## Begin on: Fri Oct 18 07:57:18 CEST 2019 ENUMERATION No. of records: 654 FAMILY (oriented family) : isomorphism classes 1 [ E1b] : 22 (18 non-degenerate) 2 [ E3b] : 82 (60 non-degenerate) 2* [E3*b] : 82 (60 non-degenerate) 2ex [E3*c] : 2 (2 non-degenerate) 2*ex [ E3c] : 2 (2 non-degenerate) 2P [ E2] : 15 (12 non-degenerate) 2Pex [ E1a] : 2 (2 non-degenerate) 3 [ E5a] : 346 (163 non-degenerate) 4 [ E4] : 36 (19 non-degenerate) 4* [ E4*] : 36 (19 non-degenerate) 4P [ E6] : 11 (2 non-degenerate) 5 [ E3a] : 7 (5 non-degenerate) 5* [E3*a] : 7 (5 non-degenerate) 5P [ E5b] : 4 (3 non-degenerate) E14.1 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {14, 14}) Quotient :: toric Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, S^2, S^-1 * A * S * B, S^-1 * B * S * A, S^-1 * Z * S * Z, Z^14, (Z^-1 * A * B^-1 * A^-1 * B)^14 ] Map:: R = (1, 16, 30, 44, 2, 18, 32, 46, 4, 20, 34, 48, 6, 22, 36, 50, 8, 24, 38, 52, 10, 26, 40, 54, 12, 28, 42, 56, 14, 27, 41, 55, 13, 25, 39, 53, 11, 23, 37, 51, 9, 21, 35, 49, 7, 19, 33, 47, 5, 17, 31, 45, 3, 15, 29, 43) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 56^56 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 28 f = 1 degree seq :: [ 56 ] E14.2 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {14, 14}) Quotient :: toric Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ S^2, A^2, B^-1 * A, S * B * S * A, (S * Z)^2, A * Z * A * Z^-1, Z^-7 * A ] Map:: R = (1, 16, 30, 44, 2, 19, 33, 47, 5, 23, 37, 51, 9, 27, 41, 55, 13, 25, 39, 53, 11, 21, 35, 49, 7, 17, 31, 45, 3, 20, 34, 48, 6, 24, 38, 52, 10, 28, 42, 56, 14, 26, 40, 54, 12, 22, 36, 50, 8, 18, 32, 46, 4, 15, 29, 43) L = (1, 31)(2, 34)(3, 29)(4, 35)(5, 38)(6, 30)(7, 32)(8, 39)(9, 42)(10, 33)(11, 36)(12, 41)(13, 40)(14, 37)(15, 45)(16, 48)(17, 43)(18, 49)(19, 52)(20, 44)(21, 46)(22, 53)(23, 56)(24, 47)(25, 50)(26, 55)(27, 54)(28, 51) local type(s) :: { ( 56^56 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 28 f = 1 degree seq :: [ 56 ] E14.3 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {14, 14}) Quotient :: toric Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ S^2, B * A^-1, Z^2 * A^2, (Z^-1, A), S * B * S * A, (S * Z)^2, A^-5 * Z^2, A^-1 * Z^6 ] Map:: R = (1, 16, 30, 44, 2, 20, 34, 48, 6, 25, 39, 53, 11, 27, 41, 55, 13, 24, 38, 52, 10, 17, 31, 45, 3, 21, 35, 49, 7, 19, 33, 47, 5, 22, 36, 50, 8, 26, 40, 54, 12, 28, 42, 56, 14, 23, 37, 51, 9, 18, 32, 46, 4, 15, 29, 43) L = (1, 31)(2, 35)(3, 37)(4, 38)(5, 29)(6, 33)(7, 32)(8, 30)(9, 41)(10, 42)(11, 36)(12, 34)(13, 40)(14, 39)(15, 47)(16, 50)(17, 43)(18, 49)(19, 48)(20, 54)(21, 44)(22, 53)(23, 45)(24, 46)(25, 56)(26, 55)(27, 51)(28, 52) local type(s) :: { ( 56^56 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 28 f = 1 degree seq :: [ 56 ] E14.4 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {14, 14}) Quotient :: toric Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, Z^2 * A^-1, S * B * S * A, (S * Z)^2, A^7, (B^-1 * Z)^14 ] Map:: R = (1, 16, 30, 44, 2, 17, 31, 45, 3, 20, 34, 48, 6, 21, 35, 49, 7, 24, 38, 52, 10, 25, 39, 53, 11, 28, 42, 56, 14, 27, 41, 55, 13, 26, 40, 54, 12, 23, 37, 51, 9, 22, 36, 50, 8, 19, 33, 47, 5, 18, 32, 46, 4, 15, 29, 43) L = (1, 31)(2, 34)(3, 35)(4, 30)(5, 29)(6, 38)(7, 39)(8, 32)(9, 33)(10, 42)(11, 41)(12, 36)(13, 37)(14, 40)(15, 47)(16, 46)(17, 43)(18, 50)(19, 51)(20, 44)(21, 45)(22, 54)(23, 55)(24, 48)(25, 49)(26, 56)(27, 53)(28, 52) local type(s) :: { ( 56^56 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 28 f = 1 degree seq :: [ 56 ] E14.5 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {14, 14}) Quotient :: toric Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ S^2, B * A^-1, Z^2 * A, (S * Z)^2, S * A * S * B, A^7, A^2 * Z^-1 * B * A^3 * Z^-1, (B * Z)^14 ] Map:: R = (1, 16, 30, 44, 2, 19, 33, 47, 5, 20, 34, 48, 6, 23, 37, 51, 9, 24, 38, 52, 10, 27, 41, 55, 13, 28, 42, 56, 14, 25, 39, 53, 11, 26, 40, 54, 12, 21, 35, 49, 7, 22, 36, 50, 8, 17, 31, 45, 3, 18, 32, 46, 4, 15, 29, 43) L = (1, 31)(2, 32)(3, 35)(4, 36)(5, 29)(6, 30)(7, 39)(8, 40)(9, 33)(10, 34)(11, 41)(12, 42)(13, 37)(14, 38)(15, 47)(16, 48)(17, 43)(18, 44)(19, 51)(20, 52)(21, 45)(22, 46)(23, 55)(24, 56)(25, 49)(26, 50)(27, 53)(28, 54) local type(s) :: { ( 56^56 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 28 f = 1 degree seq :: [ 56 ] E14.6 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {14, 14}) Quotient :: toric Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ S^2, B * A^-1, B * A^-1, S * A * S * B, (S * Z)^2, (Z, A^-1), A^-1 * Z * B^-1 * A^-1 * Z, Z^2 * A * Z^2 ] Map:: R = (1, 16, 30, 44, 2, 20, 34, 48, 6, 26, 40, 54, 12, 19, 33, 47, 5, 22, 36, 50, 8, 23, 37, 51, 9, 28, 42, 56, 14, 27, 41, 55, 13, 24, 38, 52, 10, 17, 31, 45, 3, 21, 35, 49, 7, 25, 39, 53, 11, 18, 32, 46, 4, 15, 29, 43) L = (1, 31)(2, 35)(3, 37)(4, 38)(5, 29)(6, 39)(7, 42)(8, 30)(9, 34)(10, 36)(11, 41)(12, 32)(13, 33)(14, 40)(15, 47)(16, 50)(17, 43)(18, 54)(19, 55)(20, 51)(21, 44)(22, 52)(23, 45)(24, 46)(25, 48)(26, 56)(27, 53)(28, 49) local type(s) :: { ( 56^56 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 28 f = 1 degree seq :: [ 56 ] E14.7 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {14, 14}) Quotient :: toric Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ S^2, A^-1 * B, S * B * S * A, (S * Z)^2, (Z, A^-1), A^3 * Z^2, Z * A * B * Z * A, A^-1 * Z^4 ] Map:: R = (1, 16, 30, 44, 2, 20, 34, 48, 6, 24, 38, 52, 10, 17, 31, 45, 3, 21, 35, 49, 7, 27, 41, 55, 13, 28, 42, 56, 14, 23, 37, 51, 9, 26, 40, 54, 12, 19, 33, 47, 5, 22, 36, 50, 8, 25, 39, 53, 11, 18, 32, 46, 4, 15, 29, 43) L = (1, 31)(2, 35)(3, 37)(4, 38)(5, 29)(6, 41)(7, 40)(8, 30)(9, 39)(10, 42)(11, 34)(12, 32)(13, 33)(14, 36)(15, 47)(16, 50)(17, 43)(18, 54)(19, 55)(20, 53)(21, 44)(22, 56)(23, 45)(24, 46)(25, 51)(26, 49)(27, 48)(28, 52) local type(s) :: { ( 56^56 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 28 f = 1 degree seq :: [ 56 ] E14.8 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Z^2, S^2, B * A^-1, (S * Z)^2, S * B * S * A, A * Z * A^-1 * Z, A^13 ] Map:: R = (1, 28, 54, 80, 2, 27, 53, 79)(3, 31, 57, 83, 5, 29, 55, 81)(4, 32, 58, 84, 6, 30, 56, 82)(7, 35, 61, 87, 9, 33, 59, 85)(8, 36, 62, 88, 10, 34, 60, 86)(11, 39, 65, 91, 13, 37, 63, 89)(12, 40, 66, 92, 14, 38, 64, 90)(15, 43, 69, 95, 17, 41, 67, 93)(16, 44, 70, 96, 18, 42, 68, 94)(19, 47, 73, 99, 21, 45, 71, 97)(20, 48, 74, 100, 22, 46, 72, 98)(23, 51, 77, 103, 25, 49, 75, 101)(24, 52, 78, 104, 26, 50, 76, 102) L = (1, 55)(2, 57)(3, 59)(4, 53)(5, 61)(6, 54)(7, 63)(8, 56)(9, 65)(10, 58)(11, 67)(12, 60)(13, 69)(14, 62)(15, 71)(16, 64)(17, 73)(18, 66)(19, 75)(20, 68)(21, 77)(22, 70)(23, 76)(24, 72)(25, 78)(26, 74)(27, 82)(28, 84)(29, 79)(30, 86)(31, 80)(32, 88)(33, 81)(34, 90)(35, 83)(36, 92)(37, 85)(38, 94)(39, 87)(40, 96)(41, 89)(42, 98)(43, 91)(44, 100)(45, 93)(46, 102)(47, 95)(48, 104)(49, 97)(50, 101)(51, 99)(52, 103) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 13 e = 52 f = 13 degree seq :: [ 8^13 ] E14.9 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Z^2, S^2, A^2, B^-1 * A, S * B * S * A, (S * Z)^2, (A * Z)^13 ] Map:: R = (1, 28, 54, 80, 2, 27, 53, 79)(3, 31, 57, 83, 5, 29, 55, 81)(4, 32, 58, 84, 6, 30, 56, 82)(7, 35, 61, 87, 9, 33, 59, 85)(8, 36, 62, 88, 10, 34, 60, 86)(11, 39, 65, 91, 13, 37, 63, 89)(12, 44, 70, 96, 18, 38, 64, 90)(14, 50, 76, 102, 24, 40, 66, 92)(15, 49, 75, 101, 23, 41, 67, 93)(16, 52, 78, 104, 26, 42, 68, 94)(17, 51, 77, 103, 25, 43, 69, 95)(19, 48, 74, 100, 22, 45, 71, 97)(20, 47, 73, 99, 21, 46, 72, 98) L = (1, 55)(2, 56)(3, 53)(4, 54)(5, 59)(6, 60)(7, 57)(8, 58)(9, 63)(10, 64)(11, 61)(12, 62)(13, 75)(14, 77)(15, 78)(16, 74)(17, 73)(18, 76)(19, 72)(20, 71)(21, 69)(22, 68)(23, 65)(24, 70)(25, 66)(26, 67)(27, 81)(28, 82)(29, 79)(30, 80)(31, 85)(32, 86)(33, 83)(34, 84)(35, 89)(36, 90)(37, 87)(38, 88)(39, 101)(40, 103)(41, 104)(42, 100)(43, 99)(44, 102)(45, 98)(46, 97)(47, 95)(48, 94)(49, 91)(50, 96)(51, 92)(52, 93) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 13 e = 52 f = 13 degree seq :: [ 8^13 ] E14.10 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Z^2, S^2, A^-1 * B^-1, S * B * S * A, (S * Z)^2, A * Z * B^-1 * Z, A^7 * B^-6 ] Map:: non-degenerate R = (1, 28, 54, 80, 2, 27, 53, 79)(3, 32, 58, 84, 6, 29, 55, 81)(4, 31, 57, 83, 5, 30, 56, 82)(7, 36, 62, 88, 10, 33, 59, 85)(8, 35, 61, 87, 9, 34, 60, 86)(11, 40, 66, 92, 14, 37, 63, 89)(12, 39, 65, 91, 13, 38, 64, 90)(15, 44, 70, 96, 18, 41, 67, 93)(16, 43, 69, 95, 17, 42, 68, 94)(19, 48, 74, 100, 22, 45, 71, 97)(20, 47, 73, 99, 21, 46, 72, 98)(23, 52, 78, 104, 26, 49, 75, 101)(24, 51, 77, 103, 25, 50, 76, 102) L = (1, 55)(2, 57)(3, 59)(4, 53)(5, 61)(6, 54)(7, 63)(8, 56)(9, 65)(10, 58)(11, 67)(12, 60)(13, 69)(14, 62)(15, 71)(16, 64)(17, 73)(18, 66)(19, 75)(20, 68)(21, 77)(22, 70)(23, 76)(24, 72)(25, 78)(26, 74)(27, 81)(28, 83)(29, 85)(30, 79)(31, 87)(32, 80)(33, 89)(34, 82)(35, 91)(36, 84)(37, 93)(38, 86)(39, 95)(40, 88)(41, 97)(42, 90)(43, 99)(44, 92)(45, 101)(46, 94)(47, 103)(48, 96)(49, 102)(50, 98)(51, 104)(52, 100) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 13 e = 52 f = 13 degree seq :: [ 8^13 ] E14.11 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C26 (small group id <26, 2>) Aut = C26 x C2 (small group id <52, 5>) |r| :: 2 Presentation :: [ Z^2, S^2, B^-1 * A^-1, S * A * S * B, (S * Z)^2, B * Z * B^-1 * Z, A * Z * A^-1 * Z, A^7 * B^-6 ] Map:: non-degenerate R = (1, 28, 54, 80, 2, 27, 53, 79)(3, 31, 57, 83, 5, 29, 55, 81)(4, 32, 58, 84, 6, 30, 56, 82)(7, 35, 61, 87, 9, 33, 59, 85)(8, 36, 62, 88, 10, 34, 60, 86)(11, 39, 65, 91, 13, 37, 63, 89)(12, 40, 66, 92, 14, 38, 64, 90)(15, 43, 69, 95, 17, 41, 67, 93)(16, 44, 70, 96, 18, 42, 68, 94)(19, 47, 73, 99, 21, 45, 71, 97)(20, 48, 74, 100, 22, 46, 72, 98)(23, 51, 77, 103, 25, 49, 75, 101)(24, 52, 78, 104, 26, 50, 76, 102) L = (1, 55)(2, 57)(3, 59)(4, 53)(5, 61)(6, 54)(7, 63)(8, 56)(9, 65)(10, 58)(11, 67)(12, 60)(13, 69)(14, 62)(15, 71)(16, 64)(17, 73)(18, 66)(19, 75)(20, 68)(21, 77)(22, 70)(23, 76)(24, 72)(25, 78)(26, 74)(27, 81)(28, 83)(29, 85)(30, 79)(31, 87)(32, 80)(33, 89)(34, 82)(35, 91)(36, 84)(37, 93)(38, 86)(39, 95)(40, 88)(41, 97)(42, 90)(43, 99)(44, 92)(45, 101)(46, 94)(47, 103)(48, 96)(49, 102)(50, 98)(51, 104)(52, 100) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 13 e = 52 f = 13 degree seq :: [ 8^13 ] E14.12 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^7, (Y3 * Y2^-1)^15, (Y3^-1 * Y1^-1)^15 ] Map:: R = (1, 16, 2, 17, 6, 21, 10, 25, 14, 29, 13, 28, 9, 24, 5, 20, 3, 18, 7, 22, 11, 26, 15, 30, 12, 27, 8, 23, 4, 19)(31, 46, 33, 48, 32, 47, 37, 52, 36, 51, 41, 56, 40, 55, 45, 60, 44, 59, 42, 57, 43, 58, 38, 53, 39, 54, 34, 49, 35, 50) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.13 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-7, (Y3^-1 * Y1^-1)^15, (Y3 * Y2^-1)^15 ] Map:: R = (1, 16, 2, 17, 6, 21, 10, 25, 14, 29, 12, 27, 8, 23, 3, 18, 5, 20, 7, 22, 11, 26, 15, 30, 13, 28, 9, 24, 4, 19)(31, 46, 33, 48, 34, 49, 38, 53, 39, 54, 42, 57, 43, 58, 44, 59, 45, 60, 40, 55, 41, 56, 36, 51, 37, 52, 32, 47, 35, 50) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.14 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2, Y3^3, Y3 * Y1^-2 * Y2^-1, (Y3^-1, Y1), Y1^2 * Y3^-1 * Y2, (Y3^-1, Y2), (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^2 * Y2, (R * Y2)^2, Y3 * Y1 * Y3 * Y1 * Y2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 16, 2, 17, 8, 23, 12, 27, 14, 29, 7, 22, 11, 26, 6, 21, 3, 18, 9, 24, 4, 19, 10, 25, 15, 30, 13, 28, 5, 20)(31, 46, 33, 48, 32, 47, 39, 54, 38, 53, 34, 49, 42, 57, 40, 55, 44, 59, 45, 60, 37, 52, 43, 58, 41, 56, 35, 50, 36, 51) L = (1, 34)(2, 40)(3, 42)(4, 37)(5, 39)(6, 38)(7, 31)(8, 45)(9, 44)(10, 41)(11, 32)(12, 43)(13, 33)(14, 35)(15, 36)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.15 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y3^-1, Y1 * Y2^-1 * Y1, Y1 * Y3^-1 * Y2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^5, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-2 * Y2^-1, Y2^15, (Y3^-1 * Y1^-1)^15 ] Map:: non-degenerate R = (1, 16, 2, 17, 3, 18, 4, 19, 8, 23, 9, 24, 10, 25, 14, 29, 15, 30, 13, 28, 12, 27, 11, 26, 7, 22, 6, 21, 5, 20)(31, 46, 33, 48, 38, 53, 40, 55, 45, 60, 42, 57, 37, 52, 35, 50, 32, 47, 34, 49, 39, 54, 44, 59, 43, 58, 41, 56, 36, 51) L = (1, 34)(2, 38)(3, 39)(4, 40)(5, 33)(6, 32)(7, 31)(8, 44)(9, 45)(10, 43)(11, 35)(12, 36)(13, 37)(14, 42)(15, 41)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible Dual of E14.16 Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.16 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3, Y1 * Y3^-1 * Y2, Y2^-2 * Y3^-1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y1^3 * Y3, (R * Y2)^2, Y3^5 ] Map:: non-degenerate R = (1, 16, 2, 17, 8, 23, 7, 22, 6, 21, 10, 25, 15, 30, 11, 26, 12, 27, 14, 29, 13, 28, 3, 18, 4, 19, 9, 24, 5, 20)(31, 46, 33, 48, 41, 56, 37, 52, 35, 50, 43, 58, 45, 60, 38, 53, 39, 54, 44, 59, 40, 55, 32, 47, 34, 49, 42, 57, 36, 51) L = (1, 34)(2, 39)(3, 42)(4, 44)(5, 33)(6, 32)(7, 31)(8, 35)(9, 43)(10, 38)(11, 36)(12, 40)(13, 41)(14, 45)(15, 37)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible Dual of E14.15 Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.17 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2 * Y3, (Y1, Y3^-1), Y1^-2 * Y2^-2, (Y2^-1 * Y1^-1)^2, Y1^2 * Y2^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y1), Y3 * Y1 * Y2^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1^2 ] Map:: non-degenerate R = (1, 17, 2, 18, 8, 24, 3, 19, 9, 25, 6, 22, 11, 27, 5, 21)(4, 20, 10, 26, 16, 32, 7, 23, 12, 28, 15, 31, 13, 29, 14, 30)(33, 49, 35, 51, 43, 59, 34, 50, 41, 57, 37, 53, 40, 56, 38, 54)(36, 52, 39, 55, 45, 61, 42, 58, 44, 60, 46, 62, 48, 64, 47, 63) L = (1, 36)(2, 42)(3, 39)(4, 38)(5, 46)(6, 47)(7, 33)(8, 48)(9, 44)(10, 43)(11, 45)(12, 34)(13, 35)(14, 41)(15, 40)(16, 37)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^16 ) } Outer automorphisms :: reflexible Dual of E14.36 Graph:: bipartite v = 4 e = 32 f = 2 degree seq :: [ 16^4 ] E14.18 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2 * Y3, Y2 * Y1^3, (Y2, Y1^-1), Y2^-3 * Y1^-1, Y1^2 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y1^-1), Y2 * Y1 * Y3^-1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 17, 2, 18, 8, 24, 6, 22, 11, 27, 3, 19, 9, 25, 5, 21)(4, 20, 10, 26, 13, 29, 15, 31, 16, 32, 7, 23, 12, 28, 14, 30)(33, 49, 35, 51, 40, 56, 37, 53, 43, 59, 34, 50, 41, 57, 38, 54)(36, 52, 39, 55, 45, 61, 46, 62, 48, 64, 42, 58, 44, 60, 47, 63) L = (1, 36)(2, 42)(3, 39)(4, 38)(5, 46)(6, 47)(7, 33)(8, 45)(9, 44)(10, 43)(11, 48)(12, 34)(13, 35)(14, 40)(15, 41)(16, 37)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^16 ) } Outer automorphisms :: reflexible Dual of E14.35 Graph:: bipartite v = 4 e = 32 f = 2 degree seq :: [ 16^4 ] E14.19 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^8, (Y3^-1 * Y1^-1)^8, (Y3 * Y2^-1)^16 ] Map:: R = (1, 17, 2, 18, 6, 22, 10, 26, 14, 30, 13, 29, 9, 25, 4, 20)(3, 19, 5, 21, 7, 23, 11, 27, 15, 31, 16, 32, 12, 28, 8, 24)(33, 49, 35, 51, 36, 52, 40, 56, 41, 57, 44, 60, 45, 61, 48, 64, 46, 62, 47, 63, 42, 58, 43, 59, 38, 54, 39, 55, 34, 50, 37, 53) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.20 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^8, (Y3^-1 * Y1^-1)^8, (Y3 * Y2^-1)^16 ] Map:: R = (1, 17, 2, 18, 6, 22, 10, 26, 14, 30, 12, 28, 8, 24, 4, 20)(3, 19, 7, 23, 11, 27, 15, 31, 16, 32, 13, 29, 9, 25, 5, 21)(33, 49, 35, 51, 34, 50, 39, 55, 38, 54, 43, 59, 42, 58, 47, 63, 46, 62, 48, 64, 44, 60, 45, 61, 40, 56, 41, 57, 36, 52, 37, 53) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.21 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (Y2^-1, Y1), (R * Y3)^2, Y1 * Y2 * Y1 * Y2 * Y1, Y1 * Y2^-1 * Y1 * Y2^-3, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^8, (Y3 * Y2^-1)^16 ] Map:: R = (1, 17, 2, 18, 6, 22, 13, 29, 15, 31, 9, 25, 11, 27, 4, 20)(3, 19, 7, 23, 12, 28, 5, 21, 8, 24, 14, 30, 16, 32, 10, 26)(33, 49, 35, 51, 41, 57, 46, 62, 38, 54, 44, 60, 36, 52, 42, 58, 47, 63, 40, 56, 34, 50, 39, 55, 43, 59, 48, 64, 45, 61, 37, 53) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.22 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y1, Y2), (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1^2, Y2^-1 * Y1^-1 * Y2^-3 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^8, (Y3 * Y2^-1)^16 ] Map:: R = (1, 17, 2, 18, 6, 22, 9, 25, 15, 31, 13, 29, 11, 27, 4, 20)(3, 19, 7, 23, 14, 30, 16, 32, 12, 28, 5, 21, 8, 24, 10, 26)(33, 49, 35, 51, 41, 57, 48, 64, 43, 59, 40, 56, 34, 50, 39, 55, 47, 63, 44, 60, 36, 52, 42, 58, 38, 54, 46, 62, 45, 61, 37, 53) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.23 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1 * Y2, Y1 * Y3 * Y1^-1 * Y3, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y2)^2, Y1^4 * Y3 ] Map:: non-degenerate R = (1, 17, 2, 18, 7, 23, 12, 28, 4, 20, 8, 24, 14, 30, 5, 21)(3, 19, 6, 22, 9, 25, 15, 31, 10, 26, 13, 29, 16, 32, 11, 27)(33, 49, 35, 51, 37, 53, 43, 59, 46, 62, 48, 64, 40, 56, 45, 61, 36, 52, 42, 58, 44, 60, 47, 63, 39, 55, 41, 57, 34, 50, 38, 54) L = (1, 36)(2, 40)(3, 42)(4, 33)(5, 44)(6, 45)(7, 46)(8, 34)(9, 48)(10, 35)(11, 47)(12, 37)(13, 38)(14, 39)(15, 43)(16, 41)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E14.26 Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.24 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, Y2 * Y3 * Y2^-1 * Y3, (R * Y3)^2, Y3 * Y1^4 ] Map:: non-degenerate R = (1, 17, 2, 18, 7, 23, 11, 27, 4, 20, 9, 25, 13, 29, 5, 21)(3, 19, 8, 24, 15, 31, 12, 28, 10, 26, 16, 32, 14, 30, 6, 22)(33, 49, 35, 51, 34, 50, 40, 56, 39, 55, 47, 63, 43, 59, 44, 60, 36, 52, 42, 58, 41, 57, 48, 64, 45, 61, 46, 62, 37, 53, 38, 54) L = (1, 36)(2, 41)(3, 42)(4, 33)(5, 43)(6, 44)(7, 45)(8, 48)(9, 34)(10, 35)(11, 37)(12, 38)(13, 39)(14, 47)(15, 46)(16, 40)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E14.25 Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.25 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y3 * Y1^-1, Y1 * Y3 * Y2^-2, Y2^2 * Y1^-1 * Y3, (Y2^-1, Y1^-1), Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y2^2 * Y1^3, (R * Y2 * Y3)^2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y1 ] Map:: non-degenerate R = (1, 17, 2, 18, 7, 23, 12, 28, 4, 20, 9, 25, 13, 29, 5, 21)(3, 19, 8, 24, 14, 30, 6, 22, 10, 26, 15, 31, 16, 32, 11, 27)(33, 49, 35, 51, 41, 57, 47, 63, 39, 55, 46, 62, 37, 53, 43, 59, 36, 52, 42, 58, 34, 50, 40, 56, 45, 61, 48, 64, 44, 60, 38, 54) L = (1, 36)(2, 41)(3, 42)(4, 33)(5, 44)(6, 43)(7, 45)(8, 47)(9, 34)(10, 35)(11, 38)(12, 37)(13, 39)(14, 48)(15, 40)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E14.24 Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.26 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y2^-1, Y1^-1), Y1 * Y3 * Y2^2, Y2^-1 * Y1^-1 * Y3 * Y2^-1, (R * Y1)^2, Y1^-1 * Y2^-1 * Y3 * Y2^-1, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2)^2, Y2^-1 * Y1^2 * Y2^-1 * Y1, Y3 * Y1^4 ] Map:: non-degenerate R = (1, 17, 2, 18, 7, 23, 11, 27, 4, 20, 9, 25, 14, 30, 5, 21)(3, 19, 8, 24, 15, 31, 16, 32, 12, 28, 6, 22, 10, 26, 13, 29)(33, 49, 35, 51, 43, 59, 48, 64, 46, 62, 42, 58, 34, 50, 40, 56, 36, 52, 44, 60, 37, 53, 45, 61, 39, 55, 47, 63, 41, 57, 38, 54) L = (1, 36)(2, 41)(3, 44)(4, 33)(5, 43)(6, 40)(7, 46)(8, 38)(9, 34)(10, 47)(11, 37)(12, 35)(13, 48)(14, 39)(15, 42)(16, 45)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E14.23 Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.27 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^2, Y1 * Y3^-1 * Y1, Y3^4, (R * Y2)^2, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^8 ] Map:: non-degenerate R = (1, 17, 2, 18, 4, 20, 8, 24, 12, 28, 14, 30, 7, 23, 5, 21)(3, 19, 6, 22, 9, 25, 13, 29, 15, 31, 16, 32, 11, 27, 10, 26)(33, 49, 35, 51, 37, 53, 42, 58, 39, 55, 43, 59, 46, 62, 48, 64, 44, 60, 47, 63, 40, 56, 45, 61, 36, 52, 41, 57, 34, 50, 38, 54) L = (1, 36)(2, 40)(3, 41)(4, 44)(5, 34)(6, 45)(7, 33)(8, 46)(9, 47)(10, 38)(11, 35)(12, 39)(13, 48)(14, 37)(15, 43)(16, 42)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E14.32 Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.28 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y1, Y1 * Y3 * Y1, Y3^4, (Y2^-1, Y3^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2 ] Map:: non-degenerate R = (1, 17, 2, 18, 7, 23, 9, 25, 12, 28, 13, 29, 4, 20, 5, 21)(3, 19, 8, 24, 11, 27, 15, 31, 16, 32, 14, 30, 10, 26, 6, 22)(33, 49, 35, 51, 34, 50, 40, 56, 39, 55, 43, 59, 41, 57, 47, 63, 44, 60, 48, 64, 45, 61, 46, 62, 36, 52, 42, 58, 37, 53, 38, 54) L = (1, 36)(2, 37)(3, 42)(4, 44)(5, 45)(6, 46)(7, 33)(8, 38)(9, 34)(10, 48)(11, 35)(12, 39)(13, 41)(14, 47)(15, 40)(16, 43)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E14.34 Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.29 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y3 * Y1^-1 * Y2^-2, Y1 * Y2 * Y3^-1 * Y2, Y3^4, (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y2), (R * Y2)^2, Y2^-2 * Y1 * Y3^-2 ] Map:: non-degenerate R = (1, 17, 2, 18, 7, 23, 10, 26, 15, 31, 11, 27, 4, 20, 5, 21)(3, 19, 8, 24, 14, 30, 6, 22, 9, 25, 16, 32, 12, 28, 13, 29)(33, 49, 35, 51, 43, 59, 48, 64, 39, 55, 46, 62, 37, 53, 45, 61, 47, 63, 41, 57, 34, 50, 40, 56, 36, 52, 44, 60, 42, 58, 38, 54) L = (1, 36)(2, 37)(3, 44)(4, 47)(5, 43)(6, 40)(7, 33)(8, 45)(9, 46)(10, 34)(11, 42)(12, 41)(13, 48)(14, 35)(15, 39)(16, 38)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E14.31 Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.30 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y1, (Y2, Y1^-1), Y2 * Y3^-1 * Y2 * Y1^-1, (R * Y3)^2, Y3^4, Y2^2 * Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y1)^2, Y2 * Y1 * Y3^2 * Y2, (Y1 * Y3)^8 ] Map:: non-degenerate R = (1, 17, 2, 18, 4, 20, 9, 25, 13, 29, 15, 31, 7, 23, 5, 21)(3, 19, 8, 24, 11, 27, 16, 32, 14, 30, 6, 22, 10, 26, 12, 28)(33, 49, 35, 51, 41, 57, 48, 64, 39, 55, 42, 58, 34, 50, 40, 56, 45, 61, 46, 62, 37, 53, 44, 60, 36, 52, 43, 59, 47, 63, 38, 54) L = (1, 36)(2, 41)(3, 43)(4, 45)(5, 34)(6, 44)(7, 33)(8, 48)(9, 47)(10, 35)(11, 46)(12, 40)(13, 39)(14, 42)(15, 37)(16, 38)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E14.33 Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.31 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1, Y1^-2 * Y3^-1, (R * Y2)^2, (Y2^-1, Y3^-1), (R * Y3)^2, Y3^4, (R * Y1)^2 ] Map:: non-degenerate R = (1, 17, 2, 18, 7, 23, 9, 25, 12, 28, 13, 29, 4, 20, 5, 21)(3, 19, 6, 22, 8, 24, 14, 30, 15, 31, 16, 32, 10, 26, 11, 27)(33, 49, 35, 51, 37, 53, 43, 59, 36, 52, 42, 58, 45, 61, 48, 64, 44, 60, 47, 63, 41, 57, 46, 62, 39, 55, 40, 56, 34, 50, 38, 54) L = (1, 36)(2, 37)(3, 42)(4, 44)(5, 45)(6, 43)(7, 33)(8, 35)(9, 34)(10, 47)(11, 48)(12, 39)(13, 41)(14, 38)(15, 40)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E14.29 Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.32 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2, Y1 * Y3^-1 * Y1, (R * Y3)^2, Y3^4, (Y3^-1, Y2), (R * Y1)^2, (R * Y2)^2 ] Map:: non-degenerate R = (1, 17, 2, 18, 4, 20, 9, 25, 12, 28, 13, 29, 7, 23, 5, 21)(3, 19, 8, 24, 10, 26, 15, 31, 16, 32, 14, 30, 11, 27, 6, 22)(33, 49, 35, 51, 34, 50, 40, 56, 36, 52, 42, 58, 41, 57, 47, 63, 44, 60, 48, 64, 45, 61, 46, 62, 39, 55, 43, 59, 37, 53, 38, 54) L = (1, 36)(2, 41)(3, 42)(4, 44)(5, 34)(6, 40)(7, 33)(8, 47)(9, 45)(10, 48)(11, 35)(12, 39)(13, 37)(14, 38)(15, 46)(16, 43)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E14.27 Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.33 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y1^-2 * Y3, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y3^-1, Y2^-1), (Y1, Y2^-1), Y1 * Y2 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y1 * Y3, Y3^4, (R * Y2)^2, Y3 * Y2^-4 ] Map:: non-degenerate R = (1, 17, 2, 18, 4, 20, 9, 25, 15, 31, 11, 27, 7, 23, 5, 21)(3, 19, 8, 24, 12, 28, 6, 22, 10, 26, 16, 32, 14, 30, 13, 29)(33, 49, 35, 51, 43, 59, 48, 64, 36, 52, 44, 60, 37, 53, 45, 61, 47, 63, 42, 58, 34, 50, 40, 56, 39, 55, 46, 62, 41, 57, 38, 54) L = (1, 36)(2, 41)(3, 44)(4, 47)(5, 34)(6, 48)(7, 33)(8, 38)(9, 43)(10, 46)(11, 37)(12, 42)(13, 40)(14, 35)(15, 39)(16, 45)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E14.30 Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.34 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y1, (Y2, Y1^-1), Y2^-2 * Y1 * Y3^-1, Y1 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, Y3^4, (R * Y2)^2, (R * Y1)^2, Y2 * Y3^-1 * Y1 * Y2 * Y3^-1, Y2^2 * Y1 * Y3^-2 ] Map:: non-degenerate R = (1, 17, 2, 18, 7, 23, 10, 26, 13, 29, 14, 30, 4, 20, 5, 21)(3, 19, 8, 24, 12, 28, 15, 31, 16, 32, 6, 22, 9, 25, 11, 27)(33, 49, 35, 51, 42, 58, 47, 63, 36, 52, 41, 57, 34, 50, 40, 56, 45, 61, 48, 64, 37, 53, 43, 59, 39, 55, 44, 60, 46, 62, 38, 54) L = (1, 36)(2, 37)(3, 41)(4, 45)(5, 46)(6, 47)(7, 33)(8, 43)(9, 48)(10, 34)(11, 38)(12, 35)(13, 39)(14, 42)(15, 40)(16, 44)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E14.28 Graph:: bipartite v = 3 e = 32 f = 3 degree seq :: [ 16^2, 32 ] E14.35 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1, Y2 * Y1^-3, (R * Y1)^2, (Y1, Y3^-1), R * Y2 * R * Y3^-1, Y3^2 * Y1^-1 * Y2^-2 * Y3, (Y1^-1 * Y3^-1)^8, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 17, 2, 18, 6, 22, 3, 19, 7, 23, 12, 28, 9, 25, 13, 29, 16, 32, 15, 31, 10, 26, 14, 30, 11, 27, 4, 20, 8, 24, 5, 21)(33, 49, 35, 51, 41, 57, 47, 63, 43, 59, 37, 53, 38, 54, 44, 60, 48, 64, 46, 62, 40, 56, 34, 50, 39, 55, 45, 61, 42, 58, 36, 52) L = (1, 36)(2, 40)(3, 33)(4, 42)(5, 43)(6, 37)(7, 34)(8, 46)(9, 35)(10, 45)(11, 47)(12, 38)(13, 39)(14, 48)(15, 41)(16, 44)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16^32 ) } Outer automorphisms :: reflexible Dual of E14.18 Graph:: bipartite v = 2 e = 32 f = 4 degree seq :: [ 32^2 ] E14.36 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1, (Y1, Y2^-1), Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y1 * Y3^-1 * Y1 * Y2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y2^7 * Y1^-1, Y2^3 * Y1^-5, (Y3^-1 * Y1^-1)^8 ] Map:: non-degenerate R = (1, 17, 2, 18, 6, 22, 11, 27, 15, 31, 13, 29, 10, 26, 3, 19, 7, 23, 4, 20, 8, 24, 12, 28, 16, 32, 14, 30, 9, 25, 5, 21)(33, 49, 35, 51, 41, 57, 45, 61, 48, 64, 43, 59, 40, 56, 34, 50, 39, 55, 37, 53, 42, 58, 46, 62, 47, 63, 44, 60, 38, 54, 36, 52) L = (1, 36)(2, 40)(3, 33)(4, 38)(5, 39)(6, 44)(7, 34)(8, 43)(9, 35)(10, 37)(11, 48)(12, 47)(13, 41)(14, 42)(15, 46)(16, 45)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16^32 ) } Outer automorphisms :: reflexible Dual of E14.17 Graph:: bipartite v = 2 e = 32 f = 4 degree seq :: [ 32^2 ] E14.37 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 9, 9}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^3 * Y1^2, (R * Y2 * Y3^-1)^2, Y1^6, (Y3^-1 * Y1^-1)^6, (Y3 * Y2^-1)^9 ] Map:: R = (1, 19, 2, 20, 6, 24, 14, 32, 11, 29, 4, 22)(3, 21, 7, 25, 13, 31, 16, 34, 18, 36, 10, 28)(5, 23, 8, 26, 15, 33, 17, 35, 9, 27, 12, 30)(37, 55, 39, 57, 45, 63, 47, 65, 54, 72, 51, 69, 42, 60, 49, 67, 41, 59)(38, 56, 43, 61, 48, 66, 40, 58, 46, 64, 53, 71, 50, 68, 52, 70, 44, 62) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 36 f = 5 degree seq :: [ 12^3, 18^2 ] E14.38 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 9, 9}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y2^3 * Y1^-2, Y1^6, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^6, (Y3 * Y2^-1)^9 ] Map:: R = (1, 19, 2, 20, 6, 24, 14, 32, 11, 29, 4, 22)(3, 21, 7, 25, 15, 33, 18, 36, 13, 31, 10, 28)(5, 23, 8, 26, 9, 27, 16, 34, 17, 35, 12, 30)(37, 55, 39, 57, 45, 63, 42, 60, 51, 69, 53, 71, 47, 65, 49, 67, 41, 59)(38, 56, 43, 61, 52, 70, 50, 68, 54, 72, 48, 66, 40, 58, 46, 64, 44, 62) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 36 f = 5 degree seq :: [ 12^3, 18^2 ] E14.39 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 9, 9}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1 * Y3 * Y1, (Y2, Y1^-1), Y2^3 * Y3^-1, (R * Y1)^2, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (Y3 * Y1^-1)^2, Y3 * Y2^-1 * Y1^-1 * Y3 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 10, 28, 4, 22, 5, 23)(3, 21, 8, 26, 14, 32, 17, 35, 12, 30, 13, 31)(6, 24, 9, 27, 16, 34, 18, 36, 11, 29, 15, 33)(37, 55, 39, 57, 47, 65, 40, 58, 48, 66, 52, 70, 43, 61, 50, 68, 42, 60)(38, 56, 44, 62, 51, 69, 41, 59, 49, 67, 54, 72, 46, 64, 53, 71, 45, 63) L = (1, 40)(2, 41)(3, 48)(4, 43)(5, 46)(6, 47)(7, 37)(8, 49)(9, 51)(10, 38)(11, 52)(12, 50)(13, 53)(14, 39)(15, 54)(16, 42)(17, 44)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E14.40 Graph:: bipartite v = 5 e = 36 f = 5 degree seq :: [ 12^3, 18^2 ] E14.40 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 9, 9}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1 * Y3 * Y1, (Y2, Y3), Y2^-3 * Y3^-1, (R * Y2)^2, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 10, 28, 4, 22, 5, 23)(3, 21, 8, 26, 14, 32, 18, 36, 12, 30, 13, 31)(6, 24, 9, 27, 11, 29, 17, 35, 15, 33, 16, 34)(37, 55, 39, 57, 47, 65, 43, 61, 50, 68, 51, 69, 40, 58, 48, 66, 42, 60)(38, 56, 44, 62, 53, 71, 46, 64, 54, 72, 52, 70, 41, 59, 49, 67, 45, 63) L = (1, 40)(2, 41)(3, 48)(4, 43)(5, 46)(6, 51)(7, 37)(8, 49)(9, 52)(10, 38)(11, 42)(12, 50)(13, 54)(14, 39)(15, 47)(16, 53)(17, 45)(18, 44)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E14.39 Graph:: bipartite v = 5 e = 36 f = 5 degree seq :: [ 12^3, 18^2 ] E14.41 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y2^-1, Y1^-1), Y1^-1 * Y2^-3, Y3^-1 * Y2 * Y3^-1 * Y1, Y2^-1 * Y3^2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2)^2, (Y3^-1 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 8, 26, 14, 32)(4, 22, 9, 27, 15, 33)(6, 24, 10, 28, 12, 30)(7, 25, 11, 29, 16, 34)(13, 31, 17, 35, 18, 36)(37, 55, 39, 57, 48, 66, 41, 59, 50, 68, 46, 64, 38, 56, 44, 62, 42, 60)(40, 58, 49, 67, 43, 61, 51, 69, 54, 72, 52, 70, 45, 63, 53, 71, 47, 65) L = (1, 40)(2, 45)(3, 49)(4, 44)(5, 51)(6, 47)(7, 37)(8, 53)(9, 50)(10, 52)(11, 38)(12, 43)(13, 42)(14, 54)(15, 39)(16, 41)(17, 46)(18, 48)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 36^6 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E14.56 Graph:: bipartite v = 8 e = 36 f = 2 degree seq :: [ 6^6, 18^2 ] E14.42 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3 * Y2^-1 * Y3, Y2 * Y1^-1 * Y2^2, Y2^3 * Y1^-1, (Y3^-1, Y1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 8, 26, 13, 31)(4, 22, 9, 27, 14, 32)(6, 24, 10, 28, 15, 33)(7, 25, 11, 29, 16, 34)(12, 30, 18, 36, 17, 35)(37, 55, 39, 57, 46, 64, 38, 56, 44, 62, 51, 69, 41, 59, 49, 67, 42, 60)(40, 58, 48, 66, 47, 65, 45, 63, 54, 72, 52, 70, 50, 68, 53, 71, 43, 61) L = (1, 40)(2, 45)(3, 48)(4, 39)(5, 50)(6, 43)(7, 37)(8, 54)(9, 44)(10, 47)(11, 38)(12, 46)(13, 53)(14, 49)(15, 52)(16, 41)(17, 42)(18, 51)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 36^6 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E14.55 Graph:: bipartite v = 8 e = 36 f = 2 degree seq :: [ 6^6, 18^2 ] E14.43 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y2 * Y1 * Y2, (R * Y3)^2, (Y3, Y2^-1), (R * Y2)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1^2, Y1^-3 * Y3^-1 * Y1^-1, (Y2^-1 * Y3)^18 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 16, 34, 7, 25, 4, 22, 9, 27, 15, 33, 5, 23)(3, 21, 6, 24, 10, 28, 17, 35, 13, 31, 11, 29, 14, 32, 18, 36, 12, 30)(37, 55, 39, 57, 41, 59, 48, 66, 51, 69, 54, 72, 45, 63, 50, 68, 40, 58, 47, 65, 43, 61, 49, 67, 52, 70, 53, 71, 44, 62, 46, 64, 38, 56, 42, 60) L = (1, 40)(2, 45)(3, 47)(4, 38)(5, 43)(6, 50)(7, 37)(8, 51)(9, 44)(10, 54)(11, 42)(12, 49)(13, 39)(14, 46)(15, 52)(16, 41)(17, 48)(18, 53)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E14.51 Graph:: bipartite v = 3 e = 36 f = 7 degree seq :: [ 18^2, 36 ] E14.44 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y1, (Y2 * Y3)^2, Y2^2 * Y3^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y2^-1), (R * Y2)^2, Y2^-1 * Y1 * Y2^-3, Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 ] Map:: non-degenerate R = (1, 19, 2, 20, 4, 22, 9, 27, 15, 33, 11, 29, 18, 36, 7, 25, 5, 23)(3, 21, 8, 26, 12, 30, 17, 35, 6, 24, 10, 28, 16, 34, 14, 32, 13, 31)(37, 55, 39, 57, 47, 65, 46, 64, 38, 56, 44, 62, 54, 72, 52, 70, 40, 58, 48, 66, 43, 61, 50, 68, 45, 63, 53, 71, 41, 59, 49, 67, 51, 69, 42, 60) L = (1, 40)(2, 45)(3, 48)(4, 51)(5, 38)(6, 52)(7, 37)(8, 53)(9, 47)(10, 50)(11, 43)(12, 42)(13, 44)(14, 39)(15, 54)(16, 49)(17, 46)(18, 41)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E14.54 Graph:: bipartite v = 3 e = 36 f = 7 degree seq :: [ 18^2, 36 ] E14.45 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-2, Y2^2 * Y3^-1, (Y1^-1 * Y2)^2, (R * Y3)^2, (Y1, Y2), (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^2, Y1 * Y3^4 ] Map:: non-degenerate R = (1, 19, 2, 20, 4, 22, 9, 27, 12, 30, 16, 34, 14, 32, 7, 25, 5, 23)(3, 21, 8, 26, 11, 29, 17, 35, 18, 36, 15, 33, 13, 31, 6, 24, 10, 28)(37, 55, 39, 57, 40, 58, 47, 65, 48, 66, 54, 72, 50, 68, 49, 67, 41, 59, 46, 64, 38, 56, 44, 62, 45, 63, 53, 71, 52, 70, 51, 69, 43, 61, 42, 60) L = (1, 40)(2, 45)(3, 47)(4, 48)(5, 38)(6, 39)(7, 37)(8, 53)(9, 52)(10, 44)(11, 54)(12, 50)(13, 46)(14, 41)(15, 42)(16, 43)(17, 51)(18, 49)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E14.53 Graph:: bipartite v = 3 e = 36 f = 7 degree seq :: [ 18^2, 36 ] E14.46 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3 * Y2^-1, Y1^-1 * Y3^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1), Y1^-2 * Y3^-1 * Y1^-2 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 15, 33, 7, 25, 4, 22, 10, 28, 13, 31, 5, 23)(3, 21, 9, 27, 16, 34, 14, 32, 6, 24, 11, 29, 17, 35, 18, 36, 12, 30)(37, 55, 39, 57, 40, 58, 47, 65, 38, 56, 45, 63, 46, 64, 53, 71, 44, 62, 52, 70, 49, 67, 54, 72, 51, 69, 50, 68, 41, 59, 48, 66, 43, 61, 42, 60) L = (1, 40)(2, 46)(3, 47)(4, 38)(5, 43)(6, 39)(7, 37)(8, 49)(9, 53)(10, 44)(11, 45)(12, 42)(13, 51)(14, 48)(15, 41)(16, 54)(17, 52)(18, 50)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E14.50 Graph:: bipartite v = 3 e = 36 f = 7 degree seq :: [ 18^2, 36 ] E14.47 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^2, Y2^-1 * Y1^2 * Y2^-1, (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y3), Y2^2 * Y1 * Y3 * Y1, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 17, 35, 7, 25, 4, 22, 10, 28, 15, 33, 5, 23)(3, 21, 9, 27, 18, 36, 14, 32, 13, 31, 12, 30, 16, 34, 6, 24, 11, 29)(37, 55, 39, 57, 44, 62, 54, 72, 43, 61, 49, 67, 46, 64, 52, 70, 41, 59, 47, 65, 38, 56, 45, 63, 53, 71, 50, 68, 40, 58, 48, 66, 51, 69, 42, 60) L = (1, 40)(2, 46)(3, 48)(4, 38)(5, 43)(6, 50)(7, 37)(8, 51)(9, 52)(10, 44)(11, 49)(12, 45)(13, 39)(14, 47)(15, 53)(16, 54)(17, 41)(18, 42)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E14.49 Graph:: bipartite v = 3 e = 36 f = 7 degree seq :: [ 18^2, 36 ] E14.48 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y2^-1, Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), (R * Y2)^2, Y1 * Y3^4 ] Map:: non-degenerate R = (1, 19, 2, 20, 4, 22, 8, 26, 12, 30, 15, 33, 14, 32, 7, 25, 5, 23)(3, 21, 6, 24, 9, 27, 13, 31, 16, 34, 18, 36, 17, 35, 11, 29, 10, 28)(37, 55, 39, 57, 41, 59, 46, 64, 43, 61, 47, 65, 50, 68, 53, 71, 51, 69, 54, 72, 48, 66, 52, 70, 44, 62, 49, 67, 40, 58, 45, 63, 38, 56, 42, 60) L = (1, 40)(2, 44)(3, 45)(4, 48)(5, 38)(6, 49)(7, 37)(8, 51)(9, 52)(10, 42)(11, 39)(12, 50)(13, 54)(14, 41)(15, 43)(16, 53)(17, 46)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E14.52 Graph:: bipartite v = 3 e = 36 f = 7 degree seq :: [ 18^2, 36 ] E14.49 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^2 * Y3 * Y2^-1, Y3^-1 * Y2 * Y1^-2, Y2 * Y1^-1 * Y3^-1 * Y1^-1, (Y3, Y1^-1), (Y3 * Y1^-1)^2, (R * Y2)^2, (Y2^-1, Y3^-1), Y2 * Y3^-3, (R * Y3)^2, (Y1^-1, Y2^-1), (R * Y1)^2, Y1^12 * Y2^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 17, 35, 13, 31, 15, 33, 6, 24, 11, 29, 7, 25, 12, 30, 4, 22, 10, 28, 3, 21, 9, 27, 16, 34, 18, 36, 14, 32, 5, 23)(37, 55, 39, 57, 42, 60)(38, 56, 45, 63, 47, 65)(40, 58, 49, 67, 50, 68)(41, 59, 46, 64, 51, 69)(43, 61, 44, 62, 52, 70)(48, 66, 53, 71, 54, 72) L = (1, 40)(2, 46)(3, 49)(4, 44)(5, 48)(6, 50)(7, 37)(8, 39)(9, 51)(10, 53)(11, 41)(12, 38)(13, 52)(14, 43)(15, 54)(16, 42)(17, 45)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E14.47 Graph:: bipartite v = 7 e = 36 f = 3 degree seq :: [ 6^6, 36 ] E14.50 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y3 * Y1^2, Y2 * Y3^-3, (Y1^-1, Y2), (R * Y1)^2, (Y2, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 10, 28, 15, 33, 16, 34, 6, 24, 9, 27, 17, 35, 18, 36, 11, 29, 12, 30, 3, 21, 8, 26, 13, 31, 14, 32, 4, 22, 5, 23)(37, 55, 39, 57, 42, 60)(38, 56, 44, 62, 45, 63)(40, 58, 47, 65, 51, 69)(41, 59, 48, 66, 52, 70)(43, 61, 49, 67, 53, 71)(46, 64, 50, 68, 54, 72) L = (1, 40)(2, 41)(3, 47)(4, 49)(5, 50)(6, 51)(7, 37)(8, 48)(9, 52)(10, 38)(11, 53)(12, 54)(13, 39)(14, 44)(15, 43)(16, 46)(17, 42)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E14.46 Graph:: bipartite v = 7 e = 36 f = 3 degree seq :: [ 6^6, 36 ] E14.51 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^3, (Y3^-1, Y2^-1), Y3 * Y2 * Y1^2, (Y3^-1, Y1^-1), Y3^3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3^-1 * Y2^-1 * Y1^-2, (R * Y2)^2, Y1^-4 * Y3 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 16, 34, 4, 22, 10, 28, 6, 24, 11, 29, 15, 33, 18, 36, 17, 35, 14, 32, 3, 21, 9, 27, 7, 25, 12, 30, 13, 31, 5, 23)(37, 55, 39, 57, 42, 60)(38, 56, 45, 63, 47, 65)(40, 58, 49, 67, 53, 71)(41, 59, 50, 68, 46, 64)(43, 61, 51, 69, 44, 62)(48, 66, 54, 72, 52, 70) L = (1, 40)(2, 46)(3, 49)(4, 51)(5, 52)(6, 53)(7, 37)(8, 42)(9, 41)(10, 54)(11, 50)(12, 38)(13, 44)(14, 48)(15, 39)(16, 47)(17, 43)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E14.43 Graph:: bipartite v = 7 e = 36 f = 3 degree seq :: [ 6^6, 36 ] E14.52 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^-2 * Y2^-1 * Y3^-1, (Y3^-1 * Y1)^2, Y3^-3 * Y2^-1, Y1^-2 * Y3^-1 * Y2^-1, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, Y1^-1 * Y3^2 * Y1^-1, (Y2, Y1^-1), (R * Y1)^2, Y1^6 * Y2^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 17, 35, 16, 34, 14, 32, 3, 21, 9, 27, 7, 25, 12, 30, 4, 22, 10, 28, 6, 24, 11, 29, 15, 33, 18, 36, 13, 31, 5, 23)(37, 55, 39, 57, 42, 60)(38, 56, 45, 63, 47, 65)(40, 58, 49, 67, 52, 70)(41, 59, 50, 68, 46, 64)(43, 61, 51, 69, 44, 62)(48, 66, 54, 72, 53, 71) L = (1, 40)(2, 46)(3, 49)(4, 44)(5, 48)(6, 52)(7, 37)(8, 42)(9, 41)(10, 53)(11, 50)(12, 38)(13, 43)(14, 54)(15, 39)(16, 51)(17, 47)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E14.48 Graph:: bipartite v = 7 e = 36 f = 3 degree seq :: [ 6^6, 36 ] E14.53 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y3 * Y1^2, Y2^-1 * Y3^-3, (Y2, Y3^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y1^-1, Y2^-1), Y2^-1 * Y1 * Y3^-1 * Y1 * Y3^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 10, 28, 11, 29, 12, 30, 3, 21, 8, 26, 13, 31, 18, 36, 16, 34, 17, 35, 6, 24, 9, 27, 14, 32, 15, 33, 4, 22, 5, 23)(37, 55, 39, 57, 42, 60)(38, 56, 44, 62, 45, 63)(40, 58, 47, 65, 52, 70)(41, 59, 48, 66, 53, 71)(43, 61, 49, 67, 50, 68)(46, 64, 54, 72, 51, 69) L = (1, 40)(2, 41)(3, 47)(4, 50)(5, 51)(6, 52)(7, 37)(8, 48)(9, 53)(10, 38)(11, 43)(12, 46)(13, 39)(14, 42)(15, 45)(16, 49)(17, 54)(18, 44)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E14.45 Graph:: bipartite v = 7 e = 36 f = 3 degree seq :: [ 6^6, 36 ] E14.54 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^3, (Y2^-1, Y3), Y1 * Y2^-1 * Y1 * Y3, (Y2, Y1^-1), Y2 * Y3^-1 * Y1^-2, Y3^-3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y1^2 * Y3^-2, Y2 * Y1 * Y3 * Y2 * Y1 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 15, 33, 4, 22, 10, 28, 3, 21, 9, 27, 14, 32, 18, 36, 13, 31, 17, 35, 6, 24, 11, 29, 7, 25, 12, 30, 16, 34, 5, 23)(37, 55, 39, 57, 42, 60)(38, 56, 45, 63, 47, 65)(40, 58, 49, 67, 52, 70)(41, 59, 46, 64, 53, 71)(43, 61, 44, 62, 50, 68)(48, 66, 51, 69, 54, 72) L = (1, 40)(2, 46)(3, 49)(4, 50)(5, 51)(6, 52)(7, 37)(8, 39)(9, 53)(10, 54)(11, 41)(12, 38)(13, 43)(14, 42)(15, 45)(16, 44)(17, 48)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E14.44 Graph:: bipartite v = 7 e = 36 f = 3 degree seq :: [ 6^6, 36 ] E14.55 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (Y2, Y1^-1), (Y2^-1, Y1), (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^2 * Y1^-2 * Y2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-3, (Y3 * Y2^-1)^3, (Y3^-1 * Y1^-1)^9 ] Map:: non-degenerate R = (1, 19, 2, 20, 6, 24, 14, 32, 13, 31, 18, 36, 10, 28, 3, 21, 7, 25, 15, 33, 12, 30, 5, 23, 8, 26, 16, 34, 9, 27, 17, 35, 11, 29, 4, 22)(37, 55, 39, 57, 45, 63, 50, 68, 48, 66, 40, 58, 46, 64, 52, 70, 42, 60, 51, 69, 47, 65, 54, 72, 44, 62, 38, 56, 43, 61, 53, 71, 49, 67, 41, 59) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 49)(15, 48)(16, 45)(17, 47)(18, 46)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E14.42 Graph:: bipartite v = 2 e = 36 f = 8 degree seq :: [ 36^2 ] E14.56 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1 * Y2 * Y1^-1, (Y3^-1, Y2^-1), (Y3, Y1^-1), Y3 * Y2^-2 * Y1, Y1^-1 * Y3 * Y2 * Y1^-1, Y3^-1 * Y2^-1 * Y1^2, Y3^2 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-2 * Y2^-1 * Y1^-2, Y1 * Y3 * Y2^16, 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 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 16, 34, 15, 33, 7, 25, 12, 30, 3, 21, 9, 27, 17, 35, 14, 32, 6, 24, 11, 29, 4, 22, 10, 28, 18, 36, 13, 31, 5, 23)(37, 55, 39, 57, 46, 64, 52, 70, 50, 68, 41, 59, 48, 66, 40, 58, 44, 62, 53, 71, 49, 67, 43, 61, 47, 65, 38, 56, 45, 63, 54, 72, 51, 69, 42, 60) L = (1, 40)(2, 46)(3, 44)(4, 45)(5, 47)(6, 48)(7, 37)(8, 54)(9, 52)(10, 53)(11, 39)(12, 38)(13, 42)(14, 43)(15, 41)(16, 49)(17, 51)(18, 50)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E14.41 Graph:: bipartite v = 2 e = 36 f = 8 degree seq :: [ 36^2 ] E14.57 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 10, 10}) Quotient :: edge^2 Aut^+ = C5 : C4 (small group id <20, 1>) Aut = C4 x D10 (small group id <40, 5>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1, Y1^4, Y1 * Y3 * Y2 * Y3, R * Y1 * R * Y2, (R * Y3)^2, Y2^4, Y1^-2 * Y2^-1 * Y3 * Y2^-1 * Y3, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-3 ] Map:: non-degenerate R = (1, 21, 4, 24, 11, 31, 19, 39, 14, 34, 6, 26, 13, 33, 20, 40, 12, 32, 5, 25)(2, 22, 7, 27, 15, 35, 18, 38, 10, 30, 3, 23, 9, 29, 17, 37, 16, 36, 8, 28)(41, 42, 46, 43)(44, 48, 53, 50)(45, 47, 54, 49)(51, 56, 60, 58)(52, 55, 59, 57)(61, 63, 66, 62)(64, 70, 73, 68)(65, 69, 74, 67)(71, 78, 80, 76)(72, 77, 79, 75) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 40^4 ), ( 40^20 ) } Outer automorphisms :: reflexible Dual of E14.60 Graph:: bipartite v = 12 e = 40 f = 2 degree seq :: [ 4^10, 20^2 ] E14.58 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 10, 10}) Quotient :: edge^2 Aut^+ = C5 : C4 (small group id <20, 1>) Aut = C4 x D10 (small group id <40, 5>) |r| :: 2 Presentation :: [ R^2, Y2^4, Y3 * Y2^-1 * Y3^-1 * Y1^-1, Y1 * Y2 * Y3^-2, Y1^4, R * Y1 * R * Y2, Y1^2 * Y2^2, Y2^-1 * Y3^-2 * Y1^-1, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, Y1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 21, 4, 24, 9, 29, 15, 35, 20, 40, 8, 28, 19, 39, 11, 31, 13, 33, 7, 27)(2, 22, 10, 30, 6, 26, 18, 38, 17, 37, 5, 25, 16, 36, 3, 23, 14, 34, 12, 32)(41, 42, 48, 45)(43, 53, 46, 55)(44, 52, 59, 57)(47, 50, 60, 56)(49, 54, 51, 58)(61, 63, 68, 66)(62, 69, 65, 71)(64, 76, 79, 70)(67, 74, 80, 78)(72, 75, 77, 73) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 40^4 ), ( 40^20 ) } Outer automorphisms :: reflexible Dual of E14.61 Graph:: bipartite v = 12 e = 40 f = 2 degree seq :: [ 4^10, 20^2 ] E14.59 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 10, 10}) Quotient :: edge^2 Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, Y3^4, Y1^-1 * Y3 * Y2 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3^-2 * Y2^-1 * Y3^2 * Y1^-1, Y1^2 * Y3^-2 * Y2^-3, Y1^4 * Y3^2 * Y2^-1, Y2^10 ] Map:: non-degenerate R = (1, 21, 4, 24, 12, 32, 5, 25)(2, 22, 7, 27, 16, 36, 8, 28)(3, 23, 10, 30, 20, 40, 11, 31)(6, 26, 14, 34, 17, 37, 15, 35)(9, 29, 18, 38, 13, 33, 19, 39)(41, 42, 46, 53, 60, 52, 56, 57, 49, 43)(44, 50, 58, 55, 48, 45, 51, 59, 54, 47)(61, 63, 69, 77, 76, 72, 80, 73, 66, 62)(64, 67, 74, 79, 71, 65, 68, 75, 78, 70) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 16^8 ), ( 16^10 ) } Outer automorphisms :: reflexible Dual of E14.62 Graph:: bipartite v = 9 e = 40 f = 5 degree seq :: [ 8^5, 10^4 ] E14.60 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 10, 10}) Quotient :: loop^2 Aut^+ = C5 : C4 (small group id <20, 1>) Aut = C4 x D10 (small group id <40, 5>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1, Y1^4, Y1 * Y3 * Y2 * Y3, R * Y1 * R * Y2, (R * Y3)^2, Y2^4, Y1^-2 * Y2^-1 * Y3 * Y2^-1 * Y3, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-3 ] Map:: non-degenerate R = (1, 21, 41, 61, 4, 24, 44, 64, 11, 31, 51, 71, 19, 39, 59, 79, 14, 34, 54, 74, 6, 26, 46, 66, 13, 33, 53, 73, 20, 40, 60, 80, 12, 32, 52, 72, 5, 25, 45, 65)(2, 22, 42, 62, 7, 27, 47, 67, 15, 35, 55, 75, 18, 38, 58, 78, 10, 30, 50, 70, 3, 23, 43, 63, 9, 29, 49, 69, 17, 37, 57, 77, 16, 36, 56, 76, 8, 28, 48, 68) L = (1, 22)(2, 26)(3, 21)(4, 28)(5, 27)(6, 23)(7, 34)(8, 33)(9, 25)(10, 24)(11, 36)(12, 35)(13, 30)(14, 29)(15, 39)(16, 40)(17, 32)(18, 31)(19, 37)(20, 38)(41, 63)(42, 61)(43, 66)(44, 70)(45, 69)(46, 62)(47, 65)(48, 64)(49, 74)(50, 73)(51, 78)(52, 77)(53, 68)(54, 67)(55, 72)(56, 71)(57, 79)(58, 80)(59, 75)(60, 76) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E14.57 Transitivity :: VT+ Graph:: bipartite v = 2 e = 40 f = 12 degree seq :: [ 40^2 ] E14.61 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 10, 10}) Quotient :: loop^2 Aut^+ = C5 : C4 (small group id <20, 1>) Aut = C4 x D10 (small group id <40, 5>) |r| :: 2 Presentation :: [ R^2, Y2^4, Y3 * Y2^-1 * Y3^-1 * Y1^-1, Y1 * Y2 * Y3^-2, Y1^4, R * Y1 * R * Y2, Y1^2 * Y2^2, Y2^-1 * Y3^-2 * Y1^-1, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, Y1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 21, 41, 61, 4, 24, 44, 64, 9, 29, 49, 69, 15, 35, 55, 75, 20, 40, 60, 80, 8, 28, 48, 68, 19, 39, 59, 79, 11, 31, 51, 71, 13, 33, 53, 73, 7, 27, 47, 67)(2, 22, 42, 62, 10, 30, 50, 70, 6, 26, 46, 66, 18, 38, 58, 78, 17, 37, 57, 77, 5, 25, 45, 65, 16, 36, 56, 76, 3, 23, 43, 63, 14, 34, 54, 74, 12, 32, 52, 72) L = (1, 22)(2, 28)(3, 33)(4, 32)(5, 21)(6, 35)(7, 30)(8, 25)(9, 34)(10, 40)(11, 38)(12, 39)(13, 26)(14, 31)(15, 23)(16, 27)(17, 24)(18, 29)(19, 37)(20, 36)(41, 63)(42, 69)(43, 68)(44, 76)(45, 71)(46, 61)(47, 74)(48, 66)(49, 65)(50, 64)(51, 62)(52, 75)(53, 72)(54, 80)(55, 77)(56, 79)(57, 73)(58, 67)(59, 70)(60, 78) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E14.58 Transitivity :: VT+ Graph:: bipartite v = 2 e = 40 f = 12 degree seq :: [ 40^2 ] E14.62 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 10, 10}) Quotient :: loop^2 Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, Y3^4, Y1^-1 * Y3 * Y2 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3^-2 * Y2^-1 * Y3^2 * Y1^-1, Y1^2 * Y3^-2 * Y2^-3, Y1^4 * Y3^2 * Y2^-1, Y2^10 ] Map:: non-degenerate R = (1, 21, 41, 61, 4, 24, 44, 64, 12, 32, 52, 72, 5, 25, 45, 65)(2, 22, 42, 62, 7, 27, 47, 67, 16, 36, 56, 76, 8, 28, 48, 68)(3, 23, 43, 63, 10, 30, 50, 70, 20, 40, 60, 80, 11, 31, 51, 71)(6, 26, 46, 66, 14, 34, 54, 74, 17, 37, 57, 77, 15, 35, 55, 75)(9, 29, 49, 69, 18, 38, 58, 78, 13, 33, 53, 73, 19, 39, 59, 79) L = (1, 22)(2, 26)(3, 21)(4, 30)(5, 31)(6, 33)(7, 24)(8, 25)(9, 23)(10, 38)(11, 39)(12, 36)(13, 40)(14, 27)(15, 28)(16, 37)(17, 29)(18, 35)(19, 34)(20, 32)(41, 63)(42, 61)(43, 69)(44, 67)(45, 68)(46, 62)(47, 74)(48, 75)(49, 77)(50, 64)(51, 65)(52, 80)(53, 66)(54, 79)(55, 78)(56, 72)(57, 76)(58, 70)(59, 71)(60, 73) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E14.59 Transitivity :: VT+ Graph:: v = 5 e = 40 f = 9 degree seq :: [ 16^5 ] E14.63 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 10, 10}) Quotient :: dipole Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^4, (R * Y2 * Y3^-1)^2, Y1^-2 * Y2^5, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^10 ] Map:: R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 8, 28, 13, 33, 10, 30)(5, 25, 7, 27, 14, 34, 11, 31)(9, 29, 16, 36, 20, 40, 18, 38)(12, 32, 15, 35, 17, 37, 19, 39)(41, 61, 43, 63, 49, 69, 57, 77, 54, 74, 46, 66, 53, 73, 60, 80, 52, 72, 45, 65)(42, 62, 47, 67, 55, 75, 58, 78, 50, 70, 44, 64, 51, 71, 59, 79, 56, 76, 48, 68) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 7 e = 40 f = 7 degree seq :: [ 8^5, 20^2 ] E14.64 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 10, 10}) Quotient :: dipole Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1, (Y2^-1 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y1^-2, Y2^-1 * Y3^-1 * Y1^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3^-2 * Y2^-2, Y1^-1 * Y2 * Y3 * Y1^-1, (R * Y2)^2, (R * Y1)^2, Y2 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y3^-2 * Y2^2 * Y3^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 11, 31, 7, 27, 10, 30)(4, 24, 12, 32, 6, 26, 9, 29)(13, 33, 19, 39, 14, 34, 20, 40)(15, 35, 17, 37, 16, 36, 18, 38)(41, 61, 43, 63, 53, 73, 56, 76, 44, 64, 48, 68, 47, 67, 54, 74, 55, 75, 46, 66)(42, 62, 49, 69, 57, 77, 60, 80, 50, 70, 45, 65, 52, 72, 58, 78, 59, 79, 51, 71) L = (1, 44)(2, 50)(3, 48)(4, 55)(5, 51)(6, 56)(7, 41)(8, 46)(9, 45)(10, 59)(11, 60)(12, 42)(13, 47)(14, 43)(15, 53)(16, 54)(17, 52)(18, 49)(19, 57)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E14.66 Graph:: bipartite v = 7 e = 40 f = 7 degree seq :: [ 8^5, 20^2 ] E14.65 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 10, 10}) Quotient :: dipole Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, Y1^-1 * Y2^-1 * Y1 * Y2^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, Y1^4, Y1^-2 * Y3^2 * Y2, Y1^-2 * Y2 * Y3^2, Y3^5 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 11, 31, 20, 40, 14, 34)(4, 24, 12, 32, 19, 39, 16, 36)(6, 26, 9, 29, 15, 35, 17, 37)(7, 27, 10, 30, 13, 33, 18, 38)(41, 61, 43, 63, 44, 64, 53, 73, 55, 75, 48, 68, 60, 80, 59, 79, 47, 67, 46, 66)(42, 62, 49, 69, 50, 70, 56, 76, 54, 74, 45, 65, 57, 77, 58, 78, 52, 72, 51, 71) L = (1, 44)(2, 50)(3, 53)(4, 55)(5, 58)(6, 43)(7, 41)(8, 59)(9, 56)(10, 54)(11, 49)(12, 42)(13, 48)(14, 57)(15, 60)(16, 45)(17, 52)(18, 51)(19, 46)(20, 47)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 7 e = 40 f = 7 degree seq :: [ 8^5, 20^2 ] E14.66 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 10, 10}) Quotient :: dipole Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, Y2 * Y1^-1 * Y2 * Y1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y1^4, Y1^-2 * Y3^2 * Y2^-1, Y1^-2 * Y2^-1 * Y3^2, Y1^-2 * Y3^-1 * Y2 * Y3^-1, Y3^5 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 11, 31, 15, 35, 13, 33)(4, 24, 12, 32, 14, 34, 16, 36)(6, 26, 9, 29, 20, 40, 18, 38)(7, 27, 10, 30, 17, 37, 19, 39)(41, 61, 43, 63, 47, 67, 54, 74, 60, 80, 48, 68, 55, 75, 57, 77, 44, 64, 46, 66)(42, 62, 49, 69, 52, 72, 59, 79, 53, 73, 45, 65, 58, 78, 56, 76, 50, 70, 51, 71) L = (1, 44)(2, 50)(3, 46)(4, 55)(5, 59)(6, 57)(7, 41)(8, 54)(9, 51)(10, 58)(11, 56)(12, 42)(13, 52)(14, 43)(15, 60)(16, 45)(17, 48)(18, 53)(19, 49)(20, 47)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E14.64 Graph:: bipartite v = 7 e = 40 f = 7 degree seq :: [ 8^5, 20^2 ] E14.67 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 10, 10}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y1^-2 * Y2^5, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^10 ] Map:: R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 7, 27, 13, 33, 10, 30)(5, 25, 8, 28, 14, 34, 11, 31)(9, 29, 15, 35, 20, 40, 18, 38)(12, 32, 16, 36, 17, 37, 19, 39)(41, 61, 43, 63, 49, 69, 57, 77, 54, 74, 46, 66, 53, 73, 60, 80, 52, 72, 45, 65)(42, 62, 47, 67, 55, 75, 59, 79, 51, 71, 44, 64, 50, 70, 58, 78, 56, 76, 48, 68) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 7 e = 40 f = 7 degree seq :: [ 8^5, 20^2 ] E14.68 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 5, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (Y3^-1, Y1^-1), Y1^4, Y2^5, (Y3 * Y2^-1)^5, Y3^-20 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 5, 25)(3, 23, 7, 27, 13, 33, 10, 30)(4, 24, 8, 28, 14, 34, 12, 32)(9, 29, 15, 35, 19, 39, 17, 37)(11, 31, 16, 36, 20, 40, 18, 38)(41, 61, 43, 63, 49, 69, 51, 71, 44, 64)(42, 62, 47, 67, 55, 75, 56, 76, 48, 68)(45, 65, 50, 70, 57, 77, 58, 78, 52, 72)(46, 66, 53, 73, 59, 79, 60, 80, 54, 74) L = (1, 44)(2, 48)(3, 41)(4, 51)(5, 52)(6, 54)(7, 42)(8, 56)(9, 43)(10, 45)(11, 49)(12, 58)(13, 46)(14, 60)(15, 47)(16, 55)(17, 50)(18, 57)(19, 53)(20, 59)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E14.75 Graph:: bipartite v = 9 e = 40 f = 5 degree seq :: [ 8^5, 10^4 ] E14.69 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 5, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, Y2 * Y3^2, (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1), Y1^4, (R * Y2)^2, 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 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 9, 29, 17, 37, 13, 33)(4, 24, 10, 30, 18, 38, 14, 34)(6, 26, 11, 31, 19, 39, 15, 35)(7, 27, 12, 32, 20, 40, 16, 36)(41, 61, 43, 63, 44, 64, 47, 67, 46, 66)(42, 62, 49, 69, 50, 70, 52, 72, 51, 71)(45, 65, 53, 73, 54, 74, 56, 76, 55, 75)(48, 68, 57, 77, 58, 78, 60, 80, 59, 79) L = (1, 44)(2, 50)(3, 47)(4, 46)(5, 54)(6, 43)(7, 41)(8, 58)(9, 52)(10, 51)(11, 49)(12, 42)(13, 56)(14, 55)(15, 53)(16, 45)(17, 60)(18, 59)(19, 57)(20, 48)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E14.74 Graph:: bipartite v = 9 e = 40 f = 5 degree seq :: [ 8^5, 10^4 ] E14.70 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 5, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, Y2 * Y3^-2, (Y3^-1, Y1), (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1), Y1^4, (R * Y2)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 9, 29, 17, 37, 13, 33)(4, 24, 10, 30, 18, 38, 14, 34)(6, 26, 11, 31, 19, 39, 15, 35)(7, 27, 12, 32, 20, 40, 16, 36)(41, 61, 43, 63, 47, 67, 44, 64, 46, 66)(42, 62, 49, 69, 52, 72, 50, 70, 51, 71)(45, 65, 53, 73, 56, 76, 54, 74, 55, 75)(48, 68, 57, 77, 60, 80, 58, 78, 59, 79) L = (1, 44)(2, 50)(3, 46)(4, 43)(5, 54)(6, 47)(7, 41)(8, 58)(9, 51)(10, 49)(11, 52)(12, 42)(13, 55)(14, 53)(15, 56)(16, 45)(17, 59)(18, 57)(19, 60)(20, 48)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E14.73 Graph:: bipartite v = 9 e = 40 f = 5 degree seq :: [ 8^5, 10^4 ] E14.71 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 5, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-2, Y2^-1 * Y1 * Y2^-1, Y1 * Y2 * Y1, (Y3, Y1), (Y3^-1, Y2), (Y2^-1, Y3^-1), (R * Y3)^2, (Y1^-1, Y3^-1), (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y1 * Y3^-3, (Y2 * Y3 * Y1 * Y3)^10 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 3, 23, 5, 25)(4, 24, 8, 28, 14, 34, 10, 30, 13, 33)(7, 27, 9, 29, 16, 36, 11, 31, 15, 35)(12, 32, 18, 38, 20, 40, 19, 39, 17, 37)(41, 61, 43, 63, 42, 62, 45, 65, 46, 66)(44, 64, 50, 70, 48, 68, 53, 73, 54, 74)(47, 67, 51, 71, 49, 69, 55, 75, 56, 76)(52, 72, 59, 79, 58, 78, 57, 77, 60, 80) L = (1, 44)(2, 48)(3, 50)(4, 52)(5, 53)(6, 54)(7, 41)(8, 58)(9, 42)(10, 59)(11, 43)(12, 49)(13, 57)(14, 60)(15, 45)(16, 46)(17, 47)(18, 56)(19, 55)(20, 51)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) } Outer automorphisms :: reflexible Dual of E14.72 Graph:: bipartite v = 8 e = 40 f = 6 degree seq :: [ 10^8 ] E14.72 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 5, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y1^-2 * Y3^-1, (Y2^-1, Y1^-1), Y1^-2 * Y3 * Y1^-1, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, (R * Y2)^2, Y1^-1 * Y3^2 * Y2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 4, 24, 10, 30, 6, 26, 11, 31, 17, 37, 16, 36, 20, 40, 13, 33, 18, 38, 15, 35, 19, 39, 14, 34, 3, 23, 9, 29, 7, 27, 12, 32, 5, 25)(41, 61, 43, 63, 53, 73, 46, 66)(42, 62, 49, 69, 58, 78, 51, 71)(44, 64, 52, 72, 59, 79, 56, 76)(45, 65, 54, 74, 60, 80, 50, 70)(47, 67, 55, 75, 57, 77, 48, 68) L = (1, 44)(2, 50)(3, 52)(4, 51)(5, 48)(6, 56)(7, 41)(8, 46)(9, 45)(10, 57)(11, 60)(12, 42)(13, 59)(14, 47)(15, 43)(16, 58)(17, 53)(18, 54)(19, 49)(20, 55)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10^8 ), ( 10^40 ) } Outer automorphisms :: reflexible Dual of E14.71 Graph:: bipartite v = 6 e = 40 f = 8 degree seq :: [ 8^5, 40 ] E14.73 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 5, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y1)^2, (Y1, Y2^-1), (R * Y3)^2, Y1 * Y2^4, Y1^5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^-1)^5 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 11, 31, 4, 24)(3, 23, 7, 27, 14, 34, 18, 38, 10, 30)(5, 25, 8, 28, 15, 35, 19, 39, 12, 32)(9, 29, 13, 33, 16, 36, 20, 40, 17, 37)(41, 61, 43, 63, 49, 69, 52, 72, 44, 64, 50, 70, 57, 77, 59, 79, 51, 71, 58, 78, 60, 80, 55, 75, 46, 66, 54, 74, 56, 76, 48, 68, 42, 62, 47, 67, 53, 73, 45, 65) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 51)(7, 54)(8, 55)(9, 53)(10, 43)(11, 44)(12, 45)(13, 56)(14, 58)(15, 59)(16, 60)(17, 49)(18, 50)(19, 52)(20, 57)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E14.70 Graph:: bipartite v = 5 e = 40 f = 9 degree seq :: [ 10^4, 40 ] E14.74 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 5, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y1^-1, Y3^-1 * Y1^-2, Y1 * Y3^-2, (Y2^-1, Y1), (R * Y3)^2, (R * Y1)^2, (Y2, Y3), (R * Y2)^2, Y3^-1 * Y2^-4, (Y2^-1 * Y3)^4 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 4, 24, 5, 25)(3, 23, 8, 28, 13, 33, 11, 31, 12, 32)(6, 26, 9, 29, 17, 37, 14, 34, 15, 35)(10, 30, 18, 38, 20, 40, 16, 36, 19, 39)(41, 61, 43, 63, 50, 70, 57, 77, 47, 67, 53, 73, 60, 80, 55, 75, 45, 65, 52, 72, 59, 79, 49, 69, 42, 62, 48, 68, 58, 78, 54, 74, 44, 64, 51, 71, 56, 76, 46, 66) L = (1, 44)(2, 45)(3, 51)(4, 42)(5, 47)(6, 54)(7, 41)(8, 52)(9, 55)(10, 56)(11, 48)(12, 53)(13, 43)(14, 49)(15, 57)(16, 58)(17, 46)(18, 59)(19, 60)(20, 50)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E14.69 Graph:: bipartite v = 5 e = 40 f = 9 degree seq :: [ 10^4, 40 ] E14.75 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 5, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-2, Y3^-1 * Y1^-1 * Y3^-1, Y1 * Y3^-1 * Y1, (Y1^-1, Y2), (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3), Y2 * Y3 * Y2^3, (Y2^-1 * Y3)^4 ] Map:: non-degenerate R = (1, 21, 2, 22, 4, 24, 7, 27, 5, 25)(3, 23, 8, 28, 11, 31, 13, 33, 12, 32)(6, 26, 9, 29, 14, 34, 17, 37, 15, 35)(10, 30, 18, 38, 16, 36, 19, 39, 20, 40)(41, 61, 43, 63, 50, 70, 57, 77, 47, 67, 53, 73, 59, 79, 49, 69, 42, 62, 48, 68, 58, 78, 55, 75, 45, 65, 52, 72, 60, 80, 54, 74, 44, 64, 51, 71, 56, 76, 46, 66) L = (1, 44)(2, 47)(3, 51)(4, 45)(5, 42)(6, 54)(7, 41)(8, 53)(9, 57)(10, 56)(11, 52)(12, 48)(13, 43)(14, 55)(15, 49)(16, 60)(17, 46)(18, 59)(19, 50)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E14.68 Graph:: bipartite v = 5 e = 40 f = 9 degree seq :: [ 10^4, 40 ] E14.76 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^2, Y1 * Y2 * Y1 * Y2^-1, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, Y2 * Y1 * Y3 * Y2^-1 * Y1 * Y3^-1, Y1 * Y2^5, (Y3 * Y2^-1)^20 ] Map:: non-degenerate R = (1, 21, 2, 22)(3, 23, 7, 27)(4, 24, 8, 28)(5, 25, 9, 29)(6, 26, 10, 30)(11, 31, 15, 35)(12, 32, 16, 36)(13, 33, 17, 37)(14, 34, 18, 38)(19, 39, 20, 40)(41, 61, 43, 63, 51, 71, 58, 78, 49, 69, 42, 62, 47, 67, 55, 75, 54, 74, 45, 65)(44, 64, 46, 66, 52, 72, 59, 79, 57, 77, 48, 68, 50, 70, 56, 76, 60, 80, 53, 73) L = (1, 44)(2, 48)(3, 46)(4, 45)(5, 53)(6, 41)(7, 50)(8, 49)(9, 57)(10, 42)(11, 52)(12, 43)(13, 54)(14, 60)(15, 56)(16, 47)(17, 58)(18, 59)(19, 51)(20, 55)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 40^4 ), ( 40^20 ) } Outer automorphisms :: reflexible Dual of E14.83 Graph:: bipartite v = 12 e = 40 f = 2 degree seq :: [ 4^10, 20^2 ] E14.77 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1 * Y1 * Y2^-1, (Y2, Y1^-1), (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y2^2 * Y1^-1 * Y3, Y2^2 * Y3 * Y1^-1, Y1^2 * Y3^2, (R * Y2)^2, Y3 * Y1^-4, Y2 * Y1 * Y2 * Y1^2, Y3^5, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 16, 36, 4, 24, 10, 30, 7, 27, 12, 32, 15, 35, 5, 25)(3, 23, 9, 29, 18, 38, 6, 26, 11, 31, 19, 39, 14, 34, 17, 37, 20, 40, 13, 33)(41, 61, 43, 63, 52, 72, 57, 77, 44, 64, 51, 71, 42, 62, 49, 69, 55, 75, 60, 80, 50, 70, 59, 79, 48, 68, 58, 78, 45, 65, 53, 73, 47, 67, 54, 74, 56, 76, 46, 66) L = (1, 44)(2, 50)(3, 51)(4, 55)(5, 56)(6, 57)(7, 41)(8, 47)(9, 59)(10, 45)(11, 60)(12, 42)(13, 46)(14, 43)(15, 48)(16, 52)(17, 49)(18, 54)(19, 53)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E14.81 Graph:: bipartite v = 3 e = 40 f = 11 degree seq :: [ 20^2, 40 ] E14.78 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, Y1^2 * Y3^2, (R * Y3)^2, (Y2^-1, Y3^-1), (Y1^-1, Y3^-1), (R * Y2)^2, (R * Y1)^2, Y3^5, Y3 * Y1^-4, Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 16, 36, 4, 24, 9, 29, 7, 27, 11, 31, 15, 35, 5, 25)(3, 23, 6, 26, 10, 30, 19, 39, 12, 32, 17, 37, 14, 34, 18, 38, 20, 40, 13, 33)(41, 61, 43, 63, 45, 65, 53, 73, 55, 75, 60, 80, 51, 71, 58, 78, 47, 67, 54, 74, 49, 69, 57, 77, 44, 64, 52, 72, 56, 76, 59, 79, 48, 68, 50, 70, 42, 62, 46, 66) L = (1, 44)(2, 49)(3, 52)(4, 55)(5, 56)(6, 57)(7, 41)(8, 47)(9, 45)(10, 54)(11, 42)(12, 60)(13, 59)(14, 43)(15, 48)(16, 51)(17, 53)(18, 46)(19, 58)(20, 50)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E14.82 Graph:: bipartite v = 3 e = 40 f = 11 degree seq :: [ 20^2, 40 ] E14.79 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1 * Y2^-1, Y3^2 * Y1^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2)^2, (Y3^-1, Y2), Y3 * Y1^-4, Y3^5, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 15, 35, 4, 24, 10, 30, 7, 27, 11, 31, 14, 34, 5, 25)(3, 23, 9, 29, 19, 39, 16, 36, 12, 32, 18, 38, 13, 33, 20, 40, 17, 37, 6, 26)(41, 61, 43, 63, 42, 62, 49, 69, 48, 68, 59, 79, 55, 75, 56, 76, 44, 64, 52, 72, 50, 70, 58, 78, 47, 67, 53, 73, 51, 71, 60, 80, 54, 74, 57, 77, 45, 65, 46, 66) L = (1, 44)(2, 50)(3, 52)(4, 54)(5, 55)(6, 56)(7, 41)(8, 47)(9, 58)(10, 45)(11, 42)(12, 57)(13, 43)(14, 48)(15, 51)(16, 60)(17, 59)(18, 46)(19, 53)(20, 49)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E14.80 Graph:: bipartite v = 3 e = 40 f = 11 degree seq :: [ 20^2, 40 ] E14.80 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y3^-1 * Y2, (Y1, Y3^-1), Y1^4 * Y3, Y1^-1 * Y2 * Y3^2 * Y1^-1, Y2 * Y3^-2 * Y1^2, Y3^5, Y3^-1 * Y2 * Y1^-1 * Y3^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 17, 37, 6, 26, 10, 30, 11, 31, 19, 39, 18, 38, 12, 32, 3, 23, 8, 28, 14, 34, 20, 40, 13, 33, 15, 35, 4, 24, 9, 29, 16, 36, 5, 25)(41, 61, 43, 63)(42, 62, 48, 68)(44, 64, 51, 71)(45, 65, 52, 72)(46, 66, 53, 73)(47, 67, 54, 74)(49, 69, 59, 79)(50, 70, 55, 75)(56, 76, 58, 78)(57, 77, 60, 80) L = (1, 44)(2, 49)(3, 51)(4, 54)(5, 55)(6, 41)(7, 56)(8, 59)(9, 60)(10, 42)(11, 47)(12, 50)(13, 43)(14, 58)(15, 48)(16, 53)(17, 45)(18, 46)(19, 57)(20, 52)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E14.79 Graph:: bipartite v = 11 e = 40 f = 3 degree seq :: [ 4^10, 40 ] E14.81 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1^-1 * Y2 * Y3 * Y1^-1, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^-2 * Y3 * Y2, (R * Y3)^2, (R * Y2)^2, Y3^5, Y2 * Y3^2 * Y1 * Y3^2 * Y1, Y1^14 * Y3^-2 * Y2 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 15, 35, 12, 32, 17, 37, 19, 39, 13, 33, 6, 26, 10, 30, 3, 23, 8, 28, 4, 24, 9, 29, 16, 36, 20, 40, 14, 34, 18, 38, 11, 31, 5, 25)(41, 61, 43, 63)(42, 62, 48, 68)(44, 64, 47, 67)(45, 65, 50, 70)(46, 66, 51, 71)(49, 69, 55, 75)(52, 72, 56, 76)(53, 73, 58, 78)(54, 74, 59, 79)(57, 77, 60, 80) L = (1, 44)(2, 49)(3, 47)(4, 52)(5, 48)(6, 41)(7, 56)(8, 55)(9, 57)(10, 42)(11, 43)(12, 54)(13, 45)(14, 46)(15, 60)(16, 59)(17, 58)(18, 50)(19, 51)(20, 53)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E14.77 Graph:: bipartite v = 11 e = 40 f = 3 degree seq :: [ 4^10, 40 ] E14.82 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^-1 * Y2 * Y3, Y1^-1 * Y3^-1 * Y2 * Y1^-1, Y3 * Y2 * Y1^2, Y1^-1 * Y2 * Y1^-1 * Y3^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3^5, Y3^-2 * Y1^16 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 15, 35, 14, 34, 18, 38, 19, 39, 13, 33, 4, 24, 9, 29, 3, 23, 8, 28, 6, 26, 10, 30, 16, 36, 20, 40, 12, 32, 17, 37, 11, 31, 5, 25)(41, 61, 43, 63)(42, 62, 48, 68)(44, 64, 51, 71)(45, 65, 49, 69)(46, 66, 47, 67)(50, 70, 55, 75)(52, 72, 59, 79)(53, 73, 57, 77)(54, 74, 56, 76)(58, 78, 60, 80) L = (1, 44)(2, 49)(3, 51)(4, 52)(5, 53)(6, 41)(7, 43)(8, 45)(9, 57)(10, 42)(11, 59)(12, 54)(13, 60)(14, 46)(15, 48)(16, 47)(17, 58)(18, 50)(19, 56)(20, 55)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E14.78 Graph:: bipartite v = 11 e = 40 f = 3 degree seq :: [ 4^10, 40 ] E14.83 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1 * Y3^2, Y3^-1 * Y1^-3, (Y3, Y1^-1), (Y3 * Y2^-1)^2, (Y3, Y2^-1), (R * Y1)^2, (R * Y3)^2, Y2^2 * Y1^-1 * Y2, Y3^-1 * Y2^-1 * Y3^-1 * Y1, (Y2^-1, Y1^-1), Y2 * Y3 * Y2 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 7, 27, 12, 32, 19, 39, 13, 33, 3, 23, 9, 29, 17, 37, 14, 34, 20, 40, 16, 36, 6, 26, 11, 31, 18, 38, 15, 35, 4, 24, 10, 30, 5, 25)(41, 61, 43, 63, 51, 71, 42, 62, 49, 69, 58, 78, 48, 68, 57, 77, 55, 75, 47, 67, 54, 74, 44, 64, 52, 72, 60, 80, 50, 70, 59, 79, 56, 76, 45, 65, 53, 73, 46, 66) L = (1, 44)(2, 50)(3, 52)(4, 51)(5, 55)(6, 54)(7, 41)(8, 45)(9, 59)(10, 58)(11, 60)(12, 42)(13, 47)(14, 43)(15, 46)(16, 57)(17, 53)(18, 56)(19, 48)(20, 49)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 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 E14.76 Graph:: bipartite v = 2 e = 40 f = 12 degree seq :: [ 40^2 ] E14.84 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 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, 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^-7 * Y1, (Y3 * Y2^-1)^21 ] Map:: R = (1, 22, 2, 23, 4, 25)(3, 24, 6, 27, 9, 30)(5, 26, 7, 28, 10, 31)(8, 29, 12, 33, 15, 36)(11, 32, 13, 34, 16, 37)(14, 35, 18, 39, 20, 41)(17, 38, 19, 40, 21, 42)(43, 64, 45, 66, 50, 71, 56, 77, 61, 82, 55, 76, 49, 70, 44, 65, 48, 69, 54, 75, 60, 81, 63, 84, 58, 79, 52, 73, 46, 67, 51, 72, 57, 78, 62, 83, 59, 80, 53, 74, 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) :: { ( 6, 42, 6, 42, 6, 42 ), ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 8 e = 42 f = 8 degree seq :: [ 6^7, 42 ] E14.85 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 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, 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^-7 * Y1^-1, (Y3 * Y2^-1)^21 ] Map:: R = (1, 22, 2, 23, 4, 25)(3, 24, 6, 27, 9, 30)(5, 26, 7, 28, 10, 31)(8, 29, 12, 33, 15, 36)(11, 32, 13, 34, 16, 37)(14, 35, 18, 39, 21, 42)(17, 38, 19, 40, 20, 41)(43, 64, 45, 66, 50, 71, 56, 77, 62, 83, 58, 79, 52, 73, 46, 67, 51, 72, 57, 78, 63, 84, 61, 82, 55, 76, 49, 70, 44, 65, 48, 69, 54, 75, 60, 81, 59, 80, 53, 74, 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) :: { ( 6, 42, 6, 42, 6, 42 ), ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 8 e = 42 f = 8 degree seq :: [ 6^7, 42 ] E14.86 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 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, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^-7 * Y1^-1, (Y3 * Y2^-1)^21 ] Map:: non-degenerate R = (1, 22, 2, 23, 4, 25)(3, 24, 6, 27, 9, 30)(5, 26, 7, 28, 10, 31)(8, 29, 12, 33, 15, 36)(11, 32, 13, 34, 16, 37)(14, 35, 18, 39, 21, 42)(17, 38, 19, 40, 20, 41)(43, 64, 45, 66, 50, 71, 56, 77, 62, 83, 58, 79, 52, 73, 46, 67, 51, 72, 57, 78, 63, 84, 61, 82, 55, 76, 49, 70, 44, 65, 48, 69, 54, 75, 60, 81, 59, 80, 53, 74, 47, 68) L = (1, 44)(2, 46)(3, 48)(4, 43)(5, 49)(6, 51)(7, 52)(8, 54)(9, 45)(10, 47)(11, 55)(12, 57)(13, 58)(14, 60)(15, 50)(16, 53)(17, 61)(18, 63)(19, 62)(20, 59)(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) :: { ( 6, 42, 6, 42, 6, 42 ), ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 8 e = 42 f = 8 degree seq :: [ 6^7, 42 ] E14.87 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 6}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y3^4, Y3 * Y2^2 * Y3, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3^-1 * Y1^-2 * Y3^-1, Y3 * Y2 * Y3 * Y2^-1, Y3^-2 * Y1^2, Y1^-1 * Y2^2 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y1^-1, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 6, 30, 9, 33)(4, 28, 15, 39, 7, 31, 16, 40)(10, 34, 19, 43, 12, 36, 20, 44)(13, 37, 21, 45, 14, 38, 22, 46)(17, 41, 23, 47, 18, 42, 24, 48)(49, 73, 51, 75, 56, 80, 54, 78)(50, 74, 57, 81, 53, 77, 59, 83)(52, 76, 62, 86, 55, 79, 61, 85)(58, 82, 66, 90, 60, 84, 65, 89)(63, 87, 69, 93, 64, 88, 70, 94)(67, 91, 71, 95, 68, 92, 72, 96) L = (1, 52)(2, 58)(3, 61)(4, 56)(5, 60)(6, 62)(7, 49)(8, 55)(9, 65)(10, 53)(11, 66)(12, 50)(13, 54)(14, 51)(15, 67)(16, 68)(17, 59)(18, 57)(19, 64)(20, 63)(21, 72)(22, 71)(23, 69)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E14.88 Graph:: bipartite v = 12 e = 48 f = 10 degree seq :: [ 8^12 ] E14.88 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 6}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y3^4, Y2^4, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y3 * Y2^-1, Y3^-2 * Y2^2, Y2^-1 * Y3^-2 * Y2^-1, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, R * Y2 * R * Y2^-1, Y1^-1 * Y3^2 * Y1^-2, Y2 * Y1^-2 * Y2 * Y1, Y1 * Y3 * Y1^-1 * Y3 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 14, 38, 18, 42, 5, 29)(3, 27, 13, 37, 11, 35, 6, 30, 19, 43, 9, 33)(4, 28, 17, 41, 12, 36, 7, 31, 20, 44, 10, 34)(15, 39, 21, 45, 24, 48, 16, 40, 22, 46, 23, 47)(49, 73, 51, 75, 62, 86, 54, 78)(50, 74, 57, 81, 66, 90, 59, 83)(52, 76, 64, 88, 55, 79, 63, 87)(53, 77, 61, 85, 56, 80, 67, 91)(58, 82, 70, 94, 60, 84, 69, 93)(65, 89, 72, 96, 68, 92, 71, 95) L = (1, 52)(2, 58)(3, 63)(4, 62)(5, 65)(6, 64)(7, 49)(8, 68)(9, 69)(10, 66)(11, 70)(12, 50)(13, 71)(14, 55)(15, 54)(16, 51)(17, 56)(18, 60)(19, 72)(20, 53)(21, 59)(22, 57)(23, 67)(24, 61)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^8 ), ( 8^12 ) } Outer automorphisms :: reflexible Dual of E14.87 Graph:: bipartite v = 10 e = 48 f = 12 degree seq :: [ 8^6, 12^4 ] E14.89 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 4, 6, 6}) Quotient :: edge^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y3^3, (R * Y3)^2, R * Y2 * R * Y1, Y1^2 * Y3 * Y1^-1 * Y3, (Y1^-1 * Y3^-1)^3, Y1^6, Y2^6, Y1^2 * Y3^-1 * Y2 * Y3 * Y1 * Y3^-1, (Y1^-1 * Y3^-1 * Y2^-1)^4 ] Map:: non-degenerate R = (1, 25, 3, 27, 5, 29)(2, 26, 7, 31, 8, 32)(4, 28, 11, 35, 13, 37)(6, 30, 14, 38, 17, 41)(9, 33, 20, 44, 21, 45)(10, 34, 12, 36, 23, 47)(15, 39, 22, 46, 18, 42)(16, 40, 19, 43, 24, 48)(49, 50, 54, 64, 60, 52)(51, 57, 56, 67, 70, 58)(53, 62, 69, 72, 59, 63)(55, 66, 65, 71, 68, 61)(73, 74, 78, 88, 84, 76)(75, 81, 80, 91, 94, 82)(77, 86, 93, 96, 83, 87)(79, 90, 89, 95, 92, 85) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^6 ) } Outer automorphisms :: reflexible Dual of E14.92 Graph:: simple bipartite v = 16 e = 48 f = 6 degree seq :: [ 6^16 ] E14.90 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 4, 6, 6}) Quotient :: edge^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-1 * Y2^-1, Y3 * Y2^-1 * Y1^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3^-1 * Y2, R * Y1 * R * Y2, Y3^4, (R * Y3)^2, Y1^2 * Y3^-1 * Y2 * Y3^-1, Y3 * Y2 * Y1 * Y2^-2, Y3 * Y2^2 * Y3 * Y1, Y2^6 ] Map:: polytopal non-degenerate R = (1, 25, 4, 28, 18, 42, 7, 31)(2, 26, 10, 34, 20, 44, 12, 36)(3, 27, 15, 39, 23, 47, 17, 41)(5, 29, 13, 37, 8, 32, 21, 45)(6, 30, 9, 33, 14, 38, 24, 48)(11, 35, 22, 46, 16, 40, 19, 43)(49, 50, 56, 66, 68, 53)(51, 61, 59, 71, 69, 64)(52, 63, 72, 55, 65, 57)(54, 70, 58, 62, 67, 60)(73, 75, 86, 90, 95, 78)(74, 81, 88, 92, 96, 83)(76, 82, 93, 79, 84, 85)(77, 91, 87, 80, 94, 89) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^6 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E14.91 Graph:: bipartite v = 14 e = 48 f = 8 degree seq :: [ 6^8, 8^6 ] E14.91 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 4, 6, 6}) Quotient :: loop^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y3^3, (R * Y3)^2, R * Y2 * R * Y1, Y1^2 * Y3 * Y1^-1 * Y3, (Y1^-1 * Y3^-1)^3, Y1^6, Y2^6, Y1^2 * Y3^-1 * Y2 * Y3 * Y1 * Y3^-1, (Y1^-1 * Y3^-1 * Y2^-1)^4 ] Map:: polytopal non-degenerate R = (1, 25, 49, 73, 3, 27, 51, 75, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 8, 32, 56, 80)(4, 28, 52, 76, 11, 35, 59, 83, 13, 37, 61, 85)(6, 30, 54, 78, 14, 38, 62, 86, 17, 41, 65, 89)(9, 33, 57, 81, 20, 44, 68, 92, 21, 45, 69, 93)(10, 34, 58, 82, 12, 36, 60, 84, 23, 47, 71, 95)(15, 39, 63, 87, 22, 46, 70, 94, 18, 42, 66, 90)(16, 40, 64, 88, 19, 43, 67, 91, 24, 48, 72, 96) L = (1, 26)(2, 30)(3, 33)(4, 25)(5, 38)(6, 40)(7, 42)(8, 43)(9, 32)(10, 27)(11, 39)(12, 28)(13, 31)(14, 45)(15, 29)(16, 36)(17, 47)(18, 41)(19, 46)(20, 37)(21, 48)(22, 34)(23, 44)(24, 35)(49, 74)(50, 78)(51, 81)(52, 73)(53, 86)(54, 88)(55, 90)(56, 91)(57, 80)(58, 75)(59, 87)(60, 76)(61, 79)(62, 93)(63, 77)(64, 84)(65, 95)(66, 89)(67, 94)(68, 85)(69, 96)(70, 82)(71, 92)(72, 83) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E14.90 Transitivity :: VT+ Graph:: v = 8 e = 48 f = 14 degree seq :: [ 12^8 ] E14.92 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 4, 6, 6}) Quotient :: loop^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-1 * Y2^-1, Y3 * Y2^-1 * Y1^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3^-1 * Y2, R * Y1 * R * Y2, Y3^4, (R * Y3)^2, Y1^2 * Y3^-1 * Y2 * Y3^-1, Y3 * Y2 * Y1 * Y2^-2, Y3 * Y2^2 * Y3 * Y1, Y2^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 18, 42, 66, 90, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 20, 44, 68, 92, 12, 36, 60, 84)(3, 27, 51, 75, 15, 39, 63, 87, 23, 47, 71, 95, 17, 41, 65, 89)(5, 29, 53, 77, 13, 37, 61, 85, 8, 32, 56, 80, 21, 45, 69, 93)(6, 30, 54, 78, 9, 33, 57, 81, 14, 38, 62, 86, 24, 48, 72, 96)(11, 35, 59, 83, 22, 46, 70, 94, 16, 40, 64, 88, 19, 43, 67, 91) L = (1, 26)(2, 32)(3, 37)(4, 39)(5, 25)(6, 46)(7, 41)(8, 42)(9, 28)(10, 38)(11, 47)(12, 30)(13, 35)(14, 43)(15, 48)(16, 27)(17, 33)(18, 44)(19, 36)(20, 29)(21, 40)(22, 34)(23, 45)(24, 31)(49, 75)(50, 81)(51, 86)(52, 82)(53, 91)(54, 73)(55, 84)(56, 94)(57, 88)(58, 93)(59, 74)(60, 85)(61, 76)(62, 90)(63, 80)(64, 92)(65, 77)(66, 95)(67, 87)(68, 96)(69, 79)(70, 89)(71, 78)(72, 83) local type(s) :: { ( 6^16 ) } Outer automorphisms :: reflexible Dual of E14.89 Transitivity :: VT+ Graph:: v = 6 e = 48 f = 16 degree seq :: [ 16^6 ] E14.93 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2 * Y1^-1 * Y3, Y3^3, (R * Y3^-1)^2, (R * Y1)^2, (R * Y3)^2, Y2^4, Y1^-1 * Y2^-2 * Y3 * Y2^-1, Y1 * Y3 * Y1^-1 * Y3^-1 * Y2^-1, Y2 * Y1 * Y3^-1 * Y2 * Y3 * Y1^-1, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 11, 35, 7, 31)(4, 28, 15, 39, 16, 40)(6, 30, 20, 44, 21, 45)(8, 32, 22, 46, 10, 34)(9, 33, 23, 47, 13, 37)(12, 36, 17, 41, 14, 38)(18, 42, 24, 48, 19, 43)(49, 73, 51, 75, 60, 84, 54, 78)(50, 74, 56, 80, 65, 89, 52, 76)(53, 77, 66, 90, 62, 86, 57, 81)(55, 79, 63, 87, 69, 93, 70, 94)(58, 82, 71, 95, 64, 88, 72, 96)(59, 83, 67, 91, 68, 92, 61, 85) L = (1, 52)(2, 57)(3, 61)(4, 55)(5, 54)(6, 67)(7, 49)(8, 69)(9, 58)(10, 50)(11, 70)(12, 56)(13, 62)(14, 51)(15, 71)(16, 65)(17, 66)(18, 64)(19, 53)(20, 63)(21, 60)(22, 72)(23, 68)(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) :: { ( 12^6 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E14.98 Graph:: bipartite v = 14 e = 48 f = 8 degree seq :: [ 6^8, 8^6 ] E14.94 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y2, Y3^3, Y1^-1 * Y3 * Y2 * Y1^-1, Y1^4, Y1^-2 * Y3^-1 * Y2^-1, Y3^-1 * Y1^-2 * Y2^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 13, 37, 7, 31, 14, 38)(4, 28, 15, 39, 6, 30, 16, 40)(9, 33, 17, 41, 12, 36, 18, 42)(10, 34, 19, 43, 11, 35, 20, 44)(21, 45, 24, 48, 22, 46, 23, 47)(49, 73, 51, 75, 52, 76, 56, 80, 55, 79, 54, 78)(50, 74, 57, 81, 58, 82, 53, 77, 60, 84, 59, 83)(61, 85, 68, 92, 69, 93, 62, 86, 67, 91, 70, 94)(63, 87, 71, 95, 66, 90, 64, 88, 72, 96, 65, 89) L = (1, 52)(2, 58)(3, 56)(4, 55)(5, 59)(6, 51)(7, 49)(8, 54)(9, 53)(10, 60)(11, 57)(12, 50)(13, 69)(14, 70)(15, 66)(16, 65)(17, 71)(18, 72)(19, 61)(20, 62)(21, 67)(22, 68)(23, 64)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E14.96 Graph:: bipartite v = 10 e = 48 f = 12 degree seq :: [ 8^6, 12^4 ] E14.95 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1 * Y2^-1, (R * Y3^-1)^2, Y2^-1 * Y1 * Y3 * Y2^-1, (R * Y1)^2, Y3^-2 * Y2 * Y1, Y1^4, Y1^-2 * Y2^-3, Y1^-1 * Y2 * 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, 5, 29)(3, 27, 12, 36, 21, 45, 7, 31)(4, 28, 15, 39, 18, 42, 16, 40)(6, 30, 14, 38, 10, 34, 20, 44)(9, 33, 19, 43, 17, 41, 11, 35)(13, 37, 24, 48, 22, 46, 23, 47)(49, 73, 51, 75, 58, 82, 56, 80, 69, 93, 54, 78)(50, 74, 57, 81, 66, 90, 53, 77, 65, 89, 52, 76)(55, 79, 64, 88, 61, 85, 60, 84, 63, 87, 70, 94)(59, 83, 62, 86, 71, 95, 67, 91, 68, 92, 72, 96) L = (1, 52)(2, 58)(3, 61)(4, 60)(5, 54)(6, 59)(7, 49)(8, 66)(9, 71)(10, 67)(11, 50)(12, 56)(13, 68)(14, 51)(15, 57)(16, 65)(17, 72)(18, 55)(19, 53)(20, 69)(21, 70)(22, 62)(23, 64)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E14.97 Graph:: bipartite v = 10 e = 48 f = 12 degree seq :: [ 8^6, 12^4 ] E14.96 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y3 * Y1^2, Y3^3, Y2 * Y3^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 10, 34, 4, 28, 5, 29)(3, 27, 11, 35, 9, 33, 23, 47, 12, 36, 13, 37)(6, 30, 17, 41, 19, 43, 24, 48, 15, 39, 18, 42)(8, 32, 21, 45, 20, 44, 14, 38, 22, 46, 16, 40)(49, 73, 51, 75, 54, 78)(50, 74, 56, 80, 57, 81)(52, 76, 62, 86, 61, 85)(53, 77, 63, 87, 64, 88)(55, 79, 65, 89, 68, 92)(58, 82, 71, 95, 72, 96)(59, 83, 70, 94, 67, 91)(60, 84, 69, 93, 66, 90) L = (1, 52)(2, 53)(3, 60)(4, 55)(5, 58)(6, 63)(7, 49)(8, 70)(9, 51)(10, 50)(11, 61)(12, 57)(13, 71)(14, 69)(15, 67)(16, 62)(17, 66)(18, 72)(19, 54)(20, 56)(21, 64)(22, 68)(23, 59)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E14.94 Graph:: bipartite v = 12 e = 48 f = 10 degree seq :: [ 6^8, 12^4 ] E14.97 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y2 * Y3 * Y2^-1 * Y1^-1, Y3^-1 * Y1^2 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y3^2 * Y1^-1 * Y2^-1, Y2 * Y3 * Y1^2 * Y3^-1, (Y3 * Y2)^3, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1)^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 24, 48, 19, 43, 5, 29)(3, 27, 13, 37, 11, 35, 23, 47, 7, 31, 14, 38)(4, 28, 16, 40, 12, 36, 20, 44, 9, 33, 17, 41)(6, 30, 18, 42, 21, 45, 10, 34, 15, 39, 22, 46)(49, 73, 51, 75, 54, 78)(50, 74, 57, 81, 59, 83)(52, 76, 56, 80, 66, 90)(53, 77, 63, 87, 68, 92)(55, 79, 65, 89, 70, 94)(58, 82, 72, 96, 71, 95)(60, 84, 69, 93, 61, 85)(62, 86, 67, 91, 64, 88) L = (1, 52)(2, 58)(3, 57)(4, 61)(5, 59)(6, 60)(7, 49)(8, 62)(9, 66)(10, 65)(11, 70)(12, 50)(13, 72)(14, 69)(15, 51)(16, 63)(17, 67)(18, 71)(19, 54)(20, 55)(21, 53)(22, 56)(23, 64)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E14.95 Graph:: bipartite v = 12 e = 48 f = 10 degree seq :: [ 6^8, 12^4 ] E14.98 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, Y1^2 * Y3 * Y2^-1, Y3 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2^2 * Y1^-1, Y2 * Y3^-1 * Y2^-1 * Y1 * Y3^-1, Y1 * Y3 * Y1^2 * Y2, Y2 * Y3^-1 * Y2 * Y1^-1 * Y2, (Y3^-1 * Y1)^3, (R * Y2 * Y3^-1)^2, Y1^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 24, 48, 18, 42, 5, 29)(3, 27, 13, 37, 11, 35, 19, 43, 12, 36, 16, 40)(4, 28, 15, 39, 20, 44, 9, 33, 21, 45, 17, 41)(6, 30, 22, 46, 7, 31, 14, 38, 10, 34, 23, 47)(49, 73, 51, 75, 62, 86, 72, 96, 67, 91, 54, 78)(50, 74, 57, 81, 64, 88, 66, 90, 52, 76, 59, 83)(53, 77, 58, 82, 65, 89, 56, 80, 70, 94, 68, 92)(55, 79, 60, 84, 63, 87, 71, 95, 61, 85, 69, 93) L = (1, 52)(2, 58)(3, 63)(4, 55)(5, 67)(6, 65)(7, 49)(8, 51)(9, 71)(10, 60)(11, 62)(12, 50)(13, 66)(14, 68)(15, 56)(16, 54)(17, 64)(18, 70)(19, 69)(20, 59)(21, 53)(22, 61)(23, 72)(24, 57)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E14.93 Graph:: bipartite v = 8 e = 48 f = 14 degree seq :: [ 12^8 ] E14.99 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y3^3 * Y1^-1, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^2 * Y1^-1, (Y2^-1 * Y3^-1)^2, Y1^4, (Y1^-1 * Y3^-1)^3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 13, 37, 19, 43, 9, 33)(4, 28, 10, 34, 20, 44, 17, 41)(6, 30, 15, 39, 21, 45, 11, 35)(7, 31, 12, 36, 22, 46, 18, 42)(14, 38, 24, 48, 16, 40, 23, 47)(49, 73, 51, 75, 58, 82, 72, 96, 66, 90, 54, 78)(50, 74, 57, 81, 68, 92, 62, 86, 55, 79, 59, 83)(52, 76, 64, 88, 70, 94, 63, 87, 53, 77, 61, 85)(56, 80, 67, 91, 65, 89, 71, 95, 60, 84, 69, 93) L = (1, 52)(2, 58)(3, 62)(4, 60)(5, 65)(6, 57)(7, 49)(8, 68)(9, 71)(10, 70)(11, 67)(12, 50)(13, 72)(14, 69)(15, 51)(16, 54)(17, 55)(18, 53)(19, 64)(20, 66)(21, 61)(22, 56)(23, 63)(24, 59)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E14.100 Graph:: bipartite v = 10 e = 48 f = 12 degree seq :: [ 8^6, 12^4 ] E14.100 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y2 * Y1^2, (Y3^-1 * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y2)^2, Y3^-4 * Y2, Y1 * Y3 * Y1 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 9, 33, 3, 27, 5, 29)(4, 28, 13, 37, 15, 39, 17, 41, 11, 35, 10, 34)(7, 31, 16, 40, 18, 42, 8, 32, 12, 36, 19, 43)(14, 38, 21, 45, 20, 44, 22, 46, 23, 47, 24, 48)(49, 73, 51, 75, 54, 78)(50, 74, 53, 77, 57, 81)(52, 76, 59, 83, 63, 87)(55, 79, 60, 84, 66, 90)(56, 80, 64, 88, 67, 91)(58, 82, 65, 89, 61, 85)(62, 86, 71, 95, 68, 92)(69, 93, 72, 96, 70, 94) L = (1, 52)(2, 56)(3, 59)(4, 62)(5, 64)(6, 63)(7, 49)(8, 69)(9, 67)(10, 50)(11, 71)(12, 51)(13, 57)(14, 60)(15, 68)(16, 72)(17, 53)(18, 54)(19, 70)(20, 55)(21, 65)(22, 58)(23, 66)(24, 61)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E14.99 Graph:: bipartite v = 12 e = 48 f = 10 degree seq :: [ 6^8, 12^4 ] E14.101 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 8, 8}) 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, Y2^-1 * Y1^-1, Y2^3, Y1^3, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, Y3^8 ] Map:: non-degenerate R = (1, 25, 4, 28, 10, 34, 16, 40, 22, 46, 17, 41, 11, 35, 5, 29)(2, 26, 6, 30, 12, 36, 18, 42, 23, 47, 19, 43, 13, 37, 7, 31)(3, 27, 8, 32, 14, 38, 20, 44, 24, 48, 21, 45, 15, 39, 9, 33)(49, 50, 51)(52, 56, 54)(53, 57, 55)(58, 60, 62)(59, 61, 63)(64, 68, 66)(65, 69, 67)(70, 71, 72)(73, 75, 74)(76, 78, 80)(77, 79, 81)(82, 86, 84)(83, 87, 85)(88, 90, 92)(89, 91, 93)(94, 96, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 32^3 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E14.103 Graph:: simple bipartite v = 19 e = 48 f = 3 degree seq :: [ 3^16, 16^3 ] E14.102 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 8, 8}) Quotient :: edge^2 Aut^+ = C3 : C8 (small group id <24, 1>) Aut = C8 x S3 (small group id <48, 4>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, Y3^3, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y2 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1^-1, Y1^8, Y2^8 ] Map:: non-degenerate R = (1, 25, 4, 28, 5, 29)(2, 26, 7, 31, 8, 32)(3, 27, 10, 34, 11, 35)(6, 30, 13, 37, 14, 38)(9, 33, 16, 40, 17, 41)(12, 36, 19, 43, 20, 44)(15, 39, 21, 45, 22, 46)(18, 42, 23, 47, 24, 48)(49, 50, 54, 60, 66, 63, 57, 51)(52, 56, 61, 68, 71, 70, 64, 59)(53, 55, 62, 67, 72, 69, 65, 58)(73, 75, 81, 87, 90, 84, 78, 74)(76, 83, 88, 94, 95, 92, 85, 80)(77, 82, 89, 93, 96, 91, 86, 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) :: { ( 12^6 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E14.104 Graph:: simple bipartite v = 14 e = 48 f = 8 degree seq :: [ 6^8, 8^6 ] E14.103 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 8, 8}) 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, Y2^-1 * Y1^-1, Y2^3, Y1^3, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, Y3^8 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 10, 34, 58, 82, 16, 40, 64, 88, 22, 46, 70, 94, 17, 41, 65, 89, 11, 35, 59, 83, 5, 29, 53, 77)(2, 26, 50, 74, 6, 30, 54, 78, 12, 36, 60, 84, 18, 42, 66, 90, 23, 47, 71, 95, 19, 43, 67, 91, 13, 37, 61, 85, 7, 31, 55, 79)(3, 27, 51, 75, 8, 32, 56, 80, 14, 38, 62, 86, 20, 44, 68, 92, 24, 48, 72, 96, 21, 45, 69, 93, 15, 39, 63, 87, 9, 33, 57, 81) L = (1, 26)(2, 27)(3, 25)(4, 32)(5, 33)(6, 28)(7, 29)(8, 30)(9, 31)(10, 36)(11, 37)(12, 38)(13, 39)(14, 34)(15, 35)(16, 44)(17, 45)(18, 40)(19, 41)(20, 42)(21, 43)(22, 47)(23, 48)(24, 46)(49, 75)(50, 73)(51, 74)(52, 78)(53, 79)(54, 80)(55, 81)(56, 76)(57, 77)(58, 86)(59, 87)(60, 82)(61, 83)(62, 84)(63, 85)(64, 90)(65, 91)(66, 92)(67, 93)(68, 88)(69, 89)(70, 96)(71, 94)(72, 95) local type(s) :: { ( 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16 ) } Outer automorphisms :: reflexible Dual of E14.101 Transitivity :: VT+ Graph:: v = 3 e = 48 f = 19 degree seq :: [ 32^3 ] E14.104 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 8, 8}) Quotient :: loop^2 Aut^+ = C3 : C8 (small group id <24, 1>) Aut = C8 x S3 (small group id <48, 4>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, Y3^3, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y2 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1^-1, Y1^8, Y2^8 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 8, 32, 56, 80)(3, 27, 51, 75, 10, 34, 58, 82, 11, 35, 59, 83)(6, 30, 54, 78, 13, 37, 61, 85, 14, 38, 62, 86)(9, 33, 57, 81, 16, 40, 64, 88, 17, 41, 65, 89)(12, 36, 60, 84, 19, 43, 67, 91, 20, 44, 68, 92)(15, 39, 63, 87, 21, 45, 69, 93, 22, 46, 70, 94)(18, 42, 66, 90, 23, 47, 71, 95, 24, 48, 72, 96) L = (1, 26)(2, 30)(3, 25)(4, 32)(5, 31)(6, 36)(7, 38)(8, 37)(9, 27)(10, 29)(11, 28)(12, 42)(13, 44)(14, 43)(15, 33)(16, 35)(17, 34)(18, 39)(19, 48)(20, 47)(21, 41)(22, 40)(23, 46)(24, 45)(49, 75)(50, 73)(51, 81)(52, 83)(53, 82)(54, 74)(55, 77)(56, 76)(57, 87)(58, 89)(59, 88)(60, 78)(61, 80)(62, 79)(63, 90)(64, 94)(65, 93)(66, 84)(67, 86)(68, 85)(69, 96)(70, 95)(71, 92)(72, 91) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E14.102 Transitivity :: VT+ Graph:: bipartite v = 8 e = 48 f = 14 degree seq :: [ 12^8 ] E14.105 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ 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 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^8, (Y3 * Y2^-1)^8 ] Map:: R = (1, 25, 2, 26, 4, 28)(3, 27, 8, 32, 6, 30)(5, 29, 10, 34, 7, 31)(9, 33, 12, 36, 14, 38)(11, 35, 13, 37, 16, 40)(15, 39, 20, 44, 18, 42)(17, 41, 22, 46, 19, 43)(21, 45, 23, 47, 24, 48)(49, 73, 51, 75, 57, 81, 63, 87, 69, 93, 65, 89, 59, 83, 53, 77)(50, 74, 54, 78, 60, 84, 66, 90, 71, 95, 67, 91, 61, 85, 55, 79)(52, 76, 56, 80, 62, 86, 68, 92, 72, 96, 70, 94, 64, 88, 58, 82) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 11 e = 48 f = 11 degree seq :: [ 6^8, 16^3 ] E14.106 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, Y1^3, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^8, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28)(3, 27, 8, 32, 6, 30)(5, 29, 10, 34, 7, 31)(9, 33, 12, 36, 14, 38)(11, 35, 13, 37, 16, 40)(15, 39, 20, 44, 18, 42)(17, 41, 22, 46, 19, 43)(21, 45, 23, 47, 24, 48)(49, 73, 51, 75, 57, 81, 63, 87, 69, 93, 65, 89, 59, 83, 53, 77)(50, 74, 54, 78, 60, 84, 66, 90, 71, 95, 67, 91, 61, 85, 55, 79)(52, 76, 56, 80, 62, 86, 68, 92, 72, 96, 70, 94, 64, 88, 58, 82) L = (1, 50)(2, 52)(3, 56)(4, 49)(5, 58)(6, 51)(7, 53)(8, 54)(9, 60)(10, 55)(11, 61)(12, 62)(13, 64)(14, 57)(15, 68)(16, 59)(17, 70)(18, 63)(19, 65)(20, 66)(21, 71)(22, 67)(23, 72)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 11 e = 48 f = 11 degree seq :: [ 6^8, 16^3 ] E14.107 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 8, 8}) 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, R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^8, (Y3 * Y2^-1)^8 ] Map:: R = (1, 25, 2, 26, 4, 28)(3, 27, 6, 30, 9, 33)(5, 29, 7, 31, 10, 34)(8, 32, 12, 36, 15, 39)(11, 35, 13, 37, 16, 40)(14, 38, 18, 42, 21, 45)(17, 41, 19, 43, 22, 46)(20, 44, 23, 47, 24, 48)(49, 73, 51, 75, 56, 80, 62, 86, 68, 92, 65, 89, 59, 83, 53, 77)(50, 74, 54, 78, 60, 84, 66, 90, 71, 95, 67, 91, 61, 85, 55, 79)(52, 76, 57, 81, 63, 87, 69, 93, 72, 96, 70, 94, 64, 88, 58, 82) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 11 e = 48 f = 11 degree seq :: [ 6^8, 16^3 ] E14.108 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-2, Y3^3, (Y3^-1 * Y1^-1)^2, Y1 * Y2 * Y1 * Y2^-1, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y2^3 * Y1^-1, Y3^-1 * Y2^-1 * Y1 * Y3 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 9, 33, 7, 31, 5, 29)(3, 27, 11, 35, 13, 37, 20, 44, 14, 38, 8, 32)(6, 30, 16, 40, 17, 41, 21, 45, 15, 39, 10, 34)(12, 36, 19, 43, 24, 48, 18, 42, 22, 46, 23, 47)(49, 73, 51, 75, 60, 84, 69, 93, 57, 81, 68, 92, 66, 90, 54, 78)(50, 74, 56, 80, 67, 91, 65, 89, 55, 79, 61, 85, 70, 94, 58, 82)(52, 76, 62, 86, 72, 96, 64, 88, 53, 77, 59, 83, 71, 95, 63, 87) L = (1, 52)(2, 57)(3, 61)(4, 55)(5, 50)(6, 65)(7, 49)(8, 59)(9, 53)(10, 64)(11, 68)(12, 72)(13, 62)(14, 51)(15, 54)(16, 69)(17, 63)(18, 71)(19, 66)(20, 56)(21, 58)(22, 60)(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) :: { ( 4, 16, 4, 16, 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 E14.109 Graph:: bipartite v = 7 e = 48 f = 15 degree seq :: [ 12^4, 16^3 ] E14.109 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1^4, Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 12, 36, 3, 27, 8, 32, 16, 40, 5, 29)(4, 28, 10, 34, 17, 41, 21, 45, 11, 35, 20, 44, 23, 47, 14, 38)(6, 30, 9, 33, 18, 42, 22, 46, 13, 37, 19, 43, 24, 48, 15, 39)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 59, 83)(53, 77, 60, 84)(54, 78, 61, 85)(55, 79, 64, 88)(57, 81, 67, 91)(58, 82, 68, 92)(62, 86, 69, 93)(63, 87, 70, 94)(65, 89, 71, 95)(66, 90, 72, 96) L = (1, 52)(2, 57)(3, 59)(4, 54)(5, 63)(6, 49)(7, 65)(8, 67)(9, 58)(10, 50)(11, 61)(12, 70)(13, 51)(14, 53)(15, 62)(16, 71)(17, 66)(18, 55)(19, 68)(20, 56)(21, 60)(22, 69)(23, 72)(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 ) } Outer automorphisms :: reflexible Dual of E14.108 Graph:: bipartite v = 15 e = 48 f = 7 degree seq :: [ 4^12, 16^3 ] E14.110 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 4, 4, 12}) Quotient :: edge^2 Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = C24 : C2 (small group id <48, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y2^4, Y1^4, Y1 * Y3 * Y1^-1 * Y3, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, Y1 * Y2^2 * Y1, Y1^-1 * Y2^-1 * Y3^-3, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 4, 28, 15, 39, 9, 33, 23, 47, 22, 46, 8, 32, 21, 45, 24, 48, 11, 35, 20, 44, 7, 31)(2, 26, 10, 34, 17, 41, 6, 30, 19, 43, 16, 40, 5, 29, 18, 42, 14, 38, 3, 27, 13, 37, 12, 36)(49, 50, 56, 53)(51, 59, 54, 57)(52, 60, 69, 64)(55, 58, 70, 66)(61, 72, 67, 63)(62, 68, 65, 71)(73, 75, 80, 78)(74, 81, 77, 83)(76, 86, 93, 89)(79, 85, 94, 91)(82, 87, 90, 96)(84, 95, 88, 92) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^4 ), ( 12^24 ) } Outer automorphisms :: reflexible Dual of E14.113 Graph:: bipartite v = 14 e = 48 f = 8 degree seq :: [ 4^12, 24^2 ] E14.111 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 4, 4, 12}) Quotient :: edge^2 Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = C24 : C2 (small group id <48, 6>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2^2 * Y1^2, Y1^-1 * Y2^2 * Y1^-1, Y1^4, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, R * Y2 * R * Y1, Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, Y2^-1 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 25, 4, 28, 7, 31)(2, 26, 10, 34, 12, 36)(3, 27, 13, 37, 14, 38)(5, 29, 17, 41, 15, 39)(6, 30, 18, 42, 16, 40)(8, 32, 19, 43, 20, 44)(9, 33, 21, 45, 22, 46)(11, 35, 24, 48, 23, 47)(49, 50, 56, 53)(51, 59, 54, 57)(52, 60, 67, 63)(55, 58, 68, 65)(61, 71, 66, 70)(62, 72, 64, 69)(73, 75, 80, 78)(74, 81, 77, 83)(76, 86, 91, 88)(79, 85, 92, 90)(82, 94, 89, 95)(84, 93, 87, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 48^4 ), ( 48^6 ) } Outer automorphisms :: reflexible Dual of E14.112 Graph:: simple bipartite v = 20 e = 48 f = 2 degree seq :: [ 4^12, 6^8 ] E14.112 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 4, 4, 12}) Quotient :: loop^2 Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = C24 : C2 (small group id <48, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y2^4, Y1^4, Y1 * Y3 * Y1^-1 * Y3, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, Y1 * Y2^2 * Y1, Y1^-1 * Y2^-1 * Y3^-3, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 15, 39, 63, 87, 9, 33, 57, 81, 23, 47, 71, 95, 22, 46, 70, 94, 8, 32, 56, 80, 21, 45, 69, 93, 24, 48, 72, 96, 11, 35, 59, 83, 20, 44, 68, 92, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 17, 41, 65, 89, 6, 30, 54, 78, 19, 43, 67, 91, 16, 40, 64, 88, 5, 29, 53, 77, 18, 42, 66, 90, 14, 38, 62, 86, 3, 27, 51, 75, 13, 37, 61, 85, 12, 36, 60, 84) L = (1, 26)(2, 32)(3, 35)(4, 36)(5, 25)(6, 33)(7, 34)(8, 29)(9, 27)(10, 46)(11, 30)(12, 45)(13, 48)(14, 44)(15, 37)(16, 28)(17, 47)(18, 31)(19, 39)(20, 41)(21, 40)(22, 42)(23, 38)(24, 43)(49, 75)(50, 81)(51, 80)(52, 86)(53, 83)(54, 73)(55, 85)(56, 78)(57, 77)(58, 87)(59, 74)(60, 95)(61, 94)(62, 93)(63, 90)(64, 92)(65, 76)(66, 96)(67, 79)(68, 84)(69, 89)(70, 91)(71, 88)(72, 82) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E14.111 Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 20 degree seq :: [ 48^2 ] E14.113 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 4, 4, 12}) Quotient :: loop^2 Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = C24 : C2 (small group id <48, 6>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2^2 * Y1^2, Y1^-1 * Y2^2 * Y1^-1, Y1^4, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, R * Y2 * R * Y1, Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, Y2^-1 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 12, 36, 60, 84)(3, 27, 51, 75, 13, 37, 61, 85, 14, 38, 62, 86)(5, 29, 53, 77, 17, 41, 65, 89, 15, 39, 63, 87)(6, 30, 54, 78, 18, 42, 66, 90, 16, 40, 64, 88)(8, 32, 56, 80, 19, 43, 67, 91, 20, 44, 68, 92)(9, 33, 57, 81, 21, 45, 69, 93, 22, 46, 70, 94)(11, 35, 59, 83, 24, 48, 72, 96, 23, 47, 71, 95) L = (1, 26)(2, 32)(3, 35)(4, 36)(5, 25)(6, 33)(7, 34)(8, 29)(9, 27)(10, 44)(11, 30)(12, 43)(13, 47)(14, 48)(15, 28)(16, 45)(17, 31)(18, 46)(19, 39)(20, 41)(21, 38)(22, 37)(23, 42)(24, 40)(49, 75)(50, 81)(51, 80)(52, 86)(53, 83)(54, 73)(55, 85)(56, 78)(57, 77)(58, 94)(59, 74)(60, 93)(61, 92)(62, 91)(63, 96)(64, 76)(65, 95)(66, 79)(67, 88)(68, 90)(69, 87)(70, 89)(71, 82)(72, 84) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E14.110 Transitivity :: VT+ Graph:: bipartite v = 8 e = 48 f = 14 degree seq :: [ 12^8 ] E14.114 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^4, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^4, (R * Y1)^2, R * Y2 * R * Y2^-1, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, (Y1, Y3^-1), Y2 * Y3^2 * Y2 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 12, 36, 8, 32)(4, 28, 9, 33, 16, 40)(6, 30, 17, 41, 10, 34)(7, 31, 11, 35, 18, 42)(13, 37, 19, 43, 22, 46)(14, 38, 23, 47, 20, 44)(15, 39, 24, 48, 21, 45)(49, 73, 51, 75, 61, 85, 54, 78)(50, 74, 56, 80, 67, 91, 58, 82)(52, 76, 63, 87, 55, 79, 62, 86)(53, 77, 60, 84, 70, 94, 65, 89)(57, 81, 69, 93, 59, 83, 68, 92)(64, 88, 72, 96, 66, 90, 71, 95) L = (1, 52)(2, 57)(3, 62)(4, 61)(5, 64)(6, 63)(7, 49)(8, 68)(9, 67)(10, 69)(11, 50)(12, 71)(13, 55)(14, 54)(15, 51)(16, 70)(17, 72)(18, 53)(19, 59)(20, 58)(21, 56)(22, 66)(23, 65)(24, 60)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E14.116 Graph:: simple bipartite v = 14 e = 48 f = 8 degree seq :: [ 6^8, 8^6 ] E14.115 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y3^-1, Y1), Y2^4, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, Y3^-4 * Y1, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y3, Y3 * Y1 * Y2 * Y3^-1 * Y2, R * Y2 * Y1 * R * Y2^-1, Y2^-2 * Y3^2 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 12, 36, 8, 32)(4, 28, 9, 33, 17, 41)(6, 30, 19, 43, 10, 34)(7, 31, 11, 35, 20, 44)(13, 37, 22, 46, 16, 40)(14, 38, 18, 42, 23, 47)(15, 39, 24, 48, 21, 45)(49, 73, 51, 75, 61, 85, 54, 78)(50, 74, 56, 80, 70, 94, 58, 82)(52, 76, 63, 87, 68, 92, 66, 90)(53, 77, 60, 84, 64, 88, 67, 91)(55, 79, 62, 86, 57, 81, 69, 93)(59, 83, 71, 95, 65, 89, 72, 96) L = (1, 52)(2, 57)(3, 62)(4, 64)(5, 65)(6, 69)(7, 49)(8, 71)(9, 61)(10, 72)(11, 50)(12, 66)(13, 68)(14, 58)(15, 51)(16, 59)(17, 70)(18, 54)(19, 63)(20, 53)(21, 56)(22, 55)(23, 67)(24, 60)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E14.117 Graph:: simple bipartite v = 14 e = 48 f = 8 degree seq :: [ 6^8, 8^6 ] E14.116 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y3^-2 * Y1^-2, (R * Y3)^2, Y2^-3 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2 * Y1^-1 * Y2 * Y1, Y3^4, Y3 * Y1 * Y3 * Y1^-1, Y1^4, Y2 * Y1^-2 * Y2 * Y3^-1 * Y2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y1 * Y2^-2 * Y1^-1, Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 19, 43, 15, 39)(4, 28, 12, 36, 7, 31, 10, 34)(6, 30, 9, 33, 20, 44, 18, 42)(13, 37, 22, 46, 17, 41, 23, 47)(14, 38, 21, 45, 16, 40, 24, 48)(49, 73, 51, 75, 61, 85, 55, 79, 64, 88, 68, 92, 56, 80, 67, 91, 65, 89, 52, 76, 62, 86, 54, 78)(50, 74, 57, 81, 69, 93, 60, 84, 71, 95, 63, 87, 53, 77, 66, 90, 72, 96, 58, 82, 70, 94, 59, 83) L = (1, 52)(2, 58)(3, 62)(4, 56)(5, 60)(6, 65)(7, 49)(8, 55)(9, 70)(10, 53)(11, 72)(12, 50)(13, 54)(14, 67)(15, 69)(16, 51)(17, 68)(18, 71)(19, 64)(20, 61)(21, 59)(22, 66)(23, 57)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E14.114 Graph:: bipartite v = 8 e = 48 f = 14 degree seq :: [ 8^6, 24^2 ] E14.117 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1 * Y1^2, Y2 * Y3^2 * Y2, Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y1^-2 * Y3^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^3, Y3^-2 * Y2 * Y1 * Y3 * Y2^-2 * Y1^-1, Y3^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 7, 31, 10, 34)(4, 28, 12, 36, 6, 30, 9, 33)(13, 37, 19, 43, 14, 38, 20, 44)(15, 39, 17, 41, 16, 40, 18, 42)(21, 45, 24, 48, 22, 46, 23, 47)(49, 73, 51, 75, 61, 85, 69, 93, 64, 88, 52, 76, 56, 80, 55, 79, 62, 86, 70, 94, 63, 87, 54, 78)(50, 74, 57, 81, 65, 89, 71, 95, 68, 92, 58, 82, 53, 77, 60, 84, 66, 90, 72, 96, 67, 91, 59, 83) L = (1, 52)(2, 58)(3, 56)(4, 63)(5, 59)(6, 64)(7, 49)(8, 54)(9, 53)(10, 67)(11, 68)(12, 50)(13, 55)(14, 51)(15, 69)(16, 70)(17, 60)(18, 57)(19, 71)(20, 72)(21, 62)(22, 61)(23, 66)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E14.115 Graph:: bipartite v = 8 e = 48 f = 14 degree seq :: [ 8^6, 24^2 ] E14.118 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 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, Y1^3, Y2^-1 * Y3^-2 * Y2^-1, (Y2, Y1^-1), Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y2^-1, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (Y1, Y3^-1), Y2^4, Y3^-12 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 8, 32, 14, 38)(4, 28, 9, 33, 16, 40)(6, 30, 10, 34, 17, 41)(7, 31, 11, 35, 18, 42)(12, 36, 19, 43, 22, 46)(13, 37, 20, 44, 23, 47)(15, 39, 21, 45, 24, 48)(49, 73, 51, 75, 60, 84, 54, 78)(50, 74, 56, 80, 67, 91, 58, 82)(52, 76, 63, 87, 55, 79, 61, 85)(53, 77, 62, 86, 70, 94, 65, 89)(57, 81, 69, 93, 59, 83, 68, 92)(64, 88, 72, 96, 66, 90, 71, 95) L = (1, 52)(2, 57)(3, 61)(4, 60)(5, 64)(6, 63)(7, 49)(8, 68)(9, 67)(10, 69)(11, 50)(12, 55)(13, 54)(14, 71)(15, 51)(16, 70)(17, 72)(18, 53)(19, 59)(20, 58)(21, 56)(22, 66)(23, 65)(24, 62)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E14.119 Graph:: simple bipartite v = 14 e = 48 f = 8 degree seq :: [ 6^8, 8^6 ] E14.119 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 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, Y1^-1 * Y3^2 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, Y2^-3 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y3^4, Y1^4, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1, Y1^-1 * Y2 * Y3^2 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 13, 37, 19, 43, 9, 33)(4, 28, 12, 36, 7, 31, 10, 34)(6, 30, 18, 42, 20, 44, 11, 35)(14, 38, 21, 45, 17, 41, 24, 48)(15, 39, 22, 46, 16, 40, 23, 47)(49, 73, 51, 75, 62, 86, 55, 79, 64, 88, 68, 92, 56, 80, 67, 91, 65, 89, 52, 76, 63, 87, 54, 78)(50, 74, 57, 81, 69, 93, 60, 84, 71, 95, 66, 90, 53, 77, 61, 85, 72, 96, 58, 82, 70, 94, 59, 83) L = (1, 52)(2, 58)(3, 63)(4, 56)(5, 60)(6, 65)(7, 49)(8, 55)(9, 70)(10, 53)(11, 72)(12, 50)(13, 71)(14, 54)(15, 67)(16, 51)(17, 68)(18, 69)(19, 64)(20, 62)(21, 59)(22, 61)(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) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E14.118 Graph:: bipartite v = 8 e = 48 f = 14 degree seq :: [ 8^6, 24^2 ] E14.120 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y3^-2 * Y2^-1, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1, Y3^6, Y2^-2 * Y3^2 * Y2^-2, Y2^-2 * Y1 * Y3^-2 * Y1, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 14, 38)(5, 29, 9, 33)(6, 30, 17, 41)(8, 32, 13, 37)(10, 34, 16, 40)(11, 35, 18, 42)(12, 36, 23, 47)(15, 39, 20, 44)(19, 43, 22, 46)(21, 45, 24, 48)(49, 73, 51, 75, 59, 83, 69, 93, 63, 87, 53, 77)(50, 74, 55, 79, 66, 90, 72, 96, 68, 92, 57, 81)(52, 76, 60, 84, 54, 78, 61, 85, 70, 94, 64, 88)(56, 80, 67, 91, 58, 82, 62, 86, 71, 95, 65, 89) L = (1, 52)(2, 56)(3, 60)(4, 63)(5, 64)(6, 49)(7, 67)(8, 68)(9, 65)(10, 50)(11, 54)(12, 53)(13, 51)(14, 55)(15, 70)(16, 69)(17, 72)(18, 58)(19, 57)(20, 71)(21, 61)(22, 59)(23, 66)(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) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E14.126 Graph:: simple bipartite v = 16 e = 48 f = 6 degree seq :: [ 4^12, 12^4 ] E14.121 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^2 * Y3, Y3 * Y1 * Y2 * Y1, (R * Y3)^2, (Y3, Y2^-1), (R * Y1)^2, (R * Y2)^2, Y3^-2 * Y2^4, (Y2 * Y3^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 10, 34)(4, 28, 9, 33)(5, 29, 8, 32)(6, 30, 7, 31)(11, 35, 16, 40)(12, 36, 17, 41)(13, 37, 18, 42)(14, 38, 19, 43)(15, 39, 20, 44)(21, 45, 24, 48)(22, 46, 23, 47)(49, 73, 51, 75, 59, 83, 69, 93, 62, 86, 53, 77)(50, 74, 55, 79, 64, 88, 71, 95, 67, 91, 57, 81)(52, 76, 60, 84, 54, 78, 61, 85, 70, 94, 63, 87)(56, 80, 65, 89, 58, 82, 66, 90, 72, 96, 68, 92) L = (1, 52)(2, 56)(3, 60)(4, 62)(5, 63)(6, 49)(7, 65)(8, 67)(9, 68)(10, 50)(11, 54)(12, 53)(13, 51)(14, 70)(15, 69)(16, 58)(17, 57)(18, 55)(19, 72)(20, 71)(21, 61)(22, 59)(23, 66)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E14.125 Graph:: simple bipartite v = 16 e = 48 f = 6 degree seq :: [ 4^12, 12^4 ] E14.122 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, (Y2^-1 * Y3^-1)^2, R * Y2 * Y1 * R * Y2, Y3^2 * Y1 * Y2^2, Y2 * Y1 * Y3 * Y2^-1 * Y3^-1, Y3 * Y2^-1 * Y3 * Y2^-3 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 8, 32)(5, 29, 9, 33)(6, 30, 10, 34)(11, 35, 20, 44)(12, 36, 14, 38)(13, 37, 19, 43)(15, 39, 18, 42)(16, 40, 17, 41)(21, 45, 24, 48)(22, 46, 23, 47)(49, 73, 51, 75, 59, 83, 69, 93, 66, 90, 53, 77)(50, 74, 55, 79, 68, 92, 72, 96, 63, 87, 57, 81)(52, 76, 62, 86, 58, 82, 61, 85, 71, 95, 64, 88)(54, 78, 67, 91, 70, 94, 65, 89, 56, 80, 60, 84) L = (1, 52)(2, 56)(3, 60)(4, 63)(5, 65)(6, 49)(7, 62)(8, 66)(9, 64)(10, 50)(11, 58)(12, 57)(13, 51)(14, 53)(15, 70)(16, 69)(17, 72)(18, 71)(19, 55)(20, 54)(21, 67)(22, 59)(23, 68)(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) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E14.127 Graph:: simple bipartite v = 16 e = 48 f = 6 degree seq :: [ 4^12, 12^4 ] E14.123 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y2, (Y1, Y2^-1), (Y2^-1 * Y1)^2, Y1^-1 * Y2^2 * Y1^-1, (R * Y3)^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y2^2 * Y1^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 21, 45, 17, 41, 5, 29)(3, 27, 9, 33, 22, 46, 18, 42, 6, 30, 11, 35)(4, 28, 14, 38, 23, 47, 12, 36, 19, 43, 15, 39)(7, 31, 20, 44, 13, 37, 16, 40, 24, 48, 10, 34)(49, 73, 51, 75, 56, 80, 70, 94, 65, 89, 54, 78)(50, 74, 57, 81, 69, 93, 66, 90, 53, 77, 59, 83)(52, 76, 61, 85, 71, 95, 72, 96, 67, 91, 55, 79)(58, 82, 63, 87, 68, 92, 62, 86, 64, 88, 60, 84) L = (1, 52)(2, 58)(3, 61)(4, 51)(5, 64)(6, 55)(7, 49)(8, 71)(9, 63)(10, 57)(11, 60)(12, 50)(13, 56)(14, 53)(15, 69)(16, 59)(17, 67)(18, 62)(19, 54)(20, 66)(21, 68)(22, 72)(23, 70)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E14.124 Graph:: bipartite v = 8 e = 48 f = 14 degree seq :: [ 12^8 ] E14.124 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1^-2 * Y3^-1 * Y2, Y3 * Y2 * Y3^-1 * Y2, Y3^-1 * Y1^-2 * Y2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, Y1^-1 * Y3^-1 * Y1^3 * Y3^-1, Y3^-1 * Y1^-1 * Y3^3 * Y1^-1, Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 17, 41, 16, 40, 22, 46, 24, 48, 23, 47, 14, 38, 21, 45, 12, 36, 5, 29)(3, 27, 11, 35, 6, 30, 15, 39, 18, 42, 9, 33, 20, 44, 8, 32, 19, 43, 10, 34, 4, 28, 13, 37)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 60, 84)(53, 77, 57, 81)(54, 78, 55, 79)(58, 82, 65, 89)(59, 83, 71, 95)(61, 85, 70, 94)(62, 86, 67, 91)(63, 87, 69, 93)(64, 88, 66, 90)(68, 92, 72, 96) L = (1, 52)(2, 57)(3, 60)(4, 62)(5, 63)(6, 49)(7, 51)(8, 53)(9, 69)(10, 50)(11, 70)(12, 67)(13, 65)(14, 68)(15, 71)(16, 54)(17, 56)(18, 55)(19, 72)(20, 64)(21, 59)(22, 58)(23, 61)(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) :: { ( 12^4 ), ( 12^24 ) } Outer automorphisms :: reflexible Dual of E14.123 Graph:: bipartite v = 14 e = 48 f = 8 degree seq :: [ 4^12, 24^2 ] E14.125 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, (Y3 * Y2^-1)^2, (Y3, Y1^-1), (Y3 * Y1^-1)^2, (R * Y3)^2, Y3^-2 * Y1^2, (R * Y1)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2, Y3^-2 * Y1^-4, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 21, 45, 16, 40, 5, 29)(3, 27, 6, 30, 10, 34, 23, 47, 24, 48, 13, 37)(4, 28, 9, 33, 22, 46, 17, 41, 7, 31, 11, 35)(12, 36, 18, 42, 20, 44, 15, 39, 14, 38, 19, 43)(49, 73, 51, 75, 53, 77, 61, 85, 64, 88, 72, 96, 69, 93, 71, 95, 56, 80, 58, 82, 50, 74, 54, 78)(52, 76, 63, 87, 59, 83, 68, 92, 55, 79, 66, 90, 65, 89, 60, 84, 70, 94, 67, 91, 57, 81, 62, 86) L = (1, 52)(2, 57)(3, 60)(4, 56)(5, 59)(6, 66)(7, 49)(8, 70)(9, 69)(10, 68)(11, 50)(12, 58)(13, 67)(14, 51)(15, 61)(16, 55)(17, 53)(18, 71)(19, 54)(20, 72)(21, 65)(22, 64)(23, 63)(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) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ), ( 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 E14.121 Graph:: bipartite v = 6 e = 48 f = 16 degree seq :: [ 12^4, 24^2 ] E14.126 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, (Y3, Y1^-1), Y2 * Y3^-1 * Y2^-1 * Y1, Y2^2 * Y3^-1 * Y1^-1, Y3 * Y1 * Y2^-2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y3^-2 * Y1^2, (R * Y3)^2, Y3^6, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1^-3 * Y2^-1 * Y1^-1, Y2^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 15, 39, 5, 29)(3, 27, 13, 37, 20, 44, 16, 40, 24, 48, 11, 35)(4, 28, 10, 34, 21, 45, 17, 41, 7, 31, 12, 36)(6, 30, 14, 38, 22, 46, 9, 33, 23, 47, 18, 42)(49, 73, 51, 75, 58, 82, 71, 95, 63, 87, 72, 96, 60, 84, 70, 94, 56, 80, 68, 92, 65, 89, 54, 78)(50, 74, 57, 81, 69, 93, 64, 88, 53, 77, 62, 86, 52, 76, 61, 85, 67, 91, 66, 90, 55, 79, 59, 83) L = (1, 52)(2, 58)(3, 57)(4, 56)(5, 60)(6, 59)(7, 49)(8, 69)(9, 68)(10, 67)(11, 70)(12, 50)(13, 71)(14, 51)(15, 55)(16, 54)(17, 53)(18, 72)(19, 65)(20, 66)(21, 63)(22, 61)(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) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ), ( 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 E14.120 Graph:: bipartite v = 6 e = 48 f = 16 degree seq :: [ 12^4, 24^2 ] E14.127 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-2, Y3 * Y2 * Y1^-2, (Y2 * Y1^-1)^2, (Y3, Y2^-1), (R * Y3)^2, Y3^-1 * Y1^-1 * Y2 * Y1, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y1^4, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y2^-3 * Y1^-1, (Y1^-1 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 15, 39, 5, 29)(3, 27, 10, 34, 20, 44, 16, 40, 7, 31, 11, 35)(4, 28, 9, 33, 21, 45, 17, 41, 6, 30, 12, 36)(13, 37, 22, 46, 18, 42, 24, 48, 14, 38, 23, 47)(49, 73, 51, 75, 61, 85, 69, 93, 63, 87, 55, 79, 62, 86, 52, 76, 56, 80, 68, 92, 66, 90, 54, 78)(50, 74, 57, 81, 70, 94, 64, 88, 53, 77, 60, 84, 71, 95, 58, 82, 67, 91, 65, 89, 72, 96, 59, 83) L = (1, 52)(2, 58)(3, 56)(4, 61)(5, 59)(6, 62)(7, 49)(8, 69)(9, 67)(10, 70)(11, 71)(12, 50)(13, 68)(14, 51)(15, 54)(16, 72)(17, 53)(18, 55)(19, 64)(20, 63)(21, 66)(22, 65)(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) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ), ( 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 E14.122 Graph:: bipartite v = 6 e = 48 f = 16 degree seq :: [ 12^4, 24^2 ] E14.128 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 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^-1, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2^-1 * Y1 * Y2 * Y1, Y1^4, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^6 * Y1^-1, (Y3 * Y2^-1)^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 9, 33, 13, 37, 7, 31)(5, 29, 11, 35, 14, 38, 8, 32)(10, 34, 15, 39, 21, 45, 17, 41)(12, 36, 16, 40, 22, 46, 19, 43)(18, 42, 24, 48, 20, 44, 23, 47)(49, 73, 51, 75, 58, 82, 66, 90, 70, 94, 62, 86, 54, 78, 61, 85, 69, 93, 68, 92, 60, 84, 53, 77)(50, 74, 55, 79, 63, 87, 71, 95, 67, 91, 59, 83, 52, 76, 57, 81, 65, 89, 72, 96, 64, 88, 56, 80) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 59)(6, 52)(7, 51)(8, 53)(9, 61)(10, 63)(11, 62)(12, 64)(13, 55)(14, 56)(15, 69)(16, 70)(17, 58)(18, 72)(19, 60)(20, 71)(21, 65)(22, 67)(23, 66)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E14.129 Graph:: bipartite v = 8 e = 48 f = 14 degree seq :: [ 8^6, 24^2 ] E14.129 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 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, Y2^2, Y3 * Y2 * Y3, Y3^-2 * Y2, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y1, (R * Y2)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1, Y2 * Y1^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 15, 39, 19, 43, 11, 35, 3, 27, 8, 32, 16, 40, 22, 46, 14, 38, 5, 29)(4, 28, 10, 34, 17, 41, 24, 48, 21, 45, 13, 37, 6, 30, 9, 33, 18, 42, 23, 47, 20, 44, 12, 36)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 54, 78)(53, 77, 59, 83)(55, 79, 64, 88)(57, 81, 58, 82)(60, 84, 61, 85)(62, 86, 67, 91)(63, 87, 70, 94)(65, 89, 66, 90)(68, 92, 69, 93)(71, 95, 72, 96) L = (1, 52)(2, 57)(3, 54)(4, 51)(5, 61)(6, 49)(7, 65)(8, 58)(9, 56)(10, 50)(11, 60)(12, 53)(13, 59)(14, 68)(15, 71)(16, 66)(17, 64)(18, 55)(19, 69)(20, 67)(21, 62)(22, 72)(23, 70)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 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 E14.128 Graph:: bipartite v = 14 e = 48 f = 8 degree seq :: [ 4^12, 24^2 ] E14.130 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y2, Y3), (Y2^-1, Y1^-1), (Y3^-1 * Y1^-1)^2, (R * Y2)^2, Y3^-1 * Y2^-4 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 8, 32, 13, 37)(4, 28, 9, 33, 7, 31)(6, 30, 10, 34, 16, 40)(11, 35, 19, 43, 23, 47)(12, 36, 20, 44, 14, 38)(15, 39, 21, 45, 18, 42)(17, 41, 22, 46, 24, 48)(49, 73, 51, 75, 59, 83, 66, 90, 55, 79, 62, 86, 72, 96, 64, 88, 53, 77, 61, 85, 71, 95, 69, 93, 57, 81, 68, 92, 70, 94, 58, 82, 50, 74, 56, 80, 67, 91, 63, 87, 52, 76, 60, 84, 65, 89, 54, 78) L = (1, 52)(2, 57)(3, 60)(4, 50)(5, 55)(6, 63)(7, 49)(8, 68)(9, 53)(10, 69)(11, 65)(12, 56)(13, 62)(14, 51)(15, 58)(16, 66)(17, 67)(18, 54)(19, 70)(20, 61)(21, 64)(22, 71)(23, 72)(24, 59)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E14.131 Graph:: bipartite v = 9 e = 48 f = 13 degree seq :: [ 6^8, 48 ] E14.131 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3 * Y2, (R * Y2)^2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y1^-1, Y1^2 * Y3^-1 * Y1^2, Y3 * Y2 * Y1 * Y3^2 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 14, 38, 4, 28, 9, 33, 18, 42, 23, 47, 13, 37, 20, 44, 22, 46, 12, 36, 3, 27, 8, 32, 17, 41, 21, 45, 11, 35, 19, 43, 24, 48, 16, 40, 6, 30, 10, 34, 15, 39, 5, 29)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 59, 83)(53, 77, 60, 84)(54, 78, 61, 85)(55, 79, 65, 89)(57, 81, 67, 91)(58, 82, 68, 92)(62, 86, 69, 93)(63, 87, 70, 94)(64, 88, 71, 95)(66, 90, 72, 96) L = (1, 52)(2, 57)(3, 59)(4, 61)(5, 62)(6, 49)(7, 66)(8, 67)(9, 68)(10, 50)(11, 54)(12, 69)(13, 51)(14, 71)(15, 55)(16, 53)(17, 72)(18, 70)(19, 58)(20, 56)(21, 64)(22, 65)(23, 60)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 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 E14.130 Graph:: bipartite v = 13 e = 48 f = 9 degree seq :: [ 4^12, 48 ] E14.132 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 14}) Quotient :: dipole Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^7 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 5, 33)(4, 32, 7, 35)(6, 34, 8, 36)(9, 37, 13, 41)(10, 38, 12, 40)(11, 39, 15, 43)(14, 42, 16, 44)(17, 45, 21, 49)(18, 46, 20, 48)(19, 47, 23, 51)(22, 50, 24, 52)(25, 53, 28, 56)(26, 54, 27, 55)(57, 85, 59, 87, 58, 86, 61, 89)(60, 88, 66, 94, 63, 91, 68, 96)(62, 90, 65, 93, 64, 92, 69, 97)(67, 95, 74, 102, 71, 99, 76, 104)(70, 98, 73, 101, 72, 100, 77, 105)(75, 103, 82, 110, 79, 107, 83, 111)(78, 106, 81, 109, 80, 108, 84, 112) L = (1, 60)(2, 63)(3, 65)(4, 67)(5, 69)(6, 57)(7, 71)(8, 58)(9, 73)(10, 59)(11, 75)(12, 61)(13, 77)(14, 62)(15, 79)(16, 64)(17, 81)(18, 66)(19, 78)(20, 68)(21, 84)(22, 70)(23, 80)(24, 72)(25, 82)(26, 74)(27, 76)(28, 83)(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 ) } Outer automorphisms :: reflexible Dual of E14.133 Graph:: bipartite v = 21 e = 56 f = 9 degree seq :: [ 4^14, 8^7 ] E14.133 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 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, Y3^-2 * Y2^2, (Y3, Y2^-1), Y3 * Y1 * Y2 * Y1, Y2^-1 * Y3 * Y1^-2, Y3 * Y1^-1 * Y2 * Y1^-1, Y2 * Y3^-1 * Y1^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^4, Y3^-1 * Y2^-6, Y3^7 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 5, 33)(3, 31, 11, 39, 4, 32, 12, 40)(6, 34, 9, 37, 7, 35, 10, 38)(13, 41, 19, 47, 14, 42, 20, 48)(15, 43, 17, 45, 16, 44, 18, 46)(21, 49, 27, 55, 22, 50, 28, 56)(23, 51, 25, 53, 24, 52, 26, 54)(57, 85, 59, 87, 69, 97, 77, 105, 80, 108, 72, 100, 63, 91, 64, 92, 60, 88, 70, 98, 78, 106, 79, 107, 71, 99, 62, 90)(58, 86, 65, 93, 73, 101, 81, 109, 84, 112, 76, 104, 68, 96, 61, 89, 66, 94, 74, 102, 82, 110, 83, 111, 75, 103, 67, 95) L = (1, 60)(2, 66)(3, 70)(4, 69)(5, 65)(6, 64)(7, 57)(8, 59)(9, 74)(10, 73)(11, 61)(12, 58)(13, 78)(14, 77)(15, 63)(16, 62)(17, 82)(18, 81)(19, 68)(20, 67)(21, 79)(22, 80)(23, 72)(24, 71)(25, 83)(26, 84)(27, 76)(28, 75)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 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 E14.132 Graph:: bipartite v = 9 e = 56 f = 21 degree seq :: [ 8^7, 28^2 ] E14.134 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^14 * Y1, (Y3 * Y2^-1)^28 ] Map:: R = (1, 29, 2, 30)(3, 31, 5, 33)(4, 32, 6, 34)(7, 35, 9, 37)(8, 36, 10, 38)(11, 39, 13, 41)(12, 40, 14, 42)(15, 43, 17, 45)(16, 44, 18, 46)(19, 47, 21, 49)(20, 48, 22, 50)(23, 51, 25, 53)(24, 52, 26, 54)(27, 55, 28, 56)(57, 85, 59, 87, 63, 91, 67, 95, 71, 99, 75, 103, 79, 107, 83, 111, 82, 110, 78, 106, 74, 102, 70, 98, 66, 94, 62, 90, 58, 86, 61, 89, 65, 93, 69, 97, 73, 101, 77, 105, 81, 109, 84, 112, 80, 108, 76, 104, 72, 100, 68, 96, 64, 92, 60, 88) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 15 e = 56 f = 15 degree seq :: [ 4^14, 56 ] E14.135 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^14, (T2^-1 * T1^-1)^29 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 27, 28, 24, 20, 16, 12, 8, 4, 2, 6, 10, 14, 18, 22, 26, 29, 25, 21, 17, 13, 9, 5)(30, 31, 32, 35, 36, 39, 40, 43, 44, 47, 48, 51, 52, 55, 56, 58, 57, 54, 53, 50, 49, 46, 45, 42, 41, 38, 37, 34, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.151 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.136 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^2, (F * T2)^2, (F * T1)^2, T1 * T2^-14 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 27, 26, 22, 18, 14, 10, 6, 2, 4, 8, 12, 16, 20, 24, 28, 29, 25, 21, 17, 13, 9, 5)(30, 31, 34, 35, 38, 39, 42, 43, 46, 47, 50, 51, 54, 55, 58, 56, 57, 52, 53, 48, 49, 44, 45, 40, 41, 36, 37, 32, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.148 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.137 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2^9, (T1^-1 * T2^-1)^29 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 26, 20, 14, 8, 2, 7, 13, 19, 25, 28, 22, 16, 10, 4, 6, 12, 18, 24, 29, 23, 17, 11, 5)(30, 31, 35, 32, 36, 41, 38, 42, 47, 44, 48, 53, 50, 54, 58, 56, 57, 52, 55, 51, 46, 49, 45, 40, 43, 39, 34, 37, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.153 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.138 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^-1 * T1^-1, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-1 * T2^-9 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 24, 18, 12, 6, 4, 10, 16, 22, 28, 26, 20, 14, 8, 2, 7, 13, 19, 25, 29, 23, 17, 11, 5)(30, 31, 35, 34, 37, 41, 40, 43, 47, 46, 49, 53, 52, 55, 56, 58, 57, 50, 54, 51, 44, 48, 45, 38, 42, 39, 32, 36, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.149 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.139 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-1 * T2 * T1^-3, T2 * T1 * T2^6, (T1^-1 * T2^-1)^29 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 20, 12, 4, 10, 18, 26, 29, 27, 19, 11, 6, 14, 22, 28, 24, 16, 8, 2, 7, 15, 23, 21, 13, 5)(30, 31, 35, 39, 32, 36, 43, 47, 38, 44, 51, 55, 46, 52, 57, 58, 54, 50, 53, 56, 49, 42, 45, 48, 41, 34, 37, 40, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.154 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.140 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^4 * T2, T2^6 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 3, 9, 17, 24, 16, 8, 2, 7, 15, 23, 28, 22, 14, 6, 11, 19, 26, 29, 27, 20, 12, 4, 10, 18, 25, 21, 13, 5)(30, 31, 35, 41, 34, 37, 43, 49, 42, 45, 51, 56, 50, 53, 57, 58, 54, 46, 52, 55, 47, 38, 44, 48, 39, 32, 36, 40, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.150 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.141 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1^-1), T1^-2 * T2 * T1^-3, T1^-1 * T2^6, T2 * T1 * T2 * T1 * T2^3 * T1^2, T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 27, 26, 16, 6, 15, 25, 28, 21, 11, 14, 24, 29, 22, 12, 4, 10, 20, 23, 13, 5)(30, 31, 35, 43, 39, 32, 36, 44, 53, 49, 38, 46, 54, 58, 52, 48, 56, 57, 51, 42, 47, 55, 50, 41, 34, 37, 45, 40, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.155 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.142 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-5, T2 * T1 * T2^5, T2^-1 * T1 * T2^-1 * T1^2 * T2^-3 * T1, T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^2 * T2^-2 ] Map:: non-degenerate R = (1, 3, 9, 19, 22, 12, 4, 10, 20, 28, 24, 14, 11, 21, 29, 26, 16, 6, 15, 25, 27, 18, 8, 2, 7, 17, 23, 13, 5)(30, 31, 35, 43, 41, 34, 37, 45, 53, 51, 42, 47, 55, 57, 48, 52, 56, 58, 49, 38, 46, 54, 50, 39, 32, 36, 44, 40, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.152 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.143 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (T1^-1, T2), (F * T1)^2, (F * T2)^2, (T1, T2), T2^-4 * T1^3, T1^-2 * T2^-1 * T1^-1 * T2^-2 * T1^-2, T1^-17 * T2 * T1 * T2, T2 * T1^21, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-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, 14, 27, 23, 11, 21, 18, 8, 2, 7, 17, 29, 26, 24, 12, 4, 10, 20, 16, 6, 15, 28, 22, 25, 13, 5)(30, 31, 35, 43, 55, 54, 50, 39, 32, 36, 44, 56, 53, 42, 47, 49, 38, 46, 57, 52, 41, 34, 37, 45, 48, 58, 51, 40, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.158 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.144 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T2^-3 * T1^-3 * T2^-1, T2^3 * T1^-5 ] Map:: non-degenerate R = (1, 3, 9, 19, 22, 28, 16, 6, 15, 24, 12, 4, 10, 20, 26, 29, 18, 8, 2, 7, 17, 23, 11, 21, 27, 14, 25, 13, 5)(30, 31, 35, 43, 55, 48, 52, 41, 34, 37, 45, 56, 49, 38, 46, 53, 42, 47, 57, 50, 39, 32, 36, 44, 54, 58, 51, 40, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.156 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.145 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1 * T2 * T1 * T2^2, T1^-1 * T2 * T1^-8, T1^-1 * T2^13 ] Map:: non-degenerate R = (1, 3, 9, 11, 18, 23, 25, 26, 28, 21, 14, 16, 8, 2, 7, 12, 4, 10, 17, 19, 24, 29, 27, 20, 22, 15, 6, 13, 5)(30, 31, 35, 43, 49, 55, 53, 47, 39, 32, 36, 42, 45, 51, 57, 58, 52, 46, 38, 41, 34, 37, 44, 50, 56, 54, 48, 40, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.159 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.146 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1 * T2^-2 * T1, T1^-3 * T2^-1 * T1^-6, (T1^-1 * T2^-1)^29 ] Map:: non-degenerate R = (1, 3, 9, 6, 15, 22, 20, 27, 29, 24, 17, 19, 12, 4, 10, 8, 2, 7, 16, 14, 21, 28, 26, 23, 25, 18, 11, 13, 5)(30, 31, 35, 43, 49, 55, 53, 47, 41, 34, 37, 38, 45, 51, 57, 58, 54, 48, 42, 39, 32, 36, 44, 50, 56, 52, 46, 40, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.157 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.147 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {29, 29, 29}) Quotient :: edge Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2^5 * T1^-2, T2^2 * T1^5 ] Map:: non-degenerate R = (1, 3, 9, 19, 16, 6, 15, 22, 28, 29, 24, 12, 4, 10, 20, 18, 8, 2, 7, 17, 27, 26, 14, 23, 11, 21, 25, 13, 5)(30, 31, 35, 43, 53, 42, 47, 48, 56, 57, 50, 39, 32, 36, 44, 52, 41, 34, 37, 45, 55, 58, 54, 49, 38, 46, 51, 40, 33) L = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.160 Transitivity :: ET+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.148 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1, (F * T1)^2, (F * T2)^2, T2^29, T1^29, (T2^-1 * T1^-1)^29 ] Map:: non-degenerate R = (1, 30, 2, 31, 6, 35, 14, 43, 19, 48, 28, 57, 24, 53, 13, 42, 18, 47, 21, 50, 10, 39, 3, 32, 7, 36, 15, 44, 26, 55, 29, 58, 23, 52, 12, 41, 5, 34, 8, 37, 16, 45, 20, 49, 9, 38, 17, 46, 27, 56, 25, 54, 22, 51, 11, 40, 4, 33) L = (1, 31)(2, 35)(3, 36)(4, 30)(5, 37)(6, 43)(7, 44)(8, 45)(9, 46)(10, 32)(11, 33)(12, 34)(13, 47)(14, 48)(15, 55)(16, 49)(17, 56)(18, 50)(19, 57)(20, 38)(21, 39)(22, 40)(23, 41)(24, 42)(25, 51)(26, 58)(27, 54)(28, 53)(29, 52) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.136 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.149 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^14, (T2^-1 * T1^-1)^29 ] Map:: non-degenerate R = (1, 30, 3, 32, 7, 36, 11, 40, 15, 44, 19, 48, 23, 52, 27, 56, 28, 57, 24, 53, 20, 49, 16, 45, 12, 41, 8, 37, 4, 33, 2, 31, 6, 35, 10, 39, 14, 43, 18, 47, 22, 51, 26, 55, 29, 58, 25, 54, 21, 50, 17, 46, 13, 42, 9, 38, 5, 34) L = (1, 31)(2, 32)(3, 35)(4, 30)(5, 33)(6, 36)(7, 39)(8, 34)(9, 37)(10, 40)(11, 43)(12, 38)(13, 41)(14, 44)(15, 47)(16, 42)(17, 45)(18, 48)(19, 51)(20, 46)(21, 49)(22, 52)(23, 55)(24, 50)(25, 53)(26, 56)(27, 58)(28, 54)(29, 57) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.138 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.150 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2^9, (T1^-1 * T2^-1)^29 ] Map:: non-degenerate R = (1, 30, 3, 32, 9, 38, 15, 44, 21, 50, 27, 56, 26, 55, 20, 49, 14, 43, 8, 37, 2, 31, 7, 36, 13, 42, 19, 48, 25, 54, 28, 57, 22, 51, 16, 45, 10, 39, 4, 33, 6, 35, 12, 41, 18, 47, 24, 53, 29, 58, 23, 52, 17, 46, 11, 40, 5, 34) L = (1, 31)(2, 35)(3, 36)(4, 30)(5, 37)(6, 32)(7, 41)(8, 33)(9, 42)(10, 34)(11, 43)(12, 38)(13, 47)(14, 39)(15, 48)(16, 40)(17, 49)(18, 44)(19, 53)(20, 45)(21, 54)(22, 46)(23, 55)(24, 50)(25, 58)(26, 51)(27, 57)(28, 52)(29, 56) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.140 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.151 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^-1 * T1^-1, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-1 * T2^-9 ] Map:: non-degenerate R = (1, 30, 3, 32, 9, 38, 15, 44, 21, 50, 27, 56, 24, 53, 18, 47, 12, 41, 6, 35, 4, 33, 10, 39, 16, 45, 22, 51, 28, 57, 26, 55, 20, 49, 14, 43, 8, 37, 2, 31, 7, 36, 13, 42, 19, 48, 25, 54, 29, 58, 23, 52, 17, 46, 11, 40, 5, 34) L = (1, 31)(2, 35)(3, 36)(4, 30)(5, 37)(6, 34)(7, 33)(8, 41)(9, 42)(10, 32)(11, 43)(12, 40)(13, 39)(14, 47)(15, 48)(16, 38)(17, 49)(18, 46)(19, 45)(20, 53)(21, 54)(22, 44)(23, 55)(24, 52)(25, 51)(26, 56)(27, 58)(28, 50)(29, 57) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.135 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.152 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-1 * T2 * T1^-3, T2 * T1 * T2^6, (T1^-1 * T2^-1)^29 ] Map:: non-degenerate R = (1, 30, 3, 32, 9, 38, 17, 46, 25, 54, 20, 49, 12, 41, 4, 33, 10, 39, 18, 47, 26, 55, 29, 58, 27, 56, 19, 48, 11, 40, 6, 35, 14, 43, 22, 51, 28, 57, 24, 53, 16, 45, 8, 37, 2, 31, 7, 36, 15, 44, 23, 52, 21, 50, 13, 42, 5, 34) L = (1, 31)(2, 35)(3, 36)(4, 30)(5, 37)(6, 39)(7, 43)(8, 40)(9, 44)(10, 32)(11, 33)(12, 34)(13, 45)(14, 47)(15, 51)(16, 48)(17, 52)(18, 38)(19, 41)(20, 42)(21, 53)(22, 55)(23, 57)(24, 56)(25, 50)(26, 46)(27, 49)(28, 58)(29, 54) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.142 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.153 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^4 * T2, T2^6 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 30, 3, 32, 9, 38, 17, 46, 24, 53, 16, 45, 8, 37, 2, 31, 7, 36, 15, 44, 23, 52, 28, 57, 22, 51, 14, 43, 6, 35, 11, 40, 19, 48, 26, 55, 29, 58, 27, 56, 20, 49, 12, 41, 4, 33, 10, 39, 18, 47, 25, 54, 21, 50, 13, 42, 5, 34) L = (1, 31)(2, 35)(3, 36)(4, 30)(5, 37)(6, 41)(7, 40)(8, 43)(9, 44)(10, 32)(11, 33)(12, 34)(13, 45)(14, 49)(15, 48)(16, 51)(17, 52)(18, 38)(19, 39)(20, 42)(21, 53)(22, 56)(23, 55)(24, 57)(25, 46)(26, 47)(27, 50)(28, 58)(29, 54) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.137 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.154 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-5, T2 * T1 * T2^5, T2^-1 * T1 * T2^-1 * T1^2 * T2^-3 * T1, T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^2 * T2^-2 ] Map:: non-degenerate R = (1, 30, 3, 32, 9, 38, 19, 48, 22, 51, 12, 41, 4, 33, 10, 39, 20, 49, 28, 57, 24, 53, 14, 43, 11, 40, 21, 50, 29, 58, 26, 55, 16, 45, 6, 35, 15, 44, 25, 54, 27, 56, 18, 47, 8, 37, 2, 31, 7, 36, 17, 46, 23, 52, 13, 42, 5, 34) L = (1, 31)(2, 35)(3, 36)(4, 30)(5, 37)(6, 43)(7, 44)(8, 45)(9, 46)(10, 32)(11, 33)(12, 34)(13, 47)(14, 41)(15, 40)(16, 53)(17, 54)(18, 55)(19, 52)(20, 38)(21, 39)(22, 42)(23, 56)(24, 51)(25, 50)(26, 57)(27, 58)(28, 48)(29, 49) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.139 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.155 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-1 * T2^-4, T1^2 * T2 * T1^4, T1 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-2 * T1, T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 30, 3, 32, 9, 38, 19, 48, 12, 41, 4, 33, 10, 39, 20, 49, 27, 56, 23, 52, 11, 40, 21, 50, 28, 57, 24, 53, 14, 43, 22, 51, 29, 58, 26, 55, 16, 45, 6, 35, 15, 44, 25, 54, 18, 47, 8, 37, 2, 31, 7, 36, 17, 46, 13, 42, 5, 34) L = (1, 31)(2, 35)(3, 36)(4, 30)(5, 37)(6, 43)(7, 44)(8, 45)(9, 46)(10, 32)(11, 33)(12, 34)(13, 47)(14, 52)(15, 51)(16, 53)(17, 54)(18, 55)(19, 42)(20, 38)(21, 39)(22, 40)(23, 41)(24, 56)(25, 58)(26, 57)(27, 48)(28, 49)(29, 50) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.141 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.156 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2^3, T1^-1 * T2 * T1^-6 ] Map:: non-degenerate R = (1, 30, 3, 32, 9, 38, 12, 41, 4, 33, 10, 39, 18, 47, 21, 50, 11, 40, 19, 48, 26, 55, 27, 56, 20, 49, 22, 51, 28, 57, 29, 58, 24, 53, 14, 43, 23, 52, 25, 54, 16, 45, 6, 35, 15, 44, 17, 46, 8, 37, 2, 31, 7, 36, 13, 42, 5, 34) L = (1, 31)(2, 35)(3, 36)(4, 30)(5, 37)(6, 43)(7, 44)(8, 45)(9, 42)(10, 32)(11, 33)(12, 34)(13, 46)(14, 51)(15, 52)(16, 53)(17, 54)(18, 38)(19, 39)(20, 40)(21, 41)(22, 48)(23, 57)(24, 49)(25, 58)(26, 47)(27, 50)(28, 55)(29, 56) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.144 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.157 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (T1^-1, T2), (F * T1)^2, (F * T2)^2, (T1, T2), T2^-4 * T1^3, T1^-2 * T2^-1 * T1^-1 * T2^-2 * T1^-2, T1^-17 * T2 * T1 * T2, T2 * T1^21, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-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, 30, 3, 32, 9, 38, 19, 48, 14, 43, 27, 56, 23, 52, 11, 40, 21, 50, 18, 47, 8, 37, 2, 31, 7, 36, 17, 46, 29, 58, 26, 55, 24, 53, 12, 41, 4, 33, 10, 39, 20, 49, 16, 45, 6, 35, 15, 44, 28, 57, 22, 51, 25, 54, 13, 42, 5, 34) L = (1, 31)(2, 35)(3, 36)(4, 30)(5, 37)(6, 43)(7, 44)(8, 45)(9, 46)(10, 32)(11, 33)(12, 34)(13, 47)(14, 55)(15, 56)(16, 48)(17, 57)(18, 49)(19, 58)(20, 38)(21, 39)(22, 40)(23, 41)(24, 42)(25, 50)(26, 54)(27, 53)(28, 52)(29, 51) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.146 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.158 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1 * T2^-2 * T1, T1^-3 * T2^-1 * T1^-6, (T1^-1 * T2^-1)^29 ] Map:: non-degenerate R = (1, 30, 3, 32, 9, 38, 6, 35, 15, 44, 22, 51, 20, 49, 27, 56, 29, 58, 24, 53, 17, 46, 19, 48, 12, 41, 4, 33, 10, 39, 8, 37, 2, 31, 7, 36, 16, 45, 14, 43, 21, 50, 28, 57, 26, 55, 23, 52, 25, 54, 18, 47, 11, 40, 13, 42, 5, 34) L = (1, 31)(2, 35)(3, 36)(4, 30)(5, 37)(6, 43)(7, 44)(8, 38)(9, 45)(10, 32)(11, 33)(12, 34)(13, 39)(14, 49)(15, 50)(16, 51)(17, 40)(18, 41)(19, 42)(20, 55)(21, 56)(22, 57)(23, 46)(24, 47)(25, 48)(26, 53)(27, 52)(28, 58)(29, 54) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.143 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.159 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, T2^-3 * T1^-1, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-1 * T1^-9 ] Map:: non-degenerate R = (1, 30, 3, 32, 9, 38, 4, 33, 10, 39, 15, 44, 11, 40, 16, 45, 21, 50, 17, 46, 22, 51, 27, 56, 23, 52, 28, 57, 24, 53, 29, 58, 26, 55, 18, 47, 25, 54, 20, 49, 12, 41, 19, 48, 14, 43, 6, 35, 13, 42, 8, 37, 2, 31, 7, 36, 5, 34) L = (1, 31)(2, 35)(3, 36)(4, 30)(5, 37)(6, 41)(7, 42)(8, 43)(9, 34)(10, 32)(11, 33)(12, 47)(13, 48)(14, 49)(15, 38)(16, 39)(17, 40)(18, 53)(19, 54)(20, 55)(21, 44)(22, 45)(23, 46)(24, 56)(25, 58)(26, 57)(27, 50)(28, 51)(29, 52) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.145 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.160 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {29, 29, 29}) Quotient :: loop Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2^-1), T1^3 * T2^-1 * T1 * T2^-2, T1^-1 * T2^-1 * T1^-1 * T2^-4 * T1^-1, T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 30, 3, 32, 9, 38, 19, 48, 29, 58, 22, 51, 18, 47, 8, 37, 2, 31, 7, 36, 17, 46, 28, 57, 23, 52, 11, 40, 21, 50, 16, 45, 6, 35, 15, 44, 27, 56, 24, 53, 12, 41, 4, 33, 10, 39, 20, 49, 14, 43, 26, 55, 25, 54, 13, 42, 5, 34) L = (1, 31)(2, 35)(3, 36)(4, 30)(5, 37)(6, 43)(7, 44)(8, 45)(9, 46)(10, 32)(11, 33)(12, 34)(13, 47)(14, 48)(15, 55)(16, 49)(17, 56)(18, 50)(19, 57)(20, 38)(21, 39)(22, 40)(23, 41)(24, 42)(25, 51)(26, 58)(27, 54)(28, 53)(29, 52) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.147 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.161 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^2 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^14 * Y2, Y2 * Y1^-14 ] Map:: R = (1, 30, 2, 31, 6, 35, 10, 39, 14, 43, 18, 47, 22, 51, 26, 55, 28, 57, 24, 53, 20, 49, 16, 45, 12, 41, 8, 37, 3, 32, 5, 34, 7, 36, 11, 40, 15, 44, 19, 48, 23, 52, 27, 56, 29, 58, 25, 54, 21, 50, 17, 46, 13, 42, 9, 38, 4, 33)(59, 88, 61, 90, 62, 91, 66, 95, 67, 96, 70, 99, 71, 100, 74, 103, 75, 104, 78, 107, 79, 108, 82, 111, 83, 112, 86, 115, 87, 116, 84, 113, 85, 114, 80, 109, 81, 110, 76, 105, 77, 106, 72, 101, 73, 102, 68, 97, 69, 98, 64, 93, 65, 94, 60, 89, 63, 92) L = (1, 62)(2, 59)(3, 66)(4, 67)(5, 61)(6, 60)(7, 63)(8, 70)(9, 71)(10, 64)(11, 65)(12, 74)(13, 75)(14, 68)(15, 69)(16, 78)(17, 79)(18, 72)(19, 73)(20, 82)(21, 83)(22, 76)(23, 77)(24, 86)(25, 87)(26, 80)(27, 81)(28, 84)(29, 85)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.174 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.162 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y2^-2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2, Y3^-1), Y3^6 * Y2^-1 * Y1^-6 * Y3 * Y1^-1, Y3^-1 * Y1^8 * 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 * Y1^-1 ] Map:: R = (1, 30, 2, 31, 6, 35, 10, 39, 14, 43, 18, 47, 22, 51, 26, 55, 29, 58, 25, 54, 21, 50, 17, 46, 13, 42, 9, 38, 5, 34, 3, 32, 7, 36, 11, 40, 15, 44, 19, 48, 23, 52, 27, 56, 28, 57, 24, 53, 20, 49, 16, 45, 12, 41, 8, 37, 4, 33)(59, 88, 61, 90, 60, 89, 65, 94, 64, 93, 69, 98, 68, 97, 73, 102, 72, 101, 77, 106, 76, 105, 81, 110, 80, 109, 85, 114, 84, 113, 86, 115, 87, 116, 82, 111, 83, 112, 78, 107, 79, 108, 74, 103, 75, 104, 70, 99, 71, 100, 66, 95, 67, 96, 62, 91, 63, 92) L = (1, 62)(2, 59)(3, 63)(4, 66)(5, 67)(6, 60)(7, 61)(8, 70)(9, 71)(10, 64)(11, 65)(12, 74)(13, 75)(14, 68)(15, 69)(16, 78)(17, 79)(18, 72)(19, 73)(20, 82)(21, 83)(22, 76)(23, 77)(24, 86)(25, 87)(26, 80)(27, 81)(28, 85)(29, 84)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.182 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.163 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3 * Y2^-3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^6 * Y3^-4 * Y2, Y1^4 * Y2 * Y1 * Y3^-5, Y3 * Y2^-1 * Y3^9 ] Map:: R = (1, 30, 2, 31, 6, 35, 12, 41, 18, 47, 24, 53, 27, 56, 21, 50, 15, 44, 9, 38, 5, 34, 8, 37, 14, 43, 20, 49, 26, 55, 28, 57, 22, 51, 16, 45, 10, 39, 3, 32, 7, 36, 13, 42, 19, 48, 25, 54, 29, 58, 23, 52, 17, 46, 11, 40, 4, 33)(59, 88, 61, 90, 67, 96, 62, 91, 68, 97, 73, 102, 69, 98, 74, 103, 79, 108, 75, 104, 80, 109, 85, 114, 81, 110, 86, 115, 82, 111, 87, 116, 84, 113, 76, 105, 83, 112, 78, 107, 70, 99, 77, 106, 72, 101, 64, 93, 71, 100, 66, 95, 60, 89, 65, 94, 63, 92) L = (1, 62)(2, 59)(3, 68)(4, 69)(5, 67)(6, 60)(7, 61)(8, 63)(9, 73)(10, 74)(11, 75)(12, 64)(13, 65)(14, 66)(15, 79)(16, 80)(17, 81)(18, 70)(19, 71)(20, 72)(21, 85)(22, 86)(23, 87)(24, 76)(25, 77)(26, 78)(27, 82)(28, 84)(29, 83)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.186 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.164 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y2^-1, Y1^-1), Y2^-2 * Y3^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1^3 * Y3^-2 * Y1^5, Y1^-3 * Y2^-2 * Y1^-4 * Y2 * Y3^4 * Y2 * Y3^8 * Y2^-1, (Y3 * Y2^-1)^29 ] Map:: R = (1, 30, 2, 31, 6, 35, 12, 41, 18, 47, 24, 53, 27, 56, 21, 50, 15, 44, 9, 38, 3, 32, 7, 36, 13, 42, 19, 48, 25, 54, 29, 58, 23, 52, 17, 46, 11, 40, 5, 34, 8, 37, 14, 43, 20, 49, 26, 55, 28, 57, 22, 51, 16, 45, 10, 39, 4, 33)(59, 88, 61, 90, 66, 95, 60, 89, 65, 94, 72, 101, 64, 93, 71, 100, 78, 107, 70, 99, 77, 106, 84, 113, 76, 105, 83, 112, 86, 115, 82, 111, 87, 116, 80, 109, 85, 114, 81, 110, 74, 103, 79, 108, 75, 104, 68, 97, 73, 102, 69, 98, 62, 91, 67, 96, 63, 92) L = (1, 62)(2, 59)(3, 67)(4, 68)(5, 69)(6, 60)(7, 61)(8, 63)(9, 73)(10, 74)(11, 75)(12, 64)(13, 65)(14, 66)(15, 79)(16, 80)(17, 81)(18, 70)(19, 71)(20, 72)(21, 85)(22, 86)(23, 87)(24, 76)(25, 77)(26, 78)(27, 82)(28, 84)(29, 83)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.180 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.165 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2^2 * Y3^-1 * Y2^2, Y3 * Y2 * Y3^6, Y3^-4 * Y1^25 ] Map:: R = (1, 30, 2, 31, 6, 35, 14, 43, 22, 51, 19, 48, 10, 39, 3, 32, 7, 36, 15, 44, 23, 52, 28, 57, 26, 55, 18, 47, 9, 38, 13, 42, 17, 46, 25, 54, 29, 58, 27, 56, 21, 50, 12, 41, 5, 34, 8, 37, 16, 45, 24, 53, 20, 49, 11, 40, 4, 33)(59, 88, 61, 90, 67, 96, 70, 99, 62, 91, 68, 97, 76, 105, 79, 108, 69, 98, 77, 106, 84, 113, 85, 114, 78, 107, 80, 109, 86, 115, 87, 116, 82, 111, 72, 101, 81, 110, 83, 112, 74, 103, 64, 93, 73, 102, 75, 104, 66, 95, 60, 89, 65, 94, 71, 100, 63, 92) L = (1, 62)(2, 59)(3, 68)(4, 69)(5, 70)(6, 60)(7, 61)(8, 63)(9, 76)(10, 77)(11, 78)(12, 79)(13, 67)(14, 64)(15, 65)(16, 66)(17, 71)(18, 84)(19, 80)(20, 82)(21, 85)(22, 72)(23, 73)(24, 74)(25, 75)(26, 86)(27, 87)(28, 81)(29, 83)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.183 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.166 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y2)^2, (Y2, Y3^-1), (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), Y2^-1 * Y1 * Y2^-3, Y2 * Y3^3 * Y2^-1 * Y1^3, Y1 * Y2 * Y1^6, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 30, 2, 31, 6, 35, 14, 43, 22, 51, 20, 49, 12, 41, 5, 34, 8, 37, 16, 45, 24, 53, 28, 57, 27, 56, 21, 50, 13, 42, 9, 38, 17, 46, 25, 54, 29, 58, 26, 55, 18, 47, 10, 39, 3, 32, 7, 36, 15, 44, 23, 52, 19, 48, 11, 40, 4, 33)(59, 88, 61, 90, 67, 96, 66, 95, 60, 89, 65, 94, 75, 104, 74, 103, 64, 93, 73, 102, 83, 112, 82, 111, 72, 101, 81, 110, 87, 116, 86, 115, 80, 109, 77, 106, 84, 113, 85, 114, 78, 107, 69, 98, 76, 105, 79, 108, 70, 99, 62, 91, 68, 97, 71, 100, 63, 92) L = (1, 62)(2, 59)(3, 68)(4, 69)(5, 70)(6, 60)(7, 61)(8, 63)(9, 71)(10, 76)(11, 77)(12, 78)(13, 79)(14, 64)(15, 65)(16, 66)(17, 67)(18, 84)(19, 81)(20, 80)(21, 85)(22, 72)(23, 73)(24, 74)(25, 75)(26, 87)(27, 86)(28, 82)(29, 83)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.178 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.167 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y2)^2, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y3^3 * Y1^3, Y2^-1 * Y3 * Y2^-4, Y2 * Y1^3 * Y3^-3, Y1^2 * Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y2^2, Y1^29, Y2^-1 * Y3^2 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^2 * Y3^2 * Y2^-1 ] Map:: R = (1, 30, 2, 31, 6, 35, 14, 43, 23, 52, 12, 41, 5, 34, 8, 37, 16, 45, 24, 53, 27, 56, 19, 48, 13, 42, 18, 47, 26, 55, 28, 57, 20, 49, 9, 38, 17, 46, 25, 54, 29, 58, 21, 50, 10, 39, 3, 32, 7, 36, 15, 44, 22, 51, 11, 40, 4, 33)(59, 88, 61, 90, 67, 96, 77, 106, 70, 99, 62, 91, 68, 97, 78, 107, 85, 114, 81, 110, 69, 98, 79, 108, 86, 115, 82, 111, 72, 101, 80, 109, 87, 116, 84, 113, 74, 103, 64, 93, 73, 102, 83, 112, 76, 105, 66, 95, 60, 89, 65, 94, 75, 104, 71, 100, 63, 92) L = (1, 62)(2, 59)(3, 68)(4, 69)(5, 70)(6, 60)(7, 61)(8, 63)(9, 78)(10, 79)(11, 80)(12, 81)(13, 77)(14, 64)(15, 65)(16, 66)(17, 67)(18, 71)(19, 85)(20, 86)(21, 87)(22, 73)(23, 72)(24, 74)(25, 75)(26, 76)(27, 82)(28, 84)(29, 83)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.179 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.168 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (Y2^-1, Y1), (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y2 * Y3 * Y2^-2 * Y3^-1 * Y2, Y2^3 * Y1^-1 * Y2^2, Y1 * Y2^-1 * Y1^2 * Y3^-3, Y1^4 * Y2^-1 * Y3^-2, Y3 * Y2 * Y3 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 30, 2, 31, 6, 35, 14, 43, 20, 49, 10, 39, 3, 32, 7, 36, 15, 44, 24, 53, 27, 56, 19, 48, 9, 38, 17, 46, 25, 54, 29, 58, 23, 52, 13, 42, 18, 47, 26, 55, 28, 57, 22, 51, 12, 41, 5, 34, 8, 37, 16, 45, 21, 50, 11, 40, 4, 33)(59, 88, 61, 90, 67, 96, 76, 105, 66, 95, 60, 89, 65, 94, 75, 104, 84, 113, 74, 103, 64, 93, 73, 102, 83, 112, 86, 115, 79, 108, 72, 101, 82, 111, 87, 116, 80, 109, 69, 98, 78, 107, 85, 114, 81, 110, 70, 99, 62, 91, 68, 97, 77, 106, 71, 100, 63, 92) L = (1, 62)(2, 59)(3, 68)(4, 69)(5, 70)(6, 60)(7, 61)(8, 63)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 64)(15, 65)(16, 66)(17, 67)(18, 71)(19, 85)(20, 72)(21, 74)(22, 86)(23, 87)(24, 73)(25, 75)(26, 76)(27, 82)(28, 84)(29, 83)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.177 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.169 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-2 * Y1^-2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-1 * Y3 * Y2^-1 * Y3^-2, Y2^-1 * Y1^-1 * Y2^2 * Y3^-1 * Y2^-1, Y1^2 * Y2 * Y1 * Y2^2 * Y3^-1, Y2 * Y3 * Y2 * Y3 * Y2^3 * Y1^-1, Y1^7 * Y3 * Y2^-2 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 30, 2, 31, 6, 35, 14, 43, 25, 54, 28, 57, 20, 49, 9, 38, 17, 46, 23, 52, 12, 41, 5, 34, 8, 37, 16, 45, 26, 55, 29, 58, 21, 50, 10, 39, 3, 32, 7, 36, 15, 44, 24, 53, 13, 42, 18, 47, 27, 56, 19, 48, 22, 51, 11, 40, 4, 33)(59, 88, 61, 90, 67, 96, 77, 106, 84, 113, 72, 101, 82, 111, 70, 99, 62, 91, 68, 97, 78, 107, 85, 114, 74, 103, 64, 93, 73, 102, 81, 110, 69, 98, 79, 108, 86, 115, 76, 105, 66, 95, 60, 89, 65, 94, 75, 104, 80, 109, 87, 116, 83, 112, 71, 100, 63, 92) L = (1, 62)(2, 59)(3, 68)(4, 69)(5, 70)(6, 60)(7, 61)(8, 63)(9, 78)(10, 79)(11, 80)(12, 81)(13, 82)(14, 64)(15, 65)(16, 66)(17, 67)(18, 71)(19, 85)(20, 86)(21, 87)(22, 77)(23, 75)(24, 73)(25, 72)(26, 74)(27, 76)(28, 83)(29, 84)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.176 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.170 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y3, Y3 * Y1, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (Y1, Y2^-1), (R * Y2)^2, Y2^-1 * Y3^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-2 * Y2^-1, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1, Y3^2 * Y2^-1 * Y3 * Y2^-4, Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3 * Y1^-1 ] Map:: R = (1, 30, 2, 31, 6, 35, 14, 43, 19, 48, 28, 57, 24, 53, 13, 42, 18, 47, 21, 50, 10, 39, 3, 32, 7, 36, 15, 44, 26, 55, 29, 58, 23, 52, 12, 41, 5, 34, 8, 37, 16, 45, 20, 49, 9, 38, 17, 46, 27, 56, 25, 54, 22, 51, 11, 40, 4, 33)(59, 88, 61, 90, 67, 96, 77, 106, 87, 116, 80, 109, 76, 105, 66, 95, 60, 89, 65, 94, 75, 104, 86, 115, 81, 110, 69, 98, 79, 108, 74, 103, 64, 93, 73, 102, 85, 114, 82, 111, 70, 99, 62, 91, 68, 97, 78, 107, 72, 101, 84, 113, 83, 112, 71, 100, 63, 92) L = (1, 62)(2, 59)(3, 68)(4, 69)(5, 70)(6, 60)(7, 61)(8, 63)(9, 78)(10, 79)(11, 80)(12, 81)(13, 82)(14, 64)(15, 65)(16, 66)(17, 67)(18, 71)(19, 72)(20, 74)(21, 76)(22, 83)(23, 87)(24, 86)(25, 85)(26, 73)(27, 75)(28, 77)(29, 84)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.185 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.171 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2 * Y3 * Y2 * Y3^2, Y1^2 * Y2^-1 * Y1 * Y2^-1, Y2^-1 * Y3 * 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 ] Map:: R = (1, 30, 2, 31, 6, 35, 9, 38, 15, 44, 20, 49, 22, 51, 27, 56, 29, 58, 24, 53, 19, 48, 17, 46, 12, 41, 5, 34, 8, 37, 10, 39, 3, 32, 7, 36, 14, 43, 16, 45, 21, 50, 26, 55, 28, 57, 25, 54, 23, 52, 18, 47, 13, 42, 11, 40, 4, 33)(59, 88, 61, 90, 67, 96, 74, 103, 80, 109, 86, 115, 82, 111, 76, 105, 70, 99, 62, 91, 68, 97, 64, 93, 72, 101, 78, 107, 84, 113, 87, 116, 81, 110, 75, 104, 69, 98, 66, 95, 60, 89, 65, 94, 73, 102, 79, 108, 85, 114, 83, 112, 77, 106, 71, 100, 63, 92) L = (1, 62)(2, 59)(3, 68)(4, 69)(5, 70)(6, 60)(7, 61)(8, 63)(9, 64)(10, 66)(11, 71)(12, 75)(13, 76)(14, 65)(15, 67)(16, 72)(17, 77)(18, 81)(19, 82)(20, 73)(21, 74)(22, 78)(23, 83)(24, 87)(25, 86)(26, 79)(27, 80)(28, 84)(29, 85)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.184 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.172 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y1^-1, (Y3^-1, Y2^-1), (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^2, Y2^7 * 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 ] Map:: R = (1, 30, 2, 31, 6, 35, 13, 42, 15, 44, 20, 49, 25, 54, 27, 56, 29, 58, 23, 52, 16, 45, 18, 47, 10, 39, 3, 32, 7, 36, 12, 41, 5, 34, 8, 37, 14, 43, 19, 48, 21, 50, 26, 55, 28, 57, 22, 51, 24, 53, 17, 46, 9, 38, 11, 40, 4, 33)(59, 88, 61, 90, 67, 96, 74, 103, 80, 109, 85, 114, 79, 108, 73, 102, 66, 95, 60, 89, 65, 94, 69, 98, 76, 105, 82, 111, 87, 116, 84, 113, 78, 107, 72, 101, 64, 93, 70, 99, 62, 91, 68, 97, 75, 104, 81, 110, 86, 115, 83, 112, 77, 106, 71, 100, 63, 92) L = (1, 62)(2, 59)(3, 68)(4, 69)(5, 70)(6, 60)(7, 61)(8, 63)(9, 75)(10, 76)(11, 67)(12, 65)(13, 64)(14, 66)(15, 71)(16, 81)(17, 82)(18, 74)(19, 72)(20, 73)(21, 77)(22, 86)(23, 87)(24, 80)(25, 78)(26, 79)(27, 83)(28, 84)(29, 85)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.175 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.173 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^3 * Y2 * Y1 * Y2 * Y3^-1, Y2^-1 * Y1 * Y2^-4 * Y1, Y2 * Y1 * Y2 * Y1 * Y3^-3, Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * 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 * Y2^-1 * Y3 * Y2^-1 * Y3^2 ] Map:: R = (1, 30, 2, 31, 6, 35, 14, 43, 24, 53, 13, 42, 18, 47, 19, 48, 27, 56, 28, 57, 21, 50, 10, 39, 3, 32, 7, 36, 15, 44, 23, 52, 12, 41, 5, 34, 8, 37, 16, 45, 26, 55, 29, 58, 25, 54, 20, 49, 9, 38, 17, 46, 22, 51, 11, 40, 4, 33)(59, 88, 61, 90, 67, 96, 77, 106, 74, 103, 64, 93, 73, 102, 80, 109, 86, 115, 87, 116, 82, 111, 70, 99, 62, 91, 68, 97, 78, 107, 76, 105, 66, 95, 60, 89, 65, 94, 75, 104, 85, 114, 84, 113, 72, 101, 81, 110, 69, 98, 79, 108, 83, 112, 71, 100, 63, 92) L = (1, 62)(2, 59)(3, 68)(4, 69)(5, 70)(6, 60)(7, 61)(8, 63)(9, 78)(10, 79)(11, 80)(12, 81)(13, 82)(14, 64)(15, 65)(16, 66)(17, 67)(18, 71)(19, 76)(20, 83)(21, 86)(22, 75)(23, 73)(24, 72)(25, 87)(26, 74)(27, 77)(28, 85)(29, 84)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.181 Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.174 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y2 * Y3, (R * Y1)^2, (R * Y3)^2, Y2^29, (Y3 * Y2^-1)^29, (Y3^-1 * Y1^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 62, 91, 64, 93, 66, 95, 68, 97, 70, 99, 79, 108, 87, 116, 86, 115, 85, 114, 84, 113, 83, 112, 81, 110, 82, 111, 80, 109, 78, 107, 77, 106, 76, 105, 75, 104, 74, 103, 72, 101, 73, 102, 71, 100, 69, 98, 67, 96, 65, 94, 63, 92, 61, 90) L = (1, 61)(2, 59)(3, 63)(4, 60)(5, 65)(6, 62)(7, 67)(8, 64)(9, 69)(10, 66)(11, 71)(12, 68)(13, 73)(14, 74)(15, 72)(16, 75)(17, 76)(18, 77)(19, 78)(20, 80)(21, 70)(22, 82)(23, 83)(24, 81)(25, 84)(26, 85)(27, 86)(28, 87)(29, 79)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.161 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.175 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y2 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y3^-14, (Y3^-1 * Y1^-1)^29, (Y3 * Y2^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 63, 92, 64, 93, 67, 96, 68, 97, 71, 100, 72, 101, 75, 104, 76, 105, 79, 108, 80, 109, 83, 112, 84, 113, 87, 116, 85, 114, 86, 115, 81, 110, 82, 111, 77, 106, 78, 107, 73, 102, 74, 103, 69, 98, 70, 99, 65, 94, 66, 95, 61, 90, 62, 91) L = (1, 61)(2, 62)(3, 65)(4, 66)(5, 59)(6, 60)(7, 69)(8, 70)(9, 63)(10, 64)(11, 73)(12, 74)(13, 67)(14, 68)(15, 77)(16, 78)(17, 71)(18, 72)(19, 81)(20, 82)(21, 75)(22, 76)(23, 85)(24, 86)(25, 79)(26, 80)(27, 84)(28, 87)(29, 83)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.172 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.176 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3 * Y3, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^-3 * Y2^2 * Y3^-6, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-4, (Y3^-1 * Y1^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 64, 93, 63, 92, 66, 95, 70, 99, 69, 98, 72, 101, 76, 105, 75, 104, 78, 107, 82, 111, 81, 110, 84, 113, 85, 114, 87, 116, 86, 115, 79, 108, 83, 112, 80, 109, 73, 102, 77, 106, 74, 103, 67, 96, 71, 100, 68, 97, 61, 90, 65, 94, 62, 91) L = (1, 61)(2, 65)(3, 67)(4, 68)(5, 59)(6, 62)(7, 71)(8, 60)(9, 73)(10, 74)(11, 63)(12, 64)(13, 77)(14, 66)(15, 79)(16, 80)(17, 69)(18, 70)(19, 83)(20, 72)(21, 85)(22, 86)(23, 75)(24, 76)(25, 87)(26, 78)(27, 82)(28, 84)(29, 81)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.169 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.177 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3 * Y2^4, Y3^-1 * Y2 * Y3^-6, (Y2^-1 * Y3)^29, (Y3^-1 * Y1^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 64, 93, 70, 99, 63, 92, 66, 95, 72, 101, 78, 107, 71, 100, 74, 103, 80, 109, 85, 114, 79, 108, 82, 111, 86, 115, 87, 116, 83, 112, 75, 104, 81, 110, 84, 113, 76, 105, 67, 96, 73, 102, 77, 106, 68, 97, 61, 90, 65, 94, 69, 98, 62, 91) L = (1, 61)(2, 65)(3, 67)(4, 68)(5, 59)(6, 69)(7, 73)(8, 60)(9, 75)(10, 76)(11, 77)(12, 62)(13, 63)(14, 64)(15, 81)(16, 66)(17, 82)(18, 83)(19, 84)(20, 70)(21, 71)(22, 72)(23, 86)(24, 74)(25, 79)(26, 87)(27, 78)(28, 80)(29, 85)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.168 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.178 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3^-1 * Y2^-5, Y3^2 * Y2 * Y3^4, Y2^2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-3, Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2, (Y3^-1 * Y1^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 64, 93, 72, 101, 70, 99, 63, 92, 66, 95, 74, 103, 82, 111, 80, 109, 71, 100, 76, 105, 84, 113, 86, 115, 77, 106, 81, 110, 85, 114, 87, 116, 78, 107, 67, 96, 75, 104, 83, 112, 79, 108, 68, 97, 61, 90, 65, 94, 73, 102, 69, 98, 62, 91) L = (1, 61)(2, 65)(3, 67)(4, 68)(5, 59)(6, 73)(7, 75)(8, 60)(9, 77)(10, 78)(11, 79)(12, 62)(13, 63)(14, 69)(15, 83)(16, 64)(17, 81)(18, 66)(19, 80)(20, 86)(21, 87)(22, 70)(23, 71)(24, 72)(25, 85)(26, 74)(27, 76)(28, 82)(29, 84)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.166 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.179 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3^-5 * Y2^-1, Y2 * Y3 * Y2^5, Y2^2 * Y3^-2 * Y2^-2 * Y3^2, (Y2^-1 * Y3)^29, (Y3^-1 * Y1^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 64, 93, 72, 101, 81, 110, 70, 99, 63, 92, 66, 95, 74, 103, 82, 111, 85, 114, 77, 106, 71, 100, 76, 105, 84, 113, 86, 115, 78, 107, 67, 96, 75, 104, 83, 112, 87, 116, 79, 108, 68, 97, 61, 90, 65, 94, 73, 102, 80, 109, 69, 98, 62, 91) L = (1, 61)(2, 65)(3, 67)(4, 68)(5, 59)(6, 73)(7, 75)(8, 60)(9, 77)(10, 78)(11, 79)(12, 62)(13, 63)(14, 80)(15, 83)(16, 64)(17, 71)(18, 66)(19, 70)(20, 85)(21, 86)(22, 87)(23, 69)(24, 72)(25, 76)(26, 74)(27, 81)(28, 82)(29, 84)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.167 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.180 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y3^-1 * Y2 * Y3^-3, Y2^-2 * Y3^-1 * Y2^-5, (Y3^-1 * Y1^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 64, 93, 72, 101, 80, 109, 78, 107, 70, 99, 63, 92, 66, 95, 74, 103, 82, 111, 86, 115, 85, 114, 79, 108, 71, 100, 67, 96, 75, 104, 83, 112, 87, 116, 84, 113, 76, 105, 68, 97, 61, 90, 65, 94, 73, 102, 81, 110, 77, 106, 69, 98, 62, 91) L = (1, 61)(2, 65)(3, 67)(4, 68)(5, 59)(6, 73)(7, 75)(8, 60)(9, 66)(10, 71)(11, 76)(12, 62)(13, 63)(14, 81)(15, 83)(16, 64)(17, 74)(18, 79)(19, 84)(20, 69)(21, 70)(22, 77)(23, 87)(24, 72)(25, 82)(26, 85)(27, 78)(28, 80)(29, 86)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.164 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.181 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y3^4 * Y2^3, Y2 * Y3 * Y2^2 * Y3^3, Y3^2 * Y2^-1 * Y3 * Y2^-4, Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^2 * Y3 * Y2, (Y3^-1 * Y1^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 64, 93, 72, 101, 84, 113, 77, 106, 81, 110, 70, 99, 63, 92, 66, 95, 74, 103, 85, 114, 78, 107, 67, 96, 75, 104, 82, 111, 71, 100, 76, 105, 86, 115, 79, 108, 68, 97, 61, 90, 65, 94, 73, 102, 83, 112, 87, 116, 80, 109, 69, 98, 62, 91) L = (1, 61)(2, 65)(3, 67)(4, 68)(5, 59)(6, 73)(7, 75)(8, 60)(9, 77)(10, 78)(11, 79)(12, 62)(13, 63)(14, 83)(15, 82)(16, 64)(17, 81)(18, 66)(19, 80)(20, 84)(21, 85)(22, 86)(23, 69)(24, 70)(25, 71)(26, 87)(27, 72)(28, 74)(29, 76)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.173 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.182 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y3^-1 * Y2^2 * Y3^-2, Y3^-1 * Y2^-9, Y2^-1 * Y3^-1 * Y2^-8, (Y3^-1 * Y1^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 64, 93, 72, 101, 78, 107, 84, 113, 82, 111, 76, 105, 70, 99, 63, 92, 66, 95, 67, 96, 74, 103, 80, 109, 86, 115, 87, 116, 83, 112, 77, 106, 71, 100, 68, 97, 61, 90, 65, 94, 73, 102, 79, 108, 85, 114, 81, 110, 75, 104, 69, 98, 62, 91) L = (1, 61)(2, 65)(3, 67)(4, 68)(5, 59)(6, 73)(7, 74)(8, 60)(9, 64)(10, 66)(11, 71)(12, 62)(13, 63)(14, 79)(15, 80)(16, 72)(17, 77)(18, 69)(19, 70)(20, 85)(21, 86)(22, 78)(23, 83)(24, 75)(25, 76)(26, 81)(27, 87)(28, 84)(29, 82)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.162 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.183 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^-1 * Y3^-3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^4 * Y3^-1 * Y2^-4 * Y3, Y2^4 * Y3^-2 * Y2^5, (Y3^-1 * Y1^-1)^29, (Y3 * Y2^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 64, 93, 70, 99, 76, 105, 82, 111, 85, 114, 79, 108, 73, 102, 67, 96, 63, 92, 66, 95, 72, 101, 78, 107, 84, 113, 86, 115, 80, 109, 74, 103, 68, 97, 61, 90, 65, 94, 71, 100, 77, 106, 83, 112, 87, 116, 81, 110, 75, 104, 69, 98, 62, 91) L = (1, 61)(2, 65)(3, 67)(4, 68)(5, 59)(6, 71)(7, 63)(8, 60)(9, 62)(10, 73)(11, 74)(12, 77)(13, 66)(14, 64)(15, 69)(16, 79)(17, 80)(18, 83)(19, 72)(20, 70)(21, 75)(22, 85)(23, 86)(24, 87)(25, 78)(26, 76)(27, 81)(28, 82)(29, 84)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.165 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.184 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3^-1, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^2 * Y3 * Y2 * Y3^2 * Y2, Y2^-1 * Y3 * Y2^-1 * Y3^4 * Y2^-1, 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^-3 * Y2 * Y3^-3 * Y2 * Y3^-3 * Y2 * Y3^-2 * Y2^-1 * Y3^-1, (Y3^-1 * Y1^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 64, 93, 72, 101, 83, 112, 86, 115, 78, 107, 67, 96, 75, 104, 81, 110, 70, 99, 63, 92, 66, 95, 74, 103, 84, 113, 87, 116, 79, 108, 68, 97, 61, 90, 65, 94, 73, 102, 82, 111, 71, 100, 76, 105, 85, 114, 77, 106, 80, 109, 69, 98, 62, 91) L = (1, 61)(2, 65)(3, 67)(4, 68)(5, 59)(6, 73)(7, 75)(8, 60)(9, 77)(10, 78)(11, 79)(12, 62)(13, 63)(14, 82)(15, 81)(16, 64)(17, 80)(18, 66)(19, 84)(20, 85)(21, 86)(22, 87)(23, 69)(24, 70)(25, 71)(26, 72)(27, 74)(28, 76)(29, 83)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.171 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.185 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y3), Y2^5 * Y3^-2, Y2^2 * Y3^5, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 64, 93, 72, 101, 78, 107, 67, 96, 75, 104, 83, 112, 85, 114, 87, 116, 81, 110, 70, 99, 63, 92, 66, 95, 74, 103, 79, 108, 68, 97, 61, 90, 65, 94, 73, 102, 84, 113, 86, 115, 77, 106, 82, 111, 71, 100, 76, 105, 80, 109, 69, 98, 62, 91) L = (1, 61)(2, 65)(3, 67)(4, 68)(5, 59)(6, 73)(7, 75)(8, 60)(9, 77)(10, 78)(11, 79)(12, 62)(13, 63)(14, 84)(15, 83)(16, 64)(17, 82)(18, 66)(19, 81)(20, 86)(21, 72)(22, 74)(23, 69)(24, 70)(25, 71)(26, 85)(27, 76)(28, 87)(29, 80)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.170 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.186 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {29, 29, 29}) Quotient :: dipole Aut^+ = C29 (small group id <29, 1>) Aut = D58 (small group id <58, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y2^2 * Y3^-1 * Y2 * Y3^-1, Y3^8 * Y2 * Y3, (Y3^-1 * Y1^-1)^29 ] Map:: R = (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 88, 60, 89, 64, 93, 67, 96, 73, 102, 78, 107, 80, 109, 85, 114, 87, 116, 82, 111, 77, 106, 75, 104, 70, 99, 63, 92, 66, 95, 68, 97, 61, 90, 65, 94, 72, 101, 74, 103, 79, 108, 84, 113, 86, 115, 83, 112, 81, 110, 76, 105, 71, 100, 69, 98, 62, 91) L = (1, 61)(2, 65)(3, 67)(4, 68)(5, 59)(6, 72)(7, 73)(8, 60)(9, 74)(10, 64)(11, 66)(12, 62)(13, 63)(14, 78)(15, 79)(16, 80)(17, 69)(18, 70)(19, 71)(20, 84)(21, 85)(22, 86)(23, 75)(24, 76)(25, 77)(26, 87)(27, 83)(28, 82)(29, 81)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.163 Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.187 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 5, 10}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y1 * Y2^-1)^2, (Y3, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y3 * Y1 * Y3^-1, Y3^5 * Y2, Y1 * Y2 * Y3^-1 * Y1 * Y3 * Y2^-1, (Y2^-1 * Y3)^5 ] Map:: polytopal non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 13, 43)(5, 35, 7, 37)(6, 36, 17, 47)(8, 38, 11, 41)(10, 40, 16, 46)(12, 42, 19, 49)(14, 44, 26, 56)(15, 45, 21, 51)(18, 48, 30, 60)(20, 50, 28, 58)(22, 52, 24, 54)(23, 53, 25, 55)(27, 57, 29, 59)(61, 91, 63, 93, 65, 95)(62, 92, 67, 97, 69, 99)(64, 94, 71, 101, 75, 105)(66, 96, 72, 102, 76, 106)(68, 98, 73, 103, 81, 111)(70, 100, 79, 109, 77, 107)(74, 104, 83, 113, 88, 118)(78, 108, 84, 114, 87, 117)(80, 110, 85, 115, 86, 116)(82, 112, 90, 120, 89, 119) L = (1, 64)(2, 68)(3, 71)(4, 74)(5, 75)(6, 61)(7, 73)(8, 80)(9, 81)(10, 62)(11, 83)(12, 63)(13, 85)(14, 87)(15, 88)(16, 65)(17, 69)(18, 66)(19, 67)(20, 89)(21, 86)(22, 70)(23, 78)(24, 72)(25, 82)(26, 90)(27, 76)(28, 84)(29, 77)(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 ) } Outer automorphisms :: reflexible Dual of E14.190 Graph:: simple bipartite v = 25 e = 60 f = 9 degree seq :: [ 4^15, 6^10 ] E14.188 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 5, 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, Y3^2, Y1^3, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y2 * Y3 * Y2^-1, (Y2^-1, Y1^-1), Y2^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 7, 37, 12, 42)(4, 34, 13, 43, 8, 38)(6, 36, 9, 39, 15, 45)(10, 40, 17, 47, 22, 52)(11, 41, 23, 53, 18, 48)(14, 44, 24, 54, 19, 49)(16, 46, 20, 50, 26, 56)(21, 51, 29, 59, 27, 57)(25, 55, 30, 60, 28, 58)(61, 91, 63, 93, 70, 100, 76, 106, 66, 96)(62, 92, 67, 97, 77, 107, 80, 110, 69, 99)(64, 94, 71, 101, 81, 111, 85, 115, 74, 104)(65, 95, 72, 102, 82, 112, 86, 116, 75, 105)(68, 98, 78, 108, 87, 117, 88, 118, 79, 109)(73, 103, 83, 113, 89, 119, 90, 120, 84, 114) L = (1, 64)(2, 68)(3, 71)(4, 61)(5, 73)(6, 74)(7, 78)(8, 62)(9, 79)(10, 81)(11, 63)(12, 83)(13, 65)(14, 66)(15, 84)(16, 85)(17, 87)(18, 67)(19, 69)(20, 88)(21, 70)(22, 89)(23, 72)(24, 75)(25, 76)(26, 90)(27, 77)(28, 80)(29, 82)(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, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E14.189 Graph:: simple bipartite v = 16 e = 60 f = 18 degree seq :: [ 6^10, 10^6 ] E14.189 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 5, 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, Y2^2, Y3^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-5, Y2 * Y1 * Y3 * Y2 * Y3 * Y1^-1, Y1^-1 * Y2 * Y1 * Y2 * Y3 * Y2, Y2 * Y3 * Y1 * Y2 * Y1^-1 * Y3, Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, (R * Y2 * Y3)^2 ] Map:: non-degenerate R = (1, 31, 2, 32, 6, 36, 16, 46, 13, 43, 4, 34, 8, 38, 18, 48, 15, 45, 5, 35)(3, 33, 9, 39, 17, 47, 28, 58, 23, 53, 10, 40, 22, 52, 29, 59, 25, 55, 11, 41)(7, 37, 19, 49, 27, 57, 24, 54, 12, 42, 20, 50, 30, 60, 26, 56, 14, 44, 21, 51)(61, 91, 63, 93)(62, 92, 67, 97)(64, 94, 72, 102)(65, 95, 74, 104)(66, 96, 77, 107)(68, 98, 82, 112)(69, 99, 80, 110)(70, 100, 81, 111)(71, 101, 84, 114)(73, 103, 83, 113)(75, 105, 85, 115)(76, 106, 87, 117)(78, 108, 90, 120)(79, 109, 89, 119)(86, 116, 88, 118) L = (1, 64)(2, 68)(3, 70)(4, 61)(5, 73)(6, 78)(7, 80)(8, 62)(9, 82)(10, 63)(11, 83)(12, 81)(13, 65)(14, 84)(15, 76)(16, 75)(17, 89)(18, 66)(19, 90)(20, 67)(21, 72)(22, 69)(23, 71)(24, 74)(25, 88)(26, 87)(27, 86)(28, 85)(29, 77)(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) :: { ( 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 E14.188 Graph:: bipartite v = 18 e = 60 f = 16 degree seq :: [ 4^15, 20^3 ] E14.190 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 5, 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^-2 * Y1^-2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (Y3^-1, Y1^-1), (Y3 * Y2^-1)^2, Y1^-1 * Y2^4, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-1, Y3^-1 * Y1 * Y3^-2 * Y1, Y1^5, Y2 * Y3^3 * Y2, (Y1^-1 * Y3^-1)^3, (R * Y2 * Y3^-1)^2 ] Map:: polytopal non-degenerate R = (1, 31, 2, 32, 8, 38, 13, 43, 5, 35)(3, 33, 9, 39, 6, 36, 11, 41, 15, 45)(4, 34, 10, 40, 25, 55, 24, 54, 19, 49)(7, 37, 12, 42, 18, 48, 29, 59, 20, 50)(14, 44, 26, 56, 21, 51, 30, 60, 23, 53)(16, 46, 27, 57, 22, 52, 17, 47, 28, 58)(61, 91, 63, 93, 73, 103, 71, 101, 62, 92, 69, 99, 65, 95, 75, 105, 68, 98, 66, 96)(64, 94, 77, 107, 84, 114, 87, 117, 70, 100, 88, 118, 79, 109, 82, 112, 85, 115, 76, 106)(67, 97, 81, 111, 89, 119, 74, 104, 72, 102, 90, 120, 80, 110, 86, 116, 78, 108, 83, 113) L = (1, 64)(2, 70)(3, 74)(4, 78)(5, 79)(6, 81)(7, 61)(8, 85)(9, 86)(10, 89)(11, 90)(12, 62)(13, 84)(14, 82)(15, 83)(16, 63)(17, 71)(18, 68)(19, 72)(20, 65)(21, 88)(22, 66)(23, 87)(24, 67)(25, 80)(26, 77)(27, 69)(28, 75)(29, 73)(30, 76)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 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 E14.187 Graph:: bipartite v = 9 e = 60 f = 25 degree seq :: [ 10^6, 20^3 ] E14.191 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 5, 10}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2), Y2^-1 * Y1 * Y2 * Y1, Y3^3 * Y2^2, Y2^5, Y3 * Y2 * Y1 * Y3^-2 * Y1, Y2^-1 * Y3 * Y1 * Y3 * Y1 * Y2^-1, Y3^-1 * Y2 * Y3^-1 * Y1 * Y3 * Y1 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 7, 37)(4, 34, 14, 44)(5, 35, 9, 39)(6, 36, 19, 49)(8, 38, 24, 54)(10, 40, 29, 59)(11, 41, 21, 51)(12, 42, 25, 55)(13, 43, 26, 56)(15, 45, 22, 52)(16, 46, 23, 53)(17, 47, 27, 57)(18, 48, 30, 60)(20, 50, 28, 58)(61, 91, 63, 93, 71, 101, 77, 107, 65, 95)(62, 92, 67, 97, 81, 111, 87, 117, 69, 99)(64, 94, 72, 102, 80, 110, 89, 119, 76, 106)(66, 96, 73, 103, 84, 114, 75, 105, 78, 108)(68, 98, 82, 112, 90, 120, 79, 109, 86, 116)(70, 100, 83, 113, 74, 104, 85, 115, 88, 118) L = (1, 64)(2, 68)(3, 72)(4, 75)(5, 76)(6, 61)(7, 82)(8, 85)(9, 86)(10, 62)(11, 80)(12, 78)(13, 63)(14, 81)(15, 77)(16, 84)(17, 89)(18, 65)(19, 83)(20, 66)(21, 90)(22, 88)(23, 67)(24, 71)(25, 87)(26, 74)(27, 79)(28, 69)(29, 73)(30, 70)(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 ) } Outer automorphisms :: reflexible Dual of E14.192 Graph:: simple bipartite v = 21 e = 60 f = 13 degree seq :: [ 4^15, 10^6 ] E14.192 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 5, 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, Y3^2, Y1^3, (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, (Y3 * Y1^-1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-5 * Y3 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 10, 40, 7, 37)(4, 34, 13, 43, 8, 38)(6, 36, 15, 45, 9, 39)(11, 41, 17, 47, 21, 51)(12, 42, 18, 48, 22, 52)(14, 44, 19, 49, 25, 55)(16, 46, 20, 50, 26, 56)(23, 53, 29, 59, 27, 57)(24, 54, 30, 60, 28, 58)(61, 91, 63, 93, 71, 101, 83, 113, 74, 104, 64, 94, 72, 102, 84, 114, 76, 106, 66, 96)(62, 92, 67, 97, 77, 107, 87, 117, 79, 109, 68, 98, 78, 108, 88, 118, 80, 110, 69, 99)(65, 95, 70, 100, 81, 111, 89, 119, 85, 115, 73, 103, 82, 112, 90, 120, 86, 116, 75, 105) L = (1, 64)(2, 68)(3, 72)(4, 61)(5, 73)(6, 74)(7, 78)(8, 62)(9, 79)(10, 82)(11, 84)(12, 63)(13, 65)(14, 66)(15, 85)(16, 83)(17, 88)(18, 67)(19, 69)(20, 87)(21, 90)(22, 70)(23, 76)(24, 71)(25, 75)(26, 89)(27, 80)(28, 77)(29, 86)(30, 81)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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 E14.191 Graph:: bipartite v = 13 e = 60 f = 21 degree seq :: [ 6^10, 20^3 ] E14.193 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 15, 15}) Quotient :: halfedge^2 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, Y3^2, Y3 * Y2, (R * Y1)^2, R * Y3 * R * Y2, Y1^2 * Y2 * Y1 * Y2 * Y1^2, Y2 * Y1 * Y2 * Y1^-2 * Y2 * Y1^2 * Y2 * Y1^-1 ] Map:: R = (1, 32, 2, 35, 5, 41, 11, 47, 17, 54, 24, 59, 29, 56, 26, 58, 28, 60, 30, 57, 27, 46, 16, 52, 22, 40, 10, 34, 4, 31)(3, 37, 7, 45, 15, 50, 20, 39, 9, 49, 19, 53, 23, 42, 12, 51, 21, 55, 25, 44, 14, 36, 6, 43, 13, 48, 18, 38, 8, 33) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 20)(13, 22)(14, 24)(15, 26)(18, 28)(19, 27)(23, 29)(25, 30)(31, 33)(32, 36)(34, 39)(35, 42)(37, 46)(38, 47)(40, 51)(41, 50)(43, 52)(44, 54)(45, 56)(48, 58)(49, 57)(53, 59)(55, 60) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.194 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 15, 15}) Quotient :: halfedge^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3, Y1^2 * Y2 * Y1^-1 * Y2 * Y1^2 ] Map:: R = (1, 32, 2, 35, 5, 41, 11, 46, 16, 55, 25, 59, 29, 58, 28, 56, 26, 60, 30, 57, 27, 47, 17, 52, 22, 40, 10, 34, 4, 31)(3, 37, 7, 45, 15, 44, 14, 36, 6, 43, 13, 54, 24, 51, 21, 42, 12, 53, 23, 50, 20, 39, 9, 49, 19, 48, 18, 38, 8, 33) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 19)(13, 25)(14, 22)(15, 26)(18, 28)(20, 27)(23, 29)(24, 30)(31, 33)(32, 36)(34, 39)(35, 42)(37, 46)(38, 47)(40, 51)(41, 49)(43, 55)(44, 52)(45, 56)(48, 58)(50, 57)(53, 59)(54, 60) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.195 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 15, 15}) Quotient :: halfedge^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y1 * Y2 * Y1 * Y3 * Y1, Y1 * Y2 * Y3 * Y2 * Y1^-1 * Y3, Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y2, Y1^-1 * Y2 * Y1^2 * Y3 * Y1^-1, Y3 * Y1 * Y2 * Y3 * Y2 * Y1^-1, Y1^15 ] Map:: non-degenerate R = (1, 32, 2, 36, 6, 48, 18, 54, 24, 58, 28, 43, 13, 52, 22, 56, 26, 40, 10, 50, 20, 57, 27, 60, 30, 47, 17, 35, 5, 31)(3, 39, 9, 49, 19, 51, 21, 37, 7, 46, 16, 55, 25, 59, 29, 44, 14, 34, 4, 42, 12, 45, 15, 53, 23, 38, 8, 41, 11, 33) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 14)(8, 22)(9, 24)(10, 25)(11, 27)(12, 20)(16, 28)(17, 29)(18, 23)(19, 26)(21, 30)(31, 34)(32, 38)(33, 40)(35, 46)(36, 49)(37, 50)(39, 47)(41, 58)(42, 54)(43, 51)(44, 57)(45, 56)(48, 55)(52, 59)(53, 60) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.196 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y2 * R * Y1, (R * Y3)^2, Y3^2 * Y1 * Y3 * Y1 * Y3^2, Y3 * Y1 * Y3^-2 * Y2 * Y3^2 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 31, 3, 33, 8, 38, 18, 48, 13, 43, 25, 55, 30, 60, 24, 54, 26, 56, 29, 59, 23, 53, 11, 41, 22, 52, 10, 40, 4, 34)(2, 32, 5, 35, 12, 42, 20, 50, 9, 39, 19, 49, 28, 58, 17, 47, 21, 51, 27, 57, 16, 46, 7, 37, 15, 45, 14, 44, 6, 36)(61, 62)(63, 67)(64, 69)(65, 71)(66, 73)(68, 77)(70, 81)(72, 84)(74, 86)(75, 82)(76, 85)(78, 80)(79, 83)(87, 89)(88, 90)(91, 92)(93, 97)(94, 99)(95, 101)(96, 103)(98, 107)(100, 111)(102, 114)(104, 116)(105, 112)(106, 115)(108, 110)(109, 113)(117, 119)(118, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 60, 60 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E14.201 Graph:: simple bipartite v = 32 e = 60 f = 2 degree seq :: [ 2^30, 30^2 ] E14.197 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 15, 15}) Quotient :: edge^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y2 * R * Y1, (R * Y3)^2, Y3^2 * Y1 * Y3^-1 * Y1 * Y3^2 ] Map:: R = (1, 31, 3, 33, 8, 38, 18, 48, 11, 41, 23, 53, 29, 59, 26, 56, 24, 54, 30, 60, 25, 55, 13, 43, 22, 52, 10, 40, 4, 34)(2, 32, 5, 35, 12, 42, 16, 46, 7, 37, 15, 45, 27, 57, 21, 51, 17, 47, 28, 58, 20, 50, 9, 39, 19, 49, 14, 44, 6, 36)(61, 62)(63, 67)(64, 69)(65, 71)(66, 73)(68, 77)(70, 81)(72, 84)(74, 86)(75, 83)(76, 82)(78, 79)(80, 85)(87, 90)(88, 89)(91, 92)(93, 97)(94, 99)(95, 101)(96, 103)(98, 107)(100, 111)(102, 114)(104, 116)(105, 113)(106, 112)(108, 109)(110, 115)(117, 120)(118, 119) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 60, 60 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E14.202 Graph:: simple bipartite v = 32 e = 60 f = 2 degree seq :: [ 2^30, 30^2 ] E14.198 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 15, 15}) Quotient :: edge^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y3^-2 * Y1 * Y3^-1, Y1 * Y3^-2 * Y2 * Y3^2, Y1 * Y3^-2 * Y2 * Y3^2, Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y1, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, Y3 * Y1 * Y3^-2 * Y2 * Y3, Y3^15 ] Map:: R = (1, 31, 4, 34, 14, 44, 29, 59, 21, 51, 20, 50, 6, 36, 19, 49, 26, 56, 9, 39, 22, 52, 23, 53, 30, 60, 17, 47, 5, 35)(2, 32, 7, 37, 16, 46, 28, 58, 12, 42, 11, 41, 3, 33, 10, 40, 27, 57, 18, 48, 13, 43, 15, 45, 25, 55, 24, 54, 8, 38)(61, 62)(63, 69)(64, 72)(65, 75)(66, 78)(67, 81)(68, 83)(70, 77)(71, 80)(73, 82)(74, 87)(76, 86)(79, 84)(85, 89)(88, 90)(91, 93)(92, 96)(94, 103)(95, 106)(97, 112)(98, 104)(99, 115)(100, 111)(101, 113)(102, 109)(105, 110)(107, 114)(108, 120)(116, 117)(118, 119) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 60, 60 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E14.203 Graph:: simple bipartite v = 32 e = 60 f = 2 degree seq :: [ 2^30, 30^2 ] E14.199 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 15, 15}) Quotient :: edge^2 Aut^+ = D30 (small group id <30, 3>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y1 * R * Y2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y2^-1, Y1^-1), (Y3 * Y1^-1)^2, Y1^2 * Y2^-1 * Y1^2, Y2 * Y1^-1 * Y2^3, (Y3 * Y1 * Y2^-1)^2, Y2^-1 * Y1^-2 * Y2^-2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 31, 4, 34)(2, 32, 9, 39)(3, 33, 12, 42)(5, 35, 14, 44)(6, 36, 15, 45)(7, 37, 20, 50)(8, 38, 22, 52)(10, 40, 23, 53)(11, 41, 24, 54)(13, 43, 25, 55)(16, 46, 26, 56)(17, 47, 27, 57)(18, 48, 28, 58)(19, 49, 29, 59)(21, 51, 30, 60)(61, 62, 67, 73, 63, 68, 79, 78, 71, 81, 77, 66, 70, 76, 65)(64, 74, 86, 83, 75, 87, 90, 84, 88, 89, 82, 72, 85, 80, 69)(91, 93, 101, 100, 92, 98, 111, 106, 97, 109, 107, 95, 103, 108, 96)(94, 105, 118, 115, 104, 117, 119, 110, 116, 120, 112, 99, 113, 114, 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) :: { ( 8^4 ), ( 8^15 ) } Outer automorphisms :: reflexible Dual of E14.204 Graph:: simple bipartite v = 19 e = 60 f = 15 degree seq :: [ 4^15, 15^4 ] E14.200 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 15, 15}) Quotient :: edge^2 Aut^+ = C5 x S3 (small group id <30, 1>) Aut = C10 x S3 (small group id <60, 11>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^-1 * Y2^-2 * Y1 * Y2 * Y1^-1, Y1 * Y3 * Y1 * Y3 * Y2^-3, Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-2, Y1 * Y3 * Y1^2 * Y2^-2 * Y3, Y2^4 * Y3 * Y1^-1 * Y3, Y3 * Y1^2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y1^-2, Y1^15 ] Map:: non-degenerate R = (1, 31, 4, 34)(2, 32, 6, 36)(3, 33, 8, 38)(5, 35, 12, 42)(7, 37, 16, 46)(9, 39, 20, 50)(10, 40, 22, 52)(11, 41, 18, 48)(13, 43, 15, 45)(14, 44, 25, 55)(17, 47, 26, 56)(19, 49, 27, 57)(21, 51, 28, 58)(23, 53, 29, 59)(24, 54, 30, 60)(61, 62, 65, 71, 82, 85, 89, 87, 88, 90, 86, 80, 75, 67, 63)(64, 69, 79, 78, 68, 77, 83, 72, 76, 84, 74, 66, 73, 81, 70)(91, 93, 97, 105, 110, 116, 120, 118, 117, 119, 115, 112, 101, 95, 92)(94, 100, 111, 103, 96, 104, 114, 106, 102, 113, 107, 98, 108, 109, 99) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 8^4 ), ( 8^15 ) } Outer automorphisms :: reflexible Dual of E14.205 Graph:: simple bipartite v = 19 e = 60 f = 15 degree seq :: [ 4^15, 15^4 ] E14.201 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y2 * R * Y1, (R * Y3)^2, Y3^2 * Y1 * Y3 * Y1 * Y3^2, Y3 * Y1 * Y3^-2 * Y2 * Y3^2 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 31, 61, 91, 3, 33, 63, 93, 8, 38, 68, 98, 18, 48, 78, 108, 13, 43, 73, 103, 25, 55, 85, 115, 30, 60, 90, 120, 24, 54, 84, 114, 26, 56, 86, 116, 29, 59, 89, 119, 23, 53, 83, 113, 11, 41, 71, 101, 22, 52, 82, 112, 10, 40, 70, 100, 4, 34, 64, 94)(2, 32, 62, 92, 5, 35, 65, 95, 12, 42, 72, 102, 20, 50, 80, 110, 9, 39, 69, 99, 19, 49, 79, 109, 28, 58, 88, 118, 17, 47, 77, 107, 21, 51, 81, 111, 27, 57, 87, 117, 16, 46, 76, 106, 7, 37, 67, 97, 15, 45, 75, 105, 14, 44, 74, 104, 6, 36, 66, 96) L = (1, 32)(2, 31)(3, 37)(4, 39)(5, 41)(6, 43)(7, 33)(8, 47)(9, 34)(10, 51)(11, 35)(12, 54)(13, 36)(14, 56)(15, 52)(16, 55)(17, 38)(18, 50)(19, 53)(20, 48)(21, 40)(22, 45)(23, 49)(24, 42)(25, 46)(26, 44)(27, 59)(28, 60)(29, 57)(30, 58)(61, 92)(62, 91)(63, 97)(64, 99)(65, 101)(66, 103)(67, 93)(68, 107)(69, 94)(70, 111)(71, 95)(72, 114)(73, 96)(74, 116)(75, 112)(76, 115)(77, 98)(78, 110)(79, 113)(80, 108)(81, 100)(82, 105)(83, 109)(84, 102)(85, 106)(86, 104)(87, 119)(88, 120)(89, 117)(90, 118) local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) } Outer automorphisms :: reflexible Dual of E14.196 Transitivity :: VT+ Graph:: bipartite v = 2 e = 60 f = 32 degree seq :: [ 60^2 ] E14.202 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 15, 15}) Quotient :: loop^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y2 * R * Y1, (R * Y3)^2, Y3^2 * Y1 * Y3^-1 * Y1 * Y3^2 ] Map:: R = (1, 31, 61, 91, 3, 33, 63, 93, 8, 38, 68, 98, 18, 48, 78, 108, 11, 41, 71, 101, 23, 53, 83, 113, 29, 59, 89, 119, 26, 56, 86, 116, 24, 54, 84, 114, 30, 60, 90, 120, 25, 55, 85, 115, 13, 43, 73, 103, 22, 52, 82, 112, 10, 40, 70, 100, 4, 34, 64, 94)(2, 32, 62, 92, 5, 35, 65, 95, 12, 42, 72, 102, 16, 46, 76, 106, 7, 37, 67, 97, 15, 45, 75, 105, 27, 57, 87, 117, 21, 51, 81, 111, 17, 47, 77, 107, 28, 58, 88, 118, 20, 50, 80, 110, 9, 39, 69, 99, 19, 49, 79, 109, 14, 44, 74, 104, 6, 36, 66, 96) L = (1, 32)(2, 31)(3, 37)(4, 39)(5, 41)(6, 43)(7, 33)(8, 47)(9, 34)(10, 51)(11, 35)(12, 54)(13, 36)(14, 56)(15, 53)(16, 52)(17, 38)(18, 49)(19, 48)(20, 55)(21, 40)(22, 46)(23, 45)(24, 42)(25, 50)(26, 44)(27, 60)(28, 59)(29, 58)(30, 57)(61, 92)(62, 91)(63, 97)(64, 99)(65, 101)(66, 103)(67, 93)(68, 107)(69, 94)(70, 111)(71, 95)(72, 114)(73, 96)(74, 116)(75, 113)(76, 112)(77, 98)(78, 109)(79, 108)(80, 115)(81, 100)(82, 106)(83, 105)(84, 102)(85, 110)(86, 104)(87, 120)(88, 119)(89, 118)(90, 117) local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 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 E14.197 Transitivity :: VT+ Graph:: bipartite v = 2 e = 60 f = 32 degree seq :: [ 60^2 ] E14.203 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 15, 15}) Quotient :: loop^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y3^-2 * Y1 * Y3^-1, Y1 * Y3^-2 * Y2 * Y3^2, Y1 * Y3^-2 * Y2 * Y3^2, Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y1, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, Y3 * Y1 * Y3^-2 * Y2 * Y3, Y3^15 ] Map:: R = (1, 31, 61, 91, 4, 34, 64, 94, 14, 44, 74, 104, 29, 59, 89, 119, 21, 51, 81, 111, 20, 50, 80, 110, 6, 36, 66, 96, 19, 49, 79, 109, 26, 56, 86, 116, 9, 39, 69, 99, 22, 52, 82, 112, 23, 53, 83, 113, 30, 60, 90, 120, 17, 47, 77, 107, 5, 35, 65, 95)(2, 32, 62, 92, 7, 37, 67, 97, 16, 46, 76, 106, 28, 58, 88, 118, 12, 42, 72, 102, 11, 41, 71, 101, 3, 33, 63, 93, 10, 40, 70, 100, 27, 57, 87, 117, 18, 48, 78, 108, 13, 43, 73, 103, 15, 45, 75, 105, 25, 55, 85, 115, 24, 54, 84, 114, 8, 38, 68, 98) L = (1, 32)(2, 31)(3, 39)(4, 42)(5, 45)(6, 48)(7, 51)(8, 53)(9, 33)(10, 47)(11, 50)(12, 34)(13, 52)(14, 57)(15, 35)(16, 56)(17, 40)(18, 36)(19, 54)(20, 41)(21, 37)(22, 43)(23, 38)(24, 49)(25, 59)(26, 46)(27, 44)(28, 60)(29, 55)(30, 58)(61, 93)(62, 96)(63, 91)(64, 103)(65, 106)(66, 92)(67, 112)(68, 104)(69, 115)(70, 111)(71, 113)(72, 109)(73, 94)(74, 98)(75, 110)(76, 95)(77, 114)(78, 120)(79, 102)(80, 105)(81, 100)(82, 97)(83, 101)(84, 107)(85, 99)(86, 117)(87, 116)(88, 119)(89, 118)(90, 108) local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) } Outer automorphisms :: reflexible Dual of E14.198 Transitivity :: VT+ Graph:: bipartite v = 2 e = 60 f = 32 degree seq :: [ 60^2 ] E14.204 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 15, 15}) Quotient :: loop^2 Aut^+ = D30 (small group id <30, 3>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y1 * R * Y2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y2^-1, Y1^-1), (Y3 * Y1^-1)^2, Y1^2 * Y2^-1 * Y1^2, Y2 * Y1^-1 * Y2^3, (Y3 * Y1 * Y2^-1)^2, Y2^-1 * Y1^-2 * Y2^-2 * Y1^-1 ] Map:: polytopal 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, 14, 44, 74, 104)(6, 36, 66, 96, 15, 45, 75, 105)(7, 37, 67, 97, 20, 50, 80, 110)(8, 38, 68, 98, 22, 52, 82, 112)(10, 40, 70, 100, 23, 53, 83, 113)(11, 41, 71, 101, 24, 54, 84, 114)(13, 43, 73, 103, 25, 55, 85, 115)(16, 46, 76, 106, 26, 56, 86, 116)(17, 47, 77, 107, 27, 57, 87, 117)(18, 48, 78, 108, 28, 58, 88, 118)(19, 49, 79, 109, 29, 59, 89, 119)(21, 51, 81, 111, 30, 60, 90, 120) L = (1, 32)(2, 37)(3, 38)(4, 44)(5, 31)(6, 40)(7, 43)(8, 49)(9, 34)(10, 46)(11, 51)(12, 55)(13, 33)(14, 56)(15, 57)(16, 35)(17, 36)(18, 41)(19, 48)(20, 39)(21, 47)(22, 42)(23, 45)(24, 58)(25, 50)(26, 53)(27, 60)(28, 59)(29, 52)(30, 54)(61, 93)(62, 98)(63, 101)(64, 105)(65, 103)(66, 91)(67, 109)(68, 111)(69, 113)(70, 92)(71, 100)(72, 94)(73, 108)(74, 117)(75, 118)(76, 97)(77, 95)(78, 96)(79, 107)(80, 116)(81, 106)(82, 99)(83, 114)(84, 102)(85, 104)(86, 120)(87, 119)(88, 115)(89, 110)(90, 112) local type(s) :: { ( 4, 15, 4, 15, 4, 15, 4, 15 ) } Outer automorphisms :: reflexible Dual of E14.199 Transitivity :: VT+ Graph:: v = 15 e = 60 f = 19 degree seq :: [ 8^15 ] E14.205 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 15, 15}) Quotient :: loop^2 Aut^+ = C5 x S3 (small group id <30, 1>) Aut = C10 x S3 (small group id <60, 11>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^-1 * Y2^-2 * Y1 * Y2 * Y1^-1, Y1 * Y3 * Y1 * Y3 * Y2^-3, Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-2, Y1 * Y3 * Y1^2 * Y2^-2 * Y3, Y2^4 * Y3 * Y1^-1 * Y3, Y3 * Y1^2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y1^-2, Y1^15 ] Map:: non-degenerate R = (1, 31, 61, 91, 4, 34, 64, 94)(2, 32, 62, 92, 6, 36, 66, 96)(3, 33, 63, 93, 8, 38, 68, 98)(5, 35, 65, 95, 12, 42, 72, 102)(7, 37, 67, 97, 16, 46, 76, 106)(9, 39, 69, 99, 20, 50, 80, 110)(10, 40, 70, 100, 22, 52, 82, 112)(11, 41, 71, 101, 18, 48, 78, 108)(13, 43, 73, 103, 15, 45, 75, 105)(14, 44, 74, 104, 25, 55, 85, 115)(17, 47, 77, 107, 26, 56, 86, 116)(19, 49, 79, 109, 27, 57, 87, 117)(21, 51, 81, 111, 28, 58, 88, 118)(23, 53, 83, 113, 29, 59, 89, 119)(24, 54, 84, 114, 30, 60, 90, 120) L = (1, 32)(2, 35)(3, 31)(4, 39)(5, 41)(6, 43)(7, 33)(8, 47)(9, 49)(10, 34)(11, 52)(12, 46)(13, 51)(14, 36)(15, 37)(16, 54)(17, 53)(18, 38)(19, 48)(20, 45)(21, 40)(22, 55)(23, 42)(24, 44)(25, 59)(26, 50)(27, 58)(28, 60)(29, 57)(30, 56)(61, 93)(62, 91)(63, 97)(64, 100)(65, 92)(66, 104)(67, 105)(68, 108)(69, 94)(70, 111)(71, 95)(72, 113)(73, 96)(74, 114)(75, 110)(76, 102)(77, 98)(78, 109)(79, 99)(80, 116)(81, 103)(82, 101)(83, 107)(84, 106)(85, 112)(86, 120)(87, 119)(88, 117)(89, 115)(90, 118) local type(s) :: { ( 4, 15, 4, 15, 4, 15, 4, 15 ) } Outer automorphisms :: reflexible Dual of E14.200 Transitivity :: VT+ Graph:: v = 15 e = 60 f = 19 degree seq :: [ 8^15 ] E14.206 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 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 :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2 * Y1 * Y2^2, Y2 * Y1 * Y2^-2 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^15 ] Map:: R = (1, 31, 2, 32)(3, 33, 7, 37)(4, 34, 9, 39)(5, 35, 11, 41)(6, 36, 13, 43)(8, 38, 17, 47)(10, 40, 21, 51)(12, 42, 24, 54)(14, 44, 26, 56)(15, 45, 22, 52)(16, 46, 25, 55)(18, 48, 20, 50)(19, 49, 23, 53)(27, 57, 29, 59)(28, 58, 30, 60)(61, 91, 63, 93, 68, 98, 78, 108, 73, 103, 85, 115, 90, 120, 84, 114, 86, 116, 89, 119, 83, 113, 71, 101, 82, 112, 70, 100, 64, 94)(62, 92, 65, 95, 72, 102, 80, 110, 69, 99, 79, 109, 88, 118, 77, 107, 81, 111, 87, 117, 76, 106, 67, 97, 75, 105, 74, 104, 66, 96) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.207 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) 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, Y1^2, R^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^-1 * Y1 * Y2^2, (Y3 * Y2^-1)^15 ] Map:: R = (1, 31, 2, 32)(3, 33, 7, 37)(4, 34, 9, 39)(5, 35, 11, 41)(6, 36, 13, 43)(8, 38, 17, 47)(10, 40, 21, 51)(12, 42, 24, 54)(14, 44, 26, 56)(15, 45, 23, 53)(16, 46, 22, 52)(18, 48, 19, 49)(20, 50, 25, 55)(27, 57, 30, 60)(28, 58, 29, 59)(61, 91, 63, 93, 68, 98, 78, 108, 71, 101, 83, 113, 89, 119, 86, 116, 84, 114, 90, 120, 85, 115, 73, 103, 82, 112, 70, 100, 64, 94)(62, 92, 65, 95, 72, 102, 76, 106, 67, 97, 75, 105, 87, 117, 81, 111, 77, 107, 88, 118, 80, 110, 69, 99, 79, 109, 74, 104, 66, 96) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.208 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 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 :: [ Y1^2, R^2, Y3^3, (R * Y3)^2, (Y3^-1, Y2^-1), (Y1 * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y3^-1 * Y1 * Y2^-1 * Y1, Y3 * Y2^-5, Y2 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^2 * Y3 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 11, 41)(4, 34, 10, 40)(5, 35, 16, 46)(6, 36, 8, 38)(7, 37, 14, 44)(9, 39, 15, 45)(12, 42, 24, 54)(13, 43, 20, 50)(17, 47, 29, 59)(18, 48, 22, 52)(19, 49, 26, 56)(21, 51, 30, 60)(23, 53, 27, 57)(25, 55, 28, 58)(61, 91, 63, 93, 72, 102, 85, 115, 75, 105, 64, 94, 73, 103, 86, 116, 90, 120, 78, 108, 66, 96, 74, 104, 87, 117, 77, 107, 65, 95)(62, 92, 67, 97, 79, 109, 88, 118, 76, 106, 68, 98, 80, 110, 84, 114, 89, 119, 82, 112, 70, 100, 71, 101, 83, 113, 81, 111, 69, 99) L = (1, 64)(2, 68)(3, 73)(4, 66)(5, 75)(6, 61)(7, 80)(8, 70)(9, 76)(10, 62)(11, 67)(12, 86)(13, 74)(14, 63)(15, 78)(16, 82)(17, 85)(18, 65)(19, 84)(20, 71)(21, 88)(22, 69)(23, 79)(24, 83)(25, 90)(26, 87)(27, 72)(28, 89)(29, 81)(30, 77)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.209 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) Quotient :: dipole Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, Y2^3 * Y3^-2, Y3^5, Y2 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1, Y2 * Y1 * Y3 * Y2^2 * Y1 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 11, 41)(4, 34, 10, 40)(5, 35, 17, 47)(6, 36, 8, 38)(7, 37, 21, 51)(9, 39, 27, 57)(12, 42, 26, 56)(13, 43, 23, 53)(14, 44, 28, 58)(15, 45, 30, 60)(16, 46, 22, 52)(18, 48, 24, 54)(19, 49, 29, 59)(20, 50, 25, 55)(61, 91, 63, 93, 72, 102, 75, 105, 81, 111, 79, 109, 66, 96, 74, 104, 76, 106, 64, 94, 73, 103, 87, 117, 80, 110, 78, 108, 65, 95)(62, 92, 67, 97, 82, 112, 85, 115, 71, 101, 89, 119, 70, 100, 84, 114, 86, 116, 68, 98, 83, 113, 77, 107, 90, 120, 88, 118, 69, 99) L = (1, 64)(2, 68)(3, 73)(4, 75)(5, 76)(6, 61)(7, 83)(8, 85)(9, 86)(10, 62)(11, 88)(12, 87)(13, 81)(14, 63)(15, 80)(16, 72)(17, 89)(18, 74)(19, 65)(20, 66)(21, 78)(22, 77)(23, 71)(24, 67)(25, 90)(26, 82)(27, 79)(28, 84)(29, 69)(30, 70)(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 ) } Outer automorphisms :: reflexible Dual of E14.211 Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.210 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) Quotient :: dipole Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-3 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y1 * Y2 * Y3^-1 * Y1 * 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 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 11, 41)(4, 34, 10, 40)(5, 35, 17, 47)(6, 36, 8, 38)(7, 37, 14, 44)(9, 39, 16, 46)(12, 42, 25, 55)(13, 43, 24, 54)(15, 45, 22, 52)(18, 48, 21, 51)(19, 49, 29, 59)(20, 50, 28, 58)(23, 53, 26, 56)(27, 57, 30, 60)(61, 91, 63, 93, 72, 102, 66, 96, 74, 104, 86, 116, 78, 108, 88, 118, 89, 119, 75, 105, 87, 117, 76, 106, 64, 94, 73, 103, 65, 95)(62, 92, 67, 97, 79, 109, 70, 100, 71, 101, 83, 113, 82, 112, 84, 114, 85, 115, 81, 111, 90, 120, 77, 107, 68, 98, 80, 110, 69, 99) L = (1, 64)(2, 68)(3, 73)(4, 75)(5, 76)(6, 61)(7, 80)(8, 81)(9, 77)(10, 62)(11, 67)(12, 65)(13, 87)(14, 63)(15, 78)(16, 89)(17, 85)(18, 66)(19, 69)(20, 90)(21, 82)(22, 70)(23, 79)(24, 71)(25, 83)(26, 72)(27, 88)(28, 74)(29, 86)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.211 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) Quotient :: dipole Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2^-1, Y3^-1), Y2^-3 * Y3, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, Y1 * Y2^-1 * Y3^-1 * Y1 * Y2, Y3^5 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 11, 41)(4, 34, 10, 40)(5, 35, 16, 46)(6, 36, 8, 38)(7, 37, 13, 43)(9, 39, 17, 47)(12, 42, 25, 55)(14, 44, 24, 54)(15, 45, 22, 52)(18, 48, 21, 51)(19, 49, 30, 60)(20, 50, 27, 57)(23, 53, 26, 56)(28, 58, 29, 59)(61, 91, 63, 93, 72, 102, 64, 94, 73, 103, 86, 116, 75, 105, 87, 117, 90, 120, 78, 108, 88, 118, 77, 107, 66, 96, 74, 104, 65, 95)(62, 92, 67, 97, 79, 109, 68, 98, 71, 101, 83, 113, 81, 111, 84, 114, 85, 115, 82, 112, 89, 119, 76, 106, 70, 100, 80, 110, 69, 99) L = (1, 64)(2, 68)(3, 73)(4, 75)(5, 72)(6, 61)(7, 71)(8, 81)(9, 79)(10, 62)(11, 84)(12, 86)(13, 87)(14, 63)(15, 78)(16, 69)(17, 65)(18, 66)(19, 83)(20, 67)(21, 82)(22, 70)(23, 85)(24, 89)(25, 76)(26, 90)(27, 88)(28, 74)(29, 80)(30, 77)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 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 E14.209 Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.212 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 15, 15}) 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, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^2 * Y3 * Y2 * Y3 * Y2^-2, Y1 * Y3 * Y2^2 * Y1^-2 * Y3, Y1^3 * Y2^-1 * Y3 * Y1^-1 * Y3, Y1^3 * Y3 * Y1^-1 * Y3 * Y2^-1, Y1^15 ] Map:: non-degenerate R = (1, 31, 4, 34)(2, 32, 6, 36)(3, 33, 8, 38)(5, 35, 12, 42)(7, 37, 16, 46)(9, 39, 20, 50)(10, 40, 22, 52)(11, 41, 17, 47)(13, 43, 25, 55)(14, 44, 15, 45)(18, 48, 26, 56)(19, 49, 27, 57)(21, 51, 28, 58)(23, 53, 29, 59)(24, 54, 30, 60)(61, 62, 65, 71, 80, 85, 89, 88, 87, 90, 86, 82, 75, 67, 63)(64, 69, 79, 74, 66, 73, 84, 76, 72, 83, 78, 68, 77, 81, 70)(91, 93, 97, 105, 112, 116, 120, 117, 118, 119, 115, 110, 101, 95, 92)(94, 100, 111, 107, 98, 108, 113, 102, 106, 114, 103, 96, 104, 109, 99) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 8^4 ), ( 8^15 ) } Outer automorphisms :: reflexible Dual of E14.213 Graph:: simple bipartite v = 19 e = 60 f = 15 degree seq :: [ 4^15, 15^4 ] E14.213 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 15, 15}) 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, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^2 * Y3 * Y2 * Y3 * Y2^-2, Y1 * Y3 * Y2^2 * Y1^-2 * Y3, Y1^3 * Y2^-1 * Y3 * Y1^-1 * Y3, Y1^3 * Y3 * Y1^-1 * Y3 * Y2^-1, Y1^15 ] Map:: non-degenerate R = (1, 31, 61, 91, 4, 34, 64, 94)(2, 32, 62, 92, 6, 36, 66, 96)(3, 33, 63, 93, 8, 38, 68, 98)(5, 35, 65, 95, 12, 42, 72, 102)(7, 37, 67, 97, 16, 46, 76, 106)(9, 39, 69, 99, 20, 50, 80, 110)(10, 40, 70, 100, 22, 52, 82, 112)(11, 41, 71, 101, 17, 47, 77, 107)(13, 43, 73, 103, 25, 55, 85, 115)(14, 44, 74, 104, 15, 45, 75, 105)(18, 48, 78, 108, 26, 56, 86, 116)(19, 49, 79, 109, 27, 57, 87, 117)(21, 51, 81, 111, 28, 58, 88, 118)(23, 53, 83, 113, 29, 59, 89, 119)(24, 54, 84, 114, 30, 60, 90, 120) L = (1, 32)(2, 35)(3, 31)(4, 39)(5, 41)(6, 43)(7, 33)(8, 47)(9, 49)(10, 34)(11, 50)(12, 53)(13, 54)(14, 36)(15, 37)(16, 42)(17, 51)(18, 38)(19, 44)(20, 55)(21, 40)(22, 45)(23, 48)(24, 46)(25, 59)(26, 52)(27, 60)(28, 57)(29, 58)(30, 56)(61, 93)(62, 91)(63, 97)(64, 100)(65, 92)(66, 104)(67, 105)(68, 108)(69, 94)(70, 111)(71, 95)(72, 106)(73, 96)(74, 109)(75, 112)(76, 114)(77, 98)(78, 113)(79, 99)(80, 101)(81, 107)(82, 116)(83, 102)(84, 103)(85, 110)(86, 120)(87, 118)(88, 119)(89, 115)(90, 117) local type(s) :: { ( 4, 15, 4, 15, 4, 15, 4, 15 ) } Outer automorphisms :: reflexible Dual of E14.212 Transitivity :: VT+ Graph:: v = 15 e = 60 f = 19 degree seq :: [ 8^15 ] E14.214 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 15, 15}) Quotient :: halfedge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3, (R * Y1)^2, Y1^-1 * Y3 * Y1^-1 * Y2, R * Y2 * R * Y3, Y1^15 ] Map:: R = (1, 32, 2, 35, 5, 39, 9, 43, 13, 47, 17, 51, 21, 55, 25, 58, 28, 54, 24, 50, 20, 46, 16, 42, 12, 38, 8, 34, 4, 31)(3, 37, 7, 41, 11, 45, 15, 49, 19, 53, 23, 57, 27, 60, 30, 59, 29, 56, 26, 52, 22, 48, 18, 44, 14, 40, 10, 36, 6, 33) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 29)(28, 30)(31, 33)(32, 36)(34, 37)(35, 40)(38, 41)(39, 44)(42, 45)(43, 48)(46, 49)(47, 52)(50, 53)(51, 56)(54, 57)(55, 59)(58, 60) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.215 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 15, 15}) Quotient :: halfedge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y1 * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3 * Y2)^3, Y1^2 * Y3 * Y1^-3 * Y2, Y1^2 * Y2 * Y3 * Y2 * Y1^-3 * Y3, Y2 * Y1^-1 * Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y1 * Y2 * Y1^-3 * Y3 * Y1 ] Map:: non-degenerate R = (1, 32, 2, 36, 6, 44, 14, 50, 20, 40, 10, 47, 17, 56, 26, 60, 30, 53, 23, 42, 12, 48, 18, 54, 24, 43, 13, 35, 5, 31)(3, 39, 9, 49, 19, 46, 16, 38, 8, 34, 4, 41, 11, 52, 22, 59, 29, 57, 27, 51, 21, 58, 28, 55, 25, 45, 15, 37, 7, 33) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 25)(16, 24)(17, 27)(20, 28)(22, 30)(26, 29)(31, 34)(32, 38)(33, 40)(35, 41)(36, 46)(37, 47)(39, 50)(42, 51)(43, 52)(44, 49)(45, 56)(48, 57)(53, 58)(54, 59)(55, 60) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.216 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 15, 15}) Quotient :: halfedge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, (Y2 * Y1)^2, Y1 * Y3 * Y1^-2 * Y2 * Y3 * Y2, Y1^-5 * Y3 * Y1 * Y2 ] Map:: non-degenerate R = (1, 32, 2, 36, 6, 44, 14, 56, 26, 53, 23, 42, 12, 48, 18, 50, 20, 40, 10, 47, 17, 58, 28, 55, 25, 43, 13, 35, 5, 31)(3, 39, 9, 49, 19, 54, 24, 60, 30, 59, 29, 51, 21, 46, 16, 38, 8, 34, 4, 41, 11, 52, 22, 57, 27, 45, 15, 37, 7, 33) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 20)(17, 29)(22, 26)(24, 25)(28, 30)(31, 34)(32, 38)(33, 40)(35, 41)(36, 46)(37, 47)(39, 50)(42, 54)(43, 52)(44, 51)(45, 58)(48, 49)(53, 60)(55, 57)(56, 59) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible Dual of E14.217 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.217 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 15, 15}) Quotient :: halfedge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1 * Y2 * Y3, Y2 * Y1^-1 * Y3, R * Y3 * R * Y2, (R * Y1)^2, Y1^15 ] Map:: non-degenerate R = (1, 32, 2, 36, 6, 40, 10, 44, 14, 48, 18, 52, 22, 56, 26, 59, 29, 55, 25, 51, 21, 47, 17, 43, 13, 39, 9, 35, 5, 31)(3, 38, 8, 42, 12, 46, 16, 50, 20, 54, 24, 58, 28, 60, 30, 57, 27, 53, 23, 49, 19, 45, 15, 41, 11, 37, 7, 34, 4, 33) L = (1, 3)(2, 4)(5, 8)(6, 7)(9, 12)(10, 11)(13, 16)(14, 15)(17, 20)(18, 19)(21, 24)(22, 23)(25, 28)(26, 27)(29, 30)(31, 34)(32, 37)(33, 35)(36, 41)(38, 39)(40, 45)(42, 43)(44, 49)(46, 47)(48, 53)(50, 51)(52, 57)(54, 55)(56, 60)(58, 59) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible Dual of E14.216 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.218 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 15, 15}) Quotient :: edge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y3^15 ] Map:: R = (1, 31, 3, 33, 7, 37, 11, 41, 15, 45, 19, 49, 23, 53, 27, 57, 28, 58, 24, 54, 20, 50, 16, 46, 12, 42, 8, 38, 4, 34)(2, 32, 5, 35, 9, 39, 13, 43, 17, 47, 21, 51, 25, 55, 29, 59, 30, 60, 26, 56, 22, 52, 18, 48, 14, 44, 10, 40, 6, 36)(61, 62)(63, 66)(64, 65)(67, 70)(68, 69)(71, 74)(72, 73)(75, 78)(76, 77)(79, 82)(80, 81)(83, 86)(84, 85)(87, 90)(88, 89)(91, 92)(93, 96)(94, 95)(97, 100)(98, 99)(101, 104)(102, 103)(105, 108)(106, 107)(109, 112)(110, 111)(113, 116)(114, 115)(117, 120)(118, 119) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 60, 60 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E14.223 Graph:: simple bipartite v = 32 e = 60 f = 2 degree seq :: [ 2^30, 30^2 ] E14.219 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 15, 15}) Quotient :: edge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y3)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3 * Y1 * Y3^-2 * Y2 * Y1 * Y2, Y3^-3 * Y1 * Y3 * Y2 * Y3^-2 ] Map:: R = (1, 31, 4, 34, 12, 42, 24, 54, 27, 57, 16, 46, 6, 36, 15, 45, 21, 51, 9, 39, 20, 50, 30, 60, 25, 55, 13, 43, 5, 35)(2, 32, 7, 37, 17, 47, 28, 58, 23, 53, 11, 41, 3, 33, 10, 40, 22, 52, 14, 44, 26, 56, 29, 59, 19, 49, 18, 48, 8, 38)(61, 62)(63, 69)(64, 68)(65, 67)(66, 74)(70, 81)(71, 80)(72, 78)(73, 77)(75, 82)(76, 86)(79, 84)(83, 90)(85, 88)(87, 89)(91, 93)(92, 96)(94, 101)(95, 100)(97, 106)(98, 105)(99, 109)(102, 113)(103, 112)(104, 115)(107, 117)(108, 111)(110, 119)(114, 118)(116, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 60, 60 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E14.226 Graph:: simple bipartite v = 32 e = 60 f = 2 degree seq :: [ 2^30, 30^2 ] E14.220 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 15, 15}) Quotient :: edge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^3, Y3^-2 * Y2 * Y1 * Y3^-3, Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y3^3 * Y2 ] Map:: R = (1, 31, 4, 34, 12, 42, 23, 53, 20, 50, 9, 39, 19, 49, 29, 59, 27, 57, 16, 46, 6, 36, 15, 45, 24, 54, 13, 43, 5, 35)(2, 32, 7, 37, 17, 47, 28, 58, 26, 56, 14, 44, 25, 55, 30, 60, 22, 52, 11, 41, 3, 33, 10, 40, 21, 51, 18, 48, 8, 38)(61, 62)(63, 69)(64, 68)(65, 67)(66, 74)(70, 80)(71, 79)(72, 78)(73, 77)(75, 86)(76, 85)(81, 83)(82, 89)(84, 88)(87, 90)(91, 93)(92, 96)(94, 101)(95, 100)(97, 106)(98, 105)(99, 104)(102, 112)(103, 111)(107, 117)(108, 114)(109, 116)(110, 115)(113, 120)(118, 119) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 60, 60 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E14.225 Graph:: simple bipartite v = 32 e = 60 f = 2 degree seq :: [ 2^30, 30^2 ] E14.221 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 15, 15}) Quotient :: edge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3^3 * Y1, (Y1 * Y2)^5 ] Map:: R = (1, 31, 4, 34, 12, 42, 9, 39, 18, 48, 25, 55, 23, 53, 29, 59, 27, 57, 20, 50, 22, 52, 15, 45, 6, 36, 13, 43, 5, 35)(2, 32, 7, 37, 16, 46, 14, 44, 21, 51, 28, 58, 26, 56, 30, 60, 24, 54, 17, 47, 19, 49, 11, 41, 3, 33, 10, 40, 8, 38)(61, 62)(63, 69)(64, 68)(65, 67)(66, 74)(70, 72)(71, 78)(73, 76)(75, 81)(77, 83)(79, 85)(80, 86)(82, 88)(84, 89)(87, 90)(91, 93)(92, 96)(94, 101)(95, 100)(97, 105)(98, 103)(99, 107)(102, 109)(104, 110)(106, 112)(108, 114)(111, 117)(113, 116)(115, 120)(118, 119) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 60, 60 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E14.224 Graph:: simple bipartite v = 32 e = 60 f = 2 degree seq :: [ 2^30, 30^2 ] E14.222 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 15, 15}) Quotient :: edge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y3 * Y2^-1, Y2^15, Y1^15 ] Map:: non-degenerate R = (1, 31, 4, 34)(2, 32, 6, 36)(3, 33, 8, 38)(5, 35, 10, 40)(7, 37, 12, 42)(9, 39, 14, 44)(11, 41, 16, 46)(13, 43, 18, 48)(15, 45, 20, 50)(17, 47, 22, 52)(19, 49, 24, 54)(21, 51, 26, 56)(23, 53, 28, 58)(25, 55, 29, 59)(27, 57, 30, 60)(61, 62, 65, 69, 73, 77, 81, 85, 87, 83, 79, 75, 71, 67, 63)(64, 68, 72, 76, 80, 84, 88, 90, 89, 86, 82, 78, 74, 70, 66)(91, 93, 97, 101, 105, 109, 113, 117, 115, 111, 107, 103, 99, 95, 92)(94, 96, 100, 104, 108, 112, 116, 119, 120, 118, 114, 110, 106, 102, 98) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 8^4 ), ( 8^15 ) } Outer automorphisms :: reflexible Dual of E14.227 Graph:: simple bipartite v = 19 e = 60 f = 15 degree seq :: [ 4^15, 15^4 ] E14.223 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 15, 15}) Quotient :: loop^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y3^15 ] Map:: R = (1, 31, 61, 91, 3, 33, 63, 93, 7, 37, 67, 97, 11, 41, 71, 101, 15, 45, 75, 105, 19, 49, 79, 109, 23, 53, 83, 113, 27, 57, 87, 117, 28, 58, 88, 118, 24, 54, 84, 114, 20, 50, 80, 110, 16, 46, 76, 106, 12, 42, 72, 102, 8, 38, 68, 98, 4, 34, 64, 94)(2, 32, 62, 92, 5, 35, 65, 95, 9, 39, 69, 99, 13, 43, 73, 103, 17, 47, 77, 107, 21, 51, 81, 111, 25, 55, 85, 115, 29, 59, 89, 119, 30, 60, 90, 120, 26, 56, 86, 116, 22, 52, 82, 112, 18, 48, 78, 108, 14, 44, 74, 104, 10, 40, 70, 100, 6, 36, 66, 96) L = (1, 32)(2, 31)(3, 36)(4, 35)(5, 34)(6, 33)(7, 40)(8, 39)(9, 38)(10, 37)(11, 44)(12, 43)(13, 42)(14, 41)(15, 48)(16, 47)(17, 46)(18, 45)(19, 52)(20, 51)(21, 50)(22, 49)(23, 56)(24, 55)(25, 54)(26, 53)(27, 60)(28, 59)(29, 58)(30, 57)(61, 92)(62, 91)(63, 96)(64, 95)(65, 94)(66, 93)(67, 100)(68, 99)(69, 98)(70, 97)(71, 104)(72, 103)(73, 102)(74, 101)(75, 108)(76, 107)(77, 106)(78, 105)(79, 112)(80, 111)(81, 110)(82, 109)(83, 116)(84, 115)(85, 114)(86, 113)(87, 120)(88, 119)(89, 118)(90, 117) local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 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 E14.218 Transitivity :: VT+ Graph:: bipartite v = 2 e = 60 f = 32 degree seq :: [ 60^2 ] E14.224 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 15, 15}) Quotient :: loop^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y3)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3 * Y1 * Y3^-2 * Y2 * Y1 * Y2, Y3^-3 * Y1 * Y3 * Y2 * Y3^-2 ] Map:: R = (1, 31, 61, 91, 4, 34, 64, 94, 12, 42, 72, 102, 24, 54, 84, 114, 27, 57, 87, 117, 16, 46, 76, 106, 6, 36, 66, 96, 15, 45, 75, 105, 21, 51, 81, 111, 9, 39, 69, 99, 20, 50, 80, 110, 30, 60, 90, 120, 25, 55, 85, 115, 13, 43, 73, 103, 5, 35, 65, 95)(2, 32, 62, 92, 7, 37, 67, 97, 17, 47, 77, 107, 28, 58, 88, 118, 23, 53, 83, 113, 11, 41, 71, 101, 3, 33, 63, 93, 10, 40, 70, 100, 22, 52, 82, 112, 14, 44, 74, 104, 26, 56, 86, 116, 29, 59, 89, 119, 19, 49, 79, 109, 18, 48, 78, 108, 8, 38, 68, 98) L = (1, 32)(2, 31)(3, 39)(4, 38)(5, 37)(6, 44)(7, 35)(8, 34)(9, 33)(10, 51)(11, 50)(12, 48)(13, 47)(14, 36)(15, 52)(16, 56)(17, 43)(18, 42)(19, 54)(20, 41)(21, 40)(22, 45)(23, 60)(24, 49)(25, 58)(26, 46)(27, 59)(28, 55)(29, 57)(30, 53)(61, 93)(62, 96)(63, 91)(64, 101)(65, 100)(66, 92)(67, 106)(68, 105)(69, 109)(70, 95)(71, 94)(72, 113)(73, 112)(74, 115)(75, 98)(76, 97)(77, 117)(78, 111)(79, 99)(80, 119)(81, 108)(82, 103)(83, 102)(84, 118)(85, 104)(86, 120)(87, 107)(88, 114)(89, 110)(90, 116) local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) } Outer automorphisms :: reflexible Dual of E14.221 Transitivity :: VT+ Graph:: bipartite v = 2 e = 60 f = 32 degree seq :: [ 60^2 ] E14.225 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 15, 15}) Quotient :: loop^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^3, Y3^-2 * Y2 * Y1 * Y3^-3, Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y3^3 * Y2 ] Map:: R = (1, 31, 61, 91, 4, 34, 64, 94, 12, 42, 72, 102, 23, 53, 83, 113, 20, 50, 80, 110, 9, 39, 69, 99, 19, 49, 79, 109, 29, 59, 89, 119, 27, 57, 87, 117, 16, 46, 76, 106, 6, 36, 66, 96, 15, 45, 75, 105, 24, 54, 84, 114, 13, 43, 73, 103, 5, 35, 65, 95)(2, 32, 62, 92, 7, 37, 67, 97, 17, 47, 77, 107, 28, 58, 88, 118, 26, 56, 86, 116, 14, 44, 74, 104, 25, 55, 85, 115, 30, 60, 90, 120, 22, 52, 82, 112, 11, 41, 71, 101, 3, 33, 63, 93, 10, 40, 70, 100, 21, 51, 81, 111, 18, 48, 78, 108, 8, 38, 68, 98) L = (1, 32)(2, 31)(3, 39)(4, 38)(5, 37)(6, 44)(7, 35)(8, 34)(9, 33)(10, 50)(11, 49)(12, 48)(13, 47)(14, 36)(15, 56)(16, 55)(17, 43)(18, 42)(19, 41)(20, 40)(21, 53)(22, 59)(23, 51)(24, 58)(25, 46)(26, 45)(27, 60)(28, 54)(29, 52)(30, 57)(61, 93)(62, 96)(63, 91)(64, 101)(65, 100)(66, 92)(67, 106)(68, 105)(69, 104)(70, 95)(71, 94)(72, 112)(73, 111)(74, 99)(75, 98)(76, 97)(77, 117)(78, 114)(79, 116)(80, 115)(81, 103)(82, 102)(83, 120)(84, 108)(85, 110)(86, 109)(87, 107)(88, 119)(89, 118)(90, 113) local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) } Outer automorphisms :: reflexible Dual of E14.220 Transitivity :: VT+ Graph:: bipartite v = 2 e = 60 f = 32 degree seq :: [ 60^2 ] E14.226 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 15, 15}) Quotient :: loop^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3^3 * Y1, (Y1 * Y2)^5 ] Map:: R = (1, 31, 61, 91, 4, 34, 64, 94, 12, 42, 72, 102, 9, 39, 69, 99, 18, 48, 78, 108, 25, 55, 85, 115, 23, 53, 83, 113, 29, 59, 89, 119, 27, 57, 87, 117, 20, 50, 80, 110, 22, 52, 82, 112, 15, 45, 75, 105, 6, 36, 66, 96, 13, 43, 73, 103, 5, 35, 65, 95)(2, 32, 62, 92, 7, 37, 67, 97, 16, 46, 76, 106, 14, 44, 74, 104, 21, 51, 81, 111, 28, 58, 88, 118, 26, 56, 86, 116, 30, 60, 90, 120, 24, 54, 84, 114, 17, 47, 77, 107, 19, 49, 79, 109, 11, 41, 71, 101, 3, 33, 63, 93, 10, 40, 70, 100, 8, 38, 68, 98) L = (1, 32)(2, 31)(3, 39)(4, 38)(5, 37)(6, 44)(7, 35)(8, 34)(9, 33)(10, 42)(11, 48)(12, 40)(13, 46)(14, 36)(15, 51)(16, 43)(17, 53)(18, 41)(19, 55)(20, 56)(21, 45)(22, 58)(23, 47)(24, 59)(25, 49)(26, 50)(27, 60)(28, 52)(29, 54)(30, 57)(61, 93)(62, 96)(63, 91)(64, 101)(65, 100)(66, 92)(67, 105)(68, 103)(69, 107)(70, 95)(71, 94)(72, 109)(73, 98)(74, 110)(75, 97)(76, 112)(77, 99)(78, 114)(79, 102)(80, 104)(81, 117)(82, 106)(83, 116)(84, 108)(85, 120)(86, 113)(87, 111)(88, 119)(89, 118)(90, 115) local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 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 E14.219 Transitivity :: VT+ Graph:: bipartite v = 2 e = 60 f = 32 degree seq :: [ 60^2 ] E14.227 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 15, 15}) Quotient :: loop^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y3 * Y2^-1, Y2^15, Y1^15 ] Map:: non-degenerate R = (1, 31, 61, 91, 4, 34, 64, 94)(2, 32, 62, 92, 6, 36, 66, 96)(3, 33, 63, 93, 8, 38, 68, 98)(5, 35, 65, 95, 10, 40, 70, 100)(7, 37, 67, 97, 12, 42, 72, 102)(9, 39, 69, 99, 14, 44, 74, 104)(11, 41, 71, 101, 16, 46, 76, 106)(13, 43, 73, 103, 18, 48, 78, 108)(15, 45, 75, 105, 20, 50, 80, 110)(17, 47, 77, 107, 22, 52, 82, 112)(19, 49, 79, 109, 24, 54, 84, 114)(21, 51, 81, 111, 26, 56, 86, 116)(23, 53, 83, 113, 28, 58, 88, 118)(25, 55, 85, 115, 29, 59, 89, 119)(27, 57, 87, 117, 30, 60, 90, 120) L = (1, 32)(2, 35)(3, 31)(4, 38)(5, 39)(6, 34)(7, 33)(8, 42)(9, 43)(10, 36)(11, 37)(12, 46)(13, 47)(14, 40)(15, 41)(16, 50)(17, 51)(18, 44)(19, 45)(20, 54)(21, 55)(22, 48)(23, 49)(24, 58)(25, 57)(26, 52)(27, 53)(28, 60)(29, 56)(30, 59)(61, 93)(62, 91)(63, 97)(64, 96)(65, 92)(66, 100)(67, 101)(68, 94)(69, 95)(70, 104)(71, 105)(72, 98)(73, 99)(74, 108)(75, 109)(76, 102)(77, 103)(78, 112)(79, 113)(80, 106)(81, 107)(82, 116)(83, 117)(84, 110)(85, 111)(86, 119)(87, 115)(88, 114)(89, 120)(90, 118) local type(s) :: { ( 4, 15, 4, 15, 4, 15, 4, 15 ) } Outer automorphisms :: reflexible Dual of E14.222 Transitivity :: VT+ Graph:: v = 15 e = 60 f = 19 degree seq :: [ 8^15 ] E14.228 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) 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, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^15, (Y3 * Y2^-1)^15 ] Map:: R = (1, 31, 2, 32)(3, 33, 5, 35)(4, 34, 6, 36)(7, 37, 9, 39)(8, 38, 10, 40)(11, 41, 13, 43)(12, 42, 14, 44)(15, 45, 17, 47)(16, 46, 18, 48)(19, 49, 21, 51)(20, 50, 22, 52)(23, 53, 25, 55)(24, 54, 26, 56)(27, 57, 29, 59)(28, 58, 30, 60)(61, 91, 63, 93, 67, 97, 71, 101, 75, 105, 79, 109, 83, 113, 87, 117, 88, 118, 84, 114, 80, 110, 76, 106, 72, 102, 68, 98, 64, 94)(62, 92, 65, 95, 69, 99, 73, 103, 77, 107, 81, 111, 85, 115, 89, 119, 90, 120, 86, 116, 82, 112, 78, 108, 74, 104, 70, 100, 66, 96) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.229 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ 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, Y2^15, (Y3 * Y2^-1)^15 ] Map:: R = (1, 31, 2, 32)(3, 33, 6, 36)(4, 34, 5, 35)(7, 37, 10, 40)(8, 38, 9, 39)(11, 41, 14, 44)(12, 42, 13, 43)(15, 45, 18, 48)(16, 46, 17, 47)(19, 49, 22, 52)(20, 50, 21, 51)(23, 53, 26, 56)(24, 54, 25, 55)(27, 57, 30, 60)(28, 58, 29, 59)(61, 91, 63, 93, 67, 97, 71, 101, 75, 105, 79, 109, 83, 113, 87, 117, 88, 118, 84, 114, 80, 110, 76, 106, 72, 102, 68, 98, 64, 94)(62, 92, 65, 95, 69, 99, 73, 103, 77, 107, 81, 111, 85, 115, 89, 119, 90, 120, 86, 116, 82, 112, 78, 108, 74, 104, 70, 100, 66, 96) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.230 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (Y3, Y2), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y3 * Y2^-5, Y2 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^2 * Y3 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 10, 40)(5, 35, 7, 37)(6, 36, 8, 38)(11, 41, 21, 51)(12, 42, 22, 52)(13, 43, 20, 50)(14, 44, 19, 49)(15, 45, 17, 47)(16, 46, 18, 48)(23, 53, 29, 59)(24, 54, 30, 60)(25, 55, 27, 57)(26, 56, 28, 58)(61, 91, 63, 93, 71, 101, 83, 113, 74, 104, 64, 94, 72, 102, 84, 114, 86, 116, 76, 106, 66, 96, 73, 103, 85, 115, 75, 105, 65, 95)(62, 92, 67, 97, 77, 107, 87, 117, 80, 110, 68, 98, 78, 108, 88, 118, 90, 120, 82, 112, 70, 100, 79, 109, 89, 119, 81, 111, 69, 99) L = (1, 64)(2, 68)(3, 72)(4, 66)(5, 74)(6, 61)(7, 78)(8, 70)(9, 80)(10, 62)(11, 84)(12, 73)(13, 63)(14, 76)(15, 83)(16, 65)(17, 88)(18, 79)(19, 67)(20, 82)(21, 87)(22, 69)(23, 86)(24, 85)(25, 71)(26, 75)(27, 90)(28, 89)(29, 77)(30, 81)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.231 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y3^-1 * Y1)^2, (Y2 * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^-2 * Y2^3, Y3^5, Y3^-1 * Y2^-2 * Y3^-2 * Y2^-1 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 10, 40)(5, 35, 7, 37)(6, 36, 8, 38)(11, 41, 24, 54)(12, 42, 25, 55)(13, 43, 23, 53)(14, 44, 26, 56)(15, 45, 21, 51)(16, 46, 19, 49)(17, 47, 20, 50)(18, 48, 22, 52)(27, 57, 30, 60)(28, 58, 29, 59)(61, 91, 63, 93, 71, 101, 74, 104, 88, 118, 77, 107, 66, 96, 73, 103, 75, 105, 64, 94, 72, 102, 87, 117, 78, 108, 76, 106, 65, 95)(62, 92, 67, 97, 79, 109, 82, 112, 90, 120, 85, 115, 70, 100, 81, 111, 83, 113, 68, 98, 80, 110, 89, 119, 86, 116, 84, 114, 69, 99) 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, 78)(15, 71)(16, 73)(17, 65)(18, 66)(19, 89)(20, 90)(21, 67)(22, 86)(23, 79)(24, 81)(25, 69)(26, 70)(27, 77)(28, 76)(29, 85)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 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 E14.233 Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.232 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-3 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2, Y3^-1), (R * Y2)^2, (Y2 * 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 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 10, 40)(5, 35, 7, 37)(6, 36, 8, 38)(11, 41, 18, 48)(12, 42, 17, 47)(13, 43, 21, 51)(14, 44, 22, 52)(15, 45, 19, 49)(16, 46, 20, 50)(23, 53, 28, 58)(24, 54, 27, 57)(25, 55, 30, 60)(26, 56, 29, 59)(61, 91, 63, 93, 71, 101, 66, 96, 73, 103, 83, 113, 76, 106, 85, 115, 86, 116, 74, 104, 84, 114, 75, 105, 64, 94, 72, 102, 65, 95)(62, 92, 67, 97, 77, 107, 70, 100, 79, 109, 87, 117, 82, 112, 89, 119, 90, 120, 80, 110, 88, 118, 81, 111, 68, 98, 78, 108, 69, 99) L = (1, 64)(2, 68)(3, 72)(4, 74)(5, 75)(6, 61)(7, 78)(8, 80)(9, 81)(10, 62)(11, 65)(12, 84)(13, 63)(14, 76)(15, 86)(16, 66)(17, 69)(18, 88)(19, 67)(20, 82)(21, 90)(22, 70)(23, 71)(24, 85)(25, 73)(26, 83)(27, 77)(28, 89)(29, 79)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.233 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^-3, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3, Y2), (Y2^-1 * Y1)^2, (R * Y2)^2, Y3^5 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 10, 40)(5, 35, 7, 37)(6, 36, 8, 38)(11, 41, 19, 49)(12, 42, 21, 51)(13, 43, 17, 47)(14, 44, 22, 52)(15, 45, 18, 48)(16, 46, 20, 50)(23, 53, 29, 59)(24, 54, 30, 60)(25, 55, 27, 57)(26, 56, 28, 58)(61, 91, 63, 93, 71, 101, 64, 94, 72, 102, 83, 113, 74, 104, 84, 114, 86, 116, 76, 106, 85, 115, 75, 105, 66, 96, 73, 103, 65, 95)(62, 92, 67, 97, 77, 107, 68, 98, 78, 108, 87, 117, 80, 110, 88, 118, 90, 120, 82, 112, 89, 119, 81, 111, 70, 100, 79, 109, 69, 99) L = (1, 64)(2, 68)(3, 72)(4, 74)(5, 71)(6, 61)(7, 78)(8, 80)(9, 77)(10, 62)(11, 83)(12, 84)(13, 63)(14, 76)(15, 65)(16, 66)(17, 87)(18, 88)(19, 67)(20, 82)(21, 69)(22, 70)(23, 86)(24, 85)(25, 73)(26, 75)(27, 90)(28, 89)(29, 79)(30, 81)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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 E14.231 Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.234 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2^15, (Y3 * Y2^-1)^15 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 6, 36)(4, 34, 5, 35)(7, 37, 10, 40)(8, 38, 9, 39)(11, 41, 14, 44)(12, 42, 13, 43)(15, 45, 18, 48)(16, 46, 17, 47)(19, 49, 22, 52)(20, 50, 21, 51)(23, 53, 26, 56)(24, 54, 25, 55)(27, 57, 30, 60)(28, 58, 29, 59)(61, 91, 63, 93, 67, 97, 71, 101, 75, 105, 79, 109, 83, 113, 87, 117, 88, 118, 84, 114, 80, 110, 76, 106, 72, 102, 68, 98, 64, 94)(62, 92, 65, 95, 69, 99, 73, 103, 77, 107, 81, 111, 85, 115, 89, 119, 90, 120, 86, 116, 82, 112, 78, 108, 74, 104, 70, 100, 66, 96) L = (1, 64)(2, 66)(3, 61)(4, 68)(5, 62)(6, 70)(7, 63)(8, 72)(9, 65)(10, 74)(11, 67)(12, 76)(13, 69)(14, 78)(15, 71)(16, 80)(17, 73)(18, 82)(19, 75)(20, 84)(21, 77)(22, 86)(23, 79)(24, 88)(25, 81)(26, 90)(27, 83)(28, 87)(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) :: { ( 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 E14.236 Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.235 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, Y2 * Y3^7 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 10, 40)(5, 35, 7, 37)(6, 36, 8, 38)(11, 41, 17, 47)(12, 42, 18, 48)(13, 43, 15, 45)(14, 44, 16, 46)(19, 49, 25, 55)(20, 50, 26, 56)(21, 51, 23, 53)(22, 52, 24, 54)(27, 57, 30, 60)(28, 58, 29, 59)(61, 91, 63, 93, 64, 94, 71, 101, 72, 102, 79, 109, 80, 110, 87, 117, 88, 118, 82, 112, 81, 111, 74, 104, 73, 103, 66, 96, 65, 95)(62, 92, 67, 97, 68, 98, 75, 105, 76, 106, 83, 113, 84, 114, 89, 119, 90, 120, 86, 116, 85, 115, 78, 108, 77, 107, 70, 100, 69, 99) L = (1, 64)(2, 68)(3, 71)(4, 72)(5, 63)(6, 61)(7, 75)(8, 76)(9, 67)(10, 62)(11, 79)(12, 80)(13, 65)(14, 66)(15, 83)(16, 84)(17, 69)(18, 70)(19, 87)(20, 88)(21, 73)(22, 74)(23, 89)(24, 90)(25, 77)(26, 78)(27, 82)(28, 81)(29, 86)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.236 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 15, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y2^-7 * Y3^-1 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 10, 40)(5, 35, 7, 37)(6, 36, 8, 38)(11, 41, 17, 47)(12, 42, 18, 48)(13, 43, 15, 45)(14, 44, 16, 46)(19, 49, 25, 55)(20, 50, 26, 56)(21, 51, 23, 53)(22, 52, 24, 54)(27, 57, 30, 60)(28, 58, 29, 59)(61, 91, 63, 93, 71, 101, 79, 109, 87, 117, 82, 112, 74, 104, 66, 96, 64, 94, 72, 102, 80, 110, 88, 118, 81, 111, 73, 103, 65, 95)(62, 92, 67, 97, 75, 105, 83, 113, 89, 119, 86, 116, 78, 108, 70, 100, 68, 98, 76, 106, 84, 114, 90, 120, 85, 115, 77, 107, 69, 99) L = (1, 64)(2, 68)(3, 72)(4, 63)(5, 66)(6, 61)(7, 76)(8, 67)(9, 70)(10, 62)(11, 80)(12, 71)(13, 74)(14, 65)(15, 84)(16, 75)(17, 78)(18, 69)(19, 88)(20, 79)(21, 82)(22, 73)(23, 90)(24, 83)(25, 86)(26, 77)(27, 81)(28, 87)(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) :: { ( 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 E14.234 Graph:: bipartite v = 17 e = 60 f = 17 degree seq :: [ 4^15, 30^2 ] E14.237 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {15, 30, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T1^2 * T2^-2, T2^6 * T1 * T2^8, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 6, 12, 15, 20, 23, 28, 29, 26, 21, 18, 13, 10, 4, 8, 2, 7, 11, 16, 19, 24, 27, 30, 25, 22, 17, 14, 9, 5)(31, 32, 36, 41, 45, 49, 53, 57, 59, 55, 51, 47, 43, 39, 34)(33, 37, 42, 46, 50, 54, 58, 60, 56, 52, 48, 44, 40, 35, 38) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 60^15 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E14.243 Transitivity :: ET+ Graph:: bipartite v = 3 e = 30 f = 1 degree seq :: [ 15^2, 30 ] E14.238 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {15, 30, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1, (F * T2)^2, (F * T1)^2, T1^15 ] Map:: non-degenerate R = (1, 3, 4, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29, 30, 26, 27, 22, 23, 18, 19, 14, 15, 10, 11, 6, 7, 2, 5)(31, 32, 36, 40, 44, 48, 52, 56, 59, 55, 51, 47, 43, 39, 34)(33, 35, 37, 41, 45, 49, 53, 57, 60, 58, 54, 50, 46, 42, 38) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 60^15 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E14.242 Transitivity :: ET+ Graph:: bipartite v = 3 e = 30 f = 1 degree seq :: [ 15^2, 30 ] E14.239 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {15, 30, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-2 * T1^-4, T2^-6 * T1^3 ] Map:: non-degenerate R = (1, 3, 9, 19, 27, 23, 14, 12, 4, 10, 20, 28, 24, 16, 6, 15, 11, 21, 29, 26, 18, 8, 2, 7, 17, 25, 30, 22, 13, 5)(31, 32, 36, 44, 43, 48, 54, 57, 60, 59, 50, 39, 47, 41, 34)(33, 37, 45, 42, 35, 38, 46, 53, 52, 56, 58, 49, 55, 51, 40) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 60^15 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E14.241 Transitivity :: ET+ Graph:: bipartite v = 3 e = 30 f = 1 degree seq :: [ 15^2, 30 ] E14.240 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {15, 30, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T2 * T1 * T2^3 * T1, T2 * T1^-1 * T2^2 * T1^3 * T2, T1^-6 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 11, 21, 28, 30, 25, 14, 24, 18, 8, 2, 7, 17, 12, 4, 10, 20, 27, 22, 23, 29, 26, 16, 6, 15, 13, 5)(31, 32, 36, 44, 53, 51, 40, 33, 37, 45, 54, 59, 58, 50, 39, 47, 43, 48, 56, 60, 57, 49, 42, 35, 38, 46, 55, 52, 41, 34) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible Dual of E14.244 Transitivity :: ET+ Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.241 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {15, 30, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T1^2 * T2^-2, T2^6 * T1 * T2^8, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 31, 3, 33, 6, 36, 12, 42, 15, 45, 20, 50, 23, 53, 28, 58, 29, 59, 26, 56, 21, 51, 18, 48, 13, 43, 10, 40, 4, 34, 8, 38, 2, 32, 7, 37, 11, 41, 16, 46, 19, 49, 24, 54, 27, 57, 30, 60, 25, 55, 22, 52, 17, 47, 14, 44, 9, 39, 5, 35) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 41)(7, 42)(8, 33)(9, 34)(10, 35)(11, 45)(12, 46)(13, 39)(14, 40)(15, 49)(16, 50)(17, 43)(18, 44)(19, 53)(20, 54)(21, 47)(22, 48)(23, 57)(24, 58)(25, 51)(26, 52)(27, 59)(28, 60)(29, 55)(30, 56) local type(s) :: { ( 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30 ) } Outer automorphisms :: reflexible Dual of E14.239 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 30 f = 3 degree seq :: [ 60 ] E14.242 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {15, 30, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1, (F * T2)^2, (F * T1)^2, T1^15 ] Map:: non-degenerate R = (1, 31, 3, 33, 4, 34, 8, 38, 9, 39, 12, 42, 13, 43, 16, 46, 17, 47, 20, 50, 21, 51, 24, 54, 25, 55, 28, 58, 29, 59, 30, 60, 26, 56, 27, 57, 22, 52, 23, 53, 18, 48, 19, 49, 14, 44, 15, 45, 10, 40, 11, 41, 6, 36, 7, 37, 2, 32, 5, 35) L = (1, 32)(2, 36)(3, 35)(4, 31)(5, 37)(6, 40)(7, 41)(8, 33)(9, 34)(10, 44)(11, 45)(12, 38)(13, 39)(14, 48)(15, 49)(16, 42)(17, 43)(18, 52)(19, 53)(20, 46)(21, 47)(22, 56)(23, 57)(24, 50)(25, 51)(26, 59)(27, 60)(28, 54)(29, 55)(30, 58) local type(s) :: { ( 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30 ) } Outer automorphisms :: reflexible Dual of E14.238 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 30 f = 3 degree seq :: [ 60 ] E14.243 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {15, 30, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-2 * T1^-4, T2^-6 * T1^3 ] Map:: non-degenerate R = (1, 31, 3, 33, 9, 39, 19, 49, 27, 57, 23, 53, 14, 44, 12, 42, 4, 34, 10, 40, 20, 50, 28, 58, 24, 54, 16, 46, 6, 36, 15, 45, 11, 41, 21, 51, 29, 59, 26, 56, 18, 48, 8, 38, 2, 32, 7, 37, 17, 47, 25, 55, 30, 60, 22, 52, 13, 43, 5, 35) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 44)(7, 45)(8, 46)(9, 47)(10, 33)(11, 34)(12, 35)(13, 48)(14, 43)(15, 42)(16, 53)(17, 41)(18, 54)(19, 55)(20, 39)(21, 40)(22, 56)(23, 52)(24, 57)(25, 51)(26, 58)(27, 60)(28, 49)(29, 50)(30, 59) local type(s) :: { ( 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30 ) } Outer automorphisms :: reflexible Dual of E14.237 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 30 f = 3 degree seq :: [ 60 ] E14.244 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {15, 30, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1^-2, (T2 * T1^-1)^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T2^-1 * T1^2 * T2^-1, T1^2 * T2^13, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 31, 3, 33, 6, 36, 12, 42, 15, 45, 20, 50, 23, 53, 28, 58, 30, 60, 25, 55, 22, 52, 17, 47, 14, 44, 9, 39, 5, 35)(2, 32, 7, 37, 11, 41, 16, 46, 19, 49, 24, 54, 27, 57, 29, 59, 26, 56, 21, 51, 18, 48, 13, 43, 10, 40, 4, 34, 8, 38) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 41)(7, 42)(8, 33)(9, 34)(10, 35)(11, 45)(12, 46)(13, 39)(14, 40)(15, 49)(16, 50)(17, 43)(18, 44)(19, 53)(20, 54)(21, 47)(22, 48)(23, 57)(24, 58)(25, 51)(26, 52)(27, 60)(28, 59)(29, 55)(30, 56) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible Dual of E14.240 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.245 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y2^-1, Y1^-1), (R * Y1)^2, Y2 * Y3 * Y1^-1 * Y2, Y2 * Y3 * Y2 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y1^6 * Y2 * Y1 * Y2 * Y3^-6, Y1^15, (Y1 * Y3^-1)^15, (Y3 * Y2^-1)^30 ] Map:: R = (1, 31, 2, 32, 6, 36, 11, 41, 15, 45, 19, 49, 23, 53, 27, 57, 29, 59, 25, 55, 21, 51, 17, 47, 13, 43, 9, 39, 4, 34)(3, 33, 7, 37, 12, 42, 16, 46, 20, 50, 24, 54, 28, 58, 30, 60, 26, 56, 22, 52, 18, 48, 14, 44, 10, 40, 5, 35, 8, 38)(61, 91, 63, 93, 66, 96, 72, 102, 75, 105, 80, 110, 83, 113, 88, 118, 89, 119, 86, 116, 81, 111, 78, 108, 73, 103, 70, 100, 64, 94, 68, 98, 62, 92, 67, 97, 71, 101, 76, 106, 79, 109, 84, 114, 87, 117, 90, 120, 85, 115, 82, 112, 77, 107, 74, 104, 69, 99, 65, 95) L = (1, 64)(2, 61)(3, 68)(4, 69)(5, 70)(6, 62)(7, 63)(8, 65)(9, 73)(10, 74)(11, 66)(12, 67)(13, 77)(14, 78)(15, 71)(16, 72)(17, 81)(18, 82)(19, 75)(20, 76)(21, 85)(22, 86)(23, 79)(24, 80)(25, 89)(26, 90)(27, 83)(28, 84)(29, 87)(30, 88)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ), ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) } Outer automorphisms :: reflexible Dual of E14.252 Graph:: bipartite v = 3 e = 60 f = 31 degree seq :: [ 30^2, 60 ] E14.246 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 30, 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, Y2^2 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^15, Y1^15 ] Map:: R = (1, 31, 2, 32, 6, 36, 10, 40, 14, 44, 18, 48, 22, 52, 26, 56, 29, 59, 25, 55, 21, 51, 17, 47, 13, 43, 9, 39, 4, 34)(3, 33, 5, 35, 7, 37, 11, 41, 15, 45, 19, 49, 23, 53, 27, 57, 30, 60, 28, 58, 24, 54, 20, 50, 16, 46, 12, 42, 8, 38)(61, 91, 63, 93, 64, 94, 68, 98, 69, 99, 72, 102, 73, 103, 76, 106, 77, 107, 80, 110, 81, 111, 84, 114, 85, 115, 88, 118, 89, 119, 90, 120, 86, 116, 87, 117, 82, 112, 83, 113, 78, 108, 79, 109, 74, 104, 75, 105, 70, 100, 71, 101, 66, 96, 67, 97, 62, 92, 65, 95) L = (1, 64)(2, 61)(3, 68)(4, 69)(5, 63)(6, 62)(7, 65)(8, 72)(9, 73)(10, 66)(11, 67)(12, 76)(13, 77)(14, 70)(15, 71)(16, 80)(17, 81)(18, 74)(19, 75)(20, 84)(21, 85)(22, 78)(23, 79)(24, 88)(25, 89)(26, 82)(27, 83)(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) :: { ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ), ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) } Outer automorphisms :: reflexible Dual of E14.251 Graph:: bipartite v = 3 e = 60 f = 31 degree seq :: [ 30^2, 60 ] E14.247 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1^3 * Y2 * Y3^-1, Y3^3 * Y2^-2 * Y1^-1, Y1^2 * Y2^-1 * Y3^-1 * Y2^-5 ] Map:: R = (1, 31, 2, 32, 6, 36, 14, 44, 13, 43, 18, 48, 24, 54, 27, 57, 30, 60, 29, 59, 20, 50, 9, 39, 17, 47, 11, 41, 4, 34)(3, 33, 7, 37, 15, 45, 12, 42, 5, 35, 8, 38, 16, 46, 23, 53, 22, 52, 26, 56, 28, 58, 19, 49, 25, 55, 21, 51, 10, 40)(61, 91, 63, 93, 69, 99, 79, 109, 87, 117, 83, 113, 74, 104, 72, 102, 64, 94, 70, 100, 80, 110, 88, 118, 84, 114, 76, 106, 66, 96, 75, 105, 71, 101, 81, 111, 89, 119, 86, 116, 78, 108, 68, 98, 62, 92, 67, 97, 77, 107, 85, 115, 90, 120, 82, 112, 73, 103, 65, 95) L = (1, 64)(2, 61)(3, 70)(4, 71)(5, 72)(6, 62)(7, 63)(8, 65)(9, 80)(10, 81)(11, 77)(12, 75)(13, 74)(14, 66)(15, 67)(16, 68)(17, 69)(18, 73)(19, 88)(20, 89)(21, 85)(22, 83)(23, 76)(24, 78)(25, 79)(26, 82)(27, 84)(28, 86)(29, 90)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ), ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) } Outer automorphisms :: reflexible Dual of E14.250 Graph:: bipartite v = 3 e = 60 f = 31 degree seq :: [ 30^2, 60 ] E14.248 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2, Y1), Y1 * Y2 * Y1^3 * Y2, Y2^6 * Y1^-1 * Y2, (Y3^-1 * Y1^-1)^15 ] Map:: R = (1, 31, 2, 32, 6, 36, 14, 44, 13, 43, 18, 48, 24, 54, 29, 59, 27, 57, 19, 49, 25, 55, 21, 51, 10, 40, 3, 33, 7, 37, 15, 45, 12, 42, 5, 35, 8, 38, 16, 46, 23, 53, 22, 52, 26, 56, 30, 60, 28, 58, 20, 50, 9, 39, 17, 47, 11, 41, 4, 34)(61, 91, 63, 93, 69, 99, 79, 109, 86, 116, 78, 108, 68, 98, 62, 92, 67, 97, 77, 107, 85, 115, 90, 120, 84, 114, 76, 106, 66, 96, 75, 105, 71, 101, 81, 111, 88, 118, 89, 119, 83, 113, 74, 104, 72, 102, 64, 94, 70, 100, 80, 110, 87, 117, 82, 112, 73, 103, 65, 95) L = (1, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 75)(7, 77)(8, 62)(9, 79)(10, 80)(11, 81)(12, 64)(13, 65)(14, 72)(15, 71)(16, 66)(17, 85)(18, 68)(19, 86)(20, 87)(21, 88)(22, 73)(23, 74)(24, 76)(25, 90)(26, 78)(27, 82)(28, 89)(29, 83)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 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 E14.249 Graph:: bipartite v = 2 e = 60 f = 32 degree seq :: [ 60^2 ] E14.249 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^-2 * Y3^-2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3^-1), Y2^5 * Y3^6 * Y2, Y2^-1 * Y3^14, Y2^15, 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^-1 * Y1^-1)^30 ] Map:: R = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)(61, 91, 62, 92, 66, 96, 71, 101, 75, 105, 79, 109, 83, 113, 87, 117, 90, 120, 85, 115, 82, 112, 77, 107, 74, 104, 69, 99, 64, 94)(63, 93, 67, 97, 65, 95, 68, 98, 72, 102, 76, 106, 80, 110, 84, 114, 88, 118, 89, 119, 86, 116, 81, 111, 78, 108, 73, 103, 70, 100) L = (1, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 65)(7, 64)(8, 62)(9, 73)(10, 74)(11, 68)(12, 66)(13, 77)(14, 78)(15, 72)(16, 71)(17, 81)(18, 82)(19, 76)(20, 75)(21, 85)(22, 86)(23, 80)(24, 79)(25, 89)(26, 90)(27, 84)(28, 83)(29, 87)(30, 88)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 60, 60 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E14.248 Graph:: simple bipartite v = 32 e = 60 f = 2 degree seq :: [ 2^30, 30^2 ] E14.250 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^-2 * Y1^2, (Y3, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-14, Y3^15, (Y3 * Y2^-1)^15, 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 ] Map:: R = (1, 31, 2, 32, 6, 36, 11, 41, 15, 45, 19, 49, 23, 53, 27, 57, 30, 60, 26, 56, 22, 52, 18, 48, 14, 44, 10, 40, 5, 35, 8, 38, 3, 33, 7, 37, 12, 42, 16, 46, 20, 50, 24, 54, 28, 58, 29, 59, 25, 55, 21, 51, 17, 47, 13, 43, 9, 39, 4, 34)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 114)(85, 115)(86, 116)(87, 117)(88, 118)(89, 119)(90, 120) L = (1, 63)(2, 67)(3, 66)(4, 68)(5, 61)(6, 72)(7, 71)(8, 62)(9, 65)(10, 64)(11, 76)(12, 75)(13, 70)(14, 69)(15, 80)(16, 79)(17, 74)(18, 73)(19, 84)(20, 83)(21, 78)(22, 77)(23, 88)(24, 87)(25, 82)(26, 81)(27, 89)(28, 90)(29, 86)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) } Outer automorphisms :: reflexible Dual of E14.247 Graph:: bipartite v = 31 e = 60 f = 3 degree seq :: [ 2^30, 60 ] E14.251 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y2, R^2, Y3 * Y1^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^15, (Y3^7 * Y1^-1)^2, (Y3 * Y2^-1)^15 ] Map:: R = (1, 31, 2, 32, 5, 35, 6, 36, 9, 39, 10, 40, 13, 43, 14, 44, 17, 47, 18, 48, 21, 51, 22, 52, 25, 55, 26, 56, 29, 59, 30, 60, 27, 57, 28, 58, 23, 53, 24, 54, 19, 49, 20, 50, 15, 45, 16, 46, 11, 41, 12, 42, 7, 37, 8, 38, 3, 33, 4, 34)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 114)(85, 115)(86, 116)(87, 117)(88, 118)(89, 119)(90, 120) L = (1, 63)(2, 64)(3, 67)(4, 68)(5, 61)(6, 62)(7, 71)(8, 72)(9, 65)(10, 66)(11, 75)(12, 76)(13, 69)(14, 70)(15, 79)(16, 80)(17, 73)(18, 74)(19, 83)(20, 84)(21, 77)(22, 78)(23, 87)(24, 88)(25, 81)(26, 82)(27, 89)(28, 90)(29, 85)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) } Outer automorphisms :: reflexible Dual of E14.246 Graph:: bipartite v = 31 e = 60 f = 3 degree seq :: [ 2^30, 60 ] E14.252 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1, Y3), (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^-1 * Y3^-3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3 * Y1^-3 * Y3^2 * Y1^-1, (Y3 * Y2^-1)^15 ] Map:: R = (1, 31, 2, 32, 6, 36, 14, 44, 23, 53, 27, 57, 19, 49, 12, 42, 5, 35, 8, 38, 16, 46, 25, 55, 28, 58, 20, 50, 9, 39, 17, 47, 13, 43, 18, 48, 26, 56, 29, 59, 21, 51, 10, 40, 3, 33, 7, 37, 15, 45, 24, 54, 30, 60, 22, 52, 11, 41, 4, 34)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 114)(85, 115)(86, 116)(87, 117)(88, 118)(89, 119)(90, 120) L = (1, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 75)(7, 77)(8, 62)(9, 79)(10, 80)(11, 81)(12, 64)(13, 65)(14, 84)(15, 73)(16, 66)(17, 72)(18, 68)(19, 71)(20, 87)(21, 88)(22, 89)(23, 90)(24, 78)(25, 74)(26, 76)(27, 82)(28, 83)(29, 85)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) } Outer automorphisms :: reflexible Dual of E14.245 Graph:: bipartite v = 31 e = 60 f = 3 degree seq :: [ 2^30, 60 ] E14.253 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 8, 16}) Quotient :: halfedge^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1 * Y2 * Y3, Y2 * Y1^-1 * Y3, R * Y3 * R * Y2, (R * Y1)^2, Y1^16 ] Map:: non-degenerate R = (1, 34, 2, 38, 6, 42, 10, 46, 14, 50, 18, 54, 22, 58, 26, 62, 30, 61, 29, 57, 25, 53, 21, 49, 17, 45, 13, 41, 9, 37, 5, 33)(3, 40, 8, 44, 12, 48, 16, 52, 20, 56, 24, 60, 28, 64, 32, 63, 31, 59, 27, 55, 23, 51, 19, 47, 15, 43, 11, 39, 7, 36, 4, 35) L = (1, 3)(2, 4)(5, 8)(6, 7)(9, 12)(10, 11)(13, 16)(14, 15)(17, 20)(18, 19)(21, 24)(22, 23)(25, 28)(26, 27)(29, 32)(30, 31)(33, 36)(34, 39)(35, 37)(38, 43)(40, 41)(42, 47)(44, 45)(46, 51)(48, 49)(50, 55)(52, 53)(54, 59)(56, 57)(58, 63)(60, 61)(62, 64) local type(s) :: { ( 16^32 ) } Outer automorphisms :: reflexible Dual of E14.255 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 32 f = 4 degree seq :: [ 32^2 ] E14.254 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 8, 16}) Quotient :: halfedge^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y1^2 * Y2 * Y1^-3 * Y3, Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y2 * Y1 * Y2, Y1 * Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 ] Map:: non-degenerate R = (1, 34, 2, 38, 6, 46, 14, 55, 23, 44, 12, 50, 18, 59, 27, 64, 32, 62, 30, 52, 20, 42, 10, 49, 17, 57, 25, 45, 13, 37, 5, 33)(3, 41, 9, 51, 19, 61, 29, 60, 28, 53, 21, 56, 24, 63, 31, 58, 26, 48, 16, 40, 8, 36, 4, 43, 11, 54, 22, 47, 15, 39, 7, 35) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 22)(16, 27)(17, 28)(20, 24)(25, 29)(26, 32)(30, 31)(33, 36)(34, 40)(35, 42)(37, 43)(38, 48)(39, 49)(41, 52)(44, 56)(45, 54)(46, 58)(47, 57)(50, 53)(51, 62)(55, 63)(59, 60)(61, 64) local type(s) :: { ( 16^32 ) } Outer automorphisms :: reflexible Dual of E14.256 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 32 f = 4 degree seq :: [ 32^2 ] E14.255 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 8, 16}) Quotient :: halfedge^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y1^-1 * Y2)^2, (R * Y1)^2, (Y1^-1 * Y3)^2, Y3 * Y1^-1 * Y2 * Y3 * Y2, Y1^8 ] Map:: non-degenerate R = (1, 34, 2, 38, 6, 46, 14, 54, 22, 53, 21, 45, 13, 37, 5, 33)(3, 41, 9, 50, 18, 58, 26, 61, 29, 55, 23, 47, 15, 39, 7, 35)(4, 43, 11, 51, 19, 59, 27, 62, 30, 56, 24, 48, 16, 40, 8, 36)(10, 49, 17, 57, 25, 63, 31, 64, 32, 60, 28, 52, 20, 44, 12, 42) 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, 29)(24, 25)(27, 32)(30, 31)(33, 36)(34, 40)(35, 42)(37, 43)(38, 48)(39, 49)(41, 44)(45, 51)(46, 56)(47, 57)(50, 52)(53, 59)(54, 62)(55, 63)(58, 60)(61, 64) local type(s) :: { ( 32^16 ) } Outer automorphisms :: reflexible Dual of E14.253 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 32 f = 2 degree seq :: [ 16^4 ] E14.256 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 8, 16}) Quotient :: halfedge^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y1^-1 * Y3)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, Y2 * Y1^-1 * Y3 * Y2 * Y3, Y1^8, (Y2 * Y1 * Y3)^16 ] Map:: non-degenerate R = (1, 34, 2, 38, 6, 46, 14, 54, 22, 53, 21, 45, 13, 37, 5, 33)(3, 41, 9, 50, 18, 58, 26, 61, 29, 55, 23, 47, 15, 39, 7, 35)(4, 43, 11, 52, 20, 60, 28, 62, 30, 56, 24, 48, 16, 40, 8, 36)(10, 44, 12, 49, 17, 57, 25, 63, 31, 64, 32, 59, 27, 51, 19, 42) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 17)(10, 11)(13, 18)(14, 23)(16, 25)(19, 20)(21, 26)(22, 29)(24, 31)(27, 28)(30, 32)(33, 36)(34, 40)(35, 42)(37, 43)(38, 48)(39, 44)(41, 51)(45, 52)(46, 56)(47, 49)(50, 59)(53, 60)(54, 62)(55, 57)(58, 64)(61, 63) local type(s) :: { ( 32^16 ) } Outer automorphisms :: reflexible Dual of E14.254 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 32 f = 2 degree seq :: [ 16^4 ] E14.257 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 16}) Quotient :: edge^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2, Y3^8, Y3^3 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 33, 4, 36, 12, 44, 20, 52, 28, 60, 21, 53, 13, 45, 5, 37)(2, 34, 7, 39, 15, 47, 23, 55, 30, 62, 24, 56, 16, 48, 8, 40)(3, 35, 10, 42, 18, 50, 26, 58, 32, 64, 27, 59, 19, 51, 11, 43)(6, 38, 14, 46, 22, 54, 29, 61, 31, 63, 25, 57, 17, 49, 9, 41)(65, 66)(67, 73)(68, 72)(69, 71)(70, 75)(74, 81)(76, 80)(77, 79)(78, 83)(82, 89)(84, 88)(85, 87)(86, 91)(90, 95)(92, 94)(93, 96)(97, 99)(98, 102)(100, 107)(101, 106)(103, 105)(104, 110)(108, 115)(109, 114)(111, 113)(112, 118)(116, 123)(117, 122)(119, 121)(120, 125)(124, 128)(126, 127) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64, 64 ), ( 64^16 ) } Outer automorphisms :: reflexible Dual of E14.264 Graph:: simple bipartite v = 36 e = 64 f = 2 degree seq :: [ 2^32, 16^4 ] E14.258 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 16}) Quotient :: edge^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y3 * Y1 * Y2 * Y1 * Y2, Y3^8 ] Map:: R = (1, 33, 4, 36, 12, 44, 20, 52, 28, 60, 21, 53, 13, 45, 5, 37)(2, 34, 7, 39, 15, 47, 23, 55, 30, 62, 24, 56, 16, 48, 8, 40)(3, 35, 10, 42, 18, 50, 26, 58, 32, 64, 27, 59, 19, 51, 11, 43)(6, 38, 9, 41, 17, 49, 25, 57, 31, 63, 29, 61, 22, 54, 14, 46)(65, 66)(67, 73)(68, 72)(69, 71)(70, 74)(75, 81)(76, 80)(77, 79)(78, 82)(83, 89)(84, 88)(85, 87)(86, 90)(91, 95)(92, 94)(93, 96)(97, 99)(98, 102)(100, 107)(101, 106)(103, 110)(104, 105)(108, 115)(109, 114)(111, 118)(112, 113)(116, 123)(117, 122)(119, 125)(120, 121)(124, 128)(126, 127) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64, 64 ), ( 64^16 ) } Outer automorphisms :: reflexible Dual of E14.263 Graph:: simple bipartite v = 36 e = 64 f = 2 degree seq :: [ 2^32, 16^4 ] E14.259 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 16}) Quotient :: edge^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3, Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3^16 ] Map:: R = (1, 33, 4, 36, 8, 40, 12, 44, 16, 48, 20, 52, 24, 56, 28, 60, 32, 64, 29, 61, 25, 57, 21, 53, 17, 49, 13, 45, 9, 41, 5, 37)(2, 34, 3, 35, 7, 39, 11, 43, 15, 47, 19, 51, 23, 55, 27, 59, 31, 63, 30, 62, 26, 58, 22, 54, 18, 50, 14, 46, 10, 42, 6, 38)(65, 66)(67, 69)(68, 70)(71, 73)(72, 74)(75, 77)(76, 78)(79, 81)(80, 82)(83, 85)(84, 86)(87, 89)(88, 90)(91, 93)(92, 94)(95, 96)(97, 99)(98, 100)(101, 103)(102, 104)(105, 107)(106, 108)(109, 111)(110, 112)(113, 115)(114, 116)(117, 119)(118, 120)(121, 123)(122, 124)(125, 127)(126, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 32 ), ( 32^32 ) } Outer automorphisms :: reflexible Dual of E14.262 Graph:: simple bipartite v = 34 e = 64 f = 4 degree seq :: [ 2^32, 32^2 ] E14.260 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 16}) Quotient :: edge^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1)^2, Y2 * Y3^-2 * Y1 * Y2 * Y1, Y1 * Y3^-7 * Y2, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y3^-3 * Y2 ] Map:: R = (1, 33, 4, 36, 12, 44, 21, 53, 29, 61, 27, 59, 19, 51, 9, 41, 16, 48, 6, 38, 15, 47, 24, 56, 30, 62, 22, 54, 13, 45, 5, 37)(2, 34, 7, 39, 17, 49, 25, 57, 32, 64, 31, 63, 23, 55, 14, 46, 11, 43, 3, 35, 10, 42, 20, 52, 28, 60, 26, 58, 18, 50, 8, 40)(65, 66)(67, 73)(68, 72)(69, 71)(70, 78)(74, 83)(75, 80)(76, 82)(77, 81)(79, 87)(84, 91)(85, 90)(86, 89)(88, 95)(92, 93)(94, 96)(97, 99)(98, 102)(100, 107)(101, 106)(103, 112)(104, 111)(105, 113)(108, 110)(109, 116)(114, 120)(115, 121)(117, 119)(118, 124)(122, 126)(123, 128)(125, 127) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 32 ), ( 32^32 ) } Outer automorphisms :: reflexible Dual of E14.261 Graph:: simple bipartite v = 34 e = 64 f = 4 degree seq :: [ 2^32, 32^2 ] E14.261 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 16}) Quotient :: loop^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2, Y3^8, Y3^3 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 33, 65, 97, 4, 36, 68, 100, 12, 44, 76, 108, 20, 52, 84, 116, 28, 60, 92, 124, 21, 53, 85, 117, 13, 45, 77, 109, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 15, 47, 79, 111, 23, 55, 87, 119, 30, 62, 94, 126, 24, 56, 88, 120, 16, 48, 80, 112, 8, 40, 72, 104)(3, 35, 67, 99, 10, 42, 74, 106, 18, 50, 82, 114, 26, 58, 90, 122, 32, 64, 96, 128, 27, 59, 91, 123, 19, 51, 83, 115, 11, 43, 75, 107)(6, 38, 70, 102, 14, 46, 78, 110, 22, 54, 86, 118, 29, 61, 93, 125, 31, 63, 95, 127, 25, 57, 89, 121, 17, 49, 81, 113, 9, 41, 73, 105) L = (1, 34)(2, 33)(3, 41)(4, 40)(5, 39)(6, 43)(7, 37)(8, 36)(9, 35)(10, 49)(11, 38)(12, 48)(13, 47)(14, 51)(15, 45)(16, 44)(17, 42)(18, 57)(19, 46)(20, 56)(21, 55)(22, 59)(23, 53)(24, 52)(25, 50)(26, 63)(27, 54)(28, 62)(29, 64)(30, 60)(31, 58)(32, 61)(65, 99)(66, 102)(67, 97)(68, 107)(69, 106)(70, 98)(71, 105)(72, 110)(73, 103)(74, 101)(75, 100)(76, 115)(77, 114)(78, 104)(79, 113)(80, 118)(81, 111)(82, 109)(83, 108)(84, 123)(85, 122)(86, 112)(87, 121)(88, 125)(89, 119)(90, 117)(91, 116)(92, 128)(93, 120)(94, 127)(95, 126)(96, 124) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E14.260 Transitivity :: VT+ Graph:: bipartite v = 4 e = 64 f = 34 degree seq :: [ 32^4 ] E14.262 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 16}) Quotient :: loop^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y3 * Y1 * Y2 * Y1 * Y2, Y3^8 ] Map:: R = (1, 33, 65, 97, 4, 36, 68, 100, 12, 44, 76, 108, 20, 52, 84, 116, 28, 60, 92, 124, 21, 53, 85, 117, 13, 45, 77, 109, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 15, 47, 79, 111, 23, 55, 87, 119, 30, 62, 94, 126, 24, 56, 88, 120, 16, 48, 80, 112, 8, 40, 72, 104)(3, 35, 67, 99, 10, 42, 74, 106, 18, 50, 82, 114, 26, 58, 90, 122, 32, 64, 96, 128, 27, 59, 91, 123, 19, 51, 83, 115, 11, 43, 75, 107)(6, 38, 70, 102, 9, 41, 73, 105, 17, 49, 81, 113, 25, 57, 89, 121, 31, 63, 95, 127, 29, 61, 93, 125, 22, 54, 86, 118, 14, 46, 78, 110) L = (1, 34)(2, 33)(3, 41)(4, 40)(5, 39)(6, 42)(7, 37)(8, 36)(9, 35)(10, 38)(11, 49)(12, 48)(13, 47)(14, 50)(15, 45)(16, 44)(17, 43)(18, 46)(19, 57)(20, 56)(21, 55)(22, 58)(23, 53)(24, 52)(25, 51)(26, 54)(27, 63)(28, 62)(29, 64)(30, 60)(31, 59)(32, 61)(65, 99)(66, 102)(67, 97)(68, 107)(69, 106)(70, 98)(71, 110)(72, 105)(73, 104)(74, 101)(75, 100)(76, 115)(77, 114)(78, 103)(79, 118)(80, 113)(81, 112)(82, 109)(83, 108)(84, 123)(85, 122)(86, 111)(87, 125)(88, 121)(89, 120)(90, 117)(91, 116)(92, 128)(93, 119)(94, 127)(95, 126)(96, 124) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E14.259 Transitivity :: VT+ Graph:: bipartite v = 4 e = 64 f = 34 degree seq :: [ 32^4 ] E14.263 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 16}) Quotient :: loop^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3, Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3^16 ] Map:: R = (1, 33, 65, 97, 4, 36, 68, 100, 8, 40, 72, 104, 12, 44, 76, 108, 16, 48, 80, 112, 20, 52, 84, 116, 24, 56, 88, 120, 28, 60, 92, 124, 32, 64, 96, 128, 29, 61, 93, 125, 25, 57, 89, 121, 21, 53, 85, 117, 17, 49, 81, 113, 13, 45, 77, 109, 9, 41, 73, 105, 5, 37, 69, 101)(2, 34, 66, 98, 3, 35, 67, 99, 7, 39, 71, 103, 11, 43, 75, 107, 15, 47, 79, 111, 19, 51, 83, 115, 23, 55, 87, 119, 27, 59, 91, 123, 31, 63, 95, 127, 30, 62, 94, 126, 26, 58, 90, 122, 22, 54, 86, 118, 18, 50, 82, 114, 14, 46, 78, 110, 10, 42, 74, 106, 6, 38, 70, 102) L = (1, 34)(2, 33)(3, 37)(4, 38)(5, 35)(6, 36)(7, 41)(8, 42)(9, 39)(10, 40)(11, 45)(12, 46)(13, 43)(14, 44)(15, 49)(16, 50)(17, 47)(18, 48)(19, 53)(20, 54)(21, 51)(22, 52)(23, 57)(24, 58)(25, 55)(26, 56)(27, 61)(28, 62)(29, 59)(30, 60)(31, 64)(32, 63)(65, 99)(66, 100)(67, 97)(68, 98)(69, 103)(70, 104)(71, 101)(72, 102)(73, 107)(74, 108)(75, 105)(76, 106)(77, 111)(78, 112)(79, 109)(80, 110)(81, 115)(82, 116)(83, 113)(84, 114)(85, 119)(86, 120)(87, 117)(88, 118)(89, 123)(90, 124)(91, 121)(92, 122)(93, 127)(94, 128)(95, 125)(96, 126) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E14.258 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 36 degree seq :: [ 64^2 ] E14.264 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 16}) Quotient :: loop^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1)^2, Y2 * Y3^-2 * Y1 * Y2 * Y1, Y1 * Y3^-7 * Y2, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y3^-3 * Y2 ] Map:: R = (1, 33, 65, 97, 4, 36, 68, 100, 12, 44, 76, 108, 21, 53, 85, 117, 29, 61, 93, 125, 27, 59, 91, 123, 19, 51, 83, 115, 9, 41, 73, 105, 16, 48, 80, 112, 6, 38, 70, 102, 15, 47, 79, 111, 24, 56, 88, 120, 30, 62, 94, 126, 22, 54, 86, 118, 13, 45, 77, 109, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 17, 49, 81, 113, 25, 57, 89, 121, 32, 64, 96, 128, 31, 63, 95, 127, 23, 55, 87, 119, 14, 46, 78, 110, 11, 43, 75, 107, 3, 35, 67, 99, 10, 42, 74, 106, 20, 52, 84, 116, 28, 60, 92, 124, 26, 58, 90, 122, 18, 50, 82, 114, 8, 40, 72, 104) L = (1, 34)(2, 33)(3, 41)(4, 40)(5, 39)(6, 46)(7, 37)(8, 36)(9, 35)(10, 51)(11, 48)(12, 50)(13, 49)(14, 38)(15, 55)(16, 43)(17, 45)(18, 44)(19, 42)(20, 59)(21, 58)(22, 57)(23, 47)(24, 63)(25, 54)(26, 53)(27, 52)(28, 61)(29, 60)(30, 64)(31, 56)(32, 62)(65, 99)(66, 102)(67, 97)(68, 107)(69, 106)(70, 98)(71, 112)(72, 111)(73, 113)(74, 101)(75, 100)(76, 110)(77, 116)(78, 108)(79, 104)(80, 103)(81, 105)(82, 120)(83, 121)(84, 109)(85, 119)(86, 124)(87, 117)(88, 114)(89, 115)(90, 126)(91, 128)(92, 118)(93, 127)(94, 122)(95, 125)(96, 123) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E14.257 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 36 degree seq :: [ 64^2 ] E14.265 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, Y2^8, (Y3 * Y2^-1)^16 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 10, 42)(5, 37, 7, 39)(6, 38, 8, 40)(11, 43, 18, 50)(12, 44, 17, 49)(13, 45, 16, 48)(14, 46, 15, 47)(19, 51, 26, 58)(20, 52, 25, 57)(21, 53, 24, 56)(22, 54, 23, 55)(27, 59, 30, 62)(28, 60, 32, 64)(29, 61, 31, 63)(65, 97, 67, 99, 75, 107, 83, 115, 91, 123, 86, 118, 78, 110, 69, 101)(66, 98, 71, 103, 79, 111, 87, 119, 94, 126, 90, 122, 82, 114, 73, 105)(68, 100, 70, 102, 76, 108, 84, 116, 92, 124, 93, 125, 85, 117, 77, 109)(72, 104, 74, 106, 80, 112, 88, 120, 95, 127, 96, 128, 89, 121, 81, 113) L = (1, 68)(2, 72)(3, 70)(4, 69)(5, 77)(6, 65)(7, 74)(8, 73)(9, 81)(10, 66)(11, 76)(12, 67)(13, 78)(14, 85)(15, 80)(16, 71)(17, 82)(18, 89)(19, 84)(20, 75)(21, 86)(22, 93)(23, 88)(24, 79)(25, 90)(26, 96)(27, 92)(28, 83)(29, 91)(30, 95)(31, 87)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E14.270 Graph:: simple bipartite v = 20 e = 64 f = 18 degree seq :: [ 4^16, 16^4 ] E14.266 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y2^8 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 10, 42)(5, 37, 7, 39)(6, 38, 8, 40)(11, 43, 17, 49)(12, 44, 18, 50)(13, 45, 15, 47)(14, 46, 16, 48)(19, 51, 25, 57)(20, 52, 26, 58)(21, 53, 23, 55)(22, 54, 24, 56)(27, 59, 30, 62)(28, 60, 32, 64)(29, 61, 31, 63)(65, 97, 67, 99, 75, 107, 83, 115, 91, 123, 85, 117, 77, 109, 69, 101)(66, 98, 71, 103, 79, 111, 87, 119, 94, 126, 89, 121, 81, 113, 73, 105)(68, 100, 76, 108, 84, 116, 92, 124, 93, 125, 86, 118, 78, 110, 70, 102)(72, 104, 80, 112, 88, 120, 95, 127, 96, 128, 90, 122, 82, 114, 74, 106) L = (1, 68)(2, 72)(3, 76)(4, 67)(5, 70)(6, 65)(7, 80)(8, 71)(9, 74)(10, 66)(11, 84)(12, 75)(13, 78)(14, 69)(15, 88)(16, 79)(17, 82)(18, 73)(19, 92)(20, 83)(21, 86)(22, 77)(23, 95)(24, 87)(25, 90)(26, 81)(27, 93)(28, 91)(29, 85)(30, 96)(31, 94)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E14.269 Graph:: simple bipartite v = 20 e = 64 f = 18 degree seq :: [ 4^16, 16^4 ] E14.267 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3, Y2), (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y2 * Y3 * Y2^2 * Y3, Y3 * Y2^-1 * Y3^3 * Y2^-1, Y3^-10 * Y2 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 10, 42)(5, 37, 7, 39)(6, 38, 8, 40)(11, 43, 24, 56)(12, 44, 25, 57)(13, 45, 23, 55)(14, 46, 26, 58)(15, 47, 21, 53)(16, 48, 19, 51)(17, 49, 20, 52)(18, 50, 22, 54)(27, 59, 32, 64)(28, 60, 31, 63)(29, 61, 30, 62)(65, 97, 67, 99, 75, 107, 82, 114, 92, 124, 78, 110, 80, 112, 69, 101)(66, 98, 71, 103, 83, 115, 90, 122, 95, 127, 86, 118, 88, 120, 73, 105)(68, 100, 76, 108, 81, 113, 70, 102, 77, 109, 91, 123, 93, 125, 79, 111)(72, 104, 84, 116, 89, 121, 74, 106, 85, 117, 94, 126, 96, 128, 87, 119) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 79)(6, 65)(7, 84)(8, 86)(9, 87)(10, 66)(11, 81)(12, 80)(13, 67)(14, 91)(15, 92)(16, 93)(17, 69)(18, 70)(19, 89)(20, 88)(21, 71)(22, 94)(23, 95)(24, 96)(25, 73)(26, 74)(27, 75)(28, 77)(29, 82)(30, 83)(31, 85)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E14.272 Graph:: simple bipartite v = 20 e = 64 f = 18 degree seq :: [ 4^16, 16^4 ] E14.268 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3), (R * Y1)^2, (Y2 * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, Y2^-2 * Y3 * Y2^-1 * Y3, Y3 * Y2 * Y3^3 * Y2 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 10, 42)(5, 37, 7, 39)(6, 38, 8, 40)(11, 43, 24, 56)(12, 44, 25, 57)(13, 45, 23, 55)(14, 46, 26, 58)(15, 47, 21, 53)(16, 48, 19, 51)(17, 49, 20, 52)(18, 50, 22, 54)(27, 59, 32, 64)(28, 60, 31, 63)(29, 61, 30, 62)(65, 97, 67, 99, 75, 107, 78, 110, 92, 124, 82, 114, 80, 112, 69, 101)(66, 98, 71, 103, 83, 115, 86, 118, 95, 127, 90, 122, 88, 120, 73, 105)(68, 100, 76, 108, 91, 123, 93, 125, 81, 113, 70, 102, 77, 109, 79, 111)(72, 104, 84, 116, 94, 126, 96, 128, 89, 121, 74, 106, 85, 117, 87, 119) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 79)(6, 65)(7, 84)(8, 86)(9, 87)(10, 66)(11, 91)(12, 92)(13, 67)(14, 93)(15, 75)(16, 77)(17, 69)(18, 70)(19, 94)(20, 95)(21, 71)(22, 96)(23, 83)(24, 85)(25, 73)(26, 74)(27, 82)(28, 81)(29, 80)(30, 90)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E14.271 Graph:: simple bipartite v = 20 e = 64 f = 18 degree seq :: [ 4^16, 16^4 ] E14.269 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^8, Y1^16 ] Map:: non-degenerate R = (1, 33, 2, 34, 5, 37, 9, 41, 13, 45, 17, 49, 21, 53, 25, 57, 29, 61, 28, 60, 24, 56, 20, 52, 16, 48, 12, 44, 8, 40, 4, 36)(3, 35, 7, 39, 11, 43, 15, 47, 19, 51, 23, 55, 27, 59, 31, 63, 32, 64, 30, 62, 26, 58, 22, 54, 18, 50, 14, 46, 10, 42, 6, 38)(65, 97, 67, 99)(66, 98, 70, 102)(68, 100, 71, 103)(69, 101, 74, 106)(72, 104, 75, 107)(73, 105, 78, 110)(76, 108, 79, 111)(77, 109, 82, 114)(80, 112, 83, 115)(81, 113, 86, 118)(84, 116, 87, 119)(85, 117, 90, 122)(88, 120, 91, 123)(89, 121, 94, 126)(92, 124, 95, 127)(93, 125, 96, 128) L = (1, 66)(2, 69)(3, 71)(4, 65)(5, 73)(6, 67)(7, 75)(8, 68)(9, 77)(10, 70)(11, 79)(12, 72)(13, 81)(14, 74)(15, 83)(16, 76)(17, 85)(18, 78)(19, 87)(20, 80)(21, 89)(22, 82)(23, 91)(24, 84)(25, 93)(26, 86)(27, 95)(28, 88)(29, 92)(30, 90)(31, 96)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 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 E14.266 Graph:: bipartite v = 18 e = 64 f = 20 degree seq :: [ 4^16, 32^2 ] E14.270 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1 * Y3^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, Y1^-3 * Y3 * Y1^-2, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 17, 49, 15, 47, 4, 36, 9, 41, 19, 51, 28, 60, 26, 58, 14, 46, 6, 38, 10, 42, 20, 52, 16, 48, 5, 37)(3, 35, 11, 43, 23, 55, 29, 61, 21, 53, 12, 44, 24, 56, 31, 63, 32, 64, 30, 62, 22, 54, 13, 45, 25, 57, 27, 59, 18, 50, 8, 40)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 77, 109)(69, 101, 75, 107)(70, 102, 76, 108)(71, 103, 82, 114)(73, 105, 86, 118)(74, 106, 85, 117)(78, 110, 88, 120)(79, 111, 89, 121)(80, 112, 87, 119)(81, 113, 91, 123)(83, 115, 94, 126)(84, 116, 93, 125)(90, 122, 95, 127)(92, 124, 96, 128) L = (1, 68)(2, 73)(3, 76)(4, 78)(5, 79)(6, 65)(7, 83)(8, 85)(9, 70)(10, 66)(11, 88)(12, 86)(13, 67)(14, 69)(15, 90)(16, 81)(17, 92)(18, 93)(19, 74)(20, 71)(21, 94)(22, 72)(23, 95)(24, 77)(25, 75)(26, 80)(27, 87)(28, 84)(29, 96)(30, 82)(31, 89)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 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 E14.265 Graph:: bipartite v = 18 e = 64 f = 20 degree seq :: [ 4^16, 32^2 ] E14.271 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-3, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^-1 * Y1 * Y3^-4, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 6, 38, 10, 42, 18, 50, 16, 48, 22, 54, 28, 60, 26, 58, 14, 46, 21, 53, 15, 47, 4, 36, 9, 41, 5, 37)(3, 35, 11, 43, 20, 52, 13, 45, 23, 55, 30, 62, 25, 57, 31, 63, 32, 64, 29, 61, 24, 56, 27, 59, 19, 51, 12, 44, 17, 49, 8, 40)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 77, 109)(69, 101, 75, 107)(70, 102, 76, 108)(71, 103, 81, 113)(73, 105, 84, 116)(74, 106, 83, 115)(78, 110, 89, 121)(79, 111, 87, 119)(80, 112, 88, 120)(82, 114, 91, 123)(85, 117, 94, 126)(86, 118, 93, 125)(90, 122, 95, 127)(92, 124, 96, 128) L = (1, 68)(2, 73)(3, 76)(4, 78)(5, 79)(6, 65)(7, 69)(8, 83)(9, 85)(10, 66)(11, 81)(12, 88)(13, 67)(14, 86)(15, 90)(16, 70)(17, 91)(18, 71)(19, 93)(20, 72)(21, 92)(22, 74)(23, 75)(24, 95)(25, 77)(26, 80)(27, 96)(28, 82)(29, 89)(30, 84)(31, 87)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 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 E14.268 Graph:: bipartite v = 18 e = 64 f = 20 degree seq :: [ 4^16, 32^2 ] E14.272 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y1^-1)^2, Y1^-1 * Y3^2 * Y1^-1, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-7 * Y1^-1, (Y1^-1 * Y3^-1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 16, 48, 25, 57, 24, 56, 15, 47, 6, 38, 10, 42, 4, 36, 9, 41, 18, 50, 27, 59, 23, 55, 14, 46, 5, 37)(3, 35, 11, 43, 21, 53, 29, 61, 32, 64, 28, 60, 20, 52, 13, 45, 19, 51, 12, 44, 22, 54, 30, 62, 31, 63, 26, 58, 17, 49, 8, 40)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 77, 109)(69, 101, 75, 107)(70, 102, 76, 108)(71, 103, 81, 113)(73, 105, 84, 116)(74, 106, 83, 115)(78, 110, 85, 117)(79, 111, 86, 118)(80, 112, 90, 122)(82, 114, 92, 124)(87, 119, 93, 125)(88, 120, 94, 126)(89, 121, 95, 127)(91, 123, 96, 128) L = (1, 68)(2, 73)(3, 76)(4, 71)(5, 74)(6, 65)(7, 82)(8, 83)(9, 80)(10, 66)(11, 86)(12, 85)(13, 67)(14, 70)(15, 69)(16, 91)(17, 77)(18, 89)(19, 75)(20, 72)(21, 94)(22, 93)(23, 79)(24, 78)(25, 87)(26, 84)(27, 88)(28, 81)(29, 95)(30, 96)(31, 92)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 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 E14.267 Graph:: bipartite v = 18 e = 64 f = 20 degree seq :: [ 4^16, 32^2 ] E14.273 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1, T1^8, 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, 28, 20, 27, 32, 30, 22, 29, 31, 24, 14, 23, 25, 16, 6, 15, 17, 8, 2, 7, 13, 5)(33, 34, 38, 46, 54, 52, 43, 36)(35, 39, 47, 55, 61, 59, 51, 42)(37, 40, 48, 56, 62, 60, 53, 44)(41, 45, 49, 57, 63, 64, 58, 50) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^8 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E14.281 Transitivity :: ET+ Graph:: bipartite v = 5 e = 32 f = 1 degree seq :: [ 8^4, 32 ] E14.274 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^-1, T1^8, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 3, 9, 8, 2, 7, 17, 16, 6, 15, 25, 24, 14, 23, 31, 30, 22, 29, 32, 27, 19, 26, 28, 20, 11, 18, 21, 12, 4, 10, 13, 5)(33, 34, 38, 46, 54, 51, 43, 36)(35, 39, 47, 55, 61, 58, 50, 42)(37, 40, 48, 56, 62, 59, 52, 44)(41, 49, 57, 63, 64, 60, 53, 45) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^8 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E14.282 Transitivity :: ET+ Graph:: bipartite v = 5 e = 32 f = 1 degree seq :: [ 8^4, 32 ] E14.275 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^3, T1^-8, T1^8, T1 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-2 * T1 ] Map:: non-degenerate R = (1, 3, 9, 19, 22, 32, 28, 16, 6, 15, 24, 12, 4, 10, 20, 30, 26, 29, 18, 8, 2, 7, 17, 23, 11, 21, 31, 27, 14, 25, 13, 5)(33, 34, 38, 46, 58, 54, 43, 36)(35, 39, 47, 57, 61, 64, 53, 42)(37, 40, 48, 59, 62, 51, 55, 44)(41, 49, 56, 45, 50, 60, 63, 52) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^8 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E14.279 Transitivity :: ET+ Graph:: bipartite v = 5 e = 32 f = 1 degree seq :: [ 8^4, 32 ] E14.276 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-4 * T1^3, T1^-8, T1^8, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 3, 9, 19, 14, 27, 31, 23, 11, 21, 18, 8, 2, 7, 17, 29, 26, 32, 24, 12, 4, 10, 20, 16, 6, 15, 28, 30, 22, 25, 13, 5)(33, 34, 38, 46, 58, 54, 43, 36)(35, 39, 47, 59, 64, 57, 53, 42)(37, 40, 48, 51, 61, 62, 55, 44)(41, 49, 60, 63, 56, 45, 50, 52) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^8 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E14.280 Transitivity :: ET+ Graph:: bipartite v = 5 e = 32 f = 1 degree seq :: [ 8^4, 32 ] E14.277 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^10, (T2^-1 * T1^-1)^8 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 32, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 28, 22, 16, 10, 4, 6, 12, 18, 24, 30, 29, 23, 17, 11, 5)(33, 34, 38, 35, 39, 44, 41, 45, 50, 47, 51, 56, 53, 57, 62, 59, 63, 61, 64, 60, 55, 58, 54, 49, 52, 48, 43, 46, 42, 37, 40, 36) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16^32 ) } Outer automorphisms :: reflexible Dual of E14.283 Transitivity :: ET+ Graph:: bipartite v = 2 e = 32 f = 4 degree seq :: [ 32^2 ] E14.278 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (T1, T2^-1), (F * T1)^2, (F * T2)^2, T2^-1 * T1^-5, T2^-4 * T1 * T2^-1 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 26, 16, 6, 15, 25, 32, 30, 22, 12, 4, 10, 20, 28, 18, 8, 2, 7, 17, 27, 31, 24, 14, 11, 21, 29, 23, 13, 5)(33, 34, 38, 46, 44, 37, 40, 48, 56, 54, 45, 50, 58, 63, 62, 55, 60, 51, 59, 64, 61, 52, 41, 49, 57, 53, 42, 35, 39, 47, 43, 36) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16^32 ) } Outer automorphisms :: reflexible Dual of E14.284 Transitivity :: ET+ Graph:: bipartite v = 2 e = 32 f = 4 degree seq :: [ 32^2 ] E14.279 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1, T1^8, 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, 33, 3, 35, 9, 41, 12, 44, 4, 36, 10, 42, 18, 50, 21, 53, 11, 43, 19, 51, 26, 58, 28, 60, 20, 52, 27, 59, 32, 64, 30, 62, 22, 54, 29, 61, 31, 63, 24, 56, 14, 46, 23, 55, 25, 57, 16, 48, 6, 38, 15, 47, 17, 49, 8, 40, 2, 34, 7, 39, 13, 45, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 46)(7, 47)(8, 48)(9, 45)(10, 35)(11, 36)(12, 37)(13, 49)(14, 54)(15, 55)(16, 56)(17, 57)(18, 41)(19, 42)(20, 43)(21, 44)(22, 52)(23, 61)(24, 62)(25, 63)(26, 50)(27, 51)(28, 53)(29, 59)(30, 60)(31, 64)(32, 58) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E14.275 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 5 degree seq :: [ 64 ] E14.280 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^-1, T1^8, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 8, 40, 2, 34, 7, 39, 17, 49, 16, 48, 6, 38, 15, 47, 25, 57, 24, 56, 14, 46, 23, 55, 31, 63, 30, 62, 22, 54, 29, 61, 32, 64, 27, 59, 19, 51, 26, 58, 28, 60, 20, 52, 11, 43, 18, 50, 21, 53, 12, 44, 4, 36, 10, 42, 13, 45, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 46)(7, 47)(8, 48)(9, 49)(10, 35)(11, 36)(12, 37)(13, 41)(14, 54)(15, 55)(16, 56)(17, 57)(18, 42)(19, 43)(20, 44)(21, 45)(22, 51)(23, 61)(24, 62)(25, 63)(26, 50)(27, 52)(28, 53)(29, 58)(30, 59)(31, 64)(32, 60) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E14.276 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 5 degree seq :: [ 64 ] E14.281 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^3, T1^-8, T1^8, T1 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-2 * T1 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 19, 51, 22, 54, 32, 64, 28, 60, 16, 48, 6, 38, 15, 47, 24, 56, 12, 44, 4, 36, 10, 42, 20, 52, 30, 62, 26, 58, 29, 61, 18, 50, 8, 40, 2, 34, 7, 39, 17, 49, 23, 55, 11, 43, 21, 53, 31, 63, 27, 59, 14, 46, 25, 57, 13, 45, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 46)(7, 47)(8, 48)(9, 49)(10, 35)(11, 36)(12, 37)(13, 50)(14, 58)(15, 57)(16, 59)(17, 56)(18, 60)(19, 55)(20, 41)(21, 42)(22, 43)(23, 44)(24, 45)(25, 61)(26, 54)(27, 62)(28, 63)(29, 64)(30, 51)(31, 52)(32, 53) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E14.273 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 5 degree seq :: [ 64 ] E14.282 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-4 * T1^3, T1^-8, T1^8, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 19, 51, 14, 46, 27, 59, 31, 63, 23, 55, 11, 43, 21, 53, 18, 50, 8, 40, 2, 34, 7, 39, 17, 49, 29, 61, 26, 58, 32, 64, 24, 56, 12, 44, 4, 36, 10, 42, 20, 52, 16, 48, 6, 38, 15, 47, 28, 60, 30, 62, 22, 54, 25, 57, 13, 45, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 46)(7, 47)(8, 48)(9, 49)(10, 35)(11, 36)(12, 37)(13, 50)(14, 58)(15, 59)(16, 51)(17, 60)(18, 52)(19, 61)(20, 41)(21, 42)(22, 43)(23, 44)(24, 45)(25, 53)(26, 54)(27, 64)(28, 63)(29, 62)(30, 55)(31, 56)(32, 57) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E14.274 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 5 degree seq :: [ 64 ] E14.283 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^4, T2^8, T1 * T2^-3 * T1 * T2^-2 * T1^2 * T2^-2 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 17, 49, 25, 57, 21, 53, 13, 45, 5, 37)(2, 34, 7, 39, 15, 47, 23, 55, 30, 62, 24, 56, 16, 48, 8, 40)(4, 36, 10, 42, 18, 50, 26, 58, 31, 63, 28, 60, 20, 52, 12, 44)(6, 38, 11, 43, 19, 51, 27, 59, 32, 64, 29, 61, 22, 54, 14, 46) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 44)(7, 43)(8, 46)(9, 47)(10, 35)(11, 36)(12, 37)(13, 48)(14, 52)(15, 51)(16, 54)(17, 55)(18, 41)(19, 42)(20, 45)(21, 56)(22, 60)(23, 59)(24, 61)(25, 62)(26, 49)(27, 50)(28, 53)(29, 63)(30, 64)(31, 57)(32, 58) local type(s) :: { ( 32^16 ) } Outer automorphisms :: reflexible Dual of E14.277 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 32 f = 2 degree seq :: [ 16^4 ] E14.284 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^4, T2^8, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 17, 49, 25, 57, 21, 53, 13, 45, 5, 37)(2, 34, 7, 39, 15, 47, 23, 55, 30, 62, 24, 56, 16, 48, 8, 40)(4, 36, 10, 42, 18, 50, 26, 58, 31, 63, 28, 60, 20, 52, 12, 44)(6, 38, 14, 46, 22, 54, 29, 61, 32, 64, 27, 59, 19, 51, 11, 43) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 42)(7, 46)(8, 43)(9, 47)(10, 35)(11, 36)(12, 37)(13, 48)(14, 50)(15, 54)(16, 51)(17, 55)(18, 41)(19, 44)(20, 45)(21, 56)(22, 58)(23, 61)(24, 59)(25, 62)(26, 49)(27, 52)(28, 53)(29, 63)(30, 64)(31, 57)(32, 60) local type(s) :: { ( 32^16 ) } Outer automorphisms :: reflexible Dual of E14.278 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 32 f = 2 degree seq :: [ 16^4 ] E14.285 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (Y2, Y1^-1), Y3 * Y2^4, Y3^8, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 22, 54, 19, 51, 11, 43, 4, 36)(3, 35, 7, 39, 15, 47, 23, 55, 29, 61, 26, 58, 18, 50, 10, 42)(5, 37, 8, 40, 16, 48, 24, 56, 30, 62, 27, 59, 20, 52, 12, 44)(9, 41, 17, 49, 25, 57, 31, 63, 32, 64, 28, 60, 21, 53, 13, 45)(65, 97, 67, 99, 73, 105, 72, 104, 66, 98, 71, 103, 81, 113, 80, 112, 70, 102, 79, 111, 89, 121, 88, 120, 78, 110, 87, 119, 95, 127, 94, 126, 86, 118, 93, 125, 96, 128, 91, 123, 83, 115, 90, 122, 92, 124, 84, 116, 75, 107, 82, 114, 85, 117, 76, 108, 68, 100, 74, 106, 77, 109, 69, 101) L = (1, 68)(2, 65)(3, 74)(4, 75)(5, 76)(6, 66)(7, 67)(8, 69)(9, 77)(10, 82)(11, 83)(12, 84)(13, 85)(14, 70)(15, 71)(16, 72)(17, 73)(18, 90)(19, 86)(20, 91)(21, 92)(22, 78)(23, 79)(24, 80)(25, 81)(26, 93)(27, 94)(28, 96)(29, 87)(30, 88)(31, 89)(32, 95)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) } Outer automorphisms :: reflexible Dual of E14.296 Graph:: bipartite v = 5 e = 64 f = 33 degree seq :: [ 16^4, 64 ] E14.286 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), Y2^4 * Y1, Y1^8, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 22, 54, 20, 52, 11, 43, 4, 36)(3, 35, 7, 39, 15, 47, 23, 55, 29, 61, 27, 59, 19, 51, 10, 42)(5, 37, 8, 40, 16, 48, 24, 56, 30, 62, 28, 60, 21, 53, 12, 44)(9, 41, 13, 45, 17, 49, 25, 57, 31, 63, 32, 64, 26, 58, 18, 50)(65, 97, 67, 99, 73, 105, 76, 108, 68, 100, 74, 106, 82, 114, 85, 117, 75, 107, 83, 115, 90, 122, 92, 124, 84, 116, 91, 123, 96, 128, 94, 126, 86, 118, 93, 125, 95, 127, 88, 120, 78, 110, 87, 119, 89, 121, 80, 112, 70, 102, 79, 111, 81, 113, 72, 104, 66, 98, 71, 103, 77, 109, 69, 101) L = (1, 68)(2, 65)(3, 74)(4, 75)(5, 76)(6, 66)(7, 67)(8, 69)(9, 82)(10, 83)(11, 84)(12, 85)(13, 73)(14, 70)(15, 71)(16, 72)(17, 77)(18, 90)(19, 91)(20, 86)(21, 92)(22, 78)(23, 79)(24, 80)(25, 81)(26, 96)(27, 93)(28, 94)(29, 87)(30, 88)(31, 89)(32, 95)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) } Outer automorphisms :: reflexible Dual of E14.295 Graph:: bipartite v = 5 e = 64 f = 33 degree seq :: [ 16^4, 64 ] E14.287 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, (Y2, Y1^-1), (R * Y3)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-2 * Y3^-1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y2^-2, Y1^7 * Y3^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 26, 58, 22, 54, 11, 43, 4, 36)(3, 35, 7, 39, 15, 47, 27, 59, 32, 64, 25, 57, 21, 53, 10, 42)(5, 37, 8, 40, 16, 48, 19, 51, 29, 61, 30, 62, 23, 55, 12, 44)(9, 41, 17, 49, 28, 60, 31, 63, 24, 56, 13, 45, 18, 50, 20, 52)(65, 97, 67, 99, 73, 105, 83, 115, 78, 110, 91, 123, 95, 127, 87, 119, 75, 107, 85, 117, 82, 114, 72, 104, 66, 98, 71, 103, 81, 113, 93, 125, 90, 122, 96, 128, 88, 120, 76, 108, 68, 100, 74, 106, 84, 116, 80, 112, 70, 102, 79, 111, 92, 124, 94, 126, 86, 118, 89, 121, 77, 109, 69, 101) L = (1, 68)(2, 65)(3, 74)(4, 75)(5, 76)(6, 66)(7, 67)(8, 69)(9, 84)(10, 85)(11, 86)(12, 87)(13, 88)(14, 70)(15, 71)(16, 72)(17, 73)(18, 77)(19, 80)(20, 82)(21, 89)(22, 90)(23, 94)(24, 95)(25, 96)(26, 78)(27, 79)(28, 81)(29, 83)(30, 93)(31, 92)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) } Outer automorphisms :: reflexible Dual of E14.294 Graph:: bipartite v = 5 e = 64 f = 33 degree seq :: [ 16^4, 64 ] E14.288 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, Y1 * Y3, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^2 * Y1 * Y2^2 * Y1 * Y3^-1, Y2 * Y3^-1 * Y1 * Y2^3 * Y3^-1, Y1^8, Y1^3 * Y2^-1 * Y1 * Y3^-1 * Y2^-3, Y2^-1 * Y3 * Y2^-1 * Y1^-2 * Y2^-3 * Y3^7 * Y2 * Y1^-1 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 26, 58, 22, 54, 11, 43, 4, 36)(3, 35, 7, 39, 15, 47, 25, 57, 29, 61, 32, 64, 21, 53, 10, 42)(5, 37, 8, 40, 16, 48, 27, 59, 30, 62, 19, 51, 23, 55, 12, 44)(9, 41, 17, 49, 24, 56, 13, 45, 18, 50, 28, 60, 31, 63, 20, 52)(65, 97, 67, 99, 73, 105, 83, 115, 86, 118, 96, 128, 92, 124, 80, 112, 70, 102, 79, 111, 88, 120, 76, 108, 68, 100, 74, 106, 84, 116, 94, 126, 90, 122, 93, 125, 82, 114, 72, 104, 66, 98, 71, 103, 81, 113, 87, 119, 75, 107, 85, 117, 95, 127, 91, 123, 78, 110, 89, 121, 77, 109, 69, 101) L = (1, 68)(2, 65)(3, 74)(4, 75)(5, 76)(6, 66)(7, 67)(8, 69)(9, 84)(10, 85)(11, 86)(12, 87)(13, 88)(14, 70)(15, 71)(16, 72)(17, 73)(18, 77)(19, 94)(20, 95)(21, 96)(22, 90)(23, 83)(24, 81)(25, 79)(26, 78)(27, 80)(28, 82)(29, 89)(30, 91)(31, 92)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) } Outer automorphisms :: reflexible Dual of E14.293 Graph:: bipartite v = 5 e = 64 f = 33 degree seq :: [ 16^4, 64 ] E14.289 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y2^3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1^10, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 33, 2, 34, 6, 38, 12, 44, 18, 50, 24, 56, 30, 62, 27, 59, 21, 53, 15, 47, 9, 41, 3, 35, 7, 39, 13, 45, 19, 51, 25, 57, 31, 63, 29, 61, 23, 55, 17, 49, 11, 43, 5, 37, 8, 40, 14, 46, 20, 52, 26, 58, 32, 64, 28, 60, 22, 54, 16, 48, 10, 42, 4, 36)(65, 97, 67, 99, 72, 104, 66, 98, 71, 103, 78, 110, 70, 102, 77, 109, 84, 116, 76, 108, 83, 115, 90, 122, 82, 114, 89, 121, 96, 128, 88, 120, 95, 127, 92, 124, 94, 126, 93, 125, 86, 118, 91, 123, 87, 119, 80, 112, 85, 117, 81, 113, 74, 106, 79, 111, 75, 107, 68, 100, 73, 105, 69, 101) L = (1, 67)(2, 71)(3, 72)(4, 73)(5, 65)(6, 77)(7, 78)(8, 66)(9, 69)(10, 79)(11, 68)(12, 83)(13, 84)(14, 70)(15, 75)(16, 85)(17, 74)(18, 89)(19, 90)(20, 76)(21, 81)(22, 91)(23, 80)(24, 95)(25, 96)(26, 82)(27, 87)(28, 94)(29, 86)(30, 93)(31, 92)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E14.292 Graph:: bipartite v = 2 e = 64 f = 36 degree seq :: [ 64^2 ] E14.290 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^-1 * Y2^-5, Y1^-1 * Y2 * Y1^-2 * Y2 * Y1^-3, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 24, 56, 20, 52, 9, 41, 17, 49, 27, 59, 32, 64, 30, 62, 23, 55, 12, 44, 5, 37, 8, 40, 16, 48, 26, 58, 21, 53, 10, 42, 3, 35, 7, 39, 15, 47, 25, 57, 31, 63, 29, 61, 19, 51, 13, 45, 18, 50, 28, 60, 22, 54, 11, 43, 4, 36)(65, 97, 67, 99, 73, 105, 83, 115, 76, 108, 68, 100, 74, 106, 84, 116, 93, 125, 87, 119, 75, 107, 85, 117, 88, 120, 95, 127, 94, 126, 86, 118, 90, 122, 78, 110, 89, 121, 96, 128, 92, 124, 80, 112, 70, 102, 79, 111, 91, 123, 82, 114, 72, 104, 66, 98, 71, 103, 81, 113, 77, 109, 69, 101) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 81)(8, 66)(9, 83)(10, 84)(11, 85)(12, 68)(13, 69)(14, 89)(15, 91)(16, 70)(17, 77)(18, 72)(19, 76)(20, 93)(21, 88)(22, 90)(23, 75)(24, 95)(25, 96)(26, 78)(27, 82)(28, 80)(29, 87)(30, 86)(31, 94)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E14.291 Graph:: bipartite v = 2 e = 64 f = 36 degree seq :: [ 64^2 ] E14.291 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y3^4 * Y2, Y2^8, (Y2^-1 * Y3)^32, (Y3^-1 * Y1^-1)^32 ] Map:: R = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)(65, 97, 66, 98, 70, 102, 78, 110, 86, 118, 84, 116, 75, 107, 68, 100)(67, 99, 71, 103, 79, 111, 87, 119, 93, 125, 91, 123, 83, 115, 74, 106)(69, 101, 72, 104, 80, 112, 88, 120, 94, 126, 92, 124, 85, 117, 76, 108)(73, 105, 77, 109, 81, 113, 89, 121, 95, 127, 96, 128, 90, 122, 82, 114) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 77)(8, 66)(9, 76)(10, 82)(11, 83)(12, 68)(13, 69)(14, 87)(15, 81)(16, 70)(17, 72)(18, 85)(19, 90)(20, 91)(21, 75)(22, 93)(23, 89)(24, 78)(25, 80)(26, 92)(27, 96)(28, 84)(29, 95)(30, 86)(31, 88)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64, 64 ), ( 64^16 ) } Outer automorphisms :: reflexible Dual of E14.290 Graph:: simple bipartite v = 36 e = 64 f = 2 degree seq :: [ 2^32, 16^4 ] E14.292 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3^-4 * Y2, Y2^8, 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^-2 * Y2^-1, (Y3^-1 * Y1^-1)^32 ] Map:: R = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)(65, 97, 66, 98, 70, 102, 78, 110, 86, 118, 83, 115, 75, 107, 68, 100)(67, 99, 71, 103, 79, 111, 87, 119, 93, 125, 90, 122, 82, 114, 74, 106)(69, 101, 72, 104, 80, 112, 88, 120, 94, 126, 91, 123, 84, 116, 76, 108)(73, 105, 81, 113, 89, 121, 95, 127, 96, 128, 92, 124, 85, 117, 77, 109) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 81)(8, 66)(9, 72)(10, 77)(11, 82)(12, 68)(13, 69)(14, 87)(15, 89)(16, 70)(17, 80)(18, 85)(19, 90)(20, 75)(21, 76)(22, 93)(23, 95)(24, 78)(25, 88)(26, 92)(27, 83)(28, 84)(29, 96)(30, 86)(31, 94)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64, 64 ), ( 64^16 ) } Outer automorphisms :: reflexible Dual of E14.289 Graph:: simple bipartite v = 36 e = 64 f = 2 degree seq :: [ 2^32, 16^4 ] E14.293 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3 * Y1^4, (R * Y2 * Y3^-1)^2, Y3^8, (Y3 * Y2^-1)^8, 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, 33, 2, 34, 6, 38, 12, 44, 5, 37, 8, 40, 14, 46, 20, 52, 13, 45, 16, 48, 22, 54, 28, 60, 21, 53, 24, 56, 29, 61, 31, 63, 25, 57, 30, 62, 32, 64, 26, 58, 17, 49, 23, 55, 27, 59, 18, 50, 9, 41, 15, 47, 19, 51, 10, 42, 3, 35, 7, 39, 11, 43, 4, 36)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 75)(7, 79)(8, 66)(9, 81)(10, 82)(11, 83)(12, 68)(13, 69)(14, 70)(15, 87)(16, 72)(17, 89)(18, 90)(19, 91)(20, 76)(21, 77)(22, 78)(23, 94)(24, 80)(25, 85)(26, 95)(27, 96)(28, 84)(29, 86)(30, 88)(31, 92)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16, 64 ), ( 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64 ) } Outer automorphisms :: reflexible Dual of E14.288 Graph:: bipartite v = 33 e = 64 f = 5 degree seq :: [ 2^32, 64 ] E14.294 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^-1 * Y1^4, (R * Y2 * Y3^-1)^2, Y3^8, (Y3 * Y2^-1)^8, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 33, 2, 34, 6, 38, 10, 42, 3, 35, 7, 39, 14, 46, 18, 50, 9, 41, 15, 47, 22, 54, 26, 58, 17, 49, 23, 55, 29, 61, 31, 63, 25, 57, 30, 62, 32, 64, 28, 60, 21, 53, 24, 56, 27, 59, 20, 52, 13, 45, 16, 48, 19, 51, 12, 44, 5, 37, 8, 40, 11, 43, 4, 36)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 78)(7, 79)(8, 66)(9, 81)(10, 82)(11, 70)(12, 68)(13, 69)(14, 86)(15, 87)(16, 72)(17, 89)(18, 90)(19, 75)(20, 76)(21, 77)(22, 93)(23, 94)(24, 80)(25, 85)(26, 95)(27, 83)(28, 84)(29, 96)(30, 88)(31, 92)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16, 64 ), ( 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64 ) } Outer automorphisms :: reflexible Dual of E14.287 Graph:: bipartite v = 33 e = 64 f = 5 degree seq :: [ 2^32, 64 ] E14.295 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^3 * Y1^4, Y3^-8, Y3^8, Y3^-1 * Y1 * Y3^-1 * Y1^2 * Y3^-3 * Y1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 25, 57, 28, 60, 31, 63, 20, 52, 9, 41, 17, 49, 23, 55, 12, 44, 5, 37, 8, 40, 16, 48, 26, 58, 29, 61, 32, 64, 21, 53, 10, 42, 3, 35, 7, 39, 15, 47, 24, 56, 13, 45, 18, 50, 27, 59, 30, 62, 19, 51, 22, 54, 11, 43, 4, 36)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 81)(8, 66)(9, 83)(10, 84)(11, 85)(12, 68)(13, 69)(14, 88)(15, 87)(16, 70)(17, 86)(18, 72)(19, 93)(20, 94)(21, 95)(22, 96)(23, 75)(24, 76)(25, 77)(26, 78)(27, 80)(28, 82)(29, 89)(30, 90)(31, 91)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16, 64 ), ( 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64 ) } Outer automorphisms :: reflexible Dual of E14.286 Graph:: bipartite v = 33 e = 64 f = 5 degree seq :: [ 2^32, 64 ] E14.296 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^4 * Y3^-3, Y3^8, Y3^16, (Y3 * Y2^-1)^8, Y3^24, 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 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 19, 51, 28, 60, 31, 63, 24, 56, 13, 45, 18, 50, 21, 53, 10, 42, 3, 35, 7, 39, 15, 47, 26, 58, 29, 61, 30, 62, 23, 55, 12, 44, 5, 37, 8, 40, 16, 48, 20, 52, 9, 41, 17, 49, 27, 59, 32, 64, 25, 57, 22, 54, 11, 43, 4, 36)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 81)(8, 66)(9, 83)(10, 84)(11, 85)(12, 68)(13, 69)(14, 90)(15, 91)(16, 70)(17, 92)(18, 72)(19, 93)(20, 78)(21, 80)(22, 82)(23, 75)(24, 76)(25, 77)(26, 96)(27, 95)(28, 94)(29, 89)(30, 86)(31, 87)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16, 64 ), ( 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64 ) } Outer automorphisms :: reflexible Dual of E14.285 Graph:: bipartite v = 33 e = 64 f = 5 degree seq :: [ 2^32, 64 ] E14.297 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 35, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T1^5, T2^-7 * T1^2, (T1^-1 * T2^-1)^35 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 25, 15, 6, 14, 24, 34, 32, 22, 12, 4, 10, 19, 29, 27, 17, 8, 2, 7, 16, 26, 35, 31, 21, 11, 20, 30, 33, 23, 13, 5)(36, 37, 41, 46, 39)(38, 42, 49, 55, 45)(40, 43, 50, 56, 47)(44, 51, 59, 65, 54)(48, 52, 60, 66, 57)(53, 61, 69, 68, 64)(58, 62, 63, 70, 67) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 70^5 ), ( 70^35 ) } Outer automorphisms :: reflexible Dual of E14.303 Transitivity :: ET+ Graph:: bipartite v = 8 e = 35 f = 1 degree seq :: [ 5^7, 35 ] E14.298 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 35, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^-7 * T1^-1, (T1^-1 * T2^-1)^35 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 22, 12, 4, 10, 19, 29, 34, 31, 21, 11, 20, 30, 35, 33, 25, 15, 6, 14, 24, 32, 27, 17, 8, 2, 7, 16, 26, 23, 13, 5)(36, 37, 41, 46, 39)(38, 42, 49, 55, 45)(40, 43, 50, 56, 47)(44, 51, 59, 65, 54)(48, 52, 60, 66, 57)(53, 61, 67, 70, 64)(58, 62, 68, 69, 63) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 70^5 ), ( 70^35 ) } Outer automorphisms :: reflexible Dual of E14.302 Transitivity :: ET+ Graph:: bipartite v = 8 e = 35 f = 1 degree seq :: [ 5^7, 35 ] E14.299 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 35, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^7 * T1^-1, (T1^-1 * T2^-1)^35 ] Map:: non-degenerate R = (1, 3, 9, 18, 27, 17, 8, 2, 7, 16, 26, 33, 25, 15, 6, 14, 24, 32, 35, 30, 21, 11, 20, 29, 34, 31, 22, 12, 4, 10, 19, 28, 23, 13, 5)(36, 37, 41, 46, 39)(38, 42, 49, 55, 45)(40, 43, 50, 56, 47)(44, 51, 59, 64, 54)(48, 52, 60, 65, 57)(53, 61, 67, 69, 63)(58, 62, 68, 70, 66) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 70^5 ), ( 70^35 ) } Outer automorphisms :: reflexible Dual of E14.301 Transitivity :: ET+ Graph:: bipartite v = 8 e = 35 f = 1 degree seq :: [ 5^7, 35 ] E14.300 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 35, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1 * T2^-1 * T1 * T2^-3 * T1, T1^2 * T2 * T1^6, (T1^-1 * T2^-1)^5 ] Map:: non-degenerate R = (1, 3, 9, 19, 14, 27, 34, 32, 23, 11, 21, 18, 8, 2, 7, 17, 29, 26, 30, 33, 24, 12, 4, 10, 20, 16, 6, 15, 28, 35, 31, 22, 25, 13, 5)(36, 37, 41, 49, 61, 66, 58, 47, 40, 43, 51, 54, 64, 70, 67, 59, 48, 53, 55, 44, 52, 63, 69, 68, 60, 56, 45, 38, 42, 50, 62, 65, 57, 46, 39) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 10^35 ) } Outer automorphisms :: reflexible Dual of E14.304 Transitivity :: ET+ Graph:: bipartite v = 2 e = 35 f = 7 degree seq :: [ 35^2 ] E14.301 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 35, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T1^5, T2^-7 * T1^2, (T1^-1 * T2^-1)^35 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 18, 53, 28, 63, 25, 60, 15, 50, 6, 41, 14, 49, 24, 59, 34, 69, 32, 67, 22, 57, 12, 47, 4, 39, 10, 45, 19, 54, 29, 64, 27, 62, 17, 52, 8, 43, 2, 37, 7, 42, 16, 51, 26, 61, 35, 70, 31, 66, 21, 56, 11, 46, 20, 55, 30, 65, 33, 68, 23, 58, 13, 48, 5, 40) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 46)(7, 49)(8, 50)(9, 51)(10, 38)(11, 39)(12, 40)(13, 52)(14, 55)(15, 56)(16, 59)(17, 60)(18, 61)(19, 44)(20, 45)(21, 47)(22, 48)(23, 62)(24, 65)(25, 66)(26, 69)(27, 63)(28, 70)(29, 53)(30, 54)(31, 57)(32, 58)(33, 64)(34, 68)(35, 67) local type(s) :: { ( 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35 ) } Outer automorphisms :: reflexible Dual of E14.299 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 35 f = 8 degree seq :: [ 70 ] E14.302 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 35, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^-7 * T1^-1, (T1^-1 * T2^-1)^35 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 18, 53, 28, 63, 22, 57, 12, 47, 4, 39, 10, 45, 19, 54, 29, 64, 34, 69, 31, 66, 21, 56, 11, 46, 20, 55, 30, 65, 35, 70, 33, 68, 25, 60, 15, 50, 6, 41, 14, 49, 24, 59, 32, 67, 27, 62, 17, 52, 8, 43, 2, 37, 7, 42, 16, 51, 26, 61, 23, 58, 13, 48, 5, 40) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 46)(7, 49)(8, 50)(9, 51)(10, 38)(11, 39)(12, 40)(13, 52)(14, 55)(15, 56)(16, 59)(17, 60)(18, 61)(19, 44)(20, 45)(21, 47)(22, 48)(23, 62)(24, 65)(25, 66)(26, 67)(27, 68)(28, 58)(29, 53)(30, 54)(31, 57)(32, 70)(33, 69)(34, 63)(35, 64) local type(s) :: { ( 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35 ) } Outer automorphisms :: reflexible Dual of E14.298 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 35 f = 8 degree seq :: [ 70 ] E14.303 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 35, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^7 * T1^-1, (T1^-1 * T2^-1)^35 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 18, 53, 27, 62, 17, 52, 8, 43, 2, 37, 7, 42, 16, 51, 26, 61, 33, 68, 25, 60, 15, 50, 6, 41, 14, 49, 24, 59, 32, 67, 35, 70, 30, 65, 21, 56, 11, 46, 20, 55, 29, 64, 34, 69, 31, 66, 22, 57, 12, 47, 4, 39, 10, 45, 19, 54, 28, 63, 23, 58, 13, 48, 5, 40) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 46)(7, 49)(8, 50)(9, 51)(10, 38)(11, 39)(12, 40)(13, 52)(14, 55)(15, 56)(16, 59)(17, 60)(18, 61)(19, 44)(20, 45)(21, 47)(22, 48)(23, 62)(24, 64)(25, 65)(26, 67)(27, 68)(28, 53)(29, 54)(30, 57)(31, 58)(32, 69)(33, 70)(34, 63)(35, 66) local type(s) :: { ( 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35 ) } Outer automorphisms :: reflexible Dual of E14.297 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 35 f = 8 degree seq :: [ 70 ] E14.304 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 35, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-5, T2^5, T2^-2 * T1^7, (T1^-1 * T2^-1)^35 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 13, 48, 5, 40)(2, 37, 7, 42, 17, 52, 18, 53, 8, 43)(4, 39, 10, 45, 19, 54, 23, 58, 12, 47)(6, 41, 15, 50, 27, 62, 28, 63, 16, 51)(11, 46, 20, 55, 29, 64, 33, 68, 22, 57)(14, 49, 25, 60, 35, 70, 31, 66, 26, 61)(21, 56, 30, 65, 24, 59, 34, 69, 32, 67) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 49)(7, 50)(8, 51)(9, 52)(10, 38)(11, 39)(12, 40)(13, 53)(14, 59)(15, 60)(16, 61)(17, 62)(18, 63)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 64)(25, 69)(26, 65)(27, 70)(28, 66)(29, 54)(30, 55)(31, 56)(32, 57)(33, 58)(34, 68)(35, 67) local type(s) :: { ( 35^10 ) } Outer automorphisms :: reflexible Dual of E14.300 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 35 f = 2 degree seq :: [ 10^7 ] E14.305 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), (R * Y2)^2, Y1^-2 * Y3^2 * Y1^-1, Y2 * Y3 * Y2 * Y3 * Y1 * Y2^-2 * Y1, Y2^-1 * Y1 * Y2^-2 * Y1 * Y2^-4, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 36, 2, 37, 6, 41, 11, 46, 4, 39)(3, 38, 7, 42, 14, 49, 20, 55, 10, 45)(5, 40, 8, 43, 15, 50, 21, 56, 12, 47)(9, 44, 16, 51, 24, 59, 30, 65, 19, 54)(13, 48, 17, 52, 25, 60, 31, 66, 22, 57)(18, 53, 26, 61, 34, 69, 33, 68, 29, 64)(23, 58, 27, 62, 28, 63, 35, 70, 32, 67)(71, 106, 73, 108, 79, 114, 88, 123, 98, 133, 95, 130, 85, 120, 76, 111, 84, 119, 94, 129, 104, 139, 102, 137, 92, 127, 82, 117, 74, 109, 80, 115, 89, 124, 99, 134, 97, 132, 87, 122, 78, 113, 72, 107, 77, 112, 86, 121, 96, 131, 105, 140, 101, 136, 91, 126, 81, 116, 90, 125, 100, 135, 103, 138, 93, 128, 83, 118, 75, 110) L = (1, 74)(2, 71)(3, 80)(4, 81)(5, 82)(6, 72)(7, 73)(8, 75)(9, 89)(10, 90)(11, 76)(12, 91)(13, 92)(14, 77)(15, 78)(16, 79)(17, 83)(18, 99)(19, 100)(20, 84)(21, 85)(22, 101)(23, 102)(24, 86)(25, 87)(26, 88)(27, 93)(28, 97)(29, 103)(30, 94)(31, 95)(32, 105)(33, 104)(34, 96)(35, 98)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ), ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ) } Outer automorphisms :: reflexible Dual of E14.312 Graph:: bipartite v = 8 e = 70 f = 36 degree seq :: [ 10^7, 70 ] E14.306 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y3)^2, (Y2, Y1^-1), (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1^5, Y3^5, Y3 * Y2^-7, 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 * Y3^2 * Y2^2 ] Map:: R = (1, 36, 2, 37, 6, 41, 11, 46, 4, 39)(3, 38, 7, 42, 14, 49, 20, 55, 10, 45)(5, 40, 8, 43, 15, 50, 21, 56, 12, 47)(9, 44, 16, 51, 24, 59, 30, 65, 19, 54)(13, 48, 17, 52, 25, 60, 31, 66, 22, 57)(18, 53, 26, 61, 32, 67, 35, 70, 29, 64)(23, 58, 27, 62, 33, 68, 34, 69, 28, 63)(71, 106, 73, 108, 79, 114, 88, 123, 98, 133, 92, 127, 82, 117, 74, 109, 80, 115, 89, 124, 99, 134, 104, 139, 101, 136, 91, 126, 81, 116, 90, 125, 100, 135, 105, 140, 103, 138, 95, 130, 85, 120, 76, 111, 84, 119, 94, 129, 102, 137, 97, 132, 87, 122, 78, 113, 72, 107, 77, 112, 86, 121, 96, 131, 93, 128, 83, 118, 75, 110) L = (1, 74)(2, 71)(3, 80)(4, 81)(5, 82)(6, 72)(7, 73)(8, 75)(9, 89)(10, 90)(11, 76)(12, 91)(13, 92)(14, 77)(15, 78)(16, 79)(17, 83)(18, 99)(19, 100)(20, 84)(21, 85)(22, 101)(23, 98)(24, 86)(25, 87)(26, 88)(27, 93)(28, 104)(29, 105)(30, 94)(31, 95)(32, 96)(33, 97)(34, 103)(35, 102)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ), ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ) } Outer automorphisms :: reflexible Dual of E14.311 Graph:: bipartite v = 8 e = 70 f = 36 degree seq :: [ 10^7, 70 ] E14.307 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y1^5, Y2^7 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 36, 2, 37, 6, 41, 11, 46, 4, 39)(3, 38, 7, 42, 14, 49, 20, 55, 10, 45)(5, 40, 8, 43, 15, 50, 21, 56, 12, 47)(9, 44, 16, 51, 24, 59, 29, 64, 19, 54)(13, 48, 17, 52, 25, 60, 30, 65, 22, 57)(18, 53, 26, 61, 32, 67, 34, 69, 28, 63)(23, 58, 27, 62, 33, 68, 35, 70, 31, 66)(71, 106, 73, 108, 79, 114, 88, 123, 97, 132, 87, 122, 78, 113, 72, 107, 77, 112, 86, 121, 96, 131, 103, 138, 95, 130, 85, 120, 76, 111, 84, 119, 94, 129, 102, 137, 105, 140, 100, 135, 91, 126, 81, 116, 90, 125, 99, 134, 104, 139, 101, 136, 92, 127, 82, 117, 74, 109, 80, 115, 89, 124, 98, 133, 93, 128, 83, 118, 75, 110) L = (1, 74)(2, 71)(3, 80)(4, 81)(5, 82)(6, 72)(7, 73)(8, 75)(9, 89)(10, 90)(11, 76)(12, 91)(13, 92)(14, 77)(15, 78)(16, 79)(17, 83)(18, 98)(19, 99)(20, 84)(21, 85)(22, 100)(23, 101)(24, 86)(25, 87)(26, 88)(27, 93)(28, 104)(29, 94)(30, 95)(31, 105)(32, 96)(33, 97)(34, 102)(35, 103)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ), ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ) } Outer automorphisms :: reflexible Dual of E14.310 Graph:: bipartite v = 8 e = 70 f = 36 degree seq :: [ 10^7, 70 ] E14.308 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y1^3 * Y2^-1 * Y1 * Y2^-2, Y2^7 * Y1 * Y2, (Y3^-1 * Y1^-1)^5 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 19, 54, 28, 63, 35, 70, 31, 66, 24, 59, 13, 48, 18, 53, 21, 56, 10, 45, 3, 38, 7, 42, 15, 50, 26, 61, 29, 64, 33, 68, 30, 65, 23, 58, 12, 47, 5, 40, 8, 43, 16, 51, 20, 55, 9, 44, 17, 52, 27, 62, 34, 69, 32, 67, 25, 60, 22, 57, 11, 46, 4, 39)(71, 106, 73, 108, 79, 114, 89, 124, 99, 134, 102, 137, 94, 129, 82, 117, 74, 109, 80, 115, 90, 125, 84, 119, 96, 131, 104, 139, 101, 136, 93, 128, 81, 116, 91, 126, 86, 121, 76, 111, 85, 120, 97, 132, 105, 140, 100, 135, 92, 127, 88, 123, 78, 113, 72, 107, 77, 112, 87, 122, 98, 133, 103, 138, 95, 130, 83, 118, 75, 110) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 89)(10, 90)(11, 91)(12, 74)(13, 75)(14, 96)(15, 97)(16, 76)(17, 98)(18, 78)(19, 99)(20, 84)(21, 86)(22, 88)(23, 81)(24, 82)(25, 83)(26, 104)(27, 105)(28, 103)(29, 102)(30, 92)(31, 93)(32, 94)(33, 95)(34, 101)(35, 100)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 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 E14.309 Graph:: bipartite v = 2 e = 70 f = 42 degree seq :: [ 70^2 ] E14.309 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2), (R * Y2)^2, Y2^5, Y2^5, Y3^7 * Y2^2, (Y2^-1 * Y3)^35, (Y3^-1 * Y1^-1)^35 ] Map:: R = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70)(71, 106, 72, 107, 76, 111, 81, 116, 74, 109)(73, 108, 77, 112, 84, 119, 90, 125, 80, 115)(75, 110, 78, 113, 85, 120, 91, 126, 82, 117)(79, 114, 86, 121, 94, 129, 100, 135, 89, 124)(83, 118, 87, 122, 95, 130, 101, 136, 92, 127)(88, 123, 96, 131, 103, 138, 105, 140, 99, 134)(93, 128, 97, 132, 104, 139, 98, 133, 102, 137) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 84)(7, 86)(8, 72)(9, 88)(10, 89)(11, 90)(12, 74)(13, 75)(14, 94)(15, 76)(16, 96)(17, 78)(18, 98)(19, 99)(20, 100)(21, 81)(22, 82)(23, 83)(24, 103)(25, 85)(26, 102)(27, 87)(28, 101)(29, 104)(30, 105)(31, 91)(32, 92)(33, 93)(34, 95)(35, 97)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 70, 70 ), ( 70^10 ) } Outer automorphisms :: reflexible Dual of E14.308 Graph:: simple bipartite v = 42 e = 70 f = 2 degree seq :: [ 2^35, 10^7 ] E14.310 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^-5, Y3^5, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^7, (Y3 * Y2^-1)^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 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 24, 59, 29, 64, 19, 54, 9, 44, 17, 52, 27, 62, 35, 70, 32, 67, 22, 57, 12, 47, 5, 40, 8, 43, 16, 51, 26, 61, 30, 65, 20, 55, 10, 45, 3, 38, 7, 42, 15, 50, 25, 60, 34, 69, 33, 68, 23, 58, 13, 48, 18, 53, 28, 63, 31, 66, 21, 56, 11, 46, 4, 39)(71, 106)(72, 107)(73, 108)(74, 109)(75, 110)(76, 111)(77, 112)(78, 113)(79, 114)(80, 115)(81, 116)(82, 117)(83, 118)(84, 119)(85, 120)(86, 121)(87, 122)(88, 123)(89, 124)(90, 125)(91, 126)(92, 127)(93, 128)(94, 129)(95, 130)(96, 131)(97, 132)(98, 133)(99, 134)(100, 135)(101, 136)(102, 137)(103, 138)(104, 139)(105, 140) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 83)(10, 89)(11, 90)(12, 74)(13, 75)(14, 95)(15, 97)(16, 76)(17, 88)(18, 78)(19, 93)(20, 99)(21, 100)(22, 81)(23, 82)(24, 104)(25, 105)(26, 84)(27, 98)(28, 86)(29, 103)(30, 94)(31, 96)(32, 91)(33, 92)(34, 102)(35, 101)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 10, 70 ), ( 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70 ) } Outer automorphisms :: reflexible Dual of E14.307 Graph:: bipartite v = 36 e = 70 f = 8 degree seq :: [ 2^35, 70 ] E14.311 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^5, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-7, (Y3 * Y2^-1)^5, Y1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^2 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 24, 59, 22, 57, 12, 47, 5, 40, 8, 43, 16, 51, 26, 61, 32, 67, 31, 66, 23, 58, 13, 48, 18, 53, 28, 63, 34, 69, 35, 70, 29, 64, 19, 54, 9, 44, 17, 52, 27, 62, 33, 68, 30, 65, 20, 55, 10, 45, 3, 38, 7, 42, 15, 50, 25, 60, 21, 56, 11, 46, 4, 39)(71, 106)(72, 107)(73, 108)(74, 109)(75, 110)(76, 111)(77, 112)(78, 113)(79, 114)(80, 115)(81, 116)(82, 117)(83, 118)(84, 119)(85, 120)(86, 121)(87, 122)(88, 123)(89, 124)(90, 125)(91, 126)(92, 127)(93, 128)(94, 129)(95, 130)(96, 131)(97, 132)(98, 133)(99, 134)(100, 135)(101, 136)(102, 137)(103, 138)(104, 139)(105, 140) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 83)(10, 89)(11, 90)(12, 74)(13, 75)(14, 95)(15, 97)(16, 76)(17, 88)(18, 78)(19, 93)(20, 99)(21, 100)(22, 81)(23, 82)(24, 91)(25, 103)(26, 84)(27, 98)(28, 86)(29, 101)(30, 105)(31, 92)(32, 94)(33, 104)(34, 96)(35, 102)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 10, 70 ), ( 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70 ) } Outer automorphisms :: reflexible Dual of E14.306 Graph:: bipartite v = 36 e = 70 f = 8 degree seq :: [ 2^35, 70 ] E14.312 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^5, (R * Y2 * Y3^-1)^2, Y3 * Y1^-7, (Y3 * Y2^-1)^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 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 24, 59, 20, 55, 10, 45, 3, 38, 7, 42, 15, 50, 25, 60, 32, 67, 29, 64, 19, 54, 9, 44, 17, 52, 27, 62, 33, 68, 35, 70, 31, 66, 23, 58, 13, 48, 18, 53, 28, 63, 34, 69, 30, 65, 22, 57, 12, 47, 5, 40, 8, 43, 16, 51, 26, 61, 21, 56, 11, 46, 4, 39)(71, 106)(72, 107)(73, 108)(74, 109)(75, 110)(76, 111)(77, 112)(78, 113)(79, 114)(80, 115)(81, 116)(82, 117)(83, 118)(84, 119)(85, 120)(86, 121)(87, 122)(88, 123)(89, 124)(90, 125)(91, 126)(92, 127)(93, 128)(94, 129)(95, 130)(96, 131)(97, 132)(98, 133)(99, 134)(100, 135)(101, 136)(102, 137)(103, 138)(104, 139)(105, 140) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 83)(10, 89)(11, 90)(12, 74)(13, 75)(14, 95)(15, 97)(16, 76)(17, 88)(18, 78)(19, 93)(20, 99)(21, 94)(22, 81)(23, 82)(24, 102)(25, 103)(26, 84)(27, 98)(28, 86)(29, 101)(30, 91)(31, 92)(32, 105)(33, 104)(34, 96)(35, 100)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 10, 70 ), ( 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70 ) } Outer automorphisms :: reflexible Dual of E14.305 Graph:: bipartite v = 36 e = 70 f = 8 degree seq :: [ 2^35, 70 ] E14.313 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 6, 9}) Quotient :: halfedge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y1^-1 * Y2)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y2 * Y1^-1 * Y3 * Y2 * Y3, Y1^9, (Y2 * Y1 * Y3)^6 ] Map:: non-degenerate R = (1, 38, 2, 42, 6, 50, 14, 58, 22, 65, 29, 57, 21, 49, 13, 41, 5, 37)(3, 45, 9, 54, 18, 62, 26, 69, 33, 66, 30, 59, 23, 51, 15, 43, 7, 39)(4, 47, 11, 56, 20, 64, 28, 71, 35, 67, 31, 60, 24, 52, 16, 44, 8, 40)(10, 48, 12, 53, 17, 61, 25, 68, 32, 72, 36, 70, 34, 63, 27, 55, 19, 46) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 17)(10, 11)(13, 18)(14, 23)(16, 25)(19, 20)(21, 26)(22, 30)(24, 32)(27, 28)(29, 33)(31, 36)(34, 35)(37, 40)(38, 44)(39, 46)(41, 47)(42, 52)(43, 48)(45, 55)(49, 56)(50, 60)(51, 53)(54, 63)(57, 64)(58, 67)(59, 61)(62, 70)(65, 71)(66, 68)(69, 72) local type(s) :: { ( 12^18 ) } Outer automorphisms :: reflexible Dual of E14.314 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 36 f = 6 degree seq :: [ 18^4 ] E14.314 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 6, 9}) Quotient :: halfedge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^2, Y1^6, Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3, Y1 * Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y1^2 ] Map:: non-degenerate R = (1, 38, 2, 42, 6, 50, 14, 49, 13, 41, 5, 37)(3, 45, 9, 55, 19, 61, 25, 51, 15, 43, 7, 39)(4, 47, 11, 58, 22, 62, 26, 52, 16, 44, 8, 40)(10, 53, 17, 63, 27, 69, 33, 66, 30, 56, 20, 46)(12, 54, 18, 64, 28, 70, 34, 67, 31, 59, 23, 48)(21, 60, 24, 68, 32, 72, 36, 71, 35, 65, 29, 57) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 25)(16, 28)(17, 29)(20, 24)(22, 31)(26, 34)(27, 35)(30, 32)(33, 36)(37, 40)(38, 44)(39, 46)(41, 47)(42, 52)(43, 53)(45, 56)(48, 60)(49, 58)(50, 62)(51, 63)(54, 57)(55, 66)(59, 68)(61, 69)(64, 65)(67, 72)(70, 71) local type(s) :: { ( 18^12 ) } Outer automorphisms :: reflexible Dual of E14.313 Transitivity :: VT+ AT Graph:: bipartite v = 6 e = 36 f = 4 degree seq :: [ 12^6 ] E14.315 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 9}) Quotient :: edge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, (Y3 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^6, Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, (Y1 * Y3^-1 * Y2)^9 ] Map:: R = (1, 37, 4, 40, 12, 48, 24, 60, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 28, 64, 18, 54, 8, 44)(3, 39, 10, 46, 22, 58, 32, 68, 23, 59, 11, 47)(6, 42, 15, 51, 26, 62, 34, 70, 27, 63, 16, 52)(9, 45, 20, 56, 30, 66, 36, 72, 31, 67, 21, 57)(14, 50, 19, 55, 29, 65, 35, 71, 33, 69, 25, 61)(73, 74)(75, 81)(76, 80)(77, 79)(78, 86)(82, 93)(83, 92)(84, 90)(85, 89)(87, 97)(88, 91)(94, 103)(95, 102)(96, 100)(98, 105)(99, 101)(104, 108)(106, 107)(109, 111)(110, 114)(112, 119)(113, 118)(115, 124)(116, 123)(117, 127)(120, 131)(121, 130)(122, 128)(125, 135)(126, 134)(129, 137)(132, 140)(133, 138)(136, 142)(139, 143)(141, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 36, 36 ), ( 36^12 ) } Outer automorphisms :: reflexible Dual of E14.318 Graph:: simple bipartite v = 42 e = 72 f = 4 degree seq :: [ 2^36, 12^6 ] E14.316 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 9}) Quotient :: edge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2, Y3^9, Y3^3 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 37, 4, 40, 12, 48, 20, 56, 28, 64, 29, 65, 21, 57, 13, 49, 5, 41)(2, 38, 7, 43, 15, 51, 23, 59, 31, 67, 32, 68, 24, 60, 16, 52, 8, 44)(3, 39, 10, 46, 18, 54, 26, 62, 34, 70, 35, 71, 27, 63, 19, 55, 11, 47)(6, 42, 14, 50, 22, 58, 30, 66, 36, 72, 33, 69, 25, 61, 17, 53, 9, 45)(73, 74)(75, 81)(76, 80)(77, 79)(78, 83)(82, 89)(84, 88)(85, 87)(86, 91)(90, 97)(92, 96)(93, 95)(94, 99)(98, 105)(100, 104)(101, 103)(102, 107)(106, 108)(109, 111)(110, 114)(112, 119)(113, 118)(115, 117)(116, 122)(120, 127)(121, 126)(123, 125)(124, 130)(128, 135)(129, 134)(131, 133)(132, 138)(136, 143)(137, 142)(139, 141)(140, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 24, 24 ), ( 24^18 ) } Outer automorphisms :: reflexible Dual of E14.317 Graph:: simple bipartite v = 40 e = 72 f = 6 degree seq :: [ 2^36, 18^4 ] E14.317 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 9}) Quotient :: loop^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, (Y3 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^6, Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, (Y1 * Y3^-1 * Y2)^9 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 12, 48, 84, 120, 24, 60, 96, 132, 13, 49, 85, 121, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 17, 53, 89, 125, 28, 64, 100, 136, 18, 54, 90, 126, 8, 44, 80, 116)(3, 39, 75, 111, 10, 46, 82, 118, 22, 58, 94, 130, 32, 68, 104, 140, 23, 59, 95, 131, 11, 47, 83, 119)(6, 42, 78, 114, 15, 51, 87, 123, 26, 62, 98, 134, 34, 70, 106, 142, 27, 63, 99, 135, 16, 52, 88, 124)(9, 45, 81, 117, 20, 56, 92, 128, 30, 66, 102, 138, 36, 72, 108, 144, 31, 67, 103, 139, 21, 57, 93, 129)(14, 50, 86, 122, 19, 55, 91, 127, 29, 65, 101, 137, 35, 71, 107, 143, 33, 69, 105, 141, 25, 61, 97, 133) L = (1, 38)(2, 37)(3, 45)(4, 44)(5, 43)(6, 50)(7, 41)(8, 40)(9, 39)(10, 57)(11, 56)(12, 54)(13, 53)(14, 42)(15, 61)(16, 55)(17, 49)(18, 48)(19, 52)(20, 47)(21, 46)(22, 67)(23, 66)(24, 64)(25, 51)(26, 69)(27, 65)(28, 60)(29, 63)(30, 59)(31, 58)(32, 72)(33, 62)(34, 71)(35, 70)(36, 68)(73, 111)(74, 114)(75, 109)(76, 119)(77, 118)(78, 110)(79, 124)(80, 123)(81, 127)(82, 113)(83, 112)(84, 131)(85, 130)(86, 128)(87, 116)(88, 115)(89, 135)(90, 134)(91, 117)(92, 122)(93, 137)(94, 121)(95, 120)(96, 140)(97, 138)(98, 126)(99, 125)(100, 142)(101, 129)(102, 133)(103, 143)(104, 132)(105, 144)(106, 136)(107, 139)(108, 141) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E14.316 Transitivity :: VT+ Graph:: bipartite v = 6 e = 72 f = 40 degree seq :: [ 24^6 ] E14.318 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 9}) Quotient :: loop^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2, Y3^9, Y3^3 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 12, 48, 84, 120, 20, 56, 92, 128, 28, 64, 100, 136, 29, 65, 101, 137, 21, 57, 93, 129, 13, 49, 85, 121, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 15, 51, 87, 123, 23, 59, 95, 131, 31, 67, 103, 139, 32, 68, 104, 140, 24, 60, 96, 132, 16, 52, 88, 124, 8, 44, 80, 116)(3, 39, 75, 111, 10, 46, 82, 118, 18, 54, 90, 126, 26, 62, 98, 134, 34, 70, 106, 142, 35, 71, 107, 143, 27, 63, 99, 135, 19, 55, 91, 127, 11, 47, 83, 119)(6, 42, 78, 114, 14, 50, 86, 122, 22, 58, 94, 130, 30, 66, 102, 138, 36, 72, 108, 144, 33, 69, 105, 141, 25, 61, 97, 133, 17, 53, 89, 125, 9, 45, 81, 117) L = (1, 38)(2, 37)(3, 45)(4, 44)(5, 43)(6, 47)(7, 41)(8, 40)(9, 39)(10, 53)(11, 42)(12, 52)(13, 51)(14, 55)(15, 49)(16, 48)(17, 46)(18, 61)(19, 50)(20, 60)(21, 59)(22, 63)(23, 57)(24, 56)(25, 54)(26, 69)(27, 58)(28, 68)(29, 67)(30, 71)(31, 65)(32, 64)(33, 62)(34, 72)(35, 66)(36, 70)(73, 111)(74, 114)(75, 109)(76, 119)(77, 118)(78, 110)(79, 117)(80, 122)(81, 115)(82, 113)(83, 112)(84, 127)(85, 126)(86, 116)(87, 125)(88, 130)(89, 123)(90, 121)(91, 120)(92, 135)(93, 134)(94, 124)(95, 133)(96, 138)(97, 131)(98, 129)(99, 128)(100, 143)(101, 142)(102, 132)(103, 141)(104, 144)(105, 139)(106, 137)(107, 136)(108, 140) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E14.315 Transitivity :: VT+ Graph:: bipartite v = 4 e = 72 f = 42 degree seq :: [ 36^4 ] E14.319 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 9}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2, Y3^-1), (R * Y2)^2, (Y2^-1 * Y1)^2, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 10, 46)(5, 41, 7, 43)(6, 42, 8, 44)(11, 47, 21, 57)(12, 48, 22, 58)(13, 49, 20, 56)(14, 50, 19, 55)(15, 51, 17, 53)(16, 52, 18, 54)(23, 59, 28, 64)(24, 60, 32, 68)(25, 61, 31, 67)(26, 62, 30, 66)(27, 63, 29, 65)(33, 69, 36, 72)(34, 70, 35, 71)(73, 109, 75, 111, 83, 119, 95, 131, 87, 123, 77, 113)(74, 110, 79, 115, 89, 125, 100, 136, 93, 129, 81, 117)(76, 112, 84, 120, 96, 132, 105, 141, 98, 134, 86, 122)(78, 114, 85, 121, 97, 133, 106, 142, 99, 135, 88, 124)(80, 116, 90, 126, 101, 137, 107, 143, 103, 139, 92, 128)(82, 118, 91, 127, 102, 138, 108, 144, 104, 140, 94, 130) L = (1, 76)(2, 80)(3, 84)(4, 85)(5, 86)(6, 73)(7, 90)(8, 91)(9, 92)(10, 74)(11, 96)(12, 97)(13, 75)(14, 78)(15, 98)(16, 77)(17, 101)(18, 102)(19, 79)(20, 82)(21, 103)(22, 81)(23, 105)(24, 106)(25, 83)(26, 88)(27, 87)(28, 107)(29, 108)(30, 89)(31, 94)(32, 93)(33, 99)(34, 95)(35, 104)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E14.321 Graph:: simple bipartite v = 24 e = 72 f = 22 degree seq :: [ 4^18, 12^6 ] E14.320 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 9}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-3, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2, Y3^-1), (R * Y2)^2, 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 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 10, 46)(5, 41, 7, 43)(6, 42, 8, 44)(11, 47, 22, 58)(12, 48, 20, 56)(13, 49, 21, 57)(14, 50, 18, 54)(15, 51, 19, 55)(16, 52, 17, 53)(23, 59, 28, 64)(24, 60, 31, 67)(25, 61, 32, 68)(26, 62, 29, 65)(27, 63, 30, 66)(33, 69, 36, 72)(34, 70, 35, 71)(73, 109, 75, 111, 83, 119, 95, 131, 88, 124, 77, 113)(74, 110, 79, 115, 89, 125, 100, 136, 94, 130, 81, 117)(76, 112, 84, 120, 96, 132, 105, 141, 99, 135, 87, 123)(78, 114, 85, 121, 97, 133, 106, 142, 98, 134, 86, 122)(80, 116, 90, 126, 101, 137, 107, 143, 104, 140, 93, 129)(82, 118, 91, 127, 102, 138, 108, 144, 103, 139, 92, 128) L = (1, 76)(2, 80)(3, 84)(4, 86)(5, 87)(6, 73)(7, 90)(8, 92)(9, 93)(10, 74)(11, 96)(12, 78)(13, 75)(14, 77)(15, 98)(16, 99)(17, 101)(18, 82)(19, 79)(20, 81)(21, 103)(22, 104)(23, 105)(24, 85)(25, 83)(26, 88)(27, 106)(28, 107)(29, 91)(30, 89)(31, 94)(32, 108)(33, 97)(34, 95)(35, 102)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E14.322 Graph:: simple bipartite v = 24 e = 72 f = 22 degree seq :: [ 4^18, 12^6 ] E14.321 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 9}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1^-1 * Y3^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^9, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 15, 51, 23, 59, 29, 65, 21, 57, 13, 49, 5, 41)(3, 39, 10, 46, 19, 55, 27, 63, 34, 70, 31, 67, 24, 60, 16, 52, 8, 44)(4, 40, 9, 45, 17, 53, 25, 61, 32, 68, 30, 66, 22, 58, 14, 50, 6, 42)(11, 47, 20, 56, 28, 64, 35, 71, 36, 72, 33, 69, 26, 62, 18, 54, 12, 48)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 84, 120)(77, 113, 82, 118)(78, 114, 83, 119)(79, 115, 88, 124)(81, 117, 90, 126)(85, 121, 91, 127)(86, 122, 92, 128)(87, 123, 96, 132)(89, 125, 98, 134)(93, 129, 99, 135)(94, 130, 100, 136)(95, 131, 103, 139)(97, 133, 105, 141)(101, 137, 106, 142)(102, 138, 107, 143)(104, 140, 108, 144) L = (1, 76)(2, 81)(3, 83)(4, 74)(5, 78)(6, 73)(7, 89)(8, 84)(9, 79)(10, 92)(11, 82)(12, 75)(13, 86)(14, 77)(15, 97)(16, 90)(17, 87)(18, 80)(19, 100)(20, 91)(21, 94)(22, 85)(23, 104)(24, 98)(25, 95)(26, 88)(27, 107)(28, 99)(29, 102)(30, 93)(31, 105)(32, 101)(33, 96)(34, 108)(35, 106)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E14.319 Graph:: simple bipartite v = 22 e = 72 f = 24 degree seq :: [ 4^18, 18^4 ] E14.322 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 9}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1, Y1^-1), (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y3 * Y1 * Y3^3, Y3 * Y1^-3 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 19, 55, 14, 50, 18, 54, 25, 61, 16, 52, 5, 41)(3, 39, 11, 47, 26, 62, 35, 71, 29, 65, 30, 66, 32, 68, 20, 56, 8, 44)(4, 40, 9, 45, 21, 57, 31, 67, 17, 53, 6, 42, 10, 46, 22, 58, 15, 51)(12, 48, 27, 63, 36, 72, 34, 70, 24, 60, 13, 49, 28, 64, 33, 69, 23, 59)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 85, 121)(77, 113, 83, 119)(78, 114, 84, 120)(79, 115, 92, 128)(81, 117, 96, 132)(82, 118, 95, 131)(86, 122, 102, 138)(87, 123, 100, 136)(88, 124, 98, 134)(89, 125, 99, 135)(90, 126, 101, 137)(91, 127, 104, 140)(93, 129, 106, 142)(94, 130, 105, 141)(97, 133, 107, 143)(103, 139, 108, 144) L = (1, 76)(2, 81)(3, 84)(4, 86)(5, 87)(6, 73)(7, 93)(8, 95)(9, 90)(10, 74)(11, 99)(12, 101)(13, 75)(14, 89)(15, 91)(16, 94)(17, 77)(18, 78)(19, 103)(20, 105)(21, 97)(22, 79)(23, 107)(24, 80)(25, 82)(26, 108)(27, 102)(28, 83)(29, 96)(30, 85)(31, 88)(32, 100)(33, 98)(34, 92)(35, 106)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E14.320 Graph:: simple bipartite v = 22 e = 72 f = 24 degree seq :: [ 4^18, 18^4 ] E14.323 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 18, 18}) Quotient :: edge Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T1^-6, T2^6 * T1^-2 ] Map:: non-degenerate R = (1, 3, 9, 19, 28, 16, 6, 15, 27, 36, 32, 22, 11, 21, 31, 24, 13, 5)(2, 7, 17, 29, 35, 26, 14, 25, 34, 33, 23, 12, 4, 10, 20, 30, 18, 8)(37, 38, 42, 50, 47, 40)(39, 43, 51, 61, 57, 46)(41, 44, 52, 62, 58, 48)(45, 53, 63, 70, 67, 56)(49, 54, 64, 71, 68, 59)(55, 65, 72, 69, 60, 66) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 36^6 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E14.327 Transitivity :: ET+ Graph:: bipartite v = 8 e = 36 f = 2 degree seq :: [ 6^6, 18^2 ] E14.324 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 18, 18}) Quotient :: edge Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^6, T1^-2 * T2^-6 ] Map:: non-degenerate R = (1, 3, 9, 19, 31, 22, 11, 21, 33, 36, 28, 16, 6, 15, 27, 24, 13, 5)(2, 7, 17, 29, 23, 12, 4, 10, 20, 32, 35, 26, 14, 25, 34, 30, 18, 8)(37, 38, 42, 50, 47, 40)(39, 43, 51, 61, 57, 46)(41, 44, 52, 62, 58, 48)(45, 53, 63, 70, 69, 56)(49, 54, 64, 71, 67, 59)(55, 65, 60, 66, 72, 68) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 36^6 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E14.326 Transitivity :: ET+ Graph:: bipartite v = 8 e = 36 f = 2 degree seq :: [ 6^6, 18^2 ] E14.325 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 18, 18}) Quotient :: edge Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-3 * T1, T1^3 * T2^-2 * T1^-1 * T2^-2, T1 * T2 * T1^7 * T2 ] Map:: non-degenerate R = (1, 3, 9, 16, 6, 15, 26, 33, 23, 32, 28, 35, 30, 21, 11, 19, 13, 5)(2, 7, 17, 25, 14, 24, 34, 36, 31, 29, 20, 27, 22, 12, 4, 10, 18, 8)(37, 38, 42, 50, 59, 67, 66, 58, 49, 54, 45, 53, 62, 70, 64, 56, 47, 40)(39, 43, 51, 60, 68, 65, 57, 48, 41, 44, 52, 61, 69, 72, 71, 63, 55, 46) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12^18 ) } Outer automorphisms :: reflexible Dual of E14.328 Transitivity :: ET+ Graph:: bipartite v = 4 e = 36 f = 6 degree seq :: [ 18^4 ] E14.326 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 18, 18}) Quotient :: loop Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T1^-6, T2^6 * T1^-2 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 28, 64, 16, 52, 6, 42, 15, 51, 27, 63, 36, 72, 32, 68, 22, 58, 11, 47, 21, 57, 31, 67, 24, 60, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 29, 65, 35, 71, 26, 62, 14, 50, 25, 61, 34, 70, 33, 69, 23, 59, 12, 48, 4, 40, 10, 46, 20, 56, 30, 66, 18, 54, 8, 44) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 47)(15, 61)(16, 62)(17, 63)(18, 64)(19, 65)(20, 45)(21, 46)(22, 48)(23, 49)(24, 66)(25, 57)(26, 58)(27, 70)(28, 71)(29, 72)(30, 55)(31, 56)(32, 59)(33, 60)(34, 67)(35, 68)(36, 69) local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E14.324 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 36 f = 8 degree seq :: [ 36^2 ] E14.327 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 18, 18}) Quotient :: loop Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^6, T1^-2 * T2^-6 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 31, 67, 22, 58, 11, 47, 21, 57, 33, 69, 36, 72, 28, 64, 16, 52, 6, 42, 15, 51, 27, 63, 24, 60, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 29, 65, 23, 59, 12, 48, 4, 40, 10, 46, 20, 56, 32, 68, 35, 71, 26, 62, 14, 50, 25, 61, 34, 70, 30, 66, 18, 54, 8, 44) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 47)(15, 61)(16, 62)(17, 63)(18, 64)(19, 65)(20, 45)(21, 46)(22, 48)(23, 49)(24, 66)(25, 57)(26, 58)(27, 70)(28, 71)(29, 60)(30, 72)(31, 59)(32, 55)(33, 56)(34, 69)(35, 67)(36, 68) local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E14.323 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 36 f = 8 degree seq :: [ 36^2 ] E14.328 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 18, 18}) Quotient :: loop Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-6, T2^2 * T1^-6 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 30, 66, 18, 54, 8, 44)(4, 40, 10, 46, 20, 56, 31, 67, 24, 60, 12, 48)(6, 42, 15, 51, 28, 64, 36, 72, 29, 65, 16, 52)(11, 47, 21, 57, 25, 61, 34, 70, 33, 69, 23, 59)(14, 50, 26, 62, 35, 71, 32, 68, 22, 58, 27, 63) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 56)(26, 70)(27, 57)(28, 71)(29, 58)(30, 72)(31, 55)(32, 59)(33, 60)(34, 67)(35, 69)(36, 68) local type(s) :: { ( 18^12 ) } Outer automorphisms :: reflexible Dual of E14.325 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 36 f = 4 degree seq :: [ 12^6 ] E14.329 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3^6, Y1^6, Y2^-1 * Y3 * Y2^-5 * Y1^-1, Y3^-3 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2^-2 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 25, 61, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 26, 62, 22, 58, 12, 48)(9, 45, 17, 53, 27, 63, 34, 70, 33, 69, 20, 56)(13, 49, 18, 54, 28, 64, 35, 71, 31, 67, 23, 59)(19, 55, 29, 65, 24, 60, 30, 66, 36, 72, 32, 68)(73, 109, 75, 111, 81, 117, 91, 127, 103, 139, 94, 130, 83, 119, 93, 129, 105, 141, 108, 144, 100, 136, 88, 124, 78, 114, 87, 123, 99, 135, 96, 132, 85, 121, 77, 113)(74, 110, 79, 115, 89, 125, 101, 137, 95, 131, 84, 120, 76, 112, 82, 118, 92, 128, 104, 140, 107, 143, 98, 134, 86, 122, 97, 133, 106, 142, 102, 138, 90, 126, 80, 116) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 92)(10, 93)(11, 86)(12, 94)(13, 95)(14, 78)(15, 79)(16, 80)(17, 81)(18, 85)(19, 104)(20, 105)(21, 97)(22, 98)(23, 103)(24, 101)(25, 87)(26, 88)(27, 89)(28, 90)(29, 91)(30, 96)(31, 107)(32, 108)(33, 106)(34, 99)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E14.333 Graph:: bipartite v = 8 e = 72 f = 38 degree seq :: [ 12^6, 36^2 ] E14.330 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3 * Y1, Y3^-1 * Y1^-1, Y1^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^6, Y2^2 * Y3 * Y2^4 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 25, 61, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 26, 62, 22, 58, 12, 48)(9, 45, 17, 53, 27, 63, 34, 70, 31, 67, 20, 56)(13, 49, 18, 54, 28, 64, 35, 71, 32, 68, 23, 59)(19, 55, 29, 65, 36, 72, 33, 69, 24, 60, 30, 66)(73, 109, 75, 111, 81, 117, 91, 127, 100, 136, 88, 124, 78, 114, 87, 123, 99, 135, 108, 144, 104, 140, 94, 130, 83, 119, 93, 129, 103, 139, 96, 132, 85, 121, 77, 113)(74, 110, 79, 115, 89, 125, 101, 137, 107, 143, 98, 134, 86, 122, 97, 133, 106, 142, 105, 141, 95, 131, 84, 120, 76, 112, 82, 118, 92, 128, 102, 138, 90, 126, 80, 116) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 92)(10, 93)(11, 86)(12, 94)(13, 95)(14, 78)(15, 79)(16, 80)(17, 81)(18, 85)(19, 102)(20, 103)(21, 97)(22, 98)(23, 104)(24, 105)(25, 87)(26, 88)(27, 89)(28, 90)(29, 91)(30, 96)(31, 106)(32, 107)(33, 108)(34, 99)(35, 100)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 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 E14.334 Graph:: bipartite v = 8 e = 72 f = 38 degree seq :: [ 12^6, 36^2 ] E14.331 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2 * Y1^-1 * Y2 * Y1^-3, Y1 * Y2 * Y1 * Y2^7, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 9, 45, 17, 53, 24, 60, 31, 67, 27, 63, 33, 69, 30, 66, 34, 70, 28, 64, 21, 57, 13, 49, 18, 54, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 23, 59, 19, 55, 25, 61, 32, 68, 36, 72, 35, 71, 29, 65, 22, 58, 26, 62, 20, 56, 12, 48, 5, 41, 8, 44, 16, 52, 10, 46)(73, 109, 75, 111, 81, 117, 91, 127, 99, 135, 107, 143, 100, 136, 92, 128, 83, 119, 88, 124, 78, 114, 87, 123, 96, 132, 104, 140, 102, 138, 94, 130, 85, 121, 77, 113)(74, 110, 79, 115, 89, 125, 97, 133, 105, 141, 101, 137, 93, 129, 84, 120, 76, 112, 82, 118, 86, 122, 95, 131, 103, 139, 108, 144, 106, 142, 98, 134, 90, 126, 80, 116) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 86)(11, 88)(12, 76)(13, 77)(14, 95)(15, 96)(16, 78)(17, 97)(18, 80)(19, 99)(20, 83)(21, 84)(22, 85)(23, 103)(24, 104)(25, 105)(26, 90)(27, 107)(28, 92)(29, 93)(30, 94)(31, 108)(32, 102)(33, 101)(34, 98)(35, 100)(36, 106)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E14.332 Graph:: bipartite v = 4 e = 72 f = 42 degree seq :: [ 36^4 ] E14.332 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (Y3^-1, Y2), (R * Y3)^2, (R * Y2)^2, Y2^6, Y3^6 * Y2^-2, (Y3^-1 * Y1^-1)^18 ] Map:: R = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)(73, 109, 74, 110, 78, 114, 86, 122, 83, 119, 76, 112)(75, 111, 79, 115, 87, 123, 97, 133, 93, 129, 82, 118)(77, 113, 80, 116, 88, 124, 98, 134, 94, 130, 84, 120)(81, 117, 89, 125, 99, 135, 106, 142, 103, 139, 92, 128)(85, 121, 90, 126, 100, 136, 107, 143, 104, 140, 95, 131)(91, 127, 101, 137, 108, 144, 105, 141, 96, 132, 102, 138) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 97)(15, 99)(16, 78)(17, 101)(18, 80)(19, 100)(20, 102)(21, 103)(22, 83)(23, 84)(24, 85)(25, 106)(26, 86)(27, 108)(28, 88)(29, 107)(30, 90)(31, 96)(32, 94)(33, 95)(34, 105)(35, 98)(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) :: { ( 36, 36 ), ( 36^12 ) } Outer automorphisms :: reflexible Dual of E14.331 Graph:: simple bipartite v = 42 e = 72 f = 4 degree seq :: [ 2^36, 12^6 ] E14.333 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^-6, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^-6, (Y3 * Y2^-1)^6 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 25, 61, 20, 56, 9, 45, 17, 53, 28, 64, 35, 71, 33, 69, 24, 60, 13, 49, 18, 54, 29, 65, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 26, 62, 34, 70, 31, 67, 19, 55, 30, 66, 36, 72, 32, 68, 23, 59, 12, 48, 5, 41, 8, 44, 16, 52, 27, 63, 21, 57, 10, 46)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 98)(15, 100)(16, 78)(17, 102)(18, 80)(19, 85)(20, 103)(21, 97)(22, 99)(23, 83)(24, 84)(25, 106)(26, 107)(27, 86)(28, 108)(29, 88)(30, 90)(31, 96)(32, 94)(33, 95)(34, 105)(35, 104)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12, 36 ), ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E14.329 Graph:: simple bipartite v = 38 e = 72 f = 8 degree seq :: [ 2^36, 36^2 ] E14.334 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^6, Y3^-2 * Y1^-6, (Y3 * Y2^-1)^6 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 25, 61, 24, 60, 13, 49, 18, 54, 29, 65, 35, 71, 32, 68, 20, 56, 9, 45, 17, 53, 28, 64, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 26, 62, 23, 59, 12, 48, 5, 41, 8, 44, 16, 52, 27, 63, 34, 70, 31, 67, 19, 55, 30, 66, 36, 72, 33, 69, 21, 57, 10, 46)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 98)(15, 100)(16, 78)(17, 102)(18, 80)(19, 85)(20, 103)(21, 104)(22, 105)(23, 83)(24, 84)(25, 95)(26, 94)(27, 86)(28, 108)(29, 88)(30, 90)(31, 96)(32, 106)(33, 107)(34, 97)(35, 99)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12, 36 ), ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E14.330 Graph:: simple bipartite v = 38 e = 72 f = 8 degree seq :: [ 2^36, 36^2 ] E14.335 :: Family: { 5P } :: Oriented family(ies): { E5b } Signature :: (0; {3, 3, 3, 3}) Quotient :: dipole Aut^+ = C13 : C3 (small group id <39, 1>) Aut = (C13 : C3) : C2 (small group id <78, 1>) |r| :: 2 Presentation :: [ 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, (Y3^-1 * Y1^-1)^3, (Y1 * Y2^-1)^3, (Y3 * Y2^-1)^3, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 ] Map:: R = (1, 40, 2, 41, 4, 43)(3, 42, 8, 47, 9, 48)(5, 44, 12, 51, 13, 52)(6, 45, 14, 53, 15, 54)(7, 46, 16, 55, 17, 56)(10, 49, 21, 60, 22, 61)(11, 50, 23, 62, 24, 63)(18, 57, 33, 72, 34, 73)(19, 58, 26, 65, 28, 67)(20, 59, 35, 74, 36, 75)(25, 64, 32, 71, 38, 77)(27, 66, 39, 78, 30, 69)(29, 68, 31, 70, 37, 76)(79, 118, 81, 120, 83, 122)(80, 119, 84, 123, 85, 124)(82, 121, 88, 127, 89, 128)(86, 125, 96, 135, 97, 136)(87, 126, 94, 133, 98, 137)(90, 129, 103, 142, 100, 139)(91, 130, 104, 143, 105, 144)(92, 131, 106, 145, 107, 146)(93, 132, 101, 140, 108, 147)(95, 134, 109, 148, 110, 149)(99, 138, 115, 154, 111, 150)(102, 141, 112, 151, 113, 152)(114, 153, 116, 155, 117, 156) L = (1, 79)(2, 80)(3, 81)(4, 82)(5, 83)(6, 84)(7, 85)(8, 86)(9, 87)(10, 88)(11, 89)(12, 90)(13, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 97)(20, 98)(21, 99)(22, 100)(23, 101)(24, 102)(25, 103)(26, 104)(27, 105)(28, 106)(29, 107)(30, 108)(31, 109)(32, 110)(33, 111)(34, 112)(35, 113)(36, 114)(37, 115)(38, 116)(39, 117)(40, 118)(41, 119)(42, 120)(43, 121)(44, 122)(45, 123)(46, 124)(47, 125)(48, 126)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 133)(56, 134)(57, 135)(58, 136)(59, 137)(60, 138)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 145)(68, 146)(69, 147)(70, 148)(71, 149)(72, 150)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156) local type(s) :: { ( 6^6 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT Graph:: bipartite v = 26 e = 78 f = 26 degree seq :: [ 6^26 ] E14.336 :: Family: { 5P } :: Oriented family(ies): { E5b } Signature :: (0; {3, 3, 3, 3}) Quotient :: dipole Aut^+ = C13 : C3 (small group id <39, 1>) Aut = C2 x (C13 : C3) (small group id <78, 2>) |r| :: 6 Presentation :: [ Y3^3, Y1^3, R^2 * Y3^-1, Y2^3, Y3 * Y1 * Y3^-1 * Y2, Y2 * R^-1 * Y1 * R, Y1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1, Y2 * Y1^-1 * R * Y1^-1 * R^-1, (Y2 * Y1^-1)^3 ] Map:: polyhedral non-degenerate R = (1, 40, 2, 41, 5, 44)(3, 42, 12, 51, 14, 53)(4, 43, 16, 55, 13, 52)(6, 45, 23, 62, 24, 63)(7, 46, 26, 65, 27, 66)(8, 47, 28, 67, 30, 69)(9, 48, 17, 56, 29, 68)(10, 49, 32, 71, 33, 72)(11, 50, 34, 73, 35, 74)(15, 54, 37, 76, 21, 60)(18, 57, 38, 77, 19, 58)(20, 59, 31, 70, 39, 78)(22, 61, 36, 75, 25, 64)(79, 118, 81, 120, 84, 123)(80, 119, 86, 125, 88, 127)(82, 121, 95, 134, 96, 135)(83, 122, 97, 136, 99, 138)(85, 124, 100, 139, 89, 128)(87, 126, 109, 148, 90, 129)(91, 130, 113, 152, 111, 150)(92, 131, 110, 149, 114, 153)(93, 132, 104, 143, 108, 147)(94, 133, 106, 145, 98, 137)(101, 140, 112, 151, 116, 155)(102, 141, 117, 156, 105, 144)(103, 142, 115, 154, 107, 146) L = (1, 82)(2, 87)(3, 91)(4, 85)(5, 98)(6, 94)(7, 79)(8, 107)(9, 89)(10, 95)(11, 80)(12, 112)(13, 93)(14, 96)(15, 81)(16, 103)(17, 105)(18, 104)(19, 117)(20, 100)(21, 109)(22, 83)(23, 86)(24, 111)(25, 84)(26, 92)(27, 88)(28, 114)(29, 101)(30, 90)(31, 113)(32, 97)(33, 115)(34, 108)(35, 99)(36, 116)(37, 102)(38, 106)(39, 110)(40, 118)(41, 119)(42, 120)(43, 121)(44, 122)(45, 123)(46, 124)(47, 125)(48, 126)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 133)(56, 134)(57, 135)(58, 136)(59, 137)(60, 138)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 145)(68, 146)(69, 147)(70, 148)(71, 149)(72, 150)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156) local type(s) :: { ( 6^6 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT Graph:: simple bipartite v = 26 e = 78 f = 26 degree seq :: [ 6^26 ] E14.337 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y2^2, R^2, Y2 * Y3^-2, (Y1 * Y2)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1 * Y1)^10 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 6, 46)(4, 44, 9, 49)(5, 45, 10, 50)(7, 47, 11, 51)(8, 48, 12, 52)(13, 53, 17, 57)(14, 54, 18, 58)(15, 55, 19, 59)(16, 56, 20, 60)(21, 61, 25, 65)(22, 62, 26, 66)(23, 63, 27, 67)(24, 64, 28, 68)(29, 69, 33, 73)(30, 70, 34, 74)(31, 71, 35, 75)(32, 72, 36, 76)(37, 77, 40, 80)(38, 78, 39, 79)(81, 121, 83, 123)(82, 122, 86, 126)(84, 124, 85, 125)(87, 127, 88, 128)(89, 129, 90, 130)(91, 131, 92, 132)(93, 133, 94, 134)(95, 135, 96, 136)(97, 137, 98, 138)(99, 139, 100, 140)(101, 141, 102, 142)(103, 143, 104, 144)(105, 145, 106, 146)(107, 147, 108, 148)(109, 149, 110, 150)(111, 151, 112, 152)(113, 153, 114, 154)(115, 155, 116, 156)(117, 157, 118, 158)(119, 159, 120, 160) L = (1, 84)(2, 87)(3, 85)(4, 83)(5, 81)(6, 88)(7, 86)(8, 82)(9, 93)(10, 94)(11, 95)(12, 96)(13, 90)(14, 89)(15, 92)(16, 91)(17, 101)(18, 102)(19, 103)(20, 104)(21, 98)(22, 97)(23, 100)(24, 99)(25, 109)(26, 110)(27, 111)(28, 112)(29, 106)(30, 105)(31, 108)(32, 107)(33, 117)(34, 118)(35, 119)(36, 120)(37, 114)(38, 113)(39, 116)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E14.348 Graph:: simple bipartite v = 40 e = 80 f = 14 degree seq :: [ 4^40 ] E14.338 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y2^2, R^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y2, (Y2 * Y1)^4, Y3 * Y1 * Y2 * Y3 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 9, 49)(5, 45, 11, 51)(6, 46, 13, 53)(8, 48, 16, 56)(10, 50, 19, 59)(12, 52, 21, 61)(14, 54, 24, 64)(15, 55, 20, 60)(17, 57, 26, 66)(18, 58, 27, 67)(22, 62, 30, 70)(23, 63, 31, 71)(25, 65, 33, 73)(28, 68, 36, 76)(29, 69, 37, 77)(32, 72, 40, 80)(34, 74, 39, 79)(35, 75, 38, 78)(81, 121, 83, 123)(82, 122, 85, 125)(84, 124, 90, 130)(86, 126, 94, 134)(87, 127, 95, 135)(88, 128, 97, 137)(89, 129, 96, 136)(91, 131, 100, 140)(92, 132, 102, 142)(93, 133, 101, 141)(98, 138, 108, 148)(99, 139, 106, 146)(103, 143, 112, 152)(104, 144, 110, 150)(105, 145, 114, 154)(107, 147, 113, 153)(109, 149, 118, 158)(111, 151, 117, 157)(115, 155, 120, 160)(116, 156, 119, 159) L = (1, 84)(2, 86)(3, 88)(4, 81)(5, 92)(6, 82)(7, 94)(8, 83)(9, 98)(10, 91)(11, 90)(12, 85)(13, 103)(14, 87)(15, 102)(16, 105)(17, 100)(18, 89)(19, 108)(20, 97)(21, 109)(22, 95)(23, 93)(24, 112)(25, 96)(26, 114)(27, 115)(28, 99)(29, 101)(30, 118)(31, 119)(32, 104)(33, 117)(34, 106)(35, 107)(36, 120)(37, 113)(38, 110)(39, 111)(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 ) } Outer automorphisms :: reflexible Dual of E14.347 Graph:: simple bipartite v = 40 e = 80 f = 14 degree seq :: [ 4^40 ] E14.339 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 10}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, Y2^4, 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 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 10, 50)(5, 45, 7, 47)(6, 46, 8, 48)(11, 51, 18, 58)(12, 52, 23, 63)(13, 53, 22, 62)(14, 54, 24, 64)(15, 55, 20, 60)(16, 56, 19, 59)(17, 57, 21, 61)(25, 65, 32, 72)(26, 66, 31, 71)(27, 67, 35, 75)(28, 68, 36, 76)(29, 69, 33, 73)(30, 70, 34, 74)(37, 77, 40, 80)(38, 78, 39, 79)(81, 121, 83, 123, 91, 131, 85, 125)(82, 122, 87, 127, 98, 138, 89, 129)(84, 124, 92, 132, 105, 145, 95, 135)(86, 126, 93, 133, 106, 146, 96, 136)(88, 128, 99, 139, 111, 151, 102, 142)(90, 130, 100, 140, 112, 152, 103, 143)(94, 134, 107, 147, 117, 157, 110, 150)(97, 137, 108, 148, 118, 158, 109, 149)(101, 141, 113, 153, 119, 159, 116, 156)(104, 144, 114, 154, 120, 160, 115, 155) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 99)(8, 101)(9, 102)(10, 82)(11, 105)(12, 107)(13, 83)(14, 109)(15, 110)(16, 85)(17, 86)(18, 111)(19, 113)(20, 87)(21, 115)(22, 116)(23, 89)(24, 90)(25, 117)(26, 91)(27, 97)(28, 93)(29, 96)(30, 118)(31, 119)(32, 98)(33, 104)(34, 100)(35, 103)(36, 120)(37, 108)(38, 106)(39, 114)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E14.343 Graph:: simple bipartite v = 30 e = 80 f = 24 degree seq :: [ 4^20, 8^10 ] E14.340 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, R^2, Y2 * Y1 * Y2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, (Y3 * Y2^-1)^10 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42)(3, 43, 5, 45)(4, 44, 6, 46)(7, 47, 10, 50)(8, 48, 9, 49)(11, 51, 12, 52)(13, 53, 14, 54)(15, 55, 16, 56)(17, 57, 18, 58)(19, 59, 20, 60)(21, 61, 22, 62)(23, 63, 24, 64)(25, 65, 26, 66)(27, 67, 28, 68)(29, 69, 30, 70)(31, 71, 32, 72)(33, 73, 34, 74)(35, 75, 36, 76)(37, 77, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 82, 122, 85, 125)(84, 124, 88, 128, 86, 126, 89, 129)(87, 127, 91, 131, 90, 130, 92, 132)(93, 133, 97, 137, 94, 134, 98, 138)(95, 135, 99, 139, 96, 136, 100, 140)(101, 141, 105, 145, 102, 142, 106, 146)(103, 143, 107, 147, 104, 144, 108, 148)(109, 149, 113, 153, 110, 150, 114, 154)(111, 151, 115, 155, 112, 152, 116, 156)(117, 157, 120, 160, 118, 158, 119, 159) L = (1, 84)(2, 86)(3, 87)(4, 81)(5, 90)(6, 82)(7, 83)(8, 93)(9, 94)(10, 85)(11, 95)(12, 96)(13, 88)(14, 89)(15, 91)(16, 92)(17, 101)(18, 102)(19, 103)(20, 104)(21, 97)(22, 98)(23, 99)(24, 100)(25, 109)(26, 110)(27, 111)(28, 112)(29, 105)(30, 106)(31, 107)(32, 108)(33, 117)(34, 118)(35, 119)(36, 120)(37, 113)(38, 114)(39, 115)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E14.345 Graph:: bipartite v = 30 e = 80 f = 24 degree seq :: [ 4^20, 8^10 ] E14.341 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, R^2, Y2^4, (Y3 * Y1)^2, (R * Y3)^2, Y2^2 * Y3 * Y1, (R * Y1)^2, (R * Y2 * Y3)^2, Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 7, 47)(5, 45, 10, 50)(6, 46, 11, 51)(8, 48, 12, 52)(13, 53, 17, 57)(14, 54, 18, 58)(15, 55, 19, 59)(16, 56, 20, 60)(21, 61, 25, 65)(22, 62, 26, 66)(23, 63, 27, 67)(24, 64, 28, 68)(29, 69, 33, 73)(30, 70, 34, 74)(31, 71, 35, 75)(32, 72, 36, 76)(37, 77, 40, 80)(38, 78, 39, 79)(81, 121, 83, 123, 87, 127, 85, 125)(82, 122, 86, 126, 84, 124, 88, 128)(89, 129, 93, 133, 90, 130, 94, 134)(91, 131, 95, 135, 92, 132, 96, 136)(97, 137, 101, 141, 98, 138, 102, 142)(99, 139, 103, 143, 100, 140, 104, 144)(105, 145, 109, 149, 106, 146, 110, 150)(107, 147, 111, 151, 108, 148, 112, 152)(113, 153, 117, 157, 114, 154, 118, 158)(115, 155, 119, 159, 116, 156, 120, 160) L = (1, 84)(2, 87)(3, 90)(4, 81)(5, 89)(6, 92)(7, 82)(8, 91)(9, 85)(10, 83)(11, 88)(12, 86)(13, 98)(14, 97)(15, 100)(16, 99)(17, 94)(18, 93)(19, 96)(20, 95)(21, 106)(22, 105)(23, 108)(24, 107)(25, 102)(26, 101)(27, 104)(28, 103)(29, 114)(30, 113)(31, 116)(32, 115)(33, 110)(34, 109)(35, 112)(36, 111)(37, 119)(38, 120)(39, 117)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E14.344 Graph:: bipartite v = 30 e = 80 f = 24 degree seq :: [ 4^20, 8^10 ] E14.342 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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^-2 * Y3^-2, (Y2^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y3^4, (Y3^-1 * Y1)^2, Y3^-1 * Y2^2 * Y3^-1, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, R * Y2 * Y3 * R * Y2^-1 * Y3^-1, Y2^-1 * R * Y3^2 * R * Y2^-1, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 10, 50)(5, 45, 7, 47)(6, 46, 8, 48)(11, 51, 16, 56)(12, 52, 17, 57)(13, 53, 18, 58)(14, 54, 19, 59)(15, 55, 20, 60)(21, 61, 26, 66)(22, 62, 25, 65)(23, 63, 28, 68)(24, 64, 27, 67)(29, 69, 33, 73)(30, 70, 34, 74)(31, 71, 35, 75)(32, 72, 36, 76)(37, 77, 40, 80)(38, 78, 39, 79)(81, 121, 83, 123, 91, 131, 85, 125)(82, 122, 87, 127, 96, 136, 89, 129)(84, 124, 94, 134, 86, 126, 95, 135)(88, 128, 99, 139, 90, 130, 100, 140)(92, 132, 101, 141, 93, 133, 102, 142)(97, 137, 105, 145, 98, 138, 106, 146)(103, 143, 111, 151, 104, 144, 112, 152)(107, 147, 115, 155, 108, 148, 116, 156)(109, 149, 117, 157, 110, 150, 118, 158)(113, 153, 119, 159, 114, 154, 120, 160) L = (1, 84)(2, 88)(3, 92)(4, 91)(5, 93)(6, 81)(7, 97)(8, 96)(9, 98)(10, 82)(11, 86)(12, 85)(13, 83)(14, 103)(15, 104)(16, 90)(17, 89)(18, 87)(19, 107)(20, 108)(21, 109)(22, 110)(23, 95)(24, 94)(25, 113)(26, 114)(27, 100)(28, 99)(29, 102)(30, 101)(31, 118)(32, 117)(33, 106)(34, 105)(35, 120)(36, 119)(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, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E14.346 Graph:: simple bipartite v = 30 e = 80 f = 24 degree seq :: [ 4^20, 8^10 ] E14.343 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 10}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (Y2 * Y1^-1)^2, Y1^2 * Y3^-1 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^3 * Y1^-1 * Y3^-1 * Y1^-1, Y3^6 * Y1 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 14, 54, 23, 63, 34, 74, 31, 71, 18, 58, 16, 56, 5, 45)(3, 43, 11, 51, 24, 64, 27, 67, 37, 77, 40, 80, 35, 75, 28, 68, 19, 59, 8, 48)(4, 44, 9, 49, 20, 60, 29, 69, 32, 72, 30, 70, 17, 57, 6, 46, 10, 50, 15, 55)(12, 52, 25, 65, 36, 76, 38, 78, 39, 79, 33, 73, 22, 62, 13, 53, 26, 66, 21, 61)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 93, 133)(85, 125, 91, 131)(86, 126, 92, 132)(87, 127, 99, 139)(89, 129, 102, 142)(90, 130, 101, 141)(94, 134, 108, 148)(95, 135, 106, 146)(96, 136, 104, 144)(97, 137, 105, 145)(98, 138, 107, 147)(100, 140, 113, 153)(103, 143, 115, 155)(109, 149, 119, 159)(110, 150, 116, 156)(111, 151, 117, 157)(112, 152, 118, 158)(114, 154, 120, 160) L = (1, 84)(2, 89)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 101)(9, 103)(10, 82)(11, 105)(12, 107)(13, 83)(14, 109)(15, 87)(16, 90)(17, 85)(18, 86)(19, 106)(20, 114)(21, 104)(22, 88)(23, 112)(24, 116)(25, 117)(26, 91)(27, 118)(28, 93)(29, 111)(30, 96)(31, 97)(32, 98)(33, 99)(34, 110)(35, 102)(36, 120)(37, 119)(38, 115)(39, 108)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 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 E14.339 Graph:: simple bipartite v = 24 e = 80 f = 30 degree seq :: [ 4^20, 20^4 ] E14.344 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, (R * Y2)^2, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y2 * Y1 * Y3 * Y1 * Y3, Y1^10 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 15, 55, 23, 63, 31, 71, 30, 70, 22, 62, 14, 54, 5, 45)(3, 43, 7, 47, 16, 56, 24, 64, 32, 72, 38, 78, 35, 75, 27, 67, 19, 59, 10, 50)(4, 44, 11, 51, 20, 60, 28, 68, 36, 76, 40, 80, 33, 73, 26, 66, 17, 57, 12, 52)(8, 48, 9, 49, 13, 53, 21, 61, 29, 69, 37, 77, 39, 79, 34, 74, 25, 65, 18, 58)(81, 121, 83, 123)(82, 122, 87, 127)(84, 124, 89, 129)(85, 125, 90, 130)(86, 126, 96, 136)(88, 128, 92, 132)(91, 131, 93, 133)(94, 134, 99, 139)(95, 135, 104, 144)(97, 137, 98, 138)(100, 140, 101, 141)(102, 142, 107, 147)(103, 143, 112, 152)(105, 145, 106, 146)(108, 148, 109, 149)(110, 150, 115, 155)(111, 151, 118, 158)(113, 153, 114, 154)(116, 156, 117, 157)(119, 159, 120, 160) L = (1, 84)(2, 88)(3, 89)(4, 81)(5, 93)(6, 97)(7, 92)(8, 82)(9, 83)(10, 91)(11, 90)(12, 87)(13, 85)(14, 100)(15, 105)(16, 98)(17, 86)(18, 96)(19, 101)(20, 94)(21, 99)(22, 109)(23, 113)(24, 106)(25, 95)(26, 104)(27, 108)(28, 107)(29, 102)(30, 116)(31, 119)(32, 114)(33, 103)(34, 112)(35, 117)(36, 110)(37, 115)(38, 120)(39, 111)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E14.341 Graph:: simple bipartite v = 24 e = 80 f = 30 degree seq :: [ 4^20, 20^4 ] E14.345 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, (R * Y2)^2, Y1^-1 * Y3 * Y1^-1 * Y2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^10 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42, 6, 46, 13, 53, 21, 61, 29, 69, 28, 68, 20, 60, 12, 52, 5, 45)(3, 43, 9, 49, 17, 57, 25, 65, 33, 73, 37, 77, 30, 70, 23, 63, 14, 54, 8, 48)(4, 44, 11, 51, 19, 59, 27, 67, 35, 75, 36, 76, 31, 71, 22, 62, 15, 55, 7, 47)(10, 50, 16, 56, 24, 64, 32, 72, 38, 78, 40, 80, 39, 79, 34, 74, 26, 66, 18, 58)(81, 121, 83, 123)(82, 122, 87, 127)(84, 124, 90, 130)(85, 125, 91, 131)(86, 126, 94, 134)(88, 128, 96, 136)(89, 129, 98, 138)(92, 132, 97, 137)(93, 133, 102, 142)(95, 135, 104, 144)(99, 139, 106, 146)(100, 140, 107, 147)(101, 141, 110, 150)(103, 143, 112, 152)(105, 145, 114, 154)(108, 148, 113, 153)(109, 149, 116, 156)(111, 151, 118, 158)(115, 155, 119, 159)(117, 157, 120, 160) L = (1, 84)(2, 88)(3, 90)(4, 81)(5, 89)(6, 95)(7, 96)(8, 82)(9, 85)(10, 83)(11, 98)(12, 99)(13, 103)(14, 104)(15, 86)(16, 87)(17, 106)(18, 91)(19, 92)(20, 105)(21, 111)(22, 112)(23, 93)(24, 94)(25, 100)(26, 97)(27, 114)(28, 115)(29, 117)(30, 118)(31, 101)(32, 102)(33, 119)(34, 107)(35, 108)(36, 120)(37, 109)(38, 110)(39, 113)(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 ) } Outer automorphisms :: reflexible Dual of E14.340 Graph:: simple bipartite v = 24 e = 80 f = 30 degree seq :: [ 4^20, 20^4 ] E14.346 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y3^4, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^3 * Y3^-1 * Y1^-2 * Y3^-1 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 18, 58, 30, 70, 15, 55, 24, 64, 31, 71, 16, 56, 5, 45)(3, 43, 11, 51, 25, 65, 37, 77, 36, 76, 28, 68, 40, 80, 33, 73, 19, 59, 8, 48)(4, 44, 14, 54, 29, 69, 21, 61, 10, 50, 6, 46, 17, 57, 32, 72, 20, 60, 9, 49)(12, 52, 22, 62, 34, 74, 39, 79, 27, 67, 13, 53, 23, 63, 35, 75, 38, 78, 26, 66)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 93, 133)(85, 125, 91, 131)(86, 126, 92, 132)(87, 127, 99, 139)(89, 129, 103, 143)(90, 130, 102, 142)(94, 134, 107, 147)(95, 135, 108, 148)(96, 136, 105, 145)(97, 137, 106, 146)(98, 138, 113, 153)(100, 140, 115, 155)(101, 141, 114, 154)(104, 144, 116, 156)(109, 149, 119, 159)(110, 150, 120, 160)(111, 151, 117, 157)(112, 152, 118, 158) L = (1, 84)(2, 89)(3, 92)(4, 95)(5, 94)(6, 81)(7, 100)(8, 102)(9, 104)(10, 82)(11, 106)(12, 108)(13, 83)(14, 110)(15, 86)(16, 109)(17, 85)(18, 112)(19, 114)(20, 111)(21, 87)(22, 116)(23, 88)(24, 90)(25, 118)(26, 120)(27, 91)(28, 93)(29, 98)(30, 97)(31, 101)(32, 96)(33, 119)(34, 117)(35, 99)(36, 103)(37, 115)(38, 113)(39, 105)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 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 E14.342 Graph:: simple bipartite v = 24 e = 80 f = 30 degree seq :: [ 4^20, 20^4 ] E14.347 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2 * Y1 * Y2, R * Y2 * R * Y2^-1, (Y3 * Y1^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1, (R * Y3)^2, (Y2^-1 * Y3)^2, (R * Y1)^2, Y1^4, Y2^-1 * Y1 * Y2 * Y1 * Y2^-3 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42, 7, 47, 5, 45)(3, 43, 10, 50, 18, 58, 13, 53)(4, 44, 14, 54, 19, 59, 9, 49)(6, 46, 8, 48, 20, 60, 16, 56)(11, 51, 24, 64, 32, 72, 27, 67)(12, 52, 28, 68, 33, 73, 23, 63)(15, 55, 29, 69, 34, 74, 22, 62)(17, 57, 21, 61, 25, 65, 31, 71)(26, 66, 38, 78, 40, 80, 36, 76)(30, 70, 39, 79, 37, 77, 35, 75)(81, 121, 83, 123, 91, 131, 105, 145, 100, 140, 87, 127, 98, 138, 112, 152, 97, 137, 86, 126)(82, 122, 88, 128, 101, 141, 107, 147, 93, 133, 85, 125, 96, 136, 111, 151, 104, 144, 90, 130)(84, 124, 95, 135, 110, 150, 120, 160, 113, 153, 99, 139, 114, 154, 117, 157, 106, 146, 92, 132)(89, 129, 103, 143, 116, 156, 119, 159, 109, 149, 94, 134, 108, 148, 118, 158, 115, 155, 102, 142) L = (1, 84)(2, 89)(3, 92)(4, 81)(5, 94)(6, 95)(7, 99)(8, 102)(9, 82)(10, 103)(11, 106)(12, 83)(13, 108)(14, 85)(15, 86)(16, 109)(17, 110)(18, 113)(19, 87)(20, 114)(21, 115)(22, 88)(23, 90)(24, 116)(25, 117)(26, 91)(27, 118)(28, 93)(29, 96)(30, 97)(31, 119)(32, 120)(33, 98)(34, 100)(35, 101)(36, 104)(37, 105)(38, 107)(39, 111)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4^8 ), ( 4^20 ) } Outer automorphisms :: reflexible Dual of E14.338 Graph:: bipartite v = 14 e = 80 f = 40 degree seq :: [ 8^10, 20^4 ] E14.348 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y2^-1 * Y1^-1)^2, (Y2^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^10 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 9, 49, 13, 53, 8, 48)(5, 45, 11, 51, 14, 54, 7, 47)(10, 50, 16, 56, 21, 61, 17, 57)(12, 52, 15, 55, 22, 62, 19, 59)(18, 58, 25, 65, 29, 69, 24, 64)(20, 60, 27, 67, 30, 70, 23, 63)(26, 66, 32, 72, 36, 76, 33, 73)(28, 68, 31, 71, 37, 77, 35, 75)(34, 74, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 90, 130, 98, 138, 106, 146, 114, 154, 108, 148, 100, 140, 92, 132, 85, 125)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 112, 152, 104, 144, 96, 136, 88, 128)(84, 124, 91, 131, 99, 139, 107, 147, 115, 155, 119, 159, 113, 153, 105, 145, 97, 137, 89, 129)(86, 126, 93, 133, 101, 141, 109, 149, 116, 156, 120, 160, 117, 157, 110, 150, 102, 142, 94, 134) L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 91)(6, 84)(7, 85)(8, 83)(9, 93)(10, 96)(11, 94)(12, 95)(13, 88)(14, 87)(15, 102)(16, 101)(17, 90)(18, 105)(19, 92)(20, 107)(21, 97)(22, 99)(23, 100)(24, 98)(25, 109)(26, 112)(27, 110)(28, 111)(29, 104)(30, 103)(31, 117)(32, 116)(33, 106)(34, 119)(35, 108)(36, 113)(37, 115)(38, 114)(39, 120)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4^8 ), ( 4^20 ) } Outer automorphisms :: reflexible Dual of E14.337 Graph:: bipartite v = 14 e = 80 f = 40 degree seq :: [ 8^10, 20^4 ] E14.349 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = C2 x ((C10 x C2) : C2) (small group id <80, 44>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^-2 * Y3, Y3^2 * Y2^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y3^-2 * Y1 * Y2^2 * Y1, (Y3 * Y1 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3^-1 * Y1, Y2 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3^-1 * Y2)^10 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 11, 51)(4, 44, 10, 50)(5, 45, 17, 57)(6, 46, 8, 48)(7, 47, 18, 58)(9, 49, 24, 64)(12, 52, 19, 59)(13, 53, 22, 62)(14, 54, 23, 63)(15, 55, 20, 60)(16, 56, 21, 61)(25, 65, 33, 73)(26, 66, 36, 76)(27, 67, 34, 74)(28, 68, 35, 75)(29, 69, 37, 77)(30, 70, 40, 80)(31, 71, 38, 78)(32, 72, 39, 79)(81, 121, 83, 123, 92, 132, 85, 125)(82, 122, 87, 127, 99, 139, 89, 129)(84, 124, 95, 135, 86, 126, 96, 136)(88, 128, 102, 142, 90, 130, 103, 143)(91, 131, 105, 145, 97, 137, 106, 146)(93, 133, 107, 147, 94, 134, 108, 148)(98, 138, 109, 149, 104, 144, 110, 150)(100, 140, 111, 151, 101, 141, 112, 152)(113, 153, 119, 159, 116, 156, 118, 158)(114, 154, 117, 157, 115, 155, 120, 160) L = (1, 84)(2, 88)(3, 93)(4, 92)(5, 94)(6, 81)(7, 100)(8, 99)(9, 101)(10, 82)(11, 103)(12, 86)(13, 85)(14, 83)(15, 98)(16, 104)(17, 102)(18, 96)(19, 90)(20, 89)(21, 87)(22, 91)(23, 97)(24, 95)(25, 114)(26, 115)(27, 113)(28, 116)(29, 118)(30, 119)(31, 117)(32, 120)(33, 108)(34, 106)(35, 105)(36, 107)(37, 112)(38, 110)(39, 109)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E14.350 Graph:: simple bipartite v = 30 e = 80 f = 24 degree seq :: [ 4^20, 8^10 ] E14.350 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = C2 x ((C10 x C2) : C2) (small group id <80, 44>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, Y3^-1 * Y1 * Y3 * Y1, Y3^4, (R * Y2 * Y3^-1)^2, Y1^2 * Y3^-1 * Y1^-3 * Y3^-1, Y1 * Y2 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y2 * Y1 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 18, 58, 30, 70, 15, 55, 24, 64, 31, 71, 16, 56, 5, 45)(3, 43, 8, 48, 19, 59, 33, 73, 38, 78, 26, 66, 36, 76, 39, 79, 27, 67, 12, 52)(4, 44, 14, 54, 29, 69, 21, 61, 10, 50, 6, 46, 17, 57, 32, 72, 20, 60, 9, 49)(11, 51, 25, 65, 37, 77, 35, 75, 23, 63, 13, 53, 28, 68, 40, 80, 34, 74, 22, 62)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 93, 133)(85, 125, 92, 132)(86, 126, 91, 131)(87, 127, 99, 139)(89, 129, 103, 143)(90, 130, 102, 142)(94, 134, 108, 148)(95, 135, 106, 146)(96, 136, 107, 147)(97, 137, 105, 145)(98, 138, 113, 153)(100, 140, 115, 155)(101, 141, 114, 154)(104, 144, 116, 156)(109, 149, 120, 160)(110, 150, 118, 158)(111, 151, 119, 159)(112, 152, 117, 157) L = (1, 84)(2, 89)(3, 91)(4, 95)(5, 94)(6, 81)(7, 100)(8, 102)(9, 104)(10, 82)(11, 106)(12, 105)(13, 83)(14, 110)(15, 86)(16, 109)(17, 85)(18, 112)(19, 114)(20, 111)(21, 87)(22, 116)(23, 88)(24, 90)(25, 118)(26, 93)(27, 117)(28, 92)(29, 98)(30, 97)(31, 101)(32, 96)(33, 120)(34, 119)(35, 99)(36, 103)(37, 113)(38, 108)(39, 115)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 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 E14.349 Graph:: simple bipartite v = 24 e = 80 f = 30 degree seq :: [ 4^20, 20^4 ] E14.351 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 8, 10}) Quotient :: edge Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^8, T1^-3 * T2^-5 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 26, 40, 25, 13, 5)(2, 7, 17, 31, 36, 24, 39, 32, 18, 8)(4, 11, 22, 37, 28, 14, 27, 34, 20, 10)(6, 15, 29, 38, 23, 12, 21, 35, 30, 16)(41, 42, 46, 54, 66, 64, 52, 44)(43, 48, 55, 68, 80, 76, 61, 50)(45, 47, 56, 67, 73, 79, 63, 51)(49, 58, 69, 77, 65, 71, 75, 60)(53, 57, 70, 74, 59, 72, 78, 62) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 16^8 ), ( 16^10 ) } Outer automorphisms :: reflexible Dual of E14.352 Transitivity :: ET+ Graph:: bipartite v = 9 e = 40 f = 5 degree seq :: [ 8^5, 10^4 ] E14.352 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 8, 10}) Quotient :: loop Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-2 * T2^-1, T2^-2 * T1^6, T2^-1 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1, T1^-2 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 41, 3, 43, 10, 50, 21, 61, 26, 66, 15, 55, 6, 46, 5, 45)(2, 42, 7, 47, 4, 44, 12, 52, 22, 62, 27, 67, 14, 54, 8, 48)(9, 49, 19, 59, 11, 51, 23, 63, 28, 68, 25, 65, 13, 53, 20, 60)(16, 56, 29, 69, 17, 57, 31, 71, 24, 64, 32, 72, 18, 58, 30, 70)(33, 73, 39, 79, 34, 74, 37, 77, 36, 76, 38, 78, 35, 75, 40, 80) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 53)(6, 54)(7, 56)(8, 58)(9, 45)(10, 44)(11, 43)(12, 57)(13, 55)(14, 66)(15, 68)(16, 48)(17, 47)(18, 67)(19, 73)(20, 75)(21, 51)(22, 50)(23, 74)(24, 52)(25, 76)(26, 62)(27, 64)(28, 61)(29, 77)(30, 79)(31, 78)(32, 80)(33, 60)(34, 59)(35, 65)(36, 63)(37, 70)(38, 69)(39, 72)(40, 71) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E14.351 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 40 f = 9 degree seq :: [ 16^5 ] E14.353 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 10}) Quotient :: dipole Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^8, Y1^2 * Y2^-2 * Y1^2 * Y2^-3, Y2^10, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 26, 66, 24, 64, 12, 52, 4, 44)(3, 43, 8, 48, 15, 55, 28, 68, 40, 80, 36, 76, 21, 61, 10, 50)(5, 45, 7, 47, 16, 56, 27, 67, 33, 73, 39, 79, 23, 63, 11, 51)(9, 49, 18, 58, 29, 69, 37, 77, 25, 65, 31, 71, 35, 75, 20, 60)(13, 53, 17, 57, 30, 70, 34, 74, 19, 59, 32, 72, 38, 78, 22, 62)(81, 121, 83, 123, 89, 129, 99, 139, 113, 153, 106, 146, 120, 160, 105, 145, 93, 133, 85, 125)(82, 122, 87, 127, 97, 137, 111, 151, 116, 156, 104, 144, 119, 159, 112, 152, 98, 138, 88, 128)(84, 124, 91, 131, 102, 142, 117, 157, 108, 148, 94, 134, 107, 147, 114, 154, 100, 140, 90, 130)(86, 126, 95, 135, 109, 149, 118, 158, 103, 143, 92, 132, 101, 141, 115, 155, 110, 150, 96, 136) L = (1, 83)(2, 87)(3, 89)(4, 91)(5, 81)(6, 95)(7, 97)(8, 82)(9, 99)(10, 84)(11, 102)(12, 101)(13, 85)(14, 107)(15, 109)(16, 86)(17, 111)(18, 88)(19, 113)(20, 90)(21, 115)(22, 117)(23, 92)(24, 119)(25, 93)(26, 120)(27, 114)(28, 94)(29, 118)(30, 96)(31, 116)(32, 98)(33, 106)(34, 100)(35, 110)(36, 104)(37, 108)(38, 103)(39, 112)(40, 105)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E14.354 Graph:: bipartite v = 9 e = 80 f = 45 degree seq :: [ 16^5, 20^4 ] E14.354 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 10}) Quotient :: dipole Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^8, Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-3 * Y2, (Y3^-1 * Y1^-1)^10 ] Map:: R = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(81, 121, 82, 122, 86, 126, 94, 134, 106, 146, 104, 144, 92, 132, 84, 124)(83, 123, 88, 128, 95, 135, 108, 148, 120, 160, 116, 156, 101, 141, 90, 130)(85, 125, 87, 127, 96, 136, 107, 147, 113, 153, 119, 159, 103, 143, 91, 131)(89, 129, 98, 138, 109, 149, 117, 157, 105, 145, 111, 151, 115, 155, 100, 140)(93, 133, 97, 137, 110, 150, 114, 154, 99, 139, 112, 152, 118, 158, 102, 142) L = (1, 83)(2, 87)(3, 89)(4, 91)(5, 81)(6, 95)(7, 97)(8, 82)(9, 99)(10, 84)(11, 102)(12, 101)(13, 85)(14, 107)(15, 109)(16, 86)(17, 111)(18, 88)(19, 113)(20, 90)(21, 115)(22, 117)(23, 92)(24, 119)(25, 93)(26, 120)(27, 114)(28, 94)(29, 118)(30, 96)(31, 116)(32, 98)(33, 106)(34, 100)(35, 110)(36, 104)(37, 108)(38, 103)(39, 112)(40, 105)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 16, 20 ), ( 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20 ) } Outer automorphisms :: reflexible Dual of E14.353 Graph:: simple bipartite v = 45 e = 80 f = 9 degree seq :: [ 2^40, 16^5 ] E14.355 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {8, 8, 10}) Quotient :: edge Aut^+ = C5 : C8 (small group id <40, 3>) Aut = C5 : C8 (small group id <40, 3>) |r| :: 1 Presentation :: [ X1^-1 * X2^-1 * X1^2 * X2^-1 * X1^-1, X2^-3 * X1 * X2 * X1^-1, X2 * X1 * X2^3 * X1^-1, X2^-1 * X1^3 * X2 * X1 * X2^-1, X1^8 ] Map:: non-degenerate R = (1, 2, 6, 18, 38, 35, 13, 4)(3, 9, 20, 37, 39, 22, 31, 11)(5, 15, 19, 32, 40, 26, 34, 16)(7, 21, 30, 17, 27, 36, 14, 23)(8, 24, 29, 10, 28, 33, 12, 25)(41, 43, 50, 63, 80, 78, 79, 65, 57, 45)(42, 47, 62, 55, 68, 75, 67, 49, 66, 48)(44, 52, 72, 51, 70, 58, 69, 56, 77, 54)(46, 59, 76, 64, 71, 53, 74, 61, 73, 60) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 16^8 ), ( 16^10 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: bipartite v = 9 e = 40 f = 5 degree seq :: [ 8^5, 10^4 ] E14.356 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {8, 8, 10}) Quotient :: loop Aut^+ = C5 : C8 (small group id <40, 3>) Aut = C5 : C8 (small group id <40, 3>) |r| :: 1 Presentation :: [ X2^-1 * X1 * X2^-1 * X1^-3, X2 * X1^-1 * X2^-3 * X1^-1, X2 * X1^2 * X2^-2 * X1, X2^2 * X1 * X2 * X1^-2, X2^-1 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1^-2 * X2^-1, X1^-1 * X2 * X1^-1 * X2^5, X1^8 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 18, 58, 34, 74, 30, 70, 13, 53, 4, 44)(3, 43, 9, 49, 25, 65, 8, 48, 24, 64, 39, 79, 31, 71, 11, 51)(5, 45, 15, 55, 27, 67, 37, 77, 29, 69, 12, 52, 32, 72, 16, 56)(7, 47, 21, 61, 10, 50, 20, 60, 38, 78, 28, 68, 17, 57, 23, 63)(14, 54, 19, 59, 36, 76, 22, 62, 35, 75, 33, 73, 40, 80, 26, 66) L = (1, 43)(2, 47)(3, 50)(4, 52)(5, 41)(6, 59)(7, 62)(8, 42)(9, 67)(10, 69)(11, 70)(12, 65)(13, 73)(14, 44)(15, 71)(16, 60)(17, 45)(18, 55)(19, 77)(20, 46)(21, 79)(22, 51)(23, 53)(24, 57)(25, 75)(26, 48)(27, 80)(28, 49)(29, 74)(30, 78)(31, 54)(32, 76)(33, 56)(34, 64)(35, 58)(36, 68)(37, 63)(38, 66)(39, 72)(40, 61) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 5 e = 40 f = 9 degree seq :: [ 16^5 ] E14.357 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {8, 8, 10}) Quotient :: loop Aut^+ = C5 : C8 (small group id <40, 3>) Aut = (C5 : C8) : C2 (small group id <80, 29>) |r| :: 2 Presentation :: [ F^2, F * T1 * F * T2, T2^2 * T1 * T2 * T1^-2, T2^2 * T1^-2 * T2^-1 * T1^-1, T2 * T1^3 * T2 * T1^-1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2, T2^8 ] Map:: non-degenerate R = (1, 3, 10, 29, 34, 24, 17, 5)(2, 7, 22, 11, 30, 38, 26, 8)(4, 12, 25, 35, 18, 15, 31, 14)(6, 19, 37, 23, 13, 33, 16, 20)(9, 27, 40, 21, 39, 32, 36, 28)(41, 42, 46, 58, 74, 70, 53, 44)(43, 49, 65, 48, 64, 79, 71, 51)(45, 55, 67, 77, 69, 52, 72, 56)(47, 61, 50, 60, 78, 68, 57, 63)(54, 59, 76, 62, 75, 73, 80, 66) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^8 ) } Outer automorphisms :: reflexible Dual of E14.358 Transitivity :: ET+ VT AT Graph:: bipartite v = 10 e = 40 f = 4 degree seq :: [ 8^10 ] E14.358 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {8, 8, 10}) Quotient :: edge Aut^+ = C5 : C8 (small group id <40, 3>) Aut = (C5 : C8) : C2 (small group id <80, 29>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, F * T1 * T2 * F * T1^-1, T2^-1 * T1 * T2 * T1^-1 * T2^-2, T2^3 * T1^-1 * T2 * T1, T2 * T1^2 * T2 * T1^-2, T2 * T1^3 * T2^2 * T1, T1 * T2^-1 * T1^3 * T2^-2, T1^8 ] Map:: non-degenerate R = (1, 41, 3, 43, 10, 50, 23, 63, 40, 80, 38, 78, 39, 79, 25, 65, 17, 57, 5, 45)(2, 42, 7, 47, 22, 62, 15, 55, 28, 68, 35, 75, 27, 67, 9, 49, 26, 66, 8, 48)(4, 44, 12, 52, 32, 72, 11, 51, 30, 70, 18, 58, 29, 69, 16, 56, 37, 77, 14, 54)(6, 46, 19, 59, 36, 76, 24, 64, 31, 71, 13, 53, 34, 74, 21, 61, 33, 73, 20, 60) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 55)(6, 58)(7, 61)(8, 64)(9, 60)(10, 68)(11, 43)(12, 65)(13, 44)(14, 63)(15, 59)(16, 45)(17, 67)(18, 78)(19, 72)(20, 77)(21, 70)(22, 71)(23, 47)(24, 69)(25, 48)(26, 74)(27, 76)(28, 73)(29, 50)(30, 57)(31, 51)(32, 80)(33, 52)(34, 56)(35, 53)(36, 54)(37, 79)(38, 75)(39, 62)(40, 66) local type(s) :: { ( 8^20 ) } Outer automorphisms :: reflexible Dual of E14.357 Transitivity :: ET+ VT+ Graph:: bipartite v = 4 e = 40 f = 10 degree seq :: [ 20^4 ] E14.359 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {8, 8, 10}) Quotient :: edge^2 Aut^+ = C5 : C8 (small group id <40, 3>) Aut = (C5 : C8) : C2 (small group id <80, 29>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1^2 * Y3^-1 * Y1^-1 * Y2, Y1^2 * Y3 * Y2^-2, Y1^2 * Y2^-2 * Y3^-1, Y1 * Y3^-3 * Y2, Y2 * Y1 * Y2^-1 * Y3^-1 * Y2, Y1 * Y3 * Y2 * Y3^-2, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y1^8, Y2^8 ] Map:: polytopal non-degenerate R = (1, 41, 4, 44, 17, 57, 12, 52, 38, 78, 40, 80, 37, 77, 23, 63, 31, 71, 7, 47)(2, 42, 9, 49, 33, 73, 28, 68, 19, 59, 39, 79, 27, 67, 6, 46, 25, 65, 11, 51)(3, 43, 5, 45, 21, 61, 16, 56, 18, 58, 34, 74, 32, 72, 29, 69, 30, 70, 15, 55)(8, 48, 13, 53, 14, 54, 36, 76, 20, 60, 22, 62, 26, 66, 10, 50, 35, 75, 24, 64)(81, 82, 88, 112, 120, 119, 102, 85)(83, 92, 89, 90, 114, 111, 107, 94)(84, 86, 104, 95, 117, 113, 100, 98)(87, 108, 93, 96, 118, 105, 106, 110)(91, 116, 109, 97, 99, 115, 101, 103)(121, 123, 133, 153, 160, 154, 146, 126)(122, 127, 149, 134, 159, 158, 141, 130)(124, 136, 128, 131, 157, 150, 142, 139)(125, 140, 129, 137, 152, 144, 147, 143)(132, 135, 155, 148, 151, 138, 156, 145) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4^8 ), ( 4^20 ) } Outer automorphisms :: reflexible Dual of E14.362 Graph:: bipartite v = 14 e = 80 f = 40 degree seq :: [ 8^10, 20^4 ] E14.360 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {8, 8, 10}) Quotient :: edge^2 Aut^+ = C5 : C8 (small group id <40, 3>) Aut = (C5 : C8) : C2 (small group id <80, 29>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2^2 * Y1^-2 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-2 * Y1^2, Y2 * Y1^3 * Y2 * Y1^-1, Y2^8, (Y1^-1 * Y3^-1 * Y2^-1)^10 ] Map:: R = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(81, 82, 86, 98, 114, 110, 93, 84)(83, 89, 105, 88, 104, 119, 111, 91)(85, 95, 107, 117, 109, 92, 112, 96)(87, 101, 90, 100, 118, 108, 97, 103)(94, 99, 116, 102, 115, 113, 120, 106)(121, 123, 130, 149, 154, 144, 137, 125)(122, 127, 142, 131, 150, 158, 146, 128)(124, 132, 145, 155, 138, 135, 151, 134)(126, 139, 157, 143, 133, 153, 136, 140)(129, 147, 160, 141, 159, 152, 156, 148) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 40, 40 ), ( 40^8 ) } Outer automorphisms :: reflexible Dual of E14.361 Graph:: simple bipartite v = 50 e = 80 f = 4 degree seq :: [ 2^40, 8^10 ] E14.361 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {8, 8, 10}) Quotient :: loop^2 Aut^+ = C5 : C8 (small group id <40, 3>) Aut = (C5 : C8) : C2 (small group id <80, 29>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1^2 * Y3^-1 * Y1^-1 * Y2, Y1^2 * Y3 * Y2^-2, Y1^2 * Y2^-2 * Y3^-1, Y1 * Y3^-3 * Y2, Y2 * Y1 * Y2^-1 * Y3^-1 * Y2, Y1 * Y3 * Y2 * Y3^-2, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y1^8, Y2^8 ] Map:: R = (1, 41, 81, 121, 4, 44, 84, 124, 17, 57, 97, 137, 12, 52, 92, 132, 38, 78, 118, 158, 40, 80, 120, 160, 37, 77, 117, 157, 23, 63, 103, 143, 31, 71, 111, 151, 7, 47, 87, 127)(2, 42, 82, 122, 9, 49, 89, 129, 33, 73, 113, 153, 28, 68, 108, 148, 19, 59, 99, 139, 39, 79, 119, 159, 27, 67, 107, 147, 6, 46, 86, 126, 25, 65, 105, 145, 11, 51, 91, 131)(3, 43, 83, 123, 5, 45, 85, 125, 21, 61, 101, 141, 16, 56, 96, 136, 18, 58, 98, 138, 34, 74, 114, 154, 32, 72, 112, 152, 29, 69, 109, 149, 30, 70, 110, 150, 15, 55, 95, 135)(8, 48, 88, 128, 13, 53, 93, 133, 14, 54, 94, 134, 36, 76, 116, 156, 20, 60, 100, 140, 22, 62, 102, 142, 26, 66, 106, 146, 10, 50, 90, 130, 35, 75, 115, 155, 24, 64, 104, 144) L = (1, 42)(2, 48)(3, 52)(4, 46)(5, 41)(6, 64)(7, 68)(8, 72)(9, 50)(10, 74)(11, 76)(12, 49)(13, 56)(14, 43)(15, 77)(16, 78)(17, 59)(18, 44)(19, 75)(20, 58)(21, 63)(22, 45)(23, 51)(24, 55)(25, 66)(26, 70)(27, 54)(28, 53)(29, 57)(30, 47)(31, 67)(32, 80)(33, 60)(34, 71)(35, 61)(36, 69)(37, 73)(38, 65)(39, 62)(40, 79)(81, 123)(82, 127)(83, 133)(84, 136)(85, 140)(86, 121)(87, 149)(88, 131)(89, 137)(90, 122)(91, 157)(92, 135)(93, 153)(94, 159)(95, 155)(96, 128)(97, 152)(98, 156)(99, 124)(100, 129)(101, 130)(102, 139)(103, 125)(104, 147)(105, 132)(106, 126)(107, 143)(108, 151)(109, 134)(110, 142)(111, 138)(112, 144)(113, 160)(114, 146)(115, 148)(116, 145)(117, 150)(118, 141)(119, 158)(120, 154) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E14.360 Transitivity :: VT+ Graph:: bipartite v = 4 e = 80 f = 50 degree seq :: [ 40^4 ] E14.362 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {8, 8, 10}) Quotient :: loop^2 Aut^+ = C5 : C8 (small group id <40, 3>) Aut = (C5 : C8) : C2 (small group id <80, 29>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2^2 * Y1^-2 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-2 * Y1^2, Y2 * Y1^3 * Y2 * Y1^-1, Y2^8, (Y1^-1 * Y3^-1 * Y2^-1)^10 ] Map:: polytopal non-degenerate R = (1, 41, 81, 121)(2, 42, 82, 122)(3, 43, 83, 123)(4, 44, 84, 124)(5, 45, 85, 125)(6, 46, 86, 126)(7, 47, 87, 127)(8, 48, 88, 128)(9, 49, 89, 129)(10, 50, 90, 130)(11, 51, 91, 131)(12, 52, 92, 132)(13, 53, 93, 133)(14, 54, 94, 134)(15, 55, 95, 135)(16, 56, 96, 136)(17, 57, 97, 137)(18, 58, 98, 138)(19, 59, 99, 139)(20, 60, 100, 140)(21, 61, 101, 141)(22, 62, 102, 142)(23, 63, 103, 143)(24, 64, 104, 144)(25, 65, 105, 145)(26, 66, 106, 146)(27, 67, 107, 147)(28, 68, 108, 148)(29, 69, 109, 149)(30, 70, 110, 150)(31, 71, 111, 151)(32, 72, 112, 152)(33, 73, 113, 153)(34, 74, 114, 154)(35, 75, 115, 155)(36, 76, 116, 156)(37, 77, 117, 157)(38, 78, 118, 158)(39, 79, 119, 159)(40, 80, 120, 160) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 55)(6, 58)(7, 61)(8, 64)(9, 65)(10, 60)(11, 43)(12, 72)(13, 44)(14, 59)(15, 67)(16, 45)(17, 63)(18, 74)(19, 76)(20, 78)(21, 50)(22, 75)(23, 47)(24, 79)(25, 48)(26, 54)(27, 77)(28, 57)(29, 52)(30, 53)(31, 51)(32, 56)(33, 80)(34, 70)(35, 73)(36, 62)(37, 69)(38, 68)(39, 71)(40, 66)(81, 123)(82, 127)(83, 130)(84, 132)(85, 121)(86, 139)(87, 142)(88, 122)(89, 147)(90, 149)(91, 150)(92, 145)(93, 153)(94, 124)(95, 151)(96, 140)(97, 125)(98, 135)(99, 157)(100, 126)(101, 159)(102, 131)(103, 133)(104, 137)(105, 155)(106, 128)(107, 160)(108, 129)(109, 154)(110, 158)(111, 134)(112, 156)(113, 136)(114, 144)(115, 138)(116, 148)(117, 143)(118, 146)(119, 152)(120, 141) local type(s) :: { ( 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E14.359 Transitivity :: VT+ Graph:: simple bipartite v = 40 e = 80 f = 14 degree seq :: [ 4^40 ] E14.363 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 20, 20}) Quotient :: edge Aut^+ = C5 x Q8 (small group id <40, 11>) Aut = (C4 x D10) : C2 (small group id <80, 42>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2^10 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 18, 26, 34, 38, 30, 22, 14, 6, 13, 21, 29, 37, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 35, 27, 19, 11, 4, 9, 17, 25, 33, 40, 32, 24, 16, 8)(41, 42, 46, 44)(43, 49, 53, 47)(45, 51, 54, 48)(50, 55, 61, 57)(52, 56, 62, 59)(58, 65, 69, 63)(60, 67, 70, 64)(66, 71, 77, 73)(68, 72, 78, 75)(74, 80, 76, 79) 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) :: { ( 40^4 ), ( 40^20 ) } Outer automorphisms :: reflexible Dual of E14.364 Transitivity :: ET+ Graph:: bipartite v = 12 e = 40 f = 2 degree seq :: [ 4^10, 20^2 ] E14.364 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 20, 20}) Quotient :: loop Aut^+ = C5 x Q8 (small group id <40, 11>) Aut = (C4 x D10) : C2 (small group id <80, 42>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2^10 * T1^-1 ] Map:: non-degenerate R = (1, 41, 3, 43, 10, 50, 18, 58, 26, 66, 34, 74, 38, 78, 30, 70, 22, 62, 14, 54, 6, 46, 13, 53, 21, 61, 29, 69, 37, 77, 36, 76, 28, 68, 20, 60, 12, 52, 5, 45)(2, 42, 7, 47, 15, 55, 23, 63, 31, 71, 39, 79, 35, 75, 27, 67, 19, 59, 11, 51, 4, 44, 9, 49, 17, 57, 25, 65, 33, 73, 40, 80, 32, 72, 24, 64, 16, 56, 8, 48) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 51)(6, 44)(7, 43)(8, 45)(9, 53)(10, 55)(11, 54)(12, 56)(13, 47)(14, 48)(15, 61)(16, 62)(17, 50)(18, 65)(19, 52)(20, 67)(21, 57)(22, 59)(23, 58)(24, 60)(25, 69)(26, 71)(27, 70)(28, 72)(29, 63)(30, 64)(31, 77)(32, 78)(33, 66)(34, 80)(35, 68)(36, 79)(37, 73)(38, 75)(39, 74)(40, 76) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E14.363 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 40 f = 12 degree seq :: [ 40^2 ] E14.365 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 20, 20}) Quotient :: dipole Aut^+ = C5 x Q8 (small group id <40, 11>) Aut = (C4 x D10) : C2 (small group id <80, 42>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2^-1 * Y1 * Y2 * Y3^-1, Y3 * Y2 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^9 * Y3^-2 * Y2, 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 ] Map:: R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 9, 49, 13, 53, 7, 47)(5, 45, 11, 51, 14, 54, 8, 48)(10, 50, 15, 55, 21, 61, 17, 57)(12, 52, 16, 56, 22, 62, 19, 59)(18, 58, 25, 65, 29, 69, 23, 63)(20, 60, 27, 67, 30, 70, 24, 64)(26, 66, 31, 71, 37, 77, 33, 73)(28, 68, 32, 72, 38, 78, 35, 75)(34, 74, 40, 80, 36, 76, 39, 79)(81, 121, 83, 123, 90, 130, 98, 138, 106, 146, 114, 154, 118, 158, 110, 150, 102, 142, 94, 134, 86, 126, 93, 133, 101, 141, 109, 149, 117, 157, 116, 156, 108, 148, 100, 140, 92, 132, 85, 125)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 119, 159, 115, 155, 107, 147, 99, 139, 91, 131, 84, 124, 89, 129, 97, 137, 105, 145, 113, 153, 120, 160, 112, 152, 104, 144, 96, 136, 88, 128) L = (1, 84)(2, 81)(3, 87)(4, 86)(5, 88)(6, 82)(7, 93)(8, 94)(9, 83)(10, 97)(11, 85)(12, 99)(13, 89)(14, 91)(15, 90)(16, 92)(17, 101)(18, 103)(19, 102)(20, 104)(21, 95)(22, 96)(23, 109)(24, 110)(25, 98)(26, 113)(27, 100)(28, 115)(29, 105)(30, 107)(31, 106)(32, 108)(33, 117)(34, 119)(35, 118)(36, 120)(37, 111)(38, 112)(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) :: { ( 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 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 E14.366 Graph:: bipartite v = 12 e = 80 f = 42 degree seq :: [ 8^10, 40^2 ] E14.366 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 20, 20}) Quotient :: dipole Aut^+ = C5 x Q8 (small group id <40, 11>) Aut = (C4 x D10) : C2 (small group id <80, 42>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y1^-1 * Y3^-1 * Y1^-4 * Y3^-1 * Y1^-5 ] Map:: R = (1, 41, 2, 42, 6, 46, 13, 53, 21, 61, 29, 69, 37, 77, 33, 73, 25, 65, 17, 57, 9, 49, 16, 56, 24, 64, 32, 72, 40, 80, 36, 76, 28, 68, 20, 60, 12, 52, 4, 44)(3, 43, 8, 48, 14, 54, 23, 63, 30, 70, 39, 79, 35, 75, 27, 67, 19, 59, 11, 51, 5, 45, 7, 47, 15, 55, 22, 62, 31, 71, 38, 78, 34, 74, 26, 66, 18, 58, 10, 50)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 89)(4, 91)(5, 81)(6, 94)(7, 96)(8, 82)(9, 85)(10, 84)(11, 97)(12, 98)(13, 102)(14, 104)(15, 86)(16, 88)(17, 90)(18, 105)(19, 92)(20, 107)(21, 110)(22, 112)(23, 93)(24, 95)(25, 99)(26, 100)(27, 113)(28, 114)(29, 118)(30, 120)(31, 101)(32, 103)(33, 106)(34, 117)(35, 108)(36, 119)(37, 115)(38, 116)(39, 109)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) } Outer automorphisms :: reflexible Dual of E14.365 Graph:: simple bipartite v = 42 e = 80 f = 12 degree seq :: [ 2^40, 40^2 ] E14.367 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 8, 40}) Quotient :: edge Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^8 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 23, 13, 5)(2, 7, 16, 26, 35, 27, 17, 8)(4, 10, 19, 29, 36, 32, 22, 12)(6, 14, 24, 33, 39, 34, 25, 15)(11, 20, 30, 37, 40, 38, 31, 21)(41, 42, 46, 51, 44)(43, 47, 54, 60, 50)(45, 48, 55, 61, 52)(49, 56, 64, 70, 59)(53, 57, 65, 71, 62)(58, 66, 73, 77, 69)(63, 67, 74, 78, 72)(68, 75, 79, 80, 76) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 80^5 ), ( 80^8 ) } Outer automorphisms :: reflexible Dual of E14.371 Transitivity :: ET+ Graph:: simple bipartite v = 13 e = 40 f = 1 degree seq :: [ 5^8, 8^5 ] E14.368 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 8, 40}) Quotient :: edge Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^5 * T1^-3, T1^8, (T1^-1 * T2^-1)^5 ] Map:: non-degenerate R = (1, 3, 9, 19, 28, 14, 27, 39, 35, 23, 11, 21, 32, 18, 8, 2, 7, 17, 31, 38, 26, 37, 36, 24, 12, 4, 10, 20, 30, 16, 6, 15, 29, 40, 34, 22, 33, 25, 13, 5)(41, 42, 46, 54, 66, 62, 51, 44)(43, 47, 55, 67, 77, 73, 61, 50)(45, 48, 56, 68, 78, 74, 63, 52)(49, 57, 69, 79, 76, 65, 72, 60)(53, 58, 70, 59, 71, 80, 75, 64) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10^8 ), ( 10^40 ) } Outer automorphisms :: reflexible Dual of E14.372 Transitivity :: ET+ Graph:: bipartite v = 6 e = 40 f = 8 degree seq :: [ 8^5, 40 ] E14.369 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 8, 40}) Quotient :: edge Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^5, T2^2 * T1^-8, (T1^-1 * T2^-1)^8 ] 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, 34, 40, 32)(24, 35, 39, 31, 36)(41, 42, 46, 54, 64, 74, 69, 59, 49, 57, 67, 77, 79, 72, 62, 52, 45, 48, 56, 66, 76, 70, 60, 50, 43, 47, 55, 65, 75, 80, 73, 63, 53, 58, 68, 78, 71, 61, 51, 44) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 16^5 ), ( 16^40 ) } Outer automorphisms :: reflexible Dual of E14.370 Transitivity :: ET+ Graph:: bipartite v = 9 e = 40 f = 5 degree seq :: [ 5^8, 40 ] E14.370 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 8, 40}) Quotient :: loop Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^8 ] Map:: non-degenerate R = (1, 41, 3, 43, 9, 49, 18, 58, 28, 68, 23, 63, 13, 53, 5, 45)(2, 42, 7, 47, 16, 56, 26, 66, 35, 75, 27, 67, 17, 57, 8, 48)(4, 44, 10, 50, 19, 59, 29, 69, 36, 76, 32, 72, 22, 62, 12, 52)(6, 46, 14, 54, 24, 64, 33, 73, 39, 79, 34, 74, 25, 65, 15, 55)(11, 51, 20, 60, 30, 70, 37, 77, 40, 80, 38, 78, 31, 71, 21, 61) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 51)(7, 54)(8, 55)(9, 56)(10, 43)(11, 44)(12, 45)(13, 57)(14, 60)(15, 61)(16, 64)(17, 65)(18, 66)(19, 49)(20, 50)(21, 52)(22, 53)(23, 67)(24, 70)(25, 71)(26, 73)(27, 74)(28, 75)(29, 58)(30, 59)(31, 62)(32, 63)(33, 77)(34, 78)(35, 79)(36, 68)(37, 69)(38, 72)(39, 80)(40, 76) local type(s) :: { ( 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40 ) } Outer automorphisms :: reflexible Dual of E14.369 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 40 f = 9 degree seq :: [ 16^5 ] E14.371 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 8, 40}) Quotient :: loop Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^5 * T1^-3, T1^8, (T1^-1 * T2^-1)^5 ] Map:: non-degenerate R = (1, 41, 3, 43, 9, 49, 19, 59, 28, 68, 14, 54, 27, 67, 39, 79, 35, 75, 23, 63, 11, 51, 21, 61, 32, 72, 18, 58, 8, 48, 2, 42, 7, 47, 17, 57, 31, 71, 38, 78, 26, 66, 37, 77, 36, 76, 24, 64, 12, 52, 4, 44, 10, 50, 20, 60, 30, 70, 16, 56, 6, 46, 15, 55, 29, 69, 40, 80, 34, 74, 22, 62, 33, 73, 25, 65, 13, 53, 5, 45) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 54)(7, 55)(8, 56)(9, 57)(10, 43)(11, 44)(12, 45)(13, 58)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 72)(26, 62)(27, 77)(28, 78)(29, 79)(30, 59)(31, 80)(32, 60)(33, 61)(34, 63)(35, 64)(36, 65)(37, 73)(38, 74)(39, 76)(40, 75) local type(s) :: { ( 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8 ) } Outer automorphisms :: reflexible Dual of E14.367 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 40 f = 13 degree seq :: [ 80 ] E14.372 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 8, 40}) Quotient :: loop Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^5, T2^2 * T1^-8, (T1^-1 * T2^-1)^8 ] Map:: non-degenerate R = (1, 41, 3, 43, 9, 49, 13, 53, 5, 45)(2, 42, 7, 47, 17, 57, 18, 58, 8, 48)(4, 44, 10, 50, 19, 59, 23, 63, 12, 52)(6, 46, 15, 55, 27, 67, 28, 68, 16, 56)(11, 51, 20, 60, 29, 69, 33, 73, 22, 62)(14, 54, 25, 65, 37, 77, 38, 78, 26, 66)(21, 61, 30, 70, 34, 74, 40, 80, 32, 72)(24, 64, 35, 75, 39, 79, 31, 71, 36, 76) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 54)(7, 55)(8, 56)(9, 57)(10, 43)(11, 44)(12, 45)(13, 58)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 59)(30, 60)(31, 61)(32, 62)(33, 63)(34, 69)(35, 80)(36, 70)(37, 79)(38, 71)(39, 72)(40, 73) local type(s) :: { ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) } Outer automorphisms :: reflexible Dual of E14.368 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 40 f = 6 degree seq :: [ 10^8 ] E14.373 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 8, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y1^5, Y2^8, Y3^40 ] Map:: R = (1, 41, 2, 42, 6, 46, 11, 51, 4, 44)(3, 43, 7, 47, 14, 54, 20, 60, 10, 50)(5, 45, 8, 48, 15, 55, 21, 61, 12, 52)(9, 49, 16, 56, 24, 64, 30, 70, 19, 59)(13, 53, 17, 57, 25, 65, 31, 71, 22, 62)(18, 58, 26, 66, 33, 73, 37, 77, 29, 69)(23, 63, 27, 67, 34, 74, 38, 78, 32, 72)(28, 68, 35, 75, 39, 79, 40, 80, 36, 76)(81, 121, 83, 123, 89, 129, 98, 138, 108, 148, 103, 143, 93, 133, 85, 125)(82, 122, 87, 127, 96, 136, 106, 146, 115, 155, 107, 147, 97, 137, 88, 128)(84, 124, 90, 130, 99, 139, 109, 149, 116, 156, 112, 152, 102, 142, 92, 132)(86, 126, 94, 134, 104, 144, 113, 153, 119, 159, 114, 154, 105, 145, 95, 135)(91, 131, 100, 140, 110, 150, 117, 157, 120, 160, 118, 158, 111, 151, 101, 141) L = (1, 84)(2, 81)(3, 90)(4, 91)(5, 92)(6, 82)(7, 83)(8, 85)(9, 99)(10, 100)(11, 86)(12, 101)(13, 102)(14, 87)(15, 88)(16, 89)(17, 93)(18, 109)(19, 110)(20, 94)(21, 95)(22, 111)(23, 112)(24, 96)(25, 97)(26, 98)(27, 103)(28, 116)(29, 117)(30, 104)(31, 105)(32, 118)(33, 106)(34, 107)(35, 108)(36, 120)(37, 113)(38, 114)(39, 115)(40, 119)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 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 E14.376 Graph:: bipartite v = 13 e = 80 f = 41 degree seq :: [ 10^8, 16^5 ] E14.374 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 8, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^5 * Y1^-3, Y1^8, (Y3^-1 * Y1^-1)^5 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 26, 66, 22, 62, 11, 51, 4, 44)(3, 43, 7, 47, 15, 55, 27, 67, 37, 77, 33, 73, 21, 61, 10, 50)(5, 45, 8, 48, 16, 56, 28, 68, 38, 78, 34, 74, 23, 63, 12, 52)(9, 49, 17, 57, 29, 69, 39, 79, 36, 76, 25, 65, 32, 72, 20, 60)(13, 53, 18, 58, 30, 70, 19, 59, 31, 71, 40, 80, 35, 75, 24, 64)(81, 121, 83, 123, 89, 129, 99, 139, 108, 148, 94, 134, 107, 147, 119, 159, 115, 155, 103, 143, 91, 131, 101, 141, 112, 152, 98, 138, 88, 128, 82, 122, 87, 127, 97, 137, 111, 151, 118, 158, 106, 146, 117, 157, 116, 156, 104, 144, 92, 132, 84, 124, 90, 130, 100, 140, 110, 150, 96, 136, 86, 126, 95, 135, 109, 149, 120, 160, 114, 154, 102, 142, 113, 153, 105, 145, 93, 133, 85, 125) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 95)(7, 97)(8, 82)(9, 99)(10, 100)(11, 101)(12, 84)(13, 85)(14, 107)(15, 109)(16, 86)(17, 111)(18, 88)(19, 108)(20, 110)(21, 112)(22, 113)(23, 91)(24, 92)(25, 93)(26, 117)(27, 119)(28, 94)(29, 120)(30, 96)(31, 118)(32, 98)(33, 105)(34, 102)(35, 103)(36, 104)(37, 116)(38, 106)(39, 115)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ), ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 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 E14.375 Graph:: bipartite v = 6 e = 80 f = 48 degree seq :: [ 16^5, 80 ] E14.375 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 8, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y2^-5, Y2^5, Y3^-8 * Y2^-2, (Y2^-1 * Y3)^8, (Y3^-1 * Y1^-1)^40 ] Map:: R = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(81, 121, 82, 122, 86, 126, 91, 131, 84, 124)(83, 123, 87, 127, 94, 134, 100, 140, 90, 130)(85, 125, 88, 128, 95, 135, 101, 141, 92, 132)(89, 129, 96, 136, 104, 144, 110, 150, 99, 139)(93, 133, 97, 137, 105, 145, 111, 151, 102, 142)(98, 138, 106, 146, 114, 154, 120, 160, 109, 149)(103, 143, 107, 147, 115, 155, 118, 158, 112, 152)(108, 148, 116, 156, 113, 153, 117, 157, 119, 159) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 94)(7, 96)(8, 82)(9, 98)(10, 99)(11, 100)(12, 84)(13, 85)(14, 104)(15, 86)(16, 106)(17, 88)(18, 108)(19, 109)(20, 110)(21, 91)(22, 92)(23, 93)(24, 114)(25, 95)(26, 116)(27, 97)(28, 118)(29, 119)(30, 120)(31, 101)(32, 102)(33, 103)(34, 113)(35, 105)(36, 112)(37, 107)(38, 111)(39, 115)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 16, 80 ), ( 16, 80, 16, 80, 16, 80, 16, 80, 16, 80 ) } Outer automorphisms :: reflexible Dual of E14.374 Graph:: simple bipartite v = 48 e = 80 f = 6 degree seq :: [ 2^40, 10^8 ] E14.376 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 8, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^2 * Y1^-8, Y3^10, (Y3 * Y2^-1)^5 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 24, 64, 34, 74, 29, 69, 19, 59, 9, 49, 17, 57, 27, 67, 37, 77, 39, 79, 32, 72, 22, 62, 12, 52, 5, 45, 8, 48, 16, 56, 26, 66, 36, 76, 30, 70, 20, 60, 10, 50, 3, 43, 7, 47, 15, 55, 25, 65, 35, 75, 40, 80, 33, 73, 23, 63, 13, 53, 18, 58, 28, 68, 38, 78, 31, 71, 21, 61, 11, 51, 4, 44)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 95)(7, 97)(8, 82)(9, 93)(10, 99)(11, 100)(12, 84)(13, 85)(14, 105)(15, 107)(16, 86)(17, 98)(18, 88)(19, 103)(20, 109)(21, 110)(22, 91)(23, 92)(24, 115)(25, 117)(26, 94)(27, 108)(28, 96)(29, 113)(30, 114)(31, 116)(32, 101)(33, 102)(34, 120)(35, 119)(36, 104)(37, 118)(38, 106)(39, 111)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 10, 16 ), ( 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16 ) } Outer automorphisms :: reflexible Dual of E14.373 Graph:: bipartite v = 41 e = 80 f = 13 degree seq :: [ 2^40, 80 ] E14.377 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 8, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1^5, Y2^2 * Y3 * Y2^6 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3^-1 * Y1 * Y3^-1 * Y2^-2 * Y1 * Y3^-1 * Y2^-2 * Y1 * Y3^-1 * Y2^-2 * Y1 * Y3^-1 * Y2^-2 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 41, 2, 42, 6, 46, 11, 51, 4, 44)(3, 43, 7, 47, 14, 54, 20, 60, 10, 50)(5, 45, 8, 48, 15, 55, 21, 61, 12, 52)(9, 49, 16, 56, 24, 64, 30, 70, 19, 59)(13, 53, 17, 57, 25, 65, 31, 71, 22, 62)(18, 58, 26, 66, 34, 74, 38, 78, 29, 69)(23, 63, 27, 67, 35, 75, 39, 79, 32, 72)(28, 68, 36, 76, 40, 80, 33, 73, 37, 77)(81, 121, 83, 123, 89, 129, 98, 138, 108, 148, 115, 155, 105, 145, 95, 135, 86, 126, 94, 134, 104, 144, 114, 154, 120, 160, 112, 152, 102, 142, 92, 132, 84, 124, 90, 130, 99, 139, 109, 149, 117, 157, 107, 147, 97, 137, 88, 128, 82, 122, 87, 127, 96, 136, 106, 146, 116, 156, 119, 159, 111, 151, 101, 141, 91, 131, 100, 140, 110, 150, 118, 158, 113, 153, 103, 143, 93, 133, 85, 125) L = (1, 84)(2, 81)(3, 90)(4, 91)(5, 92)(6, 82)(7, 83)(8, 85)(9, 99)(10, 100)(11, 86)(12, 101)(13, 102)(14, 87)(15, 88)(16, 89)(17, 93)(18, 109)(19, 110)(20, 94)(21, 95)(22, 111)(23, 112)(24, 96)(25, 97)(26, 98)(27, 103)(28, 117)(29, 118)(30, 104)(31, 105)(32, 119)(33, 120)(34, 106)(35, 107)(36, 108)(37, 113)(38, 114)(39, 115)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E14.378 Graph:: bipartite v = 9 e = 80 f = 45 degree seq :: [ 10^8, 80 ] E14.378 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 8, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1), (R * Y2 * Y3^-1)^2, Y3^5 * Y1^-3, Y1^8, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^40 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 26, 66, 22, 62, 11, 51, 4, 44)(3, 43, 7, 47, 15, 55, 27, 67, 37, 77, 33, 73, 21, 61, 10, 50)(5, 45, 8, 48, 16, 56, 28, 68, 38, 78, 34, 74, 23, 63, 12, 52)(9, 49, 17, 57, 29, 69, 39, 79, 36, 76, 25, 65, 32, 72, 20, 60)(13, 53, 18, 58, 30, 70, 19, 59, 31, 71, 40, 80, 35, 75, 24, 64)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 95)(7, 97)(8, 82)(9, 99)(10, 100)(11, 101)(12, 84)(13, 85)(14, 107)(15, 109)(16, 86)(17, 111)(18, 88)(19, 108)(20, 110)(21, 112)(22, 113)(23, 91)(24, 92)(25, 93)(26, 117)(27, 119)(28, 94)(29, 120)(30, 96)(31, 118)(32, 98)(33, 105)(34, 102)(35, 103)(36, 104)(37, 116)(38, 106)(39, 115)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 10, 80 ), ( 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80 ) } Outer automorphisms :: reflexible Dual of E14.377 Graph:: simple bipartite v = 45 e = 80 f = 9 degree seq :: [ 2^40, 16^5 ] E14.379 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y2^3, (Y3^-1, Y2^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2)^2, Y3^7 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 10, 52)(5, 47, 9, 51)(6, 48, 8, 50)(11, 53, 18, 60)(12, 54, 17, 59)(13, 55, 22, 64)(14, 56, 21, 63)(15, 57, 20, 62)(16, 58, 19, 61)(23, 65, 30, 72)(24, 66, 29, 71)(25, 67, 34, 76)(26, 68, 33, 75)(27, 69, 32, 74)(28, 70, 31, 73)(35, 77, 40, 82)(36, 78, 39, 81)(37, 79, 42, 84)(38, 80, 41, 83)(85, 127, 87, 129, 89, 131)(86, 128, 91, 133, 93, 135)(88, 130, 95, 137, 98, 140)(90, 132, 96, 138, 99, 141)(92, 134, 101, 143, 104, 146)(94, 136, 102, 144, 105, 147)(97, 139, 107, 149, 110, 152)(100, 142, 108, 150, 111, 153)(103, 145, 113, 155, 116, 158)(106, 148, 114, 156, 117, 159)(109, 151, 119, 161, 121, 163)(112, 154, 120, 162, 122, 164)(115, 157, 123, 165, 125, 167)(118, 160, 124, 166, 126, 168) L = (1, 88)(2, 92)(3, 95)(4, 97)(5, 98)(6, 85)(7, 101)(8, 103)(9, 104)(10, 86)(11, 107)(12, 87)(13, 109)(14, 110)(15, 89)(16, 90)(17, 113)(18, 91)(19, 115)(20, 116)(21, 93)(22, 94)(23, 119)(24, 96)(25, 112)(26, 121)(27, 99)(28, 100)(29, 123)(30, 102)(31, 118)(32, 125)(33, 105)(34, 106)(35, 120)(36, 108)(37, 122)(38, 111)(39, 124)(40, 114)(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 ) } Outer automorphisms :: reflexible Dual of E14.380 Graph:: simple bipartite v = 35 e = 84 f = 23 degree seq :: [ 4^21, 6^14 ] E14.380 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 21}) Quotient :: dipole Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y2 * Y3)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y3^-3 * Y1^-3, Y1^2 * Y2 * Y1 * Y3^-1 * Y2, Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1^-1, Y3^-4 * Y1^3, Y1^21 ] Map:: non-degenerate R = (1, 43, 2, 44, 7, 49, 21, 63, 36, 78, 16, 58, 4, 46, 9, 51, 23, 65, 20, 62, 30, 72, 35, 77, 15, 57, 29, 71, 19, 61, 6, 48, 10, 52, 24, 66, 34, 76, 18, 60, 5, 47)(3, 45, 11, 53, 31, 73, 40, 82, 39, 81, 22, 64, 12, 54, 28, 70, 17, 59, 33, 75, 42, 84, 38, 80, 27, 69, 8, 50, 25, 67, 14, 56, 32, 74, 41, 83, 37, 79, 26, 68, 13, 55)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 98, 140)(89, 131, 101, 143)(90, 132, 96, 138)(91, 133, 106, 148)(93, 135, 112, 154)(94, 136, 110, 152)(95, 137, 113, 155)(97, 139, 107, 149)(99, 141, 117, 159)(100, 142, 115, 157)(102, 144, 116, 158)(103, 145, 109, 151)(104, 146, 111, 153)(105, 147, 121, 163)(108, 150, 122, 164)(114, 156, 123, 165)(118, 160, 124, 166)(119, 161, 125, 167)(120, 162, 126, 168) L = (1, 88)(2, 93)(3, 96)(4, 99)(5, 100)(6, 85)(7, 107)(8, 110)(9, 113)(10, 86)(11, 112)(12, 111)(13, 106)(14, 87)(15, 118)(16, 119)(17, 109)(18, 120)(19, 89)(20, 90)(21, 104)(22, 122)(23, 103)(24, 91)(25, 97)(26, 123)(27, 121)(28, 92)(29, 102)(30, 94)(31, 101)(32, 95)(33, 98)(34, 105)(35, 108)(36, 114)(37, 124)(38, 125)(39, 126)(40, 117)(41, 115)(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) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 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 E14.379 Graph:: bipartite v = 23 e = 84 f = 35 degree seq :: [ 4^21, 42^2 ] E14.381 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 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, (Y2 * Y1)^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, Y1^-2 * Y3 * Y2 * Y1^-4, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3, Y1^-9 * Y2 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 44, 2, 48, 6, 56, 14, 68, 26, 65, 23, 54, 12, 60, 18, 72, 30, 78, 36, 83, 41, 84, 42, 80, 38, 76, 34, 62, 20, 52, 10, 59, 17, 71, 29, 67, 25, 55, 13, 47, 5, 43)(3, 51, 9, 61, 19, 75, 33, 82, 40, 73, 31, 63, 21, 77, 35, 74, 32, 66, 24, 79, 37, 81, 39, 70, 28, 58, 16, 50, 8, 46, 4, 53, 11, 64, 22, 69, 27, 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, 27)(16, 30)(17, 31)(20, 35)(22, 26)(24, 38)(25, 33)(28, 36)(29, 40)(32, 34)(37, 42)(39, 41)(43, 46)(44, 50)(45, 52)(47, 53)(48, 58)(49, 59)(51, 62)(54, 66)(55, 64)(56, 70)(57, 71)(60, 74)(61, 76)(63, 78)(65, 79)(67, 69)(68, 81)(72, 77)(73, 83)(75, 80)(82, 84) local type(s) :: { ( 6^42 ) } Outer automorphisms :: reflexible Dual of E14.382 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 42 f = 14 degree seq :: [ 42^2 ] E14.382 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 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, Y1^3, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3 * Y1)^2, (Y3 * Y2)^7, (Y2 * Y1 * Y3)^21 ] Map:: non-degenerate R = (1, 44, 2, 47, 5, 43)(3, 50, 8, 48, 6, 45)(4, 52, 10, 49, 7, 46)(9, 54, 12, 56, 14, 51)(11, 55, 13, 58, 16, 53)(15, 62, 20, 60, 18, 57)(17, 64, 22, 61, 19, 59)(21, 66, 24, 68, 26, 63)(23, 67, 25, 70, 28, 65)(27, 74, 32, 72, 30, 69)(29, 76, 34, 73, 31, 71)(33, 78, 36, 80, 38, 75)(35, 79, 37, 82, 40, 77)(39, 84, 42, 83, 41, 81) 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, 41)(38, 42)(43, 46)(44, 49)(45, 51)(47, 52)(48, 54)(50, 56)(53, 59)(55, 61)(57, 63)(58, 64)(60, 66)(62, 68)(65, 71)(67, 73)(69, 75)(70, 76)(72, 78)(74, 80)(77, 81)(79, 83)(82, 84) local type(s) :: { ( 42^6 ) } Outer automorphisms :: reflexible Dual of E14.381 Transitivity :: VT+ AT Graph:: bipartite v = 14 e = 42 f = 2 degree seq :: [ 6^14 ] E14.383 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 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, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^7, (Y3 * Y1 * Y2)^21 ] Map:: R = (1, 43, 4, 46, 5, 47)(2, 44, 7, 49, 8, 50)(3, 45, 10, 52, 11, 53)(6, 48, 13, 55, 14, 56)(9, 51, 16, 58, 17, 59)(12, 54, 19, 61, 20, 62)(15, 57, 22, 64, 23, 65)(18, 60, 25, 67, 26, 68)(21, 63, 28, 70, 29, 71)(24, 66, 31, 73, 32, 74)(27, 69, 34, 76, 35, 77)(30, 72, 37, 79, 38, 80)(33, 75, 39, 81, 40, 82)(36, 78, 41, 83, 42, 84)(85, 86)(87, 93)(88, 92)(89, 91)(90, 96)(94, 101)(95, 100)(97, 104)(98, 103)(99, 105)(102, 108)(106, 113)(107, 112)(109, 116)(110, 115)(111, 117)(114, 120)(118, 124)(119, 123)(121, 126)(122, 125)(127, 129)(128, 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, 162)(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 ), ( 84^6 ) } Outer automorphisms :: reflexible Dual of E14.386 Graph:: simple bipartite v = 56 e = 84 f = 2 degree seq :: [ 2^42, 6^14 ] E14.384 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 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, (Y3 * Y2)^2, Y3^-5 * Y1 * Y3 * Y2, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2, Y3 * Y1 * Y3^-2 * Y2 * Y1 * Y2 * Y1 * Y2 ] Map:: R = (1, 43, 4, 46, 12, 54, 24, 66, 30, 72, 16, 58, 6, 48, 15, 57, 29, 71, 33, 75, 41, 83, 39, 81, 26, 68, 37, 79, 21, 63, 9, 51, 20, 62, 36, 78, 25, 67, 13, 55, 5, 47)(2, 44, 7, 49, 17, 59, 31, 73, 23, 65, 11, 53, 3, 45, 10, 52, 22, 64, 38, 80, 42, 84, 35, 77, 19, 61, 34, 76, 28, 70, 14, 56, 27, 69, 40, 82, 32, 74, 18, 60, 8, 50)(85, 86)(87, 93)(88, 92)(89, 91)(90, 98)(94, 105)(95, 104)(96, 102)(97, 101)(99, 112)(100, 111)(103, 117)(106, 121)(107, 120)(108, 116)(109, 115)(110, 122)(113, 118)(114, 124)(119, 125)(123, 126)(127, 129)(128, 132)(130, 137)(131, 136)(133, 142)(134, 141)(135, 145)(138, 149)(139, 148)(140, 152)(143, 156)(144, 155)(146, 161)(147, 160)(150, 157)(151, 164)(153, 165)(154, 163)(158, 159)(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) :: { ( 12, 12 ), ( 12^42 ) } Outer automorphisms :: reflexible Dual of E14.385 Graph:: simple bipartite v = 44 e = 84 f = 14 degree seq :: [ 2^42, 42^2 ] E14.385 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 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, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^7, (Y3 * Y1 * Y2)^21 ] Map:: R = (1, 43, 85, 127, 4, 46, 88, 130, 5, 47, 89, 131)(2, 44, 86, 128, 7, 49, 91, 133, 8, 50, 92, 134)(3, 45, 87, 129, 10, 52, 94, 136, 11, 53, 95, 137)(6, 48, 90, 132, 13, 55, 97, 139, 14, 56, 98, 140)(9, 51, 93, 135, 16, 58, 100, 142, 17, 59, 101, 143)(12, 54, 96, 138, 19, 61, 103, 145, 20, 62, 104, 146)(15, 57, 99, 141, 22, 64, 106, 148, 23, 65, 107, 149)(18, 60, 102, 144, 25, 67, 109, 151, 26, 68, 110, 152)(21, 63, 105, 147, 28, 70, 112, 154, 29, 71, 113, 155)(24, 66, 108, 150, 31, 73, 115, 157, 32, 74, 116, 158)(27, 69, 111, 153, 34, 76, 118, 160, 35, 77, 119, 161)(30, 72, 114, 156, 37, 79, 121, 163, 38, 80, 122, 164)(33, 75, 117, 159, 39, 81, 123, 165, 40, 82, 124, 166)(36, 78, 120, 162, 41, 83, 125, 167, 42, 84, 126, 168) L = (1, 44)(2, 43)(3, 51)(4, 50)(5, 49)(6, 54)(7, 47)(8, 46)(9, 45)(10, 59)(11, 58)(12, 48)(13, 62)(14, 61)(15, 63)(16, 53)(17, 52)(18, 66)(19, 56)(20, 55)(21, 57)(22, 71)(23, 70)(24, 60)(25, 74)(26, 73)(27, 75)(28, 65)(29, 64)(30, 78)(31, 68)(32, 67)(33, 69)(34, 82)(35, 81)(36, 72)(37, 84)(38, 83)(39, 77)(40, 76)(41, 80)(42, 79)(85, 129)(86, 132)(87, 127)(88, 137)(89, 136)(90, 128)(91, 140)(92, 139)(93, 141)(94, 131)(95, 130)(96, 144)(97, 134)(98, 133)(99, 135)(100, 149)(101, 148)(102, 138)(103, 152)(104, 151)(105, 153)(106, 143)(107, 142)(108, 156)(109, 146)(110, 145)(111, 147)(112, 161)(113, 160)(114, 150)(115, 164)(116, 163)(117, 162)(118, 155)(119, 154)(120, 159)(121, 158)(122, 157)(123, 168)(124, 167)(125, 166)(126, 165) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E14.384 Transitivity :: VT+ Graph:: bipartite v = 14 e = 84 f = 44 degree seq :: [ 12^14 ] E14.386 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 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, (Y3 * Y2)^2, Y3^-5 * Y1 * Y3 * Y2, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2, Y3 * Y1 * Y3^-2 * Y2 * Y1 * Y2 * Y1 * Y2 ] Map:: R = (1, 43, 85, 127, 4, 46, 88, 130, 12, 54, 96, 138, 24, 66, 108, 150, 30, 72, 114, 156, 16, 58, 100, 142, 6, 48, 90, 132, 15, 57, 99, 141, 29, 71, 113, 155, 33, 75, 117, 159, 41, 83, 125, 167, 39, 81, 123, 165, 26, 68, 110, 152, 37, 79, 121, 163, 21, 63, 105, 147, 9, 51, 93, 135, 20, 62, 104, 146, 36, 78, 120, 162, 25, 67, 109, 151, 13, 55, 97, 139, 5, 47, 89, 131)(2, 44, 86, 128, 7, 49, 91, 133, 17, 59, 101, 143, 31, 73, 115, 157, 23, 65, 107, 149, 11, 53, 95, 137, 3, 45, 87, 129, 10, 52, 94, 136, 22, 64, 106, 148, 38, 80, 122, 164, 42, 84, 126, 168, 35, 77, 119, 161, 19, 61, 103, 145, 34, 76, 118, 160, 28, 70, 112, 154, 14, 56, 98, 140, 27, 69, 111, 153, 40, 82, 124, 166, 32, 74, 116, 158, 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, 70)(16, 69)(17, 55)(18, 54)(19, 75)(20, 53)(21, 52)(22, 79)(23, 78)(24, 74)(25, 73)(26, 80)(27, 58)(28, 57)(29, 76)(30, 82)(31, 67)(32, 66)(33, 61)(34, 71)(35, 83)(36, 65)(37, 64)(38, 68)(39, 84)(40, 72)(41, 77)(42, 81)(85, 129)(86, 132)(87, 127)(88, 137)(89, 136)(90, 128)(91, 142)(92, 141)(93, 145)(94, 131)(95, 130)(96, 149)(97, 148)(98, 152)(99, 134)(100, 133)(101, 156)(102, 155)(103, 135)(104, 161)(105, 160)(106, 139)(107, 138)(108, 157)(109, 164)(110, 140)(111, 165)(112, 163)(113, 144)(114, 143)(115, 150)(116, 159)(117, 158)(118, 147)(119, 146)(120, 168)(121, 154)(122, 151)(123, 153)(124, 167)(125, 166)(126, 162) 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 ) } Outer automorphisms :: reflexible Dual of E14.383 Transitivity :: VT+ Graph:: bipartite v = 2 e = 84 f = 56 degree seq :: [ 84^2 ] E14.387 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y2)^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, 21, 63)(12, 54, 20, 62)(13, 55, 22, 64)(14, 56, 18, 60)(15, 57, 17, 59)(16, 58, 19, 61)(23, 65, 33, 75)(24, 66, 32, 74)(25, 67, 34, 76)(26, 68, 30, 72)(27, 69, 29, 71)(28, 70, 31, 73)(35, 77, 42, 84)(36, 78, 41, 83)(37, 79, 40, 82)(38, 80, 39, 81)(85, 127, 87, 129, 89, 131)(86, 128, 91, 133, 93, 135)(88, 130, 95, 137, 98, 140)(90, 132, 96, 138, 99, 141)(92, 134, 101, 143, 104, 146)(94, 136, 102, 144, 105, 147)(97, 139, 107, 149, 110, 152)(100, 142, 108, 150, 111, 153)(103, 145, 113, 155, 116, 158)(106, 148, 114, 156, 117, 159)(109, 151, 119, 161, 121, 163)(112, 154, 120, 162, 122, 164)(115, 157, 123, 165, 125, 167)(118, 160, 124, 166, 126, 168) L = (1, 88)(2, 92)(3, 95)(4, 97)(5, 98)(6, 85)(7, 101)(8, 103)(9, 104)(10, 86)(11, 107)(12, 87)(13, 109)(14, 110)(15, 89)(16, 90)(17, 113)(18, 91)(19, 115)(20, 116)(21, 93)(22, 94)(23, 119)(24, 96)(25, 112)(26, 121)(27, 99)(28, 100)(29, 123)(30, 102)(31, 118)(32, 125)(33, 105)(34, 106)(35, 120)(36, 108)(37, 122)(38, 111)(39, 124)(40, 114)(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 ) } Outer automorphisms :: reflexible Dual of E14.389 Graph:: simple bipartite v = 35 e = 84 f = 23 degree seq :: [ 4^21, 6^14 ] E14.388 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y2)^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 * Y3^2 ] 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, 21, 63)(12, 54, 20, 62)(13, 55, 22, 64)(14, 56, 18, 60)(15, 57, 17, 59)(16, 58, 19, 61)(23, 65, 33, 75)(24, 66, 32, 74)(25, 67, 34, 76)(26, 68, 30, 72)(27, 69, 29, 71)(28, 70, 31, 73)(35, 77, 41, 83)(36, 78, 42, 84)(37, 79, 39, 81)(38, 80, 40, 82)(85, 127, 87, 129, 89, 131)(86, 128, 91, 133, 93, 135)(88, 130, 95, 137, 98, 140)(90, 132, 96, 138, 99, 141)(92, 134, 101, 143, 104, 146)(94, 136, 102, 144, 105, 147)(97, 139, 107, 149, 110, 152)(100, 142, 108, 150, 111, 153)(103, 145, 113, 155, 116, 158)(106, 148, 114, 156, 117, 159)(109, 151, 119, 161, 122, 164)(112, 154, 120, 162, 121, 163)(115, 157, 123, 165, 126, 168)(118, 160, 124, 166, 125, 167) L = (1, 88)(2, 92)(3, 95)(4, 97)(5, 98)(6, 85)(7, 101)(8, 103)(9, 104)(10, 86)(11, 107)(12, 87)(13, 109)(14, 110)(15, 89)(16, 90)(17, 113)(18, 91)(19, 115)(20, 116)(21, 93)(22, 94)(23, 119)(24, 96)(25, 121)(26, 122)(27, 99)(28, 100)(29, 123)(30, 102)(31, 125)(32, 126)(33, 105)(34, 106)(35, 112)(36, 108)(37, 111)(38, 120)(39, 118)(40, 114)(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) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E14.390 Graph:: simple bipartite v = 35 e = 84 f = 23 degree seq :: [ 4^21, 6^14 ] E14.389 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^-2 * Y1^-1 * Y3^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-2, Y1^5 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 43, 2, 44, 7, 49, 19, 61, 34, 76, 15, 57, 4, 46, 9, 51, 21, 63, 18, 60, 26, 68, 33, 75, 14, 56, 25, 67, 17, 59, 6, 48, 10, 52, 22, 64, 32, 74, 16, 58, 5, 47)(3, 45, 11, 53, 27, 69, 40, 82, 36, 78, 23, 65, 12, 54, 28, 70, 39, 81, 31, 73, 42, 84, 38, 80, 30, 72, 37, 79, 24, 66, 13, 55, 29, 71, 41, 83, 35, 77, 20, 62, 8, 50)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 97, 139)(89, 131, 95, 137)(90, 132, 96, 138)(91, 133, 104, 146)(93, 135, 108, 150)(94, 136, 107, 149)(98, 140, 115, 157)(99, 141, 113, 155)(100, 142, 111, 153)(101, 143, 112, 154)(102, 144, 114, 156)(103, 145, 119, 161)(105, 147, 121, 163)(106, 148, 120, 162)(109, 151, 123, 165)(110, 152, 122, 164)(116, 158, 124, 166)(117, 159, 126, 168)(118, 160, 125, 167) L = (1, 88)(2, 93)(3, 96)(4, 98)(5, 99)(6, 85)(7, 105)(8, 107)(9, 109)(10, 86)(11, 112)(12, 114)(13, 87)(14, 116)(15, 117)(16, 118)(17, 89)(18, 90)(19, 102)(20, 120)(21, 101)(22, 91)(23, 122)(24, 92)(25, 100)(26, 94)(27, 123)(28, 121)(29, 95)(30, 119)(31, 97)(32, 103)(33, 106)(34, 110)(35, 124)(36, 126)(37, 104)(38, 125)(39, 108)(40, 115)(41, 111)(42, 113)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 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 E14.387 Graph:: bipartite v = 23 e = 84 f = 35 degree seq :: [ 4^21, 42^2 ] E14.390 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3, Y1^-1), Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^4 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 43, 2, 44, 7, 49, 19, 61, 33, 75, 14, 56, 25, 67, 17, 59, 6, 48, 10, 52, 22, 64, 34, 76, 15, 57, 4, 46, 9, 51, 21, 63, 18, 60, 26, 68, 32, 74, 16, 58, 5, 47)(3, 45, 11, 53, 27, 69, 40, 82, 38, 80, 30, 72, 37, 79, 24, 66, 13, 55, 29, 71, 41, 83, 36, 78, 23, 65, 12, 54, 28, 70, 39, 81, 31, 73, 42, 84, 35, 77, 20, 62, 8, 50)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 97, 139)(89, 131, 95, 137)(90, 132, 96, 138)(91, 133, 104, 146)(93, 135, 108, 150)(94, 136, 107, 149)(98, 140, 115, 157)(99, 141, 113, 155)(100, 142, 111, 153)(101, 143, 112, 154)(102, 144, 114, 156)(103, 145, 119, 161)(105, 147, 121, 163)(106, 148, 120, 162)(109, 151, 123, 165)(110, 152, 122, 164)(116, 158, 124, 166)(117, 159, 126, 168)(118, 160, 125, 167) L = (1, 88)(2, 93)(3, 96)(4, 98)(5, 99)(6, 85)(7, 105)(8, 107)(9, 109)(10, 86)(11, 112)(12, 114)(13, 87)(14, 116)(15, 117)(16, 118)(17, 89)(18, 90)(19, 102)(20, 120)(21, 101)(22, 91)(23, 122)(24, 92)(25, 100)(26, 94)(27, 123)(28, 121)(29, 95)(30, 119)(31, 97)(32, 106)(33, 110)(34, 103)(35, 125)(36, 124)(37, 104)(38, 126)(39, 108)(40, 115)(41, 111)(42, 113)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 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 E14.388 Graph:: bipartite v = 23 e = 84 f = 35 degree seq :: [ 4^21, 42^2 ] E14.391 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 6, 21}) Quotient :: edge Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1)^2, (F * T1)^2, (F * T2)^2, T2 * T1^-3 * T2 * T1, (T2^-1 * T1^-1 * T2^-1)^2, T1 * T2^-2 * T1^-1 * T2^5 ] Map:: non-degenerate R = (1, 3, 10, 25, 37, 31, 19, 12, 21, 33, 42, 41, 30, 18, 6, 17, 29, 40, 28, 15, 5)(2, 7, 20, 32, 36, 24, 13, 4, 11, 26, 38, 35, 23, 9, 16, 14, 27, 39, 34, 22, 8)(43, 44, 48, 58, 54, 46)(45, 51, 59, 55, 63, 50)(47, 53, 60, 49, 61, 56)(52, 66, 71, 64, 75, 65)(57, 69, 72, 68, 73, 62)(67, 76, 82, 77, 84, 78)(70, 74, 83, 81, 79, 80) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 12^6 ), ( 12^21 ) } Outer automorphisms :: reflexible Dual of E14.392 Transitivity :: ET+ Graph:: bipartite v = 9 e = 42 f = 7 degree seq :: [ 6^7, 21^2 ] E14.392 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 6, 21}) Quotient :: loop Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ F^2, T1^2 * T2^-2, (F * T1)^2, (F * T2)^2, T2^6, T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^21 ] Map:: non-degenerate R = (1, 43, 3, 45, 6, 48, 15, 57, 11, 53, 5, 47)(2, 44, 7, 49, 14, 56, 12, 54, 4, 46, 8, 50)(9, 51, 19, 61, 13, 55, 21, 63, 10, 52, 20, 62)(16, 58, 22, 64, 18, 60, 24, 66, 17, 59, 23, 65)(25, 67, 31, 73, 27, 69, 33, 75, 26, 68, 32, 74)(28, 70, 34, 76, 30, 72, 36, 78, 29, 71, 35, 77)(37, 79, 40, 82, 39, 81, 42, 84, 38, 80, 41, 83) L = (1, 44)(2, 48)(3, 51)(4, 43)(5, 52)(6, 56)(7, 58)(8, 59)(9, 57)(10, 45)(11, 46)(12, 60)(13, 47)(14, 53)(15, 55)(16, 54)(17, 49)(18, 50)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 63)(26, 61)(27, 62)(28, 66)(29, 64)(30, 65)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 75)(38, 73)(39, 74)(40, 78)(41, 76)(42, 77) local type(s) :: { ( 6, 21, 6, 21, 6, 21, 6, 21, 6, 21, 6, 21 ) } Outer automorphisms :: reflexible Dual of E14.391 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 42 f = 9 degree seq :: [ 12^7 ] E14.393 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 21}) Quotient :: dipole Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y1^-1 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^2, (Y1 * Y2^2)^2, Y1^6, Y2^-2 * Y1^-2 * Y2^-5, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 43, 2, 44, 6, 48, 16, 58, 12, 54, 4, 46)(3, 45, 9, 51, 17, 59, 13, 55, 21, 63, 8, 50)(5, 47, 11, 53, 18, 60, 7, 49, 19, 61, 14, 56)(10, 52, 24, 66, 29, 71, 22, 64, 33, 75, 23, 65)(15, 57, 27, 69, 30, 72, 26, 68, 31, 73, 20, 62)(25, 67, 34, 76, 40, 82, 35, 77, 42, 84, 36, 78)(28, 70, 32, 74, 41, 83, 39, 81, 37, 79, 38, 80)(85, 127, 87, 129, 94, 136, 109, 151, 121, 163, 115, 157, 103, 145, 96, 138, 105, 147, 117, 159, 126, 168, 125, 167, 114, 156, 102, 144, 90, 132, 101, 143, 113, 155, 124, 166, 112, 154, 99, 141, 89, 131)(86, 128, 91, 133, 104, 146, 116, 158, 120, 162, 108, 150, 97, 139, 88, 130, 95, 137, 110, 152, 122, 164, 119, 161, 107, 149, 93, 135, 100, 142, 98, 140, 111, 153, 123, 165, 118, 160, 106, 148, 92, 134) L = (1, 87)(2, 91)(3, 94)(4, 95)(5, 85)(6, 101)(7, 104)(8, 86)(9, 100)(10, 109)(11, 110)(12, 105)(13, 88)(14, 111)(15, 89)(16, 98)(17, 113)(18, 90)(19, 96)(20, 116)(21, 117)(22, 92)(23, 93)(24, 97)(25, 121)(26, 122)(27, 123)(28, 99)(29, 124)(30, 102)(31, 103)(32, 120)(33, 126)(34, 106)(35, 107)(36, 108)(37, 115)(38, 119)(39, 118)(40, 112)(41, 114)(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) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E14.394 Graph:: bipartite v = 9 e = 84 f = 49 degree seq :: [ 12^7, 42^2 ] E14.394 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 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, R^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y3)^2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y3 * Y2^3, (Y3^2 * Y2^-1)^2, Y3^-3 * Y2 * Y3^2 * Y2^-1 * Y3^-2, (Y3^-1 * Y1^-1)^21 ] 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, 100, 142, 97, 139, 88, 130)(87, 129, 93, 135, 101, 143, 92, 134, 105, 147, 95, 137)(89, 131, 98, 140, 102, 144, 96, 138, 104, 146, 91, 133)(94, 136, 108, 150, 113, 155, 107, 149, 117, 159, 106, 148)(99, 141, 110, 152, 114, 156, 103, 145, 115, 157, 111, 153)(109, 151, 118, 160, 125, 167, 120, 162, 124, 166, 119, 161)(112, 154, 116, 158, 121, 163, 123, 165, 126, 168, 122, 164) L = (1, 87)(2, 91)(3, 94)(4, 96)(5, 85)(6, 101)(7, 103)(8, 86)(9, 88)(10, 109)(11, 100)(12, 110)(13, 105)(14, 111)(15, 89)(16, 98)(17, 113)(18, 90)(19, 116)(20, 97)(21, 117)(22, 92)(23, 93)(24, 95)(25, 121)(26, 122)(27, 123)(28, 99)(29, 125)(30, 102)(31, 104)(32, 120)(33, 124)(34, 106)(35, 107)(36, 108)(37, 114)(38, 118)(39, 119)(40, 112)(41, 126)(42, 115)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 12, 42 ), ( 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42 ) } Outer automorphisms :: reflexible Dual of E14.393 Graph:: simple bipartite v = 49 e = 84 f = 9 degree seq :: [ 2^42, 12^7 ] E14.395 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 42, 42}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^14 * T1, (T1^-1 * T2^-1)^42 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 26, 32, 38, 40, 34, 28, 22, 16, 10, 4, 9, 15, 21, 27, 33, 39, 42, 37, 31, 25, 19, 13, 7, 2, 6, 12, 18, 24, 30, 36, 41, 35, 29, 23, 17, 11, 5)(43, 44, 46)(45, 48, 51)(47, 49, 52)(50, 54, 57)(53, 55, 58)(56, 60, 63)(59, 61, 64)(62, 66, 69)(65, 67, 70)(68, 72, 75)(71, 73, 76)(74, 78, 81)(77, 79, 82)(80, 83, 84) 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) :: { ( 84^3 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E14.396 Transitivity :: ET+ Graph:: bipartite v = 15 e = 42 f = 1 degree seq :: [ 3^14, 42 ] E14.396 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 42, 42}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^14 * T1, (T1^-1 * T2^-1)^42 ] Map:: non-degenerate R = (1, 43, 3, 45, 8, 50, 14, 56, 20, 62, 26, 68, 32, 74, 38, 80, 40, 82, 34, 76, 28, 70, 22, 64, 16, 58, 10, 52, 4, 46, 9, 51, 15, 57, 21, 63, 27, 69, 33, 75, 39, 81, 42, 84, 37, 79, 31, 73, 25, 67, 19, 61, 13, 55, 7, 49, 2, 44, 6, 48, 12, 54, 18, 60, 24, 66, 30, 72, 36, 78, 41, 83, 35, 77, 29, 71, 23, 65, 17, 59, 11, 53, 5, 47) L = (1, 44)(2, 46)(3, 48)(4, 43)(5, 49)(6, 51)(7, 52)(8, 54)(9, 45)(10, 47)(11, 55)(12, 57)(13, 58)(14, 60)(15, 50)(16, 53)(17, 61)(18, 63)(19, 64)(20, 66)(21, 56)(22, 59)(23, 67)(24, 69)(25, 70)(26, 72)(27, 62)(28, 65)(29, 73)(30, 75)(31, 76)(32, 78)(33, 68)(34, 71)(35, 79)(36, 81)(37, 82)(38, 83)(39, 74)(40, 77)(41, 84)(42, 80) local type(s) :: { ( 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42, 3, 42 ) } Outer automorphisms :: reflexible Dual of E14.395 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 42 f = 15 degree seq :: [ 84 ] E14.397 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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 * Y1^-2, Y1^3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y2^14 * 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 ] Map:: R = (1, 43, 2, 44, 4, 46)(3, 45, 6, 48, 9, 51)(5, 47, 7, 49, 10, 52)(8, 50, 12, 54, 15, 57)(11, 53, 13, 55, 16, 58)(14, 56, 18, 60, 21, 63)(17, 59, 19, 61, 22, 64)(20, 62, 24, 66, 27, 69)(23, 65, 25, 67, 28, 70)(26, 68, 30, 72, 33, 75)(29, 71, 31, 73, 34, 76)(32, 74, 36, 78, 39, 81)(35, 77, 37, 79, 40, 82)(38, 80, 41, 83, 42, 84)(85, 127, 87, 129, 92, 134, 98, 140, 104, 146, 110, 152, 116, 158, 122, 164, 124, 166, 118, 160, 112, 154, 106, 148, 100, 142, 94, 136, 88, 130, 93, 135, 99, 141, 105, 147, 111, 153, 117, 159, 123, 165, 126, 168, 121, 163, 115, 157, 109, 151, 103, 145, 97, 139, 91, 133, 86, 128, 90, 132, 96, 138, 102, 144, 108, 150, 114, 156, 120, 162, 125, 167, 119, 161, 113, 155, 107, 149, 101, 143, 95, 137, 89, 131) L = (1, 88)(2, 85)(3, 93)(4, 86)(5, 94)(6, 87)(7, 89)(8, 99)(9, 90)(10, 91)(11, 100)(12, 92)(13, 95)(14, 105)(15, 96)(16, 97)(17, 106)(18, 98)(19, 101)(20, 111)(21, 102)(22, 103)(23, 112)(24, 104)(25, 107)(26, 117)(27, 108)(28, 109)(29, 118)(30, 110)(31, 113)(32, 123)(33, 114)(34, 115)(35, 124)(36, 116)(37, 119)(38, 126)(39, 120)(40, 121)(41, 122)(42, 125)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 2, 84, 2, 84, 2, 84 ), ( 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 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 E14.398 Graph:: bipartite v = 15 e = 84 f = 43 degree seq :: [ 6^14, 84 ] E14.398 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 42, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^14, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 43, 2, 44, 6, 48, 12, 54, 18, 60, 24, 66, 30, 72, 36, 78, 41, 83, 35, 77, 29, 71, 23, 65, 17, 59, 11, 53, 5, 47, 8, 50, 14, 56, 20, 62, 26, 68, 32, 74, 38, 80, 42, 84, 39, 81, 33, 75, 27, 69, 21, 63, 15, 57, 9, 51, 3, 45, 7, 49, 13, 55, 19, 61, 25, 67, 31, 73, 37, 79, 40, 82, 34, 76, 28, 70, 22, 64, 16, 58, 10, 52, 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, 89)(4, 93)(5, 85)(6, 97)(7, 92)(8, 86)(9, 95)(10, 99)(11, 88)(12, 103)(13, 98)(14, 90)(15, 101)(16, 105)(17, 94)(18, 109)(19, 104)(20, 96)(21, 107)(22, 111)(23, 100)(24, 115)(25, 110)(26, 102)(27, 113)(28, 117)(29, 106)(30, 121)(31, 116)(32, 108)(33, 119)(34, 123)(35, 112)(36, 124)(37, 122)(38, 114)(39, 125)(40, 126)(41, 118)(42, 120)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 6, 84 ), ( 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84 ) } Outer automorphisms :: reflexible Dual of E14.397 Graph:: bipartite v = 43 e = 84 f = 15 degree seq :: [ 2^42, 84 ] E14.399 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 8}) Quotient :: dipole Aut^+ = (C3 x D8) : C2 (small group id <48, 15>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y3^3, Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y1 * Y3^-1 * Y2 * Y1 * Y2, (Y2 * Y1)^8 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 12, 60)(5, 53, 13, 61)(6, 54, 14, 62)(7, 55, 17, 65)(8, 56, 18, 66)(10, 58, 16, 64)(11, 59, 15, 63)(19, 67, 25, 73)(20, 68, 26, 74)(21, 69, 27, 75)(22, 70, 28, 76)(23, 71, 29, 77)(24, 72, 30, 78)(31, 79, 37, 85)(32, 80, 38, 86)(33, 81, 39, 87)(34, 82, 40, 88)(35, 83, 41, 89)(36, 84, 42, 90)(43, 91, 46, 94)(44, 92, 48, 96)(45, 93, 47, 95)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 106, 154)(101, 149, 107, 155)(103, 151, 111, 159)(104, 152, 112, 160)(105, 153, 115, 163)(108, 156, 117, 165)(109, 157, 116, 164)(110, 158, 118, 166)(113, 161, 120, 168)(114, 162, 119, 167)(121, 169, 127, 175)(122, 170, 129, 177)(123, 171, 128, 176)(124, 172, 130, 178)(125, 173, 132, 180)(126, 174, 131, 179)(133, 181, 139, 187)(134, 182, 141, 189)(135, 183, 140, 188)(136, 184, 142, 190)(137, 185, 144, 192)(138, 186, 143, 191) L = (1, 100)(2, 103)(3, 106)(4, 107)(5, 97)(6, 111)(7, 112)(8, 98)(9, 116)(10, 101)(11, 99)(12, 115)(13, 117)(14, 119)(15, 104)(16, 102)(17, 118)(18, 120)(19, 109)(20, 108)(21, 105)(22, 114)(23, 113)(24, 110)(25, 128)(26, 127)(27, 129)(28, 131)(29, 130)(30, 132)(31, 123)(32, 122)(33, 121)(34, 126)(35, 125)(36, 124)(37, 140)(38, 139)(39, 141)(40, 143)(41, 142)(42, 144)(43, 135)(44, 134)(45, 133)(46, 138)(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) :: { ( 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E14.404 Graph:: simple bipartite v = 48 e = 96 f = 22 degree seq :: [ 4^48 ] E14.400 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 8}) 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, Y2^3, (Y3^-1, Y2^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y2)^2, Y3^8 * Y2, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 21, 69)(12, 60, 20, 68)(13, 61, 22, 70)(14, 62, 18, 66)(15, 63, 17, 65)(16, 64, 19, 67)(23, 71, 33, 81)(24, 72, 32, 80)(25, 73, 34, 82)(26, 74, 30, 78)(27, 75, 29, 77)(28, 76, 31, 79)(35, 83, 45, 93)(36, 84, 44, 92)(37, 85, 46, 94)(38, 86, 42, 90)(39, 87, 41, 89)(40, 88, 43, 91)(47, 95, 48, 96)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 107, 155, 110, 158)(102, 150, 108, 156, 111, 159)(104, 152, 113, 161, 116, 164)(106, 154, 114, 162, 117, 165)(109, 157, 119, 167, 122, 170)(112, 160, 120, 168, 123, 171)(115, 163, 125, 173, 128, 176)(118, 166, 126, 174, 129, 177)(121, 169, 131, 179, 134, 182)(124, 172, 132, 180, 135, 183)(127, 175, 137, 185, 140, 188)(130, 178, 138, 186, 141, 189)(133, 181, 136, 184, 143, 191)(139, 187, 142, 190, 144, 192) L = (1, 100)(2, 104)(3, 107)(4, 109)(5, 110)(6, 97)(7, 113)(8, 115)(9, 116)(10, 98)(11, 119)(12, 99)(13, 121)(14, 122)(15, 101)(16, 102)(17, 125)(18, 103)(19, 127)(20, 128)(21, 105)(22, 106)(23, 131)(24, 108)(25, 133)(26, 134)(27, 111)(28, 112)(29, 137)(30, 114)(31, 139)(32, 140)(33, 117)(34, 118)(35, 136)(36, 120)(37, 135)(38, 143)(39, 123)(40, 124)(41, 142)(42, 126)(43, 141)(44, 144)(45, 129)(46, 130)(47, 132)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E14.402 Graph:: simple bipartite v = 40 e = 96 f = 30 degree seq :: [ 4^24, 6^16 ] E14.401 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 8}) Quotient :: dipole Aut^+ = (C3 x D8) : C2 (small group id <48, 15>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y2^-1 * Y3 * Y2^-1 * Y3^-1, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, R * Y2 * R * Y2^-1, Y3^8 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 21, 69)(12, 60, 19, 67)(13, 61, 18, 66)(14, 62, 22, 70)(15, 63, 17, 65)(16, 64, 20, 68)(23, 71, 33, 81)(24, 72, 31, 79)(25, 73, 30, 78)(26, 74, 34, 82)(27, 75, 29, 77)(28, 76, 32, 80)(35, 83, 44, 92)(36, 84, 42, 90)(37, 85, 41, 89)(38, 86, 43, 91)(39, 87, 40, 88)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 109, 157, 107, 155)(102, 150, 111, 159, 108, 156)(104, 152, 115, 163, 113, 161)(106, 154, 117, 165, 114, 162)(110, 158, 119, 167, 121, 169)(112, 160, 120, 168, 123, 171)(116, 164, 125, 173, 127, 175)(118, 166, 126, 174, 129, 177)(122, 170, 133, 181, 131, 179)(124, 172, 135, 183, 132, 180)(128, 176, 138, 186, 136, 184)(130, 178, 140, 188, 137, 185)(134, 182, 141, 189, 142, 190)(139, 187, 143, 191, 144, 192) L = (1, 100)(2, 104)(3, 107)(4, 110)(5, 109)(6, 97)(7, 113)(8, 116)(9, 115)(10, 98)(11, 119)(12, 99)(13, 121)(14, 122)(15, 101)(16, 102)(17, 125)(18, 103)(19, 127)(20, 128)(21, 105)(22, 106)(23, 131)(24, 108)(25, 133)(26, 134)(27, 111)(28, 112)(29, 136)(30, 114)(31, 138)(32, 139)(33, 117)(34, 118)(35, 141)(36, 120)(37, 142)(38, 124)(39, 123)(40, 143)(41, 126)(42, 144)(43, 130)(44, 129)(45, 132)(46, 135)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E14.403 Graph:: simple bipartite v = 40 e = 96 f = 30 degree seq :: [ 4^24, 6^16 ] E14.402 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 8}) 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), (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^3 * Y1^3, (R * Y2 * Y3^-1)^2, Y3^6 * Y1^-2, Y3^4 * Y1^-1 * Y3 * Y1^-1 * Y3, Y1^8 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 35, 83, 32, 80, 16, 64, 5, 53)(3, 51, 11, 59, 27, 75, 43, 91, 46, 94, 36, 84, 20, 68, 8, 56)(4, 52, 9, 57, 21, 69, 18, 66, 26, 74, 40, 88, 34, 82, 15, 63)(6, 54, 10, 58, 22, 70, 37, 85, 33, 81, 14, 62, 25, 73, 17, 65)(12, 60, 28, 76, 42, 90, 31, 79, 45, 93, 47, 95, 38, 86, 23, 71)(13, 61, 29, 77, 44, 92, 48, 96, 41, 89, 30, 78, 39, 87, 24, 72)(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, 138, 186)(122, 170, 137, 185)(128, 176, 139, 187)(129, 177, 141, 189)(130, 178, 140, 188)(131, 179, 142, 190)(133, 181, 143, 191)(136, 184, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 110)(5, 111)(6, 97)(7, 117)(8, 119)(9, 121)(10, 98)(11, 124)(12, 126)(13, 99)(14, 128)(15, 129)(16, 130)(17, 101)(18, 102)(19, 114)(20, 134)(21, 113)(22, 103)(23, 137)(24, 104)(25, 112)(26, 106)(27, 138)(28, 135)(29, 107)(30, 132)(31, 109)(32, 136)(33, 131)(34, 133)(35, 122)(36, 143)(37, 115)(38, 144)(39, 116)(40, 118)(41, 142)(42, 120)(43, 127)(44, 123)(45, 125)(46, 141)(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 ) } Outer automorphisms :: reflexible Dual of E14.400 Graph:: simple bipartite v = 30 e = 96 f = 40 degree seq :: [ 4^24, 16^6 ] E14.403 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 8}) Quotient :: dipole Aut^+ = (C3 x D8) : C2 (small group id <48, 15>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-2 * Y3^-1, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y1)^3, Y1^-2 * Y3^2 * Y1^-4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 35, 83, 33, 81, 15, 63, 5, 53)(3, 51, 11, 59, 27, 75, 43, 91, 46, 94, 36, 84, 20, 68, 8, 56)(4, 52, 14, 62, 6, 54, 18, 66, 21, 69, 39, 87, 32, 80, 16, 64)(9, 57, 24, 72, 10, 58, 26, 74, 37, 85, 34, 82, 17, 65, 25, 73)(12, 60, 29, 77, 13, 61, 31, 79, 44, 92, 48, 96, 38, 86, 30, 78)(22, 70, 40, 88, 23, 71, 42, 90, 28, 76, 45, 93, 47, 95, 41, 89)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 109, 157)(101, 149, 107, 155)(102, 150, 108, 156)(103, 151, 116, 164)(105, 153, 119, 167)(106, 154, 118, 166)(110, 158, 125, 173)(111, 159, 123, 171)(112, 160, 127, 175)(113, 161, 124, 172)(114, 162, 126, 174)(115, 163, 132, 180)(117, 165, 134, 182)(120, 168, 136, 184)(121, 169, 138, 186)(122, 170, 137, 185)(128, 176, 140, 188)(129, 177, 139, 187)(130, 178, 141, 189)(131, 179, 142, 190)(133, 181, 143, 191)(135, 183, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 113)(6, 97)(7, 102)(8, 118)(9, 101)(10, 98)(11, 119)(12, 116)(13, 99)(14, 121)(15, 128)(16, 130)(17, 129)(18, 120)(19, 106)(20, 134)(21, 103)(22, 132)(23, 104)(24, 110)(25, 112)(26, 114)(27, 109)(28, 107)(29, 136)(30, 137)(31, 138)(32, 131)(33, 133)(34, 135)(35, 117)(36, 143)(37, 115)(38, 142)(39, 122)(40, 126)(41, 144)(42, 125)(43, 124)(44, 123)(45, 127)(46, 140)(47, 139)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E14.401 Graph:: simple bipartite v = 30 e = 96 f = 40 degree seq :: [ 4^24, 16^6 ] E14.404 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 8}) Quotient :: dipole Aut^+ = (C3 x D8) : C2 (small group id <48, 15>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^3, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y2^-1 * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^8 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 10, 58, 7, 55)(4, 52, 13, 61, 8, 56)(6, 54, 15, 63, 9, 57)(11, 59, 17, 65, 21, 69)(12, 60, 18, 66, 22, 70)(14, 62, 19, 67, 25, 73)(16, 64, 20, 68, 27, 75)(23, 71, 33, 81, 29, 77)(24, 72, 34, 82, 30, 78)(26, 74, 37, 85, 31, 79)(28, 76, 39, 87, 32, 80)(35, 83, 40, 88, 43, 91)(36, 84, 41, 89, 44, 92)(38, 86, 42, 90, 46, 94)(45, 93, 48, 96, 47, 95)(97, 145, 99, 147, 107, 155, 119, 167, 131, 179, 124, 172, 112, 160, 102, 150)(98, 146, 103, 151, 113, 161, 125, 173, 136, 184, 128, 176, 116, 164, 105, 153)(100, 148, 110, 158, 122, 170, 134, 182, 141, 189, 132, 180, 120, 168, 108, 156)(101, 149, 106, 154, 117, 165, 129, 177, 139, 187, 135, 183, 123, 171, 111, 159)(104, 152, 115, 163, 127, 175, 138, 186, 143, 191, 137, 185, 126, 174, 114, 162)(109, 157, 121, 169, 133, 181, 142, 190, 144, 192, 140, 188, 130, 178, 118, 166) L = (1, 100)(2, 104)(3, 108)(4, 97)(5, 109)(6, 110)(7, 114)(8, 98)(9, 115)(10, 118)(11, 120)(12, 99)(13, 101)(14, 102)(15, 121)(16, 122)(17, 126)(18, 103)(19, 105)(20, 127)(21, 130)(22, 106)(23, 132)(24, 107)(25, 111)(26, 112)(27, 133)(28, 134)(29, 137)(30, 113)(31, 116)(32, 138)(33, 140)(34, 117)(35, 141)(36, 119)(37, 123)(38, 124)(39, 142)(40, 143)(41, 125)(42, 128)(43, 144)(44, 129)(45, 131)(46, 135)(47, 136)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^6 ), ( 4^16 ) } Outer automorphisms :: reflexible Dual of E14.399 Graph:: simple bipartite v = 22 e = 96 f = 48 degree seq :: [ 6^16, 16^6 ] E14.405 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 8}) 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, Y2^3, Y2^-1 * Y3 * Y2^-1 * Y3^-1, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, R * Y2 * R * Y2^-1, Y3^8 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 10, 58)(5, 53, 9, 57)(6, 54, 8, 56)(11, 59, 18, 66)(12, 60, 17, 65)(13, 61, 21, 69)(14, 62, 22, 70)(15, 63, 19, 67)(16, 64, 20, 68)(23, 71, 30, 78)(24, 72, 29, 77)(25, 73, 33, 81)(26, 74, 34, 82)(27, 75, 31, 79)(28, 76, 32, 80)(35, 83, 41, 89)(36, 84, 40, 88)(37, 85, 44, 92)(38, 86, 43, 91)(39, 87, 42, 90)(45, 93, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 109, 157, 107, 155)(102, 150, 111, 159, 108, 156)(104, 152, 115, 163, 113, 161)(106, 154, 117, 165, 114, 162)(110, 158, 119, 167, 121, 169)(112, 160, 120, 168, 123, 171)(116, 164, 125, 173, 127, 175)(118, 166, 126, 174, 129, 177)(122, 170, 133, 181, 131, 179)(124, 172, 135, 183, 132, 180)(128, 176, 138, 186, 136, 184)(130, 178, 140, 188, 137, 185)(134, 182, 141, 189, 142, 190)(139, 187, 143, 191, 144, 192) L = (1, 100)(2, 104)(3, 107)(4, 110)(5, 109)(6, 97)(7, 113)(8, 116)(9, 115)(10, 98)(11, 119)(12, 99)(13, 121)(14, 122)(15, 101)(16, 102)(17, 125)(18, 103)(19, 127)(20, 128)(21, 105)(22, 106)(23, 131)(24, 108)(25, 133)(26, 134)(27, 111)(28, 112)(29, 136)(30, 114)(31, 138)(32, 139)(33, 117)(34, 118)(35, 141)(36, 120)(37, 142)(38, 124)(39, 123)(40, 143)(41, 126)(42, 144)(43, 130)(44, 129)(45, 132)(46, 135)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E14.406 Graph:: simple bipartite v = 40 e = 96 f = 30 degree seq :: [ 4^24, 6^16 ] E14.406 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 8}) 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, Y3^-2 * Y1^-2, (R * Y1)^2, (Y1 * Y3^-1 * Y2)^2, Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y1^-1 * Y2 * Y3 * Y1, Y3^2 * Y2 * Y1^-2 * Y2, Y1^-2 * Y3^2 * Y1^-4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 21, 69, 37, 85, 35, 83, 16, 64, 5, 53)(3, 51, 11, 59, 31, 79, 43, 91, 46, 94, 41, 89, 22, 70, 13, 61)(4, 52, 15, 63, 6, 54, 20, 68, 23, 71, 42, 90, 34, 82, 17, 65)(8, 56, 24, 72, 18, 66, 32, 80, 45, 93, 48, 96, 38, 86, 26, 74)(9, 57, 28, 76, 10, 58, 30, 78, 39, 87, 36, 84, 19, 67, 29, 77)(12, 60, 27, 75, 14, 62, 33, 81, 44, 92, 47, 95, 40, 88, 25, 73)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 114, 162)(102, 150, 108, 156)(103, 151, 118, 166)(105, 153, 123, 171)(106, 154, 121, 169)(107, 155, 125, 173)(109, 157, 124, 172)(111, 159, 120, 168)(112, 160, 127, 175)(113, 161, 128, 176)(115, 163, 129, 177)(116, 164, 122, 170)(117, 165, 134, 182)(119, 167, 136, 184)(126, 174, 137, 185)(130, 178, 140, 188)(131, 179, 141, 189)(132, 180, 139, 187)(133, 181, 142, 190)(135, 183, 143, 191)(138, 186, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 115)(6, 97)(7, 102)(8, 121)(9, 101)(10, 98)(11, 120)(12, 118)(13, 122)(14, 99)(15, 125)(16, 130)(17, 132)(18, 123)(19, 131)(20, 124)(21, 106)(22, 136)(23, 103)(24, 109)(25, 134)(26, 137)(27, 104)(28, 111)(29, 113)(30, 116)(31, 110)(32, 107)(33, 114)(34, 133)(35, 135)(36, 138)(37, 119)(38, 143)(39, 117)(40, 142)(41, 144)(42, 126)(43, 128)(44, 127)(45, 129)(46, 140)(47, 141)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E14.405 Graph:: simple bipartite v = 30 e = 96 f = 40 degree seq :: [ 4^24, 16^6 ] E14.407 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y2^2, R^2, Y3^-3 * Y2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 11, 59)(5, 53, 12, 60)(7, 55, 15, 63)(8, 56, 16, 64)(9, 57, 17, 65)(10, 58, 18, 66)(13, 61, 23, 71)(14, 62, 24, 72)(19, 67, 33, 81)(20, 68, 34, 82)(21, 69, 35, 83)(22, 70, 36, 84)(25, 73, 32, 80)(26, 74, 39, 87)(27, 75, 40, 88)(28, 76, 29, 77)(30, 78, 41, 89)(31, 79, 42, 90)(37, 85, 45, 93)(38, 86, 46, 94)(43, 91, 48, 96)(44, 92, 47, 95)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 105, 153)(101, 149, 106, 154)(103, 151, 109, 157)(104, 152, 110, 158)(107, 155, 113, 161)(108, 156, 114, 162)(111, 159, 119, 167)(112, 160, 120, 168)(115, 163, 125, 173)(116, 164, 126, 174)(117, 165, 127, 175)(118, 166, 128, 176)(121, 169, 132, 180)(122, 170, 133, 181)(123, 171, 134, 182)(124, 172, 129, 177)(130, 178, 137, 185)(131, 179, 138, 186)(135, 183, 141, 189)(136, 184, 142, 190)(139, 187, 140, 188)(143, 191, 144, 192) L = (1, 100)(2, 103)(3, 105)(4, 106)(5, 97)(6, 109)(7, 110)(8, 98)(9, 101)(10, 99)(11, 115)(12, 117)(13, 104)(14, 102)(15, 121)(16, 123)(17, 125)(18, 127)(19, 126)(20, 107)(21, 128)(22, 108)(23, 132)(24, 134)(25, 133)(26, 111)(27, 129)(28, 112)(29, 116)(30, 113)(31, 118)(32, 114)(33, 120)(34, 139)(35, 130)(36, 122)(37, 119)(38, 124)(39, 143)(40, 135)(41, 140)(42, 137)(43, 138)(44, 131)(45, 144)(46, 141)(47, 142)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E14.412 Graph:: simple bipartite v = 48 e = 96 f = 22 degree seq :: [ 4^48 ] E14.408 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y3^2, R^2, Y2^3, Y2 * Y1 * Y2^-1 * Y1, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 7, 55)(5, 53, 8, 56)(9, 57, 13, 61)(10, 58, 14, 62)(11, 59, 15, 63)(12, 60, 16, 64)(17, 65, 23, 71)(18, 66, 24, 72)(19, 67, 25, 73)(20, 68, 26, 74)(21, 69, 27, 75)(22, 70, 28, 76)(29, 77, 34, 82)(30, 78, 37, 85)(31, 79, 36, 84)(32, 80, 38, 86)(33, 81, 39, 87)(35, 83, 40, 88)(41, 89, 44, 92)(42, 90, 45, 93)(43, 91, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 101, 149)(98, 146, 102, 150, 104, 152)(100, 148, 106, 154, 107, 155)(103, 151, 110, 158, 111, 159)(105, 153, 113, 161, 114, 162)(108, 156, 117, 165, 118, 166)(109, 157, 119, 167, 120, 168)(112, 160, 123, 171, 124, 172)(115, 163, 127, 175, 128, 176)(116, 164, 129, 177, 130, 178)(121, 169, 132, 180, 134, 182)(122, 170, 135, 183, 125, 173)(126, 174, 137, 185, 136, 184)(131, 179, 133, 181, 140, 188)(138, 186, 144, 192, 142, 190)(139, 187, 141, 189, 143, 191) L = (1, 100)(2, 103)(3, 105)(4, 97)(5, 108)(6, 109)(7, 98)(8, 112)(9, 99)(10, 115)(11, 116)(12, 101)(13, 102)(14, 121)(15, 122)(16, 104)(17, 125)(18, 126)(19, 106)(20, 107)(21, 131)(22, 132)(23, 130)(24, 133)(25, 110)(26, 111)(27, 136)(28, 127)(29, 113)(30, 114)(31, 124)(32, 138)(33, 139)(34, 119)(35, 117)(36, 118)(37, 120)(38, 141)(39, 142)(40, 123)(41, 143)(42, 128)(43, 129)(44, 144)(45, 134)(46, 135)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E14.411 Graph:: simple bipartite v = 40 e = 96 f = 30 degree seq :: [ 4^24, 6^16 ] E14.409 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y3^2, R^2, Y2^3, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, Y3 * Y2^-1 * Y3 * Y1 * Y2 * Y1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1, (Y1 * Y2^-1)^8 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 13, 61)(6, 54, 15, 63)(8, 56, 19, 67)(10, 58, 17, 65)(11, 59, 16, 64)(12, 60, 20, 68)(14, 62, 18, 66)(21, 69, 36, 84)(22, 70, 37, 85)(23, 71, 34, 82)(24, 72, 38, 86)(25, 73, 39, 87)(26, 74, 31, 79)(27, 75, 40, 88)(28, 76, 29, 77)(30, 78, 41, 89)(32, 80, 42, 90)(33, 81, 43, 91)(35, 83, 44, 92)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 101, 149)(98, 146, 102, 150, 104, 152)(100, 148, 107, 155, 108, 156)(103, 151, 113, 161, 114, 162)(105, 153, 117, 165, 118, 166)(106, 154, 119, 167, 120, 168)(109, 157, 121, 169, 122, 170)(110, 158, 123, 171, 124, 172)(111, 159, 125, 173, 126, 174)(112, 160, 127, 175, 128, 176)(115, 163, 129, 177, 130, 178)(116, 164, 131, 179, 132, 180)(133, 181, 141, 189, 136, 184)(134, 182, 142, 190, 135, 183)(137, 185, 143, 191, 140, 188)(138, 186, 144, 192, 139, 187) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 110)(6, 112)(7, 98)(8, 116)(9, 113)(10, 99)(11, 111)(12, 115)(13, 114)(14, 101)(15, 107)(16, 102)(17, 105)(18, 109)(19, 108)(20, 104)(21, 130)(22, 134)(23, 132)(24, 133)(25, 136)(26, 125)(27, 135)(28, 127)(29, 122)(30, 138)(31, 124)(32, 137)(33, 140)(34, 117)(35, 139)(36, 119)(37, 120)(38, 118)(39, 123)(40, 121)(41, 128)(42, 126)(43, 131)(44, 129)(45, 143)(46, 144)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E14.410 Graph:: simple bipartite v = 40 e = 96 f = 30 degree seq :: [ 4^24, 6^16 ] E14.410 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y2 * Y1^4, (Y3 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 10, 58, 3, 51, 7, 55, 14, 62, 5, 53)(4, 52, 11, 59, 22, 70, 20, 68, 9, 57, 19, 67, 24, 72, 12, 60)(8, 56, 17, 65, 31, 79, 30, 78, 16, 64, 29, 77, 32, 80, 18, 66)(13, 61, 25, 73, 38, 86, 33, 81, 21, 69, 34, 82, 36, 84, 23, 71)(15, 63, 27, 75, 41, 89, 39, 87, 26, 74, 40, 88, 42, 90, 28, 76)(35, 83, 45, 93, 48, 96, 43, 91, 37, 85, 46, 94, 47, 95, 44, 92)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 105, 153)(101, 149, 106, 154)(102, 150, 110, 158)(104, 152, 112, 160)(107, 155, 115, 163)(108, 156, 116, 164)(109, 157, 117, 165)(111, 159, 122, 170)(113, 161, 125, 173)(114, 162, 126, 174)(118, 166, 120, 168)(119, 167, 129, 177)(121, 169, 130, 178)(123, 171, 136, 184)(124, 172, 135, 183)(127, 175, 128, 176)(131, 179, 133, 181)(132, 180, 134, 182)(137, 185, 138, 186)(139, 187, 140, 188)(141, 189, 142, 190)(143, 191, 144, 192) L = (1, 100)(2, 104)(3, 105)(4, 97)(5, 109)(6, 111)(7, 112)(8, 98)(9, 99)(10, 117)(11, 119)(12, 113)(13, 101)(14, 122)(15, 102)(16, 103)(17, 108)(18, 123)(19, 129)(20, 125)(21, 106)(22, 131)(23, 107)(24, 133)(25, 135)(26, 110)(27, 114)(28, 130)(29, 116)(30, 136)(31, 139)(32, 140)(33, 115)(34, 124)(35, 118)(36, 141)(37, 120)(38, 142)(39, 121)(40, 126)(41, 143)(42, 144)(43, 127)(44, 128)(45, 132)(46, 134)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E14.409 Graph:: bipartite v = 30 e = 96 f = 40 degree seq :: [ 4^24, 16^6 ] E14.411 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, (Y3 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^-2 * Y3 * Y2 * Y1^-2, Y3 * Y2 * Y1 * Y2 * Y3 * Y1^-1, (Y3 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 17, 65, 10, 58, 21, 69, 16, 64, 5, 53)(3, 51, 9, 57, 25, 73, 13, 61, 4, 52, 12, 60, 28, 76, 11, 59)(7, 55, 20, 68, 35, 83, 24, 72, 8, 56, 23, 71, 36, 84, 22, 70)(14, 62, 29, 77, 39, 87, 26, 74, 15, 63, 30, 78, 40, 88, 27, 75)(18, 66, 31, 79, 41, 89, 34, 82, 19, 67, 33, 81, 42, 90, 32, 80)(37, 85, 45, 93, 48, 96, 43, 91, 38, 86, 46, 94, 47, 95, 44, 92)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 110, 158)(102, 150, 114, 162)(104, 152, 117, 165)(105, 153, 122, 170)(107, 155, 119, 167)(108, 156, 123, 171)(109, 157, 116, 164)(111, 159, 113, 161)(112, 160, 115, 163)(118, 166, 129, 177)(120, 168, 127, 175)(121, 169, 133, 181)(124, 172, 134, 182)(125, 173, 128, 176)(126, 174, 130, 178)(131, 179, 139, 187)(132, 180, 140, 188)(135, 183, 142, 190)(136, 184, 141, 189)(137, 185, 143, 191)(138, 186, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 111)(6, 115)(7, 117)(8, 98)(9, 123)(10, 99)(11, 116)(12, 122)(13, 119)(14, 113)(15, 101)(16, 114)(17, 110)(18, 112)(19, 102)(20, 107)(21, 103)(22, 127)(23, 109)(24, 129)(25, 134)(26, 108)(27, 105)(28, 133)(29, 130)(30, 128)(31, 118)(32, 126)(33, 120)(34, 125)(35, 140)(36, 139)(37, 124)(38, 121)(39, 141)(40, 142)(41, 144)(42, 143)(43, 132)(44, 131)(45, 135)(46, 136)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E14.408 Graph:: bipartite v = 30 e = 96 f = 40 degree seq :: [ 4^24, 16^6 ] E14.412 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y1 * Y3^-2, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, (Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y3^-1 * Y2^3, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 11, 59, 14, 62)(4, 52, 9, 57, 7, 55)(6, 54, 18, 66, 8, 56)(10, 58, 26, 74, 17, 65)(12, 60, 30, 78, 32, 80)(13, 61, 25, 73, 15, 63)(16, 64, 22, 70, 28, 76)(19, 67, 24, 72, 21, 69)(20, 68, 33, 81, 31, 79)(23, 71, 37, 85, 40, 88)(27, 75, 38, 86, 39, 87)(29, 77, 42, 90, 35, 83)(34, 82, 36, 84, 41, 89)(43, 91, 48, 96, 45, 93)(44, 92, 46, 94, 47, 95)(97, 145, 99, 147, 108, 156, 120, 168, 105, 153, 121, 169, 116, 164, 102, 150)(98, 146, 104, 152, 119, 167, 118, 166, 103, 151, 115, 163, 123, 171, 106, 154)(100, 148, 112, 160, 125, 173, 107, 155, 101, 149, 113, 161, 132, 180, 111, 159)(109, 157, 130, 178, 139, 187, 126, 174, 110, 158, 131, 179, 142, 190, 129, 177)(114, 162, 127, 175, 140, 188, 134, 182, 117, 165, 128, 176, 141, 189, 133, 181)(122, 170, 135, 183, 143, 191, 138, 186, 124, 172, 136, 184, 144, 192, 137, 185) L = (1, 100)(2, 105)(3, 109)(4, 98)(5, 103)(6, 115)(7, 97)(8, 117)(9, 101)(10, 112)(11, 121)(12, 127)(13, 107)(14, 111)(15, 99)(16, 122)(17, 124)(18, 120)(19, 114)(20, 128)(21, 102)(22, 113)(23, 135)(24, 104)(25, 110)(26, 118)(27, 136)(28, 106)(29, 130)(30, 116)(31, 126)(32, 129)(33, 108)(34, 138)(35, 137)(36, 131)(37, 123)(38, 119)(39, 133)(40, 134)(41, 125)(42, 132)(43, 140)(44, 144)(45, 143)(46, 141)(47, 139)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^6 ), ( 4^16 ) } Outer automorphisms :: reflexible Dual of E14.407 Graph:: bipartite v = 22 e = 96 f = 48 degree seq :: [ 6^16, 16^6 ] E14.413 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 6, 8}) Quotient :: edge Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^6, T2^8 ] Map:: non-degenerate R = (1, 3, 9, 19, 31, 24, 13, 5)(2, 7, 17, 29, 40, 30, 18, 8)(4, 11, 22, 34, 41, 32, 20, 10)(6, 15, 27, 38, 46, 39, 28, 16)(12, 21, 33, 42, 47, 43, 35, 23)(14, 25, 36, 44, 48, 45, 37, 26)(49, 50, 54, 62, 60, 52)(51, 56, 63, 74, 69, 58)(53, 55, 64, 73, 71, 59)(57, 66, 75, 85, 81, 68)(61, 65, 76, 84, 83, 70)(67, 78, 86, 93, 90, 80)(72, 77, 87, 92, 91, 82)(79, 88, 94, 96, 95, 89) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^6 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E14.414 Transitivity :: ET+ Graph:: simple bipartite v = 14 e = 48 f = 8 degree seq :: [ 6^8, 8^6 ] E14.414 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 6, 8}) Quotient :: loop Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1^2, (F * T1)^2, (F * T2)^2, T2^-2 * T1^4, T2^6, (T2 * T1)^8 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 15, 63, 6, 54, 5, 53)(2, 50, 7, 55, 4, 52, 12, 60, 14, 62, 8, 56)(9, 57, 19, 67, 11, 59, 21, 69, 13, 61, 20, 68)(16, 64, 22, 70, 17, 65, 24, 72, 18, 66, 23, 71)(25, 73, 31, 79, 26, 74, 33, 81, 27, 75, 32, 80)(28, 76, 34, 82, 29, 77, 36, 84, 30, 78, 35, 83)(37, 85, 43, 91, 38, 86, 45, 93, 39, 87, 44, 92)(40, 88, 46, 94, 41, 89, 48, 96, 42, 90, 47, 95) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 61)(6, 62)(7, 64)(8, 66)(9, 53)(10, 52)(11, 51)(12, 65)(13, 63)(14, 58)(15, 59)(16, 56)(17, 55)(18, 60)(19, 73)(20, 75)(21, 74)(22, 76)(23, 78)(24, 77)(25, 68)(26, 67)(27, 69)(28, 71)(29, 70)(30, 72)(31, 85)(32, 87)(33, 86)(34, 88)(35, 90)(36, 89)(37, 80)(38, 79)(39, 81)(40, 83)(41, 82)(42, 84)(43, 94)(44, 95)(45, 96)(46, 92)(47, 93)(48, 91) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E14.413 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 48 f = 14 degree seq :: [ 12^8 ] E14.415 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 8}) 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 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^6, Y2^8, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 12, 60, 4, 52)(3, 51, 8, 56, 15, 63, 26, 74, 21, 69, 10, 58)(5, 53, 7, 55, 16, 64, 25, 73, 23, 71, 11, 59)(9, 57, 18, 66, 27, 75, 37, 85, 33, 81, 20, 68)(13, 61, 17, 65, 28, 76, 36, 84, 35, 83, 22, 70)(19, 67, 30, 78, 38, 86, 45, 93, 42, 90, 32, 80)(24, 72, 29, 77, 39, 87, 44, 92, 43, 91, 34, 82)(31, 79, 40, 88, 46, 94, 48, 96, 47, 95, 41, 89)(97, 145, 99, 147, 105, 153, 115, 163, 127, 175, 120, 168, 109, 157, 101, 149)(98, 146, 103, 151, 113, 161, 125, 173, 136, 184, 126, 174, 114, 162, 104, 152)(100, 148, 107, 155, 118, 166, 130, 178, 137, 185, 128, 176, 116, 164, 106, 154)(102, 150, 111, 159, 123, 171, 134, 182, 142, 190, 135, 183, 124, 172, 112, 160)(108, 156, 117, 165, 129, 177, 138, 186, 143, 191, 139, 187, 131, 179, 119, 167)(110, 158, 121, 169, 132, 180, 140, 188, 144, 192, 141, 189, 133, 181, 122, 170) L = (1, 99)(2, 103)(3, 105)(4, 107)(5, 97)(6, 111)(7, 113)(8, 98)(9, 115)(10, 100)(11, 118)(12, 117)(13, 101)(14, 121)(15, 123)(16, 102)(17, 125)(18, 104)(19, 127)(20, 106)(21, 129)(22, 130)(23, 108)(24, 109)(25, 132)(26, 110)(27, 134)(28, 112)(29, 136)(30, 114)(31, 120)(32, 116)(33, 138)(34, 137)(35, 119)(36, 140)(37, 122)(38, 142)(39, 124)(40, 126)(41, 128)(42, 143)(43, 131)(44, 144)(45, 133)(46, 135)(47, 139)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 12, 2, 12, 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 E14.416 Graph:: bipartite v = 14 e = 96 f = 56 degree seq :: [ 12^8, 16^6 ] E14.416 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 8}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^6, Y3^3 * Y2 * Y3^-5 * Y2^-1, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 102, 150, 110, 158, 108, 156, 100, 148)(99, 147, 104, 152, 111, 159, 122, 170, 117, 165, 106, 154)(101, 149, 103, 151, 112, 160, 121, 169, 119, 167, 107, 155)(105, 153, 114, 162, 123, 171, 133, 181, 129, 177, 116, 164)(109, 157, 113, 161, 124, 172, 132, 180, 131, 179, 118, 166)(115, 163, 126, 174, 134, 182, 141, 189, 138, 186, 128, 176)(120, 168, 125, 173, 135, 183, 140, 188, 139, 187, 130, 178)(127, 175, 136, 184, 142, 190, 144, 192, 143, 191, 137, 185) L = (1, 99)(2, 103)(3, 105)(4, 107)(5, 97)(6, 111)(7, 113)(8, 98)(9, 115)(10, 100)(11, 118)(12, 117)(13, 101)(14, 121)(15, 123)(16, 102)(17, 125)(18, 104)(19, 127)(20, 106)(21, 129)(22, 130)(23, 108)(24, 109)(25, 132)(26, 110)(27, 134)(28, 112)(29, 136)(30, 114)(31, 120)(32, 116)(33, 138)(34, 137)(35, 119)(36, 140)(37, 122)(38, 142)(39, 124)(40, 126)(41, 128)(42, 143)(43, 131)(44, 144)(45, 133)(46, 135)(47, 139)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E14.415 Graph:: simple bipartite v = 56 e = 96 f = 14 degree seq :: [ 2^48, 12^8 ] E14.417 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 8, 12}) Quotient :: edge Aut^+ = C3 : Q16 (small group id <48, 18>) Aut = (C8 x S3) : C2 (small group id <96, 123>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T2^4 * T1^2, T2^-2 * T1^-1 * T2^2 * T1^-1, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^12 ] Map:: non-degenerate R = (1, 3, 10, 18, 6, 17, 16, 5)(2, 7, 20, 13, 4, 12, 24, 8)(9, 25, 14, 28, 11, 27, 15, 26)(19, 29, 22, 32, 21, 31, 23, 30)(33, 41, 35, 44, 34, 43, 36, 42)(37, 45, 39, 48, 38, 47, 40, 46)(49, 50, 54, 52)(51, 57, 65, 59)(53, 62, 66, 63)(55, 67, 60, 69)(56, 70, 61, 71)(58, 72, 64, 68)(73, 81, 75, 82)(74, 83, 76, 84)(77, 85, 79, 86)(78, 87, 80, 88)(89, 94, 91, 96)(90, 93, 92, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^8 ) } Outer automorphisms :: reflexible Dual of E14.421 Transitivity :: ET+ Graph:: bipartite v = 18 e = 48 f = 4 degree seq :: [ 4^12, 8^6 ] E14.418 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 8, 12}) Quotient :: edge Aut^+ = C3 : Q16 (small group id <48, 18>) Aut = (C8 x S3) : C2 (small group id <96, 123>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1, T2 * T1^-1 * T2 * T1^3, T1^-2 * T2 * T1 * T2 * T1^-1, T2^2 * T1 * T2^2 * T1^-1, T2 * T1^-2 * T2^-1 * T1^-2, T1 * T2^5 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 10, 28, 39, 21, 36, 24, 42, 35, 17, 5)(2, 7, 22, 40, 31, 11, 30, 16, 34, 44, 26, 8)(4, 12, 32, 45, 27, 9, 18, 15, 33, 46, 29, 14)(6, 19, 37, 47, 41, 23, 13, 25, 43, 48, 38, 20)(49, 50, 54, 66, 84, 78, 61, 52)(51, 57, 73, 56, 72, 62, 67, 59)(53, 63, 71, 55, 69, 60, 68, 64)(58, 74, 85, 75, 90, 79, 91, 77)(65, 70, 86, 81, 87, 82, 89, 80)(76, 93, 96, 92, 83, 94, 95, 88) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^8 ), ( 8^12 ) } Outer automorphisms :: reflexible Dual of E14.422 Transitivity :: ET+ Graph:: bipartite v = 10 e = 48 f = 12 degree seq :: [ 8^6, 12^4 ] E14.419 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 8, 12}) Quotient :: edge Aut^+ = C3 : Q16 (small group id <48, 18>) Aut = (C8 x S3) : C2 (small group id <96, 123>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-2 * T1 * T2^-2 * T1^-1, T2 * T1^-2 * T2^-1 * T1^-2, T1^3 * T2^2 * T1^3, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^8 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 38, 19)(9, 26, 15, 27)(11, 29, 16, 30)(13, 25, 35, 33)(17, 36, 32, 37)(20, 41, 23, 42)(22, 43, 24, 44)(31, 46, 34, 45)(39, 47, 40, 48)(49, 50, 54, 65, 83, 76, 58, 69, 86, 80, 61, 52)(51, 57, 73, 88, 67, 64, 53, 63, 81, 87, 66, 59)(55, 68, 60, 79, 85, 72, 56, 71, 62, 82, 84, 70)(74, 90, 77, 92, 95, 94, 75, 89, 78, 91, 96, 93) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^4 ), ( 16^12 ) } Outer automorphisms :: reflexible Dual of E14.420 Transitivity :: ET+ Graph:: bipartite v = 16 e = 48 f = 6 degree seq :: [ 4^12, 12^4 ] E14.420 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 8, 12}) Quotient :: loop Aut^+ = C3 : Q16 (small group id <48, 18>) Aut = (C8 x S3) : C2 (small group id <96, 123>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T2^4 * T1^2, T2^-2 * T1^-1 * T2^2 * T1^-1, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^12 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 18, 66, 6, 54, 17, 65, 16, 64, 5, 53)(2, 50, 7, 55, 20, 68, 13, 61, 4, 52, 12, 60, 24, 72, 8, 56)(9, 57, 25, 73, 14, 62, 28, 76, 11, 59, 27, 75, 15, 63, 26, 74)(19, 67, 29, 77, 22, 70, 32, 80, 21, 69, 31, 79, 23, 71, 30, 78)(33, 81, 41, 89, 35, 83, 44, 92, 34, 82, 43, 91, 36, 84, 42, 90)(37, 85, 45, 93, 39, 87, 48, 96, 38, 86, 47, 95, 40, 88, 46, 94) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 67)(8, 70)(9, 65)(10, 72)(11, 51)(12, 69)(13, 71)(14, 66)(15, 53)(16, 68)(17, 59)(18, 63)(19, 60)(20, 58)(21, 55)(22, 61)(23, 56)(24, 64)(25, 81)(26, 83)(27, 82)(28, 84)(29, 85)(30, 87)(31, 86)(32, 88)(33, 75)(34, 73)(35, 76)(36, 74)(37, 79)(38, 77)(39, 80)(40, 78)(41, 94)(42, 93)(43, 96)(44, 95)(45, 92)(46, 91)(47, 90)(48, 89) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E14.419 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 48 f = 16 degree seq :: [ 16^6 ] E14.421 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 8, 12}) Quotient :: loop Aut^+ = C3 : Q16 (small group id <48, 18>) Aut = (C8 x S3) : C2 (small group id <96, 123>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1, T2 * T1^-1 * T2 * T1^3, T1^-2 * T2 * T1 * T2 * T1^-1, T2^2 * T1 * T2^2 * T1^-1, T2 * T1^-2 * T2^-1 * T1^-2, T1 * T2^5 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 28, 76, 39, 87, 21, 69, 36, 84, 24, 72, 42, 90, 35, 83, 17, 65, 5, 53)(2, 50, 7, 55, 22, 70, 40, 88, 31, 79, 11, 59, 30, 78, 16, 64, 34, 82, 44, 92, 26, 74, 8, 56)(4, 52, 12, 60, 32, 80, 45, 93, 27, 75, 9, 57, 18, 66, 15, 63, 33, 81, 46, 94, 29, 77, 14, 62)(6, 54, 19, 67, 37, 85, 47, 95, 41, 89, 23, 71, 13, 61, 25, 73, 43, 91, 48, 96, 38, 86, 20, 68) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 69)(8, 72)(9, 73)(10, 74)(11, 51)(12, 68)(13, 52)(14, 67)(15, 71)(16, 53)(17, 70)(18, 84)(19, 59)(20, 64)(21, 60)(22, 86)(23, 55)(24, 62)(25, 56)(26, 85)(27, 90)(28, 93)(29, 58)(30, 61)(31, 91)(32, 65)(33, 87)(34, 89)(35, 94)(36, 78)(37, 75)(38, 81)(39, 82)(40, 76)(41, 80)(42, 79)(43, 77)(44, 83)(45, 96)(46, 95)(47, 88)(48, 92) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E14.417 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 48 f = 18 degree seq :: [ 24^4 ] E14.422 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 8, 12}) Quotient :: loop Aut^+ = C3 : Q16 (small group id <48, 18>) Aut = (C8 x S3) : C2 (small group id <96, 123>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-2 * T1 * T2^-2 * T1^-1, T2 * T1^-2 * T2^-1 * T1^-2, T1^3 * T2^2 * T1^3, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^8 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 5, 53)(2, 50, 7, 55, 21, 69, 8, 56)(4, 52, 12, 60, 28, 76, 14, 62)(6, 54, 18, 66, 38, 86, 19, 67)(9, 57, 26, 74, 15, 63, 27, 75)(11, 59, 29, 77, 16, 64, 30, 78)(13, 61, 25, 73, 35, 83, 33, 81)(17, 65, 36, 84, 32, 80, 37, 85)(20, 68, 41, 89, 23, 71, 42, 90)(22, 70, 43, 91, 24, 72, 44, 92)(31, 79, 46, 94, 34, 82, 45, 93)(39, 87, 47, 95, 40, 88, 48, 96) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 65)(7, 68)(8, 71)(9, 73)(10, 69)(11, 51)(12, 79)(13, 52)(14, 82)(15, 81)(16, 53)(17, 83)(18, 59)(19, 64)(20, 60)(21, 86)(22, 55)(23, 62)(24, 56)(25, 88)(26, 90)(27, 89)(28, 58)(29, 92)(30, 91)(31, 85)(32, 61)(33, 87)(34, 84)(35, 76)(36, 70)(37, 72)(38, 80)(39, 66)(40, 67)(41, 78)(42, 77)(43, 96)(44, 95)(45, 74)(46, 75)(47, 94)(48, 93) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E14.418 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 48 f = 10 degree seq :: [ 8^12 ] E14.423 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 12}) Quotient :: dipole Aut^+ = C3 : Q16 (small group id <48, 18>) Aut = (C8 x S3) : C2 (small group id <96, 123>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2^-1 * Y1^-2 * Y2 * Y1^-2, Y2^3 * Y1^-1 * Y3 * Y2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-2 * Y1^-1 * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y1^-1, Y2^2 * Y3 * Y2^-2 * Y1^-1, Y2^-1 * R * Y2^2 * R * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 24, 72, 16, 64, 20, 68)(25, 73, 33, 81, 27, 75, 34, 82)(26, 74, 35, 83, 28, 76, 36, 84)(29, 77, 37, 85, 31, 79, 38, 86)(30, 78, 39, 87, 32, 80, 40, 88)(41, 89, 46, 94, 43, 91, 48, 96)(42, 90, 45, 93, 44, 92, 47, 95)(97, 145, 99, 147, 106, 154, 114, 162, 102, 150, 113, 161, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 109, 157, 100, 148, 108, 156, 120, 168, 104, 152)(105, 153, 121, 169, 110, 158, 124, 172, 107, 155, 123, 171, 111, 159, 122, 170)(115, 163, 125, 173, 118, 166, 128, 176, 117, 165, 127, 175, 119, 167, 126, 174)(129, 177, 137, 185, 131, 179, 140, 188, 130, 178, 139, 187, 132, 180, 138, 186)(133, 181, 141, 189, 135, 183, 144, 192, 134, 182, 143, 191, 136, 184, 142, 190) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 116)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 120)(17, 105)(18, 110)(19, 103)(20, 112)(21, 108)(22, 104)(23, 109)(24, 106)(25, 130)(26, 132)(27, 129)(28, 131)(29, 134)(30, 136)(31, 133)(32, 135)(33, 121)(34, 123)(35, 122)(36, 124)(37, 125)(38, 127)(39, 126)(40, 128)(41, 144)(42, 143)(43, 142)(44, 141)(45, 138)(46, 137)(47, 140)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E14.426 Graph:: bipartite v = 18 e = 96 f = 52 degree seq :: [ 8^12, 16^6 ] E14.424 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 12}) Quotient :: dipole Aut^+ = C3 : Q16 (small group id <48, 18>) Aut = (C8 x S3) : C2 (small group id <96, 123>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1^2 * Y2 * Y1^2, Y2^-1 * Y1 * Y2^-1 * Y1^-3, Y1^-2 * Y2 * Y1 * Y2 * Y1^-1, Y2^-2 * Y1^-1 * Y2^-2 * Y1, Y1 * Y2^5 * Y1 * Y2^-1, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 36, 84, 30, 78, 13, 61, 4, 52)(3, 51, 9, 57, 25, 73, 8, 56, 24, 72, 14, 62, 19, 67, 11, 59)(5, 53, 15, 63, 23, 71, 7, 55, 21, 69, 12, 60, 20, 68, 16, 64)(10, 58, 26, 74, 37, 85, 27, 75, 42, 90, 31, 79, 43, 91, 29, 77)(17, 65, 22, 70, 38, 86, 33, 81, 39, 87, 34, 82, 41, 89, 32, 80)(28, 76, 45, 93, 48, 96, 44, 92, 35, 83, 46, 94, 47, 95, 40, 88)(97, 145, 99, 147, 106, 154, 124, 172, 135, 183, 117, 165, 132, 180, 120, 168, 138, 186, 131, 179, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 136, 184, 127, 175, 107, 155, 126, 174, 112, 160, 130, 178, 140, 188, 122, 170, 104, 152)(100, 148, 108, 156, 128, 176, 141, 189, 123, 171, 105, 153, 114, 162, 111, 159, 129, 177, 142, 190, 125, 173, 110, 158)(102, 150, 115, 163, 133, 181, 143, 191, 137, 185, 119, 167, 109, 157, 121, 169, 139, 187, 144, 192, 134, 182, 116, 164) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 114)(10, 124)(11, 126)(12, 128)(13, 121)(14, 100)(15, 129)(16, 130)(17, 101)(18, 111)(19, 133)(20, 102)(21, 132)(22, 136)(23, 109)(24, 138)(25, 139)(26, 104)(27, 105)(28, 135)(29, 110)(30, 112)(31, 107)(32, 141)(33, 142)(34, 140)(35, 113)(36, 120)(37, 143)(38, 116)(39, 117)(40, 127)(41, 119)(42, 131)(43, 144)(44, 122)(45, 123)(46, 125)(47, 137)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 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 E14.425 Graph:: bipartite v = 10 e = 96 f = 60 degree seq :: [ 16^6, 24^4 ] E14.425 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 12}) Quotient :: dipole Aut^+ = C3 : Q16 (small group id <48, 18>) Aut = (C8 x S3) : C2 (small group id <96, 123>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2 * Y3^-1 * Y2^2 * Y3 * Y2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-2 * Y2^-1 * Y3^-2, Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y3^-6 * Y2^-1, (Y3^-1 * Y1^-1)^12 ] Map:: R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 102, 150, 100, 148)(99, 147, 105, 153, 113, 161, 107, 155)(101, 149, 110, 158, 114, 162, 111, 159)(103, 151, 115, 163, 108, 156, 117, 165)(104, 152, 118, 166, 109, 157, 119, 167)(106, 154, 120, 168, 131, 179, 124, 172)(112, 160, 116, 164, 132, 180, 127, 175)(121, 169, 136, 184, 125, 173, 133, 181)(122, 170, 139, 187, 126, 174, 138, 186)(123, 171, 141, 189, 130, 178, 142, 190)(128, 176, 137, 185, 129, 177, 134, 182)(135, 183, 143, 191, 140, 188, 144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 116)(8, 98)(9, 121)(10, 123)(11, 125)(12, 127)(13, 100)(14, 128)(15, 129)(16, 101)(17, 131)(18, 102)(19, 133)(20, 135)(21, 136)(22, 138)(23, 139)(24, 104)(25, 110)(26, 105)(27, 132)(28, 109)(29, 111)(30, 107)(31, 140)(32, 142)(33, 141)(34, 112)(35, 130)(36, 114)(37, 118)(38, 115)(39, 124)(40, 119)(41, 117)(42, 144)(43, 143)(44, 120)(45, 122)(46, 126)(47, 134)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24 ) } Outer automorphisms :: reflexible Dual of E14.424 Graph:: simple bipartite v = 60 e = 96 f = 10 degree seq :: [ 2^48, 8^12 ] E14.426 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 12}) Quotient :: dipole Aut^+ = C3 : Q16 (small group id <48, 18>) Aut = (C8 x S3) : C2 (small group id <96, 123>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1 * Y3^-2 * Y1^-1, (Y3 * Y2^-1)^4, Y1^3 * Y3^2 * Y1^3, Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1, (Y3 * Y1^-1)^8 ] Map:: R = (1, 49, 2, 50, 6, 54, 17, 65, 35, 83, 28, 76, 10, 58, 21, 69, 38, 86, 32, 80, 13, 61, 4, 52)(3, 51, 9, 57, 25, 73, 40, 88, 19, 67, 16, 64, 5, 53, 15, 63, 33, 81, 39, 87, 18, 66, 11, 59)(7, 55, 20, 68, 12, 60, 31, 79, 37, 85, 24, 72, 8, 56, 23, 71, 14, 62, 34, 82, 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)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 114)(7, 117)(8, 98)(9, 122)(10, 101)(11, 125)(12, 124)(13, 121)(14, 100)(15, 123)(16, 126)(17, 132)(18, 134)(19, 102)(20, 137)(21, 104)(22, 139)(23, 138)(24, 140)(25, 131)(26, 111)(27, 105)(28, 110)(29, 112)(30, 107)(31, 142)(32, 133)(33, 109)(34, 141)(35, 129)(36, 128)(37, 113)(38, 115)(39, 143)(40, 144)(41, 119)(42, 116)(43, 120)(44, 118)(45, 127)(46, 130)(47, 136)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E14.423 Graph:: simple bipartite v = 52 e = 96 f = 18 degree seq :: [ 2^48, 24^4 ] E14.427 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 12}) Quotient :: dipole Aut^+ = C3 : Q16 (small group id <48, 18>) Aut = (C8 x S3) : C2 (small group id <96, 123>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3 * Y1, Y3^-1 * Y1^-1, Y3^4, (R * Y1)^2, Y1 * Y3^-2 * Y1, (R * Y3)^2, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y3^2 * Y2^-1 * Y1^-2, Y2^-1 * R * Y2^2 * R * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1^-1 * Y2^-2 * Y3^-1, Y2^4 * Y3^-1 * Y2^-2 * Y3^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1, (Y3 * Y2)^8 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 24, 72, 35, 83, 28, 76)(16, 64, 20, 68, 36, 84, 31, 79)(25, 73, 40, 88, 29, 77, 37, 85)(26, 74, 43, 91, 30, 78, 42, 90)(27, 75, 45, 93, 34, 82, 46, 94)(32, 80, 41, 89, 33, 81, 38, 86)(39, 87, 47, 95, 44, 92, 48, 96)(97, 145, 99, 147, 106, 154, 123, 171, 132, 180, 114, 162, 102, 150, 113, 161, 131, 179, 130, 178, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 135, 183, 124, 172, 109, 157, 100, 148, 108, 156, 127, 175, 140, 188, 120, 168, 104, 152)(105, 153, 121, 169, 110, 158, 128, 176, 142, 190, 126, 174, 107, 155, 125, 173, 111, 159, 129, 177, 141, 189, 122, 170)(115, 163, 133, 181, 118, 166, 138, 186, 144, 192, 137, 185, 117, 165, 136, 184, 119, 167, 139, 187, 143, 191, 134, 182) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 124)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 127)(17, 105)(18, 110)(19, 103)(20, 112)(21, 108)(22, 104)(23, 109)(24, 106)(25, 133)(26, 138)(27, 142)(28, 131)(29, 136)(30, 139)(31, 132)(32, 134)(33, 137)(34, 141)(35, 120)(36, 116)(37, 125)(38, 129)(39, 144)(40, 121)(41, 128)(42, 126)(43, 122)(44, 143)(45, 123)(46, 130)(47, 135)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 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 E14.428 Graph:: bipartite v = 16 e = 96 f = 54 degree seq :: [ 8^12, 24^4 ] E14.428 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 12}) Quotient :: dipole Aut^+ = C3 : Q16 (small group id <48, 18>) Aut = (C8 x S3) : C2 (small group id <96, 123>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-2, Y1^-2 * Y3 * Y1 * Y3 * Y1^-1, Y1^-1 * Y3^2 * Y1 * Y3^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3^5 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 36, 84, 30, 78, 13, 61, 4, 52)(3, 51, 9, 57, 25, 73, 8, 56, 24, 72, 14, 62, 19, 67, 11, 59)(5, 53, 15, 63, 23, 71, 7, 55, 21, 69, 12, 60, 20, 68, 16, 64)(10, 58, 26, 74, 37, 85, 27, 75, 42, 90, 31, 79, 43, 91, 29, 77)(17, 65, 22, 70, 38, 86, 33, 81, 39, 87, 34, 82, 41, 89, 32, 80)(28, 76, 45, 93, 48, 96, 44, 92, 35, 83, 46, 94, 47, 95, 40, 88)(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, 114)(10, 124)(11, 126)(12, 128)(13, 121)(14, 100)(15, 129)(16, 130)(17, 101)(18, 111)(19, 133)(20, 102)(21, 132)(22, 136)(23, 109)(24, 138)(25, 139)(26, 104)(27, 105)(28, 135)(29, 110)(30, 112)(31, 107)(32, 141)(33, 142)(34, 140)(35, 113)(36, 120)(37, 143)(38, 116)(39, 117)(40, 127)(41, 119)(42, 131)(43, 144)(44, 122)(45, 123)(46, 125)(47, 137)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E14.427 Graph:: simple bipartite v = 54 e = 96 f = 16 degree seq :: [ 2^48, 16^6 ] E14.429 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 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, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^16 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 33, 39, 45, 41, 35, 29, 23, 17, 11, 5)(2, 6, 12, 18, 24, 30, 36, 42, 47, 43, 37, 31, 25, 19, 13, 7)(4, 8, 14, 20, 26, 32, 38, 44, 48, 46, 40, 34, 28, 22, 16, 10)(49, 50, 52)(51, 56, 54)(53, 58, 55)(57, 60, 62)(59, 61, 64)(63, 68, 66)(65, 70, 67)(69, 72, 74)(71, 73, 76)(75, 80, 78)(77, 82, 79)(81, 84, 86)(83, 85, 88)(87, 92, 90)(89, 94, 91)(93, 95, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 32^3 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E14.430 Transitivity :: ET+ Graph:: simple bipartite v = 19 e = 48 f = 3 degree seq :: [ 3^16, 16^3 ] E14.430 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 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, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^16 ] Map:: non-degenerate R = (1, 49, 3, 51, 9, 57, 15, 63, 21, 69, 27, 75, 33, 81, 39, 87, 45, 93, 41, 89, 35, 83, 29, 77, 23, 71, 17, 65, 11, 59, 5, 53)(2, 50, 6, 54, 12, 60, 18, 66, 24, 72, 30, 78, 36, 84, 42, 90, 47, 95, 43, 91, 37, 85, 31, 79, 25, 73, 19, 67, 13, 61, 7, 55)(4, 52, 8, 56, 14, 62, 20, 68, 26, 74, 32, 80, 38, 86, 44, 92, 48, 96, 46, 94, 40, 88, 34, 82, 28, 76, 22, 70, 16, 64, 10, 58) L = (1, 50)(2, 52)(3, 56)(4, 49)(5, 58)(6, 51)(7, 53)(8, 54)(9, 60)(10, 55)(11, 61)(12, 62)(13, 64)(14, 57)(15, 68)(16, 59)(17, 70)(18, 63)(19, 65)(20, 66)(21, 72)(22, 67)(23, 73)(24, 74)(25, 76)(26, 69)(27, 80)(28, 71)(29, 82)(30, 75)(31, 77)(32, 78)(33, 84)(34, 79)(35, 85)(36, 86)(37, 88)(38, 81)(39, 92)(40, 83)(41, 94)(42, 87)(43, 89)(44, 90)(45, 95)(46, 91)(47, 96)(48, 93) local type(s) :: { ( 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16 ) } Outer automorphisms :: reflexible Dual of E14.429 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 48 f = 19 degree seq :: [ 32^3 ] E14.431 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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^-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, Y2^16, 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 ] Map:: R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 6, 54)(5, 53, 10, 58, 7, 55)(9, 57, 12, 60, 14, 62)(11, 59, 13, 61, 16, 64)(15, 63, 20, 68, 18, 66)(17, 65, 22, 70, 19, 67)(21, 69, 24, 72, 26, 74)(23, 71, 25, 73, 28, 76)(27, 75, 32, 80, 30, 78)(29, 77, 34, 82, 31, 79)(33, 81, 36, 84, 38, 86)(35, 83, 37, 85, 40, 88)(39, 87, 44, 92, 42, 90)(41, 89, 46, 94, 43, 91)(45, 93, 47, 95, 48, 96)(97, 145, 99, 147, 105, 153, 111, 159, 117, 165, 123, 171, 129, 177, 135, 183, 141, 189, 137, 185, 131, 179, 125, 173, 119, 167, 113, 161, 107, 155, 101, 149)(98, 146, 102, 150, 108, 156, 114, 162, 120, 168, 126, 174, 132, 180, 138, 186, 143, 191, 139, 187, 133, 181, 127, 175, 121, 169, 115, 163, 109, 157, 103, 151)(100, 148, 104, 152, 110, 158, 116, 164, 122, 170, 128, 176, 134, 182, 140, 188, 144, 192, 142, 190, 136, 184, 130, 178, 124, 172, 118, 166, 112, 160, 106, 154) L = (1, 100)(2, 97)(3, 102)(4, 98)(5, 103)(6, 104)(7, 106)(8, 99)(9, 110)(10, 101)(11, 112)(12, 105)(13, 107)(14, 108)(15, 114)(16, 109)(17, 115)(18, 116)(19, 118)(20, 111)(21, 122)(22, 113)(23, 124)(24, 117)(25, 119)(26, 120)(27, 126)(28, 121)(29, 127)(30, 128)(31, 130)(32, 123)(33, 134)(34, 125)(35, 136)(36, 129)(37, 131)(38, 132)(39, 138)(40, 133)(41, 139)(42, 140)(43, 142)(44, 135)(45, 144)(46, 137)(47, 141)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 32, 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 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 E14.432 Graph:: bipartite v = 19 e = 96 f = 51 degree seq :: [ 6^16, 32^3 ] E14.432 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^16 ] Map:: R = (1, 49, 2, 50, 6, 54, 12, 60, 18, 66, 24, 72, 30, 78, 36, 84, 42, 90, 41, 89, 35, 83, 29, 77, 23, 71, 17, 65, 11, 59, 4, 52)(3, 51, 8, 56, 13, 61, 20, 68, 25, 73, 32, 80, 37, 85, 44, 92, 47, 95, 45, 93, 39, 87, 33, 81, 27, 75, 21, 69, 15, 63, 9, 57)(5, 53, 7, 55, 14, 62, 19, 67, 26, 74, 31, 79, 38, 86, 43, 91, 48, 96, 46, 94, 40, 88, 34, 82, 28, 76, 22, 70, 16, 64, 10, 58)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 101)(4, 106)(5, 97)(6, 109)(7, 104)(8, 98)(9, 100)(10, 105)(11, 111)(12, 115)(13, 110)(14, 102)(15, 112)(16, 107)(17, 118)(18, 121)(19, 116)(20, 108)(21, 113)(22, 117)(23, 123)(24, 127)(25, 122)(26, 114)(27, 124)(28, 119)(29, 130)(30, 133)(31, 128)(32, 120)(33, 125)(34, 129)(35, 135)(36, 139)(37, 134)(38, 126)(39, 136)(40, 131)(41, 142)(42, 143)(43, 140)(44, 132)(45, 137)(46, 141)(47, 144)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 32 ), ( 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32 ) } Outer automorphisms :: reflexible Dual of E14.431 Graph:: simple bipartite v = 51 e = 96 f = 19 degree seq :: [ 2^48, 32^3 ] E14.433 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 24}) Quotient :: edge Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^2 * T2^-1 * T1^-2, T2^6, T2 * T1 * T2^-2 * T1^-1 * T2, T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T1^-1 * T2^-3)^8 ] Map:: non-degenerate R = (1, 3, 10, 27, 16, 5)(2, 7, 20, 38, 24, 8)(4, 12, 28, 45, 31, 13)(6, 17, 34, 46, 35, 18)(9, 25, 43, 32, 14, 26)(11, 29, 44, 33, 15, 30)(19, 36, 47, 41, 22, 37)(21, 39, 48, 42, 23, 40)(49, 50, 54, 52)(51, 57, 65, 59)(53, 62, 66, 63)(55, 67, 60, 69)(56, 70, 61, 71)(58, 68, 82, 76)(64, 72, 83, 79)(73, 87, 77, 84)(74, 88, 78, 85)(75, 91, 94, 92)(80, 90, 81, 89)(86, 95, 93, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 48^4 ), ( 48^6 ) } Outer automorphisms :: reflexible Dual of E14.437 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 48 f = 2 degree seq :: [ 4^12, 6^8 ] E14.434 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 24}) Quotient :: edge Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^2 * T1^-1)^2, T2 * T1^2 * T2^-1 * T1^-2, T1^6, T1^-1 * T2 * T1^-1 * T2^-3, T2 * T1 * T2^-2 * T1^-2 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^4, T1^-2 * T2^16 ] Map:: non-degenerate R = (1, 3, 10, 30, 48, 25, 46, 34, 13, 32, 45, 21, 44, 35, 43, 20, 6, 19, 41, 23, 47, 24, 17, 5)(2, 7, 22, 11, 31, 15, 36, 14, 4, 12, 33, 40, 37, 16, 29, 39, 18, 38, 28, 9, 27, 42, 26, 8)(49, 50, 54, 66, 61, 52)(51, 57, 67, 88, 80, 59)(53, 63, 68, 90, 82, 64)(55, 69, 86, 78, 60, 71)(56, 72, 87, 83, 62, 73)(58, 77, 89, 84, 93, 74)(65, 81, 91, 70, 94, 76)(75, 92, 85, 96, 79, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^6 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E14.438 Transitivity :: ET+ Graph:: bipartite v = 10 e = 48 f = 12 degree seq :: [ 6^8, 24^2 ] E14.435 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 24}) Quotient :: edge Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, T1^-1 * T2^-1 * T1^2 * T2^-1 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, T1^-2 * T2^-1 * T1^-1 * T2 * T1^-3, (T2 * T1^-1)^6 ] 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, 32, 45, 29)(17, 36, 47, 37)(20, 41, 23, 42)(22, 43, 24, 44)(31, 46, 34, 35)(33, 38, 48, 40)(49, 50, 54, 65, 83, 78, 92, 73, 89, 96, 93, 75, 58, 69, 87, 95, 94, 76, 91, 74, 90, 81, 61, 52)(51, 57, 67, 88, 79, 60, 72, 56, 71, 84, 80, 64, 53, 63, 66, 86, 82, 62, 70, 55, 68, 85, 77, 59) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^4 ), ( 12^24 ) } Outer automorphisms :: reflexible Dual of E14.436 Transitivity :: ET+ Graph:: bipartite v = 14 e = 48 f = 8 degree seq :: [ 4^12, 24^2 ] E14.436 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 24}) Quotient :: loop Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^2 * T2^-1 * T1^-2, T2^6, T2 * T1 * T2^-2 * T1^-1 * T2, T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T1^-1 * T2^-3)^8 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 27, 75, 16, 64, 5, 53)(2, 50, 7, 55, 20, 68, 38, 86, 24, 72, 8, 56)(4, 52, 12, 60, 28, 76, 45, 93, 31, 79, 13, 61)(6, 54, 17, 65, 34, 82, 46, 94, 35, 83, 18, 66)(9, 57, 25, 73, 43, 91, 32, 80, 14, 62, 26, 74)(11, 59, 29, 77, 44, 92, 33, 81, 15, 63, 30, 78)(19, 67, 36, 84, 47, 95, 41, 89, 22, 70, 37, 85)(21, 69, 39, 87, 48, 96, 42, 90, 23, 71, 40, 88) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 67)(8, 70)(9, 65)(10, 68)(11, 51)(12, 69)(13, 71)(14, 66)(15, 53)(16, 72)(17, 59)(18, 63)(19, 60)(20, 82)(21, 55)(22, 61)(23, 56)(24, 83)(25, 87)(26, 88)(27, 91)(28, 58)(29, 84)(30, 85)(31, 64)(32, 90)(33, 89)(34, 76)(35, 79)(36, 73)(37, 74)(38, 95)(39, 77)(40, 78)(41, 80)(42, 81)(43, 94)(44, 75)(45, 96)(46, 92)(47, 93)(48, 86) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E14.435 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 48 f = 14 degree seq :: [ 12^8 ] E14.437 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 24}) Quotient :: loop Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^2 * T1^-1)^2, T2 * T1^2 * T2^-1 * T1^-2, T1^6, T1^-1 * T2 * T1^-1 * T2^-3, T2 * T1 * T2^-2 * T1^-2 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^4, T1^-2 * T2^16 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 30, 78, 48, 96, 25, 73, 46, 94, 34, 82, 13, 61, 32, 80, 45, 93, 21, 69, 44, 92, 35, 83, 43, 91, 20, 68, 6, 54, 19, 67, 41, 89, 23, 71, 47, 95, 24, 72, 17, 65, 5, 53)(2, 50, 7, 55, 22, 70, 11, 59, 31, 79, 15, 63, 36, 84, 14, 62, 4, 52, 12, 60, 33, 81, 40, 88, 37, 85, 16, 64, 29, 77, 39, 87, 18, 66, 38, 86, 28, 76, 9, 57, 27, 75, 42, 90, 26, 74, 8, 56) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 69)(8, 72)(9, 67)(10, 77)(11, 51)(12, 71)(13, 52)(14, 73)(15, 68)(16, 53)(17, 81)(18, 61)(19, 88)(20, 90)(21, 86)(22, 94)(23, 55)(24, 87)(25, 56)(26, 58)(27, 92)(28, 65)(29, 89)(30, 60)(31, 95)(32, 59)(33, 91)(34, 64)(35, 62)(36, 93)(37, 96)(38, 78)(39, 83)(40, 80)(41, 84)(42, 82)(43, 70)(44, 85)(45, 74)(46, 76)(47, 75)(48, 79) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E14.433 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 48 f = 20 degree seq :: [ 48^2 ] E14.438 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 24}) Quotient :: loop Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, T1^-1 * T2^-1 * T1^2 * T2^-1 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, T1^-2 * T2^-1 * T1^-1 * T2 * T1^-3, (T2 * T1^-1)^6 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 5, 53)(2, 50, 7, 55, 21, 69, 8, 56)(4, 52, 12, 60, 27, 75, 14, 62)(6, 54, 18, 66, 39, 87, 19, 67)(9, 57, 25, 73, 15, 63, 26, 74)(11, 59, 28, 76, 16, 64, 30, 78)(13, 61, 32, 80, 45, 93, 29, 77)(17, 65, 36, 84, 47, 95, 37, 85)(20, 68, 41, 89, 23, 71, 42, 90)(22, 70, 43, 91, 24, 72, 44, 92)(31, 79, 46, 94, 34, 82, 35, 83)(33, 81, 38, 86, 48, 96, 40, 88) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 65)(7, 68)(8, 71)(9, 67)(10, 69)(11, 51)(12, 72)(13, 52)(14, 70)(15, 66)(16, 53)(17, 83)(18, 86)(19, 88)(20, 85)(21, 87)(22, 55)(23, 84)(24, 56)(25, 89)(26, 90)(27, 58)(28, 91)(29, 59)(30, 92)(31, 60)(32, 64)(33, 61)(34, 62)(35, 78)(36, 80)(37, 77)(38, 82)(39, 95)(40, 79)(41, 96)(42, 81)(43, 74)(44, 73)(45, 75)(46, 76)(47, 94)(48, 93) local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E14.434 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 48 f = 10 degree seq :: [ 8^12 ] E14.439 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 24}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^4, Y1^2 * Y3^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, Y2^6, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 20, 68, 34, 82, 28, 76)(16, 64, 24, 72, 35, 83, 31, 79)(25, 73, 39, 87, 29, 77, 36, 84)(26, 74, 40, 88, 30, 78, 37, 85)(27, 75, 43, 91, 46, 94, 44, 92)(32, 80, 42, 90, 33, 81, 41, 89)(38, 86, 47, 95, 45, 93, 48, 96)(97, 145, 99, 147, 106, 154, 123, 171, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 134, 182, 120, 168, 104, 152)(100, 148, 108, 156, 124, 172, 141, 189, 127, 175, 109, 157)(102, 150, 113, 161, 130, 178, 142, 190, 131, 179, 114, 162)(105, 153, 121, 169, 139, 187, 128, 176, 110, 158, 122, 170)(107, 155, 125, 173, 140, 188, 129, 177, 111, 159, 126, 174)(115, 163, 132, 180, 143, 191, 137, 185, 118, 166, 133, 181)(117, 165, 135, 183, 144, 192, 138, 186, 119, 167, 136, 184) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 124)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 127)(17, 105)(18, 110)(19, 103)(20, 106)(21, 108)(22, 104)(23, 109)(24, 112)(25, 132)(26, 133)(27, 140)(28, 130)(29, 135)(30, 136)(31, 131)(32, 137)(33, 138)(34, 116)(35, 120)(36, 125)(37, 126)(38, 144)(39, 121)(40, 122)(41, 129)(42, 128)(43, 123)(44, 142)(45, 143)(46, 139)(47, 134)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 48, 2, 48, 2, 48, 2, 48 ), ( 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48 ) } Outer automorphisms :: reflexible Dual of E14.442 Graph:: bipartite v = 20 e = 96 f = 50 degree seq :: [ 8^12, 12^8 ] E14.440 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 24}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^2 * Y1^-1)^2, Y1^6, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2^-3 * Y1^-1, Y2 * Y1 * Y2^-2 * Y1^-2 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y1^-2 * Y2^16 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 40, 88, 32, 80, 11, 59)(5, 53, 15, 63, 20, 68, 42, 90, 34, 82, 16, 64)(7, 55, 21, 69, 38, 86, 30, 78, 12, 60, 23, 71)(8, 56, 24, 72, 39, 87, 35, 83, 14, 62, 25, 73)(10, 58, 29, 77, 41, 89, 36, 84, 45, 93, 26, 74)(17, 65, 33, 81, 43, 91, 22, 70, 46, 94, 28, 76)(27, 75, 44, 92, 37, 85, 48, 96, 31, 79, 47, 95)(97, 145, 99, 147, 106, 154, 126, 174, 144, 192, 121, 169, 142, 190, 130, 178, 109, 157, 128, 176, 141, 189, 117, 165, 140, 188, 131, 179, 139, 187, 116, 164, 102, 150, 115, 163, 137, 185, 119, 167, 143, 191, 120, 168, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 107, 155, 127, 175, 111, 159, 132, 180, 110, 158, 100, 148, 108, 156, 129, 177, 136, 184, 133, 181, 112, 160, 125, 173, 135, 183, 114, 162, 134, 182, 124, 172, 105, 153, 123, 171, 138, 186, 122, 170, 104, 152) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 123)(10, 126)(11, 127)(12, 129)(13, 128)(14, 100)(15, 132)(16, 125)(17, 101)(18, 134)(19, 137)(20, 102)(21, 140)(22, 107)(23, 143)(24, 113)(25, 142)(26, 104)(27, 138)(28, 105)(29, 135)(30, 144)(31, 111)(32, 141)(33, 136)(34, 109)(35, 139)(36, 110)(37, 112)(38, 124)(39, 114)(40, 133)(41, 119)(42, 122)(43, 116)(44, 131)(45, 117)(46, 130)(47, 120)(48, 121)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E14.441 Graph:: bipartite v = 10 e = 96 f = 60 degree seq :: [ 12^8, 48^2 ] E14.441 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 24}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, Y3 * Y2 * Y3^-2 * Y2 * Y3, Y3^4 * Y2^-1 * Y3 * Y2 * Y3, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, (Y3^3 * Y2^-1)^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, 100, 148)(99, 147, 105, 153, 113, 161, 107, 155)(101, 149, 110, 158, 114, 162, 111, 159)(103, 151, 115, 163, 108, 156, 117, 165)(104, 152, 118, 166, 109, 157, 119, 167)(106, 154, 123, 171, 131, 179, 116, 164)(112, 160, 127, 175, 132, 180, 120, 168)(121, 169, 133, 181, 125, 173, 136, 184)(122, 170, 137, 185, 126, 174, 134, 182)(124, 172, 142, 190, 143, 191, 140, 188)(128, 176, 138, 186, 129, 177, 139, 187)(130, 178, 141, 189, 144, 192, 135, 183) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 116)(8, 98)(9, 121)(10, 124)(11, 125)(12, 123)(13, 100)(14, 126)(15, 122)(16, 101)(17, 131)(18, 102)(19, 133)(20, 135)(21, 136)(22, 137)(23, 134)(24, 104)(25, 140)(26, 105)(27, 141)(28, 139)(29, 142)(30, 107)(31, 109)(32, 110)(33, 111)(34, 112)(35, 143)(36, 114)(37, 144)(38, 115)(39, 128)(40, 130)(41, 117)(42, 118)(43, 119)(44, 120)(45, 129)(46, 127)(47, 138)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12, 48 ), ( 12, 48, 12, 48, 12, 48, 12, 48 ) } Outer automorphisms :: reflexible Dual of E14.440 Graph:: simple bipartite v = 60 e = 96 f = 10 degree seq :: [ 2^48, 8^12 ] E14.442 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 24}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1^-2 * Y3^-1 * Y1, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, (Y1^-2 * Y3^-1 * Y1^-1)^2, (Y3 * Y2^-1)^4, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-3, Y1^24 ] Map:: R = (1, 49, 2, 50, 6, 54, 17, 65, 35, 83, 30, 78, 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, 33, 81, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 40, 88, 31, 79, 12, 60, 24, 72, 8, 56, 23, 71, 36, 84, 32, 80, 16, 64, 5, 53, 15, 63, 18, 66, 38, 86, 34, 82, 14, 62, 22, 70, 7, 55, 20, 68, 37, 85, 29, 77, 11, 59)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 114)(7, 117)(8, 98)(9, 121)(10, 101)(11, 124)(12, 123)(13, 128)(14, 100)(15, 122)(16, 126)(17, 132)(18, 135)(19, 102)(20, 137)(21, 104)(22, 139)(23, 138)(24, 140)(25, 111)(26, 105)(27, 110)(28, 112)(29, 109)(30, 107)(31, 142)(32, 141)(33, 134)(34, 131)(35, 127)(36, 143)(37, 113)(38, 144)(39, 115)(40, 129)(41, 119)(42, 116)(43, 120)(44, 118)(45, 125)(46, 130)(47, 133)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E14.439 Graph:: simple bipartite v = 50 e = 96 f = 20 degree seq :: [ 2^48, 48^2 ] E14.443 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 24}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y1^2 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2^2 * Y1^-1 * Y2^-1, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2^-2 * Y1^-1 * Y2, Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^3 * Y3 * Y2^3 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 27, 75, 35, 83, 20, 68)(16, 64, 31, 79, 36, 84, 24, 72)(25, 73, 37, 85, 29, 77, 40, 88)(26, 74, 41, 89, 30, 78, 38, 86)(28, 76, 46, 94, 47, 95, 44, 92)(32, 80, 42, 90, 33, 81, 43, 91)(34, 82, 45, 93, 48, 96, 39, 87)(97, 145, 99, 147, 106, 154, 124, 172, 139, 187, 119, 167, 134, 182, 115, 163, 133, 181, 144, 192, 132, 180, 114, 162, 102, 150, 113, 161, 131, 179, 143, 191, 138, 186, 118, 166, 137, 185, 117, 165, 136, 184, 130, 178, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 135, 183, 128, 176, 110, 158, 126, 174, 107, 155, 125, 173, 142, 190, 127, 175, 109, 157, 100, 148, 108, 156, 123, 171, 141, 189, 129, 177, 111, 159, 122, 170, 105, 153, 121, 169, 140, 188, 120, 168, 104, 152) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 116)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 120)(17, 105)(18, 110)(19, 103)(20, 131)(21, 108)(22, 104)(23, 109)(24, 132)(25, 136)(26, 134)(27, 106)(28, 140)(29, 133)(30, 137)(31, 112)(32, 139)(33, 138)(34, 135)(35, 123)(36, 127)(37, 121)(38, 126)(39, 144)(40, 125)(41, 122)(42, 128)(43, 129)(44, 143)(45, 130)(46, 124)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E14.444 Graph:: bipartite v = 14 e = 96 f = 56 degree seq :: [ 8^12, 48^2 ] E14.444 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 24}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y3^-2)^2, Y1^6, Y3 * Y1^-1 * Y3^-3 * Y1^-1, Y1^-1 * Y3 * Y1^2 * Y3^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3^3 * Y1^-3, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 40, 88, 32, 80, 11, 59)(5, 53, 15, 63, 20, 68, 42, 90, 34, 82, 16, 64)(7, 55, 21, 69, 38, 86, 30, 78, 12, 60, 23, 71)(8, 56, 24, 72, 39, 87, 35, 83, 14, 62, 25, 73)(10, 58, 29, 77, 41, 89, 36, 84, 45, 93, 26, 74)(17, 65, 33, 81, 43, 91, 22, 70, 46, 94, 28, 76)(27, 75, 44, 92, 37, 85, 48, 96, 31, 79, 47, 95)(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, 126)(11, 127)(12, 129)(13, 128)(14, 100)(15, 132)(16, 125)(17, 101)(18, 134)(19, 137)(20, 102)(21, 140)(22, 107)(23, 143)(24, 113)(25, 142)(26, 104)(27, 138)(28, 105)(29, 135)(30, 144)(31, 111)(32, 141)(33, 136)(34, 109)(35, 139)(36, 110)(37, 112)(38, 124)(39, 114)(40, 133)(41, 119)(42, 122)(43, 116)(44, 131)(45, 117)(46, 130)(47, 120)(48, 121)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E14.443 Graph:: simple bipartite v = 56 e = 96 f = 14 degree seq :: [ 2^48, 12^8 ] E14.445 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C13 : C4 (small group id <52, 3>) Aut = C2 x (C13 : C4) (small group id <104, 12>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2, Y2 * Y1, Y2^-1 * Y1^-1, Y1^3 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y1, Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3, Y2 * Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 53, 4, 56)(2, 54, 6, 58)(3, 55, 7, 59)(5, 57, 10, 62)(8, 60, 16, 68)(9, 61, 17, 69)(11, 63, 21, 73)(12, 64, 22, 74)(13, 65, 24, 76)(14, 66, 25, 77)(15, 67, 26, 78)(18, 70, 30, 82)(19, 71, 31, 83)(20, 72, 32, 84)(23, 75, 35, 87)(27, 79, 40, 92)(28, 80, 41, 93)(29, 81, 42, 94)(33, 85, 45, 97)(34, 86, 37, 89)(36, 88, 39, 91)(38, 90, 49, 101)(43, 95, 47, 99)(44, 96, 51, 103)(46, 98, 48, 100)(50, 102, 52, 104)(105, 106, 109, 107)(108, 112, 119, 113)(110, 115, 124, 116)(111, 117, 127, 118)(114, 122, 133, 123)(120, 129, 141, 131)(121, 132, 137, 125)(126, 138, 147, 134)(128, 135, 145, 140)(130, 142, 152, 143)(136, 148, 153, 144)(139, 150, 156, 151)(146, 154, 155, 149)(157, 159, 161, 158)(160, 165, 171, 164)(162, 168, 176, 167)(163, 170, 179, 169)(166, 175, 185, 174)(172, 183, 193, 181)(173, 177, 189, 184)(178, 186, 199, 190)(180, 192, 197, 187)(182, 195, 204, 194)(188, 196, 205, 200)(191, 203, 208, 202)(198, 201, 207, 206) L = (1, 105)(2, 106)(3, 107)(4, 108)(5, 109)(6, 110)(7, 111)(8, 112)(9, 113)(10, 114)(11, 115)(12, 116)(13, 117)(14, 118)(15, 119)(16, 120)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 129)(26, 130)(27, 131)(28, 132)(29, 133)(30, 134)(31, 135)(32, 136)(33, 137)(34, 138)(35, 139)(36, 140)(37, 141)(38, 142)(39, 143)(40, 144)(41, 145)(42, 146)(43, 147)(44, 148)(45, 149)(46, 150)(47, 151)(48, 152)(49, 153)(50, 154)(51, 155)(52, 156)(53, 157)(54, 158)(55, 159)(56, 160)(57, 161)(58, 162)(59, 163)(60, 164)(61, 165)(62, 166)(63, 167)(64, 168)(65, 169)(66, 170)(67, 171)(68, 172)(69, 173)(70, 174)(71, 175)(72, 176)(73, 177)(74, 178)(75, 179)(76, 180)(77, 181)(78, 182)(79, 183)(80, 184)(81, 185)(82, 186)(83, 187)(84, 188)(85, 189)(86, 190)(87, 191)(88, 192)(89, 193)(90, 194)(91, 195)(92, 196)(93, 197)(94, 198)(95, 199)(96, 200)(97, 201)(98, 202)(99, 203)(100, 204)(101, 205)(102, 206)(103, 207)(104, 208) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E14.448 Graph:: simple bipartite v = 52 e = 104 f = 26 degree seq :: [ 4^52 ] E14.446 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C13 : C4 (small group id <52, 3>) Aut = C2 x (C13 : C4) (small group id <104, 12>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1, Y2^4, Y1^2 * Y2^-2, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y1^-1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y3, Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 53, 4, 56)(2, 54, 6, 58)(3, 55, 7, 59)(5, 57, 10, 62)(8, 60, 16, 68)(9, 61, 17, 69)(11, 63, 21, 73)(12, 64, 22, 74)(13, 65, 24, 76)(14, 66, 25, 77)(15, 67, 26, 78)(18, 70, 30, 82)(19, 71, 31, 83)(20, 72, 32, 84)(23, 75, 35, 87)(27, 79, 40, 92)(28, 80, 41, 93)(29, 81, 42, 94)(33, 85, 36, 88)(34, 86, 38, 90)(37, 89, 47, 99)(39, 91, 49, 101)(43, 95, 44, 96)(45, 97, 48, 100)(46, 98, 52, 104)(50, 102, 51, 103)(105, 106, 109, 107)(108, 112, 119, 113)(110, 115, 124, 116)(111, 117, 127, 118)(114, 122, 133, 123)(120, 129, 141, 131)(121, 132, 137, 125)(126, 138, 144, 134)(128, 135, 147, 140)(130, 142, 152, 143)(136, 148, 155, 149)(139, 145, 153, 150)(146, 151, 156, 154)(157, 159, 161, 158)(160, 165, 171, 164)(162, 168, 176, 167)(163, 170, 179, 169)(166, 175, 185, 174)(172, 183, 193, 181)(173, 177, 189, 184)(178, 186, 196, 190)(180, 192, 199, 187)(182, 195, 204, 194)(188, 201, 207, 200)(191, 202, 205, 197)(198, 206, 208, 203) L = (1, 105)(2, 106)(3, 107)(4, 108)(5, 109)(6, 110)(7, 111)(8, 112)(9, 113)(10, 114)(11, 115)(12, 116)(13, 117)(14, 118)(15, 119)(16, 120)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 129)(26, 130)(27, 131)(28, 132)(29, 133)(30, 134)(31, 135)(32, 136)(33, 137)(34, 138)(35, 139)(36, 140)(37, 141)(38, 142)(39, 143)(40, 144)(41, 145)(42, 146)(43, 147)(44, 148)(45, 149)(46, 150)(47, 151)(48, 152)(49, 153)(50, 154)(51, 155)(52, 156)(53, 157)(54, 158)(55, 159)(56, 160)(57, 161)(58, 162)(59, 163)(60, 164)(61, 165)(62, 166)(63, 167)(64, 168)(65, 169)(66, 170)(67, 171)(68, 172)(69, 173)(70, 174)(71, 175)(72, 176)(73, 177)(74, 178)(75, 179)(76, 180)(77, 181)(78, 182)(79, 183)(80, 184)(81, 185)(82, 186)(83, 187)(84, 188)(85, 189)(86, 190)(87, 191)(88, 192)(89, 193)(90, 194)(91, 195)(92, 196)(93, 197)(94, 198)(95, 199)(96, 200)(97, 201)(98, 202)(99, 203)(100, 204)(101, 205)(102, 206)(103, 207)(104, 208) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E14.447 Graph:: simple bipartite v = 52 e = 104 f = 26 degree seq :: [ 4^52 ] E14.447 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C13 : C4 (small group id <52, 3>) Aut = C2 x (C13 : C4) (small group id <104, 12>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2, Y2 * Y1, Y2^-1 * Y1^-1, Y1^3 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y1, Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3, Y2 * Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 53, 105, 157, 4, 56, 108, 160)(2, 54, 106, 158, 6, 58, 110, 162)(3, 55, 107, 159, 7, 59, 111, 163)(5, 57, 109, 161, 10, 62, 114, 166)(8, 60, 112, 164, 16, 68, 120, 172)(9, 61, 113, 165, 17, 69, 121, 173)(11, 63, 115, 167, 21, 73, 125, 177)(12, 64, 116, 168, 22, 74, 126, 178)(13, 65, 117, 169, 24, 76, 128, 180)(14, 66, 118, 170, 25, 77, 129, 181)(15, 67, 119, 171, 26, 78, 130, 182)(18, 70, 122, 174, 30, 82, 134, 186)(19, 71, 123, 175, 31, 83, 135, 187)(20, 72, 124, 176, 32, 84, 136, 188)(23, 75, 127, 179, 35, 87, 139, 191)(27, 79, 131, 183, 40, 92, 144, 196)(28, 80, 132, 184, 41, 93, 145, 197)(29, 81, 133, 185, 42, 94, 146, 198)(33, 85, 137, 189, 45, 97, 149, 201)(34, 86, 138, 190, 37, 89, 141, 193)(36, 88, 140, 192, 39, 91, 143, 195)(38, 90, 142, 194, 49, 101, 153, 205)(43, 95, 147, 199, 47, 99, 151, 203)(44, 96, 148, 200, 51, 103, 155, 207)(46, 98, 150, 202, 48, 100, 152, 204)(50, 102, 154, 206, 52, 104, 156, 208) L = (1, 54)(2, 57)(3, 53)(4, 60)(5, 55)(6, 63)(7, 65)(8, 67)(9, 56)(10, 70)(11, 72)(12, 58)(13, 75)(14, 59)(15, 61)(16, 77)(17, 80)(18, 81)(19, 62)(20, 64)(21, 69)(22, 86)(23, 66)(24, 83)(25, 89)(26, 90)(27, 68)(28, 85)(29, 71)(30, 74)(31, 93)(32, 96)(33, 73)(34, 95)(35, 98)(36, 76)(37, 79)(38, 100)(39, 78)(40, 84)(41, 88)(42, 102)(43, 82)(44, 101)(45, 94)(46, 104)(47, 87)(48, 91)(49, 92)(50, 103)(51, 97)(52, 99)(105, 159)(106, 157)(107, 161)(108, 165)(109, 158)(110, 168)(111, 170)(112, 160)(113, 171)(114, 175)(115, 162)(116, 176)(117, 163)(118, 179)(119, 164)(120, 183)(121, 177)(122, 166)(123, 185)(124, 167)(125, 189)(126, 186)(127, 169)(128, 192)(129, 172)(130, 195)(131, 193)(132, 173)(133, 174)(134, 199)(135, 180)(136, 196)(137, 184)(138, 178)(139, 203)(140, 197)(141, 181)(142, 182)(143, 204)(144, 205)(145, 187)(146, 201)(147, 190)(148, 188)(149, 207)(150, 191)(151, 208)(152, 194)(153, 200)(154, 198)(155, 206)(156, 202) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E14.446 Transitivity :: VT+ Graph:: bipartite v = 26 e = 104 f = 52 degree seq :: [ 8^26 ] E14.448 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C13 : C4 (small group id <52, 3>) Aut = C2 x (C13 : C4) (small group id <104, 12>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1, Y2^4, Y1^2 * Y2^-2, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y1^-1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y3, Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 53, 105, 157, 4, 56, 108, 160)(2, 54, 106, 158, 6, 58, 110, 162)(3, 55, 107, 159, 7, 59, 111, 163)(5, 57, 109, 161, 10, 62, 114, 166)(8, 60, 112, 164, 16, 68, 120, 172)(9, 61, 113, 165, 17, 69, 121, 173)(11, 63, 115, 167, 21, 73, 125, 177)(12, 64, 116, 168, 22, 74, 126, 178)(13, 65, 117, 169, 24, 76, 128, 180)(14, 66, 118, 170, 25, 77, 129, 181)(15, 67, 119, 171, 26, 78, 130, 182)(18, 70, 122, 174, 30, 82, 134, 186)(19, 71, 123, 175, 31, 83, 135, 187)(20, 72, 124, 176, 32, 84, 136, 188)(23, 75, 127, 179, 35, 87, 139, 191)(27, 79, 131, 183, 40, 92, 144, 196)(28, 80, 132, 184, 41, 93, 145, 197)(29, 81, 133, 185, 42, 94, 146, 198)(33, 85, 137, 189, 36, 88, 140, 192)(34, 86, 138, 190, 38, 90, 142, 194)(37, 89, 141, 193, 47, 99, 151, 203)(39, 91, 143, 195, 49, 101, 153, 205)(43, 95, 147, 199, 44, 96, 148, 200)(45, 97, 149, 201, 48, 100, 152, 204)(46, 98, 150, 202, 52, 104, 156, 208)(50, 102, 154, 206, 51, 103, 155, 207) L = (1, 54)(2, 57)(3, 53)(4, 60)(5, 55)(6, 63)(7, 65)(8, 67)(9, 56)(10, 70)(11, 72)(12, 58)(13, 75)(14, 59)(15, 61)(16, 77)(17, 80)(18, 81)(19, 62)(20, 64)(21, 69)(22, 86)(23, 66)(24, 83)(25, 89)(26, 90)(27, 68)(28, 85)(29, 71)(30, 74)(31, 95)(32, 96)(33, 73)(34, 92)(35, 93)(36, 76)(37, 79)(38, 100)(39, 78)(40, 82)(41, 101)(42, 99)(43, 88)(44, 103)(45, 84)(46, 87)(47, 104)(48, 91)(49, 98)(50, 94)(51, 97)(52, 102)(105, 159)(106, 157)(107, 161)(108, 165)(109, 158)(110, 168)(111, 170)(112, 160)(113, 171)(114, 175)(115, 162)(116, 176)(117, 163)(118, 179)(119, 164)(120, 183)(121, 177)(122, 166)(123, 185)(124, 167)(125, 189)(126, 186)(127, 169)(128, 192)(129, 172)(130, 195)(131, 193)(132, 173)(133, 174)(134, 196)(135, 180)(136, 201)(137, 184)(138, 178)(139, 202)(140, 199)(141, 181)(142, 182)(143, 204)(144, 190)(145, 191)(146, 206)(147, 187)(148, 188)(149, 207)(150, 205)(151, 198)(152, 194)(153, 197)(154, 208)(155, 200)(156, 203) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E14.445 Transitivity :: VT+ Graph:: bipartite v = 26 e = 104 f = 52 degree seq :: [ 8^26 ] E14.449 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 28}) Quotient :: dipole Aut^+ = D56 (small group id <56, 5>) Aut = C2 x D56 (small group id <112, 29>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (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 ] Map:: non-degenerate R = (1, 57, 2, 58)(3, 59, 5, 61)(4, 60, 8, 64)(6, 62, 10, 66)(7, 63, 11, 67)(9, 65, 13, 69)(12, 68, 16, 72)(14, 70, 18, 74)(15, 71, 19, 75)(17, 73, 21, 77)(20, 76, 24, 80)(22, 78, 26, 82)(23, 79, 27, 83)(25, 81, 32, 88)(28, 84, 31, 87)(29, 85, 45, 101)(30, 86, 49, 105)(33, 89, 43, 99)(34, 90, 47, 103)(35, 91, 50, 106)(36, 92, 52, 108)(37, 93, 55, 111)(38, 94, 51, 107)(39, 95, 48, 104)(40, 96, 56, 112)(41, 97, 53, 109)(42, 98, 54, 110)(44, 100, 46, 102)(113, 169, 115, 171)(114, 170, 117, 173)(116, 172, 119, 175)(118, 174, 121, 177)(120, 176, 123, 179)(122, 178, 125, 181)(124, 180, 127, 183)(126, 182, 129, 185)(128, 184, 131, 187)(130, 186, 133, 189)(132, 188, 135, 191)(134, 190, 137, 193)(136, 192, 139, 195)(138, 194, 144, 200)(140, 196, 157, 213)(141, 197, 143, 199)(142, 198, 145, 201)(146, 202, 148, 204)(147, 203, 149, 205)(150, 206, 152, 208)(151, 207, 153, 209)(154, 210, 158, 214)(155, 211, 161, 217)(156, 212, 166, 222)(159, 215, 164, 220)(160, 216, 165, 221)(162, 218, 167, 223)(163, 219, 168, 224) L = (1, 116)(2, 118)(3, 119)(4, 113)(5, 121)(6, 114)(7, 115)(8, 124)(9, 117)(10, 126)(11, 127)(12, 120)(13, 129)(14, 122)(15, 123)(16, 132)(17, 125)(18, 134)(19, 135)(20, 128)(21, 137)(22, 130)(23, 131)(24, 140)(25, 133)(26, 155)(27, 157)(28, 136)(29, 159)(30, 162)(31, 164)(32, 161)(33, 167)(34, 163)(35, 160)(36, 168)(37, 165)(38, 166)(39, 158)(40, 156)(41, 154)(42, 153)(43, 138)(44, 152)(45, 139)(46, 151)(47, 141)(48, 147)(49, 144)(50, 142)(51, 146)(52, 143)(53, 149)(54, 150)(55, 145)(56, 148)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 56, 4, 56 ) } Outer automorphisms :: reflexible Dual of E14.450 Graph:: simple bipartite v = 56 e = 112 f = 30 degree seq :: [ 4^56 ] E14.450 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 28}) 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, Y3^2, (R * Y2)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, Y2 * Y3 * Y1^14, Y1^-1 * Y2 * Y1^6 * Y3 * Y1^-7 ] Map:: non-degenerate R = (1, 57, 2, 58, 6, 62, 13, 69, 21, 77, 29, 85, 37, 93, 45, 101, 53, 109, 50, 106, 42, 98, 34, 90, 26, 82, 18, 74, 10, 66, 16, 72, 24, 80, 32, 88, 40, 96, 48, 104, 56, 112, 52, 108, 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, 55, 111, 47, 103, 39, 95, 31, 87, 23, 79, 15, 71, 8, 64, 4, 60, 11, 67, 19, 75, 27, 83, 35, 91, 43, 99, 51, 107, 54, 110, 46, 102, 38, 94, 30, 86, 22, 78, 14, 70, 7, 63)(113, 169, 115, 171)(114, 170, 119, 175)(116, 172, 122, 178)(117, 173, 121, 177)(118, 174, 126, 182)(120, 176, 128, 184)(123, 179, 130, 186)(124, 180, 129, 185)(125, 181, 134, 190)(127, 183, 136, 192)(131, 187, 138, 194)(132, 188, 137, 193)(133, 189, 142, 198)(135, 191, 144, 200)(139, 195, 146, 202)(140, 196, 145, 201)(141, 197, 150, 206)(143, 199, 152, 208)(147, 203, 154, 210)(148, 204, 153, 209)(149, 205, 158, 214)(151, 207, 160, 216)(155, 211, 162, 218)(156, 212, 161, 217)(157, 213, 166, 222)(159, 215, 168, 224)(163, 219, 165, 221)(164, 220, 167, 223) L = (1, 116)(2, 120)(3, 122)(4, 113)(5, 123)(6, 127)(7, 128)(8, 114)(9, 130)(10, 115)(11, 117)(12, 131)(13, 135)(14, 136)(15, 118)(16, 119)(17, 138)(18, 121)(19, 124)(20, 139)(21, 143)(22, 144)(23, 125)(24, 126)(25, 146)(26, 129)(27, 132)(28, 147)(29, 151)(30, 152)(31, 133)(32, 134)(33, 154)(34, 137)(35, 140)(36, 155)(37, 159)(38, 160)(39, 141)(40, 142)(41, 162)(42, 145)(43, 148)(44, 163)(45, 167)(46, 168)(47, 149)(48, 150)(49, 165)(50, 153)(51, 156)(52, 166)(53, 161)(54, 164)(55, 157)(56, 158)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4^4 ), ( 4^56 ) } Outer automorphisms :: reflexible Dual of E14.449 Graph:: bipartite v = 30 e = 112 f = 56 degree seq :: [ 4^28, 56^2 ] E14.451 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 28}) Quotient :: edge Aut^+ = C7 : Q8 (small group id <56, 3>) Aut = (C28 x C2) : C2 (small group id <112, 30>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^-1, T2^2 * T1^-2 * T2^-2 * T1^-2, T2^12 * T1^-1 * T2^-2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 49, 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, 50, 42, 34, 26, 18, 10, 4, 11, 19, 27, 35, 43, 51, 56, 48, 40, 32, 24, 16, 8)(57, 58, 62, 60)(59, 64, 69, 66)(61, 63, 70, 67)(65, 72, 77, 74)(68, 71, 78, 75)(73, 80, 85, 82)(76, 79, 86, 83)(81, 88, 93, 90)(84, 87, 94, 91)(89, 96, 101, 98)(92, 95, 102, 99)(97, 104, 109, 106)(100, 103, 110, 107)(105, 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) :: { ( 8^4 ), ( 8^28 ) } Outer automorphisms :: reflexible Dual of E14.452 Transitivity :: ET+ Graph:: bipartite v = 16 e = 56 f = 14 degree seq :: [ 4^14, 28^2 ] E14.452 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 28}) Quotient :: loop Aut^+ = C7 : Q8 (small group id <56, 3>) Aut = (C28 x C2) : C2 (small group id <112, 30>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^2, T1^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-2 * T2^-1, T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 57, 3, 59, 6, 62, 5, 61)(2, 58, 7, 63, 4, 60, 8, 64)(9, 65, 13, 69, 10, 66, 14, 70)(11, 67, 15, 71, 12, 68, 16, 72)(17, 73, 21, 77, 18, 74, 22, 78)(19, 75, 23, 79, 20, 76, 24, 80)(25, 81, 29, 85, 26, 82, 30, 86)(27, 83, 31, 87, 28, 84, 32, 88)(33, 89, 37, 93, 34, 90, 38, 94)(35, 91, 39, 95, 36, 92, 40, 96)(41, 97, 45, 101, 42, 98, 46, 102)(43, 99, 47, 103, 44, 100, 48, 104)(49, 105, 53, 109, 50, 106, 54, 110)(51, 107, 55, 111, 52, 108, 56, 112) L = (1, 58)(2, 62)(3, 65)(4, 57)(5, 66)(6, 60)(7, 67)(8, 68)(9, 61)(10, 59)(11, 64)(12, 63)(13, 73)(14, 74)(15, 75)(16, 76)(17, 70)(18, 69)(19, 72)(20, 71)(21, 81)(22, 82)(23, 83)(24, 84)(25, 78)(26, 77)(27, 80)(28, 79)(29, 89)(30, 90)(31, 91)(32, 92)(33, 86)(34, 85)(35, 88)(36, 87)(37, 97)(38, 98)(39, 99)(40, 100)(41, 94)(42, 93)(43, 96)(44, 95)(45, 105)(46, 106)(47, 107)(48, 108)(49, 102)(50, 101)(51, 104)(52, 103)(53, 112)(54, 111)(55, 109)(56, 110) local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E14.451 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 14 e = 56 f = 16 degree seq :: [ 8^14 ] E14.453 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 28}) Quotient :: dipole Aut^+ = C7 : Q8 (small group id <56, 3>) Aut = (C28 x C2) : C2 (small group id <112, 30>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^6 * Y1^-1 * Y2^-8 * Y1^-1 ] Map:: R = (1, 57, 2, 58, 6, 62, 4, 60)(3, 59, 8, 64, 13, 69, 10, 66)(5, 61, 7, 63, 14, 70, 11, 67)(9, 65, 16, 72, 21, 77, 18, 74)(12, 68, 15, 71, 22, 78, 19, 75)(17, 73, 24, 80, 29, 85, 26, 82)(20, 76, 23, 79, 30, 86, 27, 83)(25, 81, 32, 88, 37, 93, 34, 90)(28, 84, 31, 87, 38, 94, 35, 91)(33, 89, 40, 96, 45, 101, 42, 98)(36, 92, 39, 95, 46, 102, 43, 99)(41, 97, 48, 104, 53, 109, 50, 106)(44, 100, 47, 103, 54, 110, 51, 107)(49, 105, 56, 112, 52, 108, 55, 111)(113, 169, 115, 171, 121, 177, 129, 185, 137, 193, 145, 201, 153, 209, 161, 217, 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, 162, 218, 154, 210, 146, 202, 138, 194, 130, 186, 122, 178, 116, 172, 123, 179, 131, 187, 139, 195, 147, 203, 155, 211, 163, 219, 168, 224, 160, 216, 152, 208, 144, 200, 136, 192, 128, 184, 120, 176) L = (1, 115)(2, 119)(3, 121)(4, 123)(5, 113)(6, 125)(7, 127)(8, 114)(9, 129)(10, 116)(11, 131)(12, 117)(13, 133)(14, 118)(15, 135)(16, 120)(17, 137)(18, 122)(19, 139)(20, 124)(21, 141)(22, 126)(23, 143)(24, 128)(25, 145)(26, 130)(27, 147)(28, 132)(29, 149)(30, 134)(31, 151)(32, 136)(33, 153)(34, 138)(35, 155)(36, 140)(37, 157)(38, 142)(39, 159)(40, 144)(41, 161)(42, 146)(43, 163)(44, 148)(45, 165)(46, 150)(47, 167)(48, 152)(49, 166)(50, 154)(51, 168)(52, 156)(53, 164)(54, 158)(55, 162)(56, 160)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E14.454 Graph:: bipartite v = 16 e = 112 f = 70 degree seq :: [ 8^14, 56^2 ] E14.454 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 28}) Quotient :: dipole Aut^+ = C7 : Q8 (small group id <56, 3>) Aut = (C28 x C2) : C2 (small group id <112, 30>) |r| :: 2 Presentation :: [ Y1, R^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-2 * Y2^-2 * Y3^2 * Y2^-1, Y3^4 * Y2^-1 * Y3^-10 * Y2^-1, (Y3^-1 * Y1^-1)^28 ] 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, 116, 172)(115, 171, 120, 176, 125, 181, 122, 178)(117, 173, 119, 175, 126, 182, 123, 179)(121, 177, 128, 184, 133, 189, 130, 186)(124, 180, 127, 183, 134, 190, 131, 187)(129, 185, 136, 192, 141, 197, 138, 194)(132, 188, 135, 191, 142, 198, 139, 195)(137, 193, 144, 200, 149, 205, 146, 202)(140, 196, 143, 199, 150, 206, 147, 203)(145, 201, 152, 208, 157, 213, 154, 210)(148, 204, 151, 207, 158, 214, 155, 211)(153, 209, 160, 216, 165, 221, 162, 218)(156, 212, 159, 215, 166, 222, 163, 219)(161, 217, 168, 224, 164, 220, 167, 223) L = (1, 115)(2, 119)(3, 121)(4, 123)(5, 113)(6, 125)(7, 127)(8, 114)(9, 129)(10, 116)(11, 131)(12, 117)(13, 133)(14, 118)(15, 135)(16, 120)(17, 137)(18, 122)(19, 139)(20, 124)(21, 141)(22, 126)(23, 143)(24, 128)(25, 145)(26, 130)(27, 147)(28, 132)(29, 149)(30, 134)(31, 151)(32, 136)(33, 153)(34, 138)(35, 155)(36, 140)(37, 157)(38, 142)(39, 159)(40, 144)(41, 161)(42, 146)(43, 163)(44, 148)(45, 165)(46, 150)(47, 167)(48, 152)(49, 166)(50, 154)(51, 168)(52, 156)(53, 164)(54, 158)(55, 162)(56, 160)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 8, 56 ), ( 8, 56, 8, 56, 8, 56, 8, 56 ) } Outer automorphisms :: reflexible Dual of E14.453 Graph:: simple bipartite v = 70 e = 112 f = 16 degree seq :: [ 2^56, 8^14 ] E14.455 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 56, 56}) Quotient :: regular Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^28 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 36, 32, 29, 30, 33, 37, 40, 43, 45, 47, 54, 52, 50, 49, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 42, 39, 35, 31, 34, 38, 41, 44, 46, 48, 56, 55, 53, 51, 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, 42)(28, 49)(29, 31)(30, 34)(32, 35)(33, 38)(36, 39)(37, 41)(40, 44)(43, 46)(45, 48)(47, 56)(50, 51)(52, 53)(54, 55) local type(s) :: { ( 56^56 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 28 f = 1 degree seq :: [ 56 ] E14.456 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 56, 56}) Quotient :: edge Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^28 * T1 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 29, 31, 34, 36, 38, 40, 42, 44, 46, 48, 51, 53, 55, 45, 26, 22, 18, 14, 10, 6, 2, 5, 9, 13, 17, 21, 25, 33, 30, 32, 35, 37, 39, 41, 43, 50, 47, 49, 52, 54, 56, 28, 24, 20, 16, 12, 8, 4)(57, 58)(59, 61)(60, 62)(63, 65)(64, 66)(67, 69)(68, 70)(71, 73)(72, 74)(75, 77)(76, 78)(79, 81)(80, 82)(83, 89)(84, 101)(85, 86)(87, 88)(90, 91)(92, 93)(94, 95)(96, 97)(98, 99)(100, 106)(102, 103)(104, 105)(107, 108)(109, 110)(111, 112) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 112, 112 ), ( 112^56 ) } Outer automorphisms :: reflexible Dual of E14.457 Transitivity :: ET+ Graph:: bipartite v = 29 e = 56 f = 1 degree seq :: [ 2^28, 56 ] E14.457 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 56, 56}) Quotient :: loop Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^28 * T1 ] Map:: R = (1, 57, 3, 59, 7, 63, 11, 67, 15, 71, 19, 75, 23, 79, 27, 83, 30, 86, 33, 89, 35, 91, 37, 93, 39, 95, 41, 97, 43, 99, 49, 105, 46, 102, 48, 104, 51, 107, 53, 109, 55, 111, 45, 101, 26, 82, 22, 78, 18, 74, 14, 70, 10, 66, 6, 62, 2, 58, 5, 61, 9, 65, 13, 69, 17, 73, 21, 77, 25, 81, 32, 88, 29, 85, 31, 87, 34, 90, 36, 92, 38, 94, 40, 96, 42, 98, 44, 100, 47, 103, 50, 106, 52, 108, 54, 110, 56, 112, 28, 84, 24, 80, 20, 76, 16, 72, 12, 68, 8, 64, 4, 60) L = (1, 58)(2, 57)(3, 61)(4, 62)(5, 59)(6, 60)(7, 65)(8, 66)(9, 63)(10, 64)(11, 69)(12, 70)(13, 67)(14, 68)(15, 73)(16, 74)(17, 71)(18, 72)(19, 77)(20, 78)(21, 75)(22, 76)(23, 81)(24, 82)(25, 79)(26, 80)(27, 88)(28, 101)(29, 86)(30, 85)(31, 89)(32, 83)(33, 87)(34, 91)(35, 90)(36, 93)(37, 92)(38, 95)(39, 94)(40, 97)(41, 96)(42, 99)(43, 98)(44, 105)(45, 84)(46, 103)(47, 102)(48, 106)(49, 100)(50, 104)(51, 108)(52, 107)(53, 110)(54, 109)(55, 112)(56, 111) local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) } Outer automorphisms :: reflexible Dual of E14.456 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 56 f = 29 degree seq :: [ 112 ] E14.458 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 56, 56}) Quotient :: dipole Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 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, Y2^28 * Y1, (Y3 * Y2^-1)^56 ] Map:: R = (1, 57, 2, 58)(3, 59, 5, 61)(4, 60, 6, 62)(7, 63, 9, 65)(8, 64, 10, 66)(11, 67, 13, 69)(12, 68, 14, 70)(15, 71, 17, 73)(16, 72, 18, 74)(19, 75, 21, 77)(20, 76, 22, 78)(23, 79, 25, 81)(24, 80, 26, 82)(27, 83, 32, 88)(28, 84, 45, 101)(29, 85, 30, 86)(31, 87, 33, 89)(34, 90, 35, 91)(36, 92, 37, 93)(38, 94, 39, 95)(40, 96, 41, 97)(42, 98, 43, 99)(44, 100, 49, 105)(46, 102, 47, 103)(48, 104, 50, 106)(51, 107, 52, 108)(53, 109, 54, 110)(55, 111, 56, 112)(113, 169, 115, 171, 119, 175, 123, 179, 127, 183, 131, 187, 135, 191, 139, 195, 142, 198, 145, 201, 147, 203, 149, 205, 151, 207, 153, 209, 155, 211, 161, 217, 158, 214, 160, 216, 163, 219, 165, 221, 167, 223, 157, 213, 138, 194, 134, 190, 130, 186, 126, 182, 122, 178, 118, 174, 114, 170, 117, 173, 121, 177, 125, 181, 129, 185, 133, 189, 137, 193, 144, 200, 141, 197, 143, 199, 146, 202, 148, 204, 150, 206, 152, 208, 154, 210, 156, 212, 159, 215, 162, 218, 164, 220, 166, 222, 168, 224, 140, 196, 136, 192, 132, 188, 128, 184, 124, 180, 120, 176, 116, 172) L = (1, 114)(2, 113)(3, 117)(4, 118)(5, 115)(6, 116)(7, 121)(8, 122)(9, 119)(10, 120)(11, 125)(12, 126)(13, 123)(14, 124)(15, 129)(16, 130)(17, 127)(18, 128)(19, 133)(20, 134)(21, 131)(22, 132)(23, 137)(24, 138)(25, 135)(26, 136)(27, 144)(28, 157)(29, 142)(30, 141)(31, 145)(32, 139)(33, 143)(34, 147)(35, 146)(36, 149)(37, 148)(38, 151)(39, 150)(40, 153)(41, 152)(42, 155)(43, 154)(44, 161)(45, 140)(46, 159)(47, 158)(48, 162)(49, 156)(50, 160)(51, 164)(52, 163)(53, 166)(54, 165)(55, 168)(56, 167)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) } Outer automorphisms :: reflexible Dual of E14.459 Graph:: bipartite v = 29 e = 112 f = 57 degree seq :: [ 4^28, 112 ] E14.459 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 56, 56}) Quotient :: dipole Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1^28 ] Map:: R = (1, 57, 2, 58, 5, 61, 9, 65, 13, 69, 17, 73, 21, 77, 25, 81, 29, 85, 30, 86, 32, 88, 35, 91, 37, 93, 39, 95, 41, 97, 43, 99, 46, 102, 47, 103, 49, 105, 52, 108, 54, 110, 45, 101, 27, 83, 23, 79, 19, 75, 15, 71, 11, 67, 7, 63, 3, 59, 6, 62, 10, 66, 14, 70, 18, 74, 22, 78, 26, 82, 34, 90, 31, 87, 33, 89, 36, 92, 38, 94, 40, 96, 42, 98, 44, 100, 51, 107, 48, 104, 50, 106, 53, 109, 55, 111, 56, 112, 28, 84, 24, 80, 20, 76, 16, 72, 12, 68, 8, 64, 4, 60)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224) L = (1, 115)(2, 118)(3, 113)(4, 119)(5, 122)(6, 114)(7, 116)(8, 123)(9, 126)(10, 117)(11, 120)(12, 127)(13, 130)(14, 121)(15, 124)(16, 131)(17, 134)(18, 125)(19, 128)(20, 135)(21, 138)(22, 129)(23, 132)(24, 139)(25, 146)(26, 133)(27, 136)(28, 157)(29, 143)(30, 145)(31, 141)(32, 148)(33, 142)(34, 137)(35, 150)(36, 144)(37, 152)(38, 147)(39, 154)(40, 149)(41, 156)(42, 151)(43, 163)(44, 153)(45, 140)(46, 160)(47, 162)(48, 158)(49, 165)(50, 159)(51, 155)(52, 167)(53, 161)(54, 168)(55, 164)(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, 112 ), ( 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112 ) } Outer automorphisms :: reflexible Dual of E14.458 Graph:: bipartite v = 57 e = 112 f = 29 degree seq :: [ 2^56, 112 ] E14.460 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 29, 58}) Quotient :: regular Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 4>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-29 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 32, 34, 36, 38, 40, 42, 44, 45, 46, 48, 50, 52, 54, 56, 43, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 29, 30, 31, 33, 35, 37, 39, 41, 47, 49, 51, 53, 55, 57, 58, 28, 24, 20, 16, 12, 8, 4) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 29)(28, 43)(30, 32)(31, 34)(33, 36)(35, 38)(37, 40)(39, 42)(41, 44)(45, 47)(46, 49)(48, 51)(50, 53)(52, 55)(54, 57)(56, 58) local type(s) :: { ( 29^58 ) } Outer automorphisms :: reflexible Dual of E14.461 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 29 f = 2 degree seq :: [ 58 ] E14.461 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 29, 58}) Quotient :: regular Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 4>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^29 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 35, 31, 34, 38, 40, 42, 44, 46, 55, 51, 48, 49, 52, 56, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 36, 32, 29, 30, 33, 37, 39, 41, 43, 45, 54, 50, 53, 57, 58, 47, 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, 36)(28, 47)(29, 31)(30, 34)(32, 35)(33, 38)(37, 40)(39, 42)(41, 44)(43, 46)(45, 55)(48, 50)(49, 53)(51, 54)(52, 57)(56, 58) local type(s) :: { ( 58^29 ) } Outer automorphisms :: reflexible Dual of E14.460 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 29 f = 1 degree seq :: [ 29^2 ] E14.462 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 29, 58}) Quotient :: edge Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 4>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^29 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 33, 35, 37, 39, 41, 44, 45, 47, 49, 51, 53, 55, 57, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 30, 32, 34, 36, 38, 40, 42, 46, 48, 50, 52, 54, 56, 58, 43, 26, 22, 18, 14, 10, 6)(59, 60)(61, 63)(62, 64)(65, 67)(66, 68)(69, 71)(70, 72)(73, 75)(74, 76)(77, 79)(78, 80)(81, 83)(82, 84)(85, 87)(86, 101)(88, 89)(90, 91)(92, 93)(94, 95)(96, 97)(98, 99)(100, 102)(103, 104)(105, 106)(107, 108)(109, 110)(111, 112)(113, 114)(115, 116) L = (1, 59)(2, 60)(3, 61)(4, 62)(5, 63)(6, 64)(7, 65)(8, 66)(9, 67)(10, 68)(11, 69)(12, 70)(13, 71)(14, 72)(15, 73)(16, 74)(17, 75)(18, 76)(19, 77)(20, 78)(21, 79)(22, 80)(23, 81)(24, 82)(25, 83)(26, 84)(27, 85)(28, 86)(29, 87)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 116, 116 ), ( 116^29 ) } Outer automorphisms :: reflexible Dual of E14.466 Transitivity :: ET+ Graph:: simple bipartite v = 31 e = 58 f = 1 degree seq :: [ 2^29, 29^2 ] E14.463 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 29, 58}) Quotient :: edge Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 4>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^12 * T2^-1 * T1 * T2^-13, T2^-2 * T1^27, T2^11 * T1^10 * T2^-1 * T1^13 * T2^-1 * T1^13 * T2^-1 * T1 ] Map:: non-degenerate R = (1, 3, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 56, 51, 48, 43, 40, 35, 32, 27, 24, 19, 16, 11, 8, 2, 7, 4, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 55, 52, 47, 44, 39, 36, 31, 28, 23, 20, 15, 12, 6, 5)(59, 60, 64, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 115, 112, 107, 104, 99, 96, 91, 88, 83, 80, 75, 72, 67, 62)(61, 65, 63, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 116, 111, 108, 103, 100, 95, 92, 87, 84, 79, 76, 71, 68) L = (1, 59)(2, 60)(3, 61)(4, 62)(5, 63)(6, 64)(7, 65)(8, 66)(9, 67)(10, 68)(11, 69)(12, 70)(13, 71)(14, 72)(15, 73)(16, 74)(17, 75)(18, 76)(19, 77)(20, 78)(21, 79)(22, 80)(23, 81)(24, 82)(25, 83)(26, 84)(27, 85)(28, 86)(29, 87)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 4^29 ), ( 4^58 ) } Outer automorphisms :: reflexible Dual of E14.467 Transitivity :: ET+ Graph:: bipartite v = 3 e = 58 f = 29 degree seq :: [ 29^2, 58 ] E14.464 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 29, 58}) Quotient :: edge Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 4>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-29 ] 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, 29)(28, 43)(30, 32)(31, 34)(33, 36)(35, 38)(37, 40)(39, 42)(41, 44)(45, 47)(46, 49)(48, 51)(50, 53)(52, 55)(54, 57)(56, 58)(59, 60, 63, 67, 71, 75, 79, 83, 90, 92, 94, 96, 98, 100, 102, 103, 104, 106, 108, 110, 112, 114, 101, 85, 81, 77, 73, 69, 65, 61, 64, 68, 72, 76, 80, 84, 87, 88, 89, 91, 93, 95, 97, 99, 105, 107, 109, 111, 113, 115, 116, 86, 82, 78, 74, 70, 66, 62) L = (1, 59)(2, 60)(3, 61)(4, 62)(5, 63)(6, 64)(7, 65)(8, 66)(9, 67)(10, 68)(11, 69)(12, 70)(13, 71)(14, 72)(15, 73)(16, 74)(17, 75)(18, 76)(19, 77)(20, 78)(21, 79)(22, 80)(23, 81)(24, 82)(25, 83)(26, 84)(27, 85)(28, 86)(29, 87)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116) local type(s) :: { ( 58, 58 ), ( 58^58 ) } Outer automorphisms :: reflexible Dual of E14.465 Transitivity :: ET+ Graph:: bipartite v = 30 e = 58 f = 2 degree seq :: [ 2^29, 58 ] E14.465 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 29, 58}) Quotient :: loop Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 4>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^29 ] Map:: R = (1, 59, 3, 61, 7, 65, 11, 69, 15, 73, 19, 77, 23, 81, 27, 85, 38, 96, 34, 92, 30, 88, 33, 91, 37, 95, 41, 99, 43, 101, 45, 103, 47, 105, 58, 116, 56, 114, 53, 111, 50, 108, 52, 110, 28, 86, 24, 82, 20, 78, 16, 74, 12, 70, 8, 66, 4, 62)(2, 60, 5, 63, 9, 67, 13, 71, 17, 75, 21, 79, 25, 83, 40, 98, 36, 94, 32, 90, 29, 87, 31, 89, 35, 93, 39, 97, 42, 100, 44, 102, 46, 104, 48, 106, 57, 115, 55, 113, 51, 109, 54, 112, 49, 107, 26, 84, 22, 80, 18, 76, 14, 72, 10, 68, 6, 64) L = (1, 60)(2, 59)(3, 63)(4, 64)(5, 61)(6, 62)(7, 67)(8, 68)(9, 65)(10, 66)(11, 71)(12, 72)(13, 69)(14, 70)(15, 75)(16, 76)(17, 73)(18, 74)(19, 79)(20, 80)(21, 77)(22, 78)(23, 83)(24, 84)(25, 81)(26, 82)(27, 98)(28, 107)(29, 88)(30, 87)(31, 91)(32, 92)(33, 89)(34, 90)(35, 95)(36, 96)(37, 93)(38, 94)(39, 99)(40, 85)(41, 97)(42, 101)(43, 100)(44, 103)(45, 102)(46, 105)(47, 104)(48, 116)(49, 86)(50, 109)(51, 108)(52, 112)(53, 113)(54, 110)(55, 111)(56, 115)(57, 114)(58, 106) local type(s) :: { ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.464 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 58 f = 30 degree seq :: [ 58^2 ] E14.466 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 29, 58}) Quotient :: loop Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 4>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^12 * T2^-1 * T1 * T2^-13, T2^-2 * T1^27, T2^11 * T1^10 * T2^-1 * T1^13 * T2^-1 * T1^13 * T2^-1 * T1 ] Map:: R = (1, 59, 3, 61, 9, 67, 13, 71, 17, 75, 21, 79, 25, 83, 29, 87, 33, 91, 37, 95, 41, 99, 45, 103, 49, 107, 53, 111, 57, 115, 56, 114, 51, 109, 48, 106, 43, 101, 40, 98, 35, 93, 32, 90, 27, 85, 24, 82, 19, 77, 16, 74, 11, 69, 8, 66, 2, 60, 7, 65, 4, 62, 10, 68, 14, 72, 18, 76, 22, 80, 26, 84, 30, 88, 34, 92, 38, 96, 42, 100, 46, 104, 50, 108, 54, 112, 58, 116, 55, 113, 52, 110, 47, 105, 44, 102, 39, 97, 36, 94, 31, 89, 28, 86, 23, 81, 20, 78, 15, 73, 12, 70, 6, 64, 5, 63) L = (1, 60)(2, 64)(3, 65)(4, 59)(5, 66)(6, 69)(7, 63)(8, 70)(9, 62)(10, 61)(11, 73)(12, 74)(13, 68)(14, 67)(15, 77)(16, 78)(17, 72)(18, 71)(19, 81)(20, 82)(21, 76)(22, 75)(23, 85)(24, 86)(25, 80)(26, 79)(27, 89)(28, 90)(29, 84)(30, 83)(31, 93)(32, 94)(33, 88)(34, 87)(35, 97)(36, 98)(37, 92)(38, 91)(39, 101)(40, 102)(41, 96)(42, 95)(43, 105)(44, 106)(45, 100)(46, 99)(47, 109)(48, 110)(49, 104)(50, 103)(51, 113)(52, 114)(53, 108)(54, 107)(55, 115)(56, 116)(57, 112)(58, 111) local type(s) :: { ( 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29, 2, 29 ) } Outer automorphisms :: reflexible Dual of E14.462 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 58 f = 31 degree seq :: [ 116 ] E14.467 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 29, 58}) Quotient :: loop Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 4>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-29 ] Map:: non-degenerate R = (1, 59, 3, 61)(2, 60, 6, 64)(4, 62, 7, 65)(5, 63, 10, 68)(8, 66, 11, 69)(9, 67, 14, 72)(12, 70, 15, 73)(13, 71, 18, 76)(16, 74, 19, 77)(17, 75, 22, 80)(20, 78, 23, 81)(21, 79, 26, 84)(24, 82, 27, 85)(25, 83, 36, 94)(28, 86, 47, 105)(29, 87, 31, 89)(30, 88, 34, 92)(32, 90, 35, 93)(33, 91, 38, 96)(37, 95, 40, 98)(39, 97, 42, 100)(41, 99, 44, 102)(43, 101, 46, 104)(45, 103, 55, 113)(48, 106, 50, 108)(49, 107, 53, 111)(51, 109, 54, 112)(52, 110, 57, 115)(56, 114, 58, 116) L = (1, 60)(2, 63)(3, 64)(4, 59)(5, 67)(6, 68)(7, 61)(8, 62)(9, 71)(10, 72)(11, 65)(12, 66)(13, 75)(14, 76)(15, 69)(16, 70)(17, 79)(18, 80)(19, 73)(20, 74)(21, 83)(22, 84)(23, 77)(24, 78)(25, 93)(26, 94)(27, 81)(28, 82)(29, 88)(30, 91)(31, 92)(32, 87)(33, 95)(34, 96)(35, 89)(36, 90)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 112)(46, 113)(47, 85)(48, 107)(49, 110)(50, 111)(51, 106)(52, 114)(53, 115)(54, 108)(55, 109)(56, 105)(57, 116)(58, 86) local type(s) :: { ( 29, 58, 29, 58 ) } Outer automorphisms :: reflexible Dual of E14.463 Transitivity :: ET+ VT+ AT Graph:: v = 29 e = 58 f = 3 degree seq :: [ 4^29 ] E14.468 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 29, 58}) Quotient :: dipole Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 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, Y2^29, (Y3 * Y2^-1)^58 ] Map:: R = (1, 59, 2, 60)(3, 61, 5, 63)(4, 62, 6, 64)(7, 65, 9, 67)(8, 66, 10, 68)(11, 69, 13, 71)(12, 70, 14, 72)(15, 73, 17, 75)(16, 74, 18, 76)(19, 77, 21, 79)(20, 78, 22, 80)(23, 81, 25, 83)(24, 82, 26, 84)(27, 85, 33, 91)(28, 86, 45, 103)(29, 87, 30, 88)(31, 89, 32, 90)(34, 92, 35, 93)(36, 94, 37, 95)(38, 96, 39, 97)(40, 98, 41, 99)(42, 100, 43, 101)(44, 102, 50, 108)(46, 104, 47, 105)(48, 106, 49, 107)(51, 109, 52, 110)(53, 111, 54, 112)(55, 113, 56, 114)(57, 115, 58, 116)(117, 175, 119, 177, 123, 181, 127, 185, 131, 189, 135, 193, 139, 197, 143, 201, 145, 203, 147, 205, 150, 208, 152, 210, 154, 212, 156, 214, 158, 216, 160, 218, 162, 220, 164, 222, 167, 225, 169, 227, 171, 229, 173, 231, 144, 202, 140, 198, 136, 194, 132, 190, 128, 186, 124, 182, 120, 178)(118, 176, 121, 179, 125, 183, 129, 187, 133, 191, 137, 195, 141, 199, 149, 207, 146, 204, 148, 206, 151, 209, 153, 211, 155, 213, 157, 215, 159, 217, 166, 224, 163, 221, 165, 223, 168, 226, 170, 228, 172, 230, 174, 232, 161, 219, 142, 200, 138, 196, 134, 192, 130, 188, 126, 184, 122, 180) L = (1, 118)(2, 117)(3, 121)(4, 122)(5, 119)(6, 120)(7, 125)(8, 126)(9, 123)(10, 124)(11, 129)(12, 130)(13, 127)(14, 128)(15, 133)(16, 134)(17, 131)(18, 132)(19, 137)(20, 138)(21, 135)(22, 136)(23, 141)(24, 142)(25, 139)(26, 140)(27, 149)(28, 161)(29, 146)(30, 145)(31, 148)(32, 147)(33, 143)(34, 151)(35, 150)(36, 153)(37, 152)(38, 155)(39, 154)(40, 157)(41, 156)(42, 159)(43, 158)(44, 166)(45, 144)(46, 163)(47, 162)(48, 165)(49, 164)(50, 160)(51, 168)(52, 167)(53, 170)(54, 169)(55, 172)(56, 171)(57, 174)(58, 173)(59, 175)(60, 176)(61, 177)(62, 178)(63, 179)(64, 180)(65, 181)(66, 182)(67, 183)(68, 184)(69, 185)(70, 186)(71, 187)(72, 188)(73, 189)(74, 190)(75, 191)(76, 192)(77, 193)(78, 194)(79, 195)(80, 196)(81, 197)(82, 198)(83, 199)(84, 200)(85, 201)(86, 202)(87, 203)(88, 204)(89, 205)(90, 206)(91, 207)(92, 208)(93, 209)(94, 210)(95, 211)(96, 212)(97, 213)(98, 214)(99, 215)(100, 216)(101, 217)(102, 218)(103, 219)(104, 220)(105, 221)(106, 222)(107, 223)(108, 224)(109, 225)(110, 226)(111, 227)(112, 228)(113, 229)(114, 230)(115, 231)(116, 232) local type(s) :: { ( 2, 116, 2, 116 ), ( 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116 ) } Outer automorphisms :: reflexible Dual of E14.471 Graph:: bipartite v = 31 e = 116 f = 59 degree seq :: [ 4^29, 58^2 ] E14.469 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 29, 58}) Quotient :: dipole Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y2^2 * Y1^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1, Y1^-1), Y1^-1 * Y2^28, Y1^29 ] Map:: R = (1, 59, 2, 60, 6, 64, 11, 69, 15, 73, 19, 77, 23, 81, 27, 85, 31, 89, 35, 93, 39, 97, 43, 101, 47, 105, 51, 109, 55, 113, 57, 115, 54, 112, 49, 107, 46, 104, 41, 99, 38, 96, 33, 91, 30, 88, 25, 83, 22, 80, 17, 75, 14, 72, 9, 67, 4, 62)(3, 61, 7, 65, 5, 63, 8, 66, 12, 70, 16, 74, 20, 78, 24, 82, 28, 86, 32, 90, 36, 94, 40, 98, 44, 102, 48, 106, 52, 110, 56, 114, 58, 116, 53, 111, 50, 108, 45, 103, 42, 100, 37, 95, 34, 92, 29, 87, 26, 84, 21, 79, 18, 76, 13, 71, 10, 68)(117, 175, 119, 177, 125, 183, 129, 187, 133, 191, 137, 195, 141, 199, 145, 203, 149, 207, 153, 211, 157, 215, 161, 219, 165, 223, 169, 227, 173, 231, 172, 230, 167, 225, 164, 222, 159, 217, 156, 214, 151, 209, 148, 206, 143, 201, 140, 198, 135, 193, 132, 190, 127, 185, 124, 182, 118, 176, 123, 181, 120, 178, 126, 184, 130, 188, 134, 192, 138, 196, 142, 200, 146, 204, 150, 208, 154, 212, 158, 216, 162, 220, 166, 224, 170, 228, 174, 232, 171, 229, 168, 226, 163, 221, 160, 218, 155, 213, 152, 210, 147, 205, 144, 202, 139, 197, 136, 194, 131, 189, 128, 186, 122, 180, 121, 179) L = (1, 119)(2, 123)(3, 125)(4, 126)(5, 117)(6, 121)(7, 120)(8, 118)(9, 129)(10, 130)(11, 124)(12, 122)(13, 133)(14, 134)(15, 128)(16, 127)(17, 137)(18, 138)(19, 132)(20, 131)(21, 141)(22, 142)(23, 136)(24, 135)(25, 145)(26, 146)(27, 140)(28, 139)(29, 149)(30, 150)(31, 144)(32, 143)(33, 153)(34, 154)(35, 148)(36, 147)(37, 157)(38, 158)(39, 152)(40, 151)(41, 161)(42, 162)(43, 156)(44, 155)(45, 165)(46, 166)(47, 160)(48, 159)(49, 169)(50, 170)(51, 164)(52, 163)(53, 173)(54, 174)(55, 168)(56, 167)(57, 172)(58, 171)(59, 175)(60, 176)(61, 177)(62, 178)(63, 179)(64, 180)(65, 181)(66, 182)(67, 183)(68, 184)(69, 185)(70, 186)(71, 187)(72, 188)(73, 189)(74, 190)(75, 191)(76, 192)(77, 193)(78, 194)(79, 195)(80, 196)(81, 197)(82, 198)(83, 199)(84, 200)(85, 201)(86, 202)(87, 203)(88, 204)(89, 205)(90, 206)(91, 207)(92, 208)(93, 209)(94, 210)(95, 211)(96, 212)(97, 213)(98, 214)(99, 215)(100, 216)(101, 217)(102, 218)(103, 219)(104, 220)(105, 221)(106, 222)(107, 223)(108, 224)(109, 225)(110, 226)(111, 227)(112, 228)(113, 229)(114, 230)(115, 231)(116, 232) 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 ) } Outer automorphisms :: reflexible Dual of E14.470 Graph:: bipartite v = 3 e = 116 f = 87 degree seq :: [ 58^2, 116 ] E14.470 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 29, 58}) Quotient :: dipole Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 4>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y3^29 * Y2, (Y3^-1 * Y1^-1)^58 ] Map:: R = (1, 59)(2, 60)(3, 61)(4, 62)(5, 63)(6, 64)(7, 65)(8, 66)(9, 67)(10, 68)(11, 69)(12, 70)(13, 71)(14, 72)(15, 73)(16, 74)(17, 75)(18, 76)(19, 77)(20, 78)(21, 79)(22, 80)(23, 81)(24, 82)(25, 83)(26, 84)(27, 85)(28, 86)(29, 87)(30, 88)(31, 89)(32, 90)(33, 91)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 99)(42, 100)(43, 101)(44, 102)(45, 103)(46, 104)(47, 105)(48, 106)(49, 107)(50, 108)(51, 109)(52, 110)(53, 111)(54, 112)(55, 113)(56, 114)(57, 115)(58, 116)(117, 175, 118, 176)(119, 177, 121, 179)(120, 178, 122, 180)(123, 181, 125, 183)(124, 182, 126, 184)(127, 185, 129, 187)(128, 186, 130, 188)(131, 189, 133, 191)(132, 190, 134, 192)(135, 193, 137, 195)(136, 194, 138, 196)(139, 197, 141, 199)(140, 198, 142, 200)(143, 201, 152, 210)(144, 202, 163, 221)(145, 203, 146, 204)(147, 205, 149, 207)(148, 206, 150, 208)(151, 209, 153, 211)(154, 212, 155, 213)(156, 214, 157, 215)(158, 216, 159, 217)(160, 218, 161, 219)(162, 220, 171, 229)(164, 222, 165, 223)(166, 224, 168, 226)(167, 225, 169, 227)(170, 228, 172, 230)(173, 231, 174, 232) L = (1, 119)(2, 121)(3, 123)(4, 117)(5, 125)(6, 118)(7, 127)(8, 120)(9, 129)(10, 122)(11, 131)(12, 124)(13, 133)(14, 126)(15, 135)(16, 128)(17, 137)(18, 130)(19, 139)(20, 132)(21, 141)(22, 134)(23, 143)(24, 136)(25, 152)(26, 138)(27, 150)(28, 140)(29, 147)(30, 149)(31, 151)(32, 145)(33, 153)(34, 146)(35, 154)(36, 148)(37, 155)(38, 156)(39, 157)(40, 158)(41, 159)(42, 160)(43, 161)(44, 162)(45, 171)(46, 169)(47, 142)(48, 166)(49, 168)(50, 170)(51, 164)(52, 172)(53, 165)(54, 173)(55, 167)(56, 174)(57, 163)(58, 144)(59, 175)(60, 176)(61, 177)(62, 178)(63, 179)(64, 180)(65, 181)(66, 182)(67, 183)(68, 184)(69, 185)(70, 186)(71, 187)(72, 188)(73, 189)(74, 190)(75, 191)(76, 192)(77, 193)(78, 194)(79, 195)(80, 196)(81, 197)(82, 198)(83, 199)(84, 200)(85, 201)(86, 202)(87, 203)(88, 204)(89, 205)(90, 206)(91, 207)(92, 208)(93, 209)(94, 210)(95, 211)(96, 212)(97, 213)(98, 214)(99, 215)(100, 216)(101, 217)(102, 218)(103, 219)(104, 220)(105, 221)(106, 222)(107, 223)(108, 224)(109, 225)(110, 226)(111, 227)(112, 228)(113, 229)(114, 230)(115, 231)(116, 232) local type(s) :: { ( 58, 116 ), ( 58, 116, 58, 116 ) } Outer automorphisms :: reflexible Dual of E14.469 Graph:: simple bipartite v = 87 e = 116 f = 3 degree seq :: [ 2^58, 4^29 ] E14.471 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 29, 58}) Quotient :: dipole Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 4>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-29 ] Map:: R = (1, 59, 2, 60, 5, 63, 9, 67, 13, 71, 17, 75, 21, 79, 25, 83, 29, 87, 30, 88, 32, 90, 35, 93, 37, 95, 39, 97, 41, 99, 43, 101, 46, 104, 47, 105, 49, 107, 52, 110, 54, 112, 56, 114, 45, 103, 27, 85, 23, 81, 19, 77, 15, 73, 11, 69, 7, 65, 3, 61, 6, 64, 10, 68, 14, 72, 18, 76, 22, 80, 26, 84, 34, 92, 31, 89, 33, 91, 36, 94, 38, 96, 40, 98, 42, 100, 44, 102, 51, 109, 48, 106, 50, 108, 53, 111, 55, 113, 57, 115, 58, 116, 28, 86, 24, 82, 20, 78, 16, 74, 12, 70, 8, 66, 4, 62)(117, 175)(118, 176)(119, 177)(120, 178)(121, 179)(122, 180)(123, 181)(124, 182)(125, 183)(126, 184)(127, 185)(128, 186)(129, 187)(130, 188)(131, 189)(132, 190)(133, 191)(134, 192)(135, 193)(136, 194)(137, 195)(138, 196)(139, 197)(140, 198)(141, 199)(142, 200)(143, 201)(144, 202)(145, 203)(146, 204)(147, 205)(148, 206)(149, 207)(150, 208)(151, 209)(152, 210)(153, 211)(154, 212)(155, 213)(156, 214)(157, 215)(158, 216)(159, 217)(160, 218)(161, 219)(162, 220)(163, 221)(164, 222)(165, 223)(166, 224)(167, 225)(168, 226)(169, 227)(170, 228)(171, 229)(172, 230)(173, 231)(174, 232) L = (1, 119)(2, 122)(3, 117)(4, 123)(5, 126)(6, 118)(7, 120)(8, 127)(9, 130)(10, 121)(11, 124)(12, 131)(13, 134)(14, 125)(15, 128)(16, 135)(17, 138)(18, 129)(19, 132)(20, 139)(21, 142)(22, 133)(23, 136)(24, 143)(25, 150)(26, 137)(27, 140)(28, 161)(29, 147)(30, 149)(31, 145)(32, 152)(33, 146)(34, 141)(35, 154)(36, 148)(37, 156)(38, 151)(39, 158)(40, 153)(41, 160)(42, 155)(43, 167)(44, 157)(45, 144)(46, 164)(47, 166)(48, 162)(49, 169)(50, 163)(51, 159)(52, 171)(53, 165)(54, 173)(55, 168)(56, 174)(57, 170)(58, 172)(59, 175)(60, 176)(61, 177)(62, 178)(63, 179)(64, 180)(65, 181)(66, 182)(67, 183)(68, 184)(69, 185)(70, 186)(71, 187)(72, 188)(73, 189)(74, 190)(75, 191)(76, 192)(77, 193)(78, 194)(79, 195)(80, 196)(81, 197)(82, 198)(83, 199)(84, 200)(85, 201)(86, 202)(87, 203)(88, 204)(89, 205)(90, 206)(91, 207)(92, 208)(93, 209)(94, 210)(95, 211)(96, 212)(97, 213)(98, 214)(99, 215)(100, 216)(101, 217)(102, 218)(103, 219)(104, 220)(105, 221)(106, 222)(107, 223)(108, 224)(109, 225)(110, 226)(111, 227)(112, 228)(113, 229)(114, 230)(115, 231)(116, 232) local type(s) :: { ( 4, 58 ), ( 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58, 4, 58 ) } Outer automorphisms :: reflexible Dual of E14.468 Graph:: bipartite v = 59 e = 116 f = 31 degree seq :: [ 2^58, 116 ] E14.472 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 29, 58}) Quotient :: dipole Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 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, Y2^29 * Y1, (Y3 * Y2^-1)^29 ] Map:: R = (1, 59, 2, 60)(3, 61, 5, 63)(4, 62, 6, 64)(7, 65, 9, 67)(8, 66, 10, 68)(11, 69, 13, 71)(12, 70, 14, 72)(15, 73, 17, 75)(16, 74, 18, 76)(19, 77, 21, 79)(20, 78, 22, 80)(23, 81, 25, 83)(24, 82, 26, 84)(27, 85, 33, 91)(28, 86, 45, 103)(29, 87, 30, 88)(31, 89, 32, 90)(34, 92, 35, 93)(36, 94, 37, 95)(38, 96, 39, 97)(40, 98, 41, 99)(42, 100, 43, 101)(44, 102, 50, 108)(46, 104, 47, 105)(48, 106, 49, 107)(51, 109, 52, 110)(53, 111, 54, 112)(55, 113, 56, 114)(57, 115, 58, 116)(117, 175, 119, 177, 123, 181, 127, 185, 131, 189, 135, 193, 139, 197, 143, 201, 145, 203, 147, 205, 150, 208, 152, 210, 154, 212, 156, 214, 158, 216, 160, 218, 162, 220, 164, 222, 167, 225, 169, 227, 171, 229, 173, 231, 161, 219, 142, 200, 138, 196, 134, 192, 130, 188, 126, 184, 122, 180, 118, 176, 121, 179, 125, 183, 129, 187, 133, 191, 137, 195, 141, 199, 149, 207, 146, 204, 148, 206, 151, 209, 153, 211, 155, 213, 157, 215, 159, 217, 166, 224, 163, 221, 165, 223, 168, 226, 170, 228, 172, 230, 174, 232, 144, 202, 140, 198, 136, 194, 132, 190, 128, 186, 124, 182, 120, 178) L = (1, 118)(2, 117)(3, 121)(4, 122)(5, 119)(6, 120)(7, 125)(8, 126)(9, 123)(10, 124)(11, 129)(12, 130)(13, 127)(14, 128)(15, 133)(16, 134)(17, 131)(18, 132)(19, 137)(20, 138)(21, 135)(22, 136)(23, 141)(24, 142)(25, 139)(26, 140)(27, 149)(28, 161)(29, 146)(30, 145)(31, 148)(32, 147)(33, 143)(34, 151)(35, 150)(36, 153)(37, 152)(38, 155)(39, 154)(40, 157)(41, 156)(42, 159)(43, 158)(44, 166)(45, 144)(46, 163)(47, 162)(48, 165)(49, 164)(50, 160)(51, 168)(52, 167)(53, 170)(54, 169)(55, 172)(56, 171)(57, 174)(58, 173)(59, 175)(60, 176)(61, 177)(62, 178)(63, 179)(64, 180)(65, 181)(66, 182)(67, 183)(68, 184)(69, 185)(70, 186)(71, 187)(72, 188)(73, 189)(74, 190)(75, 191)(76, 192)(77, 193)(78, 194)(79, 195)(80, 196)(81, 197)(82, 198)(83, 199)(84, 200)(85, 201)(86, 202)(87, 203)(88, 204)(89, 205)(90, 206)(91, 207)(92, 208)(93, 209)(94, 210)(95, 211)(96, 212)(97, 213)(98, 214)(99, 215)(100, 216)(101, 217)(102, 218)(103, 219)(104, 220)(105, 221)(106, 222)(107, 223)(108, 224)(109, 225)(110, 226)(111, 227)(112, 228)(113, 229)(114, 230)(115, 231)(116, 232) local type(s) :: { ( 2, 58, 2, 58 ), ( 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58, 2, 58 ) } Outer automorphisms :: reflexible Dual of E14.473 Graph:: bipartite v = 30 e = 116 f = 60 degree seq :: [ 4^29, 116 ] E14.473 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 29, 58}) Quotient :: dipole Aut^+ = C58 (small group id <58, 2>) Aut = D116 (small group id <116, 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 * Y1^12 * Y3^-1 * Y1 * Y3^-13, Y3^-2 * Y1^27, (Y3 * Y2^-1)^58 ] Map:: R = (1, 59, 2, 60, 6, 64, 11, 69, 15, 73, 19, 77, 23, 81, 27, 85, 31, 89, 35, 93, 39, 97, 43, 101, 47, 105, 51, 109, 55, 113, 57, 115, 54, 112, 49, 107, 46, 104, 41, 99, 38, 96, 33, 91, 30, 88, 25, 83, 22, 80, 17, 75, 14, 72, 9, 67, 4, 62)(3, 61, 7, 65, 5, 63, 8, 66, 12, 70, 16, 74, 20, 78, 24, 82, 28, 86, 32, 90, 36, 94, 40, 98, 44, 102, 48, 106, 52, 110, 56, 114, 58, 116, 53, 111, 50, 108, 45, 103, 42, 100, 37, 95, 34, 92, 29, 87, 26, 84, 21, 79, 18, 76, 13, 71, 10, 68)(117, 175)(118, 176)(119, 177)(120, 178)(121, 179)(122, 180)(123, 181)(124, 182)(125, 183)(126, 184)(127, 185)(128, 186)(129, 187)(130, 188)(131, 189)(132, 190)(133, 191)(134, 192)(135, 193)(136, 194)(137, 195)(138, 196)(139, 197)(140, 198)(141, 199)(142, 200)(143, 201)(144, 202)(145, 203)(146, 204)(147, 205)(148, 206)(149, 207)(150, 208)(151, 209)(152, 210)(153, 211)(154, 212)(155, 213)(156, 214)(157, 215)(158, 216)(159, 217)(160, 218)(161, 219)(162, 220)(163, 221)(164, 222)(165, 223)(166, 224)(167, 225)(168, 226)(169, 227)(170, 228)(171, 229)(172, 230)(173, 231)(174, 232) L = (1, 119)(2, 123)(3, 125)(4, 126)(5, 117)(6, 121)(7, 120)(8, 118)(9, 129)(10, 130)(11, 124)(12, 122)(13, 133)(14, 134)(15, 128)(16, 127)(17, 137)(18, 138)(19, 132)(20, 131)(21, 141)(22, 142)(23, 136)(24, 135)(25, 145)(26, 146)(27, 140)(28, 139)(29, 149)(30, 150)(31, 144)(32, 143)(33, 153)(34, 154)(35, 148)(36, 147)(37, 157)(38, 158)(39, 152)(40, 151)(41, 161)(42, 162)(43, 156)(44, 155)(45, 165)(46, 166)(47, 160)(48, 159)(49, 169)(50, 170)(51, 164)(52, 163)(53, 173)(54, 174)(55, 168)(56, 167)(57, 172)(58, 171)(59, 175)(60, 176)(61, 177)(62, 178)(63, 179)(64, 180)(65, 181)(66, 182)(67, 183)(68, 184)(69, 185)(70, 186)(71, 187)(72, 188)(73, 189)(74, 190)(75, 191)(76, 192)(77, 193)(78, 194)(79, 195)(80, 196)(81, 197)(82, 198)(83, 199)(84, 200)(85, 201)(86, 202)(87, 203)(88, 204)(89, 205)(90, 206)(91, 207)(92, 208)(93, 209)(94, 210)(95, 211)(96, 212)(97, 213)(98, 214)(99, 215)(100, 216)(101, 217)(102, 218)(103, 219)(104, 220)(105, 221)(106, 222)(107, 223)(108, 224)(109, 225)(110, 226)(111, 227)(112, 228)(113, 229)(114, 230)(115, 231)(116, 232) local type(s) :: { ( 4, 116 ), ( 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116, 4, 116 ) } Outer automorphisms :: reflexible Dual of E14.472 Graph:: simple bipartite v = 60 e = 116 f = 30 degree seq :: [ 2^58, 58^2 ] E14.474 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 15}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2 * Y1 * Y2 * Y1)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 7, 67)(4, 64, 9, 69)(5, 65, 10, 70)(6, 66, 12, 72)(8, 68, 15, 75)(11, 71, 20, 80)(13, 73, 23, 83)(14, 74, 25, 85)(16, 76, 28, 88)(17, 77, 30, 90)(18, 78, 31, 91)(19, 79, 33, 93)(21, 81, 36, 96)(22, 82, 38, 98)(24, 84, 34, 94)(26, 86, 32, 92)(27, 87, 44, 104)(29, 89, 45, 105)(35, 95, 53, 113)(37, 97, 54, 114)(39, 99, 48, 108)(40, 100, 50, 110)(41, 101, 49, 109)(42, 102, 55, 115)(43, 103, 56, 116)(46, 106, 51, 111)(47, 107, 52, 112)(57, 117, 60, 120)(58, 118, 59, 119)(121, 181, 123, 183)(122, 182, 125, 185)(124, 184, 128, 188)(126, 186, 131, 191)(127, 187, 133, 193)(129, 189, 136, 196)(130, 190, 138, 198)(132, 192, 141, 201)(134, 194, 144, 204)(135, 195, 146, 206)(137, 197, 149, 209)(139, 199, 152, 212)(140, 200, 154, 214)(142, 202, 157, 217)(143, 203, 159, 219)(145, 205, 161, 221)(147, 207, 163, 223)(148, 208, 160, 220)(150, 210, 166, 226)(151, 211, 168, 228)(153, 213, 170, 230)(155, 215, 172, 232)(156, 216, 169, 229)(158, 218, 175, 235)(162, 222, 177, 237)(164, 224, 178, 238)(165, 225, 176, 236)(167, 227, 174, 234)(171, 231, 179, 239)(173, 233, 180, 240) L = (1, 124)(2, 126)(3, 128)(4, 121)(5, 131)(6, 122)(7, 134)(8, 123)(9, 137)(10, 139)(11, 125)(12, 142)(13, 144)(14, 127)(15, 147)(16, 149)(17, 129)(18, 152)(19, 130)(20, 155)(21, 157)(22, 132)(23, 160)(24, 133)(25, 162)(26, 163)(27, 135)(28, 159)(29, 136)(30, 167)(31, 169)(32, 138)(33, 171)(34, 172)(35, 140)(36, 168)(37, 141)(38, 176)(39, 148)(40, 143)(41, 177)(42, 145)(43, 146)(44, 173)(45, 175)(46, 174)(47, 150)(48, 156)(49, 151)(50, 179)(51, 153)(52, 154)(53, 164)(54, 166)(55, 165)(56, 158)(57, 161)(58, 180)(59, 170)(60, 178)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E14.478 Graph:: simple bipartite v = 60 e = 120 f = 34 degree seq :: [ 4^60 ] E14.475 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 15}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^6, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 6, 66)(4, 64, 11, 71)(5, 65, 13, 73)(7, 67, 17, 77)(8, 68, 19, 79)(9, 69, 21, 81)(10, 70, 23, 83)(12, 72, 18, 78)(14, 74, 20, 80)(15, 75, 29, 89)(16, 76, 31, 91)(22, 82, 30, 90)(24, 84, 32, 92)(25, 85, 41, 101)(26, 86, 43, 103)(27, 87, 42, 102)(28, 88, 44, 104)(33, 93, 49, 109)(34, 94, 51, 111)(35, 95, 50, 110)(36, 96, 52, 112)(37, 97, 53, 113)(38, 98, 55, 115)(39, 99, 54, 114)(40, 100, 56, 116)(45, 105, 57, 117)(46, 106, 59, 119)(47, 107, 58, 118)(48, 108, 60, 120)(121, 181, 123, 183)(122, 182, 126, 186)(124, 184, 130, 190)(125, 185, 129, 189)(127, 187, 136, 196)(128, 188, 135, 195)(131, 191, 143, 203)(132, 192, 144, 204)(133, 193, 141, 201)(134, 194, 142, 202)(137, 197, 151, 211)(138, 198, 152, 212)(139, 199, 149, 209)(140, 200, 150, 210)(145, 205, 160, 220)(146, 206, 158, 218)(147, 207, 159, 219)(148, 208, 157, 217)(153, 213, 168, 228)(154, 214, 166, 226)(155, 215, 167, 227)(156, 216, 165, 225)(161, 221, 176, 236)(162, 222, 174, 234)(163, 223, 175, 235)(164, 224, 173, 233)(169, 229, 180, 240)(170, 230, 178, 238)(171, 231, 179, 239)(172, 232, 177, 237) L = (1, 124)(2, 127)(3, 129)(4, 132)(5, 121)(6, 135)(7, 138)(8, 122)(9, 142)(10, 123)(11, 145)(12, 147)(13, 146)(14, 125)(15, 150)(16, 126)(17, 153)(18, 155)(19, 154)(20, 128)(21, 157)(22, 159)(23, 158)(24, 130)(25, 162)(26, 131)(27, 134)(28, 133)(29, 165)(30, 167)(31, 166)(32, 136)(33, 170)(34, 137)(35, 140)(36, 139)(37, 174)(38, 141)(39, 144)(40, 143)(41, 171)(42, 148)(43, 172)(44, 169)(45, 178)(46, 149)(47, 152)(48, 151)(49, 163)(50, 156)(51, 164)(52, 161)(53, 179)(54, 160)(55, 180)(56, 177)(57, 175)(58, 168)(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) :: { ( 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E14.479 Graph:: simple bipartite v = 60 e = 120 f = 34 degree seq :: [ 4^60 ] E14.476 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 15}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1 * Y3 * Y2 * Y1 * Y2)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 7, 67)(4, 64, 9, 69)(5, 65, 10, 70)(6, 66, 12, 72)(8, 68, 15, 75)(11, 71, 20, 80)(13, 73, 23, 83)(14, 74, 25, 85)(16, 76, 28, 88)(17, 77, 30, 90)(18, 78, 31, 91)(19, 79, 33, 93)(21, 81, 36, 96)(22, 82, 38, 98)(24, 84, 34, 94)(26, 86, 32, 92)(27, 87, 42, 102)(29, 89, 43, 103)(35, 95, 47, 107)(37, 97, 48, 108)(39, 99, 49, 109)(40, 100, 50, 110)(41, 101, 51, 111)(44, 104, 53, 113)(45, 105, 54, 114)(46, 106, 55, 115)(52, 112, 56, 116)(57, 117, 60, 120)(58, 118, 59, 119)(121, 181, 123, 183)(122, 182, 125, 185)(124, 184, 128, 188)(126, 186, 131, 191)(127, 187, 133, 193)(129, 189, 136, 196)(130, 190, 138, 198)(132, 192, 141, 201)(134, 194, 144, 204)(135, 195, 146, 206)(137, 197, 149, 209)(139, 199, 152, 212)(140, 200, 154, 214)(142, 202, 157, 217)(143, 203, 159, 219)(145, 205, 160, 220)(147, 207, 161, 221)(148, 208, 158, 218)(150, 210, 156, 216)(151, 211, 164, 224)(153, 213, 165, 225)(155, 215, 166, 226)(162, 222, 170, 230)(163, 223, 171, 231)(167, 227, 174, 234)(168, 228, 175, 235)(169, 229, 177, 237)(172, 232, 178, 238)(173, 233, 179, 239)(176, 236, 180, 240) L = (1, 124)(2, 126)(3, 128)(4, 121)(5, 131)(6, 122)(7, 134)(8, 123)(9, 137)(10, 139)(11, 125)(12, 142)(13, 144)(14, 127)(15, 147)(16, 149)(17, 129)(18, 152)(19, 130)(20, 155)(21, 157)(22, 132)(23, 158)(24, 133)(25, 153)(26, 161)(27, 135)(28, 159)(29, 136)(30, 151)(31, 150)(32, 138)(33, 145)(34, 166)(35, 140)(36, 164)(37, 141)(38, 143)(39, 148)(40, 165)(41, 146)(42, 169)(43, 172)(44, 156)(45, 160)(46, 154)(47, 173)(48, 176)(49, 162)(50, 177)(51, 178)(52, 163)(53, 167)(54, 179)(55, 180)(56, 168)(57, 170)(58, 171)(59, 174)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E14.477 Graph:: simple bipartite v = 60 e = 120 f = 34 degree seq :: [ 4^60 ] E14.477 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 15}) 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, (R * Y2)^2, (Y1^-1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, Y1^2 * Y2 * Y1 * Y2 * Y1^2, Y2 * Y1^2 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-2 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 6, 66, 15, 75, 25, 85, 38, 98, 52, 112, 40, 100, 46, 106, 55, 115, 43, 103, 22, 82, 32, 92, 14, 74, 5, 65)(3, 63, 9, 69, 21, 81, 30, 90, 13, 73, 29, 89, 35, 95, 16, 76, 31, 91, 39, 99, 20, 80, 7, 67, 18, 78, 26, 86, 11, 71)(4, 64, 12, 72, 27, 87, 47, 107, 42, 102, 57, 117, 60, 120, 58, 118, 56, 116, 59, 119, 54, 114, 45, 105, 33, 93, 17, 77, 8, 68)(10, 70, 24, 84, 44, 104, 36, 96, 19, 79, 37, 97, 53, 113, 48, 108, 34, 94, 51, 111, 50, 110, 28, 88, 49, 109, 41, 101, 23, 83)(121, 181, 123, 183)(122, 182, 127, 187)(124, 184, 130, 190)(125, 185, 133, 193)(126, 186, 136, 196)(128, 188, 139, 199)(129, 189, 142, 202)(131, 191, 145, 205)(132, 192, 148, 208)(134, 194, 151, 211)(135, 195, 150, 210)(137, 197, 154, 214)(138, 198, 152, 212)(140, 200, 158, 218)(141, 201, 160, 220)(143, 203, 162, 222)(144, 204, 165, 225)(146, 206, 166, 226)(147, 207, 168, 228)(149, 209, 163, 223)(153, 213, 169, 229)(155, 215, 172, 232)(156, 216, 167, 227)(157, 217, 174, 234)(159, 219, 175, 235)(161, 221, 176, 236)(164, 224, 178, 238)(170, 230, 177, 237)(171, 231, 179, 239)(173, 233, 180, 240) L = (1, 124)(2, 128)(3, 130)(4, 121)(5, 132)(6, 137)(7, 139)(8, 122)(9, 143)(10, 123)(11, 144)(12, 125)(13, 148)(14, 147)(15, 153)(16, 154)(17, 126)(18, 156)(19, 127)(20, 157)(21, 161)(22, 162)(23, 129)(24, 131)(25, 165)(26, 164)(27, 134)(28, 133)(29, 170)(30, 169)(31, 168)(32, 167)(33, 135)(34, 136)(35, 171)(36, 138)(37, 140)(38, 174)(39, 173)(40, 176)(41, 141)(42, 142)(43, 177)(44, 146)(45, 145)(46, 178)(47, 152)(48, 151)(49, 150)(50, 149)(51, 155)(52, 179)(53, 159)(54, 158)(55, 180)(56, 160)(57, 163)(58, 166)(59, 172)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4^4 ), ( 4^30 ) } Outer automorphisms :: reflexible Dual of E14.476 Graph:: simple bipartite v = 34 e = 120 f = 60 degree seq :: [ 4^30, 30^4 ] E14.478 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 15}) 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, (R * Y2)^2, (Y1^-1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, Y1^2 * Y2 * Y1^-1 * Y2 * Y1^2 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 6, 66, 15, 75, 22, 82, 37, 97, 51, 111, 46, 106, 40, 100, 53, 113, 45, 105, 25, 85, 32, 92, 14, 74, 5, 65)(3, 63, 9, 69, 21, 81, 20, 80, 7, 67, 18, 78, 36, 96, 31, 91, 16, 76, 34, 94, 30, 90, 13, 73, 29, 89, 26, 86, 11, 71)(4, 64, 12, 72, 27, 87, 47, 107, 44, 104, 58, 118, 60, 120, 56, 116, 57, 117, 59, 119, 55, 115, 42, 102, 33, 93, 17, 77, 8, 68)(10, 70, 24, 84, 43, 103, 50, 110, 28, 88, 49, 109, 52, 112, 35, 95, 48, 108, 54, 114, 38, 98, 19, 79, 39, 99, 41, 101, 23, 83)(121, 181, 123, 183)(122, 182, 127, 187)(124, 184, 130, 190)(125, 185, 133, 193)(126, 186, 136, 196)(128, 188, 139, 199)(129, 189, 142, 202)(131, 191, 145, 205)(132, 192, 148, 208)(134, 194, 151, 211)(135, 195, 149, 209)(137, 197, 155, 215)(138, 198, 157, 217)(140, 200, 152, 212)(141, 201, 160, 220)(143, 203, 162, 222)(144, 204, 164, 224)(146, 206, 166, 226)(147, 207, 168, 228)(150, 210, 165, 225)(153, 213, 170, 230)(154, 214, 171, 231)(156, 216, 173, 233)(158, 218, 175, 235)(159, 219, 167, 227)(161, 221, 176, 236)(163, 223, 177, 237)(169, 229, 178, 238)(172, 232, 179, 239)(174, 234, 180, 240) L = (1, 124)(2, 128)(3, 130)(4, 121)(5, 132)(6, 137)(7, 139)(8, 122)(9, 143)(10, 123)(11, 144)(12, 125)(13, 148)(14, 147)(15, 153)(16, 155)(17, 126)(18, 158)(19, 127)(20, 159)(21, 161)(22, 162)(23, 129)(24, 131)(25, 164)(26, 163)(27, 134)(28, 133)(29, 170)(30, 169)(31, 168)(32, 167)(33, 135)(34, 172)(35, 136)(36, 174)(37, 175)(38, 138)(39, 140)(40, 176)(41, 141)(42, 142)(43, 146)(44, 145)(45, 178)(46, 177)(47, 152)(48, 151)(49, 150)(50, 149)(51, 179)(52, 154)(53, 180)(54, 156)(55, 157)(56, 160)(57, 166)(58, 165)(59, 171)(60, 173)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4^4 ), ( 4^30 ) } Outer automorphisms :: reflexible Dual of E14.474 Graph:: simple bipartite v = 34 e = 120 f = 60 degree seq :: [ 4^30, 30^4 ] E14.479 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 15}) 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 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y1 * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^3 * Y1 * Y3^-1 * Y1, (Y3 * Y1^-2)^2, Y1 * Y3 * Y1^-4 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 7, 67, 21, 81, 39, 99, 20, 80, 30, 90, 47, 107, 58, 118, 40, 100, 15, 75, 27, 87, 43, 103, 18, 78, 5, 65)(3, 63, 11, 71, 31, 91, 52, 112, 51, 111, 37, 97, 57, 117, 60, 120, 59, 119, 48, 108, 34, 94, 55, 115, 44, 104, 22, 82, 8, 68)(4, 64, 14, 74, 38, 98, 28, 88, 9, 69, 6, 66, 19, 79, 42, 102, 23, 83, 10, 70, 29, 89, 17, 77, 41, 101, 24, 84, 16, 76)(12, 72, 26, 86, 50, 110, 56, 116, 32, 92, 13, 73, 36, 96, 45, 105, 53, 113, 33, 93, 49, 109, 25, 85, 46, 106, 54, 114, 35, 95)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 133, 193)(125, 185, 131, 191)(126, 186, 132, 192)(127, 187, 142, 202)(129, 189, 146, 206)(130, 190, 145, 205)(134, 194, 152, 212)(135, 195, 157, 217)(136, 196, 156, 216)(137, 197, 153, 213)(138, 198, 151, 211)(139, 199, 155, 215)(140, 200, 154, 214)(141, 201, 164, 224)(143, 203, 166, 226)(144, 204, 165, 225)(147, 207, 171, 231)(148, 208, 170, 230)(149, 209, 169, 229)(150, 210, 168, 228)(158, 218, 176, 236)(159, 219, 175, 235)(160, 220, 177, 237)(161, 221, 173, 233)(162, 222, 174, 234)(163, 223, 172, 232)(167, 227, 179, 239)(178, 238, 180, 240) L = (1, 124)(2, 129)(3, 132)(4, 135)(5, 137)(6, 121)(7, 143)(8, 145)(9, 147)(10, 122)(11, 152)(12, 154)(13, 123)(14, 125)(15, 149)(16, 150)(17, 160)(18, 162)(19, 159)(20, 126)(21, 161)(22, 165)(23, 163)(24, 127)(25, 168)(26, 128)(27, 136)(28, 167)(29, 140)(30, 130)(31, 173)(32, 175)(33, 131)(34, 169)(35, 177)(36, 171)(37, 133)(38, 141)(39, 134)(40, 139)(41, 138)(42, 178)(43, 148)(44, 176)(45, 179)(46, 142)(47, 144)(48, 156)(49, 157)(50, 172)(51, 146)(52, 166)(53, 164)(54, 151)(55, 155)(56, 180)(57, 153)(58, 158)(59, 170)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4^4 ), ( 4^30 ) } Outer automorphisms :: reflexible Dual of E14.475 Graph:: simple bipartite v = 34 e = 120 f = 60 degree seq :: [ 4^30, 30^4 ] E14.480 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 15}) Quotient :: dipole Aut^+ = D60 (small group id <60, 12>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^15 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 5, 65)(4, 64, 8, 68)(6, 66, 10, 70)(7, 67, 11, 71)(9, 69, 13, 73)(12, 72, 16, 76)(14, 74, 18, 78)(15, 75, 19, 79)(17, 77, 21, 81)(20, 80, 24, 84)(22, 82, 26, 86)(23, 83, 27, 87)(25, 85, 44, 104)(28, 88, 41, 101)(29, 89, 53, 113)(30, 90, 54, 114)(31, 91, 56, 116)(32, 92, 55, 115)(33, 93, 58, 118)(34, 94, 52, 112)(35, 95, 59, 119)(36, 96, 60, 120)(37, 97, 57, 117)(38, 98, 51, 111)(39, 99, 50, 110)(40, 100, 47, 107)(42, 102, 46, 106)(43, 103, 49, 109)(45, 105, 48, 108)(121, 181, 123, 183)(122, 182, 125, 185)(124, 184, 127, 187)(126, 186, 129, 189)(128, 188, 131, 191)(130, 190, 133, 193)(132, 192, 135, 195)(134, 194, 137, 197)(136, 196, 139, 199)(138, 198, 141, 201)(140, 200, 143, 203)(142, 202, 145, 205)(144, 204, 147, 207)(146, 206, 164, 224)(148, 208, 171, 231)(149, 209, 151, 211)(150, 210, 153, 213)(152, 212, 155, 215)(154, 214, 157, 217)(156, 216, 159, 219)(158, 218, 161, 221)(160, 220, 163, 223)(162, 222, 165, 225)(166, 226, 168, 228)(167, 227, 169, 229)(170, 230, 180, 240)(172, 232, 177, 237)(173, 233, 176, 236)(174, 234, 178, 238)(175, 235, 179, 239) L = (1, 124)(2, 126)(3, 127)(4, 121)(5, 129)(6, 122)(7, 123)(8, 132)(9, 125)(10, 134)(11, 135)(12, 128)(13, 137)(14, 130)(15, 131)(16, 140)(17, 133)(18, 142)(19, 143)(20, 136)(21, 145)(22, 138)(23, 139)(24, 148)(25, 141)(26, 170)(27, 171)(28, 144)(29, 172)(30, 175)(31, 177)(32, 167)(33, 179)(34, 166)(35, 169)(36, 173)(37, 168)(38, 174)(39, 176)(40, 162)(41, 178)(42, 160)(43, 165)(44, 180)(45, 163)(46, 154)(47, 152)(48, 157)(49, 155)(50, 146)(51, 147)(52, 149)(53, 156)(54, 158)(55, 150)(56, 159)(57, 151)(58, 161)(59, 153)(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) :: { ( 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E14.481 Graph:: simple bipartite v = 60 e = 120 f = 34 degree seq :: [ 4^60 ] E14.481 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 15}) Quotient :: dipole Aut^+ = D60 (small group id <60, 12>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, Y1^15 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 6, 66, 13, 73, 21, 81, 29, 89, 37, 97, 45, 105, 52, 112, 44, 104, 36, 96, 28, 88, 20, 80, 12, 72, 5, 65)(3, 63, 9, 69, 17, 77, 25, 85, 33, 93, 41, 101, 49, 109, 56, 116, 53, 113, 46, 106, 38, 98, 30, 90, 22, 82, 14, 74, 7, 67)(4, 64, 11, 71, 19, 79, 27, 87, 35, 95, 43, 103, 51, 111, 58, 118, 54, 114, 47, 107, 39, 99, 31, 91, 23, 83, 15, 75, 8, 68)(10, 70, 16, 76, 24, 84, 32, 92, 40, 100, 48, 108, 55, 115, 59, 119, 60, 120, 57, 117, 50, 110, 42, 102, 34, 94, 26, 86, 18, 78)(121, 181, 123, 183)(122, 182, 127, 187)(124, 184, 130, 190)(125, 185, 129, 189)(126, 186, 134, 194)(128, 188, 136, 196)(131, 191, 138, 198)(132, 192, 137, 197)(133, 193, 142, 202)(135, 195, 144, 204)(139, 199, 146, 206)(140, 200, 145, 205)(141, 201, 150, 210)(143, 203, 152, 212)(147, 207, 154, 214)(148, 208, 153, 213)(149, 209, 158, 218)(151, 211, 160, 220)(155, 215, 162, 222)(156, 216, 161, 221)(157, 217, 166, 226)(159, 219, 168, 228)(163, 223, 170, 230)(164, 224, 169, 229)(165, 225, 173, 233)(167, 227, 175, 235)(171, 231, 177, 237)(172, 232, 176, 236)(174, 234, 179, 239)(178, 238, 180, 240) L = (1, 124)(2, 128)(3, 130)(4, 121)(5, 131)(6, 135)(7, 136)(8, 122)(9, 138)(10, 123)(11, 125)(12, 139)(13, 143)(14, 144)(15, 126)(16, 127)(17, 146)(18, 129)(19, 132)(20, 147)(21, 151)(22, 152)(23, 133)(24, 134)(25, 154)(26, 137)(27, 140)(28, 155)(29, 159)(30, 160)(31, 141)(32, 142)(33, 162)(34, 145)(35, 148)(36, 163)(37, 167)(38, 168)(39, 149)(40, 150)(41, 170)(42, 153)(43, 156)(44, 171)(45, 174)(46, 175)(47, 157)(48, 158)(49, 177)(50, 161)(51, 164)(52, 178)(53, 179)(54, 165)(55, 166)(56, 180)(57, 169)(58, 172)(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) :: { ( 4^4 ), ( 4^30 ) } Outer automorphisms :: reflexible Dual of E14.480 Graph:: simple bipartite v = 34 e = 120 f = 60 degree seq :: [ 4^30, 30^4 ] E14.482 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 15}) Quotient :: edge Aut^+ = C15 : C4 (small group id <60, 3>) Aut = (C30 x C2) : C2 (small group id <120, 30>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1 * T2 * T1^-1, T2^15 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 49, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 58, 57, 50, 42, 34, 26, 18, 10)(6, 13, 21, 29, 37, 45, 53, 59, 60, 54, 46, 38, 30, 22, 14)(61, 62, 66, 64)(63, 68, 73, 70)(65, 67, 74, 71)(69, 76, 81, 78)(72, 75, 82, 79)(77, 84, 89, 86)(80, 83, 90, 87)(85, 92, 97, 94)(88, 91, 98, 95)(93, 100, 105, 102)(96, 99, 106, 103)(101, 108, 113, 110)(104, 107, 114, 111)(109, 116, 119, 117)(112, 115, 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) :: { ( 8^4 ), ( 8^15 ) } Outer automorphisms :: reflexible Dual of E14.483 Transitivity :: ET+ Graph:: simple bipartite v = 19 e = 60 f = 15 degree seq :: [ 4^15, 15^4 ] E14.483 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 15}) Quotient :: loop Aut^+ = C15 : C4 (small group id <60, 3>) Aut = (C30 x C2) : C2 (small group id <120, 30>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, T2^-2 * T1^2, (F * T2)^2, (F * T1)^2, T2^4, (T2 * T1)^15 ] Map:: non-degenerate R = (1, 61, 3, 63, 6, 66, 5, 65)(2, 62, 7, 67, 4, 64, 8, 68)(9, 69, 13, 73, 10, 70, 14, 74)(11, 71, 15, 75, 12, 72, 16, 76)(17, 77, 21, 81, 18, 78, 22, 82)(19, 79, 23, 83, 20, 80, 24, 84)(25, 85, 29, 89, 26, 86, 30, 90)(27, 87, 45, 105, 28, 88, 47, 107)(31, 91, 49, 109, 34, 94, 51, 111)(32, 92, 52, 112, 33, 93, 54, 114)(35, 95, 57, 117, 36, 96, 59, 119)(37, 97, 60, 120, 38, 98, 58, 118)(39, 99, 53, 113, 40, 100, 55, 115)(41, 101, 56, 116, 42, 102, 50, 110)(43, 103, 48, 108, 44, 104, 46, 106) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 70)(6, 64)(7, 71)(8, 72)(9, 65)(10, 63)(11, 68)(12, 67)(13, 77)(14, 78)(15, 79)(16, 80)(17, 74)(18, 73)(19, 76)(20, 75)(21, 85)(22, 86)(23, 87)(24, 88)(25, 82)(26, 81)(27, 84)(28, 83)(29, 94)(30, 91)(31, 89)(32, 105)(33, 107)(34, 90)(35, 111)(36, 109)(37, 114)(38, 112)(39, 119)(40, 117)(41, 118)(42, 120)(43, 115)(44, 113)(45, 93)(46, 110)(47, 92)(48, 116)(49, 95)(50, 108)(51, 96)(52, 97)(53, 103)(54, 98)(55, 104)(56, 106)(57, 99)(58, 102)(59, 100)(60, 101) local type(s) :: { ( 4, 15, 4, 15, 4, 15, 4, 15 ) } Outer automorphisms :: reflexible Dual of E14.482 Transitivity :: ET+ VT+ AT Graph:: v = 15 e = 60 f = 19 degree seq :: [ 8^15 ] E14.484 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 15}) Quotient :: dipole Aut^+ = C15 : C4 (small group id <60, 3>) Aut = (C30 x C2) : C2 (small group id <120, 30>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1^-1 * Y2^-1 * Y1 * Y2^-1, (Y3^-1 * Y1^-1)^4, Y2^15 ] Map:: R = (1, 61, 2, 62, 6, 66, 4, 64)(3, 63, 8, 68, 13, 73, 10, 70)(5, 65, 7, 67, 14, 74, 11, 71)(9, 69, 16, 76, 21, 81, 18, 78)(12, 72, 15, 75, 22, 82, 19, 79)(17, 77, 24, 84, 29, 89, 26, 86)(20, 80, 23, 83, 30, 90, 27, 87)(25, 85, 32, 92, 37, 97, 34, 94)(28, 88, 31, 91, 38, 98, 35, 95)(33, 93, 40, 100, 45, 105, 42, 102)(36, 96, 39, 99, 46, 106, 43, 103)(41, 101, 48, 108, 53, 113, 50, 110)(44, 104, 47, 107, 54, 114, 51, 111)(49, 109, 56, 116, 59, 119, 57, 117)(52, 112, 55, 115, 60, 120, 58, 118)(121, 181, 123, 183, 129, 189, 137, 197, 145, 205, 153, 213, 161, 221, 169, 229, 172, 232, 164, 224, 156, 216, 148, 208, 140, 200, 132, 192, 125, 185)(122, 182, 127, 187, 135, 195, 143, 203, 151, 211, 159, 219, 167, 227, 175, 235, 176, 236, 168, 228, 160, 220, 152, 212, 144, 204, 136, 196, 128, 188)(124, 184, 131, 191, 139, 199, 147, 207, 155, 215, 163, 223, 171, 231, 178, 238, 177, 237, 170, 230, 162, 222, 154, 214, 146, 206, 138, 198, 130, 190)(126, 186, 133, 193, 141, 201, 149, 209, 157, 217, 165, 225, 173, 233, 179, 239, 180, 240, 174, 234, 166, 226, 158, 218, 150, 210, 142, 202, 134, 194) L = (1, 123)(2, 127)(3, 129)(4, 131)(5, 121)(6, 133)(7, 135)(8, 122)(9, 137)(10, 124)(11, 139)(12, 125)(13, 141)(14, 126)(15, 143)(16, 128)(17, 145)(18, 130)(19, 147)(20, 132)(21, 149)(22, 134)(23, 151)(24, 136)(25, 153)(26, 138)(27, 155)(28, 140)(29, 157)(30, 142)(31, 159)(32, 144)(33, 161)(34, 146)(35, 163)(36, 148)(37, 165)(38, 150)(39, 167)(40, 152)(41, 169)(42, 154)(43, 171)(44, 156)(45, 173)(46, 158)(47, 175)(48, 160)(49, 172)(50, 162)(51, 178)(52, 164)(53, 179)(54, 166)(55, 176)(56, 168)(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) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 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 E14.485 Graph:: bipartite v = 19 e = 120 f = 75 degree seq :: [ 8^15, 30^4 ] E14.485 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 15}) Quotient :: dipole Aut^+ = C15 : C4 (small group id <60, 3>) Aut = (C30 x C2) : C2 (small group id <120, 30>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^15 ] Map:: R = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)(121, 181, 122, 182, 126, 186, 124, 184)(123, 183, 128, 188, 133, 193, 130, 190)(125, 185, 127, 187, 134, 194, 131, 191)(129, 189, 136, 196, 141, 201, 138, 198)(132, 192, 135, 195, 142, 202, 139, 199)(137, 197, 144, 204, 149, 209, 146, 206)(140, 200, 143, 203, 150, 210, 147, 207)(145, 205, 152, 212, 157, 217, 154, 214)(148, 208, 151, 211, 158, 218, 155, 215)(153, 213, 160, 220, 165, 225, 162, 222)(156, 216, 159, 219, 166, 226, 163, 223)(161, 221, 168, 228, 173, 233, 170, 230)(164, 224, 167, 227, 174, 234, 171, 231)(169, 229, 176, 236, 179, 239, 177, 237)(172, 232, 175, 235, 180, 240, 178, 238) L = (1, 123)(2, 127)(3, 129)(4, 131)(5, 121)(6, 133)(7, 135)(8, 122)(9, 137)(10, 124)(11, 139)(12, 125)(13, 141)(14, 126)(15, 143)(16, 128)(17, 145)(18, 130)(19, 147)(20, 132)(21, 149)(22, 134)(23, 151)(24, 136)(25, 153)(26, 138)(27, 155)(28, 140)(29, 157)(30, 142)(31, 159)(32, 144)(33, 161)(34, 146)(35, 163)(36, 148)(37, 165)(38, 150)(39, 167)(40, 152)(41, 169)(42, 154)(43, 171)(44, 156)(45, 173)(46, 158)(47, 175)(48, 160)(49, 172)(50, 162)(51, 178)(52, 164)(53, 179)(54, 166)(55, 176)(56, 168)(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) :: { ( 8, 30 ), ( 8, 30, 8, 30, 8, 30, 8, 30 ) } Outer automorphisms :: reflexible Dual of E14.484 Graph:: simple bipartite v = 75 e = 120 f = 19 degree seq :: [ 2^60, 8^15 ] E14.486 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {4, 4, 15}) Quotient :: edge Aut^+ = C15 : C4 (small group id <60, 7>) Aut = C15 : C4 (small group id <60, 7>) |r| :: 1 Presentation :: [ X1^4, X2 * X1 * X2^-1 * X1^-1 * X2, (X2^-1 * X1^-1)^4, (X2 * X1^-1)^4, X2^15 ] Map:: polytopal non-degenerate R = (1, 2, 6, 4)(3, 9, 23, 11)(5, 14, 32, 15)(7, 19, 26, 10)(8, 21, 35, 16)(12, 28, 52, 29)(13, 30, 53, 31)(17, 37, 41, 20)(18, 38, 43, 22)(24, 47, 49, 25)(27, 51, 44, 42)(33, 46, 58, 36)(34, 54, 40, 39)(45, 57, 59, 48)(50, 60, 56, 55)(61, 63, 70, 85, 101, 119, 114, 90, 88, 111, 120, 103, 96, 76, 65)(62, 67, 80, 100, 112, 116, 93, 74, 69, 84, 108, 113, 104, 82, 68)(64, 72, 71, 87, 86, 110, 109, 98, 97, 118, 117, 95, 94, 75, 73)(66, 77, 89, 106, 83, 105, 102, 81, 79, 99, 115, 92, 107, 91, 78) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 8^4 ), ( 8^15 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 19 e = 60 f = 15 degree seq :: [ 4^15, 15^4 ] E14.487 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {4, 4, 15}) Quotient :: loop Aut^+ = C15 : C4 (small group id <60, 7>) Aut = C15 : C4 (small group id <60, 7>) |r| :: 1 Presentation :: [ X2^4, X1^4, X2^-1 * X1^-1 * X2^-1 * X1 * X2 * X1^-1, X2 * X1 * X2^-1 * X1^-1 * X2 * X1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 6, 66, 4, 64)(3, 63, 9, 69, 23, 83, 11, 71)(5, 65, 14, 74, 32, 92, 15, 75)(7, 67, 18, 78, 39, 99, 20, 80)(8, 68, 21, 81, 43, 103, 22, 82)(10, 70, 25, 85, 47, 107, 26, 86)(12, 72, 28, 88, 48, 108, 30, 90)(13, 73, 24, 84, 46, 106, 31, 91)(16, 76, 34, 94, 53, 113, 36, 96)(17, 77, 37, 97, 56, 116, 38, 98)(19, 79, 40, 100, 57, 117, 41, 101)(27, 87, 49, 109, 33, 93, 50, 110)(29, 89, 45, 105, 60, 120, 51, 111)(35, 95, 54, 114, 52, 112, 55, 115)(42, 102, 58, 118, 44, 104, 59, 119) L = (1, 63)(2, 67)(3, 70)(4, 72)(5, 61)(6, 76)(7, 79)(8, 62)(9, 80)(10, 65)(11, 87)(12, 89)(13, 64)(14, 78)(15, 91)(16, 95)(17, 66)(18, 96)(19, 68)(20, 102)(21, 94)(22, 75)(23, 100)(24, 69)(25, 99)(26, 103)(27, 97)(28, 71)(29, 73)(30, 104)(31, 98)(32, 112)(33, 74)(34, 90)(35, 77)(36, 93)(37, 88)(38, 82)(39, 114)(40, 113)(41, 116)(42, 84)(43, 120)(44, 81)(45, 83)(46, 117)(47, 118)(48, 85)(49, 86)(50, 115)(51, 92)(52, 119)(53, 105)(54, 108)(55, 106)(56, 107)(57, 110)(58, 101)(59, 111)(60, 109) local type(s) :: { ( 4, 15, 4, 15, 4, 15, 4, 15 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: simple v = 15 e = 60 f = 19 degree seq :: [ 8^15 ] E14.488 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {4, 4, 15}) Quotient :: loop Aut^+ = C15 : C4 (small group id <60, 7>) Aut = S3 x (C5 : C4) (small group id <120, 36>) |r| :: 2 Presentation :: [ F^2, F * T1 * F * T2, T1^4, T2^4, T2^-1 * T1 * T2 * T1 * T2 * T1^-1, T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 5)(2, 7, 19, 8)(4, 12, 29, 13)(6, 16, 35, 17)(9, 24, 34, 18)(11, 27, 37, 28)(14, 22, 36, 33)(15, 20, 42, 31)(21, 38, 30, 44)(23, 40, 59, 45)(25, 48, 58, 46)(26, 43, 55, 49)(32, 41, 56, 52)(39, 54, 50, 57)(47, 53, 51, 60)(61, 62, 66, 64)(63, 69, 83, 71)(65, 74, 92, 75)(67, 78, 99, 80)(68, 81, 103, 82)(70, 85, 107, 86)(72, 84, 106, 90)(73, 91, 109, 88)(76, 94, 113, 96)(77, 97, 116, 98)(79, 100, 118, 101)(87, 108, 93, 110)(89, 111, 117, 112)(95, 114, 105, 115)(102, 119, 104, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 30^4 ) } Outer automorphisms :: reflexible Dual of E14.489 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 30 e = 60 f = 4 degree seq :: [ 4^30 ] E14.489 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {4, 4, 15}) Quotient :: edge Aut^+ = C15 : C4 (small group id <60, 7>) Aut = S3 x (C5 : C4) (small group id <120, 36>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, T1^4, F * T1 * T2 * F * T1^-1, T2^2 * T1^-1 * T2^-1 * T1, (T1 * T2)^4, (T2 * T1^-1)^4, T2^15 ] Map:: polytopal non-degenerate R = (1, 61, 3, 63, 10, 70, 26, 86, 49, 109, 60, 120, 44, 104, 22, 82, 20, 80, 41, 101, 59, 119, 53, 113, 36, 96, 16, 76, 5, 65)(2, 62, 7, 67, 9, 69, 24, 84, 25, 85, 47, 107, 48, 108, 38, 98, 37, 97, 58, 118, 57, 117, 35, 95, 33, 93, 14, 74, 8, 68)(4, 64, 12, 72, 28, 88, 51, 111, 39, 99, 56, 116, 34, 94, 15, 75, 11, 71, 27, 87, 50, 110, 42, 102, 54, 114, 31, 91, 13, 73)(6, 66, 17, 77, 19, 79, 40, 100, 23, 83, 45, 105, 46, 106, 30, 90, 29, 89, 52, 112, 55, 115, 32, 92, 43, 103, 21, 81, 18, 78) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 74)(6, 64)(7, 79)(8, 81)(9, 83)(10, 85)(11, 63)(12, 70)(13, 76)(14, 92)(15, 65)(16, 95)(17, 88)(18, 91)(19, 99)(20, 67)(21, 102)(22, 68)(23, 71)(24, 106)(25, 89)(26, 108)(27, 86)(28, 109)(29, 72)(30, 73)(31, 113)(32, 75)(33, 112)(34, 96)(35, 90)(36, 118)(37, 77)(38, 78)(39, 80)(40, 94)(41, 84)(42, 82)(43, 87)(44, 93)(45, 110)(46, 114)(47, 115)(48, 103)(49, 97)(50, 120)(51, 104)(52, 111)(53, 98)(54, 101)(55, 116)(56, 119)(57, 105)(58, 100)(59, 107)(60, 117) local type(s) :: { ( 4^30 ) } Outer automorphisms :: reflexible Dual of E14.488 Transitivity :: ET+ VT+ Graph:: bipartite v = 4 e = 60 f = 30 degree seq :: [ 30^4 ] E14.490 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 15}) Quotient :: edge^2 Aut^+ = C15 : C4 (small group id <60, 7>) Aut = S3 x (C5 : C4) (small group id <120, 36>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y2^-1 * Y3^-2 * Y1^-1, Y2^4, Y3 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y1^-1, Y1^-1 * Y2^-1 * Y3^13 ] Map:: polytopal non-degenerate R = (1, 61, 4, 64, 17, 77, 43, 103, 48, 108, 59, 119, 33, 93, 28, 88, 29, 89, 50, 110, 56, 116, 40, 100, 35, 95, 12, 72, 7, 67)(2, 62, 9, 69, 6, 66, 23, 83, 19, 79, 46, 106, 44, 104, 47, 107, 53, 113, 57, 117, 38, 98, 34, 94, 51, 111, 24, 84, 11, 71)(3, 63, 5, 65, 21, 81, 27, 87, 54, 114, 30, 90, 52, 112, 25, 85, 16, 76, 18, 78, 45, 105, 49, 109, 55, 115, 36, 96, 15, 75)(8, 68, 26, 86, 10, 70, 31, 91, 22, 82, 37, 97, 13, 73, 14, 74, 39, 99, 60, 120, 41, 101, 42, 102, 58, 118, 32, 92, 20, 80)(121, 122, 128, 125)(123, 132, 154, 134)(124, 126, 142, 138)(127, 144, 162, 136)(129, 130, 150, 149)(131, 152, 175, 148)(133, 156, 170, 143)(135, 160, 167, 140)(137, 139, 159, 141)(145, 155, 177, 151)(146, 147, 168, 173)(153, 171, 180, 174)(157, 169, 179, 158)(161, 172, 176, 166)(163, 164, 178, 165)(181, 183, 193, 186)(182, 187, 205, 190)(184, 196, 221, 199)(185, 200, 224, 197)(188, 191, 213, 207)(189, 208, 229, 202)(192, 195, 212, 204)(194, 218, 228, 201)(198, 211, 233, 223)(203, 209, 234, 219)(206, 227, 236, 210)(214, 215, 232, 240)(216, 217, 237, 220)(222, 231, 239, 225)(226, 230, 235, 238) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4^4 ), ( 4^30 ) } Outer automorphisms :: reflexible Dual of E14.493 Graph:: simple bipartite v = 34 e = 120 f = 60 degree seq :: [ 4^30, 30^4 ] E14.491 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 15}) Quotient :: edge^2 Aut^+ = C15 : C4 (small group id <60, 7>) Aut = S3 x (C5 : C4) (small group id <120, 36>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y2^4, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, (Y1^-1 * Y3^-1 * Y2^-1)^15 ] 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, 124)(123, 129, 143, 131)(125, 134, 152, 135)(127, 138, 159, 140)(128, 141, 163, 142)(130, 145, 167, 146)(132, 144, 166, 150)(133, 151, 169, 148)(136, 154, 173, 156)(137, 157, 176, 158)(139, 160, 178, 161)(147, 168, 153, 170)(149, 171, 177, 172)(155, 174, 165, 175)(162, 179, 164, 180)(181, 183, 190, 185)(182, 187, 199, 188)(184, 192, 209, 193)(186, 196, 215, 197)(189, 204, 214, 198)(191, 207, 217, 208)(194, 202, 216, 213)(195, 200, 222, 211)(201, 218, 210, 224)(203, 220, 239, 225)(205, 228, 238, 226)(206, 223, 235, 229)(212, 221, 236, 232)(219, 234, 230, 237)(227, 233, 231, 240) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 60, 60 ), ( 60^4 ) } Outer automorphisms :: reflexible Dual of E14.492 Graph:: simple bipartite v = 90 e = 120 f = 4 degree seq :: [ 2^60, 4^30 ] E14.492 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 15}) Quotient :: loop^2 Aut^+ = C15 : C4 (small group id <60, 7>) Aut = S3 x (C5 : C4) (small group id <120, 36>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y2^-1 * Y3^-2 * Y1^-1, Y2^4, Y3 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y1^-1, Y1^-1 * Y2^-1 * Y3^13 ] Map:: R = (1, 61, 121, 181, 4, 64, 124, 184, 17, 77, 137, 197, 43, 103, 163, 223, 48, 108, 168, 228, 59, 119, 179, 239, 33, 93, 153, 213, 28, 88, 148, 208, 29, 89, 149, 209, 50, 110, 170, 230, 56, 116, 176, 236, 40, 100, 160, 220, 35, 95, 155, 215, 12, 72, 132, 192, 7, 67, 127, 187)(2, 62, 122, 182, 9, 69, 129, 189, 6, 66, 126, 186, 23, 83, 143, 203, 19, 79, 139, 199, 46, 106, 166, 226, 44, 104, 164, 224, 47, 107, 167, 227, 53, 113, 173, 233, 57, 117, 177, 237, 38, 98, 158, 218, 34, 94, 154, 214, 51, 111, 171, 231, 24, 84, 144, 204, 11, 71, 131, 191)(3, 63, 123, 183, 5, 65, 125, 185, 21, 81, 141, 201, 27, 87, 147, 207, 54, 114, 174, 234, 30, 90, 150, 210, 52, 112, 172, 232, 25, 85, 145, 205, 16, 76, 136, 196, 18, 78, 138, 198, 45, 105, 165, 225, 49, 109, 169, 229, 55, 115, 175, 235, 36, 96, 156, 216, 15, 75, 135, 195)(8, 68, 128, 188, 26, 86, 146, 206, 10, 70, 130, 190, 31, 91, 151, 211, 22, 82, 142, 202, 37, 97, 157, 217, 13, 73, 133, 193, 14, 74, 134, 194, 39, 99, 159, 219, 60, 120, 180, 240, 41, 101, 161, 221, 42, 102, 162, 222, 58, 118, 178, 238, 32, 92, 152, 212, 20, 80, 140, 200) L = (1, 62)(2, 68)(3, 72)(4, 66)(5, 61)(6, 82)(7, 84)(8, 65)(9, 70)(10, 90)(11, 92)(12, 94)(13, 96)(14, 63)(15, 100)(16, 67)(17, 79)(18, 64)(19, 99)(20, 75)(21, 77)(22, 78)(23, 73)(24, 102)(25, 95)(26, 87)(27, 108)(28, 71)(29, 69)(30, 89)(31, 85)(32, 115)(33, 111)(34, 74)(35, 117)(36, 110)(37, 109)(38, 97)(39, 81)(40, 107)(41, 112)(42, 76)(43, 104)(44, 118)(45, 103)(46, 101)(47, 80)(48, 113)(49, 119)(50, 83)(51, 120)(52, 116)(53, 86)(54, 93)(55, 88)(56, 106)(57, 91)(58, 105)(59, 98)(60, 114)(121, 183)(122, 187)(123, 193)(124, 196)(125, 200)(126, 181)(127, 205)(128, 191)(129, 208)(130, 182)(131, 213)(132, 195)(133, 186)(134, 218)(135, 212)(136, 221)(137, 185)(138, 211)(139, 184)(140, 224)(141, 194)(142, 189)(143, 209)(144, 192)(145, 190)(146, 227)(147, 188)(148, 229)(149, 234)(150, 206)(151, 233)(152, 204)(153, 207)(154, 215)(155, 232)(156, 217)(157, 237)(158, 228)(159, 203)(160, 216)(161, 199)(162, 231)(163, 198)(164, 197)(165, 222)(166, 230)(167, 236)(168, 201)(169, 202)(170, 235)(171, 239)(172, 240)(173, 223)(174, 219)(175, 238)(176, 210)(177, 220)(178, 226)(179, 225)(180, 214) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E14.491 Transitivity :: VT+ Graph:: bipartite v = 4 e = 120 f = 90 degree seq :: [ 60^4 ] E14.493 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 15}) Quotient :: loop^2 Aut^+ = C15 : C4 (small group id <60, 7>) Aut = S3 x (C5 : C4) (small group id <120, 36>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y2^4, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, (Y1^-1 * Y3^-1 * Y2^-1)^15 ] 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, 74)(6, 64)(7, 78)(8, 81)(9, 83)(10, 85)(11, 63)(12, 84)(13, 91)(14, 92)(15, 65)(16, 94)(17, 97)(18, 99)(19, 100)(20, 67)(21, 103)(22, 68)(23, 71)(24, 106)(25, 107)(26, 70)(27, 108)(28, 73)(29, 111)(30, 72)(31, 109)(32, 75)(33, 110)(34, 113)(35, 114)(36, 76)(37, 116)(38, 77)(39, 80)(40, 118)(41, 79)(42, 119)(43, 82)(44, 120)(45, 115)(46, 90)(47, 86)(48, 93)(49, 88)(50, 87)(51, 117)(52, 89)(53, 96)(54, 105)(55, 95)(56, 98)(57, 112)(58, 101)(59, 104)(60, 102)(121, 183)(122, 187)(123, 190)(124, 192)(125, 181)(126, 196)(127, 199)(128, 182)(129, 204)(130, 185)(131, 207)(132, 209)(133, 184)(134, 202)(135, 200)(136, 215)(137, 186)(138, 189)(139, 188)(140, 222)(141, 218)(142, 216)(143, 220)(144, 214)(145, 228)(146, 223)(147, 217)(148, 191)(149, 193)(150, 224)(151, 195)(152, 221)(153, 194)(154, 198)(155, 197)(156, 213)(157, 208)(158, 210)(159, 234)(160, 239)(161, 236)(162, 211)(163, 235)(164, 201)(165, 203)(166, 205)(167, 233)(168, 238)(169, 206)(170, 237)(171, 240)(172, 212)(173, 231)(174, 230)(175, 229)(176, 232)(177, 219)(178, 226)(179, 225)(180, 227) local type(s) :: { ( 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E14.490 Transitivity :: VT+ Graph:: simple bipartite v = 60 e = 120 f = 34 degree seq :: [ 4^60 ] E14.494 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 30, 30}) Quotient :: regular Aut^+ = C30 x C2 (small group id <60, 13>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^30 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 40, 36, 32, 29, 30, 33, 37, 41, 44, 47, 49, 58, 56, 54, 52, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 46, 43, 39, 35, 31, 34, 38, 42, 45, 48, 50, 60, 59, 57, 55, 53, 51, 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, 46)(28, 51)(29, 31)(30, 34)(32, 35)(33, 38)(36, 39)(37, 42)(40, 43)(41, 45)(44, 48)(47, 50)(49, 60)(52, 53)(54, 55)(56, 57)(58, 59) local type(s) :: { ( 30^30 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 30 f = 2 degree seq :: [ 30^2 ] E14.495 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 30, 30}) Quotient :: edge Aut^+ = C30 x C2 (small group id <60, 13>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^30 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 33, 35, 37, 39, 41, 44, 45, 47, 49, 51, 53, 55, 57, 60, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 30, 32, 34, 36, 38, 40, 42, 46, 48, 50, 52, 54, 56, 59, 58, 43, 26, 22, 18, 14, 10, 6)(61, 62)(63, 65)(64, 66)(67, 69)(68, 70)(71, 73)(72, 74)(75, 77)(76, 78)(79, 81)(80, 82)(83, 85)(84, 86)(87, 89)(88, 103)(90, 91)(92, 93)(94, 95)(96, 97)(98, 99)(100, 101)(102, 104)(105, 106)(107, 108)(109, 110)(111, 112)(113, 114)(115, 116)(117, 119)(118, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 60, 60 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E14.496 Transitivity :: ET+ Graph:: simple bipartite v = 32 e = 60 f = 2 degree seq :: [ 2^30, 30^2 ] E14.496 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 30, 30}) Quotient :: loop Aut^+ = C30 x C2 (small group id <60, 13>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^30 ] Map:: R = (1, 61, 3, 63, 7, 67, 11, 71, 15, 75, 19, 79, 23, 83, 27, 87, 31, 91, 33, 93, 35, 95, 37, 97, 39, 99, 41, 101, 44, 104, 45, 105, 47, 107, 49, 109, 51, 111, 53, 113, 55, 115, 57, 117, 60, 120, 28, 88, 24, 84, 20, 80, 16, 76, 12, 72, 8, 68, 4, 64)(2, 62, 5, 65, 9, 69, 13, 73, 17, 77, 21, 81, 25, 85, 29, 89, 30, 90, 32, 92, 34, 94, 36, 96, 38, 98, 40, 100, 42, 102, 46, 106, 48, 108, 50, 110, 52, 112, 54, 114, 56, 116, 59, 119, 58, 118, 43, 103, 26, 86, 22, 82, 18, 78, 14, 74, 10, 70, 6, 66) L = (1, 62)(2, 61)(3, 65)(4, 66)(5, 63)(6, 64)(7, 69)(8, 70)(9, 67)(10, 68)(11, 73)(12, 74)(13, 71)(14, 72)(15, 77)(16, 78)(17, 75)(18, 76)(19, 81)(20, 82)(21, 79)(22, 80)(23, 85)(24, 86)(25, 83)(26, 84)(27, 89)(28, 103)(29, 87)(30, 91)(31, 90)(32, 93)(33, 92)(34, 95)(35, 94)(36, 97)(37, 96)(38, 99)(39, 98)(40, 101)(41, 100)(42, 104)(43, 88)(44, 102)(45, 106)(46, 105)(47, 108)(48, 107)(49, 110)(50, 109)(51, 112)(52, 111)(53, 114)(54, 113)(55, 116)(56, 115)(57, 119)(58, 120)(59, 117)(60, 118) local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) } Outer automorphisms :: reflexible Dual of E14.495 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 60 f = 32 degree seq :: [ 60^2 ] E14.497 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 30, 30}) Quotient :: dipole Aut^+ = C30 x C2 (small group id <60, 13>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^30, (Y3 * Y2^-1)^30 ] Map:: R = (1, 61, 2, 62)(3, 63, 5, 65)(4, 64, 6, 66)(7, 67, 9, 69)(8, 68, 10, 70)(11, 71, 13, 73)(12, 72, 14, 74)(15, 75, 17, 77)(16, 76, 18, 78)(19, 79, 21, 81)(20, 80, 22, 82)(23, 83, 25, 85)(24, 84, 26, 86)(27, 87, 41, 101)(28, 88, 49, 109)(29, 89, 30, 90)(31, 91, 33, 93)(32, 92, 34, 94)(35, 95, 37, 97)(36, 96, 38, 98)(39, 99, 40, 100)(42, 102, 43, 103)(44, 104, 45, 105)(46, 106, 47, 107)(48, 108, 60, 120)(50, 110, 51, 111)(52, 112, 54, 114)(53, 113, 55, 115)(56, 116, 58, 118)(57, 117, 59, 119)(121, 181, 123, 183, 127, 187, 131, 191, 135, 195, 139, 199, 143, 203, 147, 207, 156, 216, 152, 212, 149, 209, 151, 211, 155, 215, 159, 219, 162, 222, 164, 224, 166, 226, 168, 228, 177, 237, 173, 233, 170, 230, 172, 232, 176, 236, 148, 208, 144, 204, 140, 200, 136, 196, 132, 192, 128, 188, 124, 184)(122, 182, 125, 185, 129, 189, 133, 193, 137, 197, 141, 201, 145, 205, 161, 221, 158, 218, 154, 214, 150, 210, 153, 213, 157, 217, 160, 220, 163, 223, 165, 225, 167, 227, 180, 240, 179, 239, 175, 235, 171, 231, 174, 234, 178, 238, 169, 229, 146, 206, 142, 202, 138, 198, 134, 194, 130, 190, 126, 186) L = (1, 122)(2, 121)(3, 125)(4, 126)(5, 123)(6, 124)(7, 129)(8, 130)(9, 127)(10, 128)(11, 133)(12, 134)(13, 131)(14, 132)(15, 137)(16, 138)(17, 135)(18, 136)(19, 141)(20, 142)(21, 139)(22, 140)(23, 145)(24, 146)(25, 143)(26, 144)(27, 161)(28, 169)(29, 150)(30, 149)(31, 153)(32, 154)(33, 151)(34, 152)(35, 157)(36, 158)(37, 155)(38, 156)(39, 160)(40, 159)(41, 147)(42, 163)(43, 162)(44, 165)(45, 164)(46, 167)(47, 166)(48, 180)(49, 148)(50, 171)(51, 170)(52, 174)(53, 175)(54, 172)(55, 173)(56, 178)(57, 179)(58, 176)(59, 177)(60, 168)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 60, 2, 60 ), ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) } Outer automorphisms :: reflexible Dual of E14.498 Graph:: bipartite v = 32 e = 120 f = 62 degree seq :: [ 4^30, 60^2 ] E14.498 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 30, 30}) Quotient :: dipole Aut^+ = C30 x C2 (small group id <60, 13>) Aut = C2 x C2 x D30 (small group id <120, 46>) |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^-30, Y1^30 ] Map:: R = (1, 61, 2, 62, 5, 65, 9, 69, 13, 73, 17, 77, 21, 81, 25, 85, 31, 91, 34, 94, 36, 96, 38, 98, 40, 100, 42, 102, 44, 104, 49, 109, 46, 106, 47, 107, 50, 110, 52, 112, 54, 114, 56, 116, 58, 118, 28, 88, 24, 84, 20, 80, 16, 76, 12, 72, 8, 68, 4, 64)(3, 63, 6, 66, 10, 70, 14, 74, 18, 78, 22, 82, 26, 86, 32, 92, 29, 89, 30, 90, 33, 93, 35, 95, 37, 97, 39, 99, 41, 101, 43, 103, 48, 108, 51, 111, 53, 113, 55, 115, 57, 117, 59, 119, 60, 120, 45, 105, 27, 87, 23, 83, 19, 79, 15, 75, 11, 71, 7, 67)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 126)(3, 121)(4, 127)(5, 130)(6, 122)(7, 124)(8, 131)(9, 134)(10, 125)(11, 128)(12, 135)(13, 138)(14, 129)(15, 132)(16, 139)(17, 142)(18, 133)(19, 136)(20, 143)(21, 146)(22, 137)(23, 140)(24, 147)(25, 152)(26, 141)(27, 144)(28, 165)(29, 151)(30, 154)(31, 149)(32, 145)(33, 156)(34, 150)(35, 158)(36, 153)(37, 160)(38, 155)(39, 162)(40, 157)(41, 164)(42, 159)(43, 169)(44, 161)(45, 148)(46, 168)(47, 171)(48, 166)(49, 163)(50, 173)(51, 167)(52, 175)(53, 170)(54, 177)(55, 172)(56, 179)(57, 174)(58, 180)(59, 176)(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, 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 E14.497 Graph:: simple bipartite v = 62 e = 120 f = 32 degree seq :: [ 2^60, 60^2 ] E14.499 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 10, 35}) Quotient :: regular Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^3 * T2 * T1^-1 * T2 * T1^3, T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 33, 16, 28, 45, 60, 65, 51, 32, 48, 62, 69, 68, 54, 50, 64, 70, 67, 53, 35, 49, 63, 66, 52, 34, 17, 29, 42, 22, 10, 4)(3, 7, 15, 31, 30, 14, 6, 13, 27, 47, 46, 26, 12, 25, 44, 61, 58, 41, 24, 43, 59, 57, 40, 21, 39, 56, 55, 38, 20, 9, 19, 37, 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, 39)(25, 45)(26, 42)(27, 48)(30, 49)(31, 50)(36, 54)(37, 51)(38, 53)(40, 52)(43, 60)(44, 62)(46, 63)(47, 64)(55, 68)(56, 65)(57, 67)(58, 66)(59, 69)(61, 70) local type(s) :: { ( 10^35 ) } Outer automorphisms :: reflexible Dual of E14.500 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 35 f = 7 degree seq :: [ 35^2 ] E14.500 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 10, 35}) Quotient :: regular Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^10, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 32, 31, 19, 10, 4)(3, 7, 12, 22, 33, 47, 43, 28, 17, 8)(6, 13, 21, 34, 46, 45, 30, 18, 9, 14)(15, 25, 35, 49, 60, 57, 42, 27, 16, 26)(23, 36, 48, 61, 59, 44, 29, 38, 24, 37)(39, 53, 62, 70, 68, 56, 41, 55, 40, 54)(50, 63, 69, 67, 58, 66, 52, 65, 51, 64) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 33)(22, 35)(25, 39)(26, 40)(27, 41)(28, 42)(31, 43)(32, 46)(34, 48)(36, 50)(37, 51)(38, 52)(44, 58)(45, 59)(47, 60)(49, 62)(53, 66)(54, 67)(55, 63)(56, 64)(57, 68)(61, 69)(65, 70) local type(s) :: { ( 35^10 ) } Outer automorphisms :: reflexible Dual of E14.499 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 7 e = 35 f = 2 degree seq :: [ 10^7 ] E14.501 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 35}) Quotient :: edge Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^10, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 ] Map:: R = (1, 3, 8, 17, 28, 43, 31, 19, 10, 4)(2, 5, 12, 22, 35, 50, 38, 24, 14, 6)(7, 15, 26, 41, 56, 45, 30, 18, 9, 16)(11, 20, 33, 48, 63, 52, 37, 23, 13, 21)(25, 39, 54, 67, 59, 44, 29, 42, 27, 40)(32, 46, 61, 69, 66, 51, 36, 49, 34, 47)(53, 64, 70, 62, 58, 60, 57, 68, 55, 65)(71, 72)(73, 77)(74, 79)(75, 81)(76, 83)(78, 82)(80, 84)(85, 95)(86, 97)(87, 96)(88, 99)(89, 100)(90, 102)(91, 104)(92, 103)(93, 106)(94, 107)(98, 105)(101, 108)(109, 123)(110, 125)(111, 124)(112, 127)(113, 126)(114, 128)(115, 129)(116, 130)(117, 132)(118, 131)(119, 134)(120, 133)(121, 135)(122, 136)(137, 140)(138, 139) L = (1, 71)(2, 72)(3, 73)(4, 74)(5, 75)(6, 76)(7, 77)(8, 78)(9, 79)(10, 80)(11, 81)(12, 82)(13, 83)(14, 84)(15, 85)(16, 86)(17, 87)(18, 88)(19, 89)(20, 90)(21, 91)(22, 92)(23, 93)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 70, 70 ), ( 70^10 ) } Outer automorphisms :: reflexible Dual of E14.505 Transitivity :: ET+ Graph:: simple bipartite v = 42 e = 70 f = 2 degree seq :: [ 2^35, 10^7 ] E14.502 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 35}) Quotient :: edge Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, T2^-1 * T1 * T2 * T1^-1 * T2^-5, T2^3 * T1^-1 * T2 * T1^-2 * T2^2 * T1^-1, T1^10, T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1 * T2^4 * T1^2 * T2^2 * T1^2 * T2^2 * T1^2 * T2^2 * T1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 48, 39, 20, 13, 28, 51, 70, 66, 41, 30, 53, 62, 43, 69, 67, 55, 61, 34, 21, 42, 68, 65, 38, 18, 6, 17, 36, 59, 33, 15, 5)(2, 7, 19, 40, 45, 23, 9, 4, 12, 29, 54, 46, 24, 11, 27, 52, 64, 58, 47, 26, 50, 60, 37, 32, 57, 49, 63, 35, 16, 14, 31, 56, 44, 22, 8)(71, 72, 76, 86, 104, 130, 123, 97, 83, 74)(73, 79, 87, 78, 91, 105, 132, 120, 98, 81)(75, 84, 88, 107, 131, 122, 100, 82, 90, 77)(80, 94, 106, 93, 112, 92, 113, 133, 121, 96)(85, 102, 108, 134, 125, 99, 111, 89, 109, 101)(95, 117, 129, 116, 138, 115, 139, 114, 140, 119)(103, 128, 135, 124, 137, 110, 136, 126, 118, 127) L = (1, 71)(2, 72)(3, 73)(4, 74)(5, 75)(6, 76)(7, 77)(8, 78)(9, 79)(10, 80)(11, 81)(12, 82)(13, 83)(14, 84)(15, 85)(16, 86)(17, 87)(18, 88)(19, 89)(20, 90)(21, 91)(22, 92)(23, 93)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 4^10 ), ( 4^35 ) } Outer automorphisms :: reflexible Dual of E14.506 Transitivity :: ET+ Graph:: bipartite v = 9 e = 70 f = 35 degree seq :: [ 10^7, 35^2 ] E14.503 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 35}) Quotient :: edge Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^3 * T2 * T1^-1 * T2 * T1^3, T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 ] Map:: 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, 39)(25, 45)(26, 42)(27, 48)(30, 49)(31, 50)(36, 54)(37, 51)(38, 53)(40, 52)(43, 60)(44, 62)(46, 63)(47, 64)(55, 68)(56, 65)(57, 67)(58, 66)(59, 69)(61, 70)(71, 72, 75, 81, 93, 103, 86, 98, 115, 130, 135, 121, 102, 118, 132, 139, 138, 124, 120, 134, 140, 137, 123, 105, 119, 133, 136, 122, 104, 87, 99, 112, 92, 80, 74)(73, 77, 85, 101, 100, 84, 76, 83, 97, 117, 116, 96, 82, 95, 114, 131, 128, 111, 94, 113, 129, 127, 110, 91, 109, 126, 125, 108, 90, 79, 89, 107, 106, 88, 78) L = (1, 71)(2, 72)(3, 73)(4, 74)(5, 75)(6, 76)(7, 77)(8, 78)(9, 79)(10, 80)(11, 81)(12, 82)(13, 83)(14, 84)(15, 85)(16, 86)(17, 87)(18, 88)(19, 89)(20, 90)(21, 91)(22, 92)(23, 93)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 20, 20 ), ( 20^35 ) } Outer automorphisms :: reflexible Dual of E14.504 Transitivity :: ET+ Graph:: simple bipartite v = 37 e = 70 f = 7 degree seq :: [ 2^35, 35^2 ] E14.504 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 35}) Quotient :: loop Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^10, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 ] Map:: R = (1, 71, 3, 73, 8, 78, 17, 87, 28, 98, 43, 113, 31, 101, 19, 89, 10, 80, 4, 74)(2, 72, 5, 75, 12, 82, 22, 92, 35, 105, 50, 120, 38, 108, 24, 94, 14, 84, 6, 76)(7, 77, 15, 85, 26, 96, 41, 111, 56, 126, 45, 115, 30, 100, 18, 88, 9, 79, 16, 86)(11, 81, 20, 90, 33, 103, 48, 118, 63, 133, 52, 122, 37, 107, 23, 93, 13, 83, 21, 91)(25, 95, 39, 109, 54, 124, 67, 137, 59, 129, 44, 114, 29, 99, 42, 112, 27, 97, 40, 110)(32, 102, 46, 116, 61, 131, 69, 139, 66, 136, 51, 121, 36, 106, 49, 119, 34, 104, 47, 117)(53, 123, 64, 134, 70, 140, 62, 132, 58, 128, 60, 130, 57, 127, 68, 138, 55, 125, 65, 135) L = (1, 72)(2, 71)(3, 77)(4, 79)(5, 81)(6, 83)(7, 73)(8, 82)(9, 74)(10, 84)(11, 75)(12, 78)(13, 76)(14, 80)(15, 95)(16, 97)(17, 96)(18, 99)(19, 100)(20, 102)(21, 104)(22, 103)(23, 106)(24, 107)(25, 85)(26, 87)(27, 86)(28, 105)(29, 88)(30, 89)(31, 108)(32, 90)(33, 92)(34, 91)(35, 98)(36, 93)(37, 94)(38, 101)(39, 123)(40, 125)(41, 124)(42, 127)(43, 126)(44, 128)(45, 129)(46, 130)(47, 132)(48, 131)(49, 134)(50, 133)(51, 135)(52, 136)(53, 109)(54, 111)(55, 110)(56, 113)(57, 112)(58, 114)(59, 115)(60, 116)(61, 118)(62, 117)(63, 120)(64, 119)(65, 121)(66, 122)(67, 140)(68, 139)(69, 138)(70, 137) local type(s) :: { ( 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35 ) } Outer automorphisms :: reflexible Dual of E14.503 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 70 f = 37 degree seq :: [ 20^7 ] E14.505 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 35}) Quotient :: loop Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, T2^-1 * T1 * T2 * T1^-1 * T2^-5, T2^3 * T1^-1 * T2 * T1^-2 * T2^2 * T1^-1, T1^10, T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1 * T2^4 * T1^2 * T2^2 * T1^2 * T2^2 * T1^2 * T2^2 * T1 ] Map:: R = (1, 71, 3, 73, 10, 80, 25, 95, 48, 118, 39, 109, 20, 90, 13, 83, 28, 98, 51, 121, 70, 140, 66, 136, 41, 111, 30, 100, 53, 123, 62, 132, 43, 113, 69, 139, 67, 137, 55, 125, 61, 131, 34, 104, 21, 91, 42, 112, 68, 138, 65, 135, 38, 108, 18, 88, 6, 76, 17, 87, 36, 106, 59, 129, 33, 103, 15, 85, 5, 75)(2, 72, 7, 77, 19, 89, 40, 110, 45, 115, 23, 93, 9, 79, 4, 74, 12, 82, 29, 99, 54, 124, 46, 116, 24, 94, 11, 81, 27, 97, 52, 122, 64, 134, 58, 128, 47, 117, 26, 96, 50, 120, 60, 130, 37, 107, 32, 102, 57, 127, 49, 119, 63, 133, 35, 105, 16, 86, 14, 84, 31, 101, 56, 126, 44, 114, 22, 92, 8, 78) L = (1, 72)(2, 76)(3, 79)(4, 71)(5, 84)(6, 86)(7, 75)(8, 91)(9, 87)(10, 94)(11, 73)(12, 90)(13, 74)(14, 88)(15, 102)(16, 104)(17, 78)(18, 107)(19, 109)(20, 77)(21, 105)(22, 113)(23, 112)(24, 106)(25, 117)(26, 80)(27, 83)(28, 81)(29, 111)(30, 82)(31, 85)(32, 108)(33, 128)(34, 130)(35, 132)(36, 93)(37, 131)(38, 134)(39, 101)(40, 136)(41, 89)(42, 92)(43, 133)(44, 140)(45, 139)(46, 138)(47, 129)(48, 127)(49, 95)(50, 98)(51, 96)(52, 100)(53, 97)(54, 137)(55, 99)(56, 118)(57, 103)(58, 135)(59, 116)(60, 123)(61, 122)(62, 120)(63, 121)(64, 125)(65, 124)(66, 126)(67, 110)(68, 115)(69, 114)(70, 119) 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 ) } Outer automorphisms :: reflexible Dual of E14.501 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 70 f = 42 degree seq :: [ 70^2 ] E14.506 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 35}) Quotient :: loop Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^3 * T2 * T1^-1 * T2 * T1^3, T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 ] Map:: polytopal non-degenerate R = (1, 71, 3, 73)(2, 72, 6, 76)(4, 74, 9, 79)(5, 75, 12, 82)(7, 77, 16, 86)(8, 78, 17, 87)(10, 80, 21, 91)(11, 81, 24, 94)(13, 83, 28, 98)(14, 84, 29, 99)(15, 85, 32, 102)(18, 88, 35, 105)(19, 89, 33, 103)(20, 90, 34, 104)(22, 92, 41, 111)(23, 93, 39, 109)(25, 95, 45, 115)(26, 96, 42, 112)(27, 97, 48, 118)(30, 100, 49, 119)(31, 101, 50, 120)(36, 106, 54, 124)(37, 107, 51, 121)(38, 108, 53, 123)(40, 110, 52, 122)(43, 113, 60, 130)(44, 114, 62, 132)(46, 116, 63, 133)(47, 117, 64, 134)(55, 125, 68, 138)(56, 126, 65, 135)(57, 127, 67, 137)(58, 128, 66, 136)(59, 129, 69, 139)(61, 131, 70, 140) L = (1, 72)(2, 75)(3, 77)(4, 71)(5, 81)(6, 83)(7, 85)(8, 73)(9, 89)(10, 74)(11, 93)(12, 95)(13, 97)(14, 76)(15, 101)(16, 98)(17, 99)(18, 78)(19, 107)(20, 79)(21, 109)(22, 80)(23, 103)(24, 113)(25, 114)(26, 82)(27, 117)(28, 115)(29, 112)(30, 84)(31, 100)(32, 118)(33, 86)(34, 87)(35, 119)(36, 88)(37, 106)(38, 90)(39, 126)(40, 91)(41, 94)(42, 92)(43, 129)(44, 131)(45, 130)(46, 96)(47, 116)(48, 132)(49, 133)(50, 134)(51, 102)(52, 104)(53, 105)(54, 120)(55, 108)(56, 125)(57, 110)(58, 111)(59, 127)(60, 135)(61, 128)(62, 139)(63, 136)(64, 140)(65, 121)(66, 122)(67, 123)(68, 124)(69, 138)(70, 137) local type(s) :: { ( 10, 35, 10, 35 ) } Outer automorphisms :: reflexible Dual of E14.502 Transitivity :: ET+ VT+ AT Graph:: simple v = 35 e = 70 f = 9 degree seq :: [ 4^35 ] E14.507 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 35}) Quotient :: dipole Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, Y2^10, Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^35 ] Map:: R = (1, 71, 2, 72)(3, 73, 7, 77)(4, 74, 9, 79)(5, 75, 11, 81)(6, 76, 13, 83)(8, 78, 12, 82)(10, 80, 14, 84)(15, 85, 25, 95)(16, 86, 27, 97)(17, 87, 26, 96)(18, 88, 29, 99)(19, 89, 30, 100)(20, 90, 32, 102)(21, 91, 34, 104)(22, 92, 33, 103)(23, 93, 36, 106)(24, 94, 37, 107)(28, 98, 35, 105)(31, 101, 38, 108)(39, 109, 53, 123)(40, 110, 55, 125)(41, 111, 54, 124)(42, 112, 57, 127)(43, 113, 56, 126)(44, 114, 58, 128)(45, 115, 59, 129)(46, 116, 60, 130)(47, 117, 62, 132)(48, 118, 61, 131)(49, 119, 64, 134)(50, 120, 63, 133)(51, 121, 65, 135)(52, 122, 66, 136)(67, 137, 70, 140)(68, 138, 69, 139)(141, 211, 143, 213, 148, 218, 157, 227, 168, 238, 183, 253, 171, 241, 159, 229, 150, 220, 144, 214)(142, 212, 145, 215, 152, 222, 162, 232, 175, 245, 190, 260, 178, 248, 164, 234, 154, 224, 146, 216)(147, 217, 155, 225, 166, 236, 181, 251, 196, 266, 185, 255, 170, 240, 158, 228, 149, 219, 156, 226)(151, 221, 160, 230, 173, 243, 188, 258, 203, 273, 192, 262, 177, 247, 163, 233, 153, 223, 161, 231)(165, 235, 179, 249, 194, 264, 207, 277, 199, 269, 184, 254, 169, 239, 182, 252, 167, 237, 180, 250)(172, 242, 186, 256, 201, 271, 209, 279, 206, 276, 191, 261, 176, 246, 189, 259, 174, 244, 187, 257)(193, 263, 204, 274, 210, 280, 202, 272, 198, 268, 200, 270, 197, 267, 208, 278, 195, 265, 205, 275) L = (1, 142)(2, 141)(3, 147)(4, 149)(5, 151)(6, 153)(7, 143)(8, 152)(9, 144)(10, 154)(11, 145)(12, 148)(13, 146)(14, 150)(15, 165)(16, 167)(17, 166)(18, 169)(19, 170)(20, 172)(21, 174)(22, 173)(23, 176)(24, 177)(25, 155)(26, 157)(27, 156)(28, 175)(29, 158)(30, 159)(31, 178)(32, 160)(33, 162)(34, 161)(35, 168)(36, 163)(37, 164)(38, 171)(39, 193)(40, 195)(41, 194)(42, 197)(43, 196)(44, 198)(45, 199)(46, 200)(47, 202)(48, 201)(49, 204)(50, 203)(51, 205)(52, 206)(53, 179)(54, 181)(55, 180)(56, 183)(57, 182)(58, 184)(59, 185)(60, 186)(61, 188)(62, 187)(63, 190)(64, 189)(65, 191)(66, 192)(67, 210)(68, 209)(69, 208)(70, 207)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280) local type(s) :: { ( 2, 70, 2, 70 ), ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ) } Outer automorphisms :: reflexible Dual of E14.510 Graph:: bipartite v = 42 e = 140 f = 72 degree seq :: [ 4^35, 20^7 ] E14.508 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 35}) Quotient :: dipole Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y3^-1 * Y1^-1)^2, (Y2 * Y1)^2, R * Y2 * R * Y3, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1^2 * Y2 * Y1^-1, Y1^-1 * Y2^-1 * Y1 * Y2^6, Y2 * Y1^-1 * Y2^3 * Y1^-3 * Y2^2, Y1^10 ] Map:: R = (1, 71, 2, 72, 6, 76, 16, 86, 34, 104, 60, 130, 53, 123, 27, 97, 13, 83, 4, 74)(3, 73, 9, 79, 17, 87, 8, 78, 21, 91, 35, 105, 62, 132, 50, 120, 28, 98, 11, 81)(5, 75, 14, 84, 18, 88, 37, 107, 61, 131, 52, 122, 30, 100, 12, 82, 20, 90, 7, 77)(10, 80, 24, 94, 36, 106, 23, 93, 42, 112, 22, 92, 43, 113, 63, 133, 51, 121, 26, 96)(15, 85, 32, 102, 38, 108, 64, 134, 55, 125, 29, 99, 41, 111, 19, 89, 39, 109, 31, 101)(25, 95, 47, 117, 59, 129, 46, 116, 68, 138, 45, 115, 69, 139, 44, 114, 70, 140, 49, 119)(33, 103, 58, 128, 65, 135, 54, 124, 67, 137, 40, 110, 66, 136, 56, 126, 48, 118, 57, 127)(141, 211, 143, 213, 150, 220, 165, 235, 188, 258, 179, 249, 160, 230, 153, 223, 168, 238, 191, 261, 210, 280, 206, 276, 181, 251, 170, 240, 193, 263, 202, 272, 183, 253, 209, 279, 207, 277, 195, 265, 201, 271, 174, 244, 161, 231, 182, 252, 208, 278, 205, 275, 178, 248, 158, 228, 146, 216, 157, 227, 176, 246, 199, 269, 173, 243, 155, 225, 145, 215)(142, 212, 147, 217, 159, 229, 180, 250, 185, 255, 163, 233, 149, 219, 144, 214, 152, 222, 169, 239, 194, 264, 186, 256, 164, 234, 151, 221, 167, 237, 192, 262, 204, 274, 198, 268, 187, 257, 166, 236, 190, 260, 200, 270, 177, 247, 172, 242, 197, 267, 189, 259, 203, 273, 175, 245, 156, 226, 154, 224, 171, 241, 196, 266, 184, 254, 162, 232, 148, 218) L = (1, 143)(2, 147)(3, 150)(4, 152)(5, 141)(6, 157)(7, 159)(8, 142)(9, 144)(10, 165)(11, 167)(12, 169)(13, 168)(14, 171)(15, 145)(16, 154)(17, 176)(18, 146)(19, 180)(20, 153)(21, 182)(22, 148)(23, 149)(24, 151)(25, 188)(26, 190)(27, 192)(28, 191)(29, 194)(30, 193)(31, 196)(32, 197)(33, 155)(34, 161)(35, 156)(36, 199)(37, 172)(38, 158)(39, 160)(40, 185)(41, 170)(42, 208)(43, 209)(44, 162)(45, 163)(46, 164)(47, 166)(48, 179)(49, 203)(50, 200)(51, 210)(52, 204)(53, 202)(54, 186)(55, 201)(56, 184)(57, 189)(58, 187)(59, 173)(60, 177)(61, 174)(62, 183)(63, 175)(64, 198)(65, 178)(66, 181)(67, 195)(68, 205)(69, 207)(70, 206)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E14.509 Graph:: bipartite v = 9 e = 140 f = 105 degree seq :: [ 20^7, 70^2 ] E14.509 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 35}) Quotient :: dipole Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y3 * Y2 * Y3^-1 * Y2 * Y3^5, Y3^2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^2 * Y2, (Y3^-1 * Y1^-1)^35 ] Map:: polytopal R = (1, 71)(2, 72)(3, 73)(4, 74)(5, 75)(6, 76)(7, 77)(8, 78)(9, 79)(10, 80)(11, 81)(12, 82)(13, 83)(14, 84)(15, 85)(16, 86)(17, 87)(18, 88)(19, 89)(20, 90)(21, 91)(22, 92)(23, 93)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)(141, 211, 142, 212)(143, 213, 147, 217)(144, 214, 149, 219)(145, 215, 151, 221)(146, 216, 153, 223)(148, 218, 157, 227)(150, 220, 161, 231)(152, 222, 165, 235)(154, 224, 169, 239)(155, 225, 163, 233)(156, 226, 167, 237)(158, 228, 175, 245)(159, 229, 164, 234)(160, 230, 168, 238)(162, 232, 181, 251)(166, 236, 186, 256)(170, 240, 190, 260)(171, 241, 184, 254)(172, 242, 188, 258)(173, 243, 183, 253)(174, 244, 182, 252)(176, 246, 179, 249)(177, 247, 185, 255)(178, 248, 189, 259)(180, 250, 187, 257)(191, 261, 202, 272)(192, 262, 200, 270)(193, 263, 204, 274)(194, 264, 199, 269)(195, 265, 206, 276)(196, 266, 201, 271)(197, 267, 205, 275)(198, 268, 203, 273)(207, 277, 210, 280)(208, 278, 209, 279) L = (1, 143)(2, 145)(3, 148)(4, 141)(5, 152)(6, 142)(7, 155)(8, 158)(9, 159)(10, 144)(11, 163)(12, 166)(13, 167)(14, 146)(15, 171)(16, 147)(17, 173)(18, 176)(19, 177)(20, 149)(21, 179)(22, 150)(23, 183)(24, 151)(25, 184)(26, 172)(27, 182)(28, 153)(29, 188)(30, 154)(31, 191)(32, 156)(33, 192)(34, 157)(35, 194)(36, 164)(37, 170)(38, 160)(39, 196)(40, 161)(41, 175)(42, 162)(43, 199)(44, 200)(45, 165)(46, 202)(47, 168)(48, 204)(49, 169)(50, 186)(51, 193)(52, 207)(53, 174)(54, 208)(55, 178)(56, 195)(57, 180)(58, 181)(59, 201)(60, 209)(61, 185)(62, 210)(63, 187)(64, 203)(65, 189)(66, 190)(67, 198)(68, 197)(69, 206)(70, 205)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280) local type(s) :: { ( 20, 70 ), ( 20, 70, 20, 70 ) } Outer automorphisms :: reflexible Dual of E14.508 Graph:: simple bipartite v = 105 e = 140 f = 9 degree seq :: [ 2^70, 4^35 ] E14.510 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 35}) Quotient :: dipole Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3, Y1^5 * Y3 * Y1^-1 * Y3 * Y1, Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 ] Map:: R = (1, 71, 2, 72, 5, 75, 11, 81, 23, 93, 33, 103, 16, 86, 28, 98, 45, 115, 60, 130, 65, 135, 51, 121, 32, 102, 48, 118, 62, 132, 69, 139, 68, 138, 54, 124, 50, 120, 64, 134, 70, 140, 67, 137, 53, 123, 35, 105, 49, 119, 63, 133, 66, 136, 52, 122, 34, 104, 17, 87, 29, 99, 42, 112, 22, 92, 10, 80, 4, 74)(3, 73, 7, 77, 15, 85, 31, 101, 30, 100, 14, 84, 6, 76, 13, 83, 27, 97, 47, 117, 46, 116, 26, 96, 12, 82, 25, 95, 44, 114, 61, 131, 58, 128, 41, 111, 24, 94, 43, 113, 59, 129, 57, 127, 40, 110, 21, 91, 39, 109, 56, 126, 55, 125, 38, 108, 20, 90, 9, 79, 19, 89, 37, 107, 36, 106, 18, 88, 8, 78)(141, 211)(142, 212)(143, 213)(144, 214)(145, 215)(146, 216)(147, 217)(148, 218)(149, 219)(150, 220)(151, 221)(152, 222)(153, 223)(154, 224)(155, 225)(156, 226)(157, 227)(158, 228)(159, 229)(160, 230)(161, 231)(162, 232)(163, 233)(164, 234)(165, 235)(166, 236)(167, 237)(168, 238)(169, 239)(170, 240)(171, 241)(172, 242)(173, 243)(174, 244)(175, 245)(176, 246)(177, 247)(178, 248)(179, 249)(180, 250)(181, 251)(182, 252)(183, 253)(184, 254)(185, 255)(186, 256)(187, 257)(188, 258)(189, 259)(190, 260)(191, 261)(192, 262)(193, 263)(194, 264)(195, 265)(196, 266)(197, 267)(198, 268)(199, 269)(200, 270)(201, 271)(202, 272)(203, 273)(204, 274)(205, 275)(206, 276)(207, 277)(208, 278)(209, 279)(210, 280) L = (1, 143)(2, 146)(3, 141)(4, 149)(5, 152)(6, 142)(7, 156)(8, 157)(9, 144)(10, 161)(11, 164)(12, 145)(13, 168)(14, 169)(15, 172)(16, 147)(17, 148)(18, 175)(19, 173)(20, 174)(21, 150)(22, 181)(23, 179)(24, 151)(25, 185)(26, 182)(27, 188)(28, 153)(29, 154)(30, 189)(31, 190)(32, 155)(33, 159)(34, 160)(35, 158)(36, 194)(37, 191)(38, 193)(39, 163)(40, 192)(41, 162)(42, 166)(43, 200)(44, 202)(45, 165)(46, 203)(47, 204)(48, 167)(49, 170)(50, 171)(51, 177)(52, 180)(53, 178)(54, 176)(55, 208)(56, 205)(57, 207)(58, 206)(59, 209)(60, 183)(61, 210)(62, 184)(63, 186)(64, 187)(65, 196)(66, 198)(67, 197)(68, 195)(69, 199)(70, 201)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280) local type(s) :: { ( 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 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 E14.507 Graph:: simple bipartite v = 72 e = 140 f = 42 degree seq :: [ 2^70, 70^2 ] E14.511 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 35}) Quotient :: dipole Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, Y2^3 * Y1 * Y2^-1 * Y1 * Y2^3, Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1 * Y2^2 * Y1, (Y3 * Y2^-1)^10 ] Map:: R = (1, 71, 2, 72)(3, 73, 7, 77)(4, 74, 9, 79)(5, 75, 11, 81)(6, 76, 13, 83)(8, 78, 17, 87)(10, 80, 21, 91)(12, 82, 25, 95)(14, 84, 29, 99)(15, 85, 23, 93)(16, 86, 27, 97)(18, 88, 35, 105)(19, 89, 24, 94)(20, 90, 28, 98)(22, 92, 41, 111)(26, 96, 46, 116)(30, 100, 50, 120)(31, 101, 44, 114)(32, 102, 48, 118)(33, 103, 43, 113)(34, 104, 42, 112)(36, 106, 39, 109)(37, 107, 45, 115)(38, 108, 49, 119)(40, 110, 47, 117)(51, 121, 62, 132)(52, 122, 60, 130)(53, 123, 64, 134)(54, 124, 59, 129)(55, 125, 66, 136)(56, 126, 61, 131)(57, 127, 65, 135)(58, 128, 63, 133)(67, 137, 70, 140)(68, 138, 69, 139)(141, 211, 143, 213, 148, 218, 158, 228, 176, 246, 164, 234, 151, 221, 163, 233, 183, 253, 199, 269, 201, 271, 185, 255, 165, 235, 184, 254, 200, 270, 209, 279, 206, 276, 190, 260, 186, 256, 202, 272, 210, 280, 205, 275, 189, 259, 169, 239, 188, 258, 204, 274, 203, 273, 187, 257, 168, 238, 153, 223, 167, 237, 182, 252, 162, 232, 150, 220, 144, 214)(142, 212, 145, 215, 152, 222, 166, 236, 172, 242, 156, 226, 147, 217, 155, 225, 171, 241, 191, 261, 193, 263, 174, 244, 157, 227, 173, 243, 192, 262, 207, 277, 198, 268, 181, 251, 175, 245, 194, 264, 208, 278, 197, 267, 180, 250, 161, 231, 179, 249, 196, 266, 195, 265, 178, 248, 160, 230, 149, 219, 159, 229, 177, 247, 170, 240, 154, 224, 146, 216) L = (1, 142)(2, 141)(3, 147)(4, 149)(5, 151)(6, 153)(7, 143)(8, 157)(9, 144)(10, 161)(11, 145)(12, 165)(13, 146)(14, 169)(15, 163)(16, 167)(17, 148)(18, 175)(19, 164)(20, 168)(21, 150)(22, 181)(23, 155)(24, 159)(25, 152)(26, 186)(27, 156)(28, 160)(29, 154)(30, 190)(31, 184)(32, 188)(33, 183)(34, 182)(35, 158)(36, 179)(37, 185)(38, 189)(39, 176)(40, 187)(41, 162)(42, 174)(43, 173)(44, 171)(45, 177)(46, 166)(47, 180)(48, 172)(49, 178)(50, 170)(51, 202)(52, 200)(53, 204)(54, 199)(55, 206)(56, 201)(57, 205)(58, 203)(59, 194)(60, 192)(61, 196)(62, 191)(63, 198)(64, 193)(65, 197)(66, 195)(67, 210)(68, 209)(69, 208)(70, 207)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280) local type(s) :: { ( 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 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 E14.512 Graph:: bipartite v = 37 e = 140 f = 77 degree seq :: [ 4^35, 70^2 ] E14.512 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 35}) Quotient :: dipole Aut^+ = C5 x D14 (small group id <70, 2>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^-2 * Y3 * Y1^2, Y1 * Y3^-1 * Y1^-3 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3 * Y1^-1 * Y3^-5, (Y3^2 * Y1^-3)^2, (Y3 * Y2^-1)^35 ] Map:: R = (1, 71, 2, 72, 6, 76, 16, 86, 34, 104, 60, 130, 53, 123, 27, 97, 13, 83, 4, 74)(3, 73, 9, 79, 17, 87, 8, 78, 21, 91, 35, 105, 62, 132, 50, 120, 28, 98, 11, 81)(5, 75, 14, 84, 18, 88, 37, 107, 61, 131, 52, 122, 30, 100, 12, 82, 20, 90, 7, 77)(10, 80, 24, 94, 36, 106, 23, 93, 42, 112, 22, 92, 43, 113, 63, 133, 51, 121, 26, 96)(15, 85, 32, 102, 38, 108, 64, 134, 55, 125, 29, 99, 41, 111, 19, 89, 39, 109, 31, 101)(25, 95, 47, 117, 59, 129, 46, 116, 68, 138, 45, 115, 69, 139, 44, 114, 70, 140, 49, 119)(33, 103, 58, 128, 65, 135, 54, 124, 67, 137, 40, 110, 66, 136, 56, 126, 48, 118, 57, 127)(141, 211)(142, 212)(143, 213)(144, 214)(145, 215)(146, 216)(147, 217)(148, 218)(149, 219)(150, 220)(151, 221)(152, 222)(153, 223)(154, 224)(155, 225)(156, 226)(157, 227)(158, 228)(159, 229)(160, 230)(161, 231)(162, 232)(163, 233)(164, 234)(165, 235)(166, 236)(167, 237)(168, 238)(169, 239)(170, 240)(171, 241)(172, 242)(173, 243)(174, 244)(175, 245)(176, 246)(177, 247)(178, 248)(179, 249)(180, 250)(181, 251)(182, 252)(183, 253)(184, 254)(185, 255)(186, 256)(187, 257)(188, 258)(189, 259)(190, 260)(191, 261)(192, 262)(193, 263)(194, 264)(195, 265)(196, 266)(197, 267)(198, 268)(199, 269)(200, 270)(201, 271)(202, 272)(203, 273)(204, 274)(205, 275)(206, 276)(207, 277)(208, 278)(209, 279)(210, 280) L = (1, 143)(2, 147)(3, 150)(4, 152)(5, 141)(6, 157)(7, 159)(8, 142)(9, 144)(10, 165)(11, 167)(12, 169)(13, 168)(14, 171)(15, 145)(16, 154)(17, 176)(18, 146)(19, 180)(20, 153)(21, 182)(22, 148)(23, 149)(24, 151)(25, 188)(26, 190)(27, 192)(28, 191)(29, 194)(30, 193)(31, 196)(32, 197)(33, 155)(34, 161)(35, 156)(36, 199)(37, 172)(38, 158)(39, 160)(40, 185)(41, 170)(42, 208)(43, 209)(44, 162)(45, 163)(46, 164)(47, 166)(48, 179)(49, 203)(50, 200)(51, 210)(52, 204)(53, 202)(54, 186)(55, 201)(56, 184)(57, 189)(58, 187)(59, 173)(60, 177)(61, 174)(62, 183)(63, 175)(64, 198)(65, 178)(66, 181)(67, 195)(68, 205)(69, 207)(70, 206)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280) local type(s) :: { ( 4, 70 ), ( 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70 ) } Outer automorphisms :: reflexible Dual of E14.511 Graph:: simple bipartite v = 77 e = 140 f = 37 degree seq :: [ 2^70, 20^7 ] E14.513 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 3}) Quotient :: edge^2 Aut^+ = (C13 : C3) : C2 (small group id <78, 1>) Aut = C2 x ((C13 : C3) : C2) (small group id <156, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2, Y1^2 * Y2^-1, Y2^3, (R * Y3)^2, R * Y2 * R * Y1, 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^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 79, 4, 82)(2, 80, 5, 83)(3, 81, 6, 84)(7, 85, 13, 91)(8, 86, 14, 92)(9, 87, 15, 93)(10, 88, 16, 94)(11, 89, 17, 95)(12, 90, 18, 96)(19, 97, 31, 109)(20, 98, 32, 110)(21, 99, 33, 111)(22, 100, 34, 112)(23, 101, 35, 113)(24, 102, 36, 114)(25, 103, 37, 115)(26, 104, 38, 116)(27, 105, 39, 117)(28, 106, 40, 118)(29, 107, 41, 119)(30, 108, 42, 120)(43, 121, 58, 136)(44, 122, 59, 137)(45, 123, 60, 138)(46, 124, 61, 139)(47, 125, 62, 140)(48, 126, 63, 141)(49, 127, 64, 142)(50, 128, 65, 143)(51, 129, 66, 144)(52, 130, 67, 145)(53, 131, 68, 146)(54, 132, 69, 147)(55, 133, 70, 148)(56, 134, 71, 149)(57, 135, 72, 150)(73, 151, 76, 154)(74, 152, 77, 155)(75, 153, 78, 156)(157, 158, 159)(160, 163, 164)(161, 165, 166)(162, 167, 168)(169, 175, 176)(170, 177, 178)(171, 179, 180)(172, 181, 182)(173, 183, 184)(174, 185, 186)(187, 198, 199)(188, 200, 201)(189, 202, 203)(190, 204, 191)(192, 205, 206)(193, 207, 208)(194, 209, 195)(196, 210, 211)(197, 212, 213)(214, 220, 229)(215, 230, 224)(216, 223, 217)(218, 227, 226)(219, 225, 231)(221, 228, 222)(232, 234, 233)(235, 237, 236)(238, 242, 241)(239, 244, 243)(240, 246, 245)(247, 254, 253)(248, 256, 255)(249, 258, 257)(250, 260, 259)(251, 262, 261)(252, 264, 263)(265, 277, 276)(266, 279, 278)(267, 281, 280)(268, 269, 282)(270, 284, 283)(271, 286, 285)(272, 273, 287)(274, 289, 288)(275, 291, 290)(292, 307, 298)(293, 302, 308)(294, 295, 301)(296, 304, 305)(297, 309, 303)(299, 300, 306)(310, 311, 312) L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312) local type(s) :: { ( 8^3 ), ( 8^4 ) } Outer automorphisms :: reflexible Dual of E14.516 Graph:: simple bipartite v = 91 e = 156 f = 39 degree seq :: [ 3^52, 4^39 ] E14.514 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 3}) Quotient :: edge^2 Aut^+ = (C13 : C3) : C2 (small group id <78, 1>) Aut = C2 x ((C13 : C3) : C2) (small group id <156, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y1^2 * Y2^-1, Y2^3, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1^-1, Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1 * Y3 * Y1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 79, 4, 82)(2, 80, 5, 83)(3, 81, 6, 84)(7, 85, 13, 91)(8, 86, 14, 92)(9, 87, 15, 93)(10, 88, 16, 94)(11, 89, 17, 95)(12, 90, 18, 96)(19, 97, 31, 109)(20, 98, 32, 110)(21, 99, 33, 111)(22, 100, 34, 112)(23, 101, 35, 113)(24, 102, 36, 114)(25, 103, 37, 115)(26, 104, 38, 116)(27, 105, 39, 117)(28, 106, 40, 118)(29, 107, 41, 119)(30, 108, 42, 120)(43, 121, 58, 136)(44, 122, 59, 137)(45, 123, 60, 138)(46, 124, 61, 139)(47, 125, 62, 140)(48, 126, 63, 141)(49, 127, 64, 142)(50, 128, 65, 143)(51, 129, 66, 144)(52, 130, 67, 145)(53, 131, 68, 146)(54, 132, 69, 147)(55, 133, 70, 148)(56, 134, 71, 149)(57, 135, 72, 150)(73, 151, 76, 154)(74, 152, 77, 155)(75, 153, 78, 156)(157, 158, 159)(160, 163, 164)(161, 165, 166)(162, 167, 168)(169, 175, 176)(170, 177, 178)(171, 179, 180)(172, 181, 182)(173, 183, 184)(174, 185, 186)(187, 198, 199)(188, 200, 201)(189, 202, 203)(190, 204, 191)(192, 205, 206)(193, 207, 208)(194, 209, 195)(196, 210, 211)(197, 212, 213)(214, 229, 223)(215, 222, 221)(216, 225, 217)(218, 224, 230)(219, 231, 228)(220, 227, 226)(232, 234, 233)(235, 237, 236)(238, 242, 241)(239, 244, 243)(240, 246, 245)(247, 254, 253)(248, 256, 255)(249, 258, 257)(250, 260, 259)(251, 262, 261)(252, 264, 263)(265, 277, 276)(266, 279, 278)(267, 281, 280)(268, 269, 282)(270, 284, 283)(271, 286, 285)(272, 273, 287)(274, 289, 288)(275, 291, 290)(292, 301, 307)(293, 299, 300)(294, 295, 303)(296, 308, 302)(297, 306, 309)(298, 304, 305)(310, 311, 312) L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312) local type(s) :: { ( 8^3 ), ( 8^4 ) } Outer automorphisms :: reflexible Dual of E14.515 Graph:: simple bipartite v = 91 e = 156 f = 39 degree seq :: [ 3^52, 4^39 ] E14.515 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 3}) Quotient :: loop^2 Aut^+ = (C13 : C3) : C2 (small group id <78, 1>) Aut = C2 x ((C13 : C3) : C2) (small group id <156, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2, Y1^2 * Y2^-1, Y2^3, (R * Y3)^2, R * Y2 * R * Y1, 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^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 79, 157, 235, 4, 82, 160, 238)(2, 80, 158, 236, 5, 83, 161, 239)(3, 81, 159, 237, 6, 84, 162, 240)(7, 85, 163, 241, 13, 91, 169, 247)(8, 86, 164, 242, 14, 92, 170, 248)(9, 87, 165, 243, 15, 93, 171, 249)(10, 88, 166, 244, 16, 94, 172, 250)(11, 89, 167, 245, 17, 95, 173, 251)(12, 90, 168, 246, 18, 96, 174, 252)(19, 97, 175, 253, 31, 109, 187, 265)(20, 98, 176, 254, 32, 110, 188, 266)(21, 99, 177, 255, 33, 111, 189, 267)(22, 100, 178, 256, 34, 112, 190, 268)(23, 101, 179, 257, 35, 113, 191, 269)(24, 102, 180, 258, 36, 114, 192, 270)(25, 103, 181, 259, 37, 115, 193, 271)(26, 104, 182, 260, 38, 116, 194, 272)(27, 105, 183, 261, 39, 117, 195, 273)(28, 106, 184, 262, 40, 118, 196, 274)(29, 107, 185, 263, 41, 119, 197, 275)(30, 108, 186, 264, 42, 120, 198, 276)(43, 121, 199, 277, 58, 136, 214, 292)(44, 122, 200, 278, 59, 137, 215, 293)(45, 123, 201, 279, 60, 138, 216, 294)(46, 124, 202, 280, 61, 139, 217, 295)(47, 125, 203, 281, 62, 140, 218, 296)(48, 126, 204, 282, 63, 141, 219, 297)(49, 127, 205, 283, 64, 142, 220, 298)(50, 128, 206, 284, 65, 143, 221, 299)(51, 129, 207, 285, 66, 144, 222, 300)(52, 130, 208, 286, 67, 145, 223, 301)(53, 131, 209, 287, 68, 146, 224, 302)(54, 132, 210, 288, 69, 147, 225, 303)(55, 133, 211, 289, 70, 148, 226, 304)(56, 134, 212, 290, 71, 149, 227, 305)(57, 135, 213, 291, 72, 150, 228, 306)(73, 151, 229, 307, 76, 154, 232, 310)(74, 152, 230, 308, 77, 155, 233, 311)(75, 153, 231, 309, 78, 156, 234, 312) L = (1, 80)(2, 81)(3, 79)(4, 85)(5, 87)(6, 89)(7, 86)(8, 82)(9, 88)(10, 83)(11, 90)(12, 84)(13, 97)(14, 99)(15, 101)(16, 103)(17, 105)(18, 107)(19, 98)(20, 91)(21, 100)(22, 92)(23, 102)(24, 93)(25, 104)(26, 94)(27, 106)(28, 95)(29, 108)(30, 96)(31, 120)(32, 122)(33, 124)(34, 126)(35, 112)(36, 127)(37, 129)(38, 131)(39, 116)(40, 132)(41, 134)(42, 121)(43, 109)(44, 123)(45, 110)(46, 125)(47, 111)(48, 113)(49, 128)(50, 114)(51, 130)(52, 115)(53, 117)(54, 133)(55, 118)(56, 135)(57, 119)(58, 142)(59, 152)(60, 145)(61, 138)(62, 149)(63, 147)(64, 151)(65, 150)(66, 143)(67, 139)(68, 137)(69, 153)(70, 140)(71, 148)(72, 144)(73, 136)(74, 146)(75, 141)(76, 156)(77, 154)(78, 155)(157, 237)(158, 235)(159, 236)(160, 242)(161, 244)(162, 246)(163, 238)(164, 241)(165, 239)(166, 243)(167, 240)(168, 245)(169, 254)(170, 256)(171, 258)(172, 260)(173, 262)(174, 264)(175, 247)(176, 253)(177, 248)(178, 255)(179, 249)(180, 257)(181, 250)(182, 259)(183, 251)(184, 261)(185, 252)(186, 263)(187, 277)(188, 279)(189, 281)(190, 269)(191, 282)(192, 284)(193, 286)(194, 273)(195, 287)(196, 289)(197, 291)(198, 265)(199, 276)(200, 266)(201, 278)(202, 267)(203, 280)(204, 268)(205, 270)(206, 283)(207, 271)(208, 285)(209, 272)(210, 274)(211, 288)(212, 275)(213, 290)(214, 307)(215, 302)(216, 295)(217, 301)(218, 304)(219, 309)(220, 292)(221, 300)(222, 306)(223, 294)(224, 308)(225, 297)(226, 305)(227, 296)(228, 299)(229, 298)(230, 293)(231, 303)(232, 311)(233, 312)(234, 310) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E14.514 Transitivity :: VT+ Graph:: v = 39 e = 156 f = 91 degree seq :: [ 8^39 ] E14.516 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 3}) Quotient :: loop^2 Aut^+ = (C13 : C3) : C2 (small group id <78, 1>) Aut = C2 x ((C13 : C3) : C2) (small group id <156, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y1^2 * Y2^-1, Y2^3, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1^-1, Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1 * Y3 * Y1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 79, 157, 235, 4, 82, 160, 238)(2, 80, 158, 236, 5, 83, 161, 239)(3, 81, 159, 237, 6, 84, 162, 240)(7, 85, 163, 241, 13, 91, 169, 247)(8, 86, 164, 242, 14, 92, 170, 248)(9, 87, 165, 243, 15, 93, 171, 249)(10, 88, 166, 244, 16, 94, 172, 250)(11, 89, 167, 245, 17, 95, 173, 251)(12, 90, 168, 246, 18, 96, 174, 252)(19, 97, 175, 253, 31, 109, 187, 265)(20, 98, 176, 254, 32, 110, 188, 266)(21, 99, 177, 255, 33, 111, 189, 267)(22, 100, 178, 256, 34, 112, 190, 268)(23, 101, 179, 257, 35, 113, 191, 269)(24, 102, 180, 258, 36, 114, 192, 270)(25, 103, 181, 259, 37, 115, 193, 271)(26, 104, 182, 260, 38, 116, 194, 272)(27, 105, 183, 261, 39, 117, 195, 273)(28, 106, 184, 262, 40, 118, 196, 274)(29, 107, 185, 263, 41, 119, 197, 275)(30, 108, 186, 264, 42, 120, 198, 276)(43, 121, 199, 277, 58, 136, 214, 292)(44, 122, 200, 278, 59, 137, 215, 293)(45, 123, 201, 279, 60, 138, 216, 294)(46, 124, 202, 280, 61, 139, 217, 295)(47, 125, 203, 281, 62, 140, 218, 296)(48, 126, 204, 282, 63, 141, 219, 297)(49, 127, 205, 283, 64, 142, 220, 298)(50, 128, 206, 284, 65, 143, 221, 299)(51, 129, 207, 285, 66, 144, 222, 300)(52, 130, 208, 286, 67, 145, 223, 301)(53, 131, 209, 287, 68, 146, 224, 302)(54, 132, 210, 288, 69, 147, 225, 303)(55, 133, 211, 289, 70, 148, 226, 304)(56, 134, 212, 290, 71, 149, 227, 305)(57, 135, 213, 291, 72, 150, 228, 306)(73, 151, 229, 307, 76, 154, 232, 310)(74, 152, 230, 308, 77, 155, 233, 311)(75, 153, 231, 309, 78, 156, 234, 312) L = (1, 80)(2, 81)(3, 79)(4, 85)(5, 87)(6, 89)(7, 86)(8, 82)(9, 88)(10, 83)(11, 90)(12, 84)(13, 97)(14, 99)(15, 101)(16, 103)(17, 105)(18, 107)(19, 98)(20, 91)(21, 100)(22, 92)(23, 102)(24, 93)(25, 104)(26, 94)(27, 106)(28, 95)(29, 108)(30, 96)(31, 120)(32, 122)(33, 124)(34, 126)(35, 112)(36, 127)(37, 129)(38, 131)(39, 116)(40, 132)(41, 134)(42, 121)(43, 109)(44, 123)(45, 110)(46, 125)(47, 111)(48, 113)(49, 128)(50, 114)(51, 130)(52, 115)(53, 117)(54, 133)(55, 118)(56, 135)(57, 119)(58, 151)(59, 144)(60, 147)(61, 138)(62, 146)(63, 153)(64, 149)(65, 137)(66, 143)(67, 136)(68, 152)(69, 139)(70, 142)(71, 148)(72, 141)(73, 145)(74, 140)(75, 150)(76, 156)(77, 154)(78, 155)(157, 237)(158, 235)(159, 236)(160, 242)(161, 244)(162, 246)(163, 238)(164, 241)(165, 239)(166, 243)(167, 240)(168, 245)(169, 254)(170, 256)(171, 258)(172, 260)(173, 262)(174, 264)(175, 247)(176, 253)(177, 248)(178, 255)(179, 249)(180, 257)(181, 250)(182, 259)(183, 251)(184, 261)(185, 252)(186, 263)(187, 277)(188, 279)(189, 281)(190, 269)(191, 282)(192, 284)(193, 286)(194, 273)(195, 287)(196, 289)(197, 291)(198, 265)(199, 276)(200, 266)(201, 278)(202, 267)(203, 280)(204, 268)(205, 270)(206, 283)(207, 271)(208, 285)(209, 272)(210, 274)(211, 288)(212, 275)(213, 290)(214, 301)(215, 299)(216, 295)(217, 303)(218, 308)(219, 306)(220, 304)(221, 300)(222, 293)(223, 307)(224, 296)(225, 294)(226, 305)(227, 298)(228, 309)(229, 292)(230, 302)(231, 297)(232, 311)(233, 312)(234, 310) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E14.513 Transitivity :: VT+ Graph:: v = 39 e = 156 f = 91 degree seq :: [ 8^39 ] E14.517 :: Family: { 5P } :: Oriented family(ies): { E5b } Signature :: (0; {2, 2, 3, 3}) Quotient :: dipole Aut^+ = (C13 : C3) : C2 (small group id <78, 1>) Aut = (C13 : C4) : C3 (small group id <156, 7>) |r| :: 12 Presentation :: [ Y1^2, Y2^2, R^2 * Y3^-1, R^-1 * Y1 * R * Y2, Y2 * R^-1 * Y1 * R, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y1, Y3^-1 * Y2 * Y1 * Y3^-2 * Y1, Y3^6, (Y3 * Y2)^3, R * Y1 * Y2 * Y1 * R^-1 * Y2, Y2 * Y3^2 * Y2 * Y3^-1 * Y1 * Y3^2 ] Map:: polyhedral non-degenerate R = (1, 79, 2, 80)(3, 81, 9, 87)(4, 82, 12, 90)(5, 83, 15, 93)(6, 84, 18, 96)(7, 85, 21, 99)(8, 86, 24, 102)(10, 88, 26, 104)(11, 89, 31, 109)(13, 91, 35, 113)(14, 92, 25, 103)(16, 94, 23, 101)(17, 95, 19, 97)(20, 98, 46, 124)(22, 100, 50, 128)(27, 105, 57, 135)(28, 106, 56, 134)(29, 107, 60, 138)(30, 108, 54, 132)(32, 110, 59, 137)(33, 111, 58, 136)(34, 112, 55, 133)(36, 114, 61, 139)(37, 115, 63, 141)(38, 116, 64, 142)(39, 117, 45, 123)(40, 118, 49, 127)(41, 119, 43, 121)(42, 120, 68, 146)(44, 122, 71, 149)(47, 125, 70, 148)(48, 126, 69, 147)(51, 129, 72, 150)(52, 130, 74, 152)(53, 131, 75, 153)(62, 140, 77, 155)(65, 143, 76, 154)(66, 144, 73, 151)(67, 145, 78, 156)(157, 235, 159, 237)(158, 236, 162, 240)(160, 238, 169, 247)(161, 239, 172, 250)(163, 241, 178, 256)(164, 242, 181, 259)(165, 243, 183, 261)(166, 244, 185, 263)(167, 245, 188, 266)(168, 246, 177, 255)(170, 248, 193, 271)(171, 249, 195, 273)(173, 251, 197, 275)(174, 252, 198, 276)(175, 253, 200, 278)(176, 254, 203, 281)(179, 257, 208, 286)(180, 258, 210, 288)(182, 260, 212, 290)(184, 262, 204, 282)(186, 264, 201, 279)(187, 265, 219, 297)(189, 267, 199, 277)(190, 268, 220, 298)(191, 269, 216, 294)(192, 270, 207, 285)(194, 272, 222, 300)(196, 274, 213, 291)(202, 280, 230, 308)(205, 283, 231, 309)(206, 284, 227, 305)(209, 287, 233, 311)(211, 289, 224, 302)(214, 292, 234, 312)(215, 293, 232, 310)(217, 295, 229, 307)(218, 296, 228, 306)(221, 299, 226, 304)(223, 301, 225, 303) L = (1, 160)(2, 163)(3, 166)(4, 170)(5, 157)(6, 175)(7, 179)(8, 158)(9, 184)(10, 186)(11, 159)(12, 180)(13, 188)(14, 194)(15, 174)(16, 196)(17, 161)(18, 199)(19, 201)(20, 162)(21, 171)(22, 203)(23, 209)(24, 165)(25, 211)(26, 164)(27, 214)(28, 215)(29, 172)(30, 218)(31, 213)(32, 198)(33, 167)(34, 168)(35, 221)(36, 169)(37, 207)(38, 173)(39, 220)(40, 206)(41, 202)(42, 225)(43, 226)(44, 181)(45, 229)(46, 224)(47, 183)(48, 176)(49, 177)(50, 232)(51, 178)(52, 192)(53, 182)(54, 231)(55, 191)(56, 187)(57, 197)(58, 193)(59, 190)(60, 230)(61, 185)(62, 189)(63, 233)(64, 227)(65, 228)(66, 234)(67, 195)(68, 212)(69, 208)(70, 205)(71, 219)(72, 200)(73, 204)(74, 222)(75, 216)(76, 217)(77, 223)(78, 210)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312) local type(s) :: { ( 6^4 ) } Outer automorphisms :: reflexible Dual of E14.518 Transitivity :: VT Graph:: simple bipartite v = 78 e = 156 f = 52 degree seq :: [ 4^78 ] E14.518 :: Family: { 5P } :: Oriented family(ies): { E5b } Signature :: (0; {2, 2, 3, 3}) Quotient :: dipole Aut^+ = (C13 : C3) : C2 (small group id <78, 1>) Aut = (C13 : C4) : C3 (small group id <156, 7>) |r| :: 12 Presentation :: [ Y1^3, Y2^3, R^2 * Y3^-1, Y2 * R^-1 * Y1 * R, (Y3^-1 * Y1^-1)^2, (Y3 * Y2^-1)^2, R^-1 * Y1^-1 * R^-1 * Y2 * Y3^-1, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, Y1 * Y2 * Y3^-1 * Y2 * Y1 * Y3, (Y2 * Y1^-1)^3, (Y2 * Y3 * Y1^-1)^2, Y3^6, Y2^-1 * R * Y1^-1 * Y2^-1 * Y1^-1 * R^-1, Y1 * Y3 * Y2^-1 * Y1^-1 * Y2 * Y3 * Y2, Y2 * Y1^-1 * Y2 * Y1 * Y2^-1 * R * Y1 * R^-1 ] Map:: polyhedral non-degenerate R = (1, 79, 2, 80, 5, 83)(3, 81, 12, 90, 14, 92)(4, 82, 16, 94, 19, 97)(6, 84, 23, 101, 25, 103)(7, 85, 27, 105, 9, 87)(8, 86, 30, 108, 29, 107)(10, 88, 35, 113, 18, 96)(11, 89, 24, 102, 21, 99)(13, 91, 42, 120, 37, 115)(15, 93, 46, 124, 40, 118)(17, 95, 49, 127, 36, 114)(20, 98, 54, 132, 38, 116)(22, 100, 58, 136, 34, 112)(26, 104, 57, 135, 61, 139)(28, 106, 55, 133, 65, 143)(31, 109, 53, 131, 48, 126)(32, 110, 71, 149, 43, 121)(33, 111, 72, 150, 59, 137)(39, 117, 66, 144, 47, 125)(41, 119, 62, 140, 44, 122)(45, 123, 50, 128, 73, 151)(51, 129, 64, 142, 60, 138)(52, 130, 70, 148, 68, 146)(56, 134, 78, 156, 69, 147)(63, 141, 76, 154, 67, 145)(74, 152, 77, 155, 75, 153)(157, 235, 159, 237, 162, 240)(158, 236, 164, 242, 166, 244)(160, 238, 173, 251, 171, 249)(161, 239, 176, 254, 178, 256)(163, 241, 180, 258, 184, 262)(165, 243, 189, 267, 188, 266)(167, 245, 175, 253, 193, 271)(168, 246, 195, 273, 197, 275)(169, 247, 199, 277, 182, 260)(170, 248, 191, 269, 201, 279)(172, 250, 183, 261, 204, 282)(174, 252, 208, 286, 207, 285)(177, 255, 213, 291, 212, 290)(179, 257, 216, 294, 194, 272)(181, 259, 218, 296, 219, 297)(185, 263, 214, 292, 223, 301)(186, 264, 200, 278, 224, 302)(187, 265, 225, 303, 192, 270)(190, 268, 203, 281, 206, 284)(196, 274, 215, 293, 211, 289)(198, 276, 202, 280, 231, 309)(205, 283, 217, 295, 228, 306)(209, 287, 227, 305, 230, 308)(210, 288, 226, 304, 222, 300)(220, 298, 232, 310, 229, 307)(221, 299, 234, 312, 233, 311) L = (1, 160)(2, 165)(3, 169)(4, 174)(5, 177)(6, 180)(7, 157)(8, 187)(9, 190)(10, 175)(11, 158)(12, 196)(13, 200)(14, 172)(15, 159)(16, 161)(17, 206)(18, 209)(19, 168)(20, 211)(21, 181)(22, 183)(23, 217)(24, 210)(25, 198)(26, 162)(27, 186)(28, 214)(29, 163)(30, 199)(31, 226)(32, 164)(33, 219)(34, 221)(35, 205)(36, 166)(37, 179)(38, 167)(39, 230)(40, 229)(41, 193)(42, 170)(43, 232)(44, 233)(45, 202)(46, 222)(47, 171)(48, 191)(49, 216)(50, 189)(51, 173)(52, 212)(53, 185)(54, 225)(55, 195)(56, 176)(57, 207)(58, 228)(59, 178)(60, 234)(61, 223)(62, 188)(63, 213)(64, 182)(65, 194)(66, 184)(67, 227)(68, 204)(69, 220)(70, 231)(71, 197)(72, 201)(73, 192)(74, 208)(75, 218)(76, 215)(77, 203)(78, 224)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312) local type(s) :: { ( 4^6 ) } Outer automorphisms :: reflexible Dual of E14.517 Transitivity :: VT Graph:: simple bipartite v = 52 e = 156 f = 78 degree seq :: [ 6^52 ] E14.519 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 6, 6}) Quotient :: edge Aut^+ = (C13 : C3) : C2 (small group id <78, 1>) Aut = (C13 : C3) : C2 (small group id <78, 1>) |r| :: 1 Presentation :: [ X1^3, (X2 * X1^-1)^2, X2^6, X2^-3 * X1^-1 * X2^-1 * X1^-1 * X2^-2 * X1^-1 * X2^-2 * X1^-1, (X2^-1 * X1^-1)^6 ] 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, 65)(59, 68, 69)(61, 76, 63)(66, 67, 75)(74, 77, 78)(79, 81, 87, 98, 91, 83)(80, 84, 93, 107, 94, 85)(82, 88, 99, 115, 100, 89)(86, 95, 109, 127, 110, 96)(90, 101, 117, 137, 118, 102)(92, 104, 120, 141, 121, 105)(97, 111, 129, 152, 130, 112)(103, 113, 131, 142, 139, 119)(106, 122, 143, 155, 144, 123)(108, 124, 145, 138, 146, 125)(114, 132, 153, 156, 151, 133)(116, 134, 150, 128, 149, 135)(126, 147, 136, 154, 140, 148) L = (1, 79)(2, 80)(3, 81)(4, 82)(5, 83)(6, 84)(7, 85)(8, 86)(9, 87)(10, 88)(11, 89)(12, 90)(13, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 97)(20, 98)(21, 99)(22, 100)(23, 101)(24, 102)(25, 103)(26, 104)(27, 105)(28, 106)(29, 107)(30, 108)(31, 109)(32, 110)(33, 111)(34, 112)(35, 113)(36, 114)(37, 115)(38, 116)(39, 117)(40, 118)(41, 119)(42, 120)(43, 121)(44, 122)(45, 123)(46, 124)(47, 125)(48, 126)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 133)(56, 134)(57, 135)(58, 136)(59, 137)(60, 138)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 145)(68, 146)(69, 147)(70, 148)(71, 149)(72, 150)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156) local type(s) :: { ( 12^3 ), ( 12^6 ) } Outer automorphisms :: chiral Dual of E14.520 Transitivity :: ET+ Graph:: simple bipartite v = 39 e = 78 f = 13 degree seq :: [ 3^26, 6^13 ] E14.520 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 6, 6}) Quotient :: loop Aut^+ = (C13 : C3) : C2 (small group id <78, 1>) Aut = (C13 : C3) : C2 (small group id <78, 1>) |r| :: 1 Presentation :: [ (X2^-2 * X1^-1)^2, (X1^-1 * X2^-1 * X1^-1)^2, X2^-1 * X1^-1 * X2 * X1 * X2 * X1^-1, X1^6, X2^6, X2^2 * X1^-1 * X2 * X1^-1 * X2 * X1^-2 ] Map:: polytopal non-degenerate R = (1, 79, 2, 80, 6, 84, 18, 96, 13, 91, 4, 82)(3, 81, 9, 87, 27, 105, 55, 133, 33, 111, 11, 89)(5, 83, 15, 93, 38, 116, 44, 122, 19, 97, 16, 94)(7, 85, 21, 99, 14, 92, 34, 112, 51, 129, 23, 101)(8, 86, 24, 102, 52, 130, 68, 146, 41, 119, 25, 103)(10, 88, 29, 107, 57, 135, 78, 156, 60, 138, 31, 109)(12, 90, 28, 106, 42, 120, 69, 147, 63, 141, 36, 114)(17, 95, 40, 118, 62, 140, 76, 154, 49, 127, 22, 100)(20, 98, 45, 123, 74, 152, 65, 143, 37, 115, 46, 124)(26, 104, 54, 132, 32, 110, 58, 136, 72, 150, 43, 121)(30, 108, 59, 137, 67, 145, 47, 125, 75, 153, 50, 128)(35, 113, 56, 134, 77, 155, 66, 144, 71, 149, 53, 131)(39, 117, 64, 142, 70, 148, 61, 139, 73, 151, 48, 126) L = (1, 81)(2, 85)(3, 88)(4, 90)(5, 79)(6, 97)(7, 100)(8, 80)(9, 99)(10, 108)(11, 110)(12, 113)(13, 115)(14, 82)(15, 101)(16, 103)(17, 83)(18, 119)(19, 121)(20, 84)(21, 94)(22, 126)(23, 128)(24, 122)(25, 124)(26, 86)(27, 91)(28, 87)(29, 92)(30, 95)(31, 123)(32, 139)(33, 131)(34, 89)(35, 136)(36, 140)(37, 142)(38, 127)(39, 93)(40, 129)(41, 145)(42, 96)(43, 149)(44, 151)(45, 146)(46, 106)(47, 98)(48, 104)(49, 147)(50, 155)(51, 109)(52, 150)(53, 102)(54, 116)(55, 114)(56, 105)(57, 111)(58, 107)(59, 112)(60, 148)(61, 152)(62, 153)(63, 117)(64, 154)(65, 156)(66, 118)(67, 138)(68, 144)(69, 143)(70, 120)(71, 125)(72, 133)(73, 135)(74, 137)(75, 130)(76, 134)(77, 141)(78, 132) local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: chiral Dual of E14.519 Transitivity :: ET+ VT+ Graph:: v = 13 e = 78 f = 39 degree seq :: [ 12^13 ] E14.521 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 6, 6}) Quotient :: edge Aut^+ = C2 x (C13 : C3) (small group id <78, 2>) Aut = C2 x (C13 : C3) (small group id <78, 2>) |r| :: 1 Presentation :: [ X1^3, X2^6, X2 * X1 * X2 * X1 * X2^-2 * X1, X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2^-1 ] 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, 44, 53)(25, 42, 56)(27, 58, 48)(28, 47, 35)(34, 49, 65)(36, 63, 62)(37, 61, 66)(45, 64, 46)(51, 71, 72)(54, 59, 68)(55, 73, 77)(57, 78, 75)(60, 76, 69)(67, 70, 74)(79, 81, 87, 103, 93, 83)(80, 84, 95, 120, 99, 85)(82, 89, 108, 134, 112, 90)(86, 100, 129, 117, 111, 101)(88, 105, 137, 118, 138, 106)(91, 113, 133, 102, 132, 114)(92, 115, 94, 104, 135, 116)(96, 122, 148, 128, 149, 123)(97, 124, 146, 119, 145, 125)(98, 126, 107, 121, 147, 127)(109, 139, 155, 143, 156, 140)(110, 141, 152, 130, 151, 142)(131, 153, 136, 150, 144, 154) L = (1, 79)(2, 80)(3, 81)(4, 82)(5, 83)(6, 84)(7, 85)(8, 86)(9, 87)(10, 88)(11, 89)(12, 90)(13, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 97)(20, 98)(21, 99)(22, 100)(23, 101)(24, 102)(25, 103)(26, 104)(27, 105)(28, 106)(29, 107)(30, 108)(31, 109)(32, 110)(33, 111)(34, 112)(35, 113)(36, 114)(37, 115)(38, 116)(39, 117)(40, 118)(41, 119)(42, 120)(43, 121)(44, 122)(45, 123)(46, 124)(47, 125)(48, 126)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 133)(56, 134)(57, 135)(58, 136)(59, 137)(60, 138)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 145)(68, 146)(69, 147)(70, 148)(71, 149)(72, 150)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156) local type(s) :: { ( 12^3 ), ( 12^6 ) } Outer automorphisms :: chiral Dual of E14.522 Transitivity :: ET+ Graph:: simple bipartite v = 39 e = 78 f = 13 degree seq :: [ 3^26, 6^13 ] E14.522 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 6, 6}) Quotient :: loop Aut^+ = C2 x (C13 : C3) (small group id <78, 2>) Aut = C2 x (C13 : C3) (small group id <78, 2>) |r| :: 1 Presentation :: [ X1^6, X2^6, X1^2 * X2^3 * X1, (X2^-1 * X1^-1)^3, X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1^-1 ] Map:: non-degenerate R = (1, 79, 2, 80, 6, 84, 18, 96, 13, 91, 4, 82)(3, 81, 9, 87, 27, 105, 17, 95, 33, 111, 11, 89)(5, 83, 15, 93, 31, 109, 10, 88, 30, 108, 16, 94)(7, 85, 21, 99, 45, 123, 26, 104, 50, 128, 23, 101)(8, 86, 24, 102, 48, 126, 22, 100, 47, 125, 25, 103)(12, 90, 35, 113, 42, 120, 19, 97, 41, 119, 36, 114)(14, 92, 37, 115, 44, 122, 20, 98, 43, 121, 28, 106)(29, 107, 49, 127, 77, 155, 57, 135, 72, 150, 58, 136)(32, 110, 61, 139, 67, 145, 55, 133, 78, 156, 54, 132)(34, 112, 53, 131, 38, 116, 56, 134, 76, 154, 59, 137)(39, 117, 64, 142, 69, 147, 60, 138, 70, 148, 63, 141)(40, 118, 62, 140, 74, 152, 46, 124, 68, 146, 66, 144)(51, 129, 71, 149, 52, 130, 73, 151, 65, 143, 75, 153) L = (1, 81)(2, 85)(3, 88)(4, 90)(5, 79)(6, 97)(7, 100)(8, 80)(9, 106)(10, 96)(11, 110)(12, 98)(13, 104)(14, 82)(15, 116)(16, 118)(17, 83)(18, 95)(19, 92)(20, 84)(21, 94)(22, 91)(23, 127)(24, 130)(25, 132)(26, 86)(27, 133)(28, 135)(29, 87)(30, 137)(31, 124)(32, 134)(33, 122)(34, 89)(35, 126)(36, 140)(37, 142)(38, 138)(39, 93)(40, 128)(41, 103)(42, 146)(43, 148)(44, 107)(45, 150)(46, 99)(47, 153)(48, 145)(49, 151)(50, 109)(51, 101)(52, 154)(53, 102)(54, 113)(55, 112)(56, 105)(57, 111)(58, 152)(59, 117)(60, 108)(61, 155)(62, 147)(63, 114)(64, 149)(65, 115)(66, 156)(67, 119)(68, 141)(69, 120)(70, 143)(71, 121)(72, 129)(73, 123)(74, 139)(75, 131)(76, 125)(77, 144)(78, 136) local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: chiral Dual of E14.521 Transitivity :: ET+ VT+ Graph:: v = 13 e = 78 f = 39 degree seq :: [ 12^13 ] E14.523 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 20}) Quotient :: regular Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^-2 * T2 * T1^5 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1, (T1 * T2)^8, T1^20 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 65, 78, 75, 79, 76, 80, 77, 64, 46, 31, 19, 10, 4)(3, 7, 15, 25, 39, 55, 74, 54, 72, 52, 71, 53, 73, 63, 66, 49, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 61, 70, 60, 43, 58, 41, 57, 42, 59, 67, 48, 34, 21, 14)(16, 26, 17, 28, 35, 51, 68, 62, 45, 30, 37, 23, 36, 24, 38, 50, 69, 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, 69)(56, 67)(57, 75)(58, 76)(59, 65)(60, 77)(64, 74)(71, 79)(72, 80)(73, 78) local type(s) :: { ( 8^20 ) } Outer automorphisms :: reflexible Dual of E14.524 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 40 f = 10 degree seq :: [ 20^4 ] E14.524 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 20}) Quotient :: regular Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, T1^8, T2 * T1^-1 * T2 * T1^2 * 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^-1 * 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, 79, 74, 77, 76, 78, 75, 80) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 31)(22, 33)(25, 37)(26, 38)(27, 39)(28, 40)(32, 42)(34, 44)(35, 45)(36, 46)(41, 51)(43, 52)(47, 57)(48, 58)(49, 59)(50, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80) local type(s) :: { ( 20^8 ) } Outer automorphisms :: reflexible Dual of E14.523 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 10 e = 40 f = 4 degree seq :: [ 8^10 ] E14.525 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 20}) Quotient :: edge Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |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^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 ] Map:: R = (1, 3, 8, 17, 28, 19, 10, 4)(2, 5, 12, 22, 34, 24, 14, 6)(7, 15, 9, 18, 30, 40, 27, 16)(11, 20, 13, 23, 36, 45, 33, 21)(25, 37, 26, 39, 50, 41, 29, 38)(31, 42, 32, 44, 55, 46, 35, 43)(47, 57, 48, 59, 51, 60, 49, 58)(52, 61, 53, 63, 56, 64, 54, 62)(65, 73, 66, 75, 68, 76, 67, 74)(69, 77, 70, 79, 72, 80, 71, 78)(81, 82)(83, 87)(84, 89)(85, 91)(86, 93)(88, 94)(90, 92)(95, 105)(96, 106)(97, 107)(98, 109)(99, 110)(100, 111)(101, 112)(102, 113)(103, 115)(104, 116)(108, 114)(117, 127)(118, 128)(119, 129)(120, 130)(121, 131)(122, 132)(123, 133)(124, 134)(125, 135)(126, 136)(137, 145)(138, 146)(139, 147)(140, 148)(141, 149)(142, 150)(143, 151)(144, 152)(153, 159)(154, 160)(155, 157)(156, 158) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 40, 40 ), ( 40^8 ) } Outer automorphisms :: reflexible Dual of E14.529 Transitivity :: ET+ Graph:: simple bipartite v = 50 e = 80 f = 4 degree seq :: [ 2^40, 8^10 ] E14.526 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 20}) Quotient :: edge Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |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 * T2^9 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 21, 36, 52, 68, 74, 58, 42, 26, 41, 57, 73, 72, 56, 40, 25, 13, 5)(2, 7, 17, 31, 47, 63, 79, 65, 49, 33, 24, 37, 53, 69, 80, 64, 48, 32, 18, 8)(4, 11, 23, 39, 55, 71, 76, 60, 44, 28, 14, 27, 43, 59, 75, 67, 51, 35, 20, 9)(6, 15, 29, 45, 61, 77, 70, 54, 38, 22, 12, 19, 34, 50, 66, 78, 62, 46, 30, 16)(81, 82, 86, 94, 106, 104, 92, 84)(83, 89, 99, 113, 121, 108, 95, 88)(85, 91, 102, 117, 122, 107, 96, 87)(90, 98, 109, 124, 137, 129, 114, 100)(93, 97, 110, 123, 138, 133, 118, 103)(101, 115, 130, 145, 153, 140, 125, 112)(105, 119, 134, 149, 154, 139, 126, 111)(116, 128, 141, 156, 152, 159, 146, 131)(120, 127, 142, 155, 148, 160, 150, 135)(132, 147, 158, 143, 136, 151, 157, 144) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4^8 ), ( 4^20 ) } Outer automorphisms :: reflexible Dual of E14.530 Transitivity :: ET+ Graph:: bipartite v = 14 e = 80 f = 40 degree seq :: [ 8^10, 20^4 ] E14.527 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 20}) Quotient :: edge Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^-2 * T2 * T1^5 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1, (T2 * T1)^8, T1^20 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 62)(45, 63)(46, 61)(47, 66)(49, 68)(51, 70)(55, 69)(56, 67)(57, 75)(58, 76)(59, 65)(60, 77)(64, 74)(71, 79)(72, 80)(73, 78)(81, 82, 85, 91, 100, 112, 127, 145, 158, 155, 159, 156, 160, 157, 144, 126, 111, 99, 90, 84)(83, 87, 95, 105, 119, 135, 154, 134, 152, 132, 151, 133, 153, 143, 146, 129, 113, 102, 92, 88)(86, 93, 89, 98, 109, 124, 141, 150, 140, 123, 138, 121, 137, 122, 139, 147, 128, 114, 101, 94)(96, 106, 97, 108, 115, 131, 148, 142, 125, 110, 117, 103, 116, 104, 118, 130, 149, 136, 120, 107) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 16, 16 ), ( 16^20 ) } Outer automorphisms :: reflexible Dual of E14.528 Transitivity :: ET+ Graph:: simple bipartite v = 44 e = 80 f = 10 degree seq :: [ 2^40, 20^4 ] E14.528 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 20}) Quotient :: loop Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |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^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 ] Map:: R = (1, 81, 3, 83, 8, 88, 17, 97, 28, 108, 19, 99, 10, 90, 4, 84)(2, 82, 5, 85, 12, 92, 22, 102, 34, 114, 24, 104, 14, 94, 6, 86)(7, 87, 15, 95, 9, 89, 18, 98, 30, 110, 40, 120, 27, 107, 16, 96)(11, 91, 20, 100, 13, 93, 23, 103, 36, 116, 45, 125, 33, 113, 21, 101)(25, 105, 37, 117, 26, 106, 39, 119, 50, 130, 41, 121, 29, 109, 38, 118)(31, 111, 42, 122, 32, 112, 44, 124, 55, 135, 46, 126, 35, 115, 43, 123)(47, 127, 57, 137, 48, 128, 59, 139, 51, 131, 60, 140, 49, 129, 58, 138)(52, 132, 61, 141, 53, 133, 63, 143, 56, 136, 64, 144, 54, 134, 62, 142)(65, 145, 73, 153, 66, 146, 75, 155, 68, 148, 76, 156, 67, 147, 74, 154)(69, 149, 77, 157, 70, 150, 79, 159, 72, 152, 80, 160, 71, 151, 78, 158) L = (1, 82)(2, 81)(3, 87)(4, 89)(5, 91)(6, 93)(7, 83)(8, 94)(9, 84)(10, 92)(11, 85)(12, 90)(13, 86)(14, 88)(15, 105)(16, 106)(17, 107)(18, 109)(19, 110)(20, 111)(21, 112)(22, 113)(23, 115)(24, 116)(25, 95)(26, 96)(27, 97)(28, 114)(29, 98)(30, 99)(31, 100)(32, 101)(33, 102)(34, 108)(35, 103)(36, 104)(37, 127)(38, 128)(39, 129)(40, 130)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(46, 136)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(73, 159)(74, 160)(75, 157)(76, 158)(77, 155)(78, 156)(79, 153)(80, 154) local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E14.527 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 80 f = 44 degree seq :: [ 16^10 ] E14.529 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 20}) Quotient :: loop Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |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 * T2^9 * T1^-2 ] Map:: R = (1, 81, 3, 83, 10, 90, 21, 101, 36, 116, 52, 132, 68, 148, 74, 154, 58, 138, 42, 122, 26, 106, 41, 121, 57, 137, 73, 153, 72, 152, 56, 136, 40, 120, 25, 105, 13, 93, 5, 85)(2, 82, 7, 87, 17, 97, 31, 111, 47, 127, 63, 143, 79, 159, 65, 145, 49, 129, 33, 113, 24, 104, 37, 117, 53, 133, 69, 149, 80, 160, 64, 144, 48, 128, 32, 112, 18, 98, 8, 88)(4, 84, 11, 91, 23, 103, 39, 119, 55, 135, 71, 151, 76, 156, 60, 140, 44, 124, 28, 108, 14, 94, 27, 107, 43, 123, 59, 139, 75, 155, 67, 147, 51, 131, 35, 115, 20, 100, 9, 89)(6, 86, 15, 95, 29, 109, 45, 125, 61, 141, 77, 157, 70, 150, 54, 134, 38, 118, 22, 102, 12, 92, 19, 99, 34, 114, 50, 130, 66, 146, 78, 158, 62, 142, 46, 126, 30, 110, 16, 96) L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 91)(6, 94)(7, 85)(8, 83)(9, 99)(10, 98)(11, 102)(12, 84)(13, 97)(14, 106)(15, 88)(16, 87)(17, 110)(18, 109)(19, 113)(20, 90)(21, 115)(22, 117)(23, 93)(24, 92)(25, 119)(26, 104)(27, 96)(28, 95)(29, 124)(30, 123)(31, 105)(32, 101)(33, 121)(34, 100)(35, 130)(36, 128)(37, 122)(38, 103)(39, 134)(40, 127)(41, 108)(42, 107)(43, 138)(44, 137)(45, 112)(46, 111)(47, 142)(48, 141)(49, 114)(50, 145)(51, 116)(52, 147)(53, 118)(54, 149)(55, 120)(56, 151)(57, 129)(58, 133)(59, 126)(60, 125)(61, 156)(62, 155)(63, 136)(64, 132)(65, 153)(66, 131)(67, 158)(68, 160)(69, 154)(70, 135)(71, 157)(72, 159)(73, 140)(74, 139)(75, 148)(76, 152)(77, 144)(78, 143)(79, 146)(80, 150) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E14.525 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 80 f = 50 degree seq :: [ 40^4 ] E14.530 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 20}) Quotient :: loop Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^-2 * T2 * T1^5 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1, (T2 * T1)^8, T1^20 ] Map:: polytopal non-degenerate R = (1, 81, 3, 83)(2, 82, 6, 86)(4, 84, 9, 89)(5, 85, 12, 92)(7, 87, 16, 96)(8, 88, 17, 97)(10, 90, 15, 95)(11, 91, 21, 101)(13, 93, 23, 103)(14, 94, 24, 104)(18, 98, 30, 110)(19, 99, 29, 109)(20, 100, 33, 113)(22, 102, 35, 115)(25, 105, 40, 120)(26, 106, 41, 121)(27, 107, 42, 122)(28, 108, 43, 123)(31, 111, 39, 119)(32, 112, 48, 128)(34, 114, 50, 130)(36, 116, 52, 132)(37, 117, 53, 133)(38, 118, 54, 134)(44, 124, 62, 142)(45, 125, 63, 143)(46, 126, 61, 141)(47, 127, 66, 146)(49, 129, 68, 148)(51, 131, 70, 150)(55, 135, 69, 149)(56, 136, 67, 147)(57, 137, 75, 155)(58, 138, 76, 156)(59, 139, 65, 145)(60, 140, 77, 157)(64, 144, 74, 154)(71, 151, 79, 159)(72, 152, 80, 160)(73, 153, 78, 158) L = (1, 82)(2, 85)(3, 87)(4, 81)(5, 91)(6, 93)(7, 95)(8, 83)(9, 98)(10, 84)(11, 100)(12, 88)(13, 89)(14, 86)(15, 105)(16, 106)(17, 108)(18, 109)(19, 90)(20, 112)(21, 94)(22, 92)(23, 116)(24, 118)(25, 119)(26, 97)(27, 96)(28, 115)(29, 124)(30, 117)(31, 99)(32, 127)(33, 102)(34, 101)(35, 131)(36, 104)(37, 103)(38, 130)(39, 135)(40, 107)(41, 137)(42, 139)(43, 138)(44, 141)(45, 110)(46, 111)(47, 145)(48, 114)(49, 113)(50, 149)(51, 148)(52, 151)(53, 153)(54, 152)(55, 154)(56, 120)(57, 122)(58, 121)(59, 147)(60, 123)(61, 150)(62, 125)(63, 146)(64, 126)(65, 158)(66, 129)(67, 128)(68, 142)(69, 136)(70, 140)(71, 133)(72, 132)(73, 143)(74, 134)(75, 159)(76, 160)(77, 144)(78, 155)(79, 156)(80, 157) local type(s) :: { ( 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E14.526 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 40 e = 80 f = 14 degree seq :: [ 4^40 ] E14.531 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 20}) Quotient :: dipole Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (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^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^20 ] Map:: R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 9, 89)(5, 85, 11, 91)(6, 86, 13, 93)(8, 88, 14, 94)(10, 90, 12, 92)(15, 95, 25, 105)(16, 96, 26, 106)(17, 97, 27, 107)(18, 98, 29, 109)(19, 99, 30, 110)(20, 100, 31, 111)(21, 101, 32, 112)(22, 102, 33, 113)(23, 103, 35, 115)(24, 104, 36, 116)(28, 108, 34, 114)(37, 117, 47, 127)(38, 118, 48, 128)(39, 119, 49, 129)(40, 120, 50, 130)(41, 121, 51, 131)(42, 122, 52, 132)(43, 123, 53, 133)(44, 124, 54, 134)(45, 125, 55, 135)(46, 126, 56, 136)(57, 137, 65, 145)(58, 138, 66, 146)(59, 139, 67, 147)(60, 140, 68, 148)(61, 141, 69, 149)(62, 142, 70, 150)(63, 143, 71, 151)(64, 144, 72, 152)(73, 153, 79, 159)(74, 154, 80, 160)(75, 155, 77, 157)(76, 156, 78, 158)(161, 241, 163, 243, 168, 248, 177, 257, 188, 268, 179, 259, 170, 250, 164, 244)(162, 242, 165, 245, 172, 252, 182, 262, 194, 274, 184, 264, 174, 254, 166, 246)(167, 247, 175, 255, 169, 249, 178, 258, 190, 270, 200, 280, 187, 267, 176, 256)(171, 251, 180, 260, 173, 253, 183, 263, 196, 276, 205, 285, 193, 273, 181, 261)(185, 265, 197, 277, 186, 266, 199, 279, 210, 290, 201, 281, 189, 269, 198, 278)(191, 271, 202, 282, 192, 272, 204, 284, 215, 295, 206, 286, 195, 275, 203, 283)(207, 287, 217, 297, 208, 288, 219, 299, 211, 291, 220, 300, 209, 289, 218, 298)(212, 292, 221, 301, 213, 293, 223, 303, 216, 296, 224, 304, 214, 294, 222, 302)(225, 305, 233, 313, 226, 306, 235, 315, 228, 308, 236, 316, 227, 307, 234, 314)(229, 309, 237, 317, 230, 310, 239, 319, 232, 312, 240, 320, 231, 311, 238, 318) L = (1, 162)(2, 161)(3, 167)(4, 169)(5, 171)(6, 173)(7, 163)(8, 174)(9, 164)(10, 172)(11, 165)(12, 170)(13, 166)(14, 168)(15, 185)(16, 186)(17, 187)(18, 189)(19, 190)(20, 191)(21, 192)(22, 193)(23, 195)(24, 196)(25, 175)(26, 176)(27, 177)(28, 194)(29, 178)(30, 179)(31, 180)(32, 181)(33, 182)(34, 188)(35, 183)(36, 184)(37, 207)(38, 208)(39, 209)(40, 210)(41, 211)(42, 212)(43, 213)(44, 214)(45, 215)(46, 216)(47, 197)(48, 198)(49, 199)(50, 200)(51, 201)(52, 202)(53, 203)(54, 204)(55, 205)(56, 206)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 217)(66, 218)(67, 219)(68, 220)(69, 221)(70, 222)(71, 223)(72, 224)(73, 239)(74, 240)(75, 237)(76, 238)(77, 235)(78, 236)(79, 233)(80, 234)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) } Outer automorphisms :: reflexible Dual of E14.534 Graph:: bipartite v = 50 e = 160 f = 84 degree seq :: [ 4^40, 16^10 ] E14.532 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 20}) Quotient :: dipole Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2^-1)^2, (Y2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y1^8, Y1^-1 * Y2^-1 * Y1^2 * Y2^-9 * Y1^-1 ] Map:: R = (1, 81, 2, 82, 6, 86, 14, 94, 26, 106, 24, 104, 12, 92, 4, 84)(3, 83, 9, 89, 19, 99, 33, 113, 41, 121, 28, 108, 15, 95, 8, 88)(5, 85, 11, 91, 22, 102, 37, 117, 42, 122, 27, 107, 16, 96, 7, 87)(10, 90, 18, 98, 29, 109, 44, 124, 57, 137, 49, 129, 34, 114, 20, 100)(13, 93, 17, 97, 30, 110, 43, 123, 58, 138, 53, 133, 38, 118, 23, 103)(21, 101, 35, 115, 50, 130, 65, 145, 73, 153, 60, 140, 45, 125, 32, 112)(25, 105, 39, 119, 54, 134, 69, 149, 74, 154, 59, 139, 46, 126, 31, 111)(36, 116, 48, 128, 61, 141, 76, 156, 72, 152, 79, 159, 66, 146, 51, 131)(40, 120, 47, 127, 62, 142, 75, 155, 68, 148, 80, 160, 70, 150, 55, 135)(52, 132, 67, 147, 78, 158, 63, 143, 56, 136, 71, 151, 77, 157, 64, 144)(161, 241, 163, 243, 170, 250, 181, 261, 196, 276, 212, 292, 228, 308, 234, 314, 218, 298, 202, 282, 186, 266, 201, 281, 217, 297, 233, 313, 232, 312, 216, 296, 200, 280, 185, 265, 173, 253, 165, 245)(162, 242, 167, 247, 177, 257, 191, 271, 207, 287, 223, 303, 239, 319, 225, 305, 209, 289, 193, 273, 184, 264, 197, 277, 213, 293, 229, 309, 240, 320, 224, 304, 208, 288, 192, 272, 178, 258, 168, 248)(164, 244, 171, 251, 183, 263, 199, 279, 215, 295, 231, 311, 236, 316, 220, 300, 204, 284, 188, 268, 174, 254, 187, 267, 203, 283, 219, 299, 235, 315, 227, 307, 211, 291, 195, 275, 180, 260, 169, 249)(166, 246, 175, 255, 189, 269, 205, 285, 221, 301, 237, 317, 230, 310, 214, 294, 198, 278, 182, 262, 172, 252, 179, 259, 194, 274, 210, 290, 226, 306, 238, 318, 222, 302, 206, 286, 190, 270, 176, 256) L = (1, 163)(2, 167)(3, 170)(4, 171)(5, 161)(6, 175)(7, 177)(8, 162)(9, 164)(10, 181)(11, 183)(12, 179)(13, 165)(14, 187)(15, 189)(16, 166)(17, 191)(18, 168)(19, 194)(20, 169)(21, 196)(22, 172)(23, 199)(24, 197)(25, 173)(26, 201)(27, 203)(28, 174)(29, 205)(30, 176)(31, 207)(32, 178)(33, 184)(34, 210)(35, 180)(36, 212)(37, 213)(38, 182)(39, 215)(40, 185)(41, 217)(42, 186)(43, 219)(44, 188)(45, 221)(46, 190)(47, 223)(48, 192)(49, 193)(50, 226)(51, 195)(52, 228)(53, 229)(54, 198)(55, 231)(56, 200)(57, 233)(58, 202)(59, 235)(60, 204)(61, 237)(62, 206)(63, 239)(64, 208)(65, 209)(66, 238)(67, 211)(68, 234)(69, 240)(70, 214)(71, 236)(72, 216)(73, 232)(74, 218)(75, 227)(76, 220)(77, 230)(78, 222)(79, 225)(80, 224)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E14.533 Graph:: bipartite v = 14 e = 160 f = 120 degree seq :: [ 16^10, 40^4 ] E14.533 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 20}) Quotient :: dipole Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^7 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^20 ] Map:: polytopal R = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)(161, 241, 162, 242)(163, 243, 167, 247)(164, 244, 169, 249)(165, 245, 171, 251)(166, 246, 173, 253)(168, 248, 174, 254)(170, 250, 172, 252)(175, 255, 185, 265)(176, 256, 186, 266)(177, 257, 187, 267)(178, 258, 189, 269)(179, 259, 190, 270)(180, 260, 192, 272)(181, 261, 193, 273)(182, 262, 194, 274)(183, 263, 196, 276)(184, 264, 197, 277)(188, 268, 198, 278)(191, 271, 195, 275)(199, 279, 215, 295)(200, 280, 216, 296)(201, 281, 217, 297)(202, 282, 218, 298)(203, 283, 219, 299)(204, 284, 221, 301)(205, 285, 222, 302)(206, 286, 223, 303)(207, 287, 225, 305)(208, 288, 226, 306)(209, 289, 227, 307)(210, 290, 228, 308)(211, 291, 229, 309)(212, 292, 231, 311)(213, 293, 232, 312)(214, 294, 233, 313)(220, 300, 234, 314)(224, 304, 230, 310)(235, 315, 238, 318)(236, 316, 240, 320)(237, 317, 239, 319) L = (1, 163)(2, 165)(3, 168)(4, 161)(5, 172)(6, 162)(7, 175)(8, 177)(9, 178)(10, 164)(11, 180)(12, 182)(13, 183)(14, 166)(15, 169)(16, 167)(17, 188)(18, 190)(19, 170)(20, 173)(21, 171)(22, 195)(23, 197)(24, 174)(25, 199)(26, 201)(27, 176)(28, 203)(29, 200)(30, 205)(31, 179)(32, 207)(33, 209)(34, 181)(35, 211)(36, 208)(37, 213)(38, 184)(39, 186)(40, 185)(41, 218)(42, 187)(43, 220)(44, 189)(45, 223)(46, 191)(47, 193)(48, 192)(49, 228)(50, 194)(51, 230)(52, 196)(53, 233)(54, 198)(55, 235)(56, 237)(57, 236)(58, 229)(59, 202)(60, 227)(61, 234)(62, 204)(63, 232)(64, 206)(65, 238)(66, 240)(67, 239)(68, 219)(69, 210)(70, 217)(71, 224)(72, 212)(73, 222)(74, 214)(75, 216)(76, 215)(77, 221)(78, 226)(79, 225)(80, 231)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 16, 40 ), ( 16, 40, 16, 40 ) } Outer automorphisms :: reflexible Dual of E14.532 Graph:: simple bipartite v = 120 e = 160 f = 14 degree seq :: [ 2^80, 4^40 ] E14.534 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 20}) Quotient :: dipole Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y3 * Y1^2)^2, Y1^-4 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-3, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^9 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: R = (1, 81, 2, 82, 5, 85, 11, 91, 20, 100, 32, 112, 47, 127, 65, 145, 78, 158, 75, 155, 79, 159, 76, 156, 80, 160, 77, 157, 64, 144, 46, 126, 31, 111, 19, 99, 10, 90, 4, 84)(3, 83, 7, 87, 15, 95, 25, 105, 39, 119, 55, 135, 74, 154, 54, 134, 72, 152, 52, 132, 71, 151, 53, 133, 73, 153, 63, 143, 66, 146, 49, 129, 33, 113, 22, 102, 12, 92, 8, 88)(6, 86, 13, 93, 9, 89, 18, 98, 29, 109, 44, 124, 61, 141, 70, 150, 60, 140, 43, 123, 58, 138, 41, 121, 57, 137, 42, 122, 59, 139, 67, 147, 48, 128, 34, 114, 21, 101, 14, 94)(16, 96, 26, 106, 17, 97, 28, 108, 35, 115, 51, 131, 68, 148, 62, 142, 45, 125, 30, 110, 37, 117, 23, 103, 36, 116, 24, 104, 38, 118, 50, 130, 69, 149, 56, 136, 40, 120, 27, 107)(161, 241)(162, 242)(163, 243)(164, 244)(165, 245)(166, 246)(167, 247)(168, 248)(169, 249)(170, 250)(171, 251)(172, 252)(173, 253)(174, 254)(175, 255)(176, 256)(177, 257)(178, 258)(179, 259)(180, 260)(181, 261)(182, 262)(183, 263)(184, 264)(185, 265)(186, 266)(187, 267)(188, 268)(189, 269)(190, 270)(191, 271)(192, 272)(193, 273)(194, 274)(195, 275)(196, 276)(197, 277)(198, 278)(199, 279)(200, 280)(201, 281)(202, 282)(203, 283)(204, 284)(205, 285)(206, 286)(207, 287)(208, 288)(209, 289)(210, 290)(211, 291)(212, 292)(213, 293)(214, 294)(215, 295)(216, 296)(217, 297)(218, 298)(219, 299)(220, 300)(221, 301)(222, 302)(223, 303)(224, 304)(225, 305)(226, 306)(227, 307)(228, 308)(229, 309)(230, 310)(231, 311)(232, 312)(233, 313)(234, 314)(235, 315)(236, 316)(237, 317)(238, 318)(239, 319)(240, 320) L = (1, 163)(2, 166)(3, 161)(4, 169)(5, 172)(6, 162)(7, 176)(8, 177)(9, 164)(10, 175)(11, 181)(12, 165)(13, 183)(14, 184)(15, 170)(16, 167)(17, 168)(18, 190)(19, 189)(20, 193)(21, 171)(22, 195)(23, 173)(24, 174)(25, 200)(26, 201)(27, 202)(28, 203)(29, 179)(30, 178)(31, 199)(32, 208)(33, 180)(34, 210)(35, 182)(36, 212)(37, 213)(38, 214)(39, 191)(40, 185)(41, 186)(42, 187)(43, 188)(44, 222)(45, 223)(46, 221)(47, 226)(48, 192)(49, 228)(50, 194)(51, 230)(52, 196)(53, 197)(54, 198)(55, 229)(56, 227)(57, 235)(58, 236)(59, 225)(60, 237)(61, 206)(62, 204)(63, 205)(64, 234)(65, 219)(66, 207)(67, 216)(68, 209)(69, 215)(70, 211)(71, 239)(72, 240)(73, 238)(74, 224)(75, 217)(76, 218)(77, 220)(78, 233)(79, 231)(80, 232)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 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 E14.531 Graph:: simple bipartite v = 84 e = 160 f = 50 degree seq :: [ 2^80, 40^4 ] E14.535 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 20}) Quotient :: dipole Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1)^2, Y2^7 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1, Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 9, 89)(5, 85, 11, 91)(6, 86, 13, 93)(8, 88, 14, 94)(10, 90, 12, 92)(15, 95, 25, 105)(16, 96, 26, 106)(17, 97, 27, 107)(18, 98, 29, 109)(19, 99, 30, 110)(20, 100, 32, 112)(21, 101, 33, 113)(22, 102, 34, 114)(23, 103, 36, 116)(24, 104, 37, 117)(28, 108, 38, 118)(31, 111, 35, 115)(39, 119, 55, 135)(40, 120, 56, 136)(41, 121, 57, 137)(42, 122, 58, 138)(43, 123, 59, 139)(44, 124, 61, 141)(45, 125, 62, 142)(46, 126, 63, 143)(47, 127, 65, 145)(48, 128, 66, 146)(49, 129, 67, 147)(50, 130, 68, 148)(51, 131, 69, 149)(52, 132, 71, 151)(53, 133, 72, 152)(54, 134, 73, 153)(60, 140, 74, 154)(64, 144, 70, 150)(75, 155, 78, 158)(76, 156, 80, 160)(77, 157, 79, 159)(161, 241, 163, 243, 168, 248, 177, 257, 188, 268, 203, 283, 220, 300, 227, 307, 239, 319, 225, 305, 238, 318, 226, 306, 240, 320, 231, 311, 224, 304, 206, 286, 191, 271, 179, 259, 170, 250, 164, 244)(162, 242, 165, 245, 172, 252, 182, 262, 195, 275, 211, 291, 230, 310, 217, 297, 236, 316, 215, 295, 235, 315, 216, 296, 237, 317, 221, 301, 234, 314, 214, 294, 198, 278, 184, 264, 174, 254, 166, 246)(167, 247, 175, 255, 169, 249, 178, 258, 190, 270, 205, 285, 223, 303, 232, 312, 212, 292, 196, 276, 208, 288, 192, 272, 207, 287, 193, 273, 209, 289, 228, 308, 219, 299, 202, 282, 187, 267, 176, 256)(171, 251, 180, 260, 173, 253, 183, 263, 197, 277, 213, 293, 233, 313, 222, 302, 204, 284, 189, 269, 200, 280, 185, 265, 199, 279, 186, 266, 201, 281, 218, 298, 229, 309, 210, 290, 194, 274, 181, 261) L = (1, 162)(2, 161)(3, 167)(4, 169)(5, 171)(6, 173)(7, 163)(8, 174)(9, 164)(10, 172)(11, 165)(12, 170)(13, 166)(14, 168)(15, 185)(16, 186)(17, 187)(18, 189)(19, 190)(20, 192)(21, 193)(22, 194)(23, 196)(24, 197)(25, 175)(26, 176)(27, 177)(28, 198)(29, 178)(30, 179)(31, 195)(32, 180)(33, 181)(34, 182)(35, 191)(36, 183)(37, 184)(38, 188)(39, 215)(40, 216)(41, 217)(42, 218)(43, 219)(44, 221)(45, 222)(46, 223)(47, 225)(48, 226)(49, 227)(50, 228)(51, 229)(52, 231)(53, 232)(54, 233)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 234)(61, 204)(62, 205)(63, 206)(64, 230)(65, 207)(66, 208)(67, 209)(68, 210)(69, 211)(70, 224)(71, 212)(72, 213)(73, 214)(74, 220)(75, 238)(76, 240)(77, 239)(78, 235)(79, 237)(80, 236)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E14.536 Graph:: bipartite v = 44 e = 160 f = 90 degree seq :: [ 4^40, 40^4 ] E14.536 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 20}) Quotient :: dipole Aut^+ = (C5 x Q8) : C2 (small group id <80, 17>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^8, Y1^-1 * Y3^-1 * Y1^2 * Y3^-9 * Y1^-1, (Y3 * Y2^-1)^20 ] Map:: R = (1, 81, 2, 82, 6, 86, 14, 94, 26, 106, 24, 104, 12, 92, 4, 84)(3, 83, 9, 89, 19, 99, 33, 113, 41, 121, 28, 108, 15, 95, 8, 88)(5, 85, 11, 91, 22, 102, 37, 117, 42, 122, 27, 107, 16, 96, 7, 87)(10, 90, 18, 98, 29, 109, 44, 124, 57, 137, 49, 129, 34, 114, 20, 100)(13, 93, 17, 97, 30, 110, 43, 123, 58, 138, 53, 133, 38, 118, 23, 103)(21, 101, 35, 115, 50, 130, 65, 145, 73, 153, 60, 140, 45, 125, 32, 112)(25, 105, 39, 119, 54, 134, 69, 149, 74, 154, 59, 139, 46, 126, 31, 111)(36, 116, 48, 128, 61, 141, 76, 156, 72, 152, 79, 159, 66, 146, 51, 131)(40, 120, 47, 127, 62, 142, 75, 155, 68, 148, 80, 160, 70, 150, 55, 135)(52, 132, 67, 147, 78, 158, 63, 143, 56, 136, 71, 151, 77, 157, 64, 144)(161, 241)(162, 242)(163, 243)(164, 244)(165, 245)(166, 246)(167, 247)(168, 248)(169, 249)(170, 250)(171, 251)(172, 252)(173, 253)(174, 254)(175, 255)(176, 256)(177, 257)(178, 258)(179, 259)(180, 260)(181, 261)(182, 262)(183, 263)(184, 264)(185, 265)(186, 266)(187, 267)(188, 268)(189, 269)(190, 270)(191, 271)(192, 272)(193, 273)(194, 274)(195, 275)(196, 276)(197, 277)(198, 278)(199, 279)(200, 280)(201, 281)(202, 282)(203, 283)(204, 284)(205, 285)(206, 286)(207, 287)(208, 288)(209, 289)(210, 290)(211, 291)(212, 292)(213, 293)(214, 294)(215, 295)(216, 296)(217, 297)(218, 298)(219, 299)(220, 300)(221, 301)(222, 302)(223, 303)(224, 304)(225, 305)(226, 306)(227, 307)(228, 308)(229, 309)(230, 310)(231, 311)(232, 312)(233, 313)(234, 314)(235, 315)(236, 316)(237, 317)(238, 318)(239, 319)(240, 320) L = (1, 163)(2, 167)(3, 170)(4, 171)(5, 161)(6, 175)(7, 177)(8, 162)(9, 164)(10, 181)(11, 183)(12, 179)(13, 165)(14, 187)(15, 189)(16, 166)(17, 191)(18, 168)(19, 194)(20, 169)(21, 196)(22, 172)(23, 199)(24, 197)(25, 173)(26, 201)(27, 203)(28, 174)(29, 205)(30, 176)(31, 207)(32, 178)(33, 184)(34, 210)(35, 180)(36, 212)(37, 213)(38, 182)(39, 215)(40, 185)(41, 217)(42, 186)(43, 219)(44, 188)(45, 221)(46, 190)(47, 223)(48, 192)(49, 193)(50, 226)(51, 195)(52, 228)(53, 229)(54, 198)(55, 231)(56, 200)(57, 233)(58, 202)(59, 235)(60, 204)(61, 237)(62, 206)(63, 239)(64, 208)(65, 209)(66, 238)(67, 211)(68, 234)(69, 240)(70, 214)(71, 236)(72, 216)(73, 232)(74, 218)(75, 227)(76, 220)(77, 230)(78, 222)(79, 225)(80, 224)(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, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E14.535 Graph:: simple bipartite v = 90 e = 160 f = 44 degree seq :: [ 2^80, 16^10 ] E14.537 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 42}) Quotient :: regular Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2 * T1^-1)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-3 * T2 * T1^4 * T2 * T1^-7 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 39, 53, 65, 77, 73, 60, 49, 33, 16, 28, 42, 35, 46, 58, 70, 82, 84, 83, 72, 61, 48, 32, 45, 34, 17, 29, 43, 56, 68, 80, 76, 64, 52, 38, 22, 10, 4)(3, 7, 15, 31, 47, 59, 71, 78, 69, 55, 40, 30, 14, 6, 13, 27, 21, 37, 51, 63, 75, 81, 67, 54, 44, 26, 12, 25, 20, 9, 19, 36, 50, 62, 74, 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, 83)(75, 77)(76, 79)(81, 84) local type(s) :: { ( 6^42 ) } Outer automorphisms :: reflexible Dual of E14.538 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 42 f = 14 degree seq :: [ 42^2 ] E14.538 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 42}) Quotient :: regular Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^6, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 ] Map:: non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 12, 20, 17, 8)(6, 13, 19, 18, 9, 14)(15, 23, 27, 25, 16, 24)(21, 28, 26, 30, 22, 29)(31, 37, 33, 39, 32, 38)(34, 40, 36, 42, 35, 41)(43, 49, 45, 51, 44, 50)(46, 52, 48, 54, 47, 53)(55, 61, 57, 63, 56, 62)(58, 64, 60, 66, 59, 65)(67, 73, 69, 75, 68, 74)(70, 76, 72, 78, 71, 77)(79, 82, 81, 84, 80, 83) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 19)(13, 21)(14, 22)(18, 26)(20, 27)(23, 31)(24, 32)(25, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72)(73, 79)(74, 80)(75, 81)(76, 82)(77, 83)(78, 84) local type(s) :: { ( 42^6 ) } Outer automorphisms :: reflexible Dual of E14.537 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 14 e = 42 f = 2 degree seq :: [ 6^14 ] E14.539 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 42}) Quotient :: edge Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * 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^-3 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1 ] Map:: R = (1, 3, 8, 17, 10, 4)(2, 5, 12, 21, 14, 6)(7, 15, 24, 18, 9, 16)(11, 19, 28, 22, 13, 20)(23, 31, 26, 33, 25, 32)(27, 34, 30, 36, 29, 35)(37, 43, 39, 45, 38, 44)(40, 46, 42, 48, 41, 47)(49, 55, 51, 57, 50, 56)(52, 58, 54, 60, 53, 59)(61, 67, 63, 69, 62, 68)(64, 70, 66, 72, 65, 71)(73, 79, 75, 81, 74, 80)(76, 82, 78, 84, 77, 83)(85, 86)(87, 91)(88, 93)(89, 95)(90, 97)(92, 96)(94, 98)(99, 107)(100, 109)(101, 108)(102, 110)(103, 111)(104, 113)(105, 112)(106, 114)(115, 121)(116, 122)(117, 123)(118, 124)(119, 125)(120, 126)(127, 133)(128, 134)(129, 135)(130, 136)(131, 137)(132, 138)(139, 145)(140, 146)(141, 147)(142, 148)(143, 149)(144, 150)(151, 157)(152, 158)(153, 159)(154, 160)(155, 161)(156, 162)(163, 166)(164, 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 ), ( 84^6 ) } Outer automorphisms :: reflexible Dual of E14.543 Transitivity :: ET+ Graph:: simple bipartite v = 56 e = 84 f = 2 degree seq :: [ 2^42, 6^14 ] E14.540 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 42}) Quotient :: edge Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2 * T1^-1 * T2, T2 * T1^-1 * T2 * T1^3, (T2^2 * T1^-1)^2, T1 * T2^-13 * T1^-1 * T2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 37, 49, 61, 73, 79, 67, 55, 43, 31, 20, 13, 21, 33, 45, 57, 69, 81, 84, 78, 66, 54, 42, 30, 18, 6, 17, 29, 41, 53, 65, 77, 76, 64, 52, 40, 28, 15, 5)(2, 7, 19, 32, 44, 56, 68, 80, 71, 59, 47, 35, 23, 9, 4, 12, 26, 38, 50, 62, 74, 83, 72, 60, 48, 36, 24, 11, 16, 14, 27, 39, 51, 63, 75, 82, 70, 58, 46, 34, 22, 8)(85, 86, 90, 100, 97, 88)(87, 93, 101, 92, 105, 95)(89, 98, 102, 96, 104, 91)(94, 108, 113, 107, 117, 106)(99, 110, 114, 103, 115, 111)(109, 118, 125, 120, 129, 119)(112, 116, 126, 123, 127, 122)(121, 131, 137, 130, 141, 132)(124, 135, 138, 134, 139, 128)(133, 144, 149, 143, 153, 142)(136, 146, 150, 140, 151, 147)(145, 154, 161, 156, 165, 155)(148, 152, 162, 159, 163, 158)(157, 164, 160, 166, 168, 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) :: { ( 4^6 ), ( 4^42 ) } Outer automorphisms :: reflexible Dual of E14.544 Transitivity :: ET+ Graph:: bipartite v = 16 e = 84 f = 42 degree seq :: [ 6^14, 42^2 ] E14.541 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 42}) Quotient :: edge Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-3)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-3 * T2 * T1^4 * T2 * T1^-7 ] 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, 83)(75, 77)(76, 79)(81, 84)(85, 86, 89, 95, 107, 123, 137, 149, 161, 157, 144, 133, 117, 100, 112, 126, 119, 130, 142, 154, 166, 168, 167, 156, 145, 132, 116, 129, 118, 101, 113, 127, 140, 152, 164, 160, 148, 136, 122, 106, 94, 88)(87, 91, 99, 115, 131, 143, 155, 162, 153, 139, 124, 114, 98, 90, 97, 111, 105, 121, 135, 147, 159, 165, 151, 138, 128, 110, 96, 109, 104, 93, 103, 120, 134, 146, 158, 163, 150, 141, 125, 108, 102, 92) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 12, 12 ), ( 12^42 ) } Outer automorphisms :: reflexible Dual of E14.542 Transitivity :: ET+ Graph:: simple bipartite v = 44 e = 84 f = 14 degree seq :: [ 2^42, 42^2 ] E14.542 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 42}) Quotient :: loop Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * 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^-3 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1 ] Map:: R = (1, 85, 3, 87, 8, 92, 17, 101, 10, 94, 4, 88)(2, 86, 5, 89, 12, 96, 21, 105, 14, 98, 6, 90)(7, 91, 15, 99, 24, 108, 18, 102, 9, 93, 16, 100)(11, 95, 19, 103, 28, 112, 22, 106, 13, 97, 20, 104)(23, 107, 31, 115, 26, 110, 33, 117, 25, 109, 32, 116)(27, 111, 34, 118, 30, 114, 36, 120, 29, 113, 35, 119)(37, 121, 43, 127, 39, 123, 45, 129, 38, 122, 44, 128)(40, 124, 46, 130, 42, 126, 48, 132, 41, 125, 47, 131)(49, 133, 55, 139, 51, 135, 57, 141, 50, 134, 56, 140)(52, 136, 58, 142, 54, 138, 60, 144, 53, 137, 59, 143)(61, 145, 67, 151, 63, 147, 69, 153, 62, 146, 68, 152)(64, 148, 70, 154, 66, 150, 72, 156, 65, 149, 71, 155)(73, 157, 79, 163, 75, 159, 81, 165, 74, 158, 80, 164)(76, 160, 82, 166, 78, 162, 84, 168, 77, 161, 83, 167) L = (1, 86)(2, 85)(3, 91)(4, 93)(5, 95)(6, 97)(7, 87)(8, 96)(9, 88)(10, 98)(11, 89)(12, 92)(13, 90)(14, 94)(15, 107)(16, 109)(17, 108)(18, 110)(19, 111)(20, 113)(21, 112)(22, 114)(23, 99)(24, 101)(25, 100)(26, 102)(27, 103)(28, 105)(29, 104)(30, 106)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 115)(38, 116)(39, 117)(40, 118)(41, 119)(42, 120)(43, 133)(44, 134)(45, 135)(46, 136)(47, 137)(48, 138)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156)(79, 166)(80, 167)(81, 168)(82, 163)(83, 164)(84, 165) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E14.541 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 14 e = 84 f = 44 degree seq :: [ 12^14 ] E14.543 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 42}) Quotient :: loop Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2 * T1^-1 * T2, T2 * T1^-1 * T2 * T1^3, (T2^2 * T1^-1)^2, T1 * T2^-13 * T1^-1 * T2 ] Map:: R = (1, 85, 3, 87, 10, 94, 25, 109, 37, 121, 49, 133, 61, 145, 73, 157, 79, 163, 67, 151, 55, 139, 43, 127, 31, 115, 20, 104, 13, 97, 21, 105, 33, 117, 45, 129, 57, 141, 69, 153, 81, 165, 84, 168, 78, 162, 66, 150, 54, 138, 42, 126, 30, 114, 18, 102, 6, 90, 17, 101, 29, 113, 41, 125, 53, 137, 65, 149, 77, 161, 76, 160, 64, 148, 52, 136, 40, 124, 28, 112, 15, 99, 5, 89)(2, 86, 7, 91, 19, 103, 32, 116, 44, 128, 56, 140, 68, 152, 80, 164, 71, 155, 59, 143, 47, 131, 35, 119, 23, 107, 9, 93, 4, 88, 12, 96, 26, 110, 38, 122, 50, 134, 62, 146, 74, 158, 83, 167, 72, 156, 60, 144, 48, 132, 36, 120, 24, 108, 11, 95, 16, 100, 14, 98, 27, 111, 39, 123, 51, 135, 63, 147, 75, 159, 82, 166, 70, 154, 58, 142, 46, 130, 34, 118, 22, 106, 8, 92) L = (1, 86)(2, 90)(3, 93)(4, 85)(5, 98)(6, 100)(7, 89)(8, 105)(9, 101)(10, 108)(11, 87)(12, 104)(13, 88)(14, 102)(15, 110)(16, 97)(17, 92)(18, 96)(19, 115)(20, 91)(21, 95)(22, 94)(23, 117)(24, 113)(25, 118)(26, 114)(27, 99)(28, 116)(29, 107)(30, 103)(31, 111)(32, 126)(33, 106)(34, 125)(35, 109)(36, 129)(37, 131)(38, 112)(39, 127)(40, 135)(41, 120)(42, 123)(43, 122)(44, 124)(45, 119)(46, 141)(47, 137)(48, 121)(49, 144)(50, 139)(51, 138)(52, 146)(53, 130)(54, 134)(55, 128)(56, 151)(57, 132)(58, 133)(59, 153)(60, 149)(61, 154)(62, 150)(63, 136)(64, 152)(65, 143)(66, 140)(67, 147)(68, 162)(69, 142)(70, 161)(71, 145)(72, 165)(73, 164)(74, 148)(75, 163)(76, 166)(77, 156)(78, 159)(79, 158)(80, 160)(81, 155)(82, 168)(83, 157)(84, 167) 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 ) } Outer automorphisms :: reflexible Dual of E14.539 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 84 f = 56 degree seq :: [ 84^2 ] E14.544 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 42}) Quotient :: loop Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-3)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-3 * T2 * T1^4 * T2 * T1^-7 ] Map:: polytopal non-degenerate R = (1, 85, 3, 87)(2, 86, 6, 90)(4, 88, 9, 93)(5, 89, 12, 96)(7, 91, 16, 100)(8, 92, 17, 101)(10, 94, 21, 105)(11, 95, 24, 108)(13, 97, 28, 112)(14, 98, 29, 113)(15, 99, 32, 116)(18, 102, 35, 119)(19, 103, 33, 117)(20, 104, 34, 118)(22, 106, 31, 115)(23, 107, 40, 124)(25, 109, 42, 126)(26, 110, 43, 127)(27, 111, 45, 129)(30, 114, 46, 130)(36, 120, 48, 132)(37, 121, 49, 133)(38, 122, 50, 134)(39, 123, 54, 138)(41, 125, 56, 140)(44, 128, 58, 142)(47, 131, 60, 144)(51, 135, 61, 145)(52, 136, 63, 147)(53, 137, 66, 150)(55, 139, 68, 152)(57, 141, 70, 154)(59, 143, 72, 156)(62, 146, 73, 157)(64, 148, 71, 155)(65, 149, 78, 162)(67, 151, 80, 164)(69, 153, 82, 166)(74, 158, 83, 167)(75, 159, 77, 161)(76, 160, 79, 163)(81, 165, 84, 168) L = (1, 86)(2, 89)(3, 91)(4, 85)(5, 95)(6, 97)(7, 99)(8, 87)(9, 103)(10, 88)(11, 107)(12, 109)(13, 111)(14, 90)(15, 115)(16, 112)(17, 113)(18, 92)(19, 120)(20, 93)(21, 121)(22, 94)(23, 123)(24, 102)(25, 104)(26, 96)(27, 105)(28, 126)(29, 127)(30, 98)(31, 131)(32, 129)(33, 100)(34, 101)(35, 130)(36, 134)(37, 135)(38, 106)(39, 137)(40, 114)(41, 108)(42, 119)(43, 140)(44, 110)(45, 118)(46, 142)(47, 143)(48, 116)(49, 117)(50, 146)(51, 147)(52, 122)(53, 149)(54, 128)(55, 124)(56, 152)(57, 125)(58, 154)(59, 155)(60, 133)(61, 132)(62, 158)(63, 159)(64, 136)(65, 161)(66, 141)(67, 138)(68, 164)(69, 139)(70, 166)(71, 162)(72, 145)(73, 144)(74, 163)(75, 165)(76, 148)(77, 157)(78, 153)(79, 150)(80, 160)(81, 151)(82, 168)(83, 156)(84, 167) local type(s) :: { ( 6, 42, 6, 42 ) } Outer automorphisms :: reflexible Dual of E14.540 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 42 e = 84 f = 16 degree seq :: [ 4^42 ] E14.545 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 42}) Quotient :: dipole Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |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, Y2^6, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^42 ] Map:: R = (1, 85, 2, 86)(3, 87, 7, 91)(4, 88, 9, 93)(5, 89, 11, 95)(6, 90, 13, 97)(8, 92, 12, 96)(10, 94, 14, 98)(15, 99, 23, 107)(16, 100, 25, 109)(17, 101, 24, 108)(18, 102, 26, 110)(19, 103, 27, 111)(20, 104, 29, 113)(21, 105, 28, 112)(22, 106, 30, 114)(31, 115, 37, 121)(32, 116, 38, 122)(33, 117, 39, 123)(34, 118, 40, 124)(35, 119, 41, 125)(36, 120, 42, 126)(43, 127, 49, 133)(44, 128, 50, 134)(45, 129, 51, 135)(46, 130, 52, 136)(47, 131, 53, 137)(48, 132, 54, 138)(55, 139, 61, 145)(56, 140, 62, 146)(57, 141, 63, 147)(58, 142, 64, 148)(59, 143, 65, 149)(60, 144, 66, 150)(67, 151, 73, 157)(68, 152, 74, 158)(69, 153, 75, 159)(70, 154, 76, 160)(71, 155, 77, 161)(72, 156, 78, 162)(79, 163, 82, 166)(80, 164, 83, 167)(81, 165, 84, 168)(169, 253, 171, 255, 176, 260, 185, 269, 178, 262, 172, 256)(170, 254, 173, 257, 180, 264, 189, 273, 182, 266, 174, 258)(175, 259, 183, 267, 192, 276, 186, 270, 177, 261, 184, 268)(179, 263, 187, 271, 196, 280, 190, 274, 181, 265, 188, 272)(191, 275, 199, 283, 194, 278, 201, 285, 193, 277, 200, 284)(195, 279, 202, 286, 198, 282, 204, 288, 197, 281, 203, 287)(205, 289, 211, 295, 207, 291, 213, 297, 206, 290, 212, 296)(208, 292, 214, 298, 210, 294, 216, 300, 209, 293, 215, 299)(217, 301, 223, 307, 219, 303, 225, 309, 218, 302, 224, 308)(220, 304, 226, 310, 222, 306, 228, 312, 221, 305, 227, 311)(229, 313, 235, 319, 231, 315, 237, 321, 230, 314, 236, 320)(232, 316, 238, 322, 234, 318, 240, 324, 233, 317, 239, 323)(241, 325, 247, 331, 243, 327, 249, 333, 242, 326, 248, 332)(244, 328, 250, 334, 246, 330, 252, 336, 245, 329, 251, 335) L = (1, 170)(2, 169)(3, 175)(4, 177)(5, 179)(6, 181)(7, 171)(8, 180)(9, 172)(10, 182)(11, 173)(12, 176)(13, 174)(14, 178)(15, 191)(16, 193)(17, 192)(18, 194)(19, 195)(20, 197)(21, 196)(22, 198)(23, 183)(24, 185)(25, 184)(26, 186)(27, 187)(28, 189)(29, 188)(30, 190)(31, 205)(32, 206)(33, 207)(34, 208)(35, 209)(36, 210)(37, 199)(38, 200)(39, 201)(40, 202)(41, 203)(42, 204)(43, 217)(44, 218)(45, 219)(46, 220)(47, 221)(48, 222)(49, 211)(50, 212)(51, 213)(52, 214)(53, 215)(54, 216)(55, 229)(56, 230)(57, 231)(58, 232)(59, 233)(60, 234)(61, 223)(62, 224)(63, 225)(64, 226)(65, 227)(66, 228)(67, 241)(68, 242)(69, 243)(70, 244)(71, 245)(72, 246)(73, 235)(74, 236)(75, 237)(76, 238)(77, 239)(78, 240)(79, 250)(80, 251)(81, 252)(82, 247)(83, 248)(84, 249)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 2, 84, 2, 84 ), ( 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84 ) } Outer automorphisms :: reflexible Dual of E14.548 Graph:: bipartite v = 56 e = 168 f = 86 degree seq :: [ 4^42, 12^14 ] E14.546 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 42}) Quotient :: dipole Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y2^-1 * Y1 * Y2^-1)^2, Y2 * Y1^-1 * Y2 * Y1^3, Y2 * Y1^-1 * Y2 * Y1^-3, Y1 * Y2^-13 * Y1^-1 * Y2 ] Map:: R = (1, 85, 2, 86, 6, 90, 16, 100, 13, 97, 4, 88)(3, 87, 9, 93, 17, 101, 8, 92, 21, 105, 11, 95)(5, 89, 14, 98, 18, 102, 12, 96, 20, 104, 7, 91)(10, 94, 24, 108, 29, 113, 23, 107, 33, 117, 22, 106)(15, 99, 26, 110, 30, 114, 19, 103, 31, 115, 27, 111)(25, 109, 34, 118, 41, 125, 36, 120, 45, 129, 35, 119)(28, 112, 32, 116, 42, 126, 39, 123, 43, 127, 38, 122)(37, 121, 47, 131, 53, 137, 46, 130, 57, 141, 48, 132)(40, 124, 51, 135, 54, 138, 50, 134, 55, 139, 44, 128)(49, 133, 60, 144, 65, 149, 59, 143, 69, 153, 58, 142)(52, 136, 62, 146, 66, 150, 56, 140, 67, 151, 63, 147)(61, 145, 70, 154, 77, 161, 72, 156, 81, 165, 71, 155)(64, 148, 68, 152, 78, 162, 75, 159, 79, 163, 74, 158)(73, 157, 80, 164, 76, 160, 82, 166, 84, 168, 83, 167)(169, 253, 171, 255, 178, 262, 193, 277, 205, 289, 217, 301, 229, 313, 241, 325, 247, 331, 235, 319, 223, 307, 211, 295, 199, 283, 188, 272, 181, 265, 189, 273, 201, 285, 213, 297, 225, 309, 237, 321, 249, 333, 252, 336, 246, 330, 234, 318, 222, 306, 210, 294, 198, 282, 186, 270, 174, 258, 185, 269, 197, 281, 209, 293, 221, 305, 233, 317, 245, 329, 244, 328, 232, 316, 220, 304, 208, 292, 196, 280, 183, 267, 173, 257)(170, 254, 175, 259, 187, 271, 200, 284, 212, 296, 224, 308, 236, 320, 248, 332, 239, 323, 227, 311, 215, 299, 203, 287, 191, 275, 177, 261, 172, 256, 180, 264, 194, 278, 206, 290, 218, 302, 230, 314, 242, 326, 251, 335, 240, 324, 228, 312, 216, 300, 204, 288, 192, 276, 179, 263, 184, 268, 182, 266, 195, 279, 207, 291, 219, 303, 231, 315, 243, 327, 250, 334, 238, 322, 226, 310, 214, 298, 202, 286, 190, 274, 176, 260) L = (1, 171)(2, 175)(3, 178)(4, 180)(5, 169)(6, 185)(7, 187)(8, 170)(9, 172)(10, 193)(11, 184)(12, 194)(13, 189)(14, 195)(15, 173)(16, 182)(17, 197)(18, 174)(19, 200)(20, 181)(21, 201)(22, 176)(23, 177)(24, 179)(25, 205)(26, 206)(27, 207)(28, 183)(29, 209)(30, 186)(31, 188)(32, 212)(33, 213)(34, 190)(35, 191)(36, 192)(37, 217)(38, 218)(39, 219)(40, 196)(41, 221)(42, 198)(43, 199)(44, 224)(45, 225)(46, 202)(47, 203)(48, 204)(49, 229)(50, 230)(51, 231)(52, 208)(53, 233)(54, 210)(55, 211)(56, 236)(57, 237)(58, 214)(59, 215)(60, 216)(61, 241)(62, 242)(63, 243)(64, 220)(65, 245)(66, 222)(67, 223)(68, 248)(69, 249)(70, 226)(71, 227)(72, 228)(73, 247)(74, 251)(75, 250)(76, 232)(77, 244)(78, 234)(79, 235)(80, 239)(81, 252)(82, 238)(83, 240)(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, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E14.547 Graph:: bipartite v = 16 e = 168 f = 126 degree seq :: [ 12^14, 84^2 ] E14.547 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 42}) Quotient :: dipole Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^3 * Y2)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y3^7 * Y2 * Y3^-7 * Y2, (Y3^-1 * Y1^-1)^42 ] Map:: polytopal R = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)(169, 253, 170, 254)(171, 255, 175, 259)(172, 256, 177, 261)(173, 257, 179, 263)(174, 258, 181, 265)(176, 260, 185, 269)(178, 262, 189, 273)(180, 264, 193, 277)(182, 266, 197, 281)(183, 267, 191, 275)(184, 268, 195, 279)(186, 270, 198, 282)(187, 271, 192, 276)(188, 272, 196, 280)(190, 274, 194, 278)(199, 283, 209, 293)(200, 284, 213, 297)(201, 285, 207, 291)(202, 286, 212, 296)(203, 287, 215, 299)(204, 288, 210, 294)(205, 289, 208, 292)(206, 290, 218, 302)(211, 295, 221, 305)(214, 298, 224, 308)(216, 300, 225, 309)(217, 301, 228, 312)(219, 303, 222, 306)(220, 304, 231, 315)(223, 307, 234, 318)(226, 310, 237, 321)(227, 311, 236, 320)(229, 313, 238, 322)(230, 314, 233, 317)(232, 316, 235, 319)(239, 323, 249, 333)(240, 324, 248, 332)(241, 325, 247, 331)(242, 326, 246, 330)(243, 327, 245, 329)(244, 328, 250, 334)(251, 335, 252, 336) L = (1, 171)(2, 173)(3, 176)(4, 169)(5, 180)(6, 170)(7, 183)(8, 186)(9, 187)(10, 172)(11, 191)(12, 194)(13, 195)(14, 174)(15, 199)(16, 175)(17, 201)(18, 203)(19, 204)(20, 177)(21, 205)(22, 178)(23, 207)(24, 179)(25, 209)(26, 211)(27, 212)(28, 181)(29, 213)(30, 182)(31, 189)(32, 184)(33, 188)(34, 185)(35, 217)(36, 218)(37, 219)(38, 190)(39, 197)(40, 192)(41, 196)(42, 193)(43, 223)(44, 224)(45, 225)(46, 198)(47, 200)(48, 202)(49, 229)(50, 230)(51, 231)(52, 206)(53, 208)(54, 210)(55, 235)(56, 236)(57, 237)(58, 214)(59, 215)(60, 216)(61, 241)(62, 242)(63, 243)(64, 220)(65, 221)(66, 222)(67, 247)(68, 248)(69, 249)(70, 226)(71, 227)(72, 228)(73, 245)(74, 250)(75, 251)(76, 232)(77, 233)(78, 234)(79, 239)(80, 244)(81, 252)(82, 238)(83, 240)(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) :: { ( 12, 84 ), ( 12, 84, 12, 84 ) } Outer automorphisms :: reflexible Dual of E14.546 Graph:: simple bipartite v = 126 e = 168 f = 16 degree seq :: [ 2^84, 4^42 ] E14.548 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 42}) Quotient :: dipole Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3, (Y3 * Y1^-3)^2, Y1^-4 * Y3 * Y1^4 * Y3 * Y1^-6 ] Map:: R = (1, 85, 2, 86, 5, 89, 11, 95, 23, 107, 39, 123, 53, 137, 65, 149, 77, 161, 73, 157, 60, 144, 49, 133, 33, 117, 16, 100, 28, 112, 42, 126, 35, 119, 46, 130, 58, 142, 70, 154, 82, 166, 84, 168, 83, 167, 72, 156, 61, 145, 48, 132, 32, 116, 45, 129, 34, 118, 17, 101, 29, 113, 43, 127, 56, 140, 68, 152, 80, 164, 76, 160, 64, 148, 52, 136, 38, 122, 22, 106, 10, 94, 4, 88)(3, 87, 7, 91, 15, 99, 31, 115, 47, 131, 59, 143, 71, 155, 78, 162, 69, 153, 55, 139, 40, 124, 30, 114, 14, 98, 6, 90, 13, 97, 27, 111, 21, 105, 37, 121, 51, 135, 63, 147, 75, 159, 81, 165, 67, 151, 54, 138, 44, 128, 26, 110, 12, 96, 25, 109, 20, 104, 9, 93, 19, 103, 36, 120, 50, 134, 62, 146, 74, 158, 79, 163, 66, 150, 57, 141, 41, 125, 24, 108, 18, 102, 8, 92)(169, 253)(170, 254)(171, 255)(172, 256)(173, 257)(174, 258)(175, 259)(176, 260)(177, 261)(178, 262)(179, 263)(180, 264)(181, 265)(182, 266)(183, 267)(184, 268)(185, 269)(186, 270)(187, 271)(188, 272)(189, 273)(190, 274)(191, 275)(192, 276)(193, 277)(194, 278)(195, 279)(196, 280)(197, 281)(198, 282)(199, 283)(200, 284)(201, 285)(202, 286)(203, 287)(204, 288)(205, 289)(206, 290)(207, 291)(208, 292)(209, 293)(210, 294)(211, 295)(212, 296)(213, 297)(214, 298)(215, 299)(216, 300)(217, 301)(218, 302)(219, 303)(220, 304)(221, 305)(222, 306)(223, 307)(224, 308)(225, 309)(226, 310)(227, 311)(228, 312)(229, 313)(230, 314)(231, 315)(232, 316)(233, 317)(234, 318)(235, 319)(236, 320)(237, 321)(238, 322)(239, 323)(240, 324)(241, 325)(242, 326)(243, 327)(244, 328)(245, 329)(246, 330)(247, 331)(248, 332)(249, 333)(250, 334)(251, 335)(252, 336) L = (1, 171)(2, 174)(3, 169)(4, 177)(5, 180)(6, 170)(7, 184)(8, 185)(9, 172)(10, 189)(11, 192)(12, 173)(13, 196)(14, 197)(15, 200)(16, 175)(17, 176)(18, 203)(19, 201)(20, 202)(21, 178)(22, 199)(23, 208)(24, 179)(25, 210)(26, 211)(27, 213)(28, 181)(29, 182)(30, 214)(31, 190)(32, 183)(33, 187)(34, 188)(35, 186)(36, 216)(37, 217)(38, 218)(39, 222)(40, 191)(41, 224)(42, 193)(43, 194)(44, 226)(45, 195)(46, 198)(47, 228)(48, 204)(49, 205)(50, 206)(51, 229)(52, 231)(53, 234)(54, 207)(55, 236)(56, 209)(57, 238)(58, 212)(59, 240)(60, 215)(61, 219)(62, 241)(63, 220)(64, 239)(65, 246)(66, 221)(67, 248)(68, 223)(69, 250)(70, 225)(71, 232)(72, 227)(73, 230)(74, 251)(75, 245)(76, 247)(77, 243)(78, 233)(79, 244)(80, 235)(81, 252)(82, 237)(83, 242)(84, 249)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 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 E14.545 Graph:: simple bipartite v = 86 e = 168 f = 56 degree seq :: [ 2^84, 84^2 ] E14.549 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 42}) Quotient :: dipole Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |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^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^6, Y2^13 * Y1 * Y2^-1 * Y1, (Y2^-1 * R * Y2^-6)^2 ] Map:: R = (1, 85, 2, 86)(3, 87, 7, 91)(4, 88, 9, 93)(5, 89, 11, 95)(6, 90, 13, 97)(8, 92, 17, 101)(10, 94, 21, 105)(12, 96, 25, 109)(14, 98, 29, 113)(15, 99, 23, 107)(16, 100, 27, 111)(18, 102, 30, 114)(19, 103, 24, 108)(20, 104, 28, 112)(22, 106, 26, 110)(31, 115, 41, 125)(32, 116, 45, 129)(33, 117, 39, 123)(34, 118, 44, 128)(35, 119, 47, 131)(36, 120, 42, 126)(37, 121, 40, 124)(38, 122, 50, 134)(43, 127, 53, 137)(46, 130, 56, 140)(48, 132, 57, 141)(49, 133, 60, 144)(51, 135, 54, 138)(52, 136, 63, 147)(55, 139, 66, 150)(58, 142, 69, 153)(59, 143, 68, 152)(61, 145, 70, 154)(62, 146, 65, 149)(64, 148, 67, 151)(71, 155, 81, 165)(72, 156, 80, 164)(73, 157, 79, 163)(74, 158, 78, 162)(75, 159, 77, 161)(76, 160, 82, 166)(83, 167, 84, 168)(169, 253, 171, 255, 176, 260, 186, 270, 203, 287, 217, 301, 229, 313, 241, 325, 245, 329, 233, 317, 221, 305, 208, 292, 192, 276, 179, 263, 191, 275, 207, 291, 197, 281, 213, 297, 225, 309, 237, 321, 249, 333, 252, 336, 246, 330, 234, 318, 222, 306, 210, 294, 193, 277, 209, 293, 196, 280, 181, 265, 195, 279, 212, 296, 224, 308, 236, 320, 248, 332, 244, 328, 232, 316, 220, 304, 206, 290, 190, 274, 178, 262, 172, 256)(170, 254, 173, 257, 180, 264, 194, 278, 211, 295, 223, 307, 235, 319, 247, 331, 239, 323, 227, 311, 215, 299, 200, 284, 184, 268, 175, 259, 183, 267, 199, 283, 189, 273, 205, 289, 219, 303, 231, 315, 243, 327, 251, 335, 240, 324, 228, 312, 216, 300, 202, 286, 185, 269, 201, 285, 188, 272, 177, 261, 187, 271, 204, 288, 218, 302, 230, 314, 242, 326, 250, 334, 238, 322, 226, 310, 214, 298, 198, 282, 182, 266, 174, 258) L = (1, 170)(2, 169)(3, 175)(4, 177)(5, 179)(6, 181)(7, 171)(8, 185)(9, 172)(10, 189)(11, 173)(12, 193)(13, 174)(14, 197)(15, 191)(16, 195)(17, 176)(18, 198)(19, 192)(20, 196)(21, 178)(22, 194)(23, 183)(24, 187)(25, 180)(26, 190)(27, 184)(28, 188)(29, 182)(30, 186)(31, 209)(32, 213)(33, 207)(34, 212)(35, 215)(36, 210)(37, 208)(38, 218)(39, 201)(40, 205)(41, 199)(42, 204)(43, 221)(44, 202)(45, 200)(46, 224)(47, 203)(48, 225)(49, 228)(50, 206)(51, 222)(52, 231)(53, 211)(54, 219)(55, 234)(56, 214)(57, 216)(58, 237)(59, 236)(60, 217)(61, 238)(62, 233)(63, 220)(64, 235)(65, 230)(66, 223)(67, 232)(68, 227)(69, 226)(70, 229)(71, 249)(72, 248)(73, 247)(74, 246)(75, 245)(76, 250)(77, 243)(78, 242)(79, 241)(80, 240)(81, 239)(82, 244)(83, 252)(84, 251)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E14.550 Graph:: bipartite v = 44 e = 168 f = 98 degree seq :: [ 4^42, 84^2 ] E14.550 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 42}) Quotient :: dipole Aut^+ = C6 x D14 (small group id <84, 12>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-2, Y3^-1 * Y1 * Y3^-1 * Y1^-3, (Y3^-2 * Y1)^2, Y3^-2 * Y1 * Y3^11 * Y1 * Y3^-1, (Y3 * Y2^-1)^42 ] Map:: R = (1, 85, 2, 86, 6, 90, 16, 100, 13, 97, 4, 88)(3, 87, 9, 93, 17, 101, 8, 92, 21, 105, 11, 95)(5, 89, 14, 98, 18, 102, 12, 96, 20, 104, 7, 91)(10, 94, 24, 108, 29, 113, 23, 107, 33, 117, 22, 106)(15, 99, 26, 110, 30, 114, 19, 103, 31, 115, 27, 111)(25, 109, 34, 118, 41, 125, 36, 120, 45, 129, 35, 119)(28, 112, 32, 116, 42, 126, 39, 123, 43, 127, 38, 122)(37, 121, 47, 131, 53, 137, 46, 130, 57, 141, 48, 132)(40, 124, 51, 135, 54, 138, 50, 134, 55, 139, 44, 128)(49, 133, 60, 144, 65, 149, 59, 143, 69, 153, 58, 142)(52, 136, 62, 146, 66, 150, 56, 140, 67, 151, 63, 147)(61, 145, 70, 154, 77, 161, 72, 156, 81, 165, 71, 155)(64, 148, 68, 152, 78, 162, 75, 159, 79, 163, 74, 158)(73, 157, 80, 164, 76, 160, 82, 166, 84, 168, 83, 167)(169, 253)(170, 254)(171, 255)(172, 256)(173, 257)(174, 258)(175, 259)(176, 260)(177, 261)(178, 262)(179, 263)(180, 264)(181, 265)(182, 266)(183, 267)(184, 268)(185, 269)(186, 270)(187, 271)(188, 272)(189, 273)(190, 274)(191, 275)(192, 276)(193, 277)(194, 278)(195, 279)(196, 280)(197, 281)(198, 282)(199, 283)(200, 284)(201, 285)(202, 286)(203, 287)(204, 288)(205, 289)(206, 290)(207, 291)(208, 292)(209, 293)(210, 294)(211, 295)(212, 296)(213, 297)(214, 298)(215, 299)(216, 300)(217, 301)(218, 302)(219, 303)(220, 304)(221, 305)(222, 306)(223, 307)(224, 308)(225, 309)(226, 310)(227, 311)(228, 312)(229, 313)(230, 314)(231, 315)(232, 316)(233, 317)(234, 318)(235, 319)(236, 320)(237, 321)(238, 322)(239, 323)(240, 324)(241, 325)(242, 326)(243, 327)(244, 328)(245, 329)(246, 330)(247, 331)(248, 332)(249, 333)(250, 334)(251, 335)(252, 336) L = (1, 171)(2, 175)(3, 178)(4, 180)(5, 169)(6, 185)(7, 187)(8, 170)(9, 172)(10, 193)(11, 184)(12, 194)(13, 189)(14, 195)(15, 173)(16, 182)(17, 197)(18, 174)(19, 200)(20, 181)(21, 201)(22, 176)(23, 177)(24, 179)(25, 205)(26, 206)(27, 207)(28, 183)(29, 209)(30, 186)(31, 188)(32, 212)(33, 213)(34, 190)(35, 191)(36, 192)(37, 217)(38, 218)(39, 219)(40, 196)(41, 221)(42, 198)(43, 199)(44, 224)(45, 225)(46, 202)(47, 203)(48, 204)(49, 229)(50, 230)(51, 231)(52, 208)(53, 233)(54, 210)(55, 211)(56, 236)(57, 237)(58, 214)(59, 215)(60, 216)(61, 241)(62, 242)(63, 243)(64, 220)(65, 245)(66, 222)(67, 223)(68, 248)(69, 249)(70, 226)(71, 227)(72, 228)(73, 247)(74, 251)(75, 250)(76, 232)(77, 244)(78, 234)(79, 235)(80, 239)(81, 252)(82, 238)(83, 240)(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) :: { ( 4, 84 ), ( 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84 ) } Outer automorphisms :: reflexible Dual of E14.549 Graph:: simple bipartite v = 98 e = 168 f = 44 degree seq :: [ 2^84, 12^14 ] E14.551 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 16}) Quotient :: regular Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1)^2, T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2, T1^16 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 61, 73, 72, 60, 46, 31, 19, 10, 4)(3, 7, 15, 25, 39, 55, 67, 79, 84, 75, 62, 49, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 58, 70, 82, 85, 74, 63, 48, 34, 21, 14)(16, 26, 17, 28, 35, 51, 64, 77, 86, 93, 89, 80, 68, 56, 40, 27)(23, 36, 24, 38, 50, 65, 76, 87, 92, 91, 83, 71, 59, 45, 30, 37)(41, 53, 42, 57, 69, 81, 90, 95, 96, 94, 88, 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, 84)(75, 86)(77, 88)(79, 89)(80, 90)(85, 92)(87, 94)(91, 95)(93, 96) local type(s) :: { ( 6^16 ) } Outer automorphisms :: reflexible Dual of E14.552 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 6 e = 48 f = 16 degree seq :: [ 16^6 ] E14.552 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 16}) Quotient :: regular Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1)^2, T1^6, T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 20, 12, 8)(6, 13, 9, 18, 19, 14)(16, 23, 17, 25, 27, 24)(21, 28, 22, 30, 26, 29)(31, 37, 32, 39, 33, 38)(34, 40, 35, 42, 36, 41)(43, 49, 44, 51, 45, 50)(46, 52, 47, 54, 48, 53)(55, 61, 56, 63, 57, 62)(58, 64, 59, 66, 60, 65)(67, 73, 68, 75, 69, 74)(70, 76, 71, 78, 72, 77)(79, 85, 80, 87, 81, 86)(82, 88, 83, 90, 84, 89)(91, 94, 92, 95, 93, 96) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 19)(13, 21)(14, 22)(18, 26)(20, 27)(23, 31)(24, 32)(25, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72)(73, 79)(74, 80)(75, 81)(76, 82)(77, 83)(78, 84)(85, 91)(86, 92)(87, 93)(88, 94)(89, 95)(90, 96) local type(s) :: { ( 16^6 ) } Outer automorphisms :: reflexible Dual of E14.551 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 16 e = 48 f = 6 degree seq :: [ 6^16 ] E14.553 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 16}) Quotient :: edge Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^6, (T2 * T1)^16 ] Map:: polytopal R = (1, 3, 8, 17, 10, 4)(2, 5, 12, 21, 14, 6)(7, 15, 9, 18, 25, 16)(11, 19, 13, 22, 29, 20)(23, 31, 24, 33, 26, 32)(27, 34, 28, 36, 30, 35)(37, 43, 38, 45, 39, 44)(40, 46, 41, 48, 42, 47)(49, 55, 50, 57, 51, 56)(52, 58, 53, 60, 54, 59)(61, 67, 62, 69, 63, 68)(64, 70, 65, 72, 66, 71)(73, 79, 74, 81, 75, 80)(76, 82, 77, 84, 78, 83)(85, 91, 86, 93, 87, 92)(88, 94, 89, 96, 90, 95)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 110)(106, 108)(111, 119)(112, 120)(113, 121)(114, 122)(115, 123)(116, 124)(117, 125)(118, 126)(127, 133)(128, 134)(129, 135)(130, 136)(131, 137)(132, 138)(139, 145)(140, 146)(141, 147)(142, 148)(143, 149)(144, 150)(151, 157)(152, 158)(153, 159)(154, 160)(155, 161)(156, 162)(163, 169)(164, 170)(165, 171)(166, 172)(167, 173)(168, 174)(175, 181)(176, 182)(177, 183)(178, 184)(179, 185)(180, 186)(187, 190)(188, 192)(189, 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 ), ( 32^6 ) } Outer automorphisms :: reflexible Dual of E14.557 Transitivity :: ET+ Graph:: simple bipartite v = 64 e = 96 f = 6 degree seq :: [ 2^48, 6^16 ] E14.554 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 16}) Quotient :: edge Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^6, T2^16 ] Map:: polytopal non-degenerate R = (1, 3, 10, 21, 33, 45, 57, 69, 81, 72, 60, 48, 36, 24, 13, 5)(2, 7, 17, 29, 41, 53, 65, 77, 88, 78, 66, 54, 42, 30, 18, 8)(4, 11, 23, 35, 47, 59, 71, 83, 90, 80, 68, 56, 44, 32, 20, 9)(6, 15, 27, 39, 51, 63, 75, 86, 94, 87, 76, 64, 52, 40, 28, 16)(12, 19, 31, 43, 55, 67, 79, 89, 95, 91, 82, 70, 58, 46, 34, 22)(14, 25, 37, 49, 61, 73, 84, 92, 96, 93, 85, 74, 62, 50, 38, 26)(97, 98, 102, 110, 108, 100)(99, 105, 115, 122, 111, 104)(101, 107, 118, 121, 112, 103)(106, 114, 123, 134, 127, 116)(109, 113, 124, 133, 130, 119)(117, 128, 139, 146, 135, 126)(120, 131, 142, 145, 136, 125)(129, 138, 147, 158, 151, 140)(132, 137, 148, 157, 154, 143)(141, 152, 163, 170, 159, 150)(144, 155, 166, 169, 160, 149)(153, 162, 171, 181, 175, 164)(156, 161, 172, 180, 178, 167)(165, 176, 185, 189, 182, 174)(168, 179, 187, 188, 183, 173)(177, 184, 190, 192, 191, 186) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^6 ), ( 4^16 ) } Outer automorphisms :: reflexible Dual of E14.558 Transitivity :: ET+ Graph:: simple bipartite v = 22 e = 96 f = 48 degree seq :: [ 6^16, 16^6 ] E14.555 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 16}) Quotient :: edge Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, T1^16 ] 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, 84)(75, 86)(77, 88)(79, 89)(80, 90)(85, 92)(87, 94)(91, 95)(93, 96)(97, 98, 101, 107, 116, 128, 143, 157, 169, 168, 156, 142, 127, 115, 106, 100)(99, 103, 111, 121, 135, 151, 163, 175, 180, 171, 158, 145, 129, 118, 108, 104)(102, 109, 105, 114, 125, 140, 154, 166, 178, 181, 170, 159, 144, 130, 117, 110)(112, 122, 113, 124, 131, 147, 160, 173, 182, 189, 185, 176, 164, 152, 136, 123)(119, 132, 120, 134, 146, 161, 172, 183, 188, 187, 179, 167, 155, 141, 126, 133)(137, 149, 138, 153, 165, 177, 186, 191, 192, 190, 184, 174, 162, 150, 139, 148) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12, 12 ), ( 12^16 ) } Outer automorphisms :: reflexible Dual of E14.556 Transitivity :: ET+ Graph:: simple bipartite v = 54 e = 96 f = 16 degree seq :: [ 2^48, 16^6 ] E14.556 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 16}) Quotient :: loop Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^6, (T2 * T1)^16 ] Map:: R = (1, 97, 3, 99, 8, 104, 17, 113, 10, 106, 4, 100)(2, 98, 5, 101, 12, 108, 21, 117, 14, 110, 6, 102)(7, 103, 15, 111, 9, 105, 18, 114, 25, 121, 16, 112)(11, 107, 19, 115, 13, 109, 22, 118, 29, 125, 20, 116)(23, 119, 31, 127, 24, 120, 33, 129, 26, 122, 32, 128)(27, 123, 34, 130, 28, 124, 36, 132, 30, 126, 35, 131)(37, 133, 43, 139, 38, 134, 45, 141, 39, 135, 44, 140)(40, 136, 46, 142, 41, 137, 48, 144, 42, 138, 47, 143)(49, 145, 55, 151, 50, 146, 57, 153, 51, 147, 56, 152)(52, 148, 58, 154, 53, 149, 60, 156, 54, 150, 59, 155)(61, 157, 67, 163, 62, 158, 69, 165, 63, 159, 68, 164)(64, 160, 70, 166, 65, 161, 72, 168, 66, 162, 71, 167)(73, 169, 79, 175, 74, 170, 81, 177, 75, 171, 80, 176)(76, 172, 82, 178, 77, 173, 84, 180, 78, 174, 83, 179)(85, 181, 91, 187, 86, 182, 93, 189, 87, 183, 92, 188)(88, 184, 94, 190, 89, 185, 96, 192, 90, 186, 95, 191) L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 110)(9, 100)(10, 108)(11, 101)(12, 106)(13, 102)(14, 104)(15, 119)(16, 120)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 133)(32, 134)(33, 135)(34, 136)(35, 137)(36, 138)(37, 127)(38, 128)(39, 129)(40, 130)(41, 131)(42, 132)(43, 145)(44, 146)(45, 147)(46, 148)(47, 149)(48, 150)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 157)(56, 158)(57, 159)(58, 160)(59, 161)(60, 162)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 169)(68, 170)(69, 171)(70, 172)(71, 173)(72, 174)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 181)(80, 182)(81, 183)(82, 184)(83, 185)(84, 186)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180)(91, 190)(92, 192)(93, 191)(94, 187)(95, 189)(96, 188) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E14.555 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 96 f = 54 degree seq :: [ 12^16 ] E14.557 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 16}) Quotient :: loop Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^6, T2^16 ] Map:: R = (1, 97, 3, 99, 10, 106, 21, 117, 33, 129, 45, 141, 57, 153, 69, 165, 81, 177, 72, 168, 60, 156, 48, 144, 36, 132, 24, 120, 13, 109, 5, 101)(2, 98, 7, 103, 17, 113, 29, 125, 41, 137, 53, 149, 65, 161, 77, 173, 88, 184, 78, 174, 66, 162, 54, 150, 42, 138, 30, 126, 18, 114, 8, 104)(4, 100, 11, 107, 23, 119, 35, 131, 47, 143, 59, 155, 71, 167, 83, 179, 90, 186, 80, 176, 68, 164, 56, 152, 44, 140, 32, 128, 20, 116, 9, 105)(6, 102, 15, 111, 27, 123, 39, 135, 51, 147, 63, 159, 75, 171, 86, 182, 94, 190, 87, 183, 76, 172, 64, 160, 52, 148, 40, 136, 28, 124, 16, 112)(12, 108, 19, 115, 31, 127, 43, 139, 55, 151, 67, 163, 79, 175, 89, 185, 95, 191, 91, 187, 82, 178, 70, 166, 58, 154, 46, 142, 34, 130, 22, 118)(14, 110, 25, 121, 37, 133, 49, 145, 61, 157, 73, 169, 84, 180, 92, 188, 96, 192, 93, 189, 85, 181, 74, 170, 62, 158, 50, 146, 38, 134, 26, 122) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 107)(6, 110)(7, 101)(8, 99)(9, 115)(10, 114)(11, 118)(12, 100)(13, 113)(14, 108)(15, 104)(16, 103)(17, 124)(18, 123)(19, 122)(20, 106)(21, 128)(22, 121)(23, 109)(24, 131)(25, 112)(26, 111)(27, 134)(28, 133)(29, 120)(30, 117)(31, 116)(32, 139)(33, 138)(34, 119)(35, 142)(36, 137)(37, 130)(38, 127)(39, 126)(40, 125)(41, 148)(42, 147)(43, 146)(44, 129)(45, 152)(46, 145)(47, 132)(48, 155)(49, 136)(50, 135)(51, 158)(52, 157)(53, 144)(54, 141)(55, 140)(56, 163)(57, 162)(58, 143)(59, 166)(60, 161)(61, 154)(62, 151)(63, 150)(64, 149)(65, 172)(66, 171)(67, 170)(68, 153)(69, 176)(70, 169)(71, 156)(72, 179)(73, 160)(74, 159)(75, 181)(76, 180)(77, 168)(78, 165)(79, 164)(80, 185)(81, 184)(82, 167)(83, 187)(84, 178)(85, 175)(86, 174)(87, 173)(88, 190)(89, 189)(90, 177)(91, 188)(92, 183)(93, 182)(94, 192)(95, 186)(96, 191) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E14.553 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 96 f = 64 degree seq :: [ 32^6 ] E14.558 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 16}) Quotient :: loop Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, T1^16 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99)(2, 98, 6, 102)(4, 100, 9, 105)(5, 101, 12, 108)(7, 103, 16, 112)(8, 104, 17, 113)(10, 106, 15, 111)(11, 107, 21, 117)(13, 109, 23, 119)(14, 110, 24, 120)(18, 114, 30, 126)(19, 115, 29, 125)(20, 116, 33, 129)(22, 118, 35, 131)(25, 121, 40, 136)(26, 122, 41, 137)(27, 123, 42, 138)(28, 124, 43, 139)(31, 127, 39, 135)(32, 128, 48, 144)(34, 130, 50, 146)(36, 132, 52, 148)(37, 133, 53, 149)(38, 134, 54, 150)(44, 140, 59, 155)(45, 141, 57, 153)(46, 142, 58, 154)(47, 143, 62, 158)(49, 145, 64, 160)(51, 147, 66, 162)(55, 151, 68, 164)(56, 152, 69, 165)(60, 156, 67, 163)(61, 157, 74, 170)(63, 159, 76, 172)(65, 161, 78, 174)(70, 166, 83, 179)(71, 167, 81, 177)(72, 168, 82, 178)(73, 169, 84, 180)(75, 171, 86, 182)(77, 173, 88, 184)(79, 175, 89, 185)(80, 176, 90, 186)(85, 181, 92, 188)(87, 183, 94, 190)(91, 187, 95, 191)(93, 189, 96, 192) L = (1, 98)(2, 101)(3, 103)(4, 97)(5, 107)(6, 109)(7, 111)(8, 99)(9, 114)(10, 100)(11, 116)(12, 104)(13, 105)(14, 102)(15, 121)(16, 122)(17, 124)(18, 125)(19, 106)(20, 128)(21, 110)(22, 108)(23, 132)(24, 134)(25, 135)(26, 113)(27, 112)(28, 131)(29, 140)(30, 133)(31, 115)(32, 143)(33, 118)(34, 117)(35, 147)(36, 120)(37, 119)(38, 146)(39, 151)(40, 123)(41, 149)(42, 153)(43, 148)(44, 154)(45, 126)(46, 127)(47, 157)(48, 130)(49, 129)(50, 161)(51, 160)(52, 137)(53, 138)(54, 139)(55, 163)(56, 136)(57, 165)(58, 166)(59, 141)(60, 142)(61, 169)(62, 145)(63, 144)(64, 173)(65, 172)(66, 150)(67, 175)(68, 152)(69, 177)(70, 178)(71, 155)(72, 156)(73, 168)(74, 159)(75, 158)(76, 183)(77, 182)(78, 162)(79, 180)(80, 164)(81, 186)(82, 181)(83, 167)(84, 171)(85, 170)(86, 189)(87, 188)(88, 174)(89, 176)(90, 191)(91, 179)(92, 187)(93, 185)(94, 184)(95, 192)(96, 190) local type(s) :: { ( 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E14.554 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 48 e = 96 f = 22 degree seq :: [ 4^48 ] E14.559 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 16}) Quotient :: dipole Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |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)^16 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 14, 110)(10, 106, 12, 108)(15, 111, 23, 119)(16, 112, 24, 120)(17, 113, 25, 121)(18, 114, 26, 122)(19, 115, 27, 123)(20, 116, 28, 124)(21, 117, 29, 125)(22, 118, 30, 126)(31, 127, 37, 133)(32, 128, 38, 134)(33, 129, 39, 135)(34, 130, 40, 136)(35, 131, 41, 137)(36, 132, 42, 138)(43, 139, 49, 145)(44, 140, 50, 146)(45, 141, 51, 147)(46, 142, 52, 148)(47, 143, 53, 149)(48, 144, 54, 150)(55, 151, 61, 157)(56, 152, 62, 158)(57, 153, 63, 159)(58, 154, 64, 160)(59, 155, 65, 161)(60, 156, 66, 162)(67, 163, 73, 169)(68, 164, 74, 170)(69, 165, 75, 171)(70, 166, 76, 172)(71, 167, 77, 173)(72, 168, 78, 174)(79, 175, 85, 181)(80, 176, 86, 182)(81, 177, 87, 183)(82, 178, 88, 184)(83, 179, 89, 185)(84, 180, 90, 186)(91, 187, 94, 190)(92, 188, 96, 192)(93, 189, 95, 191)(193, 289, 195, 291, 200, 296, 209, 305, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 213, 309, 206, 302, 198, 294)(199, 295, 207, 303, 201, 297, 210, 306, 217, 313, 208, 304)(203, 299, 211, 307, 205, 301, 214, 310, 221, 317, 212, 308)(215, 311, 223, 319, 216, 312, 225, 321, 218, 314, 224, 320)(219, 315, 226, 322, 220, 316, 228, 324, 222, 318, 227, 323)(229, 325, 235, 331, 230, 326, 237, 333, 231, 327, 236, 332)(232, 328, 238, 334, 233, 329, 240, 336, 234, 330, 239, 335)(241, 337, 247, 343, 242, 338, 249, 345, 243, 339, 248, 344)(244, 340, 250, 346, 245, 341, 252, 348, 246, 342, 251, 347)(253, 349, 259, 355, 254, 350, 261, 357, 255, 351, 260, 356)(256, 352, 262, 358, 257, 353, 264, 360, 258, 354, 263, 359)(265, 361, 271, 367, 266, 362, 273, 369, 267, 363, 272, 368)(268, 364, 274, 370, 269, 365, 276, 372, 270, 366, 275, 371)(277, 373, 283, 379, 278, 374, 285, 381, 279, 375, 284, 380)(280, 376, 286, 382, 281, 377, 288, 384, 282, 378, 287, 383) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 206)(9, 196)(10, 204)(11, 197)(12, 202)(13, 198)(14, 200)(15, 215)(16, 216)(17, 217)(18, 218)(19, 219)(20, 220)(21, 221)(22, 222)(23, 207)(24, 208)(25, 209)(26, 210)(27, 211)(28, 212)(29, 213)(30, 214)(31, 229)(32, 230)(33, 231)(34, 232)(35, 233)(36, 234)(37, 223)(38, 224)(39, 225)(40, 226)(41, 227)(42, 228)(43, 241)(44, 242)(45, 243)(46, 244)(47, 245)(48, 246)(49, 235)(50, 236)(51, 237)(52, 238)(53, 239)(54, 240)(55, 253)(56, 254)(57, 255)(58, 256)(59, 257)(60, 258)(61, 247)(62, 248)(63, 249)(64, 250)(65, 251)(66, 252)(67, 265)(68, 266)(69, 267)(70, 268)(71, 269)(72, 270)(73, 259)(74, 260)(75, 261)(76, 262)(77, 263)(78, 264)(79, 277)(80, 278)(81, 279)(82, 280)(83, 281)(84, 282)(85, 271)(86, 272)(87, 273)(88, 274)(89, 275)(90, 276)(91, 286)(92, 288)(93, 287)(94, 283)(95, 285)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E14.562 Graph:: bipartite v = 64 e = 192 f = 102 degree seq :: [ 4^48, 12^16 ] E14.560 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 16}) Quotient :: dipole Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^6, Y2^16 ] Map:: R = (1, 97, 2, 98, 6, 102, 14, 110, 12, 108, 4, 100)(3, 99, 9, 105, 19, 115, 26, 122, 15, 111, 8, 104)(5, 101, 11, 107, 22, 118, 25, 121, 16, 112, 7, 103)(10, 106, 18, 114, 27, 123, 38, 134, 31, 127, 20, 116)(13, 109, 17, 113, 28, 124, 37, 133, 34, 130, 23, 119)(21, 117, 32, 128, 43, 139, 50, 146, 39, 135, 30, 126)(24, 120, 35, 131, 46, 142, 49, 145, 40, 136, 29, 125)(33, 129, 42, 138, 51, 147, 62, 158, 55, 151, 44, 140)(36, 132, 41, 137, 52, 148, 61, 157, 58, 154, 47, 143)(45, 141, 56, 152, 67, 163, 74, 170, 63, 159, 54, 150)(48, 144, 59, 155, 70, 166, 73, 169, 64, 160, 53, 149)(57, 153, 66, 162, 75, 171, 85, 181, 79, 175, 68, 164)(60, 156, 65, 161, 76, 172, 84, 180, 82, 178, 71, 167)(69, 165, 80, 176, 89, 185, 93, 189, 86, 182, 78, 174)(72, 168, 83, 179, 91, 187, 92, 188, 87, 183, 77, 173)(81, 177, 88, 184, 94, 190, 96, 192, 95, 191, 90, 186)(193, 289, 195, 291, 202, 298, 213, 309, 225, 321, 237, 333, 249, 345, 261, 357, 273, 369, 264, 360, 252, 348, 240, 336, 228, 324, 216, 312, 205, 301, 197, 293)(194, 290, 199, 295, 209, 305, 221, 317, 233, 329, 245, 341, 257, 353, 269, 365, 280, 376, 270, 366, 258, 354, 246, 342, 234, 330, 222, 318, 210, 306, 200, 296)(196, 292, 203, 299, 215, 311, 227, 323, 239, 335, 251, 347, 263, 359, 275, 371, 282, 378, 272, 368, 260, 356, 248, 344, 236, 332, 224, 320, 212, 308, 201, 297)(198, 294, 207, 303, 219, 315, 231, 327, 243, 339, 255, 351, 267, 363, 278, 374, 286, 382, 279, 375, 268, 364, 256, 352, 244, 340, 232, 328, 220, 316, 208, 304)(204, 300, 211, 307, 223, 319, 235, 331, 247, 343, 259, 355, 271, 367, 281, 377, 287, 383, 283, 379, 274, 370, 262, 358, 250, 346, 238, 334, 226, 322, 214, 310)(206, 302, 217, 313, 229, 325, 241, 337, 253, 349, 265, 361, 276, 372, 284, 380, 288, 384, 285, 381, 277, 373, 266, 362, 254, 350, 242, 338, 230, 326, 218, 314) L = (1, 195)(2, 199)(3, 202)(4, 203)(5, 193)(6, 207)(7, 209)(8, 194)(9, 196)(10, 213)(11, 215)(12, 211)(13, 197)(14, 217)(15, 219)(16, 198)(17, 221)(18, 200)(19, 223)(20, 201)(21, 225)(22, 204)(23, 227)(24, 205)(25, 229)(26, 206)(27, 231)(28, 208)(29, 233)(30, 210)(31, 235)(32, 212)(33, 237)(34, 214)(35, 239)(36, 216)(37, 241)(38, 218)(39, 243)(40, 220)(41, 245)(42, 222)(43, 247)(44, 224)(45, 249)(46, 226)(47, 251)(48, 228)(49, 253)(50, 230)(51, 255)(52, 232)(53, 257)(54, 234)(55, 259)(56, 236)(57, 261)(58, 238)(59, 263)(60, 240)(61, 265)(62, 242)(63, 267)(64, 244)(65, 269)(66, 246)(67, 271)(68, 248)(69, 273)(70, 250)(71, 275)(72, 252)(73, 276)(74, 254)(75, 278)(76, 256)(77, 280)(78, 258)(79, 281)(80, 260)(81, 264)(82, 262)(83, 282)(84, 284)(85, 266)(86, 286)(87, 268)(88, 270)(89, 287)(90, 272)(91, 274)(92, 288)(93, 277)(94, 279)(95, 283)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 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 E14.561 Graph:: bipartite v = 22 e = 192 f = 144 degree seq :: [ 12^16, 32^6 ] E14.561 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 16}) Quotient :: dipole Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, Y3^6 * Y2 * Y3^-10 * Y2, (Y3^-1 * Y1^-1)^16 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290)(195, 291, 199, 295)(196, 292, 201, 297)(197, 293, 203, 299)(198, 294, 205, 301)(200, 296, 206, 302)(202, 298, 204, 300)(207, 303, 217, 313)(208, 304, 218, 314)(209, 305, 219, 315)(210, 306, 221, 317)(211, 307, 222, 318)(212, 308, 224, 320)(213, 309, 225, 321)(214, 310, 226, 322)(215, 311, 228, 324)(216, 312, 229, 325)(220, 316, 230, 326)(223, 319, 227, 323)(231, 327, 240, 336)(232, 328, 239, 335)(233, 329, 244, 340)(234, 330, 247, 343)(235, 331, 248, 344)(236, 332, 241, 337)(237, 333, 250, 346)(238, 334, 251, 347)(242, 338, 253, 349)(243, 339, 254, 350)(245, 341, 256, 352)(246, 342, 257, 353)(249, 345, 258, 354)(252, 348, 255, 351)(259, 355, 268, 364)(260, 356, 271, 367)(261, 357, 272, 368)(262, 358, 265, 361)(263, 359, 274, 370)(264, 360, 275, 371)(266, 362, 276, 372)(267, 363, 277, 373)(269, 365, 279, 375)(270, 366, 280, 376)(273, 369, 278, 374)(281, 377, 286, 382)(282, 378, 287, 383)(283, 379, 284, 380)(285, 381, 288, 384) L = (1, 195)(2, 197)(3, 200)(4, 193)(5, 204)(6, 194)(7, 207)(8, 209)(9, 210)(10, 196)(11, 212)(12, 214)(13, 215)(14, 198)(15, 201)(16, 199)(17, 220)(18, 222)(19, 202)(20, 205)(21, 203)(22, 227)(23, 229)(24, 206)(25, 231)(26, 233)(27, 208)(28, 235)(29, 232)(30, 237)(31, 211)(32, 239)(33, 241)(34, 213)(35, 243)(36, 240)(37, 245)(38, 216)(39, 218)(40, 217)(41, 247)(42, 219)(43, 249)(44, 221)(45, 251)(46, 223)(47, 225)(48, 224)(49, 253)(50, 226)(51, 255)(52, 228)(53, 257)(54, 230)(55, 259)(56, 234)(57, 261)(58, 236)(59, 263)(60, 238)(61, 265)(62, 242)(63, 267)(64, 244)(65, 269)(66, 246)(67, 271)(68, 248)(69, 273)(70, 250)(71, 275)(72, 252)(73, 276)(74, 254)(75, 278)(76, 256)(77, 280)(78, 258)(79, 281)(80, 260)(81, 264)(82, 262)(83, 282)(84, 284)(85, 266)(86, 270)(87, 268)(88, 285)(89, 287)(90, 272)(91, 274)(92, 288)(93, 277)(94, 279)(95, 283)(96, 286)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 12, 32 ), ( 12, 32, 12, 32 ) } Outer automorphisms :: reflexible Dual of E14.560 Graph:: simple bipartite v = 144 e = 192 f = 22 degree seq :: [ 2^96, 4^48 ] E14.562 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 16}) Quotient :: dipole Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |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)^6, Y1^16 ] Map:: polytopal R = (1, 97, 2, 98, 5, 101, 11, 107, 20, 116, 32, 128, 47, 143, 61, 157, 73, 169, 72, 168, 60, 156, 46, 142, 31, 127, 19, 115, 10, 106, 4, 100)(3, 99, 7, 103, 15, 111, 25, 121, 39, 135, 55, 151, 67, 163, 79, 175, 84, 180, 75, 171, 62, 158, 49, 145, 33, 129, 22, 118, 12, 108, 8, 104)(6, 102, 13, 109, 9, 105, 18, 114, 29, 125, 44, 140, 58, 154, 70, 166, 82, 178, 85, 181, 74, 170, 63, 159, 48, 144, 34, 130, 21, 117, 14, 110)(16, 112, 26, 122, 17, 113, 28, 124, 35, 131, 51, 147, 64, 160, 77, 173, 86, 182, 93, 189, 89, 185, 80, 176, 68, 164, 56, 152, 40, 136, 27, 123)(23, 119, 36, 132, 24, 120, 38, 134, 50, 146, 65, 161, 76, 172, 87, 183, 92, 188, 91, 187, 83, 179, 71, 167, 59, 155, 45, 141, 30, 126, 37, 133)(41, 137, 53, 149, 42, 138, 57, 153, 69, 165, 81, 177, 90, 186, 95, 191, 96, 192, 94, 190, 88, 184, 78, 174, 66, 162, 54, 150, 43, 139, 52, 148)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 198)(3, 193)(4, 201)(5, 204)(6, 194)(7, 208)(8, 209)(9, 196)(10, 207)(11, 213)(12, 197)(13, 215)(14, 216)(15, 202)(16, 199)(17, 200)(18, 222)(19, 221)(20, 225)(21, 203)(22, 227)(23, 205)(24, 206)(25, 232)(26, 233)(27, 234)(28, 235)(29, 211)(30, 210)(31, 231)(32, 240)(33, 212)(34, 242)(35, 214)(36, 244)(37, 245)(38, 246)(39, 223)(40, 217)(41, 218)(42, 219)(43, 220)(44, 251)(45, 249)(46, 250)(47, 254)(48, 224)(49, 256)(50, 226)(51, 258)(52, 228)(53, 229)(54, 230)(55, 260)(56, 261)(57, 237)(58, 238)(59, 236)(60, 259)(61, 266)(62, 239)(63, 268)(64, 241)(65, 270)(66, 243)(67, 252)(68, 247)(69, 248)(70, 275)(71, 273)(72, 274)(73, 276)(74, 253)(75, 278)(76, 255)(77, 280)(78, 257)(79, 281)(80, 282)(81, 263)(82, 264)(83, 262)(84, 265)(85, 284)(86, 267)(87, 286)(88, 269)(89, 271)(90, 272)(91, 287)(92, 277)(93, 288)(94, 279)(95, 283)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 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 E14.559 Graph:: simple bipartite v = 102 e = 192 f = 64 degree seq :: [ 2^96, 32^6 ] E14.563 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 16}) Quotient :: dipole Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |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, Y2^16 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 14, 110)(10, 106, 12, 108)(15, 111, 25, 121)(16, 112, 26, 122)(17, 113, 27, 123)(18, 114, 29, 125)(19, 115, 30, 126)(20, 116, 32, 128)(21, 117, 33, 129)(22, 118, 34, 130)(23, 119, 36, 132)(24, 120, 37, 133)(28, 124, 38, 134)(31, 127, 35, 131)(39, 135, 48, 144)(40, 136, 47, 143)(41, 137, 52, 148)(42, 138, 55, 151)(43, 139, 56, 152)(44, 140, 49, 145)(45, 141, 58, 154)(46, 142, 59, 155)(50, 146, 61, 157)(51, 147, 62, 158)(53, 149, 64, 160)(54, 150, 65, 161)(57, 153, 66, 162)(60, 156, 63, 159)(67, 163, 76, 172)(68, 164, 79, 175)(69, 165, 80, 176)(70, 166, 73, 169)(71, 167, 82, 178)(72, 168, 83, 179)(74, 170, 84, 180)(75, 171, 85, 181)(77, 173, 87, 183)(78, 174, 88, 184)(81, 177, 86, 182)(89, 185, 94, 190)(90, 186, 95, 191)(91, 187, 92, 188)(93, 189, 96, 192)(193, 289, 195, 291, 200, 296, 209, 305, 220, 316, 235, 331, 249, 345, 261, 357, 273, 369, 264, 360, 252, 348, 238, 334, 223, 319, 211, 307, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 214, 310, 227, 323, 243, 339, 255, 351, 267, 363, 278, 374, 270, 366, 258, 354, 246, 342, 230, 326, 216, 312, 206, 302, 198, 294)(199, 295, 207, 303, 201, 297, 210, 306, 222, 318, 237, 333, 251, 347, 263, 359, 275, 371, 282, 378, 272, 368, 260, 356, 248, 344, 234, 330, 219, 315, 208, 304)(203, 299, 212, 308, 205, 301, 215, 311, 229, 325, 245, 341, 257, 353, 269, 365, 280, 376, 285, 381, 277, 373, 266, 362, 254, 350, 242, 338, 226, 322, 213, 309)(217, 313, 231, 327, 218, 314, 233, 329, 247, 343, 259, 355, 271, 367, 281, 377, 287, 383, 283, 379, 274, 370, 262, 358, 250, 346, 236, 332, 221, 317, 232, 328)(224, 320, 239, 335, 225, 321, 241, 337, 253, 349, 265, 361, 276, 372, 284, 380, 288, 384, 286, 382, 279, 375, 268, 364, 256, 352, 244, 340, 228, 324, 240, 336) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 206)(9, 196)(10, 204)(11, 197)(12, 202)(13, 198)(14, 200)(15, 217)(16, 218)(17, 219)(18, 221)(19, 222)(20, 224)(21, 225)(22, 226)(23, 228)(24, 229)(25, 207)(26, 208)(27, 209)(28, 230)(29, 210)(30, 211)(31, 227)(32, 212)(33, 213)(34, 214)(35, 223)(36, 215)(37, 216)(38, 220)(39, 240)(40, 239)(41, 244)(42, 247)(43, 248)(44, 241)(45, 250)(46, 251)(47, 232)(48, 231)(49, 236)(50, 253)(51, 254)(52, 233)(53, 256)(54, 257)(55, 234)(56, 235)(57, 258)(58, 237)(59, 238)(60, 255)(61, 242)(62, 243)(63, 252)(64, 245)(65, 246)(66, 249)(67, 268)(68, 271)(69, 272)(70, 265)(71, 274)(72, 275)(73, 262)(74, 276)(75, 277)(76, 259)(77, 279)(78, 280)(79, 260)(80, 261)(81, 278)(82, 263)(83, 264)(84, 266)(85, 267)(86, 273)(87, 269)(88, 270)(89, 286)(90, 287)(91, 284)(92, 283)(93, 288)(94, 281)(95, 282)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 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 E14.564 Graph:: bipartite v = 54 e = 192 f = 112 degree seq :: [ 4^48, 32^6 ] E14.564 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 16}) Quotient :: dipole Aut^+ = (C3 x D16) : C2 (small group id <96, 33>) Aut = $<192, 469>$ (small group id <192, 469>) |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)^16 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 14, 110, 12, 108, 4, 100)(3, 99, 9, 105, 19, 115, 26, 122, 15, 111, 8, 104)(5, 101, 11, 107, 22, 118, 25, 121, 16, 112, 7, 103)(10, 106, 18, 114, 27, 123, 38, 134, 31, 127, 20, 116)(13, 109, 17, 113, 28, 124, 37, 133, 34, 130, 23, 119)(21, 117, 32, 128, 43, 139, 50, 146, 39, 135, 30, 126)(24, 120, 35, 131, 46, 142, 49, 145, 40, 136, 29, 125)(33, 129, 42, 138, 51, 147, 62, 158, 55, 151, 44, 140)(36, 132, 41, 137, 52, 148, 61, 157, 58, 154, 47, 143)(45, 141, 56, 152, 67, 163, 74, 170, 63, 159, 54, 150)(48, 144, 59, 155, 70, 166, 73, 169, 64, 160, 53, 149)(57, 153, 66, 162, 75, 171, 85, 181, 79, 175, 68, 164)(60, 156, 65, 161, 76, 172, 84, 180, 82, 178, 71, 167)(69, 165, 80, 176, 89, 185, 93, 189, 86, 182, 78, 174)(72, 168, 83, 179, 91, 187, 92, 188, 87, 183, 77, 173)(81, 177, 88, 184, 94, 190, 96, 192, 95, 191, 90, 186)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 203)(5, 193)(6, 207)(7, 209)(8, 194)(9, 196)(10, 213)(11, 215)(12, 211)(13, 197)(14, 217)(15, 219)(16, 198)(17, 221)(18, 200)(19, 223)(20, 201)(21, 225)(22, 204)(23, 227)(24, 205)(25, 229)(26, 206)(27, 231)(28, 208)(29, 233)(30, 210)(31, 235)(32, 212)(33, 237)(34, 214)(35, 239)(36, 216)(37, 241)(38, 218)(39, 243)(40, 220)(41, 245)(42, 222)(43, 247)(44, 224)(45, 249)(46, 226)(47, 251)(48, 228)(49, 253)(50, 230)(51, 255)(52, 232)(53, 257)(54, 234)(55, 259)(56, 236)(57, 261)(58, 238)(59, 263)(60, 240)(61, 265)(62, 242)(63, 267)(64, 244)(65, 269)(66, 246)(67, 271)(68, 248)(69, 273)(70, 250)(71, 275)(72, 252)(73, 276)(74, 254)(75, 278)(76, 256)(77, 280)(78, 258)(79, 281)(80, 260)(81, 264)(82, 262)(83, 282)(84, 284)(85, 266)(86, 286)(87, 268)(88, 270)(89, 287)(90, 272)(91, 274)(92, 288)(93, 277)(94, 279)(95, 283)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E14.563 Graph:: simple bipartite v = 112 e = 192 f = 54 degree seq :: [ 2^96, 12^16 ] E14.565 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 56}) Quotient :: regular Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T2 * T1^-1 * T2 * T1^27, T1^-2 * T2 * T1^13 * T2 * T1^-13 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 106, 98, 90, 82, 74, 66, 58, 50, 42, 34, 26, 16, 23, 17, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 108, 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97, 105, 111, 102, 95, 86, 79, 70, 63, 54, 47, 38, 31, 21, 14, 6, 13, 9, 18, 27, 35, 43, 51, 59, 67, 75, 83, 91, 99, 107, 110, 103, 94, 87, 78, 71, 62, 55, 46, 39, 30, 22, 12, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 70)(63, 72)(67, 74)(68, 75)(69, 78)(71, 80)(73, 82)(76, 81)(77, 86)(79, 88)(83, 90)(84, 91)(85, 94)(87, 96)(89, 98)(92, 97)(93, 102)(95, 104)(99, 106)(100, 107)(101, 110)(103, 112)(105, 109)(108, 111) local type(s) :: { ( 4^56 ) } Outer automorphisms :: reflexible Dual of E14.566 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 56 f = 28 degree seq :: [ 56^2 ] E14.566 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 56}) Quotient :: regular Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |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^-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, 51, 32, 52)(35, 55, 38, 56)(36, 57, 37, 58)(39, 59, 40, 60)(41, 61, 42, 62)(43, 63, 44, 64)(45, 65, 46, 66)(47, 67, 48, 68)(49, 69, 50, 70)(53, 73, 54, 74)(71, 91, 72, 92)(75, 95, 76, 96)(77, 97, 78, 98)(79, 99, 80, 100)(81, 101, 82, 102)(83, 103, 84, 104)(85, 105, 86, 106)(87, 107, 88, 108)(89, 109, 90, 110)(93, 112, 94, 111) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 38)(34, 35)(36, 52)(37, 51)(39, 55)(40, 56)(41, 57)(42, 58)(43, 59)(44, 60)(45, 61)(46, 62)(47, 63)(48, 64)(49, 65)(50, 66)(53, 67)(54, 68)(69, 71)(70, 72)(73, 76)(74, 75)(77, 92)(78, 91)(79, 95)(80, 96)(81, 97)(82, 98)(83, 99)(84, 100)(85, 101)(86, 102)(87, 103)(88, 104)(89, 105)(90, 106)(93, 107)(94, 108)(109, 111)(110, 112) local type(s) :: { ( 56^4 ) } Outer automorphisms :: reflexible Dual of E14.565 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 28 e = 56 f = 2 degree seq :: [ 4^28 ] E14.567 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 56}) Quotient :: edge Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] 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, 61, 34, 62)(35, 64, 42, 65)(36, 67, 45, 68)(37, 69, 38, 70)(39, 71, 40, 72)(41, 74, 43, 63)(44, 76, 46, 66)(47, 77, 48, 78)(49, 79, 50, 80)(51, 75, 52, 73)(53, 81, 54, 82)(55, 83, 56, 84)(57, 85, 58, 86)(59, 87, 60, 88)(89, 111, 90, 112)(91, 105, 102, 106)(92, 98, 93, 97)(94, 107, 104, 108)(95, 100, 96, 99)(101, 109, 103, 110)(113, 114)(115, 119)(116, 121)(117, 122)(118, 124)(120, 123)(125, 129)(126, 130)(127, 131)(128, 132)(133, 137)(134, 138)(135, 139)(136, 140)(141, 145)(142, 146)(143, 164)(144, 163)(147, 175)(148, 178)(149, 179)(150, 180)(151, 176)(152, 177)(153, 185)(154, 186)(155, 187)(156, 173)(157, 188)(158, 174)(159, 181)(160, 182)(161, 183)(162, 184)(165, 189)(166, 190)(167, 191)(168, 192)(169, 193)(170, 194)(171, 195)(172, 196)(197, 201)(198, 202)(199, 213)(200, 215)(203, 222)(204, 217)(205, 218)(206, 224)(207, 219)(208, 220)(209, 212)(210, 211)(214, 221)(216, 223) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 112, 112 ), ( 112^4 ) } Outer automorphisms :: reflexible Dual of E14.571 Transitivity :: ET+ Graph:: simple bipartite v = 84 e = 112 f = 2 degree seq :: [ 2^56, 4^28 ] E14.568 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 56}) Quotient :: edge Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1^-1)^2, (T2^-1 * T1^-1)^2, T2^27 * T1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 110, 102, 94, 86, 78, 70, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 108, 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 111, 105, 97, 89, 81, 73, 65, 57, 49, 41, 33, 25, 17, 9, 4, 11, 19, 27, 35, 43, 51, 59, 67, 75, 83, 91, 99, 107, 112, 104, 96, 88, 80, 72, 64, 56, 48, 40, 32, 24, 16, 8)(113, 114, 118, 116)(115, 121, 125, 120)(117, 123, 126, 119)(122, 128, 133, 129)(124, 127, 134, 131)(130, 137, 141, 136)(132, 139, 142, 135)(138, 144, 149, 145)(140, 143, 150, 147)(146, 153, 157, 152)(148, 155, 158, 151)(154, 160, 165, 161)(156, 159, 166, 163)(162, 169, 173, 168)(164, 171, 174, 167)(170, 176, 181, 177)(172, 175, 182, 179)(178, 185, 189, 184)(180, 187, 190, 183)(186, 192, 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, 220, 223) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4^4 ), ( 4^56 ) } Outer automorphisms :: reflexible Dual of E14.572 Transitivity :: ET+ Graph:: bipartite v = 30 e = 112 f = 56 degree seq :: [ 4^28, 56^2 ] E14.569 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 56}) Quotient :: edge Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T2 * T1^-1 * T2 * T1^27, T1^-2 * T2 * T1^13 * T2 * T1^-13 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 70)(63, 72)(67, 74)(68, 75)(69, 78)(71, 80)(73, 82)(76, 81)(77, 86)(79, 88)(83, 90)(84, 91)(85, 94)(87, 96)(89, 98)(92, 97)(93, 102)(95, 104)(99, 106)(100, 107)(101, 110)(103, 112)(105, 109)(108, 111)(113, 114, 117, 123, 132, 141, 149, 157, 165, 173, 181, 189, 197, 205, 213, 221, 218, 210, 202, 194, 186, 178, 170, 162, 154, 146, 138, 128, 135, 129, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 220, 212, 204, 196, 188, 180, 172, 164, 156, 148, 140, 131, 122, 116)(115, 119, 127, 137, 145, 153, 161, 169, 177, 185, 193, 201, 209, 217, 223, 214, 207, 198, 191, 182, 175, 166, 159, 150, 143, 133, 126, 118, 125, 121, 130, 139, 147, 155, 163, 171, 179, 187, 195, 203, 211, 219, 222, 215, 206, 199, 190, 183, 174, 167, 158, 151, 142, 134, 124, 120) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 8, 8 ), ( 8^56 ) } Outer automorphisms :: reflexible Dual of E14.570 Transitivity :: ET+ Graph:: simple bipartite v = 58 e = 112 f = 28 degree seq :: [ 2^56, 56^2 ] E14.570 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 56}) Quotient :: loop Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 113, 3, 115, 8, 120, 4, 116)(2, 114, 5, 117, 11, 123, 6, 118)(7, 119, 13, 125, 9, 121, 14, 126)(10, 122, 15, 127, 12, 124, 16, 128)(17, 129, 21, 133, 18, 130, 22, 134)(19, 131, 23, 135, 20, 132, 24, 136)(25, 137, 29, 141, 26, 138, 30, 142)(27, 139, 31, 143, 28, 140, 32, 144)(33, 145, 44, 156, 34, 146, 46, 158)(35, 147, 62, 174, 42, 154, 64, 176)(36, 148, 66, 178, 45, 157, 68, 180)(37, 149, 70, 182, 38, 150, 65, 177)(39, 151, 75, 187, 40, 152, 61, 173)(41, 153, 59, 171, 43, 155, 57, 169)(47, 159, 72, 184, 48, 160, 69, 181)(49, 161, 77, 189, 50, 162, 74, 186)(51, 163, 87, 199, 52, 164, 85, 197)(53, 165, 91, 203, 54, 166, 89, 201)(55, 167, 95, 207, 56, 168, 93, 205)(58, 170, 99, 211, 60, 172, 97, 209)(63, 175, 109, 221, 80, 192, 110, 222)(67, 179, 111, 223, 83, 195, 112, 224)(71, 183, 106, 218, 73, 185, 108, 220)(76, 188, 102, 214, 78, 190, 104, 216)(79, 191, 107, 219, 81, 193, 105, 217)(82, 194, 103, 215, 84, 196, 101, 213)(86, 198, 100, 212, 88, 200, 98, 210)(90, 202, 96, 208, 92, 204, 94, 206) L = (1, 114)(2, 113)(3, 119)(4, 121)(5, 122)(6, 124)(7, 115)(8, 123)(9, 116)(10, 117)(11, 120)(12, 118)(13, 129)(14, 130)(15, 131)(16, 132)(17, 125)(18, 126)(19, 127)(20, 128)(21, 137)(22, 138)(23, 139)(24, 140)(25, 133)(26, 134)(27, 135)(28, 136)(29, 145)(30, 146)(31, 169)(32, 171)(33, 141)(34, 142)(35, 173)(36, 177)(37, 181)(38, 184)(39, 186)(40, 189)(41, 174)(42, 187)(43, 176)(44, 178)(45, 182)(46, 180)(47, 197)(48, 199)(49, 201)(50, 203)(51, 205)(52, 207)(53, 209)(54, 211)(55, 213)(56, 215)(57, 143)(58, 217)(59, 144)(60, 219)(61, 147)(62, 153)(63, 216)(64, 155)(65, 148)(66, 156)(67, 220)(68, 158)(69, 149)(70, 157)(71, 210)(72, 150)(73, 212)(74, 151)(75, 154)(76, 206)(77, 152)(78, 208)(79, 221)(80, 214)(81, 222)(82, 223)(83, 218)(84, 224)(85, 159)(86, 204)(87, 160)(88, 202)(89, 161)(90, 200)(91, 162)(92, 198)(93, 163)(94, 188)(95, 164)(96, 190)(97, 165)(98, 183)(99, 166)(100, 185)(101, 167)(102, 192)(103, 168)(104, 175)(105, 170)(106, 195)(107, 172)(108, 179)(109, 191)(110, 193)(111, 194)(112, 196) local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56 ) } Outer automorphisms :: reflexible Dual of E14.569 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 28 e = 112 f = 58 degree seq :: [ 8^28 ] E14.571 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 56}) Quotient :: loop Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1^-1)^2, (T2^-1 * T1^-1)^2, T2^27 * T1 * T2^-1 * T1^-1 ] Map:: R = (1, 113, 3, 115, 10, 122, 18, 130, 26, 138, 34, 146, 42, 154, 50, 162, 58, 170, 66, 178, 74, 186, 82, 194, 90, 202, 98, 210, 106, 218, 110, 222, 102, 214, 94, 206, 86, 198, 78, 190, 70, 182, 62, 174, 54, 166, 46, 158, 38, 150, 30, 142, 22, 134, 14, 126, 6, 118, 13, 125, 21, 133, 29, 141, 37, 149, 45, 157, 53, 165, 61, 173, 69, 181, 77, 189, 85, 197, 93, 205, 101, 213, 109, 221, 108, 220, 100, 212, 92, 204, 84, 196, 76, 188, 68, 180, 60, 172, 52, 164, 44, 156, 36, 148, 28, 140, 20, 132, 12, 124, 5, 117)(2, 114, 7, 119, 15, 127, 23, 135, 31, 143, 39, 151, 47, 159, 55, 167, 63, 175, 71, 183, 79, 191, 87, 199, 95, 207, 103, 215, 111, 223, 105, 217, 97, 209, 89, 201, 81, 193, 73, 185, 65, 177, 57, 169, 49, 161, 41, 153, 33, 145, 25, 137, 17, 129, 9, 121, 4, 116, 11, 123, 19, 131, 27, 139, 35, 147, 43, 155, 51, 163, 59, 171, 67, 179, 75, 187, 83, 195, 91, 203, 99, 211, 107, 219, 112, 224, 104, 216, 96, 208, 88, 200, 80, 192, 72, 184, 64, 176, 56, 168, 48, 160, 40, 152, 32, 144, 24, 136, 16, 128, 8, 120) 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, 166)(48, 165)(49, 154)(50, 169)(51, 156)(52, 171)(53, 161)(54, 163)(55, 164)(56, 162)(57, 173)(58, 176)(59, 174)(60, 175)(61, 168)(62, 167)(63, 182)(64, 181)(65, 170)(66, 185)(67, 172)(68, 187)(69, 177)(70, 179)(71, 180)(72, 178)(73, 189)(74, 192)(75, 190)(76, 191)(77, 184)(78, 183)(79, 198)(80, 197)(81, 186)(82, 201)(83, 188)(84, 203)(85, 193)(86, 195)(87, 196)(88, 194)(89, 205)(90, 208)(91, 206)(92, 207)(93, 200)(94, 199)(95, 214)(96, 213)(97, 202)(98, 217)(99, 204)(100, 219)(101, 209)(102, 211)(103, 212)(104, 210)(105, 221)(106, 224)(107, 222)(108, 223)(109, 216)(110, 215)(111, 218)(112, 220) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E14.567 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 112 f = 84 degree seq :: [ 112^2 ] E14.572 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 56}) Quotient :: loop Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T2 * T1^-1 * T2 * T1^27, T1^-2 * T2 * T1^13 * T2 * T1^-13 ] 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, 26, 138)(19, 131, 27, 139)(20, 132, 30, 142)(22, 134, 32, 144)(25, 137, 34, 146)(28, 140, 33, 145)(29, 141, 38, 150)(31, 143, 40, 152)(35, 147, 42, 154)(36, 148, 43, 155)(37, 149, 46, 158)(39, 151, 48, 160)(41, 153, 50, 162)(44, 156, 49, 161)(45, 157, 54, 166)(47, 159, 56, 168)(51, 163, 58, 170)(52, 164, 59, 171)(53, 165, 62, 174)(55, 167, 64, 176)(57, 169, 66, 178)(60, 172, 65, 177)(61, 173, 70, 182)(63, 175, 72, 184)(67, 179, 74, 186)(68, 180, 75, 187)(69, 181, 78, 190)(71, 183, 80, 192)(73, 185, 82, 194)(76, 188, 81, 193)(77, 189, 86, 198)(79, 191, 88, 200)(83, 195, 90, 202)(84, 196, 91, 203)(85, 197, 94, 206)(87, 199, 96, 208)(89, 201, 98, 210)(92, 204, 97, 209)(93, 205, 102, 214)(95, 207, 104, 216)(99, 211, 106, 218)(100, 212, 107, 219)(101, 213, 110, 222)(103, 215, 112, 224)(105, 217, 109, 221)(108, 220, 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, 135)(17, 136)(18, 139)(19, 122)(20, 141)(21, 126)(22, 124)(23, 129)(24, 144)(25, 145)(26, 128)(27, 147)(28, 131)(29, 149)(30, 134)(31, 133)(32, 152)(33, 153)(34, 138)(35, 155)(36, 140)(37, 157)(38, 143)(39, 142)(40, 160)(41, 161)(42, 146)(43, 163)(44, 148)(45, 165)(46, 151)(47, 150)(48, 168)(49, 169)(50, 154)(51, 171)(52, 156)(53, 173)(54, 159)(55, 158)(56, 176)(57, 177)(58, 162)(59, 179)(60, 164)(61, 181)(62, 167)(63, 166)(64, 184)(65, 185)(66, 170)(67, 187)(68, 172)(69, 189)(70, 175)(71, 174)(72, 192)(73, 193)(74, 178)(75, 195)(76, 180)(77, 197)(78, 183)(79, 182)(80, 200)(81, 201)(82, 186)(83, 203)(84, 188)(85, 205)(86, 191)(87, 190)(88, 208)(89, 209)(90, 194)(91, 211)(92, 196)(93, 213)(94, 199)(95, 198)(96, 216)(97, 217)(98, 202)(99, 219)(100, 204)(101, 221)(102, 207)(103, 206)(104, 224)(105, 223)(106, 210)(107, 222)(108, 212)(109, 218)(110, 215)(111, 214)(112, 220) local type(s) :: { ( 4, 56, 4, 56 ) } Outer automorphisms :: reflexible Dual of E14.568 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 56 e = 112 f = 30 degree seq :: [ 4^56 ] E14.573 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 56}) Quotient :: dipole Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^56 ] Map:: R = (1, 113, 2, 114)(3, 115, 7, 119)(4, 116, 9, 121)(5, 117, 10, 122)(6, 118, 12, 124)(8, 120, 11, 123)(13, 125, 17, 129)(14, 126, 18, 130)(15, 127, 19, 131)(16, 128, 20, 132)(21, 133, 25, 137)(22, 134, 26, 138)(23, 135, 27, 139)(24, 136, 28, 140)(29, 141, 33, 145)(30, 142, 34, 146)(31, 143, 38, 150)(32, 144, 37, 149)(35, 147, 53, 165)(36, 148, 60, 172)(39, 151, 57, 169)(40, 152, 55, 167)(41, 153, 59, 171)(42, 154, 61, 173)(43, 155, 64, 176)(44, 156, 63, 175)(45, 157, 67, 179)(46, 158, 69, 181)(47, 159, 72, 184)(48, 160, 74, 186)(49, 161, 77, 189)(50, 162, 79, 191)(51, 163, 81, 193)(52, 164, 83, 195)(54, 166, 85, 197)(56, 168, 87, 199)(58, 170, 94, 206)(62, 174, 102, 214)(65, 177, 91, 203)(66, 178, 89, 201)(68, 180, 98, 210)(70, 182, 93, 205)(71, 183, 97, 209)(73, 185, 103, 215)(75, 187, 100, 212)(76, 188, 101, 213)(78, 190, 108, 220)(80, 192, 107, 219)(82, 194, 111, 223)(84, 196, 109, 221)(86, 198, 104, 216)(88, 200, 112, 224)(90, 202, 99, 211)(92, 204, 110, 222)(95, 207, 105, 217)(96, 208, 106, 218)(225, 337, 227, 339, 232, 344, 228, 340)(226, 338, 229, 341, 235, 347, 230, 342)(231, 343, 237, 349, 233, 345, 238, 350)(234, 346, 239, 351, 236, 348, 240, 352)(241, 353, 245, 357, 242, 354, 246, 358)(243, 355, 247, 359, 244, 356, 248, 360)(249, 361, 253, 365, 250, 362, 254, 366)(251, 363, 255, 367, 252, 364, 256, 368)(257, 369, 277, 389, 258, 370, 279, 391)(259, 371, 281, 393, 264, 376, 283, 395)(260, 372, 285, 397, 267, 379, 287, 399)(261, 373, 288, 400, 262, 374, 284, 396)(263, 375, 291, 403, 265, 377, 293, 405)(266, 378, 296, 408, 268, 380, 298, 410)(269, 381, 301, 413, 270, 382, 303, 415)(271, 383, 305, 417, 272, 384, 307, 419)(273, 385, 309, 421, 274, 386, 311, 423)(275, 387, 313, 425, 276, 388, 315, 427)(278, 390, 318, 430, 280, 392, 317, 429)(282, 394, 322, 434, 294, 406, 321, 433)(286, 398, 327, 439, 299, 411, 325, 437)(289, 401, 324, 436, 290, 402, 326, 438)(292, 404, 332, 444, 295, 407, 331, 443)(297, 409, 335, 447, 300, 412, 333, 445)(302, 414, 328, 440, 304, 416, 336, 448)(306, 418, 323, 435, 308, 420, 334, 446)(310, 422, 329, 441, 312, 424, 330, 442)(314, 426, 320, 432, 316, 428, 319, 431) L = (1, 226)(2, 225)(3, 231)(4, 233)(5, 234)(6, 236)(7, 227)(8, 235)(9, 228)(10, 229)(11, 232)(12, 230)(13, 241)(14, 242)(15, 243)(16, 244)(17, 237)(18, 238)(19, 239)(20, 240)(21, 249)(22, 250)(23, 251)(24, 252)(25, 245)(26, 246)(27, 247)(28, 248)(29, 257)(30, 258)(31, 262)(32, 261)(33, 253)(34, 254)(35, 277)(36, 284)(37, 256)(38, 255)(39, 281)(40, 279)(41, 283)(42, 285)(43, 288)(44, 287)(45, 291)(46, 293)(47, 296)(48, 298)(49, 301)(50, 303)(51, 305)(52, 307)(53, 259)(54, 309)(55, 264)(56, 311)(57, 263)(58, 318)(59, 265)(60, 260)(61, 266)(62, 326)(63, 268)(64, 267)(65, 315)(66, 313)(67, 269)(68, 322)(69, 270)(70, 317)(71, 321)(72, 271)(73, 327)(74, 272)(75, 324)(76, 325)(77, 273)(78, 332)(79, 274)(80, 331)(81, 275)(82, 335)(83, 276)(84, 333)(85, 278)(86, 328)(87, 280)(88, 336)(89, 290)(90, 323)(91, 289)(92, 334)(93, 294)(94, 282)(95, 329)(96, 330)(97, 295)(98, 292)(99, 314)(100, 299)(101, 300)(102, 286)(103, 297)(104, 310)(105, 319)(106, 320)(107, 304)(108, 302)(109, 308)(110, 316)(111, 306)(112, 312)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112 ) } Outer automorphisms :: reflexible Dual of E14.576 Graph:: bipartite v = 84 e = 224 f = 114 degree seq :: [ 4^56, 8^28 ] E14.574 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 56}) Quotient :: dipole Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |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^-28 * Y1^-1 ] Map:: R = (1, 113, 2, 114, 6, 118, 4, 116)(3, 115, 9, 121, 13, 125, 8, 120)(5, 117, 11, 123, 14, 126, 7, 119)(10, 122, 16, 128, 21, 133, 17, 129)(12, 124, 15, 127, 22, 134, 19, 131)(18, 130, 25, 137, 29, 141, 24, 136)(20, 132, 27, 139, 30, 142, 23, 135)(26, 138, 32, 144, 37, 149, 33, 145)(28, 140, 31, 143, 38, 150, 35, 147)(34, 146, 41, 153, 45, 157, 40, 152)(36, 148, 43, 155, 46, 158, 39, 151)(42, 154, 48, 160, 53, 165, 49, 161)(44, 156, 47, 159, 54, 166, 51, 163)(50, 162, 57, 169, 61, 173, 56, 168)(52, 164, 59, 171, 62, 174, 55, 167)(58, 170, 64, 176, 69, 181, 65, 177)(60, 172, 63, 175, 70, 182, 67, 179)(66, 178, 73, 185, 77, 189, 72, 184)(68, 180, 75, 187, 78, 190, 71, 183)(74, 186, 80, 192, 85, 197, 81, 193)(76, 188, 79, 191, 86, 198, 83, 195)(82, 194, 89, 201, 93, 205, 88, 200)(84, 196, 91, 203, 94, 206, 87, 199)(90, 202, 96, 208, 101, 213, 97, 209)(92, 204, 95, 207, 102, 214, 99, 211)(98, 210, 105, 217, 109, 221, 104, 216)(100, 212, 107, 219, 110, 222, 103, 215)(106, 218, 112, 224, 108, 220, 111, 223)(225, 337, 227, 339, 234, 346, 242, 354, 250, 362, 258, 370, 266, 378, 274, 386, 282, 394, 290, 402, 298, 410, 306, 418, 314, 426, 322, 434, 330, 442, 334, 446, 326, 438, 318, 430, 310, 422, 302, 414, 294, 406, 286, 398, 278, 390, 270, 382, 262, 374, 254, 366, 246, 358, 238, 350, 230, 342, 237, 349, 245, 357, 253, 365, 261, 373, 269, 381, 277, 389, 285, 397, 293, 405, 301, 413, 309, 421, 317, 429, 325, 437, 333, 445, 332, 444, 324, 436, 316, 428, 308, 420, 300, 412, 292, 404, 284, 396, 276, 388, 268, 380, 260, 372, 252, 364, 244, 356, 236, 348, 229, 341)(226, 338, 231, 343, 239, 351, 247, 359, 255, 367, 263, 375, 271, 383, 279, 391, 287, 399, 295, 407, 303, 415, 311, 423, 319, 431, 327, 439, 335, 447, 329, 441, 321, 433, 313, 425, 305, 417, 297, 409, 289, 401, 281, 393, 273, 385, 265, 377, 257, 369, 249, 361, 241, 353, 233, 345, 228, 340, 235, 347, 243, 355, 251, 363, 259, 371, 267, 379, 275, 387, 283, 395, 291, 403, 299, 411, 307, 419, 315, 427, 323, 435, 331, 443, 336, 448, 328, 440, 320, 432, 312, 424, 304, 416, 296, 408, 288, 400, 280, 392, 272, 384, 264, 376, 256, 368, 248, 360, 240, 352, 232, 344) L = (1, 227)(2, 231)(3, 234)(4, 235)(5, 225)(6, 237)(7, 239)(8, 226)(9, 228)(10, 242)(11, 243)(12, 229)(13, 245)(14, 230)(15, 247)(16, 232)(17, 233)(18, 250)(19, 251)(20, 236)(21, 253)(22, 238)(23, 255)(24, 240)(25, 241)(26, 258)(27, 259)(28, 244)(29, 261)(30, 246)(31, 263)(32, 248)(33, 249)(34, 266)(35, 267)(36, 252)(37, 269)(38, 254)(39, 271)(40, 256)(41, 257)(42, 274)(43, 275)(44, 260)(45, 277)(46, 262)(47, 279)(48, 264)(49, 265)(50, 282)(51, 283)(52, 268)(53, 285)(54, 270)(55, 287)(56, 272)(57, 273)(58, 290)(59, 291)(60, 276)(61, 293)(62, 278)(63, 295)(64, 280)(65, 281)(66, 298)(67, 299)(68, 284)(69, 301)(70, 286)(71, 303)(72, 288)(73, 289)(74, 306)(75, 307)(76, 292)(77, 309)(78, 294)(79, 311)(80, 296)(81, 297)(82, 314)(83, 315)(84, 300)(85, 317)(86, 302)(87, 319)(88, 304)(89, 305)(90, 322)(91, 323)(92, 308)(93, 325)(94, 310)(95, 327)(96, 312)(97, 313)(98, 330)(99, 331)(100, 316)(101, 333)(102, 318)(103, 335)(104, 320)(105, 321)(106, 334)(107, 336)(108, 324)(109, 332)(110, 326)(111, 329)(112, 328)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E14.575 Graph:: bipartite v = 30 e = 224 f = 168 degree seq :: [ 8^28, 112^2 ] E14.575 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 56}) Quotient :: dipole Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |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, Y3^25 * Y2 * Y3^-3 * Y2, (Y3^-1 * Y1^-1)^56 ] 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, 244, 356)(240, 352, 247, 359)(241, 353, 249, 361)(242, 354, 245, 357)(243, 355, 251, 363)(246, 358, 253, 365)(248, 360, 255, 367)(250, 362, 256, 368)(252, 364, 254, 366)(257, 369, 263, 375)(258, 370, 265, 377)(259, 371, 261, 373)(260, 372, 267, 379)(262, 374, 269, 381)(264, 376, 271, 383)(266, 378, 272, 384)(268, 380, 270, 382)(273, 385, 279, 391)(274, 386, 281, 393)(275, 387, 277, 389)(276, 388, 283, 395)(278, 390, 285, 397)(280, 392, 287, 399)(282, 394, 288, 400)(284, 396, 286, 398)(289, 401, 295, 407)(290, 402, 297, 409)(291, 403, 293, 405)(292, 404, 299, 411)(294, 406, 301, 413)(296, 408, 303, 415)(298, 410, 304, 416)(300, 412, 302, 414)(305, 417, 311, 423)(306, 418, 313, 425)(307, 419, 309, 421)(308, 420, 315, 427)(310, 422, 317, 429)(312, 424, 319, 431)(314, 426, 320, 432)(316, 428, 318, 430)(321, 433, 327, 439)(322, 434, 329, 441)(323, 435, 325, 437)(324, 436, 331, 443)(326, 438, 333, 445)(328, 440, 335, 447)(330, 442, 336, 448)(332, 444, 334, 446) 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, 250)(18, 251)(19, 234)(20, 237)(21, 235)(22, 254)(23, 255)(24, 238)(25, 240)(26, 258)(27, 259)(28, 243)(29, 245)(30, 262)(31, 263)(32, 248)(33, 249)(34, 266)(35, 267)(36, 252)(37, 253)(38, 270)(39, 271)(40, 256)(41, 257)(42, 274)(43, 275)(44, 260)(45, 261)(46, 278)(47, 279)(48, 264)(49, 265)(50, 282)(51, 283)(52, 268)(53, 269)(54, 286)(55, 287)(56, 272)(57, 273)(58, 290)(59, 291)(60, 276)(61, 277)(62, 294)(63, 295)(64, 280)(65, 281)(66, 298)(67, 299)(68, 284)(69, 285)(70, 302)(71, 303)(72, 288)(73, 289)(74, 306)(75, 307)(76, 292)(77, 293)(78, 310)(79, 311)(80, 296)(81, 297)(82, 314)(83, 315)(84, 300)(85, 301)(86, 318)(87, 319)(88, 304)(89, 305)(90, 322)(91, 323)(92, 308)(93, 309)(94, 326)(95, 327)(96, 312)(97, 313)(98, 330)(99, 331)(100, 316)(101, 317)(102, 334)(103, 335)(104, 320)(105, 321)(106, 333)(107, 336)(108, 324)(109, 325)(110, 329)(111, 332)(112, 328)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 8, 112 ), ( 8, 112, 8, 112 ) } Outer automorphisms :: reflexible Dual of E14.574 Graph:: simple bipartite v = 168 e = 224 f = 30 degree seq :: [ 2^112, 4^56 ] E14.576 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 56}) Quotient :: dipole Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y3 * Y1^-2)^2, (Y3 * Y1)^4, Y3 * Y1^-1 * Y3 * Y1^27, Y1^-2 * Y3 * Y1^13 * Y3 * Y1^-13 ] Map:: R = (1, 113, 2, 114, 5, 117, 11, 123, 20, 132, 29, 141, 37, 149, 45, 157, 53, 165, 61, 173, 69, 181, 77, 189, 85, 197, 93, 205, 101, 213, 109, 221, 106, 218, 98, 210, 90, 202, 82, 194, 74, 186, 66, 178, 58, 170, 50, 162, 42, 154, 34, 146, 26, 138, 16, 128, 23, 135, 17, 129, 24, 136, 32, 144, 40, 152, 48, 160, 56, 168, 64, 176, 72, 184, 80, 192, 88, 200, 96, 208, 104, 216, 112, 224, 108, 220, 100, 212, 92, 204, 84, 196, 76, 188, 68, 180, 60, 172, 52, 164, 44, 156, 36, 148, 28, 140, 19, 131, 10, 122, 4, 116)(3, 115, 7, 119, 15, 127, 25, 137, 33, 145, 41, 153, 49, 161, 57, 169, 65, 177, 73, 185, 81, 193, 89, 201, 97, 209, 105, 217, 111, 223, 102, 214, 95, 207, 86, 198, 79, 191, 70, 182, 63, 175, 54, 166, 47, 159, 38, 150, 31, 143, 21, 133, 14, 126, 6, 118, 13, 125, 9, 121, 18, 130, 27, 139, 35, 147, 43, 155, 51, 163, 59, 171, 67, 179, 75, 187, 83, 195, 91, 203, 99, 211, 107, 219, 110, 222, 103, 215, 94, 206, 87, 199, 78, 190, 71, 183, 62, 174, 55, 167, 46, 158, 39, 151, 30, 142, 22, 134, 12, 124, 8, 120)(225, 337)(226, 338)(227, 339)(228, 340)(229, 341)(230, 342)(231, 343)(232, 344)(233, 345)(234, 346)(235, 347)(236, 348)(237, 349)(238, 350)(239, 351)(240, 352)(241, 353)(242, 354)(243, 355)(244, 356)(245, 357)(246, 358)(247, 359)(248, 360)(249, 361)(250, 362)(251, 363)(252, 364)(253, 365)(254, 366)(255, 367)(256, 368)(257, 369)(258, 370)(259, 371)(260, 372)(261, 373)(262, 374)(263, 375)(264, 376)(265, 377)(266, 378)(267, 379)(268, 380)(269, 381)(270, 382)(271, 383)(272, 384)(273, 385)(274, 386)(275, 387)(276, 388)(277, 389)(278, 390)(279, 391)(280, 392)(281, 393)(282, 394)(283, 395)(284, 396)(285, 397)(286, 398)(287, 399)(288, 400)(289, 401)(290, 402)(291, 403)(292, 404)(293, 405)(294, 406)(295, 407)(296, 408)(297, 409)(298, 410)(299, 411)(300, 412)(301, 413)(302, 414)(303, 415)(304, 416)(305, 417)(306, 418)(307, 419)(308, 420)(309, 421)(310, 422)(311, 423)(312, 424)(313, 425)(314, 426)(315, 427)(316, 428)(317, 429)(318, 430)(319, 431)(320, 432)(321, 433)(322, 434)(323, 435)(324, 436)(325, 437)(326, 438)(327, 439)(328, 440)(329, 441)(330, 442)(331, 443)(332, 444)(333, 445)(334, 446)(335, 447)(336, 448) L = (1, 227)(2, 230)(3, 225)(4, 233)(5, 236)(6, 226)(7, 240)(8, 241)(9, 228)(10, 239)(11, 245)(12, 229)(13, 247)(14, 248)(15, 234)(16, 231)(17, 232)(18, 250)(19, 251)(20, 254)(21, 235)(22, 256)(23, 237)(24, 238)(25, 258)(26, 242)(27, 243)(28, 257)(29, 262)(30, 244)(31, 264)(32, 246)(33, 252)(34, 249)(35, 266)(36, 267)(37, 270)(38, 253)(39, 272)(40, 255)(41, 274)(42, 259)(43, 260)(44, 273)(45, 278)(46, 261)(47, 280)(48, 263)(49, 268)(50, 265)(51, 282)(52, 283)(53, 286)(54, 269)(55, 288)(56, 271)(57, 290)(58, 275)(59, 276)(60, 289)(61, 294)(62, 277)(63, 296)(64, 279)(65, 284)(66, 281)(67, 298)(68, 299)(69, 302)(70, 285)(71, 304)(72, 287)(73, 306)(74, 291)(75, 292)(76, 305)(77, 310)(78, 293)(79, 312)(80, 295)(81, 300)(82, 297)(83, 314)(84, 315)(85, 318)(86, 301)(87, 320)(88, 303)(89, 322)(90, 307)(91, 308)(92, 321)(93, 326)(94, 309)(95, 328)(96, 311)(97, 316)(98, 313)(99, 330)(100, 331)(101, 334)(102, 317)(103, 336)(104, 319)(105, 333)(106, 323)(107, 324)(108, 335)(109, 329)(110, 325)(111, 332)(112, 327)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E14.573 Graph:: simple bipartite v = 114 e = 224 f = 84 degree seq :: [ 2^112, 112^2 ] E14.577 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 56}) Quotient :: dipole Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^4, Y2^3 * Y1 * Y2^-25 * 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, 20, 132)(16, 128, 23, 135)(17, 129, 25, 137)(18, 130, 21, 133)(19, 131, 27, 139)(22, 134, 29, 141)(24, 136, 31, 143)(26, 138, 32, 144)(28, 140, 30, 142)(33, 145, 39, 151)(34, 146, 41, 153)(35, 147, 37, 149)(36, 148, 43, 155)(38, 150, 45, 157)(40, 152, 47, 159)(42, 154, 48, 160)(44, 156, 46, 158)(49, 161, 55, 167)(50, 162, 57, 169)(51, 163, 53, 165)(52, 164, 59, 171)(54, 166, 61, 173)(56, 168, 63, 175)(58, 170, 64, 176)(60, 172, 62, 174)(65, 177, 71, 183)(66, 178, 73, 185)(67, 179, 69, 181)(68, 180, 75, 187)(70, 182, 77, 189)(72, 184, 79, 191)(74, 186, 80, 192)(76, 188, 78, 190)(81, 193, 87, 199)(82, 194, 89, 201)(83, 195, 85, 197)(84, 196, 91, 203)(86, 198, 93, 205)(88, 200, 95, 207)(90, 202, 96, 208)(92, 204, 94, 206)(97, 209, 103, 215)(98, 210, 105, 217)(99, 211, 101, 213)(100, 212, 107, 219)(102, 214, 109, 221)(104, 216, 111, 223)(106, 218, 112, 224)(108, 220, 110, 222)(225, 337, 227, 339, 232, 344, 241, 353, 250, 362, 258, 370, 266, 378, 274, 386, 282, 394, 290, 402, 298, 410, 306, 418, 314, 426, 322, 434, 330, 442, 333, 445, 325, 437, 317, 429, 309, 421, 301, 413, 293, 405, 285, 397, 277, 389, 269, 381, 261, 373, 253, 365, 245, 357, 235, 347, 244, 356, 237, 349, 247, 359, 255, 367, 263, 375, 271, 383, 279, 391, 287, 399, 295, 407, 303, 415, 311, 423, 319, 431, 327, 439, 335, 447, 332, 444, 324, 436, 316, 428, 308, 420, 300, 412, 292, 404, 284, 396, 276, 388, 268, 380, 260, 372, 252, 364, 243, 355, 234, 346, 228, 340)(226, 338, 229, 341, 236, 348, 246, 358, 254, 366, 262, 374, 270, 382, 278, 390, 286, 398, 294, 406, 302, 414, 310, 422, 318, 430, 326, 438, 334, 446, 329, 441, 321, 433, 313, 425, 305, 417, 297, 409, 289, 401, 281, 393, 273, 385, 265, 377, 257, 369, 249, 361, 240, 352, 231, 343, 239, 351, 233, 345, 242, 354, 251, 363, 259, 371, 267, 379, 275, 387, 283, 395, 291, 403, 299, 411, 307, 419, 315, 427, 323, 435, 331, 443, 336, 448, 328, 440, 320, 432, 312, 424, 304, 416, 296, 408, 288, 400, 280, 392, 272, 384, 264, 376, 256, 368, 248, 360, 238, 350, 230, 342) L = (1, 226)(2, 225)(3, 231)(4, 233)(5, 235)(6, 237)(7, 227)(8, 238)(9, 228)(10, 236)(11, 229)(12, 234)(13, 230)(14, 232)(15, 244)(16, 247)(17, 249)(18, 245)(19, 251)(20, 239)(21, 242)(22, 253)(23, 240)(24, 255)(25, 241)(26, 256)(27, 243)(28, 254)(29, 246)(30, 252)(31, 248)(32, 250)(33, 263)(34, 265)(35, 261)(36, 267)(37, 259)(38, 269)(39, 257)(40, 271)(41, 258)(42, 272)(43, 260)(44, 270)(45, 262)(46, 268)(47, 264)(48, 266)(49, 279)(50, 281)(51, 277)(52, 283)(53, 275)(54, 285)(55, 273)(56, 287)(57, 274)(58, 288)(59, 276)(60, 286)(61, 278)(62, 284)(63, 280)(64, 282)(65, 295)(66, 297)(67, 293)(68, 299)(69, 291)(70, 301)(71, 289)(72, 303)(73, 290)(74, 304)(75, 292)(76, 302)(77, 294)(78, 300)(79, 296)(80, 298)(81, 311)(82, 313)(83, 309)(84, 315)(85, 307)(86, 317)(87, 305)(88, 319)(89, 306)(90, 320)(91, 308)(92, 318)(93, 310)(94, 316)(95, 312)(96, 314)(97, 327)(98, 329)(99, 325)(100, 331)(101, 323)(102, 333)(103, 321)(104, 335)(105, 322)(106, 336)(107, 324)(108, 334)(109, 326)(110, 332)(111, 328)(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, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E14.578 Graph:: bipartite v = 58 e = 224 f = 140 degree seq :: [ 4^56, 112^2 ] E14.578 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 56}) Quotient :: dipole Aut^+ = C56 : C2 (small group id <112, 5>) Aut = (C2 x D56) : C2 (small group id <224, 103>) |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^-28 * Y1^-1, (Y3 * Y2^-1)^56 ] Map:: R = (1, 113, 2, 114, 6, 118, 4, 116)(3, 115, 9, 121, 13, 125, 8, 120)(5, 117, 11, 123, 14, 126, 7, 119)(10, 122, 16, 128, 21, 133, 17, 129)(12, 124, 15, 127, 22, 134, 19, 131)(18, 130, 25, 137, 29, 141, 24, 136)(20, 132, 27, 139, 30, 142, 23, 135)(26, 138, 32, 144, 37, 149, 33, 145)(28, 140, 31, 143, 38, 150, 35, 147)(34, 146, 41, 153, 45, 157, 40, 152)(36, 148, 43, 155, 46, 158, 39, 151)(42, 154, 48, 160, 53, 165, 49, 161)(44, 156, 47, 159, 54, 166, 51, 163)(50, 162, 57, 169, 61, 173, 56, 168)(52, 164, 59, 171, 62, 174, 55, 167)(58, 170, 64, 176, 69, 181, 65, 177)(60, 172, 63, 175, 70, 182, 67, 179)(66, 178, 73, 185, 77, 189, 72, 184)(68, 180, 75, 187, 78, 190, 71, 183)(74, 186, 80, 192, 85, 197, 81, 193)(76, 188, 79, 191, 86, 198, 83, 195)(82, 194, 89, 201, 93, 205, 88, 200)(84, 196, 91, 203, 94, 206, 87, 199)(90, 202, 96, 208, 101, 213, 97, 209)(92, 204, 95, 207, 102, 214, 99, 211)(98, 210, 105, 217, 109, 221, 104, 216)(100, 212, 107, 219, 110, 222, 103, 215)(106, 218, 112, 224, 108, 220, 111, 223)(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, 237)(7, 239)(8, 226)(9, 228)(10, 242)(11, 243)(12, 229)(13, 245)(14, 230)(15, 247)(16, 232)(17, 233)(18, 250)(19, 251)(20, 236)(21, 253)(22, 238)(23, 255)(24, 240)(25, 241)(26, 258)(27, 259)(28, 244)(29, 261)(30, 246)(31, 263)(32, 248)(33, 249)(34, 266)(35, 267)(36, 252)(37, 269)(38, 254)(39, 271)(40, 256)(41, 257)(42, 274)(43, 275)(44, 260)(45, 277)(46, 262)(47, 279)(48, 264)(49, 265)(50, 282)(51, 283)(52, 268)(53, 285)(54, 270)(55, 287)(56, 272)(57, 273)(58, 290)(59, 291)(60, 276)(61, 293)(62, 278)(63, 295)(64, 280)(65, 281)(66, 298)(67, 299)(68, 284)(69, 301)(70, 286)(71, 303)(72, 288)(73, 289)(74, 306)(75, 307)(76, 292)(77, 309)(78, 294)(79, 311)(80, 296)(81, 297)(82, 314)(83, 315)(84, 300)(85, 317)(86, 302)(87, 319)(88, 304)(89, 305)(90, 322)(91, 323)(92, 308)(93, 325)(94, 310)(95, 327)(96, 312)(97, 313)(98, 330)(99, 331)(100, 316)(101, 333)(102, 318)(103, 335)(104, 320)(105, 321)(106, 334)(107, 336)(108, 324)(109, 332)(110, 326)(111, 329)(112, 328)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 4, 112 ), ( 4, 112, 4, 112, 4, 112, 4, 112 ) } Outer automorphisms :: reflexible Dual of E14.577 Graph:: simple bipartite v = 140 e = 224 f = 58 degree seq :: [ 2^112, 8^28 ] E14.579 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 5}) 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, T2^4, (F * T1)^2, (F * T2)^2, T2^2 * T1 * T2^-2 * T1^-1, T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, (T2^-1 * T1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 3, 9, 5)(2, 6, 16, 7)(4, 11, 22, 12)(8, 20, 13, 21)(10, 23, 14, 24)(15, 29, 18, 30)(17, 31, 19, 32)(25, 41, 27, 42)(26, 43, 28, 44)(33, 53, 35, 54)(34, 55, 36, 56)(37, 57, 39, 58)(38, 47, 40, 45)(46, 65, 48, 66)(49, 67, 51, 68)(50, 61, 52, 59)(60, 77, 62, 78)(63, 79, 64, 80)(69, 89, 71, 90)(70, 75, 72, 73)(74, 91, 76, 92)(81, 101, 83, 102)(82, 87, 84, 85)(86, 103, 88, 104)(93, 111, 95, 112)(94, 99, 96, 97)(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, 173)(164, 184, 174)(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) :: { ( 10^3 ), ( 10^4 ) } Outer automorphisms :: reflexible Dual of E14.583 Transitivity :: ET+ Graph:: simple bipartite v = 70 e = 120 f = 24 degree seq :: [ 3^40, 4^30 ] E14.580 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 5}) 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, T1^4, (F * T2)^2, (F * T1)^2, T2^5, T1 * T2^-1 * T1^2 * T2 * T1, (T2^-1 * T1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 3, 10, 16, 5)(2, 7, 20, 24, 8)(4, 12, 29, 30, 13)(6, 17, 35, 36, 18)(9, 22, 41, 47, 25)(11, 23, 42, 50, 28)(14, 31, 52, 40, 21)(15, 32, 54, 37, 19)(26, 45, 65, 69, 48)(27, 46, 66, 70, 49)(33, 55, 75, 74, 53)(34, 56, 76, 71, 51)(38, 57, 77, 79, 59)(39, 58, 78, 80, 60)(43, 63, 83, 82, 62)(44, 64, 84, 81, 61)(67, 87, 103, 102, 86)(68, 88, 104, 101, 85)(72, 91, 107, 109, 93)(73, 92, 108, 110, 94)(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, 155, 147)(136, 153, 156, 154)(140, 158, 149, 159)(144, 163, 150, 164)(145, 165, 148, 166)(151, 171, 152, 173)(157, 177, 160, 178)(161, 181, 162, 182)(167, 187, 170, 188)(168, 175, 169, 176)(172, 192, 174, 193)(179, 183, 180, 184)(185, 205, 186, 206)(189, 209, 190, 210)(191, 211, 194, 212)(195, 215, 196, 216)(197, 213, 198, 214)(199, 217, 200, 218)(201, 207, 202, 208)(203, 219, 204, 220)(221, 225, 222, 226)(223, 235, 224, 236)(227, 231, 228, 232)(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 ), ( 6^5 ) } Outer automorphisms :: reflexible Dual of E14.584 Transitivity :: ET+ Graph:: simple bipartite v = 54 e = 120 f = 40 degree seq :: [ 4^30, 5^24 ] E14.581 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 5}) 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, T1^5, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-2 * T2^-1, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-2 * T2^-1, T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2, (T2^-1 * T1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 11, 13)(6, 16, 17)(9, 23, 24)(10, 25, 27)(12, 30, 31)(14, 35, 36)(15, 37, 39)(18, 43, 33)(19, 44, 46)(20, 38, 48)(21, 49, 51)(22, 29, 52)(26, 57, 58)(28, 53, 42)(32, 54, 64)(34, 56, 65)(40, 67, 69)(41, 50, 71)(45, 66, 74)(47, 73, 75)(55, 63, 78)(59, 61, 84)(60, 85, 86)(62, 72, 88)(68, 76, 92)(70, 91, 93)(77, 79, 100)(80, 82, 102)(81, 103, 96)(83, 101, 105)(87, 94, 107)(89, 90, 108)(95, 113, 110)(97, 98, 114)(99, 106, 115)(104, 116, 117)(109, 119, 118)(111, 112, 120)(121, 122, 126, 132, 124)(123, 129, 142, 146, 130)(125, 134, 154, 158, 135)(127, 138, 147, 165, 139)(128, 140, 167, 170, 141)(131, 148, 179, 180, 149)(133, 152, 183, 155, 153)(136, 157, 166, 188, 160)(137, 161, 190, 192, 162)(143, 163, 159, 171, 173)(144, 151, 182, 199, 174)(145, 175, 200, 201, 176)(150, 169, 189, 207, 181)(156, 178, 203, 210, 186)(164, 185, 209, 215, 193)(168, 194, 216, 218, 196)(172, 197, 219, 221, 198)(177, 184, 206, 224, 202)(187, 195, 217, 229, 211)(191, 212, 230, 232, 214)(204, 213, 231, 236, 220)(205, 208, 227, 238, 226)(222, 235, 240, 234, 228)(223, 225, 237, 239, 233) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 8^3 ), ( 8^5 ) } Outer automorphisms :: reflexible Dual of E14.582 Transitivity :: ET+ Graph:: simple bipartite v = 64 e = 120 f = 30 degree seq :: [ 3^40, 5^24 ] E14.582 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 5}) Quotient :: loop Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^4, (F * T1)^2, (F * T2)^2, T2^2 * T1 * T2^-2 * T1^-1, T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, (T2^-1 * T1^-1)^5 ] Map:: polytopal 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, 47, 167, 40, 160, 45, 165)(46, 166, 65, 185, 48, 168, 66, 186)(49, 169, 67, 187, 51, 171, 68, 188)(50, 170, 61, 181, 52, 172, 59, 179)(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, 75, 195, 72, 192, 73, 193)(74, 194, 91, 211, 76, 196, 92, 212)(81, 201, 101, 221, 83, 203, 102, 222)(82, 202, 87, 207, 84, 204, 85, 205)(86, 206, 103, 223, 88, 208, 104, 224)(93, 213, 111, 231, 95, 215, 112, 232)(94, 214, 99, 219, 96, 216, 97, 217)(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, 163)(54, 164)(55, 189)(56, 191)(57, 193)(58, 195)(59, 180)(60, 161)(61, 182)(62, 162)(63, 173)(64, 174)(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, 5, 3, 5, 3, 5, 3, 5 ) } Outer automorphisms :: reflexible Dual of E14.581 Transitivity :: ET+ VT+ AT Graph:: v = 30 e = 120 f = 64 degree seq :: [ 8^30 ] E14.583 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 5}) 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, T1^4, (F * T2)^2, (F * T1)^2, T2^5, T1 * T2^-1 * T1^2 * T2 * T1, (T2^-1 * T1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123, 10, 130, 16, 136, 5, 125)(2, 122, 7, 127, 20, 140, 24, 144, 8, 128)(4, 124, 12, 132, 29, 149, 30, 150, 13, 133)(6, 126, 17, 137, 35, 155, 36, 156, 18, 138)(9, 129, 22, 142, 41, 161, 47, 167, 25, 145)(11, 131, 23, 143, 42, 162, 50, 170, 28, 148)(14, 134, 31, 151, 52, 172, 40, 160, 21, 141)(15, 135, 32, 152, 54, 174, 37, 157, 19, 139)(26, 146, 45, 165, 65, 185, 69, 189, 48, 168)(27, 147, 46, 166, 66, 186, 70, 190, 49, 169)(33, 153, 55, 175, 75, 195, 74, 194, 53, 173)(34, 154, 56, 176, 76, 196, 71, 191, 51, 171)(38, 158, 57, 177, 77, 197, 79, 199, 59, 179)(39, 159, 58, 178, 78, 198, 80, 200, 60, 180)(43, 163, 63, 183, 83, 203, 82, 202, 62, 182)(44, 164, 64, 184, 84, 204, 81, 201, 61, 181)(67, 187, 87, 207, 103, 223, 102, 222, 86, 206)(68, 188, 88, 208, 104, 224, 101, 221, 85, 205)(72, 192, 91, 211, 107, 227, 109, 229, 93, 213)(73, 193, 92, 212, 108, 228, 110, 230, 94, 214)(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, 153)(17, 131)(18, 135)(19, 132)(20, 158)(21, 127)(22, 133)(23, 128)(24, 163)(25, 165)(26, 155)(27, 130)(28, 166)(29, 159)(30, 164)(31, 171)(32, 173)(33, 156)(34, 136)(35, 147)(36, 154)(37, 177)(38, 149)(39, 140)(40, 178)(41, 181)(42, 182)(43, 150)(44, 144)(45, 148)(46, 145)(47, 187)(48, 175)(49, 176)(50, 188)(51, 152)(52, 192)(53, 151)(54, 193)(55, 169)(56, 168)(57, 160)(58, 157)(59, 183)(60, 184)(61, 162)(62, 161)(63, 180)(64, 179)(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, 213)(78, 214)(79, 217)(80, 218)(81, 207)(82, 208)(83, 219)(84, 220)(85, 186)(86, 185)(87, 202)(88, 201)(89, 190)(90, 189)(91, 194)(92, 191)(93, 198)(94, 197)(95, 196)(96, 195)(97, 200)(98, 199)(99, 204)(100, 203)(101, 225)(102, 226)(103, 235)(104, 236)(105, 222)(106, 221)(107, 231)(108, 232)(109, 233)(110, 234)(111, 228)(112, 227)(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 ) } Outer automorphisms :: reflexible Dual of E14.579 Transitivity :: ET+ VT+ AT Graph:: simple v = 24 e = 120 f = 70 degree seq :: [ 10^24 ] E14.584 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 5}) 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, T1^5, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-2 * T2^-1, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-2 * T2^-1, T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2, (T2^-1 * T1^-1)^4 ] 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, 16, 136, 17, 137)(9, 129, 23, 143, 24, 144)(10, 130, 25, 145, 27, 147)(12, 132, 30, 150, 31, 151)(14, 134, 35, 155, 36, 156)(15, 135, 37, 157, 39, 159)(18, 138, 43, 163, 33, 153)(19, 139, 44, 164, 46, 166)(20, 140, 38, 158, 48, 168)(21, 141, 49, 169, 51, 171)(22, 142, 29, 149, 52, 172)(26, 146, 57, 177, 58, 178)(28, 148, 53, 173, 42, 162)(32, 152, 54, 174, 64, 184)(34, 154, 56, 176, 65, 185)(40, 160, 67, 187, 69, 189)(41, 161, 50, 170, 71, 191)(45, 165, 66, 186, 74, 194)(47, 167, 73, 193, 75, 195)(55, 175, 63, 183, 78, 198)(59, 179, 61, 181, 84, 204)(60, 180, 85, 205, 86, 206)(62, 182, 72, 192, 88, 208)(68, 188, 76, 196, 92, 212)(70, 190, 91, 211, 93, 213)(77, 197, 79, 199, 100, 220)(80, 200, 82, 202, 102, 222)(81, 201, 103, 223, 96, 216)(83, 203, 101, 221, 105, 225)(87, 207, 94, 214, 107, 227)(89, 209, 90, 210, 108, 228)(95, 215, 113, 233, 110, 230)(97, 217, 98, 218, 114, 234)(99, 219, 106, 226, 115, 235)(104, 224, 116, 236, 117, 237)(109, 229, 119, 239, 118, 238)(111, 231, 112, 232, 120, 240) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 134)(6, 132)(7, 138)(8, 140)(9, 142)(10, 123)(11, 148)(12, 124)(13, 152)(14, 154)(15, 125)(16, 157)(17, 161)(18, 147)(19, 127)(20, 167)(21, 128)(22, 146)(23, 163)(24, 151)(25, 175)(26, 130)(27, 165)(28, 179)(29, 131)(30, 169)(31, 182)(32, 183)(33, 133)(34, 158)(35, 153)(36, 178)(37, 166)(38, 135)(39, 171)(40, 136)(41, 190)(42, 137)(43, 159)(44, 185)(45, 139)(46, 188)(47, 170)(48, 194)(49, 189)(50, 141)(51, 173)(52, 197)(53, 143)(54, 144)(55, 200)(56, 145)(57, 184)(58, 203)(59, 180)(60, 149)(61, 150)(62, 199)(63, 155)(64, 206)(65, 209)(66, 156)(67, 195)(68, 160)(69, 207)(70, 192)(71, 212)(72, 162)(73, 164)(74, 216)(75, 217)(76, 168)(77, 219)(78, 172)(79, 174)(80, 201)(81, 176)(82, 177)(83, 210)(84, 213)(85, 208)(86, 224)(87, 181)(88, 227)(89, 215)(90, 186)(91, 187)(92, 230)(93, 231)(94, 191)(95, 193)(96, 218)(97, 229)(98, 196)(99, 221)(100, 204)(101, 198)(102, 235)(103, 225)(104, 202)(105, 237)(106, 205)(107, 238)(108, 222)(109, 211)(110, 232)(111, 236)(112, 214)(113, 223)(114, 228)(115, 240)(116, 220)(117, 239)(118, 226)(119, 233)(120, 234) local type(s) :: { ( 4, 5, 4, 5, 4, 5 ) } Outer automorphisms :: reflexible Dual of E14.580 Transitivity :: ET+ VT+ AT Graph:: simple v = 40 e = 120 f = 54 degree seq :: [ 6^40 ] E14.585 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 5}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-2 * Y1^-1 * Y2^-1, Y3 * Y2^-2 * Y3^-1 * Y2^-2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 ] 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, 53, 173)(44, 164, 64, 184, 54, 174)(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, 287, 407, 280, 400, 285, 405)(286, 406, 305, 425, 288, 408, 306, 426)(289, 409, 307, 427, 291, 411, 308, 428)(290, 410, 301, 421, 292, 412, 299, 419)(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, 315, 435, 312, 432, 313, 433)(314, 434, 331, 451, 316, 436, 332, 452)(321, 441, 341, 461, 323, 443, 342, 462)(322, 442, 327, 447, 324, 444, 325, 445)(326, 446, 343, 463, 328, 448, 344, 464)(333, 453, 351, 471, 335, 455, 352, 472)(334, 454, 339, 459, 336, 456, 337, 457)(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, 293)(44, 294)(45, 269)(46, 285)(47, 270)(48, 287)(49, 271)(50, 289)(51, 272)(52, 291)(53, 303)(54, 304)(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, 10, 2, 10, 2, 10 ), ( 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E14.588 Graph:: bipartite v = 70 e = 240 f = 144 degree seq :: [ 6^40, 8^30 ] E14.586 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 5}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y3)^2, (R * Y1)^2, Y2^5, Y1 * Y2^-1 * Y1^2 * Y2 * Y1, (Y1 * Y2)^3, (Y3^-1 * Y1^-1)^3 ] 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, 35, 155, 27, 147)(16, 136, 33, 153, 36, 156, 34, 154)(20, 140, 38, 158, 29, 149, 39, 159)(24, 144, 43, 163, 30, 150, 44, 164)(25, 145, 45, 165, 28, 148, 46, 166)(31, 151, 51, 171, 32, 152, 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, 55, 175, 49, 169, 56, 176)(52, 172, 72, 192, 54, 174, 73, 193)(59, 179, 63, 183, 60, 180, 64, 184)(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, 93, 213, 78, 198, 94, 214)(79, 199, 97, 217, 80, 200, 98, 218)(81, 201, 87, 207, 82, 202, 88, 208)(83, 203, 99, 219, 84, 204, 100, 220)(101, 221, 105, 225, 102, 222, 106, 226)(103, 223, 115, 235, 104, 224, 116, 236)(107, 227, 111, 231, 108, 228, 112, 232)(109, 229, 113, 233, 110, 230, 114, 234)(117, 237, 120, 240, 118, 238, 119, 239)(241, 361, 243, 363, 250, 370, 256, 376, 245, 365)(242, 362, 247, 367, 260, 380, 264, 384, 248, 368)(244, 364, 252, 372, 269, 389, 270, 390, 253, 373)(246, 366, 257, 377, 275, 395, 276, 396, 258, 378)(249, 369, 262, 382, 281, 401, 287, 407, 265, 385)(251, 371, 263, 383, 282, 402, 290, 410, 268, 388)(254, 374, 271, 391, 292, 412, 280, 400, 261, 381)(255, 375, 272, 392, 294, 414, 277, 397, 259, 379)(266, 386, 285, 405, 305, 425, 309, 429, 288, 408)(267, 387, 286, 406, 306, 426, 310, 430, 289, 409)(273, 393, 295, 415, 315, 435, 314, 434, 293, 413)(274, 394, 296, 416, 316, 436, 311, 431, 291, 411)(278, 398, 297, 417, 317, 437, 319, 439, 299, 419)(279, 399, 298, 418, 318, 438, 320, 440, 300, 420)(283, 403, 303, 423, 323, 443, 322, 442, 302, 422)(284, 404, 304, 424, 324, 444, 321, 441, 301, 421)(307, 427, 327, 447, 343, 463, 342, 462, 326, 446)(308, 428, 328, 448, 344, 464, 341, 461, 325, 445)(312, 432, 331, 451, 347, 467, 349, 469, 333, 453)(313, 433, 332, 452, 348, 468, 350, 470, 334, 454)(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, 256)(11, 263)(12, 269)(13, 244)(14, 271)(15, 272)(16, 245)(17, 275)(18, 246)(19, 255)(20, 264)(21, 254)(22, 281)(23, 282)(24, 248)(25, 249)(26, 285)(27, 286)(28, 251)(29, 270)(30, 253)(31, 292)(32, 294)(33, 295)(34, 296)(35, 276)(36, 258)(37, 259)(38, 297)(39, 298)(40, 261)(41, 287)(42, 290)(43, 303)(44, 304)(45, 305)(46, 306)(47, 265)(48, 266)(49, 267)(50, 268)(51, 274)(52, 280)(53, 273)(54, 277)(55, 315)(56, 316)(57, 317)(58, 318)(59, 278)(60, 279)(61, 284)(62, 283)(63, 323)(64, 324)(65, 309)(66, 310)(67, 327)(68, 328)(69, 288)(70, 289)(71, 291)(72, 331)(73, 332)(74, 293)(75, 314)(76, 311)(77, 319)(78, 320)(79, 299)(80, 300)(81, 301)(82, 302)(83, 322)(84, 321)(85, 308)(86, 307)(87, 343)(88, 344)(89, 345)(90, 346)(91, 347)(92, 348)(93, 312)(94, 313)(95, 330)(96, 329)(97, 353)(98, 354)(99, 338)(100, 337)(101, 325)(102, 326)(103, 342)(104, 341)(105, 357)(106, 358)(107, 349)(108, 350)(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 ) } Outer automorphisms :: reflexible Dual of E14.587 Graph:: bipartite v = 54 e = 240 f = 160 degree seq :: [ 8^30, 10^24 ] E14.587 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 5}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, Y3^5, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3^2, (Y3 * Y2^-1)^4, Y3^2 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y2 * Y3 * Y2 * Y3 * Y2^2 * Y3^-3 * Y2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2 * Y3)^5 ] 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, 265, 385)(251, 371, 268, 388, 270, 390)(252, 372, 271, 391, 272, 392)(255, 375, 278, 398, 279, 399)(257, 377, 282, 402, 283, 403)(261, 381, 262, 382, 288, 408)(263, 383, 285, 405, 290, 410)(266, 386, 275, 395, 286, 406)(267, 387, 287, 407, 295, 415)(269, 389, 298, 418, 277, 397)(273, 393, 280, 400, 301, 421)(274, 394, 302, 422, 297, 417)(276, 396, 293, 413, 299, 419)(281, 401, 296, 416, 308, 428)(284, 404, 300, 420, 312, 432)(289, 409, 315, 435, 316, 436)(291, 411, 292, 412, 318, 438)(294, 414, 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, 255)(10, 266)(11, 269)(12, 244)(13, 274)(14, 276)(15, 245)(16, 280)(17, 261)(18, 275)(19, 285)(20, 287)(21, 247)(22, 289)(23, 248)(24, 292)(25, 260)(26, 271)(27, 250)(28, 278)(29, 273)(30, 286)(31, 296)(32, 300)(33, 252)(34, 284)(35, 253)(36, 303)(37, 254)(38, 305)(39, 290)(40, 307)(41, 256)(42, 310)(43, 272)(44, 258)(45, 299)(46, 259)(47, 313)(48, 308)(49, 291)(50, 317)(51, 263)(52, 319)(53, 264)(54, 265)(55, 282)(56, 267)(57, 268)(58, 323)(59, 270)(60, 324)(61, 302)(62, 326)(63, 304)(64, 277)(65, 322)(66, 279)(67, 309)(68, 333)(69, 281)(70, 335)(71, 283)(72, 298)(73, 294)(74, 288)(75, 339)(76, 295)(77, 330)(78, 337)(79, 320)(80, 293)(81, 315)(82, 297)(83, 344)(84, 311)(85, 301)(86, 346)(87, 341)(88, 329)(89, 348)(90, 306)(91, 349)(92, 312)(93, 338)(94, 345)(95, 316)(96, 331)(97, 351)(98, 314)(99, 353)(100, 318)(101, 355)(102, 321)(103, 327)(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, 10 ), ( 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E14.586 Graph:: simple bipartite v = 160 e = 240 f = 54 degree seq :: [ 2^120, 6^40 ] E14.588 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 5}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, Y1^5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-2 * Y3^-1, Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-2 * Y3^-1, Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3, (Y3^-1 * Y1^-1)^4 ] Map:: polytopal R = (1, 121, 2, 122, 6, 126, 12, 132, 4, 124)(3, 123, 9, 129, 22, 142, 26, 146, 10, 130)(5, 125, 14, 134, 34, 154, 38, 158, 15, 135)(7, 127, 18, 138, 27, 147, 45, 165, 19, 139)(8, 128, 20, 140, 47, 167, 50, 170, 21, 141)(11, 131, 28, 148, 59, 179, 60, 180, 29, 149)(13, 133, 32, 152, 63, 183, 35, 155, 33, 153)(16, 136, 37, 157, 46, 166, 68, 188, 40, 160)(17, 137, 41, 161, 70, 190, 72, 192, 42, 162)(23, 143, 43, 163, 39, 159, 51, 171, 53, 173)(24, 144, 31, 151, 62, 182, 79, 199, 54, 174)(25, 145, 55, 175, 80, 200, 81, 201, 56, 176)(30, 150, 49, 169, 69, 189, 87, 207, 61, 181)(36, 156, 58, 178, 83, 203, 90, 210, 66, 186)(44, 164, 65, 185, 89, 209, 95, 215, 73, 193)(48, 168, 74, 194, 96, 216, 98, 218, 76, 196)(52, 172, 77, 197, 99, 219, 101, 221, 78, 198)(57, 177, 64, 184, 86, 206, 104, 224, 82, 202)(67, 187, 75, 195, 97, 217, 109, 229, 91, 211)(71, 191, 92, 212, 110, 230, 112, 232, 94, 214)(84, 204, 93, 213, 111, 231, 116, 236, 100, 220)(85, 205, 88, 208, 107, 227, 118, 238, 106, 226)(102, 222, 115, 235, 120, 240, 114, 234, 108, 228)(103, 223, 105, 225, 117, 237, 119, 239, 113, 233)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 247)(3, 245)(4, 251)(5, 241)(6, 256)(7, 248)(8, 242)(9, 263)(10, 265)(11, 253)(12, 270)(13, 244)(14, 275)(15, 277)(16, 257)(17, 246)(18, 283)(19, 284)(20, 278)(21, 289)(22, 269)(23, 264)(24, 249)(25, 267)(26, 297)(27, 250)(28, 293)(29, 292)(30, 271)(31, 252)(32, 294)(33, 258)(34, 296)(35, 276)(36, 254)(37, 279)(38, 288)(39, 255)(40, 307)(41, 290)(42, 268)(43, 273)(44, 286)(45, 306)(46, 259)(47, 313)(48, 260)(49, 291)(50, 311)(51, 261)(52, 262)(53, 282)(54, 304)(55, 303)(56, 305)(57, 298)(58, 266)(59, 301)(60, 325)(61, 324)(62, 312)(63, 318)(64, 272)(65, 274)(66, 314)(67, 309)(68, 316)(69, 280)(70, 331)(71, 281)(72, 328)(73, 315)(74, 285)(75, 287)(76, 332)(77, 319)(78, 295)(79, 340)(80, 322)(81, 343)(82, 342)(83, 341)(84, 299)(85, 326)(86, 300)(87, 334)(88, 302)(89, 330)(90, 348)(91, 333)(92, 308)(93, 310)(94, 347)(95, 353)(96, 321)(97, 338)(98, 354)(99, 346)(100, 317)(101, 345)(102, 320)(103, 336)(104, 356)(105, 323)(106, 355)(107, 327)(108, 329)(109, 359)(110, 335)(111, 352)(112, 360)(113, 350)(114, 337)(115, 339)(116, 357)(117, 344)(118, 349)(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 ) } Outer automorphisms :: reflexible Dual of E14.585 Graph:: simple bipartite v = 144 e = 240 f = 70 degree seq :: [ 2^120, 10^24 ] E14.589 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 5}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y3^3, Y3 * Y1^-2, (R * Y3)^2, (R * Y1)^2, Y2^5, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, (Y3 * Y2^-1)^4, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2^-2 * Y3^-1, Y1 * Y2^-1 * Y1 * Y2^-2 * Y3 * Y2^2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-2 ] Map:: R = (1, 121, 2, 122, 4, 124)(3, 123, 8, 128, 10, 130)(5, 125, 13, 133, 14, 134)(6, 126, 16, 136, 18, 138)(7, 127, 19, 139, 20, 140)(9, 129, 24, 144, 25, 145)(11, 131, 28, 148, 30, 150)(12, 132, 31, 151, 32, 152)(15, 135, 38, 158, 39, 159)(17, 137, 35, 155, 42, 162)(21, 141, 47, 167, 48, 168)(22, 142, 40, 160, 37, 157)(23, 143, 49, 169, 50, 170)(26, 146, 33, 153, 55, 175)(27, 147, 56, 176, 57, 177)(29, 149, 45, 165, 60, 180)(34, 154, 41, 161, 53, 173)(36, 156, 43, 163, 64, 184)(44, 164, 59, 179, 68, 188)(46, 166, 61, 181, 72, 192)(51, 171, 77, 197, 78, 198)(52, 172, 58, 178, 80, 200)(54, 174, 75, 195, 82, 202)(62, 182, 65, 185, 86, 206)(63, 183, 87, 207, 88, 208)(66, 186, 81, 201, 90, 210)(67, 187, 69, 189, 92, 212)(70, 190, 73, 193, 94, 214)(71, 191, 95, 215, 96, 216)(74, 194, 93, 213, 98, 218)(76, 196, 83, 203, 100, 220)(79, 199, 101, 221, 102, 222)(84, 204, 85, 205, 106, 226)(89, 209, 103, 223, 108, 228)(91, 211, 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, 255, 375, 245, 365)(242, 362, 246, 366, 257, 377, 261, 381, 247, 367)(244, 364, 251, 371, 269, 389, 273, 393, 252, 372)(248, 368, 262, 382, 260, 380, 286, 406, 263, 383)(250, 370, 266, 386, 294, 414, 298, 418, 267, 387)(253, 373, 274, 394, 302, 422, 303, 423, 275, 395)(254, 374, 276, 396, 299, 419, 268, 388, 277, 397)(256, 376, 280, 400, 272, 392, 297, 417, 281, 401)(258, 378, 279, 399, 306, 426, 309, 429, 283, 403)(259, 379, 284, 404, 310, 430, 311, 431, 285, 405)(264, 384, 271, 391, 290, 410, 316, 436, 291, 411)(265, 385, 292, 412, 319, 439, 321, 441, 293, 413)(270, 390, 288, 408, 314, 434, 325, 445, 301, 421)(278, 398, 296, 416, 318, 438, 329, 449, 305, 425)(282, 402, 307, 427, 331, 451, 333, 453, 308, 428)(287, 407, 304, 424, 328, 448, 337, 457, 313, 433)(289, 409, 300, 420, 324, 444, 339, 459, 315, 435)(295, 415, 312, 432, 336, 456, 345, 465, 323, 443)(317, 437, 322, 442, 344, 464, 354, 474, 341, 461)(320, 440, 340, 460, 353, 473, 356, 476, 343, 463)(326, 446, 342, 462, 355, 475, 350, 470, 332, 452)(327, 447, 330, 450, 348, 468, 358, 478, 347, 467)(334, 454, 349, 469, 359, 479, 357, 477, 346, 466)(335, 455, 338, 458, 352, 472, 360, 480, 351, 471) L = (1, 244)(2, 241)(3, 250)(4, 242)(5, 254)(6, 258)(7, 260)(8, 243)(9, 265)(10, 248)(11, 270)(12, 272)(13, 245)(14, 253)(15, 279)(16, 246)(17, 282)(18, 256)(19, 247)(20, 259)(21, 288)(22, 277)(23, 290)(24, 249)(25, 264)(26, 295)(27, 297)(28, 251)(29, 300)(30, 268)(31, 252)(32, 271)(33, 266)(34, 293)(35, 257)(36, 304)(37, 280)(38, 255)(39, 278)(40, 262)(41, 274)(42, 275)(43, 276)(44, 308)(45, 269)(46, 312)(47, 261)(48, 287)(49, 263)(50, 289)(51, 318)(52, 320)(53, 281)(54, 322)(55, 273)(56, 267)(57, 296)(58, 292)(59, 284)(60, 285)(61, 286)(62, 326)(63, 328)(64, 283)(65, 302)(66, 330)(67, 332)(68, 299)(69, 307)(70, 334)(71, 336)(72, 301)(73, 310)(74, 338)(75, 294)(76, 340)(77, 291)(78, 317)(79, 342)(80, 298)(81, 306)(82, 315)(83, 316)(84, 346)(85, 324)(86, 305)(87, 303)(88, 327)(89, 348)(90, 321)(91, 349)(92, 309)(93, 314)(94, 313)(95, 311)(96, 335)(97, 352)(98, 333)(99, 353)(100, 323)(101, 319)(102, 341)(103, 329)(104, 357)(105, 344)(106, 325)(107, 331)(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 ) } Outer automorphisms :: reflexible Dual of E14.590 Graph:: bipartite v = 64 e = 240 f = 150 degree seq :: [ 6^40, 10^24 ] E14.590 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 5}) 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, Y1^4, (R * Y3)^2, (R * Y1)^2, Y3^5, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3, Y1^-1 * Y3^-1 * Y1^-2 * Y3 * Y1^-1, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^5 ] Map:: polytopal 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, 35, 155, 27, 147)(16, 136, 33, 153, 36, 156, 34, 154)(20, 140, 38, 158, 29, 149, 39, 159)(24, 144, 43, 163, 30, 150, 44, 164)(25, 145, 45, 165, 28, 148, 46, 166)(31, 151, 51, 171, 32, 152, 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, 55, 175, 49, 169, 56, 176)(52, 172, 72, 192, 54, 174, 73, 193)(59, 179, 63, 183, 60, 180, 64, 184)(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, 93, 213, 78, 198, 94, 214)(79, 199, 97, 217, 80, 200, 98, 218)(81, 201, 87, 207, 82, 202, 88, 208)(83, 203, 99, 219, 84, 204, 100, 220)(101, 221, 105, 225, 102, 222, 106, 226)(103, 223, 115, 235, 104, 224, 116, 236)(107, 227, 111, 231, 108, 228, 112, 232)(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, 256)(11, 263)(12, 269)(13, 244)(14, 271)(15, 272)(16, 245)(17, 275)(18, 246)(19, 255)(20, 264)(21, 254)(22, 281)(23, 282)(24, 248)(25, 249)(26, 285)(27, 286)(28, 251)(29, 270)(30, 253)(31, 292)(32, 294)(33, 295)(34, 296)(35, 276)(36, 258)(37, 259)(38, 297)(39, 298)(40, 261)(41, 287)(42, 290)(43, 303)(44, 304)(45, 305)(46, 306)(47, 265)(48, 266)(49, 267)(50, 268)(51, 274)(52, 280)(53, 273)(54, 277)(55, 315)(56, 316)(57, 317)(58, 318)(59, 278)(60, 279)(61, 284)(62, 283)(63, 323)(64, 324)(65, 309)(66, 310)(67, 327)(68, 328)(69, 288)(70, 289)(71, 291)(72, 331)(73, 332)(74, 293)(75, 314)(76, 311)(77, 319)(78, 320)(79, 299)(80, 300)(81, 301)(82, 302)(83, 322)(84, 321)(85, 308)(86, 307)(87, 343)(88, 344)(89, 345)(90, 346)(91, 347)(92, 348)(93, 312)(94, 313)(95, 330)(96, 329)(97, 353)(98, 354)(99, 338)(100, 337)(101, 325)(102, 326)(103, 342)(104, 341)(105, 357)(106, 358)(107, 349)(108, 350)(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, 10 ), ( 6, 10, 6, 10, 6, 10, 6, 10 ) } Outer automorphisms :: reflexible Dual of E14.589 Graph:: simple bipartite v = 150 e = 240 f = 64 degree seq :: [ 2^120, 8^30 ] E14.591 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 30}) Quotient :: regular Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T1^30 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 97, 106, 108, 112, 118, 102, 95, 91, 87, 83, 76, 82, 77, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 101, 107, 110, 111, 120, 98, 94, 89, 86, 80, 74, 66, 73, 69, 78, 55, 46, 39, 30, 22, 12, 8)(6, 13, 9, 18, 27, 35, 43, 51, 59, 103, 114, 105, 116, 117, 100, 93, 90, 85, 81, 72, 68, 63, 67, 75, 54, 47, 38, 31, 21, 14)(16, 23, 17, 24, 32, 40, 48, 56, 99, 119, 115, 109, 113, 104, 96, 92, 88, 84, 79, 70, 64, 61, 62, 65, 71, 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, 78)(55, 99)(57, 71)(60, 101)(61, 105)(62, 107)(63, 109)(64, 111)(65, 103)(66, 113)(67, 97)(68, 108)(69, 115)(70, 117)(72, 104)(73, 106)(74, 112)(75, 119)(76, 116)(77, 114)(79, 98)(80, 96)(81, 118)(82, 110)(83, 120)(84, 93)(85, 92)(86, 102)(87, 100)(88, 89)(90, 95)(91, 94) local type(s) :: { ( 4^30 ) } Outer automorphisms :: reflexible Dual of E14.592 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 60 f = 30 degree seq :: [ 30^4 ] E14.592 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 30}) Quotient :: regular Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^30 ] 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, 37)(36, 54, 40, 53)(38, 57, 39, 55)(41, 60, 42, 56)(43, 59, 44, 58)(45, 62, 46, 61)(47, 64, 48, 63)(49, 66, 50, 65)(51, 68, 52, 67)(69, 73, 70, 74)(71, 75, 72, 76)(77, 94, 78, 93)(79, 96, 80, 95)(81, 98, 82, 97)(83, 100, 84, 99)(85, 102, 86, 101)(87, 104, 88, 103)(89, 106, 90, 105)(91, 108, 92, 107)(109, 113, 110, 114)(111, 115, 112, 116)(117, 120, 118, 119) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 53)(34, 54)(35, 55)(36, 56)(37, 57)(38, 58)(39, 59)(40, 60)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 66)(47, 67)(48, 68)(49, 69)(50, 70)(51, 71)(52, 72)(73, 93)(74, 94)(75, 95)(76, 96)(77, 97)(78, 98)(79, 99)(80, 100)(81, 101)(82, 102)(83, 103)(84, 104)(85, 105)(86, 106)(87, 107)(88, 108)(89, 109)(90, 110)(91, 111)(92, 112)(113, 119)(114, 120)(115, 118)(116, 117) local type(s) :: { ( 30^4 ) } Outer automorphisms :: reflexible Dual of E14.591 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 30 e = 60 f = 4 degree seq :: [ 4^30 ] E14.593 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 30}) Quotient :: edge Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^30 ] 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, 46, 34, 44)(35, 62, 42, 64)(36, 66, 45, 68)(37, 70, 38, 65)(39, 75, 40, 61)(41, 57, 43, 59)(47, 72, 48, 69)(49, 77, 50, 74)(51, 87, 52, 85)(53, 91, 54, 89)(55, 95, 56, 93)(58, 99, 60, 97)(63, 110, 80, 112)(67, 113, 83, 114)(71, 116, 73, 111)(76, 119, 78, 109)(79, 105, 81, 107)(82, 101, 84, 103)(86, 117, 88, 115)(90, 120, 92, 118)(94, 108, 96, 106)(98, 104, 100, 102)(121, 122)(123, 127)(124, 129)(125, 130)(126, 132)(128, 131)(133, 137)(134, 138)(135, 139)(136, 140)(141, 145)(142, 146)(143, 147)(144, 148)(149, 153)(150, 154)(151, 177)(152, 179)(155, 181)(156, 185)(157, 189)(158, 192)(159, 194)(160, 197)(161, 182)(162, 195)(163, 184)(164, 186)(165, 190)(166, 188)(167, 205)(168, 207)(169, 209)(170, 211)(171, 213)(172, 215)(173, 217)(174, 219)(175, 221)(176, 223)(178, 225)(180, 227)(183, 229)(187, 231)(191, 235)(193, 237)(196, 238)(198, 240)(199, 230)(200, 239)(201, 232)(202, 233)(203, 236)(204, 234)(206, 226)(208, 228)(210, 222)(212, 224)(214, 220)(216, 218) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 60, 60 ), ( 60^4 ) } Outer automorphisms :: reflexible Dual of E14.597 Transitivity :: ET+ Graph:: simple bipartite v = 90 e = 120 f = 4 degree seq :: [ 2^60, 4^30 ] E14.594 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 30}) Quotient :: edge Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^30 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 113, 116, 105, 102, 91, 87, 75, 71, 62, 69, 76, 85, 92, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 111, 119, 107, 110, 94, 97, 78, 81, 63, 66, 65, 82, 80, 98, 96, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 59, 115, 114, 117, 101, 103, 86, 89, 70, 73, 61, 74, 72, 90, 88, 104, 57, 49, 41, 33, 25, 17, 9)(6, 13, 21, 29, 37, 45, 53, 109, 120, 118, 112, 108, 99, 95, 83, 79, 67, 64, 68, 77, 84, 93, 100, 106, 54, 46, 38, 30, 22, 14)(121, 122, 126, 124)(123, 129, 133, 128)(125, 131, 134, 127)(130, 136, 141, 137)(132, 135, 142, 139)(138, 145, 149, 144)(140, 147, 150, 143)(146, 152, 157, 153)(148, 151, 158, 155)(154, 161, 165, 160)(156, 163, 166, 159)(162, 168, 173, 169)(164, 167, 174, 171)(170, 177, 229, 176)(172, 179, 226, 175)(178, 216, 240, 224)(180, 231, 220, 235)(181, 215, 186, 211)(182, 206, 184, 217)(183, 203, 193, 207)(185, 219, 194, 222)(187, 209, 191, 198)(188, 223, 189, 214)(190, 199, 201, 195)(192, 228, 202, 225)(196, 221, 197, 230)(200, 232, 210, 236)(204, 237, 205, 227)(208, 238, 218, 233)(212, 234, 213, 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) :: { ( 4^4 ), ( 4^30 ) } Outer automorphisms :: reflexible Dual of E14.598 Transitivity :: ET+ Graph:: simple bipartite v = 34 e = 120 f = 60 degree seq :: [ 4^30, 30^4 ] E14.595 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 30}) Quotient :: edge Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^30 ] 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, 85)(55, 61)(57, 88)(60, 65)(62, 92)(63, 94)(64, 96)(66, 99)(67, 101)(68, 103)(69, 105)(70, 107)(71, 109)(72, 111)(73, 113)(74, 115)(75, 114)(76, 118)(77, 110)(78, 119)(79, 120)(80, 106)(81, 104)(82, 117)(83, 100)(84, 116)(86, 97)(87, 112)(89, 108)(90, 95)(91, 102)(93, 98)(121, 122, 125, 131, 140, 149, 157, 165, 173, 190, 194, 198, 202, 207, 211, 213, 215, 220, 226, 234, 231, 221, 180, 172, 164, 156, 148, 139, 130, 124)(123, 127, 135, 145, 153, 161, 169, 177, 185, 188, 192, 196, 200, 204, 210, 217, 222, 230, 237, 225, 235, 214, 205, 175, 166, 159, 150, 142, 132, 128)(126, 133, 129, 138, 147, 155, 163, 171, 179, 184, 187, 191, 195, 199, 203, 209, 218, 224, 232, 233, 239, 219, 227, 212, 174, 167, 158, 151, 141, 134)(136, 143, 137, 144, 152, 160, 168, 176, 181, 182, 183, 186, 189, 193, 197, 201, 206, 228, 236, 240, 238, 229, 223, 216, 208, 178, 170, 162, 154, 146) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 8, 8 ), ( 8^30 ) } Outer automorphisms :: reflexible Dual of E14.596 Transitivity :: ET+ Graph:: simple bipartite v = 64 e = 120 f = 30 degree seq :: [ 2^60, 30^4 ] E14.596 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 30}) Quotient :: loop Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^30 ] Map:: R = (1, 121, 3, 123, 8, 128, 4, 124)(2, 122, 5, 125, 11, 131, 6, 126)(7, 127, 13, 133, 9, 129, 14, 134)(10, 130, 15, 135, 12, 132, 16, 136)(17, 137, 21, 141, 18, 138, 22, 142)(19, 139, 23, 143, 20, 140, 24, 144)(25, 145, 29, 149, 26, 146, 30, 150)(27, 147, 31, 151, 28, 148, 32, 152)(33, 153, 61, 181, 34, 154, 62, 182)(35, 155, 64, 184, 42, 162, 65, 185)(36, 156, 67, 187, 45, 165, 68, 188)(37, 157, 69, 189, 38, 158, 70, 190)(39, 159, 71, 191, 40, 160, 72, 192)(41, 161, 74, 194, 43, 163, 63, 183)(44, 164, 76, 196, 46, 166, 66, 186)(47, 167, 77, 197, 48, 168, 78, 198)(49, 169, 79, 199, 50, 170, 80, 200)(51, 171, 75, 195, 52, 172, 73, 193)(53, 173, 81, 201, 54, 174, 82, 202)(55, 175, 83, 203, 56, 176, 84, 204)(57, 177, 85, 205, 58, 178, 86, 206)(59, 179, 87, 207, 60, 180, 88, 208)(89, 209, 117, 237, 90, 210, 118, 238)(91, 211, 114, 234, 102, 222, 113, 233)(92, 212, 109, 229, 93, 213, 110, 230)(94, 214, 116, 236, 104, 224, 115, 235)(95, 215, 111, 231, 96, 216, 112, 232)(97, 217, 108, 228, 98, 218, 107, 227)(99, 219, 106, 226, 100, 220, 105, 225)(101, 221, 120, 240, 103, 223, 119, 239) L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 130)(6, 132)(7, 123)(8, 131)(9, 124)(10, 125)(11, 128)(12, 126)(13, 137)(14, 138)(15, 139)(16, 140)(17, 133)(18, 134)(19, 135)(20, 136)(21, 145)(22, 146)(23, 147)(24, 148)(25, 141)(26, 142)(27, 143)(28, 144)(29, 153)(30, 154)(31, 172)(32, 171)(33, 149)(34, 150)(35, 183)(36, 186)(37, 187)(38, 188)(39, 184)(40, 185)(41, 193)(42, 194)(43, 195)(44, 181)(45, 196)(46, 182)(47, 189)(48, 190)(49, 191)(50, 192)(51, 152)(52, 151)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 164)(62, 166)(63, 155)(64, 159)(65, 160)(66, 156)(67, 157)(68, 158)(69, 167)(70, 168)(71, 169)(72, 170)(73, 161)(74, 162)(75, 163)(76, 165)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 209)(86, 210)(87, 221)(88, 223)(89, 205)(90, 206)(91, 239)(92, 234)(93, 233)(94, 238)(95, 236)(96, 235)(97, 231)(98, 232)(99, 229)(100, 230)(101, 207)(102, 240)(103, 208)(104, 237)(105, 228)(106, 227)(107, 226)(108, 225)(109, 219)(110, 220)(111, 217)(112, 218)(113, 213)(114, 212)(115, 216)(116, 215)(117, 224)(118, 214)(119, 211)(120, 222) local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30 ) } Outer automorphisms :: reflexible Dual of E14.595 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 30 e = 120 f = 64 degree seq :: [ 8^30 ] E14.597 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 30}) Quotient :: loop Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^30 ] Map:: R = (1, 121, 3, 123, 10, 130, 18, 138, 26, 146, 34, 154, 42, 162, 50, 170, 58, 178, 98, 218, 114, 234, 109, 229, 102, 222, 106, 226, 118, 238, 94, 214, 89, 209, 85, 205, 81, 201, 77, 197, 73, 193, 66, 186, 60, 180, 52, 172, 44, 164, 36, 156, 28, 148, 20, 140, 12, 132, 5, 125)(2, 122, 7, 127, 15, 135, 23, 143, 31, 151, 39, 159, 47, 167, 55, 175, 95, 215, 101, 221, 110, 230, 115, 235, 105, 225, 112, 232, 97, 217, 91, 211, 87, 207, 83, 203, 79, 199, 75, 195, 69, 189, 64, 184, 71, 191, 56, 176, 48, 168, 40, 160, 32, 152, 24, 144, 16, 136, 8, 128)(4, 124, 11, 131, 19, 139, 27, 147, 35, 155, 43, 163, 51, 171, 59, 179, 99, 219, 103, 223, 108, 228, 117, 237, 107, 227, 119, 239, 96, 216, 90, 210, 86, 206, 82, 202, 78, 198, 74, 194, 68, 188, 62, 182, 67, 187, 57, 177, 49, 169, 41, 161, 33, 153, 25, 145, 17, 137, 9, 129)(6, 126, 13, 133, 21, 141, 29, 149, 37, 157, 45, 165, 53, 173, 93, 213, 113, 233, 104, 224, 116, 236, 120, 240, 111, 231, 100, 220, 92, 212, 88, 208, 84, 204, 80, 200, 76, 196, 72, 192, 65, 185, 61, 181, 63, 183, 70, 190, 54, 174, 46, 166, 38, 158, 30, 150, 22, 142, 14, 134) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 131)(6, 124)(7, 125)(8, 123)(9, 133)(10, 136)(11, 134)(12, 135)(13, 128)(14, 127)(15, 142)(16, 141)(17, 130)(18, 145)(19, 132)(20, 147)(21, 137)(22, 139)(23, 140)(24, 138)(25, 149)(26, 152)(27, 150)(28, 151)(29, 144)(30, 143)(31, 158)(32, 157)(33, 146)(34, 161)(35, 148)(36, 163)(37, 153)(38, 155)(39, 156)(40, 154)(41, 165)(42, 168)(43, 166)(44, 167)(45, 160)(46, 159)(47, 174)(48, 173)(49, 162)(50, 177)(51, 164)(52, 179)(53, 169)(54, 171)(55, 172)(56, 170)(57, 213)(58, 191)(59, 190)(60, 215)(61, 221)(62, 224)(63, 219)(64, 218)(65, 228)(66, 223)(67, 178)(68, 234)(69, 236)(70, 175)(71, 233)(72, 235)(73, 230)(74, 240)(75, 229)(76, 227)(77, 237)(78, 222)(79, 231)(80, 232)(81, 225)(82, 220)(83, 226)(84, 216)(85, 239)(86, 238)(87, 212)(88, 211)(89, 217)(90, 208)(91, 214)(92, 206)(93, 176)(94, 210)(95, 183)(96, 209)(97, 204)(98, 182)(99, 180)(100, 203)(101, 186)(102, 199)(103, 181)(104, 184)(105, 196)(106, 202)(107, 201)(108, 193)(109, 194)(110, 185)(111, 198)(112, 205)(113, 187)(114, 189)(115, 197)(116, 188)(117, 192)(118, 207)(119, 200)(120, 195) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E14.593 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 120 f = 90 degree seq :: [ 60^4 ] E14.598 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 30}) Quotient :: loop Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^30 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123)(2, 122, 6, 126)(4, 124, 9, 129)(5, 125, 12, 132)(7, 127, 16, 136)(8, 128, 17, 137)(10, 130, 15, 135)(11, 131, 21, 141)(13, 133, 23, 143)(14, 134, 24, 144)(18, 138, 26, 146)(19, 139, 27, 147)(20, 140, 30, 150)(22, 142, 32, 152)(25, 145, 34, 154)(28, 148, 33, 153)(29, 149, 38, 158)(31, 151, 40, 160)(35, 155, 42, 162)(36, 156, 43, 163)(37, 157, 46, 166)(39, 159, 48, 168)(41, 161, 50, 170)(44, 164, 49, 169)(45, 165, 54, 174)(47, 167, 56, 176)(51, 171, 58, 178)(52, 172, 59, 179)(53, 173, 63, 183)(55, 175, 87, 207)(57, 177, 61, 181)(60, 180, 89, 209)(62, 182, 91, 211)(64, 184, 96, 216)(65, 185, 98, 218)(66, 186, 85, 205)(67, 187, 101, 221)(68, 188, 103, 223)(69, 189, 105, 225)(70, 190, 107, 227)(71, 191, 109, 229)(72, 192, 111, 231)(73, 193, 113, 233)(74, 194, 115, 235)(75, 195, 117, 237)(76, 196, 116, 236)(77, 197, 112, 232)(78, 198, 120, 240)(79, 199, 119, 239)(80, 200, 108, 228)(81, 201, 104, 224)(82, 202, 118, 238)(83, 203, 114, 234)(84, 204, 102, 222)(86, 206, 99, 219)(88, 208, 110, 230)(90, 210, 106, 226)(92, 212, 97, 217)(93, 213, 100, 220)(94, 214, 95, 215) L = (1, 122)(2, 125)(3, 127)(4, 121)(5, 131)(6, 133)(7, 135)(8, 123)(9, 138)(10, 124)(11, 140)(12, 128)(13, 129)(14, 126)(15, 145)(16, 143)(17, 144)(18, 147)(19, 130)(20, 149)(21, 134)(22, 132)(23, 137)(24, 152)(25, 153)(26, 136)(27, 155)(28, 139)(29, 157)(30, 142)(31, 141)(32, 160)(33, 161)(34, 146)(35, 163)(36, 148)(37, 165)(38, 151)(39, 150)(40, 168)(41, 169)(42, 154)(43, 171)(44, 156)(45, 173)(46, 159)(47, 158)(48, 176)(49, 177)(50, 162)(51, 179)(52, 164)(53, 205)(54, 167)(55, 166)(56, 207)(57, 209)(58, 170)(59, 211)(60, 172)(61, 178)(62, 181)(63, 175)(64, 174)(65, 182)(66, 184)(67, 183)(68, 185)(69, 187)(70, 186)(71, 180)(72, 188)(73, 190)(74, 189)(75, 191)(76, 192)(77, 194)(78, 193)(79, 195)(80, 196)(81, 198)(82, 197)(83, 199)(84, 200)(85, 225)(86, 202)(87, 216)(88, 201)(89, 218)(90, 203)(91, 229)(92, 204)(93, 210)(94, 213)(95, 208)(96, 221)(97, 206)(98, 237)(99, 214)(100, 217)(101, 227)(102, 215)(103, 239)(104, 219)(105, 233)(106, 222)(107, 235)(108, 220)(109, 223)(110, 212)(111, 234)(112, 224)(113, 232)(114, 228)(115, 240)(116, 226)(117, 231)(118, 230)(119, 236)(120, 238) local type(s) :: { ( 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E14.594 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 60 e = 120 f = 34 degree seq :: [ 4^60 ] E14.599 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 30}) Quotient :: dipole Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^30 ] Map:: R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 10, 130)(6, 126, 12, 132)(8, 128, 11, 131)(13, 133, 17, 137)(14, 134, 18, 138)(15, 135, 19, 139)(16, 136, 20, 140)(21, 141, 25, 145)(22, 142, 26, 146)(23, 143, 27, 147)(24, 144, 28, 148)(29, 149, 33, 153)(30, 150, 34, 154)(31, 151, 35, 155)(32, 152, 40, 160)(36, 156, 53, 173)(37, 157, 54, 174)(38, 158, 55, 175)(39, 159, 56, 176)(41, 161, 57, 177)(42, 162, 58, 178)(43, 163, 59, 179)(44, 164, 60, 180)(45, 165, 61, 181)(46, 166, 62, 182)(47, 167, 63, 183)(48, 168, 64, 184)(49, 169, 65, 185)(50, 170, 66, 186)(51, 171, 67, 187)(52, 172, 68, 188)(69, 189, 73, 193)(70, 190, 74, 194)(71, 191, 75, 195)(72, 192, 76, 196)(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)(89, 209, 105, 225)(90, 210, 106, 226)(91, 211, 107, 227)(92, 212, 108, 228)(109, 229, 113, 233)(110, 230, 114, 234)(111, 231, 115, 235)(112, 232, 116, 236)(117, 237, 120, 240)(118, 238, 119, 239)(241, 361, 243, 363, 248, 368, 244, 364)(242, 362, 245, 365, 251, 371, 246, 366)(247, 367, 253, 373, 249, 369, 254, 374)(250, 370, 255, 375, 252, 372, 256, 376)(257, 377, 261, 381, 258, 378, 262, 382)(259, 379, 263, 383, 260, 380, 264, 384)(265, 385, 269, 389, 266, 386, 270, 390)(267, 387, 271, 391, 268, 388, 272, 392)(273, 393, 293, 413, 274, 394, 294, 414)(275, 395, 295, 415, 280, 400, 296, 416)(276, 396, 297, 417, 277, 397, 298, 418)(278, 398, 299, 419, 279, 399, 300, 420)(281, 401, 301, 421, 282, 402, 302, 422)(283, 403, 303, 423, 284, 404, 304, 424)(285, 405, 305, 425, 286, 406, 306, 426)(287, 407, 307, 427, 288, 408, 308, 428)(289, 409, 309, 429, 290, 410, 310, 430)(291, 411, 311, 431, 292, 412, 312, 432)(313, 433, 333, 453, 314, 434, 334, 454)(315, 435, 335, 455, 316, 436, 336, 456)(317, 437, 337, 457, 318, 438, 338, 458)(319, 439, 339, 459, 320, 440, 340, 460)(321, 441, 341, 461, 322, 442, 342, 462)(323, 443, 343, 463, 324, 444, 344, 464)(325, 445, 345, 465, 326, 446, 346, 466)(327, 447, 347, 467, 328, 448, 348, 468)(329, 449, 349, 469, 330, 450, 350, 470)(331, 451, 351, 471, 332, 452, 352, 472)(353, 473, 360, 480, 354, 474, 359, 479)(355, 475, 358, 478, 356, 476, 357, 477) L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 250)(6, 252)(7, 243)(8, 251)(9, 244)(10, 245)(11, 248)(12, 246)(13, 257)(14, 258)(15, 259)(16, 260)(17, 253)(18, 254)(19, 255)(20, 256)(21, 265)(22, 266)(23, 267)(24, 268)(25, 261)(26, 262)(27, 263)(28, 264)(29, 273)(30, 274)(31, 275)(32, 280)(33, 269)(34, 270)(35, 271)(36, 293)(37, 294)(38, 295)(39, 296)(40, 272)(41, 297)(42, 298)(43, 299)(44, 300)(45, 301)(46, 302)(47, 303)(48, 304)(49, 305)(50, 306)(51, 307)(52, 308)(53, 276)(54, 277)(55, 278)(56, 279)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 313)(70, 314)(71, 315)(72, 316)(73, 309)(74, 310)(75, 311)(76, 312)(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, 345)(90, 346)(91, 347)(92, 348)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 353)(110, 354)(111, 355)(112, 356)(113, 349)(114, 350)(115, 351)(116, 352)(117, 360)(118, 359)(119, 358)(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, 60, 2, 60 ), ( 2, 60, 2, 60, 2, 60, 2, 60 ) } Outer automorphisms :: reflexible Dual of E14.602 Graph:: bipartite v = 90 e = 240 f = 124 degree seq :: [ 4^60, 8^30 ] E14.600 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 30}) Quotient :: dipole Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1)^2, Y1^4, Y2^30 ] Map:: R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 13, 133, 8, 128)(5, 125, 11, 131, 14, 134, 7, 127)(10, 130, 16, 136, 21, 141, 17, 137)(12, 132, 15, 135, 22, 142, 19, 139)(18, 138, 25, 145, 29, 149, 24, 144)(20, 140, 27, 147, 30, 150, 23, 143)(26, 146, 32, 152, 37, 157, 33, 153)(28, 148, 31, 151, 38, 158, 35, 155)(34, 154, 41, 161, 45, 165, 40, 160)(36, 156, 43, 163, 46, 166, 39, 159)(42, 162, 48, 168, 53, 173, 49, 169)(44, 164, 47, 167, 54, 174, 51, 171)(50, 170, 57, 177, 65, 185, 56, 176)(52, 172, 59, 179, 93, 213, 55, 175)(58, 178, 91, 211, 61, 181, 95, 215)(60, 180, 64, 184, 98, 218, 62, 182)(63, 183, 99, 219, 69, 189, 101, 221)(66, 186, 104, 224, 68, 188, 106, 226)(67, 187, 107, 227, 73, 193, 109, 229)(70, 190, 112, 232, 72, 192, 114, 234)(71, 191, 115, 235, 77, 197, 117, 237)(74, 194, 120, 240, 76, 196, 116, 236)(75, 195, 118, 238, 81, 201, 113, 233)(78, 198, 108, 228, 80, 200, 119, 239)(79, 199, 105, 225, 85, 205, 110, 230)(82, 202, 111, 231, 84, 204, 100, 220)(83, 203, 102, 222, 89, 209, 97, 217)(86, 206, 96, 216, 88, 208, 92, 212)(87, 207, 94, 214, 103, 223, 90, 210)(241, 361, 243, 363, 250, 370, 258, 378, 266, 386, 274, 394, 282, 402, 290, 410, 298, 418, 309, 429, 313, 433, 317, 437, 321, 441, 325, 445, 329, 449, 343, 463, 336, 456, 340, 460, 348, 468, 356, 476, 352, 472, 346, 466, 300, 420, 292, 412, 284, 404, 276, 396, 268, 388, 260, 380, 252, 372, 245, 365)(242, 362, 247, 367, 255, 375, 263, 383, 271, 391, 279, 399, 287, 407, 295, 415, 304, 424, 308, 428, 312, 432, 316, 436, 320, 440, 324, 444, 328, 448, 334, 454, 337, 457, 345, 465, 353, 473, 355, 475, 349, 469, 339, 459, 331, 451, 296, 416, 288, 408, 280, 400, 272, 392, 264, 384, 256, 376, 248, 368)(244, 364, 251, 371, 259, 379, 267, 387, 275, 395, 283, 403, 291, 411, 299, 419, 302, 422, 306, 426, 310, 430, 314, 434, 318, 438, 322, 442, 326, 446, 330, 450, 342, 462, 350, 470, 358, 478, 357, 477, 347, 467, 341, 461, 335, 455, 297, 417, 289, 409, 281, 401, 273, 393, 265, 385, 257, 377, 249, 369)(246, 366, 253, 373, 261, 381, 269, 389, 277, 397, 285, 405, 293, 413, 305, 425, 301, 421, 303, 423, 307, 427, 311, 431, 315, 435, 319, 439, 323, 443, 327, 447, 332, 452, 351, 471, 359, 479, 360, 480, 354, 474, 344, 464, 338, 458, 333, 453, 294, 414, 286, 406, 278, 398, 270, 390, 262, 382, 254, 374) L = (1, 243)(2, 247)(3, 250)(4, 251)(5, 241)(6, 253)(7, 255)(8, 242)(9, 244)(10, 258)(11, 259)(12, 245)(13, 261)(14, 246)(15, 263)(16, 248)(17, 249)(18, 266)(19, 267)(20, 252)(21, 269)(22, 254)(23, 271)(24, 256)(25, 257)(26, 274)(27, 275)(28, 260)(29, 277)(30, 262)(31, 279)(32, 264)(33, 265)(34, 282)(35, 283)(36, 268)(37, 285)(38, 270)(39, 287)(40, 272)(41, 273)(42, 290)(43, 291)(44, 276)(45, 293)(46, 278)(47, 295)(48, 280)(49, 281)(50, 298)(51, 299)(52, 284)(53, 305)(54, 286)(55, 304)(56, 288)(57, 289)(58, 309)(59, 302)(60, 292)(61, 303)(62, 306)(63, 307)(64, 308)(65, 301)(66, 310)(67, 311)(68, 312)(69, 313)(70, 314)(71, 315)(72, 316)(73, 317)(74, 318)(75, 319)(76, 320)(77, 321)(78, 322)(79, 323)(80, 324)(81, 325)(82, 326)(83, 327)(84, 328)(85, 329)(86, 330)(87, 332)(88, 334)(89, 343)(90, 342)(91, 296)(92, 351)(93, 294)(94, 337)(95, 297)(96, 340)(97, 345)(98, 333)(99, 331)(100, 348)(101, 335)(102, 350)(103, 336)(104, 338)(105, 353)(106, 300)(107, 341)(108, 356)(109, 339)(110, 358)(111, 359)(112, 346)(113, 355)(114, 344)(115, 349)(116, 352)(117, 347)(118, 357)(119, 360)(120, 354)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E14.601 Graph:: bipartite v = 34 e = 240 f = 180 degree seq :: [ 8^30, 60^4 ] E14.601 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 30}) Quotient :: dipole Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^30 ] Map:: polytopal R = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(241, 361, 242, 362)(243, 363, 247, 367)(244, 364, 249, 369)(245, 365, 251, 371)(246, 366, 253, 373)(248, 368, 254, 374)(250, 370, 252, 372)(255, 375, 260, 380)(256, 376, 263, 383)(257, 377, 265, 385)(258, 378, 261, 381)(259, 379, 267, 387)(262, 382, 269, 389)(264, 384, 271, 391)(266, 386, 272, 392)(268, 388, 270, 390)(273, 393, 279, 399)(274, 394, 281, 401)(275, 395, 277, 397)(276, 396, 283, 403)(278, 398, 285, 405)(280, 400, 287, 407)(282, 402, 288, 408)(284, 404, 286, 406)(289, 409, 295, 415)(290, 410, 297, 417)(291, 411, 293, 413)(292, 412, 299, 419)(294, 414, 346, 466)(296, 416, 336, 456)(298, 418, 349, 469)(300, 420, 326, 446)(301, 421, 342, 462)(302, 422, 340, 460)(303, 423, 348, 468)(304, 424, 339, 459)(305, 425, 351, 471)(306, 426, 341, 461)(307, 427, 334, 454)(308, 428, 352, 472)(309, 429, 344, 464)(310, 430, 331, 451)(311, 431, 338, 458)(312, 432, 350, 470)(313, 433, 347, 467)(314, 434, 328, 448)(315, 435, 345, 465)(316, 436, 335, 455)(317, 437, 353, 473)(318, 438, 354, 474)(319, 439, 325, 445)(320, 440, 343, 463)(321, 441, 332, 452)(322, 442, 355, 475)(323, 443, 356, 476)(324, 444, 329, 449)(327, 447, 357, 477)(330, 450, 358, 478)(333, 453, 359, 479)(337, 457, 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, 266)(18, 267)(19, 250)(20, 253)(21, 251)(22, 270)(23, 271)(24, 254)(25, 256)(26, 274)(27, 275)(28, 259)(29, 261)(30, 278)(31, 279)(32, 264)(33, 265)(34, 282)(35, 283)(36, 268)(37, 269)(38, 286)(39, 287)(40, 272)(41, 273)(42, 290)(43, 291)(44, 276)(45, 277)(46, 294)(47, 295)(48, 280)(49, 281)(50, 298)(51, 299)(52, 284)(53, 285)(54, 326)(55, 336)(56, 288)(57, 289)(58, 327)(59, 337)(60, 292)(61, 311)(62, 307)(63, 320)(64, 321)(65, 315)(66, 316)(67, 314)(68, 313)(69, 302)(70, 329)(71, 310)(72, 309)(73, 301)(74, 325)(75, 306)(76, 324)(77, 323)(78, 305)(79, 335)(80, 304)(81, 319)(82, 318)(83, 303)(84, 332)(85, 331)(86, 330)(87, 312)(88, 341)(89, 328)(90, 308)(91, 339)(92, 338)(93, 322)(94, 345)(95, 334)(96, 333)(97, 317)(98, 343)(99, 342)(100, 351)(101, 340)(102, 348)(103, 347)(104, 354)(105, 344)(106, 293)(107, 356)(108, 352)(109, 296)(110, 355)(111, 350)(112, 353)(113, 300)(114, 357)(115, 349)(116, 358)(117, 359)(118, 360)(119, 297)(120, 346)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 8, 60 ), ( 8, 60, 8, 60 ) } Outer automorphisms :: reflexible Dual of E14.600 Graph:: simple bipartite v = 180 e = 240 f = 34 degree seq :: [ 2^120, 4^60 ] E14.602 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 30}) Quotient :: dipole Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |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, Y1^30 ] Map:: polytopal R = (1, 121, 2, 122, 5, 125, 11, 131, 20, 140, 29, 149, 37, 157, 45, 165, 53, 173, 65, 185, 69, 189, 73, 193, 78, 198, 82, 202, 86, 206, 91, 211, 120, 240, 119, 239, 115, 235, 111, 231, 107, 227, 103, 223, 60, 180, 52, 172, 44, 164, 36, 156, 28, 148, 19, 139, 10, 130, 4, 124)(3, 123, 7, 127, 15, 135, 25, 145, 33, 153, 41, 161, 49, 169, 57, 177, 74, 194, 63, 183, 75, 195, 71, 191, 83, 203, 80, 200, 93, 213, 88, 208, 118, 238, 113, 233, 110, 230, 105, 225, 102, 222, 98, 218, 89, 209, 55, 175, 46, 166, 39, 159, 30, 150, 22, 142, 12, 132, 8, 128)(6, 126, 13, 133, 9, 129, 18, 138, 27, 147, 35, 155, 43, 163, 51, 171, 59, 179, 61, 181, 70, 190, 67, 187, 79, 199, 76, 196, 87, 207, 84, 204, 116, 236, 94, 214, 114, 234, 109, 229, 106, 226, 101, 221, 99, 219, 96, 216, 54, 174, 47, 167, 38, 158, 31, 151, 21, 141, 14, 134)(16, 136, 23, 143, 17, 137, 24, 144, 32, 152, 40, 160, 48, 168, 56, 176, 66, 186, 62, 182, 64, 184, 68, 188, 72, 192, 77, 197, 81, 201, 85, 205, 90, 210, 117, 237, 112, 232, 108, 228, 104, 224, 100, 220, 97, 217, 95, 215, 92, 212, 58, 178, 50, 170, 42, 162, 34, 154, 26, 146)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 246)(3, 241)(4, 249)(5, 252)(6, 242)(7, 256)(8, 257)(9, 244)(10, 255)(11, 261)(12, 245)(13, 263)(14, 264)(15, 250)(16, 247)(17, 248)(18, 266)(19, 267)(20, 270)(21, 251)(22, 272)(23, 253)(24, 254)(25, 274)(26, 258)(27, 259)(28, 273)(29, 278)(30, 260)(31, 280)(32, 262)(33, 268)(34, 265)(35, 282)(36, 283)(37, 286)(38, 269)(39, 288)(40, 271)(41, 290)(42, 275)(43, 276)(44, 289)(45, 294)(46, 277)(47, 296)(48, 279)(49, 284)(50, 281)(51, 298)(52, 299)(53, 329)(54, 285)(55, 306)(56, 287)(57, 332)(58, 291)(59, 292)(60, 314)(61, 335)(62, 336)(63, 337)(64, 338)(65, 339)(66, 295)(67, 340)(68, 341)(69, 342)(70, 343)(71, 344)(72, 345)(73, 346)(74, 300)(75, 347)(76, 348)(77, 349)(78, 350)(79, 351)(80, 352)(81, 353)(82, 354)(83, 355)(84, 357)(85, 334)(86, 358)(87, 359)(88, 330)(89, 293)(90, 328)(91, 356)(92, 297)(93, 360)(94, 325)(95, 301)(96, 302)(97, 303)(98, 304)(99, 305)(100, 307)(101, 308)(102, 309)(103, 310)(104, 311)(105, 312)(106, 313)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 331)(117, 324)(118, 326)(119, 327)(120, 333)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E14.599 Graph:: simple bipartite v = 124 e = 240 f = 90 degree seq :: [ 2^120, 60^4 ] E14.603 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 30}) Quotient :: dipole Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^30 ] Map:: R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 14, 134)(10, 130, 12, 132)(15, 135, 20, 140)(16, 136, 23, 143)(17, 137, 25, 145)(18, 138, 21, 141)(19, 139, 27, 147)(22, 142, 29, 149)(24, 144, 31, 151)(26, 146, 32, 152)(28, 148, 30, 150)(33, 153, 39, 159)(34, 154, 41, 161)(35, 155, 37, 157)(36, 156, 43, 163)(38, 158, 45, 165)(40, 160, 47, 167)(42, 162, 48, 168)(44, 164, 46, 166)(49, 169, 55, 175)(50, 170, 57, 177)(51, 171, 53, 173)(52, 172, 59, 179)(54, 174, 102, 222)(56, 176, 91, 211)(58, 178, 105, 225)(60, 180, 88, 208)(61, 181, 107, 227)(62, 182, 108, 228)(63, 183, 109, 229)(64, 184, 103, 223)(65, 185, 110, 230)(66, 186, 100, 220)(67, 187, 111, 231)(68, 188, 112, 232)(69, 189, 113, 233)(70, 190, 99, 219)(71, 191, 104, 224)(72, 192, 114, 234)(73, 193, 115, 235)(74, 194, 101, 221)(75, 195, 106, 226)(76, 196, 96, 216)(77, 197, 116, 236)(78, 198, 117, 237)(79, 199, 94, 214)(80, 200, 118, 238)(81, 201, 98, 218)(82, 202, 119, 239)(83, 203, 120, 240)(84, 204, 92, 212)(85, 205, 97, 217)(86, 206, 90, 210)(87, 207, 95, 215)(89, 209, 93, 213)(241, 361, 243, 363, 248, 368, 257, 377, 266, 386, 274, 394, 282, 402, 290, 410, 298, 418, 312, 432, 309, 429, 302, 422, 307, 427, 314, 434, 325, 445, 329, 449, 335, 455, 338, 458, 344, 464, 358, 478, 355, 475, 360, 480, 300, 420, 292, 412, 284, 404, 276, 396, 268, 388, 259, 379, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 262, 382, 270, 390, 278, 398, 286, 406, 294, 414, 328, 448, 308, 428, 313, 433, 301, 421, 311, 431, 310, 430, 327, 447, 326, 446, 337, 457, 336, 456, 351, 471, 346, 466, 353, 473, 357, 477, 345, 465, 296, 416, 288, 408, 280, 400, 272, 392, 264, 384, 254, 374, 246, 366)(247, 367, 255, 375, 249, 369, 258, 378, 267, 387, 275, 395, 283, 403, 291, 411, 299, 419, 317, 437, 323, 443, 303, 423, 320, 440, 304, 424, 321, 441, 319, 439, 333, 453, 332, 452, 341, 461, 340, 460, 348, 468, 350, 470, 354, 474, 359, 479, 297, 417, 289, 409, 281, 401, 273, 393, 265, 385, 256, 376)(251, 371, 260, 380, 253, 373, 263, 383, 271, 391, 279, 399, 287, 407, 295, 415, 331, 451, 322, 442, 318, 438, 305, 425, 315, 435, 306, 426, 316, 436, 324, 444, 330, 450, 334, 454, 339, 459, 343, 463, 347, 467, 349, 469, 352, 472, 356, 476, 342, 462, 293, 413, 285, 405, 277, 397, 269, 389, 261, 381) L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 254)(9, 244)(10, 252)(11, 245)(12, 250)(13, 246)(14, 248)(15, 260)(16, 263)(17, 265)(18, 261)(19, 267)(20, 255)(21, 258)(22, 269)(23, 256)(24, 271)(25, 257)(26, 272)(27, 259)(28, 270)(29, 262)(30, 268)(31, 264)(32, 266)(33, 279)(34, 281)(35, 277)(36, 283)(37, 275)(38, 285)(39, 273)(40, 287)(41, 274)(42, 288)(43, 276)(44, 286)(45, 278)(46, 284)(47, 280)(48, 282)(49, 295)(50, 297)(51, 293)(52, 299)(53, 291)(54, 342)(55, 289)(56, 331)(57, 290)(58, 345)(59, 292)(60, 328)(61, 347)(62, 348)(63, 349)(64, 343)(65, 350)(66, 340)(67, 351)(68, 352)(69, 353)(70, 339)(71, 344)(72, 354)(73, 355)(74, 341)(75, 346)(76, 336)(77, 356)(78, 357)(79, 334)(80, 358)(81, 338)(82, 359)(83, 360)(84, 332)(85, 337)(86, 330)(87, 335)(88, 300)(89, 333)(90, 326)(91, 296)(92, 324)(93, 329)(94, 319)(95, 327)(96, 316)(97, 325)(98, 321)(99, 310)(100, 306)(101, 314)(102, 294)(103, 304)(104, 311)(105, 298)(106, 315)(107, 301)(108, 302)(109, 303)(110, 305)(111, 307)(112, 308)(113, 309)(114, 312)(115, 313)(116, 317)(117, 318)(118, 320)(119, 322)(120, 323)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E14.604 Graph:: bipartite v = 64 e = 240 f = 150 degree seq :: [ 4^60, 60^4 ] E14.604 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 30}) Quotient :: dipole Aut^+ = (C30 x C2) : C2 (small group id <120, 30>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^30 ] Map:: polytopal R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 13, 133, 8, 128)(5, 125, 11, 131, 14, 134, 7, 127)(10, 130, 16, 136, 21, 141, 17, 137)(12, 132, 15, 135, 22, 142, 19, 139)(18, 138, 25, 145, 29, 149, 24, 144)(20, 140, 27, 147, 30, 150, 23, 143)(26, 146, 32, 152, 37, 157, 33, 153)(28, 148, 31, 151, 38, 158, 35, 155)(34, 154, 41, 161, 45, 165, 40, 160)(36, 156, 43, 163, 46, 166, 39, 159)(42, 162, 48, 168, 53, 173, 49, 169)(44, 164, 47, 167, 54, 174, 51, 171)(50, 170, 57, 177, 111, 231, 56, 176)(52, 172, 59, 179, 117, 237, 55, 175)(58, 178, 116, 236, 107, 227, 120, 240)(60, 180, 102, 222, 119, 239, 112, 232)(61, 181, 76, 196, 66, 186, 77, 197)(62, 182, 82, 202, 64, 184, 72, 192)(63, 183, 85, 205, 73, 193, 84, 204)(65, 185, 69, 189, 74, 194, 68, 188)(67, 187, 80, 200, 71, 191, 90, 210)(70, 190, 92, 212, 81, 201, 93, 213)(75, 195, 98, 218, 79, 199, 88, 208)(78, 198, 101, 221, 89, 209, 100, 220)(83, 203, 96, 216, 87, 207, 106, 226)(86, 206, 108, 228, 97, 217, 109, 229)(91, 211, 113, 233, 95, 215, 104, 224)(94, 214, 115, 235, 105, 225, 114, 234)(99, 219, 110, 230, 103, 223, 118, 238)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 247)(3, 250)(4, 251)(5, 241)(6, 253)(7, 255)(8, 242)(9, 244)(10, 258)(11, 259)(12, 245)(13, 261)(14, 246)(15, 263)(16, 248)(17, 249)(18, 266)(19, 267)(20, 252)(21, 269)(22, 254)(23, 271)(24, 256)(25, 257)(26, 274)(27, 275)(28, 260)(29, 277)(30, 262)(31, 279)(32, 264)(33, 265)(34, 282)(35, 283)(36, 268)(37, 285)(38, 270)(39, 287)(40, 272)(41, 273)(42, 290)(43, 291)(44, 276)(45, 293)(46, 278)(47, 295)(48, 280)(49, 281)(50, 298)(51, 299)(52, 284)(53, 351)(54, 286)(55, 342)(56, 288)(57, 289)(58, 339)(59, 352)(60, 292)(61, 314)(62, 309)(63, 306)(64, 308)(65, 322)(66, 305)(67, 304)(68, 317)(69, 316)(70, 313)(71, 302)(72, 330)(73, 301)(74, 312)(75, 311)(76, 325)(77, 324)(78, 321)(79, 307)(80, 338)(81, 303)(82, 320)(83, 319)(84, 333)(85, 332)(86, 329)(87, 315)(88, 346)(89, 310)(90, 328)(91, 327)(92, 341)(93, 340)(94, 337)(95, 323)(96, 353)(97, 318)(98, 336)(99, 335)(100, 349)(101, 348)(102, 345)(103, 331)(104, 358)(105, 326)(106, 344)(107, 343)(108, 355)(109, 354)(110, 360)(111, 347)(112, 334)(113, 350)(114, 300)(115, 359)(116, 296)(117, 294)(118, 356)(119, 357)(120, 297)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 60 ), ( 4, 60, 4, 60, 4, 60, 4, 60 ) } Outer automorphisms :: reflexible Dual of E14.603 Graph:: simple bipartite v = 150 e = 240 f = 64 degree seq :: [ 2^120, 8^30 ] E14.605 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 6, 6}) Quotient :: halfedge Aut^+ = C2 x ((C13 : C3) : C2) (small group id <156, 8>) Aut = C2 x ((C13 : C3) : C2) (small group id <156, 8>) |r| :: 1 Presentation :: [ X2^2, X1^6, (X2 * X1^-2 * X2 * X1^-1)^2, (X1 * X2)^6, X2 * X1^-3 * X2 * X1^3 * X2 * X1^2 * X2 * X1^-2, X2 * X1^2 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * 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, 138, 97, 57)(35, 65, 105, 130, 85, 49)(37, 68, 76, 118, 111, 69)(46, 81, 123, 114, 72, 82)(54, 92, 135, 107, 121, 79)(55, 93, 116, 83, 126, 94)(59, 86, 64, 91, 125, 99)(60, 100, 141, 153, 137, 101)(63, 87, 131, 155, 142, 104)(67, 108, 145, 150, 120, 109)(84, 127, 113, 119, 149, 128)(90, 122, 152, 139, 102, 134)(96, 124, 147, 144, 106, 132)(103, 129, 148, 146, 156, 136)(110, 143, 154, 133, 151, 140) 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, 137)(94, 131)(95, 139)(97, 115)(98, 140)(100, 135)(104, 127)(105, 143)(109, 134)(111, 142)(112, 130)(114, 146)(117, 147)(118, 148)(121, 151)(123, 153)(126, 154)(128, 152)(138, 156)(141, 149)(144, 150)(145, 155) local type(s) :: { ( 6^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 26 e = 78 f = 26 degree seq :: [ 6^26 ] E14.606 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 6, 6}) Quotient :: halfedge Aut^+ = C2 x ((C13 : C3) : C2) (small group id <156, 8>) Aut = C2 x ((C13 : C3) : C2) (small group id <156, 8>) |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 * X2 * X1^-1 * 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, 122, 149, 131, 146, 132)(103, 133, 139, 129, 150, 126)(104, 125, 105, 130, 145, 127)(106, 134, 141, 128, 142, 135)(107, 136, 148, 121, 140, 137)(123, 143, 124, 147, 138, 144)(151, 154, 152, 155, 153, 156) 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, 136)(109, 135)(110, 134)(111, 138)(112, 139)(113, 140)(114, 141)(115, 142)(116, 143)(117, 144)(118, 145)(119, 146)(120, 147)(132, 151)(133, 152)(137, 153)(148, 154)(149, 155)(150, 156) local type(s) :: { ( 6^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 26 e = 78 f = 26 degree seq :: [ 6^26 ] E14.607 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 6, 6}) Quotient :: edge Aut^+ = C2 x ((C13 : C3) : C2) (small group id <156, 8>) Aut = C2 x ((C13 : C3) : C2) (small group id <156, 8>) |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^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * 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, 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, 113)(99, 129)(102, 133)(103, 119)(104, 118)(108, 125)(109, 124)(110, 123)(111, 138)(114, 141)(117, 145)(126, 150)(127, 139)(128, 151)(130, 153)(131, 144)(132, 143)(134, 148)(135, 147)(136, 146)(137, 152)(140, 154)(142, 156)(149, 155)(157, 159, 164, 174, 166, 160)(158, 161, 168, 181, 170, 162)(163, 171, 186, 177, 188, 172)(165, 175, 190, 173, 189, 176)(167, 178, 194, 184, 196, 179)(169, 182, 198, 180, 197, 183)(185, 201, 225, 206, 227, 202)(187, 204, 229, 203, 228, 205)(191, 209, 233, 207, 232, 210)(192, 211, 235, 208, 234, 212)(193, 213, 239, 218, 241, 214)(195, 216, 243, 215, 242, 217)(199, 221, 247, 219, 246, 222)(200, 223, 249, 220, 248, 224)(226, 254, 284, 253, 283, 255)(230, 258, 287, 256, 286, 259)(231, 260, 236, 257, 288, 261)(237, 264, 291, 262, 290, 265)(238, 266, 293, 263, 292, 267)(240, 269, 296, 268, 295, 270)(244, 273, 299, 271, 298, 274)(245, 275, 250, 272, 300, 276)(251, 279, 303, 277, 302, 280)(252, 281, 305, 278, 304, 282)(285, 308, 289, 307, 294, 309)(297, 311, 301, 310, 306, 312) L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312) local type(s) :: { ( 12, 12 ), ( 12^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 104 e = 156 f = 26 degree seq :: [ 2^78, 6^26 ] E14.608 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 6, 6}) Quotient :: edge Aut^+ = C2 x ((C13 : C3) : C2) (small group id <156, 8>) Aut = C2 x ((C13 : C3) : C2) (small group id <156, 8>) |r| :: 1 Presentation :: [ X1^2, X2^6, (X1 * X2 * X1 * X2^2)^2, X2^-1 * X1 * X2^-1 * X1 * X2^4 * X1 * X2^-1 * X1 * X2^-1, X2 * X1 * X2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1, X2^-1 * X1 * X2^2 * X1 * X2^-2 * X1 * X2^3 * X1 * X2^-2 ] 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, 138)(98, 132)(100, 141)(101, 123)(102, 115)(104, 126)(106, 144)(108, 130)(110, 120)(112, 146)(114, 136)(118, 148)(122, 151)(128, 154)(134, 156)(137, 150)(139, 152)(140, 147)(142, 149)(143, 155)(145, 153)(157, 159, 164, 174, 166, 160)(158, 161, 168, 181, 170, 162)(163, 171, 186, 213, 188, 172)(165, 175, 193, 225, 195, 176)(167, 178, 199, 232, 201, 179)(169, 182, 206, 244, 208, 183)(173, 189, 217, 256, 219, 190)(177, 196, 228, 270, 229, 197)(180, 202, 236, 278, 238, 203)(184, 209, 247, 292, 248, 210)(185, 211, 194, 226, 249, 212)(187, 214, 252, 295, 253, 215)(191, 220, 260, 281, 262, 221)(192, 222, 261, 299, 264, 223)(198, 230, 207, 245, 271, 231)(200, 233, 274, 305, 275, 234)(204, 239, 282, 259, 284, 240)(205, 241, 283, 309, 286, 242)(216, 254, 273, 267, 296, 255)(218, 257, 298, 268, 227, 258)(224, 265, 301, 312, 297, 266)(235, 276, 251, 289, 306, 277)(237, 279, 308, 290, 246, 280)(243, 287, 311, 302, 307, 288)(250, 285, 269, 300, 304, 293)(263, 291, 310, 294, 303, 272) L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312) local type(s) :: { ( 12, 12 ), ( 12^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 104 e = 156 f = 26 degree seq :: [ 2^78, 6^26 ] E14.609 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 6, 6}) Quotient :: edge Aut^+ = C2 x ((C13 : C3) : C2) (small group id <156, 8>) Aut = C2 x ((C13 : C3) : C2) (small group id <156, 8>) |r| :: 1 Presentation :: [ (X2 * X1)^2, X1^6, (X1^-1 * X2^2)^2, X2^6, X1^-1 * X2^-1 * X1^2 * X2^-1 * X1 * X2^-1 * X1^-2 * X2 * X1^-2, X1^-1 * X2^-1 * X1 * X2 * X1^-2 * X2 * X1^-1 * X2 * X1^-2 * X2^-2 * 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, 127, 84, 48)(26, 42, 69, 103, 87, 51)(27, 54, 91, 133, 93, 55)(32, 36, 66, 106, 100, 61)(37, 68, 108, 142, 107, 67)(43, 76, 118, 99, 120, 77)(49, 85, 128, 141, 113, 81)(53, 90, 132, 154, 130, 88)(56, 82, 111, 70, 110, 94)(58, 64, 102, 138, 136, 96)(62, 101, 104, 140, 121, 78)(75, 117, 150, 126, 148, 115)(79, 122, 97, 137, 147, 112)(83, 125, 152, 156, 144, 124)(89, 131, 139, 155, 151, 119)(92, 123, 143, 109, 145, 134)(116, 149, 129, 153, 135, 146)(157, 159, 166, 182, 171, 161)(158, 163, 175, 198, 178, 164)(160, 168, 186, 207, 180, 165)(162, 173, 193, 225, 196, 174)(167, 183, 170, 190, 209, 181)(169, 188, 206, 243, 214, 185)(172, 191, 220, 259, 223, 192)(176, 199, 177, 202, 231, 197)(179, 204, 239, 215, 187, 205)(184, 212, 246, 219, 248, 210)(189, 211, 245, 208, 244, 218)(194, 226, 195, 229, 265, 224)(200, 234, 273, 236, 275, 232)(201, 233, 272, 230, 271, 235)(203, 237, 279, 254, 280, 238)(213, 252, 285, 242, 217, 253)(216, 255, 281, 240, 282, 241)(221, 260, 222, 263, 295, 258)(227, 268, 301, 270, 302, 266)(228, 267, 300, 264, 299, 269)(247, 290, 303, 288, 250, 291)(249, 262, 257, 286, 294, 287)(251, 278, 304, 283, 305, 276)(256, 289, 309, 292, 310, 293)(261, 297, 311, 298, 312, 296)(274, 307, 284, 306, 277, 308) L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312) local type(s) :: { ( 4^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 52 e = 156 f = 78 degree seq :: [ 6^52 ] E14.610 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 6, 6}) Quotient :: loop Aut^+ = C2 x ((C13 : C3) : C2) (small group id <156, 8>) Aut = C2 x ((C13 : C3) : C2) (small group id <156, 8>) |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^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1 ] Map:: polytopal non-degenerate R = (1, 157, 2, 158)(3, 159, 7, 163)(4, 160, 9, 165)(5, 161, 11, 167)(6, 162, 13, 169)(8, 164, 17, 173)(10, 166, 21, 177)(12, 168, 24, 180)(14, 170, 28, 184)(15, 171, 29, 185)(16, 172, 31, 187)(18, 174, 25, 181)(19, 175, 35, 191)(20, 176, 36, 192)(22, 178, 37, 193)(23, 179, 39, 195)(26, 182, 43, 199)(27, 183, 44, 200)(30, 186, 47, 203)(32, 188, 50, 206)(33, 189, 51, 207)(34, 190, 52, 208)(38, 194, 59, 215)(40, 196, 62, 218)(41, 197, 63, 219)(42, 198, 64, 220)(45, 201, 68, 224)(46, 202, 70, 226)(48, 204, 74, 230)(49, 205, 75, 231)(53, 209, 80, 236)(54, 210, 81, 237)(55, 211, 82, 238)(56, 212, 57, 213)(58, 214, 84, 240)(60, 216, 88, 244)(61, 217, 89, 245)(65, 221, 94, 250)(66, 222, 95, 251)(67, 223, 96, 252)(69, 225, 97, 253)(71, 227, 93, 249)(72, 228, 100, 256)(73, 229, 101, 257)(76, 232, 105, 261)(77, 233, 106, 262)(78, 234, 107, 263)(79, 235, 85, 241)(83, 239, 112, 268)(86, 242, 115, 271)(87, 243, 116, 272)(90, 246, 120, 276)(91, 247, 121, 277)(92, 248, 122, 278)(98, 254, 113, 269)(99, 255, 129, 285)(102, 258, 133, 289)(103, 259, 119, 275)(104, 260, 118, 274)(108, 264, 125, 281)(109, 265, 124, 280)(110, 266, 123, 279)(111, 267, 138, 294)(114, 270, 141, 297)(117, 273, 145, 301)(126, 282, 150, 306)(127, 283, 139, 295)(128, 284, 151, 307)(130, 286, 153, 309)(131, 287, 144, 300)(132, 288, 143, 299)(134, 290, 148, 304)(135, 291, 147, 303)(136, 292, 146, 302)(137, 293, 152, 308)(140, 296, 154, 310)(142, 298, 156, 312)(149, 305, 155, 311) L = (1, 159)(2, 161)(3, 164)(4, 157)(5, 168)(6, 158)(7, 171)(8, 174)(9, 175)(10, 160)(11, 178)(12, 181)(13, 182)(14, 162)(15, 186)(16, 163)(17, 189)(18, 166)(19, 190)(20, 165)(21, 188)(22, 194)(23, 167)(24, 197)(25, 170)(26, 198)(27, 169)(28, 196)(29, 201)(30, 177)(31, 204)(32, 172)(33, 176)(34, 173)(35, 209)(36, 211)(37, 213)(38, 184)(39, 216)(40, 179)(41, 183)(42, 180)(43, 221)(44, 223)(45, 225)(46, 185)(47, 228)(48, 229)(49, 187)(50, 227)(51, 232)(52, 234)(53, 233)(54, 191)(55, 235)(56, 192)(57, 239)(58, 193)(59, 242)(60, 243)(61, 195)(62, 241)(63, 246)(64, 248)(65, 247)(66, 199)(67, 249)(68, 200)(69, 206)(70, 254)(71, 202)(72, 205)(73, 203)(74, 258)(75, 260)(76, 210)(77, 207)(78, 212)(79, 208)(80, 257)(81, 264)(82, 266)(83, 218)(84, 269)(85, 214)(86, 217)(87, 215)(88, 273)(89, 275)(90, 222)(91, 219)(92, 224)(93, 220)(94, 272)(95, 279)(96, 281)(97, 283)(98, 284)(99, 226)(100, 286)(101, 288)(102, 287)(103, 230)(104, 236)(105, 231)(106, 290)(107, 292)(108, 291)(109, 237)(110, 293)(111, 238)(112, 295)(113, 296)(114, 240)(115, 298)(116, 300)(117, 299)(118, 244)(119, 250)(120, 245)(121, 302)(122, 304)(123, 303)(124, 251)(125, 305)(126, 252)(127, 255)(128, 253)(129, 308)(130, 259)(131, 256)(132, 261)(133, 307)(134, 265)(135, 262)(136, 267)(137, 263)(138, 309)(139, 270)(140, 268)(141, 311)(142, 274)(143, 271)(144, 276)(145, 310)(146, 280)(147, 277)(148, 282)(149, 278)(150, 312)(151, 294)(152, 289)(153, 285)(154, 306)(155, 301)(156, 297) local type(s) :: { ( 6^4 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: simple bipartite v = 78 e = 156 f = 52 degree seq :: [ 4^78 ] E14.611 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 6, 6}) Quotient :: loop Aut^+ = C2 x ((C13 : C3) : C2) (small group id <156, 8>) Aut = C2 x ((C13 : C3) : C2) (small group id <156, 8>) |r| :: 1 Presentation :: [ (X2 * X1)^2, X1^6, (X1^-1 * X2^2)^2, X2^6, X1^-1 * X2^-1 * X1^2 * X2^-1 * X1 * X2^-1 * X1^-2 * X2 * X1^-2, X1^-1 * X2^-1 * X1 * X2 * X1^-2 * X2 * X1^-1 * X2 * X1^-2 * X2^-2 * X1^-1 ] Map:: R = (1, 157, 2, 158, 6, 162, 16, 172, 13, 169, 4, 160)(3, 159, 9, 165, 23, 179, 47, 203, 28, 184, 11, 167)(5, 161, 14, 170, 33, 189, 44, 200, 20, 176, 7, 163)(8, 164, 21, 177, 45, 201, 71, 227, 38, 194, 17, 173)(10, 166, 25, 181, 52, 208, 80, 236, 46, 202, 22, 178)(12, 168, 29, 185, 57, 213, 95, 251, 60, 216, 31, 187)(15, 171, 30, 186, 59, 215, 98, 254, 63, 219, 34, 190)(18, 174, 39, 195, 72, 228, 105, 261, 65, 221, 35, 191)(19, 175, 41, 197, 74, 230, 114, 270, 73, 229, 40, 196)(24, 180, 50, 206, 86, 242, 127, 283, 84, 240, 48, 204)(26, 182, 42, 198, 69, 225, 103, 259, 87, 243, 51, 207)(27, 183, 54, 210, 91, 247, 133, 289, 93, 249, 55, 211)(32, 188, 36, 192, 66, 222, 106, 262, 100, 256, 61, 217)(37, 193, 68, 224, 108, 264, 142, 298, 107, 263, 67, 223)(43, 199, 76, 232, 118, 274, 99, 255, 120, 276, 77, 233)(49, 205, 85, 241, 128, 284, 141, 297, 113, 269, 81, 237)(53, 209, 90, 246, 132, 288, 154, 310, 130, 286, 88, 244)(56, 212, 82, 238, 111, 267, 70, 226, 110, 266, 94, 250)(58, 214, 64, 220, 102, 258, 138, 294, 136, 292, 96, 252)(62, 218, 101, 257, 104, 260, 140, 296, 121, 277, 78, 234)(75, 231, 117, 273, 150, 306, 126, 282, 148, 304, 115, 271)(79, 235, 122, 278, 97, 253, 137, 293, 147, 303, 112, 268)(83, 239, 125, 281, 152, 308, 156, 312, 144, 300, 124, 280)(89, 245, 131, 287, 139, 295, 155, 311, 151, 307, 119, 275)(92, 248, 123, 279, 143, 299, 109, 265, 145, 301, 134, 290)(116, 272, 149, 305, 129, 285, 153, 309, 135, 291, 146, 302) L = (1, 159)(2, 163)(3, 166)(4, 168)(5, 157)(6, 173)(7, 175)(8, 158)(9, 160)(10, 182)(11, 183)(12, 186)(13, 188)(14, 190)(15, 161)(16, 191)(17, 193)(18, 162)(19, 198)(20, 199)(21, 202)(22, 164)(23, 204)(24, 165)(25, 167)(26, 171)(27, 170)(28, 212)(29, 169)(30, 207)(31, 205)(32, 206)(33, 211)(34, 209)(35, 220)(36, 172)(37, 225)(38, 226)(39, 229)(40, 174)(41, 176)(42, 178)(43, 177)(44, 234)(45, 233)(46, 231)(47, 237)(48, 239)(49, 179)(50, 243)(51, 180)(52, 244)(53, 181)(54, 184)(55, 245)(56, 246)(57, 252)(58, 185)(59, 187)(60, 255)(61, 253)(62, 189)(63, 248)(64, 259)(65, 260)(66, 263)(67, 192)(68, 194)(69, 196)(70, 195)(71, 268)(72, 267)(73, 265)(74, 271)(75, 197)(76, 200)(77, 272)(78, 273)(79, 201)(80, 275)(81, 279)(82, 203)(83, 215)(84, 282)(85, 216)(86, 217)(87, 214)(88, 218)(89, 208)(90, 219)(91, 290)(92, 210)(93, 262)(94, 291)(95, 278)(96, 285)(97, 213)(98, 280)(99, 281)(100, 289)(101, 286)(102, 221)(103, 223)(104, 222)(105, 297)(106, 257)(107, 295)(108, 299)(109, 224)(110, 227)(111, 300)(112, 301)(113, 228)(114, 302)(115, 235)(116, 230)(117, 236)(118, 307)(119, 232)(120, 251)(121, 308)(122, 304)(123, 254)(124, 238)(125, 240)(126, 241)(127, 305)(128, 306)(129, 242)(130, 294)(131, 249)(132, 250)(133, 309)(134, 303)(135, 247)(136, 310)(137, 256)(138, 287)(139, 258)(140, 261)(141, 311)(142, 312)(143, 269)(144, 264)(145, 270)(146, 266)(147, 288)(148, 283)(149, 276)(150, 277)(151, 284)(152, 274)(153, 292)(154, 293)(155, 298)(156, 296) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: bipartite v = 26 e = 156 f = 104 degree seq :: [ 12^26 ] E14.612 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 6, 6}) Quotient :: loop Aut^+ = C2 x ((C13 : C3) : C2) (small group id <156, 8>) Aut = C2 x ((C13 : C3) : C2) (small group id <156, 8>) |r| :: 1 Presentation :: [ (X1 * X2)^2, X2^6, (X1 * X2^-1 * X1)^2, X1^6, X1^-1 * X2^-2 * X1^3 * X2^2 * X1^-2, X1^-2 * X2^2 * X1^-3 * X2^-2 * X1^-1, X2 * X1^-1 * X2^3 * X1 * X2^-2 * X1 * X2^-2 * X1^-1 ] Map:: R = (1, 157, 2, 158, 6, 162, 16, 172, 13, 169, 4, 160)(3, 159, 9, 165, 23, 179, 35, 191, 18, 174, 11, 167)(5, 161, 14, 170, 31, 187, 36, 192, 20, 176, 7, 163)(8, 164, 21, 177, 12, 168, 29, 185, 38, 194, 17, 173)(10, 166, 25, 181, 51, 207, 64, 220, 48, 204, 27, 183)(15, 171, 34, 190, 43, 199, 65, 221, 61, 217, 32, 188)(19, 175, 40, 196, 71, 227, 59, 215, 33, 189, 42, 198)(22, 178, 46, 202, 69, 225, 57, 213, 78, 234, 44, 200)(24, 180, 49, 205, 28, 184, 39, 195, 70, 226, 47, 203)(26, 182, 53, 209, 90, 246, 102, 258, 87, 243, 54, 210)(30, 186, 45, 201, 68, 224, 37, 193, 66, 222, 58, 214)(41, 197, 73, 229, 113, 269, 95, 251, 110, 266, 74, 230)(50, 206, 85, 241, 105, 261, 67, 223, 104, 260, 83, 239)(52, 208, 88, 244, 55, 211, 82, 238, 125, 281, 86, 242)(56, 212, 84, 240, 124, 280, 81, 237, 108, 264, 94, 250)(60, 216, 97, 253, 117, 273, 76, 232, 63, 219, 99, 255)(62, 218, 100, 256, 109, 265, 72, 228, 111, 267, 75, 231)(77, 233, 118, 274, 143, 299, 107, 263, 80, 236, 120, 276)(79, 235, 121, 277, 96, 252, 103, 259, 138, 294, 106, 262)(89, 245, 116, 272, 148, 304, 123, 279, 145, 301, 131, 287)(91, 247, 122, 278, 92, 248, 130, 286, 151, 307, 133, 289)(93, 249, 132, 288, 139, 295, 129, 285, 152, 308, 119, 275)(98, 254, 135, 291, 147, 303, 112, 268, 142, 298, 137, 293)(101, 257, 126, 282, 140, 296, 136, 292, 141, 297, 128, 284)(114, 270, 144, 300, 115, 271, 146, 302, 127, 283, 149, 305)(134, 290, 150, 306, 155, 311, 154, 310, 156, 312, 153, 309) L = (1, 159)(2, 163)(3, 166)(4, 168)(5, 157)(6, 173)(7, 175)(8, 158)(9, 160)(10, 182)(11, 184)(12, 186)(13, 187)(14, 188)(15, 161)(16, 191)(17, 193)(18, 162)(19, 197)(20, 199)(21, 200)(22, 164)(23, 203)(24, 165)(25, 167)(26, 171)(27, 211)(28, 212)(29, 169)(30, 206)(31, 215)(32, 216)(33, 170)(34, 210)(35, 220)(36, 172)(37, 223)(38, 225)(39, 174)(40, 176)(41, 178)(42, 231)(43, 232)(44, 233)(45, 177)(46, 230)(47, 237)(48, 179)(49, 239)(50, 180)(51, 242)(52, 181)(53, 183)(54, 248)(55, 249)(56, 245)(57, 185)(58, 252)(59, 251)(60, 254)(61, 246)(62, 189)(63, 190)(64, 258)(65, 192)(66, 194)(67, 195)(68, 262)(69, 263)(70, 261)(71, 265)(72, 196)(73, 198)(74, 271)(75, 272)(76, 268)(77, 275)(78, 269)(79, 201)(80, 202)(81, 279)(82, 204)(83, 282)(84, 205)(85, 214)(86, 285)(87, 207)(88, 287)(89, 208)(90, 289)(91, 209)(92, 290)(93, 276)(94, 270)(95, 213)(96, 291)(97, 217)(98, 218)(99, 284)(100, 293)(101, 219)(102, 221)(103, 222)(104, 224)(105, 297)(106, 298)(107, 295)(108, 226)(109, 301)(110, 227)(111, 303)(112, 228)(113, 305)(114, 229)(115, 306)(116, 250)(117, 296)(118, 234)(119, 235)(120, 247)(121, 308)(122, 236)(123, 238)(124, 302)(125, 304)(126, 309)(127, 240)(128, 241)(129, 299)(130, 243)(131, 256)(132, 244)(133, 310)(134, 257)(135, 255)(136, 253)(137, 294)(138, 288)(139, 259)(140, 260)(141, 311)(142, 273)(143, 286)(144, 264)(145, 280)(146, 266)(147, 277)(148, 267)(149, 312)(150, 278)(151, 274)(152, 281)(153, 283)(154, 292)(155, 300)(156, 307) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: bipartite v = 26 e = 156 f = 104 degree seq :: [ 12^26 ] E14.613 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 7}) Quotient :: regular Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^3, T1^7, T2 * T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-3 * T2 * T1^-3, (T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-2)^2, (T2 * T1^2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-3 * T2 * T1^-3)^2, T2 * T1^3 * T2 * T1^-2 * T2 * T1^3 * T2 * T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-3 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 11, 20, 10, 4)(3, 7, 15, 26, 30, 17, 8)(6, 13, 24, 39, 42, 25, 14)(9, 18, 31, 49, 46, 28, 16)(12, 22, 37, 57, 60, 38, 23)(19, 33, 52, 77, 76, 51, 32)(21, 35, 55, 81, 84, 56, 36)(27, 44, 67, 97, 100, 68, 45)(29, 47, 70, 102, 91, 62, 40)(34, 54, 80, 115, 114, 79, 53)(41, 63, 92, 130, 123, 86, 58)(43, 65, 95, 134, 137, 96, 66)(48, 72, 105, 147, 146, 104, 71)(50, 74, 108, 151, 154, 109, 75)(59, 87, 124, 172, 165, 118, 82)(61, 89, 127, 176, 179, 128, 90)(64, 94, 133, 185, 184, 132, 93)(69, 101, 142, 197, 193, 139, 98)(73, 106, 149, 206, 209, 150, 107)(78, 112, 158, 217, 220, 159, 113)(83, 119, 166, 228, 224, 162, 116)(85, 121, 169, 232, 235, 170, 122)(88, 126, 175, 241, 240, 174, 125)(99, 140, 194, 264, 257, 188, 135)(103, 144, 201, 272, 275, 202, 145)(110, 155, 214, 290, 286, 211, 152)(111, 156, 215, 292, 295, 216, 157)(117, 163, 225, 304, 307, 226, 164)(120, 168, 231, 313, 312, 230, 167)(129, 180, 247, 333, 329, 244, 177)(131, 182, 250, 337, 340, 251, 183)(136, 189, 258, 348, 279, 205, 148)(138, 191, 261, 352, 355, 262, 192)(141, 196, 267, 361, 360, 266, 195)(143, 199, 270, 366, 369, 271, 200)(153, 212, 287, 387, 380, 281, 207)(160, 221, 300, 403, 399, 297, 218)(161, 222, 301, 405, 408, 302, 223)(171, 236, 319, 428, 424, 316, 233)(173, 238, 322, 432, 435, 323, 239)(178, 245, 330, 443, 344, 254, 186)(181, 248, 335, 449, 452, 336, 249)(187, 255, 345, 461, 464, 346, 256)(190, 260, 351, 470, 469, 350, 259)(198, 208, 282, 381, 485, 365, 269)(203, 276, 374, 494, 410, 371, 273)(204, 277, 375, 496, 499, 376, 278)(210, 284, 384, 442, 508, 385, 285)(213, 289, 390, 514, 513, 389, 288)(219, 298, 400, 526, 521, 394, 293)(227, 308, 414, 490, 370, 411, 305)(229, 310, 417, 503, 763, 418, 311)(234, 317, 425, 779, 439, 326, 242)(237, 320, 430, 751, 555, 431, 321)(243, 327, 440, 386, 509, 441, 328)(246, 332, 446, 800, 618, 445, 331)(252, 341, 457, 810, 532, 454, 338)(253, 342, 458, 812, 570, 459, 343)(263, 356, 474, 423, 315, 422, 353)(265, 358, 477, 832, 1061, 478, 359)(268, 363, 482, 731, 551, 483, 364)(274, 372, 491, 759, 1034, 487, 367)(280, 378, 501, 419, 582, 502, 379)(283, 383, 506, 856, 707, 505, 382)(291, 294, 395, 522, 871, 518, 392)(296, 397, 462, 347, 465, 525, 398)(299, 402, 529, 876, 574, 528, 401)(303, 409, 536, 738, 453, 533, 406)(306, 412, 769, 1039, 1073, 421, 314)(309, 415, 773, 817, 563, 557, 416)(318, 427, 757, 960, 642, 537, 426)(324, 436, 701, 520, 393, 519, 433)(325, 437, 790, 889, 558, 633, 438)(334, 368, 488, 842, 1068, 1005, 448)(339, 455, 807, 691, 994, 733, 450)(349, 467, 813, 460, 816, 1044, 468)(354, 472, 827, 877, 1076, 481, 362)(357, 475, 830, 712, 549, 581, 476)(373, 493, 845, 921, 597, 541, 492)(377, 500, 851, 670, 504, 685, 497)(388, 511, 862, 1072, 1058, 1009, 512)(391, 516, 866, 696, 546, 600, 517)(396, 524, 783, 962, 768, 544, 523)(404, 407, 534, 878, 1077, 1026, 531)(413, 709, 689, 984, 673, 538, 652)(420, 613, 932, 858, 548, 666, 906)(429, 451, 805, 1056, 1084, 968, 881)(434, 692, 744, 693, 996, 793, 785)(444, 778, 1046, 792, 1053, 971, 661)(447, 736, 976, 665, 543, 593, 859)(456, 808, 1003, 931, 612, 545, 664)(463, 820, 1060, 1091, 1064, 835, 471)(466, 823, 1048, 854, 579, 562, 730)(473, 782, 798, 945, 628, 539, 610)(479, 576, 724, 913, 486, 567, 833)(480, 584, 907, 863, 565, 684, 902)(484, 802, 956, 639, 872, 753, 838)(489, 590, 777, 926, 803, 553, 831)(495, 498, 849, 1071, 1082, 986, 993)(507, 723, 1014, 1042, 1074, 868, 515)(510, 860, 980, 668, 559, 596, 920)(527, 677, 987, 1085, 1029, 964, 649)(530, 637, 954, 741, 542, 629, 822)(535, 659, 726, 1001, 715, 540, 680)(547, 745, 850, 678, 703, 988, 821)(550, 627, 789, 875, 963, 953, 636)(552, 697, 898, 719, 650, 965, 885)(554, 695, 841, 981, 1016, 787, 602)(556, 867, 799, 647, 764, 967, 887)(560, 732, 888, 770, 623, 939, 891)(561, 892, 758, 607, 846, 947, 893)(564, 641, 959, 1035, 927, 873, 688)(566, 573, 788, 797, 970, 1023, 735)(568, 740, 1025, 955, 990, 729, 631)(569, 895, 737, 699, 717, 992, 897)(571, 791, 883, 879, 644, 824, 847)(572, 828, 690, 630, 946, 925, 901)(575, 672, 983, 995, 949, 754, 654)(577, 588, 852, 1047, 937, 1055, 796)(578, 752, 894, 864, 604, 809, 784)(580, 771, 669, 681, 825, 952, 905)(583, 617, 814, 1057, 914, 1032, 756)(585, 794, 1054, 934, 998, 694, 608)(586, 908, 855, 760, 675, 985, 910)(587, 749, 727, 601, 869, 903, 912)(589, 714, 1011, 997, 974, 686, 682)(591, 605, 734, 1021, 923, 1024, 739)(592, 880, 708, 721, 1013, 979, 915)(594, 916, 884, 969, 656, 716, 765)(595, 720, 638, 653, 966, 930, 919)(598, 755, 1031, 942, 975, 663, 648)(599, 922, 806, 843, 743, 861, 924)(603, 657, 750, 1028, 904, 1040, 818)(606, 767, 1038, 1019, 943, 725, 722)(609, 761, 658, 774, 1043, 1008, 928)(611, 929, 890, 936, 616, 710, 704)(614, 687, 991, 917, 944, 626, 679)(615, 933, 870, 1027, 746, 742, 826)(619, 819, 1059, 973, 950, 634, 700)(620, 624, 667, 978, 909, 982, 671)(621, 780, 748, 834, 865, 1022, 938)(622, 645, 711, 1007, 896, 1010, 713)(625, 941, 882, 1006, 705, 674, 718)(632, 706, 839, 1051, 918, 781, 776)(635, 951, 899, 958, 640, 660, 651)(643, 676, 662, 972, 886, 1037, 766)(646, 848, 1070, 1066, 957, 702, 836)(655, 747, 728, 1018, 900, 1041, 775)(683, 804, 786, 1050, 911, 844, 874)(698, 1000, 1063, 1081, 935, 762, 772)(795, 837, 1065, 1092, 1078, 940, 801)(811, 815, 999, 1080, 1087, 1012, 1017)(829, 840, 1067, 1090, 1079, 961, 1033)(853, 977, 1052, 1088, 1062, 1004, 857)(948, 1020, 1083, 1089, 1036, 1049, 1002)(989, 1030, 1075, 1086, 1069, 1045, 1015) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 21)(14, 22)(15, 27)(17, 29)(18, 32)(20, 34)(23, 35)(24, 40)(25, 41)(26, 43)(28, 44)(30, 48)(31, 50)(33, 53)(36, 54)(37, 58)(38, 59)(39, 61)(42, 64)(45, 65)(46, 69)(47, 71)(49, 73)(51, 74)(52, 78)(55, 82)(56, 83)(57, 85)(60, 88)(62, 89)(63, 93)(66, 72)(67, 98)(68, 99)(70, 103)(75, 106)(76, 110)(77, 111)(79, 112)(80, 116)(81, 117)(84, 120)(86, 121)(87, 125)(90, 94)(91, 129)(92, 131)(95, 135)(96, 136)(97, 138)(100, 141)(101, 107)(102, 143)(104, 144)(105, 148)(108, 152)(109, 153)(113, 156)(114, 160)(115, 161)(118, 163)(119, 167)(122, 126)(123, 171)(124, 173)(127, 177)(128, 178)(130, 181)(132, 182)(133, 186)(134, 187)(137, 190)(139, 191)(140, 195)(142, 198)(145, 199)(146, 203)(147, 204)(149, 207)(150, 208)(151, 210)(154, 213)(155, 157)(158, 218)(159, 219)(162, 222)(164, 168)(165, 227)(166, 229)(169, 233)(170, 234)(172, 237)(174, 238)(175, 242)(176, 243)(179, 246)(180, 200)(183, 248)(184, 252)(185, 253)(188, 255)(189, 259)(192, 196)(193, 263)(194, 265)(197, 268)(201, 273)(202, 274)(205, 277)(206, 280)(209, 283)(211, 284)(212, 288)(214, 291)(215, 293)(216, 294)(217, 296)(220, 299)(221, 223)(224, 303)(225, 305)(226, 306)(228, 309)(230, 310)(231, 314)(232, 315)(235, 318)(236, 249)(239, 320)(240, 324)(241, 325)(244, 327)(245, 331)(247, 334)(250, 338)(251, 339)(254, 342)(256, 260)(257, 347)(258, 349)(261, 353)(262, 354)(264, 357)(266, 358)(267, 362)(269, 363)(270, 367)(271, 368)(272, 370)(275, 373)(276, 278)(279, 377)(281, 378)(282, 382)(285, 289)(286, 386)(287, 388)(290, 391)(292, 393)(295, 396)(297, 397)(298, 401)(300, 404)(301, 406)(302, 407)(304, 410)(307, 413)(308, 321)(311, 415)(312, 419)(313, 420)(316, 422)(317, 426)(319, 429)(322, 433)(323, 434)(326, 437)(328, 332)(329, 442)(330, 444)(333, 447)(335, 450)(336, 451)(337, 453)(340, 456)(341, 343)(344, 460)(345, 462)(346, 463)(348, 466)(350, 467)(351, 471)(352, 424)(355, 473)(356, 364)(359, 475)(360, 479)(361, 480)(365, 484)(366, 486)(369, 489)(371, 411)(372, 492)(374, 495)(375, 497)(376, 498)(379, 383)(380, 503)(381, 504)(384, 440)(385, 507)(387, 510)(389, 511)(390, 515)(392, 516)(394, 519)(395, 523)(398, 402)(399, 461)(400, 527)(403, 530)(405, 532)(408, 535)(409, 416)(412, 652)(414, 772)(417, 501)(418, 775)(421, 613)(423, 427)(425, 780)(428, 782)(430, 785)(431, 698)(432, 521)(435, 789)(436, 438)(439, 792)(441, 795)(443, 797)(445, 778)(446, 801)(448, 736)(449, 803)(452, 758)(454, 533)(455, 664)(457, 811)(458, 813)(459, 815)(464, 822)(465, 476)(468, 823)(469, 812)(470, 719)(472, 610)(474, 829)(477, 833)(478, 766)(481, 584)(482, 838)(483, 840)(485, 841)(487, 567)(488, 831)(490, 493)(491, 761)(494, 709)(496, 707)(499, 850)(500, 730)(502, 853)(505, 685)(506, 857)(508, 859)(509, 517)(512, 860)(513, 863)(514, 864)(518, 746)(520, 524)(522, 872)(525, 874)(526, 875)(528, 677)(529, 844)(531, 637)(534, 680)(536, 836)(537, 748)(538, 806)(539, 708)(540, 870)(541, 658)(542, 855)(543, 669)(544, 753)(545, 619)(546, 737)(547, 882)(548, 883)(549, 638)(550, 598)(551, 799)(552, 884)(553, 733)(554, 589)(555, 690)(556, 886)(557, 646)(558, 888)(559, 614)(560, 890)(561, 793)(562, 606)(563, 727)(564, 585)(565, 894)(566, 651)(568, 575)(569, 896)(570, 898)(571, 899)(572, 900)(573, 632)(574, 784)(576, 902)(577, 624)(578, 903)(579, 704)(580, 904)(581, 683)(582, 906)(583, 605)(586, 909)(587, 911)(588, 603)(590, 913)(591, 645)(592, 914)(593, 723)(594, 917)(595, 918)(596, 655)(597, 891)(599, 923)(600, 837)(601, 925)(602, 765)(604, 868)(607, 926)(608, 676)(609, 927)(611, 930)(612, 847)(615, 934)(616, 935)(617, 622)(618, 889)(620, 657)(621, 937)(623, 940)(625, 942)(626, 943)(627, 692)(628, 885)(629, 820)(630, 947)(631, 718)(633, 948)(634, 949)(635, 952)(636, 910)(639, 955)(640, 957)(641, 643)(642, 858)(644, 961)(647, 962)(648, 744)(649, 963)(650, 835)(653, 967)(654, 826)(656, 968)(659, 810)(660, 706)(661, 970)(662, 973)(663, 974)(665, 821)(666, 977)(667, 979)(668, 897)(670, 981)(671, 964)(672, 674)(673, 741)(675, 986)(678, 856)(679, 747)(681, 988)(682, 956)(684, 989)(686, 990)(687, 992)(688, 924)(689, 993)(691, 995)(693, 997)(694, 950)(695, 802)(696, 715)(697, 999)(699, 1001)(700, 807)(701, 1002)(702, 1003)(703, 1004)(705, 1005)(710, 767)(711, 1008)(712, 887)(713, 1009)(714, 716)(717, 1012)(720, 804)(721, 965)(722, 851)(724, 1015)(725, 1016)(726, 1017)(728, 1019)(729, 975)(731, 768)(732, 1020)(734, 1022)(735, 905)(738, 808)(739, 928)(740, 742)(743, 1026)(745, 849)(749, 848)(750, 1029)(751, 893)(752, 1030)(754, 998)(755, 985)(756, 938)(757, 1033)(759, 1035)(760, 984)(762, 845)(763, 920)(764, 1036)(769, 922)(770, 800)(771, 1014)(773, 1041)(774, 939)(776, 1044)(777, 1045)(779, 1047)(781, 1048)(783, 1049)(786, 1051)(787, 944)(788, 816)(790, 1046)(791, 1052)(794, 861)(796, 915)(798, 881)(805, 892)(809, 987)(814, 1058)(817, 901)(818, 971)(819, 824)(825, 1062)(827, 880)(828, 1000)(830, 1037)(832, 1034)(834, 932)(839, 1066)(842, 994)(843, 954)(846, 1069)(852, 1053)(854, 919)(862, 907)(865, 1073)(866, 1027)(867, 1067)(869, 1075)(871, 1025)(873, 1024)(876, 912)(877, 1057)(878, 933)(879, 960)(895, 1065)(908, 1060)(916, 1080)(921, 936)(929, 1083)(931, 958)(941, 1071)(945, 969)(946, 1086)(951, 1088)(953, 982)(959, 1061)(966, 1089)(972, 1090)(976, 1006)(978, 1091)(980, 1010)(983, 1068)(991, 1087)(996, 1056)(1007, 1092)(1011, 1084)(1013, 1064)(1018, 1063)(1021, 1039)(1023, 1040)(1028, 1042)(1031, 1082)(1032, 1055)(1038, 1081)(1043, 1078)(1050, 1070)(1054, 1077)(1059, 1079)(1072, 1076)(1074, 1085) local type(s) :: { ( 3^7 ) } Outer automorphisms :: reflexible Dual of E14.617 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 156 e = 546 f = 364 degree seq :: [ 7^156 ] E14.614 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 7}) Quotient :: regular Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^3, T1^7, (T1 * T2 * T1^-2 * T2 * T1^3 * T2 * T1^-2 * T2 * T1)^2, T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^3 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-2 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 11, 20, 10, 4)(3, 7, 15, 26, 30, 17, 8)(6, 13, 24, 39, 42, 25, 14)(9, 18, 31, 49, 46, 28, 16)(12, 22, 37, 57, 60, 38, 23)(19, 33, 52, 77, 76, 51, 32)(21, 35, 55, 81, 84, 56, 36)(27, 44, 67, 97, 100, 68, 45)(29, 47, 70, 102, 91, 62, 40)(34, 54, 80, 115, 114, 79, 53)(41, 63, 92, 130, 123, 86, 58)(43, 65, 95, 134, 137, 96, 66)(48, 72, 105, 147, 146, 104, 71)(50, 74, 108, 151, 154, 109, 75)(59, 87, 124, 172, 165, 118, 82)(61, 89, 127, 176, 179, 128, 90)(64, 94, 133, 185, 184, 132, 93)(69, 101, 142, 197, 193, 139, 98)(73, 106, 149, 206, 209, 150, 107)(78, 112, 158, 217, 220, 159, 113)(83, 119, 166, 228, 224, 162, 116)(85, 121, 169, 232, 235, 170, 122)(88, 126, 175, 241, 240, 174, 125)(99, 140, 194, 264, 257, 188, 135)(103, 144, 201, 272, 275, 202, 145)(110, 155, 214, 290, 286, 211, 152)(111, 156, 215, 292, 295, 216, 157)(117, 163, 225, 304, 307, 226, 164)(120, 168, 231, 313, 312, 230, 167)(129, 180, 247, 333, 329, 244, 177)(131, 182, 250, 337, 340, 251, 183)(136, 189, 258, 348, 279, 205, 148)(138, 191, 261, 352, 355, 262, 192)(141, 196, 267, 361, 360, 266, 195)(143, 199, 270, 366, 369, 271, 200)(153, 212, 287, 387, 380, 281, 207)(160, 221, 300, 403, 399, 297, 218)(161, 222, 301, 405, 408, 302, 223)(171, 236, 319, 428, 424, 316, 233)(173, 238, 322, 432, 435, 323, 239)(178, 245, 330, 443, 344, 254, 186)(181, 248, 335, 449, 452, 336, 249)(187, 255, 345, 461, 464, 346, 256)(190, 260, 351, 470, 469, 350, 259)(198, 208, 282, 381, 487, 365, 269)(203, 276, 374, 498, 494, 371, 273)(204, 277, 375, 500, 503, 376, 278)(210, 284, 384, 511, 514, 385, 285)(213, 289, 390, 520, 519, 389, 288)(219, 298, 400, 534, 527, 394, 293)(227, 308, 414, 804, 1081, 411, 305)(229, 310, 417, 739, 890, 418, 311)(234, 317, 425, 817, 439, 326, 242)(237, 320, 430, 617, 910, 431, 321)(243, 327, 440, 611, 699, 441, 328)(246, 332, 446, 731, 697, 445, 331)(252, 341, 457, 844, 766, 454, 338)(253, 342, 458, 573, 767, 459, 343)(263, 356, 476, 858, 1048, 473, 353)(265, 358, 479, 860, 810, 480, 359)(268, 363, 484, 575, 979, 485, 364)(274, 372, 495, 876, 1092, 489, 367)(280, 378, 505, 579, 704, 506, 379)(283, 383, 510, 886, 703, 509, 382)(291, 294, 395, 528, 762, 524, 392)(296, 397, 531, 693, 770, 532, 398)(299, 402, 537, 666, 727, 536, 401)(303, 409, 544, 917, 1088, 541, 406)(306, 412, 801, 771, 853, 421, 314)(309, 415, 807, 638, 789, 854, 416)(315, 422, 815, 634, 659, 1069, 423)(318, 427, 819, 764, 657, 903, 426)(324, 436, 826, 976, 832, 878, 433)(325, 437, 828, 559, 833, 1067, 438)(334, 368, 490, 871, 868, 1091, 448)(339, 455, 724, 535, 909, 683, 450)(347, 465, 846, 748, 1078, 678, 462)(349, 467, 742, 779, 1085, 825, 468)(354, 474, 855, 805, 821, 483, 362)(357, 477, 859, 604, 1012, 830, 478)(370, 492, 874, 681, 708, 1087, 493)(373, 497, 879, 721, 672, 898, 496)(377, 504, 702, 893, 1074, 665, 501)(386, 515, 892, 884, 1023, 774, 512)(388, 517, 716, 820, 434, 824, 518)(391, 522, 899, 565, 963, 1079, 523)(393, 525, 870, 569, 671, 1039, 526)(396, 530, 904, 1035, 670, 760, 529)(404, 407, 542, 914, 730, 1089, 539)(410, 799, 1018, 607, 623, 1036, 842)(413, 561, 958, 829, 621, 786, 802)(419, 580, 873, 952, 986, 1064, 808)(420, 813, 940, 552, 937, 1080, 732)(429, 451, 840, 521, 513, 889, 809)(442, 647, 1058, 798, 887, 712, 831)(444, 834, 695, 839, 862, 1072, 661)(447, 763, 991, 583, 989, 1082, 1059)(453, 735, 768, 715, 746, 867, 650)(456, 615, 508, 758, 706, 777, 841)(460, 780, 516, 772, 1045, 631, 845)(463, 849, 1086, 709, 752, 1049, 471)(466, 676, 822, 685, 835, 753, 797)(472, 750, 1068, 656, 674, 1077, 743)(475, 585, 994, 784, 645, 1055, 856)(481, 562, 756, 985, 787, 794, 861)(482, 863, 913, 550, 788, 1047, 718)(486, 866, 669, 877, 1050, 636, 865)(488, 869, 791, 556, 726, 1017, 755)(491, 553, 812, 1003, 725, 737, 872)(499, 502, 882, 1084, 700, 897, 1083)(507, 740, 783, 710, 1065, 653, 885)(533, 594, 1004, 966, 847, 895, 906)(538, 905, 951, 557, 949, 1066, 765)(540, 912, 864, 588, 643, 1037, 936)(543, 551, 935, 1054, 642, 723, 915)(545, 919, 1057, 662, 640, 932, 922)(546, 923, 1043, 628, 668, 947, 883)(547, 908, 1022, 689, 687, 953, 800)(548, 927, 1051, 701, 619, 925, 929)(549, 930, 1011, 600, 698, 960, 933)(554, 942, 1030, 667, 602, 921, 944)(555, 945, 1031, 618, 658, 943, 875)(558, 948, 984, 577, 729, 974, 816)(560, 888, 1015, 722, 590, 926, 957)(563, 848, 1010, 639, 622, 928, 961)(564, 690, 996, 811, 806, 1000, 733)(566, 962, 1002, 592, 761, 988, 850)(567, 769, 992, 759, 572, 934, 968)(568, 969, 1016, 605, 673, 956, 793)(570, 971, 1046, 785, 609, 941, 973)(571, 745, 983, 686, 593, 939, 975)(574, 719, 970, 907, 918, 1021, 682)(576, 978, 1020, 608, 823, 1005, 982)(578, 955, 993, 584, 707, 967, 736)(581, 796, 1001, 654, 610, 950, 852)(582, 663, 803, 920, 980, 1032, 720)(586, 734, 946, 954, 1013, 911, 635)(587, 881, 1034, 632, 646, 972, 751)(589, 997, 1024, 902, 591, 959, 999)(595, 738, 1019, 679, 633, 965, 1006)(596, 629, 916, 924, 880, 1052, 757)(597, 1007, 1060, 1033, 620, 827, 1009)(598, 684, 857, 938, 894, 790, 664)(599, 995, 901, 626, 1040, 1038, 891)(601, 792, 931, 977, 1044, 814, 613)(603, 637, 754, 843, 964, 837, 691)(606, 981, 1025, 612, 692, 998, 713)(614, 1026, 900, 1053, 641, 987, 1028)(616, 717, 782, 851, 773, 728, 630)(624, 778, 1041, 694, 655, 990, 896)(625, 838, 1056, 648, 680, 1008, 775)(627, 818, 1063, 649, 1061, 1070, 1042)(644, 1029, 1076, 675, 714, 1027, 781)(651, 696, 744, 749, 711, 677, 652)(660, 776, 1062, 741, 688, 1014, 1071)(705, 1075, 1090, 747, 795, 1073, 836) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 21)(14, 22)(15, 27)(17, 29)(18, 32)(20, 34)(23, 35)(24, 40)(25, 41)(26, 43)(28, 44)(30, 48)(31, 50)(33, 53)(36, 54)(37, 58)(38, 59)(39, 61)(42, 64)(45, 65)(46, 69)(47, 71)(49, 73)(51, 74)(52, 78)(55, 82)(56, 83)(57, 85)(60, 88)(62, 89)(63, 93)(66, 72)(67, 98)(68, 99)(70, 103)(75, 106)(76, 110)(77, 111)(79, 112)(80, 116)(81, 117)(84, 120)(86, 121)(87, 125)(90, 94)(91, 129)(92, 131)(95, 135)(96, 136)(97, 138)(100, 141)(101, 107)(102, 143)(104, 144)(105, 148)(108, 152)(109, 153)(113, 156)(114, 160)(115, 161)(118, 163)(119, 167)(122, 126)(123, 171)(124, 173)(127, 177)(128, 178)(130, 181)(132, 182)(133, 186)(134, 187)(137, 190)(139, 191)(140, 195)(142, 198)(145, 199)(146, 203)(147, 204)(149, 207)(150, 208)(151, 210)(154, 213)(155, 157)(158, 218)(159, 219)(162, 222)(164, 168)(165, 227)(166, 229)(169, 233)(170, 234)(172, 237)(174, 238)(175, 242)(176, 243)(179, 246)(180, 200)(183, 248)(184, 252)(185, 253)(188, 255)(189, 259)(192, 196)(193, 263)(194, 265)(197, 268)(201, 273)(202, 274)(205, 277)(206, 280)(209, 283)(211, 284)(212, 288)(214, 291)(215, 293)(216, 294)(217, 296)(220, 299)(221, 223)(224, 303)(225, 305)(226, 306)(228, 309)(230, 310)(231, 314)(232, 315)(235, 318)(236, 249)(239, 320)(240, 324)(241, 325)(244, 327)(245, 331)(247, 334)(250, 338)(251, 339)(254, 342)(256, 260)(257, 347)(258, 349)(261, 353)(262, 354)(264, 357)(266, 358)(267, 362)(269, 363)(270, 367)(271, 368)(272, 370)(275, 373)(276, 278)(279, 377)(281, 378)(282, 382)(285, 289)(286, 386)(287, 388)(290, 391)(292, 393)(295, 396)(297, 397)(298, 401)(300, 404)(301, 406)(302, 407)(304, 410)(307, 413)(308, 321)(311, 415)(312, 419)(313, 420)(316, 422)(317, 426)(319, 429)(322, 433)(323, 434)(326, 437)(328, 332)(329, 442)(330, 444)(333, 447)(335, 450)(336, 451)(337, 453)(340, 456)(341, 343)(344, 460)(345, 462)(346, 463)(348, 466)(350, 467)(351, 471)(352, 472)(355, 475)(356, 364)(359, 477)(360, 481)(361, 482)(365, 486)(366, 488)(369, 491)(371, 492)(372, 496)(374, 499)(375, 501)(376, 502)(379, 383)(380, 507)(381, 508)(384, 512)(385, 513)(387, 516)(389, 517)(390, 521)(392, 522)(394, 525)(395, 529)(398, 402)(399, 533)(400, 535)(403, 538)(405, 540)(408, 543)(409, 416)(411, 799)(412, 802)(414, 805)(417, 808)(418, 810)(421, 813)(423, 427)(424, 656)(425, 818)(428, 620)(430, 820)(431, 821)(432, 822)(435, 825)(436, 438)(439, 830)(440, 831)(441, 705)(443, 783)(445, 834)(446, 836)(448, 763)(449, 806)(452, 800)(454, 735)(455, 841)(457, 741)(458, 845)(459, 688)(461, 847)(464, 850)(465, 478)(468, 676)(469, 613)(470, 619)(473, 750)(474, 856)(476, 747)(479, 861)(480, 862)(483, 863)(484, 865)(485, 795)(487, 867)(489, 869)(490, 872)(493, 497)(494, 607)(495, 877)(498, 609)(500, 880)(503, 883)(504, 797)(505, 885)(506, 644)(509, 758)(510, 781)(511, 887)(514, 891)(515, 523)(518, 772)(519, 682)(520, 687)(524, 900)(526, 530)(527, 753)(528, 879)(531, 906)(532, 868)(534, 702)(536, 909)(537, 871)(539, 905)(541, 912)(542, 915)(544, 876)(545, 920)(546, 924)(547, 811)(548, 843)(549, 931)(550, 907)(551, 936)(552, 938)(553, 755)(554, 782)(555, 946)(556, 787)(557, 851)(558, 952)(559, 954)(560, 744)(561, 842)(562, 718)(563, 857)(564, 725)(565, 964)(566, 966)(567, 696)(568, 970)(569, 832)(570, 749)(571, 754)(572, 976)(573, 977)(574, 689)(575, 980)(576, 884)(577, 651)(578, 985)(579, 986)(580, 732)(581, 803)(582, 670)(583, 894)(584, 717)(585, 743)(586, 662)(587, 996)(588, 766)(589, 711)(590, 844)(591, 858)(592, 652)(593, 1003)(594, 765)(595, 916)(596, 703)(597, 773)(598, 628)(599, 798)(600, 616)(601, 701)(602, 886)(603, 642)(604, 1013)(605, 684)(606, 1017)(608, 677)(610, 1022)(611, 1023)(612, 792)(614, 837)(615, 650)(617, 918)(618, 637)(621, 630)(622, 1035)(623, 785)(624, 1037)(625, 1039)(626, 728)(627, 748)(629, 667)(631, 1044)(632, 734)(633, 1047)(634, 1048)(635, 697)(636, 1032)(638, 794)(639, 663)(640, 731)(641, 804)(643, 722)(645, 691)(646, 1057)(647, 1059)(648, 873)(649, 790)(653, 1064)(654, 719)(655, 1067)(657, 664)(658, 1054)(659, 902)(660, 1036)(661, 710)(665, 1052)(666, 737)(668, 764)(669, 917)(671, 759)(672, 720)(673, 1043)(674, 1033)(675, 1004)(678, 895)(679, 756)(680, 1080)(681, 1081)(683, 1000)(685, 878)(686, 690)(692, 1051)(693, 1078)(694, 826)(695, 911)(698, 829)(699, 982)(700, 1069)(704, 816)(706, 757)(707, 1011)(708, 1053)(709, 892)(712, 774)(713, 812)(714, 1066)(715, 1088)(716, 1021)(721, 760)(723, 784)(724, 893)(726, 736)(727, 733)(729, 1002)(730, 1077)(738, 1030)(739, 1065)(740, 780)(742, 814)(745, 1031)(746, 866)(751, 908)(752, 1079)(761, 1020)(762, 1087)(767, 933)(768, 864)(769, 984)(770, 1042)(771, 1058)(775, 904)(776, 1046)(777, 1074)(778, 1015)(779, 1045)(786, 901)(788, 793)(789, 791)(796, 1010)(801, 995)(807, 860)(809, 827)(815, 1068)(817, 846)(819, 1084)(823, 999)(824, 1085)(828, 1012)(833, 875)(835, 870)(838, 992)(839, 859)(840, 953)(848, 1016)(849, 988)(852, 919)(853, 1082)(854, 1092)(855, 987)(874, 1018)(881, 983)(882, 947)(888, 968)(889, 1038)(890, 1072)(896, 935)(897, 1024)(898, 1050)(899, 1026)(903, 1063)(910, 913)(914, 994)(921, 1027)(922, 979)(923, 1006)(925, 1049)(926, 1062)(927, 975)(928, 1008)(929, 963)(930, 1025)(932, 1073)(934, 1041)(937, 961)(939, 998)(940, 989)(941, 1083)(942, 993)(943, 990)(944, 949)(945, 1034)(948, 1056)(950, 972)(951, 1007)(955, 1019)(956, 965)(957, 971)(958, 1071)(959, 1090)(960, 1014)(962, 1076)(967, 981)(969, 1001)(973, 997)(974, 1029)(978, 1086)(991, 1061)(1005, 1075)(1009, 1040)(1028, 1055)(1060, 1089)(1070, 1091) local type(s) :: { ( 3^7 ) } Outer automorphisms :: reflexible Dual of E14.616 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 156 e = 546 f = 364 degree seq :: [ 7^156 ] E14.615 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 7}) Quotient :: regular Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^3, T1^7, (T2 * T1^3 * T2 * T1^-3)^3, T2 * T1^-2 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-3 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 11, 20, 10, 4)(3, 7, 15, 26, 30, 17, 8)(6, 13, 24, 39, 42, 25, 14)(9, 18, 31, 49, 46, 28, 16)(12, 22, 37, 57, 60, 38, 23)(19, 33, 52, 77, 76, 51, 32)(21, 35, 55, 81, 84, 56, 36)(27, 44, 67, 97, 100, 68, 45)(29, 47, 70, 102, 91, 62, 40)(34, 54, 80, 115, 114, 79, 53)(41, 63, 92, 130, 123, 86, 58)(43, 65, 95, 134, 137, 96, 66)(48, 72, 105, 147, 146, 104, 71)(50, 74, 108, 151, 154, 109, 75)(59, 87, 124, 172, 165, 118, 82)(61, 89, 127, 176, 179, 128, 90)(64, 94, 133, 185, 184, 132, 93)(69, 101, 142, 197, 193, 139, 98)(73, 106, 149, 206, 209, 150, 107)(78, 112, 158, 217, 220, 159, 113)(83, 119, 166, 228, 224, 162, 116)(85, 121, 169, 232, 235, 170, 122)(88, 126, 175, 241, 240, 174, 125)(99, 140, 194, 264, 257, 188, 135)(103, 144, 201, 272, 275, 202, 145)(110, 155, 214, 290, 286, 211, 152)(111, 156, 215, 292, 295, 216, 157)(117, 163, 225, 304, 307, 226, 164)(120, 168, 231, 313, 312, 230, 167)(129, 180, 247, 333, 329, 244, 177)(131, 182, 250, 337, 340, 251, 183)(136, 189, 258, 348, 279, 205, 148)(138, 191, 261, 352, 355, 262, 192)(141, 196, 267, 361, 360, 266, 195)(143, 199, 270, 366, 369, 271, 200)(153, 212, 287, 387, 380, 281, 207)(160, 221, 300, 403, 399, 297, 218)(161, 222, 301, 405, 408, 302, 223)(171, 236, 319, 428, 424, 316, 233)(173, 238, 322, 432, 435, 323, 239)(178, 245, 330, 443, 344, 254, 186)(181, 248, 335, 449, 452, 336, 249)(187, 255, 345, 461, 464, 346, 256)(190, 260, 351, 420, 469, 350, 259)(198, 208, 282, 381, 486, 365, 269)(203, 276, 374, 497, 493, 371, 273)(204, 277, 375, 499, 502, 376, 278)(210, 284, 384, 509, 512, 385, 285)(213, 289, 390, 518, 517, 389, 288)(219, 298, 400, 531, 525, 394, 293)(227, 308, 414, 758, 929, 411, 305)(229, 310, 417, 760, 641, 418, 311)(234, 317, 425, 630, 439, 326, 242)(237, 320, 430, 768, 848, 431, 321)(243, 327, 440, 777, 802, 441, 328)(246, 332, 446, 535, 691, 445, 331)(252, 341, 457, 481, 816, 454, 338)(253, 342, 458, 527, 396, 459, 343)(263, 356, 475, 810, 970, 472, 353)(265, 358, 478, 812, 607, 479, 359)(268, 363, 483, 755, 413, 484, 364)(274, 372, 494, 675, 869, 488, 367)(280, 378, 504, 826, 490, 505, 379)(283, 383, 438, 325, 437, 508, 382)(291, 294, 395, 526, 595, 522, 392)(296, 397, 528, 850, 669, 529, 398)(299, 402, 534, 857, 678, 533, 401)(303, 409, 540, 847, 900, 538, 406)(306, 412, 754, 605, 880, 421, 314)(309, 415, 753, 1066, 735, 798, 416)(315, 422, 552, 896, 1046, 1039, 423)(318, 427, 521, 391, 520, 697, 426)(324, 436, 739, 487, 823, 598, 433)(334, 368, 489, 825, 585, 942, 448)(339, 455, 723, 710, 877, 660, 450)(347, 465, 745, 1068, 949, 837, 462)(349, 467, 546, 879, 653, 1010, 468)(354, 473, 806, 649, 866, 482, 362)(357, 476, 805, 1067, 842, 700, 477)(370, 491, 544, 873, 726, 1025, 492)(373, 496, 828, 765, 632, 792, 495)(377, 503, 702, 1053, 909, 717, 500)(386, 513, 676, 772, 993, 662, 510)(388, 515, 559, 918, 591, 980, 516)(393, 523, 575, 813, 480, 796, 524)(404, 407, 539, 862, 581, 892, 536)(410, 751, 557, 911, 846, 811, 819)(419, 470, 463, 685, 1003, 615, 761)(429, 451, 590, 947, 568, 944, 1001)(434, 773, 686, 763, 888, 628, 769)(442, 781, 690, 1044, 965, 719, 778)(444, 784, 550, 891, 619, 1008, 955)(447, 613, 732, 807, 474, 657, 1031)(453, 790, 541, 865, 730, 1038, 889)(456, 597, 987, 1032, 658, 988, 793)(460, 799, 749, 1051, 931, 776, 797)(466, 588, 976, 1059, 714, 836, 833)(471, 803, 548, 884, 844, 1045, 870)(485, 820, 666, 815, 894, 687, 818)(498, 501, 537, 860, 564, 919, 728)(506, 838, 832, 1065, 939, 1080, 835)(507, 839, 543, 872, 695, 1030, 916)(511, 736, 1022, 680, 874, 596, 519)(514, 582, 969, 1089, 1034, 661, 785)(530, 786, 650, 715, 1014, 634, 851)(532, 856, 571, 953, 577, 961, 990)(542, 868, 789, 1056, 904, 747, 871)(545, 876, 1088, 1073, 886, 693, 878)(547, 882, 757, 1072, 923, 830, 883)(549, 887, 1061, 1087, 875, 647, 890)(551, 893, 1085, 1079, 898, 713, 895)(553, 899, 708, 1055, 946, 1082, 901)(554, 902, 1040, 1069, 867, 625, 905)(555, 906, 638, 1020, 926, 724, 907)(556, 908, 809, 841, 913, 767, 910)(558, 914, 1036, 1071, 852, 617, 917)(560, 921, 1015, 759, 770, 609, 924)(561, 925, 1081, 1064, 779, 682, 927)(562, 928, 673, 800, 972, 1092, 912)(563, 930, 734, 722, 933, 1074, 932)(565, 934, 1052, 1050, 737, 636, 936)(566, 937, 1012, 864, 881, 587, 940)(567, 941, 627, 1013, 935, 667, 943)(569, 948, 656, 701, 986, 1091, 945)(570, 950, 1019, 1054, 762, 603, 952)(572, 954, 1076, 771, 718, 741, 782)(573, 956, 645, 1024, 984, 780, 897)(574, 957, 795, 684, 958, 1083, 821)(576, 959, 1070, 1029, 679, 664, 843)(578, 963, 600, 991, 960, 703, 920)(579, 964, 622, 748, 822, 1084, 922)(580, 966, 699, 665, 968, 1090, 967)(583, 858, 612, 849, 775, 738, 885)(584, 788, 659, 1033, 915, 639, 971)(586, 973, 1007, 834, 709, 620, 975)(589, 977, 1049, 1009, 648, 696, 725)(592, 982, 602, 994, 978, 750, 814)(593, 983, 623, 694, 720, 1060, 938)(594, 831, 716, 853, 903, 601, 985)(599, 989, 1086, 1016, 633, 721, 854)(604, 791, 704, 637, 997, 1078, 996)(606, 729, 663, 1035, 951, 621, 998)(608, 999, 1028, 1021, 674, 654, 787)(610, 845, 616, 1004, 1000, 698, 827)(611, 804, 640, 652, 783, 1062, 962)(614, 840, 801, 626, 1002, 1077, 774)(618, 1006, 1063, 981, 629, 731, 668)(624, 855, 1023, 794, 689, 671, 742)(631, 727, 635, 1017, 974, 655, 979)(642, 740, 1037, 992, 644, 706, 683)(643, 859, 646, 1026, 1011, 733, 744)(651, 670, 681, 1041, 995, 672, 752)(677, 705, 712, 1057, 1005, 707, 861)(688, 764, 692, 1047, 1027, 808, 863)(711, 746, 766, 1048, 1018, 756, 743)(817, 829, 1075, 1058, 1042, 1043, 824) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 21)(14, 22)(15, 27)(17, 29)(18, 32)(20, 34)(23, 35)(24, 40)(25, 41)(26, 43)(28, 44)(30, 48)(31, 50)(33, 53)(36, 54)(37, 58)(38, 59)(39, 61)(42, 64)(45, 65)(46, 69)(47, 71)(49, 73)(51, 74)(52, 78)(55, 82)(56, 83)(57, 85)(60, 88)(62, 89)(63, 93)(66, 72)(67, 98)(68, 99)(70, 103)(75, 106)(76, 110)(77, 111)(79, 112)(80, 116)(81, 117)(84, 120)(86, 121)(87, 125)(90, 94)(91, 129)(92, 131)(95, 135)(96, 136)(97, 138)(100, 141)(101, 107)(102, 143)(104, 144)(105, 148)(108, 152)(109, 153)(113, 156)(114, 160)(115, 161)(118, 163)(119, 167)(122, 126)(123, 171)(124, 173)(127, 177)(128, 178)(130, 181)(132, 182)(133, 186)(134, 187)(137, 190)(139, 191)(140, 195)(142, 198)(145, 199)(146, 203)(147, 204)(149, 207)(150, 208)(151, 210)(154, 213)(155, 157)(158, 218)(159, 219)(162, 222)(164, 168)(165, 227)(166, 229)(169, 233)(170, 234)(172, 237)(174, 238)(175, 242)(176, 243)(179, 246)(180, 200)(183, 248)(184, 252)(185, 253)(188, 255)(189, 259)(192, 196)(193, 263)(194, 265)(197, 268)(201, 273)(202, 274)(205, 277)(206, 280)(209, 283)(211, 284)(212, 288)(214, 291)(215, 293)(216, 294)(217, 296)(220, 299)(221, 223)(224, 303)(225, 305)(226, 306)(228, 309)(230, 310)(231, 314)(232, 315)(235, 318)(236, 249)(239, 320)(240, 324)(241, 325)(244, 327)(245, 331)(247, 334)(250, 338)(251, 339)(254, 342)(256, 260)(257, 347)(258, 349)(261, 353)(262, 354)(264, 357)(266, 358)(267, 362)(269, 363)(270, 367)(271, 368)(272, 370)(275, 373)(276, 278)(279, 377)(281, 378)(282, 382)(285, 289)(286, 386)(287, 388)(290, 391)(292, 393)(295, 396)(297, 397)(298, 401)(300, 404)(301, 406)(302, 407)(304, 410)(307, 413)(308, 321)(311, 415)(312, 419)(313, 420)(316, 422)(317, 426)(319, 429)(322, 433)(323, 434)(326, 437)(328, 332)(329, 442)(330, 444)(333, 447)(335, 450)(336, 451)(337, 453)(340, 456)(341, 343)(344, 460)(345, 462)(346, 463)(348, 466)(350, 467)(351, 470)(352, 471)(355, 474)(356, 364)(359, 476)(360, 480)(361, 481)(365, 485)(366, 487)(369, 490)(371, 491)(372, 495)(374, 498)(375, 500)(376, 501)(379, 383)(380, 506)(381, 507)(384, 510)(385, 511)(387, 514)(389, 515)(390, 519)(392, 520)(394, 523)(395, 527)(398, 402)(399, 530)(400, 532)(403, 535)(405, 537)(408, 502)(409, 416)(411, 751)(412, 755)(414, 759)(417, 761)(418, 594)(421, 469)(423, 427)(424, 573)(425, 724)(428, 765)(430, 769)(431, 770)(432, 747)(435, 774)(436, 438)(439, 543)(440, 778)(441, 650)(443, 782)(445, 784)(446, 786)(448, 613)(449, 685)(452, 464)(454, 790)(455, 793)(457, 796)(458, 797)(459, 524)(461, 590)(465, 477)(468, 588)(472, 803)(473, 807)(475, 811)(478, 813)(479, 584)(482, 816)(483, 818)(484, 819)(486, 821)(488, 823)(489, 826)(492, 496)(493, 596)(494, 703)(497, 518)(499, 539)(503, 833)(504, 835)(505, 739)(508, 839)(509, 625)(512, 842)(513, 521)(516, 582)(517, 728)(522, 555)(525, 547)(526, 776)(528, 851)(529, 612)(531, 854)(533, 856)(534, 858)(536, 691)(538, 860)(540, 864)(541, 866)(542, 869)(544, 874)(545, 877)(546, 880)(548, 885)(549, 888)(550, 892)(551, 894)(552, 897)(553, 900)(554, 903)(556, 909)(557, 912)(558, 915)(559, 919)(560, 922)(561, 926)(562, 929)(563, 931)(564, 901)(565, 935)(566, 938)(567, 942)(568, 945)(569, 949)(570, 951)(571, 911)(572, 955)(574, 916)(575, 883)(576, 960)(577, 962)(578, 944)(579, 965)(580, 939)(581, 910)(583, 970)(585, 967)(586, 974)(587, 896)(589, 978)(591, 981)(592, 921)(593, 984)(595, 932)(597, 889)(598, 871)(599, 990)(600, 992)(601, 993)(602, 995)(603, 884)(604, 923)(605, 895)(606, 980)(607, 996)(608, 1000)(609, 777)(610, 937)(611, 972)(614, 904)(615, 878)(616, 1005)(617, 873)(618, 1007)(619, 1009)(620, 902)(621, 775)(622, 1010)(623, 1008)(624, 1011)(626, 1012)(627, 794)(628, 1014)(629, 946)(630, 927)(631, 961)(632, 1001)(633, 886)(634, 890)(635, 1018)(636, 865)(637, 1019)(638, 1021)(639, 1022)(640, 1020)(641, 1016)(642, 1023)(643, 950)(644, 986)(645, 1025)(646, 1027)(647, 850)(648, 913)(649, 936)(651, 991)(652, 1028)(653, 1029)(654, 887)(655, 716)(656, 1030)(657, 870)(658, 1015)(659, 733)(660, 1003)(661, 875)(662, 905)(663, 808)(664, 868)(665, 1036)(666, 834)(667, 806)(668, 815)(669, 1034)(670, 1037)(671, 914)(672, 822)(673, 1038)(674, 933)(675, 843)(676, 1039)(677, 994)(678, 846)(679, 898)(680, 917)(681, 1042)(682, 872)(683, 1013)(684, 1040)(686, 698)(687, 754)(688, 973)(689, 968)(690, 1045)(692, 1048)(693, 760)(694, 1049)(695, 1050)(696, 876)(697, 907)(699, 1051)(700, 867)(701, 1052)(702, 1054)(704, 1053)(705, 1041)(706, 934)(707, 720)(708, 1056)(709, 958)(710, 725)(711, 1004)(712, 1058)(713, 879)(714, 844)(715, 768)(717, 862)(718, 852)(719, 924)(721, 882)(722, 1061)(723, 750)(726, 771)(727, 1062)(729, 1063)(730, 1064)(731, 893)(732, 943)(734, 1065)(735, 1046)(736, 1067)(737, 779)(738, 952)(740, 1043)(741, 799)(742, 1033)(743, 999)(744, 997)(745, 1069)(746, 1057)(748, 1070)(749, 1071)(752, 959)(753, 985)(756, 783)(757, 1073)(758, 1032)(762, 836)(763, 787)(764, 1017)(766, 1075)(767, 891)(772, 1066)(773, 1077)(780, 940)(781, 1031)(785, 838)(788, 1078)(789, 1079)(791, 908)(792, 920)(795, 1068)(798, 881)(800, 1081)(801, 847)(802, 848)(804, 925)(805, 971)(809, 1072)(810, 857)(812, 830)(814, 988)(817, 1026)(820, 1083)(824, 855)(825, 1080)(827, 1002)(828, 956)(829, 1047)(831, 1086)(832, 1087)(837, 947)(840, 899)(841, 1088)(845, 1060)(849, 1089)(853, 975)(859, 1035)(861, 977)(863, 1006)(906, 1074)(918, 1082)(928, 987)(930, 966)(941, 1090)(948, 957)(953, 1092)(954, 983)(963, 1091)(964, 976)(969, 998)(979, 989)(982, 1084)(1024, 1076)(1044, 1059)(1055, 1085) local type(s) :: { ( 3^7 ) } Outer automorphisms :: reflexible Dual of E14.618 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 156 e = 546 f = 364 degree seq :: [ 7^156 ] E14.616 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 7}) Quotient :: regular Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^7, (T2 * T1 * T2 * T1^-1)^7, (T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1)^2 ] Map:: polyhedral non-degenerate R = (1, 2, 4)(3, 6, 7)(5, 9, 10)(8, 13, 14)(11, 17, 18)(12, 19, 20)(15, 23, 24)(16, 25, 26)(21, 31, 32)(22, 33, 34)(27, 39, 40)(28, 41, 42)(29, 43, 44)(30, 45, 46)(35, 51, 52)(36, 53, 54)(37, 55, 56)(38, 57, 58)(47, 66, 67)(48, 68, 69)(49, 70, 71)(50, 72, 59)(60, 79, 80)(61, 81, 82)(62, 83, 84)(63, 85, 86)(64, 87, 88)(65, 89, 90)(73, 97, 98)(74, 99, 100)(75, 101, 102)(76, 103, 104)(77, 105, 106)(78, 107, 108)(91, 119, 120)(92, 121, 122)(93, 123, 124)(94, 125, 126)(95, 127, 128)(96, 129, 130)(109, 141, 142)(110, 143, 144)(111, 145, 146)(112, 147, 148)(113, 149, 150)(114, 151, 152)(115, 153, 154)(116, 155, 156)(117, 157, 158)(118, 159, 160)(131, 171, 172)(132, 173, 174)(133, 175, 176)(134, 177, 178)(135, 179, 180)(136, 181, 182)(137, 183, 184)(138, 185, 186)(139, 187, 188)(140, 189, 190)(161, 207, 208)(162, 209, 210)(163, 211, 212)(164, 213, 214)(165, 215, 216)(166, 217, 218)(167, 219, 220)(168, 221, 222)(169, 223, 224)(170, 225, 226)(191, 243, 244)(192, 245, 246)(193, 247, 248)(194, 249, 250)(195, 251, 252)(196, 253, 254)(197, 255, 256)(198, 257, 258)(199, 259, 260)(200, 261, 262)(201, 263, 264)(202, 265, 266)(203, 267, 268)(204, 269, 270)(205, 271, 272)(206, 273, 227)(228, 452, 798)(229, 454, 806)(230, 456, 856)(231, 458, 859)(232, 363, 379)(233, 460, 310)(234, 461, 753)(235, 463, 413)(236, 464, 863)(237, 466, 291)(238, 468, 594)(239, 470, 872)(240, 472, 876)(241, 473, 697)(242, 312, 274)(275, 519, 846)(276, 491, 858)(277, 522, 936)(278, 524, 804)(279, 378, 351)(280, 434, 317)(281, 526, 794)(282, 528, 440)(283, 529, 941)(284, 531, 289)(285, 533, 610)(286, 535, 947)(287, 537, 905)(288, 538, 726)(290, 514, 542)(292, 544, 546)(293, 486, 547)(294, 548, 550)(295, 551, 552)(296, 553, 554)(297, 527, 520)(298, 556, 557)(299, 558, 559)(300, 429, 425)(301, 561, 563)(302, 564, 565)(303, 566, 567)(304, 462, 453)(305, 569, 571)(306, 572, 494)(307, 573, 574)(308, 388, 383)(309, 576, 578)(311, 580, 582)(313, 584, 585)(314, 586, 587)(315, 409, 404)(316, 589, 591)(318, 593, 595)(319, 596, 422)(320, 597, 599)(321, 497, 495)(322, 601, 602)(323, 603, 604)(324, 372, 367)(325, 606, 608)(326, 609, 611)(327, 612, 449)(328, 613, 615)(329, 513, 617)(330, 618, 619)(331, 620, 621)(332, 381, 432)(333, 508, 406)(334, 624, 625)(335, 356, 344)(336, 465, 628)(337, 629, 630)(338, 507, 400)(339, 631, 633)(340, 634, 636)(341, 402, 469)(342, 638, 369)(343, 640, 641)(345, 530, 644)(346, 645, 411)(347, 647, 650)(348, 444, 653)(349, 654, 655)(350, 656, 658)(352, 659, 662)(353, 365, 534)(354, 664, 385)(355, 666, 667)(357, 430, 670)(358, 671, 438)(359, 673, 676)(360, 395, 679)(361, 680, 681)(362, 682, 683)(364, 686, 689)(366, 691, 692)(368, 694, 696)(370, 698, 700)(371, 701, 427)(373, 704, 390)(374, 657, 708)(375, 417, 711)(376, 712, 713)(377, 714, 715)(380, 718, 501)(382, 721, 722)(384, 724, 488)(386, 727, 728)(387, 729, 457)(389, 732, 735)(391, 738, 739)(392, 740, 741)(393, 401, 480)(394, 744, 747)(396, 521, 751)(397, 485, 754)(398, 755, 756)(399, 757, 758)(403, 762, 763)(405, 764, 766)(407, 767, 768)(408, 769, 523)(410, 772, 775)(412, 778, 506)(414, 781, 782)(415, 423, 784)(416, 752, 787)(418, 426, 791)(419, 792, 795)(420, 796, 500)(421, 797, 799)(424, 802, 803)(428, 807, 699)(431, 812, 813)(433, 814, 816)(435, 817, 818)(436, 819, 590)(437, 822, 825)(439, 828, 742)(441, 830, 831)(442, 450, 833)(443, 793, 836)(445, 455, 840)(446, 841, 842)(447, 843, 844)(448, 845, 847)(451, 850, 851)(459, 860, 660)(467, 868, 869)(471, 874, 875)(474, 879, 880)(475, 881, 607)(476, 483, 577)(477, 885, 886)(478, 543, 887)(479, 496, 889)(481, 865, 710)(482, 709, 894)(484, 895, 896)(487, 870, 570)(489, 900, 901)(490, 902, 730)(492, 904, 906)(493, 646, 663)(498, 911, 774)(499, 773, 888)(502, 915, 684)(503, 511, 545)(504, 917, 918)(505, 562, 723)(509, 922, 903)(510, 882, 783)(512, 853, 873)(515, 927, 635)(516, 539, 930)(517, 931, 932)(518, 815, 933)(525, 938, 687)(532, 945, 898)(536, 890, 949)(540, 952, 852)(541, 944, 950)(549, 866, 877)(555, 954, 835)(560, 957, 746)(568, 962, 786)(575, 967, 688)(579, 971, 893)(581, 693, 946)(583, 987, 988)(588, 976, 719)(592, 908, 995)(598, 642, 1002)(600, 1006, 1007)(605, 985, 661)(614, 668, 1017)(616, 921, 1019)(622, 862, 672)(623, 801, 1025)(626, 1004, 632)(627, 909, 788)(637, 940, 705)(639, 849, 929)(643, 1020, 837)(648, 1037, 923)(649, 703, 1038)(651, 1041, 1042)(652, 1043, 943)(665, 760, 1051)(669, 1032, 748)(674, 1056, 916)(675, 731, 1057)(677, 854, 1060)(678, 899, 811)(685, 1065, 770)(690, 777, 839)(695, 1044, 864)(702, 717, 1069)(706, 1070, 1071)(707, 771, 914)(716, 871, 1076)(720, 827, 750)(725, 1061, 942)(733, 1079, 829)(734, 809, 1080)(736, 951, 1082)(737, 790, 761)(743, 924, 821)(745, 919, 1063)(749, 1062, 1066)(759, 1053, 1085)(765, 1049, 810)(776, 1068, 1088)(779, 1083, 824)(780, 823, 1090)(785, 999, 1074)(789, 1073, 913)(800, 1027, 1081)(805, 1054, 1013)(808, 1086, 969)(820, 1075, 1089)(826, 878, 1084)(832, 1092, 884)(834, 1014, 1046)(838, 1045, 1050)(848, 1034, 1087)(855, 1035, 1028)(857, 1067, 991)(861, 1078, 979)(867, 1048, 1091)(883, 1064, 912)(891, 920, 983)(892, 978, 1072)(897, 992, 1008)(907, 1012, 1059)(910, 1058, 1009)(925, 990, 939)(926, 955, 1029)(928, 1021, 1031)(934, 948, 1077)(935, 1036, 996)(937, 1040, 970)(953, 958, 997)(956, 982, 1005)(959, 968, 975)(960, 1052, 1022)(961, 994, 1018)(963, 977, 984)(964, 1026, 1024)(965, 1055, 1000)(966, 972, 986)(973, 1033, 1010)(974, 1047, 1015)(980, 998, 1003)(981, 1011, 993)(989, 1039, 1023)(1001, 1016, 1030) L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 12)(9, 15)(10, 16)(13, 21)(14, 22)(17, 27)(18, 28)(19, 29)(20, 30)(23, 35)(24, 36)(25, 37)(26, 38)(31, 47)(32, 48)(33, 49)(34, 50)(39, 59)(40, 60)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 51)(52, 73)(53, 74)(54, 75)(55, 76)(56, 77)(57, 78)(58, 66)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 85)(86, 114)(87, 115)(88, 116)(89, 117)(90, 118)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 103)(104, 136)(105, 137)(106, 138)(107, 139)(108, 140)(119, 161)(120, 162)(121, 163)(122, 164)(123, 165)(124, 125)(126, 166)(127, 167)(128, 168)(129, 169)(130, 170)(141, 191)(142, 192)(143, 193)(144, 145)(146, 194)(147, 195)(148, 196)(149, 197)(150, 198)(151, 199)(152, 200)(153, 201)(154, 202)(155, 203)(156, 157)(158, 204)(159, 205)(160, 206)(171, 227)(172, 228)(173, 229)(174, 175)(176, 230)(177, 231)(178, 232)(179, 233)(180, 234)(181, 235)(182, 236)(183, 237)(184, 238)(185, 239)(186, 187)(188, 240)(189, 241)(190, 242)(207, 274)(208, 275)(209, 276)(210, 211)(212, 277)(213, 278)(214, 279)(215, 280)(216, 281)(217, 282)(218, 283)(219, 284)(220, 285)(221, 286)(222, 223)(224, 287)(225, 288)(226, 243)(244, 370)(245, 478)(246, 480)(247, 462)(248, 481)(249, 483)(250, 484)(251, 486)(252, 487)(253, 489)(254, 255)(256, 355)(257, 493)(258, 495)(259, 497)(260, 498)(261, 500)(262, 263)(264, 316)(265, 505)(266, 507)(267, 508)(268, 509)(269, 511)(270, 512)(271, 514)(272, 515)(273, 386)(289, 309)(290, 303)(291, 325)(292, 296)(293, 336)(294, 299)(295, 345)(297, 307)(298, 357)(300, 314)(301, 368)(302, 341)(304, 323)(305, 384)(306, 353)(308, 331)(310, 334)(311, 405)(312, 407)(313, 332)(315, 322)(317, 343)(318, 426)(319, 369)(320, 433)(321, 435)(324, 330)(326, 455)(327, 385)(328, 471)(329, 474)(333, 366)(335, 349)(337, 521)(338, 406)(339, 536)(340, 539)(342, 382)(344, 361)(346, 427)(347, 648)(348, 651)(350, 657)(351, 434)(352, 660)(354, 403)(356, 376)(358, 457)(359, 674)(360, 677)(362, 647)(363, 684)(364, 687)(365, 424)(367, 391)(371, 431)(372, 398)(373, 523)(374, 706)(375, 709)(377, 673)(378, 716)(379, 460)(380, 699)(381, 451)(383, 412)(387, 467)(388, 420)(389, 733)(390, 736)(392, 613)(393, 742)(394, 745)(395, 590)(396, 749)(397, 752)(399, 732)(400, 759)(401, 453)(402, 518)(404, 439)(408, 532)(409, 447)(410, 773)(411, 776)(413, 779)(414, 631)(415, 739)(416, 785)(417, 607)(418, 789)(419, 793)(421, 772)(422, 800)(423, 520)(425, 450)(428, 808)(429, 491)(430, 810)(432, 502)(436, 820)(437, 823)(438, 826)(440, 809)(441, 597)(442, 506)(443, 834)(444, 577)(445, 838)(446, 744)(448, 822)(449, 848)(452, 852)(454, 527)(456, 819)(458, 551)(459, 861)(461, 862)(463, 513)(464, 844)(465, 864)(466, 863)(468, 870)(469, 871)(470, 638)(472, 877)(473, 544)(475, 867)(476, 883)(477, 659)(479, 681)(482, 892)(485, 627)(488, 878)(490, 882)(492, 845)(494, 907)(496, 550)(499, 832)(501, 913)(503, 731)(504, 580)(510, 855)(516, 928)(517, 686)(519, 918)(522, 881)(524, 556)(525, 939)(526, 940)(528, 634)(529, 756)(530, 942)(531, 941)(533, 946)(534, 900)(535, 664)(537, 950)(538, 548)(540, 569)(541, 593)(542, 873)(543, 561)(545, 609)(546, 948)(547, 896)(549, 629)(552, 956)(553, 646)(554, 960)(555, 656)(557, 961)(558, 672)(559, 964)(560, 682)(562, 564)(563, 966)(565, 970)(566, 705)(567, 973)(568, 714)(570, 572)(571, 975)(573, 719)(574, 981)(575, 740)(576, 748)(578, 857)(579, 757)(581, 584)(582, 984)(583, 718)(585, 991)(586, 661)(587, 993)(588, 781)(589, 788)(591, 937)(592, 797)(594, 596)(595, 997)(598, 601)(599, 1003)(600, 671)(602, 1010)(603, 688)(604, 1011)(605, 830)(606, 837)(608, 1012)(610, 612)(611, 903)(614, 618)(615, 897)(616, 704)(617, 753)(619, 1022)(620, 632)(621, 1024)(622, 885)(623, 904)(624, 746)(625, 1026)(626, 917)(628, 1027)(630, 1029)(633, 1031)(635, 645)(636, 794)(637, 931)(639, 971)(640, 786)(641, 1033)(642, 887)(643, 792)(644, 1034)(649, 654)(650, 1039)(652, 679)(653, 710)(655, 934)(658, 1048)(662, 1050)(663, 987)(665, 908)(666, 835)(667, 1052)(668, 952)(669, 841)(670, 1053)(675, 680)(676, 1058)(678, 711)(683, 1064)(685, 884)(689, 1066)(690, 962)(691, 893)(692, 1067)(693, 859)(694, 1013)(695, 902)(696, 1068)(697, 1006)(698, 769)(700, 972)(701, 727)(702, 801)(703, 944)(707, 712)(708, 1072)(713, 853)(715, 1075)(717, 821)(720, 954)(721, 995)(722, 1040)(723, 804)(724, 1028)(725, 1065)(726, 921)(728, 959)(729, 767)(730, 849)(734, 738)(735, 925)(737, 754)(741, 1083)(743, 780)(747, 1071)(750, 755)(751, 1074)(758, 945)(760, 770)(761, 957)(762, 906)(763, 1059)(764, 996)(765, 1069)(766, 951)(768, 963)(771, 866)(774, 778)(775, 1086)(777, 795)(782, 1080)(783, 829)(784, 798)(787, 923)(790, 796)(791, 1046)(799, 812)(802, 1025)(803, 1018)(805, 924)(806, 1043)(807, 817)(811, 967)(813, 1081)(814, 974)(815, 1051)(816, 854)(818, 980)(824, 828)(825, 1078)(827, 842)(831, 911)(833, 846)(836, 916)(839, 843)(840, 1063)(847, 868)(850, 929)(851, 895)(856, 982)(858, 899)(860, 879)(865, 976)(869, 1087)(872, 926)(874, 983)(875, 894)(876, 1077)(880, 992)(886, 1057)(888, 1055)(889, 905)(890, 965)(891, 1079)(898, 1085)(901, 1091)(909, 955)(910, 919)(912, 915)(914, 932)(920, 1062)(922, 1032)(927, 1002)(930, 938)(933, 1005)(935, 1092)(936, 994)(943, 985)(947, 953)(949, 1041)(958, 1020)(968, 1044)(969, 1088)(977, 1061)(978, 999)(979, 1084)(986, 1049)(988, 1038)(989, 1014)(990, 1082)(998, 1054)(1000, 1073)(1001, 1037)(1004, 1019)(1007, 1017)(1008, 1035)(1009, 1060)(1015, 1045)(1016, 1056)(1021, 1036)(1023, 1042)(1030, 1070)(1047, 1090)(1076, 1089) local type(s) :: { ( 7^3 ) } Outer automorphisms :: reflexible Dual of E14.614 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 364 e = 546 f = 156 degree seq :: [ 3^364 ] E14.617 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 7}) Quotient :: regular Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^7, (T2 * T1 * T2 * T1^-1)^6 ] Map:: polyhedral non-degenerate R = (1, 2, 4)(3, 6, 7)(5, 9, 10)(8, 13, 14)(11, 17, 18)(12, 19, 20)(15, 23, 24)(16, 25, 26)(21, 31, 32)(22, 33, 34)(27, 39, 40)(28, 41, 42)(29, 43, 44)(30, 45, 46)(35, 51, 52)(36, 53, 54)(37, 55, 56)(38, 57, 58)(47, 66, 67)(48, 68, 69)(49, 70, 71)(50, 72, 59)(60, 79, 80)(61, 81, 82)(62, 83, 84)(63, 85, 86)(64, 87, 88)(65, 89, 90)(73, 97, 98)(74, 99, 100)(75, 101, 102)(76, 103, 104)(77, 105, 106)(78, 107, 108)(91, 119, 120)(92, 121, 122)(93, 123, 124)(94, 125, 126)(95, 127, 128)(96, 129, 130)(109, 141, 142)(110, 143, 144)(111, 145, 146)(112, 147, 148)(113, 149, 150)(114, 151, 152)(115, 153, 154)(116, 155, 156)(117, 157, 158)(118, 159, 160)(131, 171, 172)(132, 173, 174)(133, 175, 176)(134, 177, 178)(135, 179, 180)(136, 181, 182)(137, 183, 184)(138, 185, 186)(139, 187, 188)(140, 189, 190)(161, 207, 208)(162, 209, 210)(163, 211, 212)(164, 213, 214)(165, 215, 216)(166, 217, 218)(167, 219, 220)(168, 221, 222)(169, 223, 224)(170, 225, 226)(191, 243, 244)(192, 245, 246)(193, 247, 248)(194, 249, 250)(195, 251, 238)(196, 252, 253)(197, 254, 255)(198, 256, 257)(199, 258, 259)(200, 260, 261)(201, 262, 263)(202, 264, 265)(203, 266, 267)(204, 268, 269)(205, 270, 271)(206, 272, 227)(228, 478, 361)(229, 480, 827)(230, 475, 446)(231, 483, 283)(232, 485, 667)(233, 487, 393)(234, 489, 694)(235, 491, 303)(236, 493, 569)(237, 495, 824)(239, 498, 934)(240, 500, 327)(241, 502, 744)(242, 504, 273)(274, 546, 375)(275, 548, 859)(276, 423, 476)(277, 550, 691)(278, 552, 360)(279, 554, 696)(280, 556, 309)(281, 558, 571)(282, 560, 856)(284, 530, 964)(285, 564, 338)(286, 566, 771)(287, 459, 455)(288, 499, 492)(289, 428, 424)(290, 563, 557)(291, 387, 383)(292, 577, 580)(293, 581, 583)(294, 405, 401)(295, 514, 588)(296, 589, 591)(297, 359, 355)(298, 449, 432)(299, 596, 599)(300, 600, 602)(301, 374, 370)(302, 481, 391)(304, 608, 610)(305, 611, 614)(306, 482, 616)(307, 348, 344)(308, 549, 409)(310, 623, 625)(311, 626, 628)(312, 521, 630)(313, 354, 389)(314, 567, 372)(315, 333, 322)(316, 636, 453)(317, 612, 640)(318, 641, 643)(319, 450, 645)(320, 369, 407)(321, 461, 346)(323, 651, 488)(324, 538, 656)(325, 657, 659)(326, 660, 662)(328, 597, 665)(329, 666, 668)(330, 406, 484)(331, 343, 430)(332, 503, 357)(334, 675, 553)(335, 678, 681)(336, 682, 684)(337, 536, 686)(339, 578, 689)(340, 690, 692)(341, 429, 534)(342, 388, 451)(345, 700, 703)(347, 706, 385)(349, 710, 713)(350, 714, 716)(351, 531, 718)(352, 586, 720)(353, 721, 722)(356, 727, 730)(358, 698, 403)(362, 570, 738)(363, 739, 734)(364, 460, 468)(365, 743, 746)(366, 683, 748)(367, 465, 750)(368, 606, 752)(371, 754, 757)(373, 725, 426)(376, 574, 765)(377, 766, 762)(378, 501, 416)(379, 770, 773)(380, 715, 775)(381, 413, 777)(382, 621, 779)(384, 781, 783)(386, 649, 447)(390, 788, 791)(392, 780, 457)(394, 568, 797)(395, 798, 709)(396, 565, 439)(397, 509, 803)(398, 658, 805)(399, 436, 532)(400, 527, 808)(402, 810, 811)(404, 673, 477)(408, 815, 817)(410, 809, 496)(411, 582, 822)(412, 823, 724)(414, 826, 769)(415, 747, 820)(417, 654, 831)(418, 512, 833)(419, 572, 835)(420, 836, 674)(421, 479, 510)(422, 624, 841)(425, 844, 846)(427, 634, 545)(431, 850, 852)(433, 843, 561)(434, 590, 855)(435, 525, 507)(437, 858, 801)(438, 774, 787)(440, 679, 864)(441, 865, 867)(442, 575, 869)(443, 870, 635)(444, 547, 761)(445, 639, 875)(448, 708, 473)(452, 879, 881)(454, 853, 884)(456, 885, 887)(458, 617, 891)(462, 892, 873)(463, 601, 895)(464, 896, 543)(466, 898, 742)(467, 804, 794)(469, 711, 523)(470, 903, 905)(471, 584, 907)(472, 908, 650)(474, 609, 913)(486, 922, 924)(490, 792, 927)(494, 928, 930)(497, 592, 933)(505, 937, 911)(506, 918, 839)(508, 829, 753)(511, 941, 642)(513, 676, 944)(515, 945, 947)(516, 948, 573)(517, 951, 767)(518, 897, 919)(519, 952, 618)(520, 954, 723)(522, 664, 957)(524, 959, 526)(528, 615, 962)(529, 963, 939)(533, 840, 760)(535, 967, 740)(537, 969, 647)(539, 970, 971)(540, 972, 579)(541, 975, 914)(542, 594, 976)(544, 861, 699)(551, 958, 882)(555, 818, 968)(559, 977, 984)(562, 603, 987)(576, 876, 992)(585, 915, 993)(587, 663, 994)(593, 921, 997)(595, 857, 998)(598, 687, 999)(604, 980, 1002)(605, 1003, 1004)(607, 629, 1005)(613, 736, 1006)(619, 1008, 1009)(620, 825, 979)(622, 644, 1011)(627, 763, 950)(631, 1012, 802)(632, 1013, 1015)(633, 1016, 1017)(637, 1018, 1019)(638, 768, 1020)(646, 1021, 745)(648, 1023, 1024)(652, 1025, 1026)(653, 800, 1027)(655, 669, 1028)(661, 807, 1000)(670, 1029, 772)(671, 1030, 1031)(672, 1032, 956)(677, 741, 1034)(680, 693, 1035)(685, 751, 1007)(688, 1033, 795)(695, 1040, 712)(697, 1037, 1010)(701, 1042, 1043)(702, 838, 1044)(704, 1046, 828)(705, 1047, 1048)(707, 1049, 874)(717, 778, 995)(719, 974, 735)(726, 936, 900)(728, 1052, 965)(729, 872, 1045)(731, 1054, 860)(732, 1055, 1056)(733, 1057, 912)(737, 986, 832)(749, 830, 990)(755, 1061, 1062)(756, 910, 1053)(758, 1063, 899)(759, 1064, 1065)(764, 890, 866)(776, 863, 961)(782, 955, 925)(784, 1069, 940)(785, 1070, 1071)(786, 1072, 854)(789, 929, 1073)(790, 916, 1068)(793, 983, 1074)(796, 932, 904)(799, 920, 991)(806, 902, 989)(812, 1078, 893)(813, 1079, 1080)(814, 943, 894)(816, 978, 1077)(819, 886, 1081)(821, 849, 946)(834, 868, 906)(837, 1076, 996)(842, 935, 988)(845, 1082, 883)(847, 1084, 938)(848, 1085, 1086)(851, 877, 1083)(862, 1039, 949)(871, 1060, 1001)(878, 1087, 1075)(880, 1088, 985)(888, 1089, 1066)(889, 923, 1090)(901, 1041, 1058)(909, 1067, 973)(917, 960, 1059)(926, 1091, 982)(931, 981, 1092)(942, 1051, 1036)(953, 1050, 1014)(966, 1022, 1038) L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 12)(9, 15)(10, 16)(13, 21)(14, 22)(17, 27)(18, 28)(19, 29)(20, 30)(23, 35)(24, 36)(25, 37)(26, 38)(31, 47)(32, 48)(33, 49)(34, 50)(39, 59)(40, 60)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 51)(52, 73)(53, 74)(54, 75)(55, 76)(56, 77)(57, 78)(58, 66)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 85)(86, 114)(87, 115)(88, 116)(89, 117)(90, 118)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 103)(104, 136)(105, 137)(106, 138)(107, 139)(108, 140)(119, 161)(120, 162)(121, 163)(122, 164)(123, 165)(124, 125)(126, 166)(127, 167)(128, 168)(129, 169)(130, 170)(141, 191)(142, 192)(143, 193)(144, 145)(146, 194)(147, 195)(148, 196)(149, 197)(150, 198)(151, 199)(152, 200)(153, 201)(154, 202)(155, 203)(156, 157)(158, 204)(159, 205)(160, 206)(171, 227)(172, 228)(173, 229)(174, 175)(176, 230)(177, 231)(178, 232)(179, 233)(180, 234)(181, 235)(182, 236)(183, 237)(184, 238)(185, 239)(186, 187)(188, 240)(189, 241)(190, 242)(207, 273)(208, 274)(209, 275)(210, 211)(212, 276)(213, 264)(214, 277)(215, 278)(216, 279)(217, 280)(218, 281)(219, 282)(220, 283)(221, 284)(222, 223)(224, 285)(225, 286)(226, 243)(244, 507)(245, 509)(246, 511)(247, 512)(248, 466)(249, 514)(250, 516)(251, 517)(252, 518)(253, 254)(255, 521)(256, 523)(257, 524)(258, 526)(259, 527)(260, 529)(261, 262)(263, 532)(265, 535)(266, 536)(267, 537)(268, 538)(269, 540)(270, 541)(271, 397)(272, 543)(287, 568)(288, 570)(289, 572)(290, 574)(291, 575)(292, 578)(293, 582)(294, 584)(295, 586)(296, 590)(297, 592)(298, 594)(299, 597)(300, 601)(301, 603)(302, 605)(303, 606)(304, 609)(305, 612)(306, 615)(307, 617)(308, 619)(309, 621)(310, 624)(311, 608)(312, 629)(313, 631)(314, 633)(315, 634)(316, 637)(317, 639)(318, 623)(319, 644)(320, 646)(321, 648)(322, 649)(323, 652)(324, 654)(325, 658)(326, 589)(327, 663)(328, 664)(329, 657)(330, 669)(331, 670)(332, 672)(333, 673)(334, 676)(335, 679)(336, 683)(337, 600)(338, 687)(339, 688)(340, 682)(341, 693)(342, 695)(343, 697)(344, 698)(345, 701)(346, 704)(347, 707)(348, 708)(349, 711)(350, 715)(351, 581)(352, 719)(353, 714)(354, 723)(355, 725)(356, 728)(357, 731)(358, 733)(359, 510)(360, 482)(361, 736)(362, 737)(363, 721)(364, 741)(365, 744)(366, 747)(367, 563)(368, 751)(369, 539)(370, 706)(371, 755)(372, 758)(373, 760)(374, 761)(375, 763)(376, 764)(377, 666)(378, 768)(379, 771)(380, 774)(381, 459)(382, 778)(383, 780)(384, 726)(385, 784)(386, 786)(387, 439)(388, 470)(389, 503)(390, 789)(391, 792)(392, 794)(393, 450)(394, 796)(395, 690)(396, 800)(398, 804)(399, 499)(400, 807)(401, 809)(402, 753)(403, 812)(404, 814)(405, 468)(406, 418)(407, 567)(408, 793)(409, 818)(410, 820)(411, 821)(412, 641)(413, 825)(414, 827)(415, 829)(416, 428)(417, 830)(419, 834)(420, 739)(421, 838)(422, 840)(423, 577)(424, 843)(425, 699)(426, 847)(427, 849)(429, 441)(430, 461)(431, 819)(432, 853)(433, 787)(434, 854)(435, 611)(436, 857)(437, 859)(438, 861)(440, 863)(442, 868)(443, 766)(444, 872)(445, 874)(446, 876)(447, 877)(448, 776)(449, 534)(451, 481)(452, 759)(453, 882)(454, 775)(455, 810)(456, 650)(457, 888)(458, 890)(460, 515)(462, 883)(463, 894)(464, 626)(465, 897)(467, 900)(469, 902)(471, 906)(472, 798)(473, 910)(474, 912)(475, 596)(476, 915)(477, 916)(478, 743)(479, 806)(480, 865)(483, 920)(484, 549)(485, 620)(486, 705)(487, 667)(488, 881)(489, 831)(490, 805)(491, 862)(492, 844)(493, 845)(494, 674)(495, 569)(496, 878)(497, 932)(498, 531)(500, 678)(501, 914)(502, 935)(504, 724)(505, 925)(506, 939)(508, 908)(513, 943)(519, 823)(520, 955)(522, 956)(525, 921)(528, 961)(530, 660)(533, 965)(542, 904)(544, 836)(545, 978)(546, 770)(547, 749)(548, 903)(550, 595)(551, 732)(552, 691)(553, 924)(554, 864)(555, 748)(556, 901)(557, 781)(558, 782)(559, 635)(560, 571)(561, 917)(562, 986)(564, 710)(565, 842)(566, 945)(573, 951)(576, 991)(579, 975)(580, 885)(583, 727)(585, 967)(587, 988)(588, 928)(591, 754)(593, 996)(598, 947)(599, 977)(602, 700)(604, 1001)(607, 989)(610, 788)(613, 867)(614, 909)(616, 651)(618, 973)(622, 990)(625, 815)(627, 905)(628, 837)(630, 675)(632, 1014)(636, 645)(638, 941)(640, 850)(642, 833)(643, 871)(647, 1022)(653, 1006)(655, 995)(656, 966)(659, 879)(661, 971)(662, 799)(665, 892)(668, 953)(671, 942)(677, 950)(680, 1000)(681, 1036)(684, 922)(685, 1010)(686, 740)(689, 937)(692, 1038)(694, 1039)(696, 1041)(702, 999)(703, 817)(709, 949)(712, 1007)(713, 1050)(716, 958)(717, 954)(718, 767)(720, 918)(722, 1051)(729, 972)(730, 852)(734, 1058)(735, 1024)(738, 1059)(742, 930)(745, 974)(746, 1060)(750, 824)(752, 858)(756, 994)(757, 791)(762, 959)(765, 1066)(769, 984)(772, 957)(773, 1067)(777, 856)(779, 898)(783, 873)(785, 968)(790, 1005)(795, 1017)(797, 1075)(801, 887)(802, 1033)(803, 1076)(808, 826)(811, 911)(813, 884)(816, 1011)(822, 938)(828, 875)(832, 1004)(835, 1080)(839, 846)(841, 899)(848, 927)(851, 962)(855, 940)(860, 913)(866, 1009)(869, 1086)(870, 936)(880, 1028)(886, 948)(889, 1063)(891, 1088)(893, 895)(896, 980)(907, 1071)(919, 1047)(923, 1035)(926, 1021)(929, 992)(931, 1046)(933, 1090)(934, 1030)(944, 969)(946, 1019)(952, 1052)(960, 1045)(963, 970)(964, 1013)(976, 1056)(979, 1055)(981, 1040)(982, 1029)(983, 993)(985, 1054)(987, 1092)(997, 1061)(998, 1064)(1002, 1042)(1003, 1065)(1008, 1048)(1012, 1091)(1015, 1025)(1016, 1074)(1018, 1031)(1020, 1070)(1023, 1081)(1026, 1072)(1027, 1079)(1032, 1073)(1034, 1085)(1037, 1082)(1043, 1057)(1044, 1087)(1049, 1062)(1053, 1089)(1068, 1084)(1069, 1077)(1078, 1083) local type(s) :: { ( 7^3 ) } Outer automorphisms :: reflexible Dual of E14.613 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 364 e = 546 f = 156 degree seq :: [ 3^364 ] E14.618 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 7}) Quotient :: regular Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^7, (T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1)^3 ] Map:: polyhedral non-degenerate R = (1, 2, 4)(3, 6, 7)(5, 9, 10)(8, 13, 14)(11, 17, 18)(12, 19, 20)(15, 23, 24)(16, 25, 26)(21, 31, 32)(22, 33, 34)(27, 39, 40)(28, 41, 42)(29, 43, 44)(30, 45, 46)(35, 51, 52)(36, 53, 54)(37, 55, 56)(38, 57, 58)(47, 66, 67)(48, 68, 69)(49, 70, 71)(50, 72, 59)(60, 79, 80)(61, 81, 82)(62, 83, 84)(63, 85, 86)(64, 87, 88)(65, 89, 90)(73, 97, 98)(74, 99, 100)(75, 101, 102)(76, 103, 104)(77, 105, 106)(78, 107, 108)(91, 119, 120)(92, 121, 122)(93, 123, 124)(94, 125, 126)(95, 127, 128)(96, 129, 130)(109, 141, 142)(110, 143, 144)(111, 145, 146)(112, 147, 148)(113, 149, 150)(114, 151, 152)(115, 153, 154)(116, 155, 156)(117, 157, 158)(118, 159, 160)(131, 171, 172)(132, 173, 174)(133, 175, 176)(134, 177, 178)(135, 179, 180)(136, 181, 182)(137, 183, 184)(138, 185, 186)(139, 187, 188)(140, 189, 190)(161, 207, 208)(162, 209, 210)(163, 211, 212)(164, 213, 214)(165, 215, 216)(166, 217, 218)(167, 219, 220)(168, 221, 222)(169, 223, 224)(170, 225, 226)(191, 243, 244)(192, 245, 246)(193, 247, 248)(194, 249, 250)(195, 251, 252)(196, 253, 254)(197, 255, 256)(198, 257, 258)(199, 259, 260)(200, 261, 262)(201, 263, 264)(202, 265, 266)(203, 267, 268)(204, 269, 270)(205, 271, 272)(206, 273, 227)(228, 472, 839)(229, 411, 365)(230, 475, 843)(231, 477, 301)(232, 452, 361)(233, 479, 848)(234, 481, 850)(235, 483, 395)(236, 429, 465)(237, 486, 856)(238, 488, 859)(239, 490, 860)(240, 492, 865)(241, 363, 334)(242, 495, 274)(275, 538, 924)(276, 434, 380)(277, 541, 927)(278, 445, 295)(279, 484, 376)(280, 544, 928)(281, 546, 929)(282, 548, 360)(283, 390, 416)(284, 550, 934)(285, 552, 919)(286, 554, 936)(287, 556, 941)(288, 378, 348)(289, 421, 425)(290, 443, 386)(291, 398, 454)(292, 470, 403)(293, 366, 487)(294, 515, 356)(296, 381, 551)(297, 567, 372)(298, 349, 570)(299, 414, 572)(300, 573, 344)(302, 324, 577)(303, 437, 579)(304, 580, 392)(305, 582, 329)(306, 377, 585)(307, 335, 587)(308, 463, 589)(309, 590, 408)(310, 592, 312)(311, 396, 595)(313, 500, 598)(314, 359, 600)(315, 525, 602)(316, 603, 431)(317, 605, 319)(318, 362, 608)(320, 610, 612)(321, 375, 614)(322, 615, 617)(323, 618, 450)(325, 419, 622)(326, 623, 401)(327, 625, 340)(328, 338, 628)(330, 630, 632)(331, 394, 634)(332, 635, 637)(333, 638, 480)(336, 441, 643)(337, 501, 423)(339, 352, 514)(341, 648, 650)(342, 400, 652)(343, 653, 655)(345, 657, 659)(346, 417, 661)(347, 662, 545)(350, 468, 667)(351, 668, 384)(353, 531, 672)(354, 368, 674)(355, 675, 676)(357, 678, 680)(358, 439, 682)(364, 686, 688)(367, 537, 692)(369, 694, 654)(370, 383, 532)(371, 697, 698)(373, 700, 702)(374, 466, 704)(379, 707, 709)(382, 712, 714)(385, 717, 718)(387, 720, 701)(388, 506, 722)(389, 723, 616)(391, 726, 727)(393, 729, 730)(397, 733, 735)(399, 499, 738)(402, 741, 742)(404, 744, 658)(405, 745, 747)(406, 748, 636)(407, 750, 751)(409, 724, 753)(410, 526, 755)(412, 757, 759)(413, 521, 471)(415, 762, 764)(418, 505, 767)(420, 768, 770)(422, 436, 772)(424, 774, 775)(426, 777, 679)(427, 778, 780)(428, 781, 601)(430, 782, 783)(432, 749, 785)(433, 786, 788)(435, 790, 792)(438, 795, 512)(440, 798, 800)(442, 502, 802)(444, 462, 725)(446, 805, 631)(447, 806, 808)(448, 809, 639)(449, 810, 811)(451, 695, 813)(453, 815, 816)(455, 553, 489)(456, 818, 791)(457, 820, 588)(458, 529, 507)(459, 821, 822)(460, 533, 824)(461, 825, 827)(464, 830, 807)(467, 833, 519)(469, 835, 837)(473, 840, 597)(474, 841, 842)(476, 844, 663)(478, 846, 847)(482, 649, 851)(485, 854, 855)(491, 863, 826)(493, 866, 571)(494, 862, 867)(496, 869, 870)(497, 871, 872)(498, 873, 875)(503, 644, 879)(504, 880, 882)(508, 885, 887)(509, 888, 889)(510, 736, 890)(511, 891, 893)(513, 894, 543)(516, 898, 518)(517, 524, 696)(520, 645, 902)(522, 903, 905)(523, 906, 908)(527, 911, 746)(528, 754, 913)(530, 914, 916)(534, 715, 920)(535, 897, 834)(536, 921, 923)(539, 881, 611)(540, 925, 926)(542, 900, 619)(547, 671, 930)(549, 932, 933)(555, 939, 758)(557, 942, 578)(558, 938, 943)(559, 794, 831)(560, 829, 763)(561, 876, 912)(562, 761, 796)(563, 944, 945)(564, 910, 713)(565, 711, 878)(566, 895, 946)(568, 948, 737)(569, 949, 950)(574, 953, 691)(575, 690, 954)(576, 917, 955)(581, 958, 771)(583, 960, 666)(584, 665, 961)(586, 963, 964)(591, 907, 803)(593, 967, 621)(594, 620, 968)(596, 832, 970)(599, 971, 972)(604, 973, 838)(606, 974, 642)(607, 641, 975)(609, 765, 976)(613, 977, 978)(624, 982, 789)(626, 965, 684)(627, 683, 983)(629, 797, 985)(633, 986, 987)(640, 947, 766)(646, 705, 989)(647, 731, 990)(651, 991, 992)(656, 883, 994)(660, 995, 996)(664, 952, 799)(669, 997, 756)(670, 957, 732)(673, 998, 999)(677, 1001, 1002)(681, 1003, 1004)(685, 739, 1005)(687, 874, 1006)(689, 959, 886)(693, 1007, 706)(699, 1008, 1009)(703, 1010, 915)(708, 922, 1011)(710, 966, 1012)(716, 1013, 1014)(719, 1015, 1016)(721, 1017, 1000)(728, 1018, 1019)(734, 1020, 1021)(740, 1022, 1023)(743, 1024, 1025)(752, 1026, 1027)(760, 956, 1030)(769, 1032, 1033)(773, 1035, 1036)(776, 1037, 1038)(779, 1039, 993)(784, 1040, 1041)(787, 1042, 861)(793, 877, 1044)(801, 1047, 1048)(804, 1050, 1051)(812, 857, 1052)(814, 1053, 1054)(817, 1046, 1055)(819, 1056, 979)(823, 1057, 937)(828, 951, 1058)(836, 1061, 1029)(845, 1063, 1064)(849, 935, 1065)(852, 1066, 1045)(853, 1067, 1069)(858, 1060, 909)(864, 1072, 988)(868, 1073, 1074)(884, 940, 1076)(892, 1068, 904)(896, 1078, 1075)(899, 1080, 1043)(901, 1062, 1034)(918, 1031, 1082)(931, 1086, 1059)(962, 1088, 1071)(969, 1089, 1087)(980, 1090, 1084)(981, 1077, 1049)(984, 1083, 1081)(1028, 1085, 1070)(1079, 1091, 1092) L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 12)(9, 15)(10, 16)(13, 21)(14, 22)(17, 27)(18, 28)(19, 29)(20, 30)(23, 35)(24, 36)(25, 37)(26, 38)(31, 47)(32, 48)(33, 49)(34, 50)(39, 59)(40, 60)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 51)(52, 73)(53, 74)(54, 75)(55, 76)(56, 77)(57, 78)(58, 66)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 85)(86, 114)(87, 115)(88, 116)(89, 117)(90, 118)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 103)(104, 136)(105, 137)(106, 138)(107, 139)(108, 140)(119, 161)(120, 162)(121, 163)(122, 164)(123, 165)(124, 125)(126, 166)(127, 167)(128, 168)(129, 169)(130, 170)(141, 191)(142, 192)(143, 193)(144, 145)(146, 194)(147, 195)(148, 196)(149, 197)(150, 198)(151, 199)(152, 200)(153, 201)(154, 202)(155, 203)(156, 157)(158, 204)(159, 205)(160, 206)(171, 227)(172, 228)(173, 229)(174, 175)(176, 230)(177, 231)(178, 232)(179, 233)(180, 234)(181, 235)(182, 236)(183, 237)(184, 238)(185, 239)(186, 187)(188, 240)(189, 241)(190, 242)(207, 274)(208, 275)(209, 276)(210, 211)(212, 277)(213, 278)(214, 279)(215, 280)(216, 281)(217, 282)(218, 283)(219, 284)(220, 285)(221, 286)(222, 223)(224, 287)(225, 288)(226, 243)(244, 498)(245, 377)(246, 501)(247, 503)(248, 504)(249, 505)(250, 507)(251, 509)(252, 510)(253, 511)(254, 255)(256, 513)(257, 514)(258, 516)(259, 518)(260, 520)(261, 521)(262, 263)(264, 523)(265, 470)(266, 526)(267, 528)(268, 530)(269, 441)(270, 532)(271, 534)(272, 535)(273, 536)(289, 559)(290, 560)(291, 561)(292, 562)(293, 563)(294, 564)(295, 565)(296, 566)(297, 568)(298, 569)(299, 571)(300, 574)(301, 575)(302, 576)(303, 578)(304, 581)(305, 583)(306, 584)(307, 586)(308, 588)(309, 591)(310, 593)(311, 594)(312, 596)(313, 597)(314, 599)(315, 601)(316, 604)(317, 606)(318, 607)(319, 609)(320, 611)(321, 613)(322, 616)(323, 619)(324, 620)(325, 621)(326, 624)(327, 626)(328, 627)(329, 629)(330, 631)(331, 633)(332, 636)(333, 639)(334, 640)(335, 641)(336, 642)(337, 644)(338, 645)(339, 646)(340, 647)(341, 649)(342, 651)(343, 654)(344, 656)(345, 658)(346, 660)(347, 663)(348, 664)(349, 665)(350, 666)(351, 669)(352, 670)(353, 671)(354, 673)(355, 650)(356, 677)(357, 679)(358, 681)(359, 683)(360, 684)(361, 479)(362, 538)(363, 685)(364, 687)(365, 689)(366, 690)(367, 691)(368, 693)(369, 695)(370, 696)(371, 672)(372, 699)(373, 701)(374, 703)(375, 705)(376, 544)(378, 706)(379, 708)(380, 710)(381, 711)(382, 713)(383, 715)(384, 716)(385, 612)(386, 719)(387, 489)(388, 721)(389, 724)(390, 725)(391, 704)(392, 728)(393, 680)(394, 731)(395, 732)(396, 472)(397, 734)(398, 736)(399, 737)(400, 739)(401, 740)(402, 632)(403, 743)(404, 553)(405, 746)(406, 749)(407, 661)(408, 752)(409, 702)(410, 754)(411, 756)(412, 758)(413, 760)(414, 761)(415, 763)(416, 550)(417, 765)(418, 766)(419, 556)(420, 769)(421, 488)(422, 771)(423, 773)(424, 598)(425, 776)(426, 455)(427, 779)(428, 729)(429, 772)(430, 682)(431, 784)(432, 659)(433, 787)(434, 789)(435, 791)(436, 793)(437, 794)(438, 796)(439, 797)(440, 799)(442, 801)(443, 552)(444, 803)(445, 804)(446, 777)(447, 807)(448, 741)(449, 634)(450, 812)(451, 730)(452, 814)(453, 579)(454, 817)(456, 819)(457, 700)(458, 738)(459, 722)(460, 823)(461, 826)(462, 828)(463, 829)(464, 831)(465, 486)(466, 832)(467, 834)(468, 492)(469, 836)(471, 838)(473, 720)(474, 764)(475, 798)(476, 774)(477, 845)(478, 600)(480, 849)(481, 625)(482, 753)(483, 852)(484, 853)(485, 589)(487, 858)(490, 861)(491, 864)(493, 657)(494, 692)(495, 868)(496, 747)(497, 780)(499, 847)(500, 876)(502, 878)(506, 883)(508, 886)(512, 540)(515, 897)(517, 900)(519, 901)(522, 904)(524, 909)(525, 910)(527, 912)(529, 888)(531, 917)(533, 919)(537, 894)(539, 744)(541, 833)(542, 717)(543, 614)(545, 905)(546, 628)(547, 785)(548, 931)(549, 572)(551, 918)(554, 937)(555, 940)(557, 678)(558, 714)(567, 947)(570, 951)(573, 952)(577, 956)(580, 957)(582, 959)(585, 962)(587, 877)(590, 965)(592, 966)(595, 969)(602, 884)(603, 902)(605, 880)(608, 914)(610, 944)(615, 948)(617, 979)(618, 974)(622, 980)(623, 924)(630, 895)(635, 953)(637, 988)(638, 960)(643, 984)(648, 949)(652, 865)(653, 958)(655, 993)(662, 967)(667, 896)(668, 839)(674, 941)(675, 907)(676, 1000)(686, 968)(688, 827)(694, 963)(697, 973)(698, 911)(707, 975)(709, 759)(712, 811)(718, 1004)(723, 971)(726, 982)(727, 830)(733, 961)(735, 792)(742, 915)(745, 1001)(748, 977)(750, 879)(751, 762)(755, 1028)(757, 983)(767, 981)(768, 954)(770, 872)(775, 996)(778, 1008)(781, 986)(782, 997)(783, 795)(786, 859)(788, 1043)(790, 989)(800, 887)(802, 822)(805, 851)(806, 1015)(808, 899)(809, 991)(810, 848)(813, 881)(815, 874)(816, 987)(818, 1018)(820, 995)(821, 1007)(824, 906)(825, 990)(835, 890)(837, 870)(840, 930)(841, 1024)(842, 908)(843, 867)(844, 998)(846, 928)(850, 1066)(854, 922)(855, 972)(856, 1070)(857, 1068)(860, 1071)(862, 1063)(863, 1026)(866, 1003)(869, 920)(871, 1005)(873, 885)(875, 1075)(882, 1077)(889, 1069)(891, 1029)(892, 935)(893, 1064)(898, 1079)(903, 976)(913, 1044)(916, 1083)(921, 1034)(923, 1084)(925, 1037)(926, 1085)(927, 943)(929, 1086)(932, 1020)(933, 978)(934, 1080)(936, 1087)(938, 1050)(939, 1040)(942, 1010)(945, 1039)(946, 1017)(950, 1056)(955, 1072)(964, 1076)(970, 1065)(985, 1052)(992, 1082)(994, 1027)(999, 1055)(1002, 1041)(1006, 1013)(1009, 1019)(1011, 1022)(1012, 1062)(1014, 1038)(1016, 1023)(1021, 1035)(1025, 1036)(1030, 1057)(1031, 1032)(1033, 1053)(1042, 1058)(1045, 1091)(1046, 1047)(1048, 1067)(1049, 1073)(1051, 1054)(1059, 1092)(1060, 1061)(1074, 1081)(1078, 1088)(1089, 1090) local type(s) :: { ( 7^3 ) } Outer automorphisms :: reflexible Dual of E14.615 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 364 e = 546 f = 156 degree seq :: [ 3^364 ] E14.619 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2 * T1)^7, (T1 * T2^-1 * T1 * T2)^7, (T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1)^2 ] Map:: polytopal R = (1, 3, 4)(2, 5, 6)(7, 11, 12)(8, 13, 14)(9, 15, 16)(10, 17, 18)(19, 27, 28)(20, 29, 30)(21, 31, 32)(22, 33, 34)(23, 35, 36)(24, 37, 38)(25, 39, 40)(26, 41, 42)(43, 58, 59)(44, 60, 61)(45, 62, 63)(46, 64, 65)(47, 66, 67)(48, 68, 69)(49, 70, 71)(50, 72, 51)(52, 73, 74)(53, 75, 76)(54, 77, 78)(55, 79, 80)(56, 81, 82)(57, 83, 84)(85, 107, 108)(86, 109, 110)(87, 111, 112)(88, 113, 114)(89, 115, 116)(90, 117, 118)(91, 119, 120)(92, 121, 122)(93, 123, 124)(94, 125, 126)(95, 127, 128)(96, 129, 130)(97, 131, 132)(98, 133, 134)(99, 135, 136)(100, 137, 138)(101, 139, 140)(102, 141, 142)(103, 143, 144)(104, 145, 146)(105, 147, 148)(106, 149, 150)(151, 187, 188)(152, 189, 190)(153, 191, 192)(154, 193, 194)(155, 195, 196)(156, 197, 198)(157, 199, 200)(158, 201, 202)(159, 203, 204)(160, 205, 206)(161, 207, 208)(162, 209, 210)(163, 211, 212)(164, 213, 214)(165, 215, 216)(166, 217, 218)(167, 219, 220)(168, 221, 222)(169, 223, 224)(170, 225, 226)(171, 227, 228)(172, 229, 230)(173, 231, 232)(174, 233, 234)(175, 235, 236)(176, 237, 238)(177, 239, 240)(178, 241, 242)(179, 243, 244)(180, 245, 246)(181, 247, 248)(182, 249, 250)(183, 251, 252)(184, 253, 254)(185, 255, 256)(186, 257, 258)(259, 501, 575)(260, 503, 625)(261, 365, 560)(262, 505, 499)(263, 506, 766)(264, 419, 301)(265, 509, 683)(266, 510, 323)(267, 512, 794)(268, 514, 383)(269, 516, 691)(270, 517, 630)(271, 502, 562)(272, 520, 698)(273, 450, 274)(275, 522, 600)(276, 524, 636)(277, 337, 564)(278, 526, 822)(279, 527, 891)(280, 500, 294)(281, 530, 700)(282, 531, 343)(283, 533, 821)(284, 535, 350)(285, 537, 708)(286, 423, 609)(287, 523, 566)(288, 540, 640)(289, 405, 401)(290, 417, 386)(291, 412, 440)(292, 367, 455)(293, 424, 474)(295, 372, 353)(296, 410, 377)(297, 364, 344)(298, 422, 393)(299, 511, 551)(300, 532, 553)(302, 554, 555)(303, 557, 558)(304, 327, 407)(305, 336, 333)(306, 508, 432)(307, 360, 324)(308, 529, 446)(309, 329, 325)(310, 570, 458)(311, 369, 318)(312, 574, 484)(313, 576, 577)(314, 579, 580)(315, 331, 414)(316, 581, 582)(317, 466, 584)(319, 585, 586)(320, 588, 589)(321, 338, 426)(322, 590, 591)(326, 596, 404)(328, 599, 601)(330, 572, 443)(332, 606, 607)(334, 611, 389)(335, 614, 616)(339, 621, 622)(340, 569, 624)(341, 361, 515)(342, 626, 627)(345, 632, 633)(346, 595, 635)(347, 366, 536)(348, 613, 637)(349, 561, 639)(351, 641, 642)(352, 492, 644)(354, 648, 649)(355, 610, 650)(356, 358, 652)(357, 598, 653)(359, 656, 658)(362, 662, 380)(363, 664, 666)(368, 668, 671)(370, 655, 395)(371, 676, 678)(373, 568, 460)(374, 565, 681)(375, 682, 684)(376, 686, 687)(378, 690, 692)(379, 654, 693)(381, 605, 695)(382, 550, 697)(384, 699, 701)(385, 703, 704)(387, 707, 709)(388, 661, 710)(390, 573, 712)(391, 713, 715)(392, 717, 718)(394, 721, 723)(396, 620, 725)(397, 548, 727)(398, 427, 728)(399, 729, 731)(400, 733, 734)(402, 737, 739)(403, 674, 741)(406, 618, 744)(408, 663, 434)(409, 749, 751)(411, 594, 498)(413, 660, 755)(415, 612, 448)(416, 760, 762)(418, 603, 765)(420, 675, 463)(421, 770, 772)(425, 673, 776)(428, 597, 488)(429, 781, 783)(430, 784, 786)(431, 779, 788)(433, 791, 793)(435, 631, 720)(436, 542, 796)(437, 518, 797)(438, 798, 774)(439, 801, 802)(441, 805, 807)(442, 747, 809)(444, 811, 813)(445, 815, 816)(447, 818, 820)(449, 496, 790)(451, 547, 724)(452, 538, 824)(453, 825, 489)(454, 461, 828)(456, 831, 833)(457, 758, 835)(459, 837, 839)(462, 842, 745)(464, 647, 689)(465, 740, 714)(467, 541, 847)(468, 823, 844)(469, 849, 850)(470, 851, 753)(471, 853, 722)(472, 763, 646)(473, 856, 857)(475, 860, 862)(476, 539, 571)(477, 768, 800)(478, 491, 479)(480, 868, 870)(481, 871, 615)(482, 563, 651)(483, 874, 875)(485, 877, 878)(486, 819, 879)(487, 880, 829)(490, 634, 730)(493, 549, 694)(494, 883, 882)(495, 885, 886)(497, 888, 738)(504, 748, 629)(507, 898, 900)(513, 746, 906)(519, 604, 546)(521, 911, 912)(525, 759, 608)(528, 916, 917)(534, 757, 923)(543, 928, 669)(544, 863, 619)(545, 929, 680)(552, 855, 764)(556, 930, 743)(559, 711, 893)(567, 742, 867)(578, 852, 754)(583, 932, 670)(587, 799, 775)(592, 936, 657)(593, 810, 780)(602, 836, 909)(617, 789, 967)(623, 826, 905)(628, 952, 665)(638, 887, 960)(643, 957, 677)(645, 840, 769)(659, 817, 992)(667, 719, 996)(672, 876, 998)(679, 688, 896)(685, 969, 750)(696, 974, 944)(702, 975, 761)(705, 1022, 913)(706, 914, 752)(716, 979, 771)(726, 986, 938)(732, 919, 782)(735, 1011, 1042)(736, 1043, 773)(756, 950, 1037)(767, 1004, 848)(777, 943, 1016)(778, 1052, 884)(785, 971, 808)(787, 869, 899)(792, 890, 926)(795, 995, 941)(803, 1026, 1063)(804, 1051, 901)(806, 1017, 1068)(812, 977, 834)(814, 1014, 894)(827, 902, 838)(830, 1038, 918)(832, 981, 864)(841, 861, 1012)(843, 951, 866)(845, 954, 1080)(846, 1001, 948)(854, 903, 1005)(858, 1046, 1057)(859, 1047, 946)(865, 966, 1085)(872, 915, 1020)(873, 1035, 927)(881, 942, 1062)(889, 933, 1078)(892, 1018, 949)(895, 1025, 1032)(897, 1006, 973)(904, 990, 1049)(907, 1010, 1073)(908, 1045, 1009)(910, 1054, 1075)(920, 1019, 964)(921, 1067, 1072)(922, 993, 1000)(924, 940, 1003)(925, 1066, 1024)(931, 1034, 962)(934, 1084, 1065)(935, 1013, 965)(937, 1055, 1008)(939, 1041, 1091)(945, 1021, 1076)(947, 1028, 987)(953, 1069, 1023)(955, 989, 982)(956, 1029, 985)(958, 1086, 1044)(959, 978, 972)(961, 984, 1039)(963, 1007, 1060)(968, 1031, 1070)(970, 1089, 1064)(976, 1082, 1077)(980, 1074, 1083)(983, 1056, 1030)(988, 1061, 1092)(991, 1087, 1048)(994, 1090, 999)(997, 1071, 1053)(1002, 1033, 1088)(1015, 1058, 1081)(1027, 1040, 1050)(1036, 1079, 1059)(1093, 1094)(1095, 1099)(1096, 1100)(1097, 1101)(1098, 1102)(1103, 1111)(1104, 1112)(1105, 1113)(1106, 1114)(1107, 1115)(1108, 1116)(1109, 1117)(1110, 1118)(1119, 1135)(1120, 1136)(1121, 1137)(1122, 1138)(1123, 1139)(1124, 1140)(1125, 1141)(1126, 1142)(1127, 1143)(1128, 1144)(1129, 1145)(1130, 1146)(1131, 1147)(1132, 1148)(1133, 1149)(1134, 1150)(1151, 1177)(1152, 1178)(1153, 1179)(1154, 1180)(1155, 1181)(1156, 1182)(1157, 1158)(1159, 1183)(1160, 1184)(1161, 1185)(1162, 1186)(1163, 1187)(1164, 1188)(1165, 1189)(1166, 1190)(1167, 1191)(1168, 1192)(1169, 1193)(1170, 1171)(1172, 1194)(1173, 1195)(1174, 1196)(1175, 1197)(1176, 1198)(1199, 1243)(1200, 1244)(1201, 1245)(1202, 1246)(1203, 1247)(1204, 1205)(1206, 1248)(1207, 1249)(1208, 1250)(1209, 1251)(1210, 1252)(1211, 1253)(1212, 1254)(1213, 1255)(1214, 1256)(1215, 1257)(1216, 1217)(1218, 1258)(1219, 1259)(1220, 1260)(1221, 1261)(1222, 1262)(1223, 1263)(1224, 1264)(1225, 1265)(1226, 1227)(1228, 1266)(1229, 1267)(1230, 1268)(1231, 1269)(1232, 1270)(1233, 1271)(1234, 1272)(1235, 1273)(1236, 1274)(1237, 1275)(1238, 1239)(1240, 1276)(1241, 1277)(1242, 1278)(1279, 1350)(1280, 1351)(1281, 1352)(1282, 1283)(1284, 1353)(1285, 1354)(1286, 1355)(1287, 1356)(1288, 1357)(1289, 1358)(1290, 1359)(1291, 1360)(1292, 1361)(1293, 1362)(1294, 1295)(1296, 1363)(1297, 1364)(1298, 1365)(1299, 1366)(1300, 1367)(1301, 1368)(1302, 1303)(1304, 1369)(1305, 1370)(1306, 1371)(1307, 1372)(1308, 1373)(1309, 1374)(1310, 1375)(1311, 1376)(1312, 1377)(1313, 1378)(1314, 1315)(1316, 1379)(1317, 1380)(1318, 1319)(1320, 1552)(1321, 1553)(1322, 1554)(1323, 1419)(1324, 1557)(1325, 1558)(1326, 1560)(1327, 1519)(1328, 1563)(1329, 1564)(1330, 1331)(1332, 1568)(1333, 1471)(1334, 1570)(1335, 1571)(1336, 1573)(1337, 1574)(1338, 1339)(1340, 1535)(1341, 1578)(1342, 1579)(1343, 1459)(1344, 1582)(1345, 1584)(1346, 1586)(1347, 1453)(1348, 1589)(1349, 1590)(1381, 1633)(1382, 1634)(1383, 1635)(1384, 1636)(1385, 1637)(1386, 1638)(1387, 1639)(1388, 1640)(1389, 1641)(1390, 1642)(1391, 1562)(1392, 1644)(1393, 1580)(1394, 1530)(1395, 1648)(1396, 1540)(1397, 1651)(1398, 1653)(1399, 1655)(1400, 1657)(1401, 1659)(1402, 1661)(1403, 1616)(1404, 1665)(1405, 1545)(1406, 1670)(1407, 1487)(1408, 1491)(1409, 1675)(1410, 1526)(1411, 1588)(1412, 1679)(1413, 1472)(1414, 1476)(1415, 1684)(1416, 1555)(1417, 1685)(1418, 1687)(1420, 1690)(1421, 1694)(1422, 1680)(1423, 1595)(1424, 1697)(1425, 1700)(1426, 1702)(1427, 1705)(1428, 1709)(1429, 1671)(1430, 1632)(1431, 1712)(1432, 1715)(1433, 1481)(1434, 1443)(1435, 1720)(1436, 1721)(1437, 1723)(1438, 1726)(1439, 1448)(1440, 1467)(1441, 1730)(1442, 1496)(1444, 1735)(1445, 1737)(1446, 1739)(1447, 1622)(1449, 1483)(1450, 1746)(1451, 1682)(1452, 1751)(1454, 1753)(1455, 1718)(1456, 1759)(1457, 1649)(1458, 1612)(1460, 1673)(1461, 1764)(1462, 1766)(1463, 1733)(1464, 1771)(1465, 1624)(1466, 1572)(1468, 1777)(1469, 1587)(1470, 1781)(1473, 1522)(1474, 1788)(1475, 1550)(1477, 1794)(1478, 1797)(1479, 1556)(1480, 1601)(1482, 1536)(1484, 1808)(1485, 1544)(1486, 1812)(1488, 1548)(1489, 1818)(1490, 1524)(1492, 1824)(1493, 1827)(1494, 1527)(1495, 1832)(1497, 1609)(1498, 1646)(1499, 1837)(1500, 1839)(1501, 1774)(1502, 1844)(1503, 1516)(1504, 1515)(1505, 1668)(1506, 1848)(1507, 1850)(1508, 1791)(1509, 1855)(1510, 1603)(1511, 1858)(1512, 1860)(1513, 1805)(1514, 1865)(1517, 1677)(1518, 1869)(1520, 1871)(1521, 1821)(1523, 1879)(1525, 1882)(1528, 1887)(1529, 1538)(1531, 1892)(1532, 1895)(1533, 1541)(1534, 1900)(1537, 1906)(1539, 1817)(1542, 1857)(1543, 1915)(1546, 1919)(1547, 1921)(1549, 1926)(1551, 1917)(1559, 1938)(1561, 1576)(1565, 1901)(1566, 1950)(1567, 1581)(1569, 1956)(1575, 1965)(1577, 1787)(1583, 1836)(1585, 1604)(1591, 1982)(1592, 1983)(1593, 1825)(1594, 1778)(1596, 1930)(1597, 1610)(1598, 1988)(1599, 1876)(1600, 1993)(1602, 1995)(1605, 1713)(1606, 1886)(1607, 1974)(1608, 1945)(1611, 1907)(1613, 1890)(1614, 1893)(1615, 1795)(1617, 1874)(1618, 1630)(1619, 2006)(1620, 1903)(1621, 2010)(1623, 2012)(1625, 1985)(1626, 1724)(1627, 1913)(1628, 2016)(1629, 2018)(1631, 1809)(1643, 2013)(1645, 2025)(1647, 2026)(1650, 2029)(1652, 2030)(1654, 2032)(1656, 2033)(1658, 2035)(1660, 2036)(1662, 2038)(1663, 2039)(1664, 2040)(1666, 2041)(1667, 2042)(1669, 2043)(1672, 2045)(1674, 2046)(1676, 2048)(1678, 1990)(1681, 2050)(1683, 2017)(1686, 2052)(1688, 2054)(1689, 2047)(1691, 1954)(1692, 1968)(1693, 2031)(1695, 1962)(1696, 2027)(1698, 1940)(1699, 2034)(1701, 1997)(1703, 2057)(1704, 2051)(1706, 1899)(1707, 1909)(1708, 2037)(1710, 1905)(1711, 2023)(1714, 2008)(1716, 2062)(1717, 2063)(1719, 1870)(1722, 1867)(1725, 1862)(1727, 2068)(1728, 2069)(1729, 2000)(1731, 2072)(1732, 2073)(1734, 1849)(1736, 2076)(1738, 1846)(1740, 1976)(1741, 1841)(1742, 2080)(1743, 1991)(1744, 2079)(1745, 1987)(1747, 2064)(1748, 1925)(1749, 1811)(1750, 2053)(1752, 1807)(1754, 2074)(1755, 2070)(1756, 1831)(1757, 1881)(1758, 2055)(1760, 1878)(1761, 1951)(1762, 1780)(1763, 2056)(1765, 1776)(1767, 2081)(1768, 1801)(1769, 1928)(1770, 2060)(1772, 1896)(1773, 2094)(1775, 2097)(1779, 2099)(1782, 2101)(1783, 2103)(1784, 1852)(1785, 2104)(1786, 1986)(1789, 2107)(1790, 2109)(1792, 2111)(1793, 1838)(1796, 2113)(1798, 1835)(1799, 2116)(1800, 2118)(1802, 2119)(1803, 1863)(1804, 1999)(1806, 2121)(1810, 2123)(1813, 2124)(1814, 2114)(1815, 1873)(1816, 2019)(1819, 2128)(1820, 1936)(1822, 2131)(1823, 1859)(1826, 2133)(1828, 1856)(1829, 1937)(1830, 2138)(1833, 2007)(1834, 1842)(1840, 2105)(1843, 2075)(1845, 1922)(1847, 1946)(1851, 2120)(1853, 1902)(1854, 2089)(1861, 2126)(1864, 2065)(1866, 1984)(1868, 2077)(1872, 2095)(1875, 2083)(1877, 2147)(1880, 2148)(1883, 1970)(1884, 1932)(1885, 2003)(1888, 2002)(1889, 2078)(1891, 2152)(1894, 2154)(1897, 2157)(1898, 2159)(1904, 2161)(1908, 2163)(1910, 2165)(1911, 1977)(1912, 1929)(1914, 1971)(1916, 2087)(1918, 2168)(1920, 1941)(1923, 1935)(1924, 2170)(1927, 1989)(1931, 2058)(1933, 2067)(1934, 2088)(1939, 2082)(1942, 2066)(1943, 1957)(1944, 2162)(1947, 2140)(1948, 1963)(1949, 2009)(1952, 2164)(1953, 2176)(1955, 1966)(1958, 2142)(1959, 1975)(1960, 1973)(1961, 2178)(1964, 1992)(1967, 2179)(1969, 2180)(1972, 2135)(1978, 2093)(1979, 2183)(1980, 1994)(1981, 2096)(1996, 2171)(1998, 2100)(2001, 2108)(2004, 2086)(2005, 2139)(2011, 2160)(2014, 2146)(2015, 2115)(2020, 2085)(2021, 2091)(2022, 2145)(2024, 2122)(2028, 2098)(2044, 2112)(2049, 2132)(2059, 2129)(2061, 2153)(2071, 2174)(2084, 2090)(2092, 2177)(2102, 2173)(2106, 2181)(2110, 2149)(2117, 2175)(2125, 2151)(2127, 2166)(2130, 2155)(2134, 2143)(2136, 2144)(2137, 2156)(2141, 2182)(2150, 2167)(2158, 2169)(2172, 2184) L = (1, 1093)(2, 1094)(3, 1095)(4, 1096)(5, 1097)(6, 1098)(7, 1099)(8, 1100)(9, 1101)(10, 1102)(11, 1103)(12, 1104)(13, 1105)(14, 1106)(15, 1107)(16, 1108)(17, 1109)(18, 1110)(19, 1111)(20, 1112)(21, 1113)(22, 1114)(23, 1115)(24, 1116)(25, 1117)(26, 1118)(27, 1119)(28, 1120)(29, 1121)(30, 1122)(31, 1123)(32, 1124)(33, 1125)(34, 1126)(35, 1127)(36, 1128)(37, 1129)(38, 1130)(39, 1131)(40, 1132)(41, 1133)(42, 1134)(43, 1135)(44, 1136)(45, 1137)(46, 1138)(47, 1139)(48, 1140)(49, 1141)(50, 1142)(51, 1143)(52, 1144)(53, 1145)(54, 1146)(55, 1147)(56, 1148)(57, 1149)(58, 1150)(59, 1151)(60, 1152)(61, 1153)(62, 1154)(63, 1155)(64, 1156)(65, 1157)(66, 1158)(67, 1159)(68, 1160)(69, 1161)(70, 1162)(71, 1163)(72, 1164)(73, 1165)(74, 1166)(75, 1167)(76, 1168)(77, 1169)(78, 1170)(79, 1171)(80, 1172)(81, 1173)(82, 1174)(83, 1175)(84, 1176)(85, 1177)(86, 1178)(87, 1179)(88, 1180)(89, 1181)(90, 1182)(91, 1183)(92, 1184)(93, 1185)(94, 1186)(95, 1187)(96, 1188)(97, 1189)(98, 1190)(99, 1191)(100, 1192)(101, 1193)(102, 1194)(103, 1195)(104, 1196)(105, 1197)(106, 1198)(107, 1199)(108, 1200)(109, 1201)(110, 1202)(111, 1203)(112, 1204)(113, 1205)(114, 1206)(115, 1207)(116, 1208)(117, 1209)(118, 1210)(119, 1211)(120, 1212)(121, 1213)(122, 1214)(123, 1215)(124, 1216)(125, 1217)(126, 1218)(127, 1219)(128, 1220)(129, 1221)(130, 1222)(131, 1223)(132, 1224)(133, 1225)(134, 1226)(135, 1227)(136, 1228)(137, 1229)(138, 1230)(139, 1231)(140, 1232)(141, 1233)(142, 1234)(143, 1235)(144, 1236)(145, 1237)(146, 1238)(147, 1239)(148, 1240)(149, 1241)(150, 1242)(151, 1243)(152, 1244)(153, 1245)(154, 1246)(155, 1247)(156, 1248)(157, 1249)(158, 1250)(159, 1251)(160, 1252)(161, 1253)(162, 1254)(163, 1255)(164, 1256)(165, 1257)(166, 1258)(167, 1259)(168, 1260)(169, 1261)(170, 1262)(171, 1263)(172, 1264)(173, 1265)(174, 1266)(175, 1267)(176, 1268)(177, 1269)(178, 1270)(179, 1271)(180, 1272)(181, 1273)(182, 1274)(183, 1275)(184, 1276)(185, 1277)(186, 1278)(187, 1279)(188, 1280)(189, 1281)(190, 1282)(191, 1283)(192, 1284)(193, 1285)(194, 1286)(195, 1287)(196, 1288)(197, 1289)(198, 1290)(199, 1291)(200, 1292)(201, 1293)(202, 1294)(203, 1295)(204, 1296)(205, 1297)(206, 1298)(207, 1299)(208, 1300)(209, 1301)(210, 1302)(211, 1303)(212, 1304)(213, 1305)(214, 1306)(215, 1307)(216, 1308)(217, 1309)(218, 1310)(219, 1311)(220, 1312)(221, 1313)(222, 1314)(223, 1315)(224, 1316)(225, 1317)(226, 1318)(227, 1319)(228, 1320)(229, 1321)(230, 1322)(231, 1323)(232, 1324)(233, 1325)(234, 1326)(235, 1327)(236, 1328)(237, 1329)(238, 1330)(239, 1331)(240, 1332)(241, 1333)(242, 1334)(243, 1335)(244, 1336)(245, 1337)(246, 1338)(247, 1339)(248, 1340)(249, 1341)(250, 1342)(251, 1343)(252, 1344)(253, 1345)(254, 1346)(255, 1347)(256, 1348)(257, 1349)(258, 1350)(259, 1351)(260, 1352)(261, 1353)(262, 1354)(263, 1355)(264, 1356)(265, 1357)(266, 1358)(267, 1359)(268, 1360)(269, 1361)(270, 1362)(271, 1363)(272, 1364)(273, 1365)(274, 1366)(275, 1367)(276, 1368)(277, 1369)(278, 1370)(279, 1371)(280, 1372)(281, 1373)(282, 1374)(283, 1375)(284, 1376)(285, 1377)(286, 1378)(287, 1379)(288, 1380)(289, 1381)(290, 1382)(291, 1383)(292, 1384)(293, 1385)(294, 1386)(295, 1387)(296, 1388)(297, 1389)(298, 1390)(299, 1391)(300, 1392)(301, 1393)(302, 1394)(303, 1395)(304, 1396)(305, 1397)(306, 1398)(307, 1399)(308, 1400)(309, 1401)(310, 1402)(311, 1403)(312, 1404)(313, 1405)(314, 1406)(315, 1407)(316, 1408)(317, 1409)(318, 1410)(319, 1411)(320, 1412)(321, 1413)(322, 1414)(323, 1415)(324, 1416)(325, 1417)(326, 1418)(327, 1419)(328, 1420)(329, 1421)(330, 1422)(331, 1423)(332, 1424)(333, 1425)(334, 1426)(335, 1427)(336, 1428)(337, 1429)(338, 1430)(339, 1431)(340, 1432)(341, 1433)(342, 1434)(343, 1435)(344, 1436)(345, 1437)(346, 1438)(347, 1439)(348, 1440)(349, 1441)(350, 1442)(351, 1443)(352, 1444)(353, 1445)(354, 1446)(355, 1447)(356, 1448)(357, 1449)(358, 1450)(359, 1451)(360, 1452)(361, 1453)(362, 1454)(363, 1455)(364, 1456)(365, 1457)(366, 1458)(367, 1459)(368, 1460)(369, 1461)(370, 1462)(371, 1463)(372, 1464)(373, 1465)(374, 1466)(375, 1467)(376, 1468)(377, 1469)(378, 1470)(379, 1471)(380, 1472)(381, 1473)(382, 1474)(383, 1475)(384, 1476)(385, 1477)(386, 1478)(387, 1479)(388, 1480)(389, 1481)(390, 1482)(391, 1483)(392, 1484)(393, 1485)(394, 1486)(395, 1487)(396, 1488)(397, 1489)(398, 1490)(399, 1491)(400, 1492)(401, 1493)(402, 1494)(403, 1495)(404, 1496)(405, 1497)(406, 1498)(407, 1499)(408, 1500)(409, 1501)(410, 1502)(411, 1503)(412, 1504)(413, 1505)(414, 1506)(415, 1507)(416, 1508)(417, 1509)(418, 1510)(419, 1511)(420, 1512)(421, 1513)(422, 1514)(423, 1515)(424, 1516)(425, 1517)(426, 1518)(427, 1519)(428, 1520)(429, 1521)(430, 1522)(431, 1523)(432, 1524)(433, 1525)(434, 1526)(435, 1527)(436, 1528)(437, 1529)(438, 1530)(439, 1531)(440, 1532)(441, 1533)(442, 1534)(443, 1535)(444, 1536)(445, 1537)(446, 1538)(447, 1539)(448, 1540)(449, 1541)(450, 1542)(451, 1543)(452, 1544)(453, 1545)(454, 1546)(455, 1547)(456, 1548)(457, 1549)(458, 1550)(459, 1551)(460, 1552)(461, 1553)(462, 1554)(463, 1555)(464, 1556)(465, 1557)(466, 1558)(467, 1559)(468, 1560)(469, 1561)(470, 1562)(471, 1563)(472, 1564)(473, 1565)(474, 1566)(475, 1567)(476, 1568)(477, 1569)(478, 1570)(479, 1571)(480, 1572)(481, 1573)(482, 1574)(483, 1575)(484, 1576)(485, 1577)(486, 1578)(487, 1579)(488, 1580)(489, 1581)(490, 1582)(491, 1583)(492, 1584)(493, 1585)(494, 1586)(495, 1587)(496, 1588)(497, 1589)(498, 1590)(499, 1591)(500, 1592)(501, 1593)(502, 1594)(503, 1595)(504, 1596)(505, 1597)(506, 1598)(507, 1599)(508, 1600)(509, 1601)(510, 1602)(511, 1603)(512, 1604)(513, 1605)(514, 1606)(515, 1607)(516, 1608)(517, 1609)(518, 1610)(519, 1611)(520, 1612)(521, 1613)(522, 1614)(523, 1615)(524, 1616)(525, 1617)(526, 1618)(527, 1619)(528, 1620)(529, 1621)(530, 1622)(531, 1623)(532, 1624)(533, 1625)(534, 1626)(535, 1627)(536, 1628)(537, 1629)(538, 1630)(539, 1631)(540, 1632)(541, 1633)(542, 1634)(543, 1635)(544, 1636)(545, 1637)(546, 1638)(547, 1639)(548, 1640)(549, 1641)(550, 1642)(551, 1643)(552, 1644)(553, 1645)(554, 1646)(555, 1647)(556, 1648)(557, 1649)(558, 1650)(559, 1651)(560, 1652)(561, 1653)(562, 1654)(563, 1655)(564, 1656)(565, 1657)(566, 1658)(567, 1659)(568, 1660)(569, 1661)(570, 1662)(571, 1663)(572, 1664)(573, 1665)(574, 1666)(575, 1667)(576, 1668)(577, 1669)(578, 1670)(579, 1671)(580, 1672)(581, 1673)(582, 1674)(583, 1675)(584, 1676)(585, 1677)(586, 1678)(587, 1679)(588, 1680)(589, 1681)(590, 1682)(591, 1683)(592, 1684)(593, 1685)(594, 1686)(595, 1687)(596, 1688)(597, 1689)(598, 1690)(599, 1691)(600, 1692)(601, 1693)(602, 1694)(603, 1695)(604, 1696)(605, 1697)(606, 1698)(607, 1699)(608, 1700)(609, 1701)(610, 1702)(611, 1703)(612, 1704)(613, 1705)(614, 1706)(615, 1707)(616, 1708)(617, 1709)(618, 1710)(619, 1711)(620, 1712)(621, 1713)(622, 1714)(623, 1715)(624, 1716)(625, 1717)(626, 1718)(627, 1719)(628, 1720)(629, 1721)(630, 1722)(631, 1723)(632, 1724)(633, 1725)(634, 1726)(635, 1727)(636, 1728)(637, 1729)(638, 1730)(639, 1731)(640, 1732)(641, 1733)(642, 1734)(643, 1735)(644, 1736)(645, 1737)(646, 1738)(647, 1739)(648, 1740)(649, 1741)(650, 1742)(651, 1743)(652, 1744)(653, 1745)(654, 1746)(655, 1747)(656, 1748)(657, 1749)(658, 1750)(659, 1751)(660, 1752)(661, 1753)(662, 1754)(663, 1755)(664, 1756)(665, 1757)(666, 1758)(667, 1759)(668, 1760)(669, 1761)(670, 1762)(671, 1763)(672, 1764)(673, 1765)(674, 1766)(675, 1767)(676, 1768)(677, 1769)(678, 1770)(679, 1771)(680, 1772)(681, 1773)(682, 1774)(683, 1775)(684, 1776)(685, 1777)(686, 1778)(687, 1779)(688, 1780)(689, 1781)(690, 1782)(691, 1783)(692, 1784)(693, 1785)(694, 1786)(695, 1787)(696, 1788)(697, 1789)(698, 1790)(699, 1791)(700, 1792)(701, 1793)(702, 1794)(703, 1795)(704, 1796)(705, 1797)(706, 1798)(707, 1799)(708, 1800)(709, 1801)(710, 1802)(711, 1803)(712, 1804)(713, 1805)(714, 1806)(715, 1807)(716, 1808)(717, 1809)(718, 1810)(719, 1811)(720, 1812)(721, 1813)(722, 1814)(723, 1815)(724, 1816)(725, 1817)(726, 1818)(727, 1819)(728, 1820)(729, 1821)(730, 1822)(731, 1823)(732, 1824)(733, 1825)(734, 1826)(735, 1827)(736, 1828)(737, 1829)(738, 1830)(739, 1831)(740, 1832)(741, 1833)(742, 1834)(743, 1835)(744, 1836)(745, 1837)(746, 1838)(747, 1839)(748, 1840)(749, 1841)(750, 1842)(751, 1843)(752, 1844)(753, 1845)(754, 1846)(755, 1847)(756, 1848)(757, 1849)(758, 1850)(759, 1851)(760, 1852)(761, 1853)(762, 1854)(763, 1855)(764, 1856)(765, 1857)(766, 1858)(767, 1859)(768, 1860)(769, 1861)(770, 1862)(771, 1863)(772, 1864)(773, 1865)(774, 1866)(775, 1867)(776, 1868)(777, 1869)(778, 1870)(779, 1871)(780, 1872)(781, 1873)(782, 1874)(783, 1875)(784, 1876)(785, 1877)(786, 1878)(787, 1879)(788, 1880)(789, 1881)(790, 1882)(791, 1883)(792, 1884)(793, 1885)(794, 1886)(795, 1887)(796, 1888)(797, 1889)(798, 1890)(799, 1891)(800, 1892)(801, 1893)(802, 1894)(803, 1895)(804, 1896)(805, 1897)(806, 1898)(807, 1899)(808, 1900)(809, 1901)(810, 1902)(811, 1903)(812, 1904)(813, 1905)(814, 1906)(815, 1907)(816, 1908)(817, 1909)(818, 1910)(819, 1911)(820, 1912)(821, 1913)(822, 1914)(823, 1915)(824, 1916)(825, 1917)(826, 1918)(827, 1919)(828, 1920)(829, 1921)(830, 1922)(831, 1923)(832, 1924)(833, 1925)(834, 1926)(835, 1927)(836, 1928)(837, 1929)(838, 1930)(839, 1931)(840, 1932)(841, 1933)(842, 1934)(843, 1935)(844, 1936)(845, 1937)(846, 1938)(847, 1939)(848, 1940)(849, 1941)(850, 1942)(851, 1943)(852, 1944)(853, 1945)(854, 1946)(855, 1947)(856, 1948)(857, 1949)(858, 1950)(859, 1951)(860, 1952)(861, 1953)(862, 1954)(863, 1955)(864, 1956)(865, 1957)(866, 1958)(867, 1959)(868, 1960)(869, 1961)(870, 1962)(871, 1963)(872, 1964)(873, 1965)(874, 1966)(875, 1967)(876, 1968)(877, 1969)(878, 1970)(879, 1971)(880, 1972)(881, 1973)(882, 1974)(883, 1975)(884, 1976)(885, 1977)(886, 1978)(887, 1979)(888, 1980)(889, 1981)(890, 1982)(891, 1983)(892, 1984)(893, 1985)(894, 1986)(895, 1987)(896, 1988)(897, 1989)(898, 1990)(899, 1991)(900, 1992)(901, 1993)(902, 1994)(903, 1995)(904, 1996)(905, 1997)(906, 1998)(907, 1999)(908, 2000)(909, 2001)(910, 2002)(911, 2003)(912, 2004)(913, 2005)(914, 2006)(915, 2007)(916, 2008)(917, 2009)(918, 2010)(919, 2011)(920, 2012)(921, 2013)(922, 2014)(923, 2015)(924, 2016)(925, 2017)(926, 2018)(927, 2019)(928, 2020)(929, 2021)(930, 2022)(931, 2023)(932, 2024)(933, 2025)(934, 2026)(935, 2027)(936, 2028)(937, 2029)(938, 2030)(939, 2031)(940, 2032)(941, 2033)(942, 2034)(943, 2035)(944, 2036)(945, 2037)(946, 2038)(947, 2039)(948, 2040)(949, 2041)(950, 2042)(951, 2043)(952, 2044)(953, 2045)(954, 2046)(955, 2047)(956, 2048)(957, 2049)(958, 2050)(959, 2051)(960, 2052)(961, 2053)(962, 2054)(963, 2055)(964, 2056)(965, 2057)(966, 2058)(967, 2059)(968, 2060)(969, 2061)(970, 2062)(971, 2063)(972, 2064)(973, 2065)(974, 2066)(975, 2067)(976, 2068)(977, 2069)(978, 2070)(979, 2071)(980, 2072)(981, 2073)(982, 2074)(983, 2075)(984, 2076)(985, 2077)(986, 2078)(987, 2079)(988, 2080)(989, 2081)(990, 2082)(991, 2083)(992, 2084)(993, 2085)(994, 2086)(995, 2087)(996, 2088)(997, 2089)(998, 2090)(999, 2091)(1000, 2092)(1001, 2093)(1002, 2094)(1003, 2095)(1004, 2096)(1005, 2097)(1006, 2098)(1007, 2099)(1008, 2100)(1009, 2101)(1010, 2102)(1011, 2103)(1012, 2104)(1013, 2105)(1014, 2106)(1015, 2107)(1016, 2108)(1017, 2109)(1018, 2110)(1019, 2111)(1020, 2112)(1021, 2113)(1022, 2114)(1023, 2115)(1024, 2116)(1025, 2117)(1026, 2118)(1027, 2119)(1028, 2120)(1029, 2121)(1030, 2122)(1031, 2123)(1032, 2124)(1033, 2125)(1034, 2126)(1035, 2127)(1036, 2128)(1037, 2129)(1038, 2130)(1039, 2131)(1040, 2132)(1041, 2133)(1042, 2134)(1043, 2135)(1044, 2136)(1045, 2137)(1046, 2138)(1047, 2139)(1048, 2140)(1049, 2141)(1050, 2142)(1051, 2143)(1052, 2144)(1053, 2145)(1054, 2146)(1055, 2147)(1056, 2148)(1057, 2149)(1058, 2150)(1059, 2151)(1060, 2152)(1061, 2153)(1062, 2154)(1063, 2155)(1064, 2156)(1065, 2157)(1066, 2158)(1067, 2159)(1068, 2160)(1069, 2161)(1070, 2162)(1071, 2163)(1072, 2164)(1073, 2165)(1074, 2166)(1075, 2167)(1076, 2168)(1077, 2169)(1078, 2170)(1079, 2171)(1080, 2172)(1081, 2173)(1082, 2174)(1083, 2175)(1084, 2176)(1085, 2177)(1086, 2178)(1087, 2179)(1088, 2180)(1089, 2181)(1090, 2182)(1091, 2183)(1092, 2184) local type(s) :: { ( 14, 14 ), ( 14^3 ) } Outer automorphisms :: reflexible Dual of E14.632 Transitivity :: ET+ Graph:: simple bipartite v = 910 e = 1092 f = 156 degree seq :: [ 2^546, 3^364 ] E14.620 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1)^7, (T1 * T2^-1 * T1 * T2)^6 ] Map:: polytopal R = (1, 3, 4)(2, 5, 6)(7, 11, 12)(8, 13, 14)(9, 15, 16)(10, 17, 18)(19, 27, 28)(20, 29, 30)(21, 31, 32)(22, 33, 34)(23, 35, 36)(24, 37, 38)(25, 39, 40)(26, 41, 42)(43, 58, 59)(44, 60, 61)(45, 62, 63)(46, 64, 65)(47, 66, 67)(48, 68, 69)(49, 70, 71)(50, 72, 51)(52, 73, 74)(53, 75, 76)(54, 77, 78)(55, 79, 80)(56, 81, 82)(57, 83, 84)(85, 107, 108)(86, 109, 110)(87, 111, 112)(88, 113, 114)(89, 115, 116)(90, 117, 118)(91, 119, 120)(92, 121, 122)(93, 123, 124)(94, 125, 126)(95, 127, 128)(96, 129, 130)(97, 131, 132)(98, 133, 134)(99, 135, 136)(100, 137, 138)(101, 139, 140)(102, 141, 142)(103, 143, 144)(104, 145, 146)(105, 147, 148)(106, 149, 150)(151, 187, 188)(152, 189, 190)(153, 191, 192)(154, 193, 194)(155, 195, 196)(156, 197, 198)(157, 199, 200)(158, 201, 202)(159, 203, 204)(160, 205, 206)(161, 207, 208)(162, 209, 210)(163, 211, 212)(164, 213, 214)(165, 215, 216)(166, 217, 218)(167, 219, 220)(168, 221, 222)(169, 223, 224)(170, 225, 226)(171, 227, 228)(172, 229, 230)(173, 231, 232)(174, 233, 234)(175, 235, 236)(176, 237, 238)(177, 239, 240)(178, 241, 242)(179, 243, 244)(180, 245, 246)(181, 247, 248)(182, 249, 250)(183, 251, 252)(184, 253, 254)(185, 255, 256)(186, 257, 258)(259, 509, 907)(260, 511, 911)(261, 513, 918)(262, 515, 283)(263, 288, 544)(264, 399, 768)(265, 437, 781)(266, 517, 923)(267, 310, 589)(268, 305, 404)(269, 519, 392)(270, 521, 929)(271, 523, 930)(272, 322, 273)(274, 525, 934)(275, 527, 936)(276, 529, 942)(277, 293, 561)(278, 436, 825)(279, 454, 698)(280, 531, 945)(281, 299, 576)(282, 321, 409)(284, 534, 429)(285, 536, 952)(286, 538, 955)(287, 541, 462)(289, 547, 549)(290, 551, 552)(291, 554, 556)(292, 558, 559)(294, 526, 494)(295, 565, 501)(296, 568, 471)(297, 570, 572)(298, 506, 574)(300, 579, 432)(301, 581, 583)(302, 452, 585)(303, 413, 472)(304, 510, 588)(306, 537, 591)(307, 593, 450)(308, 584, 596)(309, 397, 598)(311, 467, 395)(312, 597, 604)(313, 434, 605)(314, 607, 502)(315, 573, 610)(316, 377, 612)(317, 586, 470)(318, 430, 375)(319, 611, 618)(320, 474, 619)(323, 420, 623)(324, 522, 625)(325, 418, 503)(326, 484, 403)(327, 411, 629)(328, 631, 518)(329, 634, 635)(330, 557, 638)(331, 345, 498)(332, 587, 641)(333, 448, 343)(334, 639, 645)(335, 533, 646)(336, 648, 649)(337, 567, 652)(338, 366, 654)(339, 563, 656)(340, 393, 364)(341, 653, 659)(342, 550, 662)(344, 590, 665)(346, 663, 669)(347, 670, 671)(348, 673, 674)(349, 578, 677)(350, 386, 678)(351, 560, 680)(352, 373, 384)(353, 683, 408)(354, 361, 686)(355, 688, 532)(356, 691, 359)(357, 406, 694)(358, 696, 417)(360, 700, 702)(362, 415, 706)(363, 540, 709)(365, 622, 712)(367, 710, 716)(368, 717, 719)(369, 721, 722)(370, 592, 725)(371, 423, 726)(372, 475, 727)(374, 546, 731)(376, 624, 734)(378, 732, 738)(379, 739, 464)(380, 742, 463)(381, 601, 745)(382, 442, 679)(383, 543, 746)(385, 628, 749)(387, 747, 753)(388, 754, 733)(389, 756, 757)(390, 606, 760)(391, 455, 708)(394, 553, 763)(396, 630, 744)(398, 764, 767)(400, 730, 428)(401, 615, 771)(402, 487, 655)(405, 775, 777)(407, 514, 780)(410, 783, 785)(412, 530, 788)(414, 792, 794)(416, 720, 798)(419, 801, 803)(421, 806, 808)(422, 685, 497)(424, 681, 812)(425, 813, 664)(426, 814, 815)(427, 633, 818)(431, 564, 820)(433, 687, 676)(435, 821, 824)(438, 661, 447)(439, 642, 829)(440, 830, 614)(441, 693, 752)(443, 728, 834)(444, 835, 711)(445, 837, 838)(446, 647, 841)(449, 569, 844)(451, 695, 724)(453, 845, 847)(456, 657, 850)(457, 851, 640)(458, 797, 852)(459, 853, 854)(460, 855, 505)(461, 658, 859)(465, 507, 861)(466, 478, 799)(468, 862, 863)(469, 575, 865)(473, 699, 651)(476, 866, 869)(477, 870, 496)(479, 632, 872)(480, 637, 495)(481, 873, 875)(482, 666, 877)(483, 878, 600)(485, 705, 715)(486, 562, 881)(488, 883, 885)(489, 761, 887)(490, 888, 748)(491, 807, 890)(492, 891, 892)(493, 672, 895)(499, 899, 900)(500, 580, 902)(504, 682, 759)(508, 903, 906)(512, 915, 913)(516, 741, 921)(520, 927, 926)(524, 905, 931)(528, 939, 937)(535, 950, 856)(539, 959, 957)(542, 962, 961)(545, 964, 963)(548, 967, 966)(555, 973, 972)(566, 898, 978)(571, 982, 981)(577, 842, 987)(582, 991, 938)(594, 876, 857)(595, 897, 791)(599, 1001, 943)(602, 1004, 953)(603, 1006, 914)(608, 828, 816)(609, 920, 774)(613, 1014, 932)(616, 1018, 908)(617, 1020, 958)(620, 894, 912)(621, 1023, 1024)(626, 840, 956)(627, 1027, 879)(636, 849, 839)(643, 1035, 901)(644, 1016, 805)(650, 770, 758)(660, 811, 893)(667, 1047, 843)(668, 946, 787)(675, 743, 723)(684, 1022, 1045)(689, 998, 1013)(690, 817, 904)(692, 1037, 1053)(697, 1008, 1033)(701, 1009, 1000)(703, 858, 1060)(704, 1039, 1051)(707, 833, 796)(713, 1063, 827)(714, 1065, 762)(718, 1025, 1007)(729, 751, 922)(735, 1057, 848)(736, 1070, 819)(737, 886, 779)(740, 1026, 992)(750, 1073, 871)(755, 1028, 1021)(765, 1050, 809)(766, 1077, 864)(769, 924, 983)(772, 933, 860)(773, 1078, 1079)(776, 993, 990)(778, 1011, 1049)(782, 960, 969)(784, 999, 994)(786, 1031, 1029)(789, 1083, 925)(790, 1084, 867)(793, 984, 948)(795, 997, 1041)(800, 916, 975)(802, 1012, 985)(804, 1043, 941)(810, 1087, 1067)(822, 1054, 831)(823, 1059, 968)(826, 947, 974)(832, 1090, 1072)(836, 1055, 1015)(846, 1080, 874)(868, 940, 880)(882, 1091, 1062)(884, 1056, 1082)(889, 1061, 1002)(896, 935, 1089)(909, 1092, 949)(910, 1075, 995)(917, 954, 1068)(919, 1005, 1017)(928, 1032, 976)(944, 989, 1034)(951, 1040, 979)(965, 1074, 1069)(970, 1088, 1044)(971, 1064, 1076)(977, 1058, 1085)(980, 1046, 1086)(986, 1052, 1081)(988, 1071, 1036)(996, 1048, 1042)(1003, 1066, 1019)(1010, 1038, 1030)(1093, 1094)(1095, 1099)(1096, 1100)(1097, 1101)(1098, 1102)(1103, 1111)(1104, 1112)(1105, 1113)(1106, 1114)(1107, 1115)(1108, 1116)(1109, 1117)(1110, 1118)(1119, 1135)(1120, 1136)(1121, 1137)(1122, 1138)(1123, 1139)(1124, 1140)(1125, 1141)(1126, 1142)(1127, 1143)(1128, 1144)(1129, 1145)(1130, 1146)(1131, 1147)(1132, 1148)(1133, 1149)(1134, 1150)(1151, 1177)(1152, 1178)(1153, 1179)(1154, 1180)(1155, 1181)(1156, 1182)(1157, 1158)(1159, 1183)(1160, 1184)(1161, 1185)(1162, 1186)(1163, 1187)(1164, 1188)(1165, 1189)(1166, 1190)(1167, 1191)(1168, 1192)(1169, 1193)(1170, 1171)(1172, 1194)(1173, 1195)(1174, 1196)(1175, 1197)(1176, 1198)(1199, 1243)(1200, 1244)(1201, 1245)(1202, 1246)(1203, 1247)(1204, 1205)(1206, 1248)(1207, 1249)(1208, 1250)(1209, 1251)(1210, 1252)(1211, 1253)(1212, 1254)(1213, 1255)(1214, 1256)(1215, 1257)(1216, 1217)(1218, 1258)(1219, 1259)(1220, 1260)(1221, 1261)(1222, 1262)(1223, 1263)(1224, 1264)(1225, 1265)(1226, 1227)(1228, 1266)(1229, 1267)(1230, 1268)(1231, 1269)(1232, 1270)(1233, 1271)(1234, 1272)(1235, 1273)(1236, 1274)(1237, 1275)(1238, 1239)(1240, 1276)(1241, 1277)(1242, 1278)(1279, 1350)(1280, 1351)(1281, 1352)(1282, 1283)(1284, 1353)(1285, 1354)(1286, 1355)(1287, 1356)(1288, 1357)(1289, 1358)(1290, 1359)(1291, 1360)(1292, 1328)(1293, 1361)(1294, 1295)(1296, 1362)(1297, 1363)(1298, 1364)(1299, 1365)(1300, 1366)(1301, 1367)(1302, 1303)(1304, 1368)(1305, 1341)(1306, 1369)(1307, 1370)(1308, 1371)(1309, 1372)(1310, 1373)(1311, 1374)(1312, 1375)(1313, 1376)(1314, 1315)(1316, 1377)(1317, 1378)(1318, 1319)(1320, 1550)(1321, 1552)(1322, 1554)(1323, 1556)(1324, 1558)(1325, 1560)(1326, 1562)(1327, 1564)(1329, 1567)(1330, 1331)(1332, 1571)(1333, 1573)(1334, 1495)(1335, 1576)(1336, 1578)(1337, 1580)(1338, 1339)(1340, 1583)(1342, 1586)(1343, 1588)(1344, 1589)(1345, 1591)(1346, 1593)(1347, 1595)(1348, 1597)(1349, 1599)(1379, 1632)(1380, 1635)(1381, 1638)(1382, 1642)(1383, 1645)(1384, 1649)(1385, 1652)(1386, 1655)(1387, 1656)(1388, 1659)(1389, 1661)(1390, 1665)(1391, 1667)(1392, 1670)(1393, 1672)(1394, 1676)(1395, 1678)(1396, 1679)(1397, 1681)(1398, 1682)(1399, 1684)(1400, 1686)(1401, 1689)(1402, 1691)(1403, 1693)(1404, 1694)(1405, 1673)(1406, 1698)(1407, 1700)(1408, 1703)(1409, 1705)(1410, 1707)(1411, 1708)(1412, 1662)(1413, 1668)(1414, 1712)(1415, 1714)(1416, 1716)(1417, 1657)(1418, 1718)(1419, 1720)(1420, 1722)(1421, 1725)(1422, 1728)(1423, 1731)(1424, 1709)(1425, 1734)(1426, 1735)(1427, 1646)(1428, 1739)(1429, 1742)(1430, 1745)(1431, 1736)(1432, 1749)(1433, 1750)(1434, 1752)(1435, 1755)(1436, 1695)(1437, 1758)(1438, 1759)(1439, 1639)(1440, 1764)(1441, 1767)(1442, 1726)(1443, 1760)(1444, 1773)(1445, 1774)(1446, 1777)(1447, 1779)(1448, 1782)(1449, 1785)(1450, 1787)(1451, 1790)(1452, 1791)(1453, 1795)(1454, 1797)(1455, 1799)(1456, 1802)(1457, 1674)(1458, 1805)(1459, 1806)(1460, 1643)(1461, 1812)(1462, 1815)(1463, 1740)(1464, 1807)(1465, 1820)(1466, 1821)(1467, 1824)(1468, 1687)(1469, 1827)(1470, 1828)(1471, 1633)(1472, 1833)(1473, 1835)(1474, 1699)(1475, 1829)(1476, 1839)(1477, 1663)(1478, 1842)(1479, 1843)(1480, 1650)(1481, 1606)(1482, 1850)(1483, 1765)(1484, 1844)(1485, 1853)(1486, 1854)(1487, 1856)(1488, 1701)(1489, 1857)(1490, 1858)(1491, 1636)(1492, 1627)(1493, 1862)(1494, 1685)(1496, 1864)(1497, 1866)(1498, 1584)(1499, 1871)(1500, 1873)(1501, 1874)(1502, 1572)(1503, 1865)(1504, 1879)(1505, 1881)(1506, 1883)(1507, 1537)(1508, 1888)(1509, 1891)(1510, 1892)(1511, 1530)(1512, 1882)(1513, 1897)(1514, 1647)(1515, 1902)(1516, 1903)(1517, 1660)(1518, 1622)(1519, 1908)(1520, 1813)(1521, 1841)(1522, 1575)(1523, 1911)(1524, 1913)(1525, 1729)(1526, 1914)(1527, 1915)(1528, 1653)(1529, 1634)(1531, 1920)(1532, 1559)(1533, 1658)(1534, 1924)(1535, 1925)(1536, 1598)(1538, 1931)(1539, 1834)(1540, 1934)(1541, 1935)(1542, 1937)(1543, 1743)(1544, 1582)(1545, 1938)(1546, 1640)(1547, 1612)(1548, 1941)(1549, 1671)(1551, 1898)(1553, 1949)(1555, 1848)(1557, 1804)(1561, 1956)(1563, 1958)(1565, 1753)(1566, 1960)(1568, 1918)(1569, 1618)(1570, 1637)(1574, 1968)(1577, 1669)(1579, 1974)(1581, 1978)(1585, 1985)(1587, 1822)(1590, 1990)(1592, 1993)(1594, 1995)(1596, 1768)(1600, 1997)(1601, 1810)(1602, 2001)(1603, 1763)(1604, 2006)(1605, 2009)(1607, 1680)(1608, 2014)(1609, 1775)(1610, 2016)(1611, 2017)(1613, 1928)(1614, 2002)(1615, 1711)(1616, 2024)(1617, 1832)(1619, 1811)(1620, 2030)(1621, 2033)(1623, 1783)(1624, 2039)(1625, 2040)(1626, 2041)(1628, 1847)(1629, 2027)(1630, 1738)(1631, 2050)(1641, 1999)(1644, 2026)(1648, 2044)(1651, 1973)(1654, 1861)(1664, 2021)(1666, 2056)(1675, 1964)(1677, 2054)(1683, 1947)(1688, 2090)(1690, 2059)(1692, 2038)(1696, 2100)(1697, 1965)(1702, 2101)(1704, 2065)(1706, 2108)(1710, 2114)(1713, 2051)(1715, 2117)(1717, 2118)(1719, 2007)(1721, 2120)(1723, 2046)(1724, 1981)(1727, 2115)(1730, 2085)(1732, 2106)(1733, 2010)(1737, 2129)(1741, 1945)(1744, 2091)(1746, 2074)(1747, 2112)(1748, 2034)(1751, 2119)(1754, 2076)(1756, 2093)(1757, 1944)(1761, 2131)(1762, 2082)(1766, 1906)(1769, 2104)(1770, 2083)(1771, 2098)(1772, 1982)(1776, 2031)(1778, 1991)(1780, 1896)(1781, 2144)(1784, 1884)(1786, 2147)(1788, 1954)(1789, 2148)(1792, 1878)(1793, 2150)(1794, 2151)(1796, 1867)(1798, 2153)(1800, 2012)(1801, 2067)(1803, 1957)(1808, 2103)(1809, 2086)(1814, 1929)(1816, 1996)(1817, 2124)(1818, 1989)(1819, 1952)(1823, 1972)(1825, 1975)(1826, 2004)(1830, 2123)(1831, 2092)(1836, 2048)(1837, 2132)(1838, 2061)(1840, 1912)(1845, 2089)(1846, 2077)(1849, 1983)(1851, 2152)(1852, 2136)(1855, 1923)(1859, 2135)(1860, 2105)(1863, 2128)(1868, 2138)(1869, 2172)(1870, 1875)(1872, 2173)(1876, 2156)(1877, 2169)(1880, 2174)(1885, 2126)(1886, 2023)(1887, 1893)(1889, 2087)(1890, 2177)(1894, 2166)(1895, 2162)(1899, 2121)(1900, 2029)(1901, 1936)(1904, 2097)(1905, 2068)(1907, 2170)(1909, 1984)(1910, 2154)(1916, 1955)(1917, 2125)(1919, 2096)(1921, 2134)(1922, 2057)(1926, 2081)(1927, 2071)(1930, 1950)(1932, 2171)(1933, 2161)(1939, 2160)(1940, 1994)(1942, 2111)(1943, 2062)(1946, 2176)(1948, 2157)(1951, 2164)(1953, 1988)(1959, 1986)(1961, 2015)(1962, 2137)(1963, 2110)(1966, 2035)(1967, 2113)(1969, 2122)(1970, 2063)(1971, 2184)(1976, 2073)(1977, 2060)(1979, 2072)(1980, 2080)(1987, 2168)(1992, 2053)(1998, 2167)(2000, 2045)(2003, 2075)(2005, 2049)(2008, 2133)(2011, 2019)(2013, 2178)(2018, 2139)(2020, 2180)(2022, 2099)(2025, 2143)(2028, 2066)(2032, 2109)(2036, 2042)(2037, 2055)(2043, 2183)(2047, 2084)(2052, 2141)(2058, 2107)(2064, 2094)(2069, 2079)(2070, 2078)(2088, 2142)(2095, 2146)(2102, 2149)(2116, 2181)(2127, 2159)(2130, 2155)(2140, 2165)(2145, 2175)(2158, 2179)(2163, 2182) L = (1, 1093)(2, 1094)(3, 1095)(4, 1096)(5, 1097)(6, 1098)(7, 1099)(8, 1100)(9, 1101)(10, 1102)(11, 1103)(12, 1104)(13, 1105)(14, 1106)(15, 1107)(16, 1108)(17, 1109)(18, 1110)(19, 1111)(20, 1112)(21, 1113)(22, 1114)(23, 1115)(24, 1116)(25, 1117)(26, 1118)(27, 1119)(28, 1120)(29, 1121)(30, 1122)(31, 1123)(32, 1124)(33, 1125)(34, 1126)(35, 1127)(36, 1128)(37, 1129)(38, 1130)(39, 1131)(40, 1132)(41, 1133)(42, 1134)(43, 1135)(44, 1136)(45, 1137)(46, 1138)(47, 1139)(48, 1140)(49, 1141)(50, 1142)(51, 1143)(52, 1144)(53, 1145)(54, 1146)(55, 1147)(56, 1148)(57, 1149)(58, 1150)(59, 1151)(60, 1152)(61, 1153)(62, 1154)(63, 1155)(64, 1156)(65, 1157)(66, 1158)(67, 1159)(68, 1160)(69, 1161)(70, 1162)(71, 1163)(72, 1164)(73, 1165)(74, 1166)(75, 1167)(76, 1168)(77, 1169)(78, 1170)(79, 1171)(80, 1172)(81, 1173)(82, 1174)(83, 1175)(84, 1176)(85, 1177)(86, 1178)(87, 1179)(88, 1180)(89, 1181)(90, 1182)(91, 1183)(92, 1184)(93, 1185)(94, 1186)(95, 1187)(96, 1188)(97, 1189)(98, 1190)(99, 1191)(100, 1192)(101, 1193)(102, 1194)(103, 1195)(104, 1196)(105, 1197)(106, 1198)(107, 1199)(108, 1200)(109, 1201)(110, 1202)(111, 1203)(112, 1204)(113, 1205)(114, 1206)(115, 1207)(116, 1208)(117, 1209)(118, 1210)(119, 1211)(120, 1212)(121, 1213)(122, 1214)(123, 1215)(124, 1216)(125, 1217)(126, 1218)(127, 1219)(128, 1220)(129, 1221)(130, 1222)(131, 1223)(132, 1224)(133, 1225)(134, 1226)(135, 1227)(136, 1228)(137, 1229)(138, 1230)(139, 1231)(140, 1232)(141, 1233)(142, 1234)(143, 1235)(144, 1236)(145, 1237)(146, 1238)(147, 1239)(148, 1240)(149, 1241)(150, 1242)(151, 1243)(152, 1244)(153, 1245)(154, 1246)(155, 1247)(156, 1248)(157, 1249)(158, 1250)(159, 1251)(160, 1252)(161, 1253)(162, 1254)(163, 1255)(164, 1256)(165, 1257)(166, 1258)(167, 1259)(168, 1260)(169, 1261)(170, 1262)(171, 1263)(172, 1264)(173, 1265)(174, 1266)(175, 1267)(176, 1268)(177, 1269)(178, 1270)(179, 1271)(180, 1272)(181, 1273)(182, 1274)(183, 1275)(184, 1276)(185, 1277)(186, 1278)(187, 1279)(188, 1280)(189, 1281)(190, 1282)(191, 1283)(192, 1284)(193, 1285)(194, 1286)(195, 1287)(196, 1288)(197, 1289)(198, 1290)(199, 1291)(200, 1292)(201, 1293)(202, 1294)(203, 1295)(204, 1296)(205, 1297)(206, 1298)(207, 1299)(208, 1300)(209, 1301)(210, 1302)(211, 1303)(212, 1304)(213, 1305)(214, 1306)(215, 1307)(216, 1308)(217, 1309)(218, 1310)(219, 1311)(220, 1312)(221, 1313)(222, 1314)(223, 1315)(224, 1316)(225, 1317)(226, 1318)(227, 1319)(228, 1320)(229, 1321)(230, 1322)(231, 1323)(232, 1324)(233, 1325)(234, 1326)(235, 1327)(236, 1328)(237, 1329)(238, 1330)(239, 1331)(240, 1332)(241, 1333)(242, 1334)(243, 1335)(244, 1336)(245, 1337)(246, 1338)(247, 1339)(248, 1340)(249, 1341)(250, 1342)(251, 1343)(252, 1344)(253, 1345)(254, 1346)(255, 1347)(256, 1348)(257, 1349)(258, 1350)(259, 1351)(260, 1352)(261, 1353)(262, 1354)(263, 1355)(264, 1356)(265, 1357)(266, 1358)(267, 1359)(268, 1360)(269, 1361)(270, 1362)(271, 1363)(272, 1364)(273, 1365)(274, 1366)(275, 1367)(276, 1368)(277, 1369)(278, 1370)(279, 1371)(280, 1372)(281, 1373)(282, 1374)(283, 1375)(284, 1376)(285, 1377)(286, 1378)(287, 1379)(288, 1380)(289, 1381)(290, 1382)(291, 1383)(292, 1384)(293, 1385)(294, 1386)(295, 1387)(296, 1388)(297, 1389)(298, 1390)(299, 1391)(300, 1392)(301, 1393)(302, 1394)(303, 1395)(304, 1396)(305, 1397)(306, 1398)(307, 1399)(308, 1400)(309, 1401)(310, 1402)(311, 1403)(312, 1404)(313, 1405)(314, 1406)(315, 1407)(316, 1408)(317, 1409)(318, 1410)(319, 1411)(320, 1412)(321, 1413)(322, 1414)(323, 1415)(324, 1416)(325, 1417)(326, 1418)(327, 1419)(328, 1420)(329, 1421)(330, 1422)(331, 1423)(332, 1424)(333, 1425)(334, 1426)(335, 1427)(336, 1428)(337, 1429)(338, 1430)(339, 1431)(340, 1432)(341, 1433)(342, 1434)(343, 1435)(344, 1436)(345, 1437)(346, 1438)(347, 1439)(348, 1440)(349, 1441)(350, 1442)(351, 1443)(352, 1444)(353, 1445)(354, 1446)(355, 1447)(356, 1448)(357, 1449)(358, 1450)(359, 1451)(360, 1452)(361, 1453)(362, 1454)(363, 1455)(364, 1456)(365, 1457)(366, 1458)(367, 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2178)(1087, 2179)(1088, 2180)(1089, 2181)(1090, 2182)(1091, 2183)(1092, 2184) local type(s) :: { ( 14, 14 ), ( 14^3 ) } Outer automorphisms :: reflexible Dual of E14.631 Transitivity :: ET+ Graph:: simple bipartite v = 910 e = 1092 f = 156 degree seq :: [ 2^546, 3^364 ] E14.621 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2 * T1)^7, (T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2)^3 ] Map:: polytopal R = (1, 3, 4)(2, 5, 6)(7, 11, 12)(8, 13, 14)(9, 15, 16)(10, 17, 18)(19, 27, 28)(20, 29, 30)(21, 31, 32)(22, 33, 34)(23, 35, 36)(24, 37, 38)(25, 39, 40)(26, 41, 42)(43, 58, 59)(44, 60, 61)(45, 62, 63)(46, 64, 65)(47, 66, 67)(48, 68, 69)(49, 70, 71)(50, 72, 51)(52, 73, 74)(53, 75, 76)(54, 77, 78)(55, 79, 80)(56, 81, 82)(57, 83, 84)(85, 107, 108)(86, 109, 110)(87, 111, 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2117)(1722, 2123)(1724, 1776)(1725, 2101)(1726, 2055)(1728, 1975)(1731, 1882)(1733, 1932)(1734, 2129)(1736, 1883)(1738, 2016)(1740, 2096)(1741, 2105)(1743, 2133)(1744, 1866)(1745, 2135)(1748, 1947)(1751, 2109)(1752, 2052)(1754, 2115)(1757, 1861)(1759, 1911)(1762, 1836)(1764, 2050)(1766, 1828)(1770, 1899)(1772, 1962)(1775, 1806)(1778, 2046)(1780, 2054)(1781, 1794)(1785, 1942)(1787, 1940)(1790, 2119)(1791, 1951)(1793, 2151)(1795, 2153)(1797, 2139)(1800, 2142)(1801, 2041)(1803, 2124)(1808, 2032)(1810, 1990)(1812, 2127)(1813, 2102)(1815, 2158)(1816, 1855)(1817, 2136)(1818, 2155)(1820, 2144)(1821, 1985)(1823, 2090)(1825, 2132)(1826, 2009)(1827, 2161)(1829, 2163)(1832, 2146)(1833, 2037)(1838, 2042)(1840, 2034)(1842, 2110)(1844, 2167)(1845, 1875)(1846, 2165)(1848, 2148)(1854, 2067)(1859, 2040)(1865, 1948)(1874, 2071)(1879, 2012)(1886, 1903)(1889, 2150)(1890, 2029)(1891, 2177)(1893, 2176)(1895, 1946)(1896, 2043)(1901, 1987)(1905, 2111)(1906, 2179)(1907, 1955)(1908, 2169)(1909, 1968)(1910, 2180)(1912, 2181)(1914, 2138)(1915, 1938)(1920, 2053)(1921, 2014)(1923, 2143)(1925, 2174)(1927, 2015)(1929, 2171)(1931, 2047)(1934, 2038)(1935, 2093)(1939, 2166)(1944, 2134)(1949, 2103)(1952, 2021)(1953, 2182)(1954, 2156)(1957, 2173)(1961, 2004)(1963, 2178)(1965, 2126)(1969, 2057)(1973, 2140)(1974, 2118)(1978, 2056)(1979, 2074)(1984, 2001)(1989, 2002)(1995, 2099)(1998, 2106)(2000, 2157)(2018, 2164)(2022, 2131)(2025, 2107)(2044, 2183)(2048, 2184)(2062, 2112)(2064, 2159)(2069, 2149)(2073, 2160)(2079, 2145)(2082, 2095)(2085, 2152)(2088, 2147)(2092, 2141)(2097, 2162)(2100, 2137)(2104, 2154)(2108, 2125)(2113, 2168)(2116, 2130)(2120, 2175)(2122, 2170)(2128, 2172) L = (1, 1093)(2, 1094)(3, 1095)(4, 1096)(5, 1097)(6, 1098)(7, 1099)(8, 1100)(9, 1101)(10, 1102)(11, 1103)(12, 1104)(13, 1105)(14, 1106)(15, 1107)(16, 1108)(17, 1109)(18, 1110)(19, 1111)(20, 1112)(21, 1113)(22, 1114)(23, 1115)(24, 1116)(25, 1117)(26, 1118)(27, 1119)(28, 1120)(29, 1121)(30, 1122)(31, 1123)(32, 1124)(33, 1125)(34, 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1222)(131, 1223)(132, 1224)(133, 1225)(134, 1226)(135, 1227)(136, 1228)(137, 1229)(138, 1230)(139, 1231)(140, 1232)(141, 1233)(142, 1234)(143, 1235)(144, 1236)(145, 1237)(146, 1238)(147, 1239)(148, 1240)(149, 1241)(150, 1242)(151, 1243)(152, 1244)(153, 1245)(154, 1246)(155, 1247)(156, 1248)(157, 1249)(158, 1250)(159, 1251)(160, 1252)(161, 1253)(162, 1254)(163, 1255)(164, 1256)(165, 1257)(166, 1258)(167, 1259)(168, 1260)(169, 1261)(170, 1262)(171, 1263)(172, 1264)(173, 1265)(174, 1266)(175, 1267)(176, 1268)(177, 1269)(178, 1270)(179, 1271)(180, 1272)(181, 1273)(182, 1274)(183, 1275)(184, 1276)(185, 1277)(186, 1278)(187, 1279)(188, 1280)(189, 1281)(190, 1282)(191, 1283)(192, 1284)(193, 1285)(194, 1286)(195, 1287)(196, 1288)(197, 1289)(198, 1290)(199, 1291)(200, 1292)(201, 1293)(202, 1294)(203, 1295)(204, 1296)(205, 1297)(206, 1298)(207, 1299)(208, 1300)(209, 1301)(210, 1302)(211, 1303)(212, 1304)(213, 1305)(214, 1306)(215, 1307)(216, 1308)(217, 1309)(218, 1310)(219, 1311)(220, 1312)(221, 1313)(222, 1314)(223, 1315)(224, 1316)(225, 1317)(226, 1318)(227, 1319)(228, 1320)(229, 1321)(230, 1322)(231, 1323)(232, 1324)(233, 1325)(234, 1326)(235, 1327)(236, 1328)(237, 1329)(238, 1330)(239, 1331)(240, 1332)(241, 1333)(242, 1334)(243, 1335)(244, 1336)(245, 1337)(246, 1338)(247, 1339)(248, 1340)(249, 1341)(250, 1342)(251, 1343)(252, 1344)(253, 1345)(254, 1346)(255, 1347)(256, 1348)(257, 1349)(258, 1350)(259, 1351)(260, 1352)(261, 1353)(262, 1354)(263, 1355)(264, 1356)(265, 1357)(266, 1358)(267, 1359)(268, 1360)(269, 1361)(270, 1362)(271, 1363)(272, 1364)(273, 1365)(274, 1366)(275, 1367)(276, 1368)(277, 1369)(278, 1370)(279, 1371)(280, 1372)(281, 1373)(282, 1374)(283, 1375)(284, 1376)(285, 1377)(286, 1378)(287, 1379)(288, 1380)(289, 1381)(290, 1382)(291, 1383)(292, 1384)(293, 1385)(294, 1386)(295, 1387)(296, 1388)(297, 1389)(298, 1390)(299, 1391)(300, 1392)(301, 1393)(302, 1394)(303, 1395)(304, 1396)(305, 1397)(306, 1398)(307, 1399)(308, 1400)(309, 1401)(310, 1402)(311, 1403)(312, 1404)(313, 1405)(314, 1406)(315, 1407)(316, 1408)(317, 1409)(318, 1410)(319, 1411)(320, 1412)(321, 1413)(322, 1414)(323, 1415)(324, 1416)(325, 1417)(326, 1418)(327, 1419)(328, 1420)(329, 1421)(330, 1422)(331, 1423)(332, 1424)(333, 1425)(334, 1426)(335, 1427)(336, 1428)(337, 1429)(338, 1430)(339, 1431)(340, 1432)(341, 1433)(342, 1434)(343, 1435)(344, 1436)(345, 1437)(346, 1438)(347, 1439)(348, 1440)(349, 1441)(350, 1442)(351, 1443)(352, 1444)(353, 1445)(354, 1446)(355, 1447)(356, 1448)(357, 1449)(358, 1450)(359, 1451)(360, 1452)(361, 1453)(362, 1454)(363, 1455)(364, 1456)(365, 1457)(366, 1458)(367, 1459)(368, 1460)(369, 1461)(370, 1462)(371, 1463)(372, 1464)(373, 1465)(374, 1466)(375, 1467)(376, 1468)(377, 1469)(378, 1470)(379, 1471)(380, 1472)(381, 1473)(382, 1474)(383, 1475)(384, 1476)(385, 1477)(386, 1478)(387, 1479)(388, 1480)(389, 1481)(390, 1482)(391, 1483)(392, 1484)(393, 1485)(394, 1486)(395, 1487)(396, 1488)(397, 1489)(398, 1490)(399, 1491)(400, 1492)(401, 1493)(402, 1494)(403, 1495)(404, 1496)(405, 1497)(406, 1498)(407, 1499)(408, 1500)(409, 1501)(410, 1502)(411, 1503)(412, 1504)(413, 1505)(414, 1506)(415, 1507)(416, 1508)(417, 1509)(418, 1510)(419, 1511)(420, 1512)(421, 1513)(422, 1514)(423, 1515)(424, 1516)(425, 1517)(426, 1518)(427, 1519)(428, 1520)(429, 1521)(430, 1522)(431, 1523)(432, 1524)(433, 1525)(434, 1526)(435, 1527)(436, 1528)(437, 1529)(438, 1530)(439, 1531)(440, 1532)(441, 1533)(442, 1534)(443, 1535)(444, 1536)(445, 1537)(446, 1538)(447, 1539)(448, 1540)(449, 1541)(450, 1542)(451, 1543)(452, 1544)(453, 1545)(454, 1546)(455, 1547)(456, 1548)(457, 1549)(458, 1550)(459, 1551)(460, 1552)(461, 1553)(462, 1554)(463, 1555)(464, 1556)(465, 1557)(466, 1558)(467, 1559)(468, 1560)(469, 1561)(470, 1562)(471, 1563)(472, 1564)(473, 1565)(474, 1566)(475, 1567)(476, 1568)(477, 1569)(478, 1570)(479, 1571)(480, 1572)(481, 1573)(482, 1574)(483, 1575)(484, 1576)(485, 1577)(486, 1578)(487, 1579)(488, 1580)(489, 1581)(490, 1582)(491, 1583)(492, 1584)(493, 1585)(494, 1586)(495, 1587)(496, 1588)(497, 1589)(498, 1590)(499, 1591)(500, 1592)(501, 1593)(502, 1594)(503, 1595)(504, 1596)(505, 1597)(506, 1598)(507, 1599)(508, 1600)(509, 1601)(510, 1602)(511, 1603)(512, 1604)(513, 1605)(514, 1606)(515, 1607)(516, 1608)(517, 1609)(518, 1610)(519, 1611)(520, 1612)(521, 1613)(522, 1614)(523, 1615)(524, 1616)(525, 1617)(526, 1618)(527, 1619)(528, 1620)(529, 1621)(530, 1622)(531, 1623)(532, 1624)(533, 1625)(534, 1626)(535, 1627)(536, 1628)(537, 1629)(538, 1630)(539, 1631)(540, 1632)(541, 1633)(542, 1634)(543, 1635)(544, 1636)(545, 1637)(546, 1638)(547, 1639)(548, 1640)(549, 1641)(550, 1642)(551, 1643)(552, 1644)(553, 1645)(554, 1646)(555, 1647)(556, 1648)(557, 1649)(558, 1650)(559, 1651)(560, 1652)(561, 1653)(562, 1654)(563, 1655)(564, 1656)(565, 1657)(566, 1658)(567, 1659)(568, 1660)(569, 1661)(570, 1662)(571, 1663)(572, 1664)(573, 1665)(574, 1666)(575, 1667)(576, 1668)(577, 1669)(578, 1670)(579, 1671)(580, 1672)(581, 1673)(582, 1674)(583, 1675)(584, 1676)(585, 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1768)(677, 1769)(678, 1770)(679, 1771)(680, 1772)(681, 1773)(682, 1774)(683, 1775)(684, 1776)(685, 1777)(686, 1778)(687, 1779)(688, 1780)(689, 1781)(690, 1782)(691, 1783)(692, 1784)(693, 1785)(694, 1786)(695, 1787)(696, 1788)(697, 1789)(698, 1790)(699, 1791)(700, 1792)(701, 1793)(702, 1794)(703, 1795)(704, 1796)(705, 1797)(706, 1798)(707, 1799)(708, 1800)(709, 1801)(710, 1802)(711, 1803)(712, 1804)(713, 1805)(714, 1806)(715, 1807)(716, 1808)(717, 1809)(718, 1810)(719, 1811)(720, 1812)(721, 1813)(722, 1814)(723, 1815)(724, 1816)(725, 1817)(726, 1818)(727, 1819)(728, 1820)(729, 1821)(730, 1822)(731, 1823)(732, 1824)(733, 1825)(734, 1826)(735, 1827)(736, 1828)(737, 1829)(738, 1830)(739, 1831)(740, 1832)(741, 1833)(742, 1834)(743, 1835)(744, 1836)(745, 1837)(746, 1838)(747, 1839)(748, 1840)(749, 1841)(750, 1842)(751, 1843)(752, 1844)(753, 1845)(754, 1846)(755, 1847)(756, 1848)(757, 1849)(758, 1850)(759, 1851)(760, 1852)(761, 1853)(762, 1854)(763, 1855)(764, 1856)(765, 1857)(766, 1858)(767, 1859)(768, 1860)(769, 1861)(770, 1862)(771, 1863)(772, 1864)(773, 1865)(774, 1866)(775, 1867)(776, 1868)(777, 1869)(778, 1870)(779, 1871)(780, 1872)(781, 1873)(782, 1874)(783, 1875)(784, 1876)(785, 1877)(786, 1878)(787, 1879)(788, 1880)(789, 1881)(790, 1882)(791, 1883)(792, 1884)(793, 1885)(794, 1886)(795, 1887)(796, 1888)(797, 1889)(798, 1890)(799, 1891)(800, 1892)(801, 1893)(802, 1894)(803, 1895)(804, 1896)(805, 1897)(806, 1898)(807, 1899)(808, 1900)(809, 1901)(810, 1902)(811, 1903)(812, 1904)(813, 1905)(814, 1906)(815, 1907)(816, 1908)(817, 1909)(818, 1910)(819, 1911)(820, 1912)(821, 1913)(822, 1914)(823, 1915)(824, 1916)(825, 1917)(826, 1918)(827, 1919)(828, 1920)(829, 1921)(830, 1922)(831, 1923)(832, 1924)(833, 1925)(834, 1926)(835, 1927)(836, 1928)(837, 1929)(838, 1930)(839, 1931)(840, 1932)(841, 1933)(842, 1934)(843, 1935)(844, 1936)(845, 1937)(846, 1938)(847, 1939)(848, 1940)(849, 1941)(850, 1942)(851, 1943)(852, 1944)(853, 1945)(854, 1946)(855, 1947)(856, 1948)(857, 1949)(858, 1950)(859, 1951)(860, 1952)(861, 1953)(862, 1954)(863, 1955)(864, 1956)(865, 1957)(866, 1958)(867, 1959)(868, 1960)(869, 1961)(870, 1962)(871, 1963)(872, 1964)(873, 1965)(874, 1966)(875, 1967)(876, 1968)(877, 1969)(878, 1970)(879, 1971)(880, 1972)(881, 1973)(882, 1974)(883, 1975)(884, 1976)(885, 1977)(886, 1978)(887, 1979)(888, 1980)(889, 1981)(890, 1982)(891, 1983)(892, 1984)(893, 1985)(894, 1986)(895, 1987)(896, 1988)(897, 1989)(898, 1990)(899, 1991)(900, 1992)(901, 1993)(902, 1994)(903, 1995)(904, 1996)(905, 1997)(906, 1998)(907, 1999)(908, 2000)(909, 2001)(910, 2002)(911, 2003)(912, 2004)(913, 2005)(914, 2006)(915, 2007)(916, 2008)(917, 2009)(918, 2010)(919, 2011)(920, 2012)(921, 2013)(922, 2014)(923, 2015)(924, 2016)(925, 2017)(926, 2018)(927, 2019)(928, 2020)(929, 2021)(930, 2022)(931, 2023)(932, 2024)(933, 2025)(934, 2026)(935, 2027)(936, 2028)(937, 2029)(938, 2030)(939, 2031)(940, 2032)(941, 2033)(942, 2034)(943, 2035)(944, 2036)(945, 2037)(946, 2038)(947, 2039)(948, 2040)(949, 2041)(950, 2042)(951, 2043)(952, 2044)(953, 2045)(954, 2046)(955, 2047)(956, 2048)(957, 2049)(958, 2050)(959, 2051)(960, 2052)(961, 2053)(962, 2054)(963, 2055)(964, 2056)(965, 2057)(966, 2058)(967, 2059)(968, 2060)(969, 2061)(970, 2062)(971, 2063)(972, 2064)(973, 2065)(974, 2066)(975, 2067)(976, 2068)(977, 2069)(978, 2070)(979, 2071)(980, 2072)(981, 2073)(982, 2074)(983, 2075)(984, 2076)(985, 2077)(986, 2078)(987, 2079)(988, 2080)(989, 2081)(990, 2082)(991, 2083)(992, 2084)(993, 2085)(994, 2086)(995, 2087)(996, 2088)(997, 2089)(998, 2090)(999, 2091)(1000, 2092)(1001, 2093)(1002, 2094)(1003, 2095)(1004, 2096)(1005, 2097)(1006, 2098)(1007, 2099)(1008, 2100)(1009, 2101)(1010, 2102)(1011, 2103)(1012, 2104)(1013, 2105)(1014, 2106)(1015, 2107)(1016, 2108)(1017, 2109)(1018, 2110)(1019, 2111)(1020, 2112)(1021, 2113)(1022, 2114)(1023, 2115)(1024, 2116)(1025, 2117)(1026, 2118)(1027, 2119)(1028, 2120)(1029, 2121)(1030, 2122)(1031, 2123)(1032, 2124)(1033, 2125)(1034, 2126)(1035, 2127)(1036, 2128)(1037, 2129)(1038, 2130)(1039, 2131)(1040, 2132)(1041, 2133)(1042, 2134)(1043, 2135)(1044, 2136)(1045, 2137)(1046, 2138)(1047, 2139)(1048, 2140)(1049, 2141)(1050, 2142)(1051, 2143)(1052, 2144)(1053, 2145)(1054, 2146)(1055, 2147)(1056, 2148)(1057, 2149)(1058, 2150)(1059, 2151)(1060, 2152)(1061, 2153)(1062, 2154)(1063, 2155)(1064, 2156)(1065, 2157)(1066, 2158)(1067, 2159)(1068, 2160)(1069, 2161)(1070, 2162)(1071, 2163)(1072, 2164)(1073, 2165)(1074, 2166)(1075, 2167)(1076, 2168)(1077, 2169)(1078, 2170)(1079, 2171)(1080, 2172)(1081, 2173)(1082, 2174)(1083, 2175)(1084, 2176)(1085, 2177)(1086, 2178)(1087, 2179)(1088, 2180)(1089, 2181)(1090, 2182)(1091, 2183)(1092, 2184) local type(s) :: { ( 14, 14 ), ( 14^3 ) } Outer automorphisms :: reflexible Dual of E14.633 Transitivity :: ET+ Graph:: simple bipartite v = 910 e = 1092 f = 156 degree seq :: [ 2^546, 3^364 ] E14.622 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T2^7, (T1 * T2^-2)^6, T2 * T1^-1 * T2^-2 * T1 * T2^3 * T1^-1 * T2^-1 * T1 * T2^-2 * T1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1, T2^2 * T1^-1 * T2^2 * T1^-1 * T2^-2 * T1 * T2^3 * T1^-1 * T2 * T1^-1 * T2^-2 * T1 * T2^-3 * T1^-1 * T2 * T1^-1 * T2^-3 * T1^-1 * T2 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 3, 9, 19, 26, 13, 5)(2, 6, 14, 27, 32, 16, 7)(4, 11, 22, 40, 34, 17, 8)(10, 21, 39, 63, 59, 35, 18)(12, 23, 42, 68, 71, 43, 24)(15, 29, 50, 78, 81, 51, 30)(20, 38, 62, 94, 92, 60, 36)(25, 44, 72, 108, 111, 73, 45)(28, 49, 77, 116, 114, 75, 47)(31, 52, 82, 124, 127, 83, 53)(33, 55, 85, 129, 132, 86, 56)(37, 61, 93, 140, 112, 74, 46)(41, 67, 101, 151, 149, 99, 65)(48, 76, 115, 169, 128, 84, 54)(57, 66, 100, 150, 194, 133, 87)(58, 88, 134, 195, 198, 135, 89)(64, 98, 147, 212, 210, 145, 96)(69, 104, 155, 224, 222, 153, 102)(70, 105, 156, 226, 229, 157, 106)(79, 120, 176, 250, 248, 174, 118)(80, 121, 177, 252, 255, 178, 122)(90, 97, 146, 211, 280, 199, 136)(91, 137, 200, 281, 284, 201, 138)(95, 144, 208, 292, 290, 206, 142)(103, 154, 223, 310, 230, 158, 107)(109, 161, 233, 324, 322, 231, 159)(110, 162, 234, 326, 328, 235, 163)(113, 166, 238, 331, 334, 239, 167)(117, 173, 246, 342, 340, 244, 171)(119, 175, 249, 346, 256, 179, 123)(125, 182, 259, 359, 357, 257, 180)(126, 183, 260, 361, 363, 261, 184)(130, 189, 266, 369, 367, 264, 187)(131, 190, 267, 371, 373, 268, 191)(139, 143, 207, 291, 393, 285, 202)(141, 205, 288, 397, 395, 286, 203)(148, 214, 300, 409, 412, 301, 215)(152, 220, 306, 418, 416, 304, 218)(160, 232, 323, 436, 329, 236, 164)(165, 204, 287, 396, 446, 330, 237)(168, 172, 245, 341, 453, 335, 240)(170, 243, 338, 457, 455, 336, 241)(181, 258, 358, 480, 364, 262, 185)(186, 242, 337, 456, 489, 365, 263)(188, 265, 368, 493, 374, 269, 192)(193, 270, 375, 501, 503, 376, 271)(196, 275, 380, 508, 506, 378, 273)(197, 276, 381, 469, 348, 251, 277)(209, 293, 403, 530, 533, 404, 294)(213, 299, 228, 318, 430, 407, 297)(216, 219, 305, 417, 543, 413, 302)(217, 303, 414, 544, 504, 377, 272)(221, 307, 419, 549, 551, 420, 308)(225, 314, 254, 353, 474, 425, 312)(227, 317, 429, 560, 558, 427, 315)(247, 343, 463, 590, 592, 464, 344)(253, 352, 473, 601, 599, 471, 350)(274, 379, 507, 633, 511, 382, 278)(279, 383, 512, 639, 566, 437, 384)(282, 388, 516, 645, 643, 514, 386)(283, 389, 517, 620, 495, 370, 390)(289, 398, 526, 654, 657, 527, 399)(295, 298, 408, 537, 665, 534, 405)(296, 406, 535, 666, 641, 513, 385)(309, 313, 426, 556, 683, 552, 421)(311, 424, 392, 519, 648, 553, 422)(316, 428, 559, 691, 563, 431, 319)(320, 423, 554, 685, 607, 481, 432)(321, 433, 564, 697, 635, 509, 434)(325, 440, 333, 450, 578, 568, 438)(327, 443, 572, 706, 704, 570, 441)(332, 449, 577, 711, 709, 575, 447)(339, 458, 586, 720, 723, 587, 459)(345, 349, 470, 597, 730, 593, 465)(347, 468, 452, 580, 714, 594, 466)(351, 472, 600, 738, 604, 475, 354)(355, 467, 595, 732, 618, 494, 476)(356, 477, 605, 744, 693, 561, 478)(360, 484, 411, 541, 671, 609, 482)(362, 487, 613, 753, 751, 611, 485)(366, 490, 616, 755, 740, 602, 491)(372, 499, 624, 764, 762, 622, 497)(387, 515, 644, 783, 647, 518, 391)(394, 521, 650, 789, 792, 651, 522)(400, 402, 486, 612, 752, 658, 528)(401, 529, 659, 800, 788, 649, 520)(410, 540, 532, 663, 803, 669, 538)(415, 545, 674, 812, 815, 675, 546)(435, 439, 569, 702, 834, 699, 565)(442, 571, 705, 816, 676, 547, 444)(445, 567, 700, 835, 826, 692, 573)(448, 576, 710, 846, 713, 579, 451)(454, 582, 716, 852, 855, 717, 583)(460, 462, 498, 623, 763, 724, 588)(461, 589, 682, 819, 851, 715, 581)(479, 483, 610, 749, 880, 746, 606)(488, 608, 747, 881, 872, 739, 614)(492, 496, 621, 760, 892, 757, 617)(500, 619, 758, 893, 772, 634, 625)(502, 628, 768, 905, 903, 766, 626)(505, 630, 770, 907, 900, 765, 631)(510, 637, 775, 912, 868, 733, 596)(523, 525, 627, 767, 904, 793, 652)(524, 653, 794, 856, 718, 584, 574)(531, 662, 656, 798, 931, 801, 660)(536, 562, 695, 829, 938, 806, 667)(539, 670, 809, 940, 811, 672, 542)(548, 677, 729, 865, 916, 779, 673)(550, 680, 722, 861, 950, 817, 678)(555, 603, 742, 875, 955, 822, 686)(557, 688, 824, 956, 841, 707, 689)(585, 719, 857, 899, 769, 629, 615)(591, 727, 814, 947, 984, 863, 725)(598, 735, 870, 989, 887, 754, 736)(632, 636, 774, 911, 1015, 909, 771)(638, 773, 910, 1016, 919, 784, 776)(640, 778, 915, 1021, 1020, 914, 777)(642, 780, 917, 1022, 1018, 913, 781)(646, 785, 921, 1026, 1005, 894, 759)(655, 797, 791, 927, 1031, 929, 795)(661, 802, 934, 1035, 936, 804, 664)(668, 807, 891, 1003, 1028, 924, 805)(679, 818, 951, 1024, 918, 782, 681)(684, 787, 923, 1027, 1048, 953, 821)(687, 823, 833, 963, 1047, 952, 820)(690, 694, 828, 960, 1052, 958, 825)(696, 827, 959, 1053, 971, 847, 830)(698, 832, 954, 1049, 1055, 962, 831)(701, 712, 848, 973, 1057, 965, 836)(703, 838, 966, 1029, 925, 790, 839)(708, 843, 969, 1059, 1039, 961, 844)(721, 860, 854, 978, 1066, 980, 858)(726, 864, 985, 1061, 970, 845, 728)(731, 850, 975, 1063, 1071, 987, 867)(734, 869, 879, 996, 1070, 986, 866)(737, 741, 874, 993, 1073, 991, 871)(743, 873, 992, 1074, 1040, 941, 876)(745, 878, 988, 1019, 1076, 995, 877)(748, 810, 942, 1042, 1078, 998, 882)(750, 884, 999, 1064, 976, 853, 885)(756, 890, 937, 1038, 1080, 1002, 889)(761, 896, 1007, 1082, 1012, 906, 897)(786, 920, 1025, 1056, 964, 837, 922)(796, 930, 983, 1069, 1034, 932, 799)(808, 935, 1036, 1090, 1050, 994, 939)(813, 946, 902, 1010, 1084, 1043, 944)(840, 842, 968, 1058, 1072, 990, 967)(849, 972, 1062, 1077, 997, 883, 974)(859, 981, 933, 1033, 1068, 982, 862)(886, 888, 1001, 1079, 1014, 908, 1000)(895, 1006, 943, 1041, 1091, 1081, 1004)(898, 901, 1009, 1083, 1051, 957, 1008)(926, 1030, 1075, 1092, 1060, 1032, 928)(945, 1044, 949, 1046, 1089, 1045, 948)(977, 1065, 1017, 1087, 1037, 1067, 979)(1011, 1013, 1086, 1054, 1088, 1023, 1085)(1093, 1094, 1096)(1095, 1100, 1102)(1097, 1104, 1098)(1099, 1107, 1103)(1101, 1110, 1112)(1105, 1117, 1115)(1106, 1116, 1120)(1108, 1123, 1121)(1109, 1125, 1113)(1111, 1128, 1129)(1114, 1122, 1133)(1118, 1138, 1136)(1119, 1139, 1140)(1124, 1146, 1144)(1126, 1149, 1147)(1127, 1150, 1130)(1131, 1148, 1156)(1132, 1157, 1158)(1134, 1137, 1161)(1135, 1162, 1141)(1142, 1145, 1171)(1143, 1172, 1159)(1151, 1182, 1180)(1152, 1183, 1153)(1154, 1181, 1187)(1155, 1188, 1189)(1160, 1194, 1195)(1163, 1199, 1197)(1164, 1166, 1201)(1165, 1202, 1196)(1167, 1205, 1168)(1169, 1198, 1209)(1170, 1210, 1211)(1173, 1215, 1213)(1174, 1176, 1217)(1175, 1218, 1212)(1177, 1179, 1222)(1178, 1223, 1190)(1184, 1231, 1229)(1185, 1230, 1233)(1186, 1234, 1235)(1191, 1240, 1192)(1193, 1214, 1244)(1200, 1251, 1252)(1203, 1256, 1254)(1204, 1257, 1253)(1206, 1260, 1258)(1207, 1259, 1262)(1208, 1263, 1264)(1216, 1272, 1273)(1219, 1277, 1275)(1220, 1278, 1274)(1221, 1279, 1280)(1224, 1284, 1282)(1225, 1285, 1281)(1226, 1228, 1288)(1227, 1289, 1236)(1232, 1295, 1296)(1237, 1301, 1238)(1239, 1283, 1305)(1241, 1308, 1306)(1242, 1307, 1309)(1243, 1310, 1311)(1245, 1313, 1246)(1247, 1255, 1317)(1248, 1250, 1319)(1249, 1320, 1265)(1261, 1333, 1334)(1266, 1339, 1267)(1268, 1276, 1343)(1269, 1271, 1345)(1270, 1346, 1312)(1286, 1364, 1362)(1287, 1365, 1366)(1290, 1370, 1368)(1291, 1371, 1367)(1292, 1294, 1374)(1293, 1375, 1297)(1298, 1381, 1299)(1300, 1369, 1353)(1302, 1387, 1385)(1303, 1386, 1388)(1304, 1389, 1390)(1314, 1401, 1399)(1315, 1400, 1403)(1316, 1404, 1405)(1318, 1407, 1408)(1321, 1411, 1410)(1322, 1412, 1409)(1323, 1413, 1324)(1325, 1329, 1417)(1326, 1328, 1419)(1327, 1398, 1406)(1330, 1332, 1424)(1331, 1425, 1335)(1336, 1431, 1337)(1338, 1391, 1360)(1340, 1437, 1435)(1341, 1436, 1439)(1342, 1440, 1441)(1344, 1442, 1443)(1347, 1446, 1445)(1348, 1447, 1444)(1349, 1448, 1350)(1351, 1355, 1452)(1352, 1354, 1454)(1356, 1458, 1357)(1358, 1363, 1462)(1359, 1361, 1464)(1372, 1477, 1475)(1373, 1478, 1479)(1376, 1483, 1481)(1377, 1484, 1480)(1378, 1486, 1379)(1380, 1482, 1468)(1382, 1492, 1490)(1383, 1491, 1493)(1384, 1455, 1494)(1392, 1394, 1502)(1393, 1503, 1395)(1396, 1507, 1397)(1402, 1514, 1515)(1414, 1527, 1525)(1415, 1526, 1529)(1416, 1530, 1531)(1418, 1533, 1534)(1420, 1536, 1510)(1421, 1537, 1535)(1422, 1430, 1532)(1423, 1539, 1540)(1426, 1543, 1542)(1427, 1544, 1541)(1428, 1546, 1429)(1432, 1552, 1550)(1433, 1551, 1553)(1434, 1465, 1554)(1438, 1558, 1559)(1449, 1571, 1569)(1450, 1570, 1573)(1451, 1574, 1575)(1453, 1577, 1578)(1456, 1580, 1579)(1457, 1506, 1576)(1459, 1584, 1582)(1460, 1583, 1586)(1461, 1587, 1588)(1463, 1589, 1590)(1466, 1592, 1591)(1467, 1469, 1594)(1470, 1597, 1471)(1472, 1476, 1601)(1473, 1474, 1602)(1485, 1612, 1611)(1487, 1615, 1613)(1488, 1614, 1616)(1489, 1595, 1617)(1495, 1497, 1623)(1496, 1624, 1498)(1499, 1628, 1500)(1501, 1630, 1631)(1504, 1634, 1633)(1505, 1627, 1632)(1508, 1639, 1637)(1509, 1638, 1640)(1511, 1513, 1642)(1512, 1608, 1516)(1517, 1647, 1518)(1519, 1649, 1520)(1521, 1524, 1653)(1522, 1523, 1654)(1528, 1658, 1659)(1538, 1666, 1549)(1545, 1673, 1672)(1547, 1676, 1674)(1548, 1675, 1677)(1555, 1557, 1683)(1556, 1669, 1560)(1561, 1688, 1562)(1563, 1690, 1564)(1565, 1568, 1694)(1566, 1567, 1695)(1572, 1699, 1700)(1581, 1707, 1636)(1585, 1710, 1711)(1593, 1718, 1719)(1596, 1721, 1720)(1598, 1724, 1722)(1599, 1723, 1726)(1600, 1727, 1728)(1603, 1730, 1729)(1604, 1605, 1732)(1606, 1734, 1607)(1609, 1610, 1738)(1618, 1620, 1747)(1619, 1748, 1621)(1622, 1752, 1753)(1625, 1756, 1755)(1626, 1751, 1754)(1629, 1759, 1760)(1635, 1765, 1758)(1641, 1770, 1771)(1643, 1773, 1737)(1644, 1774, 1772)(1645, 1776, 1646)(1648, 1778, 1779)(1650, 1782, 1780)(1651, 1781, 1784)(1652, 1785, 1786)(1655, 1788, 1787)(1656, 1657, 1790)(1660, 1793, 1661)(1662, 1795, 1663)(1664, 1665, 1799)(1667, 1800, 1668)(1670, 1671, 1804)(1678, 1680, 1813)(1679, 1814, 1681)(1682, 1817, 1818)(1684, 1820, 1803)(1685, 1821, 1819)(1686, 1823, 1687)(1689, 1825, 1826)(1691, 1829, 1827)(1692, 1828, 1831)(1693, 1832, 1833)(1696, 1835, 1834)(1697, 1698, 1837)(1701, 1840, 1702)(1703, 1842, 1704)(1705, 1706, 1846)(1708, 1709, 1848)(1712, 1851, 1713)(1714, 1853, 1715)(1716, 1717, 1857)(1725, 1864, 1865)(1731, 1869, 1792)(1733, 1871, 1870)(1735, 1874, 1872)(1736, 1873, 1876)(1739, 1878, 1877)(1740, 1741, 1879)(1742, 1744, 1882)(1743, 1883, 1745)(1746, 1887, 1888)(1749, 1891, 1890)(1750, 1886, 1889)(1757, 1897, 1892)(1761, 1900, 1762)(1763, 1764, 1902)(1766, 1768, 1905)(1767, 1906, 1769)(1775, 1912, 1911)(1777, 1913, 1839)(1783, 1918, 1919)(1789, 1923, 1866)(1791, 1925, 1924)(1794, 1928, 1929)(1796, 1932, 1930)(1797, 1931, 1885)(1798, 1933, 1934)(1801, 1937, 1935)(1802, 1936, 1939)(1805, 1941, 1940)(1806, 1807, 1942)(1808, 1810, 1945)(1809, 1946, 1811)(1812, 1950, 1951)(1815, 1954, 1953)(1816, 1949, 1952)(1822, 1958, 1957)(1824, 1959, 1850)(1830, 1964, 1965)(1836, 1969, 1920)(1838, 1971, 1970)(1841, 1974, 1975)(1843, 1978, 1976)(1844, 1977, 1948)(1845, 1979, 1980)(1847, 1981, 1966)(1849, 1983, 1982)(1852, 1986, 1987)(1854, 1990, 1988)(1855, 1989, 1991)(1856, 1992, 1993)(1858, 1994, 1859)(1860, 1861, 1998)(1862, 1863, 2000)(1867, 1868, 2005)(1875, 2011, 2012)(1880, 2016, 2015)(1881, 2017, 2018)(1884, 2020, 2019)(1893, 2025, 1894)(1895, 1896, 2027)(1898, 2029, 1899)(1901, 2031, 2033)(1903, 2035, 2034)(1904, 2036, 2037)(1907, 2040, 2039)(1908, 1996, 2038)(1909, 2041, 1910)(1914, 2046, 1915)(1916, 1917, 2049)(1921, 1922, 2053)(1926, 2056, 2055)(1927, 2006, 2051)(1938, 2063, 2064)(1943, 2044, 2067)(1944, 2068, 2069)(1947, 2071, 2070)(1955, 2075, 1956)(1960, 2080, 1961)(1962, 1963, 2082)(1967, 1968, 2086)(1972, 2089, 2088)(1973, 2045, 2084)(1984, 2096, 2095)(1985, 2079, 2002)(1995, 2103, 2102)(1997, 2104, 2105)(1999, 2106, 2101)(2001, 2091, 2092)(2003, 2054, 2109)(2004, 2110, 2111)(2007, 2008, 2078)(2009, 2010, 2115)(2013, 2014, 2057)(2021, 2077, 2022)(2023, 2024, 2125)(2026, 2073, 2072)(2028, 2129, 2128)(2030, 2131, 2130)(2032, 2132, 2133)(2042, 2074, 2138)(2043, 2136, 2135)(2047, 2142, 2141)(2048, 2143, 2060)(2050, 2099, 2100)(2052, 2087, 2146)(2058, 2059, 2083)(2061, 2062, 2152)(2065, 2066, 2090)(2076, 2137, 2161)(2081, 2164, 2093)(2085, 2094, 2167)(2097, 2134, 2098)(2107, 2157, 2156)(2108, 2163, 2117)(2112, 2154, 2145)(2113, 2162, 2169)(2114, 2180, 2168)(2116, 2176, 2177)(2118, 2149, 2170)(2119, 2120, 2173)(2121, 2165, 2122)(2123, 2124, 2153)(2126, 2181, 2160)(2127, 2158, 2159)(2139, 2148, 2155)(2140, 2183, 2166)(2144, 2178, 2174)(2147, 2182, 2179)(2150, 2175, 2171)(2151, 2184, 2172) L = (1, 1093)(2, 1094)(3, 1095)(4, 1096)(5, 1097)(6, 1098)(7, 1099)(8, 1100)(9, 1101)(10, 1102)(11, 1103)(12, 1104)(13, 1105)(14, 1106)(15, 1107)(16, 1108)(17, 1109)(18, 1110)(19, 1111)(20, 1112)(21, 1113)(22, 1114)(23, 1115)(24, 1116)(25, 1117)(26, 1118)(27, 1119)(28, 1120)(29, 1121)(30, 1122)(31, 1123)(32, 1124)(33, 1125)(34, 1126)(35, 1127)(36, 1128)(37, 1129)(38, 1130)(39, 1131)(40, 1132)(41, 1133)(42, 1134)(43, 1135)(44, 1136)(45, 1137)(46, 1138)(47, 1139)(48, 1140)(49, 1141)(50, 1142)(51, 1143)(52, 1144)(53, 1145)(54, 1146)(55, 1147)(56, 1148)(57, 1149)(58, 1150)(59, 1151)(60, 1152)(61, 1153)(62, 1154)(63, 1155)(64, 1156)(65, 1157)(66, 1158)(67, 1159)(68, 1160)(69, 1161)(70, 1162)(71, 1163)(72, 1164)(73, 1165)(74, 1166)(75, 1167)(76, 1168)(77, 1169)(78, 1170)(79, 1171)(80, 1172)(81, 1173)(82, 1174)(83, 1175)(84, 1176)(85, 1177)(86, 1178)(87, 1179)(88, 1180)(89, 1181)(90, 1182)(91, 1183)(92, 1184)(93, 1185)(94, 1186)(95, 1187)(96, 1188)(97, 1189)(98, 1190)(99, 1191)(100, 1192)(101, 1193)(102, 1194)(103, 1195)(104, 1196)(105, 1197)(106, 1198)(107, 1199)(108, 1200)(109, 1201)(110, 1202)(111, 1203)(112, 1204)(113, 1205)(114, 1206)(115, 1207)(116, 1208)(117, 1209)(118, 1210)(119, 1211)(120, 1212)(121, 1213)(122, 1214)(123, 1215)(124, 1216)(125, 1217)(126, 1218)(127, 1219)(128, 1220)(129, 1221)(130, 1222)(131, 1223)(132, 1224)(133, 1225)(134, 1226)(135, 1227)(136, 1228)(137, 1229)(138, 1230)(139, 1231)(140, 1232)(141, 1233)(142, 1234)(143, 1235)(144, 1236)(145, 1237)(146, 1238)(147, 1239)(148, 1240)(149, 1241)(150, 1242)(151, 1243)(152, 1244)(153, 1245)(154, 1246)(155, 1247)(156, 1248)(157, 1249)(158, 1250)(159, 1251)(160, 1252)(161, 1253)(162, 1254)(163, 1255)(164, 1256)(165, 1257)(166, 1258)(167, 1259)(168, 1260)(169, 1261)(170, 1262)(171, 1263)(172, 1264)(173, 1265)(174, 1266)(175, 1267)(176, 1268)(177, 1269)(178, 1270)(179, 1271)(180, 1272)(181, 1273)(182, 1274)(183, 1275)(184, 1276)(185, 1277)(186, 1278)(187, 1279)(188, 1280)(189, 1281)(190, 1282)(191, 1283)(192, 1284)(193, 1285)(194, 1286)(195, 1287)(196, 1288)(197, 1289)(198, 1290)(199, 1291)(200, 1292)(201, 1293)(202, 1294)(203, 1295)(204, 1296)(205, 1297)(206, 1298)(207, 1299)(208, 1300)(209, 1301)(210, 1302)(211, 1303)(212, 1304)(213, 1305)(214, 1306)(215, 1307)(216, 1308)(217, 1309)(218, 1310)(219, 1311)(220, 1312)(221, 1313)(222, 1314)(223, 1315)(224, 1316)(225, 1317)(226, 1318)(227, 1319)(228, 1320)(229, 1321)(230, 1322)(231, 1323)(232, 1324)(233, 1325)(234, 1326)(235, 1327)(236, 1328)(237, 1329)(238, 1330)(239, 1331)(240, 1332)(241, 1333)(242, 1334)(243, 1335)(244, 1336)(245, 1337)(246, 1338)(247, 1339)(248, 1340)(249, 1341)(250, 1342)(251, 1343)(252, 1344)(253, 1345)(254, 1346)(255, 1347)(256, 1348)(257, 1349)(258, 1350)(259, 1351)(260, 1352)(261, 1353)(262, 1354)(263, 1355)(264, 1356)(265, 1357)(266, 1358)(267, 1359)(268, 1360)(269, 1361)(270, 1362)(271, 1363)(272, 1364)(273, 1365)(274, 1366)(275, 1367)(276, 1368)(277, 1369)(278, 1370)(279, 1371)(280, 1372)(281, 1373)(282, 1374)(283, 1375)(284, 1376)(285, 1377)(286, 1378)(287, 1379)(288, 1380)(289, 1381)(290, 1382)(291, 1383)(292, 1384)(293, 1385)(294, 1386)(295, 1387)(296, 1388)(297, 1389)(298, 1390)(299, 1391)(300, 1392)(301, 1393)(302, 1394)(303, 1395)(304, 1396)(305, 1397)(306, 1398)(307, 1399)(308, 1400)(309, 1401)(310, 1402)(311, 1403)(312, 1404)(313, 1405)(314, 1406)(315, 1407)(316, 1408)(317, 1409)(318, 1410)(319, 1411)(320, 1412)(321, 1413)(322, 1414)(323, 1415)(324, 1416)(325, 1417)(326, 1418)(327, 1419)(328, 1420)(329, 1421)(330, 1422)(331, 1423)(332, 1424)(333, 1425)(334, 1426)(335, 1427)(336, 1428)(337, 1429)(338, 1430)(339, 1431)(340, 1432)(341, 1433)(342, 1434)(343, 1435)(344, 1436)(345, 1437)(346, 1438)(347, 1439)(348, 1440)(349, 1441)(350, 1442)(351, 1443)(352, 1444)(353, 1445)(354, 1446)(355, 1447)(356, 1448)(357, 1449)(358, 1450)(359, 1451)(360, 1452)(361, 1453)(362, 1454)(363, 1455)(364, 1456)(365, 1457)(366, 1458)(367, 1459)(368, 1460)(369, 1461)(370, 1462)(371, 1463)(372, 1464)(373, 1465)(374, 1466)(375, 1467)(376, 1468)(377, 1469)(378, 1470)(379, 1471)(380, 1472)(381, 1473)(382, 1474)(383, 1475)(384, 1476)(385, 1477)(386, 1478)(387, 1479)(388, 1480)(389, 1481)(390, 1482)(391, 1483)(392, 1484)(393, 1485)(394, 1486)(395, 1487)(396, 1488)(397, 1489)(398, 1490)(399, 1491)(400, 1492)(401, 1493)(402, 1494)(403, 1495)(404, 1496)(405, 1497)(406, 1498)(407, 1499)(408, 1500)(409, 1501)(410, 1502)(411, 1503)(412, 1504)(413, 1505)(414, 1506)(415, 1507)(416, 1508)(417, 1509)(418, 1510)(419, 1511)(420, 1512)(421, 1513)(422, 1514)(423, 1515)(424, 1516)(425, 1517)(426, 1518)(427, 1519)(428, 1520)(429, 1521)(430, 1522)(431, 1523)(432, 1524)(433, 1525)(434, 1526)(435, 1527)(436, 1528)(437, 1529)(438, 1530)(439, 1531)(440, 1532)(441, 1533)(442, 1534)(443, 1535)(444, 1536)(445, 1537)(446, 1538)(447, 1539)(448, 1540)(449, 1541)(450, 1542)(451, 1543)(452, 1544)(453, 1545)(454, 1546)(455, 1547)(456, 1548)(457, 1549)(458, 1550)(459, 1551)(460, 1552)(461, 1553)(462, 1554)(463, 1555)(464, 1556)(465, 1557)(466, 1558)(467, 1559)(468, 1560)(469, 1561)(470, 1562)(471, 1563)(472, 1564)(473, 1565)(474, 1566)(475, 1567)(476, 1568)(477, 1569)(478, 1570)(479, 1571)(480, 1572)(481, 1573)(482, 1574)(483, 1575)(484, 1576)(485, 1577)(486, 1578)(487, 1579)(488, 1580)(489, 1581)(490, 1582)(491, 1583)(492, 1584)(493, 1585)(494, 1586)(495, 1587)(496, 1588)(497, 1589)(498, 1590)(499, 1591)(500, 1592)(501, 1593)(502, 1594)(503, 1595)(504, 1596)(505, 1597)(506, 1598)(507, 1599)(508, 1600)(509, 1601)(510, 1602)(511, 1603)(512, 1604)(513, 1605)(514, 1606)(515, 1607)(516, 1608)(517, 1609)(518, 1610)(519, 1611)(520, 1612)(521, 1613)(522, 1614)(523, 1615)(524, 1616)(525, 1617)(526, 1618)(527, 1619)(528, 1620)(529, 1621)(530, 1622)(531, 1623)(532, 1624)(533, 1625)(534, 1626)(535, 1627)(536, 1628)(537, 1629)(538, 1630)(539, 1631)(540, 1632)(541, 1633)(542, 1634)(543, 1635)(544, 1636)(545, 1637)(546, 1638)(547, 1639)(548, 1640)(549, 1641)(550, 1642)(551, 1643)(552, 1644)(553, 1645)(554, 1646)(555, 1647)(556, 1648)(557, 1649)(558, 1650)(559, 1651)(560, 1652)(561, 1653)(562, 1654)(563, 1655)(564, 1656)(565, 1657)(566, 1658)(567, 1659)(568, 1660)(569, 1661)(570, 1662)(571, 1663)(572, 1664)(573, 1665)(574, 1666)(575, 1667)(576, 1668)(577, 1669)(578, 1670)(579, 1671)(580, 1672)(581, 1673)(582, 1674)(583, 1675)(584, 1676)(585, 1677)(586, 1678)(587, 1679)(588, 1680)(589, 1681)(590, 1682)(591, 1683)(592, 1684)(593, 1685)(594, 1686)(595, 1687)(596, 1688)(597, 1689)(598, 1690)(599, 1691)(600, 1692)(601, 1693)(602, 1694)(603, 1695)(604, 1696)(605, 1697)(606, 1698)(607, 1699)(608, 1700)(609, 1701)(610, 1702)(611, 1703)(612, 1704)(613, 1705)(614, 1706)(615, 1707)(616, 1708)(617, 1709)(618, 1710)(619, 1711)(620, 1712)(621, 1713)(622, 1714)(623, 1715)(624, 1716)(625, 1717)(626, 1718)(627, 1719)(628, 1720)(629, 1721)(630, 1722)(631, 1723)(632, 1724)(633, 1725)(634, 1726)(635, 1727)(636, 1728)(637, 1729)(638, 1730)(639, 1731)(640, 1732)(641, 1733)(642, 1734)(643, 1735)(644, 1736)(645, 1737)(646, 1738)(647, 1739)(648, 1740)(649, 1741)(650, 1742)(651, 1743)(652, 1744)(653, 1745)(654, 1746)(655, 1747)(656, 1748)(657, 1749)(658, 1750)(659, 1751)(660, 1752)(661, 1753)(662, 1754)(663, 1755)(664, 1756)(665, 1757)(666, 1758)(667, 1759)(668, 1760)(669, 1761)(670, 1762)(671, 1763)(672, 1764)(673, 1765)(674, 1766)(675, 1767)(676, 1768)(677, 1769)(678, 1770)(679, 1771)(680, 1772)(681, 1773)(682, 1774)(683, 1775)(684, 1776)(685, 1777)(686, 1778)(687, 1779)(688, 1780)(689, 1781)(690, 1782)(691, 1783)(692, 1784)(693, 1785)(694, 1786)(695, 1787)(696, 1788)(697, 1789)(698, 1790)(699, 1791)(700, 1792)(701, 1793)(702, 1794)(703, 1795)(704, 1796)(705, 1797)(706, 1798)(707, 1799)(708, 1800)(709, 1801)(710, 1802)(711, 1803)(712, 1804)(713, 1805)(714, 1806)(715, 1807)(716, 1808)(717, 1809)(718, 1810)(719, 1811)(720, 1812)(721, 1813)(722, 1814)(723, 1815)(724, 1816)(725, 1817)(726, 1818)(727, 1819)(728, 1820)(729, 1821)(730, 1822)(731, 1823)(732, 1824)(733, 1825)(734, 1826)(735, 1827)(736, 1828)(737, 1829)(738, 1830)(739, 1831)(740, 1832)(741, 1833)(742, 1834)(743, 1835)(744, 1836)(745, 1837)(746, 1838)(747, 1839)(748, 1840)(749, 1841)(750, 1842)(751, 1843)(752, 1844)(753, 1845)(754, 1846)(755, 1847)(756, 1848)(757, 1849)(758, 1850)(759, 1851)(760, 1852)(761, 1853)(762, 1854)(763, 1855)(764, 1856)(765, 1857)(766, 1858)(767, 1859)(768, 1860)(769, 1861)(770, 1862)(771, 1863)(772, 1864)(773, 1865)(774, 1866)(775, 1867)(776, 1868)(777, 1869)(778, 1870)(779, 1871)(780, 1872)(781, 1873)(782, 1874)(783, 1875)(784, 1876)(785, 1877)(786, 1878)(787, 1879)(788, 1880)(789, 1881)(790, 1882)(791, 1883)(792, 1884)(793, 1885)(794, 1886)(795, 1887)(796, 1888)(797, 1889)(798, 1890)(799, 1891)(800, 1892)(801, 1893)(802, 1894)(803, 1895)(804, 1896)(805, 1897)(806, 1898)(807, 1899)(808, 1900)(809, 1901)(810, 1902)(811, 1903)(812, 1904)(813, 1905)(814, 1906)(815, 1907)(816, 1908)(817, 1909)(818, 1910)(819, 1911)(820, 1912)(821, 1913)(822, 1914)(823, 1915)(824, 1916)(825, 1917)(826, 1918)(827, 1919)(828, 1920)(829, 1921)(830, 1922)(831, 1923)(832, 1924)(833, 1925)(834, 1926)(835, 1927)(836, 1928)(837, 1929)(838, 1930)(839, 1931)(840, 1932)(841, 1933)(842, 1934)(843, 1935)(844, 1936)(845, 1937)(846, 1938)(847, 1939)(848, 1940)(849, 1941)(850, 1942)(851, 1943)(852, 1944)(853, 1945)(854, 1946)(855, 1947)(856, 1948)(857, 1949)(858, 1950)(859, 1951)(860, 1952)(861, 1953)(862, 1954)(863, 1955)(864, 1956)(865, 1957)(866, 1958)(867, 1959)(868, 1960)(869, 1961)(870, 1962)(871, 1963)(872, 1964)(873, 1965)(874, 1966)(875, 1967)(876, 1968)(877, 1969)(878, 1970)(879, 1971)(880, 1972)(881, 1973)(882, 1974)(883, 1975)(884, 1976)(885, 1977)(886, 1978)(887, 1979)(888, 1980)(889, 1981)(890, 1982)(891, 1983)(892, 1984)(893, 1985)(894, 1986)(895, 1987)(896, 1988)(897, 1989)(898, 1990)(899, 1991)(900, 1992)(901, 1993)(902, 1994)(903, 1995)(904, 1996)(905, 1997)(906, 1998)(907, 1999)(908, 2000)(909, 2001)(910, 2002)(911, 2003)(912, 2004)(913, 2005)(914, 2006)(915, 2007)(916, 2008)(917, 2009)(918, 2010)(919, 2011)(920, 2012)(921, 2013)(922, 2014)(923, 2015)(924, 2016)(925, 2017)(926, 2018)(927, 2019)(928, 2020)(929, 2021)(930, 2022)(931, 2023)(932, 2024)(933, 2025)(934, 2026)(935, 2027)(936, 2028)(937, 2029)(938, 2030)(939, 2031)(940, 2032)(941, 2033)(942, 2034)(943, 2035)(944, 2036)(945, 2037)(946, 2038)(947, 2039)(948, 2040)(949, 2041)(950, 2042)(951, 2043)(952, 2044)(953, 2045)(954, 2046)(955, 2047)(956, 2048)(957, 2049)(958, 2050)(959, 2051)(960, 2052)(961, 2053)(962, 2054)(963, 2055)(964, 2056)(965, 2057)(966, 2058)(967, 2059)(968, 2060)(969, 2061)(970, 2062)(971, 2063)(972, 2064)(973, 2065)(974, 2066)(975, 2067)(976, 2068)(977, 2069)(978, 2070)(979, 2071)(980, 2072)(981, 2073)(982, 2074)(983, 2075)(984, 2076)(985, 2077)(986, 2078)(987, 2079)(988, 2080)(989, 2081)(990, 2082)(991, 2083)(992, 2084)(993, 2085)(994, 2086)(995, 2087)(996, 2088)(997, 2089)(998, 2090)(999, 2091)(1000, 2092)(1001, 2093)(1002, 2094)(1003, 2095)(1004, 2096)(1005, 2097)(1006, 2098)(1007, 2099)(1008, 2100)(1009, 2101)(1010, 2102)(1011, 2103)(1012, 2104)(1013, 2105)(1014, 2106)(1015, 2107)(1016, 2108)(1017, 2109)(1018, 2110)(1019, 2111)(1020, 2112)(1021, 2113)(1022, 2114)(1023, 2115)(1024, 2116)(1025, 2117)(1026, 2118)(1027, 2119)(1028, 2120)(1029, 2121)(1030, 2122)(1031, 2123)(1032, 2124)(1033, 2125)(1034, 2126)(1035, 2127)(1036, 2128)(1037, 2129)(1038, 2130)(1039, 2131)(1040, 2132)(1041, 2133)(1042, 2134)(1043, 2135)(1044, 2136)(1045, 2137)(1046, 2138)(1047, 2139)(1048, 2140)(1049, 2141)(1050, 2142)(1051, 2143)(1052, 2144)(1053, 2145)(1054, 2146)(1055, 2147)(1056, 2148)(1057, 2149)(1058, 2150)(1059, 2151)(1060, 2152)(1061, 2153)(1062, 2154)(1063, 2155)(1064, 2156)(1065, 2157)(1066, 2158)(1067, 2159)(1068, 2160)(1069, 2161)(1070, 2162)(1071, 2163)(1072, 2164)(1073, 2165)(1074, 2166)(1075, 2167)(1076, 2168)(1077, 2169)(1078, 2170)(1079, 2171)(1080, 2172)(1081, 2173)(1082, 2174)(1083, 2175)(1084, 2176)(1085, 2177)(1086, 2178)(1087, 2179)(1088, 2180)(1089, 2181)(1090, 2182)(1091, 2183)(1092, 2184) local type(s) :: { ( 4^3 ), ( 4^7 ) } Outer automorphisms :: reflexible Dual of E14.634 Transitivity :: ET+ Graph:: simple bipartite v = 520 e = 1092 f = 546 degree seq :: [ 3^364, 7^156 ] E14.623 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T2^7, T2^-1 * T1 * T2 * T1 * T2^-5, T2^3 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^3, (T2^2 * T1^-1)^7, T2^-1 * T1 * T2^-2 * T1 * T2^-3 * T1^-1 * T2 * T1^-1 * T2^3 * T1^-1 * T2 * T1^-1 * T2^-3 * T1 * T2^-2 * T1 ] Map:: polyhedral non-degenerate R = (1, 3, 9, 19, 26, 13, 5)(2, 6, 14, 27, 32, 16, 7)(4, 11, 22, 40, 34, 17, 8)(10, 21, 39, 63, 59, 35, 18)(12, 23, 42, 68, 71, 43, 24)(15, 29, 50, 78, 81, 51, 30)(20, 38, 62, 94, 92, 60, 36)(25, 44, 72, 108, 111, 73, 45)(28, 49, 77, 116, 114, 75, 47)(31, 52, 82, 124, 127, 83, 53)(33, 55, 85, 129, 132, 86, 56)(37, 61, 93, 140, 112, 74, 46)(41, 67, 101, 151, 149, 99, 65)(48, 76, 115, 169, 128, 84, 54)(57, 66, 100, 150, 194, 133, 87)(58, 88, 134, 195, 198, 135, 89)(64, 98, 147, 212, 210, 145, 96)(69, 104, 155, 224, 222, 153, 102)(70, 105, 156, 226, 229, 157, 106)(79, 120, 176, 250, 248, 174, 118)(80, 121, 177, 252, 255, 178, 122)(90, 97, 146, 211, 280, 199, 136)(91, 137, 200, 281, 284, 201, 138)(95, 144, 208, 292, 290, 206, 142)(103, 154, 223, 311, 230, 158, 107)(109, 161, 233, 326, 324, 231, 159)(110, 162, 234, 328, 331, 235, 163)(113, 166, 238, 334, 337, 239, 167)(117, 173, 246, 345, 343, 244, 171)(119, 175, 249, 350, 256, 179, 123)(125, 182, 259, 365, 363, 257, 180)(126, 183, 260, 367, 370, 261, 184)(130, 189, 266, 376, 374, 264, 187)(131, 190, 267, 378, 381, 268, 191)(139, 143, 207, 291, 402, 285, 202)(141, 205, 288, 406, 404, 286, 203)(148, 214, 301, 422, 425, 302, 215)(152, 220, 307, 431, 429, 305, 218)(160, 232, 325, 452, 332, 236, 164)(165, 204, 287, 405, 465, 333, 237)(168, 172, 245, 344, 473, 338, 240)(170, 243, 341, 477, 475, 339, 241)(181, 258, 364, 505, 371, 262, 185)(186, 242, 340, 476, 517, 372, 263)(188, 265, 375, 521, 382, 269, 192)(193, 270, 383, 532, 535, 384, 271)(196, 275, 388, 540, 538, 386, 273)(197, 276, 389, 542, 544, 390, 277)(209, 294, 415, 571, 574, 416, 295)(213, 300, 421, 580, 578, 419, 298)(216, 219, 306, 430, 588, 426, 303)(217, 304, 427, 589, 536, 385, 272)(221, 308, 433, 597, 600, 434, 309)(225, 315, 441, 608, 606, 439, 313)(227, 318, 444, 612, 610, 442, 316)(228, 319, 445, 614, 616, 446, 320)(247, 347, 486, 658, 661, 487, 348)(251, 354, 494, 669, 667, 492, 352)(253, 357, 497, 673, 671, 495, 355)(254, 358, 498, 675, 677, 499, 359)(274, 387, 539, 722, 545, 391, 278)(279, 392, 546, 728, 731, 547, 393)(282, 397, 551, 736, 734, 549, 395)(283, 398, 552, 738, 739, 553, 399)(289, 408, 565, 749, 676, 566, 409)(293, 414, 369, 513, 692, 569, 412)(296, 299, 420, 579, 760, 575, 417)(297, 418, 576, 761, 732, 548, 394)(310, 314, 440, 607, 788, 601, 435)(312, 438, 604, 792, 790, 602, 436)(317, 443, 611, 799, 617, 447, 321)(322, 437, 603, 791, 805, 618, 448)(323, 449, 619, 806, 809, 620, 450)(327, 456, 627, 814, 813, 625, 454)(329, 459, 630, 666, 816, 628, 457)(330, 460, 631, 781, 595, 432, 461)(335, 468, 639, 733, 824, 637, 466)(336, 469, 640, 756, 826, 641, 470)(342, 479, 652, 725, 543, 653, 480)(346, 485, 380, 529, 710, 656, 483)(349, 353, 493, 668, 845, 662, 488)(351, 491, 665, 849, 847, 663, 489)(356, 496, 672, 853, 678, 500, 360)(361, 490, 664, 848, 858, 679, 501)(362, 502, 680, 859, 861, 681, 503)(366, 509, 688, 864, 721, 686, 507)(368, 512, 691, 577, 763, 689, 510)(373, 518, 698, 872, 807, 699, 519)(377, 525, 706, 875, 798, 704, 523)(379, 528, 709, 605, 793, 707, 526)(396, 550, 735, 843, 660, 554, 400)(401, 555, 740, 897, 899, 741, 556)(403, 558, 743, 839, 878, 744, 559)(407, 564, 534, 716, 884, 747, 562)(410, 413, 570, 754, 907, 751, 567)(411, 568, 752, 908, 900, 742, 557)(423, 583, 768, 823, 895, 766, 581)(424, 584, 769, 784, 914, 770, 585)(428, 591, 777, 802, 615, 778, 592)(451, 455, 626, 674, 855, 810, 621)(453, 624, 730, 892, 934, 811, 622)(458, 629, 817, 937, 819, 632, 462)(463, 623, 812, 935, 940, 820, 633)(464, 634, 821, 834, 650, 478, 635)(467, 638, 825, 758, 573, 642, 471)(472, 643, 827, 943, 945, 828, 644)(474, 646, 830, 922, 818, 831, 647)(481, 484, 657, 840, 953, 837, 654)(482, 655, 838, 954, 946, 829, 645)(504, 508, 687, 541, 724, 808, 682)(506, 685, 804, 931, 963, 862, 683)(511, 690, 866, 966, 868, 693, 514)(515, 684, 863, 964, 968, 869, 694)(516, 695, 870, 917, 775, 590, 696)(520, 524, 705, 613, 801, 860, 700)(522, 703, 857, 960, 972, 873, 701)(527, 708, 877, 975, 879, 711, 530)(531, 702, 874, 973, 977, 880, 712)(533, 715, 883, 753, 867, 881, 713)(537, 719, 887, 783, 598, 785, 720)(560, 563, 748, 904, 993, 901, 745)(561, 746, 902, 994, 942, 822, 636)(572, 757, 852, 670, 851, 910, 755)(582, 767, 737, 786, 599, 771, 586)(587, 772, 915, 1000, 912, 762, 773)(593, 596, 782, 923, 1008, 920, 779)(594, 780, 921, 1009, 1003, 916, 774)(609, 796, 896, 841, 659, 842, 797)(648, 651, 835, 950, 1028, 947, 832)(649, 833, 948, 1029, 970, 871, 697)(714, 882, 978, 1045, 980, 885, 717)(718, 776, 918, 1005, 1046, 981, 886)(723, 787, 924, 1010, 1047, 982, 888)(726, 836, 951, 936, 815, 850, 727)(729, 891, 985, 903, 979, 983, 889)(750, 905, 974, 876, 794, 795, 856)(759, 911, 999, 1057, 997, 909, 854)(764, 765, 803, 919, 1006, 965, 865)(789, 925, 1011, 949, 941, 1012, 926)(800, 844, 939, 1021, 1065, 1015, 930)(846, 955, 1031, 1004, 969, 1032, 956)(890, 984, 1048, 1080, 1049, 986, 893)(894, 913, 1001, 1060, 1081, 1050, 987)(898, 990, 1018, 933, 1017, 1051, 988)(906, 996, 1056, 1084, 1054, 995, 976)(927, 929, 989, 1052, 1082, 1064, 1013)(928, 1014, 1055, 1085, 1066, 1016, 932)(938, 952, 992, 1053, 1083, 1067, 1020)(944, 1025, 1037, 962, 1036, 1069, 1023)(957, 959, 1024, 1070, 1088, 1074, 1033)(958, 1034, 1072, 1090, 1075, 1035, 961)(967, 1007, 1027, 1071, 1089, 1076, 1039)(971, 1041, 1078, 1059, 1002, 1061, 1042)(991, 998, 1058, 1086, 1068, 1022, 1019)(1026, 1030, 1073, 1091, 1077, 1040, 1038)(1043, 1062, 1063, 1087, 1092, 1079, 1044)(1093, 1094, 1096)(1095, 1100, 1102)(1097, 1104, 1098)(1099, 1107, 1103)(1101, 1110, 1112)(1105, 1117, 1115)(1106, 1116, 1120)(1108, 1123, 1121)(1109, 1125, 1113)(1111, 1128, 1129)(1114, 1122, 1133)(1118, 1138, 1136)(1119, 1139, 1140)(1124, 1146, 1144)(1126, 1149, 1147)(1127, 1150, 1130)(1131, 1148, 1156)(1132, 1157, 1158)(1134, 1137, 1161)(1135, 1162, 1141)(1142, 1145, 1171)(1143, 1172, 1159)(1151, 1182, 1180)(1152, 1183, 1153)(1154, 1181, 1187)(1155, 1188, 1189)(1160, 1194, 1195)(1163, 1199, 1197)(1164, 1166, 1201)(1165, 1202, 1196)(1167, 1205, 1168)(1169, 1198, 1209)(1170, 1210, 1211)(1173, 1215, 1213)(1174, 1176, 1217)(1175, 1218, 1212)(1177, 1179, 1222)(1178, 1223, 1190)(1184, 1231, 1229)(1185, 1230, 1233)(1186, 1234, 1235)(1191, 1240, 1192)(1193, 1214, 1244)(1200, 1251, 1252)(1203, 1256, 1254)(1204, 1257, 1253)(1206, 1260, 1258)(1207, 1259, 1262)(1208, 1263, 1264)(1216, 1272, 1273)(1219, 1277, 1275)(1220, 1278, 1274)(1221, 1279, 1280)(1224, 1284, 1282)(1225, 1285, 1281)(1226, 1228, 1288)(1227, 1289, 1236)(1232, 1295, 1296)(1237, 1301, 1238)(1239, 1283, 1305)(1241, 1308, 1306)(1242, 1307, 1309)(1243, 1310, 1311)(1245, 1313, 1246)(1247, 1255, 1317)(1248, 1250, 1319)(1249, 1320, 1265)(1261, 1333, 1334)(1266, 1339, 1267)(1268, 1276, 1343)(1269, 1271, 1345)(1270, 1346, 1312)(1286, 1364, 1362)(1287, 1365, 1366)(1290, 1370, 1368)(1291, 1371, 1367)(1292, 1294, 1374)(1293, 1375, 1297)(1298, 1381, 1299)(1300, 1369, 1385)(1302, 1388, 1386)(1303, 1387, 1389)(1304, 1390, 1391)(1314, 1402, 1400)(1315, 1401, 1404)(1316, 1405, 1406)(1318, 1408, 1409)(1321, 1413, 1411)(1322, 1414, 1410)(1323, 1415, 1324)(1325, 1329, 1419)(1326, 1328, 1421)(1327, 1422, 1407)(1330, 1332, 1427)(1331, 1428, 1335)(1336, 1434, 1337)(1338, 1412, 1438)(1340, 1441, 1439)(1341, 1440, 1443)(1342, 1444, 1445)(1344, 1447, 1448)(1347, 1452, 1450)(1348, 1453, 1449)(1349, 1454, 1350)(1351, 1355, 1458)(1352, 1354, 1460)(1353, 1461, 1446)(1356, 1465, 1357)(1358, 1363, 1469)(1359, 1361, 1471)(1360, 1472, 1392)(1372, 1486, 1484)(1373, 1487, 1488)(1376, 1492, 1490)(1377, 1493, 1489)(1378, 1495, 1379)(1380, 1491, 1499)(1382, 1502, 1500)(1383, 1501, 1503)(1384, 1504, 1505)(1393, 1395, 1515)(1394, 1516, 1396)(1397, 1520, 1398)(1399, 1451, 1524)(1403, 1528, 1529)(1416, 1543, 1541)(1417, 1542, 1545)(1418, 1546, 1547)(1420, 1549, 1550)(1423, 1554, 1552)(1424, 1555, 1551)(1425, 1556, 1548)(1426, 1558, 1559)(1429, 1563, 1561)(1430, 1564, 1560)(1431, 1566, 1432)(1433, 1562, 1570)(1435, 1573, 1571)(1436, 1572, 1574)(1437, 1575, 1576)(1442, 1581, 1582)(1455, 1596, 1594)(1456, 1595, 1598)(1457, 1599, 1600)(1459, 1602, 1603)(1462, 1606, 1605)(1463, 1607, 1604)(1464, 1608, 1601)(1466, 1612, 1610)(1467, 1611, 1614)(1468, 1615, 1616)(1470, 1618, 1619)(1473, 1622, 1621)(1474, 1623, 1620)(1475, 1477, 1625)(1476, 1626, 1617)(1478, 1629, 1479)(1480, 1485, 1633)(1481, 1483, 1635)(1482, 1586, 1506)(1494, 1649, 1647)(1496, 1652, 1650)(1497, 1651, 1653)(1498, 1654, 1655)(1507, 1509, 1664)(1508, 1665, 1510)(1511, 1669, 1512)(1513, 1577, 1538)(1514, 1673, 1674)(1517, 1678, 1676)(1518, 1679, 1675)(1519, 1677, 1682)(1521, 1685, 1683)(1522, 1684, 1686)(1523, 1687, 1688)(1525, 1527, 1690)(1526, 1691, 1530)(1531, 1697, 1532)(1533, 1553, 1591)(1534, 1701, 1535)(1536, 1540, 1705)(1537, 1539, 1707)(1544, 1714, 1715)(1557, 1728, 1726)(1565, 1737, 1735)(1567, 1740, 1738)(1568, 1739, 1741)(1569, 1742, 1743)(1578, 1580, 1751)(1579, 1752, 1583)(1584, 1758, 1585)(1587, 1762, 1588)(1589, 1593, 1766)(1590, 1592, 1768)(1597, 1775, 1776)(1609, 1789, 1787)(1613, 1793, 1794)(1624, 1805, 1806)(1627, 1809, 1808)(1628, 1810, 1807)(1630, 1813, 1811)(1631, 1812, 1815)(1632, 1779, 1778)(1634, 1817, 1818)(1636, 1819, 1761)(1637, 1747, 1745)(1638, 1640, 1821)(1639, 1822, 1816)(1641, 1825, 1642)(1643, 1648, 1829)(1644, 1646, 1753)(1645, 1798, 1656)(1657, 1659, 1842)(1658, 1770, 1660)(1661, 1845, 1662)(1663, 1847, 1848)(1666, 1732, 1734)(1667, 1851, 1849)(1668, 1850, 1854)(1670, 1856, 1855)(1671, 1783, 1786)(1672, 1708, 1857)(1680, 1866, 1864)(1681, 1867, 1868)(1689, 1875, 1876)(1692, 1861, 1863)(1693, 1879, 1877)(1694, 1881, 1695)(1696, 1878, 1833)(1698, 1886, 1885)(1699, 1801, 1804)(1700, 1769, 1887)(1702, 1890, 1888)(1703, 1889, 1892)(1704, 1797, 1796)(1706, 1894, 1895)(1709, 1872, 1870)(1710, 1896, 1893)(1711, 1713, 1899)(1712, 1900, 1716)(1717, 1765, 1718)(1719, 1727, 1733)(1720, 1907, 1721)(1722, 1725, 1760)(1723, 1724, 1910)(1729, 1915, 1730)(1731, 1736, 1827)(1744, 1746, 1928)(1748, 1931, 1749)(1750, 1933, 1830)(1754, 1936, 1934)(1755, 1938, 1756)(1757, 1935, 1920)(1759, 1942, 1908)(1763, 1905, 1943)(1764, 1944, 1946)(1767, 1841, 1948)(1771, 1949, 1947)(1772, 1774, 1901)(1773, 1952, 1777)(1780, 1788, 1862)(1781, 1957, 1782)(1784, 1785, 1959)(1790, 1792, 1953)(1791, 1902, 1795)(1799, 1968, 1800)(1802, 1803, 1970)(1814, 1980, 1930)(1820, 1981, 1982)(1823, 1985, 1984)(1824, 1986, 1983)(1826, 1987, 1916)(1828, 1859, 1858)(1831, 1988, 1967)(1832, 1834, 1990)(1835, 1837, 1932)(1836, 1971, 1838)(1839, 1995, 1840)(1843, 1998, 1997)(1844, 1945, 2001)(1846, 1975, 1978)(1852, 1961, 2003)(1853, 2004, 2005)(1860, 1865, 1917)(1869, 1871, 2011)(1873, 2014, 1874)(1880, 1972, 2016)(1882, 2019, 2017)(1883, 2018, 2020)(1884, 1991, 2021)(1891, 2022, 2013)(1897, 2024, 2023)(1898, 1964, 1951)(1903, 2025, 1904)(1906, 1918, 2002)(1909, 2028, 2030)(1911, 1925, 1923)(1912, 2031, 1937)(1913, 1914, 2033)(1919, 1921, 2036)(1922, 1924, 2015)(1926, 2041, 1927)(1929, 2044, 2043)(1939, 2049, 2047)(1940, 2048, 2050)(1941, 2037, 2051)(1950, 2053, 2052)(1954, 2054, 1955)(1956, 2006, 1979)(1958, 2057, 2059)(1960, 1974, 1973)(1962, 1963, 2061)(1965, 2063, 1966)(1969, 2066, 2068)(1976, 1977, 2071)(1989, 2080, 2081)(1992, 2083, 2082)(1993, 2084, 2045)(1994, 2067, 2087)(1996, 2077, 2079)(1999, 2073, 2088)(2000, 2089, 2090)(2007, 2008, 2094)(2009, 2096, 2010)(2012, 2099, 2098)(2026, 2078, 2109)(2027, 2110, 2111)(2029, 2112, 2040)(2032, 2114, 2113)(2034, 2106, 2104)(2035, 2115, 2116)(2038, 2118, 2117)(2039, 2119, 2100)(2042, 2103, 2105)(2046, 2074, 2122)(2055, 2108, 2128)(2056, 2129, 2130)(2058, 2131, 2070)(2060, 2132, 2091)(2062, 2126, 2124)(2064, 2127, 2133)(2065, 2134, 2135)(2069, 2136, 2102)(2072, 2076, 2075)(2085, 2142, 2145)(2086, 2146, 2147)(2092, 2151, 2093)(2095, 2154, 2153)(2097, 2123, 2125)(2101, 2107, 2155)(2120, 2156, 2163)(2121, 2159, 2164)(2137, 2168, 2140)(2138, 2166, 2148)(2139, 2171, 2165)(2141, 2144, 2143)(2149, 2169, 2150)(2152, 2170, 2167)(2157, 2160, 2179)(2158, 2162, 2161)(2172, 2181, 2174)(2173, 2182, 2175)(2176, 2180, 2177)(2178, 2183, 2184) L = (1, 1093)(2, 1094)(3, 1095)(4, 1096)(5, 1097)(6, 1098)(7, 1099)(8, 1100)(9, 1101)(10, 1102)(11, 1103)(12, 1104)(13, 1105)(14, 1106)(15, 1107)(16, 1108)(17, 1109)(18, 1110)(19, 1111)(20, 1112)(21, 1113)(22, 1114)(23, 1115)(24, 1116)(25, 1117)(26, 1118)(27, 1119)(28, 1120)(29, 1121)(30, 1122)(31, 1123)(32, 1124)(33, 1125)(34, 1126)(35, 1127)(36, 1128)(37, 1129)(38, 1130)(39, 1131)(40, 1132)(41, 1133)(42, 1134)(43, 1135)(44, 1136)(45, 1137)(46, 1138)(47, 1139)(48, 1140)(49, 1141)(50, 1142)(51, 1143)(52, 1144)(53, 1145)(54, 1146)(55, 1147)(56, 1148)(57, 1149)(58, 1150)(59, 1151)(60, 1152)(61, 1153)(62, 1154)(63, 1155)(64, 1156)(65, 1157)(66, 1158)(67, 1159)(68, 1160)(69, 1161)(70, 1162)(71, 1163)(72, 1164)(73, 1165)(74, 1166)(75, 1167)(76, 1168)(77, 1169)(78, 1170)(79, 1171)(80, 1172)(81, 1173)(82, 1174)(83, 1175)(84, 1176)(85, 1177)(86, 1178)(87, 1179)(88, 1180)(89, 1181)(90, 1182)(91, 1183)(92, 1184)(93, 1185)(94, 1186)(95, 1187)(96, 1188)(97, 1189)(98, 1190)(99, 1191)(100, 1192)(101, 1193)(102, 1194)(103, 1195)(104, 1196)(105, 1197)(106, 1198)(107, 1199)(108, 1200)(109, 1201)(110, 1202)(111, 1203)(112, 1204)(113, 1205)(114, 1206)(115, 1207)(116, 1208)(117, 1209)(118, 1210)(119, 1211)(120, 1212)(121, 1213)(122, 1214)(123, 1215)(124, 1216)(125, 1217)(126, 1218)(127, 1219)(128, 1220)(129, 1221)(130, 1222)(131, 1223)(132, 1224)(133, 1225)(134, 1226)(135, 1227)(136, 1228)(137, 1229)(138, 1230)(139, 1231)(140, 1232)(141, 1233)(142, 1234)(143, 1235)(144, 1236)(145, 1237)(146, 1238)(147, 1239)(148, 1240)(149, 1241)(150, 1242)(151, 1243)(152, 1244)(153, 1245)(154, 1246)(155, 1247)(156, 1248)(157, 1249)(158, 1250)(159, 1251)(160, 1252)(161, 1253)(162, 1254)(163, 1255)(164, 1256)(165, 1257)(166, 1258)(167, 1259)(168, 1260)(169, 1261)(170, 1262)(171, 1263)(172, 1264)(173, 1265)(174, 1266)(175, 1267)(176, 1268)(177, 1269)(178, 1270)(179, 1271)(180, 1272)(181, 1273)(182, 1274)(183, 1275)(184, 1276)(185, 1277)(186, 1278)(187, 1279)(188, 1280)(189, 1281)(190, 1282)(191, 1283)(192, 1284)(193, 1285)(194, 1286)(195, 1287)(196, 1288)(197, 1289)(198, 1290)(199, 1291)(200, 1292)(201, 1293)(202, 1294)(203, 1295)(204, 1296)(205, 1297)(206, 1298)(207, 1299)(208, 1300)(209, 1301)(210, 1302)(211, 1303)(212, 1304)(213, 1305)(214, 1306)(215, 1307)(216, 1308)(217, 1309)(218, 1310)(219, 1311)(220, 1312)(221, 1313)(222, 1314)(223, 1315)(224, 1316)(225, 1317)(226, 1318)(227, 1319)(228, 1320)(229, 1321)(230, 1322)(231, 1323)(232, 1324)(233, 1325)(234, 1326)(235, 1327)(236, 1328)(237, 1329)(238, 1330)(239, 1331)(240, 1332)(241, 1333)(242, 1334)(243, 1335)(244, 1336)(245, 1337)(246, 1338)(247, 1339)(248, 1340)(249, 1341)(250, 1342)(251, 1343)(252, 1344)(253, 1345)(254, 1346)(255, 1347)(256, 1348)(257, 1349)(258, 1350)(259, 1351)(260, 1352)(261, 1353)(262, 1354)(263, 1355)(264, 1356)(265, 1357)(266, 1358)(267, 1359)(268, 1360)(269, 1361)(270, 1362)(271, 1363)(272, 1364)(273, 1365)(274, 1366)(275, 1367)(276, 1368)(277, 1369)(278, 1370)(279, 1371)(280, 1372)(281, 1373)(282, 1374)(283, 1375)(284, 1376)(285, 1377)(286, 1378)(287, 1379)(288, 1380)(289, 1381)(290, 1382)(291, 1383)(292, 1384)(293, 1385)(294, 1386)(295, 1387)(296, 1388)(297, 1389)(298, 1390)(299, 1391)(300, 1392)(301, 1393)(302, 1394)(303, 1395)(304, 1396)(305, 1397)(306, 1398)(307, 1399)(308, 1400)(309, 1401)(310, 1402)(311, 1403)(312, 1404)(313, 1405)(314, 1406)(315, 1407)(316, 1408)(317, 1409)(318, 1410)(319, 1411)(320, 1412)(321, 1413)(322, 1414)(323, 1415)(324, 1416)(325, 1417)(326, 1418)(327, 1419)(328, 1420)(329, 1421)(330, 1422)(331, 1423)(332, 1424)(333, 1425)(334, 1426)(335, 1427)(336, 1428)(337, 1429)(338, 1430)(339, 1431)(340, 1432)(341, 1433)(342, 1434)(343, 1435)(344, 1436)(345, 1437)(346, 1438)(347, 1439)(348, 1440)(349, 1441)(350, 1442)(351, 1443)(352, 1444)(353, 1445)(354, 1446)(355, 1447)(356, 1448)(357, 1449)(358, 1450)(359, 1451)(360, 1452)(361, 1453)(362, 1454)(363, 1455)(364, 1456)(365, 1457)(366, 1458)(367, 1459)(368, 1460)(369, 1461)(370, 1462)(371, 1463)(372, 1464)(373, 1465)(374, 1466)(375, 1467)(376, 1468)(377, 1469)(378, 1470)(379, 1471)(380, 1472)(381, 1473)(382, 1474)(383, 1475)(384, 1476)(385, 1477)(386, 1478)(387, 1479)(388, 1480)(389, 1481)(390, 1482)(391, 1483)(392, 1484)(393, 1485)(394, 1486)(395, 1487)(396, 1488)(397, 1489)(398, 1490)(399, 1491)(400, 1492)(401, 1493)(402, 1494)(403, 1495)(404, 1496)(405, 1497)(406, 1498)(407, 1499)(408, 1500)(409, 1501)(410, 1502)(411, 1503)(412, 1504)(413, 1505)(414, 1506)(415, 1507)(416, 1508)(417, 1509)(418, 1510)(419, 1511)(420, 1512)(421, 1513)(422, 1514)(423, 1515)(424, 1516)(425, 1517)(426, 1518)(427, 1519)(428, 1520)(429, 1521)(430, 1522)(431, 1523)(432, 1524)(433, 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2071)(980, 2072)(981, 2073)(982, 2074)(983, 2075)(984, 2076)(985, 2077)(986, 2078)(987, 2079)(988, 2080)(989, 2081)(990, 2082)(991, 2083)(992, 2084)(993, 2085)(994, 2086)(995, 2087)(996, 2088)(997, 2089)(998, 2090)(999, 2091)(1000, 2092)(1001, 2093)(1002, 2094)(1003, 2095)(1004, 2096)(1005, 2097)(1006, 2098)(1007, 2099)(1008, 2100)(1009, 2101)(1010, 2102)(1011, 2103)(1012, 2104)(1013, 2105)(1014, 2106)(1015, 2107)(1016, 2108)(1017, 2109)(1018, 2110)(1019, 2111)(1020, 2112)(1021, 2113)(1022, 2114)(1023, 2115)(1024, 2116)(1025, 2117)(1026, 2118)(1027, 2119)(1028, 2120)(1029, 2121)(1030, 2122)(1031, 2123)(1032, 2124)(1033, 2125)(1034, 2126)(1035, 2127)(1036, 2128)(1037, 2129)(1038, 2130)(1039, 2131)(1040, 2132)(1041, 2133)(1042, 2134)(1043, 2135)(1044, 2136)(1045, 2137)(1046, 2138)(1047, 2139)(1048, 2140)(1049, 2141)(1050, 2142)(1051, 2143)(1052, 2144)(1053, 2145)(1054, 2146)(1055, 2147)(1056, 2148)(1057, 2149)(1058, 2150)(1059, 2151)(1060, 2152)(1061, 2153)(1062, 2154)(1063, 2155)(1064, 2156)(1065, 2157)(1066, 2158)(1067, 2159)(1068, 2160)(1069, 2161)(1070, 2162)(1071, 2163)(1072, 2164)(1073, 2165)(1074, 2166)(1075, 2167)(1076, 2168)(1077, 2169)(1078, 2170)(1079, 2171)(1080, 2172)(1081, 2173)(1082, 2174)(1083, 2175)(1084, 2176)(1085, 2177)(1086, 2178)(1087, 2179)(1088, 2180)(1089, 2181)(1090, 2182)(1091, 2183)(1092, 2184) local type(s) :: { ( 4^3 ), ( 4^7 ) } Outer automorphisms :: reflexible Dual of E14.635 Transitivity :: ET+ Graph:: simple bipartite v = 520 e = 1092 f = 546 degree seq :: [ 3^364, 7^156 ] E14.624 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T2^-2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T2^-2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T2^7, (T2^-2 * T1 * T2^-3 * T1)^3 ] Map:: polyhedral non-degenerate R = (1, 3, 9, 19, 26, 13, 5)(2, 6, 14, 27, 32, 16, 7)(4, 11, 22, 40, 34, 17, 8)(10, 21, 39, 63, 59, 35, 18)(12, 23, 42, 68, 71, 43, 24)(15, 29, 50, 78, 81, 51, 30)(20, 38, 62, 94, 92, 60, 36)(25, 44, 72, 108, 111, 73, 45)(28, 49, 77, 116, 114, 75, 47)(31, 52, 82, 124, 127, 83, 53)(33, 55, 85, 129, 132, 86, 56)(37, 61, 93, 140, 112, 74, 46)(41, 67, 101, 151, 149, 99, 65)(48, 76, 115, 169, 128, 84, 54)(57, 66, 100, 150, 194, 133, 87)(58, 88, 134, 195, 198, 135, 89)(64, 98, 147, 212, 210, 145, 96)(69, 104, 155, 224, 222, 153, 102)(70, 105, 156, 226, 229, 157, 106)(79, 120, 176, 250, 248, 174, 118)(80, 121, 177, 252, 255, 178, 122)(90, 97, 146, 211, 280, 199, 136)(91, 137, 200, 281, 284, 201, 138)(95, 144, 208, 292, 290, 206, 142)(103, 154, 223, 311, 230, 158, 107)(109, 161, 233, 326, 324, 231, 159)(110, 162, 234, 328, 331, 235, 163)(113, 166, 238, 334, 337, 239, 167)(117, 173, 246, 345, 343, 244, 171)(119, 175, 249, 350, 256, 179, 123)(125, 182, 259, 365, 363, 257, 180)(126, 183, 260, 367, 370, 261, 184)(130, 189, 266, 376, 374, 264, 187)(131, 190, 267, 378, 381, 268, 191)(139, 143, 207, 291, 402, 285, 202)(141, 205, 288, 406, 404, 286, 203)(148, 214, 301, 422, 425, 302, 215)(152, 220, 307, 431, 429, 305, 218)(160, 232, 325, 452, 332, 236, 164)(165, 204, 287, 405, 465, 333, 237)(168, 172, 245, 344, 473, 338, 240)(170, 243, 341, 477, 475, 339, 241)(181, 258, 364, 505, 371, 262, 185)(186, 242, 340, 476, 411, 372, 263)(188, 265, 375, 520, 382, 269, 192)(193, 270, 383, 531, 482, 384, 271)(196, 275, 388, 538, 536, 386, 273)(197, 276, 389, 540, 543, 390, 277)(209, 294, 415, 563, 566, 416, 295)(213, 300, 421, 570, 569, 419, 298)(216, 219, 306, 430, 557, 426, 303)(217, 304, 427, 463, 534, 385, 272)(221, 308, 433, 585, 588, 434, 309)(225, 315, 441, 593, 592, 439, 313)(227, 318, 444, 597, 596, 442, 316)(228, 319, 445, 599, 601, 446, 320)(247, 347, 486, 627, 630, 487, 348)(251, 354, 494, 634, 633, 492, 352)(253, 357, 497, 638, 637, 495, 355)(254, 358, 498, 640, 642, 499, 359)(274, 387, 537, 582, 544, 391, 278)(279, 392, 545, 489, 351, 491, 393)(282, 397, 549, 677, 675, 547, 395)(283, 398, 550, 679, 682, 551, 399)(289, 408, 559, 685, 652, 516, 409)(293, 414, 562, 688, 687, 561, 412)(296, 299, 420, 462, 458, 567, 417)(297, 418, 448, 322, 437, 546, 394)(310, 314, 440, 515, 511, 589, 435)(312, 438, 501, 361, 490, 590, 436)(317, 443, 560, 410, 413, 447, 321)(323, 449, 602, 726, 729, 603, 450)(327, 456, 609, 733, 732, 607, 454)(329, 459, 579, 706, 735, 610, 457)(330, 460, 568, 695, 737, 611, 461)(335, 468, 615, 742, 740, 613, 466)(336, 469, 616, 744, 747, 617, 470)(342, 479, 623, 749, 662, 533, 480)(346, 485, 626, 752, 751, 625, 483)(349, 353, 493, 530, 526, 631, 488)(356, 496, 624, 481, 484, 500, 360)(362, 502, 643, 772, 775, 644, 503)(366, 509, 649, 779, 778, 647, 507)(368, 512, 407, 558, 684, 650, 510)(369, 513, 591, 713, 782, 651, 514)(373, 517, 653, 783, 786, 654, 518)(377, 524, 659, 790, 789, 657, 522)(379, 527, 478, 622, 748, 660, 525)(380, 528, 632, 759, 793, 661, 529)(396, 548, 676, 696, 683, 552, 400)(401, 553, 474, 621, 521, 656, 554)(403, 555, 506, 646, 705, 578, 556)(423, 574, 701, 825, 823, 699, 572)(424, 575, 702, 827, 830, 703, 576)(428, 580, 666, 738, 612, 464, 581)(432, 584, 707, 799, 669, 541, 583)(451, 455, 608, 725, 722, 730, 604)(453, 606, 620, 472, 619, 532, 605)(467, 614, 741, 714, 716, 618, 471)(504, 508, 648, 771, 768, 776, 645)(519, 523, 658, 673, 670, 787, 655)(535, 663, 794, 898, 900, 795, 664)(539, 629, 757, 870, 903, 797, 667)(542, 671, 788, 892, 905, 800, 672)(564, 692, 818, 919, 917, 816, 690)(565, 693, 819, 920, 839, 720, 598)(571, 698, 821, 910, 806, 680, 697)(573, 700, 824, 760, 762, 704, 577)(586, 710, 811, 912, 933, 832, 708)(587, 711, 834, 935, 875, 766, 639)(594, 717, 836, 937, 858, 745, 715)(595, 718, 837, 939, 913, 812, 686)(600, 723, 731, 846, 944, 841, 724)(628, 756, 863, 956, 961, 868, 754)(635, 763, 872, 964, 927, 828, 761)(636, 764, 873, 966, 957, 864, 750)(641, 769, 777, 882, 971, 877, 770)(665, 668, 798, 810, 807, 901, 796)(674, 801, 906, 950, 852, 736, 802)(678, 785, 890, 978, 990, 908, 804)(681, 808, 902, 985, 992, 911, 809)(689, 815, 915, 945, 842, 727, 814)(691, 817, 918, 893, 895, 820, 694)(709, 833, 934, 847, 849, 835, 712)(719, 721, 840, 862, 859, 941, 838)(728, 844, 947, 1017, 953, 856, 743)(734, 850, 948, 1018, 1009, 936, 848)(739, 853, 951, 975, 886, 781, 854)(746, 860, 942, 1000, 1023, 955, 861)(753, 867, 959, 972, 878, 773, 866)(755, 869, 962, 883, 885, 871, 758)(765, 767, 876, 930, 928, 968, 874)(774, 880, 974, 1036, 1004, 925, 826)(780, 813, 914, 994, 986, 963, 884)(784, 889, 831, 931, 1005, 976, 887)(791, 865, 958, 1025, 999, 921, 894)(792, 896, 822, 923, 1002, 980, 897)(803, 805, 909, 845, 843, 946, 907)(829, 929, 969, 1010, 1019, 949, 851)(855, 857, 954, 881, 879, 973, 952)(888, 977, 1003, 924, 926, 979, 891)(899, 983, 922, 1001, 1048, 1040, 981)(904, 987, 916, 996, 1046, 1043, 988)(932, 1006, 1051, 1056, 1015, 943, 1007)(938, 1012, 1053, 1054, 1013, 940, 1011)(960, 1027, 1060, 1065, 1034, 970, 1028)(965, 1031, 1062, 1063, 1032, 967, 1030)(982, 1041, 1047, 997, 998, 1042, 984)(989, 1016, 995, 1045, 1070, 1057, 1020)(991, 1044, 993, 1014, 1055, 1052, 1008)(1021, 1035, 1026, 1059, 1078, 1066, 1037)(1022, 1058, 1024, 1033, 1064, 1061, 1029)(1038, 1050, 1073, 1083, 1067, 1039, 1049)(1068, 1072, 1086, 1090, 1084, 1069, 1071)(1074, 1076, 1075, 1085, 1091, 1087, 1077)(1079, 1081, 1080, 1088, 1092, 1089, 1082)(1093, 1094, 1096)(1095, 1100, 1102)(1097, 1104, 1098)(1099, 1107, 1103)(1101, 1110, 1112)(1105, 1117, 1115)(1106, 1116, 1120)(1108, 1123, 1121)(1109, 1125, 1113)(1111, 1128, 1129)(1114, 1122, 1133)(1118, 1138, 1136)(1119, 1139, 1140)(1124, 1146, 1144)(1126, 1149, 1147)(1127, 1150, 1130)(1131, 1148, 1156)(1132, 1157, 1158)(1134, 1137, 1161)(1135, 1162, 1141)(1142, 1145, 1171)(1143, 1172, 1159)(1151, 1182, 1180)(1152, 1183, 1153)(1154, 1181, 1187)(1155, 1188, 1189)(1160, 1194, 1195)(1163, 1199, 1197)(1164, 1166, 1201)(1165, 1202, 1196)(1167, 1205, 1168)(1169, 1198, 1209)(1170, 1210, 1211)(1173, 1215, 1213)(1174, 1176, 1217)(1175, 1218, 1212)(1177, 1179, 1222)(1178, 1223, 1190)(1184, 1231, 1229)(1185, 1230, 1233)(1186, 1234, 1235)(1191, 1240, 1192)(1193, 1214, 1244)(1200, 1251, 1252)(1203, 1256, 1254)(1204, 1257, 1253)(1206, 1260, 1258)(1207, 1259, 1262)(1208, 1263, 1264)(1216, 1272, 1273)(1219, 1277, 1275)(1220, 1278, 1274)(1221, 1279, 1280)(1224, 1284, 1282)(1225, 1285, 1281)(1226, 1228, 1288)(1227, 1289, 1236)(1232, 1295, 1296)(1237, 1301, 1238)(1239, 1283, 1305)(1241, 1308, 1306)(1242, 1307, 1309)(1243, 1310, 1311)(1245, 1313, 1246)(1247, 1255, 1317)(1248, 1250, 1319)(1249, 1320, 1265)(1261, 1333, 1334)(1266, 1339, 1267)(1268, 1276, 1343)(1269, 1271, 1345)(1270, 1346, 1312)(1286, 1364, 1362)(1287, 1365, 1366)(1290, 1370, 1368)(1291, 1371, 1367)(1292, 1294, 1374)(1293, 1375, 1297)(1298, 1381, 1299)(1300, 1369, 1385)(1302, 1388, 1386)(1303, 1387, 1389)(1304, 1390, 1391)(1314, 1402, 1400)(1315, 1401, 1404)(1316, 1405, 1406)(1318, 1408, 1409)(1321, 1413, 1411)(1322, 1414, 1410)(1323, 1415, 1324)(1325, 1329, 1419)(1326, 1328, 1421)(1327, 1422, 1407)(1330, 1332, 1427)(1331, 1428, 1335)(1336, 1434, 1337)(1338, 1412, 1438)(1340, 1441, 1439)(1341, 1440, 1443)(1342, 1444, 1445)(1344, 1447, 1448)(1347, 1452, 1450)(1348, 1453, 1449)(1349, 1454, 1350)(1351, 1355, 1458)(1352, 1354, 1460)(1353, 1461, 1446)(1356, 1465, 1357)(1358, 1363, 1469)(1359, 1361, 1471)(1360, 1472, 1392)(1372, 1486, 1484)(1373, 1487, 1488)(1376, 1492, 1490)(1377, 1493, 1489)(1378, 1495, 1379)(1380, 1491, 1499)(1382, 1502, 1500)(1383, 1501, 1503)(1384, 1504, 1505)(1393, 1395, 1515)(1394, 1516, 1396)(1397, 1520, 1398)(1399, 1451, 1524)(1403, 1528, 1529)(1416, 1543, 1541)(1417, 1542, 1545)(1418, 1546, 1547)(1420, 1549, 1550)(1423, 1554, 1552)(1424, 1555, 1551)(1425, 1556, 1548)(1426, 1558, 1559)(1429, 1563, 1561)(1430, 1564, 1560)(1431, 1566, 1432)(1433, 1562, 1570)(1435, 1573, 1571)(1436, 1572, 1574)(1437, 1575, 1576)(1442, 1581, 1582)(1455, 1596, 1594)(1456, 1595, 1598)(1457, 1599, 1600)(1459, 1602, 1603)(1462, 1607, 1605)(1463, 1498, 1604)(1464, 1608, 1601)(1466, 1611, 1609)(1467, 1610, 1613)(1468, 1614, 1615)(1470, 1617, 1618)(1473, 1622, 1620)(1474, 1569, 1619)(1475, 1477, 1624)(1476, 1625, 1616)(1478, 1627, 1479)(1480, 1485, 1631)(1481, 1483, 1633)(1482, 1634, 1506)(1494, 1568, 1645)(1496, 1597, 1647)(1497, 1648, 1649)(1507, 1509, 1656)(1508, 1657, 1510)(1511, 1660, 1512)(1513, 1621, 1663)(1514, 1664, 1665)(1517, 1669, 1667)(1518, 1670, 1666)(1519, 1668, 1671)(1521, 1674, 1672)(1522, 1673, 1557)(1523, 1675, 1636)(1525, 1527, 1678)(1526, 1679, 1530)(1531, 1683, 1532)(1533, 1553, 1686)(1534, 1687, 1535)(1536, 1540, 1690)(1537, 1539, 1653)(1538, 1692, 1577)(1544, 1697, 1626)(1565, 1623, 1711)(1567, 1612, 1713)(1578, 1580, 1720)(1579, 1721, 1583)(1584, 1724, 1585)(1586, 1606, 1727)(1587, 1728, 1588)(1589, 1593, 1731)(1590, 1592, 1717)(1591, 1733, 1676)(1628, 1757, 1755)(1629, 1756, 1758)(1630, 1759, 1760)(1632, 1761, 1762)(1635, 1765, 1763)(1637, 1638, 1682)(1639, 1766, 1640)(1641, 1646, 1770)(1642, 1644, 1772)(1643, 1773, 1650)(1651, 1652, 1778)(1654, 1764, 1781)(1655, 1782, 1783)(1658, 1786, 1785)(1659, 1702, 1784)(1661, 1788, 1787)(1662, 1789, 1775)(1677, 1800, 1801)(1680, 1804, 1803)(1681, 1742, 1802)(1684, 1806, 1805)(1685, 1807, 1808)(1688, 1811, 1810)(1689, 1812, 1813)(1691, 1779, 1814)(1693, 1817, 1815)(1694, 1696, 1819)(1695, 1820, 1698)(1699, 1823, 1700)(1701, 1704, 1826)(1703, 1828, 1809)(1705, 1831, 1706)(1707, 1712, 1835)(1708, 1710, 1837)(1709, 1838, 1714)(1715, 1716, 1842)(1718, 1816, 1845)(1719, 1846, 1847)(1722, 1850, 1849)(1723, 1752, 1848)(1725, 1852, 1851)(1726, 1853, 1854)(1729, 1857, 1856)(1730, 1858, 1859)(1732, 1843, 1860)(1734, 1863, 1861)(1735, 1737, 1865)(1736, 1866, 1738)(1739, 1869, 1740)(1741, 1744, 1872)(1743, 1873, 1855)(1745, 1747, 1876)(1746, 1877, 1748)(1749, 1880, 1750)(1751, 1754, 1883)(1753, 1884, 1790)(1767, 1895, 1893)(1768, 1894, 1829)(1769, 1896, 1897)(1771, 1898, 1899)(1774, 1902, 1900)(1776, 1901, 1903)(1777, 1904, 1905)(1780, 1906, 1822)(1791, 1914, 1792)(1793, 1797, 1918)(1794, 1796, 1920)(1795, 1921, 1798)(1799, 1862, 1923)(1818, 1934, 1935)(1821, 1937, 1936)(1824, 1939, 1938)(1825, 1940, 1941)(1827, 1943, 1910)(1830, 1887, 1942)(1832, 1947, 1945)(1833, 1946, 1874)(1834, 1948, 1949)(1836, 1950, 1951)(1839, 1954, 1952)(1840, 1953, 1955)(1841, 1956, 1957)(1844, 1958, 1868)(1864, 1970, 1971)(1867, 1973, 1972)(1870, 1975, 1974)(1871, 1976, 1977)(1875, 1979, 1980)(1878, 1983, 1982)(1879, 1891, 1981)(1881, 1985, 1984)(1882, 1986, 1987)(1885, 1916, 1988)(1886, 1888, 1991)(1889, 1994, 1890)(1892, 1996, 1907)(1908, 2008, 1909)(1911, 1912, 2013)(1913, 1989, 2014)(1915, 2016, 2015)(1917, 2017, 2018)(1919, 2019, 2020)(1922, 2022, 2021)(1924, 2024, 1925)(1926, 1927, 2028)(1928, 1944, 2030)(1929, 1930, 2032)(1931, 2034, 1932)(1933, 2035, 1959)(1960, 2052, 1961)(1962, 1963, 2055)(1964, 1978, 2057)(1965, 1966, 2059)(1967, 2061, 1968)(1969, 2062, 2023)(1990, 2073, 2074)(1992, 2076, 2040)(1993, 2002, 2075)(1995, 2078, 2077)(1997, 2010, 2079)(1998, 1999, 2081)(2000, 2039, 2001)(2003, 2083, 2004)(2005, 2085, 2006)(2007, 2080, 2087)(2009, 2089, 2088)(2011, 2041, 2090)(2012, 2091, 2092)(2025, 2100, 2098)(2026, 2099, 2036)(2027, 2101, 2102)(2029, 2103, 2033)(2031, 2105, 2106)(2037, 2108, 2038)(2042, 2112, 2104)(2043, 2044, 2113)(2045, 2066, 2046)(2047, 2114, 2048)(2049, 2116, 2050)(2051, 2107, 2118)(2053, 2121, 2119)(2054, 2120, 2063)(2056, 2122, 2060)(2058, 2124, 2125)(2064, 2127, 2065)(2067, 2129, 2123)(2068, 2130, 2069)(2070, 2071, 2096)(2072, 2131, 2093)(2082, 2128, 2109)(2084, 2086, 2136)(2094, 2095, 2141)(2097, 2126, 2142)(2110, 2134, 2111)(2115, 2117, 2150)(2132, 2160, 2133)(2135, 2161, 2137)(2138, 2139, 2163)(2140, 2159, 2164)(2143, 2144, 2166)(2145, 2149, 2167)(2146, 2168, 2147)(2148, 2169, 2151)(2152, 2153, 2171)(2154, 2158, 2172)(2155, 2173, 2156)(2157, 2174, 2165)(2162, 2176, 2177)(2170, 2179, 2180)(2175, 2181, 2178)(2182, 2184, 2183) L = (1, 1093)(2, 1094)(3, 1095)(4, 1096)(5, 1097)(6, 1098)(7, 1099)(8, 1100)(9, 1101)(10, 1102)(11, 1103)(12, 1104)(13, 1105)(14, 1106)(15, 1107)(16, 1108)(17, 1109)(18, 1110)(19, 1111)(20, 1112)(21, 1113)(22, 1114)(23, 1115)(24, 1116)(25, 1117)(26, 1118)(27, 1119)(28, 1120)(29, 1121)(30, 1122)(31, 1123)(32, 1124)(33, 1125)(34, 1126)(35, 1127)(36, 1128)(37, 1129)(38, 1130)(39, 1131)(40, 1132)(41, 1133)(42, 1134)(43, 1135)(44, 1136)(45, 1137)(46, 1138)(47, 1139)(48, 1140)(49, 1141)(50, 1142)(51, 1143)(52, 1144)(53, 1145)(54, 1146)(55, 1147)(56, 1148)(57, 1149)(58, 1150)(59, 1151)(60, 1152)(61, 1153)(62, 1154)(63, 1155)(64, 1156)(65, 1157)(66, 1158)(67, 1159)(68, 1160)(69, 1161)(70, 1162)(71, 1163)(72, 1164)(73, 1165)(74, 1166)(75, 1167)(76, 1168)(77, 1169)(78, 1170)(79, 1171)(80, 1172)(81, 1173)(82, 1174)(83, 1175)(84, 1176)(85, 1177)(86, 1178)(87, 1179)(88, 1180)(89, 1181)(90, 1182)(91, 1183)(92, 1184)(93, 1185)(94, 1186)(95, 1187)(96, 1188)(97, 1189)(98, 1190)(99, 1191)(100, 1192)(101, 1193)(102, 1194)(103, 1195)(104, 1196)(105, 1197)(106, 1198)(107, 1199)(108, 1200)(109, 1201)(110, 1202)(111, 1203)(112, 1204)(113, 1205)(114, 1206)(115, 1207)(116, 1208)(117, 1209)(118, 1210)(119, 1211)(120, 1212)(121, 1213)(122, 1214)(123, 1215)(124, 1216)(125, 1217)(126, 1218)(127, 1219)(128, 1220)(129, 1221)(130, 1222)(131, 1223)(132, 1224)(133, 1225)(134, 1226)(135, 1227)(136, 1228)(137, 1229)(138, 1230)(139, 1231)(140, 1232)(141, 1233)(142, 1234)(143, 1235)(144, 1236)(145, 1237)(146, 1238)(147, 1239)(148, 1240)(149, 1241)(150, 1242)(151, 1243)(152, 1244)(153, 1245)(154, 1246)(155, 1247)(156, 1248)(157, 1249)(158, 1250)(159, 1251)(160, 1252)(161, 1253)(162, 1254)(163, 1255)(164, 1256)(165, 1257)(166, 1258)(167, 1259)(168, 1260)(169, 1261)(170, 1262)(171, 1263)(172, 1264)(173, 1265)(174, 1266)(175, 1267)(176, 1268)(177, 1269)(178, 1270)(179, 1271)(180, 1272)(181, 1273)(182, 1274)(183, 1275)(184, 1276)(185, 1277)(186, 1278)(187, 1279)(188, 1280)(189, 1281)(190, 1282)(191, 1283)(192, 1284)(193, 1285)(194, 1286)(195, 1287)(196, 1288)(197, 1289)(198, 1290)(199, 1291)(200, 1292)(201, 1293)(202, 1294)(203, 1295)(204, 1296)(205, 1297)(206, 1298)(207, 1299)(208, 1300)(209, 1301)(210, 1302)(211, 1303)(212, 1304)(213, 1305)(214, 1306)(215, 1307)(216, 1308)(217, 1309)(218, 1310)(219, 1311)(220, 1312)(221, 1313)(222, 1314)(223, 1315)(224, 1316)(225, 1317)(226, 1318)(227, 1319)(228, 1320)(229, 1321)(230, 1322)(231, 1323)(232, 1324)(233, 1325)(234, 1326)(235, 1327)(236, 1328)(237, 1329)(238, 1330)(239, 1331)(240, 1332)(241, 1333)(242, 1334)(243, 1335)(244, 1336)(245, 1337)(246, 1338)(247, 1339)(248, 1340)(249, 1341)(250, 1342)(251, 1343)(252, 1344)(253, 1345)(254, 1346)(255, 1347)(256, 1348)(257, 1349)(258, 1350)(259, 1351)(260, 1352)(261, 1353)(262, 1354)(263, 1355)(264, 1356)(265, 1357)(266, 1358)(267, 1359)(268, 1360)(269, 1361)(270, 1362)(271, 1363)(272, 1364)(273, 1365)(274, 1366)(275, 1367)(276, 1368)(277, 1369)(278, 1370)(279, 1371)(280, 1372)(281, 1373)(282, 1374)(283, 1375)(284, 1376)(285, 1377)(286, 1378)(287, 1379)(288, 1380)(289, 1381)(290, 1382)(291, 1383)(292, 1384)(293, 1385)(294, 1386)(295, 1387)(296, 1388)(297, 1389)(298, 1390)(299, 1391)(300, 1392)(301, 1393)(302, 1394)(303, 1395)(304, 1396)(305, 1397)(306, 1398)(307, 1399)(308, 1400)(309, 1401)(310, 1402)(311, 1403)(312, 1404)(313, 1405)(314, 1406)(315, 1407)(316, 1408)(317, 1409)(318, 1410)(319, 1411)(320, 1412)(321, 1413)(322, 1414)(323, 1415)(324, 1416)(325, 1417)(326, 1418)(327, 1419)(328, 1420)(329, 1421)(330, 1422)(331, 1423)(332, 1424)(333, 1425)(334, 1426)(335, 1427)(336, 1428)(337, 1429)(338, 1430)(339, 1431)(340, 1432)(341, 1433)(342, 1434)(343, 1435)(344, 1436)(345, 1437)(346, 1438)(347, 1439)(348, 1440)(349, 1441)(350, 1442)(351, 1443)(352, 1444)(353, 1445)(354, 1446)(355, 1447)(356, 1448)(357, 1449)(358, 1450)(359, 1451)(360, 1452)(361, 1453)(362, 1454)(363, 1455)(364, 1456)(365, 1457)(366, 1458)(367, 1459)(368, 1460)(369, 1461)(370, 1462)(371, 1463)(372, 1464)(373, 1465)(374, 1466)(375, 1467)(376, 1468)(377, 1469)(378, 1470)(379, 1471)(380, 1472)(381, 1473)(382, 1474)(383, 1475)(384, 1476)(385, 1477)(386, 1478)(387, 1479)(388, 1480)(389, 1481)(390, 1482)(391, 1483)(392, 1484)(393, 1485)(394, 1486)(395, 1487)(396, 1488)(397, 1489)(398, 1490)(399, 1491)(400, 1492)(401, 1493)(402, 1494)(403, 1495)(404, 1496)(405, 1497)(406, 1498)(407, 1499)(408, 1500)(409, 1501)(410, 1502)(411, 1503)(412, 1504)(413, 1505)(414, 1506)(415, 1507)(416, 1508)(417, 1509)(418, 1510)(419, 1511)(420, 1512)(421, 1513)(422, 1514)(423, 1515)(424, 1516)(425, 1517)(426, 1518)(427, 1519)(428, 1520)(429, 1521)(430, 1522)(431, 1523)(432, 1524)(433, 1525)(434, 1526)(435, 1527)(436, 1528)(437, 1529)(438, 1530)(439, 1531)(440, 1532)(441, 1533)(442, 1534)(443, 1535)(444, 1536)(445, 1537)(446, 1538)(447, 1539)(448, 1540)(449, 1541)(450, 1542)(451, 1543)(452, 1544)(453, 1545)(454, 1546)(455, 1547)(456, 1548)(457, 1549)(458, 1550)(459, 1551)(460, 1552)(461, 1553)(462, 1554)(463, 1555)(464, 1556)(465, 1557)(466, 1558)(467, 1559)(468, 1560)(469, 1561)(470, 1562)(471, 1563)(472, 1564)(473, 1565)(474, 1566)(475, 1567)(476, 1568)(477, 1569)(478, 1570)(479, 1571)(480, 1572)(481, 1573)(482, 1574)(483, 1575)(484, 1576)(485, 1577)(486, 1578)(487, 1579)(488, 1580)(489, 1581)(490, 1582)(491, 1583)(492, 1584)(493, 1585)(494, 1586)(495, 1587)(496, 1588)(497, 1589)(498, 1590)(499, 1591)(500, 1592)(501, 1593)(502, 1594)(503, 1595)(504, 1596)(505, 1597)(506, 1598)(507, 1599)(508, 1600)(509, 1601)(510, 1602)(511, 1603)(512, 1604)(513, 1605)(514, 1606)(515, 1607)(516, 1608)(517, 1609)(518, 1610)(519, 1611)(520, 1612)(521, 1613)(522, 1614)(523, 1615)(524, 1616)(525, 1617)(526, 1618)(527, 1619)(528, 1620)(529, 1621)(530, 1622)(531, 1623)(532, 1624)(533, 1625)(534, 1626)(535, 1627)(536, 1628)(537, 1629)(538, 1630)(539, 1631)(540, 1632)(541, 1633)(542, 1634)(543, 1635)(544, 1636)(545, 1637)(546, 1638)(547, 1639)(548, 1640)(549, 1641)(550, 1642)(551, 1643)(552, 1644)(553, 1645)(554, 1646)(555, 1647)(556, 1648)(557, 1649)(558, 1650)(559, 1651)(560, 1652)(561, 1653)(562, 1654)(563, 1655)(564, 1656)(565, 1657)(566, 1658)(567, 1659)(568, 1660)(569, 1661)(570, 1662)(571, 1663)(572, 1664)(573, 1665)(574, 1666)(575, 1667)(576, 1668)(577, 1669)(578, 1670)(579, 1671)(580, 1672)(581, 1673)(582, 1674)(583, 1675)(584, 1676)(585, 1677)(586, 1678)(587, 1679)(588, 1680)(589, 1681)(590, 1682)(591, 1683)(592, 1684)(593, 1685)(594, 1686)(595, 1687)(596, 1688)(597, 1689)(598, 1690)(599, 1691)(600, 1692)(601, 1693)(602, 1694)(603, 1695)(604, 1696)(605, 1697)(606, 1698)(607, 1699)(608, 1700)(609, 1701)(610, 1702)(611, 1703)(612, 1704)(613, 1705)(614, 1706)(615, 1707)(616, 1708)(617, 1709)(618, 1710)(619, 1711)(620, 1712)(621, 1713)(622, 1714)(623, 1715)(624, 1716)(625, 1717)(626, 1718)(627, 1719)(628, 1720)(629, 1721)(630, 1722)(631, 1723)(632, 1724)(633, 1725)(634, 1726)(635, 1727)(636, 1728)(637, 1729)(638, 1730)(639, 1731)(640, 1732)(641, 1733)(642, 1734)(643, 1735)(644, 1736)(645, 1737)(646, 1738)(647, 1739)(648, 1740)(649, 1741)(650, 1742)(651, 1743)(652, 1744)(653, 1745)(654, 1746)(655, 1747)(656, 1748)(657, 1749)(658, 1750)(659, 1751)(660, 1752)(661, 1753)(662, 1754)(663, 1755)(664, 1756)(665, 1757)(666, 1758)(667, 1759)(668, 1760)(669, 1761)(670, 1762)(671, 1763)(672, 1764)(673, 1765)(674, 1766)(675, 1767)(676, 1768)(677, 1769)(678, 1770)(679, 1771)(680, 1772)(681, 1773)(682, 1774)(683, 1775)(684, 1776)(685, 1777)(686, 1778)(687, 1779)(688, 1780)(689, 1781)(690, 1782)(691, 1783)(692, 1784)(693, 1785)(694, 1786)(695, 1787)(696, 1788)(697, 1789)(698, 1790)(699, 1791)(700, 1792)(701, 1793)(702, 1794)(703, 1795)(704, 1796)(705, 1797)(706, 1798)(707, 1799)(708, 1800)(709, 1801)(710, 1802)(711, 1803)(712, 1804)(713, 1805)(714, 1806)(715, 1807)(716, 1808)(717, 1809)(718, 1810)(719, 1811)(720, 1812)(721, 1813)(722, 1814)(723, 1815)(724, 1816)(725, 1817)(726, 1818)(727, 1819)(728, 1820)(729, 1821)(730, 1822)(731, 1823)(732, 1824)(733, 1825)(734, 1826)(735, 1827)(736, 1828)(737, 1829)(738, 1830)(739, 1831)(740, 1832)(741, 1833)(742, 1834)(743, 1835)(744, 1836)(745, 1837)(746, 1838)(747, 1839)(748, 1840)(749, 1841)(750, 1842)(751, 1843)(752, 1844)(753, 1845)(754, 1846)(755, 1847)(756, 1848)(757, 1849)(758, 1850)(759, 1851)(760, 1852)(761, 1853)(762, 1854)(763, 1855)(764, 1856)(765, 1857)(766, 1858)(767, 1859)(768, 1860)(769, 1861)(770, 1862)(771, 1863)(772, 1864)(773, 1865)(774, 1866)(775, 1867)(776, 1868)(777, 1869)(778, 1870)(779, 1871)(780, 1872)(781, 1873)(782, 1874)(783, 1875)(784, 1876)(785, 1877)(786, 1878)(787, 1879)(788, 1880)(789, 1881)(790, 1882)(791, 1883)(792, 1884)(793, 1885)(794, 1886)(795, 1887)(796, 1888)(797, 1889)(798, 1890)(799, 1891)(800, 1892)(801, 1893)(802, 1894)(803, 1895)(804, 1896)(805, 1897)(806, 1898)(807, 1899)(808, 1900)(809, 1901)(810, 1902)(811, 1903)(812, 1904)(813, 1905)(814, 1906)(815, 1907)(816, 1908)(817, 1909)(818, 1910)(819, 1911)(820, 1912)(821, 1913)(822, 1914)(823, 1915)(824, 1916)(825, 1917)(826, 1918)(827, 1919)(828, 1920)(829, 1921)(830, 1922)(831, 1923)(832, 1924)(833, 1925)(834, 1926)(835, 1927)(836, 1928)(837, 1929)(838, 1930)(839, 1931)(840, 1932)(841, 1933)(842, 1934)(843, 1935)(844, 1936)(845, 1937)(846, 1938)(847, 1939)(848, 1940)(849, 1941)(850, 1942)(851, 1943)(852, 1944)(853, 1945)(854, 1946)(855, 1947)(856, 1948)(857, 1949)(858, 1950)(859, 1951)(860, 1952)(861, 1953)(862, 1954)(863, 1955)(864, 1956)(865, 1957)(866, 1958)(867, 1959)(868, 1960)(869, 1961)(870, 1962)(871, 1963)(872, 1964)(873, 1965)(874, 1966)(875, 1967)(876, 1968)(877, 1969)(878, 1970)(879, 1971)(880, 1972)(881, 1973)(882, 1974)(883, 1975)(884, 1976)(885, 1977)(886, 1978)(887, 1979)(888, 1980)(889, 1981)(890, 1982)(891, 1983)(892, 1984)(893, 1985)(894, 1986)(895, 1987)(896, 1988)(897, 1989)(898, 1990)(899, 1991)(900, 1992)(901, 1993)(902, 1994)(903, 1995)(904, 1996)(905, 1997)(906, 1998)(907, 1999)(908, 2000)(909, 2001)(910, 2002)(911, 2003)(912, 2004)(913, 2005)(914, 2006)(915, 2007)(916, 2008)(917, 2009)(918, 2010)(919, 2011)(920, 2012)(921, 2013)(922, 2014)(923, 2015)(924, 2016)(925, 2017)(926, 2018)(927, 2019)(928, 2020)(929, 2021)(930, 2022)(931, 2023)(932, 2024)(933, 2025)(934, 2026)(935, 2027)(936, 2028)(937, 2029)(938, 2030)(939, 2031)(940, 2032)(941, 2033)(942, 2034)(943, 2035)(944, 2036)(945, 2037)(946, 2038)(947, 2039)(948, 2040)(949, 2041)(950, 2042)(951, 2043)(952, 2044)(953, 2045)(954, 2046)(955, 2047)(956, 2048)(957, 2049)(958, 2050)(959, 2051)(960, 2052)(961, 2053)(962, 2054)(963, 2055)(964, 2056)(965, 2057)(966, 2058)(967, 2059)(968, 2060)(969, 2061)(970, 2062)(971, 2063)(972, 2064)(973, 2065)(974, 2066)(975, 2067)(976, 2068)(977, 2069)(978, 2070)(979, 2071)(980, 2072)(981, 2073)(982, 2074)(983, 2075)(984, 2076)(985, 2077)(986, 2078)(987, 2079)(988, 2080)(989, 2081)(990, 2082)(991, 2083)(992, 2084)(993, 2085)(994, 2086)(995, 2087)(996, 2088)(997, 2089)(998, 2090)(999, 2091)(1000, 2092)(1001, 2093)(1002, 2094)(1003, 2095)(1004, 2096)(1005, 2097)(1006, 2098)(1007, 2099)(1008, 2100)(1009, 2101)(1010, 2102)(1011, 2103)(1012, 2104)(1013, 2105)(1014, 2106)(1015, 2107)(1016, 2108)(1017, 2109)(1018, 2110)(1019, 2111)(1020, 2112)(1021, 2113)(1022, 2114)(1023, 2115)(1024, 2116)(1025, 2117)(1026, 2118)(1027, 2119)(1028, 2120)(1029, 2121)(1030, 2122)(1031, 2123)(1032, 2124)(1033, 2125)(1034, 2126)(1035, 2127)(1036, 2128)(1037, 2129)(1038, 2130)(1039, 2131)(1040, 2132)(1041, 2133)(1042, 2134)(1043, 2135)(1044, 2136)(1045, 2137)(1046, 2138)(1047, 2139)(1048, 2140)(1049, 2141)(1050, 2142)(1051, 2143)(1052, 2144)(1053, 2145)(1054, 2146)(1055, 2147)(1056, 2148)(1057, 2149)(1058, 2150)(1059, 2151)(1060, 2152)(1061, 2153)(1062, 2154)(1063, 2155)(1064, 2156)(1065, 2157)(1066, 2158)(1067, 2159)(1068, 2160)(1069, 2161)(1070, 2162)(1071, 2163)(1072, 2164)(1073, 2165)(1074, 2166)(1075, 2167)(1076, 2168)(1077, 2169)(1078, 2170)(1079, 2171)(1080, 2172)(1081, 2173)(1082, 2174)(1083, 2175)(1084, 2176)(1085, 2177)(1086, 2178)(1087, 2179)(1088, 2180)(1089, 2181)(1090, 2182)(1091, 2183)(1092, 2184) local type(s) :: { ( 4^3 ), ( 4^7 ) } Outer automorphisms :: reflexible Dual of E14.636 Transitivity :: ET+ Graph:: simple bipartite v = 520 e = 1092 f = 546 degree seq :: [ 3^364, 7^156 ] E14.625 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^7, T2 * T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-3 * T2 * T1^-3, (T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-2)^2, T2 * T1^3 * T2 * T1^-2 * T2 * T1^3 * T2 * T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-3, (T2 * T1^2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-3 * T2 * T1^-3)^2 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 21)(14, 22)(15, 27)(17, 29)(18, 32)(20, 34)(23, 35)(24, 40)(25, 41)(26, 43)(28, 44)(30, 48)(31, 50)(33, 53)(36, 54)(37, 58)(38, 59)(39, 61)(42, 64)(45, 65)(46, 69)(47, 71)(49, 73)(51, 74)(52, 78)(55, 82)(56, 83)(57, 85)(60, 88)(62, 89)(63, 93)(66, 72)(67, 98)(68, 99)(70, 103)(75, 106)(76, 110)(77, 111)(79, 112)(80, 116)(81, 117)(84, 120)(86, 121)(87, 125)(90, 94)(91, 129)(92, 131)(95, 135)(96, 136)(97, 138)(100, 141)(101, 107)(102, 143)(104, 144)(105, 148)(108, 152)(109, 153)(113, 156)(114, 160)(115, 161)(118, 163)(119, 167)(122, 126)(123, 171)(124, 173)(127, 177)(128, 178)(130, 181)(132, 182)(133, 186)(134, 187)(137, 190)(139, 191)(140, 195)(142, 198)(145, 199)(146, 203)(147, 204)(149, 207)(150, 208)(151, 210)(154, 213)(155, 157)(158, 218)(159, 219)(162, 222)(164, 168)(165, 227)(166, 229)(169, 233)(170, 234)(172, 237)(174, 238)(175, 242)(176, 243)(179, 246)(180, 200)(183, 248)(184, 252)(185, 253)(188, 255)(189, 259)(192, 196)(193, 263)(194, 265)(197, 268)(201, 273)(202, 274)(205, 277)(206, 280)(209, 283)(211, 284)(212, 288)(214, 291)(215, 293)(216, 294)(217, 296)(220, 299)(221, 223)(224, 303)(225, 305)(226, 306)(228, 309)(230, 310)(231, 314)(232, 315)(235, 318)(236, 249)(239, 320)(240, 324)(241, 325)(244, 327)(245, 331)(247, 334)(250, 338)(251, 339)(254, 342)(256, 260)(257, 347)(258, 349)(261, 353)(262, 354)(264, 357)(266, 358)(267, 362)(269, 363)(270, 367)(271, 368)(272, 370)(275, 373)(276, 278)(279, 377)(281, 378)(282, 382)(285, 289)(286, 386)(287, 388)(290, 391)(292, 393)(295, 396)(297, 397)(298, 401)(300, 404)(301, 406)(302, 407)(304, 410)(307, 413)(308, 321)(311, 415)(312, 419)(313, 420)(316, 422)(317, 426)(319, 429)(322, 433)(323, 434)(326, 437)(328, 332)(329, 442)(330, 444)(333, 447)(335, 450)(336, 451)(337, 453)(340, 456)(341, 343)(344, 460)(345, 462)(346, 463)(348, 466)(350, 467)(351, 471)(352, 424)(355, 473)(356, 364)(359, 475)(360, 479)(361, 480)(365, 484)(366, 486)(369, 489)(371, 411)(372, 492)(374, 495)(375, 497)(376, 498)(379, 383)(380, 503)(381, 504)(384, 440)(385, 507)(387, 510)(389, 511)(390, 515)(392, 516)(394, 519)(395, 523)(398, 402)(399, 461)(400, 527)(403, 530)(405, 532)(408, 535)(409, 416)(412, 758)(414, 759)(417, 501)(418, 763)(421, 649)(423, 427)(425, 767)(428, 537)(430, 731)(431, 773)(432, 521)(435, 590)(436, 438)(439, 781)(441, 783)(443, 546)(445, 787)(446, 790)(448, 561)(449, 592)(452, 796)(454, 533)(455, 800)(457, 803)(458, 752)(459, 807)(464, 671)(465, 476)(468, 543)(469, 805)(470, 550)(472, 815)(474, 816)(477, 820)(478, 822)(481, 669)(482, 661)(483, 826)(485, 565)(487, 710)(488, 831)(490, 493)(491, 833)(494, 539)(496, 637)(499, 719)(500, 736)(502, 842)(505, 844)(506, 847)(508, 614)(509, 517)(512, 562)(513, 853)(514, 578)(518, 857)(520, 524)(522, 711)(525, 862)(526, 540)(528, 863)(529, 866)(531, 612)(534, 870)(536, 872)(538, 871)(541, 802)(542, 877)(544, 832)(545, 846)(547, 880)(548, 881)(549, 882)(551, 766)(552, 873)(553, 886)(554, 834)(555, 829)(556, 888)(557, 889)(558, 789)(559, 891)(560, 749)(563, 747)(564, 760)(566, 898)(567, 900)(568, 823)(569, 813)(570, 903)(571, 905)(572, 684)(573, 910)(574, 741)(575, 681)(576, 890)(577, 868)(579, 913)(580, 915)(581, 768)(582, 706)(583, 920)(584, 703)(585, 836)(586, 923)(587, 924)(588, 633)(589, 929)(591, 631)(593, 904)(594, 933)(595, 935)(596, 764)(597, 700)(598, 909)(599, 793)(600, 708)(601, 941)(602, 784)(603, 665)(604, 817)(605, 753)(606, 854)(607, 947)(608, 883)(609, 756)(610, 865)(611, 949)(613, 952)(615, 663)(616, 742)(617, 662)(618, 771)(619, 925)(620, 958)(621, 960)(622, 867)(623, 748)(624, 928)(625, 963)(626, 965)(627, 734)(628, 688)(629, 728)(630, 856)(632, 695)(634, 824)(635, 974)(636, 975)(638, 969)(639, 644)(640, 659)(641, 894)(642, 730)(643, 667)(645, 878)(646, 702)(647, 983)(648, 984)(650, 901)(651, 986)(652, 859)(653, 746)(654, 683)(655, 951)(656, 991)(657, 993)(658, 804)(660, 732)(664, 982)(666, 785)(668, 1000)(670, 948)(672, 869)(673, 1003)(674, 875)(675, 693)(676, 876)(677, 765)(678, 988)(679, 1006)(680, 1008)(682, 794)(685, 1012)(686, 830)(687, 780)(689, 818)(690, 729)(691, 737)(692, 843)(694, 887)(696, 919)(697, 1016)(698, 1018)(699, 902)(701, 797)(704, 944)(705, 837)(707, 723)(709, 1024)(712, 1001)(713, 861)(714, 733)(715, 1015)(716, 1026)(717, 1027)(718, 917)(720, 1029)(721, 1030)(722, 792)(724, 961)(725, 1032)(726, 1033)(727, 848)(735, 893)(738, 1037)(739, 772)(740, 957)(743, 757)(744, 1040)(745, 770)(750, 835)(751, 819)(754, 821)(755, 855)(761, 967)(762, 912)(769, 1038)(774, 798)(775, 980)(776, 931)(777, 1054)(778, 1055)(779, 1035)(782, 936)(786, 1058)(788, 1059)(791, 874)(795, 1063)(799, 1065)(801, 908)(806, 907)(808, 932)(809, 994)(810, 1069)(811, 1070)(812, 918)(814, 1072)(825, 885)(827, 858)(828, 1075)(838, 1028)(839, 1060)(840, 1042)(841, 939)(845, 1073)(849, 953)(850, 1080)(851, 1081)(852, 976)(860, 1051)(864, 1084)(879, 937)(884, 962)(892, 989)(895, 1089)(896, 1013)(897, 940)(899, 1041)(906, 1007)(911, 1062)(914, 992)(916, 1017)(921, 1045)(922, 981)(926, 990)(927, 930)(934, 1046)(938, 985)(942, 1090)(943, 1091)(945, 997)(946, 1083)(950, 964)(954, 955)(956, 1049)(959, 1014)(966, 1077)(968, 1022)(970, 1031)(971, 972)(973, 1064)(977, 999)(978, 1056)(979, 987)(995, 1048)(996, 1005)(998, 1023)(1002, 1036)(1004, 1068)(1009, 1057)(1010, 1011)(1019, 1086)(1020, 1082)(1021, 1025)(1034, 1039)(1043, 1044)(1047, 1052)(1050, 1092)(1053, 1071)(1061, 1088)(1066, 1076)(1067, 1085)(1074, 1078)(1079, 1087)(1093, 1094, 1097, 1103, 1112, 1102, 1096)(1095, 1099, 1107, 1118, 1122, 1109, 1100)(1098, 1105, 1116, 1131, 1134, 1117, 1106)(1101, 1110, 1123, 1141, 1138, 1120, 1108)(1104, 1114, 1129, 1149, 1152, 1130, 1115)(1111, 1125, 1144, 1169, 1168, 1143, 1124)(1113, 1127, 1147, 1173, 1176, 1148, 1128)(1119, 1136, 1159, 1189, 1192, 1160, 1137)(1121, 1139, 1162, 1194, 1183, 1154, 1132)(1126, 1146, 1172, 1207, 1206, 1171, 1145)(1133, 1155, 1184, 1222, 1215, 1178, 1150)(1135, 1157, 1187, 1226, 1229, 1188, 1158)(1140, 1164, 1197, 1239, 1238, 1196, 1163)(1142, 1166, 1200, 1243, 1246, 1201, 1167)(1151, 1179, 1216, 1264, 1257, 1210, 1174)(1153, 1181, 1219, 1268, 1271, 1220, 1182)(1156, 1186, 1225, 1277, 1276, 1224, 1185)(1161, 1193, 1234, 1289, 1285, 1231, 1190)(1165, 1198, 1241, 1298, 1301, 1242, 1199)(1170, 1204, 1250, 1309, 1312, 1251, 1205)(1175, 1211, 1258, 1320, 1316, 1254, 1208)(1177, 1213, 1261, 1324, 1327, 1262, 1214)(1180, 1218, 1267, 1333, 1332, 1266, 1217)(1191, 1232, 1286, 1356, 1349, 1280, 1227)(1195, 1236, 1293, 1364, 1367, 1294, 1237)(1202, 1247, 1306, 1382, 1378, 1303, 1244)(1203, 1248, 1307, 1384, 1387, 1308, 1249)(1209, 1255, 1317, 1396, 1399, 1318, 1256)(1212, 1260, 1323, 1405, 1404, 1322, 1259)(1221, 1272, 1339, 1425, 1421, 1336, 1269)(1223, 1274, 1342, 1429, 1432, 1343, 1275)(1228, 1281, 1350, 1440, 1371, 1297, 1240)(1230, 1283, 1353, 1444, 1447, 1354, 1284)(1233, 1288, 1359, 1453, 1452, 1358, 1287)(1235, 1291, 1362, 1458, 1461, 1363, 1292)(1245, 1304, 1379, 1479, 1472, 1373, 1299)(1252, 1313, 1392, 1495, 1491, 1389, 1310)(1253, 1314, 1393, 1497, 1500, 1394, 1315)(1263, 1328, 1411, 1520, 1516, 1408, 1325)(1265, 1330, 1414, 1524, 1527, 1415, 1331)(1270, 1337, 1422, 1535, 1436, 1346, 1278)(1273, 1340, 1427, 1541, 1544, 1428, 1341)(1279, 1347, 1437, 1553, 1556, 1438, 1348)(1282, 1352, 1443, 1562, 1561, 1442, 1351)(1290, 1300, 1374, 1473, 1577, 1457, 1361)(1295, 1368, 1466, 1586, 1502, 1463, 1365)(1296, 1369, 1467, 1588, 1591, 1468, 1370)(1302, 1376, 1476, 1534, 1600, 1477, 1377)(1305, 1381, 1482, 1606, 1605, 1481, 1380)(1311, 1390, 1492, 1618, 1613, 1486, 1385)(1319, 1400, 1506, 1582, 1462, 1503, 1397)(1321, 1402, 1509, 1595, 1834, 1510, 1403)(1326, 1409, 1517, 1858, 1531, 1418, 1334)(1329, 1412, 1522, 1863, 1893, 1523, 1413)(1335, 1419, 1532, 1478, 1601, 1533, 1420)(1338, 1424, 1538, 1881, 1796, 1537, 1423)(1344, 1433, 1549, 1894, 1624, 1546, 1430)(1345, 1434, 1550, 1897, 1694, 1551, 1435)(1355, 1448, 1566, 1515, 1407, 1514, 1445)(1357, 1450, 1569, 1911, 1787, 1570, 1451)(1360, 1455, 1574, 1916, 1784, 1575, 1456)(1366, 1464, 1583, 1924, 1843, 1579, 1459)(1372, 1470, 1593, 1511, 1666, 1594, 1471)(1375, 1475, 1598, 1938, 1729, 1597, 1474)(1383, 1386, 1487, 1614, 1928, 1610, 1484)(1388, 1489, 1554, 1439, 1557, 1617, 1490)(1391, 1494, 1621, 1957, 2047, 1620, 1493)(1395, 1501, 1628, 1963, 1545, 1625, 1498)(1398, 1504, 1849, 1983, 2152, 1513, 1406)(1401, 1507, 1774, 2075, 2022, 1991, 1508)(1410, 1519, 1693, 1995, 1853, 1944, 1518)(1416, 1528, 1870, 1612, 1485, 1611, 1525)(1417, 1529, 1872, 2036, 1696, 2035, 1530)(1426, 1460, 1580, 1922, 1845, 2137, 1540)(1431, 1547, 1891, 1974, 1778, 1837, 1542)(1441, 1559, 1844, 1552, 1877, 2149, 1560)(1446, 1564, 1906, 1978, 1793, 1573, 1454)(1449, 1567, 1910, 2092, 1989, 2038, 1568)(1465, 1585, 1681, 2020, 2091, 1976, 1584)(1469, 1592, 1932, 1969, 1596, 1936, 1589)(1480, 1603, 1804, 1889, 1746, 2082, 1604)(1483, 1608, 1948, 2104, 1791, 2070, 1609)(1488, 1616, 1790, 1926, 1726, 1966, 1615)(1496, 1499, 1626, 1961, 1997, 2182, 1623)(1505, 1631, 1718, 2016, 1842, 1819, 1850)(1512, 1741, 2067, 2059, 1719, 2058, 1833)(1521, 1543, 1887, 2066, 1780, 2105, 2002)(1526, 1868, 2145, 1981, 1727, 1766, 1823)(1536, 1879, 1779, 1873, 1815, 2123, 1973)(1539, 1653, 1986, 2116, 1904, 2045, 1706)(1548, 1630, 1705, 2043, 2115, 1984, 1892)(1555, 1901, 2150, 2005, 1947, 2100, 1563)(1558, 1635, 1756, 2080, 2064, 2008, 1828)(1565, 1629, 1665, 2001, 2130, 1971, 1907)(1571, 1656, 1987, 1965, 1578, 1802, 1912)(1572, 1761, 2093, 1945, 1676, 1869, 1852)(1576, 1919, 2159, 1972, 1803, 1883, 1753)(1581, 1644, 1903, 1841, 1684, 1862, 1923)(1587, 1590, 1930, 2050, 1885, 2154, 2057)(1599, 1941, 2171, 1990, 1752, 1864, 1607)(1602, 1654, 1913, 2129, 2014, 2048, 1708)(1619, 1955, 1765, 1824, 1715, 1898, 2012)(1622, 1704, 2039, 1927, 1750, 2086, 1763)(1627, 1633, 1749, 1992, 1777, 1884, 1962)(1632, 1675, 2011, 2143, 1998, 2023, 1682)(1634, 1730, 2053, 2103, 2006, 1950, 1657)(1636, 1685, 2024, 2113, 2030, 2065, 1724)(1637, 1818, 1860, 1801, 1838, 2120, 1811)(1638, 1640, 1797, 2107, 2037, 2026, 1758)(1639, 1762, 2028, 2136, 2042, 1890, 1677)(1641, 1711, 2049, 2139, 2056, 1937, 1697)(1642, 1772, 2027, 1861, 1767, 2096, 1876)(1643, 1648, 1854, 2072, 2060, 2051, 1799)(1645, 1668, 2004, 2088, 2071, 2094, 1775)(1646, 1943, 1800, 1760, 1959, 2170, 1935)(1647, 1832, 2009, 2111, 2077, 1825, 1663)(1649, 1742, 2040, 2177, 2084, 1813, 1720)(1650, 1809, 2052, 2069, 1731, 1920, 1909)(1651, 1660, 1900, 2031, 2087, 2079, 1857)(1652, 1942, 1776, 1710, 1967, 2155, 1888)(1655, 1874, 1993, 2163, 2099, 1783, 1691)(1658, 1700, 1929, 2062, 2106, 2131, 1840)(1659, 1902, 1759, 1830, 1856, 2142, 1994)(1661, 1786, 2061, 2134, 2109, 1880, 1751)(1662, 1871, 1951, 2090, 1757, 1812, 1826)(1664, 1817, 1725, 1739, 1968, 2176, 2000)(1667, 1816, 1979, 2180, 2073, 1735, 1717)(1669, 1810, 2017, 2157, 2081, 1744, 1734)(1670, 1831, 2095, 2046, 1707, 1808, 1795)(1671, 1674, 1788, 1999, 2126, 2114, 1794)(1672, 1688, 1846, 2018, 2128, 2140, 1848)(1673, 1789, 1709, 1807, 1975, 2179, 2010)(1678, 1737, 2074, 2101, 2138, 2112, 1792)(1679, 2003, 1829, 1952, 1798, 1878, 1896)(1680, 1771, 1755, 1702, 1953, 2132, 2019)(1683, 1770, 1970, 2158, 2032, 1692, 1748)(1686, 1714, 1781, 1914, 2156, 2178, 1960)(1687, 1847, 1738, 1867, 1982, 2164, 2029)(1689, 1827, 2044, 1964, 2133, 1836, 1820)(1690, 1988, 2122, 2102, 1773, 1743, 1785)(1695, 1747, 1985, 2174, 2089, 1754, 1703)(1698, 1768, 1886, 1855, 2141, 2153, 1905)(1699, 2034, 1806, 2117, 1915, 1835, 1940)(1701, 1933, 1996, 1925, 2054, 1713, 1782)(1712, 1745, 1733, 2013, 2165, 2135, 1839)(1716, 1977, 2151, 2063, 1723, 1740, 1736)(1721, 1805, 1958, 1954, 2175, 2168, 2015)(1722, 1949, 1866, 2144, 1921, 1764, 1814)(1728, 1931, 1769, 2097, 1980, 1859, 2068)(1732, 1917, 2021, 1851, 1865, 1956, 1946)(1821, 2119, 1882, 1875, 2148, 2184, 2007)(1822, 2127, 2033, 1908, 1918, 2166, 2025)(1895, 1899, 2160, 2078, 2055, 2161, 2085)(1934, 2169, 2121, 2041, 2108, 2125, 1939)(2076, 2083, 2173, 2110, 2147, 2183, 2167)(2098, 2124, 2172, 2162, 2181, 2146, 2118) L = (1, 1093)(2, 1094)(3, 1095)(4, 1096)(5, 1097)(6, 1098)(7, 1099)(8, 1100)(9, 1101)(10, 1102)(11, 1103)(12, 1104)(13, 1105)(14, 1106)(15, 1107)(16, 1108)(17, 1109)(18, 1110)(19, 1111)(20, 1112)(21, 1113)(22, 1114)(23, 1115)(24, 1116)(25, 1117)(26, 1118)(27, 1119)(28, 1120)(29, 1121)(30, 1122)(31, 1123)(32, 1124)(33, 1125)(34, 1126)(35, 1127)(36, 1128)(37, 1129)(38, 1130)(39, 1131)(40, 1132)(41, 1133)(42, 1134)(43, 1135)(44, 1136)(45, 1137)(46, 1138)(47, 1139)(48, 1140)(49, 1141)(50, 1142)(51, 1143)(52, 1144)(53, 1145)(54, 1146)(55, 1147)(56, 1148)(57, 1149)(58, 1150)(59, 1151)(60, 1152)(61, 1153)(62, 1154)(63, 1155)(64, 1156)(65, 1157)(66, 1158)(67, 1159)(68, 1160)(69, 1161)(70, 1162)(71, 1163)(72, 1164)(73, 1165)(74, 1166)(75, 1167)(76, 1168)(77, 1169)(78, 1170)(79, 1171)(80, 1172)(81, 1173)(82, 1174)(83, 1175)(84, 1176)(85, 1177)(86, 1178)(87, 1179)(88, 1180)(89, 1181)(90, 1182)(91, 1183)(92, 1184)(93, 1185)(94, 1186)(95, 1187)(96, 1188)(97, 1189)(98, 1190)(99, 1191)(100, 1192)(101, 1193)(102, 1194)(103, 1195)(104, 1196)(105, 1197)(106, 1198)(107, 1199)(108, 1200)(109, 1201)(110, 1202)(111, 1203)(112, 1204)(113, 1205)(114, 1206)(115, 1207)(116, 1208)(117, 1209)(118, 1210)(119, 1211)(120, 1212)(121, 1213)(122, 1214)(123, 1215)(124, 1216)(125, 1217)(126, 1218)(127, 1219)(128, 1220)(129, 1221)(130, 1222)(131, 1223)(132, 1224)(133, 1225)(134, 1226)(135, 1227)(136, 1228)(137, 1229)(138, 1230)(139, 1231)(140, 1232)(141, 1233)(142, 1234)(143, 1235)(144, 1236)(145, 1237)(146, 1238)(147, 1239)(148, 1240)(149, 1241)(150, 1242)(151, 1243)(152, 1244)(153, 1245)(154, 1246)(155, 1247)(156, 1248)(157, 1249)(158, 1250)(159, 1251)(160, 1252)(161, 1253)(162, 1254)(163, 1255)(164, 1256)(165, 1257)(166, 1258)(167, 1259)(168, 1260)(169, 1261)(170, 1262)(171, 1263)(172, 1264)(173, 1265)(174, 1266)(175, 1267)(176, 1268)(177, 1269)(178, 1270)(179, 1271)(180, 1272)(181, 1273)(182, 1274)(183, 1275)(184, 1276)(185, 1277)(186, 1278)(187, 1279)(188, 1280)(189, 1281)(190, 1282)(191, 1283)(192, 1284)(193, 1285)(194, 1286)(195, 1287)(196, 1288)(197, 1289)(198, 1290)(199, 1291)(200, 1292)(201, 1293)(202, 1294)(203, 1295)(204, 1296)(205, 1297)(206, 1298)(207, 1299)(208, 1300)(209, 1301)(210, 1302)(211, 1303)(212, 1304)(213, 1305)(214, 1306)(215, 1307)(216, 1308)(217, 1309)(218, 1310)(219, 1311)(220, 1312)(221, 1313)(222, 1314)(223, 1315)(224, 1316)(225, 1317)(226, 1318)(227, 1319)(228, 1320)(229, 1321)(230, 1322)(231, 1323)(232, 1324)(233, 1325)(234, 1326)(235, 1327)(236, 1328)(237, 1329)(238, 1330)(239, 1331)(240, 1332)(241, 1333)(242, 1334)(243, 1335)(244, 1336)(245, 1337)(246, 1338)(247, 1339)(248, 1340)(249, 1341)(250, 1342)(251, 1343)(252, 1344)(253, 1345)(254, 1346)(255, 1347)(256, 1348)(257, 1349)(258, 1350)(259, 1351)(260, 1352)(261, 1353)(262, 1354)(263, 1355)(264, 1356)(265, 1357)(266, 1358)(267, 1359)(268, 1360)(269, 1361)(270, 1362)(271, 1363)(272, 1364)(273, 1365)(274, 1366)(275, 1367)(276, 1368)(277, 1369)(278, 1370)(279, 1371)(280, 1372)(281, 1373)(282, 1374)(283, 1375)(284, 1376)(285, 1377)(286, 1378)(287, 1379)(288, 1380)(289, 1381)(290, 1382)(291, 1383)(292, 1384)(293, 1385)(294, 1386)(295, 1387)(296, 1388)(297, 1389)(298, 1390)(299, 1391)(300, 1392)(301, 1393)(302, 1394)(303, 1395)(304, 1396)(305, 1397)(306, 1398)(307, 1399)(308, 1400)(309, 1401)(310, 1402)(311, 1403)(312, 1404)(313, 1405)(314, 1406)(315, 1407)(316, 1408)(317, 1409)(318, 1410)(319, 1411)(320, 1412)(321, 1413)(322, 1414)(323, 1415)(324, 1416)(325, 1417)(326, 1418)(327, 1419)(328, 1420)(329, 1421)(330, 1422)(331, 1423)(332, 1424)(333, 1425)(334, 1426)(335, 1427)(336, 1428)(337, 1429)(338, 1430)(339, 1431)(340, 1432)(341, 1433)(342, 1434)(343, 1435)(344, 1436)(345, 1437)(346, 1438)(347, 1439)(348, 1440)(349, 1441)(350, 1442)(351, 1443)(352, 1444)(353, 1445)(354, 1446)(355, 1447)(356, 1448)(357, 1449)(358, 1450)(359, 1451)(360, 1452)(361, 1453)(362, 1454)(363, 1455)(364, 1456)(365, 1457)(366, 1458)(367, 1459)(368, 1460)(369, 1461)(370, 1462)(371, 1463)(372, 1464)(373, 1465)(374, 1466)(375, 1467)(376, 1468)(377, 1469)(378, 1470)(379, 1471)(380, 1472)(381, 1473)(382, 1474)(383, 1475)(384, 1476)(385, 1477)(386, 1478)(387, 1479)(388, 1480)(389, 1481)(390, 1482)(391, 1483)(392, 1484)(393, 1485)(394, 1486)(395, 1487)(396, 1488)(397, 1489)(398, 1490)(399, 1491)(400, 1492)(401, 1493)(402, 1494)(403, 1495)(404, 1496)(405, 1497)(406, 1498)(407, 1499)(408, 1500)(409, 1501)(410, 1502)(411, 1503)(412, 1504)(413, 1505)(414, 1506)(415, 1507)(416, 1508)(417, 1509)(418, 1510)(419, 1511)(420, 1512)(421, 1513)(422, 1514)(423, 1515)(424, 1516)(425, 1517)(426, 1518)(427, 1519)(428, 1520)(429, 1521)(430, 1522)(431, 1523)(432, 1524)(433, 1525)(434, 1526)(435, 1527)(436, 1528)(437, 1529)(438, 1530)(439, 1531)(440, 1532)(441, 1533)(442, 1534)(443, 1535)(444, 1536)(445, 1537)(446, 1538)(447, 1539)(448, 1540)(449, 1541)(450, 1542)(451, 1543)(452, 1544)(453, 1545)(454, 1546)(455, 1547)(456, 1548)(457, 1549)(458, 1550)(459, 1551)(460, 1552)(461, 1553)(462, 1554)(463, 1555)(464, 1556)(465, 1557)(466, 1558)(467, 1559)(468, 1560)(469, 1561)(470, 1562)(471, 1563)(472, 1564)(473, 1565)(474, 1566)(475, 1567)(476, 1568)(477, 1569)(478, 1570)(479, 1571)(480, 1572)(481, 1573)(482, 1574)(483, 1575)(484, 1576)(485, 1577)(486, 1578)(487, 1579)(488, 1580)(489, 1581)(490, 1582)(491, 1583)(492, 1584)(493, 1585)(494, 1586)(495, 1587)(496, 1588)(497, 1589)(498, 1590)(499, 1591)(500, 1592)(501, 1593)(502, 1594)(503, 1595)(504, 1596)(505, 1597)(506, 1598)(507, 1599)(508, 1600)(509, 1601)(510, 1602)(511, 1603)(512, 1604)(513, 1605)(514, 1606)(515, 1607)(516, 1608)(517, 1609)(518, 1610)(519, 1611)(520, 1612)(521, 1613)(522, 1614)(523, 1615)(524, 1616)(525, 1617)(526, 1618)(527, 1619)(528, 1620)(529, 1621)(530, 1622)(531, 1623)(532, 1624)(533, 1625)(534, 1626)(535, 1627)(536, 1628)(537, 1629)(538, 1630)(539, 1631)(540, 1632)(541, 1633)(542, 1634)(543, 1635)(544, 1636)(545, 1637)(546, 1638)(547, 1639)(548, 1640)(549, 1641)(550, 1642)(551, 1643)(552, 1644)(553, 1645)(554, 1646)(555, 1647)(556, 1648)(557, 1649)(558, 1650)(559, 1651)(560, 1652)(561, 1653)(562, 1654)(563, 1655)(564, 1656)(565, 1657)(566, 1658)(567, 1659)(568, 1660)(569, 1661)(570, 1662)(571, 1663)(572, 1664)(573, 1665)(574, 1666)(575, 1667)(576, 1668)(577, 1669)(578, 1670)(579, 1671)(580, 1672)(581, 1673)(582, 1674)(583, 1675)(584, 1676)(585, 1677)(586, 1678)(587, 1679)(588, 1680)(589, 1681)(590, 1682)(591, 1683)(592, 1684)(593, 1685)(594, 1686)(595, 1687)(596, 1688)(597, 1689)(598, 1690)(599, 1691)(600, 1692)(601, 1693)(602, 1694)(603, 1695)(604, 1696)(605, 1697)(606, 1698)(607, 1699)(608, 1700)(609, 1701)(610, 1702)(611, 1703)(612, 1704)(613, 1705)(614, 1706)(615, 1707)(616, 1708)(617, 1709)(618, 1710)(619, 1711)(620, 1712)(621, 1713)(622, 1714)(623, 1715)(624, 1716)(625, 1717)(626, 1718)(627, 1719)(628, 1720)(629, 1721)(630, 1722)(631, 1723)(632, 1724)(633, 1725)(634, 1726)(635, 1727)(636, 1728)(637, 1729)(638, 1730)(639, 1731)(640, 1732)(641, 1733)(642, 1734)(643, 1735)(644, 1736)(645, 1737)(646, 1738)(647, 1739)(648, 1740)(649, 1741)(650, 1742)(651, 1743)(652, 1744)(653, 1745)(654, 1746)(655, 1747)(656, 1748)(657, 1749)(658, 1750)(659, 1751)(660, 1752)(661, 1753)(662, 1754)(663, 1755)(664, 1756)(665, 1757)(666, 1758)(667, 1759)(668, 1760)(669, 1761)(670, 1762)(671, 1763)(672, 1764)(673, 1765)(674, 1766)(675, 1767)(676, 1768)(677, 1769)(678, 1770)(679, 1771)(680, 1772)(681, 1773)(682, 1774)(683, 1775)(684, 1776)(685, 1777)(686, 1778)(687, 1779)(688, 1780)(689, 1781)(690, 1782)(691, 1783)(692, 1784)(693, 1785)(694, 1786)(695, 1787)(696, 1788)(697, 1789)(698, 1790)(699, 1791)(700, 1792)(701, 1793)(702, 1794)(703, 1795)(704, 1796)(705, 1797)(706, 1798)(707, 1799)(708, 1800)(709, 1801)(710, 1802)(711, 1803)(712, 1804)(713, 1805)(714, 1806)(715, 1807)(716, 1808)(717, 1809)(718, 1810)(719, 1811)(720, 1812)(721, 1813)(722, 1814)(723, 1815)(724, 1816)(725, 1817)(726, 1818)(727, 1819)(728, 1820)(729, 1821)(730, 1822)(731, 1823)(732, 1824)(733, 1825)(734, 1826)(735, 1827)(736, 1828)(737, 1829)(738, 1830)(739, 1831)(740, 1832)(741, 1833)(742, 1834)(743, 1835)(744, 1836)(745, 1837)(746, 1838)(747, 1839)(748, 1840)(749, 1841)(750, 1842)(751, 1843)(752, 1844)(753, 1845)(754, 1846)(755, 1847)(756, 1848)(757, 1849)(758, 1850)(759, 1851)(760, 1852)(761, 1853)(762, 1854)(763, 1855)(764, 1856)(765, 1857)(766, 1858)(767, 1859)(768, 1860)(769, 1861)(770, 1862)(771, 1863)(772, 1864)(773, 1865)(774, 1866)(775, 1867)(776, 1868)(777, 1869)(778, 1870)(779, 1871)(780, 1872)(781, 1873)(782, 1874)(783, 1875)(784, 1876)(785, 1877)(786, 1878)(787, 1879)(788, 1880)(789, 1881)(790, 1882)(791, 1883)(792, 1884)(793, 1885)(794, 1886)(795, 1887)(796, 1888)(797, 1889)(798, 1890)(799, 1891)(800, 1892)(801, 1893)(802, 1894)(803, 1895)(804, 1896)(805, 1897)(806, 1898)(807, 1899)(808, 1900)(809, 1901)(810, 1902)(811, 1903)(812, 1904)(813, 1905)(814, 1906)(815, 1907)(816, 1908)(817, 1909)(818, 1910)(819, 1911)(820, 1912)(821, 1913)(822, 1914)(823, 1915)(824, 1916)(825, 1917)(826, 1918)(827, 1919)(828, 1920)(829, 1921)(830, 1922)(831, 1923)(832, 1924)(833, 1925)(834, 1926)(835, 1927)(836, 1928)(837, 1929)(838, 1930)(839, 1931)(840, 1932)(841, 1933)(842, 1934)(843, 1935)(844, 1936)(845, 1937)(846, 1938)(847, 1939)(848, 1940)(849, 1941)(850, 1942)(851, 1943)(852, 1944)(853, 1945)(854, 1946)(855, 1947)(856, 1948)(857, 1949)(858, 1950)(859, 1951)(860, 1952)(861, 1953)(862, 1954)(863, 1955)(864, 1956)(865, 1957)(866, 1958)(867, 1959)(868, 1960)(869, 1961)(870, 1962)(871, 1963)(872, 1964)(873, 1965)(874, 1966)(875, 1967)(876, 1968)(877, 1969)(878, 1970)(879, 1971)(880, 1972)(881, 1973)(882, 1974)(883, 1975)(884, 1976)(885, 1977)(886, 1978)(887, 1979)(888, 1980)(889, 1981)(890, 1982)(891, 1983)(892, 1984)(893, 1985)(894, 1986)(895, 1987)(896, 1988)(897, 1989)(898, 1990)(899, 1991)(900, 1992)(901, 1993)(902, 1994)(903, 1995)(904, 1996)(905, 1997)(906, 1998)(907, 1999)(908, 2000)(909, 2001)(910, 2002)(911, 2003)(912, 2004)(913, 2005)(914, 2006)(915, 2007)(916, 2008)(917, 2009)(918, 2010)(919, 2011)(920, 2012)(921, 2013)(922, 2014)(923, 2015)(924, 2016)(925, 2017)(926, 2018)(927, 2019)(928, 2020)(929, 2021)(930, 2022)(931, 2023)(932, 2024)(933, 2025)(934, 2026)(935, 2027)(936, 2028)(937, 2029)(938, 2030)(939, 2031)(940, 2032)(941, 2033)(942, 2034)(943, 2035)(944, 2036)(945, 2037)(946, 2038)(947, 2039)(948, 2040)(949, 2041)(950, 2042)(951, 2043)(952, 2044)(953, 2045)(954, 2046)(955, 2047)(956, 2048)(957, 2049)(958, 2050)(959, 2051)(960, 2052)(961, 2053)(962, 2054)(963, 2055)(964, 2056)(965, 2057)(966, 2058)(967, 2059)(968, 2060)(969, 2061)(970, 2062)(971, 2063)(972, 2064)(973, 2065)(974, 2066)(975, 2067)(976, 2068)(977, 2069)(978, 2070)(979, 2071)(980, 2072)(981, 2073)(982, 2074)(983, 2075)(984, 2076)(985, 2077)(986, 2078)(987, 2079)(988, 2080)(989, 2081)(990, 2082)(991, 2083)(992, 2084)(993, 2085)(994, 2086)(995, 2087)(996, 2088)(997, 2089)(998, 2090)(999, 2091)(1000, 2092)(1001, 2093)(1002, 2094)(1003, 2095)(1004, 2096)(1005, 2097)(1006, 2098)(1007, 2099)(1008, 2100)(1009, 2101)(1010, 2102)(1011, 2103)(1012, 2104)(1013, 2105)(1014, 2106)(1015, 2107)(1016, 2108)(1017, 2109)(1018, 2110)(1019, 2111)(1020, 2112)(1021, 2113)(1022, 2114)(1023, 2115)(1024, 2116)(1025, 2117)(1026, 2118)(1027, 2119)(1028, 2120)(1029, 2121)(1030, 2122)(1031, 2123)(1032, 2124)(1033, 2125)(1034, 2126)(1035, 2127)(1036, 2128)(1037, 2129)(1038, 2130)(1039, 2131)(1040, 2132)(1041, 2133)(1042, 2134)(1043, 2135)(1044, 2136)(1045, 2137)(1046, 2138)(1047, 2139)(1048, 2140)(1049, 2141)(1050, 2142)(1051, 2143)(1052, 2144)(1053, 2145)(1054, 2146)(1055, 2147)(1056, 2148)(1057, 2149)(1058, 2150)(1059, 2151)(1060, 2152)(1061, 2153)(1062, 2154)(1063, 2155)(1064, 2156)(1065, 2157)(1066, 2158)(1067, 2159)(1068, 2160)(1069, 2161)(1070, 2162)(1071, 2163)(1072, 2164)(1073, 2165)(1074, 2166)(1075, 2167)(1076, 2168)(1077, 2169)(1078, 2170)(1079, 2171)(1080, 2172)(1081, 2173)(1082, 2174)(1083, 2175)(1084, 2176)(1085, 2177)(1086, 2178)(1087, 2179)(1088, 2180)(1089, 2181)(1090, 2182)(1091, 2183)(1092, 2184) local type(s) :: { ( 6, 6 ), ( 6^7 ) } Outer automorphisms :: reflexible Dual of E14.629 Transitivity :: ET+ Graph:: simple bipartite v = 702 e = 1092 f = 364 degree seq :: [ 2^546, 7^156 ] E14.626 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^7, (T1^-2 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-1)^2, T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^3 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-2 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 21)(14, 22)(15, 27)(17, 29)(18, 32)(20, 34)(23, 35)(24, 40)(25, 41)(26, 43)(28, 44)(30, 48)(31, 50)(33, 53)(36, 54)(37, 58)(38, 59)(39, 61)(42, 64)(45, 65)(46, 69)(47, 71)(49, 73)(51, 74)(52, 78)(55, 82)(56, 83)(57, 85)(60, 88)(62, 89)(63, 93)(66, 72)(67, 98)(68, 99)(70, 103)(75, 106)(76, 110)(77, 111)(79, 112)(80, 116)(81, 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1769, 2036, 2010)(1640, 2013, 2092, 1735, 1724, 2009, 2016)(1641, 2017, 2102, 1701, 1804, 1972, 2020)(1643, 2023, 2131, 1752, 1823, 1932, 2026)(1644, 1983, 2083, 1779, 1703, 2025, 2029)(1646, 1947, 2077, 1711, 1722, 2005, 1935)(1647, 2034, 2078, 1677, 1799, 2033, 1952)(1650, 1868, 2061, 1814, 1680, 2027, 2042)(1652, 2046, 2104, 1833, 1733, 2052, 2047)(1653, 1845, 2054, 1749, 1690, 2004, 1977)(1656, 2048, 2093, 1692, 1759, 2015, 1874)(1659, 1828, 2049, 1849, 1662, 2040, 2055)(1661, 1892, 2070, 1726, 1709, 2008, 1866)(1664, 1810, 2041, 1793, 1675, 2014, 2062)(1666, 2032, 2084, 1682, 1775, 2028, 1841)(1668, 2065, 2087, 1885, 1706, 2068, 2066)(1670, 1829, 2156, 1846, 2161, 2106, 1877)(1671, 1861, 1946, 1895, 1673, 2053, 1962)(1672, 1839, 2067, 1744, 1732, 2018, 1927)(1674, 2074, 2115, 1911, 1745, 2081, 2075)(1678, 1973, 2098, 1705, 1747, 2024, 1806)(1684, 1919, 2071, 2000, 1687, 2069, 1965)(1685, 1862, 2164, 1887, 2167, 1987, 1819)(1686, 1791, 2051, 1771, 1702, 2035, 2088)(1688, 1990, 2125, 2141, 1772, 2096, 2091)(1694, 1800, 2150, 1949, 2175, 2127, 1863)(1696, 1873, 2080, 1755, 1753, 2044, 1882)(1698, 2100, 1982, 2116, 1720, 2097, 1884)(1699, 1879, 2165, 1966, 2160, 2132, 1764)(1713, 1760, 2136, 1970, 2177, 2140, 1922)(1715, 1933, 2095, 1719, 1777, 2057, 1824)(1718, 1821, 2155, 2183, 2168, 1989, 1801)(1721, 1917, 2120, 2135, 1756, 2117, 1999)(1723, 1993, 2174, 2181, 2151, 1950, 1737)(1727, 1767, 1910, 2172, 2179, 2148, 1830)(1729, 1870, 1939, 1796, 1783, 2064, 1995)(1739, 2072, 2112, 1742, 1812, 1979, 1825)(1741, 1857, 1969, 2176, 1959, 1871, 1761)(1784, 1838, 1889, 1903, 1852, 1817, 1786)(1802, 2105, 1957, 1803, 1888, 1929, 1915) L = (1, 1093)(2, 1094)(3, 1095)(4, 1096)(5, 1097)(6, 1098)(7, 1099)(8, 1100)(9, 1101)(10, 1102)(11, 1103)(12, 1104)(13, 1105)(14, 1106)(15, 1107)(16, 1108)(17, 1109)(18, 1110)(19, 1111)(20, 1112)(21, 1113)(22, 1114)(23, 1115)(24, 1116)(25, 1117)(26, 1118)(27, 1119)(28, 1120)(29, 1121)(30, 1122)(31, 1123)(32, 1124)(33, 1125)(34, 1126)(35, 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1223)(132, 1224)(133, 1225)(134, 1226)(135, 1227)(136, 1228)(137, 1229)(138, 1230)(139, 1231)(140, 1232)(141, 1233)(142, 1234)(143, 1235)(144, 1236)(145, 1237)(146, 1238)(147, 1239)(148, 1240)(149, 1241)(150, 1242)(151, 1243)(152, 1244)(153, 1245)(154, 1246)(155, 1247)(156, 1248)(157, 1249)(158, 1250)(159, 1251)(160, 1252)(161, 1253)(162, 1254)(163, 1255)(164, 1256)(165, 1257)(166, 1258)(167, 1259)(168, 1260)(169, 1261)(170, 1262)(171, 1263)(172, 1264)(173, 1265)(174, 1266)(175, 1267)(176, 1268)(177, 1269)(178, 1270)(179, 1271)(180, 1272)(181, 1273)(182, 1274)(183, 1275)(184, 1276)(185, 1277)(186, 1278)(187, 1279)(188, 1280)(189, 1281)(190, 1282)(191, 1283)(192, 1284)(193, 1285)(194, 1286)(195, 1287)(196, 1288)(197, 1289)(198, 1290)(199, 1291)(200, 1292)(201, 1293)(202, 1294)(203, 1295)(204, 1296)(205, 1297)(206, 1298)(207, 1299)(208, 1300)(209, 1301)(210, 1302)(211, 1303)(212, 1304)(213, 1305)(214, 1306)(215, 1307)(216, 1308)(217, 1309)(218, 1310)(219, 1311)(220, 1312)(221, 1313)(222, 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1405)(314, 1406)(315, 1407)(316, 1408)(317, 1409)(318, 1410)(319, 1411)(320, 1412)(321, 1413)(322, 1414)(323, 1415)(324, 1416)(325, 1417)(326, 1418)(327, 1419)(328, 1420)(329, 1421)(330, 1422)(331, 1423)(332, 1424)(333, 1425)(334, 1426)(335, 1427)(336, 1428)(337, 1429)(338, 1430)(339, 1431)(340, 1432)(341, 1433)(342, 1434)(343, 1435)(344, 1436)(345, 1437)(346, 1438)(347, 1439)(348, 1440)(349, 1441)(350, 1442)(351, 1443)(352, 1444)(353, 1445)(354, 1446)(355, 1447)(356, 1448)(357, 1449)(358, 1450)(359, 1451)(360, 1452)(361, 1453)(362, 1454)(363, 1455)(364, 1456)(365, 1457)(366, 1458)(367, 1459)(368, 1460)(369, 1461)(370, 1462)(371, 1463)(372, 1464)(373, 1465)(374, 1466)(375, 1467)(376, 1468)(377, 1469)(378, 1470)(379, 1471)(380, 1472)(381, 1473)(382, 1474)(383, 1475)(384, 1476)(385, 1477)(386, 1478)(387, 1479)(388, 1480)(389, 1481)(390, 1482)(391, 1483)(392, 1484)(393, 1485)(394, 1486)(395, 1487)(396, 1488)(397, 1489)(398, 1490)(399, 1491)(400, 1492)(401, 1493)(402, 1494)(403, 1495)(404, 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1587)(496, 1588)(497, 1589)(498, 1590)(499, 1591)(500, 1592)(501, 1593)(502, 1594)(503, 1595)(504, 1596)(505, 1597)(506, 1598)(507, 1599)(508, 1600)(509, 1601)(510, 1602)(511, 1603)(512, 1604)(513, 1605)(514, 1606)(515, 1607)(516, 1608)(517, 1609)(518, 1610)(519, 1611)(520, 1612)(521, 1613)(522, 1614)(523, 1615)(524, 1616)(525, 1617)(526, 1618)(527, 1619)(528, 1620)(529, 1621)(530, 1622)(531, 1623)(532, 1624)(533, 1625)(534, 1626)(535, 1627)(536, 1628)(537, 1629)(538, 1630)(539, 1631)(540, 1632)(541, 1633)(542, 1634)(543, 1635)(544, 1636)(545, 1637)(546, 1638)(547, 1639)(548, 1640)(549, 1641)(550, 1642)(551, 1643)(552, 1644)(553, 1645)(554, 1646)(555, 1647)(556, 1648)(557, 1649)(558, 1650)(559, 1651)(560, 1652)(561, 1653)(562, 1654)(563, 1655)(564, 1656)(565, 1657)(566, 1658)(567, 1659)(568, 1660)(569, 1661)(570, 1662)(571, 1663)(572, 1664)(573, 1665)(574, 1666)(575, 1667)(576, 1668)(577, 1669)(578, 1670)(579, 1671)(580, 1672)(581, 1673)(582, 1674)(583, 1675)(584, 1676)(585, 1677)(586, 1678)(587, 1679)(588, 1680)(589, 1681)(590, 1682)(591, 1683)(592, 1684)(593, 1685)(594, 1686)(595, 1687)(596, 1688)(597, 1689)(598, 1690)(599, 1691)(600, 1692)(601, 1693)(602, 1694)(603, 1695)(604, 1696)(605, 1697)(606, 1698)(607, 1699)(608, 1700)(609, 1701)(610, 1702)(611, 1703)(612, 1704)(613, 1705)(614, 1706)(615, 1707)(616, 1708)(617, 1709)(618, 1710)(619, 1711)(620, 1712)(621, 1713)(622, 1714)(623, 1715)(624, 1716)(625, 1717)(626, 1718)(627, 1719)(628, 1720)(629, 1721)(630, 1722)(631, 1723)(632, 1724)(633, 1725)(634, 1726)(635, 1727)(636, 1728)(637, 1729)(638, 1730)(639, 1731)(640, 1732)(641, 1733)(642, 1734)(643, 1735)(644, 1736)(645, 1737)(646, 1738)(647, 1739)(648, 1740)(649, 1741)(650, 1742)(651, 1743)(652, 1744)(653, 1745)(654, 1746)(655, 1747)(656, 1748)(657, 1749)(658, 1750)(659, 1751)(660, 1752)(661, 1753)(662, 1754)(663, 1755)(664, 1756)(665, 1757)(666, 1758)(667, 1759)(668, 1760)(669, 1761)(670, 1762)(671, 1763)(672, 1764)(673, 1765)(674, 1766)(675, 1767)(676, 1768)(677, 1769)(678, 1770)(679, 1771)(680, 1772)(681, 1773)(682, 1774)(683, 1775)(684, 1776)(685, 1777)(686, 1778)(687, 1779)(688, 1780)(689, 1781)(690, 1782)(691, 1783)(692, 1784)(693, 1785)(694, 1786)(695, 1787)(696, 1788)(697, 1789)(698, 1790)(699, 1791)(700, 1792)(701, 1793)(702, 1794)(703, 1795)(704, 1796)(705, 1797)(706, 1798)(707, 1799)(708, 1800)(709, 1801)(710, 1802)(711, 1803)(712, 1804)(713, 1805)(714, 1806)(715, 1807)(716, 1808)(717, 1809)(718, 1810)(719, 1811)(720, 1812)(721, 1813)(722, 1814)(723, 1815)(724, 1816)(725, 1817)(726, 1818)(727, 1819)(728, 1820)(729, 1821)(730, 1822)(731, 1823)(732, 1824)(733, 1825)(734, 1826)(735, 1827)(736, 1828)(737, 1829)(738, 1830)(739, 1831)(740, 1832)(741, 1833)(742, 1834)(743, 1835)(744, 1836)(745, 1837)(746, 1838)(747, 1839)(748, 1840)(749, 1841)(750, 1842)(751, 1843)(752, 1844)(753, 1845)(754, 1846)(755, 1847)(756, 1848)(757, 1849)(758, 1850)(759, 1851)(760, 1852)(761, 1853)(762, 1854)(763, 1855)(764, 1856)(765, 1857)(766, 1858)(767, 1859)(768, 1860)(769, 1861)(770, 1862)(771, 1863)(772, 1864)(773, 1865)(774, 1866)(775, 1867)(776, 1868)(777, 1869)(778, 1870)(779, 1871)(780, 1872)(781, 1873)(782, 1874)(783, 1875)(784, 1876)(785, 1877)(786, 1878)(787, 1879)(788, 1880)(789, 1881)(790, 1882)(791, 1883)(792, 1884)(793, 1885)(794, 1886)(795, 1887)(796, 1888)(797, 1889)(798, 1890)(799, 1891)(800, 1892)(801, 1893)(802, 1894)(803, 1895)(804, 1896)(805, 1897)(806, 1898)(807, 1899)(808, 1900)(809, 1901)(810, 1902)(811, 1903)(812, 1904)(813, 1905)(814, 1906)(815, 1907)(816, 1908)(817, 1909)(818, 1910)(819, 1911)(820, 1912)(821, 1913)(822, 1914)(823, 1915)(824, 1916)(825, 1917)(826, 1918)(827, 1919)(828, 1920)(829, 1921)(830, 1922)(831, 1923)(832, 1924)(833, 1925)(834, 1926)(835, 1927)(836, 1928)(837, 1929)(838, 1930)(839, 1931)(840, 1932)(841, 1933)(842, 1934)(843, 1935)(844, 1936)(845, 1937)(846, 1938)(847, 1939)(848, 1940)(849, 1941)(850, 1942)(851, 1943)(852, 1944)(853, 1945)(854, 1946)(855, 1947)(856, 1948)(857, 1949)(858, 1950)(859, 1951)(860, 1952)(861, 1953)(862, 1954)(863, 1955)(864, 1956)(865, 1957)(866, 1958)(867, 1959)(868, 1960)(869, 1961)(870, 1962)(871, 1963)(872, 1964)(873, 1965)(874, 1966)(875, 1967)(876, 1968)(877, 1969)(878, 1970)(879, 1971)(880, 1972)(881, 1973)(882, 1974)(883, 1975)(884, 1976)(885, 1977)(886, 1978)(887, 1979)(888, 1980)(889, 1981)(890, 1982)(891, 1983)(892, 1984)(893, 1985)(894, 1986)(895, 1987)(896, 1988)(897, 1989)(898, 1990)(899, 1991)(900, 1992)(901, 1993)(902, 1994)(903, 1995)(904, 1996)(905, 1997)(906, 1998)(907, 1999)(908, 2000)(909, 2001)(910, 2002)(911, 2003)(912, 2004)(913, 2005)(914, 2006)(915, 2007)(916, 2008)(917, 2009)(918, 2010)(919, 2011)(920, 2012)(921, 2013)(922, 2014)(923, 2015)(924, 2016)(925, 2017)(926, 2018)(927, 2019)(928, 2020)(929, 2021)(930, 2022)(931, 2023)(932, 2024)(933, 2025)(934, 2026)(935, 2027)(936, 2028)(937, 2029)(938, 2030)(939, 2031)(940, 2032)(941, 2033)(942, 2034)(943, 2035)(944, 2036)(945, 2037)(946, 2038)(947, 2039)(948, 2040)(949, 2041)(950, 2042)(951, 2043)(952, 2044)(953, 2045)(954, 2046)(955, 2047)(956, 2048)(957, 2049)(958, 2050)(959, 2051)(960, 2052)(961, 2053)(962, 2054)(963, 2055)(964, 2056)(965, 2057)(966, 2058)(967, 2059)(968, 2060)(969, 2061)(970, 2062)(971, 2063)(972, 2064)(973, 2065)(974, 2066)(975, 2067)(976, 2068)(977, 2069)(978, 2070)(979, 2071)(980, 2072)(981, 2073)(982, 2074)(983, 2075)(984, 2076)(985, 2077)(986, 2078)(987, 2079)(988, 2080)(989, 2081)(990, 2082)(991, 2083)(992, 2084)(993, 2085)(994, 2086)(995, 2087)(996, 2088)(997, 2089)(998, 2090)(999, 2091)(1000, 2092)(1001, 2093)(1002, 2094)(1003, 2095)(1004, 2096)(1005, 2097)(1006, 2098)(1007, 2099)(1008, 2100)(1009, 2101)(1010, 2102)(1011, 2103)(1012, 2104)(1013, 2105)(1014, 2106)(1015, 2107)(1016, 2108)(1017, 2109)(1018, 2110)(1019, 2111)(1020, 2112)(1021, 2113)(1022, 2114)(1023, 2115)(1024, 2116)(1025, 2117)(1026, 2118)(1027, 2119)(1028, 2120)(1029, 2121)(1030, 2122)(1031, 2123)(1032, 2124)(1033, 2125)(1034, 2126)(1035, 2127)(1036, 2128)(1037, 2129)(1038, 2130)(1039, 2131)(1040, 2132)(1041, 2133)(1042, 2134)(1043, 2135)(1044, 2136)(1045, 2137)(1046, 2138)(1047, 2139)(1048, 2140)(1049, 2141)(1050, 2142)(1051, 2143)(1052, 2144)(1053, 2145)(1054, 2146)(1055, 2147)(1056, 2148)(1057, 2149)(1058, 2150)(1059, 2151)(1060, 2152)(1061, 2153)(1062, 2154)(1063, 2155)(1064, 2156)(1065, 2157)(1066, 2158)(1067, 2159)(1068, 2160)(1069, 2161)(1070, 2162)(1071, 2163)(1072, 2164)(1073, 2165)(1074, 2166)(1075, 2167)(1076, 2168)(1077, 2169)(1078, 2170)(1079, 2171)(1080, 2172)(1081, 2173)(1082, 2174)(1083, 2175)(1084, 2176)(1085, 2177)(1086, 2178)(1087, 2179)(1088, 2180)(1089, 2181)(1090, 2182)(1091, 2183)(1092, 2184) local type(s) :: { ( 6, 6 ), ( 6^7 ) } Outer automorphisms :: reflexible Dual of E14.628 Transitivity :: ET+ Graph:: simple bipartite v = 702 e = 1092 f = 364 degree seq :: [ 2^546, 7^156 ] E14.627 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^7, (T2 * T1^3 * T2 * T1^-3)^3, T2 * T1^-2 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-3 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 21)(14, 22)(15, 27)(17, 29)(18, 32)(20, 34)(23, 35)(24, 40)(25, 41)(26, 43)(28, 44)(30, 48)(31, 50)(33, 53)(36, 54)(37, 58)(38, 59)(39, 61)(42, 64)(45, 65)(46, 69)(47, 71)(49, 73)(51, 74)(52, 78)(55, 82)(56, 83)(57, 85)(60, 88)(62, 89)(63, 93)(66, 72)(67, 98)(68, 99)(70, 103)(75, 106)(76, 110)(77, 111)(79, 112)(80, 116)(81, 117)(84, 120)(86, 121)(87, 125)(90, 94)(91, 129)(92, 131)(95, 135)(96, 136)(97, 138)(100, 141)(101, 107)(102, 143)(104, 144)(105, 148)(108, 152)(109, 153)(113, 156)(114, 160)(115, 161)(118, 163)(119, 167)(122, 126)(123, 171)(124, 173)(127, 177)(128, 178)(130, 181)(132, 182)(133, 186)(134, 187)(137, 190)(139, 191)(140, 195)(142, 198)(145, 199)(146, 203)(147, 204)(149, 207)(150, 208)(151, 210)(154, 213)(155, 157)(158, 218)(159, 219)(162, 222)(164, 168)(165, 227)(166, 229)(169, 233)(170, 234)(172, 237)(174, 238)(175, 242)(176, 243)(179, 246)(180, 200)(183, 248)(184, 252)(185, 253)(188, 255)(189, 259)(192, 196)(193, 263)(194, 265)(197, 268)(201, 273)(202, 274)(205, 277)(206, 280)(209, 283)(211, 284)(212, 288)(214, 291)(215, 293)(216, 294)(217, 296)(220, 299)(221, 223)(224, 303)(225, 305)(226, 306)(228, 309)(230, 310)(231, 314)(232, 315)(235, 318)(236, 249)(239, 320)(240, 324)(241, 325)(244, 327)(245, 331)(247, 334)(250, 338)(251, 339)(254, 342)(256, 260)(257, 347)(258, 349)(261, 353)(262, 354)(264, 357)(266, 358)(267, 362)(269, 363)(270, 367)(271, 368)(272, 370)(275, 373)(276, 278)(279, 377)(281, 378)(282, 382)(285, 289)(286, 386)(287, 388)(290, 391)(292, 393)(295, 396)(297, 397)(298, 401)(300, 404)(301, 406)(302, 407)(304, 410)(307, 413)(308, 321)(311, 415)(312, 419)(313, 420)(316, 422)(317, 426)(319, 429)(322, 433)(323, 434)(326, 437)(328, 332)(329, 442)(330, 444)(333, 447)(335, 450)(336, 451)(337, 453)(340, 456)(341, 343)(344, 460)(345, 462)(346, 463)(348, 466)(350, 467)(351, 470)(352, 471)(355, 474)(356, 364)(359, 476)(360, 480)(361, 481)(365, 485)(366, 487)(369, 490)(371, 491)(372, 495)(374, 498)(375, 500)(376, 501)(379, 383)(380, 506)(381, 507)(384, 510)(385, 511)(387, 514)(389, 515)(390, 519)(392, 520)(394, 523)(395, 527)(398, 402)(399, 530)(400, 532)(403, 535)(405, 537)(408, 502)(409, 416)(411, 708)(412, 755)(414, 758)(417, 762)(418, 745)(421, 469)(423, 427)(424, 738)(425, 770)(428, 773)(430, 600)(431, 543)(432, 777)(435, 781)(436, 438)(439, 784)(440, 711)(441, 610)(443, 788)(445, 566)(446, 724)(448, 789)(449, 791)(452, 464)(454, 620)(455, 796)(457, 798)(458, 630)(459, 524)(461, 794)(465, 477)(468, 642)(472, 658)(473, 808)(475, 811)(478, 813)(479, 805)(482, 703)(483, 591)(484, 550)(486, 816)(488, 754)(489, 818)(492, 496)(493, 783)(494, 760)(497, 518)(499, 539)(503, 802)(504, 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1743, 1912, 2056)(1706, 1710, 2064, 2108, 1814, 2132, 1919)(1708, 1837, 2091, 1739, 2090, 1762, 1779)(1714, 2070, 1798, 1813, 1729, 1781, 2071)(1716, 2068, 2078, 1725, 2077, 1825, 1720)(1719, 1794, 2125, 2119, 2151, 2114, 1771)(1727, 1731, 1893, 2127, 1877, 2162, 1944)(1753, 1758, 2105, 2145, 2158, 2143, 1833)(1777, 1818, 1926, 2174, 2154, 1871, 1811) L = (1, 1093)(2, 1094)(3, 1095)(4, 1096)(5, 1097)(6, 1098)(7, 1099)(8, 1100)(9, 1101)(10, 1102)(11, 1103)(12, 1104)(13, 1105)(14, 1106)(15, 1107)(16, 1108)(17, 1109)(18, 1110)(19, 1111)(20, 1112)(21, 1113)(22, 1114)(23, 1115)(24, 1116)(25, 1117)(26, 1118)(27, 1119)(28, 1120)(29, 1121)(30, 1122)(31, 1123)(32, 1124)(33, 1125)(34, 1126)(35, 1127)(36, 1128)(37, 1129)(38, 1130)(39, 1131)(40, 1132)(41, 1133)(42, 1134)(43, 1135)(44, 1136)(45, 1137)(46, 1138)(47, 1139)(48, 1140)(49, 1141)(50, 1142)(51, 1143)(52, 1144)(53, 1145)(54, 1146)(55, 1147)(56, 1148)(57, 1149)(58, 1150)(59, 1151)(60, 1152)(61, 1153)(62, 1154)(63, 1155)(64, 1156)(65, 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1888)(797, 1889)(798, 1890)(799, 1891)(800, 1892)(801, 1893)(802, 1894)(803, 1895)(804, 1896)(805, 1897)(806, 1898)(807, 1899)(808, 1900)(809, 1901)(810, 1902)(811, 1903)(812, 1904)(813, 1905)(814, 1906)(815, 1907)(816, 1908)(817, 1909)(818, 1910)(819, 1911)(820, 1912)(821, 1913)(822, 1914)(823, 1915)(824, 1916)(825, 1917)(826, 1918)(827, 1919)(828, 1920)(829, 1921)(830, 1922)(831, 1923)(832, 1924)(833, 1925)(834, 1926)(835, 1927)(836, 1928)(837, 1929)(838, 1930)(839, 1931)(840, 1932)(841, 1933)(842, 1934)(843, 1935)(844, 1936)(845, 1937)(846, 1938)(847, 1939)(848, 1940)(849, 1941)(850, 1942)(851, 1943)(852, 1944)(853, 1945)(854, 1946)(855, 1947)(856, 1948)(857, 1949)(858, 1950)(859, 1951)(860, 1952)(861, 1953)(862, 1954)(863, 1955)(864, 1956)(865, 1957)(866, 1958)(867, 1959)(868, 1960)(869, 1961)(870, 1962)(871, 1963)(872, 1964)(873, 1965)(874, 1966)(875, 1967)(876, 1968)(877, 1969)(878, 1970)(879, 1971)(880, 1972)(881, 1973)(882, 1974)(883, 1975)(884, 1976)(885, 1977)(886, 1978)(887, 1979)(888, 1980)(889, 1981)(890, 1982)(891, 1983)(892, 1984)(893, 1985)(894, 1986)(895, 1987)(896, 1988)(897, 1989)(898, 1990)(899, 1991)(900, 1992)(901, 1993)(902, 1994)(903, 1995)(904, 1996)(905, 1997)(906, 1998)(907, 1999)(908, 2000)(909, 2001)(910, 2002)(911, 2003)(912, 2004)(913, 2005)(914, 2006)(915, 2007)(916, 2008)(917, 2009)(918, 2010)(919, 2011)(920, 2012)(921, 2013)(922, 2014)(923, 2015)(924, 2016)(925, 2017)(926, 2018)(927, 2019)(928, 2020)(929, 2021)(930, 2022)(931, 2023)(932, 2024)(933, 2025)(934, 2026)(935, 2027)(936, 2028)(937, 2029)(938, 2030)(939, 2031)(940, 2032)(941, 2033)(942, 2034)(943, 2035)(944, 2036)(945, 2037)(946, 2038)(947, 2039)(948, 2040)(949, 2041)(950, 2042)(951, 2043)(952, 2044)(953, 2045)(954, 2046)(955, 2047)(956, 2048)(957, 2049)(958, 2050)(959, 2051)(960, 2052)(961, 2053)(962, 2054)(963, 2055)(964, 2056)(965, 2057)(966, 2058)(967, 2059)(968, 2060)(969, 2061)(970, 2062)(971, 2063)(972, 2064)(973, 2065)(974, 2066)(975, 2067)(976, 2068)(977, 2069)(978, 2070)(979, 2071)(980, 2072)(981, 2073)(982, 2074)(983, 2075)(984, 2076)(985, 2077)(986, 2078)(987, 2079)(988, 2080)(989, 2081)(990, 2082)(991, 2083)(992, 2084)(993, 2085)(994, 2086)(995, 2087)(996, 2088)(997, 2089)(998, 2090)(999, 2091)(1000, 2092)(1001, 2093)(1002, 2094)(1003, 2095)(1004, 2096)(1005, 2097)(1006, 2098)(1007, 2099)(1008, 2100)(1009, 2101)(1010, 2102)(1011, 2103)(1012, 2104)(1013, 2105)(1014, 2106)(1015, 2107)(1016, 2108)(1017, 2109)(1018, 2110)(1019, 2111)(1020, 2112)(1021, 2113)(1022, 2114)(1023, 2115)(1024, 2116)(1025, 2117)(1026, 2118)(1027, 2119)(1028, 2120)(1029, 2121)(1030, 2122)(1031, 2123)(1032, 2124)(1033, 2125)(1034, 2126)(1035, 2127)(1036, 2128)(1037, 2129)(1038, 2130)(1039, 2131)(1040, 2132)(1041, 2133)(1042, 2134)(1043, 2135)(1044, 2136)(1045, 2137)(1046, 2138)(1047, 2139)(1048, 2140)(1049, 2141)(1050, 2142)(1051, 2143)(1052, 2144)(1053, 2145)(1054, 2146)(1055, 2147)(1056, 2148)(1057, 2149)(1058, 2150)(1059, 2151)(1060, 2152)(1061, 2153)(1062, 2154)(1063, 2155)(1064, 2156)(1065, 2157)(1066, 2158)(1067, 2159)(1068, 2160)(1069, 2161)(1070, 2162)(1071, 2163)(1072, 2164)(1073, 2165)(1074, 2166)(1075, 2167)(1076, 2168)(1077, 2169)(1078, 2170)(1079, 2171)(1080, 2172)(1081, 2173)(1082, 2174)(1083, 2175)(1084, 2176)(1085, 2177)(1086, 2178)(1087, 2179)(1088, 2180)(1089, 2181)(1090, 2182)(1091, 2183)(1092, 2184) local type(s) :: { ( 6, 6 ), ( 6^7 ) } Outer automorphisms :: reflexible Dual of E14.630 Transitivity :: ET+ Graph:: simple bipartite v = 702 e = 1092 f = 364 degree seq :: [ 2^546, 7^156 ] E14.628 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2 * T1)^7, (T1 * T2^-1 * T1 * T2)^7, (T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1)^2 ] Map:: R = (1, 1093, 3, 1095, 4, 1096)(2, 1094, 5, 1097, 6, 1098)(7, 1099, 11, 1103, 12, 1104)(8, 1100, 13, 1105, 14, 1106)(9, 1101, 15, 1107, 16, 1108)(10, 1102, 17, 1109, 18, 1110)(19, 1111, 27, 1119, 28, 1120)(20, 1112, 29, 1121, 30, 1122)(21, 1113, 31, 1123, 32, 1124)(22, 1114, 33, 1125, 34, 1126)(23, 1115, 35, 1127, 36, 1128)(24, 1116, 37, 1129, 38, 1130)(25, 1117, 39, 1131, 40, 1132)(26, 1118, 41, 1133, 42, 1134)(43, 1135, 58, 1150, 59, 1151)(44, 1136, 60, 1152, 61, 1153)(45, 1137, 62, 1154, 63, 1155)(46, 1138, 64, 1156, 65, 1157)(47, 1139, 66, 1158, 67, 1159)(48, 1140, 68, 1160, 69, 1161)(49, 1141, 70, 1162, 71, 1163)(50, 1142, 72, 1164, 51, 1143)(52, 1144, 73, 1165, 74, 1166)(53, 1145, 75, 1167, 76, 1168)(54, 1146, 77, 1169, 78, 1170)(55, 1147, 79, 1171, 80, 1172)(56, 1148, 81, 1173, 82, 1174)(57, 1149, 83, 1175, 84, 1176)(85, 1177, 107, 1199, 108, 1200)(86, 1178, 109, 1201, 110, 1202)(87, 1179, 111, 1203, 112, 1204)(88, 1180, 113, 1205, 114, 1206)(89, 1181, 115, 1207, 116, 1208)(90, 1182, 117, 1209, 118, 1210)(91, 1183, 119, 1211, 120, 1212)(92, 1184, 121, 1213, 122, 1214)(93, 1185, 123, 1215, 124, 1216)(94, 1186, 125, 1217, 126, 1218)(95, 1187, 127, 1219, 128, 1220)(96, 1188, 129, 1221, 130, 1222)(97, 1189, 131, 1223, 132, 1224)(98, 1190, 133, 1225, 134, 1226)(99, 1191, 135, 1227, 136, 1228)(100, 1192, 137, 1229, 138, 1230)(101, 1193, 139, 1231, 140, 1232)(102, 1194, 141, 1233, 142, 1234)(103, 1195, 143, 1235, 144, 1236)(104, 1196, 145, 1237, 146, 1238)(105, 1197, 147, 1239, 148, 1240)(106, 1198, 149, 1241, 150, 1242)(151, 1243, 187, 1279, 188, 1280)(152, 1244, 189, 1281, 190, 1282)(153, 1245, 191, 1283, 192, 1284)(154, 1246, 193, 1285, 194, 1286)(155, 1247, 195, 1287, 196, 1288)(156, 1248, 197, 1289, 198, 1290)(157, 1249, 199, 1291, 200, 1292)(158, 1250, 201, 1293, 202, 1294)(159, 1251, 203, 1295, 204, 1296)(160, 1252, 205, 1297, 206, 1298)(161, 1253, 207, 1299, 208, 1300)(162, 1254, 209, 1301, 210, 1302)(163, 1255, 211, 1303, 212, 1304)(164, 1256, 213, 1305, 214, 1306)(165, 1257, 215, 1307, 216, 1308)(166, 1258, 217, 1309, 218, 1310)(167, 1259, 219, 1311, 220, 1312)(168, 1260, 221, 1313, 222, 1314)(169, 1261, 223, 1315, 224, 1316)(170, 1262, 225, 1317, 226, 1318)(171, 1263, 227, 1319, 228, 1320)(172, 1264, 229, 1321, 230, 1322)(173, 1265, 231, 1323, 232, 1324)(174, 1266, 233, 1325, 234, 1326)(175, 1267, 235, 1327, 236, 1328)(176, 1268, 237, 1329, 238, 1330)(177, 1269, 239, 1331, 240, 1332)(178, 1270, 241, 1333, 242, 1334)(179, 1271, 243, 1335, 244, 1336)(180, 1272, 245, 1337, 246, 1338)(181, 1273, 247, 1339, 248, 1340)(182, 1274, 249, 1341, 250, 1342)(183, 1275, 251, 1343, 252, 1344)(184, 1276, 253, 1345, 254, 1346)(185, 1277, 255, 1347, 256, 1348)(186, 1278, 257, 1349, 258, 1350)(259, 1351, 499, 1591, 996, 2088)(260, 1352, 301, 1393, 584, 1676)(261, 1353, 402, 1494, 706, 1798)(262, 1354, 380, 1472, 822, 1914)(263, 1355, 504, 1596, 348, 1440)(264, 1356, 505, 1597, 693, 1785)(265, 1357, 506, 1598, 1002, 2094)(266, 1358, 508, 1600, 803, 1895)(267, 1359, 510, 1602, 449, 1541)(268, 1360, 511, 1603, 390, 1482)(269, 1361, 512, 1604, 478, 1570)(270, 1362, 338, 1430, 720, 1812)(271, 1363, 514, 1606, 999, 2091)(272, 1364, 317, 1409, 646, 1738)(273, 1365, 517, 1609, 274, 1366)(275, 1367, 519, 1611, 1007, 2099)(276, 1368, 294, 1386, 557, 1649)(277, 1369, 442, 1534, 776, 1868)(278, 1370, 388, 1480, 841, 1933)(279, 1371, 524, 1616, 373, 1465)(280, 1372, 525, 1617, 625, 1717)(281, 1373, 427, 1519, 900, 1992)(282, 1374, 528, 1620, 880, 1972)(283, 1375, 530, 1622, 395, 1487)(284, 1376, 531, 1623, 431, 1523)(285, 1377, 532, 1624, 1014, 2106)(286, 1378, 344, 1436, 715, 1807)(287, 1379, 534, 1626, 1010, 2102)(288, 1380, 304, 1396, 595, 1687)(289, 1381, 538, 1630, 540, 1632)(290, 1382, 542, 1634, 544, 1636)(291, 1383, 546, 1638, 548, 1640)(292, 1384, 550, 1642, 480, 1572)(293, 1385, 553, 1645, 555, 1647)(295, 1387, 560, 1652, 562, 1654)(296, 1388, 564, 1656, 566, 1658)(297, 1389, 568, 1660, 570, 1662)(298, 1390, 572, 1664, 574, 1666)(299, 1391, 576, 1668, 578, 1670)(300, 1392, 580, 1672, 582, 1674)(302, 1394, 587, 1679, 589, 1681)(303, 1395, 591, 1683, 593, 1685)(305, 1397, 598, 1690, 600, 1692)(306, 1398, 602, 1694, 604, 1696)(307, 1399, 606, 1698, 608, 1700)(308, 1400, 610, 1702, 612, 1704)(309, 1401, 614, 1706, 616, 1708)(310, 1402, 618, 1710, 620, 1712)(311, 1403, 622, 1714, 624, 1716)(312, 1404, 626, 1718, 628, 1720)(313, 1405, 630, 1722, 632, 1724)(314, 1406, 634, 1726, 636, 1728)(315, 1407, 638, 1730, 640, 1732)(316, 1408, 642, 1734, 644, 1736)(318, 1410, 649, 1741, 651, 1743)(319, 1411, 653, 1745, 655, 1747)(320, 1412, 657, 1749, 659, 1751)(321, 1413, 661, 1753, 663, 1755)(322, 1414, 665, 1757, 475, 1567)(323, 1415, 668, 1760, 670, 1762)(324, 1416, 672, 1764, 674, 1766)(325, 1417, 676, 1768, 678, 1770)(326, 1418, 679, 1771, 681, 1773)(327, 1419, 682, 1774, 684, 1776)(328, 1420, 686, 1778, 688, 1780)(329, 1421, 690, 1782, 692, 1784)(330, 1422, 694, 1786, 696, 1788)(331, 1423, 698, 1790, 700, 1792)(332, 1424, 516, 1608, 703, 1795)(333, 1425, 705, 1797, 502, 1594)(334, 1426, 707, 1799, 709, 1801)(335, 1427, 711, 1803, 713, 1805)(336, 1428, 521, 1613, 533, 1625)(337, 1429, 717, 1809, 719, 1811)(339, 1431, 461, 1553, 724, 1816)(340, 1432, 726, 1818, 728, 1820)(341, 1433, 702, 1794, 731, 1823)(342, 1434, 733, 1825, 735, 1827)(343, 1435, 736, 1828, 738, 1830)(345, 1437, 741, 1833, 743, 1835)(346, 1438, 745, 1837, 747, 1839)(347, 1439, 749, 1841, 470, 1562)(349, 1441, 753, 1845, 755, 1847)(350, 1442, 673, 1765, 758, 1850)(351, 1443, 759, 1851, 761, 1853)(352, 1444, 732, 1824, 763, 1855)(353, 1445, 691, 1783, 496, 1588)(354, 1446, 766, 1858, 768, 1860)(355, 1447, 770, 1862, 772, 1864)(356, 1448, 536, 1628, 774, 1866)(357, 1449, 775, 1867, 522, 1614)(358, 1450, 777, 1869, 779, 1871)(359, 1451, 780, 1872, 782, 1874)(360, 1452, 421, 1513, 428, 1520)(361, 1453, 430, 1522, 784, 1876)(362, 1454, 786, 1878, 422, 1514)(363, 1455, 787, 1879, 710, 1802)(364, 1456, 789, 1881, 791, 1883)(365, 1457, 501, 1593, 513, 1605)(366, 1458, 793, 1885, 783, 1875)(367, 1459, 795, 1887, 797, 1889)(368, 1460, 407, 1499, 414, 1506)(369, 1461, 416, 1508, 798, 1890)(370, 1462, 800, 1892, 408, 1500)(371, 1463, 801, 1893, 685, 1777)(372, 1464, 804, 1896, 806, 1898)(374, 1466, 467, 1559, 808, 1900)(375, 1467, 687, 1779, 811, 1903)(376, 1468, 812, 1904, 814, 1906)(377, 1469, 697, 1789, 815, 1907)(378, 1470, 623, 1715, 817, 1909)(379, 1471, 492, 1584, 820, 1912)(381, 1473, 825, 1917, 827, 1919)(382, 1474, 821, 1913, 830, 1922)(383, 1475, 619, 1711, 832, 1924)(384, 1476, 833, 1925, 835, 1927)(385, 1477, 664, 1756, 836, 1928)(386, 1478, 677, 1769, 458, 1550)(387, 1479, 838, 1930, 840, 1932)(389, 1481, 487, 1579, 845, 1937)(391, 1483, 712, 1804, 848, 1940)(392, 1484, 849, 1941, 851, 1943)(393, 1485, 667, 1759, 852, 1944)(394, 1486, 607, 1699, 854, 1946)(396, 1488, 857, 1949, 460, 1552)(397, 1489, 860, 1952, 862, 1954)(398, 1490, 856, 1948, 865, 1957)(399, 1491, 603, 1695, 867, 1959)(400, 1492, 868, 1960, 870, 1962)(401, 1493, 645, 1737, 837, 1929)(403, 1495, 871, 1963, 873, 1965)(404, 1496, 874, 1966, 485, 1577)(405, 1497, 876, 1968, 701, 1793)(406, 1498, 877, 1969, 878, 1970)(409, 1501, 879, 1971, 415, 1507)(410, 1502, 859, 1951, 617, 1709)(411, 1503, 881, 1973, 883, 1975)(412, 1504, 884, 1976, 773, 1865)(413, 1505, 885, 1977, 491, 1583)(417, 1509, 887, 1979, 671, 1763)(418, 1510, 888, 1980, 890, 1982)(419, 1511, 891, 1983, 893, 1985)(420, 1512, 894, 1986, 895, 1987)(423, 1515, 896, 1988, 429, 1521)(424, 1516, 824, 1916, 601, 1693)(425, 1517, 897, 1989, 898, 1990)(426, 1518, 899, 1991, 792, 1884)(432, 1524, 781, 1873, 903, 1995)(433, 1525, 904, 1996, 906, 1998)(434, 1526, 474, 1566, 794, 1886)(435, 1527, 569, 1661, 908, 2000)(436, 1528, 910, 2002, 912, 2004)(437, 1529, 913, 2005, 915, 2007)(438, 1530, 909, 2001, 918, 2010)(439, 1531, 611, 1703, 920, 2012)(440, 1532, 921, 2013, 923, 2015)(441, 1533, 594, 1686, 765, 1857)(443, 1535, 886, 1978, 924, 2016)(444, 1536, 469, 1561, 926, 2018)(445, 1537, 790, 1882, 927, 2019)(446, 1538, 928, 2020, 930, 2022)(447, 1539, 613, 1705, 846, 1938)(448, 1540, 599, 1691, 932, 2024)(450, 1542, 934, 2026, 936, 2028)(451, 1543, 937, 2029, 939, 2031)(452, 1544, 933, 2025, 942, 2034)(453, 1545, 573, 1665, 944, 2036)(454, 1546, 945, 2037, 947, 2039)(455, 1547, 493, 1585, 818, 1910)(456, 1548, 796, 1888, 949, 2041)(457, 1549, 950, 2042, 952, 2044)(459, 1551, 561, 1653, 954, 2046)(462, 1554, 956, 2048, 518, 1610)(463, 1555, 722, 1814, 716, 1808)(464, 1556, 957, 2049, 959, 2051)(465, 1557, 960, 2052, 962, 2054)(466, 1558, 882, 1974, 486, 1578)(468, 1560, 931, 2023, 965, 2057)(471, 1563, 627, 1719, 968, 2060)(472, 1564, 969, 2061, 971, 2063)(473, 1565, 583, 1675, 740, 1832)(476, 1568, 901, 1993, 973, 2065)(477, 1569, 911, 2003, 479, 1571)(481, 1573, 805, 1897, 976, 2068)(482, 1574, 527, 1619, 978, 2070)(483, 1575, 597, 1689, 809, 1901)(484, 1576, 615, 1707, 979, 2071)(488, 1580, 919, 2011, 983, 2075)(489, 1581, 843, 1935, 609, 1701)(490, 1582, 984, 2076, 986, 2078)(494, 1586, 981, 2073, 941, 2033)(495, 1587, 988, 2080, 989, 2081)(497, 1589, 565, 1657, 992, 2084)(498, 1590, 993, 2085, 995, 2087)(500, 1592, 980, 2072, 997, 2089)(503, 1595, 998, 2090, 515, 1607)(507, 1599, 1003, 2095, 855, 1947)(509, 1601, 987, 2079, 714, 1806)(520, 1612, 1008, 2100, 966, 2058)(523, 1615, 1009, 2101, 535, 1627)(526, 1618, 769, 1861, 571, 1663)(529, 1621, 1012, 2104, 762, 1854)(537, 1629, 641, 1733, 637, 1729)(539, 1631, 1015, 2107, 1016, 2108)(541, 1633, 660, 1752, 656, 1748)(543, 1635, 1017, 2109, 1005, 2097)(545, 1637, 590, 1682, 586, 1678)(547, 1639, 1018, 2110, 1019, 2111)(549, 1641, 633, 1725, 629, 1721)(551, 1643, 975, 2067, 1021, 2113)(552, 1644, 579, 1671, 575, 1667)(554, 1646, 1022, 2114, 1024, 2116)(556, 1648, 652, 1744, 648, 1740)(558, 1650, 1025, 2117, 1027, 2119)(559, 1651, 729, 1821, 725, 1817)(563, 1655, 748, 1840, 744, 1836)(567, 1659, 756, 1848, 752, 1844)(577, 1669, 970, 2062, 1028, 2120)(581, 1673, 1029, 2121, 1031, 2123)(585, 1677, 1032, 2124, 964, 2056)(588, 1680, 922, 2014, 1033, 2125)(592, 1684, 1034, 2126, 1035, 2127)(596, 1688, 1036, 2128, 917, 2009)(605, 1697, 802, 1894, 828, 1920)(621, 1713, 788, 1880, 863, 1955)(631, 1723, 946, 2038, 1037, 2129)(635, 1727, 1038, 2130, 1040, 2132)(639, 1731, 869, 1961, 1041, 2133)(643, 1735, 1042, 2134, 1044, 2136)(647, 1739, 1045, 2137, 864, 1956)(650, 1742, 994, 2086, 1046, 2138)(654, 1746, 1047, 2139, 1048, 2140)(658, 1750, 834, 1926, 1049, 2141)(662, 1754, 1039, 2131, 1051, 2143)(666, 1758, 972, 2064, 829, 1921)(669, 1761, 1053, 2145, 785, 1877)(675, 1767, 708, 1800, 916, 2008)(680, 1772, 955, 2047, 1000, 2092)(683, 1775, 963, 2055, 704, 1796)(689, 1781, 778, 1870, 940, 2032)(695, 1787, 1054, 2146, 1011, 2103)(699, 1791, 1056, 2148, 799, 1891)(718, 1810, 1006, 2098, 1055, 2147)(721, 1813, 1030, 2122, 1058, 2150)(723, 1815, 1059, 2151, 1060, 2152)(727, 1819, 760, 1852, 1061, 2153)(730, 1822, 1043, 2135, 1063, 2155)(734, 1826, 1064, 2156, 754, 1846)(737, 1829, 892, 1984, 1052, 2144)(739, 1831, 1023, 2115, 982, 2074)(742, 1834, 1065, 2157, 1066, 2158)(746, 1838, 813, 1905, 1067, 2159)(750, 1842, 967, 2059, 1069, 2161)(751, 1843, 1001, 2093, 1070, 2162)(757, 1849, 1050, 2142, 1072, 2164)(764, 1856, 990, 2082, 935, 2027)(767, 1859, 1073, 2165, 1074, 2166)(771, 1863, 850, 1942, 1075, 2167)(807, 1899, 977, 2069, 1076, 2168)(810, 1902, 1062, 2154, 1078, 2170)(816, 1908, 1020, 2112, 858, 1950)(819, 1911, 961, 2053, 1080, 2172)(823, 1915, 853, 1945, 1026, 2118)(826, 1918, 905, 1997, 1081, 2173)(831, 1923, 1068, 2160, 1082, 2174)(839, 1931, 1084, 2176, 1085, 2177)(842, 1934, 907, 1999, 958, 2050)(844, 1936, 929, 2021, 1086, 2178)(847, 1939, 1071, 2163, 1087, 2179)(861, 1953, 951, 2043, 1088, 2180)(866, 1958, 1057, 2149, 1089, 2181)(872, 1964, 1083, 2175, 1090, 2182)(875, 1967, 953, 2045, 914, 2006)(889, 1981, 1004, 2096, 1013, 2105)(902, 1994, 1077, 2169, 1091, 2183)(925, 2017, 991, 2083, 938, 2030)(943, 2035, 985, 2077, 974, 2066)(948, 2040, 1079, 2171, 1092, 2184) L = (1, 1094)(2, 1093)(3, 1099)(4, 1100)(5, 1101)(6, 1102)(7, 1095)(8, 1096)(9, 1097)(10, 1098)(11, 1111)(12, 1112)(13, 1113)(14, 1114)(15, 1115)(16, 1116)(17, 1117)(18, 1118)(19, 1103)(20, 1104)(21, 1105)(22, 1106)(23, 1107)(24, 1108)(25, 1109)(26, 1110)(27, 1135)(28, 1136)(29, 1137)(30, 1138)(31, 1139)(32, 1140)(33, 1141)(34, 1142)(35, 1143)(36, 1144)(37, 1145)(38, 1146)(39, 1147)(40, 1148)(41, 1149)(42, 1150)(43, 1119)(44, 1120)(45, 1121)(46, 1122)(47, 1123)(48, 1124)(49, 1125)(50, 1126)(51, 1127)(52, 1128)(53, 1129)(54, 1130)(55, 1131)(56, 1132)(57, 1133)(58, 1134)(59, 1177)(60, 1178)(61, 1179)(62, 1180)(63, 1181)(64, 1182)(65, 1158)(66, 1157)(67, 1183)(68, 1184)(69, 1185)(70, 1186)(71, 1187)(72, 1188)(73, 1189)(74, 1190)(75, 1191)(76, 1192)(77, 1193)(78, 1171)(79, 1170)(80, 1194)(81, 1195)(82, 1196)(83, 1197)(84, 1198)(85, 1151)(86, 1152)(87, 1153)(88, 1154)(89, 1155)(90, 1156)(91, 1159)(92, 1160)(93, 1161)(94, 1162)(95, 1163)(96, 1164)(97, 1165)(98, 1166)(99, 1167)(100, 1168)(101, 1169)(102, 1172)(103, 1173)(104, 1174)(105, 1175)(106, 1176)(107, 1243)(108, 1244)(109, 1245)(110, 1246)(111, 1247)(112, 1205)(113, 1204)(114, 1248)(115, 1249)(116, 1250)(117, 1251)(118, 1252)(119, 1253)(120, 1254)(121, 1255)(122, 1256)(123, 1257)(124, 1217)(125, 1216)(126, 1258)(127, 1259)(128, 1260)(129, 1261)(130, 1262)(131, 1263)(132, 1264)(133, 1265)(134, 1227)(135, 1226)(136, 1266)(137, 1267)(138, 1268)(139, 1269)(140, 1270)(141, 1271)(142, 1272)(143, 1273)(144, 1274)(145, 1275)(146, 1239)(147, 1238)(148, 1276)(149, 1277)(150, 1278)(151, 1199)(152, 1200)(153, 1201)(154, 1202)(155, 1203)(156, 1206)(157, 1207)(158, 1208)(159, 1209)(160, 1210)(161, 1211)(162, 1212)(163, 1213)(164, 1214)(165, 1215)(166, 1218)(167, 1219)(168, 1220)(169, 1221)(170, 1222)(171, 1223)(172, 1224)(173, 1225)(174, 1228)(175, 1229)(176, 1230)(177, 1231)(178, 1232)(179, 1233)(180, 1234)(181, 1235)(182, 1236)(183, 1237)(184, 1240)(185, 1241)(186, 1242)(187, 1350)(188, 1351)(189, 1352)(190, 1283)(191, 1282)(192, 1353)(193, 1354)(194, 1355)(195, 1356)(196, 1357)(197, 1358)(198, 1359)(199, 1360)(200, 1361)(201, 1362)(202, 1295)(203, 1294)(204, 1363)(205, 1364)(206, 1365)(207, 1366)(208, 1367)(209, 1368)(210, 1303)(211, 1302)(212, 1369)(213, 1370)(214, 1371)(215, 1372)(216, 1373)(217, 1374)(218, 1375)(219, 1376)(220, 1377)(221, 1378)(222, 1315)(223, 1314)(224, 1379)(225, 1380)(226, 1319)(227, 1318)(228, 1550)(229, 1552)(230, 1553)(231, 1555)(232, 1557)(233, 1450)(234, 1558)(235, 1559)(236, 1561)(237, 1562)(238, 1331)(239, 1330)(240, 1418)(241, 1567)(242, 1569)(243, 1571)(244, 1510)(245, 1572)(246, 1339)(247, 1338)(248, 1526)(249, 1577)(250, 1579)(251, 1581)(252, 1583)(253, 1511)(254, 1584)(255, 1585)(256, 1587)(257, 1588)(258, 1279)(259, 1280)(260, 1281)(261, 1284)(262, 1285)(263, 1286)(264, 1287)(265, 1288)(266, 1289)(267, 1290)(268, 1291)(269, 1292)(270, 1293)(271, 1296)(272, 1297)(273, 1298)(274, 1299)(275, 1300)(276, 1301)(277, 1304)(278, 1305)(279, 1306)(280, 1307)(281, 1308)(282, 1309)(283, 1310)(284, 1311)(285, 1312)(286, 1313)(287, 1316)(288, 1317)(289, 1629)(290, 1633)(291, 1637)(292, 1641)(293, 1644)(294, 1648)(295, 1651)(296, 1655)(297, 1659)(298, 1663)(299, 1667)(300, 1671)(301, 1675)(302, 1678)(303, 1682)(304, 1686)(305, 1689)(306, 1693)(307, 1697)(308, 1701)(309, 1705)(310, 1709)(311, 1713)(312, 1717)(313, 1721)(314, 1725)(315, 1729)(316, 1733)(317, 1737)(318, 1740)(319, 1744)(320, 1748)(321, 1752)(322, 1756)(323, 1759)(324, 1763)(325, 1767)(326, 1332)(327, 1566)(328, 1777)(329, 1781)(330, 1785)(331, 1789)(332, 1793)(333, 1796)(334, 1534)(335, 1802)(336, 1806)(337, 1808)(338, 1618)(339, 1814)(340, 1817)(341, 1821)(342, 1824)(343, 1565)(344, 1516)(345, 1832)(346, 1836)(347, 1840)(348, 1597)(349, 1844)(350, 1848)(351, 1828)(352, 1533)(353, 1502)(354, 1857)(355, 1861)(356, 1865)(357, 1576)(358, 1325)(359, 1801)(360, 1854)(361, 1875)(362, 1877)(363, 1494)(364, 1871)(365, 1884)(366, 1540)(367, 1776)(368, 1829)(369, 1614)(370, 1891)(371, 1478)(372, 1895)(373, 1617)(374, 1575)(375, 1901)(376, 1741)(377, 1547)(378, 1509)(379, 1910)(380, 1913)(381, 1916)(382, 1920)(383, 1894)(384, 1809)(385, 1493)(386, 1463)(387, 1929)(388, 1845)(389, 1935)(390, 1539)(391, 1938)(392, 1722)(393, 1523)(394, 1497)(395, 1623)(396, 1948)(397, 1951)(398, 1955)(399, 1880)(400, 1786)(401, 1477)(402, 1455)(403, 1928)(404, 1818)(405, 1486)(406, 1708)(407, 1742)(408, 1514)(409, 1921)(410, 1445)(411, 1972)(412, 1527)(413, 1762)(414, 1810)(415, 1594)(416, 1846)(417, 1470)(418, 1336)(419, 1345)(420, 1692)(421, 1723)(422, 1500)(423, 1956)(424, 1436)(425, 1985)(426, 1551)(427, 1792)(428, 1787)(429, 1770)(430, 1819)(431, 1485)(432, 1944)(433, 1730)(434, 1340)(435, 1504)(436, 2001)(437, 1979)(438, 2008)(439, 1800)(440, 1718)(441, 1444)(442, 1426)(443, 1855)(444, 1837)(445, 1886)(446, 1679)(447, 1482)(448, 1458)(449, 1603)(450, 2025)(451, 1893)(452, 2032)(453, 1870)(454, 1771)(455, 1469)(456, 1907)(457, 1749)(458, 1320)(459, 1518)(460, 1321)(461, 1322)(462, 2023)(463, 1323)(464, 1968)(465, 1324)(466, 1326)(467, 1327)(468, 2055)(469, 1328)(470, 1329)(471, 1775)(472, 1702)(473, 1435)(474, 1419)(475, 1333)(476, 1830)(477, 1334)(478, 1862)(479, 1335)(480, 1337)(481, 1868)(482, 1668)(483, 1466)(484, 1449)(485, 1341)(486, 1900)(487, 1342)(488, 2073)(489, 1343)(490, 1879)(491, 1344)(492, 1346)(493, 1347)(494, 2079)(495, 1348)(496, 1349)(497, 1601)(498, 1606)(499, 2004)(500, 1700)(501, 1731)(502, 1507)(503, 2009)(504, 1755)(505, 1440)(506, 1827)(507, 2087)(508, 1856)(509, 1589)(510, 1632)(511, 1541)(512, 2018)(513, 1719)(514, 1590)(515, 1784)(516, 1838)(517, 1909)(518, 1626)(519, 2028)(520, 1662)(521, 1680)(522, 1461)(523, 2033)(524, 1823)(525, 1465)(526, 1430)(527, 2048)(528, 1908)(529, 2097)(530, 1640)(531, 1487)(532, 2044)(533, 1772)(534, 1610)(535, 1716)(536, 1750)(537, 1381)(538, 1859)(539, 1878)(540, 1602)(541, 1382)(542, 1834)(543, 1892)(544, 1974)(545, 1383)(546, 1911)(547, 1797)(548, 1622)(549, 1384)(550, 1931)(551, 1867)(552, 1385)(553, 1947)(554, 1768)(555, 1912)(556, 1386)(557, 1964)(558, 1885)(559, 1387)(560, 1746)(561, 1971)(562, 1981)(563, 1388)(564, 1815)(565, 1890)(566, 1897)(567, 1389)(568, 1727)(569, 1988)(570, 1612)(571, 1390)(572, 1843)(573, 1876)(574, 1882)(575, 1391)(576, 1574)(577, 1782)(578, 1932)(579, 1392)(580, 1990)(581, 1714)(582, 1860)(583, 1393)(584, 2040)(585, 1976)(586, 1394)(587, 1538)(588, 1613)(589, 1965)(590, 1395)(591, 1975)(592, 1698)(593, 1835)(594, 1396)(595, 1994)(596, 1991)(597, 1397)(598, 1735)(599, 2090)(600, 1512)(601, 1398)(602, 1899)(603, 1795)(604, 1804)(605, 1399)(606, 1684)(607, 2101)(608, 1592)(609, 1400)(610, 1564)(611, 1866)(612, 1873)(613, 1401)(614, 1754)(615, 2092)(616, 1498)(617, 1402)(618, 1936)(619, 1766)(620, 1779)(621, 1403)(622, 1673)(623, 2089)(624, 1627)(625, 1404)(626, 1532)(627, 1605)(628, 1888)(629, 1405)(630, 1484)(631, 1513)(632, 2016)(633, 1406)(634, 1982)(635, 1660)(636, 1747)(637, 1407)(638, 1525)(639, 1593)(640, 2041)(641, 1408)(642, 1898)(643, 1690)(644, 1816)(645, 1409)(646, 1939)(647, 2104)(648, 1410)(649, 1468)(650, 1499)(651, 2065)(652, 1411)(653, 2099)(654, 1652)(655, 1728)(656, 1412)(657, 1549)(658, 1628)(659, 1995)(660, 1413)(661, 1883)(662, 1706)(663, 1596)(664, 1414)(665, 1902)(666, 2144)(667, 1415)(668, 1822)(669, 2103)(670, 1505)(671, 1416)(672, 1863)(673, 1780)(674, 1711)(675, 1417)(676, 1646)(677, 2058)(678, 1521)(679, 1546)(680, 1625)(681, 1963)(682, 1842)(683, 1563)(684, 1459)(685, 1420)(686, 1918)(687, 1712)(688, 1765)(689, 1421)(690, 1669)(691, 1987)(692, 1607)(693, 1422)(694, 1492)(695, 1520)(696, 1978)(697, 1423)(698, 1849)(699, 2147)(700, 1519)(701, 1424)(702, 1805)(703, 1695)(704, 1425)(705, 1639)(706, 2105)(707, 1813)(708, 1531)(709, 1451)(710, 1427)(711, 1953)(712, 1696)(713, 1794)(714, 1428)(715, 1970)(716, 1429)(717, 1476)(718, 1506)(719, 1993)(720, 1889)(721, 1799)(722, 1431)(723, 1656)(724, 1736)(725, 1432)(726, 1496)(727, 1522)(728, 2019)(729, 1433)(730, 1760)(731, 1616)(732, 1434)(733, 1923)(734, 2138)(735, 1598)(736, 1443)(737, 1460)(738, 1568)(739, 1869)(740, 1437)(741, 2088)(742, 1634)(743, 1685)(744, 1438)(745, 1536)(746, 1608)(747, 1940)(748, 1439)(749, 1874)(750, 1774)(751, 1664)(752, 1441)(753, 1480)(754, 1508)(755, 2068)(756, 1442)(757, 1790)(758, 1937)(759, 1958)(760, 2129)(761, 2052)(762, 1452)(763, 1535)(764, 1600)(765, 1446)(766, 2102)(767, 1630)(768, 1674)(769, 1447)(770, 1570)(771, 1764)(772, 1903)(773, 1448)(774, 1703)(775, 1643)(776, 1573)(777, 1831)(778, 1545)(779, 1456)(780, 2006)(781, 1704)(782, 1841)(783, 1453)(784, 1665)(785, 1454)(786, 1631)(787, 1582)(788, 1491)(789, 2030)(790, 1666)(791, 1753)(792, 1457)(793, 1650)(794, 1537)(795, 2050)(796, 1720)(797, 1812)(798, 1657)(799, 1462)(800, 1635)(801, 1543)(802, 1475)(803, 1464)(804, 2077)(805, 1658)(806, 1734)(807, 1694)(808, 1578)(809, 1467)(810, 1757)(811, 1864)(812, 2011)(813, 2133)(814, 2171)(815, 1548)(816, 1620)(817, 1609)(818, 1471)(819, 1638)(820, 1647)(821, 1472)(822, 2042)(823, 2071)(824, 1473)(825, 2106)(826, 1778)(827, 1924)(828, 1474)(829, 1501)(830, 2096)(831, 1825)(832, 1919)(833, 2035)(834, 2125)(835, 2175)(836, 1495)(837, 1479)(838, 2091)(839, 1642)(840, 1670)(841, 1966)(842, 2145)(843, 1481)(844, 1710)(845, 1850)(846, 1483)(847, 1738)(848, 1839)(849, 2026)(850, 2141)(851, 2169)(852, 1524)(853, 1983)(854, 2003)(855, 1645)(856, 1488)(857, 1996)(858, 2024)(859, 1489)(860, 2081)(861, 1803)(862, 1959)(863, 1490)(864, 1515)(865, 2100)(866, 1851)(867, 1954)(868, 2083)(869, 2120)(870, 2176)(871, 1773)(872, 1649)(873, 1681)(874, 1933)(875, 2148)(876, 1556)(877, 2057)(878, 1807)(879, 1653)(880, 1503)(881, 2149)(882, 1636)(883, 1683)(884, 1677)(885, 2118)(886, 1788)(887, 1529)(888, 2075)(889, 1654)(890, 1726)(891, 1945)(892, 2108)(893, 1517)(894, 2010)(895, 1783)(896, 1661)(897, 2160)(898, 1672)(899, 1688)(900, 2112)(901, 1811)(902, 1687)(903, 1751)(904, 1949)(905, 2153)(906, 2080)(907, 2085)(908, 2027)(909, 1528)(910, 2020)(911, 1946)(912, 1591)(913, 2179)(914, 1872)(915, 2012)(916, 1530)(917, 1595)(918, 1986)(919, 1904)(920, 2007)(921, 2180)(922, 2123)(923, 2165)(924, 1724)(925, 2064)(926, 1604)(927, 1820)(928, 2002)(929, 2159)(930, 2163)(931, 1554)(932, 1950)(933, 1542)(934, 1941)(935, 2000)(936, 1611)(937, 2183)(938, 1881)(939, 2036)(940, 1544)(941, 1615)(942, 2072)(943, 1925)(944, 2031)(945, 2045)(946, 2116)(947, 2053)(948, 1676)(949, 1732)(950, 1914)(951, 2156)(952, 1624)(953, 2037)(954, 2074)(955, 2056)(956, 1619)(957, 2170)(958, 1887)(959, 2060)(960, 1853)(961, 2039)(962, 2115)(963, 1560)(964, 2047)(965, 1969)(966, 1769)(967, 2177)(968, 2051)(969, 2173)(970, 2127)(971, 2157)(972, 2017)(973, 1743)(974, 2137)(975, 2155)(976, 1847)(977, 2167)(978, 2154)(979, 1915)(980, 2034)(981, 1580)(982, 2046)(983, 1980)(984, 2184)(985, 1896)(986, 2084)(987, 1586)(988, 1998)(989, 1952)(990, 2094)(991, 1960)(992, 2078)(993, 1999)(994, 2111)(995, 1599)(996, 1833)(997, 1715)(998, 1691)(999, 1930)(1000, 1707)(1001, 2178)(1002, 2082)(1003, 2142)(1004, 1922)(1005, 1621)(1006, 2113)(1007, 1745)(1008, 1957)(1009, 1699)(1010, 1858)(1011, 1761)(1012, 1739)(1013, 1798)(1014, 1917)(1015, 2161)(1016, 1984)(1017, 2150)(1018, 2143)(1019, 2086)(1020, 1992)(1021, 2098)(1022, 2136)(1023, 2054)(1024, 2038)(1025, 2164)(1026, 1977)(1027, 2146)(1028, 1961)(1029, 2132)(1030, 2182)(1031, 2014)(1032, 2174)(1033, 1926)(1034, 2140)(1035, 2062)(1036, 2181)(1037, 1852)(1038, 2152)(1039, 2166)(1040, 2121)(1041, 1905)(1042, 2158)(1043, 2172)(1044, 2114)(1045, 2066)(1046, 1826)(1047, 2162)(1048, 2126)(1049, 1942)(1050, 2095)(1051, 2110)(1052, 1758)(1053, 1934)(1054, 2119)(1055, 1791)(1056, 1967)(1057, 1973)(1058, 2109)(1059, 2168)(1060, 2130)(1061, 1997)(1062, 2070)(1063, 2067)(1064, 2043)(1065, 2063)(1066, 2134)(1067, 2021)(1068, 1989)(1069, 2107)(1070, 2139)(1071, 2022)(1072, 2117)(1073, 2015)(1074, 2131)(1075, 2069)(1076, 2151)(1077, 1943)(1078, 2049)(1079, 1906)(1080, 2135)(1081, 2061)(1082, 2124)(1083, 1927)(1084, 1962)(1085, 2059)(1086, 2093)(1087, 2005)(1088, 2013)(1089, 2128)(1090, 2122)(1091, 2029)(1092, 2076) local type(s) :: { ( 2, 7, 2, 7, 2, 7 ) } Outer automorphisms :: reflexible Dual of E14.626 Transitivity :: ET+ VT+ AT Graph:: v = 364 e = 1092 f = 702 degree seq :: [ 6^364 ] E14.629 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1)^7, (T1 * T2^-1 * T1 * T2)^6 ] Map:: R = (1, 1093, 3, 1095, 4, 1096)(2, 1094, 5, 1097, 6, 1098)(7, 1099, 11, 1103, 12, 1104)(8, 1100, 13, 1105, 14, 1106)(9, 1101, 15, 1107, 16, 1108)(10, 1102, 17, 1109, 18, 1110)(19, 1111, 27, 1119, 28, 1120)(20, 1112, 29, 1121, 30, 1122)(21, 1113, 31, 1123, 32, 1124)(22, 1114, 33, 1125, 34, 1126)(23, 1115, 35, 1127, 36, 1128)(24, 1116, 37, 1129, 38, 1130)(25, 1117, 39, 1131, 40, 1132)(26, 1118, 41, 1133, 42, 1134)(43, 1135, 58, 1150, 59, 1151)(44, 1136, 60, 1152, 61, 1153)(45, 1137, 62, 1154, 63, 1155)(46, 1138, 64, 1156, 65, 1157)(47, 1139, 66, 1158, 67, 1159)(48, 1140, 68, 1160, 69, 1161)(49, 1141, 70, 1162, 71, 1163)(50, 1142, 72, 1164, 51, 1143)(52, 1144, 73, 1165, 74, 1166)(53, 1145, 75, 1167, 76, 1168)(54, 1146, 77, 1169, 78, 1170)(55, 1147, 79, 1171, 80, 1172)(56, 1148, 81, 1173, 82, 1174)(57, 1149, 83, 1175, 84, 1176)(85, 1177, 107, 1199, 108, 1200)(86, 1178, 109, 1201, 110, 1202)(87, 1179, 111, 1203, 112, 1204)(88, 1180, 113, 1205, 114, 1206)(89, 1181, 115, 1207, 116, 1208)(90, 1182, 117, 1209, 118, 1210)(91, 1183, 119, 1211, 120, 1212)(92, 1184, 121, 1213, 122, 1214)(93, 1185, 123, 1215, 124, 1216)(94, 1186, 125, 1217, 126, 1218)(95, 1187, 127, 1219, 128, 1220)(96, 1188, 129, 1221, 130, 1222)(97, 1189, 131, 1223, 132, 1224)(98, 1190, 133, 1225, 134, 1226)(99, 1191, 135, 1227, 136, 1228)(100, 1192, 137, 1229, 138, 1230)(101, 1193, 139, 1231, 140, 1232)(102, 1194, 141, 1233, 142, 1234)(103, 1195, 143, 1235, 144, 1236)(104, 1196, 145, 1237, 146, 1238)(105, 1197, 147, 1239, 148, 1240)(106, 1198, 149, 1241, 150, 1242)(151, 1243, 187, 1279, 188, 1280)(152, 1244, 189, 1281, 190, 1282)(153, 1245, 191, 1283, 192, 1284)(154, 1246, 193, 1285, 194, 1286)(155, 1247, 195, 1287, 196, 1288)(156, 1248, 197, 1289, 198, 1290)(157, 1249, 199, 1291, 200, 1292)(158, 1250, 201, 1293, 202, 1294)(159, 1251, 203, 1295, 204, 1296)(160, 1252, 205, 1297, 206, 1298)(161, 1253, 207, 1299, 208, 1300)(162, 1254, 209, 1301, 210, 1302)(163, 1255, 211, 1303, 212, 1304)(164, 1256, 213, 1305, 214, 1306)(165, 1257, 215, 1307, 216, 1308)(166, 1258, 217, 1309, 218, 1310)(167, 1259, 219, 1311, 220, 1312)(168, 1260, 221, 1313, 222, 1314)(169, 1261, 223, 1315, 224, 1316)(170, 1262, 225, 1317, 226, 1318)(171, 1263, 227, 1319, 228, 1320)(172, 1264, 229, 1321, 230, 1322)(173, 1265, 231, 1323, 232, 1324)(174, 1266, 233, 1325, 234, 1326)(175, 1267, 235, 1327, 236, 1328)(176, 1268, 237, 1329, 238, 1330)(177, 1269, 239, 1331, 240, 1332)(178, 1270, 241, 1333, 242, 1334)(179, 1271, 243, 1335, 244, 1336)(180, 1272, 245, 1337, 246, 1338)(181, 1273, 247, 1339, 248, 1340)(182, 1274, 249, 1341, 250, 1342)(183, 1275, 251, 1343, 252, 1344)(184, 1276, 253, 1345, 254, 1346)(185, 1277, 255, 1347, 256, 1348)(186, 1278, 257, 1349, 258, 1350)(259, 1351, 509, 1601, 952, 2044)(260, 1352, 511, 1603, 955, 2047)(261, 1353, 513, 1605, 929, 2021)(262, 1354, 515, 1607, 283, 1375)(263, 1355, 292, 1384, 565, 1657)(264, 1356, 400, 1492, 798, 1890)(265, 1357, 410, 1502, 819, 1911)(266, 1358, 520, 1612, 968, 2060)(267, 1359, 304, 1396, 599, 1691)(268, 1360, 316, 1408, 438, 1530)(269, 1361, 523, 1615, 366, 1458)(270, 1362, 524, 1616, 972, 2064)(271, 1363, 526, 1618, 974, 2066)(272, 1364, 335, 1427, 273, 1365)(274, 1366, 529, 1621, 977, 2069)(275, 1367, 531, 1623, 901, 1993)(276, 1368, 533, 1625, 981, 2073)(277, 1369, 298, 1390, 584, 1676)(278, 1370, 445, 1537, 881, 1973)(279, 1371, 418, 1510, 782, 1874)(280, 1372, 538, 1630, 989, 2081)(281, 1373, 295, 1387, 575, 1667)(282, 1374, 333, 1425, 453, 1545)(284, 1376, 542, 1634, 406, 1498)(285, 1377, 543, 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1799, 1062, 2154, 1064, 2156)(709, 1801, 1016, 2108, 1020, 2112)(711, 1803, 1032, 2124, 747, 1839)(713, 1805, 783, 1875, 1049, 2141)(716, 1808, 862, 1954, 844, 1936)(719, 1811, 1066, 2158, 1067, 2159)(721, 1813, 738, 1830, 991, 2083)(722, 1814, 1068, 2160, 1070, 2162)(724, 1816, 903, 1995, 908, 2000)(726, 1818, 1047, 2139, 809, 1901)(728, 1820, 869, 1961, 925, 2017)(731, 1823, 916, 2008, 953, 2045)(734, 1826, 1071, 2163, 1072, 2164)(736, 1828, 963, 2055, 1021, 2113)(740, 1832, 761, 1853, 1056, 2148)(743, 1835, 829, 1921, 807, 1899)(746, 1838, 970, 2062, 1073, 2165)(748, 1840, 966, 2058, 1075, 2167)(752, 1844, 1054, 2146, 847, 1939)(757, 1849, 879, 1971, 998, 2090)(775, 1867, 1065, 2157, 804, 1896)(796, 1888, 973, 2065, 842, 1934)(799, 1891, 995, 2087, 947, 2039)(802, 1894, 986, 2078, 1038, 2130)(810, 1902, 988, 2080, 1077, 2169)(814, 1906, 1063, 2155, 959, 2051)(818, 1910, 1006, 2098, 933, 2025)(822, 1914, 894, 1986, 864, 1956)(824, 1916, 855, 1947, 907, 1999)(832, 1924, 857, 1949, 949, 2041)(836, 1928, 1069, 2161, 982, 2074)(840, 1932, 1001, 2093, 1043, 2135)(848, 1940, 1078, 2170, 1080, 2172)(867, 1959, 1074, 2166, 1081, 2173)(876, 1968, 1082, 2174, 971, 2063)(891, 1983, 1083, 2175, 996, 2088)(905, 1997, 1060, 2152, 1086, 2178)(910, 2002, 983, 2075, 1087, 2179)(941, 2033, 1089, 2181, 951, 2043)(956, 2048, 1079, 2171, 1091, 2183)(960, 2052, 1088, 2180, 1084, 2176)(975, 2067, 1076, 2168, 1092, 2184)(980, 2072, 1090, 2182, 1085, 2177) L = (1, 1094)(2, 1093)(3, 1099)(4, 1100)(5, 1101)(6, 1102)(7, 1095)(8, 1096)(9, 1097)(10, 1098)(11, 1111)(12, 1112)(13, 1113)(14, 1114)(15, 1115)(16, 1116)(17, 1117)(18, 1118)(19, 1103)(20, 1104)(21, 1105)(22, 1106)(23, 1107)(24, 1108)(25, 1109)(26, 1110)(27, 1135)(28, 1136)(29, 1137)(30, 1138)(31, 1139)(32, 1140)(33, 1141)(34, 1142)(35, 1143)(36, 1144)(37, 1145)(38, 1146)(39, 1147)(40, 1148)(41, 1149)(42, 1150)(43, 1119)(44, 1120)(45, 1121)(46, 1122)(47, 1123)(48, 1124)(49, 1125)(50, 1126)(51, 1127)(52, 1128)(53, 1129)(54, 1130)(55, 1131)(56, 1132)(57, 1133)(58, 1134)(59, 1177)(60, 1178)(61, 1179)(62, 1180)(63, 1181)(64, 1182)(65, 1158)(66, 1157)(67, 1183)(68, 1184)(69, 1185)(70, 1186)(71, 1187)(72, 1188)(73, 1189)(74, 1190)(75, 1191)(76, 1192)(77, 1193)(78, 1171)(79, 1170)(80, 1194)(81, 1195)(82, 1196)(83, 1197)(84, 1198)(85, 1151)(86, 1152)(87, 1153)(88, 1154)(89, 1155)(90, 1156)(91, 1159)(92, 1160)(93, 1161)(94, 1162)(95, 1163)(96, 1164)(97, 1165)(98, 1166)(99, 1167)(100, 1168)(101, 1169)(102, 1172)(103, 1173)(104, 1174)(105, 1175)(106, 1176)(107, 1243)(108, 1244)(109, 1245)(110, 1246)(111, 1247)(112, 1205)(113, 1204)(114, 1248)(115, 1249)(116, 1250)(117, 1251)(118, 1252)(119, 1253)(120, 1254)(121, 1255)(122, 1256)(123, 1257)(124, 1217)(125, 1216)(126, 1258)(127, 1259)(128, 1260)(129, 1261)(130, 1262)(131, 1263)(132, 1264)(133, 1265)(134, 1227)(135, 1226)(136, 1266)(137, 1267)(138, 1268)(139, 1269)(140, 1270)(141, 1271)(142, 1272)(143, 1273)(144, 1274)(145, 1275)(146, 1239)(147, 1238)(148, 1276)(149, 1277)(150, 1278)(151, 1199)(152, 1200)(153, 1201)(154, 1202)(155, 1203)(156, 1206)(157, 1207)(158, 1208)(159, 1209)(160, 1210)(161, 1211)(162, 1212)(163, 1213)(164, 1214)(165, 1215)(166, 1218)(167, 1219)(168, 1220)(169, 1221)(170, 1222)(171, 1223)(172, 1224)(173, 1225)(174, 1228)(175, 1229)(176, 1230)(177, 1231)(178, 1232)(179, 1233)(180, 1234)(181, 1235)(182, 1236)(183, 1237)(184, 1240)(185, 1241)(186, 1242)(187, 1350)(188, 1351)(189, 1352)(190, 1283)(191, 1282)(192, 1353)(193, 1354)(194, 1355)(195, 1356)(196, 1357)(197, 1358)(198, 1359)(199, 1360)(200, 1328)(201, 1361)(202, 1295)(203, 1294)(204, 1362)(205, 1363)(206, 1364)(207, 1365)(208, 1366)(209, 1367)(210, 1303)(211, 1302)(212, 1368)(213, 1341)(214, 1369)(215, 1370)(216, 1371)(217, 1372)(218, 1373)(219, 1374)(220, 1375)(221, 1376)(222, 1315)(223, 1314)(224, 1377)(225, 1378)(226, 1319)(227, 1318)(228, 1555)(229, 1556)(230, 1558)(231, 1560)(232, 1562)(233, 1564)(234, 1566)(235, 1568)(236, 1292)(237, 1571)(238, 1331)(239, 1330)(240, 1574)(241, 1575)(242, 1526)(243, 1577)(244, 1579)(245, 1581)(246, 1339)(247, 1338)(248, 1584)(249, 1305)(250, 1586)(251, 1588)(252, 1590)(253, 1592)(254, 1594)(255, 1596)(256, 1598)(257, 1600)(258, 1279)(259, 1280)(260, 1281)(261, 1284)(262, 1285)(263, 1286)(264, 1287)(265, 1288)(266, 1289)(267, 1290)(268, 1291)(269, 1293)(270, 1296)(271, 1297)(272, 1298)(273, 1299)(274, 1300)(275, 1301)(276, 1304)(277, 1306)(278, 1307)(279, 1308)(280, 1309)(281, 1310)(282, 1311)(283, 1312)(284, 1313)(285, 1316)(286, 1317)(287, 1639)(288, 1643)(289, 1647)(290, 1650)(291, 1653)(292, 1656)(293, 1659)(294, 1662)(295, 1666)(296, 1669)(297, 1673)(298, 1675)(299, 1678)(300, 1680)(301, 1682)(302, 1685)(303, 1687)(304, 1690)(305, 1693)(306, 1697)(307, 1700)(308, 1703)(309, 1707)(310, 1701)(311, 1694)(312, 1711)(313, 1712)(314, 1670)(315, 1718)(316, 1691)(317, 1704)(318, 1722)(319, 1723)(320, 1663)(321, 1729)(322, 1732)(323, 1735)(324, 1739)(325, 1742)(326, 1745)(327, 1748)(328, 1751)(329, 1754)(330, 1758)(331, 1761)(332, 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1557)(788, 2024)(789, 1608)(790, 1486)(791, 1487)(792, 1785)(793, 1854)(794, 2155)(795, 1491)(796, 2032)(797, 2002)(798, 1705)(799, 1493)(800, 1585)(801, 2127)(802, 1495)(803, 1496)(804, 2094)(805, 2090)(806, 1497)(807, 1950)(808, 2156)(809, 1499)(810, 2082)(811, 2023)(812, 1500)(813, 1523)(814, 1501)(815, 1533)(816, 2006)(817, 2004)(818, 1502)(819, 1541)(820, 1546)(821, 1503)(822, 2104)(823, 1936)(824, 1504)(825, 1505)(826, 2027)(827, 1956)(828, 1506)(829, 2059)(830, 2162)(831, 1507)(832, 1952)(833, 2031)(834, 1508)(835, 1619)(836, 1509)(837, 1548)(838, 2132)(839, 2137)(840, 1510)(841, 1511)(842, 2096)(843, 2045)(844, 1915)(845, 2164)(846, 2114)(847, 1514)(848, 1999)(849, 1978)(850, 1515)(851, 1565)(852, 2134)(853, 2060)(854, 1580)(855, 1589)(856, 1518)(857, 2109)(858, 1899)(859, 1625)(860, 1924)(861, 1521)(862, 2149)(863, 2167)(864, 1919)(865, 1629)(866, 2014)(867, 1524)(868, 1593)(869, 2048)(870, 1730)(871, 2076)(872, 1528)(873, 1792)(874, 1532)(875, 1853)(876, 1868)(877, 2161)(878, 1536)(879, 2062)(880, 2172)(881, 1737)(882, 1814)(883, 2035)(884, 2072)(885, 1740)(886, 1941)(887, 1859)(888, 2081)(889, 2150)(890, 1867)(891, 1786)(892, 2146)(893, 1551)(894, 2087)(895, 2176)(896, 1749)(897, 2126)(898, 1554)(899, 1776)(900, 2133)(901, 2079)(902, 1726)(903, 1860)(904, 1832)(905, 1621)(906, 2046)(907, 1940)(908, 1563)(909, 1875)(910, 1889)(911, 2166)(912, 1909)(913, 1835)(914, 1908)(915, 1570)(916, 2158)(917, 2169)(918, 1756)(919, 2179)(920, 1672)(921, 1717)(922, 1958)(923, 2175)(924, 1840)(925, 1747)(926, 1655)(927, 2180)(928, 1877)(929, 1734)(930, 1759)(931, 1903)(932, 1880)(933, 2036)(934, 2038)(935, 1918)(936, 2173)(937, 1763)(938, 1846)(939, 1925)(940, 1888)(941, 1770)(942, 2139)(943, 1975)(944, 2025)(945, 1849)(946, 2026)(947, 2124)(948, 1599)(949, 2085)(950, 2182)(951, 1601)(952, 1642)(953, 1935)(954, 1998)(955, 2056)(956, 1961)(957, 2131)(958, 1605)(959, 1606)(960, 2113)(961, 1679)(962, 1797)(963, 1777)(964, 2047)(965, 1611)(966, 2115)(967, 1921)(968, 1945)(969, 1615)(970, 1971)(971, 1616)(972, 1665)(973, 1833)(974, 2181)(975, 1620)(976, 1766)(977, 1649)(978, 1850)(979, 2159)(980, 1976)(981, 1744)(982, 1626)(983, 2130)(984, 1963)(985, 1864)(986, 1721)(987, 1993)(988, 2120)(989, 1980)(990, 1902)(991, 1633)(992, 2163)(993, 2041)(994, 1634)(995, 1986)(996, 1635)(997, 1646)(998, 1897)(999, 2178)(1000, 2136)(1001, 1710)(1002, 1896)(1003, 1827)(1004, 1934)(1005, 1800)(1006, 1686)(1007, 2184)(1008, 1812)(1009, 1805)(1010, 2183)(1011, 1815)(1012, 1914)(1013, 1750)(1014, 1823)(1015, 1841)(1016, 1793)(1017, 1949)(1018, 1731)(1019, 1820)(1020, 2177)(1021, 2052)(1022, 1938)(1023, 2058)(1024, 1741)(1025, 1689)(1026, 1808)(1027, 1872)(1028, 2080)(1029, 1699)(1030, 1696)(1031, 2160)(1032, 2039)(1033, 1760)(1034, 1989)(1035, 1893)(1036, 2170)(1037, 1706)(1038, 2075)(1039, 2049)(1040, 1930)(1041, 1992)(1042, 1944)(1043, 2174)(1044, 2092)(1045, 1931)(1046, 2145)(1047, 2034)(1048, 1809)(1049, 1738)(1050, 2154)(1051, 2165)(1052, 1824)(1053, 2138)(1054, 1984)(1055, 1836)(1056, 1757)(1057, 1954)(1058, 1981)(1059, 1847)(1060, 1782)(1061, 1821)(1062, 2142)(1063, 1886)(1064, 1900)(1065, 1806)(1066, 2008)(1067, 2071)(1068, 2123)(1069, 1969)(1070, 1922)(1071, 2084)(1072, 1937)(1073, 2143)(1074, 2003)(1075, 1955)(1076, 2171)(1077, 2009)(1078, 2128)(1079, 2168)(1080, 1972)(1081, 2028)(1082, 2135)(1083, 2015)(1084, 1987)(1085, 2112)(1086, 2091)(1087, 2011)(1088, 2019)(1089, 2066)(1090, 2042)(1091, 2102)(1092, 2099) local type(s) :: { ( 2, 7, 2, 7, 2, 7 ) } Outer automorphisms :: reflexible Dual of E14.625 Transitivity :: ET+ VT+ AT Graph:: v = 364 e = 1092 f = 702 degree seq :: [ 6^364 ] E14.630 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2 * T1)^7, (T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2)^3 ] Map:: R = (1, 1093, 3, 1095, 4, 1096)(2, 1094, 5, 1097, 6, 1098)(7, 1099, 11, 1103, 12, 1104)(8, 1100, 13, 1105, 14, 1106)(9, 1101, 15, 1107, 16, 1108)(10, 1102, 17, 1109, 18, 1110)(19, 1111, 27, 1119, 28, 1120)(20, 1112, 29, 1121, 30, 1122)(21, 1113, 31, 1123, 32, 1124)(22, 1114, 33, 1125, 34, 1126)(23, 1115, 35, 1127, 36, 1128)(24, 1116, 37, 1129, 38, 1130)(25, 1117, 39, 1131, 40, 1132)(26, 1118, 41, 1133, 42, 1134)(43, 1135, 58, 1150, 59, 1151)(44, 1136, 60, 1152, 61, 1153)(45, 1137, 62, 1154, 63, 1155)(46, 1138, 64, 1156, 65, 1157)(47, 1139, 66, 1158, 67, 1159)(48, 1140, 68, 1160, 69, 1161)(49, 1141, 70, 1162, 71, 1163)(50, 1142, 72, 1164, 51, 1143)(52, 1144, 73, 1165, 74, 1166)(53, 1145, 75, 1167, 76, 1168)(54, 1146, 77, 1169, 78, 1170)(55, 1147, 79, 1171, 80, 1172)(56, 1148, 81, 1173, 82, 1174)(57, 1149, 83, 1175, 84, 1176)(85, 1177, 107, 1199, 108, 1200)(86, 1178, 109, 1201, 110, 1202)(87, 1179, 111, 1203, 112, 1204)(88, 1180, 113, 1205, 114, 1206)(89, 1181, 115, 1207, 116, 1208)(90, 1182, 117, 1209, 118, 1210)(91, 1183, 119, 1211, 120, 1212)(92, 1184, 121, 1213, 122, 1214)(93, 1185, 123, 1215, 124, 1216)(94, 1186, 125, 1217, 126, 1218)(95, 1187, 127, 1219, 128, 1220)(96, 1188, 129, 1221, 130, 1222)(97, 1189, 131, 1223, 132, 1224)(98, 1190, 133, 1225, 134, 1226)(99, 1191, 135, 1227, 136, 1228)(100, 1192, 137, 1229, 138, 1230)(101, 1193, 139, 1231, 140, 1232)(102, 1194, 141, 1233, 142, 1234)(103, 1195, 143, 1235, 144, 1236)(104, 1196, 145, 1237, 146, 1238)(105, 1197, 147, 1239, 148, 1240)(106, 1198, 149, 1241, 150, 1242)(151, 1243, 187, 1279, 188, 1280)(152, 1244, 189, 1281, 190, 1282)(153, 1245, 191, 1283, 192, 1284)(154, 1246, 193, 1285, 194, 1286)(155, 1247, 195, 1287, 196, 1288)(156, 1248, 197, 1289, 198, 1290)(157, 1249, 199, 1291, 200, 1292)(158, 1250, 201, 1293, 202, 1294)(159, 1251, 203, 1295, 204, 1296)(160, 1252, 205, 1297, 206, 1298)(161, 1253, 207, 1299, 208, 1300)(162, 1254, 209, 1301, 210, 1302)(163, 1255, 211, 1303, 212, 1304)(164, 1256, 213, 1305, 214, 1306)(165, 1257, 215, 1307, 216, 1308)(166, 1258, 217, 1309, 218, 1310)(167, 1259, 219, 1311, 220, 1312)(168, 1260, 221, 1313, 222, 1314)(169, 1261, 223, 1315, 224, 1316)(170, 1262, 225, 1317, 226, 1318)(171, 1263, 227, 1319, 228, 1320)(172, 1264, 229, 1321, 230, 1322)(173, 1265, 231, 1323, 232, 1324)(174, 1266, 233, 1325, 234, 1326)(175, 1267, 235, 1327, 236, 1328)(176, 1268, 237, 1329, 238, 1330)(177, 1269, 239, 1331, 240, 1332)(178, 1270, 241, 1333, 242, 1334)(179, 1271, 243, 1335, 244, 1336)(180, 1272, 245, 1337, 246, 1338)(181, 1273, 247, 1339, 248, 1340)(182, 1274, 249, 1341, 250, 1342)(183, 1275, 251, 1343, 252, 1344)(184, 1276, 253, 1345, 254, 1346)(185, 1277, 255, 1347, 256, 1348)(186, 1278, 257, 1349, 258, 1350)(259, 1351, 467, 1559, 731, 1823)(260, 1352, 469, 1561, 702, 1794)(261, 1353, 471, 1563, 533, 1625)(262, 1354, 473, 1565, 862, 1954)(263, 1355, 304, 1396, 541, 1633)(264, 1356, 474, 1566, 345, 1437)(265, 1357, 407, 1499, 762, 1854)(266, 1358, 475, 1567, 400, 1492)(267, 1359, 352, 1444, 644, 1736)(268, 1360, 476, 1568, 303, 1395)(269, 1361, 478, 1570, 868, 1960)(270, 1362, 480, 1572, 562, 1654)(271, 1363, 482, 1574, 695, 1787)(272, 1364, 484, 1576, 874, 1966)(273, 1365, 289, 1381, 274, 1366)(275, 1367, 488, 1580, 869, 1961)(276, 1368, 490, 1582, 714, 1806)(277, 1369, 492, 1584, 555, 1647)(278, 1370, 494, 1586, 883, 1975)(279, 1371, 306, 1398, 544, 1636)(280, 1372, 497, 1589, 353, 1445)(281, 1373, 421, 1513, 788, 1880)(282, 1374, 498, 1590, 414, 1506)(283, 1375, 360, 1452, 662, 1754)(284, 1376, 499, 1591, 305, 1397)(285, 1377, 500, 1592, 887, 1979)(286, 1378, 501, 1593, 536, 1628)(287, 1379, 503, 1595, 707, 1799)(288, 1380, 505, 1597, 726, 1818)(290, 1382, 446, 1538, 444, 1536)(291, 1383, 510, 1602, 511, 1603)(292, 1384, 513, 1605, 514, 1606)(293, 1385, 516, 1608, 517, 1609)(294, 1386, 519, 1611, 520, 1612)(295, 1387, 522, 1614, 523, 1615)(296, 1388, 432, 1524, 525, 1617)(297, 1389, 527, 1619, 459, 1551)(298, 1390, 529, 1621, 530, 1622)(299, 1391, 531, 1623, 532, 1624)(300, 1392, 403, 1495, 534, 1626)(301, 1393, 535, 1627, 418, 1510)(302, 1394, 537, 1629, 538, 1630)(307, 1399, 435, 1527, 546, 1638)(308, 1400, 548, 1640, 429, 1521)(309, 1401, 461, 1553, 550, 1642)(310, 1402, 552, 1644, 455, 1547)(311, 1403, 553, 1645, 554, 1646)(312, 1404, 417, 1509, 556, 1648)(313, 1405, 557, 1649, 367, 1459)(314, 1406, 464, 1556, 558, 1650)(315, 1407, 559, 1651, 428, 1520)(316, 1408, 366, 1458, 560, 1652)(317, 1409, 561, 1653, 404, 1496)(318, 1410, 563, 1655, 564, 1656)(319, 1411, 566, 1658, 567, 1659)(320, 1412, 458, 1550, 569, 1661)(321, 1413, 571, 1663, 433, 1525)(322, 1414, 573, 1665, 574, 1666)(323, 1415, 576, 1668, 392, 1484)(324, 1416, 495, 1587, 578, 1670)(325, 1417, 580, 1672, 581, 1673)(326, 1418, 583, 1675, 584, 1676)(327, 1419, 586, 1678, 479, 1571)(328, 1420, 389, 1481, 588, 1680)(329, 1421, 590, 1682, 380, 1472)(330, 1422, 592, 1684, 593, 1685)(331, 1423, 595, 1687, 596, 1688)(332, 1424, 598, 1690, 599, 1691)(333, 1425, 601, 1693, 602, 1694)(334, 1426, 377, 1469, 604, 1696)(335, 1427, 606, 1698, 607, 1699)(336, 1428, 609, 1701, 610, 1702)(337, 1429, 612, 1704, 613, 1705)(338, 1430, 615, 1707, 616, 1708)(339, 1431, 617, 1709, 454, 1546)(340, 1432, 346, 1438, 618, 1710)(341, 1433, 620, 1712, 621, 1713)(342, 1434, 623, 1715, 624, 1716)(343, 1435, 625, 1717, 359, 1451)(344, 1436, 438, 1530, 626, 1718)(347, 1439, 630, 1722, 631, 1723)(348, 1440, 633, 1725, 634, 1726)(349, 1441, 636, 1728, 637, 1729)(350, 1442, 639, 1731, 640, 1732)(351, 1443, 383, 1475, 642, 1734)(354, 1446, 647, 1739, 374, 1466)(355, 1447, 649, 1741, 650, 1742)(356, 1448, 652, 1744, 653, 1745)(357, 1449, 655, 1747, 656, 1748)(358, 1450, 658, 1750, 659, 1751)(361, 1453, 664, 1756, 665, 1757)(362, 1454, 667, 1759, 668, 1760)(363, 1455, 670, 1762, 671, 1763)(364, 1456, 673, 1765, 674, 1766)(365, 1457, 395, 1487, 676, 1768)(368, 1460, 680, 1772, 386, 1478)(369, 1461, 682, 1774, 683, 1775)(370, 1462, 685, 1777, 686, 1778)(371, 1463, 688, 1780, 689, 1781)(372, 1464, 691, 1783, 692, 1784)(373, 1465, 693, 1785, 694, 1786)(375, 1467, 697, 1789, 698, 1790)(376, 1468, 700, 1792, 701, 1793)(378, 1470, 703, 1795, 704, 1796)(379, 1471, 705, 1797, 706, 1798)(381, 1473, 709, 1801, 710, 1802)(382, 1474, 712, 1804, 713, 1805)(384, 1476, 715, 1807, 716, 1808)(385, 1477, 718, 1810, 719, 1811)(387, 1479, 722, 1814, 723, 1815)(388, 1480, 725, 1817, 481, 1573)(390, 1482, 727, 1819, 728, 1820)(391, 1483, 729, 1821, 730, 1822)(393, 1485, 493, 1585, 733, 1825)(394, 1486, 735, 1827, 736, 1828)(396, 1488, 739, 1831, 740, 1832)(397, 1489, 742, 1834, 743, 1835)(398, 1490, 745, 1837, 746, 1838)(399, 1491, 748, 1840, 749, 1841)(401, 1493, 752, 1844, 753, 1845)(402, 1494, 485, 1577, 755, 1847)(405, 1497, 758, 1850, 468, 1560)(406, 1498, 759, 1851, 760, 1852)(408, 1500, 764, 1856, 765, 1857)(409, 1501, 672, 1764, 766, 1858)(410, 1502, 768, 1860, 769, 1861)(411, 1503, 771, 1863, 772, 1864)(412, 1504, 773, 1865, 681, 1773)(413, 1505, 775, 1867, 776, 1868)(415, 1507, 778, 1870, 779, 1871)(416, 1508, 506, 1598, 781, 1873)(419, 1511, 784, 1876, 489, 1581)(420, 1512, 785, 1877, 786, 1878)(422, 1514, 790, 1882, 791, 1883)(423, 1515, 751, 1843, 793, 1885)(424, 1516, 795, 1887, 796, 1888)(425, 1517, 798, 1890, 756, 1848)(426, 1518, 521, 1613, 524, 1616)(427, 1519, 800, 1892, 801, 1893)(430, 1522, 803, 1895, 804, 1896)(431, 1523, 806, 1898, 807, 1899)(434, 1526, 809, 1901, 504, 1596)(436, 1528, 811, 1903, 812, 1904)(437, 1529, 813, 1905, 814, 1906)(439, 1531, 570, 1662, 572, 1664)(440, 1532, 817, 1909, 818, 1910)(441, 1533, 638, 1730, 819, 1911)(442, 1534, 717, 1809, 720, 1812)(443, 1535, 821, 1913, 822, 1914)(445, 1537, 825, 1917, 826, 1918)(447, 1539, 829, 1921, 830, 1922)(448, 1540, 831, 1923, 833, 1925)(449, 1541, 737, 1829, 738, 1830)(450, 1542, 835, 1927, 648, 1740)(451, 1543, 837, 1929, 838, 1930)(452, 1544, 565, 1657, 568, 1660)(453, 1545, 839, 1931, 840, 1932)(456, 1548, 843, 1935, 844, 1936)(457, 1549, 470, 1562, 846, 1938)(460, 1552, 848, 1940, 832, 1924)(462, 1554, 849, 1941, 850, 1942)(463, 1555, 851, 1943, 852, 1944)(465, 1557, 526, 1618, 528, 1620)(466, 1558, 782, 1874, 856, 1948)(472, 1564, 861, 1953, 502, 1594)(477, 1569, 853, 1945, 866, 1958)(483, 1575, 872, 1964, 873, 1965)(486, 1578, 877, 1969, 678, 1770)(487, 1579, 677, 1769, 878, 1970)(491, 1583, 882, 1974, 870, 1962)(496, 1588, 884, 1976, 802, 1894)(507, 1599, 515, 1607, 518, 1610)(508, 1600, 509, 1601, 512, 1604)(539, 1631, 551, 1643, 605, 1697)(540, 1632, 608, 1700, 582, 1674)(542, 1634, 579, 1671, 611, 1703)(543, 1635, 614, 1706, 545, 1637)(547, 1639, 619, 1711, 597, 1689)(549, 1641, 594, 1686, 622, 1714)(575, 1667, 696, 1788, 635, 1727)(577, 1669, 632, 1724, 699, 1791)(585, 1677, 708, 1800, 654, 1746)(587, 1679, 651, 1743, 711, 1803)(589, 1681, 721, 1813, 669, 1761)(591, 1683, 666, 1758, 724, 1816)(600, 1692, 732, 1824, 687, 1779)(603, 1695, 684, 1776, 734, 1826)(627, 1719, 855, 1947, 857, 1949)(628, 1720, 859, 1951, 747, 1839)(629, 1721, 744, 1836, 860, 1952)(641, 1733, 763, 1855, 871, 1963)(643, 1735, 876, 1968, 827, 1919)(645, 1737, 823, 1915, 879, 1971)(646, 1738, 881, 1973, 774, 1866)(657, 1749, 888, 1980, 792, 1884)(660, 1752, 789, 1881, 889, 1981)(661, 1753, 891, 1983, 797, 1889)(663, 1755, 794, 1886, 951, 2043)(675, 1767, 816, 1908, 960, 2052)(679, 1771, 963, 2055, 836, 1928)(690, 1782, 969, 2061, 741, 1833)(750, 1842, 842, 1934, 937, 2029)(754, 1846, 900, 1992, 1014, 2106)(757, 1849, 1016, 2108, 899, 1991)(761, 1853, 931, 2023, 910, 2002)(767, 1859, 1021, 2113, 770, 1862)(777, 1869, 909, 2001, 947, 2039)(780, 1872, 902, 1994, 1029, 2121)(783, 1875, 1031, 2123, 901, 1993)(787, 1879, 942, 2034, 810, 1902)(799, 1891, 892, 1984, 854, 1946)(805, 1897, 1034, 2126, 1041, 2133)(808, 1900, 1025, 2117, 903, 1995)(815, 1907, 952, 2044, 917, 2009)(820, 1912, 904, 1996, 913, 2005)(824, 1916, 1045, 2137, 828, 1920)(834, 1926, 920, 2012, 905, 1997)(841, 1933, 916, 2008, 875, 1967)(845, 1937, 906, 1998, 1022, 2114)(847, 1939, 1051, 2143, 864, 1956)(858, 1950, 989, 2081, 956, 2048)(863, 1955, 948, 2040, 1056, 2148)(865, 1957, 946, 2038, 976, 2068)(867, 1959, 935, 2027, 1057, 2149)(880, 1972, 1033, 2125, 1008, 2100)(885, 1977, 1065, 2157, 1066, 2158)(886, 1978, 919, 2011, 983, 2075)(890, 1982, 973, 2065, 934, 2026)(893, 1985, 978, 2070, 914, 2006)(894, 1986, 985, 2077, 932, 2024)(895, 1987, 970, 2062, 992, 2084)(896, 1988, 994, 2086, 907, 1999)(897, 1989, 912, 2004, 999, 2091)(898, 1990, 1001, 2093, 954, 2046)(908, 2000, 1060, 2152, 1006, 2098)(911, 2003, 1038, 2130, 1058, 2150)(915, 2007, 1070, 2162, 1037, 2129)(918, 2010, 1007, 2099, 1071, 2163)(921, 2013, 930, 2022, 929, 2021)(922, 2014, 939, 2031, 938, 2030)(923, 2015, 941, 2033, 940, 2032)(924, 2016, 950, 2042, 949, 2041)(925, 2017, 1076, 2168, 1064, 2156)(926, 2018, 961, 2053, 959, 2051)(927, 2019, 964, 2056, 962, 2054)(928, 2020, 1059, 2151, 1079, 2171)(933, 2025, 1072, 2164, 968, 2060)(936, 2028, 1026, 2118, 1073, 2165)(943, 2035, 1074, 2166, 1020, 2112)(944, 2036, 986, 2078, 997, 2089)(945, 2037, 955, 2047, 1075, 2167)(953, 2045, 957, 2049, 1062, 2154)(958, 2050, 1048, 2140, 1077, 2169)(965, 2057, 1078, 2170, 1044, 2136)(966, 2058, 971, 2063, 1061, 2153)(967, 2059, 1003, 2095, 981, 2073)(972, 2064, 1040, 2132, 991, 2083)(974, 2066, 1012, 2104, 1011, 2103)(975, 2067, 988, 2080, 1013, 2105)(977, 2069, 1017, 2109, 1015, 2107)(979, 2071, 1068, 2160, 1047, 2139)(980, 2072, 1046, 2138, 1054, 2146)(982, 2074, 1030, 2122, 1028, 2120)(984, 2076, 1032, 2124, 1004, 2096)(987, 2079, 1000, 2092, 1052, 2144)(990, 2082, 1005, 2097, 1009, 2101)(993, 2085, 1042, 2134, 1010, 2102)(995, 2087, 1053, 2145, 1024, 2116)(996, 2088, 1023, 2115, 1069, 2161)(998, 2090, 1035, 2127, 1050, 2142)(1002, 2094, 1036, 2128, 1039, 2131)(1018, 2110, 1080, 2172, 1063, 2155)(1019, 2111, 1084, 2176, 1067, 2159)(1027, 2119, 1055, 2147, 1086, 2178)(1043, 2135, 1083, 2175, 1082, 2174)(1049, 2141, 1081, 2173, 1088, 2180)(1085, 2177, 1087, 2179, 1091, 2183)(1089, 2181, 1090, 2182, 1092, 2184) L = (1, 1094)(2, 1093)(3, 1099)(4, 1100)(5, 1101)(6, 1102)(7, 1095)(8, 1096)(9, 1097)(10, 1098)(11, 1111)(12, 1112)(13, 1113)(14, 1114)(15, 1115)(16, 1116)(17, 1117)(18, 1118)(19, 1103)(20, 1104)(21, 1105)(22, 1106)(23, 1107)(24, 1108)(25, 1109)(26, 1110)(27, 1135)(28, 1136)(29, 1137)(30, 1138)(31, 1139)(32, 1140)(33, 1141)(34, 1142)(35, 1143)(36, 1144)(37, 1145)(38, 1146)(39, 1147)(40, 1148)(41, 1149)(42, 1150)(43, 1119)(44, 1120)(45, 1121)(46, 1122)(47, 1123)(48, 1124)(49, 1125)(50, 1126)(51, 1127)(52, 1128)(53, 1129)(54, 1130)(55, 1131)(56, 1132)(57, 1133)(58, 1134)(59, 1177)(60, 1178)(61, 1179)(62, 1180)(63, 1181)(64, 1182)(65, 1158)(66, 1157)(67, 1183)(68, 1184)(69, 1185)(70, 1186)(71, 1187)(72, 1188)(73, 1189)(74, 1190)(75, 1191)(76, 1192)(77, 1193)(78, 1171)(79, 1170)(80, 1194)(81, 1195)(82, 1196)(83, 1197)(84, 1198)(85, 1151)(86, 1152)(87, 1153)(88, 1154)(89, 1155)(90, 1156)(91, 1159)(92, 1160)(93, 1161)(94, 1162)(95, 1163)(96, 1164)(97, 1165)(98, 1166)(99, 1167)(100, 1168)(101, 1169)(102, 1172)(103, 1173)(104, 1174)(105, 1175)(106, 1176)(107, 1243)(108, 1244)(109, 1245)(110, 1246)(111, 1247)(112, 1205)(113, 1204)(114, 1248)(115, 1249)(116, 1250)(117, 1251)(118, 1252)(119, 1253)(120, 1254)(121, 1255)(122, 1256)(123, 1257)(124, 1217)(125, 1216)(126, 1258)(127, 1259)(128, 1260)(129, 1261)(130, 1262)(131, 1263)(132, 1264)(133, 1265)(134, 1227)(135, 1226)(136, 1266)(137, 1267)(138, 1268)(139, 1269)(140, 1270)(141, 1271)(142, 1272)(143, 1273)(144, 1274)(145, 1275)(146, 1239)(147, 1238)(148, 1276)(149, 1277)(150, 1278)(151, 1199)(152, 1200)(153, 1201)(154, 1202)(155, 1203)(156, 1206)(157, 1207)(158, 1208)(159, 1209)(160, 1210)(161, 1211)(162, 1212)(163, 1213)(164, 1214)(165, 1215)(166, 1218)(167, 1219)(168, 1220)(169, 1221)(170, 1222)(171, 1223)(172, 1224)(173, 1225)(174, 1228)(175, 1229)(176, 1230)(177, 1231)(178, 1232)(179, 1233)(180, 1234)(181, 1235)(182, 1236)(183, 1237)(184, 1240)(185, 1241)(186, 1242)(187, 1350)(188, 1351)(189, 1352)(190, 1283)(191, 1282)(192, 1353)(193, 1354)(194, 1355)(195, 1356)(196, 1357)(197, 1358)(198, 1359)(199, 1360)(200, 1361)(201, 1362)(202, 1295)(203, 1294)(204, 1363)(205, 1364)(206, 1365)(207, 1366)(208, 1367)(209, 1368)(210, 1303)(211, 1302)(212, 1369)(213, 1370)(214, 1371)(215, 1372)(216, 1373)(217, 1374)(218, 1375)(219, 1376)(220, 1377)(221, 1378)(222, 1315)(223, 1314)(224, 1379)(225, 1380)(226, 1319)(227, 1318)(228, 1518)(229, 1519)(230, 1521)(231, 1435)(232, 1436)(233, 1407)(234, 1408)(235, 1527)(236, 1529)(237, 1531)(238, 1331)(239, 1330)(240, 1534)(241, 1535)(242, 1536)(243, 1538)(244, 1540)(245, 1541)(246, 1339)(247, 1338)(248, 1544)(249, 1545)(250, 1547)(251, 1405)(252, 1406)(253, 1431)(254, 1432)(255, 1553)(256, 1555)(257, 1557)(258, 1279)(259, 1280)(260, 1281)(261, 1284)(262, 1285)(263, 1286)(264, 1287)(265, 1288)(266, 1289)(267, 1290)(268, 1291)(269, 1292)(270, 1293)(271, 1296)(272, 1297)(273, 1298)(274, 1299)(275, 1300)(276, 1301)(277, 1304)(278, 1305)(279, 1306)(280, 1307)(281, 1308)(282, 1309)(283, 1310)(284, 1311)(285, 1312)(286, 1313)(287, 1316)(288, 1317)(289, 1599)(290, 1600)(291, 1601)(292, 1604)(293, 1607)(294, 1610)(295, 1613)(296, 1616)(297, 1618)(298, 1620)(299, 1563)(300, 1625)(301, 1593)(302, 1628)(303, 1631)(304, 1632)(305, 1634)(306, 1635)(307, 1637)(308, 1639)(309, 1641)(310, 1643)(311, 1584)(312, 1647)(313, 1343)(314, 1344)(315, 1325)(316, 1326)(317, 1572)(318, 1654)(319, 1657)(320, 1660)(321, 1662)(322, 1664)(323, 1667)(324, 1669)(325, 1671)(326, 1674)(327, 1677)(328, 1679)(329, 1681)(330, 1683)(331, 1686)(332, 1689)(333, 1692)(334, 1695)(335, 1697)(336, 1700)(337, 1703)(338, 1706)(339, 1345)(340, 1346)(341, 1711)(342, 1714)(343, 1323)(344, 1324)(345, 1719)(346, 1720)(347, 1721)(348, 1724)(349, 1727)(350, 1730)(351, 1733)(352, 1735)(353, 1737)(354, 1738)(355, 1740)(356, 1743)(357, 1746)(358, 1749)(359, 1752)(360, 1753)(361, 1755)(362, 1758)(363, 1761)(364, 1764)(365, 1767)(366, 1769)(367, 1770)(368, 1771)(369, 1773)(370, 1776)(371, 1779)(372, 1782)(373, 1574)(374, 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1488)(739, 2095)(740, 1510)(741, 1489)(742, 1522)(743, 1828)(744, 1490)(745, 1789)(746, 1512)(747, 1491)(748, 2101)(749, 1525)(750, 1492)(751, 1493)(752, 2048)(753, 1819)(754, 1494)(755, 1731)(756, 1496)(757, 1497)(758, 1723)(759, 1893)(760, 2104)(761, 1499)(762, 1603)(763, 1500)(764, 1704)(765, 2088)(766, 1793)(767, 1502)(768, 1974)(769, 1982)(770, 1503)(771, 2089)(772, 1965)(773, 1801)(774, 1505)(775, 2087)(776, 1702)(777, 1506)(778, 2100)(779, 1943)(780, 1508)(781, 1750)(782, 1509)(783, 1511)(784, 1742)(785, 1822)(786, 2059)(787, 1513)(788, 1606)(789, 1514)(790, 1550)(791, 2128)(792, 1515)(793, 1805)(794, 1516)(795, 1814)(796, 1554)(797, 1517)(798, 2103)(799, 2043)(800, 1655)(801, 1851)(802, 1520)(803, 2026)(804, 1795)(805, 1523)(806, 1970)(807, 1765)(808, 1526)(809, 1757)(810, 1923)(811, 1954)(812, 2097)(813, 2045)(814, 1688)(815, 1530)(816, 1532)(817, 1715)(818, 2072)(819, 1573)(820, 2052)(821, 1684)(822, 1934)(823, 1579)(824, 1537)(825, 2012)(826, 1950)(827, 1578)(828, 1539)(829, 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1917)(921, 2164)(922, 2165)(923, 2166)(924, 2167)(925, 2006)(926, 2169)(927, 2170)(928, 2011)(929, 2106)(930, 2143)(931, 1722)(932, 2064)(933, 2028)(934, 1895)(935, 1728)(936, 2025)(937, 1732)(938, 2172)(939, 2108)(940, 2121)(941, 2158)(942, 1741)(943, 2037)(944, 1942)(945, 2035)(946, 2079)(947, 1751)(948, 1975)(949, 2133)(950, 2123)(951, 1891)(952, 1756)(953, 1905)(954, 2080)(955, 2050)(956, 1844)(957, 1762)(958, 2047)(959, 2151)(960, 1912)(961, 2117)(962, 2114)(963, 1926)(964, 2156)(965, 2060)(966, 1778)(967, 1878)(968, 2057)(969, 1946)(970, 2096)(971, 1932)(972, 2024)(973, 1786)(974, 2157)(975, 2134)(976, 1790)(977, 2176)(978, 1792)(979, 1929)(980, 1910)(981, 1921)(982, 2178)(983, 1802)(984, 2142)(985, 1804)(986, 1807)(987, 2038)(988, 2046)(989, 1811)(990, 2168)(991, 2109)(992, 1815)(993, 2175)(994, 1817)(995, 1867)(996, 1857)(997, 1863)(998, 2180)(999, 1825)(1000, 2120)(1001, 1827)(1002, 2171)(1003, 1831)(1004, 2062)(1005, 1904)(1006, 2122)(1007, 2102)(1008, 1870)(1009, 1840)(1010, 2099)(1011, 1890)(1012, 1852)(1013, 2160)(1014, 2021)(1015, 2130)(1016, 2031)(1017, 2083)(1018, 2004)(1019, 2112)(1020, 2111)(1021, 1984)(1022, 2054)(1023, 2149)(1024, 2148)(1025, 2053)(1026, 2119)(1027, 2118)(1028, 2092)(1029, 2032)(1030, 2098)(1031, 2042)(1032, 2146)(1033, 1948)(1034, 1988)(1035, 2129)(1036, 1883)(1037, 2127)(1038, 2107)(1039, 1935)(1040, 2145)(1041, 2041)(1042, 2067)(1043, 2136)(1044, 2135)(1045, 1953)(1046, 2154)(1047, 2153)(1048, 2141)(1049, 2140)(1050, 2076)(1051, 2022)(1052, 2161)(1053, 2132)(1054, 2124)(1055, 2179)(1056, 2116)(1057, 2115)(1058, 1962)(1059, 2051)(1060, 1964)(1061, 2139)(1062, 2138)(1063, 1972)(1064, 2056)(1065, 2066)(1066, 2033)(1067, 2177)(1068, 2105)(1069, 2144)(1070, 1996)(1071, 1997)(1072, 2013)(1073, 2014)(1074, 2015)(1075, 2016)(1076, 2082)(1077, 2018)(1078, 2019)(1079, 2094)(1080, 2030)(1081, 2182)(1082, 2181)(1083, 2085)(1084, 2069)(1085, 2159)(1086, 2074)(1087, 2147)(1088, 2090)(1089, 2174)(1090, 2173)(1091, 2184)(1092, 2183) local type(s) :: { ( 2, 7, 2, 7, 2, 7 ) } Outer automorphisms :: reflexible Dual of E14.627 Transitivity :: ET+ VT+ AT Graph:: v = 364 e = 1092 f = 702 degree seq :: [ 6^364 ] E14.631 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T2^7, (T1 * T2^-2)^6, T2 * T1^-1 * T2^-2 * T1 * T2^3 * T1^-1 * T2^-1 * T1 * T2^-2 * T1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1, T2^2 * T1^-1 * T2^2 * T1^-1 * T2^-2 * T1 * T2^3 * T1^-1 * T2 * T1^-1 * T2^-2 * T1 * T2^-3 * T1^-1 * T2 * T1^-1 * T2^-3 * T1^-1 * T2 * T1^-1 ] Map:: R = (1, 1093, 3, 1095, 9, 1101, 19, 1111, 26, 1118, 13, 1105, 5, 1097)(2, 1094, 6, 1098, 14, 1106, 27, 1119, 32, 1124, 16, 1108, 7, 1099)(4, 1096, 11, 1103, 22, 1114, 40, 1132, 34, 1126, 17, 1109, 8, 1100)(10, 1102, 21, 1113, 39, 1131, 63, 1155, 59, 1151, 35, 1127, 18, 1110)(12, 1104, 23, 1115, 42, 1134, 68, 1160, 71, 1163, 43, 1135, 24, 1116)(15, 1107, 29, 1121, 50, 1142, 78, 1170, 81, 1173, 51, 1143, 30, 1122)(20, 1112, 38, 1130, 62, 1154, 94, 1186, 92, 1184, 60, 1152, 36, 1128)(25, 1117, 44, 1136, 72, 1164, 108, 1200, 111, 1203, 73, 1165, 45, 1137)(28, 1120, 49, 1141, 77, 1169, 116, 1208, 114, 1206, 75, 1167, 47, 1139)(31, 1123, 52, 1144, 82, 1174, 124, 1216, 127, 1219, 83, 1175, 53, 1145)(33, 1125, 55, 1147, 85, 1177, 129, 1221, 132, 1224, 86, 1178, 56, 1148)(37, 1129, 61, 1153, 93, 1185, 140, 1232, 112, 1204, 74, 1166, 46, 1138)(41, 1133, 67, 1159, 101, 1193, 151, 1243, 149, 1241, 99, 1191, 65, 1157)(48, 1140, 76, 1168, 115, 1207, 169, 1261, 128, 1220, 84, 1176, 54, 1146)(57, 1149, 66, 1158, 100, 1192, 150, 1242, 194, 1286, 133, 1225, 87, 1179)(58, 1150, 88, 1180, 134, 1226, 195, 1287, 198, 1290, 135, 1227, 89, 1181)(64, 1156, 98, 1190, 147, 1239, 212, 1304, 210, 1302, 145, 1237, 96, 1188)(69, 1161, 104, 1196, 155, 1247, 224, 1316, 222, 1314, 153, 1245, 102, 1194)(70, 1162, 105, 1197, 156, 1248, 226, 1318, 229, 1321, 157, 1249, 106, 1198)(79, 1171, 120, 1212, 176, 1268, 250, 1342, 248, 1340, 174, 1266, 118, 1210)(80, 1172, 121, 1213, 177, 1269, 252, 1344, 255, 1347, 178, 1270, 122, 1214)(90, 1182, 97, 1189, 146, 1238, 211, 1303, 280, 1372, 199, 1291, 136, 1228)(91, 1183, 137, 1229, 200, 1292, 281, 1373, 284, 1376, 201, 1293, 138, 1230)(95, 1187, 144, 1236, 208, 1300, 292, 1384, 290, 1382, 206, 1298, 142, 1234)(103, 1195, 154, 1246, 223, 1315, 310, 1402, 230, 1322, 158, 1250, 107, 1199)(109, 1201, 161, 1253, 233, 1325, 324, 1416, 322, 1414, 231, 1323, 159, 1251)(110, 1202, 162, 1254, 234, 1326, 326, 1418, 328, 1420, 235, 1327, 163, 1255)(113, 1205, 166, 1258, 238, 1330, 331, 1423, 334, 1426, 239, 1331, 167, 1259)(117, 1209, 173, 1265, 246, 1338, 342, 1434, 340, 1432, 244, 1336, 171, 1263)(119, 1211, 175, 1267, 249, 1341, 346, 1438, 256, 1348, 179, 1271, 123, 1215)(125, 1217, 182, 1274, 259, 1351, 359, 1451, 357, 1449, 257, 1349, 180, 1272)(126, 1218, 183, 1275, 260, 1352, 361, 1453, 363, 1455, 261, 1353, 184, 1276)(130, 1222, 189, 1281, 266, 1358, 369, 1461, 367, 1459, 264, 1356, 187, 1279)(131, 1223, 190, 1282, 267, 1359, 371, 1463, 373, 1465, 268, 1360, 191, 1283)(139, 1231, 143, 1235, 207, 1299, 291, 1383, 393, 1485, 285, 1377, 202, 1294)(141, 1233, 205, 1297, 288, 1380, 397, 1489, 395, 1487, 286, 1378, 203, 1295)(148, 1240, 214, 1306, 300, 1392, 409, 1501, 412, 1504, 301, 1393, 215, 1307)(152, 1244, 220, 1312, 306, 1398, 418, 1510, 416, 1508, 304, 1396, 218, 1310)(160, 1252, 232, 1324, 323, 1415, 436, 1528, 329, 1421, 236, 1328, 164, 1256)(165, 1257, 204, 1296, 287, 1379, 396, 1488, 446, 1538, 330, 1422, 237, 1329)(168, 1260, 172, 1264, 245, 1337, 341, 1433, 453, 1545, 335, 1427, 240, 1332)(170, 1262, 243, 1335, 338, 1430, 457, 1549, 455, 1547, 336, 1428, 241, 1333)(181, 1273, 258, 1350, 358, 1450, 480, 1572, 364, 1456, 262, 1354, 185, 1277)(186, 1278, 242, 1334, 337, 1429, 456, 1548, 489, 1581, 365, 1457, 263, 1355)(188, 1280, 265, 1357, 368, 1460, 493, 1585, 374, 1466, 269, 1361, 192, 1284)(193, 1285, 270, 1362, 375, 1467, 501, 1593, 503, 1595, 376, 1468, 271, 1363)(196, 1288, 275, 1367, 380, 1472, 508, 1600, 506, 1598, 378, 1470, 273, 1365)(197, 1289, 276, 1368, 381, 1473, 469, 1561, 348, 1440, 251, 1343, 277, 1369)(209, 1301, 293, 1385, 403, 1495, 530, 1622, 533, 1625, 404, 1496, 294, 1386)(213, 1305, 299, 1391, 228, 1320, 318, 1410, 430, 1522, 407, 1499, 297, 1389)(216, 1308, 219, 1311, 305, 1397, 417, 1509, 543, 1635, 413, 1505, 302, 1394)(217, 1309, 303, 1395, 414, 1506, 544, 1636, 504, 1596, 377, 1469, 272, 1364)(221, 1313, 307, 1399, 419, 1511, 549, 1641, 551, 1643, 420, 1512, 308, 1400)(225, 1317, 314, 1406, 254, 1346, 353, 1445, 474, 1566, 425, 1517, 312, 1404)(227, 1319, 317, 1409, 429, 1521, 560, 1652, 558, 1650, 427, 1519, 315, 1407)(247, 1339, 343, 1435, 463, 1555, 590, 1682, 592, 1684, 464, 1556, 344, 1436)(253, 1345, 352, 1444, 473, 1565, 601, 1693, 599, 1691, 471, 1563, 350, 1442)(274, 1366, 379, 1471, 507, 1599, 633, 1725, 511, 1603, 382, 1474, 278, 1370)(279, 1371, 383, 1475, 512, 1604, 639, 1731, 566, 1658, 437, 1529, 384, 1476)(282, 1374, 388, 1480, 516, 1608, 645, 1737, 643, 1735, 514, 1606, 386, 1478)(283, 1375, 389, 1481, 517, 1609, 620, 1712, 495, 1587, 370, 1462, 390, 1482)(289, 1381, 398, 1490, 526, 1618, 654, 1746, 657, 1749, 527, 1619, 399, 1491)(295, 1387, 298, 1390, 408, 1500, 537, 1629, 665, 1757, 534, 1626, 405, 1497)(296, 1388, 406, 1498, 535, 1627, 666, 1758, 641, 1733, 513, 1605, 385, 1477)(309, 1401, 313, 1405, 426, 1518, 556, 1648, 683, 1775, 552, 1644, 421, 1513)(311, 1403, 424, 1516, 392, 1484, 519, 1611, 648, 1740, 553, 1645, 422, 1514)(316, 1408, 428, 1520, 559, 1651, 691, 1783, 563, 1655, 431, 1523, 319, 1411)(320, 1412, 423, 1515, 554, 1646, 685, 1777, 607, 1699, 481, 1573, 432, 1524)(321, 1413, 433, 1525, 564, 1656, 697, 1789, 635, 1727, 509, 1601, 434, 1526)(325, 1417, 440, 1532, 333, 1425, 450, 1542, 578, 1670, 568, 1660, 438, 1530)(327, 1419, 443, 1535, 572, 1664, 706, 1798, 704, 1796, 570, 1662, 441, 1533)(332, 1424, 449, 1541, 577, 1669, 711, 1803, 709, 1801, 575, 1667, 447, 1539)(339, 1431, 458, 1550, 586, 1678, 720, 1812, 723, 1815, 587, 1679, 459, 1551)(345, 1437, 349, 1441, 470, 1562, 597, 1689, 730, 1822, 593, 1685, 465, 1557)(347, 1439, 468, 1560, 452, 1544, 580, 1672, 714, 1806, 594, 1686, 466, 1558)(351, 1443, 472, 1564, 600, 1692, 738, 1830, 604, 1696, 475, 1567, 354, 1446)(355, 1447, 467, 1559, 595, 1687, 732, 1824, 618, 1710, 494, 1586, 476, 1568)(356, 1448, 477, 1569, 605, 1697, 744, 1836, 693, 1785, 561, 1653, 478, 1570)(360, 1452, 484, 1576, 411, 1503, 541, 1633, 671, 1763, 609, 1701, 482, 1574)(362, 1454, 487, 1579, 613, 1705, 753, 1845, 751, 1843, 611, 1703, 485, 1577)(366, 1458, 490, 1582, 616, 1708, 755, 1847, 740, 1832, 602, 1694, 491, 1583)(372, 1464, 499, 1591, 624, 1716, 764, 1856, 762, 1854, 622, 1714, 497, 1589)(387, 1479, 515, 1607, 644, 1736, 783, 1875, 647, 1739, 518, 1610, 391, 1483)(394, 1486, 521, 1613, 650, 1742, 789, 1881, 792, 1884, 651, 1743, 522, 1614)(400, 1492, 402, 1494, 486, 1578, 612, 1704, 752, 1844, 658, 1750, 528, 1620)(401, 1493, 529, 1621, 659, 1751, 800, 1892, 788, 1880, 649, 1741, 520, 1612)(410, 1502, 540, 1632, 532, 1624, 663, 1755, 803, 1895, 669, 1761, 538, 1630)(415, 1507, 545, 1637, 674, 1766, 812, 1904, 815, 1907, 675, 1767, 546, 1638)(435, 1527, 439, 1531, 569, 1661, 702, 1794, 834, 1926, 699, 1791, 565, 1657)(442, 1534, 571, 1663, 705, 1797, 816, 1908, 676, 1768, 547, 1639, 444, 1536)(445, 1537, 567, 1659, 700, 1792, 835, 1927, 826, 1918, 692, 1784, 573, 1665)(448, 1540, 576, 1668, 710, 1802, 846, 1938, 713, 1805, 579, 1671, 451, 1543)(454, 1546, 582, 1674, 716, 1808, 852, 1944, 855, 1947, 717, 1809, 583, 1675)(460, 1552, 462, 1554, 498, 1590, 623, 1715, 763, 1855, 724, 1816, 588, 1680)(461, 1553, 589, 1681, 682, 1774, 819, 1911, 851, 1943, 715, 1807, 581, 1673)(479, 1571, 483, 1575, 610, 1702, 749, 1841, 880, 1972, 746, 1838, 606, 1698)(488, 1580, 608, 1700, 747, 1839, 881, 1973, 872, 1964, 739, 1831, 614, 1706)(492, 1584, 496, 1588, 621, 1713, 760, 1852, 892, 1984, 757, 1849, 617, 1709)(500, 1592, 619, 1711, 758, 1850, 893, 1985, 772, 1864, 634, 1726, 625, 1717)(502, 1594, 628, 1720, 768, 1860, 905, 1997, 903, 1995, 766, 1858, 626, 1718)(505, 1597, 630, 1722, 770, 1862, 907, 1999, 900, 1992, 765, 1857, 631, 1723)(510, 1602, 637, 1729, 775, 1867, 912, 2004, 868, 1960, 733, 1825, 596, 1688)(523, 1615, 525, 1617, 627, 1719, 767, 1859, 904, 1996, 793, 1885, 652, 1744)(524, 1616, 653, 1745, 794, 1886, 856, 1948, 718, 1810, 584, 1676, 574, 1666)(531, 1623, 662, 1754, 656, 1748, 798, 1890, 931, 2023, 801, 1893, 660, 1752)(536, 1628, 562, 1654, 695, 1787, 829, 1921, 938, 2030, 806, 1898, 667, 1759)(539, 1631, 670, 1762, 809, 1901, 940, 2032, 811, 1903, 672, 1764, 542, 1634)(548, 1640, 677, 1769, 729, 1821, 865, 1957, 916, 2008, 779, 1871, 673, 1765)(550, 1642, 680, 1772, 722, 1814, 861, 1953, 950, 2042, 817, 1909, 678, 1770)(555, 1647, 603, 1695, 742, 1834, 875, 1967, 955, 2047, 822, 1914, 686, 1778)(557, 1649, 688, 1780, 824, 1916, 956, 2048, 841, 1933, 707, 1799, 689, 1781)(585, 1677, 719, 1811, 857, 1949, 899, 1991, 769, 1861, 629, 1721, 615, 1707)(591, 1683, 727, 1819, 814, 1906, 947, 2039, 984, 2076, 863, 1955, 725, 1817)(598, 1690, 735, 1827, 870, 1962, 989, 2081, 887, 1979, 754, 1846, 736, 1828)(632, 1724, 636, 1728, 774, 1866, 911, 2003, 1015, 2107, 909, 2001, 771, 1863)(638, 1730, 773, 1865, 910, 2002, 1016, 2108, 919, 2011, 784, 1876, 776, 1868)(640, 1732, 778, 1870, 915, 2007, 1021, 2113, 1020, 2112, 914, 2006, 777, 1869)(642, 1734, 780, 1872, 917, 2009, 1022, 2114, 1018, 2110, 913, 2005, 781, 1873)(646, 1738, 785, 1877, 921, 2013, 1026, 2118, 1005, 2097, 894, 1986, 759, 1851)(655, 1747, 797, 1889, 791, 1883, 927, 2019, 1031, 2123, 929, 2021, 795, 1887)(661, 1753, 802, 1894, 934, 2026, 1035, 2127, 936, 2028, 804, 1896, 664, 1756)(668, 1760, 807, 1899, 891, 1983, 1003, 2095, 1028, 2120, 924, 2016, 805, 1897)(679, 1771, 818, 1910, 951, 2043, 1024, 2116, 918, 2010, 782, 1874, 681, 1773)(684, 1776, 787, 1879, 923, 2015, 1027, 2119, 1048, 2140, 953, 2045, 821, 1913)(687, 1779, 823, 1915, 833, 1925, 963, 2055, 1047, 2139, 952, 2044, 820, 1912)(690, 1782, 694, 1786, 828, 1920, 960, 2052, 1052, 2144, 958, 2050, 825, 1917)(696, 1788, 827, 1919, 959, 2051, 1053, 2145, 971, 2063, 847, 1939, 830, 1922)(698, 1790, 832, 1924, 954, 2046, 1049, 2141, 1055, 2147, 962, 2054, 831, 1923)(701, 1793, 712, 1804, 848, 1940, 973, 2065, 1057, 2149, 965, 2057, 836, 1928)(703, 1795, 838, 1930, 966, 2058, 1029, 2121, 925, 2017, 790, 1882, 839, 1931)(708, 1800, 843, 1935, 969, 2061, 1059, 2151, 1039, 2131, 961, 2053, 844, 1936)(721, 1813, 860, 1952, 854, 1946, 978, 2070, 1066, 2158, 980, 2072, 858, 1950)(726, 1818, 864, 1956, 985, 2077, 1061, 2153, 970, 2062, 845, 1937, 728, 1820)(731, 1823, 850, 1942, 975, 2067, 1063, 2155, 1071, 2163, 987, 2079, 867, 1959)(734, 1826, 869, 1961, 879, 1971, 996, 2088, 1070, 2162, 986, 2078, 866, 1958)(737, 1829, 741, 1833, 874, 1966, 993, 2085, 1073, 2165, 991, 2083, 871, 1963)(743, 1835, 873, 1965, 992, 2084, 1074, 2166, 1040, 2132, 941, 2033, 876, 1968)(745, 1837, 878, 1970, 988, 2080, 1019, 2111, 1076, 2168, 995, 2087, 877, 1969)(748, 1840, 810, 1902, 942, 2034, 1042, 2134, 1078, 2170, 998, 2090, 882, 1974)(750, 1842, 884, 1976, 999, 2091, 1064, 2156, 976, 2068, 853, 1945, 885, 1977)(756, 1848, 890, 1982, 937, 2029, 1038, 2130, 1080, 2172, 1002, 2094, 889, 1981)(761, 1853, 896, 1988, 1007, 2099, 1082, 2174, 1012, 2104, 906, 1998, 897, 1989)(786, 1878, 920, 2012, 1025, 2117, 1056, 2148, 964, 2056, 837, 1929, 922, 2014)(796, 1888, 930, 2022, 983, 2075, 1069, 2161, 1034, 2126, 932, 2024, 799, 1891)(808, 1900, 935, 2027, 1036, 2128, 1090, 2182, 1050, 2142, 994, 2086, 939, 2031)(813, 1905, 946, 2038, 902, 1994, 1010, 2102, 1084, 2176, 1043, 2135, 944, 2036)(840, 1932, 842, 1934, 968, 2060, 1058, 2150, 1072, 2164, 990, 2082, 967, 2059)(849, 1941, 972, 2064, 1062, 2154, 1077, 2169, 997, 2089, 883, 1975, 974, 2066)(859, 1951, 981, 2073, 933, 2025, 1033, 2125, 1068, 2160, 982, 2074, 862, 1954)(886, 1978, 888, 1980, 1001, 2093, 1079, 2171, 1014, 2106, 908, 2000, 1000, 2092)(895, 1987, 1006, 2098, 943, 2035, 1041, 2133, 1091, 2183, 1081, 2173, 1004, 2096)(898, 1990, 901, 1993, 1009, 2101, 1083, 2175, 1051, 2143, 957, 2049, 1008, 2100)(926, 2018, 1030, 2122, 1075, 2167, 1092, 2184, 1060, 2152, 1032, 2124, 928, 2020)(945, 2037, 1044, 2136, 949, 2041, 1046, 2138, 1089, 2181, 1045, 2137, 948, 2040)(977, 2069, 1065, 2157, 1017, 2109, 1087, 2179, 1037, 2129, 1067, 2159, 979, 2071)(1011, 2103, 1013, 2105, 1086, 2178, 1054, 2146, 1088, 2180, 1023, 2115, 1085, 2177) L = (1, 1094)(2, 1096)(3, 1100)(4, 1093)(5, 1104)(6, 1097)(7, 1107)(8, 1102)(9, 1110)(10, 1095)(11, 1099)(12, 1098)(13, 1117)(14, 1116)(15, 1103)(16, 1123)(17, 1125)(18, 1112)(19, 1128)(20, 1101)(21, 1109)(22, 1122)(23, 1105)(24, 1120)(25, 1115)(26, 1138)(27, 1139)(28, 1106)(29, 1108)(30, 1133)(31, 1121)(32, 1146)(33, 1113)(34, 1149)(35, 1150)(36, 1129)(37, 1111)(38, 1127)(39, 1148)(40, 1157)(41, 1114)(42, 1137)(43, 1162)(44, 1118)(45, 1161)(46, 1136)(47, 1140)(48, 1119)(49, 1135)(50, 1145)(51, 1172)(52, 1124)(53, 1171)(54, 1144)(55, 1126)(56, 1156)(57, 1147)(58, 1130)(59, 1182)(60, 1183)(61, 1152)(62, 1181)(63, 1188)(64, 1131)(65, 1158)(66, 1132)(67, 1143)(68, 1194)(69, 1134)(70, 1141)(71, 1199)(72, 1166)(73, 1202)(74, 1201)(75, 1205)(76, 1167)(77, 1198)(78, 1210)(79, 1142)(80, 1159)(81, 1215)(82, 1176)(83, 1218)(84, 1217)(85, 1179)(86, 1223)(87, 1222)(88, 1151)(89, 1187)(90, 1180)(91, 1153)(92, 1231)(93, 1230)(94, 1234)(95, 1154)(96, 1189)(97, 1155)(98, 1178)(99, 1240)(100, 1191)(101, 1214)(102, 1195)(103, 1160)(104, 1165)(105, 1163)(106, 1209)(107, 1197)(108, 1251)(109, 1164)(110, 1196)(111, 1256)(112, 1257)(113, 1168)(114, 1260)(115, 1259)(116, 1263)(117, 1169)(118, 1211)(119, 1170)(120, 1175)(121, 1173)(122, 1244)(123, 1213)(124, 1272)(125, 1174)(126, 1212)(127, 1277)(128, 1278)(129, 1279)(130, 1177)(131, 1190)(132, 1284)(133, 1285)(134, 1228)(135, 1289)(136, 1288)(137, 1184)(138, 1233)(139, 1229)(140, 1295)(141, 1185)(142, 1235)(143, 1186)(144, 1227)(145, 1301)(146, 1237)(147, 1283)(148, 1192)(149, 1308)(150, 1307)(151, 1310)(152, 1193)(153, 1313)(154, 1245)(155, 1255)(156, 1250)(157, 1320)(158, 1319)(159, 1252)(160, 1200)(161, 1204)(162, 1203)(163, 1317)(164, 1254)(165, 1253)(166, 1206)(167, 1262)(168, 1258)(169, 1333)(170, 1207)(171, 1264)(172, 1208)(173, 1249)(174, 1339)(175, 1266)(176, 1276)(177, 1271)(178, 1346)(179, 1345)(180, 1273)(181, 1216)(182, 1220)(183, 1219)(184, 1343)(185, 1275)(186, 1274)(187, 1280)(188, 1221)(189, 1225)(190, 1224)(191, 1305)(192, 1282)(193, 1281)(194, 1364)(195, 1365)(196, 1226)(197, 1236)(198, 1370)(199, 1371)(200, 1294)(201, 1375)(202, 1374)(203, 1296)(204, 1232)(205, 1293)(206, 1381)(207, 1298)(208, 1369)(209, 1238)(210, 1387)(211, 1386)(212, 1389)(213, 1239)(214, 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1671)(579, 1804)(580, 1545)(581, 1672)(582, 1547)(583, 1677)(584, 1674)(585, 1548)(586, 1680)(587, 1814)(588, 1813)(589, 1679)(590, 1817)(591, 1555)(592, 1820)(593, 1821)(594, 1823)(595, 1686)(596, 1562)(597, 1825)(598, 1564)(599, 1829)(600, 1828)(601, 1832)(602, 1565)(603, 1566)(604, 1835)(605, 1698)(606, 1837)(607, 1700)(608, 1572)(609, 1840)(610, 1701)(611, 1842)(612, 1703)(613, 1706)(614, 1846)(615, 1636)(616, 1709)(617, 1848)(618, 1711)(619, 1585)(620, 1851)(621, 1712)(622, 1853)(623, 1714)(624, 1717)(625, 1857)(626, 1719)(627, 1593)(628, 1596)(629, 1720)(630, 1598)(631, 1726)(632, 1722)(633, 1864)(634, 1599)(635, 1728)(636, 1600)(637, 1603)(638, 1729)(639, 1869)(640, 1604)(641, 1871)(642, 1607)(643, 1874)(644, 1873)(645, 1643)(646, 1609)(647, 1878)(648, 1741)(649, 1879)(650, 1744)(651, 1883)(652, 1882)(653, 1743)(654, 1887)(655, 1618)(656, 1621)(657, 1891)(658, 1886)(659, 1754)(660, 1753)(661, 1622)(662, 1626)(663, 1625)(664, 1755)(665, 1897)(666, 1635)(667, 1760)(668, 1629)(669, 1900)(670, 1761)(671, 1764)(672, 1902)(673, 1758)(674, 1768)(675, 1906)(676, 1905)(677, 1767)(678, 1771)(679, 1641)(680, 1644)(681, 1737)(682, 1772)(683, 1912)(684, 1646)(685, 1913)(686, 1779)(687, 1648)(688, 1650)(689, 1784)(690, 1780)(691, 1918)(692, 1651)(693, 1786)(694, 1652)(695, 1655)(696, 1787)(697, 1923)(698, 1656)(699, 1925)(700, 1731)(701, 1661)(702, 1928)(703, 1663)(704, 1932)(705, 1931)(706, 1933)(707, 1664)(708, 1668)(709, 1937)(710, 1936)(711, 1684)(712, 1670)(713, 1941)(714, 1807)(715, 1942)(716, 1810)(717, 1946)(718, 1945)(719, 1809)(720, 1950)(721, 1678)(722, 1681)(723, 1954)(724, 1949)(725, 1818)(726, 1682)(727, 1685)(728, 1803)(729, 1819)(730, 1958)(731, 1687)(732, 1959)(733, 1826)(734, 1689)(735, 1691)(736, 1831)(737, 1827)(738, 1964)(739, 1692)(740, 1833)(741, 1693)(742, 1696)(743, 1834)(744, 1969)(745, 1697)(746, 1971)(747, 1777)(748, 1702)(749, 1974)(750, 1704)(751, 1978)(752, 1977)(753, 1979)(754, 1705)(755, 1981)(756, 1708)(757, 1983)(758, 1824)(759, 1713)(760, 1986)(761, 1715)(762, 1990)(763, 1989)(764, 1992)(765, 1716)(766, 1994)(767, 1858)(768, 1861)(769, 1998)(770, 1863)(771, 2000)(772, 1865)(773, 1725)(774, 1789)(775, 1868)(776, 2005)(777, 1792)(778, 1733)(779, 1870)(780, 1735)(781, 1876)(782, 1872)(783, 2011)(784, 1736)(785, 1739)(786, 1877)(787, 1740)(788, 2016)(789, 2017)(790, 1742)(791, 1745)(792, 2020)(793, 1797)(794, 1889)(795, 1888)(796, 1746)(797, 1750)(798, 1749)(799, 1890)(800, 1757)(801, 2025)(802, 1893)(803, 1896)(804, 2027)(805, 1892)(806, 2029)(807, 1898)(808, 1762)(809, 2031)(810, 1763)(811, 2035)(812, 2036)(813, 1766)(814, 1769)(815, 2040)(816, 1996)(817, 2041)(818, 1909)(819, 1775)(820, 1911)(821, 1839)(822, 2046)(823, 1914)(824, 1917)(825, 2049)(826, 1919)(827, 1783)(828, 1836)(829, 1922)(830, 2053)(831, 1866)(832, 1791)(833, 1924)(834, 2056)(835, 2006)(836, 1929)(837, 1794)(838, 1796)(839, 1885)(840, 1930)(841, 1934)(842, 1798)(843, 1801)(844, 1939)(845, 1935)(846, 2063)(847, 1802)(848, 1805)(849, 1940)(850, 1806)(851, 2044)(852, 2068)(853, 1808)(854, 1811)(855, 2071)(856, 1844)(857, 1952)(858, 1951)(859, 1812)(860, 1816)(861, 1815)(862, 1953)(863, 2075)(864, 1955)(865, 1822)(866, 1957)(867, 1850)(868, 2080)(869, 1960)(870, 1963)(871, 2082)(872, 1965)(873, 1830)(874, 1847)(875, 1968)(876, 2086)(877, 1920)(878, 1838)(879, 1970)(880, 2089)(881, 2045)(882, 1975)(883, 1841)(884, 1843)(885, 1948)(886, 1976)(887, 1980)(888, 1845)(889, 1966)(890, 1849)(891, 1982)(892, 2096)(893, 2079)(894, 1987)(895, 1852)(896, 1854)(897, 1991)(898, 1988)(899, 1855)(900, 1993)(901, 1856)(902, 1859)(903, 2103)(904, 2038)(905, 2104)(906, 1860)(907, 2106)(908, 1862)(909, 2091)(910, 1985)(911, 2054)(912, 2110)(913, 1867)(914, 2051)(915, 2008)(916, 2078)(917, 2010)(918, 2115)(919, 2012)(920, 1875)(921, 2014)(922, 2057)(923, 1880)(924, 2015)(925, 2018)(926, 1881)(927, 1884)(928, 2019)(929, 2077)(930, 2021)(931, 2024)(932, 2125)(933, 1894)(934, 2073)(935, 1895)(936, 2129)(937, 1899)(938, 2131)(939, 2033)(940, 2132)(941, 1901)(942, 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2121)(1031, 2124)(1032, 2153)(1033, 2023)(1034, 2181)(1035, 2158)(1036, 2028)(1037, 2128)(1038, 2030)(1039, 2130)(1040, 2133)(1041, 2032)(1042, 2098)(1043, 2043)(1044, 2135)(1045, 2161)(1046, 2042)(1047, 2148)(1048, 2183)(1049, 2047)(1050, 2141)(1051, 2060)(1052, 2178)(1053, 2112)(1054, 2052)(1055, 2182)(1056, 2155)(1057, 2170)(1058, 2175)(1059, 2184)(1060, 2061)(1061, 2123)(1062, 2145)(1063, 2139)(1064, 2107)(1065, 2156)(1066, 2159)(1067, 2127)(1068, 2126)(1069, 2076)(1070, 2169)(1071, 2117)(1072, 2093)(1073, 2122)(1074, 2140)(1075, 2085)(1076, 2114)(1077, 2113)(1078, 2118)(1079, 2150)(1080, 2151)(1081, 2119)(1082, 2144)(1083, 2171)(1084, 2177)(1085, 2116)(1086, 2174)(1087, 2147)(1088, 2168)(1089, 2160)(1090, 2179)(1091, 2166)(1092, 2172) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E14.620 Transitivity :: ET+ VT+ AT Graph:: v = 156 e = 1092 f = 910 degree seq :: [ 14^156 ] E14.632 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T2^7, T2^-1 * T1 * T2 * T1 * T2^-5, T2^3 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^3, (T2^2 * T1^-1)^7, T2^-1 * T1 * T2^-2 * T1 * T2^-3 * T1^-1 * T2 * T1^-1 * T2^3 * T1^-1 * T2 * T1^-1 * T2^-3 * T1 * T2^-2 * T1 ] Map:: R = (1, 1093, 3, 1095, 9, 1101, 19, 1111, 26, 1118, 13, 1105, 5, 1097)(2, 1094, 6, 1098, 14, 1106, 27, 1119, 32, 1124, 16, 1108, 7, 1099)(4, 1096, 11, 1103, 22, 1114, 40, 1132, 34, 1126, 17, 1109, 8, 1100)(10, 1102, 21, 1113, 39, 1131, 63, 1155, 59, 1151, 35, 1127, 18, 1110)(12, 1104, 23, 1115, 42, 1134, 68, 1160, 71, 1163, 43, 1135, 24, 1116)(15, 1107, 29, 1121, 50, 1142, 78, 1170, 81, 1173, 51, 1143, 30, 1122)(20, 1112, 38, 1130, 62, 1154, 94, 1186, 92, 1184, 60, 1152, 36, 1128)(25, 1117, 44, 1136, 72, 1164, 108, 1200, 111, 1203, 73, 1165, 45, 1137)(28, 1120, 49, 1141, 77, 1169, 116, 1208, 114, 1206, 75, 1167, 47, 1139)(31, 1123, 52, 1144, 82, 1174, 124, 1216, 127, 1219, 83, 1175, 53, 1145)(33, 1125, 55, 1147, 85, 1177, 129, 1221, 132, 1224, 86, 1178, 56, 1148)(37, 1129, 61, 1153, 93, 1185, 140, 1232, 112, 1204, 74, 1166, 46, 1138)(41, 1133, 67, 1159, 101, 1193, 151, 1243, 149, 1241, 99, 1191, 65, 1157)(48, 1140, 76, 1168, 115, 1207, 169, 1261, 128, 1220, 84, 1176, 54, 1146)(57, 1149, 66, 1158, 100, 1192, 150, 1242, 194, 1286, 133, 1225, 87, 1179)(58, 1150, 88, 1180, 134, 1226, 195, 1287, 198, 1290, 135, 1227, 89, 1181)(64, 1156, 98, 1190, 147, 1239, 212, 1304, 210, 1302, 145, 1237, 96, 1188)(69, 1161, 104, 1196, 155, 1247, 224, 1316, 222, 1314, 153, 1245, 102, 1194)(70, 1162, 105, 1197, 156, 1248, 226, 1318, 229, 1321, 157, 1249, 106, 1198)(79, 1171, 120, 1212, 176, 1268, 250, 1342, 248, 1340, 174, 1266, 118, 1210)(80, 1172, 121, 1213, 177, 1269, 252, 1344, 255, 1347, 178, 1270, 122, 1214)(90, 1182, 97, 1189, 146, 1238, 211, 1303, 280, 1372, 199, 1291, 136, 1228)(91, 1183, 137, 1229, 200, 1292, 281, 1373, 284, 1376, 201, 1293, 138, 1230)(95, 1187, 144, 1236, 208, 1300, 292, 1384, 290, 1382, 206, 1298, 142, 1234)(103, 1195, 154, 1246, 223, 1315, 311, 1403, 230, 1322, 158, 1250, 107, 1199)(109, 1201, 161, 1253, 233, 1325, 326, 1418, 324, 1416, 231, 1323, 159, 1251)(110, 1202, 162, 1254, 234, 1326, 328, 1420, 331, 1423, 235, 1327, 163, 1255)(113, 1205, 166, 1258, 238, 1330, 334, 1426, 337, 1429, 239, 1331, 167, 1259)(117, 1209, 173, 1265, 246, 1338, 345, 1437, 343, 1435, 244, 1336, 171, 1263)(119, 1211, 175, 1267, 249, 1341, 350, 1442, 256, 1348, 179, 1271, 123, 1215)(125, 1217, 182, 1274, 259, 1351, 365, 1457, 363, 1455, 257, 1349, 180, 1272)(126, 1218, 183, 1275, 260, 1352, 367, 1459, 370, 1462, 261, 1353, 184, 1276)(130, 1222, 189, 1281, 266, 1358, 376, 1468, 374, 1466, 264, 1356, 187, 1279)(131, 1223, 190, 1282, 267, 1359, 378, 1470, 381, 1473, 268, 1360, 191, 1283)(139, 1231, 143, 1235, 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389, 1481, 542, 1634, 544, 1636, 390, 1482, 277, 1369)(209, 1301, 294, 1386, 415, 1507, 571, 1663, 574, 1666, 416, 1508, 295, 1387)(213, 1305, 300, 1392, 421, 1513, 580, 1672, 578, 1670, 419, 1511, 298, 1390)(216, 1308, 219, 1311, 306, 1398, 430, 1522, 588, 1680, 426, 1518, 303, 1395)(217, 1309, 304, 1396, 427, 1519, 589, 1681, 536, 1628, 385, 1477, 272, 1364)(221, 1313, 308, 1400, 433, 1525, 597, 1689, 600, 1692, 434, 1526, 309, 1401)(225, 1317, 315, 1407, 441, 1533, 608, 1700, 606, 1698, 439, 1531, 313, 1405)(227, 1319, 318, 1410, 444, 1536, 612, 1704, 610, 1702, 442, 1534, 316, 1408)(228, 1320, 319, 1411, 445, 1537, 614, 1706, 616, 1708, 446, 1538, 320, 1412)(247, 1339, 347, 1439, 486, 1578, 658, 1750, 661, 1753, 487, 1579, 348, 1440)(251, 1343, 354, 1446, 494, 1586, 669, 1761, 667, 1759, 492, 1584, 352, 1444)(253, 1345, 357, 1449, 497, 1589, 673, 1765, 671, 1763, 495, 1587, 355, 1447)(254, 1346, 358, 1450, 498, 1590, 675, 1767, 677, 1769, 499, 1591, 359, 1451)(274, 1366, 387, 1479, 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1072, 2164, 1090, 2182, 1075, 2167, 1035, 2127, 961, 2053)(967, 2059, 1007, 2099, 1027, 2119, 1071, 2163, 1089, 2181, 1076, 2168, 1039, 2131)(971, 2063, 1041, 2133, 1078, 2170, 1059, 2151, 1002, 2094, 1061, 2153, 1042, 2134)(991, 2083, 998, 2090, 1058, 2150, 1086, 2178, 1068, 2160, 1022, 2114, 1019, 2111)(1026, 2118, 1030, 2122, 1073, 2165, 1091, 2183, 1077, 2169, 1040, 2132, 1038, 2130)(1043, 2135, 1062, 2154, 1063, 2155, 1087, 2179, 1092, 2184, 1079, 2171, 1044, 2136) L = (1, 1094)(2, 1096)(3, 1100)(4, 1093)(5, 1104)(6, 1097)(7, 1107)(8, 1102)(9, 1110)(10, 1095)(11, 1099)(12, 1098)(13, 1117)(14, 1116)(15, 1103)(16, 1123)(17, 1125)(18, 1112)(19, 1128)(20, 1101)(21, 1109)(22, 1122)(23, 1105)(24, 1120)(25, 1115)(26, 1138)(27, 1139)(28, 1106)(29, 1108)(30, 1133)(31, 1121)(32, 1146)(33, 1113)(34, 1149)(35, 1150)(36, 1129)(37, 1111)(38, 1127)(39, 1148)(40, 1157)(41, 1114)(42, 1137)(43, 1162)(44, 1118)(45, 1161)(46, 1136)(47, 1140)(48, 1119)(49, 1135)(50, 1145)(51, 1172)(52, 1124)(53, 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1192)(149, 1308)(150, 1307)(151, 1310)(152, 1193)(153, 1313)(154, 1245)(155, 1255)(156, 1250)(157, 1320)(158, 1319)(159, 1252)(160, 1200)(161, 1204)(162, 1203)(163, 1317)(164, 1254)(165, 1253)(166, 1206)(167, 1262)(168, 1258)(169, 1333)(170, 1207)(171, 1264)(172, 1208)(173, 1249)(174, 1339)(175, 1266)(176, 1276)(177, 1271)(178, 1346)(179, 1345)(180, 1273)(181, 1216)(182, 1220)(183, 1219)(184, 1343)(185, 1275)(186, 1274)(187, 1280)(188, 1221)(189, 1225)(190, 1224)(191, 1305)(192, 1282)(193, 1281)(194, 1364)(195, 1365)(196, 1226)(197, 1236)(198, 1370)(199, 1371)(200, 1294)(201, 1375)(202, 1374)(203, 1296)(204, 1232)(205, 1293)(206, 1381)(207, 1298)(208, 1369)(209, 1238)(210, 1388)(211, 1387)(212, 1390)(213, 1239)(214, 1241)(215, 1309)(216, 1306)(217, 1242)(218, 1311)(219, 1243)(220, 1270)(221, 1246)(222, 1402)(223, 1401)(224, 1405)(225, 1247)(226, 1408)(227, 1248)(228, 1265)(229, 1413)(230, 1414)(231, 1415)(232, 1323)(233, 1329)(234, 1328)(235, 1422)(236, 1421)(237, 1419)(238, 1332)(239, 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2085)(1054, 2147)(1055, 2086)(1056, 2138)(1057, 2169)(1058, 2149)(1059, 2093)(1060, 2170)(1061, 2095)(1062, 2153)(1063, 2101)(1064, 2163)(1065, 2160)(1066, 2162)(1067, 2164)(1068, 2179)(1069, 2158)(1070, 2161)(1071, 2120)(1072, 2121)(1073, 2139)(1074, 2148)(1075, 2152)(1076, 2140)(1077, 2150)(1078, 2167)(1079, 2165)(1080, 2181)(1081, 2182)(1082, 2172)(1083, 2173)(1084, 2180)(1085, 2176)(1086, 2183)(1087, 2157)(1088, 2177)(1089, 2174)(1090, 2175)(1091, 2184)(1092, 2178) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E14.619 Transitivity :: ET+ VT+ AT Graph:: v = 156 e = 1092 f = 910 degree seq :: [ 14^156 ] E14.633 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T2^-2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T2^-2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T2^7, (T2^-2 * T1 * T2^-3 * T1)^3 ] Map:: R = (1, 1093, 3, 1095, 9, 1101, 19, 1111, 26, 1118, 13, 1105, 5, 1097)(2, 1094, 6, 1098, 14, 1106, 27, 1119, 32, 1124, 16, 1108, 7, 1099)(4, 1096, 11, 1103, 22, 1114, 40, 1132, 34, 1126, 17, 1109, 8, 1100)(10, 1102, 21, 1113, 39, 1131, 63, 1155, 59, 1151, 35, 1127, 18, 1110)(12, 1104, 23, 1115, 42, 1134, 68, 1160, 71, 1163, 43, 1135, 24, 1116)(15, 1107, 29, 1121, 50, 1142, 78, 1170, 81, 1173, 51, 1143, 30, 1122)(20, 1112, 38, 1130, 62, 1154, 94, 1186, 92, 1184, 60, 1152, 36, 1128)(25, 1117, 44, 1136, 72, 1164, 108, 1200, 111, 1203, 73, 1165, 45, 1137)(28, 1120, 49, 1141, 77, 1169, 116, 1208, 114, 1206, 75, 1167, 47, 1139)(31, 1123, 52, 1144, 82, 1174, 124, 1216, 127, 1219, 83, 1175, 53, 1145)(33, 1125, 55, 1147, 85, 1177, 129, 1221, 132, 1224, 86, 1178, 56, 1148)(37, 1129, 61, 1153, 93, 1185, 140, 1232, 112, 1204, 74, 1166, 46, 1138)(41, 1133, 67, 1159, 101, 1193, 151, 1243, 149, 1241, 99, 1191, 65, 1157)(48, 1140, 76, 1168, 115, 1207, 169, 1261, 128, 1220, 84, 1176, 54, 1146)(57, 1149, 66, 1158, 100, 1192, 150, 1242, 194, 1286, 133, 1225, 87, 1179)(58, 1150, 88, 1180, 134, 1226, 195, 1287, 198, 1290, 135, 1227, 89, 1181)(64, 1156, 98, 1190, 147, 1239, 212, 1304, 210, 1302, 145, 1237, 96, 1188)(69, 1161, 104, 1196, 155, 1247, 224, 1316, 222, 1314, 153, 1245, 102, 1194)(70, 1162, 105, 1197, 156, 1248, 226, 1318, 229, 1321, 157, 1249, 106, 1198)(79, 1171, 120, 1212, 176, 1268, 250, 1342, 248, 1340, 174, 1266, 118, 1210)(80, 1172, 121, 1213, 177, 1269, 252, 1344, 255, 1347, 178, 1270, 122, 1214)(90, 1182, 97, 1189, 146, 1238, 211, 1303, 280, 1372, 199, 1291, 136, 1228)(91, 1183, 137, 1229, 200, 1292, 281, 1373, 284, 1376, 201, 1293, 138, 1230)(95, 1187, 144, 1236, 208, 1300, 292, 1384, 290, 1382, 206, 1298, 142, 1234)(103, 1195, 154, 1246, 223, 1315, 311, 1403, 230, 1322, 158, 1250, 107, 1199)(109, 1201, 161, 1253, 233, 1325, 326, 1418, 324, 1416, 231, 1323, 159, 1251)(110, 1202, 162, 1254, 234, 1326, 328, 1420, 331, 1423, 235, 1327, 163, 1255)(113, 1205, 166, 1258, 238, 1330, 334, 1426, 337, 1429, 239, 1331, 167, 1259)(117, 1209, 173, 1265, 246, 1338, 345, 1437, 343, 1435, 244, 1336, 171, 1263)(119, 1211, 175, 1267, 249, 1341, 350, 1442, 256, 1348, 179, 1271, 123, 1215)(125, 1217, 182, 1274, 259, 1351, 365, 1457, 363, 1455, 257, 1349, 180, 1272)(126, 1218, 183, 1275, 260, 1352, 367, 1459, 370, 1462, 261, 1353, 184, 1276)(130, 1222, 189, 1281, 266, 1358, 376, 1468, 374, 1466, 264, 1356, 187, 1279)(131, 1223, 190, 1282, 267, 1359, 378, 1470, 381, 1473, 268, 1360, 191, 1283)(139, 1231, 143, 1235, 207, 1299, 291, 1383, 402, 1494, 285, 1377, 202, 1294)(141, 1233, 205, 1297, 288, 1380, 406, 1498, 404, 1496, 286, 1378, 203, 1295)(148, 1240, 214, 1306, 301, 1393, 422, 1514, 425, 1517, 302, 1394, 215, 1307)(152, 1244, 220, 1312, 307, 1399, 431, 1523, 429, 1521, 305, 1397, 218, 1310)(160, 1252, 232, 1324, 325, 1417, 452, 1544, 332, 1424, 236, 1328, 164, 1256)(165, 1257, 204, 1296, 287, 1379, 405, 1497, 465, 1557, 333, 1425, 237, 1329)(168, 1260, 172, 1264, 245, 1337, 344, 1436, 473, 1565, 338, 1430, 240, 1332)(170, 1262, 243, 1335, 341, 1433, 477, 1569, 475, 1567, 339, 1431, 241, 1333)(181, 1273, 258, 1350, 364, 1456, 505, 1597, 371, 1463, 262, 1354, 185, 1277)(186, 1278, 242, 1334, 340, 1432, 476, 1568, 411, 1503, 372, 1464, 263, 1355)(188, 1280, 265, 1357, 375, 1467, 520, 1612, 382, 1474, 269, 1361, 192, 1284)(193, 1285, 270, 1362, 383, 1475, 531, 1623, 482, 1574, 384, 1476, 271, 1363)(196, 1288, 275, 1367, 388, 1480, 538, 1630, 536, 1628, 386, 1478, 273, 1365)(197, 1289, 276, 1368, 389, 1481, 540, 1632, 543, 1635, 390, 1482, 277, 1369)(209, 1301, 294, 1386, 415, 1507, 563, 1655, 566, 1658, 416, 1508, 295, 1387)(213, 1305, 300, 1392, 421, 1513, 570, 1662, 569, 1661, 419, 1511, 298, 1390)(216, 1308, 219, 1311, 306, 1398, 430, 1522, 557, 1649, 426, 1518, 303, 1395)(217, 1309, 304, 1396, 427, 1519, 463, 1555, 534, 1626, 385, 1477, 272, 1364)(221, 1313, 308, 1400, 433, 1525, 585, 1677, 588, 1680, 434, 1526, 309, 1401)(225, 1317, 315, 1407, 441, 1533, 593, 1685, 592, 1684, 439, 1531, 313, 1405)(227, 1319, 318, 1410, 444, 1536, 597, 1689, 596, 1688, 442, 1534, 316, 1408)(228, 1320, 319, 1411, 445, 1537, 599, 1691, 601, 1693, 446, 1538, 320, 1412)(247, 1339, 347, 1439, 486, 1578, 627, 1719, 630, 1722, 487, 1579, 348, 1440)(251, 1343, 354, 1446, 494, 1586, 634, 1726, 633, 1725, 492, 1584, 352, 1444)(253, 1345, 357, 1449, 497, 1589, 638, 1730, 637, 1729, 495, 1587, 355, 1447)(254, 1346, 358, 1450, 498, 1590, 640, 1732, 642, 1734, 499, 1591, 359, 1451)(274, 1366, 387, 1479, 537, 1629, 582, 1674, 544, 1636, 391, 1483, 278, 1370)(279, 1371, 392, 1484, 545, 1637, 489, 1581, 351, 1443, 491, 1583, 393, 1485)(282, 1374, 397, 1489, 549, 1641, 677, 1769, 675, 1767, 547, 1639, 395, 1487)(283, 1375, 398, 1490, 550, 1642, 679, 1771, 682, 1774, 551, 1643, 399, 1491)(289, 1381, 408, 1500, 559, 1651, 685, 1777, 652, 1744, 516, 1608, 409, 1501)(293, 1385, 414, 1506, 562, 1654, 688, 1780, 687, 1779, 561, 1653, 412, 1504)(296, 1388, 299, 1391, 420, 1512, 462, 1554, 458, 1550, 567, 1659, 417, 1509)(297, 1389, 418, 1510, 448, 1540, 322, 1414, 437, 1529, 546, 1638, 394, 1486)(310, 1402, 314, 1406, 440, 1532, 515, 1607, 511, 1603, 589, 1681, 435, 1527)(312, 1404, 438, 1530, 501, 1593, 361, 1453, 490, 1582, 590, 1682, 436, 1528)(317, 1409, 443, 1535, 560, 1652, 410, 1502, 413, 1505, 447, 1539, 321, 1413)(323, 1415, 449, 1541, 602, 1694, 726, 1818, 729, 1821, 603, 1695, 450, 1542)(327, 1419, 456, 1548, 609, 1701, 733, 1825, 732, 1824, 607, 1699, 454, 1546)(329, 1421, 459, 1551, 579, 1671, 706, 1798, 735, 1827, 610, 1702, 457, 1549)(330, 1422, 460, 1552, 568, 1660, 695, 1787, 737, 1829, 611, 1703, 461, 1553)(335, 1427, 468, 1560, 615, 1707, 742, 1834, 740, 1832, 613, 1705, 466, 1558)(336, 1428, 469, 1561, 616, 1708, 744, 1836, 747, 1839, 617, 1709, 470, 1562)(342, 1434, 479, 1571, 623, 1715, 749, 1841, 662, 1754, 533, 1625, 480, 1572)(346, 1438, 485, 1577, 626, 1718, 752, 1844, 751, 1843, 625, 1717, 483, 1575)(349, 1441, 353, 1445, 493, 1585, 530, 1622, 526, 1618, 631, 1723, 488, 1580)(356, 1448, 496, 1588, 624, 1716, 481, 1573, 484, 1576, 500, 1592, 360, 1452)(362, 1454, 502, 1594, 643, 1735, 772, 1864, 775, 1867, 644, 1736, 503, 1595)(366, 1458, 509, 1601, 649, 1741, 779, 1871, 778, 1870, 647, 1739, 507, 1599)(368, 1460, 512, 1604, 407, 1499, 558, 1650, 684, 1776, 650, 1742, 510, 1602)(369, 1461, 513, 1605, 591, 1683, 713, 1805, 782, 1874, 651, 1743, 514, 1606)(373, 1465, 517, 1609, 653, 1745, 783, 1875, 786, 1878, 654, 1746, 518, 1610)(377, 1469, 524, 1616, 659, 1751, 790, 1882, 789, 1881, 657, 1749, 522, 1614)(379, 1471, 527, 1619, 478, 1570, 622, 1714, 748, 1840, 660, 1752, 525, 1617)(380, 1472, 528, 1620, 632, 1724, 759, 1851, 793, 1885, 661, 1753, 529, 1621)(396, 1488, 548, 1640, 676, 1768, 696, 1788, 683, 1775, 552, 1644, 400, 1492)(401, 1493, 553, 1645, 474, 1566, 621, 1713, 521, 1613, 656, 1748, 554, 1646)(403, 1495, 555, 1647, 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818, 1910, 919, 2011, 917, 2009, 816, 1908, 690, 1782)(565, 1657, 693, 1785, 819, 1911, 920, 2012, 839, 1931, 720, 1812, 598, 1690)(571, 1663, 698, 1790, 821, 1913, 910, 2002, 806, 1898, 680, 1772, 697, 1789)(573, 1665, 700, 1792, 824, 1916, 760, 1852, 762, 1854, 704, 1796, 577, 1669)(586, 1678, 710, 1802, 811, 1903, 912, 2004, 933, 2025, 832, 1924, 708, 1800)(587, 1679, 711, 1803, 834, 1926, 935, 2027, 875, 1967, 766, 1858, 639, 1731)(594, 1686, 717, 1809, 836, 1928, 937, 2029, 858, 1950, 745, 1837, 715, 1807)(595, 1687, 718, 1810, 837, 1929, 939, 2031, 913, 2005, 812, 1904, 686, 1778)(600, 1692, 723, 1815, 731, 1823, 846, 1938, 944, 2036, 841, 1933, 724, 1816)(628, 1720, 756, 1848, 863, 1955, 956, 2048, 961, 2053, 868, 1960, 754, 1846)(635, 1727, 763, 1855, 872, 1964, 964, 2056, 927, 2019, 828, 1920, 761, 1853)(636, 1728, 764, 1856, 873, 1965, 966, 2058, 957, 2049, 864, 1956, 750, 1842)(641, 1733, 769, 1861, 777, 1869, 882, 1974, 971, 2063, 877, 1969, 770, 1862)(665, 1757, 668, 1760, 798, 1890, 810, 1902, 807, 1899, 901, 1993, 796, 1888)(674, 1766, 801, 1893, 906, 1998, 950, 2042, 852, 1944, 736, 1828, 802, 1894)(678, 1770, 785, 1877, 890, 1982, 978, 2070, 990, 2082, 908, 2000, 804, 1896)(681, 1773, 808, 1900, 902, 1994, 985, 2077, 992, 2084, 911, 2003, 809, 1901)(689, 1781, 815, 1907, 915, 2007, 945, 2037, 842, 1934, 727, 1819, 814, 1906)(691, 1783, 817, 1909, 918, 2010, 893, 1985, 895, 1987, 820, 1912, 694, 1786)(709, 1801, 833, 1925, 934, 2026, 847, 1939, 849, 1941, 835, 1927, 712, 1804)(719, 1811, 721, 1813, 840, 1932, 862, 1954, 859, 1951, 941, 2033, 838, 1930)(728, 1820, 844, 1936, 947, 2039, 1017, 2109, 953, 2045, 856, 1948, 743, 1835)(734, 1826, 850, 1942, 948, 2040, 1018, 2110, 1009, 2101, 936, 2028, 848, 1940)(739, 1831, 853, 1945, 951, 2043, 975, 2067, 886, 1978, 781, 1873, 854, 1946)(746, 1838, 860, 1952, 942, 2034, 1000, 2092, 1023, 2115, 955, 2047, 861, 1953)(753, 1845, 867, 1959, 959, 2051, 972, 2064, 878, 1970, 773, 1865, 866, 1958)(755, 1847, 869, 1961, 962, 2054, 883, 1975, 885, 1977, 871, 1963, 758, 1850)(765, 1857, 767, 1859, 876, 1968, 930, 2022, 928, 2020, 968, 2060, 874, 1966)(774, 1866, 880, 1972, 974, 2066, 1036, 2128, 1004, 2096, 925, 2017, 826, 1918)(780, 1872, 813, 1905, 914, 2006, 994, 2086, 986, 2078, 963, 2055, 884, 1976)(784, 1876, 889, 1981, 831, 1923, 931, 2023, 1005, 2097, 976, 2068, 887, 1979)(791, 1883, 865, 1957, 958, 2050, 1025, 2117, 999, 2091, 921, 2013, 894, 1986)(792, 1884, 896, 1988, 822, 1914, 923, 2015, 1002, 2094, 980, 2072, 897, 1989)(803, 1895, 805, 1897, 909, 2001, 845, 1937, 843, 1935, 946, 2038, 907, 1999)(829, 1921, 929, 2021, 969, 2061, 1010, 2102, 1019, 2111, 949, 2041, 851, 1943)(855, 1947, 857, 1949, 954, 2046, 881, 1973, 879, 1971, 973, 2065, 952, 2044)(888, 1980, 977, 2069, 1003, 2095, 924, 2016, 926, 2018, 979, 2071, 891, 1983)(899, 1991, 983, 2075, 922, 2014, 1001, 2093, 1048, 2140, 1040, 2132, 981, 2073)(904, 1996, 987, 2079, 916, 2008, 996, 2088, 1046, 2138, 1043, 2135, 988, 2080)(932, 2024, 1006, 2098, 1051, 2143, 1056, 2148, 1015, 2107, 943, 2035, 1007, 2099)(938, 2030, 1012, 2104, 1053, 2145, 1054, 2146, 1013, 2105, 940, 2032, 1011, 2103)(960, 2052, 1027, 2119, 1060, 2152, 1065, 2157, 1034, 2126, 970, 2062, 1028, 2120)(965, 2057, 1031, 2123, 1062, 2154, 1063, 2155, 1032, 2124, 967, 2059, 1030, 2122)(982, 2074, 1041, 2133, 1047, 2139, 997, 2089, 998, 2090, 1042, 2134, 984, 2076)(989, 2081, 1016, 2108, 995, 2087, 1045, 2137, 1070, 2162, 1057, 2149, 1020, 2112)(991, 2083, 1044, 2136, 993, 2085, 1014, 2106, 1055, 2147, 1052, 2144, 1008, 2100)(1021, 2113, 1035, 2127, 1026, 2118, 1059, 2151, 1078, 2170, 1066, 2158, 1037, 2129)(1022, 2114, 1058, 2150, 1024, 2116, 1033, 2125, 1064, 2156, 1061, 2153, 1029, 2121)(1038, 2130, 1050, 2142, 1073, 2165, 1083, 2175, 1067, 2159, 1039, 2131, 1049, 2141)(1068, 2160, 1072, 2164, 1086, 2178, 1090, 2182, 1084, 2176, 1069, 2161, 1071, 2163)(1074, 2166, 1076, 2168, 1075, 2167, 1085, 2177, 1091, 2183, 1087, 2179, 1077, 2169)(1079, 2171, 1081, 2173, 1080, 2172, 1088, 2180, 1092, 2184, 1089, 2181, 1082, 2174) L = (1, 1094)(2, 1096)(3, 1100)(4, 1093)(5, 1104)(6, 1097)(7, 1107)(8, 1102)(9, 1110)(10, 1095)(11, 1099)(12, 1098)(13, 1117)(14, 1116)(15, 1103)(16, 1123)(17, 1125)(18, 1112)(19, 1128)(20, 1101)(21, 1109)(22, 1122)(23, 1105)(24, 1120)(25, 1115)(26, 1138)(27, 1139)(28, 1106)(29, 1108)(30, 1133)(31, 1121)(32, 1146)(33, 1113)(34, 1149)(35, 1150)(36, 1129)(37, 1111)(38, 1127)(39, 1148)(40, 1157)(41, 1114)(42, 1137)(43, 1162)(44, 1118)(45, 1161)(46, 1136)(47, 1140)(48, 1119)(49, 1135)(50, 1145)(51, 1172)(52, 1124)(53, 1171)(54, 1144)(55, 1126)(56, 1156)(57, 1147)(58, 1130)(59, 1182)(60, 1183)(61, 1152)(62, 1181)(63, 1188)(64, 1131)(65, 1158)(66, 1132)(67, 1143)(68, 1194)(69, 1134)(70, 1141)(71, 1199)(72, 1166)(73, 1202)(74, 1201)(75, 1205)(76, 1167)(77, 1198)(78, 1210)(79, 1142)(80, 1159)(81, 1215)(82, 1176)(83, 1218)(84, 1217)(85, 1179)(86, 1223)(87, 1222)(88, 1151)(89, 1187)(90, 1180)(91, 1153)(92, 1231)(93, 1230)(94, 1234)(95, 1154)(96, 1189)(97, 1155)(98, 1178)(99, 1240)(100, 1191)(101, 1214)(102, 1195)(103, 1160)(104, 1165)(105, 1163)(106, 1209)(107, 1197)(108, 1251)(109, 1164)(110, 1196)(111, 1256)(112, 1257)(113, 1168)(114, 1260)(115, 1259)(116, 1263)(117, 1169)(118, 1211)(119, 1170)(120, 1175)(121, 1173)(122, 1244)(123, 1213)(124, 1272)(125, 1174)(126, 1212)(127, 1277)(128, 1278)(129, 1279)(130, 1177)(131, 1190)(132, 1284)(133, 1285)(134, 1228)(135, 1289)(136, 1288)(137, 1184)(138, 1233)(139, 1229)(140, 1295)(141, 1185)(142, 1235)(143, 1186)(144, 1227)(145, 1301)(146, 1237)(147, 1283)(148, 1192)(149, 1308)(150, 1307)(151, 1310)(152, 1193)(153, 1313)(154, 1245)(155, 1255)(156, 1250)(157, 1320)(158, 1319)(159, 1252)(160, 1200)(161, 1204)(162, 1203)(163, 1317)(164, 1254)(165, 1253)(166, 1206)(167, 1262)(168, 1258)(169, 1333)(170, 1207)(171, 1264)(172, 1208)(173, 1249)(174, 1339)(175, 1266)(176, 1276)(177, 1271)(178, 1346)(179, 1345)(180, 1273)(181, 1216)(182, 1220)(183, 1219)(184, 1343)(185, 1275)(186, 1274)(187, 1280)(188, 1221)(189, 1225)(190, 1224)(191, 1305)(192, 1282)(193, 1281)(194, 1364)(195, 1365)(196, 1226)(197, 1236)(198, 1370)(199, 1371)(200, 1294)(201, 1375)(202, 1374)(203, 1296)(204, 1232)(205, 1293)(206, 1381)(207, 1298)(208, 1369)(209, 1238)(210, 1388)(211, 1387)(212, 1390)(213, 1239)(214, 1241)(215, 1309)(216, 1306)(217, 1242)(218, 1311)(219, 1243)(220, 1270)(221, 1246)(222, 1402)(223, 1401)(224, 1405)(225, 1247)(226, 1408)(227, 1248)(228, 1265)(229, 1413)(230, 1414)(231, 1415)(232, 1323)(233, 1329)(234, 1328)(235, 1422)(236, 1421)(237, 1419)(238, 1332)(239, 1428)(240, 1427)(241, 1334)(242, 1261)(243, 1331)(244, 1434)(245, 1336)(246, 1412)(247, 1267)(248, 1441)(249, 1440)(250, 1444)(251, 1268)(252, 1447)(253, 1269)(254, 1312)(255, 1452)(256, 1453)(257, 1454)(258, 1349)(259, 1355)(260, 1354)(261, 1461)(262, 1460)(263, 1458)(264, 1465)(265, 1356)(266, 1363)(267, 1361)(268, 1472)(269, 1471)(270, 1286)(271, 1469)(272, 1362)(273, 1366)(274, 1287)(275, 1291)(276, 1290)(277, 1385)(278, 1368)(279, 1367)(280, 1486)(281, 1487)(282, 1292)(283, 1297)(284, 1492)(285, 1493)(286, 1495)(287, 1378)(288, 1491)(289, 1299)(290, 1502)(291, 1501)(292, 1504)(293, 1300)(294, 1302)(295, 1389)(296, 1386)(297, 1303)(298, 1391)(299, 1304)(300, 1360)(301, 1395)(302, 1516)(303, 1515)(304, 1394)(305, 1520)(306, 1397)(307, 1451)(308, 1314)(309, 1404)(310, 1400)(311, 1528)(312, 1315)(313, 1406)(314, 1316)(315, 1327)(316, 1409)(317, 1318)(318, 1322)(319, 1321)(320, 1438)(321, 1411)(322, 1410)(323, 1324)(324, 1543)(325, 1542)(326, 1546)(327, 1325)(328, 1549)(329, 1326)(330, 1407)(331, 1554)(332, 1555)(333, 1556)(334, 1558)(335, 1330)(336, 1335)(337, 1563)(338, 1564)(339, 1566)(340, 1431)(341, 1562)(342, 1337)(343, 1573)(344, 1572)(345, 1575)(346, 1338)(347, 1340)(348, 1443)(349, 1439)(350, 1581)(351, 1341)(352, 1445)(353, 1342)(354, 1353)(355, 1448)(356, 1344)(357, 1348)(358, 1347)(359, 1524)(360, 1450)(361, 1449)(362, 1350)(363, 1596)(364, 1595)(365, 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1425)(457, 1550)(458, 1420)(459, 1424)(460, 1423)(461, 1686)(462, 1552)(463, 1551)(464, 1548)(465, 1522)(466, 1559)(467, 1426)(468, 1430)(469, 1429)(470, 1570)(471, 1561)(472, 1560)(473, 1623)(474, 1432)(475, 1612)(476, 1645)(477, 1619)(478, 1433)(479, 1435)(480, 1574)(481, 1571)(482, 1436)(483, 1576)(484, 1437)(485, 1538)(486, 1580)(487, 1721)(488, 1720)(489, 1582)(490, 1442)(491, 1579)(492, 1724)(493, 1584)(494, 1606)(495, 1728)(496, 1587)(497, 1593)(498, 1592)(499, 1733)(500, 1717)(501, 1731)(502, 1455)(503, 1598)(504, 1594)(505, 1647)(506, 1456)(507, 1600)(508, 1457)(509, 1464)(510, 1603)(511, 1459)(512, 1463)(513, 1462)(514, 1727)(515, 1605)(516, 1601)(517, 1466)(518, 1613)(519, 1609)(520, 1713)(521, 1467)(522, 1615)(523, 1468)(524, 1476)(525, 1618)(526, 1470)(527, 1474)(528, 1473)(529, 1663)(530, 1620)(531, 1711)(532, 1475)(533, 1616)(534, 1544)(535, 1479)(536, 1757)(537, 1756)(538, 1759)(539, 1480)(540, 1761)(541, 1481)(542, 1506)(543, 1765)(544, 1523)(545, 1638)(546, 1682)(547, 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1858)(639, 1589)(640, 1843)(641, 1676)(642, 1863)(643, 1737)(644, 1866)(645, 1865)(646, 1736)(647, 1869)(648, 1739)(649, 1744)(650, 1802)(651, 1873)(652, 1872)(653, 1747)(654, 1877)(655, 1876)(656, 1746)(657, 1880)(658, 1749)(659, 1754)(660, 1848)(661, 1884)(662, 1883)(663, 1628)(664, 1758)(665, 1755)(666, 1629)(667, 1760)(668, 1630)(669, 1762)(670, 1632)(671, 1635)(672, 1781)(673, 1763)(674, 1640)(675, 1895)(676, 1894)(677, 1896)(678, 1641)(679, 1898)(680, 1642)(681, 1650)(682, 1902)(683, 1662)(684, 1901)(685, 1904)(686, 1651)(687, 1814)(688, 1906)(689, 1654)(690, 1783)(691, 1655)(692, 1659)(693, 1658)(694, 1785)(695, 1661)(696, 1787)(697, 1775)(698, 1753)(699, 1914)(700, 1791)(701, 1797)(702, 1796)(703, 1921)(704, 1920)(705, 1918)(706, 1795)(707, 1862)(708, 1801)(709, 1677)(710, 1681)(711, 1680)(712, 1803)(713, 1684)(714, 1805)(715, 1808)(716, 1685)(717, 1703)(718, 1688)(719, 1810)(720, 1813)(721, 1689)(722, 1691)(723, 1693)(724, 1845)(725, 1815)(726, 1934)(727, 1694)(728, 1698)(729, 1937)(730, 1780)(731, 1700)(732, 1939)(733, 1940)(734, 1701)(735, 1943)(736, 1809)(737, 1768)(738, 1887)(739, 1706)(740, 1947)(741, 1946)(742, 1948)(743, 1707)(744, 1950)(745, 1708)(746, 1714)(747, 1954)(748, 1953)(749, 1956)(750, 1715)(751, 1860)(752, 1958)(753, 1718)(754, 1847)(755, 1719)(756, 1723)(757, 1722)(758, 1849)(759, 1725)(760, 1851)(761, 1854)(762, 1726)(763, 1743)(764, 1729)(765, 1856)(766, 1859)(767, 1730)(768, 1732)(769, 1734)(770, 1923)(771, 1861)(772, 1970)(773, 1735)(774, 1738)(775, 1973)(776, 1844)(777, 1740)(778, 1975)(779, 1976)(780, 1741)(781, 1855)(782, 1833)(783, 1979)(784, 1745)(785, 1748)(786, 1983)(787, 1891)(788, 1750)(789, 1985)(790, 1986)(791, 1751)(792, 1790)(793, 1916)(794, 1888)(795, 1942)(796, 1991)(797, 1994)(798, 1889)(799, 1981)(800, 1996)(801, 1767)(802, 1829)(803, 1893)(804, 1897)(805, 1769)(806, 1899)(807, 1771)(808, 1774)(809, 1903)(810, 1900)(811, 1776)(812, 1905)(813, 1777)(814, 1822)(815, 1892)(816, 2008)(817, 1908)(818, 1827)(819, 1912)(820, 2013)(821, 1989)(822, 1792)(823, 2016)(824, 1988)(825, 2017)(826, 1793)(827, 2019)(828, 1794)(829, 1798)(830, 2022)(831, 1799)(832, 2024)(833, 1924)(834, 1927)(835, 2028)(836, 1944)(837, 1930)(838, 2032)(839, 2034)(840, 1931)(841, 2035)(842, 1935)(843, 1818)(844, 1821)(845, 1936)(846, 1824)(847, 1938)(848, 1941)(849, 1825)(850, 1830)(851, 1910)(852, 2030)(853, 1832)(854, 1874)(855, 1945)(856, 1949)(857, 1834)(858, 1951)(859, 1836)(860, 1839)(861, 1955)(862, 1952)(863, 1840)(864, 1957)(865, 1841)(866, 1868)(867, 1933)(868, 2052)(869, 1960)(870, 1963)(871, 2055)(872, 1978)(873, 1966)(874, 2059)(875, 2061)(876, 1967)(877, 2062)(878, 1971)(879, 1864)(880, 1867)(881, 1972)(882, 1870)(883, 1974)(884, 1977)(885, 1871)(886, 2057)(887, 1980)(888, 1875)(889, 1879)(890, 1878)(891, 1982)(892, 1881)(893, 1984)(894, 1987)(895, 1882)(896, 1885)(897, 2014)(898, 2073)(899, 1886)(900, 2076)(901, 2002)(902, 1890)(903, 2078)(904, 1907)(905, 2010)(906, 1999)(907, 2081)(908, 2039)(909, 2000)(910, 2075)(911, 2083)(912, 2003)(913, 2085)(914, 2005)(915, 2080)(916, 1909)(917, 2089)(918, 2079)(919, 2041)(920, 2091)(921, 1911)(922, 1913)(923, 1915)(924, 2015)(925, 2018)(926, 1917)(927, 2020)(928, 1919)(929, 1922)(930, 2021)(931, 1969)(932, 1925)(933, 2100)(934, 2099)(935, 2101)(936, 1926)(937, 2103)(938, 1928)(939, 2105)(940, 1929)(941, 2029)(942, 1932)(943, 1959)(944, 2026)(945, 2108)(946, 2037)(947, 2001)(948, 1992)(949, 2090)(950, 2112)(951, 2044)(952, 2113)(953, 2066)(954, 2045)(955, 2114)(956, 2047)(957, 2116)(958, 2049)(959, 2107)(960, 1961)(961, 2121)(962, 2120)(963, 1962)(964, 2122)(965, 1964)(966, 2124)(967, 1965)(968, 2056)(969, 1968)(970, 2023)(971, 2054)(972, 2127)(973, 2064)(974, 2046)(975, 2129)(976, 2130)(977, 2068)(978, 2071)(979, 2096)(980, 2131)(981, 2074)(982, 1990)(983, 1993)(984, 2040)(985, 1995)(986, 2077)(987, 1997)(988, 2087)(989, 1998)(990, 2128)(991, 2004)(992, 2086)(993, 2006)(994, 2136)(995, 2007)(996, 2009)(997, 2088)(998, 2011)(999, 2092)(1000, 2012)(1001, 2072)(1002, 2095)(1003, 2141)(1004, 2070)(1005, 2126)(1006, 2025)(1007, 2036)(1008, 2098)(1009, 2102)(1010, 2027)(1011, 2033)(1012, 2042)(1013, 2106)(1014, 2031)(1015, 2118)(1016, 2038)(1017, 2082)(1018, 2134)(1019, 2110)(1020, 2104)(1021, 2043)(1022, 2048)(1023, 2117)(1024, 2050)(1025, 2150)(1026, 2051)(1027, 2053)(1028, 2063)(1029, 2119)(1030, 2060)(1031, 2067)(1032, 2125)(1033, 2058)(1034, 2142)(1035, 2065)(1036, 2109)(1037, 2123)(1038, 2069)(1039, 2093)(1040, 2160)(1041, 2132)(1042, 2111)(1043, 2161)(1044, 2084)(1045, 2135)(1046, 2139)(1047, 2163)(1048, 2159)(1049, 2094)(1050, 2097)(1051, 2144)(1052, 2166)(1053, 2149)(1054, 2168)(1055, 2146)(1056, 2169)(1057, 2167)(1058, 2115)(1059, 2148)(1060, 2153)(1061, 2171)(1062, 2158)(1063, 2173)(1064, 2155)(1065, 2174)(1066, 2172)(1067, 2164)(1068, 2133)(1069, 2137)(1070, 2176)(1071, 2138)(1072, 2140)(1073, 2157)(1074, 2143)(1075, 2145)(1076, 2147)(1077, 2151)(1078, 2179)(1079, 2152)(1080, 2154)(1081, 2156)(1082, 2165)(1083, 2181)(1084, 2177)(1085, 2162)(1086, 2175)(1087, 2180)(1088, 2170)(1089, 2178)(1090, 2184)(1091, 2182)(1092, 2183) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E14.621 Transitivity :: ET+ VT+ AT Graph:: v = 156 e = 1092 f = 910 degree seq :: [ 14^156 ] E14.634 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^7, T2 * T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-3 * T2 * T1^-3, (T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-2)^2, T2 * T1^3 * T2 * T1^-2 * T2 * T1^3 * T2 * T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-3, (T2 * T1^2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-3 * T2 * T1^-3)^2 ] Map:: polyhedral non-degenerate R = (1, 1093, 3, 1095)(2, 1094, 6, 1098)(4, 1096, 9, 1101)(5, 1097, 12, 1104)(7, 1099, 16, 1108)(8, 1100, 13, 1105)(10, 1102, 19, 1111)(11, 1103, 21, 1113)(14, 1106, 22, 1114)(15, 1107, 27, 1119)(17, 1109, 29, 1121)(18, 1110, 32, 1124)(20, 1112, 34, 1126)(23, 1115, 35, 1127)(24, 1116, 40, 1132)(25, 1117, 41, 1133)(26, 1118, 43, 1135)(28, 1120, 44, 1136)(30, 1122, 48, 1140)(31, 1123, 50, 1142)(33, 1125, 53, 1145)(36, 1128, 54, 1146)(37, 1129, 58, 1150)(38, 1130, 59, 1151)(39, 1131, 61, 1153)(42, 1134, 64, 1156)(45, 1137, 65, 1157)(46, 1138, 69, 1161)(47, 1139, 71, 1163)(49, 1141, 73, 1165)(51, 1143, 74, 1166)(52, 1144, 78, 1170)(55, 1147, 82, 1174)(56, 1148, 83, 1175)(57, 1149, 85, 1177)(60, 1152, 88, 1180)(62, 1154, 89, 1181)(63, 1155, 93, 1185)(66, 1158, 72, 1164)(67, 1159, 98, 1190)(68, 1160, 99, 1191)(70, 1162, 103, 1195)(75, 1167, 106, 1198)(76, 1168, 110, 1202)(77, 1169, 111, 1203)(79, 1171, 112, 1204)(80, 1172, 116, 1208)(81, 1173, 117, 1209)(84, 1176, 120, 1212)(86, 1178, 121, 1213)(87, 1179, 125, 1217)(90, 1182, 94, 1186)(91, 1183, 129, 1221)(92, 1184, 131, 1223)(95, 1187, 135, 1227)(96, 1188, 136, 1228)(97, 1189, 138, 1230)(100, 1192, 141, 1233)(101, 1193, 107, 1199)(102, 1194, 143, 1235)(104, 1196, 144, 1236)(105, 1197, 148, 1240)(108, 1200, 152, 1244)(109, 1201, 153, 1245)(113, 1205, 156, 1248)(114, 1206, 160, 1252)(115, 1207, 161, 1253)(118, 1210, 163, 1255)(119, 1211, 167, 1259)(122, 1214, 126, 1218)(123, 1215, 171, 1263)(124, 1216, 173, 1265)(127, 1219, 177, 1269)(128, 1220, 178, 1270)(130, 1222, 181, 1273)(132, 1224, 182, 1274)(133, 1225, 186, 1278)(134, 1226, 187, 1279)(137, 1229, 190, 1282)(139, 1231, 191, 1283)(140, 1232, 195, 1287)(142, 1234, 198, 1290)(145, 1237, 199, 1291)(146, 1238, 203, 1295)(147, 1239, 204, 1296)(149, 1241, 207, 1299)(150, 1242, 208, 1300)(151, 1243, 210, 1302)(154, 1246, 213, 1305)(155, 1247, 157, 1249)(158, 1250, 218, 1310)(159, 1251, 219, 1311)(162, 1254, 222, 1314)(164, 1256, 168, 1260)(165, 1257, 227, 1319)(166, 1258, 229, 1321)(169, 1261, 233, 1325)(170, 1262, 234, 1326)(172, 1264, 237, 1329)(174, 1266, 238, 1330)(175, 1267, 242, 1334)(176, 1268, 243, 1335)(179, 1271, 246, 1338)(180, 1272, 200, 1292)(183, 1275, 248, 1340)(184, 1276, 252, 1344)(185, 1277, 253, 1345)(188, 1280, 255, 1347)(189, 1281, 259, 1351)(192, 1284, 196, 1288)(193, 1285, 263, 1355)(194, 1286, 265, 1357)(197, 1289, 268, 1360)(201, 1293, 273, 1365)(202, 1294, 274, 1366)(205, 1297, 277, 1369)(206, 1298, 280, 1372)(209, 1301, 283, 1375)(211, 1303, 284, 1376)(212, 1304, 288, 1380)(214, 1306, 291, 1383)(215, 1307, 293, 1385)(216, 1308, 294, 1386)(217, 1309, 296, 1388)(220, 1312, 299, 1391)(221, 1313, 223, 1315)(224, 1316, 303, 1395)(225, 1317, 305, 1397)(226, 1318, 306, 1398)(228, 1320, 309, 1401)(230, 1322, 310, 1402)(231, 1323, 314, 1406)(232, 1324, 315, 1407)(235, 1327, 318, 1410)(236, 1328, 249, 1341)(239, 1331, 320, 1412)(240, 1332, 324, 1416)(241, 1333, 325, 1417)(244, 1336, 327, 1419)(245, 1337, 331, 1423)(247, 1339, 334, 1426)(250, 1342, 338, 1430)(251, 1343, 339, 1431)(254, 1346, 342, 1434)(256, 1348, 260, 1352)(257, 1349, 347, 1439)(258, 1350, 349, 1441)(261, 1353, 353, 1445)(262, 1354, 354, 1446)(264, 1356, 357, 1449)(266, 1358, 358, 1450)(267, 1359, 362, 1454)(269, 1361, 363, 1455)(270, 1362, 367, 1459)(271, 1363, 368, 1460)(272, 1364, 370, 1462)(275, 1367, 373, 1465)(276, 1368, 278, 1370)(279, 1371, 377, 1469)(281, 1373, 378, 1470)(282, 1374, 382, 1474)(285, 1377, 289, 1381)(286, 1378, 386, 1478)(287, 1379, 388, 1480)(290, 1382, 391, 1483)(292, 1384, 393, 1485)(295, 1387, 396, 1488)(297, 1389, 397, 1489)(298, 1390, 401, 1493)(300, 1392, 404, 1496)(301, 1393, 406, 1498)(302, 1394, 407, 1499)(304, 1396, 410, 1502)(307, 1399, 413, 1505)(308, 1400, 321, 1413)(311, 1403, 415, 1507)(312, 1404, 419, 1511)(313, 1405, 420, 1512)(316, 1408, 422, 1514)(317, 1409, 426, 1518)(319, 1411, 429, 1521)(322, 1414, 433, 1525)(323, 1415, 434, 1526)(326, 1418, 437, 1529)(328, 1420, 332, 1424)(329, 1421, 442, 1534)(330, 1422, 444, 1536)(333, 1425, 447, 1539)(335, 1427, 450, 1542)(336, 1428, 451, 1543)(337, 1429, 453, 1545)(340, 1432, 456, 1548)(341, 1433, 343, 1435)(344, 1436, 460, 1552)(345, 1437, 462, 1554)(346, 1438, 463, 1555)(348, 1440, 466, 1558)(350, 1442, 467, 1559)(351, 1443, 471, 1563)(352, 1444, 424, 1516)(355, 1447, 473, 1565)(356, 1448, 364, 1456)(359, 1451, 475, 1567)(360, 1452, 479, 1571)(361, 1453, 480, 1572)(365, 1457, 484, 1576)(366, 1458, 486, 1578)(369, 1461, 489, 1581)(371, 1463, 411, 1503)(372, 1464, 492, 1584)(374, 1466, 495, 1587)(375, 1467, 497, 1589)(376, 1468, 498, 1590)(379, 1471, 383, 1475)(380, 1472, 503, 1595)(381, 1473, 504, 1596)(384, 1476, 440, 1532)(385, 1477, 507, 1599)(387, 1479, 510, 1602)(389, 1481, 511, 1603)(390, 1482, 515, 1607)(392, 1484, 516, 1608)(394, 1486, 519, 1611)(395, 1487, 523, 1615)(398, 1490, 402, 1494)(399, 1491, 461, 1553)(400, 1492, 527, 1619)(403, 1495, 530, 1622)(405, 1497, 532, 1624)(408, 1500, 535, 1627)(409, 1501, 416, 1508)(412, 1504, 770, 1862)(414, 1506, 773, 1865)(417, 1509, 501, 1593)(418, 1510, 776, 1868)(421, 1513, 660, 1752)(423, 1515, 427, 1519)(425, 1517, 782, 1874)(428, 1520, 672, 1764)(430, 1522, 787, 1879)(431, 1523, 789, 1881)(432, 1524, 521, 1613)(435, 1527, 667, 1759)(436, 1528, 438, 1530)(439, 1531, 795, 1887)(441, 1533, 796, 1888)(443, 1535, 797, 1889)(445, 1537, 798, 1890)(446, 1538, 753, 1845)(448, 1540, 800, 1892)(449, 1541, 772, 1864)(452, 1544, 805, 1897)(454, 1546, 533, 1625)(455, 1547, 698, 1790)(457, 1549, 809, 1901)(458, 1550, 680, 1772)(459, 1551, 811, 1903)(464, 1556, 814, 1906)(465, 1557, 476, 1568)(468, 1560, 816, 1908)(469, 1561, 810, 1902)(470, 1562, 607, 1699)(472, 1564, 821, 1913)(474, 1566, 823, 1915)(477, 1569, 825, 1917)(478, 1570, 685, 1777)(481, 1573, 623, 1715)(482, 1574, 684, 1776)(483, 1575, 832, 1924)(485, 1577, 736, 1828)(487, 1579, 600, 1692)(488, 1580, 835, 1927)(490, 1582, 493, 1585)(491, 1583, 839, 1931)(494, 1586, 620, 1712)(496, 1588, 843, 1935)(499, 1591, 848, 1940)(500, 1592, 683, 1775)(502, 1594, 851, 1943)(505, 1597, 827, 1919)(506, 1598, 854, 1946)(508, 1600, 728, 1820)(509, 1601, 517, 1609)(512, 1604, 858, 1950)(513, 1605, 861, 1953)(514, 1606, 664, 1756)(518, 1610, 706, 1798)(520, 1612, 524, 1616)(522, 1614, 865, 1957)(525, 1617, 867, 1959)(526, 1618, 778, 1870)(528, 1620, 869, 1961)(529, 1621, 705, 1797)(531, 1623, 691, 1783)(534, 1626, 873, 1965)(536, 1628, 876, 1968)(537, 1629, 878, 1970)(538, 1630, 881, 1973)(539, 1631, 885, 1977)(540, 1632, 889, 1981)(541, 1633, 891, 1983)(542, 1634, 895, 1987)(543, 1635, 897, 1989)(544, 1636, 901, 1993)(545, 1637, 904, 1996)(546, 1638, 908, 2000)(547, 1639, 910, 2002)(548, 1640, 914, 2006)(549, 1641, 916, 2008)(550, 1642, 920, 2012)(551, 1643, 922, 2014)(552, 1644, 926, 2018)(553, 1645, 928, 2020)(554, 1646, 930, 2022)(555, 1647, 933, 2025)(556, 1648, 936, 2028)(557, 1649, 939, 2031)(558, 1650, 941, 2033)(559, 1651, 943, 2035)(560, 1652, 945, 2037)(561, 1653, 948, 2040)(562, 1654, 950, 2042)(563, 1655, 953, 2045)(564, 1656, 955, 2047)(565, 1657, 958, 2050)(566, 1658, 959, 2051)(567, 1659, 962, 2054)(568, 1660, 963, 2055)(569, 1661, 965, 2057)(570, 1662, 967, 2059)(571, 1663, 969, 2061)(572, 1664, 970, 2062)(573, 1665, 972, 2064)(574, 1666, 975, 2067)(575, 1667, 976, 2068)(576, 1668, 979, 2071)(577, 1669, 980, 2072)(578, 1670, 978, 2070)(579, 1671, 983, 2075)(580, 1672, 984, 2076)(581, 1673, 985, 2077)(582, 1674, 987, 2079)(583, 1675, 988, 2080)(584, 1676, 989, 2081)(585, 1677, 992, 2084)(586, 1678, 829, 1921)(587, 1679, 994, 2086)(588, 1680, 997, 2089)(589, 1681, 1000, 2092)(590, 1682, 999, 2091)(591, 1683, 1001, 2093)(592, 1684, 853, 1945)(593, 1685, 1003, 2095)(594, 1686, 1004, 2096)(595, 1687, 1005, 2097)(596, 1688, 1007, 2099)(597, 1689, 788, 1880)(598, 1690, 1009, 2101)(599, 1691, 957, 2049)(601, 1693, 1012, 2104)(602, 1694, 1013, 2105)(603, 1695, 1016, 2108)(604, 1696, 1019, 2111)(605, 1697, 1018, 2110)(606, 1698, 1006, 2098)(608, 1700, 1021, 2113)(609, 1701, 935, 2027)(610, 1702, 1022, 2114)(611, 1703, 731, 1823)(612, 1704, 1024, 2116)(613, 1705, 1027, 2119)(614, 1706, 1029, 2121)(615, 1707, 1030, 2122)(616, 1708, 1031, 2123)(617, 1709, 803, 1895)(618, 1710, 1020, 2112)(619, 1711, 1032, 2124)(621, 1713, 1033, 2125)(622, 1714, 982, 2074)(624, 1716, 1036, 2128)(625, 1717, 830, 1922)(626, 1718, 986, 2078)(627, 1719, 799, 1891)(628, 1720, 1038, 2130)(629, 1721, 906, 1998)(630, 1722, 845, 1937)(631, 1723, 1039, 2131)(632, 1724, 1026, 2118)(633, 1725, 1040, 2132)(634, 1726, 1014, 2106)(635, 1727, 1042, 2134)(636, 1728, 977, 2069)(637, 1729, 1043, 2135)(638, 1730, 942, 2034)(639, 1731, 1015, 2107)(640, 1732, 1045, 2137)(641, 1733, 793, 1885)(642, 1734, 1047, 2139)(643, 1735, 1028, 2120)(644, 1736, 748, 1840)(645, 1737, 1002, 2094)(646, 1738, 1048, 2140)(647, 1739, 834, 1926)(648, 1740, 833, 1925)(649, 1741, 887, 1979)(650, 1742, 1049, 2141)(651, 1743, 1051, 2143)(652, 1744, 863, 1955)(653, 1745, 1052, 2144)(654, 1746, 1053, 2145)(655, 1747, 1035, 2127)(656, 1748, 1055, 2147)(657, 1749, 998, 2090)(658, 1750, 1025, 2117)(659, 1751, 968, 2060)(661, 1753, 1037, 2129)(662, 1754, 732, 1824)(663, 1755, 966, 2058)(665, 1757, 1058, 2150)(666, 1758, 918, 2010)(668, 1760, 996, 2088)(669, 1761, 716, 1808)(670, 1762, 1008, 2100)(671, 1763, 1060, 2152)(673, 1765, 758, 1850)(674, 1766, 1044, 2136)(675, 1767, 995, 2087)(676, 1768, 840, 1932)(677, 1769, 1062, 2154)(678, 1770, 956, 2048)(679, 1771, 841, 1933)(681, 1773, 1063, 2155)(682, 1774, 1046, 2138)(686, 1778, 1064, 2156)(687, 1779, 1065, 2157)(688, 1780, 1017, 2109)(689, 1781, 860, 1952)(690, 1782, 817, 1909)(692, 1784, 828, 1920)(693, 1785, 779, 1871)(694, 1786, 934, 2026)(695, 1787, 866, 1958)(696, 1788, 862, 1954)(697, 1789, 709, 1801)(699, 1791, 880, 1972)(700, 1792, 784, 1876)(701, 1793, 775, 1867)(702, 1794, 1067, 2159)(703, 1795, 991, 2083)(704, 1796, 872, 1964)(707, 1799, 1054, 2146)(708, 1800, 927, 2019)(710, 1802, 940, 2032)(711, 1803, 870, 1962)(712, 1804, 1050, 2142)(713, 1805, 899, 1991)(714, 1806, 974, 2066)(715, 1807, 1059, 2151)(717, 1809, 973, 2065)(718, 1810, 1070, 2162)(719, 1811, 981, 2073)(720, 1812, 1071, 2163)(721, 1813, 1072, 2164)(722, 1814, 1034, 2126)(723, 1815, 744, 1836)(724, 1816, 964, 2056)(725, 1817, 837, 1929)(726, 1818, 871, 1963)(727, 1819, 905, 1997)(729, 1821, 754, 1846)(730, 1822, 746, 1838)(733, 1825, 790, 1882)(734, 1826, 883, 1975)(735, 1827, 745, 1837)(737, 1829, 961, 2053)(738, 1830, 826, 1918)(739, 1831, 902, 1994)(740, 1832, 774, 1866)(741, 1833, 1066, 2158)(742, 1834, 1041, 2133)(743, 1835, 990, 2082)(747, 1839, 777, 1869)(749, 1841, 960, 2052)(750, 1842, 783, 1875)(751, 1843, 1075, 2167)(752, 1844, 890, 1982)(755, 1847, 824, 1916)(756, 1848, 1074, 2166)(757, 1849, 768, 1860)(759, 1851, 915, 2007)(760, 1852, 819, 1911)(761, 1853, 801, 1893)(762, 1854, 931, 2023)(763, 1855, 952, 2044)(764, 1856, 844, 1936)(765, 1857, 951, 2043)(766, 1858, 1078, 2170)(767, 1859, 1010, 2102)(769, 1861, 898, 1990)(771, 1863, 886, 1978)(780, 1872, 1073, 2165)(781, 1873, 893, 1985)(785, 1877, 924, 2016)(786, 1878, 875, 1967)(791, 1883, 1080, 2172)(792, 1884, 836, 1928)(794, 1886, 921, 2013)(802, 1894, 812, 1904)(804, 1896, 923, 2015)(806, 1898, 1079, 2171)(807, 1899, 855, 1947)(808, 1900, 993, 2085)(813, 1905, 919, 2011)(815, 1907, 1069, 2161)(818, 1910, 859, 1951)(820, 1912, 946, 2038)(822, 1914, 917, 2009)(831, 1923, 949, 2041)(838, 1930, 947, 2039)(842, 1934, 912, 2004)(846, 1938, 907, 1999)(847, 1939, 911, 2003)(849, 1941, 1085, 2177)(850, 1942, 868, 1960)(852, 1944, 1082, 2174)(856, 1948, 1056, 2148)(857, 1949, 1061, 2153)(864, 1956, 909, 2001)(874, 1966, 896, 1988)(877, 1969, 1088, 2180)(879, 1971, 1076, 2168)(882, 1974, 1068, 2160)(884, 1976, 1089, 2181)(888, 1980, 1081, 2173)(892, 1984, 1057, 2149)(894, 1986, 1090, 2182)(900, 1992, 1087, 2179)(903, 1995, 1083, 2175)(913, 2005, 1084, 2176)(925, 2017, 1091, 2183)(929, 2021, 944, 2036)(932, 2024, 1086, 2178)(937, 2029, 1011, 2103)(938, 2030, 1092, 2184)(954, 2046, 1077, 2169)(971, 2063, 1023, 2115) L = (1, 1094)(2, 1097)(3, 1099)(4, 1093)(5, 1103)(6, 1105)(7, 1107)(8, 1095)(9, 1110)(10, 1096)(11, 1112)(12, 1114)(13, 1116)(14, 1098)(15, 1118)(16, 1101)(17, 1100)(18, 1123)(19, 1125)(20, 1102)(21, 1127)(22, 1129)(23, 1104)(24, 1131)(25, 1106)(26, 1122)(27, 1136)(28, 1108)(29, 1139)(30, 1109)(31, 1141)(32, 1111)(33, 1144)(34, 1146)(35, 1147)(36, 1113)(37, 1149)(38, 1115)(39, 1134)(40, 1121)(41, 1155)(42, 1117)(43, 1157)(44, 1159)(45, 1119)(46, 1120)(47, 1162)(48, 1164)(49, 1138)(50, 1166)(51, 1124)(52, 1169)(53, 1126)(54, 1172)(55, 1173)(56, 1128)(57, 1152)(58, 1133)(59, 1179)(60, 1130)(61, 1181)(62, 1132)(63, 1184)(64, 1186)(65, 1187)(66, 1135)(67, 1189)(68, 1137)(69, 1193)(70, 1194)(71, 1140)(72, 1197)(73, 1198)(74, 1200)(75, 1142)(76, 1143)(77, 1168)(78, 1204)(79, 1145)(80, 1207)(81, 1176)(82, 1151)(83, 1211)(84, 1148)(85, 1213)(86, 1150)(87, 1216)(88, 1218)(89, 1219)(90, 1153)(91, 1154)(92, 1222)(93, 1156)(94, 1225)(95, 1226)(96, 1158)(97, 1192)(98, 1161)(99, 1232)(100, 1160)(101, 1234)(102, 1183)(103, 1236)(104, 1163)(105, 1239)(106, 1241)(107, 1165)(108, 1243)(109, 1167)(110, 1247)(111, 1248)(112, 1250)(113, 1170)(114, 1171)(115, 1206)(116, 1175)(117, 1255)(118, 1174)(119, 1258)(120, 1260)(121, 1261)(122, 1177)(123, 1178)(124, 1264)(125, 1180)(126, 1267)(127, 1268)(128, 1182)(129, 1272)(130, 1215)(131, 1274)(132, 1185)(133, 1277)(134, 1229)(135, 1191)(136, 1281)(137, 1188)(138, 1283)(139, 1190)(140, 1286)(141, 1288)(142, 1289)(143, 1291)(144, 1293)(145, 1195)(146, 1196)(147, 1238)(148, 1228)(149, 1298)(150, 1199)(151, 1246)(152, 1202)(153, 1304)(154, 1201)(155, 1306)(156, 1307)(157, 1203)(158, 1309)(159, 1205)(160, 1313)(161, 1314)(162, 1208)(163, 1317)(164, 1209)(165, 1210)(166, 1320)(167, 1212)(168, 1323)(169, 1324)(170, 1214)(171, 1328)(172, 1257)(173, 1330)(174, 1217)(175, 1333)(176, 1271)(177, 1221)(178, 1337)(179, 1220)(180, 1339)(181, 1340)(182, 1342)(183, 1223)(184, 1224)(185, 1276)(186, 1270)(187, 1347)(188, 1227)(189, 1350)(190, 1352)(191, 1353)(192, 1230)(193, 1231)(194, 1356)(195, 1233)(196, 1359)(197, 1285)(198, 1300)(199, 1362)(200, 1235)(201, 1364)(202, 1237)(203, 1368)(204, 1369)(205, 1240)(206, 1301)(207, 1245)(208, 1374)(209, 1242)(210, 1376)(211, 1244)(212, 1379)(213, 1381)(214, 1382)(215, 1384)(216, 1249)(217, 1312)(218, 1252)(219, 1390)(220, 1251)(221, 1392)(222, 1393)(223, 1253)(224, 1254)(225, 1396)(226, 1256)(227, 1400)(228, 1316)(229, 1402)(230, 1259)(231, 1405)(232, 1327)(233, 1263)(234, 1409)(235, 1262)(236, 1411)(237, 1412)(238, 1414)(239, 1265)(240, 1266)(241, 1332)(242, 1326)(243, 1419)(244, 1269)(245, 1422)(246, 1424)(247, 1425)(248, 1427)(249, 1273)(250, 1429)(251, 1275)(252, 1433)(253, 1434)(254, 1278)(255, 1437)(256, 1279)(257, 1280)(258, 1440)(259, 1282)(260, 1443)(261, 1444)(262, 1284)(263, 1448)(264, 1349)(265, 1450)(266, 1287)(267, 1453)(268, 1455)(269, 1290)(270, 1458)(271, 1292)(272, 1367)(273, 1295)(274, 1464)(275, 1294)(276, 1466)(277, 1467)(278, 1296)(279, 1297)(280, 1470)(281, 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2180)(1092, 2176) local type(s) :: { ( 3, 7, 3, 7 ) } Outer automorphisms :: reflexible Dual of E14.622 Transitivity :: ET+ VT+ AT Graph:: simple v = 546 e = 1092 f = 520 degree seq :: [ 4^546 ] E14.635 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^7, (T1^-2 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-1)^2, T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^3 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-2 ] Map:: polyhedral non-degenerate R = (1, 1093, 3, 1095)(2, 1094, 6, 1098)(4, 1096, 9, 1101)(5, 1097, 12, 1104)(7, 1099, 16, 1108)(8, 1100, 13, 1105)(10, 1102, 19, 1111)(11, 1103, 21, 1113)(14, 1106, 22, 1114)(15, 1107, 27, 1119)(17, 1109, 29, 1121)(18, 1110, 32, 1124)(20, 1112, 34, 1126)(23, 1115, 35, 1127)(24, 1116, 40, 1132)(25, 1117, 41, 1133)(26, 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2076)(951, 2043, 1044, 2136)(956, 2048, 1054, 2146)(957, 2049, 1009, 2101)(962, 2054, 1007, 2099)(965, 2057, 1064, 2156)(967, 2059, 1067, 2159)(968, 2060, 1037, 2129)(970, 2062, 1070, 2162)(973, 2065, 1074, 2166)(976, 2068, 1049, 2141)(977, 2069, 1047, 2139)(982, 2074, 1024, 2116)(985, 2077, 1080, 2172)(994, 2086, 1040, 2132)(995, 2087, 1063, 2155)(1003, 2095, 1076, 2168)(1004, 2096, 1028, 2120)(1005, 2097, 1027, 2119)(1018, 2110, 1081, 2173)(1019, 2111, 1060, 2152)(1023, 2115, 1088, 2180)(1031, 2123, 1042, 2134)(1034, 2126, 1085, 2177)(1043, 2135, 1091, 2183)(1046, 2138, 1072, 2164)(1053, 2145, 1062, 2154)(1068, 2160, 1086, 2178)(1078, 2170, 1092, 2184)(1082, 2174, 1090, 2182) L = (1, 1094)(2, 1097)(3, 1099)(4, 1093)(5, 1103)(6, 1105)(7, 1107)(8, 1095)(9, 1110)(10, 1096)(11, 1112)(12, 1114)(13, 1116)(14, 1098)(15, 1118)(16, 1101)(17, 1100)(18, 1123)(19, 1125)(20, 1102)(21, 1127)(22, 1129)(23, 1104)(24, 1131)(25, 1106)(26, 1122)(27, 1136)(28, 1108)(29, 1139)(30, 1109)(31, 1141)(32, 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1272)(130, 1215)(131, 1274)(132, 1185)(133, 1277)(134, 1229)(135, 1191)(136, 1281)(137, 1188)(138, 1283)(139, 1190)(140, 1286)(141, 1288)(142, 1289)(143, 1291)(144, 1293)(145, 1195)(146, 1196)(147, 1238)(148, 1228)(149, 1298)(150, 1199)(151, 1246)(152, 1202)(153, 1304)(154, 1201)(155, 1306)(156, 1307)(157, 1203)(158, 1309)(159, 1205)(160, 1313)(161, 1314)(162, 1208)(163, 1317)(164, 1209)(165, 1210)(166, 1320)(167, 1212)(168, 1323)(169, 1324)(170, 1214)(171, 1328)(172, 1257)(173, 1330)(174, 1217)(175, 1333)(176, 1271)(177, 1221)(178, 1337)(179, 1220)(180, 1339)(181, 1340)(182, 1342)(183, 1223)(184, 1224)(185, 1276)(186, 1270)(187, 1347)(188, 1227)(189, 1350)(190, 1352)(191, 1353)(192, 1230)(193, 1231)(194, 1356)(195, 1233)(196, 1359)(197, 1285)(198, 1300)(199, 1362)(200, 1235)(201, 1364)(202, 1237)(203, 1368)(204, 1369)(205, 1240)(206, 1301)(207, 1245)(208, 1374)(209, 1242)(210, 1376)(211, 1244)(212, 1379)(213, 1381)(214, 1382)(215, 1384)(216, 1249)(217, 1312)(218, 1252)(219, 1390)(220, 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1321)(312, 1322)(313, 1404)(314, 1398)(315, 1514)(316, 1325)(317, 1517)(318, 1519)(319, 1520)(320, 1522)(321, 1329)(322, 1524)(323, 1331)(324, 1528)(325, 1529)(326, 1334)(327, 1532)(328, 1335)(329, 1336)(330, 1535)(331, 1338)(332, 1538)(333, 1421)(334, 1460)(335, 1541)(336, 1341)(337, 1432)(338, 1344)(339, 1547)(340, 1343)(341, 1549)(342, 1550)(343, 1345)(344, 1346)(345, 1553)(346, 1348)(347, 1557)(348, 1371)(349, 1559)(350, 1351)(351, 1562)(352, 1447)(353, 1355)(354, 1566)(355, 1354)(356, 1568)(357, 1569)(358, 1571)(359, 1357)(360, 1358)(361, 1452)(362, 1446)(363, 1576)(364, 1360)(365, 1361)(366, 1461)(367, 1366)(368, 1582)(369, 1363)(370, 1584)(371, 1365)(372, 1587)(373, 1589)(374, 1590)(375, 1592)(376, 1370)(377, 1596)(378, 1597)(379, 1372)(380, 1373)(381, 1579)(382, 1375)(383, 1602)(384, 1603)(385, 1377)(386, 1607)(387, 1472)(388, 1609)(389, 1380)(390, 1612)(391, 1614)(392, 1383)(393, 1617)(394, 1385)(395, 1620)(396, 1622)(397, 1623)(398, 1388)(399, 1389)(400, 1626)(401, 1391)(402, 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1757)(767, 1987)(768, 1735)(769, 1777)(770, 2169)(771, 1790)(772, 2121)(773, 1990)(774, 1828)(775, 1669)(776, 2165)(777, 1703)(778, 1525)(779, 2161)(780, 1890)(781, 1905)(782, 1610)(783, 1748)(784, 1511)(785, 1808)(786, 1572)(787, 1909)(788, 1995)(789, 2047)(790, 1925)(791, 2120)(792, 1531)(793, 2110)(794, 1958)(795, 1951)(796, 1972)(797, 1797)(798, 1575)(799, 1855)(800, 2172)(801, 1937)(802, 1560)(803, 1804)(804, 1651)(805, 2168)(806, 1570)(807, 1552)(808, 1534)(809, 1843)(810, 1705)(811, 2157)(812, 1739)(813, 2174)(814, 1941)(815, 1711)(816, 2177)(817, 1567)(818, 2140)(819, 1773)(820, 2041)(821, 1850)(822, 2179)(823, 1983)(824, 2132)(825, 1845)(826, 1548)(827, 1709)(828, 2180)(829, 2069)(830, 2066)(831, 2178)(832, 1668)(833, 2097)(834, 1608)(835, 2128)(836, 1859)(837, 1768)(838, 2104)(839, 2173)(840, 1760)(841, 1675)(842, 2039)(843, 1761)(844, 1959)(845, 1714)(846, 2176)(847, 1763)(848, 1674)(849, 1729)(850, 1573)(851, 1834)(852, 2049)(853, 1765)(854, 2009)(855, 1583)(856, 2078)(857, 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2029)(949, 2163)(950, 1695)(951, 2082)(952, 1598)(953, 1673)(954, 2006)(955, 2164)(956, 2012)(957, 1678)(958, 1796)(959, 2127)(960, 1713)(961, 2073)(962, 2001)(963, 2040)(964, 1978)(965, 2105)(966, 1686)(967, 2018)(968, 1689)(969, 1743)(970, 2024)(971, 2133)(972, 1693)(973, 2118)(974, 1551)(975, 2089)(976, 2004)(977, 1698)(978, 1911)(979, 1699)(980, 1754)(981, 2055)(982, 1533)(983, 1702)(984, 1935)(985, 2028)(986, 1775)(987, 1706)(988, 2150)(989, 1707)(990, 2093)(991, 1846)(992, 2062)(993, 2126)(994, 1912)(995, 2015)(996, 1774)(997, 2084)(998, 1717)(999, 2090)(1000, 2037)(1001, 2108)(1002, 1720)(1003, 2131)(1004, 1723)(1005, 1839)(1006, 1724)(1007, 2153)(1008, 1817)(1009, 1510)(1010, 1784)(1011, 2122)(1012, 1731)(1013, 2063)(1014, 1733)(1015, 1919)(1016, 2048)(1017, 2092)(1018, 1736)(1019, 2158)(1020, 1816)(1021, 1741)(1022, 1512)(1023, 2046)(1024, 1744)(1025, 1755)(1026, 2109)(1027, 1747)(1028, 1771)(1029, 1750)(1030, 1934)(1031, 2025)(1032, 1756)(1033, 2124)(1034, 2054)(1035, 2103)(1036, 1577)(1037, 1624)(1038, 1898)(1039, 2085)(1040, 2026)(1041, 2059)(1042, 2171)(1043, 1508)(1044, 1869)(1045, 1630)(1046, 2034)(1047, 1813)(1048, 1807)(1049, 1979)(1050, 1938)(1051, 1894)(1052, 1786)(1053, 1788)(1054, 2145)(1055, 1805)(1056, 1998)(1057, 1795)(1058, 2077)(1059, 1574)(1060, 2038)(1061, 1806)(1062, 1810)(1063, 2181)(1064, 1997)(1065, 1860)(1066, 2056)(1067, 2184)(1068, 1523)(1069, 1503)(1070, 2144)(1071, 2087)(1072, 1870)(1073, 1953)(1074, 2061)(1075, 2115)(1076, 2050)(1077, 1858)(1078, 1865)(1079, 1942)(1080, 1601)(1081, 1518)(1082, 2135)(1083, 1633)(1084, 1539)(1085, 1537)(1086, 2152)(1087, 1565)(1088, 1546)(1089, 1947)(1090, 2123)(1091, 1581)(1092, 1621) local type(s) :: { ( 3, 7, 3, 7 ) } Outer automorphisms :: reflexible Dual of E14.623 Transitivity :: ET+ VT+ AT Graph:: simple v = 546 e = 1092 f = 520 degree seq :: [ 4^546 ] E14.636 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^7, (T2 * T1^3 * T2 * T1^-3)^3, T2 * T1^-2 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-3 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2 ] Map:: polyhedral non-degenerate R = (1, 1093, 3, 1095)(2, 1094, 6, 1098)(4, 1096, 9, 1101)(5, 1097, 12, 1104)(7, 1099, 16, 1108)(8, 1100, 13, 1105)(10, 1102, 19, 1111)(11, 1103, 21, 1113)(14, 1106, 22, 1114)(15, 1107, 27, 1119)(17, 1109, 29, 1121)(18, 1110, 32, 1124)(20, 1112, 34, 1126)(23, 1115, 35, 1127)(24, 1116, 40, 1132)(25, 1117, 41, 1133)(26, 1118, 43, 1135)(28, 1120, 44, 1136)(30, 1122, 48, 1140)(31, 1123, 50, 1142)(33, 1125, 53, 1145)(36, 1128, 54, 1146)(37, 1129, 58, 1150)(38, 1130, 59, 1151)(39, 1131, 61, 1153)(42, 1134, 64, 1156)(45, 1137, 65, 1157)(46, 1138, 69, 1161)(47, 1139, 71, 1163)(49, 1141, 73, 1165)(51, 1143, 74, 1166)(52, 1144, 78, 1170)(55, 1147, 82, 1174)(56, 1148, 83, 1175)(57, 1149, 85, 1177)(60, 1152, 88, 1180)(62, 1154, 89, 1181)(63, 1155, 93, 1185)(66, 1158, 72, 1164)(67, 1159, 98, 1190)(68, 1160, 99, 1191)(70, 1162, 103, 1195)(75, 1167, 106, 1198)(76, 1168, 110, 1202)(77, 1169, 111, 1203)(79, 1171, 112, 1204)(80, 1172, 116, 1208)(81, 1173, 117, 1209)(84, 1176, 120, 1212)(86, 1178, 121, 1213)(87, 1179, 125, 1217)(90, 1182, 94, 1186)(91, 1183, 129, 1221)(92, 1184, 131, 1223)(95, 1187, 135, 1227)(96, 1188, 136, 1228)(97, 1189, 138, 1230)(100, 1192, 141, 1233)(101, 1193, 107, 1199)(102, 1194, 143, 1235)(104, 1196, 144, 1236)(105, 1197, 148, 1240)(108, 1200, 152, 1244)(109, 1201, 153, 1245)(113, 1205, 156, 1248)(114, 1206, 160, 1252)(115, 1207, 161, 1253)(118, 1210, 163, 1255)(119, 1211, 167, 1259)(122, 1214, 126, 1218)(123, 1215, 171, 1263)(124, 1216, 173, 1265)(127, 1219, 177, 1269)(128, 1220, 178, 1270)(130, 1222, 181, 1273)(132, 1224, 182, 1274)(133, 1225, 186, 1278)(134, 1226, 187, 1279)(137, 1229, 190, 1282)(139, 1231, 191, 1283)(140, 1232, 195, 1287)(142, 1234, 198, 1290)(145, 1237, 199, 1291)(146, 1238, 203, 1295)(147, 1239, 204, 1296)(149, 1241, 207, 1299)(150, 1242, 208, 1300)(151, 1243, 210, 1302)(154, 1246, 213, 1305)(155, 1247, 157, 1249)(158, 1250, 218, 1310)(159, 1251, 219, 1311)(162, 1254, 222, 1314)(164, 1256, 168, 1260)(165, 1257, 227, 1319)(166, 1258, 229, 1321)(169, 1261, 233, 1325)(170, 1262, 234, 1326)(172, 1264, 237, 1329)(174, 1266, 238, 1330)(175, 1267, 242, 1334)(176, 1268, 243, 1335)(179, 1271, 246, 1338)(180, 1272, 200, 1292)(183, 1275, 248, 1340)(184, 1276, 252, 1344)(185, 1277, 253, 1345)(188, 1280, 255, 1347)(189, 1281, 259, 1351)(192, 1284, 196, 1288)(193, 1285, 263, 1355)(194, 1286, 265, 1357)(197, 1289, 268, 1360)(201, 1293, 273, 1365)(202, 1294, 274, 1366)(205, 1297, 277, 1369)(206, 1298, 280, 1372)(209, 1301, 283, 1375)(211, 1303, 284, 1376)(212, 1304, 288, 1380)(214, 1306, 291, 1383)(215, 1307, 293, 1385)(216, 1308, 294, 1386)(217, 1309, 296, 1388)(220, 1312, 299, 1391)(221, 1313, 223, 1315)(224, 1316, 303, 1395)(225, 1317, 305, 1397)(226, 1318, 306, 1398)(228, 1320, 309, 1401)(230, 1322, 310, 1402)(231, 1323, 314, 1406)(232, 1324, 315, 1407)(235, 1327, 318, 1410)(236, 1328, 249, 1341)(239, 1331, 320, 1412)(240, 1332, 324, 1416)(241, 1333, 325, 1417)(244, 1336, 327, 1419)(245, 1337, 331, 1423)(247, 1339, 334, 1426)(250, 1342, 338, 1430)(251, 1343, 339, 1431)(254, 1346, 342, 1434)(256, 1348, 260, 1352)(257, 1349, 347, 1439)(258, 1350, 349, 1441)(261, 1353, 353, 1445)(262, 1354, 354, 1446)(264, 1356, 357, 1449)(266, 1358, 358, 1450)(267, 1359, 362, 1454)(269, 1361, 363, 1455)(270, 1362, 367, 1459)(271, 1363, 368, 1460)(272, 1364, 370, 1462)(275, 1367, 373, 1465)(276, 1368, 278, 1370)(279, 1371, 377, 1469)(281, 1373, 378, 1470)(282, 1374, 382, 1474)(285, 1377, 289, 1381)(286, 1378, 386, 1478)(287, 1379, 388, 1480)(290, 1382, 391, 1483)(292, 1384, 393, 1485)(295, 1387, 396, 1488)(297, 1389, 397, 1489)(298, 1390, 401, 1493)(300, 1392, 404, 1496)(301, 1393, 406, 1498)(302, 1394, 407, 1499)(304, 1396, 410, 1502)(307, 1399, 413, 1505)(308, 1400, 321, 1413)(311, 1403, 415, 1507)(312, 1404, 419, 1511)(313, 1405, 420, 1512)(316, 1408, 422, 1514)(317, 1409, 426, 1518)(319, 1411, 429, 1521)(322, 1414, 433, 1525)(323, 1415, 434, 1526)(326, 1418, 437, 1529)(328, 1420, 332, 1424)(329, 1421, 442, 1534)(330, 1422, 444, 1536)(333, 1425, 447, 1539)(335, 1427, 450, 1542)(336, 1428, 451, 1543)(337, 1429, 453, 1545)(340, 1432, 456, 1548)(341, 1433, 343, 1435)(344, 1436, 460, 1552)(345, 1437, 462, 1554)(346, 1438, 463, 1555)(348, 1440, 466, 1558)(350, 1442, 467, 1559)(351, 1443, 470, 1562)(352, 1444, 471, 1563)(355, 1447, 474, 1566)(356, 1448, 364, 1456)(359, 1451, 476, 1568)(360, 1452, 480, 1572)(361, 1453, 481, 1573)(365, 1457, 485, 1577)(366, 1458, 487, 1579)(369, 1461, 490, 1582)(371, 1463, 491, 1583)(372, 1464, 495, 1587)(374, 1466, 498, 1590)(375, 1467, 500, 1592)(376, 1468, 501, 1593)(379, 1471, 383, 1475)(380, 1472, 506, 1598)(381, 1473, 507, 1599)(384, 1476, 510, 1602)(385, 1477, 511, 1603)(387, 1479, 514, 1606)(389, 1481, 515, 1607)(390, 1482, 519, 1611)(392, 1484, 520, 1612)(394, 1486, 523, 1615)(395, 1487, 527, 1619)(398, 1490, 402, 1494)(399, 1491, 530, 1622)(400, 1492, 532, 1624)(403, 1495, 535, 1627)(405, 1497, 537, 1629)(408, 1500, 502, 1594)(409, 1501, 416, 1508)(411, 1503, 755, 1847)(412, 1504, 759, 1851)(414, 1506, 761, 1853)(417, 1509, 764, 1856)(418, 1510, 766, 1858)(421, 1513, 469, 1561)(423, 1515, 427, 1519)(424, 1516, 737, 1829)(425, 1517, 624, 1716)(428, 1520, 771, 1863)(430, 1522, 773, 1865)(431, 1523, 774, 1866)(432, 1524, 581, 1673)(435, 1527, 778, 1870)(436, 1528, 438, 1530)(439, 1531, 681, 1773)(440, 1532, 784, 1876)(441, 1533, 786, 1878)(443, 1535, 789, 1881)(445, 1537, 791, 1883)(446, 1538, 793, 1885)(448, 1540, 794, 1886)(449, 1541, 752, 1844)(452, 1544, 464, 1556)(454, 1546, 798, 1890)(455, 1547, 642, 1734)(457, 1549, 803, 1895)(458, 1550, 805, 1897)(459, 1551, 524, 1616)(461, 1553, 740, 1832)(465, 1557, 477, 1569)(468, 1560, 812, 1904)(472, 1564, 815, 1907)(473, 1565, 749, 1841)(475, 1567, 820, 1912)(478, 1570, 823, 1915)(479, 1571, 825, 1917)(482, 1574, 827, 1919)(483, 1575, 829, 1921)(484, 1576, 830, 1922)(486, 1578, 834, 1926)(488, 1580, 836, 1928)(489, 1581, 840, 1932)(492, 1584, 496, 1588)(493, 1585, 655, 1747)(494, 1586, 673, 1765)(497, 1589, 518, 1610)(499, 1591, 539, 1631)(503, 1595, 628, 1720)(504, 1596, 847, 1939)(505, 1597, 780, 1872)(508, 1600, 851, 1943)(509, 1601, 630, 1722)(512, 1604, 855, 1947)(513, 1605, 521, 1613)(516, 1608, 858, 1950)(517, 1609, 725, 1817)(522, 1614, 775, 1867)(525, 1617, 724, 1816)(526, 1618, 569, 1661)(528, 1620, 865, 1957)(529, 1621, 867, 1959)(531, 1623, 869, 1961)(533, 1625, 870, 1962)(534, 1626, 872, 1964)(536, 1628, 873, 1965)(538, 1630, 875, 1967)(540, 1632, 747, 1839)(541, 1633, 879, 1971)(542, 1634, 881, 1973)(543, 1635, 885, 1977)(544, 1636, 887, 1979)(545, 1637, 891, 1983)(546, 1638, 892, 1984)(547, 1639, 895, 1987)(548, 1640, 897, 1989)(549, 1641, 899, 1991)(550, 1642, 902, 1994)(551, 1643, 904, 1996)(552, 1644, 906, 1998)(553, 1645, 908, 2000)(554, 1646, 909, 2001)(555, 1647, 911, 2003)(556, 1648, 915, 2007)(557, 1649, 918, 2010)(558, 1650, 920, 2012)(559, 1651, 922, 2014)(560, 1652, 925, 2017)(561, 1653, 928, 2020)(562, 1654, 839, 1931)(563, 1655, 933, 2025)(564, 1656, 934, 2026)(565, 1657, 938, 2030)(566, 1658, 941, 2033)(567, 1659, 943, 2035)(568, 1660, 945, 2037)(570, 1662, 950, 2042)(571, 1663, 952, 2044)(572, 1664, 919, 2011)(573, 1665, 822, 1914)(574, 1666, 957, 2049)(575, 1667, 959, 2051)(576, 1668, 942, 2034)(577, 1669, 962, 2054)(578, 1670, 963, 2055)(579, 1671, 878, 1970)(580, 1672, 967, 2059)(582, 1674, 971, 2063)(583, 1675, 972, 2064)(584, 1676, 974, 2066)(585, 1677, 977, 2069)(586, 1678, 903, 1995)(587, 1679, 981, 2073)(588, 1680, 982, 2074)(589, 1681, 983, 2075)(590, 1682, 927, 2019)(591, 1683, 985, 2077)(592, 1684, 986, 2078)(593, 1685, 763, 1855)(594, 1686, 990, 2082)(595, 1687, 991, 2083)(596, 1688, 896, 1988)(597, 1689, 993, 2085)(598, 1690, 758, 1850)(599, 1691, 997, 2089)(600, 1692, 999, 2091)(601, 1693, 1000, 2092)(602, 1694, 980, 2072)(603, 1695, 1003, 2095)(604, 1696, 937, 2029)(605, 1697, 1005, 2097)(606, 1698, 832, 1924)(607, 1699, 1006, 2098)(608, 1700, 864, 1956)(609, 1701, 889, 1981)(610, 1702, 1010, 2102)(611, 1703, 860, 1952)(612, 1704, 884, 1976)(613, 1705, 1015, 2107)(614, 1706, 1016, 2108)(615, 1707, 1017, 2109)(616, 1708, 914, 2006)(617, 1709, 1020, 2112)(618, 1710, 1021, 2113)(619, 1711, 776, 1868)(620, 1712, 1014, 2106)(621, 1713, 871, 1963)(622, 1714, 1009, 2101)(623, 1715, 1024, 2116)(625, 1717, 1026, 2118)(626, 1718, 1027, 2119)(627, 1719, 956, 2048)(629, 1721, 1029, 2121)(631, 1723, 880, 1972)(632, 1724, 1032, 2124)(633, 1725, 728, 1820)(634, 1726, 890, 1982)(635, 1727, 996, 2088)(636, 1728, 1037, 2129)(637, 1729, 743, 1835)(638, 1730, 1036, 2128)(639, 1731, 1039, 2131)(640, 1732, 777, 1869)(641, 1733, 1041, 2133)(643, 1735, 1042, 2134)(644, 1736, 1012, 2104)(645, 1737, 1043, 2135)(646, 1738, 1034, 2126)(647, 1739, 818, 1910)(648, 1740, 1044, 2136)(649, 1741, 989, 2081)(650, 1742, 792, 1884)(651, 1743, 1046, 2138)(652, 1744, 1047, 2139)(653, 1745, 932, 2024)(654, 1746, 1050, 2142)(656, 1748, 838, 1930)(657, 1749, 1045, 2137)(658, 1750, 807, 1899)(659, 1751, 883, 1975)(660, 1752, 1051, 2143)(661, 1753, 732, 1824)(662, 1754, 901, 1993)(663, 1755, 966, 2058)(664, 1756, 1040, 2132)(665, 1757, 1056, 2148)(666, 1758, 680, 1772)(667, 1759, 824, 1916)(668, 1760, 1053, 2145)(669, 1761, 1058, 2150)(670, 1762, 949, 2041)(671, 1763, 1060, 2152)(672, 1764, 1054, 2146)(674, 1766, 1061, 2153)(675, 1767, 833, 1925)(676, 1768, 1007, 2099)(677, 1769, 783, 1875)(678, 1770, 886, 1978)(679, 1771, 1063, 2155)(682, 1774, 1023, 2115)(683, 1775, 894, 1986)(684, 1776, 746, 1838)(685, 1777, 1028, 2120)(686, 1778, 849, 1941)(687, 1779, 1025, 2117)(688, 1780, 1033, 2125)(689, 1781, 717, 1809)(690, 1782, 1065, 2157)(691, 1783, 1062, 2154)(692, 1784, 802, 1894)(693, 1785, 772, 1864)(694, 1786, 723, 1815)(695, 1787, 1066, 2158)(696, 1788, 796, 1888)(697, 1789, 917, 2009)(698, 1790, 844, 1936)(699, 1791, 1022, 2114)(700, 1792, 828, 1920)(701, 1793, 947, 2039)(702, 1794, 1059, 2151)(703, 1795, 1070, 2162)(704, 1796, 715, 1807)(705, 1797, 841, 1933)(706, 1798, 1048, 2140)(707, 1799, 961, 2053)(708, 1800, 1073, 2165)(709, 1801, 1067, 2159)(710, 1802, 729, 1821)(711, 1803, 1074, 2166)(712, 1804, 738, 1830)(713, 1805, 1030, 2122)(714, 1806, 978, 2070)(716, 1808, 859, 1951)(718, 1810, 1001, 2093)(719, 1811, 994, 2086)(720, 1812, 893, 1985)(721, 1813, 868, 1960)(722, 1814, 1031, 2123)(726, 1818, 877, 1969)(727, 1819, 1004, 2096)(730, 1822, 1075, 2167)(731, 1823, 1076, 2168)(733, 1825, 1077, 2169)(734, 1826, 1071, 2163)(735, 1827, 940, 2032)(736, 1828, 751, 1843)(739, 1831, 987, 2079)(741, 1833, 898, 1990)(742, 1834, 788, 1880)(744, 1836, 1052, 2144)(745, 1837, 1011, 2103)(748, 1840, 1079, 2171)(750, 1842, 1081, 2173)(753, 1845, 852, 1944)(754, 1846, 1072, 2164)(756, 1848, 843, 1935)(757, 1849, 854, 1946)(760, 1852, 1082, 2174)(762, 1854, 819, 1911)(765, 1857, 795, 1887)(767, 1859, 850, 1942)(768, 1860, 808, 1900)(769, 1861, 816, 1908)(770, 1862, 813, 1905)(779, 1871, 975, 2067)(781, 1873, 787, 1879)(782, 1874, 964, 2056)(785, 1877, 905, 1997)(790, 1882, 1057, 2149)(797, 1889, 1085, 2177)(799, 1891, 845, 1937)(800, 1892, 958, 2050)(801, 1893, 1038, 2130)(804, 1896, 935, 2027)(806, 1898, 976, 2068)(809, 1901, 930, 2022)(810, 1902, 1049, 2141)(811, 1903, 876, 1968)(814, 1906, 1080, 2172)(817, 1909, 970, 2062)(821, 1913, 1078, 2170)(826, 1918, 1055, 2147)(831, 1923, 924, 2016)(835, 1927, 1008, 2100)(837, 1929, 857, 1949)(842, 1934, 1068, 2160)(846, 1938, 1083, 2175)(848, 1940, 913, 2005)(853, 1945, 951, 2043)(856, 1948, 984, 2076)(861, 1953, 1089, 2181)(862, 1954, 1090, 2182)(863, 1955, 968, 2060)(866, 1958, 916, 2008)(874, 1966, 1064, 2156)(882, 1974, 998, 2090)(888, 1980, 1002, 2094)(900, 1992, 948, 2040)(907, 1999, 969, 2061)(910, 2002, 931, 2023)(912, 2004, 1019, 2111)(921, 2013, 979, 2071)(923, 2015, 988, 2080)(926, 2018, 955, 2047)(929, 2021, 1013, 2105)(936, 2028, 953, 2045)(939, 2031, 1035, 2127)(944, 2036, 992, 2084)(946, 2038, 995, 2087)(954, 2046, 1069, 2161)(960, 2052, 965, 2057)(973, 2065, 1018, 2110)(1084, 2176, 1086, 2178)(1087, 2179, 1088, 2180)(1091, 2183, 1092, 2184) L = (1, 1094)(2, 1097)(3, 1099)(4, 1093)(5, 1103)(6, 1105)(7, 1107)(8, 1095)(9, 1110)(10, 1096)(11, 1112)(12, 1114)(13, 1116)(14, 1098)(15, 1118)(16, 1101)(17, 1100)(18, 1123)(19, 1125)(20, 1102)(21, 1127)(22, 1129)(23, 1104)(24, 1131)(25, 1106)(26, 1122)(27, 1136)(28, 1108)(29, 1139)(30, 1109)(31, 1141)(32, 1111)(33, 1144)(34, 1146)(35, 1147)(36, 1113)(37, 1149)(38, 1115)(39, 1134)(40, 1121)(41, 1155)(42, 1117)(43, 1157)(44, 1159)(45, 1119)(46, 1120)(47, 1162)(48, 1164)(49, 1138)(50, 1166)(51, 1124)(52, 1169)(53, 1126)(54, 1172)(55, 1173)(56, 1128)(57, 1152)(58, 1133)(59, 1179)(60, 1130)(61, 1181)(62, 1132)(63, 1184)(64, 1186)(65, 1187)(66, 1135)(67, 1189)(68, 1137)(69, 1193)(70, 1194)(71, 1140)(72, 1197)(73, 1198)(74, 1200)(75, 1142)(76, 1143)(77, 1168)(78, 1204)(79, 1145)(80, 1207)(81, 1176)(82, 1151)(83, 1211)(84, 1148)(85, 1213)(86, 1150)(87, 1216)(88, 1218)(89, 1219)(90, 1153)(91, 1154)(92, 1222)(93, 1156)(94, 1225)(95, 1226)(96, 1158)(97, 1192)(98, 1161)(99, 1232)(100, 1160)(101, 1234)(102, 1183)(103, 1236)(104, 1163)(105, 1239)(106, 1241)(107, 1165)(108, 1243)(109, 1167)(110, 1247)(111, 1248)(112, 1250)(113, 1170)(114, 1171)(115, 1206)(116, 1175)(117, 1255)(118, 1174)(119, 1258)(120, 1260)(121, 1261)(122, 1177)(123, 1178)(124, 1264)(125, 1180)(126, 1267)(127, 1268)(128, 1182)(129, 1272)(130, 1215)(131, 1274)(132, 1185)(133, 1277)(134, 1229)(135, 1191)(136, 1281)(137, 1188)(138, 1283)(139, 1190)(140, 1286)(141, 1288)(142, 1289)(143, 1291)(144, 1293)(145, 1195)(146, 1196)(147, 1238)(148, 1228)(149, 1298)(150, 1199)(151, 1246)(152, 1202)(153, 1304)(154, 1201)(155, 1306)(156, 1307)(157, 1203)(158, 1309)(159, 1205)(160, 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1275)(252, 1433)(253, 1434)(254, 1278)(255, 1437)(256, 1279)(257, 1280)(258, 1440)(259, 1282)(260, 1443)(261, 1444)(262, 1284)(263, 1448)(264, 1349)(265, 1450)(266, 1287)(267, 1453)(268, 1455)(269, 1290)(270, 1458)(271, 1292)(272, 1367)(273, 1295)(274, 1464)(275, 1294)(276, 1466)(277, 1467)(278, 1296)(279, 1297)(280, 1470)(281, 1299)(282, 1473)(283, 1475)(284, 1476)(285, 1302)(286, 1303)(287, 1479)(288, 1305)(289, 1482)(290, 1378)(291, 1386)(292, 1387)(293, 1311)(294, 1487)(295, 1308)(296, 1489)(297, 1310)(298, 1492)(299, 1494)(300, 1495)(301, 1497)(302, 1315)(303, 1501)(304, 1399)(305, 1319)(306, 1504)(307, 1318)(308, 1506)(309, 1507)(310, 1509)(311, 1321)(312, 1322)(313, 1404)(314, 1398)(315, 1514)(316, 1325)(317, 1517)(318, 1519)(319, 1520)(320, 1522)(321, 1329)(322, 1524)(323, 1331)(324, 1528)(325, 1529)(326, 1334)(327, 1532)(328, 1335)(329, 1336)(330, 1535)(331, 1338)(332, 1538)(333, 1421)(334, 1460)(335, 1541)(336, 1341)(337, 1432)(338, 1344)(339, 1547)(340, 1343)(341, 1549)(342, 1550)(343, 1345)(344, 1346)(345, 1553)(346, 1348)(347, 1557)(348, 1371)(349, 1559)(350, 1351)(351, 1512)(352, 1447)(353, 1355)(354, 1565)(355, 1354)(356, 1567)(357, 1568)(358, 1570)(359, 1357)(360, 1358)(361, 1452)(362, 1446)(363, 1575)(364, 1360)(365, 1361)(366, 1461)(367, 1366)(368, 1581)(369, 1363)(370, 1583)(371, 1365)(372, 1586)(373, 1588)(374, 1589)(375, 1591)(376, 1370)(377, 1595)(378, 1596)(379, 1372)(380, 1373)(381, 1578)(382, 1375)(383, 1530)(384, 1601)(385, 1377)(386, 1605)(387, 1472)(388, 1607)(389, 1380)(390, 1610)(391, 1612)(392, 1383)(393, 1615)(394, 1385)(395, 1618)(396, 1551)(397, 1620)(398, 1388)(399, 1389)(400, 1623)(401, 1391)(402, 1626)(403, 1491)(404, 1499)(405, 1500)(406, 1395)(407, 1631)(408, 1394)(409, 1632)(410, 1847)(411, 1397)(412, 1850)(413, 1576)(414, 1677)(415, 1760)(416, 1401)(417, 1855)(418, 1403)(419, 1562)(420, 1561)(421, 1406)(422, 1678)(423, 1407)(424, 1408)(425, 1645)(426, 1410)(427, 1613)(428, 1516)(429, 1543)(430, 1864)(431, 1413)(432, 1527)(433, 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1485)(525, 1486)(526, 1651)(527, 1488)(528, 1956)(529, 1490)(530, 1885)(531, 1617)(532, 1962)(533, 1493)(534, 1963)(535, 1965)(536, 1496)(537, 1967)(538, 1498)(539, 1970)(540, 1663)(541, 1957)(542, 1602)(543, 1976)(544, 1856)(545, 1982)(546, 1876)(547, 1986)(548, 1988)(549, 1525)(550, 1993)(551, 1995)(552, 1951)(553, 1531)(554, 1915)(555, 1554)(556, 2006)(557, 2009)(558, 2011)(559, 1614)(560, 2016)(561, 2019)(562, 1939)(563, 2024)(564, 2017)(565, 2029)(566, 2032)(567, 2034)(568, 1757)(569, 1897)(570, 2041)(571, 2043)(572, 1905)(573, 2001)(574, 2048)(575, 2050)(576, 1795)(577, 2053)(578, 1998)(579, 1592)(580, 1869)(581, 1991)(582, 2062)(583, 2037)(584, 1571)(585, 2068)(586, 2070)(587, 2072)(588, 1518)(589, 2040)(590, 1790)(591, 1946)(592, 2014)(593, 1979)(594, 2081)(595, 2005)(596, 1894)(597, 1987)(598, 1921)(599, 1809)(600, 2090)(601, 2066)(602, 1710)(603, 2094)(604, 1746)(605, 1818)(606, 1926)(607, 1510)(608, 1971)(609, 1542)(610, 1925)(611, 1985)(612, 2104)(613, 2106)(614, 1841)(615, 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2080)(707, 1852)(708, 1845)(709, 2010)(710, 2132)(711, 1686)(712, 1717)(713, 1731)(714, 1996)(715, 1978)(716, 2055)(717, 1958)(718, 1750)(719, 1929)(720, 2167)(721, 1942)(722, 1569)(723, 2036)(724, 2168)(725, 1590)(726, 1802)(727, 1698)(728, 2099)(729, 1649)(730, 1952)(731, 1961)(732, 2122)(733, 1820)(734, 2057)(735, 2170)(736, 1955)(737, 2172)(738, 2127)(739, 1837)(740, 2003)(741, 2158)(742, 1752)(743, 2008)(744, 1662)(745, 2149)(746, 1782)(747, 2137)(748, 1705)(749, 1566)(750, 1681)(751, 2007)(752, 1981)(753, 2173)(754, 1729)(755, 1664)(756, 2100)(757, 1938)(758, 1639)(759, 1505)(760, 1786)(761, 1866)(762, 2025)(763, 1699)(764, 1511)(765, 2151)(766, 1835)(767, 1702)(768, 1691)(769, 1761)(770, 2012)(771, 2027)(772, 2117)(773, 1526)(774, 1769)(775, 2078)(776, 1887)(777, 1833)(778, 1999)(779, 1715)(780, 1579)(781, 1539)(782, 1912)(783, 1779)(784, 1534)(785, 2169)(786, 1785)(787, 2103)(788, 1813)(789, 1974)(790, 1873)(791, 1808)(792, 2021)(793, 1878)(794, 1706)(795, 1655)(796, 1908)(797, 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2177)(980, 2045)(981, 1966)(982, 1867)(983, 1944)(984, 1854)(985, 2082)(986, 1730)(987, 1777)(988, 1685)(989, 2084)(990, 1859)(991, 2060)(992, 2174)(993, 1735)(994, 1749)(995, 1689)(996, 1918)(997, 2143)(998, 1536)(999, 2107)(1000, 1836)(1001, 1736)(1002, 1599)(1003, 1815)(1004, 1843)(1005, 2102)(1006, 2015)(1007, 1810)(1008, 1700)(1009, 1803)(1010, 1960)(1011, 1703)(1012, 1768)(1013, 2175)(1014, 2052)(1015, 2031)(1016, 2148)(1017, 1891)(1018, 2165)(1019, 1624)(1020, 2049)(1021, 2073)(1022, 1564)(1023, 2110)(1024, 1783)(1025, 1523)(1026, 2124)(1027, 1884)(1028, 1784)(1029, 1927)(1030, 1871)(1031, 1722)(1032, 1834)(1033, 1725)(1034, 1805)(1035, 2171)(1036, 2076)(1037, 2162)(1038, 1545)(1039, 1753)(1040, 1936)(1041, 2089)(1042, 2038)(1043, 2086)(1044, 2155)(1045, 1806)(1046, 1917)(1047, 1826)(1048, 1744)(1049, 2152)(1050, 2030)(1051, 1771)(1052, 2141)(1053, 1858)(1054, 1861)(1055, 2157)(1056, 2064)(1057, 1563)(1058, 1788)(1059, 2142)(1060, 2059)(1061, 2136)(1062, 2067)(1063, 1880)(1064, 2160)(1065, 2118)(1066, 2113)(1067, 2163)(1068, 2133)(1069, 1853)(1070, 2035)(1071, 1798)(1072, 2112)(1073, 2042)(1074, 2153)(1075, 2119)(1076, 2140)(1077, 2091)(1078, 1888)(1079, 2097)(1080, 2125)(1081, 2093)(1082, 2054)(1083, 2077)(1084, 2051)(1085, 2063)(1086, 2139)(1087, 2069)(1088, 2131)(1089, 2095)(1090, 2150)(1091, 2109)(1092, 2075) local type(s) :: { ( 3, 7, 3, 7 ) } Outer automorphisms :: reflexible Dual of E14.624 Transitivity :: ET+ VT+ AT Graph:: simple v = 546 e = 1092 f = 520 degree seq :: [ 4^546 ] E14.637 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^7, (Y3 * Y2^-1)^7, (Y1 * Y2 * Y1 * Y2^-1)^7, (Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1)^2 ] Map:: R = (1, 1093, 2, 1094)(3, 1095, 7, 1099)(4, 1096, 8, 1100)(5, 1097, 9, 1101)(6, 1098, 10, 1102)(11, 1103, 19, 1111)(12, 1104, 20, 1112)(13, 1105, 21, 1113)(14, 1106, 22, 1114)(15, 1107, 23, 1115)(16, 1108, 24, 1116)(17, 1109, 25, 1117)(18, 1110, 26, 1118)(27, 1119, 43, 1135)(28, 1120, 44, 1136)(29, 1121, 45, 1137)(30, 1122, 46, 1138)(31, 1123, 47, 1139)(32, 1124, 48, 1140)(33, 1125, 49, 1141)(34, 1126, 50, 1142)(35, 1127, 51, 1143)(36, 1128, 52, 1144)(37, 1129, 53, 1145)(38, 1130, 54, 1146)(39, 1131, 55, 1147)(40, 1132, 56, 1148)(41, 1133, 57, 1149)(42, 1134, 58, 1150)(59, 1151, 85, 1177)(60, 1152, 86, 1178)(61, 1153, 87, 1179)(62, 1154, 88, 1180)(63, 1155, 89, 1181)(64, 1156, 90, 1182)(65, 1157, 66, 1158)(67, 1159, 91, 1183)(68, 1160, 92, 1184)(69, 1161, 93, 1185)(70, 1162, 94, 1186)(71, 1163, 95, 1187)(72, 1164, 96, 1188)(73, 1165, 97, 1189)(74, 1166, 98, 1190)(75, 1167, 99, 1191)(76, 1168, 100, 1192)(77, 1169, 101, 1193)(78, 1170, 79, 1171)(80, 1172, 102, 1194)(81, 1173, 103, 1195)(82, 1174, 104, 1196)(83, 1175, 105, 1197)(84, 1176, 106, 1198)(107, 1199, 151, 1243)(108, 1200, 152, 1244)(109, 1201, 153, 1245)(110, 1202, 154, 1246)(111, 1203, 155, 1247)(112, 1204, 113, 1205)(114, 1206, 156, 1248)(115, 1207, 157, 1249)(116, 1208, 158, 1250)(117, 1209, 159, 1251)(118, 1210, 160, 1252)(119, 1211, 161, 1253)(120, 1212, 162, 1254)(121, 1213, 163, 1255)(122, 1214, 164, 1256)(123, 1215, 165, 1257)(124, 1216, 125, 1217)(126, 1218, 166, 1258)(127, 1219, 167, 1259)(128, 1220, 168, 1260)(129, 1221, 169, 1261)(130, 1222, 170, 1262)(131, 1223, 171, 1263)(132, 1224, 172, 1264)(133, 1225, 173, 1265)(134, 1226, 135, 1227)(136, 1228, 174, 1266)(137, 1229, 175, 1267)(138, 1230, 176, 1268)(139, 1231, 177, 1269)(140, 1232, 178, 1270)(141, 1233, 179, 1271)(142, 1234, 180, 1272)(143, 1235, 181, 1273)(144, 1236, 182, 1274)(145, 1237, 183, 1275)(146, 1238, 147, 1239)(148, 1240, 184, 1276)(149, 1241, 185, 1277)(150, 1242, 186, 1278)(187, 1279, 258, 1350)(188, 1280, 259, 1351)(189, 1281, 260, 1352)(190, 1282, 191, 1283)(192, 1284, 261, 1353)(193, 1285, 262, 1354)(194, 1286, 263, 1355)(195, 1287, 264, 1356)(196, 1288, 265, 1357)(197, 1289, 266, 1358)(198, 1290, 267, 1359)(199, 1291, 268, 1360)(200, 1292, 269, 1361)(201, 1293, 270, 1362)(202, 1294, 203, 1295)(204, 1296, 271, 1363)(205, 1297, 272, 1364)(206, 1298, 273, 1365)(207, 1299, 274, 1366)(208, 1300, 275, 1367)(209, 1301, 276, 1368)(210, 1302, 211, 1303)(212, 1304, 277, 1369)(213, 1305, 278, 1370)(214, 1306, 279, 1371)(215, 1307, 280, 1372)(216, 1308, 281, 1373)(217, 1309, 282, 1374)(218, 1310, 283, 1375)(219, 1311, 284, 1376)(220, 1312, 285, 1377)(221, 1313, 286, 1378)(222, 1314, 223, 1315)(224, 1316, 287, 1379)(225, 1317, 288, 1380)(226, 1318, 227, 1319)(228, 1320, 406, 1498)(229, 1321, 466, 1558)(230, 1322, 468, 1560)(231, 1323, 444, 1536)(232, 1324, 469, 1561)(233, 1325, 470, 1562)(234, 1326, 472, 1564)(235, 1327, 474, 1566)(236, 1328, 475, 1567)(237, 1329, 476, 1568)(238, 1330, 239, 1331)(240, 1332, 479, 1571)(241, 1333, 481, 1573)(242, 1334, 483, 1575)(243, 1335, 484, 1576)(244, 1336, 485, 1577)(245, 1337, 487, 1579)(246, 1338, 247, 1339)(248, 1340, 347, 1439)(249, 1341, 491, 1583)(250, 1342, 493, 1585)(251, 1343, 461, 1553)(252, 1344, 494, 1586)(253, 1345, 496, 1588)(254, 1346, 498, 1590)(255, 1347, 500, 1592)(256, 1348, 501, 1593)(257, 1349, 452, 1544)(289, 1381, 551, 1643)(290, 1382, 552, 1644)(291, 1383, 553, 1645)(292, 1384, 554, 1646)(293, 1385, 555, 1647)(294, 1386, 556, 1648)(295, 1387, 557, 1649)(296, 1388, 560, 1652)(297, 1389, 563, 1655)(298, 1390, 566, 1658)(299, 1391, 569, 1661)(300, 1392, 570, 1662)(301, 1393, 571, 1663)(302, 1394, 572, 1664)(303, 1395, 573, 1665)(304, 1396, 574, 1666)(305, 1397, 575, 1667)(306, 1398, 578, 1670)(307, 1399, 581, 1673)(308, 1400, 584, 1676)(309, 1401, 586, 1678)(310, 1402, 589, 1681)(311, 1403, 592, 1684)(312, 1404, 595, 1687)(313, 1405, 597, 1689)(314, 1406, 598, 1690)(315, 1407, 495, 1587)(316, 1408, 473, 1565)(317, 1409, 600, 1692)(318, 1410, 601, 1693)(319, 1411, 603, 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1458, 704, 1796)(367, 1459, 707, 1799)(368, 1460, 710, 1802)(369, 1461, 713, 1805)(370, 1462, 716, 1808)(371, 1463, 720, 1812)(372, 1464, 723, 1815)(373, 1465, 727, 1819)(374, 1466, 728, 1820)(375, 1467, 730, 1822)(376, 1468, 733, 1825)(377, 1469, 736, 1828)(378, 1470, 739, 1831)(379, 1471, 743, 1835)(380, 1472, 393, 1485)(381, 1473, 747, 1839)(382, 1474, 748, 1840)(383, 1475, 749, 1841)(384, 1476, 679, 1771)(385, 1477, 754, 1846)(387, 1479, 757, 1849)(389, 1481, 671, 1763)(390, 1482, 759, 1851)(391, 1483, 755, 1847)(392, 1484, 763, 1855)(394, 1486, 764, 1856)(395, 1487, 765, 1857)(396, 1488, 766, 1858)(397, 1489, 530, 1622)(398, 1490, 770, 1862)(400, 1492, 772, 1864)(402, 1494, 520, 1612)(403, 1495, 774, 1866)(404, 1496, 771, 1863)(405, 1497, 777, 1869)(407, 1499, 768, 1860)(408, 1500, 783, 1875)(409, 1501, 786, 1878)(410, 1502, 790, 1882)(411, 1503, 724, 1816)(412, 1504, 792, 1884)(413, 1505, 795, 1887)(414, 1506, 798, 1890)(415, 1507, 675, 1767)(416, 1508, 804, 1896)(417, 1509, 807, 1899)(418, 1510, 811, 1903)(419, 1511, 814, 1906)(420, 1512, 787, 1879)(421, 1513, 817, 1909)(422, 1514, 819, 1911)(423, 1515, 822, 1914)(424, 1516, 752, 1844)(425, 1517, 827, 1919)(426, 1518, 830, 1922)(427, 1519, 833, 1925)(428, 1520, 691, 1783)(429, 1521, 835, 1927)(430, 1522, 838, 1930)(431, 1523, 842, 1934)(432, 1524, 660, 1752)(433, 1525, 799, 1891)(434, 1526, 848, 1940)(435, 1527, 852, 1944)(436, 1528, 789, 1881)(437, 1529, 831, 1923)(438, 1530, 857, 1949)(439, 1531, 801, 1893)(440, 1532, 860, 1952)(441, 1533, 837, 1929)(442, 1534, 862, 1954)(443, 1535, 863, 1955)(445, 1537, 866, 1958)(446, 1538, 867, 1959)(448, 1540, 545, 1637)(449, 1541, 869, 1961)(450, 1542, 732, 1824)(451, 1543, 872, 1964)(453, 1545, 874, 1966)(454, 1546, 875, 1967)(455, 1547, 876, 1968)(456, 1548, 505, 1597)(457, 1549, 879, 1971)(459, 1551, 880, 1972)(462, 1554, 883, 1975)(463, 1555, 794, 1886)(464, 1556, 886, 1978)(465, 1557, 526, 1618)(467, 1559, 890, 1982)(471, 1563, 896, 1988)(477, 1569, 653, 1745)(478, 1570, 511, 1603)(480, 1572, 700, 1792)(482, 1574, 910, 2002)(486, 1578, 915, 2007)(488, 1580, 537, 1629)(489, 1581, 916, 2008)(490, 1582, 549, 1641)(492, 1584, 921, 2013)(497, 1589, 927, 2019)(502, 1594, 932, 2024)(503, 1595, 738, 1830)(504, 1596, 901, 1993)(506, 1598, 708, 1800)(507, 1599, 568, 1660)(508, 1600, 940, 2032)(509, 1601, 941, 2033)(510, 1602, 944, 2036)(512, 1604, 634, 1726)(513, 1605, 711, 1803)(514, 1606, 823, 1915)(515, 1607, 779, 1871)(516, 1608, 858, 1950)(517, 1609, 952, 2044)(518, 1610, 815, 1907)(519, 1611, 725, 1817)(521, 1613, 933, 2025)(522, 1614, 689, 1781)(523, 1615, 961, 2053)(524, 1616, 664, 1756)(525, 1617, 824, 1916)(527, 1619, 881, 1973)(528, 1620, 929, 2021)(529, 1621, 800, 1892)(531, 1623, 644, 1736)(532, 1624, 580, 1672)(533, 1625, 854, 1946)(534, 1626, 970, 2062)(535, 1627, 972, 2064)(536, 1628, 973, 2065)(538, 1630, 647, 1739)(539, 1631, 737, 1829)(540, 1632, 873, 1965)(541, 1633, 962, 2054)(542, 1634, 912, 2004)(543, 1635, 726, 1818)(544, 1636, 788, 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1938)(826, 1918, 1003, 2095)(836, 1928, 1064, 2156)(841, 1933, 1051, 2143)(844, 1936, 885, 1977)(845, 1937, 996, 2088)(851, 1943, 968, 2060)(853, 1945, 1087, 2179)(855, 1947, 899, 1991)(856, 1948, 1047, 2139)(861, 1953, 892, 1984)(864, 1956, 1077, 2169)(868, 1960, 949, 2041)(871, 1963, 975, 2067)(877, 1969, 1052, 2144)(882, 1974, 978, 2070)(887, 1979, 1072, 2164)(888, 1980, 1034, 2126)(891, 1983, 1028, 2120)(893, 1985, 1010, 2102)(894, 1986, 938, 2030)(895, 1987, 1086, 2178)(897, 1989, 981, 2073)(898, 1990, 1081, 2173)(900, 1992, 994, 2086)(902, 1994, 1071, 2163)(903, 1995, 1038, 2130)(905, 1997, 1030, 2122)(906, 1998, 1091, 2183)(907, 1999, 1053, 2145)(908, 2000, 1022, 2114)(909, 2001, 1068, 2160)(911, 2003, 928, 2020)(913, 2005, 1024, 2116)(914, 2006, 1046, 2138)(917, 2009, 1048, 2140)(919, 2011, 1040, 2132)(920, 2012, 963, 2055)(922, 2014, 1066, 2158)(923, 2015, 1002, 2094)(925, 2017, 984, 2076)(930, 2022, 1092, 2184)(931, 2023, 990, 2082)(935, 2027, 1018, 2110)(936, 2028, 1055, 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3473, 2382, 3474)(2341, 3433, 2383, 3475, 2384, 3476)(2342, 3434, 2385, 3477, 2386, 3478)(2343, 3435, 2387, 3479, 2388, 3480)(2344, 3436, 2389, 3481, 2390, 3482)(2345, 3437, 2391, 3483, 2392, 3484)(2346, 3438, 2393, 3485, 2394, 3486)(2347, 3439, 2395, 3487, 2396, 3488)(2348, 3440, 2397, 3489, 2398, 3490)(2349, 3441, 2399, 3491, 2400, 3492)(2350, 3442, 2401, 3493, 2402, 3494)(2351, 3443, 2403, 3495, 2404, 3496)(2352, 3444, 2405, 3497, 2406, 3498)(2353, 3445, 2407, 3499, 2408, 3500)(2354, 3446, 2409, 3501, 2410, 3502)(2355, 3447, 2411, 3503, 2412, 3504)(2356, 3448, 2413, 3505, 2414, 3506)(2357, 3449, 2415, 3507, 2416, 3508)(2358, 3450, 2417, 3509, 2418, 3510)(2359, 3451, 2419, 3511, 2420, 3512)(2360, 3452, 2421, 3513, 2422, 3514)(2361, 3453, 2423, 3515, 2424, 3516)(2362, 3454, 2425, 3517, 2426, 3518)(2363, 3455, 2427, 3519, 2428, 3520)(2364, 3456, 2429, 3521, 2430, 3522)(2365, 3457, 2431, 3523, 2432, 3524)(2366, 3458, 2433, 3525, 2434, 3526)(2367, 3459, 2435, 3527, 2436, 3528)(2368, 3460, 2437, 3529, 2438, 3530)(2369, 3461, 2439, 3531, 2440, 3532)(2370, 3462, 2441, 3533, 2442, 3534)(2443, 3535, 2687, 3779, 3119, 4211)(2444, 3536, 2689, 3781, 2611, 3703)(2445, 3537, 2691, 3783, 3122, 4214)(2446, 3538, 2624, 3716, 3045, 4137)(2447, 3539, 2694, 3786, 2754, 3846)(2448, 3540, 2484, 3576, 2536, 3628)(2449, 3541, 2697, 3789, 3132, 4224)(2450, 3542, 2496, 3588, 2780, 3872)(2451, 3543, 2700, 3792, 2941, 4033)(2452, 3544, 2571, 3663, 2642, 3734)(2453, 3545, 2703, 3795, 3138, 4230)(2454, 3546, 2704, 3796, 3140, 4232)(2455, 3547, 2706, 3798, 3143, 4235)(2456, 3548, 2708, 3800, 2557, 3649)(2457, 3549, 2710, 3802, 2458, 3550)(2459, 3551, 2713, 3805, 3149, 4241)(2460, 3552, 2714, 3806, 2688, 3780)(2461, 3553, 2716, 3808, 2666, 3758)(2462, 3554, 2711, 3803, 3147, 4239)(2463, 3555, 2719, 3811, 2739, 3831)(2464, 3556, 2477, 3569, 2565, 3657)(2465, 3557, 2722, 3814, 3161, 4253)(2466, 3558, 2512, 3604, 2806, 3898)(2467, 3559, 2725, 3817, 2851, 3943)(2468, 3560, 2534, 3626, 2583, 3675)(2469, 3561, 2728, 3820, 3167, 4259)(2470, 3562, 2729, 3821, 3168, 4260)(2471, 3563, 2731, 3823, 3092, 4184)(2472, 3564, 2733, 3825, 2594, 3686)(2473, 3565, 2637, 3729, 2632, 3724)(2474, 3566, 2670, 3762, 2661, 3753)(2475, 3567, 2578, 3670, 2645, 3737)(2476, 3568, 2625, 3717, 2586, 3678)(2478, 3570, 2647, 3739, 2573, 3665)(2479, 3571, 2742, 3834, 2743, 3835)(2480, 3572, 2745, 3837, 2746, 3838)(2481, 3573, 2748, 3840, 2749, 3841)(2482, 3574, 2751, 3843, 2752, 3844)(2483, 3575, 2588, 3680, 2537, 3629)(2485, 3577, 2634, 3726, 2566, 3658)(2486, 3578, 2575, 3667, 2527, 3619)(2487, 3579, 2526, 3618, 2628, 3720)(2488, 3580, 2664, 3756, 2579, 3671)(2489, 3581, 2760, 3852, 2761, 3853)(2490, 3582, 2763, 3855, 2764, 3856)(2491, 3583, 2766, 3858, 2767, 3859)(2492, 3584, 2769, 3861, 2654, 3746)(2493, 3585, 2771, 3863, 2772, 3864)(2494, 3586, 2774, 3866, 2775, 3867)(2495, 3587, 2777, 3869, 2778, 3870)(2497, 3589, 2539, 3631, 2533, 3625)(2498, 3590, 2532, 3624, 2640, 3732)(2499, 3591, 2783, 3875, 2626, 3718)(2500, 3592, 2568, 3660, 2507, 3599)(2501, 3593, 2506, 3598, 2581, 3673)(2502, 3594, 2786, 3878, 2638, 3730)(2503, 3595, 2529, 3621, 2523, 3615)(2504, 3596, 2541, 3633, 2674, 3766)(2505, 3597, 2790, 3882, 2648, 3740)(2508, 3600, 2795, 3887, 2672, 3764)(2509, 3601, 2797, 3889, 2798, 3890)(2510, 3602, 2800, 3892, 2801, 3893)(2511, 3603, 2803, 3895, 2804, 3896)(2513, 3605, 2808, 3900, 2809, 3901)(2514, 3606, 2811, 3903, 2812, 3904)(2515, 3607, 2814, 3906, 2815, 3907)(2516, 3608, 2817, 3909, 2818, 3910)(2517, 3609, 2820, 3912, 2821, 3913)(2518, 3610, 2823, 3915, 2824, 3916)(2519, 3611, 2826, 3918, 2680, 3772)(2520, 3612, 2828, 3920, 2829, 3921)(2521, 3613, 2831, 3923, 2832, 3924)(2522, 3614, 2834, 3926, 2835, 3927)(2524, 3616, 2570, 3662, 2684, 3776)(2525, 3617, 2839, 3931, 2589, 3681)(2528, 3620, 2843, 3935, 2844, 3936)(2530, 3622, 2577, 3669, 2848, 3940)(2531, 3623, 2792, 3884, 2635, 3727)(2535, 3627, 2852, 3944, 2576, 3668)(2538, 3630, 2857, 3949, 2859, 3951)(2540, 3632, 2564, 3656, 2864, 3956)(2542, 3634, 2866, 3958, 2867, 3959)(2543, 3635, 2869, 3961, 2870, 3962)(2544, 3636, 2872, 3964, 2873, 3965)(2545, 3637, 2875, 3967, 2876, 3968)(2546, 3638, 2665, 3757, 2878, 3970)(2547, 3639, 2880, 3972, 2881, 3973)(2548, 3640, 2883, 3975, 2884, 3976)(2549, 3641, 2886, 3978, 2887, 3979)(2550, 3642, 2889, 3981, 2890, 3982)(2551, 3643, 2892, 3984, 2893, 3985)(2552, 3644, 2895, 3987, 2896, 3988)(2553, 3645, 2898, 3990, 2899, 3991)(2554, 3646, 2901, 3993, 2903, 3995)(2555, 3647, 2905, 3997, 2906, 3998)(2556, 3648, 2908, 4000, 2910, 4002)(2558, 3650, 2709, 3801, 2913, 4005)(2559, 3651, 2915, 4007, 2916, 4008)(2560, 3652, 2918, 4010, 2705, 3797)(2561, 3653, 2921, 4013, 2922, 4014)(2562, 3654, 2924, 4016, 2926, 4018)(2563, 3655, 2928, 4020, 2929, 4021)(2567, 3659, 2934, 4026, 2936, 4028)(2569, 3661, 2572, 3664, 2940, 4032)(2574, 3666, 2944, 4036, 2923, 4015)(2580, 3672, 2946, 4038, 2952, 4044)(2582, 3674, 2585, 3677, 2930, 4022)(2584, 3676, 2679, 3771, 2658, 3750)(2587, 3679, 2959, 4051, 2891, 3983)(2590, 3682, 2788, 3880, 2963, 4055)(2591, 3683, 2964, 4056, 2966, 4058)(2592, 3684, 2968, 4060, 2969, 4061)(2593, 3685, 2971, 4063, 2973, 4065)(2595, 3687, 2734, 3826, 2975, 4067)(2596, 3688, 2977, 4069, 2978, 4070)(2597, 3689, 2980, 4072, 2730, 3822)(2598, 3690, 2983, 4075, 2984, 4076)(2599, 3691, 2985, 4077, 2987, 4079)(2600, 3692, 2989, 4081, 2990, 4082)(2601, 3693, 2992, 4084, 2994, 4086)(2602, 3694, 2996, 4088, 2997, 4089)(2603, 3695, 2912, 4004, 2999, 4091)(2604, 3696, 2623, 3715, 3000, 4092)(2605, 3697, 3002, 4094, 2955, 4047)(2606, 3698, 3004, 4096, 2621, 3713)(2607, 3699, 3007, 4099, 2650, 3742)(2608, 3700, 3008, 4100, 3010, 4102)(2609, 3701, 3012, 4104, 3013, 4105)(2610, 3702, 3015, 4107, 2998, 4090)(2612, 3704, 2690, 3782, 2715, 3807)(2613, 3705, 3020, 4112, 3021, 4113)(2614, 3706, 3023, 4115, 3025, 4117)(2615, 3707, 2988, 4080, 3027, 4119)(2616, 3708, 3003, 4095, 3029, 4121)(2617, 3709, 3030, 4122, 3031, 4123)(2618, 3710, 3033, 4125, 3035, 4127)(2619, 3711, 3037, 4129, 3038, 4130)(2620, 3712, 2879, 3971, 3039, 4131)(2622, 3714, 3042, 4134, 2939, 4031)(2627, 3719, 2861, 3953, 2991, 4083)(2629, 3721, 2631, 3723, 2942, 4034)(2630, 3722, 2785, 3877, 3044, 4136)(2633, 3725, 3054, 4146, 2827, 3919)(2636, 3728, 2837, 3929, 3057, 4149)(2639, 3731, 2937, 4029, 2900, 3992)(2641, 3733, 2644, 3736, 2853, 3945)(2643, 3735, 2758, 3850, 3065, 4157)(2646, 3738, 3068, 4160, 2874, 3966)(2649, 3741, 2846, 3938, 3032, 4124)(2651, 3743, 2657, 3749, 2957, 4049)(2652, 3744, 3075, 4167, 2757, 3849)(2653, 3745, 2902, 3994, 3077, 4169)(2655, 3747, 2794, 3886, 3006, 4098)(2656, 3748, 3018, 4110, 2956, 4048)(2659, 3751, 2909, 4001, 3084, 4176)(2660, 3752, 2855, 3947, 3086, 4178)(2662, 3754, 3088, 4180, 2807, 3899)(2663, 3755, 2791, 3883, 3091, 4183)(2667, 3759, 3047, 4139, 2668, 3760)(2669, 3761, 2858, 3950, 3097, 4189)(2671, 3763, 2863, 3955, 2732, 3824)(2673, 3765, 2953, 4045, 2868, 3960)(2675, 3767, 3095, 4187, 3104, 4196)(2676, 3768, 2683, 3775, 2840, 3932)(2677, 3769, 3106, 4198, 2737, 3829)(2678, 3770, 2919, 4011, 3087, 4179)(2681, 3773, 2755, 3847, 3112, 4204)(2682, 3774, 3040, 4132, 2838, 3930)(2685, 3777, 2925, 4017, 3115, 4207)(2686, 3778, 3117, 4209, 2907, 3999)(2692, 3784, 3103, 4195, 3058, 4150)(2693, 3785, 3126, 4218, 3071, 4163)(2695, 3787, 3011, 4103, 3129, 4221)(2696, 3788, 2917, 4009, 3131, 4223)(2698, 3790, 3016, 4108, 3133, 4225)(2699, 3791, 3134, 4226, 3080, 4172)(2701, 3793, 3093, 4185, 3019, 4111)(2702, 3794, 2897, 3989, 3137, 4229)(2707, 3799, 3146, 4238, 2860, 3952)(2712, 3804, 3148, 4240, 2970, 4062)(2717, 3809, 3153, 4245, 2948, 4040)(2718, 3810, 3099, 4191, 2962, 4054)(2720, 3812, 2927, 4019, 3158, 4250)(2721, 3813, 2979, 4071, 3160, 4252)(2723, 3815, 3118, 4210, 3162, 4254)(2724, 3816, 3043, 4135, 3164, 4256)(2726, 3818, 3165, 4257, 3124, 4216)(2727, 3819, 2833, 3925, 3166, 4258)(2735, 3827, 3173, 4265, 3079, 4171)(2736, 3828, 3174, 4266, 3175, 4267)(2738, 3830, 3176, 4268, 3177, 4269)(2740, 3832, 3178, 4270, 3144, 4236)(2741, 3833, 3179, 4271, 3180, 4272)(2744, 3836, 3181, 4273, 3182, 4274)(2747, 3839, 3183, 4275, 3110, 4202)(2750, 3842, 3184, 4276, 3185, 4277)(2753, 3845, 3082, 4174, 3171, 4263)(2756, 3848, 3052, 4144, 3120, 4212)(2759, 3851, 3186, 4278, 3187, 4279)(2762, 3854, 3189, 4281, 3190, 4282)(2765, 3857, 3191, 4283, 3192, 4284)(2768, 3860, 3194, 4286, 3100, 4192)(2770, 3862, 3157, 4249, 3195, 4287)(2773, 3865, 3196, 4288, 3197, 4289)(2776, 3868, 3198, 4290, 3199, 4291)(2779, 3871, 3141, 4233, 3060, 4152)(2781, 3873, 3066, 4158, 3150, 4242)(2782, 3874, 3202, 4294, 3188, 4280)(2784, 3876, 3203, 4295, 3193, 4285)(2787, 3879, 3114, 4206, 3204, 4296)(2789, 3881, 3206, 4298, 3170, 4262)(2793, 3885, 3208, 4300, 3200, 4292)(2796, 3888, 3026, 4118, 3207, 4299)(2799, 3891, 3209, 4301, 3210, 4302)(2802, 3894, 3211, 4303, 3102, 4194)(2805, 3897, 3169, 4261, 2950, 4042)(2810, 3902, 3214, 4306, 3215, 4307)(2813, 3905, 3216, 4308, 3073, 4165)(2816, 3908, 2982, 4074, 3152, 4244)(2819, 3911, 3219, 4311, 3220, 4312)(2822, 3914, 3221, 4313, 3062, 4154)(2825, 3917, 3222, 4314, 2933, 4025)(2830, 3922, 3159, 4251, 3226, 4318)(2836, 3928, 3228, 4320, 3227, 4319)(2841, 3933, 3229, 4321, 3212, 4304)(2842, 3934, 2920, 4012, 3123, 4215)(2845, 3937, 3090, 4182, 3231, 4323)(2847, 3939, 3233, 4325, 3142, 4234)(2849, 3941, 3139, 4231, 2931, 4023)(2850, 3942, 3234, 4326, 3217, 4309)(2854, 3946, 3230, 4322, 3128, 4220)(2856, 3948, 2888, 3980, 3205, 4297)(2862, 3954, 3237, 4329, 3225, 4317)(2865, 3957, 3238, 4330, 3083, 4175)(2871, 3963, 3232, 4324, 2943, 4035)(2877, 3969, 3028, 4120, 3242, 4334)(2882, 3974, 3244, 4336, 3245, 4337)(2885, 3977, 3246, 4338, 3049, 4141)(2894, 3986, 3130, 4222, 3107, 4199)(2904, 3996, 3236, 4328, 2958, 4050)(2911, 4003, 2986, 4078, 3251, 4343)(2914, 4006, 3252, 4344, 3253, 4345)(2932, 4024, 3218, 4310, 3156, 4248)(2935, 4027, 3257, 4349, 3201, 4293)(2938, 4030, 3105, 4197, 3074, 4166)(2945, 4037, 3260, 4352, 3213, 4305)(2947, 4039, 3243, 4335, 3239, 4331)(2949, 4041, 3125, 4217, 3250, 4342)(2951, 4043, 3098, 4190, 3127, 4219)(2954, 4046, 3063, 4155, 3050, 4142)(2960, 4052, 3262, 4354, 3223, 4315)(2961, 4053, 3241, 4333, 3249, 4341)(2965, 4057, 3263, 4355, 3017, 4109)(2967, 4059, 3258, 4350, 3053, 4145)(2972, 4064, 3265, 4357, 3076, 4168)(2974, 4066, 3009, 4101, 3266, 4358)(2976, 4068, 3081, 4173, 3254, 4346)(2981, 4073, 3101, 4193, 3247, 4339)(2993, 4085, 3268, 4360, 3085, 4177)(2995, 4087, 3261, 4353, 3067, 4159)(3001, 4093, 3271, 4363, 3267, 4359)(3005, 4097, 3272, 4364, 3109, 4201)(3014, 4106, 3096, 4188, 3235, 4327)(3022, 4114, 3270, 4362, 3059, 4151)(3024, 4116, 3061, 4153, 3255, 4347)(3034, 4126, 3274, 4366, 3172, 4264)(3036, 4128, 3256, 4348, 3116, 4208)(3041, 4133, 3135, 4227, 3273, 4365)(3046, 4138, 3154, 4246, 3264, 4356)(3048, 4140, 3072, 4164, 3155, 4247)(3051, 4143, 3078, 4170, 3121, 4213)(3055, 4147, 3275, 4367, 3240, 4332)(3056, 4148, 3248, 4340, 3111, 4203)(3064, 4156, 3094, 4186, 3151, 4243)(3069, 4161, 3276, 4368, 3108, 4200)(3070, 4162, 3224, 4316, 3269, 4361)(3089, 4181, 3145, 4237, 3163, 4255)(3113, 4205, 3136, 4228, 3259, 4351) L = (1, 2186)(2, 2185)(3, 2191)(4, 2192)(5, 2193)(6, 2194)(7, 2187)(8, 2188)(9, 2189)(10, 2190)(11, 2203)(12, 2204)(13, 2205)(14, 2206)(15, 2207)(16, 2208)(17, 2209)(18, 2210)(19, 2195)(20, 2196)(21, 2197)(22, 2198)(23, 2199)(24, 2200)(25, 2201)(26, 2202)(27, 2227)(28, 2228)(29, 2229)(30, 2230)(31, 2231)(32, 2232)(33, 2233)(34, 2234)(35, 2235)(36, 2236)(37, 2237)(38, 2238)(39, 2239)(40, 2240)(41, 2241)(42, 2242)(43, 2211)(44, 2212)(45, 2213)(46, 2214)(47, 2215)(48, 2216)(49, 2217)(50, 2218)(51, 2219)(52, 2220)(53, 2221)(54, 2222)(55, 2223)(56, 2224)(57, 2225)(58, 2226)(59, 2269)(60, 2270)(61, 2271)(62, 2272)(63, 2273)(64, 2274)(65, 2250)(66, 2249)(67, 2275)(68, 2276)(69, 2277)(70, 2278)(71, 2279)(72, 2280)(73, 2281)(74, 2282)(75, 2283)(76, 2284)(77, 2285)(78, 2263)(79, 2262)(80, 2286)(81, 2287)(82, 2288)(83, 2289)(84, 2290)(85, 2243)(86, 2244)(87, 2245)(88, 2246)(89, 2247)(90, 2248)(91, 2251)(92, 2252)(93, 2253)(94, 2254)(95, 2255)(96, 2256)(97, 2257)(98, 2258)(99, 2259)(100, 2260)(101, 2261)(102, 2264)(103, 2265)(104, 2266)(105, 2267)(106, 2268)(107, 2335)(108, 2336)(109, 2337)(110, 2338)(111, 2339)(112, 2297)(113, 2296)(114, 2340)(115, 2341)(116, 2342)(117, 2343)(118, 2344)(119, 2345)(120, 2346)(121, 2347)(122, 2348)(123, 2349)(124, 2309)(125, 2308)(126, 2350)(127, 2351)(128, 2352)(129, 2353)(130, 2354)(131, 2355)(132, 2356)(133, 2357)(134, 2319)(135, 2318)(136, 2358)(137, 2359)(138, 2360)(139, 2361)(140, 2362)(141, 2363)(142, 2364)(143, 2365)(144, 2366)(145, 2367)(146, 2331)(147, 2330)(148, 2368)(149, 2369)(150, 2370)(151, 2291)(152, 2292)(153, 2293)(154, 2294)(155, 2295)(156, 2298)(157, 2299)(158, 2300)(159, 2301)(160, 2302)(161, 2303)(162, 2304)(163, 2305)(164, 2306)(165, 2307)(166, 2310)(167, 2311)(168, 2312)(169, 2313)(170, 2314)(171, 2315)(172, 2316)(173, 2317)(174, 2320)(175, 2321)(176, 2322)(177, 2323)(178, 2324)(179, 2325)(180, 2326)(181, 2327)(182, 2328)(183, 2329)(184, 2332)(185, 2333)(186, 2334)(187, 2442)(188, 2443)(189, 2444)(190, 2375)(191, 2374)(192, 2445)(193, 2446)(194, 2447)(195, 2448)(196, 2449)(197, 2450)(198, 2451)(199, 2452)(200, 2453)(201, 2454)(202, 2387)(203, 2386)(204, 2455)(205, 2456)(206, 2457)(207, 2458)(208, 2459)(209, 2460)(210, 2395)(211, 2394)(212, 2461)(213, 2462)(214, 2463)(215, 2464)(216, 2465)(217, 2466)(218, 2467)(219, 2468)(220, 2469)(221, 2470)(222, 2407)(223, 2406)(224, 2471)(225, 2472)(226, 2411)(227, 2410)(228, 2590)(229, 2650)(230, 2652)(231, 2628)(232, 2653)(233, 2654)(234, 2656)(235, 2658)(236, 2659)(237, 2660)(238, 2423)(239, 2422)(240, 2663)(241, 2665)(242, 2667)(243, 2668)(244, 2669)(245, 2671)(246, 2431)(247, 2430)(248, 2531)(249, 2675)(250, 2677)(251, 2645)(252, 2678)(253, 2680)(254, 2682)(255, 2684)(256, 2685)(257, 2636)(258, 2371)(259, 2372)(260, 2373)(261, 2376)(262, 2377)(263, 2378)(264, 2379)(265, 2380)(266, 2381)(267, 2382)(268, 2383)(269, 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4011)(1828, 4012)(1829, 4013)(1830, 4014)(1831, 4015)(1832, 4016)(1833, 4017)(1834, 4018)(1835, 4019)(1836, 4020)(1837, 4021)(1838, 4022)(1839, 4023)(1840, 4024)(1841, 4025)(1842, 4026)(1843, 4027)(1844, 4028)(1845, 4029)(1846, 4030)(1847, 4031)(1848, 4032)(1849, 4033)(1850, 4034)(1851, 4035)(1852, 4036)(1853, 4037)(1854, 4038)(1855, 4039)(1856, 4040)(1857, 4041)(1858, 4042)(1859, 4043)(1860, 4044)(1861, 4045)(1862, 4046)(1863, 4047)(1864, 4048)(1865, 4049)(1866, 4050)(1867, 4051)(1868, 4052)(1869, 4053)(1870, 4054)(1871, 4055)(1872, 4056)(1873, 4057)(1874, 4058)(1875, 4059)(1876, 4060)(1877, 4061)(1878, 4062)(1879, 4063)(1880, 4064)(1881, 4065)(1882, 4066)(1883, 4067)(1884, 4068)(1885, 4069)(1886, 4070)(1887, 4071)(1888, 4072)(1889, 4073)(1890, 4074)(1891, 4075)(1892, 4076)(1893, 4077)(1894, 4078)(1895, 4079)(1896, 4080)(1897, 4081)(1898, 4082)(1899, 4083)(1900, 4084)(1901, 4085)(1902, 4086)(1903, 4087)(1904, 4088)(1905, 4089)(1906, 4090)(1907, 4091)(1908, 4092)(1909, 4093)(1910, 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4177)(1994, 4178)(1995, 4179)(1996, 4180)(1997, 4181)(1998, 4182)(1999, 4183)(2000, 4184)(2001, 4185)(2002, 4186)(2003, 4187)(2004, 4188)(2005, 4189)(2006, 4190)(2007, 4191)(2008, 4192)(2009, 4193)(2010, 4194)(2011, 4195)(2012, 4196)(2013, 4197)(2014, 4198)(2015, 4199)(2016, 4200)(2017, 4201)(2018, 4202)(2019, 4203)(2020, 4204)(2021, 4205)(2022, 4206)(2023, 4207)(2024, 4208)(2025, 4209)(2026, 4210)(2027, 4211)(2028, 4212)(2029, 4213)(2030, 4214)(2031, 4215)(2032, 4216)(2033, 4217)(2034, 4218)(2035, 4219)(2036, 4220)(2037, 4221)(2038, 4222)(2039, 4223)(2040, 4224)(2041, 4225)(2042, 4226)(2043, 4227)(2044, 4228)(2045, 4229)(2046, 4230)(2047, 4231)(2048, 4232)(2049, 4233)(2050, 4234)(2051, 4235)(2052, 4236)(2053, 4237)(2054, 4238)(2055, 4239)(2056, 4240)(2057, 4241)(2058, 4242)(2059, 4243)(2060, 4244)(2061, 4245)(2062, 4246)(2063, 4247)(2064, 4248)(2065, 4249)(2066, 4250)(2067, 4251)(2068, 4252)(2069, 4253)(2070, 4254)(2071, 4255)(2072, 4256)(2073, 4257)(2074, 4258)(2075, 4259)(2076, 4260)(2077, 4261)(2078, 4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 2, 14, 2, 14 ), ( 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E14.647 Graph:: bipartite v = 910 e = 2184 f = 1248 degree seq :: [ 4^546, 6^364 ] E14.638 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^7, (Y1 * Y2^-1)^7, (Y1 * Y2 * Y1 * Y2^-1)^6 ] Map:: R = (1, 1093, 2, 1094)(3, 1095, 7, 1099)(4, 1096, 8, 1100)(5, 1097, 9, 1101)(6, 1098, 10, 1102)(11, 1103, 19, 1111)(12, 1104, 20, 1112)(13, 1105, 21, 1113)(14, 1106, 22, 1114)(15, 1107, 23, 1115)(16, 1108, 24, 1116)(17, 1109, 25, 1117)(18, 1110, 26, 1118)(27, 1119, 43, 1135)(28, 1120, 44, 1136)(29, 1121, 45, 1137)(30, 1122, 46, 1138)(31, 1123, 47, 1139)(32, 1124, 48, 1140)(33, 1125, 49, 1141)(34, 1126, 50, 1142)(35, 1127, 51, 1143)(36, 1128, 52, 1144)(37, 1129, 53, 1145)(38, 1130, 54, 1146)(39, 1131, 55, 1147)(40, 1132, 56, 1148)(41, 1133, 57, 1149)(42, 1134, 58, 1150)(59, 1151, 85, 1177)(60, 1152, 86, 1178)(61, 1153, 87, 1179)(62, 1154, 88, 1180)(63, 1155, 89, 1181)(64, 1156, 90, 1182)(65, 1157, 66, 1158)(67, 1159, 91, 1183)(68, 1160, 92, 1184)(69, 1161, 93, 1185)(70, 1162, 94, 1186)(71, 1163, 95, 1187)(72, 1164, 96, 1188)(73, 1165, 97, 1189)(74, 1166, 98, 1190)(75, 1167, 99, 1191)(76, 1168, 100, 1192)(77, 1169, 101, 1193)(78, 1170, 79, 1171)(80, 1172, 102, 1194)(81, 1173, 103, 1195)(82, 1174, 104, 1196)(83, 1175, 105, 1197)(84, 1176, 106, 1198)(107, 1199, 151, 1243)(108, 1200, 152, 1244)(109, 1201, 153, 1245)(110, 1202, 154, 1246)(111, 1203, 155, 1247)(112, 1204, 113, 1205)(114, 1206, 156, 1248)(115, 1207, 157, 1249)(116, 1208, 158, 1250)(117, 1209, 159, 1251)(118, 1210, 160, 1252)(119, 1211, 161, 1253)(120, 1212, 162, 1254)(121, 1213, 163, 1255)(122, 1214, 164, 1256)(123, 1215, 165, 1257)(124, 1216, 125, 1217)(126, 1218, 166, 1258)(127, 1219, 167, 1259)(128, 1220, 168, 1260)(129, 1221, 169, 1261)(130, 1222, 170, 1262)(131, 1223, 171, 1263)(132, 1224, 172, 1264)(133, 1225, 173, 1265)(134, 1226, 135, 1227)(136, 1228, 174, 1266)(137, 1229, 175, 1267)(138, 1230, 176, 1268)(139, 1231, 177, 1269)(140, 1232, 178, 1270)(141, 1233, 179, 1271)(142, 1234, 180, 1272)(143, 1235, 181, 1273)(144, 1236, 182, 1274)(145, 1237, 183, 1275)(146, 1238, 147, 1239)(148, 1240, 184, 1276)(149, 1241, 185, 1277)(150, 1242, 186, 1278)(187, 1279, 258, 1350)(188, 1280, 259, 1351)(189, 1281, 260, 1352)(190, 1282, 191, 1283)(192, 1284, 261, 1353)(193, 1285, 262, 1354)(194, 1286, 263, 1355)(195, 1287, 264, 1356)(196, 1288, 265, 1357)(197, 1289, 266, 1358)(198, 1290, 267, 1359)(199, 1291, 268, 1360)(200, 1292, 236, 1328)(201, 1293, 269, 1361)(202, 1294, 203, 1295)(204, 1296, 270, 1362)(205, 1297, 271, 1363)(206, 1298, 272, 1364)(207, 1299, 273, 1365)(208, 1300, 274, 1366)(209, 1301, 275, 1367)(210, 1302, 211, 1303)(212, 1304, 276, 1368)(213, 1305, 249, 1341)(214, 1306, 277, 1369)(215, 1307, 278, 1370)(216, 1308, 279, 1371)(217, 1309, 280, 1372)(218, 1310, 281, 1373)(219, 1311, 282, 1374)(220, 1312, 283, 1375)(221, 1313, 284, 1376)(222, 1314, 223, 1315)(224, 1316, 285, 1377)(225, 1317, 286, 1378)(226, 1318, 227, 1319)(228, 1320, 436, 1528)(229, 1321, 307, 1399)(230, 1322, 438, 1530)(231, 1323, 440, 1532)(232, 1324, 442, 1534)(233, 1325, 444, 1536)(234, 1326, 446, 1538)(235, 1327, 448, 1540)(237, 1329, 451, 1543)(238, 1330, 239, 1331)(240, 1332, 453, 1545)(241, 1333, 300, 1392)(242, 1334, 454, 1546)(243, 1335, 456, 1548)(244, 1336, 457, 1549)(245, 1337, 346, 1438)(246, 1338, 247, 1339)(248, 1340, 460, 1552)(250, 1342, 462, 1554)(251, 1343, 464, 1556)(252, 1344, 466, 1558)(253, 1345, 356, 1448)(254, 1346, 469, 1561)(255, 1347, 471, 1563)(256, 1348, 473, 1565)(257, 1349, 475, 1567)(287, 1379, 326, 1418)(288, 1380, 333, 1425)(289, 1381, 322, 1414)(290, 1382, 329, 1421)(291, 1383, 360, 1452)(292, 1384, 368, 1460)(293, 1385, 373, 1465)(294, 1386, 354, 1446)(295, 1387, 364, 1456)(296, 1388, 377, 1469)(297, 1389, 416, 1508)(298, 1390, 362, 1454)(299, 1391, 428, 1520)(301, 1393, 441, 1533)(302, 1394, 375, 1467)(303, 1395, 465, 1557)(304, 1396, 420, 1512)(305, 1397, 432, 1524)(306, 1398, 449, 1541)(308, 1400, 472, 1564)(309, 1401, 572, 1664)(310, 1402, 418, 1510)(311, 1403, 579, 1671)(312, 1404, 582, 1674)(313, 1405, 430, 1522)(314, 1406, 589, 1681)(315, 1407, 592, 1684)(316, 1408, 445, 1537)(317, 1409, 599, 1691)(318, 1410, 602, 1694)(319, 1411, 468, 1560)(320, 1412, 609, 1701)(321, 1413, 612, 1704)(323, 1415, 619, 1711)(324, 1416, 621, 1713)(325, 1417, 463, 1555)(327, 1419, 631, 1723)(328, 1420, 634, 1726)(330, 1422, 641, 1733)(331, 1423, 643, 1735)(332, 1424, 427, 1519)(334, 1426, 652, 1744)(335, 1427, 620, 1712)(336, 1428, 658, 1750)(337, 1429, 661, 1753)(338, 1430, 536, 1628)(339, 1431, 666, 1758)(340, 1432, 633, 1725)(341, 1433, 673, 1765)(342, 1434, 676, 1768)(343, 1435, 522, 1614)(344, 1436, 642, 1734)(345, 1437, 685, 1777)(347, 1439, 690, 1782)(348, 1440, 538, 1630)(349, 1441, 695, 1787)(350, 1442, 654, 1746)(351, 1443, 702, 1794)(352, 1444, 705, 1797)(353, 1445, 520, 1612)(355, 1447, 712, 1804)(357, 1449, 718, 1810)(358, 1450, 719, 1811)(359, 1451, 372, 1464)(361, 1453, 646, 1738)(363, 1455, 731, 1823)(365, 1457, 737, 1829)(366, 1458, 739, 1831)(367, 1459, 415, 1507)(369, 1461, 721, 1813)(370, 1462, 748, 1840)(371, 1463, 749, 1841)(374, 1466, 624, 1716)(376, 1468, 761, 1853)(378, 1470, 741, 1833)(379, 1471, 767, 1859)(380, 1472, 439, 1531)(381, 1473, 772, 1864)(382, 1474, 414, 1506)(383, 1475, 776, 1868)(384, 1476, 559, 1651)(385, 1477, 780, 1872)(386, 1478, 728, 1820)(387, 1479, 785, 1877)(388, 1480, 788, 1880)(389, 1481, 516, 1608)(390, 1482, 792, 1884)(391, 1483, 426, 1518)(392, 1484, 797, 1889)(393, 1485, 562, 1654)(394, 1486, 800, 1892)(395, 1487, 708, 1800)(396, 1488, 806, 1898)(397, 1489, 809, 1901)(398, 1490, 437, 1529)(399, 1491, 813, 1905)(400, 1492, 565, 1657)(401, 1493, 816, 1908)(402, 1494, 758, 1850)(403, 1495, 488, 1580)(404, 1496, 823, 1915)(405, 1497, 518, 1610)(406, 1498, 826, 1918)(407, 1499, 461, 1553)(408, 1500, 831, 1923)(409, 1501, 570, 1662)(410, 1502, 834, 1926)(411, 1503, 679, 1771)(412, 1504, 839, 1931)(413, 1505, 842, 1934)(417, 1509, 595, 1687)(419, 1511, 771, 1863)(421, 1513, 645, 1737)(422, 1514, 858, 1950)(423, 1515, 860, 1952)(424, 1516, 757, 1849)(425, 1517, 863, 1955)(429, 1521, 571, 1663)(431, 1523, 862, 1954)(433, 1525, 692, 1784)(434, 1526, 880, 1972)(435, 1527, 882, 1974)(443, 1535, 575, 1667)(447, 1539, 744, 1836)(450, 1542, 623, 1715)(452, 1544, 905, 1997)(455, 1547, 909, 2001)(458, 1550, 727, 1819)(459, 1551, 913, 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4238)(2683, 3775, 3010, 4102, 3149, 4241)(2684, 3776, 3150, 4242, 3151, 4243)(2688, 3780, 2804, 3896, 3155, 4247)(2690, 3782, 3158, 4250, 3159, 4251)(2691, 3783, 3160, 4252, 2738, 3830)(2694, 3786, 2722, 3814, 3164, 4256)(2696, 3788, 2936, 4028, 3107, 4199)(2698, 3790, 3168, 4260, 3169, 4261)(2700, 3792, 3171, 4263, 3172, 4264)(2702, 3794, 3152, 4244, 3174, 4266)(2704, 3796, 3176, 4268, 3177, 4269)(2706, 3798, 3178, 4270, 3179, 4271)(2711, 3803, 3131, 4223, 3182, 4274)(2717, 3809, 3184, 4276, 3185, 4277)(2720, 3812, 3186, 4278, 3119, 4211)(2727, 3819, 3113, 4205, 3190, 4282)(2732, 3824, 3194, 4286, 3195, 4287)(2752, 3844, 3205, 4297, 3175, 4267)(2756, 3848, 3202, 4294, 3207, 4299)(2763, 3855, 3210, 4302, 3008, 4100)(2766, 3858, 3214, 4306, 3215, 4307)(2773, 3865, 3217, 4309, 3134, 4226)(2776, 3868, 3200, 4292, 3221, 4313)(2783, 3875, 3224, 4316, 2974, 4066)(2786, 3878, 3213, 4305, 3227, 4319)(2791, 3883, 2969, 4061, 3165, 4257)(2793, 3885, 3148, 4240, 3189, 4281)(2801, 3893, 3236, 4328, 3170, 4262)(2805, 3897, 3092, 4184, 3239, 4331)(2823, 3915, 3235, 4327, 3173, 4265)(2826, 3918, 3122, 4214, 3110, 4202)(2827, 3919, 3246, 4338, 3248, 4340)(2842, 3934, 3228, 4320, 2996, 4088)(2845, 3937, 3220, 4312, 3254, 4346)(2848, 3940, 2990, 4082, 3018, 4110)(2850, 3942, 2999, 4091, 3193, 4285)(2857, 3949, 3255, 4347, 2893, 3985)(2860, 3952, 3199, 4291, 3258, 4350)(2864, 3956, 2886, 3978, 3140, 4232)(2869, 3961, 3216, 4308, 2959, 4051)(2873, 3965, 2976, 4068, 3208, 4300)(2874, 3966, 3232, 4324, 3257, 4349)(2877, 3969, 3023, 4115, 2984, 4076)(2879, 3971, 2962, 4054, 3144, 4236)(2889, 3981, 3191, 4283, 3138, 4230)(2900, 3992, 3229, 4321, 3180, 4272)(2903, 3995, 3264, 4356, 3266, 4358)(2919, 4011, 3204, 4296, 3181, 4273)(2923, 4015, 3269, 4361, 3261, 4353)(2933, 4025, 3272, 4364, 3133, 4225)(2949, 4041, 3128, 4220, 3183, 4275)(2951, 4043, 3267, 4359, 3256, 4348)(2956, 4048, 3196, 4288, 2980, 4072)(2960, 4052, 3100, 4192, 3225, 4317)(2964, 4056, 2982, 4074, 3167, 4259)(2972, 4064, 3097, 4189, 3161, 4253)(2981, 4073, 3259, 4351, 3253, 4345)(2993, 4085, 3187, 4279, 3014, 4106)(2997, 4089, 3234, 4326, 3211, 4303)(3000, 4092, 3016, 4108, 3125, 4217)(3007, 4099, 3047, 4139, 3273, 4365)(3015, 4107, 3156, 4248, 3260, 4352)(3026, 4118, 3274, 4366, 3154, 4246)(3040, 4132, 3270, 4362, 3188, 4280)(3042, 4134, 3271, 4363, 3245, 4337)(3044, 4136, 3088, 4180, 3275, 4367)(3054, 4146, 3233, 4325, 3068, 4160)(3062, 4154, 3249, 4341, 3192, 4284)(3064, 4156, 3251, 4343, 3230, 4322)(3066, 4158, 3096, 4188, 3276, 4368)(3078, 4170, 3223, 4315, 3198, 4290)(3085, 4177, 3268, 4360, 3197, 4289)(3089, 4181, 3262, 4354, 3163, 4255)(3091, 4183, 3105, 4197, 3263, 4355)(3099, 4191, 3265, 4357, 3143, 4235)(3109, 4201, 3147, 4239, 3203, 4295)(3117, 4209, 3240, 4332, 3142, 4234)(3120, 4212, 3242, 4334, 3218, 4310)(3123, 4215, 3247, 4339, 3209, 4301)(3166, 4258, 3238, 4330, 3222, 4314)(3201, 4293, 3226, 4318, 3244, 4336)(3206, 4298, 3212, 4304, 3237, 4329)(3219, 4311, 3243, 4335, 3241, 4333)(3231, 4323, 3252, 4344, 3250, 4342) L = (1, 2186)(2, 2185)(3, 2191)(4, 2192)(5, 2193)(6, 2194)(7, 2187)(8, 2188)(9, 2189)(10, 2190)(11, 2203)(12, 2204)(13, 2205)(14, 2206)(15, 2207)(16, 2208)(17, 2209)(18, 2210)(19, 2195)(20, 2196)(21, 2197)(22, 2198)(23, 2199)(24, 2200)(25, 2201)(26, 2202)(27, 2227)(28, 2228)(29, 2229)(30, 2230)(31, 2231)(32, 2232)(33, 2233)(34, 2234)(35, 2235)(36, 2236)(37, 2237)(38, 2238)(39, 2239)(40, 2240)(41, 2241)(42, 2242)(43, 2211)(44, 2212)(45, 2213)(46, 2214)(47, 2215)(48, 2216)(49, 2217)(50, 2218)(51, 2219)(52, 2220)(53, 2221)(54, 2222)(55, 2223)(56, 2224)(57, 2225)(58, 2226)(59, 2269)(60, 2270)(61, 2271)(62, 2272)(63, 2273)(64, 2274)(65, 2250)(66, 2249)(67, 2275)(68, 2276)(69, 2277)(70, 2278)(71, 2279)(72, 2280)(73, 2281)(74, 2282)(75, 2283)(76, 2284)(77, 2285)(78, 2263)(79, 2262)(80, 2286)(81, 2287)(82, 2288)(83, 2289)(84, 2290)(85, 2243)(86, 2244)(87, 2245)(88, 2246)(89, 2247)(90, 2248)(91, 2251)(92, 2252)(93, 2253)(94, 2254)(95, 2255)(96, 2256)(97, 2257)(98, 2258)(99, 2259)(100, 2260)(101, 2261)(102, 2264)(103, 2265)(104, 2266)(105, 2267)(106, 2268)(107, 2335)(108, 2336)(109, 2337)(110, 2338)(111, 2339)(112, 2297)(113, 2296)(114, 2340)(115, 2341)(116, 2342)(117, 2343)(118, 2344)(119, 2345)(120, 2346)(121, 2347)(122, 2348)(123, 2349)(124, 2309)(125, 2308)(126, 2350)(127, 2351)(128, 2352)(129, 2353)(130, 2354)(131, 2355)(132, 2356)(133, 2357)(134, 2319)(135, 2318)(136, 2358)(137, 2359)(138, 2360)(139, 2361)(140, 2362)(141, 2363)(142, 2364)(143, 2365)(144, 2366)(145, 2367)(146, 2331)(147, 2330)(148, 2368)(149, 2369)(150, 2370)(151, 2291)(152, 2292)(153, 2293)(154, 2294)(155, 2295)(156, 2298)(157, 2299)(158, 2300)(159, 2301)(160, 2302)(161, 2303)(162, 2304)(163, 2305)(164, 2306)(165, 2307)(166, 2310)(167, 2311)(168, 2312)(169, 2313)(170, 2314)(171, 2315)(172, 2316)(173, 2317)(174, 2320)(175, 2321)(176, 2322)(177, 2323)(178, 2324)(179, 2325)(180, 2326)(181, 2327)(182, 2328)(183, 2329)(184, 2332)(185, 2333)(186, 2334)(187, 2442)(188, 2443)(189, 2444)(190, 2375)(191, 2374)(192, 2445)(193, 2446)(194, 2447)(195, 2448)(196, 2449)(197, 2450)(198, 2451)(199, 2452)(200, 2420)(201, 2453)(202, 2387)(203, 2386)(204, 2454)(205, 2455)(206, 2456)(207, 2457)(208, 2458)(209, 2459)(210, 2395)(211, 2394)(212, 2460)(213, 2433)(214, 2461)(215, 2462)(216, 2463)(217, 2464)(218, 2465)(219, 2466)(220, 2467)(221, 2468)(222, 2407)(223, 2406)(224, 2469)(225, 2470)(226, 2411)(227, 2410)(228, 2620)(229, 2491)(230, 2622)(231, 2624)(232, 2626)(233, 2628)(234, 2630)(235, 2632)(236, 2384)(237, 2635)(238, 2423)(239, 2422)(240, 2637)(241, 2484)(242, 2638)(243, 2640)(244, 2641)(245, 2530)(246, 2431)(247, 2430)(248, 2644)(249, 2397)(250, 2646)(251, 2648)(252, 2650)(253, 2540)(254, 2653)(255, 2655)(256, 2657)(257, 2659)(258, 2371)(259, 2372)(260, 2373)(261, 2376)(262, 2377)(263, 2378)(264, 2379)(265, 2380)(266, 2381)(267, 2382)(268, 2383)(269, 2385)(270, 2388)(271, 2389)(272, 2390)(273, 2391)(274, 2392)(275, 2393)(276, 2396)(277, 2398)(278, 2399)(279, 2400)(280, 2401)(281, 2402)(282, 2403)(283, 2404)(284, 2405)(285, 2408)(286, 2409)(287, 2510)(288, 2517)(289, 2506)(290, 2513)(291, 2544)(292, 2552)(293, 2557)(294, 2538)(295, 2548)(296, 2561)(297, 2600)(298, 2546)(299, 2612)(300, 2425)(301, 2625)(302, 2559)(303, 2649)(304, 2604)(305, 2616)(306, 2633)(307, 2413)(308, 2656)(309, 2756)(310, 2602)(311, 2763)(312, 2766)(313, 2614)(314, 2773)(315, 2776)(316, 2629)(317, 2783)(318, 2786)(319, 2652)(320, 2793)(321, 2796)(322, 2473)(323, 2803)(324, 2805)(325, 2647)(326, 2471)(327, 2815)(328, 2818)(329, 2474)(330, 2825)(331, 2827)(332, 2611)(333, 2472)(334, 2836)(335, 2804)(336, 2842)(337, 2845)(338, 2720)(339, 2850)(340, 2817)(341, 2857)(342, 2860)(343, 2706)(344, 2826)(345, 2869)(346, 2429)(347, 2874)(348, 2722)(349, 2879)(350, 2838)(351, 2886)(352, 2889)(353, 2704)(354, 2478)(355, 2896)(356, 2437)(357, 2902)(358, 2903)(359, 2556)(360, 2475)(361, 2830)(362, 2482)(363, 2915)(364, 2479)(365, 2921)(366, 2923)(367, 2599)(368, 2476)(369, 2905)(370, 2932)(371, 2933)(372, 2543)(373, 2477)(374, 2808)(375, 2486)(376, 2945)(377, 2480)(378, 2925)(379, 2951)(380, 2623)(381, 2956)(382, 2598)(383, 2960)(384, 2743)(385, 2964)(386, 2912)(387, 2969)(388, 2972)(389, 2700)(390, 2976)(391, 2610)(392, 2981)(393, 2746)(394, 2984)(395, 2892)(396, 2990)(397, 2993)(398, 2621)(399, 2997)(400, 2749)(401, 3000)(402, 2942)(403, 2672)(404, 3007)(405, 2702)(406, 3010)(407, 2645)(408, 3015)(409, 2754)(410, 3018)(411, 2863)(412, 3023)(413, 3026)(414, 2566)(415, 2551)(416, 2481)(417, 2779)(418, 2494)(419, 2955)(420, 2488)(421, 2829)(422, 3042)(423, 3044)(424, 2941)(425, 3047)(426, 2575)(427, 2516)(428, 2483)(429, 2755)(430, 2497)(431, 3046)(432, 2489)(433, 2876)(434, 3064)(435, 3066)(436, 2412)(437, 2582)(438, 2414)(439, 2564)(440, 2415)(441, 2485)(442, 2416)(443, 2759)(444, 2417)(445, 2500)(446, 2418)(447, 2928)(448, 2419)(449, 2490)(450, 2807)(451, 2421)(452, 3089)(453, 2424)(454, 2426)(455, 3093)(456, 2427)(457, 2428)(458, 2911)(459, 3097)(460, 2432)(461, 2591)(462, 2434)(463, 2509)(464, 2435)(465, 2487)(466, 2436)(467, 2747)(468, 2503)(469, 2438)(470, 3095)(471, 2439)(472, 2492)(473, 2440)(474, 2847)(475, 2441)(476, 3120)(477, 2798)(478, 3123)(479, 3125)(480, 2979)(481, 3068)(482, 2691)(483, 3131)(484, 3132)(485, 3133)(486, 2708)(487, 3001)(488, 2587)(489, 3028)(490, 3080)(491, 3140)(492, 2790)(493, 3142)(494, 3144)(495, 2922)(496, 3147)(497, 2810)(498, 3099)(499, 3016)(500, 2872)(501, 3152)(502, 3153)(503, 3154)(504, 2711)(505, 3156)(506, 3126)(507, 2666)(508, 3049)(509, 3163)(510, 2778)(511, 3165)(512, 2820)(513, 3166)(514, 3167)(515, 3170)(516, 2573)(517, 3173)(518, 2589)(519, 3175)(520, 2537)(521, 3130)(522, 2527)(523, 3180)(524, 2670)(525, 3090)(526, 3181)(527, 2688)(528, 3157)(529, 3159)(530, 3036)(531, 3043)(532, 3183)(533, 3110)(534, 2901)(535, 3006)(536, 2522)(537, 2971)(538, 2532)(539, 3012)(540, 3058)(541, 3065)(542, 3188)(543, 3189)(544, 2920)(545, 3136)(546, 2952)(547, 3192)(548, 3193)(549, 2824)(550, 2978)(551, 3112)(552, 3121)(553, 3197)(554, 3134)(555, 2950)(556, 3198)(557, 2924)(558, 2992)(559, 2568)(560, 3124)(561, 2888)(562, 2577)(563, 2651)(564, 3025)(565, 2584)(566, 3074)(567, 3203)(568, 3113)(569, 2859)(570, 2593)(571, 2613)(572, 2493)(573, 2871)(574, 3119)(575, 2627)(576, 3201)(577, 3077)(578, 3041)(579, 2495)(580, 3212)(581, 2828)(582, 2496)(583, 2958)(584, 3179)(585, 2998)(586, 3091)(587, 3008)(588, 3063)(589, 2498)(590, 3219)(591, 2904)(592, 2499)(593, 2844)(594, 2694)(595, 2601)(596, 3206)(597, 3055)(598, 3086)(599, 2501)(600, 3226)(601, 2806)(602, 2502)(603, 2995)(604, 3177)(605, 2961)(606, 2676)(607, 2974)(608, 3118)(609, 2504)(610, 3231)(611, 2934)(612, 2505)(613, 3146)(614, 2661)(615, 3209)(616, 3234)(617, 3194)(618, 2986)(619, 2507)(620, 2519)(621, 2508)(622, 2785)(623, 2634)(624, 2558)(625, 3169)(626, 2681)(627, 3143)(628, 3242)(629, 3184)(630, 2881)(631, 2511)(632, 3172)(633, 2524)(634, 2512)(635, 3195)(636, 2696)(637, 3222)(638, 3100)(639, 3145)(640, 2733)(641, 2514)(642, 2528)(643, 2515)(644, 2765)(645, 2605)(646, 2545)(647, 3127)(648, 2973)(649, 3151)(650, 3251)(651, 2852)(652, 2518)(653, 3174)(654, 2534)(655, 3241)(656, 2940)(657, 3098)(658, 2520)(659, 3105)(660, 2777)(661, 2521)(662, 2891)(663, 2658)(664, 2996)(665, 3239)(666, 2523)(667, 3252)(668, 2835)(669, 3027)(670, 3223)(671, 3033)(672, 3106)(673, 2525)(674, 3085)(675, 2753)(676, 2526)(677, 2954)(678, 2875)(679, 2595)(680, 2893)(681, 3221)(682, 3250)(683, 2910)(684, 3048)(685, 2529)(686, 3051)(687, 2757)(688, 2684)(689, 2982)(690, 2531)(691, 2862)(692, 2617)(693, 2959)(694, 3248)(695, 2533)(696, 3243)(697, 2814)(698, 3067)(699, 3135)(700, 3076)(701, 3052)(702, 2535)(703, 3040)(704, 2745)(705, 2536)(706, 2927)(707, 2846)(708, 2579)(709, 2864)(710, 3207)(711, 3262)(712, 2539)(713, 3185)(714, 3115)(715, 3259)(716, 3168)(717, 2718)(718, 2541)(719, 2542)(720, 2775)(721, 2553)(722, 3149)(723, 2994)(724, 3004)(725, 3267)(726, 2867)(727, 2642)(728, 2570)(729, 3139)(730, 3260)(731, 2547)(732, 3190)(733, 3240)(734, 3232)(735, 3024)(736, 2728)(737, 2549)(738, 2679)(739, 2550)(740, 2741)(741, 2562)(742, 3002)(743, 2890)(744, 2631)(745, 3271)(746, 3182)(747, 3162)(748, 2554)(749, 2555)(750, 2795)(751, 3208)(752, 2957)(753, 2968)(754, 3269)(755, 3171)(756, 2840)(757, 2608)(758, 2586)(759, 3082)(760, 3253)(761, 2560)(762, 3160)(763, 3249)(764, 3220)(765, 2991)(766, 2739)(767, 2563)(768, 2730)(769, 2966)(770, 2861)(771, 2603)(772, 2565)(773, 2936)(774, 2767)(775, 2877)(776, 2567)(777, 2789)(778, 2980)(779, 3266)(780, 2569)(781, 3078)(782, 2953)(783, 3158)(784, 2937)(785, 2571)(786, 3062)(787, 2721)(788, 2572)(789, 2832)(790, 2791)(791, 3215)(792, 2574)(793, 3021)(794, 2734)(795, 2664)(796, 2962)(797, 2576)(798, 2873)(799, 3261)(800, 2578)(801, 3237)(802, 2802)(803, 3045)(804, 3011)(805, 3030)(806, 2580)(807, 2949)(808, 2742)(809, 2581)(810, 2907)(811, 2787)(812, 2848)(813, 2583)(814, 2769)(815, 3014)(816, 2585)(817, 2671)(818, 2926)(819, 3229)(820, 2908)(821, 3117)(822, 2719)(823, 2588)(824, 2771)(825, 3227)(826, 2590)(827, 2988)(828, 2723)(829, 3037)(830, 2999)(831, 2592)(832, 2683)(833, 3256)(834, 2594)(835, 3244)(836, 3094)(837, 2977)(838, 3072)(839, 2596)(840, 2919)(841, 2748)(842, 2597)(843, 2853)(844, 2673)(845, 3216)(846, 2989)(847, 3246)(848, 3069)(849, 2855)(850, 3233)(851, 3257)(852, 2714)(853, 3013)(854, 3128)(855, 3199)(856, 2887)(857, 2762)(858, 2606)(859, 2715)(860, 2607)(861, 2987)(862, 2615)(863, 2609)(864, 2868)(865, 2692)(866, 3196)(867, 2870)(868, 2885)(869, 3264)(870, 3176)(871, 2781)(872, 3102)(873, 3225)(874, 2724)(875, 3137)(876, 3270)(877, 3213)(878, 2970)(879, 2772)(880, 2618)(881, 2725)(882, 2619)(883, 2882)(884, 2665)(885, 3032)(886, 3073)(887, 3228)(888, 3022)(889, 3070)(890, 2750)(891, 3092)(892, 2884)(893, 2761)(894, 2965)(895, 3254)(896, 2674)(897, 3204)(898, 2943)(899, 3268)(900, 3191)(901, 2858)(902, 2782)(903, 3245)(904, 3255)(905, 2636)(906, 2709)(907, 2770)(908, 3075)(909, 2639)(910, 3020)(911, 2654)(912, 3224)(913, 2643)(914, 2841)(915, 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4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 2, 14, 2, 14 ), ( 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E14.646 Graph:: bipartite v = 910 e = 2184 f = 1248 degree seq :: [ 4^546, 6^364 ] E14.639 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^7, (Y3 * Y2^-1)^7, (Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1)^3 ] Map:: R = (1, 1093, 2, 1094)(3, 1095, 7, 1099)(4, 1096, 8, 1100)(5, 1097, 9, 1101)(6, 1098, 10, 1102)(11, 1103, 19, 1111)(12, 1104, 20, 1112)(13, 1105, 21, 1113)(14, 1106, 22, 1114)(15, 1107, 23, 1115)(16, 1108, 24, 1116)(17, 1109, 25, 1117)(18, 1110, 26, 1118)(27, 1119, 43, 1135)(28, 1120, 44, 1136)(29, 1121, 45, 1137)(30, 1122, 46, 1138)(31, 1123, 47, 1139)(32, 1124, 48, 1140)(33, 1125, 49, 1141)(34, 1126, 50, 1142)(35, 1127, 51, 1143)(36, 1128, 52, 1144)(37, 1129, 53, 1145)(38, 1130, 54, 1146)(39, 1131, 55, 1147)(40, 1132, 56, 1148)(41, 1133, 57, 1149)(42, 1134, 58, 1150)(59, 1151, 85, 1177)(60, 1152, 86, 1178)(61, 1153, 87, 1179)(62, 1154, 88, 1180)(63, 1155, 89, 1181)(64, 1156, 90, 1182)(65, 1157, 66, 1158)(67, 1159, 91, 1183)(68, 1160, 92, 1184)(69, 1161, 93, 1185)(70, 1162, 94, 1186)(71, 1163, 95, 1187)(72, 1164, 96, 1188)(73, 1165, 97, 1189)(74, 1166, 98, 1190)(75, 1167, 99, 1191)(76, 1168, 100, 1192)(77, 1169, 101, 1193)(78, 1170, 79, 1171)(80, 1172, 102, 1194)(81, 1173, 103, 1195)(82, 1174, 104, 1196)(83, 1175, 105, 1197)(84, 1176, 106, 1198)(107, 1199, 151, 1243)(108, 1200, 152, 1244)(109, 1201, 153, 1245)(110, 1202, 154, 1246)(111, 1203, 155, 1247)(112, 1204, 113, 1205)(114, 1206, 156, 1248)(115, 1207, 157, 1249)(116, 1208, 158, 1250)(117, 1209, 159, 1251)(118, 1210, 160, 1252)(119, 1211, 161, 1253)(120, 1212, 162, 1254)(121, 1213, 163, 1255)(122, 1214, 164, 1256)(123, 1215, 165, 1257)(124, 1216, 125, 1217)(126, 1218, 166, 1258)(127, 1219, 167, 1259)(128, 1220, 168, 1260)(129, 1221, 169, 1261)(130, 1222, 170, 1262)(131, 1223, 171, 1263)(132, 1224, 172, 1264)(133, 1225, 173, 1265)(134, 1226, 135, 1227)(136, 1228, 174, 1266)(137, 1229, 175, 1267)(138, 1230, 176, 1268)(139, 1231, 177, 1269)(140, 1232, 178, 1270)(141, 1233, 179, 1271)(142, 1234, 180, 1272)(143, 1235, 181, 1273)(144, 1236, 182, 1274)(145, 1237, 183, 1275)(146, 1238, 147, 1239)(148, 1240, 184, 1276)(149, 1241, 185, 1277)(150, 1242, 186, 1278)(187, 1279, 258, 1350)(188, 1280, 259, 1351)(189, 1281, 260, 1352)(190, 1282, 191, 1283)(192, 1284, 261, 1353)(193, 1285, 262, 1354)(194, 1286, 263, 1355)(195, 1287, 264, 1356)(196, 1288, 265, 1357)(197, 1289, 266, 1358)(198, 1290, 267, 1359)(199, 1291, 268, 1360)(200, 1292, 269, 1361)(201, 1293, 270, 1362)(202, 1294, 203, 1295)(204, 1296, 271, 1363)(205, 1297, 272, 1364)(206, 1298, 273, 1365)(207, 1299, 274, 1366)(208, 1300, 275, 1367)(209, 1301, 276, 1368)(210, 1302, 211, 1303)(212, 1304, 277, 1369)(213, 1305, 278, 1370)(214, 1306, 279, 1371)(215, 1307, 280, 1372)(216, 1308, 281, 1373)(217, 1309, 282, 1374)(218, 1310, 283, 1375)(219, 1311, 284, 1376)(220, 1312, 285, 1377)(221, 1313, 286, 1378)(222, 1314, 223, 1315)(224, 1316, 287, 1379)(225, 1317, 288, 1380)(226, 1318, 227, 1319)(228, 1320, 457, 1549)(229, 1321, 459, 1551)(230, 1322, 461, 1553)(231, 1323, 463, 1555)(232, 1324, 445, 1537)(233, 1325, 464, 1556)(234, 1326, 466, 1558)(235, 1327, 444, 1536)(236, 1328, 468, 1560)(237, 1329, 469, 1561)(238, 1330, 239, 1331)(240, 1332, 472, 1564)(241, 1333, 473, 1565)(242, 1334, 475, 1567)(243, 1335, 477, 1569)(244, 1336, 479, 1571)(245, 1337, 480, 1572)(246, 1338, 247, 1339)(248, 1340, 482, 1574)(249, 1341, 484, 1576)(250, 1342, 486, 1578)(251, 1343, 488, 1580)(252, 1344, 489, 1581)(253, 1345, 490, 1582)(254, 1346, 492, 1584)(255, 1347, 494, 1586)(256, 1348, 381, 1473)(257, 1349, 495, 1587)(289, 1381, 536, 1628)(290, 1382, 538, 1630)(291, 1383, 540, 1632)(292, 1384, 542, 1634)(293, 1385, 544, 1636)(294, 1386, 546, 1638)(295, 1387, 548, 1640)(296, 1388, 551, 1643)(297, 1389, 553, 1645)(298, 1390, 556, 1648)(299, 1391, 559, 1651)(300, 1392, 562, 1654)(301, 1393, 565, 1657)(302, 1394, 568, 1660)(303, 1395, 571, 1663)(304, 1396, 574, 1666)(305, 1397, 577, 1669)(306, 1398, 580, 1672)(307, 1399, 583, 1675)(308, 1400, 586, 1678)(309, 1401, 589, 1681)(310, 1402, 592, 1684)(311, 1403, 595, 1687)(312, 1404, 597, 1689)(313, 1405, 599, 1691)(314, 1406, 602, 1694)(315, 1407, 604, 1696)(316, 1408, 607, 1699)(317, 1409, 610, 1702)(318, 1410, 612, 1704)(319, 1411, 614, 1706)(320, 1412, 617, 1709)(321, 1413, 619, 1711)(322, 1414, 621, 1713)(323, 1415, 624, 1716)(324, 1416, 627, 1719)(325, 1417, 630, 1722)(326, 1418, 633, 1725)(327, 1419, 636, 1728)(328, 1420, 639, 1731)(329, 1421, 642, 1734)(330, 1422, 644, 1736)(331, 1423, 648, 1740)(332, 1424, 651, 1743)(333, 1425, 654, 1746)(334, 1426, 656, 1748)(335, 1427, 660, 1752)(336, 1428, 663, 1755)(337, 1429, 665, 1757)(338, 1430, 668, 1760)(339, 1431, 671, 1763)(340, 1432, 673, 1765)(341, 1433, 675, 1767)(342, 1434, 658, 1750)(343, 1435, 679, 1771)(344, 1436, 681, 1773)(345, 1437, 684, 1776)(346, 1438, 687, 1779)(347, 1439, 689, 1781)(348, 1440, 691, 1783)(349, 1441, 635, 1727)(350, 1442, 695, 1787)(351, 1443, 697, 1789)(352, 1444, 701, 1793)(353, 1445, 703, 1795)(354, 1446, 706, 1798)(355, 1447, 708, 1800)(356, 1448, 711, 1803)(357, 1449, 714, 1806)(358, 1450, 717, 1809)(359, 1451, 718, 1810)(360, 1452, 721, 1813)(361, 1453, 723, 1815)(362, 1454, 726, 1818)(363, 1455, 730, 1822)(364, 1456, 732, 1824)(365, 1457, 735, 1827)(366, 1458, 737, 1829)(367, 1459, 739, 1831)(368, 1460, 742, 1834)(369, 1461, 745, 1837)(370, 1462, 747, 1839)(371, 1463, 749, 1841)(372, 1464, 750, 1842)(373, 1465, 753, 1845)(374, 1466, 755, 1847)(375, 1467, 758, 1850)(376, 1468, 760, 1852)(377, 1469, 762, 1854)(378, 1470, 582, 1674)(379, 1471, 768, 1860)(380, 1472, 769, 1861)(382, 1474, 773, 1865)(383, 1475, 775, 1867)(384, 1476, 623, 1715)(385, 1477, 780, 1872)(386, 1478, 501, 1593)(387, 1479, 783, 1875)(388, 1480, 785, 1877)(389, 1481, 787, 1879)(390, 1482, 570, 1662)(391, 1483, 793, 1885)(392, 1484, 794, 1886)(393, 1485, 797, 1889)(394, 1486, 799, 1891)(395, 1487, 646, 1738)(396, 1488, 803, 1895)(397, 1489, 804, 1896)(398, 1490, 806, 1898)(399, 1491, 736, 1828)(400, 1492, 809, 1901)(401, 1493, 812, 1904)(402, 1494, 792, 1884)(403, 1495, 813, 1905)(404, 1496, 814, 1906)(405, 1497, 816, 1908)(406, 1498, 817, 1909)(407, 1499, 820, 1912)(408, 1500, 807, 1899)(409, 1501, 822, 1914)(410, 1502, 751, 1843)(411, 1503, 826, 1918)(412, 1504, 828, 1920)(413, 1505, 829, 1921)(414, 1506, 830, 1922)(415, 1507, 832, 1924)(416, 1508, 707, 1799)(417, 1509, 835, 1927)(418, 1510, 805, 1897)(419, 1511, 767, 1859)(420, 1512, 838, 1930)(421, 1513, 839, 1931)(422, 1514, 841, 1933)(423, 1515, 842, 1934)(424, 1516, 846, 1938)(425, 1517, 833, 1925)(426, 1518, 848, 1940)(427, 1519, 724, 1816)(428, 1520, 852, 1944)(429, 1521, 854, 1946)(430, 1522, 856, 1948)(431, 1523, 523, 1615)(432, 1524, 743, 1835)(433, 1525, 860, 1952)(434, 1526, 862, 1954)(435, 1527, 863, 1955)(436, 1528, 576, 1668)(437, 1529, 866, 1958)(438, 1530, 819, 1911)(439, 1531, 869, 1961)(440, 1532, 872, 1964)(441, 1533, 874, 1966)(442, 1534, 699, 1791)(443, 1535, 876, 1968)(446, 1538, 879, 1971)(447, 1539, 789, 1881)(448, 1540, 881, 1973)(449, 1541, 552, 1644)(450, 1542, 884, 1976)(451, 1543, 734, 1826)(452, 1544, 887, 1979)(453, 1545, 890, 1982)(454, 1546, 892, 1984)(455, 1547, 715, 1807)(456, 1548, 895, 1987)(458, 1550, 899, 1991)(460, 1552, 901, 1993)(462, 1554, 588, 1680)(465, 1557, 909, 2001)(467, 1559, 844, 1936)(470, 1562, 527, 1619)(471, 1563, 918, 2010)(474, 1566, 922, 2014)(476, 1568, 728, 1820)(478, 1570, 925, 2017)(481, 1573, 930, 2022)(483, 1575, 764, 1856)(485, 1577, 873, 1965)(487, 1579, 547, 1639)(491, 1583, 941, 2033)(493, 1585, 705, 1797)(496, 1588, 947, 2039)(497, 1589, 722, 1814)(498, 1590, 731, 1823)(499, 1591, 951, 2043)(500, 1592, 818, 1910)(502, 1594, 683, 1775)(503, 1595, 682, 1774)(504, 1596, 791, 1883)(505, 1597, 834, 1926)(506, 1598, 954, 2046)(507, 1599, 956, 2048)(508, 1600, 882, 1974)(509, 1601, 960, 2052)(510, 1602, 912, 2004)(511, 1603, 962, 2054)(512, 1604, 965, 2057)(513, 1605, 657, 1749)(514, 1606, 650, 1742)(515, 1607, 948, 2040)(516, 1608, 969, 2061)(517, 1609, 972, 2064)(518, 1610, 952, 2044)(519, 1611, 655, 1747)(520, 1612, 748, 1840)(521, 1613, 975, 2067)(522, 1614, 733, 1825)(524, 1616, 754, 1846)(525, 1617, 865, 1957)(526, 1618, 950, 2042)(528, 1620, 788, 1880)(529, 1621, 924, 2016)(530, 1622, 974, 2066)(531, 1623, 981, 2073)(532, 1624, 983, 2075)(533, 1625, 709, 1801)(534, 1626, 702, 1794)(535, 1627, 985, 2077)(537, 1629, 891, 1983)(539, 1631, 857, 1949)(541, 1633, 798, 1890)(543, 1635, 774, 1866)(545, 1637, 877, 1969)(549, 1641, 926, 2018)(550, 1642, 900, 1992)(554, 1646, 908, 2000)(555, 1647, 690, 1782)(557, 1649, 1006, 2098)(558, 1650, 761, 1853)(560, 1652, 955, 2047)(561, 1653, 674, 1766)(563, 1655, 1013, 2105)(564, 1656, 786, 1878)(566, 1658, 1004, 2096)(567, 1659, 1016, 2108)(569, 1661, 1002, 2094)(572, 1664, 902, 1994)(573, 1665, 1020, 2112)(575, 1667, 1017, 2109)(578, 1670, 1009, 2101)(579, 1671, 1023, 2115)(581, 1673, 998, 2090)(584, 1676, 864, 1956)(585, 1677, 1028, 2120)(587, 1679, 1025, 2117)(590, 1682, 976, 2068)(591, 1683, 606, 1698)(593, 1685, 1032, 2124)(594, 1686, 861, 1953)(596, 1688, 1033, 2125)(598, 1690, 664, 1756)(600, 1692, 1008, 2100)(601, 1693, 880, 1972)(603, 1695, 1027, 2119)(605, 1697, 940, 2032)(608, 1700, 1039, 2131)(609, 1701, 896, 1988)(611, 1703, 953, 2045)(613, 1705, 641, 1733)(615, 1707, 1003, 2095)(616, 1708, 931, 2023)(618, 1710, 1019, 2111)(620, 1712, 1022, 2114)(622, 1714, 989, 2081)(625, 1717, 883, 1975)(626, 1718, 921, 2013)(628, 1720, 1042, 2134)(629, 1721, 680, 1772)(631, 1723, 927, 2019)(632, 1724, 1045, 2137)(634, 1726, 919, 2011)(637, 1729, 790, 1882)(638, 1730, 1041, 2133)(640, 1732, 1047, 2139)(643, 1735, 1015, 2107)(645, 1737, 987, 2079)(647, 1739, 999, 2091)(649, 1741, 936, 2028)(652, 1744, 1050, 2142)(653, 1745, 696, 1788)(659, 1751, 875, 1967)(661, 1753, 765, 1857)(662, 1754, 1035, 2127)(666, 1758, 903, 1995)(667, 1759, 855, 1947)(669, 1761, 916, 2008)(670, 1762, 1005, 2097)(672, 1764, 1000, 2092)(676, 1768, 971, 2063)(677, 1769, 973, 2065)(678, 1770, 840, 1932)(685, 1777, 870, 1962)(686, 1778, 1012, 2104)(688, 1780, 980, 2072)(692, 1784, 1057, 2149)(693, 1785, 1058, 2150)(694, 1786, 815, 1907)(698, 1790, 992, 2084)(700, 1792, 1014, 2106)(704, 1796, 932, 2024)(710, 1802, 894, 1986)(712, 1804, 1007, 2099)(713, 1805, 778, 1870)(716, 1808, 1018, 2110)(719, 1811, 929, 2021)(720, 1812, 781, 1873)(725, 1817, 802, 1894)(727, 1819, 995, 2087)(729, 1821, 1021, 2113)(738, 1830, 859, 1951)(740, 1832, 966, 2058)(741, 1833, 801, 1893)(744, 1836, 1026, 2118)(746, 1838, 1059, 2151)(752, 1844, 779, 1871)(756, 1848, 888, 1980)(757, 1849, 963, 2055)(759, 1851, 847, 1939)(763, 1855, 942, 2034)(766, 1858, 831, 1923)(770, 1862, 795, 1887)(771, 1863, 982, 2074)(772, 1864, 961, 2053)(776, 1868, 1067, 2159)(777, 1869, 1051, 2143)(782, 1874, 915, 2007)(784, 1876, 821, 1913)(796, 1888, 946, 2038)(800, 1892, 1043, 2135)(808, 1900, 878, 1970)(810, 1902, 837, 1929)(811, 1903, 836, 1928)(823, 1915, 849, 1941)(824, 1916, 893, 1985)(825, 1917, 1048, 2140)(827, 1919, 1069, 2161)(843, 1935, 897, 1989)(845, 1937, 904, 1996)(850, 1942, 858, 1950)(851, 1943, 1053, 2145)(853, 1945, 967, 2059)(867, 1959, 949, 2041)(868, 1960, 1070, 2162)(871, 1963, 964, 2056)(885, 1977, 1073, 2165)(886, 1978, 1072, 2164)(889, 1981, 898, 1990)(905, 1997, 1001, 2093)(906, 1998, 1024, 2116)(907, 1999, 937, 2029)(910, 2002, 935, 2027)(911, 2003, 1075, 2167)(913, 2005, 1081, 2173)(914, 2006, 1083, 2175)(917, 2009, 1082, 2174)(920, 2012, 1065, 2157)(923, 2015, 1080, 2172)(928, 2020, 1046, 2138)(933, 2025, 1078, 2170)(934, 2026, 1085, 2177)(938, 2030, 986, 2078)(939, 2031, 984, 2076)(943, 2035, 1077, 2169)(944, 2036, 958, 2050)(945, 2037, 957, 2049)(959, 2051, 1037, 2129)(968, 2060, 1061, 2153)(970, 2062, 991, 2083)(977, 2069, 1055, 2147)(978, 2070, 1079, 2171)(979, 2071, 1040, 2132)(988, 2080, 1074, 2166)(990, 2082, 1088, 2180)(993, 2085, 1091, 2183)(994, 2086, 1063, 2155)(996, 2088, 1064, 2156)(997, 2089, 1071, 2163)(1010, 2102, 1089, 2181)(1011, 2103, 1062, 2154)(1029, 2121, 1036, 2128)(1030, 2122, 1076, 2168)(1031, 2123, 1052, 2144)(1034, 2126, 1060, 2152)(1038, 2130, 1044, 2136)(1049, 2141, 1054, 2146)(1056, 2148, 1086, 2178)(1066, 2158, 1092, 2184)(1068, 2160, 1090, 2182)(1084, 2176, 1087, 2179)(2185, 3277, 2187, 3279, 2188, 3280)(2186, 3278, 2189, 3281, 2190, 3282)(2191, 3283, 2195, 3287, 2196, 3288)(2192, 3284, 2197, 3289, 2198, 3290)(2193, 3285, 2199, 3291, 2200, 3292)(2194, 3286, 2201, 3293, 2202, 3294)(2203, 3295, 2211, 3303, 2212, 3304)(2204, 3296, 2213, 3305, 2214, 3306)(2205, 3297, 2215, 3307, 2216, 3308)(2206, 3298, 2217, 3309, 2218, 3310)(2207, 3299, 2219, 3311, 2220, 3312)(2208, 3300, 2221, 3313, 2222, 3314)(2209, 3301, 2223, 3315, 2224, 3316)(2210, 3302, 2225, 3317, 2226, 3318)(2227, 3319, 2242, 3334, 2243, 3335)(2228, 3320, 2244, 3336, 2245, 3337)(2229, 3321, 2246, 3338, 2247, 3339)(2230, 3322, 2248, 3340, 2249, 3341)(2231, 3323, 2250, 3342, 2251, 3343)(2232, 3324, 2252, 3344, 2253, 3345)(2233, 3325, 2254, 3346, 2255, 3347)(2234, 3326, 2256, 3348, 2235, 3327)(2236, 3328, 2257, 3349, 2258, 3350)(2237, 3329, 2259, 3351, 2260, 3352)(2238, 3330, 2261, 3353, 2262, 3354)(2239, 3331, 2263, 3355, 2264, 3356)(2240, 3332, 2265, 3357, 2266, 3358)(2241, 3333, 2267, 3359, 2268, 3360)(2269, 3361, 2291, 3383, 2292, 3384)(2270, 3362, 2293, 3385, 2294, 3386)(2271, 3363, 2295, 3387, 2296, 3388)(2272, 3364, 2297, 3389, 2298, 3390)(2273, 3365, 2299, 3391, 2300, 3392)(2274, 3366, 2301, 3393, 2302, 3394)(2275, 3367, 2303, 3395, 2304, 3396)(2276, 3368, 2305, 3397, 2306, 3398)(2277, 3369, 2307, 3399, 2308, 3400)(2278, 3370, 2309, 3401, 2310, 3402)(2279, 3371, 2311, 3403, 2312, 3404)(2280, 3372, 2313, 3405, 2314, 3406)(2281, 3373, 2315, 3407, 2316, 3408)(2282, 3374, 2317, 3409, 2318, 3410)(2283, 3375, 2319, 3411, 2320, 3412)(2284, 3376, 2321, 3413, 2322, 3414)(2285, 3377, 2323, 3415, 2324, 3416)(2286, 3378, 2325, 3417, 2326, 3418)(2287, 3379, 2327, 3419, 2328, 3420)(2288, 3380, 2329, 3421, 2330, 3422)(2289, 3381, 2331, 3423, 2332, 3424)(2290, 3382, 2333, 3425, 2334, 3426)(2335, 3427, 2371, 3463, 2372, 3464)(2336, 3428, 2373, 3465, 2374, 3466)(2337, 3429, 2375, 3467, 2376, 3468)(2338, 3430, 2377, 3469, 2378, 3470)(2339, 3431, 2379, 3471, 2380, 3472)(2340, 3432, 2381, 3473, 2382, 3474)(2341, 3433, 2383, 3475, 2384, 3476)(2342, 3434, 2385, 3477, 2386, 3478)(2343, 3435, 2387, 3479, 2388, 3480)(2344, 3436, 2389, 3481, 2390, 3482)(2345, 3437, 2391, 3483, 2392, 3484)(2346, 3438, 2393, 3485, 2394, 3486)(2347, 3439, 2395, 3487, 2396, 3488)(2348, 3440, 2397, 3489, 2398, 3490)(2349, 3441, 2399, 3491, 2400, 3492)(2350, 3442, 2401, 3493, 2402, 3494)(2351, 3443, 2403, 3495, 2404, 3496)(2352, 3444, 2405, 3497, 2406, 3498)(2353, 3445, 2407, 3499, 2408, 3500)(2354, 3446, 2409, 3501, 2410, 3502)(2355, 3447, 2411, 3503, 2412, 3504)(2356, 3448, 2413, 3505, 2414, 3506)(2357, 3449, 2415, 3507, 2416, 3508)(2358, 3450, 2417, 3509, 2418, 3510)(2359, 3451, 2419, 3511, 2420, 3512)(2360, 3452, 2421, 3513, 2422, 3514)(2361, 3453, 2423, 3515, 2424, 3516)(2362, 3454, 2425, 3517, 2426, 3518)(2363, 3455, 2427, 3519, 2428, 3520)(2364, 3456, 2429, 3521, 2430, 3522)(2365, 3457, 2431, 3523, 2432, 3524)(2366, 3458, 2433, 3525, 2434, 3526)(2367, 3459, 2435, 3527, 2436, 3528)(2368, 3460, 2437, 3529, 2438, 3530)(2369, 3461, 2439, 3531, 2440, 3532)(2370, 3462, 2441, 3533, 2442, 3534)(2443, 3535, 2495, 3587, 2527, 3619)(2444, 3536, 2682, 3774, 2967, 4059)(2445, 3537, 2622, 3714, 3051, 4143)(2446, 3538, 2685, 3777, 3136, 4228)(2447, 3539, 2686, 3778, 3025, 4117)(2448, 3540, 2606, 3698, 2603, 3695)(2449, 3541, 2503, 3595, 2799, 3891)(2450, 3542, 2690, 3782, 3139, 4231)(2451, 3543, 2618, 3710, 3010, 4102)(2452, 3544, 2595, 3687, 3011, 4103)(2453, 3545, 2473, 3565, 2614, 3706)(2454, 3546, 2695, 3787, 3147, 4239)(2455, 3547, 2526, 3618, 2569, 3661)(2456, 3548, 2698, 3790, 2871, 3963)(2457, 3549, 2700, 3792, 2458, 3550)(2459, 3551, 2498, 3590, 2502, 3594)(2460, 3552, 2704, 3796, 2927, 4019)(2461, 3553, 2635, 3727, 3069, 4161)(2462, 3554, 2707, 3799, 3016, 4108)(2463, 3555, 2708, 3800, 3140, 4232)(2464, 3556, 2691, 3783, 2687, 3779)(2465, 3557, 2522, 3614, 2853, 3945)(2466, 3558, 2711, 3803, 3160, 4252)(2467, 3559, 2631, 3723, 2929, 4021)(2468, 3560, 2553, 3645, 2930, 4022)(2469, 3561, 2475, 3567, 2627, 3719)(2470, 3562, 2715, 3807, 3166, 4258)(2471, 3563, 2501, 3593, 2534, 3626)(2472, 3564, 2718, 3810, 2942, 4034)(2474, 3566, 2637, 3729, 2652, 3744)(2476, 3568, 2662, 3754, 2565, 3657)(2477, 3569, 2577, 3669, 2702, 3794)(2478, 3570, 2624, 3716, 2599, 3691)(2479, 3571, 2566, 3658, 2734, 3826)(2480, 3572, 2655, 3747, 2582, 3674)(2481, 3573, 2738, 3830, 2530, 3622)(2482, 3574, 2741, 3833, 2559, 3651)(2483, 3575, 2744, 3836, 2523, 3615)(2484, 3576, 2747, 3839, 2571, 3663)(2485, 3577, 2531, 3623, 2751, 3843)(2486, 3578, 2753, 3845, 2591, 3683)(2487, 3579, 2560, 3652, 2757, 3849)(2488, 3580, 2759, 3851, 2549, 3641)(2489, 3581, 2524, 3616, 2763, 3855)(2490, 3582, 2765, 3857, 2608, 3700)(2491, 3583, 2572, 3664, 2769, 3861)(2492, 3584, 2771, 3863, 2538, 3630)(2493, 3585, 2774, 3866, 2513, 3605)(2494, 3586, 2777, 3869, 2616, 3708)(2496, 3588, 2663, 3755, 2504, 3596)(2497, 3589, 2784, 3876, 2629, 3721)(2499, 3591, 2789, 3881, 2505, 3597)(2500, 3592, 2792, 3884, 2639, 3731)(2506, 3598, 2806, 3898, 2693, 3785)(2507, 3599, 2617, 3709, 2810, 3902)(2508, 3600, 2812, 3904, 2544, 3636)(2509, 3601, 2520, 3612, 2816, 3908)(2510, 3602, 2818, 3910, 2713, 3805)(2511, 3603, 2630, 3722, 2822, 3914)(2512, 3604, 2824, 3916, 2517, 3609)(2514, 3606, 2829, 3921, 2831, 3923)(2515, 3607, 2640, 3732, 2834, 3926)(2516, 3608, 2836, 3928, 2555, 3647)(2518, 3610, 2841, 3933, 2843, 3935)(2519, 3611, 2665, 3757, 2846, 3938)(2521, 3613, 2850, 3942, 2579, 3671)(2525, 3617, 2860, 3952, 2626, 3718)(2528, 3620, 2866, 3958, 2568, 3660)(2529, 3621, 2869, 3961, 2673, 3765)(2532, 3624, 2876, 3968, 2660, 3752)(2533, 3625, 2557, 3649, 2656, 3748)(2535, 3627, 2882, 3974, 2884, 3976)(2536, 3628, 2613, 3705, 2886, 3978)(2537, 3629, 2888, 3980, 2587, 3679)(2539, 3631, 2893, 3985, 2894, 3986)(2540, 3632, 2896, 3988, 2870, 3962)(2541, 3633, 2833, 3925, 2900, 3992)(2542, 3634, 2701, 3793, 2678, 3770)(2543, 3635, 2903, 3995, 2597, 3689)(2545, 3637, 2908, 4000, 2909, 4001)(2546, 3638, 2911, 4003, 2913, 4005)(2547, 3639, 2596, 3688, 2915, 4007)(2548, 3640, 2917, 4009, 2604, 3696)(2550, 3642, 2906, 3998, 2922, 4014)(2551, 3643, 2924, 4016, 2854, 3946)(2552, 3644, 2809, 3901, 2928, 4020)(2554, 3646, 2932, 4024, 2580, 3672)(2556, 3648, 2935, 4027, 2936, 4028)(2558, 3650, 2940, 4032, 2941, 4033)(2561, 3653, 2947, 4039, 2949, 4041)(2562, 3654, 2563, 3655, 2951, 4043)(2564, 3656, 2954, 4046, 2955, 4047)(2567, 3659, 2960, 4052, 2962, 4054)(2570, 3662, 2699, 3791, 2966, 4058)(2573, 3665, 2972, 4064, 2974, 4066)(2574, 3666, 2575, 3667, 2976, 4068)(2576, 3668, 2979, 4071, 2980, 4072)(2578, 3670, 2705, 3797, 2985, 4077)(2581, 3673, 2989, 4081, 2688, 3780)(2583, 3675, 2839, 3931, 2992, 4084)(2584, 3676, 2994, 4086, 2658, 3750)(2585, 3677, 2821, 3913, 2984, 4076)(2586, 3678, 2647, 3739, 2589, 3681)(2588, 3680, 2926, 4018, 2999, 4091)(2590, 3682, 3002, 4094, 2709, 3801)(2592, 3684, 2891, 3983, 3005, 4097)(2593, 3685, 3007, 4099, 2800, 3892)(2594, 3686, 2768, 3860, 3009, 4101)(2598, 3690, 2996, 4088, 3015, 4107)(2600, 3692, 2815, 3907, 3018, 4110)(2601, 3693, 3020, 4112, 2625, 3717)(2602, 3694, 2845, 3937, 2961, 4053)(2605, 3697, 2898, 3990, 3024, 4116)(2607, 3699, 3027, 4119, 3029, 4121)(2609, 3701, 2920, 4012, 3031, 4123)(2610, 3702, 3033, 4125, 2785, 3877)(2611, 3703, 2756, 3848, 3035, 4127)(2612, 3704, 3037, 4129, 2628, 3720)(2615, 3707, 2719, 3811, 3042, 4134)(2619, 3711, 3026, 4118, 3048, 4140)(2620, 3712, 2621, 3713, 3012, 4104)(2623, 3715, 3054, 4146, 3055, 4147)(2632, 3724, 3066, 4158, 3067, 4159)(2633, 3725, 2634, 3726, 2931, 4023)(2636, 3728, 3072, 4164, 3073, 4165)(2638, 3730, 2683, 3775, 3077, 4169)(2641, 3733, 2651, 3743, 3082, 4174)(2642, 3734, 3036, 4128, 2650, 3742)(2643, 3735, 2939, 4031, 3084, 4176)(2644, 3736, 3001, 4093, 3086, 4178)(2645, 3737, 3039, 4131, 3000, 4092)(2646, 3738, 2649, 3741, 3038, 4130)(2648, 3740, 3090, 4182, 3092, 4184)(2653, 3745, 3097, 4189, 3099, 4191)(2654, 3746, 3100, 4192, 3101, 4193)(2657, 3749, 3105, 4197, 2855, 3947)(2659, 3751, 3107, 4199, 2661, 3753)(2664, 3756, 3113, 4205, 2899, 3991)(2666, 3758, 2677, 3769, 3117, 4209)(2667, 3759, 2901, 3993, 2676, 3768)(2668, 3760, 3076, 4168, 2990, 4082)(2669, 3761, 3119, 4211, 3120, 4212)(2670, 3762, 2904, 3996, 3121, 4213)(2671, 3763, 2675, 3767, 2902, 3994)(2672, 3764, 3091, 4183, 3087, 4179)(2674, 3766, 3053, 4145, 3124, 4216)(2679, 3771, 3128, 4220, 3130, 4222)(2680, 3772, 3132, 4224, 3133, 4225)(2681, 3773, 2762, 3854, 3134, 4226)(2684, 3776, 2897, 3989, 2877, 3969)(2689, 3781, 2828, 3920, 3137, 4229)(2692, 3784, 3141, 4233, 3143, 4235)(2694, 3786, 2991, 4083, 3145, 4237)(2696, 3788, 3150, 4242, 2748, 3840)(2697, 3789, 2733, 3825, 3152, 4244)(2703, 3795, 2804, 3896, 3023, 4115)(2706, 3798, 2912, 4004, 2948, 4040)(2710, 3802, 2881, 3973, 3125, 4217)(2712, 3804, 3161, 4253, 3163, 4255)(2714, 3806, 2921, 4013, 3164, 4256)(2716, 3808, 3021, 4113, 2778, 3870)(2717, 3809, 2750, 3842, 3168, 4260)(2720, 3812, 2983, 4075, 3004, 4096)(2721, 3813, 3170, 4262, 3171, 4263)(2722, 3814, 2959, 4051, 3030, 4122)(2723, 3815, 3172, 4264, 3173, 4265)(2724, 3816, 3058, 4150, 2919, 4011)(2725, 3817, 3174, 4266, 3176, 4268)(2726, 3818, 3106, 4198, 2890, 3982)(2727, 3819, 3177, 4269, 3179, 4271)(2728, 3820, 2875, 3967, 3144, 4236)(2729, 3821, 3180, 4272, 3103, 4195)(2730, 3822, 2946, 4038, 3108, 4200)(2731, 3823, 3181, 4273, 3182, 4274)(2732, 3824, 2859, 3951, 3183, 4275)(2735, 3827, 2971, 4063, 3059, 4151)(2736, 3828, 3185, 4277, 3186, 4278)(2737, 3829, 3115, 4207, 2905, 3997)(2739, 3831, 3118, 4210, 3114, 4206)(2740, 3832, 3189, 4281, 2838, 3930)(2742, 3834, 3098, 4190, 3191, 4283)(2743, 3835, 3064, 4156, 2933, 4025)(2745, 3837, 3194, 4286, 3063, 4155)(2746, 3838, 3196, 4288, 2814, 3906)(2749, 3841, 2791, 3883, 3198, 4290)(2752, 3844, 3047, 4139, 3078, 4170)(2754, 3846, 3178, 4270, 3201, 4293)(2755, 3847, 2849, 3941, 3202, 4294)(2758, 3850, 3065, 4157, 2986, 4078)(2760, 3852, 3104, 4196, 3102, 4194)(2761, 3853, 2776, 3868, 3205, 4297)(2764, 3856, 3085, 4177, 3043, 4135)(2766, 3858, 3175, 4267, 3209, 4301)(2767, 3859, 2865, 3957, 3210, 4302)(2770, 3862, 3057, 4149, 2963, 4055)(2772, 3864, 3195, 4287, 3056, 4148)(2773, 3865, 2970, 4062, 2997, 4089)(2775, 3867, 3214, 4306, 2969, 4061)(2779, 3871, 2953, 4045, 3200, 4292)(2780, 3872, 2916, 4008, 3110, 4202)(2781, 3873, 3045, 4137, 3013, 4105)(2782, 3874, 3127, 4219, 3044, 4136)(2783, 3875, 3219, 4311, 2803, 3895)(2786, 3878, 2868, 3960, 3204, 4296)(2787, 3879, 2988, 4080, 3188, 4280)(2788, 3880, 2945, 4037, 3022, 4114)(2790, 3882, 3221, 4313, 2944, 4036)(2793, 3885, 3129, 4221, 2995, 4087)(2794, 3886, 2978, 4070, 3207, 4299)(2795, 3887, 2887, 3979, 3061, 4153)(2796, 3888, 3080, 4172, 2987, 4079)(2797, 3889, 3070, 4162, 3079, 4171)(2798, 3890, 3225, 4317, 2826, 3918)(2801, 3893, 2852, 3944, 3212, 4304)(2802, 3894, 3014, 4106, 3193, 4285)(2805, 3897, 3217, 4309, 3062, 4154)(2807, 3899, 3083, 4175, 3226, 4318)(2808, 3900, 2937, 4029, 3227, 4319)(2811, 3903, 3075, 4167, 2878, 3970)(2813, 3905, 3215, 4307, 3074, 4166)(2817, 3909, 3211, 4303, 2968, 4060)(2819, 3911, 3131, 4223, 3231, 4323)(2820, 3912, 2952, 4044, 3232, 4324)(2823, 3915, 2982, 4074, 2950, 4042)(2825, 3917, 3218, 4310, 2981, 4073)(2827, 3919, 2998, 4090, 3111, 4203)(2830, 3922, 3046, 4138, 3234, 4326)(2832, 3924, 2964, 4056, 3235, 4327)(2835, 3927, 3041, 4133, 2862, 3954)(2837, 3929, 3222, 4314, 3040, 4132)(2840, 3932, 3203, 4295, 2943, 4035)(2842, 3934, 3071, 4163, 3229, 4321)(2844, 3936, 2977, 4069, 3237, 4329)(2847, 3939, 2958, 4050, 2975, 4067)(2848, 3940, 3224, 4316, 2957, 4049)(2851, 3943, 3239, 4331, 3008, 4100)(2856, 3948, 2934, 4026, 3206, 4298)(2857, 3949, 2874, 3966, 3049, 4141)(2858, 3950, 3088, 4180, 2873, 3965)(2861, 3953, 3081, 4173, 2925, 4017)(2863, 3955, 3157, 4249, 2914, 4006)(2864, 3956, 3052, 4144, 3156, 4248)(2867, 3959, 3240, 4332, 3034, 4126)(2872, 3964, 2907, 3999, 3199, 4291)(2879, 3971, 3242, 4334, 2885, 3977)(2880, 3972, 3095, 4187, 3243, 4335)(2883, 3975, 2973, 4065, 3116, 4208)(2889, 3981, 3238, 4330, 3060, 4152)(2892, 3984, 3184, 4276, 2956, 4048)(2895, 3987, 3050, 4142, 3245, 4337)(2910, 4002, 3068, 4160, 3123, 4215)(2918, 4010, 3112, 4204, 3109, 4201)(2923, 4015, 3093, 4185, 3248, 4340)(2938, 4030, 3250, 4342, 3151, 4243)(2965, 4057, 3252, 4344, 3253, 4345)(2993, 4085, 3254, 4346, 3255, 4347)(3003, 4095, 3213, 4305, 3190, 4282)(3006, 4098, 3256, 4348, 3258, 4350)(3017, 4109, 3158, 4250, 3096, 4188)(3019, 4111, 3259, 4351, 3089, 4181)(3028, 4120, 3220, 4312, 3197, 4289)(3032, 4124, 3261, 4353, 3122, 4214)(3094, 4186, 3167, 4259, 3260, 4352)(3126, 4218, 3270, 4362, 3244, 4336)(3135, 4227, 3262, 4354, 3247, 4339)(3138, 4230, 3187, 4279, 3271, 4363)(3142, 4234, 3230, 4322, 3216, 4308)(3146, 4238, 3228, 4320, 3155, 4247)(3148, 4240, 3153, 4245, 3263, 4355)(3149, 4241, 3273, 4365, 3272, 4364)(3154, 4246, 3169, 4261, 3257, 4349)(3159, 4251, 3274, 4366, 3249, 4341)(3162, 4254, 3208, 4300, 3192, 4284)(3165, 4257, 3233, 4325, 3223, 4315)(3236, 4328, 3241, 4333, 3265, 4357)(3246, 4338, 3251, 4343, 3276, 4368)(3264, 4356, 3268, 4360, 3266, 4358)(3267, 4359, 3269, 4361, 3275, 4367) L = (1, 2186)(2, 2185)(3, 2191)(4, 2192)(5, 2193)(6, 2194)(7, 2187)(8, 2188)(9, 2189)(10, 2190)(11, 2203)(12, 2204)(13, 2205)(14, 2206)(15, 2207)(16, 2208)(17, 2209)(18, 2210)(19, 2195)(20, 2196)(21, 2197)(22, 2198)(23, 2199)(24, 2200)(25, 2201)(26, 2202)(27, 2227)(28, 2228)(29, 2229)(30, 2230)(31, 2231)(32, 2232)(33, 2233)(34, 2234)(35, 2235)(36, 2236)(37, 2237)(38, 2238)(39, 2239)(40, 2240)(41, 2241)(42, 2242)(43, 2211)(44, 2212)(45, 2213)(46, 2214)(47, 2215)(48, 2216)(49, 2217)(50, 2218)(51, 2219)(52, 2220)(53, 2221)(54, 2222)(55, 2223)(56, 2224)(57, 2225)(58, 2226)(59, 2269)(60, 2270)(61, 2271)(62, 2272)(63, 2273)(64, 2274)(65, 2250)(66, 2249)(67, 2275)(68, 2276)(69, 2277)(70, 2278)(71, 2279)(72, 2280)(73, 2281)(74, 2282)(75, 2283)(76, 2284)(77, 2285)(78, 2263)(79, 2262)(80, 2286)(81, 2287)(82, 2288)(83, 2289)(84, 2290)(85, 2243)(86, 2244)(87, 2245)(88, 2246)(89, 2247)(90, 2248)(91, 2251)(92, 2252)(93, 2253)(94, 2254)(95, 2255)(96, 2256)(97, 2257)(98, 2258)(99, 2259)(100, 2260)(101, 2261)(102, 2264)(103, 2265)(104, 2266)(105, 2267)(106, 2268)(107, 2335)(108, 2336)(109, 2337)(110, 2338)(111, 2339)(112, 2297)(113, 2296)(114, 2340)(115, 2341)(116, 2342)(117, 2343)(118, 2344)(119, 2345)(120, 2346)(121, 2347)(122, 2348)(123, 2349)(124, 2309)(125, 2308)(126, 2350)(127, 2351)(128, 2352)(129, 2353)(130, 2354)(131, 2355)(132, 2356)(133, 2357)(134, 2319)(135, 2318)(136, 2358)(137, 2359)(138, 2360)(139, 2361)(140, 2362)(141, 2363)(142, 2364)(143, 2365)(144, 2366)(145, 2367)(146, 2331)(147, 2330)(148, 2368)(149, 2369)(150, 2370)(151, 2291)(152, 2292)(153, 2293)(154, 2294)(155, 2295)(156, 2298)(157, 2299)(158, 2300)(159, 2301)(160, 2302)(161, 2303)(162, 2304)(163, 2305)(164, 2306)(165, 2307)(166, 2310)(167, 2311)(168, 2312)(169, 2313)(170, 2314)(171, 2315)(172, 2316)(173, 2317)(174, 2320)(175, 2321)(176, 2322)(177, 2323)(178, 2324)(179, 2325)(180, 2326)(181, 2327)(182, 2328)(183, 2329)(184, 2332)(185, 2333)(186, 2334)(187, 2442)(188, 2443)(189, 2444)(190, 2375)(191, 2374)(192, 2445)(193, 2446)(194, 2447)(195, 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3777)(1594, 3778)(1595, 3779)(1596, 3780)(1597, 3781)(1598, 3782)(1599, 3783)(1600, 3784)(1601, 3785)(1602, 3786)(1603, 3787)(1604, 3788)(1605, 3789)(1606, 3790)(1607, 3791)(1608, 3792)(1609, 3793)(1610, 3794)(1611, 3795)(1612, 3796)(1613, 3797)(1614, 3798)(1615, 3799)(1616, 3800)(1617, 3801)(1618, 3802)(1619, 3803)(1620, 3804)(1621, 3805)(1622, 3806)(1623, 3807)(1624, 3808)(1625, 3809)(1626, 3810)(1627, 3811)(1628, 3812)(1629, 3813)(1630, 3814)(1631, 3815)(1632, 3816)(1633, 3817)(1634, 3818)(1635, 3819)(1636, 3820)(1637, 3821)(1638, 3822)(1639, 3823)(1640, 3824)(1641, 3825)(1642, 3826)(1643, 3827)(1644, 3828)(1645, 3829)(1646, 3830)(1647, 3831)(1648, 3832)(1649, 3833)(1650, 3834)(1651, 3835)(1652, 3836)(1653, 3837)(1654, 3838)(1655, 3839)(1656, 3840)(1657, 3841)(1658, 3842)(1659, 3843)(1660, 3844)(1661, 3845)(1662, 3846)(1663, 3847)(1664, 3848)(1665, 3849)(1666, 3850)(1667, 3851)(1668, 3852)(1669, 3853)(1670, 3854)(1671, 3855)(1672, 3856)(1673, 3857)(1674, 3858)(1675, 3859)(1676, 3860)(1677, 3861)(1678, 3862)(1679, 3863)(1680, 3864)(1681, 3865)(1682, 3866)(1683, 3867)(1684, 3868)(1685, 3869)(1686, 3870)(1687, 3871)(1688, 3872)(1689, 3873)(1690, 3874)(1691, 3875)(1692, 3876)(1693, 3877)(1694, 3878)(1695, 3879)(1696, 3880)(1697, 3881)(1698, 3882)(1699, 3883)(1700, 3884)(1701, 3885)(1702, 3886)(1703, 3887)(1704, 3888)(1705, 3889)(1706, 3890)(1707, 3891)(1708, 3892)(1709, 3893)(1710, 3894)(1711, 3895)(1712, 3896)(1713, 3897)(1714, 3898)(1715, 3899)(1716, 3900)(1717, 3901)(1718, 3902)(1719, 3903)(1720, 3904)(1721, 3905)(1722, 3906)(1723, 3907)(1724, 3908)(1725, 3909)(1726, 3910)(1727, 3911)(1728, 3912)(1729, 3913)(1730, 3914)(1731, 3915)(1732, 3916)(1733, 3917)(1734, 3918)(1735, 3919)(1736, 3920)(1737, 3921)(1738, 3922)(1739, 3923)(1740, 3924)(1741, 3925)(1742, 3926)(1743, 3927)(1744, 3928)(1745, 3929)(1746, 3930)(1747, 3931)(1748, 3932)(1749, 3933)(1750, 3934)(1751, 3935)(1752, 3936)(1753, 3937)(1754, 3938)(1755, 3939)(1756, 3940)(1757, 3941)(1758, 3942)(1759, 3943)(1760, 3944)(1761, 3945)(1762, 3946)(1763, 3947)(1764, 3948)(1765, 3949)(1766, 3950)(1767, 3951)(1768, 3952)(1769, 3953)(1770, 3954)(1771, 3955)(1772, 3956)(1773, 3957)(1774, 3958)(1775, 3959)(1776, 3960)(1777, 3961)(1778, 3962)(1779, 3963)(1780, 3964)(1781, 3965)(1782, 3966)(1783, 3967)(1784, 3968)(1785, 3969)(1786, 3970)(1787, 3971)(1788, 3972)(1789, 3973)(1790, 3974)(1791, 3975)(1792, 3976)(1793, 3977)(1794, 3978)(1795, 3979)(1796, 3980)(1797, 3981)(1798, 3982)(1799, 3983)(1800, 3984)(1801, 3985)(1802, 3986)(1803, 3987)(1804, 3988)(1805, 3989)(1806, 3990)(1807, 3991)(1808, 3992)(1809, 3993)(1810, 3994)(1811, 3995)(1812, 3996)(1813, 3997)(1814, 3998)(1815, 3999)(1816, 4000)(1817, 4001)(1818, 4002)(1819, 4003)(1820, 4004)(1821, 4005)(1822, 4006)(1823, 4007)(1824, 4008)(1825, 4009)(1826, 4010)(1827, 4011)(1828, 4012)(1829, 4013)(1830, 4014)(1831, 4015)(1832, 4016)(1833, 4017)(1834, 4018)(1835, 4019)(1836, 4020)(1837, 4021)(1838, 4022)(1839, 4023)(1840, 4024)(1841, 4025)(1842, 4026)(1843, 4027)(1844, 4028)(1845, 4029)(1846, 4030)(1847, 4031)(1848, 4032)(1849, 4033)(1850, 4034)(1851, 4035)(1852, 4036)(1853, 4037)(1854, 4038)(1855, 4039)(1856, 4040)(1857, 4041)(1858, 4042)(1859, 4043)(1860, 4044)(1861, 4045)(1862, 4046)(1863, 4047)(1864, 4048)(1865, 4049)(1866, 4050)(1867, 4051)(1868, 4052)(1869, 4053)(1870, 4054)(1871, 4055)(1872, 4056)(1873, 4057)(1874, 4058)(1875, 4059)(1876, 4060)(1877, 4061)(1878, 4062)(1879, 4063)(1880, 4064)(1881, 4065)(1882, 4066)(1883, 4067)(1884, 4068)(1885, 4069)(1886, 4070)(1887, 4071)(1888, 4072)(1889, 4073)(1890, 4074)(1891, 4075)(1892, 4076)(1893, 4077)(1894, 4078)(1895, 4079)(1896, 4080)(1897, 4081)(1898, 4082)(1899, 4083)(1900, 4084)(1901, 4085)(1902, 4086)(1903, 4087)(1904, 4088)(1905, 4089)(1906, 4090)(1907, 4091)(1908, 4092)(1909, 4093)(1910, 4094)(1911, 4095)(1912, 4096)(1913, 4097)(1914, 4098)(1915, 4099)(1916, 4100)(1917, 4101)(1918, 4102)(1919, 4103)(1920, 4104)(1921, 4105)(1922, 4106)(1923, 4107)(1924, 4108)(1925, 4109)(1926, 4110)(1927, 4111)(1928, 4112)(1929, 4113)(1930, 4114)(1931, 4115)(1932, 4116)(1933, 4117)(1934, 4118)(1935, 4119)(1936, 4120)(1937, 4121)(1938, 4122)(1939, 4123)(1940, 4124)(1941, 4125)(1942, 4126)(1943, 4127)(1944, 4128)(1945, 4129)(1946, 4130)(1947, 4131)(1948, 4132)(1949, 4133)(1950, 4134)(1951, 4135)(1952, 4136)(1953, 4137)(1954, 4138)(1955, 4139)(1956, 4140)(1957, 4141)(1958, 4142)(1959, 4143)(1960, 4144)(1961, 4145)(1962, 4146)(1963, 4147)(1964, 4148)(1965, 4149)(1966, 4150)(1967, 4151)(1968, 4152)(1969, 4153)(1970, 4154)(1971, 4155)(1972, 4156)(1973, 4157)(1974, 4158)(1975, 4159)(1976, 4160)(1977, 4161)(1978, 4162)(1979, 4163)(1980, 4164)(1981, 4165)(1982, 4166)(1983, 4167)(1984, 4168)(1985, 4169)(1986, 4170)(1987, 4171)(1988, 4172)(1989, 4173)(1990, 4174)(1991, 4175)(1992, 4176)(1993, 4177)(1994, 4178)(1995, 4179)(1996, 4180)(1997, 4181)(1998, 4182)(1999, 4183)(2000, 4184)(2001, 4185)(2002, 4186)(2003, 4187)(2004, 4188)(2005, 4189)(2006, 4190)(2007, 4191)(2008, 4192)(2009, 4193)(2010, 4194)(2011, 4195)(2012, 4196)(2013, 4197)(2014, 4198)(2015, 4199)(2016, 4200)(2017, 4201)(2018, 4202)(2019, 4203)(2020, 4204)(2021, 4205)(2022, 4206)(2023, 4207)(2024, 4208)(2025, 4209)(2026, 4210)(2027, 4211)(2028, 4212)(2029, 4213)(2030, 4214)(2031, 4215)(2032, 4216)(2033, 4217)(2034, 4218)(2035, 4219)(2036, 4220)(2037, 4221)(2038, 4222)(2039, 4223)(2040, 4224)(2041, 4225)(2042, 4226)(2043, 4227)(2044, 4228)(2045, 4229)(2046, 4230)(2047, 4231)(2048, 4232)(2049, 4233)(2050, 4234)(2051, 4235)(2052, 4236)(2053, 4237)(2054, 4238)(2055, 4239)(2056, 4240)(2057, 4241)(2058, 4242)(2059, 4243)(2060, 4244)(2061, 4245)(2062, 4246)(2063, 4247)(2064, 4248)(2065, 4249)(2066, 4250)(2067, 4251)(2068, 4252)(2069, 4253)(2070, 4254)(2071, 4255)(2072, 4256)(2073, 4257)(2074, 4258)(2075, 4259)(2076, 4260)(2077, 4261)(2078, 4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 2, 14, 2, 14 ), ( 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E14.648 Graph:: bipartite v = 910 e = 2184 f = 1248 degree seq :: [ 4^546, 6^364 ] E14.640 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y2^7, (Y2^-2 * Y1)^6, Y2 * Y1^-1 * Y2^-2 * Y1 * Y2^3 * Y1 * Y2^-1 * Y1^-1 * Y2^-2 * Y1 * Y2^-2 * Y1 * Y2^-5 * Y1^-1 * Y2^2 * Y1^-1 * Y2^2 * Y1^-1, Y2^2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-2 * Y1 * Y2^3 * Y1 * Y2^-1 * Y1 * Y2^-2 * Y1 * Y2^-3 * Y1^-1 * Y2 * Y1^-1 * Y2^-3 * Y1^-1 * Y2 * Y1^-1 ] Map:: R = (1, 1093, 2, 1094, 4, 1096)(3, 1095, 8, 1100, 10, 1102)(5, 1097, 12, 1104, 6, 1098)(7, 1099, 15, 1107, 11, 1103)(9, 1101, 18, 1110, 20, 1112)(13, 1105, 25, 1117, 23, 1115)(14, 1106, 24, 1116, 28, 1120)(16, 1108, 31, 1123, 29, 1121)(17, 1109, 33, 1125, 21, 1113)(19, 1111, 36, 1128, 37, 1129)(22, 1114, 30, 1122, 41, 1133)(26, 1118, 46, 1138, 44, 1136)(27, 1119, 47, 1139, 48, 1140)(32, 1124, 54, 1146, 52, 1144)(34, 1126, 57, 1149, 55, 1147)(35, 1127, 58, 1150, 38, 1130)(39, 1131, 56, 1148, 64, 1156)(40, 1132, 65, 1157, 66, 1158)(42, 1134, 45, 1137, 69, 1161)(43, 1135, 70, 1162, 49, 1141)(50, 1142, 53, 1145, 79, 1171)(51, 1143, 80, 1172, 67, 1159)(59, 1151, 90, 1182, 88, 1180)(60, 1152, 91, 1183, 61, 1153)(62, 1154, 89, 1181, 95, 1187)(63, 1155, 96, 1188, 97, 1189)(68, 1160, 102, 1194, 103, 1195)(71, 1163, 107, 1199, 105, 1197)(72, 1164, 74, 1166, 109, 1201)(73, 1165, 110, 1202, 104, 1196)(75, 1167, 113, 1205, 76, 1168)(77, 1169, 106, 1198, 117, 1209)(78, 1170, 118, 1210, 119, 1211)(81, 1173, 123, 1215, 121, 1213)(82, 1174, 84, 1176, 125, 1217)(83, 1175, 126, 1218, 120, 1212)(85, 1177, 87, 1179, 130, 1222)(86, 1178, 131, 1223, 98, 1190)(92, 1184, 139, 1231, 137, 1229)(93, 1185, 138, 1230, 141, 1233)(94, 1186, 142, 1234, 143, 1235)(99, 1191, 148, 1240, 100, 1192)(101, 1193, 122, 1214, 152, 1244)(108, 1200, 159, 1251, 160, 1252)(111, 1203, 164, 1256, 162, 1254)(112, 1204, 165, 1257, 161, 1253)(114, 1206, 168, 1260, 166, 1258)(115, 1207, 167, 1259, 170, 1262)(116, 1208, 171, 1263, 172, 1264)(124, 1216, 180, 1272, 181, 1273)(127, 1219, 185, 1277, 183, 1275)(128, 1220, 186, 1278, 182, 1274)(129, 1221, 187, 1279, 188, 1280)(132, 1224, 192, 1284, 190, 1282)(133, 1225, 193, 1285, 189, 1281)(134, 1226, 136, 1228, 196, 1288)(135, 1227, 197, 1289, 144, 1236)(140, 1232, 203, 1295, 204, 1296)(145, 1237, 209, 1301, 146, 1238)(147, 1239, 191, 1283, 213, 1305)(149, 1241, 216, 1308, 214, 1306)(150, 1242, 215, 1307, 217, 1309)(151, 1243, 218, 1310, 219, 1311)(153, 1245, 221, 1313, 154, 1246)(155, 1247, 163, 1255, 225, 1317)(156, 1248, 158, 1250, 227, 1319)(157, 1249, 228, 1320, 173, 1265)(169, 1261, 241, 1333, 242, 1334)(174, 1266, 247, 1339, 175, 1267)(176, 1268, 184, 1276, 251, 1343)(177, 1269, 179, 1271, 253, 1345)(178, 1270, 254, 1346, 220, 1312)(194, 1286, 272, 1364, 270, 1362)(195, 1287, 273, 1365, 274, 1366)(198, 1290, 278, 1370, 276, 1368)(199, 1291, 279, 1371, 275, 1367)(200, 1292, 202, 1294, 282, 1374)(201, 1293, 283, 1375, 205, 1297)(206, 1298, 289, 1381, 207, 1299)(208, 1300, 277, 1369, 261, 1353)(210, 1302, 295, 1387, 293, 1385)(211, 1303, 294, 1386, 296, 1388)(212, 1304, 297, 1389, 298, 1390)(222, 1314, 309, 1401, 307, 1399)(223, 1315, 308, 1400, 311, 1403)(224, 1316, 312, 1404, 313, 1405)(226, 1318, 315, 1407, 316, 1408)(229, 1321, 319, 1411, 318, 1410)(230, 1322, 320, 1412, 317, 1409)(231, 1323, 321, 1413, 232, 1324)(233, 1325, 237, 1329, 325, 1417)(234, 1326, 236, 1328, 327, 1419)(235, 1327, 306, 1398, 314, 1406)(238, 1330, 240, 1332, 332, 1424)(239, 1331, 333, 1425, 243, 1335)(244, 1336, 339, 1431, 245, 1337)(246, 1338, 299, 1391, 268, 1360)(248, 1340, 345, 1437, 343, 1435)(249, 1341, 344, 1436, 347, 1439)(250, 1342, 348, 1440, 349, 1441)(252, 1344, 350, 1442, 351, 1443)(255, 1347, 354, 1446, 353, 1445)(256, 1348, 355, 1447, 352, 1444)(257, 1349, 356, 1448, 258, 1350)(259, 1351, 263, 1355, 360, 1452)(260, 1352, 262, 1354, 362, 1454)(264, 1356, 366, 1458, 265, 1357)(266, 1358, 271, 1363, 370, 1462)(267, 1359, 269, 1361, 372, 1464)(280, 1372, 385, 1477, 383, 1475)(281, 1373, 386, 1478, 387, 1479)(284, 1376, 391, 1483, 389, 1481)(285, 1377, 392, 1484, 388, 1480)(286, 1378, 394, 1486, 287, 1379)(288, 1380, 390, 1482, 376, 1468)(290, 1382, 400, 1492, 398, 1490)(291, 1383, 399, 1491, 401, 1493)(292, 1384, 363, 1455, 402, 1494)(300, 1392, 302, 1394, 410, 1502)(301, 1393, 411, 1503, 303, 1395)(304, 1396, 415, 1507, 305, 1397)(310, 1402, 422, 1514, 423, 1515)(322, 1414, 435, 1527, 433, 1525)(323, 1415, 434, 1526, 437, 1529)(324, 1416, 438, 1530, 439, 1531)(326, 1418, 441, 1533, 442, 1534)(328, 1420, 444, 1536, 418, 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4203, 3215, 4307, 3113, 4205, 2979, 4071)(2845, 3937, 2986, 4078, 3118, 4210, 3219, 4311, 3120, 4212, 2988, 4080, 2848, 3940)(2852, 3944, 2991, 4083, 3075, 4167, 3187, 4279, 3212, 4304, 3108, 4200, 2989, 4081)(2863, 3955, 3002, 4094, 3135, 4227, 3208, 4300, 3102, 4194, 2966, 4058, 2865, 3957)(2868, 3960, 2971, 4063, 3107, 4199, 3211, 4303, 3232, 4324, 3137, 4229, 3005, 4097)(2871, 3963, 3007, 4099, 3017, 4109, 3147, 4239, 3231, 4323, 3136, 4228, 3004, 4096)(2874, 3966, 2878, 3970, 3012, 4104, 3144, 4236, 3236, 4328, 3142, 4234, 3009, 4101)(2880, 3972, 3011, 4103, 3143, 4235, 3237, 4329, 3155, 4247, 3031, 4123, 3014, 4106)(2882, 3974, 3016, 4108, 3138, 4230, 3233, 4325, 3239, 4331, 3146, 4238, 3015, 4107)(2885, 3977, 2896, 3988, 3032, 4124, 3157, 4249, 3241, 4333, 3149, 4241, 3020, 4112)(2887, 3979, 3022, 4114, 3150, 4242, 3213, 4305, 3109, 4201, 2974, 4066, 3023, 4115)(2892, 3984, 3027, 4119, 3153, 4245, 3243, 4335, 3223, 4315, 3145, 4237, 3028, 4120)(2905, 3997, 3044, 4136, 3038, 4130, 3162, 4254, 3250, 4342, 3164, 4256, 3042, 4134)(2910, 4002, 3048, 4140, 3169, 4261, 3245, 4337, 3154, 4246, 3029, 4121, 2912, 4004)(2915, 4007, 3034, 4126, 3159, 4251, 3247, 4339, 3255, 4347, 3171, 4263, 3051, 4143)(2918, 4010, 3053, 4145, 3063, 4155, 3180, 4272, 3254, 4346, 3170, 4262, 3050, 4142)(2921, 4013, 2925, 4017, 3058, 4150, 3177, 4269, 3257, 4349, 3175, 4267, 3055, 4147)(2927, 4019, 3057, 4149, 3176, 4268, 3258, 4350, 3224, 4316, 3125, 4217, 3060, 4152)(2929, 4021, 3062, 4154, 3172, 4264, 3203, 4295, 3260, 4352, 3179, 4271, 3061, 4153)(2932, 4024, 2994, 4086, 3126, 4218, 3226, 4318, 3262, 4354, 3182, 4274, 3066, 4158)(2934, 4026, 3068, 4160, 3183, 4275, 3248, 4340, 3160, 4252, 3037, 4129, 3069, 4161)(2940, 4032, 3074, 4166, 3121, 4213, 3222, 4314, 3264, 4356, 3186, 4278, 3073, 4165)(2945, 4037, 3080, 4172, 3191, 4283, 3266, 4358, 3196, 4288, 3090, 4182, 3081, 4173)(2970, 4062, 3104, 4196, 3209, 4301, 3240, 4332, 3148, 4240, 3021, 4113, 3106, 4198)(2980, 4072, 3114, 4206, 3167, 4259, 3253, 4345, 3218, 4310, 3116, 4208, 2983, 4075)(2992, 4084, 3119, 4211, 3220, 4312, 3274, 4366, 3234, 4326, 3178, 4270, 3123, 4215)(2997, 4089, 3130, 4222, 3086, 4178, 3194, 4286, 3268, 4360, 3227, 4319, 3128, 4220)(3024, 4116, 3026, 4118, 3152, 4244, 3242, 4334, 3256, 4348, 3174, 4266, 3151, 4243)(3033, 4125, 3156, 4248, 3246, 4338, 3261, 4353, 3181, 4273, 3067, 4159, 3158, 4250)(3043, 4135, 3165, 4257, 3117, 4209, 3217, 4309, 3252, 4344, 3166, 4258, 3046, 4138)(3070, 4162, 3072, 4164, 3185, 4277, 3263, 4355, 3198, 4290, 3092, 4184, 3184, 4276)(3079, 4171, 3190, 4282, 3127, 4219, 3225, 4317, 3275, 4367, 3265, 4357, 3188, 4280)(3082, 4174, 3085, 4177, 3193, 4285, 3267, 4359, 3235, 4327, 3141, 4233, 3192, 4284)(3110, 4202, 3214, 4306, 3259, 4351, 3276, 4368, 3244, 4336, 3216, 4308, 3112, 4204)(3129, 4221, 3228, 4320, 3133, 4225, 3230, 4322, 3273, 4365, 3229, 4321, 3132, 4224)(3161, 4253, 3249, 4341, 3201, 4293, 3271, 4363, 3221, 4313, 3251, 4343, 3163, 4255)(3195, 4287, 3197, 4289, 3270, 4362, 3238, 4330, 3272, 4364, 3207, 4299, 3269, 4361) L = (1, 2187)(2, 2190)(3, 2193)(4, 2195)(5, 2185)(6, 2198)(7, 2186)(8, 2188)(9, 2203)(10, 2205)(11, 2206)(12, 2207)(13, 2189)(14, 2211)(15, 2213)(16, 2191)(17, 2192)(18, 2194)(19, 2210)(20, 2222)(21, 2223)(22, 2224)(23, 2226)(24, 2196)(25, 2228)(26, 2197)(27, 2216)(28, 2233)(29, 2234)(30, 2199)(31, 2236)(32, 2200)(33, 2239)(34, 2201)(35, 2202)(36, 2204)(37, 2245)(38, 2246)(39, 2247)(40, 2218)(41, 2251)(42, 2252)(43, 2208)(44, 2256)(45, 2209)(46, 2221)(47, 2212)(48, 2260)(49, 2261)(50, 2262)(51, 2214)(52, 2266)(53, 2215)(54, 2232)(55, 2269)(56, 2217)(57, 2250)(58, 2272)(59, 2219)(60, 2220)(61, 2277)(62, 2278)(63, 2243)(64, 2282)(65, 2225)(66, 2284)(67, 2285)(68, 2255)(69, 2288)(70, 2289)(71, 2227)(72, 2292)(73, 2229)(74, 2230)(75, 2231)(76, 2299)(77, 2300)(78, 2265)(79, 2304)(80, 2305)(81, 2235)(82, 2308)(83, 2237)(84, 2238)(85, 2313)(86, 2240)(87, 2241)(88, 2318)(89, 2242)(90, 2281)(91, 2321)(92, 2244)(93, 2324)(94, 2276)(95, 2328)(96, 2248)(97, 2330)(98, 2331)(99, 2249)(100, 2334)(101, 2335)(102, 2253)(103, 2338)(104, 2339)(105, 2340)(106, 2254)(107, 2287)(108, 2295)(109, 2345)(110, 2346)(111, 2257)(112, 2258)(113, 2350)(114, 2259)(115, 2353)(116, 2298)(117, 2357)(118, 2263)(119, 2359)(120, 2360)(121, 2361)(122, 2264)(123, 2303)(124, 2311)(125, 2366)(126, 2367)(127, 2267)(128, 2268)(129, 2316)(130, 2373)(131, 2374)(132, 2270)(133, 2271)(134, 2379)(135, 2273)(136, 2274)(137, 2384)(138, 2275)(139, 2327)(140, 2296)(141, 2389)(142, 2279)(143, 2391)(144, 2392)(145, 2280)(146, 2395)(147, 2396)(148, 2398)(149, 2283)(150, 2378)(151, 2333)(152, 2404)(153, 2286)(154, 2407)(155, 2408)(156, 2410)(157, 2290)(158, 2291)(159, 2293)(160, 2416)(161, 2417)(162, 2418)(163, 2294)(164, 2344)(165, 2388)(166, 2422)(167, 2297)(168, 2356)(169, 2312)(170, 2427)(171, 2301)(172, 2429)(173, 2430)(174, 2302)(175, 2433)(176, 2434)(177, 2436)(178, 2306)(179, 2307)(180, 2309)(181, 2442)(182, 2443)(183, 2444)(184, 2310)(185, 2365)(186, 2426)(187, 2314)(188, 2449)(189, 2450)(190, 2451)(191, 2315)(192, 2372)(193, 2454)(194, 2317)(195, 2382)(196, 2459)(197, 2460)(198, 2319)(199, 2320)(200, 2465)(201, 2322)(202, 2323)(203, 2325)(204, 2471)(205, 2472)(206, 2326)(207, 2475)(208, 2476)(209, 2477)(210, 2329)(211, 2464)(212, 2394)(213, 2483)(214, 2484)(215, 2332)(216, 2403)(217, 2487)(218, 2336)(219, 2489)(220, 2490)(221, 2491)(222, 2337)(223, 2494)(224, 2406)(225, 2498)(226, 2413)(227, 2501)(228, 2502)(229, 2341)(230, 2342)(231, 2343)(232, 2507)(233, 2508)(234, 2510)(235, 2347)(236, 2348)(237, 2349)(238, 2515)(239, 2351)(240, 2352)(241, 2354)(242, 2521)(243, 2522)(244, 2355)(245, 2525)(246, 2526)(247, 2527)(248, 2358)(249, 2530)(250, 2432)(251, 2461)(252, 2439)(253, 2536)(254, 2537)(255, 2362)(256, 2363)(257, 2364)(258, 2542)(259, 2543)(260, 2545)(261, 2368)(262, 2369)(263, 2370)(264, 2371)(265, 2552)(266, 2553)(267, 2555)(268, 2375)(269, 2376)(270, 2559)(271, 2377)(272, 2401)(273, 2380)(274, 2563)(275, 2564)(276, 2565)(277, 2381)(278, 2458)(279, 2567)(280, 2383)(281, 2468)(282, 2572)(283, 2573)(284, 2385)(285, 2386)(286, 2387)(287, 2580)(288, 2581)(289, 2582)(290, 2390)(291, 2577)(292, 2474)(293, 2587)(294, 2393)(295, 2482)(296, 2590)(297, 2397)(298, 2592)(299, 2412)(300, 2593)(301, 2399)(302, 2400)(303, 2598)(304, 2402)(305, 2601)(306, 2602)(307, 2603)(308, 2405)(309, 2497)(310, 2414)(311, 2608)(312, 2409)(313, 2610)(314, 2438)(315, 2411)(316, 2612)(317, 2613)(318, 2614)(319, 2500)(320, 2607)(321, 2617)(322, 2415)(323, 2620)(324, 2506)(325, 2624)(326, 2512)(327, 2627)(328, 2419)(329, 2420)(330, 2421)(331, 2518)(332, 2633)(333, 2634)(334, 2423)(335, 2424)(336, 2425)(337, 2640)(338, 2641)(339, 2642)(340, 2428)(341, 2637)(342, 2524)(343, 2647)(344, 2431)(345, 2533)(346, 2440)(347, 2652)(348, 2435)(349, 2654)(350, 2437)(351, 2656)(352, 2657)(353, 2658)(354, 2535)(355, 2651)(356, 2661)(357, 2441)(358, 2664)(359, 2541)(360, 2668)(361, 2547)(362, 2671)(363, 2445)(364, 2446)(365, 2447)(366, 2674)(367, 2448)(368, 2677)(369, 2551)(370, 2574)(371, 2557)(372, 2683)(373, 2452)(374, 2453)(375, 2685)(376, 2455)(377, 2456)(378, 2457)(379, 2691)(380, 2692)(381, 2653)(382, 2462)(383, 2696)(384, 2463)(385, 2480)(386, 2466)(387, 2699)(388, 2700)(389, 2701)(390, 2467)(391, 2571)(392, 2703)(393, 2469)(394, 2705)(395, 2470)(396, 2630)(397, 2579)(398, 2710)(399, 2473)(400, 2586)(401, 2713)(402, 2670)(403, 2714)(404, 2478)(405, 2479)(406, 2719)(407, 2481)(408, 2721)(409, 2596)(410, 2724)(411, 2725)(412, 2485)(413, 2486)(414, 2728)(415, 2729)(416, 2488)(417, 2727)(418, 2600)(419, 2733)(420, 2492)(421, 2493)(422, 2495)(423, 2738)(424, 2576)(425, 2496)(426, 2740)(427, 2499)(428, 2743)(429, 2744)(430, 2591)(431, 2503)(432, 2504)(433, 2748)(434, 2505)(435, 2623)(436, 2513)(437, 2568)(438, 2509)(439, 2753)(440, 2517)(441, 2511)(442, 2755)(443, 2756)(444, 2626)(445, 2751)(446, 2514)(447, 2516)(448, 2760)(449, 2761)(450, 2762)(451, 2632)(452, 2764)(453, 2519)(454, 2766)(455, 2520)(456, 2673)(457, 2639)(458, 2770)(459, 2523)(460, 2646)(461, 2773)(462, 2682)(463, 2774)(464, 2528)(465, 2529)(466, 2531)(467, 2779)(468, 2636)(469, 2532)(470, 2781)(471, 2534)(472, 2784)(473, 2785)(474, 2609)(475, 2538)(476, 2539)(477, 2789)(478, 2540)(479, 2667)(480, 2548)(481, 2616)(482, 2544)(483, 2794)(484, 2595)(485, 2546)(486, 2796)(487, 2797)(488, 2792)(489, 2549)(490, 2800)(491, 2550)(492, 2680)(493, 2558)(494, 2660)(495, 2554)(496, 2805)(497, 2556)(498, 2807)(499, 2808)(500, 2803)(501, 2687)(502, 2812)(503, 2560)(504, 2561)(505, 2814)(506, 2562)(507, 2817)(508, 2690)(509, 2618)(510, 2821)(511, 2566)(512, 2823)(513, 2569)(514, 2570)(515, 2828)(516, 2829)(517, 2804)(518, 2575)(519, 2832)(520, 2585)(521, 2834)(522, 2578)(523, 2709)(524, 2837)(525, 2811)(526, 2838)(527, 2583)(528, 2584)(529, 2843)(530, 2717)(531, 2846)(532, 2847)(533, 2588)(534, 2589)(535, 2850)(536, 2746)(537, 2849)(538, 2594)(539, 2854)(540, 2716)(541, 2855)(542, 2723)(543, 2597)(544, 2688)(545, 2858)(546, 2599)(547, 2628)(548, 2861)(549, 2735)(550, 2864)(551, 2604)(552, 2605)(553, 2606)(554, 2869)(555, 2787)(556, 2867)(557, 2872)(558, 2611)(559, 2875)(560, 2742)(561, 2662)(562, 2879)(563, 2615)(564, 2881)(565, 2619)(566, 2621)(567, 2884)(568, 2622)(569, 2886)(570, 2625)(571, 2889)(572, 2890)(573, 2629)(574, 2708)(575, 2631)(576, 2894)(577, 2895)(578, 2752)(579, 2635)(580, 2898)(581, 2645)(582, 2900)(583, 2638)(584, 2758)(585, 2903)(586, 2904)(587, 2643)(588, 2644)(589, 2866)(590, 2776)(591, 2911)(592, 2648)(593, 2649)(594, 2650)(595, 2916)(596, 2694)(597, 2914)(598, 2919)(599, 2655)(600, 2922)(601, 2783)(602, 2675)(603, 2926)(604, 2659)(605, 2928)(606, 2663)(607, 2665)(608, 2931)(609, 2666)(610, 2933)(611, 2669)(612, 2936)(613, 2937)(614, 2672)(615, 2769)(616, 2939)(617, 2676)(618, 2678)(619, 2942)(620, 2679)(621, 2944)(622, 2681)(623, 2947)(624, 2948)(625, 2684)(626, 2686)(627, 2951)(628, 2952)(629, 2799)(630, 2954)(631, 2689)(632, 2820)(633, 2695)(634, 2809)(635, 2693)(636, 2958)(637, 2959)(638, 2957)(639, 2750)(640, 2962)(641, 2697)(642, 2964)(643, 2698)(644, 2967)(645, 2827)(646, 2969)(647, 2702)(648, 2737)(649, 2704)(650, 2973)(651, 2706)(652, 2707)(653, 2978)(654, 2841)(655, 2981)(656, 2982)(657, 2711)(658, 2712)(659, 2984)(660, 2715)(661, 2986)(662, 2840)(663, 2987)(664, 2845)(665, 2718)(666, 2825)(667, 2720)(668, 2991)(669, 2722)(670, 2993)(671, 2793)(672, 2726)(673, 2732)(674, 2996)(675, 2730)(676, 2731)(677, 2913)(678, 2734)(679, 3002)(680, 2906)(681, 2863)(682, 3003)(683, 2736)(684, 2971)(685, 2791)(686, 2739)(687, 3007)(688, 3008)(689, 2741)(690, 2878)(691, 2747)(692, 2757)(693, 2745)(694, 3012)(695, 3013)(696, 3011)(697, 2819)(698, 3016)(699, 2749)(700, 3019)(701, 2896)(702, 3018)(703, 3022)(704, 2754)(705, 3000)(706, 2888)(707, 2873)(708, 3027)(709, 2759)(710, 3030)(711, 2893)(712, 3032)(713, 2763)(714, 2778)(715, 2765)(716, 3036)(717, 2767)(718, 2768)(719, 3041)(720, 2907)(721, 3044)(722, 3045)(723, 2771)(724, 2772)(725, 2775)(726, 3048)(727, 2998)(728, 2910)(729, 3049)(730, 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4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E14.643 Graph:: bipartite v = 520 e = 2184 f = 1638 degree seq :: [ 6^364, 14^156 ] E14.641 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2^7, Y2^-1 * Y1 * Y2 * Y1 * Y2^-5, (Y2^2 * Y1^-1)^7, Y2 * Y1^-1 * Y2^-2 * Y1 * Y2^2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-2 * Y1 * Y2^-3 * Y1 * Y2^-2 * Y1^-1 * Y2^2 * Y1^-1, Y2^3 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-2 * Y1 * Y2^3 * Y1^-1 * Y2 * Y1^-1 * Y2^-3 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1^-1 ] Map:: R = (1, 1093, 2, 1094, 4, 1096)(3, 1095, 8, 1100, 10, 1102)(5, 1097, 12, 1104, 6, 1098)(7, 1099, 15, 1107, 11, 1103)(9, 1101, 18, 1110, 20, 1112)(13, 1105, 25, 1117, 23, 1115)(14, 1106, 24, 1116, 28, 1120)(16, 1108, 31, 1123, 29, 1121)(17, 1109, 33, 1125, 21, 1113)(19, 1111, 36, 1128, 37, 1129)(22, 1114, 30, 1122, 41, 1133)(26, 1118, 46, 1138, 44, 1136)(27, 1119, 47, 1139, 48, 1140)(32, 1124, 54, 1146, 52, 1144)(34, 1126, 57, 1149, 55, 1147)(35, 1127, 58, 1150, 38, 1130)(39, 1131, 56, 1148, 64, 1156)(40, 1132, 65, 1157, 66, 1158)(42, 1134, 45, 1137, 69, 1161)(43, 1135, 70, 1162, 49, 1141)(50, 1142, 53, 1145, 79, 1171)(51, 1143, 80, 1172, 67, 1159)(59, 1151, 90, 1182, 88, 1180)(60, 1152, 91, 1183, 61, 1153)(62, 1154, 89, 1181, 95, 1187)(63, 1155, 96, 1188, 97, 1189)(68, 1160, 102, 1194, 103, 1195)(71, 1163, 107, 1199, 105, 1197)(72, 1164, 74, 1166, 109, 1201)(73, 1165, 110, 1202, 104, 1196)(75, 1167, 113, 1205, 76, 1168)(77, 1169, 106, 1198, 117, 1209)(78, 1170, 118, 1210, 119, 1211)(81, 1173, 123, 1215, 121, 1213)(82, 1174, 84, 1176, 125, 1217)(83, 1175, 126, 1218, 120, 1212)(85, 1177, 87, 1179, 130, 1222)(86, 1178, 131, 1223, 98, 1190)(92, 1184, 139, 1231, 137, 1229)(93, 1185, 138, 1230, 141, 1233)(94, 1186, 142, 1234, 143, 1235)(99, 1191, 148, 1240, 100, 1192)(101, 1193, 122, 1214, 152, 1244)(108, 1200, 159, 1251, 160, 1252)(111, 1203, 164, 1256, 162, 1254)(112, 1204, 165, 1257, 161, 1253)(114, 1206, 168, 1260, 166, 1258)(115, 1207, 167, 1259, 170, 1262)(116, 1208, 171, 1263, 172, 1264)(124, 1216, 180, 1272, 181, 1273)(127, 1219, 185, 1277, 183, 1275)(128, 1220, 186, 1278, 182, 1274)(129, 1221, 187, 1279, 188, 1280)(132, 1224, 192, 1284, 190, 1282)(133, 1225, 193, 1285, 189, 1281)(134, 1226, 136, 1228, 196, 1288)(135, 1227, 197, 1289, 144, 1236)(140, 1232, 203, 1295, 204, 1296)(145, 1237, 209, 1301, 146, 1238)(147, 1239, 191, 1283, 213, 1305)(149, 1241, 216, 1308, 214, 1306)(150, 1242, 215, 1307, 217, 1309)(151, 1243, 218, 1310, 219, 1311)(153, 1245, 221, 1313, 154, 1246)(155, 1247, 163, 1255, 225, 1317)(156, 1248, 158, 1250, 227, 1319)(157, 1249, 228, 1320, 173, 1265)(169, 1261, 241, 1333, 242, 1334)(174, 1266, 247, 1339, 175, 1267)(176, 1268, 184, 1276, 251, 1343)(177, 1269, 179, 1271, 253, 1345)(178, 1270, 254, 1346, 220, 1312)(194, 1286, 272, 1364, 270, 1362)(195, 1287, 273, 1365, 274, 1366)(198, 1290, 278, 1370, 276, 1368)(199, 1291, 279, 1371, 275, 1367)(200, 1292, 202, 1294, 282, 1374)(201, 1293, 283, 1375, 205, 1297)(206, 1298, 289, 1381, 207, 1299)(208, 1300, 277, 1369, 293, 1385)(210, 1302, 296, 1388, 294, 1386)(211, 1303, 295, 1387, 297, 1389)(212, 1304, 298, 1390, 299, 1391)(222, 1314, 310, 1402, 308, 1400)(223, 1315, 309, 1401, 312, 1404)(224, 1316, 313, 1405, 314, 1406)(226, 1318, 316, 1408, 317, 1409)(229, 1321, 321, 1413, 319, 1411)(230, 1322, 322, 1414, 318, 1410)(231, 1323, 323, 1415, 232, 1324)(233, 1325, 237, 1329, 327, 1419)(234, 1326, 236, 1328, 329, 1421)(235, 1327, 330, 1422, 315, 1407)(238, 1330, 240, 1332, 335, 1427)(239, 1331, 336, 1428, 243, 1335)(244, 1336, 342, 1434, 245, 1337)(246, 1338, 320, 1412, 346, 1438)(248, 1340, 349, 1441, 347, 1439)(249, 1341, 348, 1440, 351, 1443)(250, 1342, 352, 1444, 353, 1445)(252, 1344, 355, 1447, 356, 1448)(255, 1347, 360, 1452, 358, 1450)(256, 1348, 361, 1453, 357, 1449)(257, 1349, 362, 1454, 258, 1350)(259, 1351, 263, 1355, 366, 1458)(260, 1352, 262, 1354, 368, 1460)(261, 1353, 369, 1461, 354, 1446)(264, 1356, 373, 1465, 265, 1357)(266, 1358, 271, 1363, 377, 1469)(267, 1359, 269, 1361, 379, 1471)(268, 1360, 380, 1472, 300, 1392)(280, 1372, 394, 1486, 392, 1484)(281, 1373, 395, 1487, 396, 1488)(284, 1376, 400, 1492, 398, 1490)(285, 1377, 401, 1493, 397, 1489)(286, 1378, 403, 1495, 287, 1379)(288, 1380, 399, 1491, 407, 1499)(290, 1382, 410, 1502, 408, 1500)(291, 1383, 409, 1501, 411, 1503)(292, 1384, 412, 1504, 413, 1505)(301, 1393, 303, 1395, 423, 1515)(302, 1394, 424, 1516, 304, 1396)(305, 1397, 428, 1520, 306, 1398)(307, 1399, 359, 1451, 432, 1524)(311, 1403, 436, 1528, 437, 1529)(324, 1416, 451, 1543, 449, 1541)(325, 1417, 450, 1542, 453, 1545)(326, 1418, 454, 1546, 455, 1547)(328, 1420, 457, 1549, 458, 1550)(331, 1423, 462, 1554, 460, 1552)(332, 1424, 463, 1555, 459, 1551)(333, 1425, 464, 1556, 456, 1548)(334, 1426, 466, 1558, 467, 1559)(337, 1429, 471, 1563, 469, 1561)(338, 1430, 472, 1564, 468, 1560)(339, 1431, 474, 1566, 340, 1432)(341, 1433, 470, 1562, 478, 1570)(343, 1435, 481, 1573, 479, 1571)(344, 1436, 480, 1572, 482, 1574)(345, 1437, 483, 1575, 484, 1576)(350, 1442, 489, 1581, 490, 1582)(363, 1455, 504, 1596, 502, 1594)(364, 1456, 503, 1595, 506, 1598)(365, 1457, 507, 1599, 508, 1600)(367, 1459, 510, 1602, 511, 1603)(370, 1462, 514, 1606, 513, 1605)(371, 1463, 515, 1607, 512, 1604)(372, 1464, 516, 1608, 509, 1601)(374, 1466, 520, 1612, 518, 1610)(375, 1467, 519, 1611, 522, 1614)(376, 1468, 523, 1615, 524, 1616)(378, 1470, 526, 1618, 527, 1619)(381, 1473, 530, 1622, 529, 1621)(382, 1474, 531, 1623, 528, 1620)(383, 1475, 385, 1477, 533, 1625)(384, 1476, 534, 1626, 525, 1617)(386, 1478, 537, 1629, 387, 1479)(388, 1480, 393, 1485, 541, 1633)(389, 1481, 391, 1483, 543, 1635)(390, 1482, 494, 1586, 414, 1506)(402, 1494, 557, 1649, 555, 1647)(404, 1496, 560, 1652, 558, 1650)(405, 1497, 559, 1651, 561, 1653)(406, 1498, 562, 1654, 563, 1655)(415, 1507, 417, 1509, 572, 1664)(416, 1508, 573, 1665, 418, 1510)(419, 1511, 577, 1669, 420, 1512)(421, 1513, 485, 1577, 446, 1538)(422, 1514, 581, 1673, 582, 1674)(425, 1517, 586, 1678, 584, 1676)(426, 1518, 587, 1679, 583, 1675)(427, 1519, 585, 1677, 590, 1682)(429, 1521, 593, 1685, 591, 1683)(430, 1522, 592, 1684, 594, 1686)(431, 1523, 595, 1687, 596, 1688)(433, 1525, 435, 1527, 598, 1690)(434, 1526, 599, 1691, 438, 1530)(439, 1531, 605, 1697, 440, 1532)(441, 1533, 461, 1553, 499, 1591)(442, 1534, 609, 1701, 443, 1535)(444, 1536, 448, 1540, 613, 1705)(445, 1537, 447, 1539, 615, 1707)(452, 1544, 622, 1714, 623, 1715)(465, 1557, 636, 1728, 634, 1726)(473, 1565, 645, 1737, 643, 1735)(475, 1567, 648, 1740, 646, 1738)(476, 1568, 647, 1739, 649, 1741)(477, 1569, 650, 1742, 651, 1743)(486, 1578, 488, 1580, 659, 1751)(487, 1579, 660, 1752, 491, 1583)(492, 1584, 666, 1758, 493, 1585)(495, 1587, 670, 1762, 496, 1588)(497, 1589, 501, 1593, 674, 1766)(498, 1590, 500, 1592, 676, 1768)(505, 1597, 683, 1775, 684, 1776)(517, 1609, 697, 1789, 695, 1787)(521, 1613, 701, 1793, 702, 1794)(532, 1624, 713, 1805, 714, 1806)(535, 1627, 717, 1809, 716, 1808)(536, 1628, 718, 1810, 715, 1807)(538, 1630, 721, 1813, 719, 1811)(539, 1631, 720, 1812, 723, 1815)(540, 1632, 687, 1779, 686, 1778)(542, 1634, 725, 1817, 726, 1818)(544, 1636, 727, 1819, 669, 1761)(545, 1637, 655, 1747, 653, 1745)(546, 1638, 548, 1640, 729, 1821)(547, 1639, 730, 1822, 724, 1816)(549, 1641, 733, 1825, 550, 1642)(551, 1643, 556, 1648, 737, 1829)(552, 1644, 554, 1646, 661, 1753)(553, 1645, 706, 1798, 564, 1656)(565, 1657, 567, 1659, 750, 1842)(566, 1658, 678, 1770, 568, 1660)(569, 1661, 753, 1845, 570, 1662)(571, 1663, 755, 1847, 756, 1848)(574, 1666, 640, 1732, 642, 1734)(575, 1667, 759, 1851, 757, 1849)(576, 1668, 758, 1850, 762, 1854)(578, 1670, 764, 1856, 763, 1855)(579, 1671, 691, 1783, 694, 1786)(580, 1672, 616, 1708, 765, 1857)(588, 1680, 774, 1866, 772, 1864)(589, 1681, 775, 1867, 776, 1868)(597, 1689, 783, 1875, 784, 1876)(600, 1692, 769, 1861, 771, 1863)(601, 1693, 787, 1879, 785, 1877)(602, 1694, 789, 1881, 603, 1695)(604, 1696, 786, 1878, 741, 1833)(606, 1698, 794, 1886, 793, 1885)(607, 1699, 709, 1801, 712, 1804)(608, 1700, 677, 1769, 795, 1887)(610, 1702, 798, 1890, 796, 1888)(611, 1703, 797, 1889, 800, 1892)(612, 1704, 705, 1797, 704, 1796)(614, 1706, 802, 1894, 803, 1895)(617, 1709, 780, 1872, 778, 1870)(618, 1710, 804, 1896, 801, 1893)(619, 1711, 621, 1713, 807, 1899)(620, 1712, 808, 1900, 624, 1716)(625, 1717, 673, 1765, 626, 1718)(627, 1719, 635, 1727, 641, 1733)(628, 1720, 815, 1907, 629, 1721)(630, 1722, 633, 1725, 668, 1760)(631, 1723, 632, 1724, 818, 1910)(637, 1729, 823, 1915, 638, 1730)(639, 1731, 644, 1736, 735, 1827)(652, 1744, 654, 1746, 836, 1928)(656, 1748, 839, 1931, 657, 1749)(658, 1750, 841, 1933, 738, 1830)(662, 1754, 844, 1936, 842, 1934)(663, 1755, 846, 1938, 664, 1756)(665, 1757, 843, 1935, 828, 1920)(667, 1759, 850, 1942, 816, 1908)(671, 1763, 813, 1905, 851, 1943)(672, 1764, 852, 1944, 854, 1946)(675, 1767, 749, 1841, 856, 1948)(679, 1771, 857, 1949, 855, 1947)(680, 1772, 682, 1774, 809, 1901)(681, 1773, 860, 1952, 685, 1777)(688, 1780, 696, 1788, 770, 1862)(689, 1781, 865, 1957, 690, 1782)(692, 1784, 693, 1785, 867, 1959)(698, 1790, 700, 1792, 861, 1953)(699, 1791, 810, 1902, 703, 1795)(707, 1799, 876, 1968, 708, 1800)(710, 1802, 711, 1803, 878, 1970)(722, 1814, 888, 1980, 838, 1930)(728, 1820, 889, 1981, 890, 1982)(731, 1823, 893, 1985, 892, 1984)(732, 1824, 894, 1986, 891, 1983)(734, 1826, 895, 1987, 824, 1916)(736, 1828, 767, 1859, 766, 1858)(739, 1831, 896, 1988, 875, 1967)(740, 1832, 742, 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2050)(849, 1941, 945, 2037, 959, 2051)(858, 1950, 961, 2053, 960, 2052)(862, 1954, 962, 2054, 863, 1955)(864, 1956, 914, 2006, 887, 1979)(866, 1958, 965, 2057, 967, 2059)(868, 1960, 882, 1974, 881, 1973)(870, 1962, 871, 1963, 969, 2061)(873, 1965, 971, 2063, 874, 1966)(877, 1969, 974, 2066, 976, 2068)(884, 1976, 885, 1977, 979, 2071)(897, 1989, 988, 2080, 989, 2081)(900, 1992, 991, 2083, 990, 2082)(901, 1993, 992, 2084, 953, 2045)(902, 1994, 975, 2067, 995, 2087)(904, 1996, 985, 2077, 987, 2079)(907, 1999, 981, 2073, 996, 2088)(908, 2000, 997, 2089, 998, 2090)(915, 2007, 916, 2008, 1002, 2094)(917, 2009, 1004, 2096, 918, 2010)(920, 2012, 1007, 2099, 1006, 2098)(934, 2026, 986, 2078, 1017, 2109)(935, 2027, 1018, 2110, 1019, 2111)(937, 2029, 1020, 2112, 948, 2040)(940, 2032, 1022, 2114, 1021, 2113)(942, 2034, 1014, 2106, 1012, 2104)(943, 2035, 1023, 2115, 1024, 2116)(946, 2038, 1026, 2118, 1025, 2117)(947, 2039, 1027, 2119, 1008, 2100)(950, 2042, 1011, 2103, 1013, 2105)(954, 2046, 982, 2074, 1030, 2122)(963, 2055, 1016, 2108, 1036, 2128)(964, 2056, 1037, 2129, 1038, 2130)(966, 2058, 1039, 2131, 978, 2070)(968, 2060, 1040, 2132, 999, 2091)(970, 2062, 1034, 2126, 1032, 2124)(972, 2064, 1035, 2127, 1041, 2133)(973, 2065, 1042, 2134, 1043, 2135)(977, 2069, 1044, 2136, 1010, 2102)(980, 2072, 984, 2076, 983, 2075)(993, 2085, 1050, 2142, 1053, 2145)(994, 2086, 1054, 2146, 1055, 2147)(1000, 2092, 1059, 2151, 1001, 2093)(1003, 2095, 1062, 2154, 1061, 2153)(1005, 2097, 1031, 2123, 1033, 2125)(1009, 2101, 1015, 2107, 1063, 2155)(1028, 2120, 1064, 2156, 1071, 2163)(1029, 2121, 1067, 2159, 1072, 2164)(1045, 2137, 1076, 2168, 1048, 2140)(1046, 2138, 1074, 2166, 1056, 2148)(1047, 2139, 1079, 2171, 1073, 2165)(1049, 2141, 1052, 2144, 1051, 2143)(1057, 2149, 1077, 2169, 1058, 2150)(1060, 2152, 1078, 2170, 1075, 2167)(1065, 2157, 1068, 2160, 1087, 2179)(1066, 2158, 1070, 2162, 1069, 2161)(1080, 2172, 1089, 2181, 1082, 2174)(1081, 2173, 1090, 2182, 1083, 2175)(1084, 2176, 1088, 2180, 1085, 2177)(1086, 2178, 1091, 2183, 1092, 2184)(2185, 3277, 2187, 3279, 2193, 3285, 2203, 3295, 2210, 3302, 2197, 3289, 2189, 3281)(2186, 3278, 2190, 3282, 2198, 3290, 2211, 3303, 2216, 3308, 2200, 3292, 2191, 3283)(2188, 3280, 2195, 3287, 2206, 3298, 2224, 3316, 2218, 3310, 2201, 3293, 2192, 3284)(2194, 3286, 2205, 3297, 2223, 3315, 2247, 3339, 2243, 3335, 2219, 3311, 2202, 3294)(2196, 3288, 2207, 3299, 2226, 3318, 2252, 3344, 2255, 3347, 2227, 3319, 2208, 3300)(2199, 3291, 2213, 3305, 2234, 3326, 2262, 3354, 2265, 3357, 2235, 3327, 2214, 3306)(2204, 3296, 2222, 3314, 2246, 3338, 2278, 3370, 2276, 3368, 2244, 3336, 2220, 3312)(2209, 3301, 2228, 3320, 2256, 3348, 2292, 3384, 2295, 3387, 2257, 3349, 2229, 3321)(2212, 3304, 2233, 3325, 2261, 3353, 2300, 3392, 2298, 3390, 2259, 3351, 2231, 3323)(2215, 3307, 2236, 3328, 2266, 3358, 2308, 3400, 2311, 3403, 2267, 3359, 2237, 3329)(2217, 3309, 2239, 3331, 2269, 3361, 2313, 3405, 2316, 3408, 2270, 3362, 2240, 3332)(2221, 3313, 2245, 3337, 2277, 3369, 2324, 3416, 2296, 3388, 2258, 3350, 2230, 3322)(2225, 3317, 2251, 3343, 2285, 3377, 2335, 3427, 2333, 3425, 2283, 3375, 2249, 3341)(2232, 3324, 2260, 3352, 2299, 3391, 2353, 3445, 2312, 3404, 2268, 3360, 2238, 3330)(2241, 3333, 2250, 3342, 2284, 3376, 2334, 3426, 2378, 3470, 2317, 3409, 2271, 3363)(2242, 3334, 2272, 3364, 2318, 3410, 2379, 3471, 2382, 3474, 2319, 3411, 2273, 3365)(2248, 3340, 2282, 3374, 2331, 3423, 2396, 3488, 2394, 3486, 2329, 3421, 2280, 3372)(2253, 3345, 2288, 3380, 2339, 3431, 2408, 3500, 2406, 3498, 2337, 3429, 2286, 3378)(2254, 3346, 2289, 3381, 2340, 3432, 2410, 3502, 2413, 3505, 2341, 3433, 2290, 3382)(2263, 3355, 2304, 3396, 2360, 3452, 2434, 3526, 2432, 3524, 2358, 3450, 2302, 3394)(2264, 3356, 2305, 3397, 2361, 3453, 2436, 3528, 2439, 3531, 2362, 3454, 2306, 3398)(2274, 3366, 2281, 3373, 2330, 3422, 2395, 3487, 2464, 3556, 2383, 3475, 2320, 3412)(2275, 3367, 2321, 3413, 2384, 3476, 2465, 3557, 2468, 3560, 2385, 3477, 2322, 3414)(2279, 3371, 2328, 3420, 2392, 3484, 2476, 3568, 2474, 3566, 2390, 3482, 2326, 3418)(2287, 3379, 2338, 3430, 2407, 3499, 2495, 3587, 2414, 3506, 2342, 3434, 2291, 3383)(2293, 3385, 2345, 3437, 2417, 3509, 2510, 3602, 2508, 3600, 2415, 3507, 2343, 3435)(2294, 3386, 2346, 3438, 2418, 3510, 2512, 3604, 2515, 3607, 2419, 3511, 2347, 3439)(2297, 3389, 2350, 3442, 2422, 3514, 2518, 3610, 2521, 3613, 2423, 3515, 2351, 3443)(2301, 3393, 2357, 3449, 2430, 3522, 2529, 3621, 2527, 3619, 2428, 3520, 2355, 3447)(2303, 3395, 2359, 3451, 2433, 3525, 2534, 3626, 2440, 3532, 2363, 3455, 2307, 3399)(2309, 3401, 2366, 3458, 2443, 3535, 2549, 3641, 2547, 3639, 2441, 3533, 2364, 3456)(2310, 3402, 2367, 3459, 2444, 3536, 2551, 3643, 2554, 3646, 2445, 3537, 2368, 3460)(2314, 3406, 2373, 3465, 2450, 3542, 2560, 3652, 2558, 3650, 2448, 3540, 2371, 3463)(2315, 3407, 2374, 3466, 2451, 3543, 2562, 3654, 2565, 3657, 2452, 3544, 2375, 3467)(2323, 3415, 2327, 3419, 2391, 3483, 2475, 3567, 2586, 3678, 2469, 3561, 2386, 3478)(2325, 3417, 2389, 3481, 2472, 3564, 2590, 3682, 2588, 3680, 2470, 3562, 2387, 3479)(2332, 3424, 2398, 3490, 2485, 3577, 2606, 3698, 2609, 3701, 2486, 3578, 2399, 3491)(2336, 3428, 2404, 3496, 2491, 3583, 2615, 3707, 2613, 3705, 2489, 3581, 2402, 3494)(2344, 3436, 2416, 3508, 2509, 3601, 2636, 3728, 2516, 3608, 2420, 3512, 2348, 3440)(2349, 3441, 2388, 3480, 2471, 3563, 2589, 3681, 2649, 3741, 2517, 3609, 2421, 3513)(2352, 3444, 2356, 3448, 2429, 3521, 2528, 3620, 2657, 3749, 2522, 3614, 2424, 3516)(2354, 3446, 2427, 3519, 2525, 3617, 2661, 3753, 2659, 3751, 2523, 3615, 2425, 3517)(2365, 3457, 2442, 3534, 2548, 3640, 2689, 3781, 2555, 3647, 2446, 3538, 2369, 3461)(2370, 3462, 2426, 3518, 2524, 3616, 2660, 3752, 2701, 3793, 2556, 3648, 2447, 3539)(2372, 3464, 2449, 3541, 2559, 3651, 2705, 3797, 2566, 3658, 2453, 3545, 2376, 3468)(2377, 3469, 2454, 3546, 2567, 3659, 2716, 3808, 2719, 3811, 2568, 3660, 2455, 3547)(2380, 3472, 2459, 3551, 2572, 3664, 2724, 3816, 2722, 3814, 2570, 3662, 2457, 3549)(2381, 3473, 2460, 3552, 2573, 3665, 2726, 3818, 2728, 3820, 2574, 3666, 2461, 3553)(2393, 3485, 2478, 3570, 2599, 3691, 2755, 3847, 2758, 3850, 2600, 3692, 2479, 3571)(2397, 3489, 2484, 3576, 2605, 3697, 2764, 3856, 2762, 3854, 2603, 3695, 2482, 3574)(2400, 3492, 2403, 3495, 2490, 3582, 2614, 3706, 2772, 3864, 2610, 3702, 2487, 3579)(2401, 3493, 2488, 3580, 2611, 3703, 2773, 3865, 2720, 3812, 2569, 3661, 2456, 3548)(2405, 3497, 2492, 3584, 2617, 3709, 2781, 3873, 2784, 3876, 2618, 3710, 2493, 3585)(2409, 3501, 2499, 3591, 2625, 3717, 2792, 3884, 2790, 3882, 2623, 3715, 2497, 3589)(2411, 3503, 2502, 3594, 2628, 3720, 2796, 3888, 2794, 3886, 2626, 3718, 2500, 3592)(2412, 3504, 2503, 3595, 2629, 3721, 2798, 3890, 2800, 3892, 2630, 3722, 2504, 3596)(2431, 3523, 2531, 3623, 2670, 3762, 2842, 3934, 2845, 3937, 2671, 3763, 2532, 3624)(2435, 3527, 2538, 3630, 2678, 3770, 2853, 3945, 2851, 3943, 2676, 3768, 2536, 3628)(2437, 3529, 2541, 3633, 2681, 3773, 2857, 3949, 2855, 3947, 2679, 3771, 2539, 3631)(2438, 3530, 2542, 3634, 2682, 3774, 2859, 3951, 2861, 3953, 2683, 3775, 2543, 3635)(2458, 3550, 2571, 3663, 2723, 3815, 2906, 3998, 2729, 3821, 2575, 3667, 2462, 3554)(2463, 3555, 2576, 3668, 2730, 3822, 2912, 4004, 2915, 4007, 2731, 3823, 2577, 3669)(2466, 3558, 2581, 3673, 2735, 3827, 2920, 4012, 2918, 4010, 2733, 3825, 2579, 3671)(2467, 3559, 2582, 3674, 2736, 3828, 2922, 4014, 2923, 4015, 2737, 3829, 2583, 3675)(2473, 3565, 2592, 3684, 2749, 3841, 2933, 4025, 2860, 3952, 2750, 3842, 2593, 3685)(2477, 3569, 2598, 3690, 2553, 3645, 2697, 3789, 2876, 3968, 2753, 3845, 2596, 3688)(2480, 3572, 2483, 3575, 2604, 3696, 2763, 3855, 2944, 4036, 2759, 3851, 2601, 3693)(2481, 3573, 2602, 3694, 2760, 3852, 2945, 4037, 2916, 4008, 2732, 3824, 2578, 3670)(2494, 3586, 2498, 3590, 2624, 3716, 2791, 3883, 2972, 4064, 2785, 3877, 2619, 3711)(2496, 3588, 2622, 3714, 2788, 3880, 2976, 4068, 2974, 4066, 2786, 3878, 2620, 3712)(2501, 3593, 2627, 3719, 2795, 3887, 2983, 4075, 2801, 3893, 2631, 3723, 2505, 3597)(2506, 3598, 2621, 3713, 2787, 3879, 2975, 4067, 2989, 4081, 2802, 3894, 2632, 3724)(2507, 3599, 2633, 3725, 2803, 3895, 2990, 4082, 2993, 4085, 2804, 3896, 2634, 3726)(2511, 3603, 2640, 3732, 2811, 3903, 2998, 4090, 2997, 4089, 2809, 3901, 2638, 3730)(2513, 3605, 2643, 3735, 2814, 3906, 2850, 3942, 3000, 4092, 2812, 3904, 2641, 3733)(2514, 3606, 2644, 3736, 2815, 3907, 2965, 4057, 2779, 3871, 2616, 3708, 2645, 3737)(2519, 3611, 2652, 3744, 2823, 3915, 2917, 4009, 3008, 4100, 2821, 3913, 2650, 3742)(2520, 3612, 2653, 3745, 2824, 3916, 2940, 4032, 3010, 4102, 2825, 3917, 2654, 3746)(2526, 3618, 2663, 3755, 2836, 3928, 2909, 4001, 2727, 3819, 2837, 3929, 2664, 3756)(2530, 3622, 2669, 3761, 2564, 3656, 2713, 3805, 2894, 3986, 2840, 3932, 2667, 3759)(2533, 3625, 2537, 3629, 2677, 3769, 2852, 3944, 3029, 4121, 2846, 3938, 2672, 3764)(2535, 3627, 2675, 3767, 2849, 3941, 3033, 4125, 3031, 4123, 2847, 3939, 2673, 3765)(2540, 3632, 2680, 3772, 2856, 3948, 3037, 4129, 2862, 3954, 2684, 3776, 2544, 3636)(2545, 3637, 2674, 3766, 2848, 3940, 3032, 4124, 3042, 4134, 2863, 3955, 2685, 3777)(2546, 3638, 2686, 3778, 2864, 3956, 3043, 4135, 3045, 4137, 2865, 3957, 2687, 3779)(2550, 3642, 2693, 3785, 2872, 3964, 3048, 4140, 2905, 3997, 2870, 3962, 2691, 3783)(2552, 3644, 2696, 3788, 2875, 3967, 2761, 3853, 2947, 4039, 2873, 3965, 2694, 3786)(2557, 3649, 2702, 3794, 2882, 3974, 3056, 4148, 2991, 4083, 2883, 3975, 2703, 3795)(2561, 3653, 2709, 3801, 2890, 3982, 3059, 4151, 2982, 4074, 2888, 3980, 2707, 3799)(2563, 3655, 2712, 3804, 2893, 3985, 2789, 3881, 2977, 4069, 2891, 3983, 2710, 3802)(2580, 3672, 2734, 3826, 2919, 4011, 3027, 4119, 2844, 3936, 2738, 3830, 2584, 3676)(2585, 3677, 2739, 3831, 2924, 4016, 3081, 4173, 3083, 4175, 2925, 4017, 2740, 3832)(2587, 3679, 2742, 3834, 2927, 4019, 3023, 4115, 3062, 4154, 2928, 4020, 2743, 3835)(2591, 3683, 2748, 3840, 2718, 3810, 2900, 3992, 3068, 4160, 2931, 4023, 2746, 3838)(2594, 3686, 2597, 3689, 2754, 3846, 2938, 4030, 3091, 4183, 2935, 4027, 2751, 3843)(2595, 3687, 2752, 3844, 2936, 4028, 3092, 4184, 3084, 4176, 2926, 4018, 2741, 3833)(2607, 3699, 2767, 3859, 2952, 4044, 3007, 4099, 3079, 4171, 2950, 4042, 2765, 3857)(2608, 3700, 2768, 3860, 2953, 4045, 2968, 4060, 3098, 4190, 2954, 4046, 2769, 3861)(2612, 3704, 2775, 3867, 2961, 4053, 2986, 4078, 2799, 3891, 2962, 4054, 2776, 3868)(2635, 3727, 2639, 3731, 2810, 3902, 2858, 3950, 3039, 4131, 2994, 4086, 2805, 3897)(2637, 3729, 2808, 3900, 2914, 4006, 3076, 4168, 3118, 4210, 2995, 4087, 2806, 3898)(2642, 3734, 2813, 3905, 3001, 4093, 3121, 4213, 3003, 4095, 2816, 3908, 2646, 3738)(2647, 3739, 2807, 3899, 2996, 4088, 3119, 4211, 3124, 4216, 3004, 4096, 2817, 3909)(2648, 3740, 2818, 3910, 3005, 4097, 3018, 4110, 2834, 3926, 2662, 3754, 2819, 3911)(2651, 3743, 2822, 3914, 3009, 4101, 2942, 4034, 2757, 3849, 2826, 3918, 2655, 3747)(2656, 3748, 2827, 3919, 3011, 4103, 3127, 4219, 3129, 4221, 3012, 4104, 2828, 3920)(2658, 3750, 2830, 3922, 3014, 4106, 3106, 4198, 3002, 4094, 3015, 4107, 2831, 3923)(2665, 3757, 2668, 3760, 2841, 3933, 3024, 4116, 3137, 4229, 3021, 4113, 2838, 3930)(2666, 3758, 2839, 3931, 3022, 4114, 3138, 4230, 3130, 4222, 3013, 4105, 2829, 3921)(2688, 3780, 2692, 3784, 2871, 3963, 2725, 3817, 2908, 4000, 2992, 4084, 2866, 3958)(2690, 3782, 2869, 3961, 2988, 4080, 3115, 4207, 3147, 4239, 3046, 4138, 2867, 3959)(2695, 3787, 2874, 3966, 3050, 4142, 3150, 4242, 3052, 4144, 2877, 3969, 2698, 3790)(2699, 3791, 2868, 3960, 3047, 4139, 3148, 4240, 3152, 4244, 3053, 4145, 2878, 3970)(2700, 3792, 2879, 3971, 3054, 4146, 3101, 4193, 2959, 4051, 2774, 3866, 2880, 3972)(2704, 3796, 2708, 3800, 2889, 3981, 2797, 3889, 2985, 4077, 3044, 4136, 2884, 3976)(2706, 3798, 2887, 3979, 3041, 4133, 3144, 4236, 3156, 4248, 3057, 4149, 2885, 3977)(2711, 3803, 2892, 3984, 3061, 4153, 3159, 4251, 3063, 4155, 2895, 3987, 2714, 3806)(2715, 3807, 2886, 3978, 3058, 4150, 3157, 4249, 3161, 4253, 3064, 4156, 2896, 3988)(2717, 3809, 2899, 3991, 3067, 4159, 2937, 4029, 3051, 4143, 3065, 4157, 2897, 3989)(2721, 3813, 2903, 3995, 3071, 4163, 2967, 4059, 2782, 3874, 2969, 4061, 2904, 3996)(2744, 3836, 2747, 3839, 2932, 4024, 3088, 4180, 3177, 4269, 3085, 4177, 2929, 4021)(2745, 3837, 2930, 4022, 3086, 4178, 3178, 4270, 3126, 4218, 3006, 4098, 2820, 3912)(2756, 3848, 2941, 4033, 3036, 4128, 2854, 3946, 3035, 4127, 3094, 4186, 2939, 4031)(2766, 3858, 2951, 4043, 2921, 4013, 2970, 4062, 2783, 3875, 2955, 4047, 2770, 3862)(2771, 3863, 2956, 4048, 3099, 4191, 3184, 4276, 3096, 4188, 2946, 4038, 2957, 4049)(2777, 3869, 2780, 3872, 2966, 4058, 3107, 4199, 3192, 4284, 3104, 4196, 2963, 4055)(2778, 3870, 2964, 4056, 3105, 4197, 3193, 4285, 3187, 4279, 3100, 4192, 2958, 4050)(2793, 3885, 2980, 4072, 3080, 4172, 3025, 4117, 2843, 3935, 3026, 4118, 2981, 4073)(2832, 3924, 2835, 3927, 3019, 4111, 3134, 4226, 3212, 4304, 3131, 4223, 3016, 4108)(2833, 3925, 3017, 4109, 3132, 4224, 3213, 4305, 3154, 4246, 3055, 4147, 2881, 3973)(2898, 3990, 3066, 4158, 3162, 4254, 3229, 4321, 3164, 4256, 3069, 4161, 2901, 3993)(2902, 3994, 2960, 4052, 3102, 4194, 3189, 4281, 3230, 4322, 3165, 4257, 3070, 4162)(2907, 3999, 2971, 4063, 3108, 4200, 3194, 4286, 3231, 4323, 3166, 4258, 3072, 4164)(2910, 4002, 3020, 4112, 3135, 4227, 3120, 4212, 2999, 4091, 3034, 4126, 2911, 4003)(2913, 4005, 3075, 4167, 3169, 4261, 3087, 4179, 3163, 4255, 3167, 4259, 3073, 4165)(2934, 4026, 3089, 4181, 3158, 4250, 3060, 4152, 2978, 4070, 2979, 4071, 3040, 4132)(2943, 4035, 3095, 4187, 3183, 4275, 3241, 4333, 3181, 4273, 3093, 4185, 3038, 4130)(2948, 4040, 2949, 4041, 2987, 4079, 3103, 4195, 3190, 4282, 3149, 4241, 3049, 4141)(2973, 4065, 3109, 4201, 3195, 4287, 3133, 4225, 3125, 4217, 3196, 4288, 3110, 4202)(2984, 4076, 3028, 4120, 3123, 4215, 3205, 4297, 3249, 4341, 3199, 4291, 3114, 4206)(3030, 4122, 3139, 4231, 3215, 4307, 3188, 4280, 3153, 4245, 3216, 4308, 3140, 4232)(3074, 4166, 3168, 4260, 3232, 4324, 3264, 4356, 3233, 4325, 3170, 4262, 3077, 4169)(3078, 4170, 3097, 4189, 3185, 4277, 3244, 4336, 3265, 4357, 3234, 4326, 3171, 4263)(3082, 4174, 3174, 4266, 3202, 4294, 3117, 4209, 3201, 4293, 3235, 4327, 3172, 4264)(3090, 4182, 3180, 4272, 3240, 4332, 3268, 4360, 3238, 4330, 3179, 4271, 3160, 4252)(3111, 4203, 3113, 4205, 3173, 4265, 3236, 4328, 3266, 4358, 3248, 4340, 3197, 4289)(3112, 4204, 3198, 4290, 3239, 4331, 3269, 4361, 3250, 4342, 3200, 4292, 3116, 4208)(3122, 4214, 3136, 4228, 3176, 4268, 3237, 4329, 3267, 4359, 3251, 4343, 3204, 4296)(3128, 4220, 3209, 4301, 3221, 4313, 3146, 4238, 3220, 4312, 3253, 4345, 3207, 4299)(3141, 4233, 3143, 4235, 3208, 4300, 3254, 4346, 3272, 4364, 3258, 4350, 3217, 4309)(3142, 4234, 3218, 4310, 3256, 4348, 3274, 4366, 3259, 4351, 3219, 4311, 3145, 4237)(3151, 4243, 3191, 4283, 3211, 4303, 3255, 4347, 3273, 4365, 3260, 4352, 3223, 4315)(3155, 4247, 3225, 4317, 3262, 4354, 3243, 4335, 3186, 4278, 3245, 4337, 3226, 4318)(3175, 4267, 3182, 4274, 3242, 4334, 3270, 4362, 3252, 4344, 3206, 4298, 3203, 4295)(3210, 4302, 3214, 4306, 3257, 4349, 3275, 4367, 3261, 4353, 3224, 4316, 3222, 4314)(3227, 4319, 3246, 4338, 3247, 4339, 3271, 4363, 3276, 4368, 3263, 4355, 3228, 4320) L = (1, 2187)(2, 2190)(3, 2193)(4, 2195)(5, 2185)(6, 2198)(7, 2186)(8, 2188)(9, 2203)(10, 2205)(11, 2206)(12, 2207)(13, 2189)(14, 2211)(15, 2213)(16, 2191)(17, 2192)(18, 2194)(19, 2210)(20, 2222)(21, 2223)(22, 2224)(23, 2226)(24, 2196)(25, 2228)(26, 2197)(27, 2216)(28, 2233)(29, 2234)(30, 2199)(31, 2236)(32, 2200)(33, 2239)(34, 2201)(35, 2202)(36, 2204)(37, 2245)(38, 2246)(39, 2247)(40, 2218)(41, 2251)(42, 2252)(43, 2208)(44, 2256)(45, 2209)(46, 2221)(47, 2212)(48, 2260)(49, 2261)(50, 2262)(51, 2214)(52, 2266)(53, 2215)(54, 2232)(55, 2269)(56, 2217)(57, 2250)(58, 2272)(59, 2219)(60, 2220)(61, 2277)(62, 2278)(63, 2243)(64, 2282)(65, 2225)(66, 2284)(67, 2285)(68, 2255)(69, 2288)(70, 2289)(71, 2227)(72, 2292)(73, 2229)(74, 2230)(75, 2231)(76, 2299)(77, 2300)(78, 2265)(79, 2304)(80, 2305)(81, 2235)(82, 2308)(83, 2237)(84, 2238)(85, 2313)(86, 2240)(87, 2241)(88, 2318)(89, 2242)(90, 2281)(91, 2321)(92, 2244)(93, 2324)(94, 2276)(95, 2328)(96, 2248)(97, 2330)(98, 2331)(99, 2249)(100, 2334)(101, 2335)(102, 2253)(103, 2338)(104, 2339)(105, 2340)(106, 2254)(107, 2287)(108, 2295)(109, 2345)(110, 2346)(111, 2257)(112, 2258)(113, 2350)(114, 2259)(115, 2353)(116, 2298)(117, 2357)(118, 2263)(119, 2359)(120, 2360)(121, 2361)(122, 2264)(123, 2303)(124, 2311)(125, 2366)(126, 2367)(127, 2267)(128, 2268)(129, 2316)(130, 2373)(131, 2374)(132, 2270)(133, 2271)(134, 2379)(135, 2273)(136, 2274)(137, 2384)(138, 2275)(139, 2327)(140, 2296)(141, 2389)(142, 2279)(143, 2391)(144, 2392)(145, 2280)(146, 2395)(147, 2396)(148, 2398)(149, 2283)(150, 2378)(151, 2333)(152, 2404)(153, 2286)(154, 2407)(155, 2408)(156, 2410)(157, 2290)(158, 2291)(159, 2293)(160, 2416)(161, 2417)(162, 2418)(163, 2294)(164, 2344)(165, 2388)(166, 2422)(167, 2297)(168, 2356)(169, 2312)(170, 2427)(171, 2301)(172, 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3674)(1491, 3675)(1492, 3676)(1493, 3677)(1494, 3678)(1495, 3679)(1496, 3680)(1497, 3681)(1498, 3682)(1499, 3683)(1500, 3684)(1501, 3685)(1502, 3686)(1503, 3687)(1504, 3688)(1505, 3689)(1506, 3690)(1507, 3691)(1508, 3692)(1509, 3693)(1510, 3694)(1511, 3695)(1512, 3696)(1513, 3697)(1514, 3698)(1515, 3699)(1516, 3700)(1517, 3701)(1518, 3702)(1519, 3703)(1520, 3704)(1521, 3705)(1522, 3706)(1523, 3707)(1524, 3708)(1525, 3709)(1526, 3710)(1527, 3711)(1528, 3712)(1529, 3713)(1530, 3714)(1531, 3715)(1532, 3716)(1533, 3717)(1534, 3718)(1535, 3719)(1536, 3720)(1537, 3721)(1538, 3722)(1539, 3723)(1540, 3724)(1541, 3725)(1542, 3726)(1543, 3727)(1544, 3728)(1545, 3729)(1546, 3730)(1547, 3731)(1548, 3732)(1549, 3733)(1550, 3734)(1551, 3735)(1552, 3736)(1553, 3737)(1554, 3738)(1555, 3739)(1556, 3740)(1557, 3741)(1558, 3742)(1559, 3743)(1560, 3744)(1561, 3745)(1562, 3746)(1563, 3747)(1564, 3748)(1565, 3749)(1566, 3750)(1567, 3751)(1568, 3752)(1569, 3753)(1570, 3754)(1571, 3755)(1572, 3756)(1573, 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3840)(1657, 3841)(1658, 3842)(1659, 3843)(1660, 3844)(1661, 3845)(1662, 3846)(1663, 3847)(1664, 3848)(1665, 3849)(1666, 3850)(1667, 3851)(1668, 3852)(1669, 3853)(1670, 3854)(1671, 3855)(1672, 3856)(1673, 3857)(1674, 3858)(1675, 3859)(1676, 3860)(1677, 3861)(1678, 3862)(1679, 3863)(1680, 3864)(1681, 3865)(1682, 3866)(1683, 3867)(1684, 3868)(1685, 3869)(1686, 3870)(1687, 3871)(1688, 3872)(1689, 3873)(1690, 3874)(1691, 3875)(1692, 3876)(1693, 3877)(1694, 3878)(1695, 3879)(1696, 3880)(1697, 3881)(1698, 3882)(1699, 3883)(1700, 3884)(1701, 3885)(1702, 3886)(1703, 3887)(1704, 3888)(1705, 3889)(1706, 3890)(1707, 3891)(1708, 3892)(1709, 3893)(1710, 3894)(1711, 3895)(1712, 3896)(1713, 3897)(1714, 3898)(1715, 3899)(1716, 3900)(1717, 3901)(1718, 3902)(1719, 3903)(1720, 3904)(1721, 3905)(1722, 3906)(1723, 3907)(1724, 3908)(1725, 3909)(1726, 3910)(1727, 3911)(1728, 3912)(1729, 3913)(1730, 3914)(1731, 3915)(1732, 3916)(1733, 3917)(1734, 3918)(1735, 3919)(1736, 3920)(1737, 3921)(1738, 3922)(1739, 3923)(1740, 3924)(1741, 3925)(1742, 3926)(1743, 3927)(1744, 3928)(1745, 3929)(1746, 3930)(1747, 3931)(1748, 3932)(1749, 3933)(1750, 3934)(1751, 3935)(1752, 3936)(1753, 3937)(1754, 3938)(1755, 3939)(1756, 3940)(1757, 3941)(1758, 3942)(1759, 3943)(1760, 3944)(1761, 3945)(1762, 3946)(1763, 3947)(1764, 3948)(1765, 3949)(1766, 3950)(1767, 3951)(1768, 3952)(1769, 3953)(1770, 3954)(1771, 3955)(1772, 3956)(1773, 3957)(1774, 3958)(1775, 3959)(1776, 3960)(1777, 3961)(1778, 3962)(1779, 3963)(1780, 3964)(1781, 3965)(1782, 3966)(1783, 3967)(1784, 3968)(1785, 3969)(1786, 3970)(1787, 3971)(1788, 3972)(1789, 3973)(1790, 3974)(1791, 3975)(1792, 3976)(1793, 3977)(1794, 3978)(1795, 3979)(1796, 3980)(1797, 3981)(1798, 3982)(1799, 3983)(1800, 3984)(1801, 3985)(1802, 3986)(1803, 3987)(1804, 3988)(1805, 3989)(1806, 3990)(1807, 3991)(1808, 3992)(1809, 3993)(1810, 3994)(1811, 3995)(1812, 3996)(1813, 3997)(1814, 3998)(1815, 3999)(1816, 4000)(1817, 4001)(1818, 4002)(1819, 4003)(1820, 4004)(1821, 4005)(1822, 4006)(1823, 4007)(1824, 4008)(1825, 4009)(1826, 4010)(1827, 4011)(1828, 4012)(1829, 4013)(1830, 4014)(1831, 4015)(1832, 4016)(1833, 4017)(1834, 4018)(1835, 4019)(1836, 4020)(1837, 4021)(1838, 4022)(1839, 4023)(1840, 4024)(1841, 4025)(1842, 4026)(1843, 4027)(1844, 4028)(1845, 4029)(1846, 4030)(1847, 4031)(1848, 4032)(1849, 4033)(1850, 4034)(1851, 4035)(1852, 4036)(1853, 4037)(1854, 4038)(1855, 4039)(1856, 4040)(1857, 4041)(1858, 4042)(1859, 4043)(1860, 4044)(1861, 4045)(1862, 4046)(1863, 4047)(1864, 4048)(1865, 4049)(1866, 4050)(1867, 4051)(1868, 4052)(1869, 4053)(1870, 4054)(1871, 4055)(1872, 4056)(1873, 4057)(1874, 4058)(1875, 4059)(1876, 4060)(1877, 4061)(1878, 4062)(1879, 4063)(1880, 4064)(1881, 4065)(1882, 4066)(1883, 4067)(1884, 4068)(1885, 4069)(1886, 4070)(1887, 4071)(1888, 4072)(1889, 4073)(1890, 4074)(1891, 4075)(1892, 4076)(1893, 4077)(1894, 4078)(1895, 4079)(1896, 4080)(1897, 4081)(1898, 4082)(1899, 4083)(1900, 4084)(1901, 4085)(1902, 4086)(1903, 4087)(1904, 4088)(1905, 4089)(1906, 4090)(1907, 4091)(1908, 4092)(1909, 4093)(1910, 4094)(1911, 4095)(1912, 4096)(1913, 4097)(1914, 4098)(1915, 4099)(1916, 4100)(1917, 4101)(1918, 4102)(1919, 4103)(1920, 4104)(1921, 4105)(1922, 4106)(1923, 4107)(1924, 4108)(1925, 4109)(1926, 4110)(1927, 4111)(1928, 4112)(1929, 4113)(1930, 4114)(1931, 4115)(1932, 4116)(1933, 4117)(1934, 4118)(1935, 4119)(1936, 4120)(1937, 4121)(1938, 4122)(1939, 4123)(1940, 4124)(1941, 4125)(1942, 4126)(1943, 4127)(1944, 4128)(1945, 4129)(1946, 4130)(1947, 4131)(1948, 4132)(1949, 4133)(1950, 4134)(1951, 4135)(1952, 4136)(1953, 4137)(1954, 4138)(1955, 4139)(1956, 4140)(1957, 4141)(1958, 4142)(1959, 4143)(1960, 4144)(1961, 4145)(1962, 4146)(1963, 4147)(1964, 4148)(1965, 4149)(1966, 4150)(1967, 4151)(1968, 4152)(1969, 4153)(1970, 4154)(1971, 4155)(1972, 4156)(1973, 4157)(1974, 4158)(1975, 4159)(1976, 4160)(1977, 4161)(1978, 4162)(1979, 4163)(1980, 4164)(1981, 4165)(1982, 4166)(1983, 4167)(1984, 4168)(1985, 4169)(1986, 4170)(1987, 4171)(1988, 4172)(1989, 4173)(1990, 4174)(1991, 4175)(1992, 4176)(1993, 4177)(1994, 4178)(1995, 4179)(1996, 4180)(1997, 4181)(1998, 4182)(1999, 4183)(2000, 4184)(2001, 4185)(2002, 4186)(2003, 4187)(2004, 4188)(2005, 4189)(2006, 4190)(2007, 4191)(2008, 4192)(2009, 4193)(2010, 4194)(2011, 4195)(2012, 4196)(2013, 4197)(2014, 4198)(2015, 4199)(2016, 4200)(2017, 4201)(2018, 4202)(2019, 4203)(2020, 4204)(2021, 4205)(2022, 4206)(2023, 4207)(2024, 4208)(2025, 4209)(2026, 4210)(2027, 4211)(2028, 4212)(2029, 4213)(2030, 4214)(2031, 4215)(2032, 4216)(2033, 4217)(2034, 4218)(2035, 4219)(2036, 4220)(2037, 4221)(2038, 4222)(2039, 4223)(2040, 4224)(2041, 4225)(2042, 4226)(2043, 4227)(2044, 4228)(2045, 4229)(2046, 4230)(2047, 4231)(2048, 4232)(2049, 4233)(2050, 4234)(2051, 4235)(2052, 4236)(2053, 4237)(2054, 4238)(2055, 4239)(2056, 4240)(2057, 4241)(2058, 4242)(2059, 4243)(2060, 4244)(2061, 4245)(2062, 4246)(2063, 4247)(2064, 4248)(2065, 4249)(2066, 4250)(2067, 4251)(2068, 4252)(2069, 4253)(2070, 4254)(2071, 4255)(2072, 4256)(2073, 4257)(2074, 4258)(2075, 4259)(2076, 4260)(2077, 4261)(2078, 4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E14.644 Graph:: bipartite v = 520 e = 2184 f = 1638 degree seq :: [ 6^364, 14^156 ] E14.642 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2^7, (Y2^2 * Y1^-1 * Y2^3 * Y1^-1)^3 ] Map:: R = (1, 1093, 2, 1094, 4, 1096)(3, 1095, 8, 1100, 10, 1102)(5, 1097, 12, 1104, 6, 1098)(7, 1099, 15, 1107, 11, 1103)(9, 1101, 18, 1110, 20, 1112)(13, 1105, 25, 1117, 23, 1115)(14, 1106, 24, 1116, 28, 1120)(16, 1108, 31, 1123, 29, 1121)(17, 1109, 33, 1125, 21, 1113)(19, 1111, 36, 1128, 37, 1129)(22, 1114, 30, 1122, 41, 1133)(26, 1118, 46, 1138, 44, 1136)(27, 1119, 47, 1139, 48, 1140)(32, 1124, 54, 1146, 52, 1144)(34, 1126, 57, 1149, 55, 1147)(35, 1127, 58, 1150, 38, 1130)(39, 1131, 56, 1148, 64, 1156)(40, 1132, 65, 1157, 66, 1158)(42, 1134, 45, 1137, 69, 1161)(43, 1135, 70, 1162, 49, 1141)(50, 1142, 53, 1145, 79, 1171)(51, 1143, 80, 1172, 67, 1159)(59, 1151, 90, 1182, 88, 1180)(60, 1152, 91, 1183, 61, 1153)(62, 1154, 89, 1181, 95, 1187)(63, 1155, 96, 1188, 97, 1189)(68, 1160, 102, 1194, 103, 1195)(71, 1163, 107, 1199, 105, 1197)(72, 1164, 74, 1166, 109, 1201)(73, 1165, 110, 1202, 104, 1196)(75, 1167, 113, 1205, 76, 1168)(77, 1169, 106, 1198, 117, 1209)(78, 1170, 118, 1210, 119, 1211)(81, 1173, 123, 1215, 121, 1213)(82, 1174, 84, 1176, 125, 1217)(83, 1175, 126, 1218, 120, 1212)(85, 1177, 87, 1179, 130, 1222)(86, 1178, 131, 1223, 98, 1190)(92, 1184, 139, 1231, 137, 1229)(93, 1185, 138, 1230, 141, 1233)(94, 1186, 142, 1234, 143, 1235)(99, 1191, 148, 1240, 100, 1192)(101, 1193, 122, 1214, 152, 1244)(108, 1200, 159, 1251, 160, 1252)(111, 1203, 164, 1256, 162, 1254)(112, 1204, 165, 1257, 161, 1253)(114, 1206, 168, 1260, 166, 1258)(115, 1207, 167, 1259, 170, 1262)(116, 1208, 171, 1263, 172, 1264)(124, 1216, 180, 1272, 181, 1273)(127, 1219, 185, 1277, 183, 1275)(128, 1220, 186, 1278, 182, 1274)(129, 1221, 187, 1279, 188, 1280)(132, 1224, 192, 1284, 190, 1282)(133, 1225, 193, 1285, 189, 1281)(134, 1226, 136, 1228, 196, 1288)(135, 1227, 197, 1289, 144, 1236)(140, 1232, 203, 1295, 204, 1296)(145, 1237, 209, 1301, 146, 1238)(147, 1239, 191, 1283, 213, 1305)(149, 1241, 216, 1308, 214, 1306)(150, 1242, 215, 1307, 217, 1309)(151, 1243, 218, 1310, 219, 1311)(153, 1245, 221, 1313, 154, 1246)(155, 1247, 163, 1255, 225, 1317)(156, 1248, 158, 1250, 227, 1319)(157, 1249, 228, 1320, 173, 1265)(169, 1261, 241, 1333, 242, 1334)(174, 1266, 247, 1339, 175, 1267)(176, 1268, 184, 1276, 251, 1343)(177, 1269, 179, 1271, 253, 1345)(178, 1270, 254, 1346, 220, 1312)(194, 1286, 272, 1364, 270, 1362)(195, 1287, 273, 1365, 274, 1366)(198, 1290, 278, 1370, 276, 1368)(199, 1291, 279, 1371, 275, 1367)(200, 1292, 202, 1294, 282, 1374)(201, 1293, 283, 1375, 205, 1297)(206, 1298, 289, 1381, 207, 1299)(208, 1300, 277, 1369, 293, 1385)(210, 1302, 296, 1388, 294, 1386)(211, 1303, 295, 1387, 297, 1389)(212, 1304, 298, 1390, 299, 1391)(222, 1314, 310, 1402, 308, 1400)(223, 1315, 309, 1401, 312, 1404)(224, 1316, 313, 1405, 314, 1406)(226, 1318, 316, 1408, 317, 1409)(229, 1321, 321, 1413, 319, 1411)(230, 1322, 322, 1414, 318, 1410)(231, 1323, 323, 1415, 232, 1324)(233, 1325, 237, 1329, 327, 1419)(234, 1326, 236, 1328, 329, 1421)(235, 1327, 330, 1422, 315, 1407)(238, 1330, 240, 1332, 335, 1427)(239, 1331, 336, 1428, 243, 1335)(244, 1336, 342, 1434, 245, 1337)(246, 1338, 320, 1412, 346, 1438)(248, 1340, 349, 1441, 347, 1439)(249, 1341, 348, 1440, 351, 1443)(250, 1342, 352, 1444, 353, 1445)(252, 1344, 355, 1447, 356, 1448)(255, 1347, 360, 1452, 358, 1450)(256, 1348, 361, 1453, 357, 1449)(257, 1349, 362, 1454, 258, 1350)(259, 1351, 263, 1355, 366, 1458)(260, 1352, 262, 1354, 368, 1460)(261, 1353, 369, 1461, 354, 1446)(264, 1356, 373, 1465, 265, 1357)(266, 1358, 271, 1363, 377, 1469)(267, 1359, 269, 1361, 379, 1471)(268, 1360, 380, 1472, 300, 1392)(280, 1372, 394, 1486, 392, 1484)(281, 1373, 395, 1487, 396, 1488)(284, 1376, 400, 1492, 398, 1490)(285, 1377, 401, 1493, 397, 1489)(286, 1378, 403, 1495, 287, 1379)(288, 1380, 399, 1491, 407, 1499)(290, 1382, 410, 1502, 408, 1500)(291, 1383, 409, 1501, 411, 1503)(292, 1384, 412, 1504, 413, 1505)(301, 1393, 303, 1395, 423, 1515)(302, 1394, 424, 1516, 304, 1396)(305, 1397, 428, 1520, 306, 1398)(307, 1399, 359, 1451, 432, 1524)(311, 1403, 436, 1528, 437, 1529)(324, 1416, 451, 1543, 449, 1541)(325, 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4075, 2853, 3945, 2725, 3817, 2767, 3859)(2635, 3727, 2639, 3731, 2792, 3884, 2909, 4001, 2906, 3998, 2914, 4006, 2788, 3880)(2637, 3729, 2790, 3882, 2804, 3896, 2656, 3748, 2803, 3895, 2716, 3808, 2789, 3881)(2651, 3743, 2798, 3890, 2925, 4017, 2898, 3990, 2900, 3992, 2802, 3894, 2655, 3747)(2688, 3780, 2692, 3784, 2832, 3924, 2955, 4047, 2952, 4044, 2960, 4052, 2829, 3921)(2703, 3795, 2707, 3799, 2842, 3934, 2857, 3949, 2854, 3946, 2971, 4063, 2839, 3931)(2719, 3811, 2847, 3939, 2978, 4070, 3082, 4174, 3084, 4176, 2979, 4071, 2848, 3940)(2723, 3815, 2813, 3905, 2941, 4033, 3054, 4146, 3087, 4179, 2981, 4073, 2851, 3943)(2726, 3818, 2855, 3947, 2972, 4064, 3076, 4168, 3089, 4181, 2984, 4076, 2856, 3948)(2748, 3840, 2876, 3968, 3002, 4094, 3103, 4195, 3101, 4193, 3000, 4092, 2874, 3966)(2749, 3841, 2877, 3969, 3003, 4095, 3104, 4196, 3023, 4115, 2904, 3996, 2782, 3874)(2755, 3847, 2882, 3974, 3005, 4097, 3094, 4186, 2990, 4082, 2864, 3956, 2881, 3973)(2757, 3849, 2884, 3976, 3008, 4100, 2944, 4036, 2946, 4038, 2888, 3980, 2761, 3853)(2770, 3862, 2894, 3986, 2995, 4087, 3096, 4188, 3117, 4209, 3016, 4108, 2892, 3984)(2771, 3863, 2895, 3987, 3018, 4110, 3119, 4211, 3059, 4151, 2950, 4042, 2823, 3915)(2778, 3870, 2901, 3993, 3020, 4112, 3121, 4213, 3042, 4134, 2929, 4021, 2899, 3991)(2779, 3871, 2902, 3994, 3021, 4113, 3123, 4215, 3097, 4189, 2996, 4088, 2870, 3962)(2784, 3876, 2907, 3999, 2915, 4007, 3030, 4122, 3128, 4220, 3025, 4117, 2908, 4000)(2812, 3904, 2940, 4032, 3047, 4139, 3140, 4232, 3145, 4237, 3052, 4144, 2938, 4030)(2819, 3911, 2947, 4039, 3056, 4148, 3148, 4240, 3111, 4203, 3012, 4104, 2945, 4037)(2820, 3912, 2948, 4040, 3057, 4149, 3150, 4242, 3141, 4233, 3048, 4140, 2934, 4026)(2825, 3917, 2953, 4045, 2961, 4053, 3066, 4158, 3155, 4247, 3061, 4153, 2954, 4046)(2849, 3941, 2852, 3944, 2982, 4074, 2994, 4086, 2991, 4083, 3085, 4177, 2980, 4072)(2858, 3950, 2985, 4077, 3090, 4182, 3134, 4226, 3036, 4128, 2920, 4012, 2986, 4078)(2862, 3954, 2969, 4061, 3074, 4166, 3162, 4254, 3174, 4266, 3092, 4184, 2988, 4080)(2865, 3957, 2992, 4084, 3086, 4178, 3169, 4261, 3176, 4268, 3095, 4187, 2993, 4085)(2873, 3965, 2999, 4091, 3099, 4191, 3129, 4221, 3026, 4118, 2911, 4003, 2998, 4090)(2875, 3967, 3001, 4093, 3102, 4194, 3077, 4169, 3079, 4171, 3004, 4096, 2878, 3970)(2893, 3985, 3017, 4109, 3118, 4210, 3031, 4123, 3033, 4125, 3019, 4111, 2896, 3988)(2903, 3995, 2905, 3997, 3024, 4116, 3046, 4138, 3043, 4135, 3125, 4217, 3022, 4114)(2912, 4004, 3028, 4120, 3131, 4223, 3201, 4293, 3137, 4229, 3040, 4132, 2927, 4019)(2918, 4010, 3034, 4126, 3132, 4224, 3202, 4294, 3193, 4285, 3120, 4212, 3032, 4124)(2923, 4015, 3037, 4129, 3135, 4227, 3159, 4251, 3070, 4162, 2965, 4057, 3038, 4130)(2930, 4022, 3044, 4136, 3126, 4218, 3184, 4276, 3207, 4299, 3139, 4231, 3045, 4137)(2937, 4029, 3051, 4143, 3143, 4235, 3156, 4248, 3062, 4154, 2957, 4049, 3050, 4142)(2939, 4031, 3053, 4145, 3146, 4238, 3067, 4159, 3069, 4161, 3055, 4147, 2942, 4034)(2949, 4041, 2951, 4043, 3060, 4152, 3114, 4206, 3112, 4204, 3152, 4244, 3058, 4150)(2958, 4050, 3064, 4156, 3158, 4250, 3220, 4312, 3188, 4280, 3109, 4201, 3010, 4102)(2964, 4056, 2997, 4089, 3098, 4190, 3178, 4270, 3170, 4262, 3147, 4239, 3068, 4160)(2968, 4060, 3073, 4165, 3015, 4107, 3115, 4207, 3189, 4281, 3160, 4252, 3071, 4163)(2975, 4067, 3049, 4141, 3142, 4234, 3209, 4301, 3183, 4275, 3105, 4197, 3078, 4170)(2976, 4068, 3080, 4172, 3006, 4098, 3107, 4199, 3186, 4278, 3164, 4256, 3081, 4173)(2987, 4079, 2989, 4081, 3093, 4185, 3029, 4121, 3027, 4119, 3130, 4222, 3091, 4183)(3013, 4105, 3113, 4205, 3153, 4245, 3194, 4286, 3203, 4295, 3133, 4225, 3035, 4127)(3039, 4131, 3041, 4133, 3138, 4230, 3065, 4157, 3063, 4155, 3157, 4249, 3136, 4228)(3072, 4164, 3161, 4253, 3187, 4279, 3108, 4200, 3110, 4202, 3163, 4255, 3075, 4167)(3083, 4175, 3167, 4259, 3106, 4198, 3185, 4277, 3232, 4324, 3224, 4316, 3165, 4257)(3088, 4180, 3171, 4263, 3100, 4192, 3180, 4272, 3230, 4322, 3227, 4319, 3172, 4264)(3116, 4208, 3190, 4282, 3235, 4327, 3240, 4332, 3199, 4291, 3127, 4219, 3191, 4283)(3122, 4214, 3196, 4288, 3237, 4329, 3238, 4330, 3197, 4289, 3124, 4216, 3195, 4287)(3144, 4236, 3211, 4303, 3244, 4336, 3249, 4341, 3218, 4310, 3154, 4246, 3212, 4304)(3149, 4241, 3215, 4307, 3246, 4338, 3247, 4339, 3216, 4308, 3151, 4243, 3214, 4306)(3166, 4258, 3225, 4317, 3231, 4323, 3181, 4273, 3182, 4274, 3226, 4318, 3168, 4260)(3173, 4265, 3200, 4292, 3179, 4271, 3229, 4321, 3254, 4346, 3241, 4333, 3204, 4296)(3175, 4267, 3228, 4320, 3177, 4269, 3198, 4290, 3239, 4331, 3236, 4328, 3192, 4284)(3205, 4297, 3219, 4311, 3210, 4302, 3243, 4335, 3262, 4354, 3250, 4342, 3221, 4313)(3206, 4298, 3242, 4334, 3208, 4300, 3217, 4309, 3248, 4340, 3245, 4337, 3213, 4305)(3222, 4314, 3234, 4326, 3257, 4349, 3267, 4359, 3251, 4343, 3223, 4315, 3233, 4325)(3252, 4344, 3256, 4348, 3270, 4362, 3274, 4366, 3268, 4360, 3253, 4345, 3255, 4347)(3258, 4350, 3260, 4352, 3259, 4351, 3269, 4361, 3275, 4367, 3271, 4363, 3261, 4353)(3263, 4355, 3265, 4357, 3264, 4356, 3272, 4364, 3276, 4368, 3273, 4365, 3266, 4358) L = (1, 2187)(2, 2190)(3, 2193)(4, 2195)(5, 2185)(6, 2198)(7, 2186)(8, 2188)(9, 2203)(10, 2205)(11, 2206)(12, 2207)(13, 2189)(14, 2211)(15, 2213)(16, 2191)(17, 2192)(18, 2194)(19, 2210)(20, 2222)(21, 2223)(22, 2224)(23, 2226)(24, 2196)(25, 2228)(26, 2197)(27, 2216)(28, 2233)(29, 2234)(30, 2199)(31, 2236)(32, 2200)(33, 2239)(34, 2201)(35, 2202)(36, 2204)(37, 2245)(38, 2246)(39, 2247)(40, 2218)(41, 2251)(42, 2252)(43, 2208)(44, 2256)(45, 2209)(46, 2221)(47, 2212)(48, 2260)(49, 2261)(50, 2262)(51, 2214)(52, 2266)(53, 2215)(54, 2232)(55, 2269)(56, 2217)(57, 2250)(58, 2272)(59, 2219)(60, 2220)(61, 2277)(62, 2278)(63, 2243)(64, 2282)(65, 2225)(66, 2284)(67, 2285)(68, 2255)(69, 2288)(70, 2289)(71, 2227)(72, 2292)(73, 2229)(74, 2230)(75, 2231)(76, 2299)(77, 2300)(78, 2265)(79, 2304)(80, 2305)(81, 2235)(82, 2308)(83, 2237)(84, 2238)(85, 2313)(86, 2240)(87, 2241)(88, 2318)(89, 2242)(90, 2281)(91, 2321)(92, 2244)(93, 2324)(94, 2276)(95, 2328)(96, 2248)(97, 2330)(98, 2331)(99, 2249)(100, 2334)(101, 2335)(102, 2253)(103, 2338)(104, 2339)(105, 2340)(106, 2254)(107, 2287)(108, 2295)(109, 2345)(110, 2346)(111, 2257)(112, 2258)(113, 2350)(114, 2259)(115, 2353)(116, 2298)(117, 2357)(118, 2263)(119, 2359)(120, 2360)(121, 2361)(122, 2264)(123, 2303)(124, 2311)(125, 2366)(126, 2367)(127, 2267)(128, 2268)(129, 2316)(130, 2373)(131, 2374)(132, 2270)(133, 2271)(134, 2379)(135, 2273)(136, 2274)(137, 2384)(138, 2275)(139, 2327)(140, 2296)(141, 2389)(142, 2279)(143, 2391)(144, 2392)(145, 2280)(146, 2395)(147, 2396)(148, 2398)(149, 2283)(150, 2378)(151, 2333)(152, 2404)(153, 2286)(154, 2407)(155, 2408)(156, 2410)(157, 2290)(158, 2291)(159, 2293)(160, 2416)(161, 2417)(162, 2418)(163, 2294)(164, 2344)(165, 2388)(166, 2422)(167, 2297)(168, 2356)(169, 2312)(170, 2427)(171, 2301)(172, 2429)(173, 2430)(174, 2302)(175, 2433)(176, 2434)(177, 2436)(178, 2306)(179, 2307)(180, 2309)(181, 2442)(182, 2443)(183, 2444)(184, 2310)(185, 2365)(186, 2426)(187, 2314)(188, 2449)(189, 2450)(190, 2451)(191, 2315)(192, 2372)(193, 2454)(194, 2317)(195, 2382)(196, 2459)(197, 2460)(198, 2319)(199, 2320)(200, 2465)(201, 2322)(202, 2323)(203, 2325)(204, 2471)(205, 2472)(206, 2326)(207, 2475)(208, 2476)(209, 2478)(210, 2329)(211, 2464)(212, 2394)(213, 2484)(214, 2485)(215, 2332)(216, 2403)(217, 2488)(218, 2336)(219, 2490)(220, 2491)(221, 2492)(222, 2337)(223, 2495)(224, 2406)(225, 2499)(226, 2413)(227, 2502)(228, 2503)(229, 2341)(230, 2342)(231, 2343)(232, 2509)(233, 2510)(234, 2512)(235, 2347)(236, 2348)(237, 2349)(238, 2518)(239, 2351)(240, 2352)(241, 2354)(242, 2524)(243, 2525)(244, 2355)(245, 2528)(246, 2529)(247, 2531)(248, 2358)(249, 2534)(250, 2432)(251, 2538)(252, 2439)(253, 2541)(254, 2542)(255, 2362)(256, 2363)(257, 2364)(258, 2548)(259, 2549)(260, 2551)(261, 2368)(262, 2369)(263, 2370)(264, 2371)(265, 2559)(266, 2560)(267, 2562)(268, 2375)(269, 2376)(270, 2567)(271, 2377)(272, 2401)(273, 2380)(274, 2571)(275, 2572)(276, 2573)(277, 2381)(278, 2458)(279, 2576)(280, 2383)(281, 2468)(282, 2581)(283, 2582)(284, 2385)(285, 2386)(286, 2387)(287, 2589)(288, 2590)(289, 2592)(290, 2390)(291, 2586)(292, 2474)(293, 2598)(294, 2599)(295, 2393)(296, 2483)(297, 2602)(298, 2397)(299, 2604)(300, 2605)(301, 2606)(302, 2399)(303, 2400)(304, 2611)(305, 2402)(306, 2614)(307, 2615)(308, 2617)(309, 2405)(310, 2498)(311, 2414)(312, 2622)(313, 2409)(314, 2624)(315, 2625)(316, 2411)(317, 2627)(318, 2628)(319, 2629)(320, 2412)(321, 2501)(322, 2621)(323, 2633)(324, 2415)(325, 2636)(326, 2508)(327, 2640)(328, 2515)(329, 2643)(330, 2644)(331, 2419)(332, 2420)(333, 2421)(334, 2521)(335, 2652)(336, 2653)(337, 2423)(338, 2424)(339, 2425)(340, 2660)(341, 2661)(342, 2663)(343, 2428)(344, 2657)(345, 2527)(346, 2669)(347, 2670)(348, 2431)(349, 2537)(350, 2440)(351, 2675)(352, 2435)(353, 2677)(354, 2678)(355, 2437)(356, 2680)(357, 2681)(358, 2682)(359, 2438)(360, 2540)(361, 2674)(362, 2686)(363, 2441)(364, 2689)(365, 2547)(366, 2693)(367, 2554)(368, 2696)(369, 2697)(370, 2445)(371, 2446)(372, 2447)(373, 2701)(374, 2448)(375, 2704)(376, 2558)(377, 2708)(378, 2565)(379, 2711)(380, 2712)(381, 2452)(382, 2453)(383, 2715)(384, 2455)(385, 2456)(386, 2457)(387, 2721)(388, 2722)(389, 2724)(390, 2461)(391, 2462)(392, 2729)(393, 2463)(394, 2481)(395, 2466)(396, 2732)(397, 2733)(398, 2734)(399, 2467)(400, 2580)(401, 2737)(402, 2469)(403, 2739)(404, 2470)(405, 2649)(406, 2588)(407, 2742)(408, 2743)(409, 2473)(410, 2597)(411, 2556)(412, 2477)(413, 2631)(414, 2746)(415, 2747)(416, 2479)(417, 2480)(418, 2632)(419, 2482)(420, 2646)(421, 2754)(422, 2609)(423, 2758)(424, 2759)(425, 2486)(426, 2487)(427, 2647)(428, 2764)(429, 2489)(430, 2741)(431, 2613)(432, 2768)(433, 2769)(434, 2493)(435, 2494)(436, 2496)(437, 2730)(438, 2685)(439, 2497)(440, 2699)(441, 2777)(442, 2500)(443, 2744)(444, 2781)(445, 2783)(446, 2504)(447, 2505)(448, 2506)(449, 2786)(450, 2507)(451, 2639)(452, 2516)(453, 2790)(454, 2511)(455, 2792)(456, 2793)(457, 2513)(458, 2751)(459, 2763)(460, 2752)(461, 2514)(462, 2642)(463, 2718)(464, 2765)(465, 2517)(466, 2519)(467, 2798)(468, 2799)(469, 2800)(470, 2520)(471, 2651)(472, 2803)(473, 2522)(474, 2805)(475, 2523)(476, 2595)(477, 2659)(478, 2806)(479, 2807)(480, 2526)(481, 2668)(482, 2568)(483, 2530)(484, 2684)(485, 2810)(486, 2811)(487, 2532)(488, 2533)(489, 2535)(490, 2774)(491, 2577)(492, 2536)(493, 2714)(494, 2818)(495, 2539)(496, 2808)(497, 2822)(498, 2824)(499, 2543)(500, 2544)(501, 2545)(502, 2827)(503, 2546)(504, 2692)(505, 2555)(506, 2830)(507, 2550)(508, 2832)(509, 2833)(510, 2552)(511, 2773)(512, 2591)(513, 2775)(514, 2553)(515, 2695)(516, 2593)(517, 2837)(518, 2557)(519, 2707)(520, 2566)(521, 2840)(522, 2561)(523, 2842)(524, 2843)(525, 2563)(526, 2815)(527, 2662)(528, 2816)(529, 2564)(530, 2710)(531, 2666)(532, 2789)(533, 2664)(534, 2569)(535, 2847)(536, 2570)(537, 2766)(538, 2720)(539, 2813)(540, 2727)(541, 2767)(542, 2855)(543, 2574)(544, 2575)(545, 2673)(546, 2578)(547, 2579)(548, 2860)(549, 2861)(550, 2863)(551, 2583)(552, 2584)(553, 2658)(554, 2585)(555, 2690)(556, 2587)(557, 2610)(558, 2868)(559, 2869)(560, 2594)(561, 2596)(562, 2872)(563, 2750)(564, 2876)(565, 2877)(566, 2600)(567, 2601)(568, 2879)(569, 2603)(570, 2753)(571, 2882)(572, 2607)(573, 2884)(574, 2885)(575, 2886)(576, 2608)(577, 2757)(578, 2740)(579, 2890)(580, 2850)(581, 2612)(582, 2728)(583, 2616)(584, 2891)(585, 2772)(586, 2894)(587, 2895)(588, 2618)(589, 2619)(590, 2620)(591, 2897)(592, 2623)(593, 2776)(594, 2901)(595, 2902)(596, 2626)(597, 2780)(598, 2749)(599, 2785)(600, 2907)(601, 2630)(602, 2910)(603, 2634)(604, 2635)(605, 2637)(606, 2804)(607, 2638)(608, 2909)(609, 2917)(610, 2641)(611, 2645)(612, 2648)(613, 2650)(614, 2925)(615, 2926)(616, 2928)(617, 2654)(618, 2655)(619, 2716)(620, 2656)(621, 2705)(622, 2932)(623, 2933)(624, 2665)(625, 2667)(626, 2936)(627, 2814)(628, 2940)(629, 2941)(630, 2671)(631, 2672)(632, 2943)(633, 2676)(634, 2817)(635, 2947)(636, 2948)(637, 2679)(638, 2821)(639, 2771)(640, 2826)(641, 2953)(642, 2683)(643, 2956)(644, 2687)(645, 2688)(646, 2889)(647, 2691)(648, 2955)(649, 2963)(650, 2694)(651, 2698)(652, 2700)(653, 2967)(654, 2702)(655, 2703)(656, 2738)(657, 2706)(658, 2857)(659, 2974)(660, 2709)(661, 2713)(662, 2717)(663, 2978)(664, 2719)(665, 2852)(666, 2922)(667, 2723)(668, 2982)(669, 2725)(670, 2971)(671, 2972)(672, 2726)(673, 2854)(674, 2985)(675, 2731)(676, 2880)(677, 2859)(678, 2969)(679, 2866)(680, 2881)(681, 2992)(682, 2735)(683, 2736)(684, 2834)(685, 2836)(686, 2779)(687, 2745)(688, 2871)(689, 2999)(690, 2748)(691, 3001)(692, 3002)(693, 3003)(694, 2875)(695, 2921)(696, 2867)(697, 2755)(698, 3005)(699, 2756)(700, 3008)(701, 3009)(702, 3011)(703, 2760)(704, 2761)(705, 2762)(706, 2919)(707, 2983)(708, 2770)(709, 3017)(710, 2995)(711, 3018)(712, 2893)(713, 2966)(714, 2900)(715, 2778)(716, 2802)(717, 3020)(718, 3021)(719, 2905)(720, 2782)(721, 3024)(722, 2914)(723, 2915)(724, 2784)(725, 2906)(726, 2913)(727, 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4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E14.645 Graph:: bipartite v = 520 e = 2184 f = 1638 degree seq :: [ 6^364, 14^156 ] E14.643 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, Y3^7, (Y3^-1 * Y1^-1)^7, Y3^2 * Y2 * Y3^2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^2 * Y2 * Y3^3 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2, Y3^2 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 ] Map:: polytopal R = (1, 1093)(2, 1094)(3, 1095)(4, 1096)(5, 1097)(6, 1098)(7, 1099)(8, 1100)(9, 1101)(10, 1102)(11, 1103)(12, 1104)(13, 1105)(14, 1106)(15, 1107)(16, 1108)(17, 1109)(18, 1110)(19, 1111)(20, 1112)(21, 1113)(22, 1114)(23, 1115)(24, 1116)(25, 1117)(26, 1118)(27, 1119)(28, 1120)(29, 1121)(30, 1122)(31, 1123)(32, 1124)(33, 1125)(34, 1126)(35, 1127)(36, 1128)(37, 1129)(38, 1130)(39, 1131)(40, 1132)(41, 1133)(42, 1134)(43, 1135)(44, 1136)(45, 1137)(46, 1138)(47, 1139)(48, 1140)(49, 1141)(50, 1142)(51, 1143)(52, 1144)(53, 1145)(54, 1146)(55, 1147)(56, 1148)(57, 1149)(58, 1150)(59, 1151)(60, 1152)(61, 1153)(62, 1154)(63, 1155)(64, 1156)(65, 1157)(66, 1158)(67, 1159)(68, 1160)(69, 1161)(70, 1162)(71, 1163)(72, 1164)(73, 1165)(74, 1166)(75, 1167)(76, 1168)(77, 1169)(78, 1170)(79, 1171)(80, 1172)(81, 1173)(82, 1174)(83, 1175)(84, 1176)(85, 1177)(86, 1178)(87, 1179)(88, 1180)(89, 1181)(90, 1182)(91, 1183)(92, 1184)(93, 1185)(94, 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2178)(1087, 2179)(1088, 2180)(1089, 2181)(1090, 2182)(1091, 2183)(1092, 2184)(2185, 3277, 2186, 3278)(2187, 3279, 2191, 3283)(2188, 3280, 2193, 3285)(2189, 3281, 2195, 3287)(2190, 3282, 2197, 3289)(2192, 3284, 2200, 3292)(2194, 3286, 2203, 3295)(2196, 3288, 2206, 3298)(2198, 3290, 2209, 3301)(2199, 3291, 2211, 3303)(2201, 3293, 2214, 3306)(2202, 3294, 2215, 3307)(2204, 3296, 2218, 3310)(2205, 3297, 2219, 3311)(2207, 3299, 2222, 3314)(2208, 3300, 2223, 3315)(2210, 3302, 2226, 3318)(2212, 3304, 2228, 3320)(2213, 3305, 2230, 3322)(2216, 3308, 2234, 3326)(2217, 3309, 2236, 3328)(2220, 3312, 2240, 3332)(2221, 3313, 2241, 3333)(2224, 3316, 2245, 3337)(2225, 3317, 2246, 3338)(2227, 3319, 2249, 3341)(2229, 3321, 2252, 3344)(2231, 3323, 2254, 3346)(2232, 3324, 2238, 3330)(2233, 3325, 2257, 3349)(2235, 3327, 2260, 3352)(2237, 3329, 2262, 3354)(2239, 3331, 2265, 3357)(2242, 3334, 2269, 3361)(2243, 3335, 2248, 3340)(2244, 3336, 2272, 3364)(2247, 3339, 2276, 3368)(2250, 3342, 2280, 3372)(2251, 3343, 2281, 3373)(2253, 3345, 2284, 3376)(2255, 3347, 2287, 3379)(2256, 3348, 2288, 3380)(2258, 3350, 2291, 3383)(2259, 3351, 2292, 3384)(2261, 3353, 2295, 3387)(2263, 3355, 2298, 3390)(2264, 3356, 2299, 3391)(2266, 3358, 2302, 3394)(2267, 3359, 2294, 3386)(2268, 3360, 2304, 3396)(2270, 3362, 2307, 3399)(2271, 3363, 2308, 3400)(2273, 3365, 2311, 3403)(2274, 3366, 2283, 3375)(2275, 3367, 2313, 3405)(2277, 3369, 2316, 3408)(2278, 3370, 2317, 3409)(2279, 3371, 2319, 3411)(2282, 3374, 2323, 3415)(2285, 3377, 2327, 3419)(2286, 3378, 2328, 3420)(2289, 3381, 2332, 3424)(2290, 3382, 2333, 3425)(2293, 3385, 2337, 3429)(2296, 3388, 2341, 3433)(2297, 3389, 2342, 3434)(2300, 3392, 2346, 3438)(2301, 3393, 2347, 3439)(2303, 3395, 2350, 3442)(2305, 3397, 2353, 3445)(2306, 3398, 2354, 3446)(2309, 3401, 2358, 3450)(2310, 3402, 2359, 3451)(2312, 3404, 2362, 3454)(2314, 3406, 2365, 3457)(2315, 3407, 2366, 3458)(2318, 3410, 2370, 3462)(2320, 3412, 2372, 3464)(2321, 3413, 2330, 3422)(2322, 3414, 2374, 3466)(2324, 3416, 2377, 3469)(2325, 3417, 2378, 3470)(2326, 3418, 2380, 3472)(2329, 3421, 2384, 3476)(2331, 3423, 2387, 3479)(2334, 3426, 2391, 3483)(2335, 3427, 2344, 3436)(2336, 3428, 2393, 3485)(2338, 3430, 2396, 3488)(2339, 3431, 2397, 3489)(2340, 3432, 2399, 3491)(2343, 3435, 2403, 3495)(2345, 3437, 2406, 3498)(2348, 3440, 2410, 3502)(2349, 3441, 2356, 3448)(2351, 3443, 2413, 3505)(2352, 3444, 2414, 3506)(2355, 3447, 2418, 3510)(2357, 3449, 2421, 3513)(2360, 3452, 2425, 3517)(2361, 3453, 2368, 3460)(2363, 3455, 2428, 3520)(2364, 3456, 2429, 3521)(2367, 3459, 2433, 3525)(2369, 3461, 2436, 3528)(2371, 3463, 2439, 3531)(2373, 3465, 2442, 3534)(2375, 3467, 2445, 3537)(2376, 3468, 2446, 3538)(2379, 3471, 2450, 3542)(2381, 3473, 2452, 3544)(2382, 3474, 2389, 3481)(2383, 3475, 2454, 3546)(2385, 3477, 2457, 3549)(2386, 3478, 2458, 3550)(2388, 3480, 2461, 3553)(2390, 3482, 2464, 3556)(2392, 3484, 2467, 3559)(2394, 3486, 2470, 3562)(2395, 3487, 2471, 3563)(2398, 3490, 2475, 3567)(2400, 3492, 2477, 3569)(2401, 3493, 2408, 3500)(2402, 3494, 2479, 3571)(2404, 3496, 2482, 3574)(2405, 3497, 2483, 3575)(2407, 3499, 2486, 3578)(2409, 3501, 2488, 3580)(2411, 3503, 2491, 3583)(2412, 3504, 2493, 3585)(2415, 3507, 2497, 3589)(2416, 3508, 2423, 3515)(2417, 3509, 2499, 3591)(2419, 3511, 2502, 3594)(2420, 3512, 2503, 3595)(2422, 3514, 2506, 3598)(2424, 3516, 2509, 3601)(2426, 3518, 2512, 3604)(2427, 3519, 2514, 3606)(2430, 3522, 2518, 3610)(2431, 3523, 2438, 3530)(2432, 3524, 2520, 3612)(2434, 3526, 2523, 3615)(2435, 3527, 2524, 3616)(2437, 3529, 2527, 3619)(2440, 3532, 2530, 3622)(2441, 3533, 2448, 3540)(2443, 3535, 2533, 3625)(2444, 3536, 2534, 3626)(2447, 3539, 2538, 3630)(2449, 3541, 2541, 3633)(2451, 3543, 2544, 3636)(2453, 3545, 2547, 3639)(2455, 3547, 2550, 3642)(2456, 3548, 2551, 3643)(2459, 3551, 2555, 3647)(2460, 3552, 2556, 3648)(2462, 3554, 2559, 3651)(2463, 3555, 2560, 3652)(2465, 3557, 2563, 3655)(2466, 3558, 2473, 3565)(2468, 3560, 2566, 3658)(2469, 3561, 2567, 3659)(2472, 3564, 2571, 3663)(2474, 3566, 2574, 3666)(2476, 3568, 2577, 3669)(2478, 3570, 2580, 3672)(2480, 3572, 2583, 3675)(2481, 3573, 2584, 3676)(2484, 3576, 2588, 3680)(2485, 3577, 2589, 3681)(2487, 3579, 2592, 3684)(2489, 3581, 2595, 3687)(2490, 3582, 2495, 3587)(2492, 3584, 2598, 3690)(2494, 3586, 2600, 3692)(2496, 3588, 2603, 3695)(2498, 3590, 2606, 3698)(2500, 3592, 2609, 3701)(2501, 3593, 2610, 3702)(2504, 3596, 2614, 3706)(2505, 3597, 2615, 3707)(2507, 3599, 2618, 3710)(2508, 3600, 2619, 3711)(2510, 3602, 2622, 3714)(2511, 3603, 2516, 3608)(2513, 3605, 2625, 3717)(2515, 3607, 2627, 3719)(2517, 3609, 2630, 3722)(2519, 3611, 2633, 3725)(2521, 3613, 2636, 3728)(2522, 3614, 2637, 3729)(2525, 3617, 2641, 3733)(2526, 3618, 2642, 3734)(2528, 3620, 2645, 3737)(2529, 3621, 2594, 3686)(2531, 3623, 2648, 3740)(2532, 3624, 2650, 3742)(2535, 3627, 2654, 3746)(2536, 3628, 2543, 3635)(2537, 3629, 2656, 3748)(2539, 3631, 2659, 3751)(2540, 3632, 2660, 3752)(2542, 3634, 2663, 3755)(2545, 3637, 2631, 3723)(2546, 3638, 2553, 3645)(2548, 3640, 2667, 3759)(2549, 3641, 2668, 3760)(2552, 3644, 2672, 3764)(2554, 3646, 2675, 3767)(2557, 3649, 2679, 3771)(2558, 3650, 2680, 3772)(2561, 3653, 2684, 3776)(2562, 3654, 2621, 3713)(2564, 3656, 2686, 3778)(2565, 3657, 2688, 3780)(2568, 3660, 2692, 3784)(2569, 3661, 2576, 3668)(2570, 3662, 2694, 3786)(2572, 3664, 2697, 3789)(2573, 3665, 2698, 3790)(2575, 3667, 2701, 3793)(2578, 3670, 2604, 3696)(2579, 3671, 2586, 3678)(2581, 3673, 2705, 3797)(2582, 3674, 2706, 3798)(2585, 3677, 2710, 3802)(2587, 3679, 2713, 3805)(2590, 3682, 2717, 3809)(2591, 3683, 2682, 3774)(2593, 3685, 2720, 3812)(2596, 3688, 2769, 3861)(2597, 3689, 2813, 3905)(2599, 3691, 2969, 4061)(2601, 3693, 2947, 4039)(2602, 3694, 2972, 4064)(2605, 3697, 2612, 3704)(2607, 3699, 2975, 4067)(2608, 3700, 2778, 3870)(2611, 3703, 2810, 3902)(2613, 3705, 2982, 4074)(2616, 3708, 2985, 4077)(2617, 3709, 2987, 4079)(2620, 3712, 2990, 4082)(2623, 3715, 2784, 3876)(2624, 3716, 2994, 4086)(2626, 3718, 2997, 4089)(2628, 3720, 2901, 3993)(2629, 3721, 2887, 3979)(2632, 3724, 2639, 3731)(2634, 3726, 3004, 4096)(2635, 3727, 3005, 4097)(2638, 3730, 2723, 3815)(2640, 3732, 2758, 3850)(2643, 3735, 2914, 4006)(2644, 3736, 2995, 4087)(2646, 3738, 3015, 4107)(2647, 3739, 2652, 3744)(2649, 3741, 2968, 4060)(2651, 3743, 2722, 3814)(2653, 3745, 2716, 3808)(2655, 3747, 2824, 3916)(2657, 3749, 3024, 4116)(2658, 3750, 2892, 3984)(2661, 3753, 3027, 4119)(2662, 3754, 2984, 4076)(2664, 3756, 2881, 3973)(2665, 3757, 2747, 3839)(2666, 3758, 2776, 3868)(2669, 3761, 2707, 3799)(2670, 3762, 2677, 3769)(2671, 3763, 3033, 4125)(2673, 3765, 3035, 4127)(2674, 3766, 2911, 4003)(2676, 3768, 3036, 4128)(2678, 3770, 2691, 3783)(2681, 3773, 2763, 3855)(2683, 3775, 3041, 4133)(2685, 3777, 2690, 3782)(2687, 3779, 3043, 4135)(2689, 3781, 2867, 3959)(2693, 3785, 2863, 3955)(2695, 3787, 3049, 4141)(2696, 3788, 3050, 4142)(2699, 3791, 3054, 4146)(2700, 3792, 3056, 4148)(2702, 3794, 2838, 3930)(2703, 3795, 2753, 3845)(2704, 3796, 3059, 4151)(2708, 3800, 2715, 3807)(2709, 3801, 2938, 4030)(2711, 3803, 2871, 3963)(2712, 3804, 3044, 4136)(2714, 3806, 2744, 3836)(2718, 3810, 2735, 3827)(2719, 3811, 2749, 3841)(2721, 3813, 2967, 4059)(2724, 3816, 3075, 4167)(2725, 3817, 3077, 4169)(2726, 3818, 3029, 4121)(2727, 3819, 3025, 4117)(2728, 3820, 3083, 4175)(2729, 3821, 3085, 4177)(2730, 3822, 3088, 4180)(2731, 3823, 3089, 4181)(2732, 3824, 3091, 4183)(2733, 3825, 3069, 4161)(2734, 3826, 3097, 4189)(2736, 3828, 3099, 4191)(2737, 3829, 3026, 4118)(2738, 3830, 3102, 4194)(2739, 3831, 3106, 4198)(2740, 3832, 3013, 4105)(2741, 3833, 3108, 4200)(2742, 3834, 3110, 4202)(2743, 3835, 3014, 4106)(2745, 3837, 3117, 4209)(2746, 3838, 3121, 4213)(2748, 3840, 3123, 4215)(2750, 3842, 3010, 4102)(2751, 3843, 3129, 4221)(2752, 3844, 3133, 4225)(2754, 3846, 3134, 4226)(2755, 3847, 3136, 4228)(2756, 3848, 3138, 4230)(2757, 3849, 3140, 4232)(2759, 3851, 3144, 4236)(2760, 3852, 3148, 4240)(2761, 3853, 3149, 4241)(2762, 3854, 3153, 4245)(2764, 3856, 3155, 4247)(2765, 3857, 3032, 4124)(2766, 3858, 3159, 4251)(2767, 3859, 3066, 4158)(2768, 3860, 3166, 4258)(2770, 3862, 3167, 4259)(2771, 3863, 3171, 4263)(2772, 3864, 3172, 4264)(2773, 3865, 3174, 4266)(2774, 3866, 3048, 4140)(2775, 3867, 3175, 4267)(2777, 3869, 2977, 4069)(2779, 3871, 3178, 4270)(2780, 3872, 3137, 4229)(2781, 3873, 3182, 4274)(2782, 3874, 3184, 4276)(2783, 3875, 3187, 4279)(2785, 3877, 3188, 4280)(2786, 3878, 3181, 4273)(2787, 3879, 3191, 4283)(2788, 3880, 3193, 4285)(2789, 3881, 2974, 4066)(2790, 3882, 3194, 4286)(2791, 3883, 3062, 4154)(2792, 3884, 3197, 4289)(2793, 3885, 3199, 4291)(2794, 3886, 2958, 4050)(2795, 3887, 3204, 4296)(2796, 3888, 3206, 4298)(2797, 3889, 3124, 4216)(2798, 3890, 2988, 4080)(2799, 3891, 3209, 4301)(2800, 3892, 2936, 4028)(2801, 3893, 3212, 4304)(2802, 3894, 3213, 4305)(2803, 3895, 3215, 4307)(2804, 3896, 3109, 4201)(2805, 3897, 3218, 4310)(2806, 3898, 3220, 4312)(2807, 3899, 3042, 4134)(2808, 3900, 3111, 4203)(2809, 3901, 2946, 4038)(2811, 3903, 3225, 4317)(2812, 3904, 3051, 4143)(2814, 3906, 3226, 4318)(2815, 3907, 3100, 4192)(2816, 3908, 3229, 4321)(2817, 3909, 2976, 4068)(2818, 3910, 3214, 4306)(2819, 3911, 2954, 4046)(2820, 3912, 3232, 4324)(2821, 3913, 3235, 4327)(2822, 3914, 2876, 3968)(2823, 3915, 3236, 4328)(2825, 3917, 3237, 4329)(2826, 3918, 3156, 4248)(2827, 3919, 3240, 4332)(2828, 3920, 3003, 4095)(2829, 3921, 3243, 4335)(2830, 3922, 3012, 4104)(2831, 3923, 3246, 4338)(2832, 3924, 2941, 4033)(2833, 3925, 3018, 4110)(2834, 3926, 2999, 4091)(2835, 3927, 3023, 4115)(2836, 3928, 2856, 3948)(2837, 3929, 3249, 4341)(2839, 3931, 3060, 4152)(2840, 3932, 3139, 4231)(2841, 3933, 2960, 4052)(2842, 3934, 3253, 4345)(2843, 3935, 2964, 4056)(2844, 3936, 2989, 4081)(2845, 3937, 3257, 4349)(2846, 3938, 2916, 4008)(2847, 3939, 2973, 4065)(2848, 3940, 2983, 4075)(2849, 3941, 3084, 4176)(2850, 3942, 3223, 4315)(2851, 3943, 3007, 4099)(2852, 3944, 2872, 3964)(2853, 3945, 3222, 4314)(2854, 3946, 2926, 4018)(2855, 3947, 3244, 4336)(2857, 3949, 3200, 4292)(2858, 3950, 3258, 4350)(2859, 3951, 2944, 4036)(2860, 3952, 3090, 4182)(2861, 3953, 3020, 4112)(2862, 3954, 3210, 4302)(2864, 3956, 3227, 4319)(2865, 3957, 3017, 4109)(2866, 3958, 3252, 4344)(2868, 3960, 3261, 4353)(2869, 3961, 2940, 4032)(2870, 3962, 3208, 4300)(2873, 3965, 3207, 4299)(2874, 3966, 2904, 3996)(2875, 3967, 3031, 4123)(2877, 3969, 3219, 4311)(2878, 3970, 3264, 4356)(2879, 3971, 3265, 4357)(2880, 3972, 3065, 4157)(2882, 3974, 3216, 4308)(2883, 3975, 3016, 4108)(2884, 3976, 3239, 4331)(2885, 3977, 2951, 4043)(2886, 3978, 2900, 3992)(2888, 3980, 3241, 4333)(2889, 3981, 2907, 3999)(2890, 3982, 3267, 4359)(2891, 3983, 3260, 4352)(2893, 3985, 2949, 4041)(2894, 3986, 3006, 4098)(2895, 3987, 3076, 4168)(2896, 3988, 3128, 4220)(2897, 3989, 2924, 4016)(2898, 3990, 3251, 4343)(2899, 3991, 3228, 4320)(2902, 3994, 2921, 4013)(2903, 3995, 2929, 4021)(2905, 3997, 3162, 4254)(2906, 3998, 3266, 4358)(2908, 4000, 3247, 4339)(2909, 4001, 2996, 4088)(2910, 4002, 3192, 4284)(2912, 4004, 3233, 4325)(2913, 4005, 3052, 4144)(2915, 4007, 3256, 4348)(2917, 4009, 2992, 4084)(2918, 4010, 2962, 4054)(2919, 4011, 3078, 4170)(2920, 4012, 3116, 4208)(2922, 4014, 3238, 4330)(2923, 4015, 3217, 4309)(2925, 4017, 3047, 4139)(2927, 4019, 3147, 4239)(2928, 4020, 3259, 4351)(2930, 4022, 3092, 4184)(2931, 4023, 3230, 4322)(2932, 4024, 3196, 4288)(2933, 4025, 3272, 4364)(2934, 4026, 3009, 4101)(2935, 4027, 2957, 4049)(2937, 4029, 3179, 4271)(2939, 4031, 3186, 4278)(2942, 4034, 3019, 4111)(2943, 4035, 3189, 4281)(2945, 4037, 3270, 4362)(2948, 4040, 3071, 4163)(2950, 4042, 3268, 4360)(2952, 4044, 3170, 4262)(2953, 4045, 3068, 4160)(2955, 4047, 3169, 4261)(2956, 4048, 2963, 4055)(2959, 4051, 3248, 4340)(2961, 4053, 2971, 4063)(2965, 4057, 3180, 4272)(2966, 4058, 3271, 4363)(2970, 4062, 3195, 4287)(2978, 4070, 3201, 4293)(2979, 4071, 3224, 4316)(2980, 4072, 3112, 4204)(2981, 4073, 3070, 4162)(2986, 4078, 3273, 4365)(2991, 4083, 3073, 4165)(2993, 4085, 3269, 4361)(2998, 4090, 3274, 4366)(3000, 4092, 3255, 4347)(3001, 4093, 3185, 4277)(3002, 4094, 3231, 4323)(3008, 4100, 3122, 4214)(3011, 4103, 3045, 4137)(3021, 4113, 3105, 4197)(3022, 4114, 3242, 4334)(3028, 4120, 3245, 4337)(3030, 4122, 3263, 4355)(3034, 4126, 3146, 4238)(3037, 4129, 3165, 4257)(3038, 4130, 3157, 4249)(3039, 4131, 3154, 4246)(3040, 4132, 3064, 4156)(3046, 4138, 3254, 4346)(3053, 4145, 3067, 4159)(3055, 4147, 3086, 4178)(3057, 4149, 3096, 4188)(3058, 4150, 3234, 4326)(3061, 4153, 3132, 4224)(3063, 4155, 3131, 4223)(3072, 4164, 3104, 4196)(3074, 4166, 3095, 4187)(3079, 4171, 3161, 4253)(3080, 4172, 3176, 4268)(3081, 4173, 3276, 4368)(3082, 4174, 3115, 4207)(3087, 4179, 3127, 4219)(3093, 4185, 3145, 4237)(3094, 4186, 3125, 4217)(3098, 4190, 3151, 4243)(3101, 4193, 3160, 4252)(3103, 4195, 3113, 4205)(3107, 4199, 3164, 4256)(3114, 4206, 3262, 4354)(3118, 4210, 3158, 4250)(3119, 4211, 3275, 4367)(3120, 4212, 3177, 4269)(3126, 4218, 3143, 4235)(3130, 4222, 3142, 4234)(3135, 4227, 3202, 4294)(3141, 4233, 3250, 4342)(3150, 4242, 3211, 4303)(3152, 4244, 3168, 4260)(3163, 4255, 3203, 4295)(3173, 4265, 3221, 4313)(3183, 4275, 3198, 4290)(3190, 4282, 3205, 4297) L = (1, 2187)(2, 2189)(3, 2192)(4, 2185)(5, 2196)(6, 2186)(7, 2197)(8, 2201)(9, 2202)(10, 2188)(11, 2193)(12, 2207)(13, 2208)(14, 2190)(15, 2191)(16, 2211)(17, 2204)(18, 2216)(19, 2217)(20, 2194)(21, 2195)(22, 2219)(23, 2210)(24, 2224)(25, 2225)(26, 2198)(27, 2227)(28, 2199)(29, 2200)(30, 2230)(31, 2203)(32, 2235)(33, 2237)(34, 2238)(35, 2239)(36, 2205)(37, 2206)(38, 2241)(39, 2209)(40, 2229)(41, 2247)(42, 2248)(43, 2250)(44, 2251)(45, 2212)(46, 2253)(47, 2213)(48, 2214)(49, 2215)(50, 2257)(51, 2220)(52, 2218)(53, 2263)(54, 2264)(55, 2266)(56, 2267)(57, 2268)(58, 2221)(59, 2222)(60, 2223)(61, 2272)(62, 2226)(63, 2277)(64, 2278)(65, 2228)(66, 2255)(67, 2282)(68, 2283)(69, 2285)(70, 2286)(71, 2231)(72, 2232)(73, 2290)(74, 2233)(75, 2234)(76, 2292)(77, 2236)(78, 2295)(79, 2258)(80, 2300)(81, 2240)(82, 2270)(83, 2303)(84, 2305)(85, 2306)(86, 2242)(87, 2243)(88, 2310)(89, 2244)(90, 2245)(91, 2246)(92, 2313)(93, 2273)(94, 2318)(95, 2249)(96, 2319)(97, 2252)(98, 2324)(99, 2325)(100, 2254)(101, 2289)(102, 2329)(103, 2330)(104, 2331)(105, 2256)(106, 2334)(107, 2335)(108, 2336)(109, 2259)(110, 2260)(111, 2340)(112, 2261)(113, 2262)(114, 2342)(115, 2288)(116, 2296)(117, 2265)(118, 2347)(119, 2351)(120, 2269)(121, 2309)(122, 2355)(123, 2356)(124, 2357)(125, 2271)(126, 2360)(127, 2361)(128, 2274)(129, 2364)(130, 2275)(131, 2276)(132, 2366)(133, 2308)(134, 2314)(135, 2371)(136, 2279)(137, 2280)(138, 2281)(139, 2374)(140, 2320)(141, 2379)(142, 2284)(143, 2380)(144, 2287)(145, 2385)(146, 2386)(147, 2388)(148, 2389)(149, 2291)(150, 2338)(151, 2392)(152, 2394)(153, 2395)(154, 2293)(155, 2294)(156, 2400)(157, 2401)(158, 2402)(159, 2297)(160, 2298)(161, 2299)(162, 2406)(163, 2409)(164, 2301)(165, 2302)(166, 2397)(167, 2348)(168, 2304)(169, 2414)(170, 2307)(171, 2419)(172, 2420)(173, 2422)(174, 2423)(175, 2311)(176, 2363)(177, 2426)(178, 2427)(179, 2312)(180, 2430)(181, 2431)(182, 2432)(183, 2315)(184, 2316)(185, 2317)(186, 2436)(187, 2440)(188, 2441)(189, 2321)(190, 2444)(191, 2322)(192, 2323)(193, 2446)(194, 2362)(195, 2375)(196, 2451)(197, 2326)(198, 2327)(199, 2328)(200, 2454)(201, 2381)(202, 2459)(203, 2332)(204, 2462)(205, 2463)(206, 2333)(207, 2464)(208, 2468)(209, 2337)(210, 2398)(211, 2472)(212, 2473)(213, 2474)(214, 2339)(215, 2341)(216, 2404)(217, 2478)(218, 2480)(219, 2481)(220, 2343)(221, 2344)(222, 2485)(223, 2345)(224, 2346)(225, 2489)(226, 2490)(227, 2349)(228, 2350)(229, 2493)(230, 2496)(231, 2352)(232, 2353)(233, 2354)(234, 2499)(235, 2415)(236, 2504)(237, 2358)(238, 2507)(239, 2508)(240, 2359)(241, 2509)(242, 2513)(243, 2515)(244, 2516)(245, 2365)(246, 2434)(247, 2519)(248, 2521)(249, 2522)(250, 2367)(251, 2368)(252, 2526)(253, 2369)(254, 2370)(255, 2372)(256, 2443)(257, 2531)(258, 2532)(259, 2373)(260, 2535)(261, 2536)(262, 2537)(263, 2376)(264, 2377)(265, 2378)(266, 2541)(267, 2545)(268, 2546)(269, 2382)(270, 2549)(271, 2383)(272, 2384)(273, 2551)(274, 2442)(275, 2455)(276, 2387)(277, 2556)(278, 2407)(279, 2561)(280, 2562)(281, 2390)(282, 2391)(283, 2483)(284, 2465)(285, 2393)(286, 2567)(287, 2396)(288, 2572)(289, 2573)(290, 2575)(291, 2576)(292, 2399)(293, 2577)(294, 2581)(295, 2403)(296, 2484)(297, 2585)(298, 2586)(299, 2587)(300, 2405)(301, 2590)(302, 2591)(303, 2408)(304, 2410)(305, 2492)(306, 2596)(307, 2597)(308, 2411)(309, 2599)(310, 2412)(311, 2413)(312, 2604)(313, 2605)(314, 2416)(315, 2608)(316, 2417)(317, 2418)(318, 2610)(319, 2491)(320, 2500)(321, 2421)(322, 2615)(323, 2437)(324, 2620)(325, 2621)(326, 2424)(327, 2425)(328, 2524)(329, 2510)(330, 2428)(331, 2628)(332, 2629)(333, 2429)(334, 2630)(335, 2634)(336, 2433)(337, 2525)(338, 2638)(339, 2639)(340, 2640)(341, 2435)(342, 2643)(343, 2644)(344, 2438)(345, 2439)(346, 2594)(347, 2649)(348, 2651)(349, 2652)(350, 2445)(351, 2539)(352, 2655)(353, 2657)(354, 2658)(355, 2447)(356, 2448)(357, 2662)(358, 2449)(359, 2450)(360, 2452)(361, 2548)(362, 2665)(363, 2666)(364, 2453)(365, 2669)(366, 2670)(367, 2671)(368, 2456)(369, 2457)(370, 2458)(371, 2675)(372, 2678)(373, 2460)(374, 2461)(375, 2680)(376, 2547)(377, 2557)(378, 2622)(379, 2685)(380, 2466)(381, 2467)(382, 2688)(383, 2691)(384, 2469)(385, 2470)(386, 2471)(387, 2694)(388, 2568)(389, 2699)(390, 2475)(391, 2601)(392, 2702)(393, 2603)(394, 2476)(395, 2477)(396, 2592)(397, 2578)(398, 2479)(399, 2706)(400, 2482)(401, 2711)(402, 2712)(403, 2714)(404, 2715)(405, 2486)(406, 2593)(407, 2718)(408, 2719)(409, 2487)(410, 2488)(411, 2529)(412, 2647)(413, 2967)(414, 2968)(415, 2925)(416, 2846)(417, 2494)(418, 2495)(419, 2497)(420, 2607)(421, 2703)(422, 2974)(423, 2498)(424, 2977)(425, 2978)(426, 2979)(427, 2501)(428, 2502)(429, 2503)(430, 2982)(431, 2984)(432, 2505)(433, 2506)(434, 2987)(435, 2606)(436, 2616)(437, 2563)(438, 2687)(439, 2511)(440, 2512)(441, 2994)(442, 2514)(443, 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3068)(535, 3069)(536, 3070)(537, 3071)(538, 3073)(539, 2971)(540, 3076)(541, 3078)(542, 3080)(543, 2921)(544, 3084)(545, 3086)(546, 2897)(547, 3090)(548, 3092)(549, 3094)(550, 2999)(551, 2883)(552, 3100)(553, 3027)(554, 3103)(555, 2954)(556, 2865)(557, 3109)(558, 3111)(559, 3015)(560, 3114)(561, 3118)(562, 2852)(563, 2911)(564, 3124)(565, 2720)(566, 3126)(567, 3130)(568, 2872)(569, 2886)(570, 2828)(571, 3137)(572, 3139)(573, 3141)(574, 2641)(575, 3145)(576, 3062)(577, 3150)(578, 2819)(579, 2841)(580, 3156)(581, 3157)(582, 3160)(583, 3163)(584, 2834)(585, 2972)(586, 3168)(587, 2924)(588, 2786)(589, 3148)(590, 3049)(591, 3171)(592, 2667)(593, 2635)(594, 2609)(595, 3161)(596, 3181)(597, 2791)(598, 3037)(599, 2902)(600, 2976)(601, 2773)(602, 3136)(603, 3192)(604, 3187)(605, 2975)(606, 3146)(607, 3174)(608, 2780)(609, 3195)(610, 3201)(611, 2815)(612, 3177)(613, 3017)(614, 3106)(615, 3210)(616, 2677)(617, 3133)(618, 2613)(619, 3127)(620, 3003)(621, 3179)(622, 2804)(623, 3061)(624, 3016)(625, 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2650)(808, 2816)(809, 2862)(810, 2915)(811, 2618)(812, 2963)(813, 3191)(814, 3164)(815, 3229)(816, 2910)(817, 2730)(818, 3188)(819, 3270)(820, 3064)(821, 2778)(822, 2689)(823, 2777)(824, 2966)(825, 2838)(826, 2962)(827, 2854)(828, 2932)(829, 3274)(830, 3102)(831, 3189)(832, 2682)(833, 2995)(834, 2676)(835, 2950)(836, 2926)(837, 3251)(838, 2768)(839, 2857)(840, 3143)(841, 3128)(842, 3159)(843, 3233)(844, 2756)(845, 3226)(846, 2799)(847, 3125)(848, 3117)(849, 2672)(850, 2724)(851, 2871)(852, 2959)(853, 3272)(854, 2693)(855, 2878)(856, 2633)(857, 2811)(858, 2996)(859, 2625)(860, 2753)(861, 2636)(862, 2764)(863, 3262)(864, 3213)(865, 3203)(866, 3205)(867, 2894)(868, 2942)(869, 2851)(870, 3028)(871, 2789)(872, 2642)(873, 3238)(874, 2762)(875, 2845)(876, 3265)(877, 3266)(878, 3228)(879, 2723)(880, 2868)(881, 3158)(882, 3184)(883, 2611)(884, 2654)(885, 2983)(886, 2956)(887, 3209)(888, 2721)(889, 3225)(890, 2722)(891, 3194)(892, 3243)(893, 3178)(894, 3253)(895, 2725)(896, 3257)(897, 3221)(898, 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3672)(1489, 3673)(1490, 3674)(1491, 3675)(1492, 3676)(1493, 3677)(1494, 3678)(1495, 3679)(1496, 3680)(1497, 3681)(1498, 3682)(1499, 3683)(1500, 3684)(1501, 3685)(1502, 3686)(1503, 3687)(1504, 3688)(1505, 3689)(1506, 3690)(1507, 3691)(1508, 3692)(1509, 3693)(1510, 3694)(1511, 3695)(1512, 3696)(1513, 3697)(1514, 3698)(1515, 3699)(1516, 3700)(1517, 3701)(1518, 3702)(1519, 3703)(1520, 3704)(1521, 3705)(1522, 3706)(1523, 3707)(1524, 3708)(1525, 3709)(1526, 3710)(1527, 3711)(1528, 3712)(1529, 3713)(1530, 3714)(1531, 3715)(1532, 3716)(1533, 3717)(1534, 3718)(1535, 3719)(1536, 3720)(1537, 3721)(1538, 3722)(1539, 3723)(1540, 3724)(1541, 3725)(1542, 3726)(1543, 3727)(1544, 3728)(1545, 3729)(1546, 3730)(1547, 3731)(1548, 3732)(1549, 3733)(1550, 3734)(1551, 3735)(1552, 3736)(1553, 3737)(1554, 3738)(1555, 3739)(1556, 3740)(1557, 3741)(1558, 3742)(1559, 3743)(1560, 3744)(1561, 3745)(1562, 3746)(1563, 3747)(1564, 3748)(1565, 3749)(1566, 3750)(1567, 3751)(1568, 3752)(1569, 3753)(1570, 3754)(1571, 3755)(1572, 3756)(1573, 3757)(1574, 3758)(1575, 3759)(1576, 3760)(1577, 3761)(1578, 3762)(1579, 3763)(1580, 3764)(1581, 3765)(1582, 3766)(1583, 3767)(1584, 3768)(1585, 3769)(1586, 3770)(1587, 3771)(1588, 3772)(1589, 3773)(1590, 3774)(1591, 3775)(1592, 3776)(1593, 3777)(1594, 3778)(1595, 3779)(1596, 3780)(1597, 3781)(1598, 3782)(1599, 3783)(1600, 3784)(1601, 3785)(1602, 3786)(1603, 3787)(1604, 3788)(1605, 3789)(1606, 3790)(1607, 3791)(1608, 3792)(1609, 3793)(1610, 3794)(1611, 3795)(1612, 3796)(1613, 3797)(1614, 3798)(1615, 3799)(1616, 3800)(1617, 3801)(1618, 3802)(1619, 3803)(1620, 3804)(1621, 3805)(1622, 3806)(1623, 3807)(1624, 3808)(1625, 3809)(1626, 3810)(1627, 3811)(1628, 3812)(1629, 3813)(1630, 3814)(1631, 3815)(1632, 3816)(1633, 3817)(1634, 3818)(1635, 3819)(1636, 3820)(1637, 3821)(1638, 3822)(1639, 3823)(1640, 3824)(1641, 3825)(1642, 3826)(1643, 3827)(1644, 3828)(1645, 3829)(1646, 3830)(1647, 3831)(1648, 3832)(1649, 3833)(1650, 3834)(1651, 3835)(1652, 3836)(1653, 3837)(1654, 3838)(1655, 3839)(1656, 3840)(1657, 3841)(1658, 3842)(1659, 3843)(1660, 3844)(1661, 3845)(1662, 3846)(1663, 3847)(1664, 3848)(1665, 3849)(1666, 3850)(1667, 3851)(1668, 3852)(1669, 3853)(1670, 3854)(1671, 3855)(1672, 3856)(1673, 3857)(1674, 3858)(1675, 3859)(1676, 3860)(1677, 3861)(1678, 3862)(1679, 3863)(1680, 3864)(1681, 3865)(1682, 3866)(1683, 3867)(1684, 3868)(1685, 3869)(1686, 3870)(1687, 3871)(1688, 3872)(1689, 3873)(1690, 3874)(1691, 3875)(1692, 3876)(1693, 3877)(1694, 3878)(1695, 3879)(1696, 3880)(1697, 3881)(1698, 3882)(1699, 3883)(1700, 3884)(1701, 3885)(1702, 3886)(1703, 3887)(1704, 3888)(1705, 3889)(1706, 3890)(1707, 3891)(1708, 3892)(1709, 3893)(1710, 3894)(1711, 3895)(1712, 3896)(1713, 3897)(1714, 3898)(1715, 3899)(1716, 3900)(1717, 3901)(1718, 3902)(1719, 3903)(1720, 3904)(1721, 3905)(1722, 3906)(1723, 3907)(1724, 3908)(1725, 3909)(1726, 3910)(1727, 3911)(1728, 3912)(1729, 3913)(1730, 3914)(1731, 3915)(1732, 3916)(1733, 3917)(1734, 3918)(1735, 3919)(1736, 3920)(1737, 3921)(1738, 3922)(1739, 3923)(1740, 3924)(1741, 3925)(1742, 3926)(1743, 3927)(1744, 3928)(1745, 3929)(1746, 3930)(1747, 3931)(1748, 3932)(1749, 3933)(1750, 3934)(1751, 3935)(1752, 3936)(1753, 3937)(1754, 3938)(1755, 3939)(1756, 3940)(1757, 3941)(1758, 3942)(1759, 3943)(1760, 3944)(1761, 3945)(1762, 3946)(1763, 3947)(1764, 3948)(1765, 3949)(1766, 3950)(1767, 3951)(1768, 3952)(1769, 3953)(1770, 3954)(1771, 3955)(1772, 3956)(1773, 3957)(1774, 3958)(1775, 3959)(1776, 3960)(1777, 3961)(1778, 3962)(1779, 3963)(1780, 3964)(1781, 3965)(1782, 3966)(1783, 3967)(1784, 3968)(1785, 3969)(1786, 3970)(1787, 3971)(1788, 3972)(1789, 3973)(1790, 3974)(1791, 3975)(1792, 3976)(1793, 3977)(1794, 3978)(1795, 3979)(1796, 3980)(1797, 3981)(1798, 3982)(1799, 3983)(1800, 3984)(1801, 3985)(1802, 3986)(1803, 3987)(1804, 3988)(1805, 3989)(1806, 3990)(1807, 3991)(1808, 3992)(1809, 3993)(1810, 3994)(1811, 3995)(1812, 3996)(1813, 3997)(1814, 3998)(1815, 3999)(1816, 4000)(1817, 4001)(1818, 4002)(1819, 4003)(1820, 4004)(1821, 4005)(1822, 4006)(1823, 4007)(1824, 4008)(1825, 4009)(1826, 4010)(1827, 4011)(1828, 4012)(1829, 4013)(1830, 4014)(1831, 4015)(1832, 4016)(1833, 4017)(1834, 4018)(1835, 4019)(1836, 4020)(1837, 4021)(1838, 4022)(1839, 4023)(1840, 4024)(1841, 4025)(1842, 4026)(1843, 4027)(1844, 4028)(1845, 4029)(1846, 4030)(1847, 4031)(1848, 4032)(1849, 4033)(1850, 4034)(1851, 4035)(1852, 4036)(1853, 4037)(1854, 4038)(1855, 4039)(1856, 4040)(1857, 4041)(1858, 4042)(1859, 4043)(1860, 4044)(1861, 4045)(1862, 4046)(1863, 4047)(1864, 4048)(1865, 4049)(1866, 4050)(1867, 4051)(1868, 4052)(1869, 4053)(1870, 4054)(1871, 4055)(1872, 4056)(1873, 4057)(1874, 4058)(1875, 4059)(1876, 4060)(1877, 4061)(1878, 4062)(1879, 4063)(1880, 4064)(1881, 4065)(1882, 4066)(1883, 4067)(1884, 4068)(1885, 4069)(1886, 4070)(1887, 4071)(1888, 4072)(1889, 4073)(1890, 4074)(1891, 4075)(1892, 4076)(1893, 4077)(1894, 4078)(1895, 4079)(1896, 4080)(1897, 4081)(1898, 4082)(1899, 4083)(1900, 4084)(1901, 4085)(1902, 4086)(1903, 4087)(1904, 4088)(1905, 4089)(1906, 4090)(1907, 4091)(1908, 4092)(1909, 4093)(1910, 4094)(1911, 4095)(1912, 4096)(1913, 4097)(1914, 4098)(1915, 4099)(1916, 4100)(1917, 4101)(1918, 4102)(1919, 4103)(1920, 4104)(1921, 4105)(1922, 4106)(1923, 4107)(1924, 4108)(1925, 4109)(1926, 4110)(1927, 4111)(1928, 4112)(1929, 4113)(1930, 4114)(1931, 4115)(1932, 4116)(1933, 4117)(1934, 4118)(1935, 4119)(1936, 4120)(1937, 4121)(1938, 4122)(1939, 4123)(1940, 4124)(1941, 4125)(1942, 4126)(1943, 4127)(1944, 4128)(1945, 4129)(1946, 4130)(1947, 4131)(1948, 4132)(1949, 4133)(1950, 4134)(1951, 4135)(1952, 4136)(1953, 4137)(1954, 4138)(1955, 4139)(1956, 4140)(1957, 4141)(1958, 4142)(1959, 4143)(1960, 4144)(1961, 4145)(1962, 4146)(1963, 4147)(1964, 4148)(1965, 4149)(1966, 4150)(1967, 4151)(1968, 4152)(1969, 4153)(1970, 4154)(1971, 4155)(1972, 4156)(1973, 4157)(1974, 4158)(1975, 4159)(1976, 4160)(1977, 4161)(1978, 4162)(1979, 4163)(1980, 4164)(1981, 4165)(1982, 4166)(1983, 4167)(1984, 4168)(1985, 4169)(1986, 4170)(1987, 4171)(1988, 4172)(1989, 4173)(1990, 4174)(1991, 4175)(1992, 4176)(1993, 4177)(1994, 4178)(1995, 4179)(1996, 4180)(1997, 4181)(1998, 4182)(1999, 4183)(2000, 4184)(2001, 4185)(2002, 4186)(2003, 4187)(2004, 4188)(2005, 4189)(2006, 4190)(2007, 4191)(2008, 4192)(2009, 4193)(2010, 4194)(2011, 4195)(2012, 4196)(2013, 4197)(2014, 4198)(2015, 4199)(2016, 4200)(2017, 4201)(2018, 4202)(2019, 4203)(2020, 4204)(2021, 4205)(2022, 4206)(2023, 4207)(2024, 4208)(2025, 4209)(2026, 4210)(2027, 4211)(2028, 4212)(2029, 4213)(2030, 4214)(2031, 4215)(2032, 4216)(2033, 4217)(2034, 4218)(2035, 4219)(2036, 4220)(2037, 4221)(2038, 4222)(2039, 4223)(2040, 4224)(2041, 4225)(2042, 4226)(2043, 4227)(2044, 4228)(2045, 4229)(2046, 4230)(2047, 4231)(2048, 4232)(2049, 4233)(2050, 4234)(2051, 4235)(2052, 4236)(2053, 4237)(2054, 4238)(2055, 4239)(2056, 4240)(2057, 4241)(2058, 4242)(2059, 4243)(2060, 4244)(2061, 4245)(2062, 4246)(2063, 4247)(2064, 4248)(2065, 4249)(2066, 4250)(2067, 4251)(2068, 4252)(2069, 4253)(2070, 4254)(2071, 4255)(2072, 4256)(2073, 4257)(2074, 4258)(2075, 4259)(2076, 4260)(2077, 4261)(2078, 4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 6, 14 ), ( 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E14.640 Graph:: simple bipartite v = 1638 e = 2184 f = 520 degree seq :: [ 2^1092, 4^546 ] E14.644 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, Y3^7, (Y3^-1 * Y1^-1)^7, (Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-2 * Y2 * Y3^2 * Y2 * Y3^-2)^2, Y3^2 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 ] Map:: polytopal R = (1, 1093)(2, 1094)(3, 1095)(4, 1096)(5, 1097)(6, 1098)(7, 1099)(8, 1100)(9, 1101)(10, 1102)(11, 1103)(12, 1104)(13, 1105)(14, 1106)(15, 1107)(16, 1108)(17, 1109)(18, 1110)(19, 1111)(20, 1112)(21, 1113)(22, 1114)(23, 1115)(24, 1116)(25, 1117)(26, 1118)(27, 1119)(28, 1120)(29, 1121)(30, 1122)(31, 1123)(32, 1124)(33, 1125)(34, 1126)(35, 1127)(36, 1128)(37, 1129)(38, 1130)(39, 1131)(40, 1132)(41, 1133)(42, 1134)(43, 1135)(44, 1136)(45, 1137)(46, 1138)(47, 1139)(48, 1140)(49, 1141)(50, 1142)(51, 1143)(52, 1144)(53, 1145)(54, 1146)(55, 1147)(56, 1148)(57, 1149)(58, 1150)(59, 1151)(60, 1152)(61, 1153)(62, 1154)(63, 1155)(64, 1156)(65, 1157)(66, 1158)(67, 1159)(68, 1160)(69, 1161)(70, 1162)(71, 1163)(72, 1164)(73, 1165)(74, 1166)(75, 1167)(76, 1168)(77, 1169)(78, 1170)(79, 1171)(80, 1172)(81, 1173)(82, 1174)(83, 1175)(84, 1176)(85, 1177)(86, 1178)(87, 1179)(88, 1180)(89, 1181)(90, 1182)(91, 1183)(92, 1184)(93, 1185)(94, 1186)(95, 1187)(96, 1188)(97, 1189)(98, 1190)(99, 1191)(100, 1192)(101, 1193)(102, 1194)(103, 1195)(104, 1196)(105, 1197)(106, 1198)(107, 1199)(108, 1200)(109, 1201)(110, 1202)(111, 1203)(112, 1204)(113, 1205)(114, 1206)(115, 1207)(116, 1208)(117, 1209)(118, 1210)(119, 1211)(120, 1212)(121, 1213)(122, 1214)(123, 1215)(124, 1216)(125, 1217)(126, 1218)(127, 1219)(128, 1220)(129, 1221)(130, 1222)(131, 1223)(132, 1224)(133, 1225)(134, 1226)(135, 1227)(136, 1228)(137, 1229)(138, 1230)(139, 1231)(140, 1232)(141, 1233)(142, 1234)(143, 1235)(144, 1236)(145, 1237)(146, 1238)(147, 1239)(148, 1240)(149, 1241)(150, 1242)(151, 1243)(152, 1244)(153, 1245)(154, 1246)(155, 1247)(156, 1248)(157, 1249)(158, 1250)(159, 1251)(160, 1252)(161, 1253)(162, 1254)(163, 1255)(164, 1256)(165, 1257)(166, 1258)(167, 1259)(168, 1260)(169, 1261)(170, 1262)(171, 1263)(172, 1264)(173, 1265)(174, 1266)(175, 1267)(176, 1268)(177, 1269)(178, 1270)(179, 1271)(180, 1272)(181, 1273)(182, 1274)(183, 1275)(184, 1276)(185, 1277)(186, 1278)(187, 1279)(188, 1280)(189, 1281)(190, 1282)(191, 1283)(192, 1284)(193, 1285)(194, 1286)(195, 1287)(196, 1288)(197, 1289)(198, 1290)(199, 1291)(200, 1292)(201, 1293)(202, 1294)(203, 1295)(204, 1296)(205, 1297)(206, 1298)(207, 1299)(208, 1300)(209, 1301)(210, 1302)(211, 1303)(212, 1304)(213, 1305)(214, 1306)(215, 1307)(216, 1308)(217, 1309)(218, 1310)(219, 1311)(220, 1312)(221, 1313)(222, 1314)(223, 1315)(224, 1316)(225, 1317)(226, 1318)(227, 1319)(228, 1320)(229, 1321)(230, 1322)(231, 1323)(232, 1324)(233, 1325)(234, 1326)(235, 1327)(236, 1328)(237, 1329)(238, 1330)(239, 1331)(240, 1332)(241, 1333)(242, 1334)(243, 1335)(244, 1336)(245, 1337)(246, 1338)(247, 1339)(248, 1340)(249, 1341)(250, 1342)(251, 1343)(252, 1344)(253, 1345)(254, 1346)(255, 1347)(256, 1348)(257, 1349)(258, 1350)(259, 1351)(260, 1352)(261, 1353)(262, 1354)(263, 1355)(264, 1356)(265, 1357)(266, 1358)(267, 1359)(268, 1360)(269, 1361)(270, 1362)(271, 1363)(272, 1364)(273, 1365)(274, 1366)(275, 1367)(276, 1368)(277, 1369)(278, 1370)(279, 1371)(280, 1372)(281, 1373)(282, 1374)(283, 1375)(284, 1376)(285, 1377)(286, 1378)(287, 1379)(288, 1380)(289, 1381)(290, 1382)(291, 1383)(292, 1384)(293, 1385)(294, 1386)(295, 1387)(296, 1388)(297, 1389)(298, 1390)(299, 1391)(300, 1392)(301, 1393)(302, 1394)(303, 1395)(304, 1396)(305, 1397)(306, 1398)(307, 1399)(308, 1400)(309, 1401)(310, 1402)(311, 1403)(312, 1404)(313, 1405)(314, 1406)(315, 1407)(316, 1408)(317, 1409)(318, 1410)(319, 1411)(320, 1412)(321, 1413)(322, 1414)(323, 1415)(324, 1416)(325, 1417)(326, 1418)(327, 1419)(328, 1420)(329, 1421)(330, 1422)(331, 1423)(332, 1424)(333, 1425)(334, 1426)(335, 1427)(336, 1428)(337, 1429)(338, 1430)(339, 1431)(340, 1432)(341, 1433)(342, 1434)(343, 1435)(344, 1436)(345, 1437)(346, 1438)(347, 1439)(348, 1440)(349, 1441)(350, 1442)(351, 1443)(352, 1444)(353, 1445)(354, 1446)(355, 1447)(356, 1448)(357, 1449)(358, 1450)(359, 1451)(360, 1452)(361, 1453)(362, 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3929, 3083, 4175)(2839, 3931, 3125, 4217)(2840, 3932, 3101, 4193)(2841, 3933, 2931, 4023)(2842, 3934, 3041, 4133)(2843, 3935, 2980, 4072)(2844, 3936, 2845, 3937)(2846, 3938, 2964, 4056)(2850, 3942, 3026, 4118)(2851, 3943, 3131, 4223)(2852, 3944, 2855, 3947)(2853, 3945, 2956, 4048)(2857, 3949, 3068, 4160)(2858, 3950, 3098, 4190)(2859, 3951, 2982, 4074)(2860, 3952, 3136, 4228)(2862, 3954, 3137, 4229)(2863, 3955, 3085, 4177)(2864, 3956, 3084, 4176)(2865, 3957, 2867, 3959)(2866, 3958, 3141, 4233)(2868, 3960, 2869, 3961)(2870, 3962, 2945, 4037)(2873, 3965, 2878, 3970)(2875, 3967, 3146, 4238)(2876, 3968, 3149, 4241)(2877, 3969, 3086, 4178)(2879, 3971, 2883, 3975)(2881, 3973, 3152, 4244)(2884, 3976, 2920, 4012)(2886, 3978, 3156, 4248)(2887, 3979, 3088, 4180)(2889, 3981, 3160, 4252)(2891, 3983, 2892, 3984)(2896, 3988, 3165, 4257)(2898, 3990, 3166, 4258)(2899, 3991, 3169, 4261)(2902, 3994, 3021, 4113)(2904, 3996, 2967, 4059)(2905, 3997, 2907, 3999)(2906, 3998, 3151, 4243)(2909, 4001, 2929, 4021)(2910, 4002, 3106, 4198)(2911, 4003, 3177, 4269)(2913, 4005, 3150, 4242)(2914, 4006, 3180, 4272)(2915, 4007, 3081, 4173)(2916, 4008, 2919, 4011)(2917, 4009, 3182, 4274)(2922, 4014, 2971, 4063)(2923, 4015, 2924, 4016)(2925, 4017, 3140, 4232)(2926, 4018, 3056, 4148)(2927, 4019, 2978, 4070)(2930, 4022, 3113, 4205)(2932, 4024, 3012, 4104)(2933, 4025, 2938, 4030)(2935, 4027, 3174, 4266)(2936, 4028, 3190, 4282)(2937, 4029, 3100, 4192)(2939, 4031, 3192, 4284)(2940, 4032, 3078, 4170)(2941, 4033, 2947, 4039)(2943, 4035, 3048, 4140)(2944, 4036, 3047, 4139)(2946, 4038, 3198, 4290)(2949, 4041, 3199, 4291)(2950, 4042, 3179, 4271)(2953, 4045, 3203, 4295)(2954, 4046, 3005, 4097)(2955, 4047, 3034, 4126)(2958, 4050, 3038, 4130)(2959, 4051, 3099, 4191)(2960, 4052, 2965, 4057)(2961, 4053, 3074, 4166)(2962, 4054, 3073, 4165)(2970, 4062, 3000, 4092)(2972, 4064, 3204, 4296)(2973, 4065, 2975, 4067)(2976, 4068, 3221, 4313)(2983, 4075, 3184, 4276)(2984, 4076, 2993, 4085)(2987, 4079, 3200, 4292)(2989, 4081, 3228, 4320)(2991, 4083, 3097, 4189)(2992, 4084, 3050, 4142)(2994, 4086, 3231, 4323)(2997, 4089, 3064, 4156)(3003, 4095, 3163, 4255)(3006, 4098, 3239, 4331)(3007, 4099, 3235, 4327)(3008, 4100, 3241, 4333)(3010, 4102, 3072, 4164)(3015, 4107, 3053, 4145)(3016, 4108, 3246, 4338)(3017, 4109, 3023, 4115)(3019, 4111, 3143, 4235)(3020, 4112, 3115, 4207)(3022, 4114, 3144, 4236)(3027, 4119, 3197, 4289)(3028, 4120, 3122, 4214)(3030, 4122, 3250, 4342)(3031, 4123, 3128, 4220)(3033, 4125, 3254, 4346)(3035, 4127, 3080, 4172)(3036, 4128, 3117, 4209)(3037, 4129, 3042, 4134)(3039, 4131, 3205, 4297)(3044, 4136, 3248, 4340)(3045, 4137, 3186, 4278)(3046, 4138, 3095, 4187)(3054, 4146, 3055, 4147)(3059, 4151, 3077, 4169)(3060, 4152, 3138, 4230)(3061, 4153, 3063, 4155)(3065, 4157, 3232, 4324)(3067, 4159, 3172, 4264)(3069, 4161, 3267, 4359)(3070, 4162, 3148, 4240)(3071, 4163, 3133, 4225)(3075, 4167, 3185, 4277)(3076, 4168, 3224, 4316)(3087, 4179, 3102, 4194)(3089, 4181, 3103, 4195)(3090, 4182, 3132, 4224)(3094, 4186, 3110, 4202)(3105, 4197, 3139, 4231)(3107, 4199, 3206, 4298)(3108, 4200, 3145, 4237)(3109, 4201, 3154, 4246)(3112, 4204, 3159, 4251)(3118, 4210, 3191, 4283)(3121, 4213, 3181, 4273)(3126, 4218, 3188, 4280)(3127, 4219, 3194, 4286)(3129, 4221, 3209, 4301)(3130, 4222, 3208, 4300)(3134, 4226, 3226, 4318)(3135, 4227, 3234, 4326)(3142, 4234, 3273, 4365)(3147, 4239, 3259, 4351)(3153, 4245, 3236, 4328)(3155, 4247, 3272, 4364)(3157, 4249, 3201, 4293)(3158, 4250, 3225, 4317)(3161, 4253, 3207, 4299)(3162, 4254, 3251, 4343)(3164, 4256, 3193, 4285)(3167, 4259, 3220, 4312)(3168, 4260, 3229, 4321)(3170, 4262, 3195, 4287)(3171, 4263, 3243, 4335)(3173, 4265, 3176, 4268)(3175, 4267, 3245, 4337)(3178, 4270, 3271, 4363)(3183, 4275, 3268, 4360)(3187, 4279, 3263, 4355)(3189, 4281, 3257, 4349)(3196, 4288, 3260, 4352)(3202, 4294, 3269, 4361)(3210, 4302, 3240, 4332)(3211, 4303, 3218, 4310)(3212, 4304, 3233, 4325)(3213, 4305, 3255, 4347)(3214, 4306, 3244, 4336)(3215, 4307, 3249, 4341)(3216, 4308, 3270, 4362)(3217, 4309, 3275, 4367)(3219, 4311, 3222, 4314)(3223, 4315, 3261, 4353)(3227, 4319, 3256, 4348)(3230, 4322, 3262, 4354)(3237, 4329, 3242, 4334)(3238, 4330, 3265, 4357)(3247, 4339, 3252, 4344)(3253, 4345, 3274, 4366)(3258, 4350, 3276, 4368)(3264, 4356, 3266, 4358) L = (1, 2187)(2, 2189)(3, 2192)(4, 2185)(5, 2196)(6, 2186)(7, 2197)(8, 2201)(9, 2202)(10, 2188)(11, 2193)(12, 2207)(13, 2208)(14, 2190)(15, 2191)(16, 2211)(17, 2204)(18, 2216)(19, 2217)(20, 2194)(21, 2195)(22, 2219)(23, 2210)(24, 2224)(25, 2225)(26, 2198)(27, 2227)(28, 2199)(29, 2200)(30, 2230)(31, 2203)(32, 2235)(33, 2237)(34, 2238)(35, 2239)(36, 2205)(37, 2206)(38, 2241)(39, 2209)(40, 2229)(41, 2247)(42, 2248)(43, 2250)(44, 2251)(45, 2212)(46, 2253)(47, 2213)(48, 2214)(49, 2215)(50, 2257)(51, 2220)(52, 2218)(53, 2263)(54, 2264)(55, 2266)(56, 2267)(57, 2268)(58, 2221)(59, 2222)(60, 2223)(61, 2272)(62, 2226)(63, 2277)(64, 2278)(65, 2228)(66, 2255)(67, 2282)(68, 2283)(69, 2285)(70, 2286)(71, 2231)(72, 2232)(73, 2290)(74, 2233)(75, 2234)(76, 2292)(77, 2236)(78, 2295)(79, 2258)(80, 2300)(81, 2240)(82, 2270)(83, 2303)(84, 2305)(85, 2306)(86, 2242)(87, 2243)(88, 2310)(89, 2244)(90, 2245)(91, 2246)(92, 2313)(93, 2273)(94, 2318)(95, 2249)(96, 2319)(97, 2252)(98, 2324)(99, 2325)(100, 2254)(101, 2289)(102, 2329)(103, 2330)(104, 2331)(105, 2256)(106, 2334)(107, 2335)(108, 2336)(109, 2259)(110, 2260)(111, 2340)(112, 2261)(113, 2262)(114, 2342)(115, 2288)(116, 2296)(117, 2265)(118, 2347)(119, 2351)(120, 2269)(121, 2309)(122, 2355)(123, 2356)(124, 2357)(125, 2271)(126, 2360)(127, 2361)(128, 2274)(129, 2364)(130, 2275)(131, 2276)(132, 2366)(133, 2308)(134, 2314)(135, 2371)(136, 2279)(137, 2280)(138, 2281)(139, 2374)(140, 2320)(141, 2379)(142, 2284)(143, 2380)(144, 2287)(145, 2385)(146, 2386)(147, 2388)(148, 2389)(149, 2291)(150, 2338)(151, 2392)(152, 2394)(153, 2395)(154, 2293)(155, 2294)(156, 2400)(157, 2401)(158, 2402)(159, 2297)(160, 2298)(161, 2299)(162, 2406)(163, 2409)(164, 2301)(165, 2302)(166, 2397)(167, 2348)(168, 2304)(169, 2414)(170, 2307)(171, 2419)(172, 2420)(173, 2422)(174, 2423)(175, 2311)(176, 2363)(177, 2426)(178, 2427)(179, 2312)(180, 2430)(181, 2431)(182, 2432)(183, 2315)(184, 2316)(185, 2317)(186, 2436)(187, 2440)(188, 2441)(189, 2321)(190, 2444)(191, 2322)(192, 2323)(193, 2446)(194, 2362)(195, 2375)(196, 2451)(197, 2326)(198, 2327)(199, 2328)(200, 2454)(201, 2381)(202, 2459)(203, 2332)(204, 2462)(205, 2463)(206, 2333)(207, 2464)(208, 2468)(209, 2337)(210, 2398)(211, 2472)(212, 2473)(213, 2474)(214, 2339)(215, 2341)(216, 2404)(217, 2478)(218, 2480)(219, 2481)(220, 2343)(221, 2344)(222, 2485)(223, 2345)(224, 2346)(225, 2489)(226, 2490)(227, 2349)(228, 2350)(229, 2493)(230, 2496)(231, 2352)(232, 2353)(233, 2354)(234, 2499)(235, 2415)(236, 2504)(237, 2358)(238, 2507)(239, 2508)(240, 2359)(241, 2509)(242, 2513)(243, 2515)(244, 2516)(245, 2365)(246, 2434)(247, 2519)(248, 2521)(249, 2522)(250, 2367)(251, 2368)(252, 2526)(253, 2369)(254, 2370)(255, 2372)(256, 2443)(257, 2531)(258, 2532)(259, 2373)(260, 2535)(261, 2536)(262, 2537)(263, 2376)(264, 2377)(265, 2378)(266, 2541)(267, 2545)(268, 2546)(269, 2382)(270, 2549)(271, 2383)(272, 2384)(273, 2551)(274, 2442)(275, 2455)(276, 2387)(277, 2556)(278, 2407)(279, 2561)(280, 2562)(281, 2390)(282, 2391)(283, 2483)(284, 2465)(285, 2393)(286, 2567)(287, 2396)(288, 2572)(289, 2573)(290, 2575)(291, 2576)(292, 2399)(293, 2577)(294, 2581)(295, 2403)(296, 2484)(297, 2585)(298, 2586)(299, 2587)(300, 2405)(301, 2590)(302, 2591)(303, 2408)(304, 2410)(305, 2492)(306, 2596)(307, 2597)(308, 2411)(309, 2599)(310, 2412)(311, 2413)(312, 2604)(313, 2605)(314, 2416)(315, 2608)(316, 2417)(317, 2418)(318, 2610)(319, 2491)(320, 2500)(321, 2421)(322, 2615)(323, 2437)(324, 2620)(325, 2621)(326, 2424)(327, 2425)(328, 2524)(329, 2510)(330, 2428)(331, 2628)(332, 2629)(333, 2429)(334, 2630)(335, 2634)(336, 2433)(337, 2525)(338, 2638)(339, 2639)(340, 2640)(341, 2435)(342, 2643)(343, 2644)(344, 2438)(345, 2439)(346, 2647)(347, 2651)(348, 2653)(349, 2654)(350, 2445)(351, 2539)(352, 2657)(353, 2659)(354, 2660)(355, 2447)(356, 2448)(357, 2664)(358, 2449)(359, 2450)(360, 2452)(361, 2548)(362, 2669)(363, 2670)(364, 2453)(365, 2673)(366, 2674)(367, 2675)(368, 2456)(369, 2457)(370, 2458)(371, 2679)(372, 2682)(373, 2460)(374, 2461)(375, 2684)(376, 2547)(377, 2557)(378, 2690)(379, 2691)(380, 2466)(381, 2467)(382, 2694)(383, 2697)(384, 2469)(385, 2470)(386, 2471)(387, 2700)(388, 2568)(389, 2705)(390, 2475)(391, 2601)(392, 2708)(393, 2709)(394, 2476)(395, 2477)(396, 2592)(397, 2578)(398, 2479)(399, 2714)(400, 2482)(401, 2719)(402, 2720)(403, 2722)(404, 2723)(405, 2486)(406, 2593)(407, 2726)(408, 2727)(409, 2487)(410, 2488)(411, 2733)(412, 2943)(413, 2945)(414, 2946)(415, 2824)(416, 2949)(417, 2494)(418, 2495)(419, 2497)(420, 2607)(421, 2954)(422, 2956)(423, 2498)(424, 2958)(425, 2959)(426, 2961)(427, 2501)(428, 2502)(429, 2503)(430, 2746)(431, 2966)(432, 2505)(433, 2506)(434, 2848)(435, 2606)(436, 2616)(437, 2970)(438, 2972)(439, 2511)(440, 2512)(441, 2795)(442, 2514)(443, 2778)(444, 2542)(445, 2811)(446, 2980)(447, 2517)(448, 2518)(449, 2645)(450, 2631)(451, 2520)(452, 2737)(453, 2523)(454, 2986)(455, 2988)(456, 2990)(457, 2992)(458, 2527)(459, 2646)(460, 2996)(461, 2998)(462, 2528)(463, 2922)(464, 2529)(465, 2530)(466, 2662)(467, 2648)(468, 2533)(469, 3005)(470, 3007)(471, 2534)(472, 2744)(473, 2982)(474, 2538)(475, 2663)(476, 3012)(477, 2978)(478, 2880)(479, 2540)(480, 2918)(481, 3015)(482, 2543)(483, 2544)(484, 2729)(485, 3019)(486, 3021)(487, 3022)(488, 2550)(489, 2677)(490, 3027)(491, 2787)(492, 3030)(493, 2552)(494, 2553)(495, 2991)(496, 2554)(497, 2555)(498, 3035)(499, 3036)(500, 3038)(501, 2558)(502, 2559)(503, 2560)(504, 2765)(505, 2563)(506, 2693)(507, 3045)(508, 3047)(509, 2564)(510, 2984)(511, 2565)(512, 2566)(513, 2964)(514, 3053)(515, 2569)(516, 2861)(517, 2570)(518, 2571)(519, 2872)(520, 2692)(521, 2701)(522, 2574)(523, 2749)(524, 2931)(525, 3059)(526, 3060)(527, 2579)(528, 2580)(529, 2782)(530, 2864)(531, 2582)(532, 2583)(533, 2584)(534, 2834)(535, 2715)(536, 2777)(537, 2588)(538, 3067)(539, 3069)(540, 2589)(541, 2731)(542, 2983)(543, 3072)(544, 3073)(545, 2843)(546, 2826)(547, 2821)(548, 2807)(549, 2971)(550, 2689)(551, 2792)(552, 2890)(553, 2877)(554, 2784)(555, 2801)(556, 2672)(557, 2816)(558, 2767)(559, 2758)(560, 3079)(561, 2603)(562, 2937)(563, 2783)(564, 2751)(565, 3082)(566, 2791)(567, 2854)(568, 2771)(569, 2750)(570, 3084)(571, 3052)(572, 3013)(573, 2766)(574, 2837)(575, 2721)(576, 2747)(577, 3086)(578, 3014)(579, 3087)(580, 2774)(581, 3089)(582, 2820)(583, 2609)(584, 2756)(585, 2741)(586, 3092)(587, 2641)(588, 2642)(589, 3094)(590, 2805)(591, 2763)(592, 2739)(593, 3096)(594, 2885)(595, 3097)(596, 2999)(597, 2764)(598, 2965)(599, 2863)(600, 2882)(601, 2789)(602, 2757)(603, 3100)(604, 3024)(605, 2728)(606, 2919)(607, 2887)(608, 2683)(609, 2780)(610, 3091)(611, 2933)(612, 2732)(613, 2856)(614, 3103)(615, 3105)(616, 2781)(617, 2915)(618, 2652)(619, 2948)(620, 3108)(621, 2840)(622, 2773)(623, 2940)(624, 2835)(625, 2753)(626, 2908)(627, 3083)(628, 2838)(629, 3110)(630, 3112)(631, 2786)(632, 2955)(633, 2900)(634, 2658)(635, 3042)(636, 2858)(637, 2997)(638, 2853)(639, 2760)(640, 3102)(641, 2928)(642, 2710)(643, 2799)(644, 3093)(645, 2873)(646, 2738)(647, 2960)(648, 3121)(649, 2800)(650, 2818)(651, 2671)(652, 2867)(653, 3046)(654, 2993)(655, 3126)(656, 2833)(657, 2804)(658, 2743)(659, 2981)(660, 2814)(661, 3066)(662, 2735)(663, 2901)(664, 3025)(665, 2916)(666, 3129)(667, 2815)(668, 2803)(669, 2957)(670, 3132)(671, 2637)(672, 2938)(673, 3134)(674, 2851)(675, 2819)(676, 2748)(677, 3029)(678, 3063)(679, 2910)(680, 3140)(681, 2906)(682, 2776)(683, 2849)(684, 2832)(685, 3085)(686, 2812)(687, 2613)(688, 3017)(689, 2831)(690, 3145)(691, 3147)(692, 2809)(693, 3150)(694, 2944)(695, 2635)(696, 2704)(697, 2825)(698, 3154)(699, 2686)(700, 2839)(701, 3074)(702, 3157)(703, 2930)(704, 2790)(705, 2769)(706, 2622)(707, 2850)(708, 3088)(709, 2619)(710, 2797)(711, 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4248)(2065, 4249)(2066, 4250)(2067, 4251)(2068, 4252)(2069, 4253)(2070, 4254)(2071, 4255)(2072, 4256)(2073, 4257)(2074, 4258)(2075, 4259)(2076, 4260)(2077, 4261)(2078, 4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 6, 14 ), ( 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E14.641 Graph:: simple bipartite v = 1638 e = 2184 f = 520 degree seq :: [ 2^1092, 4^546 ] E14.645 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, Y3^7, (Y3^-1 * Y1^-1)^7, (Y3^3 * Y2 * Y3^-3 * Y2)^3, Y3^2 * Y2 * Y3^3 * Y2 * Y3^-2 * Y2 * Y3^3 * Y2 * Y3^-2 * Y2 * Y3^2 * Y2 * Y3^-3 * Y2 * Y3^2 * Y2 * Y3^-2 * Y2 * Y3 * Y2 * Y3^-1 * Y2 ] Map:: polytopal R = (1, 1093)(2, 1094)(3, 1095)(4, 1096)(5, 1097)(6, 1098)(7, 1099)(8, 1100)(9, 1101)(10, 1102)(11, 1103)(12, 1104)(13, 1105)(14, 1106)(15, 1107)(16, 1108)(17, 1109)(18, 1110)(19, 1111)(20, 1112)(21, 1113)(22, 1114)(23, 1115)(24, 1116)(25, 1117)(26, 1118)(27, 1119)(28, 1120)(29, 1121)(30, 1122)(31, 1123)(32, 1124)(33, 1125)(34, 1126)(35, 1127)(36, 1128)(37, 1129)(38, 1130)(39, 1131)(40, 1132)(41, 1133)(42, 1134)(43, 1135)(44, 1136)(45, 1137)(46, 1138)(47, 1139)(48, 1140)(49, 1141)(50, 1142)(51, 1143)(52, 1144)(53, 1145)(54, 1146)(55, 1147)(56, 1148)(57, 1149)(58, 1150)(59, 1151)(60, 1152)(61, 1153)(62, 1154)(63, 1155)(64, 1156)(65, 1157)(66, 1158)(67, 1159)(68, 1160)(69, 1161)(70, 1162)(71, 1163)(72, 1164)(73, 1165)(74, 1166)(75, 1167)(76, 1168)(77, 1169)(78, 1170)(79, 1171)(80, 1172)(81, 1173)(82, 1174)(83, 1175)(84, 1176)(85, 1177)(86, 1178)(87, 1179)(88, 1180)(89, 1181)(90, 1182)(91, 1183)(92, 1184)(93, 1185)(94, 1186)(95, 1187)(96, 1188)(97, 1189)(98, 1190)(99, 1191)(100, 1192)(101, 1193)(102, 1194)(103, 1195)(104, 1196)(105, 1197)(106, 1198)(107, 1199)(108, 1200)(109, 1201)(110, 1202)(111, 1203)(112, 1204)(113, 1205)(114, 1206)(115, 1207)(116, 1208)(117, 1209)(118, 1210)(119, 1211)(120, 1212)(121, 1213)(122, 1214)(123, 1215)(124, 1216)(125, 1217)(126, 1218)(127, 1219)(128, 1220)(129, 1221)(130, 1222)(131, 1223)(132, 1224)(133, 1225)(134, 1226)(135, 1227)(136, 1228)(137, 1229)(138, 1230)(139, 1231)(140, 1232)(141, 1233)(142, 1234)(143, 1235)(144, 1236)(145, 1237)(146, 1238)(147, 1239)(148, 1240)(149, 1241)(150, 1242)(151, 1243)(152, 1244)(153, 1245)(154, 1246)(155, 1247)(156, 1248)(157, 1249)(158, 1250)(159, 1251)(160, 1252)(161, 1253)(162, 1254)(163, 1255)(164, 1256)(165, 1257)(166, 1258)(167, 1259)(168, 1260)(169, 1261)(170, 1262)(171, 1263)(172, 1264)(173, 1265)(174, 1266)(175, 1267)(176, 1268)(177, 1269)(178, 1270)(179, 1271)(180, 1272)(181, 1273)(182, 1274)(183, 1275)(184, 1276)(185, 1277)(186, 1278)(187, 1279)(188, 1280)(189, 1281)(190, 1282)(191, 1283)(192, 1284)(193, 1285)(194, 1286)(195, 1287)(196, 1288)(197, 1289)(198, 1290)(199, 1291)(200, 1292)(201, 1293)(202, 1294)(203, 1295)(204, 1296)(205, 1297)(206, 1298)(207, 1299)(208, 1300)(209, 1301)(210, 1302)(211, 1303)(212, 1304)(213, 1305)(214, 1306)(215, 1307)(216, 1308)(217, 1309)(218, 1310)(219, 1311)(220, 1312)(221, 1313)(222, 1314)(223, 1315)(224, 1316)(225, 1317)(226, 1318)(227, 1319)(228, 1320)(229, 1321)(230, 1322)(231, 1323)(232, 1324)(233, 1325)(234, 1326)(235, 1327)(236, 1328)(237, 1329)(238, 1330)(239, 1331)(240, 1332)(241, 1333)(242, 1334)(243, 1335)(244, 1336)(245, 1337)(246, 1338)(247, 1339)(248, 1340)(249, 1341)(250, 1342)(251, 1343)(252, 1344)(253, 1345)(254, 1346)(255, 1347)(256, 1348)(257, 1349)(258, 1350)(259, 1351)(260, 1352)(261, 1353)(262, 1354)(263, 1355)(264, 1356)(265, 1357)(266, 1358)(267, 1359)(268, 1360)(269, 1361)(270, 1362)(271, 1363)(272, 1364)(273, 1365)(274, 1366)(275, 1367)(276, 1368)(277, 1369)(278, 1370)(279, 1371)(280, 1372)(281, 1373)(282, 1374)(283, 1375)(284, 1376)(285, 1377)(286, 1378)(287, 1379)(288, 1380)(289, 1381)(290, 1382)(291, 1383)(292, 1384)(293, 1385)(294, 1386)(295, 1387)(296, 1388)(297, 1389)(298, 1390)(299, 1391)(300, 1392)(301, 1393)(302, 1394)(303, 1395)(304, 1396)(305, 1397)(306, 1398)(307, 1399)(308, 1400)(309, 1401)(310, 1402)(311, 1403)(312, 1404)(313, 1405)(314, 1406)(315, 1407)(316, 1408)(317, 1409)(318, 1410)(319, 1411)(320, 1412)(321, 1413)(322, 1414)(323, 1415)(324, 1416)(325, 1417)(326, 1418)(327, 1419)(328, 1420)(329, 1421)(330, 1422)(331, 1423)(332, 1424)(333, 1425)(334, 1426)(335, 1427)(336, 1428)(337, 1429)(338, 1430)(339, 1431)(340, 1432)(341, 1433)(342, 1434)(343, 1435)(344, 1436)(345, 1437)(346, 1438)(347, 1439)(348, 1440)(349, 1441)(350, 1442)(351, 1443)(352, 1444)(353, 1445)(354, 1446)(355, 1447)(356, 1448)(357, 1449)(358, 1450)(359, 1451)(360, 1452)(361, 1453)(362, 1454)(363, 1455)(364, 1456)(365, 1457)(366, 1458)(367, 1459)(368, 1460)(369, 1461)(370, 1462)(371, 1463)(372, 1464)(373, 1465)(374, 1466)(375, 1467)(376, 1468)(377, 1469)(378, 1470)(379, 1471)(380, 1472)(381, 1473)(382, 1474)(383, 1475)(384, 1476)(385, 1477)(386, 1478)(387, 1479)(388, 1480)(389, 1481)(390, 1482)(391, 1483)(392, 1484)(393, 1485)(394, 1486)(395, 1487)(396, 1488)(397, 1489)(398, 1490)(399, 1491)(400, 1492)(401, 1493)(402, 1494)(403, 1495)(404, 1496)(405, 1497)(406, 1498)(407, 1499)(408, 1500)(409, 1501)(410, 1502)(411, 1503)(412, 1504)(413, 1505)(414, 1506)(415, 1507)(416, 1508)(417, 1509)(418, 1510)(419, 1511)(420, 1512)(421, 1513)(422, 1514)(423, 1515)(424, 1516)(425, 1517)(426, 1518)(427, 1519)(428, 1520)(429, 1521)(430, 1522)(431, 1523)(432, 1524)(433, 1525)(434, 1526)(435, 1527)(436, 1528)(437, 1529)(438, 1530)(439, 1531)(440, 1532)(441, 1533)(442, 1534)(443, 1535)(444, 1536)(445, 1537)(446, 1538)(447, 1539)(448, 1540)(449, 1541)(450, 1542)(451, 1543)(452, 1544)(453, 1545)(454, 1546)(455, 1547)(456, 1548)(457, 1549)(458, 1550)(459, 1551)(460, 1552)(461, 1553)(462, 1554)(463, 1555)(464, 1556)(465, 1557)(466, 1558)(467, 1559)(468, 1560)(469, 1561)(470, 1562)(471, 1563)(472, 1564)(473, 1565)(474, 1566)(475, 1567)(476, 1568)(477, 1569)(478, 1570)(479, 1571)(480, 1572)(481, 1573)(482, 1574)(483, 1575)(484, 1576)(485, 1577)(486, 1578)(487, 1579)(488, 1580)(489, 1581)(490, 1582)(491, 1583)(492, 1584)(493, 1585)(494, 1586)(495, 1587)(496, 1588)(497, 1589)(498, 1590)(499, 1591)(500, 1592)(501, 1593)(502, 1594)(503, 1595)(504, 1596)(505, 1597)(506, 1598)(507, 1599)(508, 1600)(509, 1601)(510, 1602)(511, 1603)(512, 1604)(513, 1605)(514, 1606)(515, 1607)(516, 1608)(517, 1609)(518, 1610)(519, 1611)(520, 1612)(521, 1613)(522, 1614)(523, 1615)(524, 1616)(525, 1617)(526, 1618)(527, 1619)(528, 1620)(529, 1621)(530, 1622)(531, 1623)(532, 1624)(533, 1625)(534, 1626)(535, 1627)(536, 1628)(537, 1629)(538, 1630)(539, 1631)(540, 1632)(541, 1633)(542, 1634)(543, 1635)(544, 1636)(545, 1637)(546, 1638)(547, 1639)(548, 1640)(549, 1641)(550, 1642)(551, 1643)(552, 1644)(553, 1645)(554, 1646)(555, 1647)(556, 1648)(557, 1649)(558, 1650)(559, 1651)(560, 1652)(561, 1653)(562, 1654)(563, 1655)(564, 1656)(565, 1657)(566, 1658)(567, 1659)(568, 1660)(569, 1661)(570, 1662)(571, 1663)(572, 1664)(573, 1665)(574, 1666)(575, 1667)(576, 1668)(577, 1669)(578, 1670)(579, 1671)(580, 1672)(581, 1673)(582, 1674)(583, 1675)(584, 1676)(585, 1677)(586, 1678)(587, 1679)(588, 1680)(589, 1681)(590, 1682)(591, 1683)(592, 1684)(593, 1685)(594, 1686)(595, 1687)(596, 1688)(597, 1689)(598, 1690)(599, 1691)(600, 1692)(601, 1693)(602, 1694)(603, 1695)(604, 1696)(605, 1697)(606, 1698)(607, 1699)(608, 1700)(609, 1701)(610, 1702)(611, 1703)(612, 1704)(613, 1705)(614, 1706)(615, 1707)(616, 1708)(617, 1709)(618, 1710)(619, 1711)(620, 1712)(621, 1713)(622, 1714)(623, 1715)(624, 1716)(625, 1717)(626, 1718)(627, 1719)(628, 1720)(629, 1721)(630, 1722)(631, 1723)(632, 1724)(633, 1725)(634, 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1999)(908, 2000)(909, 2001)(910, 2002)(911, 2003)(912, 2004)(913, 2005)(914, 2006)(915, 2007)(916, 2008)(917, 2009)(918, 2010)(919, 2011)(920, 2012)(921, 2013)(922, 2014)(923, 2015)(924, 2016)(925, 2017)(926, 2018)(927, 2019)(928, 2020)(929, 2021)(930, 2022)(931, 2023)(932, 2024)(933, 2025)(934, 2026)(935, 2027)(936, 2028)(937, 2029)(938, 2030)(939, 2031)(940, 2032)(941, 2033)(942, 2034)(943, 2035)(944, 2036)(945, 2037)(946, 2038)(947, 2039)(948, 2040)(949, 2041)(950, 2042)(951, 2043)(952, 2044)(953, 2045)(954, 2046)(955, 2047)(956, 2048)(957, 2049)(958, 2050)(959, 2051)(960, 2052)(961, 2053)(962, 2054)(963, 2055)(964, 2056)(965, 2057)(966, 2058)(967, 2059)(968, 2060)(969, 2061)(970, 2062)(971, 2063)(972, 2064)(973, 2065)(974, 2066)(975, 2067)(976, 2068)(977, 2069)(978, 2070)(979, 2071)(980, 2072)(981, 2073)(982, 2074)(983, 2075)(984, 2076)(985, 2077)(986, 2078)(987, 2079)(988, 2080)(989, 2081)(990, 2082)(991, 2083)(992, 2084)(993, 2085)(994, 2086)(995, 2087)(996, 2088)(997, 2089)(998, 2090)(999, 2091)(1000, 2092)(1001, 2093)(1002, 2094)(1003, 2095)(1004, 2096)(1005, 2097)(1006, 2098)(1007, 2099)(1008, 2100)(1009, 2101)(1010, 2102)(1011, 2103)(1012, 2104)(1013, 2105)(1014, 2106)(1015, 2107)(1016, 2108)(1017, 2109)(1018, 2110)(1019, 2111)(1020, 2112)(1021, 2113)(1022, 2114)(1023, 2115)(1024, 2116)(1025, 2117)(1026, 2118)(1027, 2119)(1028, 2120)(1029, 2121)(1030, 2122)(1031, 2123)(1032, 2124)(1033, 2125)(1034, 2126)(1035, 2127)(1036, 2128)(1037, 2129)(1038, 2130)(1039, 2131)(1040, 2132)(1041, 2133)(1042, 2134)(1043, 2135)(1044, 2136)(1045, 2137)(1046, 2138)(1047, 2139)(1048, 2140)(1049, 2141)(1050, 2142)(1051, 2143)(1052, 2144)(1053, 2145)(1054, 2146)(1055, 2147)(1056, 2148)(1057, 2149)(1058, 2150)(1059, 2151)(1060, 2152)(1061, 2153)(1062, 2154)(1063, 2155)(1064, 2156)(1065, 2157)(1066, 2158)(1067, 2159)(1068, 2160)(1069, 2161)(1070, 2162)(1071, 2163)(1072, 2164)(1073, 2165)(1074, 2166)(1075, 2167)(1076, 2168)(1077, 2169)(1078, 2170)(1079, 2171)(1080, 2172)(1081, 2173)(1082, 2174)(1083, 2175)(1084, 2176)(1085, 2177)(1086, 2178)(1087, 2179)(1088, 2180)(1089, 2181)(1090, 2182)(1091, 2183)(1092, 2184)(2185, 3277, 2186, 3278)(2187, 3279, 2191, 3283)(2188, 3280, 2193, 3285)(2189, 3281, 2195, 3287)(2190, 3282, 2197, 3289)(2192, 3284, 2200, 3292)(2194, 3286, 2203, 3295)(2196, 3288, 2206, 3298)(2198, 3290, 2209, 3301)(2199, 3291, 2211, 3303)(2201, 3293, 2214, 3306)(2202, 3294, 2215, 3307)(2204, 3296, 2218, 3310)(2205, 3297, 2219, 3311)(2207, 3299, 2222, 3314)(2208, 3300, 2223, 3315)(2210, 3302, 2226, 3318)(2212, 3304, 2228, 3320)(2213, 3305, 2230, 3322)(2216, 3308, 2234, 3326)(2217, 3309, 2236, 3328)(2220, 3312, 2240, 3332)(2221, 3313, 2241, 3333)(2224, 3316, 2245, 3337)(2225, 3317, 2246, 3338)(2227, 3319, 2249, 3341)(2229, 3321, 2252, 3344)(2231, 3323, 2254, 3346)(2232, 3324, 2238, 3330)(2233, 3325, 2257, 3349)(2235, 3327, 2260, 3352)(2237, 3329, 2262, 3354)(2239, 3331, 2265, 3357)(2242, 3334, 2269, 3361)(2243, 3335, 2248, 3340)(2244, 3336, 2272, 3364)(2247, 3339, 2276, 3368)(2250, 3342, 2280, 3372)(2251, 3343, 2281, 3373)(2253, 3345, 2284, 3376)(2255, 3347, 2287, 3379)(2256, 3348, 2288, 3380)(2258, 3350, 2291, 3383)(2259, 3351, 2292, 3384)(2261, 3353, 2295, 3387)(2263, 3355, 2298, 3390)(2264, 3356, 2299, 3391)(2266, 3358, 2302, 3394)(2267, 3359, 2294, 3386)(2268, 3360, 2304, 3396)(2270, 3362, 2307, 3399)(2271, 3363, 2308, 3400)(2273, 3365, 2311, 3403)(2274, 3366, 2283, 3375)(2275, 3367, 2313, 3405)(2277, 3369, 2316, 3408)(2278, 3370, 2317, 3409)(2279, 3371, 2319, 3411)(2282, 3374, 2323, 3415)(2285, 3377, 2327, 3419)(2286, 3378, 2328, 3420)(2289, 3381, 2332, 3424)(2290, 3382, 2333, 3425)(2293, 3385, 2337, 3429)(2296, 3388, 2341, 3433)(2297, 3389, 2342, 3434)(2300, 3392, 2346, 3438)(2301, 3393, 2347, 3439)(2303, 3395, 2350, 3442)(2305, 3397, 2353, 3445)(2306, 3398, 2354, 3446)(2309, 3401, 2358, 3450)(2310, 3402, 2359, 3451)(2312, 3404, 2362, 3454)(2314, 3406, 2365, 3457)(2315, 3407, 2366, 3458)(2318, 3410, 2370, 3462)(2320, 3412, 2372, 3464)(2321, 3413, 2330, 3422)(2322, 3414, 2374, 3466)(2324, 3416, 2377, 3469)(2325, 3417, 2378, 3470)(2326, 3418, 2380, 3472)(2329, 3421, 2384, 3476)(2331, 3423, 2387, 3479)(2334, 3426, 2391, 3483)(2335, 3427, 2344, 3436)(2336, 3428, 2393, 3485)(2338, 3430, 2396, 3488)(2339, 3431, 2397, 3489)(2340, 3432, 2399, 3491)(2343, 3435, 2403, 3495)(2345, 3437, 2406, 3498)(2348, 3440, 2410, 3502)(2349, 3441, 2356, 3448)(2351, 3443, 2413, 3505)(2352, 3444, 2414, 3506)(2355, 3447, 2418, 3510)(2357, 3449, 2421, 3513)(2360, 3452, 2425, 3517)(2361, 3453, 2368, 3460)(2363, 3455, 2428, 3520)(2364, 3456, 2429, 3521)(2367, 3459, 2433, 3525)(2369, 3461, 2436, 3528)(2371, 3463, 2439, 3531)(2373, 3465, 2442, 3534)(2375, 3467, 2445, 3537)(2376, 3468, 2446, 3538)(2379, 3471, 2450, 3542)(2381, 3473, 2452, 3544)(2382, 3474, 2389, 3481)(2383, 3475, 2454, 3546)(2385, 3477, 2457, 3549)(2386, 3478, 2458, 3550)(2388, 3480, 2461, 3553)(2390, 3482, 2464, 3556)(2392, 3484, 2467, 3559)(2394, 3486, 2470, 3562)(2395, 3487, 2471, 3563)(2398, 3490, 2475, 3567)(2400, 3492, 2477, 3569)(2401, 3493, 2408, 3500)(2402, 3494, 2479, 3571)(2404, 3496, 2482, 3574)(2405, 3497, 2483, 3575)(2407, 3499, 2486, 3578)(2409, 3501, 2488, 3580)(2411, 3503, 2491, 3583)(2412, 3504, 2493, 3585)(2415, 3507, 2497, 3589)(2416, 3508, 2423, 3515)(2417, 3509, 2499, 3591)(2419, 3511, 2502, 3594)(2420, 3512, 2503, 3595)(2422, 3514, 2506, 3598)(2424, 3516, 2509, 3601)(2426, 3518, 2512, 3604)(2427, 3519, 2514, 3606)(2430, 3522, 2518, 3610)(2431, 3523, 2438, 3530)(2432, 3524, 2520, 3612)(2434, 3526, 2523, 3615)(2435, 3527, 2524, 3616)(2437, 3529, 2527, 3619)(2440, 3532, 2530, 3622)(2441, 3533, 2448, 3540)(2443, 3535, 2533, 3625)(2444, 3536, 2534, 3626)(2447, 3539, 2538, 3630)(2449, 3541, 2541, 3633)(2451, 3543, 2544, 3636)(2453, 3545, 2547, 3639)(2455, 3547, 2550, 3642)(2456, 3548, 2551, 3643)(2459, 3551, 2555, 3647)(2460, 3552, 2556, 3648)(2462, 3554, 2559, 3651)(2463, 3555, 2560, 3652)(2465, 3557, 2563, 3655)(2466, 3558, 2473, 3565)(2468, 3560, 2566, 3658)(2469, 3561, 2567, 3659)(2472, 3564, 2571, 3663)(2474, 3566, 2574, 3666)(2476, 3568, 2577, 3669)(2478, 3570, 2580, 3672)(2480, 3572, 2583, 3675)(2481, 3573, 2584, 3676)(2484, 3576, 2588, 3680)(2485, 3577, 2589, 3681)(2487, 3579, 2592, 3684)(2489, 3581, 2595, 3687)(2490, 3582, 2495, 3587)(2492, 3584, 2598, 3690)(2494, 3586, 2600, 3692)(2496, 3588, 2603, 3695)(2498, 3590, 2606, 3698)(2500, 3592, 2609, 3701)(2501, 3593, 2610, 3702)(2504, 3596, 2614, 3706)(2505, 3597, 2615, 3707)(2507, 3599, 2618, 3710)(2508, 3600, 2619, 3711)(2510, 3602, 2622, 3714)(2511, 3603, 2516, 3608)(2513, 3605, 2625, 3717)(2515, 3607, 2627, 3719)(2517, 3609, 2630, 3722)(2519, 3611, 2633, 3725)(2521, 3613, 2636, 3728)(2522, 3614, 2637, 3729)(2525, 3617, 2641, 3733)(2526, 3618, 2642, 3734)(2528, 3620, 2645, 3737)(2529, 3621, 2647, 3739)(2531, 3623, 2650, 3742)(2532, 3624, 2652, 3744)(2535, 3627, 2656, 3748)(2536, 3628, 2543, 3635)(2537, 3629, 2658, 3750)(2539, 3631, 2661, 3753)(2540, 3632, 2662, 3754)(2542, 3634, 2665, 3757)(2545, 3637, 2668, 3760)(2546, 3638, 2553, 3645)(2548, 3640, 2671, 3763)(2549, 3641, 2672, 3764)(2552, 3644, 2676, 3768)(2554, 3646, 2679, 3771)(2557, 3649, 2683, 3775)(2558, 3650, 2684, 3776)(2561, 3653, 2620, 3712)(2562, 3654, 2688, 3780)(2564, 3656, 2691, 3783)(2565, 3657, 2693, 3785)(2568, 3660, 2697, 3789)(2569, 3661, 2576, 3668)(2570, 3662, 2699, 3791)(2572, 3664, 2702, 3794)(2573, 3665, 2703, 3795)(2575, 3667, 2706, 3798)(2578, 3670, 2708, 3800)(2579, 3671, 2586, 3678)(2581, 3673, 2711, 3803)(2582, 3674, 2712, 3804)(2585, 3677, 2716, 3808)(2587, 3679, 2719, 3811)(2590, 3682, 2722, 3814)(2591, 3683, 2686, 3778)(2593, 3685, 2646, 3738)(2594, 3686, 2958, 4050)(2596, 3688, 2942, 4034)(2597, 3689, 2949, 4041)(2599, 3691, 2816, 3908)(2601, 3693, 2967, 4059)(2602, 3694, 2968, 4060)(2604, 3696, 2955, 4047)(2605, 3697, 2612, 3704)(2607, 3699, 2663, 3755)(2608, 3700, 2852, 3944)(2611, 3703, 2957, 4049)(2613, 3705, 2975, 4067)(2616, 3708, 2687, 3779)(2617, 3709, 2980, 4072)(2621, 3713, 2982, 4074)(2623, 3715, 2984, 4076)(2624, 3716, 2986, 4078)(2626, 3718, 2892, 3984)(2628, 3720, 2989, 4081)(2629, 3721, 2773, 3865)(2631, 3723, 2992, 4084)(2632, 3724, 2639, 3731)(2634, 3726, 2704, 3796)(2635, 3727, 2996, 4088)(2638, 3730, 2998, 4090)(2640, 3732, 2865, 3957)(2643, 3735, 2724, 3816)(2644, 3736, 2828, 3920)(2648, 3740, 3004, 4096)(2649, 3741, 2654, 3746)(2651, 3743, 3008, 4100)(2653, 3745, 3009, 4101)(2655, 3747, 2978, 4070)(2657, 3749, 2843, 3935)(2659, 3751, 2960, 4052)(2660, 3752, 2876, 3968)(2664, 3756, 2887, 3979)(2666, 3758, 2714, 3806)(2667, 3759, 2970, 4062)(2669, 3761, 3020, 4112)(2670, 3762, 2965, 4057)(2673, 3765, 2941, 4033)(2674, 3766, 2681, 3773)(2675, 3767, 2785, 3877)(2677, 3769, 3026, 4118)(2678, 3770, 3027, 4119)(2680, 3772, 3030, 4122)(2682, 3774, 2916, 4008)(2685, 3777, 3033, 4125)(2689, 3781, 2882, 3974)(2690, 3782, 2695, 3787)(2692, 3784, 3038, 4130)(2694, 3786, 2922, 4014)(2696, 3788, 2910, 4002)(2698, 3790, 2928, 4020)(2700, 3792, 3043, 4135)(2701, 3793, 3045, 4137)(2705, 3797, 2938, 4030)(2707, 3799, 3006, 4098)(2709, 3801, 3050, 4142)(2710, 3802, 3052, 4144)(2713, 3805, 3053, 4145)(2715, 3807, 2868, 3960)(2717, 3809, 3057, 4149)(2718, 3810, 2749, 3841)(2720, 3812, 3061, 4153)(2721, 3813, 3063, 4155)(2723, 3815, 3065, 4157)(2725, 3817, 2742, 3834)(2726, 3818, 2748, 3840)(2727, 3819, 2729, 3821)(2728, 3820, 2756, 3848)(2730, 3822, 2762, 3854)(2731, 3823, 2763, 3855)(2732, 3824, 2737, 3829)(2733, 3825, 2736, 3828)(2734, 3826, 2771, 3863)(2735, 3827, 2772, 3864)(2738, 3830, 2779, 3871)(2739, 3831, 2781, 3873)(2740, 3832, 2782, 3874)(2741, 3833, 2751, 3843)(2743, 3835, 2755, 3847)(2744, 3836, 2765, 3857)(2745, 3837, 2791, 3883)(2746, 3838, 2792, 3884)(2747, 3839, 2758, 3850)(2750, 3842, 2774, 3866)(2752, 3844, 2800, 3892)(2753, 3845, 2802, 3894)(2754, 3846, 2804, 3896)(2757, 3849, 2770, 3862)(2759, 3851, 2805, 3897)(2760, 3852, 2813, 3905)(2761, 3853, 2814, 3906)(2764, 3856, 2795, 3887)(2766, 3858, 2825, 3917)(2767, 3859, 2826, 3918)(2768, 3860, 2827, 3919)(2769, 3861, 2830, 3922)(2775, 3867, 2838, 3930)(2776, 3868, 2839, 3931)(2777, 3869, 2841, 3933)(2778, 3870, 2842, 3934)(2780, 3872, 2846, 3938)(2783, 3875, 2819, 3911)(2784, 3876, 2855, 3947)(2786, 3878, 2831, 3923)(2787, 3879, 2858, 3950)(2788, 3880, 2860, 3952)(2789, 3881, 2861, 3953)(2790, 3882, 2866, 3958)(2793, 3885, 2833, 3925)(2794, 3886, 2872, 3964)(2796, 3888, 2844, 3936)(2797, 3889, 2874, 3966)(2798, 3890, 2875, 3967)(2799, 3891, 2881, 3973)(2801, 3893, 2885, 3977)(2803, 3895, 2850, 3942)(2806, 3898, 2897, 3989)(2807, 3899, 2898, 3990)(2808, 3900, 2863, 3955)(2809, 3901, 2902, 3994)(2810, 3902, 2903, 3995)(2811, 3903, 2905, 3997)(2812, 3904, 2908, 4000)(2815, 3907, 2918, 4010)(2817, 3909, 2878, 3970)(2818, 3910, 2924, 4016)(2820, 3912, 2883, 3975)(2821, 3913, 2927, 4019)(2822, 3914, 2929, 4021)(2823, 3915, 2930, 4022)(2824, 3916, 2935, 4027)(2829, 3921, 2950, 4042)(2832, 3924, 2954, 4046)(2834, 3926, 2906, 3998)(2835, 3927, 2963, 4055)(2836, 3928, 2966, 4058)(2837, 3929, 2972, 4064)(2840, 3932, 2983, 4075)(2845, 3937, 3000, 4092)(2847, 3939, 3011, 4103)(2848, 3940, 2932, 4024)(2849, 3941, 3017, 4109)(2851, 3943, 2936, 4028)(2853, 3945, 3023, 4115)(2854, 3946, 3025, 4117)(2856, 3948, 3037, 4129)(2857, 3949, 3040, 4132)(2859, 3951, 2944, 4036)(2862, 3954, 3018, 4110)(2864, 3956, 3032, 4124)(2867, 3959, 3199, 4291)(2869, 3961, 2973, 4065)(2870, 3962, 3190, 4282)(2871, 3963, 3114, 4206)(2873, 3965, 3122, 4214)(2877, 3969, 3041, 4133)(2879, 3971, 3169, 4261)(2880, 3972, 3206, 4298)(2884, 3976, 3191, 4283)(2886, 3978, 2969, 4061)(2888, 3980, 3029, 4121)(2889, 3981, 3047, 4139)(2890, 3982, 2981, 4073)(2891, 3983, 3109, 4201)(2893, 3985, 3039, 4131)(2894, 3986, 2977, 4069)(2895, 3987, 3140, 4232)(2896, 3988, 3100, 4192)(2899, 3991, 3138, 4230)(2900, 3992, 3060, 4152)(2901, 3993, 3215, 4307)(2904, 3996, 2925, 4017)(2907, 3999, 3183, 4275)(2909, 4001, 2931, 4023)(2911, 4003, 3189, 4281)(2912, 4004, 3012, 4104)(2913, 4005, 2940, 4032)(2914, 4006, 3101, 4193)(2915, 4007, 3120, 4212)(2917, 4009, 3130, 4222)(2919, 4011, 3046, 4138)(2920, 4012, 3024, 4116)(2921, 4013, 3224, 4316)(2923, 4015, 3207, 4299)(2926, 4018, 3104, 4196)(2933, 4025, 3139, 4231)(2934, 4026, 3228, 4320)(2937, 4029, 3208, 4300)(2939, 4031, 2979, 4071)(2943, 4035, 3203, 4295)(2945, 4037, 3129, 4221)(2946, 4038, 2995, 4087)(2947, 4039, 3095, 4187)(2948, 4040, 3042, 4134)(2951, 4043, 3137, 4229)(2952, 4044, 2987, 4079)(2953, 4045, 3082, 4174)(2956, 4048, 3236, 4328)(2959, 4051, 3111, 4203)(2961, 4053, 3059, 4151)(2962, 4054, 3180, 4272)(2964, 4056, 3241, 4333)(2971, 4063, 3242, 4334)(2974, 4066, 3217, 4309)(2976, 4068, 3103, 4195)(2985, 4077, 3028, 4120)(2988, 4080, 3088, 4180)(2990, 4082, 3211, 4303)(2991, 4083, 3249, 4341)(2993, 4085, 3044, 4136)(2994, 4086, 3119, 4211)(2997, 4089, 3085, 4177)(2999, 4091, 3123, 4215)(3001, 4093, 3255, 4347)(3002, 4094, 3227, 4319)(3003, 4095, 3257, 4349)(3005, 4097, 3102, 4194)(3007, 4099, 3147, 4239)(3010, 4102, 3159, 4251)(3013, 4105, 3092, 4184)(3014, 4106, 3260, 4352)(3015, 4107, 3198, 4290)(3016, 4108, 3253, 4345)(3019, 4111, 3086, 4178)(3021, 4113, 3077, 4169)(3022, 4114, 3177, 4269)(3031, 4123, 3160, 4252)(3034, 4126, 3230, 4322)(3035, 4127, 3266, 4358)(3036, 4128, 3049, 4141)(3048, 4140, 3083, 4175)(3051, 4143, 3201, 4293)(3054, 4146, 3113, 4205)(3055, 4147, 3175, 4267)(3056, 4148, 3106, 4198)(3058, 4150, 3200, 4292)(3062, 4154, 3197, 4289)(3064, 4156, 3071, 4163)(3066, 4158, 3093, 4185)(3067, 4159, 3258, 4350)(3068, 4160, 3271, 4363)(3069, 4161, 3262, 4354)(3070, 4162, 3272, 4364)(3072, 4164, 3270, 4362)(3073, 4165, 3243, 4335)(3074, 4166, 3269, 4361)(3075, 4167, 3220, 4312)(3076, 4168, 3225, 4317)(3078, 4170, 3273, 4365)(3079, 4171, 3212, 4304)(3080, 4172, 3237, 4329)(3081, 4173, 3251, 4343)(3084, 4176, 3235, 4327)(3087, 4179, 3263, 4355)(3089, 4181, 3202, 4294)(3090, 4182, 3234, 4326)(3091, 4183, 3254, 4346)(3094, 4186, 3274, 4366)(3096, 4188, 3195, 4287)(3097, 4189, 3185, 4277)(3098, 4190, 3222, 4314)(3099, 4191, 3275, 4367)(3105, 4197, 3187, 4279)(3107, 4199, 3214, 4306)(3108, 4200, 3265, 4357)(3110, 4202, 3232, 4324)(3112, 4204, 3239, 4331)(3115, 4207, 3173, 4265)(3116, 4208, 3178, 4270)(3117, 4209, 3246, 4338)(3118, 4210, 3231, 4323)(3121, 4213, 3250, 4342)(3124, 4216, 3261, 4353)(3125, 4217, 3165, 4257)(3126, 4218, 3171, 4263)(3127, 4219, 3264, 4356)(3128, 4220, 3247, 4339)(3131, 4223, 3164, 4256)(3132, 4224, 3192, 4284)(3133, 4225, 3252, 4344)(3134, 4226, 3161, 4253)(3135, 4227, 3210, 4302)(3136, 4228, 3209, 4301)(3141, 4233, 3154, 4246)(3142, 4234, 3196, 4288)(3143, 4235, 3151, 4243)(3144, 4236, 3219, 4311)(3145, 4237, 3218, 4310)(3146, 4238, 3244, 4336)(3148, 4240, 3181, 4273)(3149, 4241, 3240, 4332)(3150, 4242, 3223, 4315)(3152, 4244, 3168, 4260)(3153, 4245, 3226, 4318)(3155, 4247, 3194, 4286)(3156, 4248, 3205, 4297)(3157, 4249, 3229, 4321)(3158, 4250, 3182, 4274)(3162, 4254, 3268, 4360)(3163, 4255, 3233, 4325)(3166, 4258, 3245, 4337)(3167, 4259, 3248, 4340)(3170, 4262, 3256, 4348)(3172, 4264, 3204, 4296)(3174, 4266, 3267, 4359)(3176, 4268, 3259, 4351)(3179, 4271, 3213, 4305)(3184, 4276, 3221, 4313)(3186, 4278, 3193, 4285)(3188, 4280, 3216, 4308)(3238, 4330, 3276, 4368) L = (1, 2187)(2, 2189)(3, 2192)(4, 2185)(5, 2196)(6, 2186)(7, 2197)(8, 2201)(9, 2202)(10, 2188)(11, 2193)(12, 2207)(13, 2208)(14, 2190)(15, 2191)(16, 2211)(17, 2204)(18, 2216)(19, 2217)(20, 2194)(21, 2195)(22, 2219)(23, 2210)(24, 2224)(25, 2225)(26, 2198)(27, 2227)(28, 2199)(29, 2200)(30, 2230)(31, 2203)(32, 2235)(33, 2237)(34, 2238)(35, 2239)(36, 2205)(37, 2206)(38, 2241)(39, 2209)(40, 2229)(41, 2247)(42, 2248)(43, 2250)(44, 2251)(45, 2212)(46, 2253)(47, 2213)(48, 2214)(49, 2215)(50, 2257)(51, 2220)(52, 2218)(53, 2263)(54, 2264)(55, 2266)(56, 2267)(57, 2268)(58, 2221)(59, 2222)(60, 2223)(61, 2272)(62, 2226)(63, 2277)(64, 2278)(65, 2228)(66, 2255)(67, 2282)(68, 2283)(69, 2285)(70, 2286)(71, 2231)(72, 2232)(73, 2290)(74, 2233)(75, 2234)(76, 2292)(77, 2236)(78, 2295)(79, 2258)(80, 2300)(81, 2240)(82, 2270)(83, 2303)(84, 2305)(85, 2306)(86, 2242)(87, 2243)(88, 2310)(89, 2244)(90, 2245)(91, 2246)(92, 2313)(93, 2273)(94, 2318)(95, 2249)(96, 2319)(97, 2252)(98, 2324)(99, 2325)(100, 2254)(101, 2289)(102, 2329)(103, 2330)(104, 2331)(105, 2256)(106, 2334)(107, 2335)(108, 2336)(109, 2259)(110, 2260)(111, 2340)(112, 2261)(113, 2262)(114, 2342)(115, 2288)(116, 2296)(117, 2265)(118, 2347)(119, 2351)(120, 2269)(121, 2309)(122, 2355)(123, 2356)(124, 2357)(125, 2271)(126, 2360)(127, 2361)(128, 2274)(129, 2364)(130, 2275)(131, 2276)(132, 2366)(133, 2308)(134, 2314)(135, 2371)(136, 2279)(137, 2280)(138, 2281)(139, 2374)(140, 2320)(141, 2379)(142, 2284)(143, 2380)(144, 2287)(145, 2385)(146, 2386)(147, 2388)(148, 2389)(149, 2291)(150, 2338)(151, 2392)(152, 2394)(153, 2395)(154, 2293)(155, 2294)(156, 2400)(157, 2401)(158, 2402)(159, 2297)(160, 2298)(161, 2299)(162, 2406)(163, 2409)(164, 2301)(165, 2302)(166, 2397)(167, 2348)(168, 2304)(169, 2414)(170, 2307)(171, 2419)(172, 2420)(173, 2422)(174, 2423)(175, 2311)(176, 2363)(177, 2426)(178, 2427)(179, 2312)(180, 2430)(181, 2431)(182, 2432)(183, 2315)(184, 2316)(185, 2317)(186, 2436)(187, 2440)(188, 2441)(189, 2321)(190, 2444)(191, 2322)(192, 2323)(193, 2446)(194, 2362)(195, 2375)(196, 2451)(197, 2326)(198, 2327)(199, 2328)(200, 2454)(201, 2381)(202, 2459)(203, 2332)(204, 2462)(205, 2463)(206, 2333)(207, 2464)(208, 2468)(209, 2337)(210, 2398)(211, 2472)(212, 2473)(213, 2474)(214, 2339)(215, 2341)(216, 2404)(217, 2478)(218, 2480)(219, 2481)(220, 2343)(221, 2344)(222, 2485)(223, 2345)(224, 2346)(225, 2489)(226, 2490)(227, 2349)(228, 2350)(229, 2493)(230, 2496)(231, 2352)(232, 2353)(233, 2354)(234, 2499)(235, 2415)(236, 2504)(237, 2358)(238, 2507)(239, 2508)(240, 2359)(241, 2509)(242, 2513)(243, 2515)(244, 2516)(245, 2365)(246, 2434)(247, 2519)(248, 2521)(249, 2522)(250, 2367)(251, 2368)(252, 2526)(253, 2369)(254, 2370)(255, 2372)(256, 2443)(257, 2531)(258, 2532)(259, 2373)(260, 2535)(261, 2536)(262, 2537)(263, 2376)(264, 2377)(265, 2378)(266, 2541)(267, 2545)(268, 2546)(269, 2382)(270, 2549)(271, 2383)(272, 2384)(273, 2551)(274, 2442)(275, 2455)(276, 2387)(277, 2556)(278, 2407)(279, 2561)(280, 2562)(281, 2390)(282, 2391)(283, 2483)(284, 2465)(285, 2393)(286, 2567)(287, 2396)(288, 2572)(289, 2573)(290, 2575)(291, 2576)(292, 2399)(293, 2577)(294, 2581)(295, 2403)(296, 2484)(297, 2585)(298, 2586)(299, 2587)(300, 2405)(301, 2590)(302, 2591)(303, 2408)(304, 2410)(305, 2492)(306, 2596)(307, 2597)(308, 2411)(309, 2599)(310, 2412)(311, 2413)(312, 2604)(313, 2605)(314, 2416)(315, 2608)(316, 2417)(317, 2418)(318, 2610)(319, 2491)(320, 2500)(321, 2421)(322, 2615)(323, 2437)(324, 2620)(325, 2621)(326, 2424)(327, 2425)(328, 2524)(329, 2510)(330, 2428)(331, 2628)(332, 2629)(333, 2429)(334, 2630)(335, 2634)(336, 2433)(337, 2525)(338, 2638)(339, 2639)(340, 2640)(341, 2435)(342, 2643)(343, 2644)(344, 2438)(345, 2439)(346, 2647)(347, 2651)(348, 2653)(349, 2654)(350, 2445)(351, 2539)(352, 2657)(353, 2659)(354, 2660)(355, 2447)(356, 2448)(357, 2664)(358, 2449)(359, 2450)(360, 2452)(361, 2548)(362, 2669)(363, 2670)(364, 2453)(365, 2673)(366, 2674)(367, 2675)(368, 2456)(369, 2457)(370, 2458)(371, 2679)(372, 2682)(373, 2460)(374, 2461)(375, 2684)(376, 2547)(377, 2557)(378, 2689)(379, 2690)(380, 2466)(381, 2467)(382, 2693)(383, 2696)(384, 2469)(385, 2470)(386, 2471)(387, 2699)(388, 2568)(389, 2704)(390, 2475)(391, 2601)(392, 2681)(393, 2707)(394, 2476)(395, 2477)(396, 2592)(397, 2578)(398, 2479)(399, 2712)(400, 2482)(401, 2717)(402, 2718)(403, 2720)(404, 2666)(405, 2486)(406, 2593)(407, 2723)(408, 2724)(409, 2487)(410, 2488)(411, 2958)(412, 2961)(413, 2962)(414, 2964)(415, 2965)(416, 2789)(417, 2494)(418, 2495)(419, 2497)(420, 2607)(421, 2971)(422, 2960)(423, 2498)(424, 2840)(425, 2843)(426, 2764)(427, 2501)(428, 2502)(429, 2503)(430, 2975)(431, 2977)(432, 2505)(433, 2506)(434, 2980)(435, 2606)(436, 2616)(437, 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2948)(529, 2582)(530, 2583)(531, 2584)(532, 2868)(533, 2713)(534, 3059)(535, 2588)(536, 3062)(537, 2589)(538, 3063)(539, 3066)(540, 3035)(541, 3067)(542, 3070)(543, 3068)(544, 3075)(545, 3071)(546, 3079)(547, 3081)(548, 3073)(549, 3085)(550, 3088)(551, 3090)(552, 3077)(553, 3082)(554, 3095)(555, 3097)(556, 3099)(557, 3083)(558, 3086)(559, 3103)(560, 3101)(561, 3106)(562, 3108)(563, 3092)(564, 3093)(565, 3050)(566, 3109)(567, 3100)(568, 3114)(569, 3116)(570, 3118)(571, 3008)(572, 3104)(573, 3121)(574, 3033)(575, 3025)(576, 3126)(577, 3128)(578, 3111)(579, 3057)(580, 3060)(581, 2972)(582, 3130)(583, 3132)(584, 3134)(585, 3136)(586, 2625)(587, 3122)(588, 3123)(589, 2984)(590, 2935)(591, 3140)(592, 3142)(593, 3143)(594, 3145)(595, 3037)(596, 3146)(597, 3046)(598, 2702)(599, 2949)(600, 3147)(601, 2676)(602, 2930)(603, 3152)(604, 3154)(605, 3156)(606, 3157)(607, 3138)(608, 2989)(609, 2652)(610, 3055)(611, 2957)(612, 2966)(613, 3162)(614, 3164)(615, 3165)(616, 2905)(617, 3167)(618, 2912)(619, 2637)(620, 3149)(621, 2881)(622, 2987)(623, 3170)(624, 2876)(625, 2624)(626, 2974)(627, 3173)(628, 3174)(629, 2889)(630, 3159)(631, 2946)(632, 2600)(633, 2861)(634, 2937)(635, 2902)(636, 2924)(637, 3043)(638, 3181)(639, 2907)(640, 2701)(641, 2875)(642, 2921)(643, 2981)(644, 2618)(645, 3182)(646, 3014)(647, 2841)(648, 2913)(649, 2922)(650, 2903)(651, 2710)(652, 2884)(653, 3187)(654, 2860)(655, 2901)(656, 3188)(657, 2940)(658, 3176)(659, 2714)(660, 2827)(661, 2890)(662, 3179)(663, 2870)(664, 2828)(665, 3034)(666, 2858)(667, 3017)(668, 2609)(669, 3194)(670, 2879)(671, 2929)(672, 3195)(673, 3166)(674, 2849)(675, 2686)(676, 3023)(677, 2967)(678, 3028)(679, 2813)(680, 3047)(681, 2641)(682, 3184)(683, 2853)(684, 2874)(685, 3040)(686, 3201)(687, 2864)(688, 2950)(689, 3202)(690, 2857)(691, 3190)(692, 2661)(693, 3203)(694, 2802)(695, 3012)(696, 3172)(697, 2952)(698, 3001)(699, 2791)(700, 2899)(701, 3193)(702, 2877)(703, 2665)(704, 2792)(705, 3051)(706, 3210)(707, 2933)(708, 2963)(709, 2885)(710, 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3666)(1483, 3667)(1484, 3668)(1485, 3669)(1486, 3670)(1487, 3671)(1488, 3672)(1489, 3673)(1490, 3674)(1491, 3675)(1492, 3676)(1493, 3677)(1494, 3678)(1495, 3679)(1496, 3680)(1497, 3681)(1498, 3682)(1499, 3683)(1500, 3684)(1501, 3685)(1502, 3686)(1503, 3687)(1504, 3688)(1505, 3689)(1506, 3690)(1507, 3691)(1508, 3692)(1509, 3693)(1510, 3694)(1511, 3695)(1512, 3696)(1513, 3697)(1514, 3698)(1515, 3699)(1516, 3700)(1517, 3701)(1518, 3702)(1519, 3703)(1520, 3704)(1521, 3705)(1522, 3706)(1523, 3707)(1524, 3708)(1525, 3709)(1526, 3710)(1527, 3711)(1528, 3712)(1529, 3713)(1530, 3714)(1531, 3715)(1532, 3716)(1533, 3717)(1534, 3718)(1535, 3719)(1536, 3720)(1537, 3721)(1538, 3722)(1539, 3723)(1540, 3724)(1541, 3725)(1542, 3726)(1543, 3727)(1544, 3728)(1545, 3729)(1546, 3730)(1547, 3731)(1548, 3732)(1549, 3733)(1550, 3734)(1551, 3735)(1552, 3736)(1553, 3737)(1554, 3738)(1555, 3739)(1556, 3740)(1557, 3741)(1558, 3742)(1559, 3743)(1560, 3744)(1561, 3745)(1562, 3746)(1563, 3747)(1564, 3748)(1565, 3749)(1566, 3750)(1567, 3751)(1568, 3752)(1569, 3753)(1570, 3754)(1571, 3755)(1572, 3756)(1573, 3757)(1574, 3758)(1575, 3759)(1576, 3760)(1577, 3761)(1578, 3762)(1579, 3763)(1580, 3764)(1581, 3765)(1582, 3766)(1583, 3767)(1584, 3768)(1585, 3769)(1586, 3770)(1587, 3771)(1588, 3772)(1589, 3773)(1590, 3774)(1591, 3775)(1592, 3776)(1593, 3777)(1594, 3778)(1595, 3779)(1596, 3780)(1597, 3781)(1598, 3782)(1599, 3783)(1600, 3784)(1601, 3785)(1602, 3786)(1603, 3787)(1604, 3788)(1605, 3789)(1606, 3790)(1607, 3791)(1608, 3792)(1609, 3793)(1610, 3794)(1611, 3795)(1612, 3796)(1613, 3797)(1614, 3798)(1615, 3799)(1616, 3800)(1617, 3801)(1618, 3802)(1619, 3803)(1620, 3804)(1621, 3805)(1622, 3806)(1623, 3807)(1624, 3808)(1625, 3809)(1626, 3810)(1627, 3811)(1628, 3812)(1629, 3813)(1630, 3814)(1631, 3815)(1632, 3816)(1633, 3817)(1634, 3818)(1635, 3819)(1636, 3820)(1637, 3821)(1638, 3822)(1639, 3823)(1640, 3824)(1641, 3825)(1642, 3826)(1643, 3827)(1644, 3828)(1645, 3829)(1646, 3830)(1647, 3831)(1648, 3832)(1649, 3833)(1650, 3834)(1651, 3835)(1652, 3836)(1653, 3837)(1654, 3838)(1655, 3839)(1656, 3840)(1657, 3841)(1658, 3842)(1659, 3843)(1660, 3844)(1661, 3845)(1662, 3846)(1663, 3847)(1664, 3848)(1665, 3849)(1666, 3850)(1667, 3851)(1668, 3852)(1669, 3853)(1670, 3854)(1671, 3855)(1672, 3856)(1673, 3857)(1674, 3858)(1675, 3859)(1676, 3860)(1677, 3861)(1678, 3862)(1679, 3863)(1680, 3864)(1681, 3865)(1682, 3866)(1683, 3867)(1684, 3868)(1685, 3869)(1686, 3870)(1687, 3871)(1688, 3872)(1689, 3873)(1690, 3874)(1691, 3875)(1692, 3876)(1693, 3877)(1694, 3878)(1695, 3879)(1696, 3880)(1697, 3881)(1698, 3882)(1699, 3883)(1700, 3884)(1701, 3885)(1702, 3886)(1703, 3887)(1704, 3888)(1705, 3889)(1706, 3890)(1707, 3891)(1708, 3892)(1709, 3893)(1710, 3894)(1711, 3895)(1712, 3896)(1713, 3897)(1714, 3898)(1715, 3899)(1716, 3900)(1717, 3901)(1718, 3902)(1719, 3903)(1720, 3904)(1721, 3905)(1722, 3906)(1723, 3907)(1724, 3908)(1725, 3909)(1726, 3910)(1727, 3911)(1728, 3912)(1729, 3913)(1730, 3914)(1731, 3915)(1732, 3916)(1733, 3917)(1734, 3918)(1735, 3919)(1736, 3920)(1737, 3921)(1738, 3922)(1739, 3923)(1740, 3924)(1741, 3925)(1742, 3926)(1743, 3927)(1744, 3928)(1745, 3929)(1746, 3930)(1747, 3931)(1748, 3932)(1749, 3933)(1750, 3934)(1751, 3935)(1752, 3936)(1753, 3937)(1754, 3938)(1755, 3939)(1756, 3940)(1757, 3941)(1758, 3942)(1759, 3943)(1760, 3944)(1761, 3945)(1762, 3946)(1763, 3947)(1764, 3948)(1765, 3949)(1766, 3950)(1767, 3951)(1768, 3952)(1769, 3953)(1770, 3954)(1771, 3955)(1772, 3956)(1773, 3957)(1774, 3958)(1775, 3959)(1776, 3960)(1777, 3961)(1778, 3962)(1779, 3963)(1780, 3964)(1781, 3965)(1782, 3966)(1783, 3967)(1784, 3968)(1785, 3969)(1786, 3970)(1787, 3971)(1788, 3972)(1789, 3973)(1790, 3974)(1791, 3975)(1792, 3976)(1793, 3977)(1794, 3978)(1795, 3979)(1796, 3980)(1797, 3981)(1798, 3982)(1799, 3983)(1800, 3984)(1801, 3985)(1802, 3986)(1803, 3987)(1804, 3988)(1805, 3989)(1806, 3990)(1807, 3991)(1808, 3992)(1809, 3993)(1810, 3994)(1811, 3995)(1812, 3996)(1813, 3997)(1814, 3998)(1815, 3999)(1816, 4000)(1817, 4001)(1818, 4002)(1819, 4003)(1820, 4004)(1821, 4005)(1822, 4006)(1823, 4007)(1824, 4008)(1825, 4009)(1826, 4010)(1827, 4011)(1828, 4012)(1829, 4013)(1830, 4014)(1831, 4015)(1832, 4016)(1833, 4017)(1834, 4018)(1835, 4019)(1836, 4020)(1837, 4021)(1838, 4022)(1839, 4023)(1840, 4024)(1841, 4025)(1842, 4026)(1843, 4027)(1844, 4028)(1845, 4029)(1846, 4030)(1847, 4031)(1848, 4032)(1849, 4033)(1850, 4034)(1851, 4035)(1852, 4036)(1853, 4037)(1854, 4038)(1855, 4039)(1856, 4040)(1857, 4041)(1858, 4042)(1859, 4043)(1860, 4044)(1861, 4045)(1862, 4046)(1863, 4047)(1864, 4048)(1865, 4049)(1866, 4050)(1867, 4051)(1868, 4052)(1869, 4053)(1870, 4054)(1871, 4055)(1872, 4056)(1873, 4057)(1874, 4058)(1875, 4059)(1876, 4060)(1877, 4061)(1878, 4062)(1879, 4063)(1880, 4064)(1881, 4065)(1882, 4066)(1883, 4067)(1884, 4068)(1885, 4069)(1886, 4070)(1887, 4071)(1888, 4072)(1889, 4073)(1890, 4074)(1891, 4075)(1892, 4076)(1893, 4077)(1894, 4078)(1895, 4079)(1896, 4080)(1897, 4081)(1898, 4082)(1899, 4083)(1900, 4084)(1901, 4085)(1902, 4086)(1903, 4087)(1904, 4088)(1905, 4089)(1906, 4090)(1907, 4091)(1908, 4092)(1909, 4093)(1910, 4094)(1911, 4095)(1912, 4096)(1913, 4097)(1914, 4098)(1915, 4099)(1916, 4100)(1917, 4101)(1918, 4102)(1919, 4103)(1920, 4104)(1921, 4105)(1922, 4106)(1923, 4107)(1924, 4108)(1925, 4109)(1926, 4110)(1927, 4111)(1928, 4112)(1929, 4113)(1930, 4114)(1931, 4115)(1932, 4116)(1933, 4117)(1934, 4118)(1935, 4119)(1936, 4120)(1937, 4121)(1938, 4122)(1939, 4123)(1940, 4124)(1941, 4125)(1942, 4126)(1943, 4127)(1944, 4128)(1945, 4129)(1946, 4130)(1947, 4131)(1948, 4132)(1949, 4133)(1950, 4134)(1951, 4135)(1952, 4136)(1953, 4137)(1954, 4138)(1955, 4139)(1956, 4140)(1957, 4141)(1958, 4142)(1959, 4143)(1960, 4144)(1961, 4145)(1962, 4146)(1963, 4147)(1964, 4148)(1965, 4149)(1966, 4150)(1967, 4151)(1968, 4152)(1969, 4153)(1970, 4154)(1971, 4155)(1972, 4156)(1973, 4157)(1974, 4158)(1975, 4159)(1976, 4160)(1977, 4161)(1978, 4162)(1979, 4163)(1980, 4164)(1981, 4165)(1982, 4166)(1983, 4167)(1984, 4168)(1985, 4169)(1986, 4170)(1987, 4171)(1988, 4172)(1989, 4173)(1990, 4174)(1991, 4175)(1992, 4176)(1993, 4177)(1994, 4178)(1995, 4179)(1996, 4180)(1997, 4181)(1998, 4182)(1999, 4183)(2000, 4184)(2001, 4185)(2002, 4186)(2003, 4187)(2004, 4188)(2005, 4189)(2006, 4190)(2007, 4191)(2008, 4192)(2009, 4193)(2010, 4194)(2011, 4195)(2012, 4196)(2013, 4197)(2014, 4198)(2015, 4199)(2016, 4200)(2017, 4201)(2018, 4202)(2019, 4203)(2020, 4204)(2021, 4205)(2022, 4206)(2023, 4207)(2024, 4208)(2025, 4209)(2026, 4210)(2027, 4211)(2028, 4212)(2029, 4213)(2030, 4214)(2031, 4215)(2032, 4216)(2033, 4217)(2034, 4218)(2035, 4219)(2036, 4220)(2037, 4221)(2038, 4222)(2039, 4223)(2040, 4224)(2041, 4225)(2042, 4226)(2043, 4227)(2044, 4228)(2045, 4229)(2046, 4230)(2047, 4231)(2048, 4232)(2049, 4233)(2050, 4234)(2051, 4235)(2052, 4236)(2053, 4237)(2054, 4238)(2055, 4239)(2056, 4240)(2057, 4241)(2058, 4242)(2059, 4243)(2060, 4244)(2061, 4245)(2062, 4246)(2063, 4247)(2064, 4248)(2065, 4249)(2066, 4250)(2067, 4251)(2068, 4252)(2069, 4253)(2070, 4254)(2071, 4255)(2072, 4256)(2073, 4257)(2074, 4258)(2075, 4259)(2076, 4260)(2077, 4261)(2078, 4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 6, 14 ), ( 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E14.642 Graph:: simple bipartite v = 1638 e = 2184 f = 520 degree seq :: [ 2^1092, 4^546 ] E14.646 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |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)^3, Y1^7, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^3 * Y3 * Y1^2 * Y3 * Y1^-2 * Y3 * Y1^-3 * Y3 * Y1^-2, (Y3 * Y1^2 * Y3 * Y1^-2 * Y3 * Y1^2 * Y3 * Y1^-3 * Y3 * Y1^-3)^2, Y3 * Y1^3 * Y3 * Y1^-2 * Y3 * Y1^3 * Y3 * Y1^-2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-2 * Y3 * Y1^2 * Y3 * Y1^-2 * Y3 * Y1^-3 ] Map:: polytopal R = (1, 1093, 2, 1094, 5, 1097, 11, 1103, 20, 1112, 10, 1102, 4, 1096)(3, 1095, 7, 1099, 15, 1107, 26, 1118, 30, 1122, 17, 1109, 8, 1100)(6, 1098, 13, 1105, 24, 1116, 39, 1131, 42, 1134, 25, 1117, 14, 1106)(9, 1101, 18, 1110, 31, 1123, 49, 1141, 46, 1138, 28, 1120, 16, 1108)(12, 1104, 22, 1114, 37, 1129, 57, 1149, 60, 1152, 38, 1130, 23, 1115)(19, 1111, 33, 1125, 52, 1144, 77, 1169, 76, 1168, 51, 1143, 32, 1124)(21, 1113, 35, 1127, 55, 1147, 81, 1173, 84, 1176, 56, 1148, 36, 1128)(27, 1119, 44, 1136, 67, 1159, 97, 1189, 100, 1192, 68, 1160, 45, 1137)(29, 1121, 47, 1139, 70, 1162, 102, 1194, 91, 1183, 62, 1154, 40, 1132)(34, 1126, 54, 1146, 80, 1172, 115, 1207, 114, 1206, 79, 1171, 53, 1145)(41, 1133, 63, 1155, 92, 1184, 130, 1222, 123, 1215, 86, 1178, 58, 1150)(43, 1135, 65, 1157, 95, 1187, 134, 1226, 137, 1229, 96, 1188, 66, 1158)(48, 1140, 72, 1164, 105, 1197, 147, 1239, 146, 1238, 104, 1196, 71, 1163)(50, 1142, 74, 1166, 108, 1200, 151, 1243, 154, 1246, 109, 1201, 75, 1167)(59, 1151, 87, 1179, 124, 1216, 172, 1264, 165, 1257, 118, 1210, 82, 1174)(61, 1153, 89, 1181, 127, 1219, 176, 1268, 179, 1271, 128, 1220, 90, 1182)(64, 1156, 94, 1186, 133, 1225, 185, 1277, 184, 1276, 132, 1224, 93, 1185)(69, 1161, 101, 1193, 142, 1234, 197, 1289, 193, 1285, 139, 1231, 98, 1190)(73, 1165, 106, 1198, 149, 1241, 206, 1298, 209, 1301, 150, 1242, 107, 1199)(78, 1170, 112, 1204, 158, 1250, 217, 1309, 220, 1312, 159, 1251, 113, 1205)(83, 1175, 119, 1211, 166, 1258, 228, 1320, 224, 1316, 162, 1254, 116, 1208)(85, 1177, 121, 1213, 169, 1261, 232, 1324, 235, 1327, 170, 1262, 122, 1214)(88, 1180, 126, 1218, 175, 1267, 241, 1333, 240, 1332, 174, 1266, 125, 1217)(99, 1191, 140, 1232, 194, 1286, 264, 1356, 257, 1349, 188, 1280, 135, 1227)(103, 1195, 144, 1236, 201, 1293, 272, 1364, 275, 1367, 202, 1294, 145, 1237)(110, 1202, 155, 1247, 214, 1306, 290, 1382, 286, 1378, 211, 1303, 152, 1244)(111, 1203, 156, 1248, 215, 1307, 292, 1384, 295, 1387, 216, 1308, 157, 1249)(117, 1209, 163, 1255, 225, 1317, 304, 1396, 307, 1399, 226, 1318, 164, 1256)(120, 1212, 168, 1260, 231, 1323, 313, 1405, 312, 1404, 230, 1322, 167, 1259)(129, 1221, 180, 1272, 247, 1339, 333, 1425, 329, 1421, 244, 1336, 177, 1269)(131, 1223, 182, 1274, 250, 1342, 337, 1429, 340, 1432, 251, 1343, 183, 1275)(136, 1228, 189, 1281, 258, 1350, 348, 1440, 279, 1371, 205, 1297, 148, 1240)(138, 1230, 191, 1283, 261, 1353, 352, 1444, 355, 1447, 262, 1354, 192, 1284)(141, 1233, 196, 1288, 267, 1359, 361, 1453, 360, 1452, 266, 1358, 195, 1287)(143, 1235, 199, 1291, 270, 1362, 366, 1458, 369, 1461, 271, 1363, 200, 1292)(153, 1245, 212, 1304, 287, 1379, 387, 1479, 380, 1472, 281, 1373, 207, 1299)(160, 1252, 221, 1313, 300, 1392, 403, 1495, 399, 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3833)(2742, 3834)(2743, 3835)(2744, 3836)(2745, 3837)(2746, 3838)(2747, 3839)(2748, 3840)(2749, 3841)(2750, 3842)(2751, 3843)(2752, 3844)(2753, 3845)(2754, 3846)(2755, 3847)(2756, 3848)(2757, 3849)(2758, 3850)(2759, 3851)(2760, 3852)(2761, 3853)(2762, 3854)(2763, 3855)(2764, 3856)(2765, 3857)(2766, 3858)(2767, 3859)(2768, 3860)(2769, 3861)(2770, 3862)(2771, 3863)(2772, 3864)(2773, 3865)(2774, 3866)(2775, 3867)(2776, 3868)(2777, 3869)(2778, 3870)(2779, 3871)(2780, 3872)(2781, 3873)(2782, 3874)(2783, 3875)(2784, 3876)(2785, 3877)(2786, 3878)(2787, 3879)(2788, 3880)(2789, 3881)(2790, 3882)(2791, 3883)(2792, 3884)(2793, 3885)(2794, 3886)(2795, 3887)(2796, 3888)(2797, 3889)(2798, 3890)(2799, 3891)(2800, 3892)(2801, 3893)(2802, 3894)(2803, 3895)(2804, 3896)(2805, 3897)(2806, 3898)(2807, 3899)(2808, 3900)(2809, 3901)(2810, 3902)(2811, 3903)(2812, 3904)(2813, 3905)(2814, 3906)(2815, 3907)(2816, 3908)(2817, 3909)(2818, 3910)(2819, 3911)(2820, 3912)(2821, 3913)(2822, 3914)(2823, 3915)(2824, 3916)(2825, 3917)(2826, 3918)(2827, 3919)(2828, 3920)(2829, 3921)(2830, 3922)(2831, 3923)(2832, 3924)(2833, 3925)(2834, 3926)(2835, 3927)(2836, 3928)(2837, 3929)(2838, 3930)(2839, 3931)(2840, 3932)(2841, 3933)(2842, 3934)(2843, 3935)(2844, 3936)(2845, 3937)(2846, 3938)(2847, 3939)(2848, 3940)(2849, 3941)(2850, 3942)(2851, 3943)(2852, 3944)(2853, 3945)(2854, 3946)(2855, 3947)(2856, 3948)(2857, 3949)(2858, 3950)(2859, 3951)(2860, 3952)(2861, 3953)(2862, 3954)(2863, 3955)(2864, 3956)(2865, 3957)(2866, 3958)(2867, 3959)(2868, 3960)(2869, 3961)(2870, 3962)(2871, 3963)(2872, 3964)(2873, 3965)(2874, 3966)(2875, 3967)(2876, 3968)(2877, 3969)(2878, 3970)(2879, 3971)(2880, 3972)(2881, 3973)(2882, 3974)(2883, 3975)(2884, 3976)(2885, 3977)(2886, 3978)(2887, 3979)(2888, 3980)(2889, 3981)(2890, 3982)(2891, 3983)(2892, 3984)(2893, 3985)(2894, 3986)(2895, 3987)(2896, 3988)(2897, 3989)(2898, 3990)(2899, 3991)(2900, 3992)(2901, 3993)(2902, 3994)(2903, 3995)(2904, 3996)(2905, 3997)(2906, 3998)(2907, 3999)(2908, 4000)(2909, 4001)(2910, 4002)(2911, 4003)(2912, 4004)(2913, 4005)(2914, 4006)(2915, 4007)(2916, 4008)(2917, 4009)(2918, 4010)(2919, 4011)(2920, 4012)(2921, 4013)(2922, 4014)(2923, 4015)(2924, 4016)(2925, 4017)(2926, 4018)(2927, 4019)(2928, 4020)(2929, 4021)(2930, 4022)(2931, 4023)(2932, 4024)(2933, 4025)(2934, 4026)(2935, 4027)(2936, 4028)(2937, 4029)(2938, 4030)(2939, 4031)(2940, 4032)(2941, 4033)(2942, 4034)(2943, 4035)(2944, 4036)(2945, 4037)(2946, 4038)(2947, 4039)(2948, 4040)(2949, 4041)(2950, 4042)(2951, 4043)(2952, 4044)(2953, 4045)(2954, 4046)(2955, 4047)(2956, 4048)(2957, 4049)(2958, 4050)(2959, 4051)(2960, 4052)(2961, 4053)(2962, 4054)(2963, 4055)(2964, 4056)(2965, 4057)(2966, 4058)(2967, 4059)(2968, 4060)(2969, 4061)(2970, 4062)(2971, 4063)(2972, 4064)(2973, 4065)(2974, 4066)(2975, 4067)(2976, 4068)(2977, 4069)(2978, 4070)(2979, 4071)(2980, 4072)(2981, 4073)(2982, 4074)(2983, 4075)(2984, 4076)(2985, 4077)(2986, 4078)(2987, 4079)(2988, 4080)(2989, 4081)(2990, 4082)(2991, 4083)(2992, 4084)(2993, 4085)(2994, 4086)(2995, 4087)(2996, 4088)(2997, 4089)(2998, 4090)(2999, 4091)(3000, 4092)(3001, 4093)(3002, 4094)(3003, 4095)(3004, 4096)(3005, 4097)(3006, 4098)(3007, 4099)(3008, 4100)(3009, 4101)(3010, 4102)(3011, 4103)(3012, 4104)(3013, 4105)(3014, 4106)(3015, 4107)(3016, 4108)(3017, 4109)(3018, 4110)(3019, 4111)(3020, 4112)(3021, 4113)(3022, 4114)(3023, 4115)(3024, 4116)(3025, 4117)(3026, 4118)(3027, 4119)(3028, 4120)(3029, 4121)(3030, 4122)(3031, 4123)(3032, 4124)(3033, 4125)(3034, 4126)(3035, 4127)(3036, 4128)(3037, 4129)(3038, 4130)(3039, 4131)(3040, 4132)(3041, 4133)(3042, 4134)(3043, 4135)(3044, 4136)(3045, 4137)(3046, 4138)(3047, 4139)(3048, 4140)(3049, 4141)(3050, 4142)(3051, 4143)(3052, 4144)(3053, 4145)(3054, 4146)(3055, 4147)(3056, 4148)(3057, 4149)(3058, 4150)(3059, 4151)(3060, 4152)(3061, 4153)(3062, 4154)(3063, 4155)(3064, 4156)(3065, 4157)(3066, 4158)(3067, 4159)(3068, 4160)(3069, 4161)(3070, 4162)(3071, 4163)(3072, 4164)(3073, 4165)(3074, 4166)(3075, 4167)(3076, 4168)(3077, 4169)(3078, 4170)(3079, 4171)(3080, 4172)(3081, 4173)(3082, 4174)(3083, 4175)(3084, 4176)(3085, 4177)(3086, 4178)(3087, 4179)(3088, 4180)(3089, 4181)(3090, 4182)(3091, 4183)(3092, 4184)(3093, 4185)(3094, 4186)(3095, 4187)(3096, 4188)(3097, 4189)(3098, 4190)(3099, 4191)(3100, 4192)(3101, 4193)(3102, 4194)(3103, 4195)(3104, 4196)(3105, 4197)(3106, 4198)(3107, 4199)(3108, 4200)(3109, 4201)(3110, 4202)(3111, 4203)(3112, 4204)(3113, 4205)(3114, 4206)(3115, 4207)(3116, 4208)(3117, 4209)(3118, 4210)(3119, 4211)(3120, 4212)(3121, 4213)(3122, 4214)(3123, 4215)(3124, 4216)(3125, 4217)(3126, 4218)(3127, 4219)(3128, 4220)(3129, 4221)(3130, 4222)(3131, 4223)(3132, 4224)(3133, 4225)(3134, 4226)(3135, 4227)(3136, 4228)(3137, 4229)(3138, 4230)(3139, 4231)(3140, 4232)(3141, 4233)(3142, 4234)(3143, 4235)(3144, 4236)(3145, 4237)(3146, 4238)(3147, 4239)(3148, 4240)(3149, 4241)(3150, 4242)(3151, 4243)(3152, 4244)(3153, 4245)(3154, 4246)(3155, 4247)(3156, 4248)(3157, 4249)(3158, 4250)(3159, 4251)(3160, 4252)(3161, 4253)(3162, 4254)(3163, 4255)(3164, 4256)(3165, 4257)(3166, 4258)(3167, 4259)(3168, 4260)(3169, 4261)(3170, 4262)(3171, 4263)(3172, 4264)(3173, 4265)(3174, 4266)(3175, 4267)(3176, 4268)(3177, 4269)(3178, 4270)(3179, 4271)(3180, 4272)(3181, 4273)(3182, 4274)(3183, 4275)(3184, 4276)(3185, 4277)(3186, 4278)(3187, 4279)(3188, 4280)(3189, 4281)(3190, 4282)(3191, 4283)(3192, 4284)(3193, 4285)(3194, 4286)(3195, 4287)(3196, 4288)(3197, 4289)(3198, 4290)(3199, 4291)(3200, 4292)(3201, 4293)(3202, 4294)(3203, 4295)(3204, 4296)(3205, 4297)(3206, 4298)(3207, 4299)(3208, 4300)(3209, 4301)(3210, 4302)(3211, 4303)(3212, 4304)(3213, 4305)(3214, 4306)(3215, 4307)(3216, 4308)(3217, 4309)(3218, 4310)(3219, 4311)(3220, 4312)(3221, 4313)(3222, 4314)(3223, 4315)(3224, 4316)(3225, 4317)(3226, 4318)(3227, 4319)(3228, 4320)(3229, 4321)(3230, 4322)(3231, 4323)(3232, 4324)(3233, 4325)(3234, 4326)(3235, 4327)(3236, 4328)(3237, 4329)(3238, 4330)(3239, 4331)(3240, 4332)(3241, 4333)(3242, 4334)(3243, 4335)(3244, 4336)(3245, 4337)(3246, 4338)(3247, 4339)(3248, 4340)(3249, 4341)(3250, 4342)(3251, 4343)(3252, 4344)(3253, 4345)(3254, 4346)(3255, 4347)(3256, 4348)(3257, 4349)(3258, 4350)(3259, 4351)(3260, 4352)(3261, 4353)(3262, 4354)(3263, 4355)(3264, 4356)(3265, 4357)(3266, 4358)(3267, 4359)(3268, 4360)(3269, 4361)(3270, 4362)(3271, 4363)(3272, 4364)(3273, 4365)(3274, 4366)(3275, 4367)(3276, 4368) L = (1, 2187)(2, 2190)(3, 2185)(4, 2193)(5, 2196)(6, 2186)(7, 2200)(8, 2197)(9, 2188)(10, 2203)(11, 2205)(12, 2189)(13, 2192)(14, 2206)(15, 2211)(16, 2191)(17, 2213)(18, 2216)(19, 2194)(20, 2218)(21, 2195)(22, 2198)(23, 2219)(24, 2224)(25, 2225)(26, 2227)(27, 2199)(28, 2228)(29, 2201)(30, 2232)(31, 2234)(32, 2202)(33, 2237)(34, 2204)(35, 2207)(36, 2238)(37, 2242)(38, 2243)(39, 2245)(40, 2208)(41, 2209)(42, 2248)(43, 2210)(44, 2212)(45, 2249)(46, 2253)(47, 2255)(48, 2214)(49, 2257)(50, 2215)(51, 2258)(52, 2262)(53, 2217)(54, 2220)(55, 2266)(56, 2267)(57, 2269)(58, 2221)(59, 2222)(60, 2272)(61, 2223)(62, 2273)(63, 2277)(64, 2226)(65, 2229)(66, 2256)(67, 2282)(68, 2283)(69, 2230)(70, 2287)(71, 2231)(72, 2250)(73, 2233)(74, 2235)(75, 2290)(76, 2294)(77, 2295)(78, 2236)(79, 2296)(80, 2300)(81, 2301)(82, 2239)(83, 2240)(84, 2304)(85, 2241)(86, 2305)(87, 2309)(88, 2244)(89, 2246)(90, 2278)(91, 2313)(92, 2315)(93, 2247)(94, 2274)(95, 2319)(96, 2320)(97, 2322)(98, 2251)(99, 2252)(100, 2325)(101, 2291)(102, 2327)(103, 2254)(104, 2328)(105, 2332)(106, 2259)(107, 2285)(108, 2336)(109, 2337)(110, 2260)(111, 2261)(112, 2263)(113, 2340)(114, 2344)(115, 2345)(116, 2264)(117, 2265)(118, 2347)(119, 2351)(120, 2268)(121, 2270)(122, 2310)(123, 2355)(124, 2357)(125, 2271)(126, 2306)(127, 2361)(128, 2362)(129, 2275)(130, 2365)(131, 2276)(132, 2366)(133, 2370)(134, 2371)(135, 2279)(136, 2280)(137, 2374)(138, 2281)(139, 2375)(140, 2379)(141, 2284)(142, 2382)(143, 2286)(144, 2288)(145, 2383)(146, 2387)(147, 2388)(148, 2289)(149, 2391)(150, 2392)(151, 2394)(152, 2292)(153, 2293)(154, 2397)(155, 2341)(156, 2297)(157, 2339)(158, 2402)(159, 2403)(160, 2298)(161, 2299)(162, 2406)(163, 2302)(164, 2352)(165, 2411)(166, 2413)(167, 2303)(168, 2348)(169, 2417)(170, 2418)(171, 2307)(172, 2421)(173, 2308)(174, 2422)(175, 2426)(176, 2427)(177, 2311)(178, 2312)(179, 2430)(180, 2384)(181, 2314)(182, 2316)(183, 2432)(184, 2436)(185, 2437)(186, 2317)(187, 2318)(188, 2439)(189, 2443)(190, 2321)(191, 2323)(192, 2380)(193, 2447)(194, 2449)(195, 2324)(196, 2376)(197, 2452)(198, 2326)(199, 2329)(200, 2364)(201, 2457)(202, 2458)(203, 2330)(204, 2331)(205, 2461)(206, 2464)(207, 2333)(208, 2334)(209, 2467)(210, 2335)(211, 2468)(212, 2472)(213, 2338)(214, 2475)(215, 2477)(216, 2478)(217, 2480)(218, 2342)(219, 2343)(220, 2483)(221, 2407)(222, 2346)(223, 2405)(224, 2487)(225, 2489)(226, 2490)(227, 2349)(228, 2493)(229, 2350)(230, 2494)(231, 2498)(232, 2499)(233, 2353)(234, 2354)(235, 2502)(236, 2433)(237, 2356)(238, 2358)(239, 2504)(240, 2508)(241, 2509)(242, 2359)(243, 2360)(244, 2511)(245, 2515)(246, 2363)(247, 2518)(248, 2367)(249, 2420)(250, 2522)(251, 2523)(252, 2368)(253, 2369)(254, 2526)(255, 2372)(256, 2444)(257, 2531)(258, 2533)(259, 2373)(260, 2440)(261, 2537)(262, 2538)(263, 2377)(264, 2541)(265, 2378)(266, 2542)(267, 2546)(268, 2381)(269, 2547)(270, 2551)(271, 2552)(272, 2554)(273, 2385)(274, 2386)(275, 2557)(276, 2462)(277, 2389)(278, 2460)(279, 2561)(280, 2390)(281, 2562)(282, 2566)(283, 2393)(284, 2395)(285, 2473)(286, 2570)(287, 2572)(288, 2396)(289, 2469)(290, 2575)(291, 2398)(292, 2577)(293, 2399)(294, 2400)(295, 2580)(296, 2401)(297, 2581)(298, 2585)(299, 2404)(300, 2588)(301, 2590)(302, 2591)(303, 2408)(304, 2594)(305, 2409)(306, 2410)(307, 2597)(308, 2505)(309, 2412)(310, 2414)(311, 2599)(312, 2603)(313, 2604)(314, 2415)(315, 2416)(316, 2606)(317, 2610)(318, 2419)(319, 2613)(320, 2423)(321, 2492)(322, 2617)(323, 2618)(324, 2424)(325, 2425)(326, 2621)(327, 2428)(328, 2516)(329, 2626)(330, 2628)(331, 2429)(332, 2512)(333, 2631)(334, 2431)(335, 2634)(336, 2635)(337, 2637)(338, 2434)(339, 2435)(340, 2640)(341, 2527)(342, 2438)(343, 2525)(344, 2644)(345, 2646)(346, 2647)(347, 2441)(348, 2650)(349, 2442)(350, 2651)(351, 2655)(352, 2608)(353, 2445)(354, 2446)(355, 2657)(356, 2548)(357, 2448)(358, 2450)(359, 2659)(360, 2663)(361, 2664)(362, 2451)(363, 2453)(364, 2540)(365, 2668)(366, 2670)(367, 2454)(368, 2455)(369, 2673)(370, 2456)(371, 2595)(372, 2676)(373, 2459)(374, 2679)(375, 2681)(376, 2682)(377, 2463)(378, 2465)(379, 2567)(380, 2687)(381, 2688)(382, 2466)(383, 2563)(384, 2624)(385, 2691)(386, 2470)(387, 2694)(388, 2471)(389, 2695)(390, 2699)(391, 2474)(392, 2700)(393, 2476)(394, 2703)(395, 2707)(396, 2479)(397, 2481)(398, 2586)(399, 2645)(400, 2711)(401, 2482)(402, 2582)(403, 2714)(404, 2484)(405, 2716)(406, 2485)(407, 2486)(408, 2719)(409, 2600)(410, 2488)(411, 2555)(412, 2728)(413, 2491)(414, 2951)(415, 2495)(416, 2593)(417, 2685)(418, 2954)(419, 2496)(420, 2497)(421, 2957)(422, 2500)(423, 2611)(424, 2536)(425, 2838)(426, 2501)(427, 2607)(428, 2962)(429, 2503)(430, 2965)(431, 2940)(432, 2705)(433, 2506)(434, 2507)(435, 2806)(436, 2622)(437, 2510)(438, 2620)(439, 2972)(440, 2568)(441, 2974)(442, 2513)(443, 2966)(444, 2514)(445, 2978)(446, 2982)(447, 2517)(448, 2984)(449, 2985)(450, 2519)(451, 2520)(452, 2937)(453, 2521)(454, 2717)(455, 2727)(456, 2524)(457, 2992)(458, 2995)(459, 2996)(460, 2528)(461, 2583)(462, 2529)(463, 2530)(464, 2842)(465, 2660)(466, 2532)(467, 2534)(468, 3002)(469, 2994)(470, 3005)(471, 2535)(472, 2722)(473, 2539)(474, 3007)(475, 2543)(476, 2649)(477, 2780)(478, 3012)(479, 2544)(480, 2545)(481, 3016)(482, 3019)(483, 3020)(484, 2549)(485, 2873)(486, 2550)(487, 2924)(488, 2756)(489, 2553)(490, 2677)(491, 2856)(492, 2556)(493, 2674)(494, 2949)(495, 2558)(496, 3032)(497, 2559)(498, 2560)(499, 3008)(500, 2741)(501, 2601)(502, 3034)(503, 2564)(504, 2565)(505, 3038)(506, 3041)(507, 2569)(508, 2773)(509, 2701)(510, 2571)(511, 2573)(512, 3045)(513, 2901)(514, 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4068)(1885, 4069)(1886, 4070)(1887, 4071)(1888, 4072)(1889, 4073)(1890, 4074)(1891, 4075)(1892, 4076)(1893, 4077)(1894, 4078)(1895, 4079)(1896, 4080)(1897, 4081)(1898, 4082)(1899, 4083)(1900, 4084)(1901, 4085)(1902, 4086)(1903, 4087)(1904, 4088)(1905, 4089)(1906, 4090)(1907, 4091)(1908, 4092)(1909, 4093)(1910, 4094)(1911, 4095)(1912, 4096)(1913, 4097)(1914, 4098)(1915, 4099)(1916, 4100)(1917, 4101)(1918, 4102)(1919, 4103)(1920, 4104)(1921, 4105)(1922, 4106)(1923, 4107)(1924, 4108)(1925, 4109)(1926, 4110)(1927, 4111)(1928, 4112)(1929, 4113)(1930, 4114)(1931, 4115)(1932, 4116)(1933, 4117)(1934, 4118)(1935, 4119)(1936, 4120)(1937, 4121)(1938, 4122)(1939, 4123)(1940, 4124)(1941, 4125)(1942, 4126)(1943, 4127)(1944, 4128)(1945, 4129)(1946, 4130)(1947, 4131)(1948, 4132)(1949, 4133)(1950, 4134)(1951, 4135)(1952, 4136)(1953, 4137)(1954, 4138)(1955, 4139)(1956, 4140)(1957, 4141)(1958, 4142)(1959, 4143)(1960, 4144)(1961, 4145)(1962, 4146)(1963, 4147)(1964, 4148)(1965, 4149)(1966, 4150)(1967, 4151)(1968, 4152)(1969, 4153)(1970, 4154)(1971, 4155)(1972, 4156)(1973, 4157)(1974, 4158)(1975, 4159)(1976, 4160)(1977, 4161)(1978, 4162)(1979, 4163)(1980, 4164)(1981, 4165)(1982, 4166)(1983, 4167)(1984, 4168)(1985, 4169)(1986, 4170)(1987, 4171)(1988, 4172)(1989, 4173)(1990, 4174)(1991, 4175)(1992, 4176)(1993, 4177)(1994, 4178)(1995, 4179)(1996, 4180)(1997, 4181)(1998, 4182)(1999, 4183)(2000, 4184)(2001, 4185)(2002, 4186)(2003, 4187)(2004, 4188)(2005, 4189)(2006, 4190)(2007, 4191)(2008, 4192)(2009, 4193)(2010, 4194)(2011, 4195)(2012, 4196)(2013, 4197)(2014, 4198)(2015, 4199)(2016, 4200)(2017, 4201)(2018, 4202)(2019, 4203)(2020, 4204)(2021, 4205)(2022, 4206)(2023, 4207)(2024, 4208)(2025, 4209)(2026, 4210)(2027, 4211)(2028, 4212)(2029, 4213)(2030, 4214)(2031, 4215)(2032, 4216)(2033, 4217)(2034, 4218)(2035, 4219)(2036, 4220)(2037, 4221)(2038, 4222)(2039, 4223)(2040, 4224)(2041, 4225)(2042, 4226)(2043, 4227)(2044, 4228)(2045, 4229)(2046, 4230)(2047, 4231)(2048, 4232)(2049, 4233)(2050, 4234)(2051, 4235)(2052, 4236)(2053, 4237)(2054, 4238)(2055, 4239)(2056, 4240)(2057, 4241)(2058, 4242)(2059, 4243)(2060, 4244)(2061, 4245)(2062, 4246)(2063, 4247)(2064, 4248)(2065, 4249)(2066, 4250)(2067, 4251)(2068, 4252)(2069, 4253)(2070, 4254)(2071, 4255)(2072, 4256)(2073, 4257)(2074, 4258)(2075, 4259)(2076, 4260)(2077, 4261)(2078, 4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E14.638 Graph:: simple bipartite v = 1248 e = 2184 f = 910 degree seq :: [ 2^1092, 14^156 ] E14.647 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, (Y3 * Y1^-1)^3, Y1^7, (Y3 * Y1^2 * Y3 * Y1^-3 * Y3 * Y1^2 * Y3 * Y1^-2)^2, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^3 * Y3 * Y1^2 * Y3 * Y1^-2 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-2 ] Map:: polytopal R = (1, 1093, 2, 1094, 5, 1097, 11, 1103, 20, 1112, 10, 1102, 4, 1096)(3, 1095, 7, 1099, 15, 1107, 26, 1118, 30, 1122, 17, 1109, 8, 1100)(6, 1098, 13, 1105, 24, 1116, 39, 1131, 42, 1134, 25, 1117, 14, 1106)(9, 1101, 18, 1110, 31, 1123, 49, 1141, 46, 1138, 28, 1120, 16, 1108)(12, 1104, 22, 1114, 37, 1129, 57, 1149, 60, 1152, 38, 1130, 23, 1115)(19, 1111, 33, 1125, 52, 1144, 77, 1169, 76, 1168, 51, 1143, 32, 1124)(21, 1113, 35, 1127, 55, 1147, 81, 1173, 84, 1176, 56, 1148, 36, 1128)(27, 1119, 44, 1136, 67, 1159, 97, 1189, 100, 1192, 68, 1160, 45, 1137)(29, 1121, 47, 1139, 70, 1162, 102, 1194, 91, 1183, 62, 1154, 40, 1132)(34, 1126, 54, 1146, 80, 1172, 115, 1207, 114, 1206, 79, 1171, 53, 1145)(41, 1133, 63, 1155, 92, 1184, 130, 1222, 123, 1215, 86, 1178, 58, 1150)(43, 1135, 65, 1157, 95, 1187, 134, 1226, 137, 1229, 96, 1188, 66, 1158)(48, 1140, 72, 1164, 105, 1197, 147, 1239, 146, 1238, 104, 1196, 71, 1163)(50, 1142, 74, 1166, 108, 1200, 151, 1243, 154, 1246, 109, 1201, 75, 1167)(59, 1151, 87, 1179, 124, 1216, 172, 1264, 165, 1257, 118, 1210, 82, 1174)(61, 1153, 89, 1181, 127, 1219, 176, 1268, 179, 1271, 128, 1220, 90, 1182)(64, 1156, 94, 1186, 133, 1225, 185, 1277, 184, 1276, 132, 1224, 93, 1185)(69, 1161, 101, 1193, 142, 1234, 197, 1289, 193, 1285, 139, 1231, 98, 1190)(73, 1165, 106, 1198, 149, 1241, 206, 1298, 209, 1301, 150, 1242, 107, 1199)(78, 1170, 112, 1204, 158, 1250, 217, 1309, 220, 1312, 159, 1251, 113, 1205)(83, 1175, 119, 1211, 166, 1258, 228, 1320, 224, 1316, 162, 1254, 116, 1208)(85, 1177, 121, 1213, 169, 1261, 232, 1324, 235, 1327, 170, 1262, 122, 1214)(88, 1180, 126, 1218, 175, 1267, 241, 1333, 240, 1332, 174, 1266, 125, 1217)(99, 1191, 140, 1232, 194, 1286, 264, 1356, 257, 1349, 188, 1280, 135, 1227)(103, 1195, 144, 1236, 201, 1293, 272, 1364, 275, 1367, 202, 1294, 145, 1237)(110, 1202, 155, 1247, 214, 1306, 290, 1382, 286, 1378, 211, 1303, 152, 1244)(111, 1203, 156, 1248, 215, 1307, 292, 1384, 295, 1387, 216, 1308, 157, 1249)(117, 1209, 163, 1255, 225, 1317, 304, 1396, 307, 1399, 226, 1318, 164, 1256)(120, 1212, 168, 1260, 231, 1323, 313, 1405, 312, 1404, 230, 1322, 167, 1259)(129, 1221, 180, 1272, 247, 1339, 333, 1425, 329, 1421, 244, 1336, 177, 1269)(131, 1223, 182, 1274, 250, 1342, 337, 1429, 340, 1432, 251, 1343, 183, 1275)(136, 1228, 189, 1281, 258, 1350, 348, 1440, 279, 1371, 205, 1297, 148, 1240)(138, 1230, 191, 1283, 261, 1353, 352, 1444, 355, 1447, 262, 1354, 192, 1284)(141, 1233, 196, 1288, 267, 1359, 361, 1453, 360, 1452, 266, 1358, 195, 1287)(143, 1235, 199, 1291, 270, 1362, 366, 1458, 369, 1461, 271, 1363, 200, 1292)(153, 1245, 212, 1304, 287, 1379, 387, 1479, 380, 1472, 281, 1373, 207, 1299)(160, 1252, 221, 1313, 300, 1392, 403, 1495, 399, 1491, 297, 1389, 218, 1310)(161, 1253, 222, 1314, 301, 1393, 405, 1497, 408, 1500, 302, 1394, 223, 1315)(171, 1263, 236, 1328, 319, 1411, 428, 1520, 424, 1516, 316, 1408, 233, 1325)(173, 1265, 238, 1330, 322, 1414, 432, 1524, 435, 1527, 323, 1415, 239, 1331)(178, 1270, 245, 1337, 330, 1422, 443, 1535, 344, 1436, 254, 1346, 186, 1278)(181, 1273, 248, 1340, 335, 1427, 449, 1541, 452, 1544, 336, 1428, 249, 1341)(187, 1279, 255, 1347, 345, 1437, 461, 1553, 464, 1556, 346, 1438, 256, 1348)(190, 1282, 260, 1352, 351, 1443, 470, 1562, 469, 1561, 350, 1442, 259, 1351)(198, 1290, 208, 1300, 282, 1374, 381, 1473, 487, 1579, 365, 1457, 269, 1361)(203, 1295, 276, 1368, 374, 1466, 498, 1590, 494, 1586, 371, 1463, 273, 1365)(204, 1296, 277, 1369, 375, 1467, 500, 1592, 503, 1595, 376, 1468, 278, 1370)(210, 1302, 284, 1376, 384, 1476, 511, 1603, 514, 1606, 385, 1477, 285, 1377)(213, 1305, 289, 1381, 390, 1482, 520, 1612, 519, 1611, 389, 1481, 288, 1380)(219, 1311, 298, 1390, 400, 1492, 534, 1626, 527, 1619, 394, 1486, 293, 1385)(227, 1319, 308, 1400, 414, 1506, 744, 1836, 603, 1695, 411, 1503, 305, 1397)(229, 1321, 310, 1402, 417, 1509, 793, 1885, 1087, 2179, 418, 1510, 311, 1403)(234, 1326, 317, 1409, 425, 1517, 800, 1892, 439, 1531, 326, 1418, 242, 1334)(237, 1329, 320, 1412, 430, 1522, 624, 1716, 990, 2082, 431, 1523, 321, 1413)(243, 1335, 327, 1419, 440, 1532, 816, 1908, 1060, 2152, 441, 1533, 328, 1420)(246, 1338, 332, 1424, 446, 1538, 590, 1682, 997, 2089, 445, 1537, 331, 1423)(252, 1344, 341, 1433, 457, 1549, 616, 1708, 693, 1785, 454, 1546, 338, 1430)(253, 1345, 342, 1434, 458, 1550, 739, 1831, 1022, 2114, 459, 1551, 343, 1435)(263, 1355, 356, 1448, 476, 1568, 679, 1771, 640, 1732, 473, 1565, 353, 1445)(265, 1357, 358, 1450, 479, 1571, 857, 1949, 794, 1886, 480, 1572, 359, 1451)(268, 1360, 363, 1455, 484, 1576, 673, 1765, 975, 2067, 485, 1577, 364, 1456)(274, 1366, 372, 1464, 495, 1587, 877, 1969, 589, 1681, 489, 1581, 367, 1459)(280, 1372, 378, 1470, 505, 1597, 864, 1956, 1037, 2129, 506, 1598, 379, 1471)(283, 1375, 383, 1475, 510, 1602, 593, 1685, 757, 1849, 509, 1601, 382, 1474)(291, 1383, 294, 1386, 395, 1487, 528, 1620, 903, 1995, 524, 1616, 392, 1484)(296, 1388, 397, 1489, 531, 1623, 905, 1997, 1086, 2178, 532, 1624, 398, 1490)(299, 1391, 402, 1494, 537, 1629, 584, 1676, 985, 2077, 536, 1628, 401, 1493)(303, 1395, 409, 1501, 544, 1636, 807, 1899, 583, 1675, 541, 1633, 406, 1498)(306, 1398, 412, 1504, 760, 1852, 1045, 2137, 633, 1725, 421, 1513, 314, 1406)(309, 1401, 415, 1507, 581, 1673, 604, 1696, 1008, 2100, 995, 2087, 416, 1508)(315, 1407, 422, 1514, 654, 1746, 1049, 2141, 1071, 2163, 984, 2076, 423, 1515)(318, 1410, 427, 1519, 660, 1752, 571, 1663, 962, 2054, 942, 2034, 426, 1518)(324, 1416, 436, 1528, 813, 1905, 631, 1723, 731, 1823, 1028, 2120, 433, 1525)(325, 1417, 437, 1529, 575, 1667, 798, 1890, 1000, 2092, 668, 1760, 438, 1530)(334, 1426, 368, 1460, 490, 1582, 872, 1964, 906, 1998, 751, 1843, 448, 1540)(339, 1431, 455, 1547, 829, 1921, 535, 1627, 570, 1662, 876, 1968, 450, 1542)(347, 1439, 465, 1557, 840, 1932, 866, 1958, 597, 1689, 651, 1743, 462, 1554)(349, 1441, 467, 1559, 844, 1936, 971, 2063, 1088, 2180, 811, 1903, 468, 1560)(354, 1446, 474, 1566, 849, 1941, 791, 1883, 607, 1699, 483, 1575, 362, 1454)(357, 1449, 477, 1569, 563, 1655, 641, 1733, 970, 2062, 814, 1906, 478, 1570)(370, 1462, 492, 1584, 741, 1833, 1015, 2107, 1091, 2183, 972, 2064, 493, 1585)(373, 1465, 497, 1589, 618, 1710, 566, 1658, 952, 2044, 935, 2027, 496, 1588)(377, 1469, 504, 1596, 884, 1976, 951, 2043, 565, 1657, 717, 1809, 501, 1593)(386, 1478, 515, 1607, 892, 1984, 726, 1818, 638, 1730, 714, 1806, 512, 1604)(388, 1480, 517, 1609, 895, 1987, 806, 1898, 434, 1526, 809, 1901, 518, 1610)(391, 1483, 522, 1614, 557, 1649, 709, 1801, 955, 2047, 695, 1787, 523, 1615)(393, 1485, 525, 1617, 620, 1712, 1035, 2127, 1048, 2140, 702, 1794, 526, 1618)(396, 1488, 530, 1622, 785, 1877, 579, 1671, 894, 1986, 953, 2045, 529, 1621)(404, 1496, 407, 1499, 542, 1634, 764, 1856, 1059, 2151, 657, 1749, 539, 1631)(410, 1502, 700, 1792, 683, 1775, 859, 1951, 1080, 2172, 902, 1994, 749, 1841)(413, 1505, 790, 1882, 690, 1782, 561, 1653, 943, 2035, 927, 2019, 788, 1880)(419, 1511, 796, 1888, 1020, 2112, 655, 1747, 724, 1816, 899, 1991, 756, 1848)(420, 1512, 797, 1889, 562, 1654, 912, 2004, 968, 2060, 642, 1734, 855, 1947)(429, 1521, 451, 1543, 827, 1919, 521, 1613, 513, 1605, 822, 1914, 847, 1939)(442, 1534, 819, 1911, 936, 2028, 769, 1861, 612, 1704, 684, 1776, 773, 1865)(444, 1536, 574, 1666, 969, 2061, 946, 2038, 860, 1952, 910, 2002, 988, 2080)(447, 1539, 824, 1916, 553, 1645, 663, 1755, 945, 2037, 759, 1851, 889, 1981)(453, 1545, 598, 1690, 802, 1894, 983, 2075, 1092, 2184, 869, 1961, 1051, 2143)(456, 1548, 832, 1924, 508, 1600, 577, 1669, 973, 2065, 949, 2041, 830, 1922)(460, 1552, 836, 1928, 516, 1608, 893, 1985, 576, 1668, 667, 1759, 834, 1926)(463, 1555, 838, 1930, 696, 1788, 1066, 2158, 671, 1763, 804, 1896, 471, 1563)(466, 1558, 842, 1934, 601, 1693, 613, 1705, 1027, 2119, 901, 1993, 885, 1977)(472, 1564, 649, 1741, 704, 1796, 799, 1891, 1085, 2177, 950, 2042, 835, 1927)(475, 1567, 852, 1944, 646, 1738, 558, 1650, 938, 2030, 924, 2016, 850, 1942)(481, 1573, 862, 1954, 1038, 2130, 623, 1715, 843, 1935, 1016, 2108, 858, 1950)(482, 1574, 863, 1955, 586, 1678, 989, 2081, 1014, 2106, 629, 1721, 1042, 2134)(486, 1578, 867, 1959, 931, 2023, 837, 1929, 556, 1648, 780, 1872, 865, 1957)(488, 1580, 871, 1963, 596, 1688, 1007, 2099, 1033, 2125, 652, 1744, 1057, 2149)(491, 1583, 875, 1967, 882, 1974, 600, 1692, 1011, 2103, 986, 2078, 873, 1965)(499, 1591, 502, 1594, 881, 1973, 721, 1813, 1077, 2169, 707, 1799, 782, 1874)(507, 1599, 888, 1980, 820, 1912, 991, 2083, 587, 1679, 628, 1720, 887, 1979)(533, 1625, 908, 2000, 996, 2088, 686, 1778, 677, 1769, 762, 1854, 713, 1805)(538, 1630, 911, 2003, 551, 1643, 778, 1870, 941, 2033, 664, 1756, 768, 1860)(540, 1632, 737, 1829, 648, 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4326)(3235, 4327)(3236, 4328)(3237, 4329)(3238, 4330)(3239, 4331)(3240, 4332)(3241, 4333)(3242, 4334)(3243, 4335)(3244, 4336)(3245, 4337)(3246, 4338)(3247, 4339)(3248, 4340)(3249, 4341)(3250, 4342)(3251, 4343)(3252, 4344)(3253, 4345)(3254, 4346)(3255, 4347)(3256, 4348)(3257, 4349)(3258, 4350)(3259, 4351)(3260, 4352)(3261, 4353)(3262, 4354)(3263, 4355)(3264, 4356)(3265, 4357)(3266, 4358)(3267, 4359)(3268, 4360)(3269, 4361)(3270, 4362)(3271, 4363)(3272, 4364)(3273, 4365)(3274, 4366)(3275, 4367)(3276, 4368) L = (1, 2187)(2, 2190)(3, 2185)(4, 2193)(5, 2196)(6, 2186)(7, 2200)(8, 2197)(9, 2188)(10, 2203)(11, 2205)(12, 2189)(13, 2192)(14, 2206)(15, 2211)(16, 2191)(17, 2213)(18, 2216)(19, 2194)(20, 2218)(21, 2195)(22, 2198)(23, 2219)(24, 2224)(25, 2225)(26, 2227)(27, 2199)(28, 2228)(29, 2201)(30, 2232)(31, 2234)(32, 2202)(33, 2237)(34, 2204)(35, 2207)(36, 2238)(37, 2242)(38, 2243)(39, 2245)(40, 2208)(41, 2209)(42, 2248)(43, 2210)(44, 2212)(45, 2249)(46, 2253)(47, 2255)(48, 2214)(49, 2257)(50, 2215)(51, 2258)(52, 2262)(53, 2217)(54, 2220)(55, 2266)(56, 2267)(57, 2269)(58, 2221)(59, 2222)(60, 2272)(61, 2223)(62, 2273)(63, 2277)(64, 2226)(65, 2229)(66, 2256)(67, 2282)(68, 2283)(69, 2230)(70, 2287)(71, 2231)(72, 2250)(73, 2233)(74, 2235)(75, 2290)(76, 2294)(77, 2295)(78, 2236)(79, 2296)(80, 2300)(81, 2301)(82, 2239)(83, 2240)(84, 2304)(85, 2241)(86, 2305)(87, 2309)(88, 2244)(89, 2246)(90, 2278)(91, 2313)(92, 2315)(93, 2247)(94, 2274)(95, 2319)(96, 2320)(97, 2322)(98, 2251)(99, 2252)(100, 2325)(101, 2291)(102, 2327)(103, 2254)(104, 2328)(105, 2332)(106, 2259)(107, 2285)(108, 2336)(109, 2337)(110, 2260)(111, 2261)(112, 2263)(113, 2340)(114, 2344)(115, 2345)(116, 2264)(117, 2265)(118, 2347)(119, 2351)(120, 2268)(121, 2270)(122, 2310)(123, 2355)(124, 2357)(125, 2271)(126, 2306)(127, 2361)(128, 2362)(129, 2275)(130, 2365)(131, 2276)(132, 2366)(133, 2370)(134, 2371)(135, 2279)(136, 2280)(137, 2374)(138, 2281)(139, 2375)(140, 2379)(141, 2284)(142, 2382)(143, 2286)(144, 2288)(145, 2383)(146, 2387)(147, 2388)(148, 2289)(149, 2391)(150, 2392)(151, 2394)(152, 2292)(153, 2293)(154, 2397)(155, 2341)(156, 2297)(157, 2339)(158, 2402)(159, 2403)(160, 2298)(161, 2299)(162, 2406)(163, 2302)(164, 2352)(165, 2411)(166, 2413)(167, 2303)(168, 2348)(169, 2417)(170, 2418)(171, 2307)(172, 2421)(173, 2308)(174, 2422)(175, 2426)(176, 2427)(177, 2311)(178, 2312)(179, 2430)(180, 2384)(181, 2314)(182, 2316)(183, 2432)(184, 2436)(185, 2437)(186, 2317)(187, 2318)(188, 2439)(189, 2443)(190, 2321)(191, 2323)(192, 2380)(193, 2447)(194, 2449)(195, 2324)(196, 2376)(197, 2452)(198, 2326)(199, 2329)(200, 2364)(201, 2457)(202, 2458)(203, 2330)(204, 2331)(205, 2461)(206, 2464)(207, 2333)(208, 2334)(209, 2467)(210, 2335)(211, 2468)(212, 2472)(213, 2338)(214, 2475)(215, 2477)(216, 2478)(217, 2480)(218, 2342)(219, 2343)(220, 2483)(221, 2407)(222, 2346)(223, 2405)(224, 2487)(225, 2489)(226, 2490)(227, 2349)(228, 2493)(229, 2350)(230, 2494)(231, 2498)(232, 2499)(233, 2353)(234, 2354)(235, 2502)(236, 2433)(237, 2356)(238, 2358)(239, 2504)(240, 2508)(241, 2509)(242, 2359)(243, 2360)(244, 2511)(245, 2515)(246, 2363)(247, 2518)(248, 2367)(249, 2420)(250, 2522)(251, 2523)(252, 2368)(253, 2369)(254, 2526)(255, 2372)(256, 2444)(257, 2531)(258, 2533)(259, 2373)(260, 2440)(261, 2537)(262, 2538)(263, 2377)(264, 2541)(265, 2378)(266, 2542)(267, 2546)(268, 2381)(269, 2547)(270, 2551)(271, 2552)(272, 2554)(273, 2385)(274, 2386)(275, 2557)(276, 2462)(277, 2389)(278, 2460)(279, 2561)(280, 2390)(281, 2562)(282, 2566)(283, 2393)(284, 2395)(285, 2473)(286, 2570)(287, 2572)(288, 2396)(289, 2469)(290, 2575)(291, 2398)(292, 2577)(293, 2399)(294, 2400)(295, 2580)(296, 2401)(297, 2581)(298, 2585)(299, 2404)(300, 2588)(301, 2590)(302, 2591)(303, 2408)(304, 2594)(305, 2409)(306, 2410)(307, 2597)(308, 2505)(309, 2412)(310, 2414)(311, 2599)(312, 2603)(313, 2604)(314, 2415)(315, 2416)(316, 2606)(317, 2610)(318, 2419)(319, 2613)(320, 2423)(321, 2492)(322, 2617)(323, 2618)(324, 2424)(325, 2425)(326, 2621)(327, 2428)(328, 2516)(329, 2626)(330, 2628)(331, 2429)(332, 2512)(333, 2631)(334, 2431)(335, 2634)(336, 2635)(337, 2637)(338, 2434)(339, 2435)(340, 2640)(341, 2527)(342, 2438)(343, 2525)(344, 2644)(345, 2646)(346, 2647)(347, 2441)(348, 2650)(349, 2442)(350, 2651)(351, 2655)(352, 2656)(353, 2445)(354, 2446)(355, 2659)(356, 2548)(357, 2448)(358, 2450)(359, 2661)(360, 2665)(361, 2666)(362, 2451)(363, 2453)(364, 2540)(365, 2670)(366, 2672)(367, 2454)(368, 2455)(369, 2675)(370, 2456)(371, 2676)(372, 2680)(373, 2459)(374, 2683)(375, 2685)(376, 2686)(377, 2463)(378, 2465)(379, 2567)(380, 2691)(381, 2692)(382, 2466)(383, 2563)(384, 2696)(385, 2697)(386, 2470)(387, 2700)(388, 2471)(389, 2701)(390, 2705)(391, 2474)(392, 2706)(393, 2476)(394, 2709)(395, 2713)(396, 2479)(397, 2481)(398, 2586)(399, 2717)(400, 2719)(401, 2482)(402, 2582)(403, 2722)(404, 2484)(405, 2724)(406, 2485)(407, 2486)(408, 2727)(409, 2600)(410, 2488)(411, 2884)(412, 2972)(413, 2491)(414, 2975)(415, 2495)(416, 2593)(417, 2940)(418, 2978)(419, 2496)(420, 2497)(421, 2981)(422, 2500)(423, 2611)(424, 2983)(425, 2911)(426, 2501)(427, 2607)(428, 2987)(429, 2503)(430, 2990)(431, 2791)(432, 2785)(433, 2506)(434, 2507)(435, 2995)(436, 2622)(437, 2510)(438, 2620)(439, 2998)(440, 2957)(441, 3001)(442, 2513)(443, 3004)(444, 2514)(445, 2758)(446, 2968)(447, 2517)(448, 3008)(449, 3010)(450, 2519)(451, 2520)(452, 2783)(453, 2521)(454, 2782)(455, 3014)(456, 2524)(457, 2937)(458, 3018)(459, 2881)(460, 2528)(461, 2861)(462, 2529)(463, 2530)(464, 2818)(465, 2662)(466, 2532)(467, 2534)(468, 3026)(469, 2900)(470, 3030)(471, 2535)(472, 2536)(473, 2833)(474, 3034)(475, 2539)(476, 3038)(477, 2543)(478, 2649)(479, 3042)(480, 3044)(481, 2544)(482, 2545)(483, 3047)(484, 3049)(485, 2828)(486, 2549)(487, 3053)(488, 2550)(489, 3055)(490, 3057)(491, 2553)(492, 2555)(493, 2681)(494, 3043)(495, 3021)(496, 2556)(497, 2677)(498, 3063)(499, 2558)(500, 3037)(501, 2559)(502, 2560)(503, 2776)(504, 3069)(505, 3071)(506, 2945)(507, 2564)(508, 2565)(509, 2761)(510, 2873)(511, 2796)(512, 2568)(513, 2569)(514, 2892)(515, 2707)(516, 2571)(517, 2573)(518, 3077)(519, 2811)(520, 3081)(521, 2574)(522, 2576)(523, 2699)(524, 3012)(525, 2578)(526, 2714)(527, 3085)(528, 2802)(529, 2579)(530, 2710)(531, 2897)(532, 3090)(533, 2583)(534, 3068)(535, 2584)(536, 2754)(537, 3056)(538, 2587)(539, 3095)(540, 2589)(541, 2921)(542, 3097)(543, 2592)(544, 3061)(545, 3101)(546, 3102)(547, 3103)(548, 3104)(549, 3106)(550, 3108)(551, 3109)(552, 3111)(553, 3112)(554, 3114)(555, 3117)(556, 3119)(557, 3121)(558, 3123)(559, 3125)(560, 3126)(561, 3128)(562, 3129)(563, 3130)(564, 3131)(565, 3133)(566, 3137)(567, 3139)(568, 3142)(569, 3143)(570, 2720)(571, 3147)(572, 3148)(573, 3152)(574, 2629)(575, 3154)(576, 3155)(577, 2693)(578, 3159)(579, 3161)(580, 3163)(581, 3041)(582, 3164)(583, 3167)(584, 3170)(585, 3171)(586, 3174)(587, 2977)(588, 3176)(589, 3179)(590, 3182)(591, 3184)(592, 2687)(593, 3186)(594, 3188)(595, 3190)(596, 3192)(597, 3089)(598, 2638)(599, 2636)(600, 3196)(601, 2616)(602, 3198)(603, 3199)(604, 3200)(605, 3201)(606, 3166)(607, 2615)(608, 3206)(609, 3023)(610, 3208)(611, 3169)(612, 2695)(613, 3212)(614, 3214)(615, 3217)(616, 3189)(617, 3215)(618, 2712)(619, 3203)(620, 3211)(621, 3178)(622, 3221)(623, 3216)(624, 3223)(625, 3064)(626, 3150)(627, 2703)(628, 3083)(629, 3032)(630, 3227)(631, 3207)(632, 3145)(633, 2943)(634, 2648)(635, 2912)(636, 2989)(637, 3136)(638, 3000)(639, 3232)(640, 3233)(641, 3234)(642, 2967)(643, 3074)(644, 2669)(645, 3066)(646, 2948)(647, 3224)(648, 2986)(649, 2657)(650, 3197)(651, 2946)(652, 3238)(653, 3240)(654, 2888)(655, 3220)(656, 3054)(657, 2949)(658, 3244)(659, 2969)(660, 2905)(661, 3236)(662, 3157)(663, 3245)(664, 2904)(665, 2938)(666, 3181)(667, 3248)(668, 2918)(669, 3249)(670, 3118)(671, 2879)(672, 3183)(673, 3251)(674, 2874)(675, 2927)(676, 3122)(677, 2645)(678, 3253)(679, 3144)(680, 3222)(681, 2944)(682, 3005)(683, 2925)(684, 2898)(685, 3218)(686, 3202)(687, 2934)(688, 3255)(689, 2694)(690, 2858)(691, 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2994)(783, 2826)(784, 2630)(785, 2843)(786, 2960)(787, 3029)(788, 2596)(789, 3141)(790, 2933)(791, 2598)(792, 3247)(793, 2771)(794, 2602)(795, 3138)(796, 3039)(797, 2605)(798, 3017)(799, 2608)(800, 3024)(801, 3084)(802, 2832)(803, 2612)(804, 3140)(805, 2820)(806, 2614)(807, 3115)(808, 3180)(809, 3272)(810, 2966)(811, 2619)(812, 2926)(813, 2894)(814, 2623)(815, 2956)(816, 2822)(817, 2625)(818, 3099)(819, 3073)(820, 2627)(821, 2866)(822, 3067)(823, 3275)(824, 2632)(825, 3273)(826, 2633)(827, 3194)(828, 2708)(829, 3135)(830, 2639)(831, 2942)(832, 3235)(833, 2982)(834, 2642)(835, 3036)(836, 3072)(837, 2679)(838, 2913)(839, 2793)(840, 2984)(841, 3079)(842, 2652)(843, 3191)(844, 2876)(845, 2971)(846, 2654)(847, 3052)(848, 2813)(849, 2954)(850, 2658)(851, 3113)(852, 3019)(853, 2684)(854, 2660)(855, 2980)(856, 2901)(857, 2765)(858, 2663)(859, 2678)(860, 2664)(861, 3105)(862, 3226)(863, 2667)(864, 2908)(865, 2668)(866, 3149)(867, 3276)(868, 3031)(869, 2671)(870, 2840)(871, 2673)(872, 2721)(873, 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3566)(1383, 3567)(1384, 3568)(1385, 3569)(1386, 3570)(1387, 3571)(1388, 3572)(1389, 3573)(1390, 3574)(1391, 3575)(1392, 3576)(1393, 3577)(1394, 3578)(1395, 3579)(1396, 3580)(1397, 3581)(1398, 3582)(1399, 3583)(1400, 3584)(1401, 3585)(1402, 3586)(1403, 3587)(1404, 3588)(1405, 3589)(1406, 3590)(1407, 3591)(1408, 3592)(1409, 3593)(1410, 3594)(1411, 3595)(1412, 3596)(1413, 3597)(1414, 3598)(1415, 3599)(1416, 3600)(1417, 3601)(1418, 3602)(1419, 3603)(1420, 3604)(1421, 3605)(1422, 3606)(1423, 3607)(1424, 3608)(1425, 3609)(1426, 3610)(1427, 3611)(1428, 3612)(1429, 3613)(1430, 3614)(1431, 3615)(1432, 3616)(1433, 3617)(1434, 3618)(1435, 3619)(1436, 3620)(1437, 3621)(1438, 3622)(1439, 3623)(1440, 3624)(1441, 3625)(1442, 3626)(1443, 3627)(1444, 3628)(1445, 3629)(1446, 3630)(1447, 3631)(1448, 3632)(1449, 3633)(1450, 3634)(1451, 3635)(1452, 3636)(1453, 3637)(1454, 3638)(1455, 3639)(1456, 3640)(1457, 3641)(1458, 3642)(1459, 3643)(1460, 3644)(1461, 3645)(1462, 3646)(1463, 3647)(1464, 3648)(1465, 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3732)(1549, 3733)(1550, 3734)(1551, 3735)(1552, 3736)(1553, 3737)(1554, 3738)(1555, 3739)(1556, 3740)(1557, 3741)(1558, 3742)(1559, 3743)(1560, 3744)(1561, 3745)(1562, 3746)(1563, 3747)(1564, 3748)(1565, 3749)(1566, 3750)(1567, 3751)(1568, 3752)(1569, 3753)(1570, 3754)(1571, 3755)(1572, 3756)(1573, 3757)(1574, 3758)(1575, 3759)(1576, 3760)(1577, 3761)(1578, 3762)(1579, 3763)(1580, 3764)(1581, 3765)(1582, 3766)(1583, 3767)(1584, 3768)(1585, 3769)(1586, 3770)(1587, 3771)(1588, 3772)(1589, 3773)(1590, 3774)(1591, 3775)(1592, 3776)(1593, 3777)(1594, 3778)(1595, 3779)(1596, 3780)(1597, 3781)(1598, 3782)(1599, 3783)(1600, 3784)(1601, 3785)(1602, 3786)(1603, 3787)(1604, 3788)(1605, 3789)(1606, 3790)(1607, 3791)(1608, 3792)(1609, 3793)(1610, 3794)(1611, 3795)(1612, 3796)(1613, 3797)(1614, 3798)(1615, 3799)(1616, 3800)(1617, 3801)(1618, 3802)(1619, 3803)(1620, 3804)(1621, 3805)(1622, 3806)(1623, 3807)(1624, 3808)(1625, 3809)(1626, 3810)(1627, 3811)(1628, 3812)(1629, 3813)(1630, 3814)(1631, 3815)(1632, 3816)(1633, 3817)(1634, 3818)(1635, 3819)(1636, 3820)(1637, 3821)(1638, 3822)(1639, 3823)(1640, 3824)(1641, 3825)(1642, 3826)(1643, 3827)(1644, 3828)(1645, 3829)(1646, 3830)(1647, 3831)(1648, 3832)(1649, 3833)(1650, 3834)(1651, 3835)(1652, 3836)(1653, 3837)(1654, 3838)(1655, 3839)(1656, 3840)(1657, 3841)(1658, 3842)(1659, 3843)(1660, 3844)(1661, 3845)(1662, 3846)(1663, 3847)(1664, 3848)(1665, 3849)(1666, 3850)(1667, 3851)(1668, 3852)(1669, 3853)(1670, 3854)(1671, 3855)(1672, 3856)(1673, 3857)(1674, 3858)(1675, 3859)(1676, 3860)(1677, 3861)(1678, 3862)(1679, 3863)(1680, 3864)(1681, 3865)(1682, 3866)(1683, 3867)(1684, 3868)(1685, 3869)(1686, 3870)(1687, 3871)(1688, 3872)(1689, 3873)(1690, 3874)(1691, 3875)(1692, 3876)(1693, 3877)(1694, 3878)(1695, 3879)(1696, 3880)(1697, 3881)(1698, 3882)(1699, 3883)(1700, 3884)(1701, 3885)(1702, 3886)(1703, 3887)(1704, 3888)(1705, 3889)(1706, 3890)(1707, 3891)(1708, 3892)(1709, 3893)(1710, 3894)(1711, 3895)(1712, 3896)(1713, 3897)(1714, 3898)(1715, 3899)(1716, 3900)(1717, 3901)(1718, 3902)(1719, 3903)(1720, 3904)(1721, 3905)(1722, 3906)(1723, 3907)(1724, 3908)(1725, 3909)(1726, 3910)(1727, 3911)(1728, 3912)(1729, 3913)(1730, 3914)(1731, 3915)(1732, 3916)(1733, 3917)(1734, 3918)(1735, 3919)(1736, 3920)(1737, 3921)(1738, 3922)(1739, 3923)(1740, 3924)(1741, 3925)(1742, 3926)(1743, 3927)(1744, 3928)(1745, 3929)(1746, 3930)(1747, 3931)(1748, 3932)(1749, 3933)(1750, 3934)(1751, 3935)(1752, 3936)(1753, 3937)(1754, 3938)(1755, 3939)(1756, 3940)(1757, 3941)(1758, 3942)(1759, 3943)(1760, 3944)(1761, 3945)(1762, 3946)(1763, 3947)(1764, 3948)(1765, 3949)(1766, 3950)(1767, 3951)(1768, 3952)(1769, 3953)(1770, 3954)(1771, 3955)(1772, 3956)(1773, 3957)(1774, 3958)(1775, 3959)(1776, 3960)(1777, 3961)(1778, 3962)(1779, 3963)(1780, 3964)(1781, 3965)(1782, 3966)(1783, 3967)(1784, 3968)(1785, 3969)(1786, 3970)(1787, 3971)(1788, 3972)(1789, 3973)(1790, 3974)(1791, 3975)(1792, 3976)(1793, 3977)(1794, 3978)(1795, 3979)(1796, 3980)(1797, 3981)(1798, 3982)(1799, 3983)(1800, 3984)(1801, 3985)(1802, 3986)(1803, 3987)(1804, 3988)(1805, 3989)(1806, 3990)(1807, 3991)(1808, 3992)(1809, 3993)(1810, 3994)(1811, 3995)(1812, 3996)(1813, 3997)(1814, 3998)(1815, 3999)(1816, 4000)(1817, 4001)(1818, 4002)(1819, 4003)(1820, 4004)(1821, 4005)(1822, 4006)(1823, 4007)(1824, 4008)(1825, 4009)(1826, 4010)(1827, 4011)(1828, 4012)(1829, 4013)(1830, 4014)(1831, 4015)(1832, 4016)(1833, 4017)(1834, 4018)(1835, 4019)(1836, 4020)(1837, 4021)(1838, 4022)(1839, 4023)(1840, 4024)(1841, 4025)(1842, 4026)(1843, 4027)(1844, 4028)(1845, 4029)(1846, 4030)(1847, 4031)(1848, 4032)(1849, 4033)(1850, 4034)(1851, 4035)(1852, 4036)(1853, 4037)(1854, 4038)(1855, 4039)(1856, 4040)(1857, 4041)(1858, 4042)(1859, 4043)(1860, 4044)(1861, 4045)(1862, 4046)(1863, 4047)(1864, 4048)(1865, 4049)(1866, 4050)(1867, 4051)(1868, 4052)(1869, 4053)(1870, 4054)(1871, 4055)(1872, 4056)(1873, 4057)(1874, 4058)(1875, 4059)(1876, 4060)(1877, 4061)(1878, 4062)(1879, 4063)(1880, 4064)(1881, 4065)(1882, 4066)(1883, 4067)(1884, 4068)(1885, 4069)(1886, 4070)(1887, 4071)(1888, 4072)(1889, 4073)(1890, 4074)(1891, 4075)(1892, 4076)(1893, 4077)(1894, 4078)(1895, 4079)(1896, 4080)(1897, 4081)(1898, 4082)(1899, 4083)(1900, 4084)(1901, 4085)(1902, 4086)(1903, 4087)(1904, 4088)(1905, 4089)(1906, 4090)(1907, 4091)(1908, 4092)(1909, 4093)(1910, 4094)(1911, 4095)(1912, 4096)(1913, 4097)(1914, 4098)(1915, 4099)(1916, 4100)(1917, 4101)(1918, 4102)(1919, 4103)(1920, 4104)(1921, 4105)(1922, 4106)(1923, 4107)(1924, 4108)(1925, 4109)(1926, 4110)(1927, 4111)(1928, 4112)(1929, 4113)(1930, 4114)(1931, 4115)(1932, 4116)(1933, 4117)(1934, 4118)(1935, 4119)(1936, 4120)(1937, 4121)(1938, 4122)(1939, 4123)(1940, 4124)(1941, 4125)(1942, 4126)(1943, 4127)(1944, 4128)(1945, 4129)(1946, 4130)(1947, 4131)(1948, 4132)(1949, 4133)(1950, 4134)(1951, 4135)(1952, 4136)(1953, 4137)(1954, 4138)(1955, 4139)(1956, 4140)(1957, 4141)(1958, 4142)(1959, 4143)(1960, 4144)(1961, 4145)(1962, 4146)(1963, 4147)(1964, 4148)(1965, 4149)(1966, 4150)(1967, 4151)(1968, 4152)(1969, 4153)(1970, 4154)(1971, 4155)(1972, 4156)(1973, 4157)(1974, 4158)(1975, 4159)(1976, 4160)(1977, 4161)(1978, 4162)(1979, 4163)(1980, 4164)(1981, 4165)(1982, 4166)(1983, 4167)(1984, 4168)(1985, 4169)(1986, 4170)(1987, 4171)(1988, 4172)(1989, 4173)(1990, 4174)(1991, 4175)(1992, 4176)(1993, 4177)(1994, 4178)(1995, 4179)(1996, 4180)(1997, 4181)(1998, 4182)(1999, 4183)(2000, 4184)(2001, 4185)(2002, 4186)(2003, 4187)(2004, 4188)(2005, 4189)(2006, 4190)(2007, 4191)(2008, 4192)(2009, 4193)(2010, 4194)(2011, 4195)(2012, 4196)(2013, 4197)(2014, 4198)(2015, 4199)(2016, 4200)(2017, 4201)(2018, 4202)(2019, 4203)(2020, 4204)(2021, 4205)(2022, 4206)(2023, 4207)(2024, 4208)(2025, 4209)(2026, 4210)(2027, 4211)(2028, 4212)(2029, 4213)(2030, 4214)(2031, 4215)(2032, 4216)(2033, 4217)(2034, 4218)(2035, 4219)(2036, 4220)(2037, 4221)(2038, 4222)(2039, 4223)(2040, 4224)(2041, 4225)(2042, 4226)(2043, 4227)(2044, 4228)(2045, 4229)(2046, 4230)(2047, 4231)(2048, 4232)(2049, 4233)(2050, 4234)(2051, 4235)(2052, 4236)(2053, 4237)(2054, 4238)(2055, 4239)(2056, 4240)(2057, 4241)(2058, 4242)(2059, 4243)(2060, 4244)(2061, 4245)(2062, 4246)(2063, 4247)(2064, 4248)(2065, 4249)(2066, 4250)(2067, 4251)(2068, 4252)(2069, 4253)(2070, 4254)(2071, 4255)(2072, 4256)(2073, 4257)(2074, 4258)(2075, 4259)(2076, 4260)(2077, 4261)(2078, 4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E14.637 Graph:: simple bipartite v = 1248 e = 2184 f = 910 degree seq :: [ 2^1092, 14^156 ] E14.648 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |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)^3, Y1^7, (Y1^-2 * Y3 * Y1^3 * Y3 * Y1^-1)^3, Y3 * Y1^-2 * Y3 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-3 * Y3 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-2 ] Map:: polytopal R = (1, 1093, 2, 1094, 5, 1097, 11, 1103, 20, 1112, 10, 1102, 4, 1096)(3, 1095, 7, 1099, 15, 1107, 26, 1118, 30, 1122, 17, 1109, 8, 1100)(6, 1098, 13, 1105, 24, 1116, 39, 1131, 42, 1134, 25, 1117, 14, 1106)(9, 1101, 18, 1110, 31, 1123, 49, 1141, 46, 1138, 28, 1120, 16, 1108)(12, 1104, 22, 1114, 37, 1129, 57, 1149, 60, 1152, 38, 1130, 23, 1115)(19, 1111, 33, 1125, 52, 1144, 77, 1169, 76, 1168, 51, 1143, 32, 1124)(21, 1113, 35, 1127, 55, 1147, 81, 1173, 84, 1176, 56, 1148, 36, 1128)(27, 1119, 44, 1136, 67, 1159, 97, 1189, 100, 1192, 68, 1160, 45, 1137)(29, 1121, 47, 1139, 70, 1162, 102, 1194, 91, 1183, 62, 1154, 40, 1132)(34, 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3660)(2569, 3661)(2570, 3662)(2571, 3663)(2572, 3664)(2573, 3665)(2574, 3666)(2575, 3667)(2576, 3668)(2577, 3669)(2578, 3670)(2579, 3671)(2580, 3672)(2581, 3673)(2582, 3674)(2583, 3675)(2584, 3676)(2585, 3677)(2586, 3678)(2587, 3679)(2588, 3680)(2589, 3681)(2590, 3682)(2591, 3683)(2592, 3684)(2593, 3685)(2594, 3686)(2595, 3687)(2596, 3688)(2597, 3689)(2598, 3690)(2599, 3691)(2600, 3692)(2601, 3693)(2602, 3694)(2603, 3695)(2604, 3696)(2605, 3697)(2606, 3698)(2607, 3699)(2608, 3700)(2609, 3701)(2610, 3702)(2611, 3703)(2612, 3704)(2613, 3705)(2614, 3706)(2615, 3707)(2616, 3708)(2617, 3709)(2618, 3710)(2619, 3711)(2620, 3712)(2621, 3713)(2622, 3714)(2623, 3715)(2624, 3716)(2625, 3717)(2626, 3718)(2627, 3719)(2628, 3720)(2629, 3721)(2630, 3722)(2631, 3723)(2632, 3724)(2633, 3725)(2634, 3726)(2635, 3727)(2636, 3728)(2637, 3729)(2638, 3730)(2639, 3731)(2640, 3732)(2641, 3733)(2642, 3734)(2643, 3735)(2644, 3736)(2645, 3737)(2646, 3738)(2647, 3739)(2648, 3740)(2649, 3741)(2650, 3742)(2651, 3743)(2652, 3744)(2653, 3745)(2654, 3746)(2655, 3747)(2656, 3748)(2657, 3749)(2658, 3750)(2659, 3751)(2660, 3752)(2661, 3753)(2662, 3754)(2663, 3755)(2664, 3756)(2665, 3757)(2666, 3758)(2667, 3759)(2668, 3760)(2669, 3761)(2670, 3762)(2671, 3763)(2672, 3764)(2673, 3765)(2674, 3766)(2675, 3767)(2676, 3768)(2677, 3769)(2678, 3770)(2679, 3771)(2680, 3772)(2681, 3773)(2682, 3774)(2683, 3775)(2684, 3776)(2685, 3777)(2686, 3778)(2687, 3779)(2688, 3780)(2689, 3781)(2690, 3782)(2691, 3783)(2692, 3784)(2693, 3785)(2694, 3786)(2695, 3787)(2696, 3788)(2697, 3789)(2698, 3790)(2699, 3791)(2700, 3792)(2701, 3793)(2702, 3794)(2703, 3795)(2704, 3796)(2705, 3797)(2706, 3798)(2707, 3799)(2708, 3800)(2709, 3801)(2710, 3802)(2711, 3803)(2712, 3804)(2713, 3805)(2714, 3806)(2715, 3807)(2716, 3808)(2717, 3809)(2718, 3810)(2719, 3811)(2720, 3812)(2721, 3813)(2722, 3814)(2723, 3815)(2724, 3816)(2725, 3817)(2726, 3818)(2727, 3819)(2728, 3820)(2729, 3821)(2730, 3822)(2731, 3823)(2732, 3824)(2733, 3825)(2734, 3826)(2735, 3827)(2736, 3828)(2737, 3829)(2738, 3830)(2739, 3831)(2740, 3832)(2741, 3833)(2742, 3834)(2743, 3835)(2744, 3836)(2745, 3837)(2746, 3838)(2747, 3839)(2748, 3840)(2749, 3841)(2750, 3842)(2751, 3843)(2752, 3844)(2753, 3845)(2754, 3846)(2755, 3847)(2756, 3848)(2757, 3849)(2758, 3850)(2759, 3851)(2760, 3852)(2761, 3853)(2762, 3854)(2763, 3855)(2764, 3856)(2765, 3857)(2766, 3858)(2767, 3859)(2768, 3860)(2769, 3861)(2770, 3862)(2771, 3863)(2772, 3864)(2773, 3865)(2774, 3866)(2775, 3867)(2776, 3868)(2777, 3869)(2778, 3870)(2779, 3871)(2780, 3872)(2781, 3873)(2782, 3874)(2783, 3875)(2784, 3876)(2785, 3877)(2786, 3878)(2787, 3879)(2788, 3880)(2789, 3881)(2790, 3882)(2791, 3883)(2792, 3884)(2793, 3885)(2794, 3886)(2795, 3887)(2796, 3888)(2797, 3889)(2798, 3890)(2799, 3891)(2800, 3892)(2801, 3893)(2802, 3894)(2803, 3895)(2804, 3896)(2805, 3897)(2806, 3898)(2807, 3899)(2808, 3900)(2809, 3901)(2810, 3902)(2811, 3903)(2812, 3904)(2813, 3905)(2814, 3906)(2815, 3907)(2816, 3908)(2817, 3909)(2818, 3910)(2819, 3911)(2820, 3912)(2821, 3913)(2822, 3914)(2823, 3915)(2824, 3916)(2825, 3917)(2826, 3918)(2827, 3919)(2828, 3920)(2829, 3921)(2830, 3922)(2831, 3923)(2832, 3924)(2833, 3925)(2834, 3926)(2835, 3927)(2836, 3928)(2837, 3929)(2838, 3930)(2839, 3931)(2840, 3932)(2841, 3933)(2842, 3934)(2843, 3935)(2844, 3936)(2845, 3937)(2846, 3938)(2847, 3939)(2848, 3940)(2849, 3941)(2850, 3942)(2851, 3943)(2852, 3944)(2853, 3945)(2854, 3946)(2855, 3947)(2856, 3948)(2857, 3949)(2858, 3950)(2859, 3951)(2860, 3952)(2861, 3953)(2862, 3954)(2863, 3955)(2864, 3956)(2865, 3957)(2866, 3958)(2867, 3959)(2868, 3960)(2869, 3961)(2870, 3962)(2871, 3963)(2872, 3964)(2873, 3965)(2874, 3966)(2875, 3967)(2876, 3968)(2877, 3969)(2878, 3970)(2879, 3971)(2880, 3972)(2881, 3973)(2882, 3974)(2883, 3975)(2884, 3976)(2885, 3977)(2886, 3978)(2887, 3979)(2888, 3980)(2889, 3981)(2890, 3982)(2891, 3983)(2892, 3984)(2893, 3985)(2894, 3986)(2895, 3987)(2896, 3988)(2897, 3989)(2898, 3990)(2899, 3991)(2900, 3992)(2901, 3993)(2902, 3994)(2903, 3995)(2904, 3996)(2905, 3997)(2906, 3998)(2907, 3999)(2908, 4000)(2909, 4001)(2910, 4002)(2911, 4003)(2912, 4004)(2913, 4005)(2914, 4006)(2915, 4007)(2916, 4008)(2917, 4009)(2918, 4010)(2919, 4011)(2920, 4012)(2921, 4013)(2922, 4014)(2923, 4015)(2924, 4016)(2925, 4017)(2926, 4018)(2927, 4019)(2928, 4020)(2929, 4021)(2930, 4022)(2931, 4023)(2932, 4024)(2933, 4025)(2934, 4026)(2935, 4027)(2936, 4028)(2937, 4029)(2938, 4030)(2939, 4031)(2940, 4032)(2941, 4033)(2942, 4034)(2943, 4035)(2944, 4036)(2945, 4037)(2946, 4038)(2947, 4039)(2948, 4040)(2949, 4041)(2950, 4042)(2951, 4043)(2952, 4044)(2953, 4045)(2954, 4046)(2955, 4047)(2956, 4048)(2957, 4049)(2958, 4050)(2959, 4051)(2960, 4052)(2961, 4053)(2962, 4054)(2963, 4055)(2964, 4056)(2965, 4057)(2966, 4058)(2967, 4059)(2968, 4060)(2969, 4061)(2970, 4062)(2971, 4063)(2972, 4064)(2973, 4065)(2974, 4066)(2975, 4067)(2976, 4068)(2977, 4069)(2978, 4070)(2979, 4071)(2980, 4072)(2981, 4073)(2982, 4074)(2983, 4075)(2984, 4076)(2985, 4077)(2986, 4078)(2987, 4079)(2988, 4080)(2989, 4081)(2990, 4082)(2991, 4083)(2992, 4084)(2993, 4085)(2994, 4086)(2995, 4087)(2996, 4088)(2997, 4089)(2998, 4090)(2999, 4091)(3000, 4092)(3001, 4093)(3002, 4094)(3003, 4095)(3004, 4096)(3005, 4097)(3006, 4098)(3007, 4099)(3008, 4100)(3009, 4101)(3010, 4102)(3011, 4103)(3012, 4104)(3013, 4105)(3014, 4106)(3015, 4107)(3016, 4108)(3017, 4109)(3018, 4110)(3019, 4111)(3020, 4112)(3021, 4113)(3022, 4114)(3023, 4115)(3024, 4116)(3025, 4117)(3026, 4118)(3027, 4119)(3028, 4120)(3029, 4121)(3030, 4122)(3031, 4123)(3032, 4124)(3033, 4125)(3034, 4126)(3035, 4127)(3036, 4128)(3037, 4129)(3038, 4130)(3039, 4131)(3040, 4132)(3041, 4133)(3042, 4134)(3043, 4135)(3044, 4136)(3045, 4137)(3046, 4138)(3047, 4139)(3048, 4140)(3049, 4141)(3050, 4142)(3051, 4143)(3052, 4144)(3053, 4145)(3054, 4146)(3055, 4147)(3056, 4148)(3057, 4149)(3058, 4150)(3059, 4151)(3060, 4152)(3061, 4153)(3062, 4154)(3063, 4155)(3064, 4156)(3065, 4157)(3066, 4158)(3067, 4159)(3068, 4160)(3069, 4161)(3070, 4162)(3071, 4163)(3072, 4164)(3073, 4165)(3074, 4166)(3075, 4167)(3076, 4168)(3077, 4169)(3078, 4170)(3079, 4171)(3080, 4172)(3081, 4173)(3082, 4174)(3083, 4175)(3084, 4176)(3085, 4177)(3086, 4178)(3087, 4179)(3088, 4180)(3089, 4181)(3090, 4182)(3091, 4183)(3092, 4184)(3093, 4185)(3094, 4186)(3095, 4187)(3096, 4188)(3097, 4189)(3098, 4190)(3099, 4191)(3100, 4192)(3101, 4193)(3102, 4194)(3103, 4195)(3104, 4196)(3105, 4197)(3106, 4198)(3107, 4199)(3108, 4200)(3109, 4201)(3110, 4202)(3111, 4203)(3112, 4204)(3113, 4205)(3114, 4206)(3115, 4207)(3116, 4208)(3117, 4209)(3118, 4210)(3119, 4211)(3120, 4212)(3121, 4213)(3122, 4214)(3123, 4215)(3124, 4216)(3125, 4217)(3126, 4218)(3127, 4219)(3128, 4220)(3129, 4221)(3130, 4222)(3131, 4223)(3132, 4224)(3133, 4225)(3134, 4226)(3135, 4227)(3136, 4228)(3137, 4229)(3138, 4230)(3139, 4231)(3140, 4232)(3141, 4233)(3142, 4234)(3143, 4235)(3144, 4236)(3145, 4237)(3146, 4238)(3147, 4239)(3148, 4240)(3149, 4241)(3150, 4242)(3151, 4243)(3152, 4244)(3153, 4245)(3154, 4246)(3155, 4247)(3156, 4248)(3157, 4249)(3158, 4250)(3159, 4251)(3160, 4252)(3161, 4253)(3162, 4254)(3163, 4255)(3164, 4256)(3165, 4257)(3166, 4258)(3167, 4259)(3168, 4260)(3169, 4261)(3170, 4262)(3171, 4263)(3172, 4264)(3173, 4265)(3174, 4266)(3175, 4267)(3176, 4268)(3177, 4269)(3178, 4270)(3179, 4271)(3180, 4272)(3181, 4273)(3182, 4274)(3183, 4275)(3184, 4276)(3185, 4277)(3186, 4278)(3187, 4279)(3188, 4280)(3189, 4281)(3190, 4282)(3191, 4283)(3192, 4284)(3193, 4285)(3194, 4286)(3195, 4287)(3196, 4288)(3197, 4289)(3198, 4290)(3199, 4291)(3200, 4292)(3201, 4293)(3202, 4294)(3203, 4295)(3204, 4296)(3205, 4297)(3206, 4298)(3207, 4299)(3208, 4300)(3209, 4301)(3210, 4302)(3211, 4303)(3212, 4304)(3213, 4305)(3214, 4306)(3215, 4307)(3216, 4308)(3217, 4309)(3218, 4310)(3219, 4311)(3220, 4312)(3221, 4313)(3222, 4314)(3223, 4315)(3224, 4316)(3225, 4317)(3226, 4318)(3227, 4319)(3228, 4320)(3229, 4321)(3230, 4322)(3231, 4323)(3232, 4324)(3233, 4325)(3234, 4326)(3235, 4327)(3236, 4328)(3237, 4329)(3238, 4330)(3239, 4331)(3240, 4332)(3241, 4333)(3242, 4334)(3243, 4335)(3244, 4336)(3245, 4337)(3246, 4338)(3247, 4339)(3248, 4340)(3249, 4341)(3250, 4342)(3251, 4343)(3252, 4344)(3253, 4345)(3254, 4346)(3255, 4347)(3256, 4348)(3257, 4349)(3258, 4350)(3259, 4351)(3260, 4352)(3261, 4353)(3262, 4354)(3263, 4355)(3264, 4356)(3265, 4357)(3266, 4358)(3267, 4359)(3268, 4360)(3269, 4361)(3270, 4362)(3271, 4363)(3272, 4364)(3273, 4365)(3274, 4366)(3275, 4367)(3276, 4368) L = (1, 2187)(2, 2190)(3, 2185)(4, 2193)(5, 2196)(6, 2186)(7, 2200)(8, 2197)(9, 2188)(10, 2203)(11, 2205)(12, 2189)(13, 2192)(14, 2206)(15, 2211)(16, 2191)(17, 2213)(18, 2216)(19, 2194)(20, 2218)(21, 2195)(22, 2198)(23, 2219)(24, 2224)(25, 2225)(26, 2227)(27, 2199)(28, 2228)(29, 2201)(30, 2232)(31, 2234)(32, 2202)(33, 2237)(34, 2204)(35, 2207)(36, 2238)(37, 2242)(38, 2243)(39, 2245)(40, 2208)(41, 2209)(42, 2248)(43, 2210)(44, 2212)(45, 2249)(46, 2253)(47, 2255)(48, 2214)(49, 2257)(50, 2215)(51, 2258)(52, 2262)(53, 2217)(54, 2220)(55, 2266)(56, 2267)(57, 2269)(58, 2221)(59, 2222)(60, 2272)(61, 2223)(62, 2273)(63, 2277)(64, 2226)(65, 2229)(66, 2256)(67, 2282)(68, 2283)(69, 2230)(70, 2287)(71, 2231)(72, 2250)(73, 2233)(74, 2235)(75, 2290)(76, 2294)(77, 2295)(78, 2236)(79, 2296)(80, 2300)(81, 2301)(82, 2239)(83, 2240)(84, 2304)(85, 2241)(86, 2305)(87, 2309)(88, 2244)(89, 2246)(90, 2278)(91, 2313)(92, 2315)(93, 2247)(94, 2274)(95, 2319)(96, 2320)(97, 2322)(98, 2251)(99, 2252)(100, 2325)(101, 2291)(102, 2327)(103, 2254)(104, 2328)(105, 2332)(106, 2259)(107, 2285)(108, 2336)(109, 2337)(110, 2260)(111, 2261)(112, 2263)(113, 2340)(114, 2344)(115, 2345)(116, 2264)(117, 2265)(118, 2347)(119, 2351)(120, 2268)(121, 2270)(122, 2310)(123, 2355)(124, 2357)(125, 2271)(126, 2306)(127, 2361)(128, 2362)(129, 2275)(130, 2365)(131, 2276)(132, 2366)(133, 2370)(134, 2371)(135, 2279)(136, 2280)(137, 2374)(138, 2281)(139, 2375)(140, 2379)(141, 2284)(142, 2382)(143, 2286)(144, 2288)(145, 2383)(146, 2387)(147, 2388)(148, 2289)(149, 2391)(150, 2392)(151, 2394)(152, 2292)(153, 2293)(154, 2397)(155, 2341)(156, 2297)(157, 2339)(158, 2402)(159, 2403)(160, 2298)(161, 2299)(162, 2406)(163, 2302)(164, 2352)(165, 2411)(166, 2413)(167, 2303)(168, 2348)(169, 2417)(170, 2418)(171, 2307)(172, 2421)(173, 2308)(174, 2422)(175, 2426)(176, 2427)(177, 2311)(178, 2312)(179, 2430)(180, 2384)(181, 2314)(182, 2316)(183, 2432)(184, 2436)(185, 2437)(186, 2317)(187, 2318)(188, 2439)(189, 2443)(190, 2321)(191, 2323)(192, 2380)(193, 2447)(194, 2449)(195, 2324)(196, 2376)(197, 2452)(198, 2326)(199, 2329)(200, 2364)(201, 2457)(202, 2458)(203, 2330)(204, 2331)(205, 2461)(206, 2464)(207, 2333)(208, 2334)(209, 2467)(210, 2335)(211, 2468)(212, 2472)(213, 2338)(214, 2475)(215, 2477)(216, 2478)(217, 2480)(218, 2342)(219, 2343)(220, 2483)(221, 2407)(222, 2346)(223, 2405)(224, 2487)(225, 2489)(226, 2490)(227, 2349)(228, 2493)(229, 2350)(230, 2494)(231, 2498)(232, 2499)(233, 2353)(234, 2354)(235, 2502)(236, 2433)(237, 2356)(238, 2358)(239, 2504)(240, 2508)(241, 2509)(242, 2359)(243, 2360)(244, 2511)(245, 2515)(246, 2363)(247, 2518)(248, 2367)(249, 2420)(250, 2522)(251, 2523)(252, 2368)(253, 2369)(254, 2526)(255, 2372)(256, 2444)(257, 2531)(258, 2533)(259, 2373)(260, 2440)(261, 2537)(262, 2538)(263, 2377)(264, 2541)(265, 2378)(266, 2542)(267, 2546)(268, 2381)(269, 2547)(270, 2551)(271, 2552)(272, 2554)(273, 2385)(274, 2386)(275, 2557)(276, 2462)(277, 2389)(278, 2460)(279, 2561)(280, 2390)(281, 2562)(282, 2566)(283, 2393)(284, 2395)(285, 2473)(286, 2570)(287, 2572)(288, 2396)(289, 2469)(290, 2575)(291, 2398)(292, 2577)(293, 2399)(294, 2400)(295, 2580)(296, 2401)(297, 2581)(298, 2585)(299, 2404)(300, 2588)(301, 2590)(302, 2591)(303, 2408)(304, 2594)(305, 2409)(306, 2410)(307, 2597)(308, 2505)(309, 2412)(310, 2414)(311, 2599)(312, 2603)(313, 2604)(314, 2415)(315, 2416)(316, 2606)(317, 2610)(318, 2419)(319, 2613)(320, 2423)(321, 2492)(322, 2617)(323, 2618)(324, 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3978)(1795, 3979)(1796, 3980)(1797, 3981)(1798, 3982)(1799, 3983)(1800, 3984)(1801, 3985)(1802, 3986)(1803, 3987)(1804, 3988)(1805, 3989)(1806, 3990)(1807, 3991)(1808, 3992)(1809, 3993)(1810, 3994)(1811, 3995)(1812, 3996)(1813, 3997)(1814, 3998)(1815, 3999)(1816, 4000)(1817, 4001)(1818, 4002)(1819, 4003)(1820, 4004)(1821, 4005)(1822, 4006)(1823, 4007)(1824, 4008)(1825, 4009)(1826, 4010)(1827, 4011)(1828, 4012)(1829, 4013)(1830, 4014)(1831, 4015)(1832, 4016)(1833, 4017)(1834, 4018)(1835, 4019)(1836, 4020)(1837, 4021)(1838, 4022)(1839, 4023)(1840, 4024)(1841, 4025)(1842, 4026)(1843, 4027)(1844, 4028)(1845, 4029)(1846, 4030)(1847, 4031)(1848, 4032)(1849, 4033)(1850, 4034)(1851, 4035)(1852, 4036)(1853, 4037)(1854, 4038)(1855, 4039)(1856, 4040)(1857, 4041)(1858, 4042)(1859, 4043)(1860, 4044)(1861, 4045)(1862, 4046)(1863, 4047)(1864, 4048)(1865, 4049)(1866, 4050)(1867, 4051)(1868, 4052)(1869, 4053)(1870, 4054)(1871, 4055)(1872, 4056)(1873, 4057)(1874, 4058)(1875, 4059)(1876, 4060)(1877, 4061)(1878, 4062)(1879, 4063)(1880, 4064)(1881, 4065)(1882, 4066)(1883, 4067)(1884, 4068)(1885, 4069)(1886, 4070)(1887, 4071)(1888, 4072)(1889, 4073)(1890, 4074)(1891, 4075)(1892, 4076)(1893, 4077)(1894, 4078)(1895, 4079)(1896, 4080)(1897, 4081)(1898, 4082)(1899, 4083)(1900, 4084)(1901, 4085)(1902, 4086)(1903, 4087)(1904, 4088)(1905, 4089)(1906, 4090)(1907, 4091)(1908, 4092)(1909, 4093)(1910, 4094)(1911, 4095)(1912, 4096)(1913, 4097)(1914, 4098)(1915, 4099)(1916, 4100)(1917, 4101)(1918, 4102)(1919, 4103)(1920, 4104)(1921, 4105)(1922, 4106)(1923, 4107)(1924, 4108)(1925, 4109)(1926, 4110)(1927, 4111)(1928, 4112)(1929, 4113)(1930, 4114)(1931, 4115)(1932, 4116)(1933, 4117)(1934, 4118)(1935, 4119)(1936, 4120)(1937, 4121)(1938, 4122)(1939, 4123)(1940, 4124)(1941, 4125)(1942, 4126)(1943, 4127)(1944, 4128)(1945, 4129)(1946, 4130)(1947, 4131)(1948, 4132)(1949, 4133)(1950, 4134)(1951, 4135)(1952, 4136)(1953, 4137)(1954, 4138)(1955, 4139)(1956, 4140)(1957, 4141)(1958, 4142)(1959, 4143)(1960, 4144)(1961, 4145)(1962, 4146)(1963, 4147)(1964, 4148)(1965, 4149)(1966, 4150)(1967, 4151)(1968, 4152)(1969, 4153)(1970, 4154)(1971, 4155)(1972, 4156)(1973, 4157)(1974, 4158)(1975, 4159)(1976, 4160)(1977, 4161)(1978, 4162)(1979, 4163)(1980, 4164)(1981, 4165)(1982, 4166)(1983, 4167)(1984, 4168)(1985, 4169)(1986, 4170)(1987, 4171)(1988, 4172)(1989, 4173)(1990, 4174)(1991, 4175)(1992, 4176)(1993, 4177)(1994, 4178)(1995, 4179)(1996, 4180)(1997, 4181)(1998, 4182)(1999, 4183)(2000, 4184)(2001, 4185)(2002, 4186)(2003, 4187)(2004, 4188)(2005, 4189)(2006, 4190)(2007, 4191)(2008, 4192)(2009, 4193)(2010, 4194)(2011, 4195)(2012, 4196)(2013, 4197)(2014, 4198)(2015, 4199)(2016, 4200)(2017, 4201)(2018, 4202)(2019, 4203)(2020, 4204)(2021, 4205)(2022, 4206)(2023, 4207)(2024, 4208)(2025, 4209)(2026, 4210)(2027, 4211)(2028, 4212)(2029, 4213)(2030, 4214)(2031, 4215)(2032, 4216)(2033, 4217)(2034, 4218)(2035, 4219)(2036, 4220)(2037, 4221)(2038, 4222)(2039, 4223)(2040, 4224)(2041, 4225)(2042, 4226)(2043, 4227)(2044, 4228)(2045, 4229)(2046, 4230)(2047, 4231)(2048, 4232)(2049, 4233)(2050, 4234)(2051, 4235)(2052, 4236)(2053, 4237)(2054, 4238)(2055, 4239)(2056, 4240)(2057, 4241)(2058, 4242)(2059, 4243)(2060, 4244)(2061, 4245)(2062, 4246)(2063, 4247)(2064, 4248)(2065, 4249)(2066, 4250)(2067, 4251)(2068, 4252)(2069, 4253)(2070, 4254)(2071, 4255)(2072, 4256)(2073, 4257)(2074, 4258)(2075, 4259)(2076, 4260)(2077, 4261)(2078, 4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E14.639 Graph:: simple bipartite v = 1248 e = 2184 f = 910 degree seq :: [ 2^1092, 14^156 ] E14.649 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^3, (Y3 * Y2^-1)^3, Y2^7, (Y1 * Y2^-3)^6 ] Map:: R = (1, 1093, 2, 1094)(3, 1095, 7, 1099)(4, 1096, 9, 1101)(5, 1097, 11, 1103)(6, 1098, 13, 1105)(8, 1100, 16, 1108)(10, 1102, 19, 1111)(12, 1104, 22, 1114)(14, 1106, 25, 1117)(15, 1107, 27, 1119)(17, 1109, 30, 1122)(18, 1110, 31, 1123)(20, 1112, 34, 1126)(21, 1113, 35, 1127)(23, 1115, 38, 1130)(24, 1116, 39, 1131)(26, 1118, 42, 1134)(28, 1120, 44, 1136)(29, 1121, 46, 1138)(32, 1124, 50, 1142)(33, 1125, 52, 1144)(36, 1128, 56, 1148)(37, 1129, 57, 1149)(40, 1132, 61, 1153)(41, 1133, 62, 1154)(43, 1135, 65, 1157)(45, 1137, 68, 1160)(47, 1139, 70, 1162)(48, 1140, 54, 1146)(49, 1141, 73, 1165)(51, 1143, 76, 1168)(53, 1145, 78, 1170)(55, 1147, 81, 1173)(58, 1150, 85, 1177)(59, 1151, 64, 1156)(60, 1152, 88, 1180)(63, 1155, 92, 1184)(66, 1158, 96, 1188)(67, 1159, 97, 1189)(69, 1161, 100, 1192)(71, 1163, 103, 1195)(72, 1164, 104, 1196)(74, 1166, 107, 1199)(75, 1167, 108, 1200)(77, 1169, 111, 1203)(79, 1171, 114, 1206)(80, 1172, 115, 1207)(82, 1174, 118, 1210)(83, 1175, 110, 1202)(84, 1176, 120, 1212)(86, 1178, 123, 1215)(87, 1179, 124, 1216)(89, 1181, 127, 1219)(90, 1182, 99, 1191)(91, 1183, 129, 1221)(93, 1185, 132, 1224)(94, 1186, 133, 1225)(95, 1187, 135, 1227)(98, 1190, 139, 1231)(101, 1193, 143, 1235)(102, 1194, 144, 1236)(105, 1197, 148, 1240)(106, 1198, 149, 1241)(109, 1201, 153, 1245)(112, 1204, 157, 1249)(113, 1205, 158, 1250)(116, 1208, 162, 1254)(117, 1209, 163, 1255)(119, 1211, 166, 1258)(121, 1213, 169, 1261)(122, 1214, 170, 1262)(125, 1217, 174, 1266)(126, 1218, 175, 1267)(128, 1220, 178, 1270)(130, 1222, 181, 1273)(131, 1223, 182, 1274)(134, 1226, 186, 1278)(136, 1228, 188, 1280)(137, 1229, 146, 1238)(138, 1230, 190, 1282)(140, 1232, 193, 1285)(141, 1233, 194, 1286)(142, 1234, 196, 1288)(145, 1237, 200, 1292)(147, 1239, 203, 1295)(150, 1242, 207, 1299)(151, 1243, 160, 1252)(152, 1244, 209, 1301)(154, 1246, 212, 1304)(155, 1247, 213, 1305)(156, 1248, 215, 1307)(159, 1251, 219, 1311)(161, 1253, 222, 1314)(164, 1256, 226, 1318)(165, 1257, 172, 1264)(167, 1259, 229, 1321)(168, 1260, 230, 1322)(171, 1263, 234, 1326)(173, 1265, 237, 1329)(176, 1268, 241, 1333)(177, 1269, 184, 1276)(179, 1271, 244, 1336)(180, 1272, 245, 1337)(183, 1275, 249, 1341)(185, 1277, 252, 1344)(187, 1279, 255, 1347)(189, 1281, 258, 1350)(191, 1283, 261, 1353)(192, 1284, 262, 1354)(195, 1287, 266, 1358)(197, 1289, 268, 1360)(198, 1290, 205, 1297)(199, 1291, 270, 1362)(201, 1293, 273, 1365)(202, 1294, 274, 1366)(204, 1296, 277, 1369)(206, 1298, 280, 1372)(208, 1300, 283, 1375)(210, 1302, 286, 1378)(211, 1303, 287, 1379)(214, 1306, 291, 1383)(216, 1308, 293, 1385)(217, 1309, 224, 1316)(218, 1310, 295, 1387)(220, 1312, 298, 1390)(221, 1313, 299, 1391)(223, 1315, 302, 1394)(225, 1317, 304, 1396)(227, 1319, 307, 1399)(228, 1320, 309, 1401)(231, 1323, 313, 1405)(232, 1324, 239, 1331)(233, 1325, 315, 1407)(235, 1327, 318, 1410)(236, 1328, 319, 1411)(238, 1330, 322, 1414)(240, 1332, 325, 1417)(242, 1334, 328, 1420)(243, 1335, 330, 1422)(246, 1338, 334, 1426)(247, 1339, 254, 1346)(248, 1340, 336, 1428)(250, 1342, 339, 1431)(251, 1343, 340, 1432)(253, 1345, 343, 1435)(256, 1348, 346, 1438)(257, 1349, 264, 1356)(259, 1351, 349, 1441)(260, 1352, 350, 1442)(263, 1355, 354, 1446)(265, 1357, 357, 1449)(267, 1359, 360, 1452)(269, 1361, 363, 1455)(271, 1363, 366, 1458)(272, 1364, 367, 1459)(275, 1367, 371, 1463)(276, 1368, 372, 1464)(278, 1370, 375, 1467)(279, 1371, 376, 1468)(281, 1373, 379, 1471)(282, 1374, 289, 1381)(284, 1376, 382, 1474)(285, 1377, 383, 1475)(288, 1380, 387, 1479)(290, 1382, 390, 1482)(292, 1384, 393, 1485)(294, 1386, 396, 1488)(296, 1388, 399, 1491)(297, 1389, 400, 1492)(300, 1392, 404, 1496)(301, 1393, 405, 1497)(303, 1395, 408, 1500)(305, 1397, 411, 1503)(306, 1398, 311, 1403)(308, 1400, 414, 1506)(310, 1402, 416, 1508)(312, 1404, 419, 1511)(314, 1406, 422, 1514)(316, 1408, 425, 1517)(317, 1409, 426, 1518)(320, 1412, 430, 1522)(321, 1413, 431, 1523)(323, 1415, 434, 1526)(324, 1416, 435, 1527)(326, 1418, 438, 1530)(327, 1419, 332, 1424)(329, 1421, 441, 1533)(331, 1423, 443, 1535)(333, 1425, 446, 1538)(335, 1427, 449, 1541)(337, 1429, 452, 1544)(338, 1430, 453, 1545)(341, 1433, 457, 1549)(342, 1434, 458, 1550)(344, 1436, 461, 1553)(345, 1437, 410, 1502)(347, 1439, 464, 1556)(348, 1440, 466, 1558)(351, 1443, 470, 1562)(352, 1444, 359, 1451)(353, 1445, 472, 1564)(355, 1447, 475, 1567)(356, 1448, 476, 1568)(358, 1450, 479, 1571)(361, 1453, 447, 1539)(362, 1454, 369, 1461)(364, 1456, 483, 1575)(365, 1457, 484, 1576)(368, 1460, 488, 1580)(370, 1462, 491, 1583)(373, 1465, 495, 1587)(374, 1466, 496, 1588)(377, 1469, 500, 1592)(378, 1470, 437, 1529)(380, 1472, 502, 1594)(381, 1473, 504, 1596)(384, 1476, 508, 1600)(385, 1477, 392, 1484)(386, 1478, 510, 1602)(388, 1480, 513, 1605)(389, 1481, 514, 1606)(391, 1483, 517, 1609)(394, 1486, 420, 1512)(395, 1487, 402, 1494)(397, 1489, 521, 1613)(398, 1490, 522, 1614)(401, 1493, 526, 1618)(403, 1495, 529, 1621)(406, 1498, 533, 1625)(407, 1499, 498, 1590)(409, 1501, 536, 1628)(412, 1504, 783, 1875)(413, 1505, 785, 1877)(415, 1507, 787, 1879)(417, 1509, 776, 1868)(418, 1510, 758, 1850)(421, 1513, 428, 1520)(423, 1515, 649, 1741)(424, 1516, 627, 1719)(427, 1519, 797, 1889)(429, 1521, 799, 1891)(432, 1524, 803, 1895)(433, 1525, 629, 1721)(436, 1528, 805, 1897)(439, 1531, 808, 1900)(440, 1532, 716, 1808)(442, 1534, 725, 1817)(444, 1536, 666, 1758)(445, 1537, 811, 1903)(448, 1540, 455, 1547)(450, 1542, 757, 1849)(451, 1543, 815, 1907)(454, 1546, 732, 1824)(456, 1548, 655, 1747)(459, 1551, 821, 1913)(460, 1552, 823, 1915)(462, 1554, 634, 1726)(463, 1555, 468, 1560)(465, 1557, 691, 1783)(467, 1559, 737, 1829)(469, 1561, 532, 1624)(471, 1563, 828, 1920)(473, 1565, 830, 1922)(474, 1566, 832, 1924)(477, 1569, 672, 1764)(478, 1570, 801, 1893)(480, 1572, 837, 1929)(481, 1573, 838, 1930)(482, 1574, 778, 1870)(485, 1577, 523, 1615)(486, 1578, 493, 1585)(487, 1579, 842, 1934)(489, 1581, 845, 1937)(490, 1582, 696, 1788)(492, 1584, 847, 1939)(494, 1586, 507, 1599)(497, 1589, 850, 1942)(499, 1591, 851, 1943)(501, 1593, 506, 1598)(503, 1595, 698, 1790)(505, 1597, 855, 1947)(509, 1601, 857, 1949)(511, 1603, 861, 1953)(512, 1604, 645, 1737)(515, 1607, 863, 1955)(516, 1608, 679, 1771)(518, 1610, 866, 1958)(519, 1611, 868, 1960)(520, 1612, 862, 1954)(524, 1616, 531, 1623)(525, 1617, 781, 1873)(527, 1619, 621, 1713)(528, 1620, 873, 1965)(530, 1622, 703, 1795)(534, 1626, 790, 1882)(535, 1627, 724, 1816)(537, 1629, 878, 1970)(538, 1630, 880, 1972)(539, 1631, 884, 1976)(540, 1632, 887, 1979)(541, 1633, 890, 1982)(542, 1634, 894, 1986)(543, 1635, 885, 1977)(544, 1636, 900, 1992)(545, 1637, 889, 1981)(546, 1638, 905, 1997)(547, 1639, 892, 1984)(548, 1640, 909, 2001)(549, 1641, 896, 1988)(550, 1642, 914, 2006)(551, 1643, 917, 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3840, 3131, 4223, 3212, 4304, 2812, 3904, 3211, 4303, 3068, 4160, 2870, 3962)(2749, 3841, 3047, 4139, 3156, 4248, 2762, 3854, 3036, 4128, 3101, 4193, 3135, 4227)(2750, 3842, 3136, 4228, 3166, 4258, 2946, 4038, 2788, 3880, 2989, 4081, 3137, 4229)(2752, 3844, 2855, 3947, 3244, 4336, 2974, 4066, 2927, 4019, 3149, 4241, 3141, 4233)(2754, 3846, 3144, 4236, 3114, 4206, 3033, 4125, 2757, 3849, 3150, 4242, 3145, 4237)(2755, 3847, 3146, 4238, 3112, 4204, 2892, 3984, 2790, 3882, 3195, 4287, 3147, 4239)(2756, 3848, 3054, 4146, 3223, 4315, 2825, 3917, 3222, 4314, 3074, 4166, 2860, 3952)(2760, 3852, 2845, 3937, 3236, 4328, 2940, 4032, 2904, 3996, 3132, 4224, 3155, 4247)(2765, 3857, 2881, 3973, 2955, 4047, 2893, 3985, 2986, 4078, 3103, 4195, 2951, 4043)(2767, 3859, 3163, 4255, 3216, 4308, 2816, 3908, 3201, 4293, 3084, 4176, 2824, 3916)(2771, 3863, 2862, 3954, 2994, 4086, 2918, 4010, 2949, 4041, 3116, 4208, 2990, 4082)(2773, 3865, 2879, 3971, 3252, 4344, 3022, 4114, 2880, 3972, 3192, 4284, 3175, 4267)(2775, 3867, 3178, 4270, 3225, 4317, 2828, 3920, 3189, 4281, 3093, 4185, 2810, 3902)(2778, 3870, 2858, 3950, 3057, 4149, 3052, 4144, 2861, 3953, 3204, 4296, 3183, 4275)(2780, 3872, 2815, 3907, 3215, 4307, 3028, 4120, 2847, 3939, 3164, 4256, 3139, 4231)(2784, 3876, 2928, 4020, 2883, 3975, 2945, 4037, 3260, 4352, 3134, 4226, 2960, 4052)(2785, 3877, 3188, 4280, 2981, 4073, 2786, 3878, 3190, 4282, 3106, 4198, 2852, 3944)(2787, 3879, 3011, 4103, 3250, 4342, 2871, 3963, 3206, 4298, 3108, 4200, 2830, 3922)(2792, 3884, 2832, 3924, 2925, 4017, 3037, 4129, 2899, 3991, 3168, 4260, 3157, 4249)(2795, 3887, 2827, 3919, 3224, 4316, 3034, 4126, 2831, 3923, 3179, 4271, 3153, 4245)(2801, 3893, 3049, 4141, 3246, 4338, 2859, 3951, 3196, 4288, 3122, 4214, 2820, 3912)(2805, 3897, 2848, 3940, 2902, 3994, 3259, 4351, 2923, 4015, 3181, 4273, 3029, 4121)(2806, 3898, 2993, 4085, 3267, 4359, 2967, 4059, 2942, 4034, 3226, 4318, 3027, 4119)(2817, 3909, 2930, 4022, 3010, 4102, 2914, 4006, 3220, 4312, 3142, 4234, 2850, 3942)(2823, 3915, 2922, 4014, 2995, 4087, 2992, 4084, 2890, 3982, 3240, 4332, 2939, 4031)(2865, 3957, 2931, 4023, 3263, 4355, 3012, 4104, 3021, 4113, 3258, 4350, 3058, 4150)(2884, 3976, 2911, 4003, 3262, 4354, 3050, 4142, 3041, 4133, 3038, 4130, 3253, 4345)(2903, 3995, 3013, 4105, 3270, 4362, 3272, 4364, 3273, 4365, 3266, 4358, 2956, 4048)(2926, 4018, 3051, 4143, 3274, 4366, 3275, 4367, 3276, 4368, 3269, 4361, 2996, 4088) L = (1, 2186)(2, 2185)(3, 2191)(4, 2193)(5, 2195)(6, 2197)(7, 2187)(8, 2200)(9, 2188)(10, 2203)(11, 2189)(12, 2206)(13, 2190)(14, 2209)(15, 2211)(16, 2192)(17, 2214)(18, 2215)(19, 2194)(20, 2218)(21, 2219)(22, 2196)(23, 2222)(24, 2223)(25, 2198)(26, 2226)(27, 2199)(28, 2228)(29, 2230)(30, 2201)(31, 2202)(32, 2234)(33, 2236)(34, 2204)(35, 2205)(36, 2240)(37, 2241)(38, 2207)(39, 2208)(40, 2245)(41, 2246)(42, 2210)(43, 2249)(44, 2212)(45, 2252)(46, 2213)(47, 2254)(48, 2238)(49, 2257)(50, 2216)(51, 2260)(52, 2217)(53, 2262)(54, 2232)(55, 2265)(56, 2220)(57, 2221)(58, 2269)(59, 2248)(60, 2272)(61, 2224)(62, 2225)(63, 2276)(64, 2243)(65, 2227)(66, 2280)(67, 2281)(68, 2229)(69, 2284)(70, 2231)(71, 2287)(72, 2288)(73, 2233)(74, 2291)(75, 2292)(76, 2235)(77, 2295)(78, 2237)(79, 2298)(80, 2299)(81, 2239)(82, 2302)(83, 2294)(84, 2304)(85, 2242)(86, 2307)(87, 2308)(88, 2244)(89, 2311)(90, 2283)(91, 2313)(92, 2247)(93, 2316)(94, 2317)(95, 2319)(96, 2250)(97, 2251)(98, 2323)(99, 2274)(100, 2253)(101, 2327)(102, 2328)(103, 2255)(104, 2256)(105, 2332)(106, 2333)(107, 2258)(108, 2259)(109, 2337)(110, 2267)(111, 2261)(112, 2341)(113, 2342)(114, 2263)(115, 2264)(116, 2346)(117, 2347)(118, 2266)(119, 2350)(120, 2268)(121, 2353)(122, 2354)(123, 2270)(124, 2271)(125, 2358)(126, 2359)(127, 2273)(128, 2362)(129, 2275)(130, 2365)(131, 2366)(132, 2277)(133, 2278)(134, 2370)(135, 2279)(136, 2372)(137, 2330)(138, 2374)(139, 2282)(140, 2377)(141, 2378)(142, 2380)(143, 2285)(144, 2286)(145, 2384)(146, 2321)(147, 2387)(148, 2289)(149, 2290)(150, 2391)(151, 2344)(152, 2393)(153, 2293)(154, 2396)(155, 2397)(156, 2399)(157, 2296)(158, 2297)(159, 2403)(160, 2335)(161, 2406)(162, 2300)(163, 2301)(164, 2410)(165, 2356)(166, 2303)(167, 2413)(168, 2414)(169, 2305)(170, 2306)(171, 2418)(172, 2349)(173, 2421)(174, 2309)(175, 2310)(176, 2425)(177, 2368)(178, 2312)(179, 2428)(180, 2429)(181, 2314)(182, 2315)(183, 2433)(184, 2361)(185, 2436)(186, 2318)(187, 2439)(188, 2320)(189, 2442)(190, 2322)(191, 2445)(192, 2446)(193, 2324)(194, 2325)(195, 2450)(196, 2326)(197, 2452)(198, 2389)(199, 2454)(200, 2329)(201, 2457)(202, 2458)(203, 2331)(204, 2461)(205, 2382)(206, 2464)(207, 2334)(208, 2467)(209, 2336)(210, 2470)(211, 2471)(212, 2338)(213, 2339)(214, 2475)(215, 2340)(216, 2477)(217, 2408)(218, 2479)(219, 2343)(220, 2482)(221, 2483)(222, 2345)(223, 2486)(224, 2401)(225, 2488)(226, 2348)(227, 2491)(228, 2493)(229, 2351)(230, 2352)(231, 2497)(232, 2423)(233, 2499)(234, 2355)(235, 2502)(236, 2503)(237, 2357)(238, 2506)(239, 2416)(240, 2509)(241, 2360)(242, 2512)(243, 2514)(244, 2363)(245, 2364)(246, 2518)(247, 2438)(248, 2520)(249, 2367)(250, 2523)(251, 2524)(252, 2369)(253, 2527)(254, 2431)(255, 2371)(256, 2530)(257, 2448)(258, 2373)(259, 2533)(260, 2534)(261, 2375)(262, 2376)(263, 2538)(264, 2441)(265, 2541)(266, 2379)(267, 2544)(268, 2381)(269, 2547)(270, 2383)(271, 2550)(272, 2551)(273, 2385)(274, 2386)(275, 2555)(276, 2556)(277, 2388)(278, 2559)(279, 2560)(280, 2390)(281, 2563)(282, 2473)(283, 2392)(284, 2566)(285, 2567)(286, 2394)(287, 2395)(288, 2571)(289, 2466)(290, 2574)(291, 2398)(292, 2577)(293, 2400)(294, 2580)(295, 2402)(296, 2583)(297, 2584)(298, 2404)(299, 2405)(300, 2588)(301, 2589)(302, 2407)(303, 2592)(304, 2409)(305, 2595)(306, 2495)(307, 2411)(308, 2598)(309, 2412)(310, 2600)(311, 2490)(312, 2603)(313, 2415)(314, 2606)(315, 2417)(316, 2609)(317, 2610)(318, 2419)(319, 2420)(320, 2614)(321, 2615)(322, 2422)(323, 2618)(324, 2619)(325, 2424)(326, 2622)(327, 2516)(328, 2426)(329, 2625)(330, 2427)(331, 2627)(332, 2511)(333, 2630)(334, 2430)(335, 2633)(336, 2432)(337, 2636)(338, 2637)(339, 2434)(340, 2435)(341, 2641)(342, 2642)(343, 2437)(344, 2645)(345, 2594)(346, 2440)(347, 2648)(348, 2650)(349, 2443)(350, 2444)(351, 2654)(352, 2543)(353, 2656)(354, 2447)(355, 2659)(356, 2660)(357, 2449)(358, 2663)(359, 2536)(360, 2451)(361, 2631)(362, 2553)(363, 2453)(364, 2667)(365, 2668)(366, 2455)(367, 2456)(368, 2672)(369, 2546)(370, 2675)(371, 2459)(372, 2460)(373, 2679)(374, 2680)(375, 2462)(376, 2463)(377, 2684)(378, 2621)(379, 2465)(380, 2686)(381, 2688)(382, 2468)(383, 2469)(384, 2692)(385, 2576)(386, 2694)(387, 2472)(388, 2697)(389, 2698)(390, 2474)(391, 2701)(392, 2569)(393, 2476)(394, 2604)(395, 2586)(396, 2478)(397, 2705)(398, 2706)(399, 2480)(400, 2481)(401, 2710)(402, 2579)(403, 2713)(404, 2484)(405, 2485)(406, 2717)(407, 2682)(408, 2487)(409, 2720)(410, 2529)(411, 2489)(412, 2967)(413, 2969)(414, 2492)(415, 2971)(416, 2494)(417, 2960)(418, 2942)(419, 2496)(420, 2578)(421, 2612)(422, 2498)(423, 2833)(424, 2811)(425, 2500)(426, 2501)(427, 2981)(428, 2605)(429, 2983)(430, 2504)(431, 2505)(432, 2987)(433, 2813)(434, 2507)(435, 2508)(436, 2989)(437, 2562)(438, 2510)(439, 2992)(440, 2900)(441, 2513)(442, 2909)(443, 2515)(444, 2850)(445, 2995)(446, 2517)(447, 2545)(448, 2639)(449, 2519)(450, 2941)(451, 2999)(452, 2521)(453, 2522)(454, 2916)(455, 2632)(456, 2839)(457, 2525)(458, 2526)(459, 3005)(460, 3007)(461, 2528)(462, 2818)(463, 2652)(464, 2531)(465, 2875)(466, 2532)(467, 2921)(468, 2647)(469, 2716)(470, 2535)(471, 3012)(472, 2537)(473, 3014)(474, 3016)(475, 2539)(476, 2540)(477, 2856)(478, 2985)(479, 2542)(480, 3021)(481, 3022)(482, 2962)(483, 2548)(484, 2549)(485, 2707)(486, 2677)(487, 3026)(488, 2552)(489, 3029)(490, 2880)(491, 2554)(492, 3031)(493, 2670)(494, 2691)(495, 2557)(496, 2558)(497, 3034)(498, 2591)(499, 3035)(500, 2561)(501, 2690)(502, 2564)(503, 2882)(504, 2565)(505, 3039)(506, 2685)(507, 2678)(508, 2568)(509, 3041)(510, 2570)(511, 3045)(512, 2829)(513, 2572)(514, 2573)(515, 3047)(516, 2863)(517, 2575)(518, 3050)(519, 3052)(520, 3046)(521, 2581)(522, 2582)(523, 2669)(524, 2715)(525, 2965)(526, 2585)(527, 2805)(528, 3057)(529, 2587)(530, 2887)(531, 2708)(532, 2653)(533, 2590)(534, 2974)(535, 2908)(536, 2593)(537, 3062)(538, 3064)(539, 3068)(540, 3071)(541, 3074)(542, 3078)(543, 3069)(544, 3084)(545, 3073)(546, 3089)(547, 3076)(548, 3093)(549, 3080)(550, 3098)(551, 3101)(552, 3085)(553, 3106)(554, 3108)(555, 3090)(556, 3112)(557, 3114)(558, 3094)(559, 3119)(560, 3122)(561, 3100)(562, 3127)(563, 3103)(564, 3130)(565, 3133)(566, 3107)(567, 3109)(568, 3139)(569, 3142)(570, 3113)(571, 3116)(572, 3148)(573, 3018)(574, 3120)(575, 3123)(576, 3153)(577, 3055)(578, 3128)(579, 3157)(580, 3132)(581, 3160)(582, 3134)(583, 3162)(584, 2978)(585, 3166)(586, 3140)(587, 3171)(588, 3003)(589, 3155)(590, 3149)(591, 3177)(592, 3180)(593, 3154)(594, 3141)(595, 3158)(596, 3183)(597, 3043)(598, 2990)(599, 3164)(600, 3186)(601, 3187)(602, 3168)(603, 3191)(604, 2933)(605, 3172)(606, 3194)(607, 3174)(608, 3001)(609, 3121)(610, 3030)(611, 3175)(612, 2951)(613, 3179)(614, 3024)(615, 3200)(616, 3181)(617, 3203)(618, 2913)(619, 3205)(620, 3167)(621, 2711)(622, 3048)(623, 3208)(624, 3184)(625, 3095)(626, 2973)(627, 2608)(628, 3189)(629, 2617)(630, 3192)(631, 3214)(632, 3196)(633, 3217)(634, 2646)(635, 3150)(636, 2935)(637, 3219)(638, 3195)(639, 3086)(640, 2939)(641, 3201)(642, 3204)(643, 3213)(644, 3206)(645, 2696)(646, 2915)(647, 3209)(648, 3227)(649, 2607)(650, 3229)(651, 3115)(652, 2924)(653, 3232)(654, 3124)(655, 2640)(656, 3198)(657, 2901)(658, 3202)(659, 3234)(660, 3019)(661, 3199)(662, 3237)(663, 3220)(664, 3239)(665, 3102)(666, 2628)(667, 3242)(668, 3027)(669, 3190)(670, 3226)(671, 3185)(672, 2661)(673, 3228)(674, 3176)(675, 3222)(676, 2873)(677, 3233)(678, 3247)(679, 2700)(680, 3099)(681, 2932)(682, 2977)(683, 3248)(684, 3188)(685, 3070)(686, 2888)(687, 3211)(688, 3002)(689, 2860)(690, 3017)(691, 2649)(692, 3238)(693, 3235)(694, 3240)(695, 3159)(696, 2674)(697, 3251)(698, 2687)(699, 3032)(700, 2912)(701, 3254)(702, 3077)(703, 2714)(704, 2870)(705, 3161)(706, 3245)(707, 3056)(708, 3231)(709, 3146)(710, 2980)(711, 3212)(712, 3257)(713, 2970)(714, 3156)(715, 3243)(716, 2624)(717, 2841)(718, 3131)(719, 3015)(720, 3249)(721, 3244)(722, 3079)(723, 3020)(724, 2719)(725, 2626)(726, 3163)(727, 3065)(728, 2884)(729, 2802)(730, 3000)(731, 2830)(732, 2638)(733, 3061)(734, 3129)(735, 3004)(736, 3223)(737, 2651)(738, 3145)(739, 3060)(740, 2836)(741, 3054)(742, 3081)(743, 3255)(744, 3236)(745, 3072)(746, 3178)(747, 3067)(748, 2865)(749, 2788)(750, 2961)(751, 2820)(752, 3264)(753, 3224)(754, 3097)(755, 2824)(756, 3008)(757, 2634)(758, 2602)(759, 2955)(760, 3058)(761, 3125)(762, 3258)(763, 3216)(764, 3009)(765, 2986)(766, 3265)(767, 2796)(768, 3256)(769, 3126)(770, 2994)(771, 2943)(772, 2963)(773, 3260)(774, 3252)(775, 3091)(776, 2601)(777, 2934)(778, 2666)(779, 2956)(780, 2984)(781, 2709)(782, 3215)(783, 2596)(784, 3088)(785, 2597)(786, 2897)(787, 2599)(788, 3152)(789, 2810)(790, 2718)(791, 3253)(792, 3110)(793, 2866)(794, 2768)(795, 3038)(796, 2894)(797, 2611)(798, 3225)(799, 2613)(800, 2964)(801, 2662)(802, 2949)(803, 2616)(804, 3267)(805, 2620)(806, 2782)(807, 3023)(808, 2623)(809, 3111)(810, 2954)(811, 2629)(812, 3006)(813, 3044)(814, 3082)(815, 2635)(816, 2914)(817, 2792)(818, 2872)(819, 2772)(820, 2919)(821, 2643)(822, 2996)(823, 2644)(824, 2940)(825, 2948)(826, 3063)(827, 3049)(828, 2655)(829, 3083)(830, 2657)(831, 2903)(832, 2658)(833, 2874)(834, 2757)(835, 2844)(836, 2907)(837, 2664)(838, 2665)(839, 2991)(840, 2798)(841, 3272)(842, 2671)(843, 2852)(844, 3143)(845, 2673)(846, 2794)(847, 2676)(848, 2883)(849, 3266)(850, 2681)(851, 2683)(852, 3241)(853, 3096)(854, 2979)(855, 2689)(856, 3250)(857, 2693)(858, 3137)(859, 2781)(860, 2997)(861, 2695)(862, 2704)(863, 2699)(864, 2806)(865, 3011)(866, 2702)(867, 3092)(868, 2703)(869, 3147)(870, 2925)(871, 2761)(872, 2891)(873, 2712)(874, 2944)(875, 3270)(876, 2923)(877, 2917)(878, 2721)(879, 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4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E14.652 Graph:: bipartite v = 702 e = 2184 f = 1456 degree seq :: [ 4^546, 14^156 ] E14.650 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^3, (Y3 * Y2^-1)^3, Y2^7, (Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-3 * Y1 * Y2^2 * Y1 * Y2^-1)^2, Y2^2 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 ] Map:: R = (1, 1093, 2, 1094)(3, 1095, 7, 1099)(4, 1096, 9, 1101)(5, 1097, 11, 1103)(6, 1098, 13, 1105)(8, 1100, 16, 1108)(10, 1102, 19, 1111)(12, 1104, 22, 1114)(14, 1106, 25, 1117)(15, 1107, 27, 1119)(17, 1109, 30, 1122)(18, 1110, 31, 1123)(20, 1112, 34, 1126)(21, 1113, 35, 1127)(23, 1115, 38, 1130)(24, 1116, 39, 1131)(26, 1118, 42, 1134)(28, 1120, 44, 1136)(29, 1121, 46, 1138)(32, 1124, 50, 1142)(33, 1125, 52, 1144)(36, 1128, 56, 1148)(37, 1129, 57, 1149)(40, 1132, 61, 1153)(41, 1133, 62, 1154)(43, 1135, 65, 1157)(45, 1137, 68, 1160)(47, 1139, 70, 1162)(48, 1140, 54, 1146)(49, 1141, 73, 1165)(51, 1143, 76, 1168)(53, 1145, 78, 1170)(55, 1147, 81, 1173)(58, 1150, 85, 1177)(59, 1151, 64, 1156)(60, 1152, 88, 1180)(63, 1155, 92, 1184)(66, 1158, 96, 1188)(67, 1159, 97, 1189)(69, 1161, 100, 1192)(71, 1163, 103, 1195)(72, 1164, 104, 1196)(74, 1166, 107, 1199)(75, 1167, 108, 1200)(77, 1169, 111, 1203)(79, 1171, 114, 1206)(80, 1172, 115, 1207)(82, 1174, 118, 1210)(83, 1175, 110, 1202)(84, 1176, 120, 1212)(86, 1178, 123, 1215)(87, 1179, 124, 1216)(89, 1181, 127, 1219)(90, 1182, 99, 1191)(91, 1183, 129, 1221)(93, 1185, 132, 1224)(94, 1186, 133, 1225)(95, 1187, 135, 1227)(98, 1190, 139, 1231)(101, 1193, 143, 1235)(102, 1194, 144, 1236)(105, 1197, 148, 1240)(106, 1198, 149, 1241)(109, 1201, 153, 1245)(112, 1204, 157, 1249)(113, 1205, 158, 1250)(116, 1208, 162, 1254)(117, 1209, 163, 1255)(119, 1211, 166, 1258)(121, 1213, 169, 1261)(122, 1214, 170, 1262)(125, 1217, 174, 1266)(126, 1218, 175, 1267)(128, 1220, 178, 1270)(130, 1222, 181, 1273)(131, 1223, 182, 1274)(134, 1226, 186, 1278)(136, 1228, 188, 1280)(137, 1229, 146, 1238)(138, 1230, 190, 1282)(140, 1232, 193, 1285)(141, 1233, 194, 1286)(142, 1234, 196, 1288)(145, 1237, 200, 1292)(147, 1239, 203, 1295)(150, 1242, 207, 1299)(151, 1243, 160, 1252)(152, 1244, 209, 1301)(154, 1246, 212, 1304)(155, 1247, 213, 1305)(156, 1248, 215, 1307)(159, 1251, 219, 1311)(161, 1253, 222, 1314)(164, 1256, 226, 1318)(165, 1257, 172, 1264)(167, 1259, 229, 1321)(168, 1260, 230, 1322)(171, 1263, 234, 1326)(173, 1265, 237, 1329)(176, 1268, 241, 1333)(177, 1269, 184, 1276)(179, 1271, 244, 1336)(180, 1272, 245, 1337)(183, 1275, 249, 1341)(185, 1277, 252, 1344)(187, 1279, 255, 1347)(189, 1281, 258, 1350)(191, 1283, 261, 1353)(192, 1284, 262, 1354)(195, 1287, 266, 1358)(197, 1289, 268, 1360)(198, 1290, 205, 1297)(199, 1291, 270, 1362)(201, 1293, 273, 1365)(202, 1294, 274, 1366)(204, 1296, 277, 1369)(206, 1298, 280, 1372)(208, 1300, 283, 1375)(210, 1302, 286, 1378)(211, 1303, 287, 1379)(214, 1306, 291, 1383)(216, 1308, 293, 1385)(217, 1309, 224, 1316)(218, 1310, 295, 1387)(220, 1312, 298, 1390)(221, 1313, 299, 1391)(223, 1315, 302, 1394)(225, 1317, 304, 1396)(227, 1319, 307, 1399)(228, 1320, 309, 1401)(231, 1323, 313, 1405)(232, 1324, 239, 1331)(233, 1325, 315, 1407)(235, 1327, 318, 1410)(236, 1328, 319, 1411)(238, 1330, 322, 1414)(240, 1332, 325, 1417)(242, 1334, 328, 1420)(243, 1335, 330, 1422)(246, 1338, 334, 1426)(247, 1339, 254, 1346)(248, 1340, 336, 1428)(250, 1342, 339, 1431)(251, 1343, 340, 1432)(253, 1345, 343, 1435)(256, 1348, 346, 1438)(257, 1349, 264, 1356)(259, 1351, 349, 1441)(260, 1352, 350, 1442)(263, 1355, 354, 1446)(265, 1357, 357, 1449)(267, 1359, 360, 1452)(269, 1361, 363, 1455)(271, 1363, 366, 1458)(272, 1364, 367, 1459)(275, 1367, 371, 1463)(276, 1368, 372, 1464)(278, 1370, 375, 1467)(279, 1371, 376, 1468)(281, 1373, 379, 1471)(282, 1374, 289, 1381)(284, 1376, 382, 1474)(285, 1377, 383, 1475)(288, 1380, 387, 1479)(290, 1382, 390, 1482)(292, 1384, 393, 1485)(294, 1386, 396, 1488)(296, 1388, 399, 1491)(297, 1389, 400, 1492)(300, 1392, 404, 1496)(301, 1393, 405, 1497)(303, 1395, 408, 1500)(305, 1397, 411, 1503)(306, 1398, 311, 1403)(308, 1400, 414, 1506)(310, 1402, 416, 1508)(312, 1404, 419, 1511)(314, 1406, 422, 1514)(316, 1408, 425, 1517)(317, 1409, 426, 1518)(320, 1412, 430, 1522)(321, 1413, 431, 1523)(323, 1415, 434, 1526)(324, 1416, 435, 1527)(326, 1418, 438, 1530)(327, 1419, 332, 1424)(329, 1421, 441, 1533)(331, 1423, 443, 1535)(333, 1425, 446, 1538)(335, 1427, 449, 1541)(337, 1429, 452, 1544)(338, 1430, 453, 1545)(341, 1433, 457, 1549)(342, 1434, 458, 1550)(344, 1436, 461, 1553)(345, 1437, 463, 1555)(347, 1439, 466, 1558)(348, 1440, 468, 1560)(351, 1443, 472, 1564)(352, 1444, 359, 1451)(353, 1445, 474, 1566)(355, 1447, 477, 1569)(356, 1448, 478, 1570)(358, 1450, 481, 1573)(361, 1453, 484, 1576)(362, 1454, 369, 1461)(364, 1456, 487, 1579)(365, 1457, 488, 1580)(368, 1460, 492, 1584)(370, 1462, 495, 1587)(373, 1465, 499, 1591)(374, 1466, 500, 1592)(377, 1469, 504, 1596)(378, 1470, 505, 1597)(380, 1472, 508, 1600)(381, 1473, 510, 1602)(384, 1476, 514, 1606)(385, 1477, 392, 1484)(386, 1478, 516, 1608)(388, 1480, 519, 1611)(389, 1481, 520, 1612)(391, 1483, 523, 1615)(394, 1486, 526, 1618)(395, 1487, 402, 1494)(397, 1489, 529, 1621)(398, 1490, 530, 1622)(401, 1493, 534, 1626)(403, 1495, 537, 1629)(406, 1498, 541, 1633)(407, 1499, 502, 1594)(409, 1501, 544, 1636)(410, 1502, 765, 1857)(412, 1504, 611, 1703)(413, 1505, 767, 1859)(415, 1507, 770, 1862)(417, 1509, 774, 1866)(418, 1510, 776, 1868)(420, 1512, 777, 1869)(421, 1513, 428, 1520)(423, 1515, 782, 1874)(424, 1516, 784, 1876)(427, 1519, 788, 1880)(429, 1521, 791, 1883)(432, 1524, 793, 1885)(433, 1525, 573, 1665)(436, 1528, 797, 1889)(437, 1529, 798, 1890)(439, 1531, 699, 1791)(440, 1532, 595, 1687)(442, 1534, 705, 1797)(444, 1536, 802, 1894)(445, 1537, 804, 1896)(447, 1539, 807, 1899)(448, 1540, 455, 1547)(450, 1542, 809, 1901)(451, 1543, 811, 1903)(454, 1546, 571, 1663)(456, 1548, 813, 1905)(459, 1551, 758, 1850)(460, 1552, 816, 1908)(462, 1554, 820, 1912)(464, 1556, 823, 1915)(465, 1557, 470, 1562)(467, 1559, 754, 1846)(469, 1561, 591, 1683)(471, 1563, 660, 1752)(473, 1565, 688, 1780)(475, 1567, 794, 1886)(476, 1568, 830, 1922)(479, 1571, 834, 1926)(480, 1572, 836, 1928)(482, 1574, 839, 1931)(483, 1575, 841, 1933)(485, 1577, 583, 1675)(486, 1578, 843, 1935)(489, 1581, 827, 1919)(490, 1582, 497, 1589)(491, 1583, 849, 1941)(493, 1585, 853, 1945)(494, 1586, 855, 1947)(496, 1588, 857, 1949)(498, 1590, 858, 1950)(501, 1593, 661, 1753)(503, 1595, 701, 1793)(506, 1598, 864, 1956)(507, 1599, 512, 1604)(509, 1601, 869, 1961)(511, 1603, 871, 1963)(513, 1605, 874, 1966)(515, 1607, 876, 1968)(517, 1609, 879, 1971)(518, 1610, 566, 1658)(521, 1613, 884, 1976)(522, 1614, 640, 1732)(524, 1616, 716, 1808)(525, 1617, 886, 1978)(527, 1619, 638, 1730)(528, 1620, 651, 1743)(531, 1623, 891, 1983)(532, 1624, 539, 1631)(533, 1625, 771, 1863)(535, 1627, 817, 1909)(536, 1628, 814, 1906)(538, 1630, 690, 1782)(540, 1632, 894, 1986)(542, 1634, 565, 1657)(543, 1635, 896, 1988)(545, 1637, 741, 1833)(546, 1638, 677, 1769)(547, 1639, 659, 1751)(548, 1640, 664, 1756)(549, 1641, 903, 1995)(550, 1642, 711, 1803)(551, 1643, 645, 1737)(552, 1644, 906, 1998)(553, 1645, 683, 1775)(554, 1646, 628, 1720)(555, 1647, 721, 1813)(556, 1648, 908, 2000)(557, 1649, 873, 1965)(558, 1650, 694, 1786)(559, 1651, 909, 2001)(560, 1652, 910, 2002)(561, 1653, 747, 1839)(562, 1654, 615, 1707)(563, 1655, 912, 2004)(564, 1656, 790, 1882)(567, 1659, 915, 2007)(568, 1660, 917, 2009)(569, 1661, 919, 2011)(570, 1662, 576, 1668)(572, 1664, 920, 2012)(574, 1666, 921, 2013)(575, 1667, 815, 1907)(577, 1669, 922, 2014)(578, 1670, 924, 2016)(579, 1671, 779, 1871)(580, 1672, 927, 2019)(581, 1673, 929, 2021)(582, 1674, 930, 2022)(584, 1676, 749, 1841)(585, 1677, 931, 2023)(586, 1678, 932, 2024)(587, 1679, 933, 2025)(588, 1680, 935, 2027)(589, 1681, 937, 2029)(590, 1682, 938, 2030)(592, 1684, 939, 2031)(593, 1685, 940, 2032)(594, 1686, 942, 2034)(596, 1688, 944, 2036)(597, 1689, 900, 1992)(598, 1690, 948, 2040)(599, 1691, 949, 2041)(600, 1692, 786, 1878)(601, 1693, 818, 1910)(602, 1694, 687, 1779)(603, 1695, 951, 2043)(604, 1696, 953, 2045)(605, 1697, 954, 2046)(606, 1698, 748, 1840)(607, 1699, 825, 1917)(608, 1700, 831, 1923)(609, 1701, 959, 2051)(610, 1702, 763, 1855)(612, 1704, 715, 1807)(613, 1705, 846, 1938)(614, 1706, 780, 1872)(616, 1708, 844, 1936)(617, 1709, 769, 1861)(618, 1710, 964, 2056)(619, 1711, 966, 2058)(620, 1712, 963, 2055)(621, 1713, 810, 1902)(622, 1714, 970, 2062)(623, 1715, 972, 2064)(624, 1716, 974, 2066)(625, 1717, 975, 2067)(626, 1718, 904, 1996)(627, 1719, 977, 2069)(629, 1721, 743, 1835)(630, 1722, 881, 1973)(631, 1723, 734, 1826)(632, 1724, 979, 2071)(633, 1725, 880, 1972)(634, 1726, 760, 1852)(635, 1727, 986, 2078)(636, 1728, 988, 2080)(637, 1729, 989, 2081)(639, 1731, 991, 2083)(641, 1733, 861, 1953)(642, 1734, 702, 1794)(643, 1735, 801, 1893)(644, 1736, 993, 2085)(646, 1738, 897, 1989)(647, 1739, 728, 1820)(648, 1740, 995, 2087)(649, 1741, 996, 2088)(650, 1742, 997, 2089)(652, 1744, 686, 1778)(653, 1745, 723, 1815)(654, 1746, 727, 1819)(655, 1747, 1001, 2093)(656, 1748, 1003, 2095)(657, 1749, 980, 2072)(658, 1750, 1005, 2097)(662, 1754, 994, 2086)(663, 1755, 866, 1958)(665, 1757, 985, 2077)(666, 1758, 703, 1795)(667, 1759, 1007, 2099)(668, 1760, 1008, 2100)(669, 1761, 1002, 2094)(670, 1762, 714, 1806)(671, 1763, 696, 1788)(672, 1764, 1013, 2105)(673, 1765, 1014, 2106)(674, 1766, 961, 2053)(675, 1767, 863, 1955)(676, 1768, 1016, 2108)(678, 1770, 999, 2091)(679, 1771, 693, 1785)(680, 1772, 789, 1881)(681, 1773, 1019, 2111)(682, 1774, 870, 1962)(684, 1776, 925, 2017)(685, 1777, 888, 1980)(689, 1781, 1020, 2112)(691, 1783, 832, 1924)(692, 1784, 1021, 2113)(695, 1787, 1000, 2092)(697, 1789, 967, 2059)(698, 1790, 1022, 2114)(700, 1792, 1024, 2116)(704, 1796, 768, 1860)(706, 1798, 945, 2037)(707, 1799, 1011, 2103)(708, 1800, 720, 1812)(709, 1801, 746, 1838)(710, 1802, 1015, 2107)(712, 1804, 851, 1943)(713, 1805, 852, 1944)(717, 1809, 1028, 2120)(718, 1810, 1029, 2121)(719, 1811, 1030, 2122)(722, 1814, 1012, 2104)(724, 1816, 982, 2074)(725, 1817, 1017, 2109)(726, 1818, 1032, 2124)(729, 1821, 733, 1825)(730, 1822, 955, 2047)(731, 1823, 799, 1891)(732, 1824, 971, 2063)(735, 1827, 1036, 2128)(736, 1828, 901, 1993)(737, 1829, 1039, 2131)(738, 1830, 877, 1969)(739, 1831, 889, 1981)(740, 1832, 1040, 2132)(742, 1834, 958, 2050)(744, 1836, 941, 2033)(745, 1837, 1042, 2134)(750, 1842, 755, 1847)(751, 1843, 1044, 2136)(752, 1844, 854, 1946)(753, 1845, 1045, 2137)(756, 1848, 1047, 2139)(757, 1849, 1048, 2140)(759, 1851, 812, 1904)(761, 1853, 808, 1900)(762, 1854, 1050, 2142)(764, 1856, 965, 2057)(766, 1858, 987, 2079)(772, 1864, 838, 1930)(773, 1865, 840, 1932)(775, 1867, 1009, 2101)(778, 1870, 947, 2039)(781, 1873, 1059, 2151)(783, 1875, 872, 1964)(785, 1877, 862, 1954)(787, 1879, 1061, 2153)(792, 1884, 1062, 2154)(795, 1887, 803, 1895)(796, 1888, 826, 1918)(800, 1892, 978, 2070)(805, 1897, 1066, 2158)(806, 1898, 1067, 2159)(819, 1911, 1071, 2163)(821, 1913, 973, 2065)(822, 1914, 1052, 2144)(824, 1916, 1035, 2127)(828, 1920, 998, 2090)(829, 1921, 1056, 2148)(833, 1925, 1054, 2146)(835, 1927, 845, 1937)(837, 1929, 875, 1967)(842, 1934, 934, 2026)(847, 1939, 1051, 2143)(848, 1940, 899, 1991)(850, 1942, 1074, 2166)(856, 1948, 983, 2075)(859, 1951, 911, 2003)(860, 1952, 1063, 2155)(865, 1957, 984, 2076)(867, 1959, 1078, 2170)(868, 1960, 1023, 2115)(878, 1970, 1080, 2172)(882, 1974, 893, 1985)(883, 1975, 1082, 2174)(885, 1977, 1010, 2102)(887, 1979, 905, 1997)(890, 1982, 990, 2082)(892, 1984, 1084, 2176)(895, 1987, 923, 2015)(898, 1990, 1043, 2135)(902, 1994, 1033, 2125)(907, 1999, 1053, 2145)(913, 2005, 1041, 2133)(914, 2006, 1026, 2118)(916, 2008, 1065, 2157)(918, 2010, 1088, 2180)(926, 2018, 1057, 2149)(928, 2020, 1079, 2171)(936, 2028, 1075, 2167)(943, 2035, 1072, 2164)(946, 2038, 1085, 2177)(950, 2042, 1089, 2181)(952, 2044, 1049, 2141)(956, 2048, 1073, 2165)(957, 2049, 1046, 2138)(960, 2052, 1091, 2183)(962, 2054, 1037, 2129)(968, 2060, 1058, 2150)(969, 2061, 1038, 2130)(976, 2068, 1068, 2160)(981, 2073, 1083, 2175)(992, 2084, 1092, 2184)(1004, 2096, 1027, 2119)(1006, 2098, 1086, 2178)(1018, 2110, 1031, 2123)(1025, 2117, 1081, 2173)(1034, 2126, 1077, 2169)(1055, 2147, 1064, 2156)(1060, 2152, 1069, 2161)(1070, 2162, 1090, 2182)(1076, 2168, 1087, 2179)(2185, 3277, 2187, 3279, 2192, 3284, 2201, 3293, 2204, 3296, 2194, 3286, 2188, 3280)(2186, 3278, 2189, 3281, 2196, 3288, 2207, 3299, 2210, 3302, 2198, 3290, 2190, 3282)(2191, 3283, 2197, 3289, 2208, 3300, 2224, 3316, 2229, 3321, 2212, 3304, 2199, 3291)(2193, 3285, 2202, 3294, 2216, 3308, 2235, 3327, 2220, 3312, 2205, 3297, 2195, 3287)(2200, 3292, 2211, 3303, 2227, 3319, 2250, 3342, 2255, 3347, 2231, 3323, 2213, 3305)(2203, 3295, 2217, 3309, 2237, 3329, 2263, 3355, 2258, 3350, 2233, 3325, 2215, 3307)(2206, 3298, 2219, 3311, 2239, 3331, 2266, 3358, 2270, 3362, 2242, 3334, 2221, 3313)(2209, 3301, 2225, 3317, 2247, 3339, 2277, 3369, 2273, 3365, 2244, 3336, 2223, 3315)(2214, 3306, 2230, 3322, 2253, 3345, 2285, 3377, 2289, 3381, 2256, 3348, 2232, 3324)(2218, 3310, 2238, 3330, 2264, 3356, 2300, 3392, 2296, 3388, 2261, 3353, 2236, 3328)(2222, 3314, 2241, 3333, 2268, 3360, 2305, 3397, 2309, 3401, 2271, 3363, 2243, 3335)(2226, 3318, 2248, 3340, 2278, 3370, 2318, 3410, 2314, 3406, 2275, 3367, 2246, 3338)(2228, 3320, 2251, 3343, 2282, 3374, 2324, 3416, 2320, 3412, 2279, 3371, 2249, 3341)(2234, 3326, 2257, 3349, 2290, 3382, 2334, 3426, 2338, 3430, 2293, 3385, 2259, 3351)(2240, 3332, 2267, 3359, 2303, 3395, 2351, 3443, 2348, 3440, 2301, 3393, 2265, 3357)(2245, 3337, 2272, 3364, 2310, 3402, 2360, 3452, 2363, 3455, 2312, 3404, 2274, 3366)(2252, 3344, 2283, 3375, 2325, 3417, 2379, 3471, 2375, 3467, 2322, 3414, 2281, 3373)(2254, 3346, 2286, 3378, 2329, 3421, 2385, 3477, 2381, 3473, 2326, 3418, 2284, 3376)(2260, 3352, 2292, 3384, 2336, 3428, 2394, 3486, 2398, 3490, 2339, 3431, 2294, 3386)(2262, 3354, 2295, 3387, 2340, 3432, 2400, 3492, 2404, 3496, 2343, 3435, 2297, 3389)(2269, 3361, 2306, 3398, 2355, 3447, 2419, 3511, 2415, 3507, 2352, 3444, 2304, 3396)(2276, 3368, 2313, 3405, 2364, 3456, 2430, 3522, 2434, 3526, 2367, 3459, 2315, 3407)(2280, 3372, 2319, 3411, 2371, 3463, 2440, 3532, 2443, 3535, 2373, 3465, 2321, 3413)(2287, 3379, 2330, 3422, 2386, 3478, 2459, 3551, 2455, 3547, 2383, 3475, 2328, 3420)(2288, 3380, 2331, 3423, 2388, 3480, 2462, 3554, 2407, 3499, 2345, 3437, 2299, 3391)(2291, 3383, 2335, 3427, 2392, 3484, 2468, 3560, 2465, 3557, 2390, 3482, 2333, 3425)(2298, 3390, 2342, 3434, 2402, 3494, 2480, 3572, 2484, 3576, 2405, 3497, 2344, 3436)(2302, 3394, 2347, 3439, 2409, 3501, 2489, 3581, 2492, 3584, 2411, 3503, 2349, 3441)(2307, 3399, 2356, 3448, 2420, 3512, 2504, 3596, 2500, 3592, 2417, 3509, 2354, 3446)(2308, 3400, 2357, 3449, 2422, 3514, 2507, 3599, 2437, 3529, 2369, 3461, 2317, 3409)(2311, 3403, 2361, 3453, 2426, 3518, 2513, 3605, 2510, 3602, 2424, 3516, 2359, 3451)(2316, 3408, 2366, 3458, 2432, 3524, 2521, 3613, 2525, 3617, 2435, 3527, 2368, 3460)(2323, 3415, 2374, 3466, 2444, 3536, 2535, 3627, 2539, 3631, 2447, 3539, 2376, 3468)(2327, 3419, 2380, 3472, 2451, 3543, 2545, 3637, 2548, 3640, 2453, 3545, 2382, 3474)(2332, 3424, 2389, 3481, 2463, 3555, 2561, 3653, 2557, 3649, 2460, 3552, 2387, 3479)(2337, 3429, 2395, 3487, 2472, 3564, 2572, 3664, 2568, 3660, 2469, 3561, 2393, 3485)(2341, 3433, 2401, 3493, 2478, 3570, 2581, 3673, 2578, 3670, 2476, 3568, 2399, 3491)(2346, 3438, 2406, 3498, 2485, 3577, 2590, 3682, 2593, 3685, 2487, 3579, 2408, 3500)(2350, 3442, 2397, 3489, 2474, 3566, 2575, 3667, 2601, 3693, 2494, 3586, 2412, 3504)(2353, 3445, 2414, 3506, 2496, 3588, 2604, 3696, 2607, 3699, 2498, 3590, 2416, 3508)(2358, 3450, 2423, 3515, 2508, 3600, 2620, 3712, 2616, 3708, 2505, 3597, 2421, 3513)(2362, 3454, 2427, 3519, 2515, 3607, 2628, 3720, 2542, 3634, 2449, 3541, 2378, 3470)(2365, 3457, 2431, 3523, 2519, 3611, 2634, 3726, 2631, 3723, 2517, 3609, 2429, 3521)(2370, 3462, 2436, 3528, 2526, 3618, 2643, 3735, 2646, 3738, 2528, 3620, 2438, 3530)(2372, 3464, 2441, 3533, 2531, 3623, 2651, 3743, 2648, 3740, 2529, 3621, 2439, 3531)(2377, 3469, 2446, 3538, 2537, 3629, 2659, 3751, 2663, 3755, 2540, 3632, 2448, 3540)(2384, 3476, 2454, 3546, 2549, 3641, 2673, 3765, 2677, 3769, 2552, 3644, 2456, 3548)(2391, 3483, 2464, 3556, 2562, 3654, 2690, 3782, 2693, 3785, 2564, 3656, 2466, 3558)(2396, 3488, 2473, 3565, 2573, 3665, 2705, 3797, 2701, 3793, 2570, 3662, 2471, 3563)(2403, 3495, 2481, 3573, 2585, 3677, 2719, 3811, 2715, 3807, 2582, 3674, 2479, 3571)(2410, 3502, 2490, 3582, 2596, 3688, 2729, 3821, 3083, 4175, 2594, 3686, 2488, 3580)(2413, 3505, 2493, 3585, 2599, 3691, 2790, 3882, 3141, 4233, 2602, 3694, 2495, 3587)(2418, 3510, 2499, 3591, 2608, 3700, 2969, 4061, 2845, 3937, 2611, 3703, 2501, 3593)(2425, 3517, 2509, 3601, 2621, 3713, 2920, 4012, 2858, 3950, 2623, 3715, 2511, 3603)(2428, 3520, 2516, 3608, 2629, 3721, 2752, 3844, 3102, 4194, 2626, 3718, 2514, 3606)(2433, 3525, 2522, 3614, 2638, 3730, 2749, 3841, 3097, 4189, 2635, 3727, 2520, 3612)(2442, 3534, 2532, 3624, 2653, 3745, 2763, 3855, 2680, 3772, 2554, 3646, 2458, 3550)(2445, 3537, 2536, 3628, 2657, 3749, 2733, 3825, 2937, 4029, 2655, 3747, 2534, 3626)(2450, 3542, 2541, 3633, 2664, 3756, 2863, 3955, 3202, 4294, 2666, 3758, 2543, 3635)(2452, 3544, 2546, 3638, 2669, 3761, 2732, 3824, 3086, 4178, 2667, 3759, 2544, 3636)(2457, 3549, 2551, 3643, 2675, 3767, 2804, 3896, 3152, 4244, 2678, 3770, 2553, 3645)(2461, 3553, 2556, 3648, 2682, 3774, 3043, 4135, 2868, 3960, 2685, 3777, 2558, 3650)(2467, 3559, 2483, 3575, 2587, 3679, 2722, 3814, 2810, 3902, 2695, 3787, 2565, 3657)(2470, 3562, 2567, 3659, 2697, 3789, 2892, 3984, 3052, 4144, 2699, 3791, 2569, 3661)(2475, 3567, 2576, 3668, 2708, 3800, 2736, 3828, 2924, 4016, 2706, 3798, 2574, 3666)(2477, 3569, 2577, 3669, 2709, 3801, 3071, 4163, 2890, 3982, 2711, 3803, 2579, 3671)(2482, 3574, 2586, 3678, 2720, 3812, 2783, 3875, 3134, 4226, 2717, 3809, 2584, 3676)(2486, 3578, 2591, 3683, 2726, 3818, 2739, 3831, 3091, 4183, 2724, 3816, 2589, 3681)(2491, 3583, 2597, 3689, 2933, 4025, 2767, 3859, 3039, 4131, 2613, 3705, 2503, 3595)(2497, 3589, 2605, 3697, 2963, 4055, 2735, 3827, 3089, 4181, 2929, 4021, 2603, 3695)(2502, 3594, 2610, 3702, 2971, 4063, 2817, 3909, 3167, 4259, 3041, 4133, 2612, 3704)(2506, 3598, 2615, 3707, 2976, 4068, 3210, 4302, 2896, 3988, 3037, 4129, 2617, 3709)(2512, 3604, 2524, 3616, 2640, 3732, 2998, 4090, 2822, 3914, 3127, 4219, 2624, 3716)(2518, 3610, 2630, 3722, 2990, 4082, 3217, 4309, 2914, 4006, 3088, 4180, 2632, 3724)(2523, 3615, 2639, 3731, 2874, 3966, 2793, 3885, 3144, 4236, 3223, 4315, 2637, 3729)(2527, 3619, 2644, 3736, 3001, 4093, 2742, 3834, 3034, 4126, 2946, 4038, 2642, 3734)(2530, 3622, 2647, 3739, 3006, 4098, 3032, 4124, 2922, 4014, 2944, 4036, 2649, 3741)(2533, 3625, 2654, 3746, 2849, 3941, 2764, 3856, 3112, 4204, 3187, 4279, 2652, 3744)(2538, 3630, 2660, 3752, 2878, 3970, 2718, 3810, 2955, 4047, 3239, 4331, 2658, 3750)(2547, 3639, 2670, 3762, 3028, 4120, 2781, 3873, 3131, 4223, 2687, 3779, 2560, 3652)(2550, 3642, 2674, 3766, 2939, 4031, 2740, 3832, 2847, 3939, 3173, 4265, 2672, 3764)(2555, 3647, 2679, 3771, 3040, 4132, 2927, 4019, 3140, 4232, 2789, 3881, 2681, 3773)(2559, 3651, 2684, 3776, 3046, 4138, 2809, 3901, 3160, 4252, 3225, 4317, 2686, 3778)(2563, 3655, 2691, 3783, 3009, 4101, 2730, 3822, 3085, 4177, 3247, 4339, 2689, 3781)(2566, 3658, 2694, 3786, 2989, 4081, 2836, 3928, 3182, 4274, 2926, 4018, 2696, 3788)(2571, 3663, 2700, 3792, 3062, 4154, 3033, 4125, 2676, 3768, 3035, 4127, 2702, 3794)(2580, 3672, 2592, 3684, 2727, 3819, 3081, 4173, 2805, 3897, 3153, 4245, 2712, 3804)(2583, 3675, 2714, 3806, 3074, 4166, 3050, 4142, 3146, 4238, 2797, 3889, 2716, 3808)(2588, 3680, 2723, 3815, 3077, 4169, 2747, 3839, 2860, 3952, 3143, 4235, 2721, 3813)(2595, 3687, 2949, 4041, 3236, 4328, 3007, 4099, 2957, 4049, 2994, 4086, 2738, 3830)(2598, 3690, 2812, 3904, 2830, 3922, 2772, 3864, 3120, 4212, 3198, 4290, 2951, 4043)(2600, 3692, 2956, 4048, 2905, 3997, 2755, 3847, 2921, 4013, 3082, 4174, 2954, 4046)(2606, 3698, 2965, 4057, 3065, 4157, 2791, 3883, 3142, 4234, 3216, 4308, 2619, 3711)(2609, 3701, 2970, 4062, 2987, 4079, 2743, 3835, 2828, 3920, 3159, 4251, 2968, 4060)(2614, 3706, 2975, 4067, 3242, 4334, 2964, 4056, 3130, 4222, 2780, 3872, 2784, 3876)(2618, 3710, 2757, 3849, 3011, 4103, 2821, 3913, 3174, 4266, 3075, 4167, 3000, 4092)(2622, 3714, 2983, 4075, 3084, 4176, 2731, 3823, 3048, 4140, 3044, 4136, 2982, 4074)(2625, 3717, 2779, 3871, 2940, 4032, 2854, 3946, 3194, 4286, 2962, 4054, 2915, 4007)(2627, 3719, 2889, 3981, 3209, 4301, 3245, 4337, 2972, 4064, 3109, 4201, 2799, 3891)(2633, 3725, 2645, 3737, 3003, 4095, 3169, 4261, 2818, 3910, 3168, 4260, 2985, 4077)(2636, 3728, 2995, 4087, 3252, 4344, 3177, 4269, 3136, 4228, 2787, 3879, 2759, 3851)(2641, 3733, 2999, 4091, 3100, 4192, 2751, 3843, 2842, 3934, 3133, 4225, 2997, 4089)(2650, 3742, 2662, 3754, 3017, 4109, 2704, 3796, 2692, 3784, 3051, 4143, 2871, 3963)(2656, 3748, 2844, 3936, 3190, 4282, 3237, 4329, 3022, 4114, 2958, 4050, 2754, 3846)(2661, 3753, 2760, 3852, 2707, 3799, 2824, 3916, 3176, 4268, 3258, 4350, 3014, 4106)(2665, 3757, 3021, 4113, 2703, 3795, 2750, 3842, 3098, 4190, 2882, 3974, 3020, 4112)(2668, 3760, 3025, 4117, 3251, 4343, 2991, 4083, 3036, 4128, 2880, 3972, 2737, 3829)(2671, 3763, 2867, 3959, 2906, 3998, 2770, 3862, 3056, 4148, 3156, 4248, 3027, 4119)(2683, 3775, 3045, 4137, 2850, 3942, 2741, 3833, 2904, 3996, 3203, 4295, 3042, 4134)(2688, 3780, 2885, 3977, 3069, 4161, 2947, 4039, 3171, 4263, 2819, 3911, 2825, 3917)(2698, 3790, 3059, 4151, 2986, 4078, 2746, 3838, 3095, 4187, 2865, 3957, 3058, 4150)(2710, 3802, 3072, 4164, 2907, 3999, 2734, 3826, 2961, 4053, 3226, 4318, 3070, 4162)(2713, 3805, 2835, 3927, 2903, 3995, 2886, 3978, 3201, 4293, 2862, 3954, 2869, 3961)(2725, 3817, 3078, 4170, 3270, 4362, 3229, 4321, 3162, 4254, 2815, 3907, 2745, 3837)(2728, 3820, 2931, 4023, 3008, 4100, 2758, 3850, 2894, 3986, 3119, 4211, 3080, 4172)(2744, 3836, 2877, 3969, 3206, 4298, 3246, 4338, 2977, 4069, 3178, 4270, 2831, 3923)(2748, 3840, 2942, 4034, 3234, 4326, 3276, 4368, 3224, 4316, 3038, 4130, 2801, 3893)(2753, 3845, 2813, 3905, 3064, 4156, 3265, 4357, 3272, 4364, 3175, 4267, 2875, 3967)(2756, 3848, 2798, 3890, 3147, 4239, 3264, 4356, 3063, 4155, 3161, 4253, 2902, 3994)(2761, 3853, 2866, 3958, 3111, 4203, 3255, 4347, 3004, 4096, 2974, 4066, 3107, 4199)(2762, 3854, 2811, 3903, 3068, 4160, 3238, 4330, 3018, 4110, 3122, 4214, 3110, 4202)(2765, 3857, 2794, 3886, 2898, 3990, 3211, 4303, 3263, 4355, 3054, 4146, 2841, 3933)(2766, 3858, 2932, 4024, 3227, 4319, 3275, 4367, 3200, 4292, 2923, 4015, 2776, 3868)(2768, 3860, 2857, 3949, 3029, 4121, 3250, 4342, 3055, 4147, 3139, 4231, 2848, 3940)(2769, 3861, 2774, 3866, 2978, 4070, 3248, 4340, 3273, 4365, 3189, 4281, 2959, 4051)(2771, 3863, 2823, 3915, 3101, 4193, 3013, 4105, 3230, 4322, 3114, 4206, 3118, 4210)(2773, 3865, 2785, 3877, 2870, 3962, 3019, 4111, 3259, 4351, 3199, 4291, 2859, 3951)(2775, 3867, 2840, 3932, 3188, 4280, 3231, 4323, 3256, 4348, 3129, 4221, 2829, 3921)(2777, 3869, 3125, 4217, 3148, 4240, 3243, 4335, 2966, 4058, 2895, 3987, 2879, 3971)(2778, 3870, 2930, 4022, 3116, 4208, 3244, 4336, 3215, 4307, 3094, 4186, 2992, 4084)(2782, 3874, 2826, 3918, 2913, 4005, 3005, 4097, 2967, 4059, 2893, 3985, 2808, 3900)(2786, 3878, 2851, 3943, 2917, 4009, 3214, 4306, 3222, 4314, 3024, 4116, 2938, 4030)(2788, 3880, 2973, 4065, 3124, 4216, 3031, 4123, 3207, 4299, 3057, 4149, 2943, 4035)(2792, 3884, 2838, 3930, 2888, 3980, 2948, 4040, 2928, 4020, 2864, 3956, 2820, 3912)(2795, 3887, 2960, 4052, 3240, 4332, 2988, 4080, 2883, 3975, 3165, 4257, 2899, 3991)(2796, 3888, 2832, 3924, 2952, 4044, 3205, 4297, 3049, 4141, 3061, 4153, 2925, 4017)(2800, 3892, 2807, 3899, 3157, 4249, 3191, 4283, 3262, 4354, 3053, 4145, 2843, 3935)(2802, 3894, 3149, 4241, 3179, 4271, 3267, 4359, 3145, 4237, 2861, 3953, 2814, 3906)(2803, 3895, 3047, 4139, 3105, 4197, 3254, 4346, 3257, 4349, 3103, 4195, 3151, 4243)(2806, 3898, 2846, 3938, 2981, 4073, 2910, 4002, 3012, 4104, 3002, 4094, 3155, 4247)(2816, 3908, 3164, 4256, 3106, 4198, 3076, 4168, 3269, 4361, 3104, 4196, 3166, 4258)(2827, 3919, 2876, 3968, 2911, 4003, 3208, 4300, 2891, 3983, 2897, 3989, 2993, 4085)(2833, 3925, 3073, 4165, 3096, 4188, 3067, 4159, 2950, 4042, 3113, 4205, 3163, 4255)(2834, 3926, 3172, 4264, 3137, 4229, 2919, 4011, 3221, 4313, 3092, 4184, 2935, 4027)(2837, 3929, 3183, 4275, 3212, 4304, 2900, 3992, 3060, 4152, 3235, 4327, 3184, 4276)(2839, 3931, 2936, 4028, 3090, 4182, 2901, 3993, 2909, 4001, 3132, 4224, 3186, 4278)(2852, 3944, 3193, 4285, 3099, 4191, 3218, 4310, 2916, 4008, 3121, 4213, 3150, 4242)(2853, 3945, 3158, 4250, 3126, 4218, 2941, 4033, 3233, 4325, 3093, 4185, 2980, 4072)(2855, 3947, 3195, 4287, 3204, 4296, 2872, 3964, 3023, 4115, 3253, 4345, 3196, 4288)(2856, 3948, 2984, 4076, 3087, 4179, 2873, 3965, 2884, 3976, 3015, 4107, 3181, 4273)(2881, 3973, 3016, 4108, 3117, 4209, 3271, 4363, 3241, 4333, 3115, 4207, 3192, 4284)(2887, 3979, 3170, 4262, 3266, 4358, 3066, 4158, 3030, 4122, 3220, 4312, 2996, 4088)(2908, 4000, 3213, 4305, 3108, 4200, 3260, 4352, 3026, 4118, 3123, 4215, 3180, 4272)(2912, 4004, 3154, 4246, 3261, 4353, 3249, 4341, 3135, 4227, 3232, 4324, 2945, 4037)(2918, 4010, 3197, 4289, 3228, 4320, 2934, 4026, 3138, 4230, 3274, 4366, 3219, 4311)(2953, 4045, 3185, 4277, 3010, 4102, 2979, 4071, 3128, 4220, 3268, 4360, 3079, 4171) L = (1, 2186)(2, 2185)(3, 2191)(4, 2193)(5, 2195)(6, 2197)(7, 2187)(8, 2200)(9, 2188)(10, 2203)(11, 2189)(12, 2206)(13, 2190)(14, 2209)(15, 2211)(16, 2192)(17, 2214)(18, 2215)(19, 2194)(20, 2218)(21, 2219)(22, 2196)(23, 2222)(24, 2223)(25, 2198)(26, 2226)(27, 2199)(28, 2228)(29, 2230)(30, 2201)(31, 2202)(32, 2234)(33, 2236)(34, 2204)(35, 2205)(36, 2240)(37, 2241)(38, 2207)(39, 2208)(40, 2245)(41, 2246)(42, 2210)(43, 2249)(44, 2212)(45, 2252)(46, 2213)(47, 2254)(48, 2238)(49, 2257)(50, 2216)(51, 2260)(52, 2217)(53, 2262)(54, 2232)(55, 2265)(56, 2220)(57, 2221)(58, 2269)(59, 2248)(60, 2272)(61, 2224)(62, 2225)(63, 2276)(64, 2243)(65, 2227)(66, 2280)(67, 2281)(68, 2229)(69, 2284)(70, 2231)(71, 2287)(72, 2288)(73, 2233)(74, 2291)(75, 2292)(76, 2235)(77, 2295)(78, 2237)(79, 2298)(80, 2299)(81, 2239)(82, 2302)(83, 2294)(84, 2304)(85, 2242)(86, 2307)(87, 2308)(88, 2244)(89, 2311)(90, 2283)(91, 2313)(92, 2247)(93, 2316)(94, 2317)(95, 2319)(96, 2250)(97, 2251)(98, 2323)(99, 2274)(100, 2253)(101, 2327)(102, 2328)(103, 2255)(104, 2256)(105, 2332)(106, 2333)(107, 2258)(108, 2259)(109, 2337)(110, 2267)(111, 2261)(112, 2341)(113, 2342)(114, 2263)(115, 2264)(116, 2346)(117, 2347)(118, 2266)(119, 2350)(120, 2268)(121, 2353)(122, 2354)(123, 2270)(124, 2271)(125, 2358)(126, 2359)(127, 2273)(128, 2362)(129, 2275)(130, 2365)(131, 2366)(132, 2277)(133, 2278)(134, 2370)(135, 2279)(136, 2372)(137, 2330)(138, 2374)(139, 2282)(140, 2377)(141, 2378)(142, 2380)(143, 2285)(144, 2286)(145, 2384)(146, 2321)(147, 2387)(148, 2289)(149, 2290)(150, 2391)(151, 2344)(152, 2393)(153, 2293)(154, 2396)(155, 2397)(156, 2399)(157, 2296)(158, 2297)(159, 2403)(160, 2335)(161, 2406)(162, 2300)(163, 2301)(164, 2410)(165, 2356)(166, 2303)(167, 2413)(168, 2414)(169, 2305)(170, 2306)(171, 2418)(172, 2349)(173, 2421)(174, 2309)(175, 2310)(176, 2425)(177, 2368)(178, 2312)(179, 2428)(180, 2429)(181, 2314)(182, 2315)(183, 2433)(184, 2361)(185, 2436)(186, 2318)(187, 2439)(188, 2320)(189, 2442)(190, 2322)(191, 2445)(192, 2446)(193, 2324)(194, 2325)(195, 2450)(196, 2326)(197, 2452)(198, 2389)(199, 2454)(200, 2329)(201, 2457)(202, 2458)(203, 2331)(204, 2461)(205, 2382)(206, 2464)(207, 2334)(208, 2467)(209, 2336)(210, 2470)(211, 2471)(212, 2338)(213, 2339)(214, 2475)(215, 2340)(216, 2477)(217, 2408)(218, 2479)(219, 2343)(220, 2482)(221, 2483)(222, 2345)(223, 2486)(224, 2401)(225, 2488)(226, 2348)(227, 2491)(228, 2493)(229, 2351)(230, 2352)(231, 2497)(232, 2423)(233, 2499)(234, 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3979)(1796, 3980)(1797, 3981)(1798, 3982)(1799, 3983)(1800, 3984)(1801, 3985)(1802, 3986)(1803, 3987)(1804, 3988)(1805, 3989)(1806, 3990)(1807, 3991)(1808, 3992)(1809, 3993)(1810, 3994)(1811, 3995)(1812, 3996)(1813, 3997)(1814, 3998)(1815, 3999)(1816, 4000)(1817, 4001)(1818, 4002)(1819, 4003)(1820, 4004)(1821, 4005)(1822, 4006)(1823, 4007)(1824, 4008)(1825, 4009)(1826, 4010)(1827, 4011)(1828, 4012)(1829, 4013)(1830, 4014)(1831, 4015)(1832, 4016)(1833, 4017)(1834, 4018)(1835, 4019)(1836, 4020)(1837, 4021)(1838, 4022)(1839, 4023)(1840, 4024)(1841, 4025)(1842, 4026)(1843, 4027)(1844, 4028)(1845, 4029)(1846, 4030)(1847, 4031)(1848, 4032)(1849, 4033)(1850, 4034)(1851, 4035)(1852, 4036)(1853, 4037)(1854, 4038)(1855, 4039)(1856, 4040)(1857, 4041)(1858, 4042)(1859, 4043)(1860, 4044)(1861, 4045)(1862, 4046)(1863, 4047)(1864, 4048)(1865, 4049)(1866, 4050)(1867, 4051)(1868, 4052)(1869, 4053)(1870, 4054)(1871, 4055)(1872, 4056)(1873, 4057)(1874, 4058)(1875, 4059)(1876, 4060)(1877, 4061)(1878, 4062)(1879, 4063)(1880, 4064)(1881, 4065)(1882, 4066)(1883, 4067)(1884, 4068)(1885, 4069)(1886, 4070)(1887, 4071)(1888, 4072)(1889, 4073)(1890, 4074)(1891, 4075)(1892, 4076)(1893, 4077)(1894, 4078)(1895, 4079)(1896, 4080)(1897, 4081)(1898, 4082)(1899, 4083)(1900, 4084)(1901, 4085)(1902, 4086)(1903, 4087)(1904, 4088)(1905, 4089)(1906, 4090)(1907, 4091)(1908, 4092)(1909, 4093)(1910, 4094)(1911, 4095)(1912, 4096)(1913, 4097)(1914, 4098)(1915, 4099)(1916, 4100)(1917, 4101)(1918, 4102)(1919, 4103)(1920, 4104)(1921, 4105)(1922, 4106)(1923, 4107)(1924, 4108)(1925, 4109)(1926, 4110)(1927, 4111)(1928, 4112)(1929, 4113)(1930, 4114)(1931, 4115)(1932, 4116)(1933, 4117)(1934, 4118)(1935, 4119)(1936, 4120)(1937, 4121)(1938, 4122)(1939, 4123)(1940, 4124)(1941, 4125)(1942, 4126)(1943, 4127)(1944, 4128)(1945, 4129)(1946, 4130)(1947, 4131)(1948, 4132)(1949, 4133)(1950, 4134)(1951, 4135)(1952, 4136)(1953, 4137)(1954, 4138)(1955, 4139)(1956, 4140)(1957, 4141)(1958, 4142)(1959, 4143)(1960, 4144)(1961, 4145)(1962, 4146)(1963, 4147)(1964, 4148)(1965, 4149)(1966, 4150)(1967, 4151)(1968, 4152)(1969, 4153)(1970, 4154)(1971, 4155)(1972, 4156)(1973, 4157)(1974, 4158)(1975, 4159)(1976, 4160)(1977, 4161)(1978, 4162)(1979, 4163)(1980, 4164)(1981, 4165)(1982, 4166)(1983, 4167)(1984, 4168)(1985, 4169)(1986, 4170)(1987, 4171)(1988, 4172)(1989, 4173)(1990, 4174)(1991, 4175)(1992, 4176)(1993, 4177)(1994, 4178)(1995, 4179)(1996, 4180)(1997, 4181)(1998, 4182)(1999, 4183)(2000, 4184)(2001, 4185)(2002, 4186)(2003, 4187)(2004, 4188)(2005, 4189)(2006, 4190)(2007, 4191)(2008, 4192)(2009, 4193)(2010, 4194)(2011, 4195)(2012, 4196)(2013, 4197)(2014, 4198)(2015, 4199)(2016, 4200)(2017, 4201)(2018, 4202)(2019, 4203)(2020, 4204)(2021, 4205)(2022, 4206)(2023, 4207)(2024, 4208)(2025, 4209)(2026, 4210)(2027, 4211)(2028, 4212)(2029, 4213)(2030, 4214)(2031, 4215)(2032, 4216)(2033, 4217)(2034, 4218)(2035, 4219)(2036, 4220)(2037, 4221)(2038, 4222)(2039, 4223)(2040, 4224)(2041, 4225)(2042, 4226)(2043, 4227)(2044, 4228)(2045, 4229)(2046, 4230)(2047, 4231)(2048, 4232)(2049, 4233)(2050, 4234)(2051, 4235)(2052, 4236)(2053, 4237)(2054, 4238)(2055, 4239)(2056, 4240)(2057, 4241)(2058, 4242)(2059, 4243)(2060, 4244)(2061, 4245)(2062, 4246)(2063, 4247)(2064, 4248)(2065, 4249)(2066, 4250)(2067, 4251)(2068, 4252)(2069, 4253)(2070, 4254)(2071, 4255)(2072, 4256)(2073, 4257)(2074, 4258)(2075, 4259)(2076, 4260)(2077, 4261)(2078, 4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E14.653 Graph:: bipartite v = 702 e = 2184 f = 1456 degree seq :: [ 4^546, 14^156 ] E14.651 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2)^3, (Y3 * Y2^-1)^3, Y2^7, (Y2^2 * Y1 * Y2^-3 * Y1 * Y2)^3, Y2^2 * Y1 * Y2^3 * Y1 * Y2^-2 * Y1 * Y2^3 * Y1 * Y2^-2 * Y1 * Y2^2 * Y1 * Y2^-3 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 ] Map:: R = (1, 1093, 2, 1094)(3, 1095, 7, 1099)(4, 1096, 9, 1101)(5, 1097, 11, 1103)(6, 1098, 13, 1105)(8, 1100, 16, 1108)(10, 1102, 19, 1111)(12, 1104, 22, 1114)(14, 1106, 25, 1117)(15, 1107, 27, 1119)(17, 1109, 30, 1122)(18, 1110, 31, 1123)(20, 1112, 34, 1126)(21, 1113, 35, 1127)(23, 1115, 38, 1130)(24, 1116, 39, 1131)(26, 1118, 42, 1134)(28, 1120, 44, 1136)(29, 1121, 46, 1138)(32, 1124, 50, 1142)(33, 1125, 52, 1144)(36, 1128, 56, 1148)(37, 1129, 57, 1149)(40, 1132, 61, 1153)(41, 1133, 62, 1154)(43, 1135, 65, 1157)(45, 1137, 68, 1160)(47, 1139, 70, 1162)(48, 1140, 54, 1146)(49, 1141, 73, 1165)(51, 1143, 76, 1168)(53, 1145, 78, 1170)(55, 1147, 81, 1173)(58, 1150, 85, 1177)(59, 1151, 64, 1156)(60, 1152, 88, 1180)(63, 1155, 92, 1184)(66, 1158, 96, 1188)(67, 1159, 97, 1189)(69, 1161, 100, 1192)(71, 1163, 103, 1195)(72, 1164, 104, 1196)(74, 1166, 107, 1199)(75, 1167, 108, 1200)(77, 1169, 111, 1203)(79, 1171, 114, 1206)(80, 1172, 115, 1207)(82, 1174, 118, 1210)(83, 1175, 110, 1202)(84, 1176, 120, 1212)(86, 1178, 123, 1215)(87, 1179, 124, 1216)(89, 1181, 127, 1219)(90, 1182, 99, 1191)(91, 1183, 129, 1221)(93, 1185, 132, 1224)(94, 1186, 133, 1225)(95, 1187, 135, 1227)(98, 1190, 139, 1231)(101, 1193, 143, 1235)(102, 1194, 144, 1236)(105, 1197, 148, 1240)(106, 1198, 149, 1241)(109, 1201, 153, 1245)(112, 1204, 157, 1249)(113, 1205, 158, 1250)(116, 1208, 162, 1254)(117, 1209, 163, 1255)(119, 1211, 166, 1258)(121, 1213, 169, 1261)(122, 1214, 170, 1262)(125, 1217, 174, 1266)(126, 1218, 175, 1267)(128, 1220, 178, 1270)(130, 1222, 181, 1273)(131, 1223, 182, 1274)(134, 1226, 186, 1278)(136, 1228, 188, 1280)(137, 1229, 146, 1238)(138, 1230, 190, 1282)(140, 1232, 193, 1285)(141, 1233, 194, 1286)(142, 1234, 196, 1288)(145, 1237, 200, 1292)(147, 1239, 203, 1295)(150, 1242, 207, 1299)(151, 1243, 160, 1252)(152, 1244, 209, 1301)(154, 1246, 212, 1304)(155, 1247, 213, 1305)(156, 1248, 215, 1307)(159, 1251, 219, 1311)(161, 1253, 222, 1314)(164, 1256, 226, 1318)(165, 1257, 172, 1264)(167, 1259, 229, 1321)(168, 1260, 230, 1322)(171, 1263, 234, 1326)(173, 1265, 237, 1329)(176, 1268, 241, 1333)(177, 1269, 184, 1276)(179, 1271, 244, 1336)(180, 1272, 245, 1337)(183, 1275, 249, 1341)(185, 1277, 252, 1344)(187, 1279, 255, 1347)(189, 1281, 258, 1350)(191, 1283, 261, 1353)(192, 1284, 262, 1354)(195, 1287, 266, 1358)(197, 1289, 268, 1360)(198, 1290, 205, 1297)(199, 1291, 270, 1362)(201, 1293, 273, 1365)(202, 1294, 274, 1366)(204, 1296, 277, 1369)(206, 1298, 280, 1372)(208, 1300, 283, 1375)(210, 1302, 286, 1378)(211, 1303, 287, 1379)(214, 1306, 291, 1383)(216, 1308, 293, 1385)(217, 1309, 224, 1316)(218, 1310, 295, 1387)(220, 1312, 298, 1390)(221, 1313, 299, 1391)(223, 1315, 302, 1394)(225, 1317, 304, 1396)(227, 1319, 307, 1399)(228, 1320, 309, 1401)(231, 1323, 313, 1405)(232, 1324, 239, 1331)(233, 1325, 315, 1407)(235, 1327, 318, 1410)(236, 1328, 319, 1411)(238, 1330, 322, 1414)(240, 1332, 325, 1417)(242, 1334, 328, 1420)(243, 1335, 330, 1422)(246, 1338, 334, 1426)(247, 1339, 254, 1346)(248, 1340, 336, 1428)(250, 1342, 339, 1431)(251, 1343, 340, 1432)(253, 1345, 343, 1435)(256, 1348, 346, 1438)(257, 1349, 264, 1356)(259, 1351, 349, 1441)(260, 1352, 350, 1442)(263, 1355, 354, 1446)(265, 1357, 357, 1449)(267, 1359, 360, 1452)(269, 1361, 363, 1455)(271, 1363, 366, 1458)(272, 1364, 367, 1459)(275, 1367, 371, 1463)(276, 1368, 372, 1464)(278, 1370, 375, 1467)(279, 1371, 376, 1468)(281, 1373, 379, 1471)(282, 1374, 289, 1381)(284, 1376, 382, 1474)(285, 1377, 383, 1475)(288, 1380, 387, 1479)(290, 1382, 390, 1482)(292, 1384, 393, 1485)(294, 1386, 396, 1488)(296, 1388, 399, 1491)(297, 1389, 400, 1492)(300, 1392, 404, 1496)(301, 1393, 405, 1497)(303, 1395, 408, 1500)(305, 1397, 411, 1503)(306, 1398, 311, 1403)(308, 1400, 414, 1506)(310, 1402, 416, 1508)(312, 1404, 419, 1511)(314, 1406, 422, 1514)(316, 1408, 425, 1517)(317, 1409, 426, 1518)(320, 1412, 430, 1522)(321, 1413, 431, 1523)(323, 1415, 434, 1526)(324, 1416, 435, 1527)(326, 1418, 438, 1530)(327, 1419, 332, 1424)(329, 1421, 441, 1533)(331, 1423, 443, 1535)(333, 1425, 446, 1538)(335, 1427, 449, 1541)(337, 1429, 452, 1544)(338, 1430, 453, 1545)(341, 1433, 457, 1549)(342, 1434, 458, 1550)(344, 1436, 461, 1553)(345, 1437, 463, 1555)(347, 1439, 466, 1558)(348, 1440, 468, 1560)(351, 1443, 472, 1564)(352, 1444, 359, 1451)(353, 1445, 474, 1566)(355, 1447, 477, 1569)(356, 1448, 478, 1570)(358, 1450, 481, 1573)(361, 1453, 484, 1576)(362, 1454, 369, 1461)(364, 1456, 487, 1579)(365, 1457, 488, 1580)(368, 1460, 492, 1584)(370, 1462, 495, 1587)(373, 1465, 499, 1591)(374, 1466, 500, 1592)(377, 1469, 436, 1528)(378, 1470, 504, 1596)(380, 1472, 507, 1599)(381, 1473, 509, 1601)(384, 1476, 513, 1605)(385, 1477, 392, 1484)(386, 1478, 515, 1607)(388, 1480, 518, 1610)(389, 1481, 519, 1611)(391, 1483, 522, 1614)(394, 1486, 524, 1616)(395, 1487, 402, 1494)(397, 1489, 527, 1619)(398, 1490, 528, 1620)(401, 1493, 532, 1624)(403, 1495, 535, 1627)(406, 1498, 538, 1630)(407, 1499, 502, 1594)(409, 1501, 462, 1554)(410, 1502, 755, 1847)(412, 1504, 756, 1848)(413, 1505, 652, 1744)(415, 1507, 761, 1853)(417, 1509, 698, 1790)(418, 1510, 626, 1718)(420, 1512, 702, 1794)(421, 1513, 428, 1520)(423, 1515, 479, 1571)(424, 1516, 770, 1862)(427, 1519, 558, 1650)(429, 1521, 774, 1866)(432, 1524, 503, 1595)(433, 1525, 777, 1869)(437, 1529, 779, 1871)(439, 1531, 550, 1642)(440, 1532, 782, 1874)(442, 1534, 720, 1812)(444, 1536, 612, 1704)(445, 1537, 784, 1876)(447, 1539, 783, 1875)(448, 1540, 455, 1547)(450, 1542, 520, 1612)(451, 1543, 740, 1832)(454, 1546, 788, 1880)(456, 1548, 792, 1884)(459, 1551, 540, 1632)(460, 1552, 795, 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3961, 2930, 4022, 3169, 4261, 3007, 4099, 3206, 4298, 2959, 4051)(2772, 3864, 3144, 4236, 3276, 4368, 3123, 4215, 2796, 3888, 3176, 4268, 3147, 4239)(2773, 3865, 3096, 4188, 3220, 4312, 2867, 3959, 2845, 3937, 2996, 4088, 3148, 4240)(2774, 3866, 3149, 4241, 3160, 4252, 2782, 3874, 3138, 4230, 3253, 4345, 2937, 4029)(2778, 3870, 2892, 3984, 2970, 4062, 2988, 4080, 3223, 4315, 3214, 4306, 2921, 4013)(2783, 3875, 3028, 4120, 3208, 4300, 2837, 3929, 3172, 4264, 3211, 4303, 2842, 3934)(2784, 3876, 3069, 4161, 2887, 3979, 2861, 3953, 2912, 4004, 2982, 4074, 3161, 4253)(2785, 3877, 2822, 3914, 2873, 3965, 3186, 4278, 2858, 3950, 3155, 4247, 3163, 4255)(2789, 3881, 3168, 4260, 3215, 4307, 2853, 3945, 3184, 4276, 3204, 4296, 2831, 3923)(2791, 3883, 2828, 3920, 2922, 4014, 3193, 4285, 2911, 4003, 3187, 4279, 3171, 4263)(2795, 3887, 3001, 4093, 2864, 3956, 2846, 3938, 2928, 4020, 2938, 4030, 3162, 4254)(2797, 3889, 2808, 3900, 2896, 3988, 3194, 4286, 2844, 3936, 3142, 4234, 3178, 4270)(2801, 3893, 2816, 3908, 2960, 4052, 3202, 4294, 2927, 4019, 3195, 4287, 3183, 4275)(2804, 3896, 2862, 3954, 3218, 4310, 3203, 4295, 3243, 4335, 3237, 4329, 2929, 4021)(2811, 3903, 3105, 4197, 2948, 4040, 2826, 3918, 2838, 3930, 2907, 3999, 3182, 4274)(2814, 3906, 2854, 3946, 2885, 3977, 3170, 4262, 2824, 3916, 3042, 4134, 2915, 4007)(2818, 3910, 2847, 3939, 3011, 4103, 3213, 4305, 3041, 4133, 3226, 4318, 2969, 4061)(2834, 3926, 2913, 4005, 3245, 4337, 3221, 4313, 3251, 4343, 3225, 4317, 2876, 3968)(2850, 3942, 2925, 4017, 3036, 4128, 3235, 4327, 3262, 4354, 2983, 4075, 2898, 3990) L = (1, 2186)(2, 2185)(3, 2191)(4, 2193)(5, 2195)(6, 2197)(7, 2187)(8, 2200)(9, 2188)(10, 2203)(11, 2189)(12, 2206)(13, 2190)(14, 2209)(15, 2211)(16, 2192)(17, 2214)(18, 2215)(19, 2194)(20, 2218)(21, 2219)(22, 2196)(23, 2222)(24, 2223)(25, 2198)(26, 2226)(27, 2199)(28, 2228)(29, 2230)(30, 2201)(31, 2202)(32, 2234)(33, 2236)(34, 2204)(35, 2205)(36, 2240)(37, 2241)(38, 2207)(39, 2208)(40, 2245)(41, 2246)(42, 2210)(43, 2249)(44, 2212)(45, 2252)(46, 2213)(47, 2254)(48, 2238)(49, 2257)(50, 2216)(51, 2260)(52, 2217)(53, 2262)(54, 2232)(55, 2265)(56, 2220)(57, 2221)(58, 2269)(59, 2248)(60, 2272)(61, 2224)(62, 2225)(63, 2276)(64, 2243)(65, 2227)(66, 2280)(67, 2281)(68, 2229)(69, 2284)(70, 2231)(71, 2287)(72, 2288)(73, 2233)(74, 2291)(75, 2292)(76, 2235)(77, 2295)(78, 2237)(79, 2298)(80, 2299)(81, 2239)(82, 2302)(83, 2294)(84, 2304)(85, 2242)(86, 2307)(87, 2308)(88, 2244)(89, 2311)(90, 2283)(91, 2313)(92, 2247)(93, 2316)(94, 2317)(95, 2319)(96, 2250)(97, 2251)(98, 2323)(99, 2274)(100, 2253)(101, 2327)(102, 2328)(103, 2255)(104, 2256)(105, 2332)(106, 2333)(107, 2258)(108, 2259)(109, 2337)(110, 2267)(111, 2261)(112, 2341)(113, 2342)(114, 2263)(115, 2264)(116, 2346)(117, 2347)(118, 2266)(119, 2350)(120, 2268)(121, 2353)(122, 2354)(123, 2270)(124, 2271)(125, 2358)(126, 2359)(127, 2273)(128, 2362)(129, 2275)(130, 2365)(131, 2366)(132, 2277)(133, 2278)(134, 2370)(135, 2279)(136, 2372)(137, 2330)(138, 2374)(139, 2282)(140, 2377)(141, 2378)(142, 2380)(143, 2285)(144, 2286)(145, 2384)(146, 2321)(147, 2387)(148, 2289)(149, 2290)(150, 2391)(151, 2344)(152, 2393)(153, 2293)(154, 2396)(155, 2397)(156, 2399)(157, 2296)(158, 2297)(159, 2403)(160, 2335)(161, 2406)(162, 2300)(163, 2301)(164, 2410)(165, 2356)(166, 2303)(167, 2413)(168, 2414)(169, 2305)(170, 2306)(171, 2418)(172, 2349)(173, 2421)(174, 2309)(175, 2310)(176, 2425)(177, 2368)(178, 2312)(179, 2428)(180, 2429)(181, 2314)(182, 2315)(183, 2433)(184, 2361)(185, 2436)(186, 2318)(187, 2439)(188, 2320)(189, 2442)(190, 2322)(191, 2445)(192, 2446)(193, 2324)(194, 2325)(195, 2450)(196, 2326)(197, 2452)(198, 2389)(199, 2454)(200, 2329)(201, 2457)(202, 2458)(203, 2331)(204, 2461)(205, 2382)(206, 2464)(207, 2334)(208, 2467)(209, 2336)(210, 2470)(211, 2471)(212, 2338)(213, 2339)(214, 2475)(215, 2340)(216, 2477)(217, 2408)(218, 2479)(219, 2343)(220, 2482)(221, 2483)(222, 2345)(223, 2486)(224, 2401)(225, 2488)(226, 2348)(227, 2491)(228, 2493)(229, 2351)(230, 2352)(231, 2497)(232, 2423)(233, 2499)(234, 2355)(235, 2502)(236, 2503)(237, 2357)(238, 2506)(239, 2416)(240, 2509)(241, 2360)(242, 2512)(243, 2514)(244, 2363)(245, 2364)(246, 2518)(247, 2438)(248, 2520)(249, 2367)(250, 2523)(251, 2524)(252, 2369)(253, 2527)(254, 2431)(255, 2371)(256, 2530)(257, 2448)(258, 2373)(259, 2533)(260, 2534)(261, 2375)(262, 2376)(263, 2538)(264, 2441)(265, 2541)(266, 2379)(267, 2544)(268, 2381)(269, 2547)(270, 2383)(271, 2550)(272, 2551)(273, 2385)(274, 2386)(275, 2555)(276, 2556)(277, 2388)(278, 2559)(279, 2560)(280, 2390)(281, 2563)(282, 2473)(283, 2392)(284, 2566)(285, 2567)(286, 2394)(287, 2395)(288, 2571)(289, 2466)(290, 2574)(291, 2398)(292, 2577)(293, 2400)(294, 2580)(295, 2402)(296, 2583)(297, 2584)(298, 2404)(299, 2405)(300, 2588)(301, 2589)(302, 2407)(303, 2592)(304, 2409)(305, 2595)(306, 2495)(307, 2411)(308, 2598)(309, 2412)(310, 2600)(311, 2490)(312, 2603)(313, 2415)(314, 2606)(315, 2417)(316, 2609)(317, 2610)(318, 2419)(319, 2420)(320, 2614)(321, 2615)(322, 2422)(323, 2618)(324, 2619)(325, 2424)(326, 2622)(327, 2516)(328, 2426)(329, 2625)(330, 2427)(331, 2627)(332, 2511)(333, 2630)(334, 2430)(335, 2633)(336, 2432)(337, 2636)(338, 2637)(339, 2434)(340, 2435)(341, 2641)(342, 2642)(343, 2437)(344, 2645)(345, 2647)(346, 2440)(347, 2650)(348, 2652)(349, 2443)(350, 2444)(351, 2656)(352, 2543)(353, 2658)(354, 2447)(355, 2661)(356, 2662)(357, 2449)(358, 2665)(359, 2536)(360, 2451)(361, 2668)(362, 2553)(363, 2453)(364, 2671)(365, 2672)(366, 2455)(367, 2456)(368, 2676)(369, 2546)(370, 2679)(371, 2459)(372, 2460)(373, 2683)(374, 2684)(375, 2462)(376, 2463)(377, 2620)(378, 2688)(379, 2465)(380, 2691)(381, 2693)(382, 2468)(383, 2469)(384, 2697)(385, 2576)(386, 2699)(387, 2472)(388, 2702)(389, 2703)(390, 2474)(391, 2706)(392, 2569)(393, 2476)(394, 2708)(395, 2586)(396, 2478)(397, 2711)(398, 2712)(399, 2480)(400, 2481)(401, 2716)(402, 2579)(403, 2719)(404, 2484)(405, 2485)(406, 2722)(407, 2686)(408, 2487)(409, 2646)(410, 2939)(411, 2489)(412, 2940)(413, 2836)(414, 2492)(415, 2945)(416, 2494)(417, 2882)(418, 2810)(419, 2496)(420, 2886)(421, 2612)(422, 2498)(423, 2663)(424, 2954)(425, 2500)(426, 2501)(427, 2742)(428, 2605)(429, 2958)(430, 2504)(431, 2505)(432, 2687)(433, 2961)(434, 2507)(435, 2508)(436, 2561)(437, 2963)(438, 2510)(439, 2734)(440, 2966)(441, 2513)(442, 2904)(443, 2515)(444, 2796)(445, 2968)(446, 2517)(447, 2967)(448, 2639)(449, 2519)(450, 2704)(451, 2924)(452, 2521)(453, 2522)(454, 2972)(455, 2632)(456, 2976)(457, 2525)(458, 2526)(459, 2724)(460, 2979)(461, 2528)(462, 2593)(463, 2529)(464, 2874)(465, 2654)(466, 2531)(467, 2787)(468, 2532)(469, 2986)(470, 2649)(471, 2990)(472, 2535)(473, 2955)(474, 2537)(475, 2951)(476, 2881)(477, 2539)(478, 2540)(479, 2607)(480, 2997)(481, 2542)(482, 2714)(483, 3000)(484, 2545)(485, 3001)(486, 2860)(487, 2548)(488, 2549)(489, 3006)(490, 2681)(491, 3008)(492, 2552)(493, 2992)(494, 2864)(495, 2554)(496, 2809)(497, 2674)(498, 3013)(499, 2557)(500, 2558)(501, 2732)(502, 2591)(503, 2616)(504, 2562)(505, 2861)(506, 2695)(507, 2564)(508, 3020)(509, 2565)(510, 2760)(511, 2690)(512, 3025)(513, 2568)(514, 2756)(515, 2570)(516, 2875)(517, 3029)(518, 2572)(519, 2573)(520, 2634)(521, 3031)(522, 2575)(523, 3032)(524, 2578)(525, 2726)(526, 3034)(527, 2581)(528, 2582)(529, 2841)(530, 2666)(531, 2935)(532, 2585)(533, 2765)(534, 3039)(535, 2587)(536, 3040)(537, 2894)(538, 2590)(539, 3042)(540, 2643)(541, 3045)(542, 2709)(543, 3050)(544, 3054)(545, 3057)(546, 3060)(547, 3063)(548, 2685)(549, 3069)(550, 2623)(551, 3074)(552, 3077)(553, 3080)(554, 3083)(555, 3087)(556, 3090)(557, 3088)(558, 2611)(559, 3096)(560, 3098)(561, 3064)(562, 3100)(563, 3103)(564, 3105)(565, 3075)(566, 3043)(567, 3070)(568, 3113)(569, 3115)(570, 3118)(571, 3120)(572, 2698)(573, 3051)(574, 3125)(575, 3002)(576, 2694)(577, 3128)(578, 3058)(579, 3130)(580, 3093)(581, 2717)(582, 3055)(583, 3137)(584, 3138)(585, 3141)(586, 3142)(587, 3144)(588, 3046)(589, 3084)(590, 2973)(591, 3061)(592, 3152)(593, 3153)(594, 3154)(595, 3155)(596, 3157)(597, 3049)(598, 3078)(599, 3143)(600, 3111)(601, 3162)(602, 3164)(603, 2651)(604, 3167)(605, 3156)(606, 3132)(607, 3170)(608, 3172)(609, 3136)(610, 3067)(611, 3127)(612, 2628)(613, 3161)(614, 3179)(615, 2941)(616, 3181)(617, 3182)(618, 3184)(619, 3151)(620, 3186)(621, 3187)(622, 3018)(623, 2957)(624, 3106)(625, 2680)(626, 2602)(627, 3101)(628, 3139)(629, 3072)(630, 3185)(631, 3192)(632, 2974)(633, 3150)(634, 3194)(635, 3195)(636, 3191)(637, 2919)(638, 3044)(639, 3198)(640, 3108)(641, 2987)(642, 3174)(643, 3201)(644, 2932)(645, 3135)(646, 3102)(647, 3148)(648, 3205)(649, 3180)(650, 3193)(651, 3206)(652, 2597)(653, 3119)(654, 3097)(655, 3009)(656, 3166)(657, 2713)(658, 3133)(659, 3212)(660, 3126)(661, 3116)(662, 2964)(663, 3169)(664, 3190)(665, 3109)(666, 3202)(667, 3214)(668, 2965)(669, 3023)(670, 3089)(671, 3014)(672, 3217)(673, 2943)(674, 3131)(675, 3121)(676, 2670)(677, 2689)(678, 2988)(679, 3200)(680, 2678)(681, 3134)(682, 3158)(683, 3146)(684, 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3175)(776, 3041)(777, 2617)(778, 3024)(779, 2621)(780, 2846)(781, 2852)(782, 2624)(783, 2631)(784, 2629)(785, 3197)(786, 3262)(787, 3079)(788, 2638)(789, 2774)(790, 2816)(791, 2942)(792, 2640)(793, 3224)(794, 3261)(795, 2644)(796, 2868)(797, 3082)(798, 3265)(799, 3238)(800, 3225)(801, 3053)(802, 2653)(803, 2825)(804, 2862)(805, 3056)(806, 2655)(807, 3022)(808, 2677)(809, 3005)(810, 3266)(811, 3076)(812, 3267)(813, 2664)(814, 3123)(815, 3065)(816, 2667)(817, 2669)(818, 2759)(819, 2879)(820, 3268)(821, 2993)(822, 2673)(823, 2896)(824, 2675)(825, 2839)(826, 3019)(827, 3221)(828, 3241)(829, 2682)(830, 2855)(831, 3270)(832, 3189)(833, 3173)(834, 2806)(835, 3010)(836, 2692)(837, 2916)(838, 2991)(839, 2853)(840, 2962)(841, 2696)(842, 3038)(843, 3147)(844, 2911)(845, 2701)(846, 2870)(847, 2705)(848, 2707)(849, 2890)(850, 2710)(851, 3210)(852, 3245)(853, 3204)(854, 3026)(855, 2718)(856, 2720)(857, 2960)(858, 2723)(859, 2750)(860, 2822)(861, 2725)(862, 2772)(863, 2947)(864, 2900)(865, 2781)(866, 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4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E14.654 Graph:: bipartite v = 702 e = 2184 f = 1456 degree seq :: [ 4^546, 14^156 ] E14.652 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^3, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^7, (Y3 * Y2^-1)^7, (Y3^-2 * Y1)^6, Y3 * Y1^-1 * Y3^-2 * Y1 * Y3^3 * Y1^-1 * Y3^-1 * Y1 * Y3^-2 * Y1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1, Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^-2 * Y1 * Y3^3 * Y1^-1 * Y3 * Y1^-1 * Y3^-2 * Y1 * Y3^-3 * Y1^-1 * Y3 * Y1^-1 * Y3^-3 * Y1^-1 * Y3 * Y1^-1 ] Map:: polytopal R = (1, 1093, 2, 1094, 4, 1096)(3, 1095, 8, 1100, 10, 1102)(5, 1097, 12, 1104, 6, 1098)(7, 1099, 15, 1107, 11, 1103)(9, 1101, 18, 1110, 20, 1112)(13, 1105, 25, 1117, 23, 1115)(14, 1106, 24, 1116, 28, 1120)(16, 1108, 31, 1123, 29, 1121)(17, 1109, 33, 1125, 21, 1113)(19, 1111, 36, 1128, 37, 1129)(22, 1114, 30, 1122, 41, 1133)(26, 1118, 46, 1138, 44, 1136)(27, 1119, 47, 1139, 48, 1140)(32, 1124, 54, 1146, 52, 1144)(34, 1126, 57, 1149, 55, 1147)(35, 1127, 58, 1150, 38, 1130)(39, 1131, 56, 1148, 64, 1156)(40, 1132, 65, 1157, 66, 1158)(42, 1134, 45, 1137, 69, 1161)(43, 1135, 70, 1162, 49, 1141)(50, 1142, 53, 1145, 79, 1171)(51, 1143, 80, 1172, 67, 1159)(59, 1151, 90, 1182, 88, 1180)(60, 1152, 91, 1183, 61, 1153)(62, 1154, 89, 1181, 95, 1187)(63, 1155, 96, 1188, 97, 1189)(68, 1160, 102, 1194, 103, 1195)(71, 1163, 107, 1199, 105, 1197)(72, 1164, 74, 1166, 109, 1201)(73, 1165, 110, 1202, 104, 1196)(75, 1167, 113, 1205, 76, 1168)(77, 1169, 106, 1198, 117, 1209)(78, 1170, 118, 1210, 119, 1211)(81, 1173, 123, 1215, 121, 1213)(82, 1174, 84, 1176, 125, 1217)(83, 1175, 126, 1218, 120, 1212)(85, 1177, 87, 1179, 130, 1222)(86, 1178, 131, 1223, 98, 1190)(92, 1184, 139, 1231, 137, 1229)(93, 1185, 138, 1230, 141, 1233)(94, 1186, 142, 1234, 143, 1235)(99, 1191, 148, 1240, 100, 1192)(101, 1193, 122, 1214, 152, 1244)(108, 1200, 159, 1251, 160, 1252)(111, 1203, 164, 1256, 162, 1254)(112, 1204, 165, 1257, 161, 1253)(114, 1206, 168, 1260, 166, 1258)(115, 1207, 167, 1259, 170, 1262)(116, 1208, 171, 1263, 172, 1264)(124, 1216, 180, 1272, 181, 1273)(127, 1219, 185, 1277, 183, 1275)(128, 1220, 186, 1278, 182, 1274)(129, 1221, 187, 1279, 188, 1280)(132, 1224, 192, 1284, 190, 1282)(133, 1225, 193, 1285, 189, 1281)(134, 1226, 136, 1228, 196, 1288)(135, 1227, 197, 1289, 144, 1236)(140, 1232, 203, 1295, 204, 1296)(145, 1237, 209, 1301, 146, 1238)(147, 1239, 191, 1283, 213, 1305)(149, 1241, 216, 1308, 214, 1306)(150, 1242, 215, 1307, 217, 1309)(151, 1243, 218, 1310, 219, 1311)(153, 1245, 221, 1313, 154, 1246)(155, 1247, 163, 1255, 225, 1317)(156, 1248, 158, 1250, 227, 1319)(157, 1249, 228, 1320, 173, 1265)(169, 1261, 241, 1333, 242, 1334)(174, 1266, 247, 1339, 175, 1267)(176, 1268, 184, 1276, 251, 1343)(177, 1269, 179, 1271, 253, 1345)(178, 1270, 254, 1346, 220, 1312)(194, 1286, 272, 1364, 270, 1362)(195, 1287, 273, 1365, 274, 1366)(198, 1290, 278, 1370, 276, 1368)(199, 1291, 279, 1371, 275, 1367)(200, 1292, 202, 1294, 282, 1374)(201, 1293, 283, 1375, 205, 1297)(206, 1298, 289, 1381, 207, 1299)(208, 1300, 277, 1369, 261, 1353)(210, 1302, 295, 1387, 293, 1385)(211, 1303, 294, 1386, 296, 1388)(212, 1304, 297, 1389, 298, 1390)(222, 1314, 309, 1401, 307, 1399)(223, 1315, 308, 1400, 311, 1403)(224, 1316, 312, 1404, 313, 1405)(226, 1318, 315, 1407, 316, 1408)(229, 1321, 319, 1411, 318, 1410)(230, 1322, 320, 1412, 317, 1409)(231, 1323, 321, 1413, 232, 1324)(233, 1325, 237, 1329, 325, 1417)(234, 1326, 236, 1328, 327, 1419)(235, 1327, 306, 1398, 314, 1406)(238, 1330, 240, 1332, 332, 1424)(239, 1331, 333, 1425, 243, 1335)(244, 1336, 339, 1431, 245, 1337)(246, 1338, 299, 1391, 268, 1360)(248, 1340, 345, 1437, 343, 1435)(249, 1341, 344, 1436, 347, 1439)(250, 1342, 348, 1440, 349, 1441)(252, 1344, 350, 1442, 351, 1443)(255, 1347, 354, 1446, 353, 1445)(256, 1348, 355, 1447, 352, 1444)(257, 1349, 356, 1448, 258, 1350)(259, 1351, 263, 1355, 360, 1452)(260, 1352, 262, 1354, 362, 1454)(264, 1356, 366, 1458, 265, 1357)(266, 1358, 271, 1363, 370, 1462)(267, 1359, 269, 1361, 372, 1464)(280, 1372, 385, 1477, 383, 1475)(281, 1373, 386, 1478, 387, 1479)(284, 1376, 391, 1483, 389, 1481)(285, 1377, 392, 1484, 388, 1480)(286, 1378, 394, 1486, 287, 1379)(288, 1380, 390, 1482, 376, 1468)(290, 1382, 400, 1492, 398, 1490)(291, 1383, 399, 1491, 401, 1493)(292, 1384, 363, 1455, 402, 1494)(300, 1392, 302, 1394, 410, 1502)(301, 1393, 411, 1503, 303, 1395)(304, 1396, 415, 1507, 305, 1397)(310, 1402, 422, 1514, 423, 1515)(322, 1414, 435, 1527, 433, 1525)(323, 1415, 434, 1526, 437, 1529)(324, 1416, 438, 1530, 439, 1531)(326, 1418, 441, 1533, 442, 1534)(328, 1420, 444, 1536, 418, 1510)(329, 1421, 445, 1537, 443, 1535)(330, 1422, 338, 1430, 440, 1532)(331, 1423, 447, 1539, 448, 1540)(334, 1426, 451, 1543, 450, 1542)(335, 1427, 452, 1544, 449, 1541)(336, 1428, 454, 1546, 337, 1429)(340, 1432, 460, 1552, 458, 1550)(341, 1433, 459, 1551, 461, 1553)(342, 1434, 373, 1465, 462, 1554)(346, 1438, 466, 1558, 467, 1559)(357, 1449, 479, 1571, 477, 1569)(358, 1450, 478, 1570, 481, 1573)(359, 1451, 482, 1574, 483, 1575)(361, 1453, 485, 1577, 486, 1578)(364, 1456, 488, 1580, 487, 1579)(365, 1457, 414, 1506, 484, 1576)(367, 1459, 492, 1584, 490, 1582)(368, 1460, 491, 1583, 494, 1586)(369, 1461, 495, 1587, 496, 1588)(371, 1463, 497, 1589, 498, 1590)(374, 1466, 500, 1592, 499, 1591)(375, 1467, 377, 1469, 502, 1594)(378, 1470, 505, 1597, 379, 1471)(380, 1472, 384, 1476, 509, 1601)(381, 1473, 382, 1474, 510, 1602)(393, 1485, 520, 1612, 519, 1611)(395, 1487, 523, 1615, 521, 1613)(396, 1488, 522, 1614, 524, 1616)(397, 1489, 503, 1595, 525, 1617)(403, 1495, 405, 1497, 531, 1623)(404, 1496, 532, 1624, 406, 1498)(407, 1499, 536, 1628, 408, 1500)(409, 1501, 538, 1630, 539, 1631)(412, 1504, 542, 1634, 541, 1633)(413, 1505, 535, 1627, 540, 1632)(416, 1508, 547, 1639, 545, 1637)(417, 1509, 546, 1638, 548, 1640)(419, 1511, 421, 1513, 550, 1642)(420, 1512, 516, 1608, 424, 1516)(425, 1517, 555, 1647, 426, 1518)(427, 1519, 557, 1649, 428, 1520)(429, 1521, 432, 1524, 561, 1653)(430, 1522, 431, 1523, 562, 1654)(436, 1528, 566, 1658, 567, 1659)(446, 1538, 574, 1666, 457, 1549)(453, 1545, 581, 1673, 580, 1672)(455, 1547, 584, 1676, 582, 1674)(456, 1548, 583, 1675, 585, 1677)(463, 1555, 465, 1557, 591, 1683)(464, 1556, 577, 1669, 468, 1560)(469, 1561, 596, 1688, 470, 1562)(471, 1563, 598, 1690, 472, 1564)(473, 1565, 476, 1568, 602, 1694)(474, 1566, 475, 1567, 603, 1695)(480, 1572, 607, 1699, 608, 1700)(489, 1581, 615, 1707, 544, 1636)(493, 1585, 618, 1710, 619, 1711)(501, 1593, 626, 1718, 627, 1719)(504, 1596, 629, 1721, 628, 1720)(506, 1598, 632, 1724, 630, 1722)(507, 1599, 631, 1723, 634, 1726)(508, 1600, 635, 1727, 636, 1728)(511, 1603, 638, 1730, 637, 1729)(512, 1604, 513, 1605, 640, 1732)(514, 1606, 642, 1734, 515, 1607)(517, 1609, 518, 1610, 646, 1738)(526, 1618, 528, 1620, 655, 1747)(527, 1619, 656, 1748, 529, 1621)(530, 1622, 660, 1752, 661, 1753)(533, 1625, 664, 1756, 663, 1755)(534, 1626, 659, 1751, 662, 1754)(537, 1629, 667, 1759, 668, 1760)(543, 1635, 673, 1765, 666, 1758)(549, 1641, 678, 1770, 679, 1771)(551, 1643, 681, 1773, 645, 1737)(552, 1644, 682, 1774, 680, 1772)(553, 1645, 684, 1776, 554, 1646)(556, 1648, 686, 1778, 687, 1779)(558, 1650, 690, 1782, 688, 1780)(559, 1651, 689, 1781, 692, 1784)(560, 1652, 693, 1785, 694, 1786)(563, 1655, 696, 1788, 695, 1787)(564, 1656, 565, 1657, 698, 1790)(568, 1660, 701, 1793, 569, 1661)(570, 1662, 703, 1795, 571, 1663)(572, 1664, 573, 1665, 707, 1799)(575, 1667, 708, 1800, 576, 1668)(578, 1670, 579, 1671, 712, 1804)(586, 1678, 588, 1680, 721, 1813)(587, 1679, 722, 1814, 589, 1681)(590, 1682, 725, 1817, 726, 1818)(592, 1684, 728, 1820, 711, 1803)(593, 1685, 729, 1821, 727, 1819)(594, 1686, 731, 1823, 595, 1687)(597, 1689, 733, 1825, 734, 1826)(599, 1691, 737, 1829, 735, 1827)(600, 1692, 736, 1828, 739, 1831)(601, 1693, 740, 1832, 741, 1833)(604, 1696, 743, 1835, 742, 1834)(605, 1697, 606, 1698, 745, 1837)(609, 1701, 748, 1840, 610, 1702)(611, 1703, 750, 1842, 612, 1704)(613, 1705, 614, 1706, 754, 1846)(616, 1708, 617, 1709, 756, 1848)(620, 1712, 759, 1851, 621, 1713)(622, 1714, 761, 1853, 623, 1715)(624, 1716, 625, 1717, 765, 1857)(633, 1725, 772, 1864, 773, 1865)(639, 1731, 777, 1869, 700, 1792)(641, 1733, 779, 1871, 778, 1870)(643, 1735, 782, 1874, 780, 1872)(644, 1736, 781, 1873, 784, 1876)(647, 1739, 786, 1878, 785, 1877)(648, 1740, 649, 1741, 787, 1879)(650, 1742, 652, 1744, 790, 1882)(651, 1743, 791, 1883, 653, 1745)(654, 1746, 795, 1887, 796, 1888)(657, 1749, 799, 1891, 798, 1890)(658, 1750, 794, 1886, 797, 1889)(665, 1757, 805, 1897, 800, 1892)(669, 1761, 808, 1900, 670, 1762)(671, 1763, 672, 1764, 810, 1902)(674, 1766, 676, 1768, 813, 1905)(675, 1767, 814, 1906, 677, 1769)(683, 1775, 820, 1912, 819, 1911)(685, 1777, 821, 1913, 747, 1839)(691, 1783, 826, 1918, 827, 1919)(697, 1789, 831, 1923, 774, 1866)(699, 1791, 833, 1925, 832, 1924)(702, 1794, 836, 1928, 837, 1929)(704, 1796, 840, 1932, 838, 1930)(705, 1797, 839, 1931, 793, 1885)(706, 1798, 841, 1933, 842, 1934)(709, 1801, 845, 1937, 843, 1935)(710, 1802, 844, 1936, 847, 1939)(713, 1805, 849, 1941, 848, 1940)(714, 1806, 715, 1807, 850, 1942)(716, 1808, 718, 1810, 853, 1945)(717, 1809, 854, 1946, 719, 1811)(720, 1812, 858, 1950, 859, 1951)(723, 1815, 862, 1954, 861, 1953)(724, 1816, 857, 1949, 860, 1952)(730, 1822, 866, 1958, 865, 1957)(732, 1824, 867, 1959, 758, 1850)(738, 1830, 872, 1964, 873, 1965)(744, 1836, 877, 1969, 828, 1920)(746, 1838, 879, 1971, 878, 1970)(749, 1841, 882, 1974, 883, 1975)(751, 1843, 886, 1978, 884, 1976)(752, 1844, 885, 1977, 856, 1948)(753, 1845, 887, 1979, 888, 1980)(755, 1847, 889, 1981, 874, 1966)(757, 1849, 891, 1983, 890, 1982)(760, 1852, 894, 1986, 895, 1987)(762, 1854, 898, 1990, 896, 1988)(763, 1855, 897, 1989, 899, 1991)(764, 1856, 900, 1992, 901, 1993)(766, 1858, 902, 1994, 767, 1859)(768, 1860, 769, 1861, 906, 1998)(770, 1862, 771, 1863, 908, 2000)(775, 1867, 776, 1868, 913, 2005)(783, 1875, 919, 2011, 920, 2012)(788, 1880, 924, 2016, 923, 2015)(789, 1881, 925, 2017, 926, 2018)(792, 1884, 928, 2020, 927, 2019)(801, 1893, 933, 2025, 802, 1894)(803, 1895, 804, 1896, 935, 2027)(806, 1898, 937, 2029, 807, 1899)(809, 1901, 939, 2031, 941, 2033)(811, 1903, 943, 2035, 942, 2034)(812, 1904, 944, 2036, 945, 2037)(815, 1907, 948, 2040, 947, 2039)(816, 1908, 904, 1996, 946, 2038)(817, 1909, 949, 2041, 818, 1910)(822, 1914, 954, 2046, 823, 1915)(824, 1916, 825, 1917, 957, 2049)(829, 1921, 830, 1922, 961, 2053)(834, 1926, 964, 2056, 963, 2055)(835, 1927, 914, 2006, 959, 2051)(846, 1938, 971, 2063, 972, 2064)(851, 1943, 952, 2044, 975, 2067)(852, 1944, 976, 2068, 977, 2069)(855, 1947, 979, 2071, 978, 2070)(863, 1955, 983, 2075, 864, 1956)(868, 1960, 988, 2080, 869, 1961)(870, 1962, 871, 1963, 990, 2082)(875, 1967, 876, 1968, 994, 2086)(880, 1972, 997, 2089, 996, 2088)(881, 1973, 953, 2045, 992, 2084)(892, 1984, 1004, 2096, 1003, 2095)(893, 1985, 987, 2079, 910, 2002)(903, 1995, 1011, 2103, 1010, 2102)(905, 1997, 1012, 2104, 1013, 2105)(907, 1999, 1014, 2106, 1009, 2101)(909, 2001, 999, 2091, 1000, 2092)(911, 2003, 962, 2054, 1017, 2109)(912, 2004, 1018, 2110, 1019, 2111)(915, 2007, 916, 2008, 986, 2078)(917, 2009, 918, 2010, 1023, 2115)(921, 2013, 922, 2014, 965, 2057)(929, 2021, 985, 2077, 930, 2022)(931, 2023, 932, 2024, 1033, 2125)(934, 2026, 981, 2073, 980, 2072)(936, 2028, 1037, 2129, 1036, 2128)(938, 2030, 1039, 2131, 1038, 2130)(940, 2032, 1040, 2132, 1041, 2133)(950, 2042, 982, 2074, 1046, 2138)(951, 2043, 1044, 2136, 1043, 2135)(955, 2047, 1050, 2142, 1049, 2141)(956, 2048, 1051, 2143, 968, 2060)(958, 2050, 1007, 2099, 1008, 2100)(960, 2052, 995, 2087, 1054, 2146)(966, 2058, 967, 2059, 991, 2083)(969, 2061, 970, 2062, 1060, 2152)(973, 2065, 974, 2066, 998, 2090)(984, 2076, 1045, 2137, 1069, 2161)(989, 2081, 1072, 2164, 1001, 2093)(993, 2085, 1002, 2094, 1075, 2167)(1005, 2097, 1042, 2134, 1006, 2098)(1015, 2107, 1065, 2157, 1064, 2156)(1016, 2108, 1071, 2163, 1025, 2117)(1020, 2112, 1062, 2154, 1053, 2145)(1021, 2113, 1070, 2162, 1077, 2169)(1022, 2114, 1088, 2180, 1076, 2168)(1024, 2116, 1084, 2176, 1085, 2177)(1026, 2118, 1057, 2149, 1078, 2170)(1027, 2119, 1028, 2120, 1081, 2173)(1029, 2121, 1073, 2165, 1030, 2122)(1031, 2123, 1032, 2124, 1061, 2153)(1034, 2126, 1089, 2181, 1068, 2160)(1035, 2127, 1066, 2158, 1067, 2159)(1047, 2139, 1056, 2148, 1063, 2155)(1048, 2140, 1091, 2183, 1074, 2166)(1052, 2144, 1086, 2178, 1082, 2174)(1055, 2147, 1090, 2182, 1087, 2179)(1058, 2150, 1083, 2175, 1079, 2171)(1059, 2151, 1092, 2184, 1080, 2172)(2185, 3277)(2186, 3278)(2187, 3279)(2188, 3280)(2189, 3281)(2190, 3282)(2191, 3283)(2192, 3284)(2193, 3285)(2194, 3286)(2195, 3287)(2196, 3288)(2197, 3289)(2198, 3290)(2199, 3291)(2200, 3292)(2201, 3293)(2202, 3294)(2203, 3295)(2204, 3296)(2205, 3297)(2206, 3298)(2207, 3299)(2208, 3300)(2209, 3301)(2210, 3302)(2211, 3303)(2212, 3304)(2213, 3305)(2214, 3306)(2215, 3307)(2216, 3308)(2217, 3309)(2218, 3310)(2219, 3311)(2220, 3312)(2221, 3313)(2222, 3314)(2223, 3315)(2224, 3316)(2225, 3317)(2226, 3318)(2227, 3319)(2228, 3320)(2229, 3321)(2230, 3322)(2231, 3323)(2232, 3324)(2233, 3325)(2234, 3326)(2235, 3327)(2236, 3328)(2237, 3329)(2238, 3330)(2239, 3331)(2240, 3332)(2241, 3333)(2242, 3334)(2243, 3335)(2244, 3336)(2245, 3337)(2246, 3338)(2247, 3339)(2248, 3340)(2249, 3341)(2250, 3342)(2251, 3343)(2252, 3344)(2253, 3345)(2254, 3346)(2255, 3347)(2256, 3348)(2257, 3349)(2258, 3350)(2259, 3351)(2260, 3352)(2261, 3353)(2262, 3354)(2263, 3355)(2264, 3356)(2265, 3357)(2266, 3358)(2267, 3359)(2268, 3360)(2269, 3361)(2270, 3362)(2271, 3363)(2272, 3364)(2273, 3365)(2274, 3366)(2275, 3367)(2276, 3368)(2277, 3369)(2278, 3370)(2279, 3371)(2280, 3372)(2281, 3373)(2282, 3374)(2283, 3375)(2284, 3376)(2285, 3377)(2286, 3378)(2287, 3379)(2288, 3380)(2289, 3381)(2290, 3382)(2291, 3383)(2292, 3384)(2293, 3385)(2294, 3386)(2295, 3387)(2296, 3388)(2297, 3389)(2298, 3390)(2299, 3391)(2300, 3392)(2301, 3393)(2302, 3394)(2303, 3395)(2304, 3396)(2305, 3397)(2306, 3398)(2307, 3399)(2308, 3400)(2309, 3401)(2310, 3402)(2311, 3403)(2312, 3404)(2313, 3405)(2314, 3406)(2315, 3407)(2316, 3408)(2317, 3409)(2318, 3410)(2319, 3411)(2320, 3412)(2321, 3413)(2322, 3414)(2323, 3415)(2324, 3416)(2325, 3417)(2326, 3418)(2327, 3419)(2328, 3420)(2329, 3421)(2330, 3422)(2331, 3423)(2332, 3424)(2333, 3425)(2334, 3426)(2335, 3427)(2336, 3428)(2337, 3429)(2338, 3430)(2339, 3431)(2340, 3432)(2341, 3433)(2342, 3434)(2343, 3435)(2344, 3436)(2345, 3437)(2346, 3438)(2347, 3439)(2348, 3440)(2349, 3441)(2350, 3442)(2351, 3443)(2352, 3444)(2353, 3445)(2354, 3446)(2355, 3447)(2356, 3448)(2357, 3449)(2358, 3450)(2359, 3451)(2360, 3452)(2361, 3453)(2362, 3454)(2363, 3455)(2364, 3456)(2365, 3457)(2366, 3458)(2367, 3459)(2368, 3460)(2369, 3461)(2370, 3462)(2371, 3463)(2372, 3464)(2373, 3465)(2374, 3466)(2375, 3467)(2376, 3468)(2377, 3469)(2378, 3470)(2379, 3471)(2380, 3472)(2381, 3473)(2382, 3474)(2383, 3475)(2384, 3476)(2385, 3477)(2386, 3478)(2387, 3479)(2388, 3480)(2389, 3481)(2390, 3482)(2391, 3483)(2392, 3484)(2393, 3485)(2394, 3486)(2395, 3487)(2396, 3488)(2397, 3489)(2398, 3490)(2399, 3491)(2400, 3492)(2401, 3493)(2402, 3494)(2403, 3495)(2404, 3496)(2405, 3497)(2406, 3498)(2407, 3499)(2408, 3500)(2409, 3501)(2410, 3502)(2411, 3503)(2412, 3504)(2413, 3505)(2414, 3506)(2415, 3507)(2416, 3508)(2417, 3509)(2418, 3510)(2419, 3511)(2420, 3512)(2421, 3513)(2422, 3514)(2423, 3515)(2424, 3516)(2425, 3517)(2426, 3518)(2427, 3519)(2428, 3520)(2429, 3521)(2430, 3522)(2431, 3523)(2432, 3524)(2433, 3525)(2434, 3526)(2435, 3527)(2436, 3528)(2437, 3529)(2438, 3530)(2439, 3531)(2440, 3532)(2441, 3533)(2442, 3534)(2443, 3535)(2444, 3536)(2445, 3537)(2446, 3538)(2447, 3539)(2448, 3540)(2449, 3541)(2450, 3542)(2451, 3543)(2452, 3544)(2453, 3545)(2454, 3546)(2455, 3547)(2456, 3548)(2457, 3549)(2458, 3550)(2459, 3551)(2460, 3552)(2461, 3553)(2462, 3554)(2463, 3555)(2464, 3556)(2465, 3557)(2466, 3558)(2467, 3559)(2468, 3560)(2469, 3561)(2470, 3562)(2471, 3563)(2472, 3564)(2473, 3565)(2474, 3566)(2475, 3567)(2476, 3568)(2477, 3569)(2478, 3570)(2479, 3571)(2480, 3572)(2481, 3573)(2482, 3574)(2483, 3575)(2484, 3576)(2485, 3577)(2486, 3578)(2487, 3579)(2488, 3580)(2489, 3581)(2490, 3582)(2491, 3583)(2492, 3584)(2493, 3585)(2494, 3586)(2495, 3587)(2496, 3588)(2497, 3589)(2498, 3590)(2499, 3591)(2500, 3592)(2501, 3593)(2502, 3594)(2503, 3595)(2504, 3596)(2505, 3597)(2506, 3598)(2507, 3599)(2508, 3600)(2509, 3601)(2510, 3602)(2511, 3603)(2512, 3604)(2513, 3605)(2514, 3606)(2515, 3607)(2516, 3608)(2517, 3609)(2518, 3610)(2519, 3611)(2520, 3612)(2521, 3613)(2522, 3614)(2523, 3615)(2524, 3616)(2525, 3617)(2526, 3618)(2527, 3619)(2528, 3620)(2529, 3621)(2530, 3622)(2531, 3623)(2532, 3624)(2533, 3625)(2534, 3626)(2535, 3627)(2536, 3628)(2537, 3629)(2538, 3630)(2539, 3631)(2540, 3632)(2541, 3633)(2542, 3634)(2543, 3635)(2544, 3636)(2545, 3637)(2546, 3638)(2547, 3639)(2548, 3640)(2549, 3641)(2550, 3642)(2551, 3643)(2552, 3644)(2553, 3645)(2554, 3646)(2555, 3647)(2556, 3648)(2557, 3649)(2558, 3650)(2559, 3651)(2560, 3652)(2561, 3653)(2562, 3654)(2563, 3655)(2564, 3656)(2565, 3657)(2566, 3658)(2567, 3659)(2568, 3660)(2569, 3661)(2570, 3662)(2571, 3663)(2572, 3664)(2573, 3665)(2574, 3666)(2575, 3667)(2576, 3668)(2577, 3669)(2578, 3670)(2579, 3671)(2580, 3672)(2581, 3673)(2582, 3674)(2583, 3675)(2584, 3676)(2585, 3677)(2586, 3678)(2587, 3679)(2588, 3680)(2589, 3681)(2590, 3682)(2591, 3683)(2592, 3684)(2593, 3685)(2594, 3686)(2595, 3687)(2596, 3688)(2597, 3689)(2598, 3690)(2599, 3691)(2600, 3692)(2601, 3693)(2602, 3694)(2603, 3695)(2604, 3696)(2605, 3697)(2606, 3698)(2607, 3699)(2608, 3700)(2609, 3701)(2610, 3702)(2611, 3703)(2612, 3704)(2613, 3705)(2614, 3706)(2615, 3707)(2616, 3708)(2617, 3709)(2618, 3710)(2619, 3711)(2620, 3712)(2621, 3713)(2622, 3714)(2623, 3715)(2624, 3716)(2625, 3717)(2626, 3718)(2627, 3719)(2628, 3720)(2629, 3721)(2630, 3722)(2631, 3723)(2632, 3724)(2633, 3725)(2634, 3726)(2635, 3727)(2636, 3728)(2637, 3729)(2638, 3730)(2639, 3731)(2640, 3732)(2641, 3733)(2642, 3734)(2643, 3735)(2644, 3736)(2645, 3737)(2646, 3738)(2647, 3739)(2648, 3740)(2649, 3741)(2650, 3742)(2651, 3743)(2652, 3744)(2653, 3745)(2654, 3746)(2655, 3747)(2656, 3748)(2657, 3749)(2658, 3750)(2659, 3751)(2660, 3752)(2661, 3753)(2662, 3754)(2663, 3755)(2664, 3756)(2665, 3757)(2666, 3758)(2667, 3759)(2668, 3760)(2669, 3761)(2670, 3762)(2671, 3763)(2672, 3764)(2673, 3765)(2674, 3766)(2675, 3767)(2676, 3768)(2677, 3769)(2678, 3770)(2679, 3771)(2680, 3772)(2681, 3773)(2682, 3774)(2683, 3775)(2684, 3776)(2685, 3777)(2686, 3778)(2687, 3779)(2688, 3780)(2689, 3781)(2690, 3782)(2691, 3783)(2692, 3784)(2693, 3785)(2694, 3786)(2695, 3787)(2696, 3788)(2697, 3789)(2698, 3790)(2699, 3791)(2700, 3792)(2701, 3793)(2702, 3794)(2703, 3795)(2704, 3796)(2705, 3797)(2706, 3798)(2707, 3799)(2708, 3800)(2709, 3801)(2710, 3802)(2711, 3803)(2712, 3804)(2713, 3805)(2714, 3806)(2715, 3807)(2716, 3808)(2717, 3809)(2718, 3810)(2719, 3811)(2720, 3812)(2721, 3813)(2722, 3814)(2723, 3815)(2724, 3816)(2725, 3817)(2726, 3818)(2727, 3819)(2728, 3820)(2729, 3821)(2730, 3822)(2731, 3823)(2732, 3824)(2733, 3825)(2734, 3826)(2735, 3827)(2736, 3828)(2737, 3829)(2738, 3830)(2739, 3831)(2740, 3832)(2741, 3833)(2742, 3834)(2743, 3835)(2744, 3836)(2745, 3837)(2746, 3838)(2747, 3839)(2748, 3840)(2749, 3841)(2750, 3842)(2751, 3843)(2752, 3844)(2753, 3845)(2754, 3846)(2755, 3847)(2756, 3848)(2757, 3849)(2758, 3850)(2759, 3851)(2760, 3852)(2761, 3853)(2762, 3854)(2763, 3855)(2764, 3856)(2765, 3857)(2766, 3858)(2767, 3859)(2768, 3860)(2769, 3861)(2770, 3862)(2771, 3863)(2772, 3864)(2773, 3865)(2774, 3866)(2775, 3867)(2776, 3868)(2777, 3869)(2778, 3870)(2779, 3871)(2780, 3872)(2781, 3873)(2782, 3874)(2783, 3875)(2784, 3876)(2785, 3877)(2786, 3878)(2787, 3879)(2788, 3880)(2789, 3881)(2790, 3882)(2791, 3883)(2792, 3884)(2793, 3885)(2794, 3886)(2795, 3887)(2796, 3888)(2797, 3889)(2798, 3890)(2799, 3891)(2800, 3892)(2801, 3893)(2802, 3894)(2803, 3895)(2804, 3896)(2805, 3897)(2806, 3898)(2807, 3899)(2808, 3900)(2809, 3901)(2810, 3902)(2811, 3903)(2812, 3904)(2813, 3905)(2814, 3906)(2815, 3907)(2816, 3908)(2817, 3909)(2818, 3910)(2819, 3911)(2820, 3912)(2821, 3913)(2822, 3914)(2823, 3915)(2824, 3916)(2825, 3917)(2826, 3918)(2827, 3919)(2828, 3920)(2829, 3921)(2830, 3922)(2831, 3923)(2832, 3924)(2833, 3925)(2834, 3926)(2835, 3927)(2836, 3928)(2837, 3929)(2838, 3930)(2839, 3931)(2840, 3932)(2841, 3933)(2842, 3934)(2843, 3935)(2844, 3936)(2845, 3937)(2846, 3938)(2847, 3939)(2848, 3940)(2849, 3941)(2850, 3942)(2851, 3943)(2852, 3944)(2853, 3945)(2854, 3946)(2855, 3947)(2856, 3948)(2857, 3949)(2858, 3950)(2859, 3951)(2860, 3952)(2861, 3953)(2862, 3954)(2863, 3955)(2864, 3956)(2865, 3957)(2866, 3958)(2867, 3959)(2868, 3960)(2869, 3961)(2870, 3962)(2871, 3963)(2872, 3964)(2873, 3965)(2874, 3966)(2875, 3967)(2876, 3968)(2877, 3969)(2878, 3970)(2879, 3971)(2880, 3972)(2881, 3973)(2882, 3974)(2883, 3975)(2884, 3976)(2885, 3977)(2886, 3978)(2887, 3979)(2888, 3980)(2889, 3981)(2890, 3982)(2891, 3983)(2892, 3984)(2893, 3985)(2894, 3986)(2895, 3987)(2896, 3988)(2897, 3989)(2898, 3990)(2899, 3991)(2900, 3992)(2901, 3993)(2902, 3994)(2903, 3995)(2904, 3996)(2905, 3997)(2906, 3998)(2907, 3999)(2908, 4000)(2909, 4001)(2910, 4002)(2911, 4003)(2912, 4004)(2913, 4005)(2914, 4006)(2915, 4007)(2916, 4008)(2917, 4009)(2918, 4010)(2919, 4011)(2920, 4012)(2921, 4013)(2922, 4014)(2923, 4015)(2924, 4016)(2925, 4017)(2926, 4018)(2927, 4019)(2928, 4020)(2929, 4021)(2930, 4022)(2931, 4023)(2932, 4024)(2933, 4025)(2934, 4026)(2935, 4027)(2936, 4028)(2937, 4029)(2938, 4030)(2939, 4031)(2940, 4032)(2941, 4033)(2942, 4034)(2943, 4035)(2944, 4036)(2945, 4037)(2946, 4038)(2947, 4039)(2948, 4040)(2949, 4041)(2950, 4042)(2951, 4043)(2952, 4044)(2953, 4045)(2954, 4046)(2955, 4047)(2956, 4048)(2957, 4049)(2958, 4050)(2959, 4051)(2960, 4052)(2961, 4053)(2962, 4054)(2963, 4055)(2964, 4056)(2965, 4057)(2966, 4058)(2967, 4059)(2968, 4060)(2969, 4061)(2970, 4062)(2971, 4063)(2972, 4064)(2973, 4065)(2974, 4066)(2975, 4067)(2976, 4068)(2977, 4069)(2978, 4070)(2979, 4071)(2980, 4072)(2981, 4073)(2982, 4074)(2983, 4075)(2984, 4076)(2985, 4077)(2986, 4078)(2987, 4079)(2988, 4080)(2989, 4081)(2990, 4082)(2991, 4083)(2992, 4084)(2993, 4085)(2994, 4086)(2995, 4087)(2996, 4088)(2997, 4089)(2998, 4090)(2999, 4091)(3000, 4092)(3001, 4093)(3002, 4094)(3003, 4095)(3004, 4096)(3005, 4097)(3006, 4098)(3007, 4099)(3008, 4100)(3009, 4101)(3010, 4102)(3011, 4103)(3012, 4104)(3013, 4105)(3014, 4106)(3015, 4107)(3016, 4108)(3017, 4109)(3018, 4110)(3019, 4111)(3020, 4112)(3021, 4113)(3022, 4114)(3023, 4115)(3024, 4116)(3025, 4117)(3026, 4118)(3027, 4119)(3028, 4120)(3029, 4121)(3030, 4122)(3031, 4123)(3032, 4124)(3033, 4125)(3034, 4126)(3035, 4127)(3036, 4128)(3037, 4129)(3038, 4130)(3039, 4131)(3040, 4132)(3041, 4133)(3042, 4134)(3043, 4135)(3044, 4136)(3045, 4137)(3046, 4138)(3047, 4139)(3048, 4140)(3049, 4141)(3050, 4142)(3051, 4143)(3052, 4144)(3053, 4145)(3054, 4146)(3055, 4147)(3056, 4148)(3057, 4149)(3058, 4150)(3059, 4151)(3060, 4152)(3061, 4153)(3062, 4154)(3063, 4155)(3064, 4156)(3065, 4157)(3066, 4158)(3067, 4159)(3068, 4160)(3069, 4161)(3070, 4162)(3071, 4163)(3072, 4164)(3073, 4165)(3074, 4166)(3075, 4167)(3076, 4168)(3077, 4169)(3078, 4170)(3079, 4171)(3080, 4172)(3081, 4173)(3082, 4174)(3083, 4175)(3084, 4176)(3085, 4177)(3086, 4178)(3087, 4179)(3088, 4180)(3089, 4181)(3090, 4182)(3091, 4183)(3092, 4184)(3093, 4185)(3094, 4186)(3095, 4187)(3096, 4188)(3097, 4189)(3098, 4190)(3099, 4191)(3100, 4192)(3101, 4193)(3102, 4194)(3103, 4195)(3104, 4196)(3105, 4197)(3106, 4198)(3107, 4199)(3108, 4200)(3109, 4201)(3110, 4202)(3111, 4203)(3112, 4204)(3113, 4205)(3114, 4206)(3115, 4207)(3116, 4208)(3117, 4209)(3118, 4210)(3119, 4211)(3120, 4212)(3121, 4213)(3122, 4214)(3123, 4215)(3124, 4216)(3125, 4217)(3126, 4218)(3127, 4219)(3128, 4220)(3129, 4221)(3130, 4222)(3131, 4223)(3132, 4224)(3133, 4225)(3134, 4226)(3135, 4227)(3136, 4228)(3137, 4229)(3138, 4230)(3139, 4231)(3140, 4232)(3141, 4233)(3142, 4234)(3143, 4235)(3144, 4236)(3145, 4237)(3146, 4238)(3147, 4239)(3148, 4240)(3149, 4241)(3150, 4242)(3151, 4243)(3152, 4244)(3153, 4245)(3154, 4246)(3155, 4247)(3156, 4248)(3157, 4249)(3158, 4250)(3159, 4251)(3160, 4252)(3161, 4253)(3162, 4254)(3163, 4255)(3164, 4256)(3165, 4257)(3166, 4258)(3167, 4259)(3168, 4260)(3169, 4261)(3170, 4262)(3171, 4263)(3172, 4264)(3173, 4265)(3174, 4266)(3175, 4267)(3176, 4268)(3177, 4269)(3178, 4270)(3179, 4271)(3180, 4272)(3181, 4273)(3182, 4274)(3183, 4275)(3184, 4276)(3185, 4277)(3186, 4278)(3187, 4279)(3188, 4280)(3189, 4281)(3190, 4282)(3191, 4283)(3192, 4284)(3193, 4285)(3194, 4286)(3195, 4287)(3196, 4288)(3197, 4289)(3198, 4290)(3199, 4291)(3200, 4292)(3201, 4293)(3202, 4294)(3203, 4295)(3204, 4296)(3205, 4297)(3206, 4298)(3207, 4299)(3208, 4300)(3209, 4301)(3210, 4302)(3211, 4303)(3212, 4304)(3213, 4305)(3214, 4306)(3215, 4307)(3216, 4308)(3217, 4309)(3218, 4310)(3219, 4311)(3220, 4312)(3221, 4313)(3222, 4314)(3223, 4315)(3224, 4316)(3225, 4317)(3226, 4318)(3227, 4319)(3228, 4320)(3229, 4321)(3230, 4322)(3231, 4323)(3232, 4324)(3233, 4325)(3234, 4326)(3235, 4327)(3236, 4328)(3237, 4329)(3238, 4330)(3239, 4331)(3240, 4332)(3241, 4333)(3242, 4334)(3243, 4335)(3244, 4336)(3245, 4337)(3246, 4338)(3247, 4339)(3248, 4340)(3249, 4341)(3250, 4342)(3251, 4343)(3252, 4344)(3253, 4345)(3254, 4346)(3255, 4347)(3256, 4348)(3257, 4349)(3258, 4350)(3259, 4351)(3260, 4352)(3261, 4353)(3262, 4354)(3263, 4355)(3264, 4356)(3265, 4357)(3266, 4358)(3267, 4359)(3268, 4360)(3269, 4361)(3270, 4362)(3271, 4363)(3272, 4364)(3273, 4365)(3274, 4366)(3275, 4367)(3276, 4368) L = (1, 2187)(2, 2190)(3, 2193)(4, 2195)(5, 2185)(6, 2198)(7, 2186)(8, 2188)(9, 2203)(10, 2205)(11, 2206)(12, 2207)(13, 2189)(14, 2211)(15, 2213)(16, 2191)(17, 2192)(18, 2194)(19, 2210)(20, 2222)(21, 2223)(22, 2224)(23, 2226)(24, 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3710)(1527, 3711)(1528, 3712)(1529, 3713)(1530, 3714)(1531, 3715)(1532, 3716)(1533, 3717)(1534, 3718)(1535, 3719)(1536, 3720)(1537, 3721)(1538, 3722)(1539, 3723)(1540, 3724)(1541, 3725)(1542, 3726)(1543, 3727)(1544, 3728)(1545, 3729)(1546, 3730)(1547, 3731)(1548, 3732)(1549, 3733)(1550, 3734)(1551, 3735)(1552, 3736)(1553, 3737)(1554, 3738)(1555, 3739)(1556, 3740)(1557, 3741)(1558, 3742)(1559, 3743)(1560, 3744)(1561, 3745)(1562, 3746)(1563, 3747)(1564, 3748)(1565, 3749)(1566, 3750)(1567, 3751)(1568, 3752)(1569, 3753)(1570, 3754)(1571, 3755)(1572, 3756)(1573, 3757)(1574, 3758)(1575, 3759)(1576, 3760)(1577, 3761)(1578, 3762)(1579, 3763)(1580, 3764)(1581, 3765)(1582, 3766)(1583, 3767)(1584, 3768)(1585, 3769)(1586, 3770)(1587, 3771)(1588, 3772)(1589, 3773)(1590, 3774)(1591, 3775)(1592, 3776)(1593, 3777)(1594, 3778)(1595, 3779)(1596, 3780)(1597, 3781)(1598, 3782)(1599, 3783)(1600, 3784)(1601, 3785)(1602, 3786)(1603, 3787)(1604, 3788)(1605, 3789)(1606, 3790)(1607, 3791)(1608, 3792)(1609, 3793)(1610, 3794)(1611, 3795)(1612, 3796)(1613, 3797)(1614, 3798)(1615, 3799)(1616, 3800)(1617, 3801)(1618, 3802)(1619, 3803)(1620, 3804)(1621, 3805)(1622, 3806)(1623, 3807)(1624, 3808)(1625, 3809)(1626, 3810)(1627, 3811)(1628, 3812)(1629, 3813)(1630, 3814)(1631, 3815)(1632, 3816)(1633, 3817)(1634, 3818)(1635, 3819)(1636, 3820)(1637, 3821)(1638, 3822)(1639, 3823)(1640, 3824)(1641, 3825)(1642, 3826)(1643, 3827)(1644, 3828)(1645, 3829)(1646, 3830)(1647, 3831)(1648, 3832)(1649, 3833)(1650, 3834)(1651, 3835)(1652, 3836)(1653, 3837)(1654, 3838)(1655, 3839)(1656, 3840)(1657, 3841)(1658, 3842)(1659, 3843)(1660, 3844)(1661, 3845)(1662, 3846)(1663, 3847)(1664, 3848)(1665, 3849)(1666, 3850)(1667, 3851)(1668, 3852)(1669, 3853)(1670, 3854)(1671, 3855)(1672, 3856)(1673, 3857)(1674, 3858)(1675, 3859)(1676, 3860)(1677, 3861)(1678, 3862)(1679, 3863)(1680, 3864)(1681, 3865)(1682, 3866)(1683, 3867)(1684, 3868)(1685, 3869)(1686, 3870)(1687, 3871)(1688, 3872)(1689, 3873)(1690, 3874)(1691, 3875)(1692, 3876)(1693, 3877)(1694, 3878)(1695, 3879)(1696, 3880)(1697, 3881)(1698, 3882)(1699, 3883)(1700, 3884)(1701, 3885)(1702, 3886)(1703, 3887)(1704, 3888)(1705, 3889)(1706, 3890)(1707, 3891)(1708, 3892)(1709, 3893)(1710, 3894)(1711, 3895)(1712, 3896)(1713, 3897)(1714, 3898)(1715, 3899)(1716, 3900)(1717, 3901)(1718, 3902)(1719, 3903)(1720, 3904)(1721, 3905)(1722, 3906)(1723, 3907)(1724, 3908)(1725, 3909)(1726, 3910)(1727, 3911)(1728, 3912)(1729, 3913)(1730, 3914)(1731, 3915)(1732, 3916)(1733, 3917)(1734, 3918)(1735, 3919)(1736, 3920)(1737, 3921)(1738, 3922)(1739, 3923)(1740, 3924)(1741, 3925)(1742, 3926)(1743, 3927)(1744, 3928)(1745, 3929)(1746, 3930)(1747, 3931)(1748, 3932)(1749, 3933)(1750, 3934)(1751, 3935)(1752, 3936)(1753, 3937)(1754, 3938)(1755, 3939)(1756, 3940)(1757, 3941)(1758, 3942)(1759, 3943)(1760, 3944)(1761, 3945)(1762, 3946)(1763, 3947)(1764, 3948)(1765, 3949)(1766, 3950)(1767, 3951)(1768, 3952)(1769, 3953)(1770, 3954)(1771, 3955)(1772, 3956)(1773, 3957)(1774, 3958)(1775, 3959)(1776, 3960)(1777, 3961)(1778, 3962)(1779, 3963)(1780, 3964)(1781, 3965)(1782, 3966)(1783, 3967)(1784, 3968)(1785, 3969)(1786, 3970)(1787, 3971)(1788, 3972)(1789, 3973)(1790, 3974)(1791, 3975)(1792, 3976)(1793, 3977)(1794, 3978)(1795, 3979)(1796, 3980)(1797, 3981)(1798, 3982)(1799, 3983)(1800, 3984)(1801, 3985)(1802, 3986)(1803, 3987)(1804, 3988)(1805, 3989)(1806, 3990)(1807, 3991)(1808, 3992)(1809, 3993)(1810, 3994)(1811, 3995)(1812, 3996)(1813, 3997)(1814, 3998)(1815, 3999)(1816, 4000)(1817, 4001)(1818, 4002)(1819, 4003)(1820, 4004)(1821, 4005)(1822, 4006)(1823, 4007)(1824, 4008)(1825, 4009)(1826, 4010)(1827, 4011)(1828, 4012)(1829, 4013)(1830, 4014)(1831, 4015)(1832, 4016)(1833, 4017)(1834, 4018)(1835, 4019)(1836, 4020)(1837, 4021)(1838, 4022)(1839, 4023)(1840, 4024)(1841, 4025)(1842, 4026)(1843, 4027)(1844, 4028)(1845, 4029)(1846, 4030)(1847, 4031)(1848, 4032)(1849, 4033)(1850, 4034)(1851, 4035)(1852, 4036)(1853, 4037)(1854, 4038)(1855, 4039)(1856, 4040)(1857, 4041)(1858, 4042)(1859, 4043)(1860, 4044)(1861, 4045)(1862, 4046)(1863, 4047)(1864, 4048)(1865, 4049)(1866, 4050)(1867, 4051)(1868, 4052)(1869, 4053)(1870, 4054)(1871, 4055)(1872, 4056)(1873, 4057)(1874, 4058)(1875, 4059)(1876, 4060)(1877, 4061)(1878, 4062)(1879, 4063)(1880, 4064)(1881, 4065)(1882, 4066)(1883, 4067)(1884, 4068)(1885, 4069)(1886, 4070)(1887, 4071)(1888, 4072)(1889, 4073)(1890, 4074)(1891, 4075)(1892, 4076)(1893, 4077)(1894, 4078)(1895, 4079)(1896, 4080)(1897, 4081)(1898, 4082)(1899, 4083)(1900, 4084)(1901, 4085)(1902, 4086)(1903, 4087)(1904, 4088)(1905, 4089)(1906, 4090)(1907, 4091)(1908, 4092)(1909, 4093)(1910, 4094)(1911, 4095)(1912, 4096)(1913, 4097)(1914, 4098)(1915, 4099)(1916, 4100)(1917, 4101)(1918, 4102)(1919, 4103)(1920, 4104)(1921, 4105)(1922, 4106)(1923, 4107)(1924, 4108)(1925, 4109)(1926, 4110)(1927, 4111)(1928, 4112)(1929, 4113)(1930, 4114)(1931, 4115)(1932, 4116)(1933, 4117)(1934, 4118)(1935, 4119)(1936, 4120)(1937, 4121)(1938, 4122)(1939, 4123)(1940, 4124)(1941, 4125)(1942, 4126)(1943, 4127)(1944, 4128)(1945, 4129)(1946, 4130)(1947, 4131)(1948, 4132)(1949, 4133)(1950, 4134)(1951, 4135)(1952, 4136)(1953, 4137)(1954, 4138)(1955, 4139)(1956, 4140)(1957, 4141)(1958, 4142)(1959, 4143)(1960, 4144)(1961, 4145)(1962, 4146)(1963, 4147)(1964, 4148)(1965, 4149)(1966, 4150)(1967, 4151)(1968, 4152)(1969, 4153)(1970, 4154)(1971, 4155)(1972, 4156)(1973, 4157)(1974, 4158)(1975, 4159)(1976, 4160)(1977, 4161)(1978, 4162)(1979, 4163)(1980, 4164)(1981, 4165)(1982, 4166)(1983, 4167)(1984, 4168)(1985, 4169)(1986, 4170)(1987, 4171)(1988, 4172)(1989, 4173)(1990, 4174)(1991, 4175)(1992, 4176)(1993, 4177)(1994, 4178)(1995, 4179)(1996, 4180)(1997, 4181)(1998, 4182)(1999, 4183)(2000, 4184)(2001, 4185)(2002, 4186)(2003, 4187)(2004, 4188)(2005, 4189)(2006, 4190)(2007, 4191)(2008, 4192)(2009, 4193)(2010, 4194)(2011, 4195)(2012, 4196)(2013, 4197)(2014, 4198)(2015, 4199)(2016, 4200)(2017, 4201)(2018, 4202)(2019, 4203)(2020, 4204)(2021, 4205)(2022, 4206)(2023, 4207)(2024, 4208)(2025, 4209)(2026, 4210)(2027, 4211)(2028, 4212)(2029, 4213)(2030, 4214)(2031, 4215)(2032, 4216)(2033, 4217)(2034, 4218)(2035, 4219)(2036, 4220)(2037, 4221)(2038, 4222)(2039, 4223)(2040, 4224)(2041, 4225)(2042, 4226)(2043, 4227)(2044, 4228)(2045, 4229)(2046, 4230)(2047, 4231)(2048, 4232)(2049, 4233)(2050, 4234)(2051, 4235)(2052, 4236)(2053, 4237)(2054, 4238)(2055, 4239)(2056, 4240)(2057, 4241)(2058, 4242)(2059, 4243)(2060, 4244)(2061, 4245)(2062, 4246)(2063, 4247)(2064, 4248)(2065, 4249)(2066, 4250)(2067, 4251)(2068, 4252)(2069, 4253)(2070, 4254)(2071, 4255)(2072, 4256)(2073, 4257)(2074, 4258)(2075, 4259)(2076, 4260)(2077, 4261)(2078, 4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 4, 14 ), ( 4, 14, 4, 14, 4, 14 ) } Outer automorphisms :: reflexible Dual of E14.649 Graph:: simple bipartite v = 1456 e = 2184 f = 702 degree seq :: [ 2^1092, 6^364 ] E14.653 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^3, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^7, Y3^-1 * Y1 * Y3 * Y1 * Y3^-5, Y3^3 * Y1^-1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3^3, (Y3 * Y2^-1)^7, (Y3^2 * Y1^-1)^7, Y3^-1 * Y1 * Y3^-2 * Y1 * Y3^-3 * Y1^-1 * Y3 * Y1^-1 * Y3^3 * Y1^-1 * Y3 * Y1^-1 * Y3^-3 * Y1 * Y3^-2 * Y1 ] Map:: polytopal R = (1, 1093, 2, 1094, 4, 1096)(3, 1095, 8, 1100, 10, 1102)(5, 1097, 12, 1104, 6, 1098)(7, 1099, 15, 1107, 11, 1103)(9, 1101, 18, 1110, 20, 1112)(13, 1105, 25, 1117, 23, 1115)(14, 1106, 24, 1116, 28, 1120)(16, 1108, 31, 1123, 29, 1121)(17, 1109, 33, 1125, 21, 1113)(19, 1111, 36, 1128, 37, 1129)(22, 1114, 30, 1122, 41, 1133)(26, 1118, 46, 1138, 44, 1136)(27, 1119, 47, 1139, 48, 1140)(32, 1124, 54, 1146, 52, 1144)(34, 1126, 57, 1149, 55, 1147)(35, 1127, 58, 1150, 38, 1130)(39, 1131, 56, 1148, 64, 1156)(40, 1132, 65, 1157, 66, 1158)(42, 1134, 45, 1137, 69, 1161)(43, 1135, 70, 1162, 49, 1141)(50, 1142, 53, 1145, 79, 1171)(51, 1143, 80, 1172, 67, 1159)(59, 1151, 90, 1182, 88, 1180)(60, 1152, 91, 1183, 61, 1153)(62, 1154, 89, 1181, 95, 1187)(63, 1155, 96, 1188, 97, 1189)(68, 1160, 102, 1194, 103, 1195)(71, 1163, 107, 1199, 105, 1197)(72, 1164, 74, 1166, 109, 1201)(73, 1165, 110, 1202, 104, 1196)(75, 1167, 113, 1205, 76, 1168)(77, 1169, 106, 1198, 117, 1209)(78, 1170, 118, 1210, 119, 1211)(81, 1173, 123, 1215, 121, 1213)(82, 1174, 84, 1176, 125, 1217)(83, 1175, 126, 1218, 120, 1212)(85, 1177, 87, 1179, 130, 1222)(86, 1178, 131, 1223, 98, 1190)(92, 1184, 139, 1231, 137, 1229)(93, 1185, 138, 1230, 141, 1233)(94, 1186, 142, 1234, 143, 1235)(99, 1191, 148, 1240, 100, 1192)(101, 1193, 122, 1214, 152, 1244)(108, 1200, 159, 1251, 160, 1252)(111, 1203, 164, 1256, 162, 1254)(112, 1204, 165, 1257, 161, 1253)(114, 1206, 168, 1260, 166, 1258)(115, 1207, 167, 1259, 170, 1262)(116, 1208, 171, 1263, 172, 1264)(124, 1216, 180, 1272, 181, 1273)(127, 1219, 185, 1277, 183, 1275)(128, 1220, 186, 1278, 182, 1274)(129, 1221, 187, 1279, 188, 1280)(132, 1224, 192, 1284, 190, 1282)(133, 1225, 193, 1285, 189, 1281)(134, 1226, 136, 1228, 196, 1288)(135, 1227, 197, 1289, 144, 1236)(140, 1232, 203, 1295, 204, 1296)(145, 1237, 209, 1301, 146, 1238)(147, 1239, 191, 1283, 213, 1305)(149, 1241, 216, 1308, 214, 1306)(150, 1242, 215, 1307, 217, 1309)(151, 1243, 218, 1310, 219, 1311)(153, 1245, 221, 1313, 154, 1246)(155, 1247, 163, 1255, 225, 1317)(156, 1248, 158, 1250, 227, 1319)(157, 1249, 228, 1320, 173, 1265)(169, 1261, 241, 1333, 242, 1334)(174, 1266, 247, 1339, 175, 1267)(176, 1268, 184, 1276, 251, 1343)(177, 1269, 179, 1271, 253, 1345)(178, 1270, 254, 1346, 220, 1312)(194, 1286, 272, 1364, 270, 1362)(195, 1287, 273, 1365, 274, 1366)(198, 1290, 278, 1370, 276, 1368)(199, 1291, 279, 1371, 275, 1367)(200, 1292, 202, 1294, 282, 1374)(201, 1293, 283, 1375, 205, 1297)(206, 1298, 289, 1381, 207, 1299)(208, 1300, 277, 1369, 293, 1385)(210, 1302, 296, 1388, 294, 1386)(211, 1303, 295, 1387, 297, 1389)(212, 1304, 298, 1390, 299, 1391)(222, 1314, 310, 1402, 308, 1400)(223, 1315, 309, 1401, 312, 1404)(224, 1316, 313, 1405, 314, 1406)(226, 1318, 316, 1408, 317, 1409)(229, 1321, 321, 1413, 319, 1411)(230, 1322, 322, 1414, 318, 1410)(231, 1323, 323, 1415, 232, 1324)(233, 1325, 237, 1329, 327, 1419)(234, 1326, 236, 1328, 329, 1421)(235, 1327, 330, 1422, 315, 1407)(238, 1330, 240, 1332, 335, 1427)(239, 1331, 336, 1428, 243, 1335)(244, 1336, 342, 1434, 245, 1337)(246, 1338, 320, 1412, 346, 1438)(248, 1340, 349, 1441, 347, 1439)(249, 1341, 348, 1440, 351, 1443)(250, 1342, 352, 1444, 353, 1445)(252, 1344, 355, 1447, 356, 1448)(255, 1347, 360, 1452, 358, 1450)(256, 1348, 361, 1453, 357, 1449)(257, 1349, 362, 1454, 258, 1350)(259, 1351, 263, 1355, 366, 1458)(260, 1352, 262, 1354, 368, 1460)(261, 1353, 369, 1461, 354, 1446)(264, 1356, 373, 1465, 265, 1357)(266, 1358, 271, 1363, 377, 1469)(267, 1359, 269, 1361, 379, 1471)(268, 1360, 380, 1472, 300, 1392)(280, 1372, 394, 1486, 392, 1484)(281, 1373, 395, 1487, 396, 1488)(284, 1376, 400, 1492, 398, 1490)(285, 1377, 401, 1493, 397, 1489)(286, 1378, 403, 1495, 287, 1379)(288, 1380, 399, 1491, 407, 1499)(290, 1382, 410, 1502, 408, 1500)(291, 1383, 409, 1501, 411, 1503)(292, 1384, 412, 1504, 413, 1505)(301, 1393, 303, 1395, 423, 1515)(302, 1394, 424, 1516, 304, 1396)(305, 1397, 428, 1520, 306, 1398)(307, 1399, 359, 1451, 432, 1524)(311, 1403, 436, 1528, 437, 1529)(324, 1416, 451, 1543, 449, 1541)(325, 1417, 450, 1542, 453, 1545)(326, 1418, 454, 1546, 455, 1547)(328, 1420, 457, 1549, 458, 1550)(331, 1423, 462, 1554, 460, 1552)(332, 1424, 463, 1555, 459, 1551)(333, 1425, 464, 1556, 456, 1548)(334, 1426, 466, 1558, 467, 1559)(337, 1429, 471, 1563, 469, 1561)(338, 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3967)(2876, 3968)(2877, 3969)(2878, 3970)(2879, 3971)(2880, 3972)(2881, 3973)(2882, 3974)(2883, 3975)(2884, 3976)(2885, 3977)(2886, 3978)(2887, 3979)(2888, 3980)(2889, 3981)(2890, 3982)(2891, 3983)(2892, 3984)(2893, 3985)(2894, 3986)(2895, 3987)(2896, 3988)(2897, 3989)(2898, 3990)(2899, 3991)(2900, 3992)(2901, 3993)(2902, 3994)(2903, 3995)(2904, 3996)(2905, 3997)(2906, 3998)(2907, 3999)(2908, 4000)(2909, 4001)(2910, 4002)(2911, 4003)(2912, 4004)(2913, 4005)(2914, 4006)(2915, 4007)(2916, 4008)(2917, 4009)(2918, 4010)(2919, 4011)(2920, 4012)(2921, 4013)(2922, 4014)(2923, 4015)(2924, 4016)(2925, 4017)(2926, 4018)(2927, 4019)(2928, 4020)(2929, 4021)(2930, 4022)(2931, 4023)(2932, 4024)(2933, 4025)(2934, 4026)(2935, 4027)(2936, 4028)(2937, 4029)(2938, 4030)(2939, 4031)(2940, 4032)(2941, 4033)(2942, 4034)(2943, 4035)(2944, 4036)(2945, 4037)(2946, 4038)(2947, 4039)(2948, 4040)(2949, 4041)(2950, 4042)(2951, 4043)(2952, 4044)(2953, 4045)(2954, 4046)(2955, 4047)(2956, 4048)(2957, 4049)(2958, 4050)(2959, 4051)(2960, 4052)(2961, 4053)(2962, 4054)(2963, 4055)(2964, 4056)(2965, 4057)(2966, 4058)(2967, 4059)(2968, 4060)(2969, 4061)(2970, 4062)(2971, 4063)(2972, 4064)(2973, 4065)(2974, 4066)(2975, 4067)(2976, 4068)(2977, 4069)(2978, 4070)(2979, 4071)(2980, 4072)(2981, 4073)(2982, 4074)(2983, 4075)(2984, 4076)(2985, 4077)(2986, 4078)(2987, 4079)(2988, 4080)(2989, 4081)(2990, 4082)(2991, 4083)(2992, 4084)(2993, 4085)(2994, 4086)(2995, 4087)(2996, 4088)(2997, 4089)(2998, 4090)(2999, 4091)(3000, 4092)(3001, 4093)(3002, 4094)(3003, 4095)(3004, 4096)(3005, 4097)(3006, 4098)(3007, 4099)(3008, 4100)(3009, 4101)(3010, 4102)(3011, 4103)(3012, 4104)(3013, 4105)(3014, 4106)(3015, 4107)(3016, 4108)(3017, 4109)(3018, 4110)(3019, 4111)(3020, 4112)(3021, 4113)(3022, 4114)(3023, 4115)(3024, 4116)(3025, 4117)(3026, 4118)(3027, 4119)(3028, 4120)(3029, 4121)(3030, 4122)(3031, 4123)(3032, 4124)(3033, 4125)(3034, 4126)(3035, 4127)(3036, 4128)(3037, 4129)(3038, 4130)(3039, 4131)(3040, 4132)(3041, 4133)(3042, 4134)(3043, 4135)(3044, 4136)(3045, 4137)(3046, 4138)(3047, 4139)(3048, 4140)(3049, 4141)(3050, 4142)(3051, 4143)(3052, 4144)(3053, 4145)(3054, 4146)(3055, 4147)(3056, 4148)(3057, 4149)(3058, 4150)(3059, 4151)(3060, 4152)(3061, 4153)(3062, 4154)(3063, 4155)(3064, 4156)(3065, 4157)(3066, 4158)(3067, 4159)(3068, 4160)(3069, 4161)(3070, 4162)(3071, 4163)(3072, 4164)(3073, 4165)(3074, 4166)(3075, 4167)(3076, 4168)(3077, 4169)(3078, 4170)(3079, 4171)(3080, 4172)(3081, 4173)(3082, 4174)(3083, 4175)(3084, 4176)(3085, 4177)(3086, 4178)(3087, 4179)(3088, 4180)(3089, 4181)(3090, 4182)(3091, 4183)(3092, 4184)(3093, 4185)(3094, 4186)(3095, 4187)(3096, 4188)(3097, 4189)(3098, 4190)(3099, 4191)(3100, 4192)(3101, 4193)(3102, 4194)(3103, 4195)(3104, 4196)(3105, 4197)(3106, 4198)(3107, 4199)(3108, 4200)(3109, 4201)(3110, 4202)(3111, 4203)(3112, 4204)(3113, 4205)(3114, 4206)(3115, 4207)(3116, 4208)(3117, 4209)(3118, 4210)(3119, 4211)(3120, 4212)(3121, 4213)(3122, 4214)(3123, 4215)(3124, 4216)(3125, 4217)(3126, 4218)(3127, 4219)(3128, 4220)(3129, 4221)(3130, 4222)(3131, 4223)(3132, 4224)(3133, 4225)(3134, 4226)(3135, 4227)(3136, 4228)(3137, 4229)(3138, 4230)(3139, 4231)(3140, 4232)(3141, 4233)(3142, 4234)(3143, 4235)(3144, 4236)(3145, 4237)(3146, 4238)(3147, 4239)(3148, 4240)(3149, 4241)(3150, 4242)(3151, 4243)(3152, 4244)(3153, 4245)(3154, 4246)(3155, 4247)(3156, 4248)(3157, 4249)(3158, 4250)(3159, 4251)(3160, 4252)(3161, 4253)(3162, 4254)(3163, 4255)(3164, 4256)(3165, 4257)(3166, 4258)(3167, 4259)(3168, 4260)(3169, 4261)(3170, 4262)(3171, 4263)(3172, 4264)(3173, 4265)(3174, 4266)(3175, 4267)(3176, 4268)(3177, 4269)(3178, 4270)(3179, 4271)(3180, 4272)(3181, 4273)(3182, 4274)(3183, 4275)(3184, 4276)(3185, 4277)(3186, 4278)(3187, 4279)(3188, 4280)(3189, 4281)(3190, 4282)(3191, 4283)(3192, 4284)(3193, 4285)(3194, 4286)(3195, 4287)(3196, 4288)(3197, 4289)(3198, 4290)(3199, 4291)(3200, 4292)(3201, 4293)(3202, 4294)(3203, 4295)(3204, 4296)(3205, 4297)(3206, 4298)(3207, 4299)(3208, 4300)(3209, 4301)(3210, 4302)(3211, 4303)(3212, 4304)(3213, 4305)(3214, 4306)(3215, 4307)(3216, 4308)(3217, 4309)(3218, 4310)(3219, 4311)(3220, 4312)(3221, 4313)(3222, 4314)(3223, 4315)(3224, 4316)(3225, 4317)(3226, 4318)(3227, 4319)(3228, 4320)(3229, 4321)(3230, 4322)(3231, 4323)(3232, 4324)(3233, 4325)(3234, 4326)(3235, 4327)(3236, 4328)(3237, 4329)(3238, 4330)(3239, 4331)(3240, 4332)(3241, 4333)(3242, 4334)(3243, 4335)(3244, 4336)(3245, 4337)(3246, 4338)(3247, 4339)(3248, 4340)(3249, 4341)(3250, 4342)(3251, 4343)(3252, 4344)(3253, 4345)(3254, 4346)(3255, 4347)(3256, 4348)(3257, 4349)(3258, 4350)(3259, 4351)(3260, 4352)(3261, 4353)(3262, 4354)(3263, 4355)(3264, 4356)(3265, 4357)(3266, 4358)(3267, 4359)(3268, 4360)(3269, 4361)(3270, 4362)(3271, 4363)(3272, 4364)(3273, 4365)(3274, 4366)(3275, 4367)(3276, 4368) L = (1, 2187)(2, 2190)(3, 2193)(4, 2195)(5, 2185)(6, 2198)(7, 2186)(8, 2188)(9, 2203)(10, 2205)(11, 2206)(12, 2207)(13, 2189)(14, 2211)(15, 2213)(16, 2191)(17, 2192)(18, 2194)(19, 2210)(20, 2222)(21, 2223)(22, 2224)(23, 2226)(24, 2196)(25, 2228)(26, 2197)(27, 2216)(28, 2233)(29, 2234)(30, 2199)(31, 2236)(32, 2200)(33, 2239)(34, 2201)(35, 2202)(36, 2204)(37, 2245)(38, 2246)(39, 2247)(40, 2218)(41, 2251)(42, 2252)(43, 2208)(44, 2256)(45, 2209)(46, 2221)(47, 2212)(48, 2260)(49, 2261)(50, 2262)(51, 2214)(52, 2266)(53, 2215)(54, 2232)(55, 2269)(56, 2217)(57, 2250)(58, 2272)(59, 2219)(60, 2220)(61, 2277)(62, 2278)(63, 2243)(64, 2282)(65, 2225)(66, 2284)(67, 2285)(68, 2255)(69, 2288)(70, 2289)(71, 2227)(72, 2292)(73, 2229)(74, 2230)(75, 2231)(76, 2299)(77, 2300)(78, 2265)(79, 2304)(80, 2305)(81, 2235)(82, 2308)(83, 2237)(84, 2238)(85, 2313)(86, 2240)(87, 2241)(88, 2318)(89, 2242)(90, 2281)(91, 2321)(92, 2244)(93, 2324)(94, 2276)(95, 2328)(96, 2248)(97, 2330)(98, 2331)(99, 2249)(100, 2334)(101, 2335)(102, 2253)(103, 2338)(104, 2339)(105, 2340)(106, 2254)(107, 2287)(108, 2295)(109, 2345)(110, 2346)(111, 2257)(112, 2258)(113, 2350)(114, 2259)(115, 2353)(116, 2298)(117, 2357)(118, 2263)(119, 2359)(120, 2360)(121, 2361)(122, 2264)(123, 2303)(124, 2311)(125, 2366)(126, 2367)(127, 2267)(128, 2268)(129, 2316)(130, 2373)(131, 2374)(132, 2270)(133, 2271)(134, 2379)(135, 2273)(136, 2274)(137, 2384)(138, 2275)(139, 2327)(140, 2296)(141, 2389)(142, 2279)(143, 2391)(144, 2392)(145, 2280)(146, 2395)(147, 2396)(148, 2398)(149, 2283)(150, 2378)(151, 2333)(152, 2404)(153, 2286)(154, 2407)(155, 2408)(156, 2410)(157, 2290)(158, 2291)(159, 2293)(160, 2416)(161, 2417)(162, 2418)(163, 2294)(164, 2344)(165, 2388)(166, 2422)(167, 2297)(168, 2356)(169, 2312)(170, 2427)(171, 2301)(172, 2429)(173, 2430)(174, 2302)(175, 2433)(176, 2434)(177, 2436)(178, 2306)(179, 2307)(180, 2309)(181, 2442)(182, 2443)(183, 2444)(184, 2310)(185, 2365)(186, 2426)(187, 2314)(188, 2449)(189, 2450)(190, 2451)(191, 2315)(192, 2372)(193, 2454)(194, 2317)(195, 2382)(196, 2459)(197, 2460)(198, 2319)(199, 2320)(200, 2465)(201, 2322)(202, 2323)(203, 2325)(204, 2471)(205, 2472)(206, 2326)(207, 2475)(208, 2476)(209, 2478)(210, 2329)(211, 2464)(212, 2394)(213, 2484)(214, 2485)(215, 2332)(216, 2403)(217, 2488)(218, 2336)(219, 2490)(220, 2491)(221, 2492)(222, 2337)(223, 2495)(224, 2406)(225, 2499)(226, 2413)(227, 2502)(228, 2503)(229, 2341)(230, 2342)(231, 2343)(232, 2509)(233, 2510)(234, 2512)(235, 2347)(236, 2348)(237, 2349)(238, 2518)(239, 2351)(240, 2352)(241, 2354)(242, 2524)(243, 2525)(244, 2355)(245, 2528)(246, 2529)(247, 2531)(248, 2358)(249, 2534)(250, 2432)(251, 2538)(252, 2439)(253, 2541)(254, 2542)(255, 2362)(256, 2363)(257, 2364)(258, 2548)(259, 2549)(260, 2551)(261, 2368)(262, 2369)(263, 2370)(264, 2371)(265, 2559)(266, 2560)(267, 2562)(268, 2375)(269, 2376)(270, 2567)(271, 2377)(272, 2401)(273, 2380)(274, 2571)(275, 2572)(276, 2573)(277, 2381)(278, 2458)(279, 2576)(280, 2383)(281, 2468)(282, 2581)(283, 2582)(284, 2385)(285, 2386)(286, 2387)(287, 2589)(288, 2590)(289, 2592)(290, 2390)(291, 2586)(292, 2474)(293, 2598)(294, 2599)(295, 2393)(296, 2483)(297, 2602)(298, 2397)(299, 2604)(300, 2605)(301, 2606)(302, 2399)(303, 2400)(304, 2611)(305, 2402)(306, 2614)(307, 2615)(308, 2617)(309, 2405)(310, 2498)(311, 2414)(312, 2622)(313, 2409)(314, 2624)(315, 2625)(316, 2411)(317, 2627)(318, 2628)(319, 2629)(320, 2412)(321, 2501)(322, 2621)(323, 2633)(324, 2415)(325, 2636)(326, 2508)(327, 2640)(328, 2515)(329, 2643)(330, 2644)(331, 2419)(332, 2420)(333, 2421)(334, 2521)(335, 2652)(336, 2653)(337, 2423)(338, 2424)(339, 2425)(340, 2660)(341, 2661)(342, 2663)(343, 2428)(344, 2657)(345, 2527)(346, 2669)(347, 2670)(348, 2431)(349, 2537)(350, 2440)(351, 2675)(352, 2435)(353, 2677)(354, 2678)(355, 2437)(356, 2680)(357, 2681)(358, 2682)(359, 2438)(360, 2540)(361, 2674)(362, 2686)(363, 2441)(364, 2689)(365, 2547)(366, 2693)(367, 2554)(368, 2696)(369, 2697)(370, 2445)(371, 2446)(372, 2447)(373, 2702)(374, 2448)(375, 2705)(376, 2558)(377, 2709)(378, 2565)(379, 2712)(380, 2713)(381, 2452)(382, 2453)(383, 2716)(384, 2455)(385, 2456)(386, 2457)(387, 2723)(388, 2724)(389, 2726)(390, 2461)(391, 2462)(392, 2730)(393, 2463)(394, 2481)(395, 2466)(396, 2734)(397, 2735)(398, 2736)(399, 2467)(400, 2580)(401, 2739)(402, 2469)(403, 2742)(404, 2470)(405, 2649)(406, 2588)(407, 2748)(408, 2749)(409, 2473)(410, 2597)(411, 2752)(412, 2477)(413, 2754)(414, 2553)(415, 2755)(416, 2479)(417, 2480)(418, 2760)(419, 2482)(420, 2763)(421, 2764)(422, 2609)(423, 2767)(424, 2768)(425, 2486)(426, 2487)(427, 2773)(428, 2775)(429, 2489)(430, 2772)(431, 2613)(432, 2645)(433, 2781)(434, 2493)(435, 2494)(436, 2496)(437, 2787)(438, 2788)(439, 2497)(440, 2791)(441, 2792)(442, 2500)(443, 2795)(444, 2796)(445, 2798)(446, 2504)(447, 2505)(448, 2506)(449, 2803)(450, 2507)(451, 2639)(452, 2516)(453, 2808)(454, 2511)(455, 2810)(456, 2811)(457, 2513)(458, 2813)(459, 2814)(460, 2815)(461, 2514)(462, 2642)(463, 2807)(464, 2818)(465, 2517)(466, 2519)(467, 2822)(468, 2823)(469, 2824)(470, 2520)(471, 2651)(472, 2827)(473, 2522)(474, 2830)(475, 2523)(476, 2701)(477, 2659)(478, 2819)(479, 2836)(480, 2526)(481, 2668)(482, 2839)(483, 2530)(484, 2841)(485, 2564)(486, 2842)(487, 2532)(488, 2533)(489, 2535)(490, 2848)(491, 2849)(492, 2536)(493, 2852)(494, 2853)(495, 2539)(496, 2856)(497, 2857)(498, 2859)(499, 2543)(500, 2544)(501, 2545)(502, 2864)(503, 2546)(504, 2692)(505, 2555)(506, 2869)(507, 2550)(508, 2871)(509, 2872)(510, 2552)(511, 2874)(512, 2875)(513, 2876)(514, 2695)(515, 2868)(516, 2879)(517, 2556)(518, 2882)(519, 2557)(520, 2708)(521, 2566)(522, 2887)(523, 2561)(524, 2889)(525, 2890)(526, 2563)(527, 2892)(528, 2893)(529, 2894)(530, 2711)(531, 2886)(532, 2719)(533, 2899)(534, 2900)(535, 2568)(536, 2569)(537, 2903)(538, 2570)(539, 2906)(540, 2722)(541, 2908)(542, 2728)(543, 2837)(544, 2574)(545, 2575)(546, 2912)(547, 2577)(548, 2578)(549, 2579)(550, 2919)(551, 2920)(552, 2922)(553, 2583)(554, 2584)(555, 2924)(556, 2585)(557, 2595)(558, 2927)(559, 2587)(560, 2747)(561, 2930)(562, 2591)(563, 2932)(564, 2718)(565, 2933)(566, 2593)(567, 2594)(568, 2936)(569, 2596)(570, 2938)(571, 2758)(572, 2941)(573, 2826)(574, 2600)(575, 2601)(576, 2945)(577, 2947)(578, 2603)(579, 2944)(580, 2762)(581, 2607)(582, 2951)(583, 2952)(584, 2953)(585, 2608)(586, 2766)(587, 2956)(588, 2610)(589, 2720)(590, 2880)(591, 2961)(592, 2612)(593, 2780)(594, 2964)(595, 2616)(596, 2966)(597, 2784)(598, 2969)(599, 2955)(600, 2618)(601, 2619)(602, 2620)(603, 2975)(604, 2976)(605, 2977)(606, 2623)(607, 2972)(608, 2790)(609, 2980)(610, 2626)(611, 2983)(612, 2794)(613, 2985)(614, 2800)(615, 2962)(616, 2630)(617, 2631)(618, 2632)(619, 2990)(620, 2634)(621, 2635)(622, 2637)(623, 2996)(624, 2914)(625, 2638)(626, 2858)(627, 2998)(628, 2641)(629, 3001)(630, 2850)(631, 2965)(632, 2646)(633, 2647)(634, 3005)(635, 2648)(636, 2745)(637, 2650)(638, 3009)(639, 2917)(640, 2940)(641, 2654)(642, 2655)(643, 3011)(644, 2656)(645, 2666)(646, 3014)(647, 2658)(648, 2835)(649, 3017)(650, 2662)(651, 3019)(652, 2909)(653, 2664)(654, 2665)(655, 3022)(656, 2667)(657, 3024)(658, 2845)(659, 3026)(660, 2738)(661, 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4202)(2019, 4203)(2020, 4204)(2021, 4205)(2022, 4206)(2023, 4207)(2024, 4208)(2025, 4209)(2026, 4210)(2027, 4211)(2028, 4212)(2029, 4213)(2030, 4214)(2031, 4215)(2032, 4216)(2033, 4217)(2034, 4218)(2035, 4219)(2036, 4220)(2037, 4221)(2038, 4222)(2039, 4223)(2040, 4224)(2041, 4225)(2042, 4226)(2043, 4227)(2044, 4228)(2045, 4229)(2046, 4230)(2047, 4231)(2048, 4232)(2049, 4233)(2050, 4234)(2051, 4235)(2052, 4236)(2053, 4237)(2054, 4238)(2055, 4239)(2056, 4240)(2057, 4241)(2058, 4242)(2059, 4243)(2060, 4244)(2061, 4245)(2062, 4246)(2063, 4247)(2064, 4248)(2065, 4249)(2066, 4250)(2067, 4251)(2068, 4252)(2069, 4253)(2070, 4254)(2071, 4255)(2072, 4256)(2073, 4257)(2074, 4258)(2075, 4259)(2076, 4260)(2077, 4261)(2078, 4262)(2079, 4263)(2080, 4264)(2081, 4265)(2082, 4266)(2083, 4267)(2084, 4268)(2085, 4269)(2086, 4270)(2087, 4271)(2088, 4272)(2089, 4273)(2090, 4274)(2091, 4275)(2092, 4276)(2093, 4277)(2094, 4278)(2095, 4279)(2096, 4280)(2097, 4281)(2098, 4282)(2099, 4283)(2100, 4284)(2101, 4285)(2102, 4286)(2103, 4287)(2104, 4288)(2105, 4289)(2106, 4290)(2107, 4291)(2108, 4292)(2109, 4293)(2110, 4294)(2111, 4295)(2112, 4296)(2113, 4297)(2114, 4298)(2115, 4299)(2116, 4300)(2117, 4301)(2118, 4302)(2119, 4303)(2120, 4304)(2121, 4305)(2122, 4306)(2123, 4307)(2124, 4308)(2125, 4309)(2126, 4310)(2127, 4311)(2128, 4312)(2129, 4313)(2130, 4314)(2131, 4315)(2132, 4316)(2133, 4317)(2134, 4318)(2135, 4319)(2136, 4320)(2137, 4321)(2138, 4322)(2139, 4323)(2140, 4324)(2141, 4325)(2142, 4326)(2143, 4327)(2144, 4328)(2145, 4329)(2146, 4330)(2147, 4331)(2148, 4332)(2149, 4333)(2150, 4334)(2151, 4335)(2152, 4336)(2153, 4337)(2154, 4338)(2155, 4339)(2156, 4340)(2157, 4341)(2158, 4342)(2159, 4343)(2160, 4344)(2161, 4345)(2162, 4346)(2163, 4347)(2164, 4348)(2165, 4349)(2166, 4350)(2167, 4351)(2168, 4352)(2169, 4353)(2170, 4354)(2171, 4355)(2172, 4356)(2173, 4357)(2174, 4358)(2175, 4359)(2176, 4360)(2177, 4361)(2178, 4362)(2179, 4363)(2180, 4364)(2181, 4365)(2182, 4366)(2183, 4367)(2184, 4368) local type(s) :: { ( 4, 14 ), ( 4, 14, 4, 14, 4, 14 ) } Outer automorphisms :: reflexible Dual of E14.650 Graph:: simple bipartite v = 1456 e = 2184 f = 702 degree seq :: [ 2^1092, 6^364 ] E14.654 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,13) (small group id <1092, 25>) Aut = $<2184, -1>$ (small group id <2184, -1>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^3, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3^-2 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3^7, Y3^-3 * Y1^-2 * Y3 * Y1 * Y3^-3, (Y3 * Y2^-1)^7, (Y3^-2 * Y1 * Y3^-3 * Y1)^3 ] Map:: polytopal R = (1, 1093, 2, 1094, 4, 1096)(3, 1095, 8, 1100, 10, 1102)(5, 1097, 12, 1104, 6, 1098)(7, 1099, 15, 1107, 11, 1103)(9, 1101, 18, 1110, 20, 1112)(13, 1105, 25, 1117, 23, 1115)(14, 1106, 24, 1116, 28, 1120)(16, 1108, 31, 1123, 29, 1121)(17, 1109, 33, 1125, 21, 1113)(19, 1111, 36, 1128, 37, 1129)(22, 1114, 30, 1122, 41, 1133)(26, 1118, 46, 1138, 44, 1136)(27, 1119, 47, 1139, 48, 1140)(32, 1124, 54, 1146, 52, 1144)(34, 1126, 57, 1149, 55, 1147)(35, 1127, 58, 1150, 38, 1130)(39, 1131, 56, 1148, 64, 1156)(40, 1132, 65, 1157, 66, 1158)(42, 1134, 45, 1137, 69, 1161)(43, 1135, 70, 1162, 49, 1141)(50, 1142, 53, 1145, 79, 1171)(51, 1143, 80, 1172, 67, 1159)(59, 1151, 90, 1182, 88, 1180)(60, 1152, 91, 1183, 61, 1153)(62, 1154, 89, 1181, 95, 1187)(63, 1155, 96, 1188, 97, 1189)(68, 1160, 102, 1194, 103, 1195)(71, 1163, 107, 1199, 105, 1197)(72, 1164, 74, 1166, 109, 1201)(73, 1165, 110, 1202, 104, 1196)(75, 1167, 113, 1205, 76, 1168)(77, 1169, 106, 1198, 117, 1209)(78, 1170, 118, 1210, 119, 1211)(81, 1173, 123, 1215, 121, 1213)(82, 1174, 84, 1176, 125, 1217)(83, 1175, 126, 1218, 120, 1212)(85, 1177, 87, 1179, 130, 1222)(86, 1178, 131, 1223, 98, 1190)(92, 1184, 139, 1231, 137, 1229)(93, 1185, 138, 1230, 141, 1233)(94, 1186, 142, 1234, 143, 1235)(99, 1191, 148, 1240, 100, 1192)(101, 1193, 122, 1214, 152, 1244)(108, 1200, 159, 1251, 160, 1252)(111, 1203, 164, 1256, 162, 1254)(112, 1204, 165, 1257, 161, 1253)(114, 1206, 168, 1260, 166, 1258)(115, 1207, 167, 1259, 170, 1262)(116, 1208, 171, 1263, 172, 1264)(124, 1216, 180, 1272, 181, 1273)(127, 1219, 185, 1277, 183, 1275)(128, 1220, 186, 1278, 182, 1274)(129, 1221, 187, 1279, 188, 1280)(132, 1224, 192, 1284, 190, 1282)(133, 1225, 193, 1285, 189, 1281)(134, 1226, 136, 1228, 196, 1288)(135, 1227, 197, 1289, 144, 1236)(140, 1232, 203, 1295, 204, 1296)(145, 1237, 209, 1301, 146, 1238)(147, 1239, 191, 1283, 213, 1305)(149, 1241, 216, 1308, 214, 1306)(150, 1242, 215, 1307, 217, 1309)(151, 1243, 218, 1310, 219, 1311)(153, 1245, 221, 1313, 154, 1246)(155, 1247, 163, 1255, 225, 1317)(156, 1248, 158, 1250, 227, 1319)(157, 1249, 228, 1320, 173, 1265)(169, 1261, 241, 1333, 242, 1334)(174, 1266, 247, 1339, 175, 1267)(176, 1268, 184, 1276, 251, 1343)(177, 1269, 179, 1271, 253, 1345)(178, 1270, 254, 1346, 220, 1312)(194, 1286, 272, 1364, 270, 1362)(195, 1287, 273, 1365, 274, 1366)(198, 1290, 278, 1370, 276, 1368)(199, 1291, 279, 1371, 275, 1367)(200, 1292, 202, 1294, 282, 1374)(201, 1293, 283, 1375, 205, 1297)(206, 1298, 289, 1381, 207, 1299)(208, 1300, 277, 1369, 293, 1385)(210, 1302, 296, 1388, 294, 1386)(211, 1303, 295, 1387, 297, 1389)(212, 1304, 298, 1390, 299, 1391)(222, 1314, 310, 1402, 308, 1400)(223, 1315, 309, 1401, 312, 1404)(224, 1316, 313, 1405, 314, 1406)(226, 1318, 316, 1408, 317, 1409)(229, 1321, 321, 1413, 319, 1411)(230, 1322, 322, 1414, 318, 1410)(231, 1323, 323, 1415, 232, 1324)(233, 1325, 237, 1329, 327, 1419)(234, 1326, 236, 1328, 329, 1421)(235, 1327, 330, 1422, 315, 1407)(238, 1330, 240, 1332, 335, 1427)(239, 1331, 336, 1428, 243, 1335)(244, 1336, 342, 1434, 245, 1337)(246, 1338, 320, 1412, 346, 1438)(248, 1340, 349, 1441, 347, 1439)(249, 1341, 348, 1440, 351, 1443)(250, 1342, 352, 1444, 353, 1445)(252, 1344, 355, 1447, 356, 1448)(255, 1347, 360, 1452, 358, 1450)(256, 1348, 361, 1453, 357, 1449)(257, 1349, 362, 1454, 258, 1350)(259, 1351, 263, 1355, 366, 1458)(260, 1352, 262, 1354, 368, 1460)(261, 1353, 369, 1461, 354, 1446)(264, 1356, 373, 1465, 265, 1357)(266, 1358, 271, 1363, 377, 1469)(267, 1359, 269, 1361, 379, 1471)(268, 1360, 380, 1472, 300, 1392)(280, 1372, 394, 1486, 392, 1484)(281, 1373, 395, 1487, 396, 1488)(284, 1376, 400, 1492, 398, 1490)(285, 1377, 401, 1493, 397, 1489)(286, 1378, 403, 1495, 287, 1379)(288, 1380, 399, 1491, 407, 1499)(290, 1382, 410, 1502, 408, 1500)(291, 1383, 409, 1501, 411, 1503)(292, 1384, 412, 1504, 413, 1505)(301, 1393, 303, 1395, 423, 1515)(302, 1394, 424, 1516, 304, 1396)(305, 1397, 428, 1520, 306, 1398)(307, 1399, 359, 1451, 432, 1524)(311, 1403, 436, 1528, 437, 1529)(324, 1416, 451, 1543, 449, 1541)(325, 1417, 450, 1542, 453, 1545)(326, 1418, 454, 1546, 455, 1547)(328, 1420, 457, 1549, 458, 1550)(331, 1423, 462, 1554, 460, 1552)(332, 1424, 463, 1555, 459, 1551)(333, 1425, 464, 1556, 456, 1548)(334, 1426, 466, 1558, 467, 1559)(337, 1429, 471, 1563, 469, 1561)(338, 1430, 472, 1564, 468, 1560)(339, 1431, 474, 1566, 340, 1432)(341, 1433, 470, 1562, 478, 1570)(343, 1435, 481, 1573, 479, 1571)(344, 1436, 480, 1572, 482, 1574)(345, 1437, 483, 1575, 484, 1576)(350, 1442, 489, 1581, 490, 1582)(363, 1455, 504, 1596, 502, 1594)(364, 1456, 503, 1595, 506, 1598)(365, 1457, 507, 1599, 508, 1600)(367, 1459, 510, 1602, 511, 1603)(370, 1462, 515, 1607, 513, 1605)(371, 1463, 406, 1498, 512, 1604)(372, 1464, 516, 1608, 509, 1601)(374, 1466, 519, 1611, 517, 1609)(375, 1467, 518, 1610, 521, 1613)(376, 1468, 522, 1614, 523, 1615)(378, 1470, 525, 1617, 526, 1618)(381, 1473, 530, 1622, 528, 1620)(382, 1474, 477, 1569, 527, 1619)(383, 1475, 385, 1477, 532, 1624)(384, 1476, 533, 1625, 524, 1616)(386, 1478, 535, 1627, 387, 1479)(388, 1480, 393, 1485, 539, 1631)(389, 1481, 391, 1483, 541, 1633)(390, 1482, 542, 1634, 414, 1506)(402, 1494, 476, 1568, 553, 1645)(404, 1496, 505, 1597, 555, 1647)(405, 1497, 556, 1648, 557, 1649)(415, 1507, 417, 1509, 564, 1656)(416, 1508, 565, 1657, 418, 1510)(419, 1511, 568, 1660, 420, 1512)(421, 1513, 529, 1621, 571, 1663)(422, 1514, 572, 1664, 573, 1665)(425, 1517, 577, 1669, 575, 1667)(426, 1518, 578, 1670, 574, 1666)(427, 1519, 576, 1668, 579, 1671)(429, 1521, 582, 1674, 580, 1672)(430, 1522, 581, 1673, 465, 1557)(431, 1523, 583, 1675, 544, 1636)(433, 1525, 435, 1527, 586, 1678)(434, 1526, 587, 1679, 438, 1530)(439, 1531, 591, 1683, 440, 1532)(441, 1533, 461, 1553, 594, 1686)(442, 1534, 595, 1687, 443, 1535)(444, 1536, 448, 1540, 598, 1690)(445, 1537, 447, 1539, 561, 1653)(446, 1538, 600, 1692, 485, 1577)(452, 1544, 605, 1697, 534, 1626)(473, 1565, 531, 1623, 619, 1711)(475, 1567, 520, 1612, 621, 1713)(486, 1578, 488, 1580, 628, 1720)(487, 1579, 629, 1721, 491, 1583)(492, 1584, 632, 1724, 493, 1585)(494, 1586, 514, 1606, 635, 1727)(495, 1587, 636, 1728, 496, 1588)(497, 1589, 501, 1593, 639, 1731)(498, 1590, 500, 1592, 625, 1717)(499, 1591, 641, 1733, 584, 1676)(536, 1628, 665, 1757, 663, 1755)(537, 1629, 664, 1756, 666, 1758)(538, 1630, 667, 1759, 668, 1760)(540, 1632, 669, 1761, 670, 1762)(543, 1635, 673, 1765, 671, 1763)(545, 1637, 546, 1638, 590, 1682)(547, 1639, 674, 1766, 548, 1640)(549, 1641, 554, 1646, 678, 1770)(550, 1642, 552, 1644, 680, 1772)(551, 1643, 681, 1773, 558, 1650)(559, 1651, 560, 1652, 686, 1778)(562, 1654, 672, 1764, 689, 1781)(563, 1655, 690, 1782, 691, 1783)(566, 1658, 694, 1786, 693, 1785)(567, 1659, 610, 1702, 692, 1784)(569, 1661, 696, 1788, 695, 1787)(570, 1662, 697, 1789, 683, 1775)(585, 1677, 708, 1800, 709, 1801)(588, 1680, 712, 1804, 711, 1803)(589, 1681, 650, 1742, 710, 1802)(592, 1684, 714, 1806, 713, 1805)(593, 1685, 715, 1807, 716, 1808)(596, 1688, 719, 1811, 718, 1810)(597, 1689, 720, 1812, 721, 1813)(599, 1691, 687, 1779, 722, 1814)(601, 1693, 725, 1817, 723, 1815)(602, 1694, 604, 1696, 727, 1819)(603, 1695, 728, 1820, 606, 1698)(607, 1699, 731, 1823, 608, 1700)(609, 1701, 612, 1704, 734, 1826)(611, 1703, 736, 1828, 717, 1809)(613, 1705, 739, 1831, 614, 1706)(615, 1707, 620, 1712, 743, 1835)(616, 1708, 618, 1710, 745, 1837)(617, 1709, 746, 1838, 622, 1714)(623, 1715, 624, 1716, 750, 1842)(626, 1718, 724, 1816, 753, 1845)(627, 1719, 754, 1846, 755, 1847)(630, 1722, 758, 1850, 757, 1849)(631, 1723, 660, 1752, 756, 1848)(633, 1725, 760, 1852, 759, 1851)(634, 1726, 761, 1853, 762, 1854)(637, 1729, 765, 1857, 764, 1856)(638, 1730, 766, 1858, 767, 1859)(640, 1732, 751, 1843, 768, 1860)(642, 1734, 771, 1863, 769, 1861)(643, 1735, 645, 1737, 773, 1865)(644, 1736, 774, 1866, 646, 1738)(647, 1739, 777, 1869, 648, 1740)(649, 1741, 652, 1744, 780, 1872)(651, 1743, 781, 1873, 763, 1855)(653, 1745, 655, 1747, 784, 1876)(654, 1746, 785, 1877, 656, 1748)(657, 1749, 788, 1880, 658, 1750)(659, 1751, 662, 1754, 791, 1883)(661, 1753, 792, 1884, 698, 1790)(675, 1767, 803, 1895, 801, 1893)(676, 1768, 802, 1894, 737, 1829)(677, 1769, 804, 1896, 805, 1897)(679, 1771, 806, 1898, 807, 1899)(682, 1774, 810, 1902, 808, 1900)(684, 1776, 809, 1901, 811, 1903)(685, 1777, 812, 1904, 813, 1905)(688, 1780, 814, 1906, 730, 1822)(699, 1791, 822, 1914, 700, 1792)(701, 1793, 705, 1797, 826, 1918)(702, 1794, 704, 1796, 828, 1920)(703, 1795, 829, 1921, 706, 1798)(707, 1799, 770, 1862, 831, 1923)(726, 1818, 842, 1934, 843, 1935)(729, 1821, 845, 1937, 844, 1936)(732, 1824, 847, 1939, 846, 1938)(733, 1825, 848, 1940, 849, 1941)(735, 1827, 851, 1943, 818, 1910)(738, 1830, 795, 1887, 850, 1942)(740, 1832, 855, 1947, 853, 1945)(741, 1833, 854, 1946, 782, 1874)(742, 1834, 856, 1948, 857, 1949)(744, 1836, 858, 1950, 859, 1951)(747, 1839, 862, 1954, 860, 1952)(748, 1840, 861, 1953, 863, 1955)(749, 1841, 864, 1956, 865, 1957)(752, 1844, 866, 1958, 776, 1868)(772, 1864, 878, 1970, 879, 1971)(775, 1867, 881, 1973, 880, 1972)(778, 1870, 883, 1975, 882, 1974)(779, 1871, 884, 1976, 885, 1977)(783, 1875, 887, 1979, 888, 1980)(786, 1878, 891, 1983, 890, 1982)(787, 1879, 799, 1891, 889, 1981)(789, 1881, 893, 1985, 892, 1984)(790, 1882, 894, 1986, 895, 1987)(793, 1885, 824, 1916, 896, 1988)(794, 1886, 796, 1888, 899, 1991)(797, 1889, 902, 1994, 798, 1890)(800, 1892, 904, 1996, 815, 1907)(816, 1908, 916, 2008, 817, 1909)(819, 1911, 820, 1912, 921, 2013)(821, 1913, 897, 1989, 922, 2014)(823, 1915, 924, 2016, 923, 2015)(825, 1917, 925, 2017, 926, 2018)(827, 1919, 927, 2019, 928, 2020)(830, 1922, 930, 2022, 929, 2021)(832, 1924, 932, 2024, 833, 1925)(834, 1926, 835, 1927, 936, 2028)(836, 1928, 852, 1944, 938, 2030)(837, 1929, 838, 1930, 940, 2032)(839, 1931, 942, 2034, 840, 1932)(841, 1933, 943, 2035, 867, 1959)(868, 1960, 960, 2052, 869, 1961)(870, 1962, 871, 1963, 963, 2055)(872, 1964, 886, 1978, 965, 2057)(873, 1965, 874, 1966, 967, 2059)(875, 1967, 969, 2061, 876, 1968)(877, 1969, 970, 2062, 931, 2023)(898, 1990, 981, 2073, 982, 2074)(900, 1992, 984, 2076, 948, 2040)(901, 1993, 910, 2002, 983, 2075)(903, 1995, 986, 2078, 985, 2077)(905, 1997, 918, 2010, 987, 2079)(906, 1998, 907, 1999, 989, 2081)(908, 2000, 947, 2039, 909, 2001)(911, 2003, 991, 2083, 912, 2004)(913, 2005, 993, 2085, 914, 2006)(915, 2007, 988, 2080, 995, 2087)(917, 2009, 997, 2089, 996, 2088)(919, 2011, 949, 2041, 998, 2090)(920, 2012, 999, 2091, 1000, 2092)(933, 2025, 1008, 2100, 1006, 2098)(934, 2026, 1007, 2099, 944, 2036)(935, 2027, 1009, 2101, 1010, 2102)(937, 2029, 1011, 2103, 941, 2033)(939, 2031, 1013, 2105, 1014, 2106)(945, 2037, 1016, 2108, 946, 2038)(950, 2042, 1020, 2112, 1012, 2104)(951, 2043, 952, 2044, 1021, 2113)(953, 2045, 974, 2066, 954, 2046)(955, 2047, 1022, 2114, 956, 2048)(957, 2049, 1024, 2116, 958, 2050)(959, 2051, 1015, 2107, 1026, 2118)(961, 2053, 1029, 2121, 1027, 2119)(962, 2054, 1028, 2120, 971, 2063)(964, 2056, 1030, 2122, 968, 2060)(966, 2058, 1032, 2124, 1033, 2125)(972, 2064, 1035, 2127, 973, 2065)(975, 2067, 1037, 2129, 1031, 2123)(976, 2068, 1038, 2130, 977, 2069)(978, 2070, 979, 2071, 1004, 2096)(980, 2072, 1039, 2131, 1001, 2093)(990, 2082, 1036, 2128, 1017, 2109)(992, 2084, 994, 2086, 1044, 2136)(1002, 2094, 1003, 2095, 1049, 2141)(1005, 2097, 1034, 2126, 1050, 2142)(1018, 2110, 1042, 2134, 1019, 2111)(1023, 2115, 1025, 2117, 1058, 2150)(1040, 2132, 1068, 2160, 1041, 2133)(1043, 2135, 1069, 2161, 1045, 2137)(1046, 2138, 1047, 2139, 1071, 2163)(1048, 2140, 1067, 2159, 1072, 2164)(1051, 2143, 1052, 2144, 1074, 2166)(1053, 2145, 1057, 2149, 1075, 2167)(1054, 2146, 1076, 2168, 1055, 2147)(1056, 2148, 1077, 2169, 1059, 2151)(1060, 2152, 1061, 2153, 1079, 2171)(1062, 2154, 1066, 2158, 1080, 2172)(1063, 2155, 1081, 2173, 1064, 2156)(1065, 2157, 1082, 2174, 1073, 2165)(1070, 2162, 1084, 2176, 1085, 2177)(1078, 2170, 1087, 2179, 1088, 2180)(1083, 2175, 1089, 2181, 1086, 2178)(1090, 2182, 1092, 2184, 1091, 2183)(2185, 3277)(2186, 3278)(2187, 3279)(2188, 3280)(2189, 3281)(2190, 3282)(2191, 3283)(2192, 3284)(2193, 3285)(2194, 3286)(2195, 3287)(2196, 3288)(2197, 3289)(2198, 3290)(2199, 3291)(2200, 3292)(2201, 3293)(2202, 3294)(2203, 3295)(2204, 3296)(2205, 3297)(2206, 3298)(2207, 3299)(2208, 3300)(2209, 3301)(2210, 3302)(2211, 3303)(2212, 3304)(2213, 3305)(2214, 3306)(2215, 3307)(2216, 3308)(2217, 3309)(2218, 3310)(2219, 3311)(2220, 3312)(2221, 3313)(2222, 3314)(2223, 3315)(2224, 3316)(2225, 3317)(2226, 3318)(2227, 3319)(2228, 3320)(2229, 3321)(2230, 3322)(2231, 3323)(2232, 3324)(2233, 3325)(2234, 3326)(2235, 3327)(2236, 3328)(2237, 3329)(2238, 3330)(2239, 3331)(2240, 3332)(2241, 3333)(2242, 3334)(2243, 3335)(2244, 3336)(2245, 3337)(2246, 3338)(2247, 3339)(2248, 3340)(2249, 3341)(2250, 3342)(2251, 3343)(2252, 3344)(2253, 3345)(2254, 3346)(2255, 3347)(2256, 3348)(2257, 3349)(2258, 3350)(2259, 3351)(2260, 3352)(2261, 3353)(2262, 3354)(2263, 3355)(2264, 3356)(2265, 3357)(2266, 3358)(2267, 3359)(2268, 3360)(2269, 3361)(2270, 3362)(2271, 3363)(2272, 3364)(2273, 3365)(2274, 3366)(2275, 3367)(2276, 3368)(2277, 3369)(2278, 3370)(2279, 3371)(2280, 3372)(2281, 3373)(2282, 3374)(2283, 3375)(2284, 3376)(2285, 3377)(2286, 3378)(2287, 3379)(2288, 3380)(2289, 3381)(2290, 3382)(2291, 3383)(2292, 3384)(2293, 3385)(2294, 3386)(2295, 3387)(2296, 3388)(2297, 3389)(2298, 3390)(2299, 3391)(2300, 3392)(2301, 3393)(2302, 3394)(2303, 3395)(2304, 3396)(2305, 3397)(2306, 3398)(2307, 3399)(2308, 3400)(2309, 3401)(2310, 3402)(2311, 3403)(2312, 3404)(2313, 3405)(2314, 3406)(2315, 3407)(2316, 3408)(2317, 3409)(2318, 3410)(2319, 3411)(2320, 3412)(2321, 3413)(2322, 3414)(2323, 3415)(2324, 3416)(2325, 3417)(2326, 3418)(2327, 3419)(2328, 3420)(2329, 3421)(2330, 3422)(2331, 3423)(2332, 3424)(2333, 3425)(2334, 3426)(2335, 3427)(2336, 3428)(2337, 3429)(2338, 3430)(2339, 3431)(2340, 3432)(2341, 3433)(2342, 3434)(2343, 3435)(2344, 3436)(2345, 3437)(2346, 3438)(2347, 3439)(2348, 3440)(2349, 3441)(2350, 3442)(2351, 3443)(2352, 3444)(2353, 3445)(2354, 3446)(2355, 3447)(2356, 3448)(2357, 3449)(2358, 3450)(2359, 3451)(2360, 3452)(2361, 3453)(2362, 3454)(2363, 3455)(2364, 3456)(2365, 3457)(2366, 3458)(2367, 3459)(2368, 3460)(2369, 3461)(2370, 3462)(2371, 3463)(2372, 3464)(2373, 3465)(2374, 3466)(2375, 3467)(2376, 3468)(2377, 3469)(2378, 3470)(2379, 3471)(2380, 3472)(2381, 3473)(2382, 3474)(2383, 3475)(2384, 3476)(2385, 3477)(2386, 3478)(2387, 3479)(2388, 3480)(2389, 3481)(2390, 3482)(2391, 3483)(2392, 3484)(2393, 3485)(2394, 3486)(2395, 3487)(2396, 3488)(2397, 3489)(2398, 3490)(2399, 3491)(2400, 3492)(2401, 3493)(2402, 3494)(2403, 3495)(2404, 3496)(2405, 3497)(2406, 3498)(2407, 3499)(2408, 3500)(2409, 3501)(2410, 3502)(2411, 3503)(2412, 3504)(2413, 3505)(2414, 3506)(2415, 3507)(2416, 3508)(2417, 3509)(2418, 3510)(2419, 3511)(2420, 3512)(2421, 3513)(2422, 3514)(2423, 3515)(2424, 3516)(2425, 3517)(2426, 3518)(2427, 3519)(2428, 3520)(2429, 3521)(2430, 3522)(2431, 3523)(2432, 3524)(2433, 3525)(2434, 3526)(2435, 3527)(2436, 3528)(2437, 3529)(2438, 3530)(2439, 3531)(2440, 3532)(2441, 3533)(2442, 3534)(2443, 3535)(2444, 3536)(2445, 3537)(2446, 3538)(2447, 3539)(2448, 3540)(2449, 3541)(2450, 3542)(2451, 3543)(2452, 3544)(2453, 3545)(2454, 3546)(2455, 3547)(2456, 3548)(2457, 3549)(2458, 3550)(2459, 3551)(2460, 3552)(2461, 3553)(2462, 3554)(2463, 3555)(2464, 3556)(2465, 3557)(2466, 3558)(2467, 3559)(2468, 3560)(2469, 3561)(2470, 3562)(2471, 3563)(2472, 3564)(2473, 3565)(2474, 3566)(2475, 3567)(2476, 3568)(2477, 3569)(2478, 3570)(2479, 3571)(2480, 3572)(2481, 3573)(2482, 3574)(2483, 3575)(2484, 3576)(2485, 3577)(2486, 3578)(2487, 3579)(2488, 3580)(2489, 3581)(2490, 3582)(2491, 3583)(2492, 3584)(2493, 3585)(2494, 3586)(2495, 3587)(2496, 3588)(2497, 3589)(2498, 3590)(2499, 3591)(2500, 3592)(2501, 3593)(2502, 3594)(2503, 3595)(2504, 3596)(2505, 3597)(2506, 3598)(2507, 3599)(2508, 3600)(2509, 3601)(2510, 3602)(2511, 3603)(2512, 3604)(2513, 3605)(2514, 3606)(2515, 3607)(2516, 3608)(2517, 3609)(2518, 3610)(2519, 3611)(2520, 3612)(2521, 3613)(2522, 3614)(2523, 3615)(2524, 3616)(2525, 3617)(2526, 3618)(2527, 3619)(2528, 3620)(2529, 3621)(2530, 3622)(2531, 3623)(2532, 3624)(2533, 3625)(2534, 3626)(2535, 3627)(2536, 3628)(2537, 3629)(2538, 3630)(2539, 3631)(2540, 3632)(2541, 3633)(2542, 3634)(2543, 3635)(2544, 3636)(2545, 3637)(2546, 3638)(2547, 3639)(2548, 3640)(2549, 3641)(2550, 3642)(2551, 3643)(2552, 3644)(2553, 3645)(2554, 3646)(2555, 3647)(2556, 3648)(2557, 3649)(2558, 3650)(2559, 3651)(2560, 3652)(2561, 3653)(2562, 3654)(2563, 3655)(2564, 3656)(2565, 3657)(2566, 3658)(2567, 3659)(2568, 3660)(2569, 3661)(2570, 3662)(2571, 3663)(2572, 3664)(2573, 3665)(2574, 3666)(2575, 3667)(2576, 3668)(2577, 3669)(2578, 3670)(2579, 3671)(2580, 3672)(2581, 3673)(2582, 3674)(2583, 3675)(2584, 3676)(2585, 3677)(2586, 3678)(2587, 3679)(2588, 3680)(2589, 3681)(2590, 3682)(2591, 3683)(2592, 3684)(2593, 3685)(2594, 3686)(2595, 3687)(2596, 3688)(2597, 3689)(2598, 3690)(2599, 3691)(2600, 3692)(2601, 3693)(2602, 3694)(2603, 3695)(2604, 3696)(2605, 3697)(2606, 3698)(2607, 3699)(2608, 3700)(2609, 3701)(2610, 3702)(2611, 3703)(2612, 3704)(2613, 3705)(2614, 3706)(2615, 3707)(2616, 3708)(2617, 3709)(2618, 3710)(2619, 3711)(2620, 3712)(2621, 3713)(2622, 3714)(2623, 3715)(2624, 3716)(2625, 3717)(2626, 3718)(2627, 3719)(2628, 3720)(2629, 3721)(2630, 3722)(2631, 3723)(2632, 3724)(2633, 3725)(2634, 3726)(2635, 3727)(2636, 3728)(2637, 3729)(2638, 3730)(2639, 3731)(2640, 3732)(2641, 3733)(2642, 3734)(2643, 3735)(2644, 3736)(2645, 3737)(2646, 3738)(2647, 3739)(2648, 3740)(2649, 3741)(2650, 3742)(2651, 3743)(2652, 3744)(2653, 3745)(2654, 3746)(2655, 3747)(2656, 3748)(2657, 3749)(2658, 3750)(2659, 3751)(2660, 3752)(2661, 3753)(2662, 3754)(2663, 3755)(2664, 3756)(2665, 3757)(2666, 3758)(2667, 3759)(2668, 3760)(2669, 3761)(2670, 3762)(2671, 3763)(2672, 3764)(2673, 3765)(2674, 3766)(2675, 3767)(2676, 3768)(2677, 3769)(2678, 3770)(2679, 3771)(2680, 3772)(2681, 3773)(2682, 3774)(2683, 3775)(2684, 3776)(2685, 3777)(2686, 3778)(2687, 3779)(2688, 3780)(2689, 3781)(2690, 3782)(2691, 3783)(2692, 3784)(2693, 3785)(2694, 3786)(2695, 3787)(2696, 3788)(2697, 3789)(2698, 3790)(2699, 3791)(2700, 3792)(2701, 3793)(2702, 3794)(2703, 3795)(2704, 3796)(2705, 3797)(2706, 3798)(2707, 3799)(2708, 3800)(2709, 3801)(2710, 3802)(2711, 3803)(2712, 3804)(2713, 3805)(2714, 3806)(2715, 3807)(2716, 3808)(2717, 3809)(2718, 3810)(2719, 3811)(2720, 3812)(2721, 3813)(2722, 3814)(2723, 3815)(2724, 3816)(2725, 3817)(2726, 3818)(2727, 3819)(2728, 3820)(2729, 3821)(2730, 3822)(2731, 3823)(2732, 3824)(2733, 3825)(2734, 3826)(2735, 3827)(2736, 3828)(2737, 3829)(2738, 3830)(2739, 3831)(2740, 3832)(2741, 3833)(2742, 3834)(2743, 3835)(2744, 3836)(2745, 3837)(2746, 3838)(2747, 3839)(2748, 3840)(2749, 3841)(2750, 3842)(2751, 3843)(2752, 3844)(2753, 3845)(2754, 3846)(2755, 3847)(2756, 3848)(2757, 3849)(2758, 3850)(2759, 3851)(2760, 3852)(2761, 3853)(2762, 3854)(2763, 3855)(2764, 3856)(2765, 3857)(2766, 3858)(2767, 3859)(2768, 3860)(2769, 3861)(2770, 3862)(2771, 3863)(2772, 3864)(2773, 3865)(2774, 3866)(2775, 3867)(2776, 3868)(2777, 3869)(2778, 3870)(2779, 3871)(2780, 3872)(2781, 3873)(2782, 3874)(2783, 3875)(2784, 3876)(2785, 3877)(2786, 3878)(2787, 3879)(2788, 3880)(2789, 3881)(2790, 3882)(2791, 3883)(2792, 3884)(2793, 3885)(2794, 3886)(2795, 3887)(2796, 3888)(2797, 3889)(2798, 3890)(2799, 3891)(2800, 3892)(2801, 3893)(2802, 3894)(2803, 3895)(2804, 3896)(2805, 3897)(2806, 3898)(2807, 3899)(2808, 3900)(2809, 3901)(2810, 3902)(2811, 3903)(2812, 3904)(2813, 3905)(2814, 3906)(2815, 3907)(2816, 3908)(2817, 3909)(2818, 3910)(2819, 3911)(2820, 3912)(2821, 3913)(2822, 3914)(2823, 3915)(2824, 3916)(2825, 3917)(2826, 3918)(2827, 3919)(2828, 3920)(2829, 3921)(2830, 3922)(2831, 3923)(2832, 3924)(2833, 3925)(2834, 3926)(2835, 3927)(2836, 3928)(2837, 3929)(2838, 3930)(2839, 3931)(2840, 3932)(2841, 3933)(2842, 3934)(2843, 3935)(2844, 3936)(2845, 3937)(2846, 3938)(2847, 3939)(2848, 3940)(2849, 3941)(2850, 3942)(2851, 3943)(2852, 3944)(2853, 3945)(2854, 3946)(2855, 3947)(2856, 3948)(2857, 3949)(2858, 3950)(2859, 3951)(2860, 3952)(2861, 3953)(2862, 3954)(2863, 3955)(2864, 3956)(2865, 3957)(2866, 3958)(2867, 3959)(2868, 3960)(2869, 3961)(2870, 3962)(2871, 3963)(2872, 3964)(2873, 3965)(2874, 3966)(2875, 3967)(2876, 3968)(2877, 3969)(2878, 3970)(2879, 3971)(2880, 3972)(2881, 3973)(2882, 3974)(2883, 3975)(2884, 3976)(2885, 3977)(2886, 3978)(2887, 3979)(2888, 3980)(2889, 3981)(2890, 3982)(2891, 3983)(2892, 3984)(2893, 3985)(2894, 3986)(2895, 3987)(2896, 3988)(2897, 3989)(2898, 3990)(2899, 3991)(2900, 3992)(2901, 3993)(2902, 3994)(2903, 3995)(2904, 3996)(2905, 3997)(2906, 3998)(2907, 3999)(2908, 4000)(2909, 4001)(2910, 4002)(2911, 4003)(2912, 4004)(2913, 4005)(2914, 4006)(2915, 4007)(2916, 4008)(2917, 4009)(2918, 4010)(2919, 4011)(2920, 4012)(2921, 4013)(2922, 4014)(2923, 4015)(2924, 4016)(2925, 4017)(2926, 4018)(2927, 4019)(2928, 4020)(2929, 4021)(2930, 4022)(2931, 4023)(2932, 4024)(2933, 4025)(2934, 4026)(2935, 4027)(2936, 4028)(2937, 4029)(2938, 4030)(2939, 4031)(2940, 4032)(2941, 4033)(2942, 4034)(2943, 4035)(2944, 4036)(2945, 4037)(2946, 4038)(2947, 4039)(2948, 4040)(2949, 4041)(2950, 4042)(2951, 4043)(2952, 4044)(2953, 4045)(2954, 4046)(2955, 4047)(2956, 4048)(2957, 4049)(2958, 4050)(2959, 4051)(2960, 4052)(2961, 4053)(2962, 4054)(2963, 4055)(2964, 4056)(2965, 4057)(2966, 4058)(2967, 4059)(2968, 4060)(2969, 4061)(2970, 4062)(2971, 4063)(2972, 4064)(2973, 4065)(2974, 4066)(2975, 4067)(2976, 4068)(2977, 4069)(2978, 4070)(2979, 4071)(2980, 4072)(2981, 4073)(2982, 4074)(2983, 4075)(2984, 4076)(2985, 4077)(2986, 4078)(2987, 4079)(2988, 4080)(2989, 4081)(2990, 4082)(2991, 4083)(2992, 4084)(2993, 4085)(2994, 4086)(2995, 4087)(2996, 4088)(2997, 4089)(2998, 4090)(2999, 4091)(3000, 4092)(3001, 4093)(3002, 4094)(3003, 4095)(3004, 4096)(3005, 4097)(3006, 4098)(3007, 4099)(3008, 4100)(3009, 4101)(3010, 4102)(3011, 4103)(3012, 4104)(3013, 4105)(3014, 4106)(3015, 4107)(3016, 4108)(3017, 4109)(3018, 4110)(3019, 4111)(3020, 4112)(3021, 4113)(3022, 4114)(3023, 4115)(3024, 4116)(3025, 4117)(3026, 4118)(3027, 4119)(3028, 4120)(3029, 4121)(3030, 4122)(3031, 4123)(3032, 4124)(3033, 4125)(3034, 4126)(3035, 4127)(3036, 4128)(3037, 4129)(3038, 4130)(3039, 4131)(3040, 4132)(3041, 4133)(3042, 4134)(3043, 4135)(3044, 4136)(3045, 4137)(3046, 4138)(3047, 4139)(3048, 4140)(3049, 4141)(3050, 4142)(3051, 4143)(3052, 4144)(3053, 4145)(3054, 4146)(3055, 4147)(3056, 4148)(3057, 4149)(3058, 4150)(3059, 4151)(3060, 4152)(3061, 4153)(3062, 4154)(3063, 4155)(3064, 4156)(3065, 4157)(3066, 4158)(3067, 4159)(3068, 4160)(3069, 4161)(3070, 4162)(3071, 4163)(3072, 4164)(3073, 4165)(3074, 4166)(3075, 4167)(3076, 4168)(3077, 4169)(3078, 4170)(3079, 4171)(3080, 4172)(3081, 4173)(3082, 4174)(3083, 4175)(3084, 4176)(3085, 4177)(3086, 4178)(3087, 4179)(3088, 4180)(3089, 4181)(3090, 4182)(3091, 4183)(3092, 4184)(3093, 4185)(3094, 4186)(3095, 4187)(3096, 4188)(3097, 4189)(3098, 4190)(3099, 4191)(3100, 4192)(3101, 4193)(3102, 4194)(3103, 4195)(3104, 4196)(3105, 4197)(3106, 4198)(3107, 4199)(3108, 4200)(3109, 4201)(3110, 4202)(3111, 4203)(3112, 4204)(3113, 4205)(3114, 4206)(3115, 4207)(3116, 4208)(3117, 4209)(3118, 4210)(3119, 4211)(3120, 4212)(3121, 4213)(3122, 4214)(3123, 4215)(3124, 4216)(3125, 4217)(3126, 4218)(3127, 4219)(3128, 4220)(3129, 4221)(3130, 4222)(3131, 4223)(3132, 4224)(3133, 4225)(3134, 4226)(3135, 4227)(3136, 4228)(3137, 4229)(3138, 4230)(3139, 4231)(3140, 4232)(3141, 4233)(3142, 4234)(3143, 4235)(3144, 4236)(3145, 4237)(3146, 4238)(3147, 4239)(3148, 4240)(3149, 4241)(3150, 4242)(3151, 4243)(3152, 4244)(3153, 4245)(3154, 4246)(3155, 4247)(3156, 4248)(3157, 4249)(3158, 4250)(3159, 4251)(3160, 4252)(3161, 4253)(3162, 4254)(3163, 4255)(3164, 4256)(3165, 4257)(3166, 4258)(3167, 4259)(3168, 4260)(3169, 4261)(3170, 4262)(3171, 4263)(3172, 4264)(3173, 4265)(3174, 4266)(3175, 4267)(3176, 4268)(3177, 4269)(3178, 4270)(3179, 4271)(3180, 4272)(3181, 4273)(3182, 4274)(3183, 4275)(3184, 4276)(3185, 4277)(3186, 4278)(3187, 4279)(3188, 4280)(3189, 4281)(3190, 4282)(3191, 4283)(3192, 4284)(3193, 4285)(3194, 4286)(3195, 4287)(3196, 4288)(3197, 4289)(3198, 4290)(3199, 4291)(3200, 4292)(3201, 4293)(3202, 4294)(3203, 4295)(3204, 4296)(3205, 4297)(3206, 4298)(3207, 4299)(3208, 4300)(3209, 4301)(3210, 4302)(3211, 4303)(3212, 4304)(3213, 4305)(3214, 4306)(3215, 4307)(3216, 4308)(3217, 4309)(3218, 4310)(3219, 4311)(3220, 4312)(3221, 4313)(3222, 4314)(3223, 4315)(3224, 4316)(3225, 4317)(3226, 4318)(3227, 4319)(3228, 4320)(3229, 4321)(3230, 4322)(3231, 4323)(3232, 4324)(3233, 4325)(3234, 4326)(3235, 4327)(3236, 4328)(3237, 4329)(3238, 4330)(3239, 4331)(3240, 4332)(3241, 4333)(3242, 4334)(3243, 4335)(3244, 4336)(3245, 4337)(3246, 4338)(3247, 4339)(3248, 4340)(3249, 4341)(3250, 4342)(3251, 4343)(3252, 4344)(3253, 4345)(3254, 4346)(3255, 4347)(3256, 4348)(3257, 4349)(3258, 4350)(3259, 4351)(3260, 4352)(3261, 4353)(3262, 4354)(3263, 4355)(3264, 4356)(3265, 4357)(3266, 4358)(3267, 4359)(3268, 4360)(3269, 4361)(3270, 4362)(3271, 4363)(3272, 4364)(3273, 4365)(3274, 4366)(3275, 4367)(3276, 4368) L = (1, 2187)(2, 2190)(3, 2193)(4, 2195)(5, 2185)(6, 2198)(7, 2186)(8, 2188)(9, 2203)(10, 2205)(11, 2206)(12, 2207)(13, 2189)(14, 2211)(15, 2213)(16, 2191)(17, 2192)(18, 2194)(19, 2210)(20, 2222)(21, 2223)(22, 2224)(23, 2226)(24, 2196)(25, 2228)(26, 2197)(27, 2216)(28, 2233)(29, 2234)(30, 2199)(31, 2236)(32, 2200)(33, 2239)(34, 2201)(35, 2202)(36, 2204)(37, 2245)(38, 2246)(39, 2247)(40, 2218)(41, 2251)(42, 2252)(43, 2208)(44, 2256)(45, 2209)(46, 2221)(47, 2212)(48, 2260)(49, 2261)(50, 2262)(51, 2214)(52, 2266)(53, 2215)(54, 2232)(55, 2269)(56, 2217)(57, 2250)(58, 2272)(59, 2219)(60, 2220)(61, 2277)(62, 2278)(63, 2243)(64, 2282)(65, 2225)(66, 2284)(67, 2285)(68, 2255)(69, 2288)(70, 2289)(71, 2227)(72, 2292)(73, 2229)(74, 2230)(75, 2231)(76, 2299)(77, 2300)(78, 2265)(79, 2304)(80, 2305)(81, 2235)(82, 2308)(83, 2237)(84, 2238)(85, 2313)(86, 2240)(87, 2241)(88, 2318)(89, 2242)(90, 2281)(91, 2321)(92, 2244)(93, 2324)(94, 2276)(95, 2328)(96, 2248)(97, 2330)(98, 2331)(99, 2249)(100, 2334)(101, 2335)(102, 2253)(103, 2338)(104, 2339)(105, 2340)(106, 2254)(107, 2287)(108, 2295)(109, 2345)(110, 2346)(111, 2257)(112, 2258)(113, 2350)(114, 2259)(115, 2353)(116, 2298)(117, 2357)(118, 2263)(119, 2359)(120, 2360)(121, 2361)(122, 2264)(123, 2303)(124, 2311)(125, 2366)(126, 2367)(127, 2267)(128, 2268)(129, 2316)(130, 2373)(131, 2374)(132, 2270)(133, 2271)(134, 2379)(135, 2273)(136, 2274)(137, 2384)(138, 2275)(139, 2327)(140, 2296)(141, 2389)(142, 2279)(143, 2391)(144, 2392)(145, 2280)(146, 2395)(147, 2396)(148, 2398)(149, 2283)(150, 2378)(151, 2333)(152, 2404)(153, 2286)(154, 2407)(155, 2408)(156, 2410)(157, 2290)(158, 2291)(159, 2293)(160, 2416)(161, 2417)(162, 2418)(163, 2294)(164, 2344)(165, 2388)(166, 2422)(167, 2297)(168, 2356)(169, 2312)(170, 2427)(171, 2301)(172, 2429)(173, 2430)(174, 2302)(175, 2433)(176, 2434)(177, 2436)(178, 2306)(179, 2307)(180, 2309)(181, 2442)(182, 2443)(183, 2444)(184, 2310)(185, 2365)(186, 2426)(187, 2314)(188, 2449)(189, 2450)(190, 2451)(191, 2315)(192, 2372)(193, 2454)(194, 2317)(195, 2382)(196, 2459)(197, 2460)(198, 2319)(199, 2320)(200, 2465)(201, 2322)(202, 2323)(203, 2325)(204, 2471)(205, 2472)(206, 2326)(207, 2475)(208, 2476)(209, 2478)(210, 2329)(211, 2464)(212, 2394)(213, 2484)(214, 2485)(215, 2332)(216, 2403)(217, 2488)(218, 2336)(219, 2490)(220, 2491)(221, 2492)(222, 2337)(223, 2495)(224, 2406)(225, 2499)(226, 2413)(227, 2502)(228, 2503)(229, 2341)(230, 2342)(231, 2343)(232, 2509)(233, 2510)(234, 2512)(235, 2347)(236, 2348)(237, 2349)(238, 2518)(239, 2351)(240, 2352)(241, 2354)(242, 2524)(243, 2525)(244, 2355)(245, 2528)(246, 2529)(247, 2531)(248, 2358)(249, 2534)(250, 2432)(251, 2538)(252, 2439)(253, 2541)(254, 2542)(255, 2362)(256, 2363)(257, 2364)(258, 2548)(259, 2549)(260, 2551)(261, 2368)(262, 2369)(263, 2370)(264, 2371)(265, 2559)(266, 2560)(267, 2562)(268, 2375)(269, 2376)(270, 2567)(271, 2377)(272, 2401)(273, 2380)(274, 2571)(275, 2572)(276, 2573)(277, 2381)(278, 2458)(279, 2576)(280, 2383)(281, 2468)(282, 2581)(283, 2582)(284, 2385)(285, 2386)(286, 2387)(287, 2589)(288, 2590)(289, 2592)(290, 2390)(291, 2586)(292, 2474)(293, 2598)(294, 2599)(295, 2393)(296, 2483)(297, 2602)(298, 2397)(299, 2604)(300, 2605)(301, 2606)(302, 2399)(303, 2400)(304, 2611)(305, 2402)(306, 2614)(307, 2615)(308, 2617)(309, 2405)(310, 2498)(311, 2414)(312, 2622)(313, 2409)(314, 2624)(315, 2625)(316, 2411)(317, 2627)(318, 2628)(319, 2629)(320, 2412)(321, 2501)(322, 2621)(323, 2633)(324, 2415)(325, 2636)(326, 2508)(327, 2640)(328, 2515)(329, 2643)(330, 2644)(331, 2419)(332, 2420)(333, 2421)(334, 2521)(335, 2652)(336, 2653)(337, 2423)(338, 2424)(339, 2425)(340, 2660)(341, 2661)(342, 2663)(343, 2428)(344, 2657)(345, 2527)(346, 2669)(347, 2670)(348, 2431)(349, 2537)(350, 2440)(351, 2675)(352, 2435)(353, 2677)(354, 2678)(355, 2437)(356, 2680)(357, 2681)(358, 2682)(359, 2438)(360, 2540)(361, 2674)(362, 2686)(363, 2441)(364, 2689)(365, 2547)(366, 2693)(367, 2554)(368, 2696)(369, 2697)(370, 2445)(371, 2446)(372, 2447)(373, 2701)(374, 2448)(375, 2704)(376, 2558)(377, 2708)(378, 2565)(379, 2711)(380, 2712)(381, 2452)(382, 2453)(383, 2715)(384, 2455)(385, 2456)(386, 2457)(387, 2721)(388, 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2753)(571, 2882)(572, 2607)(573, 2884)(574, 2885)(575, 2886)(576, 2608)(577, 2757)(578, 2740)(579, 2890)(580, 2850)(581, 2612)(582, 2728)(583, 2616)(584, 2891)(585, 2772)(586, 2894)(587, 2895)(588, 2618)(589, 2619)(590, 2620)(591, 2897)(592, 2623)(593, 2776)(594, 2901)(595, 2902)(596, 2626)(597, 2780)(598, 2749)(599, 2785)(600, 2907)(601, 2630)(602, 2910)(603, 2634)(604, 2635)(605, 2637)(606, 2804)(607, 2638)(608, 2909)(609, 2917)(610, 2641)(611, 2645)(612, 2648)(613, 2650)(614, 2925)(615, 2926)(616, 2928)(617, 2654)(618, 2655)(619, 2716)(620, 2656)(621, 2705)(622, 2932)(623, 2933)(624, 2665)(625, 2667)(626, 2936)(627, 2814)(628, 2940)(629, 2941)(630, 2671)(631, 2672)(632, 2943)(633, 2676)(634, 2817)(635, 2947)(636, 2948)(637, 2679)(638, 2821)(639, 2771)(640, 2826)(641, 2953)(642, 2683)(643, 2956)(644, 2687)(645, 2688)(646, 2889)(647, 2691)(648, 2955)(649, 2963)(650, 2694)(651, 2698)(652, 2700)(653, 2967)(654, 2702)(655, 2703)(656, 2738)(657, 2706)(658, 2857)(659, 2974)(660, 2709)(661, 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4368) local type(s) :: { ( 4, 14 ), ( 4, 14, 4, 14, 4, 14 ) } Outer automorphisms :: reflexible Dual of E14.651 Graph:: simple bipartite v = 1456 e = 2184 f = 702 degree seq :: [ 2^1092, 6^364 ] ## Checksum: 654 records. ## Written on: Sat Oct 19 06:41:05 CEST 2019