## Begin on: Tue Oct 15 09:30:03 CEST 2019 ENUMERATION No. of records: 550 FAMILY (oriented family) : isomorphism classes 1 [ E1b] : 21 (17 non-degenerate) 2 [ E3b] : 69 (48 non-degenerate) 2* [E3*b] : 69 (48 non-degenerate) 2ex [E3*c] : 1 (1 non-degenerate) 2*ex [ E3c] : 1 (1 non-degenerate) 2P [ E2] : 19 (12 non-degenerate) 2Pex [ E1a] : 3 (3 non-degenerate) 3 [ E5a] : 271 (124 non-degenerate) 4 [ E4] : 38 (18 non-degenerate) 4* [ E4*] : 38 (18 non-degenerate) 4P [ E6] : 10 (4 non-degenerate) 5 [ E3a] : 5 (2 non-degenerate) 5* [E3*a] : 5 (2 non-degenerate) 5P [ E5b] : 0 E7.1 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {7, 7}) Quotient :: toric Aut^+ = C7 (small group id <7, 1>) Aut = D14 (small group id <14, 1>) |r| :: 2 Presentation :: [ A, A, B, B, A, B, A, B, A, B, A, B, B, A, S^2, S^-1 * B * S * A, S^-1 * Z * S * Z, S^-1 * A * S * B, Z^7, (Z^-1 * A * B^-1 * A^-1 * B)^7 ] Map:: R = (1, 9, 16, 23, 2, 11, 18, 25, 4, 13, 20, 27, 6, 14, 21, 28, 7, 12, 19, 26, 5, 10, 17, 24, 3, 8, 15, 22) L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28) local type(s) :: { ( 28^28 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 14 f = 1 degree seq :: [ 28 ] E7.2 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {7, 7}) Quotient :: toric Aut^+ = C7 (small group id <7, 1>) Aut = D14 (small group id <14, 1>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, B^-1 * Z^-1, Z^-1 * A^-1, S * A * S * B, (S * Z)^2, B^7, Z^7, Z^3 * A^-4 ] Map:: R = (1, 9, 16, 23, 2, 11, 18, 25, 4, 13, 20, 27, 6, 14, 21, 28, 7, 12, 19, 26, 5, 10, 17, 24, 3, 8, 15, 22) L = (1, 17)(2, 15)(3, 19)(4, 16)(5, 21)(6, 18)(7, 20)(8, 23)(9, 25)(10, 22)(11, 27)(12, 24)(13, 28)(14, 26) local type(s) :: { ( 28^28 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 14 f = 1 degree seq :: [ 28 ] E7.3 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {7, 7}) Quotient :: toric Aut^+ = C7 (small group id <7, 1>) Aut = D14 (small group id <14, 1>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, Z^2 * A, S * A * S * B, (S * Z)^2, Z * A^-3, (B * Z)^7 ] Map:: R = (1, 9, 16, 23, 2, 12, 19, 26, 5, 13, 20, 27, 6, 14, 21, 28, 7, 10, 17, 24, 3, 11, 18, 25, 4, 8, 15, 22) L = (1, 17)(2, 18)(3, 20)(4, 21)(5, 15)(6, 16)(7, 19)(8, 26)(9, 27)(10, 22)(11, 23)(12, 28)(13, 24)(14, 25) local type(s) :: { ( 28^28 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 14 f = 1 degree seq :: [ 28 ] E7.4 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {4, 4}) Quotient :: toric Aut^+ = C4 x C2 (small group id <8, 2>) Aut = C2 x D8 (small group id <16, 11>) |r| :: 2 Presentation :: [ S^2, A^2, B * A, S * B * S * A, A * Z * A * Z^-1, (S * Z)^2, Z^4 ] Map:: R = (1, 10, 18, 26, 2, 13, 21, 29, 5, 12, 20, 28, 4, 9, 17, 25)(3, 14, 22, 30, 6, 16, 24, 32, 8, 15, 23, 31, 7, 11, 19, 27) L = (1, 19)(2, 22)(3, 17)(4, 23)(5, 24)(6, 18)(7, 20)(8, 21)(9, 27)(10, 30)(11, 25)(12, 31)(13, 32)(14, 26)(15, 28)(16, 29) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 16 f = 2 degree seq :: [ 16^2 ] E7.5 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {4, 4}) Quotient :: toric Aut^+ = C4 x C2 (small group id <8, 2>) Aut = (C4 x C2) : C2 (small group id <16, 13>) |r| :: 2 Presentation :: [ A^2, B^2, S^2, A * Z^-1 * A * Z, B * Z^-1 * A * Z^-1, Z^4, Z^-1 * A * B * Z^-1, A * B * Z^2, S * B * S * A, (S * Z)^2 ] Map:: non-degenerate R = (1, 10, 18, 26, 2, 14, 22, 30, 6, 13, 21, 29, 5, 9, 17, 25)(3, 15, 23, 31, 7, 12, 20, 28, 4, 16, 24, 32, 8, 11, 19, 27) L = (1, 19)(2, 23)(3, 17)(4, 22)(5, 24)(6, 20)(7, 18)(8, 21)(9, 28)(10, 32)(11, 30)(12, 25)(13, 31)(14, 27)(15, 29)(16, 26) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 16 f = 2 degree seq :: [ 16^2 ] E7.6 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {3, 3}) Quotient :: toric Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ S^2, B * A^-1, Z^3, A^-2 * Z * A^-1, (S * Z)^2, S * A * S * B ] Map:: R = (1, 11, 20, 29, 2, 13, 22, 31, 4, 10, 19, 28)(3, 15, 24, 33, 6, 17, 26, 35, 8, 12, 21, 30)(5, 16, 25, 34, 7, 18, 27, 36, 9, 14, 23, 32) L = (1, 21)(2, 24)(3, 25)(4, 26)(5, 19)(6, 27)(7, 20)(8, 23)(9, 22)(10, 32)(11, 34)(12, 28)(13, 36)(14, 35)(15, 29)(16, 30)(17, 31)(18, 33) local type(s) :: { ( 12^12 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 18 f = 3 degree seq :: [ 12^3 ] E7.7 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {3, 3}) Quotient :: toric Aut^+ = C3 x C3 (small group id <9, 2>) Aut = C3 x S3 (small group id <18, 3>) |r| :: 2 Presentation :: [ S^2, B * A, Z^3, A * B^-2, (S * Z)^2, S * A * S * B, Z^-1 * A * Z * B ] Map:: non-degenerate R = (1, 11, 20, 29, 2, 14, 23, 32, 5, 10, 19, 28)(3, 15, 24, 33, 6, 17, 26, 35, 8, 12, 21, 30)(4, 16, 25, 34, 7, 18, 27, 36, 9, 13, 22, 31) L = (1, 21)(2, 24)(3, 22)(4, 19)(5, 26)(6, 25)(7, 20)(8, 27)(9, 23)(10, 30)(11, 33)(12, 31)(13, 28)(14, 35)(15, 34)(16, 29)(17, 36)(18, 32) local type(s) :: { ( 12^12 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 18 f = 3 degree seq :: [ 12^3 ] E7.8 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = A4 (small group id <12, 3>) Aut = C2 x A4 (small group id <24, 13>) |r| :: 2 Presentation :: [ Z^2, S^2, B * A, A^2 * B^-1, (S * Z)^2, S * B * S * A, Z * A * Z * A * Z * B^-1 ] Map:: non-degenerate R = (1, 14, 26, 38, 2, 13, 25, 37)(3, 19, 31, 43, 7, 15, 27, 39)(4, 20, 32, 44, 8, 16, 28, 40)(5, 21, 33, 45, 9, 17, 29, 41)(6, 22, 34, 46, 10, 18, 30, 42)(11, 24, 36, 48, 12, 23, 35, 47) L = (1, 27)(2, 29)(3, 28)(4, 25)(5, 30)(6, 26)(7, 34)(8, 36)(9, 32)(10, 35)(11, 31)(12, 33)(13, 39)(14, 41)(15, 40)(16, 37)(17, 42)(18, 38)(19, 46)(20, 48)(21, 44)(22, 47)(23, 43)(24, 45) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 6 e = 24 f = 6 degree seq :: [ 8^6 ] E7.9 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D12 (small group id <12, 4>) Aut = C2 x C2 x S3 (small group id <24, 14>) |r| :: 2 Presentation :: [ Z^2, A^2, S^2, B * A, (S * Z)^2, S * A * S * B, (A * Z)^6 ] Map:: R = (1, 14, 26, 38, 2, 13, 25, 37)(3, 17, 29, 41, 5, 15, 27, 39)(4, 18, 30, 42, 6, 16, 28, 40)(7, 21, 33, 45, 9, 19, 31, 43)(8, 22, 34, 46, 10, 20, 32, 44)(11, 24, 36, 48, 12, 23, 35, 47) L = (1, 27)(2, 28)(3, 25)(4, 26)(5, 31)(6, 32)(7, 29)(8, 30)(9, 35)(10, 36)(11, 33)(12, 34)(13, 39)(14, 40)(15, 37)(16, 38)(17, 43)(18, 44)(19, 41)(20, 42)(21, 47)(22, 48)(23, 45)(24, 46) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 6 e = 24 f = 6 degree seq :: [ 8^6 ] E7.10 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D12 (small group id <12, 4>) Aut = C2 x C2 x S3 (small group id <24, 14>) |r| :: 2 Presentation :: [ Z^2, S^2, A^-1 * B^-1, S * B * S * A, (S * Z)^2, B * Z * A^-1 * Z, B^3 * A^-3 ] Map:: non-degenerate R = (1, 14, 26, 38, 2, 13, 25, 37)(3, 18, 30, 42, 6, 15, 27, 39)(4, 17, 29, 41, 5, 16, 28, 40)(7, 22, 34, 46, 10, 19, 31, 43)(8, 21, 33, 45, 9, 20, 32, 44)(11, 24, 36, 48, 12, 23, 35, 47) L = (1, 27)(2, 29)(3, 31)(4, 25)(5, 33)(6, 26)(7, 35)(8, 28)(9, 36)(10, 30)(11, 32)(12, 34)(13, 39)(14, 41)(15, 43)(16, 37)(17, 45)(18, 38)(19, 47)(20, 40)(21, 48)(22, 42)(23, 44)(24, 46) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 6 e = 24 f = 6 degree seq :: [ 8^6 ] E7.11 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 9, 9}) Quotient :: dipole Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, Y1^3, Y3^-1 * Y2 * Y1 * Y2, Y1^-1 * Y3 * Y2^-2, (R * Y1)^2, R * Y2 * R * Y3^-1, (Y3^-1, Y1^-1), Y1^-1 * Y2^6, Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 ] Map:: non-degenerate R = (1, 10, 2, 11, 5, 14)(3, 12, 6, 15, 9, 18)(4, 13, 7, 16, 8, 17)(19, 28, 21, 30, 26, 35, 23, 32, 27, 36, 25, 34, 20, 29, 24, 33, 22, 31) L = (1, 22)(2, 25)(3, 19)(4, 24)(5, 26)(6, 20)(7, 27)(8, 21)(9, 23)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 18^6 ), ( 18^18 ) } Outer automorphisms :: reflexible Dual of E7.14 Graph:: bipartite v = 4 e = 18 f = 2 degree seq :: [ 6^3, 18 ] E7.12 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 9, 9}) Quotient :: dipole Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y2, Y2 * Y3^-1 * Y2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1 * Y3^3 ] Map:: non-degenerate R = (1, 10, 2, 11, 5, 14)(3, 12, 8, 17, 7, 16)(4, 13, 9, 18, 6, 15)(19, 28, 21, 30, 22, 31, 20, 29, 26, 35, 27, 36, 23, 32, 25, 34, 24, 33) L = (1, 22)(2, 27)(3, 20)(4, 26)(5, 24)(6, 21)(7, 19)(8, 23)(9, 25)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 18^6 ), ( 18^18 ) } Outer automorphisms :: reflexible Dual of E7.13 Graph:: bipartite v = 4 e = 18 f = 2 degree seq :: [ 6^3, 18 ] E7.13 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 9, 9}) Quotient :: dipole Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, Y1 * Y2^2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y2 * Y1^-4, (Y3^-1 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 10, 2, 11, 6, 15, 8, 17, 3, 12, 4, 13, 7, 16, 9, 18, 5, 14)(19, 28, 21, 30, 23, 32, 26, 35, 27, 36, 24, 33, 25, 34, 20, 29, 22, 31) L = (1, 22)(2, 25)(3, 19)(4, 20)(5, 21)(6, 27)(7, 24)(8, 23)(9, 26)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E7.12 Graph:: bipartite v = 2 e = 18 f = 4 degree seq :: [ 18^2 ] E7.14 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 9, 9}) Quotient :: dipole Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y1^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), Y2^-1 * Y3 * Y2^-2 * Y1, Y1 * Y3^4 ] Map:: non-degenerate R = (1, 10, 2, 11, 4, 13, 6, 15, 9, 18, 7, 16, 8, 17, 3, 12, 5, 14)(19, 28, 21, 30, 25, 34, 24, 33, 20, 29, 23, 32, 26, 35, 27, 36, 22, 31) L = (1, 22)(2, 24)(3, 19)(4, 27)(5, 20)(6, 25)(7, 21)(8, 23)(9, 26)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E7.11 Graph:: bipartite v = 2 e = 18 f = 4 degree seq :: [ 18^2 ] E7.15 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 10, 10}) Quotient :: dipole Aut^+ = C10 (small group id <10, 2>) Aut = D20 (small group id <20, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y1 * Y3 * Y2, Y1 * Y2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^2 * Y3^-3 ] Map:: non-degenerate R = (1, 11, 2, 12)(3, 13, 6, 16)(4, 14, 5, 15)(7, 17, 8, 18)(9, 19, 10, 20)(21, 31, 23, 33, 27, 37, 30, 40, 24, 34, 22, 32, 26, 36, 28, 38, 29, 39, 25, 35) L = (1, 24)(2, 25)(3, 22)(4, 29)(5, 30)(6, 21)(7, 26)(8, 23)(9, 27)(10, 28)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40) local type(s) :: { ( 20^4 ), ( 20^20 ) } Outer automorphisms :: reflexible Dual of E7.16 Graph:: bipartite v = 6 e = 20 f = 2 degree seq :: [ 4^5, 20 ] E7.16 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 10, 10}) Quotient :: dipole Aut^+ = C10 (small group id <10, 2>) Aut = D20 (small group id <20, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-1 * Y3^-1, Y1 * Y3^-1 * Y2^-1, Y2 * Y3^-1 * Y2, Y1^-3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y3^2 * Y1 ] Map:: non-degenerate R = (1, 11, 2, 12, 8, 18, 6, 16, 4, 14, 10, 20, 7, 17, 3, 13, 9, 19, 5, 15)(21, 31, 23, 33, 24, 34, 22, 32, 29, 39, 30, 40, 28, 38, 25, 35, 27, 37, 26, 36) L = (1, 24)(2, 30)(3, 22)(4, 29)(5, 26)(6, 23)(7, 21)(8, 27)(9, 28)(10, 25)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40) local type(s) :: { ( 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 E7.15 Graph:: bipartite v = 2 e = 20 f = 6 degree seq :: [ 20^2 ] E7.17 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 4, 4}) Quotient :: edge^2 Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y3^4, Y1^2 * Y3^2, (R * Y3)^2, Y3^-1 * Y1^2 * Y3^-1, R * Y1 * R * Y2, Y2^4, Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 13, 3, 15, 6, 18, 5, 17)(2, 14, 7, 19, 4, 16, 8, 20)(9, 21, 11, 23, 10, 22, 12, 24)(25, 26, 30, 28)(27, 33, 29, 34)(31, 35, 32, 36)(37, 38, 42, 40)(39, 45, 41, 46)(43, 47, 44, 48) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 16^4 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E7.19 Graph:: bipartite v = 9 e = 24 f = 3 degree seq :: [ 4^6, 8^3 ] E7.18 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 4, 4}) Quotient :: edge^2 Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y3^4, Y3^-2 * Y1^2, (R * Y3)^2, Y3^-1 * Y1^-2 * Y3^-1, R * Y1 * R * Y2, Y2^4, Y3^-1 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 13, 3, 15, 6, 18, 5, 17)(2, 14, 7, 19, 4, 16, 8, 20)(9, 21, 12, 24, 10, 22, 11, 23)(25, 26, 30, 28)(27, 33, 29, 34)(31, 35, 32, 36)(37, 38, 42, 40)(39, 45, 41, 46)(43, 47, 44, 48) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 16^4 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E7.20 Graph:: bipartite v = 9 e = 24 f = 3 degree seq :: [ 4^6, 8^3 ] E7.19 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 4, 4}) Quotient :: loop^2 Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y3^4, Y1^2 * Y3^2, (R * Y3)^2, Y3^-1 * Y1^2 * Y3^-1, R * Y1 * R * Y2, Y2^4, Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 13, 25, 37, 3, 15, 27, 39, 6, 18, 30, 42, 5, 17, 29, 41)(2, 14, 26, 38, 7, 19, 31, 43, 4, 16, 28, 40, 8, 20, 32, 44)(9, 21, 33, 45, 11, 23, 35, 47, 10, 22, 34, 46, 12, 24, 36, 48) L = (1, 14)(2, 18)(3, 21)(4, 13)(5, 22)(6, 16)(7, 23)(8, 24)(9, 17)(10, 15)(11, 20)(12, 19)(25, 38)(26, 42)(27, 45)(28, 37)(29, 46)(30, 40)(31, 47)(32, 48)(33, 41)(34, 39)(35, 44)(36, 43) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.17 Transitivity :: VT+ Graph:: v = 3 e = 24 f = 9 degree seq :: [ 16^3 ] E7.20 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 4, 4}) Quotient :: loop^2 Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y3^4, Y3^-2 * Y1^2, (R * Y3)^2, Y3^-1 * Y1^-2 * Y3^-1, R * Y1 * R * Y2, Y2^4, Y3^-1 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 13, 25, 37, 3, 15, 27, 39, 6, 18, 30, 42, 5, 17, 29, 41)(2, 14, 26, 38, 7, 19, 31, 43, 4, 16, 28, 40, 8, 20, 32, 44)(9, 21, 33, 45, 12, 24, 36, 48, 10, 22, 34, 46, 11, 23, 35, 47) L = (1, 14)(2, 18)(3, 21)(4, 13)(5, 22)(6, 16)(7, 23)(8, 24)(9, 17)(10, 15)(11, 20)(12, 19)(25, 38)(26, 42)(27, 45)(28, 37)(29, 46)(30, 40)(31, 47)(32, 48)(33, 41)(34, 39)(35, 44)(36, 43) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.18 Transitivity :: VT+ Graph:: v = 3 e = 24 f = 9 degree seq :: [ 16^3 ] E7.21 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 4, 4, 6}) Quotient :: edge^2 Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y3 * Y1 * Y3 * Y1^-1, Y2^4, Y3^-1 * Y1^2 * Y3^-2, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 13, 3, 15, 9, 21, 6, 18, 12, 24, 5, 17)(2, 14, 7, 19, 10, 22, 4, 16, 11, 23, 8, 20)(25, 26, 30, 28)(27, 32, 36, 34)(29, 31, 33, 35)(37, 38, 42, 40)(39, 44, 48, 46)(41, 43, 45, 47) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 12^4 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E7.24 Graph:: bipartite v = 8 e = 24 f = 4 degree seq :: [ 4^6, 12^2 ] E7.22 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 4, 4, 6}) Quotient :: edge^2 Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y3^3, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1 * Y3 * Y1^-1, Y1^4, Y2^4, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 13, 3, 15, 5, 17)(2, 14, 7, 19, 8, 20)(4, 16, 10, 22, 9, 21)(6, 18, 11, 23, 12, 24)(25, 26, 30, 28)(27, 32, 35, 33)(29, 31, 36, 34)(37, 38, 42, 40)(39, 44, 47, 45)(41, 43, 48, 46) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 24^4 ), ( 24^6 ) } Outer automorphisms :: reflexible Dual of E7.23 Graph:: simple bipartite v = 10 e = 24 f = 2 degree seq :: [ 4^6, 6^4 ] E7.23 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 4, 4, 6}) Quotient :: loop^2 Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y3 * Y1 * Y3 * Y1^-1, Y2^4, Y3^-1 * Y1^2 * Y3^-2, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 13, 25, 37, 3, 15, 27, 39, 9, 21, 33, 45, 6, 18, 30, 42, 12, 24, 36, 48, 5, 17, 29, 41)(2, 14, 26, 38, 7, 19, 31, 43, 10, 22, 34, 46, 4, 16, 28, 40, 11, 23, 35, 47, 8, 20, 32, 44) L = (1, 14)(2, 18)(3, 20)(4, 13)(5, 19)(6, 16)(7, 21)(8, 24)(9, 23)(10, 15)(11, 17)(12, 22)(25, 38)(26, 42)(27, 44)(28, 37)(29, 43)(30, 40)(31, 45)(32, 48)(33, 47)(34, 39)(35, 41)(36, 46) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.22 Transitivity :: VT+ Graph:: bipartite v = 2 e = 24 f = 10 degree seq :: [ 24^2 ] E7.24 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 4, 4, 6}) Quotient :: loop^2 Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y3^3, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1 * Y3 * Y1^-1, Y1^4, Y2^4, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 13, 25, 37, 3, 15, 27, 39, 5, 17, 29, 41)(2, 14, 26, 38, 7, 19, 31, 43, 8, 20, 32, 44)(4, 16, 28, 40, 10, 22, 34, 46, 9, 21, 33, 45)(6, 18, 30, 42, 11, 23, 35, 47, 12, 24, 36, 48) L = (1, 14)(2, 18)(3, 20)(4, 13)(5, 19)(6, 16)(7, 24)(8, 23)(9, 15)(10, 17)(11, 21)(12, 22)(25, 38)(26, 42)(27, 44)(28, 37)(29, 43)(30, 40)(31, 48)(32, 47)(33, 39)(34, 41)(35, 45)(36, 46) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.21 Transitivity :: VT+ Graph:: bipartite v = 4 e = 24 f = 8 degree seq :: [ 12^4 ] E7.25 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 6}) Quotient :: dipole Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y3, Y1^3, Y3 * Y1 * Y3 * Y1^-1, Y1 * Y2 * Y1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2 ] Map:: non-degenerate R = (1, 13, 2, 14, 5, 17)(3, 15, 10, 22, 7, 19)(4, 16, 8, 20, 11, 23)(6, 18, 12, 24, 9, 21)(25, 37, 27, 39, 28, 40, 30, 42)(26, 38, 31, 43, 32, 44, 33, 45)(29, 41, 34, 46, 35, 47, 36, 48) L = (1, 28)(2, 32)(3, 30)(4, 25)(5, 35)(6, 27)(7, 33)(8, 26)(9, 31)(10, 36)(11, 29)(12, 34)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E7.27 Graph:: bipartite v = 7 e = 24 f = 5 degree seq :: [ 6^4, 8^3 ] E7.26 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 6}) Quotient :: dipole Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^2 * Y1, Y2 * Y3^-1 * Y1 * Y2, Y2^-2 * Y3 * Y1^-1, Y2^-1 * Y1 * Y3^-1 * Y2^-1, (R * Y3)^2, (Y3 * Y1^-1)^2, Y1 * Y2 * Y1 * Y2^-1, Y2^4, (R * Y1)^2, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 13, 2, 14, 5, 17)(3, 15, 11, 23, 8, 20)(4, 16, 7, 19, 10, 22)(6, 18, 12, 24, 9, 21)(25, 37, 27, 39, 34, 46, 30, 42)(26, 38, 32, 44, 28, 40, 33, 45)(29, 41, 35, 47, 31, 43, 36, 48) L = (1, 28)(2, 31)(3, 36)(4, 29)(5, 34)(6, 35)(7, 25)(8, 30)(9, 27)(10, 26)(11, 33)(12, 32)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E7.28 Graph:: bipartite v = 7 e = 24 f = 5 degree seq :: [ 6^4, 8^3 ] E7.27 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 6}) Quotient :: dipole Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^2 * Y3, Y3 * Y2^-3, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, Y1 * Y2^-1 * Y1^-1 * Y2^-1, (R * Y2)^2 ] Map:: non-degenerate R = (1, 13, 2, 14, 4, 16, 5, 17)(3, 15, 8, 20, 10, 22, 11, 23)(6, 18, 7, 19, 9, 21, 12, 24)(25, 37, 27, 39, 33, 45, 28, 40, 34, 46, 30, 42)(26, 38, 31, 43, 35, 47, 29, 41, 36, 48, 32, 44) L = (1, 28)(2, 29)(3, 34)(4, 25)(5, 26)(6, 33)(7, 36)(8, 35)(9, 30)(10, 27)(11, 32)(12, 31)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 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 E7.25 Graph:: bipartite v = 5 e = 24 f = 7 degree seq :: [ 8^3, 12^2 ] E7.28 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 6}) Quotient :: dipole Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, (R * Y1)^2, Y1^4, (R * Y3)^2, Y1^-1 * Y3 * Y1 * Y2^-1, Y2 * Y1 * Y3^-1 * Y1^-1, Y1^-2 * Y2 * Y3^-2, Y3 * Y1 * Y2 * Y1 * Y2^-1, (Y2^-2 * Y3)^2, (Y3 * Y2^-1)^3, Y2^6 ] Map:: non-degenerate R = (1, 13, 2, 14, 6, 18, 5, 17)(3, 15, 8, 20, 11, 23, 10, 22)(4, 16, 7, 19, 9, 21, 12, 24)(25, 37, 27, 39, 33, 45, 30, 42, 35, 47, 28, 40)(26, 38, 31, 43, 34, 46, 29, 41, 36, 48, 32, 44) L = (1, 28)(2, 32)(3, 25)(4, 35)(5, 34)(6, 33)(7, 26)(8, 36)(9, 27)(10, 31)(11, 30)(12, 29)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 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 E7.26 Graph:: bipartite v = 5 e = 24 f = 7 degree seq :: [ 8^3, 12^2 ] E7.29 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 6}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y3, Y1^3, Y3 * Y1 * Y3 * Y1^-1, (Y1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2 ] Map:: non-degenerate R = (1, 13, 2, 14, 5, 17)(3, 15, 7, 19, 10, 22)(4, 16, 8, 20, 11, 23)(6, 18, 9, 21, 12, 24)(25, 37, 27, 39, 28, 40, 30, 42)(26, 38, 31, 43, 32, 44, 33, 45)(29, 41, 34, 46, 35, 47, 36, 48) L = (1, 28)(2, 32)(3, 30)(4, 25)(5, 35)(6, 27)(7, 33)(8, 26)(9, 31)(10, 36)(11, 29)(12, 34)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E7.30 Graph:: bipartite v = 7 e = 24 f = 5 degree seq :: [ 6^4, 8^3 ] E7.30 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 6}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^2 * Y3, Y3 * Y2^-3, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (Y1^-1, Y2^-1), (R * Y2)^2 ] Map:: non-degenerate R = (1, 13, 2, 14, 4, 16, 5, 17)(3, 15, 7, 19, 10, 22, 11, 23)(6, 18, 8, 20, 9, 21, 12, 24)(25, 37, 27, 39, 33, 45, 28, 40, 34, 46, 30, 42)(26, 38, 31, 43, 36, 48, 29, 41, 35, 47, 32, 44) L = (1, 28)(2, 29)(3, 34)(4, 25)(5, 26)(6, 33)(7, 35)(8, 36)(9, 30)(10, 27)(11, 31)(12, 32)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 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 E7.29 Graph:: bipartite v = 5 e = 24 f = 7 degree seq :: [ 8^3, 12^2 ] E7.31 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6, 6}) Quotient :: dipole Aut^+ = C6 x C2 (small group id <12, 5>) Aut = C2 x C2 x S3 (small group id <24, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, Y3^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1, Y3 * Y1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 13, 2, 14)(3, 15, 7, 19)(4, 16, 8, 20)(5, 17, 9, 21)(6, 18, 10, 22)(11, 23, 12, 24)(25, 37, 27, 39, 28, 40, 35, 47, 30, 42, 29, 41)(26, 38, 31, 43, 32, 44, 36, 48, 34, 46, 33, 45) L = (1, 28)(2, 32)(3, 35)(4, 30)(5, 27)(6, 25)(7, 36)(8, 34)(9, 31)(10, 26)(11, 29)(12, 33)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 12^4 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E7.32 Graph:: bipartite v = 8 e = 24 f = 4 degree seq :: [ 4^6, 12^2 ] E7.32 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6, 6}) Quotient :: dipole Aut^+ = C6 x C2 (small group id <12, 5>) Aut = C2 x C2 x S3 (small group id <24, 14>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^2 * Y3^-1, Y2 * Y3^-1 * Y2, (Y1^-1 * Y2)^2, (R * Y1)^2, (R * Y2)^2, (Y1^-1, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 13, 2, 14, 4, 16, 9, 21, 7, 19, 5, 17)(3, 15, 8, 20, 11, 23, 12, 24, 6, 18, 10, 22)(25, 37, 27, 39, 28, 40, 35, 47, 31, 43, 30, 42)(26, 38, 32, 44, 33, 45, 36, 48, 29, 41, 34, 46) L = (1, 28)(2, 33)(3, 35)(4, 31)(5, 26)(6, 27)(7, 25)(8, 36)(9, 29)(10, 32)(11, 30)(12, 34)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.31 Graph:: bipartite v = 4 e = 24 f = 8 degree seq :: [ 12^4 ] E7.33 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y1^3, (R * Y3)^2, (Y2^-1 * R)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (Y2^-1, Y1^-1), Y2^4, (Y3^-1 * Y1^-1)^3, Y3^12 ] Map:: non-degenerate R = (1, 13, 2, 14, 4, 16)(3, 15, 6, 18, 9, 21)(5, 17, 7, 19, 10, 22)(8, 20, 11, 23, 12, 24)(25, 37, 27, 39, 32, 44, 29, 41)(26, 38, 30, 42, 35, 47, 31, 43)(28, 40, 33, 45, 36, 48, 34, 46) L = (1, 26)(2, 28)(3, 30)(4, 25)(5, 31)(6, 33)(7, 34)(8, 35)(9, 27)(10, 29)(11, 36)(12, 32)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 6, 24, 6, 24, 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E7.34 Graph:: bipartite v = 7 e = 24 f = 5 degree seq :: [ 6^4, 8^3 ] E7.34 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y2^3, (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y1^4 * Y2^-1, (Y3 * Y2^-1)^3, (Y1^-1 * Y3^-1)^4 ] Map:: non-degenerate R = (1, 13, 2, 14, 6, 18, 9, 21, 3, 15, 7, 19, 12, 24, 10, 22, 4, 16, 8, 20, 11, 23, 5, 17)(25, 37, 27, 39, 28, 40)(26, 38, 31, 43, 32, 44)(29, 41, 33, 45, 34, 46)(30, 42, 36, 48, 35, 47) L = (1, 28)(2, 32)(3, 25)(4, 27)(5, 34)(6, 35)(7, 26)(8, 31)(9, 29)(10, 33)(11, 36)(12, 30)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 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 E7.33 Graph:: bipartite v = 5 e = 24 f = 7 degree seq :: [ 6^4, 24 ] E7.35 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y2 * Y3^-3, Y1 * Y3 * Y1 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2^-1 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 13, 2, 14)(3, 15, 5, 17)(4, 16, 7, 19)(6, 18, 8, 20)(9, 21, 11, 23)(10, 22, 12, 24)(25, 37, 27, 39, 26, 38, 29, 41)(28, 40, 33, 45, 31, 43, 35, 47)(30, 42, 34, 46, 32, 44, 36, 48) L = (1, 28)(2, 31)(3, 33)(4, 34)(5, 35)(6, 25)(7, 36)(8, 26)(9, 32)(10, 27)(11, 30)(12, 29)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E7.38 Graph:: bipartite v = 9 e = 24 f = 3 degree seq :: [ 4^6, 8^3 ] E7.36 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (Y2^-1 * R)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, Y1^4, (Y1, Y2^-1), (Y3^-1 * Y1^-1)^2, Y1^2 * Y2^3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 13, 2, 14, 6, 18, 4, 16)(3, 15, 7, 19, 12, 24, 10, 22)(5, 17, 8, 20, 9, 21, 11, 23)(25, 37, 27, 39, 33, 45, 30, 42, 36, 48, 29, 41)(26, 38, 31, 43, 35, 47, 28, 40, 34, 46, 32, 44) L = (1, 26)(2, 30)(3, 31)(4, 25)(5, 32)(6, 28)(7, 36)(8, 33)(9, 35)(10, 27)(11, 29)(12, 34)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 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 E7.37 Graph:: bipartite v = 5 e = 24 f = 7 degree seq :: [ 8^3, 12^2 ] E7.37 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3 * Y2 * Y3, (Y1, Y3^-1), Y1^-1 * Y3^-1 * Y1^-2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (Y3^-1, Y1^-1) ] Map:: non-degenerate R = (1, 13, 2, 14, 7, 19, 6, 18, 10, 22, 11, 23, 3, 15, 8, 20, 12, 24, 4, 16, 9, 21, 5, 17)(25, 37, 27, 39)(26, 38, 32, 44)(28, 40, 30, 42)(29, 41, 35, 47)(31, 43, 36, 48)(33, 45, 34, 46) L = (1, 28)(2, 33)(3, 30)(4, 27)(5, 36)(6, 25)(7, 29)(8, 34)(9, 32)(10, 26)(11, 31)(12, 35)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 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 E7.36 Graph:: bipartite v = 7 e = 24 f = 5 degree seq :: [ 4^6, 24 ] E7.38 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2, Y1 * Y3^-2, (Y3^-1, Y2^-1), (R * Y1)^2, Y1^2 * Y3 * Y2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y2^-1 * Y3^-1)^3, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 13, 2, 14, 8, 20, 12, 24, 11, 23, 5, 17)(3, 15, 9, 21, 7, 19, 4, 16, 10, 22, 6, 18)(25, 37, 27, 39, 26, 38, 33, 45, 32, 44, 31, 43, 36, 48, 28, 40, 35, 47, 34, 46, 29, 41, 30, 42) L = (1, 28)(2, 34)(3, 35)(4, 26)(5, 31)(6, 36)(7, 25)(8, 30)(9, 29)(10, 32)(11, 33)(12, 27)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E7.35 Graph:: bipartite v = 3 e = 24 f = 9 degree seq :: [ 12^2, 24 ] E7.39 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^2 * Y2, Y2^3 * Y1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 13, 2, 14)(3, 15, 7, 19)(4, 16, 8, 20)(5, 17, 9, 21)(6, 18, 10, 22)(11, 23, 12, 24)(25, 37, 27, 39, 33, 45, 26, 38, 31, 43, 29, 41)(28, 40, 30, 42, 35, 47, 32, 44, 34, 46, 36, 48) L = (1, 28)(2, 32)(3, 30)(4, 29)(5, 36)(6, 25)(7, 34)(8, 33)(9, 35)(10, 26)(11, 27)(12, 31)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E7.40 Graph:: bipartite v = 8 e = 24 f = 4 degree seq :: [ 4^6, 12^2 ] E7.40 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y2^3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y2^-1 * R)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 13, 2, 14, 6, 18, 4, 16)(3, 15, 7, 19, 11, 23, 9, 21)(5, 17, 8, 20, 12, 24, 10, 22)(25, 37, 27, 39, 32, 44, 26, 38, 31, 43, 36, 48, 30, 42, 35, 47, 34, 46, 28, 40, 33, 45, 29, 41) L = (1, 26)(2, 30)(3, 31)(4, 25)(5, 32)(6, 28)(7, 35)(8, 36)(9, 27)(10, 29)(11, 33)(12, 34)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12 ), ( 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 E7.39 Graph:: bipartite v = 4 e = 24 f = 8 degree seq :: [ 8^3, 24 ] E7.41 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^2 * Y3^-1, Y1 * Y3^-2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (Y3^-1 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 13, 2, 14, 5, 17)(3, 15, 8, 20, 11, 23)(4, 16, 9, 21, 7, 19)(6, 18, 10, 22, 12, 24)(25, 37, 27, 39, 28, 40, 34, 46, 26, 38, 32, 44, 33, 45, 36, 48, 29, 41, 35, 47, 31, 43, 30, 42) L = (1, 28)(2, 33)(3, 34)(4, 26)(5, 31)(6, 27)(7, 25)(8, 36)(9, 29)(10, 32)(11, 30)(12, 35)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 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 E7.42 Graph:: bipartite v = 5 e = 24 f = 7 degree seq :: [ 6^4, 24 ] E7.42 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y1^2 * Y3, Y3^3 * Y2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y1^-1 * Y2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 13, 2, 14, 6, 18, 8, 20, 9, 21, 10, 22, 3, 15, 7, 19, 11, 23, 12, 24, 4, 16, 5, 17)(25, 37, 27, 39)(26, 38, 31, 43)(28, 40, 33, 45)(29, 41, 34, 46)(30, 42, 35, 47)(32, 44, 36, 48) L = (1, 28)(2, 29)(3, 33)(4, 35)(5, 36)(6, 25)(7, 34)(8, 26)(9, 30)(10, 32)(11, 27)(12, 31)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 6, 24, 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E7.41 Graph:: bipartite v = 7 e = 24 f = 5 degree seq :: [ 4^6, 24 ] E7.43 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^7 * Y1, (Y3 * Y2^-1)^14 ] Map:: R = (1, 15, 2, 16)(3, 17, 5, 19)(4, 18, 6, 20)(7, 21, 9, 23)(8, 22, 10, 24)(11, 25, 13, 27)(12, 26, 14, 28)(29, 43, 31, 45, 35, 49, 39, 53, 42, 56, 38, 52, 34, 48, 30, 44, 33, 47, 37, 51, 41, 55, 40, 54, 36, 50, 32, 46) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 8 e = 28 f = 8 degree seq :: [ 4^7, 28 ] E7.44 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {15, 15, 15}) Quotient :: edge Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ F^2, T2 * T1^2, (F * T1)^2, (F * T2)^2, T1 * T2^-7 ] Map:: non-degenerate R = (1, 3, 7, 11, 14, 10, 6, 2, 4, 8, 12, 15, 13, 9, 5)(16, 17, 20, 21, 24, 25, 28, 29, 30, 26, 27, 22, 23, 18, 19) L = (1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30) local type(s) :: { ( 30^15 ) } Outer automorphisms :: reflexible Dual of E7.45 Transitivity :: ET+ Graph:: bipartite v = 2 e = 15 f = 1 degree seq :: [ 15^2 ] E7.45 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {15, 15, 15}) Quotient :: loop Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1, (F * T2)^2, (F * T1)^2, T1^15, T2^15, (T2^-1 * T1^-1)^15 ] Map:: non-degenerate R = (1, 16, 2, 17, 4, 19, 6, 21, 8, 23, 10, 25, 12, 27, 14, 29, 15, 30, 13, 28, 11, 26, 9, 24, 7, 22, 5, 20, 3, 18) L = (1, 17)(2, 19)(3, 16)(4, 21)(5, 18)(6, 23)(7, 20)(8, 25)(9, 22)(10, 27)(11, 24)(12, 29)(13, 26)(14, 30)(15, 28) local type(s) :: { ( 15^30 ) } Outer automorphisms :: reflexible Dual of E7.44 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 15 f = 2 degree seq :: [ 30 ] E7.46 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y2^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^7 * Y2, Y2 * Y1^-7 ] 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, 34)(2, 31)(3, 38)(4, 39)(5, 33)(6, 32)(7, 35)(8, 42)(9, 43)(10, 36)(11, 37)(12, 44)(13, 45)(14, 40)(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) :: { ( 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 E7.47 Graph:: bipartite v = 2 e = 30 f = 16 degree seq :: [ 30^2 ] E7.47 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ Y1, R^2, Y2 * Y3, (R * Y3)^2, (R * Y1)^2, Y2^15, (Y3 * Y2^-1)^15, (Y3^-1 * Y1^-1)^15 ] Map:: R = (1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46, 32, 47, 34, 49, 36, 51, 38, 53, 40, 55, 42, 57, 44, 59, 45, 60, 43, 58, 41, 56, 39, 54, 37, 52, 35, 50, 33, 48) L = (1, 33)(2, 31)(3, 35)(4, 32)(5, 37)(6, 34)(7, 39)(8, 36)(9, 41)(10, 38)(11, 43)(12, 40)(13, 45)(14, 42)(15, 44)(16, 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 ), ( 30^30 ) } Outer automorphisms :: reflexible Dual of E7.46 Graph:: bipartite v = 16 e = 30 f = 2 degree seq :: [ 2^15, 30 ] E7.48 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 4}) Quotient :: dipole Aut^+ = C4 x C4 (small group id <16, 2>) Aut = (C4 x C4) : C2 (small group id <32, 34>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y1 * Y3^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1 * Y2, (Y2, Y3), Y2^4, (R * Y2)^2 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 7, 23)(4, 20, 6, 22)(5, 21, 8, 24)(9, 25, 14, 30)(10, 26, 11, 27)(12, 28, 13, 29)(15, 31, 16, 32)(33, 49, 35, 51, 41, 57, 37, 53)(34, 50, 39, 55, 46, 62, 40, 56)(36, 52, 42, 58, 47, 63, 44, 60)(38, 54, 43, 59, 48, 64, 45, 61) L = (1, 36)(2, 38)(3, 42)(4, 34)(5, 44)(6, 33)(7, 43)(8, 45)(9, 47)(10, 39)(11, 35)(12, 40)(13, 37)(14, 48)(15, 46)(16, 41)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.49 Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.49 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 4}) Quotient :: dipole Aut^+ = C4 x C4 (small group id <16, 2>) Aut = (C4 x C4) : C2 (small group id <32, 34>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y3^4, (R * Y1)^2, (Y2^-1 * R)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y1, Y2^-1), Y1^4, Y2^4 ] Map:: non-degenerate R = (1, 17, 2, 18, 6, 22, 4, 20)(3, 19, 7, 23, 12, 28, 10, 26)(5, 21, 8, 24, 13, 29, 11, 27)(9, 25, 14, 30, 16, 32, 15, 31)(33, 49, 35, 51, 41, 57, 37, 53)(34, 50, 39, 55, 46, 62, 40, 56)(36, 52, 42, 58, 47, 63, 43, 59)(38, 54, 44, 60, 48, 64, 45, 61) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 36)(7, 44)(8, 45)(9, 46)(10, 35)(11, 37)(12, 42)(13, 43)(14, 48)(15, 41)(16, 47)(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) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.48 Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.50 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 4}) Quotient :: dipole Aut^+ = C4 : C4 (small group id <16, 4>) Aut = (C4 x C2 x C2) : C2 (small group id <32, 28>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y1 * Y3^-2, Y3 * Y2^-1 * Y3 * Y2, (R * Y3)^2, Y1 * Y2 * Y1 * Y2^-1, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 7, 23)(4, 20, 6, 22)(5, 21, 8, 24)(9, 25, 14, 30)(10, 26, 11, 27)(12, 28, 13, 29)(15, 31, 16, 32)(33, 49, 35, 51, 41, 57, 37, 53)(34, 50, 39, 55, 46, 62, 40, 56)(36, 52, 43, 59, 47, 63, 44, 60)(38, 54, 42, 58, 48, 64, 45, 61) L = (1, 36)(2, 38)(3, 42)(4, 34)(5, 45)(6, 33)(7, 43)(8, 44)(9, 47)(10, 39)(11, 35)(12, 37)(13, 40)(14, 48)(15, 46)(16, 41)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.55 Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.51 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 4}) Quotient :: dipole Aut^+ = C4 : C4 (small group id <16, 4>) Aut = (C4 x C2 x C2) : C2 (small group id <32, 28>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y1)^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, Y3^4, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 5, 21)(4, 20, 7, 23)(6, 22, 8, 24)(9, 25, 13, 29)(10, 26, 12, 28)(11, 27, 14, 30)(15, 31, 16, 32)(33, 49, 35, 51, 34, 50, 37, 53)(36, 52, 42, 58, 39, 55, 44, 60)(38, 54, 41, 57, 40, 56, 45, 61)(43, 59, 47, 63, 46, 62, 48, 64) L = (1, 36)(2, 39)(3, 41)(4, 43)(5, 45)(6, 33)(7, 46)(8, 34)(9, 47)(10, 35)(11, 38)(12, 37)(13, 48)(14, 40)(15, 42)(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) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.53 Graph:: bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.52 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 4}) Quotient :: dipole Aut^+ = C4 : C4 (small group id <16, 4>) Aut = (C4 x C2 x C2) : C2 (small group id <32, 28>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3 * Y1 * Y3^-1 * Y1, Y3 * Y2 * Y3 * Y2^-1, Y2^-1 * Y1 * Y2 * Y1, Y3^4, Y2^2 * Y1 * Y3^-2, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 7, 23)(4, 20, 8, 24)(5, 21, 9, 25)(6, 22, 10, 26)(11, 27, 14, 30)(12, 28, 15, 31)(13, 29, 16, 32)(33, 49, 35, 51, 43, 59, 37, 53)(34, 50, 39, 55, 46, 62, 41, 57)(36, 52, 45, 61, 42, 58, 47, 63)(38, 54, 44, 60, 40, 56, 48, 64) L = (1, 36)(2, 40)(3, 44)(4, 46)(5, 48)(6, 33)(7, 47)(8, 43)(9, 45)(10, 34)(11, 42)(12, 41)(13, 35)(14, 38)(15, 37)(16, 39)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.54 Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.53 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 4}) Quotient :: dipole Aut^+ = C4 : C4 (small group id <16, 4>) Aut = (C4 x C2 x C2) : C2 (small group id <32, 28>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2^4, Y1^4, Y2 * Y1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4 ] Map:: non-degenerate R = (1, 17, 2, 18, 6, 22, 4, 20)(3, 19, 8, 24, 12, 28, 10, 26)(5, 21, 7, 23, 13, 29, 11, 27)(9, 25, 14, 30, 16, 32, 15, 31)(33, 49, 35, 51, 41, 57, 37, 53)(34, 50, 39, 55, 46, 62, 40, 56)(36, 52, 43, 59, 47, 63, 42, 58)(38, 54, 44, 60, 48, 64, 45, 61) L = (1, 34)(2, 38)(3, 40)(4, 33)(5, 39)(6, 36)(7, 45)(8, 44)(9, 46)(10, 35)(11, 37)(12, 42)(13, 43)(14, 48)(15, 41)(16, 47)(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) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.51 Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.54 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 4}) Quotient :: dipole Aut^+ = C4 : C4 (small group id <16, 4>) Aut = (C4 x C2 x C2) : C2 (small group id <32, 28>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y3 * Y1^-1, Y2^4, Y1^-1 * Y3^-2 * Y1^-1, Y2^-1 * Y3 * Y2 * Y1^-1, Y3 * Y2^2 * Y1^-1, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y2 * Y1 * Y2 * Y1^-1, Y1^4, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 17, 2, 18, 8, 24, 5, 21)(3, 19, 11, 27, 15, 31, 13, 29)(4, 20, 10, 26, 7, 23, 12, 28)(6, 22, 9, 25, 16, 32, 14, 30)(33, 49, 35, 51, 44, 60, 38, 54)(34, 50, 41, 57, 36, 52, 43, 59)(37, 53, 46, 62, 39, 55, 45, 61)(40, 56, 47, 63, 42, 58, 48, 64) L = (1, 36)(2, 42)(3, 41)(4, 40)(5, 44)(6, 43)(7, 33)(8, 39)(9, 47)(10, 37)(11, 48)(12, 34)(13, 38)(14, 35)(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) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.52 Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.55 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 4}) Quotient :: dipole Aut^+ = C4 : C4 (small group id <16, 4>) Aut = (C4 x C2 x C2) : C2 (small group id <32, 28>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y3^-1 * Y1^-1, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^-1 * Y3^-2 * Y1^-1, Y2^-1 * Y3^-1 * Y2 * Y1^-1, Y3^4, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, Y1^4, Y2 * Y3^-1 * Y2^-1 * Y1^-1, R * Y2 * R * Y2^-1, (Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 17, 2, 18, 8, 24, 5, 21)(3, 19, 11, 27, 15, 31, 14, 30)(4, 20, 10, 26, 7, 23, 12, 28)(6, 22, 9, 25, 16, 32, 13, 29)(33, 49, 35, 51, 42, 58, 38, 54)(34, 50, 41, 57, 39, 55, 43, 59)(36, 52, 46, 62, 37, 53, 45, 61)(40, 56, 47, 63, 44, 60, 48, 64) L = (1, 36)(2, 42)(3, 45)(4, 40)(5, 44)(6, 46)(7, 33)(8, 39)(9, 35)(10, 37)(11, 38)(12, 34)(13, 47)(14, 48)(15, 41)(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) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.50 Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.56 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 4}) Quotient :: dipole Aut^+ = (C4 x C2) : C2 (small group id <16, 13>) Aut = (C2 x D8) : C2 (small group id <32, 49>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^4, (Y2^-1 * R)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, (Y2^-1 * Y1)^2, Y2 * Y1 * Y3 * Y1 * Y3 * Y2 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 8, 24)(4, 20, 11, 27)(5, 21, 6, 22)(7, 23, 15, 31)(9, 25, 13, 29)(10, 26, 14, 30)(12, 28, 16, 32)(33, 49, 35, 51, 41, 57, 37, 53)(34, 50, 38, 54, 45, 61, 40, 56)(36, 52, 42, 58, 47, 63, 44, 60)(39, 55, 46, 62, 43, 59, 48, 64) L = (1, 36)(2, 39)(3, 42)(4, 33)(5, 44)(6, 46)(7, 34)(8, 48)(9, 47)(10, 35)(11, 45)(12, 37)(13, 43)(14, 38)(15, 41)(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) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.57 Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.57 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 4}) Quotient :: dipole Aut^+ = (C4 x C2) : C2 (small group id <16, 13>) Aut = (C2 x D8) : C2 (small group id <32, 49>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, Y3 * Y2 * Y3 * Y2^-1, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^4, (Y2^-1, Y1^-1), Y2^4 ] Map:: non-degenerate R = (1, 17, 2, 18, 7, 23, 5, 21)(3, 19, 8, 24, 6, 22, 10, 26)(4, 20, 12, 28, 14, 30, 9, 25)(11, 27, 16, 32, 13, 29, 15, 31)(33, 49, 35, 51, 39, 55, 38, 54)(34, 50, 40, 56, 37, 53, 42, 58)(36, 52, 43, 59, 46, 62, 45, 61)(41, 57, 47, 63, 44, 60, 48, 64) L = (1, 36)(2, 41)(3, 43)(4, 33)(5, 44)(6, 45)(7, 46)(8, 47)(9, 34)(10, 48)(11, 35)(12, 37)(13, 38)(14, 39)(15, 40)(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) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.56 Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.58 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 8, 8}) Quotient :: halfedge^2 Aut^+ = D16 (small group id <16, 7>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3, Y1^-1 * Y3 * Y1^-1 * Y2, R * Y3 * R * Y2, (R * Y1)^2, Y1^8 ] Map:: R = (1, 18, 2, 21, 5, 25, 9, 29, 13, 28, 12, 24, 8, 20, 4, 17)(3, 23, 7, 27, 11, 31, 15, 32, 16, 30, 14, 26, 10, 22, 6, 19) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 16)(17, 19)(18, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 32) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 16 f = 2 degree seq :: [ 16^2 ] E7.59 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 8, 8}) Quotient :: halfedge^2 Aut^+ = D16 (small group id <16, 7>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ Y2^2, Y3^2, R^2, (R * Y1)^2, (Y2 * Y3)^2, R * Y2 * R * Y3, (Y2 * Y1^-1)^2, (Y3 * Y1)^2, Y1^-1 * Y3 * Y2 * Y1^-3, Y3 * Y1^-2 * Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y1^2 ] Map:: non-degenerate R = (1, 18, 2, 22, 6, 29, 13, 26, 10, 32, 16, 28, 12, 21, 5, 17)(3, 25, 9, 31, 15, 24, 8, 20, 4, 27, 11, 30, 14, 23, 7, 19) L = (1, 3)(2, 7)(4, 10)(5, 9)(6, 14)(8, 16)(11, 13)(12, 15)(17, 20)(18, 24)(19, 26)(21, 27)(22, 31)(23, 32)(25, 29)(28, 30) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 16 f = 2 degree seq :: [ 16^2 ] E7.60 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 8}) Quotient :: edge^2 Aut^+ = D16 (small group id <16, 7>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (Y3^-1 * Y2)^2, R * Y2 * R * Y1, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^8 ] Map:: R = (1, 17, 3, 19, 7, 23, 11, 27, 15, 31, 12, 28, 8, 24, 4, 20)(2, 18, 5, 21, 9, 25, 13, 29, 16, 32, 14, 30, 10, 26, 6, 22)(33, 34)(35, 38)(36, 37)(39, 42)(40, 41)(43, 46)(44, 45)(47, 48)(49, 50)(51, 54)(52, 53)(55, 58)(56, 57)(59, 62)(60, 61)(63, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32, 32 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E7.65 Graph:: simple bipartite v = 18 e = 32 f = 2 degree seq :: [ 2^16, 16^2 ] E7.61 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 8}) Quotient :: edge^2 Aut^+ = D16 (small group id <16, 7>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, Y3^-1 * Y2 * Y3^3 * Y1, Y3 * Y2 * Y1 * Y3^-1 * Y2 * Y1 ] Map:: R = (1, 17, 4, 20, 11, 27, 14, 30, 6, 22, 13, 29, 12, 28, 5, 21)(2, 18, 7, 23, 15, 31, 10, 26, 3, 19, 9, 25, 16, 32, 8, 24)(33, 34)(35, 38)(36, 40)(37, 39)(41, 46)(42, 45)(43, 48)(44, 47)(49, 51)(50, 54)(52, 58)(53, 57)(55, 62)(56, 61)(59, 63)(60, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32, 32 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E7.66 Graph:: simple bipartite v = 18 e = 32 f = 2 degree seq :: [ 2^16, 16^2 ] E7.62 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 8}) Quotient :: edge^2 Aut^+ = C8 : C2 (small group id <16, 6>) Aut = C2 x (C8 : C2) (small group id <32, 37>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y2^-1 * Y1 * Y3, Y2^2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1^2 * Y3 * Y1^-2, Y2^8, Y1^8 ] Map:: non-degenerate R = (1, 17, 4, 20)(2, 18, 6, 22)(3, 19, 8, 24)(5, 21, 12, 28)(7, 23, 13, 29)(9, 25, 15, 31)(10, 26, 11, 27)(14, 30, 16, 32)(33, 34, 37, 43, 48, 47, 39, 35)(36, 41, 44, 40, 46, 38, 45, 42)(49, 51, 55, 63, 64, 59, 53, 50)(52, 58, 61, 54, 62, 56, 60, 57) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.67 Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.63 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 8}) Quotient :: edge^2 Aut^+ = D16 (small group id <16, 7>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1, Y1^8, Y2^8 ] Map:: non-degenerate R = (1, 17, 4, 20)(2, 18, 6, 22)(3, 19, 8, 24)(5, 21, 10, 26)(7, 23, 12, 28)(9, 25, 14, 30)(11, 27, 15, 31)(13, 29, 16, 32)(33, 34, 37, 41, 45, 43, 39, 35)(36, 40, 44, 47, 48, 46, 42, 38)(49, 51, 55, 59, 61, 57, 53, 50)(52, 54, 58, 62, 64, 63, 60, 56) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.68 Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.64 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 8}) Quotient :: edge^2 Aut^+ = QD16 (small group id <16, 8>) Aut = C2 x QD16 (small group id <32, 40>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2^2)^2, Y3 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y1, Y3 * Y2 * Y3 * Y2^-3, Y1^8 ] Map:: non-degenerate R = (1, 17, 4, 20)(2, 18, 6, 22)(3, 19, 8, 24)(5, 21, 12, 28)(7, 23, 14, 30)(9, 25, 11, 27)(10, 26, 15, 31)(13, 29, 16, 32)(33, 34, 37, 43, 48, 47, 39, 35)(36, 41, 46, 38, 45, 40, 44, 42)(49, 51, 55, 63, 64, 59, 53, 50)(52, 58, 60, 56, 61, 54, 62, 57) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.69 Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.65 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 8}) Quotient :: loop^2 Aut^+ = D16 (small group id <16, 7>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (Y3^-1 * Y2)^2, R * Y2 * R * Y1, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^8 ] Map:: R = (1, 17, 33, 49, 3, 19, 35, 51, 7, 23, 39, 55, 11, 27, 43, 59, 15, 31, 47, 63, 12, 28, 44, 60, 8, 24, 40, 56, 4, 20, 36, 52)(2, 18, 34, 50, 5, 21, 37, 53, 9, 25, 41, 57, 13, 29, 45, 61, 16, 32, 48, 64, 14, 30, 46, 62, 10, 26, 42, 58, 6, 22, 38, 54) L = (1, 18)(2, 17)(3, 22)(4, 21)(5, 20)(6, 19)(7, 26)(8, 25)(9, 24)(10, 23)(11, 30)(12, 29)(13, 28)(14, 27)(15, 32)(16, 31)(33, 50)(34, 49)(35, 54)(36, 53)(37, 52)(38, 51)(39, 58)(40, 57)(41, 56)(42, 55)(43, 62)(44, 61)(45, 60)(46, 59)(47, 64)(48, 63) 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 E7.60 Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 18 degree seq :: [ 32^2 ] E7.66 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 8}) Quotient :: loop^2 Aut^+ = D16 (small group id <16, 7>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, Y3^-1 * Y2 * Y3^3 * Y1, Y3 * Y2 * Y1 * Y3^-1 * Y2 * Y1 ] Map:: R = (1, 17, 33, 49, 4, 20, 36, 52, 11, 27, 43, 59, 14, 30, 46, 62, 6, 22, 38, 54, 13, 29, 45, 61, 12, 28, 44, 60, 5, 21, 37, 53)(2, 18, 34, 50, 7, 23, 39, 55, 15, 31, 47, 63, 10, 26, 42, 58, 3, 19, 35, 51, 9, 25, 41, 57, 16, 32, 48, 64, 8, 24, 40, 56) L = (1, 18)(2, 17)(3, 22)(4, 24)(5, 23)(6, 19)(7, 21)(8, 20)(9, 30)(10, 29)(11, 32)(12, 31)(13, 26)(14, 25)(15, 28)(16, 27)(33, 51)(34, 54)(35, 49)(36, 58)(37, 57)(38, 50)(39, 62)(40, 61)(41, 53)(42, 52)(43, 63)(44, 64)(45, 56)(46, 55)(47, 59)(48, 60) 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 E7.61 Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 18 degree seq :: [ 32^2 ] E7.67 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 8}) Quotient :: loop^2 Aut^+ = C8 : C2 (small group id <16, 6>) Aut = C2 x (C8 : C2) (small group id <32, 37>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y2^-1 * Y1 * Y3, Y2^2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1^2 * Y3 * Y1^-2, Y2^8, Y1^8 ] Map:: non-degenerate R = (1, 17, 33, 49, 4, 20, 36, 52)(2, 18, 34, 50, 6, 22, 38, 54)(3, 19, 35, 51, 8, 24, 40, 56)(5, 21, 37, 53, 12, 28, 44, 60)(7, 23, 39, 55, 13, 29, 45, 61)(9, 25, 41, 57, 15, 31, 47, 63)(10, 26, 42, 58, 11, 27, 43, 59)(14, 30, 46, 62, 16, 32, 48, 64) L = (1, 18)(2, 21)(3, 17)(4, 25)(5, 27)(6, 29)(7, 19)(8, 30)(9, 28)(10, 20)(11, 32)(12, 24)(13, 26)(14, 22)(15, 23)(16, 31)(33, 51)(34, 49)(35, 55)(36, 58)(37, 50)(38, 62)(39, 63)(40, 60)(41, 52)(42, 61)(43, 53)(44, 57)(45, 54)(46, 56)(47, 64)(48, 59) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.62 Transitivity :: VT+ Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.68 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 8}) Quotient :: loop^2 Aut^+ = D16 (small group id <16, 7>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1, Y1^8, Y2^8 ] Map:: non-degenerate R = (1, 17, 33, 49, 4, 20, 36, 52)(2, 18, 34, 50, 6, 22, 38, 54)(3, 19, 35, 51, 8, 24, 40, 56)(5, 21, 37, 53, 10, 26, 42, 58)(7, 23, 39, 55, 12, 28, 44, 60)(9, 25, 41, 57, 14, 30, 46, 62)(11, 27, 43, 59, 15, 31, 47, 63)(13, 29, 45, 61, 16, 32, 48, 64) L = (1, 18)(2, 21)(3, 17)(4, 24)(5, 25)(6, 20)(7, 19)(8, 28)(9, 29)(10, 22)(11, 23)(12, 31)(13, 27)(14, 26)(15, 32)(16, 30)(33, 51)(34, 49)(35, 55)(36, 54)(37, 50)(38, 58)(39, 59)(40, 52)(41, 53)(42, 62)(43, 61)(44, 56)(45, 57)(46, 64)(47, 60)(48, 63) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.63 Transitivity :: VT+ Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.69 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 8}) Quotient :: loop^2 Aut^+ = QD16 (small group id <16, 8>) Aut = C2 x QD16 (small group id <32, 40>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2^2)^2, Y3 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y1, Y3 * Y2 * Y3 * Y2^-3, Y1^8 ] Map:: non-degenerate R = (1, 17, 33, 49, 4, 20, 36, 52)(2, 18, 34, 50, 6, 22, 38, 54)(3, 19, 35, 51, 8, 24, 40, 56)(5, 21, 37, 53, 12, 28, 44, 60)(7, 23, 39, 55, 14, 30, 46, 62)(9, 25, 41, 57, 11, 27, 43, 59)(10, 26, 42, 58, 15, 31, 47, 63)(13, 29, 45, 61, 16, 32, 48, 64) L = (1, 18)(2, 21)(3, 17)(4, 25)(5, 27)(6, 29)(7, 19)(8, 28)(9, 30)(10, 20)(11, 32)(12, 26)(13, 24)(14, 22)(15, 23)(16, 31)(33, 51)(34, 49)(35, 55)(36, 58)(37, 50)(38, 62)(39, 63)(40, 61)(41, 52)(42, 60)(43, 53)(44, 56)(45, 54)(46, 57)(47, 64)(48, 59) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.64 Transitivity :: VT+ Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.70 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = C8 x C2 (small group id <16, 5>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ 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, Y2^8, (Y3 * Y2^-1)^8 ] Map:: R = (1, 17, 2, 18)(3, 19, 5, 21)(4, 20, 6, 22)(7, 23, 9, 25)(8, 24, 10, 26)(11, 27, 13, 29)(12, 28, 14, 30)(15, 31, 16, 32)(33, 49, 35, 51, 39, 55, 43, 59, 47, 63, 44, 60, 40, 56, 36, 52)(34, 50, 37, 53, 41, 57, 45, 61, 48, 64, 46, 62, 42, 58, 38, 54) 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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.71 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = D16 (small group id <16, 7>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^8, (Y3 * Y2^-1)^8 ] Map:: R = (1, 17, 2, 18)(3, 19, 6, 22)(4, 20, 5, 21)(7, 23, 10, 26)(8, 24, 9, 25)(11, 27, 14, 30)(12, 28, 13, 29)(15, 31, 16, 32)(33, 49, 35, 51, 39, 55, 43, 59, 47, 63, 44, 60, 40, 56, 36, 52)(34, 50, 37, 53, 41, 57, 45, 61, 48, 64, 46, 62, 42, 58, 38, 54) 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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.72 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = C8 x C2 (small group id <16, 5>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^-1 * Y3 * Y2 * Y3, (Y3 * Y1)^2, (Y2^-1 * R)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, Y1 * Y2^4 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 6, 22)(4, 20, 7, 23)(5, 21, 8, 24)(9, 25, 12, 28)(10, 26, 13, 29)(11, 27, 14, 30)(15, 31, 16, 32)(33, 49, 35, 51, 41, 57, 40, 56, 34, 50, 38, 54, 44, 60, 37, 53)(36, 52, 42, 58, 47, 63, 46, 62, 39, 55, 45, 61, 48, 64, 43, 59) L = (1, 36)(2, 39)(3, 42)(4, 33)(5, 43)(6, 45)(7, 34)(8, 46)(9, 47)(10, 35)(11, 37)(12, 48)(13, 38)(14, 40)(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) :: { ( 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 E7.73 Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.73 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = C8 x C2 (small group id <16, 5>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, Y2 * Y1 * Y2^-1 * Y1, (Y2^-1 * R)^2, Y3 * Y2^4 * Y1 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 6, 22)(4, 20, 7, 23)(5, 21, 8, 24)(9, 25, 13, 29)(10, 26, 14, 30)(11, 27, 15, 31)(12, 28, 16, 32)(33, 49, 35, 51, 41, 57, 47, 63, 39, 55, 46, 62, 44, 60, 37, 53)(34, 50, 38, 54, 45, 61, 43, 59, 36, 52, 42, 58, 48, 64, 40, 56) L = (1, 36)(2, 39)(3, 42)(4, 33)(5, 43)(6, 46)(7, 34)(8, 47)(9, 48)(10, 35)(11, 37)(12, 45)(13, 44)(14, 38)(15, 40)(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) :: { ( 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 E7.72 Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.74 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = C8 x C2 (small group id <16, 5>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (Y3 * Y1)^2, (Y2^-1 * R)^2, Y2 * Y1 * Y2^-1 * Y1, Y2^4 * Y3 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 6, 22)(4, 20, 7, 23)(5, 21, 8, 24)(9, 25, 13, 29)(10, 26, 14, 30)(11, 27, 15, 31)(12, 28, 16, 32)(33, 49, 35, 51, 41, 57, 43, 59, 36, 52, 42, 58, 44, 60, 37, 53)(34, 50, 38, 54, 45, 61, 47, 63, 39, 55, 46, 62, 48, 64, 40, 56) L = (1, 36)(2, 39)(3, 42)(4, 33)(5, 43)(6, 46)(7, 34)(8, 47)(9, 44)(10, 35)(11, 37)(12, 41)(13, 48)(14, 38)(15, 40)(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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.75 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = D16 (small group id <16, 7>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (Y3 * Y1)^2, (Y2^-1 * Y1)^2, (Y2^-1 * R)^2, Y2^4 * Y3 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 8, 24)(4, 20, 7, 23)(5, 21, 6, 22)(9, 25, 16, 32)(10, 26, 15, 31)(11, 27, 14, 30)(12, 28, 13, 29)(33, 49, 35, 51, 41, 57, 43, 59, 36, 52, 42, 58, 44, 60, 37, 53)(34, 50, 38, 54, 45, 61, 47, 63, 39, 55, 46, 62, 48, 64, 40, 56) L = (1, 36)(2, 39)(3, 42)(4, 33)(5, 43)(6, 46)(7, 34)(8, 47)(9, 44)(10, 35)(11, 37)(12, 41)(13, 48)(14, 38)(15, 40)(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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.76 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = D16 (small group id <16, 7>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, Y3^4, (Y2^-1 * Y1)^2 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 9, 25)(4, 20, 10, 26)(5, 21, 7, 23)(6, 22, 8, 24)(11, 27, 16, 32)(12, 28, 15, 31)(13, 29, 14, 30)(33, 49, 35, 51, 38, 54, 43, 59, 44, 60, 45, 61, 36, 52, 37, 53)(34, 50, 39, 55, 42, 58, 46, 62, 47, 63, 48, 64, 40, 56, 41, 57) L = (1, 36)(2, 40)(3, 37)(4, 44)(5, 45)(6, 33)(7, 41)(8, 47)(9, 48)(10, 34)(11, 35)(12, 38)(13, 43)(14, 39)(15, 42)(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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.77 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = D16 (small group id <16, 7>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^4, (Y2^-1 * Y1)^2 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 9, 25)(4, 20, 10, 26)(5, 21, 7, 23)(6, 22, 8, 24)(11, 27, 16, 32)(12, 28, 15, 31)(13, 29, 14, 30)(33, 49, 35, 51, 36, 52, 43, 59, 44, 60, 45, 61, 38, 54, 37, 53)(34, 50, 39, 55, 40, 56, 46, 62, 47, 63, 48, 64, 42, 58, 41, 57) L = (1, 36)(2, 40)(3, 43)(4, 44)(5, 35)(6, 33)(7, 46)(8, 47)(9, 39)(10, 34)(11, 45)(12, 38)(13, 37)(14, 48)(15, 42)(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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.78 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 8, 8}) Quotient :: halfedge^2 Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y2^2, Y3^2, R^2, Y3 * Y1^-1 * Y2 * Y1, (Y3 * Y2)^2, Y3 * Y1 * Y2 * Y1^-1, R * Y2 * R * Y3, (R * Y1)^2, Y1^-1 * Y2 * Y3 * Y1^-3 ] Map:: R = (1, 18, 2, 22, 6, 29, 13, 25, 9, 32, 16, 28, 12, 21, 5, 17)(3, 24, 8, 30, 14, 27, 11, 20, 4, 23, 7, 31, 15, 26, 10, 19) L = (1, 3)(2, 7)(4, 9)(5, 11)(6, 14)(8, 16)(10, 13)(12, 15)(17, 20)(18, 24)(19, 25)(21, 26)(22, 31)(23, 32)(27, 29)(28, 30) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 16 f = 2 degree seq :: [ 16^2 ] E7.79 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 8, 8}) Quotient :: halfedge^2 Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y2^2, Y3^2, R^2, Y1^2 * Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3, Y1^-1 * Y3 * Y1 * Y2, Y1^8 ] Map:: non-degenerate R = (1, 18, 2, 22, 6, 28, 12, 32, 16, 31, 15, 27, 11, 21, 5, 17)(3, 25, 9, 20, 4, 23, 7, 30, 14, 24, 8, 29, 13, 26, 10, 19) L = (1, 3)(2, 7)(4, 11)(5, 8)(6, 13)(9, 12)(10, 15)(14, 16)(17, 20)(18, 24)(19, 22)(21, 26)(23, 28)(25, 31)(27, 30)(29, 32) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 16 f = 2 degree seq :: [ 16^2 ] E7.80 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 8, 8}) Quotient :: halfedge^2 Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y2^2, Y3^2, R^2, (R * Y1)^2, R * Y2 * R * Y3, Y3 * Y1^2 * Y2, Y1^-1 * Y2 * Y1 * Y3, (Y1 * Y2)^4 ] Map:: R = (1, 18, 2, 22, 6, 28, 12, 32, 16, 31, 15, 25, 9, 21, 5, 17)(3, 24, 8, 30, 14, 23, 7, 29, 13, 27, 11, 20, 4, 26, 10, 19) L = (1, 3)(2, 7)(4, 6)(5, 11)(8, 12)(9, 14)(10, 15)(13, 16)(17, 20)(18, 24)(19, 25)(21, 23)(22, 29)(26, 28)(27, 31)(30, 32) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 16 f = 2 degree seq :: [ 16^2 ] E7.81 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 8}) Quotient :: edge^2 Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, R * Y1 * R * Y2, Y3 * Y1 * Y3^-1 * Y2, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y2, Y3 * Y1 * Y3^3 * Y1 ] Map:: R = (1, 17, 4, 20, 11, 27, 14, 30, 6, 22, 13, 29, 12, 28, 5, 21)(2, 18, 7, 23, 15, 31, 10, 26, 3, 19, 9, 25, 16, 32, 8, 24)(33, 34)(35, 38)(36, 41)(37, 42)(39, 45)(40, 46)(43, 47)(44, 48)(49, 51)(50, 54)(52, 55)(53, 56)(57, 61)(58, 62)(59, 64)(60, 63) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32, 32 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E7.86 Graph:: simple bipartite v = 18 e = 32 f = 2 degree seq :: [ 2^16, 16^2 ] E7.82 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 8}) Quotient :: edge^2 Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^2 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y2, Y3^-1 * Y2 * Y1 * Y3^-5 ] Map:: R = (1, 17, 4, 20, 6, 22, 13, 29, 16, 32, 14, 30, 9, 25, 5, 21)(2, 18, 7, 23, 3, 19, 10, 26, 15, 31, 11, 27, 12, 28, 8, 24)(33, 34)(35, 41)(36, 42)(37, 43)(38, 44)(39, 45)(40, 46)(47, 48)(49, 51)(50, 54)(52, 59)(53, 56)(55, 62)(57, 63)(58, 61)(60, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32, 32 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E7.87 Graph:: simple bipartite v = 18 e = 32 f = 2 degree seq :: [ 2^16, 16^2 ] E7.83 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 8}) Quotient :: edge^2 Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^-2 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y2, Y3 * Y2 * Y1 * Y3^5 ] Map:: R = (1, 17, 4, 20, 9, 25, 14, 30, 16, 32, 13, 29, 6, 22, 5, 21)(2, 18, 7, 23, 12, 28, 11, 27, 15, 31, 10, 26, 3, 19, 8, 24)(33, 34)(35, 41)(36, 43)(37, 42)(38, 44)(39, 46)(40, 45)(47, 48)(49, 51)(50, 54)(52, 55)(53, 59)(56, 62)(57, 63)(58, 61)(60, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32, 32 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E7.88 Graph:: simple bipartite v = 18 e = 32 f = 2 degree seq :: [ 2^16, 16^2 ] E7.84 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 8}) Quotient :: edge^2 Aut^+ = D16 (small group id <16, 7>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 4 Presentation :: [ Y3^2, (Y1^-1, Y2), (Y2^-1 * Y1^-1)^2, Y1^-2 * Y2 * Y1^-1, Y2^-1 * R^2 * Y1^-1, (Y3 * Y1)^2, Y1^2 * Y2^2, R^-1 * Y1 * R * Y2, R^-1 * Y2 * R * Y1, (Y3 * Y2^-1)^2, R^-1 * Y3 * R * Y3 ] Map:: polytopal non-degenerate R = (1, 17, 4, 20)(2, 18, 9, 25)(3, 19, 11, 27)(5, 21, 12, 28)(6, 22, 13, 29)(7, 23, 14, 30)(8, 24, 15, 31)(10, 26, 16, 32)(33, 34, 39, 35, 40, 38, 42, 37)(36, 44, 48, 45, 47, 43, 46, 41)(49, 51, 58, 50, 56, 53, 55, 54)(52, 61, 62, 60, 63, 57, 64, 59) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.89 Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.85 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 8}) Quotient :: edge^2 Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y2^-2 * Y1^-2, Y2^2 * Y1^-1 * Y2, Y2 * Y1^-3, (Y2^-1 * Y1^-1)^2, R * Y1 * R * Y2, (R * Y3)^2, (Y2^-1, Y1^-1), Y3 * Y1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 17, 4, 20)(2, 18, 9, 25)(3, 19, 11, 27)(5, 21, 13, 29)(6, 22, 12, 28)(7, 23, 14, 30)(8, 24, 15, 31)(10, 26, 16, 32)(33, 34, 39, 35, 40, 38, 42, 37)(36, 43, 48, 41, 47, 45, 46, 44)(49, 51, 58, 50, 56, 53, 55, 54)(52, 57, 62, 59, 63, 60, 64, 61) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.90 Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.86 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 8}) Quotient :: loop^2 Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, R * Y1 * R * Y2, Y3 * Y1 * Y3^-1 * Y2, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y2, Y3 * Y1 * Y3^3 * Y1 ] Map:: R = (1, 17, 33, 49, 4, 20, 36, 52, 11, 27, 43, 59, 14, 30, 46, 62, 6, 22, 38, 54, 13, 29, 45, 61, 12, 28, 44, 60, 5, 21, 37, 53)(2, 18, 34, 50, 7, 23, 39, 55, 15, 31, 47, 63, 10, 26, 42, 58, 3, 19, 35, 51, 9, 25, 41, 57, 16, 32, 48, 64, 8, 24, 40, 56) L = (1, 18)(2, 17)(3, 22)(4, 25)(5, 26)(6, 19)(7, 29)(8, 30)(9, 20)(10, 21)(11, 31)(12, 32)(13, 23)(14, 24)(15, 27)(16, 28)(33, 51)(34, 54)(35, 49)(36, 55)(37, 56)(38, 50)(39, 52)(40, 53)(41, 61)(42, 62)(43, 64)(44, 63)(45, 57)(46, 58)(47, 60)(48, 59) 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 E7.81 Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 18 degree seq :: [ 32^2 ] E7.87 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 8}) Quotient :: loop^2 Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^2 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y2, Y3^-1 * Y2 * Y1 * Y3^-5 ] Map:: R = (1, 17, 33, 49, 4, 20, 36, 52, 6, 22, 38, 54, 13, 29, 45, 61, 16, 32, 48, 64, 14, 30, 46, 62, 9, 25, 41, 57, 5, 21, 37, 53)(2, 18, 34, 50, 7, 23, 39, 55, 3, 19, 35, 51, 10, 26, 42, 58, 15, 31, 47, 63, 11, 27, 43, 59, 12, 28, 44, 60, 8, 24, 40, 56) L = (1, 18)(2, 17)(3, 25)(4, 26)(5, 27)(6, 28)(7, 29)(8, 30)(9, 19)(10, 20)(11, 21)(12, 22)(13, 23)(14, 24)(15, 32)(16, 31)(33, 51)(34, 54)(35, 49)(36, 59)(37, 56)(38, 50)(39, 62)(40, 53)(41, 63)(42, 61)(43, 52)(44, 64)(45, 58)(46, 55)(47, 57)(48, 60) 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 E7.82 Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 18 degree seq :: [ 32^2 ] E7.88 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 8}) Quotient :: loop^2 Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^-2 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y2, Y3 * Y2 * Y1 * Y3^5 ] Map:: R = (1, 17, 33, 49, 4, 20, 36, 52, 9, 25, 41, 57, 14, 30, 46, 62, 16, 32, 48, 64, 13, 29, 45, 61, 6, 22, 38, 54, 5, 21, 37, 53)(2, 18, 34, 50, 7, 23, 39, 55, 12, 28, 44, 60, 11, 27, 43, 59, 15, 31, 47, 63, 10, 26, 42, 58, 3, 19, 35, 51, 8, 24, 40, 56) L = (1, 18)(2, 17)(3, 25)(4, 27)(5, 26)(6, 28)(7, 30)(8, 29)(9, 19)(10, 21)(11, 20)(12, 22)(13, 24)(14, 23)(15, 32)(16, 31)(33, 51)(34, 54)(35, 49)(36, 55)(37, 59)(38, 50)(39, 52)(40, 62)(41, 63)(42, 61)(43, 53)(44, 64)(45, 58)(46, 56)(47, 57)(48, 60) 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 E7.83 Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 18 degree seq :: [ 32^2 ] E7.89 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 8}) Quotient :: loop^2 Aut^+ = D16 (small group id <16, 7>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 4 Presentation :: [ Y3^2, (Y1^-1, Y2), (Y2^-1 * Y1^-1)^2, Y1^-2 * Y2 * Y1^-1, Y2^-1 * R^2 * Y1^-1, (Y3 * Y1)^2, Y1^2 * Y2^2, R^-1 * Y1 * R * Y2, R^-1 * Y2 * R * Y1, (Y3 * Y2^-1)^2, R^-1 * Y3 * R * Y3 ] Map:: polytopal non-degenerate R = (1, 17, 33, 49, 4, 20, 36, 52)(2, 18, 34, 50, 9, 25, 41, 57)(3, 19, 35, 51, 11, 27, 43, 59)(5, 21, 37, 53, 12, 28, 44, 60)(6, 22, 38, 54, 13, 29, 45, 61)(7, 23, 39, 55, 14, 30, 46, 62)(8, 24, 40, 56, 15, 31, 47, 63)(10, 26, 42, 58, 16, 32, 48, 64) L = (1, 18)(2, 23)(3, 24)(4, 28)(5, 17)(6, 26)(7, 19)(8, 22)(9, 20)(10, 21)(11, 30)(12, 32)(13, 31)(14, 25)(15, 27)(16, 29)(33, 51)(34, 56)(35, 58)(36, 61)(37, 55)(38, 49)(39, 54)(40, 53)(41, 64)(42, 50)(43, 52)(44, 63)(45, 62)(46, 60)(47, 57)(48, 59) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.84 Transitivity :: VT+ Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.90 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 8}) Quotient :: loop^2 Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y2^-2 * Y1^-2, Y2^2 * Y1^-1 * Y2, Y2 * Y1^-3, (Y2^-1 * Y1^-1)^2, R * Y1 * R * Y2, (R * Y3)^2, (Y2^-1, Y1^-1), Y3 * Y1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 17, 33, 49, 4, 20, 36, 52)(2, 18, 34, 50, 9, 25, 41, 57)(3, 19, 35, 51, 11, 27, 43, 59)(5, 21, 37, 53, 13, 29, 45, 61)(6, 22, 38, 54, 12, 28, 44, 60)(7, 23, 39, 55, 14, 30, 46, 62)(8, 24, 40, 56, 15, 31, 47, 63)(10, 26, 42, 58, 16, 32, 48, 64) L = (1, 18)(2, 23)(3, 24)(4, 27)(5, 17)(6, 26)(7, 19)(8, 22)(9, 31)(10, 21)(11, 32)(12, 20)(13, 30)(14, 28)(15, 29)(16, 25)(33, 51)(34, 56)(35, 58)(36, 57)(37, 55)(38, 49)(39, 54)(40, 53)(41, 62)(42, 50)(43, 63)(44, 64)(45, 52)(46, 59)(47, 60)(48, 61) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.85 Transitivity :: VT+ Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.91 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ 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, Y2^3 * Y1 * Y2 * Y1, (Y1 * Y2^-1 * Y1 * Y2)^2, (Y3 * Y2^-1)^8 ] Map:: R = (1, 17, 2, 18)(3, 19, 7, 23)(4, 20, 9, 25)(5, 21, 11, 27)(6, 22, 13, 29)(8, 24, 12, 28)(10, 26, 14, 30)(15, 31, 16, 32)(33, 49, 35, 51, 40, 56, 45, 61, 48, 64, 43, 59, 42, 58, 36, 52)(34, 50, 37, 53, 44, 60, 41, 57, 47, 63, 39, 55, 46, 62, 38, 54) 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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.92 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ 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^-1 * Y1 * Y2^3 * Y1, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^8 ] Map:: R = (1, 17, 2, 18)(3, 19, 7, 23)(4, 20, 9, 25)(5, 21, 11, 27)(6, 22, 13, 29)(8, 24, 14, 30)(10, 26, 12, 28)(15, 31, 16, 32)(33, 49, 35, 51, 40, 56, 43, 59, 48, 64, 45, 61, 42, 58, 36, 52)(34, 50, 37, 53, 44, 60, 39, 55, 47, 63, 41, 57, 46, 62, 38, 54) 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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.93 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y2^-1 * R)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, (Y3 * Y1)^2, (R * Y1)^2, Y3 * Y2^4, Y1 * Y2^-1 * Y1 * Y3 * Y2 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 9, 25)(4, 20, 7, 23)(5, 21, 13, 29)(6, 22, 11, 27)(8, 24, 12, 28)(10, 26, 15, 31)(14, 30, 16, 32)(33, 49, 35, 51, 42, 58, 44, 60, 36, 52, 43, 59, 46, 62, 37, 53)(34, 50, 38, 54, 47, 63, 45, 61, 39, 55, 41, 57, 48, 64, 40, 56) L = (1, 36)(2, 39)(3, 43)(4, 33)(5, 44)(6, 41)(7, 34)(8, 45)(9, 38)(10, 46)(11, 35)(12, 37)(13, 40)(14, 42)(15, 48)(16, 47)(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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.94 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y2^-1 * R)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, (Y3 * Y1)^2, (R * Y1)^2, Y1 * Y2^-1 * Y3 * Y1 * Y2^-1, Y3 * Y2^4 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 9, 25)(4, 20, 7, 23)(5, 21, 13, 29)(6, 22, 12, 28)(8, 24, 11, 27)(10, 26, 16, 32)(14, 30, 15, 31)(33, 49, 35, 51, 42, 58, 44, 60, 36, 52, 43, 59, 46, 62, 37, 53)(34, 50, 38, 54, 47, 63, 41, 57, 39, 55, 45, 61, 48, 64, 40, 56) L = (1, 36)(2, 39)(3, 43)(4, 33)(5, 44)(6, 45)(7, 34)(8, 41)(9, 40)(10, 46)(11, 35)(12, 37)(13, 38)(14, 42)(15, 48)(16, 47)(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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.95 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, Y1 * Y3 * Y2 * Y3 * Y2^-1, R * Y2 * R * Y1 * Y2, Y2^4 * Y1 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 6, 22)(4, 20, 7, 23)(5, 21, 8, 24)(9, 25, 14, 30)(10, 26, 11, 27)(12, 28, 13, 29)(15, 31, 16, 32)(33, 49, 35, 51, 41, 57, 40, 56, 34, 50, 38, 54, 46, 62, 37, 53)(36, 52, 43, 59, 47, 63, 45, 61, 39, 55, 42, 58, 48, 64, 44, 60) L = (1, 36)(2, 39)(3, 42)(4, 33)(5, 45)(6, 43)(7, 34)(8, 44)(9, 47)(10, 35)(11, 38)(12, 40)(13, 37)(14, 48)(15, 41)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 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 E7.96 Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.96 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y1, Y3 * Y2 * Y1 * Y2^-1, (R * Y1)^2, Y3 * Y2^3 * Y3 * Y2, (R * Y2 * Y3)^2, (Y2^-1 * Y1)^8 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 9, 25)(4, 20, 7, 23)(5, 21, 11, 27)(6, 22, 13, 29)(8, 24, 15, 31)(10, 26, 14, 30)(12, 28, 16, 32)(33, 49, 35, 51, 42, 58, 47, 63, 39, 55, 45, 61, 44, 60, 37, 53)(34, 50, 38, 54, 46, 62, 43, 59, 36, 52, 41, 57, 48, 64, 40, 56) L = (1, 36)(2, 39)(3, 38)(4, 33)(5, 40)(6, 35)(7, 34)(8, 37)(9, 45)(10, 48)(11, 47)(12, 46)(13, 41)(14, 44)(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) :: { ( 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 E7.95 Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.97 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3 * Y2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y3^4, (R * Y3)^2, (R * Y2)^2, Y1 * Y2 * Y3^-1 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 11, 27)(4, 20, 10, 26)(5, 21, 15, 31)(6, 22, 8, 24)(7, 23, 12, 28)(9, 25, 14, 30)(13, 29, 16, 32)(33, 49, 35, 51, 38, 54, 44, 60, 45, 61, 46, 62, 36, 52, 37, 53)(34, 50, 39, 55, 42, 58, 43, 59, 48, 64, 47, 63, 40, 56, 41, 57) L = (1, 36)(2, 40)(3, 37)(4, 45)(5, 46)(6, 33)(7, 41)(8, 48)(9, 47)(10, 34)(11, 39)(12, 35)(13, 38)(14, 44)(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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.98 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 8}) Quotient :: dipole Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-1 * Y2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^4, (Y3^-1 * Y1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y3 ] Map:: non-degenerate R = (1, 17, 2, 18)(3, 19, 11, 27)(4, 20, 10, 26)(5, 21, 14, 30)(6, 22, 8, 24)(7, 23, 12, 28)(9, 25, 15, 31)(13, 29, 16, 32)(33, 49, 35, 51, 36, 52, 44, 60, 45, 61, 47, 63, 38, 54, 37, 53)(34, 50, 39, 55, 40, 56, 43, 59, 48, 64, 46, 62, 42, 58, 41, 57) L = (1, 36)(2, 40)(3, 44)(4, 45)(5, 35)(6, 33)(7, 43)(8, 48)(9, 39)(10, 34)(11, 46)(12, 47)(13, 38)(14, 41)(15, 37)(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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 32 f = 10 degree seq :: [ 4^8, 16^2 ] E7.99 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 16, 16}) Quotient :: edge Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1, (F * T2)^2, (F * T1)^2, T1^8 ] Map:: non-degenerate R = (1, 3, 4, 8, 9, 12, 13, 16, 14, 15, 10, 11, 6, 7, 2, 5)(17, 18, 22, 26, 30, 29, 25, 20)(19, 21, 23, 27, 31, 32, 28, 24) L = (1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) local type(s) :: { ( 32^8 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E7.104 Transitivity :: ET+ Graph:: bipartite v = 3 e = 16 f = 1 degree seq :: [ 8^2, 16 ] E7.100 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 16, 16}) Quotient :: edge Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^8, (T2^-1 * T1^-1)^16 ] Map:: non-degenerate R = (1, 3, 2, 7, 6, 11, 10, 15, 14, 16, 12, 13, 8, 9, 4, 5)(17, 18, 22, 26, 30, 28, 24, 20)(19, 23, 27, 31, 32, 29, 25, 21) L = (1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) local type(s) :: { ( 32^8 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E7.106 Transitivity :: ET+ Graph:: bipartite v = 3 e = 16 f = 1 degree seq :: [ 8^2, 16 ] E7.101 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 16, 16}) Quotient :: edge Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T2^2 * T1^3, T2^4 * T1^-2, T1^2 * T2^-4, T2^2 * T1^-1 * T2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 3, 9, 14, 6, 12, 4, 10, 15, 8, 2, 7, 11, 16, 13, 5)(17, 18, 22, 29, 31, 25, 27, 20)(19, 23, 28, 21, 24, 30, 32, 26) L = (1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) local type(s) :: { ( 32^8 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E7.105 Transitivity :: ET+ Graph:: bipartite v = 3 e = 16 f = 1 degree seq :: [ 8^2, 16 ] E7.102 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 16, 16}) Quotient :: edge Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1, T2), T1^2 * T2^-1 * T1 * T2^-1, T2^-1 * T1^-1 * T2^-3 * T1^-1, T2^10 * T1 ] Map:: non-degenerate R = (1, 3, 9, 16, 11, 8, 2, 7, 15, 12, 4, 10, 6, 14, 13, 5)(17, 18, 22, 25, 31, 29, 27, 20)(19, 23, 30, 32, 28, 21, 24, 26) L = (1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) local type(s) :: { ( 32^8 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E7.107 Transitivity :: ET+ Graph:: bipartite v = 3 e = 16 f = 1 degree seq :: [ 8^2, 16 ] E7.103 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 16, 16}) Quotient :: edge Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^-1 * T1^-1, (F * T1)^2, (F * T2)^2, T1 * T2^-5 ] Map:: non-degenerate R = (1, 3, 9, 14, 8, 2, 7, 13, 16, 12, 6, 4, 10, 15, 11, 5)(17, 18, 22, 21, 24, 28, 27, 30, 32, 31, 25, 29, 26, 19, 23, 20) L = (1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible Dual of E7.108 Transitivity :: ET+ Graph:: bipartite v = 2 e = 16 f = 2 degree seq :: [ 16^2 ] E7.104 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 16, 16}) Quotient :: loop Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1, (F * T2)^2, (F * T1)^2, T1^8 ] Map:: non-degenerate R = (1, 17, 3, 19, 4, 20, 8, 24, 9, 25, 12, 28, 13, 29, 16, 32, 14, 30, 15, 31, 10, 26, 11, 27, 6, 22, 7, 23, 2, 18, 5, 21) L = (1, 18)(2, 22)(3, 21)(4, 17)(5, 23)(6, 26)(7, 27)(8, 19)(9, 20)(10, 30)(11, 31)(12, 24)(13, 25)(14, 29)(15, 32)(16, 28) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E7.99 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 16 f = 3 degree seq :: [ 32 ] E7.105 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 16, 16}) Quotient :: loop Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^8, (T2^-1 * T1^-1)^16 ] Map:: non-degenerate R = (1, 17, 3, 19, 2, 18, 7, 23, 6, 22, 11, 27, 10, 26, 15, 31, 14, 30, 16, 32, 12, 28, 13, 29, 8, 24, 9, 25, 4, 20, 5, 21) L = (1, 18)(2, 22)(3, 23)(4, 17)(5, 19)(6, 26)(7, 27)(8, 20)(9, 21)(10, 30)(11, 31)(12, 24)(13, 25)(14, 28)(15, 32)(16, 29) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E7.101 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 16 f = 3 degree seq :: [ 32 ] E7.106 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 16, 16}) Quotient :: loop Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T2^2 * T1^3, T2^4 * T1^-2, T1^2 * T2^-4, T2^2 * T1^-1 * T2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 17, 3, 19, 9, 25, 14, 30, 6, 22, 12, 28, 4, 20, 10, 26, 15, 31, 8, 24, 2, 18, 7, 23, 11, 27, 16, 32, 13, 29, 5, 21) L = (1, 18)(2, 22)(3, 23)(4, 17)(5, 24)(6, 29)(7, 28)(8, 30)(9, 27)(10, 19)(11, 20)(12, 21)(13, 31)(14, 32)(15, 25)(16, 26) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E7.100 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 16 f = 3 degree seq :: [ 32 ] E7.107 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 16, 16}) Quotient :: loop Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1, T2), T1^2 * T2^-1 * T1 * T2^-1, T2^-1 * T1^-1 * T2^-3 * T1^-1, T2^10 * T1 ] Map:: non-degenerate R = (1, 17, 3, 19, 9, 25, 16, 32, 11, 27, 8, 24, 2, 18, 7, 23, 15, 31, 12, 28, 4, 20, 10, 26, 6, 22, 14, 30, 13, 29, 5, 21) L = (1, 18)(2, 22)(3, 23)(4, 17)(5, 24)(6, 25)(7, 30)(8, 26)(9, 31)(10, 19)(11, 20)(12, 21)(13, 27)(14, 32)(15, 29)(16, 28) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E7.102 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 16 f = 3 degree seq :: [ 32 ] E7.108 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 16, 16}) Quotient :: loop Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2, (F * T2)^2, (F * T1)^2, T2^8, (T2^-1 * T1^-1)^16 ] Map:: non-degenerate R = (1, 17, 3, 19, 7, 23, 11, 27, 15, 31, 13, 29, 9, 25, 5, 21)(2, 18, 6, 22, 10, 26, 14, 30, 16, 32, 12, 28, 8, 24, 4, 20) L = (1, 18)(2, 19)(3, 22)(4, 17)(5, 20)(6, 23)(7, 26)(8, 21)(9, 24)(10, 27)(11, 30)(12, 25)(13, 28)(14, 31)(15, 32)(16, 29) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible Dual of E7.103 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 16 f = 2 degree seq :: [ 16^2 ] E7.109 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 * Y1^-1, Y1 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y3^-3 * Y1^5, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ] 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, 36)(2, 33)(3, 37)(4, 40)(5, 41)(6, 34)(7, 35)(8, 44)(9, 45)(10, 38)(11, 39)(12, 46)(13, 48)(14, 42)(15, 43)(16, 47)(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) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 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 E7.117 Graph:: bipartite v = 3 e = 32 f = 17 degree seq :: [ 16^2, 32 ] E7.110 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 * Y1^-1, Y2^2 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^8, Y1^8 ] 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, 36)(2, 33)(3, 40)(4, 41)(5, 35)(6, 34)(7, 37)(8, 44)(9, 45)(10, 38)(11, 39)(12, 48)(13, 46)(14, 42)(15, 43)(16, 47)(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) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 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 E7.115 Graph:: bipartite v = 3 e = 32 f = 17 degree seq :: [ 16^2, 32 ] E7.111 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 * Y1, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^2 * Y2^-2 * Y1, Y1^2 * Y2^4, Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3^2 ] 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, 36)(2, 33)(3, 42)(4, 43)(5, 44)(6, 34)(7, 35)(8, 37)(9, 38)(10, 40)(11, 45)(12, 48)(13, 47)(14, 39)(15, 41)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 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 E7.118 Graph:: bipartite v = 3 e = 32 f = 17 degree seq :: [ 16^2, 32 ] E7.112 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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, Y2 * Y1 * Y2^-1 * Y3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y1, Y2 * Y3^-2 * Y2 * Y3^-1, Y3 * Y2^3 * Y1^-1 * Y2, Y2^-2 * Y3^-1 * Y2^2 * Y1^-1, Y1^8, (Y2^-1 * Y1^-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, 36)(2, 33)(3, 42)(4, 43)(5, 44)(6, 34)(7, 35)(8, 37)(9, 47)(10, 48)(11, 41)(12, 39)(13, 38)(14, 40)(15, 45)(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) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 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 E7.116 Graph:: bipartite v = 3 e = 32 f = 17 degree seq :: [ 16^2, 32 ] E7.113 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 * Y3^-1, Y1^-1 * Y2^-3, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-5, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 17, 2, 18, 6, 22, 12, 28, 10, 26, 3, 19, 7, 23, 13, 29, 16, 32, 15, 31, 9, 25, 5, 21, 8, 24, 14, 30, 11, 27, 4, 20)(33, 49, 35, 51, 41, 57, 36, 52, 42, 58, 47, 63, 43, 59, 44, 60, 48, 64, 46, 62, 38, 54, 45, 61, 40, 56, 34, 50, 39, 55, 37, 53) L = (1, 35)(2, 39)(3, 41)(4, 42)(5, 33)(6, 45)(7, 37)(8, 34)(9, 36)(10, 47)(11, 44)(12, 48)(13, 40)(14, 38)(15, 43)(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) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 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 E7.114 Graph:: bipartite v = 2 e = 32 f = 18 degree seq :: [ 32^2 ] E7.114 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y1, R^2, Y3 * Y2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^8, (Y3^-1 * Y1^-1)^16, (Y3 * Y2^-1)^16 ] Map:: R = (1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)(33, 49, 34, 50, 38, 54, 42, 58, 46, 62, 45, 61, 41, 57, 36, 52)(35, 51, 37, 53, 39, 55, 43, 59, 47, 63, 48, 64, 44, 60, 40, 56) L = (1, 35)(2, 37)(3, 36)(4, 40)(5, 33)(6, 39)(7, 34)(8, 41)(9, 44)(10, 43)(11, 38)(12, 45)(13, 48)(14, 47)(15, 42)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32, 32 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E7.113 Graph:: simple bipartite v = 18 e = 32 f = 2 degree seq :: [ 2^16, 16^2 ] E7.115 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^2 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^8, (Y3 * Y2^-1)^8 ] Map:: R = (1, 17, 2, 18, 5, 21, 6, 22, 9, 25, 10, 26, 13, 29, 14, 30, 15, 31, 16, 32, 11, 27, 12, 28, 7, 23, 8, 24, 3, 19, 4, 20)(33, 49)(34, 50)(35, 51)(36, 52)(37, 53)(38, 54)(39, 55)(40, 56)(41, 57)(42, 58)(43, 59)(44, 60)(45, 61)(46, 62)(47, 63)(48, 64) L = (1, 35)(2, 36)(3, 39)(4, 40)(5, 33)(6, 34)(7, 43)(8, 44)(9, 37)(10, 38)(11, 47)(12, 48)(13, 41)(14, 42)(15, 45)(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 ) } Outer automorphisms :: reflexible Dual of E7.110 Graph:: bipartite v = 17 e = 32 f = 3 degree seq :: [ 2^16, 32 ] E7.116 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^8, (Y3 * Y2^-1)^8, (Y3^-1 * Y1^-1)^16 ] Map:: R = (1, 17, 2, 18, 3, 19, 6, 22, 7, 23, 10, 26, 11, 27, 14, 30, 15, 31, 16, 32, 13, 29, 12, 28, 9, 25, 8, 24, 5, 21, 4, 20)(33, 49)(34, 50)(35, 51)(36, 52)(37, 53)(38, 54)(39, 55)(40, 56)(41, 57)(42, 58)(43, 59)(44, 60)(45, 61)(46, 62)(47, 63)(48, 64) L = (1, 35)(2, 38)(3, 39)(4, 34)(5, 33)(6, 42)(7, 43)(8, 36)(9, 37)(10, 46)(11, 47)(12, 40)(13, 41)(14, 48)(15, 45)(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 ) } Outer automorphisms :: reflexible Dual of E7.112 Graph:: bipartite v = 17 e = 32 f = 3 degree seq :: [ 2^16, 32 ] E7.117 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1, Y3^-1), (R * Y1)^2, (R * Y3)^2, Y1^2 * Y3^3, Y1^4 * Y3^-2, Y3^2 * Y1^-4, Y1^-1 * Y3 * Y1^-3 * Y3, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^8 ] Map:: R = (1, 17, 2, 18, 6, 22, 14, 30, 9, 25, 12, 28, 5, 21, 8, 24, 15, 31, 10, 26, 3, 19, 7, 23, 13, 29, 16, 32, 11, 27, 4, 20)(33, 49)(34, 50)(35, 51)(36, 52)(37, 53)(38, 54)(39, 55)(40, 56)(41, 57)(42, 58)(43, 59)(44, 60)(45, 61)(46, 62)(47, 63)(48, 64) L = (1, 35)(2, 39)(3, 41)(4, 42)(5, 33)(6, 45)(7, 44)(8, 34)(9, 43)(10, 46)(11, 47)(12, 36)(13, 37)(14, 48)(15, 38)(16, 40)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 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 E7.109 Graph:: bipartite v = 17 e = 32 f = 3 degree seq :: [ 2^16, 32 ] E7.118 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y1), Y3^-3 * Y1^2, Y3^-2 * Y1^-4, Y3^-2 * Y1^-4, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^8 ] Map:: R = (1, 17, 2, 18, 6, 22, 14, 30, 13, 29, 10, 26, 3, 19, 7, 23, 15, 31, 12, 28, 5, 21, 8, 24, 9, 25, 16, 32, 11, 27, 4, 20)(33, 49)(34, 50)(35, 51)(36, 52)(37, 53)(38, 54)(39, 55)(40, 56)(41, 57)(42, 58)(43, 59)(44, 60)(45, 61)(46, 62)(47, 63)(48, 64) L = (1, 35)(2, 39)(3, 41)(4, 42)(5, 33)(6, 47)(7, 48)(8, 34)(9, 38)(10, 40)(11, 45)(12, 36)(13, 37)(14, 44)(15, 43)(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 ) } Outer automorphisms :: reflexible Dual of E7.111 Graph:: bipartite v = 17 e = 32 f = 3 degree seq :: [ 2^16, 32 ] E7.119 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 3, 3, 6}) Quotient :: edge^2 Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^3, (Y3 * Y1^-1)^2, Y2^-1 * Y3^2 * Y1^-1, Y1^-1 * Y3^2 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, R * Y1 * R * Y2, (Y2^-1, Y1^-1), Y3 * Y1 * Y3^-1 * Y2^-1, (R * Y3)^2, Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 19, 4, 22, 8, 26, 18, 36, 15, 33, 7, 25)(2, 20, 9, 27, 13, 31, 17, 35, 6, 24, 11, 29)(3, 21, 12, 30, 10, 28, 16, 34, 5, 23, 14, 32)(37, 38, 41)(39, 44, 49)(40, 48, 47)(42, 46, 51)(43, 50, 53)(45, 54, 52)(55, 57, 60)(56, 62, 64)(58, 63, 68)(59, 67, 69)(61, 65, 70)(66, 72, 71) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 8^3 ), ( 8^12 ) } Outer automorphisms :: reflexible Dual of E7.122 Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 3^12, 12^3 ] E7.120 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 3, 3, 6}) Quotient :: edge^2 Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^3, Y2^3, R * Y1 * R * Y2, (R * Y3)^2, (Y1, Y2^-1), Y3 * Y1 * Y3 * Y2^-1, Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 19, 4, 22)(2, 20, 8, 26)(3, 21, 10, 28)(5, 23, 13, 31)(6, 24, 12, 30)(7, 25, 15, 33)(9, 27, 16, 34)(11, 29, 17, 35)(14, 32, 18, 36)(37, 38, 41)(39, 43, 47)(40, 46, 48)(42, 45, 50)(44, 51, 52)(49, 53, 54)(55, 57, 60)(56, 61, 63)(58, 62, 67)(59, 65, 68)(64, 69, 71)(66, 70, 72) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 24^3 ), ( 24^4 ) } Outer automorphisms :: reflexible Dual of E7.121 Graph:: simple bipartite v = 21 e = 36 f = 3 degree seq :: [ 3^12, 4^9 ] E7.121 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 3, 3, 6}) Quotient :: loop^2 Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^3, (Y3 * Y1^-1)^2, Y2^-1 * Y3^2 * Y1^-1, Y1^-1 * Y3^2 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, R * Y1 * R * Y2, (Y2^-1, Y1^-1), Y3 * Y1 * Y3^-1 * Y2^-1, (R * Y3)^2, Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 19, 37, 55, 4, 22, 40, 58, 8, 26, 44, 62, 18, 36, 54, 72, 15, 33, 51, 69, 7, 25, 43, 61)(2, 20, 38, 56, 9, 27, 45, 63, 13, 31, 49, 67, 17, 35, 53, 71, 6, 24, 42, 60, 11, 29, 47, 65)(3, 21, 39, 57, 12, 30, 48, 66, 10, 28, 46, 64, 16, 34, 52, 70, 5, 23, 41, 59, 14, 32, 50, 68) L = (1, 20)(2, 23)(3, 26)(4, 30)(5, 19)(6, 28)(7, 32)(8, 31)(9, 36)(10, 33)(11, 22)(12, 29)(13, 21)(14, 35)(15, 24)(16, 27)(17, 25)(18, 34)(37, 57)(38, 62)(39, 60)(40, 63)(41, 67)(42, 55)(43, 65)(44, 64)(45, 68)(46, 56)(47, 70)(48, 72)(49, 69)(50, 58)(51, 59)(52, 61)(53, 66)(54, 71) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E7.120 Transitivity :: VT+ Graph:: v = 3 e = 36 f = 21 degree seq :: [ 24^3 ] E7.122 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 3, 3, 6}) Quotient :: loop^2 Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^3, Y2^3, R * Y1 * R * Y2, (R * Y3)^2, (Y1, Y2^-1), Y3 * Y1 * Y3 * Y2^-1, Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 19, 37, 55, 4, 22, 40, 58)(2, 20, 38, 56, 8, 26, 44, 62)(3, 21, 39, 57, 10, 28, 46, 64)(5, 23, 41, 59, 13, 31, 49, 67)(6, 24, 42, 60, 12, 30, 48, 66)(7, 25, 43, 61, 15, 33, 51, 69)(9, 27, 45, 63, 16, 34, 52, 70)(11, 29, 47, 65, 17, 35, 53, 71)(14, 32, 50, 68, 18, 36, 54, 72) L = (1, 20)(2, 23)(3, 25)(4, 28)(5, 19)(6, 27)(7, 29)(8, 33)(9, 32)(10, 30)(11, 21)(12, 22)(13, 35)(14, 24)(15, 34)(16, 26)(17, 36)(18, 31)(37, 57)(38, 61)(39, 60)(40, 62)(41, 65)(42, 55)(43, 63)(44, 67)(45, 56)(46, 69)(47, 68)(48, 70)(49, 58)(50, 59)(51, 71)(52, 72)(53, 64)(54, 66) local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12 ) } Outer automorphisms :: reflexible Dual of E7.119 Transitivity :: VT+ Graph:: v = 9 e = 36 f = 15 degree seq :: [ 8^9 ] E7.123 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, Y1 * Y3 * Y1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), (R * Y2)^2, (Y2^-1 * Y1)^2 ] Map:: non-degenerate R = (1, 19, 2, 20)(3, 21, 9, 27)(4, 22, 8, 26)(5, 23, 7, 25)(6, 24, 10, 28)(11, 29, 17, 35)(12, 30, 18, 36)(13, 31, 15, 33)(14, 32, 16, 34)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 47, 65, 49, 67)(42, 60, 48, 66, 50, 68)(44, 62, 51, 69, 53, 71)(46, 64, 52, 70, 54, 72) L = (1, 40)(2, 44)(3, 47)(4, 42)(5, 49)(6, 37)(7, 51)(8, 46)(9, 53)(10, 38)(11, 48)(12, 39)(13, 50)(14, 41)(15, 52)(16, 43)(17, 54)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.139 Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 4^9, 6^6 ] E7.124 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y3, Y2), (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2)^2, Y2^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 19, 2, 20)(3, 21, 7, 25)(4, 22, 13, 31)(5, 23, 9, 27)(6, 24, 16, 34)(8, 26, 15, 33)(10, 28, 11, 29)(12, 30, 18, 36)(14, 32, 17, 35)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 47, 65, 50, 68)(42, 60, 48, 66, 51, 69)(44, 62, 52, 70, 54, 72)(46, 64, 53, 71, 49, 67) L = (1, 40)(2, 44)(3, 47)(4, 42)(5, 50)(6, 37)(7, 52)(8, 46)(9, 54)(10, 38)(11, 48)(12, 39)(13, 45)(14, 51)(15, 41)(16, 53)(17, 43)(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, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.143 Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 4^9, 6^6 ] E7.125 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y2^-1, Y3^-1), (Y1 * Y2^-1)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y3 * Y1 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 19, 2, 20)(3, 21, 9, 27)(4, 22, 13, 31)(5, 23, 7, 25)(6, 24, 16, 34)(8, 26, 11, 29)(10, 28, 15, 33)(12, 30, 17, 35)(14, 32, 18, 36)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 47, 65, 50, 68)(42, 60, 48, 66, 51, 69)(44, 62, 49, 67, 54, 72)(46, 64, 53, 71, 52, 70) L = (1, 40)(2, 44)(3, 47)(4, 42)(5, 50)(6, 37)(7, 49)(8, 46)(9, 54)(10, 38)(11, 48)(12, 39)(13, 53)(14, 51)(15, 41)(16, 45)(17, 43)(18, 52)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.141 Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 4^9, 6^6 ] E7.126 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y3, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y1 * Y3 * Y1 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 19, 2, 20)(3, 21, 7, 25)(4, 22, 13, 31)(5, 23, 9, 27)(6, 24, 16, 34)(8, 26, 12, 30)(10, 28, 14, 32)(11, 29, 18, 36)(15, 33, 17, 35)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 47, 65, 50, 68)(42, 60, 48, 66, 51, 69)(44, 62, 53, 71, 52, 70)(46, 64, 49, 67, 54, 72) L = (1, 40)(2, 44)(3, 47)(4, 42)(5, 50)(6, 37)(7, 53)(8, 46)(9, 52)(10, 38)(11, 48)(12, 39)(13, 43)(14, 51)(15, 41)(16, 54)(17, 49)(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) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.145 Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 4^9, 6^6 ] E7.127 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y2, Y3^-1), (Y1 * Y2^-1)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2^-1 * Y1 * Y3^-1 * Y1 * Y3 ] Map:: polytopal non-degenerate R = (1, 19, 2, 20)(3, 21, 9, 27)(4, 22, 13, 31)(5, 23, 7, 25)(6, 24, 16, 34)(8, 26, 14, 32)(10, 28, 12, 30)(11, 29, 17, 35)(15, 33, 18, 36)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 47, 65, 50, 68)(42, 60, 48, 66, 51, 69)(44, 62, 53, 71, 49, 67)(46, 64, 52, 70, 54, 72) L = (1, 40)(2, 44)(3, 47)(4, 42)(5, 50)(6, 37)(7, 53)(8, 46)(9, 49)(10, 38)(11, 48)(12, 39)(13, 54)(14, 51)(15, 41)(16, 43)(17, 52)(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) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.146 Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 4^9, 6^6 ] E7.128 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y2^-1, Y3), (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y2)^2, Y1 * Y2 * Y3 * Y1 * Y2, (Y2^-1 * Y3 * Y1)^2 ] Map:: non-degenerate R = (1, 19, 2, 20)(3, 21, 11, 29)(4, 22, 8, 26)(5, 23, 15, 33)(6, 24, 10, 28)(7, 25, 16, 34)(9, 27, 12, 30)(13, 31, 18, 36)(14, 32, 17, 35)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 48, 66, 50, 68)(42, 60, 49, 67, 52, 70)(44, 62, 51, 69, 54, 72)(46, 64, 53, 71, 47, 65) L = (1, 40)(2, 44)(3, 48)(4, 42)(5, 50)(6, 37)(7, 51)(8, 46)(9, 54)(10, 38)(11, 45)(12, 49)(13, 39)(14, 52)(15, 53)(16, 41)(17, 43)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.137 Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 4^9, 6^6 ] E7.129 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y3, Y2), Y1 * Y3 * Y1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 19, 2, 20)(3, 21, 11, 29)(4, 22, 8, 26)(5, 23, 15, 33)(6, 24, 10, 28)(7, 25, 14, 32)(9, 27, 13, 31)(12, 30, 18, 36)(16, 34, 17, 35)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 48, 66, 50, 68)(42, 60, 49, 67, 52, 70)(44, 62, 53, 71, 47, 65)(46, 64, 51, 69, 54, 72) L = (1, 40)(2, 44)(3, 48)(4, 42)(5, 50)(6, 37)(7, 53)(8, 46)(9, 47)(10, 38)(11, 54)(12, 49)(13, 39)(14, 52)(15, 43)(16, 41)(17, 51)(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) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.138 Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 4^9, 6^6 ] E7.130 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y3^-1 * Y1, (R * Y2)^2 ] Map:: polytopal non-degenerate R = (1, 19, 2, 20)(3, 21, 8, 26)(4, 22, 7, 25)(5, 23, 10, 28)(6, 24, 9, 27)(11, 29, 15, 33)(12, 30, 17, 35)(13, 31, 16, 34)(14, 32, 18, 36)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 47, 65, 49, 67)(42, 60, 48, 66, 50, 68)(44, 62, 51, 69, 53, 71)(46, 64, 52, 70, 54, 72) L = (1, 40)(2, 44)(3, 47)(4, 42)(5, 49)(6, 37)(7, 51)(8, 46)(9, 53)(10, 38)(11, 48)(12, 39)(13, 50)(14, 41)(15, 52)(16, 43)(17, 54)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.142 Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 4^9, 6^6 ] E7.131 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y3^-1, Y2^-1), Y1 * Y2 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2 ] Map:: polytopal non-degenerate R = (1, 19, 2, 20)(3, 21, 10, 28)(4, 22, 9, 27)(5, 23, 8, 26)(6, 24, 7, 25)(11, 29, 18, 36)(12, 30, 16, 34)(13, 31, 17, 35)(14, 32, 15, 33)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 47, 65, 49, 67)(42, 60, 48, 66, 50, 68)(44, 62, 51, 69, 53, 71)(46, 64, 52, 70, 54, 72) L = (1, 40)(2, 44)(3, 47)(4, 42)(5, 49)(6, 37)(7, 51)(8, 46)(9, 53)(10, 38)(11, 48)(12, 39)(13, 50)(14, 41)(15, 52)(16, 43)(17, 54)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.140 Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 4^9, 6^6 ] E7.132 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^3, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2 * Y1 * Y3 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y1, (Y3^-1 * Y1)^6 ] Map:: non-degenerate R = (1, 19, 2, 20)(3, 21, 7, 25)(4, 22, 8, 26)(5, 23, 9, 27)(6, 24, 10, 28)(11, 29, 15, 33)(12, 30, 17, 35)(13, 31, 16, 34)(14, 32, 18, 36)(37, 55, 39, 57, 40, 58)(38, 56, 41, 59, 42, 60)(43, 61, 47, 65, 48, 66)(44, 62, 49, 67, 50, 68)(45, 63, 51, 69, 52, 70)(46, 64, 53, 71, 54, 72) L = (1, 40)(2, 42)(3, 37)(4, 39)(5, 38)(6, 41)(7, 48)(8, 50)(9, 52)(10, 54)(11, 43)(12, 47)(13, 44)(14, 49)(15, 45)(16, 51)(17, 46)(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, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.144 Graph:: bipartite v = 15 e = 36 f = 9 degree seq :: [ 4^9, 6^6 ] E7.133 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^3, Y1^3, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, (Y3 * Y1^-1)^2, (R * Y2)^2, (R * Y1)^2, (Y2^-1, Y1^-1) ] Map:: non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 7, 25, 11, 29)(4, 22, 12, 30, 8, 26)(6, 24, 9, 27, 14, 32)(10, 28, 17, 35, 15, 33)(13, 31, 18, 36, 16, 34)(37, 55, 39, 57, 42, 60)(38, 56, 43, 61, 45, 63)(40, 58, 46, 64, 49, 67)(41, 59, 47, 65, 50, 68)(44, 62, 51, 69, 52, 70)(48, 66, 53, 71, 54, 72) L = (1, 40)(2, 44)(3, 46)(4, 37)(5, 48)(6, 49)(7, 51)(8, 38)(9, 52)(10, 39)(11, 53)(12, 41)(13, 42)(14, 54)(15, 43)(16, 45)(17, 47)(18, 50)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.135 Graph:: simple bipartite v = 12 e = 36 f = 12 degree seq :: [ 6^12 ] E7.134 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^3, Y2^-1 * Y3^2, (Y1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1)^2 ] Map:: non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 8, 26, 13, 31)(4, 22, 14, 32, 15, 33)(6, 24, 10, 28, 17, 35)(7, 25, 18, 36, 9, 27)(11, 29, 12, 30, 16, 34)(37, 55, 39, 57, 42, 60)(38, 56, 44, 62, 46, 64)(40, 58, 48, 66, 43, 61)(41, 59, 49, 67, 53, 71)(45, 63, 51, 69, 47, 65)(50, 68, 52, 70, 54, 72) L = (1, 40)(2, 45)(3, 48)(4, 39)(5, 52)(6, 43)(7, 37)(8, 51)(9, 44)(10, 47)(11, 38)(12, 42)(13, 54)(14, 41)(15, 46)(16, 49)(17, 50)(18, 53)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.136 Graph:: simple bipartite v = 12 e = 36 f = 12 degree seq :: [ 6^12 ] E7.135 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y1 * Y3 * Y1^-1, Y3 * Y1^-3, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y1^-1 * Y2 * Y1^-2, (Y3 * Y2)^3, (R * Y2 * Y3)^2, Y2 * Y1 * Y2 * Y3 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 6, 24, 4, 22, 8, 26, 5, 23)(3, 21, 9, 27, 14, 32, 10, 28, 18, 36, 11, 29)(7, 25, 15, 33, 12, 30, 16, 34, 13, 31, 17, 35)(37, 55, 39, 57)(38, 56, 43, 61)(40, 58, 48, 66)(41, 59, 49, 67)(42, 60, 50, 68)(44, 62, 54, 72)(45, 63, 52, 70)(46, 64, 53, 71)(47, 65, 51, 69) L = (1, 40)(2, 44)(3, 46)(4, 37)(5, 42)(6, 41)(7, 52)(8, 38)(9, 54)(10, 39)(11, 50)(12, 53)(13, 51)(14, 47)(15, 49)(16, 43)(17, 48)(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) :: { ( 6^4 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E7.133 Graph:: bipartite v = 12 e = 36 f = 12 degree seq :: [ 4^9, 12^3 ] E7.136 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3 * Y1^2 * Y2, Y3^2 * Y1^-2, Y2 * Y3^-1 * Y1^-2, Y3^3 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2 * Y1)^3, Y3^-1 * Y1^-1 * Y2 * Y1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 15, 33, 12, 30, 5, 23)(3, 21, 11, 29, 6, 24, 14, 32, 4, 22, 13, 31)(8, 26, 16, 34, 10, 28, 18, 36, 9, 27, 17, 35)(37, 55, 39, 57)(38, 56, 44, 62)(40, 58, 48, 66)(41, 59, 45, 63)(42, 60, 43, 61)(46, 64, 51, 69)(47, 65, 54, 72)(49, 67, 52, 70)(50, 68, 53, 71) L = (1, 40)(2, 45)(3, 48)(4, 43)(5, 46)(6, 37)(7, 39)(8, 41)(9, 51)(10, 38)(11, 52)(12, 42)(13, 53)(14, 54)(15, 44)(16, 50)(17, 47)(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) :: { ( 6^4 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E7.134 Graph:: bipartite v = 12 e = 36 f = 12 degree seq :: [ 4^9, 12^3 ] E7.137 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^3, Y2 * Y3 * Y2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y2)^2, (Y3 * Y2^-1)^2, (Y3, Y1) ] Map:: non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 12, 30, 8, 26)(4, 22, 9, 27, 14, 32)(6, 24, 15, 33, 10, 28)(7, 25, 11, 29, 16, 34)(13, 31, 18, 36, 17, 35)(37, 55, 39, 57, 43, 61, 49, 67, 40, 58, 42, 60)(38, 56, 44, 62, 47, 65, 53, 71, 45, 63, 46, 64)(41, 59, 48, 66, 52, 70, 54, 72, 50, 68, 51, 69) L = (1, 40)(2, 45)(3, 42)(4, 43)(5, 50)(6, 49)(7, 37)(8, 46)(9, 47)(10, 53)(11, 38)(12, 51)(13, 39)(14, 52)(15, 54)(16, 41)(17, 44)(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) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.128 Graph:: bipartite v = 9 e = 36 f = 15 degree seq :: [ 6^6, 12^3 ] E7.138 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^3, Y2 * Y3 * Y2, (Y1 * Y2^-1)^2, (Y3^-1, Y1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y2^-1)^2 ] Map:: non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 12, 30, 10, 28)(4, 22, 9, 27, 14, 32)(6, 24, 15, 33, 18, 36)(7, 25, 11, 29, 17, 35)(8, 26, 13, 31, 16, 34)(37, 55, 39, 57, 43, 61, 49, 67, 40, 58, 42, 60)(38, 56, 44, 62, 47, 65, 54, 72, 45, 63, 46, 64)(41, 59, 51, 69, 53, 71, 48, 66, 50, 68, 52, 70) L = (1, 40)(2, 45)(3, 42)(4, 43)(5, 50)(6, 49)(7, 37)(8, 46)(9, 47)(10, 54)(11, 38)(12, 51)(13, 39)(14, 53)(15, 52)(16, 48)(17, 41)(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) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.129 Graph:: bipartite v = 9 e = 36 f = 15 degree seq :: [ 6^6, 12^3 ] E7.139 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^3, Y2 * Y3 * Y2, (Y1, Y3^-1), (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y2)^2, (Y3 * Y2^-1)^2 ] Map:: non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 12, 30, 13, 31)(4, 22, 9, 27, 15, 33)(6, 24, 18, 36, 8, 26)(7, 25, 11, 29, 17, 35)(10, 28, 14, 32, 16, 34)(37, 55, 39, 57, 43, 61, 50, 68, 40, 58, 42, 60)(38, 56, 44, 62, 47, 65, 49, 67, 45, 63, 46, 64)(41, 59, 52, 70, 53, 71, 54, 72, 51, 69, 48, 66) L = (1, 40)(2, 45)(3, 42)(4, 43)(5, 51)(6, 50)(7, 37)(8, 46)(9, 47)(10, 49)(11, 38)(12, 54)(13, 44)(14, 39)(15, 53)(16, 48)(17, 41)(18, 52)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.123 Graph:: bipartite v = 9 e = 36 f = 15 degree seq :: [ 6^6, 12^3 ] E7.140 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2 * Y1 * Y2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3 * Y2^-1)^2, (Y3^-1, Y1^-1), Y2 * Y1^-1 * Y3 * Y2 * Y3, (R * Y2 * Y3^-1)^2 ] Map:: polytopal non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 6, 24, 9, 27)(4, 22, 8, 26, 14, 32)(7, 25, 10, 28, 15, 33)(11, 29, 16, 34, 18, 36)(12, 30, 17, 35, 13, 31)(37, 55, 39, 57, 41, 59, 45, 63, 38, 56, 42, 60)(40, 58, 49, 67, 50, 68, 53, 71, 44, 62, 48, 66)(43, 61, 52, 70, 51, 69, 47, 65, 46, 64, 54, 72) L = (1, 40)(2, 44)(3, 47)(4, 43)(5, 50)(6, 52)(7, 37)(8, 46)(9, 54)(10, 38)(11, 48)(12, 39)(13, 45)(14, 51)(15, 41)(16, 53)(17, 42)(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) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.131 Graph:: bipartite v = 9 e = 36 f = 15 degree seq :: [ 6^6, 12^3 ] E7.141 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1^-1 * Y2^2, Y3^3, (Y3^-1, Y1), (R * Y1)^2, (Y1 * Y2)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2 ] Map:: polytopal non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 8, 26, 6, 24)(4, 22, 9, 27, 14, 32)(7, 25, 10, 28, 15, 33)(11, 29, 18, 36, 16, 34)(12, 30, 13, 31, 17, 35)(37, 55, 39, 57, 38, 56, 44, 62, 41, 59, 42, 60)(40, 58, 49, 67, 45, 63, 53, 71, 50, 68, 48, 66)(43, 61, 52, 70, 46, 64, 47, 65, 51, 69, 54, 72) L = (1, 40)(2, 45)(3, 47)(4, 43)(5, 50)(6, 52)(7, 37)(8, 54)(9, 46)(10, 38)(11, 48)(12, 39)(13, 44)(14, 51)(15, 41)(16, 53)(17, 42)(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) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.125 Graph:: bipartite v = 9 e = 36 f = 15 degree seq :: [ 6^6, 12^3 ] E7.142 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^3, Y2^-1 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y1 * Y2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y3^-1, Y1^-1), Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y2^4 ] Map:: polytopal non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 12, 30, 8, 26)(4, 22, 9, 27, 15, 33)(6, 24, 13, 31, 10, 28)(7, 25, 11, 29, 16, 34)(14, 32, 18, 36, 17, 35)(37, 55, 39, 57, 47, 65, 54, 72, 51, 69, 42, 60)(38, 56, 44, 62, 52, 70, 50, 68, 40, 58, 46, 64)(41, 59, 48, 66, 43, 61, 53, 71, 45, 63, 49, 67) L = (1, 40)(2, 45)(3, 49)(4, 43)(5, 51)(6, 53)(7, 37)(8, 42)(9, 47)(10, 54)(11, 38)(12, 46)(13, 50)(14, 39)(15, 52)(16, 41)(17, 44)(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) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.130 Graph:: bipartite v = 9 e = 36 f = 15 degree seq :: [ 6^6, 12^3 ] E7.143 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^3, Y2 * Y3 * Y1 * Y2, Y2^-1 * Y1 * Y2^-1 * Y3^-1, Y3^-1 * Y1^-1 * Y2^-2, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 12, 30, 8, 26)(4, 22, 9, 27, 16, 34)(6, 24, 15, 33, 10, 28)(7, 25, 11, 29, 13, 31)(14, 32, 17, 35, 18, 36)(37, 55, 39, 57, 49, 67, 54, 72, 45, 63, 42, 60)(38, 56, 44, 62, 43, 61, 53, 71, 52, 70, 46, 64)(40, 58, 51, 69, 41, 59, 48, 66, 47, 65, 50, 68) L = (1, 40)(2, 45)(3, 46)(4, 43)(5, 52)(6, 53)(7, 37)(8, 51)(9, 47)(10, 50)(11, 38)(12, 42)(13, 41)(14, 39)(15, 54)(16, 49)(17, 48)(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) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.124 Graph:: bipartite v = 9 e = 36 f = 15 degree seq :: [ 6^6, 12^3 ] E7.144 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, Y1^3, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y2^3 * Y1^-1 * Y2^-1 * Y1^-1, Y2^6, (Y3^-1 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 19, 2, 20, 4, 22)(3, 21, 8, 26, 7, 25)(5, 23, 10, 28, 12, 30)(6, 24, 14, 32, 11, 29)(9, 27, 15, 33, 18, 36)(13, 31, 16, 34, 17, 35)(37, 55, 39, 57, 45, 63, 50, 68, 49, 67, 41, 59)(38, 56, 42, 60, 51, 69, 48, 66, 52, 70, 43, 61)(40, 58, 46, 64, 54, 72, 44, 62, 53, 71, 47, 65) L = (1, 38)(2, 40)(3, 44)(4, 37)(5, 46)(6, 50)(7, 39)(8, 43)(9, 51)(10, 48)(11, 42)(12, 41)(13, 52)(14, 47)(15, 54)(16, 53)(17, 49)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.132 Graph:: bipartite v = 9 e = 36 f = 15 degree seq :: [ 6^6, 12^3 ] E7.145 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^3, Y3 * Y1 * Y2^-2, Y3 * Y2 * Y1^-1 * Y2^-1, Y2^-1 * Y1 * Y3 * Y2^-1, Y1^-1 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y2 * Y3 * Y2 * Y1 * Y3^-1, Y3 * Y1 * Y2^4, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 12, 30, 10, 28)(4, 22, 9, 27, 14, 32)(6, 24, 13, 31, 17, 35)(7, 25, 11, 29, 16, 34)(8, 26, 18, 36, 15, 33)(37, 55, 39, 57, 45, 63, 54, 72, 52, 70, 42, 60)(38, 56, 44, 62, 50, 68, 53, 71, 43, 61, 46, 64)(40, 58, 48, 66, 47, 65, 51, 69, 41, 59, 49, 67) L = (1, 40)(2, 45)(3, 44)(4, 43)(5, 50)(6, 46)(7, 37)(8, 49)(9, 47)(10, 51)(11, 38)(12, 54)(13, 39)(14, 52)(15, 42)(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) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.126 Graph:: bipartite v = 9 e = 36 f = 15 degree seq :: [ 6^6, 12^3 ] E7.146 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^3, (Y2^-1 * Y1^-1)^2, Y3 * Y2^-2 * Y1^-1, (Y3 * Y2^-1)^2, Y2^-2 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y2^4, (Y3^-1 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 12, 30, 15, 33)(4, 22, 9, 27, 13, 31)(6, 24, 17, 35, 8, 26)(7, 25, 11, 29, 16, 34)(10, 28, 18, 36, 14, 32)(37, 55, 39, 57, 49, 67, 54, 72, 47, 65, 42, 60)(38, 56, 44, 62, 40, 58, 51, 69, 52, 70, 46, 64)(41, 59, 50, 68, 45, 63, 53, 71, 43, 61, 48, 66) L = (1, 40)(2, 45)(3, 50)(4, 43)(5, 49)(6, 48)(7, 37)(8, 39)(9, 47)(10, 42)(11, 38)(12, 46)(13, 52)(14, 44)(15, 54)(16, 41)(17, 51)(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) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.127 Graph:: bipartite v = 9 e = 36 f = 15 degree seq :: [ 6^6, 12^3 ] E7.147 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C6 x C3 (small group id <18, 5>) Aut = C2 x ((C3 x C3) : C2) (small group id <36, 13>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), Y3 * Y1 * Y3^-1 * Y1, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 19, 2, 20)(3, 21, 7, 25)(4, 22, 8, 26)(5, 23, 9, 27)(6, 24, 10, 28)(11, 29, 15, 33)(12, 30, 16, 34)(13, 31, 17, 35)(14, 32, 18, 36)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 47, 65, 49, 67)(42, 60, 48, 66, 50, 68)(44, 62, 51, 69, 53, 71)(46, 64, 52, 70, 54, 72) L = (1, 40)(2, 44)(3, 47)(4, 42)(5, 49)(6, 37)(7, 51)(8, 46)(9, 53)(10, 38)(11, 48)(12, 39)(13, 50)(14, 41)(15, 52)(16, 43)(17, 54)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.148 Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 4^9, 6^6 ] E7.148 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C6 x C3 (small group id <18, 5>) Aut = C2 x ((C3 x C3) : C2) (small group id <36, 13>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^3, Y2^2 * Y3, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1), (R * Y2)^2, (Y3 * Y2^-1)^2, (Y3, Y1) ] Map:: non-degenerate R = (1, 19, 2, 20, 5, 23)(3, 21, 8, 26, 12, 30)(4, 22, 9, 27, 14, 32)(6, 24, 10, 28, 15, 33)(7, 25, 11, 29, 16, 34)(13, 31, 17, 35, 18, 36)(37, 55, 39, 57, 43, 61, 49, 67, 40, 58, 42, 60)(38, 56, 44, 62, 47, 65, 53, 71, 45, 63, 46, 64)(41, 59, 48, 66, 52, 70, 54, 72, 50, 68, 51, 69) L = (1, 40)(2, 45)(3, 42)(4, 43)(5, 50)(6, 49)(7, 37)(8, 46)(9, 47)(10, 53)(11, 38)(12, 51)(13, 39)(14, 52)(15, 54)(16, 41)(17, 44)(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) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.147 Graph:: bipartite v = 9 e = 36 f = 15 degree seq :: [ 6^6, 12^3 ] E7.149 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 6, 6}) Quotient :: halfedge^2 Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, R * Y2 * R * Y3, (R * Y1)^2, Y2 * Y1^2 * Y2 * Y1^-2, Y1^6, Y2 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 ] Map:: R = (1, 20, 2, 23, 5, 29, 11, 28, 10, 22, 4, 19)(3, 25, 7, 30, 12, 36, 18, 34, 16, 26, 8, 21)(6, 31, 13, 35, 17, 33, 15, 27, 9, 32, 14, 24) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 13)(10, 16)(11, 17)(14, 18)(19, 21)(20, 24)(22, 27)(23, 30)(25, 33)(26, 31)(28, 34)(29, 35)(32, 36) local type(s) :: { ( 12^12 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: v = 3 e = 18 f = 3 degree seq :: [ 12^3 ] E7.150 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y3^6, (Y3^-1 * Y1)^3, Y3^-2 * Y2 * Y3^2 * Y1, Y3^2 * Y2 * Y3^-2 * Y1 ] Map:: R = (1, 19, 3, 21, 8, 26, 16, 34, 10, 28, 4, 22)(2, 20, 5, 23, 12, 30, 18, 36, 14, 32, 6, 24)(7, 25, 13, 31, 17, 35, 11, 29, 9, 27, 15, 33)(37, 38)(39, 43)(40, 45)(41, 47)(42, 49)(44, 48)(46, 50)(51, 54)(52, 53)(55, 56)(57, 61)(58, 63)(59, 65)(60, 67)(62, 66)(64, 68)(69, 72)(70, 71) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 24, 24 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E7.152 Graph:: simple bipartite v = 21 e = 36 f = 3 degree seq :: [ 2^18, 12^3 ] E7.151 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x S3 (small group id <18, 3>) Aut = C6 x S3 (small group id <36, 12>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1^6, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1^2 * Y3 * Y1^-2, Y2^6, Y3 * Y2^2 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 19, 4, 22)(2, 20, 6, 24)(3, 21, 8, 26)(5, 23, 12, 30)(7, 25, 15, 33)(9, 27, 16, 34)(10, 28, 13, 31)(11, 29, 17, 35)(14, 32, 18, 36)(37, 38, 41, 47, 43, 39)(40, 45, 48, 54, 51, 46)(42, 49, 53, 52, 44, 50)(55, 57, 61, 65, 59, 56)(58, 64, 69, 72, 66, 63)(60, 68, 62, 70, 71, 67) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 8^4 ), ( 8^6 ) } Outer automorphisms :: reflexible Dual of E7.153 Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 4^9, 6^6 ] E7.152 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y3^6, (Y3^-1 * Y1)^3, Y3^-2 * Y2 * Y3^2 * Y1, Y3^2 * Y2 * Y3^-2 * Y1 ] Map:: R = (1, 19, 37, 55, 3, 21, 39, 57, 8, 26, 44, 62, 16, 34, 52, 70, 10, 28, 46, 64, 4, 22, 40, 58)(2, 20, 38, 56, 5, 23, 41, 59, 12, 30, 48, 66, 18, 36, 54, 72, 14, 32, 50, 68, 6, 24, 42, 60)(7, 25, 43, 61, 13, 31, 49, 67, 17, 35, 53, 71, 11, 29, 47, 65, 9, 27, 45, 63, 15, 33, 51, 69) L = (1, 20)(2, 19)(3, 25)(4, 27)(5, 29)(6, 31)(7, 21)(8, 30)(9, 22)(10, 32)(11, 23)(12, 26)(13, 24)(14, 28)(15, 36)(16, 35)(17, 34)(18, 33)(37, 56)(38, 55)(39, 61)(40, 63)(41, 65)(42, 67)(43, 57)(44, 66)(45, 58)(46, 68)(47, 59)(48, 62)(49, 60)(50, 64)(51, 72)(52, 71)(53, 70)(54, 69) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E7.150 Transitivity :: VT+ Graph:: v = 3 e = 36 f = 21 degree seq :: [ 24^3 ] E7.153 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x S3 (small group id <18, 3>) Aut = C6 x S3 (small group id <36, 12>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1^6, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1^2 * Y3 * Y1^-2, Y2^6, Y3 * Y2^2 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 19, 37, 55, 4, 22, 40, 58)(2, 20, 38, 56, 6, 24, 42, 60)(3, 21, 39, 57, 8, 26, 44, 62)(5, 23, 41, 59, 12, 30, 48, 66)(7, 25, 43, 61, 15, 33, 51, 69)(9, 27, 45, 63, 16, 34, 52, 70)(10, 28, 46, 64, 13, 31, 49, 67)(11, 29, 47, 65, 17, 35, 53, 71)(14, 32, 50, 68, 18, 36, 54, 72) L = (1, 20)(2, 23)(3, 19)(4, 27)(5, 29)(6, 31)(7, 21)(8, 32)(9, 30)(10, 22)(11, 25)(12, 36)(13, 35)(14, 24)(15, 28)(16, 26)(17, 34)(18, 33)(37, 57)(38, 55)(39, 61)(40, 64)(41, 56)(42, 68)(43, 65)(44, 70)(45, 58)(46, 69)(47, 59)(48, 63)(49, 60)(50, 62)(51, 72)(52, 71)(53, 67)(54, 66) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.151 Transitivity :: VT+ Graph:: v = 9 e = 36 f = 15 degree seq :: [ 8^9 ] E7.154 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^6, Y2^2 * Y1 * Y2^-2 * Y1, (Y2 * Y1)^3, (Y3 * Y2^-1)^6 ] Map:: R = (1, 19, 2, 20)(3, 21, 7, 25)(4, 22, 9, 27)(5, 23, 11, 29)(6, 24, 13, 31)(8, 26, 12, 30)(10, 28, 14, 32)(15, 33, 18, 36)(16, 34, 17, 35)(37, 55, 39, 57, 44, 62, 52, 70, 46, 64, 40, 58)(38, 56, 41, 59, 48, 66, 54, 72, 50, 68, 42, 60)(43, 61, 49, 67, 53, 71, 47, 65, 45, 63, 51, 69) 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) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 12 e = 36 f = 12 degree seq :: [ 4^9, 12^3 ] E7.155 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 6}) Quotient :: dipole Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y1 * Y2^2 * Y3 * Y2, Y1 * Y2 * Y3 * Y1 * Y2^-1, Y1 * Y3 * Y2^3, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 19, 2, 20)(3, 21, 11, 29)(4, 22, 10, 28)(5, 23, 16, 34)(6, 24, 8, 26)(7, 25, 13, 31)(9, 27, 17, 35)(12, 30, 15, 33)(14, 32, 18, 36)(37, 55, 39, 57, 48, 66, 44, 62, 54, 72, 41, 59)(38, 56, 43, 61, 51, 69, 40, 58, 50, 68, 45, 63)(42, 60, 49, 67, 52, 70, 46, 64, 47, 65, 53, 71) L = (1, 40)(2, 44)(3, 49)(4, 42)(5, 53)(6, 37)(7, 47)(8, 46)(9, 52)(10, 38)(11, 54)(12, 45)(13, 50)(14, 39)(15, 41)(16, 48)(17, 51)(18, 43)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 12 e = 36 f = 12 degree seq :: [ 4^9, 12^3 ] E7.156 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 9, 18}) Quotient :: edge Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^2, T1^-6, T1^6 ] Map:: non-degenerate R = (1, 3, 9, 11, 18, 15, 6, 13, 5)(2, 7, 12, 4, 10, 17, 14, 16, 8)(19, 20, 24, 32, 29, 22)(21, 25, 31, 34, 36, 28)(23, 26, 33, 35, 27, 30) L = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 36^6 ), ( 36^9 ) } Outer automorphisms :: reflexible Dual of E7.164 Transitivity :: ET+ Graph:: bipartite v = 5 e = 18 f = 1 degree seq :: [ 6^3, 9^2 ] E7.157 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 9, 18}) Quotient :: edge Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^2, T1^6 ] Map:: non-degenerate R = (1, 3, 9, 6, 15, 17, 11, 13, 5)(2, 7, 16, 14, 18, 12, 4, 10, 8)(19, 20, 24, 32, 29, 22)(21, 25, 33, 36, 31, 28)(23, 26, 27, 34, 35, 30) L = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 36^6 ), ( 36^9 ) } Outer automorphisms :: reflexible Dual of E7.165 Transitivity :: ET+ Graph:: bipartite v = 5 e = 18 f = 1 degree seq :: [ 6^3, 9^2 ] E7.158 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 9, 18}) Quotient :: edge Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T2)^2, (F * T1)^2, T1^9, (T2^-1 * T1^-1)^6 ] Map:: non-degenerate R = (1, 3, 2, 7, 6, 11, 10, 15, 14, 18, 16, 17, 12, 13, 8, 9, 4, 5)(19, 20, 24, 28, 32, 34, 30, 26, 22)(21, 25, 29, 33, 36, 35, 31, 27, 23) L = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 12^9 ), ( 12^18 ) } Outer automorphisms :: reflexible Dual of E7.167 Transitivity :: ET+ Graph:: bipartite v = 3 e = 18 f = 3 degree seq :: [ 9^2, 18 ] E7.159 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 9, 18}) Quotient :: edge Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T1)^2, (F * T2)^2, T1 * T2^4, T1^4 * T2^-2, T2 * T1^-3 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 12, 4, 10, 14, 18, 11, 16, 6, 15, 17, 8, 2, 7, 13, 5)(19, 20, 24, 32, 27, 31, 35, 29, 22)(21, 25, 33, 36, 30, 23, 26, 34, 28) L = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 12^9 ), ( 12^18 ) } Outer automorphisms :: reflexible Dual of E7.166 Transitivity :: ET+ Graph:: bipartite v = 3 e = 18 f = 3 degree seq :: [ 9^2, 18 ] E7.160 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 9, 18}) Quotient :: edge Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^6, (T1^-1 * T2^-1)^9 ] Map:: non-degenerate R = (1, 3, 9, 15, 11, 5)(2, 7, 13, 18, 14, 8)(4, 6, 12, 17, 16, 10)(19, 20, 24, 21, 25, 30, 27, 31, 35, 33, 36, 34, 29, 32, 28, 23, 26, 22) L = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 18^6 ), ( 18^18 ) } Outer automorphisms :: reflexible Dual of E7.163 Transitivity :: ET+ Graph:: bipartite v = 4 e = 18 f = 2 degree seq :: [ 6^3, 18 ] E7.161 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 9, 18}) Quotient :: edge Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ F^2, T2^-1 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^6 ] Map:: non-degenerate R = (1, 3, 9, 15, 11, 5)(2, 7, 13, 18, 14, 8)(4, 10, 16, 17, 12, 6)(19, 20, 24, 23, 26, 30, 29, 32, 35, 33, 36, 34, 27, 31, 28, 21, 25, 22) L = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 18^6 ), ( 18^18 ) } Outer automorphisms :: reflexible Dual of E7.162 Transitivity :: ET+ Graph:: bipartite v = 4 e = 18 f = 2 degree seq :: [ 6^3, 18 ] E7.162 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 9, 18}) Quotient :: loop Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^2, T1^-6, T1^6 ] Map:: non-degenerate R = (1, 19, 3, 21, 9, 27, 11, 29, 18, 36, 15, 33, 6, 24, 13, 31, 5, 23)(2, 20, 7, 25, 12, 30, 4, 22, 10, 28, 17, 35, 14, 32, 16, 34, 8, 26) L = (1, 20)(2, 24)(3, 25)(4, 19)(5, 26)(6, 32)(7, 31)(8, 33)(9, 30)(10, 21)(11, 22)(12, 23)(13, 34)(14, 29)(15, 35)(16, 36)(17, 27)(18, 28) local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E7.161 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 18 f = 4 degree seq :: [ 18^2 ] E7.163 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 9, 18}) Quotient :: loop Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^2, T1^6 ] Map:: non-degenerate R = (1, 19, 3, 21, 9, 27, 6, 24, 15, 33, 17, 35, 11, 29, 13, 31, 5, 23)(2, 20, 7, 25, 16, 34, 14, 32, 18, 36, 12, 30, 4, 22, 10, 28, 8, 26) L = (1, 20)(2, 24)(3, 25)(4, 19)(5, 26)(6, 32)(7, 33)(8, 27)(9, 34)(10, 21)(11, 22)(12, 23)(13, 28)(14, 29)(15, 36)(16, 35)(17, 30)(18, 31) local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E7.160 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 18 f = 4 degree seq :: [ 18^2 ] E7.164 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 9, 18}) Quotient :: loop Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T2)^2, (F * T1)^2, T1^9, (T2^-1 * T1^-1)^6 ] Map:: non-degenerate R = (1, 19, 3, 21, 2, 20, 7, 25, 6, 24, 11, 29, 10, 28, 15, 33, 14, 32, 18, 36, 16, 34, 17, 35, 12, 30, 13, 31, 8, 26, 9, 27, 4, 22, 5, 23) L = (1, 20)(2, 24)(3, 25)(4, 19)(5, 21)(6, 28)(7, 29)(8, 22)(9, 23)(10, 32)(11, 33)(12, 26)(13, 27)(14, 34)(15, 36)(16, 30)(17, 31)(18, 35) local type(s) :: { ( 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9 ) } Outer automorphisms :: reflexible Dual of E7.156 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 18 f = 5 degree seq :: [ 36 ] E7.165 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 9, 18}) Quotient :: loop Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T1)^2, (F * T2)^2, T1 * T2^4, T1^4 * T2^-2, T2 * T1^-3 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 19, 3, 21, 9, 27, 12, 30, 4, 22, 10, 28, 14, 32, 18, 36, 11, 29, 16, 34, 6, 24, 15, 33, 17, 35, 8, 26, 2, 20, 7, 25, 13, 31, 5, 23) L = (1, 20)(2, 24)(3, 25)(4, 19)(5, 26)(6, 32)(7, 33)(8, 34)(9, 31)(10, 21)(11, 22)(12, 23)(13, 35)(14, 27)(15, 36)(16, 28)(17, 29)(18, 30) local type(s) :: { ( 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9 ) } Outer automorphisms :: reflexible Dual of E7.157 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 18 f = 5 degree seq :: [ 36 ] E7.166 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 9, 18}) Quotient :: loop Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^6, (T1^-1 * T2^-1)^9 ] Map:: non-degenerate R = (1, 19, 3, 21, 9, 27, 15, 33, 11, 29, 5, 23)(2, 20, 7, 25, 13, 31, 18, 36, 14, 32, 8, 26)(4, 22, 6, 24, 12, 30, 17, 35, 16, 34, 10, 28) L = (1, 20)(2, 24)(3, 25)(4, 19)(5, 26)(6, 21)(7, 30)(8, 22)(9, 31)(10, 23)(11, 32)(12, 27)(13, 35)(14, 28)(15, 36)(16, 29)(17, 33)(18, 34) local type(s) :: { ( 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18 ) } Outer automorphisms :: reflexible Dual of E7.159 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 18 f = 3 degree seq :: [ 12^3 ] E7.167 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 9, 18}) Quotient :: loop Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ F^2, T2^-1 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^6 ] Map:: non-degenerate R = (1, 19, 3, 21, 9, 27, 15, 33, 11, 29, 5, 23)(2, 20, 7, 25, 13, 31, 18, 36, 14, 32, 8, 26)(4, 22, 10, 28, 16, 34, 17, 35, 12, 30, 6, 24) L = (1, 20)(2, 24)(3, 25)(4, 19)(5, 26)(6, 23)(7, 22)(8, 30)(9, 31)(10, 21)(11, 32)(12, 29)(13, 28)(14, 35)(15, 36)(16, 27)(17, 33)(18, 34) local type(s) :: { ( 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18 ) } Outer automorphisms :: reflexible Dual of E7.158 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 18 f = 3 degree seq :: [ 12^3 ] E7.168 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y2^-1 * Y1 * Y2^-2 * Y1, Y1^5 * 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 ] 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, 40)(2, 37)(3, 46)(4, 47)(5, 48)(6, 38)(7, 39)(8, 41)(9, 44)(10, 49)(11, 50)(12, 53)(13, 54)(14, 42)(15, 43)(16, 45)(17, 52)(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) :: { ( 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 E7.174 Graph:: bipartite v = 5 e = 36 f = 19 degree seq :: [ 12^3, 18^2 ] E7.169 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^2 * Y3^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y3^-2 * Y2^3, Y1^6, Y3^6 ] 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, 40)(2, 37)(3, 46)(4, 47)(5, 48)(6, 38)(7, 39)(8, 41)(9, 53)(10, 54)(11, 50)(12, 45)(13, 43)(14, 42)(15, 44)(16, 49)(17, 51)(18, 52)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 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 E7.175 Graph:: bipartite v = 5 e = 36 f = 19 degree seq :: [ 12^3, 18^2 ] E7.170 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, Y1^9, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 19, 2, 20, 6, 24, 10, 28, 14, 32, 16, 34, 12, 30, 8, 26, 4, 22)(3, 21, 7, 25, 11, 29, 15, 33, 18, 36, 17, 35, 13, 31, 9, 27, 5, 23)(37, 55, 39, 57, 38, 56, 43, 61, 42, 60, 47, 65, 46, 64, 51, 69, 50, 68, 54, 72, 52, 70, 53, 71, 48, 66, 49, 67, 44, 62, 45, 63, 40, 58, 41, 59) L = (1, 39)(2, 43)(3, 38)(4, 41)(5, 37)(6, 47)(7, 42)(8, 45)(9, 40)(10, 51)(11, 46)(12, 49)(13, 44)(14, 54)(15, 50)(16, 53)(17, 48)(18, 52)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E7.172 Graph:: bipartite v = 3 e = 36 f = 21 degree seq :: [ 18^2, 36 ] E7.171 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2 * Y1 * Y2^3, Y2 * Y1^-1 * Y2 * Y1^-3, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 19, 2, 20, 6, 24, 14, 32, 9, 27, 13, 31, 17, 35, 11, 29, 4, 22)(3, 21, 7, 25, 15, 33, 18, 36, 12, 30, 5, 23, 8, 26, 16, 34, 10, 28)(37, 55, 39, 57, 45, 63, 48, 66, 40, 58, 46, 64, 50, 68, 54, 72, 47, 65, 52, 70, 42, 60, 51, 69, 53, 71, 44, 62, 38, 56, 43, 61, 49, 67, 41, 59) L = (1, 39)(2, 43)(3, 45)(4, 46)(5, 37)(6, 51)(7, 49)(8, 38)(9, 48)(10, 50)(11, 52)(12, 40)(13, 41)(14, 54)(15, 53)(16, 42)(17, 44)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E7.173 Graph:: bipartite v = 3 e = 36 f = 21 degree seq :: [ 18^2, 36 ] E7.172 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y1, R^2, Y3^-2 * Y2 * Y3^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^6, (Y3^-1 * Y1^-1)^18 ] Map:: R = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)(37, 55, 38, 56, 42, 60, 48, 66, 46, 64, 40, 58)(39, 57, 43, 61, 49, 67, 53, 71, 51, 69, 45, 63)(41, 59, 44, 62, 50, 68, 54, 72, 52, 70, 47, 65) L = (1, 39)(2, 43)(3, 44)(4, 45)(5, 37)(6, 49)(7, 50)(8, 38)(9, 41)(10, 51)(11, 40)(12, 53)(13, 54)(14, 42)(15, 47)(16, 46)(17, 52)(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) :: { ( 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E7.170 Graph:: simple bipartite v = 21 e = 36 f = 3 degree seq :: [ 2^18, 12^3 ] E7.173 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^-1 * Y3^-3, (Y2^-1 * R)^2, (R * Y3)^2, (R * Y1)^2, Y2^6, (Y3 * Y2^-1)^9, (Y3^-1 * Y1^-1)^18 ] Map:: R = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)(37, 55, 38, 56, 42, 60, 48, 66, 47, 65, 40, 58)(39, 57, 43, 61, 49, 67, 53, 71, 52, 70, 46, 64)(41, 59, 44, 62, 50, 68, 54, 72, 51, 69, 45, 63) L = (1, 39)(2, 43)(3, 45)(4, 46)(5, 37)(6, 49)(7, 41)(8, 38)(9, 40)(10, 51)(11, 52)(12, 53)(13, 44)(14, 42)(15, 47)(16, 54)(17, 50)(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) :: { ( 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E7.171 Graph:: simple bipartite v = 21 e = 36 f = 3 degree seq :: [ 2^18, 12^3 ] E7.174 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y2, R^2, Y3 * Y1^-3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^6, (Y3 * Y2^-1)^6, (Y1^-1 * Y3^-1)^9 ] Map:: R = (1, 19, 2, 20, 6, 24, 3, 21, 7, 25, 12, 30, 9, 27, 13, 31, 17, 35, 15, 33, 18, 36, 16, 34, 11, 29, 14, 32, 10, 28, 5, 23, 8, 26, 4, 22)(37, 55)(38, 56)(39, 57)(40, 58)(41, 59)(42, 60)(43, 61)(44, 62)(45, 63)(46, 64)(47, 65)(48, 66)(49, 67)(50, 68)(51, 69)(52, 70)(53, 71)(54, 72) L = (1, 39)(2, 43)(3, 45)(4, 42)(5, 37)(6, 48)(7, 49)(8, 38)(9, 51)(10, 40)(11, 41)(12, 53)(13, 54)(14, 44)(15, 47)(16, 46)(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) :: { ( 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E7.168 Graph:: bipartite v = 19 e = 36 f = 5 degree seq :: [ 2^18, 36 ] E7.175 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^-1 * Y1^-3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^6, (Y3 * Y2^-1)^6 ] Map:: R = (1, 19, 2, 20, 6, 24, 5, 23, 8, 26, 12, 30, 11, 29, 14, 32, 17, 35, 15, 33, 18, 36, 16, 34, 9, 27, 13, 31, 10, 28, 3, 21, 7, 25, 4, 22)(37, 55)(38, 56)(39, 57)(40, 58)(41, 59)(42, 60)(43, 61)(44, 62)(45, 63)(46, 64)(47, 65)(48, 66)(49, 67)(50, 68)(51, 69)(52, 70)(53, 71)(54, 72) L = (1, 39)(2, 43)(3, 45)(4, 46)(5, 37)(6, 40)(7, 49)(8, 38)(9, 51)(10, 52)(11, 41)(12, 42)(13, 54)(14, 44)(15, 47)(16, 53)(17, 48)(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) :: { ( 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E7.169 Graph:: bipartite v = 19 e = 36 f = 5 degree seq :: [ 2^18, 36 ] E7.176 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y2^-3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, 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 ] Map:: R = (1, 19, 2, 20, 6, 24, 12, 30, 11, 29, 4, 22)(3, 21, 7, 25, 13, 31, 17, 35, 16, 34, 10, 28)(5, 23, 8, 26, 14, 32, 18, 36, 15, 33, 9, 27)(37, 55, 39, 57, 45, 63, 40, 58, 46, 64, 51, 69, 47, 65, 52, 70, 54, 72, 48, 66, 53, 71, 50, 68, 42, 60, 49, 67, 44, 62, 38, 56, 43, 61, 41, 59) L = (1, 40)(2, 37)(3, 46)(4, 47)(5, 45)(6, 38)(7, 39)(8, 41)(9, 51)(10, 52)(11, 48)(12, 42)(13, 43)(14, 44)(15, 54)(16, 53)(17, 49)(18, 50)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E7.178 Graph:: bipartite v = 4 e = 36 f = 20 degree seq :: [ 12^3, 36 ] E7.177 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^3 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2^-1), 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 ] Map:: R = (1, 19, 2, 20, 6, 24, 12, 30, 10, 28, 4, 22)(3, 21, 7, 25, 13, 31, 17, 35, 15, 33, 9, 27)(5, 23, 8, 26, 14, 32, 18, 36, 16, 34, 11, 29)(37, 55, 39, 57, 44, 62, 38, 56, 43, 61, 50, 68, 42, 60, 49, 67, 54, 72, 48, 66, 53, 71, 52, 70, 46, 64, 51, 69, 47, 65, 40, 58, 45, 63, 41, 59) L = (1, 40)(2, 37)(3, 45)(4, 46)(5, 47)(6, 38)(7, 39)(8, 41)(9, 51)(10, 48)(11, 52)(12, 42)(13, 43)(14, 44)(15, 53)(16, 54)(17, 49)(18, 50)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E7.179 Graph:: bipartite v = 4 e = 36 f = 20 degree seq :: [ 12^3, 36 ] E7.178 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y2, R^2, Y1 * Y3^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^9, (Y3^-1 * Y1^-1)^6, (Y3 * Y2^-1)^18 ] Map:: R = (1, 19, 2, 20, 6, 24, 10, 28, 14, 32, 16, 34, 12, 30, 8, 26, 4, 22)(3, 21, 7, 25, 11, 29, 15, 33, 18, 36, 17, 35, 13, 31, 9, 27, 5, 23)(37, 55)(38, 56)(39, 57)(40, 58)(41, 59)(42, 60)(43, 61)(44, 62)(45, 63)(46, 64)(47, 65)(48, 66)(49, 67)(50, 68)(51, 69)(52, 70)(53, 71)(54, 72) L = (1, 39)(2, 43)(3, 38)(4, 41)(5, 37)(6, 47)(7, 42)(8, 45)(9, 40)(10, 51)(11, 46)(12, 49)(13, 44)(14, 54)(15, 50)(16, 53)(17, 48)(18, 52)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 36 ), ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E7.176 Graph:: simple bipartite v = 20 e = 36 f = 4 degree seq :: [ 2^18, 18^2 ] E7.179 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y1, Y3^-1), Y3 * Y1 * Y3^3, Y1^4 * Y3^-2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-3 * Y3 * Y1^-1, (Y3 * Y2^-1)^18 ] Map:: R = (1, 19, 2, 20, 6, 24, 14, 32, 9, 27, 13, 31, 17, 35, 11, 29, 4, 22)(3, 21, 7, 25, 15, 33, 18, 36, 12, 30, 5, 23, 8, 26, 16, 34, 10, 28)(37, 55)(38, 56)(39, 57)(40, 58)(41, 59)(42, 60)(43, 61)(44, 62)(45, 63)(46, 64)(47, 65)(48, 66)(49, 67)(50, 68)(51, 69)(52, 70)(53, 71)(54, 72) L = (1, 39)(2, 43)(3, 45)(4, 46)(5, 37)(6, 51)(7, 49)(8, 38)(9, 48)(10, 50)(11, 52)(12, 40)(13, 41)(14, 54)(15, 53)(16, 42)(17, 44)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 36 ), ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E7.177 Graph:: simple bipartite v = 20 e = 36 f = 4 degree seq :: [ 2^18, 18^2 ] E7.180 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 10, 20}) Quotient :: edge Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ F^2, T1^4, (T2, T1), (F * T2)^2, (F * T1)^2, T2^-5 * T1^2 ] Map:: non-degenerate R = (1, 3, 9, 17, 14, 6, 13, 20, 12, 5)(2, 7, 15, 19, 11, 4, 10, 18, 16, 8)(21, 22, 26, 24)(23, 27, 33, 30)(25, 28, 34, 31)(29, 35, 40, 38)(32, 36, 37, 39) L = (1, 21)(2, 22)(3, 23)(4, 24)(5, 25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40) local type(s) :: { ( 40^4 ), ( 40^10 ) } Outer automorphisms :: reflexible Dual of E7.184 Transitivity :: ET+ Graph:: bipartite v = 7 e = 20 f = 1 degree seq :: [ 4^5, 10^2 ] E7.181 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 10, 20}) Quotient :: edge Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2 * T1^-2, T2 * T1 * T2^5, (T1^-1 * T2^-1)^4 ] Map:: non-degenerate R = (1, 3, 9, 16, 18, 12, 4, 10, 6, 14, 20, 17, 11, 8, 2, 7, 15, 19, 13, 5)(21, 22, 26, 29, 35, 40, 38, 33, 31, 24)(23, 27, 34, 36, 39, 37, 32, 25, 28, 30) L = (1, 21)(2, 22)(3, 23)(4, 24)(5, 25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40) local type(s) :: { ( 8^10 ), ( 8^20 ) } Outer automorphisms :: reflexible Dual of E7.185 Transitivity :: ET+ Graph:: bipartite v = 3 e = 20 f = 5 degree seq :: [ 10^2, 20 ] E7.182 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 10, 20}) Quotient :: edge Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, T2^4, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-5, (T1^-1 * T2^-1)^10 ] Map:: non-degenerate R = (1, 3, 9, 5)(2, 7, 16, 8)(4, 10, 17, 12)(6, 14, 20, 15)(11, 13, 19, 18)(21, 22, 26, 33, 30, 23, 27, 34, 39, 37, 29, 36, 40, 38, 32, 25, 28, 35, 31, 24) L = (1, 21)(2, 22)(3, 23)(4, 24)(5, 25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40) local type(s) :: { ( 20^4 ), ( 20^20 ) } Outer automorphisms :: reflexible Dual of E7.183 Transitivity :: ET+ Graph:: bipartite v = 6 e = 20 f = 2 degree seq :: [ 4^5, 20 ] E7.183 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 10, 20}) Quotient :: loop Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ F^2, T1^4, (T2, T1), (F * T2)^2, (F * T1)^2, T2^-5 * T1^2 ] Map:: non-degenerate R = (1, 21, 3, 23, 9, 29, 17, 37, 14, 34, 6, 26, 13, 33, 20, 40, 12, 32, 5, 25)(2, 22, 7, 27, 15, 35, 19, 39, 11, 31, 4, 24, 10, 30, 18, 38, 16, 36, 8, 28) L = (1, 22)(2, 26)(3, 27)(4, 21)(5, 28)(6, 24)(7, 33)(8, 34)(9, 35)(10, 23)(11, 25)(12, 36)(13, 30)(14, 31)(15, 40)(16, 37)(17, 39)(18, 29)(19, 32)(20, 38) local type(s) :: { ( 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 E7.182 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 20 f = 6 degree seq :: [ 20^2 ] E7.184 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 10, 20}) Quotient :: loop Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2 * T1^-2, T2 * T1 * T2^5, (T1^-1 * T2^-1)^4 ] Map:: non-degenerate R = (1, 21, 3, 23, 9, 29, 16, 36, 18, 38, 12, 32, 4, 24, 10, 30, 6, 26, 14, 34, 20, 40, 17, 37, 11, 31, 8, 28, 2, 22, 7, 27, 15, 35, 19, 39, 13, 33, 5, 25) L = (1, 22)(2, 26)(3, 27)(4, 21)(5, 28)(6, 29)(7, 34)(8, 30)(9, 35)(10, 23)(11, 24)(12, 25)(13, 31)(14, 36)(15, 40)(16, 39)(17, 32)(18, 33)(19, 37)(20, 38) local type(s) :: { ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E7.180 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 20 f = 7 degree seq :: [ 40 ] E7.185 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 10, 20}) Quotient :: loop Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, T2^4, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-5, (T1^-1 * T2^-1)^10 ] Map:: non-degenerate R = (1, 21, 3, 23, 9, 29, 5, 25)(2, 22, 7, 27, 16, 36, 8, 28)(4, 24, 10, 30, 17, 37, 12, 32)(6, 26, 14, 34, 20, 40, 15, 35)(11, 31, 13, 33, 19, 39, 18, 38) L = (1, 22)(2, 26)(3, 27)(4, 21)(5, 28)(6, 33)(7, 34)(8, 35)(9, 36)(10, 23)(11, 24)(12, 25)(13, 30)(14, 39)(15, 31)(16, 40)(17, 29)(18, 32)(19, 37)(20, 38) local type(s) :: { ( 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E7.181 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 20 f = 3 degree seq :: [ 8^5 ] E7.186 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y1, Y2), Y1^4, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1^2 * Y2^-5, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: 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, 44)(2, 41)(3, 50)(4, 46)(5, 51)(6, 42)(7, 43)(8, 45)(9, 58)(10, 53)(11, 54)(12, 59)(13, 47)(14, 48)(15, 49)(16, 52)(17, 56)(18, 60)(19, 57)(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) :: { ( 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 E7.189 Graph:: bipartite v = 7 e = 40 f = 21 degree seq :: [ 8^5, 20^2 ] E7.187 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), Y2^2 * Y1^-3, Y1 * Y2^6, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 21, 2, 22, 6, 26, 9, 29, 15, 35, 20, 40, 18, 38, 13, 33, 11, 31, 4, 24)(3, 23, 7, 27, 14, 34, 16, 36, 19, 39, 17, 37, 12, 32, 5, 25, 8, 28, 10, 30)(41, 61, 43, 63, 49, 69, 56, 76, 58, 78, 52, 72, 44, 64, 50, 70, 46, 66, 54, 74, 60, 80, 57, 77, 51, 71, 48, 68, 42, 62, 47, 67, 55, 75, 59, 79, 53, 73, 45, 65) L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 54)(7, 55)(8, 42)(9, 56)(10, 46)(11, 48)(12, 44)(13, 45)(14, 60)(15, 59)(16, 58)(17, 51)(18, 52)(19, 53)(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) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E7.188 Graph:: bipartite v = 3 e = 40 f = 25 degree seq :: [ 20^2, 40 ] E7.188 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, (Y2, Y3^-1), 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^-1 * Y1^-1)^20 ] Map:: R = (1, 21)(2, 22)(3, 23)(4, 24)(5, 25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)(41, 61, 42, 62, 46, 66, 44, 64)(43, 63, 47, 67, 53, 73, 50, 70)(45, 65, 48, 68, 54, 74, 51, 71)(49, 69, 55, 75, 59, 79, 58, 78)(52, 72, 56, 76, 60, 80, 57, 77) L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 53)(7, 55)(8, 42)(9, 57)(10, 58)(11, 44)(12, 45)(13, 59)(14, 46)(15, 52)(16, 48)(17, 51)(18, 60)(19, 56)(20, 54)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E7.187 Graph:: simple bipartite v = 25 e = 40 f = 3 degree seq :: [ 2^20, 8^5 ] E7.189 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, Y3^4, (Y3^-1, Y1^-1), Y3 * Y1^-5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, (Y1^-1 * Y3^-1)^10 ] Map:: R = (1, 21, 2, 22, 6, 26, 13, 33, 10, 30, 3, 23, 7, 27, 14, 34, 19, 39, 17, 37, 9, 29, 16, 36, 20, 40, 18, 38, 12, 32, 5, 25, 8, 28, 15, 35, 11, 31, 4, 24)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 66)(47, 67)(48, 68)(49, 69)(50, 70)(51, 71)(52, 72)(53, 73)(54, 74)(55, 75)(56, 76)(57, 77)(58, 78)(59, 79)(60, 80) L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 54)(7, 56)(8, 42)(9, 45)(10, 57)(11, 53)(12, 44)(13, 59)(14, 60)(15, 46)(16, 48)(17, 52)(18, 51)(19, 58)(20, 55)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E7.186 Graph:: bipartite v = 21 e = 40 f = 7 degree seq :: [ 2^20, 40 ] E7.190 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^4, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^5 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 7, 27, 13, 33, 10, 30)(5, 25, 8, 28, 14, 34, 11, 31)(9, 29, 15, 35, 19, 39, 17, 37)(12, 32, 16, 36, 20, 40, 18, 38)(41, 61, 43, 63, 49, 69, 56, 76, 48, 68, 42, 62, 47, 67, 55, 75, 60, 80, 54, 74, 46, 66, 53, 73, 59, 79, 58, 78, 51, 71, 44, 64, 50, 70, 57, 77, 52, 72, 45, 65) L = (1, 44)(2, 41)(3, 50)(4, 46)(5, 51)(6, 42)(7, 43)(8, 45)(9, 57)(10, 53)(11, 54)(12, 58)(13, 47)(14, 48)(15, 49)(16, 52)(17, 59)(18, 60)(19, 55)(20, 56)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 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 E7.191 Graph:: bipartite v = 6 e = 40 f = 22 degree seq :: [ 8^5, 40 ] E7.191 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^5, (Y1^-1 * Y3^-1)^4, (Y3 * Y2^-1)^20 ] Map:: R = (1, 21, 2, 22, 6, 26, 9, 29, 15, 35, 20, 40, 18, 38, 13, 33, 11, 31, 4, 24)(3, 23, 7, 27, 14, 34, 16, 36, 19, 39, 17, 37, 12, 32, 5, 25, 8, 28, 10, 30)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 66)(47, 67)(48, 68)(49, 69)(50, 70)(51, 71)(52, 72)(53, 73)(54, 74)(55, 75)(56, 76)(57, 77)(58, 78)(59, 79)(60, 80) L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 54)(7, 55)(8, 42)(9, 56)(10, 46)(11, 48)(12, 44)(13, 45)(14, 60)(15, 59)(16, 58)(17, 51)(18, 52)(19, 53)(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, 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 E7.190 Graph:: simple bipartite v = 22 e = 40 f = 6 degree seq :: [ 2^20, 20^2 ] E7.192 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 21, 21}) Quotient :: edge Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^7 * T1^-1, (T1^-1 * T2^-1)^21 ] Map:: non-degenerate R = (1, 3, 8, 14, 19, 13, 7, 2, 6, 12, 18, 21, 16, 10, 4, 9, 15, 20, 17, 11, 5)(22, 23, 25)(24, 27, 30)(26, 28, 31)(29, 33, 36)(32, 34, 37)(35, 39, 41)(38, 40, 42) L = (1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42) local type(s) :: { ( 42^3 ), ( 42^21 ) } Outer automorphisms :: reflexible Dual of E7.193 Transitivity :: ET+ Graph:: bipartite v = 8 e = 21 f = 1 degree seq :: [ 3^7, 21 ] E7.193 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 21, 21}) Quotient :: loop Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^7 * T1^-1, (T1^-1 * T2^-1)^21 ] Map:: non-degenerate R = (1, 22, 3, 24, 8, 29, 14, 35, 19, 40, 13, 34, 7, 28, 2, 23, 6, 27, 12, 33, 18, 39, 21, 42, 16, 37, 10, 31, 4, 25, 9, 30, 15, 36, 20, 41, 17, 38, 11, 32, 5, 26) L = (1, 23)(2, 25)(3, 27)(4, 22)(5, 28)(6, 30)(7, 31)(8, 33)(9, 24)(10, 26)(11, 34)(12, 36)(13, 37)(14, 39)(15, 29)(16, 32)(17, 40)(18, 41)(19, 42)(20, 35)(21, 38) local type(s) :: { ( 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21 ) } Outer automorphisms :: reflexible Dual of E7.192 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 21 f = 8 degree seq :: [ 42 ] E7.194 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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^-1 * Y1^-1, Y1^3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), 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 ] 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, 46)(2, 43)(3, 51)(4, 44)(5, 52)(6, 45)(7, 47)(8, 57)(9, 48)(10, 49)(11, 58)(12, 50)(13, 53)(14, 62)(15, 54)(16, 55)(17, 63)(18, 56)(19, 59)(20, 60)(21, 61)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 2, 42, 2, 42, 2, 42 ), ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E7.195 Graph:: bipartite v = 8 e = 42 f = 22 degree seq :: [ 6^7, 42 ] E7.195 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^-7, (Y1^-1 * Y3^-1)^21 ] Map:: R = (1, 22, 2, 23, 6, 27, 12, 33, 18, 39, 15, 36, 9, 30, 3, 24, 7, 28, 13, 34, 19, 40, 21, 42, 17, 38, 11, 32, 5, 26, 8, 29, 14, 35, 20, 41, 16, 37, 10, 31, 4, 25)(43, 64)(44, 65)(45, 66)(46, 67)(47, 68)(48, 69)(49, 70)(50, 71)(51, 72)(52, 73)(53, 74)(54, 75)(55, 76)(56, 77)(57, 78)(58, 79)(59, 80)(60, 81)(61, 82)(62, 83)(63, 84) L = (1, 45)(2, 49)(3, 47)(4, 51)(5, 43)(6, 55)(7, 50)(8, 44)(9, 53)(10, 57)(11, 46)(12, 61)(13, 56)(14, 48)(15, 59)(16, 60)(17, 52)(18, 63)(19, 62)(20, 54)(21, 58)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 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 Dual of E7.194 Graph:: bipartite v = 22 e = 42 f = 8 degree seq :: [ 2^21, 42 ] E7.196 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = C4 x S3 (small group id <24, 5>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ Y2^2, Y3^2, R^2, Y1^4, (Y3 * Y2)^2, Y3 * Y1^2 * Y2, (R * Y1)^2, R * Y2 * R * Y3, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 26, 2, 30, 6, 29, 5, 25)(3, 33, 9, 28, 4, 34, 10, 27)(7, 35, 11, 32, 8, 36, 12, 31)(13, 41, 17, 38, 14, 42, 18, 37)(15, 43, 19, 40, 16, 44, 20, 39)(21, 47, 23, 46, 22, 48, 24, 45) L = (1, 3)(2, 7)(4, 6)(5, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 28)(26, 32)(27, 30)(29, 31)(33, 38)(34, 37)(35, 40)(36, 39)(41, 46)(42, 45)(43, 48)(44, 47) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 6 e = 24 f = 6 degree seq :: [ 8^6 ] E7.197 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, R * Y2 * R * Y3, Y1^4, (R * Y1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: R = (1, 26, 2, 29, 5, 28, 4, 25)(3, 31, 7, 34, 10, 32, 8, 27)(6, 35, 11, 33, 9, 36, 12, 30)(13, 41, 17, 38, 14, 42, 18, 37)(15, 43, 19, 40, 16, 44, 20, 39)(21, 47, 23, 46, 22, 48, 24, 45) 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, 27)(26, 30)(28, 33)(29, 34)(31, 37)(32, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 6 e = 24 f = 6 degree seq :: [ 8^6 ] E7.198 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, Y1^4, R * Y2 * R * Y3, (R * Y1)^2, Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1 ] Map:: R = (1, 26, 2, 29, 5, 28, 4, 25)(3, 31, 7, 34, 10, 32, 8, 27)(6, 35, 11, 33, 9, 36, 12, 30)(13, 41, 17, 38, 14, 42, 18, 37)(15, 43, 19, 40, 16, 44, 20, 39)(21, 48, 24, 46, 22, 47, 23, 45) 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, 27)(26, 30)(28, 33)(29, 34)(31, 37)(32, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 6 e = 24 f = 6 degree seq :: [ 8^6 ] E7.199 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C4 x S3 (small group id <24, 5>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, Y3^4, Y3^2 * Y2 * Y1, Y2 * Y3^2 * Y1, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 25, 4, 28, 6, 30, 5, 29)(2, 26, 7, 31, 3, 27, 8, 32)(9, 33, 13, 37, 10, 34, 14, 38)(11, 35, 15, 39, 12, 36, 16, 40)(17, 41, 21, 45, 18, 42, 22, 46)(19, 43, 23, 47, 20, 44, 24, 48)(49, 50)(51, 54)(52, 57)(53, 58)(55, 59)(56, 60)(61, 65)(62, 66)(63, 67)(64, 68)(69, 71)(70, 72)(73, 75)(74, 78)(76, 82)(77, 81)(79, 84)(80, 83)(85, 90)(86, 89)(87, 92)(88, 91)(93, 96)(94, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E7.205 Graph:: simple bipartite v = 30 e = 48 f = 6 degree seq :: [ 2^24, 8^6 ] E7.200 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 25, 3, 27, 8, 32, 4, 28)(2, 26, 5, 29, 11, 35, 6, 30)(7, 31, 13, 37, 9, 33, 14, 38)(10, 34, 15, 39, 12, 36, 16, 40)(17, 41, 21, 45, 18, 42, 22, 46)(19, 43, 23, 47, 20, 44, 24, 48)(49, 50)(51, 55)(52, 57)(53, 58)(54, 60)(56, 59)(61, 65)(62, 66)(63, 67)(64, 68)(69, 71)(70, 72)(73, 74)(75, 79)(76, 81)(77, 82)(78, 84)(80, 83)(85, 89)(86, 90)(87, 91)(88, 92)(93, 95)(94, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E7.206 Graph:: simple bipartite v = 30 e = 48 f = 6 degree seq :: [ 2^24, 8^6 ] E7.201 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 25, 3, 27, 8, 32, 4, 28)(2, 26, 5, 29, 11, 35, 6, 30)(7, 31, 13, 37, 9, 33, 14, 38)(10, 34, 15, 39, 12, 36, 16, 40)(17, 41, 21, 45, 18, 42, 22, 46)(19, 43, 23, 47, 20, 44, 24, 48)(49, 50)(51, 55)(52, 57)(53, 58)(54, 60)(56, 59)(61, 65)(62, 66)(63, 67)(64, 68)(69, 72)(70, 71)(73, 74)(75, 79)(76, 81)(77, 82)(78, 84)(80, 83)(85, 89)(86, 90)(87, 91)(88, 92)(93, 96)(94, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E7.207 Graph:: simple bipartite v = 30 e = 48 f = 6 degree seq :: [ 2^24, 8^6 ] E7.202 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C4 x S3 (small group id <24, 5>) Aut = C2 x C4 x S3 (small group id <48, 35>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, Y1^4, Y2^4, (R * Y3)^2, (Y3 * Y1^-2)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 4, 28)(2, 26, 6, 30)(3, 27, 7, 31)(5, 29, 10, 34)(8, 32, 13, 37)(9, 33, 14, 38)(11, 35, 15, 39)(12, 36, 16, 40)(17, 41, 21, 45)(18, 42, 22, 46)(19, 43, 23, 47)(20, 44, 24, 48)(49, 50, 53, 51)(52, 56, 58, 57)(54, 59, 55, 60)(61, 65, 62, 66)(63, 67, 64, 68)(69, 71, 70, 72)(73, 75, 77, 74)(76, 81, 82, 80)(78, 84, 79, 83)(85, 90, 86, 89)(87, 92, 88, 91)(93, 96, 94, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E7.208 Graph:: simple bipartite v = 24 e = 48 f = 12 degree seq :: [ 4^24 ] E7.203 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y2^4, Y1 * Y3 * Y1^-2 * Y3 * Y1, (Y1^-1 * Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 25, 3, 27)(2, 26, 6, 30)(4, 28, 9, 33)(5, 29, 10, 34)(7, 31, 13, 37)(8, 32, 14, 38)(11, 35, 15, 39)(12, 36, 16, 40)(17, 41, 21, 45)(18, 42, 22, 46)(19, 43, 23, 47)(20, 44, 24, 48)(49, 50, 53, 52)(51, 55, 58, 56)(54, 59, 57, 60)(61, 65, 62, 66)(63, 67, 64, 68)(69, 71, 70, 72)(73, 74, 77, 76)(75, 79, 82, 80)(78, 83, 81, 84)(85, 89, 86, 90)(87, 91, 88, 92)(93, 95, 94, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E7.209 Graph:: simple bipartite v = 24 e = 48 f = 12 degree seq :: [ 4^24 ] E7.204 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y2^4, Y2^-1 * Y3 * Y1^2 * Y3 * Y1^-1, (Y1^-1 * Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 25, 3, 27)(2, 26, 6, 30)(4, 28, 9, 33)(5, 29, 10, 34)(7, 31, 13, 37)(8, 32, 14, 38)(11, 35, 15, 39)(12, 36, 16, 40)(17, 41, 21, 45)(18, 42, 22, 46)(19, 43, 23, 47)(20, 44, 24, 48)(49, 50, 53, 52)(51, 55, 58, 56)(54, 59, 57, 60)(61, 65, 62, 66)(63, 67, 64, 68)(69, 72, 70, 71)(73, 74, 77, 76)(75, 79, 82, 80)(78, 83, 81, 84)(85, 89, 86, 90)(87, 91, 88, 92)(93, 96, 94, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E7.210 Graph:: simple bipartite v = 24 e = 48 f = 12 degree seq :: [ 4^24 ] E7.205 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C4 x S3 (small group id <24, 5>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, Y3^4, Y3^2 * Y2 * Y1, Y2 * Y3^2 * Y1, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 25, 49, 73, 4, 28, 52, 76, 6, 30, 54, 78, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 3, 27, 51, 75, 8, 32, 56, 80)(9, 33, 57, 81, 13, 37, 61, 85, 10, 34, 58, 82, 14, 38, 62, 86)(11, 35, 59, 83, 15, 39, 63, 87, 12, 36, 60, 84, 16, 40, 64, 88)(17, 41, 65, 89, 21, 45, 69, 93, 18, 42, 66, 90, 22, 46, 70, 94)(19, 43, 67, 91, 23, 47, 71, 95, 20, 44, 68, 92, 24, 48, 72, 96) L = (1, 26)(2, 25)(3, 30)(4, 33)(5, 34)(6, 27)(7, 35)(8, 36)(9, 28)(10, 29)(11, 31)(12, 32)(13, 41)(14, 42)(15, 43)(16, 44)(17, 37)(18, 38)(19, 39)(20, 40)(21, 47)(22, 48)(23, 45)(24, 46)(49, 75)(50, 78)(51, 73)(52, 82)(53, 81)(54, 74)(55, 84)(56, 83)(57, 77)(58, 76)(59, 80)(60, 79)(61, 90)(62, 89)(63, 92)(64, 91)(65, 86)(66, 85)(67, 88)(68, 87)(69, 96)(70, 95)(71, 94)(72, 93) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E7.199 Transitivity :: VT+ Graph:: bipartite v = 6 e = 48 f = 30 degree seq :: [ 16^6 ] E7.206 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 25, 49, 73, 3, 27, 51, 75, 8, 32, 56, 80, 4, 28, 52, 76)(2, 26, 50, 74, 5, 29, 53, 77, 11, 35, 59, 83, 6, 30, 54, 78)(7, 31, 55, 79, 13, 37, 61, 85, 9, 33, 57, 81, 14, 38, 62, 86)(10, 34, 58, 82, 15, 39, 63, 87, 12, 36, 60, 84, 16, 40, 64, 88)(17, 41, 65, 89, 21, 45, 69, 93, 18, 42, 66, 90, 22, 46, 70, 94)(19, 43, 67, 91, 23, 47, 71, 95, 20, 44, 68, 92, 24, 48, 72, 96) L = (1, 26)(2, 25)(3, 31)(4, 33)(5, 34)(6, 36)(7, 27)(8, 35)(9, 28)(10, 29)(11, 32)(12, 30)(13, 41)(14, 42)(15, 43)(16, 44)(17, 37)(18, 38)(19, 39)(20, 40)(21, 47)(22, 48)(23, 45)(24, 46)(49, 74)(50, 73)(51, 79)(52, 81)(53, 82)(54, 84)(55, 75)(56, 83)(57, 76)(58, 77)(59, 80)(60, 78)(61, 89)(62, 90)(63, 91)(64, 92)(65, 85)(66, 86)(67, 87)(68, 88)(69, 95)(70, 96)(71, 93)(72, 94) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E7.200 Transitivity :: VT+ Graph:: bipartite v = 6 e = 48 f = 30 degree seq :: [ 16^6 ] E7.207 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 25, 49, 73, 3, 27, 51, 75, 8, 32, 56, 80, 4, 28, 52, 76)(2, 26, 50, 74, 5, 29, 53, 77, 11, 35, 59, 83, 6, 30, 54, 78)(7, 31, 55, 79, 13, 37, 61, 85, 9, 33, 57, 81, 14, 38, 62, 86)(10, 34, 58, 82, 15, 39, 63, 87, 12, 36, 60, 84, 16, 40, 64, 88)(17, 41, 65, 89, 21, 45, 69, 93, 18, 42, 66, 90, 22, 46, 70, 94)(19, 43, 67, 91, 23, 47, 71, 95, 20, 44, 68, 92, 24, 48, 72, 96) L = (1, 26)(2, 25)(3, 31)(4, 33)(5, 34)(6, 36)(7, 27)(8, 35)(9, 28)(10, 29)(11, 32)(12, 30)(13, 41)(14, 42)(15, 43)(16, 44)(17, 37)(18, 38)(19, 39)(20, 40)(21, 48)(22, 47)(23, 46)(24, 45)(49, 74)(50, 73)(51, 79)(52, 81)(53, 82)(54, 84)(55, 75)(56, 83)(57, 76)(58, 77)(59, 80)(60, 78)(61, 89)(62, 90)(63, 91)(64, 92)(65, 85)(66, 86)(67, 87)(68, 88)(69, 96)(70, 95)(71, 94)(72, 93) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E7.201 Transitivity :: VT+ Graph:: bipartite v = 6 e = 48 f = 30 degree seq :: [ 16^6 ] E7.208 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C4 x S3 (small group id <24, 5>) Aut = C2 x C4 x S3 (small group id <48, 35>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, Y1^4, Y2^4, (R * Y3)^2, (Y3 * Y1^-2)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76)(2, 26, 50, 74, 6, 30, 54, 78)(3, 27, 51, 75, 7, 31, 55, 79)(5, 29, 53, 77, 10, 34, 58, 82)(8, 32, 56, 80, 13, 37, 61, 85)(9, 33, 57, 81, 14, 38, 62, 86)(11, 35, 59, 83, 15, 39, 63, 87)(12, 36, 60, 84, 16, 40, 64, 88)(17, 41, 65, 89, 21, 45, 69, 93)(18, 42, 66, 90, 22, 46, 70, 94)(19, 43, 67, 91, 23, 47, 71, 95)(20, 44, 68, 92, 24, 48, 72, 96) L = (1, 26)(2, 29)(3, 25)(4, 32)(5, 27)(6, 35)(7, 36)(8, 34)(9, 28)(10, 33)(11, 31)(12, 30)(13, 41)(14, 42)(15, 43)(16, 44)(17, 38)(18, 37)(19, 40)(20, 39)(21, 47)(22, 48)(23, 46)(24, 45)(49, 75)(50, 73)(51, 77)(52, 81)(53, 74)(54, 84)(55, 83)(56, 76)(57, 82)(58, 80)(59, 78)(60, 79)(61, 90)(62, 89)(63, 92)(64, 91)(65, 85)(66, 86)(67, 87)(68, 88)(69, 96)(70, 95)(71, 93)(72, 94) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.202 Transitivity :: VT+ Graph:: bipartite v = 12 e = 48 f = 24 degree seq :: [ 8^12 ] E7.209 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y2^4, Y1 * Y3 * Y1^-2 * Y3 * Y1, (Y1^-1 * Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 25, 49, 73, 3, 27, 51, 75)(2, 26, 50, 74, 6, 30, 54, 78)(4, 28, 52, 76, 9, 33, 57, 81)(5, 29, 53, 77, 10, 34, 58, 82)(7, 31, 55, 79, 13, 37, 61, 85)(8, 32, 56, 80, 14, 38, 62, 86)(11, 35, 59, 83, 15, 39, 63, 87)(12, 36, 60, 84, 16, 40, 64, 88)(17, 41, 65, 89, 21, 45, 69, 93)(18, 42, 66, 90, 22, 46, 70, 94)(19, 43, 67, 91, 23, 47, 71, 95)(20, 44, 68, 92, 24, 48, 72, 96) L = (1, 26)(2, 29)(3, 31)(4, 25)(5, 28)(6, 35)(7, 34)(8, 27)(9, 36)(10, 32)(11, 33)(12, 30)(13, 41)(14, 42)(15, 43)(16, 44)(17, 38)(18, 37)(19, 40)(20, 39)(21, 47)(22, 48)(23, 46)(24, 45)(49, 74)(50, 77)(51, 79)(52, 73)(53, 76)(54, 83)(55, 82)(56, 75)(57, 84)(58, 80)(59, 81)(60, 78)(61, 89)(62, 90)(63, 91)(64, 92)(65, 86)(66, 85)(67, 88)(68, 87)(69, 95)(70, 96)(71, 94)(72, 93) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.203 Transitivity :: VT+ Graph:: bipartite v = 12 e = 48 f = 24 degree seq :: [ 8^12 ] E7.210 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y2^4, Y2^-1 * Y3 * Y1^2 * Y3 * Y1^-1, (Y1^-1 * Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 25, 49, 73, 3, 27, 51, 75)(2, 26, 50, 74, 6, 30, 54, 78)(4, 28, 52, 76, 9, 33, 57, 81)(5, 29, 53, 77, 10, 34, 58, 82)(7, 31, 55, 79, 13, 37, 61, 85)(8, 32, 56, 80, 14, 38, 62, 86)(11, 35, 59, 83, 15, 39, 63, 87)(12, 36, 60, 84, 16, 40, 64, 88)(17, 41, 65, 89, 21, 45, 69, 93)(18, 42, 66, 90, 22, 46, 70, 94)(19, 43, 67, 91, 23, 47, 71, 95)(20, 44, 68, 92, 24, 48, 72, 96) L = (1, 26)(2, 29)(3, 31)(4, 25)(5, 28)(6, 35)(7, 34)(8, 27)(9, 36)(10, 32)(11, 33)(12, 30)(13, 41)(14, 42)(15, 43)(16, 44)(17, 38)(18, 37)(19, 40)(20, 39)(21, 48)(22, 47)(23, 45)(24, 46)(49, 74)(50, 77)(51, 79)(52, 73)(53, 76)(54, 83)(55, 82)(56, 75)(57, 84)(58, 80)(59, 81)(60, 78)(61, 89)(62, 90)(63, 91)(64, 92)(65, 86)(66, 85)(67, 88)(68, 87)(69, 96)(70, 95)(71, 93)(72, 94) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.204 Transitivity :: VT+ Graph:: bipartite v = 12 e = 48 f = 24 degree seq :: [ 8^12 ] E7.211 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 9, 33)(5, 29, 10, 34)(6, 30, 12, 36)(8, 32, 11, 35)(13, 37, 17, 41)(14, 38, 18, 42)(15, 39, 19, 43)(16, 40, 20, 44)(21, 45, 23, 47)(22, 46, 24, 48)(49, 73, 51, 75, 56, 80, 52, 76)(50, 74, 53, 77, 59, 83, 54, 78)(55, 79, 61, 85, 57, 81, 62, 86)(58, 82, 63, 87, 60, 84, 64, 88)(65, 89, 69, 93, 66, 90, 70, 94)(67, 91, 71, 95, 68, 92, 72, 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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 18 e = 48 f = 18 degree seq :: [ 4^12, 8^6 ] E7.212 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, Y2^4, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 9, 33)(5, 29, 10, 34)(6, 30, 12, 36)(8, 32, 11, 35)(13, 37, 17, 41)(14, 38, 18, 42)(15, 39, 19, 43)(16, 40, 20, 44)(21, 45, 24, 48)(22, 46, 23, 47)(49, 73, 51, 75, 56, 80, 52, 76)(50, 74, 53, 77, 59, 83, 54, 78)(55, 79, 61, 85, 57, 81, 62, 86)(58, 82, 63, 87, 60, 84, 64, 88)(65, 89, 69, 93, 66, 90, 70, 94)(67, 91, 71, 95, 68, 92, 72, 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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 18 e = 48 f = 18 degree seq :: [ 4^12, 8^6 ] E7.213 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^2 * Y3, (R * Y1)^2, (Y1 * Y3)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 9, 33)(4, 28, 7, 31)(5, 29, 10, 34)(6, 30, 11, 35)(8, 32, 12, 36)(13, 37, 17, 41)(14, 38, 18, 42)(15, 39, 19, 43)(16, 40, 20, 44)(21, 45, 23, 47)(22, 46, 24, 48)(49, 73, 51, 75, 52, 76, 53, 77)(50, 74, 54, 78, 55, 79, 56, 80)(57, 81, 61, 85, 58, 82, 62, 86)(59, 83, 63, 87, 60, 84, 64, 88)(65, 89, 69, 93, 66, 90, 70, 94)(67, 91, 71, 95, 68, 92, 72, 96) L = (1, 52)(2, 55)(3, 53)(4, 49)(5, 51)(6, 56)(7, 50)(8, 54)(9, 58)(10, 57)(11, 60)(12, 59)(13, 62)(14, 61)(15, 64)(16, 63)(17, 66)(18, 65)(19, 68)(20, 67)(21, 70)(22, 69)(23, 72)(24, 71)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 18 e = 48 f = 18 degree seq :: [ 4^12, 8^6 ] E7.214 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^2 * Y3, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 9, 33)(4, 28, 7, 31)(5, 29, 10, 34)(6, 30, 11, 35)(8, 32, 12, 36)(13, 37, 17, 41)(14, 38, 18, 42)(15, 39, 19, 43)(16, 40, 20, 44)(21, 45, 24, 48)(22, 46, 23, 47)(49, 73, 51, 75, 52, 76, 53, 77)(50, 74, 54, 78, 55, 79, 56, 80)(57, 81, 61, 85, 58, 82, 62, 86)(59, 83, 63, 87, 60, 84, 64, 88)(65, 89, 69, 93, 66, 90, 70, 94)(67, 91, 71, 95, 68, 92, 72, 96) L = (1, 52)(2, 55)(3, 53)(4, 49)(5, 51)(6, 56)(7, 50)(8, 54)(9, 58)(10, 57)(11, 60)(12, 59)(13, 62)(14, 61)(15, 64)(16, 63)(17, 66)(18, 65)(19, 68)(20, 67)(21, 70)(22, 69)(23, 72)(24, 71)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 18 e = 48 f = 18 degree seq :: [ 4^12, 8^6 ] E7.215 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (Y1 * Y3^-1)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y3)^2, Y2^4, Y2 * Y3 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 11, 35)(4, 28, 10, 34)(5, 29, 16, 40)(6, 30, 8, 32)(7, 31, 13, 37)(9, 33, 17, 41)(12, 36, 18, 42)(14, 38, 19, 43)(15, 39, 20, 44)(21, 45, 22, 46)(23, 47, 24, 48)(49, 73, 51, 75, 60, 84, 53, 77)(50, 74, 55, 79, 66, 90, 57, 81)(52, 76, 62, 86, 70, 94, 63, 87)(54, 78, 61, 85, 71, 95, 65, 89)(56, 80, 67, 91, 72, 96, 68, 92)(58, 82, 59, 83, 69, 93, 64, 88) L = (1, 52)(2, 56)(3, 61)(4, 54)(5, 65)(6, 49)(7, 59)(8, 58)(9, 64)(10, 50)(11, 67)(12, 70)(13, 62)(14, 51)(15, 53)(16, 68)(17, 63)(18, 72)(19, 55)(20, 57)(21, 66)(22, 71)(23, 60)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 18 e = 48 f = 18 degree seq :: [ 4^12, 8^6 ] E7.216 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y2^4, R * Y2 * Y3 * R * Y2^-1, Y2^-2 * Y3^-3, Y1 * Y2 * Y3 * Y1 * Y2 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 11, 35)(4, 28, 10, 34)(5, 29, 17, 41)(6, 30, 8, 32)(7, 31, 18, 42)(9, 33, 13, 37)(12, 36, 20, 44)(14, 38, 21, 45)(15, 39, 24, 48)(16, 40, 23, 47)(19, 43, 22, 46)(49, 73, 51, 75, 60, 84, 53, 77)(50, 74, 55, 79, 68, 92, 57, 81)(52, 76, 62, 86, 67, 91, 64, 88)(54, 78, 61, 85, 63, 87, 66, 90)(56, 80, 69, 93, 72, 96, 71, 95)(58, 82, 65, 89, 70, 94, 59, 83) L = (1, 52)(2, 56)(3, 61)(4, 63)(5, 66)(6, 49)(7, 65)(8, 70)(9, 59)(10, 50)(11, 69)(12, 67)(13, 64)(14, 51)(15, 60)(16, 53)(17, 71)(18, 62)(19, 54)(20, 72)(21, 55)(22, 68)(23, 57)(24, 58)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 18 e = 48 f = 18 degree seq :: [ 4^12, 8^6 ] E7.217 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ Y2^2, Y3^2, R^2, Y1^4, (Y3 * Y2)^2, Y3 * Y1^2 * Y2, (R * Y1)^2, R * Y2 * R * Y3, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 26, 2, 30, 6, 29, 5, 25)(3, 33, 9, 28, 4, 34, 10, 27)(7, 35, 11, 32, 8, 36, 12, 31)(13, 41, 17, 38, 14, 42, 18, 37)(15, 43, 19, 40, 16, 44, 20, 39)(21, 48, 24, 46, 22, 47, 23, 45) L = (1, 3)(2, 7)(4, 6)(5, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 28)(26, 32)(27, 30)(29, 31)(33, 38)(34, 37)(35, 40)(36, 39)(41, 46)(42, 45)(43, 48)(44, 47) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 6 e = 24 f = 6 degree seq :: [ 8^6 ] E7.218 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, Y3^4, Y3^2 * Y2 * Y1, Y2 * Y3^2 * Y1, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 25, 4, 28, 6, 30, 5, 29)(2, 26, 7, 31, 3, 27, 8, 32)(9, 33, 13, 37, 10, 34, 14, 38)(11, 35, 15, 39, 12, 36, 16, 40)(17, 41, 21, 45, 18, 42, 22, 46)(19, 43, 23, 47, 20, 44, 24, 48)(49, 50)(51, 54)(52, 57)(53, 58)(55, 59)(56, 60)(61, 65)(62, 66)(63, 67)(64, 68)(69, 72)(70, 71)(73, 75)(74, 78)(76, 82)(77, 81)(79, 84)(80, 83)(85, 90)(86, 89)(87, 92)(88, 91)(93, 95)(94, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E7.220 Graph:: simple bipartite v = 30 e = 48 f = 6 degree seq :: [ 2^24, 8^6 ] E7.219 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y1^4, Y2^2 * Y1^-2, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y3 * Y1^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 4, 28)(2, 26, 6, 30)(3, 27, 7, 31)(5, 29, 10, 34)(8, 32, 13, 37)(9, 33, 14, 38)(11, 35, 15, 39)(12, 36, 16, 40)(17, 41, 21, 45)(18, 42, 22, 46)(19, 43, 23, 47)(20, 44, 24, 48)(49, 50, 53, 51)(52, 56, 58, 57)(54, 59, 55, 60)(61, 65, 62, 66)(63, 67, 64, 68)(69, 72, 70, 71)(73, 75, 77, 74)(76, 81, 82, 80)(78, 84, 79, 83)(85, 90, 86, 89)(87, 92, 88, 91)(93, 95, 94, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E7.221 Graph:: simple bipartite v = 24 e = 48 f = 12 degree seq :: [ 4^24 ] E7.220 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, Y3^4, Y3^2 * Y2 * Y1, Y2 * Y3^2 * Y1, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 25, 49, 73, 4, 28, 52, 76, 6, 30, 54, 78, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 3, 27, 51, 75, 8, 32, 56, 80)(9, 33, 57, 81, 13, 37, 61, 85, 10, 34, 58, 82, 14, 38, 62, 86)(11, 35, 59, 83, 15, 39, 63, 87, 12, 36, 60, 84, 16, 40, 64, 88)(17, 41, 65, 89, 21, 45, 69, 93, 18, 42, 66, 90, 22, 46, 70, 94)(19, 43, 67, 91, 23, 47, 71, 95, 20, 44, 68, 92, 24, 48, 72, 96) L = (1, 26)(2, 25)(3, 30)(4, 33)(5, 34)(6, 27)(7, 35)(8, 36)(9, 28)(10, 29)(11, 31)(12, 32)(13, 41)(14, 42)(15, 43)(16, 44)(17, 37)(18, 38)(19, 39)(20, 40)(21, 48)(22, 47)(23, 46)(24, 45)(49, 75)(50, 78)(51, 73)(52, 82)(53, 81)(54, 74)(55, 84)(56, 83)(57, 77)(58, 76)(59, 80)(60, 79)(61, 90)(62, 89)(63, 92)(64, 91)(65, 86)(66, 85)(67, 88)(68, 87)(69, 95)(70, 96)(71, 93)(72, 94) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E7.218 Transitivity :: VT+ Graph:: bipartite v = 6 e = 48 f = 30 degree seq :: [ 16^6 ] E7.221 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y1^4, Y2^2 * Y1^-2, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y3 * Y1^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76)(2, 26, 50, 74, 6, 30, 54, 78)(3, 27, 51, 75, 7, 31, 55, 79)(5, 29, 53, 77, 10, 34, 58, 82)(8, 32, 56, 80, 13, 37, 61, 85)(9, 33, 57, 81, 14, 38, 62, 86)(11, 35, 59, 83, 15, 39, 63, 87)(12, 36, 60, 84, 16, 40, 64, 88)(17, 41, 65, 89, 21, 45, 69, 93)(18, 42, 66, 90, 22, 46, 70, 94)(19, 43, 67, 91, 23, 47, 71, 95)(20, 44, 68, 92, 24, 48, 72, 96) L = (1, 26)(2, 29)(3, 25)(4, 32)(5, 27)(6, 35)(7, 36)(8, 34)(9, 28)(10, 33)(11, 31)(12, 30)(13, 41)(14, 42)(15, 43)(16, 44)(17, 38)(18, 37)(19, 40)(20, 39)(21, 48)(22, 47)(23, 45)(24, 46)(49, 75)(50, 73)(51, 77)(52, 81)(53, 74)(54, 84)(55, 83)(56, 76)(57, 82)(58, 80)(59, 78)(60, 79)(61, 90)(62, 89)(63, 92)(64, 91)(65, 85)(66, 86)(67, 87)(68, 88)(69, 95)(70, 96)(71, 94)(72, 93) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.219 Transitivity :: VT+ Graph:: bipartite v = 12 e = 48 f = 24 degree seq :: [ 8^12 ] E7.222 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, Y2^4, Y3 * Y1 * Y2^-1 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 11, 35)(4, 28, 10, 34)(5, 29, 16, 40)(6, 30, 8, 32)(7, 31, 17, 41)(9, 33, 13, 37)(12, 36, 18, 42)(14, 38, 20, 44)(15, 39, 19, 43)(21, 45, 22, 46)(23, 47, 24, 48)(49, 73, 51, 75, 60, 84, 53, 77)(50, 74, 55, 79, 66, 90, 57, 81)(52, 76, 62, 86, 70, 94, 63, 87)(54, 78, 61, 85, 71, 95, 65, 89)(56, 80, 67, 91, 72, 96, 68, 92)(58, 82, 64, 88, 69, 93, 59, 83) L = (1, 52)(2, 56)(3, 61)(4, 54)(5, 65)(6, 49)(7, 64)(8, 58)(9, 59)(10, 50)(11, 68)(12, 70)(13, 62)(14, 51)(15, 53)(16, 67)(17, 63)(18, 72)(19, 55)(20, 57)(21, 66)(22, 71)(23, 60)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 18 e = 48 f = 18 degree seq :: [ 4^12, 8^6 ] E7.223 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y2^4, R * Y2 * Y3 * R * Y2^-1, Y2^-2 * Y3^-3, Y1 * Y2^-1 * Y3 * Y1 * Y2, Y2 * Y3^-2 * Y2 * Y3 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 11, 35)(4, 28, 10, 34)(5, 29, 17, 41)(6, 30, 8, 32)(7, 31, 13, 37)(9, 33, 18, 42)(12, 36, 20, 44)(14, 38, 23, 47)(15, 39, 24, 48)(16, 40, 21, 45)(19, 43, 22, 46)(49, 73, 51, 75, 60, 84, 53, 77)(50, 74, 55, 79, 68, 92, 57, 81)(52, 76, 62, 86, 67, 91, 64, 88)(54, 78, 61, 85, 63, 87, 66, 90)(56, 80, 69, 93, 72, 96, 71, 95)(58, 82, 59, 83, 70, 94, 65, 89) L = (1, 52)(2, 56)(3, 61)(4, 63)(5, 66)(6, 49)(7, 59)(8, 70)(9, 65)(10, 50)(11, 71)(12, 67)(13, 64)(14, 51)(15, 60)(16, 53)(17, 69)(18, 62)(19, 54)(20, 72)(21, 55)(22, 68)(23, 57)(24, 58)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 18 e = 48 f = 18 degree seq :: [ 4^12, 8^6 ] E7.224 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, R * Y2 * R * Y3, (R * Y1)^2, Y1^4, (Y2 * Y1)^3 ] Map:: R = (1, 26, 2, 29, 5, 28, 4, 25)(3, 31, 7, 37, 13, 32, 8, 27)(6, 35, 11, 42, 18, 36, 12, 30)(9, 39, 15, 44, 20, 38, 14, 33)(10, 40, 16, 45, 21, 41, 17, 34)(19, 47, 23, 48, 24, 46, 22, 43) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 11)(12, 16)(13, 19)(15, 17)(18, 22)(20, 23)(21, 24)(25, 27)(26, 30)(28, 33)(29, 34)(31, 38)(32, 35)(36, 40)(37, 43)(39, 41)(42, 46)(44, 47)(45, 48) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: v = 6 e = 24 f = 6 degree seq :: [ 8^6 ] E7.225 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, Y3^4, R * Y1 * R * Y2, (Y1 * Y3)^3, Y3^2 * Y1 * Y3^2 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 25, 3, 27, 8, 32, 4, 28)(2, 26, 5, 29, 11, 35, 6, 30)(7, 31, 12, 36, 18, 42, 13, 37)(9, 33, 15, 39, 16, 40, 10, 34)(14, 38, 19, 43, 23, 47, 20, 44)(17, 41, 21, 45, 24, 48, 22, 46)(49, 50)(51, 55)(52, 57)(53, 58)(54, 60)(56, 62)(59, 65)(61, 67)(63, 68)(64, 69)(66, 70)(71, 72)(73, 74)(75, 79)(76, 81)(77, 82)(78, 84)(80, 86)(83, 89)(85, 91)(87, 92)(88, 93)(90, 94)(95, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E7.227 Graph:: simple bipartite v = 30 e = 48 f = 6 degree seq :: [ 2^24, 8^6 ] E7.226 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1, R * Y1 * R * Y2, Y1^3 * Y2^-1, (R * Y3)^2, Y2^4, (Y1 * Y3)^3 ] Map:: non-degenerate R = (1, 25, 4, 28)(2, 26, 6, 30)(3, 27, 7, 31)(5, 29, 10, 34)(8, 32, 14, 38)(9, 33, 11, 35)(12, 36, 16, 40)(13, 37, 17, 41)(15, 39, 20, 44)(18, 42, 22, 46)(19, 43, 23, 47)(21, 45, 24, 48)(49, 50, 53, 51)(52, 56, 63, 57)(54, 59, 66, 60)(55, 61, 67, 62)(58, 64, 69, 65)(68, 71, 72, 70)(73, 75, 77, 74)(76, 81, 87, 80)(78, 84, 90, 83)(79, 86, 91, 85)(82, 89, 93, 88)(92, 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) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E7.228 Graph:: simple bipartite v = 24 e = 48 f = 12 degree seq :: [ 4^24 ] E7.227 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, Y3^4, R * Y1 * R * Y2, (Y1 * Y3)^3, Y3^2 * Y1 * Y3^2 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 25, 49, 73, 3, 27, 51, 75, 8, 32, 56, 80, 4, 28, 52, 76)(2, 26, 50, 74, 5, 29, 53, 77, 11, 35, 59, 83, 6, 30, 54, 78)(7, 31, 55, 79, 12, 36, 60, 84, 18, 42, 66, 90, 13, 37, 61, 85)(9, 33, 57, 81, 15, 39, 63, 87, 16, 40, 64, 88, 10, 34, 58, 82)(14, 38, 62, 86, 19, 43, 67, 91, 23, 47, 71, 95, 20, 44, 68, 92)(17, 41, 65, 89, 21, 45, 69, 93, 24, 48, 72, 96, 22, 46, 70, 94) L = (1, 26)(2, 25)(3, 31)(4, 33)(5, 34)(6, 36)(7, 27)(8, 38)(9, 28)(10, 29)(11, 41)(12, 30)(13, 43)(14, 32)(15, 44)(16, 45)(17, 35)(18, 46)(19, 37)(20, 39)(21, 40)(22, 42)(23, 48)(24, 47)(49, 74)(50, 73)(51, 79)(52, 81)(53, 82)(54, 84)(55, 75)(56, 86)(57, 76)(58, 77)(59, 89)(60, 78)(61, 91)(62, 80)(63, 92)(64, 93)(65, 83)(66, 94)(67, 85)(68, 87)(69, 88)(70, 90)(71, 96)(72, 95) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E7.225 Transitivity :: VT+ Graph:: v = 6 e = 48 f = 30 degree seq :: [ 16^6 ] E7.228 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1, R * Y1 * R * Y2, Y1^3 * Y2^-1, (R * Y3)^2, Y2^4, (Y1 * Y3)^3 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76)(2, 26, 50, 74, 6, 30, 54, 78)(3, 27, 51, 75, 7, 31, 55, 79)(5, 29, 53, 77, 10, 34, 58, 82)(8, 32, 56, 80, 14, 38, 62, 86)(9, 33, 57, 81, 11, 35, 59, 83)(12, 36, 60, 84, 16, 40, 64, 88)(13, 37, 61, 85, 17, 41, 65, 89)(15, 39, 63, 87, 20, 44, 68, 92)(18, 42, 66, 90, 22, 46, 70, 94)(19, 43, 67, 91, 23, 47, 71, 95)(21, 45, 69, 93, 24, 48, 72, 96) L = (1, 26)(2, 29)(3, 25)(4, 32)(5, 27)(6, 35)(7, 37)(8, 39)(9, 28)(10, 40)(11, 42)(12, 30)(13, 43)(14, 31)(15, 33)(16, 45)(17, 34)(18, 36)(19, 38)(20, 47)(21, 41)(22, 44)(23, 48)(24, 46)(49, 75)(50, 73)(51, 77)(52, 81)(53, 74)(54, 84)(55, 86)(56, 76)(57, 87)(58, 89)(59, 78)(60, 90)(61, 79)(62, 91)(63, 80)(64, 82)(65, 93)(66, 83)(67, 85)(68, 94)(69, 88)(70, 96)(71, 92)(72, 95) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.226 Transitivity :: VT+ Graph:: v = 12 e = 48 f = 24 degree seq :: [ 8^12 ] E7.229 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y1 * Y2)^3, (Y3 * Y2^-1)^4, Y2^2 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 ] Map:: R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 9, 33)(5, 29, 10, 34)(6, 30, 12, 36)(8, 32, 14, 38)(11, 35, 17, 41)(13, 37, 19, 43)(15, 39, 20, 44)(16, 40, 21, 45)(18, 42, 22, 46)(23, 47, 24, 48)(49, 73, 51, 75, 56, 80, 52, 76)(50, 74, 53, 77, 59, 83, 54, 78)(55, 79, 60, 84, 66, 90, 61, 85)(57, 81, 63, 87, 64, 88, 58, 82)(62, 86, 67, 91, 71, 95, 68, 92)(65, 89, 69, 93, 72, 96, 70, 94) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 18 e = 48 f = 18 degree seq :: [ 4^12, 8^6 ] E7.230 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2^-1 * Y3^-1)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y1 * Y2 * Y3^-1 * Y2^-1, Y1 * Y2^-1 * Y3 * Y1 * Y2, (R * Y2 * Y3^-1)^2 ] Map:: polytopal non-degenerate R = (1, 25, 2, 26)(3, 27, 11, 35)(4, 28, 10, 34)(5, 29, 17, 41)(6, 30, 8, 32)(7, 31, 19, 43)(9, 33, 18, 42)(12, 36, 16, 40)(13, 37, 23, 47)(14, 38, 22, 46)(15, 39, 21, 45)(20, 44, 24, 48)(49, 73, 51, 75, 60, 84, 53, 77)(50, 74, 55, 79, 62, 86, 57, 81)(52, 76, 63, 87, 71, 95, 64, 88)(54, 78, 67, 91, 65, 89, 61, 85)(56, 80, 69, 93, 72, 96, 70, 94)(58, 82, 59, 83, 66, 90, 68, 92) L = (1, 52)(2, 56)(3, 61)(4, 54)(5, 66)(6, 49)(7, 68)(8, 58)(9, 65)(10, 50)(11, 70)(12, 55)(13, 62)(14, 51)(15, 53)(16, 72)(17, 69)(18, 63)(19, 64)(20, 60)(21, 57)(22, 71)(23, 59)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 18 e = 48 f = 18 degree seq :: [ 4^12, 8^6 ] E7.231 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^-1 * Y2 * Y3 * Y2, Y3^-3 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 6, 30)(4, 28, 11, 35)(5, 29, 12, 36)(7, 31, 15, 39)(8, 32, 16, 40)(9, 33, 17, 41)(10, 34, 18, 42)(13, 37, 22, 46)(14, 38, 19, 43)(20, 44, 21, 45)(23, 47, 24, 48)(49, 73, 51, 75)(50, 74, 54, 78)(52, 76, 57, 81)(53, 77, 58, 82)(55, 79, 61, 85)(56, 80, 62, 86)(59, 83, 65, 89)(60, 84, 66, 90)(63, 87, 70, 94)(64, 88, 67, 91)(68, 92, 71, 95)(69, 93, 72, 96) L = (1, 52)(2, 55)(3, 57)(4, 58)(5, 49)(6, 61)(7, 62)(8, 50)(9, 53)(10, 51)(11, 67)(12, 69)(13, 56)(14, 54)(15, 66)(16, 68)(17, 64)(18, 72)(19, 71)(20, 59)(21, 63)(22, 60)(23, 65)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.241 Graph:: simple bipartite v = 24 e = 48 f = 12 degree seq :: [ 4^24 ] E7.232 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y1 * Y2)^2, Y1 * Y2 * Y3^-1 * Y1 * Y3, (R * Y2 * Y3^-1)^2, (Y2 * Y3)^3 ] Map:: polytopal non-degenerate R = (1, 25, 2, 26)(3, 27, 6, 30)(4, 28, 11, 35)(5, 29, 13, 37)(7, 31, 12, 36)(8, 32, 10, 34)(9, 33, 17, 41)(14, 38, 20, 44)(15, 39, 18, 42)(16, 40, 19, 43)(21, 45, 22, 46)(23, 47, 24, 48)(49, 73, 51, 75)(50, 74, 54, 78)(52, 76, 60, 84)(53, 77, 62, 86)(55, 79, 59, 83)(56, 80, 64, 88)(57, 81, 66, 90)(58, 82, 67, 91)(61, 85, 68, 92)(63, 87, 65, 89)(69, 93, 72, 96)(70, 94, 71, 95) L = (1, 52)(2, 55)(3, 57)(4, 53)(5, 49)(6, 63)(7, 56)(8, 50)(9, 58)(10, 51)(11, 68)(12, 67)(13, 54)(14, 71)(15, 61)(16, 72)(17, 64)(18, 62)(19, 70)(20, 69)(21, 59)(22, 60)(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, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.242 Graph:: simple bipartite v = 24 e = 48 f = 12 degree seq :: [ 4^24 ] E7.233 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y2)^2, (Y3 * Y1)^2, (R * Y1)^2, (Y1 * Y2^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 9, 33)(4, 28, 7, 31)(5, 29, 12, 36)(6, 30, 13, 37)(8, 32, 16, 40)(10, 34, 17, 41)(11, 35, 19, 43)(14, 38, 21, 45)(15, 39, 22, 46)(18, 42, 20, 44)(23, 47, 24, 48)(49, 73, 51, 75, 53, 77)(50, 74, 54, 78, 56, 80)(52, 76, 58, 82, 59, 83)(55, 79, 62, 86, 63, 87)(57, 81, 64, 88, 66, 90)(60, 84, 68, 92, 61, 85)(65, 89, 70, 94, 71, 95)(67, 91, 72, 96, 69, 93) L = (1, 52)(2, 55)(3, 58)(4, 49)(5, 59)(6, 62)(7, 50)(8, 63)(9, 65)(10, 51)(11, 53)(12, 67)(13, 69)(14, 54)(15, 56)(16, 70)(17, 57)(18, 71)(19, 60)(20, 72)(21, 61)(22, 64)(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, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.240 Graph:: simple bipartite v = 20 e = 48 f = 16 degree seq :: [ 4^12, 6^8 ] E7.234 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, Y3 * Y2^-1 * Y3 * Y2, (R * Y3)^2, (Y3 * Y1)^2, (R * Y2)^2, (R * Y1)^2, Y1 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y1 * Y2^-1, (Y2 * Y1 * Y2^-1 * Y1)^2 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 9, 33)(4, 28, 7, 31)(5, 29, 12, 36)(6, 30, 13, 37)(8, 32, 16, 40)(10, 34, 18, 42)(11, 35, 20, 44)(14, 38, 22, 46)(15, 39, 17, 41)(19, 43, 23, 47)(21, 45, 24, 48)(49, 73, 51, 75, 53, 77)(50, 74, 54, 78, 56, 80)(52, 76, 58, 82, 59, 83)(55, 79, 62, 86, 63, 87)(57, 81, 65, 89, 67, 91)(60, 84, 69, 93, 70, 94)(61, 85, 68, 92, 71, 95)(64, 88, 72, 96, 66, 90) L = (1, 52)(2, 55)(3, 58)(4, 49)(5, 59)(6, 62)(7, 50)(8, 63)(9, 66)(10, 51)(11, 53)(12, 68)(13, 70)(14, 54)(15, 56)(16, 65)(17, 64)(18, 57)(19, 72)(20, 60)(21, 71)(22, 61)(23, 69)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.238 Graph:: simple bipartite v = 20 e = 48 f = 16 degree seq :: [ 4^12, 6^8 ] E7.235 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1)^2, (R * Y2 * Y3)^2, R * Y2 * Y3 * Y2 * R * Y1 * Y2^-1, Y2 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 6, 30)(4, 28, 7, 31)(5, 29, 8, 32)(9, 33, 13, 37)(10, 34, 14, 38)(11, 35, 15, 39)(12, 36, 16, 40)(17, 41, 20, 44)(18, 42, 23, 47)(19, 43, 22, 46)(21, 45, 24, 48)(49, 73, 51, 75, 53, 77)(50, 74, 54, 78, 56, 80)(52, 76, 58, 82, 59, 83)(55, 79, 62, 86, 63, 87)(57, 81, 65, 89, 66, 90)(60, 84, 69, 93, 70, 94)(61, 85, 68, 92, 71, 95)(64, 88, 72, 96, 67, 91) L = (1, 52)(2, 55)(3, 57)(4, 49)(5, 60)(6, 61)(7, 50)(8, 64)(9, 51)(10, 67)(11, 68)(12, 53)(13, 54)(14, 70)(15, 65)(16, 56)(17, 63)(18, 72)(19, 58)(20, 59)(21, 71)(22, 62)(23, 69)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.239 Graph:: simple bipartite v = 20 e = 48 f = 16 degree seq :: [ 4^12, 6^8 ] E7.236 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y3 * Y2 * Y3 * Y1 * Y2^-1, Y2 * Y1 * R * Y2 * R * Y1, (R * Y2 * Y3)^2, (Y1 * Y2^-1)^3 ] Map:: polytopal non-degenerate R = (1, 25, 2, 26)(3, 27, 9, 33)(4, 28, 7, 31)(5, 29, 13, 37)(6, 30, 15, 39)(8, 32, 19, 43)(10, 34, 17, 41)(11, 35, 16, 40)(12, 36, 20, 44)(14, 38, 18, 42)(21, 45, 23, 47)(22, 46, 24, 48)(49, 73, 51, 75, 53, 77)(50, 74, 54, 78, 56, 80)(52, 76, 59, 83, 60, 84)(55, 79, 65, 89, 66, 90)(57, 81, 67, 91, 69, 93)(58, 82, 68, 92, 70, 94)(61, 85, 71, 95, 63, 87)(62, 86, 72, 96, 64, 88) L = (1, 52)(2, 55)(3, 58)(4, 49)(5, 62)(6, 64)(7, 50)(8, 68)(9, 65)(10, 51)(11, 63)(12, 67)(13, 66)(14, 53)(15, 59)(16, 54)(17, 57)(18, 61)(19, 60)(20, 56)(21, 72)(22, 71)(23, 70)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.237 Graph:: simple bipartite v = 20 e = 48 f = 16 degree seq :: [ 4^12, 6^8 ] E7.237 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^-3 * Y2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (Y3 * Y2)^2, (Y3 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 25, 2, 26, 6, 30, 3, 27, 7, 31, 5, 29)(4, 28, 10, 34, 18, 42, 9, 33, 17, 41, 11, 35)(8, 32, 15, 39, 24, 48, 14, 38, 23, 47, 16, 40)(12, 36, 20, 44, 22, 46, 13, 37, 21, 45, 19, 43)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 57, 81)(53, 77, 54, 78)(56, 80, 62, 86)(58, 82, 65, 89)(59, 83, 66, 90)(60, 84, 61, 85)(63, 87, 71, 95)(64, 88, 72, 96)(67, 91, 70, 94)(68, 92, 69, 93) L = (1, 52)(2, 56)(3, 57)(4, 49)(5, 60)(6, 61)(7, 62)(8, 50)(9, 51)(10, 67)(11, 63)(12, 53)(13, 54)(14, 55)(15, 59)(16, 69)(17, 70)(18, 71)(19, 58)(20, 72)(21, 64)(22, 65)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.236 Graph:: bipartite v = 16 e = 48 f = 20 degree seq :: [ 4^12, 12^4 ] E7.238 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y1^-3, Y3 * Y1 * Y3 * Y1^-1, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 4, 28, 8, 32, 5, 29)(3, 27, 9, 33, 17, 41, 10, 34, 19, 43, 11, 35)(7, 31, 14, 38, 24, 48, 15, 39, 20, 44, 16, 40)(12, 36, 21, 45, 18, 42, 13, 37, 23, 47, 22, 46)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 58, 82)(53, 77, 60, 84)(54, 78, 61, 85)(56, 80, 63, 87)(57, 81, 66, 90)(59, 83, 68, 92)(62, 86, 65, 89)(64, 88, 69, 93)(67, 91, 70, 94)(71, 95, 72, 96) L = (1, 52)(2, 56)(3, 58)(4, 49)(5, 54)(6, 53)(7, 63)(8, 50)(9, 67)(10, 51)(11, 65)(12, 61)(13, 60)(14, 68)(15, 55)(16, 72)(17, 59)(18, 70)(19, 57)(20, 62)(21, 71)(22, 66)(23, 69)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.234 Graph:: bipartite v = 16 e = 48 f = 20 degree seq :: [ 4^12, 12^4 ] E7.239 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, Y1^2 * Y3 * Y2 * Y1, (Y3 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 10, 34, 16, 40, 5, 29)(3, 27, 9, 33, 13, 37, 4, 28, 12, 36, 11, 35)(7, 31, 17, 41, 20, 44, 8, 32, 19, 43, 18, 42)(14, 38, 23, 47, 21, 45, 15, 39, 24, 48, 22, 46)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 58, 82)(53, 77, 62, 86)(54, 78, 63, 87)(56, 80, 64, 88)(57, 81, 69, 93)(59, 83, 67, 91)(60, 84, 70, 94)(61, 85, 65, 89)(66, 90, 71, 95)(68, 92, 72, 96) L = (1, 52)(2, 56)(3, 58)(4, 49)(5, 63)(6, 62)(7, 64)(8, 50)(9, 70)(10, 51)(11, 65)(12, 69)(13, 67)(14, 54)(15, 53)(16, 55)(17, 59)(18, 72)(19, 61)(20, 71)(21, 60)(22, 57)(23, 68)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.235 Graph:: bipartite v = 16 e = 48 f = 20 degree seq :: [ 4^12, 12^4 ] E7.240 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^-3 * Y3, Y1 * Y3 * Y1^-1 * Y3, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 4, 28, 8, 32, 5, 29)(3, 27, 9, 33, 17, 41, 10, 34, 19, 43, 11, 35)(7, 31, 14, 38, 23, 47, 15, 39, 24, 48, 16, 40)(12, 36, 20, 44, 22, 46, 13, 37, 21, 45, 18, 42)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 58, 82)(53, 77, 60, 84)(54, 78, 61, 85)(56, 80, 63, 87)(57, 81, 66, 90)(59, 83, 62, 86)(64, 88, 69, 93)(65, 89, 72, 96)(67, 91, 70, 94)(68, 92, 71, 95) L = (1, 52)(2, 56)(3, 58)(4, 49)(5, 54)(6, 53)(7, 63)(8, 50)(9, 67)(10, 51)(11, 65)(12, 61)(13, 60)(14, 72)(15, 55)(16, 71)(17, 59)(18, 70)(19, 57)(20, 69)(21, 68)(22, 66)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.233 Graph:: bipartite v = 16 e = 48 f = 20 degree seq :: [ 4^12, 12^4 ] E7.241 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^3, Y2 * Y3 * Y2, (Y2^-1 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y3 * Y2^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 12, 36, 13, 37)(4, 28, 15, 39, 16, 40)(6, 30, 19, 43, 8, 32)(7, 31, 20, 44, 9, 33)(10, 34, 22, 46, 17, 41)(11, 35, 23, 47, 18, 42)(14, 38, 21, 45, 24, 48)(49, 73, 51, 75, 55, 79, 62, 86, 52, 76, 54, 78)(50, 74, 56, 80, 59, 83, 69, 93, 57, 81, 58, 82)(53, 77, 65, 89, 63, 87, 72, 96, 66, 90, 60, 84)(61, 85, 71, 95, 67, 91, 64, 88, 70, 94, 68, 92) L = (1, 52)(2, 57)(3, 54)(4, 55)(5, 66)(6, 62)(7, 49)(8, 58)(9, 59)(10, 69)(11, 50)(12, 72)(13, 70)(14, 51)(15, 53)(16, 71)(17, 60)(18, 63)(19, 61)(20, 64)(21, 56)(22, 67)(23, 68)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4^6 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E7.231 Graph:: bipartite v = 12 e = 48 f = 24 degree seq :: [ 6^8, 12^4 ] E7.242 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^3, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^2, Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^6 ] Map:: polytopal non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 12, 36, 15, 39)(4, 28, 16, 40, 18, 42)(6, 30, 19, 43, 8, 32)(7, 31, 21, 45, 9, 33)(10, 34, 20, 44, 14, 38)(11, 35, 23, 47, 13, 37)(17, 41, 22, 46, 24, 48)(49, 73, 51, 75, 61, 85, 72, 96, 69, 93, 54, 78)(50, 74, 56, 80, 52, 76, 65, 89, 71, 95, 58, 82)(53, 77, 62, 86, 57, 81, 70, 94, 66, 90, 60, 84)(55, 79, 68, 92, 59, 83, 63, 87, 64, 88, 67, 91) L = (1, 52)(2, 57)(3, 62)(4, 55)(5, 61)(6, 68)(7, 49)(8, 51)(9, 59)(10, 63)(11, 50)(12, 67)(13, 64)(14, 56)(15, 72)(16, 53)(17, 60)(18, 71)(19, 65)(20, 70)(21, 66)(22, 54)(23, 69)(24, 58)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4^6 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E7.232 Graph:: bipartite v = 12 e = 48 f = 24 degree seq :: [ 6^8, 12^4 ] E7.243 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 12}) Quotient :: edge Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^6 ] Map:: non-degenerate R = (1, 3, 9, 17, 12, 5)(2, 7, 15, 22, 16, 8)(4, 10, 18, 23, 19, 11)(6, 13, 20, 24, 21, 14)(25, 26, 30, 28)(27, 31, 37, 34)(29, 32, 38, 35)(33, 39, 44, 42)(36, 40, 45, 43)(41, 46, 48, 47) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 24^4 ), ( 24^6 ) } Outer automorphisms :: reflexible Dual of E7.247 Transitivity :: ET+ Graph:: simple bipartite v = 10 e = 24 f = 2 degree seq :: [ 4^6, 6^4 ] E7.244 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 12}) Quotient :: edge Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T2^4 * T1^-2, T1^6 ] Map:: non-degenerate R = (1, 3, 9, 16, 6, 15, 24, 20, 11, 19, 13, 5)(2, 7, 17, 23, 14, 22, 21, 12, 4, 10, 18, 8)(25, 26, 30, 38, 35, 28)(27, 31, 39, 46, 43, 34)(29, 32, 40, 47, 44, 36)(33, 41, 48, 45, 37, 42) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 8^6 ), ( 8^12 ) } Outer automorphisms :: reflexible Dual of E7.248 Transitivity :: ET+ Graph:: bipartite v = 6 e = 24 f = 6 degree seq :: [ 6^4, 12^2 ] E7.245 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 12}) Quotient :: edge Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ F^2, T2^-4, (F * T1)^2, T2^4, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^-6 ] Map:: non-degenerate R = (1, 3, 9, 5)(2, 7, 16, 8)(4, 10, 17, 12)(6, 14, 24, 15)(11, 18, 21, 20)(13, 22, 19, 23)(25, 26, 30, 37, 45, 41, 33, 40, 48, 43, 35, 28)(27, 31, 38, 46, 44, 36, 29, 32, 39, 47, 42, 34) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 12^4 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E7.246 Transitivity :: ET+ Graph:: bipartite v = 8 e = 24 f = 4 degree seq :: [ 4^6, 12^2 ] E7.246 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 12}) Quotient :: loop Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^6 ] Map:: non-degenerate R = (1, 25, 3, 27, 9, 33, 17, 41, 12, 36, 5, 29)(2, 26, 7, 31, 15, 39, 22, 46, 16, 40, 8, 32)(4, 28, 10, 34, 18, 42, 23, 47, 19, 43, 11, 35)(6, 30, 13, 37, 20, 44, 24, 48, 21, 45, 14, 38) L = (1, 26)(2, 30)(3, 31)(4, 25)(5, 32)(6, 28)(7, 37)(8, 38)(9, 39)(10, 27)(11, 29)(12, 40)(13, 34)(14, 35)(15, 44)(16, 45)(17, 46)(18, 33)(19, 36)(20, 42)(21, 43)(22, 48)(23, 41)(24, 47) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.245 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 24 f = 8 degree seq :: [ 12^4 ] E7.247 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 12}) Quotient :: loop Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T2^4 * T1^-2, T1^6 ] Map:: non-degenerate R = (1, 25, 3, 27, 9, 33, 16, 40, 6, 30, 15, 39, 24, 48, 20, 44, 11, 35, 19, 43, 13, 37, 5, 29)(2, 26, 7, 31, 17, 41, 23, 47, 14, 38, 22, 46, 21, 45, 12, 36, 4, 28, 10, 34, 18, 42, 8, 32) L = (1, 26)(2, 30)(3, 31)(4, 25)(5, 32)(6, 38)(7, 39)(8, 40)(9, 41)(10, 27)(11, 28)(12, 29)(13, 42)(14, 35)(15, 46)(16, 47)(17, 48)(18, 33)(19, 34)(20, 36)(21, 37)(22, 43)(23, 44)(24, 45) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.243 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 24 f = 10 degree seq :: [ 24^2 ] E7.248 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 12}) Quotient :: loop Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ F^2, T2^-4, (F * T1)^2, T2^4, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^-6 ] Map:: non-degenerate R = (1, 25, 3, 27, 9, 33, 5, 29)(2, 26, 7, 31, 16, 40, 8, 32)(4, 28, 10, 34, 17, 41, 12, 36)(6, 30, 14, 38, 24, 48, 15, 39)(11, 35, 18, 42, 21, 45, 20, 44)(13, 37, 22, 46, 19, 43, 23, 47) L = (1, 26)(2, 30)(3, 31)(4, 25)(5, 32)(6, 37)(7, 38)(8, 39)(9, 40)(10, 27)(11, 28)(12, 29)(13, 45)(14, 46)(15, 47)(16, 48)(17, 33)(18, 34)(19, 35)(20, 36)(21, 41)(22, 44)(23, 42)(24, 43) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.244 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 24 f = 6 degree seq :: [ 8^6 ] E7.249 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^4, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^6, Y3^12 ] Map:: R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 7, 31, 13, 37, 10, 34)(5, 29, 8, 32, 14, 38, 11, 35)(9, 33, 15, 39, 20, 44, 18, 42)(12, 36, 16, 40, 21, 45, 19, 43)(17, 41, 22, 46, 24, 48, 23, 47)(49, 73, 51, 75, 57, 81, 65, 89, 60, 84, 53, 77)(50, 74, 55, 79, 63, 87, 70, 94, 64, 88, 56, 80)(52, 76, 58, 82, 66, 90, 71, 95, 67, 91, 59, 83)(54, 78, 61, 85, 68, 92, 72, 96, 69, 93, 62, 86) L = (1, 52)(2, 49)(3, 58)(4, 54)(5, 59)(6, 50)(7, 51)(8, 53)(9, 66)(10, 61)(11, 62)(12, 67)(13, 55)(14, 56)(15, 57)(16, 60)(17, 71)(18, 68)(19, 69)(20, 63)(21, 64)(22, 65)(23, 72)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E7.252 Graph:: bipartite v = 10 e = 48 f = 26 degree seq :: [ 8^6, 12^4 ] E7.250 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y2^-1, Y1), Y2^4 * Y1^-2, Y1^6, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 25, 2, 26, 6, 30, 14, 38, 11, 35, 4, 28)(3, 27, 7, 31, 15, 39, 22, 46, 19, 43, 10, 34)(5, 29, 8, 32, 16, 40, 23, 47, 20, 44, 12, 36)(9, 33, 17, 41, 24, 48, 21, 45, 13, 37, 18, 42)(49, 73, 51, 75, 57, 81, 64, 88, 54, 78, 63, 87, 72, 96, 68, 92, 59, 83, 67, 91, 61, 85, 53, 77)(50, 74, 55, 79, 65, 89, 71, 95, 62, 86, 70, 94, 69, 93, 60, 84, 52, 76, 58, 82, 66, 90, 56, 80) L = (1, 51)(2, 55)(3, 57)(4, 58)(5, 49)(6, 63)(7, 65)(8, 50)(9, 64)(10, 66)(11, 67)(12, 52)(13, 53)(14, 70)(15, 72)(16, 54)(17, 71)(18, 56)(19, 61)(20, 59)(21, 60)(22, 69)(23, 62)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 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 E7.251 Graph:: bipartite v = 6 e = 48 f = 30 degree seq :: [ 12^4, 24^2 ] E7.251 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, (Y2, Y3^-1), Y2^2 * Y3^6, (Y3^-1 * Y1^-1)^12 ] Map:: R = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(49, 73, 50, 74, 54, 78, 52, 76)(51, 75, 55, 79, 61, 85, 58, 82)(53, 77, 56, 80, 62, 86, 59, 83)(57, 81, 63, 87, 69, 93, 66, 90)(60, 84, 64, 88, 70, 94, 67, 91)(65, 89, 71, 95, 68, 92, 72, 96) L = (1, 51)(2, 55)(3, 57)(4, 58)(5, 49)(6, 61)(7, 63)(8, 50)(9, 65)(10, 66)(11, 52)(12, 53)(13, 69)(14, 54)(15, 71)(16, 56)(17, 70)(18, 72)(19, 59)(20, 60)(21, 68)(22, 62)(23, 67)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E7.250 Graph:: simple bipartite v = 30 e = 48 f = 6 degree seq :: [ 2^24, 8^6 ] E7.252 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^-4, (R * Y1)^2, (R * Y3)^2, Y3^4, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^2 * Y1^-6, (Y3 * Y2^-1)^4 ] Map:: R = (1, 25, 2, 26, 6, 30, 13, 37, 21, 45, 17, 41, 9, 33, 16, 40, 24, 48, 19, 43, 11, 35, 4, 28)(3, 27, 7, 31, 14, 38, 22, 46, 20, 44, 12, 36, 5, 29, 8, 32, 15, 39, 23, 47, 18, 42, 10, 34)(49, 73)(50, 74)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96) L = (1, 51)(2, 55)(3, 57)(4, 58)(5, 49)(6, 62)(7, 64)(8, 50)(9, 53)(10, 65)(11, 66)(12, 52)(13, 70)(14, 72)(15, 54)(16, 56)(17, 60)(18, 69)(19, 71)(20, 59)(21, 68)(22, 67)(23, 61)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E7.249 Graph:: simple bipartite v = 26 e = 48 f = 10 degree seq :: [ 2^24, 24^2 ] E7.253 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^4, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^6 * Y1^2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 7, 31, 13, 37, 10, 34)(5, 29, 8, 32, 14, 38, 11, 35)(9, 33, 15, 39, 21, 45, 18, 42)(12, 36, 16, 40, 22, 46, 19, 43)(17, 41, 23, 47, 20, 44, 24, 48)(49, 73, 51, 75, 57, 81, 65, 89, 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, 58, 82, 66, 90, 72, 96, 64, 88, 56, 80) L = (1, 52)(2, 49)(3, 58)(4, 54)(5, 59)(6, 50)(7, 51)(8, 53)(9, 66)(10, 61)(11, 62)(12, 67)(13, 55)(14, 56)(15, 57)(16, 60)(17, 72)(18, 69)(19, 70)(20, 71)(21, 63)(22, 64)(23, 65)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ), ( 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 E7.254 Graph:: bipartite v = 8 e = 48 f = 28 degree seq :: [ 8^6, 24^2 ] E7.254 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1), Y3^4 * Y1^-2, (R * Y2 * Y3^-1)^2, Y1^6, (Y3 * Y2^-1)^12 ] Map:: R = (1, 25, 2, 26, 6, 30, 14, 38, 11, 35, 4, 28)(3, 27, 7, 31, 15, 39, 22, 46, 19, 43, 10, 34)(5, 29, 8, 32, 16, 40, 23, 47, 20, 44, 12, 36)(9, 33, 17, 41, 24, 48, 21, 45, 13, 37, 18, 42)(49, 73)(50, 74)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96) L = (1, 51)(2, 55)(3, 57)(4, 58)(5, 49)(6, 63)(7, 65)(8, 50)(9, 64)(10, 66)(11, 67)(12, 52)(13, 53)(14, 70)(15, 72)(16, 54)(17, 71)(18, 56)(19, 61)(20, 59)(21, 60)(22, 69)(23, 62)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E7.253 Graph:: simple bipartite v = 28 e = 48 f = 8 degree seq :: [ 2^24, 12^4 ] E7.255 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 8, 24}) Quotient :: edge Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^8 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 17, 11, 5)(2, 6, 12, 18, 23, 19, 13, 7)(4, 9, 15, 21, 24, 22, 16, 10)(25, 26, 28)(27, 30, 33)(29, 31, 34)(32, 36, 39)(35, 37, 40)(38, 42, 45)(41, 43, 46)(44, 47, 48) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 48^3 ), ( 48^8 ) } Outer automorphisms :: reflexible Dual of E7.259 Transitivity :: ET+ Graph:: simple bipartite v = 11 e = 24 f = 1 degree seq :: [ 3^8, 8^3 ] E7.256 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 8, 24}) Quotient :: edge Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^-3, T2^-6 * T1^2, T1^8 ] Map:: non-degenerate R = (1, 3, 9, 19, 24, 16, 6, 15, 12, 4, 10, 20, 22, 18, 8, 2, 7, 17, 11, 21, 23, 14, 13, 5)(25, 26, 30, 38, 46, 43, 35, 28)(27, 31, 39, 37, 42, 48, 45, 34)(29, 32, 40, 47, 44, 33, 41, 36) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 6^8 ), ( 6^24 ) } Outer automorphisms :: reflexible Dual of E7.260 Transitivity :: ET+ Graph:: bipartite v = 4 e = 24 f = 8 degree seq :: [ 8^3, 24 ] E7.257 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 8, 24}) Quotient :: edge Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^8, (T1^-1 * T2^-1)^8 ] Map:: non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 9, 11)(6, 13, 14)(10, 15, 17)(12, 19, 20)(16, 21, 23)(18, 24, 22)(25, 26, 30, 36, 42, 45, 39, 33, 27, 31, 37, 43, 48, 47, 41, 35, 29, 32, 38, 44, 46, 40, 34, 28) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 16^3 ), ( 16^24 ) } Outer automorphisms :: reflexible Dual of E7.258 Transitivity :: ET+ Graph:: bipartite v = 9 e = 24 f = 3 degree seq :: [ 3^8, 24 ] E7.258 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 8, 24}) Quotient :: loop Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^8 ] Map:: non-degenerate R = (1, 25, 3, 27, 8, 32, 14, 38, 20, 44, 17, 41, 11, 35, 5, 29)(2, 26, 6, 30, 12, 36, 18, 42, 23, 47, 19, 43, 13, 37, 7, 31)(4, 28, 9, 33, 15, 39, 21, 45, 24, 48, 22, 46, 16, 40, 10, 34) L = (1, 26)(2, 28)(3, 30)(4, 25)(5, 31)(6, 33)(7, 34)(8, 36)(9, 27)(10, 29)(11, 37)(12, 39)(13, 40)(14, 42)(15, 32)(16, 35)(17, 43)(18, 45)(19, 46)(20, 47)(21, 38)(22, 41)(23, 48)(24, 44) local type(s) :: { ( 3, 24, 3, 24, 3, 24, 3, 24, 3, 24, 3, 24, 3, 24, 3, 24 ) } Outer automorphisms :: reflexible Dual of E7.257 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 24 f = 9 degree seq :: [ 16^3 ] E7.259 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 8, 24}) Quotient :: loop Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^-3, T2^-6 * T1^2, T1^8 ] Map:: non-degenerate R = (1, 25, 3, 27, 9, 33, 19, 43, 24, 48, 16, 40, 6, 30, 15, 39, 12, 36, 4, 28, 10, 34, 20, 44, 22, 46, 18, 42, 8, 32, 2, 26, 7, 31, 17, 41, 11, 35, 21, 45, 23, 47, 14, 38, 13, 37, 5, 29) L = (1, 26)(2, 30)(3, 31)(4, 25)(5, 32)(6, 38)(7, 39)(8, 40)(9, 41)(10, 27)(11, 28)(12, 29)(13, 42)(14, 46)(15, 37)(16, 47)(17, 36)(18, 48)(19, 35)(20, 33)(21, 34)(22, 43)(23, 44)(24, 45) local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8 ) } Outer automorphisms :: reflexible Dual of E7.255 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 24 f = 11 degree seq :: [ 48 ] E7.260 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 8, 24}) Quotient :: loop Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^8, (T1^-1 * T2^-1)^8 ] Map:: non-degenerate R = (1, 25, 3, 27, 5, 29)(2, 26, 7, 31, 8, 32)(4, 28, 9, 33, 11, 35)(6, 30, 13, 37, 14, 38)(10, 34, 15, 39, 17, 41)(12, 36, 19, 43, 20, 44)(16, 40, 21, 45, 23, 47)(18, 42, 24, 48, 22, 46) L = (1, 26)(2, 30)(3, 31)(4, 25)(5, 32)(6, 36)(7, 37)(8, 38)(9, 27)(10, 28)(11, 29)(12, 42)(13, 43)(14, 44)(15, 33)(16, 34)(17, 35)(18, 45)(19, 48)(20, 46)(21, 39)(22, 40)(23, 41)(24, 47) local type(s) :: { ( 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E7.256 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 24 f = 4 degree seq :: [ 6^8 ] E7.261 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^8, Y3^24 ] 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, 52)(2, 49)(3, 57)(4, 50)(5, 58)(6, 51)(7, 53)(8, 63)(9, 54)(10, 55)(11, 64)(12, 56)(13, 59)(14, 69)(15, 60)(16, 61)(17, 70)(18, 62)(19, 65)(20, 72)(21, 66)(22, 67)(23, 68)(24, 71)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 2, 48, 2, 48, 2, 48 ), ( 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48 ) } Outer automorphisms :: reflexible Dual of E7.264 Graph:: bipartite v = 11 e = 48 f = 25 degree seq :: [ 6^8, 16^3 ] E7.262 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), Y1^-3 * Y2^-3, (Y3^-1 * Y1^-1)^3, Y2^-6 * Y1^2, Y2^5 * Y1^-1 * Y2 * Y1^-1, Y1^8 ] Map:: R = (1, 25, 2, 26, 6, 30, 14, 38, 22, 46, 19, 43, 11, 35, 4, 28)(3, 27, 7, 31, 15, 39, 13, 37, 18, 42, 24, 48, 21, 45, 10, 34)(5, 29, 8, 32, 16, 40, 23, 47, 20, 44, 9, 33, 17, 41, 12, 36)(49, 73, 51, 75, 57, 81, 67, 91, 72, 96, 64, 88, 54, 78, 63, 87, 60, 84, 52, 76, 58, 82, 68, 92, 70, 94, 66, 90, 56, 80, 50, 74, 55, 79, 65, 89, 59, 83, 69, 93, 71, 95, 62, 86, 61, 85, 53, 77) L = (1, 51)(2, 55)(3, 57)(4, 58)(5, 49)(6, 63)(7, 65)(8, 50)(9, 67)(10, 68)(11, 69)(12, 52)(13, 53)(14, 61)(15, 60)(16, 54)(17, 59)(18, 56)(19, 72)(20, 70)(21, 71)(22, 66)(23, 62)(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) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 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 E7.263 Graph:: bipartite v = 4 e = 48 f = 32 degree seq :: [ 16^3, 48 ] E7.263 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2 * Y3^8, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2, (Y3^-1 * Y1^-1)^24 ] Map:: R = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(49, 73, 50, 74, 52, 76)(51, 75, 54, 78, 57, 81)(53, 77, 55, 79, 58, 82)(56, 80, 60, 84, 63, 87)(59, 83, 61, 85, 64, 88)(62, 86, 66, 90, 69, 93)(65, 89, 67, 91, 70, 94)(68, 92, 71, 95, 72, 96) L = (1, 51)(2, 54)(3, 56)(4, 57)(5, 49)(6, 60)(7, 50)(8, 62)(9, 63)(10, 52)(11, 53)(12, 66)(13, 55)(14, 68)(15, 69)(16, 58)(17, 59)(18, 71)(19, 61)(20, 70)(21, 72)(22, 64)(23, 65)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 48 ), ( 16, 48, 16, 48, 16, 48 ) } Outer automorphisms :: reflexible Dual of E7.262 Graph:: simple bipartite v = 32 e = 48 f = 4 degree seq :: [ 2^24, 6^8 ] E7.264 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^-1 * Y1^8, (Y1^-1 * Y3^-1)^8 ] Map:: R = (1, 25, 2, 26, 6, 30, 12, 36, 18, 42, 21, 45, 15, 39, 9, 33, 3, 27, 7, 31, 13, 37, 19, 43, 24, 48, 23, 47, 17, 41, 11, 35, 5, 29, 8, 32, 14, 38, 20, 44, 22, 46, 16, 40, 10, 34, 4, 28)(49, 73)(50, 74)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96) L = (1, 51)(2, 55)(3, 53)(4, 57)(5, 49)(6, 61)(7, 56)(8, 50)(9, 59)(10, 63)(11, 52)(12, 67)(13, 62)(14, 54)(15, 65)(16, 69)(17, 58)(18, 72)(19, 68)(20, 60)(21, 71)(22, 66)(23, 64)(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) :: { ( 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E7.261 Graph:: bipartite v = 25 e = 48 f = 11 degree seq :: [ 2^24, 48 ] E7.265 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^-8 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] 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, 24, 48, 23, 47)(49, 73, 51, 75, 56, 80, 62, 86, 68, 92, 67, 91, 61, 85, 55, 79, 50, 74, 54, 78, 60, 84, 66, 90, 72, 96, 70, 94, 64, 88, 58, 82, 52, 76, 57, 81, 63, 87, 69, 93, 71, 95, 65, 89, 59, 83, 53, 77) L = (1, 52)(2, 49)(3, 57)(4, 50)(5, 58)(6, 51)(7, 53)(8, 63)(9, 54)(10, 55)(11, 64)(12, 56)(13, 59)(14, 69)(15, 60)(16, 61)(17, 70)(18, 62)(19, 65)(20, 71)(21, 66)(22, 67)(23, 72)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E7.266 Graph:: bipartite v = 9 e = 48 f = 27 degree seq :: [ 6^8, 48 ] E7.266 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^2 * Y1^3 * Y3, Y1^3 * Y3^3, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^3, Y1^-2 * Y3^3 * Y1^-3, (Y3 * Y2^-1)^24 ] Map:: R = (1, 25, 2, 26, 6, 30, 14, 38, 22, 46, 19, 43, 11, 35, 4, 28)(3, 27, 7, 31, 15, 39, 13, 37, 18, 42, 24, 48, 21, 45, 10, 34)(5, 29, 8, 32, 16, 40, 23, 47, 20, 44, 9, 33, 17, 41, 12, 36)(49, 73)(50, 74)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96) L = (1, 51)(2, 55)(3, 57)(4, 58)(5, 49)(6, 63)(7, 65)(8, 50)(9, 67)(10, 68)(11, 69)(12, 52)(13, 53)(14, 61)(15, 60)(16, 54)(17, 59)(18, 56)(19, 72)(20, 70)(21, 71)(22, 66)(23, 62)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 48 ), ( 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48 ) } Outer automorphisms :: reflexible Dual of E7.265 Graph:: simple bipartite v = 27 e = 48 f = 9 degree seq :: [ 2^24, 16^3 ] E7.267 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 9, 9}) Quotient :: edge Aut^+ = C9 x C3 (small group id <27, 2>) Aut = (C9 x C3) : C2 (small group id <54, 7>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^9 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 23, 17, 11, 5)(2, 6, 12, 18, 24, 25, 19, 13, 7)(4, 9, 15, 21, 26, 27, 22, 16, 10)(28, 29, 31)(30, 33, 36)(32, 34, 37)(35, 39, 42)(38, 40, 43)(41, 45, 48)(44, 46, 49)(47, 51, 53)(50, 52, 54) L = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54) local type(s) :: { ( 18^3 ), ( 18^9 ) } Outer automorphisms :: reflexible Dual of E7.268 Transitivity :: ET+ Graph:: simple bipartite v = 12 e = 27 f = 3 degree seq :: [ 3^9, 9^3 ] E7.268 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 9, 9}) Quotient :: loop Aut^+ = C9 x C3 (small group id <27, 2>) Aut = (C9 x C3) : C2 (small group id <54, 7>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^9 ] Map:: non-degenerate R = (1, 28, 3, 30, 8, 35, 14, 41, 20, 47, 23, 50, 17, 44, 11, 38, 5, 32)(2, 29, 6, 33, 12, 39, 18, 45, 24, 51, 25, 52, 19, 46, 13, 40, 7, 34)(4, 31, 9, 36, 15, 42, 21, 48, 26, 53, 27, 54, 22, 49, 16, 43, 10, 37) L = (1, 29)(2, 31)(3, 33)(4, 28)(5, 34)(6, 36)(7, 37)(8, 39)(9, 30)(10, 32)(11, 40)(12, 42)(13, 43)(14, 45)(15, 35)(16, 38)(17, 46)(18, 48)(19, 49)(20, 51)(21, 41)(22, 44)(23, 52)(24, 53)(25, 54)(26, 47)(27, 50) local type(s) :: { ( 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9 ) } Outer automorphisms :: reflexible Dual of E7.267 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 27 f = 12 degree seq :: [ 18^3 ] E7.269 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 9}) Quotient :: dipole Aut^+ = C9 x C3 (small group id <27, 2>) Aut = (C9 x C3) : C2 (small group id <54, 7>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3^9, Y2^9 ] Map:: R = (1, 28, 2, 29, 4, 31)(3, 30, 6, 33, 9, 36)(5, 32, 7, 34, 10, 37)(8, 35, 12, 39, 15, 42)(11, 38, 13, 40, 16, 43)(14, 41, 18, 45, 21, 48)(17, 44, 19, 46, 22, 49)(20, 47, 24, 51, 26, 53)(23, 50, 25, 52, 27, 54)(55, 82, 57, 84, 62, 89, 68, 95, 74, 101, 77, 104, 71, 98, 65, 92, 59, 86)(56, 83, 60, 87, 66, 93, 72, 99, 78, 105, 79, 106, 73, 100, 67, 94, 61, 88)(58, 85, 63, 90, 69, 96, 75, 102, 80, 107, 81, 108, 76, 103, 70, 97, 64, 91) L = (1, 58)(2, 55)(3, 63)(4, 56)(5, 64)(6, 57)(7, 59)(8, 69)(9, 60)(10, 61)(11, 70)(12, 62)(13, 65)(14, 75)(15, 66)(16, 67)(17, 76)(18, 68)(19, 71)(20, 80)(21, 72)(22, 73)(23, 81)(24, 74)(25, 77)(26, 78)(27, 79)(28, 82)(29, 83)(30, 84)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 91)(38, 92)(39, 93)(40, 94)(41, 95)(42, 96)(43, 97)(44, 98)(45, 99)(46, 100)(47, 101)(48, 102)(49, 103)(50, 104)(51, 105)(52, 106)(53, 107)(54, 108) local type(s) :: { ( 2, 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 E7.270 Graph:: bipartite v = 12 e = 54 f = 30 degree seq :: [ 6^9, 18^3 ] E7.270 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 9}) Quotient :: dipole Aut^+ = C9 x C3 (small group id <27, 2>) Aut = (C9 x C3) : C2 (small group id <54, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^-9, Y1^9 ] Map:: R = (1, 28, 2, 29, 6, 33, 12, 39, 18, 45, 22, 49, 16, 43, 10, 37, 4, 31)(3, 30, 7, 34, 13, 40, 19, 46, 24, 51, 26, 53, 21, 48, 15, 42, 9, 36)(5, 32, 8, 35, 14, 41, 20, 47, 25, 52, 27, 54, 23, 50, 17, 44, 11, 38)(55, 82)(56, 83)(57, 84)(58, 85)(59, 86)(60, 87)(61, 88)(62, 89)(63, 90)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)(73, 100)(74, 101)(75, 102)(76, 103)(77, 104)(78, 105)(79, 106)(80, 107)(81, 108) L = (1, 57)(2, 61)(3, 59)(4, 63)(5, 55)(6, 67)(7, 62)(8, 56)(9, 65)(10, 69)(11, 58)(12, 73)(13, 68)(14, 60)(15, 71)(16, 75)(17, 64)(18, 78)(19, 74)(20, 66)(21, 77)(22, 80)(23, 70)(24, 79)(25, 72)(26, 81)(27, 76)(28, 82)(29, 83)(30, 84)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 91)(38, 92)(39, 93)(40, 94)(41, 95)(42, 96)(43, 97)(44, 98)(45, 99)(46, 100)(47, 101)(48, 102)(49, 103)(50, 104)(51, 105)(52, 106)(53, 107)(54, 108) local type(s) :: { ( 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 E7.269 Graph:: simple bipartite v = 30 e = 54 f = 12 degree seq :: [ 2^27, 18^3 ] E7.271 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 9, 9}) Quotient :: edge Aut^+ = C9 : C3 (small group id <27, 4>) Aut = C9 : C3 (small group id <27, 4>) |r| :: 1 Presentation :: [ X1^3, X2^2 * X1^-1 * X2 * X1, X2 * X1 * X2^-1 * X1^-1 * X2^3 ] Map:: non-degenerate R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 16, 17)(7, 18, 19)(9, 21, 12)(11, 15, 24)(20, 26, 27)(22, 25, 23)(28, 30, 36, 49, 44, 46, 54, 42, 32)(29, 33, 40, 52, 51, 48, 47, 35, 34)(31, 38, 45, 50, 37, 41, 53, 43, 39) L = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54) local type(s) :: { ( 18^3 ), ( 18^9 ) } Outer automorphisms :: chiral Dual of E7.272 Transitivity :: ET+ Graph:: simple bipartite v = 12 e = 27 f = 3 degree seq :: [ 3^9, 9^3 ] E7.272 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 9, 9}) Quotient :: loop Aut^+ = C9 : C3 (small group id <27, 4>) Aut = C9 : C3 (small group id <27, 4>) |r| :: 1 Presentation :: [ X1 * X2 * X1 * X2^-1 * X1, X1 * X2 * X1^-1 * X2^2, X2^9, X1^9 ] Map:: non-degenerate R = (1, 28, 2, 29, 6, 33, 18, 45, 26, 53, 27, 54, 23, 50, 13, 40, 4, 31)(3, 30, 9, 36, 22, 49, 17, 44, 7, 34, 12, 39, 24, 51, 21, 48, 11, 38)(5, 32, 15, 42, 14, 41, 25, 52, 20, 47, 19, 46, 10, 37, 8, 35, 16, 43) L = (1, 30)(2, 34)(3, 37)(4, 39)(5, 28)(6, 38)(7, 47)(8, 29)(9, 42)(10, 50)(11, 41)(12, 43)(13, 36)(14, 31)(15, 53)(16, 54)(17, 32)(18, 44)(19, 33)(20, 40)(21, 35)(22, 46)(23, 51)(24, 52)(25, 45)(26, 48)(27, 49) local type(s) :: { ( 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9 ) } Outer automorphisms :: chiral Dual of E7.271 Transitivity :: ET+ VT+ Graph:: v = 3 e = 27 f = 12 degree seq :: [ 18^3 ] E7.273 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 5, 33)(4, 32, 8, 36)(6, 34, 10, 38)(7, 35, 11, 39)(9, 37, 13, 41)(12, 40, 16, 44)(14, 42, 18, 46)(15, 43, 19, 47)(17, 45, 21, 49)(20, 48, 24, 52)(22, 50, 26, 54)(23, 51, 27, 55)(25, 53, 28, 56)(57, 85, 59, 87)(58, 86, 61, 89)(60, 88, 63, 91)(62, 90, 65, 93)(64, 92, 67, 95)(66, 94, 69, 97)(68, 96, 71, 99)(70, 98, 73, 101)(72, 100, 75, 103)(74, 102, 77, 105)(76, 104, 79, 107)(78, 106, 81, 109)(80, 108, 83, 111)(82, 110, 84, 112) L = (1, 60)(2, 62)(3, 63)(4, 57)(5, 65)(6, 58)(7, 59)(8, 68)(9, 61)(10, 70)(11, 71)(12, 64)(13, 73)(14, 66)(15, 67)(16, 76)(17, 69)(18, 78)(19, 79)(20, 72)(21, 81)(22, 74)(23, 75)(24, 84)(25, 77)(26, 83)(27, 82)(28, 80)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E7.274 Graph:: simple bipartite v = 28 e = 56 f = 16 degree seq :: [ 4^28 ] E7.274 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y1^-1 * Y2)^2, (Y3 * Y2)^2, Y1^4 * Y3 * Y1^-3 * Y2 ] Map:: non-degenerate R = (1, 29, 2, 30, 6, 34, 13, 41, 21, 49, 26, 54, 18, 46, 10, 38, 16, 44, 24, 52, 28, 56, 20, 48, 12, 40, 5, 33)(3, 31, 9, 37, 17, 45, 25, 53, 23, 51, 15, 43, 8, 36, 4, 32, 11, 39, 19, 47, 27, 55, 22, 50, 14, 42, 7, 35)(57, 85, 59, 87)(58, 86, 63, 91)(60, 88, 66, 94)(61, 89, 65, 93)(62, 90, 70, 98)(64, 92, 72, 100)(67, 95, 74, 102)(68, 96, 73, 101)(69, 97, 78, 106)(71, 99, 80, 108)(75, 103, 82, 110)(76, 104, 81, 109)(77, 105, 83, 111)(79, 107, 84, 112) L = (1, 60)(2, 64)(3, 66)(4, 57)(5, 67)(6, 71)(7, 72)(8, 58)(9, 74)(10, 59)(11, 61)(12, 75)(13, 79)(14, 80)(15, 62)(16, 63)(17, 82)(18, 65)(19, 68)(20, 83)(21, 81)(22, 84)(23, 69)(24, 70)(25, 77)(26, 73)(27, 76)(28, 78)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4^4 ), ( 4^28 ) } Outer automorphisms :: reflexible Dual of E7.273 Graph:: bipartite v = 16 e = 56 f = 28 degree seq :: [ 4^14, 28^2 ] E7.275 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 14}) Quotient :: edge Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, T1^4, (F * T1)^2, T2 * T1 * T2 * T1^-1, T1^-2 * T2^7 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 22, 14, 6, 13, 21, 28, 20, 12, 5)(2, 7, 15, 23, 26, 18, 10, 4, 11, 19, 27, 24, 16, 8)(29, 30, 34, 32)(31, 36, 41, 38)(33, 35, 42, 39)(37, 44, 49, 46)(40, 43, 50, 47)(45, 52, 56, 54)(48, 51, 53, 55) 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) :: { ( 8^4 ), ( 8^14 ) } Outer automorphisms :: reflexible Dual of E7.276 Transitivity :: ET+ Graph:: bipartite v = 9 e = 28 f = 7 degree seq :: [ 4^7, 14^2 ] E7.276 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 14}) Quotient :: loop Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ F^2, T2^4, T1^2 * T2^2, (F * T2)^2, T2^-1 * T1^2 * T2^-1, (F * T1)^2, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 29, 3, 31, 6, 34, 5, 33)(2, 30, 7, 35, 4, 32, 8, 36)(9, 37, 13, 41, 10, 38, 14, 42)(11, 39, 15, 43, 12, 40, 16, 44)(17, 45, 21, 49, 18, 46, 22, 50)(19, 47, 23, 51, 20, 48, 24, 52)(25, 53, 27, 55, 26, 54, 28, 56) L = (1, 30)(2, 34)(3, 37)(4, 29)(5, 38)(6, 32)(7, 39)(8, 40)(9, 33)(10, 31)(11, 36)(12, 35)(13, 45)(14, 46)(15, 47)(16, 48)(17, 42)(18, 41)(19, 44)(20, 43)(21, 53)(22, 54)(23, 55)(24, 56)(25, 50)(26, 49)(27, 52)(28, 51) local type(s) :: { ( 4, 14, 4, 14, 4, 14, 4, 14 ) } Outer automorphisms :: reflexible Dual of E7.275 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 28 f = 9 degree seq :: [ 8^7 ] E7.277 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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, Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^4, (Y3^-1 * Y1^-1)^4, Y2^-1 * Y1 * Y2^3 * Y1 * Y2^-3, Y2^14 ] Map:: R = (1, 29, 2, 30, 6, 34, 4, 32)(3, 31, 8, 36, 13, 41, 10, 38)(5, 33, 7, 35, 14, 42, 11, 39)(9, 37, 16, 44, 21, 49, 18, 46)(12, 40, 15, 43, 22, 50, 19, 47)(17, 45, 24, 52, 28, 56, 26, 54)(20, 48, 23, 51, 25, 53, 27, 55)(57, 85, 59, 87, 65, 93, 73, 101, 81, 109, 78, 106, 70, 98, 62, 90, 69, 97, 77, 105, 84, 112, 76, 104, 68, 96, 61, 89)(58, 86, 63, 91, 71, 99, 79, 107, 82, 110, 74, 102, 66, 94, 60, 88, 67, 95, 75, 103, 83, 111, 80, 108, 72, 100, 64, 92) L = (1, 59)(2, 63)(3, 65)(4, 67)(5, 57)(6, 69)(7, 71)(8, 58)(9, 73)(10, 60)(11, 75)(12, 61)(13, 77)(14, 62)(15, 79)(16, 64)(17, 81)(18, 66)(19, 83)(20, 68)(21, 84)(22, 70)(23, 82)(24, 72)(25, 78)(26, 74)(27, 80)(28, 76)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 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 E7.278 Graph:: bipartite v = 9 e = 56 f = 35 degree seq :: [ 8^7, 28^2 ] E7.278 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3^7, (Y3^-1 * Y1^-1)^14 ] Map:: R = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)(57, 85, 58, 86, 62, 90, 60, 88)(59, 87, 64, 92, 69, 97, 66, 94)(61, 89, 63, 91, 70, 98, 67, 95)(65, 93, 72, 100, 77, 105, 74, 102)(68, 96, 71, 99, 78, 106, 75, 103)(73, 101, 80, 108, 84, 112, 82, 110)(76, 104, 79, 107, 81, 109, 83, 111) L = (1, 59)(2, 63)(3, 65)(4, 67)(5, 57)(6, 69)(7, 71)(8, 58)(9, 73)(10, 60)(11, 75)(12, 61)(13, 77)(14, 62)(15, 79)(16, 64)(17, 81)(18, 66)(19, 83)(20, 68)(21, 84)(22, 70)(23, 82)(24, 72)(25, 78)(26, 74)(27, 80)(28, 76)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E7.277 Graph:: simple bipartite v = 35 e = 56 f = 9 degree seq :: [ 2^28, 8^7 ] E7.279 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 28, 28}) Quotient :: regular Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^-1, T2 * T1^14 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 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, 28) local type(s) :: { ( 28^28 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 14 f = 1 degree seq :: [ 28 ] E7.280 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 28, 28}) Quotient :: edge Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^14 * T1 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 26, 22, 18, 14, 10, 6, 2, 5, 9, 13, 17, 21, 25, 28, 24, 20, 16, 12, 8, 4)(29, 30)(31, 33)(32, 34)(35, 37)(36, 38)(39, 41)(40, 42)(43, 45)(44, 46)(47, 49)(48, 50)(51, 53)(52, 54)(55, 56) 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 ), ( 56^28 ) } Outer automorphisms :: reflexible Dual of E7.281 Transitivity :: ET+ Graph:: bipartite v = 15 e = 28 f = 1 degree seq :: [ 2^14, 28 ] E7.281 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 28, 28}) Quotient :: loop Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^14 * T1 ] Map:: R = (1, 29, 3, 31, 7, 35, 11, 39, 15, 43, 19, 47, 23, 51, 27, 55, 26, 54, 22, 50, 18, 46, 14, 42, 10, 38, 6, 34, 2, 30, 5, 33, 9, 37, 13, 41, 17, 45, 21, 49, 25, 53, 28, 56, 24, 52, 20, 48, 16, 44, 12, 40, 8, 36, 4, 32) L = (1, 30)(2, 29)(3, 33)(4, 34)(5, 31)(6, 32)(7, 37)(8, 38)(9, 35)(10, 36)(11, 41)(12, 42)(13, 39)(14, 40)(15, 45)(16, 46)(17, 43)(18, 44)(19, 49)(20, 50)(21, 47)(22, 48)(23, 53)(24, 54)(25, 51)(26, 52)(27, 56)(28, 55) local type(s) :: { ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) } Outer automorphisms :: reflexible Dual of E7.280 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 28 f = 15 degree seq :: [ 56 ] E7.282 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * 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, 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, 84)(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) :: { ( 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 E7.283 Graph:: bipartite v = 15 e = 56 f = 29 degree seq :: [ 4^14, 56 ] E7.283 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1^14 ] Map:: R = (1, 29, 2, 30, 5, 33, 9, 37, 13, 41, 17, 45, 21, 49, 25, 53, 27, 55, 23, 51, 19, 47, 15, 43, 11, 39, 7, 35, 3, 31, 6, 34, 10, 38, 14, 42, 18, 46, 22, 50, 26, 54, 28, 56, 24, 52, 20, 48, 16, 44, 12, 40, 8, 36, 4, 32)(57, 85)(58, 86)(59, 87)(60, 88)(61, 89)(62, 90)(63, 91)(64, 92)(65, 93)(66, 94)(67, 95)(68, 96)(69, 97)(70, 98)(71, 99)(72, 100)(73, 101)(74, 102)(75, 103)(76, 104)(77, 105)(78, 106)(79, 107)(80, 108)(81, 109)(82, 110)(83, 111)(84, 112) L = (1, 59)(2, 62)(3, 57)(4, 63)(5, 66)(6, 58)(7, 60)(8, 67)(9, 70)(10, 61)(11, 64)(12, 71)(13, 74)(14, 65)(15, 68)(16, 75)(17, 78)(18, 69)(19, 72)(20, 79)(21, 82)(22, 73)(23, 76)(24, 83)(25, 84)(26, 77)(27, 80)(28, 81)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) } Outer automorphisms :: reflexible Dual of E7.282 Graph:: bipartite v = 29 e = 56 f = 15 degree seq :: [ 2^28, 56 ] E7.284 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 15, 30}) Quotient :: regular Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-15 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 30, 28, 24, 20, 16, 12, 8, 4) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 29) local type(s) :: { ( 15^30 ) } Outer automorphisms :: reflexible Dual of E7.285 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 15 f = 2 degree seq :: [ 30 ] E7.285 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 15, 30}) Quotient :: regular Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^-1, T1^15 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 29, 30, 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, 29)(28, 30) local type(s) :: { ( 30^15 ) } Outer automorphisms :: reflexible Dual of E7.284 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 15 f = 1 degree seq :: [ 15^2 ] E7.286 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 15, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^15 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 30, 26, 22, 18, 14, 10, 6)(31, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 43)(42, 44)(45, 47)(46, 48)(49, 51)(50, 52)(53, 55)(54, 56)(57, 59)(58, 60) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 60, 60 ), ( 60^15 ) } Outer automorphisms :: reflexible Dual of E7.290 Transitivity :: ET+ Graph:: simple bipartite v = 17 e = 30 f = 1 degree seq :: [ 2^15, 15^2 ] E7.287 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 15, 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^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^13, T2^-2 * T1^5 * T2^-8 ] Map:: non-degenerate R = (1, 3, 9, 13, 17, 21, 25, 29, 27, 24, 19, 16, 11, 8, 2, 7, 4, 10, 14, 18, 22, 26, 30, 28, 23, 20, 15, 12, 6, 5)(31, 32, 36, 41, 45, 49, 53, 57, 60, 55, 52, 47, 44, 39, 34)(33, 37, 35, 38, 42, 46, 50, 54, 58, 59, 56, 51, 48, 43, 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) :: { ( 4^15 ), ( 4^30 ) } Outer automorphisms :: reflexible Dual of E7.291 Transitivity :: ET+ Graph:: bipartite v = 3 e = 30 f = 15 degree seq :: [ 15^2, 30 ] E7.288 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 15, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-15 ] Map:: R = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 29)(31, 32, 35, 39, 43, 47, 51, 55, 59, 57, 53, 49, 45, 41, 37, 33, 36, 40, 44, 48, 52, 56, 60, 58, 54, 50, 46, 42, 38, 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 ), ( 30^30 ) } Outer automorphisms :: reflexible Dual of E7.289 Transitivity :: ET+ Graph:: bipartite v = 16 e = 30 f = 2 degree seq :: [ 2^15, 30 ] E7.289 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 15, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^15 ] 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) L = (1, 32)(2, 31)(3, 35)(4, 36)(5, 33)(6, 34)(7, 39)(8, 40)(9, 37)(10, 38)(11, 43)(12, 44)(13, 41)(14, 42)(15, 47)(16, 48)(17, 45)(18, 46)(19, 51)(20, 52)(21, 49)(22, 50)(23, 55)(24, 56)(25, 53)(26, 54)(27, 59)(28, 60)(29, 57)(30, 58) 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 ) } Outer automorphisms :: reflexible Dual of E7.288 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 30 f = 16 degree seq :: [ 30^2 ] E7.290 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 15, 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, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^13, T2^-2 * T1^5 * T2^-8 ] Map:: R = (1, 31, 3, 33, 9, 39, 13, 43, 17, 47, 21, 51, 25, 55, 29, 59, 27, 57, 24, 54, 19, 49, 16, 46, 11, 41, 8, 38, 2, 32, 7, 37, 4, 34, 10, 40, 14, 44, 18, 48, 22, 52, 26, 56, 30, 60, 28, 58, 23, 53, 20, 50, 15, 45, 12, 42, 6, 36, 5, 35) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 41)(7, 35)(8, 42)(9, 34)(10, 33)(11, 45)(12, 46)(13, 40)(14, 39)(15, 49)(16, 50)(17, 44)(18, 43)(19, 53)(20, 54)(21, 48)(22, 47)(23, 57)(24, 58)(25, 52)(26, 51)(27, 60)(28, 59)(29, 56)(30, 55) local type(s) :: { ( 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15 ) } Outer automorphisms :: reflexible Dual of E7.286 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 30 f = 17 degree seq :: [ 60 ] E7.291 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 15, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-15 ] Map:: non-degenerate R = (1, 31, 3, 33)(2, 32, 6, 36)(4, 34, 7, 37)(5, 35, 10, 40)(8, 38, 11, 41)(9, 39, 14, 44)(12, 42, 15, 45)(13, 43, 18, 48)(16, 46, 19, 49)(17, 47, 22, 52)(20, 50, 23, 53)(21, 51, 26, 56)(24, 54, 27, 57)(25, 55, 30, 60)(28, 58, 29, 59) L = (1, 32)(2, 35)(3, 36)(4, 31)(5, 39)(6, 40)(7, 33)(8, 34)(9, 43)(10, 44)(11, 37)(12, 38)(13, 47)(14, 48)(15, 41)(16, 42)(17, 51)(18, 52)(19, 45)(20, 46)(21, 55)(22, 56)(23, 49)(24, 50)(25, 59)(26, 60)(27, 53)(28, 54)(29, 57)(30, 58) local type(s) :: { ( 15, 30, 15, 30 ) } Outer automorphisms :: reflexible Dual of E7.287 Transitivity :: ET+ VT+ AT Graph:: v = 15 e = 30 f = 3 degree seq :: [ 4^15 ] E7.292 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^15, (Y3 * Y2^-1)^30 ] Map:: R = (1, 31, 2, 32)(3, 33, 5, 35)(4, 34, 6, 36)(7, 37, 9, 39)(8, 38, 10, 40)(11, 41, 13, 43)(12, 42, 14, 44)(15, 45, 17, 47)(16, 46, 18, 48)(19, 49, 21, 51)(20, 50, 22, 52)(23, 53, 25, 55)(24, 54, 26, 56)(27, 57, 29, 59)(28, 58, 30, 60)(61, 91, 63, 93, 67, 97, 71, 101, 75, 105, 79, 109, 83, 113, 87, 117, 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, 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, 90)(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 ) } Outer automorphisms :: reflexible Dual of E7.295 Graph:: bipartite v = 17 e = 60 f = 31 degree seq :: [ 4^15, 30^2 ] E7.293 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 15, 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, (Y1, Y2^-1), (Y3^-1 * Y1^-1)^2, Y1^6 * Y2^6, Y2^10 * Y1^-5, Y1^7 * Y2^-8, Y1^15 ] Map:: R = (1, 31, 2, 32, 6, 36, 11, 41, 15, 45, 19, 49, 23, 53, 27, 57, 30, 60, 25, 55, 22, 52, 17, 47, 14, 44, 9, 39, 4, 34)(3, 33, 7, 37, 5, 35, 8, 38, 12, 42, 16, 46, 20, 50, 24, 54, 28, 58, 29, 59, 26, 56, 21, 51, 18, 48, 13, 43, 10, 40)(61, 91, 63, 93, 69, 99, 73, 103, 77, 107, 81, 111, 85, 115, 89, 119, 87, 117, 84, 114, 79, 109, 76, 106, 71, 101, 68, 98, 62, 92, 67, 97, 64, 94, 70, 100, 74, 104, 78, 108, 82, 112, 86, 116, 90, 120, 88, 118, 83, 113, 80, 110, 75, 105, 72, 102, 66, 96, 65, 95) 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) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E7.294 Graph:: bipartite v = 3 e = 60 f = 45 degree seq :: [ 30^2, 60 ] E7.294 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, Y3^15 * Y2, (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)(63, 93, 65, 95)(64, 94, 66, 96)(67, 97, 69, 99)(68, 98, 70, 100)(71, 101, 73, 103)(72, 102, 74, 104)(75, 105, 77, 107)(76, 106, 78, 108)(79, 109, 81, 111)(80, 110, 82, 112)(83, 113, 85, 115)(84, 114, 86, 116)(87, 117, 89, 119)(88, 118, 90, 120) L = (1, 63)(2, 65)(3, 67)(4, 61)(5, 69)(6, 62)(7, 71)(8, 64)(9, 73)(10, 66)(11, 75)(12, 68)(13, 77)(14, 70)(15, 79)(16, 72)(17, 81)(18, 74)(19, 83)(20, 76)(21, 85)(22, 78)(23, 87)(24, 80)(25, 89)(26, 82)(27, 90)(28, 84)(29, 88)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 30, 60 ), ( 30, 60, 30, 60 ) } Outer automorphisms :: reflexible Dual of E7.293 Graph:: simple bipartite v = 45 e = 60 f = 3 degree seq :: [ 2^30, 4^15 ] E7.295 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 15, 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, R * Y2 * R * Y2^-1, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-15 ] Map:: R = (1, 31, 2, 32, 5, 35, 9, 39, 13, 43, 17, 47, 21, 51, 25, 55, 29, 59, 27, 57, 23, 53, 19, 49, 15, 45, 11, 41, 7, 37, 3, 33, 6, 36, 10, 40, 14, 44, 18, 48, 22, 52, 26, 56, 30, 60, 28, 58, 24, 54, 20, 50, 16, 46, 12, 42, 8, 38, 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, 66)(3, 61)(4, 67)(5, 70)(6, 62)(7, 64)(8, 71)(9, 74)(10, 65)(11, 68)(12, 75)(13, 78)(14, 69)(15, 72)(16, 79)(17, 82)(18, 73)(19, 76)(20, 83)(21, 86)(22, 77)(23, 80)(24, 87)(25, 90)(26, 81)(27, 84)(28, 89)(29, 88)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E7.292 Graph:: bipartite v = 31 e = 60 f = 17 degree seq :: [ 2^30, 60 ] E7.296 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^15 * Y1, (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, 90, 120, 86, 116, 82, 112, 78, 108, 74, 104, 70, 100, 66, 96, 62, 92, 65, 95, 69, 99, 73, 103, 77, 107, 81, 111, 85, 115, 89, 119, 88, 118, 84, 114, 80, 110, 76, 106, 72, 102, 68, 98, 64, 94) L = (1, 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, 90)(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, 30, 2, 30 ), ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) } Outer automorphisms :: reflexible Dual of E7.297 Graph:: bipartite v = 16 e = 60 f = 32 degree seq :: [ 4^15, 60 ] E7.297 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 15, 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, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y1^5 * Y3^6 * Y1, Y1^-1 * Y3^14, Y1^15, (Y3 * Y2^-1)^30 ] Map:: R = (1, 31, 2, 32, 6, 36, 11, 41, 15, 45, 19, 49, 23, 53, 27, 57, 30, 60, 25, 55, 22, 52, 17, 47, 14, 44, 9, 39, 4, 34)(3, 33, 7, 37, 5, 35, 8, 38, 12, 42, 16, 46, 20, 50, 24, 54, 28, 58, 29, 59, 26, 56, 21, 51, 18, 48, 13, 43, 10, 40)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 114)(85, 115)(86, 116)(87, 117)(88, 118)(89, 119)(90, 120) L = (1, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 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) :: { ( 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 E7.296 Graph:: simple bipartite v = 32 e = 60 f = 16 degree seq :: [ 2^30, 30^2 ] E7.298 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 8}) Quotient :: dipole Aut^+ = C2 x D16 (small group id <32, 39>) Aut = C2 x C2 x D16 (small group id <64, 250>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y3)^2, (Y3 * Y1)^8 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34)(3, 35, 5, 37)(4, 36, 8, 40)(6, 38, 10, 42)(7, 39, 11, 43)(9, 41, 13, 45)(12, 44, 16, 48)(14, 46, 18, 50)(15, 47, 19, 51)(17, 49, 21, 53)(20, 52, 24, 56)(22, 54, 26, 58)(23, 55, 27, 59)(25, 57, 29, 61)(28, 60, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99)(66, 98, 69, 101)(68, 100, 71, 103)(70, 102, 73, 105)(72, 104, 75, 107)(74, 106, 77, 109)(76, 108, 79, 111)(78, 110, 81, 113)(80, 112, 83, 115)(82, 114, 85, 117)(84, 116, 87, 119)(86, 118, 89, 121)(88, 120, 91, 123)(90, 122, 93, 125)(92, 124, 95, 127)(94, 126, 96, 128) L = (1, 68)(2, 70)(3, 71)(4, 65)(5, 73)(6, 66)(7, 67)(8, 76)(9, 69)(10, 78)(11, 79)(12, 72)(13, 81)(14, 74)(15, 75)(16, 84)(17, 77)(18, 86)(19, 87)(20, 80)(21, 89)(22, 82)(23, 83)(24, 92)(25, 85)(26, 94)(27, 95)(28, 88)(29, 96)(30, 90)(31, 91)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E7.303 Graph:: simple bipartite v = 32 e = 64 f = 20 degree seq :: [ 4^32 ] E7.299 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 8}) Quotient :: dipole Aut^+ = (C2 x D8) : C2 (small group id <32, 43>) Aut = C2 x ((C2 x D8) : C2) (small group id <64, 254>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y2 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (Y1 * Y3 * Y1 * Y2)^2, (Y2 * Y1)^4, Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 9, 41)(5, 37, 10, 42)(6, 38, 12, 44)(8, 40, 15, 47)(11, 43, 20, 52)(13, 45, 18, 50)(14, 46, 21, 53)(16, 48, 19, 51)(17, 49, 27, 59)(22, 54, 32, 64)(23, 55, 29, 61)(24, 56, 28, 60)(25, 57, 30, 62)(26, 58, 31, 63)(65, 97, 67, 99)(66, 98, 69, 101)(68, 100, 72, 104)(70, 102, 75, 107)(71, 103, 77, 109)(73, 105, 80, 112)(74, 106, 82, 114)(76, 108, 85, 117)(78, 110, 87, 119)(79, 111, 88, 120)(81, 113, 90, 122)(83, 115, 92, 124)(84, 116, 93, 125)(86, 118, 95, 127)(89, 121, 96, 128)(91, 123, 94, 126) L = (1, 68)(2, 70)(3, 72)(4, 65)(5, 75)(6, 66)(7, 78)(8, 67)(9, 81)(10, 83)(11, 69)(12, 86)(13, 87)(14, 71)(15, 89)(16, 90)(17, 73)(18, 92)(19, 74)(20, 94)(21, 95)(22, 76)(23, 77)(24, 96)(25, 79)(26, 80)(27, 93)(28, 82)(29, 91)(30, 84)(31, 85)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E7.305 Graph:: simple bipartite v = 32 e = 64 f = 20 degree seq :: [ 4^32 ] E7.300 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 8}) Quotient :: dipole Aut^+ = (C2 x D8) : C2 (small group id <32, 43>) Aut = C2 x ((C2 x D8) : C2) (small group id <64, 254>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y3)^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-2 * Y1 * Y3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y2, Y3 * Y1 * Y3^-1 * Y2 * Y1 * Y2, Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 12, 44)(5, 37, 14, 46)(6, 38, 15, 47)(7, 39, 18, 50)(8, 40, 20, 52)(10, 42, 16, 48)(11, 43, 17, 49)(13, 45, 19, 51)(21, 53, 30, 62)(22, 54, 28, 60)(23, 55, 27, 59)(24, 56, 31, 63)(25, 57, 26, 58)(29, 61, 32, 64)(65, 97, 67, 99)(66, 98, 70, 102)(68, 100, 75, 107)(69, 101, 74, 106)(71, 103, 81, 113)(72, 104, 80, 112)(73, 105, 85, 117)(76, 108, 87, 119)(77, 109, 88, 120)(78, 110, 86, 118)(79, 111, 90, 122)(82, 114, 92, 124)(83, 115, 93, 125)(84, 116, 91, 123)(89, 121, 95, 127)(94, 126, 96, 128) L = (1, 68)(2, 71)(3, 74)(4, 77)(5, 65)(6, 80)(7, 83)(8, 66)(9, 86)(10, 88)(11, 67)(12, 89)(13, 69)(14, 85)(15, 91)(16, 93)(17, 70)(18, 94)(19, 72)(20, 90)(21, 76)(22, 95)(23, 73)(24, 75)(25, 78)(26, 82)(27, 96)(28, 79)(29, 81)(30, 84)(31, 87)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E7.304 Graph:: simple bipartite v = 32 e = 64 f = 20 degree seq :: [ 4^32 ] E7.301 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 8}) Quotient :: dipole Aut^+ = (C2 x D8) : C2 (small group id <32, 43>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y2 * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34)(3, 35, 6, 38)(4, 36, 11, 43)(5, 37, 13, 45)(7, 39, 16, 48)(8, 40, 18, 50)(9, 41, 19, 51)(10, 42, 21, 53)(12, 44, 17, 49)(14, 46, 24, 56)(15, 47, 26, 58)(20, 52, 25, 57)(22, 54, 28, 60)(23, 55, 27, 59)(29, 61, 32, 64)(30, 62, 31, 63)(65, 97, 67, 99)(66, 98, 70, 102)(68, 100, 74, 106)(69, 101, 73, 105)(71, 103, 79, 111)(72, 104, 78, 110)(75, 107, 85, 117)(76, 108, 84, 116)(77, 109, 83, 115)(80, 112, 90, 122)(81, 113, 89, 121)(82, 114, 88, 120)(86, 118, 93, 125)(87, 119, 94, 126)(91, 123, 95, 127)(92, 124, 96, 128) L = (1, 68)(2, 71)(3, 73)(4, 76)(5, 65)(6, 78)(7, 81)(8, 66)(9, 84)(10, 67)(11, 86)(12, 69)(13, 87)(14, 89)(15, 70)(16, 91)(17, 72)(18, 92)(19, 93)(20, 74)(21, 94)(22, 77)(23, 75)(24, 95)(25, 79)(26, 96)(27, 82)(28, 80)(29, 85)(30, 83)(31, 90)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E7.306 Graph:: simple bipartite v = 32 e = 64 f = 20 degree seq :: [ 4^32 ] E7.302 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 42>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y1)^2, (Y2 * Y3)^2, (R * Y3)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 12, 44)(5, 37, 14, 46)(6, 38, 15, 47)(7, 39, 18, 50)(8, 40, 20, 52)(10, 42, 21, 53)(11, 43, 22, 54)(13, 45, 19, 51)(16, 48, 25, 57)(17, 49, 26, 58)(23, 55, 28, 60)(24, 56, 27, 59)(29, 61, 31, 63)(30, 62, 32, 64)(65, 97, 67, 99)(66, 98, 70, 102)(68, 100, 75, 107)(69, 101, 74, 106)(71, 103, 81, 113)(72, 104, 80, 112)(73, 105, 83, 115)(76, 108, 85, 117)(77, 109, 79, 111)(78, 110, 86, 118)(82, 114, 89, 121)(84, 116, 90, 122)(87, 119, 94, 126)(88, 120, 93, 125)(91, 123, 96, 128)(92, 124, 95, 127) L = (1, 68)(2, 71)(3, 74)(4, 77)(5, 65)(6, 80)(7, 83)(8, 66)(9, 81)(10, 79)(11, 67)(12, 87)(13, 69)(14, 88)(15, 75)(16, 73)(17, 70)(18, 91)(19, 72)(20, 92)(21, 93)(22, 94)(23, 78)(24, 76)(25, 95)(26, 96)(27, 84)(28, 82)(29, 86)(30, 85)(31, 90)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E7.307 Graph:: simple bipartite v = 32 e = 64 f = 20 degree seq :: [ 4^32 ] E7.303 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 8}) Quotient :: dipole Aut^+ = C2 x D16 (small group id <32, 39>) Aut = C2 x C2 x D16 (small group id <64, 250>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (Y1^-1 * Y2)^2, Y1^8 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34, 6, 38, 13, 45, 21, 53, 20, 52, 12, 44, 5, 37)(3, 35, 9, 41, 17, 49, 25, 57, 28, 60, 22, 54, 14, 46, 7, 39)(4, 36, 11, 43, 19, 51, 27, 59, 29, 61, 23, 55, 15, 47, 8, 40)(10, 42, 16, 48, 24, 56, 30, 62, 32, 64, 31, 63, 26, 58, 18, 50)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 74, 106)(69, 101, 73, 105)(70, 102, 78, 110)(72, 104, 80, 112)(75, 107, 82, 114)(76, 108, 81, 113)(77, 109, 86, 118)(79, 111, 88, 120)(83, 115, 90, 122)(84, 116, 89, 121)(85, 117, 92, 124)(87, 119, 94, 126)(91, 123, 95, 127)(93, 125, 96, 128) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 75)(6, 79)(7, 80)(8, 66)(9, 82)(10, 67)(11, 69)(12, 83)(13, 87)(14, 88)(15, 70)(16, 71)(17, 90)(18, 73)(19, 76)(20, 91)(21, 93)(22, 94)(23, 77)(24, 78)(25, 95)(26, 81)(27, 84)(28, 96)(29, 85)(30, 86)(31, 89)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4^4 ), ( 4^16 ) } Outer automorphisms :: reflexible Dual of E7.298 Graph:: simple bipartite v = 20 e = 64 f = 32 degree seq :: [ 4^16, 16^4 ] E7.304 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 8}) Quotient :: dipole Aut^+ = (C2 x D8) : C2 (small group id <32, 43>) Aut = C2 x ((C2 x D8) : C2) (small group id <64, 254>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, Y2 * Y1^-2 * Y2 * Y1^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34, 6, 38, 15, 47, 26, 58, 21, 53, 14, 46, 5, 37)(3, 35, 9, 41, 16, 48, 13, 45, 20, 52, 7, 39, 18, 50, 11, 43)(4, 36, 12, 44, 24, 56, 31, 63, 32, 64, 27, 59, 17, 49, 8, 40)(10, 42, 23, 55, 29, 61, 19, 51, 30, 62, 25, 57, 28, 60, 22, 54)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 74, 106)(69, 101, 77, 109)(70, 102, 80, 112)(72, 104, 83, 115)(73, 105, 85, 117)(75, 107, 79, 111)(76, 108, 89, 121)(78, 110, 82, 114)(81, 113, 92, 124)(84, 116, 90, 122)(86, 118, 95, 127)(87, 119, 91, 123)(88, 120, 93, 125)(94, 126, 96, 128) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 76)(6, 81)(7, 83)(8, 66)(9, 86)(10, 67)(11, 87)(12, 69)(13, 89)(14, 88)(15, 91)(16, 92)(17, 70)(18, 93)(19, 71)(20, 94)(21, 95)(22, 73)(23, 75)(24, 78)(25, 77)(26, 96)(27, 79)(28, 80)(29, 82)(30, 84)(31, 85)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4^4 ), ( 4^16 ) } Outer automorphisms :: reflexible Dual of E7.300 Graph:: simple bipartite v = 20 e = 64 f = 32 degree seq :: [ 4^16, 16^4 ] E7.305 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 8}) Quotient :: dipole Aut^+ = (C2 x D8) : C2 (small group id <32, 43>) Aut = C2 x ((C2 x D8) : C2) (small group id <64, 254>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, Y2 * Y1^3 * Y2 * Y1^-1, (Y2 * Y1^-2)^2, (Y2 * Y1)^4 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34, 6, 38, 15, 47, 26, 58, 23, 55, 14, 46, 5, 37)(3, 35, 9, 41, 20, 52, 7, 39, 18, 50, 13, 45, 16, 48, 11, 43)(4, 36, 12, 44, 24, 56, 31, 63, 32, 64, 27, 59, 17, 49, 8, 40)(10, 42, 22, 54, 28, 60, 25, 57, 29, 61, 19, 51, 30, 62, 21, 53)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 74, 106)(69, 101, 77, 109)(70, 102, 80, 112)(72, 104, 83, 115)(73, 105, 79, 111)(75, 107, 87, 119)(76, 108, 89, 121)(78, 110, 84, 116)(81, 113, 92, 124)(82, 114, 90, 122)(85, 117, 91, 123)(86, 118, 95, 127)(88, 120, 94, 126)(93, 125, 96, 128) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 76)(6, 81)(7, 83)(8, 66)(9, 85)(10, 67)(11, 86)(12, 69)(13, 89)(14, 88)(15, 91)(16, 92)(17, 70)(18, 93)(19, 71)(20, 94)(21, 73)(22, 75)(23, 95)(24, 78)(25, 77)(26, 96)(27, 79)(28, 80)(29, 82)(30, 84)(31, 87)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4^4 ), ( 4^16 ) } Outer automorphisms :: reflexible Dual of E7.299 Graph:: simple bipartite v = 20 e = 64 f = 32 degree seq :: [ 4^16, 16^4 ] E7.306 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 8}) Quotient :: dipole Aut^+ = (C2 x D8) : C2 (small group id <32, 43>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ Y2^2, R^2, (R * Y1)^2, (Y3 * Y2)^2, Y3^4, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y1^-1 * Y3^-1 * Y1 * Y3 * Y1^-2, (R * Y2 * Y3^-1)^2 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34, 7, 39, 18, 50, 15, 47, 24, 56, 17, 49, 5, 37)(3, 35, 11, 43, 25, 57, 32, 64, 28, 60, 29, 61, 19, 51, 8, 40)(4, 36, 14, 46, 21, 53, 9, 41, 6, 38, 16, 48, 20, 52, 10, 42)(12, 44, 23, 55, 30, 62, 26, 58, 13, 45, 22, 54, 31, 63, 27, 59)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 77, 109)(69, 101, 75, 107)(70, 102, 76, 108)(71, 103, 83, 115)(73, 105, 87, 119)(74, 106, 86, 118)(78, 110, 90, 122)(79, 111, 92, 124)(80, 112, 91, 123)(81, 113, 89, 121)(82, 114, 93, 125)(84, 116, 95, 127)(85, 117, 94, 126)(88, 120, 96, 128) L = (1, 68)(2, 73)(3, 76)(4, 79)(5, 80)(6, 65)(7, 84)(8, 86)(9, 88)(10, 66)(11, 90)(12, 92)(13, 67)(14, 69)(15, 70)(16, 82)(17, 85)(18, 78)(19, 94)(20, 81)(21, 71)(22, 96)(23, 72)(24, 74)(25, 95)(26, 93)(27, 75)(28, 77)(29, 91)(30, 89)(31, 83)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4^4 ), ( 4^16 ) } Outer automorphisms :: reflexible Dual of E7.301 Graph:: simple bipartite v = 20 e = 64 f = 32 degree seq :: [ 4^16, 16^4 ] E7.307 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 42>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ Y2^2, R^2, (R * Y1)^2, (Y3 * Y2)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y3^4, Y3^-2 * Y1^-4, Y1^-1 * Y2 * Y1 * Y2 * Y1^-2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y1 * Y3 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34, 7, 39, 20, 52, 16, 48, 28, 60, 19, 51, 5, 37)(3, 35, 11, 43, 26, 58, 8, 40, 24, 56, 17, 49, 21, 53, 13, 45)(4, 36, 15, 47, 23, 55, 9, 41, 6, 38, 18, 50, 22, 54, 10, 42)(12, 44, 25, 57, 31, 63, 29, 61, 14, 46, 27, 59, 32, 64, 30, 62)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 78, 110)(69, 101, 81, 113)(70, 102, 76, 108)(71, 103, 85, 117)(73, 105, 91, 123)(74, 106, 89, 121)(75, 107, 84, 116)(77, 109, 92, 124)(79, 111, 94, 126)(80, 112, 88, 120)(82, 114, 93, 125)(83, 115, 90, 122)(86, 118, 96, 128)(87, 119, 95, 127) L = (1, 68)(2, 73)(3, 76)(4, 80)(5, 82)(6, 65)(7, 86)(8, 89)(9, 92)(10, 66)(11, 93)(12, 88)(13, 91)(14, 67)(15, 69)(16, 70)(17, 94)(18, 84)(19, 87)(20, 79)(21, 95)(22, 83)(23, 71)(24, 78)(25, 77)(26, 96)(27, 72)(28, 74)(29, 81)(30, 75)(31, 90)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4^4 ), ( 4^16 ) } Outer automorphisms :: reflexible Dual of E7.302 Graph:: simple bipartite v = 20 e = 64 f = 32 degree seq :: [ 4^16, 16^4 ] E7.308 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 8}) Quotient :: edge Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T1^-2 * T2^-1 * T1^-2 * T2, T1 * T2^-1 * T1^2 * T2 * T1, T2 * T1 * T2^2 * T1^-1 * T2, T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 19, 8)(4, 12, 25, 13)(6, 16, 28, 17)(9, 23, 14, 24)(11, 26, 15, 27)(18, 29, 21, 30)(20, 31, 22, 32)(33, 34, 38, 36)(35, 41, 48, 43)(37, 46, 49, 47)(39, 50, 44, 52)(40, 53, 45, 54)(42, 51, 60, 57)(55, 63, 58, 61)(56, 64, 59, 62) 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) :: { ( 16^4 ) } Outer automorphisms :: reflexible Dual of E7.313 Transitivity :: ET+ Graph:: simple bipartite v = 16 e = 32 f = 4 degree seq :: [ 4^16 ] E7.309 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 8}) Quotient :: edge Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^-2, T1^-1 * T2^4 * T1^-1, T2^2 * T1^-1 * T2^-2 * T1^-1, (T2^-1 * T1)^4 ] Map:: polytopal 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, 34, 38, 36)(35, 41, 49, 43)(37, 46, 50, 47)(39, 51, 44, 53)(40, 54, 45, 55)(42, 56, 48, 52)(57, 61, 59, 63)(58, 64, 60, 62) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.311 Transitivity :: ET+ Graph:: bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.310 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 8}) Quotient :: edge Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2^2 * T1^-1 * T2^2, T2 * T1^-2 * T2^-1 * T1^-2, T2 * T1 * T2^-3 * T1, T2^2 * T1 * T2^-1 * T1 * T2, (T2^-1 * T1)^4 ] Map:: non-degenerate R = (1, 3, 10, 19, 31, 22, 16, 5)(2, 7, 20, 11, 28, 15, 24, 8)(4, 12, 26, 9, 25, 14, 27, 13)(6, 17, 29, 21, 32, 23, 30, 18)(33, 34, 38, 36)(35, 41, 49, 43)(37, 46, 50, 47)(39, 51, 44, 53)(40, 54, 45, 55)(42, 56, 61, 59)(48, 52, 62, 58)(57, 63, 60, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.312 Transitivity :: ET+ Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.311 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 8}) Quotient :: loop Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T1^-2 * T2^-1 * T1^-2 * T2, T1 * T2^-1 * T1^2 * T2 * T1, T2 * T1 * T2^2 * T1^-1 * T2, T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 33, 3, 35, 10, 42, 5, 37)(2, 34, 7, 39, 19, 51, 8, 40)(4, 36, 12, 44, 25, 57, 13, 45)(6, 38, 16, 48, 28, 60, 17, 49)(9, 41, 23, 55, 14, 46, 24, 56)(11, 43, 26, 58, 15, 47, 27, 59)(18, 50, 29, 61, 21, 53, 30, 62)(20, 52, 31, 63, 22, 54, 32, 64) L = (1, 34)(2, 38)(3, 41)(4, 33)(5, 46)(6, 36)(7, 50)(8, 53)(9, 48)(10, 51)(11, 35)(12, 52)(13, 54)(14, 49)(15, 37)(16, 43)(17, 47)(18, 44)(19, 60)(20, 39)(21, 45)(22, 40)(23, 63)(24, 64)(25, 42)(26, 61)(27, 62)(28, 57)(29, 55)(30, 56)(31, 58)(32, 59) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.309 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.312 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 8}) Quotient :: loop Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T1 * T2 * T1^2 * T2^-1 * T1, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, (T2 * T1^-1)^8 ] Map:: non-degenerate R = (1, 33, 3, 35, 10, 42, 5, 37)(2, 34, 7, 39, 19, 51, 8, 40)(4, 36, 12, 44, 25, 57, 13, 45)(6, 38, 16, 48, 28, 60, 17, 49)(9, 41, 23, 55, 14, 46, 24, 56)(11, 43, 26, 58, 15, 47, 27, 59)(18, 50, 29, 61, 21, 53, 30, 62)(20, 52, 31, 63, 22, 54, 32, 64) L = (1, 34)(2, 38)(3, 41)(4, 33)(5, 46)(6, 36)(7, 50)(8, 53)(9, 48)(10, 51)(11, 35)(12, 52)(13, 54)(14, 49)(15, 37)(16, 43)(17, 47)(18, 44)(19, 60)(20, 39)(21, 45)(22, 40)(23, 62)(24, 61)(25, 42)(26, 64)(27, 63)(28, 57)(29, 59)(30, 58)(31, 56)(32, 55) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.310 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.313 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 8}) Quotient :: loop Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^-2, T1^-1 * T2^4 * T1^-1, T2^2 * T1^-1 * T2^-2 * T1^-1, (T2^-1 * T1)^4 ] Map:: non-degenerate R = (1, 33, 3, 35, 10, 42, 18, 50, 6, 38, 17, 49, 16, 48, 5, 37)(2, 34, 7, 39, 20, 52, 13, 45, 4, 36, 12, 44, 24, 56, 8, 40)(9, 41, 25, 57, 14, 46, 28, 60, 11, 43, 27, 59, 15, 47, 26, 58)(19, 51, 29, 61, 22, 54, 32, 64, 21, 53, 31, 63, 23, 55, 30, 62) L = (1, 34)(2, 38)(3, 41)(4, 33)(5, 46)(6, 36)(7, 51)(8, 54)(9, 49)(10, 56)(11, 35)(12, 53)(13, 55)(14, 50)(15, 37)(16, 52)(17, 43)(18, 47)(19, 44)(20, 42)(21, 39)(22, 45)(23, 40)(24, 48)(25, 61)(26, 64)(27, 63)(28, 62)(29, 59)(30, 58)(31, 57)(32, 60) local type(s) :: { ( 4^16 ) } Outer automorphisms :: reflexible Dual of E7.308 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 32 f = 16 degree seq :: [ 16^4 ] E7.314 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^4, Y2^4, (R * Y2 * Y3^-1)^2, Y3 * Y2^-2 * Y3^-1 * Y2^-2, (Y2^-1 * R * Y2^-1)^2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y1 * Y2 * Y3 * Y1^-1 * Y2^-1 * Y3^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2)^8 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 16, 48, 11, 43)(5, 37, 14, 46, 17, 49, 15, 47)(7, 39, 18, 50, 12, 44, 20, 52)(8, 40, 21, 53, 13, 45, 22, 54)(10, 42, 19, 51, 28, 60, 25, 57)(23, 55, 30, 62, 26, 58, 32, 64)(24, 56, 29, 61, 27, 59, 31, 63)(65, 97, 67, 99, 74, 106, 69, 101)(66, 98, 71, 103, 83, 115, 72, 104)(68, 100, 76, 108, 89, 121, 77, 109)(70, 102, 80, 112, 92, 124, 81, 113)(73, 105, 87, 119, 78, 110, 88, 120)(75, 107, 90, 122, 79, 111, 91, 123)(82, 114, 93, 125, 85, 117, 94, 126)(84, 116, 95, 127, 86, 118, 96, 128) L = (1, 68)(2, 65)(3, 75)(4, 70)(5, 79)(6, 66)(7, 84)(8, 86)(9, 67)(10, 89)(11, 80)(12, 82)(13, 85)(14, 69)(15, 81)(16, 73)(17, 78)(18, 71)(19, 74)(20, 76)(21, 72)(22, 77)(23, 96)(24, 95)(25, 92)(26, 94)(27, 93)(28, 83)(29, 88)(30, 87)(31, 91)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E7.319 Graph:: bipartite v = 16 e = 64 f = 36 degree seq :: [ 8^16 ] E7.315 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, Y1^4, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1^-1 * Y2^-4 * Y1^-1, Y2^2 * Y1 * Y2^2 * Y1^-1, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 17, 49, 11, 43)(5, 37, 14, 46, 18, 50, 15, 47)(7, 39, 19, 51, 12, 44, 21, 53)(8, 40, 22, 54, 13, 45, 23, 55)(10, 42, 24, 56, 16, 48, 20, 52)(25, 57, 29, 61, 27, 59, 31, 63)(26, 58, 32, 64, 28, 60, 30, 62)(65, 97, 67, 99, 74, 106, 82, 114, 70, 102, 81, 113, 80, 112, 69, 101)(66, 98, 71, 103, 84, 116, 77, 109, 68, 100, 76, 108, 88, 120, 72, 104)(73, 105, 89, 121, 78, 110, 92, 124, 75, 107, 91, 123, 79, 111, 90, 122)(83, 115, 93, 125, 86, 118, 96, 128, 85, 117, 95, 127, 87, 119, 94, 126) L = (1, 67)(2, 71)(3, 74)(4, 76)(5, 65)(6, 81)(7, 84)(8, 66)(9, 89)(10, 82)(11, 91)(12, 88)(13, 68)(14, 92)(15, 90)(16, 69)(17, 80)(18, 70)(19, 93)(20, 77)(21, 95)(22, 96)(23, 94)(24, 72)(25, 78)(26, 73)(27, 79)(28, 75)(29, 86)(30, 83)(31, 87)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E7.318 Graph:: bipartite v = 12 e = 64 f = 40 degree seq :: [ 8^8, 16^4 ] E7.316 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1 * Y2 * Y1^2 * Y2^-1 * Y1, Y2^3 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2^-3 * Y1^-1, Y2^2 * Y1 * Y2^2 * Y1^-1, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 17, 49, 11, 43)(5, 37, 14, 46, 18, 50, 15, 47)(7, 39, 19, 51, 12, 44, 21, 53)(8, 40, 22, 54, 13, 45, 23, 55)(10, 42, 24, 56, 29, 61, 27, 59)(16, 48, 20, 52, 30, 62, 26, 58)(25, 57, 31, 63, 28, 60, 32, 64)(65, 97, 67, 99, 74, 106, 83, 115, 95, 127, 86, 118, 80, 112, 69, 101)(66, 98, 71, 103, 84, 116, 75, 107, 92, 124, 79, 111, 88, 120, 72, 104)(68, 100, 76, 108, 90, 122, 73, 105, 89, 121, 78, 110, 91, 123, 77, 109)(70, 102, 81, 113, 93, 125, 85, 117, 96, 128, 87, 119, 94, 126, 82, 114) L = (1, 67)(2, 71)(3, 74)(4, 76)(5, 65)(6, 81)(7, 84)(8, 66)(9, 89)(10, 83)(11, 92)(12, 90)(13, 68)(14, 91)(15, 88)(16, 69)(17, 93)(18, 70)(19, 95)(20, 75)(21, 96)(22, 80)(23, 94)(24, 72)(25, 78)(26, 73)(27, 77)(28, 79)(29, 85)(30, 82)(31, 86)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E7.317 Graph:: bipartite v = 12 e = 64 f = 40 degree seq :: [ 8^8, 16^4 ] E7.317 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3^4 * Y2^2, Y3^2 * Y2 * Y3^2 * Y2^-1, Y3^-2 * Y2^-1 * Y3^2 * Y2^-1, (Y3^-1 * Y2^-1)^4, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)(65, 97, 66, 98, 70, 102, 68, 100)(67, 99, 73, 105, 81, 113, 75, 107)(69, 101, 78, 110, 82, 114, 79, 111)(71, 103, 83, 115, 76, 108, 85, 117)(72, 104, 86, 118, 77, 109, 87, 119)(74, 106, 88, 120, 80, 112, 84, 116)(89, 121, 93, 125, 91, 123, 95, 127)(90, 122, 96, 128, 92, 124, 94, 126) L = (1, 67)(2, 71)(3, 74)(4, 76)(5, 65)(6, 81)(7, 84)(8, 66)(9, 89)(10, 82)(11, 91)(12, 88)(13, 68)(14, 92)(15, 90)(16, 69)(17, 80)(18, 70)(19, 93)(20, 77)(21, 95)(22, 96)(23, 94)(24, 72)(25, 78)(26, 73)(27, 79)(28, 75)(29, 86)(30, 83)(31, 87)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E7.316 Graph:: simple bipartite v = 40 e = 64 f = 12 degree seq :: [ 2^32, 8^8 ] E7.318 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2 * Y3^-2 * Y2^-1, Y3 * Y2^-1 * Y3^-3 * Y2^-1, Y3^3 * Y2^-1 * Y3^-1 * Y2^-1, (Y3^-1 * Y1^-1)^8 ] Map:: polytopal R = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)(65, 97, 66, 98, 70, 102, 68, 100)(67, 99, 73, 105, 81, 113, 75, 107)(69, 101, 78, 110, 82, 114, 79, 111)(71, 103, 83, 115, 76, 108, 85, 117)(72, 104, 86, 118, 77, 109, 87, 119)(74, 106, 88, 120, 93, 125, 91, 123)(80, 112, 84, 116, 94, 126, 90, 122)(89, 121, 95, 127, 92, 124, 96, 128) L = (1, 67)(2, 71)(3, 74)(4, 76)(5, 65)(6, 81)(7, 84)(8, 66)(9, 89)(10, 83)(11, 92)(12, 90)(13, 68)(14, 91)(15, 88)(16, 69)(17, 93)(18, 70)(19, 95)(20, 75)(21, 96)(22, 80)(23, 94)(24, 72)(25, 78)(26, 73)(27, 77)(28, 79)(29, 85)(30, 82)(31, 86)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E7.315 Graph:: simple bipartite v = 40 e = 64 f = 12 degree seq :: [ 2^32, 8^8 ] E7.319 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-2 * Y3 * Y1^-2, Y1^-2 * Y3^-2 * Y1^-2, Y3 * Y1^2 * Y3 * Y1^-2, (Y3^-1 * Y1)^4, (Y3 * Y2^-1)^4 ] Map:: R = (1, 33, 2, 34, 6, 38, 17, 49, 10, 42, 21, 53, 13, 45, 4, 36)(3, 35, 9, 41, 19, 51, 16, 48, 5, 37, 15, 47, 18, 50, 11, 43)(7, 39, 20, 52, 12, 44, 24, 56, 8, 40, 23, 55, 14, 46, 22, 54)(25, 57, 29, 61, 27, 59, 31, 63, 26, 58, 30, 62, 28, 60, 32, 64)(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, 74)(4, 76)(5, 65)(6, 82)(7, 85)(8, 66)(9, 89)(10, 69)(11, 91)(12, 81)(13, 83)(14, 68)(15, 90)(16, 92)(17, 78)(18, 77)(19, 70)(20, 93)(21, 72)(22, 95)(23, 94)(24, 96)(25, 79)(26, 73)(27, 80)(28, 75)(29, 87)(30, 84)(31, 88)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 8 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E7.314 Graph:: simple bipartite v = 36 e = 64 f = 16 degree seq :: [ 2^32, 16^4 ] E7.320 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 8}) Quotient :: edge Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, (T1 * T2^-1 * T1)^2, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, (T2 * T1^-1)^8 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 19, 8)(4, 12, 25, 13)(6, 16, 28, 17)(9, 23, 14, 24)(11, 26, 15, 27)(18, 29, 21, 30)(20, 31, 22, 32)(33, 34, 38, 36)(35, 41, 49, 43)(37, 46, 48, 47)(39, 50, 45, 52)(40, 53, 44, 54)(42, 51, 60, 57)(55, 61, 59, 64)(56, 62, 58, 63) 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) :: { ( 16^4 ) } Outer automorphisms :: reflexible Dual of E7.325 Transitivity :: ET+ Graph:: simple bipartite v = 16 e = 32 f = 4 degree seq :: [ 4^16 ] E7.321 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 8}) Quotient :: edge Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ F^2, (T2 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T1^4, T2^3 * T1^-1 * T2^-1 * T1^-1, T1 * T2 * T1^2 * T2 * T1 * T2^2, T2^8 ] Map:: non-degenerate R = (1, 3, 10, 17, 31, 24, 14, 5)(2, 7, 18, 27, 26, 13, 20, 8)(4, 11, 22, 9, 21, 29, 25, 12)(6, 15, 28, 23, 32, 19, 30, 16)(33, 34, 38, 36)(35, 41, 51, 40)(37, 43, 55, 45)(39, 49, 61, 48)(42, 50, 60, 54)(44, 47, 59, 56)(46, 52, 62, 57)(53, 63, 58, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.323 Transitivity :: ET+ Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.322 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 8}) Quotient :: edge Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^-2, T2^4 * T1^-2, (T2^2 * T1^-1)^2, (T2^-1 * T1)^4 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 6, 17, 16, 5)(2, 7, 20, 13, 4, 12, 24, 8)(9, 25, 15, 28, 11, 27, 14, 26)(19, 29, 23, 32, 21, 31, 22, 30)(33, 34, 38, 36)(35, 41, 49, 43)(37, 46, 50, 47)(39, 51, 44, 53)(40, 54, 45, 55)(42, 52, 48, 56)(57, 63, 59, 61)(58, 64, 60, 62) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.324 Transitivity :: ET+ Graph:: bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.323 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 8}) Quotient :: loop Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, (T1 * T2^-1 * T1)^2, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, (T2 * T1^-1)^8 ] Map:: non-degenerate R = (1, 33, 3, 35, 10, 42, 5, 37)(2, 34, 7, 39, 19, 51, 8, 40)(4, 36, 12, 44, 25, 57, 13, 45)(6, 38, 16, 48, 28, 60, 17, 49)(9, 41, 23, 55, 14, 46, 24, 56)(11, 43, 26, 58, 15, 47, 27, 59)(18, 50, 29, 61, 21, 53, 30, 62)(20, 52, 31, 63, 22, 54, 32, 64) L = (1, 34)(2, 38)(3, 41)(4, 33)(5, 46)(6, 36)(7, 50)(8, 53)(9, 49)(10, 51)(11, 35)(12, 54)(13, 52)(14, 48)(15, 37)(16, 47)(17, 43)(18, 45)(19, 60)(20, 39)(21, 44)(22, 40)(23, 61)(24, 62)(25, 42)(26, 63)(27, 64)(28, 57)(29, 59)(30, 58)(31, 56)(32, 55) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.321 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.324 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 8}) Quotient :: loop Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T2 * T1^-2 * T2^-1 * T1^-2, (T2^-1 * T1 * T2^-1)^2, T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 33, 3, 35, 10, 42, 5, 37)(2, 34, 7, 39, 19, 51, 8, 40)(4, 36, 12, 44, 25, 57, 13, 45)(6, 38, 16, 48, 28, 60, 17, 49)(9, 41, 23, 55, 15, 47, 24, 56)(11, 43, 26, 58, 14, 46, 27, 59)(18, 50, 29, 61, 22, 54, 30, 62)(20, 52, 31, 63, 21, 53, 32, 64) L = (1, 34)(2, 38)(3, 41)(4, 33)(5, 46)(6, 36)(7, 50)(8, 53)(9, 48)(10, 57)(11, 35)(12, 52)(13, 54)(14, 49)(15, 37)(16, 43)(17, 47)(18, 44)(19, 42)(20, 39)(21, 45)(22, 40)(23, 61)(24, 64)(25, 60)(26, 63)(27, 62)(28, 51)(29, 58)(30, 56)(31, 55)(32, 59) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.322 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.325 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 8}) Quotient :: loop Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ F^2, (T2 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T1^4, T2^3 * T1^-1 * T2^-1 * T1^-1, T1 * T2 * T1^2 * T2 * T1 * T2^2, T2^8 ] Map:: non-degenerate R = (1, 33, 3, 35, 10, 42, 17, 49, 31, 63, 24, 56, 14, 46, 5, 37)(2, 34, 7, 39, 18, 50, 27, 59, 26, 58, 13, 45, 20, 52, 8, 40)(4, 36, 11, 43, 22, 54, 9, 41, 21, 53, 29, 61, 25, 57, 12, 44)(6, 38, 15, 47, 28, 60, 23, 55, 32, 64, 19, 51, 30, 62, 16, 48) L = (1, 34)(2, 38)(3, 41)(4, 33)(5, 43)(6, 36)(7, 49)(8, 35)(9, 51)(10, 50)(11, 55)(12, 47)(13, 37)(14, 52)(15, 59)(16, 39)(17, 61)(18, 60)(19, 40)(20, 62)(21, 63)(22, 42)(23, 45)(24, 44)(25, 46)(26, 64)(27, 56)(28, 54)(29, 48)(30, 57)(31, 58)(32, 53) local type(s) :: { ( 4^16 ) } Outer automorphisms :: reflexible Dual of E7.320 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 32 f = 16 degree seq :: [ 16^4 ] E7.326 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^4, Y2^4, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^2 * Y3^-1 * Y2, Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2 * Y3 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^2 * Y2 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 16, 48, 11, 43)(5, 37, 14, 46, 17, 49, 15, 47)(7, 39, 18, 50, 12, 44, 20, 52)(8, 40, 21, 53, 13, 45, 22, 54)(10, 42, 25, 57, 28, 60, 19, 51)(23, 55, 29, 61, 26, 58, 31, 63)(24, 56, 32, 64, 27, 59, 30, 62)(65, 97, 67, 99, 74, 106, 69, 101)(66, 98, 71, 103, 83, 115, 72, 104)(68, 100, 76, 108, 89, 121, 77, 109)(70, 102, 80, 112, 92, 124, 81, 113)(73, 105, 87, 119, 79, 111, 88, 120)(75, 107, 90, 122, 78, 110, 91, 123)(82, 114, 93, 125, 86, 118, 94, 126)(84, 116, 95, 127, 85, 117, 96, 128) L = (1, 68)(2, 65)(3, 75)(4, 70)(5, 79)(6, 66)(7, 84)(8, 86)(9, 67)(10, 83)(11, 80)(12, 82)(13, 85)(14, 69)(15, 81)(16, 73)(17, 78)(18, 71)(19, 92)(20, 76)(21, 72)(22, 77)(23, 95)(24, 94)(25, 74)(26, 93)(27, 96)(28, 89)(29, 87)(30, 91)(31, 90)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E7.331 Graph:: bipartite v = 16 e = 64 f = 36 degree seq :: [ 8^16 ] E7.327 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1^-1 * Y2^4 * Y1^-1, (Y2^2 * Y1)^2, Y2^2 * Y1 * Y2^-2 * Y1^-1, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 17, 49, 11, 43)(5, 37, 14, 46, 18, 50, 15, 47)(7, 39, 19, 51, 12, 44, 21, 53)(8, 40, 22, 54, 13, 45, 23, 55)(10, 42, 20, 52, 16, 48, 24, 56)(25, 57, 31, 63, 27, 59, 29, 61)(26, 58, 32, 64, 28, 60, 30, 62)(65, 97, 67, 99, 74, 106, 82, 114, 70, 102, 81, 113, 80, 112, 69, 101)(66, 98, 71, 103, 84, 116, 77, 109, 68, 100, 76, 108, 88, 120, 72, 104)(73, 105, 89, 121, 79, 111, 92, 124, 75, 107, 91, 123, 78, 110, 90, 122)(83, 115, 93, 125, 87, 119, 96, 128, 85, 117, 95, 127, 86, 118, 94, 126) L = (1, 67)(2, 71)(3, 74)(4, 76)(5, 65)(6, 81)(7, 84)(8, 66)(9, 89)(10, 82)(11, 91)(12, 88)(13, 68)(14, 90)(15, 92)(16, 69)(17, 80)(18, 70)(19, 93)(20, 77)(21, 95)(22, 94)(23, 96)(24, 72)(25, 79)(26, 73)(27, 78)(28, 75)(29, 87)(30, 83)(31, 86)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E7.329 Graph:: bipartite v = 12 e = 64 f = 40 degree seq :: [ 8^8, 16^4 ] E7.328 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2^3 * Y1^-1 * Y2^-1 * Y1^-1, Y1 * Y2 * Y1^2 * Y2 * Y1 * Y2^2, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 19, 51, 8, 40)(5, 37, 11, 43, 23, 55, 13, 45)(7, 39, 17, 49, 29, 61, 16, 48)(10, 42, 18, 50, 28, 60, 22, 54)(12, 44, 15, 47, 27, 59, 24, 56)(14, 46, 20, 52, 30, 62, 25, 57)(21, 53, 31, 63, 26, 58, 32, 64)(65, 97, 67, 99, 74, 106, 81, 113, 95, 127, 88, 120, 78, 110, 69, 101)(66, 98, 71, 103, 82, 114, 91, 123, 90, 122, 77, 109, 84, 116, 72, 104)(68, 100, 75, 107, 86, 118, 73, 105, 85, 117, 93, 125, 89, 121, 76, 108)(70, 102, 79, 111, 92, 124, 87, 119, 96, 128, 83, 115, 94, 126, 80, 112) L = (1, 67)(2, 71)(3, 74)(4, 75)(5, 65)(6, 79)(7, 82)(8, 66)(9, 85)(10, 81)(11, 86)(12, 68)(13, 84)(14, 69)(15, 92)(16, 70)(17, 95)(18, 91)(19, 94)(20, 72)(21, 93)(22, 73)(23, 96)(24, 78)(25, 76)(26, 77)(27, 90)(28, 87)(29, 89)(30, 80)(31, 88)(32, 83)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E7.330 Graph:: bipartite v = 12 e = 64 f = 40 degree seq :: [ 8^8, 16^4 ] E7.329 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1, R^2, (Y2^-1 * Y3^-1)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y3^-3 * Y2^-1, Y3^8, (Y3^-1 * Y1^-1)^8 ] Map:: polytopal R = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)(65, 97, 66, 98, 70, 102, 68, 100)(67, 99, 73, 105, 85, 117, 75, 107)(69, 101, 77, 109, 82, 114, 71, 103)(72, 104, 83, 115, 92, 124, 79, 111)(74, 106, 81, 113, 91, 123, 88, 120)(76, 108, 80, 112, 93, 125, 87, 119)(78, 110, 84, 116, 94, 126, 86, 118)(89, 121, 95, 127, 90, 122, 96, 128) L = (1, 67)(2, 71)(3, 74)(4, 76)(5, 65)(6, 79)(7, 81)(8, 66)(9, 68)(10, 87)(11, 89)(12, 88)(13, 86)(14, 69)(15, 91)(16, 70)(17, 75)(18, 95)(19, 78)(20, 72)(21, 94)(22, 73)(23, 96)(24, 92)(25, 93)(26, 77)(27, 82)(28, 90)(29, 84)(30, 80)(31, 85)(32, 83)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E7.327 Graph:: simple bipartite v = 40 e = 64 f = 12 degree seq :: [ 2^32, 8^8 ] E7.330 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3^4 * Y2^2, (Y3^-2 * Y2^-1)^2, (Y3^2 * Y2^-1)^2, (Y3^-1 * Y2 * Y3^-1 * Y2^-1)^2, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)(65, 97, 66, 98, 70, 102, 68, 100)(67, 99, 73, 105, 81, 113, 75, 107)(69, 101, 78, 110, 82, 114, 79, 111)(71, 103, 83, 115, 76, 108, 85, 117)(72, 104, 86, 118, 77, 109, 87, 119)(74, 106, 84, 116, 80, 112, 88, 120)(89, 121, 95, 127, 91, 123, 93, 125)(90, 122, 96, 128, 92, 124, 94, 126) L = (1, 67)(2, 71)(3, 74)(4, 76)(5, 65)(6, 81)(7, 84)(8, 66)(9, 89)(10, 82)(11, 91)(12, 88)(13, 68)(14, 90)(15, 92)(16, 69)(17, 80)(18, 70)(19, 93)(20, 77)(21, 95)(22, 94)(23, 96)(24, 72)(25, 79)(26, 73)(27, 78)(28, 75)(29, 87)(30, 83)(31, 86)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E7.328 Graph:: simple bipartite v = 40 e = 64 f = 12 degree seq :: [ 2^32, 8^8 ] E7.331 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, Y3^4, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3 * Y1^-3, Y3 * Y1 * Y3 * Y1^5, (Y3 * Y2^-1)^4 ] Map:: R = (1, 33, 2, 34, 6, 38, 15, 47, 27, 59, 24, 56, 12, 44, 4, 36)(3, 35, 9, 41, 16, 48, 29, 61, 26, 58, 13, 45, 20, 52, 8, 40)(5, 37, 11, 43, 17, 49, 7, 39, 18, 50, 28, 60, 25, 57, 14, 46)(10, 42, 22, 54, 30, 62, 23, 55, 31, 63, 19, 51, 32, 64, 21, 53)(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, 74)(4, 75)(5, 65)(6, 80)(7, 83)(8, 66)(9, 79)(10, 69)(11, 87)(12, 84)(13, 68)(14, 86)(15, 92)(16, 94)(17, 70)(18, 91)(19, 72)(20, 96)(21, 73)(22, 93)(23, 77)(24, 78)(25, 76)(26, 95)(27, 90)(28, 85)(29, 88)(30, 81)(31, 82)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 8 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E7.326 Graph:: simple bipartite v = 36 e = 64 f = 16 degree seq :: [ 2^32, 16^4 ] E7.332 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 8}) Quotient :: edge Aut^+ = C8 : C4 (small group id <32, 13>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 150>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^3 * T1^-1, T2^3 * T1 * T2^-1 * T1^-1, (T1 * T2 * T1^-1 * T2)^2, (T2 * T1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 3, 10, 21, 32, 23, 16, 5)(2, 7, 20, 9, 25, 14, 24, 8)(4, 12, 28, 11, 27, 15, 26, 13)(6, 17, 29, 19, 31, 22, 30, 18)(33, 34, 38, 36)(35, 41, 49, 43)(37, 46, 50, 47)(39, 51, 44, 53)(40, 54, 45, 55)(42, 56, 61, 58)(48, 52, 62, 60)(57, 63, 59, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.333 Transitivity :: ET+ Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.333 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 8}) Quotient :: loop Aut^+ = C8 : C4 (small group id <32, 13>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 150>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T1)^2, (F * T2)^2, T2^4, T1 * T2 * T1^-2 * T2^-1 * T1, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^8 ] Map:: polytopal non-degenerate R = (1, 33, 3, 35, 10, 42, 5, 37)(2, 34, 7, 39, 19, 51, 8, 40)(4, 36, 12, 44, 25, 57, 13, 45)(6, 38, 16, 48, 28, 60, 17, 49)(9, 41, 23, 55, 14, 46, 24, 56)(11, 43, 26, 58, 15, 47, 27, 59)(18, 50, 29, 61, 21, 53, 30, 62)(20, 52, 31, 63, 22, 54, 32, 64) L = (1, 34)(2, 38)(3, 41)(4, 33)(5, 46)(6, 36)(7, 50)(8, 53)(9, 48)(10, 51)(11, 35)(12, 52)(13, 54)(14, 49)(15, 37)(16, 43)(17, 47)(18, 44)(19, 60)(20, 39)(21, 45)(22, 40)(23, 64)(24, 63)(25, 42)(26, 62)(27, 61)(28, 57)(29, 56)(30, 55)(31, 59)(32, 58) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.332 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.334 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 13>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 150>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^2 * Y1 * Y2^2, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y2^3 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y2^-3 * Y1^-1, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 17, 49, 11, 43)(5, 37, 14, 46, 18, 50, 15, 47)(7, 39, 19, 51, 12, 44, 21, 53)(8, 40, 22, 54, 13, 45, 23, 55)(10, 42, 24, 56, 29, 61, 26, 58)(16, 48, 20, 52, 30, 62, 28, 60)(25, 57, 31, 63, 27, 59, 32, 64)(65, 97, 67, 99, 74, 106, 85, 117, 96, 128, 87, 119, 80, 112, 69, 101)(66, 98, 71, 103, 84, 116, 73, 105, 89, 121, 78, 110, 88, 120, 72, 104)(68, 100, 76, 108, 92, 124, 75, 107, 91, 123, 79, 111, 90, 122, 77, 109)(70, 102, 81, 113, 93, 125, 83, 115, 95, 127, 86, 118, 94, 126, 82, 114) L = (1, 67)(2, 71)(3, 74)(4, 76)(5, 65)(6, 81)(7, 84)(8, 66)(9, 89)(10, 85)(11, 91)(12, 92)(13, 68)(14, 88)(15, 90)(16, 69)(17, 93)(18, 70)(19, 95)(20, 73)(21, 96)(22, 94)(23, 80)(24, 72)(25, 78)(26, 77)(27, 79)(28, 75)(29, 83)(30, 82)(31, 86)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E7.335 Graph:: bipartite v = 12 e = 64 f = 40 degree seq :: [ 8^8, 16^4 ] E7.335 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 13>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 150>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3^-3 * Y2^-1, Y3 * Y2^-2 * Y3^-1 * Y2^-2, Y3^2 * Y2 * Y3^2 * Y2^-1, (Y3^-1 * Y2^-1)^4, (Y3^-1 * Y1^-1)^8 ] Map:: polytopal R = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)(65, 97, 66, 98, 70, 102, 68, 100)(67, 99, 73, 105, 81, 113, 75, 107)(69, 101, 78, 110, 82, 114, 79, 111)(71, 103, 83, 115, 76, 108, 85, 117)(72, 104, 86, 118, 77, 109, 87, 119)(74, 106, 88, 120, 93, 125, 90, 122)(80, 112, 84, 116, 94, 126, 92, 124)(89, 121, 95, 127, 91, 123, 96, 128) L = (1, 67)(2, 71)(3, 74)(4, 76)(5, 65)(6, 81)(7, 84)(8, 66)(9, 89)(10, 85)(11, 91)(12, 92)(13, 68)(14, 88)(15, 90)(16, 69)(17, 93)(18, 70)(19, 95)(20, 73)(21, 96)(22, 94)(23, 80)(24, 72)(25, 78)(26, 77)(27, 79)(28, 75)(29, 83)(30, 82)(31, 86)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E7.334 Graph:: simple bipartite v = 40 e = 64 f = 12 degree seq :: [ 2^32, 8^8 ] E7.336 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 8}) Quotient :: edge Aut^+ = C8 : C4 (small group id <32, 14>) Aut = (C8 x C2 x C2) : C2 (small group id <64, 147>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1 * T2 * T1^-1, T2^8 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 20, 12, 5)(2, 7, 15, 23, 30, 24, 16, 8)(4, 11, 19, 27, 31, 26, 18, 10)(6, 13, 21, 28, 32, 29, 22, 14)(33, 34, 38, 36)(35, 40, 45, 42)(37, 39, 46, 43)(41, 48, 53, 50)(44, 47, 54, 51)(49, 56, 60, 58)(52, 55, 61, 59)(57, 62, 64, 63) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^4 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.337 Transitivity :: ET+ Graph:: simple bipartite v = 12 e = 32 f = 8 degree seq :: [ 4^8, 8^4 ] E7.337 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 8}) Quotient :: loop Aut^+ = C8 : C4 (small group id <32, 14>) Aut = (C8 x C2 x C2) : C2 (small group id <64, 147>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, T2^-2 * T1^2, (F * T2)^2, (F * T1)^2, T2^4, (T2 * T1)^8 ] Map:: non-degenerate R = (1, 33, 3, 35, 6, 38, 5, 37)(2, 34, 7, 39, 4, 36, 8, 40)(9, 41, 13, 45, 10, 42, 14, 46)(11, 43, 15, 47, 12, 44, 16, 48)(17, 49, 21, 53, 18, 50, 22, 54)(19, 51, 23, 55, 20, 52, 24, 56)(25, 57, 29, 61, 26, 58, 30, 62)(27, 59, 31, 63, 28, 60, 32, 64) L = (1, 34)(2, 38)(3, 41)(4, 33)(5, 42)(6, 36)(7, 43)(8, 44)(9, 37)(10, 35)(11, 40)(12, 39)(13, 49)(14, 50)(15, 51)(16, 52)(17, 46)(18, 45)(19, 48)(20, 47)(21, 57)(22, 58)(23, 59)(24, 60)(25, 54)(26, 53)(27, 56)(28, 55)(29, 63)(30, 64)(31, 62)(32, 61) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.336 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 32 f = 12 degree seq :: [ 8^8 ] E7.338 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 14>) Aut = (C8 x C2 x C2) : C2 (small group id <64, 147>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y1^4, Y1^-1 * Y2^-1 * Y1 * Y2^-1, (Y3^-1 * Y1^-1)^4, Y2^8 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 8, 40, 13, 45, 10, 42)(5, 37, 7, 39, 14, 46, 11, 43)(9, 41, 16, 48, 21, 53, 18, 50)(12, 44, 15, 47, 22, 54, 19, 51)(17, 49, 24, 56, 28, 60, 26, 58)(20, 52, 23, 55, 29, 61, 27, 59)(25, 57, 30, 62, 32, 64, 31, 63)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 84, 116, 76, 108, 69, 101)(66, 98, 71, 103, 79, 111, 87, 119, 94, 126, 88, 120, 80, 112, 72, 104)(68, 100, 75, 107, 83, 115, 91, 123, 95, 127, 90, 122, 82, 114, 74, 106)(70, 102, 77, 109, 85, 117, 92, 124, 96, 128, 93, 125, 86, 118, 78, 110) L = (1, 67)(2, 71)(3, 73)(4, 75)(5, 65)(6, 77)(7, 79)(8, 66)(9, 81)(10, 68)(11, 83)(12, 69)(13, 85)(14, 70)(15, 87)(16, 72)(17, 89)(18, 74)(19, 91)(20, 76)(21, 92)(22, 78)(23, 94)(24, 80)(25, 84)(26, 82)(27, 95)(28, 96)(29, 86)(30, 88)(31, 90)(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, 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 E7.339 Graph:: bipartite v = 12 e = 64 f = 40 degree seq :: [ 8^8, 16^4 ] E7.339 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 14>) Aut = (C8 x C2 x C2) : C2 (small group id <64, 147>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^3 * Y2 * Y3^-5 * Y2^-1, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)(65, 97, 66, 98, 70, 102, 68, 100)(67, 99, 72, 104, 77, 109, 74, 106)(69, 101, 71, 103, 78, 110, 75, 107)(73, 105, 80, 112, 85, 117, 82, 114)(76, 108, 79, 111, 86, 118, 83, 115)(81, 113, 88, 120, 92, 124, 90, 122)(84, 116, 87, 119, 93, 125, 91, 123)(89, 121, 94, 126, 96, 128, 95, 127) L = (1, 67)(2, 71)(3, 73)(4, 75)(5, 65)(6, 77)(7, 79)(8, 66)(9, 81)(10, 68)(11, 83)(12, 69)(13, 85)(14, 70)(15, 87)(16, 72)(17, 89)(18, 74)(19, 91)(20, 76)(21, 92)(22, 78)(23, 94)(24, 80)(25, 84)(26, 82)(27, 95)(28, 96)(29, 86)(30, 88)(31, 90)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E7.338 Graph:: simple bipartite v = 40 e = 64 f = 12 degree seq :: [ 2^32, 8^8 ] E7.340 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 16, 16}) Quotient :: regular Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^-1, T1^16 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 30, 32, 31, 27, 23, 19, 15, 11, 7) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 32) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 16 f = 2 degree seq :: [ 16^2 ] E7.341 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 16, 16}) Quotient :: edge Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^16 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 32, 30, 26, 22, 18, 14, 10, 6)(33, 34)(35, 37)(36, 38)(39, 41)(40, 42)(43, 45)(44, 46)(47, 49)(48, 50)(51, 53)(52, 54)(55, 57)(56, 58)(59, 61)(60, 62)(63, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32, 32 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E7.342 Transitivity :: ET+ Graph:: simple bipartite v = 18 e = 32 f = 2 degree seq :: [ 2^16, 16^2 ] E7.342 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 16, 16}) Quotient :: loop Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^16 ] Map:: R = (1, 33, 3, 35, 7, 39, 11, 43, 15, 47, 19, 51, 23, 55, 27, 59, 31, 63, 28, 60, 24, 56, 20, 52, 16, 48, 12, 44, 8, 40, 4, 36)(2, 34, 5, 37, 9, 41, 13, 45, 17, 49, 21, 53, 25, 57, 29, 61, 32, 64, 30, 62, 26, 58, 22, 54, 18, 50, 14, 46, 10, 42, 6, 38) 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) 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 E7.341 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 32 f = 18 degree seq :: [ 32^2 ] E7.343 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 16}) Quotient :: dipole Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^16, (Y3 * Y2^-1)^16 ] Map:: R = (1, 33, 2, 34)(3, 35, 5, 37)(4, 36, 6, 38)(7, 39, 9, 41)(8, 40, 10, 42)(11, 43, 13, 45)(12, 44, 14, 46)(15, 47, 17, 49)(16, 48, 18, 50)(19, 51, 21, 53)(20, 52, 22, 54)(23, 55, 25, 57)(24, 56, 26, 58)(27, 59, 29, 61)(28, 60, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 71, 103, 75, 107, 79, 111, 83, 115, 87, 119, 91, 123, 95, 127, 92, 124, 88, 120, 84, 116, 80, 112, 76, 108, 72, 104, 68, 100)(66, 98, 69, 101, 73, 105, 77, 109, 81, 113, 85, 117, 89, 121, 93, 125, 96, 128, 94, 126, 90, 122, 86, 118, 82, 114, 78, 110, 74, 106, 70, 102) L = (1, 66)(2, 65)(3, 69)(4, 70)(5, 67)(6, 68)(7, 73)(8, 74)(9, 71)(10, 72)(11, 77)(12, 78)(13, 75)(14, 76)(15, 81)(16, 82)(17, 79)(18, 80)(19, 85)(20, 86)(21, 83)(22, 84)(23, 89)(24, 90)(25, 87)(26, 88)(27, 93)(28, 94)(29, 91)(30, 92)(31, 96)(32, 95)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 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 E7.344 Graph:: bipartite v = 18 e = 64 f = 34 degree seq :: [ 4^16, 32^2 ] E7.344 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 16}) Quotient :: dipole Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-16, Y1^16 ] Map:: 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, 6, 38, 10, 42, 14, 46, 18, 50, 22, 54, 26, 58, 30, 62, 32, 64, 31, 63, 27, 59, 23, 55, 19, 51, 15, 47, 11, 43, 7, 39)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 70)(3, 65)(4, 71)(5, 74)(6, 66)(7, 68)(8, 75)(9, 78)(10, 69)(11, 72)(12, 79)(13, 82)(14, 73)(15, 76)(16, 83)(17, 86)(18, 77)(19, 80)(20, 87)(21, 90)(22, 81)(23, 84)(24, 91)(25, 94)(26, 85)(27, 88)(28, 95)(29, 96)(30, 89)(31, 92)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E7.343 Graph:: simple bipartite v = 34 e = 64 f = 18 degree seq :: [ 2^32, 32^2 ] E7.345 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 16, 16}) Quotient :: regular Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1^2 * T2 * T1^-2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1 * T2 * T1^7, T1^-2 * T2 * T1^-5 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 25, 16, 24, 15, 23, 32, 28, 19, 10, 4)(3, 7, 12, 22, 30, 27, 18, 9, 14, 6, 13, 21, 31, 26, 17, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 25)(19, 27)(20, 30)(22, 32)(26, 29)(28, 31) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 16 f = 2 degree seq :: [ 16^2 ] E7.346 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 16, 16}) Quotient :: edge Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T1 * T2^-2 * T1 * T2^2, (T2 * T1 * T2^-1 * T1)^2, T2^7 * T1 * T2 * T1 ] Map:: R = (1, 3, 8, 17, 26, 31, 23, 13, 21, 11, 20, 29, 28, 19, 10, 4)(2, 5, 12, 22, 30, 27, 18, 9, 16, 7, 15, 25, 32, 24, 14, 6)(33, 34)(35, 39)(36, 41)(37, 43)(38, 45)(40, 44)(42, 46)(47, 52)(48, 53)(49, 57)(50, 55)(51, 59)(54, 61)(56, 63)(58, 62)(60, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32, 32 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E7.347 Transitivity :: ET+ Graph:: simple bipartite v = 18 e = 32 f = 2 degree seq :: [ 2^16, 16^2 ] E7.347 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 16, 16}) Quotient :: loop Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T1 * T2^-2 * T1 * T2^2, (T2 * T1 * T2^-1 * T1)^2, T2^7 * T1 * T2 * T1 ] Map:: R = (1, 33, 3, 35, 8, 40, 17, 49, 26, 58, 31, 63, 23, 55, 13, 45, 21, 53, 11, 43, 20, 52, 29, 61, 28, 60, 19, 51, 10, 42, 4, 36)(2, 34, 5, 37, 12, 44, 22, 54, 30, 62, 27, 59, 18, 50, 9, 41, 16, 48, 7, 39, 15, 47, 25, 57, 32, 64, 24, 56, 14, 46, 6, 38) L = (1, 34)(2, 33)(3, 39)(4, 41)(5, 43)(6, 45)(7, 35)(8, 44)(9, 36)(10, 46)(11, 37)(12, 40)(13, 38)(14, 42)(15, 52)(16, 53)(17, 57)(18, 55)(19, 59)(20, 47)(21, 48)(22, 61)(23, 50)(24, 63)(25, 49)(26, 62)(27, 51)(28, 64)(29, 54)(30, 58)(31, 56)(32, 60) 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 E7.346 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 32 f = 18 degree seq :: [ 32^2 ] E7.348 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 16}) Quotient :: dipole Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, (Y2^-1 * R * Y2^-1)^2, (Y2 * Y1 * Y2^-1 * Y1)^2, Y2^7 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^16 ] Map:: R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 9, 41)(5, 37, 11, 43)(6, 38, 13, 45)(8, 40, 12, 44)(10, 42, 14, 46)(15, 47, 20, 52)(16, 48, 21, 53)(17, 49, 25, 57)(18, 50, 23, 55)(19, 51, 27, 59)(22, 54, 29, 61)(24, 56, 31, 63)(26, 58, 30, 62)(28, 60, 32, 64)(65, 97, 67, 99, 72, 104, 81, 113, 90, 122, 95, 127, 87, 119, 77, 109, 85, 117, 75, 107, 84, 116, 93, 125, 92, 124, 83, 115, 74, 106, 68, 100)(66, 98, 69, 101, 76, 108, 86, 118, 94, 126, 91, 123, 82, 114, 73, 105, 80, 112, 71, 103, 79, 111, 89, 121, 96, 128, 88, 120, 78, 110, 70, 102) L = (1, 66)(2, 65)(3, 71)(4, 73)(5, 75)(6, 77)(7, 67)(8, 76)(9, 68)(10, 78)(11, 69)(12, 72)(13, 70)(14, 74)(15, 84)(16, 85)(17, 89)(18, 87)(19, 91)(20, 79)(21, 80)(22, 93)(23, 82)(24, 95)(25, 81)(26, 94)(27, 83)(28, 96)(29, 86)(30, 90)(31, 88)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E7.349 Graph:: bipartite v = 18 e = 64 f = 34 degree seq :: [ 4^16, 32^2 ] E7.349 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 16}) Quotient :: dipole Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^-2 * Y3 * Y1^2 * Y3, (Y3 * Y1^-1 * Y3 * Y1)^2, Y1^-2 * Y3 * Y1^-5 * Y3 * Y1^-1 ] Map:: R = (1, 33, 2, 34, 5, 37, 11, 43, 20, 52, 29, 61, 25, 57, 16, 48, 24, 56, 15, 47, 23, 55, 32, 64, 28, 60, 19, 51, 10, 42, 4, 36)(3, 35, 7, 39, 12, 44, 22, 54, 30, 62, 27, 59, 18, 50, 9, 41, 14, 46, 6, 38, 13, 45, 21, 53, 31, 63, 26, 58, 17, 49, 8, 40)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 70)(3, 65)(4, 73)(5, 76)(6, 66)(7, 79)(8, 80)(9, 68)(10, 81)(11, 85)(12, 69)(13, 87)(14, 88)(15, 71)(16, 72)(17, 74)(18, 89)(19, 91)(20, 94)(21, 75)(22, 96)(23, 77)(24, 78)(25, 82)(26, 93)(27, 83)(28, 95)(29, 90)(30, 84)(31, 92)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E7.348 Graph:: simple bipartite v = 34 e = 64 f = 18 degree seq :: [ 2^32, 32^2 ] E7.350 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 6}) Quotient :: halfedge^2 Aut^+ = S3 x S3 (small group id <36, 10>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y1)^2, R * Y2 * R * Y3, Y2 * Y3 * Y1 * Y3 * Y2 * Y1, (Y3 * Y2)^3, (Y3 * Y1)^6 ] Map:: non-degenerate R = (1, 38, 2, 37)(3, 43, 7, 39)(4, 45, 9, 40)(5, 47, 11, 41)(6, 49, 13, 42)(8, 48, 12, 44)(10, 50, 14, 46)(15, 59, 23, 51)(16, 60, 24, 52)(17, 61, 25, 53)(18, 62, 26, 54)(19, 63, 27, 55)(20, 64, 28, 56)(21, 65, 29, 57)(22, 66, 30, 58)(31, 70, 34, 67)(32, 71, 35, 68)(33, 72, 36, 69) L = (1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 17)(9, 18)(11, 19)(12, 21)(13, 22)(16, 25)(20, 29)(23, 31)(24, 33)(26, 32)(27, 34)(28, 36)(30, 35)(37, 40)(38, 42)(39, 44)(41, 48)(43, 52)(45, 51)(46, 53)(47, 56)(49, 55)(50, 57)(54, 61)(58, 65)(59, 68)(60, 67)(62, 69)(63, 71)(64, 70)(66, 72) local type(s) :: { ( 12^4 ) } Outer automorphisms :: reflexible Dual of E7.351 Transitivity :: VT+ AT Graph:: simple bipartite v = 18 e = 36 f = 6 degree seq :: [ 4^18 ] E7.351 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 6}) Quotient :: halfedge^2 Aut^+ = S3 x S3 (small group id <36, 10>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y2^2, Y3^2, R^2, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y3 * Y2)^3, Y1^6, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 38, 2, 42, 6, 50, 14, 46, 10, 41, 5, 37)(3, 45, 9, 51, 15, 48, 12, 40, 4, 47, 11, 39)(7, 52, 16, 49, 13, 54, 18, 44, 8, 53, 17, 43)(19, 61, 25, 57, 21, 63, 27, 56, 20, 62, 26, 55)(22, 64, 28, 60, 24, 66, 30, 59, 23, 65, 29, 58)(31, 72, 36, 69, 33, 71, 35, 68, 32, 70, 34, 67) L = (1, 3)(2, 7)(4, 6)(5, 13)(8, 14)(9, 19)(10, 15)(11, 21)(12, 20)(16, 22)(17, 24)(18, 23)(25, 31)(26, 33)(27, 32)(28, 34)(29, 36)(30, 35)(37, 40)(38, 44)(39, 46)(41, 43)(42, 51)(45, 56)(47, 55)(48, 57)(49, 50)(52, 59)(53, 58)(54, 60)(61, 68)(62, 67)(63, 69)(64, 71)(65, 70)(66, 72) local type(s) :: { ( 4^12 ) } Outer automorphisms :: reflexible Dual of E7.350 Transitivity :: VT+ AT Graph:: bipartite v = 6 e = 36 f = 18 degree seq :: [ 12^6 ] E7.352 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 6}) Quotient :: edge^2 Aut^+ = S3 x S3 (small group id <36, 10>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y2 * Y1)^3, Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 ] Map:: R = (1, 37, 4, 40)(2, 38, 6, 42)(3, 39, 8, 44)(5, 41, 12, 48)(7, 43, 15, 51)(9, 45, 17, 53)(10, 46, 18, 54)(11, 47, 19, 55)(13, 49, 21, 57)(14, 50, 22, 58)(16, 52, 23, 59)(20, 56, 27, 63)(24, 60, 31, 67)(25, 61, 32, 68)(26, 62, 33, 69)(28, 64, 34, 70)(29, 65, 35, 71)(30, 66, 36, 72)(73, 74)(75, 79)(76, 81)(77, 83)(78, 85)(80, 88)(82, 87)(84, 92)(86, 91)(89, 96)(90, 98)(93, 100)(94, 102)(95, 101)(97, 99)(103, 106)(104, 108)(105, 107)(109, 111)(110, 113)(112, 118)(114, 122)(115, 119)(116, 121)(117, 120)(123, 128)(124, 127)(125, 133)(126, 132)(129, 137)(130, 136)(131, 138)(134, 135)(139, 143)(140, 142)(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) :: { ( 24, 24 ), ( 24^4 ) } Outer automorphisms :: reflexible Dual of E7.355 Graph:: simple bipartite v = 54 e = 72 f = 6 degree seq :: [ 2^36, 4^18 ] E7.353 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 6}) Quotient :: edge^2 Aut^+ = S3 x S3 (small group id <36, 10>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^-2 * Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1, Y3 * Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 37, 4, 40, 6, 42, 15, 51, 9, 45, 5, 41)(2, 38, 7, 43, 3, 39, 10, 46, 14, 50, 8, 44)(11, 47, 19, 55, 12, 48, 21, 57, 13, 49, 20, 56)(16, 52, 22, 58, 17, 53, 24, 60, 18, 54, 23, 59)(25, 61, 31, 67, 26, 62, 33, 69, 27, 63, 32, 68)(28, 64, 34, 70, 29, 65, 36, 72, 30, 66, 35, 71)(73, 74)(75, 81)(76, 83)(77, 84)(78, 86)(79, 88)(80, 89)(82, 90)(85, 87)(91, 97)(92, 98)(93, 99)(94, 100)(95, 101)(96, 102)(103, 107)(104, 106)(105, 108)(109, 111)(110, 114)(112, 120)(113, 121)(115, 125)(116, 126)(117, 122)(118, 124)(119, 123)(127, 134)(128, 135)(129, 133)(130, 137)(131, 138)(132, 136)(139, 142)(140, 144)(141, 143) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 8, 8 ), ( 8^12 ) } Outer automorphisms :: reflexible Dual of E7.354 Graph:: simple bipartite v = 42 e = 72 f = 18 degree seq :: [ 2^36, 12^6 ] E7.354 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 6}) Quotient :: loop^2 Aut^+ = S3 x S3 (small group id <36, 10>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y2 * Y1)^3, Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112)(2, 38, 74, 110, 6, 42, 78, 114)(3, 39, 75, 111, 8, 44, 80, 116)(5, 41, 77, 113, 12, 48, 84, 120)(7, 43, 79, 115, 15, 51, 87, 123)(9, 45, 81, 117, 17, 53, 89, 125)(10, 46, 82, 118, 18, 54, 90, 126)(11, 47, 83, 119, 19, 55, 91, 127)(13, 49, 85, 121, 21, 57, 93, 129)(14, 50, 86, 122, 22, 58, 94, 130)(16, 52, 88, 124, 23, 59, 95, 131)(20, 56, 92, 128, 27, 63, 99, 135)(24, 60, 96, 132, 31, 67, 103, 139)(25, 61, 97, 133, 32, 68, 104, 140)(26, 62, 98, 134, 33, 69, 105, 141)(28, 64, 100, 136, 34, 70, 106, 142)(29, 65, 101, 137, 35, 71, 107, 143)(30, 66, 102, 138, 36, 72, 108, 144) L = (1, 38)(2, 37)(3, 43)(4, 45)(5, 47)(6, 49)(7, 39)(8, 52)(9, 40)(10, 51)(11, 41)(12, 56)(13, 42)(14, 55)(15, 46)(16, 44)(17, 60)(18, 62)(19, 50)(20, 48)(21, 64)(22, 66)(23, 65)(24, 53)(25, 63)(26, 54)(27, 61)(28, 57)(29, 59)(30, 58)(31, 70)(32, 72)(33, 71)(34, 67)(35, 69)(36, 68)(73, 111)(74, 113)(75, 109)(76, 118)(77, 110)(78, 122)(79, 119)(80, 121)(81, 120)(82, 112)(83, 115)(84, 117)(85, 116)(86, 114)(87, 128)(88, 127)(89, 133)(90, 132)(91, 124)(92, 123)(93, 137)(94, 136)(95, 138)(96, 126)(97, 125)(98, 135)(99, 134)(100, 130)(101, 129)(102, 131)(103, 143)(104, 142)(105, 144)(106, 140)(107, 139)(108, 141) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E7.353 Transitivity :: VT+ Graph:: bipartite v = 18 e = 72 f = 42 degree seq :: [ 8^18 ] E7.355 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 6}) Quotient :: loop^2 Aut^+ = S3 x S3 (small group id <36, 10>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^-2 * Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1, Y3 * Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 6, 42, 78, 114, 15, 51, 87, 123, 9, 45, 81, 117, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 3, 39, 75, 111, 10, 46, 82, 118, 14, 50, 86, 122, 8, 44, 80, 116)(11, 47, 83, 119, 19, 55, 91, 127, 12, 48, 84, 120, 21, 57, 93, 129, 13, 49, 85, 121, 20, 56, 92, 128)(16, 52, 88, 124, 22, 58, 94, 130, 17, 53, 89, 125, 24, 60, 96, 132, 18, 54, 90, 126, 23, 59, 95, 131)(25, 61, 97, 133, 31, 67, 103, 139, 26, 62, 98, 134, 33, 69, 105, 141, 27, 63, 99, 135, 32, 68, 104, 140)(28, 64, 100, 136, 34, 70, 106, 142, 29, 65, 101, 137, 36, 72, 108, 144, 30, 66, 102, 138, 35, 71, 107, 143) L = (1, 38)(2, 37)(3, 45)(4, 47)(5, 48)(6, 50)(7, 52)(8, 53)(9, 39)(10, 54)(11, 40)(12, 41)(13, 51)(14, 42)(15, 49)(16, 43)(17, 44)(18, 46)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)(31, 71)(32, 70)(33, 72)(34, 68)(35, 67)(36, 69)(73, 111)(74, 114)(75, 109)(76, 120)(77, 121)(78, 110)(79, 125)(80, 126)(81, 122)(82, 124)(83, 123)(84, 112)(85, 113)(86, 117)(87, 119)(88, 118)(89, 115)(90, 116)(91, 134)(92, 135)(93, 133)(94, 137)(95, 138)(96, 136)(97, 129)(98, 127)(99, 128)(100, 132)(101, 130)(102, 131)(103, 142)(104, 144)(105, 143)(106, 139)(107, 141)(108, 140) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E7.352 Transitivity :: VT+ Graph:: bipartite v = 6 e = 72 f = 54 degree seq :: [ 24^6 ] E7.356 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x S3 (small group id <36, 10>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (Y2 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1 * Y3 * Y1)^2, (Y2 * Y1 * Y3)^3, (Y3 * Y1)^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 9, 45)(5, 41, 10, 46)(6, 42, 12, 48)(8, 44, 15, 51)(11, 47, 20, 56)(13, 49, 23, 59)(14, 50, 21, 57)(16, 52, 19, 55)(17, 53, 28, 64)(18, 54, 29, 65)(22, 58, 32, 68)(24, 60, 27, 63)(25, 61, 34, 70)(26, 62, 35, 71)(30, 66, 31, 67)(33, 69, 36, 72)(73, 109, 75, 111)(74, 110, 77, 113)(76, 112, 80, 116)(78, 114, 83, 119)(79, 115, 85, 121)(81, 117, 88, 124)(82, 118, 90, 126)(84, 120, 93, 129)(86, 122, 96, 132)(87, 123, 97, 133)(89, 125, 99, 135)(91, 127, 102, 138)(92, 128, 98, 134)(94, 130, 103, 139)(95, 131, 105, 141)(100, 136, 107, 143)(101, 137, 108, 144)(104, 140, 106, 142) L = (1, 76)(2, 78)(3, 80)(4, 73)(5, 83)(6, 74)(7, 86)(8, 75)(9, 89)(10, 91)(11, 77)(12, 94)(13, 96)(14, 79)(15, 98)(16, 99)(17, 81)(18, 102)(19, 82)(20, 97)(21, 103)(22, 84)(23, 106)(24, 85)(25, 92)(26, 87)(27, 88)(28, 108)(29, 107)(30, 90)(31, 93)(32, 105)(33, 104)(34, 95)(35, 101)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.360 Graph:: simple bipartite v = 36 e = 72 f = 24 degree seq :: [ 4^36 ] E7.357 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x S3 (small group id <36, 10>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1, Y3^6, Y1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y3^-1, (Y3^-2 * Y2 * Y1)^2 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 12, 48)(5, 41, 14, 50)(6, 42, 16, 52)(7, 43, 19, 55)(8, 44, 21, 57)(10, 46, 24, 60)(11, 47, 26, 62)(13, 49, 22, 58)(15, 51, 20, 56)(17, 53, 29, 65)(18, 54, 28, 64)(23, 59, 31, 67)(25, 61, 33, 69)(27, 63, 32, 68)(30, 66, 35, 71)(34, 70, 36, 72)(73, 109, 75, 111)(74, 110, 78, 114)(76, 112, 83, 119)(77, 113, 82, 118)(79, 115, 90, 126)(80, 116, 89, 125)(81, 117, 92, 128)(84, 120, 99, 135)(85, 121, 88, 124)(86, 122, 98, 134)(87, 123, 97, 133)(91, 127, 103, 139)(93, 129, 100, 136)(94, 130, 105, 141)(95, 131, 106, 142)(96, 132, 107, 143)(101, 137, 108, 144)(102, 138, 104, 140) L = (1, 76)(2, 79)(3, 82)(4, 85)(5, 73)(6, 89)(7, 92)(8, 74)(9, 90)(10, 97)(11, 75)(12, 100)(13, 102)(14, 103)(15, 77)(16, 83)(17, 105)(18, 78)(19, 98)(20, 106)(21, 99)(22, 80)(23, 81)(24, 91)(25, 104)(26, 93)(27, 108)(28, 86)(29, 84)(30, 87)(31, 107)(32, 88)(33, 95)(34, 94)(35, 101)(36, 96)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.361 Graph:: simple bipartite v = 36 e = 72 f = 24 degree seq :: [ 4^36 ] E7.358 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x S3 (small group id <36, 10>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2)^3, Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y2 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 9, 45)(5, 41, 10, 46)(6, 42, 12, 48)(8, 44, 14, 50)(11, 47, 18, 54)(13, 49, 21, 57)(15, 51, 22, 58)(16, 52, 25, 61)(17, 53, 26, 62)(19, 55, 27, 63)(20, 56, 30, 66)(23, 59, 29, 65)(24, 60, 28, 64)(31, 67, 34, 70)(32, 68, 36, 72)(33, 69, 35, 71)(73, 109, 75, 111)(74, 110, 77, 113)(76, 112, 80, 116)(78, 114, 83, 119)(79, 115, 82, 118)(81, 117, 87, 123)(84, 120, 91, 127)(85, 121, 89, 125)(86, 122, 94, 130)(88, 124, 96, 132)(90, 126, 99, 135)(92, 128, 101, 137)(93, 129, 103, 139)(95, 131, 105, 141)(97, 133, 104, 140)(98, 134, 106, 142)(100, 136, 108, 144)(102, 138, 107, 143) L = (1, 76)(2, 78)(3, 80)(4, 73)(5, 83)(6, 74)(7, 85)(8, 75)(9, 88)(10, 89)(11, 77)(12, 92)(13, 79)(14, 95)(15, 96)(16, 81)(17, 82)(18, 100)(19, 101)(20, 84)(21, 104)(22, 105)(23, 86)(24, 87)(25, 103)(26, 107)(27, 108)(28, 90)(29, 91)(30, 106)(31, 97)(32, 93)(33, 94)(34, 102)(35, 98)(36, 99)(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 ) } Outer automorphisms :: reflexible Dual of E7.359 Graph:: simple bipartite v = 36 e = 72 f = 24 degree seq :: [ 4^36 ] E7.359 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x S3 (small group id <36, 10>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, Y2 * Y1^2 * Y2 * Y1^-2, Y1^6, (Y2 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 6, 42, 15, 51, 14, 50, 5, 41)(3, 39, 9, 45, 16, 52, 29, 65, 24, 60, 11, 47)(4, 40, 12, 48, 25, 61, 28, 64, 17, 53, 8, 44)(7, 43, 18, 54, 27, 63, 21, 57, 13, 49, 20, 56)(10, 46, 23, 59, 34, 70, 36, 72, 30, 66, 22, 58)(19, 55, 32, 68, 26, 62, 33, 69, 35, 71, 31, 67)(73, 109, 75, 111)(74, 110, 79, 115)(76, 112, 82, 118)(77, 113, 85, 121)(78, 114, 88, 124)(80, 116, 91, 127)(81, 117, 93, 129)(83, 119, 90, 126)(84, 120, 98, 134)(86, 122, 96, 132)(87, 123, 99, 135)(89, 125, 102, 138)(92, 128, 101, 137)(94, 130, 105, 141)(95, 131, 103, 139)(97, 133, 106, 142)(100, 136, 107, 143)(104, 140, 108, 144) L = (1, 76)(2, 80)(3, 82)(4, 73)(5, 84)(6, 89)(7, 91)(8, 74)(9, 94)(10, 75)(11, 95)(12, 77)(13, 98)(14, 97)(15, 100)(16, 102)(17, 78)(18, 103)(19, 79)(20, 104)(21, 105)(22, 81)(23, 83)(24, 106)(25, 86)(26, 85)(27, 107)(28, 87)(29, 108)(30, 88)(31, 90)(32, 92)(33, 93)(34, 96)(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) :: { ( 4^4 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E7.358 Graph:: simple bipartite v = 24 e = 72 f = 36 degree seq :: [ 4^18, 12^6 ] E7.360 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x S3 (small group id <36, 10>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, Y1^6, (Y2 * Y1^-2)^2, Y1 * Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 6, 42, 15, 51, 14, 50, 5, 41)(3, 39, 9, 45, 21, 57, 32, 68, 16, 52, 11, 47)(4, 40, 12, 48, 26, 62, 30, 66, 17, 53, 8, 44)(7, 43, 18, 54, 13, 49, 28, 64, 29, 65, 20, 56)(10, 46, 24, 60, 31, 67, 33, 69, 35, 71, 23, 59)(19, 55, 22, 58, 36, 72, 25, 61, 27, 63, 34, 70)(73, 109, 75, 111)(74, 110, 79, 115)(76, 112, 82, 118)(77, 113, 85, 121)(78, 114, 88, 124)(80, 116, 91, 127)(81, 117, 94, 130)(83, 119, 97, 133)(84, 120, 99, 135)(86, 122, 93, 129)(87, 123, 101, 137)(89, 125, 103, 139)(90, 126, 105, 141)(92, 128, 95, 131)(96, 132, 100, 136)(98, 134, 107, 143)(102, 138, 108, 144)(104, 140, 106, 142) L = (1, 76)(2, 80)(3, 82)(4, 73)(5, 84)(6, 89)(7, 91)(8, 74)(9, 95)(10, 75)(11, 96)(12, 77)(13, 99)(14, 98)(15, 102)(16, 103)(17, 78)(18, 106)(19, 79)(20, 94)(21, 107)(22, 92)(23, 81)(24, 83)(25, 100)(26, 86)(27, 85)(28, 97)(29, 108)(30, 87)(31, 88)(32, 105)(33, 104)(34, 90)(35, 93)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4^4 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E7.356 Graph:: simple bipartite v = 24 e = 72 f = 36 degree seq :: [ 4^18, 12^6 ] E7.361 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x S3 (small group id <36, 10>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^3, Y1^2 * Y3^-1, (Y2 * Y3^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 4, 40, 8, 44, 6, 42, 5, 41)(3, 39, 9, 45, 10, 46, 18, 54, 12, 48, 11, 47)(7, 43, 14, 50, 13, 49, 20, 56, 16, 52, 15, 51)(17, 53, 23, 59, 19, 55, 26, 62, 25, 61, 24, 60)(21, 57, 28, 64, 22, 58, 30, 66, 27, 63, 29, 65)(31, 67, 35, 71, 32, 68, 36, 72, 33, 69, 34, 70)(73, 109, 75, 111)(74, 110, 79, 115)(76, 112, 84, 120)(77, 113, 85, 121)(78, 114, 82, 118)(80, 116, 88, 124)(81, 117, 89, 125)(83, 119, 91, 127)(86, 122, 93, 129)(87, 123, 94, 130)(90, 126, 97, 133)(92, 128, 99, 135)(95, 131, 103, 139)(96, 132, 104, 140)(98, 134, 105, 141)(100, 136, 106, 142)(101, 137, 107, 143)(102, 138, 108, 144) L = (1, 76)(2, 80)(3, 82)(4, 78)(5, 74)(6, 73)(7, 85)(8, 77)(9, 90)(10, 84)(11, 81)(12, 75)(13, 88)(14, 92)(15, 86)(16, 79)(17, 91)(18, 83)(19, 97)(20, 87)(21, 94)(22, 99)(23, 98)(24, 95)(25, 89)(26, 96)(27, 93)(28, 102)(29, 100)(30, 101)(31, 104)(32, 105)(33, 103)(34, 107)(35, 108)(36, 106)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4^4 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E7.357 Graph:: bipartite v = 24 e = 72 f = 36 degree seq :: [ 4^18, 12^6 ] E7.362 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 12}) Quotient :: edge Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C6 x S3) : C2 (small group id <72, 23>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 5)(2, 6, 16, 7)(4, 11, 22, 12)(8, 20, 13, 21)(10, 23, 14, 24)(15, 29, 18, 30)(17, 31, 19, 32)(25, 33, 27, 34)(26, 35, 28, 36)(37, 38, 40)(39, 44, 46)(41, 49, 50)(42, 51, 53)(43, 54, 55)(45, 52, 58)(47, 61, 62)(48, 63, 64)(56, 65, 69)(57, 66, 70)(59, 67, 71)(60, 68, 72) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 24^3 ), ( 24^4 ) } Outer automorphisms :: reflexible Dual of E7.366 Transitivity :: ET+ Graph:: simple bipartite v = 21 e = 36 f = 3 degree seq :: [ 3^12, 4^9 ] E7.363 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 12}) Quotient :: edge Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C6 x S3) : C2 (small group id <72, 23>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, (T2 * T1)^3, T2^2 * T1 * T2^-2 * T1^-1, T2^2 * T1 * T2^2 * T1 * T2^2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 26, 32, 18, 6, 17, 31, 30, 16, 5)(2, 7, 20, 34, 29, 13, 4, 12, 27, 36, 24, 8)(9, 22, 33, 19, 15, 28, 11, 23, 35, 21, 14, 25)(37, 38, 42, 40)(39, 45, 53, 47)(41, 50, 54, 51)(43, 55, 48, 57)(44, 58, 49, 59)(46, 56, 67, 63)(52, 60, 68, 65)(61, 70, 64, 72)(62, 69, 66, 71) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6^4 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E7.367 Transitivity :: ET+ Graph:: bipartite v = 12 e = 36 f = 12 degree seq :: [ 4^9, 12^3 ] E7.364 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 12}) Quotient :: edge Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C6 x S3) : C2 (small group id <72, 23>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1^3 * T2^-1 * T1 * T2^-1, T1^-2 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^2 * T2^-1 * T1^-2, (T2^-1 * T1^-1)^4, T2 * T1 * T2 * T1^7 ] Map:: non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 11, 13)(6, 17, 18)(9, 23, 24)(10, 16, 25)(12, 21, 27)(14, 29, 26)(15, 30, 31)(19, 33, 28)(20, 32, 34)(22, 35, 36)(37, 38, 42, 52, 68, 59, 69, 67, 72, 62, 48, 40)(39, 45, 53, 66, 70, 65, 64, 49, 58, 44, 57, 46)(41, 50, 54, 47, 56, 43, 55, 61, 71, 60, 63, 51) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 8^3 ), ( 8^12 ) } Outer automorphisms :: reflexible Dual of E7.365 Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 36 f = 9 degree seq :: [ 3^12, 12^3 ] E7.365 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 12}) Quotient :: loop Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C6 x S3) : C2 (small group id <72, 23>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 5, 41)(2, 38, 6, 42, 16, 52, 7, 43)(4, 40, 11, 47, 22, 58, 12, 48)(8, 44, 20, 56, 13, 49, 21, 57)(10, 46, 23, 59, 14, 50, 24, 60)(15, 51, 29, 65, 18, 54, 30, 66)(17, 53, 31, 67, 19, 55, 32, 68)(25, 61, 33, 69, 27, 63, 34, 70)(26, 62, 35, 71, 28, 64, 36, 72) L = (1, 38)(2, 40)(3, 44)(4, 37)(5, 49)(6, 51)(7, 54)(8, 46)(9, 52)(10, 39)(11, 61)(12, 63)(13, 50)(14, 41)(15, 53)(16, 58)(17, 42)(18, 55)(19, 43)(20, 65)(21, 66)(22, 45)(23, 67)(24, 68)(25, 62)(26, 47)(27, 64)(28, 48)(29, 69)(30, 70)(31, 71)(32, 72)(33, 56)(34, 57)(35, 59)(36, 60) local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12 ) } Outer automorphisms :: reflexible Dual of E7.364 Transitivity :: ET+ VT+ AT Graph:: v = 9 e = 36 f = 15 degree seq :: [ 8^9 ] E7.366 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 12}) Quotient :: loop Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C6 x S3) : C2 (small group id <72, 23>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, (T2 * T1)^3, T2^2 * T1 * T2^-2 * T1^-1, T2^2 * T1 * T2^2 * T1 * T2^2 ] Map:: non-degenerate R = (1, 37, 3, 39, 10, 46, 26, 62, 32, 68, 18, 54, 6, 42, 17, 53, 31, 67, 30, 66, 16, 52, 5, 41)(2, 38, 7, 43, 20, 56, 34, 70, 29, 65, 13, 49, 4, 40, 12, 48, 27, 63, 36, 72, 24, 60, 8, 44)(9, 45, 22, 58, 33, 69, 19, 55, 15, 51, 28, 64, 11, 47, 23, 59, 35, 71, 21, 57, 14, 50, 25, 61) L = (1, 38)(2, 42)(3, 45)(4, 37)(5, 50)(6, 40)(7, 55)(8, 58)(9, 53)(10, 56)(11, 39)(12, 57)(13, 59)(14, 54)(15, 41)(16, 60)(17, 47)(18, 51)(19, 48)(20, 67)(21, 43)(22, 49)(23, 44)(24, 68)(25, 70)(26, 69)(27, 46)(28, 72)(29, 52)(30, 71)(31, 63)(32, 65)(33, 66)(34, 64)(35, 62)(36, 61) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E7.362 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 36 f = 21 degree seq :: [ 24^3 ] E7.367 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 12}) Quotient :: loop Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C6 x S3) : C2 (small group id <72, 23>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1^3 * T2^-1 * T1 * T2^-1, T1^-2 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^2 * T2^-1 * T1^-2, (T2^-1 * T1^-1)^4, T2 * T1 * T2 * T1^7 ] Map:: polytopal non-degenerate R = (1, 37, 3, 39, 5, 41)(2, 38, 7, 43, 8, 44)(4, 40, 11, 47, 13, 49)(6, 42, 17, 53, 18, 54)(9, 45, 23, 59, 24, 60)(10, 46, 16, 52, 25, 61)(12, 48, 21, 57, 27, 63)(14, 50, 29, 65, 26, 62)(15, 51, 30, 66, 31, 67)(19, 55, 33, 69, 28, 64)(20, 56, 32, 68, 34, 70)(22, 58, 35, 71, 36, 72) L = (1, 38)(2, 42)(3, 45)(4, 37)(5, 50)(6, 52)(7, 55)(8, 57)(9, 53)(10, 39)(11, 56)(12, 40)(13, 58)(14, 54)(15, 41)(16, 68)(17, 66)(18, 47)(19, 61)(20, 43)(21, 46)(22, 44)(23, 69)(24, 63)(25, 71)(26, 48)(27, 51)(28, 49)(29, 64)(30, 70)(31, 72)(32, 59)(33, 67)(34, 65)(35, 60)(36, 62) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.363 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 12 e = 36 f = 12 degree seq :: [ 6^12 ] E7.368 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12}) Quotient :: dipole Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C6 x S3) : C2 (small group id <72, 23>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3 * Y2^-2 * Y3^-1 * Y2^-2, Y2 * Y1 * Y2^2 * Y1^-1 * Y2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, (Y3 * Y2)^12 ] Map:: R = (1, 37, 2, 38, 4, 40)(3, 39, 8, 44, 10, 46)(5, 41, 13, 49, 14, 50)(6, 42, 15, 51, 17, 53)(7, 43, 18, 54, 19, 55)(9, 45, 16, 52, 22, 58)(11, 47, 25, 61, 26, 62)(12, 48, 27, 63, 28, 64)(20, 56, 29, 65, 33, 69)(21, 57, 30, 66, 34, 70)(23, 59, 31, 67, 35, 71)(24, 60, 32, 68, 36, 72)(73, 109, 75, 111, 81, 117, 77, 113)(74, 110, 78, 114, 88, 124, 79, 115)(76, 112, 83, 119, 94, 130, 84, 120)(80, 116, 92, 128, 85, 121, 93, 129)(82, 118, 95, 131, 86, 122, 96, 132)(87, 123, 101, 137, 90, 126, 102, 138)(89, 125, 103, 139, 91, 127, 104, 140)(97, 133, 105, 141, 99, 135, 106, 142)(98, 134, 107, 143, 100, 136, 108, 144) L = (1, 76)(2, 73)(3, 82)(4, 74)(5, 86)(6, 89)(7, 91)(8, 75)(9, 94)(10, 80)(11, 98)(12, 100)(13, 77)(14, 85)(15, 78)(16, 81)(17, 87)(18, 79)(19, 90)(20, 105)(21, 106)(22, 88)(23, 107)(24, 108)(25, 83)(26, 97)(27, 84)(28, 99)(29, 92)(30, 93)(31, 95)(32, 96)(33, 101)(34, 102)(35, 103)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E7.371 Graph:: bipartite v = 21 e = 72 f = 39 degree seq :: [ 6^12, 8^9 ] E7.369 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12}) Quotient :: dipole Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C6 x S3) : C2 (small group id <72, 23>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, (Y2 * Y1)^3, (Y3^-1 * Y1^-1)^3, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2^2 * Y1 * Y2^2 * Y1 * Y2^2 ] Map:: R = (1, 37, 2, 38, 6, 42, 4, 40)(3, 39, 9, 45, 17, 53, 11, 47)(5, 41, 14, 50, 18, 54, 15, 51)(7, 43, 19, 55, 12, 48, 21, 57)(8, 44, 22, 58, 13, 49, 23, 59)(10, 46, 20, 56, 31, 67, 27, 63)(16, 52, 24, 60, 32, 68, 29, 65)(25, 61, 34, 70, 28, 64, 36, 72)(26, 62, 33, 69, 30, 66, 35, 71)(73, 109, 75, 111, 82, 118, 98, 134, 104, 140, 90, 126, 78, 114, 89, 125, 103, 139, 102, 138, 88, 124, 77, 113)(74, 110, 79, 115, 92, 128, 106, 142, 101, 137, 85, 121, 76, 112, 84, 120, 99, 135, 108, 144, 96, 132, 80, 116)(81, 117, 94, 130, 105, 141, 91, 127, 87, 123, 100, 136, 83, 119, 95, 131, 107, 143, 93, 129, 86, 122, 97, 133) L = (1, 75)(2, 79)(3, 82)(4, 84)(5, 73)(6, 89)(7, 92)(8, 74)(9, 94)(10, 98)(11, 95)(12, 99)(13, 76)(14, 97)(15, 100)(16, 77)(17, 103)(18, 78)(19, 87)(20, 106)(21, 86)(22, 105)(23, 107)(24, 80)(25, 81)(26, 104)(27, 108)(28, 83)(29, 85)(30, 88)(31, 102)(32, 90)(33, 91)(34, 101)(35, 93)(36, 96)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6 ), ( 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 E7.370 Graph:: bipartite v = 12 e = 72 f = 48 degree seq :: [ 8^9, 24^3 ] E7.370 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12}) Quotient :: dipole Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C6 x S3) : C2 (small group id <72, 23>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y2^-1 * Y3^2 * Y2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-3 * Y2^-1, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^-1)^12 ] Map:: polytopal R = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)(73, 109, 74, 110, 76, 112)(75, 111, 80, 116, 82, 118)(77, 113, 85, 121, 86, 122)(78, 114, 88, 124, 90, 126)(79, 115, 91, 127, 92, 128)(81, 117, 89, 125, 97, 133)(83, 119, 100, 136, 101, 137)(84, 120, 102, 138, 96, 132)(87, 123, 93, 129, 94, 130)(95, 131, 104, 140, 107, 143)(98, 134, 103, 139, 106, 142)(99, 135, 105, 141, 108, 144) L = (1, 75)(2, 78)(3, 81)(4, 83)(5, 73)(6, 89)(7, 74)(8, 94)(9, 96)(10, 98)(11, 97)(12, 76)(13, 95)(14, 99)(15, 77)(16, 87)(17, 86)(18, 103)(19, 104)(20, 105)(21, 79)(22, 84)(23, 80)(24, 108)(25, 92)(26, 102)(27, 82)(28, 93)(29, 106)(30, 107)(31, 85)(32, 88)(33, 90)(34, 91)(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) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E7.369 Graph:: simple bipartite v = 48 e = 72 f = 12 degree seq :: [ 2^36, 6^12 ] E7.371 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12}) Quotient :: dipole Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C6 x S3) : C2 (small group id <72, 23>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-3 * Y3, Y3 * Y1^2 * Y3^-1 * Y1^-2, (Y3 * Y2^-1)^3, (Y3^-1 * Y1^-1)^4, Y3 * Y1 * Y3 * Y1^7 ] Map:: R = (1, 37, 2, 38, 6, 42, 16, 52, 32, 68, 23, 59, 33, 69, 31, 67, 36, 72, 26, 62, 12, 48, 4, 40)(3, 39, 9, 45, 17, 53, 30, 66, 34, 70, 29, 65, 28, 64, 13, 49, 22, 58, 8, 44, 21, 57, 10, 46)(5, 41, 14, 50, 18, 54, 11, 47, 20, 56, 7, 43, 19, 55, 25, 61, 35, 71, 24, 60, 27, 63, 15, 51)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 77)(4, 83)(5, 73)(6, 89)(7, 80)(8, 74)(9, 95)(10, 88)(11, 85)(12, 93)(13, 76)(14, 101)(15, 102)(16, 97)(17, 90)(18, 78)(19, 105)(20, 104)(21, 99)(22, 107)(23, 96)(24, 81)(25, 82)(26, 86)(27, 84)(28, 91)(29, 98)(30, 103)(31, 87)(32, 106)(33, 100)(34, 92)(35, 108)(36, 94)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E7.368 Graph:: simple bipartite v = 39 e = 72 f = 21 degree seq :: [ 2^36, 24^3 ] E7.372 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12}) Quotient :: dipole Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C6 x S3) : C2 (small group id <72, 23>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2^3 * Y1^-1, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, (Y2^-1 * Y3)^4 ] Map:: R = (1, 37, 2, 38, 4, 40)(3, 39, 8, 44, 10, 46)(5, 41, 13, 49, 14, 50)(6, 42, 16, 52, 18, 54)(7, 43, 19, 55, 20, 56)(9, 45, 17, 53, 24, 60)(11, 47, 26, 62, 27, 63)(12, 48, 28, 64, 29, 65)(15, 51, 21, 57, 30, 66)(22, 58, 32, 68, 31, 67)(23, 59, 33, 69, 35, 71)(25, 61, 34, 70, 36, 72)(73, 109, 75, 111, 81, 117, 91, 127, 105, 141, 88, 124, 104, 140, 101, 137, 108, 144, 99, 135, 87, 123, 77, 113)(74, 110, 78, 114, 89, 125, 100, 136, 107, 143, 98, 134, 103, 139, 86, 122, 97, 133, 82, 118, 93, 129, 79, 115)(76, 112, 83, 119, 96, 132, 85, 121, 95, 131, 80, 116, 94, 130, 92, 128, 106, 142, 90, 126, 102, 138, 84, 120) L = (1, 76)(2, 73)(3, 82)(4, 74)(5, 86)(6, 90)(7, 92)(8, 75)(9, 96)(10, 80)(11, 99)(12, 101)(13, 77)(14, 85)(15, 102)(16, 78)(17, 81)(18, 88)(19, 79)(20, 91)(21, 87)(22, 103)(23, 107)(24, 89)(25, 108)(26, 83)(27, 98)(28, 84)(29, 100)(30, 93)(31, 104)(32, 94)(33, 95)(34, 97)(35, 105)(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, 8, 2, 8, 2, 8 ), ( 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 E7.373 Graph:: bipartite v = 15 e = 72 f = 45 degree seq :: [ 6^12, 24^3 ] E7.373 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12}) Quotient :: dipole Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C6 x S3) : C2 (small group id <72, 23>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1, Y1^-1 * Y3^-1 * Y1^-2 * Y3 * Y1^-1, Y3^2 * Y1 * Y3^-2 * Y1^-1, (Y3^-1 * Y1^-1)^3, Y3^2 * Y1 * Y3^2 * Y1 * Y3^2, (Y3 * Y2^-1)^12 ] Map:: R = (1, 37, 2, 38, 6, 42, 4, 40)(3, 39, 9, 45, 17, 53, 11, 47)(5, 41, 14, 50, 18, 54, 15, 51)(7, 43, 19, 55, 12, 48, 21, 57)(8, 44, 22, 58, 13, 49, 23, 59)(10, 46, 20, 56, 31, 67, 27, 63)(16, 52, 24, 60, 32, 68, 29, 65)(25, 61, 34, 70, 28, 64, 36, 72)(26, 62, 33, 69, 30, 66, 35, 71)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 82)(4, 84)(5, 73)(6, 89)(7, 92)(8, 74)(9, 94)(10, 98)(11, 95)(12, 99)(13, 76)(14, 97)(15, 100)(16, 77)(17, 103)(18, 78)(19, 87)(20, 106)(21, 86)(22, 105)(23, 107)(24, 80)(25, 81)(26, 104)(27, 108)(28, 83)(29, 85)(30, 88)(31, 102)(32, 90)(33, 91)(34, 101)(35, 93)(36, 96)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E7.372 Graph:: simple bipartite v = 45 e = 72 f = 15 degree seq :: [ 2^36, 8^9 ] E7.374 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 21}) Quotient :: regular Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, (T1^-2 * T2 * T1^-1)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-5 * T2 * T1^2 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 32, 41, 34, 17, 29, 40, 42, 33, 16, 28, 39, 35, 38, 22, 10, 4)(3, 7, 15, 31, 26, 12, 25, 20, 9, 19, 36, 30, 14, 6, 13, 27, 21, 37, 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, 36)(25, 39)(26, 40)(27, 41)(30, 38)(37, 42) local type(s) :: { ( 6^21 ) } Outer automorphisms :: reflexible Dual of E7.375 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 21 f = 7 degree seq :: [ 21^2 ] E7.375 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 21}) Quotient :: regular Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^6, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 ] Map:: non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 12, 20, 17, 8)(6, 13, 19, 18, 9, 14)(15, 23, 27, 25, 16, 24)(21, 28, 26, 30, 22, 29)(31, 37, 33, 39, 32, 38)(34, 40, 36, 42, 35, 41) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 19)(13, 21)(14, 22)(18, 26)(20, 27)(23, 31)(24, 32)(25, 33)(28, 34)(29, 35)(30, 36)(37, 42)(38, 40)(39, 41) local type(s) :: { ( 21^6 ) } Outer automorphisms :: reflexible Dual of E7.374 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 7 e = 21 f = 2 degree seq :: [ 6^7 ] E7.376 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 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 :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * 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, 41, 39, 40, 38, 42)(43, 44)(45, 49)(46, 51)(47, 53)(48, 55)(50, 54)(52, 56)(57, 65)(58, 67)(59, 66)(60, 68)(61, 69)(62, 71)(63, 70)(64, 72)(73, 79)(74, 80)(75, 81)(76, 82)(77, 83)(78, 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) :: { ( 42, 42 ), ( 42^6 ) } Outer automorphisms :: reflexible Dual of E7.380 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 42 f = 2 degree seq :: [ 2^21, 6^7 ] E7.377 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 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, (F * T1)^2, (F * T2)^2, (T1 * T2)^2, T1^6, T1 * T2^-1 * T1^-3 * T2^-1, T1^-2 * T2 * T1^-1 * T2 * T1^-1, T2^-1 * T1^-1 * T2^4 * T1^-1 * T2^-2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 37, 30, 18, 6, 17, 29, 41, 42, 31, 20, 13, 21, 33, 40, 28, 15, 5)(2, 7, 19, 32, 36, 24, 11, 16, 14, 27, 39, 35, 23, 9, 4, 12, 26, 38, 34, 22, 8)(43, 44, 48, 58, 55, 46)(45, 51, 59, 50, 63, 53)(47, 56, 60, 54, 62, 49)(52, 66, 71, 65, 75, 64)(57, 68, 72, 61, 73, 69)(67, 76, 83, 78, 82, 77)(70, 74, 79, 81, 84, 80) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 4^6 ), ( 4^21 ) } Outer automorphisms :: reflexible Dual of E7.381 Transitivity :: ET+ Graph:: bipartite v = 9 e = 42 f = 21 degree seq :: [ 6^7, 21^2 ] E7.378 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 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 :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T2 * T1^-3)^2, T2 * T1^-5 * T2 * T1^2 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 31)(23, 36)(25, 39)(26, 40)(27, 41)(30, 38)(37, 42)(43, 44, 47, 53, 65, 74, 83, 76, 59, 71, 82, 84, 75, 58, 70, 81, 77, 80, 64, 52, 46)(45, 49, 57, 73, 68, 54, 67, 62, 51, 61, 78, 72, 56, 48, 55, 69, 63, 79, 66, 60, 50) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 12, 12 ), ( 12^21 ) } Outer automorphisms :: reflexible Dual of E7.379 Transitivity :: ET+ Graph:: simple bipartite v = 23 e = 42 f = 7 degree seq :: [ 2^21, 21^2 ] E7.379 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 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 :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 ] Map:: R = (1, 43, 3, 45, 8, 50, 17, 59, 10, 52, 4, 46)(2, 44, 5, 47, 12, 54, 21, 63, 14, 56, 6, 48)(7, 49, 15, 57, 24, 66, 18, 60, 9, 51, 16, 58)(11, 53, 19, 61, 28, 70, 22, 64, 13, 55, 20, 62)(23, 65, 31, 73, 26, 68, 33, 75, 25, 67, 32, 74)(27, 69, 34, 76, 30, 72, 36, 78, 29, 71, 35, 77)(37, 79, 41, 83, 39, 81, 40, 82, 38, 80, 42, 84) L = (1, 44)(2, 43)(3, 49)(4, 51)(5, 53)(6, 55)(7, 45)(8, 54)(9, 46)(10, 56)(11, 47)(12, 50)(13, 48)(14, 52)(15, 65)(16, 67)(17, 66)(18, 68)(19, 69)(20, 71)(21, 70)(22, 72)(23, 57)(24, 59)(25, 58)(26, 60)(27, 61)(28, 63)(29, 62)(30, 64)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 73)(38, 74)(39, 75)(40, 76)(41, 77)(42, 78) local type(s) :: { ( 2, 21, 2, 21, 2, 21, 2, 21, 2, 21, 2, 21 ) } Outer automorphisms :: reflexible Dual of E7.378 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 42 f = 23 degree seq :: [ 12^7 ] E7.380 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 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, (F * T1)^2, (F * T2)^2, (T1 * T2)^2, T1^6, T1 * T2^-1 * T1^-3 * T2^-1, T1^-2 * T2 * T1^-1 * T2 * T1^-1, T2^-1 * T1^-1 * T2^4 * T1^-1 * T2^-2 ] Map:: R = (1, 43, 3, 45, 10, 52, 25, 67, 37, 79, 30, 72, 18, 60, 6, 48, 17, 59, 29, 71, 41, 83, 42, 84, 31, 73, 20, 62, 13, 55, 21, 63, 33, 75, 40, 82, 28, 70, 15, 57, 5, 47)(2, 44, 7, 49, 19, 61, 32, 74, 36, 78, 24, 66, 11, 53, 16, 58, 14, 56, 27, 69, 39, 81, 35, 77, 23, 65, 9, 51, 4, 46, 12, 54, 26, 68, 38, 80, 34, 76, 22, 64, 8, 50) L = (1, 44)(2, 48)(3, 51)(4, 43)(5, 56)(6, 58)(7, 47)(8, 63)(9, 59)(10, 66)(11, 45)(12, 62)(13, 46)(14, 60)(15, 68)(16, 55)(17, 50)(18, 54)(19, 73)(20, 49)(21, 53)(22, 52)(23, 75)(24, 71)(25, 76)(26, 72)(27, 57)(28, 74)(29, 65)(30, 61)(31, 69)(32, 79)(33, 64)(34, 83)(35, 67)(36, 82)(37, 81)(38, 70)(39, 84)(40, 77)(41, 78)(42, 80) 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 ) } Outer automorphisms :: reflexible Dual of E7.376 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 42 f = 28 degree seq :: [ 42^2 ] E7.381 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 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 :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T2 * T1^-3)^2, T2 * T1^-5 * T2 * T1^2 ] Map:: polytopal non-degenerate R = (1, 43, 3, 45)(2, 44, 6, 48)(4, 46, 9, 51)(5, 47, 12, 54)(7, 49, 16, 58)(8, 50, 17, 59)(10, 52, 21, 63)(11, 53, 24, 66)(13, 55, 28, 70)(14, 56, 29, 71)(15, 57, 32, 74)(18, 60, 35, 77)(19, 61, 33, 75)(20, 62, 34, 76)(22, 64, 31, 73)(23, 65, 36, 78)(25, 67, 39, 81)(26, 68, 40, 82)(27, 69, 41, 83)(30, 72, 38, 80)(37, 79, 42, 84) L = (1, 44)(2, 47)(3, 49)(4, 43)(5, 53)(6, 55)(7, 57)(8, 45)(9, 61)(10, 46)(11, 65)(12, 67)(13, 69)(14, 48)(15, 73)(16, 70)(17, 71)(18, 50)(19, 78)(20, 51)(21, 79)(22, 52)(23, 74)(24, 60)(25, 62)(26, 54)(27, 63)(28, 81)(29, 82)(30, 56)(31, 68)(32, 83)(33, 58)(34, 59)(35, 80)(36, 72)(37, 66)(38, 64)(39, 77)(40, 84)(41, 76)(42, 75) local type(s) :: { ( 6, 21, 6, 21 ) } Outer automorphisms :: reflexible Dual of E7.377 Transitivity :: ET+ VT+ AT Graph:: simple v = 21 e = 42 f = 9 degree seq :: [ 4^21 ] E7.382 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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 :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, Y2^6, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^21 ] Map:: R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 9, 51)(5, 47, 11, 53)(6, 48, 13, 55)(8, 50, 12, 54)(10, 52, 14, 56)(15, 57, 23, 65)(16, 58, 25, 67)(17, 59, 24, 66)(18, 60, 26, 68)(19, 61, 27, 69)(20, 62, 29, 71)(21, 63, 28, 70)(22, 64, 30, 72)(31, 73, 37, 79)(32, 74, 38, 80)(33, 75, 39, 81)(34, 76, 40, 82)(35, 77, 41, 83)(36, 78, 42, 84)(85, 127, 87, 129, 92, 134, 101, 143, 94, 136, 88, 130)(86, 128, 89, 131, 96, 138, 105, 147, 98, 140, 90, 132)(91, 133, 99, 141, 108, 150, 102, 144, 93, 135, 100, 142)(95, 137, 103, 145, 112, 154, 106, 148, 97, 139, 104, 146)(107, 149, 115, 157, 110, 152, 117, 159, 109, 151, 116, 158)(111, 153, 118, 160, 114, 156, 120, 162, 113, 155, 119, 161)(121, 163, 125, 167, 123, 165, 124, 166, 122, 164, 126, 168) L = (1, 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, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 2, 42, 2, 42 ), ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E7.385 Graph:: bipartite v = 28 e = 84 f = 44 degree seq :: [ 4^21, 12^7 ] E7.383 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (Y2 * Y1^-1 * Y2)^2, Y1^6, Y1^3 * Y2^-1 * Y1 * Y2^-1, Y2^2 * Y1^-1 * Y2^-5 * Y1 ] Map:: R = (1, 43, 2, 44, 6, 48, 16, 58, 13, 55, 4, 46)(3, 45, 9, 51, 17, 59, 8, 50, 21, 63, 11, 53)(5, 47, 14, 56, 18, 60, 12, 54, 20, 62, 7, 49)(10, 52, 24, 66, 29, 71, 23, 65, 33, 75, 22, 64)(15, 57, 26, 68, 30, 72, 19, 61, 31, 73, 27, 69)(25, 67, 34, 76, 41, 83, 36, 78, 40, 82, 35, 77)(28, 70, 32, 74, 37, 79, 39, 81, 42, 84, 38, 80)(85, 127, 87, 129, 94, 136, 109, 151, 121, 163, 114, 156, 102, 144, 90, 132, 101, 143, 113, 155, 125, 167, 126, 168, 115, 157, 104, 146, 97, 139, 105, 147, 117, 159, 124, 166, 112, 154, 99, 141, 89, 131)(86, 128, 91, 133, 103, 145, 116, 158, 120, 162, 108, 150, 95, 137, 100, 142, 98, 140, 111, 153, 123, 165, 119, 161, 107, 149, 93, 135, 88, 130, 96, 138, 110, 152, 122, 164, 118, 160, 106, 148, 92, 134) 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) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E7.384 Graph:: bipartite v = 9 e = 84 f = 63 degree seq :: [ 12^7, 42^2 ] E7.384 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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, 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, Y2 * Y3^-5 * Y2 * Y3^2, (Y3^-1 * Y1^-1)^21 ] Map:: polytopal R = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)(85, 127, 86, 128)(87, 129, 91, 133)(88, 130, 93, 135)(89, 131, 95, 137)(90, 132, 97, 139)(92, 134, 101, 143)(94, 136, 105, 147)(96, 138, 109, 151)(98, 140, 113, 155)(99, 141, 107, 149)(100, 142, 111, 153)(102, 144, 114, 156)(103, 145, 108, 150)(104, 146, 112, 154)(106, 148, 110, 152)(115, 157, 125, 167)(116, 158, 122, 164)(117, 159, 123, 165)(118, 160, 126, 168)(119, 161, 120, 162)(121, 163, 124, 166) L = (1, 87)(2, 89)(3, 92)(4, 85)(5, 96)(6, 86)(7, 99)(8, 102)(9, 103)(10, 88)(11, 107)(12, 110)(13, 111)(14, 90)(15, 115)(16, 91)(17, 117)(18, 119)(19, 120)(20, 93)(21, 121)(22, 94)(23, 123)(24, 95)(25, 125)(26, 118)(27, 126)(28, 97)(29, 122)(30, 98)(31, 105)(32, 100)(33, 104)(34, 101)(35, 109)(36, 116)(37, 114)(38, 106)(39, 113)(40, 108)(41, 112)(42, 124)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 12, 42 ), ( 12, 42, 12, 42 ) } Outer automorphisms :: reflexible Dual of E7.383 Graph:: simple bipartite v = 63 e = 84 f = 9 degree seq :: [ 2^42, 4^21 ] E7.385 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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 :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y1^-3)^2, Y1^5 * Y3 * Y1^-2 * Y3 ] Map:: R = (1, 43, 2, 44, 5, 47, 11, 53, 23, 65, 32, 74, 41, 83, 34, 76, 17, 59, 29, 71, 40, 82, 42, 84, 33, 75, 16, 58, 28, 70, 39, 81, 35, 77, 38, 80, 22, 64, 10, 52, 4, 46)(3, 45, 7, 49, 15, 57, 31, 73, 26, 68, 12, 54, 25, 67, 20, 62, 9, 51, 19, 61, 36, 78, 30, 72, 14, 56, 6, 48, 13, 55, 27, 69, 21, 63, 37, 79, 24, 66, 18, 60, 8, 50)(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, 90)(3, 85)(4, 93)(5, 96)(6, 86)(7, 100)(8, 101)(9, 88)(10, 105)(11, 108)(12, 89)(13, 112)(14, 113)(15, 116)(16, 91)(17, 92)(18, 119)(19, 117)(20, 118)(21, 94)(22, 115)(23, 120)(24, 95)(25, 123)(26, 124)(27, 125)(28, 97)(29, 98)(30, 122)(31, 106)(32, 99)(33, 103)(34, 104)(35, 102)(36, 107)(37, 126)(38, 114)(39, 109)(40, 110)(41, 111)(42, 121)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 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 E7.382 Graph:: simple bipartite v = 44 e = 84 f = 28 degree seq :: [ 2^42, 42^2 ] E7.386 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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 :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y2^3 * Y1)^2, Y2^-3 * Y1 * Y2^2 * Y1 * Y2^-2, (Y3 * Y2^-1)^6 ] Map:: R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 9, 51)(5, 47, 11, 53)(6, 48, 13, 55)(8, 50, 17, 59)(10, 52, 21, 63)(12, 54, 25, 67)(14, 56, 29, 71)(15, 57, 23, 65)(16, 58, 27, 69)(18, 60, 30, 72)(19, 61, 24, 66)(20, 62, 28, 70)(22, 64, 26, 68)(31, 73, 41, 83)(32, 74, 38, 80)(33, 75, 39, 81)(34, 76, 42, 84)(35, 77, 36, 78)(37, 79, 40, 82)(85, 127, 87, 129, 92, 134, 102, 144, 119, 161, 109, 151, 125, 167, 112, 154, 97, 139, 111, 153, 126, 168, 124, 166, 108, 150, 95, 137, 107, 149, 123, 165, 113, 155, 122, 164, 106, 148, 94, 136, 88, 130)(86, 128, 89, 131, 96, 138, 110, 152, 118, 160, 101, 143, 117, 159, 104, 146, 93, 135, 103, 145, 120, 162, 116, 158, 100, 142, 91, 133, 99, 141, 115, 157, 105, 147, 121, 163, 114, 156, 98, 140, 90, 132) L = (1, 86)(2, 85)(3, 91)(4, 93)(5, 95)(6, 97)(7, 87)(8, 101)(9, 88)(10, 105)(11, 89)(12, 109)(13, 90)(14, 113)(15, 107)(16, 111)(17, 92)(18, 114)(19, 108)(20, 112)(21, 94)(22, 110)(23, 99)(24, 103)(25, 96)(26, 106)(27, 100)(28, 104)(29, 98)(30, 102)(31, 125)(32, 122)(33, 123)(34, 126)(35, 120)(36, 119)(37, 124)(38, 116)(39, 117)(40, 121)(41, 115)(42, 118)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E7.387 Graph:: bipartite v = 23 e = 84 f = 49 degree seq :: [ 4^21, 42^2 ] E7.387 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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 :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-3 * Y3^-1 * Y1, (Y3 * Y1^-1 * Y3)^2, Y1^3 * Y3^-1 * Y1 * Y3^-1, Y1^-1 * Y3 * Y1^-1 * Y3^-6, (Y3 * Y2^-1)^21 ] Map:: R = (1, 43, 2, 44, 6, 48, 16, 58, 13, 55, 4, 46)(3, 45, 9, 51, 17, 59, 8, 50, 21, 63, 11, 53)(5, 47, 14, 56, 18, 60, 12, 54, 20, 62, 7, 49)(10, 52, 24, 66, 29, 71, 23, 65, 33, 75, 22, 64)(15, 57, 26, 68, 30, 72, 19, 61, 31, 73, 27, 69)(25, 67, 34, 76, 41, 83, 36, 78, 40, 82, 35, 77)(28, 70, 32, 74, 37, 79, 39, 81, 42, 84, 38, 80)(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, 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) :: { ( 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E7.386 Graph:: simple bipartite v = 49 e = 84 f = 23 degree seq :: [ 2^42, 12^7 ] E7.388 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = D8 x S3 (small group id <48, 38>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y1)^2, R * Y2 * R * Y3, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, (Y2 * Y3)^4, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 50, 2, 49)(3, 55, 7, 51)(4, 57, 9, 52)(5, 59, 11, 53)(6, 61, 13, 54)(8, 60, 12, 56)(10, 62, 14, 58)(15, 73, 25, 63)(16, 74, 26, 64)(17, 75, 27, 65)(18, 77, 29, 66)(19, 78, 30, 67)(20, 79, 31, 68)(21, 80, 32, 69)(22, 81, 33, 70)(23, 83, 35, 71)(24, 84, 36, 72)(28, 82, 34, 76)(37, 90, 42, 85)(38, 91, 43, 86)(39, 92, 44, 87)(40, 95, 47, 88)(41, 94, 46, 89)(45, 96, 48, 93) L = (1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 17)(9, 18)(11, 20)(12, 22)(13, 23)(16, 27)(19, 28)(21, 33)(24, 34)(25, 37)(26, 39)(29, 38)(30, 40)(31, 42)(32, 44)(35, 43)(36, 45)(41, 47)(46, 48)(49, 52)(50, 54)(51, 56)(53, 60)(55, 64)(57, 63)(58, 67)(59, 69)(61, 68)(62, 72)(65, 76)(66, 78)(70, 82)(71, 84)(73, 86)(74, 85)(75, 88)(77, 89)(79, 91)(80, 90)(81, 93)(83, 94)(87, 95)(92, 96) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E7.390 Transitivity :: VT+ AT Graph:: simple bipartite v = 24 e = 48 f = 12 degree seq :: [ 4^24 ] E7.389 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y1)^2, R * Y2 * R * Y3, Y3 * Y2 * Y1 * Y2 * Y3 * Y1, (Y2 * Y3)^4, Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 50, 2, 49)(3, 55, 7, 51)(4, 57, 9, 52)(5, 59, 11, 53)(6, 61, 13, 54)(8, 60, 12, 56)(10, 62, 14, 58)(15, 73, 25, 63)(16, 74, 26, 64)(17, 75, 27, 65)(18, 77, 29, 66)(19, 78, 30, 67)(20, 79, 31, 68)(21, 80, 32, 69)(22, 81, 33, 70)(23, 83, 35, 71)(24, 84, 36, 72)(28, 82, 34, 76)(37, 94, 46, 85)(38, 92, 44, 86)(39, 91, 43, 87)(40, 95, 47, 88)(41, 90, 42, 89)(45, 96, 48, 93) L = (1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 17)(9, 18)(11, 20)(12, 22)(13, 23)(16, 27)(19, 28)(21, 33)(24, 34)(25, 37)(26, 39)(29, 38)(30, 40)(31, 42)(32, 44)(35, 43)(36, 45)(41, 47)(46, 48)(49, 52)(50, 54)(51, 56)(53, 60)(55, 64)(57, 63)(58, 67)(59, 69)(61, 68)(62, 72)(65, 76)(66, 78)(70, 82)(71, 84)(73, 86)(74, 85)(75, 88)(77, 89)(79, 91)(80, 90)(81, 93)(83, 94)(87, 95)(92, 96) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E7.391 Transitivity :: VT+ AT Graph:: simple bipartite v = 24 e = 48 f = 12 degree seq :: [ 4^24 ] E7.390 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = D8 x S3 (small group id <48, 38>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y2^2, Y3^2, R^2, Y1^4, R * Y2 * R * Y3, (R * Y1)^2, (Y1^-1 * Y3 * Y1^-1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y3 * Y2 * Y3 * Y1^-2 * Y2, (Y1^-1 * Y2 * Y3)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 50, 2, 54, 6, 53, 5, 49)(3, 57, 9, 65, 17, 59, 11, 51)(4, 60, 12, 66, 18, 62, 14, 52)(7, 67, 19, 63, 15, 69, 21, 55)(8, 70, 22, 64, 16, 72, 24, 56)(10, 68, 20, 61, 13, 71, 23, 58)(25, 81, 33, 75, 27, 82, 34, 73)(26, 83, 35, 76, 28, 84, 36, 74)(29, 85, 37, 79, 31, 86, 38, 77)(30, 87, 39, 80, 32, 88, 40, 78)(41, 95, 47, 91, 43, 93, 45, 89)(42, 96, 48, 92, 44, 94, 46, 90) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 17)(8, 23)(9, 25)(10, 18)(11, 27)(12, 28)(14, 26)(16, 20)(19, 29)(21, 31)(22, 32)(24, 30)(33, 41)(34, 43)(35, 44)(36, 42)(37, 45)(38, 47)(39, 48)(40, 46)(49, 52)(50, 56)(51, 58)(53, 64)(54, 66)(55, 68)(57, 74)(59, 76)(60, 73)(61, 65)(62, 75)(63, 71)(67, 78)(69, 80)(70, 77)(72, 79)(81, 90)(82, 92)(83, 89)(84, 91)(85, 94)(86, 96)(87, 93)(88, 95) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.388 Transitivity :: VT+ AT Graph:: bipartite v = 12 e = 48 f = 24 degree seq :: [ 8^12 ] E7.391 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y2^2, Y3^2, R^2, (R * Y1)^2, R * Y2 * R * Y3, Y1^4, (Y1^-1 * Y2 * Y1^-1)^2, (Y1^-1 * Y3 * Y1^-1)^2, (Y2 * Y3 * Y1^-1)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 50, 2, 54, 6, 53, 5, 49)(3, 57, 9, 65, 17, 59, 11, 51)(4, 60, 12, 66, 18, 62, 14, 52)(7, 67, 19, 63, 15, 69, 21, 55)(8, 70, 22, 64, 16, 72, 24, 56)(10, 68, 20, 61, 13, 71, 23, 58)(25, 81, 33, 75, 27, 82, 34, 73)(26, 83, 35, 76, 28, 84, 36, 74)(29, 85, 37, 79, 31, 86, 38, 77)(30, 87, 39, 80, 32, 88, 40, 78)(41, 93, 45, 91, 43, 95, 47, 89)(42, 94, 46, 92, 44, 96, 48, 90) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 17)(8, 23)(9, 25)(10, 18)(11, 27)(12, 28)(14, 26)(16, 20)(19, 29)(21, 31)(22, 32)(24, 30)(33, 41)(34, 43)(35, 44)(36, 42)(37, 45)(38, 47)(39, 48)(40, 46)(49, 52)(50, 56)(51, 58)(53, 64)(54, 66)(55, 68)(57, 74)(59, 76)(60, 73)(61, 65)(62, 75)(63, 71)(67, 78)(69, 80)(70, 77)(72, 79)(81, 90)(82, 92)(83, 89)(84, 91)(85, 94)(86, 96)(87, 93)(88, 95) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.389 Transitivity :: VT+ AT Graph:: bipartite v = 12 e = 48 f = 24 degree seq :: [ 8^12 ] E7.392 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = D8 x S3 (small group id <48, 38>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y2 * Y3 * Y2 * Y1, (Y1 * Y2)^4, (Y3 * Y2)^6 ] Map:: polytopal R = (1, 49, 4, 52)(2, 50, 6, 54)(3, 51, 8, 56)(5, 53, 12, 60)(7, 55, 16, 64)(9, 57, 18, 66)(10, 58, 19, 67)(11, 59, 21, 69)(13, 61, 23, 71)(14, 62, 24, 72)(15, 63, 25, 73)(17, 65, 27, 75)(20, 68, 31, 79)(22, 70, 33, 81)(26, 74, 37, 85)(28, 76, 39, 87)(29, 77, 40, 88)(30, 78, 41, 89)(32, 80, 42, 90)(34, 82, 44, 92)(35, 83, 45, 93)(36, 84, 46, 94)(38, 86, 47, 95)(43, 91, 48, 96)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 113)(106, 112)(108, 118)(110, 117)(111, 116)(114, 124)(115, 126)(119, 130)(120, 132)(121, 128)(122, 127)(123, 131)(125, 129)(133, 139)(134, 138)(135, 140)(136, 142)(137, 141)(143, 144)(145, 147)(146, 149)(148, 154)(150, 158)(151, 159)(152, 157)(153, 156)(155, 164)(160, 170)(161, 169)(162, 173)(163, 172)(165, 176)(166, 175)(167, 179)(168, 178)(171, 182)(174, 181)(177, 187)(180, 186)(183, 189)(184, 188)(185, 191)(190, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16, 16 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E7.398 Graph:: simple bipartite v = 72 e = 96 f = 12 degree seq :: [ 2^48, 4^24 ] E7.393 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y1 * Y2)^4, Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 ] Map:: polytopal R = (1, 49, 4, 52)(2, 50, 6, 54)(3, 51, 8, 56)(5, 53, 12, 60)(7, 55, 16, 64)(9, 57, 18, 66)(10, 58, 19, 67)(11, 59, 21, 69)(13, 61, 23, 71)(14, 62, 24, 72)(15, 63, 25, 73)(17, 65, 27, 75)(20, 68, 31, 79)(22, 70, 33, 81)(26, 74, 37, 85)(28, 76, 39, 87)(29, 77, 40, 88)(30, 78, 41, 89)(32, 80, 42, 90)(34, 82, 44, 92)(35, 83, 45, 93)(36, 84, 46, 94)(38, 86, 47, 95)(43, 91, 48, 96)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 113)(106, 112)(108, 118)(110, 117)(111, 116)(114, 124)(115, 126)(119, 130)(120, 132)(121, 128)(122, 127)(123, 131)(125, 129)(133, 139)(134, 138)(135, 143)(136, 141)(137, 142)(140, 144)(145, 147)(146, 149)(148, 154)(150, 158)(151, 159)(152, 157)(153, 156)(155, 164)(160, 170)(161, 169)(162, 173)(163, 172)(165, 176)(166, 175)(167, 179)(168, 178)(171, 182)(174, 181)(177, 187)(180, 186)(183, 190)(184, 191)(185, 188)(189, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16, 16 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E7.399 Graph:: simple bipartite v = 72 e = 96 f = 12 degree seq :: [ 2^48, 4^24 ] E7.394 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = D8 x S3 (small group id <48, 38>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y1 * Y3^2 * Y2 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: polytopal R = (1, 49, 4, 52, 14, 62, 5, 53)(2, 50, 7, 55, 22, 70, 8, 56)(3, 51, 10, 58, 17, 65, 11, 59)(6, 54, 18, 66, 9, 57, 19, 67)(12, 60, 25, 73, 15, 63, 26, 74)(13, 61, 27, 75, 16, 64, 28, 76)(20, 68, 29, 77, 23, 71, 30, 78)(21, 69, 31, 79, 24, 72, 32, 80)(33, 81, 41, 89, 35, 83, 42, 90)(34, 82, 43, 91, 36, 84, 44, 92)(37, 85, 45, 93, 39, 87, 46, 94)(38, 86, 47, 95, 40, 88, 48, 96)(97, 98)(99, 105)(100, 108)(101, 111)(102, 113)(103, 116)(104, 119)(106, 120)(107, 117)(109, 115)(110, 118)(112, 114)(121, 129)(122, 131)(123, 132)(124, 130)(125, 133)(126, 135)(127, 136)(128, 134)(137, 142)(138, 141)(139, 143)(140, 144)(145, 147)(146, 150)(148, 157)(149, 160)(151, 165)(152, 168)(153, 166)(154, 164)(155, 167)(156, 162)(158, 161)(159, 163)(169, 178)(170, 180)(171, 177)(172, 179)(173, 182)(174, 184)(175, 181)(176, 183)(185, 192)(186, 191)(187, 190)(188, 189) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 8 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.396 Graph:: simple bipartite v = 60 e = 96 f = 24 degree seq :: [ 2^48, 8^12 ] E7.395 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y1 * Y3^2 * Y2 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: polytopal R = (1, 49, 4, 52, 14, 62, 5, 53)(2, 50, 7, 55, 22, 70, 8, 56)(3, 51, 10, 58, 17, 65, 11, 59)(6, 54, 18, 66, 9, 57, 19, 67)(12, 60, 25, 73, 15, 63, 26, 74)(13, 61, 27, 75, 16, 64, 28, 76)(20, 68, 29, 77, 23, 71, 30, 78)(21, 69, 31, 79, 24, 72, 32, 80)(33, 81, 41, 89, 35, 83, 42, 90)(34, 82, 43, 91, 36, 84, 44, 92)(37, 85, 45, 93, 39, 87, 46, 94)(38, 86, 47, 95, 40, 88, 48, 96)(97, 98)(99, 105)(100, 108)(101, 111)(102, 113)(103, 116)(104, 119)(106, 120)(107, 117)(109, 115)(110, 118)(112, 114)(121, 129)(122, 131)(123, 132)(124, 130)(125, 133)(126, 135)(127, 136)(128, 134)(137, 141)(138, 142)(139, 144)(140, 143)(145, 147)(146, 150)(148, 157)(149, 160)(151, 165)(152, 168)(153, 166)(154, 164)(155, 167)(156, 162)(158, 161)(159, 163)(169, 178)(170, 180)(171, 177)(172, 179)(173, 182)(174, 184)(175, 181)(176, 183)(185, 191)(186, 192)(187, 189)(188, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 8 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.397 Graph:: simple bipartite v = 60 e = 96 f = 24 degree seq :: [ 2^48, 8^12 ] E7.396 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = D8 x S3 (small group id <48, 38>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y2 * Y3 * Y2 * Y1, (Y1 * Y2)^4, (Y3 * Y2)^6 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 6, 54, 102, 150)(3, 51, 99, 147, 8, 56, 104, 152)(5, 53, 101, 149, 12, 60, 108, 156)(7, 55, 103, 151, 16, 64, 112, 160)(9, 57, 105, 153, 18, 66, 114, 162)(10, 58, 106, 154, 19, 67, 115, 163)(11, 59, 107, 155, 21, 69, 117, 165)(13, 61, 109, 157, 23, 71, 119, 167)(14, 62, 110, 158, 24, 72, 120, 168)(15, 63, 111, 159, 25, 73, 121, 169)(17, 65, 113, 161, 27, 75, 123, 171)(20, 68, 116, 164, 31, 79, 127, 175)(22, 70, 118, 166, 33, 81, 129, 177)(26, 74, 122, 170, 37, 85, 133, 181)(28, 76, 124, 172, 39, 87, 135, 183)(29, 77, 125, 173, 40, 88, 136, 184)(30, 78, 126, 174, 41, 89, 137, 185)(32, 80, 128, 176, 42, 90, 138, 186)(34, 82, 130, 178, 44, 92, 140, 188)(35, 83, 131, 179, 45, 93, 141, 189)(36, 84, 132, 180, 46, 94, 142, 190)(38, 86, 134, 182, 47, 95, 143, 191)(43, 91, 139, 187, 48, 96, 144, 192) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 52)(10, 64)(11, 53)(12, 70)(13, 54)(14, 69)(15, 68)(16, 58)(17, 56)(18, 76)(19, 78)(20, 63)(21, 62)(22, 60)(23, 82)(24, 84)(25, 80)(26, 79)(27, 83)(28, 66)(29, 81)(30, 67)(31, 74)(32, 73)(33, 77)(34, 71)(35, 75)(36, 72)(37, 91)(38, 90)(39, 92)(40, 94)(41, 93)(42, 86)(43, 85)(44, 87)(45, 89)(46, 88)(47, 96)(48, 95)(97, 147)(98, 149)(99, 145)(100, 154)(101, 146)(102, 158)(103, 159)(104, 157)(105, 156)(106, 148)(107, 164)(108, 153)(109, 152)(110, 150)(111, 151)(112, 170)(113, 169)(114, 173)(115, 172)(116, 155)(117, 176)(118, 175)(119, 179)(120, 178)(121, 161)(122, 160)(123, 182)(124, 163)(125, 162)(126, 181)(127, 166)(128, 165)(129, 187)(130, 168)(131, 167)(132, 186)(133, 174)(134, 171)(135, 189)(136, 188)(137, 191)(138, 180)(139, 177)(140, 184)(141, 183)(142, 192)(143, 185)(144, 190) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E7.394 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 60 degree seq :: [ 8^24 ] E7.397 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y1 * Y2)^4, Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 6, 54, 102, 150)(3, 51, 99, 147, 8, 56, 104, 152)(5, 53, 101, 149, 12, 60, 108, 156)(7, 55, 103, 151, 16, 64, 112, 160)(9, 57, 105, 153, 18, 66, 114, 162)(10, 58, 106, 154, 19, 67, 115, 163)(11, 59, 107, 155, 21, 69, 117, 165)(13, 61, 109, 157, 23, 71, 119, 167)(14, 62, 110, 158, 24, 72, 120, 168)(15, 63, 111, 159, 25, 73, 121, 169)(17, 65, 113, 161, 27, 75, 123, 171)(20, 68, 116, 164, 31, 79, 127, 175)(22, 70, 118, 166, 33, 81, 129, 177)(26, 74, 122, 170, 37, 85, 133, 181)(28, 76, 124, 172, 39, 87, 135, 183)(29, 77, 125, 173, 40, 88, 136, 184)(30, 78, 126, 174, 41, 89, 137, 185)(32, 80, 128, 176, 42, 90, 138, 186)(34, 82, 130, 178, 44, 92, 140, 188)(35, 83, 131, 179, 45, 93, 141, 189)(36, 84, 132, 180, 46, 94, 142, 190)(38, 86, 134, 182, 47, 95, 143, 191)(43, 91, 139, 187, 48, 96, 144, 192) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 52)(10, 64)(11, 53)(12, 70)(13, 54)(14, 69)(15, 68)(16, 58)(17, 56)(18, 76)(19, 78)(20, 63)(21, 62)(22, 60)(23, 82)(24, 84)(25, 80)(26, 79)(27, 83)(28, 66)(29, 81)(30, 67)(31, 74)(32, 73)(33, 77)(34, 71)(35, 75)(36, 72)(37, 91)(38, 90)(39, 95)(40, 93)(41, 94)(42, 86)(43, 85)(44, 96)(45, 88)(46, 89)(47, 87)(48, 92)(97, 147)(98, 149)(99, 145)(100, 154)(101, 146)(102, 158)(103, 159)(104, 157)(105, 156)(106, 148)(107, 164)(108, 153)(109, 152)(110, 150)(111, 151)(112, 170)(113, 169)(114, 173)(115, 172)(116, 155)(117, 176)(118, 175)(119, 179)(120, 178)(121, 161)(122, 160)(123, 182)(124, 163)(125, 162)(126, 181)(127, 166)(128, 165)(129, 187)(130, 168)(131, 167)(132, 186)(133, 174)(134, 171)(135, 190)(136, 191)(137, 188)(138, 180)(139, 177)(140, 185)(141, 192)(142, 183)(143, 184)(144, 189) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E7.395 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 60 degree seq :: [ 8^24 ] E7.398 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = D8 x S3 (small group id <48, 38>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y1 * Y3^2 * Y2 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 14, 62, 110, 158, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 22, 70, 118, 166, 8, 56, 104, 152)(3, 51, 99, 147, 10, 58, 106, 154, 17, 65, 113, 161, 11, 59, 107, 155)(6, 54, 102, 150, 18, 66, 114, 162, 9, 57, 105, 153, 19, 67, 115, 163)(12, 60, 108, 156, 25, 73, 121, 169, 15, 63, 111, 159, 26, 74, 122, 170)(13, 61, 109, 157, 27, 75, 123, 171, 16, 64, 112, 160, 28, 76, 124, 172)(20, 68, 116, 164, 29, 77, 125, 173, 23, 71, 119, 167, 30, 78, 126, 174)(21, 69, 117, 165, 31, 79, 127, 175, 24, 72, 120, 168, 32, 80, 128, 176)(33, 81, 129, 177, 41, 89, 137, 185, 35, 83, 131, 179, 42, 90, 138, 186)(34, 82, 130, 178, 43, 91, 139, 187, 36, 84, 132, 180, 44, 92, 140, 188)(37, 85, 133, 181, 45, 93, 141, 189, 39, 87, 135, 183, 46, 94, 142, 190)(38, 86, 134, 182, 47, 95, 143, 191, 40, 88, 136, 184, 48, 96, 144, 192) L = (1, 50)(2, 49)(3, 57)(4, 60)(5, 63)(6, 65)(7, 68)(8, 71)(9, 51)(10, 72)(11, 69)(12, 52)(13, 67)(14, 70)(15, 53)(16, 66)(17, 54)(18, 64)(19, 61)(20, 55)(21, 59)(22, 62)(23, 56)(24, 58)(25, 81)(26, 83)(27, 84)(28, 82)(29, 85)(30, 87)(31, 88)(32, 86)(33, 73)(34, 76)(35, 74)(36, 75)(37, 77)(38, 80)(39, 78)(40, 79)(41, 94)(42, 93)(43, 95)(44, 96)(45, 90)(46, 89)(47, 91)(48, 92)(97, 147)(98, 150)(99, 145)(100, 157)(101, 160)(102, 146)(103, 165)(104, 168)(105, 166)(106, 164)(107, 167)(108, 162)(109, 148)(110, 161)(111, 163)(112, 149)(113, 158)(114, 156)(115, 159)(116, 154)(117, 151)(118, 153)(119, 155)(120, 152)(121, 178)(122, 180)(123, 177)(124, 179)(125, 182)(126, 184)(127, 181)(128, 183)(129, 171)(130, 169)(131, 172)(132, 170)(133, 175)(134, 173)(135, 176)(136, 174)(137, 192)(138, 191)(139, 190)(140, 189)(141, 188)(142, 187)(143, 186)(144, 185) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E7.392 Transitivity :: VT+ Graph:: bipartite v = 12 e = 96 f = 72 degree seq :: [ 16^12 ] E7.399 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y1 * Y3^2 * Y2 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 14, 62, 110, 158, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 22, 70, 118, 166, 8, 56, 104, 152)(3, 51, 99, 147, 10, 58, 106, 154, 17, 65, 113, 161, 11, 59, 107, 155)(6, 54, 102, 150, 18, 66, 114, 162, 9, 57, 105, 153, 19, 67, 115, 163)(12, 60, 108, 156, 25, 73, 121, 169, 15, 63, 111, 159, 26, 74, 122, 170)(13, 61, 109, 157, 27, 75, 123, 171, 16, 64, 112, 160, 28, 76, 124, 172)(20, 68, 116, 164, 29, 77, 125, 173, 23, 71, 119, 167, 30, 78, 126, 174)(21, 69, 117, 165, 31, 79, 127, 175, 24, 72, 120, 168, 32, 80, 128, 176)(33, 81, 129, 177, 41, 89, 137, 185, 35, 83, 131, 179, 42, 90, 138, 186)(34, 82, 130, 178, 43, 91, 139, 187, 36, 84, 132, 180, 44, 92, 140, 188)(37, 85, 133, 181, 45, 93, 141, 189, 39, 87, 135, 183, 46, 94, 142, 190)(38, 86, 134, 182, 47, 95, 143, 191, 40, 88, 136, 184, 48, 96, 144, 192) L = (1, 50)(2, 49)(3, 57)(4, 60)(5, 63)(6, 65)(7, 68)(8, 71)(9, 51)(10, 72)(11, 69)(12, 52)(13, 67)(14, 70)(15, 53)(16, 66)(17, 54)(18, 64)(19, 61)(20, 55)(21, 59)(22, 62)(23, 56)(24, 58)(25, 81)(26, 83)(27, 84)(28, 82)(29, 85)(30, 87)(31, 88)(32, 86)(33, 73)(34, 76)(35, 74)(36, 75)(37, 77)(38, 80)(39, 78)(40, 79)(41, 93)(42, 94)(43, 96)(44, 95)(45, 89)(46, 90)(47, 92)(48, 91)(97, 147)(98, 150)(99, 145)(100, 157)(101, 160)(102, 146)(103, 165)(104, 168)(105, 166)(106, 164)(107, 167)(108, 162)(109, 148)(110, 161)(111, 163)(112, 149)(113, 158)(114, 156)(115, 159)(116, 154)(117, 151)(118, 153)(119, 155)(120, 152)(121, 178)(122, 180)(123, 177)(124, 179)(125, 182)(126, 184)(127, 181)(128, 183)(129, 171)(130, 169)(131, 172)(132, 170)(133, 175)(134, 173)(135, 176)(136, 174)(137, 191)(138, 192)(139, 189)(140, 190)(141, 187)(142, 188)(143, 185)(144, 186) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E7.393 Transitivity :: VT+ Graph:: bipartite v = 12 e = 96 f = 72 degree seq :: [ 16^12 ] E7.400 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x S3 (small group id <48, 38>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1)^4, (Y2 * Y1 * Y3 * Y1)^2, (Y2 * Y1)^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 10, 58)(6, 54, 12, 60)(8, 56, 15, 63)(11, 59, 20, 68)(13, 61, 23, 71)(14, 62, 21, 69)(16, 64, 19, 67)(17, 65, 22, 70)(18, 66, 28, 76)(24, 72, 35, 83)(25, 73, 34, 82)(26, 74, 32, 80)(27, 75, 31, 79)(29, 77, 39, 87)(30, 78, 38, 86)(33, 81, 37, 85)(36, 84, 43, 91)(40, 88, 46, 94)(41, 89, 45, 93)(42, 90, 44, 92)(47, 95, 48, 96)(97, 145, 99, 147)(98, 146, 101, 149)(100, 148, 104, 152)(102, 150, 107, 155)(103, 151, 109, 157)(105, 153, 112, 160)(106, 154, 114, 162)(108, 156, 117, 165)(110, 158, 120, 168)(111, 159, 121, 169)(113, 161, 123, 171)(115, 163, 125, 173)(116, 164, 126, 174)(118, 166, 128, 176)(119, 167, 129, 177)(122, 170, 132, 180)(124, 172, 133, 181)(127, 175, 136, 184)(130, 178, 137, 185)(131, 179, 138, 186)(134, 182, 140, 188)(135, 183, 141, 189)(139, 187, 143, 191)(142, 190, 144, 192) L = (1, 100)(2, 102)(3, 104)(4, 97)(5, 107)(6, 98)(7, 110)(8, 99)(9, 113)(10, 115)(11, 101)(12, 118)(13, 120)(14, 103)(15, 122)(16, 123)(17, 105)(18, 125)(19, 106)(20, 127)(21, 128)(22, 108)(23, 130)(24, 109)(25, 132)(26, 111)(27, 112)(28, 134)(29, 114)(30, 136)(31, 116)(32, 117)(33, 137)(34, 119)(35, 139)(36, 121)(37, 140)(38, 124)(39, 142)(40, 126)(41, 129)(42, 143)(43, 131)(44, 133)(45, 144)(46, 135)(47, 138)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.405 Graph:: simple bipartite v = 48 e = 96 f = 36 degree seq :: [ 4^48 ] E7.401 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x S3 (small group id <48, 38>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y2 * Y1 * Y2 * Y1, (Y3^2 * Y1)^2, Y3^6, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^-2 * Y2 * Y3^2 * Y1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 12, 60)(5, 53, 14, 62)(6, 54, 16, 64)(7, 55, 19, 67)(8, 56, 21, 69)(10, 58, 24, 72)(11, 59, 26, 74)(13, 61, 22, 70)(15, 63, 20, 68)(17, 65, 33, 81)(18, 66, 35, 83)(23, 71, 36, 84)(25, 73, 34, 82)(27, 75, 32, 80)(28, 76, 37, 85)(29, 77, 40, 88)(30, 78, 41, 89)(31, 79, 38, 86)(39, 87, 45, 93)(42, 90, 48, 96)(43, 91, 47, 95)(44, 92, 46, 94)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 107, 155)(101, 149, 106, 154)(103, 151, 114, 162)(104, 152, 113, 161)(105, 153, 116, 164)(108, 156, 123, 171)(109, 157, 112, 160)(110, 158, 122, 170)(111, 159, 121, 169)(115, 163, 132, 180)(117, 165, 131, 179)(118, 166, 130, 178)(119, 167, 135, 183)(120, 168, 137, 185)(124, 172, 140, 188)(125, 173, 139, 187)(126, 174, 128, 176)(127, 175, 138, 186)(129, 177, 141, 189)(133, 181, 144, 192)(134, 182, 143, 191)(136, 184, 142, 190) L = (1, 100)(2, 103)(3, 106)(4, 109)(5, 97)(6, 113)(7, 116)(8, 98)(9, 114)(10, 121)(11, 99)(12, 124)(13, 126)(14, 127)(15, 101)(16, 107)(17, 130)(18, 102)(19, 133)(20, 135)(21, 136)(22, 104)(23, 105)(24, 138)(25, 128)(26, 140)(27, 139)(28, 110)(29, 108)(30, 111)(31, 137)(32, 112)(33, 142)(34, 119)(35, 144)(36, 143)(37, 117)(38, 115)(39, 118)(40, 141)(41, 125)(42, 122)(43, 120)(44, 123)(45, 134)(46, 131)(47, 129)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.406 Graph:: simple bipartite v = 48 e = 96 f = 36 degree seq :: [ 4^48 ] E7.402 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x S3 (small group id <48, 38>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1 * Y2 * Y1)^2, (Y3 * Y1)^4, Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 10, 58)(6, 54, 12, 60)(8, 56, 15, 63)(11, 59, 20, 68)(13, 61, 23, 71)(14, 62, 21, 69)(16, 64, 19, 67)(17, 65, 22, 70)(18, 66, 28, 76)(24, 72, 35, 83)(25, 73, 34, 82)(26, 74, 32, 80)(27, 75, 31, 79)(29, 77, 39, 87)(30, 78, 38, 86)(33, 81, 41, 89)(36, 84, 44, 92)(37, 85, 45, 93)(40, 88, 48, 96)(42, 90, 46, 94)(43, 91, 47, 95)(97, 145, 99, 147)(98, 146, 101, 149)(100, 148, 104, 152)(102, 150, 107, 155)(103, 151, 109, 157)(105, 153, 112, 160)(106, 154, 114, 162)(108, 156, 117, 165)(110, 158, 120, 168)(111, 159, 121, 169)(113, 161, 123, 171)(115, 163, 125, 173)(116, 164, 126, 174)(118, 166, 128, 176)(119, 167, 129, 177)(122, 170, 132, 180)(124, 172, 133, 181)(127, 175, 136, 184)(130, 178, 138, 186)(131, 179, 139, 187)(134, 182, 142, 190)(135, 183, 143, 191)(137, 185, 144, 192)(140, 188, 141, 189) L = (1, 100)(2, 102)(3, 104)(4, 97)(5, 107)(6, 98)(7, 110)(8, 99)(9, 113)(10, 115)(11, 101)(12, 118)(13, 120)(14, 103)(15, 122)(16, 123)(17, 105)(18, 125)(19, 106)(20, 127)(21, 128)(22, 108)(23, 130)(24, 109)(25, 132)(26, 111)(27, 112)(28, 134)(29, 114)(30, 136)(31, 116)(32, 117)(33, 138)(34, 119)(35, 140)(36, 121)(37, 142)(38, 124)(39, 144)(40, 126)(41, 143)(42, 129)(43, 141)(44, 131)(45, 139)(46, 133)(47, 137)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.404 Graph:: simple bipartite v = 48 e = 96 f = 36 degree seq :: [ 4^48 ] E7.403 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 8, 56)(6, 54, 13, 61)(10, 58, 18, 66)(11, 59, 19, 67)(12, 60, 16, 64)(14, 62, 22, 70)(15, 63, 23, 71)(17, 65, 25, 73)(20, 68, 28, 76)(21, 69, 29, 77)(24, 72, 32, 80)(26, 74, 34, 82)(27, 75, 35, 83)(30, 78, 38, 86)(31, 79, 39, 87)(33, 81, 41, 89)(36, 84, 44, 92)(37, 85, 45, 93)(40, 88, 48, 96)(42, 90, 47, 95)(43, 91, 46, 94)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 107, 155)(101, 149, 106, 154)(103, 151, 111, 159)(104, 152, 110, 158)(105, 153, 113, 161)(108, 156, 116, 164)(109, 157, 117, 165)(112, 160, 120, 168)(114, 162, 123, 171)(115, 163, 122, 170)(118, 166, 127, 175)(119, 167, 126, 174)(121, 169, 129, 177)(124, 172, 132, 180)(125, 173, 133, 181)(128, 176, 136, 184)(130, 178, 139, 187)(131, 179, 138, 186)(134, 182, 143, 191)(135, 183, 142, 190)(137, 185, 144, 192)(140, 188, 141, 189) L = (1, 100)(2, 103)(3, 106)(4, 108)(5, 97)(6, 110)(7, 112)(8, 98)(9, 114)(10, 116)(11, 99)(12, 101)(13, 118)(14, 120)(15, 102)(16, 104)(17, 122)(18, 124)(19, 105)(20, 107)(21, 126)(22, 128)(23, 109)(24, 111)(25, 130)(26, 132)(27, 113)(28, 115)(29, 134)(30, 136)(31, 117)(32, 119)(33, 138)(34, 140)(35, 121)(36, 123)(37, 142)(38, 144)(39, 125)(40, 127)(41, 143)(42, 141)(43, 129)(44, 131)(45, 139)(46, 137)(47, 133)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.407 Graph:: simple bipartite v = 48 e = 96 f = 36 degree seq :: [ 4^48 ] E7.404 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x S3 (small group id <48, 38>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (R * Y1)^2, Y1^4, (R * Y3)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 5, 53)(3, 51, 9, 57, 14, 62, 11, 59)(4, 52, 12, 60, 15, 63, 8, 56)(7, 55, 16, 64, 13, 61, 18, 66)(10, 58, 21, 69, 24, 72, 20, 68)(17, 65, 27, 75, 23, 71, 26, 74)(19, 67, 29, 77, 22, 70, 31, 79)(25, 73, 33, 81, 28, 76, 35, 83)(30, 78, 39, 87, 32, 80, 38, 86)(34, 82, 43, 91, 36, 84, 42, 90)(37, 85, 41, 89, 40, 88, 44, 92)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 109, 157)(102, 150, 110, 158)(104, 152, 113, 161)(105, 153, 115, 163)(107, 155, 118, 166)(108, 156, 119, 167)(111, 159, 120, 168)(112, 160, 121, 169)(114, 162, 124, 172)(116, 164, 126, 174)(117, 165, 128, 176)(122, 170, 130, 178)(123, 171, 132, 180)(125, 173, 133, 181)(127, 175, 136, 184)(129, 177, 137, 185)(131, 179, 140, 188)(134, 182, 141, 189)(135, 183, 142, 190)(138, 186, 143, 191)(139, 187, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 108)(6, 111)(7, 113)(8, 98)(9, 116)(10, 99)(11, 117)(12, 101)(13, 119)(14, 120)(15, 102)(16, 122)(17, 103)(18, 123)(19, 126)(20, 105)(21, 107)(22, 128)(23, 109)(24, 110)(25, 130)(26, 112)(27, 114)(28, 132)(29, 134)(30, 115)(31, 135)(32, 118)(33, 138)(34, 121)(35, 139)(36, 124)(37, 141)(38, 125)(39, 127)(40, 142)(41, 143)(42, 129)(43, 131)(44, 144)(45, 133)(46, 136)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.402 Graph:: simple bipartite v = 36 e = 96 f = 48 degree seq :: [ 4^24, 8^12 ] E7.405 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x S3 (small group id <48, 38>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^4, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 5, 53)(3, 51, 9, 57, 14, 62, 11, 59)(4, 52, 12, 60, 15, 63, 8, 56)(7, 55, 16, 64, 13, 61, 18, 66)(10, 58, 21, 69, 24, 72, 20, 68)(17, 65, 27, 75, 23, 71, 26, 74)(19, 67, 29, 77, 22, 70, 31, 79)(25, 73, 33, 81, 28, 76, 35, 83)(30, 78, 39, 87, 32, 80, 38, 86)(34, 82, 43, 91, 36, 84, 42, 90)(37, 85, 44, 92, 40, 88, 41, 89)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 109, 157)(102, 150, 110, 158)(104, 152, 113, 161)(105, 153, 115, 163)(107, 155, 118, 166)(108, 156, 119, 167)(111, 159, 120, 168)(112, 160, 121, 169)(114, 162, 124, 172)(116, 164, 126, 174)(117, 165, 128, 176)(122, 170, 130, 178)(123, 171, 132, 180)(125, 173, 133, 181)(127, 175, 136, 184)(129, 177, 137, 185)(131, 179, 140, 188)(134, 182, 141, 189)(135, 183, 142, 190)(138, 186, 143, 191)(139, 187, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 108)(6, 111)(7, 113)(8, 98)(9, 116)(10, 99)(11, 117)(12, 101)(13, 119)(14, 120)(15, 102)(16, 122)(17, 103)(18, 123)(19, 126)(20, 105)(21, 107)(22, 128)(23, 109)(24, 110)(25, 130)(26, 112)(27, 114)(28, 132)(29, 134)(30, 115)(31, 135)(32, 118)(33, 138)(34, 121)(35, 139)(36, 124)(37, 141)(38, 125)(39, 127)(40, 142)(41, 143)(42, 129)(43, 131)(44, 144)(45, 133)(46, 136)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.400 Graph:: simple bipartite v = 36 e = 96 f = 48 degree seq :: [ 4^24, 8^12 ] E7.406 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x S3 (small group id <48, 38>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^-2 * Y1^2, Y3^2 * Y1^2, (Y3^-1, Y1^-1), Y1^4, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 11, 59, 16, 64, 13, 61)(4, 52, 9, 57, 6, 54, 10, 58)(8, 56, 17, 65, 15, 63, 19, 67)(12, 60, 22, 70, 14, 62, 23, 71)(18, 66, 26, 74, 20, 68, 27, 75)(21, 69, 29, 77, 24, 72, 31, 79)(25, 73, 33, 81, 28, 76, 35, 83)(30, 78, 38, 86, 32, 80, 39, 87)(34, 82, 42, 90, 36, 84, 43, 91)(37, 85, 44, 92, 40, 88, 41, 89)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 111, 159)(102, 150, 108, 156)(103, 151, 112, 160)(105, 153, 116, 164)(106, 154, 114, 162)(107, 155, 117, 165)(109, 157, 120, 168)(113, 161, 121, 169)(115, 163, 124, 172)(118, 166, 128, 176)(119, 167, 126, 174)(122, 170, 132, 180)(123, 171, 130, 178)(125, 173, 133, 181)(127, 175, 136, 184)(129, 177, 137, 185)(131, 179, 140, 188)(134, 182, 142, 190)(135, 183, 141, 189)(138, 186, 144, 192)(139, 187, 143, 191) L = (1, 100)(2, 105)(3, 108)(4, 103)(5, 106)(6, 97)(7, 102)(8, 114)(9, 101)(10, 98)(11, 118)(12, 112)(13, 119)(14, 99)(15, 116)(16, 110)(17, 122)(18, 111)(19, 123)(20, 104)(21, 126)(22, 109)(23, 107)(24, 128)(25, 130)(26, 115)(27, 113)(28, 132)(29, 134)(30, 120)(31, 135)(32, 117)(33, 138)(34, 124)(35, 139)(36, 121)(37, 141)(38, 127)(39, 125)(40, 142)(41, 143)(42, 131)(43, 129)(44, 144)(45, 136)(46, 133)(47, 140)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.401 Graph:: simple bipartite v = 36 e = 96 f = 48 degree seq :: [ 4^24, 8^12 ] E7.407 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ Y2^2, R^2, (Y3 * Y1^-1)^2, Y1^-1 * Y3^2 * Y1^-1, (Y1^-1 * Y3^-1)^2, Y3^2 * Y1^2, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y1^-1 * Y2 * Y3^2 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 11, 59, 16, 64, 13, 61)(4, 52, 9, 57, 6, 54, 10, 58)(8, 56, 17, 65, 15, 63, 19, 67)(12, 60, 22, 70, 14, 62, 23, 71)(18, 66, 26, 74, 20, 68, 27, 75)(21, 69, 29, 77, 24, 72, 31, 79)(25, 73, 33, 81, 28, 76, 35, 83)(30, 78, 38, 86, 32, 80, 39, 87)(34, 82, 42, 90, 36, 84, 43, 91)(37, 85, 41, 89, 40, 88, 44, 92)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 111, 159)(102, 150, 108, 156)(103, 151, 112, 160)(105, 153, 116, 164)(106, 154, 114, 162)(107, 155, 117, 165)(109, 157, 120, 168)(113, 161, 121, 169)(115, 163, 124, 172)(118, 166, 128, 176)(119, 167, 126, 174)(122, 170, 132, 180)(123, 171, 130, 178)(125, 173, 133, 181)(127, 175, 136, 184)(129, 177, 137, 185)(131, 179, 140, 188)(134, 182, 142, 190)(135, 183, 141, 189)(138, 186, 144, 192)(139, 187, 143, 191) L = (1, 100)(2, 105)(3, 108)(4, 103)(5, 106)(6, 97)(7, 102)(8, 114)(9, 101)(10, 98)(11, 118)(12, 112)(13, 119)(14, 99)(15, 116)(16, 110)(17, 122)(18, 111)(19, 123)(20, 104)(21, 126)(22, 109)(23, 107)(24, 128)(25, 130)(26, 115)(27, 113)(28, 132)(29, 134)(30, 120)(31, 135)(32, 117)(33, 138)(34, 124)(35, 139)(36, 121)(37, 141)(38, 127)(39, 125)(40, 142)(41, 143)(42, 131)(43, 129)(44, 144)(45, 136)(46, 133)(47, 140)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.403 Graph:: simple bipartite v = 36 e = 96 f = 48 degree seq :: [ 4^24, 8^12 ] E7.408 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (Y3 * Y2)^2, (R * Y1)^2, R * Y2 * R * Y3, Y3 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y2, (Y3 * Y1 * Y3 * Y1 * Y2 * Y1)^2, (Y2 * Y1)^6 ] Map:: polytopal non-degenerate R = (1, 50, 2, 49)(3, 55, 7, 51)(4, 57, 9, 52)(5, 58, 10, 53)(6, 60, 12, 54)(8, 63, 15, 56)(11, 68, 20, 59)(13, 71, 23, 61)(14, 73, 25, 62)(16, 76, 28, 64)(17, 78, 30, 65)(18, 79, 31, 66)(19, 81, 33, 67)(21, 84, 36, 69)(22, 86, 38, 70)(24, 83, 35, 72)(26, 85, 37, 74)(27, 80, 32, 75)(29, 82, 34, 77)(39, 92, 44, 87)(40, 95, 47, 88)(41, 94, 46, 89)(42, 93, 45, 90)(43, 96, 48, 91) L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 13)(9, 16)(10, 18)(12, 21)(14, 24)(15, 26)(17, 29)(19, 32)(20, 34)(22, 37)(23, 39)(25, 41)(27, 43)(28, 42)(30, 40)(31, 44)(33, 46)(35, 48)(36, 47)(38, 45)(49, 52)(50, 54)(51, 56)(53, 59)(55, 62)(57, 65)(58, 67)(60, 70)(61, 72)(63, 75)(64, 77)(66, 80)(68, 83)(69, 85)(71, 88)(73, 90)(74, 91)(76, 89)(78, 87)(79, 93)(81, 95)(82, 96)(84, 94)(86, 92) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E7.409 Transitivity :: VT+ AT Graph:: simple bipartite v = 24 e = 48 f = 12 degree seq :: [ 4^24 ] E7.409 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y2^2, Y3^2, R^2, (Y3 * Y2)^2, Y1^4, (R * Y1)^2, R * Y2 * R * Y3, Y1^-1 * Y3 * Y1^-2 * Y2 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 50, 2, 54, 6, 53, 5, 49)(3, 57, 9, 65, 17, 59, 11, 51)(4, 60, 12, 64, 16, 61, 13, 52)(7, 66, 18, 63, 15, 68, 20, 55)(8, 69, 21, 62, 14, 70, 22, 56)(10, 73, 25, 76, 28, 67, 19, 58)(23, 81, 33, 75, 27, 82, 34, 71)(24, 83, 35, 74, 26, 84, 36, 72)(29, 85, 37, 80, 32, 86, 38, 77)(30, 87, 39, 79, 31, 88, 40, 78)(41, 93, 45, 92, 44, 96, 48, 89)(42, 95, 47, 91, 43, 94, 46, 90) L = (1, 3)(2, 7)(4, 10)(5, 14)(6, 16)(8, 19)(9, 23)(11, 26)(12, 27)(13, 24)(15, 25)(17, 28)(18, 29)(20, 31)(21, 32)(22, 30)(33, 41)(34, 43)(35, 44)(36, 42)(37, 45)(38, 47)(39, 48)(40, 46)(49, 52)(50, 56)(51, 58)(53, 63)(54, 65)(55, 67)(57, 72)(59, 75)(60, 74)(61, 71)(62, 73)(64, 76)(66, 78)(68, 80)(69, 79)(70, 77)(81, 90)(82, 92)(83, 91)(84, 89)(85, 94)(86, 96)(87, 95)(88, 93) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.408 Transitivity :: VT+ AT Graph:: bipartite v = 12 e = 48 f = 24 degree seq :: [ 8^12 ] E7.410 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (Y1 * Y2)^2, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1, Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 ] Map:: polytopal R = (1, 49, 4, 52)(2, 50, 6, 54)(3, 51, 7, 55)(5, 53, 10, 58)(8, 56, 16, 64)(9, 57, 17, 65)(11, 59, 21, 69)(12, 60, 22, 70)(13, 61, 24, 72)(14, 62, 25, 73)(15, 63, 26, 74)(18, 66, 32, 80)(19, 67, 33, 81)(20, 68, 34, 82)(23, 71, 39, 87)(27, 75, 40, 88)(28, 76, 41, 89)(29, 77, 42, 90)(30, 78, 43, 91)(31, 79, 44, 92)(35, 83, 45, 93)(36, 84, 46, 94)(37, 85, 47, 95)(38, 86, 48, 96)(97, 98)(99, 101)(100, 104)(102, 107)(103, 109)(105, 111)(106, 114)(108, 116)(110, 119)(112, 123)(113, 125)(115, 127)(117, 131)(118, 133)(120, 134)(121, 132)(122, 135)(124, 129)(126, 128)(130, 140)(136, 141)(137, 143)(138, 142)(139, 144)(145, 147)(146, 149)(148, 153)(150, 156)(151, 158)(152, 159)(154, 163)(155, 164)(157, 167)(160, 172)(161, 174)(162, 175)(165, 180)(166, 182)(168, 181)(169, 179)(170, 178)(171, 177)(173, 176)(183, 188)(184, 192)(185, 190)(186, 191)(187, 189) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16, 16 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E7.413 Graph:: simple bipartite v = 72 e = 96 f = 12 degree seq :: [ 2^48, 4^24 ] E7.411 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, Y2 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y1, Y3^-1 * Y2 * Y3^-2 * Y1 * Y3^-1, Y3^-1 * Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: polytopal R = (1, 49, 4, 52, 13, 61, 5, 53)(2, 50, 7, 55, 20, 68, 8, 56)(3, 51, 9, 57, 23, 71, 10, 58)(6, 54, 16, 64, 28, 76, 17, 65)(11, 59, 24, 72, 15, 63, 25, 73)(12, 60, 26, 74, 14, 62, 27, 75)(18, 66, 29, 77, 22, 70, 30, 78)(19, 67, 31, 79, 21, 69, 32, 80)(33, 81, 41, 89, 36, 84, 42, 90)(34, 82, 43, 91, 35, 83, 44, 92)(37, 85, 45, 93, 40, 88, 46, 94)(38, 86, 47, 95, 39, 87, 48, 96)(97, 98)(99, 102)(100, 107)(101, 110)(103, 114)(104, 117)(105, 118)(106, 115)(108, 113)(109, 119)(111, 112)(116, 124)(120, 129)(121, 131)(122, 132)(123, 130)(125, 133)(126, 135)(127, 136)(128, 134)(137, 141)(138, 143)(139, 142)(140, 144)(145, 147)(146, 150)(148, 156)(149, 159)(151, 163)(152, 166)(153, 165)(154, 162)(155, 161)(157, 164)(158, 160)(167, 172)(168, 178)(169, 180)(170, 179)(171, 177)(173, 182)(174, 184)(175, 183)(176, 181)(185, 192)(186, 190)(187, 191)(188, 189) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 8 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E7.412 Graph:: simple bipartite v = 60 e = 96 f = 24 degree seq :: [ 2^48, 8^12 ] E7.412 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (Y1 * Y2)^2, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1, Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 6, 54, 102, 150)(3, 51, 99, 147, 7, 55, 103, 151)(5, 53, 101, 149, 10, 58, 106, 154)(8, 56, 104, 152, 16, 64, 112, 160)(9, 57, 105, 153, 17, 65, 113, 161)(11, 59, 107, 155, 21, 69, 117, 165)(12, 60, 108, 156, 22, 70, 118, 166)(13, 61, 109, 157, 24, 72, 120, 168)(14, 62, 110, 158, 25, 73, 121, 169)(15, 63, 111, 159, 26, 74, 122, 170)(18, 66, 114, 162, 32, 80, 128, 176)(19, 67, 115, 163, 33, 81, 129, 177)(20, 68, 116, 164, 34, 82, 130, 178)(23, 71, 119, 167, 39, 87, 135, 183)(27, 75, 123, 171, 40, 88, 136, 184)(28, 76, 124, 172, 41, 89, 137, 185)(29, 77, 125, 173, 42, 90, 138, 186)(30, 78, 126, 174, 43, 91, 139, 187)(31, 79, 127, 175, 44, 92, 140, 188)(35, 83, 131, 179, 45, 93, 141, 189)(36, 84, 132, 180, 46, 94, 142, 190)(37, 85, 133, 181, 47, 95, 143, 191)(38, 86, 134, 182, 48, 96, 144, 192) L = (1, 50)(2, 49)(3, 53)(4, 56)(5, 51)(6, 59)(7, 61)(8, 52)(9, 63)(10, 66)(11, 54)(12, 68)(13, 55)(14, 71)(15, 57)(16, 75)(17, 77)(18, 58)(19, 79)(20, 60)(21, 83)(22, 85)(23, 62)(24, 86)(25, 84)(26, 87)(27, 64)(28, 81)(29, 65)(30, 80)(31, 67)(32, 78)(33, 76)(34, 92)(35, 69)(36, 73)(37, 70)(38, 72)(39, 74)(40, 93)(41, 95)(42, 94)(43, 96)(44, 82)(45, 88)(46, 90)(47, 89)(48, 91)(97, 147)(98, 149)(99, 145)(100, 153)(101, 146)(102, 156)(103, 158)(104, 159)(105, 148)(106, 163)(107, 164)(108, 150)(109, 167)(110, 151)(111, 152)(112, 172)(113, 174)(114, 175)(115, 154)(116, 155)(117, 180)(118, 182)(119, 157)(120, 181)(121, 179)(122, 178)(123, 177)(124, 160)(125, 176)(126, 161)(127, 162)(128, 173)(129, 171)(130, 170)(131, 169)(132, 165)(133, 168)(134, 166)(135, 188)(136, 192)(137, 190)(138, 191)(139, 189)(140, 183)(141, 187)(142, 185)(143, 186)(144, 184) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E7.411 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 60 degree seq :: [ 8^24 ] E7.413 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, Y2 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y1, Y3^-1 * Y2 * Y3^-2 * Y1 * Y3^-1, Y3^-1 * Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 13, 61, 109, 157, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 20, 68, 116, 164, 8, 56, 104, 152)(3, 51, 99, 147, 9, 57, 105, 153, 23, 71, 119, 167, 10, 58, 106, 154)(6, 54, 102, 150, 16, 64, 112, 160, 28, 76, 124, 172, 17, 65, 113, 161)(11, 59, 107, 155, 24, 72, 120, 168, 15, 63, 111, 159, 25, 73, 121, 169)(12, 60, 108, 156, 26, 74, 122, 170, 14, 62, 110, 158, 27, 75, 123, 171)(18, 66, 114, 162, 29, 77, 125, 173, 22, 70, 118, 166, 30, 78, 126, 174)(19, 67, 115, 163, 31, 79, 127, 175, 21, 69, 117, 165, 32, 80, 128, 176)(33, 81, 129, 177, 41, 89, 137, 185, 36, 84, 132, 180, 42, 90, 138, 186)(34, 82, 130, 178, 43, 91, 139, 187, 35, 83, 131, 179, 44, 92, 140, 188)(37, 85, 133, 181, 45, 93, 141, 189, 40, 88, 136, 184, 46, 94, 142, 190)(38, 86, 134, 182, 47, 95, 143, 191, 39, 87, 135, 183, 48, 96, 144, 192) L = (1, 50)(2, 49)(3, 54)(4, 59)(5, 62)(6, 51)(7, 66)(8, 69)(9, 70)(10, 67)(11, 52)(12, 65)(13, 71)(14, 53)(15, 64)(16, 63)(17, 60)(18, 55)(19, 58)(20, 76)(21, 56)(22, 57)(23, 61)(24, 81)(25, 83)(26, 84)(27, 82)(28, 68)(29, 85)(30, 87)(31, 88)(32, 86)(33, 72)(34, 75)(35, 73)(36, 74)(37, 77)(38, 80)(39, 78)(40, 79)(41, 93)(42, 95)(43, 94)(44, 96)(45, 89)(46, 91)(47, 90)(48, 92)(97, 147)(98, 150)(99, 145)(100, 156)(101, 159)(102, 146)(103, 163)(104, 166)(105, 165)(106, 162)(107, 161)(108, 148)(109, 164)(110, 160)(111, 149)(112, 158)(113, 155)(114, 154)(115, 151)(116, 157)(117, 153)(118, 152)(119, 172)(120, 178)(121, 180)(122, 179)(123, 177)(124, 167)(125, 182)(126, 184)(127, 183)(128, 181)(129, 171)(130, 168)(131, 170)(132, 169)(133, 176)(134, 173)(135, 175)(136, 174)(137, 192)(138, 190)(139, 191)(140, 189)(141, 188)(142, 186)(143, 187)(144, 185) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E7.410 Transitivity :: VT+ Graph:: bipartite v = 12 e = 96 f = 72 degree seq :: [ 16^12 ] E7.414 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (Y2 * Y3)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1)^4, Y3 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1, (Y2 * Y1)^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 10, 58)(6, 54, 12, 60)(8, 56, 15, 63)(11, 59, 20, 68)(13, 61, 23, 71)(14, 62, 25, 73)(16, 64, 28, 76)(17, 65, 22, 70)(18, 66, 30, 78)(19, 67, 29, 77)(21, 69, 27, 75)(24, 72, 35, 83)(26, 74, 36, 84)(31, 79, 41, 89)(32, 80, 42, 90)(33, 81, 39, 87)(34, 82, 37, 85)(38, 86, 40, 88)(43, 91, 48, 96)(44, 92, 47, 95)(45, 93, 46, 94)(97, 145, 99, 147)(98, 146, 101, 149)(100, 148, 104, 152)(102, 150, 107, 155)(103, 151, 109, 157)(105, 153, 112, 160)(106, 154, 114, 162)(108, 156, 117, 165)(110, 158, 120, 168)(111, 159, 122, 170)(113, 161, 125, 173)(115, 163, 127, 175)(116, 164, 128, 176)(118, 166, 121, 169)(119, 167, 129, 177)(123, 171, 133, 181)(124, 172, 134, 182)(126, 174, 135, 183)(130, 178, 139, 187)(131, 179, 140, 188)(132, 180, 141, 189)(136, 184, 142, 190)(137, 185, 143, 191)(138, 186, 144, 192) L = (1, 100)(2, 102)(3, 104)(4, 97)(5, 107)(6, 98)(7, 110)(8, 99)(9, 113)(10, 115)(11, 101)(12, 118)(13, 120)(14, 103)(15, 123)(16, 125)(17, 105)(18, 127)(19, 106)(20, 124)(21, 121)(22, 108)(23, 130)(24, 109)(25, 117)(26, 133)(27, 111)(28, 116)(29, 112)(30, 136)(31, 114)(32, 134)(33, 139)(34, 119)(35, 132)(36, 131)(37, 122)(38, 128)(39, 142)(40, 126)(41, 138)(42, 137)(43, 129)(44, 141)(45, 140)(46, 135)(47, 144)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.417 Graph:: simple bipartite v = 48 e = 96 f = 36 degree seq :: [ 4^48 ] E7.415 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2)^3, (Y3 * Y1)^4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 10, 58)(6, 54, 12, 60)(8, 56, 14, 62)(11, 59, 18, 66)(13, 61, 21, 69)(15, 63, 22, 70)(16, 64, 20, 68)(17, 65, 25, 73)(19, 67, 26, 74)(23, 71, 30, 78)(24, 72, 32, 80)(27, 75, 34, 82)(28, 76, 36, 84)(29, 77, 33, 81)(31, 79, 38, 86)(35, 83, 41, 89)(37, 85, 43, 91)(39, 87, 44, 92)(40, 88, 45, 93)(42, 90, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147)(98, 146, 101, 149)(100, 148, 104, 152)(102, 150, 107, 155)(103, 151, 106, 154)(105, 153, 111, 159)(108, 156, 115, 163)(109, 157, 113, 161)(110, 158, 118, 166)(112, 160, 120, 168)(114, 162, 122, 170)(116, 164, 124, 172)(117, 165, 125, 173)(119, 167, 127, 175)(121, 169, 129, 177)(123, 171, 131, 179)(126, 174, 133, 181)(128, 176, 132, 180)(130, 178, 136, 184)(134, 182, 139, 187)(135, 183, 138, 186)(137, 185, 141, 189)(140, 188, 143, 191)(142, 190, 144, 192) L = (1, 100)(2, 102)(3, 104)(4, 97)(5, 107)(6, 98)(7, 109)(8, 99)(9, 112)(10, 113)(11, 101)(12, 116)(13, 103)(14, 119)(15, 120)(16, 105)(17, 106)(18, 123)(19, 124)(20, 108)(21, 126)(22, 127)(23, 110)(24, 111)(25, 130)(26, 131)(27, 114)(28, 115)(29, 133)(30, 117)(31, 118)(32, 135)(33, 136)(34, 121)(35, 122)(36, 138)(37, 125)(38, 140)(39, 128)(40, 129)(41, 142)(42, 132)(43, 143)(44, 134)(45, 144)(46, 137)(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, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.418 Graph:: simple bipartite v = 48 e = 96 f = 36 degree seq :: [ 4^48 ] E7.416 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y2 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1)^4, (Y2 * Y1 * Y3)^3, (Y2 * Y1)^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 10, 58)(6, 54, 12, 60)(8, 56, 15, 63)(11, 59, 20, 68)(13, 61, 23, 71)(14, 62, 25, 73)(16, 64, 28, 76)(17, 65, 22, 70)(18, 66, 30, 78)(19, 67, 32, 80)(21, 69, 33, 81)(24, 72, 29, 77)(26, 74, 39, 87)(27, 75, 38, 86)(31, 79, 34, 82)(35, 83, 42, 90)(36, 84, 41, 89)(37, 85, 44, 92)(40, 88, 43, 91)(45, 93, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147)(98, 146, 101, 149)(100, 148, 104, 152)(102, 150, 107, 155)(103, 151, 109, 157)(105, 153, 112, 160)(106, 154, 114, 162)(108, 156, 117, 165)(110, 158, 120, 168)(111, 159, 122, 170)(113, 161, 125, 173)(115, 163, 127, 175)(116, 164, 123, 171)(118, 166, 130, 178)(119, 167, 131, 179)(121, 169, 133, 181)(124, 172, 136, 184)(126, 174, 138, 186)(128, 176, 140, 188)(129, 177, 137, 185)(132, 180, 141, 189)(134, 182, 142, 190)(135, 183, 143, 191)(139, 187, 144, 192) L = (1, 100)(2, 102)(3, 104)(4, 97)(5, 107)(6, 98)(7, 110)(8, 99)(9, 113)(10, 115)(11, 101)(12, 118)(13, 120)(14, 103)(15, 123)(16, 125)(17, 105)(18, 127)(19, 106)(20, 122)(21, 130)(22, 108)(23, 132)(24, 109)(25, 134)(26, 116)(27, 111)(28, 137)(29, 112)(30, 139)(31, 114)(32, 135)(33, 136)(34, 117)(35, 141)(36, 119)(37, 142)(38, 121)(39, 128)(40, 129)(41, 124)(42, 144)(43, 126)(44, 143)(45, 131)(46, 133)(47, 140)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.419 Graph:: simple bipartite v = 48 e = 96 f = 36 degree seq :: [ 4^48 ] E7.417 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1 * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^4, (R * Y3)^2, (Y3 * Y2)^2, Y1^2 * Y2 * Y1^-2 * Y2 * Y3, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y2 * Y1 * Y2 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 5, 53)(3, 51, 9, 57, 19, 67, 11, 59)(4, 52, 12, 60, 15, 63, 8, 56)(7, 55, 16, 64, 24, 72, 18, 66)(10, 58, 22, 70, 14, 62, 21, 69)(13, 61, 25, 73, 17, 65, 26, 74)(20, 68, 29, 77, 32, 80, 31, 79)(23, 71, 33, 81, 30, 78, 34, 82)(27, 75, 37, 85, 36, 84, 38, 86)(28, 76, 39, 87, 35, 83, 40, 88)(41, 89, 45, 93, 44, 92, 48, 96)(42, 90, 47, 95, 43, 91, 46, 94)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 109, 157)(102, 150, 110, 158)(104, 152, 113, 161)(105, 153, 116, 164)(107, 155, 119, 167)(108, 156, 120, 168)(111, 159, 115, 163)(112, 160, 123, 171)(114, 162, 124, 172)(117, 165, 126, 174)(118, 166, 128, 176)(121, 169, 131, 179)(122, 170, 132, 180)(125, 173, 137, 185)(127, 175, 138, 186)(129, 177, 139, 187)(130, 178, 140, 188)(133, 181, 141, 189)(134, 182, 142, 190)(135, 183, 143, 191)(136, 184, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 108)(6, 111)(7, 113)(8, 98)(9, 117)(10, 99)(11, 118)(12, 101)(13, 120)(14, 115)(15, 102)(16, 121)(17, 103)(18, 122)(19, 110)(20, 126)(21, 105)(22, 107)(23, 128)(24, 109)(25, 112)(26, 114)(27, 131)(28, 132)(29, 129)(30, 116)(31, 130)(32, 119)(33, 125)(34, 127)(35, 123)(36, 124)(37, 135)(38, 136)(39, 133)(40, 134)(41, 139)(42, 140)(43, 137)(44, 138)(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) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.414 Graph:: simple bipartite v = 36 e = 96 f = 48 degree seq :: [ 4^24, 8^12 ] E7.418 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, Y1^4, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 5, 53)(3, 51, 9, 57, 19, 67, 11, 59)(4, 52, 12, 60, 15, 63, 8, 56)(7, 55, 16, 64, 28, 76, 18, 66)(10, 58, 22, 70, 32, 80, 21, 69)(13, 61, 24, 72, 34, 82, 20, 68)(14, 62, 25, 73, 36, 84, 27, 75)(17, 65, 30, 78, 40, 88, 29, 77)(23, 71, 33, 81, 43, 91, 35, 83)(26, 74, 38, 86, 45, 93, 37, 85)(31, 79, 41, 89, 44, 92, 39, 87)(42, 90, 46, 94, 48, 96, 47, 95)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 109, 157)(102, 150, 110, 158)(104, 152, 113, 161)(105, 153, 116, 164)(107, 155, 112, 160)(108, 156, 119, 167)(111, 159, 122, 170)(114, 162, 121, 169)(115, 163, 127, 175)(117, 165, 129, 177)(118, 166, 125, 173)(120, 168, 123, 171)(124, 172, 135, 183)(126, 174, 133, 181)(128, 176, 138, 186)(130, 178, 137, 185)(131, 179, 134, 182)(132, 180, 140, 188)(136, 184, 142, 190)(139, 187, 143, 191)(141, 189, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 108)(6, 111)(7, 113)(8, 98)(9, 117)(10, 99)(11, 118)(12, 101)(13, 119)(14, 122)(15, 102)(16, 125)(17, 103)(18, 126)(19, 128)(20, 129)(21, 105)(22, 107)(23, 109)(24, 131)(25, 133)(26, 110)(27, 134)(28, 136)(29, 112)(30, 114)(31, 138)(32, 115)(33, 116)(34, 139)(35, 120)(36, 141)(37, 121)(38, 123)(39, 142)(40, 124)(41, 143)(42, 127)(43, 130)(44, 144)(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) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.415 Graph:: simple bipartite v = 36 e = 96 f = 48 degree seq :: [ 4^24, 8^12 ] E7.419 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (R * Y3)^2, Y1^4, (R * Y1)^2, Y1 * Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 5, 53)(3, 51, 9, 57, 19, 67, 11, 59)(4, 52, 12, 60, 15, 63, 8, 56)(7, 55, 16, 64, 30, 78, 18, 66)(10, 58, 22, 70, 34, 82, 21, 69)(13, 61, 25, 73, 38, 86, 26, 74)(14, 62, 27, 75, 40, 88, 29, 77)(17, 65, 20, 68, 35, 83, 32, 80)(23, 71, 24, 72, 37, 85, 36, 84)(28, 76, 31, 79, 42, 90, 39, 87)(33, 81, 43, 91, 47, 95, 41, 89)(44, 92, 45, 93, 48, 96, 46, 94)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 109, 157)(102, 150, 110, 158)(104, 152, 113, 161)(105, 153, 116, 164)(107, 155, 119, 167)(108, 156, 120, 168)(111, 159, 124, 172)(112, 160, 127, 175)(114, 162, 117, 165)(115, 163, 129, 177)(118, 166, 121, 169)(122, 170, 135, 183)(123, 171, 133, 181)(125, 173, 128, 176)(126, 174, 137, 185)(130, 178, 140, 188)(131, 179, 141, 189)(132, 180, 142, 190)(134, 182, 139, 187)(136, 184, 143, 191)(138, 186, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 108)(6, 111)(7, 113)(8, 98)(9, 117)(10, 99)(11, 118)(12, 101)(13, 120)(14, 124)(15, 102)(16, 128)(17, 103)(18, 116)(19, 130)(20, 114)(21, 105)(22, 107)(23, 121)(24, 109)(25, 119)(26, 133)(27, 135)(28, 110)(29, 127)(30, 131)(31, 125)(32, 112)(33, 140)(34, 115)(35, 126)(36, 134)(37, 122)(38, 132)(39, 123)(40, 138)(41, 141)(42, 136)(43, 142)(44, 129)(45, 137)(46, 139)(47, 144)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E7.416 Graph:: simple bipartite v = 36 e = 96 f = 48 degree seq :: [ 4^24, 8^12 ] E7.420 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 6}) Quotient :: edge Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^4, (F * T1)^2, (F * T2)^2, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, (T2 * T1^-1)^6 ] 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, 37, 27, 35)(26, 39, 28, 40)(33, 43, 34, 44)(36, 45, 38, 46)(41, 47, 42, 48)(49, 50, 52)(51, 56, 58)(53, 61, 62)(54, 63, 65)(55, 66, 67)(57, 64, 70)(59, 73, 74)(60, 75, 76)(68, 81, 80)(69, 82, 79)(71, 83, 84)(72, 85, 86)(77, 89, 88)(78, 90, 87)(91, 95, 94)(92, 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) :: { ( 12^3 ), ( 12^4 ) } Outer automorphisms :: reflexible Dual of E7.424 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 48 f = 8 degree seq :: [ 3^16, 4^12 ] E7.421 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 6}) Quotient :: edge Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^2 * T2^-1 * T1^2 * T2, (T2^-1 * T1^-1)^3, T2^6, T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, T2^-3 * T1 * T2^-3 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 27, 16, 5)(2, 7, 20, 40, 24, 8)(4, 12, 30, 47, 31, 13)(6, 17, 36, 48, 37, 18)(9, 22, 43, 34, 39, 25)(11, 23, 44, 35, 41, 29)(14, 32, 46, 26, 42, 21)(15, 33, 45, 28, 38, 19)(49, 50, 54, 52)(51, 57, 65, 59)(53, 62, 66, 63)(55, 67, 60, 69)(56, 70, 61, 71)(58, 74, 84, 76)(64, 82, 85, 83)(68, 87, 78, 89)(72, 93, 79, 94)(73, 90, 77, 86)(75, 88, 96, 95)(80, 92, 81, 91) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6^4 ), ( 6^6 ) } Outer automorphisms :: reflexible Dual of E7.425 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 48 f = 16 degree seq :: [ 4^12, 6^8 ] E7.422 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 6}) Quotient :: edge Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1^6, T1^2 * T2 * T1 * T2^-1 * T1 * T2, T1^2 * T2 * T1^-1 * T2^-1 * T1 * T2^-1, T1^2 * T2^-1 * T1 * T2^-1 * T1^-1 * T2, (T2^-1 * T1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 11, 13)(6, 17, 18)(9, 24, 25)(10, 26, 28)(12, 31, 32)(14, 36, 37)(15, 38, 40)(16, 41, 42)(19, 44, 34)(20, 23, 30)(21, 39, 33)(22, 27, 46)(29, 47, 35)(43, 45, 48)(49, 50, 54, 64, 60, 52)(51, 57, 71, 89, 75, 58)(53, 62, 83, 90, 87, 63)(55, 67, 76, 79, 93, 68)(56, 69, 73, 80, 85, 70)(59, 77, 74, 65, 86, 78)(61, 81, 91, 66, 84, 82)(72, 92, 88, 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) :: { ( 8^3 ), ( 8^6 ) } Outer automorphisms :: reflexible Dual of E7.423 Transitivity :: ET+ Graph:: simple bipartite v = 24 e = 48 f = 12 degree seq :: [ 3^16, 6^8 ] E7.423 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 6}) Quotient :: loop Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^4, (F * T1)^2, (F * T2)^2, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, (T2 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 49, 3, 51, 9, 57, 5, 53)(2, 50, 6, 54, 16, 64, 7, 55)(4, 52, 11, 59, 22, 70, 12, 60)(8, 56, 20, 68, 13, 61, 21, 69)(10, 58, 23, 71, 14, 62, 24, 72)(15, 63, 29, 77, 18, 66, 30, 78)(17, 65, 31, 79, 19, 67, 32, 80)(25, 73, 37, 85, 27, 75, 35, 83)(26, 74, 39, 87, 28, 76, 40, 88)(33, 81, 43, 91, 34, 82, 44, 92)(36, 84, 45, 93, 38, 86, 46, 94)(41, 89, 47, 95, 42, 90, 48, 96) L = (1, 50)(2, 52)(3, 56)(4, 49)(5, 61)(6, 63)(7, 66)(8, 58)(9, 64)(10, 51)(11, 73)(12, 75)(13, 62)(14, 53)(15, 65)(16, 70)(17, 54)(18, 67)(19, 55)(20, 81)(21, 82)(22, 57)(23, 83)(24, 85)(25, 74)(26, 59)(27, 76)(28, 60)(29, 89)(30, 90)(31, 69)(32, 68)(33, 80)(34, 79)(35, 84)(36, 71)(37, 86)(38, 72)(39, 78)(40, 77)(41, 88)(42, 87)(43, 95)(44, 96)(45, 92)(46, 91)(47, 94)(48, 93) local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: reflexible Dual of E7.422 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 48 f = 24 degree seq :: [ 8^12 ] E7.424 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 6}) Quotient :: loop Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^2 * T2^-1 * T1^2 * T2, (T2^-1 * T1^-1)^3, T2^6, T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, T2^-3 * T1 * T2^-3 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 3, 51, 10, 58, 27, 75, 16, 64, 5, 53)(2, 50, 7, 55, 20, 68, 40, 88, 24, 72, 8, 56)(4, 52, 12, 60, 30, 78, 47, 95, 31, 79, 13, 61)(6, 54, 17, 65, 36, 84, 48, 96, 37, 85, 18, 66)(9, 57, 22, 70, 43, 91, 34, 82, 39, 87, 25, 73)(11, 59, 23, 71, 44, 92, 35, 83, 41, 89, 29, 77)(14, 62, 32, 80, 46, 94, 26, 74, 42, 90, 21, 69)(15, 63, 33, 81, 45, 93, 28, 76, 38, 86, 19, 67) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 67)(8, 70)(9, 65)(10, 74)(11, 51)(12, 69)(13, 71)(14, 66)(15, 53)(16, 82)(17, 59)(18, 63)(19, 60)(20, 87)(21, 55)(22, 61)(23, 56)(24, 93)(25, 90)(26, 84)(27, 88)(28, 58)(29, 86)(30, 89)(31, 94)(32, 92)(33, 91)(34, 85)(35, 64)(36, 76)(37, 83)(38, 73)(39, 78)(40, 96)(41, 68)(42, 77)(43, 80)(44, 81)(45, 79)(46, 72)(47, 75)(48, 95) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E7.420 Transitivity :: ET+ VT+ AT Graph:: v = 8 e = 48 f = 28 degree seq :: [ 12^8 ] E7.425 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 6}) Quotient :: loop Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1^6, T1^2 * T2 * T1 * T2^-1 * T1 * T2, T1^2 * T2 * T1^-1 * T2^-1 * T1 * T2^-1, T1^2 * T2^-1 * T1 * T2^-1 * T1^-1 * T2, (T2^-1 * T1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 49, 3, 51, 5, 53)(2, 50, 7, 55, 8, 56)(4, 52, 11, 59, 13, 61)(6, 54, 17, 65, 18, 66)(9, 57, 24, 72, 25, 73)(10, 58, 26, 74, 28, 76)(12, 60, 31, 79, 32, 80)(14, 62, 36, 84, 37, 85)(15, 63, 38, 86, 40, 88)(16, 64, 41, 89, 42, 90)(19, 67, 44, 92, 34, 82)(20, 68, 23, 71, 30, 78)(21, 69, 39, 87, 33, 81)(22, 70, 27, 75, 46, 94)(29, 77, 47, 95, 35, 83)(43, 91, 45, 93, 48, 96) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 64)(7, 67)(8, 69)(9, 71)(10, 51)(11, 77)(12, 52)(13, 81)(14, 83)(15, 53)(16, 60)(17, 86)(18, 84)(19, 76)(20, 55)(21, 73)(22, 56)(23, 89)(24, 92)(25, 80)(26, 65)(27, 58)(28, 79)(29, 74)(30, 59)(31, 93)(32, 85)(33, 91)(34, 61)(35, 90)(36, 82)(37, 70)(38, 78)(39, 63)(40, 94)(41, 75)(42, 87)(43, 66)(44, 88)(45, 68)(46, 96)(47, 72)(48, 95) local type(s) :: { ( 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.421 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 16 e = 48 f = 20 degree seq :: [ 6^16 ] E7.426 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, Y2^4, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2^2 * Y3 * Y2^-1, Y2 * Y1 * Y2^2 * Y1^-1 * Y2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^6 ] Map:: R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 10, 58)(5, 53, 13, 61, 14, 62)(6, 54, 15, 63, 17, 65)(7, 55, 18, 66, 19, 67)(9, 57, 16, 64, 22, 70)(11, 59, 25, 73, 26, 74)(12, 60, 27, 75, 28, 76)(20, 68, 33, 81, 32, 80)(21, 69, 34, 82, 31, 79)(23, 71, 35, 83, 36, 84)(24, 72, 37, 85, 38, 86)(29, 77, 41, 89, 40, 88)(30, 78, 42, 90, 39, 87)(43, 91, 47, 95, 46, 94)(44, 92, 48, 96, 45, 93)(97, 145, 99, 147, 105, 153, 101, 149)(98, 146, 102, 150, 112, 160, 103, 151)(100, 148, 107, 155, 118, 166, 108, 156)(104, 152, 116, 164, 109, 157, 117, 165)(106, 154, 119, 167, 110, 158, 120, 168)(111, 159, 125, 173, 114, 162, 126, 174)(113, 161, 127, 175, 115, 163, 128, 176)(121, 169, 133, 181, 123, 171, 131, 179)(122, 170, 135, 183, 124, 172, 136, 184)(129, 177, 139, 187, 130, 178, 140, 188)(132, 180, 141, 189, 134, 182, 142, 190)(137, 185, 143, 191, 138, 186, 144, 192) L = (1, 100)(2, 97)(3, 106)(4, 98)(5, 110)(6, 113)(7, 115)(8, 99)(9, 118)(10, 104)(11, 122)(12, 124)(13, 101)(14, 109)(15, 102)(16, 105)(17, 111)(18, 103)(19, 114)(20, 128)(21, 127)(22, 112)(23, 132)(24, 134)(25, 107)(26, 121)(27, 108)(28, 123)(29, 136)(30, 135)(31, 130)(32, 129)(33, 116)(34, 117)(35, 119)(36, 131)(37, 120)(38, 133)(39, 138)(40, 137)(41, 125)(42, 126)(43, 142)(44, 141)(45, 144)(46, 143)(47, 139)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E7.429 Graph:: bipartite v = 28 e = 96 f = 56 degree seq :: [ 6^16, 8^12 ] E7.427 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, Y1^4, R * Y2 * R * Y3, Y1^-1 * Y2^-1 * Y1^2 * Y2 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1, (Y3^-1 * Y1^-1)^3, Y2^6, Y2^-3 * Y1 * Y2^-3 * Y1^-1 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 26, 74, 36, 84, 28, 76)(16, 64, 34, 82, 37, 85, 35, 83)(20, 68, 39, 87, 30, 78, 41, 89)(24, 72, 45, 93, 31, 79, 46, 94)(25, 73, 42, 90, 29, 77, 38, 86)(27, 75, 40, 88, 48, 96, 47, 95)(32, 80, 44, 92, 33, 81, 43, 91)(97, 145, 99, 147, 106, 154, 123, 171, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 136, 184, 120, 168, 104, 152)(100, 148, 108, 156, 126, 174, 143, 191, 127, 175, 109, 157)(102, 150, 113, 161, 132, 180, 144, 192, 133, 181, 114, 162)(105, 153, 118, 166, 139, 187, 130, 178, 135, 183, 121, 169)(107, 155, 119, 167, 140, 188, 131, 179, 137, 185, 125, 173)(110, 158, 128, 176, 142, 190, 122, 170, 138, 186, 117, 165)(111, 159, 129, 177, 141, 189, 124, 172, 134, 182, 115, 163) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 116)(8, 98)(9, 118)(10, 123)(11, 119)(12, 126)(13, 100)(14, 128)(15, 129)(16, 101)(17, 132)(18, 102)(19, 111)(20, 136)(21, 110)(22, 139)(23, 140)(24, 104)(25, 105)(26, 138)(27, 112)(28, 134)(29, 107)(30, 143)(31, 109)(32, 142)(33, 141)(34, 135)(35, 137)(36, 144)(37, 114)(38, 115)(39, 121)(40, 120)(41, 125)(42, 117)(43, 130)(44, 131)(45, 124)(46, 122)(47, 127)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E7.428 Graph:: bipartite v = 20 e = 96 f = 64 degree seq :: [ 8^12, 12^8 ] E7.428 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * Y2^-1 * Y3^-1 * Y2 * Y3, Y2 * Y3 * Y2^-1 * Y3^2 * Y2^-1 * Y3, Y2 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^2, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^-1)^6 ] Map:: polytopal R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 100, 148)(99, 147, 104, 152, 106, 154)(101, 149, 109, 157, 110, 158)(102, 150, 112, 160, 114, 162)(103, 151, 115, 163, 116, 164)(105, 153, 120, 168, 122, 170)(107, 155, 125, 173, 127, 175)(108, 156, 128, 176, 129, 177)(111, 159, 135, 183, 136, 184)(113, 161, 137, 185, 133, 181)(117, 165, 118, 166, 131, 179)(119, 167, 139, 187, 130, 178)(121, 169, 138, 186, 142, 190)(123, 171, 132, 180, 140, 188)(124, 172, 134, 182, 126, 174)(141, 189, 144, 192, 143, 191) L = (1, 99)(2, 102)(3, 105)(4, 107)(5, 97)(6, 113)(7, 98)(8, 118)(9, 121)(10, 123)(11, 126)(12, 100)(13, 131)(14, 133)(15, 101)(16, 119)(17, 138)(18, 132)(19, 139)(20, 134)(21, 103)(22, 125)(23, 104)(24, 114)(25, 111)(26, 116)(27, 128)(28, 106)(29, 135)(30, 142)(31, 140)(32, 136)(33, 122)(34, 108)(35, 141)(36, 109)(37, 129)(38, 110)(39, 112)(40, 143)(41, 127)(42, 117)(43, 144)(44, 115)(45, 120)(46, 130)(47, 124)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E7.427 Graph:: simple bipartite v = 64 e = 96 f = 20 degree seq :: [ 2^48, 6^16 ] E7.429 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^6, (Y3 * Y2^-1)^3, Y1 * Y3 * Y1^2 * Y3 * Y1 * Y3^-1, Y1^2 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y1^2 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3, (Y3^-1 * Y1^-1)^4 ] Map:: polytopal R = (1, 49, 2, 50, 6, 54, 16, 64, 12, 60, 4, 52)(3, 51, 9, 57, 23, 71, 41, 89, 27, 75, 10, 58)(5, 53, 14, 62, 35, 83, 42, 90, 39, 87, 15, 63)(7, 55, 19, 67, 28, 76, 31, 79, 45, 93, 20, 68)(8, 56, 21, 69, 25, 73, 32, 80, 37, 85, 22, 70)(11, 59, 29, 77, 26, 74, 17, 65, 38, 86, 30, 78)(13, 61, 33, 81, 43, 91, 18, 66, 36, 84, 34, 82)(24, 72, 44, 92, 40, 88, 46, 94, 48, 96, 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, 101)(4, 107)(5, 97)(6, 113)(7, 104)(8, 98)(9, 120)(10, 122)(11, 109)(12, 127)(13, 100)(14, 132)(15, 134)(16, 137)(17, 114)(18, 102)(19, 140)(20, 119)(21, 135)(22, 123)(23, 126)(24, 121)(25, 105)(26, 124)(27, 142)(28, 106)(29, 143)(30, 116)(31, 128)(32, 108)(33, 117)(34, 115)(35, 125)(36, 133)(37, 110)(38, 136)(39, 129)(40, 111)(41, 138)(42, 112)(43, 141)(44, 130)(45, 144)(46, 118)(47, 131)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E7.426 Graph:: simple bipartite v = 56 e = 96 f = 28 degree seq :: [ 2^48, 12^8 ] E7.430 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^6, Y1 * Y2 * R * Y2^2 * R * Y2^-1, Y1 * Y2 * Y3 * Y2 * Y3^-1 * Y2^2, Y1 * Y2^-1 * Y3 * Y2^-2 * Y1^-1 * Y2^-1, Y1 * Y2^2 * Y3 * Y2 * Y1^-1 * Y2^-1, Y1 * Y2^-2 * Y3 * Y2 * Y3^-1 * Y2^-1, Y1 * Y2 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-2, (Y3 * Y2^-1)^4 ] Map:: R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 10, 58)(5, 53, 13, 61, 14, 62)(6, 54, 16, 64, 18, 66)(7, 55, 19, 67, 20, 68)(9, 57, 24, 72, 26, 74)(11, 59, 29, 77, 31, 79)(12, 60, 32, 80, 33, 81)(15, 63, 39, 87, 40, 88)(17, 65, 36, 84, 23, 71)(21, 69, 44, 92, 28, 76)(22, 70, 41, 89, 38, 86)(25, 73, 43, 91, 46, 94)(27, 75, 34, 82, 37, 85)(30, 78, 35, 83, 42, 90)(45, 93, 48, 96, 47, 95)(97, 145, 99, 147, 105, 153, 121, 169, 111, 159, 101, 149)(98, 146, 102, 150, 113, 161, 139, 187, 117, 165, 103, 151)(100, 148, 107, 155, 126, 174, 142, 190, 130, 178, 108, 156)(104, 152, 118, 166, 116, 164, 135, 183, 141, 189, 119, 167)(106, 154, 123, 171, 114, 162, 136, 184, 127, 175, 124, 172)(109, 157, 131, 179, 115, 163, 120, 168, 128, 176, 132, 180)(110, 158, 133, 181, 143, 191, 122, 170, 125, 173, 134, 182)(112, 160, 137, 185, 129, 177, 140, 188, 144, 192, 138, 186) L = (1, 100)(2, 97)(3, 106)(4, 98)(5, 110)(6, 114)(7, 116)(8, 99)(9, 122)(10, 104)(11, 127)(12, 129)(13, 101)(14, 109)(15, 136)(16, 102)(17, 119)(18, 112)(19, 103)(20, 115)(21, 124)(22, 134)(23, 132)(24, 105)(25, 142)(26, 120)(27, 133)(28, 140)(29, 107)(30, 138)(31, 125)(32, 108)(33, 128)(34, 123)(35, 126)(36, 113)(37, 130)(38, 137)(39, 111)(40, 135)(41, 118)(42, 131)(43, 121)(44, 117)(45, 143)(46, 139)(47, 144)(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, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E7.431 Graph:: bipartite v = 24 e = 96 f = 60 degree seq :: [ 6^16, 12^8 ] E7.431 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y1^2 * Y3 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, (Y3^-1 * Y1^-1)^3, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^2 * Y1^-1, Y3^3 * Y1 * Y3^-3 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: polytopal R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 26, 74, 36, 84, 28, 76)(16, 64, 34, 82, 37, 85, 35, 83)(20, 68, 39, 87, 30, 78, 41, 89)(24, 72, 45, 93, 31, 79, 46, 94)(25, 73, 42, 90, 29, 77, 38, 86)(27, 75, 40, 88, 48, 96, 47, 95)(32, 80, 44, 92, 33, 81, 43, 91)(97, 145)(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, 113)(7, 116)(8, 98)(9, 118)(10, 123)(11, 119)(12, 126)(13, 100)(14, 128)(15, 129)(16, 101)(17, 132)(18, 102)(19, 111)(20, 136)(21, 110)(22, 139)(23, 140)(24, 104)(25, 105)(26, 138)(27, 112)(28, 134)(29, 107)(30, 143)(31, 109)(32, 142)(33, 141)(34, 135)(35, 137)(36, 144)(37, 114)(38, 115)(39, 121)(40, 120)(41, 125)(42, 117)(43, 130)(44, 131)(45, 124)(46, 122)(47, 127)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.430 Graph:: simple bipartite v = 60 e = 96 f = 24 degree seq :: [ 2^48, 8^12 ] E7.432 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 12}) Quotient :: regular Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2 * T1^-2 * T2 * T1, T2 * T1^3 * T2 * T1^-3, T1^12, (T1^-1 * T2)^6 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 37, 46, 44, 36, 22, 10, 4)(3, 7, 15, 24, 39, 28, 41, 35, 45, 34, 18, 8)(6, 13, 27, 38, 47, 40, 33, 17, 32, 21, 30, 14)(9, 19, 26, 12, 25, 16, 31, 43, 48, 42, 29, 20) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 30)(18, 26)(19, 27)(20, 35)(22, 34)(23, 38)(25, 40)(31, 37)(32, 43)(33, 44)(36, 42)(39, 48)(41, 46)(45, 47) local type(s) :: { ( 6^12 ) } Outer automorphisms :: reflexible Dual of E7.433 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 4 e = 24 f = 8 degree seq :: [ 12^4 ] E7.433 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 12}) Quotient :: regular Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T1^6, (T1^-1 * T2 * T1^-2)^2, T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-2 * T2, (T1^-1 * T2)^12 ] Map:: non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 22, 18, 8)(6, 13, 25, 21, 28, 14)(9, 19, 24, 12, 23, 20)(16, 30, 27, 34, 42, 31)(17, 32, 40, 29, 35, 33)(26, 38, 37, 39, 44, 36)(41, 45, 46, 47, 48, 43) 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, 32)(24, 37)(25, 31)(28, 39)(30, 41)(33, 43)(38, 45)(40, 46)(42, 47)(44, 48) local type(s) :: { ( 12^6 ) } Outer automorphisms :: reflexible Dual of E7.432 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 8 e = 24 f = 4 degree seq :: [ 6^8 ] E7.434 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 12}) Quotient :: edge Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^6, T1 * T2^-3 * T1 * T2^3, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2, (T2^-1 * T1)^12 ] Map:: R = (1, 3, 8, 18, 10, 4)(2, 5, 12, 25, 14, 6)(7, 15, 30, 21, 32, 16)(9, 19, 34, 17, 33, 20)(11, 22, 31, 28, 38, 23)(13, 26, 39, 24, 35, 27)(29, 41, 43, 42, 44, 36)(37, 45, 47, 46, 48, 40)(49, 50)(51, 55)(52, 57)(53, 59)(54, 61)(56, 65)(58, 69)(60, 72)(62, 76)(63, 77)(64, 79)(66, 73)(67, 83)(68, 84)(70, 85)(71, 78)(74, 81)(75, 88)(80, 90)(82, 91)(86, 94)(87, 95)(89, 93)(92, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24, 24 ), ( 24^6 ) } Outer automorphisms :: reflexible Dual of E7.438 Transitivity :: ET+ Graph:: simple bipartite v = 32 e = 48 f = 4 degree seq :: [ 2^24, 6^8 ] E7.435 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 12}) Quotient :: edge Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2^-1)^2, T1^6, (T2 * T1^-2)^2, T2^-1 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1, T2^12 ] Map:: polytopal non-degenerate R = (1, 3, 10, 26, 46, 37, 16, 36, 42, 35, 15, 5)(2, 7, 19, 40, 27, 29, 13, 31, 48, 43, 22, 8)(4, 12, 30, 47, 39, 18, 6, 17, 34, 45, 24, 9)(11, 28, 20, 41, 38, 44, 23, 33, 14, 32, 21, 25)(49, 50, 54, 64, 61, 52)(51, 57, 71, 84, 66, 59)(53, 62, 79, 85, 68, 55)(56, 69, 60, 77, 86, 65)(58, 73, 70, 90, 92, 75)(63, 82, 89, 94, 78, 80)(67, 76, 87, 96, 81, 72)(74, 88, 93, 83, 91, 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) :: { ( 4^6 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E7.439 Transitivity :: ET+ Graph:: bipartite v = 12 e = 48 f = 24 degree seq :: [ 6^8, 12^4 ] E7.436 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 12}) Quotient :: edge Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-2 * T2 * T1^-2 * T2 * T1, T2 * T1^3 * T2 * T1^-3, (T2 * T1^-1)^6, T1^12 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 30)(18, 26)(19, 27)(20, 35)(22, 34)(23, 38)(25, 40)(31, 37)(32, 43)(33, 44)(36, 42)(39, 48)(41, 46)(45, 47)(49, 50, 53, 59, 71, 85, 94, 92, 84, 70, 58, 52)(51, 55, 63, 72, 87, 76, 89, 83, 93, 82, 66, 56)(54, 61, 75, 86, 95, 88, 81, 65, 80, 69, 78, 62)(57, 67, 74, 60, 73, 64, 79, 91, 96, 90, 77, 68) 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, 12 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E7.437 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 48 f = 8 degree seq :: [ 2^24, 12^4 ] E7.437 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 12}) Quotient :: loop Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^6, T1 * T2^-3 * T1 * T2^3, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2, (T2^-1 * T1)^12 ] Map:: R = (1, 49, 3, 51, 8, 56, 18, 66, 10, 58, 4, 52)(2, 50, 5, 53, 12, 60, 25, 73, 14, 62, 6, 54)(7, 55, 15, 63, 30, 78, 21, 69, 32, 80, 16, 64)(9, 57, 19, 67, 34, 82, 17, 65, 33, 81, 20, 68)(11, 59, 22, 70, 31, 79, 28, 76, 38, 86, 23, 71)(13, 61, 26, 74, 39, 87, 24, 72, 35, 83, 27, 75)(29, 77, 41, 89, 43, 91, 42, 90, 44, 92, 36, 84)(37, 85, 45, 93, 47, 95, 46, 94, 48, 96, 40, 88) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 52)(10, 69)(11, 53)(12, 72)(13, 54)(14, 76)(15, 77)(16, 79)(17, 56)(18, 73)(19, 83)(20, 84)(21, 58)(22, 85)(23, 78)(24, 60)(25, 66)(26, 81)(27, 88)(28, 62)(29, 63)(30, 71)(31, 64)(32, 90)(33, 74)(34, 91)(35, 67)(36, 68)(37, 70)(38, 94)(39, 95)(40, 75)(41, 93)(42, 80)(43, 82)(44, 96)(45, 89)(46, 86)(47, 87)(48, 92) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E7.436 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 48 f = 28 degree seq :: [ 12^8 ] E7.438 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 12}) Quotient :: loop Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2^-1)^2, T1^6, (T2 * T1^-2)^2, T2^-1 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1, T2^12 ] Map:: R = (1, 49, 3, 51, 10, 58, 26, 74, 46, 94, 37, 85, 16, 64, 36, 84, 42, 90, 35, 83, 15, 63, 5, 53)(2, 50, 7, 55, 19, 67, 40, 88, 27, 75, 29, 77, 13, 61, 31, 79, 48, 96, 43, 91, 22, 70, 8, 56)(4, 52, 12, 60, 30, 78, 47, 95, 39, 87, 18, 66, 6, 54, 17, 65, 34, 82, 45, 93, 24, 72, 9, 57)(11, 59, 28, 76, 20, 68, 41, 89, 38, 86, 44, 92, 23, 71, 33, 81, 14, 62, 32, 80, 21, 69, 25, 73) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 64)(7, 53)(8, 69)(9, 71)(10, 73)(11, 51)(12, 77)(13, 52)(14, 79)(15, 82)(16, 61)(17, 56)(18, 59)(19, 76)(20, 55)(21, 60)(22, 90)(23, 84)(24, 67)(25, 70)(26, 88)(27, 58)(28, 87)(29, 86)(30, 80)(31, 85)(32, 63)(33, 72)(34, 89)(35, 91)(36, 66)(37, 68)(38, 65)(39, 96)(40, 93)(41, 94)(42, 92)(43, 95)(44, 75)(45, 83)(46, 78)(47, 74)(48, 81) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E7.434 Transitivity :: ET+ VT+ AT Graph:: v = 4 e = 48 f = 32 degree seq :: [ 24^4 ] E7.439 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 12}) Quotient :: loop Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-2 * T2 * T1^-2 * T2 * T1, T2 * T1^3 * T2 * T1^-3, (T2 * T1^-1)^6, T1^12 ] Map:: polytopal non-degenerate R = (1, 49, 3, 51)(2, 50, 6, 54)(4, 52, 9, 57)(5, 53, 12, 60)(7, 55, 16, 64)(8, 56, 17, 65)(10, 58, 21, 69)(11, 59, 24, 72)(13, 61, 28, 76)(14, 62, 29, 77)(15, 63, 30, 78)(18, 66, 26, 74)(19, 67, 27, 75)(20, 68, 35, 83)(22, 70, 34, 82)(23, 71, 38, 86)(25, 73, 40, 88)(31, 79, 37, 85)(32, 80, 43, 91)(33, 81, 44, 92)(36, 84, 42, 90)(39, 87, 48, 96)(41, 89, 46, 94)(45, 93, 47, 95) L = (1, 50)(2, 53)(3, 55)(4, 49)(5, 59)(6, 61)(7, 63)(8, 51)(9, 67)(10, 52)(11, 71)(12, 73)(13, 75)(14, 54)(15, 72)(16, 79)(17, 80)(18, 56)(19, 74)(20, 57)(21, 78)(22, 58)(23, 85)(24, 87)(25, 64)(26, 60)(27, 86)(28, 89)(29, 68)(30, 62)(31, 91)(32, 69)(33, 65)(34, 66)(35, 93)(36, 70)(37, 94)(38, 95)(39, 76)(40, 81)(41, 83)(42, 77)(43, 96)(44, 84)(45, 82)(46, 92)(47, 88)(48, 90) local type(s) :: { ( 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.435 Transitivity :: ET+ VT+ AT Graph:: simple v = 24 e = 48 f = 12 degree seq :: [ 4^24 ] E7.440 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^6, Y1 * Y2^-3 * Y1 * Y2^3, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2, (Y3 * Y2^-1)^12 ] Map:: R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 17, 65)(10, 58, 21, 69)(12, 60, 24, 72)(14, 62, 28, 76)(15, 63, 29, 77)(16, 64, 31, 79)(18, 66, 25, 73)(19, 67, 35, 83)(20, 68, 36, 84)(22, 70, 37, 85)(23, 71, 30, 78)(26, 74, 33, 81)(27, 75, 40, 88)(32, 80, 42, 90)(34, 82, 43, 91)(38, 86, 46, 94)(39, 87, 47, 95)(41, 89, 45, 93)(44, 92, 48, 96)(97, 145, 99, 147, 104, 152, 114, 162, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 121, 169, 110, 158, 102, 150)(103, 151, 111, 159, 126, 174, 117, 165, 128, 176, 112, 160)(105, 153, 115, 163, 130, 178, 113, 161, 129, 177, 116, 164)(107, 155, 118, 166, 127, 175, 124, 172, 134, 182, 119, 167)(109, 157, 122, 170, 135, 183, 120, 168, 131, 179, 123, 171)(125, 173, 137, 185, 139, 187, 138, 186, 140, 188, 132, 180)(133, 181, 141, 189, 143, 191, 142, 190, 144, 192, 136, 184) L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 113)(9, 100)(10, 117)(11, 101)(12, 120)(13, 102)(14, 124)(15, 125)(16, 127)(17, 104)(18, 121)(19, 131)(20, 132)(21, 106)(22, 133)(23, 126)(24, 108)(25, 114)(26, 129)(27, 136)(28, 110)(29, 111)(30, 119)(31, 112)(32, 138)(33, 122)(34, 139)(35, 115)(36, 116)(37, 118)(38, 142)(39, 143)(40, 123)(41, 141)(42, 128)(43, 130)(44, 144)(45, 137)(46, 134)(47, 135)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E7.443 Graph:: bipartite v = 32 e = 96 f = 52 degree seq :: [ 4^24, 12^8 ] E7.441 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2)^2, (Y3^-1 * Y1^-1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y1^6, Y1 * Y2^-2 * Y1^-2 * Y2^-2, Y2^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 16, 64, 13, 61, 4, 52)(3, 51, 9, 57, 23, 71, 36, 84, 18, 66, 11, 59)(5, 53, 14, 62, 31, 79, 37, 85, 20, 68, 7, 55)(8, 56, 21, 69, 12, 60, 29, 77, 38, 86, 17, 65)(10, 58, 25, 73, 22, 70, 42, 90, 44, 92, 27, 75)(15, 63, 34, 82, 41, 89, 46, 94, 30, 78, 32, 80)(19, 67, 28, 76, 39, 87, 48, 96, 33, 81, 24, 72)(26, 74, 40, 88, 45, 93, 35, 83, 43, 91, 47, 95)(97, 145, 99, 147, 106, 154, 122, 170, 142, 190, 133, 181, 112, 160, 132, 180, 138, 186, 131, 179, 111, 159, 101, 149)(98, 146, 103, 151, 115, 163, 136, 184, 123, 171, 125, 173, 109, 157, 127, 175, 144, 192, 139, 187, 118, 166, 104, 152)(100, 148, 108, 156, 126, 174, 143, 191, 135, 183, 114, 162, 102, 150, 113, 161, 130, 178, 141, 189, 120, 168, 105, 153)(107, 155, 124, 172, 116, 164, 137, 185, 134, 182, 140, 188, 119, 167, 129, 177, 110, 158, 128, 176, 117, 165, 121, 169) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 115)(8, 98)(9, 100)(10, 122)(11, 124)(12, 126)(13, 127)(14, 128)(15, 101)(16, 132)(17, 130)(18, 102)(19, 136)(20, 137)(21, 121)(22, 104)(23, 129)(24, 105)(25, 107)(26, 142)(27, 125)(28, 116)(29, 109)(30, 143)(31, 144)(32, 117)(33, 110)(34, 141)(35, 111)(36, 138)(37, 112)(38, 140)(39, 114)(40, 123)(41, 134)(42, 131)(43, 118)(44, 119)(45, 120)(46, 133)(47, 135)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 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 E7.442 Graph:: bipartite v = 12 e = 96 f = 72 degree seq :: [ 12^8, 24^4 ] E7.442 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2, (Y3 * Y2)^6, (Y3^-1 * Y1^-1)^12 ] Map:: polytopal 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)(99, 147, 103, 151)(100, 148, 105, 153)(101, 149, 107, 155)(102, 150, 109, 157)(104, 152, 113, 161)(106, 154, 117, 165)(108, 156, 121, 169)(110, 158, 125, 173)(111, 159, 127, 175)(112, 160, 129, 177)(114, 162, 122, 170)(115, 163, 128, 176)(116, 164, 131, 179)(118, 166, 126, 174)(119, 167, 133, 181)(120, 168, 135, 183)(123, 171, 134, 182)(124, 172, 137, 185)(130, 178, 140, 188)(132, 180, 141, 189)(136, 184, 143, 191)(138, 186, 144, 192)(139, 187, 142, 190) L = (1, 99)(2, 101)(3, 104)(4, 97)(5, 108)(6, 98)(7, 111)(8, 114)(9, 115)(10, 100)(11, 119)(12, 122)(13, 123)(14, 102)(15, 128)(16, 103)(17, 120)(18, 130)(19, 125)(20, 105)(21, 121)(22, 106)(23, 134)(24, 107)(25, 112)(26, 136)(27, 117)(28, 109)(29, 113)(30, 110)(31, 139)(32, 140)(33, 116)(34, 133)(35, 138)(36, 118)(37, 142)(38, 143)(39, 124)(40, 127)(41, 132)(42, 126)(43, 131)(44, 144)(45, 129)(46, 137)(47, 141)(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) :: { ( 12, 24 ), ( 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E7.441 Graph:: simple bipartite v = 72 e = 96 f = 12 degree seq :: [ 2^48, 4^24 ] E7.443 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1^-2 * Y3 * Y1^-2, (Y3 * Y1^-1)^6, Y1^12 ] Map:: R = (1, 49, 2, 50, 5, 53, 11, 59, 23, 71, 37, 85, 46, 94, 44, 92, 36, 84, 22, 70, 10, 58, 4, 52)(3, 51, 7, 55, 15, 63, 24, 72, 39, 87, 28, 76, 41, 89, 35, 83, 45, 93, 34, 82, 18, 66, 8, 56)(6, 54, 13, 61, 27, 75, 38, 86, 47, 95, 40, 88, 33, 81, 17, 65, 32, 80, 21, 69, 30, 78, 14, 62)(9, 57, 19, 67, 26, 74, 12, 60, 25, 73, 16, 64, 31, 79, 43, 91, 48, 96, 42, 90, 29, 77, 20, 68)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 102)(3, 97)(4, 105)(5, 108)(6, 98)(7, 112)(8, 113)(9, 100)(10, 117)(11, 120)(12, 101)(13, 124)(14, 125)(15, 126)(16, 103)(17, 104)(18, 122)(19, 123)(20, 131)(21, 106)(22, 130)(23, 134)(24, 107)(25, 136)(26, 114)(27, 115)(28, 109)(29, 110)(30, 111)(31, 133)(32, 139)(33, 140)(34, 118)(35, 116)(36, 138)(37, 127)(38, 119)(39, 144)(40, 121)(41, 142)(42, 132)(43, 128)(44, 129)(45, 143)(46, 137)(47, 141)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12 ), ( 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 E7.440 Graph:: simple bipartite v = 52 e = 96 f = 32 degree seq :: [ 2^48, 24^4 ] E7.444 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * R * Y2^2 * R * Y1 * Y2, Y2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1, Y2^12, (Y3 * Y2^-1)^6 ] Map:: R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 17, 65)(10, 58, 21, 69)(12, 60, 25, 73)(14, 62, 29, 77)(15, 63, 31, 79)(16, 64, 33, 81)(18, 66, 26, 74)(19, 67, 32, 80)(20, 68, 35, 83)(22, 70, 30, 78)(23, 71, 37, 85)(24, 72, 39, 87)(27, 75, 38, 86)(28, 76, 41, 89)(34, 82, 44, 92)(36, 84, 45, 93)(40, 88, 47, 95)(42, 90, 48, 96)(43, 91, 46, 94)(97, 145, 99, 147, 104, 152, 114, 162, 130, 178, 133, 181, 142, 190, 137, 185, 132, 180, 118, 166, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 122, 170, 136, 184, 127, 175, 139, 187, 131, 179, 138, 186, 126, 174, 110, 158, 102, 150)(103, 151, 111, 159, 128, 176, 140, 188, 144, 192, 135, 183, 124, 172, 109, 157, 123, 171, 117, 165, 121, 169, 112, 160)(105, 153, 115, 163, 125, 173, 113, 161, 120, 168, 107, 155, 119, 167, 134, 182, 143, 191, 141, 189, 129, 177, 116, 164) L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 113)(9, 100)(10, 117)(11, 101)(12, 121)(13, 102)(14, 125)(15, 127)(16, 129)(17, 104)(18, 122)(19, 128)(20, 131)(21, 106)(22, 126)(23, 133)(24, 135)(25, 108)(26, 114)(27, 134)(28, 137)(29, 110)(30, 118)(31, 111)(32, 115)(33, 112)(34, 140)(35, 116)(36, 141)(37, 119)(38, 123)(39, 120)(40, 143)(41, 124)(42, 144)(43, 142)(44, 130)(45, 132)(46, 139)(47, 136)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 12, 2, 12 ), ( 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 E7.445 Graph:: bipartite v = 28 e = 96 f = 56 degree seq :: [ 4^24, 24^4 ] E7.445 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^6, (Y3^-1 * Y1^2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-1 * Y3^-1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 16, 64, 13, 61, 4, 52)(3, 51, 9, 57, 23, 71, 36, 84, 18, 66, 11, 59)(5, 53, 14, 62, 31, 79, 37, 85, 20, 68, 7, 55)(8, 56, 21, 69, 12, 60, 29, 77, 38, 86, 17, 65)(10, 58, 25, 73, 22, 70, 42, 90, 44, 92, 27, 75)(15, 63, 34, 82, 41, 89, 46, 94, 30, 78, 32, 80)(19, 67, 28, 76, 39, 87, 48, 96, 33, 81, 24, 72)(26, 74, 40, 88, 45, 93, 35, 83, 43, 91, 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, 113)(7, 115)(8, 98)(9, 100)(10, 122)(11, 124)(12, 126)(13, 127)(14, 128)(15, 101)(16, 132)(17, 130)(18, 102)(19, 136)(20, 137)(21, 121)(22, 104)(23, 129)(24, 105)(25, 107)(26, 142)(27, 125)(28, 116)(29, 109)(30, 143)(31, 144)(32, 117)(33, 110)(34, 141)(35, 111)(36, 138)(37, 112)(38, 140)(39, 114)(40, 123)(41, 134)(42, 131)(43, 118)(44, 119)(45, 120)(46, 133)(47, 135)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E7.444 Graph:: simple bipartite v = 56 e = 96 f = 28 degree seq :: [ 2^48, 12^8 ] E7.446 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 9}) Quotient :: regular Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, (T1^-2 * T2 * T1^-1)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^9 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 38, 22, 10, 4)(3, 7, 15, 31, 46, 40, 24, 18, 8)(6, 13, 27, 21, 37, 50, 39, 30, 14)(9, 19, 36, 49, 43, 26, 12, 25, 20)(16, 28, 41, 35, 45, 52, 53, 48, 33)(17, 29, 42, 51, 54, 47, 32, 44, 34) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 31)(23, 39)(25, 41)(26, 42)(27, 44)(30, 45)(36, 47)(37, 48)(38, 49)(40, 51)(43, 52)(46, 53)(50, 54) local type(s) :: { ( 6^9 ) } Outer automorphisms :: reflexible Dual of E7.447 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 6 e = 27 f = 9 degree seq :: [ 9^6 ] E7.447 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 9}) Quotient :: regular Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^6, (T1^-1 * T2)^9 ] Map:: polytopal 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) 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, 54)(50, 52)(51, 53) local type(s) :: { ( 9^6 ) } Outer automorphisms :: reflexible Dual of E7.446 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 9 e = 27 f = 6 degree seq :: [ 6^9 ] E7.448 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 9}) Quotient :: edge Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, (T2^-1 * T1)^9 ] Map:: polytopal 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, 53, 51, 52, 50, 54)(55, 56)(57, 61)(58, 63)(59, 65)(60, 67)(62, 66)(64, 68)(69, 77)(70, 79)(71, 78)(72, 80)(73, 81)(74, 83)(75, 82)(76, 84)(85, 91)(86, 92)(87, 93)(88, 94)(89, 95)(90, 96)(97, 103)(98, 104)(99, 105)(100, 106)(101, 107)(102, 108) L = (1, 55)(2, 56)(3, 57)(4, 58)(5, 59)(6, 60)(7, 61)(8, 62)(9, 63)(10, 64)(11, 65)(12, 66)(13, 67)(14, 68)(15, 69)(16, 70)(17, 71)(18, 72)(19, 73)(20, 74)(21, 75)(22, 76)(23, 77)(24, 78)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 91)(38, 92)(39, 93)(40, 94)(41, 95)(42, 96)(43, 97)(44, 98)(45, 99)(46, 100)(47, 101)(48, 102)(49, 103)(50, 104)(51, 105)(52, 106)(53, 107)(54, 108) local type(s) :: { ( 18, 18 ), ( 18^6 ) } Outer automorphisms :: reflexible Dual of E7.452 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 54 f = 6 degree seq :: [ 2^27, 6^9 ] E7.449 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 9}) Quotient :: edge Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-2 * T2 * T1^-1 * T2 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-3, (T2^-2 * T1)^2, T1^6, T2^9 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 37, 40, 28, 15, 5)(2, 7, 19, 32, 44, 46, 34, 22, 8)(4, 12, 26, 38, 49, 47, 35, 23, 9)(6, 17, 29, 41, 51, 52, 42, 30, 18)(11, 16, 14, 27, 39, 50, 48, 36, 24)(13, 21, 33, 45, 54, 53, 43, 31, 20)(55, 56, 60, 70, 67, 58)(57, 63, 71, 62, 75, 65)(59, 68, 72, 66, 74, 61)(64, 78, 83, 77, 87, 76)(69, 80, 84, 73, 85, 81)(79, 88, 95, 90, 99, 89)(82, 86, 96, 93, 97, 92)(91, 101, 105, 100, 108, 102)(94, 104, 106, 103, 107, 98) L = (1, 55)(2, 56)(3, 57)(4, 58)(5, 59)(6, 60)(7, 61)(8, 62)(9, 63)(10, 64)(11, 65)(12, 66)(13, 67)(14, 68)(15, 69)(16, 70)(17, 71)(18, 72)(19, 73)(20, 74)(21, 75)(22, 76)(23, 77)(24, 78)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 91)(38, 92)(39, 93)(40, 94)(41, 95)(42, 96)(43, 97)(44, 98)(45, 99)(46, 100)(47, 101)(48, 102)(49, 103)(50, 104)(51, 105)(52, 106)(53, 107)(54, 108) local type(s) :: { ( 4^6 ), ( 4^9 ) } Outer automorphisms :: reflexible Dual of E7.453 Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 54 f = 27 degree seq :: [ 6^9, 9^6 ] E7.450 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 9}) Quotient :: edge Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-3)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^9 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 31)(23, 39)(25, 41)(26, 42)(27, 44)(30, 45)(36, 47)(37, 48)(38, 49)(40, 51)(43, 52)(46, 53)(50, 54)(55, 56, 59, 65, 77, 92, 76, 64, 58)(57, 61, 69, 85, 100, 94, 78, 72, 62)(60, 67, 81, 75, 91, 104, 93, 84, 68)(63, 73, 90, 103, 97, 80, 66, 79, 74)(70, 82, 95, 89, 99, 106, 107, 102, 87)(71, 83, 96, 105, 108, 101, 86, 98, 88) L = (1, 55)(2, 56)(3, 57)(4, 58)(5, 59)(6, 60)(7, 61)(8, 62)(9, 63)(10, 64)(11, 65)(12, 66)(13, 67)(14, 68)(15, 69)(16, 70)(17, 71)(18, 72)(19, 73)(20, 74)(21, 75)(22, 76)(23, 77)(24, 78)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 91)(38, 92)(39, 93)(40, 94)(41, 95)(42, 96)(43, 97)(44, 98)(45, 99)(46, 100)(47, 101)(48, 102)(49, 103)(50, 104)(51, 105)(52, 106)(53, 107)(54, 108) local type(s) :: { ( 12, 12 ), ( 12^9 ) } Outer automorphisms :: reflexible Dual of E7.451 Transitivity :: ET+ Graph:: simple bipartite v = 33 e = 54 f = 9 degree seq :: [ 2^27, 9^6 ] E7.451 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 9}) Quotient :: loop Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, (T2^-1 * T1)^9 ] Map:: R = (1, 55, 3, 57, 8, 62, 17, 71, 10, 64, 4, 58)(2, 56, 5, 59, 12, 66, 21, 75, 14, 68, 6, 60)(7, 61, 15, 69, 24, 78, 18, 72, 9, 63, 16, 70)(11, 65, 19, 73, 28, 82, 22, 76, 13, 67, 20, 74)(23, 77, 31, 85, 26, 80, 33, 87, 25, 79, 32, 86)(27, 81, 34, 88, 30, 84, 36, 90, 29, 83, 35, 89)(37, 91, 43, 97, 39, 93, 45, 99, 38, 92, 44, 98)(40, 94, 46, 100, 42, 96, 48, 102, 41, 95, 47, 101)(49, 103, 53, 107, 51, 105, 52, 106, 50, 104, 54, 108) L = (1, 56)(2, 55)(3, 61)(4, 63)(5, 65)(6, 67)(7, 57)(8, 66)(9, 58)(10, 68)(11, 59)(12, 62)(13, 60)(14, 64)(15, 77)(16, 79)(17, 78)(18, 80)(19, 81)(20, 83)(21, 82)(22, 84)(23, 69)(24, 71)(25, 70)(26, 72)(27, 73)(28, 75)(29, 74)(30, 76)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 97)(50, 98)(51, 99)(52, 100)(53, 101)(54, 102) local type(s) :: { ( 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9 ) } Outer automorphisms :: reflexible Dual of E7.450 Transitivity :: ET+ VT+ AT Graph:: v = 9 e = 54 f = 33 degree seq :: [ 12^9 ] E7.452 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 9}) Quotient :: loop Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-2 * T2 * T1^-1 * T2 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-3, (T2^-2 * T1)^2, T1^6, T2^9 ] Map:: R = (1, 55, 3, 57, 10, 64, 25, 79, 37, 91, 40, 94, 28, 82, 15, 69, 5, 59)(2, 56, 7, 61, 19, 73, 32, 86, 44, 98, 46, 100, 34, 88, 22, 76, 8, 62)(4, 58, 12, 66, 26, 80, 38, 92, 49, 103, 47, 101, 35, 89, 23, 77, 9, 63)(6, 60, 17, 71, 29, 83, 41, 95, 51, 105, 52, 106, 42, 96, 30, 84, 18, 72)(11, 65, 16, 70, 14, 68, 27, 81, 39, 93, 50, 104, 48, 102, 36, 90, 24, 78)(13, 67, 21, 75, 33, 87, 45, 99, 54, 108, 53, 107, 43, 97, 31, 85, 20, 74) L = (1, 56)(2, 60)(3, 63)(4, 55)(5, 68)(6, 70)(7, 59)(8, 75)(9, 71)(10, 78)(11, 57)(12, 74)(13, 58)(14, 72)(15, 80)(16, 67)(17, 62)(18, 66)(19, 85)(20, 61)(21, 65)(22, 64)(23, 87)(24, 83)(25, 88)(26, 84)(27, 69)(28, 86)(29, 77)(30, 73)(31, 81)(32, 96)(33, 76)(34, 95)(35, 79)(36, 99)(37, 101)(38, 82)(39, 97)(40, 104)(41, 90)(42, 93)(43, 92)(44, 94)(45, 89)(46, 108)(47, 105)(48, 91)(49, 107)(50, 106)(51, 100)(52, 103)(53, 98)(54, 102) 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 E7.448 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 54 f = 36 degree seq :: [ 18^6 ] E7.453 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 9}) Quotient :: loop Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-3)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^9 ] Map:: polytopal non-degenerate R = (1, 55, 3, 57)(2, 56, 6, 60)(4, 58, 9, 63)(5, 59, 12, 66)(7, 61, 16, 70)(8, 62, 17, 71)(10, 64, 21, 75)(11, 65, 24, 78)(13, 67, 28, 82)(14, 68, 29, 83)(15, 69, 32, 86)(18, 72, 35, 89)(19, 73, 33, 87)(20, 74, 34, 88)(22, 76, 31, 85)(23, 77, 39, 93)(25, 79, 41, 95)(26, 80, 42, 96)(27, 81, 44, 98)(30, 84, 45, 99)(36, 90, 47, 101)(37, 91, 48, 102)(38, 92, 49, 103)(40, 94, 51, 105)(43, 97, 52, 106)(46, 100, 53, 107)(50, 104, 54, 108) L = (1, 56)(2, 59)(3, 61)(4, 55)(5, 65)(6, 67)(7, 69)(8, 57)(9, 73)(10, 58)(11, 77)(12, 79)(13, 81)(14, 60)(15, 85)(16, 82)(17, 83)(18, 62)(19, 90)(20, 63)(21, 91)(22, 64)(23, 92)(24, 72)(25, 74)(26, 66)(27, 75)(28, 95)(29, 96)(30, 68)(31, 100)(32, 98)(33, 70)(34, 71)(35, 99)(36, 103)(37, 104)(38, 76)(39, 84)(40, 78)(41, 89)(42, 105)(43, 80)(44, 88)(45, 106)(46, 94)(47, 86)(48, 87)(49, 97)(50, 93)(51, 108)(52, 107)(53, 102)(54, 101) local type(s) :: { ( 6, 9, 6, 9 ) } Outer automorphisms :: reflexible Dual of E7.449 Transitivity :: ET+ VT+ AT Graph:: simple v = 27 e = 54 f = 15 degree seq :: [ 4^27 ] E7.454 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 9}) Quotient :: dipole Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, Y2^6, (Y3 * Y2^-1)^9 ] Map:: R = (1, 55, 2, 56)(3, 57, 7, 61)(4, 58, 9, 63)(5, 59, 11, 65)(6, 60, 13, 67)(8, 62, 12, 66)(10, 64, 14, 68)(15, 69, 23, 77)(16, 70, 25, 79)(17, 71, 24, 78)(18, 72, 26, 80)(19, 73, 27, 81)(20, 74, 29, 83)(21, 75, 28, 82)(22, 76, 30, 84)(31, 85, 37, 91)(32, 86, 38, 92)(33, 87, 39, 93)(34, 88, 40, 94)(35, 89, 41, 95)(36, 90, 42, 96)(43, 97, 49, 103)(44, 98, 50, 104)(45, 99, 51, 105)(46, 100, 52, 106)(47, 101, 53, 107)(48, 102, 54, 108)(109, 163, 111, 165, 116, 170, 125, 179, 118, 172, 112, 166)(110, 164, 113, 167, 120, 174, 129, 183, 122, 176, 114, 168)(115, 169, 123, 177, 132, 186, 126, 180, 117, 171, 124, 178)(119, 173, 127, 181, 136, 190, 130, 184, 121, 175, 128, 182)(131, 185, 139, 193, 134, 188, 141, 195, 133, 187, 140, 194)(135, 189, 142, 196, 138, 192, 144, 198, 137, 191, 143, 197)(145, 199, 151, 205, 147, 201, 153, 207, 146, 200, 152, 206)(148, 202, 154, 208, 150, 204, 156, 210, 149, 203, 155, 209)(157, 211, 161, 215, 159, 213, 160, 214, 158, 212, 162, 216) L = (1, 110)(2, 109)(3, 115)(4, 117)(5, 119)(6, 121)(7, 111)(8, 120)(9, 112)(10, 122)(11, 113)(12, 116)(13, 114)(14, 118)(15, 131)(16, 133)(17, 132)(18, 134)(19, 135)(20, 137)(21, 136)(22, 138)(23, 123)(24, 125)(25, 124)(26, 126)(27, 127)(28, 129)(29, 128)(30, 130)(31, 145)(32, 146)(33, 147)(34, 148)(35, 149)(36, 150)(37, 139)(38, 140)(39, 141)(40, 142)(41, 143)(42, 144)(43, 157)(44, 158)(45, 159)(46, 160)(47, 161)(48, 162)(49, 151)(50, 152)(51, 153)(52, 154)(53, 155)(54, 156)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(73, 181)(74, 182)(75, 183)(76, 184)(77, 185)(78, 186)(79, 187)(80, 188)(81, 189)(82, 190)(83, 191)(84, 192)(85, 193)(86, 194)(87, 195)(88, 196)(89, 197)(90, 198)(91, 199)(92, 200)(93, 201)(94, 202)(95, 203)(96, 204)(97, 205)(98, 206)(99, 207)(100, 208)(101, 209)(102, 210)(103, 211)(104, 212)(105, 213)(106, 214)(107, 215)(108, 216) local type(s) :: { ( 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E7.457 Graph:: bipartite v = 36 e = 108 f = 60 degree seq :: [ 4^27, 12^9 ] E7.455 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 9}) Quotient :: dipole Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-2, Y2^-1 * Y1 * Y2^-1 * Y1^3, Y1^6, Y2^9 ] Map:: R = (1, 55, 2, 56, 6, 60, 16, 70, 13, 67, 4, 58)(3, 57, 9, 63, 17, 71, 8, 62, 21, 75, 11, 65)(5, 59, 14, 68, 18, 72, 12, 66, 20, 74, 7, 61)(10, 64, 24, 78, 29, 83, 23, 77, 33, 87, 22, 76)(15, 69, 26, 80, 30, 84, 19, 73, 31, 85, 27, 81)(25, 79, 34, 88, 41, 95, 36, 90, 45, 99, 35, 89)(28, 82, 32, 86, 42, 96, 39, 93, 43, 97, 38, 92)(37, 91, 47, 101, 51, 105, 46, 100, 54, 108, 48, 102)(40, 94, 50, 104, 52, 106, 49, 103, 53, 107, 44, 98)(109, 163, 111, 165, 118, 172, 133, 187, 145, 199, 148, 202, 136, 190, 123, 177, 113, 167)(110, 164, 115, 169, 127, 181, 140, 194, 152, 206, 154, 208, 142, 196, 130, 184, 116, 170)(112, 166, 120, 174, 134, 188, 146, 200, 157, 211, 155, 209, 143, 197, 131, 185, 117, 171)(114, 168, 125, 179, 137, 191, 149, 203, 159, 213, 160, 214, 150, 204, 138, 192, 126, 180)(119, 173, 124, 178, 122, 176, 135, 189, 147, 201, 158, 212, 156, 210, 144, 198, 132, 186)(121, 175, 129, 183, 141, 195, 153, 207, 162, 216, 161, 215, 151, 205, 139, 193, 128, 182) L = (1, 111)(2, 115)(3, 118)(4, 120)(5, 109)(6, 125)(7, 127)(8, 110)(9, 112)(10, 133)(11, 124)(12, 134)(13, 129)(14, 135)(15, 113)(16, 122)(17, 137)(18, 114)(19, 140)(20, 121)(21, 141)(22, 116)(23, 117)(24, 119)(25, 145)(26, 146)(27, 147)(28, 123)(29, 149)(30, 126)(31, 128)(32, 152)(33, 153)(34, 130)(35, 131)(36, 132)(37, 148)(38, 157)(39, 158)(40, 136)(41, 159)(42, 138)(43, 139)(44, 154)(45, 162)(46, 142)(47, 143)(48, 144)(49, 155)(50, 156)(51, 160)(52, 150)(53, 151)(54, 161)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(73, 181)(74, 182)(75, 183)(76, 184)(77, 185)(78, 186)(79, 187)(80, 188)(81, 189)(82, 190)(83, 191)(84, 192)(85, 193)(86, 194)(87, 195)(88, 196)(89, 197)(90, 198)(91, 199)(92, 200)(93, 201)(94, 202)(95, 203)(96, 204)(97, 205)(98, 206)(99, 207)(100, 208)(101, 209)(102, 210)(103, 211)(104, 212)(105, 213)(106, 214)(107, 215)(108, 216) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E7.456 Graph:: bipartite v = 15 e = 108 f = 81 degree seq :: [ 12^9, 18^6 ] E7.456 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 9}) Quotient :: dipole Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |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^-1 * Y1^-1)^9 ] Map:: polytopal R = (1, 55)(2, 56)(3, 57)(4, 58)(5, 59)(6, 60)(7, 61)(8, 62)(9, 63)(10, 64)(11, 65)(12, 66)(13, 67)(14, 68)(15, 69)(16, 70)(17, 71)(18, 72)(19, 73)(20, 74)(21, 75)(22, 76)(23, 77)(24, 78)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 91)(38, 92)(39, 93)(40, 94)(41, 95)(42, 96)(43, 97)(44, 98)(45, 99)(46, 100)(47, 101)(48, 102)(49, 103)(50, 104)(51, 105)(52, 106)(53, 107)(54, 108)(109, 163, 110, 164)(111, 165, 115, 169)(112, 166, 117, 171)(113, 167, 119, 173)(114, 168, 121, 175)(116, 170, 125, 179)(118, 172, 129, 183)(120, 174, 133, 187)(122, 176, 137, 191)(123, 177, 131, 185)(124, 178, 135, 189)(126, 180, 138, 192)(127, 181, 132, 186)(128, 182, 136, 190)(130, 184, 134, 188)(139, 193, 149, 203)(140, 194, 153, 207)(141, 195, 147, 201)(142, 196, 152, 206)(143, 197, 155, 209)(144, 198, 150, 204)(145, 199, 148, 202)(146, 200, 157, 211)(151, 205, 159, 213)(154, 208, 161, 215)(156, 210, 162, 216)(158, 212, 160, 214) L = (1, 111)(2, 113)(3, 116)(4, 109)(5, 120)(6, 110)(7, 123)(8, 126)(9, 127)(10, 112)(11, 131)(12, 134)(13, 135)(14, 114)(15, 139)(16, 115)(17, 141)(18, 143)(19, 144)(20, 117)(21, 145)(22, 118)(23, 147)(24, 119)(25, 149)(26, 151)(27, 152)(28, 121)(29, 153)(30, 122)(31, 129)(32, 124)(33, 128)(34, 125)(35, 146)(36, 157)(37, 158)(38, 130)(39, 137)(40, 132)(41, 136)(42, 133)(43, 154)(44, 161)(45, 162)(46, 138)(47, 140)(48, 142)(49, 156)(50, 155)(51, 148)(52, 150)(53, 160)(54, 159)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(73, 181)(74, 182)(75, 183)(76, 184)(77, 185)(78, 186)(79, 187)(80, 188)(81, 189)(82, 190)(83, 191)(84, 192)(85, 193)(86, 194)(87, 195)(88, 196)(89, 197)(90, 198)(91, 199)(92, 200)(93, 201)(94, 202)(95, 203)(96, 204)(97, 205)(98, 206)(99, 207)(100, 208)(101, 209)(102, 210)(103, 211)(104, 212)(105, 213)(106, 214)(107, 215)(108, 216) local type(s) :: { ( 12, 18 ), ( 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E7.455 Graph:: simple bipartite v = 81 e = 108 f = 15 degree seq :: [ 2^54, 4^27 ] E7.457 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 9}) Quotient :: dipole Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^-2 * Y1 * Y3, (Y1^-1, Y3^-1, Y1^-1), Y3 * Y1^-3 * Y3^-1 * Y1^-3, Y1^9, (Y3^-1 * Y1^-1)^6 ] Map:: polytopal R = (1, 55, 2, 56, 5, 59, 11, 65, 23, 77, 38, 92, 22, 76, 10, 64, 4, 58)(3, 57, 7, 61, 15, 69, 31, 85, 46, 100, 40, 94, 24, 78, 18, 72, 8, 62)(6, 60, 13, 67, 27, 81, 21, 75, 37, 91, 50, 104, 39, 93, 30, 84, 14, 68)(9, 63, 19, 73, 36, 90, 49, 103, 43, 97, 26, 80, 12, 66, 25, 79, 20, 74)(16, 70, 28, 82, 41, 95, 35, 89, 45, 99, 52, 106, 53, 107, 48, 102, 33, 87)(17, 71, 29, 83, 42, 96, 51, 105, 54, 108, 47, 101, 32, 86, 44, 98, 34, 88)(109, 163)(110, 164)(111, 165)(112, 166)(113, 167)(114, 168)(115, 169)(116, 170)(117, 171)(118, 172)(119, 173)(120, 174)(121, 175)(122, 176)(123, 177)(124, 178)(125, 179)(126, 180)(127, 181)(128, 182)(129, 183)(130, 184)(131, 185)(132, 186)(133, 187)(134, 188)(135, 189)(136, 190)(137, 191)(138, 192)(139, 193)(140, 194)(141, 195)(142, 196)(143, 197)(144, 198)(145, 199)(146, 200)(147, 201)(148, 202)(149, 203)(150, 204)(151, 205)(152, 206)(153, 207)(154, 208)(155, 209)(156, 210)(157, 211)(158, 212)(159, 213)(160, 214)(161, 215)(162, 216) L = (1, 111)(2, 114)(3, 109)(4, 117)(5, 120)(6, 110)(7, 124)(8, 125)(9, 112)(10, 129)(11, 132)(12, 113)(13, 136)(14, 137)(15, 140)(16, 115)(17, 116)(18, 143)(19, 141)(20, 142)(21, 118)(22, 139)(23, 147)(24, 119)(25, 149)(26, 150)(27, 152)(28, 121)(29, 122)(30, 153)(31, 130)(32, 123)(33, 127)(34, 128)(35, 126)(36, 155)(37, 156)(38, 157)(39, 131)(40, 159)(41, 133)(42, 134)(43, 160)(44, 135)(45, 138)(46, 161)(47, 144)(48, 145)(49, 146)(50, 162)(51, 148)(52, 151)(53, 154)(54, 158)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(73, 181)(74, 182)(75, 183)(76, 184)(77, 185)(78, 186)(79, 187)(80, 188)(81, 189)(82, 190)(83, 191)(84, 192)(85, 193)(86, 194)(87, 195)(88, 196)(89, 197)(90, 198)(91, 199)(92, 200)(93, 201)(94, 202)(95, 203)(96, 204)(97, 205)(98, 206)(99, 207)(100, 208)(101, 209)(102, 210)(103, 211)(104, 212)(105, 213)(106, 214)(107, 215)(108, 216) local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E7.454 Graph:: simple bipartite v = 60 e = 108 f = 36 degree seq :: [ 2^54, 18^6 ] E7.458 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 9}) Quotient :: dipole Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^3 * Y1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, Y2^9, (Y3 * Y2^-1)^6 ] Map:: R = (1, 55, 2, 56)(3, 57, 7, 61)(4, 58, 9, 63)(5, 59, 11, 65)(6, 60, 13, 67)(8, 62, 17, 71)(10, 64, 21, 75)(12, 66, 25, 79)(14, 68, 29, 83)(15, 69, 23, 77)(16, 70, 27, 81)(18, 72, 30, 84)(19, 73, 24, 78)(20, 74, 28, 82)(22, 76, 26, 80)(31, 85, 41, 95)(32, 86, 45, 99)(33, 87, 39, 93)(34, 88, 44, 98)(35, 89, 47, 101)(36, 90, 42, 96)(37, 91, 40, 94)(38, 92, 49, 103)(43, 97, 51, 105)(46, 100, 53, 107)(48, 102, 54, 108)(50, 104, 52, 106)(109, 163, 111, 165, 116, 170, 126, 180, 143, 197, 146, 200, 130, 184, 118, 172, 112, 166)(110, 164, 113, 167, 120, 174, 134, 188, 151, 205, 154, 208, 138, 192, 122, 176, 114, 168)(115, 169, 123, 177, 139, 193, 129, 183, 145, 199, 158, 212, 155, 209, 140, 194, 124, 178)(117, 171, 127, 181, 144, 198, 157, 211, 156, 210, 142, 196, 125, 179, 141, 195, 128, 182)(119, 173, 131, 185, 147, 201, 137, 191, 153, 207, 162, 216, 159, 213, 148, 202, 132, 186)(121, 175, 135, 189, 152, 206, 161, 215, 160, 214, 150, 204, 133, 187, 149, 203, 136, 190) L = (1, 110)(2, 109)(3, 115)(4, 117)(5, 119)(6, 121)(7, 111)(8, 125)(9, 112)(10, 129)(11, 113)(12, 133)(13, 114)(14, 137)(15, 131)(16, 135)(17, 116)(18, 138)(19, 132)(20, 136)(21, 118)(22, 134)(23, 123)(24, 127)(25, 120)(26, 130)(27, 124)(28, 128)(29, 122)(30, 126)(31, 149)(32, 153)(33, 147)(34, 152)(35, 155)(36, 150)(37, 148)(38, 157)(39, 141)(40, 145)(41, 139)(42, 144)(43, 159)(44, 142)(45, 140)(46, 161)(47, 143)(48, 162)(49, 146)(50, 160)(51, 151)(52, 158)(53, 154)(54, 156)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(73, 181)(74, 182)(75, 183)(76, 184)(77, 185)(78, 186)(79, 187)(80, 188)(81, 189)(82, 190)(83, 191)(84, 192)(85, 193)(86, 194)(87, 195)(88, 196)(89, 197)(90, 198)(91, 199)(92, 200)(93, 201)(94, 202)(95, 203)(96, 204)(97, 205)(98, 206)(99, 207)(100, 208)(101, 209)(102, 210)(103, 211)(104, 212)(105, 213)(106, 214)(107, 215)(108, 216) 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 ) } Outer automorphisms :: reflexible Dual of E7.459 Graph:: bipartite v = 33 e = 108 f = 63 degree seq :: [ 4^27, 18^6 ] E7.459 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 9}) Quotient :: dipole Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-3, Y1^6, (Y3^-2 * Y1)^2, (Y3 * Y2^-1)^9 ] Map:: polytopal R = (1, 55, 2, 56, 6, 60, 16, 70, 13, 67, 4, 58)(3, 57, 9, 63, 17, 71, 8, 62, 21, 75, 11, 65)(5, 59, 14, 68, 18, 72, 12, 66, 20, 74, 7, 61)(10, 64, 24, 78, 29, 83, 23, 77, 33, 87, 22, 76)(15, 69, 26, 80, 30, 84, 19, 73, 31, 85, 27, 81)(25, 79, 34, 88, 41, 95, 36, 90, 45, 99, 35, 89)(28, 82, 32, 86, 42, 96, 39, 93, 43, 97, 38, 92)(37, 91, 47, 101, 51, 105, 46, 100, 54, 108, 48, 102)(40, 94, 50, 104, 52, 106, 49, 103, 53, 107, 44, 98)(109, 163)(110, 164)(111, 165)(112, 166)(113, 167)(114, 168)(115, 169)(116, 170)(117, 171)(118, 172)(119, 173)(120, 174)(121, 175)(122, 176)(123, 177)(124, 178)(125, 179)(126, 180)(127, 181)(128, 182)(129, 183)(130, 184)(131, 185)(132, 186)(133, 187)(134, 188)(135, 189)(136, 190)(137, 191)(138, 192)(139, 193)(140, 194)(141, 195)(142, 196)(143, 197)(144, 198)(145, 199)(146, 200)(147, 201)(148, 202)(149, 203)(150, 204)(151, 205)(152, 206)(153, 207)(154, 208)(155, 209)(156, 210)(157, 211)(158, 212)(159, 213)(160, 214)(161, 215)(162, 216) L = (1, 111)(2, 115)(3, 118)(4, 120)(5, 109)(6, 125)(7, 127)(8, 110)(9, 112)(10, 133)(11, 124)(12, 134)(13, 129)(14, 135)(15, 113)(16, 122)(17, 137)(18, 114)(19, 140)(20, 121)(21, 141)(22, 116)(23, 117)(24, 119)(25, 145)(26, 146)(27, 147)(28, 123)(29, 149)(30, 126)(31, 128)(32, 152)(33, 153)(34, 130)(35, 131)(36, 132)(37, 148)(38, 157)(39, 158)(40, 136)(41, 159)(42, 138)(43, 139)(44, 154)(45, 162)(46, 142)(47, 143)(48, 144)(49, 155)(50, 156)(51, 160)(52, 150)(53, 151)(54, 161)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(73, 181)(74, 182)(75, 183)(76, 184)(77, 185)(78, 186)(79, 187)(80, 188)(81, 189)(82, 190)(83, 191)(84, 192)(85, 193)(86, 194)(87, 195)(88, 196)(89, 197)(90, 198)(91, 199)(92, 200)(93, 201)(94, 202)(95, 203)(96, 204)(97, 205)(98, 206)(99, 207)(100, 208)(101, 209)(102, 210)(103, 211)(104, 212)(105, 213)(106, 214)(107, 215)(108, 216) local type(s) :: { ( 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E7.458 Graph:: simple bipartite v = 63 e = 108 f = 33 degree seq :: [ 2^54, 12^9 ] E7.460 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 6, 9}) Quotient :: halfedge Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 1 Presentation :: [ X2^2, (X1^-2 * X2 * X1^-1)^2, X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-2 * X2, X1^9 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 42, 22, 10, 4)(3, 7, 15, 31, 49, 44, 24, 18, 8)(6, 13, 27, 21, 41, 51, 43, 30, 14)(9, 19, 38, 52, 46, 26, 12, 25, 20)(16, 33, 50, 37, 28, 39, 53, 48, 34)(17, 35, 40, 54, 47, 45, 32, 29, 36) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 37)(19, 39)(20, 40)(22, 31)(23, 43)(25, 34)(26, 45)(27, 47)(30, 48)(33, 41)(35, 51)(36, 38)(42, 52)(44, 54)(46, 50)(49, 53) local type(s) :: { ( 6^9 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 6 e = 27 f = 9 degree seq :: [ 9^6 ] E7.461 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 6, 9}) Quotient :: halfedge Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 1 Presentation :: [ X2^2, X1^6, 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, 16, 28, 14)(9, 19, 33, 46, 34, 20)(12, 23, 37, 26, 39, 24)(17, 22, 36, 49, 38, 31)(21, 35, 48, 50, 41, 27)(30, 43, 51, 42, 54, 44)(32, 45, 52, 47, 53, 40) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 30)(18, 32)(19, 29)(20, 24)(23, 38)(25, 40)(28, 42)(31, 44)(33, 47)(34, 43)(35, 46)(36, 50)(37, 51)(39, 52)(41, 53)(45, 49)(48, 54) local type(s) :: { ( 9^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 9 e = 27 f = 6 degree seq :: [ 6^9 ] E7.462 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 6, 9}) Quotient :: edge Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 1 Presentation :: [ X1^2, X2^6, X2 * X1 * X2^-1 * X1 * X2 * 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, 30)(18, 26)(19, 25)(20, 32)(22, 36)(23, 37)(27, 39)(31, 41)(33, 46)(34, 38)(35, 47)(40, 52)(42, 53)(43, 54)(44, 50)(45, 51)(48, 49)(55, 57, 62, 72, 64, 58)(56, 59, 66, 79, 68, 60)(61, 69, 77, 65, 76, 70)(63, 73, 87, 101, 88, 74)(67, 80, 94, 107, 95, 81)(71, 85, 98, 83, 97, 86)(75, 89, 102, 106, 99, 84)(78, 92, 104, 90, 103, 93)(82, 96, 108, 100, 105, 91) L = (1, 55)(2, 56)(3, 57)(4, 58)(5, 59)(6, 60)(7, 61)(8, 62)(9, 63)(10, 64)(11, 65)(12, 66)(13, 67)(14, 68)(15, 69)(16, 70)(17, 71)(18, 72)(19, 73)(20, 74)(21, 75)(22, 76)(23, 77)(24, 78)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 91)(38, 92)(39, 93)(40, 94)(41, 95)(42, 96)(43, 97)(44, 98)(45, 99)(46, 100)(47, 101)(48, 102)(49, 103)(50, 104)(51, 105)(52, 106)(53, 107)(54, 108) local type(s) :: { ( 18, 18 ), ( 18^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 54 f = 6 degree seq :: [ 2^27, 6^9 ] E7.463 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 6, 9}) Quotient :: edge Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 1 Presentation :: [ (X2^-1 * X1^-1)^2, (X2 * X1^-1 * X2)^2, X1^6, X2 * X1 * X2^-1 * X1^-3 * X2, X2^9 ] Map:: polytopal non-degenerate R = (1, 2, 6, 16, 13, 4)(3, 9, 23, 43, 28, 11)(5, 14, 33, 24, 20, 7)(8, 21, 34, 15, 30, 17)(10, 25, 18, 37, 41, 22)(12, 29, 49, 53, 51, 31)(19, 32, 36, 46, 54, 38)(26, 42, 44, 52, 40, 45)(27, 47, 50, 35, 39, 48)(55, 57, 64, 80, 100, 107, 89, 69, 59)(56, 61, 73, 93, 103, 97, 96, 76, 62)(58, 66, 84, 104, 91, 108, 99, 78, 63)(60, 71, 85, 98, 77, 87, 102, 92, 72)(65, 81, 68, 88, 106, 105, 90, 70, 79)(67, 86, 74, 94, 75, 95, 101, 82, 83) L = (1, 55)(2, 56)(3, 57)(4, 58)(5, 59)(6, 60)(7, 61)(8, 62)(9, 63)(10, 64)(11, 65)(12, 66)(13, 67)(14, 68)(15, 69)(16, 70)(17, 71)(18, 72)(19, 73)(20, 74)(21, 75)(22, 76)(23, 77)(24, 78)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 91)(38, 92)(39, 93)(40, 94)(41, 95)(42, 96)(43, 97)(44, 98)(45, 99)(46, 100)(47, 101)(48, 102)(49, 103)(50, 104)(51, 105)(52, 106)(53, 107)(54, 108) local type(s) :: { ( 4^6 ), ( 4^9 ) } Outer automorphisms :: chiral Dual of E7.465 Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 54 f = 27 degree seq :: [ 6^9, 9^6 ] E7.464 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 6, 9}) Quotient :: edge Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 1 Presentation :: [ X2^2, (X1^-2 * X2 * X1^-1)^2, X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-2 * X2, X1^9 ] Map:: polytopal R = (1, 2, 5, 11, 23, 42, 22, 10, 4)(3, 7, 15, 31, 49, 44, 24, 18, 8)(6, 13, 27, 21, 41, 51, 43, 30, 14)(9, 19, 38, 52, 46, 26, 12, 25, 20)(16, 33, 50, 37, 28, 39, 53, 48, 34)(17, 35, 40, 54, 47, 45, 32, 29, 36)(55, 57)(56, 60)(58, 63)(59, 66)(61, 70)(62, 71)(64, 75)(65, 78)(67, 82)(68, 83)(69, 86)(72, 91)(73, 93)(74, 94)(76, 85)(77, 97)(79, 88)(80, 99)(81, 101)(84, 102)(87, 95)(89, 105)(90, 92)(96, 106)(98, 108)(100, 104)(103, 107) L = (1, 55)(2, 56)(3, 57)(4, 58)(5, 59)(6, 60)(7, 61)(8, 62)(9, 63)(10, 64)(11, 65)(12, 66)(13, 67)(14, 68)(15, 69)(16, 70)(17, 71)(18, 72)(19, 73)(20, 74)(21, 75)(22, 76)(23, 77)(24, 78)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 91)(38, 92)(39, 93)(40, 94)(41, 95)(42, 96)(43, 97)(44, 98)(45, 99)(46, 100)(47, 101)(48, 102)(49, 103)(50, 104)(51, 105)(52, 106)(53, 107)(54, 108) local type(s) :: { ( 12, 12 ), ( 12^9 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 33 e = 54 f = 9 degree seq :: [ 2^27, 9^6 ] E7.465 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 6, 9}) Quotient :: loop Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 1 Presentation :: [ X1^2, X2^6, X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^2 ] Map:: polytopal non-degenerate R = (1, 55, 2, 56)(3, 57, 7, 61)(4, 58, 9, 63)(5, 59, 11, 65)(6, 60, 13, 67)(8, 62, 17, 71)(10, 64, 21, 75)(12, 66, 24, 78)(14, 68, 28, 82)(15, 69, 29, 83)(16, 70, 30, 84)(18, 72, 26, 80)(19, 73, 25, 79)(20, 74, 32, 86)(22, 76, 36, 90)(23, 77, 37, 91)(27, 81, 39, 93)(31, 85, 41, 95)(33, 87, 46, 100)(34, 88, 38, 92)(35, 89, 47, 101)(40, 94, 52, 106)(42, 96, 53, 107)(43, 97, 54, 108)(44, 98, 50, 104)(45, 99, 51, 105)(48, 102, 49, 103) L = (1, 57)(2, 59)(3, 62)(4, 55)(5, 66)(6, 56)(7, 69)(8, 72)(9, 73)(10, 58)(11, 76)(12, 79)(13, 80)(14, 60)(15, 77)(16, 61)(17, 85)(18, 64)(19, 87)(20, 63)(21, 89)(22, 70)(23, 65)(24, 92)(25, 68)(26, 94)(27, 67)(28, 96)(29, 97)(30, 75)(31, 98)(32, 71)(33, 101)(34, 74)(35, 102)(36, 103)(37, 82)(38, 104)(39, 78)(40, 107)(41, 81)(42, 108)(43, 86)(44, 83)(45, 84)(46, 105)(47, 88)(48, 106)(49, 93)(50, 90)(51, 91)(52, 99)(53, 95)(54, 100) local type(s) :: { ( 6, 9, 6, 9 ) } Outer automorphisms :: chiral Dual of E7.463 Transitivity :: ET+ VT+ Graph:: simple v = 27 e = 54 f = 15 degree seq :: [ 4^27 ] E7.466 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 6, 9}) Quotient :: loop Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 1 Presentation :: [ (X2^-1 * X1^-1)^2, (X2 * X1^-1 * X2)^2, X1^6, X2 * X1 * X2^-1 * X1^-3 * X2, X2^9 ] Map:: R = (1, 55, 2, 56, 6, 60, 16, 70, 13, 67, 4, 58)(3, 57, 9, 63, 23, 77, 43, 97, 28, 82, 11, 65)(5, 59, 14, 68, 33, 87, 24, 78, 20, 74, 7, 61)(8, 62, 21, 75, 34, 88, 15, 69, 30, 84, 17, 71)(10, 64, 25, 79, 18, 72, 37, 91, 41, 95, 22, 76)(12, 66, 29, 83, 49, 103, 53, 107, 51, 105, 31, 85)(19, 73, 32, 86, 36, 90, 46, 100, 54, 108, 38, 92)(26, 80, 42, 96, 44, 98, 52, 106, 40, 94, 45, 99)(27, 81, 47, 101, 50, 104, 35, 89, 39, 93, 48, 102) L = (1, 57)(2, 61)(3, 64)(4, 66)(5, 55)(6, 71)(7, 73)(8, 56)(9, 58)(10, 80)(11, 81)(12, 84)(13, 86)(14, 88)(15, 59)(16, 79)(17, 85)(18, 60)(19, 93)(20, 94)(21, 95)(22, 62)(23, 87)(24, 63)(25, 65)(26, 100)(27, 68)(28, 83)(29, 67)(30, 104)(31, 98)(32, 74)(33, 102)(34, 106)(35, 69)(36, 70)(37, 108)(38, 72)(39, 103)(40, 75)(41, 101)(42, 76)(43, 96)(44, 77)(45, 78)(46, 107)(47, 82)(48, 92)(49, 97)(50, 91)(51, 90)(52, 105)(53, 89)(54, 99) local type(s) :: { ( 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 9 e = 54 f = 33 degree seq :: [ 12^9 ] E7.467 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 6, 9}) Quotient :: loop Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 1 Presentation :: [ X2^2, (X1^-2 * X2 * X1^-1)^2, X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-2 * X2, X1^9 ] Map:: R = (1, 55, 2, 56, 5, 59, 11, 65, 23, 77, 42, 96, 22, 76, 10, 64, 4, 58)(3, 57, 7, 61, 15, 69, 31, 85, 49, 103, 44, 98, 24, 78, 18, 72, 8, 62)(6, 60, 13, 67, 27, 81, 21, 75, 41, 95, 51, 105, 43, 97, 30, 84, 14, 68)(9, 63, 19, 73, 38, 92, 52, 106, 46, 100, 26, 80, 12, 66, 25, 79, 20, 74)(16, 70, 33, 87, 50, 104, 37, 91, 28, 82, 39, 93, 53, 107, 48, 102, 34, 88)(17, 71, 35, 89, 40, 94, 54, 108, 47, 101, 45, 99, 32, 86, 29, 83, 36, 90) L = (1, 57)(2, 60)(3, 55)(4, 63)(5, 66)(6, 56)(7, 70)(8, 71)(9, 58)(10, 75)(11, 78)(12, 59)(13, 82)(14, 83)(15, 86)(16, 61)(17, 62)(18, 91)(19, 93)(20, 94)(21, 64)(22, 85)(23, 97)(24, 65)(25, 88)(26, 99)(27, 101)(28, 67)(29, 68)(30, 102)(31, 76)(32, 69)(33, 95)(34, 79)(35, 105)(36, 92)(37, 72)(38, 90)(39, 73)(40, 74)(41, 87)(42, 106)(43, 77)(44, 108)(45, 80)(46, 104)(47, 81)(48, 84)(49, 107)(50, 100)(51, 89)(52, 96)(53, 103)(54, 98) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: bipartite v = 6 e = 54 f = 36 degree seq :: [ 18^6 ] E7.468 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 7, 7}) Quotient :: halfedge Aut^+ = (C2 x C2 x C2) : C7 (small group id <56, 11>) Aut = (C2 x C2 x C2) : C7 (small group id <56, 11>) |r| :: 1 Presentation :: [ X2^2, X1^7, (X2 * X1 * X2 * X1^-1)^2, X2 * X1^-3 * X2 * X1 * X2 * X1^2, (X1^-1 * X2)^7 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 22, 10, 4)(3, 7, 15, 30, 36, 18, 8)(6, 13, 26, 47, 38, 29, 14)(9, 19, 37, 31, 50, 39, 20)(12, 24, 44, 34, 17, 33, 25)(16, 32, 23, 43, 52, 49, 28)(21, 40, 55, 54, 51, 45, 41)(27, 48, 42, 35, 53, 56, 46) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 23)(13, 27)(14, 28)(15, 31)(18, 35)(19, 33)(20, 38)(22, 42)(24, 45)(25, 46)(26, 30)(29, 40)(32, 51)(34, 52)(36, 41)(37, 54)(39, 43)(44, 47)(48, 50)(49, 53)(55, 56) local type(s) :: { ( 7^7 ) } Outer automorphisms :: chiral negatively-selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 8 e = 28 f = 8 degree seq :: [ 7^8 ] E7.469 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 7, 7}) Quotient :: edge Aut^+ = (C2 x C2 x C2) : C7 (small group id <56, 11>) Aut = (C2 x C2 x C2) : C7 (small group id <56, 11>) |r| :: 1 Presentation :: [ X1^2, X2^7, (X2 * X1 * X2^-1 * X1)^2, X1 * X2^-3 * X1 * X2 * X1 * X2^2, (X2^-1 * X1)^7 ] Map:: polytopal R = (1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 21)(12, 25)(14, 29)(15, 31)(16, 24)(18, 36)(19, 27)(20, 38)(22, 42)(23, 43)(26, 32)(28, 46)(30, 41)(33, 40)(34, 52)(35, 50)(37, 54)(39, 53)(44, 48)(45, 49)(47, 51)(55, 56)(57, 59, 64, 74, 78, 66, 60)(58, 61, 68, 82, 86, 70, 62)(63, 71, 88, 107, 94, 89, 72)(65, 75, 93, 81, 101, 95, 76)(67, 79, 92, 109, 102, 100, 80)(69, 83, 91, 73, 90, 103, 84)(77, 96, 111, 110, 99, 108, 97)(85, 104, 112, 106, 87, 105, 98) 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) :: { ( 14, 14 ), ( 14^7 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 56 f = 8 degree seq :: [ 2^28, 7^8 ] E7.470 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 7, 7}) Quotient :: loop Aut^+ = (C2 x C2 x C2) : C7 (small group id <56, 11>) Aut = (C2 x C2 x C2) : C7 (small group id <56, 11>) |r| :: 1 Presentation :: [ (X2^-1 * X1^-1)^2, X1^7, X2^7, X1^3 * X2^-2 * X1 * X2^-1, X1^2 * X2^-1 * X1 * X2^-3, X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-2 * X1^-1 ] Map:: R = (1, 57, 2, 58, 6, 62, 16, 72, 34, 90, 13, 69, 4, 60)(3, 59, 9, 65, 23, 79, 49, 105, 37, 93, 29, 85, 11, 67)(5, 61, 14, 70, 35, 91, 31, 87, 47, 103, 20, 76, 7, 63)(8, 64, 21, 77, 27, 83, 10, 66, 25, 81, 42, 98, 17, 73)(12, 68, 30, 86, 51, 107, 55, 111, 50, 106, 39, 95, 32, 88)(15, 71, 38, 94, 28, 84, 44, 100, 54, 110, 41, 97, 36, 92)(18, 74, 26, 82, 45, 101, 19, 75, 43, 99, 24, 80, 40, 96)(22, 78, 33, 89, 46, 102, 53, 109, 56, 112, 52, 108, 48, 104) L = (1, 59)(2, 63)(3, 66)(4, 68)(5, 57)(6, 73)(7, 75)(8, 58)(9, 60)(10, 82)(11, 84)(12, 87)(13, 89)(14, 92)(15, 61)(16, 96)(17, 97)(18, 62)(19, 100)(20, 102)(21, 104)(22, 64)(23, 99)(24, 65)(25, 67)(26, 95)(27, 91)(28, 72)(29, 78)(30, 69)(31, 77)(32, 74)(33, 93)(34, 94)(35, 105)(36, 98)(37, 70)(38, 106)(39, 71)(40, 108)(41, 109)(42, 86)(43, 76)(44, 85)(45, 83)(46, 90)(47, 88)(48, 80)(49, 111)(50, 79)(51, 81)(52, 107)(53, 103)(54, 101)(55, 112)(56, 110) local type(s) :: { ( 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 8 e = 56 f = 36 degree seq :: [ 14^8 ] E7.471 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {2, 7, 7}) Quotient :: loop Aut^+ = (C2 x C2 x C2) : C7 (small group id <56, 11>) Aut = C2 x ((C2 x C2 x C2) : C7) (small group id <112, 41>) |r| :: 2 Presentation :: [ F^2, F * T1 * F * T2, (T2^-1 * T1^-1)^2, T1^7, T2^7, T1^3 * T2^-2 * T1 * T2^-1, T1^2 * T2^-1 * T1 * T2^-3, T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-2 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 3, 10, 26, 39, 15, 5)(2, 7, 19, 44, 29, 22, 8)(4, 12, 31, 21, 48, 24, 9)(6, 17, 41, 53, 47, 32, 18)(11, 28, 16, 40, 52, 51, 25)(13, 33, 37, 14, 36, 42, 30)(20, 46, 34, 38, 50, 23, 43)(27, 35, 49, 55, 56, 54, 45)(57, 58, 62, 72, 90, 69, 60)(59, 65, 79, 105, 93, 85, 67)(61, 70, 91, 87, 103, 76, 63)(64, 77, 83, 66, 81, 98, 73)(68, 86, 107, 111, 106, 95, 88)(71, 94, 84, 100, 110, 97, 92)(74, 82, 101, 75, 99, 80, 96)(78, 89, 102, 109, 112, 108, 104) 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) :: { ( 4^7 ) } Outer automorphisms :: reflexible Dual of E7.472 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 16 e = 56 f = 28 degree seq :: [ 7^16 ] E7.472 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {2, 7, 7}) Quotient :: edge Aut^+ = (C2 x C2 x C2) : C7 (small group id <56, 11>) Aut = C2 x ((C2 x C2 x C2) : C7) (small group id <112, 41>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, F * T1 * T2 * F * T1^-1, T1^7, (T2 * T1 * T2 * T1^-1)^2, T2 * T1^3 * T2 * T1^-2 * T2 * T1^-1, F * T2 * T1^3 * F * T1^-1 * T2 * T1^-2, (T2 * T1^-1)^7 ] Map:: polyhedral non-degenerate R = (1, 57, 3, 59)(2, 58, 6, 62)(4, 60, 9, 65)(5, 61, 12, 68)(7, 63, 16, 72)(8, 64, 17, 73)(10, 66, 21, 77)(11, 67, 23, 79)(13, 69, 27, 83)(14, 70, 28, 84)(15, 71, 31, 87)(18, 74, 35, 91)(19, 75, 33, 89)(20, 76, 38, 94)(22, 78, 42, 98)(24, 80, 45, 101)(25, 81, 46, 102)(26, 82, 30, 86)(29, 85, 40, 96)(32, 88, 51, 107)(34, 90, 52, 108)(36, 92, 41, 97)(37, 93, 54, 110)(39, 95, 43, 99)(44, 100, 47, 103)(48, 104, 50, 106)(49, 105, 53, 109)(55, 111, 56, 112) L = (1, 58)(2, 61)(3, 63)(4, 57)(5, 67)(6, 69)(7, 71)(8, 59)(9, 75)(10, 60)(11, 78)(12, 80)(13, 82)(14, 62)(15, 86)(16, 88)(17, 89)(18, 64)(19, 93)(20, 65)(21, 96)(22, 66)(23, 99)(24, 100)(25, 68)(26, 103)(27, 104)(28, 72)(29, 70)(30, 92)(31, 106)(32, 79)(33, 81)(34, 73)(35, 109)(36, 74)(37, 87)(38, 85)(39, 76)(40, 111)(41, 77)(42, 91)(43, 108)(44, 90)(45, 97)(46, 83)(47, 94)(48, 98)(49, 84)(50, 95)(51, 101)(52, 105)(53, 112)(54, 107)(55, 110)(56, 102) local type(s) :: { ( 7^4 ) } Outer automorphisms :: reflexible Dual of E7.471 Transitivity :: ET+ VT+ Graph:: simple v = 28 e = 56 f = 16 degree seq :: [ 4^28 ] E7.473 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 7, 7}) Quotient :: edge^2 Aut^+ = (C2 x C2 x C2) : C7 (small group id <56, 11>) Aut = C2 x ((C2 x C2 x C2) : C7) (small group id <112, 41>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, (Y1^-1 * Y3^-1 * Y2^-1)^2, Y1^7, Y2^7, Y1^3 * Y2^-2 * Y1 * Y2^-1, Y1^2 * Y2^-1 * Y1 * Y2^-3, Y2 * Y1^2 * Y2 * Y1^-1 * Y2^-2 * Y1^-1 ] Map:: polytopal R = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)(113, 114, 118, 128, 146, 125, 116)(115, 121, 135, 161, 149, 141, 123)(117, 126, 147, 143, 159, 132, 119)(120, 133, 139, 122, 137, 154, 129)(124, 142, 163, 167, 162, 151, 144)(127, 150, 140, 156, 166, 153, 148)(130, 138, 157, 131, 155, 136, 152)(134, 145, 158, 165, 168, 164, 160)(169, 171, 178, 194, 207, 183, 173)(170, 175, 187, 212, 197, 190, 176)(172, 180, 199, 189, 216, 192, 177)(174, 185, 209, 221, 215, 200, 186)(179, 196, 184, 208, 220, 219, 193)(181, 201, 205, 182, 204, 210, 198)(188, 214, 202, 206, 218, 191, 211)(195, 203, 217, 223, 224, 222, 213) 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 ), ( 8^7 ) } Outer automorphisms :: reflexible Dual of E7.476 Graph:: simple bipartite v = 72 e = 112 f = 28 degree seq :: [ 2^56, 7^16 ] E7.474 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 7, 7}) Quotient :: edge^2 Aut^+ = (C2 x C2 x C2) : C7 (small group id <56, 11>) Aut = C2 x ((C2 x C2 x C2) : C7) (small group id <112, 41>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^-1 * Y3 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, (Y2^-1 * Y3 * Y1^-1)^2, Y1^2 * Y2^-1 * Y3 * Y1^-2 * Y2, Y1 * Y2^-1 * Y1 * Y3 * Y2^3, Y1^7, Y2^7, Y1^2 * Y2^-1 * Y1 * Y2^-2 * Y1, Y1 * Y2^-1 * Y1^2 * Y2^-3 ] Map:: polyhedral non-degenerate R = (1, 57, 4, 60)(2, 58, 8, 64)(3, 59, 5, 61)(6, 62, 18, 74)(7, 63, 21, 77)(9, 65, 26, 82)(10, 66, 29, 85)(11, 67, 12, 68)(13, 69, 14, 70)(15, 71, 16, 72)(17, 73, 46, 102)(19, 75, 49, 105)(20, 76, 47, 103)(22, 78, 45, 101)(23, 79, 24, 80)(25, 81, 50, 106)(27, 83, 48, 104)(28, 84, 51, 107)(30, 86, 54, 110)(31, 87, 40, 96)(32, 88, 33, 89)(34, 90, 35, 91)(36, 92, 37, 93)(38, 94, 39, 95)(41, 97, 42, 98)(43, 99, 44, 100)(52, 108, 53, 109)(55, 111, 56, 112)(113, 114, 119, 132, 156, 128, 117)(115, 122, 140, 138, 139, 147, 124)(116, 118, 129, 157, 146, 151, 126)(120, 121, 137, 144, 150, 165, 136)(123, 143, 167, 166, 158, 159, 145)(125, 141, 142, 161, 162, 155, 149)(127, 152, 135, 130, 131, 160, 154)(133, 134, 153, 148, 164, 168, 163)(169, 171, 179, 200, 218, 187, 174)(170, 172, 181, 204, 210, 195, 177)(173, 183, 209, 213, 214, 198, 178)(175, 176, 191, 199, 180, 202, 190)(182, 206, 201, 188, 189, 196, 197)(184, 211, 193, 194, 219, 223, 208)(185, 186, 192, 220, 205, 212, 215)(203, 216, 217, 222, 224, 221, 207) 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 ), ( 4^7 ) } Outer automorphisms :: reflexible Dual of E7.475 Graph:: simple bipartite v = 44 e = 112 f = 56 degree seq :: [ 4^28, 7^16 ] E7.475 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 7, 7}) Quotient :: loop^2 Aut^+ = (C2 x C2 x C2) : C7 (small group id <56, 11>) Aut = C2 x ((C2 x C2 x C2) : C7) (small group id <112, 41>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, (Y1^-1 * Y3^-1 * Y2^-1)^2, Y1^7, Y2^7, Y1^3 * Y2^-2 * Y1 * Y2^-1, Y1^2 * Y2^-1 * Y1 * Y2^-3, Y2 * Y1^2 * Y2 * Y1^-1 * Y2^-2 * Y1^-1 ] Map:: polyhedral non-degenerate R = (1, 57, 113, 169)(2, 58, 114, 170)(3, 59, 115, 171)(4, 60, 116, 172)(5, 61, 117, 173)(6, 62, 118, 174)(7, 63, 119, 175)(8, 64, 120, 176)(9, 65, 121, 177)(10, 66, 122, 178)(11, 67, 123, 179)(12, 68, 124, 180)(13, 69, 125, 181)(14, 70, 126, 182)(15, 71, 127, 183)(16, 72, 128, 184)(17, 73, 129, 185)(18, 74, 130, 186)(19, 75, 131, 187)(20, 76, 132, 188)(21, 77, 133, 189)(22, 78, 134, 190)(23, 79, 135, 191)(24, 80, 136, 192)(25, 81, 137, 193)(26, 82, 138, 194)(27, 83, 139, 195)(28, 84, 140, 196)(29, 85, 141, 197)(30, 86, 142, 198)(31, 87, 143, 199)(32, 88, 144, 200)(33, 89, 145, 201)(34, 90, 146, 202)(35, 91, 147, 203)(36, 92, 148, 204)(37, 93, 149, 205)(38, 94, 150, 206)(39, 95, 151, 207)(40, 96, 152, 208)(41, 97, 153, 209)(42, 98, 154, 210)(43, 99, 155, 211)(44, 100, 156, 212)(45, 101, 157, 213)(46, 102, 158, 214)(47, 103, 159, 215)(48, 104, 160, 216)(49, 105, 161, 217)(50, 106, 162, 218)(51, 107, 163, 219)(52, 108, 164, 220)(53, 109, 165, 221)(54, 110, 166, 222)(55, 111, 167, 223)(56, 112, 168, 224) L = (1, 58)(2, 62)(3, 65)(4, 57)(5, 70)(6, 72)(7, 61)(8, 77)(9, 79)(10, 81)(11, 59)(12, 86)(13, 60)(14, 91)(15, 94)(16, 90)(17, 64)(18, 82)(19, 99)(20, 63)(21, 83)(22, 89)(23, 105)(24, 96)(25, 98)(26, 101)(27, 66)(28, 100)(29, 67)(30, 107)(31, 103)(32, 68)(33, 102)(34, 69)(35, 87)(36, 71)(37, 85)(38, 84)(39, 88)(40, 74)(41, 92)(42, 73)(43, 80)(44, 110)(45, 75)(46, 109)(47, 76)(48, 78)(49, 93)(50, 95)(51, 111)(52, 104)(53, 112)(54, 97)(55, 106)(56, 108)(113, 171)(114, 175)(115, 178)(116, 180)(117, 169)(118, 185)(119, 187)(120, 170)(121, 172)(122, 194)(123, 196)(124, 199)(125, 201)(126, 204)(127, 173)(128, 208)(129, 209)(130, 174)(131, 212)(132, 214)(133, 216)(134, 176)(135, 211)(136, 177)(137, 179)(138, 207)(139, 203)(140, 184)(141, 190)(142, 181)(143, 189)(144, 186)(145, 205)(146, 206)(147, 217)(148, 210)(149, 182)(150, 218)(151, 183)(152, 220)(153, 221)(154, 198)(155, 188)(156, 197)(157, 195)(158, 202)(159, 200)(160, 192)(161, 223)(162, 191)(163, 193)(164, 219)(165, 215)(166, 213)(167, 224)(168, 222) local type(s) :: { ( 4, 7, 4, 7 ) } Outer automorphisms :: reflexible Dual of E7.474 Transitivity :: VT+ Graph:: simple v = 56 e = 112 f = 44 degree seq :: [ 4^56 ] E7.476 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 7, 7}) Quotient :: loop^2 Aut^+ = (C2 x C2 x C2) : C7 (small group id <56, 11>) Aut = C2 x ((C2 x C2 x C2) : C7) (small group id <112, 41>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^-1 * Y3 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, (Y2^-1 * Y3 * Y1^-1)^2, Y1^2 * Y2^-1 * Y3 * Y1^-2 * Y2, Y1 * Y2^-1 * Y1 * Y3 * Y2^3, Y1^7, Y2^7, Y1^2 * Y2^-1 * Y1 * Y2^-2 * Y1, Y1 * Y2^-1 * Y1^2 * Y2^-3 ] Map:: R = (1, 57, 113, 169, 4, 60, 116, 172)(2, 58, 114, 170, 8, 64, 120, 176)(3, 59, 115, 171, 5, 61, 117, 173)(6, 62, 118, 174, 18, 74, 130, 186)(7, 63, 119, 175, 21, 77, 133, 189)(9, 65, 121, 177, 26, 82, 138, 194)(10, 66, 122, 178, 29, 85, 141, 197)(11, 67, 123, 179, 12, 68, 124, 180)(13, 69, 125, 181, 14, 70, 126, 182)(15, 71, 127, 183, 16, 72, 128, 184)(17, 73, 129, 185, 46, 102, 158, 214)(19, 75, 131, 187, 49, 105, 161, 217)(20, 76, 132, 188, 47, 103, 159, 215)(22, 78, 134, 190, 45, 101, 157, 213)(23, 79, 135, 191, 24, 80, 136, 192)(25, 81, 137, 193, 50, 106, 162, 218)(27, 83, 139, 195, 48, 104, 160, 216)(28, 84, 140, 196, 51, 107, 163, 219)(30, 86, 142, 198, 54, 110, 166, 222)(31, 87, 143, 199, 40, 96, 152, 208)(32, 88, 144, 200, 33, 89, 145, 201)(34, 90, 146, 202, 35, 91, 147, 203)(36, 92, 148, 204, 37, 93, 149, 205)(38, 94, 150, 206, 39, 95, 151, 207)(41, 97, 153, 209, 42, 98, 154, 210)(43, 99, 155, 211, 44, 100, 156, 212)(52, 108, 164, 220, 53, 109, 165, 221)(55, 111, 167, 223, 56, 112, 168, 224) L = (1, 58)(2, 63)(3, 66)(4, 62)(5, 57)(6, 73)(7, 76)(8, 65)(9, 81)(10, 84)(11, 87)(12, 59)(13, 85)(14, 60)(15, 96)(16, 61)(17, 101)(18, 75)(19, 104)(20, 100)(21, 78)(22, 97)(23, 74)(24, 64)(25, 88)(26, 83)(27, 91)(28, 82)(29, 86)(30, 105)(31, 111)(32, 94)(33, 67)(34, 95)(35, 68)(36, 108)(37, 69)(38, 109)(39, 70)(40, 79)(41, 92)(42, 71)(43, 93)(44, 72)(45, 90)(46, 103)(47, 89)(48, 98)(49, 106)(50, 99)(51, 77)(52, 112)(53, 80)(54, 102)(55, 110)(56, 107)(113, 171)(114, 172)(115, 179)(116, 181)(117, 183)(118, 169)(119, 176)(120, 191)(121, 170)(122, 173)(123, 200)(124, 202)(125, 204)(126, 206)(127, 209)(128, 211)(129, 186)(130, 192)(131, 174)(132, 189)(133, 196)(134, 175)(135, 199)(136, 220)(137, 194)(138, 219)(139, 177)(140, 197)(141, 182)(142, 178)(143, 180)(144, 218)(145, 188)(146, 190)(147, 216)(148, 210)(149, 212)(150, 201)(151, 203)(152, 184)(153, 213)(154, 195)(155, 193)(156, 215)(157, 214)(158, 198)(159, 185)(160, 217)(161, 222)(162, 187)(163, 223)(164, 205)(165, 207)(166, 224)(167, 208)(168, 221) local type(s) :: { ( 2, 7, 2, 7, 2, 7, 2, 7 ) } Outer automorphisms :: reflexible Dual of E7.473 Transitivity :: VT+ Graph:: v = 28 e = 112 f = 72 degree seq :: [ 8^28 ] E7.477 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 28}) Quotient :: regular Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T1^-2 * T2 * T1^5 * T2 * T1^-7 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 50, 42, 34, 26, 16, 23, 17, 24, 32, 40, 48, 56, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 54, 47, 38, 31, 21, 14, 6, 13, 9, 18, 27, 35, 43, 51, 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, 53)(52, 55) local type(s) :: { ( 4^28 ) } Outer automorphisms :: reflexible Dual of E7.478 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 28 f = 14 degree seq :: [ 28^2 ] E7.478 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 28}) Quotient :: regular Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 2, 5, 4)(3, 7, 10, 8)(6, 11, 9, 12)(13, 17, 14, 18)(15, 19, 16, 20)(21, 25, 22, 26)(23, 27, 24, 28)(29, 33, 30, 34)(31, 35, 32, 36)(37, 41, 38, 42)(39, 43, 40, 44)(45, 49, 46, 50)(47, 51, 48, 52)(53, 55, 54, 56) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 53)(50, 54)(51, 55)(52, 56) local type(s) :: { ( 28^4 ) } Outer automorphisms :: reflexible Dual of E7.477 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 14 e = 28 f = 2 degree seq :: [ 4^14 ] E7.479 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 28}) Quotient :: edge Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 9, 14)(10, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)(33, 37, 34, 38)(35, 39, 36, 40)(41, 45, 42, 46)(43, 47, 44, 48)(49, 53, 50, 54)(51, 55, 52, 56)(57, 58)(59, 63)(60, 65)(61, 66)(62, 68)(64, 67)(69, 73)(70, 74)(71, 75)(72, 76)(77, 81)(78, 82)(79, 83)(80, 84)(85, 89)(86, 90)(87, 91)(88, 92)(93, 97)(94, 98)(95, 99)(96, 100)(101, 105)(102, 106)(103, 107)(104, 108)(109, 111)(110, 112) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 56, 56 ), ( 56^4 ) } Outer automorphisms :: reflexible Dual of E7.483 Transitivity :: ET+ Graph:: simple bipartite v = 42 e = 56 f = 2 degree seq :: [ 2^28, 4^14 ] E7.480 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 28}) Quotient :: edge Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^-1 * T2^-14 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 49, 41, 33, 25, 17, 9, 4, 11, 19, 27, 35, 43, 51, 56, 48, 40, 32, 24, 16, 8)(57, 58, 62, 60)(59, 65, 69, 64)(61, 67, 70, 63)(66, 72, 77, 73)(68, 71, 78, 75)(74, 81, 85, 80)(76, 83, 86, 79)(82, 88, 93, 89)(84, 87, 94, 91)(90, 97, 101, 96)(92, 99, 102, 95)(98, 104, 109, 105)(100, 103, 110, 107)(106, 111, 108, 112) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4^4 ), ( 4^28 ) } Outer automorphisms :: reflexible Dual of E7.484 Transitivity :: ET+ Graph:: bipartite v = 16 e = 56 f = 28 degree seq :: [ 4^14, 28^2 ] E7.481 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 28}) Quotient :: edge Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^-2 * T2 * T1^5 * T2 * T1^-7 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 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, 53)(52, 55)(57, 58, 61, 67, 76, 85, 93, 101, 109, 106, 98, 90, 82, 72, 79, 73, 80, 88, 96, 104, 112, 108, 100, 92, 84, 75, 66, 60)(59, 63, 71, 81, 89, 97, 105, 110, 103, 94, 87, 77, 70, 62, 69, 65, 74, 83, 91, 99, 107, 111, 102, 95, 86, 78, 68, 64) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 8, 8 ), ( 8^28 ) } Outer automorphisms :: reflexible Dual of E7.482 Transitivity :: ET+ Graph:: simple bipartite v = 30 e = 56 f = 14 degree seq :: [ 2^28, 28^2 ] E7.482 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 28}) Quotient :: loop Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 57, 3, 59, 8, 64, 4, 60)(2, 58, 5, 61, 11, 67, 6, 62)(7, 63, 13, 69, 9, 65, 14, 70)(10, 66, 15, 71, 12, 68, 16, 72)(17, 73, 21, 77, 18, 74, 22, 78)(19, 75, 23, 79, 20, 76, 24, 80)(25, 81, 29, 85, 26, 82, 30, 86)(27, 83, 31, 87, 28, 84, 32, 88)(33, 89, 37, 93, 34, 90, 38, 94)(35, 91, 39, 95, 36, 92, 40, 96)(41, 97, 45, 101, 42, 98, 46, 102)(43, 99, 47, 103, 44, 100, 48, 104)(49, 105, 53, 109, 50, 106, 54, 110)(51, 107, 55, 111, 52, 108, 56, 112) L = (1, 58)(2, 57)(3, 63)(4, 65)(5, 66)(6, 68)(7, 59)(8, 67)(9, 60)(10, 61)(11, 64)(12, 62)(13, 73)(14, 74)(15, 75)(16, 76)(17, 69)(18, 70)(19, 71)(20, 72)(21, 81)(22, 82)(23, 83)(24, 84)(25, 77)(26, 78)(27, 79)(28, 80)(29, 89)(30, 90)(31, 91)(32, 92)(33, 85)(34, 86)(35, 87)(36, 88)(37, 97)(38, 98)(39, 99)(40, 100)(41, 93)(42, 94)(43, 95)(44, 96)(45, 105)(46, 106)(47, 107)(48, 108)(49, 101)(50, 102)(51, 103)(52, 104)(53, 111)(54, 112)(55, 109)(56, 110) local type(s) :: { ( 2, 28, 2, 28, 2, 28, 2, 28 ) } Outer automorphisms :: reflexible Dual of E7.481 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 14 e = 56 f = 30 degree seq :: [ 8^14 ] E7.483 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 28}) Quotient :: loop Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^-1 * T2^-14 * T1^-1 ] Map:: R = (1, 57, 3, 59, 10, 66, 18, 74, 26, 82, 34, 90, 42, 98, 50, 106, 54, 110, 46, 102, 38, 94, 30, 86, 22, 78, 14, 70, 6, 62, 13, 69, 21, 77, 29, 85, 37, 93, 45, 101, 53, 109, 52, 108, 44, 100, 36, 92, 28, 84, 20, 76, 12, 68, 5, 61)(2, 58, 7, 63, 15, 71, 23, 79, 31, 87, 39, 95, 47, 103, 55, 111, 49, 105, 41, 97, 33, 89, 25, 81, 17, 73, 9, 65, 4, 60, 11, 67, 19, 75, 27, 83, 35, 91, 43, 99, 51, 107, 56, 112, 48, 104, 40, 96, 32, 88, 24, 80, 16, 72, 8, 64) L = (1, 58)(2, 62)(3, 65)(4, 57)(5, 67)(6, 60)(7, 61)(8, 59)(9, 69)(10, 72)(11, 70)(12, 71)(13, 64)(14, 63)(15, 78)(16, 77)(17, 66)(18, 81)(19, 68)(20, 83)(21, 73)(22, 75)(23, 76)(24, 74)(25, 85)(26, 88)(27, 86)(28, 87)(29, 80)(30, 79)(31, 94)(32, 93)(33, 82)(34, 97)(35, 84)(36, 99)(37, 89)(38, 91)(39, 92)(40, 90)(41, 101)(42, 104)(43, 102)(44, 103)(45, 96)(46, 95)(47, 110)(48, 109)(49, 98)(50, 111)(51, 100)(52, 112)(53, 105)(54, 107)(55, 108)(56, 106) 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 E7.479 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 56 f = 42 degree seq :: [ 56^2 ] E7.484 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 28}) Quotient :: loop Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^-2 * T2 * T1^5 * T2 * T1^-7 ] Map:: polytopal non-degenerate R = (1, 57, 3, 59)(2, 58, 6, 62)(4, 60, 9, 65)(5, 61, 12, 68)(7, 63, 16, 72)(8, 64, 17, 73)(10, 66, 15, 71)(11, 67, 21, 77)(13, 69, 23, 79)(14, 70, 24, 80)(18, 74, 26, 82)(19, 75, 27, 83)(20, 76, 30, 86)(22, 78, 32, 88)(25, 81, 34, 90)(28, 84, 33, 89)(29, 85, 38, 94)(31, 87, 40, 96)(35, 91, 42, 98)(36, 92, 43, 99)(37, 93, 46, 102)(39, 95, 48, 104)(41, 97, 50, 106)(44, 100, 49, 105)(45, 101, 54, 110)(47, 103, 56, 112)(51, 107, 53, 109)(52, 108, 55, 111) L = (1, 58)(2, 61)(3, 63)(4, 57)(5, 67)(6, 69)(7, 71)(8, 59)(9, 74)(10, 60)(11, 76)(12, 64)(13, 65)(14, 62)(15, 81)(16, 79)(17, 80)(18, 83)(19, 66)(20, 85)(21, 70)(22, 68)(23, 73)(24, 88)(25, 89)(26, 72)(27, 91)(28, 75)(29, 93)(30, 78)(31, 77)(32, 96)(33, 97)(34, 82)(35, 99)(36, 84)(37, 101)(38, 87)(39, 86)(40, 104)(41, 105)(42, 90)(43, 107)(44, 92)(45, 109)(46, 95)(47, 94)(48, 112)(49, 110)(50, 98)(51, 111)(52, 100)(53, 106)(54, 103)(55, 102)(56, 108) local type(s) :: { ( 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E7.480 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 28 e = 56 f = 16 degree seq :: [ 4^28 ] E7.485 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 28}) Quotient :: dipole Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^28 ] Map:: R = (1, 57, 2, 58)(3, 59, 7, 63)(4, 60, 9, 65)(5, 61, 10, 66)(6, 62, 12, 68)(8, 64, 11, 67)(13, 69, 17, 73)(14, 70, 18, 74)(15, 71, 19, 75)(16, 72, 20, 76)(21, 77, 25, 81)(22, 78, 26, 82)(23, 79, 27, 83)(24, 80, 28, 84)(29, 85, 33, 89)(30, 86, 34, 90)(31, 87, 35, 91)(32, 88, 36, 92)(37, 93, 41, 97)(38, 94, 42, 98)(39, 95, 43, 99)(40, 96, 44, 100)(45, 101, 49, 105)(46, 102, 50, 106)(47, 103, 51, 107)(48, 104, 52, 108)(53, 109, 55, 111)(54, 110, 56, 112)(113, 169, 115, 171, 120, 176, 116, 172)(114, 170, 117, 173, 123, 179, 118, 174)(119, 175, 125, 181, 121, 177, 126, 182)(122, 178, 127, 183, 124, 180, 128, 184)(129, 185, 133, 189, 130, 186, 134, 190)(131, 187, 135, 191, 132, 188, 136, 192)(137, 193, 141, 197, 138, 194, 142, 198)(139, 195, 143, 199, 140, 196, 144, 200)(145, 201, 149, 205, 146, 202, 150, 206)(147, 203, 151, 207, 148, 204, 152, 208)(153, 209, 157, 213, 154, 210, 158, 214)(155, 211, 159, 215, 156, 212, 160, 216)(161, 217, 165, 221, 162, 218, 166, 222)(163, 219, 167, 223, 164, 220, 168, 224) L = (1, 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, 147)(32, 148)(33, 141)(34, 142)(35, 143)(36, 144)(37, 153)(38, 154)(39, 155)(40, 156)(41, 149)(42, 150)(43, 151)(44, 152)(45, 161)(46, 162)(47, 163)(48, 164)(49, 157)(50, 158)(51, 159)(52, 160)(53, 167)(54, 168)(55, 165)(56, 166)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 2, 56, 2, 56 ), ( 2, 56, 2, 56, 2, 56, 2, 56 ) } Outer automorphisms :: reflexible Dual of E7.488 Graph:: bipartite v = 42 e = 112 f = 58 degree seq :: [ 4^28, 8^14 ] E7.486 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 28}) Quotient :: dipole Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1^4, (Y2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y2^13 * Y1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 57, 2, 58, 6, 62, 4, 60)(3, 59, 9, 65, 13, 69, 8, 64)(5, 61, 11, 67, 14, 70, 7, 63)(10, 66, 16, 72, 21, 77, 17, 73)(12, 68, 15, 71, 22, 78, 19, 75)(18, 74, 25, 81, 29, 85, 24, 80)(20, 76, 27, 83, 30, 86, 23, 79)(26, 82, 32, 88, 37, 93, 33, 89)(28, 84, 31, 87, 38, 94, 35, 91)(34, 90, 41, 97, 45, 101, 40, 96)(36, 92, 43, 99, 46, 102, 39, 95)(42, 98, 48, 104, 53, 109, 49, 105)(44, 100, 47, 103, 54, 110, 51, 107)(50, 106, 55, 111, 52, 108, 56, 112)(113, 169, 115, 171, 122, 178, 130, 186, 138, 194, 146, 202, 154, 210, 162, 218, 166, 222, 158, 214, 150, 206, 142, 198, 134, 190, 126, 182, 118, 174, 125, 181, 133, 189, 141, 197, 149, 205, 157, 213, 165, 221, 164, 220, 156, 212, 148, 204, 140, 196, 132, 188, 124, 180, 117, 173)(114, 170, 119, 175, 127, 183, 135, 191, 143, 199, 151, 207, 159, 215, 167, 223, 161, 217, 153, 209, 145, 201, 137, 193, 129, 185, 121, 177, 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, 122)(4, 123)(5, 113)(6, 125)(7, 127)(8, 114)(9, 116)(10, 130)(11, 131)(12, 117)(13, 133)(14, 118)(15, 135)(16, 120)(17, 121)(18, 138)(19, 139)(20, 124)(21, 141)(22, 126)(23, 143)(24, 128)(25, 129)(26, 146)(27, 147)(28, 132)(29, 149)(30, 134)(31, 151)(32, 136)(33, 137)(34, 154)(35, 155)(36, 140)(37, 157)(38, 142)(39, 159)(40, 144)(41, 145)(42, 162)(43, 163)(44, 148)(45, 165)(46, 150)(47, 167)(48, 152)(49, 153)(50, 166)(51, 168)(52, 156)(53, 164)(54, 158)(55, 161)(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, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E7.487 Graph:: bipartite v = 16 e = 112 f = 84 degree seq :: [ 8^14, 56^2 ] E7.487 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 28}) Quotient :: dipole Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2, Y3^11 * Y2 * Y3^-1 * Y2 * Y3^2, (Y3^-1 * Y1^-1)^28 ] Map:: polytopal R = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)(113, 169, 114, 170)(115, 171, 119, 175)(116, 172, 121, 177)(117, 173, 123, 179)(118, 174, 125, 181)(120, 176, 126, 182)(122, 178, 124, 180)(127, 183, 132, 188)(128, 184, 135, 191)(129, 185, 137, 193)(130, 186, 133, 189)(131, 187, 139, 195)(134, 190, 141, 197)(136, 192, 143, 199)(138, 194, 144, 200)(140, 196, 142, 198)(145, 201, 151, 207)(146, 202, 153, 209)(147, 203, 149, 205)(148, 204, 155, 211)(150, 206, 157, 213)(152, 208, 159, 215)(154, 210, 160, 216)(156, 212, 158, 214)(161, 217, 167, 223)(162, 218, 166, 222)(163, 219, 165, 221)(164, 220, 168, 224) L = (1, 115)(2, 117)(3, 120)(4, 113)(5, 124)(6, 114)(7, 127)(8, 129)(9, 130)(10, 116)(11, 132)(12, 134)(13, 135)(14, 118)(15, 121)(16, 119)(17, 138)(18, 139)(19, 122)(20, 125)(21, 123)(22, 142)(23, 143)(24, 126)(25, 128)(26, 146)(27, 147)(28, 131)(29, 133)(30, 150)(31, 151)(32, 136)(33, 137)(34, 154)(35, 155)(36, 140)(37, 141)(38, 158)(39, 159)(40, 144)(41, 145)(42, 162)(43, 163)(44, 148)(45, 149)(46, 166)(47, 167)(48, 152)(49, 153)(50, 165)(51, 168)(52, 156)(53, 157)(54, 161)(55, 164)(56, 160)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 8, 56 ), ( 8, 56, 8, 56 ) } Outer automorphisms :: reflexible Dual of E7.486 Graph:: simple bipartite v = 84 e = 112 f = 16 degree seq :: [ 2^56, 4^28 ] E7.488 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 28}) Quotient :: dipole Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3)^2, (Y3 * Y1^-2)^2, (Y3 * Y1)^4, Y1^-2 * Y3 * Y1^5 * Y3 * Y1^-7 ] Map:: R = (1, 57, 2, 58, 5, 61, 11, 67, 20, 76, 29, 85, 37, 93, 45, 101, 53, 109, 50, 106, 42, 98, 34, 90, 26, 82, 16, 72, 23, 79, 17, 73, 24, 80, 32, 88, 40, 96, 48, 104, 56, 112, 52, 108, 44, 100, 36, 92, 28, 84, 19, 75, 10, 66, 4, 60)(3, 59, 7, 63, 15, 71, 25, 81, 33, 89, 41, 97, 49, 105, 54, 110, 47, 103, 38, 94, 31, 87, 21, 77, 14, 70, 6, 62, 13, 69, 9, 65, 18, 74, 27, 83, 35, 91, 43, 99, 51, 107, 55, 111, 46, 102, 39, 95, 30, 86, 22, 78, 12, 68, 8, 64)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224) L = (1, 115)(2, 118)(3, 113)(4, 121)(5, 124)(6, 114)(7, 128)(8, 129)(9, 116)(10, 127)(11, 133)(12, 117)(13, 135)(14, 136)(15, 122)(16, 119)(17, 120)(18, 138)(19, 139)(20, 142)(21, 123)(22, 144)(23, 125)(24, 126)(25, 146)(26, 130)(27, 131)(28, 145)(29, 150)(30, 132)(31, 152)(32, 134)(33, 140)(34, 137)(35, 154)(36, 155)(37, 158)(38, 141)(39, 160)(40, 143)(41, 162)(42, 147)(43, 148)(44, 161)(45, 166)(46, 149)(47, 168)(48, 151)(49, 156)(50, 153)(51, 165)(52, 167)(53, 163)(54, 157)(55, 164)(56, 159)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E7.485 Graph:: simple bipartite v = 58 e = 112 f = 42 degree seq :: [ 2^56, 56^2 ] E7.489 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 28}) Quotient :: dipole Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^4, Y2^9 * Y1 * Y2^-5 * Y1 ] Map:: R = (1, 57, 2, 58)(3, 59, 7, 63)(4, 60, 9, 65)(5, 61, 11, 67)(6, 62, 13, 69)(8, 64, 14, 70)(10, 66, 12, 68)(15, 71, 20, 76)(16, 72, 23, 79)(17, 73, 25, 81)(18, 74, 21, 77)(19, 75, 27, 83)(22, 78, 29, 85)(24, 80, 31, 87)(26, 82, 32, 88)(28, 84, 30, 86)(33, 89, 39, 95)(34, 90, 41, 97)(35, 91, 37, 93)(36, 92, 43, 99)(38, 94, 45, 101)(40, 96, 47, 103)(42, 98, 48, 104)(44, 100, 46, 102)(49, 105, 55, 111)(50, 106, 54, 110)(51, 107, 53, 109)(52, 108, 56, 112)(113, 169, 115, 171, 120, 176, 129, 185, 138, 194, 146, 202, 154, 210, 162, 218, 165, 221, 157, 213, 149, 205, 141, 197, 133, 189, 123, 179, 132, 188, 125, 181, 135, 191, 143, 199, 151, 207, 159, 215, 167, 223, 164, 220, 156, 212, 148, 204, 140, 196, 131, 187, 122, 178, 116, 172)(114, 170, 117, 173, 124, 180, 134, 190, 142, 198, 150, 206, 158, 214, 166, 222, 161, 217, 153, 209, 145, 201, 137, 193, 128, 184, 119, 175, 127, 183, 121, 177, 130, 186, 139, 195, 147, 203, 155, 211, 163, 219, 168, 224, 160, 216, 152, 208, 144, 200, 136, 192, 126, 182, 118, 174) L = (1, 114)(2, 113)(3, 119)(4, 121)(5, 123)(6, 125)(7, 115)(8, 126)(9, 116)(10, 124)(11, 117)(12, 122)(13, 118)(14, 120)(15, 132)(16, 135)(17, 137)(18, 133)(19, 139)(20, 127)(21, 130)(22, 141)(23, 128)(24, 143)(25, 129)(26, 144)(27, 131)(28, 142)(29, 134)(30, 140)(31, 136)(32, 138)(33, 151)(34, 153)(35, 149)(36, 155)(37, 147)(38, 157)(39, 145)(40, 159)(41, 146)(42, 160)(43, 148)(44, 158)(45, 150)(46, 156)(47, 152)(48, 154)(49, 167)(50, 166)(51, 165)(52, 168)(53, 163)(54, 162)(55, 161)(56, 164)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E7.490 Graph:: bipartite v = 30 e = 112 f = 70 degree seq :: [ 4^28, 56^2 ] E7.490 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 28}) Quotient :: dipole Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-14 * Y1^-1, (Y3 * Y2^-1)^28 ] Map:: R = (1, 57, 2, 58, 6, 62, 4, 60)(3, 59, 9, 65, 13, 69, 8, 64)(5, 61, 11, 67, 14, 70, 7, 63)(10, 66, 16, 72, 21, 77, 17, 73)(12, 68, 15, 71, 22, 78, 19, 75)(18, 74, 25, 81, 29, 85, 24, 80)(20, 76, 27, 83, 30, 86, 23, 79)(26, 82, 32, 88, 37, 93, 33, 89)(28, 84, 31, 87, 38, 94, 35, 91)(34, 90, 41, 97, 45, 101, 40, 96)(36, 92, 43, 99, 46, 102, 39, 95)(42, 98, 48, 104, 53, 109, 49, 105)(44, 100, 47, 103, 54, 110, 51, 107)(50, 106, 55, 111, 52, 108, 56, 112)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224) L = (1, 115)(2, 119)(3, 122)(4, 123)(5, 113)(6, 125)(7, 127)(8, 114)(9, 116)(10, 130)(11, 131)(12, 117)(13, 133)(14, 118)(15, 135)(16, 120)(17, 121)(18, 138)(19, 139)(20, 124)(21, 141)(22, 126)(23, 143)(24, 128)(25, 129)(26, 146)(27, 147)(28, 132)(29, 149)(30, 134)(31, 151)(32, 136)(33, 137)(34, 154)(35, 155)(36, 140)(37, 157)(38, 142)(39, 159)(40, 144)(41, 145)(42, 162)(43, 163)(44, 148)(45, 165)(46, 150)(47, 167)(48, 152)(49, 153)(50, 166)(51, 168)(52, 156)(53, 164)(54, 158)(55, 161)(56, 160)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56 ) } Outer automorphisms :: reflexible Dual of E7.489 Graph:: simple bipartite v = 70 e = 112 f = 30 degree seq :: [ 2^56, 8^14 ] E7.491 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 16}) Quotient :: regular Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T1^16 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 60, 55, 46, 39, 30, 22, 12, 8)(6, 13, 9, 18, 27, 35, 43, 51, 59, 61, 54, 47, 38, 31, 21, 14)(16, 23, 17, 24, 32, 40, 48, 56, 62, 64, 63, 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, 60)(55, 62)(57, 63)(61, 64) local type(s) :: { ( 4^16 ) } Outer automorphisms :: reflexible Dual of E7.492 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 32 f = 16 degree seq :: [ 16^4 ] E7.492 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 16}) Quotient :: regular Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^16 ] Map:: polytopal non-degenerate R = (1, 2, 5, 4)(3, 7, 10, 8)(6, 11, 9, 12)(13, 17, 14, 18)(15, 19, 16, 20)(21, 25, 22, 26)(23, 27, 24, 28)(29, 33, 30, 34)(31, 35, 32, 36)(37, 41, 38, 42)(39, 43, 40, 44)(45, 49, 46, 50)(47, 51, 48, 52)(53, 57, 54, 58)(55, 59, 56, 60)(61, 63, 62, 64) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 53)(50, 54)(51, 55)(52, 56)(57, 61)(58, 62)(59, 63)(60, 64) local type(s) :: { ( 16^4 ) } Outer automorphisms :: reflexible Dual of E7.491 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 16 e = 32 f = 4 degree seq :: [ 4^16 ] E7.493 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 16}) Quotient :: edge Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^16 ] Map:: polytopal R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 9, 14)(10, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)(33, 37, 34, 38)(35, 39, 36, 40)(41, 45, 42, 46)(43, 47, 44, 48)(49, 53, 50, 54)(51, 55, 52, 56)(57, 61, 58, 62)(59, 63, 60, 64)(65, 66)(67, 71)(68, 73)(69, 74)(70, 76)(72, 75)(77, 81)(78, 82)(79, 83)(80, 84)(85, 89)(86, 90)(87, 91)(88, 92)(93, 97)(94, 98)(95, 99)(96, 100)(101, 105)(102, 106)(103, 107)(104, 108)(109, 113)(110, 114)(111, 115)(112, 116)(117, 121)(118, 122)(119, 123)(120, 124)(125, 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 ), ( 32^4 ) } Outer automorphisms :: reflexible Dual of E7.497 Transitivity :: ET+ Graph:: simple bipartite v = 48 e = 64 f = 4 degree seq :: [ 2^32, 4^16 ] E7.494 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 16}) Quotient :: edge Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^16 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 62, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 59, 63, 57, 49, 41, 33, 25, 17, 9)(6, 13, 21, 29, 37, 45, 53, 60, 64, 61, 54, 46, 38, 30, 22, 14)(65, 66, 70, 68)(67, 73, 77, 72)(69, 75, 78, 71)(74, 80, 85, 81)(76, 79, 86, 83)(82, 89, 93, 88)(84, 91, 94, 87)(90, 96, 101, 97)(92, 95, 102, 99)(98, 105, 109, 104)(100, 107, 110, 103)(106, 112, 117, 113)(108, 111, 118, 115)(114, 121, 124, 120)(116, 123, 125, 119)(122, 126, 128, 127) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4^4 ), ( 4^16 ) } Outer automorphisms :: reflexible Dual of E7.498 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 64 f = 32 degree seq :: [ 4^16, 16^4 ] E7.495 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 16}) Quotient :: edge Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, 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, 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, 60)(55, 62)(57, 63)(61, 64)(65, 66, 69, 75, 84, 93, 101, 109, 117, 116, 108, 100, 92, 83, 74, 68)(67, 71, 79, 89, 97, 105, 113, 121, 124, 119, 110, 103, 94, 86, 76, 72)(70, 77, 73, 82, 91, 99, 107, 115, 123, 125, 118, 111, 102, 95, 85, 78)(80, 87, 81, 88, 96, 104, 112, 120, 126, 128, 127, 122, 114, 106, 98, 90) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 8 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E7.496 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 64 f = 16 degree seq :: [ 2^32, 16^4 ] E7.496 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 16}) Quotient :: loop Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^16 ] Map:: R = (1, 65, 3, 67, 8, 72, 4, 68)(2, 66, 5, 69, 11, 75, 6, 70)(7, 71, 13, 77, 9, 73, 14, 78)(10, 74, 15, 79, 12, 76, 16, 80)(17, 81, 21, 85, 18, 82, 22, 86)(19, 83, 23, 87, 20, 84, 24, 88)(25, 89, 29, 93, 26, 90, 30, 94)(27, 91, 31, 95, 28, 92, 32, 96)(33, 97, 37, 101, 34, 98, 38, 102)(35, 99, 39, 103, 36, 100, 40, 104)(41, 105, 45, 109, 42, 106, 46, 110)(43, 107, 47, 111, 44, 108, 48, 112)(49, 113, 53, 117, 50, 114, 54, 118)(51, 115, 55, 119, 52, 116, 56, 120)(57, 121, 61, 125, 58, 122, 62, 126)(59, 123, 63, 127, 60, 124, 64, 128) L = (1, 66)(2, 65)(3, 71)(4, 73)(5, 74)(6, 76)(7, 67)(8, 75)(9, 68)(10, 69)(11, 72)(12, 70)(13, 81)(14, 82)(15, 83)(16, 84)(17, 77)(18, 78)(19, 79)(20, 80)(21, 89)(22, 90)(23, 91)(24, 92)(25, 85)(26, 86)(27, 87)(28, 88)(29, 97)(30, 98)(31, 99)(32, 100)(33, 93)(34, 94)(35, 95)(36, 96)(37, 105)(38, 106)(39, 107)(40, 108)(41, 101)(42, 102)(43, 103)(44, 104)(45, 113)(46, 114)(47, 115)(48, 116)(49, 109)(50, 110)(51, 111)(52, 112)(53, 121)(54, 122)(55, 123)(56, 124)(57, 117)(58, 118)(59, 119)(60, 120)(61, 127)(62, 128)(63, 125)(64, 126) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E7.495 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 64 f = 36 degree seq :: [ 8^16 ] E7.497 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 16}) Quotient :: loop Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^16 ] Map:: R = (1, 65, 3, 67, 10, 74, 18, 82, 26, 90, 34, 98, 42, 106, 50, 114, 58, 122, 52, 116, 44, 108, 36, 100, 28, 92, 20, 84, 12, 76, 5, 69)(2, 66, 7, 71, 15, 79, 23, 87, 31, 95, 39, 103, 47, 111, 55, 119, 62, 126, 56, 120, 48, 112, 40, 104, 32, 96, 24, 88, 16, 80, 8, 72)(4, 68, 11, 75, 19, 83, 27, 91, 35, 99, 43, 107, 51, 115, 59, 123, 63, 127, 57, 121, 49, 113, 41, 105, 33, 97, 25, 89, 17, 81, 9, 73)(6, 70, 13, 77, 21, 85, 29, 93, 37, 101, 45, 109, 53, 117, 60, 124, 64, 128, 61, 125, 54, 118, 46, 110, 38, 102, 30, 94, 22, 86, 14, 78) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 75)(6, 68)(7, 69)(8, 67)(9, 77)(10, 80)(11, 78)(12, 79)(13, 72)(14, 71)(15, 86)(16, 85)(17, 74)(18, 89)(19, 76)(20, 91)(21, 81)(22, 83)(23, 84)(24, 82)(25, 93)(26, 96)(27, 94)(28, 95)(29, 88)(30, 87)(31, 102)(32, 101)(33, 90)(34, 105)(35, 92)(36, 107)(37, 97)(38, 99)(39, 100)(40, 98)(41, 109)(42, 112)(43, 110)(44, 111)(45, 104)(46, 103)(47, 118)(48, 117)(49, 106)(50, 121)(51, 108)(52, 123)(53, 113)(54, 115)(55, 116)(56, 114)(57, 124)(58, 126)(59, 125)(60, 120)(61, 119)(62, 128)(63, 122)(64, 127) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E7.493 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 64 f = 48 degree seq :: [ 32^4 ] E7.498 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 16}) Quotient :: loop Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^16 ] Map:: polytopal non-degenerate R = (1, 65, 3, 67)(2, 66, 6, 70)(4, 68, 9, 73)(5, 69, 12, 76)(7, 71, 16, 80)(8, 72, 17, 81)(10, 74, 15, 79)(11, 75, 21, 85)(13, 77, 23, 87)(14, 78, 24, 88)(18, 82, 26, 90)(19, 83, 27, 91)(20, 84, 30, 94)(22, 86, 32, 96)(25, 89, 34, 98)(28, 92, 33, 97)(29, 93, 38, 102)(31, 95, 40, 104)(35, 99, 42, 106)(36, 100, 43, 107)(37, 101, 46, 110)(39, 103, 48, 112)(41, 105, 50, 114)(44, 108, 49, 113)(45, 109, 54, 118)(47, 111, 56, 120)(51, 115, 58, 122)(52, 116, 59, 123)(53, 117, 60, 124)(55, 119, 62, 126)(57, 121, 63, 127)(61, 125, 64, 128) L = (1, 66)(2, 69)(3, 71)(4, 65)(5, 75)(6, 77)(7, 79)(8, 67)(9, 82)(10, 68)(11, 84)(12, 72)(13, 73)(14, 70)(15, 89)(16, 87)(17, 88)(18, 91)(19, 74)(20, 93)(21, 78)(22, 76)(23, 81)(24, 96)(25, 97)(26, 80)(27, 99)(28, 83)(29, 101)(30, 86)(31, 85)(32, 104)(33, 105)(34, 90)(35, 107)(36, 92)(37, 109)(38, 95)(39, 94)(40, 112)(41, 113)(42, 98)(43, 115)(44, 100)(45, 117)(46, 103)(47, 102)(48, 120)(49, 121)(50, 106)(51, 123)(52, 108)(53, 116)(54, 111)(55, 110)(56, 126)(57, 124)(58, 114)(59, 125)(60, 119)(61, 118)(62, 128)(63, 122)(64, 127) local type(s) :: { ( 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E7.494 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 32 e = 64 f = 20 degree seq :: [ 4^32 ] E7.499 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^16 ] Map:: R = (1, 65, 2, 66)(3, 67, 7, 71)(4, 68, 9, 73)(5, 69, 10, 74)(6, 70, 12, 76)(8, 72, 11, 75)(13, 77, 17, 81)(14, 78, 18, 82)(15, 79, 19, 83)(16, 80, 20, 84)(21, 85, 25, 89)(22, 86, 26, 90)(23, 87, 27, 91)(24, 88, 28, 92)(29, 93, 33, 97)(30, 94, 34, 98)(31, 95, 35, 99)(32, 96, 36, 100)(37, 101, 41, 105)(38, 102, 42, 106)(39, 103, 43, 107)(40, 104, 44, 108)(45, 109, 49, 113)(46, 110, 50, 114)(47, 111, 51, 115)(48, 112, 52, 116)(53, 117, 57, 121)(54, 118, 58, 122)(55, 119, 59, 123)(56, 120, 60, 124)(61, 125, 63, 127)(62, 126, 64, 128)(129, 193, 131, 195, 136, 200, 132, 196)(130, 194, 133, 197, 139, 203, 134, 198)(135, 199, 141, 205, 137, 201, 142, 206)(138, 202, 143, 207, 140, 204, 144, 208)(145, 209, 149, 213, 146, 210, 150, 214)(147, 211, 151, 215, 148, 212, 152, 216)(153, 217, 157, 221, 154, 218, 158, 222)(155, 219, 159, 223, 156, 220, 160, 224)(161, 225, 165, 229, 162, 226, 166, 230)(163, 227, 167, 231, 164, 228, 168, 232)(169, 233, 173, 237, 170, 234, 174, 238)(171, 235, 175, 239, 172, 236, 176, 240)(177, 241, 181, 245, 178, 242, 182, 246)(179, 243, 183, 247, 180, 244, 184, 248)(185, 249, 189, 253, 186, 250, 190, 254)(187, 251, 191, 255, 188, 252, 192, 256) L = (1, 130)(2, 129)(3, 135)(4, 137)(5, 138)(6, 140)(7, 131)(8, 139)(9, 132)(10, 133)(11, 136)(12, 134)(13, 145)(14, 146)(15, 147)(16, 148)(17, 141)(18, 142)(19, 143)(20, 144)(21, 153)(22, 154)(23, 155)(24, 156)(25, 149)(26, 150)(27, 151)(28, 152)(29, 161)(30, 162)(31, 163)(32, 164)(33, 157)(34, 158)(35, 159)(36, 160)(37, 169)(38, 170)(39, 171)(40, 172)(41, 165)(42, 166)(43, 167)(44, 168)(45, 177)(46, 178)(47, 179)(48, 180)(49, 173)(50, 174)(51, 175)(52, 176)(53, 185)(54, 186)(55, 187)(56, 188)(57, 181)(58, 182)(59, 183)(60, 184)(61, 191)(62, 192)(63, 189)(64, 190)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E7.502 Graph:: bipartite v = 48 e = 128 f = 68 degree seq :: [ 4^32, 8^16 ] E7.500 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y2^16 ] Map:: R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 13, 77, 8, 72)(5, 69, 11, 75, 14, 78, 7, 71)(10, 74, 16, 80, 21, 85, 17, 81)(12, 76, 15, 79, 22, 86, 19, 83)(18, 82, 25, 89, 29, 93, 24, 88)(20, 84, 27, 91, 30, 94, 23, 87)(26, 90, 32, 96, 37, 101, 33, 97)(28, 92, 31, 95, 38, 102, 35, 99)(34, 98, 41, 105, 45, 109, 40, 104)(36, 100, 43, 107, 46, 110, 39, 103)(42, 106, 48, 112, 53, 117, 49, 113)(44, 108, 47, 111, 54, 118, 51, 115)(50, 114, 57, 121, 60, 124, 56, 120)(52, 116, 59, 123, 61, 125, 55, 119)(58, 122, 62, 126, 64, 128, 63, 127)(129, 193, 131, 195, 138, 202, 146, 210, 154, 218, 162, 226, 170, 234, 178, 242, 186, 250, 180, 244, 172, 236, 164, 228, 156, 220, 148, 212, 140, 204, 133, 197)(130, 194, 135, 199, 143, 207, 151, 215, 159, 223, 167, 231, 175, 239, 183, 247, 190, 254, 184, 248, 176, 240, 168, 232, 160, 224, 152, 216, 144, 208, 136, 200)(132, 196, 139, 203, 147, 211, 155, 219, 163, 227, 171, 235, 179, 243, 187, 251, 191, 255, 185, 249, 177, 241, 169, 233, 161, 225, 153, 217, 145, 209, 137, 201)(134, 198, 141, 205, 149, 213, 157, 221, 165, 229, 173, 237, 181, 245, 188, 252, 192, 256, 189, 253, 182, 246, 174, 238, 166, 230, 158, 222, 150, 214, 142, 206) L = (1, 131)(2, 135)(3, 138)(4, 139)(5, 129)(6, 141)(7, 143)(8, 130)(9, 132)(10, 146)(11, 147)(12, 133)(13, 149)(14, 134)(15, 151)(16, 136)(17, 137)(18, 154)(19, 155)(20, 140)(21, 157)(22, 142)(23, 159)(24, 144)(25, 145)(26, 162)(27, 163)(28, 148)(29, 165)(30, 150)(31, 167)(32, 152)(33, 153)(34, 170)(35, 171)(36, 156)(37, 173)(38, 158)(39, 175)(40, 160)(41, 161)(42, 178)(43, 179)(44, 164)(45, 181)(46, 166)(47, 183)(48, 168)(49, 169)(50, 186)(51, 187)(52, 172)(53, 188)(54, 174)(55, 190)(56, 176)(57, 177)(58, 180)(59, 191)(60, 192)(61, 182)(62, 184)(63, 185)(64, 189)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 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 E7.501 Graph:: bipartite v = 20 e = 128 f = 96 degree seq :: [ 8^16, 32^4 ] E7.501 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y1, 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, Y3^6 * Y2 * Y3^-10 * Y2, (Y3^-1 * Y1^-1)^16 ] Map:: polytopal R = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)(129, 193, 130, 194)(131, 195, 135, 199)(132, 196, 137, 201)(133, 197, 139, 203)(134, 198, 141, 205)(136, 200, 142, 206)(138, 202, 140, 204)(143, 207, 148, 212)(144, 208, 151, 215)(145, 209, 153, 217)(146, 210, 149, 213)(147, 211, 155, 219)(150, 214, 157, 221)(152, 216, 159, 223)(154, 218, 160, 224)(156, 220, 158, 222)(161, 225, 167, 231)(162, 226, 169, 233)(163, 227, 165, 229)(164, 228, 171, 235)(166, 230, 173, 237)(168, 232, 175, 239)(170, 234, 176, 240)(172, 236, 174, 238)(177, 241, 183, 247)(178, 242, 185, 249)(179, 243, 181, 245)(180, 244, 187, 251)(182, 246, 188, 252)(184, 248, 190, 254)(186, 250, 189, 253)(191, 255, 192, 256) L = (1, 131)(2, 133)(3, 136)(4, 129)(5, 140)(6, 130)(7, 143)(8, 145)(9, 146)(10, 132)(11, 148)(12, 150)(13, 151)(14, 134)(15, 137)(16, 135)(17, 154)(18, 155)(19, 138)(20, 141)(21, 139)(22, 158)(23, 159)(24, 142)(25, 144)(26, 162)(27, 163)(28, 147)(29, 149)(30, 166)(31, 167)(32, 152)(33, 153)(34, 170)(35, 171)(36, 156)(37, 157)(38, 174)(39, 175)(40, 160)(41, 161)(42, 178)(43, 179)(44, 164)(45, 165)(46, 182)(47, 183)(48, 168)(49, 169)(50, 186)(51, 187)(52, 172)(53, 173)(54, 189)(55, 190)(56, 176)(57, 177)(58, 180)(59, 191)(60, 181)(61, 184)(62, 192)(63, 185)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32 ), ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E7.500 Graph:: simple bipartite v = 96 e = 128 f = 20 degree seq :: [ 2^64, 4^32 ] E7.502 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1)^4, Y1^16 ] Map:: polytopal R = (1, 65, 2, 66, 5, 69, 11, 75, 20, 84, 29, 93, 37, 101, 45, 109, 53, 117, 52, 116, 44, 108, 36, 100, 28, 92, 19, 83, 10, 74, 4, 68)(3, 67, 7, 71, 15, 79, 25, 89, 33, 97, 41, 105, 49, 113, 57, 121, 60, 124, 55, 119, 46, 110, 39, 103, 30, 94, 22, 86, 12, 76, 8, 72)(6, 70, 13, 77, 9, 73, 18, 82, 27, 91, 35, 99, 43, 107, 51, 115, 59, 123, 61, 125, 54, 118, 47, 111, 38, 102, 31, 95, 21, 85, 14, 78)(16, 80, 23, 87, 17, 81, 24, 88, 32, 96, 40, 104, 48, 112, 56, 120, 62, 126, 64, 128, 63, 127, 58, 122, 50, 114, 42, 106, 34, 98, 26, 90)(129, 193)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256) L = (1, 131)(2, 134)(3, 129)(4, 137)(5, 140)(6, 130)(7, 144)(8, 145)(9, 132)(10, 143)(11, 149)(12, 133)(13, 151)(14, 152)(15, 138)(16, 135)(17, 136)(18, 154)(19, 155)(20, 158)(21, 139)(22, 160)(23, 141)(24, 142)(25, 162)(26, 146)(27, 147)(28, 161)(29, 166)(30, 148)(31, 168)(32, 150)(33, 156)(34, 153)(35, 170)(36, 171)(37, 174)(38, 157)(39, 176)(40, 159)(41, 178)(42, 163)(43, 164)(44, 177)(45, 182)(46, 165)(47, 184)(48, 167)(49, 172)(50, 169)(51, 186)(52, 187)(53, 188)(54, 173)(55, 190)(56, 175)(57, 191)(58, 179)(59, 180)(60, 181)(61, 192)(62, 183)(63, 185)(64, 189)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.499 Graph:: simple bipartite v = 68 e = 128 f = 48 degree seq :: [ 2^64, 32^4 ] E7.503 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^16 ] Map:: R = (1, 65, 2, 66)(3, 67, 7, 71)(4, 68, 9, 73)(5, 69, 11, 75)(6, 70, 13, 77)(8, 72, 14, 78)(10, 74, 12, 76)(15, 79, 20, 84)(16, 80, 23, 87)(17, 81, 25, 89)(18, 82, 21, 85)(19, 83, 27, 91)(22, 86, 29, 93)(24, 88, 31, 95)(26, 90, 32, 96)(28, 92, 30, 94)(33, 97, 39, 103)(34, 98, 41, 105)(35, 99, 37, 101)(36, 100, 43, 107)(38, 102, 45, 109)(40, 104, 47, 111)(42, 106, 48, 112)(44, 108, 46, 110)(49, 113, 55, 119)(50, 114, 57, 121)(51, 115, 53, 117)(52, 116, 59, 123)(54, 118, 60, 124)(56, 120, 62, 126)(58, 122, 61, 125)(63, 127, 64, 128)(129, 193, 131, 195, 136, 200, 145, 209, 154, 218, 162, 226, 170, 234, 178, 242, 186, 250, 180, 244, 172, 236, 164, 228, 156, 220, 147, 211, 138, 202, 132, 196)(130, 194, 133, 197, 140, 204, 150, 214, 158, 222, 166, 230, 174, 238, 182, 246, 189, 253, 184, 248, 176, 240, 168, 232, 160, 224, 152, 216, 142, 206, 134, 198)(135, 199, 143, 207, 137, 201, 146, 210, 155, 219, 163, 227, 171, 235, 179, 243, 187, 251, 191, 255, 185, 249, 177, 241, 169, 233, 161, 225, 153, 217, 144, 208)(139, 203, 148, 212, 141, 205, 151, 215, 159, 223, 167, 231, 175, 239, 183, 247, 190, 254, 192, 256, 188, 252, 181, 245, 173, 237, 165, 229, 157, 221, 149, 213) L = (1, 130)(2, 129)(3, 135)(4, 137)(5, 139)(6, 141)(7, 131)(8, 142)(9, 132)(10, 140)(11, 133)(12, 138)(13, 134)(14, 136)(15, 148)(16, 151)(17, 153)(18, 149)(19, 155)(20, 143)(21, 146)(22, 157)(23, 144)(24, 159)(25, 145)(26, 160)(27, 147)(28, 158)(29, 150)(30, 156)(31, 152)(32, 154)(33, 167)(34, 169)(35, 165)(36, 171)(37, 163)(38, 173)(39, 161)(40, 175)(41, 162)(42, 176)(43, 164)(44, 174)(45, 166)(46, 172)(47, 168)(48, 170)(49, 183)(50, 185)(51, 181)(52, 187)(53, 179)(54, 188)(55, 177)(56, 190)(57, 178)(58, 189)(59, 180)(60, 182)(61, 186)(62, 184)(63, 192)(64, 191)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 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 E7.504 Graph:: bipartite v = 36 e = 128 f = 80 degree seq :: [ 4^32, 32^4 ] E7.504 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^16 ] Map:: polytopal R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 13, 77, 8, 72)(5, 69, 11, 75, 14, 78, 7, 71)(10, 74, 16, 80, 21, 85, 17, 81)(12, 76, 15, 79, 22, 86, 19, 83)(18, 82, 25, 89, 29, 93, 24, 88)(20, 84, 27, 91, 30, 94, 23, 87)(26, 90, 32, 96, 37, 101, 33, 97)(28, 92, 31, 95, 38, 102, 35, 99)(34, 98, 41, 105, 45, 109, 40, 104)(36, 100, 43, 107, 46, 110, 39, 103)(42, 106, 48, 112, 53, 117, 49, 113)(44, 108, 47, 111, 54, 118, 51, 115)(50, 114, 57, 121, 60, 124, 56, 120)(52, 116, 59, 123, 61, 125, 55, 119)(58, 122, 62, 126, 64, 128, 63, 127)(129, 193)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256) L = (1, 131)(2, 135)(3, 138)(4, 139)(5, 129)(6, 141)(7, 143)(8, 130)(9, 132)(10, 146)(11, 147)(12, 133)(13, 149)(14, 134)(15, 151)(16, 136)(17, 137)(18, 154)(19, 155)(20, 140)(21, 157)(22, 142)(23, 159)(24, 144)(25, 145)(26, 162)(27, 163)(28, 148)(29, 165)(30, 150)(31, 167)(32, 152)(33, 153)(34, 170)(35, 171)(36, 156)(37, 173)(38, 158)(39, 175)(40, 160)(41, 161)(42, 178)(43, 179)(44, 164)(45, 181)(46, 166)(47, 183)(48, 168)(49, 169)(50, 186)(51, 187)(52, 172)(53, 188)(54, 174)(55, 190)(56, 176)(57, 177)(58, 180)(59, 191)(60, 192)(61, 182)(62, 184)(63, 185)(64, 189)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E7.503 Graph:: simple bipartite v = 80 e = 128 f = 36 degree seq :: [ 2^64, 8^16 ] E7.505 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 16}) Quotient :: regular Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, (T1^-1 * T2)^4, T2 * T1^6 * T2 * T1^-2, T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^3 * T2, (T1^-3 * T2 * T1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 45, 32, 54, 63, 61, 36, 57, 44, 22, 10, 4)(3, 7, 15, 31, 52, 26, 12, 25, 49, 42, 21, 41, 46, 37, 18, 8)(6, 13, 27, 53, 43, 48, 24, 47, 40, 20, 9, 19, 38, 58, 30, 14)(16, 33, 50, 29, 56, 62, 59, 39, 55, 28, 17, 35, 51, 64, 60, 34) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 39)(20, 33)(22, 43)(23, 46)(25, 50)(26, 51)(27, 54)(30, 57)(31, 59)(34, 53)(35, 47)(37, 56)(38, 45)(40, 61)(41, 60)(42, 55)(44, 52)(48, 62)(49, 63)(58, 64) local type(s) :: { ( 4^16 ) } Outer automorphisms :: reflexible Dual of E7.506 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 32 f = 16 degree seq :: [ 16^4 ] E7.506 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 16}) Quotient :: regular Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^4, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 32, 25)(15, 26, 33, 27)(21, 35, 29, 36)(22, 37, 30, 38)(23, 34, 44, 39)(40, 49, 42, 50)(41, 51, 43, 52)(45, 53, 47, 54)(46, 55, 48, 56)(57, 64, 59, 62)(58, 63, 60, 61) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 32)(19, 33)(20, 34)(24, 40)(25, 41)(26, 42)(27, 43)(28, 39)(31, 44)(35, 45)(36, 46)(37, 47)(38, 48)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64) local type(s) :: { ( 16^4 ) } Outer automorphisms :: reflexible Dual of E7.505 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 16 e = 32 f = 4 degree seq :: [ 4^16 ] E7.507 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 16}) Quotient :: edge Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2 * T1 * T2^-1, T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: polytopal R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 24, 14)(9, 16, 29, 17)(10, 18, 32, 19)(12, 21, 37, 22)(15, 26, 43, 27)(20, 34, 48, 35)(23, 39, 28, 40)(25, 41, 30, 42)(31, 44, 36, 45)(33, 46, 38, 47)(49, 57, 51, 58)(50, 59, 52, 60)(53, 61, 55, 62)(54, 63, 56, 64)(65, 66)(67, 71)(68, 73)(69, 74)(70, 76)(72, 79)(75, 84)(77, 87)(78, 89)(80, 92)(81, 94)(82, 95)(83, 97)(85, 100)(86, 102)(88, 98)(90, 96)(91, 101)(93, 99)(103, 113)(104, 114)(105, 115)(106, 116)(107, 112)(108, 117)(109, 118)(110, 119)(111, 120)(121, 128)(122, 126)(123, 127)(124, 125) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 32 ), ( 32^4 ) } Outer automorphisms :: reflexible Dual of E7.511 Transitivity :: ET+ Graph:: simple bipartite v = 48 e = 64 f = 4 degree seq :: [ 2^32, 4^16 ] E7.508 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 16}) Quotient :: edge Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1^-1, (T2^3 * T1^-1)^2, (T2 * T1^-1)^4, T2 * T1^-1 * T2^-7 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 24, 48, 56, 39, 28, 42, 19, 41, 58, 52, 32, 14, 5)(2, 7, 17, 38, 57, 46, 23, 11, 26, 35, 31, 51, 60, 44, 20, 8)(4, 12, 27, 49, 62, 47, 25, 34, 30, 13, 29, 50, 61, 45, 22, 9)(6, 15, 33, 53, 63, 55, 37, 18, 40, 21, 43, 59, 64, 54, 36, 16)(65, 66, 70, 68)(67, 73, 85, 75)(69, 77, 82, 71)(72, 83, 98, 79)(74, 87, 97, 89)(76, 80, 99, 92)(78, 95, 100, 93)(81, 101, 91, 103)(84, 107, 86, 105)(88, 111, 123, 108)(90, 104, 94, 106)(96, 113, 119, 115)(102, 120, 114, 118)(109, 117, 110, 122)(112, 124, 127, 125)(116, 121, 128, 126) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4^4 ), ( 4^16 ) } Outer automorphisms :: reflexible Dual of E7.512 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 64 f = 32 degree seq :: [ 4^16, 16^4 ] E7.509 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 16}) Quotient :: edge Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, T2 * T1^6 * T2 * T1^-2, T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^3 * T2, (T1^-3 * T2 * T1^-1)^2 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 39)(20, 33)(22, 43)(23, 46)(25, 50)(26, 51)(27, 54)(30, 57)(31, 59)(34, 53)(35, 47)(37, 56)(38, 45)(40, 61)(41, 60)(42, 55)(44, 52)(48, 62)(49, 63)(58, 64)(65, 66, 69, 75, 87, 109, 96, 118, 127, 125, 100, 121, 108, 86, 74, 68)(67, 71, 79, 95, 116, 90, 76, 89, 113, 106, 85, 105, 110, 101, 82, 72)(70, 77, 91, 117, 107, 112, 88, 111, 104, 84, 73, 83, 102, 122, 94, 78)(80, 97, 114, 93, 120, 126, 123, 103, 119, 92, 81, 99, 115, 128, 124, 98) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 8 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E7.510 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 64 f = 16 degree seq :: [ 2^32, 16^4 ] E7.510 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 16}) Quotient :: loop Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2 * T1 * T2^-1, T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 65, 3, 67, 8, 72, 4, 68)(2, 66, 5, 69, 11, 75, 6, 70)(7, 71, 13, 77, 24, 88, 14, 78)(9, 73, 16, 80, 29, 93, 17, 81)(10, 74, 18, 82, 32, 96, 19, 83)(12, 76, 21, 85, 37, 101, 22, 86)(15, 79, 26, 90, 43, 107, 27, 91)(20, 84, 34, 98, 48, 112, 35, 99)(23, 87, 39, 103, 28, 92, 40, 104)(25, 89, 41, 105, 30, 94, 42, 106)(31, 95, 44, 108, 36, 100, 45, 109)(33, 97, 46, 110, 38, 102, 47, 111)(49, 113, 57, 121, 51, 115, 58, 122)(50, 114, 59, 123, 52, 116, 60, 124)(53, 117, 61, 125, 55, 119, 62, 126)(54, 118, 63, 127, 56, 120, 64, 128) L = (1, 66)(2, 65)(3, 71)(4, 73)(5, 74)(6, 76)(7, 67)(8, 79)(9, 68)(10, 69)(11, 84)(12, 70)(13, 87)(14, 89)(15, 72)(16, 92)(17, 94)(18, 95)(19, 97)(20, 75)(21, 100)(22, 102)(23, 77)(24, 98)(25, 78)(26, 96)(27, 101)(28, 80)(29, 99)(30, 81)(31, 82)(32, 90)(33, 83)(34, 88)(35, 93)(36, 85)(37, 91)(38, 86)(39, 113)(40, 114)(41, 115)(42, 116)(43, 112)(44, 117)(45, 118)(46, 119)(47, 120)(48, 107)(49, 103)(50, 104)(51, 105)(52, 106)(53, 108)(54, 109)(55, 110)(56, 111)(57, 128)(58, 126)(59, 127)(60, 125)(61, 124)(62, 122)(63, 123)(64, 121) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E7.509 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 64 f = 36 degree seq :: [ 8^16 ] E7.511 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 16}) Quotient :: loop Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1^-1, (T2^3 * T1^-1)^2, (T2 * T1^-1)^4, T2 * T1^-1 * T2^-7 * T1^-1 ] Map:: R = (1, 65, 3, 67, 10, 74, 24, 88, 48, 112, 56, 120, 39, 103, 28, 92, 42, 106, 19, 83, 41, 105, 58, 122, 52, 116, 32, 96, 14, 78, 5, 69)(2, 66, 7, 71, 17, 81, 38, 102, 57, 121, 46, 110, 23, 87, 11, 75, 26, 90, 35, 99, 31, 95, 51, 115, 60, 124, 44, 108, 20, 84, 8, 72)(4, 68, 12, 76, 27, 91, 49, 113, 62, 126, 47, 111, 25, 89, 34, 98, 30, 94, 13, 77, 29, 93, 50, 114, 61, 125, 45, 109, 22, 86, 9, 73)(6, 70, 15, 79, 33, 97, 53, 117, 63, 127, 55, 119, 37, 101, 18, 82, 40, 104, 21, 85, 43, 107, 59, 123, 64, 128, 54, 118, 36, 100, 16, 80) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 77)(6, 68)(7, 69)(8, 83)(9, 85)(10, 87)(11, 67)(12, 80)(13, 82)(14, 95)(15, 72)(16, 99)(17, 101)(18, 71)(19, 98)(20, 107)(21, 75)(22, 105)(23, 97)(24, 111)(25, 74)(26, 104)(27, 103)(28, 76)(29, 78)(30, 106)(31, 100)(32, 113)(33, 89)(34, 79)(35, 92)(36, 93)(37, 91)(38, 120)(39, 81)(40, 94)(41, 84)(42, 90)(43, 86)(44, 88)(45, 117)(46, 122)(47, 123)(48, 124)(49, 119)(50, 118)(51, 96)(52, 121)(53, 110)(54, 102)(55, 115)(56, 114)(57, 128)(58, 109)(59, 108)(60, 127)(61, 112)(62, 116)(63, 125)(64, 126) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E7.507 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 64 f = 48 degree seq :: [ 32^4 ] E7.512 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 16}) Quotient :: loop Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, T2 * T1^6 * T2 * T1^-2, T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^3 * T2, (T1^-3 * T2 * T1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 65, 3, 67)(2, 66, 6, 70)(4, 68, 9, 73)(5, 69, 12, 76)(7, 71, 16, 80)(8, 72, 17, 81)(10, 74, 21, 85)(11, 75, 24, 88)(13, 77, 28, 92)(14, 78, 29, 93)(15, 79, 32, 96)(18, 82, 36, 100)(19, 83, 39, 103)(20, 84, 33, 97)(22, 86, 43, 107)(23, 87, 46, 110)(25, 89, 50, 114)(26, 90, 51, 115)(27, 91, 54, 118)(30, 94, 57, 121)(31, 95, 59, 123)(34, 98, 53, 117)(35, 99, 47, 111)(37, 101, 56, 120)(38, 102, 45, 109)(40, 104, 61, 125)(41, 105, 60, 124)(42, 106, 55, 119)(44, 108, 52, 116)(48, 112, 62, 126)(49, 113, 63, 127)(58, 122, 64, 128) L = (1, 66)(2, 69)(3, 71)(4, 65)(5, 75)(6, 77)(7, 79)(8, 67)(9, 83)(10, 68)(11, 87)(12, 89)(13, 91)(14, 70)(15, 95)(16, 97)(17, 99)(18, 72)(19, 102)(20, 73)(21, 105)(22, 74)(23, 109)(24, 111)(25, 113)(26, 76)(27, 117)(28, 81)(29, 120)(30, 78)(31, 116)(32, 118)(33, 114)(34, 80)(35, 115)(36, 121)(37, 82)(38, 122)(39, 119)(40, 84)(41, 110)(42, 85)(43, 112)(44, 86)(45, 96)(46, 101)(47, 104)(48, 88)(49, 106)(50, 93)(51, 128)(52, 90)(53, 107)(54, 127)(55, 92)(56, 126)(57, 108)(58, 94)(59, 103)(60, 98)(61, 100)(62, 123)(63, 125)(64, 124) local type(s) :: { ( 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E7.508 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 32 e = 64 f = 20 degree seq :: [ 4^32 ] E7.513 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, R * Y2^-2 * R * Y1 * Y2^-2 * Y1, Y2^-1 * Y1 * Y2^-1 * R * Y2^2 * R * Y2 * Y1 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^16 ] Map:: R = (1, 65, 2, 66)(3, 67, 7, 71)(4, 68, 9, 73)(5, 69, 10, 74)(6, 70, 12, 76)(8, 72, 15, 79)(11, 75, 20, 84)(13, 77, 23, 87)(14, 78, 25, 89)(16, 80, 28, 92)(17, 81, 30, 94)(18, 82, 31, 95)(19, 83, 33, 97)(21, 85, 36, 100)(22, 86, 38, 102)(24, 88, 34, 98)(26, 90, 32, 96)(27, 91, 37, 101)(29, 93, 35, 99)(39, 103, 49, 113)(40, 104, 50, 114)(41, 105, 51, 115)(42, 106, 52, 116)(43, 107, 48, 112)(44, 108, 53, 117)(45, 109, 54, 118)(46, 110, 55, 119)(47, 111, 56, 120)(57, 121, 64, 128)(58, 122, 62, 126)(59, 123, 63, 127)(60, 124, 61, 125)(129, 193, 131, 195, 136, 200, 132, 196)(130, 194, 133, 197, 139, 203, 134, 198)(135, 199, 141, 205, 152, 216, 142, 206)(137, 201, 144, 208, 157, 221, 145, 209)(138, 202, 146, 210, 160, 224, 147, 211)(140, 204, 149, 213, 165, 229, 150, 214)(143, 207, 154, 218, 171, 235, 155, 219)(148, 212, 162, 226, 176, 240, 163, 227)(151, 215, 167, 231, 156, 220, 168, 232)(153, 217, 169, 233, 158, 222, 170, 234)(159, 223, 172, 236, 164, 228, 173, 237)(161, 225, 174, 238, 166, 230, 175, 239)(177, 241, 185, 249, 179, 243, 186, 250)(178, 242, 187, 251, 180, 244, 188, 252)(181, 245, 189, 253, 183, 247, 190, 254)(182, 246, 191, 255, 184, 248, 192, 256) L = (1, 130)(2, 129)(3, 135)(4, 137)(5, 138)(6, 140)(7, 131)(8, 143)(9, 132)(10, 133)(11, 148)(12, 134)(13, 151)(14, 153)(15, 136)(16, 156)(17, 158)(18, 159)(19, 161)(20, 139)(21, 164)(22, 166)(23, 141)(24, 162)(25, 142)(26, 160)(27, 165)(28, 144)(29, 163)(30, 145)(31, 146)(32, 154)(33, 147)(34, 152)(35, 157)(36, 149)(37, 155)(38, 150)(39, 177)(40, 178)(41, 179)(42, 180)(43, 176)(44, 181)(45, 182)(46, 183)(47, 184)(48, 171)(49, 167)(50, 168)(51, 169)(52, 170)(53, 172)(54, 173)(55, 174)(56, 175)(57, 192)(58, 190)(59, 191)(60, 189)(61, 188)(62, 186)(63, 187)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E7.516 Graph:: bipartite v = 48 e = 128 f = 68 degree seq :: [ 4^32, 8^16 ] E7.514 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, R * Y2 * R * Y3, (R * Y1)^2, Y1^4, Y1^-1 * Y2^-1 * Y1 * Y2^-2 * Y1 * Y2^-1 * Y1^-1, (Y2 * Y1^-1)^4, Y2 * Y1^-1 * Y2^-7 * Y1^-1 ] Map:: R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 21, 85, 11, 75)(5, 69, 13, 77, 18, 82, 7, 71)(8, 72, 19, 83, 34, 98, 15, 79)(10, 74, 23, 87, 33, 97, 25, 89)(12, 76, 16, 80, 35, 99, 28, 92)(14, 78, 31, 95, 36, 100, 29, 93)(17, 81, 37, 101, 27, 91, 39, 103)(20, 84, 43, 107, 22, 86, 41, 105)(24, 88, 47, 111, 59, 123, 44, 108)(26, 90, 40, 104, 30, 94, 42, 106)(32, 96, 49, 113, 55, 119, 51, 115)(38, 102, 56, 120, 50, 114, 54, 118)(45, 109, 53, 117, 46, 110, 58, 122)(48, 112, 60, 124, 63, 127, 61, 125)(52, 116, 57, 121, 64, 128, 62, 126)(129, 193, 131, 195, 138, 202, 152, 216, 176, 240, 184, 248, 167, 231, 156, 220, 170, 234, 147, 211, 169, 233, 186, 250, 180, 244, 160, 224, 142, 206, 133, 197)(130, 194, 135, 199, 145, 209, 166, 230, 185, 249, 174, 238, 151, 215, 139, 203, 154, 218, 163, 227, 159, 223, 179, 243, 188, 252, 172, 236, 148, 212, 136, 200)(132, 196, 140, 204, 155, 219, 177, 241, 190, 254, 175, 239, 153, 217, 162, 226, 158, 222, 141, 205, 157, 221, 178, 242, 189, 253, 173, 237, 150, 214, 137, 201)(134, 198, 143, 207, 161, 225, 181, 245, 191, 255, 183, 247, 165, 229, 146, 210, 168, 232, 149, 213, 171, 235, 187, 251, 192, 256, 182, 246, 164, 228, 144, 208) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 143)(7, 145)(8, 130)(9, 132)(10, 152)(11, 154)(12, 155)(13, 157)(14, 133)(15, 161)(16, 134)(17, 166)(18, 168)(19, 169)(20, 136)(21, 171)(22, 137)(23, 139)(24, 176)(25, 162)(26, 163)(27, 177)(28, 170)(29, 178)(30, 141)(31, 179)(32, 142)(33, 181)(34, 158)(35, 159)(36, 144)(37, 146)(38, 185)(39, 156)(40, 149)(41, 186)(42, 147)(43, 187)(44, 148)(45, 150)(46, 151)(47, 153)(48, 184)(49, 190)(50, 189)(51, 188)(52, 160)(53, 191)(54, 164)(55, 165)(56, 167)(57, 174)(58, 180)(59, 192)(60, 172)(61, 173)(62, 175)(63, 183)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 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 E7.515 Graph:: bipartite v = 20 e = 128 f = 96 degree seq :: [ 8^16, 32^4 ] E7.515 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^4, Y3^3 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2, Y3^-2 * Y2 * Y3^6 * Y2, (Y3^-1 * Y1^-1)^16 ] Map:: polytopal R = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)(129, 193, 130, 194)(131, 195, 135, 199)(132, 196, 137, 201)(133, 197, 139, 203)(134, 198, 141, 205)(136, 200, 145, 209)(138, 202, 149, 213)(140, 204, 153, 217)(142, 206, 157, 221)(143, 207, 156, 220)(144, 208, 160, 224)(146, 210, 164, 228)(147, 211, 166, 230)(148, 212, 151, 215)(150, 214, 171, 235)(152, 216, 174, 238)(154, 218, 178, 242)(155, 219, 180, 244)(158, 222, 185, 249)(159, 223, 176, 240)(161, 225, 183, 247)(162, 226, 173, 237)(163, 227, 181, 245)(165, 229, 186, 250)(167, 231, 177, 241)(168, 232, 184, 248)(169, 233, 175, 239)(170, 234, 182, 246)(172, 236, 179, 243)(187, 251, 190, 254)(188, 252, 191, 255)(189, 253, 192, 256) L = (1, 131)(2, 133)(3, 136)(4, 129)(5, 140)(6, 130)(7, 143)(8, 146)(9, 147)(10, 132)(11, 151)(12, 154)(13, 155)(14, 134)(15, 159)(16, 135)(17, 162)(18, 165)(19, 167)(20, 137)(21, 169)(22, 138)(23, 173)(24, 139)(25, 176)(26, 179)(27, 181)(28, 141)(29, 183)(30, 142)(31, 174)(32, 185)(33, 144)(34, 188)(35, 145)(36, 180)(37, 177)(38, 182)(39, 187)(40, 148)(41, 186)(42, 149)(43, 189)(44, 150)(45, 160)(46, 171)(47, 152)(48, 191)(49, 153)(50, 166)(51, 163)(52, 168)(53, 190)(54, 156)(55, 172)(56, 157)(57, 192)(58, 158)(59, 161)(60, 170)(61, 164)(62, 175)(63, 184)(64, 178)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32 ), ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E7.514 Graph:: simple bipartite v = 96 e = 128 f = 20 degree seq :: [ 2^64, 4^32 ] E7.516 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y3 * Y1^-1)^4, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-3, Y1^-2 * Y3 * Y1^2 * Y3 * Y1^-4 ] Map:: polytopal R = (1, 65, 2, 66, 5, 69, 11, 75, 23, 87, 45, 109, 32, 96, 54, 118, 63, 127, 61, 125, 36, 100, 57, 121, 44, 108, 22, 86, 10, 74, 4, 68)(3, 67, 7, 71, 15, 79, 31, 95, 52, 116, 26, 90, 12, 76, 25, 89, 49, 113, 42, 106, 21, 85, 41, 105, 46, 110, 37, 101, 18, 82, 8, 72)(6, 70, 13, 77, 27, 91, 53, 117, 43, 107, 48, 112, 24, 88, 47, 111, 40, 104, 20, 84, 9, 73, 19, 83, 38, 102, 58, 122, 30, 94, 14, 78)(16, 80, 33, 97, 50, 114, 29, 93, 56, 120, 62, 126, 59, 123, 39, 103, 55, 119, 28, 92, 17, 81, 35, 99, 51, 115, 64, 128, 60, 124, 34, 98)(129, 193)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256) L = (1, 131)(2, 134)(3, 129)(4, 137)(5, 140)(6, 130)(7, 144)(8, 145)(9, 132)(10, 149)(11, 152)(12, 133)(13, 156)(14, 157)(15, 160)(16, 135)(17, 136)(18, 164)(19, 167)(20, 161)(21, 138)(22, 171)(23, 174)(24, 139)(25, 178)(26, 179)(27, 182)(28, 141)(29, 142)(30, 185)(31, 187)(32, 143)(33, 148)(34, 181)(35, 175)(36, 146)(37, 184)(38, 173)(39, 147)(40, 189)(41, 188)(42, 183)(43, 150)(44, 180)(45, 166)(46, 151)(47, 163)(48, 190)(49, 191)(50, 153)(51, 154)(52, 172)(53, 162)(54, 155)(55, 170)(56, 165)(57, 158)(58, 192)(59, 159)(60, 169)(61, 168)(62, 176)(63, 177)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E7.513 Graph:: simple bipartite v = 68 e = 128 f = 48 degree seq :: [ 2^64, 32^4 ] E7.517 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * R * Y2^-1)^2, (Y2 * Y1)^4, (Y3 * Y2^-1)^4, Y2 * Y1 * Y2^-2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1, Y2^6 * Y1 * Y2^-2 * Y1, (Y2^-4 * Y1)^2 ] Map:: R = (1, 65, 2, 66)(3, 67, 7, 71)(4, 68, 9, 73)(5, 69, 11, 75)(6, 70, 13, 77)(8, 72, 17, 81)(10, 74, 21, 85)(12, 76, 25, 89)(14, 78, 29, 93)(15, 79, 28, 92)(16, 80, 32, 96)(18, 82, 36, 100)(19, 83, 38, 102)(20, 84, 23, 87)(22, 86, 43, 107)(24, 88, 46, 110)(26, 90, 50, 114)(27, 91, 52, 116)(30, 94, 57, 121)(31, 95, 48, 112)(33, 97, 55, 119)(34, 98, 45, 109)(35, 99, 53, 117)(37, 101, 58, 122)(39, 103, 49, 113)(40, 104, 56, 120)(41, 105, 47, 111)(42, 106, 54, 118)(44, 108, 51, 115)(59, 123, 62, 126)(60, 124, 63, 127)(61, 125, 64, 128)(129, 193, 131, 195, 136, 200, 146, 210, 165, 229, 177, 241, 153, 217, 176, 240, 191, 255, 184, 248, 157, 221, 183, 247, 172, 236, 150, 214, 138, 202, 132, 196)(130, 194, 133, 197, 140, 204, 154, 218, 179, 243, 163, 227, 145, 209, 162, 226, 188, 252, 170, 234, 149, 213, 169, 233, 186, 250, 158, 222, 142, 206, 134, 198)(135, 199, 143, 207, 159, 223, 174, 238, 171, 235, 189, 253, 164, 228, 180, 244, 168, 232, 148, 212, 137, 201, 147, 211, 167, 231, 187, 251, 161, 225, 144, 208)(139, 203, 151, 215, 173, 237, 160, 224, 185, 249, 192, 256, 178, 242, 166, 230, 182, 246, 156, 220, 141, 205, 155, 219, 181, 245, 190, 254, 175, 239, 152, 216) L = (1, 130)(2, 129)(3, 135)(4, 137)(5, 139)(6, 141)(7, 131)(8, 145)(9, 132)(10, 149)(11, 133)(12, 153)(13, 134)(14, 157)(15, 156)(16, 160)(17, 136)(18, 164)(19, 166)(20, 151)(21, 138)(22, 171)(23, 148)(24, 174)(25, 140)(26, 178)(27, 180)(28, 143)(29, 142)(30, 185)(31, 176)(32, 144)(33, 183)(34, 173)(35, 181)(36, 146)(37, 186)(38, 147)(39, 177)(40, 184)(41, 175)(42, 182)(43, 150)(44, 179)(45, 162)(46, 152)(47, 169)(48, 159)(49, 167)(50, 154)(51, 172)(52, 155)(53, 163)(54, 170)(55, 161)(56, 168)(57, 158)(58, 165)(59, 190)(60, 191)(61, 192)(62, 187)(63, 188)(64, 189)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E7.518 Graph:: bipartite v = 36 e = 128 f = 80 degree seq :: [ 4^32, 32^4 ] E7.518 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-2 * Y1^-2, Y3 * Y1^-2 * Y3 * Y1^-1 * Y3^2 * Y1^-1, (Y3^-1 * Y1)^4, Y3^2 * Y1^-1 * Y3^-6 * Y1, (Y3 * Y2^-1)^16 ] Map:: polytopal R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 21, 85, 11, 75)(5, 69, 13, 77, 18, 82, 7, 71)(8, 72, 19, 83, 34, 98, 15, 79)(10, 74, 23, 87, 33, 97, 25, 89)(12, 76, 16, 80, 35, 99, 28, 92)(14, 78, 31, 95, 36, 100, 29, 93)(17, 81, 37, 101, 27, 91, 39, 103)(20, 84, 43, 107, 22, 86, 41, 105)(24, 88, 47, 111, 59, 123, 44, 108)(26, 90, 40, 104, 30, 94, 42, 106)(32, 96, 49, 113, 55, 119, 51, 115)(38, 102, 56, 120, 50, 114, 54, 118)(45, 109, 53, 117, 46, 110, 58, 122)(48, 112, 60, 124, 63, 127, 61, 125)(52, 116, 57, 121, 64, 128, 62, 126)(129, 193)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 143)(7, 145)(8, 130)(9, 132)(10, 152)(11, 154)(12, 155)(13, 157)(14, 133)(15, 161)(16, 134)(17, 166)(18, 168)(19, 169)(20, 136)(21, 171)(22, 137)(23, 139)(24, 176)(25, 162)(26, 163)(27, 177)(28, 170)(29, 178)(30, 141)(31, 179)(32, 142)(33, 181)(34, 158)(35, 159)(36, 144)(37, 146)(38, 185)(39, 156)(40, 149)(41, 186)(42, 147)(43, 187)(44, 148)(45, 150)(46, 151)(47, 153)(48, 184)(49, 190)(50, 189)(51, 188)(52, 160)(53, 191)(54, 164)(55, 165)(56, 167)(57, 174)(58, 180)(59, 192)(60, 172)(61, 173)(62, 175)(63, 183)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E7.517 Graph:: simple bipartite v = 80 e = 128 f = 36 degree seq :: [ 2^64, 8^16 ] E7.519 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 3, 6}) Quotient :: edge Aut^+ = C3 x SL(2,3) (small group id <72, 25>) Aut = (C3 x SL(2,3)) : C2 (small group id <144, 125>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1 * T1^-1)^3, T2^6, T2^2 * T1^-1 * T2^3 * T1 * T2, T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 9, 25, 15, 5)(2, 6, 17, 41, 21, 7)(4, 11, 30, 55, 33, 12)(8, 22, 50, 37, 52, 23)(10, 27, 56, 38, 58, 28)(13, 34, 54, 24, 53, 35)(14, 36, 48, 26, 39, 16)(18, 43, 51, 49, 70, 44)(19, 45, 69, 40, 68, 46)(20, 47, 64, 42, 59, 29)(31, 57, 67, 65, 72, 61)(32, 62, 71, 60, 66, 63)(73, 74, 76)(75, 80, 82)(77, 85, 86)(78, 88, 90)(79, 91, 92)(81, 96, 98)(83, 101, 103)(84, 104, 94)(87, 109, 110)(89, 112, 114)(93, 120, 121)(95, 117, 123)(97, 113, 127)(99, 115, 129)(100, 119, 125)(102, 132, 124)(105, 136, 137)(106, 128, 131)(107, 118, 135)(108, 138, 133)(111, 134, 139)(116, 122, 140)(126, 141, 143)(130, 142, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6^3 ), ( 6^6 ) } Outer automorphisms :: reflexible Dual of E7.520 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 72 f = 24 degree seq :: [ 3^24, 6^12 ] E7.520 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 3, 6}) Quotient :: loop Aut^+ = C3 x SL(2,3) (small group id <72, 25>) Aut = (C3 x SL(2,3)) : C2 (small group id <144, 125>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^3, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1, T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1^-1, (T2^-1 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 5, 77)(2, 74, 6, 78, 7, 79)(4, 76, 10, 82, 11, 83)(8, 80, 18, 90, 19, 91)(9, 81, 20, 92, 21, 93)(12, 84, 26, 98, 27, 99)(13, 85, 28, 100, 29, 101)(14, 86, 30, 102, 31, 103)(15, 87, 32, 104, 33, 105)(16, 88, 34, 106, 35, 107)(17, 89, 36, 108, 37, 109)(22, 94, 43, 115, 44, 116)(23, 95, 41, 113, 45, 117)(24, 96, 46, 118, 47, 119)(25, 97, 48, 120, 49, 121)(38, 110, 60, 132, 59, 131)(39, 111, 51, 123, 61, 133)(40, 112, 52, 124, 62, 134)(42, 114, 63, 135, 55, 127)(50, 122, 66, 138, 68, 140)(53, 125, 64, 136, 69, 141)(54, 126, 70, 142, 67, 139)(56, 128, 58, 130, 71, 143)(57, 129, 72, 144, 65, 137) L = (1, 74)(2, 76)(3, 80)(4, 73)(5, 84)(6, 86)(7, 88)(8, 81)(9, 75)(10, 94)(11, 96)(12, 85)(13, 77)(14, 87)(15, 78)(16, 89)(17, 79)(18, 110)(19, 106)(20, 104)(21, 108)(22, 95)(23, 82)(24, 97)(25, 83)(26, 122)(27, 107)(28, 123)(29, 124)(30, 126)(31, 118)(32, 113)(33, 120)(34, 112)(35, 119)(36, 114)(37, 130)(38, 111)(39, 90)(40, 91)(41, 92)(42, 93)(43, 136)(44, 98)(45, 100)(46, 128)(47, 99)(48, 129)(49, 138)(50, 116)(51, 117)(52, 125)(53, 101)(54, 127)(55, 102)(56, 103)(57, 105)(58, 131)(59, 109)(60, 142)(61, 135)(62, 143)(63, 144)(64, 137)(65, 115)(66, 139)(67, 121)(68, 134)(69, 132)(70, 141)(71, 140)(72, 133) local type(s) :: { ( 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: reflexible Dual of E7.519 Transitivity :: ET+ VT+ AT Graph:: simple v = 24 e = 72 f = 36 degree seq :: [ 6^24 ] E7.521 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 6}) Quotient :: dipole Aut^+ = C3 x SL(2,3) (small group id <72, 25>) Aut = (C3 x SL(2,3)) : C2 (small group id <144, 125>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1^-1)^3, Y2^6, (Y3^-1 * Y1^-1)^3, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y2^2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 73, 2, 74, 4, 76)(3, 75, 8, 80, 10, 82)(5, 77, 13, 85, 14, 86)(6, 78, 16, 88, 18, 90)(7, 79, 19, 91, 20, 92)(9, 81, 24, 96, 26, 98)(11, 83, 29, 101, 31, 103)(12, 84, 32, 104, 22, 94)(15, 87, 37, 109, 38, 110)(17, 89, 40, 112, 42, 114)(21, 93, 48, 120, 49, 121)(23, 95, 45, 117, 51, 123)(25, 97, 41, 113, 55, 127)(27, 99, 43, 115, 57, 129)(28, 100, 47, 119, 53, 125)(30, 102, 60, 132, 52, 124)(33, 105, 64, 136, 65, 137)(34, 106, 56, 128, 59, 131)(35, 107, 46, 118, 63, 135)(36, 108, 66, 138, 61, 133)(39, 111, 62, 134, 67, 139)(44, 116, 50, 122, 68, 140)(54, 126, 69, 141, 71, 143)(58, 130, 70, 142, 72, 144)(145, 217, 147, 219, 153, 225, 169, 241, 159, 231, 149, 221)(146, 218, 150, 222, 161, 233, 185, 257, 165, 237, 151, 223)(148, 220, 155, 227, 174, 246, 199, 271, 177, 249, 156, 228)(152, 224, 166, 238, 194, 266, 181, 253, 196, 268, 167, 239)(154, 226, 171, 243, 200, 272, 182, 254, 202, 274, 172, 244)(157, 229, 178, 250, 198, 270, 168, 240, 197, 269, 179, 251)(158, 230, 180, 252, 192, 264, 170, 242, 183, 255, 160, 232)(162, 234, 187, 259, 195, 267, 193, 265, 214, 286, 188, 260)(163, 235, 189, 261, 213, 285, 184, 256, 212, 284, 190, 262)(164, 236, 191, 263, 208, 280, 186, 258, 203, 275, 173, 245)(175, 247, 201, 273, 211, 283, 209, 281, 216, 288, 205, 277)(176, 248, 206, 278, 215, 287, 204, 276, 210, 282, 207, 279) L = (1, 147)(2, 150)(3, 153)(4, 155)(5, 145)(6, 161)(7, 146)(8, 166)(9, 169)(10, 171)(11, 174)(12, 148)(13, 178)(14, 180)(15, 149)(16, 158)(17, 185)(18, 187)(19, 189)(20, 191)(21, 151)(22, 194)(23, 152)(24, 197)(25, 159)(26, 183)(27, 200)(28, 154)(29, 164)(30, 199)(31, 201)(32, 206)(33, 156)(34, 198)(35, 157)(36, 192)(37, 196)(38, 202)(39, 160)(40, 212)(41, 165)(42, 203)(43, 195)(44, 162)(45, 213)(46, 163)(47, 208)(48, 170)(49, 214)(50, 181)(51, 193)(52, 167)(53, 179)(54, 168)(55, 177)(56, 182)(57, 211)(58, 172)(59, 173)(60, 210)(61, 175)(62, 215)(63, 176)(64, 186)(65, 216)(66, 207)(67, 209)(68, 190)(69, 184)(70, 188)(71, 204)(72, 205)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 2, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E7.522 Graph:: bipartite v = 36 e = 144 f = 96 degree seq :: [ 6^24, 12^12 ] E7.522 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 6}) Quotient :: dipole Aut^+ = C3 x SL(2,3) (small group id <72, 25>) Aut = (C3 x SL(2,3)) : C2 (small group id <144, 125>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^6, (Y3 * Y2^-1)^3, Y2 * Y3^-3 * Y2^-1 * Y3^-3, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, (Y3^-1 * Y1^-1)^6 ] Map:: polytopal R = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(145, 217, 146, 218, 148, 220)(147, 219, 152, 224, 154, 226)(149, 221, 157, 229, 158, 230)(150, 222, 160, 232, 162, 234)(151, 223, 163, 235, 164, 236)(153, 225, 168, 240, 170, 242)(155, 227, 172, 244, 174, 246)(156, 228, 175, 247, 176, 248)(159, 231, 181, 253, 182, 254)(161, 233, 185, 257, 187, 259)(165, 237, 192, 264, 193, 265)(166, 238, 183, 255, 195, 267)(167, 239, 196, 268, 197, 269)(169, 241, 186, 258, 201, 273)(171, 243, 203, 275, 204, 276)(173, 245, 206, 278, 207, 279)(177, 249, 209, 281, 200, 272)(178, 250, 184, 256, 210, 282)(179, 251, 188, 260, 194, 266)(180, 252, 191, 263, 208, 280)(189, 261, 205, 277, 214, 286)(190, 262, 199, 271, 211, 283)(198, 270, 212, 284, 215, 287)(202, 274, 213, 285, 216, 288) L = (1, 147)(2, 150)(3, 153)(4, 155)(5, 145)(6, 161)(7, 146)(8, 166)(9, 169)(10, 163)(11, 173)(12, 148)(13, 178)(14, 179)(15, 149)(16, 183)(17, 186)(18, 175)(19, 189)(20, 190)(21, 151)(22, 194)(23, 152)(24, 199)(25, 159)(26, 196)(27, 154)(28, 195)(29, 201)(30, 157)(31, 197)(32, 204)(33, 156)(34, 200)(35, 202)(36, 158)(37, 198)(38, 185)(39, 211)(40, 160)(41, 171)(42, 165)(43, 210)(44, 162)(45, 182)(46, 213)(47, 164)(48, 212)(49, 206)(50, 181)(51, 203)(52, 180)(53, 193)(54, 167)(55, 174)(56, 168)(57, 177)(58, 170)(59, 209)(60, 216)(61, 172)(62, 188)(63, 214)(64, 176)(65, 215)(66, 191)(67, 192)(68, 184)(69, 187)(70, 208)(71, 205)(72, 207)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E7.521 Graph:: simple bipartite v = 96 e = 144 f = 36 degree seq :: [ 2^72, 6^24 ] E7.523 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 12}) Quotient :: regular Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, (T1^-1 * T2)^3, T1^12, (T2 * T1^-6)^2, (T2 * T1^4 * T2 * T1^-1)^2, T2 * T1^2 * T2 * T1^3 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2, T2 * T1^3 * T2 * T1^2 * T2 * T1^-2 * T2 * T1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 21, 37, 63, 62, 36, 20, 10, 4)(3, 7, 15, 27, 47, 79, 104, 91, 54, 31, 17, 8)(6, 13, 25, 43, 73, 119, 103, 128, 78, 46, 26, 14)(9, 18, 32, 55, 92, 106, 64, 105, 86, 51, 29, 16)(12, 23, 41, 69, 113, 101, 61, 102, 118, 72, 42, 24)(19, 34, 58, 97, 108, 66, 38, 65, 107, 96, 57, 33)(22, 39, 67, 109, 99, 59, 35, 60, 100, 112, 68, 40)(28, 49, 83, 110, 71, 116, 90, 134, 143, 132, 84, 50)(30, 52, 87, 111, 138, 127, 80, 129, 98, 123, 75, 44)(45, 76, 124, 136, 144, 142, 120, 95, 56, 94, 115, 70)(48, 81, 114, 140, 133, 88, 53, 89, 117, 141, 130, 82)(74, 121, 137, 131, 85, 125, 77, 126, 139, 135, 93, 122) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 38)(24, 39)(25, 44)(26, 45)(27, 48)(29, 49)(31, 53)(32, 56)(34, 59)(36, 61)(37, 64)(40, 65)(41, 70)(42, 71)(43, 74)(46, 77)(47, 80)(50, 81)(51, 85)(52, 88)(54, 90)(55, 93)(57, 94)(58, 98)(60, 101)(62, 103)(63, 104)(66, 105)(67, 110)(68, 111)(69, 114)(72, 117)(73, 120)(75, 121)(76, 125)(78, 127)(79, 128)(82, 129)(83, 131)(84, 113)(86, 124)(87, 107)(89, 116)(91, 106)(92, 134)(95, 122)(96, 133)(97, 130)(99, 123)(100, 132)(102, 119)(108, 136)(109, 137)(112, 139)(115, 140)(118, 142)(126, 138)(135, 143)(141, 144) local type(s) :: { ( 3^12 ) } Outer automorphisms :: reflexible Dual of E7.524 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 12 e = 72 f = 48 degree seq :: [ 12^12 ] E7.524 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 12}) Quotient :: regular Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1, (T1^-1 * T2)^12 ] Map:: polytopal non-degenerate R = (1, 2, 4)(3, 6, 7)(5, 9, 10)(8, 13, 14)(11, 17, 18)(12, 19, 20)(15, 23, 24)(16, 25, 26)(21, 31, 32)(22, 33, 34)(27, 39, 40)(28, 41, 42)(29, 43, 44)(30, 45, 46)(35, 51, 52)(36, 53, 54)(37, 55, 56)(38, 57, 58)(47, 67, 68)(48, 69, 70)(49, 71, 72)(50, 73, 74)(59, 83, 84)(60, 79, 85)(61, 77, 86)(62, 81, 87)(63, 88, 89)(64, 80, 90)(65, 91, 92)(66, 93, 94)(75, 99, 100)(76, 96, 101)(78, 97, 102)(82, 103, 104)(95, 113, 114)(98, 115, 116)(105, 123, 122)(106, 110, 124)(107, 111, 125)(108, 126, 118)(109, 127, 128)(112, 129, 130)(117, 133, 132)(119, 121, 134)(120, 135, 131)(136, 142, 141)(137, 139, 144)(138, 143, 140) L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 12)(9, 15)(10, 16)(13, 21)(14, 22)(17, 27)(18, 28)(19, 29)(20, 30)(23, 35)(24, 36)(25, 37)(26, 38)(31, 47)(32, 48)(33, 49)(34, 50)(39, 59)(40, 60)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 66)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(67, 95)(68, 89)(69, 86)(70, 92)(71, 96)(72, 90)(73, 97)(74, 98)(83, 105)(84, 106)(85, 107)(87, 108)(88, 109)(91, 110)(93, 111)(94, 112)(99, 117)(100, 118)(101, 119)(102, 120)(103, 121)(104, 122)(113, 129)(114, 131)(115, 127)(116, 132)(123, 136)(124, 137)(125, 138)(126, 139)(128, 140)(130, 141)(133, 142)(134, 143)(135, 144) local type(s) :: { ( 12^3 ) } Outer automorphisms :: reflexible Dual of E7.523 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 48 e = 72 f = 12 degree seq :: [ 3^48 ] E7.525 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 12}) Quotient :: edge Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1, (T2^-1 * T1)^12 ] Map:: polytopal R = (1, 3, 4)(2, 5, 6)(7, 11, 12)(8, 13, 14)(9, 15, 16)(10, 17, 18)(19, 27, 28)(20, 29, 30)(21, 31, 32)(22, 33, 34)(23, 35, 36)(24, 37, 38)(25, 39, 40)(26, 41, 42)(43, 59, 60)(44, 61, 62)(45, 63, 64)(46, 65, 66)(47, 67, 68)(48, 69, 70)(49, 71, 72)(50, 73, 74)(51, 75, 76)(52, 77, 78)(53, 79, 80)(54, 81, 82)(55, 83, 84)(56, 85, 86)(57, 87, 88)(58, 89, 90)(91, 107, 108)(92, 96, 109)(93, 97, 110)(94, 111, 112)(95, 113, 114)(98, 115, 116)(99, 117, 118)(100, 104, 119)(101, 105, 120)(102, 121, 122)(103, 123, 124)(106, 125, 126)(127, 139, 132)(128, 130, 140)(129, 141, 131)(133, 142, 138)(134, 136, 143)(135, 144, 137)(145, 146)(147, 151)(148, 152)(149, 153)(150, 154)(155, 163)(156, 164)(157, 165)(158, 166)(159, 167)(160, 168)(161, 169)(162, 170)(171, 187)(172, 188)(173, 189)(174, 190)(175, 191)(176, 192)(177, 193)(178, 194)(179, 195)(180, 196)(181, 197)(182, 198)(183, 199)(184, 200)(185, 201)(186, 202)(203, 235)(204, 236)(205, 223)(206, 237)(207, 221)(208, 229)(209, 225)(210, 238)(211, 239)(212, 228)(213, 224)(214, 232)(215, 240)(216, 230)(217, 241)(218, 242)(219, 243)(220, 244)(222, 245)(226, 246)(227, 247)(231, 248)(233, 249)(234, 250)(251, 271)(252, 266)(253, 272)(254, 273)(255, 274)(256, 262)(257, 269)(258, 275)(259, 267)(260, 276)(261, 277)(263, 278)(264, 279)(265, 280)(268, 281)(270, 282)(283, 286)(284, 288)(285, 287) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 24, 24 ), ( 24^3 ) } Outer automorphisms :: reflexible Dual of E7.529 Transitivity :: ET+ Graph:: simple bipartite v = 120 e = 144 f = 12 degree seq :: [ 2^72, 3^48 ] E7.526 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 12}) Quotient :: edge Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2 * T1)^2, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-2 * T1 * T2^2 * T1^-1 * T2^3 * T1^-1, T2^12 ] Map:: polytopal non-degenerate R = (1, 3, 9, 19, 37, 67, 113, 86, 48, 26, 13, 5)(2, 6, 14, 27, 50, 89, 129, 102, 58, 32, 16, 7)(4, 11, 22, 41, 74, 119, 136, 108, 62, 34, 17, 8)(10, 21, 40, 71, 116, 85, 125, 120, 109, 64, 35, 18)(12, 23, 43, 77, 122, 101, 112, 68, 114, 80, 44, 24)(15, 29, 53, 93, 131, 107, 128, 90, 130, 96, 54, 30)(20, 39, 70, 95, 84, 47, 83, 124, 138, 110, 65, 36)(25, 45, 81, 123, 139, 111, 66, 38, 69, 94, 82, 46)(28, 52, 92, 63, 100, 57, 99, 133, 141, 126, 87, 49)(31, 55, 97, 132, 142, 127, 88, 51, 91, 72, 98, 56)(33, 59, 103, 134, 143, 137, 118, 75, 121, 78, 104, 60)(42, 76, 115, 79, 106, 61, 105, 135, 144, 140, 117, 73)(145, 146, 148)(147, 152, 154)(149, 156, 150)(151, 159, 155)(153, 162, 164)(157, 169, 167)(158, 168, 172)(160, 175, 173)(161, 177, 165)(163, 180, 182)(166, 174, 186)(170, 191, 189)(171, 193, 195)(176, 201, 199)(178, 205, 203)(179, 207, 183)(181, 210, 212)(184, 204, 216)(185, 217, 219)(187, 190, 222)(188, 223, 196)(192, 229, 227)(194, 232, 234)(197, 200, 238)(198, 239, 220)(202, 245, 243)(206, 251, 249)(208, 241, 244)(209, 237, 213)(211, 256, 246)(214, 236, 259)(215, 235, 231)(218, 262, 264)(221, 265, 261)(224, 247, 250)(225, 228, 240)(226, 242, 248)(230, 263, 269)(233, 272, 252)(253, 281, 276)(254, 279, 275)(255, 278, 258)(257, 273, 280)(260, 270, 268)(266, 284, 277)(267, 274, 271)(282, 285, 288)(283, 286, 287) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 4^3 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E7.530 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 144 f = 72 degree seq :: [ 3^48, 12^12 ] E7.527 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 12}) Quotient :: edge Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^12, (T2 * T1^-6)^2, (T2 * T1^4 * T2 * T1^-1)^2, T2 * T1^2 * T2 * T1^3 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2, T2 * T1^3 * T2 * T1^2 * T2 * T1^-2 * T2 * T1 * T2 * T1^-1 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 38)(24, 39)(25, 44)(26, 45)(27, 48)(29, 49)(31, 53)(32, 56)(34, 59)(36, 61)(37, 64)(40, 65)(41, 70)(42, 71)(43, 74)(46, 77)(47, 80)(50, 81)(51, 85)(52, 88)(54, 90)(55, 93)(57, 94)(58, 98)(60, 101)(62, 103)(63, 104)(66, 105)(67, 110)(68, 111)(69, 114)(72, 117)(73, 120)(75, 121)(76, 125)(78, 127)(79, 128)(82, 129)(83, 131)(84, 113)(86, 124)(87, 107)(89, 116)(91, 106)(92, 134)(95, 122)(96, 133)(97, 130)(99, 123)(100, 132)(102, 119)(108, 136)(109, 137)(112, 139)(115, 140)(118, 142)(126, 138)(135, 143)(141, 144)(145, 146, 149, 155, 165, 181, 207, 206, 180, 164, 154, 148)(147, 151, 159, 171, 191, 223, 248, 235, 198, 175, 161, 152)(150, 157, 169, 187, 217, 263, 247, 272, 222, 190, 170, 158)(153, 162, 176, 199, 236, 250, 208, 249, 230, 195, 173, 160)(156, 167, 185, 213, 257, 245, 205, 246, 262, 216, 186, 168)(163, 178, 202, 241, 252, 210, 182, 209, 251, 240, 201, 177)(166, 183, 211, 253, 243, 203, 179, 204, 244, 256, 212, 184)(172, 193, 227, 254, 215, 260, 234, 278, 287, 276, 228, 194)(174, 196, 231, 255, 282, 271, 224, 273, 242, 267, 219, 188)(189, 220, 268, 280, 288, 286, 264, 239, 200, 238, 259, 214)(192, 225, 258, 284, 277, 232, 197, 233, 261, 285, 274, 226)(218, 265, 281, 275, 229, 269, 221, 270, 283, 279, 237, 266) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 6, 6 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E7.528 Transitivity :: ET+ Graph:: simple bipartite v = 84 e = 144 f = 48 degree seq :: [ 2^72, 12^12 ] E7.528 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 12}) Quotient :: loop Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1, (T2^-1 * T1)^12 ] Map:: R = (1, 145, 3, 147, 4, 148)(2, 146, 5, 149, 6, 150)(7, 151, 11, 155, 12, 156)(8, 152, 13, 157, 14, 158)(9, 153, 15, 159, 16, 160)(10, 154, 17, 161, 18, 162)(19, 163, 27, 171, 28, 172)(20, 164, 29, 173, 30, 174)(21, 165, 31, 175, 32, 176)(22, 166, 33, 177, 34, 178)(23, 167, 35, 179, 36, 180)(24, 168, 37, 181, 38, 182)(25, 169, 39, 183, 40, 184)(26, 170, 41, 185, 42, 186)(43, 187, 59, 203, 60, 204)(44, 188, 61, 205, 62, 206)(45, 189, 63, 207, 64, 208)(46, 190, 65, 209, 66, 210)(47, 191, 67, 211, 68, 212)(48, 192, 69, 213, 70, 214)(49, 193, 71, 215, 72, 216)(50, 194, 73, 217, 74, 218)(51, 195, 75, 219, 76, 220)(52, 196, 77, 221, 78, 222)(53, 197, 79, 223, 80, 224)(54, 198, 81, 225, 82, 226)(55, 199, 83, 227, 84, 228)(56, 200, 85, 229, 86, 230)(57, 201, 87, 231, 88, 232)(58, 202, 89, 233, 90, 234)(91, 235, 107, 251, 108, 252)(92, 236, 96, 240, 109, 253)(93, 237, 97, 241, 110, 254)(94, 238, 111, 255, 112, 256)(95, 239, 113, 257, 114, 258)(98, 242, 115, 259, 116, 260)(99, 243, 117, 261, 118, 262)(100, 244, 104, 248, 119, 263)(101, 245, 105, 249, 120, 264)(102, 246, 121, 265, 122, 266)(103, 247, 123, 267, 124, 268)(106, 250, 125, 269, 126, 270)(127, 271, 139, 283, 132, 276)(128, 272, 130, 274, 140, 284)(129, 273, 141, 285, 131, 275)(133, 277, 142, 286, 138, 282)(134, 278, 136, 280, 143, 287)(135, 279, 144, 288, 137, 281) L = (1, 146)(2, 145)(3, 151)(4, 152)(5, 153)(6, 154)(7, 147)(8, 148)(9, 149)(10, 150)(11, 163)(12, 164)(13, 165)(14, 166)(15, 167)(16, 168)(17, 169)(18, 170)(19, 155)(20, 156)(21, 157)(22, 158)(23, 159)(24, 160)(25, 161)(26, 162)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 235)(60, 236)(61, 223)(62, 237)(63, 221)(64, 229)(65, 225)(66, 238)(67, 239)(68, 228)(69, 224)(70, 232)(71, 240)(72, 230)(73, 241)(74, 242)(75, 243)(76, 244)(77, 207)(78, 245)(79, 205)(80, 213)(81, 209)(82, 246)(83, 247)(84, 212)(85, 208)(86, 216)(87, 248)(88, 214)(89, 249)(90, 250)(91, 203)(92, 204)(93, 206)(94, 210)(95, 211)(96, 215)(97, 217)(98, 218)(99, 219)(100, 220)(101, 222)(102, 226)(103, 227)(104, 231)(105, 233)(106, 234)(107, 271)(108, 266)(109, 272)(110, 273)(111, 274)(112, 262)(113, 269)(114, 275)(115, 267)(116, 276)(117, 277)(118, 256)(119, 278)(120, 279)(121, 280)(122, 252)(123, 259)(124, 281)(125, 257)(126, 282)(127, 251)(128, 253)(129, 254)(130, 255)(131, 258)(132, 260)(133, 261)(134, 263)(135, 264)(136, 265)(137, 268)(138, 270)(139, 286)(140, 288)(141, 287)(142, 283)(143, 285)(144, 284) local type(s) :: { ( 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E7.527 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 48 e = 144 f = 84 degree seq :: [ 6^48 ] E7.529 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 12}) Quotient :: loop Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2 * T1)^2, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-2 * T1 * T2^2 * T1^-1 * T2^3 * T1^-1, T2^12 ] Map:: R = (1, 145, 3, 147, 9, 153, 19, 163, 37, 181, 67, 211, 113, 257, 86, 230, 48, 192, 26, 170, 13, 157, 5, 149)(2, 146, 6, 150, 14, 158, 27, 171, 50, 194, 89, 233, 129, 273, 102, 246, 58, 202, 32, 176, 16, 160, 7, 151)(4, 148, 11, 155, 22, 166, 41, 185, 74, 218, 119, 263, 136, 280, 108, 252, 62, 206, 34, 178, 17, 161, 8, 152)(10, 154, 21, 165, 40, 184, 71, 215, 116, 260, 85, 229, 125, 269, 120, 264, 109, 253, 64, 208, 35, 179, 18, 162)(12, 156, 23, 167, 43, 187, 77, 221, 122, 266, 101, 245, 112, 256, 68, 212, 114, 258, 80, 224, 44, 188, 24, 168)(15, 159, 29, 173, 53, 197, 93, 237, 131, 275, 107, 251, 128, 272, 90, 234, 130, 274, 96, 240, 54, 198, 30, 174)(20, 164, 39, 183, 70, 214, 95, 239, 84, 228, 47, 191, 83, 227, 124, 268, 138, 282, 110, 254, 65, 209, 36, 180)(25, 169, 45, 189, 81, 225, 123, 267, 139, 283, 111, 255, 66, 210, 38, 182, 69, 213, 94, 238, 82, 226, 46, 190)(28, 172, 52, 196, 92, 236, 63, 207, 100, 244, 57, 201, 99, 243, 133, 277, 141, 285, 126, 270, 87, 231, 49, 193)(31, 175, 55, 199, 97, 241, 132, 276, 142, 286, 127, 271, 88, 232, 51, 195, 91, 235, 72, 216, 98, 242, 56, 200)(33, 177, 59, 203, 103, 247, 134, 278, 143, 287, 137, 281, 118, 262, 75, 219, 121, 265, 78, 222, 104, 248, 60, 204)(42, 186, 76, 220, 115, 259, 79, 223, 106, 250, 61, 205, 105, 249, 135, 279, 144, 288, 140, 284, 117, 261, 73, 217) L = (1, 146)(2, 148)(3, 152)(4, 145)(5, 156)(6, 149)(7, 159)(8, 154)(9, 162)(10, 147)(11, 151)(12, 150)(13, 169)(14, 168)(15, 155)(16, 175)(17, 177)(18, 164)(19, 180)(20, 153)(21, 161)(22, 174)(23, 157)(24, 172)(25, 167)(26, 191)(27, 193)(28, 158)(29, 160)(30, 186)(31, 173)(32, 201)(33, 165)(34, 205)(35, 207)(36, 182)(37, 210)(38, 163)(39, 179)(40, 204)(41, 217)(42, 166)(43, 190)(44, 223)(45, 170)(46, 222)(47, 189)(48, 229)(49, 195)(50, 232)(51, 171)(52, 188)(53, 200)(54, 239)(55, 176)(56, 238)(57, 199)(58, 245)(59, 178)(60, 216)(61, 203)(62, 251)(63, 183)(64, 241)(65, 237)(66, 212)(67, 256)(68, 181)(69, 209)(70, 236)(71, 235)(72, 184)(73, 219)(74, 262)(75, 185)(76, 198)(77, 265)(78, 187)(79, 196)(80, 247)(81, 228)(82, 242)(83, 192)(84, 240)(85, 227)(86, 263)(87, 215)(88, 234)(89, 272)(90, 194)(91, 231)(92, 259)(93, 213)(94, 197)(95, 220)(96, 225)(97, 244)(98, 248)(99, 202)(100, 208)(101, 243)(102, 211)(103, 250)(104, 226)(105, 206)(106, 224)(107, 249)(108, 233)(109, 281)(110, 279)(111, 278)(112, 246)(113, 273)(114, 255)(115, 214)(116, 270)(117, 221)(118, 264)(119, 269)(120, 218)(121, 261)(122, 284)(123, 274)(124, 260)(125, 230)(126, 268)(127, 267)(128, 252)(129, 280)(130, 271)(131, 254)(132, 253)(133, 266)(134, 258)(135, 275)(136, 257)(137, 276)(138, 285)(139, 286)(140, 277)(141, 288)(142, 287)(143, 283)(144, 282) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E7.525 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 144 f = 120 degree seq :: [ 24^12 ] E7.530 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 12}) Quotient :: loop Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^12, (T2 * T1^-6)^2, (T2 * T1^4 * T2 * T1^-1)^2, T2 * T1^2 * T2 * T1^3 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2, T2 * T1^3 * T2 * T1^2 * T2 * T1^-2 * T2 * T1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 145, 3, 147)(2, 146, 6, 150)(4, 148, 9, 153)(5, 149, 12, 156)(7, 151, 16, 160)(8, 152, 13, 157)(10, 154, 19, 163)(11, 155, 22, 166)(14, 158, 23, 167)(15, 159, 28, 172)(17, 161, 30, 174)(18, 162, 33, 177)(20, 164, 35, 179)(21, 165, 38, 182)(24, 168, 39, 183)(25, 169, 44, 188)(26, 170, 45, 189)(27, 171, 48, 192)(29, 173, 49, 193)(31, 175, 53, 197)(32, 176, 56, 200)(34, 178, 59, 203)(36, 180, 61, 205)(37, 181, 64, 208)(40, 184, 65, 209)(41, 185, 70, 214)(42, 186, 71, 215)(43, 187, 74, 218)(46, 190, 77, 221)(47, 191, 80, 224)(50, 194, 81, 225)(51, 195, 85, 229)(52, 196, 88, 232)(54, 198, 90, 234)(55, 199, 93, 237)(57, 201, 94, 238)(58, 202, 98, 242)(60, 204, 101, 245)(62, 206, 103, 247)(63, 207, 104, 248)(66, 210, 105, 249)(67, 211, 110, 254)(68, 212, 111, 255)(69, 213, 114, 258)(72, 216, 117, 261)(73, 217, 120, 264)(75, 219, 121, 265)(76, 220, 125, 269)(78, 222, 127, 271)(79, 223, 128, 272)(82, 226, 129, 273)(83, 227, 131, 275)(84, 228, 113, 257)(86, 230, 124, 268)(87, 231, 107, 251)(89, 233, 116, 260)(91, 235, 106, 250)(92, 236, 134, 278)(95, 239, 122, 266)(96, 240, 133, 277)(97, 241, 130, 274)(99, 243, 123, 267)(100, 244, 132, 276)(102, 246, 119, 263)(108, 252, 136, 280)(109, 253, 137, 281)(112, 256, 139, 283)(115, 259, 140, 284)(118, 262, 142, 286)(126, 270, 138, 282)(135, 279, 143, 287)(141, 285, 144, 288) L = (1, 146)(2, 149)(3, 151)(4, 145)(5, 155)(6, 157)(7, 159)(8, 147)(9, 162)(10, 148)(11, 165)(12, 167)(13, 169)(14, 150)(15, 171)(16, 153)(17, 152)(18, 176)(19, 178)(20, 154)(21, 181)(22, 183)(23, 185)(24, 156)(25, 187)(26, 158)(27, 191)(28, 193)(29, 160)(30, 196)(31, 161)(32, 199)(33, 163)(34, 202)(35, 204)(36, 164)(37, 207)(38, 209)(39, 211)(40, 166)(41, 213)(42, 168)(43, 217)(44, 174)(45, 220)(46, 170)(47, 223)(48, 225)(49, 227)(50, 172)(51, 173)(52, 231)(53, 233)(54, 175)(55, 236)(56, 238)(57, 177)(58, 241)(59, 179)(60, 244)(61, 246)(62, 180)(63, 206)(64, 249)(65, 251)(66, 182)(67, 253)(68, 184)(69, 257)(70, 189)(71, 260)(72, 186)(73, 263)(74, 265)(75, 188)(76, 268)(77, 270)(78, 190)(79, 248)(80, 273)(81, 258)(82, 192)(83, 254)(84, 194)(85, 269)(86, 195)(87, 255)(88, 197)(89, 261)(90, 278)(91, 198)(92, 250)(93, 266)(94, 259)(95, 200)(96, 201)(97, 252)(98, 267)(99, 203)(100, 256)(101, 205)(102, 262)(103, 272)(104, 235)(105, 230)(106, 208)(107, 240)(108, 210)(109, 243)(110, 215)(111, 282)(112, 212)(113, 245)(114, 284)(115, 214)(116, 234)(117, 285)(118, 216)(119, 247)(120, 239)(121, 281)(122, 218)(123, 219)(124, 280)(125, 221)(126, 283)(127, 224)(128, 222)(129, 242)(130, 226)(131, 229)(132, 228)(133, 232)(134, 287)(135, 237)(136, 288)(137, 275)(138, 271)(139, 279)(140, 277)(141, 274)(142, 264)(143, 276)(144, 286) local type(s) :: { ( 3, 12, 3, 12 ) } Outer automorphisms :: reflexible Dual of E7.526 Transitivity :: ET+ VT+ AT Graph:: simple v = 72 e = 144 f = 60 degree seq :: [ 4^72 ] E7.531 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12}) Quotient :: dipole Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 8, 152)(5, 149, 9, 153)(6, 150, 10, 154)(11, 155, 19, 163)(12, 156, 20, 164)(13, 157, 21, 165)(14, 158, 22, 166)(15, 159, 23, 167)(16, 160, 24, 168)(17, 161, 25, 169)(18, 162, 26, 170)(27, 171, 43, 187)(28, 172, 44, 188)(29, 173, 45, 189)(30, 174, 46, 190)(31, 175, 47, 191)(32, 176, 48, 192)(33, 177, 49, 193)(34, 178, 50, 194)(35, 179, 51, 195)(36, 180, 52, 196)(37, 181, 53, 197)(38, 182, 54, 198)(39, 183, 55, 199)(40, 184, 56, 200)(41, 185, 57, 201)(42, 186, 58, 202)(59, 203, 91, 235)(60, 204, 92, 236)(61, 205, 79, 223)(62, 206, 93, 237)(63, 207, 77, 221)(64, 208, 85, 229)(65, 209, 81, 225)(66, 210, 94, 238)(67, 211, 95, 239)(68, 212, 84, 228)(69, 213, 80, 224)(70, 214, 88, 232)(71, 215, 96, 240)(72, 216, 86, 230)(73, 217, 97, 241)(74, 218, 98, 242)(75, 219, 99, 243)(76, 220, 100, 244)(78, 222, 101, 245)(82, 226, 102, 246)(83, 227, 103, 247)(87, 231, 104, 248)(89, 233, 105, 249)(90, 234, 106, 250)(107, 251, 127, 271)(108, 252, 122, 266)(109, 253, 128, 272)(110, 254, 129, 273)(111, 255, 130, 274)(112, 256, 118, 262)(113, 257, 125, 269)(114, 258, 131, 275)(115, 259, 123, 267)(116, 260, 132, 276)(117, 261, 133, 277)(119, 263, 134, 278)(120, 264, 135, 279)(121, 265, 136, 280)(124, 268, 137, 281)(126, 270, 138, 282)(139, 283, 142, 286)(140, 284, 144, 288)(141, 285, 143, 287)(289, 433, 291, 435, 292, 436)(290, 434, 293, 437, 294, 438)(295, 439, 299, 443, 300, 444)(296, 440, 301, 445, 302, 446)(297, 441, 303, 447, 304, 448)(298, 442, 305, 449, 306, 450)(307, 451, 315, 459, 316, 460)(308, 452, 317, 461, 318, 462)(309, 453, 319, 463, 320, 464)(310, 454, 321, 465, 322, 466)(311, 455, 323, 467, 324, 468)(312, 456, 325, 469, 326, 470)(313, 457, 327, 471, 328, 472)(314, 458, 329, 473, 330, 474)(331, 475, 347, 491, 348, 492)(332, 476, 349, 493, 350, 494)(333, 477, 351, 495, 352, 496)(334, 478, 353, 497, 354, 498)(335, 479, 355, 499, 356, 500)(336, 480, 357, 501, 358, 502)(337, 481, 359, 503, 360, 504)(338, 482, 361, 505, 362, 506)(339, 483, 363, 507, 364, 508)(340, 484, 365, 509, 366, 510)(341, 485, 367, 511, 368, 512)(342, 486, 369, 513, 370, 514)(343, 487, 371, 515, 372, 516)(344, 488, 373, 517, 374, 518)(345, 489, 375, 519, 376, 520)(346, 490, 377, 521, 378, 522)(379, 523, 395, 539, 396, 540)(380, 524, 384, 528, 397, 541)(381, 525, 385, 529, 398, 542)(382, 526, 399, 543, 400, 544)(383, 527, 401, 545, 402, 546)(386, 530, 403, 547, 404, 548)(387, 531, 405, 549, 406, 550)(388, 532, 392, 536, 407, 551)(389, 533, 393, 537, 408, 552)(390, 534, 409, 553, 410, 554)(391, 535, 411, 555, 412, 556)(394, 538, 413, 557, 414, 558)(415, 559, 427, 571, 420, 564)(416, 560, 418, 562, 428, 572)(417, 561, 429, 573, 419, 563)(421, 565, 430, 574, 426, 570)(422, 566, 424, 568, 431, 575)(423, 567, 432, 576, 425, 569) L = (1, 290)(2, 289)(3, 295)(4, 296)(5, 297)(6, 298)(7, 291)(8, 292)(9, 293)(10, 294)(11, 307)(12, 308)(13, 309)(14, 310)(15, 311)(16, 312)(17, 313)(18, 314)(19, 299)(20, 300)(21, 301)(22, 302)(23, 303)(24, 304)(25, 305)(26, 306)(27, 331)(28, 332)(29, 333)(30, 334)(31, 335)(32, 336)(33, 337)(34, 338)(35, 339)(36, 340)(37, 341)(38, 342)(39, 343)(40, 344)(41, 345)(42, 346)(43, 315)(44, 316)(45, 317)(46, 318)(47, 319)(48, 320)(49, 321)(50, 322)(51, 323)(52, 324)(53, 325)(54, 326)(55, 327)(56, 328)(57, 329)(58, 330)(59, 379)(60, 380)(61, 367)(62, 381)(63, 365)(64, 373)(65, 369)(66, 382)(67, 383)(68, 372)(69, 368)(70, 376)(71, 384)(72, 374)(73, 385)(74, 386)(75, 387)(76, 388)(77, 351)(78, 389)(79, 349)(80, 357)(81, 353)(82, 390)(83, 391)(84, 356)(85, 352)(86, 360)(87, 392)(88, 358)(89, 393)(90, 394)(91, 347)(92, 348)(93, 350)(94, 354)(95, 355)(96, 359)(97, 361)(98, 362)(99, 363)(100, 364)(101, 366)(102, 370)(103, 371)(104, 375)(105, 377)(106, 378)(107, 415)(108, 410)(109, 416)(110, 417)(111, 418)(112, 406)(113, 413)(114, 419)(115, 411)(116, 420)(117, 421)(118, 400)(119, 422)(120, 423)(121, 424)(122, 396)(123, 403)(124, 425)(125, 401)(126, 426)(127, 395)(128, 397)(129, 398)(130, 399)(131, 402)(132, 404)(133, 405)(134, 407)(135, 408)(136, 409)(137, 412)(138, 414)(139, 430)(140, 432)(141, 431)(142, 427)(143, 429)(144, 428)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E7.534 Graph:: bipartite v = 120 e = 288 f = 156 degree seq :: [ 4^72, 6^48 ] E7.532 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12}) Quotient :: dipole Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1^-2 * Y2^2 * Y1, Y2^2 * Y1^-1 * Y2^-2 * Y1 * Y2^-3 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1^-1 * Y2^-2 * Y1 * Y2^2 * Y1^-1 * Y2^3 * Y1^-1, Y2^12 ] Map:: R = (1, 145, 2, 146, 4, 148)(3, 147, 8, 152, 10, 154)(5, 149, 12, 156, 6, 150)(7, 151, 15, 159, 11, 155)(9, 153, 18, 162, 20, 164)(13, 157, 25, 169, 23, 167)(14, 158, 24, 168, 28, 172)(16, 160, 31, 175, 29, 173)(17, 161, 33, 177, 21, 165)(19, 163, 36, 180, 38, 182)(22, 166, 30, 174, 42, 186)(26, 170, 47, 191, 45, 189)(27, 171, 49, 193, 51, 195)(32, 176, 57, 201, 55, 199)(34, 178, 61, 205, 59, 203)(35, 179, 63, 207, 39, 183)(37, 181, 66, 210, 68, 212)(40, 184, 60, 204, 72, 216)(41, 185, 73, 217, 75, 219)(43, 187, 46, 190, 78, 222)(44, 188, 79, 223, 52, 196)(48, 192, 85, 229, 83, 227)(50, 194, 88, 232, 90, 234)(53, 197, 56, 200, 94, 238)(54, 198, 95, 239, 76, 220)(58, 202, 101, 245, 99, 243)(62, 206, 107, 251, 105, 249)(64, 208, 97, 241, 100, 244)(65, 209, 93, 237, 69, 213)(67, 211, 112, 256, 102, 246)(70, 214, 92, 236, 115, 259)(71, 215, 91, 235, 87, 231)(74, 218, 118, 262, 120, 264)(77, 221, 121, 265, 117, 261)(80, 224, 103, 247, 106, 250)(81, 225, 84, 228, 96, 240)(82, 226, 98, 242, 104, 248)(86, 230, 119, 263, 125, 269)(89, 233, 128, 272, 108, 252)(109, 253, 137, 281, 132, 276)(110, 254, 135, 279, 131, 275)(111, 255, 134, 278, 114, 258)(113, 257, 129, 273, 136, 280)(116, 260, 126, 270, 124, 268)(122, 266, 140, 284, 133, 277)(123, 267, 130, 274, 127, 271)(138, 282, 141, 285, 144, 288)(139, 283, 142, 286, 143, 287)(289, 433, 291, 435, 297, 441, 307, 451, 325, 469, 355, 499, 401, 545, 374, 518, 336, 480, 314, 458, 301, 445, 293, 437)(290, 434, 294, 438, 302, 446, 315, 459, 338, 482, 377, 521, 417, 561, 390, 534, 346, 490, 320, 464, 304, 448, 295, 439)(292, 436, 299, 443, 310, 454, 329, 473, 362, 506, 407, 551, 424, 568, 396, 540, 350, 494, 322, 466, 305, 449, 296, 440)(298, 442, 309, 453, 328, 472, 359, 503, 404, 548, 373, 517, 413, 557, 408, 552, 397, 541, 352, 496, 323, 467, 306, 450)(300, 444, 311, 455, 331, 475, 365, 509, 410, 554, 389, 533, 400, 544, 356, 500, 402, 546, 368, 512, 332, 476, 312, 456)(303, 447, 317, 461, 341, 485, 381, 525, 419, 563, 395, 539, 416, 560, 378, 522, 418, 562, 384, 528, 342, 486, 318, 462)(308, 452, 327, 471, 358, 502, 383, 527, 372, 516, 335, 479, 371, 515, 412, 556, 426, 570, 398, 542, 353, 497, 324, 468)(313, 457, 333, 477, 369, 513, 411, 555, 427, 571, 399, 543, 354, 498, 326, 470, 357, 501, 382, 526, 370, 514, 334, 478)(316, 460, 340, 484, 380, 524, 351, 495, 388, 532, 345, 489, 387, 531, 421, 565, 429, 573, 414, 558, 375, 519, 337, 481)(319, 463, 343, 487, 385, 529, 420, 564, 430, 574, 415, 559, 376, 520, 339, 483, 379, 523, 360, 504, 386, 530, 344, 488)(321, 465, 347, 491, 391, 535, 422, 566, 431, 575, 425, 569, 406, 550, 363, 507, 409, 553, 366, 510, 392, 536, 348, 492)(330, 474, 364, 508, 403, 547, 367, 511, 394, 538, 349, 493, 393, 537, 423, 567, 432, 576, 428, 572, 405, 549, 361, 505) L = (1, 291)(2, 294)(3, 297)(4, 299)(5, 289)(6, 302)(7, 290)(8, 292)(9, 307)(10, 309)(11, 310)(12, 311)(13, 293)(14, 315)(15, 317)(16, 295)(17, 296)(18, 298)(19, 325)(20, 327)(21, 328)(22, 329)(23, 331)(24, 300)(25, 333)(26, 301)(27, 338)(28, 340)(29, 341)(30, 303)(31, 343)(32, 304)(33, 347)(34, 305)(35, 306)(36, 308)(37, 355)(38, 357)(39, 358)(40, 359)(41, 362)(42, 364)(43, 365)(44, 312)(45, 369)(46, 313)(47, 371)(48, 314)(49, 316)(50, 377)(51, 379)(52, 380)(53, 381)(54, 318)(55, 385)(56, 319)(57, 387)(58, 320)(59, 391)(60, 321)(61, 393)(62, 322)(63, 388)(64, 323)(65, 324)(66, 326)(67, 401)(68, 402)(69, 382)(70, 383)(71, 404)(72, 386)(73, 330)(74, 407)(75, 409)(76, 403)(77, 410)(78, 392)(79, 394)(80, 332)(81, 411)(82, 334)(83, 412)(84, 335)(85, 413)(86, 336)(87, 337)(88, 339)(89, 417)(90, 418)(91, 360)(92, 351)(93, 419)(94, 370)(95, 372)(96, 342)(97, 420)(98, 344)(99, 421)(100, 345)(101, 400)(102, 346)(103, 422)(104, 348)(105, 423)(106, 349)(107, 416)(108, 350)(109, 352)(110, 353)(111, 354)(112, 356)(113, 374)(114, 368)(115, 367)(116, 373)(117, 361)(118, 363)(119, 424)(120, 397)(121, 366)(122, 389)(123, 427)(124, 426)(125, 408)(126, 375)(127, 376)(128, 378)(129, 390)(130, 384)(131, 395)(132, 430)(133, 429)(134, 431)(135, 432)(136, 396)(137, 406)(138, 398)(139, 399)(140, 405)(141, 414)(142, 415)(143, 425)(144, 428)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 2, 4, 2, 4, 2, 4 ), ( 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 E7.533 Graph:: bipartite v = 60 e = 288 f = 216 degree seq :: [ 6^48, 24^12 ] E7.533 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12}) Quotient :: dipole Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, Y3^3 * Y2 * Y3^2 * Y2 * Y3^-2 * Y2 * Y3 * Y2 * Y3^-1 * Y2, (Y3^6 * Y2)^2, (Y3^-1 * Y1^-1)^12 ] Map:: polytopal R = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)(289, 433, 290, 434)(291, 435, 295, 439)(292, 436, 297, 441)(293, 437, 299, 443)(294, 438, 301, 445)(296, 440, 304, 448)(298, 442, 307, 451)(300, 444, 310, 454)(302, 446, 313, 457)(303, 447, 315, 459)(305, 449, 318, 462)(306, 450, 320, 464)(308, 452, 323, 467)(309, 453, 325, 469)(311, 455, 328, 472)(312, 456, 330, 474)(314, 458, 333, 477)(316, 460, 336, 480)(317, 461, 338, 482)(319, 463, 341, 485)(321, 465, 344, 488)(322, 466, 346, 490)(324, 468, 349, 493)(326, 470, 352, 496)(327, 471, 354, 498)(329, 473, 357, 501)(331, 475, 360, 504)(332, 476, 362, 506)(334, 478, 365, 509)(335, 479, 367, 511)(337, 481, 370, 514)(339, 483, 373, 517)(340, 484, 375, 519)(342, 486, 378, 522)(343, 487, 380, 524)(345, 489, 383, 527)(347, 491, 386, 530)(348, 492, 388, 532)(350, 494, 391, 535)(351, 495, 392, 536)(353, 497, 395, 539)(355, 499, 398, 542)(356, 500, 400, 544)(358, 502, 403, 547)(359, 503, 405, 549)(361, 505, 408, 552)(363, 507, 411, 555)(364, 508, 413, 557)(366, 510, 416, 560)(368, 512, 397, 541)(369, 513, 394, 538)(371, 515, 402, 546)(372, 516, 393, 537)(374, 518, 414, 558)(376, 520, 412, 556)(377, 521, 396, 540)(379, 523, 404, 548)(381, 525, 410, 554)(382, 526, 407, 551)(384, 528, 415, 559)(385, 529, 406, 550)(387, 531, 401, 545)(389, 533, 399, 543)(390, 534, 409, 553)(417, 561, 426, 570)(418, 562, 429, 573)(419, 563, 424, 568)(420, 564, 430, 574)(421, 565, 431, 575)(422, 566, 425, 569)(423, 567, 427, 571)(428, 572, 432, 576) L = (1, 291)(2, 293)(3, 296)(4, 289)(5, 300)(6, 290)(7, 301)(8, 305)(9, 306)(10, 292)(11, 297)(12, 311)(13, 312)(14, 294)(15, 295)(16, 315)(17, 319)(18, 321)(19, 322)(20, 298)(21, 299)(22, 325)(23, 329)(24, 331)(25, 332)(26, 302)(27, 335)(28, 303)(29, 304)(30, 338)(31, 342)(32, 307)(33, 345)(34, 347)(35, 348)(36, 308)(37, 351)(38, 309)(39, 310)(40, 354)(41, 358)(42, 313)(43, 361)(44, 363)(45, 364)(46, 314)(47, 368)(48, 369)(49, 316)(50, 372)(51, 317)(52, 318)(53, 375)(54, 379)(55, 320)(56, 380)(57, 384)(58, 323)(59, 387)(60, 389)(61, 390)(62, 324)(63, 393)(64, 394)(65, 326)(66, 397)(67, 327)(68, 328)(69, 400)(70, 404)(71, 330)(72, 405)(73, 409)(74, 333)(75, 412)(76, 414)(77, 415)(78, 334)(79, 336)(80, 398)(81, 395)(82, 418)(83, 337)(84, 419)(85, 413)(86, 339)(87, 411)(88, 340)(89, 341)(90, 396)(91, 350)(92, 417)(93, 343)(94, 344)(95, 407)(96, 416)(97, 346)(98, 406)(99, 422)(100, 349)(101, 421)(102, 420)(103, 403)(104, 352)(105, 373)(106, 370)(107, 425)(108, 353)(109, 426)(110, 388)(111, 355)(112, 386)(113, 356)(114, 357)(115, 371)(116, 366)(117, 424)(118, 359)(119, 360)(120, 382)(121, 391)(122, 362)(123, 381)(124, 429)(125, 365)(126, 428)(127, 427)(128, 378)(129, 367)(130, 431)(131, 385)(132, 374)(133, 376)(134, 377)(135, 383)(136, 392)(137, 432)(138, 410)(139, 399)(140, 401)(141, 402)(142, 408)(143, 423)(144, 430)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 6, 24 ), ( 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E7.532 Graph:: simple bipartite v = 216 e = 288 f = 60 degree seq :: [ 2^144, 4^72 ] E7.534 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12}) Quotient :: dipole Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |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, Y1^12, (Y3 * Y1^-6)^2, Y3 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-3 * Y3 * Y1^-2, Y1^-1 * Y3 * Y1^-3 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1 ] Map:: polytopal R = (1, 145, 2, 146, 5, 149, 11, 155, 21, 165, 37, 181, 63, 207, 62, 206, 36, 180, 20, 164, 10, 154, 4, 148)(3, 147, 7, 151, 15, 159, 27, 171, 47, 191, 79, 223, 104, 248, 91, 235, 54, 198, 31, 175, 17, 161, 8, 152)(6, 150, 13, 157, 25, 169, 43, 187, 73, 217, 119, 263, 103, 247, 128, 272, 78, 222, 46, 190, 26, 170, 14, 158)(9, 153, 18, 162, 32, 176, 55, 199, 92, 236, 106, 250, 64, 208, 105, 249, 86, 230, 51, 195, 29, 173, 16, 160)(12, 156, 23, 167, 41, 185, 69, 213, 113, 257, 101, 245, 61, 205, 102, 246, 118, 262, 72, 216, 42, 186, 24, 168)(19, 163, 34, 178, 58, 202, 97, 241, 108, 252, 66, 210, 38, 182, 65, 209, 107, 251, 96, 240, 57, 201, 33, 177)(22, 166, 39, 183, 67, 211, 109, 253, 99, 243, 59, 203, 35, 179, 60, 204, 100, 244, 112, 256, 68, 212, 40, 184)(28, 172, 49, 193, 83, 227, 110, 254, 71, 215, 116, 260, 90, 234, 134, 278, 143, 287, 132, 276, 84, 228, 50, 194)(30, 174, 52, 196, 87, 231, 111, 255, 138, 282, 127, 271, 80, 224, 129, 273, 98, 242, 123, 267, 75, 219, 44, 188)(45, 189, 76, 220, 124, 268, 136, 280, 144, 288, 142, 286, 120, 264, 95, 239, 56, 200, 94, 238, 115, 259, 70, 214)(48, 192, 81, 225, 114, 258, 140, 284, 133, 277, 88, 232, 53, 197, 89, 233, 117, 261, 141, 285, 130, 274, 82, 226)(74, 218, 121, 265, 137, 281, 131, 275, 85, 229, 125, 269, 77, 221, 126, 270, 139, 283, 135, 279, 93, 237, 122, 266)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576) L = (1, 291)(2, 294)(3, 289)(4, 297)(5, 300)(6, 290)(7, 304)(8, 301)(9, 292)(10, 307)(11, 310)(12, 293)(13, 296)(14, 311)(15, 316)(16, 295)(17, 318)(18, 321)(19, 298)(20, 323)(21, 326)(22, 299)(23, 302)(24, 327)(25, 332)(26, 333)(27, 336)(28, 303)(29, 337)(30, 305)(31, 341)(32, 344)(33, 306)(34, 347)(35, 308)(36, 349)(37, 352)(38, 309)(39, 312)(40, 353)(41, 358)(42, 359)(43, 362)(44, 313)(45, 314)(46, 365)(47, 368)(48, 315)(49, 317)(50, 369)(51, 373)(52, 376)(53, 319)(54, 378)(55, 381)(56, 320)(57, 382)(58, 386)(59, 322)(60, 389)(61, 324)(62, 391)(63, 392)(64, 325)(65, 328)(66, 393)(67, 398)(68, 399)(69, 402)(70, 329)(71, 330)(72, 405)(73, 408)(74, 331)(75, 409)(76, 413)(77, 334)(78, 415)(79, 416)(80, 335)(81, 338)(82, 417)(83, 419)(84, 401)(85, 339)(86, 412)(87, 395)(88, 340)(89, 404)(90, 342)(91, 394)(92, 422)(93, 343)(94, 345)(95, 410)(96, 421)(97, 418)(98, 346)(99, 411)(100, 420)(101, 348)(102, 407)(103, 350)(104, 351)(105, 354)(106, 379)(107, 375)(108, 424)(109, 425)(110, 355)(111, 356)(112, 427)(113, 372)(114, 357)(115, 428)(116, 377)(117, 360)(118, 430)(119, 390)(120, 361)(121, 363)(122, 383)(123, 387)(124, 374)(125, 364)(126, 426)(127, 366)(128, 367)(129, 370)(130, 385)(131, 371)(132, 388)(133, 384)(134, 380)(135, 431)(136, 396)(137, 397)(138, 414)(139, 400)(140, 403)(141, 432)(142, 406)(143, 423)(144, 429)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 4, 6 ), ( 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 E7.531 Graph:: simple bipartite v = 156 e = 288 f = 120 degree seq :: [ 2^144, 24^12 ] E7.535 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12}) Quotient :: dipole Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^3, (Y3 * Y2^-1)^3, Y2^12, Y2 * Y1 * Y2^-5 * Y1 * Y2^-5 * Y1, Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-4 * Y1 * Y2^-2 * Y1 ] Map:: R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 11, 155)(6, 150, 13, 157)(8, 152, 16, 160)(10, 154, 19, 163)(12, 156, 22, 166)(14, 158, 25, 169)(15, 159, 27, 171)(17, 161, 30, 174)(18, 162, 32, 176)(20, 164, 35, 179)(21, 165, 37, 181)(23, 167, 40, 184)(24, 168, 42, 186)(26, 170, 45, 189)(28, 172, 48, 192)(29, 173, 50, 194)(31, 175, 53, 197)(33, 177, 56, 200)(34, 178, 58, 202)(36, 180, 61, 205)(38, 182, 64, 208)(39, 183, 66, 210)(41, 185, 69, 213)(43, 187, 72, 216)(44, 188, 74, 218)(46, 190, 77, 221)(47, 191, 79, 223)(49, 193, 82, 226)(51, 195, 85, 229)(52, 196, 87, 231)(54, 198, 90, 234)(55, 199, 92, 236)(57, 201, 95, 239)(59, 203, 98, 242)(60, 204, 100, 244)(62, 206, 103, 247)(63, 207, 104, 248)(65, 209, 107, 251)(67, 211, 110, 254)(68, 212, 112, 256)(70, 214, 115, 259)(71, 215, 117, 261)(73, 217, 120, 264)(75, 219, 123, 267)(76, 220, 125, 269)(78, 222, 128, 272)(80, 224, 109, 253)(81, 225, 106, 250)(83, 227, 114, 258)(84, 228, 105, 249)(86, 230, 126, 270)(88, 232, 124, 268)(89, 233, 108, 252)(91, 235, 116, 260)(93, 237, 122, 266)(94, 238, 119, 263)(96, 240, 127, 271)(97, 241, 118, 262)(99, 243, 113, 257)(101, 245, 111, 255)(102, 246, 121, 265)(129, 273, 138, 282)(130, 274, 141, 285)(131, 275, 136, 280)(132, 276, 142, 286)(133, 277, 143, 287)(134, 278, 137, 281)(135, 279, 139, 283)(140, 284, 144, 288)(289, 433, 291, 435, 296, 440, 305, 449, 319, 463, 342, 486, 379, 523, 350, 494, 324, 468, 308, 452, 298, 442, 292, 436)(290, 434, 293, 437, 300, 444, 311, 455, 329, 473, 358, 502, 404, 548, 366, 510, 334, 478, 314, 458, 302, 446, 294, 438)(295, 439, 301, 445, 312, 456, 331, 475, 361, 505, 409, 553, 391, 535, 403, 547, 371, 515, 337, 481, 316, 460, 303, 447)(297, 441, 306, 450, 321, 465, 345, 489, 384, 528, 416, 560, 378, 522, 396, 540, 353, 497, 326, 470, 309, 453, 299, 443)(304, 448, 315, 459, 335, 479, 368, 512, 398, 542, 388, 532, 349, 493, 390, 534, 420, 564, 374, 518, 339, 483, 317, 461)(307, 451, 322, 466, 347, 491, 387, 531, 422, 566, 377, 521, 341, 485, 375, 519, 411, 555, 381, 525, 343, 487, 320, 464)(310, 454, 325, 469, 351, 495, 393, 537, 373, 517, 413, 557, 365, 509, 415, 559, 427, 571, 399, 543, 355, 499, 327, 471)(313, 457, 332, 476, 363, 507, 412, 556, 429, 573, 402, 546, 357, 501, 400, 544, 386, 530, 406, 550, 359, 503, 330, 474)(318, 462, 338, 482, 372, 516, 419, 563, 385, 529, 346, 490, 323, 467, 348, 492, 389, 533, 421, 565, 376, 520, 340, 484)(328, 472, 354, 498, 397, 541, 426, 570, 410, 554, 362, 506, 333, 477, 364, 508, 414, 558, 428, 572, 401, 545, 356, 500)(336, 480, 369, 513, 395, 539, 425, 569, 432, 576, 430, 574, 408, 552, 382, 526, 344, 488, 380, 524, 417, 561, 367, 511)(352, 496, 394, 538, 370, 514, 418, 562, 431, 575, 423, 567, 383, 527, 407, 551, 360, 504, 405, 549, 424, 568, 392, 536) L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 299)(6, 301)(7, 291)(8, 304)(9, 292)(10, 307)(11, 293)(12, 310)(13, 294)(14, 313)(15, 315)(16, 296)(17, 318)(18, 320)(19, 298)(20, 323)(21, 325)(22, 300)(23, 328)(24, 330)(25, 302)(26, 333)(27, 303)(28, 336)(29, 338)(30, 305)(31, 341)(32, 306)(33, 344)(34, 346)(35, 308)(36, 349)(37, 309)(38, 352)(39, 354)(40, 311)(41, 357)(42, 312)(43, 360)(44, 362)(45, 314)(46, 365)(47, 367)(48, 316)(49, 370)(50, 317)(51, 373)(52, 375)(53, 319)(54, 378)(55, 380)(56, 321)(57, 383)(58, 322)(59, 386)(60, 388)(61, 324)(62, 391)(63, 392)(64, 326)(65, 395)(66, 327)(67, 398)(68, 400)(69, 329)(70, 403)(71, 405)(72, 331)(73, 408)(74, 332)(75, 411)(76, 413)(77, 334)(78, 416)(79, 335)(80, 397)(81, 394)(82, 337)(83, 402)(84, 393)(85, 339)(86, 414)(87, 340)(88, 412)(89, 396)(90, 342)(91, 404)(92, 343)(93, 410)(94, 407)(95, 345)(96, 415)(97, 406)(98, 347)(99, 401)(100, 348)(101, 399)(102, 409)(103, 350)(104, 351)(105, 372)(106, 369)(107, 353)(108, 377)(109, 368)(110, 355)(111, 389)(112, 356)(113, 387)(114, 371)(115, 358)(116, 379)(117, 359)(118, 385)(119, 382)(120, 361)(121, 390)(122, 381)(123, 363)(124, 376)(125, 364)(126, 374)(127, 384)(128, 366)(129, 426)(130, 429)(131, 424)(132, 430)(133, 431)(134, 425)(135, 427)(136, 419)(137, 422)(138, 417)(139, 423)(140, 432)(141, 418)(142, 420)(143, 421)(144, 428)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 2, 6, 2, 6 ), ( 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 E7.536 Graph:: bipartite v = 84 e = 288 f = 192 degree seq :: [ 4^72, 24^12 ] E7.536 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12}) Quotient :: dipole Aut^+ = (C3 x SL(2,3)) : C2 (small group id <144, 127>) Aut = $<288, 847>$ (small group id <288, 847>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^3, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y3^2 * Y1^-1 * Y3^-2 * Y1 * Y3^-3 * Y1^-1 * Y3 * Y1^-1, Y3^2 * Y1^-1 * Y3 * Y1^-1 * Y3^2 * Y1^-1 * Y3^3 * Y1^-1, (Y3 * Y2^-1)^12 ] Map:: polytopal R = (1, 145, 2, 146, 4, 148)(3, 147, 8, 152, 10, 154)(5, 149, 12, 156, 6, 150)(7, 151, 15, 159, 11, 155)(9, 153, 18, 162, 20, 164)(13, 157, 25, 169, 23, 167)(14, 158, 24, 168, 28, 172)(16, 160, 31, 175, 29, 173)(17, 161, 33, 177, 21, 165)(19, 163, 36, 180, 38, 182)(22, 166, 30, 174, 42, 186)(26, 170, 47, 191, 45, 189)(27, 171, 49, 193, 51, 195)(32, 176, 57, 201, 55, 199)(34, 178, 61, 205, 59, 203)(35, 179, 63, 207, 39, 183)(37, 181, 66, 210, 68, 212)(40, 184, 60, 204, 72, 216)(41, 185, 73, 217, 75, 219)(43, 187, 46, 190, 78, 222)(44, 188, 79, 223, 52, 196)(48, 192, 85, 229, 83, 227)(50, 194, 88, 232, 90, 234)(53, 197, 56, 200, 94, 238)(54, 198, 95, 239, 76, 220)(58, 202, 101, 245, 99, 243)(62, 206, 107, 251, 105, 249)(64, 208, 97, 241, 100, 244)(65, 209, 93, 237, 69, 213)(67, 211, 112, 256, 102, 246)(70, 214, 92, 236, 115, 259)(71, 215, 91, 235, 87, 231)(74, 218, 118, 262, 120, 264)(77, 221, 121, 265, 117, 261)(80, 224, 103, 247, 106, 250)(81, 225, 84, 228, 96, 240)(82, 226, 98, 242, 104, 248)(86, 230, 119, 263, 125, 269)(89, 233, 128, 272, 108, 252)(109, 253, 137, 281, 132, 276)(110, 254, 135, 279, 131, 275)(111, 255, 134, 278, 114, 258)(113, 257, 129, 273, 136, 280)(116, 260, 126, 270, 124, 268)(122, 266, 140, 284, 133, 277)(123, 267, 130, 274, 127, 271)(138, 282, 141, 285, 144, 288)(139, 283, 142, 286, 143, 287)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576) L = (1, 291)(2, 294)(3, 297)(4, 299)(5, 289)(6, 302)(7, 290)(8, 292)(9, 307)(10, 309)(11, 310)(12, 311)(13, 293)(14, 315)(15, 317)(16, 295)(17, 296)(18, 298)(19, 325)(20, 327)(21, 328)(22, 329)(23, 331)(24, 300)(25, 333)(26, 301)(27, 338)(28, 340)(29, 341)(30, 303)(31, 343)(32, 304)(33, 347)(34, 305)(35, 306)(36, 308)(37, 355)(38, 357)(39, 358)(40, 359)(41, 362)(42, 364)(43, 365)(44, 312)(45, 369)(46, 313)(47, 371)(48, 314)(49, 316)(50, 377)(51, 379)(52, 380)(53, 381)(54, 318)(55, 385)(56, 319)(57, 387)(58, 320)(59, 391)(60, 321)(61, 393)(62, 322)(63, 388)(64, 323)(65, 324)(66, 326)(67, 401)(68, 402)(69, 382)(70, 383)(71, 404)(72, 386)(73, 330)(74, 407)(75, 409)(76, 403)(77, 410)(78, 392)(79, 394)(80, 332)(81, 411)(82, 334)(83, 412)(84, 335)(85, 413)(86, 336)(87, 337)(88, 339)(89, 417)(90, 418)(91, 360)(92, 351)(93, 419)(94, 370)(95, 372)(96, 342)(97, 420)(98, 344)(99, 421)(100, 345)(101, 400)(102, 346)(103, 422)(104, 348)(105, 423)(106, 349)(107, 416)(108, 350)(109, 352)(110, 353)(111, 354)(112, 356)(113, 374)(114, 368)(115, 367)(116, 373)(117, 361)(118, 363)(119, 424)(120, 397)(121, 366)(122, 389)(123, 427)(124, 426)(125, 408)(126, 375)(127, 376)(128, 378)(129, 390)(130, 384)(131, 395)(132, 430)(133, 429)(134, 431)(135, 432)(136, 396)(137, 406)(138, 398)(139, 399)(140, 405)(141, 414)(142, 415)(143, 425)(144, 428)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 4, 24 ), ( 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E7.535 Graph:: simple bipartite v = 192 e = 288 f = 84 degree seq :: [ 2^144, 6^48 ] E7.537 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 7}) Quotient :: regular Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, (T1^-1 * T2)^3, T1^7, (T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2)^2, T2 * T1^3 * T2 * T1^-2 * T2 * T1^3 * T2 * T1^-3 * 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, 309, 279, 205, 148)(138, 191, 261, 349, 352, 262, 192)(141, 196, 267, 314, 306, 266, 195)(143, 199, 270, 358, 361, 271, 200)(153, 212, 287, 365, 370, 281, 207)(160, 221, 300, 381, 379, 297, 218)(161, 222, 301, 382, 384, 302, 223)(171, 236, 319, 398, 395, 316, 233)(173, 238, 322, 400, 403, 323, 239)(178, 245, 330, 299, 344, 254, 186)(181, 248, 335, 291, 294, 336, 249)(187, 255, 345, 413, 401, 324, 256)(190, 260, 325, 404, 416, 348, 259)(198, 208, 282, 321, 237, 320, 269)(203, 276, 366, 426, 425, 363, 273)(204, 277, 367, 399, 409, 368, 278)(210, 284, 372, 429, 431, 373, 285)(213, 289, 326, 242, 234, 317, 288)(219, 298, 380, 419, 434, 376, 293)(227, 308, 388, 441, 440, 386, 305)(229, 310, 389, 442, 444, 390, 311)(243, 327, 405, 448, 443, 391, 328)(246, 332, 392, 355, 351, 407, 331)(252, 341, 280, 369, 427, 411, 338)(253, 342, 412, 428, 371, 283, 343)(263, 353, 420, 457, 456, 418, 350)(265, 354, 387, 433, 375, 408, 339)(268, 356, 402, 334, 360, 421, 357)(274, 364, 396, 318, 397, 422, 359)(296, 377, 435, 463, 465, 436, 378)(303, 347, 415, 453, 466, 438, 383)(315, 393, 445, 470, 464, 437, 394)(346, 410, 450, 474, 476, 452, 414)(362, 423, 458, 479, 481, 459, 424)(374, 432, 385, 439, 467, 462, 430)(406, 447, 451, 475, 489, 473, 449)(417, 454, 477, 491, 480, 460, 455)(446, 469, 472, 488, 497, 487, 471)(461, 482, 494, 500, 492, 478, 483)(468, 484, 486, 496, 501, 495, 485)(490, 493, 499, 503, 504, 502, 498) 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, 346)(258, 347)(261, 350)(262, 351)(264, 340)(266, 354)(267, 355)(269, 356)(270, 359)(271, 360)(272, 362)(275, 365)(276, 278)(279, 311)(281, 369)(282, 371)(285, 289)(286, 374)(287, 364)(290, 375)(292, 366)(295, 368)(297, 377)(298, 330)(300, 358)(301, 383)(302, 361)(304, 385)(307, 387)(308, 321)(312, 391)(313, 392)(316, 393)(317, 396)(319, 399)(322, 401)(323, 402)(326, 404)(328, 332)(329, 406)(333, 403)(335, 408)(336, 409)(337, 410)(341, 343)(344, 378)(345, 414)(348, 415)(349, 417)(352, 419)(353, 357)(363, 423)(367, 390)(370, 424)(372, 430)(373, 416)(376, 426)(379, 437)(380, 407)(381, 422)(382, 420)(384, 421)(386, 439)(388, 428)(389, 443)(394, 397)(395, 446)(398, 444)(400, 447)(405, 449)(411, 450)(412, 436)(413, 451)(418, 454)(425, 460)(427, 459)(429, 461)(431, 453)(432, 433)(434, 455)(435, 464)(438, 457)(440, 468)(441, 465)(442, 469)(445, 471)(448, 472)(452, 475)(456, 478)(458, 480)(462, 482)(463, 484)(466, 483)(467, 485)(470, 486)(473, 488)(474, 481)(476, 490)(477, 492)(479, 493)(487, 496)(489, 498)(491, 499)(494, 495)(497, 502)(500, 503)(501, 504) local type(s) :: { ( 3^7 ) } Outer automorphisms :: reflexible Dual of E7.538 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 72 e = 252 f = 168 degree seq :: [ 7^72 ] E7.538 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 7}) Quotient :: regular Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^7, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 ] 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, 205, 206)(132, 254, 442)(133, 256, 407)(134, 258, 445)(135, 260, 389)(136, 261, 438)(137, 253, 255)(138, 263, 406)(139, 233, 198)(140, 265, 451)(161, 192, 193)(162, 290, 472)(163, 292, 375)(164, 294, 275)(165, 296, 413)(166, 297, 398)(167, 289, 291)(168, 299, 374)(169, 216, 207)(170, 301, 475)(171, 179, 180)(172, 182, 183)(173, 175, 177)(174, 186, 187)(176, 190, 191)(178, 196, 197)(181, 203, 204)(184, 212, 213)(185, 214, 215)(188, 202, 220)(189, 221, 222)(194, 211, 230)(195, 231, 232)(199, 241, 242)(200, 226, 243)(201, 244, 245)(208, 257, 259)(209, 237, 262)(210, 264, 266)(217, 293, 295)(218, 249, 298)(219, 300, 302)(223, 385, 387)(224, 272, 390)(225, 354, 392)(227, 307, 394)(228, 395, 397)(229, 284, 400)(234, 408, 410)(235, 411, 414)(236, 366, 416)(238, 303, 418)(239, 281, 391)(240, 420, 421)(246, 429, 431)(247, 432, 425)(248, 367, 434)(250, 304, 399)(251, 436, 415)(252, 437, 439)(267, 453, 380)(268, 454, 457)(269, 344, 433)(270, 321, 365)(271, 393, 460)(273, 305, 409)(274, 306, 381)(276, 462, 379)(277, 461, 463)(278, 464, 466)(279, 467, 360)(280, 468, 401)(282, 345, 456)(283, 346, 469)(285, 310, 377)(286, 311, 378)(287, 471, 459)(288, 402, 359)(308, 430, 373)(309, 403, 481)(312, 386, 384)(313, 370, 484)(314, 352, 349)(315, 353, 350)(316, 465, 358)(317, 426, 489)(318, 363, 424)(319, 355, 492)(320, 364, 362)(322, 493, 338)(323, 450, 495)(324, 376, 448)(325, 335, 497)(326, 342, 332)(327, 343, 333)(328, 388, 361)(329, 488, 348)(330, 474, 500)(331, 351, 455)(334, 412, 341)(336, 458, 447)(337, 396, 499)(339, 480, 369)(340, 440, 502)(347, 419, 487)(356, 503, 423)(357, 427, 494)(368, 441, 479)(371, 501, 383)(372, 404, 496)(382, 491, 405)(417, 504, 443)(422, 452, 428)(435, 498, 473)(444, 476, 446)(449, 486, 490)(470, 485, 482)(477, 478, 483) 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, 267)(142, 269)(143, 270)(144, 145)(146, 273)(147, 219)(148, 276)(149, 202)(150, 277)(151, 174)(152, 240)(153, 279)(154, 281)(155, 282)(156, 157)(158, 285)(159, 227)(160, 288)(171, 261)(172, 297)(173, 305)(175, 308)(176, 310)(177, 312)(178, 314)(179, 316)(180, 318)(181, 320)(182, 322)(183, 324)(184, 326)(185, 328)(186, 329)(187, 331)(188, 332)(189, 334)(190, 335)(191, 337)(192, 339)(193, 341)(194, 342)(195, 344)(196, 345)(197, 347)(198, 349)(199, 351)(200, 352)(201, 258)(203, 355)(204, 357)(205, 359)(206, 361)(207, 362)(208, 363)(209, 364)(210, 294)(211, 260)(212, 296)(213, 368)(214, 370)(215, 372)(216, 374)(217, 376)(218, 377)(220, 379)(221, 381)(222, 383)(223, 386)(224, 388)(225, 391)(226, 321)(228, 396)(229, 398)(230, 401)(231, 403)(232, 405)(233, 406)(234, 409)(235, 412)(236, 415)(237, 311)(238, 265)(239, 419)(241, 418)(242, 423)(243, 425)(244, 426)(245, 428)(246, 430)(247, 433)(248, 397)(249, 315)(250, 301)(251, 427)(252, 438)(253, 440)(254, 286)(255, 436)(256, 442)(257, 399)(259, 447)(262, 390)(263, 319)(264, 450)(266, 446)(268, 455)(271, 459)(272, 304)(274, 461)(275, 441)(278, 465)(280, 445)(283, 295)(284, 327)(287, 404)(289, 454)(290, 350)(291, 395)(292, 472)(293, 394)(298, 414)(299, 325)(300, 474)(302, 471)(303, 432)(306, 468)(307, 411)(309, 479)(313, 462)(317, 487)(323, 494)(330, 499)(333, 420)(336, 496)(338, 402)(340, 448)(343, 437)(346, 501)(348, 369)(353, 408)(354, 458)(356, 491)(358, 380)(360, 424)(365, 429)(366, 469)(367, 503)(371, 452)(373, 407)(375, 384)(378, 385)(382, 476)(387, 495)(389, 464)(392, 417)(393, 434)(400, 457)(410, 500)(413, 486)(416, 435)(421, 467)(422, 443)(431, 489)(439, 502)(444, 473)(449, 493)(451, 480)(453, 475)(456, 478)(460, 470)(463, 488)(466, 481)(477, 497)(482, 504)(483, 492)(484, 490)(485, 498) local type(s) :: { ( 7^3 ) } Outer automorphisms :: reflexible Dual of E7.537 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 168 e = 252 f = 72 degree seq :: [ 3^168 ] E7.539 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1)^7, T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 ] Map:: polytopal R = (1, 3, 4)(2, 5, 6)(7, 11, 12)(8, 13, 14)(9, 15, 16)(10, 17, 18)(19, 27, 28)(20, 29, 30)(21, 31, 32)(22, 33, 34)(23, 35, 36)(24, 37, 38)(25, 39, 40)(26, 41, 42)(43, 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, 285, 367)(152, 287, 249)(153, 270, 377)(154, 227, 180)(155, 290, 257)(156, 222, 182)(157, 293, 475)(158, 242, 366)(159, 296, 344)(160, 298, 232)(161, 300, 395)(162, 301, 295)(163, 303, 351)(164, 255, 188)(165, 306, 263)(166, 202, 175)(167, 309, 485)(168, 286, 393)(169, 311, 359)(170, 313, 238)(171, 195, 193)(172, 201, 199)(173, 198, 196)(174, 186, 184)(176, 183, 181)(177, 217, 215)(178, 221, 219)(179, 225, 223)(185, 204, 229)(187, 253, 203)(189, 260, 218)(190, 264, 197)(191, 272, 268)(192, 280, 226)(194, 207, 258)(200, 212, 276)(205, 334, 374)(206, 338, 254)(208, 348, 380)(209, 324, 261)(210, 330, 384)(211, 343, 267)(213, 353, 389)(214, 320, 283)(216, 233, 394)(220, 239, 398)(224, 244, 405)(228, 250, 408)(230, 318, 413)(231, 358, 271)(234, 373, 418)(235, 322, 411)(236, 328, 422)(237, 363, 333)(240, 379, 426)(241, 316, 420)(243, 275, 428)(245, 383, 431)(246, 326, 415)(247, 332, 424)(248, 371, 329)(251, 388, 435)(252, 282, 437)(256, 297, 265)(259, 304, 443)(262, 312, 404)(266, 448, 274)(269, 419, 452)(273, 454, 339)(277, 457, 406)(278, 414, 459)(279, 460, 453)(281, 397, 346)(284, 464, 466)(288, 434, 467)(289, 412, 469)(291, 336, 390)(292, 347, 387)(294, 396, 317)(299, 417, 477)(302, 446, 458)(305, 421, 480)(307, 340, 386)(308, 350, 416)(310, 402, 327)(314, 425, 486)(315, 451, 407)(319, 488, 439)(321, 489, 445)(323, 468, 450)(325, 470, 463)(331, 465, 392)(335, 481, 493)(337, 430, 492)(341, 484, 494)(342, 381, 449)(345, 376, 462)(349, 474, 365)(352, 378, 372)(354, 495, 357)(355, 429, 364)(356, 432, 490)(360, 382, 479)(361, 473, 461)(362, 375, 496)(368, 391, 491)(369, 497, 444)(370, 385, 498)(399, 427, 487)(400, 455, 438)(401, 423, 499)(403, 436, 442)(409, 440, 447)(410, 433, 472)(441, 476, 483)(456, 503, 471)(478, 504, 482)(500, 502, 501)(505, 506)(507, 511)(508, 512)(509, 513)(510, 514)(515, 523)(516, 524)(517, 525)(518, 526)(519, 527)(520, 528)(521, 529)(522, 530)(531, 547)(532, 548)(533, 549)(534, 550)(535, 551)(536, 552)(537, 553)(538, 554)(539, 555)(540, 556)(541, 557)(542, 558)(543, 559)(544, 560)(545, 561)(546, 562)(563, 589)(564, 590)(565, 591)(566, 592)(567, 593)(568, 594)(569, 570)(571, 595)(572, 596)(573, 597)(574, 598)(575, 599)(576, 600)(577, 601)(578, 602)(579, 603)(580, 604)(581, 605)(582, 583)(584, 606)(585, 607)(586, 608)(587, 609)(588, 610)(611, 655)(612, 656)(613, 657)(614, 658)(615, 659)(616, 617)(618, 660)(619, 661)(620, 662)(621, 663)(622, 664)(623, 665)(624, 666)(625, 667)(626, 668)(627, 669)(628, 629)(630, 670)(631, 671)(632, 672)(633, 673)(634, 674)(635, 769)(636, 725)(637, 770)(638, 639)(640, 708)(641, 773)(642, 775)(643, 777)(644, 779)(645, 781)(646, 783)(647, 785)(648, 776)(649, 786)(650, 651)(652, 702)(653, 788)(654, 766)(675, 819)(676, 821)(677, 823)(678, 825)(679, 827)(680, 829)(681, 831)(682, 833)(683, 835)(684, 837)(685, 839)(686, 841)(687, 843)(688, 845)(689, 803)(690, 848)(691, 850)(692, 771)(693, 853)(694, 855)(695, 758)(696, 858)(697, 860)(698, 818)(699, 863)(700, 865)(701, 755)(703, 809)(704, 792)(705, 871)(706, 873)(707, 744)(709, 765)(710, 879)(711, 881)(712, 730)(713, 885)(714, 787)(715, 889)(716, 801)(717, 722)(718, 894)(719, 749)(720, 806)(721, 899)(723, 793)(724, 747)(726, 904)(727, 738)(728, 907)(729, 910)(731, 903)(732, 736)(733, 913)(734, 915)(735, 918)(737, 816)(739, 890)(740, 924)(741, 927)(742, 760)(743, 754)(745, 919)(746, 808)(748, 790)(750, 880)(751, 917)(752, 937)(753, 774)(756, 940)(757, 942)(759, 872)(761, 938)(762, 944)(763, 946)(764, 948)(767, 950)(768, 951)(772, 864)(778, 929)(780, 959)(782, 962)(784, 965)(789, 908)(791, 960)(794, 974)(795, 886)(796, 926)(797, 978)(798, 980)(799, 807)(800, 870)(802, 914)(804, 912)(805, 982)(810, 985)(811, 859)(812, 888)(813, 969)(814, 968)(815, 897)(817, 945)(820, 973)(822, 991)(824, 984)(826, 935)(828, 994)(830, 922)(832, 995)(834, 956)(836, 983)(838, 979)(840, 930)(842, 998)(844, 893)(846, 939)(847, 997)(849, 884)(851, 933)(852, 989)(854, 966)(856, 920)(857, 970)(861, 981)(862, 958)(866, 990)(867, 967)(868, 878)(869, 996)(874, 971)(875, 949)(876, 928)(877, 976)(882, 891)(883, 987)(887, 1003)(892, 975)(895, 953)(896, 954)(898, 1001)(900, 911)(901, 957)(902, 961)(905, 932)(906, 943)(909, 977)(916, 1002)(921, 986)(923, 999)(925, 963)(931, 1000)(934, 1005)(936, 947)(941, 988)(952, 993)(955, 1007)(964, 1004)(972, 1006)(992, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 673)(170, 674)(171, 675)(172, 676)(173, 677)(174, 678)(175, 679)(176, 680)(177, 681)(178, 682)(179, 683)(180, 684)(181, 685)(182, 686)(183, 687)(184, 688)(185, 689)(186, 690)(187, 691)(188, 692)(189, 693)(190, 694)(191, 695)(192, 696)(193, 697)(194, 698)(195, 699)(196, 700)(197, 701)(198, 702)(199, 703)(200, 704)(201, 705)(202, 706)(203, 707)(204, 708)(205, 709)(206, 710)(207, 711)(208, 712)(209, 713)(210, 714)(211, 715)(212, 716)(213, 717)(214, 718)(215, 719)(216, 720)(217, 721)(218, 722)(219, 723)(220, 724)(221, 725)(222, 726)(223, 727)(224, 728)(225, 729)(226, 730)(227, 731)(228, 732)(229, 733)(230, 734)(231, 735)(232, 736)(233, 737)(234, 738)(235, 739)(236, 740)(237, 741)(238, 742)(239, 743)(240, 744)(241, 745)(242, 746)(243, 747)(244, 748)(245, 749)(246, 750)(247, 751)(248, 752)(249, 753)(250, 754)(251, 755)(252, 756)(253, 757)(254, 758)(255, 759)(256, 760)(257, 761)(258, 762)(259, 763)(260, 764)(261, 765)(262, 766)(263, 767)(264, 768)(265, 769)(266, 770)(267, 771)(268, 772)(269, 773)(270, 774)(271, 775)(272, 776)(273, 777)(274, 778)(275, 779)(276, 780)(277, 781)(278, 782)(279, 783)(280, 784)(281, 785)(282, 786)(283, 787)(284, 788)(285, 789)(286, 790)(287, 791)(288, 792)(289, 793)(290, 794)(291, 795)(292, 796)(293, 797)(294, 798)(295, 799)(296, 800)(297, 801)(298, 802)(299, 803)(300, 804)(301, 805)(302, 806)(303, 807)(304, 808)(305, 809)(306, 810)(307, 811)(308, 812)(309, 813)(310, 814)(311, 815)(312, 816)(313, 817)(314, 818)(315, 819)(316, 820)(317, 821)(318, 822)(319, 823)(320, 824)(321, 825)(322, 826)(323, 827)(324, 828)(325, 829)(326, 830)(327, 831)(328, 832)(329, 833)(330, 834)(331, 835)(332, 836)(333, 837)(334, 838)(335, 839)(336, 840)(337, 841)(338, 842)(339, 843)(340, 844)(341, 845)(342, 846)(343, 847)(344, 848)(345, 849)(346, 850)(347, 851)(348, 852)(349, 853)(350, 854)(351, 855)(352, 856)(353, 857)(354, 858)(355, 859)(356, 860)(357, 861)(358, 862)(359, 863)(360, 864)(361, 865)(362, 866)(363, 867)(364, 868)(365, 869)(366, 870)(367, 871)(368, 872)(369, 873)(370, 874)(371, 875)(372, 876)(373, 877)(374, 878)(375, 879)(376, 880)(377, 881)(378, 882)(379, 883)(380, 884)(381, 885)(382, 886)(383, 887)(384, 888)(385, 889)(386, 890)(387, 891)(388, 892)(389, 893)(390, 894)(391, 895)(392, 896)(393, 897)(394, 898)(395, 899)(396, 900)(397, 901)(398, 902)(399, 903)(400, 904)(401, 905)(402, 906)(403, 907)(404, 908)(405, 909)(406, 910)(407, 911)(408, 912)(409, 913)(410, 914)(411, 915)(412, 916)(413, 917)(414, 918)(415, 919)(416, 920)(417, 921)(418, 922)(419, 923)(420, 924)(421, 925)(422, 926)(423, 927)(424, 928)(425, 929)(426, 930)(427, 931)(428, 932)(429, 933)(430, 934)(431, 935)(432, 936)(433, 937)(434, 938)(435, 939)(436, 940)(437, 941)(438, 942)(439, 943)(440, 944)(441, 945)(442, 946)(443, 947)(444, 948)(445, 949)(446, 950)(447, 951)(448, 952)(449, 953)(450, 954)(451, 955)(452, 956)(453, 957)(454, 958)(455, 959)(456, 960)(457, 961)(458, 962)(459, 963)(460, 964)(461, 965)(462, 966)(463, 967)(464, 968)(465, 969)(466, 970)(467, 971)(468, 972)(469, 973)(470, 974)(471, 975)(472, 976)(473, 977)(474, 978)(475, 979)(476, 980)(477, 981)(478, 982)(479, 983)(480, 984)(481, 985)(482, 986)(483, 987)(484, 988)(485, 989)(486, 990)(487, 991)(488, 992)(489, 993)(490, 994)(491, 995)(492, 996)(493, 997)(494, 998)(495, 999)(496, 1000)(497, 1001)(498, 1002)(499, 1003)(500, 1004)(501, 1005)(502, 1006)(503, 1007)(504, 1008) local type(s) :: { ( 14, 14 ), ( 14^3 ) } Outer automorphisms :: reflexible Dual of E7.543 Transitivity :: ET+ Graph:: simple bipartite v = 420 e = 504 f = 72 degree seq :: [ 2^252, 3^168 ] E7.540 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T2^7, T2^-5 * T1 * T2^-2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^-2 * T1 * T2^-1, T2^3 * T1^-1 * T2^2 * T1^-1 * T2^-2 * T1 * T2^-3 * T1 * T2^-3 * T1^-1 * T2 * T1^-1, T2^2 * T1^-1 * T2^-2 * T1 * T2^3 * T1^-1 * T2^2 * T1^-1 * T2^-3 * T1^-1 * T2^2 * 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, 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, 398, 285, 202)(141, 205, 288, 399, 361, 286, 203)(148, 214, 301, 413, 416, 302, 215)(152, 220, 307, 419, 397, 305, 218)(160, 232, 325, 368, 332, 236, 164)(165, 204, 287, 351, 440, 333, 237)(168, 172, 245, 344, 289, 338, 240)(170, 243, 341, 392, 279, 339, 241)(181, 258, 364, 379, 371, 262, 185)(186, 242, 340, 297, 409, 372, 263)(188, 265, 375, 329, 382, 269, 192)(193, 270, 383, 312, 423, 384, 271)(196, 275, 388, 360, 356, 386, 273)(197, 276, 389, 464, 466, 390, 277)(209, 294, 406, 310, 314, 407, 295)(213, 300, 412, 471, 439, 410, 298)(216, 219, 306, 402, 342, 417, 303)(217, 304, 418, 430, 322, 385, 272)(221, 308, 421, 349, 353, 422, 309)(225, 315, 425, 476, 458, 424, 313)(227, 318, 391, 278, 274, 387, 316)(228, 319, 427, 400, 469, 428, 320)(247, 347, 408, 296, 299, 411, 348)(251, 354, 450, 483, 463, 449, 352)(253, 357, 429, 321, 317, 426, 355)(254, 358, 451, 444, 481, 452, 359)(282, 394, 467, 462, 453, 362, 393)(283, 395, 366, 454, 486, 468, 396)(293, 405, 470, 437, 330, 436, 403)(323, 431, 414, 445, 447, 457, 432)(327, 434, 479, 491, 473, 415, 433)(335, 401, 404, 438, 435, 373, 441)(336, 442, 377, 459, 487, 480, 443)(346, 448, 482, 456, 369, 455, 446)(380, 460, 474, 420, 475, 488, 461)(465, 489, 494, 472, 495, 502, 490)(477, 493, 503, 497, 478, 492, 496)(484, 499, 504, 501, 485, 498, 500)(505, 506, 508)(507, 512, 514)(509, 516, 510)(511, 519, 515)(513, 522, 524)(517, 529, 527)(518, 528, 532)(520, 535, 533)(521, 537, 525)(523, 540, 541)(526, 534, 545)(530, 550, 548)(531, 551, 552)(536, 558, 556)(538, 561, 559)(539, 562, 542)(543, 560, 568)(544, 569, 570)(546, 549, 573)(547, 574, 553)(554, 557, 583)(555, 584, 571)(563, 594, 592)(564, 595, 565)(566, 593, 599)(567, 600, 601)(572, 606, 607)(575, 611, 609)(576, 578, 613)(577, 614, 608)(579, 617, 580)(581, 610, 621)(582, 622, 623)(585, 627, 625)(586, 588, 629)(587, 630, 624)(589, 591, 634)(590, 635, 602)(596, 643, 641)(597, 642, 645)(598, 646, 647)(603, 652, 604)(605, 626, 656)(612, 663, 664)(615, 668, 666)(616, 669, 665)(618, 672, 670)(619, 671, 674)(620, 675, 676)(628, 684, 685)(631, 689, 687)(632, 690, 686)(633, 691, 692)(636, 696, 694)(637, 697, 693)(638, 640, 700)(639, 701, 648)(644, 707, 708)(649, 713, 650)(651, 695, 717)(653, 720, 718)(654, 719, 721)(655, 722, 723)(657, 725, 658)(659, 667, 729)(660, 662, 731)(661, 732, 677)(673, 745, 746)(678, 751, 679)(680, 688, 755)(681, 683, 757)(682, 758, 724)(698, 776, 774)(699, 777, 778)(702, 782, 780)(703, 783, 779)(704, 706, 786)(705, 787, 709)(710, 793, 711)(712, 781, 797)(714, 800, 798)(715, 799, 801)(716, 802, 803)(726, 814, 812)(727, 813, 816)(728, 817, 818)(730, 820, 821)(733, 825, 823)(734, 826, 822)(735, 827, 736)(737, 741, 831)(738, 740, 833)(739, 834, 819)(742, 744, 839)(743, 840, 747)(748, 846, 749)(750, 824, 850)(752, 853, 851)(753, 852, 855)(754, 856, 857)(756, 859, 860)(759, 864, 862)(760, 865, 861)(761, 866, 762)(763, 767, 870)(764, 766, 872)(765, 873, 858)(768, 877, 769)(770, 775, 881)(771, 773, 883)(772, 884, 804)(784, 844, 843)(785, 897, 867)(788, 869, 899)(789, 901, 898)(790, 854, 791)(792, 900, 904)(794, 905, 842)(795, 848, 906)(796, 907, 908)(805, 807, 918)(806, 919, 808)(809, 902, 810)(811, 863, 924)(815, 887, 889)(828, 917, 935)(829, 936, 871)(830, 937, 920)(832, 879, 939)(835, 942, 940)(836, 875, 886)(837, 943, 938)(838, 945, 878)(841, 880, 946)(845, 947, 948)(847, 949, 921)(849, 950, 951)(868, 957, 882)(874, 961, 959)(876, 962, 958)(885, 966, 964)(888, 967, 963)(890, 930, 891)(892, 896, 955)(893, 895, 934)(894, 969, 909)(903, 931, 933)(910, 912, 925)(911, 928, 913)(914, 944, 915)(916, 965, 976)(922, 977, 968)(923, 978, 971)(926, 953, 927)(929, 941, 981)(932, 982, 952)(954, 960, 988)(956, 989, 979)(970, 995, 993)(972, 996, 973)(974, 994, 997)(975, 998, 983)(980, 1000, 990)(984, 1002, 985)(986, 1001, 1003)(987, 1004, 991)(992, 1005, 999)(1006, 1008, 1007) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 673)(170, 674)(171, 675)(172, 676)(173, 677)(174, 678)(175, 679)(176, 680)(177, 681)(178, 682)(179, 683)(180, 684)(181, 685)(182, 686)(183, 687)(184, 688)(185, 689)(186, 690)(187, 691)(188, 692)(189, 693)(190, 694)(191, 695)(192, 696)(193, 697)(194, 698)(195, 699)(196, 700)(197, 701)(198, 702)(199, 703)(200, 704)(201, 705)(202, 706)(203, 707)(204, 708)(205, 709)(206, 710)(207, 711)(208, 712)(209, 713)(210, 714)(211, 715)(212, 716)(213, 717)(214, 718)(215, 719)(216, 720)(217, 721)(218, 722)(219, 723)(220, 724)(221, 725)(222, 726)(223, 727)(224, 728)(225, 729)(226, 730)(227, 731)(228, 732)(229, 733)(230, 734)(231, 735)(232, 736)(233, 737)(234, 738)(235, 739)(236, 740)(237, 741)(238, 742)(239, 743)(240, 744)(241, 745)(242, 746)(243, 747)(244, 748)(245, 749)(246, 750)(247, 751)(248, 752)(249, 753)(250, 754)(251, 755)(252, 756)(253, 757)(254, 758)(255, 759)(256, 760)(257, 761)(258, 762)(259, 763)(260, 764)(261, 765)(262, 766)(263, 767)(264, 768)(265, 769)(266, 770)(267, 771)(268, 772)(269, 773)(270, 774)(271, 775)(272, 776)(273, 777)(274, 778)(275, 779)(276, 780)(277, 781)(278, 782)(279, 783)(280, 784)(281, 785)(282, 786)(283, 787)(284, 788)(285, 789)(286, 790)(287, 791)(288, 792)(289, 793)(290, 794)(291, 795)(292, 796)(293, 797)(294, 798)(295, 799)(296, 800)(297, 801)(298, 802)(299, 803)(300, 804)(301, 805)(302, 806)(303, 807)(304, 808)(305, 809)(306, 810)(307, 811)(308, 812)(309, 813)(310, 814)(311, 815)(312, 816)(313, 817)(314, 818)(315, 819)(316, 820)(317, 821)(318, 822)(319, 823)(320, 824)(321, 825)(322, 826)(323, 827)(324, 828)(325, 829)(326, 830)(327, 831)(328, 832)(329, 833)(330, 834)(331, 835)(332, 836)(333, 837)(334, 838)(335, 839)(336, 840)(337, 841)(338, 842)(339, 843)(340, 844)(341, 845)(342, 846)(343, 847)(344, 848)(345, 849)(346, 850)(347, 851)(348, 852)(349, 853)(350, 854)(351, 855)(352, 856)(353, 857)(354, 858)(355, 859)(356, 860)(357, 861)(358, 862)(359, 863)(360, 864)(361, 865)(362, 866)(363, 867)(364, 868)(365, 869)(366, 870)(367, 871)(368, 872)(369, 873)(370, 874)(371, 875)(372, 876)(373, 877)(374, 878)(375, 879)(376, 880)(377, 881)(378, 882)(379, 883)(380, 884)(381, 885)(382, 886)(383, 887)(384, 888)(385, 889)(386, 890)(387, 891)(388, 892)(389, 893)(390, 894)(391, 895)(392, 896)(393, 897)(394, 898)(395, 899)(396, 900)(397, 901)(398, 902)(399, 903)(400, 904)(401, 905)(402, 906)(403, 907)(404, 908)(405, 909)(406, 910)(407, 911)(408, 912)(409, 913)(410, 914)(411, 915)(412, 916)(413, 917)(414, 918)(415, 919)(416, 920)(417, 921)(418, 922)(419, 923)(420, 924)(421, 925)(422, 926)(423, 927)(424, 928)(425, 929)(426, 930)(427, 931)(428, 932)(429, 933)(430, 934)(431, 935)(432, 936)(433, 937)(434, 938)(435, 939)(436, 940)(437, 941)(438, 942)(439, 943)(440, 944)(441, 945)(442, 946)(443, 947)(444, 948)(445, 949)(446, 950)(447, 951)(448, 952)(449, 953)(450, 954)(451, 955)(452, 956)(453, 957)(454, 958)(455, 959)(456, 960)(457, 961)(458, 962)(459, 963)(460, 964)(461, 965)(462, 966)(463, 967)(464, 968)(465, 969)(466, 970)(467, 971)(468, 972)(469, 973)(470, 974)(471, 975)(472, 976)(473, 977)(474, 978)(475, 979)(476, 980)(477, 981)(478, 982)(479, 983)(480, 984)(481, 985)(482, 986)(483, 987)(484, 988)(485, 989)(486, 990)(487, 991)(488, 992)(489, 993)(490, 994)(491, 995)(492, 996)(493, 997)(494, 998)(495, 999)(496, 1000)(497, 1001)(498, 1002)(499, 1003)(500, 1004)(501, 1005)(502, 1006)(503, 1007)(504, 1008) local type(s) :: { ( 4^3 ), ( 4^7 ) } Outer automorphisms :: reflexible Dual of E7.544 Transitivity :: ET+ Graph:: simple bipartite v = 240 e = 504 f = 252 degree seq :: [ 3^168, 7^72 ] E7.541 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^7, (T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2)^2, T2 * T1^3 * T2 * T1^-2 * T2 * T1^3 * T2 * T1^-3 * T2 * T1^2 * T2 * T1^-3 ] 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, 346)(258, 347)(261, 350)(262, 351)(264, 340)(266, 354)(267, 355)(269, 356)(270, 359)(271, 360)(272, 362)(275, 365)(276, 278)(279, 311)(281, 369)(282, 371)(285, 289)(286, 374)(287, 364)(290, 375)(292, 366)(295, 368)(297, 377)(298, 330)(300, 358)(301, 383)(302, 361)(304, 385)(307, 387)(308, 321)(312, 391)(313, 392)(316, 393)(317, 396)(319, 399)(322, 401)(323, 402)(326, 404)(328, 332)(329, 406)(333, 403)(335, 408)(336, 409)(337, 410)(341, 343)(344, 378)(345, 414)(348, 415)(349, 417)(352, 419)(353, 357)(363, 423)(367, 390)(370, 424)(372, 430)(373, 416)(376, 426)(379, 437)(380, 407)(381, 422)(382, 420)(384, 421)(386, 439)(388, 428)(389, 443)(394, 397)(395, 446)(398, 444)(400, 447)(405, 449)(411, 450)(412, 436)(413, 451)(418, 454)(425, 460)(427, 459)(429, 461)(431, 453)(432, 433)(434, 455)(435, 464)(438, 457)(440, 468)(441, 465)(442, 469)(445, 471)(448, 472)(452, 475)(456, 478)(458, 480)(462, 482)(463, 484)(466, 483)(467, 485)(470, 486)(473, 488)(474, 481)(476, 490)(477, 492)(479, 493)(487, 496)(489, 498)(491, 499)(494, 495)(497, 502)(500, 503)(501, 504)(505, 506, 509, 515, 524, 514, 508)(507, 511, 519, 530, 534, 521, 512)(510, 517, 528, 543, 546, 529, 518)(513, 522, 535, 553, 550, 532, 520)(516, 526, 541, 561, 564, 542, 527)(523, 537, 556, 581, 580, 555, 536)(525, 539, 559, 585, 588, 560, 540)(531, 548, 571, 601, 604, 572, 549)(533, 551, 574, 606, 595, 566, 544)(538, 558, 584, 619, 618, 583, 557)(545, 567, 596, 634, 627, 590, 562)(547, 569, 599, 638, 641, 600, 570)(552, 576, 609, 651, 650, 608, 575)(554, 578, 612, 655, 658, 613, 579)(563, 591, 628, 676, 669, 622, 586)(565, 593, 631, 680, 683, 632, 594)(568, 598, 637, 689, 688, 636, 597)(573, 605, 646, 701, 697, 643, 602)(577, 610, 653, 710, 713, 654, 611)(582, 616, 662, 721, 724, 663, 617)(587, 623, 670, 732, 728, 666, 620)(589, 625, 673, 736, 739, 674, 626)(592, 630, 679, 745, 744, 678, 629)(603, 644, 698, 768, 761, 692, 639)(607, 648, 705, 776, 779, 706, 649)(614, 659, 718, 794, 790, 715, 656)(615, 660, 719, 796, 799, 720, 661)(621, 667, 729, 808, 811, 730, 668)(624, 672, 735, 817, 816, 734, 671)(633, 684, 751, 837, 833, 748, 681)(635, 686, 754, 841, 844, 755, 687)(640, 693, 762, 813, 783, 709, 652)(642, 695, 765, 853, 856, 766, 696)(645, 700, 771, 818, 810, 770, 699)(647, 703, 774, 862, 865, 775, 704)(657, 716, 791, 869, 874, 785, 711)(664, 725, 804, 885, 883, 801, 722)(665, 726, 805, 886, 888, 806, 727)(675, 740, 823, 902, 899, 820, 737)(677, 742, 826, 904, 907, 827, 743)(682, 749, 834, 803, 848, 758, 690)(685, 752, 839, 795, 798, 840, 753)(691, 759, 849, 917, 905, 828, 760)(694, 764, 829, 908, 920, 852, 763)(702, 712, 786, 825, 741, 824, 773)(707, 780, 870, 930, 929, 867, 777)(708, 781, 871, 903, 913, 872, 782)(714, 788, 876, 933, 935, 877, 789)(717, 793, 830, 746, 738, 821, 792)(723, 802, 884, 923, 938, 880, 797)(731, 812, 892, 945, 944, 890, 809)(733, 814, 893, 946, 948, 894, 815)(747, 831, 909, 952, 947, 895, 832)(750, 836, 896, 859, 855, 911, 835)(756, 845, 784, 873, 931, 915, 842)(757, 846, 916, 932, 875, 787, 847)(767, 857, 924, 961, 960, 922, 854)(769, 858, 891, 937, 879, 912, 843)(772, 860, 906, 838, 864, 925, 861)(778, 868, 900, 822, 901, 926, 863)(800, 881, 939, 967, 969, 940, 882)(807, 851, 919, 957, 970, 942, 887)(819, 897, 949, 974, 968, 941, 898)(850, 914, 954, 978, 980, 956, 918)(866, 927, 962, 983, 985, 963, 928)(878, 936, 889, 943, 971, 966, 934)(910, 951, 955, 979, 993, 977, 953)(921, 958, 981, 995, 984, 964, 959)(950, 973, 976, 992, 1001, 991, 975)(965, 986, 998, 1004, 996, 982, 987)(972, 988, 990, 1000, 1005, 999, 989)(994, 997, 1003, 1007, 1008, 1006, 1002) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 673)(170, 674)(171, 675)(172, 676)(173, 677)(174, 678)(175, 679)(176, 680)(177, 681)(178, 682)(179, 683)(180, 684)(181, 685)(182, 686)(183, 687)(184, 688)(185, 689)(186, 690)(187, 691)(188, 692)(189, 693)(190, 694)(191, 695)(192, 696)(193, 697)(194, 698)(195, 699)(196, 700)(197, 701)(198, 702)(199, 703)(200, 704)(201, 705)(202, 706)(203, 707)(204, 708)(205, 709)(206, 710)(207, 711)(208, 712)(209, 713)(210, 714)(211, 715)(212, 716)(213, 717)(214, 718)(215, 719)(216, 720)(217, 721)(218, 722)(219, 723)(220, 724)(221, 725)(222, 726)(223, 727)(224, 728)(225, 729)(226, 730)(227, 731)(228, 732)(229, 733)(230, 734)(231, 735)(232, 736)(233, 737)(234, 738)(235, 739)(236, 740)(237, 741)(238, 742)(239, 743)(240, 744)(241, 745)(242, 746)(243, 747)(244, 748)(245, 749)(246, 750)(247, 751)(248, 752)(249, 753)(250, 754)(251, 755)(252, 756)(253, 757)(254, 758)(255, 759)(256, 760)(257, 761)(258, 762)(259, 763)(260, 764)(261, 765)(262, 766)(263, 767)(264, 768)(265, 769)(266, 770)(267, 771)(268, 772)(269, 773)(270, 774)(271, 775)(272, 776)(273, 777)(274, 778)(275, 779)(276, 780)(277, 781)(278, 782)(279, 783)(280, 784)(281, 785)(282, 786)(283, 787)(284, 788)(285, 789)(286, 790)(287, 791)(288, 792)(289, 793)(290, 794)(291, 795)(292, 796)(293, 797)(294, 798)(295, 799)(296, 800)(297, 801)(298, 802)(299, 803)(300, 804)(301, 805)(302, 806)(303, 807)(304, 808)(305, 809)(306, 810)(307, 811)(308, 812)(309, 813)(310, 814)(311, 815)(312, 816)(313, 817)(314, 818)(315, 819)(316, 820)(317, 821)(318, 822)(319, 823)(320, 824)(321, 825)(322, 826)(323, 827)(324, 828)(325, 829)(326, 830)(327, 831)(328, 832)(329, 833)(330, 834)(331, 835)(332, 836)(333, 837)(334, 838)(335, 839)(336, 840)(337, 841)(338, 842)(339, 843)(340, 844)(341, 845)(342, 846)(343, 847)(344, 848)(345, 849)(346, 850)(347, 851)(348, 852)(349, 853)(350, 854)(351, 855)(352, 856)(353, 857)(354, 858)(355, 859)(356, 860)(357, 861)(358, 862)(359, 863)(360, 864)(361, 865)(362, 866)(363, 867)(364, 868)(365, 869)(366, 870)(367, 871)(368, 872)(369, 873)(370, 874)(371, 875)(372, 876)(373, 877)(374, 878)(375, 879)(376, 880)(377, 881)(378, 882)(379, 883)(380, 884)(381, 885)(382, 886)(383, 887)(384, 888)(385, 889)(386, 890)(387, 891)(388, 892)(389, 893)(390, 894)(391, 895)(392, 896)(393, 897)(394, 898)(395, 899)(396, 900)(397, 901)(398, 902)(399, 903)(400, 904)(401, 905)(402, 906)(403, 907)(404, 908)(405, 909)(406, 910)(407, 911)(408, 912)(409, 913)(410, 914)(411, 915)(412, 916)(413, 917)(414, 918)(415, 919)(416, 920)(417, 921)(418, 922)(419, 923)(420, 924)(421, 925)(422, 926)(423, 927)(424, 928)(425, 929)(426, 930)(427, 931)(428, 932)(429, 933)(430, 934)(431, 935)(432, 936)(433, 937)(434, 938)(435, 939)(436, 940)(437, 941)(438, 942)(439, 943)(440, 944)(441, 945)(442, 946)(443, 947)(444, 948)(445, 949)(446, 950)(447, 951)(448, 952)(449, 953)(450, 954)(451, 955)(452, 956)(453, 957)(454, 958)(455, 959)(456, 960)(457, 961)(458, 962)(459, 963)(460, 964)(461, 965)(462, 966)(463, 967)(464, 968)(465, 969)(466, 970)(467, 971)(468, 972)(469, 973)(470, 974)(471, 975)(472, 976)(473, 977)(474, 978)(475, 979)(476, 980)(477, 981)(478, 982)(479, 983)(480, 984)(481, 985)(482, 986)(483, 987)(484, 988)(485, 989)(486, 990)(487, 991)(488, 992)(489, 993)(490, 994)(491, 995)(492, 996)(493, 997)(494, 998)(495, 999)(496, 1000)(497, 1001)(498, 1002)(499, 1003)(500, 1004)(501, 1005)(502, 1006)(503, 1007)(504, 1008) local type(s) :: { ( 6, 6 ), ( 6^7 ) } Outer automorphisms :: reflexible Dual of E7.542 Transitivity :: ET+ Graph:: simple bipartite v = 324 e = 504 f = 168 degree seq :: [ 2^252, 7^72 ] E7.542 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1)^7, T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 ] Map:: R = (1, 505, 3, 507, 4, 508)(2, 506, 5, 509, 6, 510)(7, 511, 11, 515, 12, 516)(8, 512, 13, 517, 14, 518)(9, 513, 15, 519, 16, 520)(10, 514, 17, 521, 18, 522)(19, 523, 27, 531, 28, 532)(20, 524, 29, 533, 30, 534)(21, 525, 31, 535, 32, 536)(22, 526, 33, 537, 34, 538)(23, 527, 35, 539, 36, 540)(24, 528, 37, 541, 38, 542)(25, 529, 39, 543, 40, 544)(26, 530, 41, 545, 42, 546)(43, 547, 58, 562, 59, 563)(44, 548, 60, 564, 61, 565)(45, 549, 62, 566, 63, 567)(46, 550, 64, 568, 65, 569)(47, 551, 66, 570, 67, 571)(48, 552, 68, 572, 69, 573)(49, 553, 70, 574, 71, 575)(50, 554, 72, 576, 51, 555)(52, 556, 73, 577, 74, 578)(53, 557, 75, 579, 76, 580)(54, 558, 77, 581, 78, 582)(55, 559, 79, 583, 80, 584)(56, 560, 81, 585, 82, 586)(57, 561, 83, 587, 84, 588)(85, 589, 107, 611, 108, 612)(86, 590, 109, 613, 110, 614)(87, 591, 111, 615, 112, 616)(88, 592, 113, 617, 114, 618)(89, 593, 115, 619, 116, 620)(90, 594, 117, 621, 118, 622)(91, 595, 119, 623, 120, 624)(92, 596, 121, 625, 122, 626)(93, 597, 123, 627, 124, 628)(94, 598, 125, 629, 126, 630)(95, 599, 127, 631, 128, 632)(96, 600, 129, 633, 130, 634)(97, 601, 131, 635, 132, 636)(98, 602, 133, 637, 134, 638)(99, 603, 135, 639, 136, 640)(100, 604, 137, 641, 138, 642)(101, 605, 139, 643, 140, 644)(102, 606, 141, 645, 142, 646)(103, 607, 143, 647, 144, 648)(104, 608, 145, 649, 146, 650)(105, 609, 147, 651, 148, 652)(106, 610, 149, 653, 150, 654)(151, 655, 275, 779, 348, 852)(152, 656, 270, 774, 446, 950)(153, 657, 278, 782, 454, 958)(154, 658, 190, 694, 239, 743)(155, 659, 215, 719, 364, 868)(156, 660, 173, 677, 234, 738)(157, 661, 280, 784, 458, 962)(158, 662, 282, 786, 253, 757)(159, 663, 284, 788, 317, 821)(160, 664, 245, 749, 411, 915)(161, 665, 287, 791, 337, 841)(162, 666, 289, 793, 460, 964)(163, 667, 291, 795, 464, 968)(164, 668, 202, 706, 281, 785)(165, 669, 220, 724, 372, 876)(166, 670, 171, 675, 211, 715)(167, 671, 294, 798, 468, 972)(168, 672, 295, 799, 225, 729)(169, 673, 297, 801, 338, 842)(170, 674, 250, 754, 422, 926)(172, 676, 205, 709, 203, 707)(174, 678, 226, 730, 241, 745)(175, 679, 189, 693, 187, 691)(176, 680, 201, 705, 199, 703)(177, 681, 185, 689, 183, 687)(178, 682, 208, 712, 206, 710)(179, 683, 230, 734, 285, 789)(180, 684, 207, 711, 298, 802)(181, 685, 238, 742, 311, 815)(182, 686, 200, 704, 276, 780)(184, 688, 227, 731, 198, 702)(186, 690, 231, 735, 216, 720)(188, 692, 235, 739, 194, 698)(191, 695, 279, 783, 325, 829)(192, 696, 204, 708, 288, 792)(193, 697, 293, 797, 328, 832)(195, 699, 331, 835, 332, 836)(196, 700, 210, 714, 334, 838)(197, 701, 335, 839, 336, 840)(209, 713, 354, 858, 257, 761)(212, 716, 360, 864, 268, 772)(213, 717, 229, 733, 361, 865)(214, 718, 318, 822, 362, 866)(217, 721, 366, 870, 367, 871)(218, 722, 233, 737, 369, 873)(219, 723, 273, 777, 370, 874)(221, 725, 237, 741, 373, 877)(222, 726, 375, 879, 255, 759)(223, 727, 377, 881, 378, 882)(224, 728, 242, 746, 380, 884)(228, 732, 386, 890, 387, 891)(232, 736, 355, 859, 393, 897)(236, 740, 399, 903, 400, 904)(240, 744, 344, 848, 405, 909)(243, 747, 261, 765, 406, 910)(244, 748, 408, 912, 409, 913)(246, 750, 413, 917, 414, 918)(247, 751, 286, 790, 416, 920)(248, 752, 292, 796, 417, 921)(249, 753, 419, 923, 420, 924)(251, 755, 397, 901, 424, 928)(252, 756, 299, 803, 426, 930)(254, 758, 322, 826, 427, 931)(256, 760, 429, 933, 421, 925)(258, 762, 430, 934, 264, 768)(259, 763, 410, 914, 433, 937)(260, 764, 431, 935, 434, 938)(262, 766, 436, 940, 437, 941)(263, 767, 320, 824, 313, 817)(265, 769, 327, 831, 329, 833)(266, 770, 439, 943, 441, 945)(267, 771, 390, 894, 442, 946)(269, 773, 444, 948, 445, 949)(271, 775, 384, 888, 449, 953)(272, 776, 447, 951, 450, 954)(274, 778, 277, 781, 435, 939)(283, 787, 319, 823, 432, 936)(290, 794, 462, 966, 463, 967)(296, 800, 339, 843, 469, 973)(300, 804, 324, 828, 326, 830)(301, 805, 330, 834, 333, 837)(302, 806, 310, 814, 312, 816)(303, 807, 308, 812, 309, 813)(304, 808, 359, 863, 356, 860)(305, 809, 365, 869, 368, 872)(306, 810, 371, 875, 345, 849)(307, 811, 376, 880, 379, 883)(314, 818, 412, 916, 415, 919)(315, 819, 363, 867, 340, 844)(316, 820, 423, 927, 425, 929)(321, 825, 374, 878, 350, 854)(323, 827, 448, 952, 452, 956)(341, 845, 407, 911, 382, 886)(342, 846, 459, 963, 457, 961)(343, 847, 492, 996, 493, 997)(346, 850, 418, 922, 389, 893)(347, 851, 396, 900, 467, 971)(349, 853, 497, 1001, 451, 955)(351, 855, 428, 932, 395, 899)(352, 856, 486, 990, 488, 992)(353, 857, 499, 1003, 491, 995)(357, 861, 443, 947, 402, 906)(358, 862, 383, 887, 484, 988)(381, 885, 498, 1002, 487, 991)(385, 889, 480, 984, 494, 998)(388, 892, 503, 1007, 481, 985)(391, 895, 502, 1006, 479, 983)(392, 896, 489, 993, 482, 986)(394, 898, 490, 994, 466, 970)(398, 902, 476, 980, 438, 942)(401, 905, 501, 1005, 455, 959)(403, 907, 504, 1008, 475, 979)(404, 908, 496, 1000, 477, 981)(440, 944, 453, 957, 478, 982)(456, 960, 500, 1004, 465, 969)(461, 965, 474, 978, 470, 974)(471, 975, 473, 977, 472, 976)(483, 987, 485, 989, 495, 999) L = (1, 506)(2, 505)(3, 511)(4, 512)(5, 513)(6, 514)(7, 507)(8, 508)(9, 509)(10, 510)(11, 523)(12, 524)(13, 525)(14, 526)(15, 527)(16, 528)(17, 529)(18, 530)(19, 515)(20, 516)(21, 517)(22, 518)(23, 519)(24, 520)(25, 521)(26, 522)(27, 547)(28, 548)(29, 549)(30, 550)(31, 551)(32, 552)(33, 553)(34, 554)(35, 555)(36, 556)(37, 557)(38, 558)(39, 559)(40, 560)(41, 561)(42, 562)(43, 531)(44, 532)(45, 533)(46, 534)(47, 535)(48, 536)(49, 537)(50, 538)(51, 539)(52, 540)(53, 541)(54, 542)(55, 543)(56, 544)(57, 545)(58, 546)(59, 589)(60, 590)(61, 591)(62, 592)(63, 593)(64, 594)(65, 570)(66, 569)(67, 595)(68, 596)(69, 597)(70, 598)(71, 599)(72, 600)(73, 601)(74, 602)(75, 603)(76, 604)(77, 605)(78, 583)(79, 582)(80, 606)(81, 607)(82, 608)(83, 609)(84, 610)(85, 563)(86, 564)(87, 565)(88, 566)(89, 567)(90, 568)(91, 571)(92, 572)(93, 573)(94, 574)(95, 575)(96, 576)(97, 577)(98, 578)(99, 579)(100, 580)(101, 581)(102, 584)(103, 585)(104, 586)(105, 587)(106, 588)(107, 655)(108, 656)(109, 657)(110, 658)(111, 659)(112, 617)(113, 616)(114, 660)(115, 661)(116, 662)(117, 663)(118, 664)(119, 665)(120, 666)(121, 667)(122, 668)(123, 669)(124, 629)(125, 628)(126, 670)(127, 671)(128, 672)(129, 673)(130, 674)(131, 718)(132, 720)(133, 759)(134, 639)(135, 638)(136, 745)(137, 764)(138, 765)(139, 767)(140, 768)(141, 769)(142, 770)(143, 758)(144, 761)(145, 772)(146, 651)(147, 650)(148, 707)(149, 776)(150, 777)(151, 611)(152, 612)(153, 613)(154, 614)(155, 615)(156, 618)(157, 619)(158, 620)(159, 621)(160, 622)(161, 623)(162, 624)(163, 625)(164, 626)(165, 627)(166, 630)(167, 631)(168, 632)(169, 633)(170, 634)(171, 804)(172, 805)(173, 806)(174, 807)(175, 808)(176, 809)(177, 810)(178, 811)(179, 812)(180, 813)(181, 814)(182, 816)(183, 817)(184, 818)(185, 819)(186, 820)(187, 821)(188, 823)(189, 825)(190, 827)(191, 828)(192, 830)(193, 831)(194, 833)(195, 834)(196, 837)(197, 791)(198, 841)(199, 842)(200, 843)(201, 845)(202, 847)(203, 652)(204, 848)(205, 850)(206, 852)(207, 853)(208, 855)(209, 857)(210, 859)(211, 861)(212, 863)(213, 860)(214, 635)(215, 867)(216, 636)(217, 869)(218, 872)(219, 779)(220, 875)(221, 849)(222, 878)(223, 880)(224, 883)(225, 801)(226, 885)(227, 887)(228, 889)(229, 858)(230, 892)(231, 894)(232, 896)(233, 890)(234, 898)(235, 900)(236, 902)(237, 785)(238, 905)(239, 796)(240, 908)(241, 640)(242, 903)(243, 824)(244, 911)(245, 914)(246, 916)(247, 919)(248, 844)(249, 922)(250, 925)(251, 927)(252, 929)(253, 788)(254, 647)(255, 637)(256, 932)(257, 648)(258, 917)(259, 936)(260, 641)(261, 642)(262, 787)(263, 643)(264, 644)(265, 645)(266, 646)(267, 854)(268, 649)(269, 947)(270, 913)(271, 952)(272, 653)(273, 654)(274, 956)(275, 723)(276, 931)(277, 957)(278, 950)(279, 960)(280, 961)(281, 741)(282, 871)(283, 766)(284, 757)(285, 958)(286, 939)(287, 701)(288, 963)(289, 924)(290, 965)(291, 964)(292, 743)(293, 934)(294, 971)(295, 836)(296, 907)(297, 729)(298, 968)(299, 966)(300, 675)(301, 676)(302, 677)(303, 678)(304, 679)(305, 680)(306, 681)(307, 682)(308, 683)(309, 684)(310, 685)(311, 866)(312, 686)(313, 687)(314, 688)(315, 689)(316, 690)(317, 691)(318, 926)(319, 692)(320, 747)(321, 693)(322, 945)(323, 694)(324, 695)(325, 874)(326, 696)(327, 697)(328, 840)(329, 698)(330, 699)(331, 989)(332, 799)(333, 700)(334, 990)(335, 915)(336, 832)(337, 702)(338, 703)(339, 704)(340, 752)(341, 705)(342, 970)(343, 706)(344, 708)(345, 725)(346, 709)(347, 906)(348, 710)(349, 711)(350, 771)(351, 712)(352, 991)(353, 713)(354, 733)(355, 714)(356, 717)(357, 715)(358, 893)(359, 716)(360, 999)(361, 953)(362, 815)(363, 719)(364, 1005)(365, 721)(366, 987)(367, 786)(368, 722)(369, 1006)(370, 829)(371, 724)(372, 1004)(373, 928)(374, 726)(375, 1007)(376, 727)(377, 969)(378, 910)(379, 728)(380, 1008)(381, 730)(382, 899)(383, 731)(384, 985)(385, 732)(386, 737)(387, 962)(388, 734)(389, 862)(390, 735)(391, 955)(392, 736)(393, 972)(394, 738)(395, 886)(396, 739)(397, 959)(398, 740)(399, 746)(400, 938)(401, 742)(402, 851)(403, 800)(404, 744)(405, 954)(406, 882)(407, 748)(408, 1001)(409, 774)(410, 749)(411, 839)(412, 750)(413, 762)(414, 921)(415, 751)(416, 1000)(417, 918)(418, 753)(419, 1002)(420, 793)(421, 754)(422, 822)(423, 755)(424, 877)(425, 756)(426, 940)(427, 780)(428, 760)(429, 973)(430, 797)(431, 992)(432, 763)(433, 946)(434, 904)(435, 790)(436, 930)(437, 993)(438, 976)(439, 949)(440, 977)(441, 826)(442, 937)(443, 773)(444, 994)(445, 943)(446, 782)(447, 988)(448, 775)(449, 865)(450, 909)(451, 895)(452, 778)(453, 781)(454, 789)(455, 901)(456, 783)(457, 784)(458, 891)(459, 792)(460, 795)(461, 794)(462, 803)(463, 997)(464, 802)(465, 881)(466, 846)(467, 798)(468, 897)(469, 933)(470, 975)(471, 974)(472, 942)(473, 944)(474, 998)(475, 1003)(476, 986)(477, 984)(478, 995)(479, 996)(480, 981)(481, 888)(482, 980)(483, 870)(484, 951)(485, 835)(486, 838)(487, 856)(488, 935)(489, 941)(490, 948)(491, 982)(492, 983)(493, 967)(494, 978)(495, 864)(496, 920)(497, 912)(498, 923)(499, 979)(500, 876)(501, 868)(502, 873)(503, 879)(504, 884) local type(s) :: { ( 2, 7, 2, 7, 2, 7 ) } Outer automorphisms :: reflexible Dual of E7.541 Transitivity :: ET+ VT+ AT Graph:: v = 168 e = 504 f = 324 degree seq :: [ 6^168 ] E7.543 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T2^7, T2^-5 * T1 * T2^-2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^-2 * T1 * T2^-1, T2^3 * T1^-1 * T2^2 * T1^-1 * T2^-2 * T1 * T2^-3 * T1 * T2^-3 * T1^-1 * T2 * T1^-1, T2^2 * T1^-1 * T2^-2 * T1 * T2^3 * T1^-1 * T2^2 * T1^-1 * T2^-3 * T1^-1 * T2^2 * T1^-1 ] Map:: R = (1, 505, 3, 507, 9, 513, 19, 523, 26, 530, 13, 517, 5, 509)(2, 506, 6, 510, 14, 518, 27, 531, 32, 536, 16, 520, 7, 511)(4, 508, 11, 515, 22, 526, 40, 544, 34, 538, 17, 521, 8, 512)(10, 514, 21, 525, 39, 543, 63, 567, 59, 563, 35, 539, 18, 522)(12, 516, 23, 527, 42, 546, 68, 572, 71, 575, 43, 547, 24, 528)(15, 519, 29, 533, 50, 554, 78, 582, 81, 585, 51, 555, 30, 534)(20, 524, 38, 542, 62, 566, 94, 598, 92, 596, 60, 564, 36, 540)(25, 529, 44, 548, 72, 576, 108, 612, 111, 615, 73, 577, 45, 549)(28, 532, 49, 553, 77, 581, 116, 620, 114, 618, 75, 579, 47, 551)(31, 535, 52, 556, 82, 586, 124, 628, 127, 631, 83, 587, 53, 557)(33, 537, 55, 559, 85, 589, 129, 633, 132, 636, 86, 590, 56, 560)(37, 541, 61, 565, 93, 597, 140, 644, 112, 616, 74, 578, 46, 550)(41, 545, 67, 571, 101, 605, 151, 655, 149, 653, 99, 603, 65, 569)(48, 552, 76, 580, 115, 619, 169, 673, 128, 632, 84, 588, 54, 558)(57, 561, 66, 570, 100, 604, 150, 654, 194, 698, 133, 637, 87, 591)(58, 562, 88, 592, 134, 638, 195, 699, 198, 702, 135, 639, 89, 593)(64, 568, 98, 602, 147, 651, 212, 716, 210, 714, 145, 649, 96, 600)(69, 573, 104, 608, 155, 659, 224, 728, 222, 726, 153, 657, 102, 606)(70, 574, 105, 609, 156, 660, 226, 730, 229, 733, 157, 661, 106, 610)(79, 583, 120, 624, 176, 680, 250, 754, 248, 752, 174, 678, 118, 622)(80, 584, 121, 625, 177, 681, 252, 756, 255, 759, 178, 682, 122, 626)(90, 594, 97, 601, 146, 650, 211, 715, 280, 784, 199, 703, 136, 640)(91, 595, 137, 641, 200, 704, 281, 785, 284, 788, 201, 705, 138, 642)(95, 599, 144, 648, 208, 712, 292, 796, 290, 794, 206, 710, 142, 646)(103, 607, 154, 658, 223, 727, 311, 815, 230, 734, 158, 662, 107, 611)(109, 613, 161, 665, 233, 737, 326, 830, 324, 828, 231, 735, 159, 663)(110, 614, 162, 666, 234, 738, 328, 832, 331, 835, 235, 739, 163, 667)(113, 617, 166, 670, 238, 742, 334, 838, 337, 841, 239, 743, 167, 671)(117, 621, 173, 677, 246, 750, 345, 849, 343, 847, 244, 748, 171, 675)(119, 623, 175, 679, 249, 753, 350, 854, 256, 760, 179, 683, 123, 627)(125, 629, 182, 686, 259, 763, 365, 869, 363, 867, 257, 761, 180, 684)(126, 630, 183, 687, 260, 764, 367, 871, 370, 874, 261, 765, 184, 688)(130, 634, 189, 693, 266, 770, 376, 880, 374, 878, 264, 768, 187, 691)(131, 635, 190, 694, 267, 771, 378, 882, 381, 885, 268, 772, 191, 695)(139, 643, 143, 647, 207, 711, 291, 795, 398, 902, 285, 789, 202, 706)(141, 645, 205, 709, 288, 792, 399, 903, 361, 865, 286, 790, 203, 707)(148, 652, 214, 718, 301, 805, 413, 917, 416, 920, 302, 806, 215, 719)(152, 656, 220, 724, 307, 811, 419, 923, 397, 901, 305, 809, 218, 722)(160, 664, 232, 736, 325, 829, 368, 872, 332, 836, 236, 740, 164, 668)(165, 669, 204, 708, 287, 791, 351, 855, 440, 944, 333, 837, 237, 741)(168, 672, 172, 676, 245, 749, 344, 848, 289, 793, 338, 842, 240, 744)(170, 674, 243, 747, 341, 845, 392, 896, 279, 783, 339, 843, 241, 745)(181, 685, 258, 762, 364, 868, 379, 883, 371, 875, 262, 766, 185, 689)(186, 690, 242, 746, 340, 844, 297, 801, 409, 913, 372, 876, 263, 767)(188, 692, 265, 769, 375, 879, 329, 833, 382, 886, 269, 773, 192, 696)(193, 697, 270, 774, 383, 887, 312, 816, 423, 927, 384, 888, 271, 775)(196, 700, 275, 779, 388, 892, 360, 864, 356, 860, 386, 890, 273, 777)(197, 701, 276, 780, 389, 893, 464, 968, 466, 970, 390, 894, 277, 781)(209, 713, 294, 798, 406, 910, 310, 814, 314, 818, 407, 911, 295, 799)(213, 717, 300, 804, 412, 916, 471, 975, 439, 943, 410, 914, 298, 802)(216, 720, 219, 723, 306, 810, 402, 906, 342, 846, 417, 921, 303, 807)(217, 721, 304, 808, 418, 922, 430, 934, 322, 826, 385, 889, 272, 776)(221, 725, 308, 812, 421, 925, 349, 853, 353, 857, 422, 926, 309, 813)(225, 729, 315, 819, 425, 929, 476, 980, 458, 962, 424, 928, 313, 817)(227, 731, 318, 822, 391, 895, 278, 782, 274, 778, 387, 891, 316, 820)(228, 732, 319, 823, 427, 931, 400, 904, 469, 973, 428, 932, 320, 824)(247, 751, 347, 851, 408, 912, 296, 800, 299, 803, 411, 915, 348, 852)(251, 755, 354, 858, 450, 954, 483, 987, 463, 967, 449, 953, 352, 856)(253, 757, 357, 861, 429, 933, 321, 825, 317, 821, 426, 930, 355, 859)(254, 758, 358, 862, 451, 955, 444, 948, 481, 985, 452, 956, 359, 863)(282, 786, 394, 898, 467, 971, 462, 966, 453, 957, 362, 866, 393, 897)(283, 787, 395, 899, 366, 870, 454, 958, 486, 990, 468, 972, 396, 900)(293, 797, 405, 909, 470, 974, 437, 941, 330, 834, 436, 940, 403, 907)(323, 827, 431, 935, 414, 918, 445, 949, 447, 951, 457, 961, 432, 936)(327, 831, 434, 938, 479, 983, 491, 995, 473, 977, 415, 919, 433, 937)(335, 839, 401, 905, 404, 908, 438, 942, 435, 939, 373, 877, 441, 945)(336, 840, 442, 946, 377, 881, 459, 963, 487, 991, 480, 984, 443, 947)(346, 850, 448, 952, 482, 986, 456, 960, 369, 873, 455, 959, 446, 950)(380, 884, 460, 964, 474, 978, 420, 924, 475, 979, 488, 992, 461, 965)(465, 969, 489, 993, 494, 998, 472, 976, 495, 999, 502, 1006, 490, 994)(477, 981, 493, 997, 503, 1007, 497, 1001, 478, 982, 492, 996, 496, 1000)(484, 988, 499, 1003, 504, 1008, 501, 1005, 485, 989, 498, 1002, 500, 1004) L = (1, 506)(2, 508)(3, 512)(4, 505)(5, 516)(6, 509)(7, 519)(8, 514)(9, 522)(10, 507)(11, 511)(12, 510)(13, 529)(14, 528)(15, 515)(16, 535)(17, 537)(18, 524)(19, 540)(20, 513)(21, 521)(22, 534)(23, 517)(24, 532)(25, 527)(26, 550)(27, 551)(28, 518)(29, 520)(30, 545)(31, 533)(32, 558)(33, 525)(34, 561)(35, 562)(36, 541)(37, 523)(38, 539)(39, 560)(40, 569)(41, 526)(42, 549)(43, 574)(44, 530)(45, 573)(46, 548)(47, 552)(48, 531)(49, 547)(50, 557)(51, 584)(52, 536)(53, 583)(54, 556)(55, 538)(56, 568)(57, 559)(58, 542)(59, 594)(60, 595)(61, 564)(62, 593)(63, 600)(64, 543)(65, 570)(66, 544)(67, 555)(68, 606)(69, 546)(70, 553)(71, 611)(72, 578)(73, 614)(74, 613)(75, 617)(76, 579)(77, 610)(78, 622)(79, 554)(80, 571)(81, 627)(82, 588)(83, 630)(84, 629)(85, 591)(86, 635)(87, 634)(88, 563)(89, 599)(90, 592)(91, 565)(92, 643)(93, 642)(94, 646)(95, 566)(96, 601)(97, 567)(98, 590)(99, 652)(100, 603)(101, 626)(102, 607)(103, 572)(104, 577)(105, 575)(106, 621)(107, 609)(108, 663)(109, 576)(110, 608)(111, 668)(112, 669)(113, 580)(114, 672)(115, 671)(116, 675)(117, 581)(118, 623)(119, 582)(120, 587)(121, 585)(122, 656)(123, 625)(124, 684)(125, 586)(126, 624)(127, 689)(128, 690)(129, 691)(130, 589)(131, 602)(132, 696)(133, 697)(134, 640)(135, 701)(136, 700)(137, 596)(138, 645)(139, 641)(140, 707)(141, 597)(142, 647)(143, 598)(144, 639)(145, 713)(146, 649)(147, 695)(148, 604)(149, 720)(150, 719)(151, 722)(152, 605)(153, 725)(154, 657)(155, 667)(156, 662)(157, 732)(158, 731)(159, 664)(160, 612)(161, 616)(162, 615)(163, 729)(164, 666)(165, 665)(166, 618)(167, 674)(168, 670)(169, 745)(170, 619)(171, 676)(172, 620)(173, 661)(174, 751)(175, 678)(176, 688)(177, 683)(178, 758)(179, 757)(180, 685)(181, 628)(182, 632)(183, 631)(184, 755)(185, 687)(186, 686)(187, 692)(188, 633)(189, 637)(190, 636)(191, 717)(192, 694)(193, 693)(194, 776)(195, 777)(196, 638)(197, 648)(198, 782)(199, 783)(200, 706)(201, 787)(202, 786)(203, 708)(204, 644)(205, 705)(206, 793)(207, 710)(208, 781)(209, 650)(210, 800)(211, 799)(212, 802)(213, 651)(214, 653)(215, 721)(216, 718)(217, 654)(218, 723)(219, 655)(220, 682)(221, 658)(222, 814)(223, 813)(224, 817)(225, 659)(226, 820)(227, 660)(228, 677)(229, 825)(230, 826)(231, 827)(232, 735)(233, 741)(234, 740)(235, 834)(236, 833)(237, 831)(238, 744)(239, 840)(240, 839)(241, 746)(242, 673)(243, 743)(244, 846)(245, 748)(246, 824)(247, 679)(248, 853)(249, 852)(250, 856)(251, 680)(252, 859)(253, 681)(254, 724)(255, 864)(256, 865)(257, 866)(258, 761)(259, 767)(260, 766)(261, 873)(262, 872)(263, 870)(264, 877)(265, 768)(266, 775)(267, 773)(268, 884)(269, 883)(270, 698)(271, 881)(272, 774)(273, 778)(274, 699)(275, 703)(276, 702)(277, 797)(278, 780)(279, 779)(280, 844)(281, 897)(282, 704)(283, 709)(284, 869)(285, 901)(286, 854)(287, 790)(288, 900)(289, 711)(290, 905)(291, 848)(292, 907)(293, 712)(294, 714)(295, 801)(296, 798)(297, 715)(298, 803)(299, 716)(300, 772)(301, 807)(302, 919)(303, 918)(304, 806)(305, 902)(306, 809)(307, 863)(308, 726)(309, 816)(310, 812)(311, 887)(312, 727)(313, 818)(314, 728)(315, 739)(316, 821)(317, 730)(318, 734)(319, 733)(320, 850)(321, 823)(322, 822)(323, 736)(324, 917)(325, 936)(326, 937)(327, 737)(328, 879)(329, 738)(330, 819)(331, 942)(332, 875)(333, 943)(334, 945)(335, 742)(336, 747)(337, 880)(338, 794)(339, 784)(340, 843)(341, 947)(342, 749)(343, 949)(344, 906)(345, 950)(346, 750)(347, 752)(348, 855)(349, 851)(350, 791)(351, 753)(352, 857)(353, 754)(354, 765)(355, 860)(356, 756)(357, 760)(358, 759)(359, 924)(360, 862)(361, 861)(362, 762)(363, 785)(364, 957)(365, 899)(366, 763)(367, 829)(368, 764)(369, 858)(370, 961)(371, 886)(372, 962)(373, 769)(374, 838)(375, 939)(376, 946)(377, 770)(378, 868)(379, 771)(380, 804)(381, 966)(382, 836)(383, 889)(384, 967)(385, 815)(386, 930)(387, 890)(388, 896)(389, 895)(390, 969)(391, 934)(392, 955)(393, 867)(394, 789)(395, 788)(396, 904)(397, 898)(398, 810)(399, 931)(400, 792)(401, 842)(402, 795)(403, 908)(404, 796)(405, 894)(406, 912)(407, 928)(408, 925)(409, 911)(410, 944)(411, 914)(412, 965)(413, 935)(414, 805)(415, 808)(416, 830)(417, 847)(418, 977)(419, 978)(420, 811)(421, 910)(422, 953)(423, 926)(424, 913)(425, 941)(426, 891)(427, 933)(428, 982)(429, 903)(430, 893)(431, 828)(432, 871)(433, 920)(434, 837)(435, 832)(436, 835)(437, 981)(438, 940)(439, 938)(440, 915)(441, 878)(442, 841)(443, 948)(444, 845)(445, 921)(446, 951)(447, 849)(448, 932)(449, 927)(450, 960)(451, 892)(452, 989)(453, 882)(454, 876)(455, 874)(456, 988)(457, 959)(458, 958)(459, 888)(460, 885)(461, 976)(462, 964)(463, 963)(464, 922)(465, 909)(466, 995)(467, 923)(468, 996)(469, 972)(470, 994)(471, 998)(472, 916)(473, 968)(474, 971)(475, 956)(476, 1000)(477, 929)(478, 952)(479, 975)(480, 1002)(481, 984)(482, 1001)(483, 1004)(484, 954)(485, 979)(486, 980)(487, 987)(488, 1005)(489, 970)(490, 997)(491, 993)(492, 973)(493, 974)(494, 983)(495, 992)(496, 990)(497, 1003)(498, 985)(499, 986)(500, 991)(501, 999)(502, 1008)(503, 1006)(504, 1007) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E7.539 Transitivity :: ET+ VT+ AT Graph:: v = 72 e = 504 f = 420 degree seq :: [ 14^72 ] E7.544 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^7, (T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2)^2, T2 * T1^3 * T2 * T1^-2 * T2 * T1^3 * T2 * T1^-3 * T2 * T1^2 * T2 * T1^-3 ] Map:: polyhedral non-degenerate R = (1, 505, 3, 507)(2, 506, 6, 510)(4, 508, 9, 513)(5, 509, 12, 516)(7, 511, 16, 520)(8, 512, 13, 517)(10, 514, 19, 523)(11, 515, 21, 525)(14, 518, 22, 526)(15, 519, 27, 531)(17, 521, 29, 533)(18, 522, 32, 536)(20, 524, 34, 538)(23, 527, 35, 539)(24, 528, 40, 544)(25, 529, 41, 545)(26, 530, 43, 547)(28, 532, 44, 548)(30, 534, 48, 552)(31, 535, 50, 554)(33, 537, 53, 557)(36, 540, 54, 558)(37, 541, 58, 562)(38, 542, 59, 563)(39, 543, 61, 565)(42, 546, 64, 568)(45, 549, 65, 569)(46, 550, 69, 573)(47, 551, 71, 575)(49, 553, 73, 577)(51, 555, 74, 578)(52, 556, 78, 582)(55, 559, 82, 586)(56, 560, 83, 587)(57, 561, 85, 589)(60, 564, 88, 592)(62, 566, 89, 593)(63, 567, 93, 597)(66, 570, 72, 576)(67, 571, 98, 602)(68, 572, 99, 603)(70, 574, 103, 607)(75, 579, 106, 610)(76, 580, 110, 614)(77, 581, 111, 615)(79, 583, 112, 616)(80, 584, 116, 620)(81, 585, 117, 621)(84, 588, 120, 624)(86, 590, 121, 625)(87, 591, 125, 629)(90, 594, 94, 598)(91, 595, 129, 633)(92, 596, 131, 635)(95, 599, 135, 639)(96, 600, 136, 640)(97, 601, 138, 642)(100, 604, 141, 645)(101, 605, 107, 611)(102, 606, 143, 647)(104, 608, 144, 648)(105, 609, 148, 652)(108, 612, 152, 656)(109, 613, 153, 657)(113, 617, 156, 660)(114, 618, 160, 664)(115, 619, 161, 665)(118, 622, 163, 667)(119, 623, 167, 671)(122, 626, 126, 630)(123, 627, 171, 675)(124, 628, 173, 677)(127, 631, 177, 681)(128, 632, 178, 682)(130, 634, 181, 685)(132, 636, 182, 686)(133, 637, 186, 690)(134, 638, 187, 691)(137, 641, 190, 694)(139, 643, 191, 695)(140, 644, 195, 699)(142, 646, 198, 702)(145, 649, 199, 703)(146, 650, 203, 707)(147, 651, 204, 708)(149, 653, 207, 711)(150, 654, 208, 712)(151, 655, 210, 714)(154, 658, 213, 717)(155, 659, 157, 661)(158, 662, 218, 722)(159, 663, 219, 723)(162, 666, 222, 726)(164, 668, 168, 672)(165, 669, 227, 731)(166, 670, 229, 733)(169, 673, 233, 737)(170, 674, 234, 738)(172, 676, 237, 741)(174, 678, 238, 742)(175, 679, 242, 746)(176, 680, 243, 747)(179, 683, 246, 750)(180, 684, 200, 704)(183, 687, 248, 752)(184, 688, 252, 756)(185, 689, 253, 757)(188, 692, 255, 759)(189, 693, 259, 763)(192, 696, 196, 700)(193, 697, 263, 767)(194, 698, 265, 769)(197, 701, 268, 772)(201, 705, 273, 777)(202, 706, 274, 778)(205, 709, 277, 781)(206, 710, 280, 784)(209, 713, 283, 787)(211, 715, 284, 788)(212, 716, 288, 792)(214, 718, 291, 795)(215, 719, 293, 797)(216, 720, 294, 798)(217, 721, 296, 800)(220, 724, 299, 803)(221, 725, 223, 727)(224, 728, 303, 807)(225, 729, 305, 809)(226, 730, 306, 810)(228, 732, 309, 813)(230, 734, 310, 814)(231, 735, 314, 818)(232, 736, 315, 819)(235, 739, 318, 822)(236, 740, 249, 753)(239, 743, 320, 824)(240, 744, 324, 828)(241, 745, 325, 829)(244, 748, 327, 831)(245, 749, 331, 835)(247, 751, 334, 838)(250, 754, 338, 842)(251, 755, 339, 843)(254, 758, 342, 846)(256, 760, 260, 764)(257, 761, 346, 850)(258, 762, 347, 851)(261, 765, 350, 854)(262, 766, 351, 855)(264, 768, 340, 844)(266, 770, 354, 858)(267, 771, 355, 859)(269, 773, 356, 860)(270, 774, 359, 863)(271, 775, 360, 864)(272, 776, 362, 866)(275, 779, 365, 869)(276, 780, 278, 782)(279, 783, 311, 815)(281, 785, 369, 873)(282, 786, 371, 875)(285, 789, 289, 793)(286, 790, 374, 878)(287, 791, 364, 868)(290, 794, 375, 879)(292, 796, 366, 870)(295, 799, 368, 872)(297, 801, 377, 881)(298, 802, 330, 834)(300, 804, 358, 862)(301, 805, 383, 887)(302, 806, 361, 865)(304, 808, 385, 889)(307, 811, 387, 891)(308, 812, 321, 825)(312, 816, 391, 895)(313, 817, 392, 896)(316, 820, 393, 897)(317, 821, 396, 900)(319, 823, 399, 903)(322, 826, 401, 905)(323, 827, 402, 906)(326, 830, 404, 908)(328, 832, 332, 836)(329, 833, 406, 910)(333, 837, 403, 907)(335, 839, 408, 912)(336, 840, 409, 913)(337, 841, 410, 914)(341, 845, 343, 847)(344, 848, 378, 882)(345, 849, 414, 918)(348, 852, 415, 919)(349, 853, 417, 921)(352, 856, 419, 923)(353, 857, 357, 861)(363, 867, 423, 927)(367, 871, 390, 894)(370, 874, 424, 928)(372, 876, 430, 934)(373, 877, 416, 920)(376, 880, 426, 930)(379, 883, 437, 941)(380, 884, 407, 911)(381, 885, 422, 926)(382, 886, 420, 924)(384, 888, 421, 925)(386, 890, 439, 943)(388, 892, 428, 932)(389, 893, 443, 947)(394, 898, 397, 901)(395, 899, 446, 950)(398, 902, 444, 948)(400, 904, 447, 951)(405, 909, 449, 953)(411, 915, 450, 954)(412, 916, 436, 940)(413, 917, 451, 955)(418, 922, 454, 958)(425, 929, 460, 964)(427, 931, 459, 963)(429, 933, 461, 965)(431, 935, 453, 957)(432, 936, 433, 937)(434, 938, 455, 959)(435, 939, 464, 968)(438, 942, 457, 961)(440, 944, 468, 972)(441, 945, 465, 969)(442, 946, 469, 973)(445, 949, 471, 975)(448, 952, 472, 976)(452, 956, 475, 979)(456, 960, 478, 982)(458, 962, 480, 984)(462, 966, 482, 986)(463, 967, 484, 988)(466, 970, 483, 987)(467, 971, 485, 989)(470, 974, 486, 990)(473, 977, 488, 992)(474, 978, 481, 985)(476, 980, 490, 994)(477, 981, 492, 996)(479, 983, 493, 997)(487, 991, 496, 1000)(489, 993, 498, 1002)(491, 995, 499, 1003)(494, 998, 495, 999)(497, 1001, 502, 1006)(500, 1004, 503, 1007)(501, 1005, 504, 1008) L = (1, 506)(2, 509)(3, 511)(4, 505)(5, 515)(6, 517)(7, 519)(8, 507)(9, 522)(10, 508)(11, 524)(12, 526)(13, 528)(14, 510)(15, 530)(16, 513)(17, 512)(18, 535)(19, 537)(20, 514)(21, 539)(22, 541)(23, 516)(24, 543)(25, 518)(26, 534)(27, 548)(28, 520)(29, 551)(30, 521)(31, 553)(32, 523)(33, 556)(34, 558)(35, 559)(36, 525)(37, 561)(38, 527)(39, 546)(40, 533)(41, 567)(42, 529)(43, 569)(44, 571)(45, 531)(46, 532)(47, 574)(48, 576)(49, 550)(50, 578)(51, 536)(52, 581)(53, 538)(54, 584)(55, 585)(56, 540)(57, 564)(58, 545)(59, 591)(60, 542)(61, 593)(62, 544)(63, 596)(64, 598)(65, 599)(66, 547)(67, 601)(68, 549)(69, 605)(70, 606)(71, 552)(72, 609)(73, 610)(74, 612)(75, 554)(76, 555)(77, 580)(78, 616)(79, 557)(80, 619)(81, 588)(82, 563)(83, 623)(84, 560)(85, 625)(86, 562)(87, 628)(88, 630)(89, 631)(90, 565)(91, 566)(92, 634)(93, 568)(94, 637)(95, 638)(96, 570)(97, 604)(98, 573)(99, 644)(100, 572)(101, 646)(102, 595)(103, 648)(104, 575)(105, 651)(106, 653)(107, 577)(108, 655)(109, 579)(110, 659)(111, 660)(112, 662)(113, 582)(114, 583)(115, 618)(116, 587)(117, 667)(118, 586)(119, 670)(120, 672)(121, 673)(122, 589)(123, 590)(124, 676)(125, 592)(126, 679)(127, 680)(128, 594)(129, 684)(130, 627)(131, 686)(132, 597)(133, 689)(134, 641)(135, 603)(136, 693)(137, 600)(138, 695)(139, 602)(140, 698)(141, 700)(142, 701)(143, 703)(144, 705)(145, 607)(146, 608)(147, 650)(148, 640)(149, 710)(150, 611)(151, 658)(152, 614)(153, 716)(154, 613)(155, 718)(156, 719)(157, 615)(158, 721)(159, 617)(160, 725)(161, 726)(162, 620)(163, 729)(164, 621)(165, 622)(166, 732)(167, 624)(168, 735)(169, 736)(170, 626)(171, 740)(172, 669)(173, 742)(174, 629)(175, 745)(176, 683)(177, 633)(178, 749)(179, 632)(180, 751)(181, 752)(182, 754)(183, 635)(184, 636)(185, 688)(186, 682)(187, 759)(188, 639)(189, 762)(190, 764)(191, 765)(192, 642)(193, 643)(194, 768)(195, 645)(196, 771)(197, 697)(198, 712)(199, 774)(200, 647)(201, 776)(202, 649)(203, 780)(204, 781)(205, 652)(206, 713)(207, 657)(208, 786)(209, 654)(210, 788)(211, 656)(212, 791)(213, 793)(214, 794)(215, 796)(216, 661)(217, 724)(218, 664)(219, 802)(220, 663)(221, 804)(222, 805)(223, 665)(224, 666)(225, 808)(226, 668)(227, 812)(228, 728)(229, 814)(230, 671)(231, 817)(232, 739)(233, 675)(234, 821)(235, 674)(236, 823)(237, 824)(238, 826)(239, 677)(240, 678)(241, 744)(242, 738)(243, 831)(244, 681)(245, 834)(246, 836)(247, 837)(248, 839)(249, 685)(250, 841)(251, 687)(252, 845)(253, 846)(254, 690)(255, 849)(256, 691)(257, 692)(258, 813)(259, 694)(260, 829)(261, 853)(262, 696)(263, 857)(264, 761)(265, 858)(266, 699)(267, 818)(268, 860)(269, 702)(270, 862)(271, 704)(272, 779)(273, 707)(274, 868)(275, 706)(276, 870)(277, 871)(278, 708)(279, 709)(280, 873)(281, 711)(282, 825)(283, 847)(284, 876)(285, 714)(286, 715)(287, 869)(288, 717)(289, 830)(290, 790)(291, 798)(292, 799)(293, 723)(294, 840)(295, 720)(296, 881)(297, 722)(298, 884)(299, 848)(300, 885)(301, 886)(302, 727)(303, 851)(304, 811)(305, 731)(306, 770)(307, 730)(308, 892)(309, 783)(310, 893)(311, 733)(312, 734)(313, 816)(314, 810)(315, 897)(316, 737)(317, 792)(318, 901)(319, 902)(320, 773)(321, 741)(322, 904)(323, 743)(324, 760)(325, 908)(326, 746)(327, 909)(328, 747)(329, 748)(330, 803)(331, 750)(332, 896)(333, 833)(334, 864)(335, 795)(336, 753)(337, 844)(338, 756)(339, 769)(340, 755)(341, 784)(342, 916)(343, 757)(344, 758)(345, 917)(346, 914)(347, 919)(348, 763)(349, 856)(350, 767)(351, 911)(352, 766)(353, 924)(354, 891)(355, 855)(356, 906)(357, 772)(358, 865)(359, 778)(360, 925)(361, 775)(362, 927)(363, 777)(364, 900)(365, 874)(366, 930)(367, 903)(368, 782)(369, 931)(370, 785)(371, 787)(372, 933)(373, 789)(374, 936)(375, 912)(376, 797)(377, 939)(378, 800)(379, 801)(380, 923)(381, 883)(382, 888)(383, 807)(384, 806)(385, 943)(386, 809)(387, 937)(388, 945)(389, 946)(390, 815)(391, 832)(392, 859)(393, 949)(394, 819)(395, 820)(396, 822)(397, 926)(398, 899)(399, 913)(400, 907)(401, 828)(402, 838)(403, 827)(404, 920)(405, 952)(406, 951)(407, 835)(408, 843)(409, 872)(410, 954)(411, 842)(412, 932)(413, 905)(414, 850)(415, 957)(416, 852)(417, 958)(418, 854)(419, 938)(420, 961)(421, 861)(422, 863)(423, 962)(424, 866)(425, 867)(426, 929)(427, 915)(428, 875)(429, 935)(430, 878)(431, 877)(432, 889)(433, 879)(434, 880)(435, 967)(436, 882)(437, 898)(438, 887)(439, 971)(440, 890)(441, 944)(442, 948)(443, 895)(444, 894)(445, 974)(446, 973)(447, 955)(448, 947)(449, 910)(450, 978)(451, 979)(452, 918)(453, 970)(454, 981)(455, 921)(456, 922)(457, 960)(458, 983)(459, 928)(460, 959)(461, 986)(462, 934)(463, 969)(464, 941)(465, 940)(466, 942)(467, 966)(468, 988)(469, 976)(470, 968)(471, 950)(472, 992)(473, 953)(474, 980)(475, 993)(476, 956)(477, 995)(478, 987)(479, 985)(480, 964)(481, 963)(482, 998)(483, 965)(484, 990)(485, 972)(486, 1000)(487, 975)(488, 1001)(489, 977)(490, 997)(491, 984)(492, 982)(493, 1003)(494, 1004)(495, 989)(496, 1005)(497, 991)(498, 994)(499, 1007)(500, 996)(501, 999)(502, 1002)(503, 1008)(504, 1006) local type(s) :: { ( 3, 7, 3, 7 ) } Outer automorphisms :: reflexible Dual of E7.540 Transitivity :: ET+ VT+ AT Graph:: simple v = 252 e = 504 f = 240 degree seq :: [ 4^252 ] E7.545 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^7, (Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1)^2, Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 ] Map:: R = (1, 505, 2, 506)(3, 507, 7, 511)(4, 508, 8, 512)(5, 509, 9, 513)(6, 510, 10, 514)(11, 515, 19, 523)(12, 516, 20, 524)(13, 517, 21, 525)(14, 518, 22, 526)(15, 519, 23, 527)(16, 520, 24, 528)(17, 521, 25, 529)(18, 522, 26, 530)(27, 531, 43, 547)(28, 532, 44, 548)(29, 533, 45, 549)(30, 534, 46, 550)(31, 535, 47, 551)(32, 536, 48, 552)(33, 537, 49, 553)(34, 538, 50, 554)(35, 539, 51, 555)(36, 540, 52, 556)(37, 541, 53, 557)(38, 542, 54, 558)(39, 543, 55, 559)(40, 544, 56, 560)(41, 545, 57, 561)(42, 546, 58, 562)(59, 563, 85, 589)(60, 564, 86, 590)(61, 565, 87, 591)(62, 566, 88, 592)(63, 567, 89, 593)(64, 568, 90, 594)(65, 569, 66, 570)(67, 571, 91, 595)(68, 572, 92, 596)(69, 573, 93, 597)(70, 574, 94, 598)(71, 575, 95, 599)(72, 576, 96, 600)(73, 577, 97, 601)(74, 578, 98, 602)(75, 579, 99, 603)(76, 580, 100, 604)(77, 581, 101, 605)(78, 582, 79, 583)(80, 584, 102, 606)(81, 585, 103, 607)(82, 586, 104, 608)(83, 587, 105, 609)(84, 588, 106, 610)(107, 611, 151, 655)(108, 612, 152, 656)(109, 613, 153, 657)(110, 614, 154, 658)(111, 615, 155, 659)(112, 616, 113, 617)(114, 618, 156, 660)(115, 619, 157, 661)(116, 620, 158, 662)(117, 621, 159, 663)(118, 622, 160, 664)(119, 623, 161, 665)(120, 624, 162, 666)(121, 625, 163, 667)(122, 626, 164, 668)(123, 627, 165, 669)(124, 628, 125, 629)(126, 630, 166, 670)(127, 631, 167, 671)(128, 632, 168, 672)(129, 633, 169, 673)(130, 634, 170, 674)(131, 635, 258, 762)(132, 636, 259, 763)(133, 637, 260, 764)(134, 638, 135, 639)(136, 640, 262, 766)(137, 641, 264, 768)(138, 642, 266, 770)(139, 643, 229, 733)(140, 644, 268, 772)(141, 645, 235, 739)(142, 646, 270, 774)(143, 647, 272, 776)(144, 648, 273, 777)(145, 649, 275, 779)(146, 650, 147, 651)(148, 652, 278, 782)(149, 653, 280, 784)(150, 654, 210, 714)(171, 675, 307, 811)(172, 676, 308, 812)(173, 677, 279, 783)(174, 678, 254, 758)(175, 679, 311, 815)(176, 680, 312, 816)(177, 681, 224, 728)(178, 682, 246, 750)(179, 683, 215, 719)(180, 684, 263, 767)(181, 685, 316, 820)(182, 686, 317, 821)(183, 687, 318, 822)(184, 688, 319, 823)(185, 689, 191, 695)(186, 690, 251, 755)(187, 691, 322, 826)(188, 692, 209, 713)(189, 693, 221, 725)(190, 694, 325, 829)(192, 696, 274, 778)(193, 697, 329, 833)(194, 698, 219, 723)(195, 699, 212, 716)(196, 700, 334, 838)(197, 701, 335, 839)(198, 702, 336, 840)(199, 703, 337, 841)(200, 704, 338, 842)(201, 705, 339, 843)(202, 706, 341, 845)(203, 707, 342, 846)(204, 708, 343, 847)(205, 709, 296, 800)(206, 710, 289, 793)(207, 711, 344, 848)(208, 712, 346, 850)(211, 715, 349, 853)(213, 717, 218, 722)(214, 718, 353, 857)(216, 720, 356, 860)(217, 721, 358, 862)(220, 724, 363, 867)(222, 726, 227, 731)(223, 727, 366, 870)(225, 729, 369, 873)(226, 730, 371, 875)(228, 732, 375, 879)(230, 734, 301, 805)(231, 735, 355, 859)(232, 736, 378, 882)(233, 737, 379, 883)(234, 738, 284, 788)(236, 740, 327, 831)(237, 741, 383, 887)(238, 742, 384, 888)(239, 743, 368, 872)(240, 744, 376, 880)(241, 745, 386, 890)(242, 746, 306, 810)(243, 747, 291, 795)(244, 748, 276, 780)(245, 749, 249, 753)(247, 751, 394, 898)(248, 752, 396, 900)(250, 754, 399, 903)(252, 756, 257, 761)(253, 757, 402, 906)(255, 759, 404, 908)(256, 760, 406, 910)(261, 765, 269, 773)(265, 769, 397, 901)(267, 771, 417, 921)(271, 775, 421, 925)(277, 781, 429, 933)(281, 785, 432, 936)(282, 786, 434, 938)(283, 787, 389, 893)(285, 789, 437, 941)(286, 790, 372, 876)(287, 791, 393, 897)(288, 792, 381, 885)(290, 794, 441, 945)(292, 796, 425, 929)(293, 797, 377, 881)(294, 798, 303, 807)(295, 799, 445, 949)(297, 801, 447, 951)(298, 802, 380, 884)(299, 803, 403, 907)(300, 804, 345, 849)(302, 806, 450, 954)(304, 808, 433, 937)(305, 809, 382, 886)(309, 813, 453, 957)(310, 814, 454, 958)(313, 817, 455, 959)(314, 818, 456, 960)(315, 819, 457, 961)(320, 824, 458, 962)(321, 825, 416, 920)(323, 827, 431, 935)(324, 828, 461, 965)(326, 830, 464, 968)(328, 832, 395, 899)(330, 834, 467, 971)(331, 835, 449, 953)(332, 836, 419, 923)(333, 837, 468, 972)(340, 844, 423, 927)(347, 851, 472, 976)(348, 852, 405, 909)(350, 854, 475, 979)(351, 855, 476, 980)(352, 856, 470, 974)(354, 858, 410, 914)(357, 861, 370, 874)(359, 863, 409, 913)(360, 864, 440, 944)(361, 865, 481, 985)(362, 866, 478, 982)(364, 868, 477, 981)(365, 869, 463, 967)(367, 871, 438, 942)(373, 877, 413, 917)(374, 878, 444, 948)(385, 889, 418, 922)(387, 891, 424, 928)(388, 892, 408, 912)(390, 894, 471, 975)(391, 895, 415, 919)(392, 896, 448, 952)(398, 902, 411, 915)(400, 904, 469, 973)(401, 905, 460, 964)(407, 911, 439, 943)(412, 916, 451, 955)(414, 918, 426, 930)(420, 924, 436, 940)(422, 926, 462, 966)(427, 931, 496, 1000)(428, 932, 466, 970)(430, 934, 474, 978)(435, 939, 488, 992)(442, 946, 499, 1003)(443, 947, 497, 1001)(446, 950, 487, 991)(452, 956, 492, 996)(459, 963, 498, 1002)(465, 969, 490, 994)(473, 977, 484, 988)(479, 983, 486, 990)(480, 984, 482, 986)(483, 987, 495, 999)(485, 989, 500, 1004)(489, 993, 493, 997)(491, 995, 501, 1005)(494, 998, 502, 1006)(503, 1007, 504, 1008)(1009, 1513, 1011, 1515, 1012, 1516)(1010, 1514, 1013, 1517, 1014, 1518)(1015, 1519, 1019, 1523, 1020, 1524)(1016, 1520, 1021, 1525, 1022, 1526)(1017, 1521, 1023, 1527, 1024, 1528)(1018, 1522, 1025, 1529, 1026, 1530)(1027, 1531, 1035, 1539, 1036, 1540)(1028, 1532, 1037, 1541, 1038, 1542)(1029, 1533, 1039, 1543, 1040, 1544)(1030, 1534, 1041, 1545, 1042, 1546)(1031, 1535, 1043, 1547, 1044, 1548)(1032, 1536, 1045, 1549, 1046, 1550)(1033, 1537, 1047, 1551, 1048, 1552)(1034, 1538, 1049, 1553, 1050, 1554)(1051, 1555, 1066, 1570, 1067, 1571)(1052, 1556, 1068, 1572, 1069, 1573)(1053, 1557, 1070, 1574, 1071, 1575)(1054, 1558, 1072, 1576, 1073, 1577)(1055, 1559, 1074, 1578, 1075, 1579)(1056, 1560, 1076, 1580, 1077, 1581)(1057, 1561, 1078, 1582, 1079, 1583)(1058, 1562, 1080, 1584, 1059, 1563)(1060, 1564, 1081, 1585, 1082, 1586)(1061, 1565, 1083, 1587, 1084, 1588)(1062, 1566, 1085, 1589, 1086, 1590)(1063, 1567, 1087, 1591, 1088, 1592)(1064, 1568, 1089, 1593, 1090, 1594)(1065, 1569, 1091, 1595, 1092, 1596)(1093, 1597, 1115, 1619, 1116, 1620)(1094, 1598, 1117, 1621, 1118, 1622)(1095, 1599, 1119, 1623, 1120, 1624)(1096, 1600, 1121, 1625, 1122, 1626)(1097, 1601, 1123, 1627, 1124, 1628)(1098, 1602, 1125, 1629, 1126, 1630)(1099, 1603, 1127, 1631, 1128, 1632)(1100, 1604, 1129, 1633, 1130, 1634)(1101, 1605, 1131, 1635, 1132, 1636)(1102, 1606, 1133, 1637, 1134, 1638)(1103, 1607, 1135, 1639, 1136, 1640)(1104, 1608, 1137, 1641, 1138, 1642)(1105, 1609, 1139, 1643, 1140, 1644)(1106, 1610, 1141, 1645, 1142, 1646)(1107, 1611, 1143, 1647, 1144, 1648)(1108, 1612, 1145, 1649, 1146, 1650)(1109, 1613, 1147, 1651, 1148, 1652)(1110, 1614, 1149, 1653, 1150, 1654)(1111, 1615, 1151, 1655, 1152, 1656)(1112, 1616, 1153, 1657, 1154, 1658)(1113, 1617, 1155, 1659, 1156, 1660)(1114, 1618, 1157, 1661, 1158, 1662)(1159, 1663, 1180, 1684, 1261, 1765)(1160, 1664, 1291, 1795, 1259, 1763)(1161, 1665, 1194, 1698, 1329, 1833)(1162, 1666, 1294, 1798, 1446, 1950)(1163, 1667, 1292, 1796, 1444, 1948)(1164, 1668, 1297, 1801, 1448, 1952)(1165, 1669, 1206, 1710, 1290, 1794)(1166, 1670, 1300, 1804, 1287, 1791)(1167, 1671, 1181, 1685, 1317, 1821)(1168, 1672, 1301, 1805, 1364, 1868)(1169, 1673, 1183, 1687, 1231, 1735)(1170, 1674, 1303, 1807, 1229, 1733)(1171, 1675, 1197, 1701, 1332, 1836)(1172, 1676, 1306, 1810, 1456, 1960)(1173, 1677, 1304, 1808, 1454, 1958)(1174, 1678, 1309, 1813, 1457, 1961)(1175, 1679, 1209, 1713, 1348, 1852)(1176, 1680, 1312, 1816, 1315, 1819)(1177, 1681, 1179, 1683, 1285, 1789)(1178, 1682, 1313, 1817, 1282, 1786)(1182, 1686, 1318, 1822, 1237, 1741)(1184, 1688, 1222, 1726, 1243, 1747)(1185, 1689, 1321, 1825, 1242, 1746)(1186, 1690, 1322, 1826, 1213, 1717)(1187, 1691, 1323, 1827, 1250, 1754)(1188, 1692, 1293, 1797, 1207, 1711)(1189, 1693, 1211, 1715, 1214, 1718)(1190, 1694, 1204, 1708, 1238, 1742)(1191, 1695, 1205, 1709, 1208, 1712)(1192, 1696, 1198, 1702, 1246, 1750)(1193, 1697, 1328, 1832, 1299, 1803)(1195, 1699, 1305, 1809, 1210, 1714)(1196, 1700, 1331, 1835, 1311, 1815)(1199, 1703, 1334, 1838, 1335, 1839)(1200, 1704, 1336, 1840, 1266, 1770)(1201, 1705, 1338, 1842, 1216, 1720)(1202, 1706, 1339, 1843, 1340, 1844)(1203, 1707, 1341, 1845, 1280, 1784)(1212, 1716, 1264, 1768, 1272, 1776)(1215, 1719, 1353, 1857, 1288, 1792)(1217, 1721, 1355, 1859, 1352, 1856)(1218, 1722, 1356, 1860, 1316, 1820)(1219, 1723, 1358, 1862, 1240, 1744)(1220, 1724, 1278, 1782, 1359, 1863)(1221, 1725, 1360, 1864, 1344, 1848)(1223, 1727, 1362, 1866, 1363, 1867)(1224, 1728, 1365, 1869, 1319, 1823)(1225, 1729, 1367, 1871, 1245, 1749)(1226, 1730, 1368, 1872, 1369, 1873)(1227, 1731, 1370, 1874, 1347, 1851)(1228, 1732, 1372, 1876, 1248, 1752)(1230, 1734, 1373, 1877, 1351, 1855)(1232, 1736, 1375, 1879, 1376, 1880)(1233, 1737, 1378, 1882, 1320, 1824)(1234, 1738, 1380, 1884, 1236, 1740)(1235, 1739, 1381, 1885, 1382, 1886)(1239, 1743, 1384, 1888, 1385, 1889)(1241, 1745, 1256, 1760, 1388, 1892)(1244, 1748, 1389, 1893, 1390, 1894)(1247, 1751, 1386, 1890, 1393, 1897)(1249, 1753, 1275, 1779, 1395, 1899)(1251, 1755, 1396, 1900, 1397, 1901)(1252, 1756, 1398, 1902, 1296, 1800)(1253, 1757, 1399, 1903, 1383, 1887)(1254, 1758, 1400, 1904, 1401, 1905)(1255, 1759, 1403, 1907, 1324, 1828)(1257, 1761, 1405, 1909, 1406, 1910)(1258, 1762, 1408, 1912, 1308, 1812)(1260, 1764, 1409, 1913, 1387, 1891)(1262, 1766, 1274, 1778, 1411, 1915)(1263, 1767, 1413, 1917, 1325, 1829)(1265, 1769, 1415, 1919, 1416, 1920)(1267, 1771, 1417, 1921, 1418, 1922)(1268, 1772, 1314, 1818, 1419, 1923)(1269, 1773, 1295, 1799, 1391, 1895)(1270, 1774, 1346, 1850, 1421, 1925)(1271, 1775, 1422, 1926, 1423, 1927)(1273, 1777, 1424, 1928, 1326, 1830)(1276, 1780, 1426, 1930, 1377, 1881)(1277, 1781, 1402, 1906, 1428, 1932)(1279, 1783, 1430, 1934, 1431, 1935)(1281, 1785, 1432, 1936, 1434, 1938)(1283, 1787, 1345, 1849, 1435, 1939)(1284, 1788, 1436, 1940, 1394, 1898)(1286, 1790, 1392, 1896, 1439, 1943)(1289, 1793, 1441, 1945, 1327, 1831)(1298, 1802, 1450, 1954, 1451, 1955)(1302, 1806, 1452, 1956, 1453, 1957)(1307, 1811, 1354, 1858, 1443, 1947)(1310, 1814, 1459, 1963, 1429, 1933)(1330, 1834, 1467, 1971, 1468, 1972)(1333, 1837, 1470, 1974, 1471, 1975)(1337, 1841, 1473, 1977, 1474, 1978)(1342, 1846, 1477, 1981, 1478, 1982)(1343, 1847, 1447, 1951, 1469, 1973)(1349, 1853, 1460, 1964, 1433, 1937)(1350, 1854, 1479, 1983, 1476, 1980)(1357, 1861, 1481, 1985, 1482, 1986)(1361, 1865, 1485, 1989, 1486, 1990)(1366, 1870, 1487, 1991, 1488, 1992)(1371, 1875, 1490, 1994, 1458, 1962)(1374, 1878, 1483, 1987, 1480, 1984)(1379, 1883, 1491, 1995, 1492, 1996)(1404, 1908, 1493, 1997, 1494, 1998)(1407, 1911, 1438, 1942, 1449, 1953)(1410, 1914, 1475, 1979, 1472, 1976)(1412, 1916, 1495, 1999, 1496, 2000)(1414, 1918, 1497, 2001, 1498, 2002)(1420, 1924, 1499, 2003, 1501, 2005)(1425, 1929, 1502, 2006, 1503, 2007)(1427, 1931, 1489, 1993, 1484, 1988)(1437, 1941, 1455, 1959, 1466, 1970)(1440, 1944, 1504, 2008, 1500, 2004)(1442, 1946, 1505, 2009, 1506, 2010)(1445, 1949, 1465, 1969, 1461, 1965)(1462, 1966, 1464, 1968, 1463, 1967)(1507, 2011, 1511, 2015, 1508, 2012)(1509, 2013, 1512, 2016, 1510, 2014) L = (1, 1010)(2, 1009)(3, 1015)(4, 1016)(5, 1017)(6, 1018)(7, 1011)(8, 1012)(9, 1013)(10, 1014)(11, 1027)(12, 1028)(13, 1029)(14, 1030)(15, 1031)(16, 1032)(17, 1033)(18, 1034)(19, 1019)(20, 1020)(21, 1021)(22, 1022)(23, 1023)(24, 1024)(25, 1025)(26, 1026)(27, 1051)(28, 1052)(29, 1053)(30, 1054)(31, 1055)(32, 1056)(33, 1057)(34, 1058)(35, 1059)(36, 1060)(37, 1061)(38, 1062)(39, 1063)(40, 1064)(41, 1065)(42, 1066)(43, 1035)(44, 1036)(45, 1037)(46, 1038)(47, 1039)(48, 1040)(49, 1041)(50, 1042)(51, 1043)(52, 1044)(53, 1045)(54, 1046)(55, 1047)(56, 1048)(57, 1049)(58, 1050)(59, 1093)(60, 1094)(61, 1095)(62, 1096)(63, 1097)(64, 1098)(65, 1074)(66, 1073)(67, 1099)(68, 1100)(69, 1101)(70, 1102)(71, 1103)(72, 1104)(73, 1105)(74, 1106)(75, 1107)(76, 1108)(77, 1109)(78, 1087)(79, 1086)(80, 1110)(81, 1111)(82, 1112)(83, 1113)(84, 1114)(85, 1067)(86, 1068)(87, 1069)(88, 1070)(89, 1071)(90, 1072)(91, 1075)(92, 1076)(93, 1077)(94, 1078)(95, 1079)(96, 1080)(97, 1081)(98, 1082)(99, 1083)(100, 1084)(101, 1085)(102, 1088)(103, 1089)(104, 1090)(105, 1091)(106, 1092)(107, 1159)(108, 1160)(109, 1161)(110, 1162)(111, 1163)(112, 1121)(113, 1120)(114, 1164)(115, 1165)(116, 1166)(117, 1167)(118, 1168)(119, 1169)(120, 1170)(121, 1171)(122, 1172)(123, 1173)(124, 1133)(125, 1132)(126, 1174)(127, 1175)(128, 1176)(129, 1177)(130, 1178)(131, 1266)(132, 1267)(133, 1268)(134, 1143)(135, 1142)(136, 1270)(137, 1272)(138, 1274)(139, 1237)(140, 1276)(141, 1243)(142, 1278)(143, 1280)(144, 1281)(145, 1283)(146, 1155)(147, 1154)(148, 1286)(149, 1288)(150, 1218)(151, 1115)(152, 1116)(153, 1117)(154, 1118)(155, 1119)(156, 1122)(157, 1123)(158, 1124)(159, 1125)(160, 1126)(161, 1127)(162, 1128)(163, 1129)(164, 1130)(165, 1131)(166, 1134)(167, 1135)(168, 1136)(169, 1137)(170, 1138)(171, 1315)(172, 1316)(173, 1287)(174, 1262)(175, 1319)(176, 1320)(177, 1232)(178, 1254)(179, 1223)(180, 1271)(181, 1324)(182, 1325)(183, 1326)(184, 1327)(185, 1199)(186, 1259)(187, 1330)(188, 1217)(189, 1229)(190, 1333)(191, 1193)(192, 1282)(193, 1337)(194, 1227)(195, 1220)(196, 1342)(197, 1343)(198, 1344)(199, 1345)(200, 1346)(201, 1347)(202, 1349)(203, 1350)(204, 1351)(205, 1304)(206, 1297)(207, 1352)(208, 1354)(209, 1196)(210, 1158)(211, 1357)(212, 1203)(213, 1226)(214, 1361)(215, 1187)(216, 1364)(217, 1366)(218, 1221)(219, 1202)(220, 1371)(221, 1197)(222, 1235)(223, 1374)(224, 1185)(225, 1377)(226, 1379)(227, 1230)(228, 1383)(229, 1147)(230, 1309)(231, 1363)(232, 1386)(233, 1387)(234, 1292)(235, 1149)(236, 1335)(237, 1391)(238, 1392)(239, 1376)(240, 1384)(241, 1394)(242, 1314)(243, 1299)(244, 1284)(245, 1257)(246, 1186)(247, 1402)(248, 1404)(249, 1253)(250, 1407)(251, 1194)(252, 1265)(253, 1410)(254, 1182)(255, 1412)(256, 1414)(257, 1260)(258, 1139)(259, 1140)(260, 1141)(261, 1277)(262, 1144)(263, 1188)(264, 1145)(265, 1405)(266, 1146)(267, 1425)(268, 1148)(269, 1269)(270, 1150)(271, 1429)(272, 1151)(273, 1152)(274, 1200)(275, 1153)(276, 1252)(277, 1437)(278, 1156)(279, 1181)(280, 1157)(281, 1440)(282, 1442)(283, 1397)(284, 1242)(285, 1445)(286, 1380)(287, 1401)(288, 1389)(289, 1214)(290, 1449)(291, 1251)(292, 1433)(293, 1385)(294, 1311)(295, 1453)(296, 1213)(297, 1455)(298, 1388)(299, 1411)(300, 1353)(301, 1238)(302, 1458)(303, 1302)(304, 1441)(305, 1390)(306, 1250)(307, 1179)(308, 1180)(309, 1461)(310, 1462)(311, 1183)(312, 1184)(313, 1463)(314, 1464)(315, 1465)(316, 1189)(317, 1190)(318, 1191)(319, 1192)(320, 1466)(321, 1424)(322, 1195)(323, 1439)(324, 1469)(325, 1198)(326, 1472)(327, 1244)(328, 1403)(329, 1201)(330, 1475)(331, 1457)(332, 1427)(333, 1476)(334, 1204)(335, 1205)(336, 1206)(337, 1207)(338, 1208)(339, 1209)(340, 1431)(341, 1210)(342, 1211)(343, 1212)(344, 1215)(345, 1308)(346, 1216)(347, 1480)(348, 1413)(349, 1219)(350, 1483)(351, 1484)(352, 1478)(353, 1222)(354, 1418)(355, 1239)(356, 1224)(357, 1378)(358, 1225)(359, 1417)(360, 1448)(361, 1489)(362, 1486)(363, 1228)(364, 1485)(365, 1471)(366, 1231)(367, 1446)(368, 1247)(369, 1233)(370, 1365)(371, 1234)(372, 1294)(373, 1421)(374, 1452)(375, 1236)(376, 1248)(377, 1301)(378, 1240)(379, 1241)(380, 1306)(381, 1296)(382, 1313)(383, 1245)(384, 1246)(385, 1426)(386, 1249)(387, 1432)(388, 1416)(389, 1291)(390, 1479)(391, 1423)(392, 1456)(393, 1295)(394, 1255)(395, 1336)(396, 1256)(397, 1273)(398, 1419)(399, 1258)(400, 1477)(401, 1468)(402, 1261)(403, 1307)(404, 1263)(405, 1356)(406, 1264)(407, 1447)(408, 1396)(409, 1367)(410, 1362)(411, 1406)(412, 1459)(413, 1381)(414, 1434)(415, 1399)(416, 1329)(417, 1275)(418, 1393)(419, 1340)(420, 1444)(421, 1279)(422, 1470)(423, 1348)(424, 1395)(425, 1300)(426, 1422)(427, 1504)(428, 1474)(429, 1285)(430, 1482)(431, 1331)(432, 1289)(433, 1312)(434, 1290)(435, 1496)(436, 1428)(437, 1293)(438, 1375)(439, 1415)(440, 1368)(441, 1298)(442, 1507)(443, 1505)(444, 1382)(445, 1303)(446, 1495)(447, 1305)(448, 1400)(449, 1339)(450, 1310)(451, 1420)(452, 1500)(453, 1317)(454, 1318)(455, 1321)(456, 1322)(457, 1323)(458, 1328)(459, 1506)(460, 1409)(461, 1332)(462, 1430)(463, 1373)(464, 1334)(465, 1498)(466, 1436)(467, 1338)(468, 1341)(469, 1408)(470, 1360)(471, 1398)(472, 1355)(473, 1492)(474, 1438)(475, 1358)(476, 1359)(477, 1372)(478, 1370)(479, 1494)(480, 1490)(481, 1369)(482, 1488)(483, 1503)(484, 1481)(485, 1508)(486, 1487)(487, 1454)(488, 1443)(489, 1501)(490, 1473)(491, 1509)(492, 1460)(493, 1497)(494, 1510)(495, 1491)(496, 1435)(497, 1451)(498, 1467)(499, 1450)(500, 1493)(501, 1499)(502, 1502)(503, 1512)(504, 1511)(505, 1513)(506, 1514)(507, 1515)(508, 1516)(509, 1517)(510, 1518)(511, 1519)(512, 1520)(513, 1521)(514, 1522)(515, 1523)(516, 1524)(517, 1525)(518, 1526)(519, 1527)(520, 1528)(521, 1529)(522, 1530)(523, 1531)(524, 1532)(525, 1533)(526, 1534)(527, 1535)(528, 1536)(529, 1537)(530, 1538)(531, 1539)(532, 1540)(533, 1541)(534, 1542)(535, 1543)(536, 1544)(537, 1545)(538, 1546)(539, 1547)(540, 1548)(541, 1549)(542, 1550)(543, 1551)(544, 1552)(545, 1553)(546, 1554)(547, 1555)(548, 1556)(549, 1557)(550, 1558)(551, 1559)(552, 1560)(553, 1561)(554, 1562)(555, 1563)(556, 1564)(557, 1565)(558, 1566)(559, 1567)(560, 1568)(561, 1569)(562, 1570)(563, 1571)(564, 1572)(565, 1573)(566, 1574)(567, 1575)(568, 1576)(569, 1577)(570, 1578)(571, 1579)(572, 1580)(573, 1581)(574, 1582)(575, 1583)(576, 1584)(577, 1585)(578, 1586)(579, 1587)(580, 1588)(581, 1589)(582, 1590)(583, 1591)(584, 1592)(585, 1593)(586, 1594)(587, 1595)(588, 1596)(589, 1597)(590, 1598)(591, 1599)(592, 1600)(593, 1601)(594, 1602)(595, 1603)(596, 1604)(597, 1605)(598, 1606)(599, 1607)(600, 1608)(601, 1609)(602, 1610)(603, 1611)(604, 1612)(605, 1613)(606, 1614)(607, 1615)(608, 1616)(609, 1617)(610, 1618)(611, 1619)(612, 1620)(613, 1621)(614, 1622)(615, 1623)(616, 1624)(617, 1625)(618, 1626)(619, 1627)(620, 1628)(621, 1629)(622, 1630)(623, 1631)(624, 1632)(625, 1633)(626, 1634)(627, 1635)(628, 1636)(629, 1637)(630, 1638)(631, 1639)(632, 1640)(633, 1641)(634, 1642)(635, 1643)(636, 1644)(637, 1645)(638, 1646)(639, 1647)(640, 1648)(641, 1649)(642, 1650)(643, 1651)(644, 1652)(645, 1653)(646, 1654)(647, 1655)(648, 1656)(649, 1657)(650, 1658)(651, 1659)(652, 1660)(653, 1661)(654, 1662)(655, 1663)(656, 1664)(657, 1665)(658, 1666)(659, 1667)(660, 1668)(661, 1669)(662, 1670)(663, 1671)(664, 1672)(665, 1673)(666, 1674)(667, 1675)(668, 1676)(669, 1677)(670, 1678)(671, 1679)(672, 1680)(673, 1681)(674, 1682)(675, 1683)(676, 1684)(677, 1685)(678, 1686)(679, 1687)(680, 1688)(681, 1689)(682, 1690)(683, 1691)(684, 1692)(685, 1693)(686, 1694)(687, 1695)(688, 1696)(689, 1697)(690, 1698)(691, 1699)(692, 1700)(693, 1701)(694, 1702)(695, 1703)(696, 1704)(697, 1705)(698, 1706)(699, 1707)(700, 1708)(701, 1709)(702, 1710)(703, 1711)(704, 1712)(705, 1713)(706, 1714)(707, 1715)(708, 1716)(709, 1717)(710, 1718)(711, 1719)(712, 1720)(713, 1721)(714, 1722)(715, 1723)(716, 1724)(717, 1725)(718, 1726)(719, 1727)(720, 1728)(721, 1729)(722, 1730)(723, 1731)(724, 1732)(725, 1733)(726, 1734)(727, 1735)(728, 1736)(729, 1737)(730, 1738)(731, 1739)(732, 1740)(733, 1741)(734, 1742)(735, 1743)(736, 1744)(737, 1745)(738, 1746)(739, 1747)(740, 1748)(741, 1749)(742, 1750)(743, 1751)(744, 1752)(745, 1753)(746, 1754)(747, 1755)(748, 1756)(749, 1757)(750, 1758)(751, 1759)(752, 1760)(753, 1761)(754, 1762)(755, 1763)(756, 1764)(757, 1765)(758, 1766)(759, 1767)(760, 1768)(761, 1769)(762, 1770)(763, 1771)(764, 1772)(765, 1773)(766, 1774)(767, 1775)(768, 1776)(769, 1777)(770, 1778)(771, 1779)(772, 1780)(773, 1781)(774, 1782)(775, 1783)(776, 1784)(777, 1785)(778, 1786)(779, 1787)(780, 1788)(781, 1789)(782, 1790)(783, 1791)(784, 1792)(785, 1793)(786, 1794)(787, 1795)(788, 1796)(789, 1797)(790, 1798)(791, 1799)(792, 1800)(793, 1801)(794, 1802)(795, 1803)(796, 1804)(797, 1805)(798, 1806)(799, 1807)(800, 1808)(801, 1809)(802, 1810)(803, 1811)(804, 1812)(805, 1813)(806, 1814)(807, 1815)(808, 1816)(809, 1817)(810, 1818)(811, 1819)(812, 1820)(813, 1821)(814, 1822)(815, 1823)(816, 1824)(817, 1825)(818, 1826)(819, 1827)(820, 1828)(821, 1829)(822, 1830)(823, 1831)(824, 1832)(825, 1833)(826, 1834)(827, 1835)(828, 1836)(829, 1837)(830, 1838)(831, 1839)(832, 1840)(833, 1841)(834, 1842)(835, 1843)(836, 1844)(837, 1845)(838, 1846)(839, 1847)(840, 1848)(841, 1849)(842, 1850)(843, 1851)(844, 1852)(845, 1853)(846, 1854)(847, 1855)(848, 1856)(849, 1857)(850, 1858)(851, 1859)(852, 1860)(853, 1861)(854, 1862)(855, 1863)(856, 1864)(857, 1865)(858, 1866)(859, 1867)(860, 1868)(861, 1869)(862, 1870)(863, 1871)(864, 1872)(865, 1873)(866, 1874)(867, 1875)(868, 1876)(869, 1877)(870, 1878)(871, 1879)(872, 1880)(873, 1881)(874, 1882)(875, 1883)(876, 1884)(877, 1885)(878, 1886)(879, 1887)(880, 1888)(881, 1889)(882, 1890)(883, 1891)(884, 1892)(885, 1893)(886, 1894)(887, 1895)(888, 1896)(889, 1897)(890, 1898)(891, 1899)(892, 1900)(893, 1901)(894, 1902)(895, 1903)(896, 1904)(897, 1905)(898, 1906)(899, 1907)(900, 1908)(901, 1909)(902, 1910)(903, 1911)(904, 1912)(905, 1913)(906, 1914)(907, 1915)(908, 1916)(909, 1917)(910, 1918)(911, 1919)(912, 1920)(913, 1921)(914, 1922)(915, 1923)(916, 1924)(917, 1925)(918, 1926)(919, 1927)(920, 1928)(921, 1929)(922, 1930)(923, 1931)(924, 1932)(925, 1933)(926, 1934)(927, 1935)(928, 1936)(929, 1937)(930, 1938)(931, 1939)(932, 1940)(933, 1941)(934, 1942)(935, 1943)(936, 1944)(937, 1945)(938, 1946)(939, 1947)(940, 1948)(941, 1949)(942, 1950)(943, 1951)(944, 1952)(945, 1953)(946, 1954)(947, 1955)(948, 1956)(949, 1957)(950, 1958)(951, 1959)(952, 1960)(953, 1961)(954, 1962)(955, 1963)(956, 1964)(957, 1965)(958, 1966)(959, 1967)(960, 1968)(961, 1969)(962, 1970)(963, 1971)(964, 1972)(965, 1973)(966, 1974)(967, 1975)(968, 1976)(969, 1977)(970, 1978)(971, 1979)(972, 1980)(973, 1981)(974, 1982)(975, 1983)(976, 1984)(977, 1985)(978, 1986)(979, 1987)(980, 1988)(981, 1989)(982, 1990)(983, 1991)(984, 1992)(985, 1993)(986, 1994)(987, 1995)(988, 1996)(989, 1997)(990, 1998)(991, 1999)(992, 2000)(993, 2001)(994, 2002)(995, 2003)(996, 2004)(997, 2005)(998, 2006)(999, 2007)(1000, 2008)(1001, 2009)(1002, 2010)(1003, 2011)(1004, 2012)(1005, 2013)(1006, 2014)(1007, 2015)(1008, 2016) local type(s) :: { ( 2, 14, 2, 14 ), ( 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E7.548 Graph:: bipartite v = 420 e = 1008 f = 576 degree seq :: [ 4^252, 6^168 ] E7.546 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y2^7, Y2^-5 * Y1 * Y2^-2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-1, Y2^2 * Y1^-1 * Y2^-2 * Y1 * Y2^3 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-3 * Y1^-1 * Y2^2 * Y1^-1, Y2^3 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-2 * Y1 * Y2^-3 * Y1 * Y2^-3 * Y1^-1 * Y2 * Y1^-1 ] Map:: R = (1, 505, 2, 506, 4, 508)(3, 507, 8, 512, 10, 514)(5, 509, 12, 516, 6, 510)(7, 511, 15, 519, 11, 515)(9, 513, 18, 522, 20, 524)(13, 517, 25, 529, 23, 527)(14, 518, 24, 528, 28, 532)(16, 520, 31, 535, 29, 533)(17, 521, 33, 537, 21, 525)(19, 523, 36, 540, 37, 541)(22, 526, 30, 534, 41, 545)(26, 530, 46, 550, 44, 548)(27, 531, 47, 551, 48, 552)(32, 536, 54, 558, 52, 556)(34, 538, 57, 561, 55, 559)(35, 539, 58, 562, 38, 542)(39, 543, 56, 560, 64, 568)(40, 544, 65, 569, 66, 570)(42, 546, 45, 549, 69, 573)(43, 547, 70, 574, 49, 553)(50, 554, 53, 557, 79, 583)(51, 555, 80, 584, 67, 571)(59, 563, 90, 594, 88, 592)(60, 564, 91, 595, 61, 565)(62, 566, 89, 593, 95, 599)(63, 567, 96, 600, 97, 601)(68, 572, 102, 606, 103, 607)(71, 575, 107, 611, 105, 609)(72, 576, 74, 578, 109, 613)(73, 577, 110, 614, 104, 608)(75, 579, 113, 617, 76, 580)(77, 581, 106, 610, 117, 621)(78, 582, 118, 622, 119, 623)(81, 585, 123, 627, 121, 625)(82, 586, 84, 588, 125, 629)(83, 587, 126, 630, 120, 624)(85, 589, 87, 591, 130, 634)(86, 590, 131, 635, 98, 602)(92, 596, 139, 643, 137, 641)(93, 597, 138, 642, 141, 645)(94, 598, 142, 646, 143, 647)(99, 603, 148, 652, 100, 604)(101, 605, 122, 626, 152, 656)(108, 612, 159, 663, 160, 664)(111, 615, 164, 668, 162, 666)(112, 616, 165, 669, 161, 665)(114, 618, 168, 672, 166, 670)(115, 619, 167, 671, 170, 674)(116, 620, 171, 675, 172, 676)(124, 628, 180, 684, 181, 685)(127, 631, 185, 689, 183, 687)(128, 632, 186, 690, 182, 686)(129, 633, 187, 691, 188, 692)(132, 636, 192, 696, 190, 694)(133, 637, 193, 697, 189, 693)(134, 638, 136, 640, 196, 700)(135, 639, 197, 701, 144, 648)(140, 644, 203, 707, 204, 708)(145, 649, 209, 713, 146, 650)(147, 651, 191, 695, 213, 717)(149, 653, 216, 720, 214, 718)(150, 654, 215, 719, 217, 721)(151, 655, 218, 722, 219, 723)(153, 657, 221, 725, 154, 658)(155, 659, 163, 667, 225, 729)(156, 660, 158, 662, 227, 731)(157, 661, 228, 732, 173, 677)(169, 673, 241, 745, 242, 746)(174, 678, 247, 751, 175, 679)(176, 680, 184, 688, 251, 755)(177, 681, 179, 683, 253, 757)(178, 682, 254, 758, 220, 724)(194, 698, 272, 776, 270, 774)(195, 699, 273, 777, 274, 778)(198, 702, 278, 782, 276, 780)(199, 703, 279, 783, 275, 779)(200, 704, 202, 706, 282, 786)(201, 705, 283, 787, 205, 709)(206, 710, 289, 793, 207, 711)(208, 712, 277, 781, 293, 797)(210, 714, 296, 800, 294, 798)(211, 715, 295, 799, 297, 801)(212, 716, 298, 802, 299, 803)(222, 726, 310, 814, 308, 812)(223, 727, 309, 813, 312, 816)(224, 728, 313, 817, 314, 818)(226, 730, 316, 820, 317, 821)(229, 733, 321, 825, 319, 823)(230, 734, 322, 826, 318, 822)(231, 735, 323, 827, 232, 736)(233, 737, 237, 741, 327, 831)(234, 738, 236, 740, 329, 833)(235, 739, 330, 834, 315, 819)(238, 742, 240, 744, 335, 839)(239, 743, 336, 840, 243, 747)(244, 748, 342, 846, 245, 749)(246, 750, 320, 824, 346, 850)(248, 752, 349, 853, 347, 851)(249, 753, 348, 852, 351, 855)(250, 754, 352, 856, 353, 857)(252, 756, 355, 859, 356, 860)(255, 759, 360, 864, 358, 862)(256, 760, 361, 865, 357, 861)(257, 761, 362, 866, 258, 762)(259, 763, 263, 767, 366, 870)(260, 764, 262, 766, 368, 872)(261, 765, 369, 873, 354, 858)(264, 768, 373, 877, 265, 769)(266, 770, 271, 775, 377, 881)(267, 771, 269, 773, 379, 883)(268, 772, 380, 884, 300, 804)(280, 784, 340, 844, 339, 843)(281, 785, 393, 897, 363, 867)(284, 788, 365, 869, 395, 899)(285, 789, 397, 901, 394, 898)(286, 790, 350, 854, 287, 791)(288, 792, 396, 900, 400, 904)(290, 794, 401, 905, 338, 842)(291, 795, 344, 848, 402, 906)(292, 796, 403, 907, 404, 908)(301, 805, 303, 807, 414, 918)(302, 806, 415, 919, 304, 808)(305, 809, 398, 902, 306, 810)(307, 811, 359, 863, 420, 924)(311, 815, 383, 887, 385, 889)(324, 828, 413, 917, 431, 935)(325, 829, 432, 936, 367, 871)(326, 830, 433, 937, 416, 920)(328, 832, 375, 879, 435, 939)(331, 835, 438, 942, 436, 940)(332, 836, 371, 875, 382, 886)(333, 837, 439, 943, 434, 938)(334, 838, 441, 945, 374, 878)(337, 841, 376, 880, 442, 946)(341, 845, 443, 947, 444, 948)(343, 847, 445, 949, 417, 921)(345, 849, 446, 950, 447, 951)(364, 868, 453, 957, 378, 882)(370, 874, 457, 961, 455, 959)(372, 876, 458, 962, 454, 958)(381, 885, 462, 966, 460, 964)(384, 888, 463, 967, 459, 963)(386, 890, 426, 930, 387, 891)(388, 892, 392, 896, 451, 955)(389, 893, 391, 895, 430, 934)(390, 894, 465, 969, 405, 909)(399, 903, 427, 931, 429, 933)(406, 910, 408, 912, 421, 925)(407, 911, 424, 928, 409, 913)(410, 914, 440, 944, 411, 915)(412, 916, 461, 965, 472, 976)(418, 922, 473, 977, 464, 968)(419, 923, 474, 978, 467, 971)(422, 926, 449, 953, 423, 927)(425, 929, 437, 941, 477, 981)(428, 932, 478, 982, 448, 952)(450, 954, 456, 960, 484, 988)(452, 956, 485, 989, 475, 979)(466, 970, 491, 995, 489, 993)(468, 972, 492, 996, 469, 973)(470, 974, 490, 994, 493, 997)(471, 975, 494, 998, 479, 983)(476, 980, 496, 1000, 486, 990)(480, 984, 498, 1002, 481, 985)(482, 986, 497, 1001, 499, 1003)(483, 987, 500, 1004, 487, 991)(488, 992, 501, 1005, 495, 999)(502, 1006, 504, 1008, 503, 1007)(1009, 1513, 1011, 1515, 1017, 1521, 1027, 1531, 1034, 1538, 1021, 1525, 1013, 1517)(1010, 1514, 1014, 1518, 1022, 1526, 1035, 1539, 1040, 1544, 1024, 1528, 1015, 1519)(1012, 1516, 1019, 1523, 1030, 1534, 1048, 1552, 1042, 1546, 1025, 1529, 1016, 1520)(1018, 1522, 1029, 1533, 1047, 1551, 1071, 1575, 1067, 1571, 1043, 1547, 1026, 1530)(1020, 1524, 1031, 1535, 1050, 1554, 1076, 1580, 1079, 1583, 1051, 1555, 1032, 1536)(1023, 1527, 1037, 1541, 1058, 1562, 1086, 1590, 1089, 1593, 1059, 1563, 1038, 1542)(1028, 1532, 1046, 1550, 1070, 1574, 1102, 1606, 1100, 1604, 1068, 1572, 1044, 1548)(1033, 1537, 1052, 1556, 1080, 1584, 1116, 1620, 1119, 1623, 1081, 1585, 1053, 1557)(1036, 1540, 1057, 1561, 1085, 1589, 1124, 1628, 1122, 1626, 1083, 1587, 1055, 1559)(1039, 1543, 1060, 1564, 1090, 1594, 1132, 1636, 1135, 1639, 1091, 1595, 1061, 1565)(1041, 1545, 1063, 1567, 1093, 1597, 1137, 1641, 1140, 1644, 1094, 1598, 1064, 1568)(1045, 1549, 1069, 1573, 1101, 1605, 1148, 1652, 1120, 1624, 1082, 1586, 1054, 1558)(1049, 1553, 1075, 1579, 1109, 1613, 1159, 1663, 1157, 1661, 1107, 1611, 1073, 1577)(1056, 1560, 1084, 1588, 1123, 1627, 1177, 1681, 1136, 1640, 1092, 1596, 1062, 1566)(1065, 1569, 1074, 1578, 1108, 1612, 1158, 1662, 1202, 1706, 1141, 1645, 1095, 1599)(1066, 1570, 1096, 1600, 1142, 1646, 1203, 1707, 1206, 1710, 1143, 1647, 1097, 1601)(1072, 1576, 1106, 1610, 1155, 1659, 1220, 1724, 1218, 1722, 1153, 1657, 1104, 1608)(1077, 1581, 1112, 1616, 1163, 1667, 1232, 1736, 1230, 1734, 1161, 1665, 1110, 1614)(1078, 1582, 1113, 1617, 1164, 1668, 1234, 1738, 1237, 1741, 1165, 1669, 1114, 1618)(1087, 1591, 1128, 1632, 1184, 1688, 1258, 1762, 1256, 1760, 1182, 1686, 1126, 1630)(1088, 1592, 1129, 1633, 1185, 1689, 1260, 1764, 1263, 1767, 1186, 1690, 1130, 1634)(1098, 1602, 1105, 1609, 1154, 1658, 1219, 1723, 1288, 1792, 1207, 1711, 1144, 1648)(1099, 1603, 1145, 1649, 1208, 1712, 1289, 1793, 1292, 1796, 1209, 1713, 1146, 1650)(1103, 1607, 1152, 1656, 1216, 1720, 1300, 1804, 1298, 1802, 1214, 1718, 1150, 1654)(1111, 1615, 1162, 1666, 1231, 1735, 1319, 1823, 1238, 1742, 1166, 1670, 1115, 1619)(1117, 1621, 1169, 1673, 1241, 1745, 1334, 1838, 1332, 1836, 1239, 1743, 1167, 1671)(1118, 1622, 1170, 1674, 1242, 1746, 1336, 1840, 1339, 1843, 1243, 1747, 1171, 1675)(1121, 1625, 1174, 1678, 1246, 1750, 1342, 1846, 1345, 1849, 1247, 1751, 1175, 1679)(1125, 1629, 1181, 1685, 1254, 1758, 1353, 1857, 1351, 1855, 1252, 1756, 1179, 1683)(1127, 1631, 1183, 1687, 1257, 1761, 1358, 1862, 1264, 1768, 1187, 1691, 1131, 1635)(1133, 1637, 1190, 1694, 1267, 1771, 1373, 1877, 1371, 1875, 1265, 1769, 1188, 1692)(1134, 1638, 1191, 1695, 1268, 1772, 1375, 1879, 1378, 1882, 1269, 1773, 1192, 1696)(1138, 1642, 1197, 1701, 1274, 1778, 1384, 1888, 1382, 1886, 1272, 1776, 1195, 1699)(1139, 1643, 1198, 1702, 1275, 1779, 1386, 1890, 1389, 1893, 1276, 1780, 1199, 1703)(1147, 1651, 1151, 1655, 1215, 1719, 1299, 1803, 1406, 1910, 1293, 1797, 1210, 1714)(1149, 1653, 1213, 1717, 1296, 1800, 1407, 1911, 1369, 1873, 1294, 1798, 1211, 1715)(1156, 1660, 1222, 1726, 1309, 1813, 1421, 1925, 1424, 1928, 1310, 1814, 1223, 1727)(1160, 1664, 1228, 1732, 1315, 1819, 1427, 1931, 1405, 1909, 1313, 1817, 1226, 1730)(1168, 1672, 1240, 1744, 1333, 1837, 1376, 1880, 1340, 1844, 1244, 1748, 1172, 1676)(1173, 1677, 1212, 1716, 1295, 1799, 1359, 1863, 1448, 1952, 1341, 1845, 1245, 1749)(1176, 1680, 1180, 1684, 1253, 1757, 1352, 1856, 1297, 1801, 1346, 1850, 1248, 1752)(1178, 1682, 1251, 1755, 1349, 1853, 1400, 1904, 1287, 1791, 1347, 1851, 1249, 1753)(1189, 1693, 1266, 1770, 1372, 1876, 1387, 1891, 1379, 1883, 1270, 1774, 1193, 1697)(1194, 1698, 1250, 1754, 1348, 1852, 1305, 1809, 1417, 1921, 1380, 1884, 1271, 1775)(1196, 1700, 1273, 1777, 1383, 1887, 1337, 1841, 1390, 1894, 1277, 1781, 1200, 1704)(1201, 1705, 1278, 1782, 1391, 1895, 1320, 1824, 1431, 1935, 1392, 1896, 1279, 1783)(1204, 1708, 1283, 1787, 1396, 1900, 1368, 1872, 1364, 1868, 1394, 1898, 1281, 1785)(1205, 1709, 1284, 1788, 1397, 1901, 1472, 1976, 1474, 1978, 1398, 1902, 1285, 1789)(1217, 1721, 1302, 1806, 1414, 1918, 1318, 1822, 1322, 1826, 1415, 1919, 1303, 1807)(1221, 1725, 1308, 1812, 1420, 1924, 1479, 1983, 1447, 1951, 1418, 1922, 1306, 1810)(1224, 1728, 1227, 1731, 1314, 1818, 1410, 1914, 1350, 1854, 1425, 1929, 1311, 1815)(1225, 1729, 1312, 1816, 1426, 1930, 1438, 1942, 1330, 1834, 1393, 1897, 1280, 1784)(1229, 1733, 1316, 1820, 1429, 1933, 1357, 1861, 1361, 1865, 1430, 1934, 1317, 1821)(1233, 1737, 1323, 1827, 1433, 1937, 1484, 1988, 1466, 1970, 1432, 1936, 1321, 1825)(1235, 1739, 1326, 1830, 1399, 1903, 1286, 1790, 1282, 1786, 1395, 1899, 1324, 1828)(1236, 1740, 1327, 1831, 1435, 1939, 1408, 1912, 1477, 1981, 1436, 1940, 1328, 1832)(1255, 1759, 1355, 1859, 1416, 1920, 1304, 1808, 1307, 1811, 1419, 1923, 1356, 1860)(1259, 1763, 1362, 1866, 1458, 1962, 1491, 1995, 1471, 1975, 1457, 1961, 1360, 1864)(1261, 1765, 1365, 1869, 1437, 1941, 1329, 1833, 1325, 1829, 1434, 1938, 1363, 1867)(1262, 1766, 1366, 1870, 1459, 1963, 1452, 1956, 1489, 1993, 1460, 1964, 1367, 1871)(1290, 1794, 1402, 1906, 1475, 1979, 1470, 1974, 1461, 1965, 1370, 1874, 1401, 1905)(1291, 1795, 1403, 1907, 1374, 1878, 1462, 1966, 1494, 1998, 1476, 1980, 1404, 1908)(1301, 1805, 1413, 1917, 1478, 1982, 1445, 1949, 1338, 1842, 1444, 1948, 1411, 1915)(1331, 1835, 1439, 1943, 1422, 1926, 1453, 1957, 1455, 1959, 1465, 1969, 1440, 1944)(1335, 1839, 1442, 1946, 1487, 1991, 1499, 2003, 1481, 1985, 1423, 1927, 1441, 1945)(1343, 1847, 1409, 1913, 1412, 1916, 1446, 1950, 1443, 1947, 1381, 1885, 1449, 1953)(1344, 1848, 1450, 1954, 1385, 1889, 1467, 1971, 1495, 1999, 1488, 1992, 1451, 1955)(1354, 1858, 1456, 1960, 1490, 1994, 1464, 1968, 1377, 1881, 1463, 1967, 1454, 1958)(1388, 1892, 1468, 1972, 1482, 1986, 1428, 1932, 1483, 1987, 1496, 2000, 1469, 1973)(1473, 1977, 1497, 2001, 1502, 2006, 1480, 1984, 1503, 2007, 1510, 2014, 1498, 2002)(1485, 1989, 1501, 2005, 1511, 2015, 1505, 2009, 1486, 1990, 1500, 2004, 1504, 2008)(1492, 1996, 1507, 2011, 1512, 2016, 1509, 2013, 1493, 1997, 1506, 2010, 1508, 2012) L = (1, 1011)(2, 1014)(3, 1017)(4, 1019)(5, 1009)(6, 1022)(7, 1010)(8, 1012)(9, 1027)(10, 1029)(11, 1030)(12, 1031)(13, 1013)(14, 1035)(15, 1037)(16, 1015)(17, 1016)(18, 1018)(19, 1034)(20, 1046)(21, 1047)(22, 1048)(23, 1050)(24, 1020)(25, 1052)(26, 1021)(27, 1040)(28, 1057)(29, 1058)(30, 1023)(31, 1060)(32, 1024)(33, 1063)(34, 1025)(35, 1026)(36, 1028)(37, 1069)(38, 1070)(39, 1071)(40, 1042)(41, 1075)(42, 1076)(43, 1032)(44, 1080)(45, 1033)(46, 1045)(47, 1036)(48, 1084)(49, 1085)(50, 1086)(51, 1038)(52, 1090)(53, 1039)(54, 1056)(55, 1093)(56, 1041)(57, 1074)(58, 1096)(59, 1043)(60, 1044)(61, 1101)(62, 1102)(63, 1067)(64, 1106)(65, 1049)(66, 1108)(67, 1109)(68, 1079)(69, 1112)(70, 1113)(71, 1051)(72, 1116)(73, 1053)(74, 1054)(75, 1055)(76, 1123)(77, 1124)(78, 1089)(79, 1128)(80, 1129)(81, 1059)(82, 1132)(83, 1061)(84, 1062)(85, 1137)(86, 1064)(87, 1065)(88, 1142)(89, 1066)(90, 1105)(91, 1145)(92, 1068)(93, 1148)(94, 1100)(95, 1152)(96, 1072)(97, 1154)(98, 1155)(99, 1073)(100, 1158)(101, 1159)(102, 1077)(103, 1162)(104, 1163)(105, 1164)(106, 1078)(107, 1111)(108, 1119)(109, 1169)(110, 1170)(111, 1081)(112, 1082)(113, 1174)(114, 1083)(115, 1177)(116, 1122)(117, 1181)(118, 1087)(119, 1183)(120, 1184)(121, 1185)(122, 1088)(123, 1127)(124, 1135)(125, 1190)(126, 1191)(127, 1091)(128, 1092)(129, 1140)(130, 1197)(131, 1198)(132, 1094)(133, 1095)(134, 1203)(135, 1097)(136, 1098)(137, 1208)(138, 1099)(139, 1151)(140, 1120)(141, 1213)(142, 1103)(143, 1215)(144, 1216)(145, 1104)(146, 1219)(147, 1220)(148, 1222)(149, 1107)(150, 1202)(151, 1157)(152, 1228)(153, 1110)(154, 1231)(155, 1232)(156, 1234)(157, 1114)(158, 1115)(159, 1117)(160, 1240)(161, 1241)(162, 1242)(163, 1118)(164, 1168)(165, 1212)(166, 1246)(167, 1121)(168, 1180)(169, 1136)(170, 1251)(171, 1125)(172, 1253)(173, 1254)(174, 1126)(175, 1257)(176, 1258)(177, 1260)(178, 1130)(179, 1131)(180, 1133)(181, 1266)(182, 1267)(183, 1268)(184, 1134)(185, 1189)(186, 1250)(187, 1138)(188, 1273)(189, 1274)(190, 1275)(191, 1139)(192, 1196)(193, 1278)(194, 1141)(195, 1206)(196, 1283)(197, 1284)(198, 1143)(199, 1144)(200, 1289)(201, 1146)(202, 1147)(203, 1149)(204, 1295)(205, 1296)(206, 1150)(207, 1299)(208, 1300)(209, 1302)(210, 1153)(211, 1288)(212, 1218)(213, 1308)(214, 1309)(215, 1156)(216, 1227)(217, 1312)(218, 1160)(219, 1314)(220, 1315)(221, 1316)(222, 1161)(223, 1319)(224, 1230)(225, 1323)(226, 1237)(227, 1326)(228, 1327)(229, 1165)(230, 1166)(231, 1167)(232, 1333)(233, 1334)(234, 1336)(235, 1171)(236, 1172)(237, 1173)(238, 1342)(239, 1175)(240, 1176)(241, 1178)(242, 1348)(243, 1349)(244, 1179)(245, 1352)(246, 1353)(247, 1355)(248, 1182)(249, 1358)(250, 1256)(251, 1362)(252, 1263)(253, 1365)(254, 1366)(255, 1186)(256, 1187)(257, 1188)(258, 1372)(259, 1373)(260, 1375)(261, 1192)(262, 1193)(263, 1194)(264, 1195)(265, 1383)(266, 1384)(267, 1386)(268, 1199)(269, 1200)(270, 1391)(271, 1201)(272, 1225)(273, 1204)(274, 1395)(275, 1396)(276, 1397)(277, 1205)(278, 1282)(279, 1347)(280, 1207)(281, 1292)(282, 1402)(283, 1403)(284, 1209)(285, 1210)(286, 1211)(287, 1359)(288, 1407)(289, 1346)(290, 1214)(291, 1406)(292, 1298)(293, 1413)(294, 1414)(295, 1217)(296, 1307)(297, 1417)(298, 1221)(299, 1419)(300, 1420)(301, 1421)(302, 1223)(303, 1224)(304, 1426)(305, 1226)(306, 1410)(307, 1427)(308, 1429)(309, 1229)(310, 1322)(311, 1238)(312, 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1957)(950, 1958)(951, 1959)(952, 1960)(953, 1961)(954, 1962)(955, 1963)(956, 1964)(957, 1965)(958, 1966)(959, 1967)(960, 1968)(961, 1969)(962, 1970)(963, 1971)(964, 1972)(965, 1973)(966, 1974)(967, 1975)(968, 1976)(969, 1977)(970, 1978)(971, 1979)(972, 1980)(973, 1981)(974, 1982)(975, 1983)(976, 1984)(977, 1985)(978, 1986)(979, 1987)(980, 1988)(981, 1989)(982, 1990)(983, 1991)(984, 1992)(985, 1993)(986, 1994)(987, 1995)(988, 1996)(989, 1997)(990, 1998)(991, 1999)(992, 2000)(993, 2001)(994, 2002)(995, 2003)(996, 2004)(997, 2005)(998, 2006)(999, 2007)(1000, 2008)(1001, 2009)(1002, 2010)(1003, 2011)(1004, 2012)(1005, 2013)(1006, 2014)(1007, 2015)(1008, 2016) local type(s) :: { ( 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E7.547 Graph:: bipartite v = 240 e = 1008 f = 756 degree seq :: [ 6^168, 14^72 ] E7.547 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, (Y3^-1 * Y1^-1)^7, (Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-3 * Y2 * Y3^-2)^2 ] Map:: polytopal R = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 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1939)(1379, 1883, 1408, 1912)(1382, 1886, 1416, 1920)(1385, 1889, 1443, 1947)(1387, 1891, 1418, 1922)(1388, 1892, 1417, 1921)(1389, 1893, 1396, 1900)(1391, 1895, 1395, 1899)(1392, 1896, 1399, 1903)(1393, 1897, 1447, 1951)(1401, 1905, 1452, 1956)(1410, 1914, 1455, 1959)(1415, 1919, 1460, 1964)(1424, 1928, 1464, 1968)(1425, 1929, 1427, 1931)(1426, 1930, 1462, 1966)(1428, 1932, 1453, 1957)(1429, 1933, 1444, 1948)(1430, 1934, 1465, 1969)(1432, 1936, 1441, 1945)(1433, 1937, 1457, 1961)(1434, 1938, 1458, 1962)(1436, 1940, 1470, 1974)(1437, 1941, 1439, 1943)(1438, 1942, 1454, 1958)(1440, 1944, 1461, 1965)(1442, 1946, 1471, 1975)(1445, 1949, 1449, 1953)(1446, 1950, 1450, 1954)(1448, 1952, 1476, 1980)(1451, 1955, 1477, 1981)(1456, 1960, 1481, 1985)(1459, 1963, 1482, 1986)(1463, 1967, 1485, 1989)(1466, 1970, 1489, 1993)(1467, 1971, 1473, 1977)(1468, 1972, 1487, 1991)(1469, 1973, 1490, 1994)(1472, 1976, 1492, 1996)(1474, 1978, 1491, 1995)(1475, 1979, 1493, 1997)(1478, 1982, 1496, 2000)(1479, 1983, 1484, 1988)(1480, 1984, 1497, 2001)(1483, 1987, 1498, 2002)(1486, 1990, 1500, 2004)(1488, 1992, 1501, 2005)(1494, 1998, 1504, 2008)(1495, 1999, 1505, 2009)(1499, 2003, 1507, 2011)(1502, 2006, 1508, 2012)(1503, 2007, 1509, 2013)(1506, 2010, 1510, 2014)(1511, 2015, 1512, 2016) L = (1, 1011)(2, 1013)(3, 1016)(4, 1009)(5, 1020)(6, 1010)(7, 1021)(8, 1025)(9, 1026)(10, 1012)(11, 1017)(12, 1031)(13, 1032)(14, 1014)(15, 1015)(16, 1035)(17, 1028)(18, 1040)(19, 1041)(20, 1018)(21, 1019)(22, 1043)(23, 1034)(24, 1048)(25, 1049)(26, 1022)(27, 1051)(28, 1023)(29, 1024)(30, 1054)(31, 1027)(32, 1059)(33, 1061)(34, 1062)(35, 1063)(36, 1029)(37, 1030)(38, 1065)(39, 1033)(40, 1053)(41, 1071)(42, 1072)(43, 1074)(44, 1075)(45, 1036)(46, 1077)(47, 1037)(48, 1038)(49, 1039)(50, 1081)(51, 1044)(52, 1042)(53, 1087)(54, 1088)(55, 1090)(56, 1091)(57, 1092)(58, 1045)(59, 1046)(60, 1047)(61, 1096)(62, 1050)(63, 1101)(64, 1102)(65, 1052)(66, 1079)(67, 1106)(68, 1107)(69, 1109)(70, 1110)(71, 1055)(72, 1056)(73, 1114)(74, 1057)(75, 1058)(76, 1116)(77, 1060)(78, 1119)(79, 1082)(80, 1124)(81, 1064)(82, 1094)(83, 1127)(84, 1129)(85, 1130)(86, 1066)(87, 1067)(88, 1134)(89, 1068)(90, 1069)(91, 1070)(92, 1137)(93, 1097)(94, 1142)(95, 1073)(96, 1143)(97, 1076)(98, 1148)(99, 1149)(100, 1078)(101, 1113)(102, 1153)(103, 1154)(104, 1155)(105, 1080)(106, 1158)(107, 1159)(108, 1160)(109, 1083)(110, 1084)(111, 1164)(112, 1085)(113, 1086)(114, 1166)(115, 1112)(116, 1120)(117, 1089)(118, 1171)(119, 1175)(120, 1093)(121, 1133)(122, 1179)(123, 1180)(124, 1181)(125, 1095)(126, 1184)(127, 1185)(128, 1098)(129, 1188)(130, 1099)(131, 1100)(132, 1190)(133, 1132)(134, 1138)(135, 1195)(136, 1103)(137, 1104)(138, 1105)(139, 1198)(140, 1144)(141, 1203)(142, 1108)(143, 1204)(144, 1111)(145, 1209)(146, 1210)(147, 1212)(148, 1213)(149, 1115)(150, 1162)(151, 1216)(152, 1218)(153, 1219)(154, 1117)(155, 1118)(156, 1224)(157, 1225)(158, 1226)(159, 1121)(160, 1122)(161, 1123)(162, 1230)(163, 1233)(164, 1125)(165, 1126)(166, 1221)(167, 1172)(168, 1128)(169, 1238)(170, 1131)(171, 1243)(172, 1244)(173, 1246)(174, 1247)(175, 1135)(176, 1187)(177, 1250)(178, 1251)(179, 1136)(180, 1254)(181, 1255)(182, 1256)(183, 1139)(184, 1140)(185, 1141)(186, 1260)(187, 1264)(188, 1265)(189, 1145)(190, 1268)(191, 1146)(192, 1147)(193, 1270)(194, 1186)(195, 1199)(196, 1275)(197, 1150)(198, 1151)(199, 1152)(200, 1278)(201, 1205)(202, 1283)(203, 1156)(204, 1286)(205, 1287)(206, 1157)(207, 1288)(208, 1292)(209, 1161)(210, 1222)(211, 1296)(212, 1297)(213, 1298)(214, 1163)(215, 1165)(216, 1228)(217, 1302)(218, 1304)(219, 1305)(220, 1167)(221, 1168)(222, 1309)(223, 1169)(224, 1170)(225, 1313)(226, 1314)(227, 1173)(228, 1174)(229, 1317)(230, 1320)(231, 1176)(232, 1177)(233, 1178)(234, 1323)(235, 1239)(236, 1328)(237, 1182)(238, 1331)(239, 1332)(240, 1183)(241, 1333)(242, 1337)(243, 1339)(244, 1340)(245, 1189)(246, 1258)(247, 1343)(248, 1345)(249, 1346)(250, 1191)(251, 1192)(252, 1350)(253, 1193)(254, 1194)(255, 1196)(256, 1267)(257, 1355)(258, 1356)(259, 1197)(260, 1359)(261, 1360)(262, 1361)(263, 1200)(264, 1201)(265, 1202)(266, 1363)(267, 1367)(268, 1368)(269, 1206)(270, 1370)(271, 1207)(272, 1208)(273, 1318)(274, 1266)(275, 1279)(276, 1211)(277, 1374)(278, 1231)(279, 1376)(280, 1377)(281, 1214)(282, 1215)(283, 1307)(284, 1289)(285, 1217)(286, 1381)(287, 1220)(288, 1347)(289, 1373)(290, 1372)(291, 1365)(292, 1223)(293, 1384)(294, 1387)(295, 1227)(296, 1308)(297, 1389)(298, 1364)(299, 1362)(300, 1229)(301, 1391)(302, 1330)(303, 1232)(304, 1234)(305, 1316)(306, 1395)(307, 1396)(308, 1235)(309, 1398)(310, 1236)(311, 1237)(312, 1401)(313, 1402)(314, 1240)(315, 1404)(316, 1241)(317, 1242)(318, 1271)(319, 1315)(320, 1324)(321, 1245)(322, 1407)(323, 1261)(324, 1409)(325, 1410)(326, 1248)(327, 1249)(328, 1348)(329, 1334)(330, 1252)(331, 1306)(332, 1406)(333, 1253)(334, 1414)(335, 1417)(336, 1257)(337, 1349)(338, 1419)(339, 1382)(340, 1399)(341, 1259)(342, 1421)(343, 1285)(344, 1262)(345, 1263)(346, 1423)(347, 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1810)(803, 1811)(804, 1812)(805, 1813)(806, 1814)(807, 1815)(808, 1816)(809, 1817)(810, 1818)(811, 1819)(812, 1820)(813, 1821)(814, 1822)(815, 1823)(816, 1824)(817, 1825)(818, 1826)(819, 1827)(820, 1828)(821, 1829)(822, 1830)(823, 1831)(824, 1832)(825, 1833)(826, 1834)(827, 1835)(828, 1836)(829, 1837)(830, 1838)(831, 1839)(832, 1840)(833, 1841)(834, 1842)(835, 1843)(836, 1844)(837, 1845)(838, 1846)(839, 1847)(840, 1848)(841, 1849)(842, 1850)(843, 1851)(844, 1852)(845, 1853)(846, 1854)(847, 1855)(848, 1856)(849, 1857)(850, 1858)(851, 1859)(852, 1860)(853, 1861)(854, 1862)(855, 1863)(856, 1864)(857, 1865)(858, 1866)(859, 1867)(860, 1868)(861, 1869)(862, 1870)(863, 1871)(864, 1872)(865, 1873)(866, 1874)(867, 1875)(868, 1876)(869, 1877)(870, 1878)(871, 1879)(872, 1880)(873, 1881)(874, 1882)(875, 1883)(876, 1884)(877, 1885)(878, 1886)(879, 1887)(880, 1888)(881, 1889)(882, 1890)(883, 1891)(884, 1892)(885, 1893)(886, 1894)(887, 1895)(888, 1896)(889, 1897)(890, 1898)(891, 1899)(892, 1900)(893, 1901)(894, 1902)(895, 1903)(896, 1904)(897, 1905)(898, 1906)(899, 1907)(900, 1908)(901, 1909)(902, 1910)(903, 1911)(904, 1912)(905, 1913)(906, 1914)(907, 1915)(908, 1916)(909, 1917)(910, 1918)(911, 1919)(912, 1920)(913, 1921)(914, 1922)(915, 1923)(916, 1924)(917, 1925)(918, 1926)(919, 1927)(920, 1928)(921, 1929)(922, 1930)(923, 1931)(924, 1932)(925, 1933)(926, 1934)(927, 1935)(928, 1936)(929, 1937)(930, 1938)(931, 1939)(932, 1940)(933, 1941)(934, 1942)(935, 1943)(936, 1944)(937, 1945)(938, 1946)(939, 1947)(940, 1948)(941, 1949)(942, 1950)(943, 1951)(944, 1952)(945, 1953)(946, 1954)(947, 1955)(948, 1956)(949, 1957)(950, 1958)(951, 1959)(952, 1960)(953, 1961)(954, 1962)(955, 1963)(956, 1964)(957, 1965)(958, 1966)(959, 1967)(960, 1968)(961, 1969)(962, 1970)(963, 1971)(964, 1972)(965, 1973)(966, 1974)(967, 1975)(968, 1976)(969, 1977)(970, 1978)(971, 1979)(972, 1980)(973, 1981)(974, 1982)(975, 1983)(976, 1984)(977, 1985)(978, 1986)(979, 1987)(980, 1988)(981, 1989)(982, 1990)(983, 1991)(984, 1992)(985, 1993)(986, 1994)(987, 1995)(988, 1996)(989, 1997)(990, 1998)(991, 1999)(992, 2000)(993, 2001)(994, 2002)(995, 2003)(996, 2004)(997, 2005)(998, 2006)(999, 2007)(1000, 2008)(1001, 2009)(1002, 2010)(1003, 2011)(1004, 2012)(1005, 2013)(1006, 2014)(1007, 2015)(1008, 2016) local type(s) :: { ( 6, 14 ), ( 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E7.546 Graph:: simple bipartite v = 756 e = 1008 f = 240 degree seq :: [ 2^504, 4^252 ] E7.548 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y3 * Y1^-1)^3, Y1^7, (Y3 * Y1^2 * Y3 * Y1^-2 * Y3 * Y1^2 * Y3 * Y1^-1)^2, Y3 * Y1^3 * Y3 * Y1^-2 * Y3 * Y1^3 * Y3 * Y1^-3 * Y3 * Y1^2 * Y3 * Y1^-3 ] Map:: polytopal R = (1, 505, 2, 506, 5, 509, 11, 515, 20, 524, 10, 514, 4, 508)(3, 507, 7, 511, 15, 519, 26, 530, 30, 534, 17, 521, 8, 512)(6, 510, 13, 517, 24, 528, 39, 543, 42, 546, 25, 529, 14, 518)(9, 513, 18, 522, 31, 535, 49, 553, 46, 550, 28, 532, 16, 520)(12, 516, 22, 526, 37, 541, 57, 561, 60, 564, 38, 542, 23, 527)(19, 523, 33, 537, 52, 556, 77, 581, 76, 580, 51, 555, 32, 536)(21, 525, 35, 539, 55, 559, 81, 585, 84, 588, 56, 560, 36, 540)(27, 531, 44, 548, 67, 571, 97, 601, 100, 604, 68, 572, 45, 549)(29, 533, 47, 551, 70, 574, 102, 606, 91, 595, 62, 566, 40, 544)(34, 538, 54, 558, 80, 584, 115, 619, 114, 618, 79, 583, 53, 557)(41, 545, 63, 567, 92, 596, 130, 634, 123, 627, 86, 590, 58, 562)(43, 547, 65, 569, 95, 599, 134, 638, 137, 641, 96, 600, 66, 570)(48, 552, 72, 576, 105, 609, 147, 651, 146, 650, 104, 608, 71, 575)(50, 554, 74, 578, 108, 612, 151, 655, 154, 658, 109, 613, 75, 579)(59, 563, 87, 591, 124, 628, 172, 676, 165, 669, 118, 622, 82, 586)(61, 565, 89, 593, 127, 631, 176, 680, 179, 683, 128, 632, 90, 594)(64, 568, 94, 598, 133, 637, 185, 689, 184, 688, 132, 636, 93, 597)(69, 573, 101, 605, 142, 646, 197, 701, 193, 697, 139, 643, 98, 602)(73, 577, 106, 610, 149, 653, 206, 710, 209, 713, 150, 654, 107, 611)(78, 582, 112, 616, 158, 662, 217, 721, 220, 724, 159, 663, 113, 617)(83, 587, 119, 623, 166, 670, 228, 732, 224, 728, 162, 666, 116, 620)(85, 589, 121, 625, 169, 673, 232, 736, 235, 739, 170, 674, 122, 626)(88, 592, 126, 630, 175, 679, 241, 745, 240, 744, 174, 678, 125, 629)(99, 603, 140, 644, 194, 698, 264, 768, 257, 761, 188, 692, 135, 639)(103, 607, 144, 648, 201, 705, 272, 776, 275, 779, 202, 706, 145, 649)(110, 614, 155, 659, 214, 718, 290, 794, 286, 790, 211, 715, 152, 656)(111, 615, 156, 660, 215, 719, 292, 796, 295, 799, 216, 720, 157, 661)(117, 621, 163, 667, 225, 729, 304, 808, 307, 811, 226, 730, 164, 668)(120, 624, 168, 672, 231, 735, 313, 817, 312, 816, 230, 734, 167, 671)(129, 633, 180, 684, 247, 751, 333, 837, 329, 833, 244, 748, 177, 681)(131, 635, 182, 686, 250, 754, 337, 841, 340, 844, 251, 755, 183, 687)(136, 640, 189, 693, 258, 762, 309, 813, 279, 783, 205, 709, 148, 652)(138, 642, 191, 695, 261, 765, 349, 853, 352, 856, 262, 766, 192, 696)(141, 645, 196, 700, 267, 771, 314, 818, 306, 810, 266, 770, 195, 699)(143, 647, 199, 703, 270, 774, 358, 862, 361, 865, 271, 775, 200, 704)(153, 657, 212, 716, 287, 791, 365, 869, 370, 874, 281, 785, 207, 711)(160, 664, 221, 725, 300, 804, 381, 885, 379, 883, 297, 801, 218, 722)(161, 665, 222, 726, 301, 805, 382, 886, 384, 888, 302, 806, 223, 727)(171, 675, 236, 740, 319, 823, 398, 902, 395, 899, 316, 820, 233, 737)(173, 677, 238, 742, 322, 826, 400, 904, 403, 907, 323, 827, 239, 743)(178, 682, 245, 749, 330, 834, 299, 803, 344, 848, 254, 758, 186, 690)(181, 685, 248, 752, 335, 839, 291, 795, 294, 798, 336, 840, 249, 753)(187, 691, 255, 759, 345, 849, 413, 917, 401, 905, 324, 828, 256, 760)(190, 694, 260, 764, 325, 829, 404, 908, 416, 920, 348, 852, 259, 763)(198, 702, 208, 712, 282, 786, 321, 825, 237, 741, 320, 824, 269, 773)(203, 707, 276, 780, 366, 870, 426, 930, 425, 929, 363, 867, 273, 777)(204, 708, 277, 781, 367, 871, 399, 903, 409, 913, 368, 872, 278, 782)(210, 714, 284, 788, 372, 876, 429, 933, 431, 935, 373, 877, 285, 789)(213, 717, 289, 793, 326, 830, 242, 746, 234, 738, 317, 821, 288, 792)(219, 723, 298, 802, 380, 884, 419, 923, 434, 938, 376, 880, 293, 797)(227, 731, 308, 812, 388, 892, 441, 945, 440, 944, 386, 890, 305, 809)(229, 733, 310, 814, 389, 893, 442, 946, 444, 948, 390, 894, 311, 815)(243, 747, 327, 831, 405, 909, 448, 952, 443, 947, 391, 895, 328, 832)(246, 750, 332, 836, 392, 896, 355, 859, 351, 855, 407, 911, 331, 835)(252, 756, 341, 845, 280, 784, 369, 873, 427, 931, 411, 915, 338, 842)(253, 757, 342, 846, 412, 916, 428, 932, 371, 875, 283, 787, 343, 847)(263, 767, 353, 857, 420, 924, 457, 961, 456, 960, 418, 922, 350, 854)(265, 769, 354, 858, 387, 891, 433, 937, 375, 879, 408, 912, 339, 843)(268, 772, 356, 860, 402, 906, 334, 838, 360, 864, 421, 925, 357, 861)(274, 778, 364, 868, 396, 900, 318, 822, 397, 901, 422, 926, 359, 863)(296, 800, 377, 881, 435, 939, 463, 967, 465, 969, 436, 940, 378, 882)(303, 807, 347, 851, 415, 919, 453, 957, 466, 970, 438, 942, 383, 887)(315, 819, 393, 897, 445, 949, 470, 974, 464, 968, 437, 941, 394, 898)(346, 850, 410, 914, 450, 954, 474, 978, 476, 980, 452, 956, 414, 918)(362, 866, 423, 927, 458, 962, 479, 983, 481, 985, 459, 963, 424, 928)(374, 878, 432, 936, 385, 889, 439, 943, 467, 971, 462, 966, 430, 934)(406, 910, 447, 951, 451, 955, 475, 979, 489, 993, 473, 977, 449, 953)(417, 921, 454, 958, 477, 981, 491, 995, 480, 984, 460, 964, 455, 959)(446, 950, 469, 973, 472, 976, 488, 992, 497, 1001, 487, 991, 471, 975)(461, 965, 482, 986, 494, 998, 500, 1004, 492, 996, 478, 982, 483, 987)(468, 972, 484, 988, 486, 990, 496, 1000, 501, 1005, 495, 999, 485, 989)(490, 994, 493, 997, 499, 1003, 503, 1007, 504, 1008, 502, 1006, 498, 1002)(1009, 1513)(1010, 1514)(1011, 1515)(1012, 1516)(1013, 1517)(1014, 1518)(1015, 1519)(1016, 1520)(1017, 1521)(1018, 1522)(1019, 1523)(1020, 1524)(1021, 1525)(1022, 1526)(1023, 1527)(1024, 1528)(1025, 1529)(1026, 1530)(1027, 1531)(1028, 1532)(1029, 1533)(1030, 1534)(1031, 1535)(1032, 1536)(1033, 1537)(1034, 1538)(1035, 1539)(1036, 1540)(1037, 1541)(1038, 1542)(1039, 1543)(1040, 1544)(1041, 1545)(1042, 1546)(1043, 1547)(1044, 1548)(1045, 1549)(1046, 1550)(1047, 1551)(1048, 1552)(1049, 1553)(1050, 1554)(1051, 1555)(1052, 1556)(1053, 1557)(1054, 1558)(1055, 1559)(1056, 1560)(1057, 1561)(1058, 1562)(1059, 1563)(1060, 1564)(1061, 1565)(1062, 1566)(1063, 1567)(1064, 1568)(1065, 1569)(1066, 1570)(1067, 1571)(1068, 1572)(1069, 1573)(1070, 1574)(1071, 1575)(1072, 1576)(1073, 1577)(1074, 1578)(1075, 1579)(1076, 1580)(1077, 1581)(1078, 1582)(1079, 1583)(1080, 1584)(1081, 1585)(1082, 1586)(1083, 1587)(1084, 1588)(1085, 1589)(1086, 1590)(1087, 1591)(1088, 1592)(1089, 1593)(1090, 1594)(1091, 1595)(1092, 1596)(1093, 1597)(1094, 1598)(1095, 1599)(1096, 1600)(1097, 1601)(1098, 1602)(1099, 1603)(1100, 1604)(1101, 1605)(1102, 1606)(1103, 1607)(1104, 1608)(1105, 1609)(1106, 1610)(1107, 1611)(1108, 1612)(1109, 1613)(1110, 1614)(1111, 1615)(1112, 1616)(1113, 1617)(1114, 1618)(1115, 1619)(1116, 1620)(1117, 1621)(1118, 1622)(1119, 1623)(1120, 1624)(1121, 1625)(1122, 1626)(1123, 1627)(1124, 1628)(1125, 1629)(1126, 1630)(1127, 1631)(1128, 1632)(1129, 1633)(1130, 1634)(1131, 1635)(1132, 1636)(1133, 1637)(1134, 1638)(1135, 1639)(1136, 1640)(1137, 1641)(1138, 1642)(1139, 1643)(1140, 1644)(1141, 1645)(1142, 1646)(1143, 1647)(1144, 1648)(1145, 1649)(1146, 1650)(1147, 1651)(1148, 1652)(1149, 1653)(1150, 1654)(1151, 1655)(1152, 1656)(1153, 1657)(1154, 1658)(1155, 1659)(1156, 1660)(1157, 1661)(1158, 1662)(1159, 1663)(1160, 1664)(1161, 1665)(1162, 1666)(1163, 1667)(1164, 1668)(1165, 1669)(1166, 1670)(1167, 1671)(1168, 1672)(1169, 1673)(1170, 1674)(1171, 1675)(1172, 1676)(1173, 1677)(1174, 1678)(1175, 1679)(1176, 1680)(1177, 1681)(1178, 1682)(1179, 1683)(1180, 1684)(1181, 1685)(1182, 1686)(1183, 1687)(1184, 1688)(1185, 1689)(1186, 1690)(1187, 1691)(1188, 1692)(1189, 1693)(1190, 1694)(1191, 1695)(1192, 1696)(1193, 1697)(1194, 1698)(1195, 1699)(1196, 1700)(1197, 1701)(1198, 1702)(1199, 1703)(1200, 1704)(1201, 1705)(1202, 1706)(1203, 1707)(1204, 1708)(1205, 1709)(1206, 1710)(1207, 1711)(1208, 1712)(1209, 1713)(1210, 1714)(1211, 1715)(1212, 1716)(1213, 1717)(1214, 1718)(1215, 1719)(1216, 1720)(1217, 1721)(1218, 1722)(1219, 1723)(1220, 1724)(1221, 1725)(1222, 1726)(1223, 1727)(1224, 1728)(1225, 1729)(1226, 1730)(1227, 1731)(1228, 1732)(1229, 1733)(1230, 1734)(1231, 1735)(1232, 1736)(1233, 1737)(1234, 1738)(1235, 1739)(1236, 1740)(1237, 1741)(1238, 1742)(1239, 1743)(1240, 1744)(1241, 1745)(1242, 1746)(1243, 1747)(1244, 1748)(1245, 1749)(1246, 1750)(1247, 1751)(1248, 1752)(1249, 1753)(1250, 1754)(1251, 1755)(1252, 1756)(1253, 1757)(1254, 1758)(1255, 1759)(1256, 1760)(1257, 1761)(1258, 1762)(1259, 1763)(1260, 1764)(1261, 1765)(1262, 1766)(1263, 1767)(1264, 1768)(1265, 1769)(1266, 1770)(1267, 1771)(1268, 1772)(1269, 1773)(1270, 1774)(1271, 1775)(1272, 1776)(1273, 1777)(1274, 1778)(1275, 1779)(1276, 1780)(1277, 1781)(1278, 1782)(1279, 1783)(1280, 1784)(1281, 1785)(1282, 1786)(1283, 1787)(1284, 1788)(1285, 1789)(1286, 1790)(1287, 1791)(1288, 1792)(1289, 1793)(1290, 1794)(1291, 1795)(1292, 1796)(1293, 1797)(1294, 1798)(1295, 1799)(1296, 1800)(1297, 1801)(1298, 1802)(1299, 1803)(1300, 1804)(1301, 1805)(1302, 1806)(1303, 1807)(1304, 1808)(1305, 1809)(1306, 1810)(1307, 1811)(1308, 1812)(1309, 1813)(1310, 1814)(1311, 1815)(1312, 1816)(1313, 1817)(1314, 1818)(1315, 1819)(1316, 1820)(1317, 1821)(1318, 1822)(1319, 1823)(1320, 1824)(1321, 1825)(1322, 1826)(1323, 1827)(1324, 1828)(1325, 1829)(1326, 1830)(1327, 1831)(1328, 1832)(1329, 1833)(1330, 1834)(1331, 1835)(1332, 1836)(1333, 1837)(1334, 1838)(1335, 1839)(1336, 1840)(1337, 1841)(1338, 1842)(1339, 1843)(1340, 1844)(1341, 1845)(1342, 1846)(1343, 1847)(1344, 1848)(1345, 1849)(1346, 1850)(1347, 1851)(1348, 1852)(1349, 1853)(1350, 1854)(1351, 1855)(1352, 1856)(1353, 1857)(1354, 1858)(1355, 1859)(1356, 1860)(1357, 1861)(1358, 1862)(1359, 1863)(1360, 1864)(1361, 1865)(1362, 1866)(1363, 1867)(1364, 1868)(1365, 1869)(1366, 1870)(1367, 1871)(1368, 1872)(1369, 1873)(1370, 1874)(1371, 1875)(1372, 1876)(1373, 1877)(1374, 1878)(1375, 1879)(1376, 1880)(1377, 1881)(1378, 1882)(1379, 1883)(1380, 1884)(1381, 1885)(1382, 1886)(1383, 1887)(1384, 1888)(1385, 1889)(1386, 1890)(1387, 1891)(1388, 1892)(1389, 1893)(1390, 1894)(1391, 1895)(1392, 1896)(1393, 1897)(1394, 1898)(1395, 1899)(1396, 1900)(1397, 1901)(1398, 1902)(1399, 1903)(1400, 1904)(1401, 1905)(1402, 1906)(1403, 1907)(1404, 1908)(1405, 1909)(1406, 1910)(1407, 1911)(1408, 1912)(1409, 1913)(1410, 1914)(1411, 1915)(1412, 1916)(1413, 1917)(1414, 1918)(1415, 1919)(1416, 1920)(1417, 1921)(1418, 1922)(1419, 1923)(1420, 1924)(1421, 1925)(1422, 1926)(1423, 1927)(1424, 1928)(1425, 1929)(1426, 1930)(1427, 1931)(1428, 1932)(1429, 1933)(1430, 1934)(1431, 1935)(1432, 1936)(1433, 1937)(1434, 1938)(1435, 1939)(1436, 1940)(1437, 1941)(1438, 1942)(1439, 1943)(1440, 1944)(1441, 1945)(1442, 1946)(1443, 1947)(1444, 1948)(1445, 1949)(1446, 1950)(1447, 1951)(1448, 1952)(1449, 1953)(1450, 1954)(1451, 1955)(1452, 1956)(1453, 1957)(1454, 1958)(1455, 1959)(1456, 1960)(1457, 1961)(1458, 1962)(1459, 1963)(1460, 1964)(1461, 1965)(1462, 1966)(1463, 1967)(1464, 1968)(1465, 1969)(1466, 1970)(1467, 1971)(1468, 1972)(1469, 1973)(1470, 1974)(1471, 1975)(1472, 1976)(1473, 1977)(1474, 1978)(1475, 1979)(1476, 1980)(1477, 1981)(1478, 1982)(1479, 1983)(1480, 1984)(1481, 1985)(1482, 1986)(1483, 1987)(1484, 1988)(1485, 1989)(1486, 1990)(1487, 1991)(1488, 1992)(1489, 1993)(1490, 1994)(1491, 1995)(1492, 1996)(1493, 1997)(1494, 1998)(1495, 1999)(1496, 2000)(1497, 2001)(1498, 2002)(1499, 2003)(1500, 2004)(1501, 2005)(1502, 2006)(1503, 2007)(1504, 2008)(1505, 2009)(1506, 2010)(1507, 2011)(1508, 2012)(1509, 2013)(1510, 2014)(1511, 2015)(1512, 2016) L = (1, 1011)(2, 1014)(3, 1009)(4, 1017)(5, 1020)(6, 1010)(7, 1024)(8, 1021)(9, 1012)(10, 1027)(11, 1029)(12, 1013)(13, 1016)(14, 1030)(15, 1035)(16, 1015)(17, 1037)(18, 1040)(19, 1018)(20, 1042)(21, 1019)(22, 1022)(23, 1043)(24, 1048)(25, 1049)(26, 1051)(27, 1023)(28, 1052)(29, 1025)(30, 1056)(31, 1058)(32, 1026)(33, 1061)(34, 1028)(35, 1031)(36, 1062)(37, 1066)(38, 1067)(39, 1069)(40, 1032)(41, 1033)(42, 1072)(43, 1034)(44, 1036)(45, 1073)(46, 1077)(47, 1079)(48, 1038)(49, 1081)(50, 1039)(51, 1082)(52, 1086)(53, 1041)(54, 1044)(55, 1090)(56, 1091)(57, 1093)(58, 1045)(59, 1046)(60, 1096)(61, 1047)(62, 1097)(63, 1101)(64, 1050)(65, 1053)(66, 1080)(67, 1106)(68, 1107)(69, 1054)(70, 1111)(71, 1055)(72, 1074)(73, 1057)(74, 1059)(75, 1114)(76, 1118)(77, 1119)(78, 1060)(79, 1120)(80, 1124)(81, 1125)(82, 1063)(83, 1064)(84, 1128)(85, 1065)(86, 1129)(87, 1133)(88, 1068)(89, 1070)(90, 1102)(91, 1137)(92, 1139)(93, 1071)(94, 1098)(95, 1143)(96, 1144)(97, 1146)(98, 1075)(99, 1076)(100, 1149)(101, 1115)(102, 1151)(103, 1078)(104, 1152)(105, 1156)(106, 1083)(107, 1109)(108, 1160)(109, 1161)(110, 1084)(111, 1085)(112, 1087)(113, 1164)(114, 1168)(115, 1169)(116, 1088)(117, 1089)(118, 1171)(119, 1175)(120, 1092)(121, 1094)(122, 1134)(123, 1179)(124, 1181)(125, 1095)(126, 1130)(127, 1185)(128, 1186)(129, 1099)(130, 1189)(131, 1100)(132, 1190)(133, 1194)(134, 1195)(135, 1103)(136, 1104)(137, 1198)(138, 1105)(139, 1199)(140, 1203)(141, 1108)(142, 1206)(143, 1110)(144, 1112)(145, 1207)(146, 1211)(147, 1212)(148, 1113)(149, 1215)(150, 1216)(151, 1218)(152, 1116)(153, 1117)(154, 1221)(155, 1165)(156, 1121)(157, 1163)(158, 1226)(159, 1227)(160, 1122)(161, 1123)(162, 1230)(163, 1126)(164, 1176)(165, 1235)(166, 1237)(167, 1127)(168, 1172)(169, 1241)(170, 1242)(171, 1131)(172, 1245)(173, 1132)(174, 1246)(175, 1250)(176, 1251)(177, 1135)(178, 1136)(179, 1254)(180, 1208)(181, 1138)(182, 1140)(183, 1256)(184, 1260)(185, 1261)(186, 1141)(187, 1142)(188, 1263)(189, 1267)(190, 1145)(191, 1147)(192, 1204)(193, 1271)(194, 1273)(195, 1148)(196, 1200)(197, 1276)(198, 1150)(199, 1153)(200, 1188)(201, 1281)(202, 1282)(203, 1154)(204, 1155)(205, 1285)(206, 1288)(207, 1157)(208, 1158)(209, 1291)(210, 1159)(211, 1292)(212, 1296)(213, 1162)(214, 1299)(215, 1301)(216, 1302)(217, 1304)(218, 1166)(219, 1167)(220, 1307)(221, 1231)(222, 1170)(223, 1229)(224, 1311)(225, 1313)(226, 1314)(227, 1173)(228, 1317)(229, 1174)(230, 1318)(231, 1322)(232, 1323)(233, 1177)(234, 1178)(235, 1326)(236, 1257)(237, 1180)(238, 1182)(239, 1328)(240, 1332)(241, 1333)(242, 1183)(243, 1184)(244, 1335)(245, 1339)(246, 1187)(247, 1342)(248, 1191)(249, 1244)(250, 1346)(251, 1347)(252, 1192)(253, 1193)(254, 1350)(255, 1196)(256, 1268)(257, 1354)(258, 1355)(259, 1197)(260, 1264)(261, 1358)(262, 1359)(263, 1201)(264, 1348)(265, 1202)(266, 1362)(267, 1363)(268, 1205)(269, 1364)(270, 1367)(271, 1368)(272, 1370)(273, 1209)(274, 1210)(275, 1373)(276, 1286)(277, 1213)(278, 1284)(279, 1319)(280, 1214)(281, 1377)(282, 1379)(283, 1217)(284, 1219)(285, 1297)(286, 1382)(287, 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1568)(561, 1569)(562, 1570)(563, 1571)(564, 1572)(565, 1573)(566, 1574)(567, 1575)(568, 1576)(569, 1577)(570, 1578)(571, 1579)(572, 1580)(573, 1581)(574, 1582)(575, 1583)(576, 1584)(577, 1585)(578, 1586)(579, 1587)(580, 1588)(581, 1589)(582, 1590)(583, 1591)(584, 1592)(585, 1593)(586, 1594)(587, 1595)(588, 1596)(589, 1597)(590, 1598)(591, 1599)(592, 1600)(593, 1601)(594, 1602)(595, 1603)(596, 1604)(597, 1605)(598, 1606)(599, 1607)(600, 1608)(601, 1609)(602, 1610)(603, 1611)(604, 1612)(605, 1613)(606, 1614)(607, 1615)(608, 1616)(609, 1617)(610, 1618)(611, 1619)(612, 1620)(613, 1621)(614, 1622)(615, 1623)(616, 1624)(617, 1625)(618, 1626)(619, 1627)(620, 1628)(621, 1629)(622, 1630)(623, 1631)(624, 1632)(625, 1633)(626, 1634)(627, 1635)(628, 1636)(629, 1637)(630, 1638)(631, 1639)(632, 1640)(633, 1641)(634, 1642)(635, 1643)(636, 1644)(637, 1645)(638, 1646)(639, 1647)(640, 1648)(641, 1649)(642, 1650)(643, 1651)(644, 1652)(645, 1653)(646, 1654)(647, 1655)(648, 1656)(649, 1657)(650, 1658)(651, 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1841)(834, 1842)(835, 1843)(836, 1844)(837, 1845)(838, 1846)(839, 1847)(840, 1848)(841, 1849)(842, 1850)(843, 1851)(844, 1852)(845, 1853)(846, 1854)(847, 1855)(848, 1856)(849, 1857)(850, 1858)(851, 1859)(852, 1860)(853, 1861)(854, 1862)(855, 1863)(856, 1864)(857, 1865)(858, 1866)(859, 1867)(860, 1868)(861, 1869)(862, 1870)(863, 1871)(864, 1872)(865, 1873)(866, 1874)(867, 1875)(868, 1876)(869, 1877)(870, 1878)(871, 1879)(872, 1880)(873, 1881)(874, 1882)(875, 1883)(876, 1884)(877, 1885)(878, 1886)(879, 1887)(880, 1888)(881, 1889)(882, 1890)(883, 1891)(884, 1892)(885, 1893)(886, 1894)(887, 1895)(888, 1896)(889, 1897)(890, 1898)(891, 1899)(892, 1900)(893, 1901)(894, 1902)(895, 1903)(896, 1904)(897, 1905)(898, 1906)(899, 1907)(900, 1908)(901, 1909)(902, 1910)(903, 1911)(904, 1912)(905, 1913)(906, 1914)(907, 1915)(908, 1916)(909, 1917)(910, 1918)(911, 1919)(912, 1920)(913, 1921)(914, 1922)(915, 1923)(916, 1924)(917, 1925)(918, 1926)(919, 1927)(920, 1928)(921, 1929)(922, 1930)(923, 1931)(924, 1932)(925, 1933)(926, 1934)(927, 1935)(928, 1936)(929, 1937)(930, 1938)(931, 1939)(932, 1940)(933, 1941)(934, 1942)(935, 1943)(936, 1944)(937, 1945)(938, 1946)(939, 1947)(940, 1948)(941, 1949)(942, 1950)(943, 1951)(944, 1952)(945, 1953)(946, 1954)(947, 1955)(948, 1956)(949, 1957)(950, 1958)(951, 1959)(952, 1960)(953, 1961)(954, 1962)(955, 1963)(956, 1964)(957, 1965)(958, 1966)(959, 1967)(960, 1968)(961, 1969)(962, 1970)(963, 1971)(964, 1972)(965, 1973)(966, 1974)(967, 1975)(968, 1976)(969, 1977)(970, 1978)(971, 1979)(972, 1980)(973, 1981)(974, 1982)(975, 1983)(976, 1984)(977, 1985)(978, 1986)(979, 1987)(980, 1988)(981, 1989)(982, 1990)(983, 1991)(984, 1992)(985, 1993)(986, 1994)(987, 1995)(988, 1996)(989, 1997)(990, 1998)(991, 1999)(992, 2000)(993, 2001)(994, 2002)(995, 2003)(996, 2004)(997, 2005)(998, 2006)(999, 2007)(1000, 2008)(1001, 2009)(1002, 2010)(1003, 2011)(1004, 2012)(1005, 2013)(1006, 2014)(1007, 2015)(1008, 2016) local type(s) :: { ( 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E7.545 Graph:: simple bipartite v = 576 e = 1008 f = 420 degree seq :: [ 2^504, 14^72 ] E7.549 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^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)^2 ] Map:: R = (1, 505, 2, 506)(3, 507, 7, 511)(4, 508, 9, 513)(5, 509, 11, 515)(6, 510, 13, 517)(8, 512, 16, 520)(10, 514, 19, 523)(12, 516, 22, 526)(14, 518, 25, 529)(15, 519, 27, 531)(17, 521, 30, 534)(18, 522, 31, 535)(20, 524, 34, 538)(21, 525, 35, 539)(23, 527, 38, 542)(24, 528, 39, 543)(26, 530, 42, 546)(28, 532, 44, 548)(29, 533, 46, 550)(32, 536, 50, 554)(33, 537, 52, 556)(36, 540, 56, 560)(37, 541, 57, 561)(40, 544, 61, 565)(41, 545, 62, 566)(43, 547, 65, 569)(45, 549, 68, 572)(47, 551, 70, 574)(48, 552, 54, 558)(49, 553, 73, 577)(51, 555, 76, 580)(53, 557, 78, 582)(55, 559, 81, 585)(58, 562, 85, 589)(59, 563, 64, 568)(60, 564, 88, 592)(63, 567, 92, 596)(66, 570, 96, 600)(67, 571, 97, 601)(69, 573, 100, 604)(71, 575, 103, 607)(72, 576, 104, 608)(74, 578, 107, 611)(75, 579, 108, 612)(77, 581, 111, 615)(79, 583, 114, 618)(80, 584, 115, 619)(82, 586, 118, 622)(83, 587, 110, 614)(84, 588, 120, 624)(86, 590, 123, 627)(87, 591, 124, 628)(89, 593, 127, 631)(90, 594, 99, 603)(91, 595, 129, 633)(93, 597, 132, 636)(94, 598, 133, 637)(95, 599, 135, 639)(98, 602, 139, 643)(101, 605, 143, 647)(102, 606, 144, 648)(105, 609, 148, 652)(106, 610, 149, 653)(109, 613, 153, 657)(112, 616, 157, 661)(113, 617, 158, 662)(116, 620, 162, 666)(117, 621, 163, 667)(119, 623, 166, 670)(121, 625, 169, 673)(122, 626, 170, 674)(125, 629, 174, 678)(126, 630, 175, 679)(128, 632, 178, 682)(130, 634, 181, 685)(131, 635, 182, 686)(134, 638, 186, 690)(136, 640, 188, 692)(137, 641, 146, 650)(138, 642, 190, 694)(140, 644, 193, 697)(141, 645, 194, 698)(142, 646, 196, 700)(145, 649, 200, 704)(147, 651, 203, 707)(150, 654, 207, 711)(151, 655, 160, 664)(152, 656, 209, 713)(154, 658, 212, 716)(155, 659, 213, 717)(156, 660, 215, 719)(159, 663, 219, 723)(161, 665, 222, 726)(164, 668, 226, 730)(165, 669, 172, 676)(167, 671, 229, 733)(168, 672, 230, 734)(171, 675, 234, 738)(173, 677, 237, 741)(176, 680, 241, 745)(177, 681, 184, 688)(179, 683, 244, 748)(180, 684, 245, 749)(183, 687, 249, 753)(185, 689, 252, 756)(187, 691, 255, 759)(189, 693, 258, 762)(191, 695, 261, 765)(192, 696, 262, 766)(195, 699, 266, 770)(197, 701, 268, 772)(198, 702, 205, 709)(199, 703, 270, 774)(201, 705, 273, 777)(202, 706, 274, 778)(204, 708, 277, 781)(206, 710, 280, 784)(208, 712, 283, 787)(210, 714, 286, 790)(211, 715, 287, 791)(214, 718, 291, 795)(216, 720, 293, 797)(217, 721, 224, 728)(218, 722, 295, 799)(220, 724, 298, 802)(221, 725, 299, 803)(223, 727, 302, 806)(225, 729, 304, 808)(227, 731, 307, 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1786)(779, 1787)(780, 1788)(781, 1789)(782, 1790)(783, 1791)(784, 1792)(785, 1793)(786, 1794)(787, 1795)(788, 1796)(789, 1797)(790, 1798)(791, 1799)(792, 1800)(793, 1801)(794, 1802)(795, 1803)(796, 1804)(797, 1805)(798, 1806)(799, 1807)(800, 1808)(801, 1809)(802, 1810)(803, 1811)(804, 1812)(805, 1813)(806, 1814)(807, 1815)(808, 1816)(809, 1817)(810, 1818)(811, 1819)(812, 1820)(813, 1821)(814, 1822)(815, 1823)(816, 1824)(817, 1825)(818, 1826)(819, 1827)(820, 1828)(821, 1829)(822, 1830)(823, 1831)(824, 1832)(825, 1833)(826, 1834)(827, 1835)(828, 1836)(829, 1837)(830, 1838)(831, 1839)(832, 1840)(833, 1841)(834, 1842)(835, 1843)(836, 1844)(837, 1845)(838, 1846)(839, 1847)(840, 1848)(841, 1849)(842, 1850)(843, 1851)(844, 1852)(845, 1853)(846, 1854)(847, 1855)(848, 1856)(849, 1857)(850, 1858)(851, 1859)(852, 1860)(853, 1861)(854, 1862)(855, 1863)(856, 1864)(857, 1865)(858, 1866)(859, 1867)(860, 1868)(861, 1869)(862, 1870)(863, 1871)(864, 1872)(865, 1873)(866, 1874)(867, 1875)(868, 1876)(869, 1877)(870, 1878)(871, 1879)(872, 1880)(873, 1881)(874, 1882)(875, 1883)(876, 1884)(877, 1885)(878, 1886)(879, 1887)(880, 1888)(881, 1889)(882, 1890)(883, 1891)(884, 1892)(885, 1893)(886, 1894)(887, 1895)(888, 1896)(889, 1897)(890, 1898)(891, 1899)(892, 1900)(893, 1901)(894, 1902)(895, 1903)(896, 1904)(897, 1905)(898, 1906)(899, 1907)(900, 1908)(901, 1909)(902, 1910)(903, 1911)(904, 1912)(905, 1913)(906, 1914)(907, 1915)(908, 1916)(909, 1917)(910, 1918)(911, 1919)(912, 1920)(913, 1921)(914, 1922)(915, 1923)(916, 1924)(917, 1925)(918, 1926)(919, 1927)(920, 1928)(921, 1929)(922, 1930)(923, 1931)(924, 1932)(925, 1933)(926, 1934)(927, 1935)(928, 1936)(929, 1937)(930, 1938)(931, 1939)(932, 1940)(933, 1941)(934, 1942)(935, 1943)(936, 1944)(937, 1945)(938, 1946)(939, 1947)(940, 1948)(941, 1949)(942, 1950)(943, 1951)(944, 1952)(945, 1953)(946, 1954)(947, 1955)(948, 1956)(949, 1957)(950, 1958)(951, 1959)(952, 1960)(953, 1961)(954, 1962)(955, 1963)(956, 1964)(957, 1965)(958, 1966)(959, 1967)(960, 1968)(961, 1969)(962, 1970)(963, 1971)(964, 1972)(965, 1973)(966, 1974)(967, 1975)(968, 1976)(969, 1977)(970, 1978)(971, 1979)(972, 1980)(973, 1981)(974, 1982)(975, 1983)(976, 1984)(977, 1985)(978, 1986)(979, 1987)(980, 1988)(981, 1989)(982, 1990)(983, 1991)(984, 1992)(985, 1993)(986, 1994)(987, 1995)(988, 1996)(989, 1997)(990, 1998)(991, 1999)(992, 2000)(993, 2001)(994, 2002)(995, 2003)(996, 2004)(997, 2005)(998, 2006)(999, 2007)(1000, 2008)(1001, 2009)(1002, 2010)(1003, 2011)(1004, 2012)(1005, 2013)(1006, 2014)(1007, 2015)(1008, 2016) local type(s) :: { ( 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E7.550 Graph:: bipartite v = 324 e = 1008 f = 672 degree seq :: [ 4^252, 14^72 ] E7.550 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^3, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^7, Y3^-5 * Y1 * Y3^-2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^-2 * Y1 * Y3^-1, Y3^3 * Y1^-1 * Y3^2 * Y1^-1 * Y3^-2 * Y1 * Y3^-3 * Y1 * Y3^-3 * Y1^-1 * Y3 * Y1^-1, Y3^2 * Y1^-1 * Y3^-2 * Y1 * Y3^3 * Y1^-1 * Y3^2 * Y1^-1 * Y3^-3 * Y1^-1 * Y3^2 * Y1^-1 ] Map:: polytopal R = (1, 505, 2, 506, 4, 508)(3, 507, 8, 512, 10, 514)(5, 509, 12, 516, 6, 510)(7, 511, 15, 519, 11, 515)(9, 513, 18, 522, 20, 524)(13, 517, 25, 529, 23, 527)(14, 518, 24, 528, 28, 532)(16, 520, 31, 535, 29, 533)(17, 521, 33, 537, 21, 525)(19, 523, 36, 540, 37, 541)(22, 526, 30, 534, 41, 545)(26, 530, 46, 550, 44, 548)(27, 531, 47, 551, 48, 552)(32, 536, 54, 558, 52, 556)(34, 538, 57, 561, 55, 559)(35, 539, 58, 562, 38, 542)(39, 543, 56, 560, 64, 568)(40, 544, 65, 569, 66, 570)(42, 546, 45, 549, 69, 573)(43, 547, 70, 574, 49, 553)(50, 554, 53, 557, 79, 583)(51, 555, 80, 584, 67, 571)(59, 563, 90, 594, 88, 592)(60, 564, 91, 595, 61, 565)(62, 566, 89, 593, 95, 599)(63, 567, 96, 600, 97, 601)(68, 572, 102, 606, 103, 607)(71, 575, 107, 611, 105, 609)(72, 576, 74, 578, 109, 613)(73, 577, 110, 614, 104, 608)(75, 579, 113, 617, 76, 580)(77, 581, 106, 610, 117, 621)(78, 582, 118, 622, 119, 623)(81, 585, 123, 627, 121, 625)(82, 586, 84, 588, 125, 629)(83, 587, 126, 630, 120, 624)(85, 589, 87, 591, 130, 634)(86, 590, 131, 635, 98, 602)(92, 596, 139, 643, 137, 641)(93, 597, 138, 642, 141, 645)(94, 598, 142, 646, 143, 647)(99, 603, 148, 652, 100, 604)(101, 605, 122, 626, 152, 656)(108, 612, 159, 663, 160, 664)(111, 615, 164, 668, 162, 666)(112, 616, 165, 669, 161, 665)(114, 618, 168, 672, 166, 670)(115, 619, 167, 671, 170, 674)(116, 620, 171, 675, 172, 676)(124, 628, 180, 684, 181, 685)(127, 631, 185, 689, 183, 687)(128, 632, 186, 690, 182, 686)(129, 633, 187, 691, 188, 692)(132, 636, 192, 696, 190, 694)(133, 637, 193, 697, 189, 693)(134, 638, 136, 640, 196, 700)(135, 639, 197, 701, 144, 648)(140, 644, 203, 707, 204, 708)(145, 649, 209, 713, 146, 650)(147, 651, 191, 695, 213, 717)(149, 653, 216, 720, 214, 718)(150, 654, 215, 719, 217, 721)(151, 655, 218, 722, 219, 723)(153, 657, 221, 725, 154, 658)(155, 659, 163, 667, 225, 729)(156, 660, 158, 662, 227, 731)(157, 661, 228, 732, 173, 677)(169, 673, 241, 745, 242, 746)(174, 678, 247, 751, 175, 679)(176, 680, 184, 688, 251, 755)(177, 681, 179, 683, 253, 757)(178, 682, 254, 758, 220, 724)(194, 698, 272, 776, 270, 774)(195, 699, 273, 777, 274, 778)(198, 702, 278, 782, 276, 780)(199, 703, 279, 783, 275, 779)(200, 704, 202, 706, 282, 786)(201, 705, 283, 787, 205, 709)(206, 710, 289, 793, 207, 711)(208, 712, 277, 781, 293, 797)(210, 714, 296, 800, 294, 798)(211, 715, 295, 799, 297, 801)(212, 716, 298, 802, 299, 803)(222, 726, 310, 814, 308, 812)(223, 727, 309, 813, 312, 816)(224, 728, 313, 817, 314, 818)(226, 730, 316, 820, 317, 821)(229, 733, 321, 825, 319, 823)(230, 734, 322, 826, 318, 822)(231, 735, 323, 827, 232, 736)(233, 737, 237, 741, 327, 831)(234, 738, 236, 740, 329, 833)(235, 739, 330, 834, 315, 819)(238, 742, 240, 744, 335, 839)(239, 743, 336, 840, 243, 747)(244, 748, 342, 846, 245, 749)(246, 750, 320, 824, 346, 850)(248, 752, 349, 853, 347, 851)(249, 753, 348, 852, 351, 855)(250, 754, 352, 856, 353, 857)(252, 756, 355, 859, 356, 860)(255, 759, 360, 864, 358, 862)(256, 760, 361, 865, 357, 861)(257, 761, 362, 866, 258, 762)(259, 763, 263, 767, 366, 870)(260, 764, 262, 766, 368, 872)(261, 765, 369, 873, 354, 858)(264, 768, 373, 877, 265, 769)(266, 770, 271, 775, 377, 881)(267, 771, 269, 773, 379, 883)(268, 772, 380, 884, 300, 804)(280, 784, 340, 844, 339, 843)(281, 785, 393, 897, 363, 867)(284, 788, 365, 869, 395, 899)(285, 789, 397, 901, 394, 898)(286, 790, 350, 854, 287, 791)(288, 792, 396, 900, 400, 904)(290, 794, 401, 905, 338, 842)(291, 795, 344, 848, 402, 906)(292, 796, 403, 907, 404, 908)(301, 805, 303, 807, 414, 918)(302, 806, 415, 919, 304, 808)(305, 809, 398, 902, 306, 810)(307, 811, 359, 863, 420, 924)(311, 815, 383, 887, 385, 889)(324, 828, 413, 917, 431, 935)(325, 829, 432, 936, 367, 871)(326, 830, 433, 937, 416, 920)(328, 832, 375, 879, 435, 939)(331, 835, 438, 942, 436, 940)(332, 836, 371, 875, 382, 886)(333, 837, 439, 943, 434, 938)(334, 838, 441, 945, 374, 878)(337, 841, 376, 880, 442, 946)(341, 845, 443, 947, 444, 948)(343, 847, 445, 949, 417, 921)(345, 849, 446, 950, 447, 951)(364, 868, 453, 957, 378, 882)(370, 874, 457, 961, 455, 959)(372, 876, 458, 962, 454, 958)(381, 885, 462, 966, 460, 964)(384, 888, 463, 967, 459, 963)(386, 890, 426, 930, 387, 891)(388, 892, 392, 896, 451, 955)(389, 893, 391, 895, 430, 934)(390, 894, 465, 969, 405, 909)(399, 903, 427, 931, 429, 933)(406, 910, 408, 912, 421, 925)(407, 911, 424, 928, 409, 913)(410, 914, 440, 944, 411, 915)(412, 916, 461, 965, 472, 976)(418, 922, 473, 977, 464, 968)(419, 923, 474, 978, 467, 971)(422, 926, 449, 953, 423, 927)(425, 929, 437, 941, 477, 981)(428, 932, 478, 982, 448, 952)(450, 954, 456, 960, 484, 988)(452, 956, 485, 989, 475, 979)(466, 970, 491, 995, 489, 993)(468, 972, 492, 996, 469, 973)(470, 974, 490, 994, 493, 997)(471, 975, 494, 998, 479, 983)(476, 980, 496, 1000, 486, 990)(480, 984, 498, 1002, 481, 985)(482, 986, 497, 1001, 499, 1003)(483, 987, 500, 1004, 487, 991)(488, 992, 501, 1005, 495, 999)(502, 1006, 504, 1008, 503, 1007)(1009, 1513)(1010, 1514)(1011, 1515)(1012, 1516)(1013, 1517)(1014, 1518)(1015, 1519)(1016, 1520)(1017, 1521)(1018, 1522)(1019, 1523)(1020, 1524)(1021, 1525)(1022, 1526)(1023, 1527)(1024, 1528)(1025, 1529)(1026, 1530)(1027, 1531)(1028, 1532)(1029, 1533)(1030, 1534)(1031, 1535)(1032, 1536)(1033, 1537)(1034, 1538)(1035, 1539)(1036, 1540)(1037, 1541)(1038, 1542)(1039, 1543)(1040, 1544)(1041, 1545)(1042, 1546)(1043, 1547)(1044, 1548)(1045, 1549)(1046, 1550)(1047, 1551)(1048, 1552)(1049, 1553)(1050, 1554)(1051, 1555)(1052, 1556)(1053, 1557)(1054, 1558)(1055, 1559)(1056, 1560)(1057, 1561)(1058, 1562)(1059, 1563)(1060, 1564)(1061, 1565)(1062, 1566)(1063, 1567)(1064, 1568)(1065, 1569)(1066, 1570)(1067, 1571)(1068, 1572)(1069, 1573)(1070, 1574)(1071, 1575)(1072, 1576)(1073, 1577)(1074, 1578)(1075, 1579)(1076, 1580)(1077, 1581)(1078, 1582)(1079, 1583)(1080, 1584)(1081, 1585)(1082, 1586)(1083, 1587)(1084, 1588)(1085, 1589)(1086, 1590)(1087, 1591)(1088, 1592)(1089, 1593)(1090, 1594)(1091, 1595)(1092, 1596)(1093, 1597)(1094, 1598)(1095, 1599)(1096, 1600)(1097, 1601)(1098, 1602)(1099, 1603)(1100, 1604)(1101, 1605)(1102, 1606)(1103, 1607)(1104, 1608)(1105, 1609)(1106, 1610)(1107, 1611)(1108, 1612)(1109, 1613)(1110, 1614)(1111, 1615)(1112, 1616)(1113, 1617)(1114, 1618)(1115, 1619)(1116, 1620)(1117, 1621)(1118, 1622)(1119, 1623)(1120, 1624)(1121, 1625)(1122, 1626)(1123, 1627)(1124, 1628)(1125, 1629)(1126, 1630)(1127, 1631)(1128, 1632)(1129, 1633)(1130, 1634)(1131, 1635)(1132, 1636)(1133, 1637)(1134, 1638)(1135, 1639)(1136, 1640)(1137, 1641)(1138, 1642)(1139, 1643)(1140, 1644)(1141, 1645)(1142, 1646)(1143, 1647)(1144, 1648)(1145, 1649)(1146, 1650)(1147, 1651)(1148, 1652)(1149, 1653)(1150, 1654)(1151, 1655)(1152, 1656)(1153, 1657)(1154, 1658)(1155, 1659)(1156, 1660)(1157, 1661)(1158, 1662)(1159, 1663)(1160, 1664)(1161, 1665)(1162, 1666)(1163, 1667)(1164, 1668)(1165, 1669)(1166, 1670)(1167, 1671)(1168, 1672)(1169, 1673)(1170, 1674)(1171, 1675)(1172, 1676)(1173, 1677)(1174, 1678)(1175, 1679)(1176, 1680)(1177, 1681)(1178, 1682)(1179, 1683)(1180, 1684)(1181, 1685)(1182, 1686)(1183, 1687)(1184, 1688)(1185, 1689)(1186, 1690)(1187, 1691)(1188, 1692)(1189, 1693)(1190, 1694)(1191, 1695)(1192, 1696)(1193, 1697)(1194, 1698)(1195, 1699)(1196, 1700)(1197, 1701)(1198, 1702)(1199, 1703)(1200, 1704)(1201, 1705)(1202, 1706)(1203, 1707)(1204, 1708)(1205, 1709)(1206, 1710)(1207, 1711)(1208, 1712)(1209, 1713)(1210, 1714)(1211, 1715)(1212, 1716)(1213, 1717)(1214, 1718)(1215, 1719)(1216, 1720)(1217, 1721)(1218, 1722)(1219, 1723)(1220, 1724)(1221, 1725)(1222, 1726)(1223, 1727)(1224, 1728)(1225, 1729)(1226, 1730)(1227, 1731)(1228, 1732)(1229, 1733)(1230, 1734)(1231, 1735)(1232, 1736)(1233, 1737)(1234, 1738)(1235, 1739)(1236, 1740)(1237, 1741)(1238, 1742)(1239, 1743)(1240, 1744)(1241, 1745)(1242, 1746)(1243, 1747)(1244, 1748)(1245, 1749)(1246, 1750)(1247, 1751)(1248, 1752)(1249, 1753)(1250, 1754)(1251, 1755)(1252, 1756)(1253, 1757)(1254, 1758)(1255, 1759)(1256, 1760)(1257, 1761)(1258, 1762)(1259, 1763)(1260, 1764)(1261, 1765)(1262, 1766)(1263, 1767)(1264, 1768)(1265, 1769)(1266, 1770)(1267, 1771)(1268, 1772)(1269, 1773)(1270, 1774)(1271, 1775)(1272, 1776)(1273, 1777)(1274, 1778)(1275, 1779)(1276, 1780)(1277, 1781)(1278, 1782)(1279, 1783)(1280, 1784)(1281, 1785)(1282, 1786)(1283, 1787)(1284, 1788)(1285, 1789)(1286, 1790)(1287, 1791)(1288, 1792)(1289, 1793)(1290, 1794)(1291, 1795)(1292, 1796)(1293, 1797)(1294, 1798)(1295, 1799)(1296, 1800)(1297, 1801)(1298, 1802)(1299, 1803)(1300, 1804)(1301, 1805)(1302, 1806)(1303, 1807)(1304, 1808)(1305, 1809)(1306, 1810)(1307, 1811)(1308, 1812)(1309, 1813)(1310, 1814)(1311, 1815)(1312, 1816)(1313, 1817)(1314, 1818)(1315, 1819)(1316, 1820)(1317, 1821)(1318, 1822)(1319, 1823)(1320, 1824)(1321, 1825)(1322, 1826)(1323, 1827)(1324, 1828)(1325, 1829)(1326, 1830)(1327, 1831)(1328, 1832)(1329, 1833)(1330, 1834)(1331, 1835)(1332, 1836)(1333, 1837)(1334, 1838)(1335, 1839)(1336, 1840)(1337, 1841)(1338, 1842)(1339, 1843)(1340, 1844)(1341, 1845)(1342, 1846)(1343, 1847)(1344, 1848)(1345, 1849)(1346, 1850)(1347, 1851)(1348, 1852)(1349, 1853)(1350, 1854)(1351, 1855)(1352, 1856)(1353, 1857)(1354, 1858)(1355, 1859)(1356, 1860)(1357, 1861)(1358, 1862)(1359, 1863)(1360, 1864)(1361, 1865)(1362, 1866)(1363, 1867)(1364, 1868)(1365, 1869)(1366, 1870)(1367, 1871)(1368, 1872)(1369, 1873)(1370, 1874)(1371, 1875)(1372, 1876)(1373, 1877)(1374, 1878)(1375, 1879)(1376, 1880)(1377, 1881)(1378, 1882)(1379, 1883)(1380, 1884)(1381, 1885)(1382, 1886)(1383, 1887)(1384, 1888)(1385, 1889)(1386, 1890)(1387, 1891)(1388, 1892)(1389, 1893)(1390, 1894)(1391, 1895)(1392, 1896)(1393, 1897)(1394, 1898)(1395, 1899)(1396, 1900)(1397, 1901)(1398, 1902)(1399, 1903)(1400, 1904)(1401, 1905)(1402, 1906)(1403, 1907)(1404, 1908)(1405, 1909)(1406, 1910)(1407, 1911)(1408, 1912)(1409, 1913)(1410, 1914)(1411, 1915)(1412, 1916)(1413, 1917)(1414, 1918)(1415, 1919)(1416, 1920)(1417, 1921)(1418, 1922)(1419, 1923)(1420, 1924)(1421, 1925)(1422, 1926)(1423, 1927)(1424, 1928)(1425, 1929)(1426, 1930)(1427, 1931)(1428, 1932)(1429, 1933)(1430, 1934)(1431, 1935)(1432, 1936)(1433, 1937)(1434, 1938)(1435, 1939)(1436, 1940)(1437, 1941)(1438, 1942)(1439, 1943)(1440, 1944)(1441, 1945)(1442, 1946)(1443, 1947)(1444, 1948)(1445, 1949)(1446, 1950)(1447, 1951)(1448, 1952)(1449, 1953)(1450, 1954)(1451, 1955)(1452, 1956)(1453, 1957)(1454, 1958)(1455, 1959)(1456, 1960)(1457, 1961)(1458, 1962)(1459, 1963)(1460, 1964)(1461, 1965)(1462, 1966)(1463, 1967)(1464, 1968)(1465, 1969)(1466, 1970)(1467, 1971)(1468, 1972)(1469, 1973)(1470, 1974)(1471, 1975)(1472, 1976)(1473, 1977)(1474, 1978)(1475, 1979)(1476, 1980)(1477, 1981)(1478, 1982)(1479, 1983)(1480, 1984)(1481, 1985)(1482, 1986)(1483, 1987)(1484, 1988)(1485, 1989)(1486, 1990)(1487, 1991)(1488, 1992)(1489, 1993)(1490, 1994)(1491, 1995)(1492, 1996)(1493, 1997)(1494, 1998)(1495, 1999)(1496, 2000)(1497, 2001)(1498, 2002)(1499, 2003)(1500, 2004)(1501, 2005)(1502, 2006)(1503, 2007)(1504, 2008)(1505, 2009)(1506, 2010)(1507, 2011)(1508, 2012)(1509, 2013)(1510, 2014)(1511, 2015)(1512, 2016) L = (1, 1011)(2, 1014)(3, 1017)(4, 1019)(5, 1009)(6, 1022)(7, 1010)(8, 1012)(9, 1027)(10, 1029)(11, 1030)(12, 1031)(13, 1013)(14, 1035)(15, 1037)(16, 1015)(17, 1016)(18, 1018)(19, 1034)(20, 1046)(21, 1047)(22, 1048)(23, 1050)(24, 1020)(25, 1052)(26, 1021)(27, 1040)(28, 1057)(29, 1058)(30, 1023)(31, 1060)(32, 1024)(33, 1063)(34, 1025)(35, 1026)(36, 1028)(37, 1069)(38, 1070)(39, 1071)(40, 1042)(41, 1075)(42, 1076)(43, 1032)(44, 1080)(45, 1033)(46, 1045)(47, 1036)(48, 1084)(49, 1085)(50, 1086)(51, 1038)(52, 1090)(53, 1039)(54, 1056)(55, 1093)(56, 1041)(57, 1074)(58, 1096)(59, 1043)(60, 1044)(61, 1101)(62, 1102)(63, 1067)(64, 1106)(65, 1049)(66, 1108)(67, 1109)(68, 1079)(69, 1112)(70, 1113)(71, 1051)(72, 1116)(73, 1053)(74, 1054)(75, 1055)(76, 1123)(77, 1124)(78, 1089)(79, 1128)(80, 1129)(81, 1059)(82, 1132)(83, 1061)(84, 1062)(85, 1137)(86, 1064)(87, 1065)(88, 1142)(89, 1066)(90, 1105)(91, 1145)(92, 1068)(93, 1148)(94, 1100)(95, 1152)(96, 1072)(97, 1154)(98, 1155)(99, 1073)(100, 1158)(101, 1159)(102, 1077)(103, 1162)(104, 1163)(105, 1164)(106, 1078)(107, 1111)(108, 1119)(109, 1169)(110, 1170)(111, 1081)(112, 1082)(113, 1174)(114, 1083)(115, 1177)(116, 1122)(117, 1181)(118, 1087)(119, 1183)(120, 1184)(121, 1185)(122, 1088)(123, 1127)(124, 1135)(125, 1190)(126, 1191)(127, 1091)(128, 1092)(129, 1140)(130, 1197)(131, 1198)(132, 1094)(133, 1095)(134, 1203)(135, 1097)(136, 1098)(137, 1208)(138, 1099)(139, 1151)(140, 1120)(141, 1213)(142, 1103)(143, 1215)(144, 1216)(145, 1104)(146, 1219)(147, 1220)(148, 1222)(149, 1107)(150, 1202)(151, 1157)(152, 1228)(153, 1110)(154, 1231)(155, 1232)(156, 1234)(157, 1114)(158, 1115)(159, 1117)(160, 1240)(161, 1241)(162, 1242)(163, 1118)(164, 1168)(165, 1212)(166, 1246)(167, 1121)(168, 1180)(169, 1136)(170, 1251)(171, 1125)(172, 1253)(173, 1254)(174, 1126)(175, 1257)(176, 1258)(177, 1260)(178, 1130)(179, 1131)(180, 1133)(181, 1266)(182, 1267)(183, 1268)(184, 1134)(185, 1189)(186, 1250)(187, 1138)(188, 1273)(189, 1274)(190, 1275)(191, 1139)(192, 1196)(193, 1278)(194, 1141)(195, 1206)(196, 1283)(197, 1284)(198, 1143)(199, 1144)(200, 1289)(201, 1146)(202, 1147)(203, 1149)(204, 1295)(205, 1296)(206, 1150)(207, 1299)(208, 1300)(209, 1302)(210, 1153)(211, 1288)(212, 1218)(213, 1308)(214, 1309)(215, 1156)(216, 1227)(217, 1312)(218, 1160)(219, 1314)(220, 1315)(221, 1316)(222, 1161)(223, 1319)(224, 1230)(225, 1323)(226, 1237)(227, 1326)(228, 1327)(229, 1165)(230, 1166)(231, 1167)(232, 1333)(233, 1334)(234, 1336)(235, 1171)(236, 1172)(237, 1173)(238, 1342)(239, 1175)(240, 1176)(241, 1178)(242, 1348)(243, 1349)(244, 1179)(245, 1352)(246, 1353)(247, 1355)(248, 1182)(249, 1358)(250, 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1986)(979, 1987)(980, 1988)(981, 1989)(982, 1990)(983, 1991)(984, 1992)(985, 1993)(986, 1994)(987, 1995)(988, 1996)(989, 1997)(990, 1998)(991, 1999)(992, 2000)(993, 2001)(994, 2002)(995, 2003)(996, 2004)(997, 2005)(998, 2006)(999, 2007)(1000, 2008)(1001, 2009)(1002, 2010)(1003, 2011)(1004, 2012)(1005, 2013)(1006, 2014)(1007, 2015)(1008, 2016) local type(s) :: { ( 4, 14 ), ( 4, 14, 4, 14, 4, 14 ) } Outer automorphisms :: reflexible Dual of E7.549 Graph:: simple bipartite v = 672 e = 1008 f = 324 degree seq :: [ 2^504, 6^168 ] ## Checksum: 550 records. ## Written on: Tue Oct 15 13:51:45 CEST 2019