## Begin on: Sat Oct 19 21:25:50 CEST 2019 ENUMERATION No. of records: 1312 FAMILY (oriented family) : isomorphism classes 1 [ E1b] : 30 (26 non-degenerate) 2 [ E3b] : 154 (124 non-degenerate) 2* [E3*b] : 154 (124 non-degenerate) 2ex [E3*c] : 4 (4 non-degenerate) 2*ex [ E3c] : 4 (4 non-degenerate) 2P [ E2] : 30 (28 non-degenerate) 2Pex [ E1a] : 2 (2 non-degenerate) 3 [ E5a] : 738 (404 non-degenerate) 4 [ E4] : 60 (26 non-degenerate) 4* [ E4*] : 60 (26 non-degenerate) 4P [ E6] : 52 (30 non-degenerate) 5 [ E3a] : 12 (10 non-degenerate) 5* [E3*a] : 12 (10 non-degenerate) 5P [ E5b] : 0 E16.1 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {16, 16}) Quotient :: toric Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, S^2, S^-1 * A * S * B, S^-1 * B * S * A, S^-1 * Z * S * Z, Z^16, (Z^-1 * A * B^-1 * A^-1 * B)^16 ] Map:: R = (1, 18, 34, 50, 2, 20, 36, 52, 4, 22, 38, 54, 6, 24, 40, 56, 8, 26, 42, 58, 10, 28, 44, 60, 12, 30, 46, 62, 14, 32, 48, 64, 16, 31, 47, 63, 15, 29, 45, 61, 13, 27, 43, 59, 11, 25, 41, 57, 9, 23, 39, 55, 7, 21, 37, 53, 5, 19, 35, 51, 3, 17, 33, 49) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^64 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 32 f = 1 degree seq :: [ 64 ] E16.2 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {16, 16}) Quotient :: toric Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ S^2, A^2, B^-1 * A, A * Z * A * Z^-1, S * B * S * A, (S * Z)^2, A * Z^8 ] Map:: R = (1, 18, 34, 50, 2, 21, 37, 53, 5, 25, 41, 57, 9, 29, 45, 61, 13, 31, 47, 63, 15, 27, 43, 59, 11, 23, 39, 55, 7, 19, 35, 51, 3, 22, 38, 54, 6, 26, 42, 58, 10, 30, 46, 62, 14, 32, 48, 64, 16, 28, 44, 60, 12, 24, 40, 56, 8, 20, 36, 52, 4, 17, 33, 49) L = (1, 35)(2, 38)(3, 33)(4, 39)(5, 42)(6, 34)(7, 36)(8, 43)(9, 46)(10, 37)(11, 40)(12, 47)(13, 48)(14, 41)(15, 44)(16, 45)(17, 51)(18, 54)(19, 49)(20, 55)(21, 58)(22, 50)(23, 52)(24, 59)(25, 62)(26, 53)(27, 56)(28, 63)(29, 64)(30, 57)(31, 60)(32, 61) local type(s) :: { ( 64^64 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 32 f = 1 degree seq :: [ 64 ] E16.3 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {16, 16}) Quotient :: toric Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ S^2, A^-1 * B, A^-1 * B^-1 * A^-2, (S * Z)^2, Z^-1 * B * Z * A^-1, S * A * S * B, Z * B * Z^3, A^-1 * B^-1 * Z * A^-2 * Z^-1, Z * B^-2 * Z^2 * B^-1 * Z ] Map:: R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 28, 44, 60, 12, 21, 37, 53, 5, 24, 40, 56, 8, 29, 45, 61, 13, 31, 47, 63, 15, 25, 41, 57, 9, 30, 46, 62, 14, 32, 48, 64, 16, 26, 42, 58, 10, 19, 35, 51, 3, 23, 39, 55, 7, 27, 43, 59, 11, 20, 36, 52, 4, 17, 33, 49) L = (1, 35)(2, 39)(3, 41)(4, 42)(5, 33)(6, 43)(7, 46)(8, 34)(9, 37)(10, 47)(11, 48)(12, 36)(13, 38)(14, 40)(15, 44)(16, 45)(17, 53)(18, 56)(19, 49)(20, 60)(21, 57)(22, 61)(23, 50)(24, 62)(25, 51)(26, 52)(27, 54)(28, 63)(29, 64)(30, 55)(31, 58)(32, 59) local type(s) :: { ( 64^64 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 32 f = 1 degree seq :: [ 64 ] E16.4 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {16, 16}) Quotient :: toric Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, A^4, S * A * S * B, Z * B * Z^-1 * A^-1, Z^-1 * B * Z * A^-1, (S * Z)^2, Z * B^-1 * Z^3, A^-2 * Z * A^-2 * Z^-1 ] Map:: R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 26, 42, 58, 10, 19, 35, 51, 3, 23, 39, 55, 7, 29, 45, 61, 13, 31, 47, 63, 15, 25, 41, 57, 9, 30, 46, 62, 14, 32, 48, 64, 16, 28, 44, 60, 12, 21, 37, 53, 5, 24, 40, 56, 8, 27, 43, 59, 11, 20, 36, 52, 4, 17, 33, 49) L = (1, 35)(2, 39)(3, 41)(4, 42)(5, 33)(6, 45)(7, 46)(8, 34)(9, 37)(10, 47)(11, 38)(12, 36)(13, 48)(14, 40)(15, 44)(16, 43)(17, 53)(18, 56)(19, 49)(20, 60)(21, 57)(22, 59)(23, 50)(24, 62)(25, 51)(26, 52)(27, 64)(28, 63)(29, 54)(30, 55)(31, 58)(32, 61) local type(s) :: { ( 64^64 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 32 f = 1 degree seq :: [ 64 ] E16.5 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {16, 16}) Quotient :: toric Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, Z^2 * A, S * A * S * B, (S * Z)^2, A^8, (B * Z)^16 ] Map:: R = (1, 18, 34, 50, 2, 21, 37, 53, 5, 22, 38, 54, 6, 25, 41, 57, 9, 26, 42, 58, 10, 29, 45, 61, 13, 30, 46, 62, 14, 31, 47, 63, 15, 32, 48, 64, 16, 27, 43, 59, 11, 28, 44, 60, 12, 23, 39, 55, 7, 24, 40, 56, 8, 19, 35, 51, 3, 20, 36, 52, 4, 17, 33, 49) 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, 53)(18, 54)(19, 49)(20, 50)(21, 57)(22, 58)(23, 51)(24, 52)(25, 61)(26, 62)(27, 55)(28, 56)(29, 63)(30, 64)(31, 59)(32, 60) local type(s) :: { ( 64^64 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 32 f = 1 degree seq :: [ 64 ] E16.6 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {16, 16}) Quotient :: toric Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ S^2, B * A^-1, Z^2 * A^-1, S * B * S * A, (S * Z)^2, A^8, (B^-1 * Z)^16 ] Map:: R = (1, 18, 34, 50, 2, 19, 35, 51, 3, 22, 38, 54, 6, 23, 39, 55, 7, 26, 42, 58, 10, 27, 43, 59, 11, 30, 46, 62, 14, 31, 47, 63, 15, 32, 48, 64, 16, 29, 45, 61, 13, 28, 44, 60, 12, 25, 41, 57, 9, 24, 40, 56, 8, 21, 37, 53, 5, 20, 36, 52, 4, 17, 33, 49) 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, 53)(18, 52)(19, 49)(20, 56)(21, 57)(22, 50)(23, 51)(24, 60)(25, 61)(26, 54)(27, 55)(28, 64)(29, 63)(30, 58)(31, 59)(32, 62) local type(s) :: { ( 64^64 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 32 f = 1 degree seq :: [ 64 ] E16.7 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {16, 16}) Quotient :: toric Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ S^2, A * B^-1, (Z^-1, B^-1), Z^-1 * B * Z * A^-1, (S * Z)^2, S * B * S * A, Z * B * Z * A^2, B^-1 * Z^4 * B^-1 ] Map:: R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 30, 46, 62, 14, 25, 41, 57, 9, 28, 44, 60, 12, 21, 37, 53, 5, 24, 40, 56, 8, 31, 47, 63, 15, 26, 42, 58, 10, 19, 35, 51, 3, 23, 39, 55, 7, 29, 45, 61, 13, 32, 48, 64, 16, 27, 43, 59, 11, 20, 36, 52, 4, 17, 33, 49) 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, 53)(18, 56)(19, 49)(20, 60)(21, 61)(22, 63)(23, 50)(24, 64)(25, 51)(26, 52)(27, 57)(28, 55)(29, 54)(30, 58)(31, 59)(32, 62) local type(s) :: { ( 64^64 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 32 f = 1 degree seq :: [ 64 ] E16.8 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {16, 16}) Quotient :: toric Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ S^2, A^-1 * B, (S * Z)^2, (A, Z), S * A * S * B, A^-1 * Z * B^-1 * A^-1 * Z, A^-2 * Z^-4, A^8 ] Map:: R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 30, 46, 62, 14, 29, 45, 61, 13, 26, 42, 58, 10, 19, 35, 51, 3, 23, 39, 55, 7, 31, 47, 63, 15, 28, 44, 60, 12, 21, 37, 53, 5, 24, 40, 56, 8, 25, 41, 57, 9, 32, 48, 64, 16, 27, 43, 59, 11, 20, 36, 52, 4, 17, 33, 49) 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, 53)(18, 56)(19, 49)(20, 60)(21, 61)(22, 57)(23, 50)(24, 58)(25, 51)(26, 52)(27, 63)(28, 62)(29, 59)(30, 64)(31, 54)(32, 55) local type(s) :: { ( 64^64 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 32 f = 1 degree seq :: [ 64 ] E16.9 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {6, 6}) Quotient :: toric Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ S^2, B * A^-1, B^-1 * A, (Z, B), (S * Z)^2, S * B * S * A, (Z, A^-1), Z^-2 * A^-3, Z^6 ] Map:: R = (1, 20, 38, 56, 2, 24, 42, 60, 6, 32, 50, 68, 14, 29, 47, 65, 11, 22, 40, 58, 4, 19, 37, 55)(3, 25, 43, 61, 7, 31, 49, 67, 13, 34, 52, 70, 16, 36, 54, 72, 18, 28, 46, 64, 10, 21, 39, 57)(5, 26, 44, 62, 8, 33, 51, 69, 15, 35, 53, 71, 17, 27, 45, 63, 9, 30, 48, 66, 12, 23, 41, 59) L = (1, 39)(2, 43)(3, 45)(4, 46)(5, 37)(6, 49)(7, 48)(8, 38)(9, 47)(10, 53)(11, 54)(12, 40)(13, 41)(14, 52)(15, 42)(16, 44)(17, 50)(18, 51)(19, 59)(20, 62)(21, 55)(22, 66)(23, 67)(24, 69)(25, 56)(26, 70)(27, 57)(28, 58)(29, 63)(30, 61)(31, 60)(32, 71)(33, 72)(34, 68)(35, 64)(36, 65) local type(s) :: { ( 24^24 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.10 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {6, 6}) Quotient :: toric Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, B^-1 * A, (S * Z)^2, (Z, A^-1), S * B * S * A, A^-1 * Z * B^-1 * A^-1 * Z, Z^6 ] Map:: R = (1, 20, 38, 56, 2, 24, 42, 60, 6, 32, 50, 68, 14, 29, 47, 65, 11, 22, 40, 58, 4, 19, 37, 55)(3, 25, 43, 61, 7, 33, 51, 69, 15, 36, 54, 72, 18, 31, 49, 67, 13, 28, 46, 64, 10, 21, 39, 57)(5, 26, 44, 62, 8, 27, 45, 63, 9, 34, 52, 70, 16, 35, 53, 71, 17, 30, 48, 66, 12, 23, 41, 59) L = (1, 39)(2, 43)(3, 45)(4, 46)(5, 37)(6, 51)(7, 52)(8, 38)(9, 42)(10, 44)(11, 49)(12, 40)(13, 41)(14, 54)(15, 53)(16, 50)(17, 47)(18, 48)(19, 59)(20, 62)(21, 55)(22, 66)(23, 67)(24, 63)(25, 56)(26, 64)(27, 57)(28, 58)(29, 71)(30, 72)(31, 65)(32, 70)(33, 60)(34, 61)(35, 69)(36, 68) local type(s) :: { ( 24^24 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.11 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {6, 6}) Quotient :: toric Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ S^2, A^2, B^-1 * A, (S * Z)^2, S * B * S * A, (A * Z^-1)^3, A * Z^2 * A * Z^-2, Z^6 ] Map:: R = (1, 20, 38, 56, 2, 23, 41, 59, 5, 29, 47, 65, 11, 28, 46, 64, 10, 22, 40, 58, 4, 19, 37, 55)(3, 25, 43, 61, 7, 30, 48, 66, 12, 36, 54, 72, 18, 34, 52, 70, 16, 26, 44, 62, 8, 21, 39, 57)(6, 31, 49, 67, 13, 35, 53, 71, 17, 33, 51, 69, 15, 27, 45, 63, 9, 32, 50, 68, 14, 24, 42, 60) L = (1, 39)(2, 42)(3, 37)(4, 45)(5, 48)(6, 38)(7, 51)(8, 49)(9, 40)(10, 52)(11, 53)(12, 41)(13, 44)(14, 54)(15, 43)(16, 46)(17, 47)(18, 50)(19, 57)(20, 60)(21, 55)(22, 63)(23, 66)(24, 56)(25, 69)(26, 67)(27, 58)(28, 70)(29, 71)(30, 59)(31, 62)(32, 72)(33, 61)(34, 64)(35, 65)(36, 68) local type(s) :: { ( 24^24 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.12 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {6, 6}) Quotient :: toric Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ S^2, A^-1 * B^-1, A * B^-2, (S * Z)^2, Z^-1 * A^-1 * Z * A^-1, S * B * S * A, Z^-1 * B * Z * B, Z^6 ] Map:: non-degenerate R = (1, 20, 38, 56, 2, 24, 42, 60, 6, 30, 48, 66, 12, 29, 47, 65, 11, 23, 41, 59, 5, 19, 37, 55)(3, 26, 44, 62, 8, 31, 49, 67, 13, 36, 54, 72, 18, 33, 51, 69, 15, 27, 45, 63, 9, 21, 39, 57)(4, 25, 43, 61, 7, 32, 50, 68, 14, 35, 53, 71, 17, 34, 52, 70, 16, 28, 46, 64, 10, 22, 40, 58) L = (1, 39)(2, 43)(3, 40)(4, 37)(5, 46)(6, 49)(7, 44)(8, 38)(9, 41)(10, 45)(11, 51)(12, 53)(13, 50)(14, 42)(15, 52)(16, 47)(17, 54)(18, 48)(19, 57)(20, 61)(21, 58)(22, 55)(23, 64)(24, 67)(25, 62)(26, 56)(27, 59)(28, 63)(29, 69)(30, 71)(31, 68)(32, 60)(33, 70)(34, 65)(35, 72)(36, 66) local type(s) :: { ( 24^24 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.13 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {6, 6}) Quotient :: toric Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ S^2, B^3, A^3, Z^-1 * B * A * Z^-1, (Z * B^-1)^2, (Z * A^-1)^2, B * Z * A^-1 * Z^-1, (A^-1, B), (S * Z)^2, S * A * S * B, Z * B * Z^-1 * A^-1, B * Z * B^-1 * A * Z, B * Z^2 * B * A^-1 ] Map:: non-degenerate R = (1, 20, 38, 56, 2, 26, 44, 62, 8, 36, 54, 72, 18, 33, 51, 69, 15, 23, 41, 59, 5, 19, 37, 55)(3, 28, 46, 64, 10, 32, 50, 68, 14, 34, 52, 70, 16, 25, 43, 61, 7, 29, 47, 65, 11, 21, 39, 57)(4, 27, 45, 63, 9, 31, 49, 67, 13, 35, 53, 71, 17, 24, 42, 60, 6, 30, 48, 66, 12, 22, 40, 58) L = (1, 39)(2, 45)(3, 42)(4, 44)(5, 48)(6, 37)(7, 49)(8, 50)(9, 47)(10, 54)(11, 38)(12, 52)(13, 51)(14, 40)(15, 43)(16, 41)(17, 46)(18, 53)(19, 61)(20, 66)(21, 67)(22, 55)(23, 71)(24, 69)(25, 58)(26, 57)(27, 70)(28, 56)(29, 59)(30, 64)(31, 62)(32, 60)(33, 68)(34, 72)(35, 65)(36, 63) local type(s) :: { ( 24^24 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.14 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {6, 6}) Quotient :: toric Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ S^2, B^3, A^3, (A, B^-1), Z^-1 * A^-1 * B^-1 * Z^-1, (Z^-1 * A^-1)^2, (B^-1 * Z^-1)^2, (S * Z)^2, Z^-1 * B^-1 * A^-1 * Z^-1, A^-1 * Z * B * Z^-1, S * A * S * B, Z * A * Z^-1 * B^-1 ] Map:: non-degenerate R = (1, 20, 38, 56, 2, 26, 44, 62, 8, 36, 54, 72, 18, 31, 49, 67, 13, 23, 41, 59, 5, 19, 37, 55)(3, 28, 46, 64, 10, 25, 43, 61, 7, 29, 47, 65, 11, 35, 53, 71, 17, 32, 50, 68, 14, 21, 39, 57)(4, 27, 45, 63, 9, 24, 42, 60, 6, 30, 48, 66, 12, 33, 51, 69, 15, 34, 52, 70, 16, 22, 40, 58) L = (1, 39)(2, 45)(3, 42)(4, 49)(5, 52)(6, 37)(7, 51)(8, 43)(9, 47)(10, 41)(11, 38)(12, 50)(13, 53)(14, 54)(15, 44)(16, 46)(17, 40)(18, 48)(19, 61)(20, 66)(21, 69)(22, 55)(23, 63)(24, 62)(25, 58)(26, 71)(27, 68)(28, 56)(29, 72)(30, 64)(31, 57)(32, 59)(33, 67)(34, 65)(35, 60)(36, 70) local type(s) :: { ( 24^24 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.15 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {6, 6}) Quotient :: toric Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ S^2, B * A^-1, B * A^-1, A * Z^-2 * A, (S * Z)^2, S * A * S * B, A^6, A * Z^-1 * A * Z * A^-1 * Z^-1, (A^-1 * Z^-1)^3 ] Map:: R = (1, 20, 38, 56, 2, 24, 42, 60, 6, 32, 50, 68, 14, 29, 47, 65, 11, 22, 40, 58, 4, 19, 37, 55)(3, 27, 45, 63, 9, 33, 51, 69, 15, 31, 49, 67, 13, 23, 41, 59, 5, 28, 46, 64, 10, 21, 39, 57)(7, 34, 52, 70, 16, 30, 48, 66, 12, 36, 54, 72, 18, 26, 44, 62, 8, 35, 53, 71, 17, 25, 43, 61) L = (1, 39)(2, 43)(3, 42)(4, 44)(5, 37)(6, 51)(7, 50)(8, 38)(9, 52)(10, 53)(11, 41)(12, 40)(13, 54)(14, 48)(15, 47)(16, 49)(17, 45)(18, 46)(19, 59)(20, 62)(21, 55)(22, 66)(23, 65)(24, 57)(25, 56)(26, 58)(27, 71)(28, 72)(29, 69)(30, 68)(31, 70)(32, 61)(33, 60)(34, 63)(35, 64)(36, 67) local type(s) :: { ( 24^24 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.16 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {6, 6}) Quotient :: toric Aut^+ = C3 x S3 (small group id <18, 3>) Aut = S3 x S3 (small group id <36, 10>) |r| :: 2 Presentation :: [ S^2, B * A^-1, A * B * Z^2, B * Z^2 * B, S * B * S * A, (S * Z)^2, A * Z * B * Z * A^-1 * Z^-1, A * B * Z * A^-2 * Z^-1, B^2 * Z^-4, A * Z^-1 * B * Z^-1 * A * Z^-1 ] Map:: R = (1, 20, 38, 56, 2, 24, 42, 60, 6, 32, 50, 68, 14, 28, 46, 64, 10, 22, 40, 58, 4, 19, 37, 55)(3, 27, 45, 63, 9, 23, 41, 59, 5, 31, 49, 67, 13, 33, 51, 69, 15, 29, 47, 65, 11, 21, 39, 57)(7, 34, 52, 70, 16, 26, 44, 62, 8, 36, 54, 72, 18, 30, 48, 66, 12, 35, 53, 71, 17, 25, 43, 61) L = (1, 39)(2, 43)(3, 46)(4, 48)(5, 37)(6, 41)(7, 40)(8, 38)(9, 53)(10, 51)(11, 54)(12, 50)(13, 52)(14, 44)(15, 42)(16, 45)(17, 47)(18, 49)(19, 59)(20, 62)(21, 55)(22, 61)(23, 60)(24, 69)(25, 56)(26, 68)(27, 70)(28, 57)(29, 71)(30, 58)(31, 72)(32, 66)(33, 64)(34, 67)(35, 63)(36, 65) local type(s) :: { ( 24^24 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.17 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {6, 6}) Quotient :: toric Aut^+ = C6 x C3 (small group id <18, 5>) Aut = C6 x S3 (small group id <36, 12>) |r| :: 2 Presentation :: [ S^2, B * A, A * B^-2, Z^-1 * A * Z * B, (S * Z)^2, S * B * S * A, Z^-1 * B^-1 * Z * A^-1, Z^6 ] Map:: non-degenerate R = (1, 20, 38, 56, 2, 24, 42, 60, 6, 30, 48, 66, 12, 29, 47, 65, 11, 23, 41, 59, 5, 19, 37, 55)(3, 25, 43, 61, 7, 31, 49, 67, 13, 35, 53, 71, 17, 33, 51, 69, 15, 27, 45, 63, 9, 21, 39, 57)(4, 26, 44, 62, 8, 32, 50, 68, 14, 36, 54, 72, 18, 34, 52, 70, 16, 28, 46, 64, 10, 22, 40, 58) L = (1, 39)(2, 43)(3, 40)(4, 37)(5, 45)(6, 49)(7, 44)(8, 38)(9, 46)(10, 41)(11, 51)(12, 53)(13, 50)(14, 42)(15, 52)(16, 47)(17, 54)(18, 48)(19, 57)(20, 61)(21, 58)(22, 55)(23, 63)(24, 67)(25, 62)(26, 56)(27, 64)(28, 59)(29, 69)(30, 71)(31, 68)(32, 60)(33, 70)(34, 65)(35, 72)(36, 66) local type(s) :: { ( 24^24 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.18 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {6, 6}) Quotient :: toric Aut^+ = C6 x C3 (small group id <18, 5>) Aut = C6 x S3 (small group id <36, 12>) |r| :: 2 Presentation :: [ S^2, B^3, A^3, Z * A^-1 * B^-1 * Z, Z * B^-1 * A^-1 * Z, Z * A^-1 * Z * B^-1, (S * Z)^2, (A^-1, B), S * A * S * B ] Map:: non-degenerate R = (1, 20, 38, 56, 2, 26, 44, 62, 8, 36, 54, 72, 18, 33, 51, 69, 15, 23, 41, 59, 5, 19, 37, 55)(3, 27, 45, 63, 9, 32, 50, 68, 14, 35, 53, 71, 17, 25, 43, 61, 7, 30, 48, 66, 12, 21, 39, 57)(4, 28, 46, 64, 10, 31, 49, 67, 13, 34, 52, 70, 16, 24, 42, 60, 6, 29, 47, 65, 11, 22, 40, 58) L = (1, 39)(2, 45)(3, 42)(4, 44)(5, 48)(6, 37)(7, 49)(8, 50)(9, 47)(10, 54)(11, 38)(12, 52)(13, 51)(14, 40)(15, 43)(16, 41)(17, 46)(18, 53)(19, 61)(20, 66)(21, 67)(22, 55)(23, 71)(24, 69)(25, 58)(26, 57)(27, 70)(28, 56)(29, 59)(30, 64)(31, 62)(32, 60)(33, 68)(34, 72)(35, 65)(36, 63) local type(s) :: { ( 24^24 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.19 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {6, 6}) Quotient :: toric Aut^+ = C6 x C3 (small group id <18, 5>) Aut = C6 x S3 (small group id <36, 12>) |r| :: 2 Presentation :: [ S^2, B^3, A^3, (A, B^-1), B^-1 * Z^-1 * A^-1 * Z^-1, Z^-1 * A^-1 * B^-1 * Z^-1, (S * Z)^2, S * A * S * B, (Z^-1, A^-1) ] Map:: non-degenerate R = (1, 20, 38, 56, 2, 26, 44, 62, 8, 36, 54, 72, 18, 31, 49, 67, 13, 23, 41, 59, 5, 19, 37, 55)(3, 27, 45, 63, 9, 25, 43, 61, 7, 30, 48, 66, 12, 35, 53, 71, 17, 32, 50, 68, 14, 21, 39, 57)(4, 28, 46, 64, 10, 24, 42, 60, 6, 29, 47, 65, 11, 33, 51, 69, 15, 34, 52, 70, 16, 22, 40, 58) L = (1, 39)(2, 45)(3, 42)(4, 49)(5, 50)(6, 37)(7, 51)(8, 43)(9, 47)(10, 41)(11, 38)(12, 52)(13, 53)(14, 46)(15, 44)(16, 54)(17, 40)(18, 48)(19, 61)(20, 66)(21, 69)(22, 55)(23, 63)(24, 62)(25, 58)(26, 71)(27, 70)(28, 56)(29, 72)(30, 64)(31, 57)(32, 65)(33, 67)(34, 59)(35, 60)(36, 68) local type(s) :: { ( 24^24 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.20 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {6, 6}) Quotient :: toric Aut^+ = C6 x C3 (small group id <18, 5>) Aut = C2 x ((C3 x C3) : C2) (small group id <36, 13>) |r| :: 2 Presentation :: [ S^2, B * A^-1, B * A^2, (A^-1, Z), S * A * S * B, (S * Z)^2, Z^6 ] Map:: R = (1, 20, 38, 56, 2, 24, 42, 60, 6, 30, 48, 66, 12, 28, 46, 64, 10, 22, 40, 58, 4, 19, 37, 55)(3, 25, 43, 61, 7, 31, 49, 67, 13, 35, 53, 71, 17, 33, 51, 69, 15, 27, 45, 63, 9, 21, 39, 57)(5, 26, 44, 62, 8, 32, 50, 68, 14, 36, 54, 72, 18, 34, 52, 70, 16, 29, 47, 65, 11, 23, 41, 59) L = (1, 39)(2, 43)(3, 41)(4, 45)(5, 37)(6, 49)(7, 44)(8, 38)(9, 47)(10, 51)(11, 40)(12, 53)(13, 50)(14, 42)(15, 52)(16, 46)(17, 54)(18, 48)(19, 59)(20, 62)(21, 55)(22, 65)(23, 57)(24, 68)(25, 56)(26, 61)(27, 58)(28, 70)(29, 63)(30, 72)(31, 60)(32, 67)(33, 64)(34, 69)(35, 66)(36, 71) local type(s) :: { ( 24^24 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.21 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {4, 4}) Quotient :: toric Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, A * B^-1, A^-3 * B^-1, Z^-1 * A^-2 * Z^-1, (S * Z)^2, B * Z^-2 * A, S * A * S * B, A^-1 * Z^-1 * A * Z * A^-1 * Z * A^-1 * Z^-1 * A^-1 * Z^-1 ] Map:: R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 24, 44, 64, 4, 21, 41, 61)(3, 29, 49, 69, 9, 25, 45, 65, 5, 30, 50, 70, 10, 23, 43, 63)(7, 31, 51, 71, 11, 28, 48, 68, 8, 32, 52, 72, 12, 27, 47, 67)(13, 37, 57, 77, 17, 34, 54, 74, 14, 38, 58, 78, 18, 33, 53, 73)(15, 39, 59, 79, 19, 36, 56, 76, 16, 40, 60, 80, 20, 35, 55, 75) L = (1, 43)(2, 47)(3, 46)(4, 48)(5, 41)(6, 45)(7, 44)(8, 42)(9, 53)(10, 54)(11, 55)(12, 56)(13, 50)(14, 49)(15, 52)(16, 51)(17, 59)(18, 60)(19, 58)(20, 57)(21, 65)(22, 68)(23, 61)(24, 67)(25, 66)(26, 63)(27, 62)(28, 64)(29, 74)(30, 73)(31, 76)(32, 75)(33, 69)(34, 70)(35, 71)(36, 72)(37, 80)(38, 79)(39, 77)(40, 78) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 5 e = 40 f = 5 degree seq :: [ 16^5 ] E16.22 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {4, 4}) Quotient :: toric Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ S^2, A * B^-1, (B * A)^2, Z^4, Z^-1 * A^-1 * B^-1 * Z^-1, (S * Z)^2, S * A * S * B, B^-1 * Z^-1 * A * Z * A^-1 * Z^-1 * A^-1 * Z^-1 * A^-1 * Z^-1 ] Map:: R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 24, 44, 64, 4, 21, 41, 61)(3, 29, 49, 69, 9, 25, 45, 65, 5, 30, 50, 70, 10, 23, 43, 63)(7, 31, 51, 71, 11, 28, 48, 68, 8, 32, 52, 72, 12, 27, 47, 67)(13, 37, 57, 77, 17, 34, 54, 74, 14, 38, 58, 78, 18, 33, 53, 73)(15, 39, 59, 79, 19, 36, 56, 76, 16, 40, 60, 80, 20, 35, 55, 75) L = (1, 43)(2, 47)(3, 46)(4, 48)(5, 41)(6, 45)(7, 44)(8, 42)(9, 53)(10, 54)(11, 55)(12, 56)(13, 50)(14, 49)(15, 52)(16, 51)(17, 60)(18, 59)(19, 57)(20, 58)(21, 65)(22, 68)(23, 61)(24, 67)(25, 66)(26, 63)(27, 62)(28, 64)(29, 74)(30, 73)(31, 76)(32, 75)(33, 69)(34, 70)(35, 71)(36, 72)(37, 79)(38, 80)(39, 78)(40, 77) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 5 e = 40 f = 5 degree seq :: [ 16^5 ] E16.23 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {4, 4}) Quotient :: toric Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ S^2, A^-1 * B^-1, (S * Z)^2, Z^4, S * A * S * B, B * Z * A^-1 * Z^-1, A * Z * B^-1 * Z^-1, A^3 * B^-2 ] Map:: non-degenerate R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 25, 45, 65, 5, 21, 41, 61)(3, 28, 48, 68, 8, 33, 53, 73, 13, 30, 50, 70, 10, 23, 43, 63)(4, 27, 47, 67, 7, 34, 54, 74, 14, 32, 52, 72, 12, 24, 44, 64)(9, 36, 56, 76, 16, 39, 59, 79, 19, 37, 57, 77, 17, 29, 49, 69)(11, 35, 55, 75, 15, 40, 60, 80, 20, 38, 58, 78, 18, 31, 51, 71) L = (1, 43)(2, 47)(3, 49)(4, 41)(5, 52)(6, 53)(7, 55)(8, 42)(9, 51)(10, 45)(11, 44)(12, 58)(13, 59)(14, 46)(15, 56)(16, 48)(17, 50)(18, 57)(19, 60)(20, 54)(21, 63)(22, 67)(23, 69)(24, 61)(25, 72)(26, 73)(27, 75)(28, 62)(29, 71)(30, 65)(31, 64)(32, 78)(33, 79)(34, 66)(35, 76)(36, 68)(37, 70)(38, 77)(39, 80)(40, 74) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 5 e = 40 f = 5 degree seq :: [ 16^5 ] E16.24 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {4, 4}) Quotient :: toric Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ S^2, A^-1 * B^-1, A^-1 * B^-1, A * Z^-1 * A * Z, Z * B * Z^-1 * B, S * B * S * A, Z^4, (S * Z)^2, A^-1 * Z * B^-1 * Z * B * A^-2, A * Z^-1 * B^2 * A^-1 * B * Z^-1, B^-2 * A^3 * Z^2 ] Map:: non-degenerate R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 25, 45, 65, 5, 21, 41, 61)(3, 28, 48, 68, 8, 33, 53, 73, 13, 30, 50, 70, 10, 23, 43, 63)(4, 27, 47, 67, 7, 34, 54, 74, 14, 32, 52, 72, 12, 24, 44, 64)(9, 36, 56, 76, 16, 39, 59, 79, 19, 38, 58, 78, 18, 29, 49, 69)(11, 35, 55, 75, 15, 37, 57, 77, 17, 40, 60, 80, 20, 31, 51, 71) L = (1, 43)(2, 47)(3, 49)(4, 41)(5, 52)(6, 53)(7, 55)(8, 42)(9, 57)(10, 45)(11, 44)(12, 60)(13, 59)(14, 46)(15, 58)(16, 48)(17, 54)(18, 50)(19, 51)(20, 56)(21, 63)(22, 67)(23, 69)(24, 61)(25, 72)(26, 73)(27, 75)(28, 62)(29, 77)(30, 65)(31, 64)(32, 80)(33, 79)(34, 66)(35, 78)(36, 68)(37, 74)(38, 70)(39, 71)(40, 76) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 5 e = 40 f = 5 degree seq :: [ 16^5 ] E16.25 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {4, 4}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ S^2, A^-1 * B, (A^-1, Z), S * A * S * B, Z^4, (S * Z)^2, Z^-1 * B * Z * A^-1, A^2 * B * A^2 ] Map:: R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 24, 44, 64, 4, 21, 41, 61)(3, 27, 47, 67, 7, 33, 53, 73, 13, 30, 50, 70, 10, 23, 43, 63)(5, 28, 48, 68, 8, 34, 54, 74, 14, 31, 51, 71, 11, 25, 45, 65)(9, 35, 55, 75, 15, 39, 59, 79, 19, 37, 57, 77, 17, 29, 49, 69)(12, 36, 56, 76, 16, 40, 60, 80, 20, 38, 58, 78, 18, 32, 52, 72) L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 53)(7, 55)(8, 42)(9, 52)(10, 57)(11, 44)(12, 45)(13, 59)(14, 46)(15, 56)(16, 48)(17, 58)(18, 51)(19, 60)(20, 54)(21, 65)(22, 68)(23, 61)(24, 71)(25, 72)(26, 74)(27, 62)(28, 76)(29, 63)(30, 64)(31, 78)(32, 69)(33, 66)(34, 80)(35, 67)(36, 75)(37, 70)(38, 77)(39, 73)(40, 79) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 5 e = 40 f = 5 degree seq :: [ 16^5 ] E16.26 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {4, 4}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ S^2, A^-1 * B, (A, Z), S * B * S * A, Z^4, (S * Z)^2, Z^-1 * B * Z * A^-1, A^2 * Z * A^-1 * Z^-1 * B^-1, Z * B * A * Z^-1 * B^-1 * A^-1, Z^-1 * A^-1 * Z^-1 * B^-1 * A^-3 ] Map:: R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 24, 44, 64, 4, 21, 41, 61)(3, 27, 47, 67, 7, 33, 53, 73, 13, 30, 50, 70, 10, 23, 43, 63)(5, 28, 48, 68, 8, 34, 54, 74, 14, 31, 51, 71, 11, 25, 45, 65)(9, 35, 55, 75, 15, 40, 60, 80, 20, 38, 58, 78, 18, 29, 49, 69)(12, 36, 56, 76, 16, 37, 57, 77, 17, 39, 59, 79, 19, 32, 52, 72) 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, 60)(14, 46)(15, 59)(16, 48)(17, 54)(18, 56)(19, 51)(20, 52)(21, 65)(22, 68)(23, 61)(24, 71)(25, 72)(26, 74)(27, 62)(28, 76)(29, 63)(30, 64)(31, 79)(32, 80)(33, 66)(34, 77)(35, 67)(36, 78)(37, 69)(38, 70)(39, 75)(40, 73) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 5 e = 40 f = 5 degree seq :: [ 16^5 ] E16.27 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {4, 4}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = C5 x D8 (small group id <40, 10>) |r| :: 2 Presentation :: [ S^2, B^-1 * A^-1, (S * Z)^2, (A^-1, Z^-1), Z^4, S * A * S * B, (B^-1, Z^-1), A^3 * B^-2 ] Map:: non-degenerate R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 25, 45, 65, 5, 21, 41, 61)(3, 27, 47, 67, 7, 33, 53, 73, 13, 30, 50, 70, 10, 23, 43, 63)(4, 28, 48, 68, 8, 34, 54, 74, 14, 32, 52, 72, 12, 24, 44, 64)(9, 35, 55, 75, 15, 39, 59, 79, 19, 37, 57, 77, 17, 29, 49, 69)(11, 36, 56, 76, 16, 40, 60, 80, 20, 38, 58, 78, 18, 31, 51, 71) L = (1, 43)(2, 47)(3, 49)(4, 41)(5, 50)(6, 53)(7, 55)(8, 42)(9, 51)(10, 57)(11, 44)(12, 45)(13, 59)(14, 46)(15, 56)(16, 48)(17, 58)(18, 52)(19, 60)(20, 54)(21, 63)(22, 67)(23, 69)(24, 61)(25, 70)(26, 73)(27, 75)(28, 62)(29, 71)(30, 77)(31, 64)(32, 65)(33, 79)(34, 66)(35, 76)(36, 68)(37, 78)(38, 72)(39, 80)(40, 74) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 5 e = 40 f = 5 degree seq :: [ 16^5 ] E16.28 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {4, 4}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = C5 x D8 (small group id <40, 10>) |r| :: 2 Presentation :: [ S^2, B^-1 * A^-1, A^-1 * B^-1, (A^-1, Z^-1), (S * Z)^2, (Z^-1, B), Z^4, S * B * S * A, A * Z * A * B^-1 * Z * B^-2, B * Z * B^2 * Z * A^-2, Z^-2 * B^2 * A^-3 ] Map:: non-degenerate R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 25, 45, 65, 5, 21, 41, 61)(3, 27, 47, 67, 7, 33, 53, 73, 13, 30, 50, 70, 10, 23, 43, 63)(4, 28, 48, 68, 8, 34, 54, 74, 14, 32, 52, 72, 12, 24, 44, 64)(9, 35, 55, 75, 15, 39, 59, 79, 19, 38, 58, 78, 18, 29, 49, 69)(11, 36, 56, 76, 16, 37, 57, 77, 17, 40, 60, 80, 20, 31, 51, 71) L = (1, 43)(2, 47)(3, 49)(4, 41)(5, 50)(6, 53)(7, 55)(8, 42)(9, 57)(10, 58)(11, 44)(12, 45)(13, 59)(14, 46)(15, 60)(16, 48)(17, 54)(18, 56)(19, 51)(20, 52)(21, 63)(22, 67)(23, 69)(24, 61)(25, 70)(26, 73)(27, 75)(28, 62)(29, 77)(30, 78)(31, 64)(32, 65)(33, 79)(34, 66)(35, 80)(36, 68)(37, 74)(38, 76)(39, 71)(40, 72) local type(s) :: { ( 16^16 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 5 e = 40 f = 5 degree seq :: [ 16^5 ] E16.29 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 4}) Quotient :: toric Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ Z^2, S^2, A^3, B^3, B * Z * B^-1 * Z, Z * A^-1 * Z * A, (S * Z)^2, S * B * S * A, A^-1 * B * A^-1 * Z * B, B * A * B * A^-1 * B^-1 * A^-1 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 25, 49, 73)(3, 31, 55, 79, 7, 27, 51, 75)(4, 32, 56, 80, 8, 28, 52, 76)(5, 33, 57, 81, 9, 29, 53, 77)(6, 34, 58, 82, 10, 30, 54, 78)(11, 43, 67, 91, 19, 35, 59, 83)(12, 38, 62, 86, 14, 36, 60, 84)(13, 44, 68, 92, 20, 37, 61, 85)(15, 41, 65, 89, 17, 39, 63, 87)(16, 45, 69, 93, 21, 40, 64, 88)(18, 46, 70, 94, 22, 42, 66, 90)(23, 48, 72, 96, 24, 47, 71, 95) L = (1, 51)(2, 55)(3, 53)(4, 61)(5, 49)(6, 65)(7, 57)(8, 68)(9, 50)(10, 63)(11, 71)(12, 56)(13, 62)(14, 52)(15, 70)(16, 67)(17, 66)(18, 54)(19, 72)(20, 60)(21, 59)(22, 58)(23, 69)(24, 64)(25, 78)(26, 82)(27, 84)(28, 73)(29, 88)(30, 76)(31, 86)(32, 74)(33, 93)(34, 80)(35, 75)(36, 83)(37, 94)(38, 91)(39, 77)(40, 87)(41, 81)(42, 96)(43, 79)(44, 90)(45, 89)(46, 95)(47, 85)(48, 92) local type(s) :: { ( 16^8 ) } Outer automorphisms :: reflexible Dual of E16.31 Transitivity :: VT+ Graph:: v = 12 e = 48 f = 6 degree seq :: [ 8^12 ] E16.30 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 4}) Quotient :: toric Aut^+ = SL(2,3) (small group id <24, 3>) Aut = SL(2,3) : C2 (small group id <48, 33>) |r| :: 2 Presentation :: [ Z^2, S^2, A^3, B^3, Z * A^-1 * Z * A, Z * B * Z * B^-1, S * B * S * A, (S * Z)^2, A * B * A * Z * B, A * B^-1 * Z * B^-1 * A * B, A^-1 * B * A^-1 * B^-1 * A * B^-1, (B * Z * A)^4 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 25, 49, 73)(3, 31, 55, 79, 7, 27, 51, 75)(4, 32, 56, 80, 8, 28, 52, 76)(5, 33, 57, 81, 9, 29, 53, 77)(6, 34, 58, 82, 10, 30, 54, 78)(11, 42, 66, 90, 18, 35, 59, 83)(12, 43, 67, 91, 19, 36, 60, 84)(13, 40, 64, 88, 16, 37, 61, 85)(14, 44, 68, 92, 20, 38, 62, 86)(15, 45, 69, 93, 21, 39, 63, 87)(17, 46, 70, 94, 22, 41, 65, 89)(23, 48, 72, 96, 24, 47, 71, 95) L = (1, 51)(2, 55)(3, 53)(4, 61)(5, 49)(6, 65)(7, 57)(8, 64)(9, 50)(10, 70)(11, 58)(12, 71)(13, 62)(14, 52)(15, 67)(16, 68)(17, 66)(18, 54)(19, 72)(20, 56)(21, 60)(22, 59)(23, 69)(24, 63)(25, 78)(26, 82)(27, 84)(28, 73)(29, 88)(30, 76)(31, 91)(32, 74)(33, 85)(34, 80)(35, 75)(36, 83)(37, 93)(38, 94)(39, 77)(40, 87)(41, 95)(42, 79)(43, 90)(44, 89)(45, 81)(46, 96)(47, 92)(48, 86) local type(s) :: { ( 16^8 ) } Outer automorphisms :: reflexible Dual of E16.32 Transitivity :: VT+ Graph:: v = 12 e = 48 f = 6 degree seq :: [ 8^12 ] E16.31 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 4}) Quotient :: toric Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ S^2, A^3, B^3, Z * B * Z^-1 * A^-1, Z * B^-1 * A^-1 * B^-1, B^-1 * Z * A * Z^-1, B * Z^-1 * B * A, A * B * A * Z^-1, S * A * S * B, (S * Z)^2, Z^4 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 32, 56, 80, 8, 29, 53, 77, 5, 25, 49, 73)(3, 34, 58, 82, 10, 45, 69, 93, 21, 37, 61, 85, 13, 27, 51, 75)(4, 33, 57, 81, 9, 46, 70, 94, 22, 39, 63, 87, 15, 28, 52, 76)(6, 36, 60, 84, 12, 47, 71, 95, 23, 42, 66, 90, 18, 30, 54, 78)(7, 35, 59, 83, 11, 48, 72, 96, 24, 41, 65, 89, 17, 31, 55, 79)(14, 43, 67, 91, 19, 40, 64, 88, 16, 44, 68, 92, 20, 38, 62, 86) L = (1, 51)(2, 57)(3, 54)(4, 60)(5, 63)(6, 49)(7, 68)(8, 69)(9, 59)(10, 72)(11, 50)(12, 64)(13, 55)(14, 70)(15, 65)(16, 52)(17, 53)(18, 62)(19, 58)(20, 61)(21, 71)(22, 66)(23, 56)(24, 67)(25, 79)(26, 84)(27, 86)(28, 73)(29, 90)(30, 87)(31, 76)(32, 96)(33, 92)(34, 74)(35, 75)(36, 82)(37, 77)(38, 83)(39, 91)(40, 89)(41, 93)(42, 85)(43, 78)(44, 95)(45, 88)(46, 80)(47, 81)(48, 94) local type(s) :: { ( 8^16 ) } Outer automorphisms :: reflexible Dual of E16.29 Transitivity :: VT+ Graph:: v = 6 e = 48 f = 12 degree seq :: [ 16^6 ] E16.32 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 4}) Quotient :: toric Aut^+ = SL(2,3) (small group id <24, 3>) Aut = SL(2,3) : C2 (small group id <48, 33>) |r| :: 2 Presentation :: [ S^2, A^3, B * A * Z, B^3, S * B * S * A, (S * Z)^2, Z^4, B * Z^-1 * B * A^-1 * Z^-1, A * B * Z^-1 * B^-1 * A^-1 * Z^-1 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 32, 56, 80, 8, 29, 53, 77, 5, 25, 49, 73)(3, 31, 55, 79, 7, 45, 69, 93, 21, 37, 61, 85, 13, 27, 51, 75)(4, 39, 63, 87, 15, 34, 58, 82, 10, 40, 64, 88, 16, 28, 52, 76)(6, 38, 62, 86, 14, 42, 66, 90, 18, 44, 68, 92, 20, 30, 54, 78)(9, 35, 59, 83, 11, 41, 65, 89, 17, 43, 67, 91, 19, 33, 57, 81)(12, 48, 72, 96, 24, 46, 70, 94, 22, 47, 71, 95, 23, 36, 60, 84) L = (1, 51)(2, 57)(3, 54)(4, 53)(5, 65)(6, 49)(7, 64)(8, 69)(9, 58)(10, 50)(11, 68)(12, 61)(13, 63)(14, 71)(15, 60)(16, 70)(17, 52)(18, 56)(19, 62)(20, 72)(21, 66)(22, 55)(23, 67)(24, 59)(25, 79)(26, 83)(27, 86)(28, 73)(29, 91)(30, 74)(31, 76)(32, 85)(33, 88)(34, 80)(35, 78)(36, 75)(37, 82)(38, 84)(39, 96)(40, 95)(41, 87)(42, 77)(43, 90)(44, 94)(45, 92)(46, 93)(47, 81)(48, 89) local type(s) :: { ( 8^16 ) } Outer automorphisms :: reflexible Dual of E16.30 Transitivity :: VT+ Graph:: v = 6 e = 48 f = 12 degree seq :: [ 16^6 ] E16.33 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 4}) Quotient :: toric Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Z^2, S^2, B^3, A^3, S * A * S * B, (B^-1 * A^-1)^2, (B^-1 * Z)^2, (S * Z)^2, (A^-1 * Z)^2, (B * A^-1)^3, B * A^-2 * B * Z * A * B^-1 * A^-1 * B * Z * A * B^-2 * A ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 25, 49, 73)(3, 33, 57, 81, 9, 27, 51, 75)(4, 34, 58, 82, 10, 28, 52, 76)(5, 31, 55, 79, 7, 29, 53, 77)(6, 32, 56, 80, 8, 30, 54, 78)(11, 43, 67, 91, 19, 35, 59, 83)(12, 45, 69, 93, 21, 36, 60, 84)(13, 41, 65, 89, 17, 37, 61, 85)(14, 46, 70, 94, 22, 38, 62, 86)(15, 42, 66, 90, 18, 39, 63, 87)(16, 44, 68, 92, 20, 40, 64, 88)(23, 48, 72, 96, 24, 47, 71, 95) L = (1, 51)(2, 55)(3, 53)(4, 61)(5, 49)(6, 64)(7, 57)(8, 67)(9, 50)(10, 70)(11, 54)(12, 71)(13, 62)(14, 52)(15, 60)(16, 59)(17, 58)(18, 72)(19, 68)(20, 56)(21, 66)(22, 65)(23, 63)(24, 69)(25, 78)(26, 82)(27, 84)(28, 73)(29, 85)(30, 76)(31, 90)(32, 74)(33, 91)(34, 80)(35, 75)(36, 83)(37, 87)(38, 88)(39, 77)(40, 95)(41, 79)(42, 89)(43, 93)(44, 94)(45, 81)(46, 96)(47, 86)(48, 92) local type(s) :: { ( 16^8 ) } Outer automorphisms :: reflexible Dual of E16.35 Transitivity :: VT+ Graph:: v = 12 e = 48 f = 6 degree seq :: [ 8^12 ] E16.34 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 4}) Quotient :: toric Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Z^2, S^2, B^3, A^3, (B^-1 * A^-1)^2, S * A * S * B, (S * Z)^2, A^-1 * Z * B * Z, (B * A^-1)^3 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 25, 49, 73)(3, 32, 56, 80, 8, 27, 51, 75)(4, 31, 55, 79, 7, 28, 52, 76)(5, 34, 58, 82, 10, 29, 53, 77)(6, 33, 57, 81, 9, 30, 54, 78)(11, 43, 67, 91, 19, 35, 59, 83)(12, 44, 68, 92, 20, 36, 60, 84)(13, 41, 65, 89, 17, 37, 61, 85)(14, 42, 66, 90, 18, 38, 62, 86)(15, 46, 70, 94, 22, 39, 63, 87)(16, 45, 69, 93, 21, 40, 64, 88)(23, 48, 72, 96, 24, 47, 71, 95) L = (1, 51)(2, 55)(3, 53)(4, 61)(5, 49)(6, 64)(7, 57)(8, 67)(9, 50)(10, 70)(11, 54)(12, 71)(13, 62)(14, 52)(15, 60)(16, 59)(17, 58)(18, 72)(19, 68)(20, 56)(21, 66)(22, 65)(23, 63)(24, 69)(25, 78)(26, 82)(27, 84)(28, 73)(29, 85)(30, 76)(31, 90)(32, 74)(33, 91)(34, 80)(35, 75)(36, 83)(37, 87)(38, 88)(39, 77)(40, 95)(41, 79)(42, 89)(43, 93)(44, 94)(45, 81)(46, 96)(47, 86)(48, 92) local type(s) :: { ( 16^8 ) } Outer automorphisms :: reflexible Dual of E16.36 Transitivity :: VT+ Graph:: v = 12 e = 48 f = 6 degree seq :: [ 8^12 ] E16.35 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 4}) Quotient :: toric Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ S^2, B^3, A^3, A * Z * B^-1 * Z^-1, Z^-2 * B^-1 * A^-1, Z^-2 * A * B, S * B * S * A, (Z * B^-1)^2, (B^-1 * A^-1)^2, (S * Z)^2, Z^4, A^-1 * Z^-1 * A * B^-1 * Z^-1, B^-1 * Z * A^-1 * B^-1 * A * Z^-1 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 32, 56, 80, 8, 29, 53, 77, 5, 25, 49, 73)(3, 34, 58, 82, 10, 43, 67, 91, 19, 35, 59, 83, 11, 27, 51, 75)(4, 38, 62, 86, 14, 30, 54, 78, 6, 36, 60, 84, 12, 28, 52, 76)(7, 41, 65, 89, 17, 40, 64, 88, 16, 42, 66, 90, 18, 31, 55, 79)(9, 37, 61, 85, 13, 46, 70, 94, 22, 44, 68, 92, 20, 33, 57, 81)(15, 48, 72, 96, 24, 47, 71, 95, 23, 45, 69, 93, 21, 39, 63, 87) L = (1, 51)(2, 57)(3, 54)(4, 63)(5, 60)(6, 49)(7, 68)(8, 55)(9, 59)(10, 69)(11, 50)(12, 66)(13, 71)(14, 58)(15, 64)(16, 52)(17, 72)(18, 53)(19, 61)(20, 56)(21, 62)(22, 65)(23, 67)(24, 70)(25, 79)(26, 84)(27, 85)(28, 73)(29, 81)(30, 87)(31, 76)(32, 75)(33, 89)(34, 74)(35, 93)(36, 82)(37, 80)(38, 90)(39, 91)(40, 92)(41, 77)(42, 96)(43, 78)(44, 95)(45, 94)(46, 83)(47, 88)(48, 86) local type(s) :: { ( 8^16 ) } Outer automorphisms :: reflexible Dual of E16.33 Transitivity :: VT+ Graph:: v = 6 e = 48 f = 12 degree seq :: [ 16^6 ] E16.36 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 4}) Quotient :: toric Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ S^2, A^3, B^3, (Z * B)^2, S * B * S * A, B * Z^2 * A, B^-1 * Z * A * Z^-1, (A * B)^2, (Z^-1 * A^-1)^2, Z^2 * B^-1 * A^-1, (S * Z)^2, Z * A^-1 * Z * A * B^-1, Z^-1 * A^-1 * B * A * B^-1 * Z^-1 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 32, 56, 80, 8, 29, 53, 77, 5, 25, 49, 73)(3, 37, 61, 85, 13, 43, 67, 91, 19, 38, 62, 86, 14, 27, 51, 75)(4, 33, 57, 81, 9, 30, 54, 78, 6, 41, 65, 89, 17, 28, 52, 76)(7, 35, 59, 83, 11, 42, 66, 90, 18, 34, 58, 82, 10, 31, 55, 79)(12, 44, 68, 92, 20, 46, 70, 94, 22, 39, 63, 87, 15, 36, 60, 84)(16, 47, 71, 95, 23, 48, 72, 96, 24, 45, 69, 93, 21, 40, 64, 88) L = (1, 51)(2, 57)(3, 54)(4, 64)(5, 60)(6, 49)(7, 68)(8, 55)(9, 59)(10, 69)(11, 50)(12, 61)(13, 53)(14, 71)(15, 72)(16, 66)(17, 62)(18, 52)(19, 63)(20, 56)(21, 70)(22, 58)(23, 65)(24, 67)(25, 79)(26, 84)(27, 87)(28, 73)(29, 81)(30, 88)(31, 76)(32, 75)(33, 86)(34, 74)(35, 93)(36, 82)(37, 95)(38, 77)(39, 80)(40, 91)(41, 83)(42, 92)(43, 78)(44, 96)(45, 89)(46, 85)(47, 94)(48, 90) local type(s) :: { ( 8^16 ) } Outer automorphisms :: reflexible Dual of E16.34 Transitivity :: VT+ Graph:: v = 6 e = 48 f = 12 degree seq :: [ 16^6 ] E16.37 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Z^2, S^2, A * B^-1, (S * Z)^2, S * B * S * A, Z * A * B * Z * A^-2, A * Z * A^2 * B * Z * A * Z ] Map:: R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 37, 67, 97, 7, 33, 63, 93)(4, 39, 69, 99, 9, 34, 64, 94)(5, 41, 71, 101, 11, 35, 65, 95)(6, 43, 73, 103, 13, 36, 66, 96)(8, 42, 72, 102, 12, 38, 68, 98)(10, 44, 74, 104, 14, 40, 70, 100)(15, 54, 84, 114, 24, 45, 75, 105)(16, 55, 85, 115, 25, 46, 76, 106)(17, 53, 83, 113, 23, 47, 77, 107)(18, 52, 82, 112, 22, 48, 78, 108)(19, 50, 80, 110, 20, 49, 79, 109)(21, 58, 88, 118, 28, 51, 81, 111)(26, 59, 89, 119, 29, 56, 86, 116)(27, 60, 90, 120, 30, 57, 87, 117) L = (1, 63)(2, 65)(3, 68)(4, 61)(5, 72)(6, 62)(7, 75)(8, 77)(9, 76)(10, 64)(11, 80)(12, 82)(13, 81)(14, 66)(15, 83)(16, 67)(17, 86)(18, 69)(19, 70)(20, 78)(21, 71)(22, 89)(23, 73)(24, 74)(25, 90)(26, 88)(27, 79)(28, 87)(29, 85)(30, 84)(31, 94)(32, 96)(33, 91)(34, 100)(35, 92)(36, 104)(37, 106)(38, 93)(39, 108)(40, 109)(41, 111)(42, 95)(43, 113)(44, 114)(45, 97)(46, 99)(47, 98)(48, 110)(49, 117)(50, 101)(51, 103)(52, 102)(53, 105)(54, 120)(55, 119)(56, 107)(57, 118)(58, 116)(59, 112)(60, 115) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.38 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Z^2, S^2, S * B * S * A, (S * Z)^2, (B^-1, A^-1), A * Z * B^-1 * Z, A^2 * B * A^2, B * A * B^3 ] Map:: non-degenerate R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 38, 68, 98, 8, 33, 63, 93)(4, 37, 67, 97, 7, 34, 64, 94)(5, 40, 70, 100, 10, 35, 65, 95)(6, 39, 69, 99, 9, 36, 66, 96)(11, 52, 82, 112, 22, 41, 71, 101)(12, 50, 80, 110, 20, 42, 72, 102)(13, 53, 83, 113, 23, 43, 73, 103)(14, 49, 79, 109, 19, 44, 74, 104)(15, 51, 81, 111, 21, 45, 75, 105)(16, 56, 86, 116, 26, 46, 76, 106)(17, 55, 85, 115, 25, 47, 77, 107)(18, 54, 84, 114, 24, 48, 78, 108)(27, 59, 89, 119, 29, 57, 87, 117)(28, 60, 90, 120, 30, 58, 88, 118) L = (1, 63)(2, 67)(3, 71)(4, 72)(5, 61)(6, 73)(7, 79)(8, 80)(9, 62)(10, 81)(11, 77)(12, 76)(13, 87)(14, 78)(15, 64)(16, 65)(17, 66)(18, 88)(19, 85)(20, 84)(21, 89)(22, 86)(23, 68)(24, 69)(25, 70)(26, 90)(27, 74)(28, 75)(29, 82)(30, 83)(31, 96)(32, 100)(33, 103)(34, 91)(35, 107)(36, 108)(37, 111)(38, 92)(39, 115)(40, 116)(41, 117)(42, 93)(43, 118)(44, 94)(45, 95)(46, 101)(47, 104)(48, 102)(49, 119)(50, 97)(51, 120)(52, 98)(53, 99)(54, 109)(55, 112)(56, 110)(57, 105)(58, 106)(59, 113)(60, 114) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.39 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Z^2, S^2, B * A^-1, (S * Z)^2, S * A * S * B, A^-1 * Z * A^2 * Z * A^-1, A^6, A * Z * A * Z * A^-1 * Z * A * Z * A * Z ] Map:: R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 37, 67, 97, 7, 33, 63, 93)(4, 39, 69, 99, 9, 34, 64, 94)(5, 41, 71, 101, 11, 35, 65, 95)(6, 43, 73, 103, 13, 36, 66, 96)(8, 42, 72, 102, 12, 38, 68, 98)(10, 44, 74, 104, 14, 40, 70, 100)(15, 53, 83, 113, 23, 45, 75, 105)(16, 55, 85, 115, 25, 46, 76, 106)(17, 54, 84, 114, 24, 47, 77, 107)(18, 56, 86, 116, 26, 48, 78, 108)(19, 57, 87, 117, 27, 49, 79, 109)(20, 59, 89, 119, 29, 50, 80, 110)(21, 58, 88, 118, 28, 51, 81, 111)(22, 60, 90, 120, 30, 52, 82, 112) L = (1, 63)(2, 65)(3, 68)(4, 61)(5, 72)(6, 62)(7, 75)(8, 77)(9, 76)(10, 64)(11, 79)(12, 81)(13, 80)(14, 66)(15, 84)(16, 67)(17, 70)(18, 69)(19, 88)(20, 71)(21, 74)(22, 73)(23, 89)(24, 78)(25, 90)(26, 87)(27, 85)(28, 82)(29, 86)(30, 83)(31, 94)(32, 96)(33, 91)(34, 100)(35, 92)(36, 104)(37, 106)(38, 93)(39, 108)(40, 107)(41, 110)(42, 95)(43, 112)(44, 111)(45, 97)(46, 99)(47, 98)(48, 114)(49, 101)(50, 103)(51, 102)(52, 118)(53, 120)(54, 105)(55, 117)(56, 119)(57, 116)(58, 109)(59, 113)(60, 115) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.40 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Z^2, S^2, S * B * S * A, (S * Z)^2, A^-1 * Z * B * Z, (B, A), B^-4 * A, A^2 * B^-1 * A^2, A^-1 * B^-2 * A^-2 * B^-1 ] Map:: non-degenerate R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 38, 68, 98, 8, 33, 63, 93)(4, 37, 67, 97, 7, 34, 64, 94)(5, 40, 70, 100, 10, 35, 65, 95)(6, 39, 69, 99, 9, 36, 66, 96)(11, 52, 82, 112, 22, 41, 71, 101)(12, 50, 80, 110, 20, 42, 72, 102)(13, 53, 83, 113, 23, 43, 73, 103)(14, 49, 79, 109, 19, 44, 74, 104)(15, 51, 81, 111, 21, 45, 75, 105)(16, 56, 86, 116, 26, 46, 76, 106)(17, 55, 85, 115, 25, 47, 77, 107)(18, 54, 84, 114, 24, 48, 78, 108)(27, 60, 90, 120, 30, 57, 87, 117)(28, 59, 89, 119, 29, 58, 88, 118) L = (1, 63)(2, 67)(3, 71)(4, 72)(5, 61)(6, 73)(7, 79)(8, 80)(9, 62)(10, 81)(11, 75)(12, 87)(13, 76)(14, 88)(15, 64)(16, 65)(17, 66)(18, 74)(19, 83)(20, 89)(21, 84)(22, 90)(23, 68)(24, 69)(25, 70)(26, 82)(27, 78)(28, 77)(29, 86)(30, 85)(31, 96)(32, 100)(33, 103)(34, 91)(35, 107)(36, 108)(37, 111)(38, 92)(39, 115)(40, 116)(41, 106)(42, 93)(43, 104)(44, 94)(45, 95)(46, 118)(47, 117)(48, 105)(49, 114)(50, 97)(51, 112)(52, 98)(53, 99)(54, 120)(55, 119)(56, 113)(57, 101)(58, 102)(59, 109)(60, 110) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.41 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D30 (small group id <30, 3>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Z^2, A^2, S^2, B^2, S * B * S * A, (S * Z)^2, (B * A)^3, (B * Z * A)^2, B * Z * A * Z * B * Z * B * Z * B * Z ] Map:: non-degenerate R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 37, 67, 97, 7, 33, 63, 93)(4, 39, 69, 99, 9, 34, 64, 94)(5, 41, 71, 101, 11, 35, 65, 95)(6, 43, 73, 103, 13, 36, 66, 96)(8, 44, 74, 104, 14, 38, 68, 98)(10, 42, 72, 102, 12, 40, 70, 100)(15, 53, 83, 113, 23, 45, 75, 105)(16, 55, 85, 115, 25, 46, 76, 106)(17, 54, 84, 114, 24, 47, 77, 107)(18, 56, 86, 116, 26, 48, 78, 108)(19, 57, 87, 117, 27, 49, 79, 109)(20, 59, 89, 119, 29, 50, 80, 110)(21, 58, 88, 118, 28, 51, 81, 111)(22, 60, 90, 120, 30, 52, 82, 112) L = (1, 63)(2, 65)(3, 61)(4, 70)(5, 62)(6, 74)(7, 75)(8, 77)(9, 76)(10, 64)(11, 79)(12, 81)(13, 80)(14, 66)(15, 67)(16, 69)(17, 68)(18, 84)(19, 71)(20, 73)(21, 72)(22, 88)(23, 89)(24, 78)(25, 87)(26, 90)(27, 85)(28, 82)(29, 83)(30, 86)(31, 94)(32, 96)(33, 98)(34, 91)(35, 102)(36, 92)(37, 106)(38, 93)(39, 108)(40, 107)(41, 110)(42, 95)(43, 112)(44, 111)(45, 114)(46, 97)(47, 100)(48, 99)(49, 118)(50, 101)(51, 104)(52, 103)(53, 117)(54, 105)(55, 120)(56, 119)(57, 113)(58, 109)(59, 116)(60, 115) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.42 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D30 (small group id <30, 3>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Z^2, S^2, (B^-1, A), S * B * S * A, (S * Z)^2, (A * Z)^2, (B * Z)^2, A^2 * B^-1 * A^2, B^-4 * A, A^-1 * B^-2 * A^-2 * B^-1, (B^-1 * A * Z)^2, (B^-2 * A^-1 * Z)^2, (B^-1 * A^-2 * Z)^2 ] Map:: non-degenerate R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 39, 69, 99, 9, 33, 63, 93)(4, 40, 70, 100, 10, 34, 64, 94)(5, 37, 67, 97, 7, 35, 65, 95)(6, 38, 68, 98, 8, 36, 66, 96)(11, 54, 84, 114, 24, 41, 71, 101)(12, 55, 85, 115, 25, 42, 72, 102)(13, 53, 83, 113, 23, 43, 73, 103)(14, 56, 86, 116, 26, 44, 74, 104)(15, 51, 81, 111, 21, 45, 75, 105)(16, 49, 79, 109, 19, 46, 76, 106)(17, 50, 80, 110, 20, 47, 77, 107)(18, 52, 82, 112, 22, 48, 78, 108)(27, 60, 90, 120, 30, 57, 87, 117)(28, 59, 89, 119, 29, 58, 88, 118) L = (1, 63)(2, 67)(3, 71)(4, 72)(5, 61)(6, 73)(7, 79)(8, 80)(9, 62)(10, 81)(11, 75)(12, 87)(13, 76)(14, 88)(15, 64)(16, 65)(17, 66)(18, 74)(19, 83)(20, 89)(21, 84)(22, 90)(23, 68)(24, 69)(25, 70)(26, 82)(27, 78)(28, 77)(29, 86)(30, 85)(31, 96)(32, 100)(33, 103)(34, 91)(35, 107)(36, 108)(37, 111)(38, 92)(39, 115)(40, 116)(41, 106)(42, 93)(43, 104)(44, 94)(45, 95)(46, 118)(47, 117)(48, 105)(49, 114)(50, 97)(51, 112)(52, 98)(53, 99)(54, 120)(55, 119)(56, 113)(57, 101)(58, 102)(59, 109)(60, 110) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.43 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C30 (small group id <30, 4>) Aut = C10 x S3 (small group id <60, 11>) |r| :: 2 Presentation :: [ Z^2, S^2, S * B * S * A, (S * Z)^2, A^-1 * Z * A * Z, (B, A), B * Z * B^-1 * Z, A^2 * B^-1 * A^2, B^-4 * A, B^-1 * A^-2 * B^-2 * A^-1 ] Map:: non-degenerate R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 37, 67, 97, 7, 33, 63, 93)(4, 38, 68, 98, 8, 34, 64, 94)(5, 39, 69, 99, 9, 35, 65, 95)(6, 40, 70, 100, 10, 36, 66, 96)(11, 49, 79, 109, 19, 41, 71, 101)(12, 50, 80, 110, 20, 42, 72, 102)(13, 51, 81, 111, 21, 43, 73, 103)(14, 52, 82, 112, 22, 44, 74, 104)(15, 53, 83, 113, 23, 45, 75, 105)(16, 54, 84, 114, 24, 46, 76, 106)(17, 55, 85, 115, 25, 47, 77, 107)(18, 56, 86, 116, 26, 48, 78, 108)(27, 59, 89, 119, 29, 57, 87, 117)(28, 60, 90, 120, 30, 58, 88, 118) L = (1, 63)(2, 67)(3, 71)(4, 72)(5, 61)(6, 73)(7, 79)(8, 80)(9, 62)(10, 81)(11, 75)(12, 87)(13, 76)(14, 88)(15, 64)(16, 65)(17, 66)(18, 74)(19, 83)(20, 89)(21, 84)(22, 90)(23, 68)(24, 69)(25, 70)(26, 82)(27, 78)(28, 77)(29, 86)(30, 85)(31, 96)(32, 100)(33, 103)(34, 91)(35, 107)(36, 108)(37, 111)(38, 92)(39, 115)(40, 116)(41, 106)(42, 93)(43, 104)(44, 94)(45, 95)(46, 118)(47, 117)(48, 105)(49, 114)(50, 97)(51, 112)(52, 98)(53, 99)(54, 120)(55, 119)(56, 113)(57, 101)(58, 102)(59, 109)(60, 110) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.44 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C5 x S3 (small group id <30, 1>) Aut = C10 x S3 (small group id <60, 11>) |r| :: 2 Presentation :: [ Z^2, S^2, A * B, (S * Z)^2, S * A * S * B, B^2 * Z * A^2 * Z, B * Z * A * B^-1 * Z * A^-1, A^3 * Z * B^-1 * Z * A * Z ] Map:: non-degenerate R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 37, 67, 97, 7, 33, 63, 93)(4, 39, 69, 99, 9, 34, 64, 94)(5, 41, 71, 101, 11, 35, 65, 95)(6, 43, 73, 103, 13, 36, 66, 96)(8, 42, 72, 102, 12, 38, 68, 98)(10, 44, 74, 104, 14, 40, 70, 100)(15, 54, 84, 114, 24, 45, 75, 105)(16, 55, 85, 115, 25, 46, 76, 106)(17, 53, 83, 113, 23, 47, 77, 107)(18, 52, 82, 112, 22, 48, 78, 108)(19, 50, 80, 110, 20, 49, 79, 109)(21, 58, 88, 118, 28, 51, 81, 111)(26, 59, 89, 119, 29, 56, 86, 116)(27, 60, 90, 120, 30, 57, 87, 117) L = (1, 63)(2, 65)(3, 68)(4, 61)(5, 72)(6, 62)(7, 75)(8, 77)(9, 76)(10, 64)(11, 80)(12, 82)(13, 81)(14, 66)(15, 83)(16, 67)(17, 86)(18, 69)(19, 70)(20, 78)(21, 71)(22, 89)(23, 73)(24, 74)(25, 90)(26, 88)(27, 79)(28, 87)(29, 85)(30, 84)(31, 93)(32, 95)(33, 98)(34, 91)(35, 102)(36, 92)(37, 105)(38, 107)(39, 106)(40, 94)(41, 110)(42, 112)(43, 111)(44, 96)(45, 113)(46, 97)(47, 116)(48, 99)(49, 100)(50, 108)(51, 101)(52, 119)(53, 103)(54, 104)(55, 120)(56, 118)(57, 109)(58, 117)(59, 115)(60, 114) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.45 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C5 x S3 (small group id <30, 1>) Aut = C10 x S3 (small group id <60, 11>) |r| :: 2 Presentation :: [ Z^2, S^2, A * B, (S * Z)^2, S * B * S * A, Z * A^3 * B^-1 * Z * B^-1, A * Z * A * Z * B^-3, A^2 * Z * B^-1 * Z * B^-2, Z * A * Z * A * B^-3, A * Z * B^2 * Z * B^-2 * Z * A^-1 * Z, A^2 * Z * B * Z * B^-1 * Z * A^-2 * Z ] Map:: non-degenerate R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 37, 67, 97, 7, 33, 63, 93)(4, 39, 69, 99, 9, 34, 64, 94)(5, 41, 71, 101, 11, 35, 65, 95)(6, 43, 73, 103, 13, 36, 66, 96)(8, 47, 77, 107, 17, 38, 68, 98)(10, 51, 81, 111, 21, 40, 70, 100)(12, 54, 84, 114, 24, 42, 72, 102)(14, 56, 86, 116, 26, 44, 74, 104)(15, 52, 82, 112, 22, 45, 75, 105)(16, 55, 85, 115, 25, 46, 76, 106)(18, 50, 80, 110, 20, 48, 78, 108)(19, 53, 83, 113, 23, 49, 79, 109)(27, 59, 89, 119, 29, 57, 87, 117)(28, 60, 90, 120, 30, 58, 88, 118) L = (1, 63)(2, 65)(3, 68)(4, 61)(5, 72)(6, 62)(7, 75)(8, 78)(9, 79)(10, 64)(11, 82)(12, 80)(13, 85)(14, 66)(15, 74)(16, 67)(17, 81)(18, 73)(19, 88)(20, 69)(21, 87)(22, 70)(23, 71)(24, 86)(25, 90)(26, 89)(27, 76)(28, 77)(29, 83)(30, 84)(31, 93)(32, 95)(33, 98)(34, 91)(35, 102)(36, 92)(37, 105)(38, 108)(39, 109)(40, 94)(41, 112)(42, 110)(43, 115)(44, 96)(45, 104)(46, 97)(47, 111)(48, 103)(49, 118)(50, 99)(51, 117)(52, 100)(53, 101)(54, 116)(55, 120)(56, 119)(57, 106)(58, 107)(59, 113)(60, 114) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.46 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C30 (small group id <30, 4>) Aut = C6 x D10 (small group id <60, 10>) |r| :: 2 Presentation :: [ Z^2, S^2, (B^-1, A), S * B * S * A, B * Z * B^-1 * Z, (S * Z)^2, A^-1 * Z * A * Z, A * B * A^3, B^4 * A, A^-1 * B^2 * A^-2 * B ] Map:: non-degenerate R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 37, 67, 97, 7, 33, 63, 93)(4, 38, 68, 98, 8, 34, 64, 94)(5, 39, 69, 99, 9, 35, 65, 95)(6, 40, 70, 100, 10, 36, 66, 96)(11, 49, 79, 109, 19, 41, 71, 101)(12, 50, 80, 110, 20, 42, 72, 102)(13, 51, 81, 111, 21, 43, 73, 103)(14, 52, 82, 112, 22, 44, 74, 104)(15, 53, 83, 113, 23, 45, 75, 105)(16, 54, 84, 114, 24, 46, 76, 106)(17, 55, 85, 115, 25, 47, 77, 107)(18, 56, 86, 116, 26, 48, 78, 108)(27, 59, 89, 119, 29, 57, 87, 117)(28, 60, 90, 120, 30, 58, 88, 118) L = (1, 63)(2, 67)(3, 71)(4, 72)(5, 61)(6, 73)(7, 79)(8, 80)(9, 62)(10, 81)(11, 77)(12, 76)(13, 87)(14, 78)(15, 64)(16, 65)(17, 66)(18, 88)(19, 85)(20, 84)(21, 89)(22, 86)(23, 68)(24, 69)(25, 70)(26, 90)(27, 74)(28, 75)(29, 82)(30, 83)(31, 96)(32, 100)(33, 103)(34, 91)(35, 107)(36, 108)(37, 111)(38, 92)(39, 115)(40, 116)(41, 117)(42, 93)(43, 118)(44, 94)(45, 95)(46, 101)(47, 104)(48, 102)(49, 119)(50, 97)(51, 120)(52, 98)(53, 99)(54, 109)(55, 112)(56, 110)(57, 105)(58, 106)(59, 113)(60, 114) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.47 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C3 x D10 (small group id <30, 2>) Aut = C6 x D10 (small group id <60, 10>) |r| :: 2 Presentation :: [ Z^2, S^2, A * B, S * B * S * A, (S * Z)^2, A^2 * Z * B * A^-1 * Z, B^3 * A^-3, B^2 * Z * B^-2 * Z, A * Z * B * Z * A * Z * B^-1 * Z * B^-1 * Z ] Map:: non-degenerate R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 37, 67, 97, 7, 33, 63, 93)(4, 39, 69, 99, 9, 34, 64, 94)(5, 41, 71, 101, 11, 35, 65, 95)(6, 43, 73, 103, 13, 36, 66, 96)(8, 42, 72, 102, 12, 38, 68, 98)(10, 44, 74, 104, 14, 40, 70, 100)(15, 53, 83, 113, 23, 45, 75, 105)(16, 55, 85, 115, 25, 46, 76, 106)(17, 54, 84, 114, 24, 47, 77, 107)(18, 56, 86, 116, 26, 48, 78, 108)(19, 57, 87, 117, 27, 49, 79, 109)(20, 59, 89, 119, 29, 50, 80, 110)(21, 58, 88, 118, 28, 51, 81, 111)(22, 60, 90, 120, 30, 52, 82, 112) L = (1, 63)(2, 65)(3, 68)(4, 61)(5, 72)(6, 62)(7, 75)(8, 77)(9, 76)(10, 64)(11, 79)(12, 81)(13, 80)(14, 66)(15, 84)(16, 67)(17, 70)(18, 69)(19, 88)(20, 71)(21, 74)(22, 73)(23, 89)(24, 78)(25, 90)(26, 87)(27, 85)(28, 82)(29, 86)(30, 83)(31, 93)(32, 95)(33, 98)(34, 91)(35, 102)(36, 92)(37, 105)(38, 107)(39, 106)(40, 94)(41, 109)(42, 111)(43, 110)(44, 96)(45, 114)(46, 97)(47, 100)(48, 99)(49, 118)(50, 101)(51, 104)(52, 103)(53, 119)(54, 108)(55, 120)(56, 117)(57, 115)(58, 112)(59, 116)(60, 113) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.48 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C3 x D10 (small group id <30, 2>) Aut = C6 x D10 (small group id <60, 10>) |r| :: 2 Presentation :: [ Z^2, S^2, B^-1 * A^-1, (S * Z)^2, S * A * S * B, B^2 * A^-1 * Z * A * Z * A^-1, A^2 * Z * B * Z * B^-2 ] Map:: non-degenerate R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 37, 67, 97, 7, 33, 63, 93)(4, 39, 69, 99, 9, 34, 64, 94)(5, 41, 71, 101, 11, 35, 65, 95)(6, 43, 73, 103, 13, 36, 66, 96)(8, 47, 77, 107, 17, 38, 68, 98)(10, 51, 81, 111, 21, 40, 70, 100)(12, 54, 84, 114, 24, 42, 72, 102)(14, 56, 86, 116, 26, 44, 74, 104)(15, 53, 83, 113, 23, 45, 75, 105)(16, 52, 82, 112, 22, 46, 76, 106)(18, 49, 79, 109, 19, 48, 78, 108)(20, 55, 85, 115, 25, 50, 80, 110)(27, 60, 90, 120, 30, 57, 87, 117)(28, 59, 89, 119, 29, 58, 88, 118) L = (1, 63)(2, 65)(3, 68)(4, 61)(5, 72)(6, 62)(7, 75)(8, 78)(9, 79)(10, 64)(11, 83)(12, 76)(13, 82)(14, 66)(15, 87)(16, 67)(17, 88)(18, 71)(19, 74)(20, 69)(21, 77)(22, 70)(23, 89)(24, 90)(25, 73)(26, 84)(27, 81)(28, 80)(29, 86)(30, 85)(31, 93)(32, 95)(33, 98)(34, 91)(35, 102)(36, 92)(37, 105)(38, 108)(39, 109)(40, 94)(41, 113)(42, 106)(43, 112)(44, 96)(45, 117)(46, 97)(47, 118)(48, 101)(49, 104)(50, 99)(51, 107)(52, 100)(53, 119)(54, 120)(55, 103)(56, 114)(57, 111)(58, 110)(59, 116)(60, 115) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.49 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Z^2, S^2, B * A^-1, S * B * S * A, (S * Z)^2, A * Z * A^-1 * Z, A^15 ] Map:: R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 35, 65, 95, 5, 33, 63, 93)(4, 36, 66, 96, 6, 34, 64, 94)(7, 39, 69, 99, 9, 37, 67, 97)(8, 40, 70, 100, 10, 38, 68, 98)(11, 43, 73, 103, 13, 41, 71, 101)(12, 44, 74, 104, 14, 42, 72, 102)(15, 47, 77, 107, 17, 45, 75, 105)(16, 48, 78, 108, 18, 46, 76, 106)(19, 51, 81, 111, 21, 49, 79, 109)(20, 52, 82, 112, 22, 50, 80, 110)(23, 55, 85, 115, 25, 53, 83, 113)(24, 56, 86, 116, 26, 54, 84, 114)(27, 59, 89, 119, 29, 57, 87, 117)(28, 60, 90, 120, 30, 58, 88, 118) 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, 88)(28, 84)(29, 90)(30, 86)(31, 94)(32, 96)(33, 91)(34, 98)(35, 92)(36, 100)(37, 93)(38, 102)(39, 95)(40, 104)(41, 97)(42, 106)(43, 99)(44, 108)(45, 101)(46, 110)(47, 103)(48, 112)(49, 105)(50, 114)(51, 107)(52, 116)(53, 109)(54, 118)(55, 111)(56, 120)(57, 113)(58, 117)(59, 115)(60, 119) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.50 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Z^2, S^2, A^2, B^-1 * A, S * B * S * A, (S * Z)^2, (A * Z)^15 ] Map:: R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 35, 65, 95, 5, 33, 63, 93)(4, 36, 66, 96, 6, 34, 64, 94)(7, 39, 69, 99, 9, 37, 67, 97)(8, 40, 70, 100, 10, 38, 68, 98)(11, 43, 73, 103, 13, 41, 71, 101)(12, 44, 74, 104, 14, 42, 72, 102)(15, 51, 81, 111, 21, 45, 75, 105)(16, 52, 82, 112, 22, 46, 76, 106)(17, 53, 83, 113, 23, 47, 77, 107)(18, 54, 84, 114, 24, 48, 78, 108)(19, 55, 85, 115, 25, 49, 79, 109)(20, 56, 86, 116, 26, 50, 80, 110)(27, 59, 89, 119, 29, 57, 87, 117)(28, 60, 90, 120, 30, 58, 88, 118) L = (1, 63)(2, 64)(3, 61)(4, 62)(5, 67)(6, 68)(7, 65)(8, 66)(9, 71)(10, 72)(11, 69)(12, 70)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 90)(30, 89)(31, 93)(32, 94)(33, 91)(34, 92)(35, 97)(36, 98)(37, 95)(38, 96)(39, 101)(40, 102)(41, 99)(42, 100)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 103)(52, 104)(53, 105)(54, 106)(55, 107)(56, 108)(57, 109)(58, 110)(59, 120)(60, 119) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.51 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Z^2, S^2, A^-1 * B^-1, S * A * S * B, (S * Z)^2, A * Z * B^-1 * Z, A^8 * B^-7 ] Map:: non-degenerate R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 36, 66, 96, 6, 33, 63, 93)(4, 35, 65, 95, 5, 34, 64, 94)(7, 40, 70, 100, 10, 37, 67, 97)(8, 39, 69, 99, 9, 38, 68, 98)(11, 44, 74, 104, 14, 41, 71, 101)(12, 43, 73, 103, 13, 42, 72, 102)(15, 48, 78, 108, 18, 45, 75, 105)(16, 47, 77, 107, 17, 46, 76, 106)(19, 52, 82, 112, 22, 49, 79, 109)(20, 51, 81, 111, 21, 50, 80, 110)(23, 56, 86, 116, 26, 53, 83, 113)(24, 55, 85, 115, 25, 54, 84, 114)(27, 60, 90, 120, 30, 57, 87, 117)(28, 59, 89, 119, 29, 58, 88, 118) 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, 88)(28, 84)(29, 90)(30, 86)(31, 93)(32, 95)(33, 97)(34, 91)(35, 99)(36, 92)(37, 101)(38, 94)(39, 103)(40, 96)(41, 105)(42, 98)(43, 107)(44, 100)(45, 109)(46, 102)(47, 111)(48, 104)(49, 113)(50, 106)(51, 115)(52, 108)(53, 117)(54, 110)(55, 119)(56, 112)(57, 118)(58, 114)(59, 120)(60, 116) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.52 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C30 (small group id <30, 4>) Aut = C30 x C2 (small group id <60, 13>) |r| :: 2 Presentation :: [ Z^2, S^2, B^-1 * A^-1, (S * Z)^2, S * B * S * A, A * Z * A^-1 * Z, B * Z * B^-1 * Z, A^8 * B^-7 ] Map:: non-degenerate R = (1, 32, 62, 92, 2, 31, 61, 91)(3, 35, 65, 95, 5, 33, 63, 93)(4, 36, 66, 96, 6, 34, 64, 94)(7, 39, 69, 99, 9, 37, 67, 97)(8, 40, 70, 100, 10, 38, 68, 98)(11, 43, 73, 103, 13, 41, 71, 101)(12, 44, 74, 104, 14, 42, 72, 102)(15, 47, 77, 107, 17, 45, 75, 105)(16, 48, 78, 108, 18, 46, 76, 106)(19, 51, 81, 111, 21, 49, 79, 109)(20, 52, 82, 112, 22, 50, 80, 110)(23, 55, 85, 115, 25, 53, 83, 113)(24, 56, 86, 116, 26, 54, 84, 114)(27, 59, 89, 119, 29, 57, 87, 117)(28, 60, 90, 120, 30, 58, 88, 118) 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, 88)(28, 84)(29, 90)(30, 86)(31, 93)(32, 95)(33, 97)(34, 91)(35, 99)(36, 92)(37, 101)(38, 94)(39, 103)(40, 96)(41, 105)(42, 98)(43, 107)(44, 100)(45, 109)(46, 102)(47, 111)(48, 104)(49, 113)(50, 106)(51, 115)(52, 108)(53, 117)(54, 110)(55, 119)(56, 112)(57, 118)(58, 114)(59, 120)(60, 116) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.53 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^8, (Y3 * Y2^-1)^17, (Y3^-1 * Y1^-1)^17 ] Map:: R = (1, 18, 2, 19, 6, 23, 10, 27, 14, 31, 17, 34, 13, 30, 9, 26, 5, 22, 3, 20, 7, 24, 11, 28, 15, 32, 16, 33, 12, 29, 8, 25, 4, 21)(35, 52, 37, 54, 36, 53, 41, 58, 40, 57, 45, 62, 44, 61, 49, 66, 48, 65, 50, 67, 51, 68, 46, 63, 47, 64, 42, 59, 43, 60, 38, 55, 39, 56) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.54 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-8, (Y3^-1 * Y1^-1)^17, (Y3 * Y2^-1)^17 ] Map:: R = (1, 18, 2, 19, 6, 23, 10, 27, 14, 31, 16, 33, 12, 29, 8, 25, 3, 20, 5, 22, 7, 24, 11, 28, 15, 32, 17, 34, 13, 30, 9, 26, 4, 21)(35, 52, 37, 54, 38, 55, 42, 59, 43, 60, 46, 63, 47, 64, 50, 67, 51, 68, 48, 65, 49, 66, 44, 61, 45, 62, 40, 57, 41, 58, 36, 53, 39, 56) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.55 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y1^5, (Y3 * Y2^-1)^17, (Y3^-1 * Y1^-1)^17 ] Map:: R = (1, 18, 2, 19, 6, 23, 12, 29, 15, 32, 9, 26, 3, 20, 7, 24, 13, 30, 17, 34, 11, 28, 5, 22, 8, 25, 14, 31, 16, 33, 10, 27, 4, 21)(35, 52, 37, 54, 42, 59, 36, 53, 41, 58, 48, 65, 40, 57, 47, 64, 50, 67, 46, 63, 51, 68, 44, 61, 49, 66, 45, 62, 38, 55, 43, 60, 39, 56) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.56 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^-3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^-1 * Y1^-5, (Y3 * Y2^-1)^17, (Y3^-1 * Y1^-1)^17 ] Map:: R = (1, 18, 2, 19, 6, 23, 12, 29, 15, 32, 9, 26, 5, 22, 8, 25, 14, 31, 16, 33, 10, 27, 3, 20, 7, 24, 13, 30, 17, 34, 11, 28, 4, 21)(35, 52, 37, 54, 43, 60, 38, 55, 44, 61, 49, 66, 45, 62, 50, 67, 46, 63, 51, 68, 48, 65, 40, 57, 47, 64, 42, 59, 36, 53, 41, 58, 39, 56) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.57 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2 * Y1^-1 * Y2^3, Y1 * Y2 * Y1^3, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^17, (Y3 * Y2^-1)^17 ] Map:: R = (1, 18, 2, 19, 6, 23, 12, 29, 5, 22, 8, 25, 14, 31, 17, 34, 13, 30, 9, 26, 15, 32, 16, 33, 10, 27, 3, 20, 7, 24, 11, 28, 4, 21)(35, 52, 37, 54, 43, 60, 42, 59, 36, 53, 41, 58, 49, 66, 48, 65, 40, 57, 45, 62, 50, 67, 51, 68, 46, 63, 38, 55, 44, 61, 47, 64, 39, 56) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.58 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y1^-1 * Y2^-1 * Y1^-2 * Y2^-1, Y2^4 * Y1^-1 * Y2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^17, (Y3^-1 * Y1^-1)^17 ] Map:: R = (1, 18, 2, 19, 6, 23, 13, 30, 15, 32, 17, 34, 10, 27, 3, 20, 7, 24, 12, 29, 5, 22, 8, 25, 14, 31, 16, 33, 9, 26, 11, 28, 4, 21)(35, 52, 37, 54, 43, 60, 49, 66, 42, 59, 36, 53, 41, 58, 45, 62, 51, 68, 48, 65, 40, 57, 46, 63, 38, 55, 44, 61, 50, 67, 47, 64, 39, 56) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.59 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y2 * Y1^-1 * Y2 * Y1^-2, Y2^-1 * Y1^-1 * Y2^-4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^17, (Y3 * Y2^-1)^17 ] Map:: R = (1, 18, 2, 19, 6, 23, 9, 26, 15, 32, 17, 34, 12, 29, 5, 22, 8, 25, 10, 27, 3, 20, 7, 24, 14, 31, 16, 33, 13, 30, 11, 28, 4, 21)(35, 52, 37, 54, 43, 60, 50, 67, 46, 63, 38, 55, 44, 61, 40, 57, 48, 65, 51, 68, 45, 62, 42, 59, 36, 53, 41, 58, 49, 66, 47, 64, 39, 56) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.60 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y1 * Y3^-2, (R * Y3)^2, (R * Y1)^2, Y1^4 * Y3 * Y1^4, Y2^17, (Y3^-1 * Y1^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 10, 27, 14, 31, 16, 33, 12, 29, 8, 25, 3, 20, 4, 21, 7, 24, 11, 28, 15, 32, 17, 34, 13, 30, 9, 26, 5, 22)(35, 52, 37, 54, 39, 56, 42, 59, 43, 60, 46, 63, 47, 64, 50, 67, 51, 68, 48, 65, 49, 66, 44, 61, 45, 62, 40, 57, 41, 58, 36, 53, 38, 55) L = (1, 38)(2, 41)(3, 35)(4, 36)(5, 37)(6, 45)(7, 40)(8, 39)(9, 42)(10, 49)(11, 44)(12, 43)(13, 46)(14, 51)(15, 48)(16, 47)(17, 50)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.79 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.61 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y2 * Y3^-1 * Y1 * Y2, Y2 * Y1 * Y3^-1 * Y2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y1^3 * Y2^-1 * Y1 * Y2^-1 * Y1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 12, 29, 15, 32, 9, 26, 4, 21, 8, 25, 14, 31, 16, 33, 10, 27, 3, 20, 7, 24, 13, 30, 17, 34, 11, 28, 5, 22)(35, 52, 37, 54, 43, 60, 39, 56, 44, 61, 49, 66, 45, 62, 50, 67, 46, 63, 51, 68, 48, 65, 40, 57, 47, 64, 42, 59, 36, 53, 41, 58, 38, 55) L = (1, 38)(2, 42)(3, 35)(4, 41)(5, 43)(6, 48)(7, 36)(8, 47)(9, 37)(10, 39)(11, 49)(12, 50)(13, 40)(14, 51)(15, 44)(16, 45)(17, 46)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.96 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.62 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (Y2^-1, Y1^-1), Y2 * Y1^-1 * Y2 * Y3^-2, Y3 * Y1 * Y3 * Y2^-2, Y1^2 * Y3^-1 * Y1^2, Y2^17, Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y3^-1, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 12, 29, 4, 21, 8, 25, 14, 31, 17, 34, 11, 28, 9, 26, 15, 32, 16, 33, 10, 27, 3, 20, 7, 24, 13, 30, 5, 22)(35, 52, 37, 54, 43, 60, 42, 59, 36, 53, 41, 58, 49, 66, 48, 65, 40, 57, 47, 64, 50, 67, 51, 68, 46, 63, 39, 56, 44, 61, 45, 62, 38, 55) L = (1, 38)(2, 42)(3, 35)(4, 45)(5, 46)(6, 48)(7, 36)(8, 43)(9, 37)(10, 39)(11, 44)(12, 51)(13, 40)(14, 49)(15, 41)(16, 47)(17, 50)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.69 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.63 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, Y3^-2 * Y2^-2, R * Y2 * R * Y3^-1, (Y3^-1, Y1^-1), (R * Y1)^2, (Y2^-1, Y1^-1), Y2 * Y1 * Y2^2 * Y3^-1, Y2^-1 * Y1^4, Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2^-1, (Y1^-1 * Y3^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 10, 27, 3, 20, 7, 24, 14, 31, 16, 33, 9, 26, 11, 28, 15, 32, 17, 34, 12, 29, 4, 21, 8, 25, 13, 30, 5, 22)(35, 52, 37, 54, 43, 60, 46, 63, 39, 56, 44, 61, 50, 67, 51, 68, 47, 64, 40, 57, 48, 65, 49, 66, 42, 59, 36, 53, 41, 58, 45, 62, 38, 55) L = (1, 38)(2, 42)(3, 35)(4, 45)(5, 46)(6, 47)(7, 36)(8, 49)(9, 37)(10, 39)(11, 41)(12, 43)(13, 51)(14, 40)(15, 48)(16, 44)(17, 50)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.90 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.64 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y1 * Y2 * Y1^-1 * Y3, (R * Y3)^2, Y3^-1 * Y1^-1 * Y2^-1 * Y1, (R * Y1)^2, Y1^2 * Y3^-1 * Y1 * Y3^-1, Y1 * Y2^-1 * Y3 * Y1^-1 * Y3^-2, Y3^3 * Y1 * Y2^-2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y1, Y3^-12 * Y1, (Y1^-1 * Y2)^17, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 11, 28, 15, 32, 17, 34, 10, 27, 3, 20, 7, 24, 12, 29, 4, 21, 8, 25, 14, 31, 16, 33, 9, 26, 13, 30, 5, 22)(35, 52, 37, 54, 43, 60, 49, 66, 42, 59, 36, 53, 41, 58, 47, 64, 51, 68, 48, 65, 40, 57, 46, 63, 39, 56, 44, 61, 50, 67, 45, 62, 38, 55) L = (1, 38)(2, 42)(3, 35)(4, 45)(5, 46)(6, 48)(7, 36)(8, 49)(9, 37)(10, 39)(11, 50)(12, 40)(13, 41)(14, 51)(15, 43)(16, 44)(17, 47)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.101 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.65 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, (Y1, Y3^-1), Y2^-1 * Y1^2 * Y2^-1 * Y1, Y3 * Y1 * Y3 * Y1^2, Y3^-5 * Y1, Y1 * Y3^-2 * Y1^-1 * Y2^-2, Y3^-1 * Y1^7, Y3^-3 * Y2^14, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 9, 26, 15, 32, 17, 34, 12, 29, 4, 21, 8, 25, 10, 27, 3, 20, 7, 24, 14, 31, 16, 33, 11, 28, 13, 30, 5, 22)(35, 52, 37, 54, 43, 60, 50, 67, 46, 63, 39, 56, 44, 61, 40, 57, 48, 65, 51, 68, 47, 64, 42, 59, 36, 53, 41, 58, 49, 66, 45, 62, 38, 55) L = (1, 38)(2, 42)(3, 35)(4, 45)(5, 46)(6, 44)(7, 36)(8, 47)(9, 37)(10, 39)(11, 49)(12, 50)(13, 51)(14, 40)(15, 41)(16, 43)(17, 48)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.91 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.66 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, Y1 * Y3^-1 * Y1^-1 * Y2^-1, Y2 * Y1^-3, (Y3^-1, Y1^-1), (R * Y1)^2, R * Y2 * R * Y3^-1, Y2 * Y1^-1 * Y2^5, (Y1^-1 * Y3^-1)^17, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 3, 20, 7, 24, 12, 29, 9, 26, 13, 30, 16, 33, 15, 32, 17, 34, 10, 27, 14, 31, 11, 28, 4, 21, 8, 25, 5, 22)(35, 52, 37, 54, 43, 60, 49, 66, 48, 65, 42, 59, 36, 53, 41, 58, 47, 64, 51, 68, 45, 62, 39, 56, 40, 57, 46, 63, 50, 67, 44, 61, 38, 55) L = (1, 38)(2, 42)(3, 35)(4, 44)(5, 45)(6, 39)(7, 36)(8, 48)(9, 37)(10, 50)(11, 51)(12, 40)(13, 41)(14, 49)(15, 43)(16, 46)(17, 47)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.85 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.67 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y3 * Y1^-3, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, Y2 * Y1 * Y2^2 * Y3^-3, Y3 * Y1^-1 * Y3^5, Y2^17, (Y3 * Y2^-1)^17, (Y3^-1 * Y1^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 4, 21, 8, 25, 12, 29, 11, 28, 14, 31, 15, 32, 17, 34, 16, 33, 9, 26, 13, 30, 10, 27, 3, 20, 7, 24, 5, 22)(35, 52, 37, 54, 43, 60, 49, 66, 46, 63, 40, 57, 39, 56, 44, 61, 50, 67, 48, 65, 42, 59, 36, 53, 41, 58, 47, 64, 51, 68, 45, 62, 38, 55) L = (1, 38)(2, 42)(3, 35)(4, 45)(5, 40)(6, 46)(7, 36)(8, 48)(9, 37)(10, 39)(11, 51)(12, 49)(13, 41)(14, 50)(15, 43)(16, 44)(17, 47)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.98 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.68 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, (R * Y1)^2, (Y2^-1, Y1^-1), (Y3^-1, Y1^-1), (R * Y3)^2, Y1 * Y2 * Y1 * Y2^2, Y1^-1 * Y2 * Y1^-4, (Y1^-1 * Y3^-1)^17, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 14, 31, 10, 27, 3, 20, 7, 24, 11, 28, 16, 33, 17, 34, 9, 26, 12, 29, 4, 21, 8, 25, 15, 32, 13, 30, 5, 22)(35, 52, 37, 54, 43, 60, 47, 64, 48, 65, 50, 67, 42, 59, 36, 53, 41, 58, 46, 63, 39, 56, 44, 61, 51, 68, 49, 66, 40, 57, 45, 62, 38, 55) L = (1, 38)(2, 42)(3, 35)(4, 45)(5, 46)(6, 49)(7, 36)(8, 50)(9, 37)(10, 39)(11, 40)(12, 41)(13, 43)(14, 47)(15, 51)(16, 48)(17, 44)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.84 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.69 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3^-1, (Y3^-1, Y1^-1), (Y2^-1, Y1^-1), Y2^-1 * Y1 * Y2^-2 * Y1, Y1 * Y3 * Y1 * Y3^2, Y1^-1 * Y3 * Y1^-4, Y1^-1 * Y3^7, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 14, 31, 12, 29, 4, 21, 8, 25, 9, 26, 16, 33, 17, 34, 11, 28, 10, 27, 3, 20, 7, 24, 15, 32, 13, 30, 5, 22)(35, 52, 37, 54, 43, 60, 40, 57, 49, 66, 51, 68, 46, 63, 39, 56, 44, 61, 42, 59, 36, 53, 41, 58, 50, 67, 48, 65, 47, 64, 45, 62, 38, 55) L = (1, 38)(2, 42)(3, 35)(4, 45)(5, 46)(6, 43)(7, 36)(8, 44)(9, 37)(10, 39)(11, 47)(12, 51)(13, 48)(14, 50)(15, 40)(16, 41)(17, 49)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.62 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.70 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y1^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), Y1 * Y2^-4 * Y3^4, Y2^9 * Y1, (Y3 * Y2^-1)^17, (Y3^-1 * Y1^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 4, 21, 6, 23, 9, 26, 10, 27, 13, 30, 14, 31, 17, 34, 15, 32, 16, 33, 11, 28, 12, 29, 7, 24, 8, 25, 3, 20, 5, 22)(35, 52, 37, 54, 41, 58, 45, 62, 49, 66, 48, 65, 44, 61, 40, 57, 36, 53, 39, 56, 42, 59, 46, 63, 50, 67, 51, 68, 47, 64, 43, 60, 38, 55) L = (1, 38)(2, 40)(3, 35)(4, 43)(5, 36)(6, 44)(7, 37)(8, 39)(9, 47)(10, 48)(11, 41)(12, 42)(13, 51)(14, 49)(15, 45)(16, 46)(17, 50)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.94 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.71 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y2 * Y1^-2, (R * Y1)^2, (R * Y3)^2, (Y1, Y3^-1), Y1 * Y2^8, (Y1^-1 * Y3^-1)^17, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 3, 20, 6, 23, 7, 24, 10, 27, 11, 28, 14, 31, 15, 32, 16, 33, 17, 34, 12, 29, 13, 30, 8, 25, 9, 26, 4, 21, 5, 22)(35, 52, 37, 54, 41, 58, 45, 62, 49, 66, 51, 68, 47, 64, 43, 60, 39, 56, 36, 53, 40, 57, 44, 61, 48, 65, 50, 67, 46, 63, 42, 59, 38, 55) L = (1, 38)(2, 39)(3, 35)(4, 42)(5, 43)(6, 36)(7, 37)(8, 46)(9, 47)(10, 40)(11, 41)(12, 50)(13, 51)(14, 44)(15, 45)(16, 48)(17, 49)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.74 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.72 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y2, Y2^2 * Y3^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^3 * Y3 * Y1^2, Y3^7 * Y1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 14, 31, 13, 30, 7, 24, 3, 20, 9, 26, 15, 32, 17, 34, 12, 29, 6, 23, 4, 21, 10, 27, 16, 33, 11, 28, 5, 22)(35, 52, 37, 54, 38, 55, 36, 53, 43, 60, 44, 61, 42, 59, 49, 66, 50, 67, 48, 65, 51, 68, 45, 62, 47, 64, 46, 63, 39, 56, 41, 58, 40, 57) L = (1, 38)(2, 44)(3, 36)(4, 43)(5, 40)(6, 37)(7, 35)(8, 50)(9, 42)(10, 49)(11, 46)(12, 41)(13, 39)(14, 45)(15, 48)(16, 51)(17, 47)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.76 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.73 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y3, Y1^-1 * Y3^2, (R * Y2)^2, (Y2^-1, Y1), (R * Y3)^2, (R * Y1)^2, Y1^-2 * Y2^-1 * Y1^-2, Y2^-1 * Y1^-4, (Y3^-1 * Y1^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 14, 31, 6, 23, 11, 28, 17, 34, 15, 32, 7, 24, 4, 21, 10, 27, 16, 33, 12, 29, 3, 20, 9, 26, 13, 30, 5, 22)(35, 52, 37, 54, 38, 55, 45, 62, 36, 53, 43, 60, 44, 61, 51, 68, 42, 59, 47, 64, 50, 67, 49, 66, 48, 65, 39, 56, 46, 63, 41, 58, 40, 57) L = (1, 38)(2, 44)(3, 45)(4, 36)(5, 41)(6, 37)(7, 35)(8, 50)(9, 51)(10, 42)(11, 43)(12, 40)(13, 49)(14, 46)(15, 39)(16, 48)(17, 47)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.78 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.74 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-2, Y1 * Y3^2, (R * Y2)^2, (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1^-3, Y3 * Y2 * Y1^-1 * Y3 * Y1^-2 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 13, 30, 3, 20, 9, 26, 16, 33, 14, 31, 4, 21, 7, 24, 11, 28, 17, 34, 12, 29, 6, 23, 10, 27, 15, 32, 5, 22)(35, 52, 37, 54, 38, 55, 46, 63, 39, 56, 47, 64, 48, 65, 51, 68, 49, 66, 42, 59, 50, 67, 45, 62, 44, 61, 36, 53, 43, 60, 41, 58, 40, 57) L = (1, 38)(2, 41)(3, 46)(4, 39)(5, 48)(6, 37)(7, 35)(8, 45)(9, 40)(10, 43)(11, 36)(12, 47)(13, 51)(14, 49)(15, 50)(16, 44)(17, 42)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.71 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.75 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y3, Y1^-2 * Y3^-1 * Y1^-1, Y1^-1 * Y3^2 * Y2, (Y1, Y3^-1), (R * Y2)^2, (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y2 * Y1^2 * Y2 * Y1 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 7, 24, 12, 29, 17, 34, 13, 30, 3, 20, 9, 26, 15, 32, 6, 23, 11, 28, 16, 33, 14, 31, 4, 21, 10, 27, 5, 22)(35, 52, 37, 54, 38, 55, 46, 63, 45, 62, 36, 53, 43, 60, 44, 61, 51, 68, 50, 67, 42, 59, 49, 66, 39, 56, 47, 64, 48, 65, 41, 58, 40, 57) L = (1, 38)(2, 44)(3, 46)(4, 45)(5, 48)(6, 37)(7, 35)(8, 39)(9, 51)(10, 50)(11, 43)(12, 36)(13, 41)(14, 40)(15, 47)(16, 49)(17, 42)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.80 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.76 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3 * Y2^-1, (Y2^-1, Y1), Y3 * Y1^-3, Y3^-2 * Y1^-1 * Y2^-1, Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1, (Y3^-1, Y1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y3^3 * Y1^-1 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 4, 21, 10, 27, 17, 34, 15, 32, 6, 23, 11, 28, 14, 31, 3, 20, 9, 26, 16, 33, 13, 30, 7, 24, 12, 29, 5, 22)(35, 52, 37, 54, 38, 55, 47, 64, 49, 66, 39, 56, 48, 65, 42, 59, 50, 67, 51, 68, 46, 63, 45, 62, 36, 53, 43, 60, 44, 61, 41, 58, 40, 57) L = (1, 38)(2, 44)(3, 47)(4, 49)(5, 42)(6, 37)(7, 35)(8, 51)(9, 41)(10, 40)(11, 43)(12, 36)(13, 39)(14, 50)(15, 48)(16, 46)(17, 45)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.72 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.77 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y2, (Y1, Y2^-1), Y1^-1 * Y3^3, Y2^-1 * Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y3 * Y1 * Y3 * Y2 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 3, 20, 9, 26, 14, 31, 4, 21, 10, 27, 17, 34, 13, 30, 16, 33, 7, 24, 12, 29, 15, 32, 6, 23, 11, 28, 5, 22)(35, 52, 37, 54, 38, 55, 47, 64, 46, 63, 45, 62, 36, 53, 43, 60, 44, 61, 50, 67, 49, 66, 39, 56, 42, 59, 48, 65, 51, 68, 41, 58, 40, 57) L = (1, 38)(2, 44)(3, 47)(4, 46)(5, 48)(6, 37)(7, 35)(8, 51)(9, 50)(10, 49)(11, 43)(12, 36)(13, 45)(14, 41)(15, 42)(16, 39)(17, 40)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.81 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.78 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y2, (Y1, Y3^-1), (Y3^-1, Y2), Y2^-1 * Y1^-3, Y1 * Y3^3, (Y1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), Y3^-1 * Y1 * Y3^-1 * Y1 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 6, 23, 11, 28, 15, 32, 7, 24, 12, 29, 13, 30, 17, 34, 16, 33, 4, 21, 10, 27, 14, 31, 3, 20, 9, 26, 5, 22)(35, 52, 37, 54, 38, 55, 47, 64, 49, 66, 42, 59, 39, 56, 48, 65, 50, 67, 46, 63, 45, 62, 36, 53, 43, 60, 44, 61, 51, 68, 41, 58, 40, 57) L = (1, 38)(2, 44)(3, 47)(4, 49)(5, 50)(6, 37)(7, 35)(8, 48)(9, 51)(10, 41)(11, 43)(12, 36)(13, 42)(14, 46)(15, 39)(16, 45)(17, 40)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.73 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.79 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, (Y1, Y2^-1), Y1 * Y3 * Y1 * Y2, Y2 * Y1^2 * Y3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-1 * Y3^-2, Y2^-1 * Y3^-2 * Y1 * Y3^-1, Y2^-1 * Y1 * Y3^-3 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 15, 32, 14, 31, 3, 20, 9, 26, 7, 24, 12, 29, 16, 33, 4, 21, 10, 27, 6, 23, 11, 28, 17, 34, 13, 30, 5, 22)(35, 52, 37, 54, 38, 55, 47, 64, 49, 66, 46, 63, 45, 62, 36, 53, 43, 60, 44, 61, 39, 56, 48, 65, 50, 67, 51, 68, 42, 59, 41, 58, 40, 57) L = (1, 38)(2, 44)(3, 47)(4, 49)(5, 50)(6, 37)(7, 35)(8, 40)(9, 39)(10, 48)(11, 43)(12, 36)(13, 46)(14, 51)(15, 45)(16, 42)(17, 41)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.60 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.80 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, (Y1^-1, Y3^-1), Y1^2 * Y3^-1 * Y2^-1, Y2^-1 * Y1 * Y3^-1 * Y1, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y3 * Y2 * Y3^2, Y1^12 * Y2^-1 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 17, 34, 15, 32, 6, 23, 11, 28, 4, 21, 10, 27, 16, 33, 7, 24, 12, 29, 3, 20, 9, 26, 13, 30, 14, 31, 5, 22)(35, 52, 37, 54, 38, 55, 42, 59, 47, 64, 50, 67, 49, 66, 39, 56, 46, 63, 45, 62, 36, 53, 43, 60, 44, 61, 51, 68, 48, 65, 41, 58, 40, 57) L = (1, 38)(2, 44)(3, 42)(4, 47)(5, 45)(6, 37)(7, 35)(8, 50)(9, 51)(10, 48)(11, 43)(12, 36)(13, 49)(14, 40)(15, 46)(16, 39)(17, 41)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.75 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.81 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-2, Y2^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y1), Y3^2 * Y1 * Y3^2 ] Map:: non-degenerate R = (1, 18, 2, 19, 3, 20, 8, 25, 4, 21, 9, 26, 11, 28, 16, 33, 12, 29, 15, 32, 17, 34, 14, 31, 13, 30, 7, 24, 10, 27, 6, 23, 5, 22)(35, 52, 37, 54, 38, 55, 45, 62, 46, 63, 51, 68, 47, 64, 44, 61, 39, 56, 36, 53, 42, 59, 43, 60, 50, 67, 49, 66, 48, 65, 41, 58, 40, 57) L = (1, 38)(2, 43)(3, 45)(4, 46)(5, 42)(6, 37)(7, 35)(8, 50)(9, 49)(10, 36)(11, 51)(12, 47)(13, 39)(14, 40)(15, 41)(16, 48)(17, 44)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.77 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.82 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, Y1 * Y3^-2, Y1^-1 * Y2^-1 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-2 * Y2 * Y1^-2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 12, 29, 3, 20, 9, 26, 16, 33, 15, 32, 7, 24, 4, 21, 10, 27, 17, 34, 13, 30, 6, 23, 11, 28, 14, 31, 5, 22)(35, 52, 37, 54, 41, 58, 47, 64, 39, 56, 46, 63, 49, 66, 51, 68, 48, 65, 42, 59, 50, 67, 44, 61, 45, 62, 36, 53, 43, 60, 38, 55, 40, 57) L = (1, 38)(2, 44)(3, 40)(4, 36)(5, 41)(6, 43)(7, 35)(8, 51)(9, 45)(10, 42)(11, 50)(12, 47)(13, 37)(14, 49)(15, 39)(16, 48)(17, 46)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.100 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.83 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1 * Y2^-1, Y2 * Y3^-1 * Y1 * Y3^-1, Y3^-1 * Y1^-3, (Y3, Y1), (R * Y1)^2, (Y2^-1, Y1), (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1^2 * Y2^-1 * Y1, Y3^-4 * Y1^-1 * Y3^-2 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 7, 24, 12, 29, 17, 34, 15, 32, 6, 23, 11, 28, 13, 30, 3, 20, 9, 26, 16, 33, 14, 31, 4, 21, 10, 27, 5, 22)(35, 52, 37, 54, 41, 58, 48, 65, 49, 66, 39, 56, 47, 64, 42, 59, 50, 67, 51, 68, 44, 61, 45, 62, 36, 53, 43, 60, 46, 63, 38, 55, 40, 57) L = (1, 38)(2, 44)(3, 40)(4, 43)(5, 48)(6, 46)(7, 35)(8, 39)(9, 45)(10, 50)(11, 51)(12, 36)(13, 49)(14, 37)(15, 41)(16, 47)(17, 42)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.97 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.84 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^2, Y1^-1 * Y3^-3, Y1^-1 * Y3^-3, Y2^-1 * Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y1, Y3^-1), (Y2^-1, Y1^-1) ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 3, 20, 9, 26, 14, 31, 7, 24, 12, 29, 16, 33, 13, 30, 15, 32, 4, 21, 10, 27, 17, 34, 6, 23, 11, 28, 5, 22)(35, 52, 37, 54, 41, 58, 47, 64, 44, 61, 45, 62, 36, 53, 43, 60, 46, 63, 49, 66, 51, 68, 39, 56, 42, 59, 48, 65, 50, 67, 38, 55, 40, 57) L = (1, 38)(2, 44)(3, 40)(4, 48)(5, 49)(6, 50)(7, 35)(8, 51)(9, 45)(10, 41)(11, 47)(12, 36)(13, 37)(14, 39)(15, 43)(16, 42)(17, 46)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.68 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.85 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-2, (Y1, Y3^-1), Y3^3 * Y1^-1, Y2 * Y1^3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y2^-1 * Y3^2 * Y2^-1, (Y3^-1 * Y1^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 6, 23, 11, 28, 15, 32, 4, 21, 10, 27, 14, 31, 16, 33, 17, 34, 7, 24, 12, 29, 13, 30, 3, 20, 9, 26, 5, 22)(35, 52, 37, 54, 41, 58, 48, 65, 49, 66, 42, 59, 39, 56, 47, 64, 51, 68, 44, 61, 45, 62, 36, 53, 43, 60, 46, 63, 50, 67, 38, 55, 40, 57) L = (1, 38)(2, 44)(3, 40)(4, 46)(5, 49)(6, 50)(7, 35)(8, 48)(9, 45)(10, 47)(11, 51)(12, 36)(13, 42)(14, 37)(15, 41)(16, 43)(17, 39)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.66 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.86 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, (Y1^-1, Y3^-1), Y3 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, Y1^-2 * Y3 * Y2^-1, (R * Y2)^2, (R * Y3)^2, Y3^-2 * Y1 * Y2^-1 * Y1, Y3^-3 * Y1^-1 * Y2, Y3 * Y2^-1 * Y3^2 * Y1, Y1^34 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 17, 34, 13, 30, 3, 20, 9, 26, 4, 21, 10, 27, 16, 33, 7, 24, 12, 29, 6, 23, 11, 28, 15, 32, 14, 31, 5, 22)(35, 52, 37, 54, 41, 58, 48, 65, 51, 68, 44, 61, 45, 62, 36, 53, 43, 60, 46, 63, 39, 56, 47, 64, 50, 67, 49, 66, 42, 59, 38, 55, 40, 57) L = (1, 38)(2, 44)(3, 40)(4, 49)(5, 43)(6, 42)(7, 35)(8, 50)(9, 45)(10, 48)(11, 51)(12, 36)(13, 46)(14, 37)(15, 47)(16, 39)(17, 41)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.89 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.87 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^2, Y2^2 * Y3, (Y1^-1, Y3^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^3 * Y1 * Y3, Y2 * Y3^-2 * Y2 * Y1^-1 * Y3^-1, Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 9, 26, 4, 21, 8, 25, 13, 30, 16, 33, 12, 29, 15, 32, 17, 34, 11, 28, 14, 31, 7, 24, 10, 27, 3, 20, 5, 22)(35, 52, 37, 54, 41, 58, 45, 62, 49, 66, 50, 67, 42, 59, 43, 60, 36, 53, 39, 56, 44, 61, 48, 65, 51, 68, 46, 63, 47, 64, 38, 55, 40, 57) L = (1, 38)(2, 42)(3, 40)(4, 46)(5, 43)(6, 47)(7, 35)(8, 49)(9, 50)(10, 36)(11, 37)(12, 48)(13, 51)(14, 39)(15, 41)(16, 45)(17, 44)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.88 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.88 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-2, Y3 * Y2^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y3^-4, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y1 * Y2 ] Map:: non-degenerate R = (1, 18, 2, 19, 3, 20, 8, 25, 7, 24, 10, 27, 11, 28, 16, 33, 15, 32, 12, 29, 17, 34, 14, 31, 13, 30, 4, 21, 9, 26, 6, 23, 5, 22)(35, 52, 37, 54, 41, 58, 45, 62, 49, 66, 51, 68, 47, 64, 43, 60, 39, 56, 36, 53, 42, 59, 44, 61, 50, 67, 46, 63, 48, 65, 38, 55, 40, 57) L = (1, 38)(2, 43)(3, 40)(4, 46)(5, 47)(6, 48)(7, 35)(8, 39)(9, 51)(10, 36)(11, 37)(12, 44)(13, 49)(14, 50)(15, 41)(16, 42)(17, 45)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.87 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.89 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y3, Y2^2 * Y3^-1 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^2 * Y2 * Y1^2, Y1^2 * Y3^3, (Y3^-1 * Y1^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 15, 32, 6, 23, 4, 21, 10, 27, 17, 34, 12, 29, 11, 28, 13, 30, 16, 33, 7, 24, 3, 20, 9, 26, 14, 31, 5, 22)(35, 52, 37, 54, 45, 62, 38, 55, 36, 53, 43, 60, 47, 64, 44, 61, 42, 59, 48, 65, 50, 67, 51, 68, 49, 66, 39, 56, 41, 58, 46, 63, 40, 57) L = (1, 38)(2, 44)(3, 36)(4, 47)(5, 40)(6, 45)(7, 35)(8, 51)(9, 42)(10, 50)(11, 43)(12, 37)(13, 48)(14, 49)(15, 46)(16, 39)(17, 41)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.86 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.90 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y1^3 * Y2^-1, Y3 * Y2^-3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y3 * Y1^2 * Y3 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 3, 20, 9, 26, 17, 34, 12, 29, 16, 33, 7, 24, 4, 21, 10, 27, 14, 31, 13, 30, 15, 32, 6, 23, 11, 28, 5, 22)(35, 52, 37, 54, 46, 63, 38, 55, 47, 64, 45, 62, 36, 53, 43, 60, 50, 67, 44, 61, 49, 66, 39, 56, 42, 59, 51, 68, 41, 58, 48, 65, 40, 57) L = (1, 38)(2, 44)(3, 47)(4, 36)(5, 41)(6, 46)(7, 35)(8, 48)(9, 49)(10, 42)(11, 50)(12, 45)(13, 43)(14, 37)(15, 51)(16, 39)(17, 40)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.63 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.91 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y1^-1 * Y2^-1 * Y1^-2, Y3 * Y2^-3, (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y2), (R * Y2)^2, Y2^-1 * Y3 * Y1^-2 * Y3 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 6, 23, 10, 27, 13, 30, 15, 32, 16, 33, 4, 21, 7, 24, 11, 28, 12, 29, 17, 34, 14, 31, 3, 20, 9, 26, 5, 22)(35, 52, 37, 54, 46, 63, 38, 55, 47, 64, 42, 59, 39, 56, 48, 65, 45, 62, 50, 67, 44, 61, 36, 53, 43, 60, 51, 68, 41, 58, 49, 66, 40, 57) L = (1, 38)(2, 41)(3, 47)(4, 39)(5, 50)(6, 46)(7, 35)(8, 45)(9, 49)(10, 51)(11, 36)(12, 42)(13, 48)(14, 44)(15, 37)(16, 43)(17, 40)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.65 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.92 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y1, Y3^-1 * Y1^-1 * Y3^-2, Y3 * Y2^-3, Y2^-3 * Y3, Y1^-1 * Y3^-3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y3^-1), (Y1^-1, Y3^-1), Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 9, 26, 14, 31, 15, 32, 7, 24, 10, 27, 17, 34, 12, 29, 16, 33, 4, 21, 8, 25, 11, 28, 13, 30, 3, 20, 5, 22)(35, 52, 37, 54, 45, 62, 38, 55, 46, 63, 44, 61, 49, 66, 43, 60, 36, 53, 39, 56, 47, 64, 42, 59, 50, 67, 51, 68, 41, 58, 48, 65, 40, 57) L = (1, 38)(2, 42)(3, 46)(4, 49)(5, 50)(6, 45)(7, 35)(8, 41)(9, 47)(10, 36)(11, 44)(12, 43)(13, 51)(14, 37)(15, 39)(16, 48)(17, 40)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.99 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.93 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-1 * Y1, (Y1^-1, Y3^-1), Y3^-1 * Y2^3, Y1 * Y3^-3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y3 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 3, 20, 8, 25, 11, 28, 14, 31, 4, 21, 9, 26, 12, 29, 17, 34, 16, 33, 7, 24, 10, 27, 13, 30, 15, 32, 6, 23, 5, 22)(35, 52, 37, 54, 45, 62, 38, 55, 46, 63, 50, 67, 44, 61, 49, 66, 39, 56, 36, 53, 42, 59, 48, 65, 43, 60, 51, 68, 41, 58, 47, 64, 40, 57) L = (1, 38)(2, 43)(3, 46)(4, 44)(5, 48)(6, 45)(7, 35)(8, 51)(9, 47)(10, 36)(11, 50)(12, 49)(13, 37)(14, 41)(15, 42)(16, 39)(17, 40)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.95 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.94 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2 * Y3^-1, Y3 * Y2 * Y3 * Y1^-1, Y1 * Y3^-2 * Y2^-1, (Y1^-1, Y3^-1), Y3^-1 * Y2^-3, Y3 * Y1^-1 * Y2^-2, Y3 * Y2^-2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y1 * Y3 * Y2^-1 * Y3 * Y1 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 13, 30, 4, 21, 10, 27, 15, 32, 6, 23, 11, 28, 14, 31, 3, 20, 9, 26, 17, 34, 7, 24, 12, 29, 16, 33, 5, 22)(35, 52, 37, 54, 47, 64, 41, 58, 49, 66, 39, 56, 48, 65, 42, 59, 51, 68, 44, 61, 50, 67, 45, 62, 36, 53, 43, 60, 38, 55, 46, 63, 40, 57) L = (1, 38)(2, 44)(3, 46)(4, 45)(5, 47)(6, 43)(7, 35)(8, 49)(9, 50)(10, 48)(11, 51)(12, 36)(13, 40)(14, 41)(15, 37)(16, 42)(17, 39)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.70 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.95 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y2^-1 * Y1^-3, Y2 * Y3 * Y2^2, Y2 * Y1^3, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2^-1), (R * Y2)^2, (Y2, Y3), Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 6, 23, 11, 28, 15, 32, 13, 30, 17, 34, 7, 24, 4, 21, 10, 27, 12, 29, 16, 33, 14, 31, 3, 20, 9, 26, 5, 22)(35, 52, 37, 54, 46, 63, 41, 58, 49, 66, 42, 59, 39, 56, 48, 65, 44, 61, 51, 68, 45, 62, 36, 53, 43, 60, 50, 67, 38, 55, 47, 64, 40, 57) L = (1, 38)(2, 44)(3, 47)(4, 36)(5, 41)(6, 50)(7, 35)(8, 46)(9, 51)(10, 42)(11, 48)(12, 40)(13, 43)(14, 49)(15, 37)(16, 45)(17, 39)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.93 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.96 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y1, Y3 * Y2^3, (Y1^-1, Y3^-1), Y3 * Y1^-1 * Y3^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 9, 26, 12, 29, 15, 32, 4, 21, 8, 25, 16, 33, 14, 31, 17, 34, 7, 24, 10, 27, 11, 28, 13, 30, 3, 20, 5, 22)(35, 52, 37, 54, 45, 62, 41, 58, 48, 65, 42, 59, 49, 66, 43, 60, 36, 53, 39, 56, 47, 64, 44, 61, 51, 68, 50, 67, 38, 55, 46, 63, 40, 57) L = (1, 38)(2, 42)(3, 46)(4, 44)(5, 49)(6, 50)(7, 35)(8, 45)(9, 48)(10, 36)(11, 40)(12, 51)(13, 43)(14, 37)(15, 41)(16, 47)(17, 39)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.61 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.97 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-1 * Y1, Y3^-1 * Y1^-1 * Y3^-2, Y2^-2 * Y3^-1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y2)^2, Y1 * Y3^-1 * Y2^-1 * Y3^-2, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 18, 2, 19, 3, 20, 8, 25, 11, 28, 14, 31, 7, 24, 10, 27, 13, 30, 16, 33, 15, 32, 4, 21, 9, 26, 12, 29, 17, 34, 6, 23, 5, 22)(35, 52, 37, 54, 45, 62, 41, 58, 47, 64, 49, 66, 43, 60, 51, 68, 39, 56, 36, 53, 42, 59, 48, 65, 44, 61, 50, 67, 38, 55, 46, 63, 40, 57) L = (1, 38)(2, 43)(3, 46)(4, 48)(5, 49)(6, 50)(7, 35)(8, 51)(9, 41)(10, 36)(11, 40)(12, 44)(13, 37)(14, 39)(15, 45)(16, 42)(17, 47)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.83 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.98 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1 * Y3^-1, Y2 * Y1^-1 * Y3, Y1 * Y3^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^2 * Y3^-1 * Y2^2, Y1^2 * Y2^2 * Y1 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 17, 34, 14, 31, 13, 30, 7, 24, 3, 20, 9, 26, 16, 33, 6, 23, 4, 21, 10, 27, 12, 29, 11, 28, 15, 32, 5, 22)(35, 52, 37, 54, 45, 62, 48, 65, 38, 55, 36, 53, 43, 60, 49, 66, 47, 64, 44, 61, 42, 59, 50, 67, 39, 56, 41, 58, 46, 63, 51, 68, 40, 57) L = (1, 38)(2, 44)(3, 36)(4, 47)(5, 40)(6, 48)(7, 35)(8, 46)(9, 42)(10, 41)(11, 43)(12, 37)(13, 39)(14, 49)(15, 50)(16, 51)(17, 45)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.67 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.99 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y3 * Y1, Y1 * Y2^-1 * Y1^2, Y2^-1 * Y3^-1 * Y1 * Y2^-1, (Y3, Y1^-1), (R * Y3)^2, Y1 * Y2 * Y1 * Y3, (R * Y1)^2, (Y2^-1, Y1^-1), Y2 * Y1^2 * Y3, (R * Y2)^2, Y1^-1 * Y2^-2 * Y3^2, Y3^-1 * Y1 * Y2^2 * Y3^-1, Y2^-1 * Y3^-4 ] Map:: non-degenerate R = (1, 18, 2, 19, 8, 25, 3, 20, 9, 26, 7, 24, 12, 29, 14, 31, 13, 30, 16, 33, 17, 34, 15, 32, 4, 21, 10, 27, 6, 23, 11, 28, 5, 22)(35, 52, 37, 54, 46, 63, 50, 67, 38, 55, 45, 62, 36, 53, 43, 60, 48, 65, 51, 68, 44, 61, 39, 56, 42, 59, 41, 58, 47, 64, 49, 66, 40, 57) L = (1, 38)(2, 44)(3, 45)(4, 48)(5, 49)(6, 50)(7, 35)(8, 40)(9, 39)(10, 47)(11, 51)(12, 36)(13, 37)(14, 42)(15, 46)(16, 43)(17, 41)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.92 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.100 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y1 * Y2 * Y1, (R * Y1)^2, (R * Y3)^2, Y2 * Y3 * Y1 * Y3, (R * Y2)^2, Y2^4 * Y3^-1, Y2^2 * Y1^-1 * Y2^2 * Y3 ] Map:: non-degenerate R = (1, 18, 2, 19, 6, 23, 9, 26, 15, 32, 17, 34, 13, 30, 11, 28, 7, 24, 4, 21, 8, 25, 14, 31, 16, 33, 10, 27, 12, 29, 3, 20, 5, 22)(35, 52, 37, 54, 44, 61, 48, 65, 38, 55, 45, 62, 51, 68, 43, 60, 36, 53, 39, 56, 46, 63, 50, 67, 42, 59, 41, 58, 47, 64, 49, 66, 40, 57) L = (1, 38)(2, 42)(3, 45)(4, 36)(5, 41)(6, 48)(7, 35)(8, 40)(9, 50)(10, 51)(11, 39)(12, 47)(13, 37)(14, 43)(15, 44)(16, 49)(17, 46)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.82 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.101 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 17, 17, 17}) Quotient :: dipole Aut^+ = C17 (small group id <17, 1>) Aut = D34 (small group id <34, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y1 * Y2^-1 * Y1, (R * Y3)^2, (Y2, Y3^-1), (R * Y1)^2, (R * Y2)^2, Y2^2 * Y3^-1 * Y2^2, Y2^-1 * Y3 * Y1^-1 * Y2^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 18, 2, 19, 3, 20, 8, 25, 10, 27, 16, 33, 13, 30, 12, 29, 4, 21, 7, 24, 9, 26, 11, 28, 17, 34, 15, 32, 14, 31, 6, 23, 5, 22)(35, 52, 37, 54, 44, 61, 47, 64, 38, 55, 43, 60, 51, 68, 48, 65, 39, 56, 36, 53, 42, 59, 50, 67, 46, 63, 41, 58, 45, 62, 49, 66, 40, 57) L = (1, 38)(2, 41)(3, 43)(4, 39)(5, 46)(6, 47)(7, 35)(8, 45)(9, 36)(10, 51)(11, 37)(12, 40)(13, 48)(14, 50)(15, 44)(16, 49)(17, 42)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.64 Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.102 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^-1 * Y2^2, Y3 * Y2^-1 * Y3 * Y2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y2 * Y1^4 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 14, 32, 6, 24, 3, 21, 8, 26, 13, 31, 5, 23)(4, 22, 9, 27, 15, 33, 18, 36, 12, 30, 10, 28, 16, 34, 17, 35, 11, 29)(37, 55, 39, 57, 38, 56, 44, 62, 43, 61, 49, 67, 50, 68, 41, 59, 42, 60)(40, 58, 46, 64, 45, 63, 52, 70, 51, 69, 53, 71, 54, 72, 47, 65, 48, 66) L = (1, 40)(2, 45)(3, 46)(4, 37)(5, 47)(6, 48)(7, 51)(8, 52)(9, 38)(10, 39)(11, 41)(12, 42)(13, 53)(14, 54)(15, 43)(16, 44)(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) :: { ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.133 Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 18^4 ] E16.103 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1 * Y2^2, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y3, Y1 * Y3 * Y1^-1 * Y3, (R * Y2)^2, (R * Y1)^2, Y2 * Y1^-4 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 11, 29, 3, 21, 6, 24, 9, 27, 14, 32, 5, 23)(4, 22, 8, 26, 15, 33, 17, 35, 10, 28, 13, 31, 16, 34, 18, 36, 12, 30)(37, 55, 39, 57, 41, 59, 47, 65, 50, 68, 43, 61, 45, 63, 38, 56, 42, 60)(40, 58, 46, 64, 48, 66, 53, 71, 54, 72, 51, 69, 52, 70, 44, 62, 49, 67) 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) :: { ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.134 Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 18^4 ] E16.104 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2, (Y1^-1, Y3^-1), (Y3, Y2), Y3 * Y1 * Y3 * Y2, Y1 * Y2 * Y3^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^-3 * Y3, (Y2^-1 * Y1^-1)^3, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 14, 32, 6, 24, 3, 21, 9, 27, 17, 35, 5, 23)(4, 22, 10, 28, 13, 31, 18, 36, 16, 34, 12, 30, 7, 25, 11, 29, 15, 33)(37, 55, 39, 57, 38, 56, 45, 63, 44, 62, 53, 71, 50, 68, 41, 59, 42, 60)(40, 58, 48, 66, 46, 64, 43, 61, 49, 67, 47, 65, 54, 72, 51, 69, 52, 70) L = (1, 40)(2, 46)(3, 48)(4, 50)(5, 51)(6, 52)(7, 37)(8, 49)(9, 43)(10, 42)(11, 38)(12, 41)(13, 39)(14, 54)(15, 44)(16, 53)(17, 47)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.136 Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 18^4 ] E16.105 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2, (Y3^-1, Y1^-1), Y3^-2 * Y1 * Y2, (Y3, Y2^-1), Y3^-2 * Y2 * Y1, Y3^-1 * Y1 * Y3^-1 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^3 * Y3^2 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 15, 33, 6, 24, 3, 21, 9, 27, 14, 32, 5, 23)(4, 22, 10, 28, 16, 34, 7, 25, 11, 29, 12, 30, 18, 36, 17, 35, 13, 31)(37, 55, 39, 57, 38, 56, 45, 63, 44, 62, 50, 68, 51, 69, 41, 59, 42, 60)(40, 58, 48, 66, 46, 64, 54, 72, 52, 70, 53, 71, 43, 61, 49, 67, 47, 65) L = (1, 40)(2, 46)(3, 48)(4, 45)(5, 49)(6, 47)(7, 37)(8, 52)(9, 54)(10, 50)(11, 38)(12, 44)(13, 39)(14, 53)(15, 43)(16, 41)(17, 42)(18, 51)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.135 Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 18^4 ] E16.106 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^2 * Y1^-2, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^4 * Y1^5, Y1^3 * Y2^-12, (Y3^-1 * Y1^-1)^9, Y2^-26 * Y1^-1, (Y3 * Y2^-1)^18 ] Map:: R = (1, 19, 2, 20, 6, 24, 11, 29, 15, 33, 17, 35, 13, 31, 9, 27, 4, 22)(3, 21, 7, 25, 12, 30, 16, 34, 18, 36, 14, 32, 10, 28, 5, 23, 8, 26)(37, 55, 39, 57, 42, 60, 48, 66, 51, 69, 54, 72, 49, 67, 46, 64, 40, 58, 44, 62, 38, 56, 43, 61, 47, 65, 52, 70, 53, 71, 50, 68, 45, 63, 41, 59) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.107 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^2 * Y1^2, Y2^-2 * Y1^-2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^2 * Y2^-1 * Y1^2 * Y2^-3 * Y1, Y1^9, Y1^-1 * Y2^8, (Y3^-1 * Y1^-1)^9, (Y3 * Y2^-1)^18 ] Map:: R = (1, 19, 2, 20, 6, 24, 11, 29, 15, 33, 17, 35, 14, 32, 9, 27, 4, 22)(3, 21, 7, 25, 5, 23, 8, 26, 12, 30, 16, 34, 18, 36, 13, 31, 10, 28)(37, 55, 39, 57, 45, 63, 49, 67, 53, 71, 52, 70, 47, 65, 44, 62, 38, 56, 43, 61, 40, 58, 46, 64, 50, 68, 54, 72, 51, 69, 48, 66, 42, 60, 41, 59) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.108 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^9, (Y3^-1 * Y1^-1)^9, (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, 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, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.109 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^9, (Y3^-1 * Y1^-1)^9, (Y3 * Y2^-1)^18 ] Map:: R = (1, 19, 2, 20, 6, 24, 10, 28, 14, 32, 17, 35, 13, 31, 9, 27, 4, 22)(3, 21, 5, 23, 7, 25, 11, 29, 15, 33, 18, 36, 16, 34, 12, 30, 8, 26)(37, 55, 39, 57, 40, 58, 44, 62, 45, 63, 48, 66, 49, 67, 52, 70, 53, 71, 54, 72, 50, 68, 51, 69, 46, 64, 47, 65, 42, 60, 43, 61, 38, 56, 41, 59) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.110 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2, Y1), (R * Y3)^2, (R * Y1)^2, Y2^-4 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1^3 * Y2, (Y3^-1 * Y1^-1)^9, (Y3 * Y2^-1)^18 ] Map:: R = (1, 19, 2, 20, 6, 24, 14, 32, 13, 31, 9, 27, 17, 35, 11, 29, 4, 22)(3, 21, 7, 25, 15, 33, 12, 30, 5, 23, 8, 26, 16, 34, 18, 36, 10, 28)(37, 55, 39, 57, 45, 63, 44, 62, 38, 56, 43, 61, 53, 71, 52, 70, 42, 60, 51, 69, 47, 65, 54, 72, 50, 68, 48, 66, 40, 58, 46, 64, 49, 67, 41, 59) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.111 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2 * Y1 * Y2^3, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1^3, (Y3^-1 * Y1^-1)^9, (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, 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, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.112 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1 * Y2 * Y3^-1 * Y2, Y2^-2 * Y3 * Y1^-1, (Y2 * Y1^-1)^2, Y3 * Y1^-3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y3^-1), (Y3 * Y1)^9, Y3 * Y1^-1 * Y2^16 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 4, 22, 10, 28, 15, 33, 7, 25, 12, 30, 5, 23)(3, 21, 9, 27, 17, 35, 13, 31, 16, 34, 18, 36, 14, 32, 6, 24, 11, 29)(37, 55, 39, 57, 44, 62, 53, 71, 46, 64, 52, 70, 43, 61, 50, 68, 41, 59, 47, 65, 38, 56, 45, 63, 40, 58, 49, 67, 51, 69, 54, 72, 48, 66, 42, 60) L = (1, 40)(2, 46)(3, 49)(4, 43)(5, 44)(6, 45)(7, 37)(8, 51)(9, 52)(10, 48)(11, 53)(12, 38)(13, 50)(14, 39)(15, 41)(16, 42)(17, 54)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.121 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.113 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^-3 * Y3^-1, (Y1, Y3), (Y3, Y2^-1), Y1^-1 * Y2 * Y3^-1 * Y2, Y2^2 * Y3^-1 * Y1^-1, (R * Y3)^2, Y2 * Y1^-1 * Y3^-1 * Y2, (Y2^-1 * Y1^-1)^2, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 7, 25, 12, 30, 15, 33, 4, 22, 10, 28, 5, 23)(3, 21, 9, 27, 6, 24, 11, 29, 17, 35, 16, 34, 13, 31, 18, 36, 14, 32)(37, 55, 39, 57, 46, 64, 54, 72, 51, 69, 52, 70, 43, 61, 47, 65, 38, 56, 45, 63, 41, 59, 50, 68, 40, 58, 49, 67, 48, 66, 53, 71, 44, 62, 42, 60) L = (1, 40)(2, 46)(3, 49)(4, 43)(5, 51)(6, 50)(7, 37)(8, 41)(9, 54)(10, 48)(11, 39)(12, 38)(13, 47)(14, 52)(15, 44)(16, 42)(17, 45)(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) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.119 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.114 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2 * Y1^-1 * Y2, (Y1, Y3), (Y3, Y2), Y3 * Y1^3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1 * Y3)^18 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 7, 25, 11, 29, 14, 32, 4, 22, 10, 28, 5, 23)(3, 21, 9, 27, 17, 35, 13, 31, 18, 36, 15, 33, 12, 30, 16, 34, 6, 24)(37, 55, 39, 57, 38, 56, 45, 63, 44, 62, 53, 71, 43, 61, 49, 67, 47, 65, 54, 72, 50, 68, 51, 69, 40, 58, 48, 66, 46, 64, 52, 70, 41, 59, 42, 60) L = (1, 40)(2, 46)(3, 48)(4, 43)(5, 50)(6, 51)(7, 37)(8, 41)(9, 52)(10, 47)(11, 38)(12, 49)(13, 39)(14, 44)(15, 53)(16, 54)(17, 42)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.120 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.115 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2 * Y1 * Y2, (Y3^-1, Y2^-1), Y1^3 * Y3^-1, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y2 * Y3^-1 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 4, 22, 9, 27, 16, 34, 7, 25, 11, 29, 5, 23)(3, 21, 6, 24, 10, 28, 12, 30, 15, 33, 18, 36, 14, 32, 17, 35, 13, 31)(37, 55, 39, 57, 41, 59, 49, 67, 47, 65, 53, 71, 43, 61, 50, 68, 52, 70, 54, 72, 45, 63, 51, 69, 40, 58, 48, 66, 44, 62, 46, 64, 38, 56, 42, 60) L = (1, 40)(2, 45)(3, 48)(4, 43)(5, 44)(6, 51)(7, 37)(8, 52)(9, 47)(10, 54)(11, 38)(12, 50)(13, 46)(14, 39)(15, 53)(16, 41)(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) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.122 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.116 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y3^-1 * Y1^3, (Y2, Y3^-1), (Y3^-1, Y1^-1), Y1 * Y2 * Y3 * Y2, (R * Y1)^2, (R * Y2)^2, Y1 * Y3 * Y2^2, (R * Y3)^2, Y1^2 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 4, 22, 10, 28, 13, 31, 7, 25, 12, 30, 5, 23)(3, 21, 9, 27, 18, 36, 14, 32, 6, 24, 11, 29, 16, 34, 17, 35, 15, 33)(37, 55, 39, 57, 49, 67, 47, 65, 38, 56, 45, 63, 43, 61, 52, 70, 44, 62, 54, 72, 48, 66, 53, 71, 40, 58, 50, 68, 41, 59, 51, 69, 46, 64, 42, 60) L = (1, 40)(2, 46)(3, 50)(4, 43)(5, 44)(6, 53)(7, 37)(8, 49)(9, 42)(10, 48)(11, 51)(12, 38)(13, 41)(14, 52)(15, 54)(16, 39)(17, 45)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.118 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.117 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, (Y3^-1, Y2), Y2^-1 * Y1 * Y3^-1 * Y2^-1, Y1 * Y2^-2 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1), Y2^-1 * Y1 * Y2^-1 * Y3^-1, Y1^2 * Y3 * Y1, (R * Y3)^2, Y2^2 * Y1^2 * Y3^-1, (Y1^-2 * Y2)^2 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 7, 25, 12, 30, 15, 33, 4, 22, 10, 28, 5, 23)(3, 21, 9, 27, 16, 34, 14, 32, 17, 35, 6, 24, 11, 29, 18, 36, 13, 31)(37, 55, 39, 57, 48, 66, 53, 71, 41, 59, 49, 67, 43, 61, 50, 68, 46, 64, 54, 72, 44, 62, 52, 70, 40, 58, 47, 65, 38, 56, 45, 63, 51, 69, 42, 60) L = (1, 40)(2, 46)(3, 47)(4, 43)(5, 51)(6, 52)(7, 37)(8, 41)(9, 54)(10, 48)(11, 50)(12, 38)(13, 42)(14, 39)(15, 44)(16, 49)(17, 45)(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) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.123 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.118 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y3^-1 * Y1^-3, (Y2, Y3), Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, Y1^-1 * Y3^-1 * Y2^-2, (Y3^-1, Y1^-1), Y1^-1 * Y2^2 * Y1^-1, (R * Y2)^2, (Y2^-1 * Y1)^2, Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1, (R * Y1)^2, Y2^2 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 7, 25, 12, 30, 15, 33, 4, 22, 10, 28, 5, 23)(3, 21, 9, 27, 17, 35, 14, 32, 16, 34, 18, 36, 13, 31, 6, 24, 11, 29)(37, 55, 39, 57, 44, 62, 53, 71, 48, 66, 52, 70, 40, 58, 49, 67, 41, 59, 47, 65, 38, 56, 45, 63, 43, 61, 50, 68, 51, 69, 54, 72, 46, 64, 42, 60) L = (1, 40)(2, 46)(3, 49)(4, 43)(5, 51)(6, 52)(7, 37)(8, 41)(9, 42)(10, 48)(11, 54)(12, 38)(13, 50)(14, 39)(15, 44)(16, 45)(17, 47)(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) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.116 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.119 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-2 * Y3^-1 * Y1, (R * Y3)^2, (Y2 * Y1)^2, Y1 * Y3^-1 * Y2^-2, Y1^-2 * Y3 * Y1^-1, (R * Y2)^2, (Y2, Y3^-1), (R * Y1)^2, Y1^-1 * Y2^-2 * Y1^-1, Y2^6 * Y3^-1, (Y3^-1 * Y1^-1)^9 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 4, 22, 10, 28, 16, 34, 7, 25, 12, 30, 5, 23)(3, 21, 9, 27, 6, 24, 11, 29, 17, 35, 15, 33, 14, 32, 18, 36, 13, 31)(37, 55, 39, 57, 48, 66, 54, 72, 52, 70, 51, 69, 40, 58, 47, 65, 38, 56, 45, 63, 41, 59, 49, 67, 43, 61, 50, 68, 46, 64, 53, 71, 44, 62, 42, 60) L = (1, 40)(2, 46)(3, 47)(4, 43)(5, 44)(6, 51)(7, 37)(8, 52)(9, 53)(10, 48)(11, 50)(12, 38)(13, 42)(14, 39)(15, 49)(16, 41)(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) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.113 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.120 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-3, Y3^3, Y2 * Y1^-1 * Y2, Y3^-1 * Y1^3, (R * Y1)^2, (Y3^-1, Y2), (R * Y2)^2, (R * Y3)^2, Y1 * Y2 * Y1 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^9 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 4, 22, 10, 28, 16, 34, 7, 25, 11, 29, 5, 23)(3, 21, 9, 27, 14, 32, 12, 30, 18, 36, 17, 35, 13, 31, 15, 33, 6, 24)(37, 55, 39, 57, 38, 56, 45, 63, 44, 62, 50, 68, 40, 58, 48, 66, 46, 64, 54, 72, 52, 70, 53, 71, 43, 61, 49, 67, 47, 65, 51, 69, 41, 59, 42, 60) L = (1, 40)(2, 46)(3, 48)(4, 43)(5, 44)(6, 50)(7, 37)(8, 52)(9, 54)(10, 47)(11, 38)(12, 49)(13, 39)(14, 53)(15, 45)(16, 41)(17, 42)(18, 51)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.114 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.121 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2 * Y1 * Y2, (Y1, Y3^-1), Y1^-3 * Y3^-1, (R * Y3)^2, (Y2^-1, Y3^-1), (R * Y2)^2, (R * Y1)^2 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 7, 25, 11, 29, 15, 33, 4, 22, 9, 27, 5, 23)(3, 21, 6, 24, 10, 28, 14, 32, 17, 35, 18, 36, 12, 30, 16, 34, 13, 31)(37, 55, 39, 57, 41, 59, 49, 67, 45, 63, 52, 70, 40, 58, 48, 66, 51, 69, 54, 72, 47, 65, 53, 71, 43, 61, 50, 68, 44, 62, 46, 64, 38, 56, 42, 60) L = (1, 40)(2, 45)(3, 48)(4, 43)(5, 51)(6, 52)(7, 37)(8, 41)(9, 47)(10, 49)(11, 38)(12, 50)(13, 54)(14, 39)(15, 44)(16, 53)(17, 42)(18, 46)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.112 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.122 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y1 * Y3^-1 * Y2^2, Y3 * Y2^-2 * Y1^-1, Y1 * Y3 * Y1^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^2 * Y3^-1 * Y2^-2, Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 7, 25, 12, 30, 13, 31, 4, 22, 10, 28, 5, 23)(3, 21, 9, 27, 18, 36, 16, 34, 6, 24, 11, 29, 14, 32, 17, 35, 15, 33)(37, 55, 39, 57, 49, 67, 47, 65, 38, 56, 45, 63, 40, 58, 50, 68, 44, 62, 54, 72, 46, 64, 53, 71, 43, 61, 52, 70, 41, 59, 51, 69, 48, 66, 42, 60) L = (1, 40)(2, 46)(3, 50)(4, 43)(5, 49)(6, 45)(7, 37)(8, 41)(9, 53)(10, 48)(11, 54)(12, 38)(13, 44)(14, 52)(15, 47)(16, 39)(17, 42)(18, 51)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.115 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.123 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y3^-1 * Y1^3, (Y3, Y2^-1), Y2 * Y3^-1 * Y2 * Y1^-1, (Y3^-1, Y1^-1), Y2^2 * Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y1^-1 * Y3^-1 * Y2, Y3 * Y2 * Y1^-1 * Y3 * Y2, (Y3 * Y1)^9 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 4, 22, 10, 28, 16, 34, 7, 25, 12, 30, 5, 23)(3, 21, 9, 27, 17, 35, 13, 31, 15, 33, 6, 24, 11, 29, 18, 36, 14, 32)(37, 55, 39, 57, 46, 64, 51, 69, 41, 59, 50, 68, 40, 58, 49, 67, 48, 66, 54, 72, 44, 62, 53, 71, 43, 61, 47, 65, 38, 56, 45, 63, 52, 70, 42, 60) L = (1, 40)(2, 46)(3, 49)(4, 43)(5, 44)(6, 50)(7, 37)(8, 52)(9, 51)(10, 48)(11, 39)(12, 38)(13, 47)(14, 53)(15, 54)(16, 41)(17, 42)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.117 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.124 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, Y1^-2 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (Y1, Y2^-1), (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^8, Y1^2 * Y2^-1 * Y1^2 * Y2^-3 * Y1, Y1^9, (Y3 * Y2^-1)^18 ] Map:: non-degenerate R = (1, 19, 2, 20, 6, 24, 11, 29, 15, 33, 17, 35, 14, 32, 9, 27, 4, 22)(3, 21, 7, 25, 5, 23, 8, 26, 12, 30, 16, 34, 18, 36, 13, 31, 10, 28)(37, 55, 39, 57, 45, 63, 49, 67, 53, 71, 52, 70, 47, 65, 44, 62, 38, 56, 43, 61, 40, 58, 46, 64, 50, 68, 54, 72, 51, 69, 48, 66, 42, 60, 41, 59) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 47)(7, 41)(8, 48)(9, 40)(10, 39)(11, 51)(12, 52)(13, 46)(14, 45)(15, 53)(16, 54)(17, 50)(18, 49)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.130 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.125 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y1 * Y2^-2, (Y2^-1 * Y3^-1)^2, (R * Y1)^2, (Y2, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y3 * Y1^-4, Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 13, 31, 4, 22, 7, 25, 10, 28, 15, 33, 5, 23)(3, 21, 9, 27, 17, 35, 14, 32, 11, 29, 12, 30, 18, 36, 16, 34, 6, 24)(37, 55, 39, 57, 38, 56, 45, 63, 44, 62, 53, 71, 49, 67, 50, 68, 40, 58, 47, 65, 43, 61, 48, 66, 46, 64, 54, 72, 51, 69, 52, 70, 41, 59, 42, 60) L = (1, 40)(2, 43)(3, 47)(4, 41)(5, 49)(6, 50)(7, 37)(8, 46)(9, 48)(10, 38)(11, 42)(12, 39)(13, 51)(14, 52)(15, 44)(16, 53)(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) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.132 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.126 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y1, Y2^-1 * Y3^-2 * Y2^-1, (Y1^-1, Y2^-1), (R * Y3)^2, (Y3^-1 * Y2^-1)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y2^4, (Y3 * Y2^-1)^18 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 10, 28, 11, 29, 15, 33, 16, 34, 4, 22, 5, 23)(3, 21, 8, 26, 14, 32, 17, 35, 18, 36, 6, 24, 9, 27, 12, 30, 13, 31)(37, 55, 39, 57, 47, 65, 54, 72, 41, 59, 49, 67, 46, 64, 53, 71, 40, 58, 48, 66, 43, 61, 50, 68, 52, 70, 45, 63, 38, 56, 44, 62, 51, 69, 42, 60) L = (1, 40)(2, 41)(3, 48)(4, 51)(5, 52)(6, 53)(7, 37)(8, 49)(9, 54)(10, 38)(11, 43)(12, 42)(13, 45)(14, 39)(15, 46)(16, 47)(17, 44)(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) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.131 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.127 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^2, Y3^-1 * Y2^2, (Y1^-1 * Y2^-1)^2, (Y1^-1, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-4 * Y1 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 10, 28, 16, 34, 13, 31, 14, 32, 4, 22, 5, 23)(3, 21, 8, 26, 6, 24, 9, 27, 15, 33, 17, 35, 18, 36, 11, 29, 12, 30)(37, 55, 39, 57, 40, 58, 47, 65, 49, 67, 53, 71, 46, 64, 45, 63, 38, 56, 44, 62, 41, 59, 48, 66, 50, 68, 54, 72, 52, 70, 51, 69, 43, 61, 42, 60) L = (1, 40)(2, 41)(3, 47)(4, 49)(5, 50)(6, 39)(7, 37)(8, 48)(9, 44)(10, 38)(11, 53)(12, 54)(13, 46)(14, 52)(15, 42)(16, 43)(17, 45)(18, 51)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.128 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, Y1 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^9, (Y3^-1 * Y1^-1)^9, (Y3 * Y2^-1)^18 ] Map:: non-degenerate 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, 38)(2, 42)(3, 43)(4, 37)(5, 39)(6, 46)(7, 47)(8, 40)(9, 41)(10, 50)(11, 51)(12, 44)(13, 45)(14, 52)(15, 54)(16, 48)(17, 49)(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) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.129 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.129 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y2, Y1 * Y3^2, (R * Y1)^2, (R * Y3)^2, (Y1, Y2^-1), (R * Y2)^2, Y1^-2 * Y3 * Y1^-2 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 14, 32, 4, 22, 7, 25, 11, 29, 15, 33, 5, 23)(3, 21, 9, 27, 16, 34, 18, 36, 12, 30, 6, 24, 10, 28, 17, 35, 13, 31)(37, 55, 39, 57, 40, 58, 48, 66, 41, 59, 49, 67, 50, 68, 54, 72, 51, 69, 53, 71, 44, 62, 52, 70, 47, 65, 46, 64, 38, 56, 45, 63, 43, 61, 42, 60) L = (1, 40)(2, 43)(3, 48)(4, 41)(5, 50)(6, 39)(7, 37)(8, 47)(9, 42)(10, 45)(11, 38)(12, 49)(13, 54)(14, 51)(15, 44)(16, 46)(17, 52)(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) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.128 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.130 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y1^-2 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y1^-1, Y2), Y1 * Y2 * Y3^-1 * Y2 * Y3^-1, Y2^-1 * Y1^2 * Y3^-1 * Y2^-1, Y3^-1 * Y1^7 * Y3^-1 * Y1, Y2^18 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 16, 34, 4, 22, 7, 25, 11, 29, 12, 30, 5, 23)(3, 21, 9, 27, 6, 24, 10, 28, 13, 31, 15, 33, 17, 35, 18, 36, 14, 32)(37, 55, 39, 57, 48, 66, 54, 72, 43, 61, 51, 69, 52, 70, 46, 64, 38, 56, 45, 63, 41, 59, 50, 68, 47, 65, 53, 71, 40, 58, 49, 67, 44, 62, 42, 60) L = (1, 40)(2, 43)(3, 49)(4, 41)(5, 52)(6, 53)(7, 37)(8, 47)(9, 51)(10, 54)(11, 38)(12, 44)(13, 50)(14, 46)(15, 39)(16, 48)(17, 45)(18, 42)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.124 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.131 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1 * Y2^-1, Y1 * Y3 * Y1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), Y1 * Y3^-4, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 9, 27, 15, 33, 12, 30, 13, 31, 4, 22, 5, 23)(3, 21, 8, 26, 11, 29, 16, 34, 18, 36, 17, 35, 14, 32, 10, 28, 6, 24)(37, 55, 39, 57, 38, 56, 44, 62, 43, 61, 47, 65, 45, 63, 52, 70, 51, 69, 54, 72, 48, 66, 53, 71, 49, 67, 50, 68, 40, 58, 46, 64, 41, 59, 42, 60) L = (1, 40)(2, 41)(3, 46)(4, 48)(5, 49)(6, 50)(7, 37)(8, 42)(9, 38)(10, 53)(11, 39)(12, 45)(13, 51)(14, 54)(15, 43)(16, 44)(17, 52)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.126 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.132 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1), Y2^4 * Y1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^9, (Y3 * Y2^-1)^18 ] Map:: non-degenerate 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, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 49)(10, 39)(11, 40)(12, 41)(13, 53)(14, 45)(15, 54)(16, 46)(17, 47)(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, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.125 Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.133 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1 * Y3 * Y1^-1, Y1^-1 * Y2 * Y3 * Y1^-1, Y2^-1 * Y3 * Y1^2, (Y2, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^4 * Y2^-2, Y2^-2 * Y1^-3 * Y2^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 15, 33, 11, 29, 17, 35, 13, 31, 6, 24, 10, 28, 4, 22, 9, 27, 3, 21, 8, 26, 16, 34, 14, 32, 18, 36, 12, 30, 5, 23)(37, 55, 39, 57, 47, 65, 54, 72, 46, 64, 38, 56, 44, 62, 53, 71, 48, 66, 40, 58, 43, 61, 52, 70, 49, 67, 41, 59, 45, 63, 51, 69, 50, 68, 42, 60) L = (1, 40)(2, 45)(3, 43)(4, 37)(5, 46)(6, 48)(7, 39)(8, 51)(9, 38)(10, 41)(11, 52)(12, 42)(13, 54)(14, 53)(15, 44)(16, 47)(17, 50)(18, 49)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^36 ) } Outer automorphisms :: reflexible Dual of E16.102 Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.134 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y3 * Y1^2, Y2^-1 * Y1^-1 * Y3 * Y1^-1, Y2 * Y3 * Y2^-1 * Y3, Y3 * Y1^-1 * Y3 * Y1, Y3 * Y1^-2 * Y2^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2^-4 * Y3 * Y1, (Y1^-1 * Y2)^3, Y2^-1 * Y1^14 * Y2^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 15, 33, 14, 32, 18, 36, 13, 31, 3, 21, 8, 26, 4, 22, 9, 27, 6, 24, 10, 28, 16, 34, 11, 29, 17, 35, 12, 30, 5, 23)(37, 55, 39, 57, 47, 65, 51, 69, 45, 63, 41, 59, 49, 67, 52, 70, 43, 61, 40, 58, 48, 66, 54, 72, 46, 64, 38, 56, 44, 62, 53, 71, 50, 68, 42, 60) L = (1, 40)(2, 45)(3, 48)(4, 37)(5, 44)(6, 43)(7, 42)(8, 41)(9, 38)(10, 51)(11, 54)(12, 39)(13, 53)(14, 52)(15, 46)(16, 50)(17, 49)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^36 ) } Outer automorphisms :: reflexible Dual of E16.103 Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.135 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1 * Y3 * Y2, (Y2, Y1^-1), Y3^-1 * Y2^-1 * Y1 * Y2^-1, Y2^-1 * Y3 * Y2^-2, (R * Y2)^2, Y3 * Y1^-1 * Y3 * Y2^-1, Y3^-1 * Y2^-2 * Y1, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1^-2, (R * Y3)^2, Y2^-1 * Y3^-2 * Y2^-1 * Y1^-2, Y3^6 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 7, 25, 12, 30, 18, 36, 15, 33, 6, 24, 11, 29, 17, 35, 13, 31, 3, 21, 9, 27, 16, 34, 14, 32, 4, 22, 10, 28, 5, 23)(37, 55, 39, 57, 48, 66, 40, 58, 47, 65, 38, 56, 45, 63, 54, 72, 46, 64, 53, 71, 44, 62, 52, 70, 51, 69, 41, 59, 49, 67, 43, 61, 50, 68, 42, 60) L = (1, 40)(2, 46)(3, 47)(4, 45)(5, 50)(6, 48)(7, 37)(8, 41)(9, 53)(10, 52)(11, 54)(12, 38)(13, 42)(14, 39)(15, 43)(16, 49)(17, 51)(18, 44)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^36 ) } Outer automorphisms :: reflexible Dual of E16.105 Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.136 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 9, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1^-1 * Y3^-1, Y1^-1 * Y2 * Y3^-1 * Y2, Y3 * Y1^-3, (R * Y3)^2, Y1^-1 * Y3^-2 * Y2^-1, Y3^-2 * Y1^-1 * Y2^-1, (Y3^-1, Y1), (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y3^2 * Y2^-1 * Y1^-2, (Y2 * Y1)^3 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 4, 22, 10, 28, 17, 35, 15, 33, 6, 24, 11, 29, 18, 36, 14, 32, 3, 21, 9, 27, 16, 34, 13, 31, 7, 25, 12, 30, 5, 23)(37, 55, 39, 57, 46, 64, 43, 61, 47, 65, 38, 56, 45, 63, 53, 71, 48, 66, 54, 72, 44, 62, 52, 70, 51, 69, 41, 59, 50, 68, 40, 58, 49, 67, 42, 60) L = (1, 40)(2, 46)(3, 49)(4, 51)(5, 44)(6, 50)(7, 37)(8, 53)(9, 43)(10, 42)(11, 39)(12, 38)(13, 41)(14, 52)(15, 54)(16, 48)(17, 47)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^36 ) } Outer automorphisms :: reflexible Dual of E16.104 Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.137 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 18, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1 * Y3^-1 * Y2, Y1 * Y3^-2 * Y2, Y3^-2 * Y1 * Y2, Y2 * Y1 * Y2^2, (Y3^-1, Y2^-1), (Y2 * Y3)^2, (Y1^-1, Y2), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2)^2, Y2^-1 * Y1^2 * Y3 * Y2^-1, Y1 * Y2 * Y3 * Y1^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 14, 32, 17, 35, 5, 23)(3, 21, 9, 27, 18, 36, 7, 25, 12, 30, 15, 33)(4, 22, 10, 28, 13, 31, 6, 24, 11, 29, 16, 34)(37, 55, 39, 57, 49, 67, 41, 59, 51, 69, 46, 64, 53, 71, 48, 66, 40, 58, 50, 68, 43, 61, 52, 70, 44, 62, 54, 72, 47, 65, 38, 56, 45, 63, 42, 60) L = (1, 40)(2, 46)(3, 50)(4, 45)(5, 52)(6, 48)(7, 37)(8, 49)(9, 53)(10, 54)(11, 51)(12, 38)(13, 43)(14, 42)(15, 44)(16, 39)(17, 47)(18, 41)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 36^12 ), ( 36^36 ) } Outer automorphisms :: reflexible Dual of E16.139 Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 12^3, 36 ] E16.138 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 18, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y2, Y2^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^6, Y1 * Y3^6 * Y1, (Y3^-1 * Y1^-1)^18 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 14, 32, 11, 29, 5, 23)(3, 21, 9, 27, 15, 33, 18, 36, 13, 31, 7, 25)(4, 22, 10, 28, 16, 34, 17, 35, 12, 30, 6, 24)(37, 55, 39, 57, 40, 58, 38, 56, 45, 63, 46, 64, 44, 62, 51, 69, 52, 70, 50, 68, 54, 72, 53, 71, 47, 65, 49, 67, 48, 66, 41, 59, 43, 61, 42, 60) L = (1, 40)(2, 46)(3, 38)(4, 45)(5, 42)(6, 39)(7, 37)(8, 52)(9, 44)(10, 51)(11, 48)(12, 43)(13, 41)(14, 53)(15, 50)(16, 54)(17, 49)(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) :: { ( 36^12 ), ( 36^36 ) } Outer automorphisms :: reflexible Dual of E16.140 Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 12^3, 36 ] E16.139 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 18, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-1, (Y2^-1 * Y3^-1)^2, Y2^2 * Y3^2, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y3 * Y2^-2, Y1 * Y2^-2 * Y3 * Y2^-1, Y3^18 ] Map:: non-degenerate R = (1, 19, 2, 20, 4, 22, 9, 27, 15, 33, 14, 32, 13, 31, 3, 21, 8, 26, 12, 30, 17, 35, 6, 24, 10, 28, 16, 34, 11, 29, 18, 36, 7, 25, 5, 23)(37, 55, 39, 57, 47, 65, 45, 63, 53, 71, 41, 59, 49, 67, 52, 70, 40, 58, 48, 66, 43, 61, 50, 68, 46, 64, 38, 56, 44, 62, 54, 72, 51, 69, 42, 60) L = (1, 40)(2, 45)(3, 48)(4, 51)(5, 38)(6, 52)(7, 37)(8, 53)(9, 50)(10, 47)(11, 43)(12, 42)(13, 44)(14, 39)(15, 49)(16, 54)(17, 46)(18, 41)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E16.137 Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.140 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 18, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y2, Y2 * Y3^-1 * Y1, (Y3 * Y2)^2, Y2^-1 * Y3^-2 * Y2^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1^-2 * Y3, Y1^-3 * Y3^-1 * Y1^-1, Y1^-1 * Y2^14 * Y1^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 16, 34, 7, 25, 6, 24, 10, 28, 17, 35, 11, 29, 12, 30, 14, 32, 18, 36, 13, 31, 3, 21, 4, 22, 9, 27, 15, 33, 5, 23)(37, 55, 39, 57, 47, 65, 52, 70, 51, 69, 54, 72, 46, 64, 38, 56, 40, 58, 48, 66, 43, 61, 41, 59, 49, 67, 53, 71, 44, 62, 45, 63, 50, 68, 42, 60) L = (1, 40)(2, 45)(3, 48)(4, 50)(5, 39)(6, 38)(7, 37)(8, 51)(9, 54)(10, 44)(11, 43)(12, 42)(13, 47)(14, 46)(15, 49)(16, 41)(17, 52)(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) :: { ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E16.138 Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.141 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^-2 * Y2^-2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y3 * Y1 * Y3, (Y1, Y2), (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, Y1 * Y2^-4, (Y3 * Y2 * Y1)^2, Y1^10 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 11, 31, 5, 25)(3, 23, 8, 28, 6, 26, 10, 30, 13, 33)(4, 24, 9, 29, 16, 36, 19, 39, 14, 34)(12, 32, 17, 37, 15, 35, 18, 38, 20, 40)(41, 61, 43, 63, 51, 71, 50, 70, 42, 62, 48, 68, 45, 65, 53, 73, 47, 67, 46, 66)(44, 64, 52, 72, 59, 79, 58, 78, 49, 69, 57, 77, 54, 74, 60, 80, 56, 76, 55, 75) L = (1, 44)(2, 49)(3, 52)(4, 41)(5, 54)(6, 55)(7, 56)(8, 57)(9, 42)(10, 58)(11, 59)(12, 43)(13, 60)(14, 45)(15, 46)(16, 47)(17, 48)(18, 50)(19, 51)(20, 53)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^10 ), ( 20^20 ) } Outer automorphisms :: reflexible Dual of E16.146 Graph:: bipartite v = 6 e = 40 f = 4 degree seq :: [ 10^4, 20^2 ] E16.142 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^-1 * Y2^2, Y2 * Y3 * Y2^-1 * Y3, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y2)^2, Y1^5 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 13, 33, 5, 25)(3, 23, 8, 28, 15, 35, 14, 34, 6, 26)(4, 24, 9, 29, 16, 36, 18, 38, 11, 31)(10, 30, 17, 37, 20, 40, 19, 39, 12, 32)(41, 61, 43, 63, 42, 62, 48, 68, 47, 67, 55, 75, 53, 73, 54, 74, 45, 65, 46, 66)(44, 64, 50, 70, 49, 69, 57, 77, 56, 76, 60, 80, 58, 78, 59, 79, 51, 71, 52, 72) L = (1, 44)(2, 49)(3, 50)(4, 41)(5, 51)(6, 52)(7, 56)(8, 57)(9, 42)(10, 43)(11, 45)(12, 46)(13, 58)(14, 59)(15, 60)(16, 47)(17, 48)(18, 53)(19, 54)(20, 55)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^10 ), ( 20^20 ) } Outer automorphisms :: reflexible Dual of E16.148 Graph:: bipartite v = 6 e = 40 f = 4 degree seq :: [ 10^4, 20^2 ] E16.143 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, Y1^5 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 14, 34, 5, 25)(3, 23, 6, 26, 9, 29, 16, 36, 11, 31)(4, 24, 8, 28, 15, 35, 19, 39, 12, 32)(10, 30, 13, 33, 17, 37, 20, 40, 18, 38)(41, 61, 43, 63, 45, 65, 51, 71, 54, 74, 56, 76, 47, 67, 49, 69, 42, 62, 46, 66)(44, 64, 50, 70, 52, 72, 58, 78, 59, 79, 60, 80, 55, 75, 57, 77, 48, 68, 53, 73) L = (1, 44)(2, 48)(3, 50)(4, 41)(5, 52)(6, 53)(7, 55)(8, 42)(9, 57)(10, 43)(11, 58)(12, 45)(13, 46)(14, 59)(15, 47)(16, 60)(17, 49)(18, 51)(19, 54)(20, 56)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^10 ), ( 20^20 ) } Outer automorphisms :: reflexible Dual of E16.147 Graph:: bipartite v = 6 e = 40 f = 4 degree seq :: [ 10^4, 20^2 ] E16.144 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ R^2, (Y3 * Y1^-1)^2, Y1^-1 * Y2^-2 * Y1^-1, (Y2^-1 * Y3^-1)^2, Y3^-2 * Y2^-2, (R * Y1)^2, (R * Y2)^2, Y1^-2 * Y3^2, (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (Y2, Y3^-1), Y1 * Y2^-1 * Y3^2 * Y2^-1, Y3^4 * Y1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 13, 33, 5, 25)(3, 23, 9, 29, 6, 26, 11, 31, 15, 35)(4, 24, 10, 30, 18, 38, 7, 27, 12, 32)(14, 34, 19, 39, 17, 37, 16, 36, 20, 40)(41, 61, 43, 63, 53, 73, 51, 71, 42, 62, 49, 69, 45, 65, 55, 75, 48, 68, 46, 66)(44, 64, 54, 74, 47, 67, 56, 76, 50, 70, 59, 79, 52, 72, 60, 80, 58, 78, 57, 77) L = (1, 44)(2, 50)(3, 54)(4, 48)(5, 52)(6, 57)(7, 41)(8, 58)(9, 59)(10, 53)(11, 56)(12, 42)(13, 47)(14, 46)(15, 60)(16, 43)(17, 55)(18, 45)(19, 51)(20, 49)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^10 ), ( 20^20 ) } Outer automorphisms :: reflexible Dual of E16.149 Graph:: bipartite v = 6 e = 40 f = 4 degree seq :: [ 10^4, 20^2 ] E16.145 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y1^2 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y1 * Y2^-1)^2, (Y2, Y3), Y1 * Y2^-1 * Y3 * Y2^-1 * Y3, Y2^4 * Y1, (Y3^-1 * Y1^-1)^10 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 15, 35, 5, 25)(3, 23, 9, 29, 16, 36, 6, 26, 11, 31)(4, 24, 10, 30, 19, 39, 17, 37, 7, 27)(12, 32, 20, 40, 18, 38, 14, 34, 13, 33)(41, 61, 43, 63, 48, 68, 56, 76, 45, 65, 51, 71, 42, 62, 49, 69, 55, 75, 46, 66)(44, 64, 52, 72, 59, 79, 58, 78, 47, 67, 53, 73, 50, 70, 60, 80, 57, 77, 54, 74) L = (1, 44)(2, 50)(3, 52)(4, 42)(5, 47)(6, 54)(7, 41)(8, 59)(9, 60)(10, 48)(11, 53)(12, 49)(13, 43)(14, 51)(15, 57)(16, 58)(17, 45)(18, 46)(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) :: { ( 20^10 ), ( 20^20 ) } Outer automorphisms :: reflexible Dual of E16.150 Graph:: bipartite v = 6 e = 40 f = 4 degree seq :: [ 10^4, 20^2 ] E16.146 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y2, Y1^-1), (Y2^-1 * Y1^-1)^2, Y1^-2 * Y2^-2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, Y1^-1 * Y3 * Y1 * Y3, (R * Y2)^2, (R * Y1)^2, Y2 * Y3 * Y1^-1 * Y2 * Y1^-2, Y2^2 * Y1^-1 * Y3 * Y2^2 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 16, 36, 14, 34, 4, 24, 9, 29, 17, 37, 11, 31, 5, 25)(3, 23, 8, 28, 6, 26, 10, 30, 18, 38, 12, 32, 19, 39, 15, 35, 20, 40, 13, 33)(41, 61, 43, 63, 51, 71, 60, 80, 49, 69, 59, 79, 54, 74, 58, 78, 47, 67, 46, 66)(42, 62, 48, 68, 45, 65, 53, 73, 57, 77, 55, 75, 44, 64, 52, 72, 56, 76, 50, 70) L = (1, 44)(2, 49)(3, 52)(4, 41)(5, 54)(6, 55)(7, 57)(8, 59)(9, 42)(10, 60)(11, 56)(12, 43)(13, 58)(14, 45)(15, 46)(16, 51)(17, 47)(18, 53)(19, 48)(20, 50)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.141 Graph:: bipartite v = 4 e = 40 f = 6 degree seq :: [ 20^4 ] E16.147 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-2 * Y3 * Y1^-1, (Y2^-1, Y1^-1), Y3 * Y2^-1 * Y1^-1 * Y2^-1, Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y1^-5, Y1^-2 * Y2^6 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 15, 35, 11, 31, 4, 24, 9, 29, 17, 37, 14, 34, 5, 25)(3, 23, 8, 28, 16, 36, 20, 40, 19, 39, 12, 32, 6, 26, 10, 30, 18, 38, 13, 33)(41, 61, 43, 63, 51, 71, 59, 79, 54, 74, 58, 78, 47, 67, 56, 76, 49, 69, 46, 66)(42, 62, 48, 68, 44, 64, 52, 72, 45, 65, 53, 73, 55, 75, 60, 80, 57, 77, 50, 70) L = (1, 44)(2, 49)(3, 52)(4, 41)(5, 51)(6, 48)(7, 57)(8, 46)(9, 42)(10, 56)(11, 45)(12, 43)(13, 59)(14, 55)(15, 54)(16, 50)(17, 47)(18, 60)(19, 53)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.143 Graph:: bipartite v = 4 e = 40 f = 6 degree seq :: [ 20^4 ] E16.148 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y1^-1, Y2), Y2^2 * Y1^-1 * Y3, Y3 * Y2^-1 * Y1 * Y2^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-5, (R * Y2 * Y3)^2 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 15, 35, 12, 32, 4, 24, 9, 29, 17, 37, 13, 33, 5, 25)(3, 23, 8, 28, 16, 36, 14, 34, 6, 26, 10, 30, 18, 38, 20, 40, 19, 39, 11, 31)(41, 61, 43, 63, 49, 69, 58, 78, 47, 67, 56, 76, 53, 73, 59, 79, 52, 72, 46, 66)(42, 62, 48, 68, 57, 77, 60, 80, 55, 75, 54, 74, 45, 65, 51, 71, 44, 64, 50, 70) L = (1, 44)(2, 49)(3, 50)(4, 41)(5, 52)(6, 51)(7, 57)(8, 58)(9, 42)(10, 43)(11, 46)(12, 45)(13, 55)(14, 59)(15, 53)(16, 60)(17, 47)(18, 48)(19, 54)(20, 56)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.142 Graph:: bipartite v = 4 e = 40 f = 6 degree seq :: [ 20^4 ] E16.149 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, Y3 * Y1^-1, Y1^-2 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (Y1, Y2^-1), (R * Y2 * Y3^-1)^2, Y2^10, Y1^10, (Y3 * Y2^-1)^10 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 11, 31, 15, 35, 19, 39, 17, 37, 14, 34, 9, 29, 4, 24)(3, 23, 7, 27, 5, 25, 8, 28, 12, 32, 16, 36, 20, 40, 18, 38, 13, 33, 10, 30)(41, 61, 43, 63, 49, 69, 53, 73, 57, 77, 60, 80, 55, 75, 52, 72, 46, 66, 45, 65)(42, 62, 47, 67, 44, 64, 50, 70, 54, 74, 58, 78, 59, 79, 56, 76, 51, 71, 48, 68) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 51)(7, 45)(8, 52)(9, 44)(10, 43)(11, 55)(12, 56)(13, 50)(14, 49)(15, 59)(16, 60)(17, 54)(18, 53)(19, 57)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.144 Graph:: bipartite v = 4 e = 40 f = 6 degree seq :: [ 20^4 ] E16.150 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1^-1 * Y3^-1, (Y2^-1, Y1^-1), Y2^-1 * Y3^-2 * Y2^-1, Y1^-1 * Y3^-3, Y1^-1 * Y3 * Y1^-2, (Y1, Y3^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1 * Y2^-1)^2, Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-2, (Y2^-1 * Y3 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 4, 24, 10, 30, 18, 38, 15, 35, 7, 27, 12, 32, 5, 25)(3, 23, 9, 29, 17, 37, 13, 33, 20, 40, 16, 36, 6, 26, 11, 31, 19, 39, 14, 34)(41, 61, 43, 63, 50, 70, 60, 80, 52, 72, 59, 79, 48, 68, 57, 77, 55, 75, 46, 66)(42, 62, 49, 69, 58, 78, 56, 76, 45, 65, 54, 74, 44, 64, 53, 73, 47, 67, 51, 71) L = (1, 44)(2, 50)(3, 53)(4, 55)(5, 48)(6, 54)(7, 41)(8, 58)(9, 60)(10, 47)(11, 43)(12, 42)(13, 46)(14, 57)(15, 45)(16, 59)(17, 56)(18, 52)(19, 49)(20, 51)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.145 Graph:: bipartite v = 4 e = 40 f = 6 degree seq :: [ 20^4 ] E16.151 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, (R * Y2)^2, (Y2^-1, Y1), (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y1^4, Y3 * Y1^2 * Y3 * Y2^-1, Y1^-2 * Y2^-1 * Y3^2, Y3^-1 * Y1 * Y2 * Y3^-1 * Y1, Y3^5 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 9, 29, 15, 35, 13, 33)(4, 24, 10, 30, 14, 34, 16, 36)(6, 26, 11, 31, 20, 40, 18, 38)(7, 27, 12, 32, 17, 37, 19, 39)(41, 61, 43, 63, 47, 67, 54, 74, 60, 80, 48, 68, 55, 75, 57, 77, 44, 64, 46, 66)(42, 62, 49, 69, 52, 72, 56, 76, 58, 78, 45, 65, 53, 73, 59, 79, 50, 70, 51, 71) L = (1, 44)(2, 50)(3, 46)(4, 55)(5, 56)(6, 57)(7, 41)(8, 54)(9, 51)(10, 53)(11, 59)(12, 42)(13, 58)(14, 43)(15, 60)(16, 49)(17, 48)(18, 52)(19, 45)(20, 47)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20, 40, 20, 40, 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E16.158 Graph:: bipartite v = 7 e = 40 f = 3 degree seq :: [ 8^5, 20^2 ] E16.152 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, (Y1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^4, (Y3^-1, Y1^-1), Y1^-2 * Y3^2 * Y2, Y1^-2 * Y2 * Y3^2, Y3^5 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 9, 29, 20, 40, 14, 34)(4, 24, 10, 30, 19, 39, 16, 36)(6, 26, 11, 31, 15, 35, 17, 37)(7, 27, 12, 32, 13, 33, 18, 38)(41, 61, 43, 63, 44, 64, 53, 73, 55, 75, 48, 68, 60, 80, 59, 79, 47, 67, 46, 66)(42, 62, 49, 69, 50, 70, 58, 78, 57, 77, 45, 65, 54, 74, 56, 76, 52, 72, 51, 71) L = (1, 44)(2, 50)(3, 53)(4, 55)(5, 56)(6, 43)(7, 41)(8, 59)(9, 58)(10, 57)(11, 49)(12, 42)(13, 48)(14, 52)(15, 60)(16, 51)(17, 54)(18, 45)(19, 46)(20, 47)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20, 40, 20, 40, 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E16.156 Graph:: bipartite v = 7 e = 40 f = 3 degree seq :: [ 8^5, 20^2 ] E16.153 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, (Y2^-1 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3^-1, Y1^-1), Y2^-1 * Y3^-1 * Y1^-2, Y2 * Y1^-1 * Y3 * Y1^-1, (R * Y3)^2, Y1^4, (R * Y2)^2, Y3^-2 * Y2^-2, Y3^-2 * Y2^2 * Y3^-1, (Y2 * Y3^-1)^10 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 9, 29, 7, 27, 12, 32)(4, 24, 10, 30, 6, 26, 11, 31)(13, 33, 17, 37, 14, 34, 18, 38)(15, 35, 19, 39, 16, 36, 20, 40)(41, 61, 43, 63, 53, 73, 56, 76, 44, 64, 48, 68, 47, 67, 54, 74, 55, 75, 46, 66)(42, 62, 49, 69, 57, 77, 60, 80, 50, 70, 45, 65, 52, 72, 58, 78, 59, 79, 51, 71) L = (1, 44)(2, 50)(3, 48)(4, 55)(5, 51)(6, 56)(7, 41)(8, 46)(9, 45)(10, 59)(11, 60)(12, 42)(13, 47)(14, 43)(15, 53)(16, 54)(17, 52)(18, 49)(19, 57)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20, 40, 20, 40, 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E16.157 Graph:: bipartite v = 7 e = 40 f = 3 degree seq :: [ 8^5, 20^2 ] E16.154 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1 * Y3, Y2^-3 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1), Y1^-1 * Y2 * Y1^-2, Y1^-1 * Y3 * Y1^-2 * Y3, Y3 * Y1 * Y2 * Y3 * Y2, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 3, 23, 9, 29, 18, 38, 13, 33, 6, 26, 11, 31, 5, 25)(4, 24, 10, 30, 19, 39, 14, 34, 17, 37, 20, 40, 16, 36, 7, 27, 12, 32, 15, 35)(41, 61, 43, 63, 53, 73, 45, 65, 48, 68, 58, 78, 51, 71, 42, 62, 49, 69, 46, 66)(44, 64, 54, 74, 56, 76, 55, 75, 59, 79, 60, 80, 52, 72, 50, 70, 57, 77, 47, 67) L = (1, 44)(2, 50)(3, 54)(4, 43)(5, 55)(6, 47)(7, 41)(8, 59)(9, 57)(10, 49)(11, 52)(12, 42)(13, 56)(14, 53)(15, 48)(16, 45)(17, 46)(18, 60)(19, 58)(20, 51)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) } Outer automorphisms :: reflexible Dual of E16.155 Graph:: bipartite v = 4 e = 40 f = 6 degree seq :: [ 20^4 ] E16.155 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y3^-1 * Y1, Y1 * Y3^-1, (Y1, Y2^-1), (R * Y1)^2, Y2^4, (R * Y3)^2, Y1^2 * Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y1^-4, Y2^-1 * Y3 * Y2^-2 * Y1^-1 * Y2^-1, Y2^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^10 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 13, 33, 12, 32, 5, 25, 8, 28, 15, 35, 19, 39, 17, 37, 9, 29, 16, 36, 20, 40, 18, 38, 10, 30, 3, 23, 7, 27, 14, 34, 11, 31, 4, 24)(41, 61, 43, 63, 49, 69, 45, 65)(42, 62, 47, 67, 56, 76, 48, 68)(44, 64, 50, 70, 57, 77, 52, 72)(46, 66, 54, 74, 60, 80, 55, 75)(51, 71, 58, 78, 59, 79, 53, 73) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 53)(7, 54)(8, 55)(9, 56)(10, 43)(11, 44)(12, 45)(13, 52)(14, 51)(15, 59)(16, 60)(17, 49)(18, 50)(19, 57)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^8 ), ( 20^40 ) } Outer automorphisms :: reflexible Dual of E16.154 Graph:: bipartite v = 6 e = 40 f = 4 degree seq :: [ 8^5, 40 ] E16.156 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y1, Y1 * Y2^-2, (R * Y2)^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, Y3^5, (Y3^2 * Y1^-1)^2, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 9, 29, 15, 35, 17, 37, 12, 32, 13, 33, 4, 24, 5, 25)(3, 23, 8, 28, 11, 31, 16, 36, 19, 39, 20, 40, 18, 38, 14, 34, 10, 30, 6, 26)(41, 61, 43, 63, 42, 62, 48, 68, 47, 67, 51, 71, 49, 69, 56, 76, 55, 75, 59, 79, 57, 77, 60, 80, 52, 72, 58, 78, 53, 73, 54, 74, 44, 64, 50, 70, 45, 65, 46, 66) L = (1, 44)(2, 45)(3, 50)(4, 52)(5, 53)(6, 54)(7, 41)(8, 46)(9, 42)(10, 58)(11, 43)(12, 55)(13, 57)(14, 60)(15, 47)(16, 48)(17, 49)(18, 59)(19, 51)(20, 56)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E16.152 Graph:: bipartite v = 3 e = 40 f = 7 degree seq :: [ 20^2, 40 ] E16.157 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^2, Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), (R * Y2)^2, Y3^5, (Y3^-1 * Y1^-1)^10 ] Map:: non-degenerate R = (1, 21, 2, 22, 4, 24, 8, 28, 12, 32, 16, 36, 15, 35, 14, 34, 7, 27, 5, 25)(3, 23, 6, 26, 9, 29, 13, 33, 17, 37, 20, 40, 19, 39, 18, 38, 11, 31, 10, 30)(41, 61, 43, 63, 45, 65, 50, 70, 47, 67, 51, 71, 54, 74, 58, 78, 55, 75, 59, 79, 56, 76, 60, 80, 52, 72, 57, 77, 48, 68, 53, 73, 44, 64, 49, 69, 42, 62, 46, 66) L = (1, 44)(2, 48)(3, 49)(4, 52)(5, 42)(6, 53)(7, 41)(8, 56)(9, 57)(10, 46)(11, 43)(12, 55)(13, 60)(14, 45)(15, 47)(16, 54)(17, 59)(18, 50)(19, 51)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E16.153 Graph:: bipartite v = 3 e = 40 f = 7 degree seq :: [ 20^2, 40 ] E16.158 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 10, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1 * Y2 * Y3^-1, Y3^2 * Y1^-2, (Y3^-1, Y1^-1), (R * Y2)^2, Y1 * Y2^-2 * Y3, Y2^2 * Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y3^-1), (Y2^-1, Y1^-1), Y2 * Y1 * Y3^2 * Y2, Y3^5, Y1 * Y2 * Y1 * Y2 * Y1, Y3 * Y1^4, Y3 * Y1 * Y2^18 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 17, 37, 7, 27, 12, 32, 4, 24, 10, 30, 15, 35, 5, 25)(3, 23, 9, 29, 16, 36, 6, 26, 11, 31, 19, 39, 13, 33, 18, 38, 20, 40, 14, 34)(41, 61, 43, 63, 50, 70, 58, 78, 47, 67, 51, 71, 42, 62, 49, 69, 55, 75, 60, 80, 52, 72, 59, 79, 48, 68, 56, 76, 45, 65, 54, 74, 44, 64, 53, 73, 57, 77, 46, 66) L = (1, 44)(2, 50)(3, 53)(4, 48)(5, 52)(6, 54)(7, 41)(8, 55)(9, 58)(10, 57)(11, 43)(12, 42)(13, 56)(14, 59)(15, 47)(16, 60)(17, 45)(18, 46)(19, 49)(20, 51)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E16.151 Graph:: bipartite v = 3 e = 40 f = 7 degree seq :: [ 20^2, 40 ] E16.159 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y1, Y1 * Y2^-2, (Y3, Y2^-1), (Y1^-1, Y3^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^4, Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 3, 23, 5, 25)(4, 24, 8, 28, 14, 34, 10, 30, 13, 33)(7, 27, 9, 29, 16, 36, 11, 31, 15, 35)(12, 32, 17, 37, 20, 40, 18, 38, 19, 39)(41, 61, 43, 63, 42, 62, 45, 65, 46, 66)(44, 64, 50, 70, 48, 68, 53, 73, 54, 74)(47, 67, 51, 71, 49, 69, 55, 75, 56, 76)(52, 72, 58, 78, 57, 77, 59, 79, 60, 80) L = (1, 44)(2, 48)(3, 50)(4, 52)(5, 53)(6, 54)(7, 41)(8, 57)(9, 42)(10, 58)(11, 43)(12, 47)(13, 59)(14, 60)(15, 45)(16, 46)(17, 49)(18, 51)(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) :: { ( 40^10 ) } Outer automorphisms :: reflexible Dual of E16.173 Graph:: bipartite v = 8 e = 40 f = 2 degree seq :: [ 10^8 ] E16.160 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y2^4 * Y1, Y1^5, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^20 ] Map:: R = (1, 21, 2, 22, 6, 26, 11, 31, 4, 24)(3, 23, 7, 27, 14, 34, 18, 38, 10, 30)(5, 25, 8, 28, 15, 35, 19, 39, 12, 32)(9, 29, 13, 33, 16, 36, 20, 40, 17, 37)(41, 61, 43, 63, 49, 69, 52, 72, 44, 64, 50, 70, 57, 77, 59, 79, 51, 71, 58, 78, 60, 80, 55, 75, 46, 66, 54, 74, 56, 76, 48, 68, 42, 62, 47, 67, 53, 73, 45, 65) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.161 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, Y2^-4 * Y1, Y1^5, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^20 ] Map:: R = (1, 21, 2, 22, 6, 26, 11, 31, 4, 24)(3, 23, 7, 27, 14, 34, 17, 37, 10, 30)(5, 25, 8, 28, 15, 35, 18, 38, 12, 32)(9, 29, 16, 36, 20, 40, 19, 39, 13, 33)(41, 61, 43, 63, 49, 69, 48, 68, 42, 62, 47, 67, 56, 76, 55, 75, 46, 66, 54, 74, 60, 80, 58, 78, 51, 71, 57, 77, 59, 79, 52, 72, 44, 64, 50, 70, 53, 73, 45, 65) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.162 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1), Y1^-5, Y1^5, Y2^4 * Y1^-2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^20 ] Map:: R = (1, 21, 2, 22, 6, 26, 11, 31, 4, 24)(3, 23, 7, 27, 14, 34, 18, 38, 10, 30)(5, 25, 8, 28, 15, 35, 19, 39, 12, 32)(9, 29, 16, 36, 20, 40, 13, 33, 17, 37)(41, 61, 43, 63, 49, 69, 55, 75, 46, 66, 54, 74, 60, 80, 52, 72, 44, 64, 50, 70, 57, 77, 48, 68, 42, 62, 47, 67, 56, 76, 59, 79, 51, 71, 58, 78, 53, 73, 45, 65) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.163 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (Y2, Y1), (R * Y3)^2, Y1^-5, Y1^5, Y2^-4 * Y1^-2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-2 * Y1, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^20 ] Map:: R = (1, 21, 2, 22, 6, 26, 11, 31, 4, 24)(3, 23, 7, 27, 14, 34, 20, 40, 10, 30)(5, 25, 8, 28, 15, 35, 18, 38, 12, 32)(9, 29, 16, 36, 13, 33, 17, 37, 19, 39)(41, 61, 43, 63, 49, 69, 58, 78, 51, 71, 60, 80, 57, 77, 48, 68, 42, 62, 47, 67, 56, 76, 52, 72, 44, 64, 50, 70, 59, 79, 55, 75, 46, 66, 54, 74, 53, 73, 45, 65) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.164 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y2 * Y3^-1 * Y2^3, Y1^5, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2 * Y3^-1, (Y3^-1 * Y1^-1)^5 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 11, 31, 4, 24)(3, 23, 7, 27, 14, 34, 17, 37, 10, 30)(5, 25, 8, 28, 15, 35, 18, 38, 12, 32)(9, 29, 16, 36, 20, 40, 19, 39, 13, 33)(41, 61, 43, 63, 49, 69, 48, 68, 42, 62, 47, 67, 56, 76, 55, 75, 46, 66, 54, 74, 60, 80, 58, 78, 51, 71, 57, 77, 59, 79, 52, 72, 44, 64, 50, 70, 53, 73, 45, 65) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 51)(7, 54)(8, 55)(9, 56)(10, 43)(11, 44)(12, 45)(13, 49)(14, 57)(15, 58)(16, 60)(17, 50)(18, 52)(19, 53)(20, 59)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E16.171 Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.165 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-2, Y1 * Y3^2, (Y2^-1, Y1), (R * Y1)^2, (Y2, Y3), (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y3 * Y2^-3 ] Map:: non-degenerate R = (1, 21, 2, 22, 4, 24, 7, 27, 5, 25)(3, 23, 8, 28, 11, 31, 13, 33, 12, 32)(6, 26, 9, 29, 14, 34, 17, 37, 15, 35)(10, 30, 18, 38, 20, 40, 16, 36, 19, 39)(41, 61, 43, 63, 50, 70, 54, 74, 44, 64, 51, 71, 60, 80, 55, 75, 45, 65, 52, 72, 59, 79, 49, 69, 42, 62, 48, 68, 58, 78, 57, 77, 47, 67, 53, 73, 56, 76, 46, 66) L = (1, 44)(2, 47)(3, 51)(4, 45)(5, 42)(6, 54)(7, 41)(8, 53)(9, 57)(10, 60)(11, 52)(12, 48)(13, 43)(14, 55)(15, 49)(16, 50)(17, 46)(18, 56)(19, 58)(20, 59)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E16.172 Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.166 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-2, Y3^2 * Y1^-1, (Y2, Y1), (Y2, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-3 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 4, 24, 5, 25)(3, 23, 8, 28, 13, 33, 11, 31, 12, 32)(6, 26, 9, 29, 17, 37, 14, 34, 15, 35)(10, 30, 18, 38, 16, 36, 19, 39, 20, 40)(41, 61, 43, 63, 50, 70, 54, 74, 44, 64, 51, 71, 59, 79, 49, 69, 42, 62, 48, 68, 58, 78, 55, 75, 45, 65, 52, 72, 60, 80, 57, 77, 47, 67, 53, 73, 56, 76, 46, 66) L = (1, 44)(2, 45)(3, 51)(4, 42)(5, 47)(6, 54)(7, 41)(8, 52)(9, 55)(10, 59)(11, 48)(12, 53)(13, 43)(14, 49)(15, 57)(16, 50)(17, 46)(18, 60)(19, 58)(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) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E16.170 Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.167 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^2, Y1 * Y3^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y2^-1), (Y2, Y3), (R * Y2)^2, Y2^-1 * Y1^-1 * Y2^-3, (Y2^-2 * Y3)^2 ] Map:: non-degenerate R = (1, 21, 2, 22, 4, 24, 7, 27, 5, 25)(3, 23, 8, 28, 11, 31, 13, 33, 12, 32)(6, 26, 9, 29, 14, 34, 17, 37, 15, 35)(10, 30, 16, 36, 18, 38, 20, 40, 19, 39)(41, 61, 43, 63, 50, 70, 55, 75, 45, 65, 52, 72, 59, 79, 57, 77, 47, 67, 53, 73, 60, 80, 54, 74, 44, 64, 51, 71, 58, 78, 49, 69, 42, 62, 48, 68, 56, 76, 46, 66) L = (1, 44)(2, 47)(3, 51)(4, 45)(5, 42)(6, 54)(7, 41)(8, 53)(9, 57)(10, 58)(11, 52)(12, 48)(13, 43)(14, 55)(15, 49)(16, 60)(17, 46)(18, 59)(19, 56)(20, 50)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E16.169 Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.168 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-2, Y1 * Y3^-2, (Y1^-1, Y2), (R * Y1)^2, (R * Y3)^2, (Y2, Y3), (R * Y2)^2, Y2^-1 * Y1 * Y2^-3, (Y2^-2 * Y3)^2 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 4, 24, 5, 25)(3, 23, 8, 28, 13, 33, 11, 31, 12, 32)(6, 26, 9, 29, 17, 37, 14, 34, 15, 35)(10, 30, 18, 38, 20, 40, 19, 39, 16, 36)(41, 61, 43, 63, 50, 70, 49, 69, 42, 62, 48, 68, 58, 78, 57, 77, 47, 67, 53, 73, 60, 80, 54, 74, 44, 64, 51, 71, 59, 79, 55, 75, 45, 65, 52, 72, 56, 76, 46, 66) L = (1, 44)(2, 45)(3, 51)(4, 42)(5, 47)(6, 54)(7, 41)(8, 52)(9, 55)(10, 59)(11, 48)(12, 53)(13, 43)(14, 49)(15, 57)(16, 60)(17, 46)(18, 56)(19, 58)(20, 50)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.169 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (Y2^-1, Y1), (R * Y3)^2, (R * Y1)^2, Y1^-5, Y1^5, Y2^4 * Y1^-2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^20 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 11, 31, 4, 24)(3, 23, 7, 27, 14, 34, 18, 38, 10, 30)(5, 25, 8, 28, 15, 35, 19, 39, 12, 32)(9, 29, 16, 36, 20, 40, 13, 33, 17, 37)(41, 61, 43, 63, 49, 69, 55, 75, 46, 66, 54, 74, 60, 80, 52, 72, 44, 64, 50, 70, 57, 77, 48, 68, 42, 62, 47, 67, 56, 76, 59, 79, 51, 71, 58, 78, 53, 73, 45, 65) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 51)(7, 54)(8, 55)(9, 56)(10, 43)(11, 44)(12, 45)(13, 57)(14, 58)(15, 59)(16, 60)(17, 49)(18, 50)(19, 52)(20, 53)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E16.167 Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.170 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^2, Y1 * Y3^-2, (Y2, Y3^-1), (R * Y1)^2, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1^-1 * Y2^-3, Y2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 4, 24, 5, 25)(3, 23, 8, 28, 13, 33, 11, 31, 12, 32)(6, 26, 9, 29, 17, 37, 14, 34, 15, 35)(10, 30, 16, 36, 18, 38, 19, 39, 20, 40)(41, 61, 43, 63, 50, 70, 55, 75, 45, 65, 52, 72, 60, 80, 54, 74, 44, 64, 51, 71, 59, 79, 57, 77, 47, 67, 53, 73, 58, 78, 49, 69, 42, 62, 48, 68, 56, 76, 46, 66) L = (1, 44)(2, 45)(3, 51)(4, 42)(5, 47)(6, 54)(7, 41)(8, 52)(9, 55)(10, 59)(11, 48)(12, 53)(13, 43)(14, 49)(15, 57)(16, 60)(17, 46)(18, 50)(19, 56)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E16.166 Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.171 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y1 * Y3^-1 * Y1, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2), (R * Y2)^2, Y2^-2 * Y1 * Y2^-2, Y2^-2 * Y1 * Y2^-2, (Y2^-1 * Y3)^20 ] Map:: non-degenerate R = (1, 21, 2, 22, 4, 24, 7, 27, 5, 25)(3, 23, 8, 28, 11, 31, 13, 33, 12, 32)(6, 26, 9, 29, 14, 34, 17, 37, 15, 35)(10, 30, 18, 38, 19, 39, 20, 40, 16, 36)(41, 61, 43, 63, 50, 70, 49, 69, 42, 62, 48, 68, 58, 78, 54, 74, 44, 64, 51, 71, 59, 79, 57, 77, 47, 67, 53, 73, 60, 80, 55, 75, 45, 65, 52, 72, 56, 76, 46, 66) L = (1, 44)(2, 47)(3, 51)(4, 45)(5, 42)(6, 54)(7, 41)(8, 53)(9, 57)(10, 59)(11, 52)(12, 48)(13, 43)(14, 55)(15, 49)(16, 58)(17, 46)(18, 60)(19, 56)(20, 50)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E16.164 Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.172 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y1, Y1^5, Y2^-1 * Y1^-1 * Y2^-3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^2 * Y2^-2 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^5, Y3 * Y1 * Y3^-2 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 11, 31, 4, 24)(3, 23, 7, 27, 14, 34, 20, 40, 10, 30)(5, 25, 8, 28, 15, 35, 18, 38, 12, 32)(9, 29, 16, 36, 13, 33, 17, 37, 19, 39)(41, 61, 43, 63, 49, 69, 58, 78, 51, 71, 60, 80, 57, 77, 48, 68, 42, 62, 47, 67, 56, 76, 52, 72, 44, 64, 50, 70, 59, 79, 55, 75, 46, 66, 54, 74, 53, 73, 45, 65) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 51)(7, 54)(8, 55)(9, 56)(10, 43)(11, 44)(12, 45)(13, 57)(14, 60)(15, 58)(16, 53)(17, 59)(18, 52)(19, 49)(20, 50)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E16.165 Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.173 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-2 * Y3, (Y2^-1, Y1^-1), Y2 * Y1^-1 * Y3 * Y1^-1, Y1^-1 * Y3 * Y2^-2, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y2)^2, Y1^-1 * Y2^-1 * Y3 * Y2^-1, Y3^4, (R * Y1)^2, (R * Y3)^2, (Y3, Y1), Y3 * Y2 * Y1^3 * Y3 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 17, 37, 16, 36, 7, 27, 12, 32, 3, 23, 9, 29, 18, 38, 14, 34, 20, 40, 13, 33, 6, 26, 11, 31, 4, 24, 10, 30, 19, 39, 15, 35, 5, 25)(41, 61, 43, 63, 51, 71, 42, 62, 49, 69, 44, 64, 48, 68, 58, 78, 50, 70, 57, 77, 54, 74, 59, 79, 56, 76, 60, 80, 55, 75, 47, 67, 53, 73, 45, 65, 52, 72, 46, 66) L = (1, 44)(2, 50)(3, 48)(4, 54)(5, 51)(6, 49)(7, 41)(8, 59)(9, 57)(10, 60)(11, 58)(12, 42)(13, 43)(14, 47)(15, 46)(16, 45)(17, 55)(18, 56)(19, 53)(20, 52)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10^40 ) } Outer automorphisms :: reflexible Dual of E16.159 Graph:: bipartite v = 2 e = 40 f = 8 degree seq :: [ 40^2 ] E16.174 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y3, Y1^3, Y2 * Y1 * Y3 * Y1, (R * Y1)^2, Y3 * Y1 * Y2 * Y1, (R * Y3)^2, (R * Y2)^2, Y2^7, Y3^-6 * Y2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y1 * Y2 ] Map:: non-degenerate R = (1, 22, 2, 23, 5, 26)(3, 24, 8, 29, 7, 28)(4, 25, 9, 30, 6, 27)(10, 31, 15, 36, 11, 32)(12, 33, 14, 35, 13, 34)(16, 37, 18, 39, 17, 38)(19, 40, 21, 42, 20, 41)(43, 64, 45, 66, 52, 73, 58, 79, 61, 82, 56, 77, 48, 69)(44, 65, 50, 71, 57, 78, 60, 81, 63, 84, 55, 76, 46, 67)(47, 68, 49, 70, 53, 74, 59, 80, 62, 83, 54, 75, 51, 72) L = (1, 46)(2, 51)(3, 44)(4, 54)(5, 48)(6, 55)(7, 43)(8, 47)(9, 56)(10, 50)(11, 45)(12, 61)(13, 62)(14, 63)(15, 49)(16, 57)(17, 52)(18, 53)(19, 60)(20, 58)(21, 59)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 42^6 ), ( 42^14 ) } Outer automorphisms :: reflexible Dual of E16.186 Graph:: bipartite v = 10 e = 42 f = 2 degree seq :: [ 6^7, 14^3 ] E16.175 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y2, Y1^-1), Y3^-2 * Y2 * Y3^-1, (R * Y3)^2, Y2 * Y3 * Y2 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y1^-1), Y1^-1 * Y3^-1 * Y1^-1 * Y2^-2, Y2^7, Y3^-1 * Y1 * Y2^2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 ] Map:: non-degenerate R = (1, 22, 2, 23, 5, 26)(3, 24, 8, 29, 12, 33)(4, 25, 9, 30, 14, 35)(6, 27, 10, 31, 16, 37)(7, 28, 11, 32, 17, 38)(13, 34, 18, 39, 20, 41)(15, 36, 19, 40, 21, 42)(43, 64, 45, 66, 53, 74, 60, 81, 63, 84, 56, 77, 48, 69)(44, 65, 50, 71, 59, 80, 62, 83, 57, 78, 46, 67, 52, 73)(47, 68, 54, 75, 49, 70, 55, 76, 61, 82, 51, 72, 58, 79) L = (1, 46)(2, 51)(3, 52)(4, 55)(5, 56)(6, 57)(7, 43)(8, 58)(9, 60)(10, 61)(11, 44)(12, 48)(13, 45)(14, 62)(15, 49)(16, 63)(17, 47)(18, 50)(19, 53)(20, 54)(21, 59)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 42^6 ), ( 42^14 ) } Outer automorphisms :: reflexible Dual of E16.187 Graph:: bipartite v = 10 e = 42 f = 2 degree seq :: [ 6^7, 14^3 ] E16.176 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y1 * Y2 * Y1^-1 * Y3, (Y2^-1, Y1^-1), (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^2 * Y3^-1 * Y1^-2, (Y1^-1 * Y3^-1)^3, Y2 * Y1^-2 * Y3^-2 * Y1^-1, Y1 * Y3^-1 * Y1^2 * Y2 * Y1 * Y2, Y2^2 * Y3^-1 * Y1^4, Y2^21, (Y3 * Y2^-1)^21 ] Map:: non-degenerate R = (1, 22, 2, 23, 6, 27, 14, 35, 19, 40, 13, 34, 5, 26)(3, 24, 7, 28, 15, 36, 20, 41, 11, 32, 18, 39, 10, 31)(4, 25, 8, 29, 16, 37, 9, 30, 17, 38, 21, 42, 12, 33)(43, 64, 45, 66, 51, 72, 56, 77, 62, 83, 54, 75, 47, 68, 52, 73, 58, 79, 48, 69, 57, 78, 63, 84, 55, 76, 60, 81, 50, 71, 44, 65, 49, 70, 59, 80, 61, 82, 53, 74, 46, 67) L = (1, 46)(2, 50)(3, 43)(4, 53)(5, 54)(6, 58)(7, 44)(8, 60)(9, 45)(10, 47)(11, 61)(12, 62)(13, 63)(14, 51)(15, 48)(16, 52)(17, 49)(18, 55)(19, 59)(20, 56)(21, 57)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ), ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) } Outer automorphisms :: reflexible Dual of E16.182 Graph:: bipartite v = 4 e = 42 f = 8 degree seq :: [ 14^3, 42 ] E16.177 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, (Y1^-1, Y3^-1), (Y1, Y2), Y1^-1 * Y3 * Y2 * Y1^-1, Y2 * Y1^-1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^3 * Y1 * Y3 * Y2 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 18, 39, 21, 42, 14, 35, 5, 26)(3, 24, 9, 30, 13, 34, 20, 41, 16, 37, 7, 28, 12, 33)(4, 25, 10, 31, 19, 40, 17, 38, 15, 36, 6, 27, 11, 32)(43, 64, 45, 66, 46, 67, 50, 71, 55, 76, 61, 82, 63, 84, 58, 79, 57, 78, 47, 68, 54, 75, 53, 74, 44, 65, 51, 72, 52, 73, 60, 81, 62, 83, 59, 80, 56, 77, 49, 70, 48, 69) L = (1, 46)(2, 52)(3, 50)(4, 55)(5, 53)(6, 45)(7, 43)(8, 61)(9, 60)(10, 62)(11, 51)(12, 44)(13, 63)(14, 48)(15, 54)(16, 47)(17, 49)(18, 59)(19, 58)(20, 56)(21, 57)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ), ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) } Outer automorphisms :: reflexible Dual of E16.185 Graph:: bipartite v = 4 e = 42 f = 8 degree seq :: [ 14^3, 42 ] E16.178 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1 * Y2^3, (Y3^-1 * Y1^-1)^3, Y3^5 * Y2^-1, Y1^7, Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 18, 39, 21, 42, 15, 36, 5, 26)(3, 24, 9, 30, 14, 35, 13, 34, 20, 41, 16, 37, 7, 28)(4, 25, 10, 31, 19, 40, 17, 38, 12, 33, 11, 32, 6, 27)(43, 64, 45, 66, 53, 74, 47, 68, 49, 70, 54, 75, 57, 78, 58, 79, 59, 80, 63, 84, 62, 83, 61, 82, 60, 81, 55, 76, 52, 73, 50, 71, 56, 77, 46, 67, 44, 65, 51, 72, 48, 69) L = (1, 46)(2, 52)(3, 44)(4, 55)(5, 48)(6, 56)(7, 43)(8, 61)(9, 50)(10, 62)(11, 51)(12, 45)(13, 63)(14, 60)(15, 53)(16, 47)(17, 49)(18, 59)(19, 58)(20, 57)(21, 54)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ), ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) } Outer automorphisms :: reflexible Dual of E16.183 Graph:: bipartite v = 4 e = 42 f = 8 degree seq :: [ 14^3, 42 ] E16.179 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2^-1), Y3 * Y1^-1 * Y3 * Y2^-1, (R * Y3)^2, Y3^2 * Y1^-1 * Y2^-1, (R * Y1)^2, Y3^2 * Y2^-1 * Y1^-1, (R * Y2)^2, Y1 * Y3^2 * Y2^2, Y1^2 * Y3^-1 * Y1 * Y2^-1, (Y3^-1 * Y1^-1)^3, Y1^7 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 14, 35, 21, 42, 17, 38, 5, 26)(3, 24, 9, 30, 20, 41, 19, 40, 7, 28, 12, 33, 15, 36)(4, 25, 10, 31, 13, 34, 18, 39, 6, 27, 11, 32, 16, 37)(43, 64, 45, 66, 55, 76, 59, 80, 54, 75, 46, 67, 56, 77, 61, 82, 53, 74, 44, 65, 51, 72, 60, 81, 47, 68, 57, 78, 52, 73, 63, 84, 49, 70, 58, 79, 50, 71, 62, 83, 48, 69) L = (1, 46)(2, 52)(3, 56)(4, 51)(5, 58)(6, 54)(7, 43)(8, 55)(9, 63)(10, 62)(11, 57)(12, 44)(13, 61)(14, 60)(15, 50)(16, 45)(17, 53)(18, 49)(19, 47)(20, 59)(21, 48)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ), ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) } Outer automorphisms :: reflexible Dual of E16.184 Graph:: bipartite v = 4 e = 42 f = 8 degree seq :: [ 14^3, 42 ] E16.180 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 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 * Y2 * Y3^-1, Y2^3 * Y1^-1, (R * Y2)^2, (Y3^-1, Y1), (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y3 * Y1^2 * Y2 * Y1 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 19, 40, 13, 34, 16, 37, 5, 26)(3, 24, 9, 30, 18, 39, 7, 28, 12, 33, 21, 42, 14, 35)(4, 25, 10, 31, 17, 38, 6, 27, 11, 32, 20, 41, 15, 36)(43, 64, 45, 66, 53, 74, 44, 65, 51, 72, 62, 83, 50, 71, 60, 81, 57, 78, 61, 82, 49, 70, 46, 67, 55, 76, 54, 75, 52, 73, 58, 79, 63, 84, 59, 80, 47, 68, 56, 77, 48, 69) L = (1, 46)(2, 52)(3, 55)(4, 45)(5, 57)(6, 49)(7, 43)(8, 59)(9, 58)(10, 51)(11, 54)(12, 44)(13, 53)(14, 61)(15, 56)(16, 62)(17, 60)(18, 47)(19, 48)(20, 63)(21, 50)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ), ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) } Outer automorphisms :: reflexible Dual of E16.181 Graph:: bipartite v = 4 e = 42 f = 8 degree seq :: [ 14^3, 42 ] E16.181 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y2^3, Y1 * Y2^-1 * Y3^-1 * Y2, (R * Y3)^2, (Y1, Y2^-1), (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y1 * Y2 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3 * Y1^2 * Y3 * Y2^-1 * Y3 * Y1^2, (Y3^-1 * Y1^-1)^21 ] Map:: non-degenerate 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, 45, 66, 47, 68)(44, 65, 49, 70, 50, 71)(46, 67, 51, 72, 53, 74)(48, 69, 55, 76, 56, 77)(52, 73, 57, 78, 59, 80)(54, 75, 61, 82, 62, 83)(58, 79, 60, 81, 63, 84) L = (1, 44)(2, 48)(3, 49)(4, 43)(5, 50)(6, 54)(7, 55)(8, 56)(9, 45)(10, 46)(11, 47)(12, 60)(13, 61)(14, 62)(15, 51)(16, 52)(17, 53)(18, 57)(19, 63)(20, 58)(21, 59)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14, 42, 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) } Outer automorphisms :: reflexible Dual of E16.180 Graph:: bipartite v = 8 e = 42 f = 4 degree seq :: [ 6^7, 42 ] E16.182 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y3 * Y1 * Y3, (Y3^-1, Y2^-1), (Y2^-1, Y1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y2 * Y3^-1 * Y1^2 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 16, 37, 19, 40, 21, 42, 13, 34, 3, 24, 9, 30, 15, 36, 4, 25, 7, 28, 11, 32, 18, 39, 6, 27, 10, 31, 20, 41, 12, 33, 14, 35, 17, 38, 5, 26)(43, 64, 45, 66, 48, 69)(44, 65, 51, 72, 52, 73)(46, 67, 54, 75, 58, 79)(47, 68, 55, 76, 60, 81)(49, 70, 56, 77, 61, 82)(50, 71, 57, 78, 62, 83)(53, 74, 59, 80, 63, 84) L = (1, 46)(2, 49)(3, 54)(4, 47)(5, 57)(6, 58)(7, 43)(8, 53)(9, 56)(10, 61)(11, 44)(12, 55)(13, 62)(14, 45)(15, 59)(16, 60)(17, 51)(18, 50)(19, 48)(20, 63)(21, 52)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14, 42, 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) } Outer automorphisms :: reflexible Dual of E16.176 Graph:: bipartite v = 8 e = 42 f = 4 degree seq :: [ 6^7, 42 ] E16.183 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2^3, (Y3, Y2^-1), Y2^-1 * Y1^2 * Y3^-1, (R * Y3)^2, Y1^2 * Y2^-1 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (Y1^-1, Y2^-1), (Y1^-1, Y3), Y3 * Y1 * Y2^-1 * Y3^2, Y2 * Y1 * Y3^-1 * Y2 * Y1, Y2 * Y1^3 * Y3^2 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 20, 41, 18, 39, 7, 28, 12, 33, 3, 24, 9, 30, 15, 36, 19, 40, 14, 35, 13, 34, 17, 38, 6, 27, 11, 32, 4, 25, 10, 31, 21, 42, 16, 37, 5, 26)(43, 64, 45, 66, 48, 69)(44, 65, 51, 72, 53, 74)(46, 67, 50, 71, 57, 78)(47, 68, 54, 75, 59, 80)(49, 70, 55, 76, 58, 79)(52, 73, 62, 83, 61, 82)(56, 77, 63, 84, 60, 81) L = (1, 46)(2, 52)(3, 50)(4, 56)(5, 53)(6, 57)(7, 43)(8, 63)(9, 62)(10, 55)(11, 61)(12, 44)(13, 45)(14, 54)(15, 60)(16, 48)(17, 51)(18, 47)(19, 49)(20, 58)(21, 59)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14, 42, 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) } Outer automorphisms :: reflexible Dual of E16.178 Graph:: bipartite v = 8 e = 42 f = 4 degree seq :: [ 6^7, 42 ] E16.184 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y3^-2 * Y2 * Y1, (Y3, Y2^-1), (R * Y3)^2, Y3 * Y2^-1 * Y1^-1 * Y3, (R * Y2)^2, Y2^-1 * Y3 * Y1^-1 * Y3, (R * Y1)^2, Y1^3 * Y3^-1 * Y1, Y1^2 * Y3 * Y1 * Y2^-1, Y3^5 * Y1, Y3^-2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 15, 36, 4, 25, 10, 31, 14, 35, 3, 24, 9, 30, 20, 41, 19, 40, 13, 34, 21, 42, 17, 38, 6, 27, 11, 32, 18, 39, 7, 28, 12, 33, 16, 37, 5, 26)(43, 64, 45, 66, 48, 69)(44, 65, 51, 72, 53, 74)(46, 67, 55, 76, 54, 75)(47, 68, 56, 77, 59, 80)(49, 70, 57, 78, 61, 82)(50, 71, 62, 83, 60, 81)(52, 73, 63, 84, 58, 79) L = (1, 46)(2, 52)(3, 55)(4, 51)(5, 57)(6, 54)(7, 43)(8, 56)(9, 63)(10, 62)(11, 58)(12, 44)(13, 53)(14, 61)(15, 45)(16, 50)(17, 49)(18, 47)(19, 48)(20, 59)(21, 60)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14, 42, 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) } Outer automorphisms :: reflexible Dual of E16.179 Graph:: bipartite v = 8 e = 42 f = 4 degree seq :: [ 6^7, 42 ] E16.185 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y3 * Y1^2, (Y1^-1, Y2^-1), (Y2, Y3^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y2^-1 * Y3^-3, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 22, 2, 23, 7, 28, 10, 31, 19, 40, 11, 32, 12, 33, 3, 24, 8, 29, 13, 34, 20, 41, 21, 42, 16, 37, 17, 38, 6, 27, 9, 30, 18, 39, 14, 35, 15, 36, 4, 25, 5, 26)(43, 64, 45, 66, 48, 69)(44, 65, 50, 71, 51, 72)(46, 67, 53, 74, 58, 79)(47, 68, 54, 75, 59, 80)(49, 70, 55, 76, 60, 81)(52, 73, 62, 83, 56, 77)(57, 78, 61, 82, 63, 84) L = (1, 46)(2, 47)(3, 53)(4, 56)(5, 57)(6, 58)(7, 43)(8, 54)(9, 59)(10, 44)(11, 52)(12, 61)(13, 45)(14, 51)(15, 60)(16, 62)(17, 63)(18, 48)(19, 49)(20, 50)(21, 55)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14, 42, 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) } Outer automorphisms :: reflexible Dual of E16.177 Graph:: bipartite v = 8 e = 42 f = 4 degree seq :: [ 6^7, 42 ] E16.186 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y2^-1, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, (Y2^-1, Y3^-1), (R * Y2)^2, Y1^2 * Y3^-2 * Y2^-1, Y1 * Y3 * Y2^-1 * Y3^2, Y1 * Y3 * Y1^3 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 19, 40, 7, 28, 11, 32, 12, 33, 17, 38, 21, 42, 13, 34, 3, 24, 6, 27, 10, 31, 15, 36, 14, 35, 20, 41, 16, 37, 4, 25, 9, 30, 18, 39, 5, 26)(43, 64, 45, 66, 47, 68, 55, 76, 60, 81, 63, 84, 51, 72, 59, 80, 46, 67, 54, 75, 58, 79, 53, 74, 62, 83, 49, 70, 56, 77, 61, 82, 57, 78, 50, 71, 52, 73, 44, 65, 48, 69) L = (1, 46)(2, 51)(3, 54)(4, 57)(5, 58)(6, 59)(7, 43)(8, 60)(9, 56)(10, 63)(11, 44)(12, 50)(13, 53)(14, 45)(15, 55)(16, 52)(17, 61)(18, 62)(19, 47)(20, 48)(21, 49)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E16.174 Graph:: bipartite v = 2 e = 42 f = 10 degree seq :: [ 42^2 ] E16.187 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-2, Y2^-1 * Y3^-2 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y3^-1, Y2^-1), Y2 * Y3^2 * Y1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-2 * Y1 * Y2^-2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 22, 2, 23, 4, 25, 9, 30, 15, 36, 6, 27, 10, 31, 16, 37, 19, 40, 21, 42, 17, 38, 11, 32, 18, 39, 20, 41, 14, 35, 13, 34, 3, 24, 8, 29, 12, 33, 7, 28, 5, 26)(43, 64, 45, 66, 53, 74, 52, 73, 44, 65, 50, 71, 60, 81, 58, 79, 46, 67, 54, 75, 62, 83, 61, 82, 51, 72, 49, 70, 56, 77, 63, 84, 57, 78, 47, 68, 55, 76, 59, 80, 48, 69) L = (1, 46)(2, 51)(3, 54)(4, 57)(5, 44)(6, 58)(7, 43)(8, 49)(9, 48)(10, 61)(11, 62)(12, 47)(13, 50)(14, 45)(15, 52)(16, 63)(17, 60)(18, 56)(19, 59)(20, 55)(21, 53)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E16.175 Graph:: bipartite v = 2 e = 42 f = 10 degree seq :: [ 42^2 ] E16.188 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y1 * Y3 * Y2, Y1 * Y3^-1 * Y2^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^11, Y2^6 * Y3^-5, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 6, 28)(4, 26, 5, 27)(7, 29, 8, 30)(9, 31, 10, 32)(11, 33, 12, 34)(13, 35, 14, 36)(15, 37, 16, 38)(17, 39, 18, 40)(19, 41, 20, 42)(21, 43, 22, 44)(45, 67, 47, 69, 51, 73, 55, 77, 59, 81, 63, 85, 65, 87, 62, 84, 57, 79, 54, 76, 48, 70, 46, 68, 50, 72, 52, 74, 56, 78, 60, 82, 64, 86, 66, 88, 61, 83, 58, 80, 53, 75, 49, 71) L = (1, 48)(2, 49)(3, 46)(4, 53)(5, 54)(6, 45)(7, 50)(8, 47)(9, 57)(10, 58)(11, 52)(12, 51)(13, 61)(14, 62)(15, 56)(16, 55)(17, 65)(18, 66)(19, 60)(20, 59)(21, 64)(22, 63)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 44^4 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E16.192 Graph:: bipartite v = 12 e = 44 f = 2 degree seq :: [ 4^11, 44 ] E16.189 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3, Y1 * Y2^-1 * Y1 * Y2, (R * Y3)^2, Y1 * Y3^-1 * Y1 * Y3, (R * Y2)^2, (R * Y1)^2, Y3^2 * Y1 * Y2^-1 * Y3^3, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 7, 29)(4, 26, 8, 30)(5, 27, 9, 31)(6, 28, 10, 32)(11, 33, 15, 37)(12, 34, 16, 38)(13, 35, 17, 39)(14, 36, 18, 40)(19, 41, 20, 42)(21, 43, 22, 44)(45, 67, 47, 69, 50, 72, 55, 77, 58, 80, 63, 85, 66, 88, 60, 82, 61, 83, 52, 74, 53, 75, 46, 68, 51, 73, 54, 76, 59, 81, 62, 84, 64, 86, 65, 87, 56, 78, 57, 79, 48, 70, 49, 71) L = (1, 48)(2, 52)(3, 49)(4, 56)(5, 57)(6, 45)(7, 53)(8, 60)(9, 61)(10, 46)(11, 47)(12, 64)(13, 65)(14, 50)(15, 51)(16, 63)(17, 66)(18, 54)(19, 55)(20, 59)(21, 62)(22, 58)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 44^4 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E16.195 Graph:: bipartite v = 12 e = 44 f = 2 degree seq :: [ 4^11, 44 ] E16.190 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, (Y2, Y3^-1), (R * Y2)^2, Y3^-1 * Y2 * Y3^-2 * Y2, Y3 * Y1 * Y2^3, Y3 * Y2 * Y3^3 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 7, 29)(4, 26, 8, 30)(5, 27, 9, 31)(6, 28, 10, 32)(11, 33, 17, 39)(12, 34, 16, 38)(13, 35, 19, 41)(14, 36, 20, 42)(15, 37, 21, 43)(18, 40, 22, 44)(45, 67, 47, 69, 55, 77, 54, 76, 63, 85, 64, 86, 62, 84, 59, 81, 48, 70, 56, 78, 53, 75, 46, 68, 51, 73, 61, 83, 50, 72, 57, 79, 58, 80, 66, 88, 65, 87, 52, 74, 60, 82, 49, 71) L = (1, 48)(2, 52)(3, 56)(4, 58)(5, 59)(6, 45)(7, 60)(8, 64)(9, 65)(10, 46)(11, 53)(12, 66)(13, 47)(14, 55)(15, 57)(16, 62)(17, 49)(18, 50)(19, 51)(20, 61)(21, 63)(22, 54)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 44^4 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E16.193 Graph:: bipartite v = 12 e = 44 f = 2 degree seq :: [ 4^11, 44 ] E16.191 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^2 * Y3 * Y2^2, Y3 * Y1 * Y2 * Y3^2, Y1 * Y2^2 * Y3^-2 * Y2 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 7, 29)(4, 26, 8, 30)(5, 27, 9, 31)(6, 28, 10, 32)(11, 33, 19, 41)(12, 34, 18, 40)(13, 35, 20, 42)(14, 36, 17, 39)(15, 37, 21, 43)(16, 38, 22, 44)(45, 67, 47, 69, 55, 77, 61, 83, 50, 72, 57, 79, 65, 87, 52, 74, 62, 84, 66, 88, 53, 75, 46, 68, 51, 73, 63, 85, 58, 80, 54, 76, 64, 86, 59, 81, 48, 70, 56, 78, 60, 82, 49, 71) L = (1, 48)(2, 52)(3, 56)(4, 58)(5, 59)(6, 45)(7, 62)(8, 61)(9, 65)(10, 46)(11, 60)(12, 54)(13, 47)(14, 53)(15, 63)(16, 64)(17, 49)(18, 50)(19, 66)(20, 51)(21, 55)(22, 57)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 44^4 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E16.194 Graph:: bipartite v = 12 e = 44 f = 2 degree seq :: [ 4^11, 44 ] E16.192 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, Y1^2 * Y3^2, (Y1, Y2^-1), (R * Y1)^2, (R * Y2)^2, (Y1, Y3^-1), (R * Y3)^2, Y1 * Y2 * Y1 * Y3 * Y2, Y1^-1 * Y3 * Y2 * Y3 * Y1^-2, Y1^-7 * Y2^-1 * Y3^-1, Y3^11, Y1^15 * Y2^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 19, 41, 14, 36, 3, 25, 9, 31, 18, 40, 22, 44, 16, 38, 4, 26, 10, 32, 7, 29, 12, 34, 21, 43, 13, 35, 17, 39, 6, 28, 11, 33, 20, 42, 15, 37, 5, 27)(45, 67, 47, 69, 48, 70, 57, 79, 59, 81, 63, 85, 66, 88, 56, 78, 55, 77, 46, 68, 53, 75, 54, 76, 61, 83, 49, 71, 58, 80, 60, 82, 65, 87, 64, 86, 52, 74, 62, 84, 51, 73, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 59)(5, 60)(6, 47)(7, 45)(8, 51)(9, 61)(10, 49)(11, 53)(12, 46)(13, 63)(14, 65)(15, 66)(16, 64)(17, 58)(18, 50)(19, 56)(20, 62)(21, 52)(22, 55)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E16.188 Graph:: bipartite v = 2 e = 44 f = 12 degree seq :: [ 44^2 ] E16.193 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, Y1^-1 * Y3^-2 * Y1^-1, (Y1, Y3), (R * Y1)^2, (Y2^-1, Y1), (R * Y2)^2, (R * Y3)^2, Y2 * Y3^-1 * Y2 * Y1^-2, Y1^-2 * Y3^2 * Y2^-1 * Y1^-1, Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y3, Y2 * Y1^10 * Y2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 19, 41, 18, 40, 6, 28, 11, 33, 14, 36, 22, 44, 16, 38, 4, 26, 10, 32, 7, 29, 12, 34, 21, 43, 17, 39, 13, 35, 3, 25, 9, 31, 20, 42, 15, 37, 5, 27)(45, 67, 47, 69, 51, 73, 58, 80, 52, 74, 64, 86, 65, 87, 60, 82, 62, 84, 49, 71, 57, 79, 54, 76, 55, 77, 46, 68, 53, 75, 56, 78, 66, 88, 63, 85, 59, 81, 61, 83, 48, 70, 50, 72) L = (1, 48)(2, 54)(3, 50)(4, 59)(5, 60)(6, 61)(7, 45)(8, 51)(9, 55)(10, 49)(11, 57)(12, 46)(13, 62)(14, 47)(15, 66)(16, 64)(17, 63)(18, 65)(19, 56)(20, 58)(21, 52)(22, 53)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E16.190 Graph:: bipartite v = 2 e = 44 f = 12 degree seq :: [ 44^2 ] E16.194 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y2^-2, (Y3^-1 * Y1^-1)^2, (Y1^-1, Y2), (R * Y1)^2, Y1^-2 * Y3^-2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3), Y3^-3 * Y2^-2, Y2 * Y3^-2 * Y1 * Y3^-1, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1, Y1^17 * Y2^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 19, 41, 22, 44, 20, 42, 15, 37, 3, 25, 9, 31, 18, 40, 4, 26, 10, 32, 7, 29, 12, 34, 13, 35, 6, 28, 11, 33, 14, 36, 21, 43, 16, 38, 17, 39, 5, 27)(45, 67, 47, 69, 57, 79, 49, 71, 59, 81, 56, 78, 61, 83, 64, 86, 51, 73, 60, 82, 66, 88, 54, 76, 65, 87, 63, 85, 48, 70, 58, 80, 52, 74, 62, 84, 55, 77, 46, 68, 53, 75, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 61)(5, 62)(6, 63)(7, 45)(8, 51)(9, 65)(10, 49)(11, 66)(12, 46)(13, 52)(14, 64)(15, 55)(16, 47)(17, 53)(18, 60)(19, 56)(20, 50)(21, 59)(22, 57)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E16.191 Graph:: bipartite v = 2 e = 44 f = 12 degree seq :: [ 44^2 ] E16.195 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1^-1 * Y2, (Y3^-1 * Y1^-1)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y3^-2 * Y1^-2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y3^-2 * Y2^2 * Y3^-1, Y2^-1 * Y1^-2 * Y2^-1 * Y3, Y1^-3 * Y3 * Y2, Y3^-2 * Y1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 13, 35, 21, 43, 15, 37, 19, 41, 6, 28, 11, 33, 17, 39, 4, 26, 10, 32, 7, 29, 12, 34, 14, 36, 3, 25, 9, 31, 18, 40, 22, 44, 20, 42, 16, 38, 5, 27)(45, 67, 47, 69, 55, 77, 46, 68, 53, 75, 61, 83, 52, 74, 62, 84, 48, 70, 57, 79, 66, 88, 54, 76, 65, 87, 64, 86, 51, 73, 59, 81, 60, 82, 56, 78, 63, 85, 49, 71, 58, 80, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 60)(5, 61)(6, 62)(7, 45)(8, 51)(9, 65)(10, 49)(11, 66)(12, 46)(13, 56)(14, 52)(15, 47)(16, 55)(17, 64)(18, 59)(19, 53)(20, 50)(21, 58)(22, 63)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E16.189 Graph:: bipartite v = 2 e = 44 f = 12 degree seq :: [ 44^2 ] E16.196 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 6, 6, 6}) Quotient :: edge^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1 * Y3^-1, Y3 * Y2^-1 * Y1^-1 * Y2, Y2 * Y3 * Y1^-1 * Y3^-1, Y1 * Y2^-1 * Y1^-1 * Y3, Y2 * Y3^-1 * Y2^-1 * Y1, R * Y2 * R * Y1, Y1 * Y3^-1 * Y2^-1 * Y3, (R * Y3)^2, Y3^6, Y2^6, Y1^6, Y2^-2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 25, 4, 28, 15, 39, 22, 46, 21, 45, 7, 31)(2, 26, 6, 30, 16, 40, 18, 42, 12, 36, 11, 35)(3, 27, 9, 33, 17, 41, 20, 44, 24, 48, 14, 38)(5, 29, 13, 37, 23, 47, 8, 32, 10, 34, 19, 43)(49, 50, 56, 70, 66, 53)(51, 55, 58, 68, 63, 61)(52, 57, 59, 69, 72, 64)(54, 65, 71, 60, 62, 67)(73, 75, 84, 94, 92, 78)(74, 81, 85, 90, 96, 82)(76, 77, 86, 93, 80, 89)(79, 83, 95, 87, 88, 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) :: { ( 16^6 ), ( 16^12 ) } Outer automorphisms :: reflexible Dual of E16.199 Graph:: bipartite v = 12 e = 48 f = 6 degree seq :: [ 6^8, 12^4 ] E16.197 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 6, 6, 6}) Quotient :: edge^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1, Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1, R * Y1 * R * Y2, Y3^4, Y3 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, (R * Y3)^2, Y1 * Y3^-1 * Y2^2 * Y3^-1, Y1 * Y2^-2 * Y3^-1 * Y2, Y1 * Y3^-1 * Y1^-2 * Y2 ] Map:: non-degenerate R = (1, 25, 4, 28, 18, 42, 7, 31)(2, 26, 10, 34, 22, 46, 12, 36)(3, 27, 15, 39, 24, 48, 17, 41)(5, 29, 20, 44, 8, 32, 13, 37)(6, 30, 19, 43, 14, 38, 9, 33)(11, 35, 21, 45, 16, 40, 23, 47)(49, 50, 56, 66, 70, 53)(51, 61, 59, 72, 68, 64)(52, 63, 57, 55, 65, 67)(54, 71, 60, 62, 69, 58)(73, 75, 86, 90, 96, 78)(74, 81, 88, 94, 91, 83)(76, 82, 85, 79, 84, 92)(77, 93, 89, 80, 95, 87) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^6 ), ( 24^8 ) } Outer automorphisms :: reflexible Dual of E16.198 Graph:: bipartite v = 14 e = 48 f = 4 degree seq :: [ 6^8, 8^6 ] E16.198 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 6, 6, 6}) Quotient :: loop^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1 * Y3^-1, Y3 * Y2^-1 * Y1^-1 * Y2, Y2 * Y3 * Y1^-1 * Y3^-1, Y1 * Y2^-1 * Y1^-1 * Y3, Y2 * Y3^-1 * Y2^-1 * Y1, R * Y2 * R * Y1, Y1 * Y3^-1 * Y2^-1 * Y3, (R * Y3)^2, Y3^6, Y2^6, Y1^6, Y2^-2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 15, 39, 63, 87, 22, 46, 70, 94, 21, 45, 69, 93, 7, 31, 55, 79)(2, 26, 50, 74, 6, 30, 54, 78, 16, 40, 64, 88, 18, 42, 66, 90, 12, 36, 60, 84, 11, 35, 59, 83)(3, 27, 51, 75, 9, 33, 57, 81, 17, 41, 65, 89, 20, 44, 68, 92, 24, 48, 72, 96, 14, 38, 62, 86)(5, 29, 53, 77, 13, 37, 61, 85, 23, 47, 71, 95, 8, 32, 56, 80, 10, 34, 58, 82, 19, 43, 67, 91) L = (1, 26)(2, 32)(3, 31)(4, 33)(5, 25)(6, 41)(7, 34)(8, 46)(9, 35)(10, 44)(11, 45)(12, 38)(13, 27)(14, 43)(15, 37)(16, 28)(17, 47)(18, 29)(19, 30)(20, 39)(21, 48)(22, 42)(23, 36)(24, 40)(49, 75)(50, 81)(51, 84)(52, 77)(53, 86)(54, 73)(55, 83)(56, 89)(57, 85)(58, 74)(59, 95)(60, 94)(61, 90)(62, 93)(63, 88)(64, 91)(65, 76)(66, 96)(67, 79)(68, 78)(69, 80)(70, 92)(71, 87)(72, 82) 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 ) } Outer automorphisms :: reflexible Dual of E16.197 Transitivity :: VT+ Graph:: v = 4 e = 48 f = 14 degree seq :: [ 24^4 ] E16.199 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 6, 6, 6}) Quotient :: loop^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1, Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1, R * Y1 * R * Y2, Y3^4, Y3 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, (R * Y3)^2, Y1 * Y3^-1 * Y2^2 * Y3^-1, Y1 * Y2^-2 * Y3^-1 * Y2, Y1 * Y3^-1 * Y1^-2 * Y2 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 18, 42, 66, 90, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 22, 46, 70, 94, 12, 36, 60, 84)(3, 27, 51, 75, 15, 39, 63, 87, 24, 48, 72, 96, 17, 41, 65, 89)(5, 29, 53, 77, 20, 44, 68, 92, 8, 32, 56, 80, 13, 37, 61, 85)(6, 30, 54, 78, 19, 43, 67, 91, 14, 38, 62, 86, 9, 33, 57, 81)(11, 35, 59, 83, 21, 45, 69, 93, 16, 40, 64, 88, 23, 47, 71, 95) L = (1, 26)(2, 32)(3, 37)(4, 39)(5, 25)(6, 47)(7, 41)(8, 42)(9, 31)(10, 30)(11, 48)(12, 38)(13, 35)(14, 45)(15, 33)(16, 27)(17, 43)(18, 46)(19, 28)(20, 40)(21, 34)(22, 29)(23, 36)(24, 44)(49, 75)(50, 81)(51, 86)(52, 82)(53, 93)(54, 73)(55, 84)(56, 95)(57, 88)(58, 85)(59, 74)(60, 92)(61, 79)(62, 90)(63, 77)(64, 94)(65, 80)(66, 96)(67, 83)(68, 76)(69, 89)(70, 91)(71, 87)(72, 78) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.196 Transitivity :: VT+ Graph:: v = 6 e = 48 f = 12 degree seq :: [ 16^6 ] E16.200 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y2, Y3^3, (Y2^-1 * Y3^-1)^2, (R * Y3)^2, Y3^-1 * Y2^-1 * Y1^2, Y1^-1 * Y3 * Y2 * Y1^-1, Y2^-1 * Y1^-2 * Y3^-1, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y1 * Y2 * Y1 * Y3^-1 * Y1^-1, Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 13, 37, 7, 31, 14, 38)(4, 28, 15, 39, 6, 30, 16, 40)(9, 33, 17, 41, 12, 36, 18, 42)(10, 34, 19, 43, 11, 35, 20, 44)(21, 45, 23, 47, 22, 46, 24, 48)(49, 73, 51, 75, 52, 76, 56, 80, 55, 79, 54, 78)(50, 74, 57, 81, 58, 82, 53, 77, 60, 84, 59, 83)(61, 85, 67, 91, 69, 93, 62, 86, 68, 92, 70, 94)(63, 87, 71, 95, 65, 89, 64, 88, 72, 96, 66, 90) L = (1, 52)(2, 58)(3, 56)(4, 55)(5, 59)(6, 51)(7, 49)(8, 54)(9, 53)(10, 60)(11, 57)(12, 50)(13, 69)(14, 70)(15, 65)(16, 66)(17, 72)(18, 71)(19, 62)(20, 61)(21, 68)(22, 67)(23, 64)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^8 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E16.201 Graph:: bipartite v = 10 e = 48 f = 8 degree seq :: [ 8^6, 12^4 ] E16.201 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2^2 * Y3^-1, (Y2^-1 * Y3^-1)^2, Y3 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1^2 * Y2 * Y1^-1, Y2 * Y1^-3 * Y3, (Y3 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 14, 38, 18, 42, 5, 29)(3, 27, 13, 37, 11, 35, 7, 31, 22, 46, 10, 34)(4, 28, 15, 39, 21, 45, 6, 30, 20, 44, 16, 40)(9, 33, 23, 47, 17, 41, 12, 36, 24, 48, 19, 43)(49, 73, 51, 75, 52, 76, 62, 86, 55, 79, 54, 78)(50, 74, 57, 81, 58, 82, 66, 90, 60, 84, 59, 83)(53, 77, 63, 87, 65, 89, 56, 80, 68, 92, 67, 91)(61, 85, 71, 95, 64, 88, 70, 94, 72, 96, 69, 93) L = (1, 52)(2, 58)(3, 62)(4, 55)(5, 65)(6, 51)(7, 49)(8, 67)(9, 66)(10, 60)(11, 57)(12, 50)(13, 64)(14, 54)(15, 56)(16, 72)(17, 68)(18, 59)(19, 63)(20, 53)(21, 71)(22, 69)(23, 70)(24, 61)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.200 Graph:: bipartite v = 8 e = 48 f = 10 degree seq :: [ 12^8 ] E16.202 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y3^-2, Y3 * Y2 * Y1^-2, Y3 * Y2 * Y1^2, Y3 * Y1^-1 * Y2 * Y1, (R * Y1)^2, Y1^-1 * Y2 * Y3 * Y1^-1, (R * Y3)^2, (Y2^-1 * Y3^-1)^2, (R * Y2)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^6, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 12, 36, 7, 31, 9, 33)(4, 28, 11, 35, 6, 30, 10, 34)(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, 61, 85, 69, 93, 63, 87, 54, 78)(50, 74, 57, 81, 65, 89, 71, 95, 67, 91, 59, 83)(52, 76, 56, 80, 55, 79, 62, 86, 70, 94, 64, 88)(53, 77, 60, 84, 66, 90, 72, 96, 68, 92, 58, 82) L = (1, 52)(2, 58)(3, 56)(4, 63)(5, 59)(6, 64)(7, 49)(8, 54)(9, 53)(10, 67)(11, 68)(12, 50)(13, 55)(14, 51)(15, 70)(16, 69)(17, 60)(18, 57)(19, 72)(20, 71)(21, 62)(22, 61)(23, 66)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^8 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E16.203 Graph:: bipartite v = 10 e = 48 f = 8 degree seq :: [ 8^6, 12^4 ] E16.203 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y2^-2, (Y3^-1, Y2), (R * Y3)^2, Y2^-2 * Y1^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y1 * Y3^2 * Y1, (R * Y2)^2, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3, Y2 * Y1 * Y3 * Y1 * Y3^-1, Y1^-1 * Y3^-1 * Y1 * Y2 * Y3^-1, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 22, 46, 16, 40, 5, 29)(3, 27, 9, 33, 23, 47, 20, 44, 6, 30, 11, 35)(4, 28, 15, 39, 7, 31, 21, 45, 24, 48, 17, 41)(10, 34, 18, 42, 12, 36, 13, 37, 19, 43, 14, 38)(49, 73, 51, 75, 56, 80, 71, 95, 64, 88, 54, 78)(50, 74, 57, 81, 70, 94, 68, 92, 53, 77, 59, 83)(52, 76, 61, 85, 55, 79, 62, 86, 72, 96, 66, 90)(58, 82, 65, 89, 60, 84, 63, 87, 67, 91, 69, 93) L = (1, 52)(2, 58)(3, 61)(4, 64)(5, 67)(6, 66)(7, 49)(8, 55)(9, 65)(10, 53)(11, 69)(12, 50)(13, 54)(14, 51)(15, 57)(16, 72)(17, 59)(18, 71)(19, 70)(20, 63)(21, 68)(22, 60)(23, 62)(24, 56)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.202 Graph:: bipartite v = 8 e = 48 f = 10 degree seq :: [ 12^8 ] E16.204 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 6, 8, 8}) Quotient :: edge^2 Aut^+ = C3 : C8 (small group id <24, 1>) Aut = C24 : C2 (small group id <48, 5>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2^3 * Y1^-1, (Y2^-1 * Y1^-1)^2, Y2^2 * Y1^2, R * Y1 * R * Y2, Y2 * Y1^-3, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, Y3 * Y2^-2 * Y3^-1 * Y1^-2, Y1^-1 * Y2^-1 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 25, 4, 28, 7, 31)(2, 26, 10, 34, 12, 36)(3, 27, 13, 37, 14, 38)(5, 29, 17, 41, 15, 39)(6, 30, 18, 42, 16, 40)(8, 32, 19, 43, 20, 44)(9, 33, 21, 45, 22, 46)(11, 35, 24, 48, 23, 47)(49, 50, 56, 51, 57, 54, 59, 53)(52, 60, 67, 62, 69, 64, 72, 63)(55, 58, 68, 61, 70, 66, 71, 65)(73, 75, 83, 74, 81, 77, 80, 78)(76, 86, 96, 84, 93, 87, 91, 88)(79, 85, 95, 82, 94, 89, 92, 90) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^6 ), ( 24^8 ) } Outer automorphisms :: reflexible Dual of E16.207 Graph:: simple bipartite v = 14 e = 48 f = 4 degree seq :: [ 6^8, 8^6 ] E16.205 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 6, 8, 8}) Quotient :: edge^2 Aut^+ = C3 : C8 (small group id <24, 1>) Aut = C24 : C2 (small group id <48, 5>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2 * Y1^-2, Y1^-1 * Y2^-2 * Y1^-1, (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (Y2^-1, Y1^-1), Y2^3 * Y1^-1, Y1 * Y3^-1 * Y1^-1 * Y3^-1, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^-1 * Y2 * Y1 * Y3^-2, Y3^-1 * Y1 * Y3 * Y2 * Y3^-1, Y3^-1 * Y2^2 * Y3 * Y1^2 ] Map:: non-degenerate R = (1, 25, 4, 28, 15, 39, 9, 33, 20, 44, 7, 31)(2, 26, 10, 34, 17, 41, 6, 30, 19, 43, 12, 36)(3, 27, 13, 37, 16, 40, 5, 29, 18, 42, 14, 38)(8, 32, 21, 45, 23, 47, 11, 35, 24, 48, 22, 46)(49, 50, 56, 51, 57, 54, 59, 53)(52, 60, 69, 62, 68, 65, 72, 64)(55, 58, 70, 61, 63, 67, 71, 66)(73, 75, 83, 74, 81, 77, 80, 78)(76, 86, 96, 84, 92, 88, 93, 89)(79, 85, 95, 82, 87, 90, 94, 91) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^8 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E16.206 Graph:: bipartite v = 10 e = 48 f = 8 degree seq :: [ 8^6, 12^4 ] E16.206 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 6, 8, 8}) Quotient :: loop^2 Aut^+ = C3 : C8 (small group id <24, 1>) Aut = C24 : C2 (small group id <48, 5>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2^3 * Y1^-1, (Y2^-1 * Y1^-1)^2, Y2^2 * Y1^2, R * Y1 * R * Y2, Y2 * Y1^-3, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, Y3 * Y2^-2 * Y3^-1 * Y1^-2, Y1^-1 * Y2^-1 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 12, 36, 60, 84)(3, 27, 51, 75, 13, 37, 61, 85, 14, 38, 62, 86)(5, 29, 53, 77, 17, 41, 65, 89, 15, 39, 63, 87)(6, 30, 54, 78, 18, 42, 66, 90, 16, 40, 64, 88)(8, 32, 56, 80, 19, 43, 67, 91, 20, 44, 68, 92)(9, 33, 57, 81, 21, 45, 69, 93, 22, 46, 70, 94)(11, 35, 59, 83, 24, 48, 72, 96, 23, 47, 71, 95) L = (1, 26)(2, 32)(3, 33)(4, 36)(5, 25)(6, 35)(7, 34)(8, 27)(9, 30)(10, 44)(11, 29)(12, 43)(13, 46)(14, 45)(15, 28)(16, 48)(17, 31)(18, 47)(19, 38)(20, 37)(21, 40)(22, 42)(23, 41)(24, 39)(49, 75)(50, 81)(51, 83)(52, 86)(53, 80)(54, 73)(55, 85)(56, 78)(57, 77)(58, 94)(59, 74)(60, 93)(61, 95)(62, 96)(63, 91)(64, 76)(65, 92)(66, 79)(67, 88)(68, 90)(69, 87)(70, 89)(71, 82)(72, 84) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.205 Transitivity :: VT+ Graph:: bipartite v = 8 e = 48 f = 10 degree seq :: [ 12^8 ] E16.207 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 6, 8, 8}) Quotient :: loop^2 Aut^+ = C3 : C8 (small group id <24, 1>) Aut = C24 : C2 (small group id <48, 5>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2 * Y1^-2, Y1^-1 * Y2^-2 * Y1^-1, (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (Y2^-1, Y1^-1), Y2^3 * Y1^-1, Y1 * Y3^-1 * Y1^-1 * Y3^-1, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^-1 * Y2 * Y1 * Y3^-2, Y3^-1 * Y1 * Y3 * Y2 * Y3^-1, Y3^-1 * Y2^2 * Y3 * Y1^2 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 15, 39, 63, 87, 9, 33, 57, 81, 20, 44, 68, 92, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 17, 41, 65, 89, 6, 30, 54, 78, 19, 43, 67, 91, 12, 36, 60, 84)(3, 27, 51, 75, 13, 37, 61, 85, 16, 40, 64, 88, 5, 29, 53, 77, 18, 42, 66, 90, 14, 38, 62, 86)(8, 32, 56, 80, 21, 45, 69, 93, 23, 47, 71, 95, 11, 35, 59, 83, 24, 48, 72, 96, 22, 46, 70, 94) L = (1, 26)(2, 32)(3, 33)(4, 36)(5, 25)(6, 35)(7, 34)(8, 27)(9, 30)(10, 46)(11, 29)(12, 45)(13, 39)(14, 44)(15, 43)(16, 28)(17, 48)(18, 31)(19, 47)(20, 41)(21, 38)(22, 37)(23, 42)(24, 40)(49, 75)(50, 81)(51, 83)(52, 86)(53, 80)(54, 73)(55, 85)(56, 78)(57, 77)(58, 87)(59, 74)(60, 92)(61, 95)(62, 96)(63, 90)(64, 93)(65, 76)(66, 94)(67, 79)(68, 88)(69, 89)(70, 91)(71, 82)(72, 84) 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 ) } Outer automorphisms :: reflexible Dual of E16.204 Transitivity :: VT+ Graph:: bipartite v = 4 e = 48 f = 14 degree seq :: [ 24^4 ] E16.208 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-3 * Y3, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3 * Y2^-1, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2^4, Y2 * Y1^-1 * Y2 * Y1 * Y2^2 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 4, 28, 9, 33, 5, 29)(3, 27, 11, 35, 20, 44, 13, 37, 17, 41, 8, 32)(6, 30, 15, 39, 21, 45, 14, 38, 18, 42, 10, 34)(12, 36, 19, 43, 24, 48, 16, 40, 22, 46, 23, 47)(49, 73, 51, 75, 60, 84, 62, 86, 52, 76, 61, 85, 64, 88, 54, 78)(50, 74, 56, 80, 67, 91, 69, 93, 57, 81, 68, 92, 70, 94, 58, 82)(53, 77, 59, 83, 71, 95, 66, 90, 55, 79, 65, 89, 72, 96, 63, 87) L = (1, 52)(2, 57)(3, 61)(4, 49)(5, 55)(6, 62)(7, 53)(8, 68)(9, 50)(10, 69)(11, 65)(12, 64)(13, 51)(14, 54)(15, 66)(16, 60)(17, 59)(18, 63)(19, 70)(20, 56)(21, 58)(22, 67)(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) :: { ( 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 E16.210 Graph:: bipartite v = 7 e = 48 f = 11 degree seq :: [ 12^4, 16^3 ] E16.209 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y1^6, (Y3^-1 * Y1^-1)^3, Y2 * Y1^3 * Y2^3, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 14, 38, 11, 35, 4, 28)(3, 27, 9, 33, 19, 43, 24, 48, 15, 39, 7, 31)(5, 29, 12, 36, 22, 46, 21, 45, 16, 40, 8, 32)(10, 34, 17, 41, 23, 47, 13, 37, 18, 42, 20, 44)(49, 73, 51, 75, 58, 82, 69, 93, 62, 86, 72, 96, 61, 85, 53, 77)(50, 74, 55, 79, 65, 89, 70, 94, 59, 83, 67, 91, 66, 90, 56, 80)(52, 76, 57, 81, 68, 92, 64, 88, 54, 78, 63, 87, 71, 95, 60, 84) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 60)(6, 62)(7, 51)(8, 53)(9, 67)(10, 65)(11, 52)(12, 70)(13, 66)(14, 59)(15, 55)(16, 56)(17, 71)(18, 68)(19, 72)(20, 58)(21, 64)(22, 69)(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) :: { ( 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 E16.211 Graph:: bipartite v = 7 e = 48 f = 11 degree seq :: [ 12^4, 16^3 ] E16.210 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^3, Y2^-1 * Y3 * Y2 * Y3, Y1^-1 * Y3 * Y1 * Y3, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^4 * Y3, Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 13, 37, 4, 28, 9, 33, 16, 40, 5, 29)(3, 27, 10, 34, 17, 41, 21, 45, 11, 35, 20, 44, 22, 46, 12, 36)(6, 30, 8, 32, 18, 42, 23, 47, 14, 38, 19, 43, 24, 48, 15, 39)(49, 73, 51, 75, 54, 78)(50, 74, 56, 80, 58, 82)(52, 76, 59, 83, 62, 86)(53, 77, 63, 87, 60, 84)(55, 79, 65, 89, 66, 90)(57, 81, 67, 91, 68, 92)(61, 85, 71, 95, 69, 93)(64, 88, 70, 94, 72, 96) L = (1, 52)(2, 57)(3, 59)(4, 49)(5, 61)(6, 62)(7, 64)(8, 67)(9, 50)(10, 68)(11, 51)(12, 69)(13, 53)(14, 54)(15, 71)(16, 55)(17, 70)(18, 72)(19, 56)(20, 58)(21, 60)(22, 65)(23, 63)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 16, 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E16.208 Graph:: bipartite v = 11 e = 48 f = 7 degree seq :: [ 6^8, 16^3 ] E16.211 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y2^-1 * Y3^2, Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y1^-1 * Y3 * Y1 * Y3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-2, Y2 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 13, 37, 24, 48, 18, 42, 5, 29)(3, 27, 11, 35, 20, 44, 17, 41, 7, 31, 10, 34, 23, 47, 14, 38)(4, 28, 12, 36, 21, 45, 16, 40, 6, 30, 9, 33, 22, 46, 15, 39)(49, 73, 51, 75, 54, 78)(50, 74, 57, 81, 59, 83)(52, 76, 61, 85, 55, 79)(53, 77, 64, 88, 62, 86)(56, 80, 68, 92, 70, 94)(58, 82, 72, 96, 60, 84)(63, 87, 65, 89, 67, 91)(66, 90, 71, 95, 69, 93) L = (1, 52)(2, 58)(3, 61)(4, 51)(5, 65)(6, 55)(7, 49)(8, 69)(9, 72)(10, 57)(11, 60)(12, 50)(13, 54)(14, 63)(15, 53)(16, 67)(17, 64)(18, 70)(19, 62)(20, 66)(21, 68)(22, 71)(23, 56)(24, 59)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 16, 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E16.209 Graph:: bipartite v = 11 e = 48 f = 7 degree seq :: [ 6^8, 16^3 ] E16.212 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 8, 8}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-3 * Y3, (R * Y2)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (Y2^-1, Y1^-1), Y2^4 * Y3 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 4, 28, 9, 33, 5, 29)(3, 27, 8, 32, 17, 41, 12, 36, 20, 44, 13, 37)(6, 30, 10, 34, 18, 42, 14, 38, 21, 45, 15, 39)(11, 35, 19, 43, 24, 48, 16, 40, 22, 46, 23, 47)(49, 73, 51, 75, 59, 83, 62, 86, 52, 76, 60, 84, 64, 88, 54, 78)(50, 74, 56, 80, 67, 91, 69, 93, 57, 81, 68, 92, 70, 94, 58, 82)(53, 77, 61, 85, 71, 95, 66, 90, 55, 79, 65, 89, 72, 96, 63, 87) L = (1, 52)(2, 57)(3, 60)(4, 49)(5, 55)(6, 62)(7, 53)(8, 68)(9, 50)(10, 69)(11, 64)(12, 51)(13, 65)(14, 54)(15, 66)(16, 59)(17, 61)(18, 63)(19, 70)(20, 56)(21, 58)(22, 67)(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) :: { ( 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 E16.213 Graph:: bipartite v = 7 e = 48 f = 11 degree seq :: [ 12^4, 16^3 ] E16.213 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 8, 8}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^3, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y3 * Y1^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 13, 37, 4, 28, 9, 33, 15, 39, 5, 29)(3, 27, 8, 32, 17, 41, 21, 45, 11, 35, 19, 43, 22, 46, 12, 36)(6, 30, 10, 34, 18, 42, 23, 47, 14, 38, 20, 44, 24, 48, 16, 40)(49, 73, 51, 75, 54, 78)(50, 74, 56, 80, 58, 82)(52, 76, 59, 83, 62, 86)(53, 77, 60, 84, 64, 88)(55, 79, 65, 89, 66, 90)(57, 81, 67, 91, 68, 92)(61, 85, 69, 93, 71, 95)(63, 87, 70, 94, 72, 96) L = (1, 52)(2, 57)(3, 59)(4, 49)(5, 61)(6, 62)(7, 63)(8, 67)(9, 50)(10, 68)(11, 51)(12, 69)(13, 53)(14, 54)(15, 55)(16, 71)(17, 70)(18, 72)(19, 56)(20, 58)(21, 60)(22, 65)(23, 64)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 16, 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E16.212 Graph:: bipartite v = 11 e = 48 f = 7 degree seq :: [ 6^8, 16^3 ] E16.214 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 12}) Quotient :: edge^2 Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = C24 : C2 (small group id <48, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1^-2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y2^-2 * Y1^-2, Y1^4, R * Y1 * R * Y2, Y2^4, Y2 * Y1 * Y2 * Y1^-1, Y1 * Y3 * Y1^-1 * Y3, Y2 * Y3 * Y2^-1 * Y3, (R * Y3)^2, Y1^-2 * Y3^3 ] Map:: non-degenerate R = (1, 25, 4, 28, 15, 39, 8, 32, 20, 44, 7, 31)(2, 26, 10, 34, 16, 40, 5, 29, 18, 42, 12, 36)(3, 27, 13, 37, 17, 41, 6, 30, 19, 43, 14, 38)(9, 33, 21, 45, 23, 47, 11, 35, 24, 48, 22, 46)(49, 50, 56, 53)(51, 59, 54, 57)(52, 60, 68, 64)(55, 58, 63, 66)(61, 71, 67, 70)(62, 72, 65, 69)(73, 75, 80, 78)(74, 81, 77, 83)(76, 86, 92, 89)(79, 85, 87, 91)(82, 94, 90, 95)(84, 93, 88, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 48^4 ), ( 48^12 ) } Outer automorphisms :: reflexible Dual of E16.217 Graph:: bipartite v = 16 e = 48 f = 2 degree seq :: [ 4^12, 12^4 ] E16.215 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 12}) Quotient :: edge^2 Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = C24 : C2 (small group id <48, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y1 * Y2^-1, Y2^-1 * Y1^2 * Y2^-1, Y1^2 * Y2^2, Y2^4, R * Y1 * R * Y2, Y1 * Y2 * Y1^-1 * Y2, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y3, Y1 * Y3 * Y1^-1 * Y3, Y3^-1 * Y2 * Y1 * Y3^-2 ] Map:: non-degenerate R = (1, 25, 4, 28, 15, 39, 11, 35, 24, 48, 22, 46, 8, 32, 21, 45, 23, 47, 9, 33, 20, 44, 7, 31)(2, 26, 10, 34, 14, 38, 3, 27, 13, 37, 16, 40, 5, 29, 18, 42, 17, 41, 6, 30, 19, 43, 12, 36)(49, 50, 56, 53)(51, 59, 54, 57)(52, 60, 69, 64)(55, 58, 70, 66)(61, 63, 67, 71)(62, 72, 65, 68)(73, 75, 80, 78)(74, 81, 77, 83)(76, 86, 93, 89)(79, 85, 94, 91)(82, 95, 90, 87)(84, 92, 88, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^24 ) } Outer automorphisms :: reflexible Dual of E16.216 Graph:: bipartite v = 14 e = 48 f = 4 degree seq :: [ 4^12, 24^2 ] E16.216 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 12}) Quotient :: loop^2 Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = C24 : C2 (small group id <48, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1^-2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y2^-2 * Y1^-2, Y1^4, R * Y1 * R * Y2, Y2^4, Y2 * Y1 * Y2 * Y1^-1, Y1 * Y3 * Y1^-1 * Y3, Y2 * Y3 * Y2^-1 * Y3, (R * Y3)^2, Y1^-2 * Y3^3 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 15, 39, 63, 87, 8, 32, 56, 80, 20, 44, 68, 92, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 16, 40, 64, 88, 5, 29, 53, 77, 18, 42, 66, 90, 12, 36, 60, 84)(3, 27, 51, 75, 13, 37, 61, 85, 17, 41, 65, 89, 6, 30, 54, 78, 19, 43, 67, 91, 14, 38, 62, 86)(9, 33, 57, 81, 21, 45, 69, 93, 23, 47, 71, 95, 11, 35, 59, 83, 24, 48, 72, 96, 22, 46, 70, 94) L = (1, 26)(2, 32)(3, 35)(4, 36)(5, 25)(6, 33)(7, 34)(8, 29)(9, 27)(10, 39)(11, 30)(12, 44)(13, 47)(14, 48)(15, 42)(16, 28)(17, 45)(18, 31)(19, 46)(20, 40)(21, 38)(22, 37)(23, 43)(24, 41)(49, 75)(50, 81)(51, 80)(52, 86)(53, 83)(54, 73)(55, 85)(56, 78)(57, 77)(58, 94)(59, 74)(60, 93)(61, 87)(62, 92)(63, 91)(64, 96)(65, 76)(66, 95)(67, 79)(68, 89)(69, 88)(70, 90)(71, 82)(72, 84) local type(s) :: { ( 4, 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 E16.215 Transitivity :: VT+ Graph:: bipartite v = 4 e = 48 f = 14 degree seq :: [ 24^4 ] E16.217 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 12}) Quotient :: loop^2 Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = C24 : C2 (small group id <48, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y1 * Y2^-1, Y2^-1 * Y1^2 * Y2^-1, Y1^2 * Y2^2, Y2^4, R * Y1 * R * Y2, Y1 * Y2 * Y1^-1 * Y2, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y3, Y1 * Y3 * Y1^-1 * Y3, Y3^-1 * Y2 * Y1 * Y3^-2 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 15, 39, 63, 87, 11, 35, 59, 83, 24, 48, 72, 96, 22, 46, 70, 94, 8, 32, 56, 80, 21, 45, 69, 93, 23, 47, 71, 95, 9, 33, 57, 81, 20, 44, 68, 92, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 14, 38, 62, 86, 3, 27, 51, 75, 13, 37, 61, 85, 16, 40, 64, 88, 5, 29, 53, 77, 18, 42, 66, 90, 17, 41, 65, 89, 6, 30, 54, 78, 19, 43, 67, 91, 12, 36, 60, 84) L = (1, 26)(2, 32)(3, 35)(4, 36)(5, 25)(6, 33)(7, 34)(8, 29)(9, 27)(10, 46)(11, 30)(12, 45)(13, 39)(14, 48)(15, 43)(16, 28)(17, 44)(18, 31)(19, 47)(20, 38)(21, 40)(22, 42)(23, 37)(24, 41)(49, 75)(50, 81)(51, 80)(52, 86)(53, 83)(54, 73)(55, 85)(56, 78)(57, 77)(58, 95)(59, 74)(60, 92)(61, 94)(62, 93)(63, 82)(64, 96)(65, 76)(66, 87)(67, 79)(68, 88)(69, 89)(70, 91)(71, 90)(72, 84) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 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 E16.214 Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 16 degree seq :: [ 48^2 ] E16.218 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y3^2 * Y1^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3^2 * Y1^-2, (Y2^-1, Y3^-1), (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, (R * Y2)^2, Y3^4, Y2^3 * Y3^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 19, 43, 15, 39)(4, 28, 12, 36, 7, 31, 10, 34)(6, 30, 9, 33, 13, 37, 18, 42)(14, 38, 24, 48, 16, 40, 23, 47)(17, 41, 22, 46, 20, 44, 21, 45)(49, 73, 51, 75, 61, 85, 56, 80, 67, 91, 54, 78)(50, 74, 57, 81, 63, 87, 53, 77, 66, 90, 59, 83)(52, 76, 62, 86, 68, 92, 55, 79, 64, 88, 65, 89)(58, 82, 69, 93, 72, 96, 60, 84, 70, 94, 71, 95) L = (1, 52)(2, 58)(3, 62)(4, 56)(5, 60)(6, 65)(7, 49)(8, 55)(9, 69)(10, 53)(11, 71)(12, 50)(13, 68)(14, 67)(15, 72)(16, 51)(17, 61)(18, 70)(19, 64)(20, 54)(21, 66)(22, 57)(23, 63)(24, 59)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E16.220 Graph:: bipartite v = 10 e = 48 f = 8 degree seq :: [ 8^6, 12^4 ] E16.219 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2^-1, Y3 * Y1^-1 * Y3 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^4, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^2, Y2^2 * Y1^-1 * Y2^-1 * Y1^-1, Y1^-1 * Y2^-3 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 19, 43, 15, 39)(4, 28, 12, 36, 21, 45, 16, 40)(6, 30, 9, 33, 13, 37, 17, 41)(7, 31, 10, 34, 22, 46, 18, 42)(14, 38, 24, 48, 20, 44, 23, 47)(49, 73, 51, 75, 61, 85, 56, 80, 67, 91, 54, 78)(50, 74, 57, 81, 63, 87, 53, 77, 65, 89, 59, 83)(52, 76, 62, 86, 70, 94, 69, 93, 68, 92, 55, 79)(58, 82, 71, 95, 64, 88, 66, 90, 72, 96, 60, 84) L = (1, 52)(2, 58)(3, 62)(4, 51)(5, 66)(6, 55)(7, 49)(8, 69)(9, 71)(10, 57)(11, 60)(12, 50)(13, 70)(14, 61)(15, 64)(16, 53)(17, 72)(18, 65)(19, 68)(20, 54)(21, 67)(22, 56)(23, 63)(24, 59)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E16.221 Graph:: bipartite v = 10 e = 48 f = 8 degree seq :: [ 8^6, 12^4 ] E16.220 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2^-2, Y2^-1 * Y3^-2 * Y2^-1, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^-1 * Y1^-3, Y3^4, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y2^-1, (Y1^-1, Y3^-1), Y3 * Y2 * Y1^-1 * Y3^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 7, 31, 12, 36, 21, 45, 14, 38, 22, 46, 17, 41, 4, 28, 10, 34, 5, 29)(3, 27, 13, 37, 24, 48, 16, 40, 20, 44, 11, 35, 6, 30, 18, 42, 23, 47, 15, 39, 19, 43, 9, 33)(49, 73, 51, 75, 62, 86, 54, 78)(50, 74, 57, 81, 70, 94, 59, 83)(52, 76, 64, 88, 55, 79, 63, 87)(53, 77, 61, 85, 69, 93, 66, 90)(56, 80, 67, 91, 65, 89, 68, 92)(58, 82, 72, 96, 60, 84, 71, 95) L = (1, 52)(2, 58)(3, 63)(4, 62)(5, 65)(6, 64)(7, 49)(8, 53)(9, 71)(10, 70)(11, 72)(12, 50)(13, 67)(14, 55)(15, 54)(16, 51)(17, 69)(18, 68)(19, 66)(20, 61)(21, 56)(22, 60)(23, 59)(24, 57)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.218 Graph:: bipartite v = 8 e = 48 f = 10 degree seq :: [ 8^6, 24^2 ] E16.221 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1, Y2^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^2 * Y1^-5, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 13, 37, 21, 45, 18, 42, 10, 34, 16, 40, 24, 48, 19, 43, 11, 35, 4, 28)(3, 27, 9, 33, 17, 41, 23, 47, 15, 39, 8, 32, 5, 29, 12, 36, 20, 44, 22, 46, 14, 38, 7, 31)(49, 73, 51, 75, 58, 82, 53, 77)(50, 74, 55, 79, 64, 88, 56, 80)(52, 76, 57, 81, 66, 90, 60, 84)(54, 78, 62, 86, 72, 96, 63, 87)(59, 83, 65, 89, 69, 93, 68, 92)(61, 85, 70, 94, 67, 91, 71, 95) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 60)(6, 61)(7, 51)(8, 53)(9, 65)(10, 64)(11, 52)(12, 68)(13, 69)(14, 55)(15, 56)(16, 72)(17, 71)(18, 58)(19, 59)(20, 70)(21, 66)(22, 62)(23, 63)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.219 Graph:: bipartite v = 8 e = 48 f = 10 degree seq :: [ 8^6, 24^2 ] E16.222 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 12}) Quotient :: dipole Aut^+ = C3 x Q8 (small group id <24, 11>) Aut = (C4 x S3) : C2 (small group id <48, 41>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1 * Y3 * Y1^-1, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (R * Y1)^2, (Y2^-1, Y3^-1), Y3^2 * Y1^2, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y1^4, Y1^2 * Y2^-3, Y2 * Y3^-1 * Y2^2 * Y3^-1, Y3 * Y2 * Y3 * Y2^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 9, 33, 19, 43, 15, 39)(4, 28, 12, 36, 7, 31, 10, 34)(6, 30, 11, 35, 13, 37, 18, 42)(14, 38, 22, 46, 16, 40, 21, 45)(17, 41, 24, 48, 20, 44, 23, 47)(49, 73, 51, 75, 61, 85, 56, 80, 67, 91, 54, 78)(50, 74, 57, 81, 66, 90, 53, 77, 63, 87, 59, 83)(52, 76, 62, 86, 68, 92, 55, 79, 64, 88, 65, 89)(58, 82, 69, 93, 72, 96, 60, 84, 70, 94, 71, 95) L = (1, 52)(2, 58)(3, 62)(4, 56)(5, 60)(6, 65)(7, 49)(8, 55)(9, 69)(10, 53)(11, 71)(12, 50)(13, 68)(14, 67)(15, 70)(16, 51)(17, 61)(18, 72)(19, 64)(20, 54)(21, 63)(22, 57)(23, 66)(24, 59)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E16.223 Graph:: bipartite v = 10 e = 48 f = 8 degree seq :: [ 8^6, 12^4 ] E16.223 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 12}) Quotient :: dipole Aut^+ = C3 x Q8 (small group id <24, 11>) Aut = (C4 x S3) : C2 (small group id <48, 41>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-3, Y2^-1 * Y3^2 * Y2^-1, Y3 * Y2 * Y3^-1 * Y2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y2 * Y1, Y3^-2 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1), Y3^4, Y2^4, R * Y2 * R * Y2^-1, Y2 * Y1^2 * Y3^-1 * Y2^-1 * Y1, Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-2, Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 7, 31, 12, 36, 21, 45, 13, 37, 22, 46, 17, 41, 4, 28, 10, 34, 5, 29)(3, 27, 11, 35, 19, 43, 16, 40, 23, 47, 18, 42, 6, 30, 9, 33, 20, 44, 14, 38, 24, 48, 15, 39)(49, 73, 51, 75, 61, 85, 54, 78)(50, 74, 57, 81, 70, 94, 59, 83)(52, 76, 64, 88, 55, 79, 62, 86)(53, 77, 66, 90, 69, 93, 63, 87)(56, 80, 67, 91, 65, 89, 68, 92)(58, 82, 72, 96, 60, 84, 71, 95) L = (1, 52)(2, 58)(3, 62)(4, 61)(5, 65)(6, 64)(7, 49)(8, 53)(9, 71)(10, 70)(11, 72)(12, 50)(13, 55)(14, 54)(15, 68)(16, 51)(17, 69)(18, 67)(19, 63)(20, 66)(21, 56)(22, 60)(23, 59)(24, 57)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.222 Graph:: bipartite v = 8 e = 48 f = 10 degree seq :: [ 8^6, 24^2 ] E16.224 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, Y1^3, (R * Y1)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, (Y3^-1, Y1^-1), (Y2 * Y1^-1)^2, Y3^4, (R * Y2 * Y3^-1)^2, (Y3 * Y2 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 6, 30, 9, 33)(4, 28, 8, 32, 14, 38)(7, 31, 10, 34, 16, 40)(11, 35, 17, 41, 20, 44)(12, 36, 15, 39, 19, 43)(13, 37, 18, 42, 22, 46)(21, 45, 23, 47, 24, 48)(49, 73, 51, 75, 53, 77, 57, 81, 50, 74, 54, 78)(52, 76, 60, 84, 62, 86, 67, 91, 56, 80, 63, 87)(55, 79, 59, 83, 64, 88, 68, 92, 58, 82, 65, 89)(61, 85, 69, 93, 70, 94, 72, 96, 66, 90, 71, 95) L = (1, 52)(2, 56)(3, 59)(4, 61)(5, 62)(6, 65)(7, 49)(8, 66)(9, 68)(10, 50)(11, 69)(12, 51)(13, 55)(14, 70)(15, 54)(16, 53)(17, 71)(18, 58)(19, 57)(20, 72)(21, 60)(22, 64)(23, 63)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 24, 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E16.229 Graph:: bipartite v = 12 e = 48 f = 6 degree seq :: [ 6^8, 12^4 ] E16.225 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^2, Y1^3, (Y2 * Y1)^2, (R * Y1)^2, (Y3^-1, Y1), (R * Y3)^2, Y3 * Y2^-1 * Y3 * Y2, Y3^4, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 8, 32, 6, 30)(4, 28, 9, 33, 14, 38)(7, 31, 10, 34, 16, 40)(11, 35, 18, 42, 17, 41)(12, 36, 19, 43, 15, 39)(13, 37, 20, 44, 22, 46)(21, 45, 24, 48, 23, 47)(49, 73, 51, 75, 50, 74, 56, 80, 53, 77, 54, 78)(52, 76, 60, 84, 57, 81, 67, 91, 62, 86, 63, 87)(55, 79, 59, 83, 58, 82, 66, 90, 64, 88, 65, 89)(61, 85, 69, 93, 68, 92, 72, 96, 70, 94, 71, 95) L = (1, 52)(2, 57)(3, 59)(4, 61)(5, 62)(6, 65)(7, 49)(8, 66)(9, 68)(10, 50)(11, 69)(12, 51)(13, 55)(14, 70)(15, 54)(16, 53)(17, 71)(18, 72)(19, 56)(20, 58)(21, 60)(22, 64)(23, 63)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 24, 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E16.230 Graph:: bipartite v = 12 e = 48 f = 6 degree seq :: [ 6^8, 12^4 ] E16.226 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1 * Y2, Y1^3, (Y1^-1, Y3), (Y1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, Y1^-1 * Y3^4, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 8, 32, 6, 30)(4, 28, 9, 33, 15, 39)(7, 31, 10, 34, 17, 41)(11, 35, 19, 43, 18, 42)(12, 36, 16, 40, 13, 37)(14, 38, 21, 45, 20, 44)(22, 46, 24, 48, 23, 47)(49, 73, 51, 75, 50, 74, 56, 80, 53, 77, 54, 78)(52, 76, 61, 85, 57, 81, 60, 84, 63, 87, 64, 88)(55, 79, 67, 91, 58, 82, 66, 90, 65, 89, 59, 83)(62, 86, 70, 94, 69, 93, 72, 96, 68, 92, 71, 95) L = (1, 52)(2, 57)(3, 59)(4, 62)(5, 63)(6, 66)(7, 49)(8, 67)(9, 69)(10, 50)(11, 70)(12, 51)(13, 54)(14, 58)(15, 68)(16, 56)(17, 53)(18, 71)(19, 72)(20, 55)(21, 65)(22, 64)(23, 60)(24, 61)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 24, 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E16.231 Graph:: bipartite v = 12 e = 48 f = 6 degree seq :: [ 6^8, 12^4 ] E16.227 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y1^-1 * Y3 * Y1, Y2^2 * Y3 * Y1^-1, Y3 * Y1^-3, Y2 * Y1^-1 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, Y2^-2 * Y1^-2, (R * Y2 * Y3)^2, Y2^-1 * R * Y1^-1 * Y3 * R * Y2^-1, Y2 * Y3 * Y2^-1 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 4, 28, 9, 33, 5, 29)(3, 27, 11, 35, 6, 30, 12, 36, 15, 39, 13, 37)(8, 32, 16, 40, 10, 34, 17, 41, 14, 38, 18, 42)(19, 43, 22, 46, 20, 44, 23, 47, 21, 45, 24, 48)(49, 73, 51, 75, 57, 81, 63, 87, 55, 79, 54, 78)(50, 74, 56, 80, 53, 77, 62, 86, 52, 76, 58, 82)(59, 83, 67, 91, 61, 85, 69, 93, 60, 84, 68, 92)(64, 88, 70, 94, 66, 90, 72, 96, 65, 89, 71, 95) L = (1, 52)(2, 57)(3, 60)(4, 49)(5, 55)(6, 61)(7, 53)(8, 65)(9, 50)(10, 66)(11, 63)(12, 51)(13, 54)(14, 64)(15, 59)(16, 62)(17, 56)(18, 58)(19, 71)(20, 72)(21, 70)(22, 69)(23, 67)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E16.228 Graph:: bipartite v = 8 e = 48 f = 10 degree seq :: [ 12^8 ] E16.228 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^3, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2 * Y1^4, Y1 * Y3 * Y1 * Y2^-1 * Y3, Y3 * Y1^2 * Y3 * Y1^-2 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 18, 42, 6, 30, 10, 34, 20, 44, 12, 36, 3, 27, 8, 32, 17, 41, 5, 29)(4, 28, 13, 37, 19, 43, 21, 45, 15, 39, 16, 40, 22, 46, 9, 33, 11, 35, 23, 47, 24, 48, 14, 38)(49, 73, 51, 75, 54, 78)(50, 74, 56, 80, 58, 82)(52, 76, 59, 83, 63, 87)(53, 77, 60, 84, 66, 90)(55, 79, 65, 89, 68, 92)(57, 81, 69, 93, 62, 86)(61, 85, 71, 95, 64, 88)(67, 91, 72, 96, 70, 94) L = (1, 52)(2, 57)(3, 59)(4, 49)(5, 64)(6, 63)(7, 67)(8, 69)(9, 50)(10, 62)(11, 51)(12, 61)(13, 60)(14, 58)(15, 54)(16, 53)(17, 72)(18, 71)(19, 55)(20, 70)(21, 56)(22, 68)(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) :: { ( 12^6 ), ( 12^24 ) } Outer automorphisms :: reflexible Dual of E16.227 Graph:: bipartite v = 10 e = 48 f = 8 degree seq :: [ 6^8, 24^2 ] E16.229 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2^-1), Y3 * Y1 * Y2 * Y1, Y1 * Y2 * Y3^-1 * Y1, (R * Y2)^2, Y3^-1 * Y2^-3, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y3 * Y1^-2 * Y2^-1, Y3^4, Y2^-1 * Y3 * Y1^4, Y3 * Y1^-1 * Y2^-1 * Y3^-2 * Y1^-1, Y1^2 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 16, 40, 5, 29)(3, 27, 13, 37, 4, 28, 12, 36, 20, 44, 11, 35)(6, 30, 18, 42, 21, 45, 9, 33, 7, 31, 10, 34)(14, 38, 22, 46, 15, 39, 23, 47, 17, 41, 24, 48)(49, 73, 51, 75, 62, 86, 55, 79, 64, 88, 68, 92, 65, 89, 69, 93, 56, 80, 52, 76, 63, 87, 54, 78)(50, 74, 57, 81, 70, 94, 60, 84, 53, 77, 66, 90, 72, 96, 61, 85, 67, 91, 58, 82, 71, 95, 59, 83) L = (1, 52)(2, 58)(3, 63)(4, 65)(5, 57)(6, 56)(7, 49)(8, 68)(9, 71)(10, 72)(11, 67)(12, 50)(13, 53)(14, 54)(15, 69)(16, 51)(17, 55)(18, 70)(19, 66)(20, 62)(21, 64)(22, 59)(23, 61)(24, 60)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.224 Graph:: bipartite v = 6 e = 48 f = 12 degree seq :: [ 12^4, 24^2 ] E16.230 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1 * Y3 * Y1, Y2 * Y1^-1 * Y3 * Y1^-1, (R * Y3)^2, Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y2 * Y1^-1, (R * Y1)^2, Y2^-2 * Y3^-1 * Y2^-1, (Y1^-1 * Y2^-1)^2, Y3^4, (R * Y2)^2, Y3^-1 * Y2 * Y1^4, Y2 * Y3 * Y1^-1 * Y3^-2 * Y1^-1, Y1^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 17, 41, 5, 29)(3, 27, 13, 37, 20, 44, 11, 35, 4, 28, 12, 36)(6, 30, 18, 42, 7, 31, 10, 34, 21, 45, 9, 33)(14, 38, 22, 46, 16, 40, 24, 48, 15, 39, 23, 47)(49, 73, 51, 75, 62, 86, 55, 79, 56, 80, 68, 92, 64, 88, 69, 93, 65, 89, 52, 76, 63, 87, 54, 78)(50, 74, 57, 81, 70, 94, 60, 84, 67, 91, 66, 90, 72, 96, 61, 85, 53, 77, 58, 82, 71, 95, 59, 83) L = (1, 52)(2, 58)(3, 63)(4, 64)(5, 66)(6, 65)(7, 49)(8, 51)(9, 71)(10, 72)(11, 53)(12, 50)(13, 67)(14, 54)(15, 69)(16, 55)(17, 68)(18, 70)(19, 57)(20, 62)(21, 56)(22, 59)(23, 61)(24, 60)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.225 Graph:: bipartite v = 6 e = 48 f = 12 degree seq :: [ 12^4, 24^2 ] E16.231 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1 * Y3^-1 * Y1^-1, (Y3 * Y1^-1)^2, Y1 * Y2 * Y3^-1 * Y1, (Y3 * Y2)^2, (R * Y1)^2, (Y3, Y2^-1), (Y2 * Y1)^2, Y3 * Y1^-2 * Y2^-1, (R * Y2)^2, (R * Y3)^2, Y2^-2 * Y3^-2, Y1^2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3^-2 * Y1 * Y2^-2 * Y1^-1, Y2^-1 * Y3 * Y1^4, Y3^-2 * Y2^2 * Y1^-2, (Y1^-1 * Y2)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 16, 40, 5, 29)(3, 27, 12, 36, 4, 28, 11, 35, 20, 44, 15, 39)(6, 30, 10, 34, 21, 45, 18, 42, 7, 31, 9, 33)(13, 37, 22, 46, 14, 38, 23, 47, 17, 41, 24, 48)(49, 73, 51, 75, 61, 85, 69, 93, 56, 80, 52, 76, 62, 86, 55, 79, 64, 88, 68, 92, 65, 89, 54, 78)(50, 74, 57, 81, 70, 94, 63, 87, 67, 91, 58, 82, 71, 95, 60, 84, 53, 77, 66, 90, 72, 96, 59, 83) L = (1, 52)(2, 58)(3, 62)(4, 65)(5, 57)(6, 56)(7, 49)(8, 68)(9, 71)(10, 72)(11, 67)(12, 50)(13, 55)(14, 54)(15, 53)(16, 51)(17, 69)(18, 70)(19, 66)(20, 61)(21, 64)(22, 60)(23, 59)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.226 Graph:: bipartite v = 6 e = 48 f = 12 degree seq :: [ 12^4, 24^2 ] E16.232 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12, 12}) Quotient :: dipole Aut^+ = C3 x Q8 (small group id <24, 11>) Aut = (C4 x S3) : C2 (small group id <48, 41>) |r| :: 2 Presentation :: [ R^2, Y3^3 * Y1^-1, Y3 * Y2^2 * Y3, Y1^-1 * Y3 * Y2^-2, Y2^-1 * Y3 * Y1^-1 * Y2^-1, Y2 * Y3^-1 * Y2 * Y1^-1, (R * Y1)^2, (Y3^-1, Y1^-1), Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^3, Y2^-1 * Y3 * Y2 * Y3^-1 * Y1^-2, Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 13, 37, 19, 43, 9, 33)(4, 28, 10, 34, 20, 44, 14, 38)(6, 30, 17, 41, 21, 45, 11, 35)(7, 31, 12, 36, 22, 46, 18, 42)(15, 39, 24, 48, 16, 40, 23, 47)(49, 73, 51, 75, 62, 86, 71, 95, 66, 90, 69, 93, 56, 80, 67, 91, 58, 82, 72, 96, 60, 84, 54, 78)(50, 74, 57, 81, 52, 76, 64, 88, 55, 79, 65, 89, 53, 77, 61, 85, 68, 92, 63, 87, 70, 94, 59, 83) L = (1, 52)(2, 58)(3, 63)(4, 60)(5, 62)(6, 61)(7, 49)(8, 68)(9, 71)(10, 70)(11, 51)(12, 50)(13, 72)(14, 55)(15, 54)(16, 69)(17, 67)(18, 53)(19, 64)(20, 66)(21, 57)(22, 56)(23, 59)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E16.233 Graph:: bipartite v = 8 e = 48 f = 10 degree seq :: [ 8^6, 24^2 ] E16.233 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12, 12}) Quotient :: dipole Aut^+ = C3 x Q8 (small group id <24, 11>) Aut = (C4 x S3) : C2 (small group id <48, 41>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y3^2 * Y1^-2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (Y2, Y3^-1), Y2 * Y1^-4, Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y2 * Y1 * Y3, Y3 * Y2 * Y1^-1 * Y3 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 14, 38, 3, 27, 9, 33, 24, 48, 20, 44, 6, 30, 11, 35, 19, 43, 5, 29)(4, 28, 16, 40, 15, 39, 21, 45, 13, 37, 12, 36, 22, 46, 10, 34, 18, 42, 23, 47, 7, 31, 17, 41)(49, 73, 51, 75, 54, 78)(50, 74, 57, 81, 59, 83)(52, 76, 61, 85, 66, 90)(53, 77, 62, 86, 68, 92)(55, 79, 63, 87, 70, 94)(56, 80, 72, 96, 67, 91)(58, 82, 65, 89, 69, 93)(60, 84, 71, 95, 64, 88) L = (1, 52)(2, 58)(3, 61)(4, 56)(5, 60)(6, 66)(7, 49)(8, 63)(9, 65)(10, 62)(11, 69)(12, 50)(13, 72)(14, 71)(15, 51)(16, 59)(17, 68)(18, 67)(19, 55)(20, 64)(21, 53)(22, 54)(23, 57)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E16.232 Graph:: bipartite v = 10 e = 48 f = 8 degree seq :: [ 6^8, 24^2 ] E16.234 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, Y1^3, (R * Y3)^2, (Y1, Y3), (R * Y1)^2, Y2^4, (Y1, Y2^-1), (R * Y2)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 8, 32, 14, 38)(4, 28, 9, 33, 15, 39)(6, 30, 10, 34, 16, 40)(7, 31, 11, 35, 17, 41)(12, 36, 19, 43, 22, 46)(13, 37, 20, 44, 23, 47)(18, 42, 21, 45, 24, 48)(49, 73, 51, 75, 60, 84, 54, 78)(50, 74, 56, 80, 67, 91, 58, 82)(52, 76, 61, 85, 66, 90, 55, 79)(53, 77, 62, 86, 70, 94, 64, 88)(57, 81, 68, 92, 69, 93, 59, 83)(63, 87, 71, 95, 72, 96, 65, 89) L = (1, 52)(2, 57)(3, 61)(4, 51)(5, 63)(6, 55)(7, 49)(8, 68)(9, 56)(10, 59)(11, 50)(12, 66)(13, 60)(14, 71)(15, 62)(16, 65)(17, 53)(18, 54)(19, 69)(20, 67)(21, 58)(22, 72)(23, 70)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 48, 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48 ) } Outer automorphisms :: reflexible Dual of E16.240 Graph:: simple bipartite v = 14 e = 48 f = 4 degree seq :: [ 6^8, 8^6 ] E16.235 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^2, Y1^3, (Y3^-1, Y1), (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1), Y2^4, (R * Y2)^2, (Y3 * Y2^-1)^8, Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 8, 32, 13, 37)(4, 28, 9, 33, 15, 39)(6, 30, 10, 34, 17, 41)(7, 31, 11, 35, 18, 42)(12, 36, 19, 43, 22, 46)(14, 38, 20, 44, 23, 47)(16, 40, 21, 45, 24, 48)(49, 73, 51, 75, 60, 84, 54, 78)(50, 74, 56, 80, 67, 91, 58, 82)(52, 76, 55, 79, 62, 86, 64, 88)(53, 77, 61, 85, 70, 94, 65, 89)(57, 81, 59, 83, 68, 92, 69, 93)(63, 87, 66, 90, 71, 95, 72, 96) L = (1, 52)(2, 57)(3, 55)(4, 54)(5, 63)(6, 64)(7, 49)(8, 59)(9, 58)(10, 69)(11, 50)(12, 62)(13, 66)(14, 51)(15, 65)(16, 60)(17, 72)(18, 53)(19, 68)(20, 56)(21, 67)(22, 71)(23, 61)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 48, 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48 ) } Outer automorphisms :: reflexible Dual of E16.241 Graph:: simple bipartite v = 14 e = 48 f = 4 degree seq :: [ 6^8, 8^6 ] E16.236 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, Y1^-1 * Y3^3, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), (R * Y2)^2, Y1^4, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1, (Y2^-1 * Y3)^24 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 6, 30, 10, 34, 13, 37)(4, 28, 9, 33, 19, 43, 15, 39)(7, 31, 11, 35, 20, 44, 17, 41)(12, 36, 16, 40, 21, 45, 23, 47)(14, 38, 18, 42, 22, 46, 24, 48)(49, 73, 51, 75, 53, 77, 61, 85, 56, 80, 58, 82, 50, 74, 54, 78)(52, 76, 60, 84, 63, 87, 71, 95, 67, 91, 69, 93, 57, 81, 64, 88)(55, 79, 62, 86, 65, 89, 72, 96, 68, 92, 70, 94, 59, 83, 66, 90) L = (1, 52)(2, 57)(3, 60)(4, 59)(5, 63)(6, 64)(7, 49)(8, 67)(9, 68)(10, 69)(11, 50)(12, 66)(13, 71)(14, 51)(15, 55)(16, 70)(17, 53)(18, 54)(19, 65)(20, 56)(21, 72)(22, 58)(23, 62)(24, 61)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 48, 6, 48, 6, 48, 6, 48 ), ( 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48 ) } Outer automorphisms :: reflexible Dual of E16.239 Graph:: bipartite v = 9 e = 48 f = 9 degree seq :: [ 8^6, 16^3 ] E16.237 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1^-1, (Y1, Y3^-1), Y3^-3 * Y1, (R * Y3)^2, (Y3, Y2), Y1^4, (R * Y2)^2, (R * Y1)^2, Y3^-2 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 9, 33, 16, 40, 6, 30)(4, 28, 10, 34, 19, 43, 14, 38)(7, 31, 11, 35, 20, 44, 17, 41)(12, 36, 21, 45, 23, 47, 15, 39)(13, 37, 22, 46, 24, 48, 18, 42)(49, 73, 51, 75, 50, 74, 57, 81, 56, 80, 64, 88, 53, 77, 54, 78)(52, 76, 60, 84, 58, 82, 69, 93, 67, 91, 71, 95, 62, 86, 63, 87)(55, 79, 61, 85, 59, 83, 70, 94, 68, 92, 72, 96, 65, 89, 66, 90) L = (1, 52)(2, 58)(3, 60)(4, 59)(5, 62)(6, 63)(7, 49)(8, 67)(9, 69)(10, 68)(11, 50)(12, 70)(13, 51)(14, 55)(15, 61)(16, 71)(17, 53)(18, 54)(19, 65)(20, 56)(21, 72)(22, 57)(23, 66)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 48, 6, 48, 6, 48, 6, 48 ), ( 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48 ) } Outer automorphisms :: reflexible Dual of E16.238 Graph:: bipartite v = 9 e = 48 f = 9 degree seq :: [ 8^6, 16^3 ] E16.238 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y3 * Y1^-2, (Y2, Y3), (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), (R * Y2)^2, Y2 * Y3^-4, Y3^-1 * Y2 * Y1^-1 * Y3^-2 * Y1^-1, (Y3^-2 * Y2^-1)^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 9, 33, 14, 38, 21, 45, 13, 37, 12, 36, 3, 27, 8, 32, 11, 35, 20, 44, 23, 47, 24, 48, 18, 42, 16, 40, 6, 30, 10, 34, 15, 39, 22, 46, 19, 43, 17, 41, 7, 31, 5, 29)(49, 73, 51, 75, 54, 78)(50, 74, 56, 80, 58, 82)(52, 76, 59, 83, 63, 87)(53, 77, 60, 84, 64, 88)(55, 79, 61, 85, 66, 90)(57, 81, 68, 92, 70, 94)(62, 86, 71, 95, 67, 91)(65, 89, 69, 93, 72, 96) L = (1, 52)(2, 57)(3, 59)(4, 62)(5, 50)(6, 63)(7, 49)(8, 68)(9, 69)(10, 70)(11, 71)(12, 56)(13, 51)(14, 61)(15, 67)(16, 58)(17, 53)(18, 54)(19, 55)(20, 72)(21, 60)(22, 65)(23, 66)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 16, 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E16.237 Graph:: bipartite v = 9 e = 48 f = 9 degree seq :: [ 6^8, 48 ] E16.239 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^3, (Y2, Y3^-1), Y1^2 * Y3 * Y2, (R * Y3)^2, (Y2^-1, Y1), (R * Y2)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3^-1, Y1), (R * Y1)^2, Y3^-4 * Y2, Y3 * Y2 * Y1^-1 * Y3^2 * Y1^-1, Y1^18 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 20, 44, 16, 40, 23, 47, 18, 42, 14, 38, 3, 27, 9, 33, 7, 31, 12, 36, 21, 45, 17, 41, 4, 28, 10, 34, 6, 30, 11, 35, 15, 39, 22, 46, 19, 43, 24, 48, 13, 37, 5, 29)(49, 73, 51, 75, 54, 78)(50, 74, 57, 81, 59, 83)(52, 76, 61, 85, 66, 90)(53, 77, 62, 86, 58, 82)(55, 79, 63, 87, 56, 80)(60, 84, 70, 94, 68, 92)(64, 88, 69, 93, 67, 91)(65, 89, 72, 96, 71, 95) L = (1, 52)(2, 58)(3, 61)(4, 64)(5, 65)(6, 66)(7, 49)(8, 54)(9, 53)(10, 71)(11, 62)(12, 50)(13, 69)(14, 72)(15, 51)(16, 63)(17, 68)(18, 67)(19, 55)(20, 59)(21, 56)(22, 57)(23, 70)(24, 60)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 16, 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E16.236 Graph:: bipartite v = 9 e = 48 f = 9 degree seq :: [ 6^8, 48 ] E16.240 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (Y1, Y2^-1), (R * Y1)^2, (R * Y3)^2, Y1^3 * Y2^-3, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y2^-6 * Y1^-2, Y1^8, (Y3^-1 * Y1^-1)^4, Y2^24 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 14, 38, 22, 46, 19, 43, 11, 35, 4, 28)(3, 27, 7, 31, 15, 39, 23, 47, 21, 45, 13, 37, 18, 42, 10, 34)(5, 29, 8, 32, 16, 40, 9, 33, 17, 41, 24, 48, 20, 44, 12, 36)(49, 73, 51, 75, 57, 81, 62, 86, 71, 95, 68, 92, 59, 83, 66, 90, 56, 80, 50, 74, 55, 79, 65, 89, 70, 94, 69, 93, 60, 84, 52, 76, 58, 82, 64, 88, 54, 78, 63, 87, 72, 96, 67, 91, 61, 85, 53, 77) L = (1, 50)(2, 54)(3, 55)(4, 49)(5, 56)(6, 62)(7, 63)(8, 64)(9, 65)(10, 51)(11, 52)(12, 53)(13, 66)(14, 70)(15, 71)(16, 57)(17, 72)(18, 58)(19, 59)(20, 60)(21, 61)(22, 67)(23, 69)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 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 E16.234 Graph:: bipartite v = 4 e = 48 f = 14 degree seq :: [ 16^3, 48 ] E16.241 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y2^-2, (Y3, Y1^-1), Y1^-2 * Y3^-1 * Y1^-1, (Y2^-1, Y3^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y1, Y2^-1), (Y2^-1 * Y3)^3, Y3 * Y2 * Y3 * Y2^2 * Y1^-1, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 7, 31, 12, 36, 4, 28, 10, 34, 5, 29)(3, 27, 9, 33, 19, 43, 16, 40, 22, 46, 14, 38, 21, 45, 15, 39)(6, 30, 11, 35, 20, 44, 18, 42, 24, 48, 17, 41, 23, 47, 13, 37)(49, 73, 51, 75, 61, 85, 53, 77, 63, 87, 71, 95, 58, 82, 69, 93, 65, 89, 52, 76, 62, 86, 72, 96, 60, 84, 70, 94, 66, 90, 55, 79, 64, 88, 68, 92, 56, 80, 67, 91, 59, 83, 50, 74, 57, 81, 54, 78) L = (1, 52)(2, 58)(3, 62)(4, 56)(5, 60)(6, 65)(7, 49)(8, 53)(9, 69)(10, 55)(11, 71)(12, 50)(13, 72)(14, 67)(15, 70)(16, 51)(17, 68)(18, 54)(19, 63)(20, 61)(21, 64)(22, 57)(23, 66)(24, 59)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 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 E16.235 Graph:: bipartite v = 4 e = 48 f = 14 degree seq :: [ 16^3, 48 ] E16.242 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (Y2^-1, Y1^-1), (Y3 * Y2^-1)^4, Y2^8, Y3^-24 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 6, 30, 9, 33)(4, 28, 7, 31, 11, 35)(8, 32, 12, 36, 15, 39)(10, 34, 13, 37, 17, 41)(14, 38, 18, 42, 21, 45)(16, 40, 19, 43, 22, 46)(20, 44, 23, 47, 24, 48)(49, 73, 51, 75, 56, 80, 62, 86, 68, 92, 64, 88, 58, 82, 52, 76)(50, 74, 54, 78, 60, 84, 66, 90, 71, 95, 67, 91, 61, 85, 55, 79)(53, 77, 57, 81, 63, 87, 69, 93, 72, 96, 70, 94, 65, 89, 59, 83) L = (1, 52)(2, 55)(3, 49)(4, 58)(5, 59)(6, 50)(7, 61)(8, 51)(9, 53)(10, 64)(11, 65)(12, 54)(13, 67)(14, 56)(15, 57)(16, 68)(17, 70)(18, 60)(19, 71)(20, 62)(21, 63)(22, 72)(23, 66)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 48, 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E16.245 Graph:: bipartite v = 11 e = 48 f = 7 degree seq :: [ 6^8, 16^3 ] E16.243 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^3 * Y2^-1, Y3 * Y2^-3, Y3^2 * Y2^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y1^-1), (Y2^-1, Y1^-1) ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 8, 32, 14, 38)(4, 28, 9, 33, 16, 40)(6, 30, 10, 34, 17, 41)(7, 31, 11, 35, 18, 42)(12, 36, 19, 43, 22, 46)(13, 37, 20, 44, 23, 47)(15, 39, 21, 45, 24, 48)(49, 73, 51, 75, 60, 84, 52, 76, 61, 85, 55, 79, 63, 87, 54, 78)(50, 74, 56, 80, 67, 91, 57, 81, 68, 92, 59, 83, 69, 93, 58, 82)(53, 77, 62, 86, 70, 94, 64, 88, 71, 95, 66, 90, 72, 96, 65, 89) L = (1, 52)(2, 57)(3, 61)(4, 63)(5, 64)(6, 60)(7, 49)(8, 68)(9, 69)(10, 67)(11, 50)(12, 55)(13, 54)(14, 71)(15, 51)(16, 72)(17, 70)(18, 53)(19, 59)(20, 58)(21, 56)(22, 66)(23, 65)(24, 62)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 48, 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E16.244 Graph:: bipartite v = 11 e = 48 f = 7 degree seq :: [ 6^8, 16^3 ] E16.244 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, Y3^-3 * Y1, (Y2^-1, Y1), (R * Y3)^2, (R * Y1)^2, Y1^4, (R * Y2)^2, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, (Y3^-1 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 9, 33, 19, 43, 13, 37)(4, 28, 10, 34, 20, 44, 15, 39)(6, 30, 11, 35, 21, 45, 17, 41)(7, 31, 12, 36, 22, 46, 18, 42)(14, 38, 16, 40, 23, 47, 24, 48)(49, 73, 51, 75, 55, 79, 62, 86, 63, 87, 65, 89, 53, 77, 61, 85, 66, 90, 72, 96, 68, 92, 69, 93, 56, 80, 67, 91, 70, 94, 71, 95, 58, 82, 59, 83, 50, 74, 57, 81, 60, 84, 64, 88, 52, 76, 54, 78) L = (1, 52)(2, 58)(3, 54)(4, 60)(5, 63)(6, 64)(7, 49)(8, 68)(9, 59)(10, 70)(11, 71)(12, 50)(13, 65)(14, 51)(15, 55)(16, 57)(17, 62)(18, 53)(19, 69)(20, 66)(21, 72)(22, 56)(23, 67)(24, 61)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 16, 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E16.243 Graph:: bipartite v = 7 e = 48 f = 11 degree seq :: [ 8^6, 48 ] E16.245 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^3, (R * Y1)^2, (Y3, Y2), (Y2^-1, Y1), (Y1^-1, Y3^-1), Y1^4, (R * Y3)^2, (R * Y2)^2, Y1^-2 * Y3^-1 * Y2^-2, Y3 * Y1 * Y2^-1 * Y3 * Y2^-1, Y2^-1 * Y1 * Y3^-1 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 9, 33, 22, 46, 15, 39)(4, 28, 10, 34, 21, 45, 17, 41)(6, 30, 11, 35, 14, 38, 19, 43)(7, 31, 12, 36, 13, 37, 20, 44)(16, 40, 23, 47, 24, 48, 18, 42)(49, 73, 51, 75, 61, 85, 72, 96, 65, 89, 59, 83, 50, 74, 57, 81, 68, 92, 66, 90, 52, 76, 62, 86, 56, 80, 70, 94, 55, 79, 64, 88, 58, 82, 67, 91, 53, 77, 63, 87, 60, 84, 71, 95, 69, 93, 54, 78) L = (1, 52)(2, 58)(3, 62)(4, 60)(5, 65)(6, 66)(7, 49)(8, 69)(9, 67)(10, 61)(11, 64)(12, 50)(13, 56)(14, 71)(15, 59)(16, 51)(17, 55)(18, 63)(19, 72)(20, 53)(21, 68)(22, 54)(23, 57)(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, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E16.242 Graph:: bipartite v = 7 e = 48 f = 11 degree seq :: [ 8^6, 48 ] E16.246 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3, Y2), (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y3^-1 * Y1 * Y2 * Y3^-2, Y2^4 * Y1, Y2^-1 * Y3^-2 * Y2^-2 * Y3^-1, Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 8, 32)(5, 29, 9, 33)(6, 30, 10, 34)(11, 35, 16, 40)(12, 36, 19, 43)(13, 37, 14, 38)(15, 39, 18, 42)(17, 41, 20, 44)(21, 45, 24, 48)(22, 46, 23, 47)(49, 73, 51, 75, 59, 83, 57, 81, 50, 74, 55, 79, 64, 88, 53, 77)(52, 76, 60, 84, 69, 93, 66, 90, 56, 80, 67, 91, 72, 96, 63, 87)(54, 78, 61, 85, 70, 94, 68, 92, 58, 82, 62, 86, 71, 95, 65, 89) L = (1, 52)(2, 56)(3, 60)(4, 62)(5, 63)(6, 49)(7, 67)(8, 61)(9, 66)(10, 50)(11, 69)(12, 71)(13, 51)(14, 55)(15, 58)(16, 72)(17, 53)(18, 54)(19, 70)(20, 57)(21, 65)(22, 59)(23, 64)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24, 48, 24, 48 ), ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E16.253 Graph:: bipartite v = 15 e = 48 f = 3 degree seq :: [ 4^12, 16^3 ] E16.247 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^2 * Y2^-1 * Y3, (R * Y1)^2, (Y3, Y2), (R * Y3)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1, Y1 * Y2^4, Y3^-1 * Y2^-2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 8, 32)(5, 29, 9, 33)(6, 30, 10, 34)(11, 35, 15, 39)(12, 36, 17, 41)(13, 37, 18, 42)(14, 38, 19, 43)(16, 40, 20, 44)(21, 45, 23, 47)(22, 46, 24, 48)(49, 73, 51, 75, 59, 83, 57, 81, 50, 74, 55, 79, 63, 87, 53, 77)(52, 76, 60, 84, 69, 93, 67, 91, 56, 80, 65, 89, 71, 95, 62, 86)(54, 78, 61, 85, 70, 94, 68, 92, 58, 82, 66, 90, 72, 96, 64, 88) L = (1, 52)(2, 56)(3, 60)(4, 61)(5, 62)(6, 49)(7, 65)(8, 66)(9, 67)(10, 50)(11, 69)(12, 70)(13, 51)(14, 54)(15, 71)(16, 53)(17, 72)(18, 55)(19, 58)(20, 57)(21, 68)(22, 59)(23, 64)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24, 48, 24, 48 ), ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E16.252 Graph:: bipartite v = 15 e = 48 f = 3 degree seq :: [ 4^12, 16^3 ] E16.248 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y1^-2 * Y3 * Y1^-1, (Y3^-1 * Y1^-1)^2, Y1^-1 * Y3^3, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^2 * Y3^2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), Y2 * Y1 * Y2^2 * Y3^-1, Y3 * Y2^2 * Y3 * Y2, Y2^-1 * Y1 * Y2^-2 * Y1, (Y2 * Y3 * Y1)^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 4, 28, 10, 34, 7, 31, 12, 36, 5, 29)(3, 27, 9, 33, 21, 45, 14, 38, 22, 46, 16, 40, 19, 43, 15, 39)(6, 30, 11, 35, 13, 37, 17, 41, 23, 47, 20, 44, 24, 48, 18, 42)(49, 73, 51, 75, 61, 85, 56, 80, 69, 93, 71, 95, 58, 82, 70, 94, 72, 96, 60, 84, 67, 91, 54, 78)(50, 74, 57, 81, 65, 89, 52, 76, 62, 86, 68, 92, 55, 79, 64, 88, 66, 90, 53, 77, 63, 87, 59, 83) L = (1, 52)(2, 58)(3, 62)(4, 60)(5, 56)(6, 65)(7, 49)(8, 55)(9, 70)(10, 53)(11, 71)(12, 50)(13, 68)(14, 67)(15, 69)(16, 51)(17, 72)(18, 61)(19, 57)(20, 54)(21, 64)(22, 63)(23, 66)(24, 59)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E16.250 Graph:: bipartite v = 5 e = 48 f = 13 degree seq :: [ 16^3, 24^2 ] E16.249 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y1^-2 * Y3 * Y1^-1, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y1^-2 * Y3^-2, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y3^-1 * Y2^2 * Y3^-1 * Y2, Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y2^3 * Y1^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 4, 28, 10, 34, 7, 31, 12, 36, 5, 29)(3, 27, 9, 33, 19, 43, 14, 38, 22, 46, 16, 40, 23, 47, 15, 39)(6, 30, 11, 35, 21, 45, 17, 41, 24, 48, 20, 44, 13, 37, 18, 42)(49, 73, 51, 75, 61, 85, 60, 84, 71, 95, 72, 96, 58, 82, 70, 94, 69, 93, 56, 80, 67, 91, 54, 78)(50, 74, 57, 81, 66, 90, 53, 77, 63, 87, 68, 92, 55, 79, 64, 88, 65, 89, 52, 76, 62, 86, 59, 83) L = (1, 52)(2, 58)(3, 62)(4, 60)(5, 56)(6, 65)(7, 49)(8, 55)(9, 70)(10, 53)(11, 72)(12, 50)(13, 59)(14, 71)(15, 67)(16, 51)(17, 61)(18, 69)(19, 64)(20, 54)(21, 68)(22, 63)(23, 57)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E16.251 Graph:: bipartite v = 5 e = 48 f = 13 degree seq :: [ 16^3, 24^2 ] E16.250 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y2, Y3^4 * Y2, Y1^2 * Y3 * Y1 * Y2, Y2 * Y3^-1 * Y1 * Y2 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3^2 * Y1^-2 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 13, 37, 20, 44, 24, 48, 18, 42, 22, 46, 15, 39, 4, 28, 9, 33, 12, 36, 3, 27, 8, 32, 17, 41, 6, 30, 10, 34, 19, 43, 14, 38, 21, 45, 23, 47, 11, 35, 16, 40, 5, 29)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 59, 83)(53, 77, 60, 84)(54, 78, 61, 85)(55, 79, 65, 89)(57, 81, 64, 88)(58, 82, 68, 92)(62, 86, 66, 90)(63, 87, 71, 95)(67, 91, 72, 96)(69, 93, 70, 94) L = (1, 52)(2, 57)(3, 59)(4, 62)(5, 63)(6, 49)(7, 60)(8, 64)(9, 69)(10, 50)(11, 66)(12, 71)(13, 51)(14, 61)(15, 67)(16, 70)(17, 53)(18, 54)(19, 55)(20, 56)(21, 68)(22, 58)(23, 72)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 24, 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ) } Outer automorphisms :: reflexible Dual of E16.248 Graph:: bipartite v = 13 e = 48 f = 5 degree seq :: [ 4^12, 48 ] E16.251 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1^-1 * Y3^-1 * Y1^-2, (Y3, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, Y2 * Y1 * Y2 * Y1^-1, Y3^4 * Y2, Y2 * Y1 * Y3 * Y2 * Y1^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 6, 30, 10, 34, 18, 42, 16, 40, 22, 46, 23, 47, 11, 35, 19, 43, 12, 36, 3, 27, 8, 32, 17, 41, 13, 37, 20, 44, 24, 48, 14, 38, 21, 45, 15, 39, 4, 28, 9, 33, 5, 29)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 59, 83)(53, 77, 60, 84)(54, 78, 61, 85)(55, 79, 65, 89)(57, 81, 67, 91)(58, 82, 68, 92)(62, 86, 64, 88)(63, 87, 71, 95)(66, 90, 72, 96)(69, 93, 70, 94) L = (1, 52)(2, 57)(3, 59)(4, 62)(5, 63)(6, 49)(7, 53)(8, 67)(9, 69)(10, 50)(11, 64)(12, 71)(13, 51)(14, 61)(15, 72)(16, 54)(17, 60)(18, 55)(19, 70)(20, 56)(21, 68)(22, 58)(23, 66)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 24, 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ) } Outer automorphisms :: reflexible Dual of E16.249 Graph:: bipartite v = 13 e = 48 f = 5 degree seq :: [ 4^12, 48 ] E16.252 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y1^-1 * Y2^2, (Y2^-1, Y3^-1), (Y2^-1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, Y1^4 * Y2 * Y3 * Y1, (Y3^-1 * Y1^-1)^8 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 17, 41, 24, 48, 16, 40, 12, 36, 11, 35, 20, 44, 21, 45, 13, 37, 5, 29)(3, 27, 9, 33, 18, 42, 23, 47, 15, 39, 7, 31, 4, 28, 10, 34, 19, 43, 22, 46, 14, 38, 6, 30)(49, 73, 51, 75, 50, 74, 57, 81, 56, 80, 66, 90, 65, 89, 71, 95, 72, 96, 63, 87, 64, 88, 55, 79, 60, 84, 52, 76, 59, 83, 58, 82, 68, 92, 67, 91, 69, 93, 70, 94, 61, 85, 62, 86, 53, 77, 54, 78) L = (1, 52)(2, 58)(3, 59)(4, 50)(5, 55)(6, 60)(7, 49)(8, 67)(9, 68)(10, 56)(11, 57)(12, 51)(13, 63)(14, 64)(15, 53)(16, 54)(17, 70)(18, 69)(19, 65)(20, 66)(21, 71)(22, 72)(23, 61)(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, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E16.247 Graph:: bipartite v = 3 e = 48 f = 15 degree seq :: [ 24^2, 48 ] E16.253 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y3, Y3 * Y2^-2 * Y3, (Y3^-1 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^4 * Y3^2 * Y1, (Y3^-1 * Y1^-1)^8, Y1 * Y2^20 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 17, 41, 24, 48, 16, 40, 12, 36, 11, 35, 20, 44, 21, 45, 13, 37, 5, 29)(3, 27, 9, 33, 18, 42, 22, 46, 14, 38, 6, 30, 4, 28, 10, 34, 19, 43, 23, 47, 15, 39, 7, 31)(49, 73, 51, 75, 59, 83, 58, 82, 56, 80, 66, 90, 69, 93, 71, 95, 72, 96, 62, 86, 53, 77, 55, 79, 60, 84, 52, 76, 50, 74, 57, 81, 68, 92, 67, 91, 65, 89, 70, 94, 61, 85, 63, 87, 64, 88, 54, 78) L = (1, 52)(2, 58)(3, 50)(4, 59)(5, 54)(6, 60)(7, 49)(8, 67)(9, 56)(10, 68)(11, 57)(12, 51)(13, 62)(14, 64)(15, 53)(16, 55)(17, 71)(18, 65)(19, 69)(20, 66)(21, 70)(22, 72)(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) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E16.246 Graph:: bipartite v = 3 e = 48 f = 15 degree seq :: [ 24^2, 48 ] E16.254 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, Y3^-1 * Y1 * Y3 * Y1, Y2^6 * Y1, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 8, 32)(5, 29, 9, 33)(6, 30, 10, 34)(11, 35, 15, 39)(12, 36, 16, 40)(13, 37, 17, 41)(14, 38, 18, 42)(19, 43, 22, 46)(20, 44, 23, 47)(21, 45, 24, 48)(49, 73, 51, 75, 59, 83, 67, 91, 66, 90, 57, 81, 50, 74, 55, 79, 63, 87, 70, 94, 62, 86, 53, 77)(52, 76, 54, 78, 60, 84, 68, 92, 72, 96, 65, 89, 56, 80, 58, 82, 64, 88, 71, 95, 69, 93, 61, 85) L = (1, 52)(2, 56)(3, 54)(4, 53)(5, 61)(6, 49)(7, 58)(8, 57)(9, 65)(10, 50)(11, 60)(12, 51)(13, 62)(14, 69)(15, 64)(16, 55)(17, 66)(18, 72)(19, 68)(20, 59)(21, 70)(22, 71)(23, 63)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48 ) } Outer automorphisms :: reflexible Dual of E16.257 Graph:: bipartite v = 14 e = 48 f = 4 degree seq :: [ 4^12, 24^2 ] E16.255 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-1 * Y3^-1 * Y1, Y2 * Y3^2 * Y1, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2)^2, (Y2^-1, Y3), Y2 * Y3^-1 * Y2^3 * Y3^-1 * Y2, Y2^6 * Y1, (Y3^-1 * Y2)^8 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 8, 32)(5, 29, 9, 33)(6, 30, 10, 34)(11, 35, 15, 39)(12, 36, 16, 40)(13, 37, 17, 41)(14, 38, 18, 42)(19, 43, 22, 46)(20, 44, 23, 47)(21, 45, 24, 48)(49, 73, 51, 75, 59, 83, 67, 91, 66, 90, 57, 81, 50, 74, 55, 79, 63, 87, 70, 94, 62, 86, 53, 77)(52, 76, 58, 82, 64, 88, 71, 95, 72, 96, 65, 89, 56, 80, 54, 78, 60, 84, 68, 92, 69, 93, 61, 85) L = (1, 52)(2, 56)(3, 58)(4, 57)(5, 61)(6, 49)(7, 54)(8, 53)(9, 65)(10, 50)(11, 64)(12, 51)(13, 66)(14, 69)(15, 60)(16, 55)(17, 62)(18, 72)(19, 71)(20, 59)(21, 67)(22, 68)(23, 63)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48 ) } Outer automorphisms :: reflexible Dual of E16.256 Graph:: bipartite v = 14 e = 48 f = 4 degree seq :: [ 4^12, 24^2 ] E16.256 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y1), Y1^-2 * Y3 * Y1^-1, (Y3 * Y1)^2, (Y2^-1, Y1), Y1^-1 * Y3^3, (R * Y1)^2, (Y3, Y2^-1), (R * Y2)^2, Y1^-1 * Y2^-3, (R * Y3)^2, Y1^-2 * Y3^-2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3, Y1^-1 * Y2^-1 * Y1^-1 * Y3 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 4, 28, 10, 34, 7, 31, 12, 36, 5, 29)(3, 27, 9, 33, 19, 43, 14, 38, 21, 45, 16, 40, 22, 46, 15, 39)(6, 30, 11, 35, 20, 44, 17, 41, 23, 47, 18, 42, 24, 48, 13, 37)(49, 73, 51, 75, 61, 85, 53, 77, 63, 87, 72, 96, 60, 84, 70, 94, 66, 90, 55, 79, 64, 88, 71, 95, 58, 82, 69, 93, 65, 89, 52, 76, 62, 86, 68, 92, 56, 80, 67, 91, 59, 83, 50, 74, 57, 81, 54, 78) L = (1, 52)(2, 58)(3, 62)(4, 60)(5, 56)(6, 65)(7, 49)(8, 55)(9, 69)(10, 53)(11, 71)(12, 50)(13, 68)(14, 70)(15, 67)(16, 51)(17, 72)(18, 54)(19, 64)(20, 66)(21, 63)(22, 57)(23, 61)(24, 59)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 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 E16.255 Graph:: bipartite v = 4 e = 48 f = 14 degree seq :: [ 16^3, 48 ] E16.257 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-2, (Y1^-1 * Y3^-1)^2, (R * Y1)^2, Y2^-3 * Y3, Y3^2 * Y1^-1 * Y3, (Y1, Y2), (R * Y2)^2, (R * Y3)^2, (Y1, Y3^-1), (Y2^-1, Y3^-1), Y3 * Y2 * Y3 * Y2^2 * Y1^-1, Y2 * Y3 * Y1 * Y2 * Y1 * Y2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 4, 28, 10, 34, 7, 31, 12, 36, 5, 29)(3, 27, 9, 33, 19, 43, 14, 38, 22, 46, 16, 40, 23, 47, 15, 39)(6, 30, 11, 35, 20, 44, 13, 37, 21, 45, 18, 42, 24, 48, 17, 41)(49, 73, 51, 75, 61, 85, 52, 76, 62, 86, 72, 96, 60, 84, 71, 95, 59, 83, 50, 74, 57, 81, 69, 93, 58, 82, 70, 94, 65, 89, 53, 77, 63, 87, 68, 92, 56, 80, 67, 91, 66, 90, 55, 79, 64, 88, 54, 78) L = (1, 52)(2, 58)(3, 62)(4, 60)(5, 56)(6, 61)(7, 49)(8, 55)(9, 70)(10, 53)(11, 69)(12, 50)(13, 72)(14, 71)(15, 67)(16, 51)(17, 68)(18, 54)(19, 64)(20, 66)(21, 65)(22, 63)(23, 57)(24, 59)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E16.254 Graph:: bipartite v = 4 e = 48 f = 14 degree seq :: [ 16^3, 48 ] E16.258 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^8 * Y1, (Y3 * Y2^-1)^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, 70, 94, 64, 88, 58, 82, 52, 76, 57, 81, 63, 87, 69, 93, 72, 96, 67, 91, 61, 85, 55, 79, 50, 74, 54, 78, 60, 84, 66, 90, 71, 95, 65, 89, 59, 83, 53, 77) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 48, 6, 48, 6, 48 ), ( 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 9 e = 48 f = 9 degree seq :: [ 6^8, 48 ] E16.259 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^-8 * Y1, (Y3 * Y2^-1)^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, 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, 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, 48, 6, 48, 6, 48 ), ( 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 9 e = 48 f = 9 degree seq :: [ 6^8, 48 ] E16.260 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^-8 * Y1, (Y3 * Y2^-1)^24 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28)(3, 27, 6, 30, 9, 33)(5, 29, 7, 31, 10, 34)(8, 32, 12, 36, 15, 39)(11, 35, 13, 37, 16, 40)(14, 38, 18, 42, 21, 45)(17, 41, 19, 43, 22, 46)(20, 44, 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, 50)(2, 52)(3, 54)(4, 49)(5, 55)(6, 57)(7, 58)(8, 60)(9, 51)(10, 53)(11, 61)(12, 63)(13, 64)(14, 66)(15, 56)(16, 59)(17, 67)(18, 69)(19, 70)(20, 72)(21, 62)(22, 65)(23, 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) :: { ( 6, 48, 6, 48, 6, 48 ), ( 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 9 e = 48 f = 9 degree seq :: [ 6^8, 48 ] E16.261 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-2, Y3^3, Y1 * Y3^-1 * Y1, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2^-1 * Y1 * Y2^-3, Y2^-1 * Y1^-1 * Y2^2 * Y3 * Y1 * Y2^2 * Y3 * Y1 * Y2^2 * Y3 * Y1 * Y2^2 * Y3 * Y1 * Y2^2 * Y3 * Y1 * Y2^2 * Y3 * Y1 * Y2^2 * Y3 * Y1 * Y2^2 * Y3 * Y1 * Y2^2 * Y3 * Y1 * Y2^2 * Y3 * Y1 * Y2^2 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 9, 33, 7, 31, 5, 29)(3, 27, 8, 32, 12, 36, 20, 44, 14, 38, 13, 37)(6, 30, 10, 34, 15, 39, 21, 45, 18, 42, 16, 40)(11, 35, 19, 43, 22, 46, 24, 48, 23, 47, 17, 41)(49, 73, 51, 75, 59, 83, 58, 82, 50, 74, 56, 80, 67, 91, 63, 87, 52, 76, 60, 84, 70, 94, 69, 93, 57, 81, 68, 92, 72, 96, 66, 90, 55, 79, 62, 86, 71, 95, 64, 88, 53, 77, 61, 85, 65, 89, 54, 78) L = (1, 52)(2, 57)(3, 60)(4, 55)(5, 50)(6, 63)(7, 49)(8, 68)(9, 53)(10, 69)(11, 70)(12, 62)(13, 56)(14, 51)(15, 66)(16, 58)(17, 67)(18, 54)(19, 72)(20, 61)(21, 64)(22, 71)(23, 59)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E16.262 Graph:: bipartite v = 5 e = 48 f = 13 degree seq :: [ 12^4, 48 ] E16.262 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, Y2 * Y3 * Y2 * Y3^-1, Y2 * Y1^-1 * Y2 * Y1, (Y3^-1, Y1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^2 * Y3^-1 * Y1^2 * Y2, Y1^-2 * Y2 * Y3 * Y1^-2 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 17, 41, 11, 35, 21, 45, 24, 48, 16, 40, 6, 30, 10, 34, 20, 44, 12, 36, 3, 27, 8, 32, 18, 42, 14, 38, 4, 28, 9, 33, 19, 43, 23, 47, 13, 37, 22, 46, 15, 39, 5, 29)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 59, 83)(53, 77, 60, 84)(54, 78, 61, 85)(55, 79, 66, 90)(57, 81, 69, 93)(58, 82, 70, 94)(62, 86, 65, 89)(63, 87, 68, 92)(64, 88, 71, 95)(67, 91, 72, 96) L = (1, 52)(2, 57)(3, 59)(4, 54)(5, 62)(6, 49)(7, 67)(8, 69)(9, 58)(10, 50)(11, 61)(12, 65)(13, 51)(14, 64)(15, 66)(16, 53)(17, 71)(18, 72)(19, 68)(20, 55)(21, 70)(22, 56)(23, 60)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 48, 12, 48 ), ( 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48 ) } Outer automorphisms :: reflexible Dual of E16.261 Graph:: bipartite v = 13 e = 48 f = 5 degree seq :: [ 4^12, 48 ] E16.263 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 5, 5}) Quotient :: dipole Aut^+ = C5 x C5 (small group id <25, 2>) Aut = (C5 x C5) : C2 (small group id <50, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (Y3^-1, Y1^-1), Y3^-5, Y1^5, Y2^5, (Y3 * Y2^-1)^5 ] Map:: non-degenerate R = (1, 26, 2, 27, 6, 31, 13, 38, 5, 30)(3, 28, 7, 32, 14, 39, 19, 44, 10, 35)(4, 29, 8, 33, 15, 40, 21, 46, 12, 37)(9, 34, 16, 41, 22, 47, 24, 49, 18, 43)(11, 36, 17, 42, 23, 48, 25, 50, 20, 45)(51, 76, 53, 78, 59, 84, 61, 86, 54, 79)(52, 77, 57, 82, 66, 91, 67, 92, 58, 83)(55, 80, 60, 85, 68, 93, 70, 95, 62, 87)(56, 81, 64, 89, 72, 97, 73, 98, 65, 90)(63, 88, 69, 94, 74, 99, 75, 100, 71, 96) L = (1, 54)(2, 58)(3, 51)(4, 61)(5, 62)(6, 65)(7, 52)(8, 67)(9, 53)(10, 55)(11, 59)(12, 70)(13, 71)(14, 56)(15, 73)(16, 57)(17, 66)(18, 60)(19, 63)(20, 68)(21, 75)(22, 64)(23, 72)(24, 69)(25, 74)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10^10 ) } Outer automorphisms :: reflexible Dual of E16.265 Graph:: bipartite v = 10 e = 50 f = 10 degree seq :: [ 10^10 ] E16.264 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 5, 5}) Quotient :: dipole Aut^+ = C5 x C5 (small group id <25, 2>) Aut = (C5 x C5) : C2 (small group id <50, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, Y2 * Y3^2, (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1), (R * Y2)^2, Y1^5, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 26, 2, 27, 8, 33, 15, 40, 5, 30)(3, 28, 9, 34, 18, 43, 22, 47, 13, 38)(4, 29, 10, 35, 19, 44, 23, 48, 14, 39)(6, 31, 11, 36, 20, 45, 24, 49, 16, 41)(7, 32, 12, 37, 21, 46, 25, 50, 17, 42)(51, 76, 53, 78, 54, 79, 57, 82, 56, 81)(52, 77, 59, 84, 60, 85, 62, 87, 61, 86)(55, 80, 63, 88, 64, 89, 67, 92, 66, 91)(58, 83, 68, 93, 69, 94, 71, 96, 70, 95)(65, 90, 72, 97, 73, 98, 75, 100, 74, 99) L = (1, 54)(2, 60)(3, 57)(4, 56)(5, 64)(6, 53)(7, 51)(8, 69)(9, 62)(10, 61)(11, 59)(12, 52)(13, 67)(14, 66)(15, 73)(16, 63)(17, 55)(18, 71)(19, 70)(20, 68)(21, 58)(22, 75)(23, 74)(24, 72)(25, 65)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10^10 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 50 f = 10 degree seq :: [ 10^10 ] E16.265 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 5, 5}) Quotient :: dipole Aut^+ = C5 x C5 (small group id <25, 2>) Aut = (C5 x C5) : C2 (small group id <50, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, Y2 * Y3^-2, (R * Y1)^2, (Y1, Y3), (Y2^-1, Y1), (R * Y3)^2, (R * Y2)^2, Y1^5, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 26, 2, 27, 8, 33, 15, 40, 5, 30)(3, 28, 9, 34, 18, 43, 22, 47, 13, 38)(4, 29, 10, 35, 19, 44, 23, 48, 14, 39)(6, 31, 11, 36, 20, 45, 24, 49, 16, 41)(7, 32, 12, 37, 21, 46, 25, 50, 17, 42)(51, 76, 53, 78, 57, 82, 54, 79, 56, 81)(52, 77, 59, 84, 62, 87, 60, 85, 61, 86)(55, 80, 63, 88, 67, 92, 64, 89, 66, 91)(58, 83, 68, 93, 71, 96, 69, 94, 70, 95)(65, 90, 72, 97, 75, 100, 73, 98, 74, 99) L = (1, 54)(2, 60)(3, 56)(4, 53)(5, 64)(6, 57)(7, 51)(8, 69)(9, 61)(10, 59)(11, 62)(12, 52)(13, 66)(14, 63)(15, 73)(16, 67)(17, 55)(18, 70)(19, 68)(20, 71)(21, 58)(22, 74)(23, 72)(24, 75)(25, 65)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10^10 ) } Outer automorphisms :: reflexible Dual of E16.263 Graph:: bipartite v = 10 e = 50 f = 10 degree seq :: [ 10^10 ] E16.266 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 5, 5}) Quotient :: dipole Aut^+ = C5 x C5 (small group id <25, 2>) Aut = (C5 x C5) : C2 (small group id <50, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-2 * Y2, Y3 * Y1^-1 * Y2 * Y1^-1, (Y2^-1, Y1), Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y3 * Y1^3, Y2^2 * Y1 * Y3^2, Y2^5, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1, (Y3^-1 * Y1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 26, 2, 27, 8, 33, 17, 42, 5, 30)(3, 28, 9, 34, 19, 44, 7, 32, 12, 37)(4, 29, 10, 35, 18, 43, 6, 31, 11, 36)(13, 38, 21, 46, 25, 50, 14, 39, 22, 47)(15, 40, 20, 45, 24, 49, 16, 41, 23, 48)(51, 76, 53, 78, 63, 88, 70, 95, 56, 81)(52, 77, 59, 84, 71, 96, 74, 99, 61, 86)(54, 79, 58, 83, 69, 94, 75, 100, 66, 91)(55, 80, 62, 87, 72, 97, 65, 90, 68, 93)(57, 82, 64, 89, 73, 98, 60, 85, 67, 92) L = (1, 54)(2, 60)(3, 58)(4, 65)(5, 61)(6, 66)(7, 51)(8, 68)(9, 67)(10, 70)(11, 73)(12, 52)(13, 69)(14, 53)(15, 71)(16, 72)(17, 56)(18, 74)(19, 55)(20, 75)(21, 57)(22, 59)(23, 63)(24, 64)(25, 62)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10^10 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 50 f = 10 degree seq :: [ 10^10 ] E16.267 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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, Y2^3, Y1^3, Y3^3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2)^2, (Y3^-1, Y2^-1), (Y3^-1, Y1^-1), (Y1^-1 * Y3^-1)^9 ] Map:: non-degenerate R = (1, 28, 2, 29, 5, 32)(3, 30, 8, 35, 13, 40)(4, 31, 9, 36, 15, 42)(6, 33, 10, 37, 17, 44)(7, 34, 11, 38, 18, 45)(12, 39, 20, 47, 24, 51)(14, 41, 21, 48, 25, 52)(16, 43, 22, 49, 26, 53)(19, 46, 23, 50, 27, 54)(55, 82, 57, 84, 60, 87)(56, 83, 62, 89, 64, 91)(58, 85, 66, 93, 70, 97)(59, 86, 67, 94, 71, 98)(61, 88, 68, 95, 73, 100)(63, 90, 74, 101, 76, 103)(65, 92, 75, 102, 77, 104)(69, 96, 78, 105, 80, 107)(72, 99, 79, 106, 81, 108) L = (1, 58)(2, 63)(3, 66)(4, 68)(5, 69)(6, 70)(7, 55)(8, 74)(9, 75)(10, 76)(11, 56)(12, 73)(13, 78)(14, 57)(15, 79)(16, 61)(17, 80)(18, 59)(19, 60)(20, 77)(21, 62)(22, 65)(23, 64)(24, 81)(25, 67)(26, 72)(27, 71)(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) :: { ( 18^6 ) } Outer automorphisms :: reflexible Dual of E16.278 Graph:: simple bipartite v = 18 e = 54 f = 6 degree seq :: [ 6^18 ] E16.268 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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 :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^9, (Y3 * Y2^-1)^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, 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) :: { ( 6, 18, 6, 18, 6, 18 ), ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 12 e = 54 f = 12 degree seq :: [ 6^9, 18^3 ] E16.269 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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, Y3^3, Y1^3, Y3 * Y2^-3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y1^-1) ] Map:: non-degenerate R = (1, 28, 2, 29, 5, 32)(3, 30, 8, 35, 14, 41)(4, 31, 9, 36, 16, 43)(6, 33, 10, 37, 17, 44)(7, 34, 11, 38, 18, 45)(12, 39, 20, 47, 24, 51)(13, 40, 21, 48, 25, 52)(15, 42, 22, 49, 26, 53)(19, 46, 23, 50, 27, 54)(55, 82, 57, 84, 66, 93, 58, 85, 67, 94, 73, 100, 61, 88, 69, 96, 60, 87)(56, 83, 62, 89, 74, 101, 63, 90, 75, 102, 77, 104, 65, 92, 76, 103, 64, 91)(59, 86, 68, 95, 78, 105, 70, 97, 79, 106, 81, 108, 72, 99, 80, 107, 71, 98) L = (1, 58)(2, 63)(3, 67)(4, 61)(5, 70)(6, 66)(7, 55)(8, 75)(9, 65)(10, 74)(11, 56)(12, 73)(13, 69)(14, 79)(15, 57)(16, 72)(17, 78)(18, 59)(19, 60)(20, 77)(21, 76)(22, 62)(23, 64)(24, 81)(25, 80)(26, 68)(27, 71)(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, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E16.270 Graph:: bipartite v = 12 e = 54 f = 12 degree seq :: [ 6^9, 18^3 ] E16.270 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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, Y3^3, Y1^3, Y2^-3 * Y3^-1, (Y2, Y3), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (Y2, Y1^-1), (Y1^-1 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 28, 2, 29, 5, 32)(3, 30, 8, 35, 14, 41)(4, 31, 9, 36, 16, 43)(6, 33, 10, 37, 18, 45)(7, 34, 11, 38, 19, 46)(12, 39, 20, 47, 24, 51)(13, 40, 21, 48, 25, 52)(15, 42, 22, 49, 26, 53)(17, 44, 23, 50, 27, 54)(55, 82, 57, 84, 66, 93, 61, 88, 69, 96, 71, 98, 58, 85, 67, 94, 60, 87)(56, 83, 62, 89, 74, 101, 65, 92, 76, 103, 77, 104, 63, 90, 75, 102, 64, 91)(59, 86, 68, 95, 78, 105, 73, 100, 80, 107, 81, 108, 70, 97, 79, 106, 72, 99) L = (1, 58)(2, 63)(3, 67)(4, 61)(5, 70)(6, 71)(7, 55)(8, 75)(9, 65)(10, 77)(11, 56)(12, 60)(13, 69)(14, 79)(15, 57)(16, 73)(17, 66)(18, 81)(19, 59)(20, 64)(21, 76)(22, 62)(23, 74)(24, 72)(25, 80)(26, 68)(27, 78)(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, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E16.269 Graph:: bipartite v = 12 e = 54 f = 12 degree seq :: [ 6^9, 18^3 ] E16.271 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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, Y1^3, Y3^3, Y2^3 * Y1^-1, (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (Y3^-1, Y2), (Y1^-1 * Y3^-1)^3, (Y2^-1 * Y3)^9 ] Map:: non-degenerate R = (1, 28, 2, 29, 5, 32)(3, 30, 8, 35, 13, 40)(4, 31, 9, 36, 15, 42)(6, 33, 10, 37, 17, 44)(7, 34, 11, 38, 18, 45)(12, 39, 20, 47, 24, 51)(14, 41, 21, 48, 25, 52)(16, 43, 22, 49, 26, 53)(19, 46, 23, 50, 27, 54)(55, 82, 57, 84, 64, 91, 56, 83, 62, 89, 71, 98, 59, 86, 67, 94, 60, 87)(58, 85, 66, 93, 76, 103, 63, 90, 74, 101, 80, 107, 69, 96, 78, 105, 70, 97)(61, 88, 68, 95, 77, 104, 65, 92, 75, 102, 81, 108, 72, 99, 79, 106, 73, 100) L = (1, 58)(2, 63)(3, 66)(4, 61)(5, 69)(6, 70)(7, 55)(8, 74)(9, 65)(10, 76)(11, 56)(12, 68)(13, 78)(14, 57)(15, 72)(16, 73)(17, 80)(18, 59)(19, 60)(20, 75)(21, 62)(22, 77)(23, 64)(24, 79)(25, 67)(26, 81)(27, 71)(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, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E16.275 Graph:: bipartite v = 12 e = 54 f = 12 degree seq :: [ 6^9, 18^3 ] E16.272 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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, Y1^3, Y3^3, Y1^-1 * Y2^-3, (Y1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (Y3^-1, Y2), (R * Y1)^2, (Y1^-1 * Y3^-1)^3, Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 28, 2, 29, 5, 32)(3, 30, 8, 35, 14, 41)(4, 31, 9, 36, 16, 43)(6, 33, 10, 37, 12, 39)(7, 34, 11, 38, 18, 45)(13, 40, 20, 47, 26, 53)(15, 42, 21, 48, 27, 54)(17, 44, 22, 49, 24, 51)(19, 46, 23, 50, 25, 52)(55, 82, 57, 84, 66, 93, 59, 86, 68, 95, 64, 91, 56, 83, 62, 89, 60, 87)(58, 85, 67, 94, 78, 105, 70, 97, 80, 107, 76, 103, 63, 90, 74, 101, 71, 98)(61, 88, 69, 96, 79, 106, 72, 99, 81, 108, 77, 104, 65, 92, 75, 102, 73, 100) L = (1, 58)(2, 63)(3, 67)(4, 61)(5, 70)(6, 71)(7, 55)(8, 74)(9, 65)(10, 76)(11, 56)(12, 78)(13, 69)(14, 80)(15, 57)(16, 72)(17, 73)(18, 59)(19, 60)(20, 75)(21, 62)(22, 77)(23, 64)(24, 79)(25, 66)(26, 81)(27, 68)(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, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E16.277 Graph:: bipartite v = 12 e = 54 f = 12 degree seq :: [ 6^9, 18^3 ] E16.273 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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 * Y1^-1, Y1^3, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^9, (Y3 * Y2^-1)^9 ] Map:: non-degenerate 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, 56)(2, 58)(3, 60)(4, 55)(5, 61)(6, 63)(7, 64)(8, 66)(9, 57)(10, 59)(11, 67)(12, 69)(13, 70)(14, 72)(15, 62)(16, 65)(17, 73)(18, 75)(19, 76)(20, 78)(21, 68)(22, 71)(23, 79)(24, 80)(25, 81)(26, 74)(27, 77)(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, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 12 e = 54 f = 12 degree seq :: [ 6^9, 18^3 ] E16.274 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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, Y3^3, Y1^3, (Y2^-1, Y1), (R * Y1)^2, (Y3^-1, Y2), (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y1^-1), Y2^3 * Y3^-1 * Y1, Y2 * Y3 * Y2 * Y1 * Y3 * Y2 ] Map:: non-degenerate R = (1, 28, 2, 29, 5, 32)(3, 30, 8, 35, 14, 41)(4, 31, 9, 36, 16, 43)(6, 33, 10, 37, 18, 45)(7, 34, 11, 38, 19, 46)(12, 39, 17, 44, 23, 50)(13, 40, 22, 49, 27, 54)(15, 42, 20, 47, 24, 51)(21, 48, 25, 52, 26, 53)(55, 82, 57, 84, 66, 93, 70, 97, 81, 108, 79, 106, 65, 92, 74, 101, 60, 87)(56, 83, 62, 89, 71, 98, 58, 85, 67, 94, 80, 107, 73, 100, 78, 105, 64, 91)(59, 86, 68, 95, 77, 104, 63, 90, 76, 103, 75, 102, 61, 88, 69, 96, 72, 99) L = (1, 58)(2, 63)(3, 67)(4, 61)(5, 70)(6, 71)(7, 55)(8, 76)(9, 65)(10, 77)(11, 56)(12, 80)(13, 69)(14, 81)(15, 57)(16, 73)(17, 75)(18, 66)(19, 59)(20, 62)(21, 60)(22, 74)(23, 79)(24, 68)(25, 64)(26, 72)(27, 78)(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, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 12 e = 54 f = 12 degree seq :: [ 6^9, 18^3 ] E16.275 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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, Y1^3, Y3^3, (Y1^-1, Y3), (Y3^-1, Y2), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y2 * Y3^-1 * Y2^2 * Y1^-1 ] Map:: non-degenerate R = (1, 28, 2, 29, 5, 32)(3, 30, 8, 35, 14, 41)(4, 31, 9, 36, 16, 43)(6, 33, 10, 37, 18, 45)(7, 34, 11, 38, 19, 46)(12, 39, 22, 49, 17, 44)(13, 40, 23, 50, 26, 53)(15, 42, 24, 51, 20, 47)(21, 48, 25, 52, 27, 54)(55, 82, 57, 84, 66, 93, 63, 90, 77, 104, 81, 108, 73, 100, 74, 101, 60, 87)(56, 83, 62, 89, 76, 103, 70, 97, 80, 107, 75, 102, 61, 88, 69, 96, 64, 91)(58, 85, 67, 94, 79, 106, 65, 92, 78, 105, 72, 99, 59, 86, 68, 95, 71, 98) L = (1, 58)(2, 63)(3, 67)(4, 61)(5, 70)(6, 71)(7, 55)(8, 77)(9, 65)(10, 66)(11, 56)(12, 79)(13, 69)(14, 80)(15, 57)(16, 73)(17, 75)(18, 76)(19, 59)(20, 68)(21, 60)(22, 81)(23, 78)(24, 62)(25, 64)(26, 74)(27, 72)(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, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E16.271 Graph:: bipartite v = 12 e = 54 f = 12 degree seq :: [ 6^9, 18^3 ] E16.276 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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, Y1^3, Y3^3, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2), (Y3^-1, Y1^-1), (R * Y1)^2, Y3^-1 * Y1 * Y2^-3, (Y1^-1 * Y3)^3 ] Map:: non-degenerate R = (1, 28, 2, 29, 5, 32)(3, 30, 8, 35, 14, 41)(4, 31, 9, 36, 16, 43)(6, 33, 10, 37, 18, 45)(7, 34, 11, 38, 19, 46)(12, 39, 22, 49, 21, 48)(13, 40, 23, 50, 20, 47)(15, 42, 24, 51, 26, 53)(17, 44, 25, 52, 27, 54)(55, 82, 57, 84, 66, 93, 65, 92, 78, 105, 81, 108, 70, 97, 74, 101, 60, 87)(56, 83, 62, 89, 76, 103, 73, 100, 80, 107, 71, 98, 58, 85, 67, 94, 64, 91)(59, 86, 68, 95, 75, 102, 61, 88, 69, 96, 79, 106, 63, 90, 77, 104, 72, 99) L = (1, 58)(2, 63)(3, 67)(4, 61)(5, 70)(6, 71)(7, 55)(8, 77)(9, 65)(10, 79)(11, 56)(12, 64)(13, 69)(14, 74)(15, 57)(16, 73)(17, 75)(18, 81)(19, 59)(20, 80)(21, 60)(22, 72)(23, 78)(24, 62)(25, 66)(26, 68)(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, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 12 e = 54 f = 12 degree seq :: [ 6^9, 18^3 ] E16.277 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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, Y1^3, Y3^3, (Y2^-1, Y1), (R * Y2)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (Y2^-1, Y3^-1), (R * Y1)^2, Y3 * Y1 * Y2^3, (Y3 * Y1)^3 ] Map:: non-degenerate R = (1, 28, 2, 29, 5, 32)(3, 30, 8, 35, 14, 41)(4, 31, 9, 36, 16, 43)(6, 33, 10, 37, 18, 45)(7, 34, 11, 38, 19, 46)(12, 39, 21, 48, 25, 52)(13, 40, 20, 47, 24, 51)(15, 42, 22, 49, 27, 54)(17, 44, 23, 50, 26, 53)(55, 82, 57, 84, 66, 93, 73, 100, 81, 108, 77, 104, 63, 90, 74, 101, 60, 87)(56, 83, 62, 89, 75, 102, 61, 88, 69, 96, 80, 107, 70, 97, 78, 105, 64, 91)(58, 85, 67, 94, 72, 99, 59, 86, 68, 95, 79, 106, 65, 92, 76, 103, 71, 98) L = (1, 58)(2, 63)(3, 67)(4, 61)(5, 70)(6, 71)(7, 55)(8, 74)(9, 65)(10, 77)(11, 56)(12, 72)(13, 69)(14, 78)(15, 57)(16, 73)(17, 75)(18, 80)(19, 59)(20, 76)(21, 60)(22, 62)(23, 79)(24, 81)(25, 64)(26, 66)(27, 68)(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, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E16.272 Graph:: bipartite v = 12 e = 54 f = 12 degree seq :: [ 6^9, 18^3 ] E16.278 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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, Y2^2 * Y3, (Y2^-1, Y1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y1), Y1 * Y3^-1 * Y1 * Y2 * Y1, Y2 * Y3^-4, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 28, 2, 29, 8, 35, 17, 44, 25, 52, 27, 54, 14, 41, 18, 45, 5, 32)(3, 30, 9, 36, 16, 43, 4, 31, 10, 37, 22, 49, 21, 48, 26, 53, 13, 40)(6, 33, 11, 38, 23, 50, 15, 42, 24, 51, 20, 47, 7, 34, 12, 39, 19, 46)(55, 82, 57, 84, 61, 88, 68, 95, 75, 102, 69, 96, 71, 98, 58, 85, 60, 87)(56, 83, 63, 90, 66, 93, 72, 99, 80, 107, 78, 105, 79, 106, 64, 91, 65, 92)(59, 86, 67, 94, 74, 101, 81, 108, 76, 103, 77, 104, 62, 89, 70, 97, 73, 100) L = (1, 58)(2, 64)(3, 60)(4, 69)(5, 70)(6, 71)(7, 55)(8, 76)(9, 65)(10, 78)(11, 79)(12, 56)(13, 73)(14, 57)(15, 68)(16, 77)(17, 75)(18, 63)(19, 62)(20, 59)(21, 61)(22, 74)(23, 81)(24, 72)(25, 80)(26, 66)(27, 67)(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 ) } Outer automorphisms :: reflexible Dual of E16.267 Graph:: bipartite v = 6 e = 54 f = 18 degree seq :: [ 18^6 ] E16.279 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 9, 9}) Quotient :: edge^2 Aut^+ = C9 : C3 (small group id <27, 4>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, Y1^2 * Y2^-1, Y2^3, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y2^-1 * Y3^-2 * Y1^-1, Y1 * Y3 * Y2 * Y3^-4 ] Map:: non-degenerate R = (1, 28, 4, 31, 12, 39, 24, 51, 17, 44, 19, 46, 27, 54, 15, 42, 5, 32)(2, 29, 6, 33, 13, 40, 25, 52, 20, 47, 21, 48, 22, 49, 10, 37, 7, 34)(3, 30, 8, 35, 18, 45, 23, 50, 11, 38, 14, 41, 26, 53, 16, 43, 9, 36)(55, 56, 57)(58, 64, 65)(59, 67, 68)(60, 70, 71)(61, 72, 73)(62, 69, 74)(63, 66, 75)(76, 80, 81)(77, 78, 79)(82, 84, 83)(85, 92, 91)(86, 95, 94)(87, 98, 97)(88, 100, 99)(89, 101, 96)(90, 102, 93)(103, 108, 107)(104, 106, 105) 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) :: { ( 36^3 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.284 Graph:: simple bipartite v = 21 e = 54 f = 3 degree seq :: [ 3^18, 18^3 ] E16.280 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 9, 9}) Quotient :: edge^2 Aut^+ = C9 : C3 (small group id <27, 4>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, (Y1^-1, Y2), R * Y2 * R * Y1, (R * Y3)^2, Y1^-1 * Y3 * Y2^-1 * Y3^-1, Y2^-1 * Y3 * Y1 * Y2^-1 * Y3^-1, Y1 * Y3^-2 * Y1^-1 * Y3^-1, Y3 * Y2^-1 * Y3^2 * Y2, Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 28, 4, 31, 17, 44, 19, 46, 27, 54, 26, 53, 8, 35, 25, 52, 7, 34)(2, 29, 9, 36, 22, 49, 6, 33, 21, 48, 24, 51, 13, 40, 15, 42, 11, 38)(3, 30, 12, 39, 20, 47, 5, 32, 16, 43, 23, 50, 10, 37, 18, 45, 14, 41)(55, 56, 59)(57, 62, 67)(58, 69, 72)(60, 64, 73)(61, 76, 68)(63, 66, 81)(65, 77, 80)(70, 79, 75)(71, 78, 74)(82, 84, 87)(83, 89, 91)(85, 97, 90)(86, 94, 100)(88, 104, 105)(92, 98, 95)(93, 96, 106)(99, 102, 108)(101, 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) :: { ( 36^3 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.283 Graph:: simple bipartite v = 21 e = 54 f = 3 degree seq :: [ 3^18, 18^3 ] E16.281 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 9, 9}) Quotient :: edge^2 Aut^+ = C9 : C3 (small group id <27, 4>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, (Y1, Y2^-1), R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1^-1 * Y3^-1 * Y2^-1, Y1 * Y3^2 * Y1^-1 * Y3, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3, Y1 * Y3 * Y2^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 28, 4, 31, 17, 44, 8, 35, 26, 53, 27, 54, 20, 47, 25, 52, 7, 34)(2, 29, 9, 36, 23, 50, 13, 40, 18, 45, 22, 49, 6, 33, 15, 42, 11, 38)(3, 30, 12, 39, 24, 51, 10, 37, 16, 43, 21, 48, 5, 32, 19, 46, 14, 41)(55, 56, 59)(57, 62, 67)(58, 69, 66)(60, 64, 74)(61, 77, 78)(63, 70, 80)(65, 68, 81)(71, 76, 75)(72, 73, 79)(82, 84, 87)(83, 89, 91)(85, 97, 99)(86, 94, 101)(88, 102, 92)(90, 106, 93)(95, 104, 98)(96, 107, 100)(103, 108, 105) 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) :: { ( 36^3 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.282 Graph:: simple bipartite v = 21 e = 54 f = 3 degree seq :: [ 3^18, 18^3 ] E16.282 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 9, 9}) Quotient :: loop^2 Aut^+ = C9 : C3 (small group id <27, 4>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, Y1^2 * Y2^-1, Y2^3, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y2^-1 * Y3^-2 * Y1^-1, Y1 * Y3 * Y2 * Y3^-4 ] Map:: non-degenerate R = (1, 28, 55, 82, 4, 31, 58, 85, 12, 39, 66, 93, 24, 51, 78, 105, 17, 44, 71, 98, 19, 46, 73, 100, 27, 54, 81, 108, 15, 42, 69, 96, 5, 32, 59, 86)(2, 29, 56, 83, 6, 33, 60, 87, 13, 40, 67, 94, 25, 52, 79, 106, 20, 47, 74, 101, 21, 48, 75, 102, 22, 49, 76, 103, 10, 37, 64, 91, 7, 34, 61, 88)(3, 30, 57, 84, 8, 35, 62, 89, 18, 45, 72, 99, 23, 50, 77, 104, 11, 38, 65, 92, 14, 41, 68, 95, 26, 53, 80, 107, 16, 43, 70, 97, 9, 36, 63, 90) L = (1, 29)(2, 30)(3, 28)(4, 37)(5, 40)(6, 43)(7, 45)(8, 42)(9, 39)(10, 38)(11, 31)(12, 48)(13, 41)(14, 32)(15, 47)(16, 44)(17, 33)(18, 46)(19, 34)(20, 35)(21, 36)(22, 53)(23, 51)(24, 52)(25, 50)(26, 54)(27, 49)(55, 84)(56, 82)(57, 83)(58, 92)(59, 95)(60, 98)(61, 100)(62, 101)(63, 102)(64, 85)(65, 91)(66, 90)(67, 86)(68, 94)(69, 89)(70, 87)(71, 97)(72, 88)(73, 99)(74, 96)(75, 93)(76, 108)(77, 106)(78, 104)(79, 105)(80, 103)(81, 107) local type(s) :: { ( 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18 ) } Outer automorphisms :: reflexible Dual of E16.281 Transitivity :: VT+ Graph:: v = 3 e = 54 f = 21 degree seq :: [ 36^3 ] E16.283 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 9, 9}) Quotient :: loop^2 Aut^+ = C9 : C3 (small group id <27, 4>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, (Y1^-1, Y2), R * Y2 * R * Y1, (R * Y3)^2, Y1^-1 * Y3 * Y2^-1 * Y3^-1, Y2^-1 * Y3 * Y1 * Y2^-1 * Y3^-1, Y1 * Y3^-2 * Y1^-1 * Y3^-1, Y3 * Y2^-1 * Y3^2 * Y2, Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 28, 55, 82, 4, 31, 58, 85, 17, 44, 71, 98, 19, 46, 73, 100, 27, 54, 81, 108, 26, 53, 80, 107, 8, 35, 62, 89, 25, 52, 79, 106, 7, 34, 61, 88)(2, 29, 56, 83, 9, 36, 63, 90, 22, 49, 76, 103, 6, 33, 60, 87, 21, 48, 75, 102, 24, 51, 78, 105, 13, 40, 67, 94, 15, 42, 69, 96, 11, 38, 65, 92)(3, 30, 57, 84, 12, 39, 66, 93, 20, 47, 74, 101, 5, 32, 59, 86, 16, 43, 70, 97, 23, 50, 77, 104, 10, 37, 64, 91, 18, 45, 72, 99, 14, 41, 68, 95) L = (1, 29)(2, 32)(3, 35)(4, 42)(5, 28)(6, 37)(7, 49)(8, 40)(9, 39)(10, 46)(11, 50)(12, 54)(13, 30)(14, 34)(15, 45)(16, 52)(17, 51)(18, 31)(19, 33)(20, 44)(21, 43)(22, 41)(23, 53)(24, 47)(25, 48)(26, 38)(27, 36)(55, 84)(56, 89)(57, 87)(58, 97)(59, 94)(60, 82)(61, 104)(62, 91)(63, 85)(64, 83)(65, 98)(66, 96)(67, 100)(68, 92)(69, 106)(70, 90)(71, 95)(72, 102)(73, 86)(74, 103)(75, 108)(76, 107)(77, 105)(78, 88)(79, 93)(80, 101)(81, 99) local type(s) :: { ( 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18 ) } Outer automorphisms :: reflexible Dual of E16.280 Transitivity :: VT+ Graph:: v = 3 e = 54 f = 21 degree seq :: [ 36^3 ] E16.284 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 9, 9}) Quotient :: loop^2 Aut^+ = C9 : C3 (small group id <27, 4>) Aut = (C9 : C3) : C2 (small group id <54, 6>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, (Y1, Y2^-1), R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1^-1 * Y3^-1 * Y2^-1, Y1 * Y3^2 * Y1^-1 * Y3, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3, Y1 * Y3 * Y2^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 28, 55, 82, 4, 31, 58, 85, 17, 44, 71, 98, 8, 35, 62, 89, 26, 53, 80, 107, 27, 54, 81, 108, 20, 47, 74, 101, 25, 52, 79, 106, 7, 34, 61, 88)(2, 29, 56, 83, 9, 36, 63, 90, 23, 50, 77, 104, 13, 40, 67, 94, 18, 45, 72, 99, 22, 49, 76, 103, 6, 33, 60, 87, 15, 42, 69, 96, 11, 38, 65, 92)(3, 30, 57, 84, 12, 39, 66, 93, 24, 51, 78, 105, 10, 37, 64, 91, 16, 43, 70, 97, 21, 48, 75, 102, 5, 32, 59, 86, 19, 46, 73, 100, 14, 41, 68, 95) L = (1, 29)(2, 32)(3, 35)(4, 42)(5, 28)(6, 37)(7, 50)(8, 40)(9, 43)(10, 47)(11, 41)(12, 31)(13, 30)(14, 54)(15, 39)(16, 53)(17, 49)(18, 46)(19, 52)(20, 33)(21, 44)(22, 48)(23, 51)(24, 34)(25, 45)(26, 36)(27, 38)(55, 84)(56, 89)(57, 87)(58, 97)(59, 94)(60, 82)(61, 102)(62, 91)(63, 106)(64, 83)(65, 88)(66, 90)(67, 101)(68, 104)(69, 107)(70, 99)(71, 95)(72, 85)(73, 96)(74, 86)(75, 92)(76, 108)(77, 98)(78, 103)(79, 93)(80, 100)(81, 105) local type(s) :: { ( 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18 ) } Outer automorphisms :: reflexible Dual of E16.279 Transitivity :: VT+ Graph:: v = 3 e = 54 f = 21 degree seq :: [ 36^3 ] E16.285 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 7, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y3^-1 * Y1 * Y3 * Y1, (R * Y1)^2, Y2 * Y3^-2 * Y2^-1 * Y3^2, Y3^-7 * Y2^-1, (Y2^-1 * Y3)^7 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 5, 33)(4, 32, 7, 35)(6, 34, 8, 36)(9, 37, 12, 40)(10, 38, 13, 41)(11, 39, 15, 43)(14, 42, 16, 44)(17, 45, 20, 48)(18, 46, 21, 49)(19, 47, 23, 51)(22, 50, 24, 52)(25, 53, 28, 56)(26, 54, 27, 55)(57, 85, 59, 87, 58, 86, 61, 89)(60, 88, 65, 93, 63, 91, 68, 96)(62, 90, 66, 94, 64, 92, 69, 97)(67, 95, 73, 101, 71, 99, 76, 104)(70, 98, 74, 102, 72, 100, 77, 105)(75, 103, 81, 109, 79, 107, 84, 112)(78, 106, 82, 110, 80, 108, 83, 111) L = (1, 60)(2, 63)(3, 65)(4, 67)(5, 68)(6, 57)(7, 71)(8, 58)(9, 73)(10, 59)(11, 75)(12, 76)(13, 61)(14, 62)(15, 79)(16, 64)(17, 81)(18, 66)(19, 83)(20, 84)(21, 69)(22, 70)(23, 82)(24, 72)(25, 78)(26, 74)(27, 77)(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) :: { ( 14, 56, 14, 56 ), ( 14, 56, 14, 56, 14, 56, 14, 56 ) } Outer automorphisms :: reflexible Dual of E16.288 Graph:: bipartite v = 21 e = 56 f = 5 degree seq :: [ 4^14, 8^7 ] E16.286 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 7, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^4, (R * Y2 * Y3^-1)^2, Y2^7, (Y3 * Y2^-1)^28 ] Map:: non-degenerate R = (1, 29, 2, 30, 6, 34, 4, 32)(3, 31, 7, 35, 13, 41, 10, 38)(5, 33, 8, 36, 14, 42, 11, 39)(9, 37, 15, 43, 21, 49, 18, 46)(12, 40, 16, 44, 22, 50, 19, 47)(17, 45, 23, 51, 27, 55, 25, 53)(20, 48, 24, 52, 28, 56, 26, 54)(57, 85, 59, 87, 65, 93, 73, 101, 76, 104, 68, 96, 61, 89)(58, 86, 63, 91, 71, 99, 79, 107, 80, 108, 72, 100, 64, 92)(60, 88, 66, 94, 74, 102, 81, 109, 82, 110, 75, 103, 67, 95)(62, 90, 69, 97, 77, 105, 83, 111, 84, 112, 78, 106, 70, 98) L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 60)(7, 69)(8, 70)(9, 71)(10, 59)(11, 61)(12, 72)(13, 66)(14, 67)(15, 77)(16, 78)(17, 79)(18, 65)(19, 68)(20, 80)(21, 74)(22, 75)(23, 83)(24, 84)(25, 73)(26, 76)(27, 81)(28, 82)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 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 E16.287 Graph:: bipartite v = 11 e = 56 f = 15 degree seq :: [ 8^7, 14^4 ] E16.287 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 7, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^2, (R * Y3)^2, (Y1, Y3), (R * Y2)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1, Y1^-7 * Y3, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 29, 2, 30, 7, 35, 15, 43, 23, 51, 20, 48, 12, 40, 4, 32, 9, 37, 17, 45, 25, 53, 27, 55, 19, 47, 11, 39, 3, 31, 8, 36, 16, 44, 24, 52, 28, 56, 22, 50, 14, 42, 6, 34, 10, 38, 18, 46, 26, 54, 21, 49, 13, 41, 5, 33)(57, 85, 59, 87)(58, 86, 64, 92)(60, 88, 62, 90)(61, 89, 67, 95)(63, 91, 72, 100)(65, 93, 66, 94)(68, 96, 70, 98)(69, 97, 75, 103)(71, 99, 80, 108)(73, 101, 74, 102)(76, 104, 78, 106)(77, 105, 83, 111)(79, 107, 84, 112)(81, 109, 82, 110) L = (1, 60)(2, 65)(3, 62)(4, 59)(5, 68)(6, 57)(7, 73)(8, 66)(9, 64)(10, 58)(11, 70)(12, 67)(13, 76)(14, 61)(15, 81)(16, 74)(17, 72)(18, 63)(19, 78)(20, 75)(21, 79)(22, 69)(23, 83)(24, 82)(25, 80)(26, 71)(27, 84)(28, 77)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 8, 14, 8, 14 ), ( 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14 ) } Outer automorphisms :: reflexible Dual of E16.286 Graph:: bipartite v = 15 e = 56 f = 11 degree seq :: [ 4^14, 56 ] E16.288 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 7, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2^-1), Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1, Y3^-2 * Y2^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y2^-1 * Y3^-1 * Y1^5, Y2^-1 * Y3^-2 * Y2^-1 * Y1 * Y3^-1 * Y2^-1, Y2^-1 * Y3^-1 * Y1 * Y2^-4 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 19, 47, 28, 56, 14, 42, 5, 33)(3, 31, 9, 37, 7, 35, 12, 40, 21, 49, 26, 54, 15, 43)(4, 32, 10, 38, 6, 34, 11, 39, 20, 48, 25, 53, 17, 45)(13, 41, 22, 50, 16, 44, 23, 51, 18, 46, 24, 52, 27, 55)(57, 85, 59, 87, 69, 97, 81, 109, 75, 103, 68, 96, 79, 107, 66, 94, 61, 89, 71, 99, 83, 111, 76, 104, 64, 92, 63, 91, 72, 100, 60, 88, 70, 98, 82, 110, 80, 108, 67, 95, 58, 86, 65, 93, 78, 106, 73, 101, 84, 112, 77, 105, 74, 102, 62, 90) L = (1, 60)(2, 66)(3, 70)(4, 69)(5, 73)(6, 72)(7, 57)(8, 62)(9, 61)(10, 78)(11, 79)(12, 58)(13, 82)(14, 81)(15, 84)(16, 59)(17, 83)(18, 63)(19, 67)(20, 74)(21, 64)(22, 71)(23, 65)(24, 68)(25, 80)(26, 75)(27, 77)(28, 76)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E16.285 Graph:: bipartite v = 5 e = 56 f = 21 degree seq :: [ 14^4, 56 ] E16.289 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 7, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y1 * Y2^2 * Y3^-2, Y1 * Y2^-2 * Y3^2, Y3^-4 * Y2^-3, Y3^4 * Y2^3, Y2^7, Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^3 * Y2^-2 * Y3^2 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 7, 35)(4, 32, 8, 36)(5, 33, 9, 37)(6, 34, 10, 38)(11, 39, 14, 42)(12, 40, 19, 47)(13, 41, 15, 43)(16, 44, 18, 46)(17, 45, 20, 48)(21, 49, 23, 51)(22, 50, 24, 52)(25, 53, 27, 55)(26, 54, 28, 56)(57, 85, 59, 87, 67, 95, 77, 105, 81, 109, 72, 100, 61, 89)(58, 86, 63, 91, 70, 98, 79, 107, 83, 111, 74, 102, 65, 93)(60, 88, 68, 96, 78, 106, 84, 112, 76, 104, 66, 94, 71, 99)(62, 90, 69, 97, 64, 92, 75, 103, 80, 108, 82, 110, 73, 101) L = (1, 60)(2, 64)(3, 68)(4, 70)(5, 71)(6, 57)(7, 75)(8, 67)(9, 69)(10, 58)(11, 78)(12, 79)(13, 59)(14, 80)(15, 63)(16, 66)(17, 61)(18, 62)(19, 77)(20, 65)(21, 84)(22, 83)(23, 82)(24, 81)(25, 76)(26, 72)(27, 73)(28, 74)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 8, 56, 8, 56 ), ( 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56 ) } Outer automorphisms :: reflexible Dual of E16.290 Graph:: simple bipartite v = 18 e = 56 f = 8 degree seq :: [ 4^14, 14^4 ] E16.290 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 7, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y1^4, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y2^-7 * Y1^-1, (Y3 * Y2^-1)^7 ] Map:: non-degenerate R = (1, 29, 2, 30, 6, 34, 4, 32)(3, 31, 7, 35, 13, 41, 10, 38)(5, 33, 8, 36, 14, 42, 11, 39)(9, 37, 15, 43, 21, 49, 18, 46)(12, 40, 16, 44, 22, 50, 19, 47)(17, 45, 23, 51, 27, 55, 26, 54)(20, 48, 24, 52, 28, 56, 25, 53)(57, 85, 59, 87, 65, 93, 73, 101, 81, 109, 75, 103, 67, 95, 60, 88, 66, 94, 74, 102, 82, 110, 84, 112, 78, 106, 70, 98, 62, 90, 69, 97, 77, 105, 83, 111, 80, 108, 72, 100, 64, 92, 58, 86, 63, 91, 71, 99, 79, 107, 76, 104, 68, 96, 61, 89) L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 60)(7, 69)(8, 70)(9, 71)(10, 59)(11, 61)(12, 72)(13, 66)(14, 67)(15, 77)(16, 78)(17, 79)(18, 65)(19, 68)(20, 80)(21, 74)(22, 75)(23, 83)(24, 84)(25, 76)(26, 73)(27, 82)(28, 81)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4, 14, 4, 14, 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) } Outer automorphisms :: reflexible Dual of E16.289 Graph:: bipartite v = 8 e = 56 f = 18 degree seq :: [ 8^7, 56 ] E16.291 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 6, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y1^2 * Y3^-2, R * Y2 * R * Y1, (R * Y3)^2, Y3^6, (Y1^-1 * Y3^-1 * Y2^-1)^2, Y2^6, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 3, 33, 6, 36, 15, 45, 11, 41, 5, 35)(2, 32, 7, 37, 14, 44, 12, 42, 4, 34, 8, 38)(9, 39, 19, 49, 13, 43, 21, 51, 10, 40, 20, 50)(16, 46, 22, 52, 18, 48, 24, 54, 17, 47, 23, 53)(25, 55, 28, 58, 27, 57, 30, 60, 26, 56, 29, 59)(61, 62, 66, 74, 71, 64)(63, 69, 75, 73, 65, 70)(67, 76, 72, 78, 68, 77)(79, 85, 81, 87, 80, 86)(82, 88, 84, 90, 83, 89)(91, 92, 96, 104, 101, 94)(93, 99, 105, 103, 95, 100)(97, 106, 102, 108, 98, 107)(109, 115, 111, 117, 110, 116)(112, 118, 114, 120, 113, 119) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 8^6 ), ( 8^12 ) } Outer automorphisms :: reflexible Dual of E16.294 Graph:: bipartite v = 15 e = 60 f = 15 degree seq :: [ 6^10, 12^5 ] E16.292 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 6, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1, Y2^6, Y1^6, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1, (Y1^-1 * Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 31, 3, 33)(2, 32, 6, 36)(4, 34, 9, 39)(5, 35, 12, 42)(7, 37, 15, 45)(8, 38, 16, 46)(10, 40, 17, 47)(11, 41, 19, 49)(13, 43, 21, 51)(14, 44, 22, 52)(18, 48, 26, 56)(20, 50, 27, 57)(23, 53, 30, 60)(24, 54, 28, 58)(25, 55, 29, 59)(61, 62, 65, 71, 70, 64)(63, 67, 72, 80, 77, 68)(66, 73, 79, 78, 69, 74)(75, 83, 87, 85, 76, 84)(81, 88, 86, 90, 82, 89)(91, 92, 95, 101, 100, 94)(93, 97, 102, 110, 107, 98)(96, 103, 109, 108, 99, 104)(105, 113, 117, 115, 106, 114)(111, 118, 116, 120, 112, 119) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 24^4 ), ( 24^6 ) } Outer automorphisms :: reflexible Dual of E16.293 Graph:: simple bipartite v = 25 e = 60 f = 5 degree seq :: [ 4^15, 6^10 ] E16.293 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 6, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y1^2 * Y3^-2, R * Y2 * R * Y1, (R * Y3)^2, Y3^6, (Y1^-1 * Y3^-1 * Y2^-1)^2, Y2^6, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 61, 91, 3, 33, 63, 93, 6, 36, 66, 96, 15, 45, 75, 105, 11, 41, 71, 101, 5, 35, 65, 95)(2, 32, 62, 92, 7, 37, 67, 97, 14, 44, 74, 104, 12, 42, 72, 102, 4, 34, 64, 94, 8, 38, 68, 98)(9, 39, 69, 99, 19, 49, 79, 109, 13, 43, 73, 103, 21, 51, 81, 111, 10, 40, 70, 100, 20, 50, 80, 110)(16, 46, 76, 106, 22, 52, 82, 112, 18, 48, 78, 108, 24, 54, 84, 114, 17, 47, 77, 107, 23, 53, 83, 113)(25, 55, 85, 115, 28, 58, 88, 118, 27, 57, 87, 117, 30, 60, 90, 120, 26, 56, 86, 116, 29, 59, 89, 119) L = (1, 32)(2, 36)(3, 39)(4, 31)(5, 40)(6, 44)(7, 46)(8, 47)(9, 45)(10, 33)(11, 34)(12, 48)(13, 35)(14, 41)(15, 43)(16, 42)(17, 37)(18, 38)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 51)(26, 49)(27, 50)(28, 54)(29, 52)(30, 53)(61, 92)(62, 96)(63, 99)(64, 91)(65, 100)(66, 104)(67, 106)(68, 107)(69, 105)(70, 93)(71, 94)(72, 108)(73, 95)(74, 101)(75, 103)(76, 102)(77, 97)(78, 98)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 111)(86, 109)(87, 110)(88, 114)(89, 112)(90, 113) 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 E16.292 Transitivity :: VT+ Graph:: v = 5 e = 60 f = 25 degree seq :: [ 24^5 ] E16.294 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 6, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1, Y2^6, Y1^6, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1, (Y1^-1 * Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 31, 61, 91, 3, 33, 63, 93)(2, 32, 62, 92, 6, 36, 66, 96)(4, 34, 64, 94, 9, 39, 69, 99)(5, 35, 65, 95, 12, 42, 72, 102)(7, 37, 67, 97, 15, 45, 75, 105)(8, 38, 68, 98, 16, 46, 76, 106)(10, 40, 70, 100, 17, 47, 77, 107)(11, 41, 71, 101, 19, 49, 79, 109)(13, 43, 73, 103, 21, 51, 81, 111)(14, 44, 74, 104, 22, 52, 82, 112)(18, 48, 78, 108, 26, 56, 86, 116)(20, 50, 80, 110, 27, 57, 87, 117)(23, 53, 83, 113, 30, 60, 90, 120)(24, 54, 84, 114, 28, 58, 88, 118)(25, 55, 85, 115, 29, 59, 89, 119) L = (1, 32)(2, 35)(3, 37)(4, 31)(5, 41)(6, 43)(7, 42)(8, 33)(9, 44)(10, 34)(11, 40)(12, 50)(13, 49)(14, 36)(15, 53)(16, 54)(17, 38)(18, 39)(19, 48)(20, 47)(21, 58)(22, 59)(23, 57)(24, 45)(25, 46)(26, 60)(27, 55)(28, 56)(29, 51)(30, 52)(61, 92)(62, 95)(63, 97)(64, 91)(65, 101)(66, 103)(67, 102)(68, 93)(69, 104)(70, 94)(71, 100)(72, 110)(73, 109)(74, 96)(75, 113)(76, 114)(77, 98)(78, 99)(79, 108)(80, 107)(81, 118)(82, 119)(83, 117)(84, 105)(85, 106)(86, 120)(87, 115)(88, 116)(89, 111)(90, 112) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.291 Transitivity :: VT+ Graph:: v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.295 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6, 6}) Quotient :: dipole Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-1 * Y2, Y3^3, (Y2 * Y3)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1 * Y3, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 11, 41)(4, 34, 8, 38)(5, 35, 13, 43)(6, 36, 10, 40)(7, 37, 14, 44)(9, 39, 16, 46)(12, 42, 18, 48)(15, 45, 22, 52)(17, 47, 25, 55)(19, 49, 26, 56)(20, 50, 27, 57)(21, 51, 28, 58)(23, 53, 29, 59)(24, 54, 30, 60)(61, 91, 63, 93, 64, 94, 72, 102, 66, 96, 65, 95)(62, 92, 67, 97, 68, 98, 75, 105, 70, 100, 69, 99)(71, 101, 77, 107, 78, 108, 80, 110, 73, 103, 79, 109)(74, 104, 81, 111, 82, 112, 84, 114, 76, 106, 83, 113)(85, 115, 89, 119, 87, 117, 88, 118, 86, 116, 90, 120) L = (1, 64)(2, 68)(3, 72)(4, 66)(5, 63)(6, 61)(7, 75)(8, 70)(9, 67)(10, 62)(11, 78)(12, 65)(13, 71)(14, 82)(15, 69)(16, 74)(17, 80)(18, 73)(19, 77)(20, 79)(21, 84)(22, 76)(23, 81)(24, 83)(25, 87)(26, 85)(27, 86)(28, 90)(29, 88)(30, 89)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 12^4 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E16.296 Graph:: bipartite v = 20 e = 60 f = 10 degree seq :: [ 4^15, 12^5 ] E16.296 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6, 6}) Quotient :: dipole Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2^2 * Y3^-1, Y1 * Y3^-1 * Y1, (Y2 * Y3)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1^-1)^2, Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 4, 34, 9, 39, 7, 37, 5, 35)(3, 33, 11, 41, 12, 42, 15, 45, 6, 36, 13, 43)(8, 38, 16, 46, 14, 44, 18, 48, 10, 40, 17, 47)(19, 49, 25, 55, 21, 51, 27, 57, 20, 50, 26, 56)(22, 52, 28, 58, 24, 54, 30, 60, 23, 53, 29, 59)(61, 91, 63, 93, 64, 94, 72, 102, 67, 97, 66, 96)(62, 92, 68, 98, 69, 99, 74, 104, 65, 95, 70, 100)(71, 101, 79, 109, 75, 105, 81, 111, 73, 103, 80, 110)(76, 106, 82, 112, 78, 108, 84, 114, 77, 107, 83, 113)(85, 115, 88, 118, 87, 117, 90, 120, 86, 116, 89, 119) L = (1, 64)(2, 69)(3, 72)(4, 67)(5, 62)(6, 63)(7, 61)(8, 74)(9, 65)(10, 68)(11, 75)(12, 66)(13, 71)(14, 70)(15, 73)(16, 78)(17, 76)(18, 77)(19, 81)(20, 79)(21, 80)(22, 84)(23, 82)(24, 83)(25, 87)(26, 85)(27, 86)(28, 90)(29, 88)(30, 89)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.295 Graph:: bipartite v = 10 e = 60 f = 20 degree seq :: [ 12^10 ] E16.297 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y2^-1 * Y1)^2, R * Y2 * R * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y3 * Y1 * Y3^-1, Y2^-1 * Y1 * Y3^5, Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2^-1 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 13, 43)(5, 35, 7, 37)(6, 36, 17, 47)(8, 38, 14, 44)(10, 40, 16, 46)(11, 41, 19, 49)(12, 42, 20, 50)(15, 45, 21, 51)(18, 48, 22, 52)(23, 53, 25, 55)(24, 54, 29, 59)(26, 56, 30, 60)(27, 57, 28, 58)(61, 91, 63, 93, 65, 95)(62, 92, 67, 97, 69, 99)(64, 94, 74, 104, 71, 101)(66, 96, 76, 106, 72, 102)(68, 98, 73, 103, 79, 109)(70, 100, 77, 107, 80, 110)(75, 105, 83, 113, 86, 116)(78, 108, 84, 114, 88, 118)(81, 111, 90, 120, 85, 115)(82, 112, 87, 117, 89, 119) L = (1, 64)(2, 68)(3, 71)(4, 75)(5, 74)(6, 61)(7, 79)(8, 81)(9, 73)(10, 62)(11, 83)(12, 63)(13, 85)(14, 86)(15, 87)(16, 65)(17, 69)(18, 66)(19, 90)(20, 67)(21, 84)(22, 70)(23, 82)(24, 72)(25, 88)(26, 89)(27, 80)(28, 76)(29, 77)(30, 78)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E16.303 Graph:: simple bipartite v = 25 e = 60 f = 5 degree seq :: [ 4^15, 6^10 ] E16.298 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^-1 * Y2 * Y3 * Y2, (Y2 * Y1)^2, (R * Y3)^2, R * Y2 * R * Y2^-1, (R * Y1)^2, Y1 * Y2 * Y3^-1 * Y1 * Y3, Y2^-1 * Y1 * Y3 * Y1 * Y3^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y3^-3 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 13, 43)(5, 35, 7, 37)(6, 36, 17, 47)(8, 38, 11, 41)(10, 40, 12, 42)(14, 44, 19, 49)(15, 45, 20, 50)(16, 46, 21, 51)(18, 48, 22, 52)(23, 53, 30, 60)(24, 54, 27, 57)(25, 55, 26, 56)(28, 58, 29, 59)(61, 91, 63, 93, 65, 95)(62, 92, 67, 97, 69, 99)(64, 94, 74, 104, 71, 101)(66, 96, 76, 106, 72, 102)(68, 98, 79, 109, 73, 103)(70, 100, 81, 111, 77, 107)(75, 105, 83, 113, 86, 116)(78, 108, 84, 114, 88, 118)(80, 110, 85, 115, 90, 120)(82, 112, 89, 119, 87, 117) L = (1, 64)(2, 68)(3, 71)(4, 75)(5, 74)(6, 61)(7, 73)(8, 80)(9, 79)(10, 62)(11, 83)(12, 63)(13, 85)(14, 86)(15, 87)(16, 65)(17, 67)(18, 66)(19, 90)(20, 88)(21, 69)(22, 70)(23, 89)(24, 72)(25, 84)(26, 82)(27, 81)(28, 76)(29, 77)(30, 78)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E16.304 Graph:: simple bipartite v = 25 e = 60 f = 5 degree seq :: [ 4^15, 6^10 ] E16.299 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^3, (Y3 * Y1)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, Y3 * Y2^-1 * Y3 * Y2 * Y1, R * Y2 * Y1 * R * Y2, Y3 * Y1^-1 * Y2 * Y3 * Y2^-1, Y3 * Y1 * Y2^5, Y2^-1 * Y1^-1 * Y2^-3 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1^2 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 10, 40, 7, 37)(4, 34, 13, 43, 8, 38)(6, 36, 16, 46, 9, 39)(11, 41, 19, 49, 23, 53)(12, 42, 20, 50, 14, 44)(15, 45, 17, 47, 21, 51)(18, 48, 22, 52, 28, 58)(24, 54, 29, 59, 27, 57)(25, 55, 30, 60, 26, 56)(61, 91, 63, 93, 71, 101, 84, 114, 81, 111, 73, 103, 80, 110, 90, 120, 78, 108, 66, 96)(62, 92, 67, 97, 79, 109, 87, 117, 75, 105, 64, 94, 74, 104, 85, 115, 82, 112, 69, 99)(65, 95, 70, 100, 83, 113, 89, 119, 77, 107, 68, 98, 72, 102, 86, 116, 88, 118, 76, 106) L = (1, 64)(2, 68)(3, 72)(4, 61)(5, 73)(6, 77)(7, 80)(8, 62)(9, 81)(10, 74)(11, 85)(12, 63)(13, 65)(14, 70)(15, 76)(16, 75)(17, 66)(18, 87)(19, 86)(20, 67)(21, 69)(22, 89)(23, 90)(24, 88)(25, 71)(26, 79)(27, 78)(28, 84)(29, 82)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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 E16.301 Graph:: bipartite v = 13 e = 60 f = 17 degree seq :: [ 6^10, 20^3 ] E16.300 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^3, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y1 * Y3)^2, Y1 * Y2 * Y1 * Y2^-1, R * Y2 * R * Y1 * Y2, Y2 * Y1^-1 * Y3 * Y2^-1 * Y3, Y2 * Y1^-1 * Y2^-2 * Y1 * Y2, Y2 * Y1^-1 * Y2^3 * Y3 * Y2, Y2^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 10, 40, 7, 37)(4, 34, 13, 43, 8, 38)(6, 36, 16, 46, 9, 39)(11, 41, 19, 49, 23, 53)(12, 42, 14, 44, 20, 50)(15, 45, 21, 51, 17, 47)(18, 48, 22, 52, 28, 58)(24, 54, 27, 57, 29, 59)(25, 55, 26, 56, 30, 60)(61, 91, 63, 93, 71, 101, 84, 114, 81, 111, 68, 98, 80, 110, 90, 120, 78, 108, 66, 96)(62, 92, 67, 97, 79, 109, 89, 119, 77, 107, 73, 103, 72, 102, 86, 116, 82, 112, 69, 99)(64, 94, 74, 104, 85, 115, 88, 118, 76, 106, 65, 95, 70, 100, 83, 113, 87, 117, 75, 105) L = (1, 64)(2, 68)(3, 72)(4, 61)(5, 73)(6, 77)(7, 74)(8, 62)(9, 75)(10, 80)(11, 85)(12, 63)(13, 65)(14, 67)(15, 69)(16, 81)(17, 66)(18, 87)(19, 90)(20, 70)(21, 76)(22, 84)(23, 86)(24, 82)(25, 71)(26, 83)(27, 78)(28, 89)(29, 88)(30, 79)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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 E16.302 Graph:: bipartite v = 13 e = 60 f = 17 degree seq :: [ 6^10, 20^3 ] E16.301 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1 * Y3 * Y1^-1 * Y2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y2, Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2, Y1^-1 * Y3 * Y1^2 * Y2 * Y1^-1, (R * Y2 * Y3)^2, Y3 * Y2 * Y1^-1 * Y3 * Y1 * Y2, Y3 * Y1 * Y3 * Y1^4 ] Map:: non-degenerate R = (1, 31, 2, 32, 6, 36, 16, 46, 23, 53, 9, 39, 19, 49, 29, 59, 30, 60, 24, 54, 12, 42, 22, 52, 28, 58, 15, 45, 5, 35)(3, 33, 8, 38, 21, 51, 26, 56, 13, 43, 4, 34, 11, 41, 17, 47, 27, 57, 14, 44, 20, 50, 7, 37, 18, 48, 25, 55, 10, 40)(61, 91, 63, 93)(62, 92, 67, 97)(64, 94, 72, 102)(65, 95, 73, 103)(66, 96, 77, 107)(68, 98, 82, 112)(69, 99, 80, 110)(70, 100, 83, 113)(71, 101, 79, 109)(74, 104, 84, 114)(75, 105, 87, 117)(76, 106, 86, 116)(78, 108, 88, 118)(81, 111, 89, 119)(85, 115, 90, 120) L = (1, 64)(2, 68)(3, 69)(4, 61)(5, 74)(6, 78)(7, 79)(8, 62)(9, 63)(10, 84)(11, 82)(12, 80)(13, 83)(14, 65)(15, 85)(16, 87)(17, 89)(18, 66)(19, 67)(20, 72)(21, 88)(22, 71)(23, 73)(24, 70)(25, 75)(26, 90)(27, 76)(28, 81)(29, 77)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 20, 6, 20 ), ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E16.299 Graph:: bipartite v = 17 e = 60 f = 13 degree seq :: [ 4^15, 30^2 ] E16.302 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y1 * Y2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, Y1^-1 * Y2 * Y3 * Y1 * Y3 * Y2, Y2 * Y1^2 * Y3 * Y1^-2, Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y2, Y2 * Y1 * Y2 * Y1^4 ] Map:: non-degenerate R = (1, 31, 2, 32, 6, 36, 16, 46, 24, 54, 12, 42, 21, 51, 29, 59, 30, 60, 23, 53, 10, 40, 20, 50, 28, 58, 15, 45, 5, 35)(3, 33, 9, 39, 18, 48, 27, 57, 14, 44, 22, 52, 8, 38, 17, 47, 26, 56, 13, 43, 4, 34, 7, 37, 19, 49, 25, 55, 11, 41)(61, 91, 63, 93)(62, 92, 67, 97)(64, 94, 72, 102)(65, 95, 74, 104)(66, 96, 77, 107)(68, 98, 81, 111)(69, 99, 80, 110)(70, 100, 82, 112)(71, 101, 84, 114)(73, 103, 83, 113)(75, 105, 86, 116)(76, 106, 87, 117)(78, 108, 89, 119)(79, 109, 88, 118)(85, 115, 90, 120) L = (1, 64)(2, 68)(3, 70)(4, 61)(5, 71)(6, 78)(7, 80)(8, 62)(9, 81)(10, 63)(11, 65)(12, 82)(13, 84)(14, 83)(15, 87)(16, 85)(17, 88)(18, 66)(19, 89)(20, 67)(21, 69)(22, 72)(23, 74)(24, 73)(25, 76)(26, 90)(27, 75)(28, 77)(29, 79)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 20, 6, 20 ), ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E16.300 Graph:: bipartite v = 17 e = 60 f = 13 degree seq :: [ 4^15, 30^2 ] E16.303 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1 * Y2^-2, Y1^-2 * Y3^-2, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y3, Y3^-2 * Y1 * Y3^-1 * Y2^-1, Y3^-2 * Y2^-1 * Y1 * Y3^-1, Y2 * Y1 * Y3 * Y1 * Y2^-1 * Y1^-1, Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y1)^3, Y2^8 * Y1^-1 * Y3 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 15, 45, 27, 57, 17, 47, 29, 59, 24, 54, 19, 49, 5, 35)(3, 33, 13, 43, 25, 55, 11, 41, 21, 51, 26, 56, 10, 40, 30, 60, 12, 42, 16, 46)(4, 34, 18, 48, 7, 37, 23, 53, 20, 50, 28, 58, 9, 39, 6, 36, 22, 52, 14, 44)(61, 91, 63, 93, 74, 104, 68, 98, 85, 115, 78, 108, 87, 117, 81, 111, 83, 113, 89, 119, 70, 100, 88, 118, 79, 109, 72, 102, 66, 96)(62, 92, 69, 99, 86, 116, 75, 105, 82, 112, 90, 120, 77, 107, 64, 94, 76, 106, 84, 114, 67, 97, 73, 103, 65, 95, 80, 110, 71, 101) L = (1, 64)(2, 70)(3, 75)(4, 79)(5, 81)(6, 73)(7, 61)(8, 67)(9, 87)(10, 65)(11, 66)(12, 62)(13, 88)(14, 71)(15, 72)(16, 83)(17, 63)(18, 86)(19, 82)(20, 68)(21, 84)(22, 89)(23, 90)(24, 85)(25, 77)(26, 74)(27, 80)(28, 76)(29, 69)(30, 78)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 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 E16.297 Graph:: bipartite v = 5 e = 60 f = 25 degree seq :: [ 20^3, 30^2 ] E16.304 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, (Y2 * Y1)^2, Y1^-1 * Y2 * Y3^-1 * Y2^-1, Y3 * Y2^-2 * Y1^-1, (R * Y1)^2, Y1^-2 * Y3^-2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3^-2 * Y1 * Y2^-1 * Y3^-1, Y1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1, (Y3 * Y1)^3, (R * Y2 * Y3^-1)^2, Y2^10 * Y1^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 28, 58, 22, 52, 30, 60, 24, 54, 19, 49, 5, 35)(3, 33, 13, 43, 25, 55, 11, 41, 20, 50, 4, 34, 17, 47, 7, 37, 23, 53, 16, 46)(6, 36, 21, 51, 14, 44, 29, 59, 10, 40, 27, 57, 12, 42, 15, 45, 26, 56, 9, 39)(61, 91, 63, 93, 74, 104, 68, 98, 85, 115, 70, 100, 88, 118, 80, 110, 72, 102, 90, 120, 77, 107, 86, 116, 79, 109, 83, 113, 66, 96)(62, 92, 69, 99, 64, 94, 78, 108, 81, 111, 67, 97, 82, 112, 89, 119, 76, 106, 84, 114, 87, 117, 73, 103, 65, 95, 75, 105, 71, 101) L = (1, 64)(2, 70)(3, 75)(4, 79)(5, 74)(6, 82)(7, 61)(8, 67)(9, 63)(10, 65)(11, 90)(12, 62)(13, 88)(14, 84)(15, 83)(16, 68)(17, 89)(18, 72)(19, 71)(20, 81)(21, 85)(22, 86)(23, 87)(24, 66)(25, 69)(26, 78)(27, 77)(28, 76)(29, 80)(30, 73)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 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 E16.298 Graph:: bipartite v = 5 e = 60 f = 25 degree seq :: [ 20^3, 30^2 ] E16.305 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y1 * Y2^-1 * Y1 * Y2, Y1 * Y2 * Y1 * Y2^-1, (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y1)^2, Y3^2 * Y2 * Y1 * Y3^3, Y3^-1 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y1 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 7, 37)(4, 34, 8, 38)(5, 35, 9, 39)(6, 36, 10, 40)(11, 41, 17, 47)(12, 42, 18, 48)(13, 43, 19, 49)(14, 44, 20, 50)(15, 45, 21, 51)(16, 46, 22, 52)(23, 53, 28, 58)(24, 54, 29, 59)(25, 55, 27, 57)(26, 56, 30, 60)(61, 91, 63, 93, 65, 95)(62, 92, 67, 97, 69, 99)(64, 94, 71, 101, 74, 104)(66, 96, 72, 102, 75, 105)(68, 98, 77, 107, 80, 110)(70, 100, 78, 108, 81, 111)(73, 103, 83, 113, 86, 116)(76, 106, 84, 114, 87, 117)(79, 109, 88, 118, 90, 120)(82, 112, 89, 119, 85, 115) L = (1, 64)(2, 68)(3, 71)(4, 73)(5, 74)(6, 61)(7, 77)(8, 79)(9, 80)(10, 62)(11, 83)(12, 63)(13, 85)(14, 86)(15, 65)(16, 66)(17, 88)(18, 67)(19, 87)(20, 90)(21, 69)(22, 70)(23, 82)(24, 72)(25, 81)(26, 89)(27, 75)(28, 76)(29, 78)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E16.308 Graph:: simple bipartite v = 25 e = 60 f = 5 degree seq :: [ 4^15, 6^10 ] E16.306 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2^-1), (Y2, Y3), (R * Y2)^2, (Y1^-1 * Y3^-1)^2, Y1 * Y2^-1 * Y3 * Y1 * Y3 * Y2, Y2^2 * Y1 * Y3 * Y2^3, Y3 * Y2^2 * Y1 * Y2^3, (Y2^-1 * Y3)^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 13, 43)(4, 34, 9, 39, 7, 37)(6, 36, 10, 40, 16, 46)(11, 41, 19, 49, 25, 55)(12, 42, 20, 50, 14, 44)(15, 45, 21, 51, 18, 48)(17, 47, 22, 52, 28, 58)(23, 53, 30, 60, 27, 57)(24, 54, 29, 59, 26, 56)(61, 91, 63, 93, 71, 101, 83, 113, 81, 111, 69, 99, 80, 110, 89, 119, 77, 107, 66, 96)(62, 92, 68, 98, 79, 109, 90, 120, 78, 108, 67, 97, 74, 104, 86, 116, 82, 112, 70, 100)(64, 94, 72, 102, 84, 114, 88, 118, 76, 106, 65, 95, 73, 103, 85, 115, 87, 117, 75, 105) L = (1, 64)(2, 69)(3, 72)(4, 62)(5, 67)(6, 75)(7, 61)(8, 80)(9, 65)(10, 81)(11, 84)(12, 68)(13, 74)(14, 63)(15, 70)(16, 78)(17, 87)(18, 66)(19, 89)(20, 73)(21, 76)(22, 83)(23, 88)(24, 79)(25, 86)(26, 71)(27, 82)(28, 90)(29, 85)(30, 77)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E16.307 Graph:: bipartite v = 13 e = 60 f = 17 degree seq :: [ 6^10, 20^3 ] E16.307 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1, Y1^-1), Y3^-3 * Y2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1 * Y2 * Y1^-1 * Y2, Y3 * Y1^5 * Y3, (Y1^-1 * Y3^-1)^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 17, 47, 23, 53, 11, 41, 21, 51, 29, 59, 30, 60, 25, 55, 13, 43, 22, 52, 27, 57, 15, 45, 5, 35)(3, 33, 8, 38, 18, 48, 26, 56, 14, 44, 4, 34, 9, 39, 19, 49, 28, 58, 16, 46, 6, 36, 10, 40, 20, 50, 24, 54, 12, 42)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 71, 101)(65, 95, 72, 102)(66, 96, 73, 103)(67, 97, 78, 108)(69, 99, 81, 111)(70, 100, 82, 112)(74, 104, 83, 113)(75, 105, 84, 114)(76, 106, 85, 115)(77, 107, 86, 116)(79, 109, 89, 119)(80, 110, 87, 117)(88, 118, 90, 120) L = (1, 64)(2, 69)(3, 71)(4, 73)(5, 74)(6, 61)(7, 79)(8, 81)(9, 82)(10, 62)(11, 66)(12, 83)(13, 63)(14, 85)(15, 86)(16, 65)(17, 88)(18, 89)(19, 87)(20, 67)(21, 70)(22, 68)(23, 76)(24, 77)(25, 72)(26, 90)(27, 78)(28, 75)(29, 80)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 20, 6, 20 ), ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E16.306 Graph:: bipartite v = 17 e = 60 f = 13 degree seq :: [ 4^15, 30^2 ] E16.308 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, (Y3, Y1), Y3^2 * Y2^-2, (Y3, Y2^-1), (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y2^-1 * Y1 * Y3^-1 * Y1 * Y3^-1, Y2^-1 * Y1 * Y2^-2 * Y1, Y3^3 * Y1^3, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-5 * Y1^-1 * Y2^-1, Y1^10, Y3^2 * Y2^13 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 23, 53, 30, 60, 16, 46, 28, 58, 29, 59, 18, 48, 5, 35)(3, 33, 9, 39, 24, 54, 22, 52, 17, 47, 4, 34, 10, 40, 25, 55, 21, 51, 15, 45)(6, 36, 11, 41, 13, 43, 26, 56, 20, 50, 7, 37, 12, 42, 14, 44, 27, 57, 19, 49)(61, 91, 63, 93, 73, 103, 68, 98, 84, 114, 80, 110, 90, 120, 77, 107, 72, 102, 88, 118, 70, 100, 87, 117, 78, 108, 81, 111, 66, 96)(62, 92, 69, 99, 86, 116, 83, 113, 82, 112, 67, 97, 76, 106, 64, 94, 74, 104, 89, 119, 85, 115, 79, 109, 65, 95, 75, 105, 71, 101) L = (1, 64)(2, 70)(3, 74)(4, 73)(5, 77)(6, 76)(7, 61)(8, 85)(9, 87)(10, 86)(11, 88)(12, 62)(13, 89)(14, 68)(15, 72)(16, 63)(17, 71)(18, 82)(19, 90)(20, 65)(21, 67)(22, 66)(23, 81)(24, 79)(25, 80)(26, 78)(27, 83)(28, 69)(29, 84)(30, 75)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 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 E16.305 Graph:: bipartite v = 5 e = 60 f = 25 degree seq :: [ 20^3, 30^2 ] E16.309 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2), (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^5 * Y1, Y3 * Y2^-1 * Y3^2 * Y2^-2, Y3 * Y2^2 * Y3^2 * Y1, Y2^-1 * Y3^-1 * Y1 * Y2 * Y3 * Y1, Y3^-9 * Y2^-1 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 7, 37)(4, 34, 8, 38)(5, 35, 9, 39)(6, 36, 10, 40)(11, 41, 19, 49)(12, 42, 20, 50)(13, 43, 21, 51)(14, 44, 22, 52)(15, 45, 23, 53)(16, 46, 24, 54)(17, 47, 25, 55)(18, 48, 26, 56)(27, 57, 29, 59)(28, 58, 30, 60)(61, 91, 63, 93, 71, 101, 84, 114, 69, 99, 62, 92, 67, 97, 79, 109, 76, 106, 65, 95)(64, 94, 72, 102, 86, 116, 90, 120, 83, 113, 68, 98, 80, 110, 78, 108, 88, 118, 75, 105)(66, 96, 73, 103, 87, 117, 74, 104, 85, 115, 70, 100, 81, 111, 89, 119, 82, 112, 77, 107) L = (1, 64)(2, 68)(3, 72)(4, 74)(5, 75)(6, 61)(7, 80)(8, 82)(9, 83)(10, 62)(11, 86)(12, 85)(13, 63)(14, 84)(15, 87)(16, 88)(17, 65)(18, 66)(19, 78)(20, 77)(21, 67)(22, 76)(23, 89)(24, 90)(25, 69)(26, 70)(27, 71)(28, 73)(29, 79)(30, 81)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 30, 6, 30 ), ( 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30 ) } Outer automorphisms :: reflexible Dual of E16.310 Graph:: bipartite v = 18 e = 60 f = 12 degree seq :: [ 4^15, 20^3 ] E16.310 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1, Y1^3, (Y2, Y3), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y1^-1, Y2^-1), (Y3^-1 * Y1^-1)^2, Y1^-1 * Y2^5, (Y2^-1 * Y3)^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 13, 43)(4, 34, 9, 39, 7, 37)(6, 36, 10, 40, 16, 46)(11, 41, 19, 49, 24, 54)(12, 42, 20, 50, 14, 44)(15, 45, 21, 51, 18, 48)(17, 47, 22, 52, 27, 57)(23, 53, 29, 59, 25, 55)(26, 56, 30, 60, 28, 58)(61, 91, 63, 93, 71, 101, 82, 112, 70, 100, 62, 92, 68, 98, 79, 109, 87, 117, 76, 106, 65, 95, 73, 103, 84, 114, 77, 107, 66, 96)(64, 94, 72, 102, 83, 113, 90, 120, 81, 111, 69, 99, 80, 110, 89, 119, 88, 118, 78, 108, 67, 97, 74, 104, 85, 115, 86, 116, 75, 105) L = (1, 64)(2, 69)(3, 72)(4, 62)(5, 67)(6, 75)(7, 61)(8, 80)(9, 65)(10, 81)(11, 83)(12, 68)(13, 74)(14, 63)(15, 70)(16, 78)(17, 86)(18, 66)(19, 89)(20, 73)(21, 76)(22, 90)(23, 79)(24, 85)(25, 71)(26, 82)(27, 88)(28, 77)(29, 84)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E16.309 Graph:: bipartite v = 12 e = 60 f = 18 degree seq :: [ 6^10, 30^2 ] E16.311 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^3 * Y2 * Y3^3 * Y2^-1, Y3^8 * Y1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 5, 37)(4, 36, 7, 39)(6, 38, 8, 40)(9, 41, 13, 45)(10, 42, 12, 44)(11, 43, 15, 47)(14, 46, 16, 48)(17, 49, 21, 53)(18, 50, 20, 52)(19, 51, 23, 55)(22, 54, 24, 56)(25, 57, 29, 61)(26, 58, 28, 60)(27, 59, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 66, 98, 69, 101)(68, 100, 74, 106, 71, 103, 76, 108)(70, 102, 73, 105, 72, 104, 77, 109)(75, 107, 82, 114, 79, 111, 84, 116)(78, 110, 81, 113, 80, 112, 85, 117)(83, 115, 90, 122, 87, 119, 92, 124)(86, 118, 89, 121, 88, 120, 93, 125)(91, 123, 96, 128, 94, 126, 95, 127) L = (1, 68)(2, 71)(3, 73)(4, 75)(5, 77)(6, 65)(7, 79)(8, 66)(9, 81)(10, 67)(11, 83)(12, 69)(13, 85)(14, 70)(15, 87)(16, 72)(17, 89)(18, 74)(19, 91)(20, 76)(21, 93)(22, 78)(23, 94)(24, 80)(25, 95)(26, 82)(27, 88)(28, 84)(29, 96)(30, 86)(31, 92)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E16.318 Graph:: bipartite v = 24 e = 64 f = 10 degree seq :: [ 4^16, 8^8 ] E16.312 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-2 * Y2^2, Y3^-2 * Y2^-2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, Y3^4, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (Y2 * Y1)^2, R * Y2 * R * Y2^-1, (Y3^-1 * Y1 * Y3^-1)^2, Y2^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1, Y3 * Y2 * Y1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3 * Y1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 14, 46)(5, 37, 7, 39)(6, 38, 15, 47)(8, 40, 19, 51)(10, 42, 20, 52)(11, 43, 16, 48)(12, 44, 21, 53)(13, 45, 22, 54)(17, 49, 25, 57)(18, 50, 26, 58)(23, 55, 31, 63)(24, 56, 32, 64)(27, 59, 29, 61)(28, 60, 30, 62)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 80, 112, 73, 105)(68, 100, 77, 109, 70, 102, 76, 108)(72, 104, 82, 114, 74, 106, 81, 113)(78, 110, 85, 117, 79, 111, 86, 118)(83, 115, 89, 121, 84, 116, 90, 122)(87, 119, 94, 126, 88, 120, 93, 125)(91, 123, 96, 128, 92, 124, 95, 127) L = (1, 68)(2, 72)(3, 76)(4, 75)(5, 77)(6, 65)(7, 81)(8, 80)(9, 82)(10, 66)(11, 70)(12, 69)(13, 67)(14, 87)(15, 88)(16, 74)(17, 73)(18, 71)(19, 91)(20, 92)(21, 93)(22, 94)(23, 79)(24, 78)(25, 95)(26, 96)(27, 84)(28, 83)(29, 86)(30, 85)(31, 90)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E16.320 Graph:: simple bipartite v = 24 e = 64 f = 10 degree seq :: [ 4^16, 8^8 ] E16.313 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^2 * Y3, Y3^-1 * Y2^2 * Y3^-1, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^4, Y2^4, (Y2^-1 * Y1)^2, R * Y2 * R * Y2^-1, (R * Y1)^2, Y1 * Y2^2 * Y1 * Y3^-2, Y2^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1, Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 14, 46)(5, 37, 7, 39)(6, 38, 15, 47)(8, 40, 19, 51)(10, 42, 20, 52)(11, 43, 16, 48)(12, 44, 21, 53)(13, 45, 22, 54)(17, 49, 25, 57)(18, 50, 26, 58)(23, 55, 31, 63)(24, 56, 32, 64)(27, 59, 30, 62)(28, 60, 29, 61)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 80, 112, 73, 105)(68, 100, 77, 109, 70, 102, 76, 108)(72, 104, 82, 114, 74, 106, 81, 113)(78, 110, 85, 117, 79, 111, 86, 118)(83, 115, 89, 121, 84, 116, 90, 122)(87, 119, 94, 126, 88, 120, 93, 125)(91, 123, 95, 127, 92, 124, 96, 128) L = (1, 68)(2, 72)(3, 76)(4, 75)(5, 77)(6, 65)(7, 81)(8, 80)(9, 82)(10, 66)(11, 70)(12, 69)(13, 67)(14, 87)(15, 88)(16, 74)(17, 73)(18, 71)(19, 91)(20, 92)(21, 93)(22, 94)(23, 79)(24, 78)(25, 96)(26, 95)(27, 84)(28, 83)(29, 86)(30, 85)(31, 89)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E16.319 Graph:: simple bipartite v = 24 e = 64 f = 10 degree seq :: [ 4^16, 8^8 ] E16.314 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^2 * Y1^-1, Y2^4, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-2 * Y1^-2, (Y3, Y2), (R * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y3^4 * Y2, Y3^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * 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 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 6, 38, 9, 41)(4, 36, 15, 47, 21, 53, 12, 44)(7, 39, 18, 50, 22, 54, 10, 42)(13, 45, 24, 56, 17, 49, 27, 59)(14, 46, 23, 55, 19, 51, 26, 58)(16, 48, 28, 60, 29, 61, 30, 62)(20, 52, 25, 57, 31, 63, 32, 64)(65, 97, 67, 99, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 75, 107)(68, 100, 77, 109, 85, 117, 81, 113)(71, 103, 78, 110, 86, 118, 83, 115)(74, 106, 87, 119, 82, 114, 90, 122)(76, 108, 88, 120, 79, 111, 91, 123)(80, 112, 84, 116, 93, 125, 95, 127)(89, 121, 92, 124, 96, 128, 94, 126) L = (1, 68)(2, 74)(3, 77)(4, 80)(5, 82)(6, 81)(7, 65)(8, 85)(9, 87)(10, 89)(11, 90)(12, 66)(13, 84)(14, 67)(15, 69)(16, 83)(17, 95)(18, 96)(19, 70)(20, 71)(21, 93)(22, 72)(23, 92)(24, 73)(25, 91)(26, 94)(27, 75)(28, 76)(29, 78)(30, 79)(31, 86)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E16.317 Graph:: bipartite v = 16 e = 64 f = 18 degree seq :: [ 8^16 ] E16.315 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y1^2 * Y2^-2, Y2^4, Y2^-2 * Y1^-2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1^-1)^2, (Y3 * Y1^-1)^2, (Y3, Y2), Y3^4 * Y2^-1, Y3^-1 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 6, 38, 9, 41)(4, 36, 15, 47, 21, 53, 12, 44)(7, 39, 18, 50, 22, 54, 10, 42)(13, 45, 24, 56, 17, 49, 27, 59)(14, 46, 23, 55, 19, 51, 26, 58)(16, 48, 28, 60, 32, 64, 30, 62)(20, 52, 25, 57, 29, 61, 31, 63)(65, 97, 67, 99, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 75, 107)(68, 100, 77, 109, 85, 117, 81, 113)(71, 103, 78, 110, 86, 118, 83, 115)(74, 106, 87, 119, 82, 114, 90, 122)(76, 108, 88, 120, 79, 111, 91, 123)(80, 112, 93, 125, 96, 128, 84, 116)(89, 121, 94, 126, 95, 127, 92, 124) L = (1, 68)(2, 74)(3, 77)(4, 80)(5, 82)(6, 81)(7, 65)(8, 85)(9, 87)(10, 89)(11, 90)(12, 66)(13, 93)(14, 67)(15, 69)(16, 78)(17, 84)(18, 95)(19, 70)(20, 71)(21, 96)(22, 72)(23, 94)(24, 73)(25, 88)(26, 92)(27, 75)(28, 76)(29, 86)(30, 79)(31, 91)(32, 83)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E16.316 Graph:: bipartite v = 16 e = 64 f = 18 degree seq :: [ 8^16 ] E16.316 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y2 * Y1 * Y3 * Y1^-3, Y1^-4 * Y3 * Y2, Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y2 * Y1 * Y2, Y3 * Y1^2 * Y2 * Y1^-2, (Y1 * Y2)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 18, 50, 13, 45, 25, 57, 30, 62, 27, 59, 31, 63, 29, 61, 32, 64, 28, 60, 10, 42, 22, 54, 17, 49, 5, 37)(3, 35, 9, 41, 26, 58, 8, 40, 24, 56, 16, 48, 23, 55, 7, 39, 21, 53, 15, 47, 20, 52, 14, 46, 4, 36, 12, 44, 19, 51, 11, 43)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 77, 109)(69, 101, 79, 111)(70, 102, 83, 115)(72, 104, 89, 121)(73, 105, 91, 123)(74, 106, 88, 120)(75, 107, 93, 125)(76, 108, 92, 124)(78, 110, 86, 118)(80, 112, 82, 114)(81, 113, 90, 122)(84, 116, 94, 126)(85, 117, 95, 127)(87, 119, 96, 128) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 80)(6, 84)(7, 86)(8, 66)(9, 82)(10, 67)(11, 89)(12, 91)(13, 85)(14, 93)(15, 92)(16, 69)(17, 83)(18, 73)(19, 81)(20, 70)(21, 77)(22, 71)(23, 94)(24, 95)(25, 75)(26, 96)(27, 76)(28, 79)(29, 78)(30, 87)(31, 88)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8^4 ), ( 8^32 ) } Outer automorphisms :: reflexible Dual of E16.315 Graph:: bipartite v = 18 e = 64 f = 16 degree seq :: [ 4^16, 32^2 ] E16.317 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y1^-1 * Y2 * Y3 * Y1^-3, Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-1, (Y1^-2 * Y2)^2, Y3 * Y1^-1 * Y3 * Y2 * Y1 * Y2, Y2 * Y1^2 * Y3 * Y1^-2, (Y2 * Y1)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 18, 50, 10, 42, 22, 54, 30, 62, 27, 59, 31, 63, 29, 61, 32, 64, 28, 60, 13, 45, 25, 57, 17, 49, 5, 37)(3, 35, 9, 41, 20, 52, 14, 46, 4, 36, 12, 44, 23, 55, 7, 39, 21, 53, 15, 47, 26, 58, 8, 40, 24, 56, 16, 48, 19, 51, 11, 43)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 77, 109)(69, 101, 79, 111)(70, 102, 83, 115)(72, 104, 89, 121)(73, 105, 91, 123)(74, 106, 88, 120)(75, 107, 93, 125)(76, 108, 82, 114)(78, 110, 86, 118)(80, 112, 92, 124)(81, 113, 84, 116)(85, 117, 95, 127)(87, 119, 96, 128)(90, 122, 94, 126) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 80)(6, 84)(7, 86)(8, 66)(9, 92)(10, 67)(11, 89)(12, 91)(13, 85)(14, 93)(15, 82)(16, 69)(17, 87)(18, 79)(19, 94)(20, 70)(21, 77)(22, 71)(23, 81)(24, 95)(25, 75)(26, 96)(27, 76)(28, 73)(29, 78)(30, 83)(31, 88)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8^4 ), ( 8^32 ) } Outer automorphisms :: reflexible Dual of E16.314 Graph:: bipartite v = 18 e = 64 f = 16 degree seq :: [ 4^16, 32^2 ] E16.318 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y2^-1 * Y3 * Y1^2, Y3 * Y1 * Y3 * Y1^-1, Y1^-2 * Y3 * Y2^-1, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y3 * Y1^-1, Y2^-4 * Y3^-1 * Y2^-3, Y2^-4 * Y1^-1 * Y3^-1 * Y2^-3 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 4, 36, 12, 44)(6, 38, 9, 41, 7, 39, 10, 42)(13, 45, 19, 51, 14, 46, 20, 52)(15, 47, 17, 49, 16, 48, 18, 50)(21, 53, 27, 59, 22, 54, 28, 60)(23, 55, 25, 57, 24, 56, 26, 58)(29, 61, 32, 64, 30, 62, 31, 63)(65, 97, 67, 99, 77, 109, 85, 117, 93, 125, 88, 120, 80, 112, 71, 103, 72, 104, 68, 100, 78, 110, 86, 118, 94, 126, 87, 119, 79, 111, 70, 102)(66, 98, 73, 105, 81, 113, 89, 121, 95, 127, 92, 124, 84, 116, 76, 108, 69, 101, 74, 106, 82, 114, 90, 122, 96, 128, 91, 123, 83, 115, 75, 107) L = (1, 68)(2, 74)(3, 78)(4, 77)(5, 73)(6, 72)(7, 65)(8, 67)(9, 82)(10, 81)(11, 69)(12, 66)(13, 86)(14, 85)(15, 71)(16, 70)(17, 90)(18, 89)(19, 76)(20, 75)(21, 94)(22, 93)(23, 80)(24, 79)(25, 96)(26, 95)(27, 84)(28, 83)(29, 87)(30, 88)(31, 91)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E16.311 Graph:: bipartite v = 10 e = 64 f = 24 degree seq :: [ 8^8, 32^2 ] E16.319 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y1^4, Y3^-2 * Y1^-2, Y3^-2 * Y1^2, (Y1^-1 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (Y3 * Y2^-1)^2, (Y2^-1 * Y3^-1)^2, Y2^2 * Y3 * Y2^-2 * Y1^-1, Y2^-1 * Y3^-1 * Y2^2 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^16 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 21, 53, 11, 43)(4, 36, 12, 44, 7, 39, 10, 42)(6, 38, 18, 50, 22, 54, 9, 41)(14, 46, 28, 60, 31, 63, 29, 61)(15, 47, 27, 59, 16, 48, 26, 58)(17, 49, 25, 57, 19, 51, 24, 56)(20, 52, 23, 55, 32, 64, 30, 62)(65, 97, 67, 99, 78, 110, 88, 120, 76, 108, 91, 123, 96, 128, 86, 118, 72, 104, 85, 117, 95, 127, 89, 121, 74, 106, 90, 122, 84, 116, 70, 102)(66, 98, 73, 105, 87, 119, 80, 112, 68, 100, 81, 113, 93, 125, 77, 109, 69, 101, 82, 114, 94, 126, 79, 111, 71, 103, 83, 115, 92, 124, 75, 107) L = (1, 68)(2, 74)(3, 79)(4, 72)(5, 76)(6, 83)(7, 65)(8, 71)(9, 88)(10, 69)(11, 91)(12, 66)(13, 90)(14, 87)(15, 85)(16, 67)(17, 70)(18, 89)(19, 86)(20, 93)(21, 80)(22, 81)(23, 95)(24, 82)(25, 73)(26, 75)(27, 77)(28, 84)(29, 96)(30, 78)(31, 94)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E16.313 Graph:: bipartite v = 10 e = 64 f = 24 degree seq :: [ 8^8, 32^2 ] E16.320 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y3^-2 * Y1^2, Y3 * Y1 * Y3 * Y1^-1, Y1 * Y3^2 * Y1, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (R * Y3)^2, (Y2 * Y1^-1)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (Y2^-1 * Y3^-1)^2, Y2^2 * Y3^-1 * Y2^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y2^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 21, 53, 11, 43)(4, 36, 12, 44, 7, 39, 10, 42)(6, 38, 18, 50, 22, 54, 9, 41)(14, 46, 28, 60, 31, 63, 29, 61)(15, 47, 27, 59, 16, 48, 26, 58)(17, 49, 25, 57, 19, 51, 24, 56)(20, 52, 23, 55, 32, 64, 30, 62)(65, 97, 67, 99, 78, 110, 89, 121, 74, 106, 90, 122, 96, 128, 86, 118, 72, 104, 85, 117, 95, 127, 88, 120, 76, 108, 91, 123, 84, 116, 70, 102)(66, 98, 73, 105, 87, 119, 79, 111, 71, 103, 83, 115, 93, 125, 77, 109, 69, 101, 82, 114, 94, 126, 80, 112, 68, 100, 81, 113, 92, 124, 75, 107) L = (1, 68)(2, 74)(3, 79)(4, 72)(5, 76)(6, 83)(7, 65)(8, 71)(9, 88)(10, 69)(11, 91)(12, 66)(13, 90)(14, 94)(15, 85)(16, 67)(17, 70)(18, 89)(19, 86)(20, 92)(21, 80)(22, 81)(23, 78)(24, 82)(25, 73)(26, 75)(27, 77)(28, 96)(29, 84)(30, 95)(31, 87)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.312 Graph:: bipartite v = 10 e = 64 f = 24 degree seq :: [ 8^8, 32^2 ] E16.321 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^16 * Y1, (Y3 * Y2^-1)^32 ] 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, 94, 126, 90, 122, 86, 118, 82, 114, 78, 110, 74, 106, 70, 102, 66, 98, 69, 101, 73, 105, 77, 109, 81, 113, 85, 117, 89, 121, 93, 125, 96, 128, 92, 124, 88, 120, 84, 116, 80, 112, 76, 108, 72, 104, 68, 100) 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, 64, 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 17 e = 64 f = 17 degree seq :: [ 4^16, 64 ] E16.322 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {33, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, T2 * T1^2, (F * T1)^2, (F * T2)^2, T2^-16 * T1 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 30, 26, 22, 18, 14, 10, 6, 2, 4, 8, 12, 16, 20, 24, 28, 32, 33, 29, 25, 21, 17, 13, 9, 5)(34, 35, 38, 39, 42, 43, 46, 47, 50, 51, 54, 55, 58, 59, 62, 63, 66, 64, 65, 60, 61, 56, 57, 52, 53, 48, 49, 44, 45, 40, 41, 36, 37) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^33 ) } Outer automorphisms :: reflexible Dual of E16.326 Transitivity :: ET+ Graph:: bipartite v = 2 e = 33 f = 1 degree seq :: [ 33^2 ] E16.323 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {33, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-1 * T2 * T1^-3, T2 * T1 * T2^7, (T1^-1 * T2^-1)^33 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 28, 20, 12, 4, 10, 18, 26, 32, 33, 27, 19, 11, 6, 14, 22, 30, 31, 24, 16, 8, 2, 7, 15, 23, 29, 21, 13, 5)(34, 35, 39, 43, 36, 40, 47, 51, 42, 48, 55, 59, 50, 56, 63, 65, 58, 62, 64, 66, 61, 54, 57, 60, 53, 46, 49, 52, 45, 38, 41, 44, 37) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^33 ) } Outer automorphisms :: reflexible Dual of E16.328 Transitivity :: ET+ Graph:: bipartite v = 2 e = 33 f = 1 degree seq :: [ 33^2 ] E16.324 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {33, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T1)^2, (F * T2)^2, T2^-1 * T1^-2 * T2 * T1^2, T1^4 * T2 * T1, T1 * T2^-1 * T1 * T2^-5 * T1 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 24, 14, 11, 21, 31, 28, 18, 8, 2, 7, 17, 27, 32, 22, 12, 4, 10, 20, 30, 26, 16, 6, 15, 25, 33, 23, 13, 5)(34, 35, 39, 47, 45, 38, 41, 49, 57, 55, 46, 51, 59, 62, 65, 56, 61, 63, 52, 60, 66, 64, 53, 42, 50, 58, 54, 43, 36, 40, 48, 44, 37) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^33 ) } Outer automorphisms :: reflexible Dual of E16.327 Transitivity :: ET+ Graph:: bipartite v = 2 e = 33 f = 1 degree seq :: [ 33^2 ] E16.325 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {33, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (T1^-1, T2), (F * T1)^2, (F * T2)^2, T2^4 * T1^-1 * T2 * T1^-1, T1^3 * T2^-1 * T1^4, T1^2 * T2 * T1^2 * T2^3 * T1, (T1^-1 * T2^-1)^33 ] Map:: non-degenerate R = (1, 3, 9, 19, 16, 6, 15, 29, 31, 22, 26, 33, 24, 12, 4, 10, 20, 18, 8, 2, 7, 17, 30, 28, 14, 27, 32, 23, 11, 21, 25, 13, 5)(34, 35, 39, 47, 59, 54, 43, 36, 40, 48, 60, 66, 58, 53, 42, 50, 62, 65, 57, 46, 51, 52, 63, 64, 56, 45, 38, 41, 49, 61, 55, 44, 37) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^33 ) } Outer automorphisms :: reflexible Dual of E16.329 Transitivity :: ET+ Graph:: bipartite v = 2 e = 33 f = 1 degree seq :: [ 33^2 ] E16.326 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {33, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1, (F * T1)^2, (F * T2)^2, T2^33, T1^33, (T2^-1 * T1^-1)^33 ] Map:: non-degenerate R = (1, 34, 2, 35, 6, 39, 14, 47, 22, 55, 28, 61, 32, 65, 25, 58, 21, 54, 10, 43, 3, 36, 7, 40, 15, 48, 13, 46, 18, 51, 24, 57, 30, 63, 31, 64, 27, 60, 20, 53, 9, 42, 17, 50, 12, 45, 5, 38, 8, 41, 16, 49, 23, 56, 29, 62, 33, 66, 26, 59, 19, 52, 11, 44, 4, 37) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 47)(7, 48)(8, 49)(9, 50)(10, 36)(11, 37)(12, 38)(13, 51)(14, 55)(15, 46)(16, 56)(17, 45)(18, 57)(19, 44)(20, 42)(21, 43)(22, 61)(23, 62)(24, 63)(25, 54)(26, 52)(27, 53)(28, 65)(29, 66)(30, 64)(31, 60)(32, 58)(33, 59) local type(s) :: { ( 33^66 ) } Outer automorphisms :: reflexible Dual of E16.322 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 2 degree seq :: [ 66 ] E16.327 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {33, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-1 * T2 * T1^-3, T2 * T1 * T2^7, (T1^-1 * T2^-1)^33 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 17, 50, 25, 58, 28, 61, 20, 53, 12, 45, 4, 37, 10, 43, 18, 51, 26, 59, 32, 65, 33, 66, 27, 60, 19, 52, 11, 44, 6, 39, 14, 47, 22, 55, 30, 63, 31, 64, 24, 57, 16, 49, 8, 41, 2, 35, 7, 40, 15, 48, 23, 56, 29, 62, 21, 54, 13, 46, 5, 38) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 43)(7, 47)(8, 44)(9, 48)(10, 36)(11, 37)(12, 38)(13, 49)(14, 51)(15, 55)(16, 52)(17, 56)(18, 42)(19, 45)(20, 46)(21, 57)(22, 59)(23, 63)(24, 60)(25, 62)(26, 50)(27, 53)(28, 54)(29, 64)(30, 65)(31, 66)(32, 58)(33, 61) local type(s) :: { ( 33^66 ) } Outer automorphisms :: reflexible Dual of E16.324 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 2 degree seq :: [ 66 ] E16.328 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {33, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T1)^2, (F * T2)^2, T2^-1 * T1^-2 * T2 * T1^2, T1^4 * T2 * T1, T1 * T2^-1 * T1 * T2^-5 * T1 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 19, 52, 29, 62, 24, 57, 14, 47, 11, 44, 21, 54, 31, 64, 28, 61, 18, 51, 8, 41, 2, 35, 7, 40, 17, 50, 27, 60, 32, 65, 22, 55, 12, 45, 4, 37, 10, 43, 20, 53, 30, 63, 26, 59, 16, 49, 6, 39, 15, 48, 25, 58, 33, 66, 23, 56, 13, 46, 5, 38) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 47)(7, 48)(8, 49)(9, 50)(10, 36)(11, 37)(12, 38)(13, 51)(14, 45)(15, 44)(16, 57)(17, 58)(18, 59)(19, 60)(20, 42)(21, 43)(22, 46)(23, 61)(24, 55)(25, 54)(26, 62)(27, 66)(28, 63)(29, 65)(30, 52)(31, 53)(32, 56)(33, 64) local type(s) :: { ( 33^66 ) } Outer automorphisms :: reflexible Dual of E16.323 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 2 degree seq :: [ 66 ] E16.329 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {33, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-4 * T1, T1^8 * T2, (T1^-1 * T2^-1)^33 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 8, 41, 2, 35, 7, 40, 17, 50, 16, 49, 6, 39, 15, 48, 25, 58, 24, 57, 14, 47, 23, 56, 31, 64, 30, 63, 22, 55, 27, 60, 32, 65, 33, 66, 28, 61, 19, 52, 26, 59, 29, 62, 20, 53, 11, 44, 18, 51, 21, 54, 12, 45, 4, 37, 10, 43, 13, 46, 5, 38) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 47)(7, 48)(8, 49)(9, 50)(10, 36)(11, 37)(12, 38)(13, 42)(14, 55)(15, 56)(16, 57)(17, 58)(18, 43)(19, 44)(20, 45)(21, 46)(22, 61)(23, 60)(24, 63)(25, 64)(26, 51)(27, 52)(28, 53)(29, 54)(30, 66)(31, 65)(32, 59)(33, 62) local type(s) :: { ( 33^66 ) } Outer automorphisms :: reflexible Dual of E16.325 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 2 degree seq :: [ 66 ] E16.330 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {33, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^2 * Y3^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^16 * Y2, Y2 * Y1^-16 ] Map:: R = (1, 34, 2, 35, 6, 39, 10, 43, 14, 47, 18, 51, 22, 55, 26, 59, 30, 63, 32, 65, 28, 61, 24, 57, 20, 53, 16, 49, 12, 45, 8, 41, 3, 36, 5, 38, 7, 40, 11, 44, 15, 48, 19, 52, 23, 56, 27, 60, 31, 64, 33, 66, 29, 62, 25, 58, 21, 54, 17, 50, 13, 46, 9, 42, 4, 37)(67, 100, 69, 102, 70, 103, 74, 107, 75, 108, 78, 111, 79, 112, 82, 115, 83, 116, 86, 119, 87, 120, 90, 123, 91, 124, 94, 127, 95, 128, 98, 131, 99, 132, 96, 129, 97, 130, 92, 125, 93, 126, 88, 121, 89, 122, 84, 117, 85, 118, 80, 113, 81, 114, 76, 109, 77, 110, 72, 105, 73, 106, 68, 101, 71, 104) L = (1, 70)(2, 67)(3, 74)(4, 75)(5, 69)(6, 68)(7, 71)(8, 78)(9, 79)(10, 72)(11, 73)(12, 82)(13, 83)(14, 76)(15, 77)(16, 86)(17, 87)(18, 80)(19, 81)(20, 90)(21, 91)(22, 84)(23, 85)(24, 94)(25, 95)(26, 88)(27, 89)(28, 98)(29, 99)(30, 92)(31, 93)(32, 96)(33, 97)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E16.334 Graph:: bipartite v = 2 e = 66 f = 34 degree seq :: [ 66^2 ] E16.331 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {33, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2^-4 * Y1, Y1^5 * Y3^-2 * Y2 * Y3^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 22, 55, 28, 61, 20, 53, 12, 45, 5, 38, 8, 41, 16, 49, 24, 57, 30, 63, 33, 66, 29, 62, 21, 54, 13, 46, 9, 42, 17, 50, 25, 58, 31, 64, 32, 65, 26, 59, 18, 51, 10, 43, 3, 36, 7, 40, 15, 48, 23, 56, 27, 60, 19, 52, 11, 44, 4, 37)(67, 100, 69, 102, 75, 108, 74, 107, 68, 101, 73, 106, 83, 116, 82, 115, 72, 105, 81, 114, 91, 124, 90, 123, 80, 113, 89, 122, 97, 130, 96, 129, 88, 121, 93, 126, 98, 131, 99, 132, 94, 127, 85, 118, 92, 125, 95, 128, 86, 119, 77, 110, 84, 117, 87, 120, 78, 111, 70, 103, 76, 109, 79, 112, 71, 104) L = (1, 70)(2, 67)(3, 76)(4, 77)(5, 78)(6, 68)(7, 69)(8, 71)(9, 79)(10, 84)(11, 85)(12, 86)(13, 87)(14, 72)(15, 73)(16, 74)(17, 75)(18, 92)(19, 93)(20, 94)(21, 95)(22, 80)(23, 81)(24, 82)(25, 83)(26, 98)(27, 89)(28, 88)(29, 99)(30, 90)(31, 91)(32, 97)(33, 96)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E16.337 Graph:: bipartite v = 2 e = 66 f = 34 degree seq :: [ 66^2 ] E16.332 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {33, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y2^-1, Y3), (R * Y2)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y1)^2, Y1^2 * Y2 * Y3^2 * Y2^-1, Y3 * Y2^-5, Y1 * Y2 * Y3^-3 * Y2 * Y3^-3, Y1^5 * Y3^-1 * Y2^2 * Y3^-1, Y2^2 * Y3 * Y2 * Y3^5, Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y2^-2 * Y3^3, Y2^-1 * Y3^2 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^2 * Y3^2 * Y2^-1 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 24, 57, 29, 62, 19, 52, 13, 46, 18, 51, 28, 61, 31, 64, 21, 54, 10, 43, 3, 36, 7, 40, 15, 48, 25, 58, 33, 66, 23, 56, 12, 45, 5, 38, 8, 41, 16, 49, 26, 59, 30, 63, 20, 53, 9, 42, 17, 50, 27, 60, 32, 65, 22, 55, 11, 44, 4, 37)(67, 100, 69, 102, 75, 108, 85, 118, 78, 111, 70, 103, 76, 109, 86, 119, 95, 128, 89, 122, 77, 110, 87, 120, 96, 129, 90, 123, 99, 132, 88, 121, 97, 130, 92, 125, 80, 113, 91, 124, 98, 131, 94, 127, 82, 115, 72, 105, 81, 114, 93, 126, 84, 117, 74, 107, 68, 101, 73, 106, 83, 116, 79, 112, 71, 104) L = (1, 70)(2, 67)(3, 76)(4, 77)(5, 78)(6, 68)(7, 69)(8, 71)(9, 86)(10, 87)(11, 88)(12, 89)(13, 85)(14, 72)(15, 73)(16, 74)(17, 75)(18, 79)(19, 95)(20, 96)(21, 97)(22, 98)(23, 99)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 90)(30, 92)(31, 94)(32, 93)(33, 91)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E16.336 Graph:: bipartite v = 2 e = 66 f = 34 degree seq :: [ 66^2 ] E16.333 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {33, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-2 * Y1^-2, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y1^4 * Y2^-1 * Y1 * Y2^-1, Y2^4 * Y3 * Y2^3, Y2^-1 * Y3 * Y2^-2 * Y3 * Y2^-1 * Y3^2 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2^3 * Y1 * Y3^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-2 * Y2 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 20, 53, 9, 42, 17, 50, 27, 60, 33, 66, 25, 58, 29, 62, 31, 64, 23, 56, 12, 45, 5, 38, 8, 41, 16, 49, 21, 54, 10, 43, 3, 36, 7, 40, 15, 48, 26, 59, 30, 63, 19, 52, 28, 61, 32, 65, 24, 57, 13, 46, 18, 51, 22, 55, 11, 44, 4, 37)(67, 100, 69, 102, 75, 108, 85, 118, 95, 128, 84, 117, 74, 107, 68, 101, 73, 106, 83, 116, 94, 127, 97, 130, 88, 121, 82, 115, 72, 105, 81, 114, 93, 126, 98, 131, 89, 122, 77, 110, 87, 120, 80, 113, 92, 125, 99, 132, 90, 123, 78, 111, 70, 103, 76, 109, 86, 119, 96, 129, 91, 124, 79, 112, 71, 104) L = (1, 70)(2, 67)(3, 76)(4, 77)(5, 78)(6, 68)(7, 69)(8, 71)(9, 86)(10, 87)(11, 88)(12, 89)(13, 90)(14, 72)(15, 73)(16, 74)(17, 75)(18, 79)(19, 96)(20, 80)(21, 82)(22, 84)(23, 97)(24, 98)(25, 99)(26, 81)(27, 83)(28, 85)(29, 91)(30, 92)(31, 95)(32, 94)(33, 93)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E16.335 Graph:: bipartite v = 2 e = 66 f = 34 degree seq :: [ 66^2 ] E16.334 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {33, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y1, R^2, Y2 * Y3, (R * Y1)^2, (R * Y3)^2, Y2^33, (Y3 * Y2^-1)^33, (Y3^-1 * Y1^-1)^33 ] Map:: R = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66)(67, 100, 68, 101, 70, 103, 72, 105, 74, 107, 76, 109, 78, 111, 80, 113, 82, 115, 83, 116, 84, 117, 85, 118, 86, 119, 87, 120, 88, 121, 89, 122, 91, 124, 92, 125, 93, 126, 94, 127, 95, 128, 96, 129, 97, 130, 98, 131, 99, 132, 90, 123, 81, 114, 79, 112, 77, 110, 75, 108, 73, 106, 71, 104, 69, 102) L = (1, 69)(2, 67)(3, 71)(4, 68)(5, 73)(6, 70)(7, 75)(8, 72)(9, 77)(10, 74)(11, 79)(12, 76)(13, 81)(14, 78)(15, 90)(16, 80)(17, 82)(18, 83)(19, 84)(20, 85)(21, 86)(22, 87)(23, 88)(24, 99)(25, 89)(26, 91)(27, 92)(28, 93)(29, 94)(30, 95)(31, 96)(32, 97)(33, 98)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 66, 66 ), ( 66^66 ) } Outer automorphisms :: reflexible Dual of E16.330 Graph:: bipartite v = 34 e = 66 f = 2 degree seq :: [ 2^33, 66 ] E16.335 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {33, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3 * Y2^4, Y3^-1 * Y2 * Y3^-7, (Y2^-1 * Y3)^33, (Y3^-1 * Y1^-1)^33 ] Map:: R = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66)(67, 100, 68, 101, 72, 105, 78, 111, 71, 104, 74, 107, 80, 113, 86, 119, 79, 112, 82, 115, 88, 121, 94, 127, 87, 120, 90, 123, 96, 129, 99, 132, 95, 128, 91, 124, 97, 130, 98, 131, 92, 125, 83, 116, 89, 122, 93, 126, 84, 117, 75, 108, 81, 114, 85, 118, 76, 109, 69, 102, 73, 106, 77, 110, 70, 103) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 77)(7, 81)(8, 68)(9, 83)(10, 84)(11, 85)(12, 70)(13, 71)(14, 72)(15, 89)(16, 74)(17, 91)(18, 92)(19, 93)(20, 78)(21, 79)(22, 80)(23, 97)(24, 82)(25, 90)(26, 95)(27, 98)(28, 86)(29, 87)(30, 88)(31, 96)(32, 99)(33, 94)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 66, 66 ), ( 66^66 ) } Outer automorphisms :: reflexible Dual of E16.333 Graph:: bipartite v = 34 e = 66 f = 2 degree seq :: [ 2^33, 66 ] E16.336 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {33, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y3^-4 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-2 * Y3^-1 * Y2^-5, Y2^3 * Y3^-1 * Y2^2 * Y3^-3, (Y2^-1 * Y3)^33, (Y3^-1 * Y1^-1)^33 ] Map:: R = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66)(67, 100, 68, 101, 72, 105, 80, 113, 92, 125, 89, 122, 78, 111, 71, 104, 74, 107, 82, 115, 94, 127, 97, 130, 85, 118, 90, 123, 79, 112, 84, 117, 95, 128, 98, 131, 86, 119, 75, 108, 83, 116, 91, 124, 96, 129, 99, 132, 87, 120, 76, 109, 69, 102, 73, 106, 81, 114, 93, 126, 88, 121, 77, 110, 70, 103) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 81)(7, 83)(8, 68)(9, 85)(10, 86)(11, 87)(12, 70)(13, 71)(14, 93)(15, 91)(16, 72)(17, 90)(18, 74)(19, 89)(20, 97)(21, 98)(22, 99)(23, 77)(24, 78)(25, 79)(26, 88)(27, 96)(28, 80)(29, 82)(30, 84)(31, 92)(32, 94)(33, 95)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 66, 66 ), ( 66^66 ) } Outer automorphisms :: reflexible Dual of E16.332 Graph:: bipartite v = 34 e = 66 f = 2 degree seq :: [ 2^33, 66 ] E16.337 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {33, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y3), Y3^-5 * Y2, Y2^2 * Y3^-1 * Y2^4 * Y3^-1 * Y2, Y2^3 * Y3 * Y2 * Y3^2 * Y2^2, Y3^-1 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2, (Y3^-1 * Y1^-1)^33 ] Map:: R = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66)(67, 100, 68, 101, 72, 105, 80, 113, 90, 123, 95, 128, 85, 118, 75, 108, 83, 116, 93, 126, 98, 131, 88, 121, 78, 111, 71, 104, 74, 107, 82, 115, 92, 125, 96, 129, 86, 119, 76, 109, 69, 102, 73, 106, 81, 114, 91, 124, 99, 132, 89, 122, 79, 112, 84, 117, 94, 127, 97, 130, 87, 120, 77, 110, 70, 103) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 81)(7, 83)(8, 68)(9, 84)(10, 85)(11, 86)(12, 70)(13, 71)(14, 91)(15, 93)(16, 72)(17, 94)(18, 74)(19, 79)(20, 95)(21, 96)(22, 77)(23, 78)(24, 99)(25, 98)(26, 80)(27, 97)(28, 82)(29, 89)(30, 90)(31, 92)(32, 87)(33, 88)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 66, 66 ), ( 66^66 ) } Outer automorphisms :: reflexible Dual of E16.331 Graph:: bipartite v = 34 e = 66 f = 2 degree seq :: [ 2^33, 66 ] E16.338 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 17, 17}) Quotient :: halfedge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3, R * Y3 * R * Y2, Y1^-1 * Y3 * Y1^-1 * Y2, (R * Y1)^2, Y1^17 ] Map:: R = (1, 36, 2, 39, 5, 43, 9, 47, 13, 51, 17, 55, 21, 59, 25, 63, 29, 66, 32, 62, 28, 58, 24, 54, 20, 50, 16, 46, 12, 42, 8, 38, 4, 35)(3, 41, 7, 45, 11, 49, 15, 53, 19, 57, 23, 61, 27, 65, 31, 68, 34, 67, 33, 64, 30, 60, 26, 56, 22, 52, 18, 48, 14, 44, 10, 40, 6, 37) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 33)(32, 34)(35, 37)(36, 40)(38, 41)(39, 44)(42, 45)(43, 48)(46, 49)(47, 52)(50, 53)(51, 56)(54, 57)(55, 60)(58, 61)(59, 64)(62, 65)(63, 67)(66, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.339 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 17, 17}) Quotient :: halfedge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y1^-1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y1 * Y2 * Y1^-2 * Y3 * Y1, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2 * Y1 * Y3 ] Map:: non-degenerate R = (1, 36, 2, 40, 6, 48, 14, 46, 12, 52, 18, 58, 24, 65, 31, 64, 30, 63, 29, 67, 33, 61, 27, 54, 20, 44, 10, 51, 17, 47, 13, 39, 5, 35)(3, 43, 9, 53, 19, 59, 25, 55, 21, 62, 28, 68, 34, 66, 32, 60, 26, 56, 22, 57, 23, 50, 16, 42, 8, 38, 4, 45, 11, 49, 15, 41, 7, 37) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 14)(13, 19)(16, 24)(17, 25)(20, 28)(22, 30)(23, 31)(26, 29)(27, 34)(32, 33)(35, 38)(36, 42)(37, 44)(39, 45)(40, 50)(41, 51)(43, 54)(46, 56)(47, 49)(48, 57)(52, 60)(53, 61)(55, 63)(58, 66)(59, 67)(62, 64)(65, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.342 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.340 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 17, 17}) Quotient :: halfedge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y2 * Y1 * Y3 * Y1^-3, Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3, Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-5 * Y3 ] Map:: non-degenerate R = (1, 36, 2, 40, 6, 48, 14, 44, 10, 51, 17, 58, 24, 65, 31, 61, 27, 64, 30, 67, 33, 62, 28, 55, 21, 46, 12, 52, 18, 47, 13, 39, 5, 35)(3, 43, 9, 50, 16, 42, 8, 38, 4, 45, 11, 54, 20, 60, 26, 56, 22, 63, 29, 68, 34, 66, 32, 59, 25, 53, 19, 57, 23, 49, 15, 41, 7, 37) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 19)(11, 21)(13, 16)(14, 23)(17, 25)(20, 28)(22, 30)(24, 32)(26, 33)(27, 29)(31, 34)(35, 38)(36, 42)(37, 44)(39, 45)(40, 50)(41, 51)(43, 48)(46, 56)(47, 54)(49, 58)(52, 60)(53, 61)(55, 63)(57, 65)(59, 64)(62, 68)(66, 67) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.344 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.341 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 17, 17}) Quotient :: halfedge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y1^-1 * Y2)^2, (R * Y1)^2, (Y1^-1 * Y3)^2, Y3 * Y1^-1 * Y2 * Y3 * Y2, (Y3 * Y1^2)^2, Y1^8 * Y2 * Y3 ] Map:: non-degenerate R = (1, 36, 2, 40, 6, 48, 14, 56, 22, 64, 30, 62, 28, 54, 20, 46, 12, 44, 10, 51, 17, 59, 25, 67, 33, 63, 29, 55, 21, 47, 13, 39, 5, 35)(3, 43, 9, 52, 18, 60, 26, 68, 34, 66, 32, 58, 24, 50, 16, 42, 8, 38, 4, 45, 11, 53, 19, 61, 27, 65, 31, 57, 23, 49, 15, 41, 7, 37) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 10)(11, 20)(13, 18)(14, 23)(16, 17)(19, 28)(21, 26)(22, 31)(24, 25)(27, 30)(29, 34)(32, 33)(35, 38)(36, 42)(37, 44)(39, 45)(40, 50)(41, 51)(43, 46)(47, 53)(48, 58)(49, 59)(52, 54)(55, 61)(56, 66)(57, 67)(60, 62)(63, 65)(64, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.345 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.342 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 17, 17}) Quotient :: halfedge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y1^-1 * Y2)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y2 * Y1^-1 * Y3 * Y2 * Y3, Y1^-1 * Y2 * Y1 * Y3 * Y1^-6, (Y2 * Y1 * Y3)^17 ] Map:: non-degenerate R = (1, 36, 2, 40, 6, 48, 14, 56, 22, 64, 30, 61, 27, 53, 19, 44, 10, 46, 12, 51, 17, 59, 25, 67, 33, 63, 29, 55, 21, 47, 13, 39, 5, 35)(3, 43, 9, 52, 18, 60, 26, 66, 32, 58, 24, 50, 16, 42, 8, 38, 4, 45, 11, 54, 20, 62, 28, 68, 34, 65, 31, 57, 23, 49, 15, 41, 7, 37) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 17)(10, 11)(13, 18)(14, 23)(16, 25)(19, 20)(21, 26)(22, 31)(24, 33)(27, 28)(29, 32)(30, 34)(35, 38)(36, 42)(37, 44)(39, 45)(40, 50)(41, 46)(43, 53)(47, 54)(48, 58)(49, 51)(52, 61)(55, 62)(56, 66)(57, 59)(60, 64)(63, 68)(65, 67) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.339 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.343 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 17, 17}) Quotient :: halfedge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1)^2, Y1^2 * Y3 * Y1^-3 * Y2, Y3 * Y2 * Y3 * Y1^2 * Y2 * Y3 * Y2, Y1^-1 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y2 ] Map:: non-degenerate R = (1, 36, 2, 40, 6, 48, 14, 54, 20, 44, 10, 51, 17, 61, 27, 67, 33, 68, 34, 65, 31, 57, 23, 46, 12, 52, 18, 59, 25, 47, 13, 39, 5, 35)(3, 43, 9, 53, 19, 50, 16, 42, 8, 38, 4, 45, 11, 56, 22, 66, 32, 63, 29, 58, 24, 62, 28, 55, 21, 64, 30, 60, 26, 49, 15, 41, 7, 37) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 26)(16, 25)(17, 28)(20, 30)(22, 31)(24, 27)(29, 33)(32, 34)(35, 38)(36, 42)(37, 44)(39, 45)(40, 50)(41, 51)(43, 54)(46, 58)(47, 56)(48, 53)(49, 61)(52, 63)(55, 65)(57, 62)(59, 66)(60, 67)(64, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.344 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 17, 17}) Quotient :: halfedge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1 * Y2)^2, (R * Y1)^2, R * Y3 * R * Y2, (Y3 * Y1^-1)^2, Y1^2 * Y2 * Y1^-3 * Y3, Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 36, 2, 40, 6, 48, 14, 57, 23, 46, 12, 52, 18, 61, 27, 67, 33, 68, 34, 65, 31, 54, 20, 44, 10, 51, 17, 59, 25, 47, 13, 39, 5, 35)(3, 43, 9, 53, 19, 64, 30, 62, 28, 55, 21, 63, 29, 58, 24, 66, 32, 60, 26, 50, 16, 42, 8, 38, 4, 45, 11, 56, 22, 49, 15, 41, 7, 37) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 22)(16, 27)(17, 28)(20, 29)(24, 31)(25, 30)(26, 33)(32, 34)(35, 38)(36, 42)(37, 44)(39, 45)(40, 50)(41, 51)(43, 54)(46, 58)(47, 56)(48, 60)(49, 59)(52, 63)(53, 65)(55, 61)(57, 66)(62, 67)(64, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.340 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.345 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 17, 17}) Quotient :: halfedge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1 * Y2 * Y3, Y2 * Y1^-1 * Y3, R * Y2 * R * Y3, (R * Y1)^2, Y1^17 ] Map:: non-degenerate R = (1, 36, 2, 40, 6, 44, 10, 48, 14, 52, 18, 56, 22, 60, 26, 64, 30, 67, 33, 63, 29, 59, 25, 55, 21, 51, 17, 47, 13, 43, 9, 39, 5, 35)(3, 42, 8, 46, 12, 50, 16, 54, 20, 58, 24, 62, 28, 66, 32, 68, 34, 65, 31, 61, 27, 57, 23, 53, 19, 49, 15, 45, 11, 41, 7, 38, 4, 37) L = (1, 3)(2, 4)(5, 8)(6, 7)(9, 12)(10, 11)(13, 16)(14, 15)(17, 20)(18, 19)(21, 24)(22, 23)(25, 28)(26, 27)(29, 32)(30, 31)(33, 34)(35, 38)(36, 41)(37, 39)(40, 45)(42, 43)(44, 49)(46, 47)(48, 53)(50, 51)(52, 57)(54, 55)(56, 61)(58, 59)(60, 65)(62, 63)(64, 68)(66, 67) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.341 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.346 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 17, 17}) Quotient :: edge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y3^17 ] Map:: R = (1, 35, 3, 37, 7, 41, 11, 45, 15, 49, 19, 53, 23, 57, 27, 61, 31, 65, 32, 66, 28, 62, 24, 58, 20, 54, 16, 50, 12, 46, 8, 42, 4, 38)(2, 36, 5, 39, 9, 43, 13, 47, 17, 51, 21, 55, 25, 59, 29, 63, 33, 67, 34, 68, 30, 64, 26, 60, 22, 56, 18, 52, 14, 48, 10, 44, 6, 40)(69, 70)(71, 74)(72, 73)(75, 78)(76, 77)(79, 82)(80, 81)(83, 86)(84, 85)(87, 90)(88, 89)(91, 94)(92, 93)(95, 98)(96, 97)(99, 102)(100, 101)(103, 104)(105, 108)(106, 107)(109, 112)(110, 111)(113, 116)(114, 115)(117, 120)(118, 119)(121, 124)(122, 123)(125, 128)(126, 127)(129, 132)(130, 131)(133, 136)(134, 135) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.355 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.347 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 17, 17}) Quotient :: edge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^2 * Y1 * Y3^-2 * Y2, Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2, Y3^-1 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 ] Map:: R = (1, 35, 4, 38, 12, 46, 21, 55, 9, 43, 20, 54, 30, 64, 33, 67, 27, 61, 23, 57, 31, 65, 26, 60, 16, 50, 6, 40, 15, 49, 13, 47, 5, 39)(2, 36, 7, 41, 17, 51, 25, 59, 14, 48, 24, 58, 32, 66, 34, 68, 29, 63, 19, 53, 28, 62, 22, 56, 11, 45, 3, 37, 10, 44, 18, 52, 8, 42)(69, 70)(71, 77)(72, 76)(73, 75)(74, 82)(78, 89)(79, 88)(80, 86)(81, 85)(83, 93)(84, 92)(87, 95)(90, 98)(91, 97)(94, 100)(96, 101)(99, 102)(103, 105)(104, 108)(106, 113)(107, 112)(109, 118)(110, 117)(111, 121)(114, 124)(115, 120)(116, 125)(119, 128)(122, 131)(123, 130)(126, 129)(127, 133)(132, 136)(134, 135) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.360 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.348 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 17, 17}) Quotient :: edge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y3)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y2 * Y3^-4 * Y1, Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2, Y3^2 * Y1 * Y2 * Y3^3 * Y1 * Y2 * Y3^3 * Y1 * Y2 * Y3^3 * Y1 * Y2 * Y3^3 * Y1 * Y2 ] Map:: R = (1, 35, 4, 38, 12, 46, 16, 50, 6, 40, 15, 49, 26, 60, 31, 65, 23, 57, 27, 61, 33, 67, 30, 64, 21, 55, 9, 43, 20, 54, 13, 47, 5, 39)(2, 36, 7, 41, 17, 51, 11, 45, 3, 37, 10, 44, 22, 56, 29, 63, 19, 53, 28, 62, 34, 68, 32, 66, 25, 59, 14, 48, 24, 58, 18, 52, 8, 42)(69, 70)(71, 77)(72, 76)(73, 75)(74, 82)(78, 89)(79, 88)(80, 86)(81, 85)(83, 93)(84, 92)(87, 95)(90, 98)(91, 96)(94, 100)(97, 101)(99, 102)(103, 105)(104, 108)(106, 113)(107, 112)(109, 118)(110, 117)(111, 121)(114, 119)(115, 124)(116, 125)(120, 128)(122, 131)(123, 130)(126, 133)(127, 129)(132, 136)(134, 135) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.358 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.349 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 17, 17}) Quotient :: edge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, Y2 * Y3^-1 * Y1 * Y2 * Y1, Y3^-2 * Y2 * Y3^6 * Y1, Y3^3 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 35, 4, 38, 12, 46, 20, 54, 28, 62, 33, 67, 25, 59, 17, 51, 9, 43, 6, 40, 14, 48, 22, 56, 30, 64, 29, 63, 21, 55, 13, 47, 5, 39)(2, 36, 7, 41, 15, 49, 23, 57, 31, 65, 34, 68, 27, 61, 19, 53, 11, 45, 3, 37, 10, 44, 18, 52, 26, 60, 32, 66, 24, 58, 16, 50, 8, 42)(69, 70)(71, 77)(72, 76)(73, 75)(74, 79)(78, 85)(80, 84)(81, 83)(82, 87)(86, 93)(88, 92)(89, 91)(90, 95)(94, 101)(96, 100)(97, 99)(98, 102)(103, 105)(104, 108)(106, 113)(107, 112)(109, 111)(110, 116)(114, 121)(115, 120)(117, 119)(118, 124)(122, 129)(123, 128)(125, 127)(126, 132)(130, 136)(131, 134)(133, 135) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.357 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.350 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 17, 17}) Quotient :: edge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y1 * Y3^-1 * Y2 * Y1 * Y2, Y3^-6 * Y1 * Y3^2 * Y2 ] Map:: R = (1, 35, 4, 38, 12, 46, 20, 54, 28, 62, 30, 64, 22, 56, 14, 48, 6, 40, 9, 43, 17, 51, 25, 59, 33, 67, 29, 63, 21, 55, 13, 47, 5, 39)(2, 36, 7, 41, 15, 49, 23, 57, 31, 65, 27, 61, 19, 53, 11, 45, 3, 37, 10, 44, 18, 52, 26, 60, 34, 68, 32, 66, 24, 58, 16, 50, 8, 42)(69, 70)(71, 77)(72, 76)(73, 75)(74, 78)(79, 85)(80, 84)(81, 83)(82, 86)(87, 93)(88, 92)(89, 91)(90, 94)(95, 101)(96, 100)(97, 99)(98, 102)(103, 105)(104, 108)(106, 113)(107, 112)(109, 116)(110, 111)(114, 121)(115, 120)(117, 124)(118, 119)(122, 129)(123, 128)(125, 132)(126, 127)(130, 133)(131, 136)(134, 135) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.362 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.351 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 17, 17}) Quotient :: edge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3^-5 * Y1, Y2 * Y1 * Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y1, Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y2 * Y3^-1 ] Map:: R = (1, 35, 4, 38, 12, 46, 24, 58, 16, 50, 6, 40, 15, 49, 29, 63, 34, 68, 33, 67, 26, 60, 21, 55, 9, 43, 20, 54, 25, 59, 13, 47, 5, 39)(2, 36, 7, 41, 17, 51, 23, 57, 11, 45, 3, 37, 10, 44, 22, 56, 32, 66, 31, 65, 19, 53, 28, 62, 14, 48, 27, 61, 30, 64, 18, 52, 8, 42)(69, 70)(71, 77)(72, 76)(73, 75)(74, 82)(78, 89)(79, 88)(80, 86)(81, 85)(83, 96)(84, 95)(87, 97)(90, 94)(91, 93)(92, 98)(99, 102)(100, 101)(103, 105)(104, 108)(106, 113)(107, 112)(109, 118)(110, 117)(111, 121)(114, 125)(115, 124)(116, 128)(119, 126)(120, 131)(122, 133)(123, 130)(127, 134)(129, 135)(132, 136) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.356 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.352 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 17, 17}) Quotient :: edge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3 * Y1 * Y3^-4, Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1, Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y3^-1 ] Map:: R = (1, 35, 4, 38, 12, 46, 24, 58, 21, 55, 9, 43, 20, 54, 26, 60, 33, 67, 34, 68, 29, 63, 16, 50, 6, 40, 15, 49, 25, 59, 13, 47, 5, 39)(2, 36, 7, 41, 17, 51, 30, 64, 28, 62, 14, 48, 27, 61, 19, 53, 31, 65, 32, 66, 23, 57, 11, 45, 3, 37, 10, 44, 22, 56, 18, 52, 8, 42)(69, 70)(71, 77)(72, 76)(73, 75)(74, 82)(78, 89)(79, 88)(80, 86)(81, 85)(83, 96)(84, 95)(87, 97)(90, 92)(91, 94)(93, 98)(99, 102)(100, 101)(103, 105)(104, 108)(106, 113)(107, 112)(109, 118)(110, 117)(111, 121)(114, 125)(115, 124)(116, 128)(119, 131)(120, 127)(122, 129)(123, 133)(126, 134)(130, 135)(132, 136) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.361 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.353 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 17, 17}) Quotient :: edge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3, Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3^17 ] Map:: R = (1, 35, 4, 38, 8, 42, 12, 46, 16, 50, 20, 54, 24, 58, 28, 62, 32, 66, 33, 67, 29, 63, 25, 59, 21, 55, 17, 51, 13, 47, 9, 43, 5, 39)(2, 36, 3, 37, 7, 41, 11, 45, 15, 49, 19, 53, 23, 57, 27, 61, 31, 65, 34, 68, 30, 64, 26, 60, 22, 56, 18, 52, 14, 48, 10, 44, 6, 40)(69, 70)(71, 73)(72, 74)(75, 77)(76, 78)(79, 81)(80, 82)(83, 85)(84, 86)(87, 89)(88, 90)(91, 93)(92, 94)(95, 97)(96, 98)(99, 101)(100, 102)(103, 105)(104, 106)(107, 109)(108, 110)(111, 113)(112, 114)(115, 117)(116, 118)(119, 121)(120, 122)(123, 125)(124, 126)(127, 129)(128, 130)(131, 133)(132, 134)(135, 136) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.359 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.354 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 17, 17}) Quotient :: edge^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y1^-1, Y2^17, Y1^17 ] Map:: non-degenerate R = (1, 35, 4, 38)(2, 36, 6, 40)(3, 37, 8, 42)(5, 39, 10, 44)(7, 41, 12, 46)(9, 43, 14, 48)(11, 45, 16, 50)(13, 47, 18, 52)(15, 49, 20, 54)(17, 51, 22, 56)(19, 53, 24, 58)(21, 55, 26, 60)(23, 57, 28, 62)(25, 59, 30, 64)(27, 61, 32, 66)(29, 63, 33, 67)(31, 65, 34, 68)(69, 70, 73, 77, 81, 85, 89, 93, 97, 99, 95, 91, 87, 83, 79, 75, 71)(72, 76, 80, 84, 88, 92, 96, 100, 102, 101, 98, 94, 90, 86, 82, 78, 74)(103, 105, 109, 113, 117, 121, 125, 129, 133, 131, 127, 123, 119, 115, 111, 107, 104)(106, 108, 112, 116, 120, 124, 128, 132, 135, 136, 134, 130, 126, 122, 118, 114, 110) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 8^4 ), ( 8^17 ) } Outer automorphisms :: reflexible Dual of E16.363 Graph:: simple bipartite v = 21 e = 68 f = 17 degree seq :: [ 4^17, 17^4 ] E16.355 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 17, 17}) Quotient :: loop^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y3^17 ] Map:: R = (1, 35, 69, 103, 3, 37, 71, 105, 7, 41, 75, 109, 11, 45, 79, 113, 15, 49, 83, 117, 19, 53, 87, 121, 23, 57, 91, 125, 27, 61, 95, 129, 31, 65, 99, 133, 32, 66, 100, 134, 28, 62, 96, 130, 24, 58, 92, 126, 20, 54, 88, 122, 16, 50, 84, 118, 12, 46, 80, 114, 8, 42, 76, 110, 4, 38, 72, 106)(2, 36, 70, 104, 5, 39, 73, 107, 9, 43, 77, 111, 13, 47, 81, 115, 17, 51, 85, 119, 21, 55, 89, 123, 25, 59, 93, 127, 29, 63, 97, 131, 33, 67, 101, 135, 34, 68, 102, 136, 30, 64, 98, 132, 26, 60, 94, 128, 22, 56, 90, 124, 18, 52, 86, 120, 14, 48, 82, 116, 10, 44, 78, 112, 6, 40, 74, 108) L = (1, 36)(2, 35)(3, 40)(4, 39)(5, 38)(6, 37)(7, 44)(8, 43)(9, 42)(10, 41)(11, 48)(12, 47)(13, 46)(14, 45)(15, 52)(16, 51)(17, 50)(18, 49)(19, 56)(20, 55)(21, 54)(22, 53)(23, 60)(24, 59)(25, 58)(26, 57)(27, 64)(28, 63)(29, 62)(30, 61)(31, 68)(32, 67)(33, 66)(34, 65)(69, 104)(70, 103)(71, 108)(72, 107)(73, 106)(74, 105)(75, 112)(76, 111)(77, 110)(78, 109)(79, 116)(80, 115)(81, 114)(82, 113)(83, 120)(84, 119)(85, 118)(86, 117)(87, 124)(88, 123)(89, 122)(90, 121)(91, 128)(92, 127)(93, 126)(94, 125)(95, 132)(96, 131)(97, 130)(98, 129)(99, 136)(100, 135)(101, 134)(102, 133) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.346 Transitivity :: VT+ Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.356 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 17, 17}) Quotient :: loop^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^2 * Y1 * Y3^-2 * Y2, Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2, Y3^-1 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 ] Map:: R = (1, 35, 69, 103, 4, 38, 72, 106, 12, 46, 80, 114, 21, 55, 89, 123, 9, 43, 77, 111, 20, 54, 88, 122, 30, 64, 98, 132, 33, 67, 101, 135, 27, 61, 95, 129, 23, 57, 91, 125, 31, 65, 99, 133, 26, 60, 94, 128, 16, 50, 84, 118, 6, 40, 74, 108, 15, 49, 83, 117, 13, 47, 81, 115, 5, 39, 73, 107)(2, 36, 70, 104, 7, 41, 75, 109, 17, 51, 85, 119, 25, 59, 93, 127, 14, 48, 82, 116, 24, 58, 92, 126, 32, 66, 100, 134, 34, 68, 102, 136, 29, 63, 97, 131, 19, 53, 87, 121, 28, 62, 96, 130, 22, 56, 90, 124, 11, 45, 79, 113, 3, 37, 71, 105, 10, 44, 78, 112, 18, 52, 86, 120, 8, 42, 76, 110) L = (1, 36)(2, 35)(3, 43)(4, 42)(5, 41)(6, 48)(7, 39)(8, 38)(9, 37)(10, 55)(11, 54)(12, 52)(13, 51)(14, 40)(15, 59)(16, 58)(17, 47)(18, 46)(19, 61)(20, 45)(21, 44)(22, 64)(23, 63)(24, 50)(25, 49)(26, 66)(27, 53)(28, 67)(29, 57)(30, 56)(31, 68)(32, 60)(33, 62)(34, 65)(69, 105)(70, 108)(71, 103)(72, 113)(73, 112)(74, 104)(75, 118)(76, 117)(77, 121)(78, 107)(79, 106)(80, 124)(81, 120)(82, 125)(83, 110)(84, 109)(85, 128)(86, 115)(87, 111)(88, 131)(89, 130)(90, 114)(91, 116)(92, 129)(93, 133)(94, 119)(95, 126)(96, 123)(97, 122)(98, 136)(99, 127)(100, 135)(101, 134)(102, 132) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.351 Transitivity :: VT+ Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.357 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 17, 17}) Quotient :: loop^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y3)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y2 * Y3^-4 * Y1, Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2, Y3^2 * Y1 * Y2 * Y3^3 * Y1 * Y2 * Y3^3 * Y1 * Y2 * Y3^3 * Y1 * Y2 * Y3^3 * Y1 * Y2 ] Map:: R = (1, 35, 69, 103, 4, 38, 72, 106, 12, 46, 80, 114, 16, 50, 84, 118, 6, 40, 74, 108, 15, 49, 83, 117, 26, 60, 94, 128, 31, 65, 99, 133, 23, 57, 91, 125, 27, 61, 95, 129, 33, 67, 101, 135, 30, 64, 98, 132, 21, 55, 89, 123, 9, 43, 77, 111, 20, 54, 88, 122, 13, 47, 81, 115, 5, 39, 73, 107)(2, 36, 70, 104, 7, 41, 75, 109, 17, 51, 85, 119, 11, 45, 79, 113, 3, 37, 71, 105, 10, 44, 78, 112, 22, 56, 90, 124, 29, 63, 97, 131, 19, 53, 87, 121, 28, 62, 96, 130, 34, 68, 102, 136, 32, 66, 100, 134, 25, 59, 93, 127, 14, 48, 82, 116, 24, 58, 92, 126, 18, 52, 86, 120, 8, 42, 76, 110) L = (1, 36)(2, 35)(3, 43)(4, 42)(5, 41)(6, 48)(7, 39)(8, 38)(9, 37)(10, 55)(11, 54)(12, 52)(13, 51)(14, 40)(15, 59)(16, 58)(17, 47)(18, 46)(19, 61)(20, 45)(21, 44)(22, 64)(23, 62)(24, 50)(25, 49)(26, 66)(27, 53)(28, 57)(29, 67)(30, 56)(31, 68)(32, 60)(33, 63)(34, 65)(69, 105)(70, 108)(71, 103)(72, 113)(73, 112)(74, 104)(75, 118)(76, 117)(77, 121)(78, 107)(79, 106)(80, 119)(81, 124)(82, 125)(83, 110)(84, 109)(85, 114)(86, 128)(87, 111)(88, 131)(89, 130)(90, 115)(91, 116)(92, 133)(93, 129)(94, 120)(95, 127)(96, 123)(97, 122)(98, 136)(99, 126)(100, 135)(101, 134)(102, 132) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.349 Transitivity :: VT+ Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.358 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 17, 17}) Quotient :: loop^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, Y2 * Y3^-1 * Y1 * Y2 * Y1, Y3^-2 * Y2 * Y3^6 * Y1, Y3^3 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 35, 69, 103, 4, 38, 72, 106, 12, 46, 80, 114, 20, 54, 88, 122, 28, 62, 96, 130, 33, 67, 101, 135, 25, 59, 93, 127, 17, 51, 85, 119, 9, 43, 77, 111, 6, 40, 74, 108, 14, 48, 82, 116, 22, 56, 90, 124, 30, 64, 98, 132, 29, 63, 97, 131, 21, 55, 89, 123, 13, 47, 81, 115, 5, 39, 73, 107)(2, 36, 70, 104, 7, 41, 75, 109, 15, 49, 83, 117, 23, 57, 91, 125, 31, 65, 99, 133, 34, 68, 102, 136, 27, 61, 95, 129, 19, 53, 87, 121, 11, 45, 79, 113, 3, 37, 71, 105, 10, 44, 78, 112, 18, 52, 86, 120, 26, 60, 94, 128, 32, 66, 100, 134, 24, 58, 92, 126, 16, 50, 84, 118, 8, 42, 76, 110) L = (1, 36)(2, 35)(3, 43)(4, 42)(5, 41)(6, 45)(7, 39)(8, 38)(9, 37)(10, 51)(11, 40)(12, 50)(13, 49)(14, 53)(15, 47)(16, 46)(17, 44)(18, 59)(19, 48)(20, 58)(21, 57)(22, 61)(23, 55)(24, 54)(25, 52)(26, 67)(27, 56)(28, 66)(29, 65)(30, 68)(31, 63)(32, 62)(33, 60)(34, 64)(69, 105)(70, 108)(71, 103)(72, 113)(73, 112)(74, 104)(75, 111)(76, 116)(77, 109)(78, 107)(79, 106)(80, 121)(81, 120)(82, 110)(83, 119)(84, 124)(85, 117)(86, 115)(87, 114)(88, 129)(89, 128)(90, 118)(91, 127)(92, 132)(93, 125)(94, 123)(95, 122)(96, 136)(97, 134)(98, 126)(99, 135)(100, 131)(101, 133)(102, 130) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.348 Transitivity :: VT+ Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.359 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 17, 17}) Quotient :: loop^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y1 * Y3^-1 * Y2 * Y1 * Y2, Y3^-6 * Y1 * Y3^2 * Y2 ] Map:: R = (1, 35, 69, 103, 4, 38, 72, 106, 12, 46, 80, 114, 20, 54, 88, 122, 28, 62, 96, 130, 30, 64, 98, 132, 22, 56, 90, 124, 14, 48, 82, 116, 6, 40, 74, 108, 9, 43, 77, 111, 17, 51, 85, 119, 25, 59, 93, 127, 33, 67, 101, 135, 29, 63, 97, 131, 21, 55, 89, 123, 13, 47, 81, 115, 5, 39, 73, 107)(2, 36, 70, 104, 7, 41, 75, 109, 15, 49, 83, 117, 23, 57, 91, 125, 31, 65, 99, 133, 27, 61, 95, 129, 19, 53, 87, 121, 11, 45, 79, 113, 3, 37, 71, 105, 10, 44, 78, 112, 18, 52, 86, 120, 26, 60, 94, 128, 34, 68, 102, 136, 32, 66, 100, 134, 24, 58, 92, 126, 16, 50, 84, 118, 8, 42, 76, 110) L = (1, 36)(2, 35)(3, 43)(4, 42)(5, 41)(6, 44)(7, 39)(8, 38)(9, 37)(10, 40)(11, 51)(12, 50)(13, 49)(14, 52)(15, 47)(16, 46)(17, 45)(18, 48)(19, 59)(20, 58)(21, 57)(22, 60)(23, 55)(24, 54)(25, 53)(26, 56)(27, 67)(28, 66)(29, 65)(30, 68)(31, 63)(32, 62)(33, 61)(34, 64)(69, 105)(70, 108)(71, 103)(72, 113)(73, 112)(74, 104)(75, 116)(76, 111)(77, 110)(78, 107)(79, 106)(80, 121)(81, 120)(82, 109)(83, 124)(84, 119)(85, 118)(86, 115)(87, 114)(88, 129)(89, 128)(90, 117)(91, 132)(92, 127)(93, 126)(94, 123)(95, 122)(96, 133)(97, 136)(98, 125)(99, 130)(100, 135)(101, 134)(102, 131) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.353 Transitivity :: VT+ Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.360 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 17, 17}) Quotient :: loop^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3^-5 * Y1, Y2 * Y1 * Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y1, Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y2 * Y3^-1 ] Map:: R = (1, 35, 69, 103, 4, 38, 72, 106, 12, 46, 80, 114, 24, 58, 92, 126, 16, 50, 84, 118, 6, 40, 74, 108, 15, 49, 83, 117, 29, 63, 97, 131, 34, 68, 102, 136, 33, 67, 101, 135, 26, 60, 94, 128, 21, 55, 89, 123, 9, 43, 77, 111, 20, 54, 88, 122, 25, 59, 93, 127, 13, 47, 81, 115, 5, 39, 73, 107)(2, 36, 70, 104, 7, 41, 75, 109, 17, 51, 85, 119, 23, 57, 91, 125, 11, 45, 79, 113, 3, 37, 71, 105, 10, 44, 78, 112, 22, 56, 90, 124, 32, 66, 100, 134, 31, 65, 99, 133, 19, 53, 87, 121, 28, 62, 96, 130, 14, 48, 82, 116, 27, 61, 95, 129, 30, 64, 98, 132, 18, 52, 86, 120, 8, 42, 76, 110) L = (1, 36)(2, 35)(3, 43)(4, 42)(5, 41)(6, 48)(7, 39)(8, 38)(9, 37)(10, 55)(11, 54)(12, 52)(13, 51)(14, 40)(15, 62)(16, 61)(17, 47)(18, 46)(19, 63)(20, 45)(21, 44)(22, 60)(23, 59)(24, 64)(25, 57)(26, 56)(27, 50)(28, 49)(29, 53)(30, 58)(31, 68)(32, 67)(33, 66)(34, 65)(69, 105)(70, 108)(71, 103)(72, 113)(73, 112)(74, 104)(75, 118)(76, 117)(77, 121)(78, 107)(79, 106)(80, 125)(81, 124)(82, 128)(83, 110)(84, 109)(85, 126)(86, 131)(87, 111)(88, 133)(89, 130)(90, 115)(91, 114)(92, 119)(93, 134)(94, 116)(95, 135)(96, 123)(97, 120)(98, 136)(99, 122)(100, 127)(101, 129)(102, 132) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.347 Transitivity :: VT+ Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.361 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 17, 17}) Quotient :: loop^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3 * Y1 * Y3^-4, Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1, Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y3^-1 ] Map:: R = (1, 35, 69, 103, 4, 38, 72, 106, 12, 46, 80, 114, 24, 58, 92, 126, 21, 55, 89, 123, 9, 43, 77, 111, 20, 54, 88, 122, 26, 60, 94, 128, 33, 67, 101, 135, 34, 68, 102, 136, 29, 63, 97, 131, 16, 50, 84, 118, 6, 40, 74, 108, 15, 49, 83, 117, 25, 59, 93, 127, 13, 47, 81, 115, 5, 39, 73, 107)(2, 36, 70, 104, 7, 41, 75, 109, 17, 51, 85, 119, 30, 64, 98, 132, 28, 62, 96, 130, 14, 48, 82, 116, 27, 61, 95, 129, 19, 53, 87, 121, 31, 65, 99, 133, 32, 66, 100, 134, 23, 57, 91, 125, 11, 45, 79, 113, 3, 37, 71, 105, 10, 44, 78, 112, 22, 56, 90, 124, 18, 52, 86, 120, 8, 42, 76, 110) L = (1, 36)(2, 35)(3, 43)(4, 42)(5, 41)(6, 48)(7, 39)(8, 38)(9, 37)(10, 55)(11, 54)(12, 52)(13, 51)(14, 40)(15, 62)(16, 61)(17, 47)(18, 46)(19, 63)(20, 45)(21, 44)(22, 58)(23, 60)(24, 56)(25, 64)(26, 57)(27, 50)(28, 49)(29, 53)(30, 59)(31, 68)(32, 67)(33, 66)(34, 65)(69, 105)(70, 108)(71, 103)(72, 113)(73, 112)(74, 104)(75, 118)(76, 117)(77, 121)(78, 107)(79, 106)(80, 125)(81, 124)(82, 128)(83, 110)(84, 109)(85, 131)(86, 127)(87, 111)(88, 129)(89, 133)(90, 115)(91, 114)(92, 134)(93, 120)(94, 116)(95, 122)(96, 135)(97, 119)(98, 136)(99, 123)(100, 126)(101, 130)(102, 132) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.352 Transitivity :: VT+ Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.362 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 17, 17}) Quotient :: loop^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3, Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3^17 ] Map:: R = (1, 35, 69, 103, 4, 38, 72, 106, 8, 42, 76, 110, 12, 46, 80, 114, 16, 50, 84, 118, 20, 54, 88, 122, 24, 58, 92, 126, 28, 62, 96, 130, 32, 66, 100, 134, 33, 67, 101, 135, 29, 63, 97, 131, 25, 59, 93, 127, 21, 55, 89, 123, 17, 51, 85, 119, 13, 47, 81, 115, 9, 43, 77, 111, 5, 39, 73, 107)(2, 36, 70, 104, 3, 37, 71, 105, 7, 41, 75, 109, 11, 45, 79, 113, 15, 49, 83, 117, 19, 53, 87, 121, 23, 57, 91, 125, 27, 61, 95, 129, 31, 65, 99, 133, 34, 68, 102, 136, 30, 64, 98, 132, 26, 60, 94, 128, 22, 56, 90, 124, 18, 52, 86, 120, 14, 48, 82, 116, 10, 44, 78, 112, 6, 40, 74, 108) L = (1, 36)(2, 35)(3, 39)(4, 40)(5, 37)(6, 38)(7, 43)(8, 44)(9, 41)(10, 42)(11, 47)(12, 48)(13, 45)(14, 46)(15, 51)(16, 52)(17, 49)(18, 50)(19, 55)(20, 56)(21, 53)(22, 54)(23, 59)(24, 60)(25, 57)(26, 58)(27, 63)(28, 64)(29, 61)(30, 62)(31, 67)(32, 68)(33, 65)(34, 66)(69, 105)(70, 106)(71, 103)(72, 104)(73, 109)(74, 110)(75, 107)(76, 108)(77, 113)(78, 114)(79, 111)(80, 112)(81, 117)(82, 118)(83, 115)(84, 116)(85, 121)(86, 122)(87, 119)(88, 120)(89, 125)(90, 126)(91, 123)(92, 124)(93, 129)(94, 130)(95, 127)(96, 128)(97, 133)(98, 134)(99, 131)(100, 132)(101, 136)(102, 135) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.350 Transitivity :: VT+ Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.363 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 17, 17}) Quotient :: loop^2 Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y1^-1, Y2^17, Y1^17 ] Map:: non-degenerate R = (1, 35, 69, 103, 4, 38, 72, 106)(2, 36, 70, 104, 6, 40, 74, 108)(3, 37, 71, 105, 8, 42, 76, 110)(5, 39, 73, 107, 10, 44, 78, 112)(7, 41, 75, 109, 12, 46, 80, 114)(9, 43, 77, 111, 14, 48, 82, 116)(11, 45, 79, 113, 16, 50, 84, 118)(13, 47, 81, 115, 18, 52, 86, 120)(15, 49, 83, 117, 20, 54, 88, 122)(17, 51, 85, 119, 22, 56, 90, 124)(19, 53, 87, 121, 24, 58, 92, 126)(21, 55, 89, 123, 26, 60, 94, 128)(23, 57, 91, 125, 28, 62, 96, 130)(25, 59, 93, 127, 30, 64, 98, 132)(27, 61, 95, 129, 32, 66, 100, 134)(29, 63, 97, 131, 33, 67, 101, 135)(31, 65, 99, 133, 34, 68, 102, 136) L = (1, 36)(2, 39)(3, 35)(4, 42)(5, 43)(6, 38)(7, 37)(8, 46)(9, 47)(10, 40)(11, 41)(12, 50)(13, 51)(14, 44)(15, 45)(16, 54)(17, 55)(18, 48)(19, 49)(20, 58)(21, 59)(22, 52)(23, 53)(24, 62)(25, 63)(26, 56)(27, 57)(28, 66)(29, 65)(30, 60)(31, 61)(32, 68)(33, 64)(34, 67)(69, 105)(70, 103)(71, 109)(72, 108)(73, 104)(74, 112)(75, 113)(76, 106)(77, 107)(78, 116)(79, 117)(80, 110)(81, 111)(82, 120)(83, 121)(84, 114)(85, 115)(86, 124)(87, 125)(88, 118)(89, 119)(90, 128)(91, 129)(92, 122)(93, 123)(94, 132)(95, 133)(96, 126)(97, 127)(98, 135)(99, 131)(100, 130)(101, 136)(102, 134) local type(s) :: { ( 4, 17, 4, 17, 4, 17, 4, 17 ) } Outer automorphisms :: reflexible Dual of E16.354 Transitivity :: VT+ Graph:: v = 17 e = 68 f = 21 degree seq :: [ 8^17 ] E16.364 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^17, (Y3 * Y2^-1)^17 ] Map:: R = (1, 35, 2, 36)(3, 37, 5, 39)(4, 38, 6, 40)(7, 41, 9, 43)(8, 42, 10, 44)(11, 45, 13, 47)(12, 46, 14, 48)(15, 49, 17, 51)(16, 50, 18, 52)(19, 53, 21, 55)(20, 54, 22, 56)(23, 57, 25, 59)(24, 58, 26, 60)(27, 61, 29, 63)(28, 62, 30, 64)(31, 65, 33, 67)(32, 66, 34, 68)(69, 103, 71, 105, 75, 109, 79, 113, 83, 117, 87, 121, 91, 125, 95, 129, 99, 133, 100, 134, 96, 130, 92, 126, 88, 122, 84, 118, 80, 114, 76, 110, 72, 106)(70, 104, 73, 107, 77, 111, 81, 115, 85, 119, 89, 123, 93, 127, 97, 131, 101, 135, 102, 136, 98, 132, 94, 128, 90, 124, 86, 120, 82, 116, 78, 112, 74, 108) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.365 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^17, (Y3 * Y2^-1)^17 ] Map:: R = (1, 35, 2, 36)(3, 37, 6, 40)(4, 38, 5, 39)(7, 41, 10, 44)(8, 42, 9, 43)(11, 45, 14, 48)(12, 46, 13, 47)(15, 49, 18, 52)(16, 50, 17, 51)(19, 53, 22, 56)(20, 54, 21, 55)(23, 57, 26, 60)(24, 58, 25, 59)(27, 61, 30, 64)(28, 62, 29, 63)(31, 65, 34, 68)(32, 66, 33, 67)(69, 103, 71, 105, 75, 109, 79, 113, 83, 117, 87, 121, 91, 125, 95, 129, 99, 133, 100, 134, 96, 130, 92, 126, 88, 122, 84, 118, 80, 114, 76, 110, 72, 106)(70, 104, 73, 107, 77, 111, 81, 115, 85, 119, 89, 123, 93, 127, 97, 131, 101, 135, 102, 136, 98, 132, 94, 128, 90, 124, 86, 120, 82, 116, 78, 112, 74, 108) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.366 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y2^17, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 6, 40)(4, 38, 5, 39)(7, 41, 10, 44)(8, 42, 9, 43)(11, 45, 14, 48)(12, 46, 13, 47)(15, 49, 18, 52)(16, 50, 17, 51)(19, 53, 22, 56)(20, 54, 21, 55)(23, 57, 26, 60)(24, 58, 25, 59)(27, 61, 30, 64)(28, 62, 29, 63)(31, 65, 34, 68)(32, 66, 33, 67)(69, 103, 71, 105, 75, 109, 79, 113, 83, 117, 87, 121, 91, 125, 95, 129, 99, 133, 100, 134, 96, 130, 92, 126, 88, 122, 84, 118, 80, 114, 76, 110, 72, 106)(70, 104, 73, 107, 77, 111, 81, 115, 85, 119, 89, 123, 93, 127, 97, 131, 101, 135, 102, 136, 98, 132, 94, 128, 90, 124, 86, 120, 82, 116, 78, 112, 74, 108) L = (1, 72)(2, 74)(3, 69)(4, 76)(5, 70)(6, 78)(7, 71)(8, 80)(9, 73)(10, 82)(11, 75)(12, 84)(13, 77)(14, 86)(15, 79)(16, 88)(17, 81)(18, 90)(19, 83)(20, 92)(21, 85)(22, 94)(23, 87)(24, 96)(25, 89)(26, 98)(27, 91)(28, 100)(29, 93)(30, 102)(31, 95)(32, 99)(33, 97)(34, 101)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.380 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.367 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, Y2 * Y3^8 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 17, 51)(12, 46, 18, 52)(13, 47, 15, 49)(14, 48, 16, 50)(19, 53, 25, 59)(20, 54, 26, 60)(21, 55, 23, 57)(22, 56, 24, 58)(27, 61, 33, 67)(28, 62, 34, 68)(29, 63, 31, 65)(30, 64, 32, 66)(69, 103, 71, 105, 72, 106, 79, 113, 80, 114, 87, 121, 88, 122, 95, 129, 96, 130, 98, 132, 97, 131, 90, 124, 89, 123, 82, 116, 81, 115, 74, 108, 73, 107)(70, 104, 75, 109, 76, 110, 83, 117, 84, 118, 91, 125, 92, 126, 99, 133, 100, 134, 102, 136, 101, 135, 94, 128, 93, 127, 86, 120, 85, 119, 78, 112, 77, 111) L = (1, 72)(2, 76)(3, 79)(4, 80)(5, 71)(6, 69)(7, 83)(8, 84)(9, 75)(10, 70)(11, 87)(12, 88)(13, 73)(14, 74)(15, 91)(16, 92)(17, 77)(18, 78)(19, 95)(20, 96)(21, 81)(22, 82)(23, 99)(24, 100)(25, 85)(26, 86)(27, 98)(28, 97)(29, 89)(30, 90)(31, 102)(32, 101)(33, 93)(34, 94)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.368 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, Y2 * Y3^-8, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 17, 51)(12, 46, 18, 52)(13, 47, 15, 49)(14, 48, 16, 50)(19, 53, 25, 59)(20, 54, 26, 60)(21, 55, 23, 57)(22, 56, 24, 58)(27, 61, 33, 67)(28, 62, 34, 68)(29, 63, 31, 65)(30, 64, 32, 66)(69, 103, 71, 105, 74, 108, 79, 113, 82, 116, 87, 121, 90, 124, 95, 129, 98, 132, 96, 130, 97, 131, 88, 122, 89, 123, 80, 114, 81, 115, 72, 106, 73, 107)(70, 104, 75, 109, 78, 112, 83, 117, 86, 120, 91, 125, 94, 128, 99, 133, 102, 136, 100, 134, 101, 135, 92, 126, 93, 127, 84, 118, 85, 119, 76, 110, 77, 111) L = (1, 72)(2, 76)(3, 73)(4, 80)(5, 81)(6, 69)(7, 77)(8, 84)(9, 85)(10, 70)(11, 71)(12, 88)(13, 89)(14, 74)(15, 75)(16, 92)(17, 93)(18, 78)(19, 79)(20, 96)(21, 97)(22, 82)(23, 83)(24, 100)(25, 101)(26, 86)(27, 87)(28, 95)(29, 98)(30, 90)(31, 91)(32, 99)(33, 102)(34, 94)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.374 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.369 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^-3, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, (R * Y1)^2, Y2 * Y3^2 * Y2^-1 * Y3^-2, Y2^-2 * Y3^-5 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 19, 53)(12, 46, 21, 55)(13, 47, 17, 51)(14, 48, 22, 56)(15, 49, 18, 52)(16, 50, 20, 54)(23, 57, 31, 65)(24, 58, 33, 67)(25, 59, 29, 63)(26, 60, 34, 68)(27, 61, 30, 64)(28, 62, 32, 66)(69, 103, 71, 105, 79, 113, 72, 106, 80, 114, 91, 125, 82, 116, 92, 126, 96, 130, 94, 128, 95, 129, 84, 118, 93, 127, 83, 117, 74, 108, 81, 115, 73, 107)(70, 104, 75, 109, 85, 119, 76, 110, 86, 120, 97, 131, 88, 122, 98, 132, 102, 136, 100, 134, 101, 135, 90, 124, 99, 133, 89, 123, 78, 112, 87, 121, 77, 111) L = (1, 72)(2, 76)(3, 80)(4, 82)(5, 79)(6, 69)(7, 86)(8, 88)(9, 85)(10, 70)(11, 91)(12, 92)(13, 71)(14, 94)(15, 73)(16, 74)(17, 97)(18, 98)(19, 75)(20, 100)(21, 77)(22, 78)(23, 96)(24, 95)(25, 81)(26, 93)(27, 83)(28, 84)(29, 102)(30, 101)(31, 87)(32, 99)(33, 89)(34, 90)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.378 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.370 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-3, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, Y2 * Y3^-2 * Y2^-1 * Y3^2, Y3^2 * Y2^-2 * Y3^3, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 18, 52)(12, 46, 17, 51)(13, 47, 21, 55)(14, 48, 22, 56)(15, 49, 19, 53)(16, 50, 20, 54)(23, 57, 30, 64)(24, 58, 29, 63)(25, 59, 33, 67)(26, 60, 34, 68)(27, 61, 31, 65)(28, 62, 32, 66)(69, 103, 71, 105, 79, 113, 74, 108, 81, 115, 91, 125, 84, 118, 93, 127, 94, 128, 96, 130, 95, 129, 82, 116, 92, 126, 83, 117, 72, 106, 80, 114, 73, 107)(70, 104, 75, 109, 85, 119, 78, 112, 87, 121, 97, 131, 90, 124, 99, 133, 100, 134, 102, 136, 101, 135, 88, 122, 98, 132, 89, 123, 76, 110, 86, 120, 77, 111) L = (1, 72)(2, 76)(3, 80)(4, 82)(5, 83)(6, 69)(7, 86)(8, 88)(9, 89)(10, 70)(11, 73)(12, 92)(13, 71)(14, 94)(15, 95)(16, 74)(17, 77)(18, 98)(19, 75)(20, 100)(21, 101)(22, 78)(23, 79)(24, 96)(25, 81)(26, 91)(27, 93)(28, 84)(29, 85)(30, 102)(31, 87)(32, 97)(33, 99)(34, 90)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.373 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.371 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (Y3, Y2), (Y2 * Y1)^2, Y2^2 * Y3^-1 * Y2^2, Y2 * Y3^4 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 24, 58)(12, 46, 25, 59)(13, 47, 23, 57)(14, 48, 26, 60)(15, 49, 21, 55)(16, 50, 19, 53)(17, 51, 20, 54)(18, 52, 22, 56)(27, 61, 34, 68)(28, 62, 33, 67)(29, 63, 32, 66)(30, 64, 31, 65)(69, 103, 71, 105, 79, 113, 83, 117, 72, 106, 80, 114, 95, 129, 97, 131, 82, 116, 86, 120, 96, 130, 98, 132, 85, 119, 74, 108, 81, 115, 84, 118, 73, 107)(70, 104, 75, 109, 87, 121, 91, 125, 76, 110, 88, 122, 99, 133, 101, 135, 90, 124, 94, 128, 100, 134, 102, 136, 93, 127, 78, 112, 89, 123, 92, 126, 77, 111) L = (1, 72)(2, 76)(3, 80)(4, 82)(5, 83)(6, 69)(7, 88)(8, 90)(9, 91)(10, 70)(11, 95)(12, 86)(13, 71)(14, 85)(15, 97)(16, 79)(17, 73)(18, 74)(19, 99)(20, 94)(21, 75)(22, 93)(23, 101)(24, 87)(25, 77)(26, 78)(27, 96)(28, 81)(29, 98)(30, 84)(31, 100)(32, 89)(33, 102)(34, 92)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.377 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.372 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3, Y2), (R * Y2)^2, (Y2^-1 * Y1)^2, Y2^2 * Y3 * Y2^2, Y3 * Y2^-1 * Y3^3 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 24, 58)(12, 46, 25, 59)(13, 47, 23, 57)(14, 48, 26, 60)(15, 49, 21, 55)(16, 50, 19, 53)(17, 51, 20, 54)(18, 52, 22, 56)(27, 61, 33, 67)(28, 62, 34, 68)(29, 63, 31, 65)(30, 64, 32, 66)(69, 103, 71, 105, 79, 113, 85, 119, 74, 108, 81, 115, 95, 129, 98, 132, 86, 120, 82, 116, 96, 130, 97, 131, 83, 117, 72, 106, 80, 114, 84, 118, 73, 107)(70, 104, 75, 109, 87, 121, 93, 127, 78, 112, 89, 123, 99, 133, 102, 136, 94, 128, 90, 124, 100, 134, 101, 135, 91, 125, 76, 110, 88, 122, 92, 126, 77, 111) L = (1, 72)(2, 76)(3, 80)(4, 82)(5, 83)(6, 69)(7, 88)(8, 90)(9, 91)(10, 70)(11, 84)(12, 96)(13, 71)(14, 81)(15, 86)(16, 97)(17, 73)(18, 74)(19, 92)(20, 100)(21, 75)(22, 89)(23, 94)(24, 101)(25, 77)(26, 78)(27, 79)(28, 95)(29, 98)(30, 85)(31, 87)(32, 99)(33, 102)(34, 93)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.376 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.373 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3, Y2^-1), (Y2 * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^2 * Y2, Y2^-5 * Y3, Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 24, 58)(12, 46, 25, 59)(13, 47, 23, 57)(14, 48, 26, 60)(15, 49, 21, 55)(16, 50, 19, 53)(17, 51, 20, 54)(18, 52, 22, 56)(27, 61, 32, 66)(28, 62, 31, 65)(29, 63, 34, 68)(30, 64, 33, 67)(69, 103, 71, 105, 79, 113, 95, 129, 83, 117, 72, 106, 80, 114, 86, 120, 97, 131, 98, 132, 82, 116, 85, 119, 74, 108, 81, 115, 96, 130, 84, 118, 73, 107)(70, 104, 75, 109, 87, 121, 99, 133, 91, 125, 76, 110, 88, 122, 94, 128, 101, 135, 102, 136, 90, 124, 93, 127, 78, 112, 89, 123, 100, 134, 92, 126, 77, 111) L = (1, 72)(2, 76)(3, 80)(4, 82)(5, 83)(6, 69)(7, 88)(8, 90)(9, 91)(10, 70)(11, 86)(12, 85)(13, 71)(14, 84)(15, 98)(16, 95)(17, 73)(18, 74)(19, 94)(20, 93)(21, 75)(22, 92)(23, 102)(24, 99)(25, 77)(26, 78)(27, 97)(28, 79)(29, 81)(30, 96)(31, 101)(32, 87)(33, 89)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.370 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.374 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3, Y2), (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2 * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y3^2, Y2^-4 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 24, 58)(12, 46, 25, 59)(13, 47, 23, 57)(14, 48, 26, 60)(15, 49, 21, 55)(16, 50, 19, 53)(17, 51, 20, 54)(18, 52, 22, 56)(27, 61, 32, 66)(28, 62, 31, 65)(29, 63, 34, 68)(30, 64, 33, 67)(69, 103, 71, 105, 79, 113, 95, 129, 85, 119, 74, 108, 81, 115, 82, 116, 97, 131, 98, 132, 86, 120, 83, 117, 72, 106, 80, 114, 96, 130, 84, 118, 73, 107)(70, 104, 75, 109, 87, 121, 99, 133, 93, 127, 78, 112, 89, 123, 90, 124, 101, 135, 102, 136, 94, 128, 91, 125, 76, 110, 88, 122, 100, 134, 92, 126, 77, 111) L = (1, 72)(2, 76)(3, 80)(4, 82)(5, 83)(6, 69)(7, 88)(8, 90)(9, 91)(10, 70)(11, 96)(12, 97)(13, 71)(14, 79)(15, 81)(16, 86)(17, 73)(18, 74)(19, 100)(20, 101)(21, 75)(22, 87)(23, 89)(24, 94)(25, 77)(26, 78)(27, 84)(28, 98)(29, 95)(30, 85)(31, 92)(32, 102)(33, 99)(34, 93)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.368 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.375 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^2 * Y2^-1 * Y3, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1, Y2^-1), (Y2^-1 * Y1)^2, (R * Y2)^2, Y2 * Y3 * Y2^2 * Y3 * Y2^2 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 21, 55)(12, 46, 22, 56)(13, 47, 20, 54)(14, 48, 19, 53)(15, 49, 17, 51)(16, 50, 18, 52)(23, 57, 33, 67)(24, 58, 34, 68)(25, 59, 32, 66)(26, 60, 31, 65)(27, 61, 29, 63)(28, 62, 30, 64)(69, 103, 71, 105, 79, 113, 91, 125, 94, 128, 82, 116, 72, 106, 80, 114, 92, 126, 96, 130, 84, 118, 74, 108, 81, 115, 93, 127, 95, 129, 83, 117, 73, 107)(70, 104, 75, 109, 85, 119, 97, 131, 100, 134, 88, 122, 76, 110, 86, 120, 98, 132, 102, 136, 90, 124, 78, 112, 87, 121, 99, 133, 101, 135, 89, 123, 77, 111) L = (1, 72)(2, 76)(3, 80)(4, 81)(5, 82)(6, 69)(7, 86)(8, 87)(9, 88)(10, 70)(11, 92)(12, 93)(13, 71)(14, 74)(15, 94)(16, 73)(17, 98)(18, 99)(19, 75)(20, 78)(21, 100)(22, 77)(23, 96)(24, 95)(25, 79)(26, 84)(27, 91)(28, 83)(29, 102)(30, 101)(31, 85)(32, 90)(33, 97)(34, 89)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.379 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.376 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-3, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, Y2 * Y3^-2 * Y2^4, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 22, 56)(12, 46, 20, 54)(13, 47, 21, 55)(14, 48, 18, 52)(15, 49, 19, 53)(16, 50, 17, 51)(23, 57, 34, 68)(24, 58, 32, 66)(25, 59, 33, 67)(26, 60, 30, 64)(27, 61, 31, 65)(28, 62, 29, 63)(69, 103, 71, 105, 79, 113, 91, 125, 94, 128, 82, 116, 74, 108, 81, 115, 93, 127, 95, 129, 83, 117, 72, 106, 80, 114, 92, 126, 96, 130, 84, 118, 73, 107)(70, 104, 75, 109, 85, 119, 97, 131, 100, 134, 88, 122, 78, 112, 87, 121, 99, 133, 101, 135, 89, 123, 76, 110, 86, 120, 98, 132, 102, 136, 90, 124, 77, 111) L = (1, 72)(2, 76)(3, 80)(4, 82)(5, 83)(6, 69)(7, 86)(8, 88)(9, 89)(10, 70)(11, 92)(12, 74)(13, 71)(14, 73)(15, 94)(16, 95)(17, 98)(18, 78)(19, 75)(20, 77)(21, 100)(22, 101)(23, 96)(24, 81)(25, 79)(26, 84)(27, 91)(28, 93)(29, 102)(30, 87)(31, 85)(32, 90)(33, 97)(34, 99)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.372 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.377 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3, Y2^-1), (R * Y2)^2, (Y2 * Y1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2, Y3^3 * Y2^-1 * Y3^2, Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 24, 58)(12, 46, 25, 59)(13, 47, 23, 57)(14, 48, 26, 60)(15, 49, 21, 55)(16, 50, 19, 53)(17, 51, 20, 54)(18, 52, 22, 56)(27, 61, 34, 68)(28, 62, 33, 67)(29, 63, 32, 66)(30, 64, 31, 65)(69, 103, 71, 105, 79, 113, 86, 120, 96, 130, 98, 132, 83, 117, 72, 106, 80, 114, 85, 119, 74, 108, 81, 115, 95, 129, 97, 131, 82, 116, 84, 118, 73, 107)(70, 104, 75, 109, 87, 121, 94, 128, 100, 134, 102, 136, 91, 125, 76, 110, 88, 122, 93, 127, 78, 112, 89, 123, 99, 133, 101, 135, 90, 124, 92, 126, 77, 111) L = (1, 72)(2, 76)(3, 80)(4, 82)(5, 83)(6, 69)(7, 88)(8, 90)(9, 91)(10, 70)(11, 85)(12, 84)(13, 71)(14, 96)(15, 97)(16, 98)(17, 73)(18, 74)(19, 93)(20, 92)(21, 75)(22, 100)(23, 101)(24, 102)(25, 77)(26, 78)(27, 79)(28, 81)(29, 86)(30, 95)(31, 87)(32, 89)(33, 94)(34, 99)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.371 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.378 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3, Y2), (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3^3 * Y2 * Y3^2 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 24, 58)(12, 46, 25, 59)(13, 47, 23, 57)(14, 48, 26, 60)(15, 49, 21, 55)(16, 50, 19, 53)(17, 51, 20, 54)(18, 52, 22, 56)(27, 61, 34, 68)(28, 62, 33, 67)(29, 63, 32, 66)(30, 64, 31, 65)(69, 103, 71, 105, 79, 113, 82, 116, 96, 130, 98, 132, 85, 119, 74, 108, 81, 115, 83, 117, 72, 106, 80, 114, 95, 129, 97, 131, 86, 120, 84, 118, 73, 107)(70, 104, 75, 109, 87, 121, 90, 124, 100, 134, 102, 136, 93, 127, 78, 112, 89, 123, 91, 125, 76, 110, 88, 122, 99, 133, 101, 135, 94, 128, 92, 126, 77, 111) L = (1, 72)(2, 76)(3, 80)(4, 82)(5, 83)(6, 69)(7, 88)(8, 90)(9, 91)(10, 70)(11, 95)(12, 96)(13, 71)(14, 97)(15, 79)(16, 81)(17, 73)(18, 74)(19, 99)(20, 100)(21, 75)(22, 101)(23, 87)(24, 89)(25, 77)(26, 78)(27, 98)(28, 86)(29, 85)(30, 84)(31, 102)(32, 94)(33, 93)(34, 92)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.369 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.379 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y2^8 * Y3^-1, (Y3 * Y2^-1)^17 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 18, 52)(12, 46, 17, 51)(13, 47, 16, 50)(14, 48, 15, 49)(19, 53, 26, 60)(20, 54, 25, 59)(21, 55, 24, 58)(22, 56, 23, 57)(27, 61, 34, 68)(28, 62, 33, 67)(29, 63, 32, 66)(30, 64, 31, 65)(69, 103, 71, 105, 79, 113, 87, 121, 95, 129, 97, 131, 89, 123, 81, 115, 72, 106, 74, 108, 80, 114, 88, 122, 96, 130, 98, 132, 90, 124, 82, 116, 73, 107)(70, 104, 75, 109, 83, 117, 91, 125, 99, 133, 101, 135, 93, 127, 85, 119, 76, 110, 78, 112, 84, 118, 92, 126, 100, 134, 102, 136, 94, 128, 86, 120, 77, 111) L = (1, 72)(2, 76)(3, 74)(4, 73)(5, 81)(6, 69)(7, 78)(8, 77)(9, 85)(10, 70)(11, 80)(12, 71)(13, 82)(14, 89)(15, 84)(16, 75)(17, 86)(18, 93)(19, 88)(20, 79)(21, 90)(22, 97)(23, 92)(24, 83)(25, 94)(26, 101)(27, 96)(28, 87)(29, 98)(30, 95)(31, 100)(32, 91)(33, 102)(34, 99)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.375 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.380 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 17, 17}) Quotient :: dipole Aut^+ = D34 (small group id <34, 1>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, Y2^-8 * Y3^-1 ] Map:: non-degenerate R = (1, 35, 2, 36)(3, 37, 9, 43)(4, 38, 10, 44)(5, 39, 7, 41)(6, 40, 8, 42)(11, 45, 17, 51)(12, 46, 18, 52)(13, 47, 15, 49)(14, 48, 16, 50)(19, 53, 25, 59)(20, 54, 26, 60)(21, 55, 23, 57)(22, 56, 24, 58)(27, 61, 33, 67)(28, 62, 34, 68)(29, 63, 31, 65)(30, 64, 32, 66)(69, 103, 71, 105, 79, 113, 87, 121, 95, 129, 98, 132, 90, 124, 82, 116, 74, 108, 72, 106, 80, 114, 88, 122, 96, 130, 97, 131, 89, 123, 81, 115, 73, 107)(70, 104, 75, 109, 83, 117, 91, 125, 99, 133, 102, 136, 94, 128, 86, 120, 78, 112, 76, 110, 84, 118, 92, 126, 100, 134, 101, 135, 93, 127, 85, 119, 77, 111) L = (1, 72)(2, 76)(3, 80)(4, 71)(5, 74)(6, 69)(7, 84)(8, 75)(9, 78)(10, 70)(11, 88)(12, 79)(13, 82)(14, 73)(15, 92)(16, 83)(17, 86)(18, 77)(19, 96)(20, 87)(21, 90)(22, 81)(23, 100)(24, 91)(25, 94)(26, 85)(27, 97)(28, 95)(29, 98)(30, 89)(31, 101)(32, 99)(33, 102)(34, 93)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 4, 34, 4, 34 ), ( 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.366 Graph:: bipartite v = 19 e = 68 f = 19 degree seq :: [ 4^17, 34^2 ] E16.381 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T1^2 * T2^-2, T2^16 * T1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 6, 12, 15, 20, 23, 28, 31, 34, 29, 26, 21, 18, 13, 10, 4, 8, 2, 7, 11, 16, 19, 24, 27, 32, 33, 30, 25, 22, 17, 14, 9, 5)(35, 36, 40, 45, 49, 53, 57, 61, 65, 67, 63, 59, 55, 51, 47, 43, 38)(37, 41, 46, 50, 54, 58, 62, 66, 68, 64, 60, 56, 52, 48, 44, 39, 42) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.416 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.382 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T2^5 * T1^-1 * T2, T1^-1 * T2 * T1^-2 * T2 * T1^-3, T1^2 * T2 * T1^2 * T2^3 * T1, (T1^-1 * T2^-1)^34 ] Map:: non-degenerate R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 31, 30, 16, 6, 15, 29, 32, 22, 28, 14, 27, 33, 23, 11, 21, 26, 34, 24, 12, 4, 10, 20, 25, 13, 5)(35, 36, 40, 48, 60, 54, 43, 51, 63, 67, 58, 47, 52, 64, 56, 45, 38)(37, 41, 49, 61, 68, 59, 53, 65, 66, 57, 46, 39, 42, 50, 62, 55, 44) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.414 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.383 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-4 * T1^-1 * T2^-2, T1^-5 * T2^-1 * T1^-1 * T2^-1, T1^2 * T2^-1 * T1^2 * T2^-3 * T1, T1^59 * T2^-2 * T1^3 ] Map:: non-degenerate R = (1, 3, 9, 19, 24, 12, 4, 10, 20, 32, 26, 23, 11, 21, 33, 28, 14, 27, 22, 34, 30, 16, 6, 15, 29, 31, 18, 8, 2, 7, 17, 25, 13, 5)(35, 36, 40, 48, 60, 58, 47, 52, 64, 67, 54, 43, 51, 63, 56, 45, 38)(37, 41, 49, 61, 57, 46, 39, 42, 50, 62, 66, 53, 59, 65, 68, 55, 44) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.417 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.384 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1 * T2^-1 * T1 * T2^-3 * T1, T1^2 * T2 * T1^2 * T2 * T1^3, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1, T1^-2 * T2^2 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^4 * T1^-3 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 14, 27, 30, 33, 24, 12, 4, 10, 20, 16, 6, 15, 28, 34, 32, 23, 11, 21, 18, 8, 2, 7, 17, 29, 26, 31, 22, 25, 13, 5)(35, 36, 40, 48, 60, 66, 58, 47, 52, 54, 43, 51, 62, 64, 56, 45, 38)(37, 41, 49, 61, 65, 57, 46, 39, 42, 50, 53, 63, 68, 67, 59, 55, 44) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.412 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.385 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T1^-1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-3 * T2^-4, T1^-7 * T2^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 22, 32, 26, 29, 18, 8, 2, 7, 17, 23, 11, 21, 31, 34, 28, 16, 6, 15, 24, 12, 4, 10, 20, 30, 33, 27, 14, 25, 13, 5)(35, 36, 40, 48, 60, 65, 54, 43, 51, 58, 47, 52, 62, 67, 56, 45, 38)(37, 41, 49, 59, 63, 68, 64, 53, 57, 46, 39, 42, 50, 61, 66, 55, 44) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.415 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.386 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^3, T2^10 * T1^-2, T1^2 * T2^-10, T2^-1 * T1 * T2^-9 * T1 ] Map:: non-degenerate R = (1, 3, 9, 16, 22, 28, 32, 26, 20, 14, 6, 12, 4, 10, 17, 23, 29, 33, 27, 21, 15, 8, 2, 7, 11, 18, 24, 30, 34, 31, 25, 19, 13, 5)(35, 36, 40, 47, 49, 54, 59, 61, 66, 68, 63, 56, 58, 51, 43, 45, 38)(37, 41, 46, 39, 42, 48, 53, 55, 60, 65, 67, 62, 64, 57, 50, 52, 44) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.410 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.387 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1 * T2^-1 * T1 * T2^-1 * T1, T1 * T2 * T1 * T2^9, (T1^-1 * T2^-1)^34 ] Map:: non-degenerate R = (1, 3, 9, 16, 22, 28, 34, 29, 23, 17, 11, 8, 2, 7, 15, 21, 27, 33, 30, 24, 18, 12, 4, 10, 6, 14, 20, 26, 32, 31, 25, 19, 13, 5)(35, 36, 40, 43, 49, 54, 56, 61, 66, 68, 64, 59, 57, 52, 47, 45, 38)(37, 41, 48, 50, 55, 60, 62, 67, 65, 63, 58, 53, 51, 46, 39, 42, 44) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.413 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.388 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^17, (T2^-1 * T1^-1)^34 ] Map:: non-degenerate R = (1, 3, 2, 7, 6, 11, 10, 15, 14, 19, 18, 23, 22, 27, 26, 31, 30, 34, 32, 33, 28, 29, 24, 25, 20, 21, 16, 17, 12, 13, 8, 9, 4, 5)(35, 36, 40, 44, 48, 52, 56, 60, 64, 66, 62, 58, 54, 50, 46, 42, 38)(37, 41, 45, 49, 53, 57, 61, 65, 68, 67, 63, 59, 55, 51, 47, 43, 39) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.408 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.389 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1, (F * T2)^2, (F * T1)^2, T1^17 ] Map:: non-degenerate R = (1, 3, 4, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29, 32, 33, 34, 30, 31, 26, 27, 22, 23, 18, 19, 14, 15, 10, 11, 6, 7, 2, 5)(35, 36, 40, 44, 48, 52, 56, 60, 64, 67, 63, 59, 55, 51, 47, 43, 38)(37, 39, 41, 45, 49, 53, 57, 61, 65, 68, 66, 62, 58, 54, 50, 46, 42) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.411 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.390 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^3 * T2^-1 * T1 * T2^-1 * T1, T1 * T2 * T1 * T2^5, T2^3 * T1^-2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 * T2^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 30, 23, 11, 21, 14, 26, 33, 29, 18, 8, 2, 7, 17, 28, 24, 12, 4, 10, 20, 31, 34, 32, 22, 16, 6, 15, 27, 25, 13, 5)(35, 36, 40, 48, 54, 43, 51, 61, 67, 68, 64, 58, 47, 52, 56, 45, 38)(37, 41, 49, 60, 65, 53, 62, 59, 63, 66, 57, 46, 39, 42, 50, 55, 44) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.406 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.391 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^3 * T2 * T1 * T2 * T1, T2^5 * T1^-1 * T2 * T1^-1, T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-3 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 27, 16, 6, 15, 22, 31, 34, 32, 24, 12, 4, 10, 20, 29, 18, 8, 2, 7, 17, 28, 33, 26, 14, 23, 11, 21, 30, 25, 13, 5)(35, 36, 40, 48, 58, 47, 52, 61, 67, 68, 64, 54, 43, 51, 56, 45, 38)(37, 41, 49, 57, 46, 39, 42, 50, 60, 66, 59, 63, 53, 62, 65, 55, 44) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.409 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.392 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-4 * T1, T1 * T2 * T1^7 * T2, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 9, 8, 2, 7, 17, 16, 6, 15, 25, 24, 14, 23, 33, 32, 22, 31, 27, 34, 30, 28, 19, 26, 29, 20, 11, 18, 21, 12, 4, 10, 13, 5)(35, 36, 40, 48, 56, 64, 63, 55, 47, 43, 51, 59, 67, 61, 53, 45, 38)(37, 41, 49, 57, 65, 62, 54, 46, 39, 42, 50, 58, 66, 68, 60, 52, 44) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.404 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.393 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2^3, T1^2 * T2^-1 * T1 * T2^-1 * T1^5, T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^3 ] Map:: non-degenerate R = (1, 3, 9, 12, 4, 10, 18, 21, 11, 19, 26, 29, 20, 27, 30, 34, 28, 32, 22, 31, 33, 24, 14, 23, 25, 16, 6, 15, 17, 8, 2, 7, 13, 5)(35, 36, 40, 48, 56, 64, 60, 52, 43, 47, 51, 59, 67, 62, 54, 45, 38)(37, 41, 49, 57, 65, 68, 63, 55, 46, 39, 42, 50, 58, 66, 61, 53, 44) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.407 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.394 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-2 * T1^-4, T2^-8 * T1, T1 * T2^-1 * T1 * T2^-2 * T1^2 * T2^-3 * T1 ] Map:: non-degenerate R = (1, 3, 9, 19, 27, 26, 18, 8, 2, 7, 17, 25, 33, 32, 24, 16, 6, 15, 11, 21, 29, 34, 31, 23, 14, 12, 4, 10, 20, 28, 30, 22, 13, 5)(35, 36, 40, 48, 47, 52, 58, 65, 64, 61, 67, 63, 54, 43, 51, 45, 38)(37, 41, 49, 46, 39, 42, 50, 57, 56, 60, 66, 68, 62, 53, 59, 55, 44) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.403 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.395 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-3 * T2, T2^8 * T1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 27, 29, 21, 12, 4, 10, 14, 23, 31, 34, 28, 20, 11, 16, 6, 15, 24, 32, 33, 26, 18, 8, 2, 7, 17, 25, 30, 22, 13, 5)(35, 36, 40, 48, 43, 51, 58, 65, 61, 64, 67, 62, 55, 47, 52, 45, 38)(37, 41, 49, 57, 53, 59, 66, 68, 63, 56, 60, 54, 46, 39, 42, 50, 44) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 68^17 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.405 Transitivity :: ET+ Graph:: bipartite v = 3 e = 34 f = 1 degree seq :: [ 17^2, 34 ] E16.396 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T1 * T2^11, (T2^-1 * T1^-1)^17 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 33, 28, 22, 16, 10, 4, 6, 12, 18, 24, 30, 34, 32, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 29, 23, 17, 11, 5)(35, 36, 40, 37, 41, 46, 43, 47, 52, 49, 53, 58, 55, 59, 64, 61, 65, 68, 67, 63, 66, 62, 57, 60, 56, 51, 54, 50, 45, 48, 44, 39, 42, 38) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.423 Transitivity :: ET+ Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.397 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^-1 * T1^-1, (F * T1)^2, (F * T2)^2, T2^-11 * T1 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 32, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 34, 30, 24, 18, 12, 6, 4, 10, 16, 22, 28, 33, 29, 23, 17, 11, 5)(35, 36, 40, 39, 42, 46, 45, 48, 52, 51, 54, 58, 57, 60, 64, 63, 66, 68, 67, 61, 65, 62, 55, 59, 56, 49, 53, 50, 43, 47, 44, 37, 41, 38) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.419 Transitivity :: ET+ Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.398 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-2 * T2^-1 * T1^2, T1^3 * T2^-1 * T1^2, T2^6 * T1^-1 * T2, (T1^-1 * T2^-1)^17 ] Map:: non-degenerate R = (1, 3, 9, 19, 28, 18, 8, 2, 7, 17, 27, 34, 26, 16, 6, 15, 25, 33, 30, 21, 11, 14, 24, 32, 31, 22, 12, 4, 10, 20, 29, 23, 13, 5)(35, 36, 40, 48, 44, 37, 41, 49, 58, 54, 43, 51, 59, 66, 63, 53, 61, 67, 65, 57, 62, 68, 64, 56, 47, 52, 60, 55, 46, 39, 42, 50, 45, 38) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.424 Transitivity :: ET+ Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.399 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-4 * T2^-1 * T1^-1, T2^-1 * T1^-1 * T2^-6, T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 22, 12, 4, 10, 20, 30, 32, 24, 14, 11, 21, 31, 34, 26, 16, 6, 15, 25, 33, 28, 18, 8, 2, 7, 17, 27, 23, 13, 5)(35, 36, 40, 48, 46, 39, 42, 50, 58, 56, 47, 52, 60, 66, 63, 57, 62, 68, 64, 53, 61, 67, 65, 54, 43, 51, 59, 55, 44, 37, 41, 49, 45, 38) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.422 Transitivity :: ET+ Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.400 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2^3 * T1^-1 * T2 * T1^-1, T2^-3 * T1^-7, (T1^-1 * T2^-1)^17 ] Map:: non-degenerate R = (1, 3, 9, 16, 6, 15, 26, 33, 23, 32, 29, 20, 27, 22, 12, 4, 10, 18, 8, 2, 7, 17, 25, 14, 24, 34, 28, 31, 30, 21, 11, 19, 13, 5)(35, 36, 40, 48, 57, 65, 61, 53, 44, 37, 41, 49, 58, 66, 64, 56, 47, 52, 43, 51, 60, 68, 63, 55, 46, 39, 42, 50, 59, 67, 62, 54, 45, 38) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.421 Transitivity :: ET+ Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.401 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T2^-1 * T1^-1 * T2^-3 * T1^-1, T1^-6 * T2 * T1^-1 * T2^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 11, 21, 28, 31, 30, 34, 25, 14, 24, 18, 8, 2, 7, 17, 12, 4, 10, 20, 27, 22, 29, 33, 23, 32, 26, 16, 6, 15, 13, 5)(35, 36, 40, 48, 57, 65, 61, 53, 46, 39, 42, 50, 59, 67, 62, 54, 43, 51, 47, 52, 60, 68, 63, 55, 44, 37, 41, 49, 58, 66, 64, 56, 45, 38) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.418 Transitivity :: ET+ Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.402 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {17, 34, 34}) Quotient :: edge Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1 * T2^2 * T1 * T2^2 * T1 * T2, T2 * T1^-1 * T2^2 * T1^-4, T2^2 * T1^29 * T2 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 22, 30, 16, 6, 15, 29, 24, 12, 4, 10, 20, 26, 34, 32, 18, 8, 2, 7, 17, 31, 23, 11, 21, 28, 14, 27, 25, 13, 5)(35, 36, 40, 48, 60, 53, 65, 58, 47, 52, 64, 55, 44, 37, 41, 49, 61, 68, 67, 57, 46, 39, 42, 50, 62, 54, 43, 51, 63, 59, 66, 56, 45, 38) L = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.420 Transitivity :: ET+ Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.403 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T1^2 * T2^-2, T2^16 * T1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 35, 3, 37, 6, 40, 12, 46, 15, 49, 20, 54, 23, 57, 28, 62, 31, 65, 34, 68, 29, 63, 26, 60, 21, 55, 18, 52, 13, 47, 10, 44, 4, 38, 8, 42, 2, 36, 7, 41, 11, 45, 16, 50, 19, 53, 24, 58, 27, 61, 32, 66, 33, 67, 30, 64, 25, 59, 22, 56, 17, 51, 14, 48, 9, 43, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 45)(7, 46)(8, 37)(9, 38)(10, 39)(11, 49)(12, 50)(13, 43)(14, 44)(15, 53)(16, 54)(17, 47)(18, 48)(19, 57)(20, 58)(21, 51)(22, 52)(23, 61)(24, 62)(25, 55)(26, 56)(27, 65)(28, 66)(29, 59)(30, 60)(31, 67)(32, 68)(33, 63)(34, 64) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.394 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.404 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T2^5 * T1^-1 * T2, T1^-1 * T2 * T1^-2 * T2 * T1^-3, T1^2 * T2 * T1^2 * T2^3 * T1, (T1^-1 * T2^-1)^34 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 19, 53, 18, 52, 8, 42, 2, 36, 7, 41, 17, 51, 31, 65, 30, 64, 16, 50, 6, 40, 15, 49, 29, 63, 32, 66, 22, 56, 28, 62, 14, 48, 27, 61, 33, 67, 23, 57, 11, 45, 21, 55, 26, 60, 34, 68, 24, 58, 12, 46, 4, 38, 10, 44, 20, 54, 25, 59, 13, 47, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 51)(10, 37)(11, 38)(12, 39)(13, 52)(14, 60)(15, 61)(16, 62)(17, 63)(18, 64)(19, 65)(20, 43)(21, 44)(22, 45)(23, 46)(24, 47)(25, 53)(26, 54)(27, 68)(28, 55)(29, 67)(30, 56)(31, 66)(32, 57)(33, 58)(34, 59) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.392 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.405 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-4 * T1^-1 * T2^-2, T1^-5 * T2^-1 * T1^-1 * T2^-1, T1^2 * T2^-1 * T1^2 * T2^-3 * T1, T1^59 * T2^-2 * T1^3 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 19, 53, 24, 58, 12, 46, 4, 38, 10, 44, 20, 54, 32, 66, 26, 60, 23, 57, 11, 45, 21, 55, 33, 67, 28, 62, 14, 48, 27, 61, 22, 56, 34, 68, 30, 64, 16, 50, 6, 40, 15, 49, 29, 63, 31, 65, 18, 52, 8, 42, 2, 36, 7, 41, 17, 51, 25, 59, 13, 47, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 51)(10, 37)(11, 38)(12, 39)(13, 52)(14, 60)(15, 61)(16, 62)(17, 63)(18, 64)(19, 59)(20, 43)(21, 44)(22, 45)(23, 46)(24, 47)(25, 65)(26, 58)(27, 57)(28, 66)(29, 56)(30, 67)(31, 68)(32, 53)(33, 54)(34, 55) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.395 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.406 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1 * T2^-1 * T1 * T2^-3 * T1, T1^2 * T2 * T1^2 * T2 * T1^3, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1, T1^-2 * T2^2 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^4 * T1^-3 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 19, 53, 14, 48, 27, 61, 30, 64, 33, 67, 24, 58, 12, 46, 4, 38, 10, 44, 20, 54, 16, 50, 6, 40, 15, 49, 28, 62, 34, 68, 32, 66, 23, 57, 11, 45, 21, 55, 18, 52, 8, 42, 2, 36, 7, 41, 17, 51, 29, 63, 26, 60, 31, 65, 22, 56, 25, 59, 13, 47, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 51)(10, 37)(11, 38)(12, 39)(13, 52)(14, 60)(15, 61)(16, 53)(17, 62)(18, 54)(19, 63)(20, 43)(21, 44)(22, 45)(23, 46)(24, 47)(25, 55)(26, 66)(27, 65)(28, 64)(29, 68)(30, 56)(31, 57)(32, 58)(33, 59)(34, 67) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.390 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.407 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T1^-1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-3 * T2^-4, T1^-7 * T2^2 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 19, 53, 22, 56, 32, 66, 26, 60, 29, 63, 18, 52, 8, 42, 2, 36, 7, 41, 17, 51, 23, 57, 11, 45, 21, 55, 31, 65, 34, 68, 28, 62, 16, 50, 6, 40, 15, 49, 24, 58, 12, 46, 4, 38, 10, 44, 20, 54, 30, 64, 33, 67, 27, 61, 14, 48, 25, 59, 13, 47, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 51)(10, 37)(11, 38)(12, 39)(13, 52)(14, 60)(15, 59)(16, 61)(17, 58)(18, 62)(19, 57)(20, 43)(21, 44)(22, 45)(23, 46)(24, 47)(25, 63)(26, 65)(27, 66)(28, 67)(29, 68)(30, 53)(31, 54)(32, 55)(33, 56)(34, 64) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.393 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.408 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^3, T2^10 * T1^-2, T1^2 * T2^-10, T2^-1 * T1 * T2^-9 * T1 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 16, 50, 22, 56, 28, 62, 32, 66, 26, 60, 20, 54, 14, 48, 6, 40, 12, 46, 4, 38, 10, 44, 17, 51, 23, 57, 29, 63, 33, 67, 27, 61, 21, 55, 15, 49, 8, 42, 2, 36, 7, 41, 11, 45, 18, 52, 24, 58, 30, 64, 34, 68, 31, 65, 25, 59, 19, 53, 13, 47, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 47)(7, 46)(8, 48)(9, 45)(10, 37)(11, 38)(12, 39)(13, 49)(14, 53)(15, 54)(16, 52)(17, 43)(18, 44)(19, 55)(20, 59)(21, 60)(22, 58)(23, 50)(24, 51)(25, 61)(26, 65)(27, 66)(28, 64)(29, 56)(30, 57)(31, 67)(32, 68)(33, 62)(34, 63) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.388 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.409 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1 * T2^-1 * T1 * T2^-1 * T1, T1 * T2 * T1 * T2^9, (T1^-1 * T2^-1)^34 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 16, 50, 22, 56, 28, 62, 34, 68, 29, 63, 23, 57, 17, 51, 11, 45, 8, 42, 2, 36, 7, 41, 15, 49, 21, 55, 27, 61, 33, 67, 30, 64, 24, 58, 18, 52, 12, 46, 4, 38, 10, 44, 6, 40, 14, 48, 20, 54, 26, 60, 32, 66, 31, 65, 25, 59, 19, 53, 13, 47, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 43)(7, 48)(8, 44)(9, 49)(10, 37)(11, 38)(12, 39)(13, 45)(14, 50)(15, 54)(16, 55)(17, 46)(18, 47)(19, 51)(20, 56)(21, 60)(22, 61)(23, 52)(24, 53)(25, 57)(26, 62)(27, 66)(28, 67)(29, 58)(30, 59)(31, 63)(32, 68)(33, 65)(34, 64) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.391 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.410 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^17, (T2^-1 * T1^-1)^34 ] Map:: non-degenerate R = (1, 35, 3, 37, 2, 36, 7, 41, 6, 40, 11, 45, 10, 44, 15, 49, 14, 48, 19, 53, 18, 52, 23, 57, 22, 56, 27, 61, 26, 60, 31, 65, 30, 64, 34, 68, 32, 66, 33, 67, 28, 62, 29, 63, 24, 58, 25, 59, 20, 54, 21, 55, 16, 50, 17, 51, 12, 46, 13, 47, 8, 42, 9, 43, 4, 38, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 37)(6, 44)(7, 45)(8, 38)(9, 39)(10, 48)(11, 49)(12, 42)(13, 43)(14, 52)(15, 53)(16, 46)(17, 47)(18, 56)(19, 57)(20, 50)(21, 51)(22, 60)(23, 61)(24, 54)(25, 55)(26, 64)(27, 65)(28, 58)(29, 59)(30, 66)(31, 68)(32, 62)(33, 63)(34, 67) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.386 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.411 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1, (F * T2)^2, (F * T1)^2, T1^17 ] Map:: non-degenerate R = (1, 35, 3, 37, 4, 38, 8, 42, 9, 43, 12, 46, 13, 47, 16, 50, 17, 51, 20, 54, 21, 55, 24, 58, 25, 59, 28, 62, 29, 63, 32, 66, 33, 67, 34, 68, 30, 64, 31, 65, 26, 60, 27, 61, 22, 56, 23, 57, 18, 52, 19, 53, 14, 48, 15, 49, 10, 44, 11, 45, 6, 40, 7, 41, 2, 36, 5, 39) L = (1, 36)(2, 40)(3, 39)(4, 35)(5, 41)(6, 44)(7, 45)(8, 37)(9, 38)(10, 48)(11, 49)(12, 42)(13, 43)(14, 52)(15, 53)(16, 46)(17, 47)(18, 56)(19, 57)(20, 50)(21, 51)(22, 60)(23, 61)(24, 54)(25, 55)(26, 64)(27, 65)(28, 58)(29, 59)(30, 67)(31, 68)(32, 62)(33, 63)(34, 66) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.389 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.412 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^3 * T2^-1 * T1 * T2^-1 * T1, T1 * T2 * T1 * T2^5, T2^3 * T1^-2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 * T2^2 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 19, 53, 30, 64, 23, 57, 11, 45, 21, 55, 14, 48, 26, 60, 33, 67, 29, 63, 18, 52, 8, 42, 2, 36, 7, 41, 17, 51, 28, 62, 24, 58, 12, 46, 4, 38, 10, 44, 20, 54, 31, 65, 34, 68, 32, 66, 22, 56, 16, 50, 6, 40, 15, 49, 27, 61, 25, 59, 13, 47, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 51)(10, 37)(11, 38)(12, 39)(13, 52)(14, 54)(15, 60)(16, 55)(17, 61)(18, 56)(19, 62)(20, 43)(21, 44)(22, 45)(23, 46)(24, 47)(25, 63)(26, 65)(27, 67)(28, 59)(29, 66)(30, 58)(31, 53)(32, 57)(33, 68)(34, 64) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.384 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.413 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^3 * T2 * T1 * T2 * T1, T2^5 * T1^-1 * T2 * T1^-1, T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-3 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 19, 53, 27, 61, 16, 50, 6, 40, 15, 49, 22, 56, 31, 65, 34, 68, 32, 66, 24, 58, 12, 46, 4, 38, 10, 44, 20, 54, 29, 63, 18, 52, 8, 42, 2, 36, 7, 41, 17, 51, 28, 62, 33, 67, 26, 60, 14, 48, 23, 57, 11, 45, 21, 55, 30, 64, 25, 59, 13, 47, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 51)(10, 37)(11, 38)(12, 39)(13, 52)(14, 58)(15, 57)(16, 60)(17, 56)(18, 61)(19, 62)(20, 43)(21, 44)(22, 45)(23, 46)(24, 47)(25, 63)(26, 66)(27, 67)(28, 65)(29, 53)(30, 54)(31, 55)(32, 59)(33, 68)(34, 64) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.387 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.414 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-4 * T1, T1 * T2 * T1^7 * T2, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 8, 42, 2, 36, 7, 41, 17, 51, 16, 50, 6, 40, 15, 49, 25, 59, 24, 58, 14, 48, 23, 57, 33, 67, 32, 66, 22, 56, 31, 65, 27, 61, 34, 68, 30, 64, 28, 62, 19, 53, 26, 60, 29, 63, 20, 54, 11, 45, 18, 52, 21, 55, 12, 46, 4, 38, 10, 44, 13, 47, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 51)(10, 37)(11, 38)(12, 39)(13, 43)(14, 56)(15, 57)(16, 58)(17, 59)(18, 44)(19, 45)(20, 46)(21, 47)(22, 64)(23, 65)(24, 66)(25, 67)(26, 52)(27, 53)(28, 54)(29, 55)(30, 63)(31, 62)(32, 68)(33, 61)(34, 60) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.382 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.415 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2^3, T1^2 * T2^-1 * T1 * T2^-1 * T1^5, T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^3 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 12, 46, 4, 38, 10, 44, 18, 52, 21, 55, 11, 45, 19, 53, 26, 60, 29, 63, 20, 54, 27, 61, 30, 64, 34, 68, 28, 62, 32, 66, 22, 56, 31, 65, 33, 67, 24, 58, 14, 48, 23, 57, 25, 59, 16, 50, 6, 40, 15, 49, 17, 51, 8, 42, 2, 36, 7, 41, 13, 47, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 47)(10, 37)(11, 38)(12, 39)(13, 51)(14, 56)(15, 57)(16, 58)(17, 59)(18, 43)(19, 44)(20, 45)(21, 46)(22, 64)(23, 65)(24, 66)(25, 67)(26, 52)(27, 53)(28, 54)(29, 55)(30, 60)(31, 68)(32, 61)(33, 62)(34, 63) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.385 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.416 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-2 * T1^-4, T2^-8 * T1, T1 * T2^-1 * T1 * T2^-2 * T1^2 * T2^-3 * T1 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 19, 53, 27, 61, 26, 60, 18, 52, 8, 42, 2, 36, 7, 41, 17, 51, 25, 59, 33, 67, 32, 66, 24, 58, 16, 50, 6, 40, 15, 49, 11, 45, 21, 55, 29, 63, 34, 68, 31, 65, 23, 57, 14, 48, 12, 46, 4, 38, 10, 44, 20, 54, 28, 62, 30, 64, 22, 56, 13, 47, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 51)(10, 37)(11, 38)(12, 39)(13, 52)(14, 47)(15, 46)(16, 57)(17, 45)(18, 58)(19, 59)(20, 43)(21, 44)(22, 60)(23, 56)(24, 65)(25, 55)(26, 66)(27, 67)(28, 53)(29, 54)(30, 61)(31, 64)(32, 68)(33, 63)(34, 62) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.381 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.417 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-3 * T2, T2^8 * T1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 19, 53, 27, 61, 29, 63, 21, 55, 12, 46, 4, 38, 10, 44, 14, 48, 23, 57, 31, 65, 34, 68, 28, 62, 20, 54, 11, 45, 16, 50, 6, 40, 15, 49, 24, 58, 32, 66, 33, 67, 26, 60, 18, 52, 8, 42, 2, 36, 7, 41, 17, 51, 25, 59, 30, 64, 22, 56, 13, 47, 5, 39) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 51)(10, 37)(11, 38)(12, 39)(13, 52)(14, 43)(15, 57)(16, 44)(17, 58)(18, 45)(19, 59)(20, 46)(21, 47)(22, 60)(23, 53)(24, 65)(25, 66)(26, 54)(27, 64)(28, 55)(29, 56)(30, 67)(31, 61)(32, 68)(33, 62)(34, 63) local type(s) :: { ( 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34, 17, 34 ) } Outer automorphisms :: reflexible Dual of E16.383 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 34 f = 3 degree seq :: [ 68 ] E16.418 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T2 * T1^-1)^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T2^-1 * T1^2 * T2^-1, T2^7 * T1 * T2^-7 * T1^-1, T1^2 * T2^15, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 35, 3, 37, 6, 40, 12, 46, 15, 49, 20, 54, 23, 57, 28, 62, 31, 65, 33, 67, 30, 64, 25, 59, 22, 56, 17, 51, 14, 48, 9, 43, 5, 39)(2, 36, 7, 41, 11, 45, 16, 50, 19, 53, 24, 58, 27, 61, 32, 66, 34, 68, 29, 63, 26, 60, 21, 55, 18, 52, 13, 47, 10, 44, 4, 38, 8, 42) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 45)(7, 46)(8, 37)(9, 38)(10, 39)(11, 49)(12, 50)(13, 43)(14, 44)(15, 53)(16, 54)(17, 47)(18, 48)(19, 57)(20, 58)(21, 51)(22, 52)(23, 61)(24, 62)(25, 55)(26, 56)(27, 65)(28, 66)(29, 59)(30, 60)(31, 68)(32, 67)(33, 63)(34, 64) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.401 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.419 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2, (F * T2)^2, (F * T1)^2, T2^17, (T2^-1 * T1^-1)^34 ] Map:: non-degenerate R = (1, 35, 3, 37, 7, 41, 11, 45, 15, 49, 19, 53, 23, 57, 27, 61, 31, 65, 33, 67, 29, 63, 25, 59, 21, 55, 17, 51, 13, 47, 9, 43, 5, 39)(2, 36, 6, 40, 10, 44, 14, 48, 18, 52, 22, 56, 26, 60, 30, 64, 34, 68, 32, 66, 28, 62, 24, 58, 20, 54, 16, 50, 12, 46, 8, 42, 4, 38) L = (1, 36)(2, 37)(3, 40)(4, 35)(5, 38)(6, 41)(7, 44)(8, 39)(9, 42)(10, 45)(11, 48)(12, 43)(13, 46)(14, 49)(15, 52)(16, 47)(17, 50)(18, 53)(19, 56)(20, 51)(21, 54)(22, 57)(23, 60)(24, 55)(25, 58)(26, 61)(27, 64)(28, 59)(29, 62)(30, 65)(31, 68)(32, 63)(33, 66)(34, 67) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.397 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.420 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2 * T1 * T2^3, T1^-1 * T2 * T1^-1 * T2 * T1^-4, T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2, T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-3 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 19, 53, 23, 57, 11, 45, 21, 55, 26, 60, 33, 67, 34, 68, 29, 63, 16, 50, 6, 40, 15, 49, 25, 59, 13, 47, 5, 39)(2, 36, 7, 41, 17, 51, 24, 58, 12, 46, 4, 38, 10, 44, 20, 54, 31, 65, 32, 66, 22, 56, 28, 62, 14, 48, 27, 61, 30, 64, 18, 52, 8, 42) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 51)(10, 37)(11, 38)(12, 39)(13, 52)(14, 60)(15, 61)(16, 62)(17, 59)(18, 63)(19, 58)(20, 43)(21, 44)(22, 45)(23, 46)(24, 47)(25, 64)(26, 54)(27, 67)(28, 55)(29, 56)(30, 68)(31, 53)(32, 57)(33, 65)(34, 66) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.402 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.421 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-1 * T1 * T2^-4 * T1, T1 * T2 * T1^5 * T2, T1^3 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^2 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 19, 53, 16, 50, 6, 40, 15, 49, 29, 63, 34, 68, 33, 67, 26, 60, 23, 57, 11, 45, 21, 55, 25, 59, 13, 47, 5, 39)(2, 36, 7, 41, 17, 51, 30, 64, 28, 62, 14, 48, 27, 61, 22, 56, 31, 65, 32, 66, 24, 58, 12, 46, 4, 38, 10, 44, 20, 54, 18, 52, 8, 42) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 51)(10, 37)(11, 38)(12, 39)(13, 52)(14, 60)(15, 61)(16, 62)(17, 63)(18, 53)(19, 64)(20, 43)(21, 44)(22, 45)(23, 46)(24, 47)(25, 54)(26, 58)(27, 57)(28, 67)(29, 56)(30, 68)(31, 55)(32, 59)(33, 66)(34, 65) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.400 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.422 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-1 * T2 * T1^-3, T1 * T2 * T1 * T2^7, T1^-2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 17, 51, 25, 59, 33, 67, 27, 61, 19, 53, 11, 45, 6, 40, 14, 48, 22, 56, 30, 64, 29, 63, 21, 55, 13, 47, 5, 39)(2, 36, 7, 41, 15, 49, 23, 57, 31, 65, 28, 62, 20, 54, 12, 46, 4, 38, 10, 44, 18, 52, 26, 60, 34, 68, 32, 66, 24, 58, 16, 50, 8, 42) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 44)(7, 48)(8, 45)(9, 49)(10, 37)(11, 38)(12, 39)(13, 50)(14, 52)(15, 56)(16, 53)(17, 57)(18, 43)(19, 46)(20, 47)(21, 58)(22, 60)(23, 64)(24, 61)(25, 65)(26, 51)(27, 54)(28, 55)(29, 66)(30, 68)(31, 63)(32, 67)(33, 62)(34, 59) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.399 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.423 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T1 * T2 * T1^3, T2^2 * T1^-1 * T2^5 * T1^-1 * T2, T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1^-1 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 17, 51, 25, 59, 30, 64, 22, 56, 14, 48, 6, 40, 11, 45, 19, 53, 27, 61, 33, 67, 29, 63, 21, 55, 13, 47, 5, 39)(2, 36, 7, 41, 15, 49, 23, 57, 31, 65, 34, 68, 28, 62, 20, 54, 12, 46, 4, 38, 10, 44, 18, 52, 26, 60, 32, 66, 24, 58, 16, 50, 8, 42) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 46)(7, 45)(8, 48)(9, 49)(10, 37)(11, 38)(12, 39)(13, 50)(14, 54)(15, 53)(16, 56)(17, 57)(18, 43)(19, 44)(20, 47)(21, 58)(22, 62)(23, 61)(24, 64)(25, 65)(26, 51)(27, 52)(28, 55)(29, 66)(30, 68)(31, 67)(32, 59)(33, 60)(34, 63) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.396 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.424 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {17, 34, 34}) Quotient :: loop Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T2 * T1^2 * T2^-1 * T1^-2, T1^-5 * T2^-1 * T1^-1, T2^-1 * T1^-1 * T2^-4 * T1^-1 * T2^-1, (T1^-1 * T2^-1)^34 ] Map:: non-degenerate R = (1, 35, 3, 37, 9, 43, 19, 53, 31, 65, 23, 57, 11, 45, 21, 55, 33, 67, 28, 62, 16, 50, 6, 40, 15, 49, 27, 61, 25, 59, 13, 47, 5, 39)(2, 36, 7, 41, 17, 51, 29, 63, 24, 58, 12, 46, 4, 38, 10, 44, 20, 54, 32, 66, 26, 60, 14, 48, 22, 56, 34, 68, 30, 64, 18, 52, 8, 42) L = (1, 36)(2, 40)(3, 41)(4, 35)(5, 42)(6, 48)(7, 49)(8, 50)(9, 51)(10, 37)(11, 38)(12, 39)(13, 52)(14, 57)(15, 56)(16, 60)(17, 61)(18, 62)(19, 63)(20, 43)(21, 44)(22, 45)(23, 46)(24, 47)(25, 64)(26, 65)(27, 68)(28, 66)(29, 59)(30, 67)(31, 58)(32, 53)(33, 54)(34, 55) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible Dual of E16.398 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.425 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y2^-1, Y1^-1), (R * Y1)^2, Y2 * Y3 * Y1^-1 * Y2, Y2 * Y3 * Y2 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y1^7 * Y2 * Y1 * Y2 * Y3^-7, Y1^17, (Y1 * Y3^-1)^17, (Y3 * Y2^-1)^34 ] Map:: R = (1, 35, 2, 36, 6, 40, 11, 45, 15, 49, 19, 53, 23, 57, 27, 61, 31, 65, 33, 67, 29, 63, 25, 59, 21, 55, 17, 51, 13, 47, 9, 43, 4, 38)(3, 37, 7, 41, 12, 46, 16, 50, 20, 54, 24, 58, 28, 62, 32, 66, 34, 68, 30, 64, 26, 60, 22, 56, 18, 52, 14, 48, 10, 44, 5, 39, 8, 42)(69, 103, 71, 105, 74, 108, 80, 114, 83, 117, 88, 122, 91, 125, 96, 130, 99, 133, 102, 136, 97, 131, 94, 128, 89, 123, 86, 120, 81, 115, 78, 112, 72, 106, 76, 110, 70, 104, 75, 109, 79, 113, 84, 118, 87, 121, 92, 126, 95, 129, 100, 134, 101, 135, 98, 132, 93, 127, 90, 124, 85, 119, 82, 116, 77, 111, 73, 107) L = (1, 72)(2, 69)(3, 76)(4, 77)(5, 78)(6, 70)(7, 71)(8, 73)(9, 81)(10, 82)(11, 74)(12, 75)(13, 85)(14, 86)(15, 79)(16, 80)(17, 89)(18, 90)(19, 83)(20, 84)(21, 93)(22, 94)(23, 87)(24, 88)(25, 97)(26, 98)(27, 91)(28, 92)(29, 101)(30, 102)(31, 95)(32, 96)(33, 99)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.467 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.426 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^2 * Y3^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^17, Y1^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 10, 44, 14, 48, 18, 52, 22, 56, 26, 60, 30, 64, 33, 67, 29, 63, 25, 59, 21, 55, 17, 51, 13, 47, 9, 43, 4, 38)(3, 37, 5, 39, 7, 41, 11, 45, 15, 49, 19, 53, 23, 57, 27, 61, 31, 65, 34, 68, 32, 66, 28, 62, 24, 58, 20, 54, 16, 50, 12, 46, 8, 42)(69, 103, 71, 105, 72, 106, 76, 110, 77, 111, 80, 114, 81, 115, 84, 118, 85, 119, 88, 122, 89, 123, 92, 126, 93, 127, 96, 130, 97, 131, 100, 134, 101, 135, 102, 136, 98, 132, 99, 133, 94, 128, 95, 129, 90, 124, 91, 125, 86, 120, 87, 121, 82, 116, 83, 117, 78, 112, 79, 113, 74, 108, 75, 109, 70, 104, 73, 107) L = (1, 72)(2, 69)(3, 76)(4, 77)(5, 71)(6, 70)(7, 73)(8, 80)(9, 81)(10, 74)(11, 75)(12, 84)(13, 85)(14, 78)(15, 79)(16, 88)(17, 89)(18, 82)(19, 83)(20, 92)(21, 93)(22, 86)(23, 87)(24, 96)(25, 97)(26, 90)(27, 91)(28, 100)(29, 101)(30, 94)(31, 95)(32, 102)(33, 98)(34, 99)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.462 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.427 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y2^-2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3^-1), Y1^17, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 10, 44, 14, 48, 18, 52, 22, 56, 26, 60, 30, 64, 32, 66, 28, 62, 24, 58, 20, 54, 16, 50, 12, 46, 8, 42, 4, 38)(3, 37, 7, 41, 11, 45, 15, 49, 19, 53, 23, 57, 27, 61, 31, 65, 34, 68, 33, 67, 29, 63, 25, 59, 21, 55, 17, 51, 13, 47, 9, 43, 5, 39)(69, 103, 71, 105, 70, 104, 75, 109, 74, 108, 79, 113, 78, 112, 83, 117, 82, 116, 87, 121, 86, 120, 91, 125, 90, 124, 95, 129, 94, 128, 99, 133, 98, 132, 102, 136, 100, 134, 101, 135, 96, 130, 97, 131, 92, 126, 93, 127, 88, 122, 89, 123, 84, 118, 85, 119, 80, 114, 81, 115, 76, 110, 77, 111, 72, 106, 73, 107) L = (1, 72)(2, 69)(3, 73)(4, 76)(5, 77)(6, 70)(7, 71)(8, 80)(9, 81)(10, 74)(11, 75)(12, 84)(13, 85)(14, 78)(15, 79)(16, 88)(17, 89)(18, 82)(19, 83)(20, 92)(21, 93)(22, 86)(23, 87)(24, 96)(25, 97)(26, 90)(27, 91)(28, 100)(29, 101)(30, 94)(31, 95)(32, 98)(33, 102)(34, 99)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.459 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.428 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y2^-1, Y3), Y1 * Y2 * Y3 * Y2^-1, Y3 * Y2 * Y1 * Y2^-1, Y2^-1 * Y1^-1 * Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-2 * Y1 * Y2^2 * Y1^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y3^-3, Y1^4 * Y2^-1 * Y1 * Y2^-1, Y1^-1 * Y3 * Y2^-6, Y2 * Y1^-1 * Y2^3 * Y3 * Y2^2 * Y3 * Y2^2, Y2^3 * Y1^-1 * Y3^-1 * Y2^-1 * Y1 * Y3^6, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 20, 54, 9, 43, 17, 51, 27, 61, 33, 67, 34, 68, 30, 64, 24, 58, 13, 47, 18, 52, 22, 56, 11, 45, 4, 38)(3, 37, 7, 41, 15, 49, 26, 60, 31, 65, 19, 53, 28, 62, 25, 59, 29, 63, 32, 66, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 21, 55, 10, 44)(69, 103, 71, 105, 77, 111, 87, 121, 98, 132, 91, 125, 79, 113, 89, 123, 82, 116, 94, 128, 101, 135, 97, 131, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 96, 130, 92, 126, 80, 114, 72, 106, 78, 112, 88, 122, 99, 133, 102, 136, 100, 134, 90, 124, 84, 118, 74, 108, 83, 117, 95, 129, 93, 127, 81, 115, 73, 107) L = (1, 72)(2, 69)(3, 78)(4, 79)(5, 80)(6, 70)(7, 71)(8, 73)(9, 88)(10, 89)(11, 90)(12, 91)(13, 92)(14, 74)(15, 75)(16, 76)(17, 77)(18, 81)(19, 99)(20, 82)(21, 84)(22, 86)(23, 100)(24, 98)(25, 96)(26, 83)(27, 85)(28, 87)(29, 93)(30, 102)(31, 94)(32, 97)(33, 95)(34, 101)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.457 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.429 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, Y1 * Y3, Y2 * Y3 * Y2^-1 * Y1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y3 * Y1^-1 * Y2^-1 * Y3^-2, Y1^2 * Y2 * Y1 * Y2 * Y1 * Y3^-1, Y2^2 * Y1^2 * Y3^-3, Y2^4 * Y1^-1 * Y2 * Y1^-1 * Y2, Y3 * Y2^-3 * Y3 * Y2^-2 * Y3 * Y2^-3, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^2 * Y3^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 24, 58, 13, 47, 18, 52, 27, 61, 33, 67, 34, 68, 30, 64, 20, 54, 9, 43, 17, 51, 22, 56, 11, 45, 4, 38)(3, 37, 7, 41, 15, 49, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 26, 60, 32, 66, 25, 59, 29, 63, 19, 53, 28, 62, 31, 65, 21, 55, 10, 44)(69, 103, 71, 105, 77, 111, 87, 121, 95, 129, 84, 118, 74, 108, 83, 117, 90, 124, 99, 133, 102, 136, 100, 134, 92, 126, 80, 114, 72, 106, 78, 112, 88, 122, 97, 131, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 96, 130, 101, 135, 94, 128, 82, 116, 91, 125, 79, 113, 89, 123, 98, 132, 93, 127, 81, 115, 73, 107) L = (1, 72)(2, 69)(3, 78)(4, 79)(5, 80)(6, 70)(7, 71)(8, 73)(9, 88)(10, 89)(11, 90)(12, 91)(13, 92)(14, 74)(15, 75)(16, 76)(17, 77)(18, 81)(19, 97)(20, 98)(21, 99)(22, 85)(23, 83)(24, 82)(25, 100)(26, 84)(27, 86)(28, 87)(29, 93)(30, 102)(31, 96)(32, 94)(33, 95)(34, 101)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.460 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.430 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y3^-1, (R * Y3)^2, (R * Y2)^2, Y2 * Y3^-1 * Y2^3, Y3^-3 * Y2^-1 * Y3^3 * Y2, Y2 * Y3^-3 * Y2^2 * Y3 * Y2 * Y1^-1, Y1^-1 * Y2 * Y3^3 * Y2 * Y3^4, Y1^3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^4, Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3^2 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 22, 56, 30, 64, 26, 60, 18, 52, 9, 43, 13, 47, 17, 51, 25, 59, 33, 67, 28, 62, 20, 54, 11, 45, 4, 38)(3, 37, 7, 41, 15, 49, 23, 57, 31, 65, 34, 68, 29, 63, 21, 55, 12, 46, 5, 39, 8, 42, 16, 50, 24, 58, 32, 66, 27, 61, 19, 53, 10, 44)(69, 103, 71, 105, 77, 111, 80, 114, 72, 106, 78, 112, 86, 120, 89, 123, 79, 113, 87, 121, 94, 128, 97, 131, 88, 122, 95, 129, 98, 132, 102, 136, 96, 130, 100, 134, 90, 124, 99, 133, 101, 135, 92, 126, 82, 116, 91, 125, 93, 127, 84, 118, 74, 108, 83, 117, 85, 119, 76, 110, 70, 104, 75, 109, 81, 115, 73, 107) L = (1, 72)(2, 69)(3, 78)(4, 79)(5, 80)(6, 70)(7, 71)(8, 73)(9, 86)(10, 87)(11, 88)(12, 89)(13, 77)(14, 74)(15, 75)(16, 76)(17, 81)(18, 94)(19, 95)(20, 96)(21, 97)(22, 82)(23, 83)(24, 84)(25, 85)(26, 98)(27, 100)(28, 101)(29, 102)(30, 90)(31, 91)(32, 92)(33, 93)(34, 99)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.458 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.431 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), (R * Y2)^2, (Y2, Y1^-1), Y2 * Y3 * Y2^3, Y3^-1 * Y2 * Y1^4 * Y3^-3 * Y2, Y1^9 * Y2^-2, Y3^-4 * Y2^-1 * Y1 * Y3^-4 * Y2^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 22, 56, 30, 64, 29, 63, 21, 55, 13, 47, 9, 43, 17, 51, 25, 59, 33, 67, 27, 61, 19, 53, 11, 45, 4, 38)(3, 37, 7, 41, 15, 49, 23, 57, 31, 65, 28, 62, 20, 54, 12, 46, 5, 39, 8, 42, 16, 50, 24, 58, 32, 66, 34, 68, 26, 60, 18, 52, 10, 44)(69, 103, 71, 105, 77, 111, 76, 110, 70, 104, 75, 109, 85, 119, 84, 118, 74, 108, 83, 117, 93, 127, 92, 126, 82, 116, 91, 125, 101, 135, 100, 134, 90, 124, 99, 133, 95, 129, 102, 136, 98, 132, 96, 130, 87, 121, 94, 128, 97, 131, 88, 122, 79, 113, 86, 120, 89, 123, 80, 114, 72, 106, 78, 112, 81, 115, 73, 107) L = (1, 72)(2, 69)(3, 78)(4, 79)(5, 80)(6, 70)(7, 71)(8, 73)(9, 81)(10, 86)(11, 87)(12, 88)(13, 89)(14, 74)(15, 75)(16, 76)(17, 77)(18, 94)(19, 95)(20, 96)(21, 97)(22, 82)(23, 83)(24, 84)(25, 85)(26, 102)(27, 101)(28, 99)(29, 98)(30, 90)(31, 91)(32, 92)(33, 93)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.455 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.432 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (R * Y1)^2, (Y3^-1, Y2^-1), Y1^2 * Y2^-1 * Y1 * Y2^-1, Y3 * Y2 * Y3 * Y2 * Y3, Y2 * Y1 * Y2^9 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 9, 43, 15, 49, 20, 54, 22, 56, 27, 61, 32, 66, 34, 68, 30, 64, 25, 59, 23, 57, 18, 52, 13, 47, 11, 45, 4, 38)(3, 37, 7, 41, 14, 48, 16, 50, 21, 55, 26, 60, 28, 62, 33, 67, 31, 65, 29, 63, 24, 58, 19, 53, 17, 51, 12, 46, 5, 39, 8, 42, 10, 44)(69, 103, 71, 105, 77, 111, 84, 118, 90, 124, 96, 130, 102, 136, 97, 131, 91, 125, 85, 119, 79, 113, 76, 110, 70, 104, 75, 109, 83, 117, 89, 123, 95, 129, 101, 135, 98, 132, 92, 126, 86, 120, 80, 114, 72, 106, 78, 112, 74, 108, 82, 116, 88, 122, 94, 128, 100, 134, 99, 133, 93, 127, 87, 121, 81, 115, 73, 107) L = (1, 72)(2, 69)(3, 78)(4, 79)(5, 80)(6, 70)(7, 71)(8, 73)(9, 74)(10, 76)(11, 81)(12, 85)(13, 86)(14, 75)(15, 77)(16, 82)(17, 87)(18, 91)(19, 92)(20, 83)(21, 84)(22, 88)(23, 93)(24, 97)(25, 98)(26, 89)(27, 90)(28, 94)(29, 99)(30, 102)(31, 101)(32, 95)(33, 96)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.464 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.433 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y3^-1 * Y1^-1, Y1 * Y3, (Y2^-1, Y1), (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1 * Y3^-1, Y2^8 * Y1^-1 * Y2 * Y1^-1 * Y2, Y3^-15 * Y1^2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 13, 47, 15, 49, 20, 54, 25, 59, 27, 61, 32, 66, 34, 68, 29, 63, 22, 56, 24, 58, 17, 51, 9, 43, 11, 45, 4, 38)(3, 37, 7, 41, 12, 46, 5, 39, 8, 42, 14, 48, 19, 53, 21, 55, 26, 60, 31, 65, 33, 67, 28, 62, 30, 64, 23, 57, 16, 50, 18, 52, 10, 44)(69, 103, 71, 105, 77, 111, 84, 118, 90, 124, 96, 130, 100, 134, 94, 128, 88, 122, 82, 116, 74, 108, 80, 114, 72, 106, 78, 112, 85, 119, 91, 125, 97, 131, 101, 135, 95, 129, 89, 123, 83, 117, 76, 110, 70, 104, 75, 109, 79, 113, 86, 120, 92, 126, 98, 132, 102, 136, 99, 133, 93, 127, 87, 121, 81, 115, 73, 107) L = (1, 72)(2, 69)(3, 78)(4, 79)(5, 80)(6, 70)(7, 71)(8, 73)(9, 85)(10, 86)(11, 77)(12, 75)(13, 74)(14, 76)(15, 81)(16, 91)(17, 92)(18, 84)(19, 82)(20, 83)(21, 87)(22, 97)(23, 98)(24, 90)(25, 88)(26, 89)(27, 93)(28, 101)(29, 102)(30, 96)(31, 94)(32, 95)(33, 99)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.461 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.434 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y3^-1, Y2), Y2 * Y1^-1 * Y2^-1 * Y3^-1, (R * Y3)^2, (Y2, Y1^-1), (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2^-5 * Y1^-1 * Y2^-1, Y3 * Y2^-1 * Y3^2 * Y2^-1 * Y1^-3, Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-4, Y1^3 * Y2^-1 * Y1 * Y3^-1 * Y2^-3, Y3^-1 * Y1^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 26, 60, 24, 58, 13, 47, 18, 52, 30, 64, 33, 67, 20, 54, 9, 43, 17, 51, 29, 63, 22, 56, 11, 45, 4, 38)(3, 37, 7, 41, 15, 49, 27, 61, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 28, 62, 32, 66, 19, 53, 25, 59, 31, 65, 34, 68, 21, 55, 10, 44)(69, 103, 71, 105, 77, 111, 87, 121, 92, 126, 80, 114, 72, 106, 78, 112, 88, 122, 100, 134, 94, 128, 91, 125, 79, 113, 89, 123, 101, 135, 96, 130, 82, 116, 95, 129, 90, 124, 102, 136, 98, 132, 84, 118, 74, 108, 83, 117, 97, 131, 99, 133, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 93, 127, 81, 115, 73, 107) L = (1, 72)(2, 69)(3, 78)(4, 79)(5, 80)(6, 70)(7, 71)(8, 73)(9, 88)(10, 89)(11, 90)(12, 91)(13, 92)(14, 74)(15, 75)(16, 76)(17, 77)(18, 81)(19, 100)(20, 101)(21, 102)(22, 97)(23, 95)(24, 94)(25, 87)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 93)(32, 96)(33, 98)(34, 99)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.468 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.435 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (Y2, Y1^-1), Y2^-1 * Y1 * Y2^-5, Y2 * Y3 * Y2 * Y3 * Y1^-4, Y3 * Y2 * Y3^2 * Y2 * Y1^-3, Y1 * Y2 * Y1^2 * Y2^3 * Y1 * Y3^-1, Y2 * Y3 * Y2 * Y1^12, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 26, 60, 20, 54, 9, 43, 17, 51, 29, 63, 33, 67, 24, 58, 13, 47, 18, 52, 30, 64, 22, 56, 11, 45, 4, 38)(3, 37, 7, 41, 15, 49, 27, 61, 34, 68, 25, 59, 19, 53, 31, 65, 32, 66, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 28, 62, 21, 55, 10, 44)(69, 103, 71, 105, 77, 111, 87, 121, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 99, 133, 98, 132, 84, 118, 74, 108, 83, 117, 97, 131, 100, 134, 90, 124, 96, 130, 82, 116, 95, 129, 101, 135, 91, 125, 79, 113, 89, 123, 94, 128, 102, 136, 92, 126, 80, 114, 72, 106, 78, 112, 88, 122, 93, 127, 81, 115, 73, 107) L = (1, 72)(2, 69)(3, 78)(4, 79)(5, 80)(6, 70)(7, 71)(8, 73)(9, 88)(10, 89)(11, 90)(12, 91)(13, 92)(14, 74)(15, 75)(16, 76)(17, 77)(18, 81)(19, 93)(20, 94)(21, 96)(22, 98)(23, 100)(24, 101)(25, 102)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 99)(33, 97)(34, 95)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.465 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.436 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (Y3^-1, Y2^-1), (R * Y1)^2, (Y1^-1, Y2), (R * Y2)^2, (R * Y3)^2, Y2^2 * Y1^2 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y1 * Y2^2 * Y3^-1, Y2 * Y3 * Y2 * Y3^6, Y1^5 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y1 * Y2^-1 * Y1^3 * Y3^-3 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-4, Y2^-2 * Y3^-2 * Y2^-2 * Y3^-2 * Y2^-2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 26, 60, 31, 65, 20, 54, 9, 43, 17, 51, 24, 58, 13, 47, 18, 52, 28, 62, 33, 67, 22, 56, 11, 45, 4, 38)(3, 37, 7, 41, 15, 49, 25, 59, 29, 63, 34, 68, 30, 64, 19, 53, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 27, 61, 32, 66, 21, 55, 10, 44)(69, 103, 71, 105, 77, 111, 87, 121, 90, 124, 100, 134, 94, 128, 97, 131, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 91, 125, 79, 113, 89, 123, 99, 133, 102, 136, 96, 130, 84, 118, 74, 108, 83, 117, 92, 126, 80, 114, 72, 106, 78, 112, 88, 122, 98, 132, 101, 135, 95, 129, 82, 116, 93, 127, 81, 115, 73, 107) L = (1, 72)(2, 69)(3, 78)(4, 79)(5, 80)(6, 70)(7, 71)(8, 73)(9, 88)(10, 89)(11, 90)(12, 91)(13, 92)(14, 74)(15, 75)(16, 76)(17, 77)(18, 81)(19, 98)(20, 99)(21, 100)(22, 101)(23, 87)(24, 85)(25, 83)(26, 82)(27, 84)(28, 86)(29, 93)(30, 102)(31, 94)(32, 95)(33, 96)(34, 97)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.466 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.437 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, Y1 * Y3, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-2 * Y3^-1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y2^-2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y1^-3, Y1^3 * Y2 * Y1 * Y2 * Y1 * Y3^-2, Y3 * Y2^-1 * Y3 * Y2^-2 * Y3^2 * Y2^-3, Y3 * Y2^2 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y1 * Y2^-1 * Y1 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 26, 60, 32, 66, 24, 58, 13, 47, 18, 52, 20, 54, 9, 43, 17, 51, 28, 62, 30, 64, 22, 56, 11, 45, 4, 38)(3, 37, 7, 41, 15, 49, 27, 61, 31, 65, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 19, 53, 29, 63, 34, 68, 33, 67, 25, 59, 21, 55, 10, 44)(69, 103, 71, 105, 77, 111, 87, 121, 82, 116, 95, 129, 98, 132, 101, 135, 92, 126, 80, 114, 72, 106, 78, 112, 88, 122, 84, 118, 74, 108, 83, 117, 96, 130, 102, 136, 100, 134, 91, 125, 79, 113, 89, 123, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 97, 131, 94, 128, 99, 133, 90, 124, 93, 127, 81, 115, 73, 107) L = (1, 72)(2, 69)(3, 78)(4, 79)(5, 80)(6, 70)(7, 71)(8, 73)(9, 88)(10, 89)(11, 90)(12, 91)(13, 92)(14, 74)(15, 75)(16, 76)(17, 77)(18, 81)(19, 84)(20, 86)(21, 93)(22, 98)(23, 99)(24, 100)(25, 101)(26, 82)(27, 83)(28, 85)(29, 87)(30, 96)(31, 95)(32, 94)(33, 102)(34, 97)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.463 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.438 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, Y2 * Y1^-1 * Y2 * Y1^-3, Y3^3 * Y2^2 * Y1^-1, Y2 * Y3^-1 * Y2^7, Y2 * Y1^-1 * Y2 * Y1^14, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 9, 43, 17, 51, 24, 58, 31, 65, 27, 61, 30, 64, 33, 67, 28, 62, 21, 55, 13, 47, 18, 52, 11, 45, 4, 38)(3, 37, 7, 41, 15, 49, 23, 57, 19, 53, 25, 59, 32, 66, 34, 68, 29, 63, 22, 56, 26, 60, 20, 54, 12, 46, 5, 39, 8, 42, 16, 50, 10, 44)(69, 103, 71, 105, 77, 111, 87, 121, 95, 129, 97, 131, 89, 123, 80, 114, 72, 106, 78, 112, 82, 116, 91, 125, 99, 133, 102, 136, 96, 130, 88, 122, 79, 113, 84, 118, 74, 108, 83, 117, 92, 126, 100, 134, 101, 135, 94, 128, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 93, 127, 98, 132, 90, 124, 81, 115, 73, 107) L = (1, 72)(2, 69)(3, 78)(4, 79)(5, 80)(6, 70)(7, 71)(8, 73)(9, 82)(10, 84)(11, 86)(12, 88)(13, 89)(14, 74)(15, 75)(16, 76)(17, 77)(18, 81)(19, 91)(20, 94)(21, 96)(22, 97)(23, 83)(24, 85)(25, 87)(26, 90)(27, 99)(28, 101)(29, 102)(30, 95)(31, 92)(32, 93)(33, 98)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.456 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.439 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3^-1 * Y1^-1, (R * Y2)^2, (Y2, Y1^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y3 * Y2^-2 * Y1^-3, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y2^2 * Y3 * Y2^6, Y1^2 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-4, Y2^-2 * Y1^13 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 13, 47, 18, 52, 24, 58, 31, 65, 30, 64, 27, 61, 33, 67, 29, 63, 20, 54, 9, 43, 17, 51, 11, 45, 4, 38)(3, 37, 7, 41, 15, 49, 12, 46, 5, 39, 8, 42, 16, 50, 23, 57, 22, 56, 26, 60, 32, 66, 34, 68, 28, 62, 19, 53, 25, 59, 21, 55, 10, 44)(69, 103, 71, 105, 77, 111, 87, 121, 95, 129, 94, 128, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 93, 127, 101, 135, 100, 134, 92, 126, 84, 118, 74, 108, 83, 117, 79, 113, 89, 123, 97, 131, 102, 136, 99, 133, 91, 125, 82, 116, 80, 114, 72, 106, 78, 112, 88, 122, 96, 130, 98, 132, 90, 124, 81, 115, 73, 107) L = (1, 72)(2, 69)(3, 78)(4, 79)(5, 80)(6, 70)(7, 71)(8, 73)(9, 88)(10, 89)(11, 85)(12, 83)(13, 82)(14, 74)(15, 75)(16, 76)(17, 77)(18, 81)(19, 96)(20, 97)(21, 93)(22, 91)(23, 84)(24, 86)(25, 87)(26, 90)(27, 98)(28, 102)(29, 101)(30, 99)(31, 92)(32, 94)(33, 95)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.454 Graph:: bipartite v = 3 e = 68 f = 35 degree seq :: [ 34^2, 68 ] E16.440 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y2^3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^11, (Y3^-1 * Y1^-1)^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 12, 46, 18, 52, 24, 58, 30, 64, 29, 63, 23, 57, 17, 51, 11, 45, 5, 39, 8, 42, 14, 48, 20, 54, 26, 60, 32, 66, 34, 68, 33, 67, 27, 61, 21, 55, 15, 49, 9, 43, 3, 37, 7, 41, 13, 47, 19, 53, 25, 59, 31, 65, 28, 62, 22, 56, 16, 50, 10, 44, 4, 38)(69, 103, 71, 105, 76, 110, 70, 104, 75, 109, 82, 116, 74, 108, 81, 115, 88, 122, 80, 114, 87, 121, 94, 128, 86, 120, 93, 127, 100, 134, 92, 126, 99, 133, 102, 136, 98, 132, 96, 130, 101, 135, 97, 131, 90, 124, 95, 129, 91, 125, 84, 118, 89, 123, 85, 119, 78, 112, 83, 117, 79, 113, 72, 106, 77, 111, 73, 107) L = (1, 71)(2, 75)(3, 76)(4, 77)(5, 69)(6, 81)(7, 82)(8, 70)(9, 73)(10, 83)(11, 72)(12, 87)(13, 88)(14, 74)(15, 79)(16, 89)(17, 78)(18, 93)(19, 94)(20, 80)(21, 85)(22, 95)(23, 84)(24, 99)(25, 100)(26, 86)(27, 91)(28, 101)(29, 90)(30, 96)(31, 102)(32, 92)(33, 97)(34, 98)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.450 Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.441 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y2^-3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-11, (Y3^-1 * Y1^-1)^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 12, 46, 18, 52, 24, 58, 30, 64, 28, 62, 22, 56, 16, 50, 10, 44, 3, 37, 7, 41, 13, 47, 19, 53, 25, 59, 31, 65, 34, 68, 33, 67, 27, 61, 21, 55, 15, 49, 9, 43, 5, 39, 8, 42, 14, 48, 20, 54, 26, 60, 32, 66, 29, 63, 23, 57, 17, 51, 11, 45, 4, 38)(69, 103, 71, 105, 77, 111, 72, 106, 78, 112, 83, 117, 79, 113, 84, 118, 89, 123, 85, 119, 90, 124, 95, 129, 91, 125, 96, 130, 101, 135, 97, 131, 98, 132, 102, 136, 100, 134, 92, 126, 99, 133, 94, 128, 86, 120, 93, 127, 88, 122, 80, 114, 87, 121, 82, 116, 74, 108, 81, 115, 76, 110, 70, 104, 75, 109, 73, 107) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 81)(7, 73)(8, 70)(9, 72)(10, 83)(11, 84)(12, 87)(13, 76)(14, 74)(15, 79)(16, 89)(17, 90)(18, 93)(19, 82)(20, 80)(21, 85)(22, 95)(23, 96)(24, 99)(25, 88)(26, 86)(27, 91)(28, 101)(29, 98)(30, 102)(31, 94)(32, 92)(33, 97)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.453 Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.442 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1, Y2^-1), Y2^4 * Y1^-1 * Y2, Y1^-2 * Y2 * Y1^-5, (Y3^-1 * Y1^-1)^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 24, 58, 20, 54, 10, 44, 3, 37, 7, 41, 15, 49, 25, 59, 32, 66, 29, 63, 19, 53, 9, 43, 17, 51, 27, 61, 33, 67, 31, 65, 23, 57, 13, 47, 18, 52, 28, 62, 34, 68, 30, 64, 22, 56, 12, 46, 5, 39, 8, 42, 16, 50, 26, 60, 21, 55, 11, 45, 4, 38)(69, 103, 71, 105, 77, 111, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 96, 130, 84, 118, 74, 108, 83, 117, 95, 129, 102, 136, 94, 128, 82, 116, 93, 127, 101, 135, 98, 132, 89, 123, 92, 126, 100, 134, 99, 133, 90, 124, 79, 113, 88, 122, 97, 131, 91, 125, 80, 114, 72, 106, 78, 112, 87, 121, 81, 115, 73, 107) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 86)(10, 87)(11, 88)(12, 72)(13, 73)(14, 93)(15, 95)(16, 74)(17, 96)(18, 76)(19, 81)(20, 97)(21, 92)(22, 79)(23, 80)(24, 100)(25, 101)(26, 82)(27, 102)(28, 84)(29, 91)(30, 89)(31, 90)(32, 99)(33, 98)(34, 94)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.448 Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.443 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^-3 * Y1^-1 * Y2^-2, Y2^2 * Y1^-1 * Y2^3 * Y1^2, Y1^-6 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-2 * Y2^2 * Y1^-3, (Y3^-1 * Y1^-1)^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 24, 58, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 26, 60, 32, 66, 29, 63, 19, 53, 13, 47, 18, 52, 28, 62, 34, 68, 30, 64, 20, 54, 9, 43, 17, 51, 27, 61, 33, 67, 31, 65, 21, 55, 10, 44, 3, 37, 7, 41, 15, 49, 25, 59, 22, 56, 11, 45, 4, 38)(69, 103, 71, 105, 77, 111, 87, 121, 80, 114, 72, 106, 78, 112, 88, 122, 97, 131, 91, 125, 79, 113, 89, 123, 98, 132, 100, 134, 92, 126, 90, 124, 99, 133, 102, 136, 94, 128, 82, 116, 93, 127, 101, 135, 96, 130, 84, 118, 74, 108, 83, 117, 95, 129, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 81, 115, 73, 107) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 93)(15, 95)(16, 74)(17, 81)(18, 76)(19, 80)(20, 97)(21, 98)(22, 99)(23, 79)(24, 90)(25, 101)(26, 82)(27, 86)(28, 84)(29, 91)(30, 100)(31, 102)(32, 92)(33, 96)(34, 94)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.449 Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.444 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2 * Y1^-1 * Y2 * Y1^-3, Y2^-1 * Y1^-1 * Y2^-6 * Y1^-2, (Y3^-1 * Y1^-1)^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 9, 43, 17, 51, 24, 58, 31, 65, 27, 61, 33, 67, 29, 63, 22, 56, 26, 60, 20, 54, 12, 46, 5, 39, 8, 42, 16, 50, 10, 44, 3, 37, 7, 41, 15, 49, 23, 57, 19, 53, 25, 59, 32, 66, 30, 64, 34, 68, 28, 62, 21, 55, 13, 47, 18, 52, 11, 45, 4, 38)(69, 103, 71, 105, 77, 111, 87, 121, 95, 129, 102, 136, 94, 128, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 93, 127, 101, 135, 96, 130, 88, 122, 79, 113, 84, 118, 74, 108, 83, 117, 92, 126, 100, 134, 97, 131, 89, 123, 80, 114, 72, 106, 78, 112, 82, 116, 91, 125, 99, 133, 98, 132, 90, 124, 81, 115, 73, 107) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 82)(11, 84)(12, 72)(13, 73)(14, 91)(15, 92)(16, 74)(17, 93)(18, 76)(19, 95)(20, 79)(21, 80)(22, 81)(23, 99)(24, 100)(25, 101)(26, 86)(27, 102)(28, 88)(29, 89)(30, 90)(31, 98)(32, 97)(33, 96)(34, 94)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.451 Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.445 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1), Y1^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-7 * Y1^3, Y2^2 * Y1^2 * Y2^-3 * Y1^-2 * Y2, (Y3^-1 * Y1^-1)^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 13, 47, 18, 52, 24, 58, 31, 65, 30, 64, 34, 68, 28, 62, 19, 53, 25, 59, 21, 55, 10, 44, 3, 37, 7, 41, 15, 49, 12, 46, 5, 39, 8, 42, 16, 50, 23, 57, 22, 56, 26, 60, 32, 66, 27, 61, 33, 67, 29, 63, 20, 54, 9, 43, 17, 51, 11, 45, 4, 38)(69, 103, 71, 105, 77, 111, 87, 121, 95, 129, 99, 133, 91, 125, 82, 116, 80, 114, 72, 106, 78, 112, 88, 122, 96, 130, 100, 134, 92, 126, 84, 118, 74, 108, 83, 117, 79, 113, 89, 123, 97, 131, 102, 136, 94, 128, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 93, 127, 101, 135, 98, 132, 90, 124, 81, 115, 73, 107) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 80)(15, 79)(16, 74)(17, 93)(18, 76)(19, 95)(20, 96)(21, 97)(22, 81)(23, 82)(24, 84)(25, 101)(26, 86)(27, 99)(28, 100)(29, 102)(30, 90)(31, 91)(32, 92)(33, 98)(34, 94)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.447 Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.446 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^4 * Y1^-1 * Y2 * Y1^-2, Y1^-3 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, (Y3^-1 * Y1^-1)^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 26, 60, 25, 59, 32, 66, 20, 54, 9, 43, 17, 51, 29, 63, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 28, 62, 34, 68, 33, 67, 21, 55, 10, 44, 3, 37, 7, 41, 15, 49, 27, 61, 24, 58, 13, 47, 18, 52, 30, 64, 19, 53, 31, 65, 22, 56, 11, 45, 4, 38)(69, 103, 71, 105, 77, 111, 87, 121, 96, 130, 82, 116, 95, 129, 91, 125, 79, 113, 89, 123, 100, 134, 86, 120, 76, 110, 70, 104, 75, 109, 85, 119, 99, 133, 102, 136, 94, 128, 92, 126, 80, 114, 72, 106, 78, 112, 88, 122, 98, 132, 84, 118, 74, 108, 83, 117, 97, 131, 90, 124, 101, 135, 93, 127, 81, 115, 73, 107) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 95)(15, 97)(16, 74)(17, 99)(18, 76)(19, 96)(20, 98)(21, 100)(22, 101)(23, 79)(24, 80)(25, 81)(26, 92)(27, 91)(28, 82)(29, 90)(30, 84)(31, 102)(32, 86)(33, 93)(34, 94)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.452 Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.447 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^-2 * Y3^-2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3^-1), Y2^-1 * Y3^16, Y2^6 * Y3^-1 * Y2^2 * Y3^-7 * Y2, Y2^17, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^34 ] Map:: R = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68)(69, 103, 70, 104, 74, 108, 79, 113, 83, 117, 87, 121, 91, 125, 95, 129, 99, 133, 101, 135, 98, 132, 93, 127, 90, 124, 85, 119, 82, 116, 77, 111, 72, 106)(71, 105, 75, 109, 73, 107, 76, 110, 80, 114, 84, 118, 88, 122, 92, 126, 96, 130, 100, 134, 102, 136, 97, 131, 94, 128, 89, 123, 86, 120, 81, 115, 78, 112) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 73)(7, 72)(8, 70)(9, 81)(10, 82)(11, 76)(12, 74)(13, 85)(14, 86)(15, 80)(16, 79)(17, 89)(18, 90)(19, 84)(20, 83)(21, 93)(22, 94)(23, 88)(24, 87)(25, 97)(26, 98)(27, 92)(28, 91)(29, 101)(30, 102)(31, 96)(32, 95)(33, 100)(34, 99)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.445 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.448 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y3^4 * Y2^-1 * Y3^2, (Y2^-3 * Y3)^2, Y2 * Y3 * Y2^2 * Y3^3 * Y2^2, (Y2^-1 * Y3)^34, (Y3^-1 * Y1^-1)^34 ] Map:: R = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68)(69, 103, 70, 104, 74, 108, 82, 116, 94, 128, 88, 122, 77, 111, 85, 119, 97, 131, 101, 135, 92, 126, 81, 115, 86, 120, 98, 132, 90, 124, 79, 113, 72, 106)(71, 105, 75, 109, 83, 117, 95, 129, 102, 136, 93, 127, 87, 121, 99, 133, 100, 134, 91, 125, 80, 114, 73, 107, 76, 110, 84, 118, 96, 130, 89, 123, 78, 112) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 95)(15, 97)(16, 74)(17, 99)(18, 76)(19, 86)(20, 93)(21, 94)(22, 96)(23, 79)(24, 80)(25, 81)(26, 102)(27, 101)(28, 82)(29, 100)(30, 84)(31, 98)(32, 90)(33, 91)(34, 92)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.442 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.449 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2), Y3^-4 * Y2^-1 * Y3^-2, Y2^-3 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2, Y2 * Y3^-1 * Y2^3 * Y3^-3 * Y2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^2 * Y3^-1, (Y3^-1 * Y1^-1)^34 ] Map:: R = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68)(69, 103, 70, 104, 74, 108, 82, 116, 94, 128, 92, 126, 81, 115, 86, 120, 98, 132, 101, 135, 88, 122, 77, 111, 85, 119, 97, 131, 90, 124, 79, 113, 72, 106)(71, 105, 75, 109, 83, 117, 95, 129, 91, 125, 80, 114, 73, 107, 76, 110, 84, 118, 96, 130, 100, 134, 87, 121, 93, 127, 99, 133, 102, 136, 89, 123, 78, 112) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 95)(15, 97)(16, 74)(17, 93)(18, 76)(19, 92)(20, 100)(21, 101)(22, 102)(23, 79)(24, 80)(25, 81)(26, 91)(27, 90)(28, 82)(29, 99)(30, 84)(31, 86)(32, 94)(33, 96)(34, 98)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.443 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.450 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y3^-1 * Y2 * Y3^-1 * Y2^2 * Y3^-2, Y2^-6 * Y3^-1 * Y2^-1 * Y3^-1, Y2^4 * Y3 * Y2 * Y3 * Y2^2, (Y3^-1 * Y1^-1)^34 ] Map:: R = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68)(69, 103, 70, 104, 74, 108, 82, 116, 94, 128, 100, 134, 92, 126, 81, 115, 86, 120, 88, 122, 77, 111, 85, 119, 96, 130, 98, 132, 90, 124, 79, 113, 72, 106)(71, 105, 75, 109, 83, 117, 95, 129, 99, 133, 91, 125, 80, 114, 73, 107, 76, 110, 84, 118, 87, 121, 97, 131, 102, 136, 101, 135, 93, 127, 89, 123, 78, 112) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 95)(15, 96)(16, 74)(17, 97)(18, 76)(19, 82)(20, 84)(21, 86)(22, 93)(23, 79)(24, 80)(25, 81)(26, 99)(27, 98)(28, 102)(29, 94)(30, 101)(31, 90)(32, 91)(33, 92)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.440 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.451 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y2 * Y3 * Y2 * Y3^3 * Y2, Y2^6 * Y3^-1 * Y2 * Y3^-1, Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^-1 * Y3 * Y2^4, (Y3^-1 * Y1^-1)^34 ] Map:: R = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68)(69, 103, 70, 104, 74, 108, 82, 116, 94, 128, 99, 133, 88, 122, 77, 111, 85, 119, 92, 126, 81, 115, 86, 120, 96, 130, 101, 135, 90, 124, 79, 113, 72, 106)(71, 105, 75, 109, 83, 117, 93, 127, 97, 131, 102, 136, 98, 132, 87, 121, 91, 125, 80, 114, 73, 107, 76, 110, 84, 118, 95, 129, 100, 134, 89, 123, 78, 112) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 93)(15, 92)(16, 74)(17, 91)(18, 76)(19, 90)(20, 98)(21, 99)(22, 100)(23, 79)(24, 80)(25, 81)(26, 97)(27, 82)(28, 84)(29, 86)(30, 101)(31, 102)(32, 94)(33, 95)(34, 96)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.444 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.452 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (Y3^-1, Y2), (R * Y3)^2, (R * Y2)^2, Y3 * Y2 * Y3 * Y2^2, Y2 * Y3^-1 * Y2 * Y3^-9, (Y2^-1 * Y3)^34, (Y3^-1 * Y1^-1)^34 ] Map:: R = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68)(69, 103, 70, 104, 74, 108, 81, 115, 83, 117, 88, 122, 93, 127, 95, 129, 100, 134, 102, 136, 97, 131, 90, 124, 92, 126, 85, 119, 77, 111, 79, 113, 72, 106)(71, 105, 75, 109, 80, 114, 73, 107, 76, 110, 82, 116, 87, 121, 89, 123, 94, 128, 99, 133, 101, 135, 96, 130, 98, 132, 91, 125, 84, 118, 86, 120, 78, 112) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 80)(7, 79)(8, 70)(9, 84)(10, 85)(11, 86)(12, 72)(13, 73)(14, 74)(15, 76)(16, 90)(17, 91)(18, 92)(19, 81)(20, 82)(21, 83)(22, 96)(23, 97)(24, 98)(25, 87)(26, 88)(27, 89)(28, 100)(29, 101)(30, 102)(31, 93)(32, 94)(33, 95)(34, 99)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.446 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.453 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3^-2 * Y2^3, Y3^-10 * Y2^-2, Y2^2 * Y3^10, Y3^-1 * Y2^-1 * Y3^-9 * Y2^-1, (Y3^-1 * Y1^-1)^34 ] Map:: R = (1, 35)(2, 36)(3, 37)(4, 38)(5, 39)(6, 40)(7, 41)(8, 42)(9, 43)(10, 44)(11, 45)(12, 46)(13, 47)(14, 48)(15, 49)(16, 50)(17, 51)(18, 52)(19, 53)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 59)(26, 60)(27, 61)(28, 62)(29, 63)(30, 64)(31, 65)(32, 66)(33, 67)(34, 68)(69, 103, 70, 104, 74, 108, 77, 111, 83, 117, 88, 122, 90, 124, 95, 129, 100, 134, 102, 136, 98, 132, 93, 127, 91, 125, 86, 120, 81, 115, 79, 113, 72, 106)(71, 105, 75, 109, 82, 116, 84, 118, 89, 123, 94, 128, 96, 130, 101, 135, 99, 133, 97, 131, 92, 126, 87, 121, 85, 119, 80, 114, 73, 107, 76, 110, 78, 112) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 82)(7, 83)(8, 70)(9, 84)(10, 74)(11, 76)(12, 72)(13, 73)(14, 88)(15, 89)(16, 90)(17, 79)(18, 80)(19, 81)(20, 94)(21, 95)(22, 96)(23, 85)(24, 86)(25, 87)(26, 100)(27, 101)(28, 102)(29, 91)(30, 92)(31, 93)(32, 99)(33, 98)(34, 97)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.441 Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.454 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^8 * Y1 * Y3^7 * Y1, (Y3 * Y2^-1)^17, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 11, 45, 15, 49, 19, 53, 23, 57, 27, 61, 31, 65, 34, 68, 30, 64, 26, 60, 22, 56, 18, 52, 14, 48, 10, 44, 5, 39, 8, 42, 3, 37, 7, 41, 12, 46, 16, 50, 20, 54, 24, 58, 28, 62, 32, 66, 33, 67, 29, 63, 25, 59, 21, 55, 17, 51, 13, 47, 9, 43, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 74)(4, 76)(5, 69)(6, 80)(7, 79)(8, 70)(9, 73)(10, 72)(11, 84)(12, 83)(13, 78)(14, 77)(15, 88)(16, 87)(17, 82)(18, 81)(19, 92)(20, 91)(21, 86)(22, 85)(23, 96)(24, 95)(25, 90)(26, 89)(27, 100)(28, 99)(29, 94)(30, 93)(31, 101)(32, 102)(33, 98)(34, 97)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.439 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.455 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1^5, Y3^4 * Y1^-1 * Y3 * Y1^-1 * Y3, Y3 * Y1 * Y3 * Y1 * Y3^3 * Y1^2, Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1^-1, (Y3 * Y2^-1)^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 21, 55, 10, 44, 3, 37, 7, 41, 15, 49, 26, 60, 31, 65, 20, 54, 9, 43, 17, 51, 27, 61, 34, 68, 25, 59, 30, 64, 19, 53, 29, 63, 33, 67, 24, 58, 13, 47, 18, 52, 28, 62, 32, 66, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 22, 56, 11, 45, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 94)(15, 95)(16, 74)(17, 97)(18, 76)(19, 96)(20, 98)(21, 99)(22, 82)(23, 79)(24, 80)(25, 81)(26, 102)(27, 101)(28, 84)(29, 100)(30, 86)(31, 93)(32, 90)(33, 91)(34, 92)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.431 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.456 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (Y3, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^6, Y3^-2 * Y1^-1 * Y3^-4 * Y1^-1, (Y3 * Y2^-1)^17, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2 * Y3 * Y1^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 26, 60, 31, 65, 24, 58, 13, 47, 18, 52, 28, 62, 32, 66, 19, 53, 29, 63, 25, 59, 30, 64, 33, 67, 20, 54, 9, 43, 17, 51, 27, 61, 34, 68, 21, 55, 10, 44, 3, 37, 7, 41, 15, 49, 22, 56, 11, 45, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 90)(15, 95)(16, 74)(17, 97)(18, 76)(19, 99)(20, 100)(21, 101)(22, 102)(23, 79)(24, 80)(25, 81)(26, 82)(27, 93)(28, 84)(29, 92)(30, 86)(31, 91)(32, 94)(33, 96)(34, 98)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.438 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.457 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (Y1^-1, Y3^-1), (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3 * Y1^-3 * Y3, Y3 * Y1 * Y3^6 * Y1, (Y3 * Y2^-1)^17, Y1^-1 * Y3^3 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 19, 53, 28, 62, 33, 67, 30, 64, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 20, 54, 9, 43, 17, 51, 27, 61, 34, 68, 31, 65, 24, 58, 13, 47, 18, 52, 21, 55, 10, 44, 3, 37, 7, 41, 15, 49, 26, 60, 29, 63, 32, 66, 25, 59, 22, 56, 11, 45, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 94)(15, 95)(16, 74)(17, 96)(18, 76)(19, 97)(20, 82)(21, 84)(22, 86)(23, 79)(24, 80)(25, 81)(26, 102)(27, 101)(28, 100)(29, 99)(30, 90)(31, 91)(32, 92)(33, 93)(34, 98)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.428 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.458 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3, Y1), (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-3 * Y3^-1, Y3^-7 * Y1^2, (Y3 * Y2^-1)^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 25, 59, 28, 62, 29, 63, 32, 66, 21, 55, 10, 44, 3, 37, 7, 41, 15, 49, 24, 58, 13, 47, 18, 52, 27, 61, 34, 68, 31, 65, 20, 54, 9, 43, 17, 51, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 26, 60, 33, 67, 30, 64, 19, 53, 22, 56, 11, 45, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 92)(15, 91)(16, 74)(17, 90)(18, 76)(19, 97)(20, 98)(21, 99)(22, 100)(23, 79)(24, 80)(25, 81)(26, 82)(27, 84)(28, 86)(29, 95)(30, 96)(31, 101)(32, 102)(33, 93)(34, 94)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.430 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.459 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y3^3 * Y1^2, (R * Y2 * Y3^-1)^2, Y1^10 * Y3^-2, Y3^2 * Y1^-10, Y1^10 * Y3^-2, (Y3 * Y2^-1)^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 20, 54, 26, 60, 32, 66, 29, 63, 23, 57, 17, 51, 9, 43, 12, 46, 5, 39, 8, 42, 15, 49, 21, 55, 27, 61, 33, 67, 30, 64, 24, 58, 18, 52, 10, 44, 3, 37, 7, 41, 13, 47, 16, 50, 22, 56, 28, 62, 34, 68, 31, 65, 25, 59, 19, 53, 11, 45, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 81)(7, 80)(8, 70)(9, 79)(10, 85)(11, 86)(12, 72)(13, 73)(14, 84)(15, 74)(16, 76)(17, 87)(18, 91)(19, 92)(20, 90)(21, 82)(22, 83)(23, 93)(24, 97)(25, 98)(26, 96)(27, 88)(28, 89)(29, 99)(30, 100)(31, 101)(32, 102)(33, 94)(34, 95)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.427 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.460 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, Y3^-1 * Y1 * Y3^-2 * Y1, (R * Y2 * Y3^-1)^2, Y1^-3 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-5, (Y3 * Y2^-1)^17, (Y1^-1 * Y3^-1)^34 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 20, 54, 26, 60, 32, 66, 31, 65, 25, 59, 19, 53, 13, 47, 10, 44, 3, 37, 7, 41, 15, 49, 21, 55, 27, 61, 33, 67, 30, 64, 24, 58, 18, 52, 12, 46, 5, 39, 8, 42, 9, 43, 16, 50, 22, 56, 28, 62, 34, 68, 29, 63, 23, 57, 17, 51, 11, 45, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 84)(8, 70)(9, 74)(10, 76)(11, 81)(12, 72)(13, 73)(14, 89)(15, 90)(16, 82)(17, 87)(18, 79)(19, 80)(20, 95)(21, 96)(22, 88)(23, 93)(24, 85)(25, 86)(26, 101)(27, 102)(28, 94)(29, 99)(30, 91)(31, 92)(32, 98)(33, 97)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.429 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.461 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^-2 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^17, (Y3 * Y2^-1)^17, (Y3^-1 * Y1^-1)^34 ] Map:: R = (1, 35, 2, 36, 3, 37, 6, 40, 7, 41, 10, 44, 11, 45, 14, 48, 15, 49, 18, 52, 19, 53, 22, 56, 23, 57, 26, 60, 27, 61, 30, 64, 31, 65, 34, 68, 33, 67, 32, 66, 29, 63, 28, 62, 25, 59, 24, 58, 21, 55, 20, 54, 17, 51, 16, 50, 13, 47, 12, 46, 9, 43, 8, 42, 5, 39, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 74)(3, 75)(4, 70)(5, 69)(6, 78)(7, 79)(8, 72)(9, 73)(10, 82)(11, 83)(12, 76)(13, 77)(14, 86)(15, 87)(16, 80)(17, 81)(18, 90)(19, 91)(20, 84)(21, 85)(22, 94)(23, 95)(24, 88)(25, 89)(26, 98)(27, 99)(28, 92)(29, 93)(30, 102)(31, 101)(32, 96)(33, 97)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.433 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.462 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, Y3 * Y1^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^17, (Y3^8 * Y1^-1)^2, (Y3 * Y2^-1)^17 ] Map:: R = (1, 35, 2, 36, 5, 39, 6, 40, 9, 43, 10, 44, 13, 47, 14, 48, 17, 51, 18, 52, 21, 55, 22, 56, 25, 59, 26, 60, 29, 63, 30, 64, 33, 67, 34, 68, 31, 65, 32, 66, 27, 61, 28, 62, 23, 57, 24, 58, 19, 53, 20, 54, 15, 49, 16, 50, 11, 45, 12, 46, 7, 41, 8, 42, 3, 37, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 72)(3, 75)(4, 76)(5, 69)(6, 70)(7, 79)(8, 80)(9, 73)(10, 74)(11, 83)(12, 84)(13, 77)(14, 78)(15, 87)(16, 88)(17, 81)(18, 82)(19, 91)(20, 92)(21, 85)(22, 86)(23, 95)(24, 96)(25, 89)(26, 90)(27, 99)(28, 100)(29, 93)(30, 94)(31, 101)(32, 102)(33, 97)(34, 98)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.426 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.463 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-4 * Y1, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2, (Y3 * Y2^-1)^17, Y1^59 * Y3^-2 * Y1^3 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 26, 60, 24, 58, 13, 47, 18, 52, 19, 53, 30, 64, 34, 68, 31, 65, 21, 55, 10, 44, 3, 37, 7, 41, 15, 49, 27, 61, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 28, 62, 33, 67, 32, 66, 25, 59, 20, 54, 9, 43, 17, 51, 29, 63, 22, 56, 11, 45, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 95)(15, 97)(16, 74)(17, 98)(18, 76)(19, 84)(20, 86)(21, 93)(22, 99)(23, 79)(24, 80)(25, 81)(26, 91)(27, 90)(28, 82)(29, 102)(30, 96)(31, 100)(32, 92)(33, 94)(34, 101)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.437 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.464 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3^3, Y1^-1 * Y3 * Y1^-2 * Y3 * Y1^-3, (Y3 * Y2^-1)^17, Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-3 * Y3 * Y1^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 26, 60, 20, 54, 9, 43, 17, 51, 25, 59, 30, 64, 34, 68, 32, 66, 23, 57, 12, 46, 5, 39, 8, 42, 16, 50, 28, 62, 21, 55, 10, 44, 3, 37, 7, 41, 15, 49, 27, 61, 33, 67, 31, 65, 19, 53, 24, 58, 13, 47, 18, 52, 29, 63, 22, 56, 11, 45, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 95)(15, 93)(16, 74)(17, 92)(18, 76)(19, 91)(20, 99)(21, 94)(22, 96)(23, 79)(24, 80)(25, 81)(26, 101)(27, 98)(28, 82)(29, 84)(30, 86)(31, 100)(32, 90)(33, 102)(34, 97)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.432 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.465 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y1^3 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^7 * Y1, (Y3 * Y2^-1)^17, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 35, 2, 36, 6, 40, 10, 44, 3, 37, 7, 41, 14, 48, 18, 52, 9, 43, 15, 49, 22, 56, 26, 60, 17, 51, 23, 57, 30, 64, 34, 68, 25, 59, 31, 65, 29, 63, 32, 66, 33, 67, 28, 62, 21, 55, 24, 58, 27, 61, 20, 54, 13, 47, 16, 50, 19, 53, 12, 46, 5, 39, 8, 42, 11, 45, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 82)(7, 83)(8, 70)(9, 85)(10, 86)(11, 74)(12, 72)(13, 73)(14, 90)(15, 91)(16, 76)(17, 93)(18, 94)(19, 79)(20, 80)(21, 81)(22, 98)(23, 99)(24, 84)(25, 101)(26, 102)(27, 87)(28, 88)(29, 89)(30, 97)(31, 96)(32, 92)(33, 95)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.435 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.466 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1), Y3 * Y1^4, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1 * Y3^-7, Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1^-1, (Y3 * Y2^-1)^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 12, 46, 5, 39, 8, 42, 14, 48, 20, 54, 13, 47, 16, 50, 22, 56, 28, 62, 21, 55, 24, 58, 30, 64, 34, 68, 29, 63, 32, 66, 25, 59, 31, 65, 33, 67, 26, 60, 17, 51, 23, 57, 27, 61, 18, 52, 9, 43, 15, 49, 19, 53, 10, 44, 3, 37, 7, 41, 11, 45, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 79)(7, 83)(8, 70)(9, 85)(10, 86)(11, 87)(12, 72)(13, 73)(14, 74)(15, 91)(16, 76)(17, 93)(18, 94)(19, 95)(20, 80)(21, 81)(22, 82)(23, 99)(24, 84)(25, 98)(26, 100)(27, 101)(28, 88)(29, 89)(30, 90)(31, 102)(32, 92)(33, 97)(34, 96)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.436 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.467 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y3^-3 * Y1^-1, Y1^7 * Y3^-1 * Y1, (Y3 * Y2^-1)^17 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 23, 57, 29, 63, 21, 55, 10, 44, 3, 37, 7, 41, 15, 49, 24, 58, 31, 65, 34, 68, 28, 62, 20, 54, 9, 43, 17, 51, 13, 47, 18, 52, 26, 60, 32, 66, 33, 67, 27, 61, 19, 53, 12, 46, 5, 39, 8, 42, 16, 50, 25, 59, 30, 64, 22, 56, 11, 45, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 87)(10, 88)(11, 89)(12, 72)(13, 73)(14, 92)(15, 81)(16, 74)(17, 80)(18, 76)(19, 79)(20, 95)(21, 96)(22, 97)(23, 99)(24, 86)(25, 82)(26, 84)(27, 90)(28, 101)(29, 102)(30, 91)(31, 94)(32, 93)(33, 98)(34, 100)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.425 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.468 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {17, 34, 34}) Quotient :: dipole Aut^+ = C34 (small group id <34, 2>) Aut = D68 (small group id <68, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1 * Y3^-3, (R * Y2 * Y3^-1)^2, Y1^4 * Y3 * Y1^4, (Y3 * Y2^-1)^17, (Y1^-1 * Y3^-1)^34 ] Map:: R = (1, 35, 2, 36, 6, 40, 14, 48, 23, 57, 29, 63, 21, 55, 12, 46, 5, 39, 8, 42, 16, 50, 25, 59, 31, 65, 34, 68, 30, 64, 22, 56, 13, 47, 18, 52, 9, 43, 17, 51, 26, 60, 32, 66, 33, 67, 27, 61, 19, 53, 10, 44, 3, 37, 7, 41, 15, 49, 24, 58, 28, 62, 20, 54, 11, 45, 4, 38)(69, 103)(70, 104)(71, 105)(72, 106)(73, 107)(74, 108)(75, 109)(76, 110)(77, 111)(78, 112)(79, 113)(80, 114)(81, 115)(82, 116)(83, 117)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(98, 132)(99, 133)(100, 134)(101, 135)(102, 136) L = (1, 71)(2, 75)(3, 77)(4, 78)(5, 69)(6, 83)(7, 85)(8, 70)(9, 84)(10, 86)(11, 87)(12, 72)(13, 73)(14, 92)(15, 94)(16, 74)(17, 93)(18, 76)(19, 81)(20, 95)(21, 79)(22, 80)(23, 96)(24, 100)(25, 82)(26, 99)(27, 90)(28, 101)(29, 88)(30, 89)(31, 91)(32, 102)(33, 98)(34, 97)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34, 68 ), ( 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68, 34, 68 ) } Outer automorphisms :: reflexible Dual of E16.434 Graph:: bipartite v = 35 e = 68 f = 3 degree seq :: [ 2^34, 68 ] E16.469 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 4, 4}) Quotient :: edge^2 Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = C3 x ((C6 x C2) : C2) (small group id <72, 30>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, Y1^3, Y2^3, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, Y3 * Y1 * Y3^2 * Y2 * Y3, Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 37, 4, 40, 12, 48, 5, 41)(2, 38, 6, 42, 17, 53, 7, 43)(3, 39, 8, 44, 22, 58, 9, 45)(10, 46, 25, 61, 13, 49, 26, 62)(11, 47, 27, 63, 14, 50, 28, 64)(15, 51, 29, 65, 18, 54, 30, 66)(16, 52, 31, 67, 19, 55, 32, 68)(20, 56, 33, 69, 23, 59, 34, 70)(21, 57, 35, 71, 24, 60, 36, 72)(73, 74, 75)(76, 82, 83)(77, 85, 86)(78, 87, 88)(79, 90, 91)(80, 92, 93)(81, 95, 96)(84, 89, 94)(97, 101, 105)(98, 102, 106)(99, 103, 107)(100, 104, 108)(109, 111, 110)(112, 119, 118)(113, 122, 121)(114, 124, 123)(115, 127, 126)(116, 129, 128)(117, 132, 131)(120, 130, 125)(133, 141, 137)(134, 142, 138)(135, 143, 139)(136, 144, 140) 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) :: { ( 16^3 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E16.471 Graph:: simple bipartite v = 33 e = 72 f = 9 degree seq :: [ 3^24, 8^9 ] E16.470 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 4, 4}) Quotient :: edge^2 Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C3 x (C3 : C4)) : C2 (small group id <72, 21>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, Y3^3, Y2^4, Y2 * Y1^-3, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y3 * Y1, Y2 * Y3^-1 * Y1^-2 * Y3 * Y1^-1, Y3^-1 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y2 * Y3 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y3 * Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 4, 40, 5, 41)(2, 38, 7, 43, 8, 44)(3, 39, 9, 45, 10, 46)(6, 42, 15, 51, 16, 52)(11, 47, 21, 57, 22, 58)(12, 48, 23, 59, 24, 60)(13, 49, 25, 61, 26, 62)(14, 50, 27, 63, 28, 64)(17, 53, 29, 65, 30, 66)(18, 54, 31, 67, 32, 68)(19, 55, 33, 69, 34, 70)(20, 56, 35, 71, 36, 72)(73, 74, 78, 75)(76, 83, 87, 84)(77, 85, 88, 86)(79, 89, 81, 90)(80, 91, 82, 92)(93, 101, 95, 103)(94, 105, 96, 107)(97, 102, 99, 104)(98, 106, 100, 108)(109, 111, 114, 110)(112, 120, 123, 119)(113, 122, 124, 121)(115, 126, 117, 125)(116, 128, 118, 127)(129, 139, 131, 137)(130, 143, 132, 141)(133, 140, 135, 138)(134, 144, 136, 142) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.472 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.471 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 4, 4}) Quotient :: loop^2 Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = C3 x ((C6 x C2) : C2) (small group id <72, 30>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, Y1^3, Y2^3, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, Y3 * Y1 * Y3^2 * Y2 * Y3, Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 37, 73, 109, 4, 40, 76, 112, 12, 48, 84, 120, 5, 41, 77, 113)(2, 38, 74, 110, 6, 42, 78, 114, 17, 53, 89, 125, 7, 43, 79, 115)(3, 39, 75, 111, 8, 44, 80, 116, 22, 58, 94, 130, 9, 45, 81, 117)(10, 46, 82, 118, 25, 61, 97, 133, 13, 49, 85, 121, 26, 62, 98, 134)(11, 47, 83, 119, 27, 63, 99, 135, 14, 50, 86, 122, 28, 64, 100, 136)(15, 51, 87, 123, 29, 65, 101, 137, 18, 54, 90, 126, 30, 66, 102, 138)(16, 52, 88, 124, 31, 67, 103, 139, 19, 55, 91, 127, 32, 68, 104, 140)(20, 56, 92, 128, 33, 69, 105, 141, 23, 59, 95, 131, 34, 70, 106, 142)(21, 57, 93, 129, 35, 71, 107, 143, 24, 60, 96, 132, 36, 72, 108, 144) L = (1, 38)(2, 39)(3, 37)(4, 46)(5, 49)(6, 51)(7, 54)(8, 56)(9, 59)(10, 47)(11, 40)(12, 53)(13, 50)(14, 41)(15, 52)(16, 42)(17, 58)(18, 55)(19, 43)(20, 57)(21, 44)(22, 48)(23, 60)(24, 45)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 61)(34, 62)(35, 63)(36, 64)(73, 111)(74, 109)(75, 110)(76, 119)(77, 122)(78, 124)(79, 127)(80, 129)(81, 132)(82, 112)(83, 118)(84, 130)(85, 113)(86, 121)(87, 114)(88, 123)(89, 120)(90, 115)(91, 126)(92, 116)(93, 128)(94, 125)(95, 117)(96, 131)(97, 141)(98, 142)(99, 143)(100, 144)(101, 133)(102, 134)(103, 135)(104, 136)(105, 137)(106, 138)(107, 139)(108, 140) local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8 ) } Outer automorphisms :: reflexible Dual of E16.469 Transitivity :: VT+ Graph:: v = 9 e = 72 f = 33 degree seq :: [ 16^9 ] E16.472 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 4, 4}) Quotient :: loop^2 Aut^+ = C3 x (C3 : C4) (small group id <36, 6>) Aut = (C3 x (C3 : C4)) : C2 (small group id <72, 21>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, Y3^3, Y2^4, Y2 * Y1^-3, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y3 * Y1, Y2 * Y3^-1 * Y1^-2 * Y3 * Y1^-1, Y3^-1 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y2 * Y3 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y3 * Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 73, 109, 4, 40, 76, 112, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 8, 44, 80, 116)(3, 39, 75, 111, 9, 45, 81, 117, 10, 46, 82, 118)(6, 42, 78, 114, 15, 51, 87, 123, 16, 52, 88, 124)(11, 47, 83, 119, 21, 57, 93, 129, 22, 58, 94, 130)(12, 48, 84, 120, 23, 59, 95, 131, 24, 60, 96, 132)(13, 49, 85, 121, 25, 61, 97, 133, 26, 62, 98, 134)(14, 50, 86, 122, 27, 63, 99, 135, 28, 64, 100, 136)(17, 53, 89, 125, 29, 65, 101, 137, 30, 66, 102, 138)(18, 54, 90, 126, 31, 67, 103, 139, 32, 68, 104, 140)(19, 55, 91, 127, 33, 69, 105, 141, 34, 70, 106, 142)(20, 56, 92, 128, 35, 71, 107, 143, 36, 72, 108, 144) L = (1, 38)(2, 42)(3, 37)(4, 47)(5, 49)(6, 39)(7, 53)(8, 55)(9, 54)(10, 56)(11, 51)(12, 40)(13, 52)(14, 41)(15, 48)(16, 50)(17, 45)(18, 43)(19, 46)(20, 44)(21, 65)(22, 69)(23, 67)(24, 71)(25, 66)(26, 70)(27, 68)(28, 72)(29, 59)(30, 63)(31, 57)(32, 61)(33, 60)(34, 64)(35, 58)(36, 62)(73, 111)(74, 109)(75, 114)(76, 120)(77, 122)(78, 110)(79, 126)(80, 128)(81, 125)(82, 127)(83, 112)(84, 123)(85, 113)(86, 124)(87, 119)(88, 121)(89, 115)(90, 117)(91, 116)(92, 118)(93, 139)(94, 143)(95, 137)(96, 141)(97, 140)(98, 144)(99, 138)(100, 142)(101, 129)(102, 133)(103, 131)(104, 135)(105, 130)(106, 134)(107, 132)(108, 136) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.470 Transitivity :: VT+ Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.473 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 4}) 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 :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y1)^2, (R * Y3)^2, Y2^4, Y1^-1 * Y2^-2 * Y1 * Y2^-2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, (Y1, Y2^-1, Y1^-1), (Y3 * Y2^-1)^4 ] 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, 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, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 21 e = 72 f = 21 degree seq :: [ 6^12, 8^9 ] E16.474 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 4}) 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, Y3^3, Y1^3, (Y2^-1, Y1), Y3 * Y2^-1 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, Y2^4, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 14, 50)(4, 40, 9, 45, 16, 52)(6, 42, 10, 46, 18, 54)(7, 43, 11, 47, 19, 55)(12, 48, 21, 57, 27, 63)(13, 49, 22, 58, 29, 65)(15, 51, 23, 59, 30, 66)(17, 53, 24, 60, 31, 67)(20, 56, 25, 61, 32, 68)(26, 62, 33, 69, 35, 71)(28, 64, 34, 70, 36, 72)(73, 109, 75, 111, 84, 120, 78, 114)(74, 110, 80, 116, 93, 129, 82, 118)(76, 112, 87, 123, 98, 134, 89, 125)(77, 113, 86, 122, 99, 135, 90, 126)(79, 115, 85, 121, 100, 136, 92, 128)(81, 117, 95, 131, 105, 141, 96, 132)(83, 119, 94, 130, 106, 142, 97, 133)(88, 124, 102, 138, 107, 143, 103, 139)(91, 127, 101, 137, 108, 144, 104, 140) L = (1, 76)(2, 81)(3, 85)(4, 79)(5, 88)(6, 92)(7, 73)(8, 94)(9, 83)(10, 97)(11, 74)(12, 98)(13, 87)(14, 101)(15, 75)(16, 91)(17, 78)(18, 104)(19, 77)(20, 89)(21, 105)(22, 95)(23, 80)(24, 82)(25, 96)(26, 100)(27, 107)(28, 84)(29, 102)(30, 86)(31, 90)(32, 103)(33, 106)(34, 93)(35, 108)(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) :: { ( 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E16.476 Graph:: simple bipartite v = 21 e = 72 f = 21 degree seq :: [ 6^12, 8^9 ] E16.475 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 4}) 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, Y1^3, Y3^3, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y1, Y3^-1), Y3 * Y2^-1 * Y3 * Y2, Y2 * Y3 * Y1 * Y2^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 12, 48, 15, 51)(4, 40, 9, 45, 17, 53)(6, 42, 22, 58, 24, 60)(7, 43, 11, 47, 21, 57)(8, 44, 25, 61, 14, 50)(10, 46, 28, 64, 23, 59)(13, 49, 26, 62, 32, 68)(16, 52, 27, 63, 19, 55)(18, 54, 29, 65, 20, 56)(30, 66, 35, 71, 31, 67)(33, 69, 36, 72, 34, 70)(73, 109, 75, 111, 85, 121, 78, 114)(74, 110, 80, 116, 98, 134, 82, 118)(76, 112, 88, 124, 103, 139, 90, 126)(77, 113, 91, 127, 104, 140, 92, 128)(79, 115, 86, 122, 105, 141, 95, 131)(81, 117, 84, 120, 102, 138, 94, 130)(83, 119, 99, 135, 108, 144, 101, 137)(87, 123, 106, 142, 96, 132, 93, 129)(89, 125, 97, 133, 107, 143, 100, 136) L = (1, 76)(2, 81)(3, 86)(4, 79)(5, 89)(6, 95)(7, 73)(8, 99)(9, 83)(10, 101)(11, 74)(12, 80)(13, 103)(14, 88)(15, 97)(16, 75)(17, 93)(18, 78)(19, 87)(20, 96)(21, 77)(22, 82)(23, 90)(24, 100)(25, 91)(26, 102)(27, 84)(28, 92)(29, 94)(30, 108)(31, 105)(32, 107)(33, 85)(34, 104)(35, 106)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 21 e = 72 f = 21 degree seq :: [ 6^12, 8^9 ] E16.476 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 4}) 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, Y3^3, Y1^3, (Y3, Y1), (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-1 * Y3 * Y2, Y2^4, Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 12, 48, 15, 51)(4, 40, 9, 45, 17, 53)(6, 42, 22, 58, 24, 60)(7, 43, 11, 47, 21, 57)(8, 44, 25, 61, 16, 52)(10, 46, 29, 65, 18, 54)(13, 49, 26, 62, 32, 68)(14, 50, 27, 63, 19, 55)(20, 56, 23, 59, 28, 64)(30, 66, 35, 71, 33, 69)(31, 67, 36, 72, 34, 70)(73, 109, 75, 111, 85, 121, 78, 114)(74, 110, 80, 116, 98, 134, 82, 118)(76, 112, 88, 124, 103, 139, 90, 126)(77, 113, 91, 127, 104, 140, 92, 128)(79, 115, 86, 122, 105, 141, 95, 131)(81, 117, 99, 135, 108, 144, 100, 136)(83, 119, 84, 120, 102, 138, 94, 130)(87, 123, 106, 142, 96, 132, 89, 125)(93, 129, 97, 133, 107, 143, 101, 137) L = (1, 76)(2, 81)(3, 86)(4, 79)(5, 89)(6, 95)(7, 73)(8, 84)(9, 83)(10, 94)(11, 74)(12, 99)(13, 103)(14, 88)(15, 91)(16, 75)(17, 93)(18, 78)(19, 97)(20, 101)(21, 77)(22, 100)(23, 90)(24, 92)(25, 87)(26, 108)(27, 80)(28, 82)(29, 96)(30, 98)(31, 105)(32, 106)(33, 85)(34, 107)(35, 104)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E16.474 Graph:: simple bipartite v = 21 e = 72 f = 21 degree seq :: [ 6^12, 8^9 ] E16.477 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 4}) Quotient :: dipole Aut^+ = (C3 x C3) : C4 (small group id <36, 7>) Aut = (C6 x C6) : C2 (small group id <72, 35>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^3, (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-1 * Y3 * Y2, Y2^4, Y2^-1 * Y1 * Y2 * Y1, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 12, 48, 8, 44)(4, 40, 9, 45, 16, 52)(6, 42, 18, 54, 10, 46)(7, 43, 11, 47, 19, 55)(13, 49, 21, 57, 26, 62)(14, 50, 27, 63, 22, 58)(15, 51, 28, 64, 23, 59)(17, 53, 31, 67, 24, 60)(20, 56, 32, 68, 25, 61)(29, 65, 33, 69, 35, 71)(30, 66, 34, 70, 36, 72)(73, 109, 75, 111, 85, 121, 78, 114)(74, 110, 80, 116, 93, 129, 82, 118)(76, 112, 87, 123, 101, 137, 89, 125)(77, 113, 84, 120, 98, 134, 90, 126)(79, 115, 86, 122, 102, 138, 92, 128)(81, 117, 95, 131, 105, 141, 96, 132)(83, 119, 94, 130, 106, 142, 97, 133)(88, 124, 100, 136, 107, 143, 103, 139)(91, 127, 99, 135, 108, 144, 104, 140) L = (1, 76)(2, 81)(3, 86)(4, 79)(5, 88)(6, 92)(7, 73)(8, 94)(9, 83)(10, 97)(11, 74)(12, 99)(13, 101)(14, 87)(15, 75)(16, 91)(17, 78)(18, 104)(19, 77)(20, 89)(21, 105)(22, 95)(23, 80)(24, 82)(25, 96)(26, 107)(27, 100)(28, 84)(29, 102)(30, 85)(31, 90)(32, 103)(33, 106)(34, 93)(35, 108)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 21 e = 72 f = 21 degree seq :: [ 6^12, 8^9 ] E16.478 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 4, 4}) Quotient :: edge^2 Aut^+ = (C3 x C3) : C4 (small group id <36, 9>) Aut = (S3 x S3) : C2 (small group id <72, 40>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2, Y2^3, Y1^3, R * Y2 * R * Y1, (R * Y3)^2, Y3^4, (Y3^-2 * Y1^-1)^2, Y3^-1 * Y2 * Y3^-2 * Y1 * Y3^-1, Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^4 ] Map:: polytopal 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, 14, 50, 21, 57)(10, 46, 23, 59, 13, 49, 24, 60)(15, 51, 29, 65, 19, 55, 30, 66)(17, 53, 31, 67, 18, 54, 32, 68)(25, 61, 33, 69, 28, 64, 34, 70)(26, 62, 35, 71, 27, 63, 36, 72)(73, 74, 76)(75, 80, 82)(77, 85, 86)(78, 87, 89)(79, 90, 91)(81, 94, 88)(83, 97, 98)(84, 99, 100)(92, 105, 101)(93, 102, 106)(95, 107, 103)(96, 104, 108)(109, 110, 112)(111, 116, 118)(113, 121, 122)(114, 123, 125)(115, 126, 127)(117, 130, 124)(119, 133, 134)(120, 135, 136)(128, 141, 137)(129, 138, 142)(131, 143, 139)(132, 140, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 16^3 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E16.483 Graph:: simple bipartite v = 33 e = 72 f = 9 degree seq :: [ 3^24, 8^9 ] E16.479 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 4, 4}) Quotient :: edge^2 Aut^+ = (C3 x C3) : C4 (small group id <36, 9>) Aut = (S3 x S3) : C2 (small group id <72, 40>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1, Y1^3, Y2^3, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, (Y3 * Y1 * Y3)^2, (Y3 * Y2 * Y3)^2, (Y3^-1 * Y1^-1)^4, (Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 37, 4, 40, 12, 48, 5, 41)(2, 38, 6, 42, 17, 53, 7, 43)(3, 39, 8, 44, 22, 58, 9, 45)(10, 46, 25, 61, 14, 50, 26, 62)(11, 47, 27, 63, 13, 49, 28, 64)(15, 51, 29, 65, 19, 55, 30, 66)(16, 52, 31, 67, 18, 54, 32, 68)(20, 56, 33, 69, 24, 60, 34, 70)(21, 57, 35, 71, 23, 59, 36, 72)(73, 74, 75)(76, 82, 83)(77, 85, 86)(78, 87, 88)(79, 90, 91)(80, 92, 93)(81, 95, 96)(84, 94, 89)(97, 105, 101)(98, 102, 106)(99, 107, 103)(100, 104, 108)(109, 111, 110)(112, 119, 118)(113, 122, 121)(114, 124, 123)(115, 127, 126)(116, 129, 128)(117, 132, 131)(120, 125, 130)(133, 137, 141)(134, 142, 138)(135, 139, 143)(136, 144, 140) 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) :: { ( 16^3 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E16.484 Graph:: simple bipartite v = 33 e = 72 f = 9 degree seq :: [ 3^24, 8^9 ] E16.480 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 4, 4}) Quotient :: edge^2 Aut^+ = (C3 x C3) : C4 (small group id <36, 9>) Aut = C2 x ((C3 x C3) : C4) (small group id <72, 45>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, Y3^3, Y2^4, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y1^-3, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y1, Y2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-1, Y3 * Y2 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y2 * Y3 * Y1 * Y3^-1 * Y2^-1 * Y3 * Y1^-1, Y3^-1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 4, 40, 5, 41)(2, 38, 7, 43, 8, 44)(3, 39, 9, 45, 10, 46)(6, 42, 15, 51, 16, 52)(11, 47, 21, 57, 22, 58)(12, 48, 23, 59, 24, 60)(13, 49, 25, 61, 26, 62)(14, 50, 27, 63, 28, 64)(17, 53, 29, 65, 30, 66)(18, 54, 31, 67, 32, 68)(19, 55, 33, 69, 34, 70)(20, 56, 35, 71, 36, 72)(73, 74, 78, 75)(76, 83, 88, 84)(77, 85, 87, 86)(79, 89, 82, 90)(80, 91, 81, 92)(93, 102, 96, 103)(94, 106, 95, 107)(97, 101, 100, 104)(98, 105, 99, 108)(109, 111, 114, 110)(112, 120, 124, 119)(113, 122, 123, 121)(115, 126, 118, 125)(116, 128, 117, 127)(129, 139, 132, 138)(130, 143, 131, 142)(133, 140, 136, 137)(134, 144, 135, 141) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.485 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.481 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 4, 4}) Quotient :: edge^2 Aut^+ = (C3 x C3) : C4 (small group id <36, 9>) Aut = C2 x ((C3 x C3) : C4) (small group id <72, 45>) |r| :: 2 Presentation :: [ R^2, Y3^3, (R * Y3)^2, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y1^4, (Y2 * Y1^-1)^2, Y2^4, R * Y1 * R * Y2, Y1 * Y2^-2 * Y1 * Y3^-1, Y1^-2 * Y2^-1 * Y3 * Y2^-1, Y2^-2 * Y3 * Y2 * Y3^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y2 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 37, 4, 40, 7, 43)(2, 38, 10, 46, 12, 48)(3, 39, 15, 51, 16, 52)(5, 41, 22, 58, 18, 54)(6, 42, 24, 60, 17, 53)(8, 44, 28, 64, 29, 65)(9, 45, 31, 67, 23, 59)(11, 47, 21, 57, 32, 68)(13, 49, 33, 69, 25, 61)(14, 50, 34, 70, 36, 72)(19, 55, 35, 71, 27, 63)(20, 56, 30, 66, 26, 62)(73, 74, 80, 77)(75, 85, 92, 83)(76, 89, 101, 91)(78, 93, 99, 97)(79, 98, 100, 87)(81, 102, 106, 88)(82, 104, 90, 105)(84, 86, 94, 103)(95, 96, 108, 107)(109, 111, 122, 114)(110, 117, 127, 119)(112, 126, 144, 128)(113, 129, 134, 131)(115, 135, 142, 118)(116, 132, 141, 124)(120, 121, 143, 136)(123, 140, 125, 139)(130, 137, 138, 133) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.486 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.482 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 4, 4}) Quotient :: edge^2 Aut^+ = (C3 x C3) : C4 (small group id <36, 9>) Aut = C2 x ((C3 x C3) : C4) (small group id <72, 45>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1 * Y1^-1, Y3^3, Y1^4, Y2^4, Y1^4, (R * Y3)^2, (Y2 * Y1^-1)^2, Y2^4, R * Y2 * R * Y1, Y2 * Y3^-1 * Y2^-2 * Y3 * Y1^-1, Y1^-1 * Y3^-1 * Y1 * Y2 * Y3 * Y2^-1, Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y3 ] Map:: polytopal non-degenerate R = (1, 37, 4, 40, 7, 43)(2, 38, 6, 42, 11, 47)(3, 39, 13, 49, 14, 50)(5, 41, 19, 55, 20, 56)(8, 44, 10, 46, 24, 60)(9, 45, 25, 61, 26, 62)(12, 48, 29, 65, 18, 54)(15, 51, 17, 53, 31, 67)(16, 52, 32, 68, 33, 69)(21, 57, 34, 70, 30, 66)(22, 58, 23, 59, 35, 71)(27, 63, 28, 64, 36, 72)(73, 74, 80, 77)(75, 79, 94, 82)(76, 87, 96, 88)(78, 90, 92, 93)(81, 83, 99, 91)(84, 86, 102, 95)(85, 98, 107, 100)(89, 101, 105, 106)(97, 103, 108, 104)(109, 111, 120, 114)(110, 117, 121, 118)(112, 113, 126, 125)(115, 124, 137, 131)(116, 123, 133, 127)(119, 129, 122, 136)(128, 135, 139, 142)(130, 134, 140, 132)(138, 141, 144, 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) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.487 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.483 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 4, 4}) Quotient :: loop^2 Aut^+ = (C3 x C3) : C4 (small group id <36, 9>) Aut = (S3 x S3) : C2 (small group id <72, 40>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2, Y2^3, Y1^3, R * Y2 * R * Y1, (R * Y3)^2, Y3^4, (Y3^-2 * Y1^-1)^2, Y3^-1 * Y2 * Y3^-2 * Y1 * Y3^-1, Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^4 ] Map:: polytopal non-degenerate R = (1, 37, 73, 109, 3, 39, 75, 111, 9, 45, 81, 117, 5, 41, 77, 113)(2, 38, 74, 110, 6, 42, 78, 114, 16, 52, 88, 124, 7, 43, 79, 115)(4, 40, 76, 112, 11, 47, 83, 119, 22, 58, 94, 130, 12, 48, 84, 120)(8, 44, 80, 116, 20, 56, 92, 128, 14, 50, 86, 122, 21, 57, 93, 129)(10, 46, 82, 118, 23, 59, 95, 131, 13, 49, 85, 121, 24, 60, 96, 132)(15, 51, 87, 123, 29, 65, 101, 137, 19, 55, 91, 127, 30, 66, 102, 138)(17, 53, 89, 125, 31, 67, 103, 139, 18, 54, 90, 126, 32, 68, 104, 140)(25, 61, 97, 133, 33, 69, 105, 141, 28, 64, 100, 136, 34, 70, 106, 142)(26, 62, 98, 134, 35, 71, 107, 143, 27, 63, 99, 135, 36, 72, 108, 144) L = (1, 38)(2, 40)(3, 44)(4, 37)(5, 49)(6, 51)(7, 54)(8, 46)(9, 58)(10, 39)(11, 61)(12, 63)(13, 50)(14, 41)(15, 53)(16, 45)(17, 42)(18, 55)(19, 43)(20, 69)(21, 66)(22, 52)(23, 71)(24, 68)(25, 62)(26, 47)(27, 64)(28, 48)(29, 56)(30, 70)(31, 59)(32, 72)(33, 65)(34, 57)(35, 67)(36, 60)(73, 110)(74, 112)(75, 116)(76, 109)(77, 121)(78, 123)(79, 126)(80, 118)(81, 130)(82, 111)(83, 133)(84, 135)(85, 122)(86, 113)(87, 125)(88, 117)(89, 114)(90, 127)(91, 115)(92, 141)(93, 138)(94, 124)(95, 143)(96, 140)(97, 134)(98, 119)(99, 136)(100, 120)(101, 128)(102, 142)(103, 131)(104, 144)(105, 137)(106, 129)(107, 139)(108, 132) local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8 ) } Outer automorphisms :: reflexible Dual of E16.478 Transitivity :: VT+ Graph:: v = 9 e = 72 f = 33 degree seq :: [ 16^9 ] E16.484 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 4, 4}) Quotient :: loop^2 Aut^+ = (C3 x C3) : C4 (small group id <36, 9>) Aut = (S3 x S3) : C2 (small group id <72, 40>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1, Y1^3, Y2^3, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, (Y3 * Y1 * Y3)^2, (Y3 * Y2 * Y3)^2, (Y3^-1 * Y1^-1)^4, (Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 37, 73, 109, 4, 40, 76, 112, 12, 48, 84, 120, 5, 41, 77, 113)(2, 38, 74, 110, 6, 42, 78, 114, 17, 53, 89, 125, 7, 43, 79, 115)(3, 39, 75, 111, 8, 44, 80, 116, 22, 58, 94, 130, 9, 45, 81, 117)(10, 46, 82, 118, 25, 61, 97, 133, 14, 50, 86, 122, 26, 62, 98, 134)(11, 47, 83, 119, 27, 63, 99, 135, 13, 49, 85, 121, 28, 64, 100, 136)(15, 51, 87, 123, 29, 65, 101, 137, 19, 55, 91, 127, 30, 66, 102, 138)(16, 52, 88, 124, 31, 67, 103, 139, 18, 54, 90, 126, 32, 68, 104, 140)(20, 56, 92, 128, 33, 69, 105, 141, 24, 60, 96, 132, 34, 70, 106, 142)(21, 57, 93, 129, 35, 71, 107, 143, 23, 59, 95, 131, 36, 72, 108, 144) L = (1, 38)(2, 39)(3, 37)(4, 46)(5, 49)(6, 51)(7, 54)(8, 56)(9, 59)(10, 47)(11, 40)(12, 58)(13, 50)(14, 41)(15, 52)(16, 42)(17, 48)(18, 55)(19, 43)(20, 57)(21, 44)(22, 53)(23, 60)(24, 45)(25, 69)(26, 66)(27, 71)(28, 68)(29, 61)(30, 70)(31, 63)(32, 72)(33, 65)(34, 62)(35, 67)(36, 64)(73, 111)(74, 109)(75, 110)(76, 119)(77, 122)(78, 124)(79, 127)(80, 129)(81, 132)(82, 112)(83, 118)(84, 125)(85, 113)(86, 121)(87, 114)(88, 123)(89, 130)(90, 115)(91, 126)(92, 116)(93, 128)(94, 120)(95, 117)(96, 131)(97, 137)(98, 142)(99, 139)(100, 144)(101, 141)(102, 134)(103, 143)(104, 136)(105, 133)(106, 138)(107, 135)(108, 140) local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8 ) } Outer automorphisms :: reflexible Dual of E16.479 Transitivity :: VT+ Graph:: v = 9 e = 72 f = 33 degree seq :: [ 16^9 ] E16.485 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 4, 4}) Quotient :: loop^2 Aut^+ = (C3 x C3) : C4 (small group id <36, 9>) Aut = C2 x ((C3 x C3) : C4) (small group id <72, 45>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, Y3^3, Y2^4, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y1^-3, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y1, Y2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-1, Y3 * Y2 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y2 * Y3 * Y1 * Y3^-1 * Y2^-1 * Y3 * Y1^-1, Y3^-1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 73, 109, 4, 40, 76, 112, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 8, 44, 80, 116)(3, 39, 75, 111, 9, 45, 81, 117, 10, 46, 82, 118)(6, 42, 78, 114, 15, 51, 87, 123, 16, 52, 88, 124)(11, 47, 83, 119, 21, 57, 93, 129, 22, 58, 94, 130)(12, 48, 84, 120, 23, 59, 95, 131, 24, 60, 96, 132)(13, 49, 85, 121, 25, 61, 97, 133, 26, 62, 98, 134)(14, 50, 86, 122, 27, 63, 99, 135, 28, 64, 100, 136)(17, 53, 89, 125, 29, 65, 101, 137, 30, 66, 102, 138)(18, 54, 90, 126, 31, 67, 103, 139, 32, 68, 104, 140)(19, 55, 91, 127, 33, 69, 105, 141, 34, 70, 106, 142)(20, 56, 92, 128, 35, 71, 107, 143, 36, 72, 108, 144) L = (1, 38)(2, 42)(3, 37)(4, 47)(5, 49)(6, 39)(7, 53)(8, 55)(9, 56)(10, 54)(11, 52)(12, 40)(13, 51)(14, 41)(15, 50)(16, 48)(17, 46)(18, 43)(19, 45)(20, 44)(21, 66)(22, 70)(23, 71)(24, 67)(25, 65)(26, 69)(27, 72)(28, 68)(29, 64)(30, 60)(31, 57)(32, 61)(33, 63)(34, 59)(35, 58)(36, 62)(73, 111)(74, 109)(75, 114)(76, 120)(77, 122)(78, 110)(79, 126)(80, 128)(81, 127)(82, 125)(83, 112)(84, 124)(85, 113)(86, 123)(87, 121)(88, 119)(89, 115)(90, 118)(91, 116)(92, 117)(93, 139)(94, 143)(95, 142)(96, 138)(97, 140)(98, 144)(99, 141)(100, 137)(101, 133)(102, 129)(103, 132)(104, 136)(105, 134)(106, 130)(107, 131)(108, 135) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.480 Transitivity :: VT+ Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.486 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 4, 4}) Quotient :: loop^2 Aut^+ = (C3 x C3) : C4 (small group id <36, 9>) Aut = C2 x ((C3 x C3) : C4) (small group id <72, 45>) |r| :: 2 Presentation :: [ R^2, Y3^3, (R * Y3)^2, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y1^4, (Y2 * Y1^-1)^2, Y2^4, R * Y1 * R * Y2, Y1 * Y2^-2 * Y1 * Y3^-1, Y1^-2 * Y2^-1 * Y3 * Y2^-1, Y2^-2 * Y3 * Y2 * Y3^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y2 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 37, 73, 109, 4, 40, 76, 112, 7, 43, 79, 115)(2, 38, 74, 110, 10, 46, 82, 118, 12, 48, 84, 120)(3, 39, 75, 111, 15, 51, 87, 123, 16, 52, 88, 124)(5, 41, 77, 113, 22, 58, 94, 130, 18, 54, 90, 126)(6, 42, 78, 114, 24, 60, 96, 132, 17, 53, 89, 125)(8, 44, 80, 116, 28, 64, 100, 136, 29, 65, 101, 137)(9, 45, 81, 117, 31, 67, 103, 139, 23, 59, 95, 131)(11, 47, 83, 119, 21, 57, 93, 129, 32, 68, 104, 140)(13, 49, 85, 121, 33, 69, 105, 141, 25, 61, 97, 133)(14, 50, 86, 122, 34, 70, 106, 142, 36, 72, 108, 144)(19, 55, 91, 127, 35, 71, 107, 143, 27, 63, 99, 135)(20, 56, 92, 128, 30, 66, 102, 138, 26, 62, 98, 134) L = (1, 38)(2, 44)(3, 49)(4, 53)(5, 37)(6, 57)(7, 62)(8, 41)(9, 66)(10, 68)(11, 39)(12, 50)(13, 56)(14, 58)(15, 43)(16, 45)(17, 65)(18, 69)(19, 40)(20, 47)(21, 63)(22, 67)(23, 60)(24, 72)(25, 42)(26, 64)(27, 61)(28, 51)(29, 55)(30, 70)(31, 48)(32, 54)(33, 46)(34, 52)(35, 59)(36, 71)(73, 111)(74, 117)(75, 122)(76, 126)(77, 129)(78, 109)(79, 135)(80, 132)(81, 127)(82, 115)(83, 110)(84, 121)(85, 143)(86, 114)(87, 140)(88, 116)(89, 139)(90, 144)(91, 119)(92, 112)(93, 134)(94, 137)(95, 113)(96, 141)(97, 130)(98, 131)(99, 142)(100, 120)(101, 138)(102, 133)(103, 123)(104, 125)(105, 124)(106, 118)(107, 136)(108, 128) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.481 Transitivity :: VT+ Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.487 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 4, 4}) Quotient :: loop^2 Aut^+ = (C3 x C3) : C4 (small group id <36, 9>) Aut = C2 x ((C3 x C3) : C4) (small group id <72, 45>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1 * Y1^-1, Y3^3, Y1^4, Y2^4, Y1^4, (R * Y3)^2, (Y2 * Y1^-1)^2, Y2^4, R * Y2 * R * Y1, Y2 * Y3^-1 * Y2^-2 * Y3 * Y1^-1, Y1^-1 * Y3^-1 * Y1 * Y2 * Y3 * Y2^-1, Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y3 ] Map:: polytopal non-degenerate R = (1, 37, 73, 109, 4, 40, 76, 112, 7, 43, 79, 115)(2, 38, 74, 110, 6, 42, 78, 114, 11, 47, 83, 119)(3, 39, 75, 111, 13, 49, 85, 121, 14, 50, 86, 122)(5, 41, 77, 113, 19, 55, 91, 127, 20, 56, 92, 128)(8, 44, 80, 116, 10, 46, 82, 118, 24, 60, 96, 132)(9, 45, 81, 117, 25, 61, 97, 133, 26, 62, 98, 134)(12, 48, 84, 120, 29, 65, 101, 137, 18, 54, 90, 126)(15, 51, 87, 123, 17, 53, 89, 125, 31, 67, 103, 139)(16, 52, 88, 124, 32, 68, 104, 140, 33, 69, 105, 141)(21, 57, 93, 129, 34, 70, 106, 142, 30, 66, 102, 138)(22, 58, 94, 130, 23, 59, 95, 131, 35, 71, 107, 143)(27, 63, 99, 135, 28, 64, 100, 136, 36, 72, 108, 144) L = (1, 38)(2, 44)(3, 43)(4, 51)(5, 37)(6, 54)(7, 58)(8, 41)(9, 47)(10, 39)(11, 63)(12, 50)(13, 62)(14, 66)(15, 60)(16, 40)(17, 65)(18, 56)(19, 45)(20, 57)(21, 42)(22, 46)(23, 48)(24, 52)(25, 67)(26, 71)(27, 55)(28, 49)(29, 69)(30, 59)(31, 72)(32, 61)(33, 70)(34, 53)(35, 64)(36, 68)(73, 111)(74, 117)(75, 120)(76, 113)(77, 126)(78, 109)(79, 124)(80, 123)(81, 121)(82, 110)(83, 129)(84, 114)(85, 118)(86, 136)(87, 133)(88, 137)(89, 112)(90, 125)(91, 116)(92, 135)(93, 122)(94, 134)(95, 115)(96, 130)(97, 127)(98, 140)(99, 139)(100, 119)(101, 131)(102, 141)(103, 142)(104, 132)(105, 144)(106, 128)(107, 138)(108, 143) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.482 Transitivity :: VT+ Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.488 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 4}) Quotient :: dipole Aut^+ = (C3 x C3) : C4 (small group id <36, 9>) Aut = (S3 x S3) : C2 (small group id <72, 40>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y2^-2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^4, (Y1, Y2^-1, Y1^-1) ] 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, 22, 58, 16, 52)(11, 47, 25, 61, 26, 62)(12, 48, 27, 63, 28, 64)(20, 56, 33, 69, 29, 65)(21, 57, 30, 66, 34, 70)(23, 59, 35, 71, 31, 67)(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, 86, 122, 93, 129)(82, 118, 95, 131, 85, 121, 96, 132)(87, 123, 101, 137, 91, 127, 102, 138)(89, 125, 103, 139, 90, 126, 104, 140)(97, 133, 105, 141, 100, 136, 106, 142)(98, 134, 107, 143, 99, 135, 108, 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, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 21 e = 72 f = 21 degree seq :: [ 6^12, 8^9 ] E16.489 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 4}) Quotient :: dipole Aut^+ = (C3 x C3) : C4 (small group id <36, 9>) Aut = (S3 x S3) : C2 (small group id <72, 40>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3, Y1^3, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3^-1 * Y2^-2 * Y1^-1, (Y3^-1 * Y1^-1)^3, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^4 ] Map:: non-degenerate 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, 22, 58, 16, 52)(11, 47, 25, 61, 26, 62)(12, 48, 27, 63, 28, 64)(20, 56, 33, 69, 29, 65)(21, 57, 30, 66, 34, 70)(23, 59, 35, 71, 31, 67)(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, 86, 122, 93, 129)(82, 118, 95, 131, 85, 121, 96, 132)(87, 123, 101, 137, 91, 127, 102, 138)(89, 125, 103, 139, 90, 126, 104, 140)(97, 133, 105, 141, 100, 136, 106, 142)(98, 134, 107, 143, 99, 135, 108, 144) L = (1, 74)(2, 76)(3, 80)(4, 73)(5, 85)(6, 87)(7, 90)(8, 82)(9, 94)(10, 75)(11, 97)(12, 99)(13, 86)(14, 77)(15, 89)(16, 81)(17, 78)(18, 91)(19, 79)(20, 105)(21, 102)(22, 88)(23, 107)(24, 104)(25, 98)(26, 83)(27, 100)(28, 84)(29, 92)(30, 106)(31, 95)(32, 108)(33, 101)(34, 93)(35, 103)(36, 96)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 21 e = 72 f = 21 degree seq :: [ 6^12, 8^9 ] E16.490 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 3, 6}) Quotient :: edge^2 Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y3^3, (Y1 * Y2^-1)^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y1^-1 * Y3^-1, Y1 * Y3 * Y1 * Y2 * Y3^-1, Y2 * Y3^-1 * Y1 * Y2 * Y3, Y2 * Y1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 ] Map:: polytopal non-degenerate R = (1, 37, 4, 40, 7, 43)(2, 38, 9, 45, 11, 47)(3, 39, 13, 49, 14, 50)(5, 41, 19, 55, 21, 57)(6, 42, 16, 52, 23, 59)(8, 44, 17, 53, 25, 61)(10, 46, 28, 64, 30, 66)(12, 48, 27, 63, 31, 67)(15, 51, 24, 60, 22, 58)(18, 54, 29, 65, 32, 68)(20, 56, 35, 71, 36, 72)(26, 62, 33, 69, 34, 70)(73, 74, 77)(75, 84, 82)(76, 85, 88)(78, 90, 94)(79, 96, 97)(80, 98, 92)(81, 89, 100)(83, 103, 104)(86, 93, 106)(87, 99, 105)(91, 101, 107)(95, 102, 108)(109, 111, 114)(110, 116, 118)(112, 123, 125)(113, 126, 128)(115, 119, 129)(117, 135, 137)(120, 134, 130)(121, 127, 141)(122, 139, 138)(124, 136, 143)(131, 140, 132)(133, 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) :: { ( 24^3 ), ( 24^6 ) } Outer automorphisms :: reflexible Dual of E16.493 Graph:: simple bipartite v = 36 e = 72 f = 6 degree seq :: [ 3^24, 6^12 ] E16.491 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 3, 6}) Quotient :: edge^2 Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y2^3, Y1^3, R * Y2 * R * Y1, (R * Y3)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, (Y3^-1 * Y1^-1)^3, Y3^6, (Y3, Y1^-1)^2, (Y1^-1 * Y3^-1 * Y2^-1)^3 ] Map:: polytopal non-degenerate R = (1, 37, 3, 39, 9, 45, 24, 60, 15, 51, 5, 41)(2, 38, 6, 42, 17, 53, 32, 68, 21, 57, 7, 43)(4, 40, 11, 47, 25, 61, 35, 71, 30, 66, 12, 48)(8, 44, 22, 58, 34, 70, 28, 64, 13, 49, 23, 59)(10, 46, 19, 55, 31, 67, 16, 52, 14, 50, 26, 62)(18, 54, 29, 65, 36, 72, 27, 63, 20, 56, 33, 69)(73, 74, 76)(75, 80, 82)(77, 85, 86)(78, 88, 90)(79, 91, 92)(81, 89, 97)(83, 99, 100)(84, 101, 94)(87, 93, 102)(95, 107, 105)(96, 106, 103)(98, 108, 104)(109, 110, 112)(111, 116, 118)(113, 121, 122)(114, 124, 126)(115, 127, 128)(117, 125, 133)(119, 135, 136)(120, 137, 130)(123, 129, 138)(131, 143, 141)(132, 142, 139)(134, 144, 140) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^3 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E16.492 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 3^24, 12^6 ] E16.492 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 3, 6}) Quotient :: loop^2 Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y3^3, (Y1 * Y2^-1)^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y1^-1 * Y3^-1, Y1 * Y3 * Y1 * Y2 * Y3^-1, Y2 * Y3^-1 * Y1 * Y2 * Y3, Y2 * Y1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 ] Map:: polytopal non-degenerate R = (1, 37, 73, 109, 4, 40, 76, 112, 7, 43, 79, 115)(2, 38, 74, 110, 9, 45, 81, 117, 11, 47, 83, 119)(3, 39, 75, 111, 13, 49, 85, 121, 14, 50, 86, 122)(5, 41, 77, 113, 19, 55, 91, 127, 21, 57, 93, 129)(6, 42, 78, 114, 16, 52, 88, 124, 23, 59, 95, 131)(8, 44, 80, 116, 17, 53, 89, 125, 25, 61, 97, 133)(10, 46, 82, 118, 28, 64, 100, 136, 30, 66, 102, 138)(12, 48, 84, 120, 27, 63, 99, 135, 31, 67, 103, 139)(15, 51, 87, 123, 24, 60, 96, 132, 22, 58, 94, 130)(18, 54, 90, 126, 29, 65, 101, 137, 32, 68, 104, 140)(20, 56, 92, 128, 35, 71, 107, 143, 36, 72, 108, 144)(26, 62, 98, 134, 33, 69, 105, 141, 34, 70, 106, 142) L = (1, 38)(2, 41)(3, 48)(4, 49)(5, 37)(6, 54)(7, 60)(8, 62)(9, 53)(10, 39)(11, 67)(12, 46)(13, 52)(14, 57)(15, 63)(16, 40)(17, 64)(18, 58)(19, 65)(20, 44)(21, 70)(22, 42)(23, 66)(24, 61)(25, 43)(26, 56)(27, 69)(28, 45)(29, 71)(30, 72)(31, 68)(32, 47)(33, 51)(34, 50)(35, 55)(36, 59)(73, 111)(74, 116)(75, 114)(76, 123)(77, 126)(78, 109)(79, 119)(80, 118)(81, 135)(82, 110)(83, 129)(84, 134)(85, 127)(86, 139)(87, 125)(88, 136)(89, 112)(90, 128)(91, 141)(92, 113)(93, 115)(94, 120)(95, 140)(96, 131)(97, 142)(98, 130)(99, 137)(100, 143)(101, 117)(102, 122)(103, 138)(104, 132)(105, 121)(106, 144)(107, 124)(108, 133) local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12 ) } Outer automorphisms :: reflexible Dual of E16.491 Transitivity :: VT+ Graph:: v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.493 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 3, 6}) Quotient :: loop^2 Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y2^3, Y1^3, R * Y2 * R * Y1, (R * Y3)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, (Y3^-1 * Y1^-1)^3, Y3^6, (Y3, Y1^-1)^2, (Y1^-1 * Y3^-1 * Y2^-1)^3 ] Map:: polytopal non-degenerate R = (1, 37, 73, 109, 3, 39, 75, 111, 9, 45, 81, 117, 24, 60, 96, 132, 15, 51, 87, 123, 5, 41, 77, 113)(2, 38, 74, 110, 6, 42, 78, 114, 17, 53, 89, 125, 32, 68, 104, 140, 21, 57, 93, 129, 7, 43, 79, 115)(4, 40, 76, 112, 11, 47, 83, 119, 25, 61, 97, 133, 35, 71, 107, 143, 30, 66, 102, 138, 12, 48, 84, 120)(8, 44, 80, 116, 22, 58, 94, 130, 34, 70, 106, 142, 28, 64, 100, 136, 13, 49, 85, 121, 23, 59, 95, 131)(10, 46, 82, 118, 19, 55, 91, 127, 31, 67, 103, 139, 16, 52, 88, 124, 14, 50, 86, 122, 26, 62, 98, 134)(18, 54, 90, 126, 29, 65, 101, 137, 36, 72, 108, 144, 27, 63, 99, 135, 20, 56, 92, 128, 33, 69, 105, 141) L = (1, 38)(2, 40)(3, 44)(4, 37)(5, 49)(6, 52)(7, 55)(8, 46)(9, 53)(10, 39)(11, 63)(12, 65)(13, 50)(14, 41)(15, 57)(16, 54)(17, 61)(18, 42)(19, 56)(20, 43)(21, 66)(22, 48)(23, 71)(24, 70)(25, 45)(26, 72)(27, 64)(28, 47)(29, 58)(30, 51)(31, 60)(32, 62)(33, 59)(34, 67)(35, 69)(36, 68)(73, 110)(74, 112)(75, 116)(76, 109)(77, 121)(78, 124)(79, 127)(80, 118)(81, 125)(82, 111)(83, 135)(84, 137)(85, 122)(86, 113)(87, 129)(88, 126)(89, 133)(90, 114)(91, 128)(92, 115)(93, 138)(94, 120)(95, 143)(96, 142)(97, 117)(98, 144)(99, 136)(100, 119)(101, 130)(102, 123)(103, 132)(104, 134)(105, 131)(106, 139)(107, 141)(108, 140) local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: reflexible Dual of E16.490 Transitivity :: VT+ Graph:: v = 6 e = 72 f = 36 degree seq :: [ 24^6 ] E16.494 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^3, Y2^3, (Y3, Y2), (R * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), Y3 * Y1 * Y2^-1 * Y3 * Y1, (Y3 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 13, 49)(4, 40, 15, 51, 16, 52)(6, 42, 10, 46, 19, 55)(7, 43, 22, 58, 23, 59)(9, 45, 14, 50, 26, 62)(11, 47, 28, 64, 29, 65)(12, 48, 30, 66, 31, 67)(17, 53, 20, 56, 33, 69)(18, 54, 25, 61, 35, 71)(21, 57, 34, 70, 24, 60)(27, 63, 36, 72, 32, 68)(73, 109, 75, 111, 78, 114)(74, 110, 80, 116, 82, 118)(76, 112, 84, 120, 89, 125)(77, 113, 85, 121, 91, 127)(79, 115, 86, 122, 93, 129)(81, 117, 96, 132, 95, 131)(83, 119, 97, 133, 99, 135)(87, 123, 102, 138, 92, 128)(88, 124, 103, 139, 105, 141)(90, 126, 104, 140, 101, 137)(94, 130, 98, 134, 106, 142)(100, 136, 107, 143, 108, 144) L = (1, 76)(2, 81)(3, 84)(4, 79)(5, 90)(6, 89)(7, 73)(8, 96)(9, 83)(10, 95)(11, 74)(12, 86)(13, 104)(14, 75)(15, 85)(16, 100)(17, 93)(18, 92)(19, 101)(20, 77)(21, 78)(22, 103)(23, 99)(24, 97)(25, 80)(26, 105)(27, 82)(28, 106)(29, 102)(30, 91)(31, 107)(32, 87)(33, 108)(34, 88)(35, 94)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.502 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 6^24 ] E16.495 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^3, Y2^3, (Y3, Y2), (R * Y2)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y2 * Y3 * Y1, (Y3 * Y2^-1 * Y1)^2, (Y3 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 13, 49)(4, 40, 15, 51, 16, 52)(6, 42, 10, 46, 19, 55)(7, 43, 22, 58, 23, 59)(9, 45, 21, 57, 25, 61)(11, 47, 28, 64, 29, 65)(12, 48, 20, 56, 30, 66)(14, 50, 32, 68, 26, 62)(17, 53, 31, 67, 34, 70)(18, 54, 27, 63, 35, 71)(24, 60, 36, 72, 33, 69)(73, 109, 75, 111, 78, 114)(74, 110, 80, 116, 82, 118)(76, 112, 84, 120, 89, 125)(77, 113, 85, 121, 91, 127)(79, 115, 86, 122, 93, 129)(81, 117, 95, 131, 98, 134)(83, 119, 96, 132, 99, 135)(87, 123, 92, 128, 103, 139)(88, 124, 102, 138, 106, 142)(90, 126, 101, 137, 105, 141)(94, 130, 104, 140, 97, 133)(100, 136, 108, 144, 107, 143) L = (1, 76)(2, 81)(3, 84)(4, 79)(5, 90)(6, 89)(7, 73)(8, 95)(9, 83)(10, 98)(11, 74)(12, 86)(13, 101)(14, 75)(15, 91)(16, 100)(17, 93)(18, 92)(19, 105)(20, 77)(21, 78)(22, 106)(23, 96)(24, 80)(25, 102)(26, 99)(27, 82)(28, 104)(29, 103)(30, 108)(31, 85)(32, 88)(33, 87)(34, 107)(35, 94)(36, 97)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.499 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 6^24 ] E16.496 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y2^3, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y3 * Y2^-1 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y3 * Y2^-1 * Y1 * Y3^-1 * Y1, Y2 * Y1^-1 * Y3 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y1^-1, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y3 * Y1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y1^-1 * Y3^-1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 9, 45)(4, 40, 10, 46, 11, 47)(6, 42, 14, 50, 15, 51)(7, 43, 16, 52, 17, 53)(12, 48, 25, 61, 26, 62)(13, 49, 27, 63, 18, 54)(19, 55, 30, 66, 29, 65)(20, 56, 28, 64, 33, 69)(21, 57, 32, 68, 22, 58)(23, 59, 31, 67, 34, 70)(24, 60, 35, 71, 36, 72)(73, 109, 75, 111, 76, 112)(74, 110, 78, 114, 79, 115)(77, 113, 84, 120, 85, 121)(80, 116, 90, 126, 91, 127)(81, 117, 92, 128, 93, 129)(82, 118, 94, 130, 95, 131)(83, 119, 96, 132, 86, 122)(87, 123, 100, 136, 101, 137)(88, 124, 102, 138, 103, 139)(89, 125, 104, 140, 97, 133)(98, 134, 105, 141, 108, 144)(99, 135, 107, 143, 106, 142) L = (1, 76)(2, 79)(3, 73)(4, 75)(5, 85)(6, 74)(7, 78)(8, 91)(9, 93)(10, 95)(11, 86)(12, 77)(13, 84)(14, 96)(15, 101)(16, 103)(17, 97)(18, 80)(19, 90)(20, 81)(21, 92)(22, 82)(23, 94)(24, 83)(25, 104)(26, 108)(27, 106)(28, 87)(29, 100)(30, 88)(31, 102)(32, 89)(33, 98)(34, 107)(35, 99)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.500 Graph:: bipartite v = 24 e = 72 f = 18 degree seq :: [ 6^24 ] E16.497 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y3^3, Y1^3, (R * Y1)^2, (Y3^-1 * Y2^-1)^2, (R * Y3)^2, Y2 * Y1 * Y3 * Y1^-1, Y3 * R * Y2 * R * Y2^-1, Y1^-1 * Y2^-1 * Y3 * Y1 * Y2^-1, (Y3 * Y2^-1)^3, Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 11, 47, 13, 49)(4, 40, 15, 51, 17, 53)(6, 42, 9, 45, 23, 59)(7, 43, 24, 60, 19, 55)(8, 44, 21, 57, 22, 58)(10, 46, 20, 56, 25, 61)(12, 48, 28, 64, 30, 66)(14, 50, 27, 63, 31, 67)(16, 52, 34, 70, 35, 71)(18, 54, 29, 65, 36, 72)(26, 62, 32, 68, 33, 69)(73, 109, 75, 111, 78, 114)(74, 110, 80, 116, 82, 118)(76, 112, 88, 124, 90, 126)(77, 113, 91, 127, 89, 125)(79, 115, 97, 133, 84, 120)(81, 117, 100, 136, 101, 137)(83, 119, 87, 123, 98, 134)(85, 121, 103, 139, 102, 138)(86, 122, 105, 141, 94, 130)(92, 128, 104, 140, 108, 144)(93, 129, 95, 131, 107, 143)(96, 132, 99, 135, 106, 142) L = (1, 76)(2, 81)(3, 84)(4, 79)(5, 92)(6, 94)(7, 73)(8, 98)(9, 83)(10, 96)(11, 74)(12, 86)(13, 104)(14, 75)(15, 101)(16, 78)(17, 85)(18, 105)(19, 107)(20, 93)(21, 77)(22, 88)(23, 108)(24, 100)(25, 90)(26, 99)(27, 80)(28, 82)(29, 106)(30, 95)(31, 91)(32, 89)(33, 97)(34, 87)(35, 103)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.501 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 6^24 ] E16.498 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y3^3, (Y2 * Y1^-1)^2, (Y3, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^-1 * Y1^-1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, (Y3 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 12, 48, 10, 46)(4, 40, 15, 51, 16, 52)(6, 42, 18, 54, 22, 58)(7, 43, 24, 60, 25, 61)(8, 44, 26, 62, 20, 56)(9, 45, 17, 53, 28, 64)(11, 47, 31, 67, 32, 68)(13, 49, 27, 63, 33, 69)(14, 50, 21, 57, 34, 70)(19, 55, 29, 65, 36, 72)(23, 59, 30, 66, 35, 71)(73, 109, 75, 111, 78, 114)(74, 110, 80, 116, 82, 118)(76, 112, 85, 121, 89, 125)(77, 113, 90, 126, 92, 128)(79, 115, 86, 122, 95, 131)(81, 117, 99, 135, 101, 137)(83, 119, 97, 133, 102, 138)(84, 120, 98, 134, 94, 130)(87, 123, 91, 127, 105, 141)(88, 124, 100, 136, 108, 144)(93, 129, 104, 140, 107, 143)(96, 132, 103, 139, 106, 142) L = (1, 76)(2, 81)(3, 85)(4, 79)(5, 91)(6, 89)(7, 73)(8, 99)(9, 83)(10, 101)(11, 74)(12, 88)(13, 86)(14, 75)(15, 107)(16, 103)(17, 95)(18, 105)(19, 93)(20, 87)(21, 77)(22, 108)(23, 78)(24, 94)(25, 80)(26, 100)(27, 97)(28, 106)(29, 102)(30, 82)(31, 84)(32, 90)(33, 104)(34, 98)(35, 92)(36, 96)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.503 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 6^24 ] E16.499 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^3, Y3 * Y1^-3, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y1^-1 * Y2^-1 * Y1^-2, (Y1 * Y2^-1)^3, Y2 * Y1^2 * Y2^-1 * Y3 * Y1, (R * Y2 * Y3)^2, (Y1^-1 * Y2^-1)^3, (Y3 * Y2^-1)^3 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 4, 40, 9, 45, 5, 41)(3, 39, 11, 47, 21, 57, 12, 48, 26, 62, 13, 49)(6, 42, 18, 54, 22, 58, 19, 55, 27, 63, 20, 56)(8, 44, 23, 59, 14, 50, 24, 60, 16, 52, 25, 61)(10, 46, 28, 64, 15, 51, 29, 65, 17, 53, 30, 66)(31, 67, 36, 72, 32, 68, 34, 70, 33, 69, 35, 71)(73, 109, 75, 111, 78, 114)(74, 110, 80, 116, 82, 118)(76, 112, 86, 122, 87, 123)(77, 113, 88, 124, 89, 125)(79, 115, 93, 129, 94, 130)(81, 117, 98, 134, 99, 135)(83, 119, 101, 137, 103, 139)(84, 120, 102, 138, 104, 140)(85, 121, 100, 136, 105, 141)(90, 126, 106, 142, 96, 132)(91, 127, 107, 143, 97, 133)(92, 128, 108, 144, 95, 131) L = (1, 76)(2, 81)(3, 84)(4, 73)(5, 79)(6, 91)(7, 77)(8, 96)(9, 74)(10, 101)(11, 98)(12, 75)(13, 93)(14, 97)(15, 102)(16, 95)(17, 100)(18, 99)(19, 78)(20, 94)(21, 85)(22, 92)(23, 88)(24, 80)(25, 86)(26, 83)(27, 90)(28, 89)(29, 82)(30, 87)(31, 106)(32, 107)(33, 108)(34, 103)(35, 104)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6^6 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E16.495 Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.500 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, Y2^3, R * Y2 * R * Y3^-1, (R * Y1)^2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y1^6, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^3, Y3 * Y1^2 * Y3^-1 * Y1^-2 ] Map:: non-degenerate R = (1, 37, 2, 38, 6, 42, 16, 52, 15, 51, 5, 41)(3, 39, 9, 45, 17, 53, 33, 69, 26, 62, 10, 46)(4, 40, 11, 47, 18, 54, 34, 70, 30, 66, 12, 48)(7, 43, 19, 55, 31, 67, 28, 64, 13, 49, 20, 56)(8, 44, 21, 57, 32, 68, 23, 59, 14, 50, 22, 58)(24, 60, 29, 65, 36, 72, 27, 63, 25, 61, 35, 71)(73, 109, 75, 111, 76, 112)(74, 110, 79, 115, 80, 116)(77, 113, 85, 121, 86, 122)(78, 114, 89, 125, 90, 126)(81, 117, 95, 131, 96, 132)(82, 118, 93, 129, 97, 133)(83, 119, 99, 135, 100, 136)(84, 120, 101, 137, 91, 127)(87, 123, 98, 134, 102, 138)(88, 124, 103, 139, 104, 140)(92, 128, 106, 142, 107, 143)(94, 130, 108, 144, 105, 141) L = (1, 76)(2, 80)(3, 73)(4, 75)(5, 86)(6, 90)(7, 74)(8, 79)(9, 96)(10, 97)(11, 100)(12, 91)(13, 77)(14, 85)(15, 102)(16, 104)(17, 78)(18, 89)(19, 101)(20, 107)(21, 82)(22, 105)(23, 81)(24, 95)(25, 93)(26, 87)(27, 83)(28, 99)(29, 84)(30, 98)(31, 88)(32, 103)(33, 108)(34, 92)(35, 106)(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) :: { ( 6^6 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E16.496 Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.501 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2^3, (Y3^-1 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, Y1^3 * Y3 * Y2, Y1 * Y2 * Y1^-1 * Y3^-1 * Y2, Y1^2 * Y2 * Y1 * Y3, Y1 * Y3 * Y1^-1 * Y3 * Y2^-1, Y1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1, Y1 * Y3 * Y2^-1 * Y1^-1 * Y3, Y1^2 * Y3^-1 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^3 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 8, 44, 18, 54, 23, 59, 5, 41)(3, 39, 13, 49, 31, 67, 7, 43, 29, 65, 15, 51)(4, 40, 17, 53, 24, 60, 30, 66, 11, 47, 19, 55)(6, 42, 26, 62, 22, 58, 16, 52, 10, 46, 28, 64)(9, 45, 25, 61, 20, 56, 12, 48, 21, 57, 27, 63)(14, 50, 32, 68, 35, 71, 36, 72, 33, 69, 34, 70)(73, 109, 75, 111, 78, 114)(74, 110, 81, 117, 83, 119)(76, 112, 90, 126, 92, 128)(77, 113, 93, 129, 96, 132)(79, 115, 102, 138, 86, 122)(80, 116, 103, 139, 94, 130)(82, 118, 95, 131, 101, 137)(84, 120, 98, 134, 104, 140)(85, 121, 89, 125, 105, 141)(87, 123, 91, 127, 107, 143)(88, 124, 108, 144, 99, 135)(97, 133, 100, 136, 106, 142) L = (1, 76)(2, 82)(3, 86)(4, 79)(5, 94)(6, 99)(7, 73)(8, 96)(9, 104)(10, 84)(11, 85)(12, 74)(13, 95)(14, 88)(15, 80)(16, 75)(17, 81)(18, 78)(19, 93)(20, 108)(21, 106)(22, 97)(23, 83)(24, 87)(25, 77)(26, 101)(27, 90)(28, 103)(29, 105)(30, 92)(31, 107)(32, 89)(33, 98)(34, 91)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6^6 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E16.497 Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.502 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y3^3, Y2 * Y1^-2 * Y3^-1, Y1 * Y3 * Y2^-1 * Y1, (R * Y3)^2, (Y2^-1, Y3), (R * Y2)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1, Y3 * Y1^-1 * Y3 * Y1 * Y2 * Y1, Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, (Y1 * Y2)^3, (Y2^-1 * Y1)^3 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 24, 60, 17, 53, 5, 41)(3, 39, 13, 49, 22, 58, 16, 52, 4, 40, 15, 51)(6, 42, 20, 56, 7, 43, 23, 59, 14, 50, 21, 57)(9, 45, 25, 61, 18, 54, 27, 63, 10, 46, 26, 62)(11, 47, 28, 64, 12, 48, 30, 66, 19, 55, 29, 65)(31, 67, 35, 71, 32, 68, 34, 70, 33, 69, 36, 72)(73, 109, 75, 111, 78, 114)(74, 110, 81, 117, 83, 119)(76, 112, 86, 122, 89, 125)(77, 113, 82, 118, 91, 127)(79, 115, 80, 116, 94, 130)(84, 120, 96, 132, 90, 126)(85, 121, 102, 138, 103, 139)(87, 123, 100, 136, 105, 141)(88, 124, 101, 137, 104, 140)(92, 128, 106, 142, 99, 135)(93, 129, 107, 143, 97, 133)(95, 131, 108, 144, 98, 134) L = (1, 76)(2, 82)(3, 86)(4, 79)(5, 90)(6, 89)(7, 73)(8, 75)(9, 91)(10, 84)(11, 77)(12, 74)(13, 100)(14, 80)(15, 101)(16, 102)(17, 94)(18, 83)(19, 96)(20, 107)(21, 108)(22, 78)(23, 106)(24, 81)(25, 95)(26, 92)(27, 93)(28, 104)(29, 103)(30, 105)(31, 87)(32, 85)(33, 88)(34, 97)(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) :: { ( 6^6 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E16.494 Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.503 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 3, 6}) Quotient :: dipole Aut^+ = C3 x A4 (small group id <36, 11>) Aut = (C3 x A4) : C2 (small group id <72, 43>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y3^3, (Y3^-1, Y2), (R * Y2)^2, Y2^-1 * Y1^-2 * Y3^-1, Y3 * Y2 * Y1^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^3, (Y2 * Y1^-1)^3, (Y3 * Y1^-1)^3, (Y2^-1 * Y1^-1)^3, Y3^-1 * Y1^4 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 8, 44, 24, 60, 14, 50, 5, 41)(3, 39, 13, 49, 7, 43, 23, 59, 19, 55, 15, 51)(4, 40, 17, 53, 6, 42, 22, 58, 16, 52, 18, 54)(9, 45, 25, 61, 12, 48, 30, 66, 20, 56, 26, 62)(10, 46, 27, 63, 11, 47, 29, 65, 21, 57, 28, 64)(31, 67, 36, 72, 32, 68, 34, 70, 33, 69, 35, 71)(73, 109, 75, 111, 78, 114)(74, 110, 81, 117, 83, 119)(76, 112, 86, 122, 91, 127)(77, 113, 92, 128, 82, 118)(79, 115, 88, 124, 80, 116)(84, 120, 93, 129, 96, 132)(85, 121, 100, 136, 104, 140)(87, 123, 101, 137, 103, 139)(89, 125, 106, 142, 97, 133)(90, 126, 108, 144, 98, 134)(94, 130, 107, 143, 102, 138)(95, 131, 99, 135, 105, 141) L = (1, 76)(2, 82)(3, 86)(4, 79)(5, 93)(6, 91)(7, 73)(8, 78)(9, 77)(10, 84)(11, 92)(12, 74)(13, 103)(14, 88)(15, 105)(16, 75)(17, 98)(18, 102)(19, 80)(20, 96)(21, 81)(22, 97)(23, 104)(24, 83)(25, 108)(26, 107)(27, 85)(28, 87)(29, 95)(30, 106)(31, 99)(32, 101)(33, 100)(34, 90)(35, 89)(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) :: { ( 6^6 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E16.498 Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.504 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, Y2^-1 * Y3 * Y2 * Y3, Y2^-1 * Y1 * Y2 * Y1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 6, 42)(4, 40, 10, 46)(5, 41, 8, 44)(7, 43, 13, 49)(9, 45, 15, 51)(11, 47, 17, 53)(12, 48, 18, 54)(14, 50, 20, 56)(16, 52, 22, 58)(19, 55, 25, 61)(21, 57, 27, 63)(23, 59, 29, 65)(24, 60, 30, 66)(26, 62, 32, 68)(28, 64, 31, 67)(33, 69, 35, 71)(34, 70, 36, 72)(73, 109, 75, 111, 77, 113)(74, 110, 78, 114, 80, 116)(76, 112, 81, 117, 83, 119)(79, 115, 84, 120, 86, 122)(82, 118, 87, 123, 89, 125)(85, 121, 90, 126, 92, 128)(88, 124, 93, 129, 95, 131)(91, 127, 96, 132, 98, 134)(94, 130, 99, 135, 101, 137)(97, 133, 102, 138, 104, 140)(100, 136, 105, 141, 106, 142)(103, 139, 107, 143, 108, 144) L = (1, 76)(2, 79)(3, 81)(4, 73)(5, 83)(6, 84)(7, 74)(8, 86)(9, 75)(10, 88)(11, 77)(12, 78)(13, 91)(14, 80)(15, 93)(16, 82)(17, 95)(18, 96)(19, 85)(20, 98)(21, 87)(22, 100)(23, 89)(24, 90)(25, 103)(26, 92)(27, 105)(28, 94)(29, 106)(30, 107)(31, 97)(32, 108)(33, 99)(34, 101)(35, 102)(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) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.553 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.505 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 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, Y3^2, R^2, Y2^3, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, (Y3 * Y1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 8, 44)(4, 40, 10, 46)(5, 41, 6, 42)(7, 43, 13, 49)(9, 45, 15, 51)(11, 47, 16, 52)(12, 48, 18, 54)(14, 50, 19, 55)(17, 53, 23, 59)(20, 56, 26, 62)(21, 57, 27, 63)(22, 58, 28, 64)(24, 60, 30, 66)(25, 61, 31, 67)(29, 65, 32, 68)(33, 69, 36, 72)(34, 70, 35, 71)(73, 109, 75, 111, 77, 113)(74, 110, 78, 114, 80, 116)(76, 112, 81, 117, 83, 119)(79, 115, 84, 120, 86, 122)(82, 118, 88, 124, 87, 123)(85, 121, 91, 127, 90, 126)(89, 125, 94, 130, 93, 129)(92, 128, 97, 133, 96, 132)(95, 131, 99, 135, 100, 136)(98, 134, 102, 138, 103, 139)(101, 137, 105, 141, 106, 142)(104, 140, 107, 143, 108, 144) L = (1, 76)(2, 79)(3, 81)(4, 73)(5, 83)(6, 84)(7, 74)(8, 86)(9, 75)(10, 89)(11, 77)(12, 78)(13, 92)(14, 80)(15, 93)(16, 94)(17, 82)(18, 96)(19, 97)(20, 85)(21, 87)(22, 88)(23, 101)(24, 90)(25, 91)(26, 104)(27, 105)(28, 106)(29, 95)(30, 107)(31, 108)(32, 98)(33, 99)(34, 100)(35, 102)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.563 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.506 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, (Y2^-1 * Y1)^2, Y3^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 8, 44)(5, 41, 7, 43)(6, 42, 10, 46)(11, 47, 20, 56)(12, 48, 21, 57)(13, 49, 19, 55)(14, 50, 17, 53)(15, 51, 18, 54)(16, 52, 22, 58)(23, 59, 31, 67)(24, 60, 32, 68)(25, 61, 30, 66)(26, 62, 28, 64)(27, 63, 29, 65)(33, 69, 36, 72)(34, 70, 35, 71)(73, 109, 75, 111, 77, 113)(74, 110, 79, 115, 81, 117)(76, 112, 83, 119, 86, 122)(78, 114, 84, 120, 87, 123)(80, 116, 89, 125, 92, 128)(82, 118, 90, 126, 93, 129)(85, 121, 95, 131, 98, 134)(88, 124, 96, 132, 99, 135)(91, 127, 100, 136, 103, 139)(94, 130, 101, 137, 104, 140)(97, 133, 105, 141, 106, 142)(102, 138, 107, 143, 108, 144) L = (1, 76)(2, 80)(3, 83)(4, 85)(5, 86)(6, 73)(7, 89)(8, 91)(9, 92)(10, 74)(11, 95)(12, 75)(13, 97)(14, 98)(15, 77)(16, 78)(17, 100)(18, 79)(19, 102)(20, 103)(21, 81)(22, 82)(23, 105)(24, 84)(25, 88)(26, 106)(27, 87)(28, 107)(29, 90)(30, 94)(31, 108)(32, 93)(33, 96)(34, 99)(35, 101)(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) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.560 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.507 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3, Y2^-1), (Y1 * Y2^-1)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y1 * Y3 * Y1 * Y3^-1, Y2 * Y3^-1 * Y1 * Y3 * Y2^-1 * Y1, Y3^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 13, 49)(5, 41, 7, 43)(6, 42, 17, 53)(8, 44, 11, 47)(10, 46, 16, 52)(12, 48, 19, 55)(14, 50, 26, 62)(15, 51, 21, 57)(18, 54, 31, 67)(20, 56, 28, 64)(22, 58, 24, 60)(23, 59, 25, 61)(27, 63, 32, 68)(29, 65, 30, 66)(33, 69, 35, 71)(34, 70, 36, 72)(73, 109, 75, 111, 77, 113)(74, 110, 79, 115, 81, 117)(76, 112, 83, 119, 87, 123)(78, 114, 84, 120, 88, 124)(80, 116, 85, 121, 93, 129)(82, 118, 91, 127, 89, 125)(86, 122, 95, 131, 100, 136)(90, 126, 96, 132, 101, 137)(92, 128, 97, 133, 98, 134)(94, 130, 103, 139, 102, 138)(99, 135, 105, 141, 108, 144)(104, 140, 106, 142, 107, 143) L = (1, 76)(2, 80)(3, 83)(4, 86)(5, 87)(6, 73)(7, 85)(8, 92)(9, 93)(10, 74)(11, 95)(12, 75)(13, 97)(14, 99)(15, 100)(16, 77)(17, 81)(18, 78)(19, 79)(20, 104)(21, 98)(22, 82)(23, 105)(24, 84)(25, 106)(26, 107)(27, 90)(28, 108)(29, 88)(30, 89)(31, 91)(32, 94)(33, 96)(34, 103)(35, 102)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.557 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.508 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3^-1, Y2^-1), (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1, (Y3^-1 * Y1 * Y2^-1)^2, (Y1 * Y2 * Y3)^2, Y3^6 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 13, 49)(5, 41, 9, 45)(6, 42, 17, 53)(8, 44, 12, 48)(10, 46, 15, 51)(11, 47, 21, 57)(14, 50, 26, 62)(16, 52, 19, 55)(18, 54, 31, 67)(20, 56, 29, 65)(22, 58, 23, 59)(24, 60, 30, 66)(25, 61, 28, 64)(27, 63, 32, 68)(33, 69, 34, 70)(35, 71, 36, 72)(73, 109, 75, 111, 77, 113)(74, 110, 79, 115, 81, 117)(76, 112, 83, 119, 87, 123)(78, 114, 84, 120, 88, 124)(80, 116, 91, 127, 89, 125)(82, 118, 85, 121, 93, 129)(86, 122, 95, 131, 100, 136)(90, 126, 96, 132, 101, 137)(92, 128, 103, 139, 102, 138)(94, 130, 97, 133, 98, 134)(99, 135, 105, 141, 108, 144)(104, 140, 106, 142, 107, 143) L = (1, 76)(2, 80)(3, 83)(4, 86)(5, 87)(6, 73)(7, 91)(8, 92)(9, 89)(10, 74)(11, 95)(12, 75)(13, 79)(14, 99)(15, 100)(16, 77)(17, 102)(18, 78)(19, 103)(20, 104)(21, 81)(22, 82)(23, 105)(24, 84)(25, 85)(26, 93)(27, 90)(28, 108)(29, 88)(30, 107)(31, 106)(32, 94)(33, 96)(34, 97)(35, 98)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.558 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.509 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (R * Y1)^2, (Y1 * Y2^-1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y2 * Y1 * Y3 * Y1 * Y3^-1, Y3^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 13, 49)(5, 41, 7, 43)(6, 42, 17, 53)(8, 44, 15, 51)(10, 46, 12, 48)(11, 47, 19, 55)(14, 50, 26, 62)(16, 52, 21, 57)(18, 54, 31, 67)(20, 56, 23, 59)(22, 58, 29, 65)(24, 60, 30, 66)(25, 61, 28, 64)(27, 63, 32, 68)(33, 69, 34, 70)(35, 71, 36, 72)(73, 109, 75, 111, 77, 113)(74, 110, 79, 115, 81, 117)(76, 112, 83, 119, 87, 123)(78, 114, 84, 120, 88, 124)(80, 116, 91, 127, 85, 121)(82, 118, 89, 125, 93, 129)(86, 122, 95, 131, 100, 136)(90, 126, 96, 132, 101, 137)(92, 128, 98, 134, 97, 133)(94, 130, 102, 138, 103, 139)(99, 135, 105, 141, 108, 144)(104, 140, 107, 143, 106, 142) L = (1, 76)(2, 80)(3, 83)(4, 86)(5, 87)(6, 73)(7, 91)(8, 92)(9, 85)(10, 74)(11, 95)(12, 75)(13, 97)(14, 99)(15, 100)(16, 77)(17, 79)(18, 78)(19, 98)(20, 104)(21, 81)(22, 82)(23, 105)(24, 84)(25, 106)(26, 107)(27, 90)(28, 108)(29, 88)(30, 89)(31, 93)(32, 94)(33, 96)(34, 103)(35, 102)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.562 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.510 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 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, R^2, Y2^3, Y3 * Y2^-1 * Y3, (Y2 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2^-1)^2, (Y3^-1 * Y1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 12, 48)(5, 41, 7, 43)(6, 42, 13, 49)(8, 44, 15, 51)(10, 46, 16, 52)(11, 47, 17, 53)(14, 50, 21, 57)(18, 54, 25, 61)(19, 55, 26, 62)(20, 56, 27, 63)(22, 58, 28, 64)(23, 59, 29, 65)(24, 60, 30, 66)(31, 67, 35, 71)(32, 68, 34, 70)(33, 69, 36, 72)(73, 109, 75, 111, 77, 113)(74, 110, 79, 115, 81, 117)(76, 112, 83, 119, 78, 114)(80, 116, 86, 122, 82, 118)(84, 120, 85, 121, 89, 125)(87, 123, 88, 124, 93, 129)(90, 126, 92, 128, 91, 127)(94, 130, 96, 132, 95, 131)(97, 133, 98, 134, 99, 135)(100, 136, 101, 137, 102, 138)(103, 139, 105, 141, 104, 140)(106, 142, 108, 144, 107, 143) L = (1, 76)(2, 80)(3, 83)(4, 75)(5, 78)(6, 73)(7, 86)(8, 79)(9, 82)(10, 74)(11, 77)(12, 90)(13, 92)(14, 81)(15, 94)(16, 96)(17, 91)(18, 85)(19, 84)(20, 89)(21, 95)(22, 88)(23, 87)(24, 93)(25, 103)(26, 105)(27, 104)(28, 106)(29, 108)(30, 107)(31, 98)(32, 97)(33, 99)(34, 101)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.565 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.511 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y2^-1, Y2 * Y3 * Y2^-1 * Y1 * Y3 * Y1, (R * Y2 * Y3)^2, Y2 * Y1 * Y3 * Y2^-1 * Y3 * Y1, Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y1, Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y1 * Y2^-1, Y3 * Y2 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 11, 47)(5, 41, 14, 50)(6, 42, 16, 52)(7, 43, 18, 54)(8, 44, 21, 57)(10, 46, 17, 53)(12, 48, 28, 64)(13, 49, 20, 56)(15, 51, 27, 63)(19, 55, 31, 67)(22, 58, 25, 61)(23, 59, 32, 68)(24, 60, 34, 70)(26, 62, 33, 69)(29, 65, 35, 71)(30, 66, 36, 72)(73, 109, 75, 111, 77, 113)(74, 110, 78, 114, 80, 116)(76, 112, 84, 120, 85, 121)(79, 115, 91, 127, 92, 128)(81, 117, 95, 131, 96, 132)(82, 118, 97, 133, 90, 126)(83, 119, 89, 125, 99, 135)(86, 122, 98, 134, 101, 137)(87, 123, 102, 138, 103, 139)(88, 124, 104, 140, 105, 141)(93, 129, 106, 142, 107, 143)(94, 130, 108, 144, 100, 136) L = (1, 76)(2, 79)(3, 82)(4, 73)(5, 87)(6, 89)(7, 74)(8, 94)(9, 91)(10, 75)(11, 98)(12, 88)(13, 93)(14, 92)(15, 77)(16, 84)(17, 78)(18, 106)(19, 81)(20, 86)(21, 85)(22, 80)(23, 99)(24, 108)(25, 104)(26, 83)(27, 95)(28, 101)(29, 100)(30, 105)(31, 107)(32, 97)(33, 102)(34, 90)(35, 103)(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) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.554 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.512 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1 * Y3 * Y2 * Y3, (R * Y2 * Y3)^2, Y2^-1 * Y3 * Y1 * Y3 * Y2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3 * Y2^-1, Y3 * Y2 * Y1 * Y3 * Y1 * Y2^-1, Y2 * Y3 * Y1 * Y2 * Y3 * Y2 * Y1, (Y2 * Y3 * Y2^-1 * Y1)^2, (Y1 * Y2^-1)^6, (Y2 * Y1 * Y2^-1 * Y1)^3 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 11, 47)(5, 41, 14, 50)(6, 42, 16, 52)(7, 43, 18, 54)(8, 44, 21, 57)(10, 46, 25, 61)(12, 48, 19, 55)(13, 49, 28, 64)(15, 51, 22, 58)(17, 53, 31, 67)(20, 56, 26, 62)(23, 59, 32, 68)(24, 60, 35, 71)(27, 63, 34, 70)(29, 65, 33, 69)(30, 66, 36, 72)(73, 109, 75, 111, 77, 113)(74, 110, 78, 114, 80, 116)(76, 112, 84, 120, 85, 121)(79, 115, 91, 127, 92, 128)(81, 117, 95, 131, 96, 132)(82, 118, 98, 134, 99, 135)(83, 119, 97, 133, 94, 130)(86, 122, 101, 137, 102, 138)(87, 123, 90, 126, 103, 139)(88, 124, 104, 140, 105, 141)(89, 125, 100, 136, 106, 142)(93, 129, 107, 143, 108, 144) L = (1, 76)(2, 79)(3, 82)(4, 73)(5, 87)(6, 89)(7, 74)(8, 94)(9, 91)(10, 75)(11, 96)(12, 88)(13, 93)(14, 92)(15, 77)(16, 84)(17, 78)(18, 105)(19, 81)(20, 86)(21, 85)(22, 80)(23, 100)(24, 83)(25, 102)(26, 104)(27, 107)(28, 95)(29, 106)(30, 97)(31, 108)(32, 98)(33, 90)(34, 101)(35, 99)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.555 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.513 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 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, Y3^2, R^2, Y2^3, (Y1 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1 * Y2^-1)^2, Y2^-1 * Y3 * Y2 * Y1 * Y3 * Y1, (R * Y2 * Y3)^2, (Y3 * Y1 * Y3 * Y2^-1)^2, (Y3 * Y2^-1 * Y3 * Y2)^3, (Y3 * Y2^-1)^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38)(3, 39, 8, 44)(4, 40, 10, 46)(5, 41, 6, 42)(7, 43, 15, 51)(9, 45, 19, 55)(11, 47, 18, 54)(12, 48, 22, 58)(13, 49, 16, 52)(14, 50, 20, 56)(17, 53, 26, 62)(21, 57, 27, 63)(23, 59, 33, 69)(24, 60, 30, 66)(25, 61, 29, 65)(28, 64, 36, 72)(31, 67, 35, 71)(32, 68, 34, 70)(73, 109, 75, 111, 77, 113)(74, 110, 78, 114, 80, 116)(76, 112, 83, 119, 84, 120)(79, 115, 88, 124, 89, 125)(81, 117, 92, 128, 93, 129)(82, 118, 94, 130, 90, 126)(85, 121, 87, 123, 98, 134)(86, 122, 91, 127, 99, 135)(95, 131, 101, 137, 103, 139)(96, 132, 104, 140, 100, 136)(97, 133, 105, 141, 107, 143)(102, 138, 108, 144, 106, 142) L = (1, 76)(2, 79)(3, 81)(4, 73)(5, 85)(6, 86)(7, 74)(8, 90)(9, 75)(10, 95)(11, 96)(12, 97)(13, 77)(14, 78)(15, 100)(16, 101)(17, 102)(18, 80)(19, 103)(20, 104)(21, 105)(22, 106)(23, 82)(24, 83)(25, 84)(26, 107)(27, 108)(28, 87)(29, 88)(30, 89)(31, 91)(32, 92)(33, 93)(34, 94)(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) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.564 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.514 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1, Y3^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38)(3, 39, 11, 47)(4, 40, 8, 44)(5, 41, 16, 52)(6, 42, 10, 46)(7, 43, 19, 55)(9, 45, 24, 60)(12, 48, 25, 61)(13, 49, 28, 64)(14, 50, 22, 58)(15, 51, 32, 68)(17, 53, 20, 56)(18, 54, 26, 62)(21, 57, 34, 70)(23, 59, 36, 72)(27, 63, 31, 67)(29, 65, 33, 69)(30, 66, 35, 71)(73, 109, 75, 111, 77, 113)(74, 110, 79, 115, 81, 117)(76, 112, 84, 120, 87, 123)(78, 114, 85, 121, 89, 125)(80, 116, 92, 128, 95, 131)(82, 118, 93, 129, 97, 133)(83, 119, 98, 134, 99, 135)(86, 122, 96, 132, 103, 139)(88, 124, 105, 141, 94, 130)(90, 126, 101, 137, 91, 127)(100, 136, 107, 143, 104, 140)(102, 138, 108, 144, 106, 142) L = (1, 76)(2, 80)(3, 84)(4, 86)(5, 87)(6, 73)(7, 92)(8, 94)(9, 95)(10, 74)(11, 97)(12, 96)(13, 75)(14, 102)(15, 103)(16, 104)(17, 77)(18, 78)(19, 89)(20, 88)(21, 79)(22, 107)(23, 105)(24, 108)(25, 81)(26, 82)(27, 93)(28, 83)(29, 85)(30, 90)(31, 106)(32, 99)(33, 100)(34, 91)(35, 98)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.559 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.515 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y2^-1, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y3^-2 * Y1 * Y2, (Y3 * Y2 * Y1)^2, (Y3^-1 * Y2^-1 * Y1)^2, Y3^6, (Y3^-1 * Y1)^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38)(3, 39, 11, 47)(4, 40, 14, 50)(5, 41, 17, 53)(6, 42, 19, 55)(7, 43, 15, 51)(8, 44, 23, 59)(9, 45, 20, 56)(10, 46, 26, 62)(12, 48, 25, 61)(13, 49, 22, 58)(16, 52, 24, 60)(18, 54, 21, 57)(27, 63, 30, 66)(28, 64, 33, 69)(29, 65, 31, 67)(32, 68, 36, 72)(34, 70, 35, 71)(73, 109, 75, 111, 77, 113)(74, 110, 79, 115, 81, 117)(76, 112, 84, 120, 88, 124)(78, 114, 85, 121, 90, 126)(80, 116, 93, 129, 96, 132)(82, 118, 94, 130, 97, 133)(83, 119, 99, 135, 101, 137)(86, 122, 100, 136, 91, 127)(87, 123, 102, 138, 106, 142)(89, 125, 107, 143, 104, 140)(92, 128, 103, 139, 108, 144)(95, 131, 105, 141, 98, 134) L = (1, 76)(2, 80)(3, 84)(4, 87)(5, 88)(6, 73)(7, 93)(8, 83)(9, 96)(10, 74)(11, 100)(12, 102)(13, 75)(14, 104)(15, 105)(16, 106)(17, 82)(18, 77)(19, 107)(20, 78)(21, 99)(22, 79)(23, 108)(24, 101)(25, 81)(26, 103)(27, 91)(28, 89)(29, 86)(30, 98)(31, 85)(32, 97)(33, 92)(34, 95)(35, 94)(36, 90)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.556 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.516 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^2 * Y2^-1, Y2^3, (Y3^-1 * Y2^-1)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1 * Y3 * Y2 * Y1 * Y3^-1 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 11, 47)(4, 40, 13, 49)(5, 41, 14, 50)(6, 42, 15, 51)(7, 43, 16, 52)(8, 44, 18, 54)(9, 45, 19, 55)(10, 46, 20, 56)(12, 48, 17, 53)(21, 57, 29, 65)(22, 58, 33, 69)(23, 59, 36, 72)(24, 60, 32, 68)(25, 61, 30, 66)(26, 62, 34, 70)(27, 63, 35, 71)(28, 64, 31, 67)(73, 109, 75, 111, 77, 113)(74, 110, 79, 115, 81, 117)(76, 112, 84, 120, 78, 114)(80, 116, 89, 125, 82, 118)(83, 119, 93, 129, 95, 131)(85, 121, 97, 133, 99, 135)(86, 122, 100, 136, 98, 134)(87, 123, 96, 132, 94, 130)(88, 124, 101, 137, 103, 139)(90, 126, 105, 141, 107, 143)(91, 127, 108, 144, 106, 142)(92, 128, 104, 140, 102, 138) L = (1, 76)(2, 80)(3, 84)(4, 75)(5, 78)(6, 73)(7, 89)(8, 79)(9, 82)(10, 74)(11, 94)(12, 77)(13, 98)(14, 99)(15, 95)(16, 102)(17, 81)(18, 106)(19, 107)(20, 103)(21, 87)(22, 93)(23, 96)(24, 83)(25, 86)(26, 97)(27, 100)(28, 85)(29, 92)(30, 101)(31, 104)(32, 88)(33, 91)(34, 105)(35, 108)(36, 90)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.561 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.517 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (Y3 * Y1^-1)^2, (Y2^-1, Y1^-1), Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 7, 43, 12, 48)(4, 40, 13, 49, 8, 44)(6, 42, 9, 45, 15, 51)(10, 46, 17, 53, 23, 59)(11, 47, 24, 60, 18, 54)(14, 50, 25, 61, 19, 55)(16, 52, 20, 56, 27, 63)(21, 57, 28, 64, 32, 68)(22, 58, 33, 69, 29, 65)(26, 62, 34, 70, 30, 66)(31, 67, 36, 72, 35, 71)(73, 109, 75, 111, 82, 118, 93, 129, 88, 124, 78, 114)(74, 110, 79, 115, 89, 125, 100, 136, 92, 128, 81, 117)(76, 112, 83, 119, 94, 130, 103, 139, 98, 134, 86, 122)(77, 113, 84, 120, 95, 131, 104, 140, 99, 135, 87, 123)(80, 116, 90, 126, 101, 137, 107, 143, 102, 138, 91, 127)(85, 121, 96, 132, 105, 141, 108, 144, 106, 142, 97, 133) L = (1, 76)(2, 80)(3, 83)(4, 73)(5, 85)(6, 86)(7, 90)(8, 74)(9, 91)(10, 94)(11, 75)(12, 96)(13, 77)(14, 78)(15, 97)(16, 98)(17, 101)(18, 79)(19, 81)(20, 102)(21, 103)(22, 82)(23, 105)(24, 84)(25, 87)(26, 88)(27, 106)(28, 107)(29, 89)(30, 92)(31, 93)(32, 108)(33, 95)(34, 99)(35, 100)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.540 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.518 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^-2 * Y2^-2, (Y3 * Y1)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y3^6, Y3 * Y1^-1 * Y3^-3 * Y1^-1, Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y2^-1, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 14, 50)(4, 40, 16, 52, 18, 54)(6, 42, 10, 46, 21, 57)(7, 43, 22, 58, 9, 45)(11, 47, 28, 64, 20, 56)(12, 48, 23, 59, 30, 66)(13, 49, 31, 67, 27, 63)(15, 51, 33, 69, 24, 60)(17, 53, 26, 62, 34, 70)(19, 55, 32, 68, 25, 61)(29, 65, 35, 71, 36, 72)(73, 109, 75, 111, 84, 120, 101, 137, 89, 125, 78, 114)(74, 110, 80, 116, 95, 131, 107, 143, 98, 134, 82, 118)(76, 112, 85, 121, 79, 115, 87, 123, 100, 136, 91, 127)(77, 113, 86, 122, 102, 138, 108, 144, 106, 142, 93, 129)(81, 117, 96, 132, 83, 119, 97, 133, 90, 126, 99, 135)(88, 124, 103, 139, 94, 130, 105, 141, 92, 128, 104, 140) L = (1, 76)(2, 81)(3, 85)(4, 89)(5, 92)(6, 91)(7, 73)(8, 96)(9, 98)(10, 99)(11, 74)(12, 79)(13, 78)(14, 104)(15, 75)(16, 77)(17, 100)(18, 95)(19, 101)(20, 106)(21, 105)(22, 102)(23, 83)(24, 82)(25, 80)(26, 90)(27, 107)(28, 84)(29, 87)(30, 88)(31, 86)(32, 93)(33, 108)(34, 94)(35, 97)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.550 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.519 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2^-1), Y2^-1 * Y3^-1 * Y2^-1 * Y3, R * Y2 * R * Y2^-1, (Y3^-1 * Y1^-1)^2, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 13, 49)(4, 40, 9, 45, 7, 43)(6, 42, 10, 46, 16, 52)(11, 47, 19, 55, 25, 61)(12, 48, 20, 56, 14, 50)(15, 51, 21, 57, 18, 54)(17, 53, 22, 58, 28, 64)(23, 59, 30, 66, 34, 70)(24, 60, 31, 67, 26, 62)(27, 63, 32, 68, 29, 65)(33, 69, 36, 72, 35, 71)(73, 109, 75, 111, 83, 119, 95, 131, 89, 125, 78, 114)(74, 110, 80, 116, 91, 127, 102, 138, 94, 130, 82, 118)(76, 112, 87, 123, 99, 135, 105, 141, 96, 132, 84, 120)(77, 113, 85, 121, 97, 133, 106, 142, 100, 136, 88, 124)(79, 115, 90, 126, 101, 137, 107, 143, 98, 134, 86, 122)(81, 117, 93, 129, 104, 140, 108, 144, 103, 139, 92, 128) L = (1, 76)(2, 81)(3, 84)(4, 74)(5, 79)(6, 87)(7, 73)(8, 92)(9, 77)(10, 93)(11, 96)(12, 80)(13, 86)(14, 75)(15, 82)(16, 90)(17, 99)(18, 78)(19, 103)(20, 85)(21, 88)(22, 104)(23, 105)(24, 91)(25, 98)(26, 83)(27, 94)(28, 101)(29, 89)(30, 108)(31, 97)(32, 100)(33, 102)(34, 107)(35, 95)(36, 106)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.542 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.520 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2^-1), (Y2 * Y3)^2, (Y3^-1 * Y1^-1)^2, R * Y2 * Y1 * R * Y2^-1, Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y2, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 13, 49)(4, 40, 9, 45, 7, 43)(6, 42, 10, 46, 17, 53)(11, 47, 21, 57, 25, 61)(12, 48, 16, 52, 14, 50)(15, 51, 18, 54, 20, 56)(19, 55, 22, 58, 29, 65)(23, 59, 32, 68, 34, 70)(24, 60, 27, 63, 26, 62)(28, 64, 30, 66, 31, 67)(33, 69, 36, 72, 35, 71)(73, 109, 75, 111, 83, 119, 95, 131, 91, 127, 78, 114)(74, 110, 80, 116, 93, 129, 104, 140, 94, 130, 82, 118)(76, 112, 87, 123, 100, 136, 105, 141, 98, 134, 88, 124)(77, 113, 85, 121, 97, 133, 106, 142, 101, 137, 89, 125)(79, 115, 92, 128, 103, 139, 107, 143, 99, 135, 84, 120)(81, 117, 90, 126, 102, 138, 108, 144, 96, 132, 86, 122) L = (1, 76)(2, 81)(3, 84)(4, 74)(5, 79)(6, 90)(7, 73)(8, 88)(9, 77)(10, 92)(11, 96)(12, 80)(13, 86)(14, 75)(15, 78)(16, 85)(17, 87)(18, 82)(19, 103)(20, 89)(21, 99)(22, 100)(23, 105)(24, 93)(25, 98)(26, 83)(27, 97)(28, 101)(29, 102)(30, 91)(31, 94)(32, 108)(33, 104)(34, 107)(35, 95)(36, 106)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.541 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.521 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^3, (R * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 10, 46, 7, 43)(4, 40, 13, 49, 8, 44)(6, 42, 15, 51, 9, 45)(11, 47, 17, 53, 21, 57)(12, 48, 18, 54, 22, 58)(14, 50, 19, 55, 25, 61)(16, 52, 20, 56, 27, 63)(23, 59, 31, 67, 28, 64)(24, 60, 32, 68, 29, 65)(26, 62, 34, 70, 30, 66)(33, 69, 35, 71, 36, 72)(73, 109, 75, 111, 83, 119, 95, 131, 88, 124, 78, 114)(74, 110, 79, 115, 89, 125, 100, 136, 92, 128, 81, 117)(76, 112, 84, 120, 96, 132, 105, 141, 98, 134, 86, 122)(77, 113, 82, 118, 93, 129, 103, 139, 99, 135, 87, 123)(80, 116, 90, 126, 101, 137, 107, 143, 102, 138, 91, 127)(85, 121, 94, 130, 104, 140, 108, 144, 106, 142, 97, 133) L = (1, 76)(2, 80)(3, 84)(4, 73)(5, 85)(6, 86)(7, 90)(8, 74)(9, 91)(10, 94)(11, 96)(12, 75)(13, 77)(14, 78)(15, 97)(16, 98)(17, 101)(18, 79)(19, 81)(20, 102)(21, 104)(22, 82)(23, 105)(24, 83)(25, 87)(26, 88)(27, 106)(28, 107)(29, 89)(30, 92)(31, 108)(32, 93)(33, 95)(34, 99)(35, 100)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.537 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.522 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^3, Y1^3, (R * Y1)^2, (Y3 * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, R * Y2 * Y1 * R * Y2, Y2^-1 * Y3 * Y2 * Y1 * Y3, Y2^6, (Y1 * Y2^-2)^3 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 10, 46, 7, 43)(4, 40, 13, 49, 8, 44)(6, 42, 16, 52, 9, 45)(11, 47, 19, 55, 23, 59)(12, 48, 20, 56, 14, 50)(15, 51, 17, 53, 21, 57)(18, 54, 22, 58, 28, 64)(24, 60, 33, 69, 30, 66)(25, 61, 31, 67, 26, 62)(27, 63, 32, 68, 29, 65)(34, 70, 36, 72, 35, 71)(73, 109, 75, 111, 83, 119, 96, 132, 90, 126, 78, 114)(74, 110, 79, 115, 91, 127, 102, 138, 94, 130, 81, 117)(76, 112, 86, 122, 97, 133, 107, 143, 99, 135, 87, 123)(77, 113, 82, 118, 95, 131, 105, 141, 100, 136, 88, 124)(80, 116, 84, 120, 98, 134, 106, 142, 101, 137, 89, 125)(85, 121, 92, 128, 103, 139, 108, 144, 104, 140, 93, 129) L = (1, 76)(2, 80)(3, 84)(4, 73)(5, 85)(6, 89)(7, 92)(8, 74)(9, 93)(10, 86)(11, 97)(12, 75)(13, 77)(14, 82)(15, 88)(16, 87)(17, 78)(18, 99)(19, 98)(20, 79)(21, 81)(22, 101)(23, 103)(24, 106)(25, 83)(26, 91)(27, 90)(28, 104)(29, 94)(30, 108)(31, 95)(32, 100)(33, 107)(34, 96)(35, 105)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.538 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.523 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^3, (R * Y1)^2, (Y3 * Y1^-1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, Y2 * Y1^-1 * Y3 * Y2^-1 * Y3, R * Y2 * R * Y1 * Y2, Y2^6, (Y2^-1 * Y1 * Y2^-1)^3 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 10, 46, 7, 43)(4, 40, 13, 49, 8, 44)(6, 42, 16, 52, 9, 45)(11, 47, 19, 55, 23, 59)(12, 48, 14, 50, 20, 56)(15, 51, 21, 57, 17, 53)(18, 54, 22, 58, 28, 64)(24, 60, 33, 69, 30, 66)(25, 61, 26, 62, 31, 67)(27, 63, 29, 65, 32, 68)(34, 70, 35, 71, 36, 72)(73, 109, 75, 111, 83, 119, 96, 132, 90, 126, 78, 114)(74, 110, 79, 115, 91, 127, 102, 138, 94, 130, 81, 117)(76, 112, 86, 122, 97, 133, 107, 143, 99, 135, 87, 123)(77, 113, 82, 118, 95, 131, 105, 141, 100, 136, 88, 124)(80, 116, 92, 128, 103, 139, 108, 144, 104, 140, 93, 129)(84, 120, 98, 134, 106, 142, 101, 137, 89, 125, 85, 121) L = (1, 76)(2, 80)(3, 84)(4, 73)(5, 85)(6, 89)(7, 86)(8, 74)(9, 87)(10, 92)(11, 97)(12, 75)(13, 77)(14, 79)(15, 81)(16, 93)(17, 78)(18, 99)(19, 103)(20, 82)(21, 88)(22, 104)(23, 98)(24, 106)(25, 83)(26, 95)(27, 90)(28, 101)(29, 100)(30, 107)(31, 91)(32, 94)(33, 108)(34, 96)(35, 102)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.539 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.524 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 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, Y3^2, Y1^3, (Y3 * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y2 * Y3 * Y2, R * Y2 * Y1 * R * Y2^-1, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 10, 46, 7, 43)(4, 40, 13, 49, 8, 44)(6, 42, 16, 52, 9, 45)(11, 47, 19, 55, 23, 59)(12, 48, 20, 56, 15, 51)(14, 50, 17, 53, 21, 57)(18, 54, 22, 58, 28, 64)(24, 60, 33, 69, 30, 66)(25, 61, 31, 67, 26, 62)(27, 63, 32, 68, 29, 65)(34, 70, 36, 72, 35, 71)(73, 109, 75, 111, 83, 119, 96, 132, 90, 126, 78, 114)(74, 110, 79, 115, 91, 127, 102, 138, 94, 130, 81, 117)(76, 112, 86, 122, 99, 135, 107, 143, 97, 133, 87, 123)(77, 113, 82, 118, 95, 131, 105, 141, 100, 136, 88, 124)(80, 116, 89, 125, 101, 137, 106, 142, 98, 134, 84, 120)(85, 121, 93, 129, 104, 140, 108, 144, 103, 139, 92, 128) L = (1, 76)(2, 80)(3, 84)(4, 73)(5, 85)(6, 89)(7, 92)(8, 74)(9, 93)(10, 87)(11, 97)(12, 75)(13, 77)(14, 88)(15, 82)(16, 86)(17, 78)(18, 99)(19, 98)(20, 79)(21, 81)(22, 101)(23, 103)(24, 106)(25, 83)(26, 91)(27, 90)(28, 104)(29, 94)(30, 108)(31, 95)(32, 100)(33, 107)(34, 96)(35, 105)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.551 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.525 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 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, Y3^2, Y1^3, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, R * Y2 * Y1^-1 * R * Y2^-1, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 10, 46, 7, 43)(4, 40, 13, 49, 8, 44)(6, 42, 16, 52, 9, 45)(11, 47, 19, 55, 23, 59)(12, 48, 15, 51, 21, 57)(14, 50, 20, 56, 17, 53)(18, 54, 22, 58, 28, 64)(24, 60, 33, 69, 30, 66)(25, 61, 26, 62, 31, 67)(27, 63, 29, 65, 32, 68)(34, 70, 35, 71, 36, 72)(73, 109, 75, 111, 83, 119, 96, 132, 90, 126, 78, 114)(74, 110, 79, 115, 91, 127, 102, 138, 94, 130, 81, 117)(76, 112, 86, 122, 99, 135, 107, 143, 97, 133, 87, 123)(77, 113, 82, 118, 95, 131, 105, 141, 100, 136, 88, 124)(80, 116, 92, 128, 104, 140, 108, 144, 103, 139, 93, 129)(84, 120, 85, 121, 89, 125, 101, 137, 106, 142, 98, 134) L = (1, 76)(2, 80)(3, 84)(4, 73)(5, 85)(6, 89)(7, 87)(8, 74)(9, 86)(10, 93)(11, 97)(12, 75)(13, 77)(14, 81)(15, 79)(16, 92)(17, 78)(18, 99)(19, 103)(20, 88)(21, 82)(22, 104)(23, 98)(24, 106)(25, 83)(26, 95)(27, 90)(28, 101)(29, 100)(30, 107)(31, 91)(32, 94)(33, 108)(34, 96)(35, 102)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.552 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.526 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1 * Y2^-1, (Y3^-1 * Y1^-1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y2 * Y3^-1)^2, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 11, 47, 8, 44)(4, 40, 9, 45, 7, 43)(6, 42, 16, 52, 10, 46)(12, 48, 19, 55, 23, 59)(13, 49, 20, 56, 14, 50)(15, 51, 17, 53, 21, 57)(18, 54, 22, 58, 28, 64)(24, 60, 33, 69, 30, 66)(25, 61, 31, 67, 26, 62)(27, 63, 32, 68, 29, 65)(34, 70, 36, 72, 35, 71)(73, 109, 75, 111, 84, 120, 96, 132, 90, 126, 78, 114)(74, 110, 80, 116, 91, 127, 102, 138, 94, 130, 82, 118)(76, 112, 86, 122, 97, 133, 107, 143, 99, 135, 87, 123)(77, 113, 83, 119, 95, 131, 105, 141, 100, 136, 88, 124)(79, 115, 85, 121, 98, 134, 106, 142, 101, 137, 89, 125)(81, 117, 92, 128, 103, 139, 108, 144, 104, 140, 93, 129) L = (1, 76)(2, 81)(3, 85)(4, 74)(5, 79)(6, 89)(7, 73)(8, 86)(9, 77)(10, 87)(11, 92)(12, 97)(13, 83)(14, 75)(15, 78)(16, 93)(17, 88)(18, 99)(19, 103)(20, 80)(21, 82)(22, 104)(23, 98)(24, 106)(25, 91)(26, 84)(27, 94)(28, 101)(29, 90)(30, 107)(31, 95)(32, 100)(33, 108)(34, 105)(35, 96)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.535 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.527 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (Y2^-1 * Y3^-1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y2 * Y3)^2, Y1 * Y2 * Y1 * Y2^-3, Y2^6, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1 * Y2^3, Y2 * Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 11, 47, 10, 46)(4, 40, 9, 45, 7, 43)(6, 42, 17, 53, 20, 56)(8, 44, 23, 59, 18, 54)(12, 48, 24, 60, 30, 66)(13, 49, 26, 62, 14, 50)(15, 51, 19, 55, 27, 63)(16, 52, 22, 58, 25, 61)(21, 57, 28, 64, 29, 65)(31, 67, 35, 71, 32, 68)(33, 69, 34, 70, 36, 72)(73, 109, 75, 111, 84, 120, 95, 131, 93, 129, 78, 114)(74, 110, 80, 116, 96, 132, 92, 128, 100, 136, 82, 118)(76, 112, 87, 123, 103, 139, 86, 122, 106, 142, 88, 124)(77, 113, 89, 125, 102, 138, 83, 119, 101, 137, 90, 126)(79, 115, 94, 130, 104, 140, 91, 127, 105, 141, 85, 121)(81, 117, 98, 134, 107, 143, 97, 133, 108, 144, 99, 135) L = (1, 76)(2, 81)(3, 85)(4, 74)(5, 79)(6, 91)(7, 73)(8, 88)(9, 77)(10, 86)(11, 98)(12, 103)(13, 83)(14, 75)(15, 78)(16, 95)(17, 99)(18, 97)(19, 89)(20, 87)(21, 106)(22, 90)(23, 94)(24, 107)(25, 80)(26, 82)(27, 92)(28, 108)(29, 105)(30, 104)(31, 96)(32, 84)(33, 93)(34, 100)(35, 102)(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, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.536 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.528 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y3, Y2^-1), Y3^-2 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1^-1)^2, (Y2 * Y1^-1)^2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y3 * Y2 * Y1 * Y2 * Y3 * Y1^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^2, Y2^6, Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 12, 48, 10, 46)(4, 40, 16, 52, 18, 54)(6, 42, 20, 56, 23, 59)(7, 43, 24, 60, 9, 45)(8, 44, 25, 61, 22, 58)(11, 47, 31, 67, 21, 57)(13, 49, 26, 62, 34, 70)(14, 50, 27, 63, 36, 72)(15, 51, 28, 64, 33, 69)(17, 53, 29, 65, 32, 68)(19, 55, 30, 66, 35, 71)(73, 109, 75, 111, 85, 121, 97, 133, 89, 125, 78, 114)(74, 110, 80, 116, 98, 134, 95, 131, 101, 137, 82, 118)(76, 112, 86, 122, 79, 115, 87, 123, 103, 139, 91, 127)(77, 113, 92, 128, 106, 142, 84, 120, 104, 140, 94, 130)(81, 117, 99, 135, 83, 119, 100, 136, 90, 126, 102, 138)(88, 124, 105, 141, 96, 132, 107, 143, 93, 129, 108, 144) L = (1, 76)(2, 81)(3, 86)(4, 89)(5, 93)(6, 91)(7, 73)(8, 99)(9, 101)(10, 102)(11, 74)(12, 105)(13, 79)(14, 78)(15, 75)(16, 77)(17, 103)(18, 98)(19, 97)(20, 108)(21, 104)(22, 107)(23, 100)(24, 106)(25, 87)(26, 83)(27, 82)(28, 80)(29, 90)(30, 95)(31, 85)(32, 96)(33, 92)(34, 88)(35, 84)(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) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.545 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.529 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y2 * Y1^-1 * Y2, Y1^3, (R * Y1)^2, (Y1 * Y2)^2, (R * Y3)^2, (Y1 * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 6, 42)(4, 40, 9, 45, 7, 43)(10, 46, 14, 50, 11, 47)(12, 48, 15, 51, 13, 49)(16, 52, 18, 54, 17, 53)(19, 55, 21, 57, 20, 56)(22, 58, 24, 60, 23, 59)(25, 61, 27, 63, 26, 62)(28, 64, 30, 66, 29, 65)(31, 67, 33, 69, 32, 68)(34, 70, 36, 72, 35, 71)(73, 109, 75, 111, 74, 110, 80, 116, 77, 113, 78, 114)(76, 112, 84, 120, 81, 117, 87, 123, 79, 115, 85, 121)(82, 118, 88, 124, 86, 122, 90, 126, 83, 119, 89, 125)(91, 127, 97, 133, 93, 129, 99, 135, 92, 128, 98, 134)(94, 130, 100, 136, 96, 132, 102, 138, 95, 131, 101, 137)(103, 139, 106, 142, 105, 141, 108, 144, 104, 140, 107, 143) L = (1, 76)(2, 81)(3, 82)(4, 74)(5, 79)(6, 83)(7, 73)(8, 86)(9, 77)(10, 80)(11, 75)(12, 91)(13, 92)(14, 78)(15, 93)(16, 94)(17, 95)(18, 96)(19, 87)(20, 84)(21, 85)(22, 90)(23, 88)(24, 89)(25, 103)(26, 104)(27, 105)(28, 106)(29, 107)(30, 108)(31, 99)(32, 97)(33, 98)(34, 102)(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) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.543 Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.530 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y3 * Y1)^2, (Y1 * Y2)^2, Y3^2 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y3^-1 * Y1^-1 * Y2 * Y3 * Y2, Y2^-1 * Y3^-1 * Y1 * Y3 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y2^-2 * Y1^-1, Y3 * Y2^2 * Y1^-1 * Y3 * Y1^-1, Y3^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, (Y1^-1 * R * Y2^-1)^2 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 12, 48, 15, 51)(4, 40, 17, 53, 19, 55)(6, 42, 23, 59, 8, 44)(7, 43, 26, 62, 9, 45)(10, 46, 31, 67, 21, 57)(11, 47, 34, 70, 22, 58)(13, 49, 28, 64, 36, 72)(14, 50, 29, 65, 20, 56)(16, 52, 30, 66, 27, 63)(18, 54, 25, 61, 33, 69)(24, 60, 32, 68, 35, 71)(73, 109, 75, 111, 85, 121, 103, 139, 96, 132, 78, 114)(74, 110, 80, 116, 100, 136, 87, 123, 104, 140, 82, 118)(76, 112, 90, 126, 106, 142, 99, 135, 79, 115, 92, 128)(77, 113, 93, 129, 108, 144, 95, 131, 107, 143, 84, 120)(81, 117, 97, 133, 91, 127, 88, 124, 83, 119, 86, 122)(89, 125, 101, 137, 94, 130, 105, 141, 98, 134, 102, 138) L = (1, 76)(2, 81)(3, 86)(4, 85)(5, 94)(6, 88)(7, 73)(8, 101)(9, 100)(10, 102)(11, 74)(12, 99)(13, 106)(14, 103)(15, 105)(16, 75)(17, 77)(18, 84)(19, 104)(20, 95)(21, 92)(22, 108)(23, 90)(24, 79)(25, 78)(26, 107)(27, 93)(28, 91)(29, 87)(30, 80)(31, 97)(32, 83)(33, 82)(34, 96)(35, 89)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.546 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.531 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, Y3^2 * Y2^-2, (Y3^-1 * Y1^-1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y1, R * Y2 * Y1^-1 * R * Y2^-1, Y2^-1 * Y1^-1 * Y3 * Y2 * Y3, Y3^2 * Y2^4, (Y3 * Y1^-1 * Y2)^2, Y2^-3 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 12, 48, 15, 51)(4, 40, 17, 53, 19, 55)(6, 42, 23, 59, 8, 44)(7, 43, 26, 62, 9, 45)(10, 46, 31, 67, 21, 57)(11, 47, 33, 69, 22, 58)(13, 49, 28, 64, 36, 72)(14, 50, 27, 63, 34, 70)(16, 52, 18, 54, 29, 65)(20, 56, 30, 66, 25, 61)(24, 60, 32, 68, 35, 71)(73, 109, 75, 111, 85, 121, 103, 139, 96, 132, 78, 114)(74, 110, 80, 116, 100, 136, 87, 123, 104, 140, 82, 118)(76, 112, 90, 126, 105, 141, 99, 135, 79, 115, 92, 128)(77, 113, 93, 129, 108, 144, 95, 131, 107, 143, 84, 120)(81, 117, 101, 137, 91, 127, 106, 142, 83, 119, 102, 138)(86, 122, 89, 125, 97, 133, 94, 130, 88, 124, 98, 134) L = (1, 76)(2, 81)(3, 86)(4, 85)(5, 94)(6, 88)(7, 73)(8, 99)(9, 100)(10, 90)(11, 74)(12, 101)(13, 105)(14, 103)(15, 92)(16, 75)(17, 77)(18, 80)(19, 104)(20, 82)(21, 106)(22, 108)(23, 102)(24, 79)(25, 78)(26, 107)(27, 87)(28, 91)(29, 93)(30, 84)(31, 97)(32, 83)(33, 96)(34, 95)(35, 89)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.547 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.532 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y2 * Y1 * Y2, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y1 * Y2^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 6, 42, 9, 45)(4, 40, 8, 44, 7, 43)(10, 46, 14, 50, 11, 47)(12, 48, 13, 49, 15, 51)(16, 52, 17, 53, 18, 54)(19, 55, 21, 57, 20, 56)(22, 58, 24, 60, 23, 59)(25, 61, 26, 62, 27, 63)(28, 64, 29, 65, 30, 66)(31, 67, 33, 69, 32, 68)(34, 70, 36, 72, 35, 71)(73, 109, 75, 111, 77, 113, 81, 117, 74, 110, 78, 114)(76, 112, 84, 120, 79, 115, 87, 123, 80, 116, 85, 121)(82, 118, 88, 124, 83, 119, 90, 126, 86, 122, 89, 125)(91, 127, 97, 133, 92, 128, 99, 135, 93, 129, 98, 134)(94, 130, 100, 136, 95, 131, 102, 138, 96, 132, 101, 137)(103, 139, 106, 142, 104, 140, 107, 143, 105, 141, 108, 144) L = (1, 76)(2, 80)(3, 82)(4, 74)(5, 79)(6, 86)(7, 73)(8, 77)(9, 83)(10, 78)(11, 75)(12, 91)(13, 93)(14, 81)(15, 92)(16, 94)(17, 96)(18, 95)(19, 85)(20, 84)(21, 87)(22, 89)(23, 88)(24, 90)(25, 103)(26, 105)(27, 104)(28, 106)(29, 108)(30, 107)(31, 98)(32, 97)(33, 99)(34, 101)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.544 Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.533 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y2^-1 * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y3^2 * Y2^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y1, Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y2, R * Y2 * Y1 * R * Y2^-1, Y3^6, (Y2^-1 * Y1^-1 * Y3)^2, Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3^-2 * Y1 * Y2^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 12, 48, 10, 46)(4, 40, 16, 52, 19, 55)(6, 42, 21, 57, 25, 61)(7, 43, 26, 62, 9, 45)(8, 44, 28, 64, 23, 59)(11, 47, 34, 70, 22, 58)(13, 49, 29, 65, 36, 72)(14, 50, 30, 66, 27, 63)(15, 51, 31, 67, 20, 56)(17, 53, 24, 60, 33, 69)(18, 54, 32, 68, 35, 71)(73, 109, 75, 111, 85, 121, 100, 136, 90, 126, 78, 114)(74, 110, 80, 116, 101, 137, 97, 133, 104, 140, 82, 118)(76, 112, 89, 125, 79, 115, 99, 135, 106, 142, 92, 128)(77, 113, 93, 129, 108, 144, 84, 120, 107, 143, 95, 131)(81, 117, 96, 132, 83, 119, 86, 122, 91, 127, 87, 123)(88, 124, 102, 138, 98, 134, 103, 139, 94, 130, 105, 141) L = (1, 76)(2, 81)(3, 86)(4, 90)(5, 94)(6, 96)(7, 73)(8, 102)(9, 104)(10, 105)(11, 74)(12, 92)(13, 79)(14, 78)(15, 75)(16, 77)(17, 84)(18, 106)(19, 101)(20, 93)(21, 99)(22, 107)(23, 89)(24, 100)(25, 103)(26, 108)(27, 95)(28, 87)(29, 83)(30, 82)(31, 80)(32, 91)(33, 97)(34, 85)(35, 98)(36, 88)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.548 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.534 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y1^3, (R * Y3)^2, Y3^-2 * Y2^-2, (Y2^-1 * Y1)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1 * Y2 * R * Y2^-1 * R, Y2 * Y1^-1 * Y3 * Y2^-1 * Y3, Y2 * Y3^-1 * Y2 * Y3 * Y1, Y3^-2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2, Y2^-2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y1 * Y2 * Y3 * Y1^-1 * Y3 * Y2 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 12, 48, 10, 46)(4, 40, 16, 52, 19, 55)(6, 42, 21, 57, 25, 61)(7, 43, 26, 62, 9, 45)(8, 44, 28, 64, 23, 59)(11, 47, 33, 69, 22, 58)(13, 49, 29, 65, 36, 72)(14, 50, 20, 56, 32, 68)(15, 51, 17, 53, 30, 66)(18, 54, 31, 67, 35, 71)(24, 60, 27, 63, 34, 70)(73, 109, 75, 111, 85, 121, 100, 136, 90, 126, 78, 114)(74, 110, 80, 116, 101, 137, 97, 133, 103, 139, 82, 118)(76, 112, 89, 125, 79, 115, 99, 135, 105, 141, 92, 128)(77, 113, 93, 129, 108, 144, 84, 120, 107, 143, 95, 131)(81, 117, 102, 138, 83, 119, 106, 142, 91, 127, 104, 140)(86, 122, 94, 130, 87, 123, 88, 124, 96, 132, 98, 134) L = (1, 76)(2, 81)(3, 86)(4, 90)(5, 94)(6, 96)(7, 73)(8, 92)(9, 103)(10, 99)(11, 74)(12, 102)(13, 79)(14, 78)(15, 75)(16, 77)(17, 80)(18, 105)(19, 101)(20, 82)(21, 104)(22, 107)(23, 106)(24, 100)(25, 89)(26, 108)(27, 97)(28, 87)(29, 83)(30, 93)(31, 91)(32, 95)(33, 85)(34, 84)(35, 98)(36, 88)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.549 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.535 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3 * Y2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y3)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 17, 53, 16, 52, 5, 41)(3, 39, 8, 44, 18, 54, 28, 64, 25, 61, 12, 48)(4, 40, 10, 46, 19, 55, 30, 66, 26, 62, 14, 50)(6, 42, 9, 45, 20, 56, 29, 65, 27, 63, 15, 51)(11, 47, 22, 58, 31, 67, 36, 72, 33, 69, 23, 59)(13, 49, 21, 57, 32, 68, 35, 71, 34, 70, 24, 60)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 83, 119)(77, 113, 84, 120)(78, 114, 85, 121)(79, 115, 90, 126)(81, 117, 93, 129)(82, 118, 94, 130)(86, 122, 95, 131)(87, 123, 96, 132)(88, 124, 97, 133)(89, 125, 100, 136)(91, 127, 103, 139)(92, 128, 104, 140)(98, 134, 105, 141)(99, 135, 106, 142)(101, 137, 107, 143)(102, 138, 108, 144) L = (1, 76)(2, 81)(3, 83)(4, 85)(5, 87)(6, 73)(7, 91)(8, 93)(9, 94)(10, 74)(11, 78)(12, 96)(13, 75)(14, 77)(15, 95)(16, 98)(17, 101)(18, 103)(19, 104)(20, 79)(21, 82)(22, 80)(23, 84)(24, 86)(25, 105)(26, 106)(27, 88)(28, 107)(29, 108)(30, 89)(31, 92)(32, 90)(33, 99)(34, 97)(35, 102)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.526 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.536 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-3 * Y2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^6, Y3^-1 * Y1^-1 * Y3^-1 * Y1^3, Y1^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 19, 55, 16, 52, 5, 41)(3, 39, 8, 44, 20, 56, 32, 68, 29, 65, 12, 48)(4, 40, 14, 50, 21, 57, 17, 53, 26, 62, 10, 46)(6, 42, 15, 51, 22, 58, 9, 45, 25, 61, 18, 54)(11, 47, 27, 63, 33, 69, 30, 66, 36, 72, 24, 60)(13, 49, 28, 64, 34, 70, 23, 59, 35, 71, 31, 67)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 83, 119)(77, 113, 84, 120)(78, 114, 85, 121)(79, 115, 92, 128)(81, 117, 95, 131)(82, 118, 96, 132)(86, 122, 99, 135)(87, 123, 100, 136)(88, 124, 101, 137)(89, 125, 102, 138)(90, 126, 103, 139)(91, 127, 104, 140)(93, 129, 105, 141)(94, 130, 106, 142)(97, 133, 107, 143)(98, 134, 108, 144) L = (1, 76)(2, 81)(3, 83)(4, 85)(5, 87)(6, 73)(7, 93)(8, 95)(9, 96)(10, 74)(11, 78)(12, 100)(13, 75)(14, 91)(15, 102)(16, 98)(17, 77)(18, 99)(19, 90)(20, 105)(21, 106)(22, 79)(23, 82)(24, 80)(25, 88)(26, 107)(27, 104)(28, 89)(29, 108)(30, 84)(31, 86)(32, 103)(33, 94)(34, 92)(35, 101)(36, 97)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.527 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.537 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2 * Y3)^2, Y1^6, (Y3 * Y2)^3 ] Map:: non-degenerate R = (1, 37, 2, 38, 6, 42, 14, 50, 13, 49, 5, 41)(3, 39, 7, 43, 15, 51, 24, 60, 21, 57, 10, 46)(4, 40, 8, 44, 16, 52, 25, 61, 23, 59, 12, 48)(9, 45, 17, 53, 26, 62, 32, 68, 30, 66, 20, 56)(11, 47, 18, 54, 27, 63, 33, 69, 31, 67, 22, 58)(19, 55, 28, 64, 34, 70, 36, 72, 35, 71, 29, 65)(73, 109, 75, 111)(74, 110, 79, 115)(76, 112, 83, 119)(77, 113, 82, 118)(78, 114, 87, 123)(80, 116, 90, 126)(81, 117, 91, 127)(84, 120, 94, 130)(85, 121, 93, 129)(86, 122, 96, 132)(88, 124, 99, 135)(89, 125, 100, 136)(92, 128, 101, 137)(95, 131, 103, 139)(97, 133, 105, 141)(98, 134, 106, 142)(102, 138, 107, 143)(104, 140, 108, 144) L = (1, 76)(2, 80)(3, 81)(4, 73)(5, 84)(6, 88)(7, 89)(8, 74)(9, 75)(10, 92)(11, 91)(12, 77)(13, 95)(14, 97)(15, 98)(16, 78)(17, 79)(18, 100)(19, 83)(20, 82)(21, 102)(22, 101)(23, 85)(24, 104)(25, 86)(26, 87)(27, 106)(28, 90)(29, 94)(30, 93)(31, 107)(32, 96)(33, 108)(34, 99)(35, 103)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.521 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.538 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y1^-1 * Y2 * Y1, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y2 * Y1 * Y2 * Y1^-1, Y2 * Y1^-2 * Y3 * Y1^2, Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y2, (R * Y2 * Y3)^2, Y1^6, (Y1^-2 * Y2 * Y3)^3 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 6, 42, 16, 52, 15, 51, 5, 41)(3, 39, 8, 44, 21, 57, 28, 64, 25, 61, 10, 46)(4, 40, 11, 47, 17, 53, 29, 65, 26, 62, 13, 49)(7, 43, 18, 54, 31, 67, 27, 63, 14, 50, 20, 56)(9, 45, 19, 55, 30, 66, 35, 71, 33, 69, 23, 59)(12, 48, 22, 58, 32, 68, 36, 72, 34, 70, 24, 60)(73, 109, 75, 111)(74, 110, 79, 115)(76, 112, 84, 120)(77, 113, 85, 121)(78, 114, 89, 125)(80, 116, 94, 130)(81, 117, 92, 128)(82, 118, 95, 131)(83, 119, 91, 127)(86, 122, 96, 132)(87, 123, 99, 135)(88, 124, 100, 136)(90, 126, 104, 140)(93, 129, 102, 138)(97, 133, 106, 142)(98, 134, 105, 141)(101, 137, 108, 144)(103, 139, 107, 143) L = (1, 76)(2, 80)(3, 81)(4, 73)(5, 86)(6, 90)(7, 91)(8, 74)(9, 75)(10, 96)(11, 94)(12, 92)(13, 95)(14, 77)(15, 97)(16, 101)(17, 102)(18, 78)(19, 79)(20, 84)(21, 104)(22, 83)(23, 85)(24, 82)(25, 87)(26, 106)(27, 105)(28, 107)(29, 88)(30, 89)(31, 108)(32, 93)(33, 99)(34, 98)(35, 100)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.522 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.539 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1 * Y2 * Y1^-1 * Y3, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^-1 * Y2 * Y1 * Y3 * Y2, (R * Y2 * Y3)^2, Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1, Y1^-2 * Y2 * Y1^2 * Y3, Y1^6, Y1^-1 * Y3 * Y2 * Y1^-2 * Y2 * Y1^-2 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 6, 42, 16, 52, 15, 51, 5, 41)(3, 39, 9, 45, 18, 54, 28, 64, 25, 61, 11, 47)(4, 40, 7, 43, 19, 55, 29, 65, 26, 62, 13, 49)(8, 44, 17, 53, 30, 66, 27, 63, 14, 50, 22, 58)(10, 46, 20, 56, 31, 67, 35, 71, 33, 69, 23, 59)(12, 48, 21, 57, 32, 68, 36, 72, 34, 70, 24, 60)(73, 109, 75, 111)(74, 110, 79, 115)(76, 112, 84, 120)(77, 113, 86, 122)(78, 114, 89, 125)(80, 116, 93, 129)(81, 117, 92, 128)(82, 118, 94, 130)(83, 119, 96, 132)(85, 121, 95, 131)(87, 123, 98, 134)(88, 124, 100, 136)(90, 126, 104, 140)(91, 127, 103, 139)(97, 133, 105, 141)(99, 135, 106, 142)(101, 137, 108, 144)(102, 138, 107, 143) L = (1, 76)(2, 80)(3, 82)(4, 73)(5, 83)(6, 90)(7, 92)(8, 74)(9, 93)(10, 75)(11, 77)(12, 94)(13, 96)(14, 95)(15, 99)(16, 101)(17, 103)(18, 78)(19, 104)(20, 79)(21, 81)(22, 84)(23, 86)(24, 85)(25, 106)(26, 105)(27, 87)(28, 107)(29, 88)(30, 108)(31, 89)(32, 91)(33, 98)(34, 97)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.523 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.540 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y2 * Y3 * Y1 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y3 * Y2 * Y1^-1, Y2 * Y1 * Y3 * Y2 * Y3 * Y1^-1, Y1^6, (Y3 * Y2)^3 ] Map:: non-degenerate R = (1, 37, 2, 38, 6, 42, 16, 52, 15, 51, 5, 41)(3, 39, 9, 45, 17, 53, 30, 66, 25, 61, 11, 47)(4, 40, 8, 44, 18, 54, 29, 65, 26, 62, 13, 49)(7, 43, 19, 55, 28, 64, 27, 63, 14, 50, 21, 57)(10, 46, 22, 58, 31, 67, 36, 72, 33, 69, 23, 59)(12, 48, 20, 56, 32, 68, 35, 71, 34, 70, 24, 60)(73, 109, 75, 111)(74, 110, 79, 115)(76, 112, 84, 120)(77, 113, 86, 122)(78, 114, 89, 125)(80, 116, 94, 130)(81, 117, 92, 128)(82, 118, 93, 129)(83, 119, 96, 132)(85, 121, 95, 131)(87, 123, 97, 133)(88, 124, 100, 136)(90, 126, 104, 140)(91, 127, 103, 139)(98, 134, 106, 142)(99, 135, 105, 141)(101, 137, 108, 144)(102, 138, 107, 143) L = (1, 76)(2, 80)(3, 82)(4, 73)(5, 85)(6, 90)(7, 92)(8, 74)(9, 94)(10, 75)(11, 95)(12, 93)(13, 77)(14, 96)(15, 98)(16, 101)(17, 103)(18, 78)(19, 104)(20, 79)(21, 84)(22, 81)(23, 83)(24, 86)(25, 105)(26, 87)(27, 106)(28, 107)(29, 88)(30, 108)(31, 89)(32, 91)(33, 97)(34, 99)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.517 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.541 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1^-1 * Y3^2 * Y1^-1, Y3^-3 * Y2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^2 * Y1^4, (Y3^-1 * Y1 * Y2)^2, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 15, 51, 12, 48, 5, 41)(3, 39, 11, 47, 6, 42, 14, 50, 4, 40, 13, 49)(8, 44, 16, 52, 10, 46, 18, 54, 9, 45, 17, 53)(19, 55, 25, 61, 21, 57, 27, 63, 20, 56, 26, 62)(22, 58, 28, 64, 24, 60, 30, 66, 23, 59, 29, 65)(31, 67, 34, 70, 33, 69, 36, 72, 32, 68, 35, 71)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 84, 120)(77, 113, 81, 117)(78, 114, 79, 115)(82, 118, 87, 123)(83, 119, 91, 127)(85, 121, 92, 128)(86, 122, 93, 129)(88, 124, 94, 130)(89, 125, 95, 131)(90, 126, 96, 132)(97, 133, 103, 139)(98, 134, 104, 140)(99, 135, 105, 141)(100, 136, 106, 142)(101, 137, 107, 143)(102, 138, 108, 144) L = (1, 76)(2, 81)(3, 84)(4, 79)(5, 82)(6, 73)(7, 75)(8, 77)(9, 87)(10, 74)(11, 92)(12, 78)(13, 93)(14, 91)(15, 80)(16, 95)(17, 96)(18, 94)(19, 85)(20, 86)(21, 83)(22, 89)(23, 90)(24, 88)(25, 104)(26, 105)(27, 103)(28, 107)(29, 108)(30, 106)(31, 98)(32, 99)(33, 97)(34, 101)(35, 102)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.520 Graph:: bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.542 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, Y1^-1 * Y3 * Y2 * Y1^-1, Y3^-3 * Y2, Y2 * Y3 * Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y1^4, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 15, 51, 13, 49, 5, 41)(3, 39, 11, 47, 4, 40, 14, 50, 6, 42, 12, 48)(8, 44, 16, 52, 9, 45, 18, 54, 10, 46, 17, 53)(19, 55, 25, 61, 20, 56, 27, 63, 21, 57, 26, 62)(22, 58, 28, 64, 23, 59, 30, 66, 24, 60, 29, 65)(31, 67, 34, 70, 32, 68, 35, 71, 33, 69, 36, 72)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 79, 115)(77, 113, 82, 118)(78, 114, 85, 121)(81, 117, 87, 123)(83, 119, 91, 127)(84, 120, 93, 129)(86, 122, 92, 128)(88, 124, 94, 130)(89, 125, 96, 132)(90, 126, 95, 131)(97, 133, 103, 139)(98, 134, 105, 141)(99, 135, 104, 140)(100, 136, 106, 142)(101, 137, 108, 144)(102, 138, 107, 143) L = (1, 76)(2, 81)(3, 79)(4, 85)(5, 80)(6, 73)(7, 78)(8, 87)(9, 77)(10, 74)(11, 92)(12, 91)(13, 75)(14, 93)(15, 82)(16, 95)(17, 94)(18, 96)(19, 86)(20, 84)(21, 83)(22, 90)(23, 89)(24, 88)(25, 104)(26, 103)(27, 105)(28, 107)(29, 106)(30, 108)(31, 99)(32, 98)(33, 97)(34, 102)(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) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.519 Graph:: bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.543 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3 * Y2, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (R * Y1)^2, (Y2 * Y1^-1)^2, Y3^-1 * Y2 * Y3 * Y2, Y1^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 7, 43, 17, 53, 15, 51, 5, 41)(3, 39, 11, 47, 23, 59, 28, 64, 18, 54, 8, 44)(4, 40, 14, 50, 26, 62, 29, 65, 19, 55, 9, 45)(6, 42, 16, 52, 27, 63, 30, 66, 20, 56, 10, 46)(12, 48, 21, 57, 31, 67, 35, 71, 33, 69, 24, 60)(13, 49, 22, 58, 32, 68, 36, 72, 34, 70, 25, 61)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 84, 120)(77, 113, 83, 119)(78, 114, 85, 121)(79, 115, 90, 126)(81, 117, 93, 129)(82, 118, 94, 130)(86, 122, 96, 132)(87, 123, 95, 131)(88, 124, 97, 133)(89, 125, 100, 136)(91, 127, 103, 139)(92, 128, 104, 140)(98, 134, 105, 141)(99, 135, 106, 142)(101, 137, 107, 143)(102, 138, 108, 144) L = (1, 76)(2, 81)(3, 84)(4, 85)(5, 86)(6, 73)(7, 91)(8, 93)(9, 94)(10, 74)(11, 96)(12, 78)(13, 75)(14, 97)(15, 98)(16, 77)(17, 101)(18, 103)(19, 104)(20, 79)(21, 82)(22, 80)(23, 105)(24, 88)(25, 83)(26, 106)(27, 87)(28, 107)(29, 108)(30, 89)(31, 92)(32, 90)(33, 99)(34, 95)(35, 102)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.529 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.544 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-3 * Y2, Y3^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (R * Y2)^2, Y1^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 7, 43, 17, 53, 16, 52, 5, 41)(3, 39, 11, 47, 23, 59, 28, 64, 20, 56, 9, 45)(4, 40, 14, 50, 26, 62, 29, 65, 18, 54, 10, 46)(6, 42, 15, 51, 27, 63, 30, 66, 19, 55, 8, 44)(12, 48, 21, 57, 31, 67, 35, 71, 33, 69, 25, 61)(13, 49, 22, 58, 32, 68, 36, 72, 34, 70, 24, 60)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 84, 120)(77, 113, 86, 122)(78, 114, 85, 121)(79, 115, 90, 126)(81, 117, 93, 129)(82, 118, 94, 130)(83, 119, 96, 132)(87, 123, 97, 133)(88, 124, 99, 135)(89, 125, 100, 136)(91, 127, 103, 139)(92, 128, 104, 140)(95, 131, 105, 141)(98, 134, 106, 142)(101, 137, 107, 143)(102, 138, 108, 144) L = (1, 76)(2, 81)(3, 84)(4, 85)(5, 87)(6, 73)(7, 91)(8, 93)(9, 94)(10, 74)(11, 77)(12, 78)(13, 75)(14, 97)(15, 96)(16, 95)(17, 101)(18, 103)(19, 104)(20, 79)(21, 82)(22, 80)(23, 106)(24, 86)(25, 83)(26, 88)(27, 105)(28, 107)(29, 108)(30, 89)(31, 92)(32, 90)(33, 98)(34, 99)(35, 102)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.532 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.545 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1 * Y1)^2, Y1^-1 * Y3^2 * Y1^-1, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^4, (Y3 * Y2)^3, (Y1^-1 * Y3^-1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 18, 54, 15, 51, 5, 41)(3, 39, 8, 44, 19, 55, 31, 67, 26, 62, 12, 48)(4, 40, 9, 45, 20, 56, 16, 52, 6, 42, 10, 46)(11, 47, 21, 57, 32, 68, 27, 63, 13, 49, 22, 58)(14, 50, 23, 59, 33, 69, 30, 66, 17, 53, 24, 60)(25, 61, 34, 70, 29, 65, 36, 72, 28, 64, 35, 71)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 86, 122)(77, 113, 84, 120)(78, 114, 89, 125)(79, 115, 91, 127)(81, 117, 95, 131)(82, 118, 96, 132)(83, 119, 97, 133)(85, 121, 100, 136)(87, 123, 98, 134)(88, 124, 102, 138)(90, 126, 103, 139)(92, 128, 105, 141)(93, 129, 106, 142)(94, 130, 107, 143)(99, 135, 108, 144)(101, 137, 104, 140) L = (1, 76)(2, 81)(3, 83)(4, 79)(5, 82)(6, 73)(7, 92)(8, 93)(9, 90)(10, 74)(11, 91)(12, 94)(13, 75)(14, 100)(15, 78)(16, 77)(17, 101)(18, 88)(19, 104)(20, 87)(21, 103)(22, 80)(23, 107)(24, 108)(25, 89)(26, 85)(27, 84)(28, 105)(29, 86)(30, 106)(31, 99)(32, 98)(33, 97)(34, 96)(35, 102)(36, 95)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.528 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.546 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y1^-1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-2 * R * Y2 * R * Y2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-2 * Y1^2 * Y3^-1, Y3 * Y1 * Y2 * Y3^-1 * Y1 * Y2, Y1^6, Y1^-1 * Y2 * Y3^-3 * Y1^-1, (Y3 * Y2)^3, Y3^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 7, 43, 21, 57, 17, 53, 5, 41)(3, 39, 11, 47, 31, 67, 34, 70, 22, 58, 8, 44)(4, 40, 14, 50, 32, 68, 35, 71, 23, 59, 9, 45)(6, 42, 18, 54, 33, 69, 36, 72, 24, 60, 10, 46)(12, 48, 25, 61, 15, 51, 27, 63, 20, 56, 30, 66)(13, 49, 26, 62, 19, 55, 29, 65, 16, 52, 28, 64)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 87, 123)(77, 113, 83, 119)(78, 114, 91, 127)(79, 115, 94, 130)(81, 117, 99, 135)(82, 118, 101, 137)(84, 120, 104, 140)(85, 121, 105, 141)(86, 122, 97, 133)(88, 124, 96, 132)(89, 125, 103, 139)(90, 126, 98, 134)(92, 128, 95, 131)(93, 129, 106, 142)(100, 136, 108, 144)(102, 138, 107, 143) L = (1, 76)(2, 81)(3, 84)(4, 88)(5, 86)(6, 73)(7, 95)(8, 97)(9, 100)(10, 74)(11, 102)(12, 96)(13, 75)(14, 101)(15, 105)(16, 103)(17, 104)(18, 77)(19, 94)(20, 78)(21, 107)(22, 87)(23, 85)(24, 79)(25, 108)(26, 80)(27, 90)(28, 83)(29, 106)(30, 82)(31, 92)(32, 91)(33, 89)(34, 99)(35, 98)(36, 93)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.530 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.547 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y1^6, Y3^2 * Y2 * Y1^-2 * Y3, Y1^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^6, Y3^2 * Y1^-2 * Y3 * Y2 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 7, 43, 21, 57, 17, 53, 5, 41)(3, 39, 11, 47, 31, 67, 34, 70, 22, 58, 8, 44)(4, 40, 14, 50, 33, 69, 35, 71, 23, 59, 9, 45)(6, 42, 18, 54, 32, 68, 36, 72, 24, 60, 10, 46)(12, 48, 25, 61, 20, 56, 30, 66, 15, 51, 27, 63)(13, 49, 26, 62, 16, 52, 28, 64, 19, 55, 29, 65)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 87, 123)(77, 113, 83, 119)(78, 114, 91, 127)(79, 115, 94, 130)(81, 117, 99, 135)(82, 118, 101, 137)(84, 120, 95, 131)(85, 121, 96, 132)(86, 122, 102, 138)(88, 124, 104, 140)(89, 125, 103, 139)(90, 126, 100, 136)(92, 128, 105, 141)(93, 129, 106, 142)(97, 133, 107, 143)(98, 134, 108, 144) L = (1, 76)(2, 81)(3, 84)(4, 88)(5, 86)(6, 73)(7, 95)(8, 97)(9, 100)(10, 74)(11, 99)(12, 104)(13, 75)(14, 98)(15, 96)(16, 94)(17, 105)(18, 77)(19, 103)(20, 78)(21, 107)(22, 92)(23, 91)(24, 79)(25, 90)(26, 80)(27, 108)(28, 106)(29, 83)(30, 82)(31, 87)(32, 89)(33, 85)(34, 102)(35, 101)(36, 93)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.531 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.548 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-2 * Y2, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3 * Y2 * Y3 * Y2, Y1^-1 * Y3 * Y1^3 * Y2, Y3^6, Y2 * Y3^2 * Y1^-1 * Y2 * Y1^-1, Y3 * Y1^-2 * Y3^-2 * Y2 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 21, 57, 15, 51, 5, 41)(3, 39, 11, 47, 6, 42, 17, 53, 32, 68, 13, 49)(4, 40, 14, 50, 26, 62, 8, 44, 24, 60, 10, 46)(9, 45, 27, 63, 18, 54, 22, 58, 34, 70, 23, 59)(12, 48, 25, 61, 35, 71, 31, 67, 16, 52, 28, 64)(19, 55, 29, 65, 20, 56, 30, 66, 36, 72, 33, 69)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 87, 123)(77, 113, 81, 117)(78, 114, 91, 127)(79, 115, 94, 130)(82, 118, 101, 137)(83, 119, 103, 139)(84, 120, 104, 140)(85, 121, 102, 138)(86, 122, 97, 133)(88, 124, 96, 132)(89, 125, 93, 129)(90, 126, 105, 141)(92, 128, 95, 131)(98, 134, 108, 144)(99, 135, 107, 143)(100, 136, 106, 142) L = (1, 76)(2, 81)(3, 84)(4, 88)(5, 89)(6, 73)(7, 75)(8, 97)(9, 100)(10, 74)(11, 102)(12, 96)(13, 93)(14, 101)(15, 94)(16, 99)(17, 103)(18, 77)(19, 98)(20, 78)(21, 80)(22, 107)(23, 79)(24, 108)(25, 106)(26, 87)(27, 92)(28, 83)(29, 90)(30, 82)(31, 86)(32, 91)(33, 85)(34, 105)(35, 104)(36, 95)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.533 Graph:: bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.549 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^2 * Y2, Y3 * Y2 * Y3^-2 * Y2 * Y3, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2, Y3 * Y1^-4 * Y2, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * R * Y2 * R * Y3^-1 * Y1^-1, (Y3^-1 * Y2)^3, Y3 * Y2 * Y1^-1 * Y3^-2 * Y1^-1, Y3^2 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 7, 43, 21, 57, 12, 48, 5, 41)(3, 39, 11, 47, 29, 65, 10, 46, 4, 40, 13, 49)(6, 42, 18, 54, 33, 69, 17, 53, 22, 58, 19, 55)(8, 44, 24, 60, 35, 71, 23, 59, 9, 45, 25, 61)(14, 50, 26, 62, 20, 56, 30, 66, 36, 72, 32, 68)(15, 51, 27, 63, 34, 70, 31, 67, 16, 52, 28, 64)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 87, 123)(77, 113, 89, 125)(78, 114, 79, 115)(81, 117, 99, 135)(82, 118, 93, 129)(83, 119, 103, 139)(84, 120, 95, 131)(85, 121, 102, 138)(86, 122, 101, 137)(88, 124, 96, 132)(90, 126, 100, 136)(91, 127, 104, 140)(92, 128, 105, 141)(94, 130, 106, 142)(97, 133, 108, 144)(98, 134, 107, 143) L = (1, 76)(2, 81)(3, 84)(4, 88)(5, 90)(6, 73)(7, 94)(8, 77)(9, 100)(10, 74)(11, 99)(12, 96)(13, 98)(14, 75)(15, 101)(16, 97)(17, 93)(18, 103)(19, 102)(20, 78)(21, 83)(22, 87)(23, 79)(24, 106)(25, 92)(26, 80)(27, 107)(28, 91)(29, 108)(30, 82)(31, 85)(32, 89)(33, 86)(34, 105)(35, 104)(36, 95)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.534 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.550 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1, Y1^-1), (Y3, Y1), (Y3, Y1^-1), (Y3^-1, Y1), Y3^2 * Y1^-2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y3 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y2, Y3^2 * Y1^4, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y1 * Y2 * Y3^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 20, 56, 17, 53, 5, 41)(3, 39, 11, 47, 21, 57, 34, 70, 31, 67, 13, 49)(4, 40, 9, 45, 22, 58, 18, 54, 6, 42, 10, 46)(8, 44, 23, 59, 33, 69, 30, 66, 16, 52, 25, 61)(12, 48, 27, 63, 35, 71, 32, 68, 14, 50, 28, 64)(15, 51, 24, 60, 36, 72, 29, 65, 19, 55, 26, 62)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 87, 123)(77, 113, 88, 124)(78, 114, 91, 127)(79, 115, 93, 129)(81, 117, 99, 135)(82, 118, 100, 136)(83, 119, 101, 137)(84, 120, 102, 138)(85, 121, 96, 132)(86, 122, 95, 131)(89, 125, 103, 139)(90, 126, 104, 140)(92, 128, 105, 141)(94, 130, 108, 144)(97, 133, 107, 143)(98, 134, 106, 142) L = (1, 76)(2, 81)(3, 84)(4, 79)(5, 82)(6, 73)(7, 94)(8, 96)(9, 92)(10, 74)(11, 99)(12, 93)(13, 100)(14, 75)(15, 95)(16, 98)(17, 78)(18, 77)(19, 97)(20, 90)(21, 107)(22, 89)(23, 108)(24, 105)(25, 87)(26, 80)(27, 106)(28, 83)(29, 88)(30, 91)(31, 86)(32, 85)(33, 101)(34, 104)(35, 103)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.518 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.551 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 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, Y1^2 * Y3 * Y2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y1^-1, (R * Y2 * Y3)^2, (Y2 * Y1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 6, 42, 14, 50, 12, 48, 5, 41)(3, 39, 9, 45, 4, 40, 11, 47, 15, 51, 10, 46)(7, 43, 16, 52, 8, 44, 18, 54, 13, 49, 17, 53)(19, 55, 25, 61, 20, 56, 27, 63, 21, 57, 26, 62)(22, 58, 28, 64, 23, 59, 30, 66, 24, 60, 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, 80, 116)(78, 114, 87, 123)(81, 117, 91, 127)(82, 118, 92, 128)(83, 119, 93, 129)(85, 121, 86, 122)(88, 124, 94, 130)(89, 125, 95, 131)(90, 126, 96, 132)(97, 133, 103, 139)(98, 134, 104, 140)(99, 135, 105, 141)(100, 136, 106, 142)(101, 137, 107, 143)(102, 138, 108, 144) L = (1, 76)(2, 80)(3, 78)(4, 73)(5, 85)(6, 75)(7, 86)(8, 74)(9, 92)(10, 93)(11, 91)(12, 87)(13, 77)(14, 79)(15, 84)(16, 95)(17, 96)(18, 94)(19, 83)(20, 81)(21, 82)(22, 90)(23, 88)(24, 89)(25, 104)(26, 105)(27, 103)(28, 107)(29, 108)(30, 106)(31, 99)(32, 97)(33, 98)(34, 102)(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) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.524 Graph:: bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.552 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 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, Y1^-2 * Y3 * Y2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y1^-1, (R * Y2 * Y3)^2, Y1^6, Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 6, 42, 14, 50, 10, 46, 5, 41)(3, 39, 9, 45, 15, 51, 12, 48, 4, 40, 11, 47)(7, 43, 16, 52, 13, 49, 18, 54, 8, 44, 17, 53)(19, 55, 25, 61, 21, 57, 27, 63, 20, 56, 26, 62)(22, 58, 28, 64, 24, 60, 30, 66, 23, 59, 29, 65)(31, 67, 36, 72, 33, 69, 35, 71, 32, 68, 34, 70)(73, 109, 75, 111)(74, 110, 79, 115)(76, 112, 78, 114)(77, 113, 85, 121)(80, 116, 86, 122)(81, 117, 91, 127)(82, 118, 87, 123)(83, 119, 93, 129)(84, 120, 92, 128)(88, 124, 94, 130)(89, 125, 96, 132)(90, 126, 95, 131)(97, 133, 103, 139)(98, 134, 105, 141)(99, 135, 104, 140)(100, 136, 106, 142)(101, 137, 108, 144)(102, 138, 107, 143) L = (1, 76)(2, 80)(3, 82)(4, 73)(5, 79)(6, 87)(7, 77)(8, 74)(9, 92)(10, 75)(11, 91)(12, 93)(13, 86)(14, 85)(15, 78)(16, 95)(17, 94)(18, 96)(19, 83)(20, 81)(21, 84)(22, 89)(23, 88)(24, 90)(25, 104)(26, 103)(27, 105)(28, 107)(29, 106)(30, 108)(31, 98)(32, 97)(33, 99)(34, 101)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.525 Graph:: bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.553 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-3 * Y3, R * Y2 * R * Y2^-1, (R * Y3)^2, (Y2^-1 * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 4, 40, 9, 45, 5, 41)(3, 39, 10, 46, 17, 53, 12, 48, 21, 57, 13, 49)(6, 42, 8, 44, 18, 54, 14, 50, 20, 56, 15, 51)(11, 47, 22, 58, 28, 64, 24, 60, 32, 68, 25, 61)(16, 52, 19, 55, 29, 65, 26, 62, 31, 67, 27, 63)(23, 59, 30, 66, 35, 71, 33, 69, 36, 72, 34, 70)(73, 109, 75, 111, 83, 119, 95, 131, 88, 124, 78, 114)(74, 110, 80, 116, 91, 127, 102, 138, 94, 130, 82, 118)(76, 112, 86, 122, 98, 134, 105, 141, 96, 132, 84, 120)(77, 113, 87, 123, 99, 135, 106, 142, 97, 133, 85, 121)(79, 115, 89, 125, 100, 136, 107, 143, 101, 137, 90, 126)(81, 117, 93, 129, 104, 140, 108, 144, 103, 139, 92, 128) L = (1, 76)(2, 81)(3, 84)(4, 73)(5, 79)(6, 86)(7, 77)(8, 92)(9, 74)(10, 93)(11, 96)(12, 75)(13, 89)(14, 78)(15, 90)(16, 98)(17, 85)(18, 87)(19, 103)(20, 80)(21, 82)(22, 104)(23, 105)(24, 83)(25, 100)(26, 88)(27, 101)(28, 97)(29, 99)(30, 108)(31, 91)(32, 94)(33, 95)(34, 107)(35, 106)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.504 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.554 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, R * Y2 * R * Y2^-1, Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y1^-1, Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y1^2 * Y3 * Y1^-2, (Y3 * Y1^-1)^3, Y1^6, Y2^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 7, 43, 21, 57, 19, 55, 5, 41)(3, 39, 10, 46, 22, 58, 15, 51, 33, 69, 13, 49)(4, 40, 14, 50, 23, 59, 11, 47, 30, 66, 16, 52)(6, 42, 8, 44, 24, 60, 34, 70, 28, 64, 17, 53)(9, 45, 27, 63, 20, 56, 25, 61, 18, 54, 29, 65)(12, 48, 26, 62, 35, 71, 31, 67, 36, 72, 32, 68)(73, 109, 75, 111, 83, 119, 103, 139, 92, 128, 78, 114)(74, 110, 80, 116, 97, 133, 108, 144, 102, 138, 82, 118)(76, 112, 87, 123, 93, 129, 106, 142, 101, 137, 84, 120)(77, 113, 89, 125, 99, 135, 107, 143, 95, 131, 85, 121)(79, 115, 94, 130, 88, 124, 104, 140, 90, 126, 96, 132)(81, 117, 100, 136, 91, 127, 105, 141, 86, 122, 98, 134) L = (1, 76)(2, 81)(3, 84)(4, 73)(5, 90)(6, 87)(7, 95)(8, 98)(9, 74)(10, 100)(11, 101)(12, 75)(13, 96)(14, 97)(15, 78)(16, 99)(17, 104)(18, 77)(19, 102)(20, 93)(21, 92)(22, 107)(23, 79)(24, 85)(25, 86)(26, 80)(27, 88)(28, 82)(29, 83)(30, 91)(31, 106)(32, 89)(33, 108)(34, 103)(35, 94)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.511 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.555 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y3)^2, Y3 * Y2^-1 * Y1^-1 * Y2 * Y1^-2, Y1^-2 * Y2^2 * Y3 * Y1^-1, Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1, Y3 * Y1 * Y2^-2 * Y3 * Y1^-1, (Y3 * Y1^-1)^3, Y2^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 7, 43, 21, 57, 19, 55, 5, 41)(3, 39, 10, 46, 22, 58, 34, 70, 26, 62, 13, 49)(4, 40, 14, 50, 23, 59, 20, 56, 25, 61, 16, 52)(6, 42, 8, 44, 24, 60, 12, 48, 32, 68, 17, 53)(9, 45, 27, 63, 11, 47, 30, 66, 18, 54, 29, 65)(15, 51, 28, 64, 35, 71, 31, 67, 36, 72, 33, 69)(73, 109, 75, 111, 83, 119, 103, 139, 92, 128, 78, 114)(74, 110, 80, 116, 97, 133, 108, 144, 102, 138, 82, 118)(76, 112, 87, 123, 101, 137, 106, 142, 93, 129, 84, 120)(77, 113, 89, 125, 95, 131, 107, 143, 99, 135, 85, 121)(79, 115, 94, 130, 90, 126, 105, 141, 88, 124, 96, 132)(81, 117, 100, 136, 86, 122, 104, 140, 91, 127, 98, 134) L = (1, 76)(2, 81)(3, 84)(4, 73)(5, 90)(6, 87)(7, 95)(8, 98)(9, 74)(10, 100)(11, 93)(12, 75)(13, 105)(14, 102)(15, 78)(16, 99)(17, 94)(18, 77)(19, 97)(20, 101)(21, 83)(22, 89)(23, 79)(24, 107)(25, 91)(26, 80)(27, 88)(28, 82)(29, 92)(30, 86)(31, 106)(32, 108)(33, 85)(34, 103)(35, 96)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.512 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.556 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^2 * Y2^-1, (Y2 * Y1^-1)^2, (Y2, Y1^-1), Y3^2 * Y2^-2, Y3^2 * Y1^-2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2)^2, Y3^2 * Y1^4, Y1^2 * Y2^4, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 8, 44, 22, 58, 17, 53, 5, 41)(3, 39, 9, 45, 23, 59, 18, 54, 6, 42, 11, 47)(4, 40, 15, 51, 24, 60, 21, 57, 7, 43, 16, 52)(10, 46, 27, 63, 19, 55, 30, 66, 12, 48, 28, 64)(13, 49, 31, 67, 20, 56, 33, 69, 14, 50, 32, 68)(25, 61, 34, 70, 29, 65, 36, 72, 26, 62, 35, 71)(73, 109, 75, 111, 80, 116, 95, 131, 89, 125, 78, 114)(74, 110, 81, 117, 94, 130, 90, 126, 77, 113, 83, 119)(76, 112, 85, 121, 96, 132, 92, 128, 79, 115, 86, 122)(82, 118, 97, 133, 91, 127, 101, 137, 84, 120, 98, 134)(87, 123, 103, 139, 93, 129, 105, 141, 88, 124, 104, 140)(99, 135, 106, 142, 102, 138, 108, 144, 100, 136, 107, 143) L = (1, 76)(2, 82)(3, 85)(4, 80)(5, 84)(6, 86)(7, 73)(8, 96)(9, 97)(10, 94)(11, 98)(12, 74)(13, 95)(14, 75)(15, 99)(16, 100)(17, 79)(18, 101)(19, 77)(20, 78)(21, 102)(22, 91)(23, 92)(24, 89)(25, 90)(26, 81)(27, 93)(28, 87)(29, 83)(30, 88)(31, 106)(32, 107)(33, 108)(34, 105)(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) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.515 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.557 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y1), Y3 * Y1^2 * Y3, (Y2 * Y1)^2, (R * Y1)^2, Y1^-1 * Y2^-2 * Y1^-1, (R * Y2)^2, Y3^2 * Y2^-2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y3 * Y1^-1)^3, (Y3^-1 * Y1^-1)^3, Y3^-1 * Y2^-1 * Y1^2 * Y3^-1 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 8, 44, 22, 58, 13, 49, 5, 41)(3, 39, 9, 45, 6, 42, 11, 47, 23, 59, 15, 51)(4, 40, 17, 53, 7, 43, 21, 57, 24, 60, 18, 54)(10, 46, 27, 63, 12, 48, 30, 66, 19, 55, 28, 64)(14, 50, 31, 67, 16, 52, 33, 69, 20, 56, 32, 68)(25, 61, 34, 70, 26, 62, 36, 72, 29, 65, 35, 71)(73, 109, 75, 111, 85, 121, 95, 131, 80, 116, 78, 114)(74, 110, 81, 117, 77, 113, 87, 123, 94, 130, 83, 119)(76, 112, 86, 122, 96, 132, 92, 128, 79, 115, 88, 124)(82, 118, 97, 133, 91, 127, 101, 137, 84, 120, 98, 134)(89, 125, 103, 139, 90, 126, 104, 140, 93, 129, 105, 141)(99, 135, 106, 142, 100, 136, 107, 143, 102, 138, 108, 144) L = (1, 76)(2, 82)(3, 86)(4, 85)(5, 91)(6, 88)(7, 73)(8, 79)(9, 97)(10, 77)(11, 98)(12, 74)(13, 96)(14, 95)(15, 101)(16, 75)(17, 100)(18, 102)(19, 94)(20, 78)(21, 99)(22, 84)(23, 92)(24, 80)(25, 87)(26, 81)(27, 89)(28, 90)(29, 83)(30, 93)(31, 107)(32, 108)(33, 106)(34, 103)(35, 104)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.507 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.558 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, R * Y2^-1 * R * Y1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-2, Y1^-2 * Y2 * Y1 * Y2 * Y1^-1, (Y2^-2 * Y1^-1)^2, Y2^6, (Y3^-1 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 37, 2, 38, 6, 42, 16, 52, 12, 48, 4, 40)(3, 39, 9, 45, 17, 53, 13, 49, 21, 57, 8, 44)(5, 41, 11, 47, 18, 54, 7, 43, 19, 55, 14, 50)(10, 46, 24, 60, 28, 64, 22, 58, 32, 68, 23, 59)(15, 51, 27, 63, 29, 65, 26, 62, 30, 66, 20, 56)(25, 61, 31, 67, 35, 71, 33, 69, 36, 72, 34, 70)(73, 109, 75, 111, 82, 118, 97, 133, 87, 123, 77, 113)(74, 110, 79, 115, 92, 128, 103, 139, 94, 130, 80, 116)(76, 112, 83, 119, 98, 134, 106, 142, 96, 132, 85, 121)(78, 114, 89, 125, 100, 136, 107, 143, 101, 137, 90, 126)(81, 117, 88, 124, 86, 122, 99, 135, 105, 141, 95, 131)(84, 120, 93, 129, 104, 140, 108, 144, 102, 138, 91, 127) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 83)(6, 88)(7, 91)(8, 75)(9, 89)(10, 96)(11, 90)(12, 76)(13, 93)(14, 77)(15, 99)(16, 84)(17, 85)(18, 79)(19, 86)(20, 87)(21, 80)(22, 104)(23, 82)(24, 100)(25, 103)(26, 102)(27, 101)(28, 94)(29, 98)(30, 92)(31, 107)(32, 95)(33, 108)(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) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.508 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.559 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, (Y3 * Y2^-1)^2, Y3 * Y2 * Y1^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y3^2 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^4, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y1, Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y1^-1, Y2 * Y1 * Y2 * Y3^-2 * Y1^-1, Y3^-1 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^3, Y2^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 8, 44, 25, 61, 19, 55, 5, 41)(3, 39, 13, 49, 26, 62, 20, 56, 34, 70, 11, 47)(4, 40, 14, 50, 27, 63, 23, 59, 7, 43, 17, 53)(6, 42, 18, 54, 28, 64, 9, 45, 29, 65, 22, 58)(10, 46, 30, 66, 21, 57, 35, 71, 12, 48, 33, 69)(15, 51, 31, 67, 24, 60, 36, 72, 16, 52, 32, 68)(73, 109, 75, 111, 86, 122, 103, 139, 93, 129, 78, 114)(74, 110, 81, 117, 102, 138, 96, 132, 79, 115, 83, 119)(76, 112, 85, 121, 97, 133, 94, 130, 107, 143, 88, 124)(77, 113, 90, 126, 105, 141, 87, 123, 99, 135, 92, 128)(80, 116, 98, 134, 95, 131, 108, 144, 84, 120, 100, 136)(82, 118, 101, 137, 91, 127, 106, 142, 89, 125, 104, 140) L = (1, 76)(2, 82)(3, 87)(4, 80)(5, 84)(6, 83)(7, 73)(8, 99)(9, 103)(10, 97)(11, 100)(12, 74)(13, 101)(14, 102)(15, 98)(16, 75)(17, 105)(18, 104)(19, 79)(20, 78)(21, 77)(22, 108)(23, 107)(24, 106)(25, 93)(26, 96)(27, 91)(28, 85)(29, 92)(30, 95)(31, 94)(32, 81)(33, 86)(34, 88)(35, 89)(36, 90)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.514 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.560 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, (Y3 * Y2^-1)^2, Y2^-1 * Y3 * Y1^-1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^-2 * Y3^-1, Y3 * Y2 * Y1 * Y2^-1, (Y3 * Y1^-1)^3, (R * Y2 * Y3^-1)^2, Y2 * Y3^-2 * Y1 * Y2 * Y1^-1, Y3^-2 * Y1^4, Y2^2 * Y3^-1 * Y1 * Y3 * Y1, Y2 * Y3 * Y2^-3 * Y1^-1, Y3 * Y1^-1 * Y2^4, (Y3^-1 * Y1^-1)^3, Y3 * Y1^-2 * Y2^2 * Y1^-1, Y3^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 8, 44, 25, 61, 19, 55, 5, 41)(3, 39, 13, 49, 26, 62, 11, 47, 34, 70, 16, 52)(4, 40, 18, 54, 7, 43, 23, 59, 28, 64, 14, 50)(6, 42, 22, 58, 27, 63, 20, 56, 31, 67, 9, 45)(10, 46, 33, 69, 12, 48, 35, 71, 21, 57, 29, 65)(15, 51, 30, 66, 17, 53, 32, 68, 24, 60, 36, 72)(73, 109, 75, 111, 86, 122, 108, 144, 84, 120, 78, 114)(74, 110, 81, 117, 101, 137, 87, 123, 100, 136, 83, 119)(76, 112, 88, 124, 97, 133, 94, 130, 105, 141, 89, 125)(77, 113, 92, 128, 107, 143, 96, 132, 79, 115, 85, 121)(80, 116, 98, 134, 90, 126, 102, 138, 93, 129, 99, 135)(82, 118, 103, 139, 91, 127, 106, 142, 95, 131, 104, 140) L = (1, 76)(2, 82)(3, 87)(4, 91)(5, 93)(6, 85)(7, 73)(8, 79)(9, 102)(10, 77)(11, 78)(12, 74)(13, 103)(14, 107)(15, 106)(16, 99)(17, 75)(18, 101)(19, 100)(20, 108)(21, 97)(22, 104)(23, 105)(24, 98)(25, 84)(26, 89)(27, 83)(28, 80)(29, 86)(30, 92)(31, 88)(32, 81)(33, 90)(34, 96)(35, 95)(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) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.506 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.561 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, (Y3 * Y2^-1)^2, Y1^-1 * Y2 * Y3 * Y2^-1, (R * Y3)^2, Y3^2 * Y1^-2, (R * Y1)^2, Y2^2 * Y3^-1 * Y1^-1, Y3 * Y1 * Y2^-2 * Y3 * Y1^-1, Y3^2 * Y1^4, Y2^6, (Y1 * Y3)^3, Y3 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 25, 61, 18, 54, 5, 41)(3, 39, 13, 49, 26, 62, 19, 55, 34, 70, 11, 47)(4, 40, 15, 51, 27, 63, 23, 59, 7, 43, 17, 53)(6, 42, 14, 50, 28, 64, 9, 45, 29, 65, 22, 58)(10, 46, 30, 66, 20, 56, 35, 71, 12, 48, 32, 68)(16, 52, 31, 67, 24, 60, 36, 72, 21, 57, 33, 69)(73, 109, 75, 111, 82, 118, 103, 139, 95, 131, 78, 114)(74, 110, 81, 117, 99, 135, 96, 132, 107, 143, 83, 119)(76, 112, 88, 124, 102, 138, 91, 127, 77, 113, 86, 122)(79, 115, 93, 129, 104, 140, 85, 121, 97, 133, 94, 130)(80, 116, 98, 134, 92, 128, 108, 144, 89, 125, 100, 136)(84, 120, 105, 141, 87, 123, 101, 137, 90, 126, 106, 142) L = (1, 76)(2, 82)(3, 81)(4, 80)(5, 84)(6, 93)(7, 73)(8, 99)(9, 98)(10, 97)(11, 105)(12, 74)(13, 103)(14, 75)(15, 102)(16, 101)(17, 104)(18, 79)(19, 108)(20, 77)(21, 100)(22, 106)(23, 107)(24, 78)(25, 92)(26, 94)(27, 90)(28, 88)(29, 96)(30, 95)(31, 91)(32, 87)(33, 85)(34, 86)(35, 89)(36, 83)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.516 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.562 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x S3 (small group id <36, 12>) Aut = C2 x S3 x S3 (small group id <72, 46>) |r| :: 2 Presentation :: [ R^2, (Y3 * Y2^-1)^2, Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^-2 * Y3^-1, Y1 * Y2^-1 * Y3^-1 * Y2^3, Y3 * Y2 * Y1 * Y2^-1 * Y3 * Y1, Y3^3 * Y1^-1 * Y2^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y3 * Y1 * Y2^-1 * Y3, Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 8, 44, 25, 61, 19, 55, 5, 41)(3, 39, 13, 49, 26, 62, 11, 47, 33, 69, 16, 52)(4, 40, 17, 53, 7, 43, 23, 59, 28, 64, 20, 56)(6, 42, 21, 57, 27, 63, 15, 51, 29, 65, 9, 45)(10, 46, 30, 66, 12, 48, 35, 71, 14, 50, 32, 68)(18, 54, 31, 67, 22, 58, 34, 70, 24, 60, 36, 72)(73, 109, 75, 111, 86, 122, 108, 144, 95, 131, 78, 114)(74, 110, 81, 117, 76, 112, 90, 126, 107, 143, 83, 119)(77, 113, 87, 123, 100, 136, 96, 132, 102, 138, 85, 121)(79, 115, 94, 130, 104, 140, 88, 124, 97, 133, 93, 129)(80, 116, 98, 134, 82, 118, 103, 139, 92, 128, 99, 135)(84, 120, 106, 142, 89, 125, 101, 137, 91, 127, 105, 141) L = (1, 76)(2, 82)(3, 87)(4, 91)(5, 86)(6, 94)(7, 73)(8, 79)(9, 75)(10, 77)(11, 106)(12, 74)(13, 103)(14, 97)(15, 105)(16, 108)(17, 104)(18, 99)(19, 100)(20, 107)(21, 98)(22, 101)(23, 102)(24, 78)(25, 84)(26, 81)(27, 96)(28, 80)(29, 90)(30, 89)(31, 88)(32, 92)(33, 93)(34, 85)(35, 95)(36, 83)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.509 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.563 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 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, Y3^2, Y1^-3 * Y3, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y3)^2, (Y2 * Y1^-1)^2, Y3 * Y1 * Y3 * Y1^-1, (Y1^-1 * Y2^-1)^2, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 4, 40, 9, 45, 5, 41)(3, 39, 11, 47, 21, 57, 13, 49, 17, 53, 10, 46)(6, 42, 15, 51, 20, 56, 14, 50, 18, 54, 8, 44)(12, 48, 22, 58, 28, 64, 25, 61, 32, 68, 23, 59)(16, 52, 19, 55, 29, 65, 26, 62, 31, 67, 27, 63)(24, 60, 33, 69, 36, 72, 34, 70, 35, 71, 30, 66)(73, 109, 75, 111, 84, 120, 96, 132, 88, 124, 78, 114)(74, 110, 80, 116, 91, 127, 102, 138, 94, 130, 82, 118)(76, 112, 86, 122, 98, 134, 106, 142, 97, 133, 85, 121)(77, 113, 87, 123, 99, 135, 105, 141, 95, 131, 83, 119)(79, 115, 89, 125, 100, 136, 107, 143, 101, 137, 90, 126)(81, 117, 93, 129, 104, 140, 108, 144, 103, 139, 92, 128) L = (1, 76)(2, 81)(3, 85)(4, 73)(5, 79)(6, 86)(7, 77)(8, 92)(9, 74)(10, 93)(11, 89)(12, 97)(13, 75)(14, 78)(15, 90)(16, 98)(17, 83)(18, 87)(19, 103)(20, 80)(21, 82)(22, 104)(23, 100)(24, 106)(25, 84)(26, 88)(27, 101)(28, 95)(29, 99)(30, 108)(31, 91)(32, 94)(33, 107)(34, 96)(35, 105)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.505 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.564 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 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, Y3^2, (Y2^-1 * Y1^-1)^2, (Y2^-1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, R * Y2 * R * Y2^-1, Y1^6, Y3 * Y2^-2 * Y1^-3, Y3 * Y2^2 * Y1 * Y3 * Y1^-1, Y1^-1 * Y2^-2 * Y1^-1 * Y3 * Y1^-1, Y3 * Y2^-2 * Y1^3, Y2^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 7, 43, 21, 57, 19, 55, 5, 41)(3, 39, 11, 47, 26, 62, 34, 70, 22, 58, 10, 46)(4, 40, 14, 50, 23, 59, 20, 56, 25, 61, 16, 52)(6, 42, 17, 53, 33, 69, 13, 49, 24, 60, 8, 44)(9, 45, 27, 63, 12, 48, 30, 66, 18, 54, 29, 65)(15, 51, 31, 67, 36, 72, 32, 68, 35, 71, 28, 64)(73, 109, 75, 111, 84, 120, 104, 140, 92, 128, 78, 114)(74, 110, 80, 116, 97, 133, 108, 144, 102, 138, 82, 118)(76, 112, 87, 123, 101, 137, 106, 142, 93, 129, 85, 121)(77, 113, 89, 125, 95, 131, 107, 143, 99, 135, 83, 119)(79, 115, 94, 130, 90, 126, 103, 139, 88, 124, 96, 132)(81, 117, 100, 136, 86, 122, 105, 141, 91, 127, 98, 134) L = (1, 76)(2, 81)(3, 85)(4, 73)(5, 90)(6, 87)(7, 95)(8, 98)(9, 74)(10, 100)(11, 103)(12, 93)(13, 75)(14, 102)(15, 78)(16, 99)(17, 94)(18, 77)(19, 97)(20, 101)(21, 84)(22, 89)(23, 79)(24, 107)(25, 91)(26, 80)(27, 88)(28, 82)(29, 92)(30, 86)(31, 83)(32, 106)(33, 108)(34, 104)(35, 96)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.513 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.565 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 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, Y3^-1 * Y1, (Y3 * Y2^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^6, Y1^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 6, 42, 14, 50, 12, 48, 4, 40)(3, 39, 9, 45, 19, 55, 25, 61, 15, 51, 8, 44)(5, 41, 11, 47, 22, 58, 24, 60, 16, 52, 7, 43)(10, 46, 18, 54, 26, 62, 33, 69, 29, 65, 20, 56)(13, 49, 17, 53, 27, 63, 32, 68, 31, 67, 23, 59)(21, 57, 30, 66, 35, 71, 36, 72, 34, 70, 28, 64)(73, 109, 75, 111, 82, 118, 93, 129, 85, 121, 77, 113)(74, 110, 79, 115, 89, 125, 100, 136, 90, 126, 80, 116)(76, 112, 83, 119, 95, 131, 102, 138, 92, 128, 81, 117)(78, 114, 87, 123, 98, 134, 106, 142, 99, 135, 88, 124)(84, 120, 91, 127, 101, 137, 107, 143, 103, 139, 94, 130)(86, 122, 96, 132, 104, 140, 108, 144, 105, 141, 97, 133) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 83)(6, 86)(7, 77)(8, 75)(9, 91)(10, 90)(11, 94)(12, 76)(13, 89)(14, 84)(15, 80)(16, 79)(17, 99)(18, 98)(19, 97)(20, 82)(21, 102)(22, 96)(23, 85)(24, 88)(25, 87)(26, 105)(27, 104)(28, 93)(29, 92)(30, 107)(31, 95)(32, 103)(33, 101)(34, 100)(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, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.510 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.566 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x C6 (small group id <36, 14>) Aut = C2 x C2 x ((C3 x C3) : C2) (small group id <72, 49>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (R * Y1)^2, (R * Y3)^2, (Y2, Y3), (R * Y2)^2, (Y2^-1, Y1^-1), (Y3^-1 * Y1^-1)^2, Y2^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 13, 49)(4, 40, 9, 45, 7, 43)(6, 42, 10, 46, 16, 52)(11, 47, 19, 55, 25, 61)(12, 48, 20, 56, 14, 50)(15, 51, 21, 57, 18, 54)(17, 53, 22, 58, 28, 64)(23, 59, 30, 66, 34, 70)(24, 60, 31, 67, 26, 62)(27, 63, 32, 68, 29, 65)(33, 69, 36, 72, 35, 71)(73, 109, 75, 111, 83, 119, 95, 131, 89, 125, 78, 114)(74, 110, 80, 116, 91, 127, 102, 138, 94, 130, 82, 118)(76, 112, 84, 120, 96, 132, 105, 141, 99, 135, 87, 123)(77, 113, 85, 121, 97, 133, 106, 142, 100, 136, 88, 124)(79, 115, 86, 122, 98, 134, 107, 143, 101, 137, 90, 126)(81, 117, 92, 128, 103, 139, 108, 144, 104, 140, 93, 129) L = (1, 76)(2, 81)(3, 84)(4, 74)(5, 79)(6, 87)(7, 73)(8, 92)(9, 77)(10, 93)(11, 96)(12, 80)(13, 86)(14, 75)(15, 82)(16, 90)(17, 99)(18, 78)(19, 103)(20, 85)(21, 88)(22, 104)(23, 105)(24, 91)(25, 98)(26, 83)(27, 94)(28, 101)(29, 89)(30, 108)(31, 97)(32, 100)(33, 102)(34, 107)(35, 95)(36, 106)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.567 Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.567 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 6}) Quotient :: dipole Aut^+ = C6 x C6 (small group id <36, 14>) Aut = C2 x C2 x ((C3 x C3) : C2) (small group id <72, 49>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3 * Y2, (R * Y2)^2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y1^-1, Y1^6 ] Map:: polytopal non-degenerate R = (1, 37, 2, 38, 7, 43, 17, 53, 15, 51, 5, 41)(3, 39, 8, 44, 18, 54, 28, 64, 24, 60, 12, 48)(4, 40, 9, 45, 19, 55, 29, 65, 26, 62, 14, 50)(6, 42, 10, 46, 20, 56, 30, 66, 27, 63, 16, 52)(11, 47, 21, 57, 31, 67, 35, 71, 33, 69, 23, 59)(13, 49, 22, 58, 32, 68, 36, 72, 34, 70, 25, 61)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 83, 119)(77, 113, 84, 120)(78, 114, 85, 121)(79, 115, 90, 126)(81, 117, 93, 129)(82, 118, 94, 130)(86, 122, 95, 131)(87, 123, 96, 132)(88, 124, 97, 133)(89, 125, 100, 136)(91, 127, 103, 139)(92, 128, 104, 140)(98, 134, 105, 141)(99, 135, 106, 142)(101, 137, 107, 143)(102, 138, 108, 144) L = (1, 76)(2, 81)(3, 83)(4, 85)(5, 86)(6, 73)(7, 91)(8, 93)(9, 94)(10, 74)(11, 78)(12, 95)(13, 75)(14, 97)(15, 98)(16, 77)(17, 101)(18, 103)(19, 104)(20, 79)(21, 82)(22, 80)(23, 88)(24, 105)(25, 84)(26, 106)(27, 87)(28, 107)(29, 108)(30, 89)(31, 92)(32, 90)(33, 99)(34, 96)(35, 102)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.566 Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 4^18, 12^6 ] E16.568 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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 :: [ Y1^2, R^2, Y2^3, Y1 * Y2 * Y1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y1, Y1 * Y2 * Y3^-1 * Y2 * Y3^-1, Y3^-1 * Y2^-1 * Y3^-3 * Y2^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 8, 44)(5, 41, 9, 45)(6, 42, 10, 46)(11, 47, 21, 57)(12, 48, 15, 51)(13, 49, 22, 58)(14, 50, 23, 59)(16, 52, 18, 54)(17, 53, 24, 60)(19, 55, 25, 61)(20, 56, 26, 62)(27, 63, 32, 68)(28, 64, 35, 71)(29, 65, 34, 70)(30, 66, 36, 72)(31, 67, 33, 69)(73, 109, 75, 111, 77, 113)(74, 110, 79, 115, 81, 117)(76, 112, 85, 121, 87, 123)(78, 114, 90, 126, 91, 127)(80, 116, 94, 130, 84, 120)(82, 118, 88, 124, 97, 133)(83, 119, 99, 135, 96, 132)(86, 122, 100, 136, 105, 141)(89, 125, 93, 129, 104, 140)(92, 128, 101, 137, 102, 138)(95, 131, 107, 143, 103, 139)(98, 134, 106, 142, 108, 144) L = (1, 76)(2, 80)(3, 83)(4, 86)(5, 88)(6, 73)(7, 93)(8, 95)(9, 90)(10, 74)(11, 100)(12, 75)(13, 102)(14, 104)(15, 79)(16, 105)(17, 77)(18, 103)(19, 106)(20, 78)(21, 107)(22, 108)(23, 99)(24, 81)(25, 101)(26, 82)(27, 92)(28, 91)(29, 84)(30, 89)(31, 85)(32, 98)(33, 94)(34, 87)(35, 97)(36, 96)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E16.571 Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.569 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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, Y1 * Y3^-2, Y1^3, (Y3 * Y1)^2, Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1, Y3^-1 * Y2^2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * R * Y3 * Y1 * R * Y2^-1, R * Y2 * Y1 * R * Y2^-1 * Y3^-1, Y1^-1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y2 * R * Y2^-1 * Y3 * Y2^-1 * R * Y2^-1 * Y1^-1, Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 11, 47, 13, 49)(4, 40, 9, 45, 7, 43)(6, 42, 14, 50, 12, 48)(8, 44, 17, 53, 19, 55)(10, 46, 20, 56, 18, 54)(15, 51, 25, 61, 27, 63)(16, 52, 28, 64, 26, 62)(21, 57, 29, 65, 34, 70)(22, 58, 30, 66, 33, 69)(23, 59, 31, 67, 36, 72)(24, 60, 32, 68, 35, 71)(73, 109, 75, 111, 81, 117, 78, 114)(74, 110, 80, 116, 79, 115, 82, 118)(76, 112, 87, 123, 77, 113, 88, 124)(83, 119, 93, 129, 86, 122, 94, 130)(84, 120, 95, 131, 85, 121, 96, 132)(89, 125, 101, 137, 92, 128, 102, 138)(90, 126, 103, 139, 91, 127, 104, 140)(97, 133, 105, 141, 100, 136, 106, 142)(98, 134, 107, 143, 99, 135, 108, 144) L = (1, 76)(2, 81)(3, 84)(4, 74)(5, 79)(6, 85)(7, 73)(8, 90)(9, 77)(10, 91)(11, 78)(12, 83)(13, 86)(14, 75)(15, 98)(16, 99)(17, 82)(18, 89)(19, 92)(20, 80)(21, 105)(22, 106)(23, 107)(24, 108)(25, 88)(26, 97)(27, 100)(28, 87)(29, 94)(30, 93)(31, 96)(32, 95)(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) :: { ( 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E16.570 Graph:: bipartite v = 21 e = 72 f = 21 degree seq :: [ 6^12, 8^9 ] E16.570 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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, Y2^2, Y3^-3 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y1 * Y2 * Y3 * Y1, Y3^-2 * Y1 * Y3 * Y1, Y1^-2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y1^2 * Y3 * Y1^-2 * Y3^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 21, 57, 31, 67, 12, 48, 3, 39, 8, 44, 22, 58, 33, 69, 17, 53, 5, 41)(4, 40, 14, 50, 23, 59, 25, 61, 36, 72, 29, 65, 11, 47, 18, 54, 28, 64, 10, 46, 27, 63, 15, 51)(6, 42, 19, 55, 24, 60, 16, 52, 26, 62, 9, 45, 13, 49, 32, 68, 35, 71, 30, 66, 34, 70, 20, 56)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 83, 119)(77, 113, 84, 120)(78, 114, 85, 121)(79, 115, 94, 130)(81, 117, 92, 128)(82, 118, 97, 133)(86, 122, 90, 126)(87, 123, 101, 137)(88, 124, 102, 138)(89, 125, 103, 139)(91, 127, 104, 140)(93, 129, 105, 141)(95, 131, 100, 136)(96, 132, 107, 143)(98, 134, 106, 142)(99, 135, 108, 144) L = (1, 76)(2, 81)(3, 83)(4, 85)(5, 88)(6, 73)(7, 95)(8, 92)(9, 97)(10, 74)(11, 78)(12, 102)(13, 75)(14, 84)(15, 93)(16, 86)(17, 99)(18, 77)(19, 87)(20, 82)(21, 104)(22, 100)(23, 107)(24, 79)(25, 80)(26, 103)(27, 98)(28, 96)(29, 105)(30, 90)(31, 108)(32, 101)(33, 91)(34, 89)(35, 94)(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) :: { ( 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 E16.569 Graph:: bipartite v = 21 e = 72 f = 21 degree seq :: [ 4^18, 24^3 ] E16.571 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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^-1 * Y3 * Y1^2, Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y1^-1 * Y2^-1 * Y3 * Y1^-1, (Y3, Y2^-1), (R * Y3)^2, Y2^2 * Y3^-2, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3^-3 * Y2^-3, Y3^-2 * Y1^-1 * Y3 * Y2 * Y1^-1, Y3^2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 5, 41)(3, 39, 13, 49, 4, 40, 16, 52)(6, 42, 17, 53, 7, 43, 18, 54)(9, 45, 21, 57, 10, 46, 24, 60)(11, 47, 25, 61, 12, 48, 26, 62)(14, 50, 22, 58, 15, 51, 23, 59)(19, 55, 27, 63, 20, 56, 28, 64)(29, 65, 36, 72, 30, 66, 35, 71)(31, 67, 34, 70, 32, 68, 33, 69)(73, 109, 75, 111, 86, 122, 103, 139, 92, 128, 79, 115, 80, 116, 76, 112, 87, 123, 104, 140, 91, 127, 78, 114)(74, 110, 81, 117, 94, 130, 107, 143, 100, 136, 84, 120, 77, 113, 82, 118, 95, 131, 108, 144, 99, 135, 83, 119)(85, 121, 98, 134, 106, 142, 96, 132, 90, 126, 102, 138, 88, 124, 97, 133, 105, 141, 93, 129, 89, 125, 101, 137) L = (1, 76)(2, 82)(3, 87)(4, 86)(5, 81)(6, 80)(7, 73)(8, 75)(9, 95)(10, 94)(11, 77)(12, 74)(13, 97)(14, 104)(15, 103)(16, 98)(17, 102)(18, 101)(19, 79)(20, 78)(21, 90)(22, 108)(23, 107)(24, 89)(25, 106)(26, 105)(27, 84)(28, 83)(29, 88)(30, 85)(31, 91)(32, 92)(33, 96)(34, 93)(35, 99)(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, 6, 4, 6, 4, 6, 4, 6 ), ( 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 E16.568 Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 8^9, 24^3 ] E16.572 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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 :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y2 * Y3^2 * Y2^-1 * Y3^-2, Y3^6 * Y1 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 5, 41)(4, 40, 7, 43)(6, 42, 8, 44)(9, 45, 14, 50)(10, 46, 15, 51)(11, 47, 13, 49)(12, 48, 19, 55)(16, 52, 17, 53)(18, 54, 20, 56)(21, 57, 23, 59)(22, 58, 29, 65)(24, 60, 25, 61)(26, 62, 31, 67)(27, 63, 30, 66)(28, 64, 32, 68)(33, 69, 35, 71)(34, 70, 36, 72)(73, 109, 75, 111, 74, 110, 77, 113)(76, 112, 83, 119, 79, 115, 85, 121)(78, 114, 88, 124, 80, 116, 89, 125)(81, 117, 93, 129, 86, 122, 95, 131)(82, 118, 96, 132, 87, 123, 97, 133)(84, 120, 94, 130, 91, 127, 101, 137)(90, 126, 98, 134, 92, 128, 103, 139)(99, 135, 108, 144, 102, 138, 106, 142)(100, 136, 107, 143, 104, 140, 105, 141) L = (1, 76)(2, 79)(3, 81)(4, 84)(5, 86)(6, 73)(7, 91)(8, 74)(9, 94)(10, 75)(11, 97)(12, 100)(13, 96)(14, 101)(15, 77)(16, 99)(17, 102)(18, 78)(19, 104)(20, 80)(21, 88)(22, 106)(23, 89)(24, 105)(25, 107)(26, 82)(27, 83)(28, 92)(29, 108)(30, 85)(31, 87)(32, 90)(33, 93)(34, 103)(35, 95)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 24, 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E16.573 Graph:: bipartite v = 27 e = 72 f = 15 degree seq :: [ 4^18, 8^9 ] E16.573 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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, Y1 * Y3^-2, Y1^3, Y2^-1 * Y1^-1 * Y2^-1 * Y3, Y2 * Y3^-1 * Y2 * Y1, Y2 * Y3^-1 * Y2 * Y1, Y3 * Y2^-1 * Y1^-1 * Y2^-1, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2 * Y1^-1 * Y2^-2, Y3 * Y2 * Y1^-1 * Y2^9 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 11, 47, 14, 50)(4, 40, 9, 45, 7, 43)(6, 42, 18, 54, 19, 55)(8, 44, 23, 59, 21, 57)(10, 46, 26, 62, 16, 52)(12, 48, 24, 60, 31, 67)(13, 49, 25, 61, 15, 51)(17, 53, 22, 58, 28, 64)(20, 56, 27, 63, 34, 70)(29, 65, 35, 71, 33, 69)(30, 66, 36, 72, 32, 68)(73, 109, 75, 111, 84, 120, 98, 134, 107, 143, 95, 131, 81, 117, 97, 133, 108, 144, 100, 136, 92, 128, 78, 114)(74, 110, 80, 116, 96, 132, 85, 121, 105, 141, 94, 130, 79, 115, 91, 127, 104, 140, 86, 122, 99, 135, 82, 118)(76, 112, 88, 124, 102, 138, 93, 129, 106, 142, 87, 123, 77, 113, 89, 125, 103, 139, 90, 126, 101, 137, 83, 119) L = (1, 76)(2, 81)(3, 85)(4, 74)(5, 79)(6, 80)(7, 73)(8, 90)(9, 77)(10, 89)(11, 97)(12, 102)(13, 83)(14, 87)(15, 75)(16, 100)(17, 98)(18, 95)(19, 93)(20, 101)(21, 78)(22, 88)(23, 91)(24, 108)(25, 86)(26, 94)(27, 107)(28, 82)(29, 99)(30, 96)(31, 104)(32, 84)(33, 92)(34, 105)(35, 106)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 8, 4, 8, 4, 8 ), ( 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 E16.572 Graph:: bipartite v = 15 e = 72 f = 27 degree seq :: [ 6^12, 24^3 ] E16.574 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 9, 18}) Quotient :: halfedge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y3)^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (Y1^-1 * Y2)^2, (R * Y1)^2, Y1^-7 * Y2 * Y1^2 * Y3, Y1^4 * Y2 * Y1^-5 * Y3 ] Map:: non-degenerate R = (1, 38, 2, 42, 6, 49, 13, 57, 21, 65, 29, 70, 34, 62, 26, 54, 18, 46, 10, 52, 16, 60, 24, 68, 32, 72, 36, 64, 28, 56, 20, 48, 12, 41, 5, 37)(3, 45, 9, 53, 17, 61, 25, 69, 33, 67, 31, 59, 23, 51, 15, 44, 8, 40, 4, 47, 11, 55, 19, 63, 27, 71, 35, 66, 30, 58, 22, 50, 14, 43, 7, 39) L = (1, 3)(2, 7)(4, 10)(5, 9)(6, 14)(8, 16)(11, 18)(12, 17)(13, 22)(15, 24)(19, 26)(20, 25)(21, 30)(23, 32)(27, 34)(28, 33)(29, 35)(31, 36)(37, 40)(38, 44)(39, 46)(41, 47)(42, 51)(43, 52)(45, 54)(48, 55)(49, 59)(50, 60)(53, 62)(56, 63)(57, 67)(58, 68)(61, 70)(64, 71)(65, 69)(66, 72) local type(s) :: { ( 18^36 ) } Outer automorphisms :: reflexible Dual of E16.577 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.575 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 9, 18}) Quotient :: halfedge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, (Y1^-1 * Y3)^2, (Y2 * Y1^-1)^2, Y1^2 * Y2 * Y1^-1 * Y3, (Y3 * Y2)^6, (Y2 * Y1 * Y3)^9 ] Map:: non-degenerate R = (1, 38, 2, 42, 6, 48, 12, 51, 15, 56, 20, 61, 25, 63, 27, 68, 32, 72, 36, 70, 34, 65, 29, 60, 24, 58, 22, 53, 17, 46, 10, 49, 13, 41, 5, 37)(3, 45, 9, 52, 16, 54, 18, 59, 23, 64, 28, 66, 30, 71, 35, 69, 33, 67, 31, 62, 26, 57, 21, 55, 19, 50, 14, 44, 8, 40, 4, 47, 11, 43, 7, 39) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 11)(8, 15)(10, 18)(13, 16)(14, 20)(17, 23)(19, 25)(21, 27)(22, 28)(24, 30)(26, 32)(29, 35)(31, 36)(33, 34)(37, 40)(38, 44)(39, 46)(41, 47)(42, 50)(43, 49)(45, 53)(48, 55)(51, 57)(52, 58)(54, 60)(56, 62)(59, 65)(61, 67)(63, 69)(64, 70)(66, 72)(68, 71) local type(s) :: { ( 18^36 ) } Outer automorphisms :: reflexible Dual of E16.579 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.576 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 9, 18}) Quotient :: halfedge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y1^-1 * Y3)^2, Y1^2 * Y3 * Y1^-1 * Y2, (Y2 * Y3)^6 ] Map:: non-degenerate R = (1, 38, 2, 42, 6, 46, 10, 51, 15, 56, 20, 58, 22, 63, 27, 68, 32, 70, 34, 71, 35, 66, 30, 61, 25, 59, 23, 54, 18, 48, 12, 49, 13, 41, 5, 37)(3, 45, 9, 44, 8, 40, 4, 47, 11, 53, 17, 55, 19, 60, 24, 65, 29, 67, 31, 72, 36, 69, 33, 64, 28, 62, 26, 57, 21, 52, 16, 50, 14, 43, 7, 39) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 14)(8, 13)(10, 16)(11, 18)(15, 21)(17, 23)(19, 25)(20, 26)(22, 28)(24, 30)(27, 33)(29, 35)(31, 34)(32, 36)(37, 40)(38, 44)(39, 46)(41, 47)(42, 45)(43, 51)(48, 55)(49, 53)(50, 56)(52, 58)(54, 60)(57, 63)(59, 65)(61, 67)(62, 68)(64, 70)(66, 72)(69, 71) local type(s) :: { ( 18^36 ) } Outer automorphisms :: reflexible Dual of E16.578 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.577 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 9, 18}) Quotient :: halfedge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, (Y3 * Y2)^2, (Y1^-1 * Y2)^2, Y1^9 ] Map:: non-degenerate R = (1, 38, 2, 42, 6, 49, 13, 57, 21, 64, 28, 56, 20, 48, 12, 41, 5, 37)(3, 45, 9, 53, 17, 61, 25, 68, 32, 65, 29, 58, 22, 50, 14, 43, 7, 39)(4, 47, 11, 55, 19, 63, 27, 70, 34, 66, 30, 59, 23, 51, 15, 44, 8, 40)(10, 52, 16, 60, 24, 67, 31, 71, 35, 72, 36, 69, 33, 62, 26, 54, 18, 46) L = (1, 3)(2, 7)(4, 10)(5, 9)(6, 14)(8, 16)(11, 18)(12, 17)(13, 22)(15, 24)(19, 26)(20, 25)(21, 29)(23, 31)(27, 33)(28, 32)(30, 35)(34, 36)(37, 40)(38, 44)(39, 46)(41, 47)(42, 51)(43, 52)(45, 54)(48, 55)(49, 59)(50, 60)(53, 62)(56, 63)(57, 66)(58, 67)(61, 69)(64, 70)(65, 71)(68, 72) local type(s) :: { ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.574 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 18^4 ] E16.578 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 9, 18}) Quotient :: halfedge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y1^-1 * Y3)^2, Y3 * Y1^-1 * Y2 * Y3 * Y2, Y1^9 ] Map:: non-degenerate R = (1, 38, 2, 42, 6, 50, 14, 58, 22, 65, 29, 57, 21, 49, 13, 41, 5, 37)(3, 45, 9, 54, 18, 62, 26, 69, 33, 66, 30, 59, 23, 51, 15, 43, 7, 39)(4, 47, 11, 55, 19, 63, 27, 70, 34, 67, 31, 60, 24, 52, 16, 44, 8, 40)(10, 53, 17, 61, 25, 68, 32, 72, 36, 71, 35, 64, 28, 56, 20, 48, 12, 46) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 10)(11, 20)(13, 18)(14, 23)(16, 17)(19, 28)(21, 26)(22, 30)(24, 25)(27, 35)(29, 33)(31, 32)(34, 36)(37, 40)(38, 44)(39, 46)(41, 47)(42, 52)(43, 53)(45, 48)(49, 55)(50, 60)(51, 61)(54, 56)(57, 63)(58, 67)(59, 68)(62, 64)(65, 70)(66, 72)(69, 71) local type(s) :: { ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.576 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 18^4 ] E16.579 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 9, 18}) Quotient :: halfedge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1 * Y3)^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y2 * Y1^-1 * Y3 * Y1 * Y2 * Y1^-1 * Y3, Y2 * Y3 * Y1^3 * Y2 * Y3, Y1^9, Y1^-1 * Y2 * Y1^2 * Y3 * Y2 * Y3 * Y1^-3, (Y2 * Y1 * Y3)^18 ] Map:: non-degenerate R = (1, 38, 2, 42, 6, 50, 14, 62, 26, 69, 33, 61, 25, 49, 13, 41, 5, 37)(3, 45, 9, 55, 19, 66, 30, 72, 36, 65, 29, 60, 24, 51, 15, 43, 7, 39)(4, 47, 11, 58, 22, 57, 21, 68, 32, 70, 34, 63, 27, 52, 16, 44, 8, 40)(10, 53, 17, 59, 23, 48, 12, 54, 18, 64, 28, 71, 35, 67, 31, 56, 20, 46) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 24)(16, 28)(17, 22)(20, 32)(25, 30)(26, 29)(27, 35)(31, 34)(33, 36)(37, 40)(38, 44)(39, 46)(41, 47)(42, 52)(43, 53)(45, 56)(48, 60)(49, 58)(50, 63)(51, 59)(54, 65)(55, 67)(57, 61)(62, 70)(64, 72)(66, 71)(68, 69) local type(s) :: { ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.575 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 18^4 ] E16.580 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 9, 18}) Quotient :: edge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, Y3^9, (Y3 * Y1 * Y2)^18 ] Map:: R = (1, 37, 4, 40, 11, 47, 19, 55, 27, 63, 28, 64, 20, 56, 12, 48, 5, 41)(2, 38, 7, 43, 15, 51, 23, 59, 31, 67, 32, 68, 24, 60, 16, 52, 8, 44)(3, 39, 9, 45, 17, 53, 25, 61, 33, 69, 34, 70, 26, 62, 18, 54, 10, 46)(6, 42, 13, 49, 21, 57, 29, 65, 35, 71, 36, 72, 30, 66, 22, 58, 14, 50)(73, 74)(75, 78)(76, 80)(77, 79)(81, 86)(82, 85)(83, 88)(84, 87)(89, 94)(90, 93)(91, 96)(92, 95)(97, 102)(98, 101)(99, 104)(100, 103)(105, 108)(106, 107)(109, 111)(110, 114)(112, 118)(113, 117)(115, 122)(116, 121)(119, 126)(120, 125)(123, 130)(124, 129)(127, 134)(128, 133)(131, 138)(132, 137)(135, 142)(136, 141)(139, 144)(140, 143) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 72, 72 ), ( 72^18 ) } Outer automorphisms :: reflexible Dual of E16.589 Graph:: simple bipartite v = 40 e = 72 f = 2 degree seq :: [ 2^36, 18^4 ] E16.581 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 9, 18}) Quotient :: edge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y1 * Y2 * Y1 * Y3^-3 * Y2, Y3^9, Y3 * Y2 * Y3^-2 * Y1 * Y3^3 * Y2 * Y1 ] Map:: R = (1, 37, 4, 40, 12, 48, 24, 60, 32, 68, 33, 69, 25, 61, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 28, 64, 36, 72, 29, 65, 19, 55, 18, 54, 8, 44)(3, 39, 10, 46, 22, 58, 14, 50, 26, 62, 34, 70, 31, 67, 23, 59, 11, 47)(6, 42, 15, 51, 21, 57, 9, 45, 20, 56, 30, 66, 35, 71, 27, 63, 16, 52)(73, 74)(75, 81)(76, 80)(77, 79)(78, 86)(82, 93)(83, 92)(84, 90)(85, 89)(87, 94)(88, 98)(91, 96)(95, 102)(97, 100)(99, 106)(101, 104)(103, 107)(105, 108)(109, 111)(110, 114)(112, 119)(113, 118)(115, 124)(116, 123)(117, 127)(120, 131)(121, 130)(122, 133)(125, 135)(126, 129)(128, 137)(132, 139)(134, 141)(136, 143)(138, 144)(140, 142) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 72, 72 ), ( 72^18 ) } Outer automorphisms :: reflexible Dual of E16.590 Graph:: simple bipartite v = 40 e = 72 f = 2 degree seq :: [ 2^36, 18^4 ] E16.582 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 9, 18}) Quotient :: edge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1)^2, Y2 * Y3^-2 * Y1 * Y2 * Y1, Y3^9, Y1 * Y3^-3 * Y2 * Y1 * Y3^-4 * Y2, Y3^4 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 37, 4, 40, 12, 48, 21, 57, 29, 65, 30, 66, 22, 58, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 25, 61, 33, 69, 34, 70, 26, 62, 18, 54, 8, 44)(3, 39, 10, 46, 20, 56, 28, 64, 36, 72, 31, 67, 23, 59, 14, 50, 11, 47)(6, 42, 15, 51, 24, 60, 32, 68, 35, 71, 27, 63, 19, 55, 9, 45, 16, 52)(73, 74)(75, 81)(76, 80)(77, 79)(78, 86)(82, 91)(83, 88)(84, 90)(85, 89)(87, 95)(92, 99)(93, 98)(94, 97)(96, 103)(100, 107)(101, 106)(102, 105)(104, 108)(109, 111)(110, 114)(112, 119)(113, 118)(115, 124)(116, 123)(117, 125)(120, 122)(121, 128)(126, 132)(127, 133)(129, 131)(130, 136)(134, 140)(135, 141)(137, 139)(138, 144)(142, 143) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 72, 72 ), ( 72^18 ) } Outer automorphisms :: reflexible Dual of E16.591 Graph:: simple bipartite v = 40 e = 72 f = 2 degree seq :: [ 2^36, 18^4 ] E16.583 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 9, 18}) Quotient :: edge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y2 * Y1 * Y2 * Y3^3 * Y1 * Y3^3, Y3^-3 * Y1 * Y2 * Y1 * Y3^-3 * Y2, Y3^-1 * Y2 * Y3^3 * Y1 * Y3^-5, Y3^2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 37, 4, 40, 11, 47, 19, 55, 27, 63, 35, 71, 30, 66, 22, 58, 14, 50, 6, 42, 13, 49, 21, 57, 29, 65, 36, 72, 28, 64, 20, 56, 12, 48, 5, 41)(2, 38, 7, 43, 15, 51, 23, 59, 31, 67, 34, 70, 26, 62, 18, 54, 10, 46, 3, 39, 9, 45, 17, 53, 25, 61, 33, 69, 32, 68, 24, 60, 16, 52, 8, 44)(73, 74)(75, 78)(76, 80)(77, 79)(81, 86)(82, 85)(83, 88)(84, 87)(89, 94)(90, 93)(91, 96)(92, 95)(97, 102)(98, 101)(99, 104)(100, 103)(105, 107)(106, 108)(109, 111)(110, 114)(112, 118)(113, 117)(115, 122)(116, 121)(119, 126)(120, 125)(123, 130)(124, 129)(127, 134)(128, 133)(131, 138)(132, 137)(135, 142)(136, 141)(139, 143)(140, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 36, 36 ), ( 36^36 ) } Outer automorphisms :: reflexible Dual of E16.586 Graph:: simple bipartite v = 38 e = 72 f = 4 degree seq :: [ 2^36, 36^2 ] E16.584 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 9, 18}) Quotient :: edge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3^3 * Y1, (Y1 * Y2)^6 ] Map:: R = (1, 37, 4, 40, 12, 48, 9, 45, 18, 54, 25, 61, 23, 59, 30, 66, 36, 72, 32, 68, 34, 70, 27, 63, 20, 56, 22, 58, 15, 51, 6, 42, 13, 49, 5, 41)(2, 38, 7, 43, 16, 52, 14, 50, 21, 57, 28, 64, 26, 62, 33, 69, 35, 71, 29, 65, 31, 67, 24, 60, 17, 53, 19, 55, 11, 47, 3, 39, 10, 46, 8, 44)(73, 74)(75, 81)(76, 80)(77, 79)(78, 86)(82, 84)(83, 90)(85, 88)(87, 93)(89, 95)(91, 97)(92, 98)(94, 100)(96, 102)(99, 105)(101, 104)(103, 108)(106, 107)(109, 111)(110, 114)(112, 119)(113, 118)(115, 123)(116, 121)(117, 125)(120, 127)(122, 128)(124, 130)(126, 132)(129, 135)(131, 137)(133, 139)(134, 140)(136, 142)(138, 143)(141, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 36, 36 ), ( 36^36 ) } Outer automorphisms :: reflexible Dual of E16.587 Graph:: simple bipartite v = 38 e = 72 f = 4 degree seq :: [ 2^36, 36^2 ] E16.585 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 9, 18}) Quotient :: edge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3 * Y1 * Y3^-4, Y3 * Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1 ] Map:: R = (1, 37, 4, 40, 12, 48, 24, 60, 21, 57, 9, 45, 20, 56, 34, 70, 26, 62, 36, 72, 31, 67, 29, 65, 16, 52, 6, 42, 15, 51, 25, 61, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 30, 66, 28, 64, 14, 50, 27, 63, 33, 69, 19, 55, 32, 68, 35, 71, 23, 59, 11, 47, 3, 39, 10, 46, 22, 58, 18, 54, 8, 44)(73, 74)(75, 81)(76, 80)(77, 79)(78, 86)(82, 93)(83, 92)(84, 90)(85, 89)(87, 100)(88, 99)(91, 103)(94, 96)(95, 106)(97, 102)(98, 107)(101, 105)(104, 108)(109, 111)(110, 114)(112, 119)(113, 118)(115, 124)(116, 123)(117, 127)(120, 131)(121, 130)(122, 134)(125, 137)(126, 133)(128, 141)(129, 140)(132, 143)(135, 142)(136, 144)(138, 139) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 36, 36 ), ( 36^36 ) } Outer automorphisms :: reflexible Dual of E16.588 Graph:: simple bipartite v = 38 e = 72 f = 4 degree seq :: [ 2^36, 36^2 ] E16.586 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 9, 18}) Quotient :: loop^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, Y3^9, (Y3 * Y1 * Y2)^18 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 11, 47, 83, 119, 19, 55, 91, 127, 27, 63, 99, 135, 28, 64, 100, 136, 20, 56, 92, 128, 12, 48, 84, 120, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 15, 51, 87, 123, 23, 59, 95, 131, 31, 67, 103, 139, 32, 68, 104, 140, 24, 60, 96, 132, 16, 52, 88, 124, 8, 44, 80, 116)(3, 39, 75, 111, 9, 45, 81, 117, 17, 53, 89, 125, 25, 61, 97, 133, 33, 69, 105, 141, 34, 70, 106, 142, 26, 62, 98, 134, 18, 54, 90, 126, 10, 46, 82, 118)(6, 42, 78, 114, 13, 49, 85, 121, 21, 57, 93, 129, 29, 65, 101, 137, 35, 71, 107, 143, 36, 72, 108, 144, 30, 66, 102, 138, 22, 58, 94, 130, 14, 50, 86, 122) L = (1, 38)(2, 37)(3, 42)(4, 44)(5, 43)(6, 39)(7, 41)(8, 40)(9, 50)(10, 49)(11, 52)(12, 51)(13, 46)(14, 45)(15, 48)(16, 47)(17, 58)(18, 57)(19, 60)(20, 59)(21, 54)(22, 53)(23, 56)(24, 55)(25, 66)(26, 65)(27, 68)(28, 67)(29, 62)(30, 61)(31, 64)(32, 63)(33, 72)(34, 71)(35, 70)(36, 69)(73, 111)(74, 114)(75, 109)(76, 118)(77, 117)(78, 110)(79, 122)(80, 121)(81, 113)(82, 112)(83, 126)(84, 125)(85, 116)(86, 115)(87, 130)(88, 129)(89, 120)(90, 119)(91, 134)(92, 133)(93, 124)(94, 123)(95, 138)(96, 137)(97, 128)(98, 127)(99, 142)(100, 141)(101, 132)(102, 131)(103, 144)(104, 143)(105, 136)(106, 135)(107, 140)(108, 139) local type(s) :: { ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.583 Transitivity :: VT+ Graph:: bipartite v = 4 e = 72 f = 38 degree seq :: [ 36^4 ] E16.587 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 9, 18}) Quotient :: loop^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y1 * Y2 * Y1 * Y3^-3 * Y2, Y3^9, Y3 * Y2 * Y3^-2 * Y1 * Y3^3 * Y2 * Y1 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 12, 48, 84, 120, 24, 60, 96, 132, 32, 68, 104, 140, 33, 69, 105, 141, 25, 61, 97, 133, 13, 49, 85, 121, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 17, 53, 89, 125, 28, 64, 100, 136, 36, 72, 108, 144, 29, 65, 101, 137, 19, 55, 91, 127, 18, 54, 90, 126, 8, 44, 80, 116)(3, 39, 75, 111, 10, 46, 82, 118, 22, 58, 94, 130, 14, 50, 86, 122, 26, 62, 98, 134, 34, 70, 106, 142, 31, 67, 103, 139, 23, 59, 95, 131, 11, 47, 83, 119)(6, 42, 78, 114, 15, 51, 87, 123, 21, 57, 93, 129, 9, 45, 81, 117, 20, 56, 92, 128, 30, 66, 102, 138, 35, 71, 107, 143, 27, 63, 99, 135, 16, 52, 88, 124) L = (1, 38)(2, 37)(3, 45)(4, 44)(5, 43)(6, 50)(7, 41)(8, 40)(9, 39)(10, 57)(11, 56)(12, 54)(13, 53)(14, 42)(15, 58)(16, 62)(17, 49)(18, 48)(19, 60)(20, 47)(21, 46)(22, 51)(23, 66)(24, 55)(25, 64)(26, 52)(27, 70)(28, 61)(29, 68)(30, 59)(31, 71)(32, 65)(33, 72)(34, 63)(35, 67)(36, 69)(73, 111)(74, 114)(75, 109)(76, 119)(77, 118)(78, 110)(79, 124)(80, 123)(81, 127)(82, 113)(83, 112)(84, 131)(85, 130)(86, 133)(87, 116)(88, 115)(89, 135)(90, 129)(91, 117)(92, 137)(93, 126)(94, 121)(95, 120)(96, 139)(97, 122)(98, 141)(99, 125)(100, 143)(101, 128)(102, 144)(103, 132)(104, 142)(105, 134)(106, 140)(107, 136)(108, 138) local type(s) :: { ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.584 Transitivity :: VT+ Graph:: bipartite v = 4 e = 72 f = 38 degree seq :: [ 36^4 ] E16.588 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 9, 18}) Quotient :: loop^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1)^2, Y2 * Y3^-2 * Y1 * Y2 * Y1, Y3^9, Y1 * Y3^-3 * Y2 * Y1 * Y3^-4 * Y2, Y3^4 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 12, 48, 84, 120, 21, 57, 93, 129, 29, 65, 101, 137, 30, 66, 102, 138, 22, 58, 94, 130, 13, 49, 85, 121, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 17, 53, 89, 125, 25, 61, 97, 133, 33, 69, 105, 141, 34, 70, 106, 142, 26, 62, 98, 134, 18, 54, 90, 126, 8, 44, 80, 116)(3, 39, 75, 111, 10, 46, 82, 118, 20, 56, 92, 128, 28, 64, 100, 136, 36, 72, 108, 144, 31, 67, 103, 139, 23, 59, 95, 131, 14, 50, 86, 122, 11, 47, 83, 119)(6, 42, 78, 114, 15, 51, 87, 123, 24, 60, 96, 132, 32, 68, 104, 140, 35, 71, 107, 143, 27, 63, 99, 135, 19, 55, 91, 127, 9, 45, 81, 117, 16, 52, 88, 124) L = (1, 38)(2, 37)(3, 45)(4, 44)(5, 43)(6, 50)(7, 41)(8, 40)(9, 39)(10, 55)(11, 52)(12, 54)(13, 53)(14, 42)(15, 59)(16, 47)(17, 49)(18, 48)(19, 46)(20, 63)(21, 62)(22, 61)(23, 51)(24, 67)(25, 58)(26, 57)(27, 56)(28, 71)(29, 70)(30, 69)(31, 60)(32, 72)(33, 66)(34, 65)(35, 64)(36, 68)(73, 111)(74, 114)(75, 109)(76, 119)(77, 118)(78, 110)(79, 124)(80, 123)(81, 125)(82, 113)(83, 112)(84, 122)(85, 128)(86, 120)(87, 116)(88, 115)(89, 117)(90, 132)(91, 133)(92, 121)(93, 131)(94, 136)(95, 129)(96, 126)(97, 127)(98, 140)(99, 141)(100, 130)(101, 139)(102, 144)(103, 137)(104, 134)(105, 135)(106, 143)(107, 142)(108, 138) local type(s) :: { ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.585 Transitivity :: VT+ Graph:: bipartite v = 4 e = 72 f = 38 degree seq :: [ 36^4 ] E16.589 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 9, 18}) Quotient :: loop^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y2 * Y1 * Y2 * Y3^3 * Y1 * Y3^3, Y3^-3 * Y1 * Y2 * Y1 * Y3^-3 * Y2, Y3^-1 * Y2 * Y3^3 * Y1 * Y3^-5, Y3^2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 11, 47, 83, 119, 19, 55, 91, 127, 27, 63, 99, 135, 35, 71, 107, 143, 30, 66, 102, 138, 22, 58, 94, 130, 14, 50, 86, 122, 6, 42, 78, 114, 13, 49, 85, 121, 21, 57, 93, 129, 29, 65, 101, 137, 36, 72, 108, 144, 28, 64, 100, 136, 20, 56, 92, 128, 12, 48, 84, 120, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 15, 51, 87, 123, 23, 59, 95, 131, 31, 67, 103, 139, 34, 70, 106, 142, 26, 62, 98, 134, 18, 54, 90, 126, 10, 46, 82, 118, 3, 39, 75, 111, 9, 45, 81, 117, 17, 53, 89, 125, 25, 61, 97, 133, 33, 69, 105, 141, 32, 68, 104, 140, 24, 60, 96, 132, 16, 52, 88, 124, 8, 44, 80, 116) L = (1, 38)(2, 37)(3, 42)(4, 44)(5, 43)(6, 39)(7, 41)(8, 40)(9, 50)(10, 49)(11, 52)(12, 51)(13, 46)(14, 45)(15, 48)(16, 47)(17, 58)(18, 57)(19, 60)(20, 59)(21, 54)(22, 53)(23, 56)(24, 55)(25, 66)(26, 65)(27, 68)(28, 67)(29, 62)(30, 61)(31, 64)(32, 63)(33, 71)(34, 72)(35, 69)(36, 70)(73, 111)(74, 114)(75, 109)(76, 118)(77, 117)(78, 110)(79, 122)(80, 121)(81, 113)(82, 112)(83, 126)(84, 125)(85, 116)(86, 115)(87, 130)(88, 129)(89, 120)(90, 119)(91, 134)(92, 133)(93, 124)(94, 123)(95, 138)(96, 137)(97, 128)(98, 127)(99, 142)(100, 141)(101, 132)(102, 131)(103, 143)(104, 144)(105, 136)(106, 135)(107, 139)(108, 140) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E16.580 Transitivity :: VT+ Graph:: bipartite v = 2 e = 72 f = 40 degree seq :: [ 72^2 ] E16.590 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 9, 18}) Quotient :: loop^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3^3 * Y1, (Y1 * Y2)^6 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 12, 48, 84, 120, 9, 45, 81, 117, 18, 54, 90, 126, 25, 61, 97, 133, 23, 59, 95, 131, 30, 66, 102, 138, 36, 72, 108, 144, 32, 68, 104, 140, 34, 70, 106, 142, 27, 63, 99, 135, 20, 56, 92, 128, 22, 58, 94, 130, 15, 51, 87, 123, 6, 42, 78, 114, 13, 49, 85, 121, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 16, 52, 88, 124, 14, 50, 86, 122, 21, 57, 93, 129, 28, 64, 100, 136, 26, 62, 98, 134, 33, 69, 105, 141, 35, 71, 107, 143, 29, 65, 101, 137, 31, 67, 103, 139, 24, 60, 96, 132, 17, 53, 89, 125, 19, 55, 91, 127, 11, 47, 83, 119, 3, 39, 75, 111, 10, 46, 82, 118, 8, 44, 80, 116) L = (1, 38)(2, 37)(3, 45)(4, 44)(5, 43)(6, 50)(7, 41)(8, 40)(9, 39)(10, 48)(11, 54)(12, 46)(13, 52)(14, 42)(15, 57)(16, 49)(17, 59)(18, 47)(19, 61)(20, 62)(21, 51)(22, 64)(23, 53)(24, 66)(25, 55)(26, 56)(27, 69)(28, 58)(29, 68)(30, 60)(31, 72)(32, 65)(33, 63)(34, 71)(35, 70)(36, 67)(73, 111)(74, 114)(75, 109)(76, 119)(77, 118)(78, 110)(79, 123)(80, 121)(81, 125)(82, 113)(83, 112)(84, 127)(85, 116)(86, 128)(87, 115)(88, 130)(89, 117)(90, 132)(91, 120)(92, 122)(93, 135)(94, 124)(95, 137)(96, 126)(97, 139)(98, 140)(99, 129)(100, 142)(101, 131)(102, 143)(103, 133)(104, 134)(105, 144)(106, 136)(107, 138)(108, 141) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 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 E16.581 Transitivity :: VT+ Graph:: bipartite v = 2 e = 72 f = 40 degree seq :: [ 72^2 ] E16.591 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 9, 18}) Quotient :: loop^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3 * Y1 * Y3^-4, Y3 * Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 12, 48, 84, 120, 24, 60, 96, 132, 21, 57, 93, 129, 9, 45, 81, 117, 20, 56, 92, 128, 34, 70, 106, 142, 26, 62, 98, 134, 36, 72, 108, 144, 31, 67, 103, 139, 29, 65, 101, 137, 16, 52, 88, 124, 6, 42, 78, 114, 15, 51, 87, 123, 25, 61, 97, 133, 13, 49, 85, 121, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 17, 53, 89, 125, 30, 66, 102, 138, 28, 64, 100, 136, 14, 50, 86, 122, 27, 63, 99, 135, 33, 69, 105, 141, 19, 55, 91, 127, 32, 68, 104, 140, 35, 71, 107, 143, 23, 59, 95, 131, 11, 47, 83, 119, 3, 39, 75, 111, 10, 46, 82, 118, 22, 58, 94, 130, 18, 54, 90, 126, 8, 44, 80, 116) L = (1, 38)(2, 37)(3, 45)(4, 44)(5, 43)(6, 50)(7, 41)(8, 40)(9, 39)(10, 57)(11, 56)(12, 54)(13, 53)(14, 42)(15, 64)(16, 63)(17, 49)(18, 48)(19, 67)(20, 47)(21, 46)(22, 60)(23, 70)(24, 58)(25, 66)(26, 71)(27, 52)(28, 51)(29, 69)(30, 61)(31, 55)(32, 72)(33, 65)(34, 59)(35, 62)(36, 68)(73, 111)(74, 114)(75, 109)(76, 119)(77, 118)(78, 110)(79, 124)(80, 123)(81, 127)(82, 113)(83, 112)(84, 131)(85, 130)(86, 134)(87, 116)(88, 115)(89, 137)(90, 133)(91, 117)(92, 141)(93, 140)(94, 121)(95, 120)(96, 143)(97, 126)(98, 122)(99, 142)(100, 144)(101, 125)(102, 139)(103, 138)(104, 129)(105, 128)(106, 135)(107, 132)(108, 136) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E16.582 Transitivity :: VT+ Graph:: bipartite v = 2 e = 72 f = 40 degree seq :: [ 72^2 ] E16.592 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (R * Y1)^2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1, Y2^9 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 6, 42)(4, 40, 7, 43)(5, 41, 8, 44)(9, 45, 13, 49)(10, 46, 14, 50)(11, 47, 15, 51)(12, 48, 16, 52)(17, 53, 21, 57)(18, 54, 22, 58)(19, 55, 23, 59)(20, 56, 24, 60)(25, 61, 29, 65)(26, 62, 30, 66)(27, 63, 31, 67)(28, 64, 32, 68)(33, 69, 35, 71)(34, 70, 36, 72)(73, 109, 75, 111, 81, 117, 89, 125, 97, 133, 100, 136, 92, 128, 84, 120, 77, 113)(74, 110, 78, 114, 85, 121, 93, 129, 101, 137, 104, 140, 96, 132, 88, 124, 80, 116)(76, 112, 82, 118, 90, 126, 98, 134, 105, 141, 106, 142, 99, 135, 91, 127, 83, 119)(79, 115, 86, 122, 94, 130, 102, 138, 107, 143, 108, 144, 103, 139, 95, 131, 87, 123) L = (1, 76)(2, 79)(3, 82)(4, 73)(5, 83)(6, 86)(7, 74)(8, 87)(9, 90)(10, 75)(11, 77)(12, 91)(13, 94)(14, 78)(15, 80)(16, 95)(17, 98)(18, 81)(19, 84)(20, 99)(21, 102)(22, 85)(23, 88)(24, 103)(25, 105)(26, 89)(27, 92)(28, 106)(29, 107)(30, 93)(31, 96)(32, 108)(33, 97)(34, 100)(35, 101)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E16.599 Graph:: simple bipartite v = 22 e = 72 f = 20 degree seq :: [ 4^18, 18^4 ] E16.593 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (R * Y1)^2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, Y2^9 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 8, 44)(4, 40, 7, 43)(5, 41, 6, 42)(9, 45, 16, 52)(10, 46, 15, 51)(11, 47, 14, 50)(12, 48, 13, 49)(17, 53, 24, 60)(18, 54, 23, 59)(19, 55, 22, 58)(20, 56, 21, 57)(25, 61, 32, 68)(26, 62, 31, 67)(27, 63, 30, 66)(28, 64, 29, 65)(33, 69, 36, 72)(34, 70, 35, 71)(73, 109, 75, 111, 81, 117, 89, 125, 97, 133, 100, 136, 92, 128, 84, 120, 77, 113)(74, 110, 78, 114, 85, 121, 93, 129, 101, 137, 104, 140, 96, 132, 88, 124, 80, 116)(76, 112, 82, 118, 90, 126, 98, 134, 105, 141, 106, 142, 99, 135, 91, 127, 83, 119)(79, 115, 86, 122, 94, 130, 102, 138, 107, 143, 108, 144, 103, 139, 95, 131, 87, 123) L = (1, 76)(2, 79)(3, 82)(4, 73)(5, 83)(6, 86)(7, 74)(8, 87)(9, 90)(10, 75)(11, 77)(12, 91)(13, 94)(14, 78)(15, 80)(16, 95)(17, 98)(18, 81)(19, 84)(20, 99)(21, 102)(22, 85)(23, 88)(24, 103)(25, 105)(26, 89)(27, 92)(28, 106)(29, 107)(30, 93)(31, 96)(32, 108)(33, 97)(34, 100)(35, 101)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E16.600 Graph:: simple bipartite v = 22 e = 72 f = 20 degree seq :: [ 4^18, 18^4 ] E16.594 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, Y3^2 * Y2^3, Y3^6 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 10, 46)(5, 41, 7, 43)(6, 42, 8, 44)(11, 47, 24, 60)(12, 48, 25, 61)(13, 49, 23, 59)(14, 50, 26, 62)(15, 51, 21, 57)(16, 52, 19, 55)(17, 53, 20, 56)(18, 54, 22, 58)(27, 63, 36, 72)(28, 64, 35, 71)(29, 65, 34, 70)(30, 66, 33, 69)(31, 67, 32, 68)(73, 109, 75, 111, 83, 119, 90, 126, 100, 136, 102, 138, 86, 122, 88, 124, 77, 113)(74, 110, 79, 115, 91, 127, 98, 134, 105, 141, 107, 143, 94, 130, 96, 132, 81, 117)(76, 112, 84, 120, 89, 125, 78, 114, 85, 121, 99, 135, 101, 137, 103, 139, 87, 123)(80, 116, 92, 128, 97, 133, 82, 118, 93, 129, 104, 140, 106, 142, 108, 144, 95, 131) L = (1, 76)(2, 80)(3, 84)(4, 86)(5, 87)(6, 73)(7, 92)(8, 94)(9, 95)(10, 74)(11, 89)(12, 88)(13, 75)(14, 101)(15, 102)(16, 103)(17, 77)(18, 78)(19, 97)(20, 96)(21, 79)(22, 106)(23, 107)(24, 108)(25, 81)(26, 82)(27, 83)(28, 85)(29, 90)(30, 99)(31, 100)(32, 91)(33, 93)(34, 98)(35, 104)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E16.601 Graph:: simple bipartite v = 22 e = 72 f = 20 degree seq :: [ 4^18, 18^4 ] E16.595 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3, Y2), (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, Y3^-2 * Y2^3, Y3^6 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 10, 46)(5, 41, 7, 43)(6, 42, 8, 44)(11, 47, 24, 60)(12, 48, 25, 61)(13, 49, 23, 59)(14, 50, 26, 62)(15, 51, 21, 57)(16, 52, 19, 55)(17, 53, 20, 56)(18, 54, 22, 58)(27, 63, 35, 71)(28, 64, 36, 72)(29, 65, 34, 70)(30, 66, 32, 68)(31, 67, 33, 69)(73, 109, 75, 111, 83, 119, 86, 122, 100, 136, 103, 139, 90, 126, 88, 124, 77, 113)(74, 110, 79, 115, 91, 127, 94, 130, 105, 141, 108, 144, 98, 134, 96, 132, 81, 117)(76, 112, 84, 120, 99, 135, 101, 137, 102, 138, 89, 125, 78, 114, 85, 121, 87, 123)(80, 116, 92, 128, 104, 140, 106, 142, 107, 143, 97, 133, 82, 118, 93, 129, 95, 131) L = (1, 76)(2, 80)(3, 84)(4, 86)(5, 87)(6, 73)(7, 92)(8, 94)(9, 95)(10, 74)(11, 99)(12, 100)(13, 75)(14, 101)(15, 83)(16, 85)(17, 77)(18, 78)(19, 104)(20, 105)(21, 79)(22, 106)(23, 91)(24, 93)(25, 81)(26, 82)(27, 103)(28, 102)(29, 90)(30, 88)(31, 89)(32, 108)(33, 107)(34, 98)(35, 96)(36, 97)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E16.602 Graph:: simple bipartite v = 22 e = 72 f = 20 degree seq :: [ 4^18, 18^4 ] E16.596 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-2 * Y2^-1, (R * Y1)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2^-1)^2, (R * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, Y3^-2 * Y2^7, Y3^-2 * Y2^2 * Y3^-1 * Y2 * Y3^-3, (Y3 * Y2^-1)^18 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 10, 46)(5, 41, 7, 43)(6, 42, 8, 44)(11, 47, 19, 55)(12, 48, 17, 53)(13, 49, 20, 56)(14, 50, 16, 52)(15, 51, 18, 54)(21, 57, 28, 64)(22, 58, 27, 63)(23, 59, 26, 62)(24, 60, 25, 61)(29, 65, 35, 71)(30, 66, 36, 72)(31, 67, 33, 69)(32, 68, 34, 70)(73, 109, 75, 111, 83, 119, 93, 129, 101, 137, 103, 139, 96, 132, 86, 122, 77, 113)(74, 110, 79, 115, 88, 124, 97, 133, 105, 141, 107, 143, 100, 136, 91, 127, 81, 117)(76, 112, 84, 120, 78, 114, 85, 121, 94, 130, 102, 138, 104, 140, 95, 131, 87, 123)(80, 116, 89, 125, 82, 118, 90, 126, 98, 134, 106, 142, 108, 144, 99, 135, 92, 128) L = (1, 76)(2, 80)(3, 84)(4, 86)(5, 87)(6, 73)(7, 89)(8, 91)(9, 92)(10, 74)(11, 78)(12, 77)(13, 75)(14, 95)(15, 96)(16, 82)(17, 81)(18, 79)(19, 99)(20, 100)(21, 85)(22, 83)(23, 103)(24, 104)(25, 90)(26, 88)(27, 107)(28, 108)(29, 94)(30, 93)(31, 102)(32, 101)(33, 98)(34, 97)(35, 106)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E16.605 Graph:: simple bipartite v = 22 e = 72 f = 20 degree seq :: [ 4^18, 18^4 ] E16.597 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y2^9 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 10, 46)(5, 41, 7, 43)(6, 42, 8, 44)(11, 47, 17, 53)(12, 48, 18, 54)(13, 49, 15, 51)(14, 50, 16, 52)(19, 55, 25, 61)(20, 56, 26, 62)(21, 57, 23, 59)(22, 58, 24, 60)(27, 63, 33, 69)(28, 64, 34, 70)(29, 65, 31, 67)(30, 66, 32, 68)(35, 71, 36, 72)(73, 109, 75, 111, 83, 119, 91, 127, 99, 135, 101, 137, 93, 129, 85, 121, 77, 113)(74, 110, 79, 115, 87, 123, 95, 131, 103, 139, 105, 141, 97, 133, 89, 125, 81, 117)(76, 112, 84, 120, 92, 128, 100, 136, 107, 143, 102, 138, 94, 130, 86, 122, 78, 114)(80, 116, 88, 124, 96, 132, 104, 140, 108, 144, 106, 142, 98, 134, 90, 126, 82, 118) L = (1, 76)(2, 80)(3, 84)(4, 75)(5, 78)(6, 73)(7, 88)(8, 79)(9, 82)(10, 74)(11, 92)(12, 83)(13, 86)(14, 77)(15, 96)(16, 87)(17, 90)(18, 81)(19, 100)(20, 91)(21, 94)(22, 85)(23, 104)(24, 95)(25, 98)(26, 89)(27, 107)(28, 99)(29, 102)(30, 93)(31, 108)(32, 103)(33, 106)(34, 97)(35, 101)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E16.603 Graph:: simple bipartite v = 22 e = 72 f = 20 degree seq :: [ 4^18, 18^4 ] E16.598 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^3, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 10, 46)(5, 41, 7, 43)(6, 42, 8, 44)(11, 47, 24, 60)(12, 48, 25, 61)(13, 49, 23, 59)(14, 50, 26, 62)(15, 51, 21, 57)(16, 52, 19, 55)(17, 53, 20, 56)(18, 54, 22, 58)(27, 63, 35, 71)(28, 64, 36, 72)(29, 65, 34, 70)(30, 66, 32, 68)(31, 67, 33, 69)(73, 109, 75, 111, 83, 119, 99, 135, 86, 122, 90, 126, 102, 138, 88, 124, 77, 113)(74, 110, 79, 115, 91, 127, 104, 140, 94, 130, 98, 134, 107, 143, 96, 132, 81, 117)(76, 112, 84, 120, 100, 136, 103, 139, 89, 125, 78, 114, 85, 121, 101, 137, 87, 123)(80, 116, 92, 128, 105, 141, 108, 144, 97, 133, 82, 118, 93, 129, 106, 142, 95, 131) L = (1, 76)(2, 80)(3, 84)(4, 86)(5, 87)(6, 73)(7, 92)(8, 94)(9, 95)(10, 74)(11, 100)(12, 90)(13, 75)(14, 89)(15, 99)(16, 101)(17, 77)(18, 78)(19, 105)(20, 98)(21, 79)(22, 97)(23, 104)(24, 106)(25, 81)(26, 82)(27, 103)(28, 102)(29, 83)(30, 85)(31, 88)(32, 108)(33, 107)(34, 91)(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) :: { ( 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E16.604 Graph:: simple bipartite v = 22 e = 72 f = 20 degree seq :: [ 4^18, 18^4 ] E16.599 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, Y1^-9 * Y3 ] Map:: non-degenerate R = (1, 37, 2, 38, 6, 42, 13, 49, 21, 57, 29, 65, 27, 63, 19, 55, 11, 47, 4, 40, 8, 44, 15, 51, 23, 59, 31, 67, 28, 64, 20, 56, 12, 48, 5, 41)(3, 39, 7, 43, 14, 50, 22, 58, 30, 66, 35, 71, 33, 69, 25, 61, 17, 53, 9, 45, 16, 52, 24, 60, 32, 68, 36, 72, 34, 70, 26, 62, 18, 54, 10, 46)(73, 109, 75, 111)(74, 110, 79, 115)(76, 112, 81, 117)(77, 113, 82, 118)(78, 114, 86, 122)(80, 116, 88, 124)(83, 119, 89, 125)(84, 120, 90, 126)(85, 121, 94, 130)(87, 123, 96, 132)(91, 127, 97, 133)(92, 128, 98, 134)(93, 129, 102, 138)(95, 131, 104, 140)(99, 135, 105, 141)(100, 136, 106, 142)(101, 137, 107, 143)(103, 139, 108, 144) L = (1, 76)(2, 80)(3, 81)(4, 73)(5, 83)(6, 87)(7, 88)(8, 74)(9, 75)(10, 89)(11, 77)(12, 91)(13, 95)(14, 96)(15, 78)(16, 79)(17, 82)(18, 97)(19, 84)(20, 99)(21, 103)(22, 104)(23, 85)(24, 86)(25, 90)(26, 105)(27, 92)(28, 101)(29, 100)(30, 108)(31, 93)(32, 94)(33, 98)(34, 107)(35, 106)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E16.592 Graph:: bipartite v = 20 e = 72 f = 22 degree seq :: [ 4^18, 36^2 ] E16.600 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, (R * Y3)^2, Y1^-1 * Y3 * Y1 * Y3, Y1^-9 * Y3 ] Map:: non-degenerate R = (1, 37, 2, 38, 6, 42, 13, 49, 21, 57, 29, 65, 27, 63, 19, 55, 11, 47, 4, 40, 8, 44, 15, 51, 23, 59, 31, 67, 28, 64, 20, 56, 12, 48, 5, 41)(3, 39, 9, 45, 17, 53, 25, 61, 33, 69, 36, 72, 32, 68, 24, 60, 16, 52, 10, 46, 18, 54, 26, 62, 34, 70, 35, 71, 30, 66, 22, 58, 14, 50, 7, 43)(73, 109, 75, 111)(74, 110, 79, 115)(76, 112, 82, 118)(77, 113, 81, 117)(78, 114, 86, 122)(80, 116, 88, 124)(83, 119, 90, 126)(84, 120, 89, 125)(85, 121, 94, 130)(87, 123, 96, 132)(91, 127, 98, 134)(92, 128, 97, 133)(93, 129, 102, 138)(95, 131, 104, 140)(99, 135, 106, 142)(100, 136, 105, 141)(101, 137, 107, 143)(103, 139, 108, 144) L = (1, 76)(2, 80)(3, 82)(4, 73)(5, 83)(6, 87)(7, 88)(8, 74)(9, 90)(10, 75)(11, 77)(12, 91)(13, 95)(14, 96)(15, 78)(16, 79)(17, 98)(18, 81)(19, 84)(20, 99)(21, 103)(22, 104)(23, 85)(24, 86)(25, 106)(26, 89)(27, 92)(28, 101)(29, 100)(30, 108)(31, 93)(32, 94)(33, 107)(34, 97)(35, 105)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E16.593 Graph:: bipartite v = 20 e = 72 f = 22 degree seq :: [ 4^18, 36^2 ] E16.601 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^-3, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^6, (Y1^-1 * Y3^-1)^9 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 4, 40, 9, 45, 18, 54, 14, 50, 21, 57, 29, 65, 26, 62, 32, 68, 27, 63, 16, 52, 22, 58, 15, 51, 6, 42, 10, 46, 5, 41)(3, 39, 11, 47, 19, 55, 12, 48, 23, 59, 30, 66, 24, 60, 33, 69, 36, 72, 34, 70, 35, 71, 31, 67, 25, 61, 28, 64, 20, 56, 13, 49, 17, 53, 8, 44)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 85, 121)(77, 113, 83, 119)(78, 114, 84, 120)(79, 115, 89, 125)(81, 117, 92, 128)(82, 118, 91, 127)(86, 122, 97, 133)(87, 123, 95, 131)(88, 124, 96, 132)(90, 126, 100, 136)(93, 129, 103, 139)(94, 130, 102, 138)(98, 134, 106, 142)(99, 135, 105, 141)(101, 137, 107, 143)(104, 140, 108, 144) L = (1, 76)(2, 81)(3, 84)(4, 86)(5, 79)(6, 73)(7, 90)(8, 91)(9, 93)(10, 74)(11, 95)(12, 96)(13, 75)(14, 98)(15, 77)(16, 78)(17, 83)(18, 101)(19, 102)(20, 80)(21, 104)(22, 82)(23, 105)(24, 106)(25, 85)(26, 88)(27, 87)(28, 89)(29, 99)(30, 108)(31, 92)(32, 94)(33, 107)(34, 97)(35, 100)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E16.594 Graph:: bipartite v = 20 e = 72 f = 22 degree seq :: [ 4^18, 36^2 ] E16.602 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-3, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 6, 42, 10, 46, 18, 54, 16, 52, 22, 58, 29, 65, 26, 62, 32, 68, 27, 63, 14, 50, 21, 57, 15, 51, 4, 40, 9, 45, 5, 41)(3, 39, 11, 47, 20, 56, 13, 49, 23, 59, 31, 67, 25, 61, 33, 69, 36, 72, 34, 70, 35, 71, 30, 66, 24, 60, 28, 64, 19, 55, 12, 48, 17, 53, 8, 44)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 85, 121)(77, 113, 83, 119)(78, 114, 84, 120)(79, 115, 89, 125)(81, 117, 92, 128)(82, 118, 91, 127)(86, 122, 97, 133)(87, 123, 95, 131)(88, 124, 96, 132)(90, 126, 100, 136)(93, 129, 103, 139)(94, 130, 102, 138)(98, 134, 106, 142)(99, 135, 105, 141)(101, 137, 107, 143)(104, 140, 108, 144) L = (1, 76)(2, 81)(3, 84)(4, 86)(5, 87)(6, 73)(7, 77)(8, 91)(9, 93)(10, 74)(11, 89)(12, 96)(13, 75)(14, 98)(15, 99)(16, 78)(17, 100)(18, 79)(19, 102)(20, 80)(21, 104)(22, 82)(23, 83)(24, 106)(25, 85)(26, 88)(27, 101)(28, 107)(29, 90)(30, 108)(31, 92)(32, 94)(33, 95)(34, 97)(35, 105)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E16.595 Graph:: bipartite v = 20 e = 72 f = 22 degree seq :: [ 4^18, 36^2 ] E16.603 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^18, (Y3^-1 * Y1^-1)^9 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41, 9, 45, 13, 49, 17, 53, 21, 57, 25, 61, 29, 65, 33, 69, 32, 68, 28, 64, 24, 60, 20, 56, 16, 52, 12, 48, 8, 44, 4, 40)(3, 39, 7, 43, 11, 47, 15, 51, 19, 55, 23, 59, 27, 63, 31, 67, 35, 71, 36, 72, 34, 70, 30, 66, 26, 62, 22, 58, 18, 54, 14, 50, 10, 46, 6, 42)(73, 109, 75, 111)(74, 110, 78, 114)(76, 112, 79, 115)(77, 113, 82, 118)(80, 116, 83, 119)(81, 117, 86, 122)(84, 120, 87, 123)(85, 121, 90, 126)(88, 124, 91, 127)(89, 125, 94, 130)(92, 128, 95, 131)(93, 129, 98, 134)(96, 132, 99, 135)(97, 133, 102, 138)(100, 136, 103, 139)(101, 137, 106, 142)(104, 140, 107, 143)(105, 141, 108, 144) L = (1, 74)(2, 77)(3, 79)(4, 73)(5, 81)(6, 75)(7, 83)(8, 76)(9, 85)(10, 78)(11, 87)(12, 80)(13, 89)(14, 82)(15, 91)(16, 84)(17, 93)(18, 86)(19, 95)(20, 88)(21, 97)(22, 90)(23, 99)(24, 92)(25, 101)(26, 94)(27, 103)(28, 96)(29, 105)(30, 98)(31, 107)(32, 100)(33, 104)(34, 102)(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, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E16.597 Graph:: bipartite v = 20 e = 72 f = 22 degree seq :: [ 4^18, 36^2 ] E16.604 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1, Y1), (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, Y3^-3 * Y1^-1 * Y3^-2, Y3^-1 * Y1 * Y3^-2 * Y1^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y3^-3 * Y2 * Y1^-2, Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^2 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 19, 55, 18, 54, 26, 62, 15, 51, 4, 40, 9, 45, 21, 57, 17, 53, 6, 42, 10, 46, 22, 58, 14, 50, 25, 61, 16, 52, 5, 41)(3, 39, 11, 47, 27, 63, 36, 72, 31, 67, 33, 69, 23, 59, 12, 48, 28, 64, 34, 70, 24, 60, 13, 49, 29, 65, 35, 71, 30, 66, 32, 68, 20, 56, 8, 44)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 85, 121)(77, 113, 83, 119)(78, 114, 84, 120)(79, 115, 92, 128)(81, 117, 96, 132)(82, 118, 95, 131)(86, 122, 103, 139)(87, 123, 101, 137)(88, 124, 99, 135)(89, 125, 100, 136)(90, 126, 102, 138)(91, 127, 104, 140)(93, 129, 106, 142)(94, 130, 105, 141)(97, 133, 108, 144)(98, 134, 107, 143) L = (1, 76)(2, 81)(3, 84)(4, 86)(5, 87)(6, 73)(7, 93)(8, 95)(9, 97)(10, 74)(11, 100)(12, 102)(13, 75)(14, 91)(15, 94)(16, 98)(17, 77)(18, 78)(19, 89)(20, 105)(21, 88)(22, 79)(23, 107)(24, 80)(25, 90)(26, 82)(27, 106)(28, 104)(29, 83)(30, 108)(31, 85)(32, 103)(33, 101)(34, 92)(35, 99)(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, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E16.598 Graph:: bipartite v = 20 e = 72 f = 22 degree seq :: [ 4^18, 36^2 ] E16.605 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3, Y1^-1), (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, Y1^-1 * Y3^-1 * Y1^-4, Y3 * Y1^-1 * Y3^2 * Y1^-2, (R * Y2 * Y3^-1)^2, (Y2 * Y3 * Y1)^2, Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^2 * Y3^-2 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 19, 55, 17, 53, 6, 42, 10, 46, 22, 58, 14, 50, 25, 61, 18, 54, 26, 62, 15, 51, 4, 40, 9, 45, 21, 57, 16, 52, 5, 41)(3, 39, 11, 47, 27, 63, 34, 70, 24, 60, 13, 49, 29, 65, 35, 71, 30, 66, 36, 72, 31, 67, 33, 69, 23, 59, 12, 48, 28, 64, 32, 68, 20, 56, 8, 44)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 85, 121)(77, 113, 83, 119)(78, 114, 84, 120)(79, 115, 92, 128)(81, 117, 96, 132)(82, 118, 95, 131)(86, 122, 103, 139)(87, 123, 101, 137)(88, 124, 99, 135)(89, 125, 100, 136)(90, 126, 102, 138)(91, 127, 104, 140)(93, 129, 106, 142)(94, 130, 105, 141)(97, 133, 108, 144)(98, 134, 107, 143) L = (1, 76)(2, 81)(3, 84)(4, 86)(5, 87)(6, 73)(7, 93)(8, 95)(9, 97)(10, 74)(11, 100)(12, 102)(13, 75)(14, 91)(15, 94)(16, 98)(17, 77)(18, 78)(19, 88)(20, 105)(21, 90)(22, 79)(23, 107)(24, 80)(25, 89)(26, 82)(27, 104)(28, 108)(29, 83)(30, 106)(31, 85)(32, 103)(33, 101)(34, 92)(35, 99)(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, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E16.596 Graph:: bipartite v = 20 e = 72 f = 22 degree seq :: [ 4^18, 36^2 ] E16.606 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {18, 18, 18}) Quotient :: edge Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T2)^2, (F * T1)^2, T2 * T1 * T2^3 * T1, T1^-7 * T2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 3, 9, 19, 11, 21, 28, 35, 30, 33, 23, 32, 26, 16, 6, 15, 13, 5)(2, 7, 17, 12, 4, 10, 20, 27, 22, 29, 31, 36, 34, 25, 14, 24, 18, 8)(37, 38, 42, 50, 59, 67, 64, 56, 45, 53, 49, 54, 62, 70, 66, 58, 47, 40)(39, 43, 51, 60, 68, 72, 71, 63, 55, 48, 41, 44, 52, 61, 69, 65, 57, 46) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.607 Transitivity :: ET+ Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 18^4 ] E16.607 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {18, 18, 18}) Quotient :: loop Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ F^2, T1^-1 * T2^2 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^16, (T1^-1 * T2^-1)^18 ] Map:: non-degenerate R = (1, 37, 3, 39, 6, 42, 12, 48, 15, 51, 20, 56, 23, 59, 28, 64, 31, 67, 36, 72, 33, 69, 30, 66, 25, 61, 22, 58, 17, 53, 14, 50, 9, 45, 5, 41)(2, 38, 7, 43, 11, 47, 16, 52, 19, 55, 24, 60, 27, 63, 32, 68, 35, 71, 34, 70, 29, 65, 26, 62, 21, 57, 18, 54, 13, 49, 10, 46, 4, 40, 8, 44) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 47)(7, 48)(8, 39)(9, 40)(10, 41)(11, 51)(12, 52)(13, 45)(14, 46)(15, 55)(16, 56)(17, 49)(18, 50)(19, 59)(20, 60)(21, 53)(22, 54)(23, 63)(24, 64)(25, 57)(26, 58)(27, 67)(28, 68)(29, 61)(30, 62)(31, 71)(32, 72)(33, 65)(34, 66)(35, 69)(36, 70) local type(s) :: { ( 18^36 ) } Outer automorphisms :: reflexible Dual of E16.606 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.608 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {18, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y2, Y1^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y3 * Y2^-2 * Y1^-3, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y2^3 * Y3 * Y2^5 * Y1^-1, Y2^-2 * Y1^14 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 13, 49, 18, 54, 24, 60, 31, 67, 30, 66, 34, 70, 27, 63, 33, 69, 29, 65, 20, 56, 9, 45, 17, 53, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 12, 48, 5, 41, 8, 44, 16, 52, 23, 59, 22, 58, 26, 62, 32, 68, 36, 72, 35, 71, 28, 64, 19, 55, 25, 61, 21, 57, 10, 46)(73, 109, 75, 111, 81, 117, 91, 127, 99, 135, 104, 140, 96, 132, 88, 124, 78, 114, 87, 123, 83, 119, 93, 129, 101, 137, 107, 143, 102, 138, 94, 130, 85, 121, 77, 113)(74, 110, 79, 115, 89, 125, 97, 133, 105, 141, 108, 144, 103, 139, 95, 131, 86, 122, 84, 120, 76, 112, 82, 118, 92, 128, 100, 136, 106, 142, 98, 134, 90, 126, 80, 116) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 92)(10, 93)(11, 89)(12, 87)(13, 86)(14, 78)(15, 79)(16, 80)(17, 81)(18, 85)(19, 100)(20, 101)(21, 97)(22, 95)(23, 88)(24, 90)(25, 91)(26, 94)(27, 106)(28, 107)(29, 105)(30, 103)(31, 96)(32, 98)(33, 99)(34, 102)(35, 108)(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, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.609 Graph:: bipartite v = 4 e = 72 f = 38 degree seq :: [ 36^4 ] E16.609 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {18, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1, R^2, (Y2^-1 * Y3^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-2 * Y3^-2, Y3^-2 * Y2^16, (Y3 * Y2^-1)^18, (Y3^-1 * Y1^-1)^18 ] Map:: R = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)(73, 109, 74, 110, 78, 114, 83, 119, 87, 123, 91, 127, 95, 131, 99, 135, 103, 139, 107, 143, 105, 141, 102, 138, 97, 133, 94, 130, 89, 125, 86, 122, 81, 117, 76, 112)(75, 111, 79, 115, 77, 113, 80, 116, 84, 120, 88, 124, 92, 128, 96, 132, 100, 136, 104, 140, 108, 144, 106, 142, 101, 137, 98, 134, 93, 129, 90, 126, 85, 121, 82, 118) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 77)(7, 76)(8, 74)(9, 85)(10, 86)(11, 80)(12, 78)(13, 89)(14, 90)(15, 84)(16, 83)(17, 93)(18, 94)(19, 88)(20, 87)(21, 97)(22, 98)(23, 92)(24, 91)(25, 101)(26, 102)(27, 96)(28, 95)(29, 105)(30, 106)(31, 100)(32, 99)(33, 108)(34, 107)(35, 104)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 36, 36 ), ( 36^36 ) } Outer automorphisms :: reflexible Dual of E16.608 Graph:: simple bipartite v = 38 e = 72 f = 4 degree seq :: [ 2^36, 36^2 ] E16.610 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {12, 18, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^2, T1^12, T1^-24 ] Map:: non-degenerate R = (1, 3, 9, 6, 15, 22, 20, 27, 34, 32, 36, 30, 23, 25, 18, 11, 13, 5)(2, 7, 16, 14, 21, 28, 26, 33, 35, 29, 31, 24, 17, 19, 12, 4, 10, 8)(37, 38, 42, 50, 56, 62, 68, 65, 59, 53, 47, 40)(39, 43, 51, 57, 63, 69, 72, 67, 61, 55, 49, 46)(41, 44, 45, 52, 58, 64, 70, 71, 66, 60, 54, 48) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 72^12 ), ( 72^18 ) } Outer automorphisms :: reflexible Dual of E16.619 Transitivity :: ET+ Graph:: bipartite v = 5 e = 36 f = 1 degree seq :: [ 12^3, 18^2 ] E16.611 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {12, 18, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^2, T1^-12, T1^12 ] Map:: non-degenerate R = (1, 3, 9, 11, 18, 23, 25, 30, 35, 32, 34, 27, 20, 22, 15, 6, 13, 5)(2, 7, 12, 4, 10, 17, 19, 24, 29, 31, 36, 33, 26, 28, 21, 14, 16, 8)(37, 38, 42, 50, 56, 62, 68, 67, 61, 55, 47, 40)(39, 43, 49, 52, 58, 64, 70, 72, 66, 60, 54, 46)(41, 44, 51, 57, 63, 69, 71, 65, 59, 53, 45, 48) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 72^12 ), ( 72^18 ) } Outer automorphisms :: reflexible Dual of E16.618 Transitivity :: ET+ Graph:: bipartite v = 5 e = 36 f = 1 degree seq :: [ 12^3, 18^2 ] E16.612 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {12, 18, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^18, (T2^-1 * T1^-1)^12 ] Map:: non-degenerate R = (1, 3, 2, 7, 6, 11, 10, 15, 14, 19, 18, 23, 22, 27, 26, 31, 30, 35, 34, 36, 32, 33, 28, 29, 24, 25, 20, 21, 16, 17, 12, 13, 8, 9, 4, 5)(37, 38, 42, 46, 50, 54, 58, 62, 66, 70, 68, 64, 60, 56, 52, 48, 44, 40)(39, 43, 47, 51, 55, 59, 63, 67, 71, 72, 69, 65, 61, 57, 53, 49, 45, 41) 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) :: { ( 24^18 ), ( 24^36 ) } Outer automorphisms :: reflexible Dual of E16.620 Transitivity :: ET+ Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.613 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {12, 18, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^3 * T2 * T1 * T2 * T1, T1 * T2^-1 * T1 * T2^-5 * T1, T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-4 ] Map:: non-degenerate R = (1, 3, 9, 19, 30, 26, 14, 23, 11, 21, 32, 29, 18, 8, 2, 7, 17, 28, 36, 34, 24, 12, 4, 10, 20, 31, 27, 16, 6, 15, 22, 33, 35, 25, 13, 5)(37, 38, 42, 50, 60, 49, 54, 63, 66, 72, 71, 68, 56, 45, 53, 58, 47, 40)(39, 43, 51, 59, 48, 41, 44, 52, 62, 70, 61, 65, 67, 55, 64, 69, 57, 46) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 24^18 ), ( 24^36 ) } Outer automorphisms :: reflexible Dual of E16.621 Transitivity :: ET+ Graph:: bipartite v = 3 e = 36 f = 3 degree seq :: [ 18^2, 36 ] E16.614 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {12, 18, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, T2^-1 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^12 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 33, 29, 23, 17, 11, 5)(2, 7, 13, 19, 25, 31, 36, 32, 26, 20, 14, 8)(4, 10, 16, 22, 28, 34, 35, 30, 24, 18, 12, 6)(37, 38, 42, 41, 44, 48, 47, 50, 54, 53, 56, 60, 59, 62, 66, 65, 68, 71, 69, 72, 70, 63, 67, 64, 57, 61, 58, 51, 55, 52, 45, 49, 46, 39, 43, 40) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 36^12 ), ( 36^36 ) } Outer automorphisms :: reflexible Dual of E16.617 Transitivity :: ET+ Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 12^3, 36 ] E16.615 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {12, 18, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-2 * T2^-1 * T1^-1 * T2^-4, T1^-1 * T2 * T1^-1 * T2 * T1^-4, T2^3 * T1^-3 * T2^-1 * T1^-3, T1 * T2^-1 * T1^-2 * T2^2 * T1 * T2^-1 * T1^-2 * T2^2 * T1 * T2^-1 * T1^-2 * T2^2 * T1 * T2^-1 * T1^-2 * T2^2 * T1 * T2^3, T1^-1 * T2^2 * T1^25 * T2^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 22, 28, 14, 27, 25, 13, 5)(2, 7, 17, 31, 23, 11, 21, 26, 35, 32, 18, 8)(4, 10, 20, 34, 36, 30, 16, 6, 15, 29, 24, 12)(37, 38, 42, 50, 62, 56, 45, 53, 65, 61, 68, 72, 69, 59, 48, 41, 44, 52, 64, 57, 46, 39, 43, 51, 63, 71, 70, 55, 67, 60, 49, 54, 66, 58, 47, 40) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 36^12 ), ( 36^36 ) } Outer automorphisms :: reflexible Dual of E16.616 Transitivity :: ET+ Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 12^3, 36 ] E16.616 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {12, 18, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^2, T1^12, T1^-24 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 6, 42, 15, 51, 22, 58, 20, 56, 27, 63, 34, 70, 32, 68, 36, 72, 30, 66, 23, 59, 25, 61, 18, 54, 11, 47, 13, 49, 5, 41)(2, 38, 7, 43, 16, 52, 14, 50, 21, 57, 28, 64, 26, 62, 33, 69, 35, 71, 29, 65, 31, 67, 24, 60, 17, 53, 19, 55, 12, 48, 4, 40, 10, 46, 8, 44) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 45)(9, 52)(10, 39)(11, 40)(12, 41)(13, 46)(14, 56)(15, 57)(16, 58)(17, 47)(18, 48)(19, 49)(20, 62)(21, 63)(22, 64)(23, 53)(24, 54)(25, 55)(26, 68)(27, 69)(28, 70)(29, 59)(30, 60)(31, 61)(32, 65)(33, 72)(34, 71)(35, 66)(36, 67) local type(s) :: { ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E16.615 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.617 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {12, 18, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^2, T1^-12, T1^12 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 11, 47, 18, 54, 23, 59, 25, 61, 30, 66, 35, 71, 32, 68, 34, 70, 27, 63, 20, 56, 22, 58, 15, 51, 6, 42, 13, 49, 5, 41)(2, 38, 7, 43, 12, 48, 4, 40, 10, 46, 17, 53, 19, 55, 24, 60, 29, 65, 31, 67, 36, 72, 33, 69, 26, 62, 28, 64, 21, 57, 14, 50, 16, 52, 8, 44) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 49)(8, 51)(9, 48)(10, 39)(11, 40)(12, 41)(13, 52)(14, 56)(15, 57)(16, 58)(17, 45)(18, 46)(19, 47)(20, 62)(21, 63)(22, 64)(23, 53)(24, 54)(25, 55)(26, 68)(27, 69)(28, 70)(29, 59)(30, 60)(31, 61)(32, 67)(33, 71)(34, 72)(35, 65)(36, 66) local type(s) :: { ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E16.614 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.618 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {12, 18, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^18, (T2^-1 * T1^-1)^12 ] Map:: non-degenerate R = (1, 37, 3, 39, 2, 38, 7, 43, 6, 42, 11, 47, 10, 46, 15, 51, 14, 50, 19, 55, 18, 54, 23, 59, 22, 58, 27, 63, 26, 62, 31, 67, 30, 66, 35, 71, 34, 70, 36, 72, 32, 68, 33, 69, 28, 64, 29, 65, 24, 60, 25, 61, 20, 56, 21, 57, 16, 52, 17, 53, 12, 48, 13, 49, 8, 44, 9, 45, 4, 40, 5, 41) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 39)(6, 46)(7, 47)(8, 40)(9, 41)(10, 50)(11, 51)(12, 44)(13, 45)(14, 54)(15, 55)(16, 48)(17, 49)(18, 58)(19, 59)(20, 52)(21, 53)(22, 62)(23, 63)(24, 56)(25, 57)(26, 66)(27, 67)(28, 60)(29, 61)(30, 70)(31, 71)(32, 64)(33, 65)(34, 68)(35, 72)(36, 69) local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E16.611 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 36 f = 5 degree seq :: [ 72 ] E16.619 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {12, 18, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^3 * T2 * T1 * T2 * T1, T1 * T2^-1 * T1 * T2^-5 * T1, T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-4 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 30, 66, 26, 62, 14, 50, 23, 59, 11, 47, 21, 57, 32, 68, 29, 65, 18, 54, 8, 44, 2, 38, 7, 43, 17, 53, 28, 64, 36, 72, 34, 70, 24, 60, 12, 48, 4, 40, 10, 46, 20, 56, 31, 67, 27, 63, 16, 52, 6, 42, 15, 51, 22, 58, 33, 69, 35, 71, 25, 61, 13, 49, 5, 41) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 60)(15, 59)(16, 62)(17, 58)(18, 63)(19, 64)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 65)(26, 70)(27, 66)(28, 69)(29, 67)(30, 72)(31, 55)(32, 56)(33, 57)(34, 61)(35, 68)(36, 71) local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E16.610 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 36 f = 5 degree seq :: [ 72 ] E16.620 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {12, 18, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, T2^-1 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^12 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 15, 51, 21, 57, 27, 63, 33, 69, 29, 65, 23, 59, 17, 53, 11, 47, 5, 41)(2, 38, 7, 43, 13, 49, 19, 55, 25, 61, 31, 67, 36, 72, 32, 68, 26, 62, 20, 56, 14, 50, 8, 44)(4, 40, 10, 46, 16, 52, 22, 58, 28, 64, 34, 70, 35, 71, 30, 66, 24, 60, 18, 54, 12, 48, 6, 42) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 41)(7, 40)(8, 48)(9, 49)(10, 39)(11, 50)(12, 47)(13, 46)(14, 54)(15, 55)(16, 45)(17, 56)(18, 53)(19, 52)(20, 60)(21, 61)(22, 51)(23, 62)(24, 59)(25, 58)(26, 66)(27, 67)(28, 57)(29, 68)(30, 65)(31, 64)(32, 71)(33, 72)(34, 63)(35, 69)(36, 70) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.612 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.621 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {12, 18, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-2 * T2^-1 * T1^-1 * T2^-4, T1^-1 * T2 * T1^-1 * T2 * T1^-4, T2^3 * T1^-3 * T2^-1 * T1^-3, T1 * T2^-1 * T1^-2 * T2^2 * T1 * T2^-1 * T1^-2 * T2^2 * T1 * T2^-1 * T1^-2 * T2^2 * T1 * T2^-1 * T1^-2 * T2^2 * T1 * T2^3, T1^-1 * T2^2 * T1^25 * T2^2 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 33, 69, 22, 58, 28, 64, 14, 50, 27, 63, 25, 61, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 31, 67, 23, 59, 11, 47, 21, 57, 26, 62, 35, 71, 32, 68, 18, 54, 8, 44)(4, 40, 10, 46, 20, 56, 34, 70, 36, 72, 30, 66, 16, 52, 6, 42, 15, 51, 29, 65, 24, 60, 12, 48) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 68)(26, 56)(27, 71)(28, 57)(29, 61)(30, 58)(31, 60)(32, 72)(33, 59)(34, 55)(35, 70)(36, 69) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.613 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 36 f = 3 degree seq :: [ 24^3 ] E16.622 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 18, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^2 * Y3^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), Y3^-2 * Y2^3, Y3^12, Y3^12, Y1^12 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 20, 56, 26, 62, 32, 68, 31, 67, 25, 61, 19, 55, 11, 47, 4, 40)(3, 39, 7, 43, 13, 49, 16, 52, 22, 58, 28, 64, 34, 70, 36, 72, 30, 66, 24, 60, 18, 54, 10, 46)(5, 41, 8, 44, 15, 51, 21, 57, 27, 63, 33, 69, 35, 71, 29, 65, 23, 59, 17, 53, 9, 45, 12, 48)(73, 109, 75, 111, 81, 117, 83, 119, 90, 126, 95, 131, 97, 133, 102, 138, 107, 143, 104, 140, 106, 142, 99, 135, 92, 128, 94, 130, 87, 123, 78, 114, 85, 121, 77, 113)(74, 110, 79, 115, 84, 120, 76, 112, 82, 118, 89, 125, 91, 127, 96, 132, 101, 137, 103, 139, 108, 144, 105, 141, 98, 134, 100, 136, 93, 129, 86, 122, 88, 124, 80, 116) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 89)(10, 90)(11, 91)(12, 81)(13, 79)(14, 78)(15, 80)(16, 85)(17, 95)(18, 96)(19, 97)(20, 86)(21, 87)(22, 88)(23, 101)(24, 102)(25, 103)(26, 92)(27, 93)(28, 94)(29, 107)(30, 108)(31, 104)(32, 98)(33, 99)(34, 100)(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, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) } Outer automorphisms :: reflexible Dual of E16.628 Graph:: bipartite v = 5 e = 72 f = 37 degree seq :: [ 24^3, 36^2 ] E16.623 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 18, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y1 * Y2^-1 * Y1 * Y2^-2, Y1^8 * Y3^-4, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 20, 56, 26, 62, 32, 68, 29, 65, 23, 59, 17, 53, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 21, 57, 27, 63, 33, 69, 36, 72, 31, 67, 25, 61, 19, 55, 13, 49, 10, 46)(5, 41, 8, 44, 9, 45, 16, 52, 22, 58, 28, 64, 34, 70, 35, 71, 30, 66, 24, 60, 18, 54, 12, 48)(73, 109, 75, 111, 81, 117, 78, 114, 87, 123, 94, 130, 92, 128, 99, 135, 106, 142, 104, 140, 108, 144, 102, 138, 95, 131, 97, 133, 90, 126, 83, 119, 85, 121, 77, 113)(74, 110, 79, 115, 88, 124, 86, 122, 93, 129, 100, 136, 98, 134, 105, 141, 107, 143, 101, 137, 103, 139, 96, 132, 89, 125, 91, 127, 84, 120, 76, 112, 82, 118, 80, 116) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 80)(10, 85)(11, 89)(12, 90)(13, 91)(14, 78)(15, 79)(16, 81)(17, 95)(18, 96)(19, 97)(20, 86)(21, 87)(22, 88)(23, 101)(24, 102)(25, 103)(26, 92)(27, 93)(28, 94)(29, 104)(30, 107)(31, 108)(32, 98)(33, 99)(34, 100)(35, 106)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) } Outer automorphisms :: reflexible Dual of E16.629 Graph:: bipartite v = 5 e = 72 f = 37 degree seq :: [ 24^3, 36^2 ] E16.624 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 18, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, Y1^18, (Y3^-1 * Y1^-1)^12 ] Map:: R = (1, 37, 2, 38, 6, 42, 10, 46, 14, 50, 18, 54, 22, 58, 26, 62, 30, 66, 34, 70, 32, 68, 28, 64, 24, 60, 20, 56, 16, 52, 12, 48, 8, 44, 4, 40)(3, 39, 7, 43, 11, 47, 15, 51, 19, 55, 23, 59, 27, 63, 31, 67, 35, 71, 36, 72, 33, 69, 29, 65, 25, 61, 21, 57, 17, 53, 13, 49, 9, 45, 5, 41)(73, 109, 75, 111, 74, 110, 79, 115, 78, 114, 83, 119, 82, 118, 87, 123, 86, 122, 91, 127, 90, 126, 95, 131, 94, 130, 99, 135, 98, 134, 103, 139, 102, 138, 107, 143, 106, 142, 108, 144, 104, 140, 105, 141, 100, 136, 101, 137, 96, 132, 97, 133, 92, 128, 93, 129, 88, 124, 89, 125, 84, 120, 85, 121, 80, 116, 81, 117, 76, 112, 77, 113) L = (1, 75)(2, 79)(3, 74)(4, 77)(5, 73)(6, 83)(7, 78)(8, 81)(9, 76)(10, 87)(11, 82)(12, 85)(13, 80)(14, 91)(15, 86)(16, 89)(17, 84)(18, 95)(19, 90)(20, 93)(21, 88)(22, 99)(23, 94)(24, 97)(25, 92)(26, 103)(27, 98)(28, 101)(29, 96)(30, 107)(31, 102)(32, 105)(33, 100)(34, 108)(35, 106)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E16.626 Graph:: bipartite v = 3 e = 72 f = 39 degree seq :: [ 36^2, 72 ] E16.625 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 18, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1 * Y2 * Y1^4 * Y2, Y1 * Y2^-1 * Y1 * Y2^-5 * Y1, (Y3^-1 * Y1^-1)^12 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 24, 60, 13, 49, 18, 54, 27, 63, 30, 66, 36, 72, 35, 71, 32, 68, 20, 56, 9, 45, 17, 53, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 23, 59, 12, 48, 5, 41, 8, 44, 16, 52, 26, 62, 34, 70, 25, 61, 29, 65, 31, 67, 19, 55, 28, 64, 33, 69, 21, 57, 10, 46)(73, 109, 75, 111, 81, 117, 91, 127, 102, 138, 98, 134, 86, 122, 95, 131, 83, 119, 93, 129, 104, 140, 101, 137, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 100, 136, 108, 144, 106, 142, 96, 132, 84, 120, 76, 112, 82, 118, 92, 128, 103, 139, 99, 135, 88, 124, 78, 114, 87, 123, 94, 130, 105, 141, 107, 143, 97, 133, 85, 121, 77, 113) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 95)(15, 94)(16, 78)(17, 100)(18, 80)(19, 102)(20, 103)(21, 104)(22, 105)(23, 83)(24, 84)(25, 85)(26, 86)(27, 88)(28, 108)(29, 90)(30, 98)(31, 99)(32, 101)(33, 107)(34, 96)(35, 97)(36, 106)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E16.627 Graph:: bipartite v = 3 e = 72 f = 39 degree seq :: [ 36^2, 72 ] E16.626 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 18, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^-1 * Y3^3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^12, (Y3^-1 * Y1^-1)^36 ] Map:: R = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)(73, 109, 74, 110, 78, 114, 84, 120, 90, 126, 96, 132, 102, 138, 100, 136, 94, 130, 88, 124, 82, 118, 76, 112)(75, 111, 79, 115, 85, 121, 91, 127, 97, 133, 103, 139, 107, 143, 105, 141, 99, 135, 93, 129, 87, 123, 81, 117)(77, 113, 80, 116, 86, 122, 92, 128, 98, 134, 104, 140, 108, 144, 106, 142, 101, 137, 95, 131, 89, 125, 83, 119) L = (1, 75)(2, 79)(3, 80)(4, 81)(5, 73)(6, 85)(7, 86)(8, 74)(9, 77)(10, 87)(11, 76)(12, 91)(13, 92)(14, 78)(15, 83)(16, 93)(17, 82)(18, 97)(19, 98)(20, 84)(21, 89)(22, 99)(23, 88)(24, 103)(25, 104)(26, 90)(27, 95)(28, 105)(29, 94)(30, 107)(31, 108)(32, 96)(33, 101)(34, 100)(35, 106)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 36, 72 ), ( 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72 ) } Outer automorphisms :: reflexible Dual of E16.624 Graph:: simple bipartite v = 39 e = 72 f = 3 degree seq :: [ 2^36, 24^3 ] E16.627 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 18, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3 * Y2^-1 * Y3 * Y2^-4 * Y3, Y3^-1 * Y2^-1 * Y3^-5 * Y2^-1, Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^4, (Y3^-1 * Y1^-1)^36 ] Map:: R = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)(73, 109, 74, 110, 78, 114, 86, 122, 98, 134, 91, 127, 103, 139, 97, 133, 104, 140, 94, 130, 83, 119, 76, 112)(75, 111, 79, 115, 87, 123, 99, 135, 107, 143, 105, 141, 96, 132, 85, 121, 90, 126, 102, 138, 93, 129, 82, 118)(77, 113, 80, 116, 88, 124, 100, 136, 92, 128, 81, 117, 89, 125, 101, 137, 108, 144, 106, 142, 95, 131, 84, 120) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 99)(15, 101)(16, 78)(17, 103)(18, 80)(19, 105)(20, 98)(21, 100)(22, 102)(23, 83)(24, 84)(25, 85)(26, 107)(27, 108)(28, 86)(29, 97)(30, 88)(31, 96)(32, 90)(33, 95)(34, 94)(35, 106)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 36, 72 ), ( 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72, 36, 72 ) } Outer automorphisms :: reflexible Dual of E16.625 Graph:: simple bipartite v = 39 e = 72 f = 3 degree seq :: [ 2^36, 24^3 ] E16.628 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 18, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^-2 * Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^5 * Y1 * Y3^-5, Y3^12, (Y3 * Y2^-1)^12 ] Map:: R = (1, 37, 2, 38, 6, 42, 5, 41, 8, 44, 12, 48, 11, 47, 14, 50, 18, 54, 17, 53, 20, 56, 24, 60, 23, 59, 26, 62, 30, 66, 29, 65, 32, 68, 35, 71, 33, 69, 36, 72, 34, 70, 27, 63, 31, 67, 28, 64, 21, 57, 25, 61, 22, 58, 15, 51, 19, 55, 16, 52, 9, 45, 13, 49, 10, 46, 3, 39, 7, 43, 4, 40)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 76)(7, 85)(8, 74)(9, 87)(10, 88)(11, 77)(12, 78)(13, 91)(14, 80)(15, 93)(16, 94)(17, 83)(18, 84)(19, 97)(20, 86)(21, 99)(22, 100)(23, 89)(24, 90)(25, 103)(26, 92)(27, 105)(28, 106)(29, 95)(30, 96)(31, 108)(32, 98)(33, 101)(34, 107)(35, 102)(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) :: { ( 24, 36 ), ( 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36 ) } Outer automorphisms :: reflexible Dual of E16.622 Graph:: bipartite v = 37 e = 72 f = 5 degree seq :: [ 2^36, 72 ] E16.629 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 18, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y1^-2 * Y3^-1 * Y1^-1 * Y3^-4, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-4, Y3^3 * Y1^-3 * Y3^-1 * Y1^-3, (Y3 * Y2^-1)^12, Y1 * Y3^-1 * Y1^-2 * Y3^2 * Y1 * Y3^-1 * Y1^-2 * Y3^2 * Y1 * Y3^-1 * Y1^-2 * Y3^2 * Y1 * Y3^-1 * Y1^-2 * Y3^2 * Y1 * Y3^3, Y1^-1 * Y3^2 * Y1^25 * Y3^2 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 26, 62, 20, 56, 9, 45, 17, 53, 29, 65, 25, 61, 32, 68, 36, 72, 33, 69, 23, 59, 12, 48, 5, 41, 8, 44, 16, 52, 28, 64, 21, 57, 10, 46, 3, 39, 7, 43, 15, 51, 27, 63, 35, 71, 34, 70, 19, 55, 31, 67, 24, 60, 13, 49, 18, 54, 30, 66, 22, 58, 11, 47, 4, 40)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 99)(15, 101)(16, 78)(17, 103)(18, 80)(19, 105)(20, 106)(21, 98)(22, 100)(23, 83)(24, 84)(25, 85)(26, 107)(27, 97)(28, 86)(29, 96)(30, 88)(31, 95)(32, 90)(33, 94)(34, 108)(35, 104)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 24, 36 ), ( 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36, 24, 36 ) } Outer automorphisms :: reflexible Dual of E16.623 Graph:: bipartite v = 37 e = 72 f = 5 degree seq :: [ 2^36, 72 ] E16.630 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 18, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3 * Y2^-3, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y3^12, Y1^12 ] Map:: R = (1, 37, 2, 38, 6, 42, 12, 48, 18, 54, 24, 60, 30, 66, 29, 65, 23, 59, 17, 53, 11, 47, 4, 40)(3, 39, 7, 43, 13, 49, 19, 55, 25, 61, 31, 67, 35, 71, 34, 70, 28, 64, 22, 58, 16, 52, 10, 46)(5, 41, 8, 44, 14, 50, 20, 56, 26, 62, 32, 68, 36, 72, 33, 69, 27, 63, 21, 57, 15, 51, 9, 45)(73, 109, 75, 111, 81, 117, 76, 112, 82, 118, 87, 123, 83, 119, 88, 124, 93, 129, 89, 125, 94, 130, 99, 135, 95, 131, 100, 136, 105, 141, 101, 137, 106, 142, 108, 144, 102, 138, 107, 143, 104, 140, 96, 132, 103, 139, 98, 134, 90, 126, 97, 133, 92, 128, 84, 120, 91, 127, 86, 122, 78, 114, 85, 121, 80, 116, 74, 110, 79, 115, 77, 113) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 81)(6, 74)(7, 75)(8, 77)(9, 87)(10, 88)(11, 89)(12, 78)(13, 79)(14, 80)(15, 93)(16, 94)(17, 95)(18, 84)(19, 85)(20, 86)(21, 99)(22, 100)(23, 101)(24, 90)(25, 91)(26, 92)(27, 105)(28, 106)(29, 102)(30, 96)(31, 97)(32, 98)(33, 108)(34, 107)(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, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.632 Graph:: bipartite v = 4 e = 72 f = 38 degree seq :: [ 24^3, 72 ] E16.631 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 18, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3 * Y1, Y3^-1 * Y1^-1, (Y2, Y3^-1), (R * Y2)^2, (R * Y3)^2, Y1^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y1)^2, Y2^2 * Y3 * Y2^4 * Y1^-1, Y2^-1 * Y3^-2 * Y1 * Y2 * Y1^-3, Y3^3 * Y2^-1 * Y3 * Y2^-2 * Y1^-1, Y1^12, Y2^-1 * Y3^-1 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 26, 62, 25, 61, 32, 68, 19, 55, 31, 67, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 27, 63, 24, 60, 13, 49, 18, 54, 30, 66, 36, 72, 34, 70, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 28, 64, 35, 71, 33, 69, 20, 56, 9, 45, 17, 53, 29, 65, 23, 59, 12, 48)(73, 109, 75, 111, 81, 117, 91, 127, 102, 138, 88, 124, 78, 114, 87, 123, 101, 137, 94, 130, 106, 142, 107, 143, 98, 134, 96, 132, 84, 120, 76, 112, 82, 118, 92, 128, 104, 140, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 103, 139, 108, 144, 100, 136, 86, 122, 99, 135, 95, 131, 83, 119, 93, 129, 105, 141, 97, 133, 85, 121, 77, 113) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 92)(10, 93)(11, 94)(12, 95)(13, 96)(14, 78)(15, 79)(16, 80)(17, 81)(18, 85)(19, 104)(20, 105)(21, 106)(22, 103)(23, 101)(24, 99)(25, 98)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 97)(33, 107)(34, 108)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.633 Graph:: bipartite v = 4 e = 72 f = 38 degree seq :: [ 24^3, 72 ] E16.632 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 18, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, Y3 * Y1^-1 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^18, (Y3^-1 * Y1^-1)^12, (Y3 * Y2^-1)^36 ] Map:: R = (1, 37, 2, 38, 6, 42, 10, 46, 14, 50, 18, 54, 22, 58, 26, 62, 30, 66, 34, 70, 32, 68, 28, 64, 24, 60, 20, 56, 16, 52, 12, 48, 8, 44, 4, 40)(3, 39, 7, 43, 11, 47, 15, 51, 19, 55, 23, 59, 27, 63, 31, 67, 35, 71, 36, 72, 33, 69, 29, 65, 25, 61, 21, 57, 17, 53, 13, 49, 9, 45, 5, 41)(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, 74)(4, 77)(5, 73)(6, 83)(7, 78)(8, 81)(9, 76)(10, 87)(11, 82)(12, 85)(13, 80)(14, 91)(15, 86)(16, 89)(17, 84)(18, 95)(19, 90)(20, 93)(21, 88)(22, 99)(23, 94)(24, 97)(25, 92)(26, 103)(27, 98)(28, 101)(29, 96)(30, 107)(31, 102)(32, 105)(33, 100)(34, 108)(35, 106)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 24, 72 ), ( 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72 ) } Outer automorphisms :: reflexible Dual of E16.630 Graph:: simple bipartite v = 38 e = 72 f = 4 degree seq :: [ 2^36, 36^2 ] E16.633 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 18, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^3 * Y3 * Y1 * Y3 * Y1, Y1 * Y3^-1 * Y1 * Y3^-5 * Y1, Y3^-1 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^2, (Y3 * Y2^-1)^36 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 24, 60, 13, 49, 18, 54, 27, 63, 30, 66, 36, 72, 35, 71, 32, 68, 20, 56, 9, 45, 17, 53, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 23, 59, 12, 48, 5, 41, 8, 44, 16, 52, 26, 62, 34, 70, 25, 61, 29, 65, 31, 67, 19, 55, 28, 64, 33, 69, 21, 57, 10, 46)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 95)(15, 94)(16, 78)(17, 100)(18, 80)(19, 102)(20, 103)(21, 104)(22, 105)(23, 83)(24, 84)(25, 85)(26, 86)(27, 88)(28, 108)(29, 90)(30, 98)(31, 99)(32, 101)(33, 107)(34, 96)(35, 97)(36, 106)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 24, 72 ), ( 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72 ) } Outer automorphisms :: reflexible Dual of E16.631 Graph:: simple bipartite v = 38 e = 72 f = 4 degree seq :: [ 2^36, 36^2 ] E16.634 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 36, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^-4 * T2^4, T1^-1 * T2^-8, T1^9, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 26, 36, 24, 12, 4, 10, 20, 28, 14, 27, 35, 23, 11, 21, 30, 16, 6, 15, 29, 34, 22, 32, 18, 8, 2, 7, 17, 31, 33, 25, 13, 5)(37, 38, 42, 50, 62, 69, 58, 47, 40)(39, 43, 51, 63, 72, 61, 68, 57, 46)(41, 44, 52, 64, 55, 67, 70, 59, 48)(45, 53, 65, 71, 60, 49, 54, 66, 56) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 72^9 ), ( 72^36 ) } Outer automorphisms :: reflexible Dual of E16.640 Transitivity :: ET+ Graph:: bipartite v = 5 e = 36 f = 1 degree seq :: [ 9^4, 36 ] E16.635 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 36, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^-2 * T2^-4, T1^-9, T1^9, T1^3 * T2^-1 * T1 * T2^-1 * T1^3 * T2^-2 ] Map:: non-degenerate R = (1, 3, 9, 19, 11, 21, 28, 34, 30, 36, 33, 25, 14, 24, 18, 8, 2, 7, 17, 12, 4, 10, 20, 27, 22, 29, 35, 32, 23, 31, 26, 16, 6, 15, 13, 5)(37, 38, 42, 50, 59, 66, 58, 47, 40)(39, 43, 51, 60, 67, 72, 65, 57, 46)(41, 44, 52, 61, 68, 70, 63, 55, 48)(45, 53, 49, 54, 62, 69, 71, 64, 56) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 72^9 ), ( 72^36 ) } Outer automorphisms :: reflexible Dual of E16.639 Transitivity :: ET+ Graph:: bipartite v = 5 e = 36 f = 1 degree seq :: [ 9^4, 36 ] E16.636 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 36, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^-1, T1^9, (T1^-1 * T2^-1)^36 ] Map:: non-degenerate R = (1, 3, 9, 8, 2, 7, 17, 16, 6, 15, 25, 24, 14, 23, 32, 31, 22, 30, 36, 34, 27, 33, 35, 28, 19, 26, 29, 20, 11, 18, 21, 12, 4, 10, 13, 5)(37, 38, 42, 50, 58, 63, 55, 47, 40)(39, 43, 51, 59, 66, 69, 62, 54, 46)(41, 44, 52, 60, 67, 70, 64, 56, 48)(45, 53, 61, 68, 72, 71, 65, 57, 49) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 72^9 ), ( 72^36 ) } Outer automorphisms :: reflexible Dual of E16.638 Transitivity :: ET+ Graph:: bipartite v = 5 e = 36 f = 1 degree seq :: [ 9^4, 36 ] E16.637 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 36, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-5, T2^-7 * T1, T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^2 * T2^-2 ] Map:: non-degenerate R = (1, 3, 9, 19, 28, 18, 8, 2, 7, 17, 27, 34, 26, 16, 6, 15, 25, 33, 36, 32, 24, 14, 11, 21, 30, 35, 31, 22, 12, 4, 10, 20, 29, 23, 13, 5)(37, 38, 42, 50, 48, 41, 44, 52, 60, 58, 49, 54, 62, 68, 67, 59, 64, 70, 72, 71, 65, 55, 63, 69, 66, 56, 45, 53, 61, 57, 46, 39, 43, 51, 47, 40) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^36 ) } Outer automorphisms :: reflexible Dual of E16.641 Transitivity :: ET+ Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.638 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 36, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^-4 * T2^4, T1^-1 * T2^-8, T1^9, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 26, 62, 36, 72, 24, 60, 12, 48, 4, 40, 10, 46, 20, 56, 28, 64, 14, 50, 27, 63, 35, 71, 23, 59, 11, 47, 21, 57, 30, 66, 16, 52, 6, 42, 15, 51, 29, 65, 34, 70, 22, 58, 32, 68, 18, 54, 8, 44, 2, 38, 7, 43, 17, 53, 31, 67, 33, 69, 25, 61, 13, 49, 5, 41) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 68)(26, 69)(27, 72)(28, 55)(29, 71)(30, 56)(31, 70)(32, 57)(33, 58)(34, 59)(35, 60)(36, 61) local type(s) :: { ( 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36 ) } Outer automorphisms :: reflexible Dual of E16.636 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 36 f = 5 degree seq :: [ 72 ] E16.639 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 36, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^-2 * T2^-4, T1^-9, T1^9, T1^3 * T2^-1 * T1 * T2^-1 * T1^3 * T2^-2 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 11, 47, 21, 57, 28, 64, 34, 70, 30, 66, 36, 72, 33, 69, 25, 61, 14, 50, 24, 60, 18, 54, 8, 44, 2, 38, 7, 43, 17, 53, 12, 48, 4, 40, 10, 46, 20, 56, 27, 63, 22, 58, 29, 65, 35, 71, 32, 68, 23, 59, 31, 67, 26, 62, 16, 52, 6, 42, 15, 51, 13, 49, 5, 41) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 59)(15, 60)(16, 61)(17, 49)(18, 62)(19, 48)(20, 45)(21, 46)(22, 47)(23, 66)(24, 67)(25, 68)(26, 69)(27, 55)(28, 56)(29, 57)(30, 58)(31, 72)(32, 70)(33, 71)(34, 63)(35, 64)(36, 65) local type(s) :: { ( 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36 ) } Outer automorphisms :: reflexible Dual of E16.635 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 36 f = 5 degree seq :: [ 72 ] E16.640 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 36, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^-1, T1^9, (T1^-1 * T2^-1)^36 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 8, 44, 2, 38, 7, 43, 17, 53, 16, 52, 6, 42, 15, 51, 25, 61, 24, 60, 14, 50, 23, 59, 32, 68, 31, 67, 22, 58, 30, 66, 36, 72, 34, 70, 27, 63, 33, 69, 35, 71, 28, 64, 19, 55, 26, 62, 29, 65, 20, 56, 11, 47, 18, 54, 21, 57, 12, 48, 4, 40, 10, 46, 13, 49, 5, 41) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 45)(14, 58)(15, 59)(16, 60)(17, 61)(18, 46)(19, 47)(20, 48)(21, 49)(22, 63)(23, 66)(24, 67)(25, 68)(26, 54)(27, 55)(28, 56)(29, 57)(30, 69)(31, 70)(32, 72)(33, 62)(34, 64)(35, 65)(36, 71) local type(s) :: { ( 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36 ) } Outer automorphisms :: reflexible Dual of E16.634 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 36 f = 5 degree seq :: [ 72 ] E16.641 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 36, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-4 * T2^4, T2 * T1^8, T2 * T1 * T2 * T1 * T2^3 * T1^2, T2^9, T2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2 * T1^-1 * T2^-1 * T1^-2 * T2 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 26, 62, 33, 69, 25, 61, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 31, 67, 34, 70, 22, 58, 32, 68, 18, 54, 8, 44)(4, 40, 10, 46, 20, 56, 28, 64, 14, 50, 27, 63, 36, 72, 24, 60, 12, 48)(6, 42, 15, 51, 29, 65, 35, 71, 23, 59, 11, 47, 21, 57, 30, 66, 16, 52) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 68)(26, 70)(27, 69)(28, 55)(29, 72)(30, 56)(31, 71)(32, 57)(33, 58)(34, 59)(35, 60)(36, 61) local type(s) :: { ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.637 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 18^4 ] E16.642 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (Y2^-1, Y1), (Y3^-1, Y2^-1), (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y3^-1, (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y1^-1 * Y2 * Y3^-1, Y1^-2 * Y2 * Y3 * Y2^2 * Y3 * Y2, Y1^-1 * Y2 * Y1^-1 * Y2^2 * Y1^-1 * Y3 * Y2, Y1^3 * Y2 * Y3^-1 * Y2^3 * Y3^-1, Y1^9, Y2^36, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 26, 62, 33, 69, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 27, 63, 36, 72, 25, 61, 32, 68, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 28, 64, 19, 55, 31, 67, 34, 70, 23, 59, 12, 48)(9, 45, 17, 53, 29, 65, 35, 71, 24, 60, 13, 49, 18, 54, 30, 66, 20, 56)(73, 109, 75, 111, 81, 117, 91, 127, 98, 134, 108, 144, 96, 132, 84, 120, 76, 112, 82, 118, 92, 128, 100, 136, 86, 122, 99, 135, 107, 143, 95, 131, 83, 119, 93, 129, 102, 138, 88, 124, 78, 114, 87, 123, 101, 137, 106, 142, 94, 130, 104, 140, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 103, 139, 105, 141, 97, 133, 85, 121, 77, 113) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 92)(10, 93)(11, 94)(12, 95)(13, 96)(14, 78)(15, 79)(16, 80)(17, 81)(18, 85)(19, 100)(20, 102)(21, 104)(22, 105)(23, 106)(24, 107)(25, 108)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 97)(33, 98)(34, 103)(35, 101)(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) :: { ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) } Outer automorphisms :: reflexible Dual of E16.649 Graph:: bipartite v = 5 e = 72 f = 37 degree seq :: [ 18^4, 72 ] E16.643 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2), (R * Y2)^2, (Y2, Y1^-1), Y2^-1 * Y3 * Y2^-3 * Y1^-1, Y1^9, Y1^3 * Y2^-1 * Y1 * Y2^-1 * Y3^-3 * Y2^-2, Y3^18, Y2^36 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 23, 59, 30, 66, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 24, 60, 31, 67, 36, 72, 29, 65, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 25, 61, 32, 68, 34, 70, 27, 63, 19, 55, 12, 48)(9, 45, 17, 53, 13, 49, 18, 54, 26, 62, 33, 69, 35, 71, 28, 64, 20, 56)(73, 109, 75, 111, 81, 117, 91, 127, 83, 119, 93, 129, 100, 136, 106, 142, 102, 138, 108, 144, 105, 141, 97, 133, 86, 122, 96, 132, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 84, 120, 76, 112, 82, 118, 92, 128, 99, 135, 94, 130, 101, 137, 107, 143, 104, 140, 95, 131, 103, 139, 98, 134, 88, 124, 78, 114, 87, 123, 85, 121, 77, 113) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 92)(10, 93)(11, 94)(12, 91)(13, 89)(14, 78)(15, 79)(16, 80)(17, 81)(18, 85)(19, 99)(20, 100)(21, 101)(22, 102)(23, 86)(24, 87)(25, 88)(26, 90)(27, 106)(28, 107)(29, 108)(30, 95)(31, 96)(32, 97)(33, 98)(34, 104)(35, 105)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) } Outer automorphisms :: reflexible Dual of E16.648 Graph:: bipartite v = 5 e = 72 f = 37 degree seq :: [ 18^4, 72 ] E16.644 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3 * Y2^4, Y3^9, Y1^9, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 22, 58, 27, 63, 19, 55, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 23, 59, 30, 66, 33, 69, 26, 62, 18, 54, 10, 46)(5, 41, 8, 44, 16, 52, 24, 60, 31, 67, 34, 70, 28, 64, 20, 56, 12, 48)(9, 45, 17, 53, 25, 61, 32, 68, 36, 72, 35, 71, 29, 65, 21, 57, 13, 49)(73, 109, 75, 111, 81, 117, 80, 116, 74, 110, 79, 115, 89, 125, 88, 124, 78, 114, 87, 123, 97, 133, 96, 132, 86, 122, 95, 131, 104, 140, 103, 139, 94, 130, 102, 138, 108, 144, 106, 142, 99, 135, 105, 141, 107, 143, 100, 136, 91, 127, 98, 134, 101, 137, 92, 128, 83, 119, 90, 126, 93, 129, 84, 120, 76, 112, 82, 118, 85, 121, 77, 113) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 85)(10, 90)(11, 91)(12, 92)(13, 93)(14, 78)(15, 79)(16, 80)(17, 81)(18, 98)(19, 99)(20, 100)(21, 101)(22, 86)(23, 87)(24, 88)(25, 89)(26, 105)(27, 94)(28, 106)(29, 107)(30, 95)(31, 96)(32, 97)(33, 102)(34, 103)(35, 108)(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, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) } Outer automorphisms :: reflexible Dual of E16.647 Graph:: bipartite v = 5 e = 72 f = 37 degree seq :: [ 18^4, 72 ] E16.645 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^-1 * Y2^-2 * Y1 * Y2^2, Y2 * Y1 * Y2^4, Y1^-2 * Y2 * Y1^-5, (Y3^-1 * Y1^-1)^9 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 24, 60, 21, 57, 10, 46, 3, 39, 7, 43, 15, 51, 25, 61, 32, 68, 30, 66, 20, 56, 9, 45, 17, 53, 27, 63, 33, 69, 36, 72, 35, 71, 29, 65, 19, 55, 13, 49, 18, 54, 28, 64, 34, 70, 31, 67, 23, 59, 12, 48, 5, 41, 8, 44, 16, 52, 26, 62, 22, 58, 11, 47, 4, 40)(73, 109, 75, 111, 81, 117, 91, 127, 84, 120, 76, 112, 82, 118, 92, 128, 101, 137, 95, 131, 83, 119, 93, 129, 102, 138, 107, 143, 103, 139, 94, 130, 96, 132, 104, 140, 108, 144, 106, 142, 98, 134, 86, 122, 97, 133, 105, 141, 100, 136, 88, 124, 78, 114, 87, 123, 99, 135, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 85, 121, 77, 113) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 97)(15, 99)(16, 78)(17, 85)(18, 80)(19, 84)(20, 101)(21, 102)(22, 96)(23, 83)(24, 104)(25, 105)(26, 86)(27, 90)(28, 88)(29, 95)(30, 107)(31, 94)(32, 108)(33, 100)(34, 98)(35, 103)(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, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E16.646 Graph:: bipartite v = 2 e = 72 f = 40 degree seq :: [ 72^2 ] E16.646 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2), Y3^-4 * Y2^-4, Y2^-1 * Y3^8, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^2 * Y3^-2 * Y2, Y2^9, Y2 * Y3 * Y2^-2 * Y3 * Y2^2 * Y3^-1 * Y2^3 * Y3 * Y2^2 * Y3 * Y2^-2 * Y3, (Y3^-1 * Y1^-1)^36 ] Map:: R = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)(73, 109, 74, 110, 78, 114, 86, 122, 98, 134, 105, 141, 94, 130, 83, 119, 76, 112)(75, 111, 79, 115, 87, 123, 99, 135, 97, 133, 104, 140, 108, 144, 93, 129, 82, 118)(77, 113, 80, 116, 88, 124, 100, 136, 106, 142, 91, 127, 103, 139, 95, 131, 84, 120)(81, 117, 89, 125, 101, 137, 96, 132, 85, 121, 90, 126, 102, 138, 107, 143, 92, 128) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 99)(15, 101)(16, 78)(17, 103)(18, 80)(19, 105)(20, 106)(21, 107)(22, 108)(23, 83)(24, 84)(25, 85)(26, 97)(27, 96)(28, 86)(29, 95)(30, 88)(31, 94)(32, 90)(33, 104)(34, 98)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 72, 72 ), ( 72^18 ) } Outer automorphisms :: reflexible Dual of E16.645 Graph:: simple bipartite v = 40 e = 72 f = 2 degree seq :: [ 2^36, 18^4 ] E16.647 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^-1 * Y3^2 * Y1^-3, Y1 * Y3 * Y1 * Y3 * Y1 * Y3^3 * Y1, Y1^2 * Y3 * Y1^6, (Y3 * Y2^-1)^9, (Y3^2 * Y1)^12 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 26, 62, 34, 70, 23, 59, 12, 48, 5, 41, 8, 44, 16, 52, 28, 64, 19, 55, 31, 67, 35, 71, 24, 60, 13, 49, 18, 54, 30, 66, 20, 56, 9, 45, 17, 53, 29, 65, 36, 72, 25, 61, 32, 68, 21, 57, 10, 46, 3, 39, 7, 43, 15, 51, 27, 63, 33, 69, 22, 58, 11, 47, 4, 40)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 99)(15, 101)(16, 78)(17, 103)(18, 80)(19, 98)(20, 100)(21, 102)(22, 104)(23, 83)(24, 84)(25, 85)(26, 105)(27, 108)(28, 86)(29, 107)(30, 88)(31, 106)(32, 90)(33, 97)(34, 94)(35, 95)(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) :: { ( 18, 72 ), ( 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72 ) } Outer automorphisms :: reflexible Dual of E16.644 Graph:: bipartite v = 37 e = 72 f = 5 degree seq :: [ 2^36, 72 ] E16.648 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), Y3^-2 * Y1^-4, (R * Y2 * Y3^-1)^2, Y3^-9, (Y3 * Y2^-1)^9 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 13, 49, 18, 54, 24, 60, 31, 67, 30, 66, 34, 70, 36, 72, 28, 64, 19, 55, 25, 61, 21, 57, 10, 46, 3, 39, 7, 43, 15, 51, 12, 48, 5, 41, 8, 44, 16, 52, 23, 59, 22, 58, 26, 62, 32, 68, 35, 71, 27, 63, 33, 69, 29, 65, 20, 56, 9, 45, 17, 53, 11, 47, 4, 40)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 84)(15, 83)(16, 78)(17, 97)(18, 80)(19, 99)(20, 100)(21, 101)(22, 85)(23, 86)(24, 88)(25, 105)(26, 90)(27, 102)(28, 107)(29, 108)(30, 94)(31, 95)(32, 96)(33, 106)(34, 98)(35, 103)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 18, 72 ), ( 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72 ) } Outer automorphisms :: reflexible Dual of E16.643 Graph:: bipartite v = 37 e = 72 f = 5 degree seq :: [ 2^36, 72 ] E16.649 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^-1 * Y1^4, (R * Y2 * Y3^-1)^2, Y3^9, (Y3 * Y2^-1)^9, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 37, 2, 38, 6, 42, 10, 46, 3, 39, 7, 43, 14, 50, 18, 54, 9, 45, 15, 51, 22, 58, 26, 62, 17, 53, 23, 59, 30, 66, 33, 69, 25, 61, 31, 67, 36, 72, 35, 71, 29, 65, 32, 68, 34, 70, 28, 64, 21, 57, 24, 60, 27, 63, 20, 56, 13, 49, 16, 52, 19, 55, 12, 48, 5, 41, 8, 44, 11, 47, 4, 40)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 86)(7, 87)(8, 74)(9, 89)(10, 90)(11, 78)(12, 76)(13, 77)(14, 94)(15, 95)(16, 80)(17, 97)(18, 98)(19, 83)(20, 84)(21, 85)(22, 102)(23, 103)(24, 88)(25, 101)(26, 105)(27, 91)(28, 92)(29, 93)(30, 108)(31, 104)(32, 96)(33, 107)(34, 99)(35, 100)(36, 106)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 18, 72 ), ( 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72 ) } Outer automorphisms :: reflexible Dual of E16.642 Graph:: bipartite v = 37 e = 72 f = 5 degree seq :: [ 2^36, 72 ] E16.650 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 20}) Quotient :: halfedge^2 Aut^+ = D40 (small group id <40, 6>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1)^2, Y1^2 * Y3 * Y1^-3 * Y2, Y1^-1 * Y2 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 ] Map:: non-degenerate R = (1, 42, 2, 46, 6, 54, 14, 60, 20, 50, 10, 57, 17, 67, 27, 75, 35, 78, 38, 71, 31, 77, 37, 79, 39, 73, 33, 63, 23, 52, 12, 58, 18, 65, 25, 53, 13, 45, 5, 41)(3, 49, 9, 59, 19, 56, 16, 48, 8, 44, 4, 51, 11, 62, 22, 72, 32, 69, 29, 64, 24, 74, 34, 80, 40, 76, 36, 68, 28, 61, 21, 70, 30, 66, 26, 55, 15, 47, 7, 43) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 26)(16, 25)(17, 28)(20, 30)(22, 33)(24, 31)(27, 36)(29, 37)(32, 39)(34, 38)(35, 40)(41, 44)(42, 48)(43, 50)(45, 51)(46, 56)(47, 57)(49, 60)(52, 64)(53, 62)(54, 59)(55, 67)(58, 69)(61, 71)(63, 74)(65, 72)(66, 75)(68, 77)(70, 78)(73, 80)(76, 79) local type(s) :: { ( 10^40 ) } Outer automorphisms :: reflexible Dual of E16.652 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 40 f = 8 degree seq :: [ 40^2 ] E16.651 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 20}) Quotient :: halfedge^2 Aut^+ = D40 (small group id <40, 6>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y2 * Y1)^2, Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3, Y1^-4 * Y3 * Y1 * Y2 * Y1^-2, Y1^3 * Y2 * Y1^-4 * Y3, Y1^-1 * Y2 * Y3 * Y2 * Y1^2 * Y2 * Y3 * Y1^2 * Y2 * Y3 * Y1^2 * Y2, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 42, 2, 46, 6, 54, 14, 66, 26, 76, 36, 63, 23, 52, 12, 58, 18, 70, 30, 79, 39, 73, 33, 60, 20, 50, 10, 57, 17, 69, 29, 77, 37, 65, 25, 53, 13, 45, 5, 41)(3, 49, 9, 59, 19, 72, 32, 80, 40, 71, 31, 64, 24, 61, 21, 74, 34, 78, 38, 68, 28, 56, 16, 48, 8, 44, 4, 51, 11, 62, 22, 75, 35, 67, 27, 55, 15, 47, 7, 43) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 24)(20, 34)(22, 36)(25, 32)(26, 35)(28, 39)(29, 31)(33, 38)(37, 40)(41, 44)(42, 48)(43, 50)(45, 51)(46, 56)(47, 57)(49, 60)(52, 64)(53, 62)(54, 68)(55, 69)(58, 71)(59, 73)(61, 63)(65, 75)(66, 78)(67, 77)(70, 80)(72, 79)(74, 76) local type(s) :: { ( 10^40 ) } Outer automorphisms :: reflexible Dual of E16.653 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 40 f = 8 degree seq :: [ 40^2 ] E16.652 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 20}) Quotient :: halfedge^2 Aut^+ = D40 (small group id <40, 6>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^2, Y1^5, (Y3 * Y2)^4, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 42, 2, 46, 6, 53, 13, 45, 5, 41)(3, 49, 9, 58, 18, 54, 14, 47, 7, 43)(4, 51, 11, 61, 21, 55, 15, 48, 8, 44)(10, 56, 16, 64, 24, 68, 28, 59, 19, 50)(12, 57, 17, 65, 25, 71, 31, 62, 22, 52)(20, 69, 29, 76, 36, 73, 33, 66, 26, 60)(23, 72, 32, 78, 38, 74, 34, 67, 27, 63)(30, 75, 35, 79, 39, 80, 40, 77, 37, 70) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 14)(8, 17)(10, 20)(11, 22)(13, 18)(15, 25)(16, 26)(19, 29)(21, 31)(23, 30)(24, 33)(27, 35)(28, 36)(32, 37)(34, 39)(38, 40)(41, 44)(42, 48)(43, 50)(45, 51)(46, 55)(47, 56)(49, 59)(52, 63)(53, 61)(54, 64)(57, 67)(58, 68)(60, 70)(62, 72)(65, 74)(66, 75)(69, 77)(71, 78)(73, 79)(76, 80) local type(s) :: { ( 40^10 ) } Outer automorphisms :: reflexible Dual of E16.650 Transitivity :: VT+ AT Graph:: bipartite v = 8 e = 40 f = 2 degree seq :: [ 10^8 ] E16.653 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 20}) Quotient :: halfedge^2 Aut^+ = D40 (small group id <40, 6>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^2, Y1^5, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, (Y1^-1 * Y3 * Y2 * Y3 * Y2)^10 ] Map:: non-degenerate R = (1, 42, 2, 46, 6, 53, 13, 45, 5, 41)(3, 49, 9, 58, 18, 54, 14, 47, 7, 43)(4, 51, 11, 61, 21, 55, 15, 48, 8, 44)(10, 56, 16, 64, 24, 68, 28, 59, 19, 50)(12, 57, 17, 65, 25, 71, 31, 62, 22, 52)(20, 69, 29, 77, 37, 74, 34, 66, 26, 60)(23, 72, 32, 78, 38, 75, 35, 67, 27, 63)(30, 76, 36, 80, 40, 79, 39, 73, 33, 70) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 14)(8, 17)(10, 20)(11, 22)(13, 18)(15, 25)(16, 26)(19, 29)(21, 31)(23, 33)(24, 34)(27, 30)(28, 37)(32, 39)(35, 36)(38, 40)(41, 44)(42, 48)(43, 50)(45, 51)(46, 55)(47, 56)(49, 59)(52, 63)(53, 61)(54, 64)(57, 67)(58, 68)(60, 70)(62, 72)(65, 75)(66, 76)(69, 73)(71, 78)(74, 80)(77, 79) local type(s) :: { ( 40^10 ) } Outer automorphisms :: reflexible Dual of E16.651 Transitivity :: VT+ AT Graph:: bipartite v = 8 e = 40 f = 2 degree seq :: [ 10^8 ] E16.654 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 20}) Quotient :: edge^2 Aut^+ = D40 (small group id <40, 6>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^5, (Y2 * Y1)^4, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 41, 4, 44, 12, 52, 13, 53, 5, 45)(2, 42, 7, 47, 17, 57, 18, 58, 8, 48)(3, 43, 10, 50, 22, 62, 23, 63, 11, 51)(6, 46, 15, 55, 27, 67, 28, 68, 16, 56)(9, 49, 20, 60, 31, 71, 32, 72, 21, 61)(14, 54, 25, 65, 35, 75, 36, 76, 26, 66)(19, 59, 29, 69, 37, 77, 38, 78, 30, 70)(24, 64, 33, 73, 39, 79, 40, 80, 34, 74)(81, 82)(83, 89)(84, 88)(85, 87)(86, 94)(90, 101)(91, 100)(92, 98)(93, 97)(95, 106)(96, 105)(99, 104)(102, 112)(103, 111)(107, 116)(108, 115)(109, 114)(110, 113)(117, 120)(118, 119)(121, 123)(122, 126)(124, 131)(125, 130)(127, 136)(128, 135)(129, 139)(132, 143)(133, 142)(134, 144)(137, 148)(138, 147)(140, 150)(141, 149)(145, 154)(146, 153)(151, 158)(152, 157)(155, 160)(156, 159) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 80, 80 ), ( 80^10 ) } Outer automorphisms :: reflexible Dual of E16.660 Graph:: simple bipartite v = 48 e = 80 f = 2 degree seq :: [ 2^40, 10^8 ] E16.655 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 20}) Quotient :: edge^2 Aut^+ = D40 (small group id <40, 6>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^5, Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-2 * Y2 * Y1 * Y2 ] Map:: R = (1, 41, 4, 44, 12, 52, 13, 53, 5, 45)(2, 42, 7, 47, 17, 57, 18, 58, 8, 48)(3, 43, 10, 50, 22, 62, 23, 63, 11, 51)(6, 46, 15, 55, 27, 67, 28, 68, 16, 56)(9, 49, 20, 60, 32, 72, 33, 73, 21, 61)(14, 54, 25, 65, 35, 75, 36, 76, 26, 66)(19, 59, 30, 70, 38, 78, 39, 79, 31, 71)(24, 64, 29, 69, 37, 77, 40, 80, 34, 74)(81, 82)(83, 89)(84, 88)(85, 87)(86, 94)(90, 101)(91, 100)(92, 98)(93, 97)(95, 106)(96, 105)(99, 109)(102, 113)(103, 112)(104, 110)(107, 116)(108, 115)(111, 117)(114, 118)(119, 120)(121, 123)(122, 126)(124, 131)(125, 130)(127, 136)(128, 135)(129, 139)(132, 143)(133, 142)(134, 144)(137, 148)(138, 147)(140, 151)(141, 150)(145, 154)(146, 149)(152, 159)(153, 158)(155, 160)(156, 157) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 80, 80 ), ( 80^10 ) } Outer automorphisms :: reflexible Dual of E16.661 Graph:: simple bipartite v = 48 e = 80 f = 2 degree seq :: [ 2^40, 10^8 ] E16.656 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 20}) Quotient :: edge^2 Aut^+ = D40 (small group id <40, 6>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y1 * Y3^-5 * Y2, (Y2 * Y1)^4, Y3^-2 * Y1 * Y2 * Y3^-3 * Y1 * Y2 * Y1 * Y2 ] Map:: R = (1, 41, 4, 44, 12, 52, 24, 64, 21, 61, 9, 49, 20, 60, 33, 73, 40, 80, 36, 76, 26, 66, 35, 75, 38, 78, 29, 69, 16, 56, 6, 46, 15, 55, 25, 65, 13, 53, 5, 45)(2, 42, 7, 47, 17, 57, 30, 70, 28, 68, 14, 54, 27, 67, 37, 77, 39, 79, 32, 72, 19, 59, 31, 71, 34, 74, 23, 63, 11, 51, 3, 43, 10, 50, 22, 62, 18, 58, 8, 48)(81, 82)(83, 89)(84, 88)(85, 87)(86, 94)(90, 101)(91, 100)(92, 98)(93, 97)(95, 108)(96, 107)(99, 106)(102, 104)(103, 113)(105, 110)(109, 117)(111, 116)(112, 115)(114, 120)(118, 119)(121, 123)(122, 126)(124, 131)(125, 130)(127, 136)(128, 135)(129, 139)(132, 143)(133, 142)(134, 146)(137, 149)(138, 145)(140, 152)(141, 151)(144, 154)(147, 156)(148, 155)(150, 158)(153, 159)(157, 160) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 20 ), ( 20^40 ) } Outer automorphisms :: reflexible Dual of E16.658 Graph:: simple bipartite v = 42 e = 80 f = 8 degree seq :: [ 2^40, 40^2 ] E16.657 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 20}) Quotient :: edge^2 Aut^+ = D40 (small group id <40, 6>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1)^2, Y2 * Y3^-2 * Y1 * Y2 * Y1, Y3^4 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2, Y3^20 ] Map:: R = (1, 41, 4, 44, 12, 52, 21, 61, 29, 69, 37, 77, 35, 75, 27, 67, 19, 59, 9, 49, 16, 56, 6, 46, 15, 55, 24, 64, 32, 72, 38, 78, 30, 70, 22, 62, 13, 53, 5, 45)(2, 42, 7, 47, 17, 57, 25, 65, 33, 73, 40, 80, 39, 79, 31, 71, 23, 63, 14, 54, 11, 51, 3, 43, 10, 50, 20, 60, 28, 68, 36, 76, 34, 74, 26, 66, 18, 58, 8, 48)(81, 82)(83, 89)(84, 88)(85, 87)(86, 94)(90, 99)(91, 96)(92, 98)(93, 97)(95, 103)(100, 107)(101, 106)(102, 105)(104, 111)(108, 115)(109, 114)(110, 113)(112, 119)(116, 117)(118, 120)(121, 123)(122, 126)(124, 131)(125, 130)(127, 136)(128, 135)(129, 137)(132, 134)(133, 140)(138, 144)(139, 145)(141, 143)(142, 148)(146, 152)(147, 153)(149, 151)(150, 156)(154, 158)(155, 160)(157, 159) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 20 ), ( 20^40 ) } Outer automorphisms :: reflexible Dual of E16.659 Graph:: simple bipartite v = 42 e = 80 f = 8 degree seq :: [ 2^40, 40^2 ] E16.658 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 20}) Quotient :: loop^2 Aut^+ = D40 (small group id <40, 6>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^5, (Y2 * Y1)^4, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 41, 81, 121, 4, 44, 84, 124, 12, 52, 92, 132, 13, 53, 93, 133, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 17, 57, 97, 137, 18, 58, 98, 138, 8, 48, 88, 128)(3, 43, 83, 123, 10, 50, 90, 130, 22, 62, 102, 142, 23, 63, 103, 143, 11, 51, 91, 131)(6, 46, 86, 126, 15, 55, 95, 135, 27, 67, 107, 147, 28, 68, 108, 148, 16, 56, 96, 136)(9, 49, 89, 129, 20, 60, 100, 140, 31, 71, 111, 151, 32, 72, 112, 152, 21, 61, 101, 141)(14, 54, 94, 134, 25, 65, 105, 145, 35, 75, 115, 155, 36, 76, 116, 156, 26, 66, 106, 146)(19, 59, 99, 139, 29, 69, 109, 149, 37, 77, 117, 157, 38, 78, 118, 158, 30, 70, 110, 150)(24, 64, 104, 144, 33, 73, 113, 153, 39, 79, 119, 159, 40, 80, 120, 160, 34, 74, 114, 154) L = (1, 42)(2, 41)(3, 49)(4, 48)(5, 47)(6, 54)(7, 45)(8, 44)(9, 43)(10, 61)(11, 60)(12, 58)(13, 57)(14, 46)(15, 66)(16, 65)(17, 53)(18, 52)(19, 64)(20, 51)(21, 50)(22, 72)(23, 71)(24, 59)(25, 56)(26, 55)(27, 76)(28, 75)(29, 74)(30, 73)(31, 63)(32, 62)(33, 70)(34, 69)(35, 68)(36, 67)(37, 80)(38, 79)(39, 78)(40, 77)(81, 123)(82, 126)(83, 121)(84, 131)(85, 130)(86, 122)(87, 136)(88, 135)(89, 139)(90, 125)(91, 124)(92, 143)(93, 142)(94, 144)(95, 128)(96, 127)(97, 148)(98, 147)(99, 129)(100, 150)(101, 149)(102, 133)(103, 132)(104, 134)(105, 154)(106, 153)(107, 138)(108, 137)(109, 141)(110, 140)(111, 158)(112, 157)(113, 146)(114, 145)(115, 160)(116, 159)(117, 152)(118, 151)(119, 156)(120, 155) local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) } Outer automorphisms :: reflexible Dual of E16.656 Transitivity :: VT+ Graph:: bipartite v = 8 e = 80 f = 42 degree seq :: [ 20^8 ] E16.659 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 20}) Quotient :: loop^2 Aut^+ = D40 (small group id <40, 6>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^5, Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-2 * Y2 * Y1 * Y2 ] Map:: R = (1, 41, 81, 121, 4, 44, 84, 124, 12, 52, 92, 132, 13, 53, 93, 133, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 17, 57, 97, 137, 18, 58, 98, 138, 8, 48, 88, 128)(3, 43, 83, 123, 10, 50, 90, 130, 22, 62, 102, 142, 23, 63, 103, 143, 11, 51, 91, 131)(6, 46, 86, 126, 15, 55, 95, 135, 27, 67, 107, 147, 28, 68, 108, 148, 16, 56, 96, 136)(9, 49, 89, 129, 20, 60, 100, 140, 32, 72, 112, 152, 33, 73, 113, 153, 21, 61, 101, 141)(14, 54, 94, 134, 25, 65, 105, 145, 35, 75, 115, 155, 36, 76, 116, 156, 26, 66, 106, 146)(19, 59, 99, 139, 30, 70, 110, 150, 38, 78, 118, 158, 39, 79, 119, 159, 31, 71, 111, 151)(24, 64, 104, 144, 29, 69, 109, 149, 37, 77, 117, 157, 40, 80, 120, 160, 34, 74, 114, 154) L = (1, 42)(2, 41)(3, 49)(4, 48)(5, 47)(6, 54)(7, 45)(8, 44)(9, 43)(10, 61)(11, 60)(12, 58)(13, 57)(14, 46)(15, 66)(16, 65)(17, 53)(18, 52)(19, 69)(20, 51)(21, 50)(22, 73)(23, 72)(24, 70)(25, 56)(26, 55)(27, 76)(28, 75)(29, 59)(30, 64)(31, 77)(32, 63)(33, 62)(34, 78)(35, 68)(36, 67)(37, 71)(38, 74)(39, 80)(40, 79)(81, 123)(82, 126)(83, 121)(84, 131)(85, 130)(86, 122)(87, 136)(88, 135)(89, 139)(90, 125)(91, 124)(92, 143)(93, 142)(94, 144)(95, 128)(96, 127)(97, 148)(98, 147)(99, 129)(100, 151)(101, 150)(102, 133)(103, 132)(104, 134)(105, 154)(106, 149)(107, 138)(108, 137)(109, 146)(110, 141)(111, 140)(112, 159)(113, 158)(114, 145)(115, 160)(116, 157)(117, 156)(118, 153)(119, 152)(120, 155) local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) } Outer automorphisms :: reflexible Dual of E16.657 Transitivity :: VT+ Graph:: bipartite v = 8 e = 80 f = 42 degree seq :: [ 20^8 ] E16.660 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 20}) Quotient :: loop^2 Aut^+ = D40 (small group id <40, 6>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y1 * Y3^-5 * Y2, (Y2 * Y1)^4, Y3^-2 * Y1 * Y2 * Y3^-3 * Y1 * Y2 * Y1 * Y2 ] Map:: R = (1, 41, 81, 121, 4, 44, 84, 124, 12, 52, 92, 132, 24, 64, 104, 144, 21, 61, 101, 141, 9, 49, 89, 129, 20, 60, 100, 140, 33, 73, 113, 153, 40, 80, 120, 160, 36, 76, 116, 156, 26, 66, 106, 146, 35, 75, 115, 155, 38, 78, 118, 158, 29, 69, 109, 149, 16, 56, 96, 136, 6, 46, 86, 126, 15, 55, 95, 135, 25, 65, 105, 145, 13, 53, 93, 133, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 17, 57, 97, 137, 30, 70, 110, 150, 28, 68, 108, 148, 14, 54, 94, 134, 27, 67, 107, 147, 37, 77, 117, 157, 39, 79, 119, 159, 32, 72, 112, 152, 19, 59, 99, 139, 31, 71, 111, 151, 34, 74, 114, 154, 23, 63, 103, 143, 11, 51, 91, 131, 3, 43, 83, 123, 10, 50, 90, 130, 22, 62, 102, 142, 18, 58, 98, 138, 8, 48, 88, 128) L = (1, 42)(2, 41)(3, 49)(4, 48)(5, 47)(6, 54)(7, 45)(8, 44)(9, 43)(10, 61)(11, 60)(12, 58)(13, 57)(14, 46)(15, 68)(16, 67)(17, 53)(18, 52)(19, 66)(20, 51)(21, 50)(22, 64)(23, 73)(24, 62)(25, 70)(26, 59)(27, 56)(28, 55)(29, 77)(30, 65)(31, 76)(32, 75)(33, 63)(34, 80)(35, 72)(36, 71)(37, 69)(38, 79)(39, 78)(40, 74)(81, 123)(82, 126)(83, 121)(84, 131)(85, 130)(86, 122)(87, 136)(88, 135)(89, 139)(90, 125)(91, 124)(92, 143)(93, 142)(94, 146)(95, 128)(96, 127)(97, 149)(98, 145)(99, 129)(100, 152)(101, 151)(102, 133)(103, 132)(104, 154)(105, 138)(106, 134)(107, 156)(108, 155)(109, 137)(110, 158)(111, 141)(112, 140)(113, 159)(114, 144)(115, 148)(116, 147)(117, 160)(118, 150)(119, 153)(120, 157) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.654 Transitivity :: VT+ Graph:: bipartite v = 2 e = 80 f = 48 degree seq :: [ 80^2 ] E16.661 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 20}) Quotient :: loop^2 Aut^+ = D40 (small group id <40, 6>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1)^2, Y2 * Y3^-2 * Y1 * Y2 * Y1, Y3^4 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2, Y3^20 ] Map:: R = (1, 41, 81, 121, 4, 44, 84, 124, 12, 52, 92, 132, 21, 61, 101, 141, 29, 69, 109, 149, 37, 77, 117, 157, 35, 75, 115, 155, 27, 67, 107, 147, 19, 59, 99, 139, 9, 49, 89, 129, 16, 56, 96, 136, 6, 46, 86, 126, 15, 55, 95, 135, 24, 64, 104, 144, 32, 72, 112, 152, 38, 78, 118, 158, 30, 70, 110, 150, 22, 62, 102, 142, 13, 53, 93, 133, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 17, 57, 97, 137, 25, 65, 105, 145, 33, 73, 113, 153, 40, 80, 120, 160, 39, 79, 119, 159, 31, 71, 111, 151, 23, 63, 103, 143, 14, 54, 94, 134, 11, 51, 91, 131, 3, 43, 83, 123, 10, 50, 90, 130, 20, 60, 100, 140, 28, 68, 108, 148, 36, 76, 116, 156, 34, 74, 114, 154, 26, 66, 106, 146, 18, 58, 98, 138, 8, 48, 88, 128) L = (1, 42)(2, 41)(3, 49)(4, 48)(5, 47)(6, 54)(7, 45)(8, 44)(9, 43)(10, 59)(11, 56)(12, 58)(13, 57)(14, 46)(15, 63)(16, 51)(17, 53)(18, 52)(19, 50)(20, 67)(21, 66)(22, 65)(23, 55)(24, 71)(25, 62)(26, 61)(27, 60)(28, 75)(29, 74)(30, 73)(31, 64)(32, 79)(33, 70)(34, 69)(35, 68)(36, 77)(37, 76)(38, 80)(39, 72)(40, 78)(81, 123)(82, 126)(83, 121)(84, 131)(85, 130)(86, 122)(87, 136)(88, 135)(89, 137)(90, 125)(91, 124)(92, 134)(93, 140)(94, 132)(95, 128)(96, 127)(97, 129)(98, 144)(99, 145)(100, 133)(101, 143)(102, 148)(103, 141)(104, 138)(105, 139)(106, 152)(107, 153)(108, 142)(109, 151)(110, 156)(111, 149)(112, 146)(113, 147)(114, 158)(115, 160)(116, 150)(117, 159)(118, 154)(119, 157)(120, 155) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.655 Transitivity :: VT+ Graph:: bipartite v = 2 e = 80 f = 48 degree seq :: [ 80^2 ] E16.662 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 20}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3, Y2^-1), (R * Y2)^2, (Y2 * Y1)^2, Y3^4, Y2^5 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 10, 50)(5, 45, 7, 47)(6, 46, 8, 48)(11, 51, 23, 63)(12, 52, 24, 64)(13, 53, 22, 62)(14, 54, 21, 61)(15, 55, 20, 60)(16, 56, 18, 58)(17, 57, 19, 59)(25, 65, 36, 76)(26, 66, 35, 75)(27, 67, 34, 74)(28, 68, 33, 73)(29, 69, 32, 72)(30, 70, 31, 71)(37, 77, 40, 80)(38, 78, 39, 79)(81, 121, 83, 123, 91, 131, 96, 136, 85, 125)(82, 122, 87, 127, 98, 138, 103, 143, 89, 129)(84, 124, 92, 132, 105, 145, 109, 149, 95, 135)(86, 126, 93, 133, 106, 146, 110, 150, 97, 137)(88, 128, 99, 139, 111, 151, 115, 155, 102, 142)(90, 130, 100, 140, 112, 152, 116, 156, 104, 144)(94, 134, 107, 147, 117, 157, 118, 158, 108, 148)(101, 141, 113, 153, 119, 159, 120, 160, 114, 154) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 99)(8, 101)(9, 102)(10, 82)(11, 105)(12, 107)(13, 83)(14, 86)(15, 108)(16, 109)(17, 85)(18, 111)(19, 113)(20, 87)(21, 90)(22, 114)(23, 115)(24, 89)(25, 117)(26, 91)(27, 93)(28, 97)(29, 118)(30, 96)(31, 119)(32, 98)(33, 100)(34, 104)(35, 120)(36, 103)(37, 106)(38, 110)(39, 112)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E16.667 Graph:: simple bipartite v = 28 e = 80 f = 22 degree seq :: [ 4^20, 10^8 ] E16.663 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 20}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y3, Y2), (Y2 * Y1)^2, Y3^4 * Y2^-1, Y2^5 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 10, 50)(5, 45, 7, 47)(6, 46, 8, 48)(11, 51, 24, 64)(12, 52, 25, 65)(13, 53, 23, 63)(14, 54, 26, 66)(15, 55, 21, 61)(16, 56, 19, 59)(17, 57, 20, 60)(18, 58, 22, 62)(27, 67, 37, 77)(28, 68, 36, 76)(29, 69, 38, 78)(30, 70, 34, 74)(31, 71, 33, 73)(32, 72, 35, 75)(39, 79, 40, 80)(81, 121, 83, 123, 91, 131, 96, 136, 85, 125)(82, 122, 87, 127, 99, 139, 104, 144, 89, 129)(84, 124, 92, 132, 107, 147, 110, 150, 95, 135)(86, 126, 93, 133, 108, 148, 111, 151, 97, 137)(88, 128, 100, 140, 113, 153, 116, 156, 103, 143)(90, 130, 101, 141, 114, 154, 117, 157, 105, 145)(94, 134, 109, 149, 119, 159, 112, 152, 98, 138)(102, 142, 115, 155, 120, 160, 118, 158, 106, 146) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 103)(10, 82)(11, 107)(12, 109)(13, 83)(14, 93)(15, 98)(16, 110)(17, 85)(18, 86)(19, 113)(20, 115)(21, 87)(22, 101)(23, 106)(24, 116)(25, 89)(26, 90)(27, 119)(28, 91)(29, 108)(30, 112)(31, 96)(32, 97)(33, 120)(34, 99)(35, 114)(36, 118)(37, 104)(38, 105)(39, 111)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E16.668 Graph:: simple bipartite v = 28 e = 80 f = 22 degree seq :: [ 4^20, 10^8 ] E16.664 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 20}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2, Y3^-1), (Y2^-1 * Y1)^2, Y2^-5, Y2^-2 * Y3^4 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 10, 50)(5, 45, 7, 47)(6, 46, 8, 48)(11, 51, 24, 64)(12, 52, 25, 65)(13, 53, 23, 63)(14, 54, 26, 66)(15, 55, 21, 61)(16, 56, 19, 59)(17, 57, 20, 60)(18, 58, 22, 62)(27, 67, 39, 79)(28, 68, 38, 78)(29, 69, 40, 80)(30, 70, 37, 77)(31, 71, 35, 75)(32, 72, 34, 74)(33, 73, 36, 76)(81, 121, 83, 123, 91, 131, 96, 136, 85, 125)(82, 122, 87, 127, 99, 139, 104, 144, 89, 129)(84, 124, 92, 132, 107, 147, 111, 151, 95, 135)(86, 126, 93, 133, 108, 148, 112, 152, 97, 137)(88, 128, 100, 140, 114, 154, 118, 158, 103, 143)(90, 130, 101, 141, 115, 155, 119, 159, 105, 145)(94, 134, 109, 149, 113, 153, 98, 138, 110, 150)(102, 142, 116, 156, 120, 160, 106, 146, 117, 157) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 103)(10, 82)(11, 107)(12, 109)(13, 83)(14, 108)(15, 110)(16, 111)(17, 85)(18, 86)(19, 114)(20, 116)(21, 87)(22, 115)(23, 117)(24, 118)(25, 89)(26, 90)(27, 113)(28, 91)(29, 112)(30, 93)(31, 98)(32, 96)(33, 97)(34, 120)(35, 99)(36, 119)(37, 101)(38, 106)(39, 104)(40, 105)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E16.670 Graph:: simple bipartite v = 28 e = 80 f = 22 degree seq :: [ 4^20, 10^8 ] E16.665 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 20}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, Y2^-5, Y2^5, Y2^-2 * Y3^-4, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 10, 50)(5, 45, 7, 47)(6, 46, 8, 48)(11, 51, 24, 64)(12, 52, 25, 65)(13, 53, 23, 63)(14, 54, 26, 66)(15, 55, 21, 61)(16, 56, 19, 59)(17, 57, 20, 60)(18, 58, 22, 62)(27, 67, 38, 78)(28, 68, 40, 80)(29, 69, 36, 76)(30, 70, 39, 79)(31, 71, 34, 74)(32, 72, 37, 77)(33, 73, 35, 75)(81, 121, 83, 123, 91, 131, 96, 136, 85, 125)(82, 122, 87, 127, 99, 139, 104, 144, 89, 129)(84, 124, 92, 132, 107, 147, 113, 153, 95, 135)(86, 126, 93, 133, 108, 148, 111, 151, 97, 137)(88, 128, 100, 140, 114, 154, 120, 160, 103, 143)(90, 130, 101, 141, 115, 155, 118, 158, 105, 145)(94, 134, 109, 149, 98, 138, 110, 150, 112, 152)(102, 142, 116, 156, 106, 146, 117, 157, 119, 159) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 103)(10, 82)(11, 107)(12, 109)(13, 83)(14, 111)(15, 112)(16, 113)(17, 85)(18, 86)(19, 114)(20, 116)(21, 87)(22, 118)(23, 119)(24, 120)(25, 89)(26, 90)(27, 98)(28, 91)(29, 97)(30, 93)(31, 96)(32, 108)(33, 110)(34, 106)(35, 99)(36, 105)(37, 101)(38, 104)(39, 115)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E16.669 Graph:: simple bipartite v = 28 e = 80 f = 22 degree seq :: [ 4^20, 10^8 ] E16.666 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3, Y2^-1), (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3^4, Y2^5 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 10, 50)(5, 45, 9, 49)(6, 46, 8, 48)(11, 51, 18, 58)(12, 52, 20, 60)(13, 53, 19, 59)(14, 54, 21, 61)(15, 55, 24, 64)(16, 56, 23, 63)(17, 57, 22, 62)(25, 65, 32, 72)(26, 66, 31, 71)(27, 67, 33, 73)(28, 68, 34, 74)(29, 69, 36, 76)(30, 70, 35, 75)(37, 77, 39, 79)(38, 78, 40, 80)(81, 121, 83, 123, 91, 131, 96, 136, 85, 125)(82, 122, 87, 127, 98, 138, 103, 143, 89, 129)(84, 124, 92, 132, 105, 145, 109, 149, 95, 135)(86, 126, 93, 133, 106, 146, 110, 150, 97, 137)(88, 128, 99, 139, 111, 151, 115, 155, 102, 142)(90, 130, 100, 140, 112, 152, 116, 156, 104, 144)(94, 134, 107, 147, 117, 157, 118, 158, 108, 148)(101, 141, 113, 153, 119, 159, 120, 160, 114, 154) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 99)(8, 101)(9, 102)(10, 82)(11, 105)(12, 107)(13, 83)(14, 86)(15, 108)(16, 109)(17, 85)(18, 111)(19, 113)(20, 87)(21, 90)(22, 114)(23, 115)(24, 89)(25, 117)(26, 91)(27, 93)(28, 97)(29, 118)(30, 96)(31, 119)(32, 98)(33, 100)(34, 104)(35, 120)(36, 103)(37, 106)(38, 110)(39, 112)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E16.671 Graph:: simple bipartite v = 28 e = 80 f = 22 degree seq :: [ 4^20, 10^8 ] E16.667 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 20}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y3^4, (Y3^-1, Y1^-1), Y1^5 * Y3, (Y2 * Y3 * Y1)^2, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 18, 58, 17, 57, 6, 46, 10, 50, 21, 61, 32, 72, 29, 69, 14, 54, 24, 64, 35, 75, 30, 70, 15, 55, 4, 44, 9, 49, 20, 60, 16, 56, 5, 45)(3, 43, 11, 51, 25, 65, 34, 74, 23, 63, 13, 53, 27, 67, 37, 77, 40, 80, 36, 76, 28, 68, 38, 78, 39, 79, 33, 73, 22, 62, 12, 52, 26, 66, 31, 71, 19, 59, 8, 48)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 93, 133)(85, 125, 91, 131)(86, 126, 92, 132)(87, 127, 99, 139)(89, 129, 103, 143)(90, 130, 102, 142)(94, 134, 108, 148)(95, 135, 107, 147)(96, 136, 105, 145)(97, 137, 106, 146)(98, 138, 111, 151)(100, 140, 114, 154)(101, 141, 113, 153)(104, 144, 116, 156)(109, 149, 118, 158)(110, 150, 117, 157)(112, 152, 119, 159)(115, 155, 120, 160) L = (1, 84)(2, 89)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 104)(10, 82)(11, 106)(12, 108)(13, 83)(14, 86)(15, 109)(16, 110)(17, 85)(18, 96)(19, 113)(20, 115)(21, 87)(22, 116)(23, 88)(24, 90)(25, 111)(26, 118)(27, 91)(28, 93)(29, 97)(30, 112)(31, 119)(32, 98)(33, 120)(34, 99)(35, 101)(36, 103)(37, 105)(38, 107)(39, 117)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.662 Graph:: bipartite v = 22 e = 80 f = 28 degree seq :: [ 4^20, 40^2 ] E16.668 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 20}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2 * Y1^-1 * Y3, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (Y1^-1 * Y2)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-6, (Y1^-1 * Y3^-1)^5 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 17, 57, 29, 69, 26, 66, 14, 54, 4, 44, 9, 49, 19, 59, 31, 71, 28, 68, 16, 56, 6, 46, 10, 50, 20, 60, 32, 72, 27, 67, 15, 55, 5, 45)(3, 43, 11, 51, 23, 63, 35, 75, 39, 79, 33, 73, 21, 61, 12, 52, 24, 64, 36, 76, 40, 80, 34, 74, 22, 62, 13, 53, 25, 65, 37, 77, 38, 78, 30, 70, 18, 58, 8, 48)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 93, 133)(85, 125, 91, 131)(86, 126, 92, 132)(87, 127, 98, 138)(89, 129, 102, 142)(90, 130, 101, 141)(94, 134, 105, 145)(95, 135, 103, 143)(96, 136, 104, 144)(97, 137, 110, 150)(99, 139, 114, 154)(100, 140, 113, 153)(106, 146, 117, 157)(107, 147, 115, 155)(108, 148, 116, 156)(109, 149, 118, 158)(111, 151, 120, 160)(112, 152, 119, 159) L = (1, 84)(2, 89)(3, 92)(4, 90)(5, 94)(6, 81)(7, 99)(8, 101)(9, 100)(10, 82)(11, 104)(12, 105)(13, 83)(14, 86)(15, 106)(16, 85)(17, 111)(18, 113)(19, 112)(20, 87)(21, 93)(22, 88)(23, 116)(24, 117)(25, 91)(26, 96)(27, 109)(28, 95)(29, 108)(30, 119)(31, 107)(32, 97)(33, 102)(34, 98)(35, 120)(36, 118)(37, 103)(38, 115)(39, 114)(40, 110)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.663 Graph:: bipartite v = 22 e = 80 f = 28 degree seq :: [ 4^20, 40^2 ] E16.669 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 20}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^-3, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^6, (Y3^-1 * Y1^-1)^5 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 4, 44, 9, 49, 18, 58, 14, 54, 21, 61, 30, 70, 26, 66, 33, 73, 28, 68, 34, 74, 27, 67, 16, 56, 22, 62, 15, 55, 6, 46, 10, 50, 5, 45)(3, 43, 11, 51, 19, 59, 12, 52, 23, 63, 31, 71, 24, 64, 35, 75, 39, 79, 36, 76, 40, 80, 37, 77, 38, 78, 32, 72, 25, 65, 29, 69, 20, 60, 13, 53, 17, 57, 8, 48)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 93, 133)(85, 125, 91, 131)(86, 126, 92, 132)(87, 127, 97, 137)(89, 129, 100, 140)(90, 130, 99, 139)(94, 134, 105, 145)(95, 135, 103, 143)(96, 136, 104, 144)(98, 138, 109, 149)(101, 141, 112, 152)(102, 142, 111, 151)(106, 146, 117, 157)(107, 147, 115, 155)(108, 148, 116, 156)(110, 150, 118, 158)(113, 153, 120, 160)(114, 154, 119, 159) L = (1, 84)(2, 89)(3, 92)(4, 94)(5, 87)(6, 81)(7, 98)(8, 99)(9, 101)(10, 82)(11, 103)(12, 104)(13, 83)(14, 106)(15, 85)(16, 86)(17, 91)(18, 110)(19, 111)(20, 88)(21, 113)(22, 90)(23, 115)(24, 116)(25, 93)(26, 114)(27, 95)(28, 96)(29, 97)(30, 108)(31, 119)(32, 100)(33, 107)(34, 102)(35, 120)(36, 118)(37, 105)(38, 109)(39, 117)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.665 Graph:: bipartite v = 22 e = 80 f = 28 degree seq :: [ 4^20, 40^2 ] E16.670 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 20}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (R * Y3)^2, Y3^2 * Y1^-2, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, Y3^2 * Y1^18 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 16, 56, 25, 65, 33, 73, 32, 72, 24, 64, 15, 55, 6, 46, 10, 50, 4, 44, 9, 49, 18, 58, 27, 67, 35, 75, 31, 71, 23, 63, 14, 54, 5, 45)(3, 43, 11, 51, 21, 61, 29, 69, 37, 77, 40, 80, 36, 76, 28, 68, 20, 60, 13, 53, 19, 59, 12, 52, 22, 62, 30, 70, 38, 78, 39, 79, 34, 74, 26, 66, 17, 57, 8, 48)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 93, 133)(85, 125, 91, 131)(86, 126, 92, 132)(87, 127, 97, 137)(89, 129, 100, 140)(90, 130, 99, 139)(94, 134, 101, 141)(95, 135, 102, 142)(96, 136, 106, 146)(98, 138, 108, 148)(103, 143, 109, 149)(104, 144, 110, 150)(105, 145, 114, 154)(107, 147, 116, 156)(111, 151, 117, 157)(112, 152, 118, 158)(113, 153, 119, 159)(115, 155, 120, 160) L = (1, 84)(2, 89)(3, 92)(4, 87)(5, 90)(6, 81)(7, 98)(8, 99)(9, 96)(10, 82)(11, 102)(12, 101)(13, 83)(14, 86)(15, 85)(16, 107)(17, 93)(18, 105)(19, 91)(20, 88)(21, 110)(22, 109)(23, 95)(24, 94)(25, 115)(26, 100)(27, 113)(28, 97)(29, 118)(30, 117)(31, 104)(32, 103)(33, 111)(34, 108)(35, 112)(36, 106)(37, 119)(38, 120)(39, 116)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.664 Graph:: bipartite v = 22 e = 80 f = 28 degree seq :: [ 4^20, 40^2 ] E16.671 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y2 * Y3^-1)^2, (Y3, Y1), (R * Y3)^2, Y3^4, (R * Y1)^2, Y1^-5 * Y3^-1, Y3 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1^2 * Y2 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2 * Y1^-1, Y1^3 * Y3^-1 * Y1^2 * Y3^-2 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 20, 60, 19, 59, 6, 46, 10, 50, 23, 63, 36, 76, 30, 70, 15, 55, 28, 68, 40, 80, 33, 73, 16, 56, 4, 44, 9, 49, 22, 62, 18, 58, 5, 45)(3, 43, 11, 51, 21, 61, 37, 77, 32, 72, 14, 54, 25, 65, 39, 79, 34, 74, 17, 57, 26, 66, 8, 48, 24, 64, 35, 75, 29, 69, 12, 52, 27, 67, 38, 78, 31, 71, 13, 53)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 94, 134)(85, 125, 97, 137)(86, 126, 92, 132)(87, 127, 101, 141)(89, 129, 107, 147)(90, 130, 105, 145)(91, 131, 108, 148)(93, 133, 110, 150)(95, 135, 106, 146)(96, 136, 109, 149)(98, 138, 111, 151)(99, 139, 112, 152)(100, 140, 115, 155)(102, 142, 119, 159)(103, 143, 118, 158)(104, 144, 120, 160)(113, 153, 117, 157)(114, 154, 116, 156) L = (1, 84)(2, 89)(3, 92)(4, 95)(5, 96)(6, 81)(7, 102)(8, 105)(9, 108)(10, 82)(11, 107)(12, 106)(13, 109)(14, 83)(15, 86)(16, 110)(17, 112)(18, 113)(19, 85)(20, 98)(21, 118)(22, 120)(23, 87)(24, 119)(25, 91)(26, 94)(27, 88)(28, 90)(29, 97)(30, 99)(31, 115)(32, 93)(33, 116)(34, 117)(35, 114)(36, 100)(37, 111)(38, 104)(39, 101)(40, 103)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.666 Graph:: bipartite v = 22 e = 80 f = 28 degree seq :: [ 4^20, 40^2 ] E16.672 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {10, 10, 20}) Quotient :: edge Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2^-2 * T1^-1, T2^2 * T1 * T2^-2 * T1^-1, T1 * T2^-1 * T1^-2 * T2 * T1, (T2^2 * T1^-1)^2, (T2, T1^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^20 ] Map:: non-degenerate R = (1, 3, 10, 20, 6, 19, 13, 30, 17, 5)(2, 7, 22, 34, 18, 14, 4, 12, 26, 8)(9, 27, 35, 33, 16, 31, 11, 29, 15, 28)(21, 36, 32, 40, 25, 39, 23, 38, 24, 37)(41, 42, 46, 58, 57, 66, 50, 62, 53, 44)(43, 49, 59, 56, 45, 55, 60, 75, 70, 51)(47, 61, 54, 65, 48, 64, 74, 72, 52, 63)(67, 76, 71, 79, 68, 77, 73, 80, 69, 78) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 40^10 ) } Outer automorphisms :: reflexible Dual of E16.679 Transitivity :: ET+ Graph:: bipartite v = 8 e = 40 f = 2 degree seq :: [ 10^8 ] E16.673 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {10, 10, 20}) Quotient :: edge Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^2, T1^2 * T2 * T1^-2 * T2^-1, T2^2 * T1 * T2^-2 * T1^-1, T2^-1 * T1^-3 * T2^-1 * T1^-5, (T2^-1 * T1^-1)^10, T2^20 ] Map:: non-degenerate R = (1, 3, 10, 19, 28, 38, 36, 25, 12, 21, 32, 18, 6, 17, 31, 39, 33, 26, 15, 5)(2, 7, 20, 30, 37, 35, 27, 13, 4, 11, 23, 9, 16, 29, 40, 34, 24, 14, 22, 8)(41, 42, 46, 56, 68, 77, 73, 64, 52, 44)(43, 49, 57, 70, 78, 74, 66, 53, 61, 48)(45, 51, 58, 47, 59, 69, 79, 75, 65, 54)(50, 60, 71, 80, 76, 67, 55, 62, 72, 63) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^10 ), ( 20^20 ) } Outer automorphisms :: reflexible Dual of E16.677 Transitivity :: ET+ Graph:: bipartite v = 6 e = 40 f = 4 degree seq :: [ 10^4, 20^2 ] E16.674 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {10, 10, 20}) Quotient :: edge Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2^-2 * T1^-1 * T2, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T2^4 * T1^-2, (T2 * T1^-1 * T2)^2, T1^-3 * T2^-1 * T1^-1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 10, 20, 6, 19, 36, 32, 34, 25, 40, 23, 39, 24, 38, 21, 13, 30, 17, 5)(2, 7, 22, 35, 18, 16, 31, 11, 29, 15, 28, 9, 27, 37, 33, 14, 4, 12, 26, 8)(41, 42, 46, 58, 74, 69, 79, 67, 53, 44)(43, 49, 59, 54, 65, 48, 64, 75, 70, 51)(45, 55, 60, 77, 72, 52, 63, 47, 61, 56)(50, 62, 76, 71, 80, 68, 78, 73, 57, 66) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^10 ), ( 20^20 ) } Outer automorphisms :: reflexible Dual of E16.676 Transitivity :: ET+ Graph:: bipartite v = 6 e = 40 f = 4 degree seq :: [ 10^4, 20^2 ] E16.675 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {10, 10, 20}) Quotient :: edge Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-3 * T2 * T1^-1, T2^-1 * T1^-2 * T2^-3, T2^-1 * T1 * T2^2 * T1^-1 * T2^-1, (T2^-2 * T1^-1)^2, T2 * T1^2 * T2^-1 * T1^-2, T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 29, 13, 24, 39, 21, 38, 25, 40, 23, 34, 33, 37, 20, 6, 19, 17, 5)(2, 7, 22, 14, 4, 12, 30, 36, 32, 15, 28, 9, 27, 16, 31, 11, 18, 35, 26, 8)(41, 42, 46, 58, 74, 67, 78, 72, 53, 44)(43, 49, 59, 76, 73, 54, 65, 48, 64, 51)(45, 55, 60, 52, 63, 47, 61, 75, 69, 56)(50, 62, 57, 66, 77, 71, 80, 68, 79, 70) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^10 ), ( 20^20 ) } Outer automorphisms :: reflexible Dual of E16.678 Transitivity :: ET+ Graph:: bipartite v = 6 e = 40 f = 4 degree seq :: [ 10^4, 20^2 ] E16.676 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {10, 10, 20}) Quotient :: loop Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1^-2, T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1^-1, T1^2 * T2 * T1^6 * T2, (T2^-1 * T1^-1)^20 ] Map:: non-degenerate R = (1, 41, 3, 43, 6, 46, 15, 55, 26, 66, 38, 78, 33, 73, 23, 63, 11, 51, 5, 45)(2, 42, 7, 47, 14, 54, 27, 67, 37, 77, 34, 74, 22, 62, 12, 52, 4, 44, 8, 48)(9, 49, 19, 59, 28, 68, 40, 80, 35, 75, 25, 65, 13, 53, 21, 61, 10, 50, 20, 60)(16, 56, 29, 69, 39, 79, 36, 76, 24, 64, 32, 72, 18, 58, 31, 71, 17, 57, 30, 70) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 50)(6, 54)(7, 56)(8, 57)(9, 55)(10, 43)(11, 44)(12, 58)(13, 45)(14, 66)(15, 68)(16, 67)(17, 47)(18, 48)(19, 69)(20, 70)(21, 71)(22, 51)(23, 53)(24, 52)(25, 72)(26, 77)(27, 79)(28, 78)(29, 80)(30, 59)(31, 60)(32, 61)(33, 62)(34, 64)(35, 63)(36, 65)(37, 73)(38, 75)(39, 74)(40, 76) local type(s) :: { ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.674 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 40 f = 6 degree seq :: [ 20^4 ] E16.677 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {10, 10, 20}) Quotient :: loop Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2^-2 * T1^-1, T2^2 * T1 * T2^-2 * T1^-1, T1 * T2^-1 * T1^-2 * T2 * T1, (T2^2 * T1^-1)^2, (T2, T1^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^20 ] Map:: non-degenerate R = (1, 41, 3, 43, 10, 50, 20, 60, 6, 46, 19, 59, 13, 53, 30, 70, 17, 57, 5, 45)(2, 42, 7, 47, 22, 62, 34, 74, 18, 58, 14, 54, 4, 44, 12, 52, 26, 66, 8, 48)(9, 49, 27, 67, 35, 75, 33, 73, 16, 56, 31, 71, 11, 51, 29, 69, 15, 55, 28, 68)(21, 61, 36, 76, 32, 72, 40, 80, 25, 65, 39, 79, 23, 63, 38, 78, 24, 64, 37, 77) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 55)(6, 58)(7, 61)(8, 64)(9, 59)(10, 62)(11, 43)(12, 63)(13, 44)(14, 65)(15, 60)(16, 45)(17, 66)(18, 57)(19, 56)(20, 75)(21, 54)(22, 53)(23, 47)(24, 74)(25, 48)(26, 50)(27, 76)(28, 77)(29, 78)(30, 51)(31, 79)(32, 52)(33, 80)(34, 72)(35, 70)(36, 71)(37, 73)(38, 67)(39, 68)(40, 69) local type(s) :: { ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.673 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 40 f = 6 degree seq :: [ 20^4 ] E16.678 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {10, 10, 20}) Quotient :: loop Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-2 * T2^-3, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, T1 * T2^-2 * T1^3, (T2^-2 * T1^-1)^2, T2 * T1 * T2^-2 * T1^-1 * T2, (T2 * T1^-2)^2, (T2, T1^-1)^2, T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 41, 3, 43, 10, 50, 29, 69, 13, 53, 20, 60, 6, 46, 19, 59, 17, 57, 5, 45)(2, 42, 7, 47, 22, 62, 14, 54, 4, 44, 12, 52, 18, 58, 34, 74, 26, 66, 8, 48)(9, 49, 27, 67, 16, 56, 31, 71, 11, 51, 30, 70, 35, 75, 33, 73, 15, 55, 28, 68)(21, 61, 36, 76, 25, 65, 39, 79, 23, 63, 38, 78, 32, 72, 40, 80, 24, 64, 37, 77) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 55)(6, 58)(7, 61)(8, 64)(9, 59)(10, 62)(11, 43)(12, 63)(13, 44)(14, 65)(15, 60)(16, 45)(17, 66)(18, 50)(19, 75)(20, 51)(21, 74)(22, 57)(23, 47)(24, 52)(25, 48)(26, 53)(27, 76)(28, 77)(29, 56)(30, 78)(31, 79)(32, 54)(33, 80)(34, 72)(35, 69)(36, 73)(37, 70)(38, 67)(39, 68)(40, 71) local type(s) :: { ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.675 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 40 f = 6 degree seq :: [ 20^4 ] E16.679 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {10, 10, 20}) Quotient :: loop Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^2, T1^2 * T2 * T1^-2 * T2^-1, T2^2 * T1 * T2^-2 * T1^-1, T2^-1 * T1^-3 * T2^-1 * T1^-5, (T2^-1 * T1^-1)^10, T2^20 ] Map:: non-degenerate R = (1, 41, 3, 43, 10, 50, 19, 59, 28, 68, 38, 78, 36, 76, 25, 65, 12, 52, 21, 61, 32, 72, 18, 58, 6, 46, 17, 57, 31, 71, 39, 79, 33, 73, 26, 66, 15, 55, 5, 45)(2, 42, 7, 47, 20, 60, 30, 70, 37, 77, 35, 75, 27, 67, 13, 53, 4, 44, 11, 51, 23, 63, 9, 49, 16, 56, 29, 69, 40, 80, 34, 74, 24, 64, 14, 54, 22, 62, 8, 48) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 51)(6, 56)(7, 59)(8, 43)(9, 57)(10, 60)(11, 58)(12, 44)(13, 61)(14, 45)(15, 62)(16, 68)(17, 70)(18, 47)(19, 69)(20, 71)(21, 48)(22, 72)(23, 50)(24, 52)(25, 54)(26, 53)(27, 55)(28, 77)(29, 79)(30, 78)(31, 80)(32, 63)(33, 64)(34, 66)(35, 65)(36, 67)(37, 73)(38, 74)(39, 75)(40, 76) local type(s) :: { ( 10^40 ) } Outer automorphisms :: reflexible Dual of E16.672 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 40 f = 8 degree seq :: [ 40^2 ] E16.680 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y2 * Y3^-1 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y1 * Y2^2 * Y3^-1 * Y1 * Y3^-1, Y3 * Y2^4 * Y1^-1, Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2^-1, Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, Y3^2 * Y2 * Y3^-2 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y1, Y2)^2, Y1^10, Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 41, 2, 42, 6, 46, 18, 58, 17, 57, 26, 66, 10, 50, 22, 62, 13, 53, 4, 44)(3, 43, 9, 49, 19, 59, 16, 56, 5, 45, 15, 55, 20, 60, 35, 75, 30, 70, 11, 51)(7, 47, 21, 61, 14, 54, 25, 65, 8, 48, 24, 64, 34, 74, 32, 72, 12, 52, 23, 63)(27, 67, 36, 76, 31, 71, 39, 79, 28, 68, 37, 77, 33, 73, 40, 80, 29, 69, 38, 78)(81, 121, 83, 123, 90, 130, 100, 140, 86, 126, 99, 139, 93, 133, 110, 150, 97, 137, 85, 125)(82, 122, 87, 127, 102, 142, 114, 154, 98, 138, 94, 134, 84, 124, 92, 132, 106, 146, 88, 128)(89, 129, 107, 147, 115, 155, 113, 153, 96, 136, 111, 151, 91, 131, 109, 149, 95, 135, 108, 148)(101, 141, 116, 156, 112, 152, 120, 160, 105, 145, 119, 159, 103, 143, 118, 158, 104, 144, 117, 157) L = (1, 84)(2, 81)(3, 91)(4, 93)(5, 96)(6, 82)(7, 103)(8, 105)(9, 83)(10, 106)(11, 110)(12, 112)(13, 102)(14, 101)(15, 85)(16, 99)(17, 98)(18, 86)(19, 89)(20, 95)(21, 87)(22, 90)(23, 92)(24, 88)(25, 94)(26, 97)(27, 118)(28, 119)(29, 120)(30, 115)(31, 116)(32, 114)(33, 117)(34, 104)(35, 100)(36, 107)(37, 108)(38, 109)(39, 111)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 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 E16.687 Graph:: bipartite v = 8 e = 80 f = 42 degree seq :: [ 20^8 ] E16.681 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, Y2^3 * Y1^-1 * Y2^-1 * Y1^-1, Y1^2 * Y2 * Y1^-2 * Y2^-1, Y1^2 * Y2 * Y1^2 * Y2 * Y1 * Y2^2 * Y1, Y2^-1 * Y1^-3 * Y2^-1 * Y1^-5, (Y3^-1 * Y1^-1)^10 ] Map:: R = (1, 41, 2, 42, 6, 46, 16, 56, 28, 68, 37, 77, 33, 73, 24, 64, 12, 52, 4, 44)(3, 43, 9, 49, 17, 57, 30, 70, 38, 78, 34, 74, 26, 66, 13, 53, 21, 61, 8, 48)(5, 45, 11, 51, 18, 58, 7, 47, 19, 59, 29, 69, 39, 79, 35, 75, 25, 65, 14, 54)(10, 50, 20, 60, 31, 71, 40, 80, 36, 76, 27, 67, 15, 55, 22, 62, 32, 72, 23, 63)(81, 121, 83, 123, 90, 130, 99, 139, 108, 148, 118, 158, 116, 156, 105, 145, 92, 132, 101, 141, 112, 152, 98, 138, 86, 126, 97, 137, 111, 151, 119, 159, 113, 153, 106, 146, 95, 135, 85, 125)(82, 122, 87, 127, 100, 140, 110, 150, 117, 157, 115, 155, 107, 147, 93, 133, 84, 124, 91, 131, 103, 143, 89, 129, 96, 136, 109, 149, 120, 160, 114, 154, 104, 144, 94, 134, 102, 142, 88, 128) L = (1, 83)(2, 87)(3, 90)(4, 91)(5, 81)(6, 97)(7, 100)(8, 82)(9, 96)(10, 99)(11, 103)(12, 101)(13, 84)(14, 102)(15, 85)(16, 109)(17, 111)(18, 86)(19, 108)(20, 110)(21, 112)(22, 88)(23, 89)(24, 94)(25, 92)(26, 95)(27, 93)(28, 118)(29, 120)(30, 117)(31, 119)(32, 98)(33, 106)(34, 104)(35, 107)(36, 105)(37, 115)(38, 116)(39, 113)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E16.685 Graph:: bipartite v = 6 e = 80 f = 44 degree seq :: [ 20^4, 40^2 ] E16.682 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2^-2)^2, Y1^-1 * Y2 * Y1^-3 * Y2, Y2^-1 * Y1^-2 * Y2^-3, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y1 * Y2^-1 * Y1^-2 * Y2 * Y1, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^10 ] Map:: R = (1, 41, 2, 42, 6, 46, 18, 58, 34, 74, 27, 67, 38, 78, 32, 72, 13, 53, 4, 44)(3, 43, 9, 49, 19, 59, 36, 76, 33, 73, 14, 54, 25, 65, 8, 48, 24, 64, 11, 51)(5, 45, 15, 55, 20, 60, 12, 52, 23, 63, 7, 47, 21, 61, 35, 75, 29, 69, 16, 56)(10, 50, 22, 62, 17, 57, 26, 66, 37, 77, 31, 71, 40, 80, 28, 68, 39, 79, 30, 70)(81, 121, 83, 123, 90, 130, 109, 149, 93, 133, 104, 144, 119, 159, 101, 141, 118, 158, 105, 145, 120, 160, 103, 143, 114, 154, 113, 153, 117, 157, 100, 140, 86, 126, 99, 139, 97, 137, 85, 125)(82, 122, 87, 127, 102, 142, 94, 134, 84, 124, 92, 132, 110, 150, 116, 156, 112, 152, 95, 135, 108, 148, 89, 129, 107, 147, 96, 136, 111, 151, 91, 131, 98, 138, 115, 155, 106, 146, 88, 128) L = (1, 83)(2, 87)(3, 90)(4, 92)(5, 81)(6, 99)(7, 102)(8, 82)(9, 107)(10, 109)(11, 98)(12, 110)(13, 104)(14, 84)(15, 108)(16, 111)(17, 85)(18, 115)(19, 97)(20, 86)(21, 118)(22, 94)(23, 114)(24, 119)(25, 120)(26, 88)(27, 96)(28, 89)(29, 93)(30, 116)(31, 91)(32, 95)(33, 117)(34, 113)(35, 106)(36, 112)(37, 100)(38, 105)(39, 101)(40, 103)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E16.684 Graph:: bipartite v = 6 e = 80 f = 44 degree seq :: [ 20^4, 40^2 ] E16.683 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^4 * Y1^-1, Y1^-1 * Y2^-1 * Y1^-3 * Y2^-1, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y1 * Y2^-1 * Y1^-2 * Y2 * Y1, Y1^5 * Y2^-1 * Y1 * Y2^-1, (Y3^-1 * Y1^-1)^10 ] Map:: R = (1, 41, 2, 42, 6, 46, 18, 58, 34, 74, 29, 69, 39, 79, 27, 67, 13, 53, 4, 44)(3, 43, 9, 49, 19, 59, 14, 54, 25, 65, 8, 48, 24, 64, 35, 75, 30, 70, 11, 51)(5, 45, 15, 55, 20, 60, 37, 77, 32, 72, 12, 52, 23, 63, 7, 47, 21, 61, 16, 56)(10, 50, 22, 62, 36, 76, 31, 71, 40, 80, 28, 68, 38, 78, 33, 73, 17, 57, 26, 66)(81, 121, 83, 123, 90, 130, 100, 140, 86, 126, 99, 139, 116, 156, 112, 152, 114, 154, 105, 145, 120, 160, 103, 143, 119, 159, 104, 144, 118, 158, 101, 141, 93, 133, 110, 150, 97, 137, 85, 125)(82, 122, 87, 127, 102, 142, 115, 155, 98, 138, 96, 136, 111, 151, 91, 131, 109, 149, 95, 135, 108, 148, 89, 129, 107, 147, 117, 157, 113, 153, 94, 134, 84, 124, 92, 132, 106, 146, 88, 128) L = (1, 83)(2, 87)(3, 90)(4, 92)(5, 81)(6, 99)(7, 102)(8, 82)(9, 107)(10, 100)(11, 109)(12, 106)(13, 110)(14, 84)(15, 108)(16, 111)(17, 85)(18, 96)(19, 116)(20, 86)(21, 93)(22, 115)(23, 119)(24, 118)(25, 120)(26, 88)(27, 117)(28, 89)(29, 95)(30, 97)(31, 91)(32, 114)(33, 94)(34, 105)(35, 98)(36, 112)(37, 113)(38, 101)(39, 104)(40, 103)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E16.686 Graph:: bipartite v = 6 e = 80 f = 44 degree seq :: [ 20^4, 40^2 ] E16.684 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (Y2^-1 * Y3^-1)^2, (R * Y3)^2, Y2^3 * Y3 * Y2^-1 * Y3, Y3^2 * Y2 * Y3^-2 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-2, Y3^3 * Y2^-1 * Y3^3 * Y2^-3, Y3^-1 * Y2 * Y3^-1 * Y2^7, (Y3^-1 * Y1^-1)^20 ] Map:: R = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(81, 121, 82, 122, 86, 126, 96, 136, 108, 148, 117, 157, 113, 153, 106, 146, 93, 133, 84, 124)(83, 123, 89, 129, 97, 137, 88, 128, 101, 141, 109, 149, 119, 159, 115, 155, 107, 147, 91, 131)(85, 125, 94, 134, 98, 138, 111, 151, 118, 158, 114, 154, 104, 144, 92, 132, 100, 140, 87, 127)(90, 130, 99, 139, 110, 150, 103, 143, 95, 135, 102, 142, 112, 152, 120, 160, 116, 156, 105, 145) L = (1, 83)(2, 87)(3, 90)(4, 92)(5, 81)(6, 97)(7, 99)(8, 82)(9, 84)(10, 104)(11, 106)(12, 105)(13, 107)(14, 103)(15, 85)(16, 94)(17, 110)(18, 86)(19, 91)(20, 93)(21, 95)(22, 88)(23, 89)(24, 113)(25, 115)(26, 114)(27, 116)(28, 101)(29, 96)(30, 100)(31, 102)(32, 98)(33, 119)(34, 120)(35, 117)(36, 118)(37, 111)(38, 108)(39, 112)(40, 109)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E16.682 Graph:: simple bipartite v = 44 e = 80 f = 6 degree seq :: [ 2^40, 20^4 ] E16.685 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^-3 * Y3^-1, Y2^-1 * Y3^4 * Y2^-1, Y3^2 * Y2 * Y3^-2 * Y2^-1, Y2 * Y3^-1 * Y2^-2 * Y3 * Y2, Y2^5 * Y3^-1 * Y2 * Y3^-1, Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^20 ] Map:: R = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(81, 121, 82, 122, 86, 126, 98, 138, 114, 154, 109, 149, 119, 159, 107, 147, 93, 133, 84, 124)(83, 123, 89, 129, 99, 139, 94, 134, 105, 145, 88, 128, 104, 144, 115, 155, 110, 150, 91, 131)(85, 125, 95, 135, 100, 140, 117, 157, 112, 152, 92, 132, 103, 143, 87, 127, 101, 141, 96, 136)(90, 130, 102, 142, 116, 156, 111, 151, 120, 160, 108, 148, 118, 158, 113, 153, 97, 137, 106, 146) L = (1, 83)(2, 87)(3, 90)(4, 92)(5, 81)(6, 99)(7, 102)(8, 82)(9, 107)(10, 100)(11, 109)(12, 106)(13, 110)(14, 84)(15, 108)(16, 111)(17, 85)(18, 96)(19, 116)(20, 86)(21, 93)(22, 115)(23, 119)(24, 118)(25, 120)(26, 88)(27, 117)(28, 89)(29, 95)(30, 97)(31, 91)(32, 114)(33, 94)(34, 105)(35, 98)(36, 112)(37, 113)(38, 101)(39, 104)(40, 103)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E16.681 Graph:: simple bipartite v = 44 e = 80 f = 6 degree seq :: [ 2^40, 20^4 ] E16.686 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2^-2 * Y3 * Y2^2, (Y3^-1 * Y2^-1 * Y3^-1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-4 * Y2^-1, Y3^2 * Y2 * Y3^-2 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2^-3, (Y3, Y2^-1)^2, (Y3^-1 * Y1^-1)^20 ] Map:: R = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(81, 121, 82, 122, 86, 126, 98, 138, 114, 154, 107, 147, 118, 158, 112, 152, 93, 133, 84, 124)(83, 123, 89, 129, 99, 139, 116, 156, 113, 153, 94, 134, 105, 145, 88, 128, 104, 144, 91, 131)(85, 125, 95, 135, 100, 140, 92, 132, 103, 143, 87, 127, 101, 141, 115, 155, 109, 149, 96, 136)(90, 130, 102, 142, 97, 137, 106, 146, 117, 157, 111, 151, 120, 160, 108, 148, 119, 159, 110, 150) L = (1, 83)(2, 87)(3, 90)(4, 92)(5, 81)(6, 99)(7, 102)(8, 82)(9, 107)(10, 109)(11, 98)(12, 110)(13, 104)(14, 84)(15, 108)(16, 111)(17, 85)(18, 115)(19, 97)(20, 86)(21, 118)(22, 94)(23, 114)(24, 119)(25, 120)(26, 88)(27, 96)(28, 89)(29, 93)(30, 116)(31, 91)(32, 95)(33, 117)(34, 113)(35, 106)(36, 112)(37, 100)(38, 105)(39, 101)(40, 103)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E16.683 Graph:: simple bipartite v = 44 e = 80 f = 6 degree seq :: [ 2^40, 20^4 ] E16.687 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1^2 * Y3^-1 * Y1^-2, Y1^-3 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-3, (Y3 * Y2^-1)^10, (Y3^-1 * Y1^-1)^10 ] Map:: R = (1, 41, 2, 42, 6, 46, 16, 56, 28, 68, 37, 77, 36, 76, 27, 67, 15, 55, 22, 62, 32, 72, 23, 63, 10, 50, 20, 60, 31, 71, 40, 80, 33, 73, 24, 64, 12, 52, 4, 44)(3, 43, 9, 49, 17, 57, 30, 70, 38, 78, 35, 75, 25, 65, 14, 54, 5, 45, 11, 51, 18, 58, 7, 47, 19, 59, 29, 69, 39, 79, 34, 74, 26, 66, 13, 53, 21, 61, 8, 48)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 90)(4, 91)(5, 81)(6, 97)(7, 100)(8, 82)(9, 96)(10, 99)(11, 103)(12, 101)(13, 84)(14, 102)(15, 85)(16, 109)(17, 111)(18, 86)(19, 108)(20, 110)(21, 112)(22, 88)(23, 89)(24, 94)(25, 92)(26, 95)(27, 93)(28, 118)(29, 120)(30, 117)(31, 119)(32, 98)(33, 106)(34, 104)(35, 107)(36, 105)(37, 114)(38, 113)(39, 116)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 20 ), ( 20^40 ) } Outer automorphisms :: reflexible Dual of E16.680 Graph:: simple bipartite v = 42 e = 80 f = 8 degree seq :: [ 2^40, 40^2 ] E16.688 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 10, 40}) Quotient :: edge Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^8, T2^5 * T1^4 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 26, 40, 25, 13, 5)(2, 7, 17, 31, 37, 22, 36, 32, 18, 8)(4, 10, 20, 34, 28, 14, 27, 39, 24, 12)(6, 15, 29, 38, 23, 11, 21, 35, 30, 16)(41, 42, 46, 54, 66, 62, 51, 44)(43, 47, 55, 67, 80, 76, 61, 50)(45, 48, 56, 68, 73, 77, 63, 52)(49, 57, 69, 79, 65, 72, 75, 60)(53, 58, 70, 74, 59, 71, 78, 64) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 80^8 ), ( 80^10 ) } Outer automorphisms :: reflexible Dual of E16.692 Transitivity :: ET+ Graph:: bipartite v = 9 e = 40 f = 1 degree seq :: [ 8^5, 10^4 ] E16.689 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 10, 40}) Quotient :: edge Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^-1, T1^10, (T1^-1 * T2^-1)^8 ] Map:: non-degenerate R = (1, 3, 9, 8, 2, 7, 17, 16, 6, 15, 25, 24, 14, 23, 33, 32, 22, 31, 39, 38, 30, 37, 40, 35, 27, 34, 36, 28, 19, 26, 29, 20, 11, 18, 21, 12, 4, 10, 13, 5)(41, 42, 46, 54, 62, 70, 67, 59, 51, 44)(43, 47, 55, 63, 71, 77, 74, 66, 58, 50)(45, 48, 56, 64, 72, 78, 75, 68, 60, 52)(49, 57, 65, 73, 79, 80, 76, 69, 61, 53) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 16^10 ), ( 16^40 ) } Outer automorphisms :: reflexible Dual of E16.693 Transitivity :: ET+ Graph:: bipartite v = 5 e = 40 f = 5 degree seq :: [ 10^4, 40 ] E16.690 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 10, 40}) Quotient :: edge Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-5, T2^8, T2^3 * T1^-2 * T2^-3 * T1^2, (T1^3 * T2^-1)^5 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 23, 13, 5)(2, 7, 17, 27, 36, 28, 18, 8)(4, 10, 20, 30, 37, 32, 22, 12)(6, 15, 25, 34, 40, 35, 26, 16)(11, 21, 31, 38, 39, 33, 24, 14)(41, 42, 46, 54, 52, 45, 48, 56, 64, 62, 53, 58, 66, 73, 72, 63, 68, 75, 79, 77, 69, 76, 80, 78, 70, 59, 67, 74, 71, 60, 49, 57, 65, 61, 50, 43, 47, 55, 51, 44) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^8 ), ( 20^40 ) } Outer automorphisms :: reflexible Dual of E16.691 Transitivity :: ET+ Graph:: bipartite v = 6 e = 40 f = 4 degree seq :: [ 8^5, 40 ] E16.691 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 10, 40}) Quotient :: loop Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^8, T2^5 * T1^4 ] Map:: non-degenerate R = (1, 41, 3, 43, 9, 49, 19, 59, 33, 73, 26, 66, 40, 80, 25, 65, 13, 53, 5, 45)(2, 42, 7, 47, 17, 57, 31, 71, 37, 77, 22, 62, 36, 76, 32, 72, 18, 58, 8, 48)(4, 44, 10, 50, 20, 60, 34, 74, 28, 68, 14, 54, 27, 67, 39, 79, 24, 64, 12, 52)(6, 46, 15, 55, 29, 69, 38, 78, 23, 63, 11, 51, 21, 61, 35, 75, 30, 70, 16, 56) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 54)(7, 55)(8, 56)(9, 57)(10, 43)(11, 44)(12, 45)(13, 58)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 72)(26, 62)(27, 80)(28, 73)(29, 79)(30, 74)(31, 78)(32, 75)(33, 77)(34, 59)(35, 60)(36, 61)(37, 63)(38, 64)(39, 65)(40, 76) local type(s) :: { ( 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 E16.690 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 40 f = 6 degree seq :: [ 20^4 ] E16.692 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 10, 40}) Quotient :: loop Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^-1, T1^10, (T1^-1 * T2^-1)^8 ] Map:: non-degenerate R = (1, 41, 3, 43, 9, 49, 8, 48, 2, 42, 7, 47, 17, 57, 16, 56, 6, 46, 15, 55, 25, 65, 24, 64, 14, 54, 23, 63, 33, 73, 32, 72, 22, 62, 31, 71, 39, 79, 38, 78, 30, 70, 37, 77, 40, 80, 35, 75, 27, 67, 34, 74, 36, 76, 28, 68, 19, 59, 26, 66, 29, 69, 20, 60, 11, 51, 18, 58, 21, 61, 12, 52, 4, 44, 10, 50, 13, 53, 5, 45) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 54)(7, 55)(8, 56)(9, 57)(10, 43)(11, 44)(12, 45)(13, 49)(14, 62)(15, 63)(16, 64)(17, 65)(18, 50)(19, 51)(20, 52)(21, 53)(22, 70)(23, 71)(24, 72)(25, 73)(26, 58)(27, 59)(28, 60)(29, 61)(30, 67)(31, 77)(32, 78)(33, 79)(34, 66)(35, 68)(36, 69)(37, 74)(38, 75)(39, 80)(40, 76) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E16.688 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 40 f = 9 degree seq :: [ 80 ] E16.693 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 10, 40}) Quotient :: loop Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-5, T2^8, T2^3 * T1^-2 * T2^-3 * T1^2, (T1^3 * T2^-1)^5 ] Map:: non-degenerate R = (1, 41, 3, 43, 9, 49, 19, 59, 29, 69, 23, 63, 13, 53, 5, 45)(2, 42, 7, 47, 17, 57, 27, 67, 36, 76, 28, 68, 18, 58, 8, 48)(4, 44, 10, 50, 20, 60, 30, 70, 37, 77, 32, 72, 22, 62, 12, 52)(6, 46, 15, 55, 25, 65, 34, 74, 40, 80, 35, 75, 26, 66, 16, 56)(11, 51, 21, 61, 31, 71, 38, 78, 39, 79, 33, 73, 24, 64, 14, 54) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 54)(7, 55)(8, 56)(9, 57)(10, 43)(11, 44)(12, 45)(13, 58)(14, 52)(15, 51)(16, 64)(17, 65)(18, 66)(19, 67)(20, 49)(21, 50)(22, 53)(23, 68)(24, 62)(25, 61)(26, 73)(27, 74)(28, 75)(29, 76)(30, 59)(31, 60)(32, 63)(33, 72)(34, 71)(35, 79)(36, 80)(37, 69)(38, 70)(39, 77)(40, 78) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E16.689 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 40 f = 5 degree seq :: [ 16^5 ] E16.694 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 10, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^8, Y1^2 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-3, Y1^2 * Y2 * Y3^-1 * Y1 * Y2^4, Y2^10, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^2 * Y1^2 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 26, 66, 22, 62, 11, 51, 4, 44)(3, 43, 7, 47, 15, 55, 27, 67, 40, 80, 36, 76, 21, 61, 10, 50)(5, 45, 8, 48, 16, 56, 28, 68, 33, 73, 37, 77, 23, 63, 12, 52)(9, 49, 17, 57, 29, 69, 39, 79, 25, 65, 32, 72, 35, 75, 20, 60)(13, 53, 18, 58, 30, 70, 34, 74, 19, 59, 31, 71, 38, 78, 24, 64)(81, 121, 83, 123, 89, 129, 99, 139, 113, 153, 106, 146, 120, 160, 105, 145, 93, 133, 85, 125)(82, 122, 87, 127, 97, 137, 111, 151, 117, 157, 102, 142, 116, 156, 112, 152, 98, 138, 88, 128)(84, 124, 90, 130, 100, 140, 114, 154, 108, 148, 94, 134, 107, 147, 119, 159, 104, 144, 92, 132)(86, 126, 95, 135, 109, 149, 118, 158, 103, 143, 91, 131, 101, 141, 115, 155, 110, 150, 96, 136) L = (1, 84)(2, 81)(3, 90)(4, 91)(5, 92)(6, 82)(7, 83)(8, 85)(9, 100)(10, 101)(11, 102)(12, 103)(13, 104)(14, 86)(15, 87)(16, 88)(17, 89)(18, 93)(19, 114)(20, 115)(21, 116)(22, 106)(23, 117)(24, 118)(25, 119)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 105)(33, 108)(34, 110)(35, 112)(36, 120)(37, 113)(38, 111)(39, 109)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ), ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ) } Outer automorphisms :: reflexible Dual of E16.697 Graph:: bipartite v = 9 e = 80 f = 41 degree seq :: [ 16^5, 20^4 ] E16.695 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 10, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^4 * Y1^-1, Y1^10, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 22, 62, 30, 70, 27, 67, 19, 59, 11, 51, 4, 44)(3, 43, 7, 47, 15, 55, 23, 63, 31, 71, 37, 77, 34, 74, 26, 66, 18, 58, 10, 50)(5, 45, 8, 48, 16, 56, 24, 64, 32, 72, 38, 78, 35, 75, 28, 68, 20, 60, 12, 52)(9, 49, 17, 57, 25, 65, 33, 73, 39, 79, 40, 80, 36, 76, 29, 69, 21, 61, 13, 53)(81, 121, 83, 123, 89, 129, 88, 128, 82, 122, 87, 127, 97, 137, 96, 136, 86, 126, 95, 135, 105, 145, 104, 144, 94, 134, 103, 143, 113, 153, 112, 152, 102, 142, 111, 151, 119, 159, 118, 158, 110, 150, 117, 157, 120, 160, 115, 155, 107, 147, 114, 154, 116, 156, 108, 148, 99, 139, 106, 146, 109, 149, 100, 140, 91, 131, 98, 138, 101, 141, 92, 132, 84, 124, 90, 130, 93, 133, 85, 125) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 95)(7, 97)(8, 82)(9, 88)(10, 93)(11, 98)(12, 84)(13, 85)(14, 103)(15, 105)(16, 86)(17, 96)(18, 101)(19, 106)(20, 91)(21, 92)(22, 111)(23, 113)(24, 94)(25, 104)(26, 109)(27, 114)(28, 99)(29, 100)(30, 117)(31, 119)(32, 102)(33, 112)(34, 116)(35, 107)(36, 108)(37, 120)(38, 110)(39, 118)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E16.696 Graph:: bipartite v = 5 e = 80 f = 45 degree seq :: [ 20^4, 80 ] E16.696 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 10, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3^5 * Y2^-1, Y2^8, (Y2^-1 * Y3^-3)^5, (Y3^-1 * Y1^-1)^40 ] Map:: R = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(81, 121, 82, 122, 86, 126, 94, 134, 104, 144, 101, 141, 91, 131, 84, 124)(83, 123, 87, 127, 95, 135, 105, 145, 113, 153, 110, 150, 100, 140, 90, 130)(85, 125, 88, 128, 96, 136, 106, 146, 114, 154, 111, 151, 102, 142, 92, 132)(89, 129, 97, 137, 107, 147, 115, 155, 119, 159, 117, 157, 109, 149, 99, 139)(93, 133, 98, 138, 108, 148, 116, 156, 120, 160, 118, 158, 112, 152, 103, 143) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 95)(7, 97)(8, 82)(9, 98)(10, 99)(11, 100)(12, 84)(13, 85)(14, 105)(15, 107)(16, 86)(17, 108)(18, 88)(19, 93)(20, 109)(21, 110)(22, 91)(23, 92)(24, 113)(25, 115)(26, 94)(27, 116)(28, 96)(29, 103)(30, 117)(31, 101)(32, 102)(33, 119)(34, 104)(35, 120)(36, 106)(37, 112)(38, 111)(39, 118)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 80 ), ( 20, 80, 20, 80, 20, 80, 20, 80, 20, 80, 20, 80, 20, 80, 20, 80 ) } Outer automorphisms :: reflexible Dual of E16.695 Graph:: simple bipartite v = 45 e = 80 f = 5 degree seq :: [ 2^40, 16^5 ] E16.697 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 10, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-5, Y3^8, Y3^2 * Y1^-2 * Y3^-3 * Y1^2 * Y3, Y3^-2 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1 * Y3^-1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 12, 52, 5, 45, 8, 48, 16, 56, 24, 64, 22, 62, 13, 53, 18, 58, 26, 66, 33, 73, 32, 72, 23, 63, 28, 68, 35, 75, 39, 79, 37, 77, 29, 69, 36, 76, 40, 80, 38, 78, 30, 70, 19, 59, 27, 67, 34, 74, 31, 71, 20, 60, 9, 49, 17, 57, 25, 65, 21, 61, 10, 50, 3, 43, 7, 47, 15, 55, 11, 51, 4, 44)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 95)(7, 97)(8, 82)(9, 99)(10, 100)(11, 101)(12, 84)(13, 85)(14, 91)(15, 105)(16, 86)(17, 107)(18, 88)(19, 109)(20, 110)(21, 111)(22, 92)(23, 93)(24, 94)(25, 114)(26, 96)(27, 116)(28, 98)(29, 103)(30, 117)(31, 118)(32, 102)(33, 104)(34, 120)(35, 106)(36, 108)(37, 112)(38, 119)(39, 113)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 16, 20 ), ( 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20 ) } Outer automorphisms :: reflexible Dual of E16.694 Graph:: bipartite v = 41 e = 80 f = 9 degree seq :: [ 2^40, 80 ] E16.698 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 10, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), Y3 * Y2^-5, Y3^8, Y1^8, Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^3 * Y2 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 24, 64, 22, 62, 11, 51, 4, 44)(3, 43, 7, 47, 15, 55, 25, 65, 33, 73, 31, 71, 21, 61, 10, 50)(5, 45, 8, 48, 16, 56, 26, 66, 34, 74, 32, 72, 23, 63, 12, 52)(9, 49, 17, 57, 27, 67, 35, 75, 39, 79, 38, 78, 30, 70, 20, 60)(13, 53, 18, 58, 28, 68, 36, 76, 40, 80, 37, 77, 29, 69, 19, 59)(81, 121, 83, 123, 89, 129, 99, 139, 92, 132, 84, 124, 90, 130, 100, 140, 109, 149, 103, 143, 91, 131, 101, 141, 110, 150, 117, 157, 112, 152, 102, 142, 111, 151, 118, 158, 120, 160, 114, 154, 104, 144, 113, 153, 119, 159, 116, 156, 106, 146, 94, 134, 105, 145, 115, 155, 108, 148, 96, 136, 86, 126, 95, 135, 107, 147, 98, 138, 88, 128, 82, 122, 87, 127, 97, 137, 93, 133, 85, 125) L = (1, 84)(2, 81)(3, 90)(4, 91)(5, 92)(6, 82)(7, 83)(8, 85)(9, 100)(10, 101)(11, 102)(12, 103)(13, 99)(14, 86)(15, 87)(16, 88)(17, 89)(18, 93)(19, 109)(20, 110)(21, 111)(22, 104)(23, 112)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 117)(30, 118)(31, 113)(32, 114)(33, 105)(34, 106)(35, 107)(36, 108)(37, 120)(38, 119)(39, 115)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 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 E16.699 Graph:: bipartite v = 6 e = 80 f = 44 degree seq :: [ 16^5, 80 ] E16.699 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 10, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y1^-1 * Y3^4, (R * Y2 * Y3^-1)^2, Y1^10, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^40 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 22, 62, 30, 70, 27, 67, 19, 59, 11, 51, 4, 44)(3, 43, 7, 47, 15, 55, 23, 63, 31, 71, 37, 77, 34, 74, 26, 66, 18, 58, 10, 50)(5, 45, 8, 48, 16, 56, 24, 64, 32, 72, 38, 78, 35, 75, 28, 68, 20, 60, 12, 52)(9, 49, 17, 57, 25, 65, 33, 73, 39, 79, 40, 80, 36, 76, 29, 69, 21, 61, 13, 53)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 95)(7, 97)(8, 82)(9, 88)(10, 93)(11, 98)(12, 84)(13, 85)(14, 103)(15, 105)(16, 86)(17, 96)(18, 101)(19, 106)(20, 91)(21, 92)(22, 111)(23, 113)(24, 94)(25, 104)(26, 109)(27, 114)(28, 99)(29, 100)(30, 117)(31, 119)(32, 102)(33, 112)(34, 116)(35, 107)(36, 108)(37, 120)(38, 110)(39, 118)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 16, 80 ), ( 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80 ) } Outer automorphisms :: reflexible Dual of E16.698 Graph:: simple bipartite v = 44 e = 80 f = 6 degree seq :: [ 2^40, 20^4 ] E16.700 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 40, 40}) Quotient :: edge Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-5, T2^-8 * T1^-2, T2^-1 * T1 * T2^-3 * T1 * T2^-4 * T1, T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 38, 31, 21, 11, 20, 30, 40, 37, 27, 17, 8, 2, 7, 16, 26, 36, 32, 22, 12, 4, 10, 19, 29, 39, 35, 25, 15, 6, 14, 24, 34, 33, 23, 13, 5)(41, 42, 46, 51, 44)(43, 47, 54, 60, 50)(45, 48, 55, 61, 52)(49, 56, 64, 70, 59)(53, 57, 65, 71, 62)(58, 66, 74, 80, 69)(63, 67, 75, 78, 72)(68, 76, 73, 77, 79) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 80^5 ), ( 80^40 ) } Outer automorphisms :: reflexible Dual of E16.705 Transitivity :: ET+ Graph:: bipartite v = 9 e = 40 f = 1 degree seq :: [ 5^8, 40 ] E16.701 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 40, 40}) Quotient :: edge Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^8 * T1, (T1^-1 * T2^-1)^40 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 32, 22, 12, 4, 10, 19, 29, 37, 39, 31, 21, 11, 20, 30, 38, 40, 35, 25, 15, 6, 14, 24, 34, 36, 27, 17, 8, 2, 7, 16, 26, 33, 23, 13, 5)(41, 42, 46, 51, 44)(43, 47, 54, 60, 50)(45, 48, 55, 61, 52)(49, 56, 64, 70, 59)(53, 57, 65, 71, 62)(58, 66, 74, 78, 69)(63, 67, 75, 79, 72)(68, 73, 76, 80, 77) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 80^5 ), ( 80^40 ) } Outer automorphisms :: reflexible Dual of E16.704 Transitivity :: ET+ Graph:: bipartite v = 9 e = 40 f = 1 degree seq :: [ 5^8, 40 ] E16.702 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 40, 40}) Quotient :: edge Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^8 * T1^-1, (T1^-1 * T2^-1)^40 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 27, 17, 8, 2, 7, 16, 26, 36, 35, 25, 15, 6, 14, 24, 34, 40, 38, 31, 21, 11, 20, 30, 37, 39, 32, 22, 12, 4, 10, 19, 29, 33, 23, 13, 5)(41, 42, 46, 51, 44)(43, 47, 54, 60, 50)(45, 48, 55, 61, 52)(49, 56, 64, 70, 59)(53, 57, 65, 71, 62)(58, 66, 74, 77, 69)(63, 67, 75, 78, 72)(68, 76, 80, 79, 73) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 80^5 ), ( 80^40 ) } Outer automorphisms :: reflexible Dual of E16.706 Transitivity :: ET+ Graph:: bipartite v = 9 e = 40 f = 1 degree seq :: [ 5^8, 40 ] E16.703 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 40, 40}) Quotient :: edge Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T1^-1 * T2^5 * T1^-1 * T2, T1^-3 * T2 * T1^-4, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1^-3)^4 ] Map:: non-degenerate R = (1, 3, 9, 19, 30, 16, 6, 15, 29, 40, 34, 22, 26, 37, 36, 24, 12, 4, 10, 20, 32, 18, 8, 2, 7, 17, 31, 39, 28, 14, 27, 38, 35, 23, 11, 21, 33, 25, 13, 5)(41, 42, 46, 54, 66, 61, 50, 43, 47, 55, 67, 77, 73, 60, 49, 57, 69, 78, 76, 65, 72, 59, 71, 80, 75, 64, 53, 58, 70, 79, 74, 63, 52, 45, 48, 56, 68, 62, 51, 44) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10^40 ) } Outer automorphisms :: reflexible Dual of E16.707 Transitivity :: ET+ Graph:: bipartite v = 2 e = 40 f = 8 degree seq :: [ 40^2 ] E16.704 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 40, 40}) Quotient :: loop Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-5, T2^-8 * T1^-2, T2^-1 * T1 * T2^-3 * T1 * T2^-4 * T1, T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 41, 3, 43, 9, 49, 18, 58, 28, 68, 38, 78, 31, 71, 21, 61, 11, 51, 20, 60, 30, 70, 40, 80, 37, 77, 27, 67, 17, 57, 8, 48, 2, 42, 7, 47, 16, 56, 26, 66, 36, 76, 32, 72, 22, 62, 12, 52, 4, 44, 10, 50, 19, 59, 29, 69, 39, 79, 35, 75, 25, 65, 15, 55, 6, 46, 14, 54, 24, 64, 34, 74, 33, 73, 23, 63, 13, 53, 5, 45) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 51)(7, 54)(8, 55)(9, 56)(10, 43)(11, 44)(12, 45)(13, 57)(14, 60)(15, 61)(16, 64)(17, 65)(18, 66)(19, 49)(20, 50)(21, 52)(22, 53)(23, 67)(24, 70)(25, 71)(26, 74)(27, 75)(28, 76)(29, 58)(30, 59)(31, 62)(32, 63)(33, 77)(34, 80)(35, 78)(36, 73)(37, 79)(38, 72)(39, 68)(40, 69) local type(s) :: { ( 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40 ) } Outer automorphisms :: reflexible Dual of E16.701 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 40 f = 9 degree seq :: [ 80 ] E16.705 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 40, 40}) Quotient :: loop Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^8 * T1, (T1^-1 * T2^-1)^40 ] Map:: non-degenerate R = (1, 41, 3, 43, 9, 49, 18, 58, 28, 68, 32, 72, 22, 62, 12, 52, 4, 44, 10, 50, 19, 59, 29, 69, 37, 77, 39, 79, 31, 71, 21, 61, 11, 51, 20, 60, 30, 70, 38, 78, 40, 80, 35, 75, 25, 65, 15, 55, 6, 46, 14, 54, 24, 64, 34, 74, 36, 76, 27, 67, 17, 57, 8, 48, 2, 42, 7, 47, 16, 56, 26, 66, 33, 73, 23, 63, 13, 53, 5, 45) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 51)(7, 54)(8, 55)(9, 56)(10, 43)(11, 44)(12, 45)(13, 57)(14, 60)(15, 61)(16, 64)(17, 65)(18, 66)(19, 49)(20, 50)(21, 52)(22, 53)(23, 67)(24, 70)(25, 71)(26, 74)(27, 75)(28, 73)(29, 58)(30, 59)(31, 62)(32, 63)(33, 76)(34, 78)(35, 79)(36, 80)(37, 68)(38, 69)(39, 72)(40, 77) local type(s) :: { ( 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40 ) } Outer automorphisms :: reflexible Dual of E16.700 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 40 f = 9 degree seq :: [ 80 ] E16.706 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 40, 40}) Quotient :: loop Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^8 * T1^-1, (T1^-1 * T2^-1)^40 ] Map:: non-degenerate R = (1, 41, 3, 43, 9, 49, 18, 58, 28, 68, 27, 67, 17, 57, 8, 48, 2, 42, 7, 47, 16, 56, 26, 66, 36, 76, 35, 75, 25, 65, 15, 55, 6, 46, 14, 54, 24, 64, 34, 74, 40, 80, 38, 78, 31, 71, 21, 61, 11, 51, 20, 60, 30, 70, 37, 77, 39, 79, 32, 72, 22, 62, 12, 52, 4, 44, 10, 50, 19, 59, 29, 69, 33, 73, 23, 63, 13, 53, 5, 45) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 51)(7, 54)(8, 55)(9, 56)(10, 43)(11, 44)(12, 45)(13, 57)(14, 60)(15, 61)(16, 64)(17, 65)(18, 66)(19, 49)(20, 50)(21, 52)(22, 53)(23, 67)(24, 70)(25, 71)(26, 74)(27, 75)(28, 76)(29, 58)(30, 59)(31, 62)(32, 63)(33, 68)(34, 77)(35, 78)(36, 80)(37, 69)(38, 72)(39, 73)(40, 79) local type(s) :: { ( 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40, 5, 40 ) } Outer automorphisms :: reflexible Dual of E16.702 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 40 f = 9 degree seq :: [ 80 ] E16.707 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 40, 40}) Quotient :: loop Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-5, T2^5, T2^-2 * T1^-8, T1^2 * T2^-2 * T1^-1 * T2^-1 * T1^-2 * T2^-2 * T1, T1^5 * T2^-1 * T1^5 * T2^-1 * T1^5 * T2^-1 * T1^5 * T2^-1 * T1^5 * T2^-1 * T1^5 * T2^-1 * T1^5 * T2^-1 * T1^5 * T2^-1 * T1^5 * T2^-1 * T1^5 * T2^-1 * T1^5 * T2^-1 * T1^5 * T2^-1 * T1^4 * T2^-2 ] Map:: non-degenerate R = (1, 41, 3, 43, 9, 49, 13, 53, 5, 45)(2, 42, 7, 47, 17, 57, 18, 58, 8, 48)(4, 44, 10, 50, 19, 59, 23, 63, 12, 52)(6, 46, 15, 55, 27, 67, 28, 68, 16, 56)(11, 51, 20, 60, 29, 69, 33, 73, 22, 62)(14, 54, 25, 65, 37, 77, 38, 78, 26, 66)(21, 61, 30, 70, 39, 79, 34, 74, 32, 72)(24, 64, 35, 75, 31, 71, 40, 80, 36, 76) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 54)(7, 55)(8, 56)(9, 57)(10, 43)(11, 44)(12, 45)(13, 58)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 59)(30, 60)(31, 61)(32, 62)(33, 63)(34, 73)(35, 72)(36, 79)(37, 71)(38, 80)(39, 69)(40, 70) local type(s) :: { ( 40^10 ) } Outer automorphisms :: reflexible Dual of E16.703 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 40 f = 2 degree seq :: [ 10^8 ] E16.708 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y3, Y1^-1 * Y3^-1, Y3 * Y2 * Y1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^5, Y2^-2 * Y3 * Y2^-6 * Y1^-1, Y3^10, Y1 * Y2^-1 * Y1 * Y2^-3 * Y3^-1 * Y2^-4, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 41, 2, 42, 6, 46, 11, 51, 4, 44)(3, 43, 7, 47, 14, 54, 20, 60, 10, 50)(5, 45, 8, 48, 15, 55, 21, 61, 12, 52)(9, 49, 16, 56, 24, 64, 30, 70, 19, 59)(13, 53, 17, 57, 25, 65, 31, 71, 22, 62)(18, 58, 26, 66, 34, 74, 40, 80, 29, 69)(23, 63, 27, 67, 35, 75, 38, 78, 32, 72)(28, 68, 36, 76, 33, 73, 37, 77, 39, 79)(81, 121, 83, 123, 89, 129, 98, 138, 108, 148, 118, 158, 111, 151, 101, 141, 91, 131, 100, 140, 110, 150, 120, 160, 117, 157, 107, 147, 97, 137, 88, 128, 82, 122, 87, 127, 96, 136, 106, 146, 116, 156, 112, 152, 102, 142, 92, 132, 84, 124, 90, 130, 99, 139, 109, 149, 119, 159, 115, 155, 105, 145, 95, 135, 86, 126, 94, 134, 104, 144, 114, 154, 113, 153, 103, 143, 93, 133, 85, 125) L = (1, 84)(2, 81)(3, 90)(4, 91)(5, 92)(6, 82)(7, 83)(8, 85)(9, 99)(10, 100)(11, 86)(12, 101)(13, 102)(14, 87)(15, 88)(16, 89)(17, 93)(18, 109)(19, 110)(20, 94)(21, 95)(22, 111)(23, 112)(24, 96)(25, 97)(26, 98)(27, 103)(28, 119)(29, 120)(30, 104)(31, 105)(32, 118)(33, 116)(34, 106)(35, 107)(36, 108)(37, 113)(38, 115)(39, 117)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ), ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ) } Outer automorphisms :: reflexible Dual of E16.714 Graph:: bipartite v = 9 e = 80 f = 41 degree seq :: [ 10^8, 80 ] E16.709 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3^5, Y1^5, Y3 * Y2^8, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 41, 2, 42, 6, 46, 11, 51, 4, 44)(3, 43, 7, 47, 14, 54, 20, 60, 10, 50)(5, 45, 8, 48, 15, 55, 21, 61, 12, 52)(9, 49, 16, 56, 24, 64, 30, 70, 19, 59)(13, 53, 17, 57, 25, 65, 31, 71, 22, 62)(18, 58, 26, 66, 34, 74, 37, 77, 29, 69)(23, 63, 27, 67, 35, 75, 38, 78, 32, 72)(28, 68, 36, 76, 40, 80, 39, 79, 33, 73)(81, 121, 83, 123, 89, 129, 98, 138, 108, 148, 107, 147, 97, 137, 88, 128, 82, 122, 87, 127, 96, 136, 106, 146, 116, 156, 115, 155, 105, 145, 95, 135, 86, 126, 94, 134, 104, 144, 114, 154, 120, 160, 118, 158, 111, 151, 101, 141, 91, 131, 100, 140, 110, 150, 117, 157, 119, 159, 112, 152, 102, 142, 92, 132, 84, 124, 90, 130, 99, 139, 109, 149, 113, 153, 103, 143, 93, 133, 85, 125) L = (1, 84)(2, 81)(3, 90)(4, 91)(5, 92)(6, 82)(7, 83)(8, 85)(9, 99)(10, 100)(11, 86)(12, 101)(13, 102)(14, 87)(15, 88)(16, 89)(17, 93)(18, 109)(19, 110)(20, 94)(21, 95)(22, 111)(23, 112)(24, 96)(25, 97)(26, 98)(27, 103)(28, 113)(29, 117)(30, 104)(31, 105)(32, 118)(33, 119)(34, 106)(35, 107)(36, 108)(37, 114)(38, 115)(39, 120)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ), ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ) } Outer automorphisms :: reflexible Dual of E16.715 Graph:: bipartite v = 9 e = 80 f = 41 degree seq :: [ 10^8, 80 ] E16.710 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y1^5, Y2^8 * Y1, Y2^3 * Y3 * Y1^-1 * Y2^-3 * Y3^-2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 41, 2, 42, 6, 46, 11, 51, 4, 44)(3, 43, 7, 47, 14, 54, 20, 60, 10, 50)(5, 45, 8, 48, 15, 55, 21, 61, 12, 52)(9, 49, 16, 56, 24, 64, 30, 70, 19, 59)(13, 53, 17, 57, 25, 65, 31, 71, 22, 62)(18, 58, 26, 66, 34, 74, 38, 78, 29, 69)(23, 63, 27, 67, 35, 75, 39, 79, 32, 72)(28, 68, 33, 73, 36, 76, 40, 80, 37, 77)(81, 121, 83, 123, 89, 129, 98, 138, 108, 148, 112, 152, 102, 142, 92, 132, 84, 124, 90, 130, 99, 139, 109, 149, 117, 157, 119, 159, 111, 151, 101, 141, 91, 131, 100, 140, 110, 150, 118, 158, 120, 160, 115, 155, 105, 145, 95, 135, 86, 126, 94, 134, 104, 144, 114, 154, 116, 156, 107, 147, 97, 137, 88, 128, 82, 122, 87, 127, 96, 136, 106, 146, 113, 153, 103, 143, 93, 133, 85, 125) L = (1, 84)(2, 81)(3, 90)(4, 91)(5, 92)(6, 82)(7, 83)(8, 85)(9, 99)(10, 100)(11, 86)(12, 101)(13, 102)(14, 87)(15, 88)(16, 89)(17, 93)(18, 109)(19, 110)(20, 94)(21, 95)(22, 111)(23, 112)(24, 96)(25, 97)(26, 98)(27, 103)(28, 117)(29, 118)(30, 104)(31, 105)(32, 119)(33, 108)(34, 106)(35, 107)(36, 113)(37, 120)(38, 114)(39, 115)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ), ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ) } Outer automorphisms :: reflexible Dual of E16.713 Graph:: bipartite v = 9 e = 80 f = 41 degree seq :: [ 10^8, 80 ] E16.711 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2 * Y1^-1 * Y2 * Y1^-5, Y2^6 * Y1^-1 * Y2, (Y3^-1 * Y1^-1)^5 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 26, 66, 20, 60, 9, 49, 17, 57, 29, 69, 38, 78, 36, 76, 25, 65, 32, 72, 40, 80, 34, 74, 23, 63, 12, 52, 5, 45, 8, 48, 16, 56, 28, 68, 21, 61, 10, 50, 3, 43, 7, 47, 15, 55, 27, 67, 37, 77, 33, 73, 19, 59, 31, 71, 39, 79, 35, 75, 24, 64, 13, 53, 18, 58, 30, 70, 22, 62, 11, 51, 4, 44)(81, 121, 83, 123, 89, 129, 99, 139, 112, 152, 98, 138, 88, 128, 82, 122, 87, 127, 97, 137, 111, 151, 120, 160, 110, 150, 96, 136, 86, 126, 95, 135, 109, 149, 119, 159, 114, 154, 102, 142, 108, 148, 94, 134, 107, 147, 118, 158, 115, 155, 103, 143, 91, 131, 101, 141, 106, 146, 117, 157, 116, 156, 104, 144, 92, 132, 84, 124, 90, 130, 100, 140, 113, 153, 105, 145, 93, 133, 85, 125) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 95)(7, 97)(8, 82)(9, 99)(10, 100)(11, 101)(12, 84)(13, 85)(14, 107)(15, 109)(16, 86)(17, 111)(18, 88)(19, 112)(20, 113)(21, 106)(22, 108)(23, 91)(24, 92)(25, 93)(26, 117)(27, 118)(28, 94)(29, 119)(30, 96)(31, 120)(32, 98)(33, 105)(34, 102)(35, 103)(36, 104)(37, 116)(38, 115)(39, 114)(40, 110)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.712 Graph:: bipartite v = 2 e = 80 f = 48 degree seq :: [ 80^2 ] E16.712 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2), (R * Y2)^2, Y2^-5, Y2^5, Y3^8 * Y2^-2, Y2^-1 * Y3^-5 * Y2^-1 * Y3^-5 * Y2^-1 * Y3^-5 * Y2^-1 * Y3^-5 * Y2^-1 * Y3^-5 * Y2^-1 * Y3^-5 * Y2^-1 * Y3^-5 * Y2^-1 * Y3^-5 * Y2^-1 * Y3^-5 * Y2^-1 * Y3^-5 * Y2^-1 * Y3^-5 * Y2^-1 * Y3^-5 * Y2^-1 * Y3^-4 * Y2^-1, (Y3^-1 * Y1^-1)^40 ] Map:: R = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(81, 121, 82, 122, 86, 126, 91, 131, 84, 124)(83, 123, 87, 127, 94, 134, 100, 140, 90, 130)(85, 125, 88, 128, 95, 135, 101, 141, 92, 132)(89, 129, 96, 136, 104, 144, 110, 150, 99, 139)(93, 133, 97, 137, 105, 145, 111, 151, 102, 142)(98, 138, 106, 146, 114, 154, 118, 158, 109, 149)(103, 143, 107, 147, 115, 155, 119, 159, 112, 152)(108, 148, 116, 156, 120, 160, 113, 153, 117, 157) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 94)(7, 96)(8, 82)(9, 98)(10, 99)(11, 100)(12, 84)(13, 85)(14, 104)(15, 86)(16, 106)(17, 88)(18, 108)(19, 109)(20, 110)(21, 91)(22, 92)(23, 93)(24, 114)(25, 95)(26, 116)(27, 97)(28, 115)(29, 117)(30, 118)(31, 101)(32, 102)(33, 103)(34, 120)(35, 105)(36, 119)(37, 107)(38, 113)(39, 111)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 80, 80 ), ( 80^10 ) } Outer automorphisms :: reflexible Dual of E16.711 Graph:: simple bipartite v = 48 e = 80 f = 2 degree seq :: [ 2^40, 10^8 ] E16.713 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, Y3^5, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^-8, (Y3 * Y2^-1)^5 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 24, 64, 34, 74, 33, 73, 23, 63, 13, 53, 18, 58, 28, 68, 38, 78, 40, 80, 30, 70, 20, 60, 10, 50, 3, 43, 7, 47, 15, 55, 25, 65, 35, 75, 32, 72, 22, 62, 12, 52, 5, 45, 8, 48, 16, 56, 26, 66, 36, 76, 39, 79, 29, 69, 19, 59, 9, 49, 17, 57, 27, 67, 37, 77, 31, 71, 21, 61, 11, 51, 4, 44)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 95)(7, 97)(8, 82)(9, 93)(10, 99)(11, 100)(12, 84)(13, 85)(14, 105)(15, 107)(16, 86)(17, 98)(18, 88)(19, 103)(20, 109)(21, 110)(22, 91)(23, 92)(24, 115)(25, 117)(26, 94)(27, 108)(28, 96)(29, 113)(30, 119)(31, 120)(32, 101)(33, 102)(34, 112)(35, 111)(36, 104)(37, 118)(38, 106)(39, 114)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 10, 80 ), ( 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80 ) } Outer automorphisms :: reflexible Dual of E16.710 Graph:: bipartite v = 41 e = 80 f = 9 degree seq :: [ 2^40, 80 ] E16.714 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^5, (R * Y2 * Y3^-1)^2, Y3 * Y1^8, (Y3 * Y2^-1)^5, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 24, 64, 32, 72, 22, 62, 12, 52, 5, 45, 8, 48, 16, 56, 26, 66, 34, 74, 39, 79, 33, 73, 23, 63, 13, 53, 18, 58, 28, 68, 36, 76, 40, 80, 37, 77, 29, 69, 19, 59, 9, 49, 17, 57, 27, 67, 35, 75, 38, 78, 30, 70, 20, 60, 10, 50, 3, 43, 7, 47, 15, 55, 25, 65, 31, 71, 21, 61, 11, 51, 4, 44)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 95)(7, 97)(8, 82)(9, 93)(10, 99)(11, 100)(12, 84)(13, 85)(14, 105)(15, 107)(16, 86)(17, 98)(18, 88)(19, 103)(20, 109)(21, 110)(22, 91)(23, 92)(24, 111)(25, 115)(26, 94)(27, 108)(28, 96)(29, 113)(30, 117)(31, 118)(32, 101)(33, 102)(34, 104)(35, 116)(36, 106)(37, 119)(38, 120)(39, 112)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 10, 80 ), ( 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80 ) } Outer automorphisms :: reflexible Dual of E16.708 Graph:: bipartite v = 41 e = 80 f = 9 degree seq :: [ 2^40, 80 ] E16.715 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^5, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^8, (Y3 * Y2^-1)^5, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 24, 64, 30, 70, 20, 60, 10, 50, 3, 43, 7, 47, 15, 55, 25, 65, 34, 74, 37, 77, 29, 69, 19, 59, 9, 49, 17, 57, 27, 67, 35, 75, 40, 80, 39, 79, 33, 73, 23, 63, 13, 53, 18, 58, 28, 68, 36, 76, 38, 78, 32, 72, 22, 62, 12, 52, 5, 45, 8, 48, 16, 56, 26, 66, 31, 71, 21, 61, 11, 51, 4, 44)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 95)(7, 97)(8, 82)(9, 93)(10, 99)(11, 100)(12, 84)(13, 85)(14, 105)(15, 107)(16, 86)(17, 98)(18, 88)(19, 103)(20, 109)(21, 110)(22, 91)(23, 92)(24, 114)(25, 115)(26, 94)(27, 108)(28, 96)(29, 113)(30, 117)(31, 104)(32, 101)(33, 102)(34, 120)(35, 116)(36, 106)(37, 119)(38, 111)(39, 112)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 10, 80 ), ( 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80, 10, 80 ) } Outer automorphisms :: reflexible Dual of E16.709 Graph:: bipartite v = 41 e = 80 f = 9 degree seq :: [ 2^40, 80 ] E16.716 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 14, 21}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^6, T2^7 * T1^3 ] Map:: non-degenerate R = (1, 3, 9, 19, 31, 38, 26, 14, 25, 37, 36, 24, 13, 5)(2, 7, 17, 29, 41, 34, 22, 11, 21, 33, 42, 30, 18, 8)(4, 10, 20, 32, 40, 28, 16, 6, 15, 27, 39, 35, 23, 12)(43, 44, 48, 56, 53, 46)(45, 49, 57, 67, 63, 52)(47, 50, 58, 68, 64, 54)(51, 59, 69, 79, 75, 62)(55, 60, 70, 80, 76, 65)(61, 71, 81, 78, 84, 74)(66, 72, 82, 73, 83, 77) 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) :: { ( 42^6 ), ( 42^14 ) } Outer automorphisms :: reflexible Dual of E16.720 Transitivity :: ET+ Graph:: bipartite v = 10 e = 42 f = 2 degree seq :: [ 6^7, 14^3 ] E16.717 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 14, 21}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2^-1), T2 * T1^-1 * T2 * T1^-3 * T2, T1^-1 * T2^5 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2 * T1 * T2^8 * T1 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 37, 39, 31, 23, 11, 21, 16, 6, 15, 27, 35, 41, 33, 25, 13, 5)(2, 7, 17, 28, 36, 40, 32, 24, 12, 4, 10, 20, 14, 26, 34, 42, 38, 30, 22, 18, 8)(43, 44, 48, 56, 61, 70, 77, 84, 81, 74, 67, 64, 53, 46)(45, 49, 57, 68, 71, 78, 83, 80, 73, 66, 55, 60, 63, 52)(47, 50, 58, 62, 51, 59, 69, 76, 79, 82, 75, 72, 65, 54) 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) :: { ( 12^14 ), ( 12^21 ) } Outer automorphisms :: reflexible Dual of E16.721 Transitivity :: ET+ Graph:: bipartite v = 5 e = 42 f = 7 degree seq :: [ 14^3, 21^2 ] E16.718 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 14, 21}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-6, T2^-2 * T1^7 ] Map:: non-degenerate R = (1, 3, 9, 19, 13, 5)(2, 7, 17, 30, 18, 8)(4, 10, 20, 31, 24, 12)(6, 15, 28, 39, 29, 16)(11, 21, 32, 40, 36, 23)(14, 26, 38, 41, 34, 27)(22, 33, 25, 37, 42, 35)(43, 44, 48, 56, 67, 74, 62, 51, 59, 70, 80, 84, 78, 66, 55, 60, 71, 76, 64, 53, 46)(45, 49, 57, 68, 79, 82, 73, 61, 72, 81, 83, 77, 65, 54, 47, 50, 58, 69, 75, 63, 52) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 28^6 ), ( 28^21 ) } Outer automorphisms :: reflexible Dual of E16.719 Transitivity :: ET+ Graph:: bipartite v = 9 e = 42 f = 3 degree seq :: [ 6^7, 21^2 ] E16.719 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 14, 21}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^6, T2^7 * T1^3 ] Map:: non-degenerate R = (1, 43, 3, 45, 9, 51, 19, 61, 31, 73, 38, 80, 26, 68, 14, 56, 25, 67, 37, 79, 36, 78, 24, 66, 13, 55, 5, 47)(2, 44, 7, 49, 17, 59, 29, 71, 41, 83, 34, 76, 22, 64, 11, 53, 21, 63, 33, 75, 42, 84, 30, 72, 18, 60, 8, 50)(4, 46, 10, 52, 20, 62, 32, 74, 40, 82, 28, 70, 16, 58, 6, 48, 15, 57, 27, 69, 39, 81, 35, 77, 23, 65, 12, 54) L = (1, 44)(2, 48)(3, 49)(4, 43)(5, 50)(6, 56)(7, 57)(8, 58)(9, 59)(10, 45)(11, 46)(12, 47)(13, 60)(14, 53)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 51)(21, 52)(22, 54)(23, 55)(24, 72)(25, 63)(26, 64)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 61)(33, 62)(34, 65)(35, 66)(36, 84)(37, 75)(38, 76)(39, 78)(40, 73)(41, 77)(42, 74) local type(s) :: { ( 6, 21, 6, 21, 6, 21, 6, 21, 6, 21, 6, 21, 6, 21, 6, 21, 6, 21, 6, 21, 6, 21, 6, 21, 6, 21, 6, 21 ) } Outer automorphisms :: reflexible Dual of E16.718 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 42 f = 9 degree seq :: [ 28^3 ] E16.720 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 14, 21}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2^-1), T2 * T1^-1 * T2 * T1^-3 * T2, T1^-1 * T2^5 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2 * T1 * T2^8 * T1 ] Map:: non-degenerate R = (1, 43, 3, 45, 9, 51, 19, 61, 29, 71, 37, 79, 39, 81, 31, 73, 23, 65, 11, 53, 21, 63, 16, 58, 6, 48, 15, 57, 27, 69, 35, 77, 41, 83, 33, 75, 25, 67, 13, 55, 5, 47)(2, 44, 7, 49, 17, 59, 28, 70, 36, 78, 40, 82, 32, 74, 24, 66, 12, 54, 4, 46, 10, 52, 20, 62, 14, 56, 26, 68, 34, 76, 42, 84, 38, 80, 30, 72, 22, 64, 18, 60, 8, 50) L = (1, 44)(2, 48)(3, 49)(4, 43)(5, 50)(6, 56)(7, 57)(8, 58)(9, 59)(10, 45)(11, 46)(12, 47)(13, 60)(14, 61)(15, 68)(16, 62)(17, 69)(18, 63)(19, 70)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 64)(26, 71)(27, 76)(28, 77)(29, 78)(30, 65)(31, 66)(32, 67)(33, 72)(34, 79)(35, 84)(36, 83)(37, 82)(38, 73)(39, 74)(40, 75)(41, 80)(42, 81) local type(s) :: { ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E16.716 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 42 f = 10 degree seq :: [ 42^2 ] E16.721 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 14, 21}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-6, T2^-2 * T1^7 ] Map:: non-degenerate R = (1, 43, 3, 45, 9, 51, 19, 61, 13, 55, 5, 47)(2, 44, 7, 49, 17, 59, 30, 72, 18, 60, 8, 50)(4, 46, 10, 52, 20, 62, 31, 73, 24, 66, 12, 54)(6, 48, 15, 57, 28, 70, 39, 81, 29, 71, 16, 58)(11, 53, 21, 63, 32, 74, 40, 82, 36, 78, 23, 65)(14, 56, 26, 68, 38, 80, 41, 83, 34, 76, 27, 69)(22, 64, 33, 75, 25, 67, 37, 79, 42, 84, 35, 77) L = (1, 44)(2, 48)(3, 49)(4, 43)(5, 50)(6, 56)(7, 57)(8, 58)(9, 59)(10, 45)(11, 46)(12, 47)(13, 60)(14, 67)(15, 68)(16, 69)(17, 70)(18, 71)(19, 72)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 74)(26, 79)(27, 75)(28, 80)(29, 76)(30, 81)(31, 61)(32, 62)(33, 63)(34, 64)(35, 65)(36, 66)(37, 82)(38, 84)(39, 83)(40, 73)(41, 77)(42, 78) local type(s) :: { ( 14, 21, 14, 21, 14, 21, 14, 21, 14, 21, 14, 21 ) } Outer automorphisms :: reflexible Dual of E16.717 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 42 f = 5 degree seq :: [ 12^7 ] E16.722 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 14, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, Y1^-1 * Y3^-1, Y2 * Y3 * Y2^-1 * Y1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^6, Y2^2 * Y3 * Y2^5 * Y1^-2, Y2^-1 * Y1^2 * Y3^-1 * Y2^-2 * Y1^2 * Y2^3 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 11, 53, 4, 46)(3, 45, 7, 49, 15, 57, 25, 67, 21, 63, 10, 52)(5, 47, 8, 50, 16, 58, 26, 68, 22, 64, 12, 54)(9, 51, 17, 59, 27, 69, 37, 79, 33, 75, 20, 62)(13, 55, 18, 60, 28, 70, 38, 80, 34, 76, 23, 65)(19, 61, 29, 71, 39, 81, 36, 78, 42, 84, 32, 74)(24, 66, 30, 72, 40, 82, 31, 73, 41, 83, 35, 77)(85, 127, 87, 129, 93, 135, 103, 145, 115, 157, 122, 164, 110, 152, 98, 140, 109, 151, 121, 163, 120, 162, 108, 150, 97, 139, 89, 131)(86, 128, 91, 133, 101, 143, 113, 155, 125, 167, 118, 160, 106, 148, 95, 137, 105, 147, 117, 159, 126, 168, 114, 156, 102, 144, 92, 134)(88, 130, 94, 136, 104, 146, 116, 158, 124, 166, 112, 154, 100, 142, 90, 132, 99, 141, 111, 153, 123, 165, 119, 161, 107, 149, 96, 138) L = (1, 88)(2, 85)(3, 94)(4, 95)(5, 96)(6, 86)(7, 87)(8, 89)(9, 104)(10, 105)(11, 98)(12, 106)(13, 107)(14, 90)(15, 91)(16, 92)(17, 93)(18, 97)(19, 116)(20, 117)(21, 109)(22, 110)(23, 118)(24, 119)(25, 99)(26, 100)(27, 101)(28, 102)(29, 103)(30, 108)(31, 124)(32, 126)(33, 121)(34, 122)(35, 125)(36, 123)(37, 111)(38, 112)(39, 113)(40, 114)(41, 115)(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, 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 E16.725 Graph:: bipartite v = 10 e = 84 f = 44 degree seq :: [ 12^7, 28^3 ] E16.723 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 14, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2^-1), Y2 * Y1^-1 * Y2 * Y1^-3 * Y2, Y2 * Y1 * Y2^8 * Y1, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 19, 61, 28, 70, 35, 77, 42, 84, 39, 81, 32, 74, 25, 67, 22, 64, 11, 53, 4, 46)(3, 45, 7, 49, 15, 57, 26, 68, 29, 71, 36, 78, 41, 83, 38, 80, 31, 73, 24, 66, 13, 55, 18, 60, 21, 63, 10, 52)(5, 47, 8, 50, 16, 58, 20, 62, 9, 51, 17, 59, 27, 69, 34, 76, 37, 79, 40, 82, 33, 75, 30, 72, 23, 65, 12, 54)(85, 127, 87, 129, 93, 135, 103, 145, 113, 155, 121, 163, 123, 165, 115, 157, 107, 149, 95, 137, 105, 147, 100, 142, 90, 132, 99, 141, 111, 153, 119, 161, 125, 167, 117, 159, 109, 151, 97, 139, 89, 131)(86, 128, 91, 133, 101, 143, 112, 154, 120, 162, 124, 166, 116, 158, 108, 150, 96, 138, 88, 130, 94, 136, 104, 146, 98, 140, 110, 152, 118, 160, 126, 168, 122, 164, 114, 156, 106, 148, 102, 144, 92, 134) L = (1, 87)(2, 91)(3, 93)(4, 94)(5, 85)(6, 99)(7, 101)(8, 86)(9, 103)(10, 104)(11, 105)(12, 88)(13, 89)(14, 110)(15, 111)(16, 90)(17, 112)(18, 92)(19, 113)(20, 98)(21, 100)(22, 102)(23, 95)(24, 96)(25, 97)(26, 118)(27, 119)(28, 120)(29, 121)(30, 106)(31, 107)(32, 108)(33, 109)(34, 126)(35, 125)(36, 124)(37, 123)(38, 114)(39, 115)(40, 116)(41, 117)(42, 122)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E16.724 Graph:: bipartite v = 5 e = 84 f = 49 degree seq :: [ 28^3, 42^2 ] E16.724 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 14, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y2^-6, Y2^6, Y3^7 * Y2^2, (Y3^-1 * Y1^-1)^21 ] Map:: R = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)(85, 127, 86, 128, 90, 132, 98, 140, 95, 137, 88, 130)(87, 129, 91, 133, 99, 141, 109, 151, 105, 147, 94, 136)(89, 131, 92, 134, 100, 142, 110, 152, 106, 148, 96, 138)(93, 135, 101, 143, 111, 153, 121, 163, 117, 159, 104, 146)(97, 139, 102, 144, 112, 154, 122, 164, 118, 160, 107, 149)(103, 145, 113, 155, 120, 162, 124, 166, 126, 168, 116, 158)(108, 150, 114, 156, 123, 165, 125, 167, 115, 157, 119, 161) L = (1, 87)(2, 91)(3, 93)(4, 94)(5, 85)(6, 99)(7, 101)(8, 86)(9, 103)(10, 104)(11, 105)(12, 88)(13, 89)(14, 109)(15, 111)(16, 90)(17, 113)(18, 92)(19, 115)(20, 116)(21, 117)(22, 95)(23, 96)(24, 97)(25, 121)(26, 98)(27, 120)(28, 100)(29, 119)(30, 102)(31, 118)(32, 125)(33, 126)(34, 106)(35, 107)(36, 108)(37, 124)(38, 110)(39, 112)(40, 114)(41, 122)(42, 123)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 28, 42 ), ( 28, 42, 28, 42, 28, 42, 28, 42, 28, 42, 28, 42 ) } Outer automorphisms :: reflexible Dual of E16.723 Graph:: simple bipartite v = 49 e = 84 f = 5 degree seq :: [ 2^42, 12^7 ] E16.725 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 14, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^-6, (R * Y2 * Y3^-1)^2, Y3^6, Y3^-2 * Y1^7, (Y3 * Y2^-1)^6 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 25, 67, 32, 74, 20, 62, 9, 51, 17, 59, 28, 70, 38, 80, 42, 84, 36, 78, 24, 66, 13, 55, 18, 60, 29, 71, 34, 76, 22, 64, 11, 53, 4, 46)(3, 45, 7, 49, 15, 57, 26, 68, 37, 79, 40, 82, 31, 73, 19, 61, 30, 72, 39, 81, 41, 83, 35, 77, 23, 65, 12, 54, 5, 47, 8, 50, 16, 58, 27, 69, 33, 75, 21, 63, 10, 52)(85, 127)(86, 128)(87, 129)(88, 130)(89, 131)(90, 132)(91, 133)(92, 134)(93, 135)(94, 136)(95, 137)(96, 138)(97, 139)(98, 140)(99, 141)(100, 142)(101, 143)(102, 144)(103, 145)(104, 146)(105, 147)(106, 148)(107, 149)(108, 150)(109, 151)(110, 152)(111, 153)(112, 154)(113, 155)(114, 156)(115, 157)(116, 158)(117, 159)(118, 160)(119, 161)(120, 162)(121, 163)(122, 164)(123, 165)(124, 166)(125, 167)(126, 168) L = (1, 87)(2, 91)(3, 93)(4, 94)(5, 85)(6, 99)(7, 101)(8, 86)(9, 103)(10, 104)(11, 105)(12, 88)(13, 89)(14, 110)(15, 112)(16, 90)(17, 114)(18, 92)(19, 97)(20, 115)(21, 116)(22, 117)(23, 95)(24, 96)(25, 121)(26, 122)(27, 98)(28, 123)(29, 100)(30, 102)(31, 108)(32, 124)(33, 109)(34, 111)(35, 106)(36, 107)(37, 126)(38, 125)(39, 113)(40, 120)(41, 118)(42, 119)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 12, 28 ), ( 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28 ) } Outer automorphisms :: reflexible Dual of E16.722 Graph:: simple bipartite v = 44 e = 84 f = 10 degree seq :: [ 2^42, 42^2 ] E16.726 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 14, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y2^-1 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^6, Y1^6, Y3^2 * Y2^7 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 11, 53, 4, 46)(3, 45, 7, 49, 15, 57, 25, 67, 21, 63, 10, 52)(5, 47, 8, 50, 16, 58, 26, 68, 22, 64, 12, 54)(9, 51, 17, 59, 27, 69, 37, 79, 33, 75, 20, 62)(13, 55, 18, 60, 28, 70, 38, 80, 34, 76, 23, 65)(19, 61, 29, 71, 39, 81, 42, 84, 36, 78, 32, 74)(24, 66, 30, 72, 31, 73, 40, 82, 41, 83, 35, 77)(85, 127, 87, 129, 93, 135, 103, 145, 115, 157, 112, 154, 100, 142, 90, 132, 99, 141, 111, 153, 123, 165, 125, 167, 118, 160, 106, 148, 95, 137, 105, 147, 117, 159, 120, 162, 108, 150, 97, 139, 89, 131)(86, 128, 91, 133, 101, 143, 113, 155, 124, 166, 122, 164, 110, 152, 98, 140, 109, 151, 121, 163, 126, 168, 119, 161, 107, 149, 96, 138, 88, 130, 94, 136, 104, 146, 116, 158, 114, 156, 102, 144, 92, 134) L = (1, 88)(2, 85)(3, 94)(4, 95)(5, 96)(6, 86)(7, 87)(8, 89)(9, 104)(10, 105)(11, 98)(12, 106)(13, 107)(14, 90)(15, 91)(16, 92)(17, 93)(18, 97)(19, 116)(20, 117)(21, 109)(22, 110)(23, 118)(24, 119)(25, 99)(26, 100)(27, 101)(28, 102)(29, 103)(30, 108)(31, 114)(32, 120)(33, 121)(34, 122)(35, 125)(36, 126)(37, 111)(38, 112)(39, 113)(40, 115)(41, 124)(42, 123)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 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 E16.727 Graph:: bipartite v = 9 e = 84 f = 45 degree seq :: [ 12^7, 42^2 ] E16.727 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 14, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^3 * Y3^-1 * Y1 * Y3^-2, Y1^-1 * Y3^5 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1 * Y3^8 * Y1, (Y3 * Y2^-1)^21 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 19, 61, 28, 70, 35, 77, 42, 84, 39, 81, 32, 74, 25, 67, 22, 64, 11, 53, 4, 46)(3, 45, 7, 49, 15, 57, 26, 68, 29, 71, 36, 78, 41, 83, 38, 80, 31, 73, 24, 66, 13, 55, 18, 60, 21, 63, 10, 52)(5, 47, 8, 50, 16, 58, 20, 62, 9, 51, 17, 59, 27, 69, 34, 76, 37, 79, 40, 82, 33, 75, 30, 72, 23, 65, 12, 54)(85, 127)(86, 128)(87, 129)(88, 130)(89, 131)(90, 132)(91, 133)(92, 134)(93, 135)(94, 136)(95, 137)(96, 138)(97, 139)(98, 140)(99, 141)(100, 142)(101, 143)(102, 144)(103, 145)(104, 146)(105, 147)(106, 148)(107, 149)(108, 150)(109, 151)(110, 152)(111, 153)(112, 154)(113, 155)(114, 156)(115, 157)(116, 158)(117, 159)(118, 160)(119, 161)(120, 162)(121, 163)(122, 164)(123, 165)(124, 166)(125, 167)(126, 168) L = (1, 87)(2, 91)(3, 93)(4, 94)(5, 85)(6, 99)(7, 101)(8, 86)(9, 103)(10, 104)(11, 105)(12, 88)(13, 89)(14, 110)(15, 111)(16, 90)(17, 112)(18, 92)(19, 113)(20, 98)(21, 100)(22, 102)(23, 95)(24, 96)(25, 97)(26, 118)(27, 119)(28, 120)(29, 121)(30, 106)(31, 107)(32, 108)(33, 109)(34, 126)(35, 125)(36, 124)(37, 123)(38, 114)(39, 115)(40, 116)(41, 117)(42, 122)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 12, 42 ), ( 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42 ) } Outer automorphisms :: reflexible Dual of E16.726 Graph:: simple bipartite v = 45 e = 84 f = 9 degree seq :: [ 2^42, 28^3 ] E16.728 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 22, 44}) Quotient :: edge Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^-11 * T1^2 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 38, 30, 22, 14, 6, 13, 21, 29, 37, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 43, 35, 27, 19, 11, 4, 10, 18, 26, 34, 42, 40, 32, 24, 16, 8)(45, 46, 50, 48)(47, 51, 57, 54)(49, 52, 58, 55)(53, 59, 65, 62)(56, 60, 66, 63)(61, 67, 73, 70)(64, 68, 74, 71)(69, 75, 81, 78)(72, 76, 82, 79)(77, 83, 88, 86)(80, 84, 85, 87) L = (1, 45)(2, 46)(3, 47)(4, 48)(5, 49)(6, 50)(7, 51)(8, 52)(9, 53)(10, 54)(11, 55)(12, 56)(13, 57)(14, 58)(15, 59)(16, 60)(17, 61)(18, 62)(19, 63)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 88^4 ), ( 88^22 ) } Outer automorphisms :: reflexible Dual of E16.732 Transitivity :: ET+ Graph:: bipartite v = 13 e = 44 f = 1 degree seq :: [ 4^11, 22^2 ] E16.729 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 22, 44}) Quotient :: edge Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^4 * T2^4, T2^-4 * T1^-4, T2^-6 * T1^5, T2^2 * T1^35 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 41, 37, 32, 18, 8, 2, 7, 17, 31, 22, 36, 44, 40, 30, 16, 6, 15, 29, 23, 11, 21, 35, 43, 39, 28, 14, 27, 24, 12, 4, 10, 20, 34, 42, 38, 26, 25, 13, 5)(45, 46, 50, 58, 70, 81, 88, 79, 64, 53, 61, 73, 68, 57, 62, 74, 83, 86, 77, 66, 55, 48)(47, 51, 59, 71, 69, 76, 84, 87, 78, 63, 75, 67, 56, 49, 52, 60, 72, 82, 85, 80, 65, 54) L = (1, 45)(2, 46)(3, 47)(4, 48)(5, 49)(6, 50)(7, 51)(8, 52)(9, 53)(10, 54)(11, 55)(12, 56)(13, 57)(14, 58)(15, 59)(16, 60)(17, 61)(18, 62)(19, 63)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 8^22 ), ( 8^44 ) } Outer automorphisms :: reflexible Dual of E16.733 Transitivity :: ET+ Graph:: bipartite v = 3 e = 44 f = 11 degree seq :: [ 22^2, 44 ] E16.730 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 22, 44}) Quotient :: edge Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1, T1^-1), T2^-1 * T1^-11, (T1^-1 * T2^-1)^22 ] Map:: non-degenerate R = (1, 3, 9, 5)(2, 7, 16, 8)(4, 10, 17, 12)(6, 14, 24, 15)(11, 18, 25, 20)(13, 22, 32, 23)(19, 26, 33, 28)(21, 30, 40, 31)(27, 34, 41, 36)(29, 38, 44, 39)(35, 42, 43, 37)(45, 46, 50, 57, 65, 73, 81, 80, 72, 64, 56, 49, 52, 59, 67, 75, 83, 87, 85, 77, 69, 61, 53, 60, 68, 76, 84, 88, 86, 78, 70, 62, 54, 47, 51, 58, 66, 74, 82, 79, 71, 63, 55, 48) L = (1, 45)(2, 46)(3, 47)(4, 48)(5, 49)(6, 50)(7, 51)(8, 52)(9, 53)(10, 54)(11, 55)(12, 56)(13, 57)(14, 58)(15, 59)(16, 60)(17, 61)(18, 62)(19, 63)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 44^4 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E16.731 Transitivity :: ET+ Graph:: bipartite v = 12 e = 44 f = 2 degree seq :: [ 4^11, 44 ] E16.731 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 22, 44}) Quotient :: loop Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^-11 * T1^2 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 17, 61, 25, 69, 33, 77, 41, 85, 38, 82, 30, 74, 22, 66, 14, 58, 6, 50, 13, 57, 21, 65, 29, 73, 37, 81, 44, 88, 36, 80, 28, 72, 20, 64, 12, 56, 5, 49)(2, 46, 7, 51, 15, 59, 23, 67, 31, 75, 39, 83, 43, 87, 35, 79, 27, 71, 19, 63, 11, 55, 4, 48, 10, 54, 18, 62, 26, 70, 34, 78, 42, 86, 40, 84, 32, 76, 24, 68, 16, 60, 8, 52) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 48)(7, 57)(8, 58)(9, 59)(10, 47)(11, 49)(12, 60)(13, 54)(14, 55)(15, 65)(16, 66)(17, 67)(18, 53)(19, 56)(20, 68)(21, 62)(22, 63)(23, 73)(24, 74)(25, 75)(26, 61)(27, 64)(28, 76)(29, 70)(30, 71)(31, 81)(32, 82)(33, 83)(34, 69)(35, 72)(36, 84)(37, 78)(38, 79)(39, 88)(40, 85)(41, 87)(42, 77)(43, 80)(44, 86) local type(s) :: { ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E16.730 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 44 f = 12 degree seq :: [ 44^2 ] E16.732 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 22, 44}) Quotient :: loop Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^4 * T2^4, T2^-4 * T1^-4, T2^-6 * T1^5, T2^2 * T1^35 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 33, 77, 41, 85, 37, 81, 32, 76, 18, 62, 8, 52, 2, 46, 7, 51, 17, 61, 31, 75, 22, 66, 36, 80, 44, 88, 40, 84, 30, 74, 16, 60, 6, 50, 15, 59, 29, 73, 23, 67, 11, 55, 21, 65, 35, 79, 43, 87, 39, 83, 28, 72, 14, 58, 27, 71, 24, 68, 12, 56, 4, 48, 10, 54, 20, 64, 34, 78, 42, 86, 38, 82, 26, 70, 25, 69, 13, 57, 5, 49) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 58)(7, 59)(8, 60)(9, 61)(10, 47)(11, 48)(12, 49)(13, 62)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 76)(26, 81)(27, 69)(28, 82)(29, 68)(30, 83)(31, 67)(32, 84)(33, 66)(34, 63)(35, 64)(36, 65)(37, 88)(38, 85)(39, 86)(40, 87)(41, 80)(42, 77)(43, 78)(44, 79) local type(s) :: { ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ) } Outer automorphisms :: reflexible Dual of E16.728 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 44 f = 13 degree seq :: [ 88 ] E16.733 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 22, 44}) Quotient :: loop Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1, T1^-1), T2^-1 * T1^-11, (T1^-1 * T2^-1)^22 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 5, 49)(2, 46, 7, 51, 16, 60, 8, 52)(4, 48, 10, 54, 17, 61, 12, 56)(6, 50, 14, 58, 24, 68, 15, 59)(11, 55, 18, 62, 25, 69, 20, 64)(13, 57, 22, 66, 32, 76, 23, 67)(19, 63, 26, 70, 33, 77, 28, 72)(21, 65, 30, 74, 40, 84, 31, 75)(27, 71, 34, 78, 41, 85, 36, 80)(29, 73, 38, 82, 44, 88, 39, 83)(35, 79, 42, 86, 43, 87, 37, 81) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 57)(7, 58)(8, 59)(9, 60)(10, 47)(11, 48)(12, 49)(13, 65)(14, 66)(15, 67)(16, 68)(17, 53)(18, 54)(19, 55)(20, 56)(21, 73)(22, 74)(23, 75)(24, 76)(25, 61)(26, 62)(27, 63)(28, 64)(29, 81)(30, 82)(31, 83)(32, 84)(33, 69)(34, 70)(35, 71)(36, 72)(37, 80)(38, 79)(39, 87)(40, 88)(41, 77)(42, 78)(43, 85)(44, 86) local type(s) :: { ( 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E16.729 Transitivity :: ET+ VT+ AT Graph:: v = 11 e = 44 f = 3 degree seq :: [ 8^11 ] E16.734 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 22, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^4, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^-11 * Y1^2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 45, 2, 46, 6, 50, 4, 48)(3, 47, 7, 51, 13, 57, 10, 54)(5, 49, 8, 52, 14, 58, 11, 55)(9, 53, 15, 59, 21, 65, 18, 62)(12, 56, 16, 60, 22, 66, 19, 63)(17, 61, 23, 67, 29, 73, 26, 70)(20, 64, 24, 68, 30, 74, 27, 71)(25, 69, 31, 75, 37, 81, 34, 78)(28, 72, 32, 76, 38, 82, 35, 79)(33, 77, 39, 83, 44, 88, 42, 86)(36, 80, 40, 84, 41, 85, 43, 87)(89, 133, 91, 135, 97, 141, 105, 149, 113, 157, 121, 165, 129, 173, 126, 170, 118, 162, 110, 154, 102, 146, 94, 138, 101, 145, 109, 153, 117, 161, 125, 169, 132, 176, 124, 168, 116, 160, 108, 152, 100, 144, 93, 137)(90, 134, 95, 139, 103, 147, 111, 155, 119, 163, 127, 171, 131, 175, 123, 167, 115, 159, 107, 151, 99, 143, 92, 136, 98, 142, 106, 150, 114, 158, 122, 166, 130, 174, 128, 172, 120, 164, 112, 156, 104, 148, 96, 140) L = (1, 92)(2, 89)(3, 98)(4, 94)(5, 99)(6, 90)(7, 91)(8, 93)(9, 106)(10, 101)(11, 102)(12, 107)(13, 95)(14, 96)(15, 97)(16, 100)(17, 114)(18, 109)(19, 110)(20, 115)(21, 103)(22, 104)(23, 105)(24, 108)(25, 122)(26, 117)(27, 118)(28, 123)(29, 111)(30, 112)(31, 113)(32, 116)(33, 130)(34, 125)(35, 126)(36, 131)(37, 119)(38, 120)(39, 121)(40, 124)(41, 128)(42, 132)(43, 129)(44, 127)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 2, 88, 2, 88, 2, 88, 2, 88 ), ( 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88 ) } Outer automorphisms :: reflexible Dual of E16.737 Graph:: bipartite v = 13 e = 88 f = 45 degree seq :: [ 8^11, 44^2 ] E16.735 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 22, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^4 * Y1^4, (Y3^-1 * Y1^-1)^4, Y2^-6 * Y1^5, Y1^22, Y1^-44 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 37, 81, 44, 88, 35, 79, 20, 64, 9, 53, 17, 61, 29, 73, 24, 68, 13, 57, 18, 62, 30, 74, 39, 83, 42, 86, 33, 77, 22, 66, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 27, 71, 25, 69, 32, 76, 40, 84, 43, 87, 34, 78, 19, 63, 31, 75, 23, 67, 12, 56, 5, 49, 8, 52, 16, 60, 28, 72, 38, 82, 41, 85, 36, 80, 21, 65, 10, 54)(89, 133, 91, 135, 97, 141, 107, 151, 121, 165, 129, 173, 125, 169, 120, 164, 106, 150, 96, 140, 90, 134, 95, 139, 105, 149, 119, 163, 110, 154, 124, 168, 132, 176, 128, 172, 118, 162, 104, 148, 94, 138, 103, 147, 117, 161, 111, 155, 99, 143, 109, 153, 123, 167, 131, 175, 127, 171, 116, 160, 102, 146, 115, 159, 112, 156, 100, 144, 92, 136, 98, 142, 108, 152, 122, 166, 130, 174, 126, 170, 114, 158, 113, 157, 101, 145, 93, 137) L = (1, 91)(2, 95)(3, 97)(4, 98)(5, 89)(6, 103)(7, 105)(8, 90)(9, 107)(10, 108)(11, 109)(12, 92)(13, 93)(14, 115)(15, 117)(16, 94)(17, 119)(18, 96)(19, 121)(20, 122)(21, 123)(22, 124)(23, 99)(24, 100)(25, 101)(26, 113)(27, 112)(28, 102)(29, 111)(30, 104)(31, 110)(32, 106)(33, 129)(34, 130)(35, 131)(36, 132)(37, 120)(38, 114)(39, 116)(40, 118)(41, 125)(42, 126)(43, 127)(44, 128)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E16.736 Graph:: bipartite v = 3 e = 88 f = 55 degree seq :: [ 44^2, 88 ] E16.736 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 22, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y3, Y2^-1), Y3^11 * Y2^-1, (Y2^-1 * Y3)^22, (Y3^-1 * Y1^-1)^44 ] Map:: R = (1, 45)(2, 46)(3, 47)(4, 48)(5, 49)(6, 50)(7, 51)(8, 52)(9, 53)(10, 54)(11, 55)(12, 56)(13, 57)(14, 58)(15, 59)(16, 60)(17, 61)(18, 62)(19, 63)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88)(89, 133, 90, 134, 94, 138, 92, 136)(91, 135, 95, 139, 101, 145, 98, 142)(93, 137, 96, 140, 102, 146, 99, 143)(97, 141, 103, 147, 109, 153, 106, 150)(100, 144, 104, 148, 110, 154, 107, 151)(105, 149, 111, 155, 117, 161, 114, 158)(108, 152, 112, 156, 118, 162, 115, 159)(113, 157, 119, 163, 125, 169, 122, 166)(116, 160, 120, 164, 126, 170, 123, 167)(121, 165, 127, 171, 131, 175, 129, 173)(124, 168, 128, 172, 132, 176, 130, 174) L = (1, 91)(2, 95)(3, 97)(4, 98)(5, 89)(6, 101)(7, 103)(8, 90)(9, 105)(10, 106)(11, 92)(12, 93)(13, 109)(14, 94)(15, 111)(16, 96)(17, 113)(18, 114)(19, 99)(20, 100)(21, 117)(22, 102)(23, 119)(24, 104)(25, 121)(26, 122)(27, 107)(28, 108)(29, 125)(30, 110)(31, 127)(32, 112)(33, 128)(34, 129)(35, 115)(36, 116)(37, 131)(38, 118)(39, 132)(40, 120)(41, 124)(42, 123)(43, 130)(44, 126)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 44, 88 ), ( 44, 88, 44, 88, 44, 88, 44, 88 ) } Outer automorphisms :: reflexible Dual of E16.735 Graph:: simple bipartite v = 55 e = 88 f = 3 degree seq :: [ 2^44, 8^11 ] E16.737 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 22, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y3^-1 * Y1^-11, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 45, 2, 46, 6, 50, 13, 57, 21, 65, 29, 73, 37, 81, 36, 80, 28, 72, 20, 64, 12, 56, 5, 49, 8, 52, 15, 59, 23, 67, 31, 75, 39, 83, 43, 87, 41, 85, 33, 77, 25, 69, 17, 61, 9, 53, 16, 60, 24, 68, 32, 76, 40, 84, 44, 88, 42, 86, 34, 78, 26, 70, 18, 62, 10, 54, 3, 47, 7, 51, 14, 58, 22, 66, 30, 74, 38, 82, 35, 79, 27, 71, 19, 63, 11, 55, 4, 48)(89, 133)(90, 134)(91, 135)(92, 136)(93, 137)(94, 138)(95, 139)(96, 140)(97, 141)(98, 142)(99, 143)(100, 144)(101, 145)(102, 146)(103, 147)(104, 148)(105, 149)(106, 150)(107, 151)(108, 152)(109, 153)(110, 154)(111, 155)(112, 156)(113, 157)(114, 158)(115, 159)(116, 160)(117, 161)(118, 162)(119, 163)(120, 164)(121, 165)(122, 166)(123, 167)(124, 168)(125, 169)(126, 170)(127, 171)(128, 172)(129, 173)(130, 174)(131, 175)(132, 176) L = (1, 91)(2, 95)(3, 97)(4, 98)(5, 89)(6, 102)(7, 104)(8, 90)(9, 93)(10, 105)(11, 106)(12, 92)(13, 110)(14, 112)(15, 94)(16, 96)(17, 100)(18, 113)(19, 114)(20, 99)(21, 118)(22, 120)(23, 101)(24, 103)(25, 108)(26, 121)(27, 122)(28, 107)(29, 126)(30, 128)(31, 109)(32, 111)(33, 116)(34, 129)(35, 130)(36, 115)(37, 123)(38, 132)(39, 117)(40, 119)(41, 124)(42, 131)(43, 125)(44, 127)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 8, 44 ), ( 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44 ) } Outer automorphisms :: reflexible Dual of E16.734 Graph:: bipartite v = 45 e = 88 f = 13 degree seq :: [ 2^44, 88 ] E16.738 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 22, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^4, Y1^4, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3 * Y2^-11, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 45, 2, 46, 6, 50, 4, 48)(3, 47, 7, 51, 13, 57, 10, 54)(5, 49, 8, 52, 14, 58, 11, 55)(9, 53, 15, 59, 21, 65, 18, 62)(12, 56, 16, 60, 22, 66, 19, 63)(17, 61, 23, 67, 29, 73, 26, 70)(20, 64, 24, 68, 30, 74, 27, 71)(25, 69, 31, 75, 37, 81, 34, 78)(28, 72, 32, 76, 38, 82, 35, 79)(33, 77, 39, 83, 43, 87, 42, 86)(36, 80, 40, 84, 44, 88, 41, 85)(89, 133, 91, 135, 97, 141, 105, 149, 113, 157, 121, 165, 129, 173, 123, 167, 115, 159, 107, 151, 99, 143, 92, 136, 98, 142, 106, 150, 114, 158, 122, 166, 130, 174, 132, 176, 126, 170, 118, 162, 110, 154, 102, 146, 94, 138, 101, 145, 109, 153, 117, 161, 125, 169, 131, 175, 128, 172, 120, 164, 112, 156, 104, 148, 96, 140, 90, 134, 95, 139, 103, 147, 111, 155, 119, 163, 127, 171, 124, 168, 116, 160, 108, 152, 100, 144, 93, 137) L = (1, 92)(2, 89)(3, 98)(4, 94)(5, 99)(6, 90)(7, 91)(8, 93)(9, 106)(10, 101)(11, 102)(12, 107)(13, 95)(14, 96)(15, 97)(16, 100)(17, 114)(18, 109)(19, 110)(20, 115)(21, 103)(22, 104)(23, 105)(24, 108)(25, 122)(26, 117)(27, 118)(28, 123)(29, 111)(30, 112)(31, 113)(32, 116)(33, 130)(34, 125)(35, 126)(36, 129)(37, 119)(38, 120)(39, 121)(40, 124)(41, 132)(42, 131)(43, 127)(44, 128)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 2, 44, 2, 44, 2, 44, 2, 44 ), ( 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44 ) } Outer automorphisms :: reflexible Dual of E16.739 Graph:: bipartite v = 12 e = 88 f = 46 degree seq :: [ 8^11, 88 ] E16.739 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 22, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-4 * Y1^-4, Y3^-6 * Y1^5, Y1^22, Y1^-44, (Y3 * Y2^-1)^44 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 37, 81, 44, 88, 35, 79, 20, 64, 9, 53, 17, 61, 29, 73, 24, 68, 13, 57, 18, 62, 30, 74, 39, 83, 42, 86, 33, 77, 22, 66, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 27, 71, 25, 69, 32, 76, 40, 84, 43, 87, 34, 78, 19, 63, 31, 75, 23, 67, 12, 56, 5, 49, 8, 52, 16, 60, 28, 72, 38, 82, 41, 85, 36, 80, 21, 65, 10, 54)(89, 133)(90, 134)(91, 135)(92, 136)(93, 137)(94, 138)(95, 139)(96, 140)(97, 141)(98, 142)(99, 143)(100, 144)(101, 145)(102, 146)(103, 147)(104, 148)(105, 149)(106, 150)(107, 151)(108, 152)(109, 153)(110, 154)(111, 155)(112, 156)(113, 157)(114, 158)(115, 159)(116, 160)(117, 161)(118, 162)(119, 163)(120, 164)(121, 165)(122, 166)(123, 167)(124, 168)(125, 169)(126, 170)(127, 171)(128, 172)(129, 173)(130, 174)(131, 175)(132, 176) L = (1, 91)(2, 95)(3, 97)(4, 98)(5, 89)(6, 103)(7, 105)(8, 90)(9, 107)(10, 108)(11, 109)(12, 92)(13, 93)(14, 115)(15, 117)(16, 94)(17, 119)(18, 96)(19, 121)(20, 122)(21, 123)(22, 124)(23, 99)(24, 100)(25, 101)(26, 113)(27, 112)(28, 102)(29, 111)(30, 104)(31, 110)(32, 106)(33, 129)(34, 130)(35, 131)(36, 132)(37, 120)(38, 114)(39, 116)(40, 118)(41, 125)(42, 126)(43, 127)(44, 128)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 8, 88 ), ( 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88 ) } Outer automorphisms :: reflexible Dual of E16.738 Graph:: simple bipartite v = 46 e = 88 f = 12 degree seq :: [ 2^44, 44^2 ] E16.740 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 9, 45}) Quotient :: edge Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^9 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 33, 23, 13, 5)(2, 7, 16, 26, 36, 37, 27, 17, 8)(4, 10, 19, 29, 38, 41, 32, 22, 12)(6, 14, 24, 34, 42, 43, 35, 25, 15)(11, 20, 30, 39, 44, 45, 40, 31, 21)(46, 47, 51, 56, 49)(48, 52, 59, 65, 55)(50, 53, 60, 66, 57)(54, 61, 69, 75, 64)(58, 62, 70, 76, 67)(63, 71, 79, 84, 74)(68, 72, 80, 85, 77)(73, 81, 87, 89, 83)(78, 82, 88, 90, 86) L = (1, 46)(2, 47)(3, 48)(4, 49)(5, 50)(6, 51)(7, 52)(8, 53)(9, 54)(10, 55)(11, 56)(12, 57)(13, 58)(14, 59)(15, 60)(16, 61)(17, 62)(18, 63)(19, 64)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 70)(26, 71)(27, 72)(28, 73)(29, 74)(30, 75)(31, 76)(32, 77)(33, 78)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 86)(42, 87)(43, 88)(44, 89)(45, 90) local type(s) :: { ( 90^5 ), ( 90^9 ) } Outer automorphisms :: reflexible Dual of E16.744 Transitivity :: ET+ Graph:: simple bipartite v = 14 e = 45 f = 1 degree seq :: [ 5^9, 9^5 ] E16.741 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 9, 45}) Quotient :: edge Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2), T1^4 * T2^-5, T1^9, (T1^-1 * T2^-1)^5 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 26, 42, 40, 24, 12, 4, 10, 20, 34, 28, 14, 27, 43, 39, 23, 11, 21, 35, 30, 16, 6, 15, 29, 44, 38, 22, 36, 32, 18, 8, 2, 7, 17, 31, 45, 37, 41, 25, 13, 5)(46, 47, 51, 59, 71, 82, 67, 56, 49)(48, 52, 60, 72, 87, 86, 81, 66, 55)(50, 53, 61, 73, 78, 90, 83, 68, 57)(54, 62, 74, 88, 85, 70, 77, 80, 65)(58, 63, 75, 79, 64, 76, 89, 84, 69) L = (1, 46)(2, 47)(3, 48)(4, 49)(5, 50)(6, 51)(7, 52)(8, 53)(9, 54)(10, 55)(11, 56)(12, 57)(13, 58)(14, 59)(15, 60)(16, 61)(17, 62)(18, 63)(19, 64)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 70)(26, 71)(27, 72)(28, 73)(29, 74)(30, 75)(31, 76)(32, 77)(33, 78)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 86)(42, 87)(43, 88)(44, 89)(45, 90) local type(s) :: { ( 10^9 ), ( 10^45 ) } Outer automorphisms :: reflexible Dual of E16.745 Transitivity :: ET+ Graph:: bipartite v = 6 e = 45 f = 9 degree seq :: [ 9^5, 45 ] E16.742 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 9, 45}) Quotient :: edge Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^5, T2 * T1^-9, (T1^-1 * T2^-1)^9 ] Map:: non-degenerate R = (1, 3, 9, 13, 5)(2, 7, 17, 18, 8)(4, 10, 19, 23, 12)(6, 15, 27, 28, 16)(11, 20, 29, 33, 22)(14, 25, 37, 38, 26)(21, 30, 39, 41, 32)(24, 35, 43, 44, 36)(31, 34, 42, 45, 40)(46, 47, 51, 59, 69, 79, 75, 65, 55, 48, 52, 60, 70, 80, 87, 84, 74, 64, 54, 62, 72, 82, 88, 90, 86, 78, 68, 58, 63, 73, 83, 89, 85, 77, 67, 57, 50, 53, 61, 71, 81, 76, 66, 56, 49) L = (1, 46)(2, 47)(3, 48)(4, 49)(5, 50)(6, 51)(7, 52)(8, 53)(9, 54)(10, 55)(11, 56)(12, 57)(13, 58)(14, 59)(15, 60)(16, 61)(17, 62)(18, 63)(19, 64)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 70)(26, 71)(27, 72)(28, 73)(29, 74)(30, 75)(31, 76)(32, 77)(33, 78)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 86)(42, 87)(43, 88)(44, 89)(45, 90) local type(s) :: { ( 18^5 ), ( 18^45 ) } Outer automorphisms :: reflexible Dual of E16.743 Transitivity :: ET+ Graph:: bipartite v = 10 e = 45 f = 5 degree seq :: [ 5^9, 45 ] E16.743 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 9, 45}) Quotient :: loop Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^9 ] Map:: non-degenerate R = (1, 46, 3, 48, 9, 54, 18, 63, 28, 73, 33, 78, 23, 68, 13, 58, 5, 50)(2, 47, 7, 52, 16, 61, 26, 71, 36, 81, 37, 82, 27, 72, 17, 62, 8, 53)(4, 49, 10, 55, 19, 64, 29, 74, 38, 83, 41, 86, 32, 77, 22, 67, 12, 57)(6, 51, 14, 59, 24, 69, 34, 79, 42, 87, 43, 88, 35, 80, 25, 70, 15, 60)(11, 56, 20, 65, 30, 75, 39, 84, 44, 89, 45, 90, 40, 85, 31, 76, 21, 66) L = (1, 47)(2, 51)(3, 52)(4, 46)(5, 53)(6, 56)(7, 59)(8, 60)(9, 61)(10, 48)(11, 49)(12, 50)(13, 62)(14, 65)(15, 66)(16, 69)(17, 70)(18, 71)(19, 54)(20, 55)(21, 57)(22, 58)(23, 72)(24, 75)(25, 76)(26, 79)(27, 80)(28, 81)(29, 63)(30, 64)(31, 67)(32, 68)(33, 82)(34, 84)(35, 85)(36, 87)(37, 88)(38, 73)(39, 74)(40, 77)(41, 78)(42, 89)(43, 90)(44, 83)(45, 86) local type(s) :: { ( 5, 45, 5, 45, 5, 45, 5, 45, 5, 45, 5, 45, 5, 45, 5, 45, 5, 45 ) } Outer automorphisms :: reflexible Dual of E16.742 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 45 f = 10 degree seq :: [ 18^5 ] E16.744 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 9, 45}) Quotient :: loop Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2), T1^4 * T2^-5, T1^9, (T1^-1 * T2^-1)^5 ] Map:: non-degenerate R = (1, 46, 3, 48, 9, 54, 19, 64, 33, 78, 26, 71, 42, 87, 40, 85, 24, 69, 12, 57, 4, 49, 10, 55, 20, 65, 34, 79, 28, 73, 14, 59, 27, 72, 43, 88, 39, 84, 23, 68, 11, 56, 21, 66, 35, 80, 30, 75, 16, 61, 6, 51, 15, 60, 29, 74, 44, 89, 38, 83, 22, 67, 36, 81, 32, 77, 18, 63, 8, 53, 2, 47, 7, 52, 17, 62, 31, 76, 45, 90, 37, 82, 41, 86, 25, 70, 13, 58, 5, 50) L = (1, 47)(2, 51)(3, 52)(4, 46)(5, 53)(6, 59)(7, 60)(8, 61)(9, 62)(10, 48)(11, 49)(12, 50)(13, 63)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 77)(26, 82)(27, 87)(28, 78)(29, 88)(30, 79)(31, 89)(32, 80)(33, 90)(34, 64)(35, 65)(36, 66)(37, 67)(38, 68)(39, 69)(40, 70)(41, 81)(42, 86)(43, 85)(44, 84)(45, 83) local type(s) :: { ( 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9, 5, 9 ) } Outer automorphisms :: reflexible Dual of E16.740 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 45 f = 14 degree seq :: [ 90 ] E16.745 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 9, 45}) Quotient :: loop Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^5, T2 * T1^-9, (T1^-1 * T2^-1)^9 ] Map:: non-degenerate R = (1, 46, 3, 48, 9, 54, 13, 58, 5, 50)(2, 47, 7, 52, 17, 62, 18, 63, 8, 53)(4, 49, 10, 55, 19, 64, 23, 68, 12, 57)(6, 51, 15, 60, 27, 72, 28, 73, 16, 61)(11, 56, 20, 65, 29, 74, 33, 78, 22, 67)(14, 59, 25, 70, 37, 82, 38, 83, 26, 71)(21, 66, 30, 75, 39, 84, 41, 86, 32, 77)(24, 69, 35, 80, 43, 88, 44, 89, 36, 81)(31, 76, 34, 79, 42, 87, 45, 90, 40, 85) L = (1, 47)(2, 51)(3, 52)(4, 46)(5, 53)(6, 59)(7, 60)(8, 61)(9, 62)(10, 48)(11, 49)(12, 50)(13, 63)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 75)(35, 87)(36, 76)(37, 88)(38, 89)(39, 74)(40, 77)(41, 78)(42, 84)(43, 90)(44, 85)(45, 86) local type(s) :: { ( 9, 45, 9, 45, 9, 45, 9, 45, 9, 45 ) } Outer automorphisms :: reflexible Dual of E16.741 Transitivity :: ET+ VT+ AT Graph:: v = 9 e = 45 f = 6 degree seq :: [ 10^9 ] E16.746 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 9, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y1^5, Y2^9, Y3^45 ] Map:: R = (1, 46, 2, 47, 6, 51, 11, 56, 4, 49)(3, 48, 7, 52, 14, 59, 20, 65, 10, 55)(5, 50, 8, 53, 15, 60, 21, 66, 12, 57)(9, 54, 16, 61, 24, 69, 30, 75, 19, 64)(13, 58, 17, 62, 25, 70, 31, 76, 22, 67)(18, 63, 26, 71, 34, 79, 39, 84, 29, 74)(23, 68, 27, 72, 35, 80, 40, 85, 32, 77)(28, 73, 36, 81, 42, 87, 44, 89, 38, 83)(33, 78, 37, 82, 43, 88, 45, 90, 41, 86)(91, 136, 93, 138, 99, 144, 108, 153, 118, 163, 123, 168, 113, 158, 103, 148, 95, 140)(92, 137, 97, 142, 106, 151, 116, 161, 126, 171, 127, 172, 117, 162, 107, 152, 98, 143)(94, 139, 100, 145, 109, 154, 119, 164, 128, 173, 131, 176, 122, 167, 112, 157, 102, 147)(96, 141, 104, 149, 114, 159, 124, 169, 132, 177, 133, 178, 125, 170, 115, 160, 105, 150)(101, 146, 110, 155, 120, 165, 129, 174, 134, 179, 135, 180, 130, 175, 121, 166, 111, 156) L = (1, 94)(2, 91)(3, 100)(4, 101)(5, 102)(6, 92)(7, 93)(8, 95)(9, 109)(10, 110)(11, 96)(12, 111)(13, 112)(14, 97)(15, 98)(16, 99)(17, 103)(18, 119)(19, 120)(20, 104)(21, 105)(22, 121)(23, 122)(24, 106)(25, 107)(26, 108)(27, 113)(28, 128)(29, 129)(30, 114)(31, 115)(32, 130)(33, 131)(34, 116)(35, 117)(36, 118)(37, 123)(38, 134)(39, 124)(40, 125)(41, 135)(42, 126)(43, 127)(44, 132)(45, 133)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 169)(80, 170)(81, 171)(82, 172)(83, 173)(84, 174)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180) local type(s) :: { ( 2, 90, 2, 90, 2, 90, 2, 90, 2, 90 ), ( 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90 ) } Outer automorphisms :: reflexible Dual of E16.749 Graph:: bipartite v = 14 e = 90 f = 46 degree seq :: [ 10^9, 18^5 ] E16.747 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 9, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2), Y1^4 * Y2^-5, Y1^9, (Y3^-1 * Y1^-1)^5 ] Map:: R = (1, 46, 2, 47, 6, 51, 14, 59, 26, 71, 37, 82, 22, 67, 11, 56, 4, 49)(3, 48, 7, 52, 15, 60, 27, 72, 42, 87, 41, 86, 36, 81, 21, 66, 10, 55)(5, 50, 8, 53, 16, 61, 28, 73, 33, 78, 45, 90, 38, 83, 23, 68, 12, 57)(9, 54, 17, 62, 29, 74, 43, 88, 40, 85, 25, 70, 32, 77, 35, 80, 20, 65)(13, 58, 18, 63, 30, 75, 34, 79, 19, 64, 31, 76, 44, 89, 39, 84, 24, 69)(91, 136, 93, 138, 99, 144, 109, 154, 123, 168, 116, 161, 132, 177, 130, 175, 114, 159, 102, 147, 94, 139, 100, 145, 110, 155, 124, 169, 118, 163, 104, 149, 117, 162, 133, 178, 129, 174, 113, 158, 101, 146, 111, 156, 125, 170, 120, 165, 106, 151, 96, 141, 105, 150, 119, 164, 134, 179, 128, 173, 112, 157, 126, 171, 122, 167, 108, 153, 98, 143, 92, 137, 97, 142, 107, 152, 121, 166, 135, 180, 127, 172, 131, 176, 115, 160, 103, 148, 95, 140) L = (1, 93)(2, 97)(3, 99)(4, 100)(5, 91)(6, 105)(7, 107)(8, 92)(9, 109)(10, 110)(11, 111)(12, 94)(13, 95)(14, 117)(15, 119)(16, 96)(17, 121)(18, 98)(19, 123)(20, 124)(21, 125)(22, 126)(23, 101)(24, 102)(25, 103)(26, 132)(27, 133)(28, 104)(29, 134)(30, 106)(31, 135)(32, 108)(33, 116)(34, 118)(35, 120)(36, 122)(37, 131)(38, 112)(39, 113)(40, 114)(41, 115)(42, 130)(43, 129)(44, 128)(45, 127)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 169)(80, 170)(81, 171)(82, 172)(83, 173)(84, 174)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ), ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.748 Graph:: bipartite v = 6 e = 90 f = 54 degree seq :: [ 18^5, 90 ] E16.748 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 9, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y2^5, Y3^-9 * Y2^-1, (Y2^-1 * Y3)^9, (Y3^-1 * Y1^-1)^45 ] Map:: R = (1, 46)(2, 47)(3, 48)(4, 49)(5, 50)(6, 51)(7, 52)(8, 53)(9, 54)(10, 55)(11, 56)(12, 57)(13, 58)(14, 59)(15, 60)(16, 61)(17, 62)(18, 63)(19, 64)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 70)(26, 71)(27, 72)(28, 73)(29, 74)(30, 75)(31, 76)(32, 77)(33, 78)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 86)(42, 87)(43, 88)(44, 89)(45, 90)(91, 136, 92, 137, 96, 141, 101, 146, 94, 139)(93, 138, 97, 142, 104, 149, 110, 155, 100, 145)(95, 140, 98, 143, 105, 150, 111, 156, 102, 147)(99, 144, 106, 151, 114, 159, 120, 165, 109, 154)(103, 148, 107, 152, 115, 160, 121, 166, 112, 157)(108, 153, 116, 161, 124, 169, 130, 175, 119, 164)(113, 158, 117, 162, 125, 170, 131, 176, 122, 167)(118, 163, 126, 171, 132, 177, 135, 180, 129, 174)(123, 168, 127, 172, 133, 178, 134, 179, 128, 173) L = (1, 93)(2, 97)(3, 99)(4, 100)(5, 91)(6, 104)(7, 106)(8, 92)(9, 108)(10, 109)(11, 110)(12, 94)(13, 95)(14, 114)(15, 96)(16, 116)(17, 98)(18, 118)(19, 119)(20, 120)(21, 101)(22, 102)(23, 103)(24, 124)(25, 105)(26, 126)(27, 107)(28, 128)(29, 129)(30, 130)(31, 111)(32, 112)(33, 113)(34, 132)(35, 115)(36, 123)(37, 117)(38, 122)(39, 134)(40, 135)(41, 121)(42, 127)(43, 125)(44, 131)(45, 133)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 169)(80, 170)(81, 171)(82, 172)(83, 173)(84, 174)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180) local type(s) :: { ( 18, 90 ), ( 18, 90, 18, 90, 18, 90, 18, 90, 18, 90 ) } Outer automorphisms :: reflexible Dual of E16.747 Graph:: simple bipartite v = 54 e = 90 f = 6 degree seq :: [ 2^45, 10^9 ] E16.749 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 9, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^5, (R * Y2 * Y3^-1)^2, Y3 * Y1^-9, (Y3 * Y2^-1)^5, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 46, 2, 47, 6, 51, 14, 59, 24, 69, 34, 79, 30, 75, 20, 65, 10, 55, 3, 48, 7, 52, 15, 60, 25, 70, 35, 80, 42, 87, 39, 84, 29, 74, 19, 64, 9, 54, 17, 62, 27, 72, 37, 82, 43, 88, 45, 90, 41, 86, 33, 78, 23, 68, 13, 58, 18, 63, 28, 73, 38, 83, 44, 89, 40, 85, 32, 77, 22, 67, 12, 57, 5, 50, 8, 53, 16, 61, 26, 71, 36, 81, 31, 76, 21, 66, 11, 56, 4, 49)(91, 136)(92, 137)(93, 138)(94, 139)(95, 140)(96, 141)(97, 142)(98, 143)(99, 144)(100, 145)(101, 146)(102, 147)(103, 148)(104, 149)(105, 150)(106, 151)(107, 152)(108, 153)(109, 154)(110, 155)(111, 156)(112, 157)(113, 158)(114, 159)(115, 160)(116, 161)(117, 162)(118, 163)(119, 164)(120, 165)(121, 166)(122, 167)(123, 168)(124, 169)(125, 170)(126, 171)(127, 172)(128, 173)(129, 174)(130, 175)(131, 176)(132, 177)(133, 178)(134, 179)(135, 180) L = (1, 93)(2, 97)(3, 99)(4, 100)(5, 91)(6, 105)(7, 107)(8, 92)(9, 103)(10, 109)(11, 110)(12, 94)(13, 95)(14, 115)(15, 117)(16, 96)(17, 108)(18, 98)(19, 113)(20, 119)(21, 120)(22, 101)(23, 102)(24, 125)(25, 127)(26, 104)(27, 118)(28, 106)(29, 123)(30, 129)(31, 124)(32, 111)(33, 112)(34, 132)(35, 133)(36, 114)(37, 128)(38, 116)(39, 131)(40, 121)(41, 122)(42, 135)(43, 134)(44, 126)(45, 130)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 169)(80, 170)(81, 171)(82, 172)(83, 173)(84, 174)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180) local type(s) :: { ( 10, 18 ), ( 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18, 10, 18 ) } Outer automorphisms :: reflexible Dual of E16.746 Graph:: bipartite v = 46 e = 90 f = 14 degree seq :: [ 2^45, 90 ] E16.750 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 9, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y1^5, Y2^9 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 46, 2, 47, 6, 51, 11, 56, 4, 49)(3, 48, 7, 52, 14, 59, 20, 65, 10, 55)(5, 50, 8, 53, 15, 60, 21, 66, 12, 57)(9, 54, 16, 61, 24, 69, 30, 75, 19, 64)(13, 58, 17, 62, 25, 70, 31, 76, 22, 67)(18, 63, 26, 71, 34, 79, 39, 84, 29, 74)(23, 68, 27, 72, 35, 80, 40, 85, 32, 77)(28, 73, 36, 81, 42, 87, 44, 89, 38, 83)(33, 78, 37, 82, 43, 88, 45, 90, 41, 86)(91, 136, 93, 138, 99, 144, 108, 153, 118, 163, 127, 172, 117, 162, 107, 152, 98, 143, 92, 137, 97, 142, 106, 151, 116, 161, 126, 171, 133, 178, 125, 170, 115, 160, 105, 150, 96, 141, 104, 149, 114, 159, 124, 169, 132, 177, 135, 180, 130, 175, 121, 166, 111, 156, 101, 146, 110, 155, 120, 165, 129, 174, 134, 179, 131, 176, 122, 167, 112, 157, 102, 147, 94, 139, 100, 145, 109, 154, 119, 164, 128, 173, 123, 168, 113, 158, 103, 148, 95, 140) L = (1, 94)(2, 91)(3, 100)(4, 101)(5, 102)(6, 92)(7, 93)(8, 95)(9, 109)(10, 110)(11, 96)(12, 111)(13, 112)(14, 97)(15, 98)(16, 99)(17, 103)(18, 119)(19, 120)(20, 104)(21, 105)(22, 121)(23, 122)(24, 106)(25, 107)(26, 108)(27, 113)(28, 128)(29, 129)(30, 114)(31, 115)(32, 130)(33, 131)(34, 116)(35, 117)(36, 118)(37, 123)(38, 134)(39, 124)(40, 125)(41, 135)(42, 126)(43, 127)(44, 132)(45, 133)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 169)(80, 170)(81, 171)(82, 172)(83, 173)(84, 174)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E16.751 Graph:: bipartite v = 10 e = 90 f = 50 degree seq :: [ 10^9, 90 ] E16.751 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 9, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-5 * Y1^4, Y1^9, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^45 ] Map:: R = (1, 46, 2, 47, 6, 51, 14, 59, 26, 71, 37, 82, 22, 67, 11, 56, 4, 49)(3, 48, 7, 52, 15, 60, 27, 72, 42, 87, 41, 86, 36, 81, 21, 66, 10, 55)(5, 50, 8, 53, 16, 61, 28, 73, 33, 78, 45, 90, 38, 83, 23, 68, 12, 57)(9, 54, 17, 62, 29, 74, 43, 88, 40, 85, 25, 70, 32, 77, 35, 80, 20, 65)(13, 58, 18, 63, 30, 75, 34, 79, 19, 64, 31, 76, 44, 89, 39, 84, 24, 69)(91, 136)(92, 137)(93, 138)(94, 139)(95, 140)(96, 141)(97, 142)(98, 143)(99, 144)(100, 145)(101, 146)(102, 147)(103, 148)(104, 149)(105, 150)(106, 151)(107, 152)(108, 153)(109, 154)(110, 155)(111, 156)(112, 157)(113, 158)(114, 159)(115, 160)(116, 161)(117, 162)(118, 163)(119, 164)(120, 165)(121, 166)(122, 167)(123, 168)(124, 169)(125, 170)(126, 171)(127, 172)(128, 173)(129, 174)(130, 175)(131, 176)(132, 177)(133, 178)(134, 179)(135, 180) L = (1, 93)(2, 97)(3, 99)(4, 100)(5, 91)(6, 105)(7, 107)(8, 92)(9, 109)(10, 110)(11, 111)(12, 94)(13, 95)(14, 117)(15, 119)(16, 96)(17, 121)(18, 98)(19, 123)(20, 124)(21, 125)(22, 126)(23, 101)(24, 102)(25, 103)(26, 132)(27, 133)(28, 104)(29, 134)(30, 106)(31, 135)(32, 108)(33, 116)(34, 118)(35, 120)(36, 122)(37, 131)(38, 112)(39, 113)(40, 114)(41, 115)(42, 130)(43, 129)(44, 128)(45, 127)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 169)(80, 170)(81, 171)(82, 172)(83, 173)(84, 174)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180) local type(s) :: { ( 10, 90 ), ( 10, 90, 10, 90, 10, 90, 10, 90, 10, 90, 10, 90, 10, 90, 10, 90, 10, 90 ) } Outer automorphisms :: reflexible Dual of E16.750 Graph:: simple bipartite v = 50 e = 90 f = 10 degree seq :: [ 2^45, 18^5 ] E16.752 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 8, 12}) Quotient :: edge Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^3 * T1^-1 * T2^-1 * T1, T2^3 * T1 * T2^-1 * T1^-1, T2 * T1^2 * T2^-1 * T1^-2, T1^6, (T1^-1 * T2 * T1 * T2)^2, (T2^-1 * T1^-1)^12 ] Map:: non-degenerate R = (1, 3, 10, 23, 42, 25, 17, 5)(2, 7, 22, 9, 27, 15, 26, 8)(4, 12, 31, 11, 29, 16, 28, 14)(6, 19, 38, 21, 41, 24, 40, 20)(13, 30, 43, 32, 44, 34, 45, 33)(18, 35, 46, 37, 48, 39, 47, 36)(49, 50, 54, 66, 61, 52)(51, 57, 67, 85, 78, 59)(53, 63, 68, 87, 81, 64)(55, 69, 83, 80, 60, 71)(56, 72, 84, 82, 62, 73)(58, 74, 86, 95, 91, 76)(65, 70, 88, 94, 93, 79)(75, 89, 96, 92, 77, 90) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^6 ), ( 24^8 ) } Outer automorphisms :: reflexible Dual of E16.756 Transitivity :: ET+ Graph:: simple bipartite v = 14 e = 48 f = 4 degree seq :: [ 6^8, 8^6 ] E16.753 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 8, 12}) Quotient :: edge Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^3 * T2 * T1^-1, T2 * T1^-3 * T2^-1 * T1, T2^2 * T1^-1 * T2^-2 * T1, (T2 * T1 * T2^-1 * T1)^2, (T2 * T1^-1 * T2^2)^2, (T2^-1 * T1^-1)^6 ] Map:: non-degenerate R = (1, 3, 10, 28, 42, 24, 36, 21, 39, 35, 17, 5)(2, 7, 22, 40, 34, 16, 31, 11, 30, 44, 26, 8)(4, 12, 29, 46, 33, 15, 18, 9, 27, 45, 32, 14)(6, 19, 37, 47, 43, 25, 13, 23, 41, 48, 38, 20)(49, 50, 54, 66, 84, 79, 61, 52)(51, 57, 71, 55, 69, 60, 67, 59)(53, 63, 73, 56, 72, 62, 68, 64)(58, 70, 85, 75, 87, 78, 89, 77)(65, 74, 86, 81, 90, 82, 91, 80)(76, 93, 96, 88, 83, 94, 95, 92) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^8 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E16.757 Transitivity :: ET+ Graph:: bipartite v = 10 e = 48 f = 8 degree seq :: [ 8^6, 12^4 ] E16.754 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 8, 12}) Quotient :: edge Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2^-2 * T1^3, (T1^-1 * T2 * T1^-1)^2, T2^6, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 29, 17, 5)(2, 7, 22, 42, 26, 8)(4, 12, 18, 37, 34, 14)(6, 19, 39, 32, 13, 20)(9, 27, 47, 35, 15, 28)(11, 30, 38, 36, 16, 31)(21, 40, 33, 45, 24, 41)(23, 43, 48, 46, 25, 44)(49, 50, 54, 66, 58, 70, 87, 82, 65, 74, 61, 52)(51, 57, 67, 86, 77, 95, 80, 64, 53, 63, 68, 59)(55, 69, 85, 96, 90, 81, 62, 73, 56, 72, 60, 71)(75, 92, 84, 89, 83, 91, 79, 88, 76, 94, 78, 93) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^6 ), ( 16^12 ) } Outer automorphisms :: reflexible Dual of E16.755 Transitivity :: ET+ Graph:: bipartite v = 12 e = 48 f = 6 degree seq :: [ 6^8, 12^4 ] E16.755 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 8, 12}) Quotient :: loop Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^3 * T1^-1 * T2^-1 * T1, T2^3 * T1 * T2^-1 * T1^-1, T2 * T1^2 * T2^-1 * T1^-2, T1^6, (T1^-1 * T2 * T1 * T2)^2, (T2^-1 * T1^-1)^12 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 23, 71, 42, 90, 25, 73, 17, 65, 5, 53)(2, 50, 7, 55, 22, 70, 9, 57, 27, 75, 15, 63, 26, 74, 8, 56)(4, 52, 12, 60, 31, 79, 11, 59, 29, 77, 16, 64, 28, 76, 14, 62)(6, 54, 19, 67, 38, 86, 21, 69, 41, 89, 24, 72, 40, 88, 20, 68)(13, 61, 30, 78, 43, 91, 32, 80, 44, 92, 34, 82, 45, 93, 33, 81)(18, 66, 35, 83, 46, 94, 37, 85, 48, 96, 39, 87, 47, 95, 36, 84) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 69)(8, 72)(9, 67)(10, 74)(11, 51)(12, 71)(13, 52)(14, 73)(15, 68)(16, 53)(17, 70)(18, 61)(19, 85)(20, 87)(21, 83)(22, 88)(23, 55)(24, 84)(25, 56)(26, 86)(27, 89)(28, 58)(29, 90)(30, 59)(31, 65)(32, 60)(33, 64)(34, 62)(35, 80)(36, 82)(37, 78)(38, 95)(39, 81)(40, 94)(41, 96)(42, 75)(43, 76)(44, 77)(45, 79)(46, 93)(47, 91)(48, 92) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.754 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 48 f = 12 degree seq :: [ 16^6 ] E16.756 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 8, 12}) Quotient :: loop Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^3 * T2 * T1^-1, T2 * T1^-3 * T2^-1 * T1, T2^2 * T1^-1 * T2^-2 * T1, (T2 * T1 * T2^-1 * T1)^2, (T2 * T1^-1 * T2^2)^2, (T2^-1 * T1^-1)^6 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 28, 76, 42, 90, 24, 72, 36, 84, 21, 69, 39, 87, 35, 83, 17, 65, 5, 53)(2, 50, 7, 55, 22, 70, 40, 88, 34, 82, 16, 64, 31, 79, 11, 59, 30, 78, 44, 92, 26, 74, 8, 56)(4, 52, 12, 60, 29, 77, 46, 94, 33, 81, 15, 63, 18, 66, 9, 57, 27, 75, 45, 93, 32, 80, 14, 62)(6, 54, 19, 67, 37, 85, 47, 95, 43, 91, 25, 73, 13, 61, 23, 71, 41, 89, 48, 96, 38, 86, 20, 68) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 69)(8, 72)(9, 71)(10, 70)(11, 51)(12, 67)(13, 52)(14, 68)(15, 73)(16, 53)(17, 74)(18, 84)(19, 59)(20, 64)(21, 60)(22, 85)(23, 55)(24, 62)(25, 56)(26, 86)(27, 87)(28, 93)(29, 58)(30, 89)(31, 61)(32, 65)(33, 90)(34, 91)(35, 94)(36, 79)(37, 75)(38, 81)(39, 78)(40, 83)(41, 77)(42, 82)(43, 80)(44, 76)(45, 96)(46, 95)(47, 92)(48, 88) 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 ) } Outer automorphisms :: reflexible Dual of E16.752 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 48 f = 14 degree seq :: [ 24^4 ] E16.757 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 8, 12}) Quotient :: loop Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2^-2 * T1^3, (T1^-1 * T2 * T1^-1)^2, T2^6, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 29, 77, 17, 65, 5, 53)(2, 50, 7, 55, 22, 70, 42, 90, 26, 74, 8, 56)(4, 52, 12, 60, 18, 66, 37, 85, 34, 82, 14, 62)(6, 54, 19, 67, 39, 87, 32, 80, 13, 61, 20, 68)(9, 57, 27, 75, 47, 95, 35, 83, 15, 63, 28, 76)(11, 59, 30, 78, 38, 86, 36, 84, 16, 64, 31, 79)(21, 69, 40, 88, 33, 81, 45, 93, 24, 72, 41, 89)(23, 71, 43, 91, 48, 96, 46, 94, 25, 73, 44, 92) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 69)(8, 72)(9, 67)(10, 70)(11, 51)(12, 71)(13, 52)(14, 73)(15, 68)(16, 53)(17, 74)(18, 58)(19, 86)(20, 59)(21, 85)(22, 87)(23, 55)(24, 60)(25, 56)(26, 61)(27, 92)(28, 94)(29, 95)(30, 93)(31, 88)(32, 64)(33, 62)(34, 65)(35, 91)(36, 89)(37, 96)(38, 77)(39, 82)(40, 76)(41, 83)(42, 81)(43, 79)(44, 84)(45, 75)(46, 78)(47, 80)(48, 90) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.753 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 48 f = 10 degree seq :: [ 12^8 ] E16.758 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-3 * Y1^-1, Y2^-1 * Y1^-1 * Y3 * Y2 * Y3^-1 * Y1, Y3 * Y2^-2 * Y3^-1 * Y2^-2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^2, Y1^6, (Y1 * Y2 * Y1^-1 * Y2)^2, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (Y3 * Y2)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 37, 85, 30, 78, 11, 59)(5, 53, 15, 63, 20, 68, 39, 87, 33, 81, 16, 64)(7, 55, 21, 69, 35, 83, 32, 80, 12, 60, 23, 71)(8, 56, 24, 72, 36, 84, 34, 82, 14, 62, 25, 73)(10, 58, 26, 74, 38, 86, 47, 95, 43, 91, 28, 76)(17, 65, 22, 70, 40, 88, 46, 94, 45, 93, 31, 79)(27, 75, 41, 89, 48, 96, 44, 92, 29, 77, 42, 90)(97, 145, 99, 147, 106, 154, 119, 167, 138, 186, 121, 169, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 105, 153, 123, 171, 111, 159, 122, 170, 104, 152)(100, 148, 108, 156, 127, 175, 107, 155, 125, 173, 112, 160, 124, 172, 110, 158)(102, 150, 115, 163, 134, 182, 117, 165, 137, 185, 120, 168, 136, 184, 116, 164)(109, 157, 126, 174, 139, 187, 128, 176, 140, 188, 130, 178, 141, 189, 129, 177)(114, 162, 131, 179, 142, 190, 133, 181, 144, 192, 135, 183, 143, 191, 132, 180) L = (1, 100)(2, 97)(3, 107)(4, 109)(5, 112)(6, 98)(7, 119)(8, 121)(9, 99)(10, 124)(11, 126)(12, 128)(13, 114)(14, 130)(15, 101)(16, 129)(17, 127)(18, 102)(19, 105)(20, 111)(21, 103)(22, 113)(23, 108)(24, 104)(25, 110)(26, 106)(27, 138)(28, 139)(29, 140)(30, 133)(31, 141)(32, 131)(33, 135)(34, 132)(35, 117)(36, 120)(37, 115)(38, 122)(39, 116)(40, 118)(41, 123)(42, 125)(43, 143)(44, 144)(45, 142)(46, 136)(47, 134)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E16.761 Graph:: bipartite v = 14 e = 96 f = 52 degree seq :: [ 12^8, 16^6 ] E16.759 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1^-3, Y1^-2 * Y2 * Y1 * Y2^-1 * Y1^-1, Y2^2 * Y1^-1 * Y2^-2 * Y1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, (Y2 * Y1^-1 * Y2^2)^2, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 36, 84, 31, 79, 13, 61, 4, 52)(3, 51, 9, 57, 23, 71, 7, 55, 21, 69, 12, 60, 19, 67, 11, 59)(5, 53, 15, 63, 25, 73, 8, 56, 24, 72, 14, 62, 20, 68, 16, 64)(10, 58, 22, 70, 37, 85, 27, 75, 39, 87, 30, 78, 41, 89, 29, 77)(17, 65, 26, 74, 38, 86, 33, 81, 42, 90, 34, 82, 43, 91, 32, 80)(28, 76, 45, 93, 48, 96, 40, 88, 35, 83, 46, 94, 47, 95, 44, 92)(97, 145, 99, 147, 106, 154, 124, 172, 138, 186, 120, 168, 132, 180, 117, 165, 135, 183, 131, 179, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 136, 184, 130, 178, 112, 160, 127, 175, 107, 155, 126, 174, 140, 188, 122, 170, 104, 152)(100, 148, 108, 156, 125, 173, 142, 190, 129, 177, 111, 159, 114, 162, 105, 153, 123, 171, 141, 189, 128, 176, 110, 158)(102, 150, 115, 163, 133, 181, 143, 191, 139, 187, 121, 169, 109, 157, 119, 167, 137, 185, 144, 192, 134, 182, 116, 164) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 123)(10, 124)(11, 126)(12, 125)(13, 119)(14, 100)(15, 114)(16, 127)(17, 101)(18, 105)(19, 133)(20, 102)(21, 135)(22, 136)(23, 137)(24, 132)(25, 109)(26, 104)(27, 141)(28, 138)(29, 142)(30, 140)(31, 107)(32, 110)(33, 111)(34, 112)(35, 113)(36, 117)(37, 143)(38, 116)(39, 131)(40, 130)(41, 144)(42, 120)(43, 121)(44, 122)(45, 128)(46, 129)(47, 139)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ), ( 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 E16.760 Graph:: bipartite v = 10 e = 96 f = 56 degree seq :: [ 16^6, 24^4 ] E16.760 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2^-1)^2, Y3^-3 * Y2^-2 * Y3^-1, Y2 * Y3^-1 * Y2^-2 * Y3 * Y2, Y2^6, Y3^2 * Y2 * Y3^-2 * Y2^-1, Y3^2 * Y2^-1 * Y3 * Y2^-2 * Y3 * Y2^-1, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^12 ] Map:: R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 102, 150, 114, 162, 109, 157, 100, 148)(99, 147, 105, 153, 115, 163, 135, 183, 128, 176, 107, 155)(101, 149, 111, 159, 116, 164, 136, 184, 125, 173, 112, 160)(103, 151, 117, 165, 133, 181, 130, 178, 108, 156, 119, 167)(104, 152, 120, 168, 134, 182, 131, 179, 110, 158, 121, 169)(106, 154, 118, 166, 113, 161, 122, 170, 137, 185, 126, 174)(123, 171, 143, 191, 132, 180, 141, 189, 127, 175, 139, 187)(124, 172, 140, 188, 144, 192, 138, 186, 129, 177, 142, 190) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 123)(10, 125)(11, 127)(12, 126)(13, 128)(14, 100)(15, 124)(16, 129)(17, 101)(18, 133)(19, 113)(20, 102)(21, 138)(22, 110)(23, 140)(24, 139)(25, 141)(26, 104)(27, 112)(28, 105)(29, 109)(30, 134)(31, 136)(32, 137)(33, 107)(34, 142)(35, 143)(36, 111)(37, 122)(38, 114)(39, 132)(40, 144)(41, 116)(42, 121)(43, 117)(44, 131)(45, 119)(46, 120)(47, 130)(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) :: { ( 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ) } Outer automorphisms :: reflexible Dual of E16.759 Graph:: simple bipartite v = 56 e = 96 f = 10 degree seq :: [ 2^48, 12^8 ] E16.761 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3^-2 * Y1^3, (Y1^-1 * Y3 * Y1^-1)^2, Y3^6, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 10, 58, 22, 70, 39, 87, 34, 82, 17, 65, 26, 74, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 38, 86, 29, 77, 47, 95, 32, 80, 16, 64, 5, 53, 15, 63, 20, 68, 11, 59)(7, 55, 21, 69, 37, 85, 48, 96, 42, 90, 33, 81, 14, 62, 25, 73, 8, 56, 24, 72, 12, 60, 23, 71)(27, 75, 44, 92, 36, 84, 41, 89, 35, 83, 43, 91, 31, 79, 40, 88, 28, 76, 46, 94, 30, 78, 45, 93)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 123)(10, 125)(11, 126)(12, 114)(13, 116)(14, 100)(15, 124)(16, 127)(17, 101)(18, 133)(19, 135)(20, 102)(21, 136)(22, 138)(23, 139)(24, 137)(25, 140)(26, 104)(27, 143)(28, 105)(29, 113)(30, 134)(31, 107)(32, 109)(33, 141)(34, 110)(35, 111)(36, 112)(37, 130)(38, 132)(39, 128)(40, 129)(41, 117)(42, 122)(43, 144)(44, 119)(45, 120)(46, 121)(47, 131)(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) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E16.758 Graph:: simple bipartite v = 52 e = 96 f = 14 degree seq :: [ 2^48, 24^4 ] E16.762 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^2 * Y3 * Y2^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y1^6, Y3^2 * Y2 * Y3^-2 * Y2^-1, Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^-3 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 39, 87, 30, 78, 11, 59)(5, 53, 15, 63, 20, 68, 41, 89, 33, 81, 16, 64)(7, 55, 21, 69, 37, 85, 32, 80, 12, 60, 23, 71)(8, 56, 24, 72, 38, 86, 34, 82, 14, 62, 25, 73)(10, 58, 22, 70, 40, 88, 35, 83, 17, 65, 26, 74)(27, 75, 45, 93, 36, 84, 43, 91, 29, 77, 47, 95)(28, 76, 46, 94, 48, 96, 44, 92, 31, 79, 42, 90)(97, 145, 99, 147, 106, 154, 116, 164, 102, 150, 115, 163, 136, 184, 129, 177, 109, 157, 126, 174, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 134, 182, 114, 162, 133, 181, 131, 179, 110, 158, 100, 148, 108, 156, 122, 170, 104, 152)(105, 153, 123, 171, 137, 185, 144, 192, 135, 183, 132, 180, 112, 160, 127, 175, 107, 155, 125, 173, 111, 159, 124, 172)(117, 165, 138, 186, 130, 178, 143, 191, 128, 176, 142, 190, 121, 169, 141, 189, 119, 167, 140, 188, 120, 168, 139, 187) L = (1, 100)(2, 97)(3, 107)(4, 109)(5, 112)(6, 98)(7, 119)(8, 121)(9, 99)(10, 122)(11, 126)(12, 128)(13, 114)(14, 130)(15, 101)(16, 129)(17, 131)(18, 102)(19, 105)(20, 111)(21, 103)(22, 106)(23, 108)(24, 104)(25, 110)(26, 113)(27, 143)(28, 138)(29, 139)(30, 135)(31, 140)(32, 133)(33, 137)(34, 134)(35, 136)(36, 141)(37, 117)(38, 120)(39, 115)(40, 118)(41, 116)(42, 127)(43, 132)(44, 144)(45, 123)(46, 124)(47, 125)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E16.763 Graph:: bipartite v = 12 e = 96 f = 54 degree seq :: [ 12^8, 24^4 ] E16.763 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^2 * Y3 * Y1^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y1 * Y3 * Y1^-2, Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-2, Y3^2 * Y1^-1 * Y3^-2 * Y1, (Y3 * Y1^-1 * Y3^2)^2, (Y3^-1 * Y1^-1)^6, (Y3 * Y2^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 36, 84, 31, 79, 13, 61, 4, 52)(3, 51, 9, 57, 23, 71, 7, 55, 21, 69, 12, 60, 19, 67, 11, 59)(5, 53, 15, 63, 25, 73, 8, 56, 24, 72, 14, 62, 20, 68, 16, 64)(10, 58, 22, 70, 37, 85, 27, 75, 39, 87, 30, 78, 41, 89, 29, 77)(17, 65, 26, 74, 38, 86, 33, 81, 42, 90, 34, 82, 43, 91, 32, 80)(28, 76, 45, 93, 48, 96, 40, 88, 35, 83, 46, 94, 47, 95, 44, 92)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 123)(10, 124)(11, 126)(12, 125)(13, 119)(14, 100)(15, 114)(16, 127)(17, 101)(18, 105)(19, 133)(20, 102)(21, 135)(22, 136)(23, 137)(24, 132)(25, 109)(26, 104)(27, 141)(28, 138)(29, 142)(30, 140)(31, 107)(32, 110)(33, 111)(34, 112)(35, 113)(36, 117)(37, 143)(38, 116)(39, 131)(40, 130)(41, 144)(42, 120)(43, 121)(44, 122)(45, 128)(46, 129)(47, 139)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E16.762 Graph:: simple bipartite v = 54 e = 96 f = 12 degree seq :: [ 2^48, 16^6 ] E16.764 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 24}) Quotient :: halfedge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y2 * Y1)^2, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3, Y1^-1 * Y3 * Y1 * Y2 * Y3 * Y2 * Y1^-4, Y2 * Y3 * Y2 * Y1^18 * Y3 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 62, 14, 74, 26, 90, 42, 88, 40, 82, 34, 68, 20, 58, 10, 65, 17, 77, 29, 93, 45, 86, 38, 71, 23, 60, 12, 66, 18, 78, 30, 84, 36, 95, 47, 89, 41, 73, 25, 61, 13, 53, 5, 49)(3, 57, 9, 67, 19, 81, 33, 96, 48, 92, 44, 76, 28, 64, 16, 56, 8, 52, 4, 59, 11, 70, 22, 85, 37, 94, 46, 79, 31, 69, 21, 83, 35, 80, 32, 72, 24, 87, 39, 91, 43, 75, 27, 63, 15, 55, 7, 51) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 38)(24, 40)(25, 33)(26, 43)(28, 36)(29, 46)(32, 34)(37, 45)(39, 42)(41, 48)(44, 47)(49, 52)(50, 56)(51, 58)(53, 59)(54, 64)(55, 65)(57, 68)(60, 72)(61, 70)(62, 76)(63, 77)(66, 80)(67, 82)(69, 84)(71, 87)(73, 85)(74, 92)(75, 93)(78, 83)(79, 95)(81, 88)(86, 91)(89, 94)(90, 96) local type(s) :: { ( 6^48 ) } Outer automorphisms :: reflexible Dual of E16.765 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 16 degree seq :: [ 48^2 ] E16.765 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 24}) Quotient :: halfedge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^3, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3 * Y1)^2, (Y3 * Y2)^8, (Y2 * Y1 * Y3)^24 ] Map:: non-degenerate R = (1, 50, 2, 53, 5, 49)(3, 56, 8, 54, 6, 51)(4, 58, 10, 55, 7, 52)(9, 60, 12, 62, 14, 57)(11, 61, 13, 64, 16, 59)(15, 68, 20, 66, 18, 63)(17, 70, 22, 67, 19, 65)(21, 72, 24, 74, 26, 69)(23, 73, 25, 76, 28, 71)(27, 80, 32, 78, 30, 75)(29, 82, 34, 79, 31, 77)(33, 84, 36, 86, 38, 81)(35, 85, 37, 88, 40, 83)(39, 92, 44, 90, 42, 87)(41, 94, 46, 91, 43, 89)(45, 95, 47, 96, 48, 93) L = (1, 3)(2, 6)(4, 11)(5, 8)(7, 13)(9, 15)(10, 16)(12, 18)(14, 20)(17, 23)(19, 25)(21, 27)(22, 28)(24, 30)(26, 32)(29, 35)(31, 37)(33, 39)(34, 40)(36, 42)(38, 44)(41, 45)(43, 47)(46, 48)(49, 52)(50, 55)(51, 57)(53, 58)(54, 60)(56, 62)(59, 65)(61, 67)(63, 69)(64, 70)(66, 72)(68, 74)(71, 77)(73, 79)(75, 81)(76, 82)(78, 84)(80, 86)(83, 89)(85, 91)(87, 93)(88, 94)(90, 95)(92, 96) local type(s) :: { ( 48^6 ) } Outer automorphisms :: reflexible Dual of E16.764 Transitivity :: VT+ AT Graph:: bipartite v = 16 e = 48 f = 2 degree seq :: [ 6^16 ] E16.766 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 24}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^8, (Y3 * Y1 * Y2)^24 ] Map:: R = (1, 49, 4, 52, 5, 53)(2, 50, 7, 55, 8, 56)(3, 51, 10, 58, 11, 59)(6, 54, 13, 61, 14, 62)(9, 57, 16, 64, 17, 65)(12, 60, 19, 67, 20, 68)(15, 63, 22, 70, 23, 71)(18, 66, 25, 73, 26, 74)(21, 69, 28, 76, 29, 77)(24, 72, 31, 79, 32, 80)(27, 75, 34, 82, 35, 83)(30, 78, 37, 85, 38, 86)(33, 81, 40, 88, 41, 89)(36, 84, 43, 91, 44, 92)(39, 87, 45, 93, 46, 94)(42, 90, 47, 95, 48, 96)(97, 98)(99, 105)(100, 104)(101, 103)(102, 108)(106, 113)(107, 112)(109, 116)(110, 115)(111, 117)(114, 120)(118, 125)(119, 124)(121, 128)(122, 127)(123, 129)(126, 132)(130, 137)(131, 136)(133, 140)(134, 139)(135, 138)(141, 144)(142, 143)(145, 147)(146, 150)(148, 155)(149, 154)(151, 158)(152, 157)(153, 159)(156, 162)(160, 167)(161, 166)(163, 170)(164, 169)(165, 171)(168, 174)(172, 179)(173, 178)(175, 182)(176, 181)(177, 183)(180, 186)(184, 190)(185, 189)(187, 192)(188, 191) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^6 ) } Outer automorphisms :: reflexible Dual of E16.769 Graph:: simple bipartite v = 64 e = 96 f = 2 degree seq :: [ 2^48, 6^16 ] E16.767 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 24}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3^-2 * Y2 * Y1 * Y3^2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2, Y2 * Y3^-6 * Y1 * Y2 * Y1, (Y1 * Y2)^8 ] Map:: R = (1, 49, 4, 52, 12, 60, 24, 72, 40, 88, 42, 90, 26, 74, 37, 85, 21, 69, 9, 57, 20, 68, 36, 84, 44, 92, 30, 78, 16, 64, 6, 54, 15, 63, 29, 77, 33, 81, 47, 95, 41, 89, 25, 73, 13, 61, 5, 53)(2, 50, 7, 55, 17, 65, 31, 79, 45, 93, 35, 83, 19, 67, 34, 82, 28, 76, 14, 62, 27, 75, 43, 91, 39, 87, 23, 71, 11, 59, 3, 51, 10, 58, 22, 70, 38, 86, 48, 96, 46, 94, 32, 80, 18, 66, 8, 56)(97, 98)(99, 105)(100, 104)(101, 103)(102, 110)(106, 117)(107, 116)(108, 114)(109, 113)(111, 124)(112, 123)(115, 129)(118, 133)(119, 132)(120, 128)(121, 127)(122, 134)(125, 130)(126, 139)(131, 143)(135, 140)(136, 142)(137, 141)(138, 144)(145, 147)(146, 150)(148, 155)(149, 154)(151, 160)(152, 159)(153, 163)(156, 167)(157, 166)(158, 170)(161, 174)(162, 173)(164, 179)(165, 178)(168, 183)(169, 182)(171, 186)(172, 181)(175, 188)(176, 177)(180, 189)(184, 187)(185, 192)(190, 191) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12, 12 ), ( 12^48 ) } Outer automorphisms :: reflexible Dual of E16.768 Graph:: simple bipartite v = 50 e = 96 f = 16 degree seq :: [ 2^48, 48^2 ] E16.768 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 24}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^8, (Y3 * Y1 * Y2)^24 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 8, 56, 104, 152)(3, 51, 99, 147, 10, 58, 106, 154, 11, 59, 107, 155)(6, 54, 102, 150, 13, 61, 109, 157, 14, 62, 110, 158)(9, 57, 105, 153, 16, 64, 112, 160, 17, 65, 113, 161)(12, 60, 108, 156, 19, 67, 115, 163, 20, 68, 116, 164)(15, 63, 111, 159, 22, 70, 118, 166, 23, 71, 119, 167)(18, 66, 114, 162, 25, 73, 121, 169, 26, 74, 122, 170)(21, 69, 117, 165, 28, 76, 124, 172, 29, 77, 125, 173)(24, 72, 120, 168, 31, 79, 127, 175, 32, 80, 128, 176)(27, 75, 123, 171, 34, 82, 130, 178, 35, 83, 131, 179)(30, 78, 126, 174, 37, 85, 133, 181, 38, 86, 134, 182)(33, 81, 129, 177, 40, 88, 136, 184, 41, 89, 137, 185)(36, 84, 132, 180, 43, 91, 139, 187, 44, 92, 140, 188)(39, 87, 135, 183, 45, 93, 141, 189, 46, 94, 142, 190)(42, 90, 138, 186, 47, 95, 143, 191, 48, 96, 144, 192) L = (1, 50)(2, 49)(3, 57)(4, 56)(5, 55)(6, 60)(7, 53)(8, 52)(9, 51)(10, 65)(11, 64)(12, 54)(13, 68)(14, 67)(15, 69)(16, 59)(17, 58)(18, 72)(19, 62)(20, 61)(21, 63)(22, 77)(23, 76)(24, 66)(25, 80)(26, 79)(27, 81)(28, 71)(29, 70)(30, 84)(31, 74)(32, 73)(33, 75)(34, 89)(35, 88)(36, 78)(37, 92)(38, 91)(39, 90)(40, 83)(41, 82)(42, 87)(43, 86)(44, 85)(45, 96)(46, 95)(47, 94)(48, 93)(97, 147)(98, 150)(99, 145)(100, 155)(101, 154)(102, 146)(103, 158)(104, 157)(105, 159)(106, 149)(107, 148)(108, 162)(109, 152)(110, 151)(111, 153)(112, 167)(113, 166)(114, 156)(115, 170)(116, 169)(117, 171)(118, 161)(119, 160)(120, 174)(121, 164)(122, 163)(123, 165)(124, 179)(125, 178)(126, 168)(127, 182)(128, 181)(129, 183)(130, 173)(131, 172)(132, 186)(133, 176)(134, 175)(135, 177)(136, 190)(137, 189)(138, 180)(139, 192)(140, 191)(141, 185)(142, 184)(143, 188)(144, 187) local type(s) :: { ( 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48 ) } Outer automorphisms :: reflexible Dual of E16.767 Transitivity :: VT+ Graph:: bipartite v = 16 e = 96 f = 50 degree seq :: [ 12^16 ] E16.769 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 24}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3^-2 * Y2 * Y1 * Y3^2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2, Y2 * Y3^-6 * Y1 * Y2 * Y1, (Y1 * Y2)^8 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 12, 60, 108, 156, 24, 72, 120, 168, 40, 88, 136, 184, 42, 90, 138, 186, 26, 74, 122, 170, 37, 85, 133, 181, 21, 69, 117, 165, 9, 57, 105, 153, 20, 68, 116, 164, 36, 84, 132, 180, 44, 92, 140, 188, 30, 78, 126, 174, 16, 64, 112, 160, 6, 54, 102, 150, 15, 63, 111, 159, 29, 77, 125, 173, 33, 81, 129, 177, 47, 95, 143, 191, 41, 89, 137, 185, 25, 73, 121, 169, 13, 61, 109, 157, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 17, 65, 113, 161, 31, 79, 127, 175, 45, 93, 141, 189, 35, 83, 131, 179, 19, 67, 115, 163, 34, 82, 130, 178, 28, 76, 124, 172, 14, 62, 110, 158, 27, 75, 123, 171, 43, 91, 139, 187, 39, 87, 135, 183, 23, 71, 119, 167, 11, 59, 107, 155, 3, 51, 99, 147, 10, 58, 106, 154, 22, 70, 118, 166, 38, 86, 134, 182, 48, 96, 144, 192, 46, 94, 142, 190, 32, 80, 128, 176, 18, 66, 114, 162, 8, 56, 104, 152) L = (1, 50)(2, 49)(3, 57)(4, 56)(5, 55)(6, 62)(7, 53)(8, 52)(9, 51)(10, 69)(11, 68)(12, 66)(13, 65)(14, 54)(15, 76)(16, 75)(17, 61)(18, 60)(19, 81)(20, 59)(21, 58)(22, 85)(23, 84)(24, 80)(25, 79)(26, 86)(27, 64)(28, 63)(29, 82)(30, 91)(31, 73)(32, 72)(33, 67)(34, 77)(35, 95)(36, 71)(37, 70)(38, 74)(39, 92)(40, 94)(41, 93)(42, 96)(43, 78)(44, 87)(45, 89)(46, 88)(47, 83)(48, 90)(97, 147)(98, 150)(99, 145)(100, 155)(101, 154)(102, 146)(103, 160)(104, 159)(105, 163)(106, 149)(107, 148)(108, 167)(109, 166)(110, 170)(111, 152)(112, 151)(113, 174)(114, 173)(115, 153)(116, 179)(117, 178)(118, 157)(119, 156)(120, 183)(121, 182)(122, 158)(123, 186)(124, 181)(125, 162)(126, 161)(127, 188)(128, 177)(129, 176)(130, 165)(131, 164)(132, 189)(133, 172)(134, 169)(135, 168)(136, 187)(137, 192)(138, 171)(139, 184)(140, 175)(141, 180)(142, 191)(143, 190)(144, 185) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E16.766 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 64 degree seq :: [ 96^2 ] E16.770 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y3^-1), (Y2^-1 * Y1)^2, Y3^8 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 21, 69)(12, 60, 20, 68)(13, 61, 22, 70)(14, 62, 18, 66)(15, 63, 17, 65)(16, 64, 19, 67)(23, 71, 33, 81)(24, 72, 32, 80)(25, 73, 34, 82)(26, 74, 30, 78)(27, 75, 29, 77)(28, 76, 31, 79)(35, 83, 44, 92)(36, 84, 43, 91)(37, 85, 42, 90)(38, 86, 41, 89)(39, 87, 40, 88)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 107, 155, 110, 158)(102, 150, 108, 156, 111, 159)(104, 152, 113, 161, 116, 164)(106, 154, 114, 162, 117, 165)(109, 157, 119, 167, 122, 170)(112, 160, 120, 168, 123, 171)(115, 163, 125, 173, 128, 176)(118, 166, 126, 174, 129, 177)(121, 169, 131, 179, 134, 182)(124, 172, 132, 180, 135, 183)(127, 175, 136, 184, 139, 187)(130, 178, 137, 185, 140, 188)(133, 181, 141, 189, 142, 190)(138, 186, 143, 191, 144, 192) L = (1, 100)(2, 104)(3, 107)(4, 109)(5, 110)(6, 97)(7, 113)(8, 115)(9, 116)(10, 98)(11, 119)(12, 99)(13, 121)(14, 122)(15, 101)(16, 102)(17, 125)(18, 103)(19, 127)(20, 128)(21, 105)(22, 106)(23, 131)(24, 108)(25, 133)(26, 134)(27, 111)(28, 112)(29, 136)(30, 114)(31, 138)(32, 139)(33, 117)(34, 118)(35, 141)(36, 120)(37, 124)(38, 142)(39, 123)(40, 143)(41, 126)(42, 130)(43, 144)(44, 129)(45, 132)(46, 135)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E16.773 Graph:: simple bipartite v = 40 e = 96 f = 26 degree seq :: [ 4^24, 6^16 ] E16.771 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3^-1, Y2^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y2)^2, Y3^8 * Y2^-1, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 21, 69)(12, 60, 20, 68)(13, 61, 22, 70)(14, 62, 18, 66)(15, 63, 17, 65)(16, 64, 19, 67)(23, 71, 33, 81)(24, 72, 32, 80)(25, 73, 34, 82)(26, 74, 30, 78)(27, 75, 29, 77)(28, 76, 31, 79)(35, 83, 45, 93)(36, 84, 44, 92)(37, 85, 46, 94)(38, 86, 42, 90)(39, 87, 41, 89)(40, 88, 43, 91)(47, 95, 48, 96)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 107, 155, 110, 158)(102, 150, 108, 156, 111, 159)(104, 152, 113, 161, 116, 164)(106, 154, 114, 162, 117, 165)(109, 157, 119, 167, 122, 170)(112, 160, 120, 168, 123, 171)(115, 163, 125, 173, 128, 176)(118, 166, 126, 174, 129, 177)(121, 169, 131, 179, 134, 182)(124, 172, 132, 180, 135, 183)(127, 175, 137, 185, 140, 188)(130, 178, 138, 186, 141, 189)(133, 181, 143, 191, 136, 184)(139, 187, 144, 192, 142, 190) L = (1, 100)(2, 104)(3, 107)(4, 109)(5, 110)(6, 97)(7, 113)(8, 115)(9, 116)(10, 98)(11, 119)(12, 99)(13, 121)(14, 122)(15, 101)(16, 102)(17, 125)(18, 103)(19, 127)(20, 128)(21, 105)(22, 106)(23, 131)(24, 108)(25, 133)(26, 134)(27, 111)(28, 112)(29, 137)(30, 114)(31, 139)(32, 140)(33, 117)(34, 118)(35, 143)(36, 120)(37, 132)(38, 136)(39, 123)(40, 124)(41, 144)(42, 126)(43, 138)(44, 142)(45, 129)(46, 130)(47, 135)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E16.774 Graph:: simple bipartite v = 40 e = 96 f = 26 degree seq :: [ 4^24, 6^16 ] E16.772 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y3^-1), Y2^-1 * Y1 * Y2 * Y1, Y3^8 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 10, 58)(5, 53, 9, 57)(6, 54, 8, 56)(11, 59, 18, 66)(12, 60, 17, 65)(13, 61, 22, 70)(14, 62, 21, 69)(15, 63, 20, 68)(16, 64, 19, 67)(23, 71, 30, 78)(24, 72, 29, 77)(25, 73, 34, 82)(26, 74, 33, 81)(27, 75, 32, 80)(28, 76, 31, 79)(35, 83, 41, 89)(36, 84, 40, 88)(37, 85, 42, 90)(38, 86, 44, 92)(39, 87, 43, 91)(45, 93, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 107, 155, 110, 158)(102, 150, 108, 156, 111, 159)(104, 152, 113, 161, 116, 164)(106, 154, 114, 162, 117, 165)(109, 157, 119, 167, 122, 170)(112, 160, 120, 168, 123, 171)(115, 163, 125, 173, 128, 176)(118, 166, 126, 174, 129, 177)(121, 169, 131, 179, 134, 182)(124, 172, 132, 180, 135, 183)(127, 175, 136, 184, 139, 187)(130, 178, 137, 185, 140, 188)(133, 181, 141, 189, 142, 190)(138, 186, 143, 191, 144, 192) L = (1, 100)(2, 104)(3, 107)(4, 109)(5, 110)(6, 97)(7, 113)(8, 115)(9, 116)(10, 98)(11, 119)(12, 99)(13, 121)(14, 122)(15, 101)(16, 102)(17, 125)(18, 103)(19, 127)(20, 128)(21, 105)(22, 106)(23, 131)(24, 108)(25, 133)(26, 134)(27, 111)(28, 112)(29, 136)(30, 114)(31, 138)(32, 139)(33, 117)(34, 118)(35, 141)(36, 120)(37, 124)(38, 142)(39, 123)(40, 143)(41, 126)(42, 130)(43, 144)(44, 129)(45, 132)(46, 135)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E16.775 Graph:: simple bipartite v = 40 e = 96 f = 26 degree seq :: [ 4^24, 6^16 ] E16.773 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y1, Y3), (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, Y1^-3 * Y3^-3, (R * Y2 * Y3^-1)^2, Y1^-3 * Y3^5, Y1^24 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 35, 83, 33, 81, 14, 62, 25, 73, 17, 65, 6, 54, 10, 58, 22, 70, 37, 85, 34, 82, 15, 63, 4, 52, 9, 57, 21, 69, 18, 66, 26, 74, 40, 88, 32, 80, 16, 64, 5, 53)(3, 51, 11, 59, 27, 75, 43, 91, 48, 96, 41, 89, 30, 78, 39, 87, 24, 72, 13, 61, 29, 77, 44, 92, 47, 95, 38, 86, 23, 71, 12, 60, 28, 76, 42, 90, 31, 79, 45, 93, 46, 94, 36, 84, 20, 68, 8, 56)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 109, 157)(101, 149, 107, 155)(102, 150, 108, 156)(103, 151, 116, 164)(105, 153, 120, 168)(106, 154, 119, 167)(110, 158, 127, 175)(111, 159, 125, 173)(112, 160, 123, 171)(113, 161, 124, 172)(114, 162, 126, 174)(115, 163, 132, 180)(117, 165, 135, 183)(118, 166, 134, 182)(121, 169, 138, 186)(122, 170, 137, 185)(128, 176, 139, 187)(129, 177, 141, 189)(130, 178, 140, 188)(131, 179, 142, 190)(133, 181, 143, 191)(136, 184, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 110)(5, 111)(6, 97)(7, 117)(8, 119)(9, 121)(10, 98)(11, 124)(12, 126)(13, 99)(14, 128)(15, 129)(16, 130)(17, 101)(18, 102)(19, 114)(20, 134)(21, 113)(22, 103)(23, 137)(24, 104)(25, 112)(26, 106)(27, 138)(28, 135)(29, 107)(30, 132)(31, 109)(32, 133)(33, 136)(34, 131)(35, 122)(36, 143)(37, 115)(38, 144)(39, 116)(40, 118)(41, 142)(42, 120)(43, 127)(44, 123)(45, 125)(46, 140)(47, 139)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 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 E16.770 Graph:: bipartite v = 26 e = 96 f = 40 degree seq :: [ 4^24, 48^2 ] E16.774 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y3^-3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y3^4 * Y1^-4, Y1^24 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 35, 83, 34, 82, 15, 63, 4, 52, 9, 57, 21, 69, 18, 66, 26, 74, 40, 88, 33, 81, 14, 62, 25, 73, 17, 65, 6, 54, 10, 58, 22, 70, 37, 85, 32, 80, 16, 64, 5, 53)(3, 51, 11, 59, 27, 75, 43, 91, 47, 95, 38, 86, 23, 71, 12, 60, 28, 76, 42, 90, 31, 79, 45, 93, 48, 96, 41, 89, 30, 78, 39, 87, 24, 72, 13, 61, 29, 77, 44, 92, 46, 94, 36, 84, 20, 68, 8, 56)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 109, 157)(101, 149, 107, 155)(102, 150, 108, 156)(103, 151, 116, 164)(105, 153, 120, 168)(106, 154, 119, 167)(110, 158, 127, 175)(111, 159, 125, 173)(112, 160, 123, 171)(113, 161, 124, 172)(114, 162, 126, 174)(115, 163, 132, 180)(117, 165, 135, 183)(118, 166, 134, 182)(121, 169, 138, 186)(122, 170, 137, 185)(128, 176, 139, 187)(129, 177, 141, 189)(130, 178, 140, 188)(131, 179, 142, 190)(133, 181, 143, 191)(136, 184, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 110)(5, 111)(6, 97)(7, 117)(8, 119)(9, 121)(10, 98)(11, 124)(12, 126)(13, 99)(14, 128)(15, 129)(16, 130)(17, 101)(18, 102)(19, 114)(20, 134)(21, 113)(22, 103)(23, 137)(24, 104)(25, 112)(26, 106)(27, 138)(28, 135)(29, 107)(30, 132)(31, 109)(32, 131)(33, 133)(34, 136)(35, 122)(36, 143)(37, 115)(38, 144)(39, 116)(40, 118)(41, 142)(42, 120)(43, 127)(44, 123)(45, 125)(46, 139)(47, 141)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 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 E16.771 Graph:: bipartite v = 26 e = 96 f = 40 degree seq :: [ 4^24, 48^2 ] E16.775 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3, Y1), (Y2 * Y3)^2, (R * Y3)^2, (R * Y1)^2, Y3^-3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y1^2 * Y2 * Y1 * Y3^-1 * Y2, Y3^5 * Y1^-3, Y1^24 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 21, 69, 37, 85, 35, 83, 15, 63, 29, 77, 19, 67, 6, 54, 10, 58, 24, 72, 39, 87, 36, 84, 16, 64, 4, 52, 9, 57, 23, 71, 20, 68, 30, 78, 42, 90, 34, 82, 18, 66, 5, 53)(3, 51, 11, 59, 31, 79, 43, 91, 46, 94, 40, 88, 27, 75, 8, 56, 25, 73, 14, 62, 32, 80, 44, 92, 47, 95, 41, 89, 22, 70, 12, 60, 28, 76, 17, 65, 33, 81, 45, 93, 48, 96, 38, 86, 26, 74, 13, 61)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 113, 161)(102, 150, 108, 156)(103, 151, 118, 166)(105, 153, 124, 172)(106, 154, 122, 170)(107, 155, 125, 173)(109, 157, 119, 167)(111, 159, 129, 177)(112, 160, 127, 175)(114, 162, 128, 176)(115, 163, 121, 169)(116, 164, 123, 171)(117, 165, 134, 182)(120, 168, 136, 184)(126, 174, 137, 185)(130, 178, 139, 187)(131, 179, 140, 188)(132, 180, 141, 189)(133, 181, 142, 190)(135, 183, 143, 191)(138, 186, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 112)(6, 97)(7, 119)(8, 122)(9, 125)(10, 98)(11, 124)(12, 123)(13, 118)(14, 99)(15, 130)(16, 131)(17, 121)(18, 132)(19, 101)(20, 102)(21, 116)(22, 136)(23, 115)(24, 103)(25, 109)(26, 137)(27, 134)(28, 104)(29, 114)(30, 106)(31, 113)(32, 107)(33, 110)(34, 135)(35, 138)(36, 133)(37, 126)(38, 143)(39, 117)(40, 144)(41, 142)(42, 120)(43, 129)(44, 127)(45, 128)(46, 141)(47, 139)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 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 E16.772 Graph:: bipartite v = 26 e = 96 f = 40 degree seq :: [ 4^24, 48^2 ] E16.776 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 6, 24}) Quotient :: edge Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1)^2, (T2^-1 * T1)^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1^-3, (T2^-2 * T1^-1)^2, T2^4 * T1 * T2^-4 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 25, 37, 42, 30, 18, 6, 17, 29, 41, 48, 43, 31, 19, 12, 21, 33, 45, 40, 28, 15, 5)(2, 7, 20, 32, 44, 35, 23, 9, 16, 14, 27, 39, 47, 36, 24, 13, 4, 11, 26, 38, 46, 34, 22, 8)(49, 50, 54, 64, 60, 52)(51, 57, 65, 61, 69, 56)(53, 59, 66, 55, 67, 62)(58, 72, 77, 70, 81, 71)(63, 75, 78, 74, 79, 68)(73, 82, 89, 83, 93, 84)(76, 80, 90, 87, 91, 86)(85, 92, 96, 95, 88, 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) :: { ( 12^6 ), ( 12^24 ) } Outer automorphisms :: reflexible Dual of E16.777 Transitivity :: ET+ Graph:: bipartite v = 10 e = 48 f = 8 degree seq :: [ 6^8, 24^2 ] E16.777 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 6, 24}) Quotient :: loop Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ F^2, T1^2 * T2^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-2)^2, T2^2 * T1^4, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1 * T2 * T1 ] Map:: non-degenerate R = (1, 49, 3, 51, 6, 54, 15, 63, 11, 59, 5, 53)(2, 50, 7, 55, 14, 62, 12, 60, 4, 52, 8, 56)(9, 57, 19, 67, 13, 61, 21, 69, 10, 58, 20, 68)(16, 64, 22, 70, 18, 66, 24, 72, 17, 65, 23, 71)(25, 73, 31, 79, 27, 75, 33, 81, 26, 74, 32, 80)(28, 76, 34, 82, 30, 78, 36, 84, 29, 77, 35, 83)(37, 85, 43, 91, 39, 87, 45, 93, 38, 86, 44, 92)(40, 88, 46, 94, 42, 90, 48, 96, 41, 89, 47, 95) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 58)(6, 62)(7, 64)(8, 65)(9, 63)(10, 51)(11, 52)(12, 66)(13, 53)(14, 59)(15, 61)(16, 60)(17, 55)(18, 56)(19, 73)(20, 74)(21, 75)(22, 76)(23, 77)(24, 78)(25, 69)(26, 67)(27, 68)(28, 72)(29, 70)(30, 71)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 81)(38, 79)(39, 80)(40, 84)(41, 82)(42, 83)(43, 94)(44, 95)(45, 96)(46, 93)(47, 91)(48, 92) local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E16.776 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 48 f = 10 degree seq :: [ 12^8 ] E16.778 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (Y1 * Y2^-1)^2, (R * Y1)^2, Y1^-2 * Y2 * Y1 * Y2 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-3, (Y2^2 * Y1)^2, Y2^-4 * Y1 * Y2^4 * Y1^-1, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 49, 2, 50, 6, 54, 16, 64, 12, 60, 4, 52)(3, 51, 9, 57, 17, 65, 13, 61, 21, 69, 8, 56)(5, 53, 11, 59, 18, 66, 7, 55, 19, 67, 14, 62)(10, 58, 24, 72, 29, 77, 22, 70, 33, 81, 23, 71)(15, 63, 27, 75, 30, 78, 26, 74, 31, 79, 20, 68)(25, 73, 34, 82, 41, 89, 35, 83, 45, 93, 36, 84)(28, 76, 32, 80, 42, 90, 39, 87, 43, 91, 38, 86)(37, 85, 44, 92, 48, 96, 47, 95, 40, 88, 46, 94)(97, 145, 99, 147, 106, 154, 121, 169, 133, 181, 138, 186, 126, 174, 114, 162, 102, 150, 113, 161, 125, 173, 137, 185, 144, 192, 139, 187, 127, 175, 115, 163, 108, 156, 117, 165, 129, 177, 141, 189, 136, 184, 124, 172, 111, 159, 101, 149)(98, 146, 103, 151, 116, 164, 128, 176, 140, 188, 131, 179, 119, 167, 105, 153, 112, 160, 110, 158, 123, 171, 135, 183, 143, 191, 132, 180, 120, 168, 109, 157, 100, 148, 107, 155, 122, 170, 134, 182, 142, 190, 130, 178, 118, 166, 104, 152) L = (1, 99)(2, 103)(3, 106)(4, 107)(5, 97)(6, 113)(7, 116)(8, 98)(9, 112)(10, 121)(11, 122)(12, 117)(13, 100)(14, 123)(15, 101)(16, 110)(17, 125)(18, 102)(19, 108)(20, 128)(21, 129)(22, 104)(23, 105)(24, 109)(25, 133)(26, 134)(27, 135)(28, 111)(29, 137)(30, 114)(31, 115)(32, 140)(33, 141)(34, 118)(35, 119)(36, 120)(37, 138)(38, 142)(39, 143)(40, 124)(41, 144)(42, 126)(43, 127)(44, 131)(45, 136)(46, 130)(47, 132)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E16.779 Graph:: bipartite v = 10 e = 96 f = 56 degree seq :: [ 12^8, 48^2 ] E16.779 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3^-1 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-3 * Y3 * Y2^-1 * Y3, Y3 * Y2^-1 * Y3 * Y2^3, (Y3^-2 * Y2)^2, Y2 * Y3^-7 * Y2^-1 * Y3, (Y3^-1 * Y1^-1)^24 ] Map:: R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 102, 150, 112, 160, 109, 157, 100, 148)(99, 147, 105, 153, 113, 161, 104, 152, 117, 165, 107, 155)(101, 149, 110, 158, 114, 162, 108, 156, 116, 164, 103, 151)(106, 154, 120, 168, 125, 173, 119, 167, 129, 177, 118, 166)(111, 159, 122, 170, 126, 174, 115, 163, 127, 175, 123, 171)(121, 169, 130, 178, 137, 185, 132, 180, 141, 189, 131, 179)(124, 172, 128, 176, 138, 186, 135, 183, 139, 187, 134, 182)(133, 181, 140, 188, 136, 184, 142, 190, 144, 192, 143, 191) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 115)(8, 98)(9, 100)(10, 121)(11, 112)(12, 122)(13, 117)(14, 123)(15, 101)(16, 110)(17, 125)(18, 102)(19, 128)(20, 109)(21, 129)(22, 104)(23, 105)(24, 107)(25, 133)(26, 134)(27, 135)(28, 111)(29, 137)(30, 114)(31, 116)(32, 140)(33, 141)(34, 118)(35, 119)(36, 120)(37, 139)(38, 143)(39, 142)(40, 124)(41, 136)(42, 126)(43, 127)(44, 131)(45, 144)(46, 130)(47, 132)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12, 48 ), ( 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48 ) } Outer automorphisms :: reflexible Dual of E16.778 Graph:: simple bipartite v = 56 e = 96 f = 10 degree seq :: [ 2^48, 12^8 ] E16.780 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 24}) Quotient :: edge Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T2^2 * T1 * T2^-2 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2^2 * T1 * T2^2 * T1 * T2^2, T1^-1 * T2^-1 * T1^-1 * T2^-3 * T1^-1 * T2^-3 * T1^-1 * T2^-3 * T1^-1 * T2^-3 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2 ] Map:: non-degenerate R = (1, 3, 10, 27, 36, 18, 6, 17, 35, 34, 16, 5)(2, 7, 20, 39, 31, 13, 4, 12, 28, 44, 24, 8)(9, 25, 45, 33, 15, 30, 11, 29, 46, 32, 14, 26)(19, 37, 47, 43, 23, 41, 21, 40, 48, 42, 22, 38)(49, 50, 54, 52)(51, 57, 65, 59)(53, 62, 66, 63)(55, 67, 60, 69)(56, 70, 61, 71)(58, 68, 83, 76)(64, 72, 84, 79)(73, 88, 77, 85)(74, 89, 78, 86)(75, 93, 82, 94)(80, 91, 81, 90)(87, 95, 92, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 48^4 ), ( 48^12 ) } Outer automorphisms :: reflexible Dual of E16.784 Transitivity :: ET+ Graph:: bipartite v = 16 e = 48 f = 2 degree seq :: [ 4^12, 12^4 ] E16.781 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 24}) Quotient :: edge Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4 * T1^-2, T1^-1 * T2 * T1^-1 * T2 * T1^-2, T2^-2 * T1^-1 * T2 * T1^-1 * T2^-1, T2 * T1^2 * T2^-1 * T1^-2, T2 * T1 * T2^-2 * T1^-2 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^4, T2 * T1 * T2 * T1^7 ] Map:: non-degenerate R = (1, 3, 10, 20, 6, 19, 39, 23, 36, 47, 41, 21, 40, 33, 43, 48, 44, 25, 42, 32, 13, 24, 17, 5)(2, 7, 22, 11, 18, 37, 28, 9, 27, 45, 30, 38, 35, 16, 29, 46, 31, 15, 34, 14, 4, 12, 26, 8)(49, 50, 54, 66, 84, 75, 88, 83, 92, 79, 61, 52)(51, 57, 67, 86, 95, 94, 81, 62, 73, 56, 72, 59)(53, 63, 68, 60, 71, 55, 69, 85, 96, 93, 80, 64)(58, 77, 87, 82, 89, 74, 91, 70, 90, 76, 65, 78) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^12 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E16.785 Transitivity :: ET+ Graph:: bipartite v = 6 e = 48 f = 12 degree seq :: [ 12^4, 24^2 ] E16.782 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 24}) Quotient :: edge Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-2 * T1 * T2^-2 * T1^-1, T1 * T2^-1 * T1^-2 * T2^-1 * T1, T2^-1 * T1^-1 * T2^-1 * T1^-5, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, (T2 * T1^-1)^12 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 27, 14)(6, 18, 39, 19)(9, 25, 15, 26)(11, 28, 16, 30)(13, 32, 45, 29)(17, 36, 47, 37)(20, 41, 23, 42)(22, 43, 24, 44)(31, 35, 34, 46)(33, 40, 48, 38)(49, 50, 54, 65, 83, 76, 91, 74, 90, 96, 93, 75, 58, 69, 87, 95, 94, 78, 92, 73, 89, 81, 61, 52)(51, 57, 67, 88, 82, 62, 70, 55, 68, 85, 80, 64, 53, 63, 66, 86, 79, 60, 72, 56, 71, 84, 77, 59) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^24 ) } Outer automorphisms :: reflexible Dual of E16.783 Transitivity :: ET+ Graph:: bipartite v = 14 e = 48 f = 4 degree seq :: [ 4^12, 24^2 ] E16.783 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 24}) Quotient :: loop Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T2^2 * T1 * T2^-2 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2^2 * T1 * T2^2 * T1 * T2^2, T1^-1 * T2^-1 * T1^-1 * T2^-3 * T1^-1 * T2^-3 * T1^-1 * T2^-3 * T1^-1 * T2^-3 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 27, 75, 36, 84, 18, 66, 6, 54, 17, 65, 35, 83, 34, 82, 16, 64, 5, 53)(2, 50, 7, 55, 20, 68, 39, 87, 31, 79, 13, 61, 4, 52, 12, 60, 28, 76, 44, 92, 24, 72, 8, 56)(9, 57, 25, 73, 45, 93, 33, 81, 15, 63, 30, 78, 11, 59, 29, 77, 46, 94, 32, 80, 14, 62, 26, 74)(19, 67, 37, 85, 47, 95, 43, 91, 23, 71, 41, 89, 21, 69, 40, 88, 48, 96, 42, 90, 22, 70, 38, 86) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 67)(8, 70)(9, 65)(10, 68)(11, 51)(12, 69)(13, 71)(14, 66)(15, 53)(16, 72)(17, 59)(18, 63)(19, 60)(20, 83)(21, 55)(22, 61)(23, 56)(24, 84)(25, 88)(26, 89)(27, 93)(28, 58)(29, 85)(30, 86)(31, 64)(32, 91)(33, 90)(34, 94)(35, 76)(36, 79)(37, 73)(38, 74)(39, 95)(40, 77)(41, 78)(42, 80)(43, 81)(44, 96)(45, 82)(46, 75)(47, 92)(48, 87) 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 ) } Outer automorphisms :: reflexible Dual of E16.782 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 48 f = 14 degree seq :: [ 24^4 ] E16.784 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 24}) Quotient :: loop Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4 * T1^-2, T1^-1 * T2 * T1^-1 * T2 * T1^-2, T2^-2 * T1^-1 * T2 * T1^-1 * T2^-1, T2 * T1^2 * T2^-1 * T1^-2, T2 * T1 * T2^-2 * T1^-2 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^4, T2 * T1 * T2 * T1^7 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 20, 68, 6, 54, 19, 67, 39, 87, 23, 71, 36, 84, 47, 95, 41, 89, 21, 69, 40, 88, 33, 81, 43, 91, 48, 96, 44, 92, 25, 73, 42, 90, 32, 80, 13, 61, 24, 72, 17, 65, 5, 53)(2, 50, 7, 55, 22, 70, 11, 59, 18, 66, 37, 85, 28, 76, 9, 57, 27, 75, 45, 93, 30, 78, 38, 86, 35, 83, 16, 64, 29, 77, 46, 94, 31, 79, 15, 63, 34, 82, 14, 62, 4, 52, 12, 60, 26, 74, 8, 56) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 69)(8, 72)(9, 67)(10, 77)(11, 51)(12, 71)(13, 52)(14, 73)(15, 68)(16, 53)(17, 78)(18, 84)(19, 86)(20, 60)(21, 85)(22, 90)(23, 55)(24, 59)(25, 56)(26, 91)(27, 88)(28, 65)(29, 87)(30, 58)(31, 61)(32, 64)(33, 62)(34, 89)(35, 92)(36, 75)(37, 96)(38, 95)(39, 82)(40, 83)(41, 74)(42, 76)(43, 70)(44, 79)(45, 80)(46, 81)(47, 94)(48, 93) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.780 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 48 f = 16 degree seq :: [ 48^2 ] E16.785 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 24}) Quotient :: loop Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-2 * T1 * T2^-2 * T1^-1, T1 * T2^-1 * T1^-2 * T2^-1 * T1, T2^-1 * T1^-1 * T2^-1 * T1^-5, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, (T2 * T1^-1)^12 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 5, 53)(2, 50, 7, 55, 21, 69, 8, 56)(4, 52, 12, 60, 27, 75, 14, 62)(6, 54, 18, 66, 39, 87, 19, 67)(9, 57, 25, 73, 15, 63, 26, 74)(11, 59, 28, 76, 16, 64, 30, 78)(13, 61, 32, 80, 45, 93, 29, 77)(17, 65, 36, 84, 47, 95, 37, 85)(20, 68, 41, 89, 23, 71, 42, 90)(22, 70, 43, 91, 24, 72, 44, 92)(31, 79, 35, 83, 34, 82, 46, 94)(33, 81, 40, 88, 48, 96, 38, 86) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 65)(7, 68)(8, 71)(9, 67)(10, 69)(11, 51)(12, 72)(13, 52)(14, 70)(15, 66)(16, 53)(17, 83)(18, 86)(19, 88)(20, 85)(21, 87)(22, 55)(23, 84)(24, 56)(25, 89)(26, 90)(27, 58)(28, 91)(29, 59)(30, 92)(31, 60)(32, 64)(33, 61)(34, 62)(35, 76)(36, 77)(37, 80)(38, 79)(39, 95)(40, 82)(41, 81)(42, 96)(43, 74)(44, 73)(45, 75)(46, 78)(47, 94)(48, 93) local type(s) :: { ( 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E16.781 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 48 f = 6 degree seq :: [ 8^12 ] E16.786 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24}) Quotient :: dipole Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y1^-2 * Y3^2, (R * Y1)^2, Y1^4, (R * Y3)^2, Y3 * Y2 * Y1^2 * Y2^-1 * Y3, (Y2^-1 * R * Y2^-1)^2, Y2^-2 * Y3^-1 * Y2^2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^2 * Y3 * Y2^-2 * Y1, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2^4 * Y3^-1 * Y2^2 * Y1, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 20, 68, 35, 83, 28, 76)(16, 64, 24, 72, 36, 84, 31, 79)(25, 73, 40, 88, 29, 77, 37, 85)(26, 74, 41, 89, 30, 78, 38, 86)(27, 75, 45, 93, 34, 82, 46, 94)(32, 80, 43, 91, 33, 81, 42, 90)(39, 87, 47, 95, 44, 92, 48, 96)(97, 145, 99, 147, 106, 154, 123, 171, 132, 180, 114, 162, 102, 150, 113, 161, 131, 179, 130, 178, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 135, 183, 127, 175, 109, 157, 100, 148, 108, 156, 124, 172, 140, 188, 120, 168, 104, 152)(105, 153, 121, 169, 141, 189, 129, 177, 111, 159, 126, 174, 107, 155, 125, 173, 142, 190, 128, 176, 110, 158, 122, 170)(115, 163, 133, 181, 143, 191, 139, 187, 119, 167, 137, 185, 117, 165, 136, 184, 144, 192, 138, 186, 118, 166, 134, 182) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 124)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 127)(17, 105)(18, 110)(19, 103)(20, 106)(21, 108)(22, 104)(23, 109)(24, 112)(25, 133)(26, 134)(27, 142)(28, 131)(29, 136)(30, 137)(31, 132)(32, 138)(33, 139)(34, 141)(35, 116)(36, 120)(37, 125)(38, 126)(39, 144)(40, 121)(41, 122)(42, 129)(43, 128)(44, 143)(45, 123)(46, 130)(47, 135)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 48, 2, 48, 2, 48, 2, 48 ), ( 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48 ) } Outer automorphisms :: reflexible Dual of E16.789 Graph:: bipartite v = 16 e = 96 f = 50 degree seq :: [ 8^12, 24^4 ] E16.787 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24}) Quotient :: dipole Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-2 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2^-2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2 * Y1 * Y2^-2 * Y1^-2 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2 * Y1 * Y2 * Y1^7 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 36, 84, 27, 75, 40, 88, 35, 83, 44, 92, 31, 79, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 38, 86, 47, 95, 46, 94, 33, 81, 14, 62, 25, 73, 8, 56, 24, 72, 11, 59)(5, 53, 15, 63, 20, 68, 12, 60, 23, 71, 7, 55, 21, 69, 37, 85, 48, 96, 45, 93, 32, 80, 16, 64)(10, 58, 29, 77, 39, 87, 34, 82, 41, 89, 26, 74, 43, 91, 22, 70, 42, 90, 28, 76, 17, 65, 30, 78)(97, 145, 99, 147, 106, 154, 116, 164, 102, 150, 115, 163, 135, 183, 119, 167, 132, 180, 143, 191, 137, 185, 117, 165, 136, 184, 129, 177, 139, 187, 144, 192, 140, 188, 121, 169, 138, 186, 128, 176, 109, 157, 120, 168, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 107, 155, 114, 162, 133, 181, 124, 172, 105, 153, 123, 171, 141, 189, 126, 174, 134, 182, 131, 179, 112, 160, 125, 173, 142, 190, 127, 175, 111, 159, 130, 178, 110, 158, 100, 148, 108, 156, 122, 170, 104, 152) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 123)(10, 116)(11, 114)(12, 122)(13, 120)(14, 100)(15, 130)(16, 125)(17, 101)(18, 133)(19, 135)(20, 102)(21, 136)(22, 107)(23, 132)(24, 113)(25, 138)(26, 104)(27, 141)(28, 105)(29, 142)(30, 134)(31, 111)(32, 109)(33, 139)(34, 110)(35, 112)(36, 143)(37, 124)(38, 131)(39, 119)(40, 129)(41, 117)(42, 128)(43, 144)(44, 121)(45, 126)(46, 127)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E16.788 Graph:: bipartite v = 6 e = 96 f = 60 degree seq :: [ 24^4, 48^2 ] E16.788 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24}) Quotient :: dipole Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y3^-1 * Y2^-2 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2^2 * Y3 * Y2, Y3 * Y2^-1 * Y3^-2 * Y2^-1 * Y3, Y3 * Y2^-1 * Y3^5 * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1, Y3^-14 * Y2 * Y3^-1 * Y2^-1 * Y3^-3, (Y3^-1 * Y1^-1)^24 ] Map:: R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 102, 150, 100, 148)(99, 147, 105, 153, 113, 161, 107, 155)(101, 149, 110, 158, 114, 162, 111, 159)(103, 151, 115, 163, 108, 156, 117, 165)(104, 152, 118, 166, 109, 157, 119, 167)(106, 154, 123, 171, 131, 179, 116, 164)(112, 160, 127, 175, 132, 180, 120, 168)(121, 169, 133, 181, 125, 173, 136, 184)(122, 170, 137, 185, 126, 174, 134, 182)(124, 172, 140, 188, 143, 191, 141, 189)(128, 176, 138, 186, 129, 177, 139, 187)(130, 178, 135, 183, 144, 192, 142, 190) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 116)(8, 98)(9, 121)(10, 124)(11, 125)(12, 123)(13, 100)(14, 126)(15, 122)(16, 101)(17, 131)(18, 102)(19, 133)(20, 135)(21, 136)(22, 137)(23, 134)(24, 104)(25, 141)(26, 105)(27, 142)(28, 138)(29, 140)(30, 107)(31, 109)(32, 110)(33, 111)(34, 112)(35, 143)(36, 114)(37, 130)(38, 115)(39, 129)(40, 144)(41, 117)(42, 118)(43, 119)(44, 120)(45, 127)(46, 128)(47, 139)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 24, 48 ), ( 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E16.787 Graph:: simple bipartite v = 60 e = 96 f = 6 degree seq :: [ 2^48, 8^12 ] E16.789 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24}) Quotient :: dipole Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y1 * Y3^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-4, (Y3 * Y2^-1)^4 ] Map:: R = (1, 49, 2, 50, 6, 54, 17, 65, 35, 83, 28, 76, 43, 91, 26, 74, 42, 90, 48, 96, 45, 93, 27, 75, 10, 58, 21, 69, 39, 87, 47, 95, 46, 94, 30, 78, 44, 92, 25, 73, 41, 89, 33, 81, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 40, 88, 34, 82, 14, 62, 22, 70, 7, 55, 20, 68, 37, 85, 32, 80, 16, 64, 5, 53, 15, 63, 18, 66, 38, 86, 31, 79, 12, 60, 24, 72, 8, 56, 23, 71, 36, 84, 29, 77, 11, 59)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 114)(7, 117)(8, 98)(9, 121)(10, 101)(11, 124)(12, 123)(13, 128)(14, 100)(15, 122)(16, 126)(17, 132)(18, 135)(19, 102)(20, 137)(21, 104)(22, 139)(23, 138)(24, 140)(25, 111)(26, 105)(27, 110)(28, 112)(29, 109)(30, 107)(31, 131)(32, 141)(33, 136)(34, 142)(35, 130)(36, 143)(37, 113)(38, 129)(39, 115)(40, 144)(41, 119)(42, 116)(43, 120)(44, 118)(45, 125)(46, 127)(47, 133)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E16.786 Graph:: simple bipartite v = 50 e = 96 f = 16 degree seq :: [ 2^48, 48^2 ] E16.790 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24}) Quotient :: dipole Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, Y3^-2 * Y1^2, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y1^-1, Y2^-1 * Y1 * Y2^2 * Y3^-1 * Y2^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^-1 * Y3 * Y2^2 * Y1^-1 * Y2^-1, Y2 * Y3 * Y2^5 * Y1^-1, Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 27, 75, 35, 83, 20, 68)(16, 64, 31, 79, 36, 84, 24, 72)(25, 73, 37, 85, 29, 77, 40, 88)(26, 74, 41, 89, 30, 78, 38, 86)(28, 76, 44, 92, 47, 95, 45, 93)(32, 80, 42, 90, 33, 81, 43, 91)(34, 82, 39, 87, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 124, 172, 138, 186, 118, 166, 137, 185, 117, 165, 136, 184, 144, 192, 132, 180, 114, 162, 102, 150, 113, 161, 131, 179, 143, 191, 139, 187, 119, 167, 134, 182, 115, 163, 133, 181, 130, 178, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 135, 183, 129, 177, 111, 159, 122, 170, 105, 153, 121, 169, 141, 189, 127, 175, 109, 157, 100, 148, 108, 156, 123, 171, 142, 190, 128, 176, 110, 158, 126, 174, 107, 155, 125, 173, 140, 188, 120, 168, 104, 152) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 116)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 120)(17, 105)(18, 110)(19, 103)(20, 131)(21, 108)(22, 104)(23, 109)(24, 132)(25, 136)(26, 134)(27, 106)(28, 141)(29, 133)(30, 137)(31, 112)(32, 139)(33, 138)(34, 142)(35, 123)(36, 127)(37, 121)(38, 126)(39, 130)(40, 125)(41, 122)(42, 128)(43, 129)(44, 124)(45, 143)(46, 144)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E16.791 Graph:: bipartite v = 14 e = 96 f = 52 degree seq :: [ 8^12, 48^2 ] E16.791 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24}) Quotient :: dipole Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^4 * Y1^-2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-2, Y3^-2 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, Y3 * Y1 * Y3^-2 * Y1^-2 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y3 * Y1^-1 * Y3 * Y1^9, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 36, 84, 27, 75, 40, 88, 35, 83, 44, 92, 31, 79, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 38, 86, 47, 95, 46, 94, 33, 81, 14, 62, 25, 73, 8, 56, 24, 72, 11, 59)(5, 53, 15, 63, 20, 68, 12, 60, 23, 71, 7, 55, 21, 69, 37, 85, 48, 96, 45, 93, 32, 80, 16, 64)(10, 58, 29, 77, 39, 87, 34, 82, 41, 89, 26, 74, 43, 91, 22, 70, 42, 90, 28, 76, 17, 65, 30, 78)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 123)(10, 116)(11, 114)(12, 122)(13, 120)(14, 100)(15, 130)(16, 125)(17, 101)(18, 133)(19, 135)(20, 102)(21, 136)(22, 107)(23, 132)(24, 113)(25, 138)(26, 104)(27, 141)(28, 105)(29, 142)(30, 134)(31, 111)(32, 109)(33, 139)(34, 110)(35, 112)(36, 143)(37, 124)(38, 131)(39, 119)(40, 129)(41, 117)(42, 128)(43, 144)(44, 121)(45, 126)(46, 127)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E16.790 Graph:: simple bipartite v = 52 e = 96 f = 14 degree seq :: [ 2^48, 24^4 ] E16.792 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 48, 48}) Quotient :: edge Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^-16 * T1, (T1^-1 * T2^-1)^48 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 26, 32, 38, 44, 43, 37, 31, 25, 19, 13, 7, 2, 6, 12, 18, 24, 30, 36, 42, 48, 46, 40, 34, 28, 22, 16, 10, 4, 9, 15, 21, 27, 33, 39, 45, 47, 41, 35, 29, 23, 17, 11, 5)(49, 50, 52)(51, 54, 57)(53, 55, 58)(56, 60, 63)(59, 61, 64)(62, 66, 69)(65, 67, 70)(68, 72, 75)(71, 73, 76)(74, 78, 81)(77, 79, 82)(80, 84, 87)(83, 85, 88)(86, 90, 93)(89, 91, 94)(92, 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) :: { ( 96^3 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E16.793 Transitivity :: ET+ Graph:: bipartite v = 17 e = 48 f = 1 degree seq :: [ 3^16, 48 ] E16.793 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 48, 48}) Quotient :: loop Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^-16 * T1, (T1^-1 * T2^-1)^48 ] Map:: non-degenerate R = (1, 49, 3, 51, 8, 56, 14, 62, 20, 68, 26, 74, 32, 80, 38, 86, 44, 92, 43, 91, 37, 85, 31, 79, 25, 73, 19, 67, 13, 61, 7, 55, 2, 50, 6, 54, 12, 60, 18, 66, 24, 72, 30, 78, 36, 84, 42, 90, 48, 96, 46, 94, 40, 88, 34, 82, 28, 76, 22, 70, 16, 64, 10, 58, 4, 52, 9, 57, 15, 63, 21, 69, 27, 75, 33, 81, 39, 87, 45, 93, 47, 95, 41, 89, 35, 83, 29, 77, 23, 71, 17, 65, 11, 59, 5, 53) L = (1, 50)(2, 52)(3, 54)(4, 49)(5, 55)(6, 57)(7, 58)(8, 60)(9, 51)(10, 53)(11, 61)(12, 63)(13, 64)(14, 66)(15, 56)(16, 59)(17, 67)(18, 69)(19, 70)(20, 72)(21, 62)(22, 65)(23, 73)(24, 75)(25, 76)(26, 78)(27, 68)(28, 71)(29, 79)(30, 81)(31, 82)(32, 84)(33, 74)(34, 77)(35, 85)(36, 87)(37, 88)(38, 90)(39, 80)(40, 83)(41, 91)(42, 93)(43, 94)(44, 96)(45, 86)(46, 89)(47, 92)(48, 95) local type(s) :: { ( 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48 ) } Outer automorphisms :: reflexible Dual of E16.792 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 48 f = 17 degree seq :: [ 96 ] E16.794 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3^3, Y1^3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3 * Y2^16, Y2^-3 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 49, 2, 50, 4, 52)(3, 51, 6, 54, 9, 57)(5, 53, 7, 55, 10, 58)(8, 56, 12, 60, 15, 63)(11, 59, 13, 61, 16, 64)(14, 62, 18, 66, 21, 69)(17, 65, 19, 67, 22, 70)(20, 68, 24, 72, 27, 75)(23, 71, 25, 73, 28, 76)(26, 74, 30, 78, 33, 81)(29, 77, 31, 79, 34, 82)(32, 80, 36, 84, 39, 87)(35, 83, 37, 85, 40, 88)(38, 86, 42, 90, 45, 93)(41, 89, 43, 91, 46, 94)(44, 92, 48, 96, 47, 95)(97, 145, 99, 147, 104, 152, 110, 158, 116, 164, 122, 170, 128, 176, 134, 182, 140, 188, 139, 187, 133, 181, 127, 175, 121, 169, 115, 163, 109, 157, 103, 151, 98, 146, 102, 150, 108, 156, 114, 162, 120, 168, 126, 174, 132, 180, 138, 186, 144, 192, 142, 190, 136, 184, 130, 178, 124, 172, 118, 166, 112, 160, 106, 154, 100, 148, 105, 153, 111, 159, 117, 165, 123, 171, 129, 177, 135, 183, 141, 189, 143, 191, 137, 185, 131, 179, 125, 173, 119, 167, 113, 161, 107, 155, 101, 149) L = (1, 100)(2, 97)(3, 105)(4, 98)(5, 106)(6, 99)(7, 101)(8, 111)(9, 102)(10, 103)(11, 112)(12, 104)(13, 107)(14, 117)(15, 108)(16, 109)(17, 118)(18, 110)(19, 113)(20, 123)(21, 114)(22, 115)(23, 124)(24, 116)(25, 119)(26, 129)(27, 120)(28, 121)(29, 130)(30, 122)(31, 125)(32, 135)(33, 126)(34, 127)(35, 136)(36, 128)(37, 131)(38, 141)(39, 132)(40, 133)(41, 142)(42, 134)(43, 137)(44, 143)(45, 138)(46, 139)(47, 144)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 96, 2, 96, 2, 96 ), ( 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96 ) } Outer automorphisms :: reflexible Dual of E16.795 Graph:: bipartite v = 17 e = 96 f = 49 degree seq :: [ 6^16, 96 ] E16.795 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^-1 * Y1^16, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 49, 2, 50, 6, 54, 12, 60, 18, 66, 24, 72, 30, 78, 36, 84, 42, 90, 45, 93, 39, 87, 33, 81, 27, 75, 21, 69, 15, 63, 9, 57, 3, 51, 7, 55, 13, 61, 19, 67, 25, 73, 31, 79, 37, 85, 43, 91, 48, 96, 47, 95, 41, 89, 35, 83, 29, 77, 23, 71, 17, 65, 11, 59, 5, 53, 8, 56, 14, 62, 20, 68, 26, 74, 32, 80, 38, 86, 44, 92, 46, 94, 40, 88, 34, 82, 28, 76, 22, 70, 16, 64, 10, 58, 4, 52)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 101)(4, 105)(5, 97)(6, 109)(7, 104)(8, 98)(9, 107)(10, 111)(11, 100)(12, 115)(13, 110)(14, 102)(15, 113)(16, 117)(17, 106)(18, 121)(19, 116)(20, 108)(21, 119)(22, 123)(23, 112)(24, 127)(25, 122)(26, 114)(27, 125)(28, 129)(29, 118)(30, 133)(31, 128)(32, 120)(33, 131)(34, 135)(35, 124)(36, 139)(37, 134)(38, 126)(39, 137)(40, 141)(41, 130)(42, 144)(43, 140)(44, 132)(45, 143)(46, 138)(47, 136)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 96 ), ( 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96 ) } Outer automorphisms :: reflexible Dual of E16.794 Graph:: bipartite v = 49 e = 96 f = 17 degree seq :: [ 2^48, 96 ] E16.796 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 5}) Quotient :: halfedge^2 Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3, Y1^5, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y1^-2 * Y2 * Y1^-2 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 ] Map:: R = (1, 52, 2, 55, 5, 60, 10, 54, 4, 51)(3, 57, 7, 64, 14, 67, 17, 58, 8, 53)(6, 62, 12, 73, 23, 76, 26, 63, 13, 56)(9, 68, 18, 81, 31, 82, 32, 69, 19, 59)(11, 71, 21, 85, 35, 88, 38, 72, 22, 61)(15, 74, 24, 86, 36, 92, 42, 78, 28, 65)(16, 75, 25, 87, 37, 93, 43, 79, 29, 66)(20, 83, 33, 95, 45, 96, 46, 84, 34, 70)(27, 89, 39, 97, 47, 99, 49, 91, 41, 77)(30, 90, 40, 98, 48, 100, 50, 94, 44, 80) L = (1, 3)(2, 6)(4, 9)(5, 11)(7, 15)(8, 16)(10, 20)(12, 24)(13, 25)(14, 27)(17, 30)(18, 28)(19, 29)(21, 36)(22, 37)(23, 39)(26, 40)(31, 41)(32, 44)(33, 42)(34, 43)(35, 47)(38, 48)(45, 49)(46, 50)(51, 53)(52, 56)(54, 59)(55, 61)(57, 65)(58, 66)(60, 70)(62, 74)(63, 75)(64, 77)(67, 80)(68, 78)(69, 79)(71, 86)(72, 87)(73, 89)(76, 90)(81, 91)(82, 94)(83, 92)(84, 93)(85, 97)(88, 98)(95, 99)(96, 100) local type(s) :: { ( 10^10 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 10 e = 50 f = 10 degree seq :: [ 10^10 ] E16.797 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 5}) Quotient :: halfedge^2 Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y1^5, Y1 * Y2 * Y3 * Y2 * Y1^-1 * Y3, Y2 * Y3 * Y1 * Y3 * Y2 * Y1^-1, Y3 * Y2 * Y3 * Y1 * Y2 * Y1^-1, Y1 * Y3 * Y1^-2 * Y2 * Y1, Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y3 * Y1^-1, (Y2 * Y3 * Y1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 52, 2, 56, 6, 67, 17, 55, 5, 51)(3, 59, 9, 69, 19, 82, 32, 61, 11, 53)(4, 62, 12, 83, 33, 85, 35, 64, 14, 54)(7, 70, 20, 88, 38, 95, 45, 72, 22, 57)(8, 73, 23, 86, 36, 65, 15, 75, 25, 58)(10, 71, 21, 89, 39, 97, 47, 79, 29, 60)(13, 74, 24, 91, 41, 99, 49, 81, 31, 63)(16, 78, 28, 90, 40, 68, 18, 87, 37, 66)(26, 92, 42, 100, 50, 84, 34, 96, 46, 76)(27, 93, 43, 98, 48, 80, 30, 94, 44, 77) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 18)(8, 24)(9, 26)(10, 28)(11, 30)(12, 21)(14, 34)(16, 31)(17, 35)(19, 41)(20, 42)(22, 44)(23, 39)(25, 46)(27, 40)(29, 45)(32, 47)(33, 43)(36, 48)(37, 50)(38, 49)(51, 54)(52, 58)(53, 60)(55, 66)(56, 69)(57, 71)(59, 77)(61, 81)(62, 76)(63, 72)(64, 80)(65, 79)(67, 88)(68, 89)(70, 93)(73, 92)(74, 90)(75, 94)(78, 96)(82, 100)(83, 91)(84, 95)(85, 97)(86, 99)(87, 98) local type(s) :: { ( 10^10 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 10 e = 50 f = 10 degree seq :: [ 10^10 ] E16.798 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 5}) Quotient :: edge^2 Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y3^5, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^2 * Y1 * Y3^2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 ] Map:: R = (1, 51, 3, 53, 8, 58, 10, 60, 4, 54)(2, 52, 5, 55, 12, 62, 14, 64, 6, 56)(7, 57, 15, 65, 27, 77, 28, 78, 16, 66)(9, 59, 18, 68, 31, 81, 32, 82, 19, 69)(11, 61, 21, 71, 35, 85, 36, 86, 22, 72)(13, 63, 24, 74, 39, 89, 40, 90, 25, 75)(17, 67, 29, 79, 43, 93, 44, 94, 30, 80)(20, 70, 33, 83, 45, 95, 46, 96, 34, 84)(23, 73, 37, 87, 47, 97, 48, 98, 38, 88)(26, 76, 41, 91, 49, 99, 50, 100, 42, 92)(101, 102)(103, 107)(104, 109)(105, 111)(106, 113)(108, 117)(110, 120)(112, 123)(114, 126)(115, 121)(116, 124)(118, 122)(119, 125)(127, 137)(128, 141)(129, 135)(130, 139)(131, 138)(132, 142)(133, 136)(134, 140)(143, 147)(144, 149)(145, 148)(146, 150)(151, 152)(153, 157)(154, 159)(155, 161)(156, 163)(158, 167)(160, 170)(162, 173)(164, 176)(165, 171)(166, 174)(168, 172)(169, 175)(177, 187)(178, 191)(179, 185)(180, 189)(181, 188)(182, 192)(183, 186)(184, 190)(193, 197)(194, 199)(195, 198)(196, 200) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 20, 20 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E16.801 Graph:: simple bipartite v = 60 e = 100 f = 10 degree seq :: [ 2^50, 10^10 ] E16.799 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 5}) Quotient :: edge^2 Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^5, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, Y2 * Y1 * Y3 * Y1 * Y2 * Y3^-1, Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y2, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1, Y2 * Y3^2 * Y1 * Y3^-2, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y1, Y2 * Y3^-2 * Y2 * Y1 * Y3^2 * Y1, Y3^-1 * Y2 * Y3^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: polytopal R = (1, 51, 4, 54, 14, 64, 17, 67, 5, 55)(2, 52, 7, 57, 23, 73, 26, 76, 8, 58)(3, 53, 10, 60, 30, 80, 31, 81, 11, 61)(6, 56, 19, 69, 42, 92, 43, 93, 20, 70)(9, 59, 22, 72, 46, 96, 50, 100, 28, 78)(12, 62, 32, 82, 37, 87, 16, 66, 33, 83)(13, 63, 34, 84, 38, 88, 40, 90, 18, 68)(15, 65, 27, 77, 41, 91, 35, 85, 36, 86)(21, 71, 44, 94, 49, 99, 25, 75, 45, 95)(24, 74, 39, 89, 29, 79, 47, 97, 48, 98)(101, 102)(103, 109)(104, 112)(105, 115)(106, 118)(107, 121)(108, 124)(110, 129)(111, 120)(113, 122)(114, 130)(116, 128)(117, 138)(119, 141)(123, 142)(125, 140)(126, 150)(127, 145)(131, 149)(132, 144)(133, 139)(134, 147)(135, 146)(136, 148)(137, 143)(151, 153)(152, 156)(154, 163)(155, 166)(157, 172)(158, 175)(159, 177)(160, 171)(161, 174)(162, 169)(164, 185)(165, 170)(167, 176)(168, 189)(173, 197)(178, 190)(179, 191)(180, 192)(181, 200)(182, 196)(183, 195)(184, 194)(186, 199)(187, 198)(188, 193) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 20, 20 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E16.802 Graph:: simple bipartite v = 60 e = 100 f = 10 degree seq :: [ 2^50, 10^10 ] E16.800 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 5}) Quotient :: edge^2 Aut^+ = C5 x D10 (small group id <50, 3>) Aut = C10 x D10 (small group id <100, 14>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^5, Y2^5, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 51, 4, 54)(2, 52, 6, 56)(3, 53, 8, 58)(5, 55, 11, 61)(7, 57, 14, 64)(9, 59, 18, 68)(10, 60, 20, 70)(12, 62, 24, 74)(13, 63, 26, 76)(15, 65, 30, 80)(16, 66, 32, 82)(17, 67, 33, 83)(19, 69, 34, 84)(21, 71, 36, 86)(22, 72, 38, 88)(23, 73, 39, 89)(25, 75, 40, 90)(27, 77, 42, 92)(28, 78, 44, 94)(29, 79, 45, 95)(31, 81, 46, 96)(35, 85, 47, 97)(37, 87, 48, 98)(41, 91, 49, 99)(43, 93, 50, 100)(101, 102, 105, 107, 103)(104, 109, 117, 119, 110)(106, 112, 123, 125, 113)(108, 115, 129, 131, 116)(111, 121, 135, 137, 122)(114, 127, 141, 143, 128)(118, 124, 136, 142, 130)(120, 126, 138, 144, 132)(133, 139, 147, 149, 145)(134, 140, 148, 150, 146)(151, 153, 157, 155, 152)(154, 160, 169, 167, 159)(156, 163, 175, 173, 162)(158, 166, 181, 179, 165)(161, 172, 187, 185, 171)(164, 178, 193, 191, 177)(168, 180, 192, 186, 174)(170, 182, 194, 188, 176)(183, 195, 199, 197, 189)(184, 196, 200, 198, 190) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 8^4 ), ( 8^5 ) } Outer automorphisms :: reflexible Dual of E16.803 Graph:: simple bipartite v = 45 e = 100 f = 25 degree seq :: [ 4^25, 5^20 ] E16.801 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 5}) Quotient :: loop^2 Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y3^5, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^2 * Y1 * Y3^2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 ] Map:: R = (1, 51, 101, 151, 3, 53, 103, 153, 8, 58, 108, 158, 10, 60, 110, 160, 4, 54, 104, 154)(2, 52, 102, 152, 5, 55, 105, 155, 12, 62, 112, 162, 14, 64, 114, 164, 6, 56, 106, 156)(7, 57, 107, 157, 15, 65, 115, 165, 27, 77, 127, 177, 28, 78, 128, 178, 16, 66, 116, 166)(9, 59, 109, 159, 18, 68, 118, 168, 31, 81, 131, 181, 32, 82, 132, 182, 19, 69, 119, 169)(11, 61, 111, 161, 21, 71, 121, 171, 35, 85, 135, 185, 36, 86, 136, 186, 22, 72, 122, 172)(13, 63, 113, 163, 24, 74, 124, 174, 39, 89, 139, 189, 40, 90, 140, 190, 25, 75, 125, 175)(17, 67, 117, 167, 29, 79, 129, 179, 43, 93, 143, 193, 44, 94, 144, 194, 30, 80, 130, 180)(20, 70, 120, 170, 33, 83, 133, 183, 45, 95, 145, 195, 46, 96, 146, 196, 34, 84, 134, 184)(23, 73, 123, 173, 37, 87, 137, 187, 47, 97, 147, 197, 48, 98, 148, 198, 38, 88, 138, 188)(26, 76, 126, 176, 41, 91, 141, 191, 49, 99, 149, 199, 50, 100, 150, 200, 42, 92, 142, 192) L = (1, 52)(2, 51)(3, 57)(4, 59)(5, 61)(6, 63)(7, 53)(8, 67)(9, 54)(10, 70)(11, 55)(12, 73)(13, 56)(14, 76)(15, 71)(16, 74)(17, 58)(18, 72)(19, 75)(20, 60)(21, 65)(22, 68)(23, 62)(24, 66)(25, 69)(26, 64)(27, 87)(28, 91)(29, 85)(30, 89)(31, 88)(32, 92)(33, 86)(34, 90)(35, 79)(36, 83)(37, 77)(38, 81)(39, 80)(40, 84)(41, 78)(42, 82)(43, 97)(44, 99)(45, 98)(46, 100)(47, 93)(48, 95)(49, 94)(50, 96)(101, 152)(102, 151)(103, 157)(104, 159)(105, 161)(106, 163)(107, 153)(108, 167)(109, 154)(110, 170)(111, 155)(112, 173)(113, 156)(114, 176)(115, 171)(116, 174)(117, 158)(118, 172)(119, 175)(120, 160)(121, 165)(122, 168)(123, 162)(124, 166)(125, 169)(126, 164)(127, 187)(128, 191)(129, 185)(130, 189)(131, 188)(132, 192)(133, 186)(134, 190)(135, 179)(136, 183)(137, 177)(138, 181)(139, 180)(140, 184)(141, 178)(142, 182)(143, 197)(144, 199)(145, 198)(146, 200)(147, 193)(148, 195)(149, 194)(150, 196) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.798 Transitivity :: VT+ Graph:: bipartite v = 10 e = 100 f = 60 degree seq :: [ 20^10 ] E16.802 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 5}) Quotient :: loop^2 Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^5, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, Y2 * Y1 * Y3 * Y1 * Y2 * Y3^-1, Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y2, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1, Y2 * Y3^2 * Y1 * Y3^-2, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y1, Y2 * Y3^-2 * Y2 * Y1 * Y3^2 * Y1, Y3^-1 * Y2 * Y3^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 51, 101, 151, 4, 54, 104, 154, 14, 64, 114, 164, 17, 67, 117, 167, 5, 55, 105, 155)(2, 52, 102, 152, 7, 57, 107, 157, 23, 73, 123, 173, 26, 76, 126, 176, 8, 58, 108, 158)(3, 53, 103, 153, 10, 60, 110, 160, 30, 80, 130, 180, 31, 81, 131, 181, 11, 61, 111, 161)(6, 56, 106, 156, 19, 69, 119, 169, 42, 92, 142, 192, 43, 93, 143, 193, 20, 70, 120, 170)(9, 59, 109, 159, 22, 72, 122, 172, 46, 96, 146, 196, 50, 100, 150, 200, 28, 78, 128, 178)(12, 62, 112, 162, 32, 82, 132, 182, 37, 87, 137, 187, 16, 66, 116, 166, 33, 83, 133, 183)(13, 63, 113, 163, 34, 84, 134, 184, 38, 88, 138, 188, 40, 90, 140, 190, 18, 68, 118, 168)(15, 65, 115, 165, 27, 77, 127, 177, 41, 91, 141, 191, 35, 85, 135, 185, 36, 86, 136, 186)(21, 71, 121, 171, 44, 94, 144, 194, 49, 99, 149, 199, 25, 75, 125, 175, 45, 95, 145, 195)(24, 74, 124, 174, 39, 89, 139, 189, 29, 79, 129, 179, 47, 97, 147, 197, 48, 98, 148, 198) L = (1, 52)(2, 51)(3, 59)(4, 62)(5, 65)(6, 68)(7, 71)(8, 74)(9, 53)(10, 79)(11, 70)(12, 54)(13, 72)(14, 80)(15, 55)(16, 78)(17, 88)(18, 56)(19, 91)(20, 61)(21, 57)(22, 63)(23, 92)(24, 58)(25, 90)(26, 100)(27, 95)(28, 66)(29, 60)(30, 64)(31, 99)(32, 94)(33, 89)(34, 97)(35, 96)(36, 98)(37, 93)(38, 67)(39, 83)(40, 75)(41, 69)(42, 73)(43, 87)(44, 82)(45, 77)(46, 85)(47, 84)(48, 86)(49, 81)(50, 76)(101, 153)(102, 156)(103, 151)(104, 163)(105, 166)(106, 152)(107, 172)(108, 175)(109, 177)(110, 171)(111, 174)(112, 169)(113, 154)(114, 185)(115, 170)(116, 155)(117, 176)(118, 189)(119, 162)(120, 165)(121, 160)(122, 157)(123, 197)(124, 161)(125, 158)(126, 167)(127, 159)(128, 190)(129, 191)(130, 192)(131, 200)(132, 196)(133, 195)(134, 194)(135, 164)(136, 199)(137, 198)(138, 193)(139, 168)(140, 178)(141, 179)(142, 180)(143, 188)(144, 184)(145, 183)(146, 182)(147, 173)(148, 187)(149, 186)(150, 181) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.799 Transitivity :: VT+ Graph:: bipartite v = 10 e = 100 f = 60 degree seq :: [ 20^10 ] E16.803 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 5}) Quotient :: loop^2 Aut^+ = C5 x D10 (small group id <50, 3>) Aut = C10 x D10 (small group id <100, 14>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^5, Y2^5, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 51, 101, 151, 4, 54, 104, 154)(2, 52, 102, 152, 6, 56, 106, 156)(3, 53, 103, 153, 8, 58, 108, 158)(5, 55, 105, 155, 11, 61, 111, 161)(7, 57, 107, 157, 14, 64, 114, 164)(9, 59, 109, 159, 18, 68, 118, 168)(10, 60, 110, 160, 20, 70, 120, 170)(12, 62, 112, 162, 24, 74, 124, 174)(13, 63, 113, 163, 26, 76, 126, 176)(15, 65, 115, 165, 30, 80, 130, 180)(16, 66, 116, 166, 32, 82, 132, 182)(17, 67, 117, 167, 33, 83, 133, 183)(19, 69, 119, 169, 34, 84, 134, 184)(21, 71, 121, 171, 36, 86, 136, 186)(22, 72, 122, 172, 38, 88, 138, 188)(23, 73, 123, 173, 39, 89, 139, 189)(25, 75, 125, 175, 40, 90, 140, 190)(27, 77, 127, 177, 42, 92, 142, 192)(28, 78, 128, 178, 44, 94, 144, 194)(29, 79, 129, 179, 45, 95, 145, 195)(31, 81, 131, 181, 46, 96, 146, 196)(35, 85, 135, 185, 47, 97, 147, 197)(37, 87, 137, 187, 48, 98, 148, 198)(41, 91, 141, 191, 49, 99, 149, 199)(43, 93, 143, 193, 50, 100, 150, 200) L = (1, 52)(2, 55)(3, 51)(4, 59)(5, 57)(6, 62)(7, 53)(8, 65)(9, 67)(10, 54)(11, 71)(12, 73)(13, 56)(14, 77)(15, 79)(16, 58)(17, 69)(18, 74)(19, 60)(20, 76)(21, 85)(22, 61)(23, 75)(24, 86)(25, 63)(26, 88)(27, 91)(28, 64)(29, 81)(30, 68)(31, 66)(32, 70)(33, 89)(34, 90)(35, 87)(36, 92)(37, 72)(38, 94)(39, 97)(40, 98)(41, 93)(42, 80)(43, 78)(44, 82)(45, 83)(46, 84)(47, 99)(48, 100)(49, 95)(50, 96)(101, 153)(102, 151)(103, 157)(104, 160)(105, 152)(106, 163)(107, 155)(108, 166)(109, 154)(110, 169)(111, 172)(112, 156)(113, 175)(114, 178)(115, 158)(116, 181)(117, 159)(118, 180)(119, 167)(120, 182)(121, 161)(122, 187)(123, 162)(124, 168)(125, 173)(126, 170)(127, 164)(128, 193)(129, 165)(130, 192)(131, 179)(132, 194)(133, 195)(134, 196)(135, 171)(136, 174)(137, 185)(138, 176)(139, 183)(140, 184)(141, 177)(142, 186)(143, 191)(144, 188)(145, 199)(146, 200)(147, 189)(148, 190)(149, 197)(150, 198) local type(s) :: { ( 4, 5, 4, 5, 4, 5, 4, 5 ) } Outer automorphisms :: reflexible Dual of E16.800 Transitivity :: VT+ Graph:: v = 25 e = 100 f = 45 degree seq :: [ 8^25 ] E16.804 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 5}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (Y3, Y2), Y2^-1 * Y1 * Y2 * Y1, Y2^5, Y3^5 ] Map:: polytopal non-degenerate R = (1, 51, 2, 52)(3, 53, 7, 57)(4, 54, 10, 60)(5, 55, 9, 59)(6, 56, 8, 58)(11, 61, 19, 69)(12, 62, 21, 71)(13, 63, 20, 70)(14, 64, 26, 76)(15, 65, 25, 75)(16, 66, 24, 74)(17, 67, 23, 73)(18, 68, 22, 72)(27, 77, 36, 86)(28, 78, 35, 85)(29, 79, 38, 88)(30, 80, 37, 87)(31, 81, 42, 92)(32, 82, 41, 91)(33, 83, 40, 90)(34, 84, 39, 89)(43, 93, 48, 98)(44, 94, 47, 97)(45, 95, 50, 100)(46, 96, 49, 99)(101, 151, 103, 153, 111, 161, 116, 166, 105, 155)(102, 152, 107, 157, 119, 169, 124, 174, 109, 159)(104, 154, 112, 162, 127, 177, 132, 182, 115, 165)(106, 156, 113, 163, 128, 178, 133, 183, 117, 167)(108, 158, 120, 170, 135, 185, 140, 190, 123, 173)(110, 160, 121, 171, 136, 186, 141, 191, 125, 175)(114, 164, 129, 179, 143, 193, 145, 195, 131, 181)(118, 168, 130, 180, 144, 194, 146, 196, 134, 184)(122, 172, 137, 187, 147, 197, 149, 199, 139, 189)(126, 176, 138, 188, 148, 198, 150, 200, 142, 192) L = (1, 104)(2, 108)(3, 112)(4, 114)(5, 115)(6, 101)(7, 120)(8, 122)(9, 123)(10, 102)(11, 127)(12, 129)(13, 103)(14, 118)(15, 131)(16, 132)(17, 105)(18, 106)(19, 135)(20, 137)(21, 107)(22, 126)(23, 139)(24, 140)(25, 109)(26, 110)(27, 143)(28, 111)(29, 130)(30, 113)(31, 134)(32, 145)(33, 116)(34, 117)(35, 147)(36, 119)(37, 138)(38, 121)(39, 142)(40, 149)(41, 124)(42, 125)(43, 144)(44, 128)(45, 146)(46, 133)(47, 148)(48, 136)(49, 150)(50, 141)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.806 Graph:: simple bipartite v = 35 e = 100 f = 35 degree seq :: [ 4^25, 10^10 ] E16.805 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 5}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y2^5, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^5, Y2^2 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1 ] Map:: R = (1, 51, 2, 52)(3, 53, 7, 57)(4, 54, 9, 59)(5, 55, 11, 61)(6, 56, 13, 63)(8, 58, 17, 67)(10, 60, 20, 70)(12, 62, 23, 73)(14, 64, 26, 76)(15, 65, 21, 71)(16, 66, 24, 74)(18, 68, 22, 72)(19, 69, 25, 75)(27, 77, 37, 87)(28, 78, 41, 91)(29, 79, 35, 85)(30, 80, 39, 89)(31, 81, 38, 88)(32, 82, 42, 92)(33, 83, 36, 86)(34, 84, 40, 90)(43, 93, 47, 97)(44, 94, 49, 99)(45, 95, 48, 98)(46, 96, 50, 100)(101, 151, 103, 153, 108, 158, 110, 160, 104, 154)(102, 152, 105, 155, 112, 162, 114, 164, 106, 156)(107, 157, 115, 165, 127, 177, 128, 178, 116, 166)(109, 159, 118, 168, 131, 181, 132, 182, 119, 169)(111, 161, 121, 171, 135, 185, 136, 186, 122, 172)(113, 163, 124, 174, 139, 189, 140, 190, 125, 175)(117, 167, 129, 179, 143, 193, 144, 194, 130, 180)(120, 170, 133, 183, 145, 195, 146, 196, 134, 184)(123, 173, 137, 187, 147, 197, 148, 198, 138, 188)(126, 176, 141, 191, 149, 199, 150, 200, 142, 192) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 35 e = 100 f = 35 degree seq :: [ 4^25, 10^10 ] E16.806 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 5}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y3^5, Y2^5, Y1 * Y2 * Y3^-1 * Y1 * Y3 * Y2^-1, Y1 * Y2^-1 * Y3^2 * Y1 * Y2, Y2^-1 * Y1 * Y2^2 * Y3 * Y1 * Y2^-1, Y1 * Y3 * Y2 * Y1 * Y3^-2 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 51, 2, 52)(3, 53, 11, 61)(4, 54, 10, 60)(5, 55, 17, 67)(6, 56, 8, 58)(7, 57, 21, 71)(9, 59, 27, 77)(12, 62, 33, 83)(13, 63, 32, 82)(14, 64, 24, 74)(15, 65, 30, 80)(16, 66, 26, 76)(18, 68, 40, 90)(19, 69, 38, 88)(20, 70, 25, 75)(22, 72, 34, 84)(23, 73, 36, 86)(28, 78, 41, 91)(29, 79, 42, 92)(31, 81, 43, 93)(35, 85, 48, 98)(37, 87, 47, 97)(39, 89, 46, 96)(44, 94, 49, 99)(45, 95, 50, 100)(101, 151, 103, 153, 112, 162, 118, 168, 105, 155)(102, 152, 107, 157, 122, 172, 128, 178, 109, 159)(104, 154, 113, 163, 134, 184, 137, 187, 116, 166)(106, 156, 114, 164, 135, 185, 141, 191, 119, 169)(108, 158, 123, 173, 133, 183, 145, 195, 126, 176)(110, 160, 124, 174, 144, 194, 140, 190, 129, 179)(111, 161, 131, 181, 147, 197, 138, 188, 130, 180)(115, 165, 136, 186, 149, 199, 146, 196, 127, 177)(117, 167, 125, 175, 132, 182, 148, 198, 139, 189)(120, 170, 121, 171, 143, 193, 150, 200, 142, 192) L = (1, 104)(2, 108)(3, 113)(4, 115)(5, 116)(6, 101)(7, 123)(8, 125)(9, 126)(10, 102)(11, 124)(12, 134)(13, 136)(14, 103)(15, 120)(16, 127)(17, 138)(18, 137)(19, 105)(20, 106)(21, 114)(22, 133)(23, 132)(24, 107)(25, 130)(26, 117)(27, 142)(28, 145)(29, 109)(30, 110)(31, 144)(32, 111)(33, 148)(34, 149)(35, 112)(36, 121)(37, 146)(38, 129)(39, 147)(40, 128)(41, 118)(42, 119)(43, 135)(44, 122)(45, 139)(46, 150)(47, 140)(48, 131)(49, 143)(50, 141)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.804 Graph:: simple bipartite v = 35 e = 100 f = 35 degree seq :: [ 4^25, 10^10 ] E16.807 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 5}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y3^5, Y2^5, Y1 * Y2 * Y3^2 * Y1 * Y2^-1, Y3^-2 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 51, 2, 52)(3, 53, 11, 61)(4, 54, 10, 60)(5, 55, 17, 67)(6, 56, 8, 58)(7, 57, 21, 71)(9, 59, 27, 77)(12, 62, 33, 83)(13, 63, 23, 73)(14, 64, 32, 82)(15, 65, 30, 80)(16, 66, 38, 88)(18, 68, 41, 91)(19, 69, 29, 79)(20, 70, 25, 75)(22, 72, 35, 85)(24, 74, 36, 86)(26, 76, 37, 87)(28, 78, 39, 89)(31, 81, 43, 93)(34, 84, 48, 98)(40, 90, 45, 95)(42, 92, 47, 97)(44, 94, 49, 99)(46, 96, 50, 100)(101, 151, 103, 153, 112, 162, 118, 168, 105, 155)(102, 152, 107, 157, 122, 172, 128, 178, 109, 159)(104, 154, 113, 163, 134, 184, 139, 189, 116, 166)(106, 156, 114, 164, 135, 185, 142, 192, 119, 169)(108, 158, 123, 173, 144, 194, 141, 191, 126, 176)(110, 160, 124, 174, 133, 183, 146, 196, 129, 179)(111, 161, 131, 181, 147, 197, 138, 188, 125, 175)(115, 165, 121, 171, 143, 193, 150, 200, 137, 187)(117, 167, 130, 180, 132, 182, 148, 198, 140, 190)(120, 170, 136, 186, 149, 199, 145, 195, 127, 177) L = (1, 104)(2, 108)(3, 113)(4, 115)(5, 116)(6, 101)(7, 123)(8, 125)(9, 126)(10, 102)(11, 132)(12, 134)(13, 121)(14, 103)(15, 120)(16, 137)(17, 129)(18, 139)(19, 105)(20, 106)(21, 136)(22, 144)(23, 111)(24, 107)(25, 130)(26, 138)(27, 119)(28, 141)(29, 109)(30, 110)(31, 148)(32, 124)(33, 122)(34, 143)(35, 112)(36, 114)(37, 127)(38, 117)(39, 150)(40, 146)(41, 147)(42, 118)(43, 149)(44, 131)(45, 142)(46, 128)(47, 140)(48, 133)(49, 135)(50, 145)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.809 Graph:: simple bipartite v = 35 e = 100 f = 35 degree seq :: [ 4^25, 10^10 ] E16.808 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 5}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y3^-1 * Y1 * Y2^-1 * Y1 * Y2, Y3^5, Y2^5 ] Map:: polytopal non-degenerate R = (1, 51, 2, 52)(3, 53, 11, 61)(4, 54, 10, 60)(5, 55, 17, 67)(6, 56, 8, 58)(7, 57, 14, 64)(9, 59, 16, 66)(12, 62, 29, 79)(13, 63, 28, 78)(15, 65, 26, 76)(18, 68, 38, 88)(19, 69, 36, 86)(20, 70, 23, 73)(21, 71, 41, 91)(22, 72, 33, 83)(24, 74, 44, 94)(25, 75, 34, 84)(27, 77, 31, 81)(30, 80, 48, 98)(32, 82, 43, 93)(35, 85, 37, 87)(39, 89, 47, 97)(40, 90, 46, 96)(42, 92, 49, 99)(45, 95, 50, 100)(101, 151, 103, 153, 112, 162, 118, 168, 105, 155)(102, 152, 107, 157, 121, 171, 124, 174, 109, 159)(104, 154, 113, 163, 130, 180, 135, 185, 116, 166)(106, 156, 114, 164, 131, 181, 139, 189, 119, 169)(108, 158, 122, 172, 142, 192, 137, 187, 117, 167)(110, 160, 111, 161, 127, 177, 145, 195, 125, 175)(115, 165, 132, 182, 149, 199, 144, 194, 134, 184)(120, 170, 133, 183, 141, 191, 150, 200, 140, 190)(123, 173, 143, 193, 148, 198, 138, 188, 136, 186)(126, 176, 128, 178, 129, 179, 147, 197, 146, 196) L = (1, 104)(2, 108)(3, 113)(4, 115)(5, 116)(6, 101)(7, 122)(8, 123)(9, 117)(10, 102)(11, 107)(12, 130)(13, 132)(14, 103)(15, 120)(16, 134)(17, 136)(18, 135)(19, 105)(20, 106)(21, 142)(22, 143)(23, 126)(24, 137)(25, 109)(26, 110)(27, 121)(28, 111)(29, 127)(30, 149)(31, 112)(32, 133)(33, 114)(34, 140)(35, 144)(36, 146)(37, 138)(38, 147)(39, 118)(40, 119)(41, 131)(42, 148)(43, 128)(44, 150)(45, 124)(46, 125)(47, 145)(48, 129)(49, 141)(50, 139)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 35 e = 100 f = 35 degree seq :: [ 4^25, 10^10 ] E16.809 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 5}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2, Y3^-1), (R * Y2)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2^-1, Y2^5, Y3^5 ] Map:: polytopal non-degenerate R = (1, 51, 2, 52)(3, 53, 11, 61)(4, 54, 10, 60)(5, 55, 17, 67)(6, 56, 8, 58)(7, 57, 13, 63)(9, 59, 19, 69)(12, 62, 29, 79)(14, 64, 28, 78)(15, 65, 26, 76)(16, 66, 35, 85)(18, 68, 38, 88)(20, 70, 23, 73)(21, 71, 41, 91)(22, 72, 32, 82)(24, 74, 40, 90)(25, 75, 46, 96)(27, 77, 30, 80)(31, 81, 48, 98)(33, 83, 43, 93)(34, 84, 44, 94)(36, 86, 47, 97)(37, 87, 39, 89)(42, 92, 49, 99)(45, 95, 50, 100)(101, 151, 103, 153, 112, 162, 118, 168, 105, 155)(102, 152, 107, 157, 121, 171, 125, 175, 109, 159)(104, 154, 113, 163, 130, 180, 136, 186, 116, 166)(106, 156, 114, 164, 131, 181, 139, 189, 119, 169)(108, 158, 111, 161, 127, 177, 145, 195, 124, 174)(110, 160, 122, 172, 142, 192, 137, 187, 117, 167)(115, 165, 132, 182, 141, 191, 150, 200, 134, 184)(120, 170, 133, 183, 149, 199, 146, 196, 140, 190)(123, 173, 128, 178, 129, 179, 147, 197, 144, 194)(126, 176, 143, 193, 148, 198, 138, 188, 135, 185) L = (1, 104)(2, 108)(3, 113)(4, 115)(5, 116)(6, 101)(7, 111)(8, 123)(9, 124)(10, 102)(11, 128)(12, 130)(13, 132)(14, 103)(15, 120)(16, 134)(17, 109)(18, 136)(19, 105)(20, 106)(21, 127)(22, 107)(23, 126)(24, 144)(25, 145)(26, 110)(27, 129)(28, 143)(29, 148)(30, 141)(31, 112)(32, 133)(33, 114)(34, 140)(35, 117)(36, 150)(37, 125)(38, 137)(39, 118)(40, 119)(41, 149)(42, 121)(43, 122)(44, 135)(45, 147)(46, 139)(47, 138)(48, 142)(49, 131)(50, 146)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.807 Graph:: simple bipartite v = 35 e = 100 f = 35 degree seq :: [ 4^25, 10^10 ] E16.810 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 5}) Quotient :: dipole Aut^+ = (C5 x C5) : C2 (small group id <50, 4>) Aut = C2 x ((C5 x C5) : C2) (small group id <100, 15>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (Y3, Y2), (Y2^-1 * Y1)^2, Y2^5, Y3^5 ] Map:: polytopal non-degenerate R = (1, 51, 2, 52)(3, 53, 9, 59)(4, 54, 10, 60)(5, 55, 7, 57)(6, 56, 8, 58)(11, 61, 24, 74)(12, 62, 25, 75)(13, 63, 23, 73)(14, 64, 26, 76)(15, 65, 21, 71)(16, 66, 19, 69)(17, 67, 20, 70)(18, 68, 22, 72)(27, 77, 41, 91)(28, 78, 40, 90)(29, 79, 42, 92)(30, 80, 39, 89)(31, 81, 38, 88)(32, 82, 36, 86)(33, 83, 35, 85)(34, 84, 37, 87)(43, 93, 50, 100)(44, 94, 49, 99)(45, 95, 48, 98)(46, 96, 47, 97)(101, 151, 103, 153, 111, 161, 116, 166, 105, 155)(102, 152, 107, 157, 119, 169, 124, 174, 109, 159)(104, 154, 112, 162, 127, 177, 132, 182, 115, 165)(106, 156, 113, 163, 128, 178, 133, 183, 117, 167)(108, 158, 120, 170, 135, 185, 140, 190, 123, 173)(110, 160, 121, 171, 136, 186, 141, 191, 125, 175)(114, 164, 129, 179, 143, 193, 145, 195, 131, 181)(118, 168, 130, 180, 144, 194, 146, 196, 134, 184)(122, 172, 137, 187, 147, 197, 149, 199, 139, 189)(126, 176, 138, 188, 148, 198, 150, 200, 142, 192) L = (1, 104)(2, 108)(3, 112)(4, 114)(5, 115)(6, 101)(7, 120)(8, 122)(9, 123)(10, 102)(11, 127)(12, 129)(13, 103)(14, 118)(15, 131)(16, 132)(17, 105)(18, 106)(19, 135)(20, 137)(21, 107)(22, 126)(23, 139)(24, 140)(25, 109)(26, 110)(27, 143)(28, 111)(29, 130)(30, 113)(31, 134)(32, 145)(33, 116)(34, 117)(35, 147)(36, 119)(37, 138)(38, 121)(39, 142)(40, 149)(41, 124)(42, 125)(43, 144)(44, 128)(45, 146)(46, 133)(47, 148)(48, 136)(49, 150)(50, 141)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 35 e = 100 f = 35 degree seq :: [ 4^25, 10^10 ] E16.811 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 10, 10}) Quotient :: edge Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^-1 * T1^-1, T1^5, T2^10 ] Map:: non-degenerate R = (1, 3, 10, 20, 30, 40, 33, 23, 13, 5)(2, 7, 16, 26, 36, 45, 37, 27, 17, 8)(4, 9, 19, 29, 39, 47, 42, 32, 22, 12)(6, 14, 24, 34, 43, 49, 44, 35, 25, 15)(11, 18, 28, 38, 46, 50, 48, 41, 31, 21)(51, 52, 56, 61, 54)(53, 59, 68, 64, 57)(55, 62, 71, 65, 58)(60, 66, 74, 78, 69)(63, 67, 75, 81, 72)(70, 79, 88, 84, 76)(73, 82, 91, 85, 77)(80, 86, 93, 96, 89)(83, 87, 94, 98, 92)(90, 97, 100, 99, 95) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 20^5 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E16.816 Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 50 f = 5 degree seq :: [ 5^10, 10^5 ] E16.812 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 10, 10}) Quotient :: edge Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^2, T1^5, T2^-1 * T1 * T2^2 * T1^-1 * T2^-1, T2^10, (T2^-1 * T1^-1)^10 ] Map:: non-degenerate R = (1, 3, 10, 18, 37, 48, 46, 28, 15, 5)(2, 7, 19, 32, 49, 45, 31, 14, 21, 8)(4, 11, 24, 9, 23, 36, 50, 43, 29, 13)(6, 16, 33, 42, 47, 30, 38, 20, 35, 17)(12, 26, 41, 25, 40, 22, 39, 34, 44, 27)(51, 52, 56, 62, 54)(53, 59, 72, 70, 58)(55, 61, 75, 80, 64)(57, 68, 86, 84, 67)(60, 69, 83, 91, 74)(63, 76, 92, 95, 78)(65, 71, 85, 94, 79)(66, 82, 98, 93, 77)(73, 87, 99, 97, 90)(81, 88, 89, 100, 96) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 20^5 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E16.818 Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 50 f = 5 degree seq :: [ 5^10, 10^5 ] E16.813 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 10, 10}) Quotient :: edge Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^5, T1^5, (T2^-1 * T1^-2)^2, T2 * T1^-1 * T2 * T1^-1 * T2^2, (T2^-1 * T1^-2)^2, T2 * T1^-1 * T2^-2 * T1 * T2, T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 ] Map:: non-degenerate R = (1, 3, 10, 23, 43, 20, 42, 33, 17, 5)(2, 7, 21, 40, 38, 16, 31, 11, 25, 8)(4, 12, 29, 15, 28, 9, 27, 45, 36, 14)(6, 18, 39, 30, 46, 24, 44, 22, 41, 19)(13, 34, 50, 35, 49, 32, 48, 37, 47, 26)(51, 52, 56, 63, 54)(53, 59, 76, 80, 61)(55, 65, 87, 68, 66)(57, 70, 64, 85, 72)(58, 73, 95, 84, 74)(60, 71, 89, 100, 79)(62, 82, 69, 90, 83)(67, 75, 91, 97, 86)(77, 92, 81, 94, 98)(78, 93, 88, 96, 99) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 20^5 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E16.817 Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 50 f = 5 degree seq :: [ 5^10, 10^5 ] E16.814 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 10, 10}) Quotient :: edge Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^5, T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1, (T1 * T2^-1 * T1)^2, T2 * T1^-1 * T2^-2 * T1 * T2 ] Map:: non-degenerate R = (1, 3, 10, 29, 46, 23, 43, 20, 17, 5)(2, 7, 21, 16, 32, 11, 31, 39, 25, 8)(4, 12, 30, 42, 37, 15, 28, 9, 27, 14)(6, 18, 40, 24, 45, 22, 44, 38, 41, 19)(13, 34, 48, 26, 47, 36, 50, 33, 49, 35)(51, 52, 56, 63, 54)(53, 59, 76, 69, 61)(55, 65, 84, 88, 66)(57, 70, 92, 85, 72)(58, 73, 62, 83, 74)(60, 71, 90, 98, 80)(64, 86, 68, 89, 79)(67, 75, 91, 99, 77)(78, 93, 81, 94, 100)(82, 95, 97, 87, 96) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 20^5 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E16.819 Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 50 f = 5 degree seq :: [ 5^10, 10^5 ] E16.815 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 10, 10}) Quotient :: edge Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^3 * T1^-2 * T2, (T2^-2 * T1)^2, T1^-3 * T2^-2 * T1^-1, T2 * T1^2 * T2^-1 * T1^-2, (T2^-1 * T1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 3, 10, 20, 6, 19, 13, 30, 17, 5)(2, 7, 22, 34, 18, 14, 4, 12, 26, 8)(9, 27, 35, 33, 16, 31, 11, 29, 15, 28)(21, 36, 32, 40, 25, 39, 23, 38, 24, 37)(41, 49, 45, 47, 44, 48, 42, 46, 43, 50)(51, 52, 56, 68, 67, 76, 60, 72, 63, 54)(53, 59, 69, 66, 55, 65, 70, 85, 80, 61)(57, 71, 64, 75, 58, 74, 84, 82, 62, 73)(77, 91, 81, 94, 78, 93, 83, 95, 79, 92)(86, 96, 89, 99, 87, 98, 90, 100, 88, 97) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10^10 ) } Outer automorphisms :: reflexible Dual of E16.820 Transitivity :: ET+ Graph:: bipartite v = 10 e = 50 f = 10 degree seq :: [ 10^10 ] E16.816 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 10, 10}) Quotient :: loop Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^-1 * T1^-1, T1^5, T2^10 ] Map:: non-degenerate R = (1, 51, 3, 53, 10, 60, 20, 70, 30, 80, 40, 90, 33, 83, 23, 73, 13, 63, 5, 55)(2, 52, 7, 57, 16, 66, 26, 76, 36, 86, 45, 95, 37, 87, 27, 77, 17, 67, 8, 58)(4, 54, 9, 59, 19, 69, 29, 79, 39, 89, 47, 97, 42, 92, 32, 82, 22, 72, 12, 62)(6, 56, 14, 64, 24, 74, 34, 84, 43, 93, 49, 99, 44, 94, 35, 85, 25, 75, 15, 65)(11, 61, 18, 68, 28, 78, 38, 88, 46, 96, 50, 100, 48, 98, 41, 91, 31, 81, 21, 71) L = (1, 52)(2, 56)(3, 59)(4, 51)(5, 62)(6, 61)(7, 53)(8, 55)(9, 68)(10, 66)(11, 54)(12, 71)(13, 67)(14, 57)(15, 58)(16, 74)(17, 75)(18, 64)(19, 60)(20, 79)(21, 65)(22, 63)(23, 82)(24, 78)(25, 81)(26, 70)(27, 73)(28, 69)(29, 88)(30, 86)(31, 72)(32, 91)(33, 87)(34, 76)(35, 77)(36, 93)(37, 94)(38, 84)(39, 80)(40, 97)(41, 85)(42, 83)(43, 96)(44, 98)(45, 90)(46, 89)(47, 100)(48, 92)(49, 95)(50, 99) local type(s) :: { ( 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10 ) } Outer automorphisms :: reflexible Dual of E16.811 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 50 f = 15 degree seq :: [ 20^5 ] E16.817 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 10, 10}) Quotient :: loop Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^2, T1^5, T2^-1 * T1 * T2^2 * T1^-1 * T2^-1, T2^10, (T2^-1 * T1^-1)^10 ] Map:: non-degenerate R = (1, 51, 3, 53, 10, 60, 18, 68, 37, 87, 48, 98, 46, 96, 28, 78, 15, 65, 5, 55)(2, 52, 7, 57, 19, 69, 32, 82, 49, 99, 45, 95, 31, 81, 14, 64, 21, 71, 8, 58)(4, 54, 11, 61, 24, 74, 9, 59, 23, 73, 36, 86, 50, 100, 43, 93, 29, 79, 13, 63)(6, 56, 16, 66, 33, 83, 42, 92, 47, 97, 30, 80, 38, 88, 20, 70, 35, 85, 17, 67)(12, 62, 26, 76, 41, 91, 25, 75, 40, 90, 22, 72, 39, 89, 34, 84, 44, 94, 27, 77) L = (1, 52)(2, 56)(3, 59)(4, 51)(5, 61)(6, 62)(7, 68)(8, 53)(9, 72)(10, 69)(11, 75)(12, 54)(13, 76)(14, 55)(15, 71)(16, 82)(17, 57)(18, 86)(19, 83)(20, 58)(21, 85)(22, 70)(23, 87)(24, 60)(25, 80)(26, 92)(27, 66)(28, 63)(29, 65)(30, 64)(31, 88)(32, 98)(33, 91)(34, 67)(35, 94)(36, 84)(37, 99)(38, 89)(39, 100)(40, 73)(41, 74)(42, 95)(43, 77)(44, 79)(45, 78)(46, 81)(47, 90)(48, 93)(49, 97)(50, 96) local type(s) :: { ( 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10 ) } Outer automorphisms :: reflexible Dual of E16.813 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 50 f = 15 degree seq :: [ 20^5 ] E16.818 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 10, 10}) Quotient :: loop Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^5, T1^5, (T2^-1 * T1^-2)^2, T2 * T1^-1 * T2 * T1^-1 * T2^2, (T2^-1 * T1^-2)^2, T2 * T1^-1 * T2^-2 * T1 * T2, T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 ] Map:: non-degenerate R = (1, 51, 3, 53, 10, 60, 23, 73, 43, 93, 20, 70, 42, 92, 33, 83, 17, 67, 5, 55)(2, 52, 7, 57, 21, 71, 40, 90, 38, 88, 16, 66, 31, 81, 11, 61, 25, 75, 8, 58)(4, 54, 12, 62, 29, 79, 15, 65, 28, 78, 9, 59, 27, 77, 45, 95, 36, 86, 14, 64)(6, 56, 18, 68, 39, 89, 30, 80, 46, 96, 24, 74, 44, 94, 22, 72, 41, 91, 19, 69)(13, 63, 34, 84, 50, 100, 35, 85, 49, 99, 32, 82, 48, 98, 37, 87, 47, 97, 26, 76) L = (1, 52)(2, 56)(3, 59)(4, 51)(5, 65)(6, 63)(7, 70)(8, 73)(9, 76)(10, 71)(11, 53)(12, 82)(13, 54)(14, 85)(15, 87)(16, 55)(17, 75)(18, 66)(19, 90)(20, 64)(21, 89)(22, 57)(23, 95)(24, 58)(25, 91)(26, 80)(27, 92)(28, 93)(29, 60)(30, 61)(31, 94)(32, 69)(33, 62)(34, 74)(35, 72)(36, 67)(37, 68)(38, 96)(39, 100)(40, 83)(41, 97)(42, 81)(43, 88)(44, 98)(45, 84)(46, 99)(47, 86)(48, 77)(49, 78)(50, 79) local type(s) :: { ( 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10 ) } Outer automorphisms :: reflexible Dual of E16.812 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 50 f = 15 degree seq :: [ 20^5 ] E16.819 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 10, 10}) Quotient :: loop Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^5, T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1, (T1 * T2^-1 * T1)^2, T2 * T1^-1 * T2^-2 * T1 * T2 ] Map:: non-degenerate R = (1, 51, 3, 53, 10, 60, 29, 79, 46, 96, 23, 73, 43, 93, 20, 70, 17, 67, 5, 55)(2, 52, 7, 57, 21, 71, 16, 66, 32, 82, 11, 61, 31, 81, 39, 89, 25, 75, 8, 58)(4, 54, 12, 62, 30, 80, 42, 92, 37, 87, 15, 65, 28, 78, 9, 59, 27, 77, 14, 64)(6, 56, 18, 68, 40, 90, 24, 74, 45, 95, 22, 72, 44, 94, 38, 88, 41, 91, 19, 69)(13, 63, 34, 84, 48, 98, 26, 76, 47, 97, 36, 86, 50, 100, 33, 83, 49, 99, 35, 85) L = (1, 52)(2, 56)(3, 59)(4, 51)(5, 65)(6, 63)(7, 70)(8, 73)(9, 76)(10, 71)(11, 53)(12, 83)(13, 54)(14, 86)(15, 84)(16, 55)(17, 75)(18, 89)(19, 61)(20, 92)(21, 90)(22, 57)(23, 62)(24, 58)(25, 91)(26, 69)(27, 67)(28, 93)(29, 64)(30, 60)(31, 94)(32, 95)(33, 74)(34, 88)(35, 72)(36, 68)(37, 96)(38, 66)(39, 79)(40, 98)(41, 99)(42, 85)(43, 81)(44, 100)(45, 97)(46, 82)(47, 87)(48, 80)(49, 77)(50, 78) local type(s) :: { ( 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10 ) } Outer automorphisms :: reflexible Dual of E16.814 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 50 f = 15 degree seq :: [ 20^5 ] E16.820 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 10, 10}) Quotient :: loop Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1)^2, T2^5, T2 * T1^2 * T2^-1 * T1^-2, T2^-1 * T1^2 * T2 * T1^-2, T1^10, (T2^-1 * T1^-1)^10 ] Map:: polytopal non-degenerate R = (1, 51, 3, 53, 10, 60, 15, 65, 5, 55)(2, 52, 7, 57, 20, 70, 22, 72, 8, 58)(4, 54, 11, 61, 25, 75, 29, 79, 13, 63)(6, 56, 17, 67, 35, 85, 36, 86, 18, 68)(9, 59, 16, 66, 33, 83, 41, 91, 23, 73)(12, 62, 21, 71, 39, 89, 45, 95, 27, 77)(14, 64, 30, 80, 47, 97, 43, 93, 26, 76)(19, 69, 32, 82, 49, 99, 46, 96, 37, 87)(24, 74, 34, 84, 48, 98, 44, 94, 31, 81)(28, 78, 40, 90, 38, 88, 50, 100, 42, 92) L = (1, 52)(2, 56)(3, 59)(4, 51)(5, 61)(6, 66)(7, 69)(8, 53)(9, 67)(10, 74)(11, 68)(12, 54)(13, 71)(14, 55)(15, 80)(16, 82)(17, 84)(18, 57)(19, 83)(20, 88)(21, 58)(22, 89)(23, 60)(24, 85)(25, 87)(26, 62)(27, 64)(28, 63)(29, 90)(30, 86)(31, 65)(32, 98)(33, 100)(34, 99)(35, 97)(36, 75)(37, 70)(38, 91)(39, 73)(40, 72)(41, 95)(42, 76)(43, 78)(44, 77)(45, 81)(46, 79)(47, 96)(48, 92)(49, 93)(50, 94) local type(s) :: { ( 10^10 ) } Outer automorphisms :: reflexible Dual of E16.815 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 50 f = 10 degree seq :: [ 10^10 ] E16.821 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y1^-1 * Y2^-1, Y2^-1 * Y1 * Y2 * Y3^-1, Y1^5, (R * Y2 * Y3^-1)^2, Y2^10, Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 51, 2, 52, 6, 56, 11, 61, 4, 54)(3, 53, 9, 59, 18, 68, 14, 64, 7, 57)(5, 55, 12, 62, 21, 71, 15, 65, 8, 58)(10, 60, 16, 66, 24, 74, 28, 78, 19, 69)(13, 63, 17, 67, 25, 75, 31, 81, 22, 72)(20, 70, 29, 79, 38, 88, 34, 84, 26, 76)(23, 73, 32, 82, 41, 91, 35, 85, 27, 77)(30, 80, 36, 86, 43, 93, 46, 96, 39, 89)(33, 83, 37, 87, 44, 94, 48, 98, 42, 92)(40, 90, 47, 97, 50, 100, 49, 99, 45, 95)(101, 151, 103, 153, 110, 160, 120, 170, 130, 180, 140, 190, 133, 183, 123, 173, 113, 163, 105, 155)(102, 152, 107, 157, 116, 166, 126, 176, 136, 186, 145, 195, 137, 187, 127, 177, 117, 167, 108, 158)(104, 154, 109, 159, 119, 169, 129, 179, 139, 189, 147, 197, 142, 192, 132, 182, 122, 172, 112, 162)(106, 156, 114, 164, 124, 174, 134, 184, 143, 193, 149, 199, 144, 194, 135, 185, 125, 175, 115, 165)(111, 161, 118, 168, 128, 178, 138, 188, 146, 196, 150, 200, 148, 198, 141, 191, 131, 181, 121, 171) L = (1, 104)(2, 101)(3, 107)(4, 111)(5, 108)(6, 102)(7, 114)(8, 115)(9, 103)(10, 119)(11, 106)(12, 105)(13, 122)(14, 118)(15, 121)(16, 110)(17, 113)(18, 109)(19, 128)(20, 126)(21, 112)(22, 131)(23, 127)(24, 116)(25, 117)(26, 134)(27, 135)(28, 124)(29, 120)(30, 139)(31, 125)(32, 123)(33, 142)(34, 138)(35, 141)(36, 130)(37, 133)(38, 129)(39, 146)(40, 145)(41, 132)(42, 148)(43, 136)(44, 137)(45, 149)(46, 143)(47, 140)(48, 144)(49, 150)(50, 147)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 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 E16.827 Graph:: bipartite v = 15 e = 100 f = 55 degree seq :: [ 10^10, 20^5 ] E16.822 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y3^-1, (R * Y1)^2, Y1^2 * Y3^-3, Y1^5, Y2^3 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-3 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2^-1, Y3 * Y2^2 * Y3^-1 * Y2^-2, Y2^10, (Y3 * Y2^-1)^10 ] Map:: R = (1, 51, 2, 52, 6, 56, 12, 62, 4, 54)(3, 53, 9, 59, 22, 72, 20, 70, 8, 58)(5, 55, 11, 61, 25, 75, 30, 80, 14, 64)(7, 57, 18, 68, 36, 86, 34, 84, 17, 67)(10, 60, 19, 69, 33, 83, 41, 91, 24, 74)(13, 63, 26, 76, 42, 92, 45, 95, 28, 78)(15, 65, 21, 71, 35, 85, 44, 94, 29, 79)(16, 66, 32, 82, 48, 98, 43, 93, 27, 77)(23, 73, 37, 87, 49, 99, 47, 97, 40, 90)(31, 81, 38, 88, 39, 89, 50, 100, 46, 96)(101, 151, 103, 153, 110, 160, 118, 168, 137, 187, 148, 198, 146, 196, 128, 178, 115, 165, 105, 155)(102, 152, 107, 157, 119, 169, 132, 182, 149, 199, 145, 195, 131, 181, 114, 164, 121, 171, 108, 158)(104, 154, 111, 161, 124, 174, 109, 159, 123, 173, 136, 186, 150, 200, 143, 193, 129, 179, 113, 163)(106, 156, 116, 166, 133, 183, 142, 192, 147, 197, 130, 180, 138, 188, 120, 170, 135, 185, 117, 167)(112, 162, 126, 176, 141, 191, 125, 175, 140, 190, 122, 172, 139, 189, 134, 184, 144, 194, 127, 177) L = (1, 104)(2, 101)(3, 108)(4, 112)(5, 114)(6, 102)(7, 117)(8, 120)(9, 103)(10, 124)(11, 105)(12, 106)(13, 128)(14, 130)(15, 129)(16, 127)(17, 134)(18, 107)(19, 110)(20, 122)(21, 115)(22, 109)(23, 140)(24, 141)(25, 111)(26, 113)(27, 143)(28, 145)(29, 144)(30, 125)(31, 146)(32, 116)(33, 119)(34, 136)(35, 121)(36, 118)(37, 123)(38, 131)(39, 138)(40, 147)(41, 133)(42, 126)(43, 148)(44, 135)(45, 142)(46, 150)(47, 149)(48, 132)(49, 137)(50, 139)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 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 E16.829 Graph:: bipartite v = 15 e = 100 f = 55 degree seq :: [ 10^10, 20^5 ] E16.823 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y3^-3 * Y1 * Y3^-1, Y3 * Y2^-3 * Y1^-1 * Y2^-1, (Y1^-1 * Y2 * Y1^-1)^2, (Y2 * Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2 * Y1^-1 * Y2^-2 * Y1 * Y2, Y3 * Y2^2 * Y3^-1 * Y2^-2, (Y2^2 * Y3 * Y2)^2, Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 51, 2, 52, 6, 56, 13, 63, 4, 54)(3, 53, 9, 59, 26, 76, 19, 69, 11, 61)(5, 55, 15, 65, 34, 84, 38, 88, 16, 66)(7, 57, 20, 70, 42, 92, 35, 85, 22, 72)(8, 58, 23, 73, 12, 62, 33, 83, 24, 74)(10, 60, 21, 71, 40, 90, 48, 98, 30, 80)(14, 64, 36, 86, 18, 68, 39, 89, 29, 79)(17, 67, 25, 75, 41, 91, 49, 99, 27, 77)(28, 78, 43, 93, 31, 81, 44, 94, 50, 100)(32, 82, 45, 95, 47, 97, 37, 87, 46, 96)(101, 151, 103, 153, 110, 160, 129, 179, 146, 196, 123, 173, 143, 193, 120, 170, 117, 167, 105, 155)(102, 152, 107, 157, 121, 171, 116, 166, 132, 182, 111, 161, 131, 181, 139, 189, 125, 175, 108, 158)(104, 154, 112, 162, 130, 180, 142, 192, 137, 187, 115, 165, 128, 178, 109, 159, 127, 177, 114, 164)(106, 156, 118, 168, 140, 190, 124, 174, 145, 195, 122, 172, 144, 194, 138, 188, 141, 191, 119, 169)(113, 163, 134, 184, 148, 198, 126, 176, 147, 197, 136, 186, 150, 200, 133, 183, 149, 199, 135, 185) L = (1, 104)(2, 101)(3, 111)(4, 113)(5, 116)(6, 102)(7, 122)(8, 124)(9, 103)(10, 130)(11, 119)(12, 123)(13, 106)(14, 129)(15, 105)(16, 138)(17, 127)(18, 136)(19, 126)(20, 107)(21, 110)(22, 135)(23, 108)(24, 133)(25, 117)(26, 109)(27, 149)(28, 150)(29, 139)(30, 148)(31, 143)(32, 146)(33, 112)(34, 115)(35, 142)(36, 114)(37, 147)(38, 134)(39, 118)(40, 121)(41, 125)(42, 120)(43, 128)(44, 131)(45, 132)(46, 137)(47, 145)(48, 140)(49, 141)(50, 144)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 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 E16.830 Graph:: bipartite v = 15 e = 100 f = 55 degree seq :: [ 10^10, 20^5 ] E16.824 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^2 * Y3^-1 * Y1 * Y3^-1, Y1^5, Y3 * Y2^2 * Y3^-1 * Y2^-2, Y2^2 * Y3 * Y2 * Y1^-1 * Y2, Y2^-1 * Y1 * Y2^-3 * Y3^-1, Y3 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, (Y2^-1 * R * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y2^-1 * Y1^-2 * Y2^-1, Y2 * Y1^-1 * Y2^-2 * Y1 * Y2, Y2^-1 * Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, (Y1 * Y2 * Y1 * Y2^-1)^5 ] Map:: R = (1, 51, 2, 52, 6, 56, 13, 63, 4, 54)(3, 53, 9, 59, 26, 76, 30, 80, 11, 61)(5, 55, 15, 65, 37, 87, 18, 68, 16, 66)(7, 57, 20, 70, 14, 64, 35, 85, 22, 72)(8, 58, 23, 73, 45, 95, 34, 84, 24, 74)(10, 60, 21, 71, 39, 89, 50, 100, 29, 79)(12, 62, 32, 82, 19, 69, 40, 90, 33, 83)(17, 67, 25, 75, 41, 91, 47, 97, 36, 86)(27, 77, 42, 92, 31, 81, 44, 94, 48, 98)(28, 78, 43, 93, 38, 88, 46, 96, 49, 99)(101, 151, 103, 153, 110, 160, 123, 173, 143, 193, 120, 170, 142, 192, 133, 183, 117, 167, 105, 155)(102, 152, 107, 157, 121, 171, 140, 190, 138, 188, 116, 166, 131, 181, 111, 161, 125, 175, 108, 158)(104, 154, 112, 162, 129, 179, 115, 165, 128, 178, 109, 159, 127, 177, 145, 195, 136, 186, 114, 164)(106, 156, 118, 168, 139, 189, 130, 180, 146, 196, 124, 174, 144, 194, 122, 172, 141, 191, 119, 169)(113, 163, 134, 184, 150, 200, 135, 185, 149, 199, 132, 182, 148, 198, 137, 187, 147, 197, 126, 176) L = (1, 104)(2, 101)(3, 111)(4, 113)(5, 116)(6, 102)(7, 122)(8, 124)(9, 103)(10, 129)(11, 130)(12, 133)(13, 106)(14, 120)(15, 105)(16, 118)(17, 136)(18, 137)(19, 132)(20, 107)(21, 110)(22, 135)(23, 108)(24, 134)(25, 117)(26, 109)(27, 148)(28, 149)(29, 150)(30, 126)(31, 142)(32, 112)(33, 140)(34, 145)(35, 114)(36, 147)(37, 115)(38, 143)(39, 121)(40, 119)(41, 125)(42, 127)(43, 128)(44, 131)(45, 123)(46, 138)(47, 141)(48, 144)(49, 146)(50, 139)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 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 E16.828 Graph:: bipartite v = 15 e = 100 f = 55 degree seq :: [ 10^10, 20^5 ] E16.825 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-2 * Y2^2 * Y1^-2, Y2^-3 * Y1^-2 * Y2^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2^2 * Y1 * Y2^-2 * Y1^-1, (Y3^-1 * Y1^-1)^5 ] Map:: R = (1, 51, 2, 52, 6, 56, 18, 68, 10, 60, 22, 72, 17, 67, 26, 76, 13, 63, 4, 54)(3, 53, 9, 59, 19, 69, 35, 85, 29, 79, 16, 66, 5, 55, 15, 65, 20, 70, 11, 61)(7, 57, 21, 71, 34, 84, 32, 82, 14, 64, 25, 75, 8, 58, 24, 74, 12, 62, 23, 73)(27, 77, 41, 91, 33, 83, 45, 95, 31, 81, 44, 94, 28, 78, 43, 93, 30, 80, 42, 92)(36, 86, 46, 96, 40, 90, 50, 100, 39, 89, 49, 99, 37, 87, 48, 98, 38, 88, 47, 97)(101, 151, 103, 153, 110, 160, 129, 179, 113, 163, 120, 170, 106, 156, 119, 169, 117, 167, 105, 155)(102, 152, 107, 157, 122, 172, 114, 164, 104, 154, 112, 162, 118, 168, 134, 184, 126, 176, 108, 158)(109, 159, 127, 177, 116, 166, 131, 181, 111, 161, 130, 180, 135, 185, 133, 183, 115, 165, 128, 178)(121, 171, 136, 186, 125, 175, 139, 189, 123, 173, 138, 188, 132, 182, 140, 190, 124, 174, 137, 187)(141, 191, 148, 198, 144, 194, 146, 196, 142, 192, 149, 199, 145, 195, 147, 197, 143, 193, 150, 200) L = (1, 103)(2, 107)(3, 110)(4, 112)(5, 101)(6, 119)(7, 122)(8, 102)(9, 127)(10, 129)(11, 130)(12, 118)(13, 120)(14, 104)(15, 128)(16, 131)(17, 105)(18, 134)(19, 117)(20, 106)(21, 136)(22, 114)(23, 138)(24, 137)(25, 139)(26, 108)(27, 116)(28, 109)(29, 113)(30, 135)(31, 111)(32, 140)(33, 115)(34, 126)(35, 133)(36, 125)(37, 121)(38, 132)(39, 123)(40, 124)(41, 148)(42, 149)(43, 150)(44, 146)(45, 147)(46, 142)(47, 143)(48, 144)(49, 145)(50, 141)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.826 Graph:: bipartite v = 10 e = 100 f = 60 degree seq :: [ 20^10 ] E16.826 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3^-1 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, Y2^5, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-3 * Y2^-1 * Y3, Y3^-1 * Y2^2 * Y3^2 * Y2^-2 * Y3^-1, Y3^20, (Y3^-1 * Y1^-1)^10 ] Map:: polytopal R = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100)(101, 151, 102, 152, 106, 156, 113, 163, 104, 154)(103, 153, 109, 159, 122, 172, 127, 177, 111, 161)(105, 155, 114, 164, 130, 180, 119, 169, 107, 157)(108, 158, 120, 170, 137, 187, 133, 183, 116, 166)(110, 160, 118, 168, 132, 182, 144, 194, 125, 175)(112, 162, 128, 178, 146, 196, 142, 192, 124, 174)(115, 165, 121, 171, 135, 185, 139, 189, 123, 173)(117, 167, 134, 184, 148, 198, 143, 193, 129, 179)(126, 176, 136, 186, 147, 197, 150, 200, 141, 191)(131, 181, 138, 188, 149, 199, 145, 195, 140, 190) L = (1, 103)(2, 107)(3, 110)(4, 112)(5, 101)(6, 116)(7, 118)(8, 102)(9, 104)(10, 124)(11, 126)(12, 125)(13, 129)(14, 123)(15, 105)(16, 132)(17, 106)(18, 111)(19, 136)(20, 115)(21, 108)(22, 139)(23, 109)(24, 141)(25, 143)(26, 142)(27, 145)(28, 113)(29, 144)(30, 140)(31, 114)(32, 119)(33, 147)(34, 121)(35, 117)(36, 127)(37, 131)(38, 120)(39, 128)(40, 122)(41, 148)(42, 149)(43, 150)(44, 133)(45, 146)(46, 135)(47, 130)(48, 138)(49, 134)(50, 137)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 20, 20 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E16.825 Graph:: simple bipartite v = 60 e = 100 f = 10 degree seq :: [ 2^50, 10^10 ] E16.827 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^10, (Y3 * Y2^-1)^5 ] Map:: R = (1, 51, 2, 52, 6, 56, 14, 64, 24, 74, 34, 84, 33, 83, 23, 73, 12, 62, 4, 54)(3, 53, 8, 58, 15, 65, 26, 76, 35, 85, 44, 94, 40, 90, 30, 80, 20, 70, 10, 60)(5, 55, 7, 57, 16, 66, 25, 75, 36, 86, 43, 93, 42, 92, 32, 82, 22, 72, 11, 61)(9, 59, 18, 68, 27, 77, 38, 88, 45, 95, 50, 100, 47, 97, 39, 89, 29, 79, 19, 69)(13, 63, 17, 67, 28, 78, 37, 87, 46, 96, 49, 99, 48, 98, 41, 91, 31, 81, 21, 71)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200) L = (1, 103)(2, 107)(3, 109)(4, 111)(5, 101)(6, 115)(7, 117)(8, 102)(9, 113)(10, 104)(11, 121)(12, 120)(13, 105)(14, 125)(15, 127)(16, 106)(17, 118)(18, 108)(19, 110)(20, 129)(21, 119)(22, 112)(23, 132)(24, 135)(25, 137)(26, 114)(27, 128)(28, 116)(29, 131)(30, 123)(31, 122)(32, 141)(33, 140)(34, 143)(35, 145)(36, 124)(37, 138)(38, 126)(39, 130)(40, 147)(41, 139)(42, 133)(43, 149)(44, 134)(45, 146)(46, 136)(47, 148)(48, 142)(49, 150)(50, 144)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.821 Graph:: simple bipartite v = 55 e = 100 f = 15 degree seq :: [ 2^50, 20^5 ] E16.828 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y3^5, Y3 * Y1^2 * Y3^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^2, (Y3 * Y2^-1)^5, Y1^10, (Y3^-1 * Y1^-1)^10 ] Map:: R = (1, 51, 2, 52, 6, 56, 16, 66, 32, 82, 48, 98, 42, 92, 26, 76, 12, 62, 4, 54)(3, 53, 9, 59, 17, 67, 34, 84, 49, 99, 43, 93, 28, 78, 13, 63, 21, 71, 8, 58)(5, 55, 11, 61, 18, 68, 7, 57, 19, 69, 33, 83, 50, 100, 44, 94, 27, 77, 14, 64)(10, 60, 24, 74, 35, 85, 47, 97, 46, 96, 29, 79, 40, 90, 22, 72, 39, 89, 23, 73)(15, 65, 30, 80, 36, 86, 25, 75, 37, 87, 20, 70, 38, 88, 41, 91, 45, 95, 31, 81)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200) L = (1, 103)(2, 107)(3, 110)(4, 111)(5, 101)(6, 117)(7, 120)(8, 102)(9, 116)(10, 115)(11, 125)(12, 121)(13, 104)(14, 130)(15, 105)(16, 133)(17, 135)(18, 106)(19, 132)(20, 122)(21, 139)(22, 108)(23, 109)(24, 134)(25, 129)(26, 114)(27, 112)(28, 140)(29, 113)(30, 147)(31, 124)(32, 149)(33, 141)(34, 148)(35, 136)(36, 118)(37, 119)(38, 150)(39, 145)(40, 138)(41, 123)(42, 128)(43, 126)(44, 131)(45, 127)(46, 137)(47, 143)(48, 144)(49, 146)(50, 142)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.824 Graph:: simple bipartite v = 55 e = 100 f = 15 degree seq :: [ 2^50, 20^5 ] E16.829 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^5, Y3 * Y1^-3 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^2 * Y3 * Y1^-2, (Y1^-1 * Y3^-2)^2, Y1 * Y3 * Y1 * Y3 * Y1^4, (Y3 * Y2^-1)^5 ] Map:: R = (1, 51, 2, 52, 6, 56, 18, 68, 39, 89, 27, 77, 44, 94, 33, 83, 13, 63, 4, 54)(3, 53, 9, 59, 19, 69, 41, 91, 35, 85, 14, 64, 25, 75, 8, 58, 24, 74, 11, 61)(5, 55, 15, 65, 20, 70, 12, 62, 23, 73, 7, 57, 21, 71, 40, 90, 34, 84, 16, 66)(10, 60, 29, 79, 42, 92, 26, 76, 50, 100, 31, 81, 49, 99, 28, 78, 48, 98, 30, 80)(17, 67, 38, 88, 43, 93, 37, 87, 47, 97, 36, 86, 45, 95, 32, 82, 46, 96, 22, 72)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200) L = (1, 103)(2, 107)(3, 110)(4, 112)(5, 101)(6, 119)(7, 122)(8, 102)(9, 127)(10, 117)(11, 118)(12, 132)(13, 124)(14, 104)(15, 136)(16, 137)(17, 105)(18, 140)(19, 142)(20, 106)(21, 144)(22, 126)(23, 139)(24, 148)(25, 149)(26, 108)(27, 116)(28, 109)(29, 114)(30, 141)(31, 111)(32, 129)(33, 115)(34, 113)(35, 150)(36, 130)(37, 128)(38, 131)(39, 135)(40, 138)(41, 133)(42, 143)(43, 120)(44, 125)(45, 121)(46, 134)(47, 123)(48, 146)(49, 145)(50, 147)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.822 Graph:: simple bipartite v = 55 e = 100 f = 15 degree seq :: [ 2^50, 20^5 ] E16.830 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10}) Quotient :: dipole Aut^+ = C5 x D10 (small group id <50, 3>) Aut = D10 x D10 (small group id <100, 13>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^5, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2, (Y3 * Y1^-1 * Y3)^2, Y1 * Y3 * Y1^-2 * Y3^-1 * Y1, (Y3 * Y1^-3)^2, (Y3 * Y2^-1)^5 ] Map:: R = (1, 51, 2, 52, 6, 56, 18, 68, 39, 89, 30, 80, 46, 96, 27, 77, 13, 63, 4, 54)(3, 53, 9, 59, 19, 69, 14, 64, 25, 75, 8, 58, 24, 74, 40, 90, 31, 81, 11, 61)(5, 55, 15, 65, 20, 70, 42, 92, 34, 84, 12, 62, 23, 73, 7, 57, 21, 71, 16, 66)(10, 60, 29, 79, 41, 91, 32, 82, 49, 99, 28, 78, 48, 98, 35, 85, 50, 100, 26, 76)(17, 67, 33, 83, 43, 93, 22, 72, 45, 95, 37, 87, 47, 97, 36, 86, 44, 94, 38, 88)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200) L = (1, 103)(2, 107)(3, 110)(4, 112)(5, 101)(6, 119)(7, 122)(8, 102)(9, 127)(10, 117)(11, 130)(12, 133)(13, 131)(14, 104)(15, 136)(16, 137)(17, 105)(18, 116)(19, 141)(20, 106)(21, 113)(22, 126)(23, 146)(24, 148)(25, 149)(26, 108)(27, 142)(28, 109)(29, 140)(30, 115)(31, 150)(32, 111)(33, 135)(34, 139)(35, 114)(36, 132)(37, 129)(38, 128)(39, 125)(40, 118)(41, 143)(42, 138)(43, 120)(44, 121)(45, 134)(46, 124)(47, 123)(48, 147)(49, 145)(50, 144)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.823 Graph:: simple bipartite v = 55 e = 100 f = 15 degree seq :: [ 2^50, 20^5 ] E16.831 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 10, 10}) Quotient :: edge Aut^+ = C10 x C5 (small group id <50, 5>) Aut = C2 x ((C5 x C5) : C2) (small group id <100, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^10 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 38, 33, 23, 13, 5)(2, 7, 16, 26, 36, 45, 37, 27, 17, 8)(4, 10, 19, 29, 39, 46, 42, 32, 22, 12)(6, 14, 24, 34, 43, 49, 44, 35, 25, 15)(11, 20, 30, 40, 47, 50, 48, 41, 31, 21)(51, 52, 56, 61, 54)(53, 57, 64, 70, 60)(55, 58, 65, 71, 62)(59, 66, 74, 80, 69)(63, 67, 75, 81, 72)(68, 76, 84, 90, 79)(73, 77, 85, 91, 82)(78, 86, 93, 97, 89)(83, 87, 94, 98, 92)(88, 95, 99, 100, 96) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 20^5 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E16.832 Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 50 f = 5 degree seq :: [ 5^10, 10^5 ] E16.832 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 10, 10}) Quotient :: loop Aut^+ = C10 x C5 (small group id <50, 5>) Aut = C2 x ((C5 x C5) : C2) (small group id <100, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^10 ] Map:: non-degenerate R = (1, 51, 3, 53, 9, 59, 18, 68, 28, 78, 38, 88, 33, 83, 23, 73, 13, 63, 5, 55)(2, 52, 7, 57, 16, 66, 26, 76, 36, 86, 45, 95, 37, 87, 27, 77, 17, 67, 8, 58)(4, 54, 10, 60, 19, 69, 29, 79, 39, 89, 46, 96, 42, 92, 32, 82, 22, 72, 12, 62)(6, 56, 14, 64, 24, 74, 34, 84, 43, 93, 49, 99, 44, 94, 35, 85, 25, 75, 15, 65)(11, 61, 20, 70, 30, 80, 40, 90, 47, 97, 50, 100, 48, 98, 41, 91, 31, 81, 21, 71) L = (1, 52)(2, 56)(3, 57)(4, 51)(5, 58)(6, 61)(7, 64)(8, 65)(9, 66)(10, 53)(11, 54)(12, 55)(13, 67)(14, 70)(15, 71)(16, 74)(17, 75)(18, 76)(19, 59)(20, 60)(21, 62)(22, 63)(23, 77)(24, 80)(25, 81)(26, 84)(27, 85)(28, 86)(29, 68)(30, 69)(31, 72)(32, 73)(33, 87)(34, 90)(35, 91)(36, 93)(37, 94)(38, 95)(39, 78)(40, 79)(41, 82)(42, 83)(43, 97)(44, 98)(45, 99)(46, 88)(47, 89)(48, 92)(49, 100)(50, 96) local type(s) :: { ( 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10 ) } Outer automorphisms :: reflexible Dual of E16.831 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 50 f = 15 degree seq :: [ 20^5 ] E16.833 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10}) Quotient :: dipole Aut^+ = C10 x C5 (small group id <50, 5>) Aut = C2 x ((C5 x C5) : C2) (small group id <100, 15>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y1^5, Y3^10, Y2^10 ] Map:: R = (1, 51, 2, 52, 6, 56, 11, 61, 4, 54)(3, 53, 7, 57, 14, 64, 20, 70, 10, 60)(5, 55, 8, 58, 15, 65, 21, 71, 12, 62)(9, 59, 16, 66, 24, 74, 30, 80, 19, 69)(13, 63, 17, 67, 25, 75, 31, 81, 22, 72)(18, 68, 26, 76, 34, 84, 40, 90, 29, 79)(23, 73, 27, 77, 35, 85, 41, 91, 32, 82)(28, 78, 36, 86, 43, 93, 47, 97, 39, 89)(33, 83, 37, 87, 44, 94, 48, 98, 42, 92)(38, 88, 45, 95, 49, 99, 50, 100, 46, 96)(101, 151, 103, 153, 109, 159, 118, 168, 128, 178, 138, 188, 133, 183, 123, 173, 113, 163, 105, 155)(102, 152, 107, 157, 116, 166, 126, 176, 136, 186, 145, 195, 137, 187, 127, 177, 117, 167, 108, 158)(104, 154, 110, 160, 119, 169, 129, 179, 139, 189, 146, 196, 142, 192, 132, 182, 122, 172, 112, 162)(106, 156, 114, 164, 124, 174, 134, 184, 143, 193, 149, 199, 144, 194, 135, 185, 125, 175, 115, 165)(111, 161, 120, 170, 130, 180, 140, 190, 147, 197, 150, 200, 148, 198, 141, 191, 131, 181, 121, 171) L = (1, 104)(2, 101)(3, 110)(4, 111)(5, 112)(6, 102)(7, 103)(8, 105)(9, 119)(10, 120)(11, 106)(12, 121)(13, 122)(14, 107)(15, 108)(16, 109)(17, 113)(18, 129)(19, 130)(20, 114)(21, 115)(22, 131)(23, 132)(24, 116)(25, 117)(26, 118)(27, 123)(28, 139)(29, 140)(30, 124)(31, 125)(32, 141)(33, 142)(34, 126)(35, 127)(36, 128)(37, 133)(38, 146)(39, 147)(40, 134)(41, 135)(42, 148)(43, 136)(44, 137)(45, 138)(46, 150)(47, 143)(48, 144)(49, 145)(50, 149)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 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 E16.834 Graph:: bipartite v = 15 e = 100 f = 55 degree seq :: [ 10^10, 20^5 ] E16.834 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 10, 10}) Quotient :: dipole Aut^+ = C10 x C5 (small group id <50, 5>) Aut = C2 x ((C5 x C5) : C2) (small group id <100, 15>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-10, (Y3 * Y2^-1)^5, Y1^10 ] Map:: R = (1, 51, 2, 52, 6, 56, 14, 64, 24, 74, 34, 84, 31, 81, 21, 71, 11, 61, 4, 54)(3, 53, 7, 57, 15, 65, 25, 75, 35, 85, 43, 93, 40, 90, 30, 80, 20, 70, 10, 60)(5, 55, 8, 58, 16, 66, 26, 76, 36, 86, 44, 94, 41, 91, 32, 82, 22, 72, 12, 62)(9, 59, 17, 67, 27, 77, 37, 87, 45, 95, 49, 99, 47, 97, 39, 89, 29, 79, 19, 69)(13, 63, 18, 68, 28, 78, 38, 88, 46, 96, 50, 100, 48, 98, 42, 92, 33, 83, 23, 73)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200) L = (1, 103)(2, 107)(3, 109)(4, 110)(5, 101)(6, 115)(7, 117)(8, 102)(9, 113)(10, 119)(11, 120)(12, 104)(13, 105)(14, 125)(15, 127)(16, 106)(17, 118)(18, 108)(19, 123)(20, 129)(21, 130)(22, 111)(23, 112)(24, 135)(25, 137)(26, 114)(27, 128)(28, 116)(29, 133)(30, 139)(31, 140)(32, 121)(33, 122)(34, 143)(35, 145)(36, 124)(37, 138)(38, 126)(39, 142)(40, 147)(41, 131)(42, 132)(43, 149)(44, 134)(45, 146)(46, 136)(47, 148)(48, 141)(49, 150)(50, 144)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E16.833 Graph:: simple bipartite v = 55 e = 100 f = 15 degree seq :: [ 2^50, 20^5 ] E16.835 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 17, 51}) Quotient :: edge Aut^+ = C51 (small group id <51, 1>) Aut = D102 (small group id <102, 3>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^17 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 26, 32, 38, 44, 47, 41, 35, 29, 23, 17, 11, 5)(2, 6, 12, 18, 24, 30, 36, 42, 48, 49, 43, 37, 31, 25, 19, 13, 7)(4, 9, 15, 21, 27, 33, 39, 45, 50, 51, 46, 40, 34, 28, 22, 16, 10)(52, 53, 55)(54, 57, 60)(56, 58, 61)(59, 63, 66)(62, 64, 67)(65, 69, 72)(68, 70, 73)(71, 75, 78)(74, 76, 79)(77, 81, 84)(80, 82, 85)(83, 87, 90)(86, 88, 91)(89, 93, 96)(92, 94, 97)(95, 99, 101)(98, 100, 102) L = (1, 52)(2, 53)(3, 54)(4, 55)(5, 56)(6, 57)(7, 58)(8, 59)(9, 60)(10, 61)(11, 62)(12, 63)(13, 64)(14, 65)(15, 66)(16, 67)(17, 68)(18, 69)(19, 70)(20, 71)(21, 72)(22, 73)(23, 74)(24, 75)(25, 76)(26, 77)(27, 78)(28, 79)(29, 80)(30, 81)(31, 82)(32, 83)(33, 84)(34, 85)(35, 86)(36, 87)(37, 88)(38, 89)(39, 90)(40, 91)(41, 92)(42, 93)(43, 94)(44, 95)(45, 96)(46, 97)(47, 98)(48, 99)(49, 100)(50, 101)(51, 102) local type(s) :: { ( 102^3 ), ( 102^17 ) } Outer automorphisms :: reflexible Dual of E16.839 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 51 f = 1 degree seq :: [ 3^17, 17^3 ] E16.836 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 17, 51}) Quotient :: edge Aut^+ = C51 (small group id <51, 1>) Aut = D102 (small group id <102, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^-3, T2^-15 * T1^2, T1^5 * T2^-1 * T1 * T2^-1 * T1 * T2^-7 * T1, T1^17, T2^51 ] Map:: non-degenerate R = (1, 3, 9, 19, 25, 31, 37, 43, 49, 46, 42, 35, 28, 24, 16, 6, 15, 12, 4, 10, 20, 26, 32, 38, 44, 50, 47, 40, 36, 29, 22, 18, 8, 2, 7, 17, 11, 21, 27, 33, 39, 45, 51, 48, 41, 34, 30, 23, 14, 13, 5)(52, 53, 57, 65, 73, 79, 85, 91, 97, 102, 95, 88, 84, 77, 70, 62, 55)(54, 58, 66, 64, 69, 75, 81, 87, 93, 99, 101, 94, 90, 83, 76, 72, 61)(56, 59, 67, 74, 80, 86, 92, 98, 100, 96, 89, 82, 78, 71, 60, 68, 63) L = (1, 52)(2, 53)(3, 54)(4, 55)(5, 56)(6, 57)(7, 58)(8, 59)(9, 60)(10, 61)(11, 62)(12, 63)(13, 64)(14, 65)(15, 66)(16, 67)(17, 68)(18, 69)(19, 70)(20, 71)(21, 72)(22, 73)(23, 74)(24, 75)(25, 76)(26, 77)(27, 78)(28, 79)(29, 80)(30, 81)(31, 82)(32, 83)(33, 84)(34, 85)(35, 86)(36, 87)(37, 88)(38, 89)(39, 90)(40, 91)(41, 92)(42, 93)(43, 94)(44, 95)(45, 96)(46, 97)(47, 98)(48, 99)(49, 100)(50, 101)(51, 102) local type(s) :: { ( 6^17 ), ( 6^51 ) } Outer automorphisms :: reflexible Dual of E16.840 Transitivity :: ET+ Graph:: bipartite v = 4 e = 51 f = 17 degree seq :: [ 17^3, 51 ] E16.837 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 17, 51}) Quotient :: edge Aut^+ = C51 (small group id <51, 1>) Aut = D102 (small group id <102, 3>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-17, (T1^-1 * T2^-1)^17 ] Map:: non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 9, 11)(6, 13, 14)(10, 15, 17)(12, 19, 20)(16, 21, 23)(18, 25, 26)(22, 27, 29)(24, 31, 32)(28, 33, 35)(30, 37, 38)(34, 39, 41)(36, 43, 44)(40, 45, 47)(42, 49, 50)(46, 48, 51)(52, 53, 57, 63, 69, 75, 81, 87, 93, 99, 96, 90, 84, 78, 72, 66, 60, 54, 58, 64, 70, 76, 82, 88, 94, 100, 102, 98, 92, 86, 80, 74, 68, 62, 56, 59, 65, 71, 77, 83, 89, 95, 101, 97, 91, 85, 79, 73, 67, 61, 55) L = (1, 52)(2, 53)(3, 54)(4, 55)(5, 56)(6, 57)(7, 58)(8, 59)(9, 60)(10, 61)(11, 62)(12, 63)(13, 64)(14, 65)(15, 66)(16, 67)(17, 68)(18, 69)(19, 70)(20, 71)(21, 72)(22, 73)(23, 74)(24, 75)(25, 76)(26, 77)(27, 78)(28, 79)(29, 80)(30, 81)(31, 82)(32, 83)(33, 84)(34, 85)(35, 86)(36, 87)(37, 88)(38, 89)(39, 90)(40, 91)(41, 92)(42, 93)(43, 94)(44, 95)(45, 96)(46, 97)(47, 98)(48, 99)(49, 100)(50, 101)(51, 102) local type(s) :: { ( 34^3 ), ( 34^51 ) } Outer automorphisms :: reflexible Dual of E16.838 Transitivity :: ET+ Graph:: bipartite v = 18 e = 51 f = 3 degree seq :: [ 3^17, 51 ] E16.838 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 17, 51}) Quotient :: loop Aut^+ = C51 (small group id <51, 1>) Aut = D102 (small group id <102, 3>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^17 ] Map:: non-degenerate R = (1, 52, 3, 54, 8, 59, 14, 65, 20, 71, 26, 77, 32, 83, 38, 89, 44, 95, 47, 98, 41, 92, 35, 86, 29, 80, 23, 74, 17, 68, 11, 62, 5, 56)(2, 53, 6, 57, 12, 63, 18, 69, 24, 75, 30, 81, 36, 87, 42, 93, 48, 99, 49, 100, 43, 94, 37, 88, 31, 82, 25, 76, 19, 70, 13, 64, 7, 58)(4, 55, 9, 60, 15, 66, 21, 72, 27, 78, 33, 84, 39, 90, 45, 96, 50, 101, 51, 102, 46, 97, 40, 91, 34, 85, 28, 79, 22, 73, 16, 67, 10, 61) L = (1, 53)(2, 55)(3, 57)(4, 52)(5, 58)(6, 60)(7, 61)(8, 63)(9, 54)(10, 56)(11, 64)(12, 66)(13, 67)(14, 69)(15, 59)(16, 62)(17, 70)(18, 72)(19, 73)(20, 75)(21, 65)(22, 68)(23, 76)(24, 78)(25, 79)(26, 81)(27, 71)(28, 74)(29, 82)(30, 84)(31, 85)(32, 87)(33, 77)(34, 80)(35, 88)(36, 90)(37, 91)(38, 93)(39, 83)(40, 86)(41, 94)(42, 96)(43, 97)(44, 99)(45, 89)(46, 92)(47, 100)(48, 101)(49, 102)(50, 95)(51, 98) local type(s) :: { ( 3, 51, 3, 51, 3, 51, 3, 51, 3, 51, 3, 51, 3, 51, 3, 51, 3, 51, 3, 51, 3, 51, 3, 51, 3, 51, 3, 51, 3, 51, 3, 51, 3, 51 ) } Outer automorphisms :: reflexible Dual of E16.837 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 51 f = 18 degree seq :: [ 34^3 ] E16.839 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 17, 51}) Quotient :: loop Aut^+ = C51 (small group id <51, 1>) Aut = D102 (small group id <102, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^-3, T2^-15 * T1^2, T1^5 * T2^-1 * T1 * T2^-1 * T1 * T2^-7 * T1, T1^17, T2^51 ] Map:: non-degenerate R = (1, 52, 3, 54, 9, 60, 19, 70, 25, 76, 31, 82, 37, 88, 43, 94, 49, 100, 46, 97, 42, 93, 35, 86, 28, 79, 24, 75, 16, 67, 6, 57, 15, 66, 12, 63, 4, 55, 10, 61, 20, 71, 26, 77, 32, 83, 38, 89, 44, 95, 50, 101, 47, 98, 40, 91, 36, 87, 29, 80, 22, 73, 18, 69, 8, 59, 2, 53, 7, 58, 17, 68, 11, 62, 21, 72, 27, 78, 33, 84, 39, 90, 45, 96, 51, 102, 48, 99, 41, 92, 34, 85, 30, 81, 23, 74, 14, 65, 13, 64, 5, 56) L = (1, 53)(2, 57)(3, 58)(4, 52)(5, 59)(6, 65)(7, 66)(8, 67)(9, 68)(10, 54)(11, 55)(12, 56)(13, 69)(14, 73)(15, 64)(16, 74)(17, 63)(18, 75)(19, 62)(20, 60)(21, 61)(22, 79)(23, 80)(24, 81)(25, 72)(26, 70)(27, 71)(28, 85)(29, 86)(30, 87)(31, 78)(32, 76)(33, 77)(34, 91)(35, 92)(36, 93)(37, 84)(38, 82)(39, 83)(40, 97)(41, 98)(42, 99)(43, 90)(44, 88)(45, 89)(46, 102)(47, 100)(48, 101)(49, 96)(50, 94)(51, 95) local type(s) :: { ( 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17, 3, 17 ) } Outer automorphisms :: reflexible Dual of E16.835 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 51 f = 20 degree seq :: [ 102 ] E16.840 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 17, 51}) Quotient :: loop Aut^+ = C51 (small group id <51, 1>) Aut = D102 (small group id <102, 3>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-17, (T1^-1 * T2^-1)^17 ] Map:: non-degenerate R = (1, 52, 3, 54, 5, 56)(2, 53, 7, 58, 8, 59)(4, 55, 9, 60, 11, 62)(6, 57, 13, 64, 14, 65)(10, 61, 15, 66, 17, 68)(12, 63, 19, 70, 20, 71)(16, 67, 21, 72, 23, 74)(18, 69, 25, 76, 26, 77)(22, 73, 27, 78, 29, 80)(24, 75, 31, 82, 32, 83)(28, 79, 33, 84, 35, 86)(30, 81, 37, 88, 38, 89)(34, 85, 39, 90, 41, 92)(36, 87, 43, 94, 44, 95)(40, 91, 45, 96, 47, 98)(42, 93, 49, 100, 50, 101)(46, 97, 48, 99, 51, 102) L = (1, 53)(2, 57)(3, 58)(4, 52)(5, 59)(6, 63)(7, 64)(8, 65)(9, 54)(10, 55)(11, 56)(12, 69)(13, 70)(14, 71)(15, 60)(16, 61)(17, 62)(18, 75)(19, 76)(20, 77)(21, 66)(22, 67)(23, 68)(24, 81)(25, 82)(26, 83)(27, 72)(28, 73)(29, 74)(30, 87)(31, 88)(32, 89)(33, 78)(34, 79)(35, 80)(36, 93)(37, 94)(38, 95)(39, 84)(40, 85)(41, 86)(42, 99)(43, 100)(44, 101)(45, 90)(46, 91)(47, 92)(48, 96)(49, 102)(50, 97)(51, 98) local type(s) :: { ( 17, 51, 17, 51, 17, 51 ) } Outer automorphisms :: reflexible Dual of E16.836 Transitivity :: ET+ VT+ AT Graph:: v = 17 e = 51 f = 4 degree seq :: [ 6^17 ] E16.841 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 17, 51}) Quotient :: dipole Aut^+ = C51 (small group id <51, 1>) Aut = D102 (small group id <102, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^17, Y3^51 ] Map:: R = (1, 52, 2, 53, 4, 55)(3, 54, 6, 57, 9, 60)(5, 56, 7, 58, 10, 61)(8, 59, 12, 63, 15, 66)(11, 62, 13, 64, 16, 67)(14, 65, 18, 69, 21, 72)(17, 68, 19, 70, 22, 73)(20, 71, 24, 75, 27, 78)(23, 74, 25, 76, 28, 79)(26, 77, 30, 81, 33, 84)(29, 80, 31, 82, 34, 85)(32, 83, 36, 87, 39, 90)(35, 86, 37, 88, 40, 91)(38, 89, 42, 93, 45, 96)(41, 92, 43, 94, 46, 97)(44, 95, 48, 99, 50, 101)(47, 98, 49, 100, 51, 102)(103, 154, 105, 156, 110, 161, 116, 167, 122, 173, 128, 179, 134, 185, 140, 191, 146, 197, 149, 200, 143, 194, 137, 188, 131, 182, 125, 176, 119, 170, 113, 164, 107, 158)(104, 155, 108, 159, 114, 165, 120, 171, 126, 177, 132, 183, 138, 189, 144, 195, 150, 201, 151, 202, 145, 196, 139, 190, 133, 184, 127, 178, 121, 172, 115, 166, 109, 160)(106, 157, 111, 162, 117, 168, 123, 174, 129, 180, 135, 186, 141, 192, 147, 198, 152, 203, 153, 204, 148, 199, 142, 193, 136, 187, 130, 181, 124, 175, 118, 169, 112, 163) L = (1, 106)(2, 103)(3, 111)(4, 104)(5, 112)(6, 105)(7, 107)(8, 117)(9, 108)(10, 109)(11, 118)(12, 110)(13, 113)(14, 123)(15, 114)(16, 115)(17, 124)(18, 116)(19, 119)(20, 129)(21, 120)(22, 121)(23, 130)(24, 122)(25, 125)(26, 135)(27, 126)(28, 127)(29, 136)(30, 128)(31, 131)(32, 141)(33, 132)(34, 133)(35, 142)(36, 134)(37, 137)(38, 147)(39, 138)(40, 139)(41, 148)(42, 140)(43, 143)(44, 152)(45, 144)(46, 145)(47, 153)(48, 146)(49, 149)(50, 150)(51, 151)(52, 154)(53, 155)(54, 156)(55, 157)(56, 158)(57, 159)(58, 160)(59, 161)(60, 162)(61, 163)(62, 164)(63, 165)(64, 166)(65, 167)(66, 168)(67, 169)(68, 170)(69, 171)(70, 172)(71, 173)(72, 174)(73, 175)(74, 176)(75, 177)(76, 178)(77, 179)(78, 180)(79, 181)(80, 182)(81, 183)(82, 184)(83, 185)(84, 186)(85, 187)(86, 188)(87, 189)(88, 190)(89, 191)(90, 192)(91, 193)(92, 194)(93, 195)(94, 196)(95, 197)(96, 198)(97, 199)(98, 200)(99, 201)(100, 202)(101, 203)(102, 204) local type(s) :: { ( 2, 102, 2, 102, 2, 102 ), ( 2, 102, 2, 102, 2, 102, 2, 102, 2, 102, 2, 102, 2, 102, 2, 102, 2, 102, 2, 102, 2, 102, 2, 102, 2, 102, 2, 102, 2, 102, 2, 102, 2, 102 ) } Outer automorphisms :: reflexible Dual of E16.844 Graph:: bipartite v = 20 e = 102 f = 52 degree seq :: [ 6^17, 34^3 ] E16.842 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 17, 51}) Quotient :: dipole Aut^+ = C51 (small group id <51, 1>) Aut = D102 (small group id <102, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1 * Y1^-1)^3, Y2^6 * Y1^6, Y2^12 * Y1^-5, Y1^6 * Y2^-1 * Y1 * Y2^-8 * Y1, Y1^17 ] Map:: R = (1, 52, 2, 53, 6, 57, 14, 65, 22, 73, 28, 79, 34, 85, 40, 91, 46, 97, 51, 102, 44, 95, 37, 88, 33, 84, 26, 77, 19, 70, 11, 62, 4, 55)(3, 54, 7, 58, 15, 66, 13, 64, 18, 69, 24, 75, 30, 81, 36, 87, 42, 93, 48, 99, 50, 101, 43, 94, 39, 90, 32, 83, 25, 76, 21, 72, 10, 61)(5, 56, 8, 59, 16, 67, 23, 74, 29, 80, 35, 86, 41, 92, 47, 98, 49, 100, 45, 96, 38, 89, 31, 82, 27, 78, 20, 71, 9, 60, 17, 68, 12, 63)(103, 154, 105, 156, 111, 162, 121, 172, 127, 178, 133, 184, 139, 190, 145, 196, 151, 202, 148, 199, 144, 195, 137, 188, 130, 181, 126, 177, 118, 169, 108, 159, 117, 168, 114, 165, 106, 157, 112, 163, 122, 173, 128, 179, 134, 185, 140, 191, 146, 197, 152, 203, 149, 200, 142, 193, 138, 189, 131, 182, 124, 175, 120, 171, 110, 161, 104, 155, 109, 160, 119, 170, 113, 164, 123, 174, 129, 180, 135, 186, 141, 192, 147, 198, 153, 204, 150, 201, 143, 194, 136, 187, 132, 183, 125, 176, 116, 167, 115, 166, 107, 158) L = (1, 105)(2, 109)(3, 111)(4, 112)(5, 103)(6, 117)(7, 119)(8, 104)(9, 121)(10, 122)(11, 123)(12, 106)(13, 107)(14, 115)(15, 114)(16, 108)(17, 113)(18, 110)(19, 127)(20, 128)(21, 129)(22, 120)(23, 116)(24, 118)(25, 133)(26, 134)(27, 135)(28, 126)(29, 124)(30, 125)(31, 139)(32, 140)(33, 141)(34, 132)(35, 130)(36, 131)(37, 145)(38, 146)(39, 147)(40, 138)(41, 136)(42, 137)(43, 151)(44, 152)(45, 153)(46, 144)(47, 142)(48, 143)(49, 148)(50, 149)(51, 150)(52, 154)(53, 155)(54, 156)(55, 157)(56, 158)(57, 159)(58, 160)(59, 161)(60, 162)(61, 163)(62, 164)(63, 165)(64, 166)(65, 167)(66, 168)(67, 169)(68, 170)(69, 171)(70, 172)(71, 173)(72, 174)(73, 175)(74, 176)(75, 177)(76, 178)(77, 179)(78, 180)(79, 181)(80, 182)(81, 183)(82, 184)(83, 185)(84, 186)(85, 187)(86, 188)(87, 189)(88, 190)(89, 191)(90, 192)(91, 193)(92, 194)(93, 195)(94, 196)(95, 197)(96, 198)(97, 199)(98, 200)(99, 201)(100, 202)(101, 203)(102, 204) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E16.843 Graph:: bipartite v = 4 e = 102 f = 68 degree seq :: [ 34^3, 102 ] E16.843 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 17, 51}) Quotient :: dipole Aut^+ = C51 (small group id <51, 1>) Aut = D102 (small group id <102, 3>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3, Y2^-1), Y3^-17 * Y2^-1, (Y2^-1 * Y3)^17, (Y3^-1 * Y1^-1)^51 ] Map:: R = (1, 52)(2, 53)(3, 54)(4, 55)(5, 56)(6, 57)(7, 58)(8, 59)(9, 60)(10, 61)(11, 62)(12, 63)(13, 64)(14, 65)(15, 66)(16, 67)(17, 68)(18, 69)(19, 70)(20, 71)(21, 72)(22, 73)(23, 74)(24, 75)(25, 76)(26, 77)(27, 78)(28, 79)(29, 80)(30, 81)(31, 82)(32, 83)(33, 84)(34, 85)(35, 86)(36, 87)(37, 88)(38, 89)(39, 90)(40, 91)(41, 92)(42, 93)(43, 94)(44, 95)(45, 96)(46, 97)(47, 98)(48, 99)(49, 100)(50, 101)(51, 102)(103, 154, 104, 155, 106, 157)(105, 156, 108, 159, 111, 162)(107, 158, 109, 160, 112, 163)(110, 161, 114, 165, 117, 168)(113, 164, 115, 166, 118, 169)(116, 167, 120, 171, 123, 174)(119, 170, 121, 172, 124, 175)(122, 173, 126, 177, 129, 180)(125, 176, 127, 178, 130, 181)(128, 179, 132, 183, 135, 186)(131, 182, 133, 184, 136, 187)(134, 185, 138, 189, 141, 192)(137, 188, 139, 190, 142, 193)(140, 191, 144, 195, 147, 198)(143, 194, 145, 196, 148, 199)(146, 197, 150, 201, 153, 204)(149, 200, 151, 202, 152, 203) L = (1, 105)(2, 108)(3, 110)(4, 111)(5, 103)(6, 114)(7, 104)(8, 116)(9, 117)(10, 106)(11, 107)(12, 120)(13, 109)(14, 122)(15, 123)(16, 112)(17, 113)(18, 126)(19, 115)(20, 128)(21, 129)(22, 118)(23, 119)(24, 132)(25, 121)(26, 134)(27, 135)(28, 124)(29, 125)(30, 138)(31, 127)(32, 140)(33, 141)(34, 130)(35, 131)(36, 144)(37, 133)(38, 146)(39, 147)(40, 136)(41, 137)(42, 150)(43, 139)(44, 152)(45, 153)(46, 142)(47, 143)(48, 149)(49, 145)(50, 148)(51, 151)(52, 154)(53, 155)(54, 156)(55, 157)(56, 158)(57, 159)(58, 160)(59, 161)(60, 162)(61, 163)(62, 164)(63, 165)(64, 166)(65, 167)(66, 168)(67, 169)(68, 170)(69, 171)(70, 172)(71, 173)(72, 174)(73, 175)(74, 176)(75, 177)(76, 178)(77, 179)(78, 180)(79, 181)(80, 182)(81, 183)(82, 184)(83, 185)(84, 186)(85, 187)(86, 188)(87, 189)(88, 190)(89, 191)(90, 192)(91, 193)(92, 194)(93, 195)(94, 196)(95, 197)(96, 198)(97, 199)(98, 200)(99, 201)(100, 202)(101, 203)(102, 204) local type(s) :: { ( 34, 102 ), ( 34, 102, 34, 102, 34, 102 ) } Outer automorphisms :: reflexible Dual of E16.842 Graph:: simple bipartite v = 68 e = 102 f = 4 degree seq :: [ 2^51, 6^17 ] E16.844 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 17, 51}) Quotient :: dipole Aut^+ = C51 (small group id <51, 1>) Aut = D102 (small group id <102, 3>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^-17, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 52, 2, 53, 6, 57, 12, 63, 18, 69, 24, 75, 30, 81, 36, 87, 42, 93, 48, 99, 45, 96, 39, 90, 33, 84, 27, 78, 21, 72, 15, 66, 9, 60, 3, 54, 7, 58, 13, 64, 19, 70, 25, 76, 31, 82, 37, 88, 43, 94, 49, 100, 51, 102, 47, 98, 41, 92, 35, 86, 29, 80, 23, 74, 17, 68, 11, 62, 5, 56, 8, 59, 14, 65, 20, 71, 26, 77, 32, 83, 38, 89, 44, 95, 50, 101, 46, 97, 40, 91, 34, 85, 28, 79, 22, 73, 16, 67, 10, 61, 4, 55)(103, 154)(104, 155)(105, 156)(106, 157)(107, 158)(108, 159)(109, 160)(110, 161)(111, 162)(112, 163)(113, 164)(114, 165)(115, 166)(116, 167)(117, 168)(118, 169)(119, 170)(120, 171)(121, 172)(122, 173)(123, 174)(124, 175)(125, 176)(126, 177)(127, 178)(128, 179)(129, 180)(130, 181)(131, 182)(132, 183)(133, 184)(134, 185)(135, 186)(136, 187)(137, 188)(138, 189)(139, 190)(140, 191)(141, 192)(142, 193)(143, 194)(144, 195)(145, 196)(146, 197)(147, 198)(148, 199)(149, 200)(150, 201)(151, 202)(152, 203)(153, 204) L = (1, 105)(2, 109)(3, 107)(4, 111)(5, 103)(6, 115)(7, 110)(8, 104)(9, 113)(10, 117)(11, 106)(12, 121)(13, 116)(14, 108)(15, 119)(16, 123)(17, 112)(18, 127)(19, 122)(20, 114)(21, 125)(22, 129)(23, 118)(24, 133)(25, 128)(26, 120)(27, 131)(28, 135)(29, 124)(30, 139)(31, 134)(32, 126)(33, 137)(34, 141)(35, 130)(36, 145)(37, 140)(38, 132)(39, 143)(40, 147)(41, 136)(42, 151)(43, 146)(44, 138)(45, 149)(46, 150)(47, 142)(48, 153)(49, 152)(50, 144)(51, 148)(52, 154)(53, 155)(54, 156)(55, 157)(56, 158)(57, 159)(58, 160)(59, 161)(60, 162)(61, 163)(62, 164)(63, 165)(64, 166)(65, 167)(66, 168)(67, 169)(68, 170)(69, 171)(70, 172)(71, 173)(72, 174)(73, 175)(74, 176)(75, 177)(76, 178)(77, 179)(78, 180)(79, 181)(80, 182)(81, 183)(82, 184)(83, 185)(84, 186)(85, 187)(86, 188)(87, 189)(88, 190)(89, 191)(90, 192)(91, 193)(92, 194)(93, 195)(94, 196)(95, 197)(96, 198)(97, 199)(98, 200)(99, 201)(100, 202)(101, 203)(102, 204) local type(s) :: { ( 6, 34 ), ( 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34, 6, 34 ) } Outer automorphisms :: reflexible Dual of E16.841 Graph:: bipartite v = 52 e = 102 f = 20 degree seq :: [ 2^51, 102 ] E16.845 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 17, 51}) Quotient :: dipole Aut^+ = C51 (small group id <51, 1>) Aut = D102 (small group id <102, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^17 * 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 ] Map:: R = (1, 52, 2, 53, 4, 55)(3, 54, 6, 57, 9, 60)(5, 56, 7, 58, 10, 61)(8, 59, 12, 63, 15, 66)(11, 62, 13, 64, 16, 67)(14, 65, 18, 69, 21, 72)(17, 68, 19, 70, 22, 73)(20, 71, 24, 75, 27, 78)(23, 74, 25, 76, 28, 79)(26, 77, 30, 81, 33, 84)(29, 80, 31, 82, 34, 85)(32, 83, 36, 87, 39, 90)(35, 86, 37, 88, 40, 91)(38, 89, 42, 93, 45, 96)(41, 92, 43, 94, 46, 97)(44, 95, 48, 99, 50, 101)(47, 98, 49, 100, 51, 102)(103, 154, 105, 156, 110, 161, 116, 167, 122, 173, 128, 179, 134, 185, 140, 191, 146, 197, 151, 202, 145, 196, 139, 190, 133, 184, 127, 178, 121, 172, 115, 166, 109, 160, 104, 155, 108, 159, 114, 165, 120, 171, 126, 177, 132, 183, 138, 189, 144, 195, 150, 201, 153, 204, 148, 199, 142, 193, 136, 187, 130, 181, 124, 175, 118, 169, 112, 163, 106, 157, 111, 162, 117, 168, 123, 174, 129, 180, 135, 186, 141, 192, 147, 198, 152, 203, 149, 200, 143, 194, 137, 188, 131, 182, 125, 176, 119, 170, 113, 164, 107, 158) L = (1, 106)(2, 103)(3, 111)(4, 104)(5, 112)(6, 105)(7, 107)(8, 117)(9, 108)(10, 109)(11, 118)(12, 110)(13, 113)(14, 123)(15, 114)(16, 115)(17, 124)(18, 116)(19, 119)(20, 129)(21, 120)(22, 121)(23, 130)(24, 122)(25, 125)(26, 135)(27, 126)(28, 127)(29, 136)(30, 128)(31, 131)(32, 141)(33, 132)(34, 133)(35, 142)(36, 134)(37, 137)(38, 147)(39, 138)(40, 139)(41, 148)(42, 140)(43, 143)(44, 152)(45, 144)(46, 145)(47, 153)(48, 146)(49, 149)(50, 150)(51, 151)(52, 154)(53, 155)(54, 156)(55, 157)(56, 158)(57, 159)(58, 160)(59, 161)(60, 162)(61, 163)(62, 164)(63, 165)(64, 166)(65, 167)(66, 168)(67, 169)(68, 170)(69, 171)(70, 172)(71, 173)(72, 174)(73, 175)(74, 176)(75, 177)(76, 178)(77, 179)(78, 180)(79, 181)(80, 182)(81, 183)(82, 184)(83, 185)(84, 186)(85, 187)(86, 188)(87, 189)(88, 190)(89, 191)(90, 192)(91, 193)(92, 194)(93, 195)(94, 196)(95, 197)(96, 198)(97, 199)(98, 200)(99, 201)(100, 202)(101, 203)(102, 204) local type(s) :: { ( 2, 34, 2, 34, 2, 34 ), ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.846 Graph:: bipartite v = 18 e = 102 f = 54 degree seq :: [ 6^17, 102 ] E16.846 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 17, 51}) Quotient :: dipole Aut^+ = C51 (small group id <51, 1>) Aut = D102 (small group id <102, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^-3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y3^-15 * Y1^2, Y1^7 * Y3^-1 * Y1 * Y3^-8, Y1^17, (Y3 * Y2^-1)^51 ] Map:: R = (1, 52, 2, 53, 6, 57, 14, 65, 22, 73, 28, 79, 34, 85, 40, 91, 46, 97, 51, 102, 44, 95, 37, 88, 33, 84, 26, 77, 19, 70, 11, 62, 4, 55)(3, 54, 7, 58, 15, 66, 13, 64, 18, 69, 24, 75, 30, 81, 36, 87, 42, 93, 48, 99, 50, 101, 43, 94, 39, 90, 32, 83, 25, 76, 21, 72, 10, 61)(5, 56, 8, 59, 16, 67, 23, 74, 29, 80, 35, 86, 41, 92, 47, 98, 49, 100, 45, 96, 38, 89, 31, 82, 27, 78, 20, 71, 9, 60, 17, 68, 12, 63)(103, 154)(104, 155)(105, 156)(106, 157)(107, 158)(108, 159)(109, 160)(110, 161)(111, 162)(112, 163)(113, 164)(114, 165)(115, 166)(116, 167)(117, 168)(118, 169)(119, 170)(120, 171)(121, 172)(122, 173)(123, 174)(124, 175)(125, 176)(126, 177)(127, 178)(128, 179)(129, 180)(130, 181)(131, 182)(132, 183)(133, 184)(134, 185)(135, 186)(136, 187)(137, 188)(138, 189)(139, 190)(140, 191)(141, 192)(142, 193)(143, 194)(144, 195)(145, 196)(146, 197)(147, 198)(148, 199)(149, 200)(150, 201)(151, 202)(152, 203)(153, 204) L = (1, 105)(2, 109)(3, 111)(4, 112)(5, 103)(6, 117)(7, 119)(8, 104)(9, 121)(10, 122)(11, 123)(12, 106)(13, 107)(14, 115)(15, 114)(16, 108)(17, 113)(18, 110)(19, 127)(20, 128)(21, 129)(22, 120)(23, 116)(24, 118)(25, 133)(26, 134)(27, 135)(28, 126)(29, 124)(30, 125)(31, 139)(32, 140)(33, 141)(34, 132)(35, 130)(36, 131)(37, 145)(38, 146)(39, 147)(40, 138)(41, 136)(42, 137)(43, 151)(44, 152)(45, 153)(46, 144)(47, 142)(48, 143)(49, 148)(50, 149)(51, 150)(52, 154)(53, 155)(54, 156)(55, 157)(56, 158)(57, 159)(58, 160)(59, 161)(60, 162)(61, 163)(62, 164)(63, 165)(64, 166)(65, 167)(66, 168)(67, 169)(68, 170)(69, 171)(70, 172)(71, 173)(72, 174)(73, 175)(74, 176)(75, 177)(76, 178)(77, 179)(78, 180)(79, 181)(80, 182)(81, 183)(82, 184)(83, 185)(84, 186)(85, 187)(86, 188)(87, 189)(88, 190)(89, 191)(90, 192)(91, 193)(92, 194)(93, 195)(94, 196)(95, 197)(96, 198)(97, 199)(98, 200)(99, 201)(100, 202)(101, 203)(102, 204) local type(s) :: { ( 6, 102 ), ( 6, 102, 6, 102, 6, 102, 6, 102, 6, 102, 6, 102, 6, 102, 6, 102, 6, 102, 6, 102, 6, 102, 6, 102, 6, 102, 6, 102, 6, 102, 6, 102, 6, 102 ) } Outer automorphisms :: reflexible Dual of E16.845 Graph:: simple bipartite v = 54 e = 102 f = 18 degree seq :: [ 2^51, 34^3 ] E16.847 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 9}) Quotient :: halfedge^2 Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y2 * Y1^2 * Y3 * Y1^-2, Y3 * Y2 * Y1 * Y2 * Y3 * Y1^-1, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-2, Y1^2 * Y2 * Y1^-1 * Y3 * Y1^2, Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 56, 2, 60, 6, 72, 18, 89, 35, 86, 32, 98, 44, 71, 17, 59, 5, 55)(3, 63, 9, 74, 20, 100, 46, 96, 42, 70, 16, 95, 41, 87, 33, 65, 11, 57)(4, 66, 12, 88, 34, 77, 23, 61, 7, 75, 21, 99, 45, 93, 39, 68, 14, 58)(8, 78, 24, 83, 29, 97, 43, 73, 19, 90, 36, 94, 40, 69, 15, 80, 26, 62)(10, 76, 22, 92, 38, 104, 50, 81, 27, 102, 48, 108, 54, 106, 52, 84, 30, 64)(13, 79, 25, 101, 47, 105, 51, 107, 53, 85, 31, 103, 49, 82, 28, 91, 37, 67) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 19)(8, 25)(9, 27)(10, 29)(11, 31)(12, 35)(14, 38)(16, 37)(17, 39)(18, 41)(20, 47)(21, 48)(22, 42)(23, 49)(24, 32)(26, 50)(28, 43)(30, 34)(33, 52)(36, 54)(40, 53)(44, 46)(45, 51)(55, 58)(56, 62)(57, 64)(59, 70)(60, 74)(61, 76)(63, 82)(65, 86)(66, 81)(67, 90)(68, 85)(69, 84)(71, 97)(72, 99)(73, 92)(75, 91)(77, 98)(78, 102)(79, 87)(80, 103)(83, 105)(88, 101)(89, 94)(93, 106)(95, 104)(96, 107)(100, 108) local type(s) :: { ( 6^18 ) } Outer automorphisms :: reflexible Dual of E16.848 Transitivity :: VT+ AT Graph:: bipartite v = 6 e = 54 f = 18 degree seq :: [ 18^6 ] E16.848 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 9}) Quotient :: halfedge^2 Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^3, R * Y3 * R * Y2, (R * Y1)^2, Y3 * Y2 * Y1 * Y2 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y2, Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 56, 2, 59, 5, 55)(3, 62, 8, 64, 10, 57)(4, 65, 11, 67, 13, 58)(6, 70, 16, 72, 18, 60)(7, 73, 19, 75, 21, 61)(9, 71, 17, 79, 25, 63)(12, 74, 20, 84, 30, 66)(14, 86, 32, 87, 33, 68)(15, 88, 34, 89, 35, 69)(22, 90, 36, 98, 44, 76)(23, 91, 37, 100, 46, 77)(24, 99, 45, 102, 48, 78)(26, 93, 39, 104, 50, 80)(27, 94, 40, 105, 51, 81)(28, 95, 41, 101, 47, 82)(29, 92, 38, 106, 52, 83)(31, 97, 43, 107, 53, 85)(42, 103, 49, 108, 54, 96) L = (1, 3)(2, 6)(4, 12)(5, 14)(7, 20)(8, 22)(9, 24)(10, 26)(11, 28)(13, 31)(15, 30)(16, 36)(17, 38)(18, 39)(19, 41)(21, 43)(23, 45)(25, 49)(27, 48)(29, 40)(32, 44)(33, 50)(34, 47)(35, 53)(37, 52)(42, 51)(46, 54)(55, 58)(56, 61)(57, 63)(59, 69)(60, 71)(62, 77)(64, 81)(65, 76)(66, 83)(67, 80)(68, 79)(70, 91)(72, 94)(73, 90)(74, 96)(75, 93)(78, 101)(82, 92)(84, 102)(85, 106)(86, 100)(87, 105)(88, 98)(89, 104)(95, 103)(97, 108)(99, 107) local type(s) :: { ( 18^6 ) } Outer automorphisms :: reflexible Dual of E16.847 Transitivity :: VT+ AT Graph:: simple bipartite v = 18 e = 54 f = 6 degree seq :: [ 6^18 ] E16.849 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 9}) Quotient :: edge^2 Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, Y1 * Y3 * Y1 * Y2 * Y3^-1 * Y2, Y1 * Y2 * Y3^-1 * Y2 * Y1 * Y3, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y1, Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 ] Map:: polytopal R = (1, 55, 4, 58, 5, 59)(2, 56, 7, 61, 8, 62)(3, 57, 10, 64, 11, 65)(6, 60, 17, 71, 18, 72)(9, 63, 24, 78, 25, 79)(12, 66, 28, 82, 29, 83)(13, 67, 30, 84, 31, 85)(14, 68, 32, 86, 33, 87)(15, 69, 34, 88, 35, 89)(16, 70, 37, 91, 38, 92)(19, 73, 41, 95, 42, 96)(20, 74, 43, 97, 44, 98)(21, 75, 45, 99, 46, 100)(22, 76, 47, 101, 48, 102)(23, 77, 39, 93, 49, 103)(26, 80, 51, 105, 36, 90)(27, 81, 52, 106, 53, 107)(40, 94, 54, 108, 50, 104)(109, 110)(111, 117)(112, 120)(113, 122)(114, 124)(115, 127)(116, 129)(118, 134)(119, 135)(121, 132)(123, 133)(125, 147)(126, 148)(128, 145)(130, 146)(131, 155)(136, 149)(137, 153)(138, 159)(139, 160)(140, 150)(141, 154)(142, 144)(143, 161)(151, 157)(152, 162)(156, 158)(163, 165)(164, 168)(166, 175)(167, 177)(169, 182)(170, 184)(171, 185)(172, 181)(173, 183)(174, 179)(176, 180)(178, 198)(186, 212)(187, 200)(188, 201)(189, 211)(190, 205)(191, 209)(192, 203)(193, 207)(194, 206)(195, 210)(196, 204)(197, 208)(199, 215)(202, 213)(214, 216) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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) :: { ( 36, 36 ), ( 36^6 ) } Outer automorphisms :: reflexible Dual of E16.852 Graph:: simple bipartite v = 72 e = 108 f = 6 degree seq :: [ 2^54, 6^18 ] E16.850 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 9}) Quotient :: edge^2 Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1 * Y2 * Y3^-1 * Y2 * Y1, Y3^2 * Y1 * Y3^-2 * Y2, Y3^2 * Y2 * Y1 * Y2 * Y3 * Y1, Y1 * Y3 * Y2 * Y3^-4 ] Map:: polytopal R = (1, 55, 4, 58, 14, 68, 39, 93, 22, 76, 32, 86, 44, 98, 17, 71, 5, 59)(2, 56, 7, 61, 23, 77, 37, 91, 13, 67, 36, 90, 52, 106, 26, 80, 8, 62)(3, 57, 10, 64, 31, 85, 54, 108, 41, 95, 15, 69, 40, 94, 33, 87, 11, 65)(6, 60, 19, 73, 46, 100, 53, 107, 50, 104, 24, 78, 49, 103, 30, 84, 20, 74)(9, 63, 28, 82, 25, 79, 48, 102, 21, 75, 47, 101, 45, 99, 51, 105, 29, 83)(12, 66, 34, 88, 27, 81, 43, 97, 38, 92, 18, 72, 42, 96, 16, 70, 35, 89)(109, 110)(111, 117)(112, 120)(113, 123)(114, 126)(115, 129)(116, 132)(118, 138)(119, 140)(121, 136)(122, 139)(124, 137)(125, 151)(127, 141)(128, 144)(130, 150)(131, 154)(133, 146)(134, 159)(135, 161)(142, 155)(143, 157)(145, 152)(147, 160)(148, 156)(149, 158)(153, 162)(163, 165)(164, 168)(166, 175)(167, 178)(169, 184)(170, 187)(171, 189)(172, 183)(173, 186)(174, 181)(176, 200)(177, 182)(179, 188)(180, 207)(185, 191)(190, 203)(192, 205)(193, 208)(194, 196)(195, 213)(197, 210)(198, 209)(199, 211)(201, 202)(204, 212)(206, 216)(214, 215) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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, 12 ), ( 12^18 ) } Outer automorphisms :: reflexible Dual of E16.851 Graph:: simple bipartite v = 60 e = 108 f = 18 degree seq :: [ 2^54, 18^6 ] E16.851 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 9}) Quotient :: loop^2 Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, Y1 * Y3 * Y1 * Y2 * Y3^-1 * Y2, Y1 * Y2 * Y3^-1 * Y2 * Y1 * Y3, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y1, Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 ] Map:: R = (1, 55, 109, 163, 4, 58, 112, 166, 5, 59, 113, 167)(2, 56, 110, 164, 7, 61, 115, 169, 8, 62, 116, 170)(3, 57, 111, 165, 10, 64, 118, 172, 11, 65, 119, 173)(6, 60, 114, 168, 17, 71, 125, 179, 18, 72, 126, 180)(9, 63, 117, 171, 24, 78, 132, 186, 25, 79, 133, 187)(12, 66, 120, 174, 28, 82, 136, 190, 29, 83, 137, 191)(13, 67, 121, 175, 30, 84, 138, 192, 31, 85, 139, 193)(14, 68, 122, 176, 32, 86, 140, 194, 33, 87, 141, 195)(15, 69, 123, 177, 34, 88, 142, 196, 35, 89, 143, 197)(16, 70, 124, 178, 37, 91, 145, 199, 38, 92, 146, 200)(19, 73, 127, 181, 41, 95, 149, 203, 42, 96, 150, 204)(20, 74, 128, 182, 43, 97, 151, 205, 44, 98, 152, 206)(21, 75, 129, 183, 45, 99, 153, 207, 46, 100, 154, 208)(22, 76, 130, 184, 47, 101, 155, 209, 48, 102, 156, 210)(23, 77, 131, 185, 39, 93, 147, 201, 49, 103, 157, 211)(26, 80, 134, 188, 51, 105, 159, 213, 36, 90, 144, 198)(27, 81, 135, 189, 52, 106, 160, 214, 53, 107, 161, 215)(40, 94, 148, 202, 54, 108, 162, 216, 50, 104, 158, 212) L = (1, 56)(2, 55)(3, 63)(4, 66)(5, 68)(6, 70)(7, 73)(8, 75)(9, 57)(10, 80)(11, 81)(12, 58)(13, 78)(14, 59)(15, 79)(16, 60)(17, 93)(18, 94)(19, 61)(20, 91)(21, 62)(22, 92)(23, 101)(24, 67)(25, 69)(26, 64)(27, 65)(28, 95)(29, 99)(30, 105)(31, 106)(32, 96)(33, 100)(34, 90)(35, 107)(36, 88)(37, 74)(38, 76)(39, 71)(40, 72)(41, 82)(42, 86)(43, 103)(44, 108)(45, 83)(46, 87)(47, 77)(48, 104)(49, 97)(50, 102)(51, 84)(52, 85)(53, 89)(54, 98)(109, 165)(110, 168)(111, 163)(112, 175)(113, 177)(114, 164)(115, 182)(116, 184)(117, 185)(118, 181)(119, 183)(120, 179)(121, 166)(122, 180)(123, 167)(124, 198)(125, 174)(126, 176)(127, 172)(128, 169)(129, 173)(130, 170)(131, 171)(132, 212)(133, 200)(134, 201)(135, 211)(136, 205)(137, 209)(138, 203)(139, 207)(140, 206)(141, 210)(142, 204)(143, 208)(144, 178)(145, 215)(146, 187)(147, 188)(148, 213)(149, 192)(150, 196)(151, 190)(152, 194)(153, 193)(154, 197)(155, 191)(156, 195)(157, 189)(158, 186)(159, 202)(160, 216)(161, 199)(162, 214) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E16.850 Transitivity :: VT+ Graph:: bipartite v = 18 e = 108 f = 60 degree seq :: [ 12^18 ] E16.852 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 9}) Quotient :: loop^2 Aut^+ = C3 x D18 (small group id <54, 3>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1 * Y2 * Y3^-1 * Y2 * Y1, Y3^2 * Y1 * Y3^-2 * Y2, Y3^2 * Y2 * Y1 * Y2 * Y3 * Y1, Y1 * Y3 * Y2 * Y3^-4 ] Map:: R = (1, 55, 109, 163, 4, 58, 112, 166, 14, 68, 122, 176, 39, 93, 147, 201, 22, 76, 130, 184, 32, 86, 140, 194, 44, 98, 152, 206, 17, 71, 125, 179, 5, 59, 113, 167)(2, 56, 110, 164, 7, 61, 115, 169, 23, 77, 131, 185, 37, 91, 145, 199, 13, 67, 121, 175, 36, 90, 144, 198, 52, 106, 160, 214, 26, 80, 134, 188, 8, 62, 116, 170)(3, 57, 111, 165, 10, 64, 118, 172, 31, 85, 139, 193, 54, 108, 162, 216, 41, 95, 149, 203, 15, 69, 123, 177, 40, 94, 148, 202, 33, 87, 141, 195, 11, 65, 119, 173)(6, 60, 114, 168, 19, 73, 127, 181, 46, 100, 154, 208, 53, 107, 161, 215, 50, 104, 158, 212, 24, 78, 132, 186, 49, 103, 157, 211, 30, 84, 138, 192, 20, 74, 128, 182)(9, 63, 117, 171, 28, 82, 136, 190, 25, 79, 133, 187, 48, 102, 156, 210, 21, 75, 129, 183, 47, 101, 155, 209, 45, 99, 153, 207, 51, 105, 159, 213, 29, 83, 137, 191)(12, 66, 120, 174, 34, 88, 142, 196, 27, 81, 135, 189, 43, 97, 151, 205, 38, 92, 146, 200, 18, 72, 126, 180, 42, 96, 150, 204, 16, 70, 124, 178, 35, 89, 143, 197) L = (1, 56)(2, 55)(3, 63)(4, 66)(5, 69)(6, 72)(7, 75)(8, 78)(9, 57)(10, 84)(11, 86)(12, 58)(13, 82)(14, 85)(15, 59)(16, 83)(17, 97)(18, 60)(19, 87)(20, 90)(21, 61)(22, 96)(23, 100)(24, 62)(25, 92)(26, 105)(27, 107)(28, 67)(29, 70)(30, 64)(31, 68)(32, 65)(33, 73)(34, 101)(35, 103)(36, 74)(37, 98)(38, 79)(39, 106)(40, 102)(41, 104)(42, 76)(43, 71)(44, 91)(45, 108)(46, 77)(47, 88)(48, 94)(49, 89)(50, 95)(51, 80)(52, 93)(53, 81)(54, 99)(109, 165)(110, 168)(111, 163)(112, 175)(113, 178)(114, 164)(115, 184)(116, 187)(117, 189)(118, 183)(119, 186)(120, 181)(121, 166)(122, 200)(123, 182)(124, 167)(125, 188)(126, 207)(127, 174)(128, 177)(129, 172)(130, 169)(131, 191)(132, 173)(133, 170)(134, 179)(135, 171)(136, 203)(137, 185)(138, 205)(139, 208)(140, 196)(141, 213)(142, 194)(143, 210)(144, 209)(145, 211)(146, 176)(147, 202)(148, 201)(149, 190)(150, 212)(151, 192)(152, 216)(153, 180)(154, 193)(155, 198)(156, 197)(157, 199)(158, 204)(159, 195)(160, 215)(161, 214)(162, 206) 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 ) } Outer automorphisms :: reflexible Dual of E16.849 Transitivity :: VT+ Graph:: bipartite v = 6 e = 108 f = 72 degree seq :: [ 36^6 ] E16.853 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y2^3, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y2^-1), Y2^-1 * Y1 * Y2 * Y1, Y3^9 ] Map:: polytopal non-degenerate R = (1, 55, 2, 56)(3, 57, 7, 61)(4, 58, 10, 64)(5, 59, 9, 63)(6, 60, 8, 62)(11, 65, 18, 72)(12, 66, 17, 71)(13, 67, 22, 76)(14, 68, 21, 75)(15, 69, 20, 74)(16, 70, 19, 73)(23, 77, 30, 84)(24, 78, 29, 83)(25, 79, 34, 88)(26, 80, 33, 87)(27, 81, 32, 86)(28, 82, 31, 85)(35, 89, 42, 96)(36, 90, 41, 95)(37, 91, 46, 100)(38, 92, 45, 99)(39, 93, 44, 98)(40, 94, 43, 97)(47, 101, 52, 106)(48, 102, 51, 105)(49, 103, 54, 108)(50, 104, 53, 107)(109, 163, 111, 165, 113, 167)(110, 164, 115, 169, 117, 171)(112, 166, 119, 173, 122, 176)(114, 168, 120, 174, 123, 177)(116, 170, 125, 179, 128, 182)(118, 172, 126, 180, 129, 183)(121, 175, 131, 185, 134, 188)(124, 178, 132, 186, 135, 189)(127, 181, 137, 191, 140, 194)(130, 184, 138, 192, 141, 195)(133, 187, 143, 197, 146, 200)(136, 190, 144, 198, 147, 201)(139, 193, 149, 203, 152, 206)(142, 196, 150, 204, 153, 207)(145, 199, 155, 209, 157, 211)(148, 202, 156, 210, 158, 212)(151, 205, 159, 213, 161, 215)(154, 208, 160, 214, 162, 216) L = (1, 112)(2, 116)(3, 119)(4, 121)(5, 122)(6, 109)(7, 125)(8, 127)(9, 128)(10, 110)(11, 131)(12, 111)(13, 133)(14, 134)(15, 113)(16, 114)(17, 137)(18, 115)(19, 139)(20, 140)(21, 117)(22, 118)(23, 143)(24, 120)(25, 145)(26, 146)(27, 123)(28, 124)(29, 149)(30, 126)(31, 151)(32, 152)(33, 129)(34, 130)(35, 155)(36, 132)(37, 148)(38, 157)(39, 135)(40, 136)(41, 159)(42, 138)(43, 154)(44, 161)(45, 141)(46, 142)(47, 156)(48, 144)(49, 158)(50, 147)(51, 160)(52, 150)(53, 162)(54, 153)(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 ) } Outer automorphisms :: reflexible Dual of E16.856 Graph:: simple bipartite v = 45 e = 108 f = 33 degree seq :: [ 4^27, 6^18 ] E16.854 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y2^3, (Y1 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y2), Y3^-1 * Y1 * Y3^2 * Y2^-1 * Y1 * Y2, Y3 * Y2 * Y3^2 * Y2 * Y1 * Y2 * Y1, Y3^9 ] Map:: polytopal non-degenerate R = (1, 55, 2, 56)(3, 57, 11, 65)(4, 58, 10, 64)(5, 59, 16, 70)(6, 60, 8, 62)(7, 61, 19, 73)(9, 63, 24, 78)(12, 66, 30, 84)(13, 67, 28, 82)(14, 68, 26, 80)(15, 69, 35, 89)(17, 71, 37, 91)(18, 72, 22, 76)(20, 74, 42, 96)(21, 75, 32, 86)(23, 77, 34, 88)(25, 79, 44, 98)(27, 81, 41, 95)(29, 83, 33, 87)(31, 85, 49, 103)(36, 90, 40, 94)(38, 92, 45, 99)(39, 93, 47, 101)(43, 97, 54, 108)(46, 100, 53, 107)(48, 102, 50, 104)(51, 105, 52, 106)(109, 163, 111, 165, 113, 167)(110, 164, 115, 169, 117, 171)(112, 166, 120, 174, 123, 177)(114, 168, 121, 175, 125, 179)(116, 170, 128, 182, 131, 185)(118, 172, 129, 183, 133, 187)(119, 173, 135, 189, 137, 191)(122, 176, 139, 193, 142, 196)(124, 178, 144, 198, 146, 200)(126, 180, 140, 194, 147, 201)(127, 181, 149, 203, 148, 202)(130, 184, 151, 205, 143, 197)(132, 186, 141, 195, 153, 207)(134, 188, 136, 190, 154, 208)(138, 192, 155, 209, 156, 210)(145, 199, 159, 213, 157, 211)(150, 204, 161, 215, 160, 214)(152, 206, 158, 212, 162, 216) L = (1, 112)(2, 116)(3, 120)(4, 122)(5, 123)(6, 109)(7, 128)(8, 130)(9, 131)(10, 110)(11, 136)(12, 139)(13, 111)(14, 141)(15, 142)(16, 145)(17, 113)(18, 114)(19, 140)(20, 151)(21, 115)(22, 144)(23, 143)(24, 152)(25, 117)(26, 118)(27, 154)(28, 129)(29, 134)(30, 119)(31, 153)(32, 121)(33, 158)(34, 132)(35, 124)(36, 159)(37, 155)(38, 157)(39, 125)(40, 126)(41, 147)(42, 127)(43, 146)(44, 161)(45, 162)(46, 133)(47, 135)(48, 137)(49, 138)(50, 160)(51, 156)(52, 148)(53, 149)(54, 150)(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 ) } Outer automorphisms :: reflexible Dual of E16.858 Graph:: simple bipartite v = 45 e = 108 f = 33 degree seq :: [ 4^27, 6^18 ] E16.855 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y2^3, (Y1 * Y3^-1)^2, (Y2^-1, Y3^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^2 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y2, Y3^9 ] Map:: polytopal non-degenerate R = (1, 55, 2, 56)(3, 57, 11, 65)(4, 58, 10, 64)(5, 59, 16, 70)(6, 60, 8, 62)(7, 61, 19, 73)(9, 63, 24, 78)(12, 66, 30, 84)(13, 67, 28, 82)(14, 68, 26, 80)(15, 69, 35, 89)(17, 71, 37, 91)(18, 72, 22, 76)(20, 74, 31, 85)(21, 75, 42, 96)(23, 77, 45, 99)(25, 79, 39, 93)(27, 81, 41, 95)(29, 83, 40, 94)(32, 86, 48, 102)(33, 87, 36, 90)(34, 88, 47, 101)(38, 92, 46, 100)(43, 97, 54, 108)(44, 98, 53, 107)(49, 103, 52, 106)(50, 104, 51, 105)(109, 163, 111, 165, 113, 167)(110, 164, 115, 169, 117, 171)(112, 166, 120, 174, 123, 177)(114, 168, 121, 175, 125, 179)(116, 170, 128, 182, 131, 185)(118, 172, 129, 183, 133, 187)(119, 173, 135, 189, 137, 191)(122, 176, 139, 193, 142, 196)(124, 178, 144, 198, 146, 200)(126, 180, 140, 194, 147, 201)(127, 181, 149, 203, 141, 195)(130, 184, 138, 192, 152, 206)(132, 186, 148, 202, 154, 208)(134, 188, 151, 205, 145, 199)(136, 190, 155, 209, 157, 211)(143, 197, 159, 213, 156, 210)(150, 204, 161, 215, 158, 212)(153, 207, 160, 214, 162, 216) L = (1, 112)(2, 116)(3, 120)(4, 122)(5, 123)(6, 109)(7, 128)(8, 130)(9, 131)(10, 110)(11, 136)(12, 139)(13, 111)(14, 141)(15, 142)(16, 145)(17, 113)(18, 114)(19, 150)(20, 138)(21, 115)(22, 137)(23, 152)(24, 147)(25, 117)(26, 118)(27, 155)(28, 156)(29, 157)(30, 119)(31, 127)(32, 121)(33, 158)(34, 149)(35, 124)(36, 134)(37, 133)(38, 151)(39, 125)(40, 126)(41, 161)(42, 162)(43, 129)(44, 135)(45, 132)(46, 140)(47, 143)(48, 146)(49, 159)(50, 160)(51, 144)(52, 148)(53, 153)(54, 154)(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 ) } Outer automorphisms :: reflexible Dual of E16.857 Graph:: simple bipartite v = 45 e = 108 f = 33 degree seq :: [ 4^27, 6^18 ] E16.856 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y2^2, (Y2 * Y3)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y3^-3 * Y1^-3, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1^-1, Y1^2 * Y2 * Y1 * Y3^-1 * Y2, Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^9 ] Map:: polytopal non-degenerate R = (1, 55, 2, 56, 7, 61, 21, 75, 37, 91, 47, 101, 34, 88, 18, 72, 5, 59)(3, 57, 11, 65, 31, 85, 43, 97, 52, 106, 51, 105, 38, 92, 26, 80, 13, 67)(4, 58, 9, 63, 23, 77, 20, 74, 30, 84, 42, 96, 46, 100, 36, 90, 16, 70)(6, 60, 10, 64, 24, 78, 39, 93, 48, 102, 35, 89, 15, 69, 29, 83, 19, 73)(8, 62, 25, 79, 14, 68, 32, 86, 44, 98, 53, 107, 49, 103, 40, 94, 27, 81)(12, 66, 28, 82, 17, 71, 33, 87, 45, 99, 54, 108, 50, 104, 41, 95, 22, 76)(109, 163, 111, 165)(110, 164, 116, 170)(112, 166, 122, 176)(113, 167, 125, 179)(114, 168, 120, 174)(115, 169, 130, 184)(117, 171, 136, 190)(118, 172, 134, 188)(119, 173, 137, 191)(121, 175, 131, 185)(123, 177, 141, 195)(124, 178, 139, 193)(126, 180, 140, 194)(127, 181, 133, 187)(128, 182, 135, 189)(129, 183, 146, 200)(132, 186, 148, 202)(138, 192, 149, 203)(142, 196, 151, 205)(143, 197, 152, 206)(144, 198, 153, 207)(145, 199, 157, 211)(147, 201, 158, 212)(150, 204, 159, 213)(154, 208, 161, 215)(155, 209, 162, 216)(156, 210, 160, 214) L = (1, 112)(2, 117)(3, 120)(4, 123)(5, 124)(6, 109)(7, 131)(8, 134)(9, 137)(10, 110)(11, 136)(12, 135)(13, 130)(14, 111)(15, 142)(16, 143)(17, 133)(18, 144)(19, 113)(20, 114)(21, 128)(22, 148)(23, 127)(24, 115)(25, 121)(26, 149)(27, 146)(28, 116)(29, 126)(30, 118)(31, 125)(32, 119)(33, 122)(34, 154)(35, 155)(36, 156)(37, 138)(38, 158)(39, 129)(40, 159)(41, 157)(42, 132)(43, 141)(44, 139)(45, 140)(46, 147)(47, 150)(48, 145)(49, 160)(50, 161)(51, 162)(52, 153)(53, 151)(54, 152)(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, 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 E16.853 Graph:: simple bipartite v = 33 e = 108 f = 45 degree seq :: [ 4^27, 18^6 ] E16.857 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y2^2, (Y3, Y1^-1), (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y3^-1 * Y1^2 * Y3^-1 * Y2, Y2 * Y1^3 * Y3^-1 * Y1 * Y2 * Y1^-1, Y1^9 ] Map:: polytopal non-degenerate R = (1, 55, 2, 56, 7, 61, 21, 75, 49, 103, 54, 108, 41, 95, 18, 72, 5, 59)(3, 57, 11, 65, 31, 85, 52, 106, 26, 80, 43, 97, 50, 104, 38, 92, 13, 67)(4, 58, 9, 63, 23, 77, 20, 74, 30, 84, 37, 91, 53, 107, 44, 98, 16, 70)(6, 60, 10, 64, 24, 78, 51, 105, 32, 86, 42, 96, 15, 69, 29, 83, 19, 73)(8, 62, 25, 79, 35, 89, 48, 102, 39, 93, 14, 68, 34, 88, 46, 100, 27, 81)(12, 66, 33, 87, 22, 76, 40, 94, 47, 101, 17, 71, 45, 99, 28, 82, 36, 90)(109, 163, 111, 165)(110, 164, 116, 170)(112, 166, 122, 176)(113, 167, 125, 179)(114, 168, 120, 174)(115, 169, 130, 184)(117, 171, 136, 190)(118, 172, 134, 188)(119, 173, 140, 194)(121, 175, 145, 199)(123, 177, 148, 202)(124, 178, 151, 205)(126, 180, 156, 210)(127, 181, 154, 208)(128, 182, 143, 197)(129, 183, 158, 212)(131, 185, 139, 193)(132, 186, 147, 201)(133, 187, 150, 204)(135, 189, 161, 215)(137, 191, 146, 200)(138, 192, 155, 209)(141, 195, 152, 206)(142, 196, 157, 211)(144, 198, 162, 216)(149, 203, 160, 214)(153, 207, 159, 213) L = (1, 112)(2, 117)(3, 120)(4, 123)(5, 124)(6, 109)(7, 131)(8, 134)(9, 137)(10, 110)(11, 141)(12, 143)(13, 144)(14, 111)(15, 149)(16, 150)(17, 154)(18, 152)(19, 113)(20, 114)(21, 128)(22, 147)(23, 127)(24, 115)(25, 151)(26, 155)(27, 160)(28, 116)(29, 126)(30, 118)(31, 130)(32, 157)(33, 156)(34, 119)(35, 158)(36, 133)(37, 132)(38, 136)(39, 121)(40, 122)(41, 161)(42, 162)(43, 125)(44, 140)(45, 135)(46, 139)(47, 142)(48, 146)(49, 138)(50, 153)(51, 129)(52, 148)(53, 159)(54, 145)(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, 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 E16.855 Graph:: simple bipartite v = 33 e = 108 f = 45 degree seq :: [ 4^27, 18^6 ] E16.858 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y1 * Y3^-1 * Y2 * Y1^-1 * Y2, Y3^-3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y1^9 ] Map:: polytopal non-degenerate R = (1, 55, 2, 56, 7, 61, 21, 75, 41, 95, 54, 108, 35, 89, 18, 72, 5, 59)(3, 57, 11, 65, 29, 83, 49, 103, 48, 102, 45, 99, 42, 96, 32, 86, 13, 67)(4, 58, 9, 63, 23, 77, 20, 74, 28, 82, 46, 100, 53, 107, 37, 91, 16, 70)(6, 60, 10, 64, 24, 78, 43, 97, 52, 106, 36, 90, 15, 69, 27, 81, 19, 73)(8, 62, 25, 79, 47, 101, 40, 94, 38, 92, 31, 85, 51, 105, 33, 87, 14, 68)(12, 66, 30, 84, 50, 104, 34, 88, 26, 80, 22, 76, 44, 98, 39, 93, 17, 71)(109, 163, 111, 165)(110, 164, 116, 170)(112, 166, 122, 176)(113, 167, 125, 179)(114, 168, 120, 174)(115, 169, 130, 184)(117, 171, 134, 188)(118, 172, 119, 173)(121, 175, 124, 178)(123, 177, 142, 196)(126, 180, 148, 202)(127, 181, 146, 200)(128, 182, 139, 193)(129, 183, 150, 204)(131, 185, 153, 207)(132, 186, 133, 187)(135, 189, 156, 210)(136, 190, 138, 192)(137, 191, 154, 208)(140, 194, 160, 214)(141, 195, 144, 198)(143, 197, 157, 211)(145, 199, 147, 201)(149, 203, 159, 213)(151, 205, 152, 206)(155, 209, 161, 215)(158, 212, 162, 216) L = (1, 112)(2, 117)(3, 120)(4, 123)(5, 124)(6, 109)(7, 131)(8, 119)(9, 135)(10, 110)(11, 138)(12, 139)(13, 125)(14, 111)(15, 143)(16, 144)(17, 146)(18, 145)(19, 113)(20, 114)(21, 128)(22, 133)(23, 127)(24, 115)(25, 137)(26, 116)(27, 126)(28, 118)(29, 158)(30, 159)(31, 150)(32, 147)(33, 121)(34, 122)(35, 161)(36, 162)(37, 160)(38, 153)(39, 148)(40, 156)(41, 136)(42, 152)(43, 129)(44, 155)(45, 130)(46, 132)(47, 157)(48, 134)(49, 142)(50, 141)(51, 140)(52, 149)(53, 151)(54, 154)(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, 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 E16.854 Graph:: simple bipartite v = 33 e = 108 f = 45 degree seq :: [ 4^27, 18^6 ] E16.859 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 9}) Quotient :: dipole Aut^+ = (C9 x C3) : C2 (small group id <54, 7>) Aut = C2 x ((C9 x C3) : C2) (small group id <108, 27>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y2^-1), (Y2 * Y1)^2, Y3^9 ] Map:: polytopal non-degenerate R = (1, 55, 2, 56)(3, 57, 9, 63)(4, 58, 10, 64)(5, 59, 7, 61)(6, 60, 8, 62)(11, 65, 21, 75)(12, 66, 20, 74)(13, 67, 22, 76)(14, 68, 18, 72)(15, 69, 17, 71)(16, 70, 19, 73)(23, 77, 33, 87)(24, 78, 32, 86)(25, 79, 34, 88)(26, 80, 30, 84)(27, 81, 29, 83)(28, 82, 31, 85)(35, 89, 45, 99)(36, 90, 44, 98)(37, 91, 46, 100)(38, 92, 42, 96)(39, 93, 41, 95)(40, 94, 43, 97)(47, 101, 54, 108)(48, 102, 53, 107)(49, 103, 52, 106)(50, 104, 51, 105)(109, 163, 111, 165, 113, 167)(110, 164, 115, 169, 117, 171)(112, 166, 119, 173, 122, 176)(114, 168, 120, 174, 123, 177)(116, 170, 125, 179, 128, 182)(118, 172, 126, 180, 129, 183)(121, 175, 131, 185, 134, 188)(124, 178, 132, 186, 135, 189)(127, 181, 137, 191, 140, 194)(130, 184, 138, 192, 141, 195)(133, 187, 143, 197, 146, 200)(136, 190, 144, 198, 147, 201)(139, 193, 149, 203, 152, 206)(142, 196, 150, 204, 153, 207)(145, 199, 155, 209, 157, 211)(148, 202, 156, 210, 158, 212)(151, 205, 159, 213, 161, 215)(154, 208, 160, 214, 162, 216) L = (1, 112)(2, 116)(3, 119)(4, 121)(5, 122)(6, 109)(7, 125)(8, 127)(9, 128)(10, 110)(11, 131)(12, 111)(13, 133)(14, 134)(15, 113)(16, 114)(17, 137)(18, 115)(19, 139)(20, 140)(21, 117)(22, 118)(23, 143)(24, 120)(25, 145)(26, 146)(27, 123)(28, 124)(29, 149)(30, 126)(31, 151)(32, 152)(33, 129)(34, 130)(35, 155)(36, 132)(37, 148)(38, 157)(39, 135)(40, 136)(41, 159)(42, 138)(43, 154)(44, 161)(45, 141)(46, 142)(47, 156)(48, 144)(49, 158)(50, 147)(51, 160)(52, 150)(53, 162)(54, 153)(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 ) } Outer automorphisms :: reflexible Dual of E16.860 Graph:: simple bipartite v = 45 e = 108 f = 33 degree seq :: [ 4^27, 6^18 ] E16.860 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 9}) Quotient :: dipole Aut^+ = (C9 x C3) : C2 (small group id <54, 7>) Aut = C2 x ((C9 x C3) : C2) (small group id <108, 27>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^-3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y1^9 ] Map:: polytopal non-degenerate R = (1, 55, 2, 56, 7, 61, 19, 73, 35, 89, 47, 101, 32, 86, 16, 70, 5, 59)(3, 57, 11, 65, 27, 81, 43, 97, 52, 106, 49, 103, 36, 90, 20, 74, 8, 62)(4, 58, 9, 63, 21, 75, 18, 72, 26, 80, 40, 94, 46, 100, 34, 88, 15, 69)(6, 60, 10, 64, 22, 76, 37, 91, 48, 102, 33, 87, 14, 68, 25, 79, 17, 71)(12, 66, 28, 82, 42, 96, 31, 85, 45, 99, 54, 108, 50, 104, 38, 92, 23, 77)(13, 67, 29, 83, 44, 98, 53, 107, 51, 105, 41, 95, 30, 84, 39, 93, 24, 78)(109, 163, 111, 165)(110, 164, 116, 170)(112, 166, 121, 175)(113, 167, 119, 173)(114, 168, 120, 174)(115, 169, 128, 182)(117, 171, 132, 186)(118, 172, 131, 185)(122, 176, 139, 193)(123, 177, 137, 191)(124, 178, 135, 189)(125, 179, 136, 190)(126, 180, 138, 192)(127, 181, 144, 198)(129, 183, 147, 201)(130, 184, 146, 200)(133, 187, 150, 204)(134, 188, 149, 203)(140, 194, 151, 205)(141, 195, 153, 207)(142, 196, 152, 206)(143, 197, 157, 211)(145, 199, 158, 212)(148, 202, 159, 213)(154, 208, 161, 215)(155, 209, 160, 214)(156, 210, 162, 216) L = (1, 112)(2, 117)(3, 120)(4, 122)(5, 123)(6, 109)(7, 129)(8, 131)(9, 133)(10, 110)(11, 136)(12, 138)(13, 111)(14, 140)(15, 141)(16, 142)(17, 113)(18, 114)(19, 126)(20, 146)(21, 125)(22, 115)(23, 149)(24, 116)(25, 124)(26, 118)(27, 150)(28, 147)(29, 119)(30, 144)(31, 121)(32, 154)(33, 155)(34, 156)(35, 134)(36, 158)(37, 127)(38, 159)(39, 128)(40, 130)(41, 157)(42, 132)(43, 139)(44, 135)(45, 137)(46, 145)(47, 148)(48, 143)(49, 162)(50, 161)(51, 160)(52, 153)(53, 151)(54, 152)(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, 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 E16.859 Graph:: simple bipartite v = 33 e = 108 f = 45 degree seq :: [ 4^27, 18^6 ] E16.861 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 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 * T1 * T2 * T1^-1, T1^6, T2^9 ] Map:: non-degenerate R = (1, 3, 9, 19, 31, 36, 24, 13, 5)(2, 7, 17, 29, 41, 42, 30, 18, 8)(4, 11, 22, 34, 45, 43, 32, 20, 10)(6, 15, 27, 39, 49, 50, 40, 28, 16)(12, 21, 33, 44, 51, 52, 46, 35, 23)(14, 25, 37, 47, 53, 54, 48, 38, 26)(55, 56, 60, 68, 66, 58)(57, 62, 69, 80, 75, 64)(59, 61, 70, 79, 77, 65)(63, 72, 81, 92, 87, 74)(67, 71, 82, 91, 89, 76)(73, 84, 93, 102, 98, 86)(78, 83, 94, 101, 100, 88)(85, 96, 103, 108, 105, 97)(90, 95, 104, 107, 106, 99) 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) :: { ( 12^6 ), ( 12^9 ) } Outer automorphisms :: reflexible Dual of E16.864 Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 54 f = 9 degree seq :: [ 6^9, 9^6 ] E16.862 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 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, (T2^-1 * T1)^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1 * T2 * T1^-1, (T2^2 * T1)^2, T1^6, T2^9 ] Map:: non-degenerate R = (1, 3, 10, 25, 37, 40, 28, 15, 5)(2, 7, 20, 32, 44, 46, 34, 22, 8)(4, 11, 26, 38, 49, 48, 36, 24, 13)(6, 17, 29, 41, 51, 52, 42, 30, 18)(9, 16, 14, 27, 39, 50, 47, 35, 23)(12, 21, 33, 45, 54, 53, 43, 31, 19)(55, 56, 60, 70, 66, 58)(57, 63, 71, 67, 75, 62)(59, 65, 72, 61, 73, 68)(64, 78, 83, 76, 87, 77)(69, 81, 84, 80, 85, 74)(79, 88, 95, 89, 99, 90)(82, 86, 96, 93, 97, 92)(91, 101, 105, 102, 108, 100)(94, 103, 106, 98, 107, 104) 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) :: { ( 12^6 ), ( 12^9 ) } Outer automorphisms :: reflexible Dual of E16.863 Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 54 f = 9 degree seq :: [ 6^9, 9^6 ] E16.863 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 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, T1^2 * T2^-2, (F * T1)^2, (F * T2)^2, T2^2 * T1^4, (T2^-1 * T1^-1)^9 ] Map:: non-degenerate R = (1, 55, 3, 57, 6, 60, 15, 69, 11, 65, 5, 59)(2, 56, 7, 61, 14, 68, 12, 66, 4, 58, 8, 62)(9, 63, 19, 73, 13, 67, 21, 75, 10, 64, 20, 74)(16, 70, 22, 76, 18, 72, 24, 78, 17, 71, 23, 77)(25, 79, 31, 85, 27, 81, 33, 87, 26, 80, 32, 86)(28, 82, 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, 52, 106, 51, 105, 54, 108, 50, 104, 53, 107) L = (1, 56)(2, 60)(3, 63)(4, 55)(5, 64)(6, 68)(7, 70)(8, 71)(9, 69)(10, 57)(11, 58)(12, 72)(13, 59)(14, 65)(15, 67)(16, 66)(17, 61)(18, 62)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 75)(26, 73)(27, 74)(28, 78)(29, 76)(30, 77)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 87)(38, 85)(39, 86)(40, 90)(41, 88)(42, 89)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 99)(50, 97)(51, 98)(52, 102)(53, 100)(54, 101) local type(s) :: { ( 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9 ) } Outer automorphisms :: reflexible Dual of E16.862 Transitivity :: ET+ VT+ AT Graph:: v = 9 e = 54 f = 15 degree seq :: [ 12^9 ] E16.864 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 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, T2^2 * T1^2, (F * T1)^2, (F * T2)^2, T2^-2 * T1^4, T2^6, (T2 * T1)^9 ] Map:: non-degenerate R = (1, 55, 3, 57, 10, 64, 15, 69, 6, 60, 5, 59)(2, 56, 7, 61, 4, 58, 12, 66, 14, 68, 8, 62)(9, 63, 19, 73, 11, 65, 21, 75, 13, 67, 20, 74)(16, 70, 22, 76, 17, 71, 24, 78, 18, 72, 23, 77)(25, 79, 31, 85, 26, 80, 33, 87, 27, 81, 32, 86)(28, 82, 34, 88, 29, 83, 36, 90, 30, 84, 35, 89)(37, 91, 43, 97, 38, 92, 45, 99, 39, 93, 44, 98)(40, 94, 46, 100, 41, 95, 48, 102, 42, 96, 47, 101)(49, 103, 53, 107, 50, 104, 54, 108, 51, 105, 52, 106) L = (1, 56)(2, 60)(3, 63)(4, 55)(5, 67)(6, 68)(7, 70)(8, 72)(9, 59)(10, 58)(11, 57)(12, 71)(13, 69)(14, 64)(15, 65)(16, 62)(17, 61)(18, 66)(19, 79)(20, 81)(21, 80)(22, 82)(23, 84)(24, 83)(25, 74)(26, 73)(27, 75)(28, 77)(29, 76)(30, 78)(31, 91)(32, 93)(33, 92)(34, 94)(35, 96)(36, 95)(37, 86)(38, 85)(39, 87)(40, 89)(41, 88)(42, 90)(43, 103)(44, 105)(45, 104)(46, 106)(47, 108)(48, 107)(49, 98)(50, 97)(51, 99)(52, 101)(53, 100)(54, 102) local type(s) :: { ( 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9 ) } Outer automorphisms :: reflexible Dual of E16.861 Transitivity :: ET+ VT+ AT Graph:: v = 9 e = 54 f = 15 degree seq :: [ 12^9 ] E16.865 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 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 * Y1 * Y2 * Y1^-1, Y1^6, Y2^9, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 55, 2, 56, 6, 60, 14, 68, 12, 66, 4, 58)(3, 57, 8, 62, 15, 69, 26, 80, 21, 75, 10, 64)(5, 59, 7, 61, 16, 70, 25, 79, 23, 77, 11, 65)(9, 63, 18, 72, 27, 81, 38, 92, 33, 87, 20, 74)(13, 67, 17, 71, 28, 82, 37, 91, 35, 89, 22, 76)(19, 73, 30, 84, 39, 93, 48, 102, 44, 98, 32, 86)(24, 78, 29, 83, 40, 94, 47, 101, 46, 100, 34, 88)(31, 85, 42, 96, 49, 103, 54, 108, 51, 105, 43, 97)(36, 90, 41, 95, 50, 104, 53, 107, 52, 106, 45, 99)(109, 163, 111, 165, 117, 171, 127, 181, 139, 193, 144, 198, 132, 186, 121, 175, 113, 167)(110, 164, 115, 169, 125, 179, 137, 191, 149, 203, 150, 204, 138, 192, 126, 180, 116, 170)(112, 166, 119, 173, 130, 184, 142, 196, 153, 207, 151, 205, 140, 194, 128, 182, 118, 172)(114, 168, 123, 177, 135, 189, 147, 201, 157, 211, 158, 212, 148, 202, 136, 190, 124, 178)(120, 174, 129, 183, 141, 195, 152, 206, 159, 213, 160, 214, 154, 208, 143, 197, 131, 185)(122, 176, 133, 187, 145, 199, 155, 209, 161, 215, 162, 216, 156, 210, 146, 200, 134, 188) L = (1, 111)(2, 115)(3, 117)(4, 119)(5, 109)(6, 123)(7, 125)(8, 110)(9, 127)(10, 112)(11, 130)(12, 129)(13, 113)(14, 133)(15, 135)(16, 114)(17, 137)(18, 116)(19, 139)(20, 118)(21, 141)(22, 142)(23, 120)(24, 121)(25, 145)(26, 122)(27, 147)(28, 124)(29, 149)(30, 126)(31, 144)(32, 128)(33, 152)(34, 153)(35, 131)(36, 132)(37, 155)(38, 134)(39, 157)(40, 136)(41, 150)(42, 138)(43, 140)(44, 159)(45, 151)(46, 143)(47, 161)(48, 146)(49, 158)(50, 148)(51, 160)(52, 154)(53, 162)(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, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E16.867 Graph:: bipartite v = 15 e = 108 f = 63 degree seq :: [ 12^9, 18^6 ] E16.866 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 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, (Y2^-1 * Y1)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-2 * Y2^-1 * Y1^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-3, (Y2^-2 * Y1^-1)^2, Y2^9, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 55, 2, 56, 6, 60, 16, 70, 12, 66, 4, 58)(3, 57, 9, 63, 17, 71, 13, 67, 21, 75, 8, 62)(5, 59, 11, 65, 18, 72, 7, 61, 19, 73, 14, 68)(10, 64, 24, 78, 29, 83, 22, 76, 33, 87, 23, 77)(15, 69, 27, 81, 30, 84, 26, 80, 31, 85, 20, 74)(25, 79, 34, 88, 41, 95, 35, 89, 45, 99, 36, 90)(28, 82, 32, 86, 42, 96, 39, 93, 43, 97, 38, 92)(37, 91, 47, 101, 51, 105, 48, 102, 54, 108, 46, 100)(40, 94, 49, 103, 52, 106, 44, 98, 53, 107, 50, 104)(109, 163, 111, 165, 118, 172, 133, 187, 145, 199, 148, 202, 136, 190, 123, 177, 113, 167)(110, 164, 115, 169, 128, 182, 140, 194, 152, 206, 154, 208, 142, 196, 130, 184, 116, 170)(112, 166, 119, 173, 134, 188, 146, 200, 157, 211, 156, 210, 144, 198, 132, 186, 121, 175)(114, 168, 125, 179, 137, 191, 149, 203, 159, 213, 160, 214, 150, 204, 138, 192, 126, 180)(117, 171, 124, 178, 122, 176, 135, 189, 147, 201, 158, 212, 155, 209, 143, 197, 131, 185)(120, 174, 129, 183, 141, 195, 153, 207, 162, 216, 161, 215, 151, 205, 139, 193, 127, 181) L = (1, 111)(2, 115)(3, 118)(4, 119)(5, 109)(6, 125)(7, 128)(8, 110)(9, 124)(10, 133)(11, 134)(12, 129)(13, 112)(14, 135)(15, 113)(16, 122)(17, 137)(18, 114)(19, 120)(20, 140)(21, 141)(22, 116)(23, 117)(24, 121)(25, 145)(26, 146)(27, 147)(28, 123)(29, 149)(30, 126)(31, 127)(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, 156)(50, 155)(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, 12, 2, 12, 2, 12, 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 E16.868 Graph:: bipartite v = 15 e = 108 f = 63 degree seq :: [ 12^9, 18^6 ] E16.867 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 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, R^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^6, (Y3^-1 * Y1^-1)^9 ] Map:: 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, 114, 168, 122, 176, 120, 174, 112, 166)(111, 165, 116, 170, 123, 177, 134, 188, 129, 183, 118, 172)(113, 167, 115, 169, 124, 178, 133, 187, 131, 185, 119, 173)(117, 171, 126, 180, 135, 189, 146, 200, 141, 195, 128, 182)(121, 175, 125, 179, 136, 190, 145, 199, 143, 197, 130, 184)(127, 181, 138, 192, 147, 201, 156, 210, 152, 206, 140, 194)(132, 186, 137, 191, 148, 202, 155, 209, 154, 208, 142, 196)(139, 193, 150, 204, 157, 211, 162, 216, 159, 213, 151, 205)(144, 198, 149, 203, 158, 212, 161, 215, 160, 214, 153, 207) L = (1, 111)(2, 115)(3, 117)(4, 119)(5, 109)(6, 123)(7, 125)(8, 110)(9, 127)(10, 112)(11, 130)(12, 129)(13, 113)(14, 133)(15, 135)(16, 114)(17, 137)(18, 116)(19, 139)(20, 118)(21, 141)(22, 142)(23, 120)(24, 121)(25, 145)(26, 122)(27, 147)(28, 124)(29, 149)(30, 126)(31, 144)(32, 128)(33, 152)(34, 153)(35, 131)(36, 132)(37, 155)(38, 134)(39, 157)(40, 136)(41, 150)(42, 138)(43, 140)(44, 159)(45, 151)(46, 143)(47, 161)(48, 146)(49, 158)(50, 148)(51, 160)(52, 154)(53, 162)(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) :: { ( 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E16.865 Graph:: simple bipartite v = 63 e = 108 f = 15 degree seq :: [ 2^54, 12^9 ] E16.868 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 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, R^2, (Y3^-1 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y3 * Y2^3, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2, (Y3^-1 * Y1^-1)^9 ] Map:: 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, 114, 168, 124, 178, 121, 175, 112, 166)(111, 165, 117, 171, 125, 179, 116, 170, 129, 183, 119, 173)(113, 167, 122, 176, 126, 180, 120, 174, 128, 182, 115, 169)(118, 172, 132, 186, 137, 191, 131, 185, 141, 195, 130, 184)(123, 177, 134, 188, 138, 192, 127, 181, 139, 193, 135, 189)(133, 187, 142, 196, 149, 203, 144, 198, 153, 207, 143, 197)(136, 190, 140, 194, 150, 204, 147, 201, 151, 205, 146, 200)(145, 199, 155, 209, 159, 213, 154, 208, 162, 216, 156, 210)(148, 202, 158, 212, 160, 214, 157, 211, 161, 215, 152, 206) 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) :: { ( 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E16.866 Graph:: simple bipartite v = 63 e = 108 f = 15 degree seq :: [ 2^54, 12^9 ] E16.869 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {6, 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 * X1^-1)^2, X1^6, (X2^-2 * X1^-1)^2, X1 * X2 * X1^3 * X2^-2, X2^9 ] Map:: polytopal non-degenerate R = (1, 2, 6, 16, 12, 4)(3, 9, 23, 29, 21, 8)(5, 11, 28, 48, 34, 14)(7, 19, 25, 10, 26, 18)(13, 30, 51, 47, 52, 32)(15, 33, 17, 37, 40, 20)(22, 31, 36, 53, 54, 38)(24, 44, 46, 27, 42, 43)(35, 41, 49, 45, 39, 50)(55, 57, 64, 81, 101, 107, 89, 69, 59)(56, 61, 74, 95, 102, 105, 96, 76, 62)(58, 65, 83, 104, 108, 91, 100, 80, 67)(60, 71, 92, 97, 77, 82, 103, 86, 72)(63, 78, 68, 87, 70, 90, 106, 99, 79)(66, 84, 88, 98, 94, 73, 93, 75, 85) 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) :: { ( 12^6 ), ( 12^9 ) } Outer automorphisms :: chiral Dual of E16.871 Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 54 f = 9 degree seq :: [ 6^9, 9^6 ] E16.870 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {6, 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 * X1 * X2^-2 * X1^-1, X1^6, X1^2 * X2 * X1^-2 * X2^2, X2 * X1 * X2 * X1^-1 * X2^3, (X2^-1 * X1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 2, 6, 18, 13, 4)(3, 9, 25, 44, 30, 11)(5, 15, 37, 43, 39, 16)(7, 21, 47, 34, 36, 22)(8, 23, 49, 33, 31, 24)(10, 27, 20, 46, 32, 12)(14, 17, 41, 19, 45, 35)(26, 50, 53, 52, 40, 42)(28, 38, 48, 54, 51, 29)(55, 57, 64, 82, 78, 76, 96, 71, 59)(56, 61, 63, 80, 81, 95, 92, 69, 62)(58, 66, 85, 94, 70, 65, 83, 90, 68)(60, 73, 75, 102, 79, 91, 104, 77, 74)(67, 87, 93, 105, 89, 86, 106, 84, 88)(72, 97, 99, 107, 101, 103, 108, 100, 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) :: { ( 12^6 ), ( 12^9 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 54 f = 9 degree seq :: [ 6^9, 9^6 ] E16.871 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {6, 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 * X1^-1 * X2^-1 * X1 * X2 * X1^-1, X1^6, (X1^-1 * X2^-1 * X1^-1)^2, X2^6, (X1^-1 * X2^-2)^2, X2^-1 * X1^3 * X2 * X1^-1 * X2^-1 * X1^-1, X2^-3 * X1^-2 * X2 * X1^-2 ] Map:: polytopal non-degenerate R = (1, 55, 2, 56, 6, 60, 18, 72, 13, 67, 4, 58)(3, 57, 9, 63, 27, 81, 53, 107, 33, 87, 11, 65)(5, 59, 15, 69, 38, 92, 43, 97, 19, 73, 16, 70)(7, 61, 21, 75, 14, 68, 37, 91, 50, 104, 23, 77)(8, 62, 24, 78, 51, 105, 28, 82, 40, 94, 25, 79)(10, 64, 29, 83, 42, 96, 26, 80, 52, 106, 31, 85)(12, 66, 32, 86, 41, 95, 54, 108, 48, 102, 35, 89)(17, 71, 39, 93, 46, 100, 34, 88, 49, 103, 22, 76)(20, 74, 44, 98, 30, 84, 47, 101, 36, 90, 45, 99) L = (1, 57)(2, 61)(3, 64)(4, 66)(5, 55)(6, 73)(7, 76)(8, 56)(9, 82)(10, 84)(11, 86)(12, 88)(13, 90)(14, 58)(15, 78)(16, 89)(17, 59)(18, 94)(19, 96)(20, 60)(21, 101)(22, 102)(23, 63)(24, 98)(25, 65)(26, 62)(27, 67)(28, 70)(29, 68)(30, 71)(31, 95)(32, 97)(33, 100)(34, 105)(35, 99)(36, 106)(37, 69)(38, 103)(39, 104)(40, 93)(41, 72)(42, 87)(43, 75)(44, 108)(45, 77)(46, 74)(47, 79)(48, 80)(49, 81)(50, 85)(51, 83)(52, 92)(53, 91)(54, 107) local type(s) :: { ( 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9 ) } Outer automorphisms :: chiral Dual of E16.869 Transitivity :: ET+ VT+ Graph:: v = 9 e = 54 f = 15 degree seq :: [ 12^9 ] E16.872 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {6, 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 :: [ X2^6, (X2^2 * X1^-1)^2, X1^6, (X2 * X1^-2)^2, X1^-1 * X2 * X1 * X2^-1 * X1^-1 * X2^-1, X1^-1 * X2^-1 * X1^-2 * X2^-3 * X1^-1, X2^-1 * X1^3 * X2^-2 * X1^-1 * X2^-1, X1^-2 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 55, 2, 56, 6, 60, 18, 72, 13, 67, 4, 58)(3, 57, 9, 63, 27, 81, 45, 99, 20, 74, 11, 65)(5, 59, 15, 69, 34, 88, 53, 107, 38, 92, 16, 70)(7, 61, 21, 75, 47, 101, 31, 85, 41, 95, 23, 77)(8, 62, 24, 78, 12, 66, 28, 82, 51, 105, 25, 79)(10, 64, 29, 83, 43, 97, 37, 91, 52, 106, 26, 80)(14, 68, 36, 90, 40, 94, 54, 108, 49, 103, 32, 86)(17, 71, 33, 87, 46, 100, 22, 76, 48, 102, 39, 93)(19, 73, 42, 96, 30, 84, 50, 104, 35, 89, 44, 98) L = (1, 57)(2, 61)(3, 64)(4, 66)(5, 55)(6, 73)(7, 76)(8, 56)(9, 82)(10, 84)(11, 85)(12, 87)(13, 88)(14, 58)(15, 79)(16, 77)(17, 59)(18, 94)(19, 97)(20, 60)(21, 63)(22, 103)(23, 104)(24, 99)(25, 98)(26, 62)(27, 102)(28, 107)(29, 95)(30, 71)(31, 69)(32, 65)(33, 101)(34, 106)(35, 67)(36, 70)(37, 68)(38, 100)(39, 105)(40, 93)(41, 72)(42, 75)(43, 92)(44, 86)(45, 90)(46, 74)(47, 91)(48, 89)(49, 80)(50, 78)(51, 83)(52, 81)(53, 108)(54, 96) local type(s) :: { ( 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 9 e = 54 f = 15 degree seq :: [ 12^9 ] E16.873 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {6, 6, 9}) Quotient :: loop Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 2 Presentation :: [ F^2, F * T1 * F * T2, (T2 * T1^-2)^2, (T2^2 * T1^-1)^2, T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^6, T2^6, T1 * T2^-1 * T1^-3 * T2^-1 * T1^-1 * T2^-1, T2 * T1^3 * T2^-1 * T1^-1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 30, 17, 5)(2, 7, 22, 49, 26, 8)(4, 12, 33, 47, 37, 14)(6, 19, 43, 38, 46, 20)(9, 28, 53, 54, 42, 21)(11, 31, 15, 25, 44, 32)(13, 34, 52, 27, 48, 35)(16, 23, 50, 24, 45, 36)(18, 40, 39, 51, 29, 41)(55, 56, 60, 72, 67, 58)(57, 63, 81, 99, 74, 65)(59, 69, 88, 107, 92, 70)(61, 75, 101, 85, 95, 77)(62, 78, 66, 82, 105, 79)(64, 83, 97, 91, 106, 80)(68, 90, 94, 108, 103, 86)(71, 87, 100, 76, 102, 93)(73, 96, 84, 104, 89, 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) :: { ( 18^6 ) } Outer automorphisms :: reflexible Dual of E16.874 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 18 e = 54 f = 6 degree seq :: [ 6^18 ] E16.874 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {6, 6, 9}) Quotient :: edge Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, F * T1 * T2 * F * T1^-1, T2 * T1 * T2^-2 * T1^-1, T1^6, T1^2 * T2 * T1^-2 * T2^2, T2 * T1 * T2 * T1^-1 * T2^3, F * T1^-2 * T2^-1 * F * T1^2 * T2^-1, (T2^-1 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 55, 3, 57, 10, 64, 28, 82, 24, 78, 22, 76, 42, 96, 17, 71, 5, 59)(2, 56, 7, 61, 9, 63, 26, 80, 27, 81, 41, 95, 38, 92, 15, 69, 8, 62)(4, 58, 12, 66, 31, 85, 40, 94, 16, 70, 11, 65, 29, 83, 36, 90, 14, 68)(6, 60, 19, 73, 21, 75, 48, 102, 25, 79, 37, 91, 50, 104, 23, 77, 20, 74)(13, 67, 33, 87, 39, 93, 51, 105, 35, 89, 32, 86, 52, 106, 30, 84, 34, 88)(18, 72, 43, 97, 45, 99, 53, 107, 47, 101, 49, 103, 54, 108, 46, 100, 44, 98) L = (1, 56)(2, 60)(3, 63)(4, 55)(5, 69)(6, 72)(7, 75)(8, 77)(9, 79)(10, 81)(11, 57)(12, 64)(13, 58)(14, 71)(15, 91)(16, 59)(17, 95)(18, 67)(19, 99)(20, 100)(21, 101)(22, 61)(23, 103)(24, 62)(25, 98)(26, 104)(27, 74)(28, 92)(29, 82)(30, 65)(31, 78)(32, 66)(33, 85)(34, 90)(35, 68)(36, 76)(37, 97)(38, 102)(39, 70)(40, 96)(41, 73)(42, 80)(43, 93)(44, 84)(45, 89)(46, 86)(47, 88)(48, 108)(49, 87)(50, 107)(51, 83)(52, 94)(53, 106)(54, 105) local type(s) :: { ( 6^18 ) } Outer automorphisms :: reflexible Dual of E16.873 Transitivity :: ET+ VT+ Graph:: bipartite v = 6 e = 54 f = 18 degree seq :: [ 18^6 ] E16.875 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {6, 6, 9}) Quotient :: edge^2 Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y3^-2 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y3^-2, Y2 * Y3^-1 * Y1^2 * Y3 * Y2, Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y2^6, (Y2^2 * Y1^-1)^2, (Y2 * Y1^-2)^2, Y1^6, Y3^-1 * Y1^-1 * Y3^4 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 55, 4, 58, 17, 71, 38, 92, 32, 86, 33, 87, 40, 94, 12, 66, 7, 61)(2, 56, 9, 63, 6, 60, 24, 78, 19, 73, 39, 93, 48, 102, 26, 80, 11, 65)(3, 57, 5, 59, 21, 75, 51, 105, 27, 81, 16, 70, 18, 72, 41, 95, 15, 69)(8, 62, 29, 83, 10, 64, 35, 89, 23, 77, 53, 107, 25, 79, 37, 91, 31, 85)(13, 67, 14, 68, 45, 99, 49, 103, 46, 100, 20, 74, 22, 76, 47, 101, 43, 97)(28, 82, 44, 98, 30, 84, 50, 104, 34, 88, 42, 96, 36, 90, 54, 108, 52, 106)(109, 110, 116, 136, 130, 113)(111, 120, 147, 137, 138, 122)(112, 114, 131, 160, 154, 126)(115, 134, 161, 152, 151, 124)(117, 118, 142, 128, 123, 141)(119, 145, 150, 155, 159, 140)(121, 149, 146, 156, 143, 144)(125, 127, 139, 162, 153, 129)(132, 133, 158, 157, 135, 148)(163, 165, 175, 204, 187, 168)(164, 169, 189, 207, 198, 172)(166, 178, 209, 196, 191, 181)(167, 182, 212, 215, 210, 179)(170, 173, 200, 180, 211, 192)(171, 194, 183, 176, 206, 185)(174, 177, 208, 216, 199, 188)(184, 214, 197, 201, 202, 213)(186, 195, 203, 205, 190, 193) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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) :: { ( 4^6 ), ( 4^18 ) } Outer automorphisms :: reflexible Dual of E16.878 Graph:: simple bipartite v = 24 e = 108 f = 54 degree seq :: [ 6^18, 18^6 ] E16.876 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {6, 6, 9}) Quotient :: edge^2 Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y2^2 * Y1^-1)^2, (Y2 * Y1^-2)^2, Y2^6, Y1^6, Y2^-2 * Y1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-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, 110, 114, 126, 121, 112)(111, 117, 135, 153, 128, 119)(113, 123, 142, 161, 146, 124)(115, 129, 155, 139, 149, 131)(116, 132, 120, 136, 159, 133)(118, 137, 151, 145, 160, 134)(122, 144, 148, 162, 157, 140)(125, 141, 154, 130, 156, 147)(127, 150, 138, 158, 143, 152)(163, 165, 172, 192, 179, 167)(164, 169, 184, 211, 188, 170)(166, 174, 195, 209, 199, 176)(168, 181, 205, 200, 208, 182)(171, 190, 215, 216, 204, 183)(173, 193, 177, 187, 206, 194)(175, 196, 214, 189, 210, 197)(178, 185, 212, 186, 207, 198)(180, 202, 201, 213, 191, 203) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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) :: { ( 36, 36 ), ( 36^6 ) } Outer automorphisms :: reflexible Dual of E16.877 Graph:: simple bipartite v = 72 e = 108 f = 6 degree seq :: [ 2^54, 6^18 ] E16.877 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {6, 6, 9}) Quotient :: loop^2 Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y3^-2 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y3^-2, Y2 * Y3^-1 * Y1^2 * Y3 * Y2, Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y2^6, (Y2^2 * Y1^-1)^2, (Y2 * Y1^-2)^2, Y1^6, Y3^-1 * Y1^-1 * Y3^4 * Y2^-1 ] Map:: R = (1, 55, 109, 163, 4, 58, 112, 166, 17, 71, 125, 179, 38, 92, 146, 200, 32, 86, 140, 194, 33, 87, 141, 195, 40, 94, 148, 202, 12, 66, 120, 174, 7, 61, 115, 169)(2, 56, 110, 164, 9, 63, 117, 171, 6, 60, 114, 168, 24, 78, 132, 186, 19, 73, 127, 181, 39, 93, 147, 201, 48, 102, 156, 210, 26, 80, 134, 188, 11, 65, 119, 173)(3, 57, 111, 165, 5, 59, 113, 167, 21, 75, 129, 183, 51, 105, 159, 213, 27, 81, 135, 189, 16, 70, 124, 178, 18, 72, 126, 180, 41, 95, 149, 203, 15, 69, 123, 177)(8, 62, 116, 170, 29, 83, 137, 191, 10, 64, 118, 172, 35, 89, 143, 197, 23, 77, 131, 185, 53, 107, 161, 215, 25, 79, 133, 187, 37, 91, 145, 199, 31, 85, 139, 193)(13, 67, 121, 175, 14, 68, 122, 176, 45, 99, 153, 207, 49, 103, 157, 211, 46, 100, 154, 208, 20, 74, 128, 182, 22, 76, 130, 184, 47, 101, 155, 209, 43, 97, 151, 205)(28, 82, 136, 190, 44, 98, 152, 206, 30, 84, 138, 192, 50, 104, 158, 212, 34, 88, 142, 196, 42, 96, 150, 204, 36, 90, 144, 198, 54, 108, 162, 216, 52, 106, 160, 214) L = (1, 56)(2, 62)(3, 66)(4, 60)(5, 55)(6, 77)(7, 80)(8, 82)(9, 64)(10, 88)(11, 91)(12, 93)(13, 95)(14, 57)(15, 87)(16, 61)(17, 73)(18, 58)(19, 85)(20, 69)(21, 71)(22, 59)(23, 106)(24, 79)(25, 104)(26, 107)(27, 94)(28, 76)(29, 84)(30, 68)(31, 108)(32, 65)(33, 63)(34, 74)(35, 90)(36, 67)(37, 96)(38, 102)(39, 83)(40, 78)(41, 92)(42, 101)(43, 70)(44, 97)(45, 75)(46, 72)(47, 105)(48, 89)(49, 81)(50, 103)(51, 86)(52, 100)(53, 98)(54, 99)(109, 165)(110, 169)(111, 175)(112, 178)(113, 182)(114, 163)(115, 189)(116, 173)(117, 194)(118, 164)(119, 200)(120, 177)(121, 204)(122, 206)(123, 208)(124, 209)(125, 167)(126, 211)(127, 166)(128, 212)(129, 176)(130, 214)(131, 171)(132, 195)(133, 168)(134, 174)(135, 207)(136, 193)(137, 181)(138, 170)(139, 186)(140, 183)(141, 203)(142, 191)(143, 201)(144, 172)(145, 188)(146, 180)(147, 202)(148, 213)(149, 205)(150, 187)(151, 190)(152, 185)(153, 198)(154, 216)(155, 196)(156, 179)(157, 192)(158, 215)(159, 184)(160, 197)(161, 210)(162, 199) 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 ) } Outer automorphisms :: reflexible Dual of E16.876 Transitivity :: VT+ Graph:: bipartite v = 6 e = 108 f = 72 degree seq :: [ 36^6 ] E16.878 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {6, 6, 9}) Quotient :: loop^2 Aut^+ = (C9 : C3) : C2 (small group id <54, 6>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y2^2 * Y1^-1)^2, (Y2 * Y1^-2)^2, Y2^6, Y1^6, Y2^-2 * Y1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^9 ] Map:: polytopal non-degenerate R = (1, 55, 109, 163)(2, 56, 110, 164)(3, 57, 111, 165)(4, 58, 112, 166)(5, 59, 113, 167)(6, 60, 114, 168)(7, 61, 115, 169)(8, 62, 116, 170)(9, 63, 117, 171)(10, 64, 118, 172)(11, 65, 119, 173)(12, 66, 120, 174)(13, 67, 121, 175)(14, 68, 122, 176)(15, 69, 123, 177)(16, 70, 124, 178)(17, 71, 125, 179)(18, 72, 126, 180)(19, 73, 127, 181)(20, 74, 128, 182)(21, 75, 129, 183)(22, 76, 130, 184)(23, 77, 131, 185)(24, 78, 132, 186)(25, 79, 133, 187)(26, 80, 134, 188)(27, 81, 135, 189)(28, 82, 136, 190)(29, 83, 137, 191)(30, 84, 138, 192)(31, 85, 139, 193)(32, 86, 140, 194)(33, 87, 141, 195)(34, 88, 142, 196)(35, 89, 143, 197)(36, 90, 144, 198)(37, 91, 145, 199)(38, 92, 146, 200)(39, 93, 147, 201)(40, 94, 148, 202)(41, 95, 149, 203)(42, 96, 150, 204)(43, 97, 151, 205)(44, 98, 152, 206)(45, 99, 153, 207)(46, 100, 154, 208)(47, 101, 155, 209)(48, 102, 156, 210)(49, 103, 157, 211)(50, 104, 158, 212)(51, 105, 159, 213)(52, 106, 160, 214)(53, 107, 161, 215)(54, 108, 162, 216) L = (1, 56)(2, 60)(3, 63)(4, 55)(5, 69)(6, 72)(7, 75)(8, 78)(9, 81)(10, 83)(11, 57)(12, 82)(13, 58)(14, 90)(15, 88)(16, 59)(17, 87)(18, 67)(19, 96)(20, 65)(21, 101)(22, 102)(23, 61)(24, 66)(25, 62)(26, 64)(27, 99)(28, 105)(29, 97)(30, 104)(31, 95)(32, 68)(33, 100)(34, 107)(35, 98)(36, 94)(37, 106)(38, 70)(39, 71)(40, 108)(41, 77)(42, 84)(43, 91)(44, 73)(45, 74)(46, 76)(47, 85)(48, 93)(49, 86)(50, 89)(51, 79)(52, 80)(53, 92)(54, 103)(109, 165)(110, 169)(111, 172)(112, 174)(113, 163)(114, 181)(115, 184)(116, 164)(117, 190)(118, 192)(119, 193)(120, 195)(121, 196)(122, 166)(123, 187)(124, 185)(125, 167)(126, 202)(127, 205)(128, 168)(129, 171)(130, 211)(131, 212)(132, 207)(133, 206)(134, 170)(135, 210)(136, 215)(137, 203)(138, 179)(139, 177)(140, 173)(141, 209)(142, 214)(143, 175)(144, 178)(145, 176)(146, 208)(147, 213)(148, 201)(149, 180)(150, 183)(151, 200)(152, 194)(153, 198)(154, 182)(155, 199)(156, 197)(157, 188)(158, 186)(159, 191)(160, 189)(161, 216)(162, 204) local type(s) :: { ( 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E16.875 Transitivity :: VT+ Graph:: simple bipartite v = 54 e = 108 f = 24 degree seq :: [ 4^54 ] E16.879 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 18, 18}) Quotient :: edge Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^18 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 33, 39, 45, 51, 47, 41, 35, 29, 23, 17, 11, 5)(2, 6, 12, 18, 24, 30, 36, 42, 48, 53, 49, 43, 37, 31, 25, 19, 13, 7)(4, 8, 14, 20, 26, 32, 38, 44, 50, 54, 52, 46, 40, 34, 28, 22, 16, 10)(55, 56, 58)(57, 62, 60)(59, 64, 61)(63, 66, 68)(65, 67, 70)(69, 74, 72)(71, 76, 73)(75, 78, 80)(77, 79, 82)(81, 86, 84)(83, 88, 85)(87, 90, 92)(89, 91, 94)(93, 98, 96)(95, 100, 97)(99, 102, 104)(101, 103, 106)(105, 108, 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) :: { ( 36^3 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.883 Transitivity :: ET+ Graph:: simple bipartite v = 21 e = 54 f = 3 degree seq :: [ 3^18, 18^3 ] E16.880 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 18, 18}) Quotient :: edge Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1^-1, T2 * T1 * T2^-2 * T1^-1 * T2, T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1, T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, (T1^-1 * T2^-3)^2 ] Map:: non-degenerate R = (1, 3, 9, 24, 47, 31, 51, 29, 50, 54, 41, 19, 37, 16, 36, 35, 15, 5)(2, 6, 17, 38, 34, 14, 27, 10, 26, 48, 52, 30, 46, 28, 45, 43, 21, 7)(4, 11, 25, 49, 42, 20, 40, 18, 39, 53, 33, 13, 23, 8, 22, 44, 32, 12)(55, 56, 58)(57, 62, 64)(59, 67, 68)(60, 70, 72)(61, 73, 74)(63, 71, 79)(65, 82, 83)(66, 84, 85)(69, 75, 86)(76, 90, 99)(77, 91, 100)(78, 98, 102)(80, 93, 104)(81, 94, 105)(87, 95, 106)(88, 96, 101)(89, 107, 92)(97, 108, 103) 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) :: { ( 36^3 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.885 Transitivity :: ET+ Graph:: simple bipartite v = 21 e = 54 f = 3 degree seq :: [ 3^18, 18^3 ] E16.881 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 18, 18}) Quotient :: edge Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1^-1 * T2^-1, (T1^-1, T2^-1, T1), T2 * T1^-1 * T2^5 * T1^-1, (T2^-1 * T1^-1)^18 ] Map:: non-degenerate R = (1, 3, 9, 24, 41, 19, 37, 16, 36, 54, 51, 31, 49, 29, 48, 35, 15, 5)(2, 6, 17, 38, 50, 30, 46, 28, 45, 53, 34, 14, 27, 10, 26, 43, 21, 7)(4, 11, 25, 47, 33, 13, 23, 8, 22, 44, 42, 20, 40, 18, 39, 52, 32, 12)(55, 56, 58)(57, 62, 64)(59, 67, 68)(60, 70, 72)(61, 73, 74)(63, 71, 79)(65, 82, 83)(66, 84, 85)(69, 75, 86)(76, 90, 99)(77, 91, 100)(78, 98, 97)(80, 93, 102)(81, 94, 103)(87, 95, 104)(88, 96, 105)(89, 101, 107)(92, 108, 106) 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) :: { ( 36^3 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.884 Transitivity :: ET+ Graph:: simple bipartite v = 21 e = 54 f = 3 degree seq :: [ 3^18, 18^3 ] E16.882 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 18, 18}) Quotient :: edge Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-2 * T1 * T2^2 * T1^-1, T2^4 * T1^-2, (T2^-1 * T1^-1)^3, T1 * T2^2 * T1^7 ] Map:: polytopal non-degenerate R = (1, 3, 10, 20, 6, 19, 40, 52, 36, 51, 48, 54, 49, 34, 13, 30, 17, 5)(2, 7, 22, 38, 18, 37, 53, 47, 50, 45, 33, 46, 35, 14, 4, 12, 26, 8)(9, 27, 41, 32, 39, 25, 44, 23, 43, 24, 42, 21, 16, 31, 11, 29, 15, 28)(55, 56, 60, 72, 90, 104, 103, 89, 71, 80, 64, 76, 94, 107, 102, 87, 67, 58)(57, 63, 73, 93, 105, 97, 88, 70, 59, 69, 74, 95, 106, 98, 108, 96, 84, 65)(61, 75, 91, 83, 99, 81, 68, 79, 62, 78, 92, 85, 101, 82, 100, 86, 66, 77) 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) :: { ( 6^18 ) } Outer automorphisms :: reflexible Dual of E16.886 Transitivity :: ET+ Graph:: bipartite v = 6 e = 54 f = 18 degree seq :: [ 18^6 ] E16.883 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 18, 18}) Quotient :: loop Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^18 ] Map:: non-degenerate R = (1, 55, 3, 57, 9, 63, 15, 69, 21, 75, 27, 81, 33, 87, 39, 93, 45, 99, 51, 105, 47, 101, 41, 95, 35, 89, 29, 83, 23, 77, 17, 71, 11, 65, 5, 59)(2, 56, 6, 60, 12, 66, 18, 72, 24, 78, 30, 84, 36, 90, 42, 96, 48, 102, 53, 107, 49, 103, 43, 97, 37, 91, 31, 85, 25, 79, 19, 73, 13, 67, 7, 61)(4, 58, 8, 62, 14, 68, 20, 74, 26, 80, 32, 86, 38, 92, 44, 98, 50, 104, 54, 108, 52, 106, 46, 100, 40, 94, 34, 88, 28, 82, 22, 76, 16, 70, 10, 64) L = (1, 56)(2, 58)(3, 62)(4, 55)(5, 64)(6, 57)(7, 59)(8, 60)(9, 66)(10, 61)(11, 67)(12, 68)(13, 70)(14, 63)(15, 74)(16, 65)(17, 76)(18, 69)(19, 71)(20, 72)(21, 78)(22, 73)(23, 79)(24, 80)(25, 82)(26, 75)(27, 86)(28, 77)(29, 88)(30, 81)(31, 83)(32, 84)(33, 90)(34, 85)(35, 91)(36, 92)(37, 94)(38, 87)(39, 98)(40, 89)(41, 100)(42, 93)(43, 95)(44, 96)(45, 102)(46, 97)(47, 103)(48, 104)(49, 106)(50, 99)(51, 108)(52, 101)(53, 105)(54, 107) local type(s) :: { ( 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18 ) } Outer automorphisms :: reflexible Dual of E16.879 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 54 f = 21 degree seq :: [ 36^3 ] E16.884 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 18, 18}) Quotient :: loop Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1^-1, T2 * T1 * T2^-2 * T1^-1 * T2, T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1, T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, (T1^-1 * T2^-3)^2 ] Map:: non-degenerate R = (1, 55, 3, 57, 9, 63, 24, 78, 47, 101, 31, 85, 51, 105, 29, 83, 50, 104, 54, 108, 41, 95, 19, 73, 37, 91, 16, 70, 36, 90, 35, 89, 15, 69, 5, 59)(2, 56, 6, 60, 17, 71, 38, 92, 34, 88, 14, 68, 27, 81, 10, 64, 26, 80, 48, 102, 52, 106, 30, 84, 46, 100, 28, 82, 45, 99, 43, 97, 21, 75, 7, 61)(4, 58, 11, 65, 25, 79, 49, 103, 42, 96, 20, 74, 40, 94, 18, 72, 39, 93, 53, 107, 33, 87, 13, 67, 23, 77, 8, 62, 22, 76, 44, 98, 32, 86, 12, 66) L = (1, 56)(2, 58)(3, 62)(4, 55)(5, 67)(6, 70)(7, 73)(8, 64)(9, 71)(10, 57)(11, 82)(12, 84)(13, 68)(14, 59)(15, 75)(16, 72)(17, 79)(18, 60)(19, 74)(20, 61)(21, 86)(22, 90)(23, 91)(24, 98)(25, 63)(26, 93)(27, 94)(28, 83)(29, 65)(30, 85)(31, 66)(32, 69)(33, 95)(34, 96)(35, 107)(36, 99)(37, 100)(38, 89)(39, 104)(40, 105)(41, 106)(42, 101)(43, 108)(44, 102)(45, 76)(46, 77)(47, 88)(48, 78)(49, 97)(50, 80)(51, 81)(52, 87)(53, 92)(54, 103) local type(s) :: { ( 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18 ) } Outer automorphisms :: reflexible Dual of E16.881 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 54 f = 21 degree seq :: [ 36^3 ] E16.885 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 18, 18}) Quotient :: loop Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1^-1 * T2^-1, (T1^-1, T2^-1, T1), T2 * T1^-1 * T2^5 * T1^-1, (T2^-1 * T1^-1)^18 ] Map:: non-degenerate R = (1, 55, 3, 57, 9, 63, 24, 78, 41, 95, 19, 73, 37, 91, 16, 70, 36, 90, 54, 108, 51, 105, 31, 85, 49, 103, 29, 83, 48, 102, 35, 89, 15, 69, 5, 59)(2, 56, 6, 60, 17, 71, 38, 92, 50, 104, 30, 84, 46, 100, 28, 82, 45, 99, 53, 107, 34, 88, 14, 68, 27, 81, 10, 64, 26, 80, 43, 97, 21, 75, 7, 61)(4, 58, 11, 65, 25, 79, 47, 101, 33, 87, 13, 67, 23, 77, 8, 62, 22, 76, 44, 98, 42, 96, 20, 74, 40, 94, 18, 72, 39, 93, 52, 106, 32, 86, 12, 66) L = (1, 56)(2, 58)(3, 62)(4, 55)(5, 67)(6, 70)(7, 73)(8, 64)(9, 71)(10, 57)(11, 82)(12, 84)(13, 68)(14, 59)(15, 75)(16, 72)(17, 79)(18, 60)(19, 74)(20, 61)(21, 86)(22, 90)(23, 91)(24, 98)(25, 63)(26, 93)(27, 94)(28, 83)(29, 65)(30, 85)(31, 66)(32, 69)(33, 95)(34, 96)(35, 101)(36, 99)(37, 100)(38, 108)(39, 102)(40, 103)(41, 104)(42, 105)(43, 78)(44, 97)(45, 76)(46, 77)(47, 107)(48, 80)(49, 81)(50, 87)(51, 88)(52, 92)(53, 89)(54, 106) local type(s) :: { ( 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18 ) } Outer automorphisms :: reflexible Dual of E16.880 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 54 f = 21 degree seq :: [ 36^3 ] E16.886 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 18, 18}) Quotient :: loop Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2^-1 * T1, T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2^-1, (T2^-1 * T1^-3)^2 ] Map:: polytopal non-degenerate R = (1, 55, 3, 57, 5, 59)(2, 56, 7, 61, 8, 62)(4, 58, 11, 65, 13, 67)(6, 60, 17, 71, 18, 72)(9, 63, 23, 77, 24, 78)(10, 64, 25, 79, 27, 81)(12, 66, 26, 80, 30, 84)(14, 68, 32, 86, 33, 87)(15, 69, 34, 88, 35, 89)(16, 70, 37, 91, 38, 92)(19, 73, 41, 95, 42, 96)(20, 74, 43, 97, 44, 98)(21, 75, 45, 99, 46, 100)(22, 76, 47, 101, 48, 102)(28, 82, 49, 103, 53, 107)(29, 83, 52, 106, 39, 93)(31, 85, 51, 105, 36, 90)(40, 94, 50, 104, 54, 108) L = (1, 56)(2, 60)(3, 63)(4, 55)(5, 68)(6, 70)(7, 73)(8, 75)(9, 71)(10, 57)(11, 74)(12, 58)(13, 76)(14, 72)(15, 59)(16, 90)(17, 93)(18, 94)(19, 91)(20, 61)(21, 92)(22, 62)(23, 95)(24, 99)(25, 97)(26, 64)(27, 101)(28, 65)(29, 66)(30, 69)(31, 67)(32, 96)(33, 100)(34, 98)(35, 102)(36, 89)(37, 84)(38, 107)(39, 85)(40, 105)(41, 83)(42, 104)(43, 77)(44, 86)(45, 106)(46, 108)(47, 78)(48, 87)(49, 79)(50, 80)(51, 81)(52, 82)(53, 88)(54, 103) local type(s) :: { ( 18^6 ) } Outer automorphisms :: reflexible Dual of E16.882 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 18 e = 54 f = 6 degree seq :: [ 6^18 ] E16.887 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 18, 18}) Quotient :: dipole Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y3^-1, Y3 * Y2 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^18, Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 55, 2, 56, 4, 58)(3, 57, 8, 62, 6, 60)(5, 59, 10, 64, 7, 61)(9, 63, 12, 66, 14, 68)(11, 65, 13, 67, 16, 70)(15, 69, 20, 74, 18, 72)(17, 71, 22, 76, 19, 73)(21, 75, 24, 78, 26, 80)(23, 77, 25, 79, 28, 82)(27, 81, 32, 86, 30, 84)(29, 83, 34, 88, 31, 85)(33, 87, 36, 90, 38, 92)(35, 89, 37, 91, 40, 94)(39, 93, 44, 98, 42, 96)(41, 95, 46, 100, 43, 97)(45, 99, 48, 102, 50, 104)(47, 101, 49, 103, 52, 106)(51, 105, 54, 108, 53, 107)(109, 163, 111, 165, 117, 171, 123, 177, 129, 183, 135, 189, 141, 195, 147, 201, 153, 207, 159, 213, 155, 209, 149, 203, 143, 197, 137, 191, 131, 185, 125, 179, 119, 173, 113, 167)(110, 164, 114, 168, 120, 174, 126, 180, 132, 186, 138, 192, 144, 198, 150, 204, 156, 210, 161, 215, 157, 211, 151, 205, 145, 199, 139, 193, 133, 187, 127, 181, 121, 175, 115, 169)(112, 166, 116, 170, 122, 176, 128, 182, 134, 188, 140, 194, 146, 200, 152, 206, 158, 212, 162, 216, 160, 214, 154, 208, 148, 202, 142, 196, 136, 190, 130, 184, 124, 178, 118, 172) L = (1, 112)(2, 109)(3, 114)(4, 110)(5, 115)(6, 116)(7, 118)(8, 111)(9, 122)(10, 113)(11, 124)(12, 117)(13, 119)(14, 120)(15, 126)(16, 121)(17, 127)(18, 128)(19, 130)(20, 123)(21, 134)(22, 125)(23, 136)(24, 129)(25, 131)(26, 132)(27, 138)(28, 133)(29, 139)(30, 140)(31, 142)(32, 135)(33, 146)(34, 137)(35, 148)(36, 141)(37, 143)(38, 144)(39, 150)(40, 145)(41, 151)(42, 152)(43, 154)(44, 147)(45, 158)(46, 149)(47, 160)(48, 153)(49, 155)(50, 156)(51, 161)(52, 157)(53, 162)(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) :: { ( 2, 36, 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.892 Graph:: bipartite v = 21 e = 108 f = 57 degree seq :: [ 6^18, 36^3 ] E16.888 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 18, 18}) Quotient :: dipole Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^2 * Y3 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y2 * Y3^-1, Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, (Y1^-1, Y2, Y1^-1), Y2 * Y3 * Y2^5 * Y1^-1, Y2^2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1, (Y3 * Y2^-1)^18 ] Map:: R = (1, 55, 2, 56, 4, 58)(3, 57, 8, 62, 10, 64)(5, 59, 13, 67, 14, 68)(6, 60, 16, 70, 18, 72)(7, 61, 19, 73, 20, 74)(9, 63, 17, 71, 25, 79)(11, 65, 28, 82, 29, 83)(12, 66, 30, 84, 31, 85)(15, 69, 21, 75, 32, 86)(22, 76, 36, 90, 45, 99)(23, 77, 37, 91, 46, 100)(24, 78, 44, 98, 43, 97)(26, 80, 39, 93, 48, 102)(27, 81, 40, 94, 49, 103)(33, 87, 41, 95, 50, 104)(34, 88, 42, 96, 51, 105)(35, 89, 47, 101, 53, 107)(38, 92, 54, 108, 52, 106)(109, 163, 111, 165, 117, 171, 132, 186, 149, 203, 127, 181, 145, 199, 124, 178, 144, 198, 162, 216, 159, 213, 139, 193, 157, 211, 137, 191, 156, 210, 143, 197, 123, 177, 113, 167)(110, 164, 114, 168, 125, 179, 146, 200, 158, 212, 138, 192, 154, 208, 136, 190, 153, 207, 161, 215, 142, 196, 122, 176, 135, 189, 118, 172, 134, 188, 151, 205, 129, 183, 115, 169)(112, 166, 119, 173, 133, 187, 155, 209, 141, 195, 121, 175, 131, 185, 116, 170, 130, 184, 152, 206, 150, 204, 128, 182, 148, 202, 126, 180, 147, 201, 160, 214, 140, 194, 120, 174) L = (1, 112)(2, 109)(3, 118)(4, 110)(5, 122)(6, 126)(7, 128)(8, 111)(9, 133)(10, 116)(11, 137)(12, 139)(13, 113)(14, 121)(15, 140)(16, 114)(17, 117)(18, 124)(19, 115)(20, 127)(21, 123)(22, 153)(23, 154)(24, 151)(25, 125)(26, 156)(27, 157)(28, 119)(29, 136)(30, 120)(31, 138)(32, 129)(33, 158)(34, 159)(35, 161)(36, 130)(37, 131)(38, 160)(39, 134)(40, 135)(41, 141)(42, 142)(43, 152)(44, 132)(45, 144)(46, 145)(47, 143)(48, 147)(49, 148)(50, 149)(51, 150)(52, 162)(53, 155)(54, 146)(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, 36, 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.893 Graph:: bipartite v = 21 e = 108 f = 57 degree seq :: [ 6^18, 36^3 ] E16.889 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 18, 18}) Quotient :: dipole Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^3, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-2 * Y1 * Y2, Y3 * Y2^-2 * Y3^-1 * Y2^2, (Y2^-1 * R * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y2^-1 * Y3^2 * Y1^-1 * Y2 * Y3, Y3 * Y2^-3 * Y1^-1 * Y2^-3, Y3 * Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2, Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1, Y2 * Y1^-1 * Y2^2 * Y3^-3 * Y2 * Y3^-1 * Y2 * Y1^-1 * Y2 ] Map:: R = (1, 55, 2, 56, 4, 58)(3, 57, 8, 62, 10, 64)(5, 59, 13, 67, 14, 68)(6, 60, 16, 70, 18, 72)(7, 61, 19, 73, 20, 74)(9, 63, 17, 71, 25, 79)(11, 65, 28, 82, 29, 83)(12, 66, 30, 84, 31, 85)(15, 69, 21, 75, 32, 86)(22, 76, 36, 90, 45, 99)(23, 77, 37, 91, 46, 100)(24, 78, 44, 98, 48, 102)(26, 80, 39, 93, 50, 104)(27, 81, 40, 94, 51, 105)(33, 87, 41, 95, 52, 106)(34, 88, 42, 96, 47, 101)(35, 89, 53, 107, 38, 92)(43, 97, 54, 108, 49, 103)(109, 163, 111, 165, 117, 171, 132, 186, 155, 209, 139, 193, 159, 213, 137, 191, 158, 212, 162, 216, 149, 203, 127, 181, 145, 199, 124, 178, 144, 198, 143, 197, 123, 177, 113, 167)(110, 164, 114, 168, 125, 179, 146, 200, 142, 196, 122, 176, 135, 189, 118, 172, 134, 188, 156, 210, 160, 214, 138, 192, 154, 208, 136, 190, 153, 207, 151, 205, 129, 183, 115, 169)(112, 166, 119, 173, 133, 187, 157, 211, 150, 204, 128, 182, 148, 202, 126, 180, 147, 201, 161, 215, 141, 195, 121, 175, 131, 185, 116, 170, 130, 184, 152, 206, 140, 194, 120, 174) L = (1, 112)(2, 109)(3, 118)(4, 110)(5, 122)(6, 126)(7, 128)(8, 111)(9, 133)(10, 116)(11, 137)(12, 139)(13, 113)(14, 121)(15, 140)(16, 114)(17, 117)(18, 124)(19, 115)(20, 127)(21, 123)(22, 153)(23, 154)(24, 156)(25, 125)(26, 158)(27, 159)(28, 119)(29, 136)(30, 120)(31, 138)(32, 129)(33, 160)(34, 155)(35, 146)(36, 130)(37, 131)(38, 161)(39, 134)(40, 135)(41, 141)(42, 142)(43, 157)(44, 132)(45, 144)(46, 145)(47, 150)(48, 152)(49, 162)(50, 147)(51, 148)(52, 149)(53, 143)(54, 151)(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, 36, 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.894 Graph:: bipartite v = 21 e = 108 f = 57 degree seq :: [ 6^18, 36^3 ] E16.890 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 18, 18}) Quotient :: dipole Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y2^2 * Y1^-4, (Y2^-1 * Y1^2)^2, (Y3^-1 * Y1^-1)^3, Y1^-1 * Y2 * Y1^-1 * Y2^-3 * Y1^-1 * Y2^-1 ] Map:: R = (1, 55, 2, 56, 6, 60, 18, 72, 10, 64, 22, 76, 38, 92, 50, 104, 47, 101, 53, 107, 49, 103, 54, 108, 48, 102, 33, 87, 17, 71, 26, 80, 13, 67, 4, 58)(3, 57, 9, 63, 19, 73, 37, 91, 29, 83, 43, 97, 51, 105, 42, 96, 52, 106, 39, 93, 35, 89, 41, 95, 32, 86, 16, 70, 5, 59, 15, 69, 20, 74, 11, 65)(7, 61, 21, 75, 36, 90, 34, 88, 40, 94, 31, 85, 46, 100, 28, 82, 45, 99, 30, 84, 44, 98, 27, 81, 14, 68, 25, 79, 8, 62, 24, 78, 12, 66, 23, 77)(109, 163, 111, 165, 118, 172, 137, 191, 155, 209, 160, 214, 156, 210, 140, 194, 121, 175, 128, 182, 114, 168, 127, 181, 146, 200, 159, 213, 157, 211, 143, 197, 125, 179, 113, 167)(110, 164, 115, 169, 130, 184, 148, 202, 161, 215, 153, 207, 141, 195, 122, 176, 112, 166, 120, 174, 126, 180, 144, 198, 158, 212, 154, 208, 162, 216, 152, 206, 134, 188, 116, 170)(117, 171, 135, 189, 151, 205, 132, 186, 147, 201, 129, 183, 124, 178, 139, 193, 119, 173, 138, 192, 145, 199, 133, 187, 150, 204, 131, 185, 149, 203, 142, 196, 123, 177, 136, 190) L = (1, 111)(2, 115)(3, 118)(4, 120)(5, 109)(6, 127)(7, 130)(8, 110)(9, 135)(10, 137)(11, 138)(12, 126)(13, 128)(14, 112)(15, 136)(16, 139)(17, 113)(18, 144)(19, 146)(20, 114)(21, 124)(22, 148)(23, 149)(24, 147)(25, 150)(26, 116)(27, 151)(28, 117)(29, 155)(30, 145)(31, 119)(32, 121)(33, 122)(34, 123)(35, 125)(36, 158)(37, 133)(38, 159)(39, 129)(40, 161)(41, 142)(42, 131)(43, 132)(44, 134)(45, 141)(46, 162)(47, 160)(48, 140)(49, 143)(50, 154)(51, 157)(52, 156)(53, 153)(54, 152)(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, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 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 E16.891 Graph:: bipartite v = 6 e = 108 f = 72 degree seq :: [ 36^6 ] E16.891 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 18, 18}) Quotient :: dipole Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |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 * Y2^-1 * Y3^-2 * Y2 * Y3, (Y3^-2 * Y2^-1 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, (Y3^-1 * Y1^-1)^18, (Y3 * Y2^-1)^18 ] 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, 112, 166)(111, 165, 116, 170, 118, 172)(113, 167, 121, 175, 122, 176)(114, 168, 124, 178, 126, 180)(115, 169, 127, 181, 128, 182)(117, 171, 125, 179, 133, 187)(119, 173, 136, 190, 137, 191)(120, 174, 138, 192, 139, 193)(123, 177, 129, 183, 140, 194)(130, 184, 144, 198, 153, 207)(131, 185, 145, 199, 154, 208)(132, 186, 152, 206, 156, 210)(134, 188, 147, 201, 158, 212)(135, 189, 148, 202, 159, 213)(141, 195, 149, 203, 160, 214)(142, 196, 150, 204, 155, 209)(143, 197, 161, 215, 146, 200)(151, 205, 162, 216, 157, 211) L = (1, 111)(2, 114)(3, 117)(4, 119)(5, 109)(6, 125)(7, 110)(8, 130)(9, 132)(10, 134)(11, 133)(12, 112)(13, 131)(14, 135)(15, 113)(16, 144)(17, 146)(18, 147)(19, 145)(20, 148)(21, 115)(22, 152)(23, 116)(24, 155)(25, 157)(26, 156)(27, 118)(28, 153)(29, 158)(30, 154)(31, 159)(32, 120)(33, 121)(34, 122)(35, 123)(36, 143)(37, 124)(38, 142)(39, 161)(40, 126)(41, 127)(42, 128)(43, 129)(44, 140)(45, 151)(46, 136)(47, 139)(48, 160)(49, 150)(50, 162)(51, 137)(52, 138)(53, 141)(54, 149)(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) :: { ( 36, 36 ), ( 36^6 ) } Outer automorphisms :: reflexible Dual of E16.890 Graph:: simple bipartite v = 72 e = 108 f = 6 degree seq :: [ 2^54, 6^18 ] E16.892 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 18, 18}) Quotient :: dipole Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^18 ] Map:: R = (1, 55, 2, 56, 6, 60, 12, 66, 18, 72, 24, 78, 30, 84, 36, 90, 42, 96, 48, 102, 47, 101, 41, 95, 35, 89, 29, 83, 23, 77, 17, 71, 11, 65, 4, 58)(3, 57, 8, 62, 13, 67, 20, 74, 25, 79, 32, 86, 37, 91, 44, 98, 49, 103, 54, 108, 51, 105, 45, 99, 39, 93, 33, 87, 27, 81, 21, 75, 15, 69, 9, 63)(5, 59, 7, 61, 14, 68, 19, 73, 26, 80, 31, 85, 38, 92, 43, 97, 50, 104, 53, 107, 52, 106, 46, 100, 40, 94, 34, 88, 28, 82, 22, 76, 16, 70, 10, 64)(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, 113)(4, 118)(5, 109)(6, 121)(7, 116)(8, 110)(9, 112)(10, 117)(11, 123)(12, 127)(13, 122)(14, 114)(15, 124)(16, 119)(17, 130)(18, 133)(19, 128)(20, 120)(21, 125)(22, 129)(23, 135)(24, 139)(25, 134)(26, 126)(27, 136)(28, 131)(29, 142)(30, 145)(31, 140)(32, 132)(33, 137)(34, 141)(35, 147)(36, 151)(37, 146)(38, 138)(39, 148)(40, 143)(41, 154)(42, 157)(43, 152)(44, 144)(45, 149)(46, 153)(47, 159)(48, 161)(49, 158)(50, 150)(51, 160)(52, 155)(53, 162)(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) :: { ( 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E16.887 Graph:: simple bipartite v = 57 e = 108 f = 21 degree seq :: [ 2^54, 36^3 ] E16.893 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 18, 18}) Quotient :: dipole Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1^-2 * Y3 * Y1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1 * Y3 * Y1^5 * Y3, (Y3, Y1^-1, Y3^-1) ] Map:: R = (1, 55, 2, 56, 6, 60, 16, 70, 36, 90, 35, 89, 48, 102, 33, 87, 46, 100, 54, 108, 49, 103, 25, 79, 43, 97, 23, 77, 41, 95, 29, 83, 12, 66, 4, 58)(3, 57, 9, 63, 17, 71, 39, 93, 31, 85, 13, 67, 22, 76, 8, 62, 21, 75, 38, 92, 53, 107, 34, 88, 44, 98, 32, 86, 42, 96, 50, 104, 26, 80, 10, 64)(5, 59, 14, 68, 18, 72, 40, 94, 51, 105, 27, 81, 47, 101, 24, 78, 45, 99, 52, 106, 28, 82, 11, 65, 20, 74, 7, 61, 19, 73, 37, 91, 30, 84, 15, 69)(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, 113)(4, 119)(5, 109)(6, 125)(7, 116)(8, 110)(9, 131)(10, 133)(11, 121)(12, 134)(13, 112)(14, 140)(15, 142)(16, 145)(17, 126)(18, 114)(19, 149)(20, 151)(21, 153)(22, 155)(23, 132)(24, 117)(25, 135)(26, 138)(27, 118)(28, 157)(29, 160)(30, 120)(31, 159)(32, 141)(33, 122)(34, 143)(35, 123)(36, 139)(37, 146)(38, 124)(39, 137)(40, 158)(41, 150)(42, 127)(43, 152)(44, 128)(45, 154)(46, 129)(47, 156)(48, 130)(49, 161)(50, 162)(51, 144)(52, 147)(53, 136)(54, 148)(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) :: { ( 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E16.888 Graph:: simple bipartite v = 57 e = 108 f = 21 degree seq :: [ 2^54, 36^3 ] E16.894 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 18, 18}) Quotient :: dipole Aut^+ = C9 x S3 (small group id <54, 4>) Aut = S3 x D18 (small group id <108, 16>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1 * Y3 * Y1^-2 * Y3^-1 * Y1, (Y3^-1, Y1^-1, Y3), (Y1^-3 * Y3)^2, (Y3^-1 * Y1^-1)^18 ] Map:: R = (1, 55, 2, 56, 6, 60, 16, 70, 36, 90, 25, 79, 43, 97, 23, 77, 41, 95, 54, 108, 53, 107, 35, 89, 48, 102, 33, 87, 46, 100, 29, 83, 12, 66, 4, 58)(3, 57, 9, 63, 17, 71, 39, 93, 50, 104, 34, 88, 44, 98, 32, 86, 42, 96, 51, 105, 31, 85, 13, 67, 22, 76, 8, 62, 21, 75, 38, 92, 26, 80, 10, 64)(5, 59, 14, 68, 18, 72, 40, 94, 28, 82, 11, 65, 20, 74, 7, 61, 19, 73, 37, 91, 49, 103, 27, 81, 47, 101, 24, 78, 45, 99, 52, 106, 30, 84, 15, 69)(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, 113)(4, 119)(5, 109)(6, 125)(7, 116)(8, 110)(9, 131)(10, 133)(11, 121)(12, 134)(13, 112)(14, 140)(15, 142)(16, 145)(17, 126)(18, 114)(19, 149)(20, 151)(21, 153)(22, 155)(23, 132)(24, 117)(25, 135)(26, 138)(27, 118)(28, 144)(29, 148)(30, 120)(31, 157)(32, 141)(33, 122)(34, 143)(35, 123)(36, 158)(37, 146)(38, 124)(39, 162)(40, 159)(41, 150)(42, 127)(43, 152)(44, 128)(45, 154)(46, 129)(47, 156)(48, 130)(49, 161)(50, 136)(51, 137)(52, 147)(53, 139)(54, 160)(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) :: { ( 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E16.889 Graph:: simple bipartite v = 57 e = 108 f = 21 degree seq :: [ 2^54, 36^3 ] E16.895 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 18, 18}) Quotient :: edge Aut^+ = C18 x C3 (small group id <54, 9>) Aut = C2 x ((C9 x C3) : C2) (small group id <108, 27>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^18 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 26, 32, 38, 44, 50, 47, 41, 35, 29, 23, 17, 11, 5)(2, 6, 12, 18, 24, 30, 36, 42, 48, 53, 49, 43, 37, 31, 25, 19, 13, 7)(4, 9, 15, 21, 27, 33, 39, 45, 51, 54, 52, 46, 40, 34, 28, 22, 16, 10)(55, 56, 58)(57, 60, 63)(59, 61, 64)(62, 66, 69)(65, 67, 70)(68, 72, 75)(71, 73, 76)(74, 78, 81)(77, 79, 82)(80, 84, 87)(83, 85, 88)(86, 90, 93)(89, 91, 94)(92, 96, 99)(95, 97, 100)(98, 102, 105)(101, 103, 106)(104, 107, 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) :: { ( 36^3 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.896 Transitivity :: ET+ Graph:: simple bipartite v = 21 e = 54 f = 3 degree seq :: [ 3^18, 18^3 ] E16.896 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 18, 18}) Quotient :: loop Aut^+ = C18 x C3 (small group id <54, 9>) Aut = C2 x ((C9 x C3) : C2) (small group id <108, 27>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^18 ] Map:: non-degenerate R = (1, 55, 3, 57, 8, 62, 14, 68, 20, 74, 26, 80, 32, 86, 38, 92, 44, 98, 50, 104, 47, 101, 41, 95, 35, 89, 29, 83, 23, 77, 17, 71, 11, 65, 5, 59)(2, 56, 6, 60, 12, 66, 18, 72, 24, 78, 30, 84, 36, 90, 42, 96, 48, 102, 53, 107, 49, 103, 43, 97, 37, 91, 31, 85, 25, 79, 19, 73, 13, 67, 7, 61)(4, 58, 9, 63, 15, 69, 21, 75, 27, 81, 33, 87, 39, 93, 45, 99, 51, 105, 54, 108, 52, 106, 46, 100, 40, 94, 34, 88, 28, 82, 22, 76, 16, 70, 10, 64) L = (1, 56)(2, 58)(3, 60)(4, 55)(5, 61)(6, 63)(7, 64)(8, 66)(9, 57)(10, 59)(11, 67)(12, 69)(13, 70)(14, 72)(15, 62)(16, 65)(17, 73)(18, 75)(19, 76)(20, 78)(21, 68)(22, 71)(23, 79)(24, 81)(25, 82)(26, 84)(27, 74)(28, 77)(29, 85)(30, 87)(31, 88)(32, 90)(33, 80)(34, 83)(35, 91)(36, 93)(37, 94)(38, 96)(39, 86)(40, 89)(41, 97)(42, 99)(43, 100)(44, 102)(45, 92)(46, 95)(47, 103)(48, 105)(49, 106)(50, 107)(51, 98)(52, 101)(53, 108)(54, 104) local type(s) :: { ( 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18 ) } Outer automorphisms :: reflexible Dual of E16.895 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 54 f = 21 degree seq :: [ 36^3 ] E16.897 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 18, 18}) Quotient :: dipole Aut^+ = C18 x C3 (small group id <54, 9>) Aut = C2 x ((C9 x C3) : C2) (small group id <108, 27>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3^18, Y2^18 ] Map:: R = (1, 55, 2, 56, 4, 58)(3, 57, 6, 60, 9, 63)(5, 59, 7, 61, 10, 64)(8, 62, 12, 66, 15, 69)(11, 65, 13, 67, 16, 70)(14, 68, 18, 72, 21, 75)(17, 71, 19, 73, 22, 76)(20, 74, 24, 78, 27, 81)(23, 77, 25, 79, 28, 82)(26, 80, 30, 84, 33, 87)(29, 83, 31, 85, 34, 88)(32, 86, 36, 90, 39, 93)(35, 89, 37, 91, 40, 94)(38, 92, 42, 96, 45, 99)(41, 95, 43, 97, 46, 100)(44, 98, 48, 102, 51, 105)(47, 101, 49, 103, 52, 106)(50, 104, 53, 107, 54, 108)(109, 163, 111, 165, 116, 170, 122, 176, 128, 182, 134, 188, 140, 194, 146, 200, 152, 206, 158, 212, 155, 209, 149, 203, 143, 197, 137, 191, 131, 185, 125, 179, 119, 173, 113, 167)(110, 164, 114, 168, 120, 174, 126, 180, 132, 186, 138, 192, 144, 198, 150, 204, 156, 210, 161, 215, 157, 211, 151, 205, 145, 199, 139, 193, 133, 187, 127, 181, 121, 175, 115, 169)(112, 166, 117, 171, 123, 177, 129, 183, 135, 189, 141, 195, 147, 201, 153, 207, 159, 213, 162, 216, 160, 214, 154, 208, 148, 202, 142, 196, 136, 190, 130, 184, 124, 178, 118, 172) L = (1, 112)(2, 109)(3, 117)(4, 110)(5, 118)(6, 111)(7, 113)(8, 123)(9, 114)(10, 115)(11, 124)(12, 116)(13, 119)(14, 129)(15, 120)(16, 121)(17, 130)(18, 122)(19, 125)(20, 135)(21, 126)(22, 127)(23, 136)(24, 128)(25, 131)(26, 141)(27, 132)(28, 133)(29, 142)(30, 134)(31, 137)(32, 147)(33, 138)(34, 139)(35, 148)(36, 140)(37, 143)(38, 153)(39, 144)(40, 145)(41, 154)(42, 146)(43, 149)(44, 159)(45, 150)(46, 151)(47, 160)(48, 152)(49, 155)(50, 162)(51, 156)(52, 157)(53, 158)(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, 36, 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.898 Graph:: bipartite v = 21 e = 108 f = 57 degree seq :: [ 6^18, 36^3 ] E16.898 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 18, 18}) Quotient :: dipole Aut^+ = C18 x C3 (small group id <54, 9>) Aut = C2 x ((C9 x C3) : C2) (small group id <108, 27>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^-18, Y1^18 ] Map:: R = (1, 55, 2, 56, 6, 60, 12, 66, 18, 72, 24, 78, 30, 84, 36, 90, 42, 96, 48, 102, 46, 100, 40, 94, 34, 88, 28, 82, 22, 76, 16, 70, 10, 64, 4, 58)(3, 57, 7, 61, 13, 67, 19, 73, 25, 79, 31, 85, 37, 91, 43, 97, 49, 103, 53, 107, 51, 105, 45, 99, 39, 93, 33, 87, 27, 81, 21, 75, 15, 69, 9, 63)(5, 59, 8, 62, 14, 68, 20, 74, 26, 80, 32, 86, 38, 92, 44, 98, 50, 104, 54, 108, 52, 106, 47, 101, 41, 95, 35, 89, 29, 83, 23, 77, 17, 71, 11, 65)(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, 113)(4, 117)(5, 109)(6, 121)(7, 116)(8, 110)(9, 119)(10, 123)(11, 112)(12, 127)(13, 122)(14, 114)(15, 125)(16, 129)(17, 118)(18, 133)(19, 128)(20, 120)(21, 131)(22, 135)(23, 124)(24, 139)(25, 134)(26, 126)(27, 137)(28, 141)(29, 130)(30, 145)(31, 140)(32, 132)(33, 143)(34, 147)(35, 136)(36, 151)(37, 146)(38, 138)(39, 149)(40, 153)(41, 142)(42, 157)(43, 152)(44, 144)(45, 155)(46, 159)(47, 148)(48, 161)(49, 158)(50, 150)(51, 160)(52, 154)(53, 162)(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) :: { ( 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E16.897 Graph:: simple bipartite v = 57 e = 108 f = 21 degree seq :: [ 2^54, 36^3 ] E16.899 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 18, 18}) Quotient :: edge Aut^+ = C2 x (C9 : C3) (small group id <54, 11>) Aut = C2 x (C9 : C3) (small group id <54, 11>) |r| :: 1 Presentation :: [ X1^3, X2^-2 * X1 * X2 * X1 * X2 * X1, X2^2 * X1 * X2^-1 * X1 * X2^-1 * X1, X2^-1 * X1 * X2^-1 * X1 * X2^2 * X1, X2 * X1 * X2^-2 * X1 * X2 * X1, X2^2 * X1 * X2^4 * X1^-1 ] Map:: non-degenerate R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 16, 18)(7, 19, 20)(9, 24, 26)(11, 29, 31)(12, 32, 33)(15, 39, 40)(17, 27, 43)(21, 38, 48)(22, 30, 44)(23, 37, 46)(25, 42, 51)(28, 45, 35)(34, 47, 36)(41, 49, 53)(50, 52, 54)(55, 57, 63, 79, 101, 74, 100, 83, 97, 108, 102, 86, 99, 72, 98, 95, 69, 59)(56, 60, 71, 96, 93, 87, 77, 62, 76, 104, 90, 67, 89, 85, 78, 103, 75, 61)(58, 65, 84, 105, 92, 68, 91, 70, 80, 106, 94, 73, 82, 64, 81, 107, 88, 66) 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) :: { ( 36^3 ), ( 36^18 ) } Outer automorphisms :: chiral Dual of E16.900 Transitivity :: ET+ Graph:: simple bipartite v = 21 e = 54 f = 3 degree seq :: [ 3^18, 18^3 ] E16.900 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 18, 18}) Quotient :: loop Aut^+ = C2 x (C9 : C3) (small group id <54, 11>) Aut = C2 x (C9 : C3) (small group id <54, 11>) |r| :: 1 Presentation :: [ X2^2 * X1^-1 * X2 * X1^-2, X1^-3 * X2^-3, (X2^-1 * X1^-1)^3, X2^-1 * X1^4 * X2^-2 * X1^-1, X2^-2 * X1^-1 * X2^-2 * X1^-1 * X2 * X1^-1, X1^-1 * X2^-1 * X1^-1 * X2^4 * X1^-1 ] Map:: non-degenerate R = (1, 55, 2, 56, 6, 60, 18, 72, 40, 94, 39, 93, 52, 106, 29, 83, 47, 101, 54, 108, 53, 107, 33, 87, 50, 104, 38, 92, 51, 105, 31, 85, 13, 67, 4, 58)(3, 57, 9, 63, 27, 81, 17, 71, 35, 89, 12, 66, 34, 88, 43, 97, 19, 73, 42, 96, 36, 90, 45, 99, 23, 77, 7, 61, 21, 75, 46, 100, 26, 80, 11, 65)(5, 59, 15, 69, 32, 86, 41, 95, 22, 76, 48, 102, 25, 79, 8, 62, 24, 78, 49, 103, 28, 82, 14, 68, 37, 91, 44, 98, 20, 74, 10, 64, 30, 84, 16, 70) L = (1, 57)(2, 61)(3, 64)(4, 66)(5, 55)(6, 73)(7, 76)(8, 56)(9, 82)(10, 85)(11, 86)(12, 78)(13, 90)(14, 58)(15, 92)(16, 93)(17, 59)(18, 71)(19, 68)(20, 60)(21, 70)(22, 67)(23, 103)(24, 105)(25, 106)(26, 62)(27, 102)(28, 94)(29, 63)(30, 107)(31, 100)(32, 101)(33, 65)(34, 95)(35, 98)(36, 69)(37, 104)(38, 97)(39, 99)(40, 80)(41, 72)(42, 79)(43, 84)(44, 83)(45, 74)(46, 91)(47, 75)(48, 87)(49, 108)(50, 77)(51, 81)(52, 88)(53, 89)(54, 96) local type(s) :: { ( 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18 ) } Outer automorphisms :: chiral Dual of E16.899 Transitivity :: ET+ VT+ Graph:: v = 3 e = 54 f = 21 degree seq :: [ 36^3 ] E16.901 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 3}) Quotient :: dipole Aut^+ = A5 (small group id <60, 5>) Aut = S5 (small group id <120, 34>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, (Y1 * Y3 * Y2)^2, (Y3 * Y2^-1)^3, (Y3 * Y1)^3, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2, Y1 * Y2 * Y1 * R * Y2^-1 * Y1 * Y3 * R, Y3 * Y1 * Y2 * Y3 * Y2 * Y1 * Y2^-1 * Y1, Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 11, 71)(5, 65, 14, 74)(6, 66, 16, 76)(7, 67, 18, 78)(8, 68, 21, 81)(10, 70, 26, 86)(12, 72, 22, 82)(13, 73, 31, 91)(15, 75, 19, 79)(17, 77, 39, 99)(20, 80, 44, 104)(23, 83, 49, 109)(24, 84, 50, 110)(25, 85, 51, 111)(27, 87, 42, 102)(28, 88, 45, 105)(29, 89, 40, 100)(30, 90, 46, 106)(32, 92, 41, 101)(33, 93, 43, 103)(34, 94, 54, 114)(35, 95, 56, 116)(36, 96, 53, 113)(37, 97, 57, 117)(38, 98, 52, 112)(47, 107, 55, 115)(48, 108, 58, 118)(59, 119, 60, 120)(121, 181, 123, 183, 125, 185)(122, 182, 126, 186, 128, 188)(124, 184, 132, 192, 133, 193)(127, 187, 139, 199, 140, 200)(129, 189, 143, 203, 145, 205)(130, 190, 147, 207, 148, 208)(131, 191, 149, 209, 144, 204)(134, 194, 152, 212, 154, 214)(135, 195, 155, 215, 150, 210)(136, 196, 156, 216, 158, 218)(137, 197, 160, 220, 161, 221)(138, 198, 162, 222, 157, 217)(141, 201, 165, 225, 167, 227)(142, 202, 168, 228, 163, 223)(146, 206, 172, 232, 153, 213)(151, 211, 173, 233, 174, 234)(159, 219, 171, 231, 166, 226)(164, 224, 169, 229, 175, 235)(170, 230, 176, 236, 179, 239)(177, 237, 178, 238, 180, 240) L = (1, 124)(2, 127)(3, 130)(4, 121)(5, 135)(6, 137)(7, 122)(8, 142)(9, 144)(10, 123)(11, 138)(12, 150)(13, 147)(14, 153)(15, 125)(16, 157)(17, 126)(18, 131)(19, 163)(20, 160)(21, 166)(22, 128)(23, 156)(24, 129)(25, 162)(26, 170)(27, 133)(28, 155)(29, 158)(30, 132)(31, 171)(32, 175)(33, 134)(34, 176)(35, 148)(36, 143)(37, 136)(38, 149)(39, 177)(40, 140)(41, 168)(42, 145)(43, 139)(44, 172)(45, 174)(46, 141)(47, 178)(48, 161)(49, 179)(50, 146)(51, 151)(52, 164)(53, 180)(54, 165)(55, 152)(56, 154)(57, 159)(58, 167)(59, 169)(60, 173)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 6^4 ), ( 6^6 ) } Outer automorphisms :: reflexible Dual of E16.902 Graph:: simple bipartite v = 50 e = 120 f = 40 degree seq :: [ 4^30, 6^20 ] E16.902 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 3}) Quotient :: dipole Aut^+ = A5 (small group id <60, 5>) Aut = S5 (small group id <120, 34>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^3, Y1^3, (Y1^-1 * Y3)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y3 * Y2)^2, Y1^-1 * Y2 * Y3 * Y2 * Y1 * Y2^-1, (R * Y2 * Y3)^2, (Y3 * Y2 * Y1^-1)^2, Y2 * Y3 * Y2 * Y1 * Y2^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 5, 65)(3, 63, 10, 70, 12, 72)(4, 64, 13, 73, 8, 68)(6, 66, 18, 78, 20, 80)(7, 67, 21, 81, 23, 83)(9, 69, 26, 86, 28, 88)(11, 71, 32, 92, 30, 90)(14, 74, 37, 97, 27, 87)(15, 75, 31, 91, 22, 82)(16, 76, 38, 98, 39, 99)(17, 77, 40, 100, 42, 102)(19, 79, 36, 96, 43, 103)(24, 84, 50, 110, 41, 101)(25, 85, 48, 108, 35, 95)(29, 89, 53, 113, 45, 105)(33, 93, 44, 104, 54, 114)(34, 94, 56, 116, 57, 117)(46, 106, 55, 115, 58, 118)(47, 107, 59, 119, 52, 112)(49, 109, 51, 111, 60, 120)(121, 181, 123, 183, 126, 186)(122, 182, 127, 187, 129, 189)(124, 184, 134, 194, 135, 195)(125, 185, 136, 196, 137, 197)(128, 188, 144, 204, 145, 205)(130, 190, 149, 209, 151, 211)(131, 191, 143, 203, 153, 213)(132, 192, 154, 214, 155, 215)(133, 193, 156, 216, 152, 212)(138, 198, 157, 217, 164, 224)(139, 199, 165, 225, 148, 208)(140, 200, 161, 221, 166, 226)(141, 201, 167, 227, 168, 228)(142, 202, 159, 219, 169, 229)(146, 206, 170, 230, 171, 231)(147, 207, 172, 232, 162, 222)(150, 210, 158, 218, 175, 235)(160, 220, 163, 223, 176, 236)(173, 233, 179, 239, 178, 238)(174, 234, 177, 237, 180, 240) L = (1, 124)(2, 128)(3, 131)(4, 121)(5, 133)(6, 139)(7, 142)(8, 122)(9, 147)(10, 150)(11, 123)(12, 152)(13, 125)(14, 148)(15, 143)(16, 155)(17, 161)(18, 163)(19, 126)(20, 156)(21, 151)(22, 127)(23, 135)(24, 162)(25, 159)(26, 157)(27, 129)(28, 134)(29, 174)(30, 130)(31, 141)(32, 132)(33, 165)(34, 166)(35, 136)(36, 140)(37, 146)(38, 168)(39, 145)(40, 170)(41, 137)(42, 144)(43, 138)(44, 173)(45, 153)(46, 154)(47, 180)(48, 158)(49, 172)(50, 160)(51, 179)(52, 169)(53, 164)(54, 149)(55, 177)(56, 178)(57, 175)(58, 176)(59, 171)(60, 167)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.901 Graph:: simple bipartite v = 40 e = 120 f = 50 degree seq :: [ 6^40 ] E16.903 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {4, 6, 12}) Quotient :: edge Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C3 x (C5 : C4) (small group id <60, 6>) |r| :: 1 Presentation :: [ X1^4, X1^4, X2^-1 * X1^-1 * X2^2 * X1 * X2^-1, X2^6, X2 * X1 * X2 * X1^2 * X2 * X1^-1, X2 * X1^-2 * X2 * X1^3 * X2 * X1 ] Map:: non-degenerate R = (1, 2, 6, 4)(3, 9, 25, 11)(5, 14, 37, 15)(7, 19, 38, 21)(8, 22, 26, 23)(10, 20, 41, 29)(12, 32, 56, 33)(13, 34, 58, 35)(16, 24, 43, 36)(17, 40, 48, 39)(18, 42, 44, 30)(27, 51, 46, 52)(28, 50, 57, 53)(31, 55, 60, 45)(47, 54, 49, 59)(61, 63, 70, 88, 76, 65)(62, 67, 80, 106, 84, 68)(64, 72, 89, 114, 96, 73)(66, 77, 101, 115, 103, 78)(69, 86, 110, 98, 74, 87)(71, 90, 113, 99, 75, 91)(79, 104, 112, 108, 82, 105)(81, 95, 111, 93, 83, 107)(85, 94, 117, 92, 97, 109)(100, 118, 120, 116, 102, 119) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 24^4 ), ( 24^6 ) } Outer automorphisms :: chiral Dual of E16.908 Transitivity :: ET+ Graph:: simple bipartite v = 25 e = 60 f = 5 degree seq :: [ 4^15, 6^10 ] E16.904 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {4, 6, 12}) Quotient :: edge Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C3 x (C5 : C4) (small group id <60, 6>) |r| :: 1 Presentation :: [ X2^4 * X1^-2, X1^6, X1^-1 * X2 * X1^2 * X2^-1 * X1^-1, X2 * X1 * X2^-2 * X1 * X2^-1 * X1^-1, (X2^-1 * X1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 2, 6, 18, 13, 4)(3, 9, 19, 45, 32, 11)(5, 15, 20, 47, 35, 16)(7, 21, 43, 34, 12, 23)(8, 24, 44, 36, 14, 25)(10, 29, 46, 42, 17, 30)(22, 49, 37, 40, 26, 38)(27, 52, 56, 51, 31, 50)(28, 53, 48, 41, 33, 39)(54, 59, 60, 58, 55, 57)(61, 63, 70, 80, 66, 79, 106, 95, 73, 92, 77, 65)(62, 67, 82, 104, 78, 103, 97, 74, 64, 72, 86, 68)(69, 87, 81, 108, 105, 116, 94, 93, 71, 91, 83, 88)(75, 98, 117, 113, 107, 109, 119, 101, 76, 100, 118, 99)(84, 89, 114, 112, 96, 102, 120, 111, 85, 90, 115, 110) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 8^6 ), ( 8^12 ) } Outer automorphisms :: chiral Dual of E16.906 Transitivity :: ET+ Graph:: bipartite v = 15 e = 60 f = 15 degree seq :: [ 6^10, 12^5 ] E16.905 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {4, 6, 12}) Quotient :: edge Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C3 x (C5 : C4) (small group id <60, 6>) |r| :: 1 Presentation :: [ X2^4, X2^-2 * X1^-2 * X2 * X1^-1, X2 * X1 * X2^-1 * X1^-3 * X2^-1 * X1^-1, X2 * X1^-3 * X2^-1 * X1 * X2^-1 * X1^-1, X1 * X2 * X1^2 * X2^-1 * X1^-1 * X2 * X1 ] Map:: non-degenerate R = (1, 2, 6, 17, 39, 38, 52, 26, 47, 32, 13, 4)(3, 9, 25, 51, 35, 14, 34, 54, 58, 41, 29, 11)(5, 15, 31, 56, 57, 49, 22, 7, 20, 46, 27, 16)(8, 23, 10, 28, 53, 60, 43, 18, 42, 36, 48, 24)(12, 30, 55, 37, 40, 33, 50, 59, 45, 19, 44, 21)(61, 63, 70, 65)(62, 67, 81, 68)(64, 72, 91, 74)(66, 78, 71, 79)(69, 86, 105, 87)(73, 88, 114, 93)(75, 96, 115, 89)(76, 97, 113, 98)(77, 100, 82, 101)(80, 107, 118, 108)(83, 110, 85, 109)(84, 111, 90, 112)(92, 116, 119, 102)(94, 106, 120, 104)(95, 103, 117, 99) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 12^4 ), ( 12^12 ) } Outer automorphisms :: chiral Dual of E16.907 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 60 f = 10 degree seq :: [ 4^15, 12^5 ] E16.906 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {4, 6, 12}) Quotient :: loop Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C3 x (C5 : C4) (small group id <60, 6>) |r| :: 1 Presentation :: [ X1^4, X1^4, X2^-1 * X1^-1 * X2^2 * X1 * X2^-1, X2^6, X2 * X1 * X2 * X1^2 * X2 * X1^-1, X2 * X1^-2 * X2 * X1^3 * X2 * X1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 6, 66, 4, 64)(3, 63, 9, 69, 25, 85, 11, 71)(5, 65, 14, 74, 37, 97, 15, 75)(7, 67, 19, 79, 38, 98, 21, 81)(8, 68, 22, 82, 26, 86, 23, 83)(10, 70, 20, 80, 41, 101, 29, 89)(12, 72, 32, 92, 56, 116, 33, 93)(13, 73, 34, 94, 58, 118, 35, 95)(16, 76, 24, 84, 43, 103, 36, 96)(17, 77, 40, 100, 48, 108, 39, 99)(18, 78, 42, 102, 44, 104, 30, 90)(27, 87, 51, 111, 46, 106, 52, 112)(28, 88, 50, 110, 57, 117, 53, 113)(31, 91, 55, 115, 60, 120, 45, 105)(47, 107, 54, 114, 49, 109, 59, 119) L = (1, 63)(2, 67)(3, 70)(4, 72)(5, 61)(6, 77)(7, 80)(8, 62)(9, 86)(10, 88)(11, 90)(12, 89)(13, 64)(14, 87)(15, 91)(16, 65)(17, 101)(18, 66)(19, 104)(20, 106)(21, 95)(22, 105)(23, 107)(24, 68)(25, 94)(26, 110)(27, 69)(28, 76)(29, 114)(30, 113)(31, 71)(32, 97)(33, 83)(34, 117)(35, 111)(36, 73)(37, 109)(38, 74)(39, 75)(40, 118)(41, 115)(42, 119)(43, 78)(44, 112)(45, 79)(46, 84)(47, 81)(48, 82)(49, 85)(50, 98)(51, 93)(52, 108)(53, 99)(54, 96)(55, 103)(56, 102)(57, 92)(58, 120)(59, 100)(60, 116) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: chiral Dual of E16.904 Transitivity :: ET+ VT+ Graph:: simple v = 15 e = 60 f = 15 degree seq :: [ 8^15 ] E16.907 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {4, 6, 12}) Quotient :: loop Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C3 x (C5 : C4) (small group id <60, 6>) |r| :: 1 Presentation :: [ X2^4 * X1^-2, X1^6, X1^-1 * X2 * X1^2 * X2^-1 * X1^-1, X2 * X1 * X2^-2 * X1 * X2^-1 * X1^-1, (X2^-1 * X1^-1)^4 ] Map:: non-degenerate R = (1, 61, 2, 62, 6, 66, 18, 78, 13, 73, 4, 64)(3, 63, 9, 69, 19, 79, 45, 105, 32, 92, 11, 71)(5, 65, 15, 75, 20, 80, 47, 107, 35, 95, 16, 76)(7, 67, 21, 81, 43, 103, 34, 94, 12, 72, 23, 83)(8, 68, 24, 84, 44, 104, 36, 96, 14, 74, 25, 85)(10, 70, 29, 89, 46, 106, 42, 102, 17, 77, 30, 90)(22, 82, 49, 109, 37, 97, 40, 100, 26, 86, 38, 98)(27, 87, 52, 112, 56, 116, 51, 111, 31, 91, 50, 110)(28, 88, 53, 113, 48, 108, 41, 101, 33, 93, 39, 99)(54, 114, 59, 119, 60, 120, 58, 118, 55, 115, 57, 117) L = (1, 63)(2, 67)(3, 70)(4, 72)(5, 61)(6, 79)(7, 82)(8, 62)(9, 87)(10, 80)(11, 91)(12, 86)(13, 92)(14, 64)(15, 98)(16, 100)(17, 65)(18, 103)(19, 106)(20, 66)(21, 108)(22, 104)(23, 88)(24, 89)(25, 90)(26, 68)(27, 81)(28, 69)(29, 114)(30, 115)(31, 83)(32, 77)(33, 71)(34, 93)(35, 73)(36, 102)(37, 74)(38, 117)(39, 75)(40, 118)(41, 76)(42, 120)(43, 97)(44, 78)(45, 116)(46, 95)(47, 109)(48, 105)(49, 119)(50, 84)(51, 85)(52, 96)(53, 107)(54, 112)(55, 110)(56, 94)(57, 113)(58, 99)(59, 101)(60, 111) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: chiral Dual of E16.905 Transitivity :: ET+ VT+ Graph:: bipartite v = 10 e = 60 f = 20 degree seq :: [ 12^10 ] E16.908 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {4, 6, 12}) Quotient :: loop Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C3 x (C5 : C4) (small group id <60, 6>) |r| :: 1 Presentation :: [ X2^4, X2^-2 * X1^-2 * X2 * X1^-1, X2 * X1 * X2^-1 * X1^-3 * X2^-1 * X1^-1, X2 * X1^-3 * X2^-1 * X1 * X2^-1 * X1^-1, X1 * X2 * X1^2 * X2^-1 * X1^-1 * X2 * X1 ] Map:: non-degenerate R = (1, 61, 2, 62, 6, 66, 17, 77, 39, 99, 38, 98, 52, 112, 26, 86, 47, 107, 32, 92, 13, 73, 4, 64)(3, 63, 9, 69, 25, 85, 51, 111, 35, 95, 14, 74, 34, 94, 54, 114, 58, 118, 41, 101, 29, 89, 11, 71)(5, 65, 15, 75, 31, 91, 56, 116, 57, 117, 49, 109, 22, 82, 7, 67, 20, 80, 46, 106, 27, 87, 16, 76)(8, 68, 23, 83, 10, 70, 28, 88, 53, 113, 60, 120, 43, 103, 18, 78, 42, 102, 36, 96, 48, 108, 24, 84)(12, 72, 30, 90, 55, 115, 37, 97, 40, 100, 33, 93, 50, 110, 59, 119, 45, 105, 19, 79, 44, 104, 21, 81) L = (1, 63)(2, 67)(3, 70)(4, 72)(5, 61)(6, 78)(7, 81)(8, 62)(9, 86)(10, 65)(11, 79)(12, 91)(13, 88)(14, 64)(15, 96)(16, 97)(17, 100)(18, 71)(19, 66)(20, 107)(21, 68)(22, 101)(23, 110)(24, 111)(25, 109)(26, 105)(27, 69)(28, 114)(29, 75)(30, 112)(31, 74)(32, 116)(33, 73)(34, 106)(35, 103)(36, 115)(37, 113)(38, 76)(39, 95)(40, 82)(41, 77)(42, 92)(43, 117)(44, 94)(45, 87)(46, 120)(47, 118)(48, 80)(49, 83)(50, 85)(51, 90)(52, 84)(53, 98)(54, 93)(55, 89)(56, 119)(57, 99)(58, 108)(59, 102)(60, 104) 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 :: chiral Dual of E16.903 Transitivity :: ET+ VT+ Graph:: v = 5 e = 60 f = 25 degree seq :: [ 24^5 ] E16.909 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 10, 15}) Quotient :: edge Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1^-1, T2^3 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, (T2, T1^-1)^2, T1^-1 * T2^-3 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T2^10 ] Map:: non-degenerate R = (1, 3, 9, 24, 47, 56, 55, 35, 15, 5)(2, 6, 17, 38, 57, 51, 58, 43, 21, 7)(4, 11, 25, 48, 60, 46, 59, 44, 32, 12)(8, 22, 45, 31, 53, 29, 52, 33, 13, 23)(10, 26, 41, 19, 37, 16, 36, 34, 14, 27)(18, 39, 54, 30, 50, 28, 49, 42, 20, 40)(61, 62, 64)(63, 68, 70)(65, 73, 74)(66, 76, 78)(67, 79, 80)(69, 77, 85)(71, 88, 89)(72, 90, 91)(75, 81, 92)(82, 104, 99)(83, 106, 100)(84, 105, 101)(86, 109, 103)(87, 110, 111)(93, 108, 102)(94, 114, 98)(95, 112, 96)(97, 116, 113)(107, 117, 120)(115, 118, 119) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 30^3 ), ( 30^10 ) } Outer automorphisms :: reflexible Dual of E16.913 Transitivity :: ET+ Graph:: simple bipartite v = 26 e = 60 f = 4 degree seq :: [ 3^20, 10^6 ] E16.910 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 10, 15}) Quotient :: edge Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-3, (T1^-1 * T2^-1)^3, (T2^-1, T1^-1)^2, T1^10 ] Map:: polytopal non-degenerate R = (1, 3, 10, 6, 19, 41, 38, 59, 60, 55, 56, 32, 13, 17, 5)(2, 7, 21, 18, 39, 53, 58, 57, 50, 31, 33, 14, 4, 12, 8)(9, 25, 49, 40, 24, 48, 47, 23, 46, 37, 43, 29, 11, 28, 26)(15, 34, 52, 27, 51, 30, 54, 45, 22, 44, 42, 20, 16, 36, 35)(61, 62, 66, 78, 98, 118, 115, 91, 73, 64)(63, 69, 79, 100, 119, 107, 116, 97, 77, 71)(65, 75, 70, 87, 101, 114, 120, 104, 92, 76)(67, 80, 99, 95, 117, 112, 93, 90, 72, 82)(68, 83, 81, 103, 113, 88, 110, 85, 74, 84)(86, 102, 109, 96, 108, 94, 106, 111, 89, 105) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6^10 ), ( 6^15 ) } Outer automorphisms :: reflexible Dual of E16.914 Transitivity :: ET+ Graph:: bipartite v = 10 e = 60 f = 20 degree seq :: [ 10^6, 15^4 ] E16.911 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 10, 15}) Quotient :: edge Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2, T1^4 * T2 * T1 * T2, T2^-1 * T1 * T2 * T1 * T2^-1 * T1^3, (T1, T2^-1)^2 ] Map:: non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 11, 13)(6, 17, 18)(9, 24, 25)(10, 26, 28)(12, 31, 33)(14, 37, 38)(15, 39, 41)(16, 35, 42)(19, 32, 45)(20, 34, 47)(21, 49, 23)(22, 50, 51)(27, 54, 48)(29, 52, 55)(30, 40, 43)(36, 53, 56)(44, 58, 59)(46, 60, 57)(61, 62, 66, 76, 101, 111, 119, 116, 114, 120, 112, 84, 92, 72, 64)(63, 69, 83, 95, 73, 94, 104, 78, 103, 117, 110, 97, 105, 87, 70)(65, 74, 96, 102, 88, 115, 118, 109, 91, 106, 80, 67, 79, 100, 75)(68, 81, 108, 99, 107, 85, 113, 90, 71, 89, 98, 77, 93, 86, 82) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20^3 ), ( 20^15 ) } Outer automorphisms :: reflexible Dual of E16.912 Transitivity :: ET+ Graph:: simple bipartite v = 24 e = 60 f = 6 degree seq :: [ 3^20, 15^4 ] E16.912 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 10, 15}) Quotient :: loop Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1^-1, T2^3 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, (T2, T1^-1)^2, T1^-1 * T2^-3 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T2^10 ] Map:: non-degenerate R = (1, 61, 3, 63, 9, 69, 24, 84, 47, 107, 56, 116, 55, 115, 35, 95, 15, 75, 5, 65)(2, 62, 6, 66, 17, 77, 38, 98, 57, 117, 51, 111, 58, 118, 43, 103, 21, 81, 7, 67)(4, 64, 11, 71, 25, 85, 48, 108, 60, 120, 46, 106, 59, 119, 44, 104, 32, 92, 12, 72)(8, 68, 22, 82, 45, 105, 31, 91, 53, 113, 29, 89, 52, 112, 33, 93, 13, 73, 23, 83)(10, 70, 26, 86, 41, 101, 19, 79, 37, 97, 16, 76, 36, 96, 34, 94, 14, 74, 27, 87)(18, 78, 39, 99, 54, 114, 30, 90, 50, 110, 28, 88, 49, 109, 42, 102, 20, 80, 40, 100) L = (1, 62)(2, 64)(3, 68)(4, 61)(5, 73)(6, 76)(7, 79)(8, 70)(9, 77)(10, 63)(11, 88)(12, 90)(13, 74)(14, 65)(15, 81)(16, 78)(17, 85)(18, 66)(19, 80)(20, 67)(21, 92)(22, 104)(23, 106)(24, 105)(25, 69)(26, 109)(27, 110)(28, 89)(29, 71)(30, 91)(31, 72)(32, 75)(33, 108)(34, 114)(35, 112)(36, 95)(37, 116)(38, 94)(39, 82)(40, 83)(41, 84)(42, 93)(43, 86)(44, 99)(45, 101)(46, 100)(47, 117)(48, 102)(49, 103)(50, 111)(51, 87)(52, 96)(53, 97)(54, 98)(55, 118)(56, 113)(57, 120)(58, 119)(59, 115)(60, 107) local type(s) :: { ( 3, 15, 3, 15, 3, 15, 3, 15, 3, 15, 3, 15, 3, 15, 3, 15, 3, 15, 3, 15 ) } Outer automorphisms :: reflexible Dual of E16.911 Transitivity :: ET+ VT+ AT Graph:: v = 6 e = 60 f = 24 degree seq :: [ 20^6 ] E16.913 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 10, 15}) Quotient :: loop Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-3, (T1^-1 * T2^-1)^3, (T2^-1, T1^-1)^2, T1^10 ] Map:: non-degenerate R = (1, 61, 3, 63, 10, 70, 6, 66, 19, 79, 41, 101, 38, 98, 59, 119, 60, 120, 55, 115, 56, 116, 32, 92, 13, 73, 17, 77, 5, 65)(2, 62, 7, 67, 21, 81, 18, 78, 39, 99, 53, 113, 58, 118, 57, 117, 50, 110, 31, 91, 33, 93, 14, 74, 4, 64, 12, 72, 8, 68)(9, 69, 25, 85, 49, 109, 40, 100, 24, 84, 48, 108, 47, 107, 23, 83, 46, 106, 37, 97, 43, 103, 29, 89, 11, 71, 28, 88, 26, 86)(15, 75, 34, 94, 52, 112, 27, 87, 51, 111, 30, 90, 54, 114, 45, 105, 22, 82, 44, 104, 42, 102, 20, 80, 16, 76, 36, 96, 35, 95) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 75)(6, 78)(7, 80)(8, 83)(9, 79)(10, 87)(11, 63)(12, 82)(13, 64)(14, 84)(15, 70)(16, 65)(17, 71)(18, 98)(19, 100)(20, 99)(21, 103)(22, 67)(23, 81)(24, 68)(25, 74)(26, 102)(27, 101)(28, 110)(29, 105)(30, 72)(31, 73)(32, 76)(33, 90)(34, 106)(35, 117)(36, 108)(37, 77)(38, 118)(39, 95)(40, 119)(41, 114)(42, 109)(43, 113)(44, 92)(45, 86)(46, 111)(47, 116)(48, 94)(49, 96)(50, 85)(51, 89)(52, 93)(53, 88)(54, 120)(55, 91)(56, 97)(57, 112)(58, 115)(59, 107)(60, 104) local type(s) :: { ( 3, 10, 3, 10, 3, 10, 3, 10, 3, 10, 3, 10, 3, 10, 3, 10, 3, 10, 3, 10, 3, 10, 3, 10, 3, 10, 3, 10, 3, 10 ) } Outer automorphisms :: reflexible Dual of E16.909 Transitivity :: ET+ VT+ AT Graph:: v = 4 e = 60 f = 26 degree seq :: [ 30^4 ] E16.914 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 10, 15}) Quotient :: loop Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2, T1^4 * T2 * T1 * T2, T2^-1 * T1 * T2 * T1 * T2^-1 * T1^3, (T1, T2^-1)^2 ] Map:: polytopal non-degenerate R = (1, 61, 3, 63, 5, 65)(2, 62, 7, 67, 8, 68)(4, 64, 11, 71, 13, 73)(6, 66, 17, 77, 18, 78)(9, 69, 24, 84, 25, 85)(10, 70, 26, 86, 28, 88)(12, 72, 31, 91, 33, 93)(14, 74, 37, 97, 38, 98)(15, 75, 39, 99, 41, 101)(16, 76, 35, 95, 42, 102)(19, 79, 32, 92, 45, 105)(20, 80, 34, 94, 47, 107)(21, 81, 49, 109, 23, 83)(22, 82, 50, 110, 51, 111)(27, 87, 54, 114, 48, 108)(29, 89, 52, 112, 55, 115)(30, 90, 40, 100, 43, 103)(36, 96, 53, 113, 56, 116)(44, 104, 58, 118, 59, 119)(46, 106, 60, 120, 57, 117) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 74)(6, 76)(7, 79)(8, 81)(9, 83)(10, 63)(11, 89)(12, 64)(13, 94)(14, 96)(15, 65)(16, 101)(17, 93)(18, 103)(19, 100)(20, 67)(21, 108)(22, 68)(23, 95)(24, 92)(25, 113)(26, 82)(27, 70)(28, 115)(29, 98)(30, 71)(31, 106)(32, 72)(33, 86)(34, 104)(35, 73)(36, 102)(37, 105)(38, 77)(39, 107)(40, 75)(41, 111)(42, 88)(43, 117)(44, 78)(45, 87)(46, 80)(47, 85)(48, 99)(49, 91)(50, 97)(51, 119)(52, 84)(53, 90)(54, 120)(55, 118)(56, 114)(57, 110)(58, 109)(59, 116)(60, 112) local type(s) :: { ( 10, 15, 10, 15, 10, 15 ) } Outer automorphisms :: reflexible Dual of E16.910 Transitivity :: ET+ VT+ AT Graph:: simple v = 20 e = 60 f = 10 degree seq :: [ 6^20 ] E16.915 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15}) Quotient :: dipole Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-2 * Y3 * Y2^2, Y2 * Y1 * Y2^-2 * Y1^-1 * Y2, Y3 * Y2^-3 * Y3 * Y2^-1 * Y1^-1 * Y2^-1, Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y1^-1, Y3 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y2^3 * Y1^-1 * Y2 * Y1^-1, Y2^10 ] Map:: R = (1, 61, 2, 62, 4, 64)(3, 63, 8, 68, 10, 70)(5, 65, 13, 73, 14, 74)(6, 66, 16, 76, 18, 78)(7, 67, 19, 79, 20, 80)(9, 69, 17, 77, 25, 85)(11, 71, 28, 88, 29, 89)(12, 72, 30, 90, 31, 91)(15, 75, 21, 81, 32, 92)(22, 82, 44, 104, 39, 99)(23, 83, 46, 106, 40, 100)(24, 84, 45, 105, 41, 101)(26, 86, 49, 109, 43, 103)(27, 87, 50, 110, 51, 111)(33, 93, 48, 108, 42, 102)(34, 94, 54, 114, 38, 98)(35, 95, 52, 112, 36, 96)(37, 97, 56, 116, 53, 113)(47, 107, 57, 117, 60, 120)(55, 115, 58, 118, 59, 119)(121, 181, 123, 183, 129, 189, 144, 204, 167, 227, 176, 236, 175, 235, 155, 215, 135, 195, 125, 185)(122, 182, 126, 186, 137, 197, 158, 218, 177, 237, 171, 231, 178, 238, 163, 223, 141, 201, 127, 187)(124, 184, 131, 191, 145, 205, 168, 228, 180, 240, 166, 226, 179, 239, 164, 224, 152, 212, 132, 192)(128, 188, 142, 202, 165, 225, 151, 211, 173, 233, 149, 209, 172, 232, 153, 213, 133, 193, 143, 203)(130, 190, 146, 206, 161, 221, 139, 199, 157, 217, 136, 196, 156, 216, 154, 214, 134, 194, 147, 207)(138, 198, 159, 219, 174, 234, 150, 210, 170, 230, 148, 208, 169, 229, 162, 222, 140, 200, 160, 220) L = (1, 124)(2, 121)(3, 130)(4, 122)(5, 134)(6, 138)(7, 140)(8, 123)(9, 145)(10, 128)(11, 149)(12, 151)(13, 125)(14, 133)(15, 152)(16, 126)(17, 129)(18, 136)(19, 127)(20, 139)(21, 135)(22, 159)(23, 160)(24, 161)(25, 137)(26, 163)(27, 171)(28, 131)(29, 148)(30, 132)(31, 150)(32, 141)(33, 162)(34, 158)(35, 156)(36, 172)(37, 173)(38, 174)(39, 164)(40, 166)(41, 165)(42, 168)(43, 169)(44, 142)(45, 144)(46, 143)(47, 180)(48, 153)(49, 146)(50, 147)(51, 170)(52, 155)(53, 176)(54, 154)(55, 179)(56, 157)(57, 167)(58, 175)(59, 178)(60, 177)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 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 E16.918 Graph:: bipartite v = 26 e = 120 f = 64 degree seq :: [ 6^20, 20^6 ] E16.916 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15}) Quotient :: dipole Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^2 * Y2^-3, (Y1^-1 * Y2^-1)^3, (Y3^-1 * Y1^-1)^3, (Y1, Y2, Y1^-1), Y1^10 ] Map:: R = (1, 61, 2, 62, 6, 66, 18, 78, 38, 98, 58, 118, 55, 115, 31, 91, 13, 73, 4, 64)(3, 63, 9, 69, 19, 79, 40, 100, 59, 119, 47, 107, 56, 116, 37, 97, 17, 77, 11, 71)(5, 65, 15, 75, 10, 70, 27, 87, 41, 101, 54, 114, 60, 120, 44, 104, 32, 92, 16, 76)(7, 67, 20, 80, 39, 99, 35, 95, 57, 117, 52, 112, 33, 93, 30, 90, 12, 72, 22, 82)(8, 68, 23, 83, 21, 81, 43, 103, 53, 113, 28, 88, 50, 110, 25, 85, 14, 74, 24, 84)(26, 86, 42, 102, 49, 109, 36, 96, 48, 108, 34, 94, 46, 106, 51, 111, 29, 89, 45, 105)(121, 181, 123, 183, 130, 190, 126, 186, 139, 199, 161, 221, 158, 218, 179, 239, 180, 240, 175, 235, 176, 236, 152, 212, 133, 193, 137, 197, 125, 185)(122, 182, 127, 187, 141, 201, 138, 198, 159, 219, 173, 233, 178, 238, 177, 237, 170, 230, 151, 211, 153, 213, 134, 194, 124, 184, 132, 192, 128, 188)(129, 189, 145, 205, 169, 229, 160, 220, 144, 204, 168, 228, 167, 227, 143, 203, 166, 226, 157, 217, 163, 223, 149, 209, 131, 191, 148, 208, 146, 206)(135, 195, 154, 214, 172, 232, 147, 207, 171, 231, 150, 210, 174, 234, 165, 225, 142, 202, 164, 224, 162, 222, 140, 200, 136, 196, 156, 216, 155, 215) L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 139)(7, 141)(8, 122)(9, 145)(10, 126)(11, 148)(12, 128)(13, 137)(14, 124)(15, 154)(16, 156)(17, 125)(18, 159)(19, 161)(20, 136)(21, 138)(22, 164)(23, 166)(24, 168)(25, 169)(26, 129)(27, 171)(28, 146)(29, 131)(30, 174)(31, 153)(32, 133)(33, 134)(34, 172)(35, 135)(36, 155)(37, 163)(38, 179)(39, 173)(40, 144)(41, 158)(42, 140)(43, 149)(44, 162)(45, 142)(46, 157)(47, 143)(48, 167)(49, 160)(50, 151)(51, 150)(52, 147)(53, 178)(54, 165)(55, 176)(56, 152)(57, 170)(58, 177)(59, 180)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 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 E16.917 Graph:: bipartite v = 10 e = 120 f = 80 degree seq :: [ 20^6, 30^4 ] E16.917 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15}) Quotient :: dipole Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^-4 * Y2, Y3 * Y2 * Y3 * Y2 * Y3^-2 * Y2, Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y3^-3, (Y3^-1, Y2^-1)^2, (Y3^-1 * Y1^-1)^15 ] Map:: polytopal R = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)(121, 181, 122, 182, 124, 184)(123, 183, 128, 188, 130, 190)(125, 185, 133, 193, 134, 194)(126, 186, 136, 196, 138, 198)(127, 187, 139, 199, 140, 200)(129, 189, 144, 204, 146, 206)(131, 191, 149, 209, 151, 211)(132, 192, 152, 212, 153, 213)(135, 195, 159, 219, 160, 220)(137, 197, 162, 222, 164, 224)(141, 201, 158, 218, 170, 230)(142, 202, 150, 210, 171, 231)(143, 203, 167, 227, 166, 226)(145, 205, 163, 223, 156, 216)(147, 207, 165, 225, 161, 221)(148, 208, 168, 228, 155, 215)(154, 214, 169, 229, 176, 236)(157, 217, 175, 235, 174, 234)(172, 232, 177, 237, 179, 239)(173, 233, 178, 238, 180, 240) L = (1, 123)(2, 126)(3, 129)(4, 131)(5, 121)(6, 137)(7, 122)(8, 142)(9, 145)(10, 147)(11, 150)(12, 124)(13, 155)(14, 157)(15, 125)(16, 146)(17, 163)(18, 165)(19, 167)(20, 168)(21, 127)(22, 169)(23, 128)(24, 170)(25, 139)(26, 159)(27, 141)(28, 130)(29, 164)(30, 156)(31, 161)(32, 175)(33, 143)(34, 132)(35, 172)(36, 133)(37, 136)(38, 134)(39, 153)(40, 173)(41, 135)(42, 176)(43, 152)(44, 158)(45, 154)(46, 138)(47, 177)(48, 149)(49, 140)(50, 178)(51, 160)(52, 144)(53, 148)(54, 151)(55, 179)(56, 180)(57, 162)(58, 166)(59, 171)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 20, 30 ), ( 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E16.916 Graph:: simple bipartite v = 80 e = 120 f = 10 degree seq :: [ 2^60, 6^20 ] E16.918 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15}) Quotient :: dipole Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1^2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3, Y1^4 * Y3 * Y1 * Y3, Y3^-2 * Y1 * Y3^-3 * Y1^-1 * Y3^-1, (Y3^-1, Y1^-1)^2, Y3 * Y1^-3 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 61, 2, 62, 6, 66, 16, 76, 41, 101, 51, 111, 59, 119, 56, 116, 54, 114, 60, 120, 52, 112, 24, 84, 32, 92, 12, 72, 4, 64)(3, 63, 9, 69, 23, 83, 35, 95, 13, 73, 34, 94, 44, 104, 18, 78, 43, 103, 57, 117, 50, 110, 37, 97, 45, 105, 27, 87, 10, 70)(5, 65, 14, 74, 36, 96, 42, 102, 28, 88, 55, 115, 58, 118, 49, 109, 31, 91, 46, 106, 20, 80, 7, 67, 19, 79, 40, 100, 15, 75)(8, 68, 21, 81, 48, 108, 39, 99, 47, 107, 25, 85, 53, 113, 30, 90, 11, 71, 29, 89, 38, 98, 17, 77, 33, 93, 26, 86, 22, 82)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 127)(3, 125)(4, 131)(5, 121)(6, 137)(7, 128)(8, 122)(9, 144)(10, 146)(11, 133)(12, 151)(13, 124)(14, 157)(15, 159)(16, 155)(17, 138)(18, 126)(19, 152)(20, 154)(21, 169)(22, 170)(23, 141)(24, 145)(25, 129)(26, 148)(27, 174)(28, 130)(29, 172)(30, 160)(31, 153)(32, 165)(33, 132)(34, 167)(35, 162)(36, 173)(37, 158)(38, 134)(39, 161)(40, 163)(41, 135)(42, 136)(43, 150)(44, 178)(45, 139)(46, 180)(47, 140)(48, 147)(49, 143)(50, 171)(51, 142)(52, 175)(53, 176)(54, 168)(55, 149)(56, 156)(57, 166)(58, 179)(59, 164)(60, 177)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 6, 20 ), ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E16.915 Graph:: simple bipartite v = 64 e = 120 f = 26 degree seq :: [ 2^60, 30^4 ] E16.919 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15}) Quotient :: dipole Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3^2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y3^-1 * Y2^-1 * Y3^-1, Y2^-1 * Y1 * Y2^2 * Y3^-1 * Y2^-1 * Y3^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^2 * Y1, Y1 * Y2^4 * Y3^-1 * Y2, Y2^3 * Y3 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y3 * Y2^3 * Y1^-1, Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^10 ] Map:: R = (1, 61, 2, 62, 4, 64)(3, 63, 8, 68, 10, 70)(5, 65, 13, 73, 14, 74)(6, 66, 16, 76, 18, 78)(7, 67, 19, 79, 20, 80)(9, 69, 24, 84, 26, 86)(11, 71, 29, 89, 31, 91)(12, 72, 32, 92, 33, 93)(15, 75, 39, 99, 40, 100)(17, 77, 27, 87, 43, 103)(21, 81, 48, 108, 49, 109)(22, 82, 41, 101, 50, 110)(23, 83, 37, 97, 45, 105)(25, 85, 38, 98, 47, 107)(28, 88, 54, 114, 55, 115)(30, 90, 44, 104, 56, 116)(34, 94, 52, 112, 36, 96)(35, 95, 42, 102, 46, 106)(51, 111, 57, 117, 59, 119)(53, 113, 58, 118, 60, 120)(121, 181, 123, 183, 129, 189, 145, 205, 153, 213, 175, 235, 180, 240, 176, 236, 168, 228, 177, 237, 162, 222, 136, 196, 161, 221, 135, 195, 125, 185)(122, 182, 126, 186, 137, 197, 158, 218, 134, 194, 157, 217, 173, 233, 146, 206, 172, 232, 179, 239, 174, 234, 149, 209, 170, 230, 141, 201, 127, 187)(124, 184, 131, 191, 150, 210, 167, 227, 140, 200, 166, 226, 178, 238, 163, 223, 159, 219, 171, 231, 143, 203, 128, 188, 142, 202, 154, 214, 132, 192)(130, 190, 147, 207, 169, 229, 152, 212, 165, 225, 138, 198, 164, 224, 156, 216, 133, 193, 155, 215, 151, 211, 144, 204, 160, 220, 139, 199, 148, 208) L = (1, 124)(2, 121)(3, 130)(4, 122)(5, 134)(6, 138)(7, 140)(8, 123)(9, 146)(10, 128)(11, 151)(12, 153)(13, 125)(14, 133)(15, 160)(16, 126)(17, 163)(18, 136)(19, 127)(20, 139)(21, 169)(22, 170)(23, 165)(24, 129)(25, 167)(26, 144)(27, 137)(28, 175)(29, 131)(30, 176)(31, 149)(32, 132)(33, 152)(34, 156)(35, 166)(36, 172)(37, 143)(38, 145)(39, 135)(40, 159)(41, 142)(42, 155)(43, 147)(44, 150)(45, 157)(46, 162)(47, 158)(48, 141)(49, 168)(50, 161)(51, 179)(52, 154)(53, 180)(54, 148)(55, 174)(56, 164)(57, 171)(58, 173)(59, 177)(60, 178)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 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 E16.920 Graph:: bipartite v = 24 e = 120 f = 66 degree seq :: [ 6^20, 30^4 ] E16.920 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15}) Quotient :: dipole Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^-2 * Y3^3, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^3, (Y3^-1, Y1^-1)^2, Y1^10, (Y3 * Y2^-1)^15 ] Map:: R = (1, 61, 2, 62, 6, 66, 18, 78, 38, 98, 58, 118, 55, 115, 31, 91, 13, 73, 4, 64)(3, 63, 9, 69, 19, 79, 40, 100, 59, 119, 47, 107, 56, 116, 37, 97, 17, 77, 11, 71)(5, 65, 15, 75, 10, 70, 27, 87, 41, 101, 54, 114, 60, 120, 44, 104, 32, 92, 16, 76)(7, 67, 20, 80, 39, 99, 35, 95, 57, 117, 52, 112, 33, 93, 30, 90, 12, 72, 22, 82)(8, 68, 23, 83, 21, 81, 43, 103, 53, 113, 28, 88, 50, 110, 25, 85, 14, 74, 24, 84)(26, 86, 42, 102, 49, 109, 36, 96, 48, 108, 34, 94, 46, 106, 51, 111, 29, 89, 45, 105)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 139)(7, 141)(8, 122)(9, 145)(10, 126)(11, 148)(12, 128)(13, 137)(14, 124)(15, 154)(16, 156)(17, 125)(18, 159)(19, 161)(20, 136)(21, 138)(22, 164)(23, 166)(24, 168)(25, 169)(26, 129)(27, 171)(28, 146)(29, 131)(30, 174)(31, 153)(32, 133)(33, 134)(34, 172)(35, 135)(36, 155)(37, 163)(38, 179)(39, 173)(40, 144)(41, 158)(42, 140)(43, 149)(44, 162)(45, 142)(46, 157)(47, 143)(48, 167)(49, 160)(50, 151)(51, 150)(52, 147)(53, 178)(54, 165)(55, 176)(56, 152)(57, 170)(58, 177)(59, 180)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 6, 30 ), ( 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30 ) } Outer automorphisms :: reflexible Dual of E16.919 Graph:: simple bipartite v = 66 e = 120 f = 24 degree seq :: [ 2^60, 20^6 ] E16.921 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 32}) Quotient :: dipole Aut^+ = D64 (small group id <64, 52>) Aut = $<128, 991>$ (small group id <128, 991>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 5, 69)(4, 68, 8, 72)(6, 70, 10, 74)(7, 71, 11, 75)(9, 73, 13, 77)(12, 76, 16, 80)(14, 78, 18, 82)(15, 79, 19, 83)(17, 81, 21, 85)(20, 84, 24, 88)(22, 86, 26, 90)(23, 87, 27, 91)(25, 89, 29, 93)(28, 92, 32, 96)(30, 94, 33, 97)(31, 95, 36, 100)(34, 98, 49, 113)(35, 99, 52, 116)(37, 101, 53, 117)(38, 102, 56, 120)(39, 103, 54, 118)(40, 104, 55, 119)(41, 105, 57, 121)(42, 106, 58, 122)(43, 107, 59, 123)(44, 108, 60, 124)(45, 109, 61, 125)(46, 110, 62, 126)(47, 111, 63, 127)(48, 112, 64, 128)(50, 114, 51, 115)(129, 193, 131, 195)(130, 194, 133, 197)(132, 196, 135, 199)(134, 198, 137, 201)(136, 200, 139, 203)(138, 202, 141, 205)(140, 204, 143, 207)(142, 206, 145, 209)(144, 208, 147, 211)(146, 210, 149, 213)(148, 212, 151, 215)(150, 214, 153, 217)(152, 216, 155, 219)(154, 218, 157, 221)(156, 220, 159, 223)(158, 222, 177, 241)(160, 224, 164, 228)(161, 225, 162, 226)(163, 227, 166, 230)(165, 229, 167, 231)(168, 232, 170, 234)(169, 233, 171, 235)(172, 236, 174, 238)(173, 237, 175, 239)(176, 240, 179, 243)(178, 242, 192, 256)(180, 244, 184, 248)(181, 245, 182, 246)(183, 247, 186, 250)(185, 249, 187, 251)(188, 252, 190, 254)(189, 253, 191, 255) L = (1, 132)(2, 134)(3, 135)(4, 129)(5, 137)(6, 130)(7, 131)(8, 140)(9, 133)(10, 142)(11, 143)(12, 136)(13, 145)(14, 138)(15, 139)(16, 148)(17, 141)(18, 150)(19, 151)(20, 144)(21, 153)(22, 146)(23, 147)(24, 156)(25, 149)(26, 158)(27, 159)(28, 152)(29, 177)(30, 154)(31, 155)(32, 180)(33, 181)(34, 182)(35, 183)(36, 184)(37, 185)(38, 186)(39, 187)(40, 188)(41, 189)(42, 190)(43, 191)(44, 192)(45, 179)(46, 178)(47, 176)(48, 175)(49, 157)(50, 174)(51, 173)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E16.922 Graph:: simple bipartite v = 64 e = 128 f = 34 degree seq :: [ 4^64 ] E16.922 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 32}) Quotient :: dipole Aut^+ = D64 (small group id <64, 52>) Aut = $<128, 991>$ (small group id <128, 991>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, (R * Y3)^2, Y2 * Y3 * Y1^16, Y1^-1 * Y2 * Y1^7 * Y3 * Y1^-8 ] Map:: non-degenerate R = (1, 65, 2, 66, 6, 70, 13, 77, 21, 85, 29, 93, 37, 101, 45, 109, 53, 117, 61, 125, 58, 122, 50, 114, 42, 106, 34, 98, 26, 90, 18, 82, 10, 74, 16, 80, 24, 88, 32, 96, 40, 104, 48, 112, 56, 120, 64, 128, 60, 124, 52, 116, 44, 108, 36, 100, 28, 92, 20, 84, 12, 76, 5, 69)(3, 67, 9, 73, 17, 81, 25, 89, 33, 97, 41, 105, 49, 113, 57, 121, 63, 127, 55, 119, 47, 111, 39, 103, 31, 95, 23, 87, 15, 79, 8, 72, 4, 68, 11, 75, 19, 83, 27, 91, 35, 99, 43, 107, 51, 115, 59, 123, 62, 126, 54, 118, 46, 110, 38, 102, 30, 94, 22, 86, 14, 78, 7, 71)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 138, 202)(133, 197, 137, 201)(134, 198, 142, 206)(136, 200, 144, 208)(139, 203, 146, 210)(140, 204, 145, 209)(141, 205, 150, 214)(143, 207, 152, 216)(147, 211, 154, 218)(148, 212, 153, 217)(149, 213, 158, 222)(151, 215, 160, 224)(155, 219, 162, 226)(156, 220, 161, 225)(157, 221, 166, 230)(159, 223, 168, 232)(163, 227, 170, 234)(164, 228, 169, 233)(165, 229, 174, 238)(167, 231, 176, 240)(171, 235, 178, 242)(172, 236, 177, 241)(173, 237, 182, 246)(175, 239, 184, 248)(179, 243, 186, 250)(180, 244, 185, 249)(181, 245, 190, 254)(183, 247, 192, 256)(187, 251, 189, 253)(188, 252, 191, 255) L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 139)(6, 143)(7, 144)(8, 130)(9, 146)(10, 131)(11, 133)(12, 147)(13, 151)(14, 152)(15, 134)(16, 135)(17, 154)(18, 137)(19, 140)(20, 155)(21, 159)(22, 160)(23, 141)(24, 142)(25, 162)(26, 145)(27, 148)(28, 163)(29, 167)(30, 168)(31, 149)(32, 150)(33, 170)(34, 153)(35, 156)(36, 171)(37, 175)(38, 176)(39, 157)(40, 158)(41, 178)(42, 161)(43, 164)(44, 179)(45, 183)(46, 184)(47, 165)(48, 166)(49, 186)(50, 169)(51, 172)(52, 187)(53, 191)(54, 192)(55, 173)(56, 174)(57, 189)(58, 177)(59, 180)(60, 190)(61, 185)(62, 188)(63, 181)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^4 ), ( 4^64 ) } Outer automorphisms :: reflexible Dual of E16.921 Graph:: bipartite v = 34 e = 128 f = 64 degree seq :: [ 4^32, 64^2 ] E16.923 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 32}) Quotient :: edge Aut^+ = Q64 (small group id <64, 54>) Aut = $<128, 994>$ (small group id <128, 994>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^-1, T2^2 * T1^-2 * T2^-2 * T1^-2, T2^14 * T1^-1 * T2^-2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 58, 50, 42, 34, 26, 18, 10, 4, 11, 19, 27, 35, 43, 51, 59, 64, 56, 48, 40, 32, 24, 16, 8)(65, 66, 70, 68)(67, 72, 77, 74)(69, 71, 78, 75)(73, 80, 85, 82)(76, 79, 86, 83)(81, 88, 93, 90)(84, 87, 94, 91)(89, 96, 101, 98)(92, 95, 102, 99)(97, 104, 109, 106)(100, 103, 110, 107)(105, 112, 117, 114)(108, 111, 118, 115)(113, 120, 125, 122)(116, 119, 126, 123)(121, 128, 124, 127) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8^4 ), ( 8^32 ) } Outer automorphisms :: reflexible Dual of E16.924 Transitivity :: ET+ Graph:: bipartite v = 18 e = 64 f = 16 degree seq :: [ 4^16, 32^2 ] E16.924 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 32}) Quotient :: loop Aut^+ = Q64 (small group id <64, 54>) Aut = $<128, 994>$ (small group id <128, 994>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^2, T1^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-2 * T2^-1, T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 65, 3, 67, 6, 70, 5, 69)(2, 66, 7, 71, 4, 68, 8, 72)(9, 73, 13, 77, 10, 74, 14, 78)(11, 75, 15, 79, 12, 76, 16, 80)(17, 81, 21, 85, 18, 82, 22, 86)(19, 83, 23, 87, 20, 84, 24, 88)(25, 89, 29, 93, 26, 90, 30, 94)(27, 91, 31, 95, 28, 92, 32, 96)(33, 97, 37, 101, 34, 98, 38, 102)(35, 99, 39, 103, 36, 100, 40, 104)(41, 105, 45, 109, 42, 106, 46, 110)(43, 107, 47, 111, 44, 108, 48, 112)(49, 113, 53, 117, 50, 114, 54, 118)(51, 115, 55, 119, 52, 116, 56, 120)(57, 121, 61, 125, 58, 122, 62, 126)(59, 123, 63, 127, 60, 124, 64, 128) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 74)(6, 68)(7, 75)(8, 76)(9, 69)(10, 67)(11, 72)(12, 71)(13, 81)(14, 82)(15, 83)(16, 84)(17, 78)(18, 77)(19, 80)(20, 79)(21, 89)(22, 90)(23, 91)(24, 92)(25, 86)(26, 85)(27, 88)(28, 87)(29, 97)(30, 98)(31, 99)(32, 100)(33, 94)(34, 93)(35, 96)(36, 95)(37, 105)(38, 106)(39, 107)(40, 108)(41, 102)(42, 101)(43, 104)(44, 103)(45, 113)(46, 114)(47, 115)(48, 116)(49, 110)(50, 109)(51, 112)(52, 111)(53, 121)(54, 122)(55, 123)(56, 124)(57, 118)(58, 117)(59, 120)(60, 119)(61, 128)(62, 127)(63, 125)(64, 126) local type(s) :: { ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E16.923 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 64 f = 18 degree seq :: [ 8^16 ] E16.925 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 32}) Quotient :: dipole Aut^+ = Q64 (small group id <64, 54>) Aut = $<128, 994>$ (small group id <128, 994>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y1^4, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^7 * Y1^-1 * Y2^-9 * Y1^-1 ] Map:: R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 8, 72, 13, 77, 10, 74)(5, 69, 7, 71, 14, 78, 11, 75)(9, 73, 16, 80, 21, 85, 18, 82)(12, 76, 15, 79, 22, 86, 19, 83)(17, 81, 24, 88, 29, 93, 26, 90)(20, 84, 23, 87, 30, 94, 27, 91)(25, 89, 32, 96, 37, 101, 34, 98)(28, 92, 31, 95, 38, 102, 35, 99)(33, 97, 40, 104, 45, 109, 42, 106)(36, 100, 39, 103, 46, 110, 43, 107)(41, 105, 48, 112, 53, 117, 50, 114)(44, 108, 47, 111, 54, 118, 51, 115)(49, 113, 56, 120, 61, 125, 58, 122)(52, 116, 55, 119, 62, 126, 59, 123)(57, 121, 64, 128, 60, 124, 63, 127)(129, 193, 131, 195, 137, 201, 145, 209, 153, 217, 161, 225, 169, 233, 177, 241, 185, 249, 190, 254, 182, 246, 174, 238, 166, 230, 158, 222, 150, 214, 142, 206, 134, 198, 141, 205, 149, 213, 157, 221, 165, 229, 173, 237, 181, 245, 189, 253, 188, 252, 180, 244, 172, 236, 164, 228, 156, 220, 148, 212, 140, 204, 133, 197)(130, 194, 135, 199, 143, 207, 151, 215, 159, 223, 167, 231, 175, 239, 183, 247, 191, 255, 186, 250, 178, 242, 170, 234, 162, 226, 154, 218, 146, 210, 138, 202, 132, 196, 139, 203, 147, 211, 155, 219, 163, 227, 171, 235, 179, 243, 187, 251, 192, 256, 184, 248, 176, 240, 168, 232, 160, 224, 152, 216, 144, 208, 136, 200) L = (1, 131)(2, 135)(3, 137)(4, 139)(5, 129)(6, 141)(7, 143)(8, 130)(9, 145)(10, 132)(11, 147)(12, 133)(13, 149)(14, 134)(15, 151)(16, 136)(17, 153)(18, 138)(19, 155)(20, 140)(21, 157)(22, 142)(23, 159)(24, 144)(25, 161)(26, 146)(27, 163)(28, 148)(29, 165)(30, 150)(31, 167)(32, 152)(33, 169)(34, 154)(35, 171)(36, 156)(37, 173)(38, 158)(39, 175)(40, 160)(41, 177)(42, 162)(43, 179)(44, 164)(45, 181)(46, 166)(47, 183)(48, 168)(49, 185)(50, 170)(51, 187)(52, 172)(53, 189)(54, 174)(55, 191)(56, 176)(57, 190)(58, 178)(59, 192)(60, 180)(61, 188)(62, 182)(63, 186)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E16.926 Graph:: bipartite v = 18 e = 128 f = 80 degree seq :: [ 8^16, 64^2 ] E16.926 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 32}) Quotient :: dipole Aut^+ = Q64 (small group id <64, 54>) Aut = $<128, 994>$ (small group id <128, 994>) |r| :: 2 Presentation :: [ Y1, R^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3^2 * Y2^-2 * Y3^-2 * Y2^-2, Y3^14 * Y2^-1 * Y3^-2 * Y2^-1, (Y3^-1 * Y1^-1)^32 ] Map:: R = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)(129, 193, 130, 194, 134, 198, 132, 196)(131, 195, 136, 200, 141, 205, 138, 202)(133, 197, 135, 199, 142, 206, 139, 203)(137, 201, 144, 208, 149, 213, 146, 210)(140, 204, 143, 207, 150, 214, 147, 211)(145, 209, 152, 216, 157, 221, 154, 218)(148, 212, 151, 215, 158, 222, 155, 219)(153, 217, 160, 224, 165, 229, 162, 226)(156, 220, 159, 223, 166, 230, 163, 227)(161, 225, 168, 232, 173, 237, 170, 234)(164, 228, 167, 231, 174, 238, 171, 235)(169, 233, 176, 240, 181, 245, 178, 242)(172, 236, 175, 239, 182, 246, 179, 243)(177, 241, 184, 248, 189, 253, 186, 250)(180, 244, 183, 247, 190, 254, 187, 251)(185, 249, 192, 256, 188, 252, 191, 255) L = (1, 131)(2, 135)(3, 137)(4, 139)(5, 129)(6, 141)(7, 143)(8, 130)(9, 145)(10, 132)(11, 147)(12, 133)(13, 149)(14, 134)(15, 151)(16, 136)(17, 153)(18, 138)(19, 155)(20, 140)(21, 157)(22, 142)(23, 159)(24, 144)(25, 161)(26, 146)(27, 163)(28, 148)(29, 165)(30, 150)(31, 167)(32, 152)(33, 169)(34, 154)(35, 171)(36, 156)(37, 173)(38, 158)(39, 175)(40, 160)(41, 177)(42, 162)(43, 179)(44, 164)(45, 181)(46, 166)(47, 183)(48, 168)(49, 185)(50, 170)(51, 187)(52, 172)(53, 189)(54, 174)(55, 191)(56, 176)(57, 190)(58, 178)(59, 192)(60, 180)(61, 188)(62, 182)(63, 186)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64 ) } Outer automorphisms :: reflexible Dual of E16.925 Graph:: simple bipartite v = 80 e = 128 f = 18 degree seq :: [ 2^64, 8^16 ] E16.927 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 64, 64}) Quotient :: regular Aut^+ = C64 (small group id <64, 1>) Aut = $<128, 161>$ (small group id <128, 161>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^32 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 40, 36, 33, 34, 37, 41, 44, 47, 49, 51, 53, 62, 59, 56, 57, 55, 31, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 30, 46, 43, 39, 35, 38, 42, 45, 48, 50, 52, 54, 64, 63, 61, 58, 60, 32, 28, 24, 20, 16, 12, 8, 4) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 46)(32, 55)(33, 35)(34, 38)(36, 39)(37, 42)(40, 43)(41, 45)(44, 48)(47, 50)(49, 52)(51, 54)(53, 64)(56, 58)(57, 60)(59, 61)(62, 63) local type(s) :: { ( 64^64 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 32 f = 1 degree seq :: [ 64 ] E16.928 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 64, 64}) Quotient :: edge Aut^+ = C64 (small group id <64, 1>) Aut = $<128, 161>$ (small group id <128, 161>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^32 * T1 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 38, 34, 37, 41, 43, 45, 47, 49, 51, 61, 57, 54, 56, 60, 63, 53, 30, 26, 22, 18, 14, 10, 6, 2, 5, 9, 13, 17, 21, 25, 29, 40, 36, 33, 35, 39, 42, 44, 46, 48, 50, 52, 59, 55, 58, 62, 64, 32, 28, 24, 20, 16, 12, 8, 4)(65, 66)(67, 69)(68, 70)(71, 73)(72, 74)(75, 77)(76, 78)(79, 81)(80, 82)(83, 85)(84, 86)(87, 89)(88, 90)(91, 93)(92, 94)(95, 104)(96, 117)(97, 98)(99, 101)(100, 102)(103, 105)(106, 107)(108, 109)(110, 111)(112, 113)(114, 115)(116, 125)(118, 119)(120, 122)(121, 123)(124, 126)(127, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 128, 128 ), ( 128^64 ) } Outer automorphisms :: reflexible Dual of E16.929 Transitivity :: ET+ Graph:: bipartite v = 33 e = 64 f = 1 degree seq :: [ 2^32, 64 ] E16.929 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 64, 64}) Quotient :: loop Aut^+ = C64 (small group id <64, 1>) Aut = $<128, 161>$ (small group id <128, 161>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^32 * T1 ] Map:: R = (1, 65, 3, 67, 7, 71, 11, 75, 15, 79, 19, 83, 23, 87, 27, 91, 31, 95, 35, 99, 37, 101, 39, 103, 41, 105, 43, 107, 45, 109, 47, 111, 50, 114, 51, 115, 53, 117, 55, 119, 57, 121, 59, 123, 61, 125, 63, 127, 49, 113, 30, 94, 26, 90, 22, 86, 18, 82, 14, 78, 10, 74, 6, 70, 2, 66, 5, 69, 9, 73, 13, 77, 17, 81, 21, 85, 25, 89, 29, 93, 33, 97, 34, 98, 36, 100, 38, 102, 40, 104, 42, 106, 44, 108, 46, 110, 48, 112, 52, 116, 54, 118, 56, 120, 58, 122, 60, 124, 62, 126, 64, 128, 32, 96, 28, 92, 24, 88, 20, 84, 16, 80, 12, 76, 8, 72, 4, 68) 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, 97)(32, 113)(33, 95)(34, 99)(35, 98)(36, 101)(37, 100)(38, 103)(39, 102)(40, 105)(41, 104)(42, 107)(43, 106)(44, 109)(45, 108)(46, 111)(47, 110)(48, 114)(49, 96)(50, 112)(51, 116)(52, 115)(53, 118)(54, 117)(55, 120)(56, 119)(57, 122)(58, 121)(59, 124)(60, 123)(61, 126)(62, 125)(63, 128)(64, 127) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) } Outer automorphisms :: reflexible Dual of E16.928 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 64 f = 33 degree seq :: [ 128 ] E16.930 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 64, 64}) Quotient :: dipole Aut^+ = C64 (small group id <64, 1>) Aut = $<128, 161>$ (small group id <128, 161>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^32 * Y1, (Y3 * Y2^-1)^64 ] Map:: R = (1, 65, 2, 66)(3, 67, 5, 69)(4, 68, 6, 70)(7, 71, 9, 73)(8, 72, 10, 74)(11, 75, 13, 77)(12, 76, 14, 78)(15, 79, 17, 81)(16, 80, 18, 82)(19, 83, 21, 85)(20, 84, 22, 86)(23, 87, 25, 89)(24, 88, 26, 90)(27, 91, 29, 93)(28, 92, 30, 94)(31, 95, 48, 112)(32, 96, 57, 121)(33, 97, 34, 98)(35, 99, 37, 101)(36, 100, 38, 102)(39, 103, 41, 105)(40, 104, 42, 106)(43, 107, 45, 109)(44, 108, 46, 110)(47, 111, 49, 113)(50, 114, 51, 115)(52, 116, 53, 117)(54, 118, 55, 119)(56, 120, 64, 128)(58, 122, 59, 123)(60, 124, 61, 125)(62, 126, 63, 127)(129, 193, 131, 195, 135, 199, 139, 203, 143, 207, 147, 211, 151, 215, 155, 219, 159, 223, 174, 238, 170, 234, 166, 230, 162, 226, 165, 229, 169, 233, 173, 237, 177, 241, 179, 243, 181, 245, 183, 247, 192, 256, 190, 254, 188, 252, 186, 250, 185, 249, 158, 222, 154, 218, 150, 214, 146, 210, 142, 206, 138, 202, 134, 198, 130, 194, 133, 197, 137, 201, 141, 205, 145, 209, 149, 213, 153, 217, 157, 221, 176, 240, 172, 236, 168, 232, 164, 228, 161, 225, 163, 227, 167, 231, 171, 235, 175, 239, 178, 242, 180, 244, 182, 246, 184, 248, 191, 255, 189, 253, 187, 251, 160, 224, 156, 220, 152, 216, 148, 212, 144, 208, 140, 204, 136, 200, 132, 196) L = (1, 130)(2, 129)(3, 133)(4, 134)(5, 131)(6, 132)(7, 137)(8, 138)(9, 135)(10, 136)(11, 141)(12, 142)(13, 139)(14, 140)(15, 145)(16, 146)(17, 143)(18, 144)(19, 149)(20, 150)(21, 147)(22, 148)(23, 153)(24, 154)(25, 151)(26, 152)(27, 157)(28, 158)(29, 155)(30, 156)(31, 176)(32, 185)(33, 162)(34, 161)(35, 165)(36, 166)(37, 163)(38, 164)(39, 169)(40, 170)(41, 167)(42, 168)(43, 173)(44, 174)(45, 171)(46, 172)(47, 177)(48, 159)(49, 175)(50, 179)(51, 178)(52, 181)(53, 180)(54, 183)(55, 182)(56, 192)(57, 160)(58, 187)(59, 186)(60, 189)(61, 188)(62, 191)(63, 190)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 2, 128, 2, 128 ), ( 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128, 2, 128 ) } Outer automorphisms :: reflexible Dual of E16.931 Graph:: bipartite v = 33 e = 128 f = 65 degree seq :: [ 4^32, 128 ] E16.931 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 64, 64}) Quotient :: dipole Aut^+ = C64 (small group id <64, 1>) Aut = $<128, 161>$ (small group id <128, 161>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1^32 ] Map:: R = (1, 65, 2, 66, 5, 69, 9, 73, 13, 77, 17, 81, 21, 85, 25, 89, 29, 93, 47, 111, 43, 107, 39, 103, 35, 99, 38, 102, 42, 106, 46, 110, 50, 114, 52, 116, 54, 118, 56, 120, 64, 128, 62, 126, 60, 124, 58, 122, 57, 121, 31, 95, 27, 91, 23, 87, 19, 83, 15, 79, 11, 75, 7, 71, 3, 67, 6, 70, 10, 74, 14, 78, 18, 82, 22, 86, 26, 90, 30, 94, 48, 112, 44, 108, 40, 104, 36, 100, 33, 97, 34, 98, 37, 101, 41, 105, 45, 109, 49, 113, 51, 115, 53, 117, 55, 119, 63, 127, 61, 125, 59, 123, 32, 96, 28, 92, 24, 88, 20, 84, 16, 80, 12, 76, 8, 72, 4, 68)(129, 193)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256) L = (1, 131)(2, 134)(3, 129)(4, 135)(5, 138)(6, 130)(7, 132)(8, 139)(9, 142)(10, 133)(11, 136)(12, 143)(13, 146)(14, 137)(15, 140)(16, 147)(17, 150)(18, 141)(19, 144)(20, 151)(21, 154)(22, 145)(23, 148)(24, 155)(25, 158)(26, 149)(27, 152)(28, 159)(29, 176)(30, 153)(31, 156)(32, 185)(33, 163)(34, 166)(35, 161)(36, 167)(37, 170)(38, 162)(39, 164)(40, 171)(41, 174)(42, 165)(43, 168)(44, 175)(45, 178)(46, 169)(47, 172)(48, 157)(49, 180)(50, 173)(51, 182)(52, 177)(53, 184)(54, 179)(55, 192)(56, 181)(57, 160)(58, 187)(59, 186)(60, 189)(61, 188)(62, 191)(63, 190)(64, 183)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 128 ), ( 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128, 4, 128 ) } Outer automorphisms :: reflexible Dual of E16.930 Graph:: bipartite v = 65 e = 128 f = 33 degree seq :: [ 2^64, 128 ] E16.932 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 33, 66}) Quotient :: regular Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-33 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 36, 33, 34, 37, 40, 43, 45, 47, 49, 51, 57, 54, 55, 58, 61, 64, 53, 31, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 30, 42, 39, 35, 38, 41, 44, 46, 48, 50, 52, 63, 60, 56, 59, 62, 65, 66, 32, 28, 24, 20, 16, 12, 8, 4) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 42)(32, 53)(33, 35)(34, 38)(36, 39)(37, 41)(40, 44)(43, 46)(45, 48)(47, 50)(49, 52)(51, 63)(54, 56)(55, 59)(57, 60)(58, 62)(61, 65)(64, 66) local type(s) :: { ( 33^66 ) } Outer automorphisms :: reflexible Dual of E16.933 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 33 f = 2 degree seq :: [ 66 ] E16.933 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 33, 66}) Quotient :: regular Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^33 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 36, 38, 40, 42, 44, 46, 48, 50, 51, 52, 54, 56, 58, 60, 62, 64, 32, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 30, 33, 34, 35, 37, 39, 41, 43, 45, 47, 53, 55, 57, 59, 61, 63, 65, 66, 49, 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, 33)(32, 49)(34, 36)(35, 38)(37, 40)(39, 42)(41, 44)(43, 46)(45, 48)(47, 50)(51, 53)(52, 55)(54, 57)(56, 59)(58, 61)(60, 63)(62, 65)(64, 66) local type(s) :: { ( 66^33 ) } Outer automorphisms :: reflexible Dual of E16.932 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 33 f = 1 degree seq :: [ 33^2 ] E16.934 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 33, 66}) Quotient :: edge Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^33 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 33, 35, 38, 40, 42, 44, 46, 48, 50, 52, 54, 57, 59, 61, 63, 65, 32, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 37, 34, 36, 39, 41, 43, 45, 47, 49, 56, 53, 55, 58, 60, 62, 64, 66, 51, 30, 26, 22, 18, 14, 10, 6)(67, 68)(69, 71)(70, 72)(73, 75)(74, 76)(77, 79)(78, 80)(81, 83)(82, 84)(85, 87)(86, 88)(89, 91)(90, 92)(93, 95)(94, 96)(97, 103)(98, 117)(99, 100)(101, 102)(104, 105)(106, 107)(108, 109)(110, 111)(112, 113)(114, 115)(116, 122)(118, 119)(120, 121)(123, 124)(125, 126)(127, 128)(129, 130)(131, 132) L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 132, 132 ), ( 132^33 ) } Outer automorphisms :: reflexible Dual of E16.938 Transitivity :: ET+ Graph:: simple bipartite v = 35 e = 66 f = 1 degree seq :: [ 2^33, 33^2 ] E16.935 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 33, 66}) Quotient :: edge Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^14 * T2^-1 * T1 * T2^-15, T2^-2 * T1^31, T2^13 * T1^12 * T2^-1 * T1^15 * T2^-1 * T1^15 * T2^-1 * T1 ] Map:: non-degenerate R = (1, 3, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 64, 59, 56, 51, 48, 43, 40, 35, 32, 27, 24, 19, 16, 11, 8, 2, 7, 4, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 63, 60, 55, 52, 47, 44, 39, 36, 31, 28, 23, 20, 15, 12, 6, 5)(67, 68, 72, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 131, 128, 123, 120, 115, 112, 107, 104, 99, 96, 91, 88, 83, 80, 75, 70)(69, 73, 71, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 132, 127, 124, 119, 116, 111, 108, 103, 100, 95, 92, 87, 84, 79, 76) L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 4^33 ), ( 4^66 ) } Outer automorphisms :: reflexible Dual of E16.939 Transitivity :: ET+ Graph:: bipartite v = 3 e = 66 f = 33 degree seq :: [ 33^2, 66 ] E16.936 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 33, 66}) Quotient :: edge Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-33 ] Map:: R = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 36)(32, 51)(33, 35)(34, 38)(37, 40)(39, 42)(41, 44)(43, 46)(45, 48)(47, 50)(49, 55)(52, 54)(53, 57)(56, 59)(58, 61)(60, 63)(62, 65)(64, 66)(67, 68, 71, 75, 79, 83, 87, 91, 95, 101, 104, 106, 108, 110, 112, 114, 116, 121, 118, 119, 122, 124, 126, 128, 130, 117, 97, 93, 89, 85, 81, 77, 73, 69, 72, 76, 80, 84, 88, 92, 96, 102, 99, 100, 103, 105, 107, 109, 111, 113, 115, 120, 123, 125, 127, 129, 131, 132, 98, 94, 90, 86, 82, 78, 74, 70) L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 66, 66 ), ( 66^66 ) } Outer automorphisms :: reflexible Dual of E16.937 Transitivity :: ET+ Graph:: bipartite v = 34 e = 66 f = 2 degree seq :: [ 2^33, 66 ] E16.937 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 33, 66}) Quotient :: loop Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^33 ] Map:: R = (1, 67, 3, 69, 7, 73, 11, 77, 15, 81, 19, 85, 23, 89, 27, 93, 31, 97, 33, 99, 35, 101, 38, 104, 40, 106, 42, 108, 44, 110, 46, 112, 48, 114, 50, 116, 52, 118, 54, 120, 57, 123, 59, 125, 61, 127, 63, 129, 65, 131, 32, 98, 28, 94, 24, 90, 20, 86, 16, 82, 12, 78, 8, 74, 4, 70)(2, 68, 5, 71, 9, 75, 13, 79, 17, 83, 21, 87, 25, 91, 29, 95, 37, 103, 34, 100, 36, 102, 39, 105, 41, 107, 43, 109, 45, 111, 47, 113, 49, 115, 56, 122, 53, 119, 55, 121, 58, 124, 60, 126, 62, 128, 64, 130, 66, 132, 51, 117, 30, 96, 26, 92, 22, 88, 18, 84, 14, 80, 10, 76, 6, 72) L = (1, 68)(2, 67)(3, 71)(4, 72)(5, 69)(6, 70)(7, 75)(8, 76)(9, 73)(10, 74)(11, 79)(12, 80)(13, 77)(14, 78)(15, 83)(16, 84)(17, 81)(18, 82)(19, 87)(20, 88)(21, 85)(22, 86)(23, 91)(24, 92)(25, 89)(26, 90)(27, 95)(28, 96)(29, 93)(30, 94)(31, 103)(32, 117)(33, 100)(34, 99)(35, 102)(36, 101)(37, 97)(38, 105)(39, 104)(40, 107)(41, 106)(42, 109)(43, 108)(44, 111)(45, 110)(46, 113)(47, 112)(48, 115)(49, 114)(50, 122)(51, 98)(52, 119)(53, 118)(54, 121)(55, 120)(56, 116)(57, 124)(58, 123)(59, 126)(60, 125)(61, 128)(62, 127)(63, 130)(64, 129)(65, 132)(66, 131) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E16.936 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 66 f = 34 degree seq :: [ 66^2 ] E16.938 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 33, 66}) Quotient :: loop Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^14 * T2^-1 * T1 * T2^-15, T2^-2 * T1^31, T2^13 * T1^12 * T2^-1 * T1^15 * T2^-1 * T1^15 * T2^-1 * T1 ] Map:: R = (1, 67, 3, 69, 9, 75, 13, 79, 17, 83, 21, 87, 25, 91, 29, 95, 33, 99, 37, 103, 41, 107, 45, 111, 49, 115, 53, 119, 57, 123, 61, 127, 65, 131, 64, 130, 59, 125, 56, 122, 51, 117, 48, 114, 43, 109, 40, 106, 35, 101, 32, 98, 27, 93, 24, 90, 19, 85, 16, 82, 11, 77, 8, 74, 2, 68, 7, 73, 4, 70, 10, 76, 14, 80, 18, 84, 22, 88, 26, 92, 30, 96, 34, 100, 38, 104, 42, 108, 46, 112, 50, 116, 54, 120, 58, 124, 62, 128, 66, 132, 63, 129, 60, 126, 55, 121, 52, 118, 47, 113, 44, 110, 39, 105, 36, 102, 31, 97, 28, 94, 23, 89, 20, 86, 15, 81, 12, 78, 6, 72, 5, 71) L = (1, 68)(2, 72)(3, 73)(4, 67)(5, 74)(6, 77)(7, 71)(8, 78)(9, 70)(10, 69)(11, 81)(12, 82)(13, 76)(14, 75)(15, 85)(16, 86)(17, 80)(18, 79)(19, 89)(20, 90)(21, 84)(22, 83)(23, 93)(24, 94)(25, 88)(26, 87)(27, 97)(28, 98)(29, 92)(30, 91)(31, 101)(32, 102)(33, 96)(34, 95)(35, 105)(36, 106)(37, 100)(38, 99)(39, 109)(40, 110)(41, 104)(42, 103)(43, 113)(44, 114)(45, 108)(46, 107)(47, 117)(48, 118)(49, 112)(50, 111)(51, 121)(52, 122)(53, 116)(54, 115)(55, 125)(56, 126)(57, 120)(58, 119)(59, 129)(60, 130)(61, 124)(62, 123)(63, 131)(64, 132)(65, 128)(66, 127) local type(s) :: { ( 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33 ) } Outer automorphisms :: reflexible Dual of E16.934 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 66 f = 35 degree seq :: [ 132 ] E16.939 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 33, 66}) Quotient :: loop Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-33 ] Map:: non-degenerate R = (1, 67, 3, 69)(2, 68, 6, 72)(4, 70, 7, 73)(5, 71, 10, 76)(8, 74, 11, 77)(9, 75, 14, 80)(12, 78, 15, 81)(13, 79, 18, 84)(16, 82, 19, 85)(17, 83, 22, 88)(20, 86, 23, 89)(21, 87, 26, 92)(24, 90, 27, 93)(25, 91, 30, 96)(28, 94, 31, 97)(29, 95, 40, 106)(32, 98, 53, 119)(33, 99, 35, 101)(34, 100, 38, 104)(36, 102, 39, 105)(37, 103, 42, 108)(41, 107, 44, 110)(43, 109, 46, 112)(45, 111, 48, 114)(47, 113, 50, 116)(49, 115, 52, 118)(51, 117, 61, 127)(54, 120, 56, 122)(55, 121, 59, 125)(57, 123, 60, 126)(58, 124, 63, 129)(62, 128, 65, 131)(64, 130, 66, 132) L = (1, 68)(2, 71)(3, 72)(4, 67)(5, 75)(6, 76)(7, 69)(8, 70)(9, 79)(10, 80)(11, 73)(12, 74)(13, 83)(14, 84)(15, 77)(16, 78)(17, 87)(18, 88)(19, 81)(20, 82)(21, 91)(22, 92)(23, 85)(24, 86)(25, 95)(26, 96)(27, 89)(28, 90)(29, 105)(30, 106)(31, 93)(32, 94)(33, 100)(34, 103)(35, 104)(36, 99)(37, 107)(38, 108)(39, 101)(40, 102)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 126)(52, 127)(53, 97)(54, 121)(55, 124)(56, 125)(57, 120)(58, 128)(59, 129)(60, 122)(61, 123)(62, 130)(63, 131)(64, 119)(65, 132)(66, 98) local type(s) :: { ( 33, 66, 33, 66 ) } Outer automorphisms :: reflexible Dual of E16.935 Transitivity :: ET+ VT+ AT Graph:: v = 33 e = 66 f = 3 degree seq :: [ 4^33 ] E16.940 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 33, 66}) Quotient :: dipole Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^33, (Y3 * Y2^-1)^66 ] Map:: R = (1, 67, 2, 68)(3, 69, 5, 71)(4, 70, 6, 72)(7, 73, 9, 75)(8, 74, 10, 76)(11, 77, 13, 79)(12, 78, 14, 80)(15, 81, 17, 83)(16, 82, 18, 84)(19, 85, 21, 87)(20, 86, 22, 88)(23, 89, 25, 91)(24, 90, 26, 92)(27, 93, 29, 95)(28, 94, 30, 96)(31, 97, 37, 103)(32, 98, 51, 117)(33, 99, 34, 100)(35, 101, 36, 102)(38, 104, 39, 105)(40, 106, 41, 107)(42, 108, 43, 109)(44, 110, 45, 111)(46, 112, 47, 113)(48, 114, 49, 115)(50, 116, 56, 122)(52, 118, 53, 119)(54, 120, 55, 121)(57, 123, 58, 124)(59, 125, 60, 126)(61, 127, 62, 128)(63, 129, 64, 130)(65, 131, 66, 132)(133, 199, 135, 201, 139, 205, 143, 209, 147, 213, 151, 217, 155, 221, 159, 225, 163, 229, 165, 231, 167, 233, 170, 236, 172, 238, 174, 240, 176, 242, 178, 244, 180, 246, 182, 248, 184, 250, 186, 252, 189, 255, 191, 257, 193, 259, 195, 261, 197, 263, 164, 230, 160, 226, 156, 222, 152, 218, 148, 214, 144, 210, 140, 206, 136, 202)(134, 200, 137, 203, 141, 207, 145, 211, 149, 215, 153, 219, 157, 223, 161, 227, 169, 235, 166, 232, 168, 234, 171, 237, 173, 239, 175, 241, 177, 243, 179, 245, 181, 247, 188, 254, 185, 251, 187, 253, 190, 256, 192, 258, 194, 260, 196, 262, 198, 264, 183, 249, 162, 228, 158, 224, 154, 220, 150, 216, 146, 212, 142, 208, 138, 204) L = (1, 134)(2, 133)(3, 137)(4, 138)(5, 135)(6, 136)(7, 141)(8, 142)(9, 139)(10, 140)(11, 145)(12, 146)(13, 143)(14, 144)(15, 149)(16, 150)(17, 147)(18, 148)(19, 153)(20, 154)(21, 151)(22, 152)(23, 157)(24, 158)(25, 155)(26, 156)(27, 161)(28, 162)(29, 159)(30, 160)(31, 169)(32, 183)(33, 166)(34, 165)(35, 168)(36, 167)(37, 163)(38, 171)(39, 170)(40, 173)(41, 172)(42, 175)(43, 174)(44, 177)(45, 176)(46, 179)(47, 178)(48, 181)(49, 180)(50, 188)(51, 164)(52, 185)(53, 184)(54, 187)(55, 186)(56, 182)(57, 190)(58, 189)(59, 192)(60, 191)(61, 194)(62, 193)(63, 196)(64, 195)(65, 198)(66, 197)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 2, 132, 2, 132 ), ( 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132 ) } Outer automorphisms :: reflexible Dual of E16.943 Graph:: bipartite v = 35 e = 132 f = 67 degree seq :: [ 4^33, 66^2 ] E16.941 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 33, 66}) Quotient :: dipole Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y2^2 * Y1^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1, Y1^-1), Y1^-1 * Y2^32, Y1^33 ] Map:: R = (1, 67, 2, 68, 6, 72, 11, 77, 15, 81, 19, 85, 23, 89, 27, 93, 31, 97, 35, 101, 39, 105, 43, 109, 47, 113, 51, 117, 55, 121, 59, 125, 63, 129, 65, 131, 62, 128, 57, 123, 54, 120, 49, 115, 46, 112, 41, 107, 38, 104, 33, 99, 30, 96, 25, 91, 22, 88, 17, 83, 14, 80, 9, 75, 4, 70)(3, 69, 7, 73, 5, 71, 8, 74, 12, 78, 16, 82, 20, 86, 24, 90, 28, 94, 32, 98, 36, 102, 40, 106, 44, 110, 48, 114, 52, 118, 56, 122, 60, 126, 64, 130, 66, 132, 61, 127, 58, 124, 53, 119, 50, 116, 45, 111, 42, 108, 37, 103, 34, 100, 29, 95, 26, 92, 21, 87, 18, 84, 13, 79, 10, 76)(133, 199, 135, 201, 141, 207, 145, 211, 149, 215, 153, 219, 157, 223, 161, 227, 165, 231, 169, 235, 173, 239, 177, 243, 181, 247, 185, 251, 189, 255, 193, 259, 197, 263, 196, 262, 191, 257, 188, 254, 183, 249, 180, 246, 175, 241, 172, 238, 167, 233, 164, 230, 159, 225, 156, 222, 151, 217, 148, 214, 143, 209, 140, 206, 134, 200, 139, 205, 136, 202, 142, 208, 146, 212, 150, 216, 154, 220, 158, 224, 162, 228, 166, 232, 170, 236, 174, 240, 178, 244, 182, 248, 186, 252, 190, 256, 194, 260, 198, 264, 195, 261, 192, 258, 187, 253, 184, 250, 179, 245, 176, 242, 171, 237, 168, 234, 163, 229, 160, 226, 155, 221, 152, 218, 147, 213, 144, 210, 138, 204, 137, 203) L = (1, 135)(2, 139)(3, 141)(4, 142)(5, 133)(6, 137)(7, 136)(8, 134)(9, 145)(10, 146)(11, 140)(12, 138)(13, 149)(14, 150)(15, 144)(16, 143)(17, 153)(18, 154)(19, 148)(20, 147)(21, 157)(22, 158)(23, 152)(24, 151)(25, 161)(26, 162)(27, 156)(28, 155)(29, 165)(30, 166)(31, 160)(32, 159)(33, 169)(34, 170)(35, 164)(36, 163)(37, 173)(38, 174)(39, 168)(40, 167)(41, 177)(42, 178)(43, 172)(44, 171)(45, 181)(46, 182)(47, 176)(48, 175)(49, 185)(50, 186)(51, 180)(52, 179)(53, 189)(54, 190)(55, 184)(56, 183)(57, 193)(58, 194)(59, 188)(60, 187)(61, 197)(62, 198)(63, 192)(64, 191)(65, 196)(66, 195)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E16.942 Graph:: bipartite v = 3 e = 132 f = 99 degree seq :: [ 66^2, 132 ] E16.942 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 33, 66}) Quotient :: dipole Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y3^33 * Y2, (Y3^-1 * Y1^-1)^66 ] Map:: R = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)(133, 199, 134, 200)(135, 201, 137, 203)(136, 202, 138, 204)(139, 205, 141, 207)(140, 206, 142, 208)(143, 209, 145, 211)(144, 210, 146, 212)(147, 213, 149, 215)(148, 214, 150, 216)(151, 217, 153, 219)(152, 218, 154, 220)(155, 221, 157, 223)(156, 222, 158, 224)(159, 225, 161, 227)(160, 226, 162, 228)(163, 229, 181, 247)(164, 230, 189, 255)(165, 231, 166, 232)(167, 233, 169, 235)(168, 234, 170, 236)(171, 237, 173, 239)(172, 238, 174, 240)(175, 241, 177, 243)(176, 242, 178, 244)(179, 245, 180, 246)(182, 248, 183, 249)(184, 250, 185, 251)(186, 252, 187, 253)(188, 254, 198, 264)(190, 256, 191, 257)(192, 258, 193, 259)(194, 260, 195, 261)(196, 262, 197, 263) L = (1, 135)(2, 137)(3, 139)(4, 133)(5, 141)(6, 134)(7, 143)(8, 136)(9, 145)(10, 138)(11, 147)(12, 140)(13, 149)(14, 142)(15, 151)(16, 144)(17, 153)(18, 146)(19, 155)(20, 148)(21, 157)(22, 150)(23, 159)(24, 152)(25, 161)(26, 154)(27, 163)(28, 156)(29, 181)(30, 158)(31, 176)(32, 160)(33, 167)(34, 169)(35, 171)(36, 165)(37, 173)(38, 166)(39, 175)(40, 168)(41, 177)(42, 170)(43, 179)(44, 172)(45, 180)(46, 174)(47, 182)(48, 183)(49, 178)(50, 184)(51, 185)(52, 186)(53, 187)(54, 188)(55, 198)(56, 196)(57, 162)(58, 189)(59, 164)(60, 190)(61, 191)(62, 192)(63, 193)(64, 194)(65, 195)(66, 197)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 66, 132 ), ( 66, 132, 66, 132 ) } Outer automorphisms :: reflexible Dual of E16.941 Graph:: simple bipartite v = 99 e = 132 f = 3 degree seq :: [ 2^66, 4^33 ] E16.943 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 33, 66}) Quotient :: dipole Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-33 ] Map:: R = (1, 67, 2, 68, 5, 71, 9, 75, 13, 79, 17, 83, 21, 87, 25, 91, 29, 95, 36, 102, 33, 99, 34, 100, 37, 103, 40, 106, 43, 109, 45, 111, 47, 113, 49, 115, 51, 117, 57, 123, 54, 120, 55, 121, 58, 124, 61, 127, 64, 130, 53, 119, 31, 97, 27, 93, 23, 89, 19, 85, 15, 81, 11, 77, 7, 73, 3, 69, 6, 72, 10, 76, 14, 80, 18, 84, 22, 88, 26, 92, 30, 96, 42, 108, 39, 105, 35, 101, 38, 104, 41, 107, 44, 110, 46, 112, 48, 114, 50, 116, 52, 118, 63, 129, 60, 126, 56, 122, 59, 125, 62, 128, 65, 131, 66, 132, 32, 98, 28, 94, 24, 90, 20, 86, 16, 82, 12, 78, 8, 74, 4, 70)(133, 199)(134, 200)(135, 201)(136, 202)(137, 203)(138, 204)(139, 205)(140, 206)(141, 207)(142, 208)(143, 209)(144, 210)(145, 211)(146, 212)(147, 213)(148, 214)(149, 215)(150, 216)(151, 217)(152, 218)(153, 219)(154, 220)(155, 221)(156, 222)(157, 223)(158, 224)(159, 225)(160, 226)(161, 227)(162, 228)(163, 229)(164, 230)(165, 231)(166, 232)(167, 233)(168, 234)(169, 235)(170, 236)(171, 237)(172, 238)(173, 239)(174, 240)(175, 241)(176, 242)(177, 243)(178, 244)(179, 245)(180, 246)(181, 247)(182, 248)(183, 249)(184, 250)(185, 251)(186, 252)(187, 253)(188, 254)(189, 255)(190, 256)(191, 257)(192, 258)(193, 259)(194, 260)(195, 261)(196, 262)(197, 263)(198, 264) L = (1, 135)(2, 138)(3, 133)(4, 139)(5, 142)(6, 134)(7, 136)(8, 143)(9, 146)(10, 137)(11, 140)(12, 147)(13, 150)(14, 141)(15, 144)(16, 151)(17, 154)(18, 145)(19, 148)(20, 155)(21, 158)(22, 149)(23, 152)(24, 159)(25, 162)(26, 153)(27, 156)(28, 163)(29, 174)(30, 157)(31, 160)(32, 185)(33, 167)(34, 170)(35, 165)(36, 171)(37, 173)(38, 166)(39, 168)(40, 176)(41, 169)(42, 161)(43, 178)(44, 172)(45, 180)(46, 175)(47, 182)(48, 177)(49, 184)(50, 179)(51, 195)(52, 181)(53, 164)(54, 188)(55, 191)(56, 186)(57, 192)(58, 194)(59, 187)(60, 189)(61, 197)(62, 190)(63, 183)(64, 198)(65, 193)(66, 196)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 4, 66 ), ( 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66 ) } Outer automorphisms :: reflexible Dual of E16.940 Graph:: bipartite v = 67 e = 132 f = 35 degree seq :: [ 2^66, 132 ] E16.944 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 33, 66}) Quotient :: dipole Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^33 * Y1, (Y3 * Y2^-1)^33 ] Map:: R = (1, 67, 2, 68)(3, 69, 5, 71)(4, 70, 6, 72)(7, 73, 9, 75)(8, 74, 10, 76)(11, 77, 13, 79)(12, 78, 14, 80)(15, 81, 17, 83)(16, 82, 18, 84)(19, 85, 21, 87)(20, 86, 22, 88)(23, 89, 25, 91)(24, 90, 26, 92)(27, 93, 29, 95)(28, 94, 30, 96)(31, 97, 41, 107)(32, 98, 53, 119)(33, 99, 34, 100)(35, 101, 37, 103)(36, 102, 38, 104)(39, 105, 40, 106)(42, 108, 43, 109)(44, 110, 45, 111)(46, 112, 47, 113)(48, 114, 49, 115)(50, 116, 51, 117)(52, 118, 62, 128)(54, 120, 55, 121)(56, 122, 58, 124)(57, 123, 59, 125)(60, 126, 61, 127)(63, 129, 64, 130)(65, 131, 66, 132)(133, 199, 135, 201, 139, 205, 143, 209, 147, 213, 151, 217, 155, 221, 159, 225, 163, 229, 168, 234, 165, 231, 167, 233, 171, 237, 174, 240, 176, 242, 178, 244, 180, 246, 182, 248, 184, 250, 189, 255, 186, 252, 188, 254, 192, 258, 195, 261, 197, 263, 185, 251, 162, 228, 158, 224, 154, 220, 150, 216, 146, 212, 142, 208, 138, 204, 134, 200, 137, 203, 141, 207, 145, 211, 149, 215, 153, 219, 157, 223, 161, 227, 173, 239, 170, 236, 166, 232, 169, 235, 172, 238, 175, 241, 177, 243, 179, 245, 181, 247, 183, 249, 194, 260, 191, 257, 187, 253, 190, 256, 193, 259, 196, 262, 198, 264, 164, 230, 160, 226, 156, 222, 152, 218, 148, 214, 144, 210, 140, 206, 136, 202) L = (1, 134)(2, 133)(3, 137)(4, 138)(5, 135)(6, 136)(7, 141)(8, 142)(9, 139)(10, 140)(11, 145)(12, 146)(13, 143)(14, 144)(15, 149)(16, 150)(17, 147)(18, 148)(19, 153)(20, 154)(21, 151)(22, 152)(23, 157)(24, 158)(25, 155)(26, 156)(27, 161)(28, 162)(29, 159)(30, 160)(31, 173)(32, 185)(33, 166)(34, 165)(35, 169)(36, 170)(37, 167)(38, 168)(39, 172)(40, 171)(41, 163)(42, 175)(43, 174)(44, 177)(45, 176)(46, 179)(47, 178)(48, 181)(49, 180)(50, 183)(51, 182)(52, 194)(53, 164)(54, 187)(55, 186)(56, 190)(57, 191)(58, 188)(59, 189)(60, 193)(61, 192)(62, 184)(63, 196)(64, 195)(65, 198)(66, 197)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 2, 66, 2, 66 ), ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E16.945 Graph:: bipartite v = 34 e = 132 f = 68 degree seq :: [ 4^33, 132 ] E16.945 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 33, 66}) Quotient :: dipole Aut^+ = C66 (small group id <66, 4>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^-1 * Y3^-2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^14 * Y3^-1 * Y1 * Y3^-15, Y3^-2 * Y1^31, (Y3 * Y2^-1)^66 ] Map:: R = (1, 67, 2, 68, 6, 72, 11, 77, 15, 81, 19, 85, 23, 89, 27, 93, 31, 97, 35, 101, 39, 105, 43, 109, 47, 113, 51, 117, 55, 121, 59, 125, 63, 129, 65, 131, 62, 128, 57, 123, 54, 120, 49, 115, 46, 112, 41, 107, 38, 104, 33, 99, 30, 96, 25, 91, 22, 88, 17, 83, 14, 80, 9, 75, 4, 70)(3, 69, 7, 73, 5, 71, 8, 74, 12, 78, 16, 82, 20, 86, 24, 90, 28, 94, 32, 98, 36, 102, 40, 106, 44, 110, 48, 114, 52, 118, 56, 122, 60, 126, 64, 130, 66, 132, 61, 127, 58, 124, 53, 119, 50, 116, 45, 111, 42, 108, 37, 103, 34, 100, 29, 95, 26, 92, 21, 87, 18, 84, 13, 79, 10, 76)(133, 199)(134, 200)(135, 201)(136, 202)(137, 203)(138, 204)(139, 205)(140, 206)(141, 207)(142, 208)(143, 209)(144, 210)(145, 211)(146, 212)(147, 213)(148, 214)(149, 215)(150, 216)(151, 217)(152, 218)(153, 219)(154, 220)(155, 221)(156, 222)(157, 223)(158, 224)(159, 225)(160, 226)(161, 227)(162, 228)(163, 229)(164, 230)(165, 231)(166, 232)(167, 233)(168, 234)(169, 235)(170, 236)(171, 237)(172, 238)(173, 239)(174, 240)(175, 241)(176, 242)(177, 243)(178, 244)(179, 245)(180, 246)(181, 247)(182, 248)(183, 249)(184, 250)(185, 251)(186, 252)(187, 253)(188, 254)(189, 255)(190, 256)(191, 257)(192, 258)(193, 259)(194, 260)(195, 261)(196, 262)(197, 263)(198, 264) L = (1, 135)(2, 139)(3, 141)(4, 142)(5, 133)(6, 137)(7, 136)(8, 134)(9, 145)(10, 146)(11, 140)(12, 138)(13, 149)(14, 150)(15, 144)(16, 143)(17, 153)(18, 154)(19, 148)(20, 147)(21, 157)(22, 158)(23, 152)(24, 151)(25, 161)(26, 162)(27, 156)(28, 155)(29, 165)(30, 166)(31, 160)(32, 159)(33, 169)(34, 170)(35, 164)(36, 163)(37, 173)(38, 174)(39, 168)(40, 167)(41, 177)(42, 178)(43, 172)(44, 171)(45, 181)(46, 182)(47, 176)(48, 175)(49, 185)(50, 186)(51, 180)(52, 179)(53, 189)(54, 190)(55, 184)(56, 183)(57, 193)(58, 194)(59, 188)(60, 187)(61, 197)(62, 198)(63, 192)(64, 191)(65, 196)(66, 195)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 4, 132 ), ( 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132, 4, 132 ) } Outer automorphisms :: reflexible Dual of E16.944 Graph:: simple bipartite v = 68 e = 132 f = 34 degree seq :: [ 2^66, 66^2 ] E16.946 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 17}) Quotient :: dipole Aut^+ = D68 (small group id <68, 4>) Aut = C2 x C2 x D34 (small group id <136, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^17 ] Map:: polytopal non-degenerate R = (1, 69, 2, 70)(3, 71, 5, 73)(4, 72, 8, 76)(6, 74, 10, 78)(7, 75, 11, 79)(9, 77, 13, 81)(12, 80, 16, 84)(14, 82, 18, 86)(15, 83, 19, 87)(17, 85, 21, 89)(20, 88, 24, 92)(22, 90, 26, 94)(23, 91, 27, 95)(25, 93, 29, 97)(28, 96, 32, 100)(30, 98, 47, 115)(31, 99, 49, 117)(33, 101, 51, 119)(34, 102, 53, 121)(35, 103, 55, 123)(36, 104, 57, 125)(37, 105, 59, 127)(38, 106, 61, 129)(39, 107, 63, 131)(40, 108, 65, 133)(41, 109, 67, 135)(42, 110, 68, 136)(43, 111, 66, 134)(44, 112, 64, 132)(45, 113, 62, 130)(46, 114, 60, 128)(48, 116, 58, 126)(50, 118, 56, 124)(52, 120, 54, 122)(137, 205, 139, 207)(138, 206, 141, 209)(140, 208, 143, 211)(142, 210, 145, 213)(144, 212, 147, 215)(146, 214, 149, 217)(148, 216, 151, 219)(150, 218, 153, 221)(152, 220, 155, 223)(154, 222, 157, 225)(156, 224, 159, 227)(158, 226, 161, 229)(160, 228, 163, 231)(162, 230, 165, 233)(164, 232, 167, 235)(166, 234, 169, 237)(168, 236, 185, 253)(170, 238, 172, 240)(171, 239, 173, 241)(174, 242, 176, 244)(175, 243, 177, 245)(178, 246, 180, 248)(179, 247, 181, 249)(182, 250, 186, 254)(183, 251, 187, 255)(184, 252, 188, 256)(189, 257, 193, 261)(190, 258, 194, 262)(191, 259, 195, 263)(192, 260, 196, 264)(197, 265, 201, 269)(198, 266, 202, 270)(199, 267, 203, 271)(200, 268, 204, 272) L = (1, 140)(2, 142)(3, 143)(4, 137)(5, 145)(6, 138)(7, 139)(8, 148)(9, 141)(10, 150)(11, 151)(12, 144)(13, 153)(14, 146)(15, 147)(16, 156)(17, 149)(18, 158)(19, 159)(20, 152)(21, 161)(22, 154)(23, 155)(24, 164)(25, 157)(26, 166)(27, 167)(28, 160)(29, 169)(30, 162)(31, 163)(32, 172)(33, 165)(34, 185)(35, 187)(36, 168)(37, 183)(38, 189)(39, 191)(40, 193)(41, 195)(42, 197)(43, 199)(44, 201)(45, 203)(46, 204)(47, 173)(48, 202)(49, 170)(50, 200)(51, 171)(52, 198)(53, 174)(54, 192)(55, 175)(56, 190)(57, 176)(58, 196)(59, 177)(60, 194)(61, 178)(62, 188)(63, 179)(64, 186)(65, 180)(66, 184)(67, 181)(68, 182)(69, 205)(70, 206)(71, 207)(72, 208)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 257)(122, 258)(123, 259)(124, 260)(125, 261)(126, 262)(127, 263)(128, 264)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272) local type(s) :: { ( 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.947 Graph:: simple bipartite v = 68 e = 136 f = 38 degree seq :: [ 4^68 ] E16.947 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 17}) Quotient :: dipole Aut^+ = D68 (small group id <68, 4>) Aut = C2 x C2 x D34 (small group id <136, 14>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, (R * Y3)^2, Y1^17 ] Map:: polytopal non-degenerate R = (1, 69, 2, 70, 6, 74, 13, 81, 21, 89, 29, 97, 37, 105, 45, 113, 53, 121, 60, 128, 52, 120, 44, 112, 36, 104, 28, 96, 20, 88, 12, 80, 5, 73)(3, 71, 9, 77, 17, 85, 25, 93, 33, 101, 41, 109, 49, 117, 57, 125, 64, 132, 61, 129, 54, 122, 46, 114, 38, 106, 30, 98, 22, 90, 14, 82, 7, 75)(4, 72, 11, 79, 19, 87, 27, 95, 35, 103, 43, 111, 51, 119, 59, 127, 66, 134, 62, 130, 55, 123, 47, 115, 39, 107, 31, 99, 23, 91, 15, 83, 8, 76)(10, 78, 16, 84, 24, 92, 32, 100, 40, 108, 48, 116, 56, 124, 63, 131, 67, 135, 68, 136, 65, 133, 58, 126, 50, 118, 42, 110, 34, 102, 26, 94, 18, 86)(137, 205, 139, 207)(138, 206, 143, 211)(140, 208, 146, 214)(141, 209, 145, 213)(142, 210, 150, 218)(144, 212, 152, 220)(147, 215, 154, 222)(148, 216, 153, 221)(149, 217, 158, 226)(151, 219, 160, 228)(155, 223, 162, 230)(156, 224, 161, 229)(157, 225, 166, 234)(159, 227, 168, 236)(163, 231, 170, 238)(164, 232, 169, 237)(165, 233, 174, 242)(167, 235, 176, 244)(171, 239, 178, 246)(172, 240, 177, 245)(173, 241, 182, 250)(175, 243, 184, 252)(179, 247, 186, 254)(180, 248, 185, 253)(181, 249, 190, 258)(183, 251, 192, 260)(187, 255, 194, 262)(188, 256, 193, 261)(189, 257, 197, 265)(191, 259, 199, 267)(195, 263, 201, 269)(196, 264, 200, 268)(198, 266, 203, 271)(202, 270, 204, 272) L = (1, 140)(2, 144)(3, 146)(4, 137)(5, 147)(6, 151)(7, 152)(8, 138)(9, 154)(10, 139)(11, 141)(12, 155)(13, 159)(14, 160)(15, 142)(16, 143)(17, 162)(18, 145)(19, 148)(20, 163)(21, 167)(22, 168)(23, 149)(24, 150)(25, 170)(26, 153)(27, 156)(28, 171)(29, 175)(30, 176)(31, 157)(32, 158)(33, 178)(34, 161)(35, 164)(36, 179)(37, 183)(38, 184)(39, 165)(40, 166)(41, 186)(42, 169)(43, 172)(44, 187)(45, 191)(46, 192)(47, 173)(48, 174)(49, 194)(50, 177)(51, 180)(52, 195)(53, 198)(54, 199)(55, 181)(56, 182)(57, 201)(58, 185)(59, 188)(60, 202)(61, 203)(62, 189)(63, 190)(64, 204)(65, 193)(66, 196)(67, 197)(68, 200)(69, 205)(70, 206)(71, 207)(72, 208)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 257)(122, 258)(123, 259)(124, 260)(125, 261)(126, 262)(127, 263)(128, 264)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272) local type(s) :: { ( 4^4 ), ( 4^34 ) } Outer automorphisms :: reflexible Dual of E16.946 Graph:: simple bipartite v = 38 e = 136 f = 68 degree seq :: [ 4^34, 34^4 ] E16.948 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 17}) Quotient :: edge Aut^+ = C17 : C4 (small group id <68, 1>) Aut = (C34 x C2) : C2 (small group id <136, 8>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1 * T2 * T1^-1, T2^17 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 64, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 59, 66, 65, 58, 50, 42, 34, 26, 18, 10)(6, 13, 21, 29, 37, 45, 53, 61, 67, 68, 62, 54, 46, 38, 30, 22, 14)(69, 70, 74, 72)(71, 76, 81, 78)(73, 75, 82, 79)(77, 84, 89, 86)(80, 83, 90, 87)(85, 92, 97, 94)(88, 91, 98, 95)(93, 100, 105, 102)(96, 99, 106, 103)(101, 108, 113, 110)(104, 107, 114, 111)(109, 116, 121, 118)(112, 115, 122, 119)(117, 124, 129, 126)(120, 123, 130, 127)(125, 132, 135, 133)(128, 131, 136, 134) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 8^4 ), ( 8^17 ) } Outer automorphisms :: reflexible Dual of E16.949 Transitivity :: ET+ Graph:: simple bipartite v = 21 e = 68 f = 17 degree seq :: [ 4^17, 17^4 ] E16.949 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 17}) Quotient :: loop Aut^+ = C17 : C4 (small group id <68, 1>) Aut = (C34 x C2) : C2 (small group id <136, 8>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, T2^-2 * T1^2, (F * T2)^2, (F * T1)^2, T2^4, (T2 * T1)^17 ] Map:: non-degenerate R = (1, 69, 3, 71, 6, 74, 5, 73)(2, 70, 7, 75, 4, 72, 8, 76)(9, 77, 13, 81, 10, 78, 14, 82)(11, 79, 15, 83, 12, 80, 16, 84)(17, 85, 21, 89, 18, 86, 22, 90)(19, 87, 23, 91, 20, 88, 24, 92)(25, 93, 29, 97, 26, 94, 30, 98)(27, 95, 31, 99, 28, 96, 32, 100)(33, 101, 53, 121, 34, 102, 55, 123)(35, 103, 57, 125, 40, 108, 59, 127)(36, 104, 61, 129, 38, 106, 64, 132)(37, 105, 60, 128, 39, 107, 63, 131)(41, 109, 66, 134, 42, 110, 62, 130)(43, 111, 58, 126, 44, 112, 68, 136)(45, 113, 65, 133, 46, 114, 67, 135)(47, 115, 54, 122, 48, 116, 56, 124)(49, 117, 52, 120, 50, 118, 51, 119) L = (1, 70)(2, 74)(3, 77)(4, 69)(5, 78)(6, 72)(7, 79)(8, 80)(9, 73)(10, 71)(11, 76)(12, 75)(13, 85)(14, 86)(15, 87)(16, 88)(17, 82)(18, 81)(19, 84)(20, 83)(21, 93)(22, 94)(23, 95)(24, 96)(25, 90)(26, 89)(27, 92)(28, 91)(29, 101)(30, 102)(31, 107)(32, 105)(33, 98)(34, 97)(35, 123)(36, 128)(37, 99)(38, 131)(39, 100)(40, 121)(41, 127)(42, 125)(43, 132)(44, 129)(45, 130)(46, 134)(47, 136)(48, 126)(49, 135)(50, 133)(51, 124)(52, 122)(53, 103)(54, 119)(55, 108)(56, 120)(57, 109)(58, 115)(59, 110)(60, 106)(61, 111)(62, 114)(63, 104)(64, 112)(65, 117)(66, 113)(67, 118)(68, 116) local type(s) :: { ( 4, 17, 4, 17, 4, 17, 4, 17 ) } Outer automorphisms :: reflexible Dual of E16.948 Transitivity :: ET+ VT+ AT Graph:: v = 17 e = 68 f = 21 degree seq :: [ 8^17 ] E16.950 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 17}) Quotient :: dipole Aut^+ = C17 : C4 (small group id <68, 1>) Aut = (C34 x C2) : C2 (small group id <136, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^4, (Y3^-1 * Y1^-1)^4, Y2^17 ] Map:: R = (1, 69, 2, 70, 6, 74, 4, 72)(3, 71, 8, 76, 13, 81, 10, 78)(5, 73, 7, 75, 14, 82, 11, 79)(9, 77, 16, 84, 21, 89, 18, 86)(12, 80, 15, 83, 22, 90, 19, 87)(17, 85, 24, 92, 29, 97, 26, 94)(20, 88, 23, 91, 30, 98, 27, 95)(25, 93, 32, 100, 37, 105, 34, 102)(28, 96, 31, 99, 38, 106, 35, 103)(33, 101, 40, 108, 45, 113, 42, 110)(36, 104, 39, 107, 46, 114, 43, 111)(41, 109, 48, 116, 53, 121, 50, 118)(44, 112, 47, 115, 54, 122, 51, 119)(49, 117, 56, 124, 61, 129, 58, 126)(52, 120, 55, 123, 62, 130, 59, 127)(57, 125, 64, 132, 67, 135, 65, 133)(60, 128, 63, 131, 68, 136, 66, 134)(137, 205, 139, 207, 145, 213, 153, 221, 161, 229, 169, 237, 177, 245, 185, 253, 193, 261, 196, 264, 188, 256, 180, 248, 172, 240, 164, 232, 156, 224, 148, 216, 141, 209)(138, 206, 143, 211, 151, 219, 159, 227, 167, 235, 175, 243, 183, 251, 191, 259, 199, 267, 200, 268, 192, 260, 184, 252, 176, 244, 168, 236, 160, 228, 152, 220, 144, 212)(140, 208, 147, 215, 155, 223, 163, 231, 171, 239, 179, 247, 187, 255, 195, 263, 202, 270, 201, 269, 194, 262, 186, 254, 178, 246, 170, 238, 162, 230, 154, 222, 146, 214)(142, 210, 149, 217, 157, 225, 165, 233, 173, 241, 181, 249, 189, 257, 197, 265, 203, 271, 204, 272, 198, 266, 190, 258, 182, 250, 174, 242, 166, 234, 158, 226, 150, 218) L = (1, 139)(2, 143)(3, 145)(4, 147)(5, 137)(6, 149)(7, 151)(8, 138)(9, 153)(10, 140)(11, 155)(12, 141)(13, 157)(14, 142)(15, 159)(16, 144)(17, 161)(18, 146)(19, 163)(20, 148)(21, 165)(22, 150)(23, 167)(24, 152)(25, 169)(26, 154)(27, 171)(28, 156)(29, 173)(30, 158)(31, 175)(32, 160)(33, 177)(34, 162)(35, 179)(36, 164)(37, 181)(38, 166)(39, 183)(40, 168)(41, 185)(42, 170)(43, 187)(44, 172)(45, 189)(46, 174)(47, 191)(48, 176)(49, 193)(50, 178)(51, 195)(52, 180)(53, 197)(54, 182)(55, 199)(56, 184)(57, 196)(58, 186)(59, 202)(60, 188)(61, 203)(62, 190)(63, 200)(64, 192)(65, 194)(66, 201)(67, 204)(68, 198)(69, 205)(70, 206)(71, 207)(72, 208)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 257)(122, 258)(123, 259)(124, 260)(125, 261)(126, 262)(127, 263)(128, 264)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272) 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 ) } Outer automorphisms :: reflexible Dual of E16.951 Graph:: bipartite v = 21 e = 136 f = 85 degree seq :: [ 8^17, 34^4 ] E16.951 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 17}) Quotient :: dipole Aut^+ = C17 : C4 (small group id <68, 1>) Aut = (C34 x C2) : C2 (small group id <136, 8>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^17 ] Map:: R = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136)(137, 205, 138, 206, 142, 210, 140, 208)(139, 207, 144, 212, 149, 217, 146, 214)(141, 209, 143, 211, 150, 218, 147, 215)(145, 213, 152, 220, 157, 225, 154, 222)(148, 216, 151, 219, 158, 226, 155, 223)(153, 221, 160, 228, 165, 233, 162, 230)(156, 224, 159, 227, 166, 234, 163, 231)(161, 229, 168, 236, 173, 241, 170, 238)(164, 232, 167, 235, 174, 242, 171, 239)(169, 237, 176, 244, 181, 249, 178, 246)(172, 240, 175, 243, 182, 250, 179, 247)(177, 245, 184, 252, 189, 257, 186, 254)(180, 248, 183, 251, 190, 258, 187, 255)(185, 253, 192, 260, 197, 265, 194, 262)(188, 256, 191, 259, 198, 266, 195, 263)(193, 261, 200, 268, 203, 271, 201, 269)(196, 264, 199, 267, 204, 272, 202, 270) L = (1, 139)(2, 143)(3, 145)(4, 147)(5, 137)(6, 149)(7, 151)(8, 138)(9, 153)(10, 140)(11, 155)(12, 141)(13, 157)(14, 142)(15, 159)(16, 144)(17, 161)(18, 146)(19, 163)(20, 148)(21, 165)(22, 150)(23, 167)(24, 152)(25, 169)(26, 154)(27, 171)(28, 156)(29, 173)(30, 158)(31, 175)(32, 160)(33, 177)(34, 162)(35, 179)(36, 164)(37, 181)(38, 166)(39, 183)(40, 168)(41, 185)(42, 170)(43, 187)(44, 172)(45, 189)(46, 174)(47, 191)(48, 176)(49, 193)(50, 178)(51, 195)(52, 180)(53, 197)(54, 182)(55, 199)(56, 184)(57, 196)(58, 186)(59, 202)(60, 188)(61, 203)(62, 190)(63, 200)(64, 192)(65, 194)(66, 201)(67, 204)(68, 198)(69, 205)(70, 206)(71, 207)(72, 208)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 257)(122, 258)(123, 259)(124, 260)(125, 261)(126, 262)(127, 263)(128, 264)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272) local type(s) :: { ( 8, 34 ), ( 8, 34, 8, 34, 8, 34, 8, 34 ) } Outer automorphisms :: reflexible Dual of E16.950 Graph:: simple bipartite v = 85 e = 136 f = 21 degree seq :: [ 2^68, 8^17 ] E16.952 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {4, 4, 17}) Quotient :: edge Aut^+ = C17 : C4 (small group id <68, 3>) Aut = C17 : C4 (small group id <68, 3>) |r| :: 1 Presentation :: [ X1^4, (X1^-1 * X2^-1 * X1^-1)^2, X1 * X2^-1 * X1^-1 * X2^4, (X2^-1 * X1 * X2 * X1)^2, X2^-1 * X1 * X2^2 * X1^-1 * X2 * X1 * X2^-2 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 2, 6, 4)(3, 9, 18, 11)(5, 14, 17, 15)(7, 19, 13, 21)(8, 22, 12, 23)(10, 27, 42, 29)(16, 38, 41, 39)(20, 45, 33, 46)(24, 51, 32, 52)(25, 44, 31, 47)(26, 49, 30, 40)(28, 34, 43, 37)(35, 48, 36, 50)(53, 67, 56, 68)(54, 61, 55, 64)(57, 62, 58, 63)(59, 65, 60, 66)(69, 71, 78, 96, 89, 115, 132, 131, 114, 120, 136, 134, 118, 91, 108, 84, 73)(70, 75, 88, 103, 82, 102, 125, 127, 106, 95, 122, 121, 94, 77, 93, 92, 76)(72, 80, 100, 99, 79, 98, 124, 123, 97, 107, 128, 126, 105, 83, 104, 101, 81)(74, 85, 109, 117, 90, 116, 133, 135, 119, 113, 130, 129, 112, 87, 111, 110, 86) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 8^4 ), ( 8^17 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 21 e = 68 f = 17 degree seq :: [ 4^17, 17^4 ] E16.953 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {4, 4, 17}) Quotient :: loop Aut^+ = C17 : C4 (small group id <68, 3>) Aut = C17 : C4 (small group id <68, 3>) |r| :: 1 Presentation :: [ (X1^-1 * X2)^2, X1^4, X2^4, X2^2 * X1^-2 * X2 * X1 * X2 * X1 * X2 * X1, X1^-1 * X2^2 * X1^-2 * X2^-1 * X1^-1 * X2^-2 * X1^-2 * X2^-1 * X1^-1 * X2^-2 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 69, 2, 70, 6, 74, 4, 72)(3, 71, 9, 77, 18, 86, 8, 76)(5, 73, 11, 79, 22, 90, 13, 81)(7, 75, 16, 84, 28, 96, 15, 83)(10, 78, 21, 89, 35, 103, 20, 88)(12, 80, 14, 82, 26, 94, 24, 92)(17, 85, 31, 99, 48, 116, 30, 98)(19, 87, 33, 101, 50, 118, 32, 100)(23, 91, 39, 107, 54, 122, 38, 106)(25, 93, 37, 105, 47, 115, 41, 109)(27, 95, 44, 112, 56, 124, 43, 111)(29, 97, 46, 114, 58, 126, 45, 113)(34, 102, 51, 119, 40, 108, 42, 110)(36, 104, 53, 121, 62, 130, 52, 120)(49, 117, 60, 128, 66, 134, 59, 127)(55, 123, 61, 129, 67, 135, 63, 131)(57, 125, 65, 133, 68, 136, 64, 132) L = (1, 71)(2, 75)(3, 78)(4, 79)(5, 69)(6, 82)(7, 85)(8, 70)(9, 87)(10, 73)(11, 91)(12, 72)(13, 89)(14, 95)(15, 74)(16, 97)(17, 76)(18, 99)(19, 102)(20, 77)(21, 104)(22, 105)(23, 80)(24, 107)(25, 81)(26, 110)(27, 83)(28, 112)(29, 115)(30, 84)(31, 117)(32, 86)(33, 111)(34, 88)(35, 119)(36, 93)(37, 114)(38, 90)(39, 123)(40, 92)(41, 121)(42, 101)(43, 94)(44, 125)(45, 96)(46, 106)(47, 98)(48, 109)(49, 100)(50, 128)(51, 129)(52, 103)(53, 127)(54, 126)(55, 108)(56, 118)(57, 113)(58, 133)(59, 116)(60, 132)(61, 120)(62, 135)(63, 122)(64, 124)(65, 131)(66, 130)(67, 136)(68, 134) local type(s) :: { ( 4, 17, 4, 17, 4, 17, 4, 17 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 17 e = 68 f = 21 degree seq :: [ 8^17 ] E16.954 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {4, 4, 17}) Quotient :: loop Aut^+ = C17 : C4 (small group id <68, 3>) Aut = C2 x (C17 : C4) (small group id <136, 13>) |r| :: 2 Presentation :: [ F^2, F * T2 * F * T1, (T1^-1 * T2)^2, T2^4, T1^4, T2^2 * T1^-2 * T2 * T1 * T2 * T1 * T2 * T1, T1^-1 * T2^2 * T1^-2 * T2^-1 * T1^-1 * T2^-2 * T1^-2 * T2^-1 * T1^-1 * T2^-2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 5)(2, 7, 17, 8)(4, 11, 23, 12)(6, 14, 27, 15)(9, 19, 34, 20)(13, 21, 36, 25)(16, 29, 47, 30)(18, 31, 49, 32)(22, 37, 46, 38)(24, 39, 55, 40)(26, 42, 33, 43)(28, 44, 57, 45)(35, 51, 61, 52)(41, 53, 59, 48)(50, 60, 64, 56)(54, 58, 65, 63)(62, 67, 68, 66)(69, 70, 74, 72)(71, 77, 86, 76)(73, 79, 90, 81)(75, 84, 96, 83)(78, 89, 103, 88)(80, 82, 94, 92)(85, 99, 116, 98)(87, 101, 118, 100)(91, 107, 122, 106)(93, 105, 115, 109)(95, 112, 124, 111)(97, 114, 126, 113)(102, 119, 108, 110)(104, 121, 130, 120)(117, 128, 134, 127)(123, 129, 135, 131)(125, 133, 136, 132) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 34^4 ) } Outer automorphisms :: reflexible Dual of E16.955 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 34 e = 68 f = 4 degree seq :: [ 4^34 ] E16.955 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {4, 4, 17}) Quotient :: edge Aut^+ = C17 : C4 (small group id <68, 3>) Aut = C2 x (C17 : C4) (small group id <136, 13>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, T1^4, F * T1 * T2 * F * T1^-1, (T2 * T1^2)^2, (T2 * T1^-2)^2, T1 * T2^4 * T1^-1 * T2, (T2^-1 * T1 * F * T1^-1)^2, (T2^-1 * T1^-1)^4, T2 * T1^-2 * F * T2 * T1^2 * T2^-1 * F ] Map:: polytopal non-degenerate R = (1, 69, 3, 71, 10, 78, 28, 96, 21, 89, 47, 115, 64, 132, 63, 131, 46, 114, 52, 120, 68, 136, 66, 134, 50, 118, 23, 91, 40, 108, 16, 84, 5, 73)(2, 70, 7, 75, 20, 88, 35, 103, 14, 82, 34, 102, 57, 125, 59, 127, 38, 106, 27, 95, 54, 122, 53, 121, 26, 94, 9, 77, 25, 93, 24, 92, 8, 76)(4, 72, 12, 80, 32, 100, 31, 99, 11, 79, 30, 98, 56, 124, 55, 123, 29, 97, 39, 107, 60, 128, 58, 126, 37, 105, 15, 83, 36, 104, 33, 101, 13, 81)(6, 74, 17, 85, 41, 109, 49, 117, 22, 90, 48, 116, 65, 133, 67, 135, 51, 119, 45, 113, 62, 130, 61, 129, 44, 112, 19, 87, 43, 111, 42, 110, 18, 86) L = (1, 70)(2, 74)(3, 77)(4, 69)(5, 82)(6, 72)(7, 87)(8, 90)(9, 86)(10, 95)(11, 71)(12, 91)(13, 89)(14, 85)(15, 73)(16, 106)(17, 83)(18, 79)(19, 81)(20, 113)(21, 75)(22, 80)(23, 76)(24, 119)(25, 112)(26, 117)(27, 110)(28, 102)(29, 78)(30, 108)(31, 115)(32, 120)(33, 114)(34, 111)(35, 116)(36, 118)(37, 96)(38, 109)(39, 84)(40, 94)(41, 107)(42, 97)(43, 105)(44, 99)(45, 101)(46, 88)(47, 93)(48, 104)(49, 98)(50, 103)(51, 100)(52, 92)(53, 135)(54, 129)(55, 132)(56, 136)(57, 130)(58, 131)(59, 133)(60, 134)(61, 123)(62, 126)(63, 125)(64, 122)(65, 128)(66, 127)(67, 124)(68, 121) local type(s) :: { ( 4^34 ) } Outer automorphisms :: reflexible Dual of E16.954 Transitivity :: ET+ VT+ Graph:: bipartite v = 4 e = 68 f = 34 degree seq :: [ 34^4 ] E16.956 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 17}) Quotient :: edge^2 Aut^+ = C17 : C4 (small group id <68, 3>) Aut = C2 x (C17 : C4) (small group id <136, 13>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1 * Y2, Y2^4, Y1^4, (Y2 * Y1^-1)^2, Y1^4, (R * Y3)^2, Y2^4, R * Y1 * R * Y2, Y2^-1 * Y1 * Y3 * Y1^-2, Y1 * Y3^-1 * Y1^-1 * Y2 * Y1, Y3 * Y2 * Y3^-3 * Y1 ] Map:: polytopal non-degenerate R = (1, 69, 4, 72, 16, 84, 29, 97, 12, 80, 36, 104, 61, 129, 57, 125, 38, 106, 51, 119, 65, 133, 60, 128, 34, 102, 21, 89, 47, 115, 27, 95, 7, 75)(2, 70, 9, 77, 30, 98, 53, 121, 24, 92, 44, 112, 64, 132, 66, 134, 49, 117, 18, 86, 48, 116, 52, 120, 23, 91, 6, 74, 22, 90, 35, 103, 11, 79)(3, 71, 5, 73, 20, 88, 41, 109, 15, 83, 17, 85, 46, 114, 63, 131, 42, 110, 43, 111, 55, 123, 67, 135, 54, 122, 25, 93, 26, 94, 40, 108, 14, 82)(8, 76, 28, 96, 56, 124, 50, 118, 33, 101, 58, 126, 68, 136, 62, 130, 39, 107, 31, 99, 59, 127, 37, 105, 13, 81, 10, 78, 32, 100, 45, 113, 19, 87)(137, 138, 144, 141)(139, 148, 145, 146)(140, 142, 155, 153)(143, 160, 164, 162)(147, 169, 156, 157)(149, 151, 172, 158)(150, 174, 166, 167)(152, 154, 181, 179)(159, 186, 182, 183)(161, 165, 180, 168)(163, 185, 192, 191)(170, 189, 194, 176)(171, 175, 177, 187)(173, 178, 197, 184)(188, 198, 199, 201)(190, 193, 200, 195)(196, 202, 204, 203)(205, 207, 217, 210)(206, 211, 229, 214)(208, 219, 241, 222)(209, 223, 227, 225)(212, 215, 238, 230)(213, 233, 258, 235)(216, 218, 243, 226)(220, 246, 263, 248)(221, 249, 253, 251)(224, 254, 256, 255)(228, 231, 247, 236)(232, 257, 264, 259)(234, 261, 271, 262)(237, 239, 242, 244)(240, 245, 266, 252)(250, 260, 270, 269)(265, 267, 272, 268) L = (1, 137)(2, 138)(3, 139)(4, 140)(5, 141)(6, 142)(7, 143)(8, 144)(9, 145)(10, 146)(11, 147)(12, 148)(13, 149)(14, 150)(15, 151)(16, 152)(17, 153)(18, 154)(19, 155)(20, 156)(21, 157)(22, 158)(23, 159)(24, 160)(25, 161)(26, 162)(27, 163)(28, 164)(29, 165)(30, 166)(31, 167)(32, 168)(33, 169)(34, 170)(35, 171)(36, 172)(37, 173)(38, 174)(39, 175)(40, 176)(41, 177)(42, 178)(43, 179)(44, 180)(45, 181)(46, 182)(47, 183)(48, 184)(49, 185)(50, 186)(51, 187)(52, 188)(53, 189)(54, 190)(55, 191)(56, 192)(57, 193)(58, 194)(59, 195)(60, 196)(61, 197)(62, 198)(63, 199)(64, 200)(65, 201)(66, 202)(67, 203)(68, 204)(69, 205)(70, 206)(71, 207)(72, 208)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 257)(122, 258)(123, 259)(124, 260)(125, 261)(126, 262)(127, 263)(128, 264)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272) local type(s) :: { ( 4^4 ), ( 4^34 ) } Outer automorphisms :: reflexible Dual of E16.959 Graph:: simple bipartite v = 38 e = 136 f = 68 degree seq :: [ 4^34, 34^4 ] E16.957 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 17}) Quotient :: edge^2 Aut^+ = C17 : C4 (small group id <68, 3>) Aut = C2 x (C17 : C4) (small group id <136, 13>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y1^-1 * Y2)^2, Y2^4, Y1^4, Y2^2 * Y1^-2 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, (Y1^-1 * Y3^-1 * Y2^-1)^17 ] Map:: polytopal R = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136)(137, 138, 142, 140)(139, 145, 154, 144)(141, 147, 158, 149)(143, 152, 164, 151)(146, 157, 171, 156)(148, 150, 162, 160)(153, 167, 184, 166)(155, 169, 186, 168)(159, 175, 190, 174)(161, 173, 183, 177)(163, 180, 192, 179)(165, 182, 194, 181)(170, 187, 176, 178)(172, 189, 198, 188)(185, 196, 202, 195)(191, 197, 203, 199)(193, 201, 204, 200)(205, 207, 214, 209)(206, 211, 221, 212)(208, 215, 227, 216)(210, 218, 231, 219)(213, 223, 238, 224)(217, 225, 240, 229)(220, 233, 251, 234)(222, 235, 253, 236)(226, 241, 250, 242)(228, 243, 259, 244)(230, 246, 237, 247)(232, 248, 261, 249)(239, 255, 265, 256)(245, 257, 263, 252)(254, 264, 268, 260)(258, 262, 269, 267)(266, 271, 272, 270) L = (1, 137)(2, 138)(3, 139)(4, 140)(5, 141)(6, 142)(7, 143)(8, 144)(9, 145)(10, 146)(11, 147)(12, 148)(13, 149)(14, 150)(15, 151)(16, 152)(17, 153)(18, 154)(19, 155)(20, 156)(21, 157)(22, 158)(23, 159)(24, 160)(25, 161)(26, 162)(27, 163)(28, 164)(29, 165)(30, 166)(31, 167)(32, 168)(33, 169)(34, 170)(35, 171)(36, 172)(37, 173)(38, 174)(39, 175)(40, 176)(41, 177)(42, 178)(43, 179)(44, 180)(45, 181)(46, 182)(47, 183)(48, 184)(49, 185)(50, 186)(51, 187)(52, 188)(53, 189)(54, 190)(55, 191)(56, 192)(57, 193)(58, 194)(59, 195)(60, 196)(61, 197)(62, 198)(63, 199)(64, 200)(65, 201)(66, 202)(67, 203)(68, 204)(69, 205)(70, 206)(71, 207)(72, 208)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 257)(122, 258)(123, 259)(124, 260)(125, 261)(126, 262)(127, 263)(128, 264)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272) local type(s) :: { ( 68, 68 ), ( 68^4 ) } Outer automorphisms :: reflexible Dual of E16.958 Graph:: simple bipartite v = 102 e = 136 f = 4 degree seq :: [ 2^68, 4^34 ] E16.958 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 17}) Quotient :: loop^2 Aut^+ = C17 : C4 (small group id <68, 3>) Aut = C2 x (C17 : C4) (small group id <136, 13>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1 * Y2, Y2^4, Y1^4, (Y2 * Y1^-1)^2, Y1^4, (R * Y3)^2, Y2^4, R * Y1 * R * Y2, Y2^-1 * Y1 * Y3 * Y1^-2, Y1 * Y3^-1 * Y1^-1 * Y2 * Y1, Y3 * Y2 * Y3^-3 * Y1 ] Map:: R = (1, 69, 137, 205, 4, 72, 140, 208, 16, 84, 152, 220, 29, 97, 165, 233, 12, 80, 148, 216, 36, 104, 172, 240, 61, 129, 197, 265, 57, 125, 193, 261, 38, 106, 174, 242, 51, 119, 187, 255, 65, 133, 201, 269, 60, 128, 196, 264, 34, 102, 170, 238, 21, 89, 157, 225, 47, 115, 183, 251, 27, 95, 163, 231, 7, 75, 143, 211)(2, 70, 138, 206, 9, 77, 145, 213, 30, 98, 166, 234, 53, 121, 189, 257, 24, 92, 160, 228, 44, 112, 180, 248, 64, 132, 200, 268, 66, 134, 202, 270, 49, 117, 185, 253, 18, 86, 154, 222, 48, 116, 184, 252, 52, 120, 188, 256, 23, 91, 159, 227, 6, 74, 142, 210, 22, 90, 158, 226, 35, 103, 171, 239, 11, 79, 147, 215)(3, 71, 139, 207, 5, 73, 141, 209, 20, 88, 156, 224, 41, 109, 177, 245, 15, 83, 151, 219, 17, 85, 153, 221, 46, 114, 182, 250, 63, 131, 199, 267, 42, 110, 178, 246, 43, 111, 179, 247, 55, 123, 191, 259, 67, 135, 203, 271, 54, 122, 190, 258, 25, 93, 161, 229, 26, 94, 162, 230, 40, 108, 176, 244, 14, 82, 150, 218)(8, 76, 144, 212, 28, 96, 164, 232, 56, 124, 192, 260, 50, 118, 186, 254, 33, 101, 169, 237, 58, 126, 194, 262, 68, 136, 204, 272, 62, 130, 198, 266, 39, 107, 175, 243, 31, 99, 167, 235, 59, 127, 195, 263, 37, 105, 173, 241, 13, 81, 149, 217, 10, 78, 146, 214, 32, 100, 168, 236, 45, 113, 181, 249, 19, 87, 155, 223) L = (1, 70)(2, 76)(3, 80)(4, 74)(5, 69)(6, 87)(7, 92)(8, 73)(9, 78)(10, 71)(11, 101)(12, 77)(13, 83)(14, 106)(15, 104)(16, 86)(17, 72)(18, 113)(19, 85)(20, 89)(21, 79)(22, 81)(23, 118)(24, 96)(25, 97)(26, 75)(27, 117)(28, 94)(29, 112)(30, 99)(31, 82)(32, 93)(33, 88)(34, 121)(35, 107)(36, 90)(37, 110)(38, 98)(39, 109)(40, 102)(41, 119)(42, 129)(43, 84)(44, 100)(45, 111)(46, 115)(47, 91)(48, 105)(49, 124)(50, 114)(51, 103)(52, 130)(53, 126)(54, 125)(55, 95)(56, 123)(57, 132)(58, 108)(59, 122)(60, 134)(61, 116)(62, 131)(63, 133)(64, 127)(65, 120)(66, 136)(67, 128)(68, 135)(137, 207)(138, 211)(139, 217)(140, 219)(141, 223)(142, 205)(143, 229)(144, 215)(145, 233)(146, 206)(147, 238)(148, 218)(149, 210)(150, 243)(151, 241)(152, 246)(153, 249)(154, 208)(155, 227)(156, 254)(157, 209)(158, 216)(159, 225)(160, 231)(161, 214)(162, 212)(163, 247)(164, 257)(165, 258)(166, 261)(167, 213)(168, 228)(169, 239)(170, 230)(171, 242)(172, 245)(173, 222)(174, 244)(175, 226)(176, 237)(177, 266)(178, 263)(179, 236)(180, 220)(181, 253)(182, 260)(183, 221)(184, 240)(185, 251)(186, 256)(187, 224)(188, 255)(189, 264)(190, 235)(191, 232)(192, 270)(193, 271)(194, 234)(195, 248)(196, 259)(197, 267)(198, 252)(199, 272)(200, 265)(201, 250)(202, 269)(203, 262)(204, 268) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E16.957 Transitivity :: VT+ Graph:: bipartite v = 4 e = 136 f = 102 degree seq :: [ 68^4 ] E16.959 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 17}) Quotient :: loop^2 Aut^+ = C17 : C4 (small group id <68, 3>) Aut = C2 x (C17 : C4) (small group id <136, 13>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y1^-1 * Y2)^2, Y2^4, Y1^4, Y2^2 * Y1^-2 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, (Y1^-1 * Y3^-1 * Y2^-1)^17 ] Map:: polytopal non-degenerate R = (1, 69, 137, 205)(2, 70, 138, 206)(3, 71, 139, 207)(4, 72, 140, 208)(5, 73, 141, 209)(6, 74, 142, 210)(7, 75, 143, 211)(8, 76, 144, 212)(9, 77, 145, 213)(10, 78, 146, 214)(11, 79, 147, 215)(12, 80, 148, 216)(13, 81, 149, 217)(14, 82, 150, 218)(15, 83, 151, 219)(16, 84, 152, 220)(17, 85, 153, 221)(18, 86, 154, 222)(19, 87, 155, 223)(20, 88, 156, 224)(21, 89, 157, 225)(22, 90, 158, 226)(23, 91, 159, 227)(24, 92, 160, 228)(25, 93, 161, 229)(26, 94, 162, 230)(27, 95, 163, 231)(28, 96, 164, 232)(29, 97, 165, 233)(30, 98, 166, 234)(31, 99, 167, 235)(32, 100, 168, 236)(33, 101, 169, 237)(34, 102, 170, 238)(35, 103, 171, 239)(36, 104, 172, 240)(37, 105, 173, 241)(38, 106, 174, 242)(39, 107, 175, 243)(40, 108, 176, 244)(41, 109, 177, 245)(42, 110, 178, 246)(43, 111, 179, 247)(44, 112, 180, 248)(45, 113, 181, 249)(46, 114, 182, 250)(47, 115, 183, 251)(48, 116, 184, 252)(49, 117, 185, 253)(50, 118, 186, 254)(51, 119, 187, 255)(52, 120, 188, 256)(53, 121, 189, 257)(54, 122, 190, 258)(55, 123, 191, 259)(56, 124, 192, 260)(57, 125, 193, 261)(58, 126, 194, 262)(59, 127, 195, 263)(60, 128, 196, 264)(61, 129, 197, 265)(62, 130, 198, 266)(63, 131, 199, 267)(64, 132, 200, 268)(65, 133, 201, 269)(66, 134, 202, 270)(67, 135, 203, 271)(68, 136, 204, 272) L = (1, 70)(2, 74)(3, 77)(4, 69)(5, 79)(6, 72)(7, 84)(8, 71)(9, 86)(10, 89)(11, 90)(12, 82)(13, 73)(14, 94)(15, 75)(16, 96)(17, 99)(18, 76)(19, 101)(20, 78)(21, 103)(22, 81)(23, 107)(24, 80)(25, 105)(26, 92)(27, 112)(28, 83)(29, 114)(30, 85)(31, 116)(32, 87)(33, 118)(34, 119)(35, 88)(36, 121)(37, 115)(38, 91)(39, 122)(40, 110)(41, 93)(42, 102)(43, 95)(44, 124)(45, 97)(46, 126)(47, 109)(48, 98)(49, 128)(50, 100)(51, 108)(52, 104)(53, 130)(54, 106)(55, 129)(56, 111)(57, 133)(58, 113)(59, 117)(60, 134)(61, 135)(62, 120)(63, 123)(64, 125)(65, 136)(66, 127)(67, 131)(68, 132)(137, 207)(138, 211)(139, 214)(140, 215)(141, 205)(142, 218)(143, 221)(144, 206)(145, 223)(146, 209)(147, 227)(148, 208)(149, 225)(150, 231)(151, 210)(152, 233)(153, 212)(154, 235)(155, 238)(156, 213)(157, 240)(158, 241)(159, 216)(160, 243)(161, 217)(162, 246)(163, 219)(164, 248)(165, 251)(166, 220)(167, 253)(168, 222)(169, 247)(170, 224)(171, 255)(172, 229)(173, 250)(174, 226)(175, 259)(176, 228)(177, 257)(178, 237)(179, 230)(180, 261)(181, 232)(182, 242)(183, 234)(184, 245)(185, 236)(186, 264)(187, 265)(188, 239)(189, 263)(190, 262)(191, 244)(192, 254)(193, 249)(194, 269)(195, 252)(196, 268)(197, 256)(198, 271)(199, 258)(200, 260)(201, 267)(202, 266)(203, 272)(204, 270) local type(s) :: { ( 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.956 Transitivity :: VT+ Graph:: simple bipartite v = 68 e = 136 f = 38 degree seq :: [ 4^68 ] E16.960 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 34, 34}) Quotient :: regular Aut^+ = C34 x C2 (small group id <68, 5>) Aut = C2 x C2 x D34 (small group id <136, 14>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^34 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 35, 38, 40, 42, 44, 46, 48, 50, 55, 52, 53, 56, 58, 60, 62, 64, 66, 32, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 30, 36, 33, 34, 37, 39, 41, 43, 45, 47, 49, 54, 57, 59, 61, 63, 65, 67, 68, 51, 31, 27, 23, 19, 15, 11, 7) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 36)(32, 51)(33, 35)(34, 38)(37, 40)(39, 42)(41, 44)(43, 46)(45, 48)(47, 50)(49, 55)(52, 54)(53, 57)(56, 59)(58, 61)(60, 63)(62, 65)(64, 67)(66, 68) local type(s) :: { ( 34^34 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 34 f = 2 degree seq :: [ 34^2 ] E16.961 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 34, 34}) Quotient :: edge Aut^+ = C34 x C2 (small group id <68, 5>) Aut = C2 x C2 x D34 (small group id <136, 14>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^34 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 37, 39, 41, 43, 45, 47, 50, 51, 53, 55, 57, 59, 61, 63, 65, 68, 32, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 33, 34, 36, 38, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60, 62, 64, 67, 66, 49, 30, 26, 22, 18, 14, 10, 6)(69, 70)(71, 73)(72, 74)(75, 77)(76, 78)(79, 81)(80, 82)(83, 85)(84, 86)(87, 89)(88, 90)(91, 93)(92, 94)(95, 97)(96, 98)(99, 101)(100, 117)(102, 103)(104, 105)(106, 107)(108, 109)(110, 111)(112, 113)(114, 115)(116, 118)(119, 120)(121, 122)(123, 124)(125, 126)(127, 128)(129, 130)(131, 132)(133, 135)(134, 136) L = (1, 69)(2, 70)(3, 71)(4, 72)(5, 73)(6, 74)(7, 75)(8, 76)(9, 77)(10, 78)(11, 79)(12, 80)(13, 81)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 88)(21, 89)(22, 90)(23, 91)(24, 92)(25, 93)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 100)(33, 101)(34, 102)(35, 103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44, 112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 120)(53, 121)(54, 122)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136) local type(s) :: { ( 68, 68 ), ( 68^34 ) } Outer automorphisms :: reflexible Dual of E16.962 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 68 f = 2 degree seq :: [ 2^34, 34^2 ] E16.962 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 34, 34}) Quotient :: loop Aut^+ = C34 x C2 (small group id <68, 5>) Aut = C2 x C2 x D34 (small group id <136, 14>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^34 ] Map:: R = (1, 69, 3, 71, 7, 75, 11, 79, 15, 83, 19, 87, 23, 91, 27, 95, 31, 99, 35, 103, 37, 105, 39, 107, 41, 109, 43, 111, 45, 113, 47, 115, 50, 118, 51, 119, 53, 121, 55, 123, 57, 125, 59, 127, 61, 129, 63, 131, 65, 133, 68, 136, 32, 100, 28, 96, 24, 92, 20, 88, 16, 84, 12, 80, 8, 76, 4, 72)(2, 70, 5, 73, 9, 77, 13, 81, 17, 85, 21, 89, 25, 93, 29, 97, 33, 101, 34, 102, 36, 104, 38, 106, 40, 108, 42, 110, 44, 112, 46, 114, 48, 116, 52, 120, 54, 122, 56, 124, 58, 126, 60, 128, 62, 130, 64, 132, 67, 135, 66, 134, 49, 117, 30, 98, 26, 94, 22, 90, 18, 86, 14, 82, 10, 78, 6, 74) L = (1, 70)(2, 69)(3, 73)(4, 74)(5, 71)(6, 72)(7, 77)(8, 78)(9, 75)(10, 76)(11, 81)(12, 82)(13, 79)(14, 80)(15, 85)(16, 86)(17, 83)(18, 84)(19, 89)(20, 90)(21, 87)(22, 88)(23, 93)(24, 94)(25, 91)(26, 92)(27, 97)(28, 98)(29, 95)(30, 96)(31, 101)(32, 117)(33, 99)(34, 103)(35, 102)(36, 105)(37, 104)(38, 107)(39, 106)(40, 109)(41, 108)(42, 111)(43, 110)(44, 113)(45, 112)(46, 115)(47, 114)(48, 118)(49, 100)(50, 116)(51, 120)(52, 119)(53, 122)(54, 121)(55, 124)(56, 123)(57, 126)(58, 125)(59, 128)(60, 127)(61, 130)(62, 129)(63, 132)(64, 131)(65, 135)(66, 136)(67, 133)(68, 134) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.961 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 68 f = 36 degree seq :: [ 68^2 ] E16.963 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 34, 34}) Quotient :: dipole Aut^+ = C34 x C2 (small group id <68, 5>) Aut = C2 x C2 x D34 (small group id <136, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^34, (Y3 * Y2^-1)^34 ] Map:: R = (1, 69, 2, 70)(3, 71, 5, 73)(4, 72, 6, 74)(7, 75, 9, 77)(8, 76, 10, 78)(11, 79, 13, 81)(12, 80, 14, 82)(15, 83, 17, 85)(16, 84, 18, 86)(19, 87, 21, 89)(20, 88, 22, 90)(23, 91, 25, 93)(24, 92, 26, 94)(27, 95, 29, 97)(28, 96, 30, 98)(31, 99, 33, 101)(32, 100, 49, 117)(34, 102, 35, 103)(36, 104, 37, 105)(38, 106, 39, 107)(40, 108, 41, 109)(42, 110, 43, 111)(44, 112, 45, 113)(46, 114, 47, 115)(48, 116, 50, 118)(51, 119, 52, 120)(53, 121, 54, 122)(55, 123, 56, 124)(57, 125, 58, 126)(59, 127, 60, 128)(61, 129, 62, 130)(63, 131, 64, 132)(65, 133, 67, 135)(66, 134, 68, 136)(137, 205, 139, 207, 143, 211, 147, 215, 151, 219, 155, 223, 159, 227, 163, 231, 167, 235, 171, 239, 173, 241, 175, 243, 177, 245, 179, 247, 181, 249, 183, 251, 186, 254, 187, 255, 189, 257, 191, 259, 193, 261, 195, 263, 197, 265, 199, 267, 201, 269, 204, 272, 168, 236, 164, 232, 160, 228, 156, 224, 152, 220, 148, 216, 144, 212, 140, 208)(138, 206, 141, 209, 145, 213, 149, 217, 153, 221, 157, 225, 161, 229, 165, 233, 169, 237, 170, 238, 172, 240, 174, 242, 176, 244, 178, 246, 180, 248, 182, 250, 184, 252, 188, 256, 190, 258, 192, 260, 194, 262, 196, 264, 198, 266, 200, 268, 203, 271, 202, 270, 185, 253, 166, 234, 162, 230, 158, 226, 154, 222, 150, 218, 146, 214, 142, 210) L = (1, 138)(2, 137)(3, 141)(4, 142)(5, 139)(6, 140)(7, 145)(8, 146)(9, 143)(10, 144)(11, 149)(12, 150)(13, 147)(14, 148)(15, 153)(16, 154)(17, 151)(18, 152)(19, 157)(20, 158)(21, 155)(22, 156)(23, 161)(24, 162)(25, 159)(26, 160)(27, 165)(28, 166)(29, 163)(30, 164)(31, 169)(32, 185)(33, 167)(34, 171)(35, 170)(36, 173)(37, 172)(38, 175)(39, 174)(40, 177)(41, 176)(42, 179)(43, 178)(44, 181)(45, 180)(46, 183)(47, 182)(48, 186)(49, 168)(50, 184)(51, 188)(52, 187)(53, 190)(54, 189)(55, 192)(56, 191)(57, 194)(58, 193)(59, 196)(60, 195)(61, 198)(62, 197)(63, 200)(64, 199)(65, 203)(66, 204)(67, 201)(68, 202)(69, 205)(70, 206)(71, 207)(72, 208)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 257)(122, 258)(123, 259)(124, 260)(125, 261)(126, 262)(127, 263)(128, 264)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272) local type(s) :: { ( 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.964 Graph:: bipartite v = 36 e = 136 f = 70 degree seq :: [ 4^34, 68^2 ] E16.964 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 34, 34}) Quotient :: dipole Aut^+ = C34 x C2 (small group id <68, 5>) Aut = C2 x C2 x D34 (small group id <136, 14>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-34, Y1^34 ] Map:: R = (1, 69, 2, 70, 5, 73, 9, 77, 13, 81, 17, 85, 21, 89, 25, 93, 29, 97, 39, 107, 35, 103, 38, 106, 42, 110, 44, 112, 46, 114, 48, 116, 50, 118, 52, 120, 61, 129, 57, 125, 54, 122, 55, 123, 58, 126, 62, 130, 64, 132, 66, 134, 32, 100, 28, 96, 24, 92, 20, 88, 16, 84, 12, 80, 8, 76, 4, 72)(3, 71, 6, 74, 10, 78, 14, 82, 18, 86, 22, 90, 26, 94, 30, 98, 40, 108, 36, 104, 33, 101, 34, 102, 37, 105, 41, 109, 43, 111, 45, 113, 47, 115, 49, 117, 51, 119, 60, 128, 56, 124, 59, 127, 63, 131, 65, 133, 67, 135, 68, 136, 53, 121, 31, 99, 27, 95, 23, 91, 19, 87, 15, 83, 11, 79, 7, 75)(137, 205)(138, 206)(139, 207)(140, 208)(141, 209)(142, 210)(143, 211)(144, 212)(145, 213)(146, 214)(147, 215)(148, 216)(149, 217)(150, 218)(151, 219)(152, 220)(153, 221)(154, 222)(155, 223)(156, 224)(157, 225)(158, 226)(159, 227)(160, 228)(161, 229)(162, 230)(163, 231)(164, 232)(165, 233)(166, 234)(167, 235)(168, 236)(169, 237)(170, 238)(171, 239)(172, 240)(173, 241)(174, 242)(175, 243)(176, 244)(177, 245)(178, 246)(179, 247)(180, 248)(181, 249)(182, 250)(183, 251)(184, 252)(185, 253)(186, 254)(187, 255)(188, 256)(189, 257)(190, 258)(191, 259)(192, 260)(193, 261)(194, 262)(195, 263)(196, 264)(197, 265)(198, 266)(199, 267)(200, 268)(201, 269)(202, 270)(203, 271)(204, 272) L = (1, 139)(2, 142)(3, 137)(4, 143)(5, 146)(6, 138)(7, 140)(8, 147)(9, 150)(10, 141)(11, 144)(12, 151)(13, 154)(14, 145)(15, 148)(16, 155)(17, 158)(18, 149)(19, 152)(20, 159)(21, 162)(22, 153)(23, 156)(24, 163)(25, 166)(26, 157)(27, 160)(28, 167)(29, 176)(30, 161)(31, 164)(32, 189)(33, 171)(34, 174)(35, 169)(36, 175)(37, 178)(38, 170)(39, 172)(40, 165)(41, 180)(42, 173)(43, 182)(44, 177)(45, 184)(46, 179)(47, 186)(48, 181)(49, 188)(50, 183)(51, 197)(52, 185)(53, 168)(54, 192)(55, 195)(56, 190)(57, 196)(58, 199)(59, 191)(60, 193)(61, 187)(62, 201)(63, 194)(64, 203)(65, 198)(66, 204)(67, 200)(68, 202)(69, 205)(70, 206)(71, 207)(72, 208)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 257)(122, 258)(123, 259)(124, 260)(125, 261)(126, 262)(127, 263)(128, 264)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272) local type(s) :: { ( 4, 68 ), ( 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68, 4, 68 ) } Outer automorphisms :: reflexible Dual of E16.963 Graph:: simple bipartite v = 70 e = 136 f = 36 degree seq :: [ 2^68, 68^2 ] E16.965 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (C6 x S3) : C2 (small group id <72, 22>) Aut = ((C6 x C2) : C2) x S3 (small group id <144, 153>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^-1 * Y2 * Y3 * Y2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y3^4, R * Y2 * R * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74)(3, 75, 11, 83)(4, 76, 10, 82)(5, 77, 16, 88)(6, 78, 8, 80)(7, 79, 18, 90)(9, 81, 23, 95)(12, 84, 28, 100)(13, 85, 26, 98)(14, 86, 30, 102)(15, 87, 22, 94)(17, 89, 33, 105)(19, 91, 38, 110)(20, 92, 36, 108)(21, 93, 40, 112)(24, 96, 43, 115)(25, 97, 35, 107)(27, 99, 42, 114)(29, 101, 48, 120)(31, 103, 52, 124)(32, 104, 37, 109)(34, 106, 44, 116)(39, 111, 58, 130)(41, 113, 62, 134)(45, 117, 56, 128)(46, 118, 55, 127)(47, 119, 61, 133)(49, 121, 63, 135)(50, 122, 64, 136)(51, 123, 57, 129)(53, 125, 59, 131)(54, 126, 60, 132)(65, 137, 69, 141)(66, 138, 72, 144)(67, 139, 71, 143)(68, 140, 70, 142)(145, 217, 147, 219, 149, 221)(146, 218, 151, 223, 153, 225)(148, 220, 158, 230, 156, 228)(150, 222, 161, 233, 157, 229)(152, 224, 165, 237, 163, 235)(154, 226, 168, 240, 164, 236)(155, 227, 169, 241, 171, 243)(159, 231, 173, 245, 175, 247)(160, 232, 176, 248, 178, 250)(162, 234, 179, 251, 181, 253)(166, 238, 183, 255, 185, 257)(167, 239, 186, 258, 188, 260)(170, 242, 191, 263, 189, 261)(172, 244, 193, 265, 190, 262)(174, 246, 194, 266, 195, 267)(177, 249, 198, 270, 197, 269)(180, 252, 201, 273, 199, 271)(182, 254, 203, 275, 200, 272)(184, 256, 204, 276, 205, 277)(187, 259, 208, 280, 207, 279)(192, 264, 209, 281, 210, 282)(196, 268, 212, 284, 211, 283)(202, 274, 213, 285, 214, 286)(206, 278, 216, 288, 215, 287) L = (1, 148)(2, 152)(3, 156)(4, 159)(5, 158)(6, 145)(7, 163)(8, 166)(9, 165)(10, 146)(11, 170)(12, 173)(13, 147)(14, 175)(15, 150)(16, 177)(17, 149)(18, 180)(19, 183)(20, 151)(21, 185)(22, 154)(23, 187)(24, 153)(25, 189)(26, 192)(27, 191)(28, 155)(29, 157)(30, 160)(31, 161)(32, 197)(33, 196)(34, 198)(35, 199)(36, 202)(37, 201)(38, 162)(39, 164)(40, 167)(41, 168)(42, 207)(43, 206)(44, 208)(45, 209)(46, 169)(47, 210)(48, 172)(49, 171)(50, 178)(51, 176)(52, 174)(53, 212)(54, 211)(55, 213)(56, 179)(57, 214)(58, 182)(59, 181)(60, 188)(61, 186)(62, 184)(63, 216)(64, 215)(65, 190)(66, 193)(67, 194)(68, 195)(69, 200)(70, 203)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.966 Graph:: simple bipartite v = 60 e = 144 f = 54 degree seq :: [ 4^36, 6^24 ] E16.966 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (C6 x S3) : C2 (small group id <72, 22>) Aut = ((C6 x C2) : C2) x S3 (small group id <144, 153>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1 * Y3^2 * Y1, Y3^4, Y3^2 * Y1^-2, (R * Y1)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^2)^2, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74, 7, 79, 5, 77)(3, 75, 11, 83, 18, 90, 13, 85)(4, 76, 15, 87, 6, 78, 16, 88)(8, 80, 19, 91, 17, 89, 21, 93)(9, 81, 23, 95, 10, 82, 24, 96)(12, 84, 28, 100, 14, 86, 29, 101)(20, 92, 36, 108, 22, 94, 37, 109)(25, 97, 41, 113, 30, 102, 43, 115)(26, 98, 45, 117, 27, 99, 46, 118)(31, 103, 49, 121, 32, 104, 50, 122)(33, 105, 51, 123, 38, 110, 53, 125)(34, 106, 55, 127, 35, 107, 56, 128)(39, 111, 59, 131, 40, 112, 60, 132)(42, 114, 58, 130, 44, 116, 57, 129)(47, 119, 54, 126, 48, 120, 52, 124)(61, 133, 70, 142, 64, 136, 67, 139)(62, 134, 71, 143, 63, 135, 72, 144)(65, 137, 68, 140, 66, 138, 69, 141)(145, 217, 147, 219)(146, 218, 152, 224)(148, 220, 158, 230)(149, 221, 161, 233)(150, 222, 156, 228)(151, 223, 162, 234)(153, 225, 166, 238)(154, 226, 164, 236)(155, 227, 169, 241)(157, 229, 174, 246)(159, 231, 175, 247)(160, 232, 176, 248)(163, 235, 177, 249)(165, 237, 182, 254)(167, 239, 183, 255)(168, 240, 184, 256)(170, 242, 188, 260)(171, 243, 186, 258)(172, 244, 191, 263)(173, 245, 192, 264)(178, 250, 198, 270)(179, 251, 196, 268)(180, 252, 201, 273)(181, 253, 202, 274)(185, 257, 205, 277)(187, 259, 208, 280)(189, 261, 209, 281)(190, 262, 210, 282)(193, 265, 206, 278)(194, 266, 207, 279)(195, 267, 211, 283)(197, 269, 214, 286)(199, 271, 215, 287)(200, 272, 216, 288)(203, 275, 212, 284)(204, 276, 213, 285) L = (1, 148)(2, 153)(3, 156)(4, 151)(5, 154)(6, 145)(7, 150)(8, 164)(9, 149)(10, 146)(11, 170)(12, 162)(13, 171)(14, 147)(15, 168)(16, 167)(17, 166)(18, 158)(19, 178)(20, 161)(21, 179)(22, 152)(23, 159)(24, 160)(25, 186)(26, 157)(27, 155)(28, 190)(29, 189)(30, 188)(31, 183)(32, 184)(33, 196)(34, 165)(35, 163)(36, 200)(37, 199)(38, 198)(39, 176)(40, 175)(41, 206)(42, 174)(43, 207)(44, 169)(45, 172)(46, 173)(47, 209)(48, 210)(49, 205)(50, 208)(51, 212)(52, 182)(53, 213)(54, 177)(55, 180)(56, 181)(57, 215)(58, 216)(59, 211)(60, 214)(61, 194)(62, 187)(63, 185)(64, 193)(65, 192)(66, 191)(67, 204)(68, 197)(69, 195)(70, 203)(71, 202)(72, 201)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.965 Graph:: simple bipartite v = 54 e = 144 f = 60 degree seq :: [ 4^36, 8^18 ] E16.967 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (C6 x S3) : C2 (small group id <72, 23>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, (Y3 * Y1 * Y2)^2, Y3^-2 * Y2 * Y3^2 * Y2, Y3^6, (Y3^-1 * Y1 * Y2)^2, (Y3^-2 * Y1)^2, (Y3 * Y1)^4, Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1 * Y3^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74)(3, 75, 9, 81)(4, 76, 12, 84)(5, 77, 15, 87)(6, 78, 18, 90)(7, 79, 21, 93)(8, 80, 24, 96)(10, 82, 25, 97)(11, 83, 22, 94)(13, 85, 20, 92)(14, 86, 26, 98)(16, 88, 19, 91)(17, 89, 23, 95)(27, 99, 51, 123)(28, 100, 54, 126)(29, 101, 56, 128)(30, 102, 53, 125)(31, 103, 57, 129)(32, 104, 52, 124)(33, 105, 55, 127)(34, 106, 46, 118)(35, 107, 50, 122)(36, 108, 60, 132)(37, 109, 61, 133)(38, 110, 47, 119)(39, 111, 62, 134)(40, 112, 65, 137)(41, 113, 67, 139)(42, 114, 64, 136)(43, 115, 68, 140)(44, 116, 63, 135)(45, 117, 66, 138)(48, 120, 71, 143)(49, 121, 72, 144)(58, 130, 70, 142)(59, 131, 69, 141)(145, 217, 147, 219)(146, 218, 150, 222)(148, 220, 157, 229)(149, 221, 160, 232)(151, 223, 166, 238)(152, 224, 169, 241)(153, 225, 171, 243)(154, 226, 174, 246)(155, 227, 176, 248)(156, 228, 173, 245)(158, 230, 175, 247)(159, 231, 172, 244)(161, 233, 177, 249)(162, 234, 183, 255)(163, 235, 186, 258)(164, 236, 188, 260)(165, 237, 185, 257)(167, 239, 187, 259)(168, 240, 184, 256)(170, 242, 189, 261)(178, 250, 204, 276)(179, 251, 196, 268)(180, 252, 203, 275)(181, 253, 202, 274)(182, 254, 197, 269)(190, 262, 215, 287)(191, 263, 207, 279)(192, 264, 214, 286)(193, 265, 213, 285)(194, 266, 208, 280)(195, 267, 216, 288)(198, 270, 210, 282)(199, 271, 209, 281)(200, 272, 212, 284)(201, 273, 211, 283)(205, 277, 206, 278) L = (1, 148)(2, 151)(3, 154)(4, 158)(5, 145)(6, 163)(7, 167)(8, 146)(9, 172)(10, 175)(11, 147)(12, 178)(13, 176)(14, 181)(15, 182)(16, 180)(17, 149)(18, 184)(19, 187)(20, 150)(21, 190)(22, 188)(23, 193)(24, 194)(25, 192)(26, 152)(27, 196)(28, 199)(29, 153)(30, 160)(31, 203)(32, 202)(33, 155)(34, 159)(35, 156)(36, 157)(37, 161)(38, 205)(39, 207)(40, 210)(41, 162)(42, 169)(43, 214)(44, 213)(45, 164)(46, 168)(47, 165)(48, 166)(49, 170)(50, 216)(51, 212)(52, 209)(53, 171)(54, 215)(55, 206)(56, 208)(57, 173)(58, 174)(59, 177)(60, 211)(61, 179)(62, 201)(63, 198)(64, 183)(65, 204)(66, 195)(67, 197)(68, 185)(69, 186)(70, 189)(71, 200)(72, 191)(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, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E16.972 Graph:: simple bipartite v = 72 e = 144 f = 42 degree seq :: [ 4^72 ] E16.968 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (C6 x S3) : C2 (small group id <72, 23>) Aut = D24 x S3 (small group id <144, 144>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y3 * Y2^-1 * Y3^-2 * Y2 * Y3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-2, Y3^2 * Y2 * Y3^-2 * Y2^-1, (Y3 * Y2^-1)^4 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74)(3, 75, 9, 81)(4, 76, 10, 82)(5, 77, 7, 79)(6, 78, 8, 80)(11, 83, 27, 99)(12, 84, 26, 98)(13, 85, 29, 101)(14, 86, 30, 102)(15, 87, 28, 100)(16, 88, 22, 94)(17, 89, 21, 93)(18, 90, 25, 97)(19, 91, 23, 95)(20, 92, 24, 96)(31, 103, 55, 127)(32, 104, 53, 125)(33, 105, 61, 133)(34, 106, 60, 132)(35, 107, 59, 131)(36, 108, 56, 128)(37, 109, 48, 120)(38, 110, 58, 130)(39, 111, 47, 119)(40, 112, 52, 124)(41, 113, 62, 134)(42, 114, 54, 126)(43, 115, 51, 123)(44, 116, 50, 122)(45, 117, 49, 121)(46, 118, 57, 129)(63, 135, 72, 144)(64, 136, 71, 143)(65, 137, 70, 142)(66, 138, 69, 141)(67, 139, 68, 140)(145, 217, 147, 219, 149, 221)(146, 218, 151, 223, 153, 225)(148, 220, 157, 229, 159, 231)(150, 222, 162, 234, 163, 235)(152, 224, 167, 239, 169, 241)(154, 226, 172, 244, 173, 245)(155, 227, 175, 247, 177, 249)(156, 228, 178, 250, 179, 251)(158, 230, 176, 248, 184, 256)(160, 232, 187, 259, 188, 260)(161, 233, 189, 261, 183, 255)(164, 236, 180, 252, 181, 253)(165, 237, 191, 263, 193, 265)(166, 238, 194, 266, 195, 267)(168, 240, 192, 264, 200, 272)(170, 242, 203, 275, 204, 276)(171, 243, 205, 277, 199, 271)(174, 246, 196, 268, 197, 269)(182, 254, 207, 279, 210, 282)(185, 257, 190, 262, 209, 281)(186, 258, 208, 280, 211, 283)(198, 270, 212, 284, 215, 287)(201, 273, 206, 278, 214, 286)(202, 274, 213, 285, 216, 288) L = (1, 148)(2, 152)(3, 155)(4, 158)(5, 160)(6, 145)(7, 165)(8, 168)(9, 170)(10, 146)(11, 176)(12, 147)(13, 181)(14, 183)(15, 185)(16, 184)(17, 149)(18, 182)(19, 186)(20, 150)(21, 192)(22, 151)(23, 197)(24, 199)(25, 201)(26, 200)(27, 153)(28, 198)(29, 202)(30, 154)(31, 164)(32, 163)(33, 190)(34, 207)(35, 208)(36, 156)(37, 161)(38, 157)(39, 211)(40, 179)(41, 189)(42, 159)(43, 180)(44, 209)(45, 210)(46, 162)(47, 174)(48, 173)(49, 206)(50, 212)(51, 213)(52, 166)(53, 171)(54, 167)(55, 216)(56, 195)(57, 205)(58, 169)(59, 196)(60, 214)(61, 215)(62, 172)(63, 175)(64, 177)(65, 178)(66, 187)(67, 188)(68, 191)(69, 193)(70, 194)(71, 203)(72, 204)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.970 Graph:: simple bipartite v = 60 e = 144 f = 54 degree seq :: [ 4^36, 6^24 ] E16.969 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (C6 x S3) : C2 (small group id <72, 23>) Aut = C2 x ((C6 x S3) : C2) (small group id <144, 151>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3 * Y1)^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-1 * Y3^-2 * Y2 * Y3, Y1 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-3 * Y2^-1, (Y2 * Y3 * Y1)^2, Y3^-2 * Y2 * Y3^2 * Y2^-1, Y2 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^4, (Y2 * Y3^-1 * Y2 * Y1)^2 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74)(3, 75, 11, 83)(4, 76, 10, 82)(5, 77, 17, 89)(6, 78, 8, 80)(7, 79, 23, 95)(9, 81, 29, 101)(12, 84, 33, 105)(13, 85, 28, 100)(14, 86, 31, 103)(15, 87, 34, 106)(16, 88, 25, 97)(18, 90, 32, 104)(19, 91, 26, 98)(20, 92, 30, 102)(21, 93, 24, 96)(22, 94, 27, 99)(35, 107, 53, 125)(36, 108, 65, 137)(37, 109, 62, 134)(38, 110, 56, 128)(39, 111, 59, 131)(40, 112, 68, 140)(41, 113, 57, 129)(42, 114, 64, 136)(43, 115, 61, 133)(44, 116, 55, 127)(45, 117, 70, 142)(46, 118, 60, 132)(47, 119, 54, 126)(48, 120, 66, 138)(49, 121, 69, 141)(50, 122, 58, 130)(51, 123, 67, 139)(52, 124, 63, 135)(71, 143, 72, 144)(145, 217, 147, 219, 149, 221)(146, 218, 151, 223, 153, 225)(148, 220, 158, 230, 160, 232)(150, 222, 164, 236, 165, 237)(152, 224, 170, 242, 172, 244)(154, 226, 176, 248, 177, 249)(155, 227, 179, 251, 180, 252)(156, 228, 181, 253, 183, 255)(157, 229, 184, 256, 185, 257)(159, 231, 182, 254, 189, 261)(161, 233, 191, 263, 192, 264)(162, 234, 193, 265, 194, 266)(163, 235, 195, 267, 188, 260)(166, 238, 186, 258, 187, 259)(167, 239, 197, 269, 198, 270)(168, 240, 199, 271, 201, 273)(169, 241, 202, 274, 203, 275)(171, 243, 200, 272, 207, 279)(173, 245, 209, 281, 210, 282)(174, 246, 211, 283, 212, 284)(175, 247, 213, 285, 206, 278)(178, 250, 204, 276, 205, 277)(190, 262, 196, 268, 215, 287)(208, 280, 214, 286, 216, 288) L = (1, 148)(2, 152)(3, 156)(4, 159)(5, 162)(6, 145)(7, 168)(8, 171)(9, 174)(10, 146)(11, 172)(12, 182)(13, 147)(14, 187)(15, 188)(16, 190)(17, 170)(18, 189)(19, 149)(20, 173)(21, 167)(22, 150)(23, 160)(24, 200)(25, 151)(26, 205)(27, 206)(28, 208)(29, 158)(30, 207)(31, 153)(32, 161)(33, 155)(34, 154)(35, 201)(36, 212)(37, 166)(38, 165)(39, 196)(40, 209)(41, 197)(42, 157)(43, 163)(44, 198)(45, 185)(46, 195)(47, 199)(48, 211)(49, 186)(50, 215)(51, 210)(52, 164)(53, 183)(54, 194)(55, 178)(56, 177)(57, 214)(58, 191)(59, 179)(60, 169)(61, 175)(62, 180)(63, 203)(64, 213)(65, 181)(66, 193)(67, 204)(68, 216)(69, 192)(70, 176)(71, 184)(72, 202)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.971 Graph:: simple bipartite v = 60 e = 144 f = 54 degree seq :: [ 4^36, 6^24 ] E16.970 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (C6 x S3) : C2 (small group id <72, 23>) Aut = D24 x S3 (small group id <144, 144>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1^4, Y1^4, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1^-2 * Y3 * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74, 7, 79, 5, 77)(3, 75, 11, 83, 22, 94, 8, 80)(4, 76, 14, 86, 23, 95, 16, 88)(6, 78, 19, 91, 24, 96, 20, 92)(9, 81, 27, 99, 17, 89, 29, 101)(10, 82, 30, 102, 18, 90, 31, 103)(12, 84, 35, 107, 47, 119, 37, 109)(13, 85, 38, 110, 48, 120, 39, 111)(15, 87, 28, 100, 49, 121, 43, 115)(21, 93, 32, 104, 50, 122, 45, 117)(25, 97, 51, 123, 33, 105, 53, 125)(26, 98, 54, 126, 34, 106, 55, 127)(36, 108, 61, 133, 67, 139, 52, 124)(40, 112, 62, 134, 68, 140, 56, 128)(41, 113, 58, 130, 44, 116, 60, 132)(42, 114, 57, 129, 46, 118, 59, 131)(63, 135, 72, 144, 65, 137, 70, 142)(64, 136, 71, 143, 66, 138, 69, 141)(145, 217, 147, 219)(146, 218, 152, 224)(148, 220, 157, 229)(149, 221, 155, 227)(150, 222, 156, 228)(151, 223, 166, 238)(153, 225, 170, 242)(154, 226, 169, 241)(158, 230, 183, 255)(159, 231, 184, 256)(160, 232, 182, 254)(161, 233, 178, 250)(162, 234, 177, 249)(163, 235, 181, 253)(164, 236, 179, 251)(165, 237, 180, 252)(167, 239, 192, 264)(168, 240, 191, 263)(171, 243, 199, 271)(172, 244, 200, 272)(173, 245, 198, 270)(174, 246, 197, 269)(175, 247, 195, 267)(176, 248, 196, 268)(185, 257, 209, 281)(186, 258, 210, 282)(187, 259, 206, 278)(188, 260, 207, 279)(189, 261, 205, 277)(190, 262, 208, 280)(193, 265, 212, 284)(194, 266, 211, 283)(201, 273, 215, 287)(202, 274, 216, 288)(203, 275, 213, 285)(204, 276, 214, 286) L = (1, 148)(2, 153)(3, 156)(4, 159)(5, 161)(6, 145)(7, 167)(8, 169)(9, 172)(10, 146)(11, 177)(12, 180)(13, 147)(14, 174)(15, 186)(16, 175)(17, 187)(18, 149)(19, 185)(20, 188)(21, 150)(22, 191)(23, 193)(24, 151)(25, 196)(26, 152)(27, 164)(28, 202)(29, 163)(30, 201)(31, 203)(32, 154)(33, 205)(34, 155)(35, 199)(36, 208)(37, 198)(38, 207)(39, 209)(40, 157)(41, 158)(42, 194)(43, 204)(44, 160)(45, 162)(46, 165)(47, 211)(48, 166)(49, 190)(50, 168)(51, 182)(52, 214)(53, 183)(54, 213)(55, 215)(56, 170)(57, 171)(58, 189)(59, 173)(60, 176)(61, 216)(62, 178)(63, 179)(64, 212)(65, 181)(66, 184)(67, 210)(68, 192)(69, 195)(70, 206)(71, 197)(72, 200)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.968 Graph:: simple bipartite v = 54 e = 144 f = 60 degree seq :: [ 4^36, 8^18 ] E16.971 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (C6 x S3) : C2 (small group id <72, 23>) Aut = C2 x ((C6 x S3) : C2) (small group id <144, 151>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1 * Y2)^2, Y1^4, (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y1 * Y3^2 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, (Y3^-1 * Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1^-2)^2, Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y2, (Y1^-1 * Y3^-1)^3, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, Y2 * Y1 * R * Y3^-1 * Y1 * Y2 * R * Y1, Y3^5 * Y1^-2 * Y3 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74, 7, 79, 5, 77)(3, 75, 11, 83, 24, 96, 13, 85)(4, 76, 15, 87, 25, 97, 17, 89)(6, 78, 21, 93, 26, 98, 22, 94)(8, 80, 27, 99, 18, 90, 29, 101)(9, 81, 31, 103, 19, 91, 33, 105)(10, 82, 34, 106, 20, 92, 35, 107)(12, 84, 40, 112, 51, 123, 28, 100)(14, 86, 45, 117, 52, 124, 30, 102)(16, 88, 32, 104, 53, 125, 48, 120)(23, 95, 36, 108, 54, 126, 49, 121)(37, 109, 64, 136, 42, 114, 63, 135)(38, 110, 62, 134, 43, 115, 65, 137)(39, 111, 66, 138, 44, 116, 58, 130)(41, 113, 61, 133, 69, 141, 57, 129)(46, 118, 56, 128, 70, 142, 60, 132)(47, 119, 59, 131, 50, 122, 55, 127)(67, 139, 72, 144, 68, 140, 71, 143)(145, 217, 147, 219)(146, 218, 152, 224)(148, 220, 158, 230)(149, 221, 162, 234)(150, 222, 156, 228)(151, 223, 168, 240)(153, 225, 174, 246)(154, 226, 172, 244)(155, 227, 181, 253)(157, 229, 186, 258)(159, 231, 188, 260)(160, 232, 190, 262)(161, 233, 183, 255)(163, 235, 189, 261)(164, 236, 184, 256)(165, 237, 187, 259)(166, 238, 182, 254)(167, 239, 185, 257)(169, 241, 196, 268)(170, 242, 195, 267)(171, 243, 199, 271)(173, 245, 203, 275)(175, 247, 205, 277)(176, 248, 206, 278)(177, 249, 201, 273)(178, 250, 204, 276)(179, 251, 200, 272)(180, 252, 202, 274)(191, 263, 212, 284)(192, 264, 209, 281)(193, 265, 210, 282)(194, 266, 211, 283)(197, 269, 214, 286)(198, 270, 213, 285)(207, 279, 216, 288)(208, 280, 215, 287) L = (1, 148)(2, 153)(3, 156)(4, 160)(5, 163)(6, 145)(7, 169)(8, 172)(9, 176)(10, 146)(11, 182)(12, 185)(13, 187)(14, 147)(15, 178)(16, 191)(17, 179)(18, 184)(19, 192)(20, 149)(21, 186)(22, 181)(23, 150)(24, 195)(25, 197)(26, 151)(27, 200)(28, 202)(29, 204)(30, 152)(31, 166)(32, 207)(33, 165)(34, 203)(35, 199)(36, 154)(37, 161)(38, 205)(39, 155)(40, 210)(41, 211)(42, 159)(43, 201)(44, 157)(45, 162)(46, 158)(47, 198)(48, 208)(49, 164)(50, 167)(51, 213)(52, 168)(53, 194)(54, 170)(55, 177)(56, 183)(57, 171)(58, 215)(59, 175)(60, 188)(61, 173)(62, 174)(63, 193)(64, 180)(65, 189)(66, 216)(67, 214)(68, 190)(69, 212)(70, 196)(71, 209)(72, 206)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.969 Graph:: simple bipartite v = 54 e = 144 f = 60 degree seq :: [ 4^36, 8^18 ] E16.972 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (C6 x S3) : C2 (small group id <72, 23>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^3, R * Y2 * R * Y2^-1, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y3)^2, Y2^4, Y2 * Y1^-1 * Y2^2 * Y1 * Y2, Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74, 5, 77)(3, 75, 10, 82, 13, 85)(4, 76, 14, 86, 8, 80)(6, 78, 18, 90, 19, 91)(7, 79, 20, 92, 23, 95)(9, 81, 25, 97, 26, 98)(11, 83, 21, 93, 31, 103)(12, 84, 32, 104, 28, 100)(15, 87, 37, 109, 38, 110)(16, 88, 39, 111, 40, 112)(17, 89, 41, 113, 42, 114)(22, 94, 47, 119, 44, 116)(24, 96, 50, 122, 51, 123)(27, 99, 43, 115, 53, 125)(29, 101, 45, 117, 55, 127)(30, 102, 56, 128, 46, 118)(33, 105, 48, 120, 59, 131)(34, 106, 49, 121, 60, 132)(35, 107, 61, 133, 62, 134)(36, 108, 63, 135, 64, 136)(52, 124, 69, 141, 65, 137)(54, 126, 70, 142, 66, 138)(57, 129, 71, 143, 67, 139)(58, 130, 72, 144, 68, 140)(145, 217, 147, 219, 155, 227, 150, 222)(146, 218, 151, 223, 165, 237, 153, 225)(148, 220, 159, 231, 174, 246, 156, 228)(149, 221, 160, 232, 175, 247, 161, 233)(152, 224, 168, 240, 190, 262, 166, 238)(154, 226, 171, 243, 162, 234, 173, 245)(157, 229, 177, 249, 163, 235, 178, 250)(158, 230, 179, 251, 200, 272, 180, 252)(164, 236, 187, 259, 169, 241, 189, 261)(167, 239, 192, 264, 170, 242, 193, 265)(172, 244, 198, 270, 182, 254, 196, 268)(176, 248, 201, 273, 181, 253, 202, 274)(183, 255, 197, 269, 185, 257, 199, 271)(184, 256, 203, 275, 186, 258, 204, 276)(188, 260, 210, 282, 195, 267, 209, 281)(191, 263, 211, 283, 194, 266, 212, 284)(205, 277, 216, 288, 207, 279, 215, 287)(206, 278, 213, 285, 208, 280, 214, 286) L = (1, 148)(2, 152)(3, 156)(4, 145)(5, 158)(6, 159)(7, 166)(8, 146)(9, 168)(10, 172)(11, 174)(12, 147)(13, 176)(14, 149)(15, 150)(16, 180)(17, 179)(18, 182)(19, 181)(20, 188)(21, 190)(22, 151)(23, 191)(24, 153)(25, 195)(26, 194)(27, 196)(28, 154)(29, 198)(30, 155)(31, 200)(32, 157)(33, 202)(34, 201)(35, 161)(36, 160)(37, 163)(38, 162)(39, 208)(40, 207)(41, 206)(42, 205)(43, 209)(44, 164)(45, 210)(46, 165)(47, 167)(48, 212)(49, 211)(50, 170)(51, 169)(52, 171)(53, 213)(54, 173)(55, 214)(56, 175)(57, 178)(58, 177)(59, 216)(60, 215)(61, 186)(62, 185)(63, 184)(64, 183)(65, 187)(66, 189)(67, 193)(68, 192)(69, 197)(70, 199)(71, 204)(72, 203)(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) :: { ( 4^6 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.967 Graph:: simple bipartite v = 42 e = 144 f = 72 degree seq :: [ 6^24, 8^18 ] E16.973 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, (Y3 * Y2)^3, (Y3 * Y1)^4, (Y3 * Y1 * Y2 * Y1)^2, (Y2 * Y1)^4, Y2 * R * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y2 * R, Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74)(3, 75, 7, 79)(4, 76, 9, 81)(5, 77, 11, 83)(6, 78, 13, 85)(8, 80, 17, 89)(10, 82, 21, 93)(12, 84, 24, 96)(14, 86, 28, 100)(15, 87, 22, 94)(16, 88, 26, 98)(18, 90, 33, 105)(19, 91, 23, 95)(20, 92, 27, 99)(25, 97, 42, 114)(29, 101, 40, 112)(30, 102, 45, 117)(31, 103, 38, 110)(32, 104, 43, 115)(34, 106, 41, 113)(35, 107, 46, 118)(36, 108, 39, 111)(37, 109, 44, 116)(47, 119, 58, 130)(48, 120, 56, 128)(49, 121, 61, 133)(50, 122, 55, 127)(51, 123, 60, 132)(52, 124, 59, 131)(53, 125, 57, 129)(54, 126, 62, 134)(63, 135, 68, 140)(64, 136, 67, 139)(65, 137, 70, 142)(66, 138, 69, 141)(71, 143, 72, 144)(145, 217, 147, 219)(146, 218, 149, 221)(148, 220, 154, 226)(150, 222, 158, 230)(151, 223, 159, 231)(152, 224, 162, 234)(153, 225, 163, 235)(155, 227, 166, 238)(156, 228, 169, 241)(157, 229, 170, 242)(160, 232, 174, 246)(161, 233, 175, 247)(164, 236, 179, 251)(165, 237, 180, 252)(167, 239, 183, 255)(168, 240, 184, 256)(171, 243, 188, 260)(172, 244, 189, 261)(173, 245, 191, 263)(176, 248, 193, 265)(177, 249, 194, 266)(178, 250, 196, 268)(181, 253, 198, 270)(182, 254, 199, 271)(185, 257, 201, 273)(186, 258, 202, 274)(187, 259, 204, 276)(190, 262, 206, 278)(192, 264, 207, 279)(195, 267, 209, 281)(197, 269, 210, 282)(200, 272, 211, 283)(203, 275, 213, 285)(205, 277, 214, 286)(208, 280, 215, 287)(212, 284, 216, 288) L = (1, 148)(2, 150)(3, 152)(4, 145)(5, 156)(6, 146)(7, 160)(8, 147)(9, 164)(10, 162)(11, 167)(12, 149)(13, 171)(14, 169)(15, 173)(16, 151)(17, 176)(18, 154)(19, 178)(20, 153)(21, 181)(22, 182)(23, 155)(24, 185)(25, 158)(26, 187)(27, 157)(28, 190)(29, 159)(30, 191)(31, 192)(32, 161)(33, 195)(34, 163)(35, 196)(36, 197)(37, 165)(38, 166)(39, 199)(40, 200)(41, 168)(42, 203)(43, 170)(44, 204)(45, 205)(46, 172)(47, 174)(48, 175)(49, 207)(50, 208)(51, 177)(52, 179)(53, 180)(54, 210)(55, 183)(56, 184)(57, 211)(58, 212)(59, 186)(60, 188)(61, 189)(62, 214)(63, 193)(64, 194)(65, 215)(66, 198)(67, 201)(68, 202)(69, 216)(70, 206)(71, 209)(72, 213)(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, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E16.979 Graph:: simple bipartite v = 72 e = 144 f = 42 degree seq :: [ 4^72 ] E16.974 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3 * Y2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y2)^2, (Y3^-1 * Y1)^4, (Y2 * Y1 * Y3 * Y1)^2, (Y2 * Y1)^4, (Y3^-1 * Y1 * Y3 * Y1)^2 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74)(3, 75, 9, 81)(4, 76, 12, 84)(5, 77, 13, 85)(6, 78, 14, 86)(7, 79, 17, 89)(8, 80, 18, 90)(10, 82, 22, 94)(11, 83, 23, 95)(15, 87, 33, 105)(16, 88, 34, 106)(19, 91, 30, 102)(20, 92, 38, 110)(21, 93, 35, 107)(24, 96, 32, 104)(25, 97, 40, 112)(26, 98, 37, 109)(27, 99, 31, 103)(28, 100, 39, 111)(29, 101, 36, 108)(41, 113, 58, 130)(42, 114, 55, 127)(43, 115, 54, 126)(44, 116, 62, 134)(45, 117, 64, 136)(46, 118, 53, 125)(47, 119, 61, 133)(48, 120, 63, 135)(49, 121, 59, 131)(50, 122, 56, 128)(51, 123, 60, 132)(52, 124, 57, 129)(65, 137, 69, 141)(66, 138, 71, 143)(67, 139, 70, 142)(68, 140, 72, 144)(145, 217, 147, 219)(146, 218, 150, 222)(148, 220, 154, 226)(149, 221, 155, 227)(151, 223, 159, 231)(152, 224, 160, 232)(153, 225, 163, 235)(156, 228, 168, 240)(157, 229, 171, 243)(158, 230, 174, 246)(161, 233, 179, 251)(162, 234, 182, 254)(164, 236, 185, 257)(165, 237, 186, 258)(166, 238, 187, 259)(167, 239, 190, 262)(169, 241, 193, 265)(170, 242, 194, 266)(172, 244, 195, 267)(173, 245, 196, 268)(175, 247, 197, 269)(176, 248, 198, 270)(177, 249, 199, 271)(178, 250, 202, 274)(180, 252, 205, 277)(181, 253, 206, 278)(183, 255, 207, 279)(184, 256, 208, 280)(188, 260, 209, 281)(189, 261, 210, 282)(191, 263, 211, 283)(192, 264, 212, 284)(200, 272, 213, 285)(201, 273, 214, 286)(203, 275, 215, 287)(204, 276, 216, 288) L = (1, 148)(2, 151)(3, 154)(4, 155)(5, 145)(6, 159)(7, 160)(8, 146)(9, 164)(10, 149)(11, 147)(12, 169)(13, 172)(14, 175)(15, 152)(16, 150)(17, 180)(18, 183)(19, 185)(20, 186)(21, 153)(22, 188)(23, 191)(24, 193)(25, 194)(26, 156)(27, 195)(28, 196)(29, 157)(30, 197)(31, 198)(32, 158)(33, 200)(34, 203)(35, 205)(36, 206)(37, 161)(38, 207)(39, 208)(40, 162)(41, 165)(42, 163)(43, 209)(44, 210)(45, 166)(46, 211)(47, 212)(48, 167)(49, 170)(50, 168)(51, 173)(52, 171)(53, 176)(54, 174)(55, 213)(56, 214)(57, 177)(58, 215)(59, 216)(60, 178)(61, 181)(62, 179)(63, 184)(64, 182)(65, 189)(66, 187)(67, 192)(68, 190)(69, 201)(70, 199)(71, 204)(72, 202)(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, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E16.980 Graph:: simple bipartite v = 72 e = 144 f = 42 degree seq :: [ 4^72 ] E16.975 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y3 * Y2^-1 * Y1 * Y3 * Y2 * Y1, Y3^-1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y1, (Y3^-2 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y3 * Y2 * Y1, Y2 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y2^-1 * Y3^-1)^4, (Y3 * Y2^-1)^4 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74)(3, 75, 11, 83)(4, 76, 10, 82)(5, 77, 17, 89)(6, 78, 8, 80)(7, 79, 22, 94)(9, 81, 28, 100)(12, 84, 32, 104)(13, 85, 25, 97)(14, 86, 24, 96)(15, 87, 26, 98)(16, 88, 30, 102)(18, 90, 31, 103)(19, 91, 27, 99)(20, 92, 29, 101)(21, 93, 23, 95)(33, 105, 49, 121)(34, 106, 59, 131)(35, 107, 55, 127)(36, 108, 56, 128)(37, 109, 64, 136)(38, 110, 61, 133)(39, 111, 51, 123)(40, 112, 52, 124)(41, 113, 58, 130)(42, 114, 57, 129)(43, 115, 50, 122)(44, 116, 60, 132)(45, 117, 54, 126)(46, 118, 63, 135)(47, 119, 62, 134)(48, 120, 53, 125)(65, 137, 69, 141)(66, 138, 71, 143)(67, 139, 70, 142)(68, 140, 72, 144)(145, 217, 147, 219, 149, 221)(146, 218, 151, 223, 153, 225)(148, 220, 158, 230, 160, 232)(150, 222, 164, 236, 165, 237)(152, 224, 169, 241, 171, 243)(154, 226, 175, 247, 176, 248)(155, 227, 177, 249, 178, 250)(156, 228, 179, 251, 181, 253)(157, 229, 182, 254, 183, 255)(159, 231, 185, 257, 180, 252)(161, 233, 187, 259, 188, 260)(162, 234, 189, 261, 190, 262)(163, 235, 191, 263, 192, 264)(166, 238, 193, 265, 194, 266)(167, 239, 195, 267, 197, 269)(168, 240, 198, 270, 199, 271)(170, 242, 201, 273, 196, 268)(172, 244, 203, 275, 204, 276)(173, 245, 205, 277, 206, 278)(174, 246, 207, 279, 208, 280)(184, 256, 211, 283, 209, 281)(186, 258, 212, 284, 210, 282)(200, 272, 215, 287, 213, 285)(202, 274, 216, 288, 214, 286) L = (1, 148)(2, 152)(3, 156)(4, 159)(5, 162)(6, 145)(7, 167)(8, 170)(9, 173)(10, 146)(11, 169)(12, 180)(13, 147)(14, 184)(15, 150)(16, 186)(17, 171)(18, 185)(19, 149)(20, 172)(21, 166)(22, 158)(23, 196)(24, 151)(25, 200)(26, 154)(27, 202)(28, 160)(29, 201)(30, 153)(31, 161)(32, 155)(33, 195)(34, 205)(35, 209)(36, 157)(37, 210)(38, 203)(39, 193)(40, 165)(41, 163)(42, 164)(43, 197)(44, 206)(45, 211)(46, 212)(47, 204)(48, 194)(49, 179)(50, 189)(51, 213)(52, 168)(53, 214)(54, 187)(55, 177)(56, 176)(57, 174)(58, 175)(59, 181)(60, 190)(61, 215)(62, 216)(63, 188)(64, 178)(65, 183)(66, 182)(67, 192)(68, 191)(69, 199)(70, 198)(71, 208)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.977 Graph:: simple bipartite v = 60 e = 144 f = 54 degree seq :: [ 4^36, 6^24 ] E16.976 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y1 * Y3^-1)^2, Y3^4, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2^-1)^2, (Y3 * Y2 * Y1)^2, (Y2^-1 * Y3^-1)^4, Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1, (Y3 * Y2^-1)^4 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74)(3, 75, 11, 83)(4, 76, 10, 82)(5, 77, 17, 89)(6, 78, 8, 80)(7, 79, 22, 94)(9, 81, 28, 100)(12, 84, 31, 103)(13, 85, 27, 99)(14, 86, 30, 102)(15, 87, 26, 98)(16, 88, 24, 96)(18, 90, 32, 104)(19, 91, 25, 97)(20, 92, 23, 95)(21, 93, 29, 101)(33, 105, 49, 121)(34, 106, 59, 131)(35, 107, 63, 135)(36, 108, 58, 130)(37, 109, 54, 126)(38, 110, 53, 125)(39, 111, 62, 134)(40, 112, 57, 129)(41, 113, 56, 128)(42, 114, 52, 124)(43, 115, 50, 122)(44, 116, 60, 132)(45, 117, 64, 136)(46, 118, 55, 127)(47, 119, 51, 123)(48, 120, 61, 133)(65, 137, 72, 144)(66, 138, 70, 142)(67, 139, 71, 143)(68, 140, 69, 141)(145, 217, 147, 219, 149, 221)(146, 218, 151, 223, 153, 225)(148, 220, 158, 230, 160, 232)(150, 222, 164, 236, 165, 237)(152, 224, 169, 241, 171, 243)(154, 226, 175, 247, 176, 248)(155, 227, 177, 249, 178, 250)(156, 228, 179, 251, 181, 253)(157, 229, 182, 254, 183, 255)(159, 231, 185, 257, 180, 252)(161, 233, 187, 259, 188, 260)(162, 234, 189, 261, 190, 262)(163, 235, 191, 263, 192, 264)(166, 238, 193, 265, 194, 266)(167, 239, 195, 267, 197, 269)(168, 240, 198, 270, 199, 271)(170, 242, 201, 273, 196, 268)(172, 244, 203, 275, 204, 276)(173, 245, 205, 277, 206, 278)(174, 246, 207, 279, 208, 280)(184, 256, 211, 283, 209, 281)(186, 258, 212, 284, 210, 282)(200, 272, 215, 287, 213, 285)(202, 274, 216, 288, 214, 286) L = (1, 148)(2, 152)(3, 156)(4, 159)(5, 162)(6, 145)(7, 167)(8, 170)(9, 173)(10, 146)(11, 171)(12, 180)(13, 147)(14, 184)(15, 150)(16, 186)(17, 169)(18, 185)(19, 149)(20, 166)(21, 172)(22, 160)(23, 196)(24, 151)(25, 200)(26, 154)(27, 202)(28, 158)(29, 201)(30, 153)(31, 155)(32, 161)(33, 197)(34, 206)(35, 209)(36, 157)(37, 210)(38, 193)(39, 203)(40, 165)(41, 163)(42, 164)(43, 195)(44, 205)(45, 211)(46, 212)(47, 194)(48, 204)(49, 181)(50, 190)(51, 213)(52, 168)(53, 214)(54, 177)(55, 187)(56, 176)(57, 174)(58, 175)(59, 179)(60, 189)(61, 215)(62, 216)(63, 178)(64, 188)(65, 183)(66, 182)(67, 192)(68, 191)(69, 199)(70, 198)(71, 208)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.978 Graph:: simple bipartite v = 60 e = 144 f = 54 degree seq :: [ 4^36, 6^24 ] E16.977 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1 * Y2)^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1)^2, (Y3 * Y1)^3, Y3^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y2 * Y1 * Y2, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^2 * Y2 * Y1^-2 * Y2 * Y1^-1, Y2 * Y3^-1 * Y1^2 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74, 7, 79, 5, 77)(3, 75, 11, 83, 31, 103, 13, 85)(4, 76, 15, 87, 30, 102, 10, 82)(6, 78, 18, 90, 42, 114, 20, 92)(8, 80, 24, 96, 51, 123, 26, 98)(9, 81, 28, 100, 50, 122, 23, 95)(12, 84, 32, 104, 45, 117, 25, 97)(14, 86, 35, 107, 59, 131, 37, 109)(16, 88, 39, 111, 57, 129, 34, 106)(17, 89, 33, 105, 54, 126, 40, 112)(19, 91, 22, 94, 48, 120, 38, 110)(21, 93, 44, 116, 36, 108, 46, 118)(27, 99, 53, 125, 68, 140, 55, 127)(29, 101, 56, 128, 67, 139, 52, 124)(41, 113, 62, 134, 69, 141, 60, 132)(43, 115, 58, 130, 70, 142, 61, 133)(47, 119, 64, 136, 72, 144, 65, 137)(49, 121, 66, 138, 71, 143, 63, 135)(145, 217, 147, 219)(146, 218, 152, 224)(148, 220, 158, 230)(149, 221, 161, 233)(150, 222, 156, 228)(151, 223, 165, 237)(153, 225, 171, 243)(154, 226, 169, 241)(155, 227, 173, 245)(157, 229, 178, 250)(159, 231, 180, 252)(160, 232, 177, 249)(162, 234, 185, 257)(163, 235, 176, 248)(164, 236, 181, 253)(166, 238, 191, 263)(167, 239, 189, 261)(168, 240, 193, 265)(170, 242, 196, 268)(172, 244, 198, 270)(174, 246, 199, 271)(175, 247, 192, 264)(179, 251, 202, 274)(182, 254, 204, 276)(183, 255, 197, 269)(184, 256, 205, 277)(186, 258, 195, 267)(187, 259, 188, 260)(190, 262, 207, 279)(194, 266, 209, 281)(200, 272, 208, 280)(201, 273, 213, 285)(203, 275, 211, 283)(206, 278, 210, 282)(212, 284, 215, 287)(214, 286, 216, 288) L = (1, 148)(2, 153)(3, 156)(4, 160)(5, 162)(6, 145)(7, 166)(8, 169)(9, 173)(10, 146)(11, 171)(12, 177)(13, 179)(14, 147)(15, 182)(16, 150)(17, 176)(18, 187)(19, 149)(20, 183)(21, 189)(22, 193)(23, 151)(24, 191)(25, 155)(26, 197)(27, 152)(28, 164)(29, 154)(30, 200)(31, 190)(32, 188)(33, 158)(34, 159)(35, 204)(36, 157)(37, 198)(38, 202)(39, 196)(40, 206)(41, 161)(42, 194)(43, 163)(44, 185)(45, 168)(46, 208)(47, 165)(48, 174)(49, 167)(50, 210)(51, 184)(52, 172)(53, 181)(54, 170)(55, 175)(56, 207)(57, 214)(58, 178)(59, 212)(60, 180)(61, 186)(62, 209)(63, 192)(64, 199)(65, 195)(66, 205)(67, 201)(68, 216)(69, 203)(70, 215)(71, 211)(72, 213)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.975 Graph:: simple bipartite v = 54 e = 144 f = 60 degree seq :: [ 4^36, 8^18 ] E16.978 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^4, (R * Y3)^2, (Y1^-1 * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, Y1^4, Y3 * Y1 * Y3^-1 * Y1 * Y3^2, Y3^-1 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y2, (Y1^-1 * R * Y2)^2, (Y3^-1 * Y1^-1)^3, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2 * Y1 * Y3 * Y1^-2 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74, 7, 79, 5, 77)(3, 75, 11, 83, 31, 103, 13, 85)(4, 76, 15, 87, 30, 102, 10, 82)(6, 78, 18, 90, 43, 115, 20, 92)(8, 80, 24, 96, 51, 123, 26, 98)(9, 81, 28, 100, 50, 122, 23, 95)(12, 84, 35, 107, 59, 131, 34, 106)(14, 86, 37, 109, 47, 119, 27, 99)(16, 88, 32, 104, 58, 130, 40, 112)(17, 89, 41, 113, 53, 125, 42, 114)(19, 91, 22, 94, 48, 120, 39, 111)(21, 93, 44, 116, 33, 105, 46, 118)(25, 97, 55, 127, 68, 140, 54, 126)(29, 101, 52, 124, 67, 139, 56, 128)(36, 108, 61, 133, 70, 142, 62, 134)(38, 110, 57, 129, 69, 141, 60, 132)(45, 117, 65, 137, 72, 144, 64, 136)(49, 121, 63, 135, 71, 143, 66, 138)(145, 217, 147, 219)(146, 218, 152, 224)(148, 220, 158, 230)(149, 221, 161, 233)(150, 222, 156, 228)(151, 223, 165, 237)(153, 225, 171, 243)(154, 226, 169, 241)(155, 227, 176, 248)(157, 229, 180, 252)(159, 231, 179, 251)(160, 232, 170, 242)(162, 234, 181, 253)(163, 235, 182, 254)(164, 236, 177, 249)(166, 238, 191, 263)(167, 239, 189, 261)(168, 240, 196, 268)(172, 244, 199, 271)(173, 245, 190, 262)(174, 246, 197, 269)(175, 247, 194, 266)(178, 250, 200, 272)(183, 255, 195, 267)(184, 256, 204, 276)(185, 257, 205, 277)(186, 258, 193, 265)(187, 259, 201, 273)(188, 260, 207, 279)(192, 264, 209, 281)(198, 270, 210, 282)(202, 274, 212, 284)(203, 275, 214, 286)(206, 278, 208, 280)(211, 283, 216, 288)(213, 285, 215, 287) L = (1, 148)(2, 153)(3, 156)(4, 160)(5, 162)(6, 145)(7, 166)(8, 169)(9, 173)(10, 146)(11, 177)(12, 170)(13, 181)(14, 147)(15, 183)(16, 150)(17, 182)(18, 180)(19, 149)(20, 176)(21, 189)(22, 193)(23, 151)(24, 197)(25, 190)(26, 158)(27, 152)(28, 164)(29, 154)(30, 196)(31, 201)(32, 200)(33, 199)(34, 155)(35, 204)(36, 163)(37, 161)(38, 157)(39, 205)(40, 159)(41, 195)(42, 191)(43, 194)(44, 175)(45, 186)(46, 171)(47, 165)(48, 174)(49, 167)(50, 207)(51, 179)(52, 210)(53, 209)(54, 168)(55, 178)(56, 172)(57, 208)(58, 214)(59, 212)(60, 185)(61, 184)(62, 187)(63, 206)(64, 188)(65, 198)(66, 192)(67, 202)(68, 216)(69, 203)(70, 215)(71, 211)(72, 213)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.976 Graph:: simple bipartite v = 54 e = 144 f = 60 degree seq :: [ 4^36, 8^18 ] E16.979 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^3, R * Y2 * R * Y2^-1, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y3)^2, Y2^4, (Y2 * Y1^-1 * Y2)^2, (Y2^-2 * Y1^-1)^2, Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74, 5, 77)(3, 75, 10, 82, 13, 85)(4, 76, 14, 86, 8, 80)(6, 78, 18, 90, 19, 91)(7, 79, 20, 92, 23, 95)(9, 81, 25, 97, 26, 98)(11, 83, 30, 102, 21, 93)(12, 84, 32, 104, 28, 100)(15, 87, 37, 109, 38, 110)(16, 88, 39, 111, 40, 112)(17, 89, 41, 113, 42, 114)(22, 94, 47, 119, 44, 116)(24, 96, 50, 122, 51, 123)(27, 99, 52, 124, 43, 115)(29, 101, 45, 117, 55, 127)(31, 103, 46, 118, 56, 128)(33, 105, 59, 131, 48, 120)(34, 106, 49, 121, 60, 132)(35, 107, 61, 133, 62, 134)(36, 108, 63, 135, 64, 136)(53, 125, 65, 137, 69, 141)(54, 126, 70, 142, 66, 138)(57, 129, 71, 143, 67, 139)(58, 130, 68, 140, 72, 144)(145, 217, 147, 219, 155, 227, 150, 222)(146, 218, 151, 223, 165, 237, 153, 225)(148, 220, 159, 231, 175, 247, 156, 228)(149, 221, 160, 232, 174, 246, 161, 233)(152, 224, 168, 240, 190, 262, 166, 238)(154, 226, 171, 243, 163, 235, 173, 245)(157, 229, 177, 249, 162, 234, 178, 250)(158, 230, 179, 251, 200, 272, 180, 252)(164, 236, 187, 259, 170, 242, 189, 261)(167, 239, 192, 264, 169, 241, 193, 265)(172, 244, 198, 270, 181, 253, 197, 269)(176, 248, 201, 273, 182, 254, 202, 274)(183, 255, 196, 268, 186, 258, 199, 271)(184, 256, 203, 275, 185, 257, 204, 276)(188, 260, 210, 282, 194, 266, 209, 281)(191, 263, 211, 283, 195, 267, 212, 284)(205, 277, 213, 285, 208, 280, 214, 286)(206, 278, 216, 288, 207, 279, 215, 287) L = (1, 148)(2, 152)(3, 156)(4, 145)(5, 158)(6, 159)(7, 166)(8, 146)(9, 168)(10, 172)(11, 175)(12, 147)(13, 176)(14, 149)(15, 150)(16, 180)(17, 179)(18, 182)(19, 181)(20, 188)(21, 190)(22, 151)(23, 191)(24, 153)(25, 195)(26, 194)(27, 197)(28, 154)(29, 198)(30, 200)(31, 155)(32, 157)(33, 202)(34, 201)(35, 161)(36, 160)(37, 163)(38, 162)(39, 208)(40, 207)(41, 206)(42, 205)(43, 209)(44, 164)(45, 210)(46, 165)(47, 167)(48, 212)(49, 211)(50, 170)(51, 169)(52, 213)(53, 171)(54, 173)(55, 214)(56, 174)(57, 178)(58, 177)(59, 216)(60, 215)(61, 186)(62, 185)(63, 184)(64, 183)(65, 187)(66, 189)(67, 193)(68, 192)(69, 196)(70, 199)(71, 204)(72, 203)(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) :: { ( 4^6 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.973 Graph:: simple bipartite v = 42 e = 144 f = 72 degree seq :: [ 6^24, 8^18 ] E16.980 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 4}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y1^3, (Y2 * Y3^-1)^2, (Y2 * Y3^-1)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2^4, (R * Y3)^2, Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1, (Y1 * Y2^-2)^2, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1^-1)^2, Y2 * Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74, 5, 77)(3, 75, 11, 83, 14, 86)(4, 76, 9, 81, 7, 79)(6, 78, 19, 91, 21, 93)(8, 80, 24, 96, 27, 99)(10, 82, 30, 102, 31, 103)(12, 84, 36, 108, 25, 97)(13, 85, 34, 106, 15, 87)(16, 88, 43, 115, 32, 104)(17, 89, 44, 116, 46, 118)(18, 90, 47, 119, 48, 120)(20, 92, 50, 122, 22, 94)(23, 95, 45, 117, 53, 125)(26, 98, 55, 127, 28, 100)(29, 101, 62, 134, 49, 121)(33, 105, 63, 135, 54, 126)(35, 107, 56, 128, 67, 139)(37, 109, 57, 129, 38, 110)(39, 111, 58, 130, 52, 124)(40, 112, 68, 140, 59, 131)(41, 113, 60, 132, 69, 141)(42, 114, 51, 123, 61, 133)(64, 136, 71, 143, 65, 137)(66, 138, 72, 144, 70, 142)(145, 217, 147, 219, 156, 228, 150, 222)(146, 218, 152, 224, 169, 241, 154, 226)(148, 220, 160, 232, 186, 258, 159, 231)(149, 221, 161, 233, 180, 252, 162, 234)(151, 223, 164, 236, 195, 267, 167, 239)(153, 225, 173, 245, 205, 277, 172, 244)(155, 227, 177, 249, 165, 237, 179, 251)(157, 229, 183, 255, 176, 248, 182, 254)(158, 230, 184, 256, 163, 235, 185, 257)(166, 238, 181, 253, 189, 261, 196, 268)(168, 240, 198, 270, 175, 247, 200, 272)(170, 242, 202, 274, 193, 265, 201, 273)(171, 243, 203, 275, 174, 246, 204, 276)(178, 250, 210, 282, 187, 259, 209, 281)(188, 260, 207, 279, 192, 264, 211, 283)(190, 262, 212, 284, 191, 263, 213, 285)(194, 266, 208, 280, 197, 269, 214, 286)(199, 271, 216, 288, 206, 278, 215, 287) L = (1, 148)(2, 153)(3, 157)(4, 146)(5, 151)(6, 164)(7, 145)(8, 170)(9, 149)(10, 160)(11, 178)(12, 181)(13, 155)(14, 159)(15, 147)(16, 174)(17, 189)(18, 173)(19, 194)(20, 163)(21, 166)(22, 150)(23, 161)(24, 199)(25, 182)(26, 168)(27, 172)(28, 152)(29, 191)(30, 187)(31, 176)(32, 154)(33, 208)(34, 158)(35, 183)(36, 201)(37, 180)(38, 156)(39, 200)(40, 195)(41, 210)(42, 184)(43, 175)(44, 197)(45, 188)(46, 167)(47, 206)(48, 193)(49, 162)(50, 165)(51, 212)(52, 179)(53, 190)(54, 209)(55, 171)(56, 202)(57, 169)(58, 211)(59, 186)(60, 216)(61, 203)(62, 192)(63, 215)(64, 207)(65, 177)(66, 204)(67, 196)(68, 205)(69, 214)(70, 185)(71, 198)(72, 213)(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) :: { ( 4^6 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.974 Graph:: simple bipartite v = 42 e = 144 f = 72 degree seq :: [ 6^24, 8^18 ] E16.981 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 6}) Quotient :: edge Aut^+ = (C6 x S3) : C2 (small group id <72, 22>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 145>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^6, T1^-1 * T2^-2 * T1 * T2^-2, (T2 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 3, 10, 27, 16, 5)(2, 7, 20, 38, 24, 8)(4, 12, 31, 49, 28, 13)(6, 17, 34, 52, 35, 18)(9, 25, 14, 32, 47, 26)(11, 29, 15, 33, 48, 30)(19, 36, 22, 41, 57, 37)(21, 39, 23, 42, 58, 40)(43, 61, 45, 65, 50, 62)(44, 63, 46, 66, 51, 64)(53, 67, 55, 71, 59, 68)(54, 69, 56, 72, 60, 70)(73, 74, 78, 76)(75, 81, 89, 83)(77, 86, 90, 87)(79, 91, 84, 93)(80, 94, 85, 95)(82, 96, 106, 100)(88, 92, 107, 103)(97, 115, 101, 116)(98, 117, 102, 118)(99, 119, 124, 120)(104, 122, 105, 123)(108, 125, 111, 126)(109, 127, 112, 128)(110, 129, 121, 130)(113, 131, 114, 132)(133, 142, 135, 140)(134, 141, 136, 139)(137, 144, 138, 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) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.982 Transitivity :: ET+ Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.982 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 6}) Quotient :: loop Aut^+ = (C6 x S3) : C2 (small group id <72, 22>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 145>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^6, T1^-1 * T2^-2 * T1 * T2^-2, (T2 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 10, 82, 27, 99, 16, 88, 5, 77)(2, 74, 7, 79, 20, 92, 38, 110, 24, 96, 8, 80)(4, 76, 12, 84, 31, 103, 49, 121, 28, 100, 13, 85)(6, 78, 17, 89, 34, 106, 52, 124, 35, 107, 18, 90)(9, 81, 25, 97, 14, 86, 32, 104, 47, 119, 26, 98)(11, 83, 29, 101, 15, 87, 33, 105, 48, 120, 30, 102)(19, 91, 36, 108, 22, 94, 41, 113, 57, 129, 37, 109)(21, 93, 39, 111, 23, 95, 42, 114, 58, 130, 40, 112)(43, 115, 61, 133, 45, 117, 65, 137, 50, 122, 62, 134)(44, 116, 63, 135, 46, 118, 66, 138, 51, 123, 64, 136)(53, 125, 67, 139, 55, 127, 71, 143, 59, 131, 68, 140)(54, 126, 69, 141, 56, 128, 72, 144, 60, 132, 70, 142) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 86)(6, 76)(7, 91)(8, 94)(9, 89)(10, 96)(11, 75)(12, 93)(13, 95)(14, 90)(15, 77)(16, 92)(17, 83)(18, 87)(19, 84)(20, 107)(21, 79)(22, 85)(23, 80)(24, 106)(25, 115)(26, 117)(27, 119)(28, 82)(29, 116)(30, 118)(31, 88)(32, 122)(33, 123)(34, 100)(35, 103)(36, 125)(37, 127)(38, 129)(39, 126)(40, 128)(41, 131)(42, 132)(43, 101)(44, 97)(45, 102)(46, 98)(47, 124)(48, 99)(49, 130)(50, 105)(51, 104)(52, 120)(53, 111)(54, 108)(55, 112)(56, 109)(57, 121)(58, 110)(59, 114)(60, 113)(61, 142)(62, 141)(63, 140)(64, 139)(65, 144)(66, 143)(67, 134)(68, 133)(69, 136)(70, 135)(71, 137)(72, 138) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.981 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.983 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x S3) : C2 (small group id <72, 22>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 145>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^6, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^2 * Y1 * Y2^2 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y3 * Y2^-2 * Y3^-1 * Y2^-2, (Y3 * Y2)^6 ] Map:: R = (1, 73, 2, 74, 6, 78, 4, 76)(3, 75, 9, 81, 17, 89, 11, 83)(5, 77, 14, 86, 18, 90, 15, 87)(7, 79, 19, 91, 12, 84, 21, 93)(8, 80, 22, 94, 13, 85, 23, 95)(10, 82, 24, 96, 34, 106, 28, 100)(16, 88, 20, 92, 35, 107, 31, 103)(25, 97, 43, 115, 29, 101, 44, 116)(26, 98, 45, 117, 30, 102, 46, 118)(27, 99, 47, 119, 52, 124, 48, 120)(32, 104, 50, 122, 33, 105, 51, 123)(36, 108, 53, 125, 39, 111, 54, 126)(37, 109, 55, 127, 40, 112, 56, 128)(38, 110, 57, 129, 49, 121, 58, 130)(41, 113, 59, 131, 42, 114, 60, 132)(61, 133, 70, 142, 63, 135, 68, 140)(62, 134, 69, 141, 64, 136, 67, 139)(65, 137, 72, 144, 66, 138, 71, 143)(145, 217, 147, 219, 154, 226, 171, 243, 160, 232, 149, 221)(146, 218, 151, 223, 164, 236, 182, 254, 168, 240, 152, 224)(148, 220, 156, 228, 175, 247, 193, 265, 172, 244, 157, 229)(150, 222, 161, 233, 178, 250, 196, 268, 179, 251, 162, 234)(153, 225, 169, 241, 158, 230, 176, 248, 191, 263, 170, 242)(155, 227, 173, 245, 159, 231, 177, 249, 192, 264, 174, 246)(163, 235, 180, 252, 166, 238, 185, 257, 201, 273, 181, 253)(165, 237, 183, 255, 167, 239, 186, 258, 202, 274, 184, 256)(187, 259, 205, 277, 189, 261, 209, 281, 194, 266, 206, 278)(188, 260, 207, 279, 190, 262, 210, 282, 195, 267, 208, 280)(197, 269, 211, 283, 199, 271, 215, 287, 203, 275, 212, 284)(198, 270, 213, 285, 200, 272, 216, 288, 204, 276, 214, 286) L = (1, 148)(2, 145)(3, 155)(4, 150)(5, 159)(6, 146)(7, 165)(8, 167)(9, 147)(10, 172)(11, 161)(12, 163)(13, 166)(14, 149)(15, 162)(16, 175)(17, 153)(18, 158)(19, 151)(20, 160)(21, 156)(22, 152)(23, 157)(24, 154)(25, 188)(26, 190)(27, 192)(28, 178)(29, 187)(30, 189)(31, 179)(32, 195)(33, 194)(34, 168)(35, 164)(36, 198)(37, 200)(38, 202)(39, 197)(40, 199)(41, 204)(42, 203)(43, 169)(44, 173)(45, 170)(46, 174)(47, 171)(48, 196)(49, 201)(50, 176)(51, 177)(52, 191)(53, 180)(54, 183)(55, 181)(56, 184)(57, 182)(58, 193)(59, 185)(60, 186)(61, 212)(62, 211)(63, 214)(64, 213)(65, 215)(66, 216)(67, 208)(68, 207)(69, 206)(70, 205)(71, 210)(72, 209)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 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 E16.984 Graph:: bipartite v = 30 e = 144 f = 84 degree seq :: [ 8^18, 12^12 ] E16.984 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x S3) : C2 (small group id <72, 22>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 145>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^6, Y1^-1 * Y3^2 * Y1 * Y3^-2, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^4, (Y3^-1 * Y1)^6 ] Map:: polytopal R = (1, 73, 2, 74, 6, 78, 17, 89, 13, 85, 4, 76)(3, 75, 9, 81, 25, 97, 37, 109, 18, 90, 11, 83)(5, 77, 15, 87, 32, 104, 38, 110, 19, 91, 16, 88)(7, 79, 20, 92, 12, 84, 31, 103, 34, 106, 22, 94)(8, 80, 23, 95, 14, 86, 33, 105, 35, 107, 24, 96)(10, 82, 21, 93, 36, 108, 52, 124, 43, 115, 28, 100)(26, 98, 44, 116, 29, 101, 48, 120, 53, 125, 45, 117)(27, 99, 46, 118, 30, 102, 49, 121, 54, 126, 47, 119)(39, 111, 55, 127, 41, 113, 59, 131, 50, 122, 56, 128)(40, 112, 57, 129, 42, 114, 60, 132, 51, 123, 58, 130)(61, 133, 70, 142, 63, 135, 72, 144, 65, 137, 68, 140)(62, 134, 69, 141, 64, 136, 71, 143, 66, 138, 67, 139)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 162)(7, 165)(8, 146)(9, 170)(10, 149)(11, 173)(12, 172)(13, 169)(14, 148)(15, 171)(16, 174)(17, 178)(18, 180)(19, 150)(20, 183)(21, 152)(22, 185)(23, 184)(24, 186)(25, 187)(26, 159)(27, 153)(28, 158)(29, 160)(30, 155)(31, 194)(32, 157)(33, 195)(34, 196)(35, 161)(36, 163)(37, 197)(38, 198)(39, 167)(40, 164)(41, 168)(42, 166)(43, 176)(44, 205)(45, 207)(46, 206)(47, 208)(48, 209)(49, 210)(50, 177)(51, 175)(52, 179)(53, 182)(54, 181)(55, 211)(56, 213)(57, 212)(58, 214)(59, 215)(60, 216)(61, 190)(62, 188)(63, 191)(64, 189)(65, 193)(66, 192)(67, 201)(68, 199)(69, 202)(70, 200)(71, 204)(72, 203)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.983 Graph:: simple bipartite v = 84 e = 144 f = 30 degree seq :: [ 2^72, 12^12 ] E16.985 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 6}) Quotient :: edge Aut^+ = C3 x ((C6 x C2) : C2) (small group id <72, 30>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^-2 * T2 * T1^-2 * T2^-1, T2^6, (T2^-2 * T1 * T2^-1)^2, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-3 * T1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 28, 16, 5)(2, 7, 20, 45, 24, 8)(4, 12, 32, 59, 33, 13)(6, 17, 40, 64, 41, 18)(9, 25, 55, 39, 56, 26)(11, 30, 62, 38, 63, 31)(14, 34, 61, 29, 60, 35)(15, 36, 58, 27, 57, 37)(19, 42, 65, 54, 66, 43)(21, 47, 71, 53, 72, 48)(22, 49, 70, 46, 69, 50)(23, 51, 68, 44, 67, 52)(73, 74, 78, 76)(75, 81, 89, 83)(77, 86, 90, 87)(79, 91, 84, 93)(80, 94, 85, 95)(82, 99, 112, 101)(88, 110, 113, 111)(92, 116, 104, 118)(96, 125, 105, 126)(97, 114, 102, 119)(98, 121, 103, 123)(100, 131, 136, 117)(106, 115, 108, 120)(107, 122, 109, 124)(127, 139, 134, 141)(128, 144, 135, 138)(129, 137, 132, 143)(130, 142, 133, 140) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.989 Transitivity :: ET+ Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.986 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 6}) Quotient :: edge Aut^+ = C3 x ((C6 x C2) : C2) (small group id <72, 30>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^6, T2^2 * T1 * T2^-2 * T1^-1, (T2^-1 * T1)^6 ] Map:: polytopal non-degenerate R = (1, 3, 10, 27, 16, 5)(2, 7, 20, 38, 24, 8)(4, 12, 28, 49, 31, 13)(6, 17, 34, 52, 35, 18)(9, 25, 44, 32, 14, 26)(11, 29, 48, 33, 15, 30)(19, 36, 54, 41, 22, 37)(21, 39, 58, 42, 23, 40)(43, 61, 50, 65, 46, 62)(45, 63, 51, 66, 47, 64)(53, 67, 59, 71, 56, 68)(55, 69, 60, 72, 57, 70)(73, 74, 78, 76)(75, 81, 89, 83)(77, 86, 90, 87)(79, 91, 84, 93)(80, 94, 85, 95)(82, 92, 106, 100)(88, 96, 107, 103)(97, 115, 101, 117)(98, 118, 102, 119)(99, 116, 124, 120)(104, 122, 105, 123)(108, 125, 111, 127)(109, 128, 112, 129)(110, 126, 121, 130)(113, 131, 114, 132)(133, 141, 135, 139)(134, 142, 136, 140)(137, 144, 138, 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) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.988 Transitivity :: ET+ Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.987 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 6}) Quotient :: edge Aut^+ = C3 x ((C6 x C2) : C2) (small group id <72, 30>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-2 * T1 * T2^2 * T1^-1, T2^2 * T1 * T2^-2 * T1^-1, T2^6, (T1^-1 * T2 * T1^-1)^2, T1^6, T2^-3 * T1^-2 * T2^-1 * T1^-2, (T2^-1 * T1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 3, 10, 30, 17, 5)(2, 7, 22, 53, 26, 8)(4, 12, 31, 50, 39, 14)(6, 19, 46, 41, 49, 20)(9, 28, 61, 40, 15, 29)(11, 32, 45, 42, 16, 33)(13, 35, 60, 27, 59, 36)(18, 43, 67, 57, 69, 44)(21, 51, 38, 56, 24, 52)(23, 54, 66, 58, 25, 55)(34, 62, 68, 65, 37, 63)(47, 70, 64, 72, 48, 71)(73, 74, 78, 90, 85, 76)(75, 81, 99, 120, 92, 83)(77, 87, 107, 136, 113, 88)(79, 93, 122, 140, 116, 95)(80, 96, 84, 106, 129, 97)(82, 94, 118, 139, 132, 103)(86, 109, 115, 138, 125, 110)(89, 98, 121, 141, 131, 111)(91, 117, 102, 133, 108, 119)(100, 123, 114, 130, 144, 134)(101, 124, 104, 126, 142, 135)(105, 127, 143, 137, 112, 128) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 8^6 ) } Outer automorphisms :: reflexible Dual of E16.990 Transitivity :: ET+ Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 6^24 ] E16.988 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 6}) Quotient :: loop Aut^+ = C3 x ((C6 x C2) : C2) (small group id <72, 30>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^-2 * T2 * T1^-2 * T2^-1, T2^6, (T2^-2 * T1 * T2^-1)^2, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-3 * T1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 10, 82, 28, 100, 16, 88, 5, 77)(2, 74, 7, 79, 20, 92, 45, 117, 24, 96, 8, 80)(4, 76, 12, 84, 32, 104, 59, 131, 33, 105, 13, 85)(6, 78, 17, 89, 40, 112, 64, 136, 41, 113, 18, 90)(9, 81, 25, 97, 55, 127, 39, 111, 56, 128, 26, 98)(11, 83, 30, 102, 62, 134, 38, 110, 63, 135, 31, 103)(14, 86, 34, 106, 61, 133, 29, 101, 60, 132, 35, 107)(15, 87, 36, 108, 58, 130, 27, 99, 57, 129, 37, 109)(19, 91, 42, 114, 65, 137, 54, 126, 66, 138, 43, 115)(21, 93, 47, 119, 71, 143, 53, 125, 72, 144, 48, 120)(22, 94, 49, 121, 70, 142, 46, 118, 69, 141, 50, 122)(23, 95, 51, 123, 68, 140, 44, 116, 67, 139, 52, 124) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 86)(6, 76)(7, 91)(8, 94)(9, 89)(10, 99)(11, 75)(12, 93)(13, 95)(14, 90)(15, 77)(16, 110)(17, 83)(18, 87)(19, 84)(20, 116)(21, 79)(22, 85)(23, 80)(24, 125)(25, 114)(26, 121)(27, 112)(28, 131)(29, 82)(30, 119)(31, 123)(32, 118)(33, 126)(34, 115)(35, 122)(36, 120)(37, 124)(38, 113)(39, 88)(40, 101)(41, 111)(42, 102)(43, 108)(44, 104)(45, 100)(46, 92)(47, 97)(48, 106)(49, 103)(50, 109)(51, 98)(52, 107)(53, 105)(54, 96)(55, 139)(56, 144)(57, 137)(58, 142)(59, 136)(60, 143)(61, 140)(62, 141)(63, 138)(64, 117)(65, 132)(66, 128)(67, 134)(68, 130)(69, 127)(70, 133)(71, 129)(72, 135) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.986 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.989 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 6}) Quotient :: loop Aut^+ = C3 x ((C6 x C2) : C2) (small group id <72, 30>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^6, T2^2 * T1 * T2^-2 * T1^-1, (T2^-1 * T1)^6 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 10, 82, 27, 99, 16, 88, 5, 77)(2, 74, 7, 79, 20, 92, 38, 110, 24, 96, 8, 80)(4, 76, 12, 84, 28, 100, 49, 121, 31, 103, 13, 85)(6, 78, 17, 89, 34, 106, 52, 124, 35, 107, 18, 90)(9, 81, 25, 97, 44, 116, 32, 104, 14, 86, 26, 98)(11, 83, 29, 101, 48, 120, 33, 105, 15, 87, 30, 102)(19, 91, 36, 108, 54, 126, 41, 113, 22, 94, 37, 109)(21, 93, 39, 111, 58, 130, 42, 114, 23, 95, 40, 112)(43, 115, 61, 133, 50, 122, 65, 137, 46, 118, 62, 134)(45, 117, 63, 135, 51, 123, 66, 138, 47, 119, 64, 136)(53, 125, 67, 139, 59, 131, 71, 143, 56, 128, 68, 140)(55, 127, 69, 141, 60, 132, 72, 144, 57, 129, 70, 142) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 86)(6, 76)(7, 91)(8, 94)(9, 89)(10, 92)(11, 75)(12, 93)(13, 95)(14, 90)(15, 77)(16, 96)(17, 83)(18, 87)(19, 84)(20, 106)(21, 79)(22, 85)(23, 80)(24, 107)(25, 115)(26, 118)(27, 116)(28, 82)(29, 117)(30, 119)(31, 88)(32, 122)(33, 123)(34, 100)(35, 103)(36, 125)(37, 128)(38, 126)(39, 127)(40, 129)(41, 131)(42, 132)(43, 101)(44, 124)(45, 97)(46, 102)(47, 98)(48, 99)(49, 130)(50, 105)(51, 104)(52, 120)(53, 111)(54, 121)(55, 108)(56, 112)(57, 109)(58, 110)(59, 114)(60, 113)(61, 141)(62, 142)(63, 139)(64, 140)(65, 144)(66, 143)(67, 133)(68, 134)(69, 135)(70, 136)(71, 137)(72, 138) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.985 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.990 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 6}) Quotient :: loop Aut^+ = C3 x ((C6 x C2) : C2) (small group id <72, 30>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, T2 * T1 * T2^2 * T1^-1 * T2, T1^6, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-3)^2, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 10, 82, 5, 77)(2, 74, 7, 79, 21, 93, 8, 80)(4, 76, 12, 84, 28, 100, 14, 86)(6, 78, 18, 90, 43, 115, 19, 91)(9, 81, 26, 98, 15, 87, 27, 99)(11, 83, 29, 101, 16, 88, 31, 103)(13, 85, 34, 106, 59, 131, 35, 107)(17, 89, 40, 112, 64, 136, 41, 113)(20, 92, 48, 120, 23, 95, 49, 121)(22, 94, 50, 122, 24, 96, 52, 124)(25, 97, 55, 127, 38, 110, 56, 128)(30, 102, 61, 133, 39, 111, 62, 134)(32, 104, 57, 129, 36, 108, 58, 130)(33, 105, 60, 132, 37, 109, 63, 135)(42, 114, 65, 137, 45, 117, 66, 138)(44, 116, 67, 139, 46, 118, 68, 140)(47, 119, 69, 141, 53, 125, 70, 142)(51, 123, 71, 143, 54, 126, 72, 144) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 89)(7, 92)(8, 95)(9, 97)(10, 93)(11, 75)(12, 104)(13, 76)(14, 108)(15, 110)(16, 77)(17, 85)(18, 114)(19, 117)(20, 119)(21, 115)(22, 79)(23, 125)(24, 80)(25, 113)(26, 120)(27, 121)(28, 82)(29, 122)(30, 83)(31, 124)(32, 118)(33, 84)(34, 126)(35, 123)(36, 116)(37, 86)(38, 112)(39, 88)(40, 111)(41, 102)(42, 109)(43, 136)(44, 90)(45, 105)(46, 91)(47, 107)(48, 137)(49, 138)(50, 139)(51, 94)(52, 140)(53, 106)(54, 96)(55, 141)(56, 142)(57, 98)(58, 99)(59, 100)(60, 101)(61, 143)(62, 144)(63, 103)(64, 131)(65, 134)(66, 133)(67, 128)(68, 127)(69, 135)(70, 132)(71, 130)(72, 129) local type(s) :: { ( 6^8 ) } Outer automorphisms :: reflexible Dual of E16.987 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 8^18 ] E16.991 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = C3 x ((C6 x C2) : C2) (small group id <72, 30>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, Y1^4, (R * Y3)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^6, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-3 * Y3 * Y2^-3 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: R = (1, 73, 2, 74, 6, 78, 4, 76)(3, 75, 9, 81, 17, 89, 11, 83)(5, 77, 14, 86, 18, 90, 15, 87)(7, 79, 19, 91, 12, 84, 21, 93)(8, 80, 22, 94, 13, 85, 23, 95)(10, 82, 27, 99, 40, 112, 29, 101)(16, 88, 38, 110, 41, 113, 39, 111)(20, 92, 44, 116, 32, 104, 46, 118)(24, 96, 53, 125, 33, 105, 54, 126)(25, 97, 42, 114, 30, 102, 47, 119)(26, 98, 49, 121, 31, 103, 51, 123)(28, 100, 59, 131, 64, 136, 45, 117)(34, 106, 43, 115, 36, 108, 48, 120)(35, 107, 50, 122, 37, 109, 52, 124)(55, 127, 67, 139, 62, 134, 69, 141)(56, 128, 72, 144, 63, 135, 66, 138)(57, 129, 65, 137, 60, 132, 71, 143)(58, 130, 70, 142, 61, 133, 68, 140)(145, 217, 147, 219, 154, 226, 172, 244, 160, 232, 149, 221)(146, 218, 151, 223, 164, 236, 189, 261, 168, 240, 152, 224)(148, 220, 156, 228, 176, 248, 203, 275, 177, 249, 157, 229)(150, 222, 161, 233, 184, 256, 208, 280, 185, 257, 162, 234)(153, 225, 169, 241, 199, 271, 183, 255, 200, 272, 170, 242)(155, 227, 174, 246, 206, 278, 182, 254, 207, 279, 175, 247)(158, 230, 178, 250, 205, 277, 173, 245, 204, 276, 179, 251)(159, 231, 180, 252, 202, 274, 171, 243, 201, 273, 181, 253)(163, 235, 186, 258, 209, 281, 198, 270, 210, 282, 187, 259)(165, 237, 191, 263, 215, 287, 197, 269, 216, 288, 192, 264)(166, 238, 193, 265, 214, 286, 190, 262, 213, 285, 194, 266)(167, 239, 195, 267, 212, 284, 188, 260, 211, 283, 196, 268) L = (1, 148)(2, 145)(3, 155)(4, 150)(5, 159)(6, 146)(7, 165)(8, 167)(9, 147)(10, 173)(11, 161)(12, 163)(13, 166)(14, 149)(15, 162)(16, 183)(17, 153)(18, 158)(19, 151)(20, 190)(21, 156)(22, 152)(23, 157)(24, 198)(25, 191)(26, 195)(27, 154)(28, 189)(29, 184)(30, 186)(31, 193)(32, 188)(33, 197)(34, 192)(35, 196)(36, 187)(37, 194)(38, 160)(39, 185)(40, 171)(41, 182)(42, 169)(43, 178)(44, 164)(45, 208)(46, 176)(47, 174)(48, 180)(49, 170)(50, 179)(51, 175)(52, 181)(53, 168)(54, 177)(55, 213)(56, 210)(57, 215)(58, 212)(59, 172)(60, 209)(61, 214)(62, 211)(63, 216)(64, 203)(65, 201)(66, 207)(67, 199)(68, 205)(69, 206)(70, 202)(71, 204)(72, 200)(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, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E16.995 Graph:: bipartite v = 30 e = 144 f = 84 degree seq :: [ 8^18, 12^12 ] E16.992 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = C3 x ((C6 x C2) : C2) (small group id <72, 30>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^6, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y3 * Y2^2 * Y3^-1 * Y2^-2, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: R = (1, 73, 2, 74, 6, 78, 4, 76)(3, 75, 9, 81, 17, 89, 11, 83)(5, 77, 14, 86, 18, 90, 15, 87)(7, 79, 19, 91, 12, 84, 21, 93)(8, 80, 22, 94, 13, 85, 23, 95)(10, 82, 20, 92, 34, 106, 28, 100)(16, 88, 24, 96, 35, 107, 31, 103)(25, 97, 43, 115, 29, 101, 45, 117)(26, 98, 46, 118, 30, 102, 47, 119)(27, 99, 44, 116, 52, 124, 48, 120)(32, 104, 50, 122, 33, 105, 51, 123)(36, 108, 53, 125, 39, 111, 55, 127)(37, 109, 56, 128, 40, 112, 57, 129)(38, 110, 54, 126, 49, 121, 58, 130)(41, 113, 59, 131, 42, 114, 60, 132)(61, 133, 69, 141, 63, 135, 67, 139)(62, 134, 70, 142, 64, 136, 68, 140)(65, 137, 72, 144, 66, 138, 71, 143)(145, 217, 147, 219, 154, 226, 171, 243, 160, 232, 149, 221)(146, 218, 151, 223, 164, 236, 182, 254, 168, 240, 152, 224)(148, 220, 156, 228, 172, 244, 193, 265, 175, 247, 157, 229)(150, 222, 161, 233, 178, 250, 196, 268, 179, 251, 162, 234)(153, 225, 169, 241, 188, 260, 176, 248, 158, 230, 170, 242)(155, 227, 173, 245, 192, 264, 177, 249, 159, 231, 174, 246)(163, 235, 180, 252, 198, 270, 185, 257, 166, 238, 181, 253)(165, 237, 183, 255, 202, 274, 186, 258, 167, 239, 184, 256)(187, 259, 205, 277, 194, 266, 209, 281, 190, 262, 206, 278)(189, 261, 207, 279, 195, 267, 210, 282, 191, 263, 208, 280)(197, 269, 211, 283, 203, 275, 215, 287, 200, 272, 212, 284)(199, 271, 213, 285, 204, 276, 216, 288, 201, 273, 214, 286) L = (1, 148)(2, 145)(3, 155)(4, 150)(5, 159)(6, 146)(7, 165)(8, 167)(9, 147)(10, 172)(11, 161)(12, 163)(13, 166)(14, 149)(15, 162)(16, 175)(17, 153)(18, 158)(19, 151)(20, 154)(21, 156)(22, 152)(23, 157)(24, 160)(25, 189)(26, 191)(27, 192)(28, 178)(29, 187)(30, 190)(31, 179)(32, 195)(33, 194)(34, 164)(35, 168)(36, 199)(37, 201)(38, 202)(39, 197)(40, 200)(41, 204)(42, 203)(43, 169)(44, 171)(45, 173)(46, 170)(47, 174)(48, 196)(49, 198)(50, 176)(51, 177)(52, 188)(53, 180)(54, 182)(55, 183)(56, 181)(57, 184)(58, 193)(59, 185)(60, 186)(61, 211)(62, 212)(63, 213)(64, 214)(65, 215)(66, 216)(67, 207)(68, 208)(69, 205)(70, 206)(71, 210)(72, 209)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 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 E16.996 Graph:: bipartite v = 30 e = 144 f = 84 degree seq :: [ 8^18, 12^12 ] E16.993 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = C3 x ((C6 x C2) : C2) (small group id <72, 30>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1 * Y2)^2, Y2^6, Y1 * Y2 * Y1^-2 * Y2^-1 * Y1, Y1^6, Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2 * Y1^-2 * Y2^3 * Y1^-1 * Y2^-2 * Y1^-1 ] Map:: R = (1, 73, 2, 74, 6, 78, 18, 90, 13, 85, 4, 76)(3, 75, 9, 81, 19, 91, 45, 117, 32, 104, 11, 83)(5, 77, 15, 87, 20, 92, 47, 119, 36, 108, 16, 88)(7, 79, 21, 93, 43, 115, 35, 107, 12, 84, 23, 95)(8, 80, 24, 96, 44, 116, 37, 109, 14, 86, 25, 97)(10, 82, 29, 101, 46, 118, 38, 110, 58, 130, 26, 98)(17, 89, 34, 106, 48, 120, 22, 94, 51, 123, 42, 114)(27, 99, 49, 121, 41, 113, 57, 129, 31, 103, 53, 125)(28, 100, 55, 127, 66, 138, 62, 134, 33, 105, 56, 128)(30, 102, 61, 133, 67, 139, 63, 135, 70, 142, 59, 131)(39, 111, 50, 122, 68, 140, 65, 137, 40, 112, 54, 126)(52, 124, 71, 143, 60, 132, 72, 144, 64, 136, 69, 141)(145, 217, 147, 219, 154, 226, 174, 246, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 196, 268, 170, 242, 152, 224)(148, 220, 156, 228, 178, 250, 208, 280, 182, 254, 158, 230)(150, 222, 163, 235, 190, 262, 211, 283, 192, 264, 164, 236)(153, 225, 171, 243, 191, 263, 212, 284, 203, 275, 172, 244)(155, 227, 175, 247, 159, 231, 183, 255, 207, 279, 177, 249)(157, 229, 176, 248, 202, 274, 214, 286, 195, 267, 180, 252)(160, 232, 184, 256, 205, 277, 210, 282, 189, 261, 185, 257)(162, 234, 187, 259, 186, 258, 204, 276, 173, 245, 188, 260)(165, 237, 193, 265, 181, 253, 206, 278, 213, 285, 194, 266)(167, 239, 197, 269, 168, 240, 199, 271, 216, 288, 198, 270)(169, 241, 200, 272, 215, 287, 209, 281, 179, 251, 201, 273) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 171)(10, 174)(11, 175)(12, 178)(13, 176)(14, 148)(15, 183)(16, 184)(17, 149)(18, 187)(19, 190)(20, 150)(21, 193)(22, 196)(23, 197)(24, 199)(25, 200)(26, 152)(27, 191)(28, 153)(29, 188)(30, 161)(31, 159)(32, 202)(33, 155)(34, 208)(35, 201)(36, 157)(37, 206)(38, 158)(39, 207)(40, 205)(41, 160)(42, 204)(43, 186)(44, 162)(45, 185)(46, 211)(47, 212)(48, 164)(49, 181)(50, 165)(51, 180)(52, 170)(53, 168)(54, 167)(55, 216)(56, 215)(57, 169)(58, 214)(59, 172)(60, 173)(61, 210)(62, 213)(63, 177)(64, 182)(65, 179)(66, 189)(67, 192)(68, 203)(69, 194)(70, 195)(71, 209)(72, 198)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E16.994 Graph:: bipartite v = 24 e = 144 f = 90 degree seq :: [ 12^24 ] E16.994 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = C3 x ((C6 x C2) : C2) (small group id <72, 30>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2^2 * Y3 * Y2, Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3^3 * Y2^-1 * Y3^-3 * Y2^-1, Y3 * Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3, (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, 150, 222, 148, 220)(147, 219, 153, 225, 161, 233, 155, 227)(149, 221, 158, 230, 162, 234, 159, 231)(151, 223, 163, 235, 156, 228, 165, 237)(152, 224, 166, 238, 157, 229, 167, 239)(154, 226, 171, 243, 184, 256, 173, 245)(160, 232, 182, 254, 185, 257, 183, 255)(164, 236, 188, 260, 176, 248, 190, 262)(168, 240, 197, 269, 177, 249, 198, 270)(169, 241, 186, 258, 174, 246, 191, 263)(170, 242, 193, 265, 175, 247, 195, 267)(172, 244, 203, 275, 208, 280, 189, 261)(178, 250, 187, 259, 180, 252, 192, 264)(179, 251, 194, 266, 181, 253, 196, 268)(199, 271, 211, 283, 206, 278, 213, 285)(200, 272, 216, 288, 207, 279, 210, 282)(201, 273, 209, 281, 204, 276, 215, 287)(202, 274, 214, 286, 205, 277, 212, 284) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 161)(7, 164)(8, 146)(9, 169)(10, 172)(11, 174)(12, 176)(13, 148)(14, 178)(15, 180)(16, 149)(17, 184)(18, 150)(19, 186)(20, 189)(21, 191)(22, 193)(23, 195)(24, 152)(25, 199)(26, 153)(27, 201)(28, 160)(29, 204)(30, 206)(31, 155)(32, 203)(33, 157)(34, 205)(35, 158)(36, 202)(37, 159)(38, 207)(39, 200)(40, 208)(41, 162)(42, 209)(43, 163)(44, 211)(45, 168)(46, 213)(47, 215)(48, 165)(49, 214)(50, 166)(51, 212)(52, 167)(53, 216)(54, 210)(55, 183)(56, 170)(57, 181)(58, 171)(59, 177)(60, 179)(61, 173)(62, 182)(63, 175)(64, 185)(65, 198)(66, 187)(67, 196)(68, 188)(69, 194)(70, 190)(71, 197)(72, 192)(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) :: { ( 12, 12 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E16.993 Graph:: simple bipartite v = 90 e = 144 f = 24 degree seq :: [ 2^72, 8^18 ] E16.995 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = C3 x ((C6 x C2) : C2) (small group id <72, 30>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^6, Y1^-1 * Y3 * Y1^2 * Y3^-1 * Y1^-1, Y1^-1 * Y3^2 * Y1 * Y3^-2, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^-1)^6 ] Map:: polytopal R = (1, 73, 2, 74, 6, 78, 17, 89, 13, 85, 4, 76)(3, 75, 9, 81, 18, 90, 36, 108, 29, 101, 11, 83)(5, 77, 15, 87, 19, 91, 38, 110, 32, 104, 16, 88)(7, 79, 20, 92, 34, 106, 31, 103, 12, 84, 22, 94)(8, 80, 23, 95, 35, 107, 33, 105, 14, 86, 24, 96)(10, 82, 21, 93, 37, 109, 52, 124, 47, 119, 27, 99)(25, 97, 43, 115, 53, 125, 48, 120, 28, 100, 44, 116)(26, 98, 45, 117, 54, 126, 49, 121, 30, 102, 46, 118)(39, 111, 55, 127, 50, 122, 59, 131, 41, 113, 56, 128)(40, 112, 57, 129, 51, 123, 60, 132, 42, 114, 58, 130)(61, 133, 68, 140, 65, 137, 72, 144, 63, 135, 70, 142)(62, 134, 67, 139, 66, 138, 71, 143, 64, 136, 69, 141)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 162)(7, 165)(8, 146)(9, 169)(10, 149)(11, 172)(12, 171)(13, 173)(14, 148)(15, 170)(16, 174)(17, 178)(18, 181)(19, 150)(20, 183)(21, 152)(22, 185)(23, 184)(24, 186)(25, 159)(26, 153)(27, 158)(28, 160)(29, 191)(30, 155)(31, 194)(32, 157)(33, 195)(34, 196)(35, 161)(36, 197)(37, 163)(38, 198)(39, 167)(40, 164)(41, 168)(42, 166)(43, 205)(44, 207)(45, 206)(46, 208)(47, 176)(48, 209)(49, 210)(50, 177)(51, 175)(52, 179)(53, 182)(54, 180)(55, 211)(56, 213)(57, 212)(58, 214)(59, 215)(60, 216)(61, 189)(62, 187)(63, 190)(64, 188)(65, 193)(66, 192)(67, 201)(68, 199)(69, 202)(70, 200)(71, 204)(72, 203)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.991 Graph:: simple bipartite v = 84 e = 144 f = 30 degree seq :: [ 2^72, 12^12 ] E16.996 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = C3 x ((C6 x C2) : C2) (small group id <72, 30>) Aut = (C2 x S3 x S3) : C2 (small group id <144, 154>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^2 * Y1 * Y3^-2, Y1^6, (Y3 * Y1^-3)^2, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^4, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: polytopal R = (1, 73, 2, 74, 6, 78, 17, 89, 13, 85, 4, 76)(3, 75, 9, 81, 25, 97, 41, 113, 30, 102, 11, 83)(5, 77, 15, 87, 38, 110, 40, 112, 39, 111, 16, 88)(7, 79, 20, 92, 47, 119, 35, 107, 51, 123, 22, 94)(8, 80, 23, 95, 53, 125, 34, 106, 54, 126, 24, 96)(10, 82, 21, 93, 43, 115, 64, 136, 59, 131, 28, 100)(12, 84, 32, 104, 46, 118, 19, 91, 45, 117, 33, 105)(14, 86, 36, 108, 44, 116, 18, 90, 42, 114, 37, 109)(26, 98, 48, 120, 65, 137, 62, 134, 72, 144, 57, 129)(27, 99, 49, 121, 66, 138, 61, 133, 71, 143, 58, 130)(29, 101, 50, 122, 67, 139, 56, 128, 70, 142, 60, 132)(31, 103, 52, 124, 68, 140, 55, 127, 69, 141, 63, 135)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 162)(7, 165)(8, 146)(9, 170)(10, 149)(11, 173)(12, 172)(13, 178)(14, 148)(15, 171)(16, 175)(17, 184)(18, 187)(19, 150)(20, 192)(21, 152)(22, 194)(23, 193)(24, 196)(25, 199)(26, 159)(27, 153)(28, 158)(29, 160)(30, 205)(31, 155)(32, 201)(33, 204)(34, 203)(35, 157)(36, 202)(37, 207)(38, 200)(39, 206)(40, 208)(41, 161)(42, 209)(43, 163)(44, 211)(45, 210)(46, 212)(47, 213)(48, 167)(49, 164)(50, 168)(51, 215)(52, 166)(53, 214)(54, 216)(55, 182)(56, 169)(57, 180)(58, 176)(59, 179)(60, 181)(61, 183)(62, 174)(63, 177)(64, 185)(65, 189)(66, 186)(67, 190)(68, 188)(69, 197)(70, 191)(71, 198)(72, 195)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.992 Graph:: simple bipartite v = 84 e = 144 f = 30 degree seq :: [ 2^72, 12^12 ] E16.997 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 6}) Quotient :: edge Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T1 * T2^-1 * T1)^2, T2^6, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1, (T2^-3 * T1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 28, 16, 5)(2, 7, 20, 45, 24, 8)(4, 12, 32, 59, 33, 13)(6, 17, 40, 64, 41, 18)(9, 25, 55, 39, 56, 26)(11, 30, 62, 38, 63, 31)(14, 34, 61, 29, 60, 35)(15, 36, 58, 27, 57, 37)(19, 42, 65, 54, 66, 43)(21, 47, 71, 53, 72, 48)(22, 49, 70, 46, 69, 50)(23, 51, 68, 44, 67, 52)(73, 74, 78, 76)(75, 81, 90, 83)(77, 86, 89, 87)(79, 91, 85, 93)(80, 94, 84, 95)(82, 99, 113, 101)(88, 110, 112, 111)(92, 116, 105, 118)(96, 125, 104, 126)(97, 121, 103, 124)(98, 114, 102, 120)(100, 131, 136, 117)(106, 122, 109, 123)(107, 115, 108, 119)(127, 143, 135, 138)(128, 140, 134, 141)(129, 137, 133, 144)(130, 142, 132, 139) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.1001 Transitivity :: ET+ Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.998 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 6}) Quotient :: edge Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T2 * T1^-1)^2, (F * T1)^2, T1^4, T2^6, T2^-1 * T1 * T2 * T1^2 * T2^2 * T1^-1, (T2^-1 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 3, 10, 24, 14, 5)(2, 7, 18, 39, 20, 8)(4, 11, 26, 49, 28, 12)(6, 15, 33, 55, 35, 16)(9, 21, 44, 56, 34, 22)(13, 29, 32, 54, 52, 30)(17, 36, 58, 50, 27, 37)(19, 40, 25, 48, 63, 41)(23, 45, 57, 70, 62, 46)(31, 47, 66, 71, 67, 53)(38, 59, 68, 72, 69, 60)(42, 61, 43, 65, 51, 64)(73, 74, 78, 76)(75, 81, 91, 80)(77, 83, 97, 85)(79, 89, 106, 88)(82, 95, 107, 94)(84, 87, 104, 99)(86, 101, 105, 103)(90, 110, 100, 109)(92, 112, 98, 114)(93, 115, 134, 113)(96, 119, 135, 118)(102, 120, 138, 123)(108, 129, 141, 128)(111, 133, 116, 132)(117, 130, 125, 127)(121, 131, 124, 136)(122, 126, 140, 139)(137, 143, 144, 142) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E16.1000 Transitivity :: ET+ Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 4^18, 6^12 ] E16.999 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 6}) Quotient :: edge Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-2)^2, (T1^-1 * T2^2)^2, (T2^-2 * T1)^2, (T2^2 * T1^-1)^2, (T1^-1 * T2^-1 * T1^-1)^2, T2^6, T1^6, T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1, T1^-2 * T2^-2 * T1^-1 * T2^-2 * T1^-1, T1^-2 * T2^2 * T1^2 * T2^-2, (T2 * T1)^4, T2^3 * T1^-2 * T2 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 31, 17, 5)(2, 7, 22, 56, 26, 8)(4, 12, 36, 60, 40, 14)(6, 19, 48, 33, 52, 20)(9, 28, 49, 70, 50, 29)(11, 32, 15, 42, 51, 34)(13, 38, 64, 41, 55, 27)(16, 43, 66, 71, 65, 44)(18, 46, 45, 58, 30, 47)(21, 53, 68, 72, 69, 54)(23, 57, 24, 61, 35, 59)(25, 62, 37, 67, 39, 63)(73, 74, 78, 90, 85, 76)(75, 81, 99, 137, 105, 83)(77, 87, 113, 121, 91, 88)(79, 93, 86, 111, 130, 95)(80, 96, 132, 140, 118, 97)(82, 102, 120, 112, 136, 98)(84, 107, 119, 141, 128, 109)(89, 108, 124, 94, 127, 117)(92, 122, 103, 138, 110, 123)(100, 126, 106, 133, 115, 135)(101, 134, 114, 125, 116, 131)(104, 139, 143, 144, 142, 129) 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) :: { ( 8^6 ) } Outer automorphisms :: reflexible Dual of E16.1002 Transitivity :: ET+ Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 6^24 ] E16.1000 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 6}) Quotient :: loop Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T1 * T2^-1 * T1)^2, T2^6, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1, (T2^-3 * T1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 10, 82, 28, 100, 16, 88, 5, 77)(2, 74, 7, 79, 20, 92, 45, 117, 24, 96, 8, 80)(4, 76, 12, 84, 32, 104, 59, 131, 33, 105, 13, 85)(6, 78, 17, 89, 40, 112, 64, 136, 41, 113, 18, 90)(9, 81, 25, 97, 55, 127, 39, 111, 56, 128, 26, 98)(11, 83, 30, 102, 62, 134, 38, 110, 63, 135, 31, 103)(14, 86, 34, 106, 61, 133, 29, 101, 60, 132, 35, 107)(15, 87, 36, 108, 58, 130, 27, 99, 57, 129, 37, 109)(19, 91, 42, 114, 65, 137, 54, 126, 66, 138, 43, 115)(21, 93, 47, 119, 71, 143, 53, 125, 72, 144, 48, 120)(22, 94, 49, 121, 70, 142, 46, 118, 69, 141, 50, 122)(23, 95, 51, 123, 68, 140, 44, 116, 67, 139, 52, 124) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 86)(6, 76)(7, 91)(8, 94)(9, 90)(10, 99)(11, 75)(12, 95)(13, 93)(14, 89)(15, 77)(16, 110)(17, 87)(18, 83)(19, 85)(20, 116)(21, 79)(22, 84)(23, 80)(24, 125)(25, 121)(26, 114)(27, 113)(28, 131)(29, 82)(30, 120)(31, 124)(32, 126)(33, 118)(34, 122)(35, 115)(36, 119)(37, 123)(38, 112)(39, 88)(40, 111)(41, 101)(42, 102)(43, 108)(44, 105)(45, 100)(46, 92)(47, 107)(48, 98)(49, 103)(50, 109)(51, 106)(52, 97)(53, 104)(54, 96)(55, 143)(56, 140)(57, 137)(58, 142)(59, 136)(60, 139)(61, 144)(62, 141)(63, 138)(64, 117)(65, 133)(66, 127)(67, 130)(68, 134)(69, 128)(70, 132)(71, 135)(72, 129) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.998 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.1001 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 6}) Quotient :: loop Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T2 * T1^-1)^2, (F * T1)^2, T1^4, T2^6, T2^-1 * T1 * T2 * T1^2 * T2^2 * T1^-1, (T2^-1 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 10, 82, 24, 96, 14, 86, 5, 77)(2, 74, 7, 79, 18, 90, 39, 111, 20, 92, 8, 80)(4, 76, 11, 83, 26, 98, 49, 121, 28, 100, 12, 84)(6, 78, 15, 87, 33, 105, 55, 127, 35, 107, 16, 88)(9, 81, 21, 93, 44, 116, 56, 128, 34, 106, 22, 94)(13, 85, 29, 101, 32, 104, 54, 126, 52, 124, 30, 102)(17, 89, 36, 108, 58, 130, 50, 122, 27, 99, 37, 109)(19, 91, 40, 112, 25, 97, 48, 120, 63, 135, 41, 113)(23, 95, 45, 117, 57, 129, 70, 142, 62, 134, 46, 118)(31, 103, 47, 119, 66, 138, 71, 143, 67, 139, 53, 125)(38, 110, 59, 131, 68, 140, 72, 144, 69, 141, 60, 132)(42, 114, 61, 133, 43, 115, 65, 137, 51, 123, 64, 136) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 83)(6, 76)(7, 89)(8, 75)(9, 91)(10, 95)(11, 97)(12, 87)(13, 77)(14, 101)(15, 104)(16, 79)(17, 106)(18, 110)(19, 80)(20, 112)(21, 115)(22, 82)(23, 107)(24, 119)(25, 85)(26, 114)(27, 84)(28, 109)(29, 105)(30, 120)(31, 86)(32, 99)(33, 103)(34, 88)(35, 94)(36, 129)(37, 90)(38, 100)(39, 133)(40, 98)(41, 93)(42, 92)(43, 134)(44, 132)(45, 130)(46, 96)(47, 135)(48, 138)(49, 131)(50, 126)(51, 102)(52, 136)(53, 127)(54, 140)(55, 117)(56, 108)(57, 141)(58, 125)(59, 124)(60, 111)(61, 116)(62, 113)(63, 118)(64, 121)(65, 143)(66, 123)(67, 122)(68, 139)(69, 128)(70, 137)(71, 144)(72, 142) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.997 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.1002 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 6}) Quotient :: loop Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, T1^6, (T2^-2 * T1^-1)^2, T1^6, T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2 * T1^-3)^2 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 10, 82, 5, 77)(2, 74, 7, 79, 21, 93, 8, 80)(4, 76, 12, 84, 28, 100, 14, 86)(6, 78, 18, 90, 43, 115, 19, 91)(9, 81, 26, 98, 16, 88, 27, 99)(11, 83, 29, 101, 15, 87, 31, 103)(13, 85, 34, 106, 59, 131, 35, 107)(17, 89, 40, 112, 64, 136, 41, 113)(20, 92, 48, 120, 24, 96, 49, 121)(22, 94, 50, 122, 23, 95, 52, 124)(25, 97, 55, 127, 39, 111, 56, 128)(30, 102, 61, 133, 38, 110, 62, 134)(32, 104, 60, 132, 37, 109, 63, 135)(33, 105, 57, 129, 36, 108, 58, 130)(42, 114, 65, 137, 46, 118, 66, 138)(44, 116, 67, 139, 45, 117, 68, 140)(47, 119, 69, 141, 54, 126, 70, 142)(51, 123, 71, 143, 53, 125, 72, 144) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 89)(7, 92)(8, 95)(9, 97)(10, 100)(11, 75)(12, 104)(13, 76)(14, 108)(15, 110)(16, 77)(17, 85)(18, 114)(19, 117)(20, 119)(21, 82)(22, 79)(23, 125)(24, 80)(25, 113)(26, 122)(27, 130)(28, 131)(29, 120)(30, 83)(31, 135)(32, 118)(33, 84)(34, 126)(35, 123)(36, 116)(37, 86)(38, 112)(39, 88)(40, 111)(41, 102)(42, 109)(43, 93)(44, 90)(45, 105)(46, 91)(47, 107)(48, 139)(49, 103)(50, 137)(51, 94)(52, 99)(53, 106)(54, 96)(55, 140)(56, 144)(57, 98)(58, 141)(59, 136)(60, 101)(61, 138)(62, 142)(63, 143)(64, 115)(65, 134)(66, 124)(67, 128)(68, 121)(69, 133)(70, 129)(71, 127)(72, 132) local type(s) :: { ( 6^8 ) } Outer automorphisms :: reflexible Dual of E16.999 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 8^18 ] E16.1003 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, (Y2 * Y1^-2)^2, Y3^-1 * Y2 * Y1^-1 * Y3 * Y2 * Y1, Y2^6, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y3 * Y2^-3 * Y1^-1 * Y2^-3, Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1, Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: R = (1, 73, 2, 74, 6, 78, 4, 76)(3, 75, 9, 81, 18, 90, 11, 83)(5, 77, 14, 86, 17, 89, 15, 87)(7, 79, 19, 91, 13, 85, 21, 93)(8, 80, 22, 94, 12, 84, 23, 95)(10, 82, 27, 99, 41, 113, 29, 101)(16, 88, 38, 110, 40, 112, 39, 111)(20, 92, 44, 116, 33, 105, 46, 118)(24, 96, 53, 125, 32, 104, 54, 126)(25, 97, 49, 121, 31, 103, 52, 124)(26, 98, 42, 114, 30, 102, 48, 120)(28, 100, 59, 131, 64, 136, 45, 117)(34, 106, 50, 122, 37, 109, 51, 123)(35, 107, 43, 115, 36, 108, 47, 119)(55, 127, 71, 143, 63, 135, 66, 138)(56, 128, 68, 140, 62, 134, 69, 141)(57, 129, 65, 137, 61, 133, 72, 144)(58, 130, 70, 142, 60, 132, 67, 139)(145, 217, 147, 219, 154, 226, 172, 244, 160, 232, 149, 221)(146, 218, 151, 223, 164, 236, 189, 261, 168, 240, 152, 224)(148, 220, 156, 228, 176, 248, 203, 275, 177, 249, 157, 229)(150, 222, 161, 233, 184, 256, 208, 280, 185, 257, 162, 234)(153, 225, 169, 241, 199, 271, 183, 255, 200, 272, 170, 242)(155, 227, 174, 246, 206, 278, 182, 254, 207, 279, 175, 247)(158, 230, 178, 250, 205, 277, 173, 245, 204, 276, 179, 251)(159, 231, 180, 252, 202, 274, 171, 243, 201, 273, 181, 253)(163, 235, 186, 258, 209, 281, 198, 270, 210, 282, 187, 259)(165, 237, 191, 263, 215, 287, 197, 269, 216, 288, 192, 264)(166, 238, 193, 265, 214, 286, 190, 262, 213, 285, 194, 266)(167, 239, 195, 267, 212, 284, 188, 260, 211, 283, 196, 268) L = (1, 148)(2, 145)(3, 155)(4, 150)(5, 159)(6, 146)(7, 165)(8, 167)(9, 147)(10, 173)(11, 162)(12, 166)(13, 163)(14, 149)(15, 161)(16, 183)(17, 158)(18, 153)(19, 151)(20, 190)(21, 157)(22, 152)(23, 156)(24, 198)(25, 196)(26, 192)(27, 154)(28, 189)(29, 185)(30, 186)(31, 193)(32, 197)(33, 188)(34, 195)(35, 191)(36, 187)(37, 194)(38, 160)(39, 184)(40, 182)(41, 171)(42, 170)(43, 179)(44, 164)(45, 208)(46, 177)(47, 180)(48, 174)(49, 169)(50, 178)(51, 181)(52, 175)(53, 168)(54, 176)(55, 210)(56, 213)(57, 216)(58, 211)(59, 172)(60, 214)(61, 209)(62, 212)(63, 215)(64, 203)(65, 201)(66, 207)(67, 204)(68, 200)(69, 206)(70, 202)(71, 199)(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, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E16.1008 Graph:: bipartite v = 30 e = 144 f = 84 degree seq :: [ 8^18, 12^12 ] E16.1004 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y1 * Y3^-1)^2, Y1^4, Y2 * Y3 * Y2 * Y1^-1, Y2^6, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2 * Y1 * Y3^-1 * Y2^2 * Y1^-1, Y2^2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y1^-2, Y3 * Y2^-1 * Y3^2 * Y1^-1 * Y2^-1 * Y1^-2, Y1^-2 * Y3 * Y2^-1 * Y1^-1 * Y2^2 * Y3^-2 * Y2, (Y3 * Y2^-1)^6 ] Map:: R = (1, 73, 2, 74, 6, 78, 4, 76)(3, 75, 9, 81, 19, 91, 8, 80)(5, 77, 11, 83, 25, 97, 13, 85)(7, 79, 17, 89, 34, 106, 16, 88)(10, 82, 23, 95, 35, 107, 22, 94)(12, 84, 15, 87, 32, 104, 27, 99)(14, 86, 29, 101, 33, 105, 31, 103)(18, 90, 38, 110, 28, 100, 37, 109)(20, 92, 40, 112, 26, 98, 42, 114)(21, 93, 43, 115, 62, 134, 41, 113)(24, 96, 47, 119, 63, 135, 46, 118)(30, 102, 48, 120, 66, 138, 51, 123)(36, 108, 57, 129, 69, 141, 56, 128)(39, 111, 61, 133, 44, 116, 60, 132)(45, 117, 58, 130, 53, 125, 55, 127)(49, 121, 59, 131, 52, 124, 64, 136)(50, 122, 54, 126, 68, 140, 67, 139)(65, 137, 71, 143, 72, 144, 70, 142)(145, 217, 147, 219, 154, 226, 168, 240, 158, 230, 149, 221)(146, 218, 151, 223, 162, 234, 183, 255, 164, 236, 152, 224)(148, 220, 155, 227, 170, 242, 193, 265, 172, 244, 156, 228)(150, 222, 159, 231, 177, 249, 199, 271, 179, 251, 160, 232)(153, 225, 165, 237, 188, 260, 200, 272, 178, 250, 166, 238)(157, 229, 173, 245, 176, 248, 198, 270, 196, 268, 174, 246)(161, 233, 180, 252, 202, 274, 194, 266, 171, 243, 181, 253)(163, 235, 184, 256, 169, 241, 192, 264, 207, 279, 185, 257)(167, 239, 189, 261, 201, 273, 214, 286, 206, 278, 190, 262)(175, 247, 191, 263, 210, 282, 215, 287, 211, 283, 197, 269)(182, 254, 203, 275, 212, 284, 216, 288, 213, 285, 204, 276)(186, 258, 205, 277, 187, 259, 209, 281, 195, 267, 208, 280) L = (1, 148)(2, 145)(3, 152)(4, 150)(5, 157)(6, 146)(7, 160)(8, 163)(9, 147)(10, 166)(11, 149)(12, 171)(13, 169)(14, 175)(15, 156)(16, 178)(17, 151)(18, 181)(19, 153)(20, 186)(21, 185)(22, 179)(23, 154)(24, 190)(25, 155)(26, 184)(27, 176)(28, 182)(29, 158)(30, 195)(31, 177)(32, 159)(33, 173)(34, 161)(35, 167)(36, 200)(37, 172)(38, 162)(39, 204)(40, 164)(41, 206)(42, 170)(43, 165)(44, 205)(45, 199)(46, 207)(47, 168)(48, 174)(49, 208)(50, 211)(51, 210)(52, 203)(53, 202)(54, 194)(55, 197)(56, 213)(57, 180)(58, 189)(59, 193)(60, 188)(61, 183)(62, 187)(63, 191)(64, 196)(65, 214)(66, 192)(67, 212)(68, 198)(69, 201)(70, 216)(71, 209)(72, 215)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E16.1007 Graph:: bipartite v = 30 e = 144 f = 84 degree seq :: [ 8^18, 12^12 ] E16.1005 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-2 * Y1^-1)^2, (Y2 * Y1^-2)^2, Y1^6, Y2^6, Y1^2 * Y2^-2 * Y1 * Y2^-2 * Y1, (Y1^-1 * Y2^-1)^4, (Y2 * Y1^-1)^4, Y1^-1 * Y2^-3 * Y1^-2 * Y2^-1 * Y1^-1, Y1^-2 * Y2^-2 * Y1^2 * Y2^2, (Y3^-1 * Y1^-1)^4, (Y2^-1, Y1^-1)^2 ] Map:: R = (1, 73, 2, 74, 6, 78, 18, 90, 13, 85, 4, 76)(3, 75, 9, 81, 27, 99, 51, 123, 20, 92, 11, 83)(5, 77, 15, 87, 37, 109, 67, 139, 44, 116, 16, 88)(7, 79, 21, 93, 53, 125, 69, 141, 47, 119, 23, 95)(8, 80, 24, 96, 12, 84, 35, 107, 63, 135, 25, 97)(10, 82, 30, 102, 49, 121, 26, 98, 64, 136, 32, 104)(14, 86, 39, 111, 46, 118, 68, 140, 56, 128, 40, 112)(17, 89, 45, 117, 52, 124, 36, 108, 57, 129, 22, 94)(19, 91, 48, 120, 31, 103, 66, 138, 38, 110, 50, 122)(28, 100, 65, 137, 71, 143, 72, 144, 70, 142, 54, 126)(29, 101, 61, 133, 33, 105, 62, 134, 41, 113, 59, 131)(34, 106, 58, 130, 42, 114, 60, 132, 43, 115, 55, 127)(145, 217, 147, 219, 154, 226, 175, 247, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 200, 272, 170, 242, 152, 224)(148, 220, 156, 228, 180, 252, 197, 269, 174, 246, 158, 230)(150, 222, 163, 235, 193, 265, 188, 260, 196, 268, 164, 236)(153, 225, 172, 244, 160, 232, 187, 259, 194, 266, 173, 245)(155, 227, 177, 249, 211, 283, 215, 287, 210, 282, 178, 250)(157, 229, 181, 253, 208, 280, 171, 243, 201, 273, 182, 254)(159, 231, 185, 257, 192, 264, 214, 286, 195, 267, 186, 258)(162, 234, 190, 262, 189, 261, 207, 279, 176, 248, 191, 263)(165, 237, 198, 270, 169, 241, 206, 278, 183, 255, 199, 271)(167, 239, 202, 274, 179, 251, 209, 281, 184, 256, 203, 275)(168, 240, 204, 276, 212, 284, 216, 288, 213, 285, 205, 277) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 172)(10, 175)(11, 177)(12, 180)(13, 181)(14, 148)(15, 185)(16, 187)(17, 149)(18, 190)(19, 193)(20, 150)(21, 198)(22, 200)(23, 202)(24, 204)(25, 206)(26, 152)(27, 201)(28, 160)(29, 153)(30, 158)(31, 161)(32, 191)(33, 211)(34, 155)(35, 209)(36, 197)(37, 208)(38, 157)(39, 199)(40, 203)(41, 192)(42, 159)(43, 194)(44, 196)(45, 207)(46, 189)(47, 162)(48, 214)(49, 188)(50, 173)(51, 186)(52, 164)(53, 174)(54, 169)(55, 165)(56, 170)(57, 182)(58, 179)(59, 167)(60, 212)(61, 168)(62, 183)(63, 176)(64, 171)(65, 184)(66, 178)(67, 215)(68, 216)(69, 205)(70, 195)(71, 210)(72, 213)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E16.1006 Graph:: bipartite v = 24 e = 144 f = 90 degree seq :: [ 12^24 ] E16.1006 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2 * Y3 * Y2)^2, Y3^-1 * Y2^-1 * Y3^3 * Y2^-1 * Y3^-2, (Y3^-1, Y2^-1)^2, (Y3 * Y2 * Y3 * Y2^-1)^2, (Y3 * Y2^-1)^6, (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, 150, 222, 148, 220)(147, 219, 153, 225, 162, 234, 155, 227)(149, 221, 158, 230, 161, 233, 159, 231)(151, 223, 163, 235, 157, 229, 165, 237)(152, 224, 166, 238, 156, 228, 167, 239)(154, 226, 171, 243, 185, 257, 173, 245)(160, 232, 182, 254, 184, 256, 183, 255)(164, 236, 188, 260, 177, 249, 190, 262)(168, 240, 197, 269, 176, 248, 198, 270)(169, 241, 193, 265, 175, 247, 196, 268)(170, 242, 186, 258, 174, 246, 192, 264)(172, 244, 203, 275, 208, 280, 189, 261)(178, 250, 194, 266, 181, 253, 195, 267)(179, 251, 187, 259, 180, 252, 191, 263)(199, 271, 215, 287, 207, 279, 210, 282)(200, 272, 212, 284, 206, 278, 213, 285)(201, 273, 209, 281, 205, 277, 216, 288)(202, 274, 214, 286, 204, 276, 211, 283) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 161)(7, 164)(8, 146)(9, 169)(10, 172)(11, 174)(12, 176)(13, 148)(14, 178)(15, 180)(16, 149)(17, 184)(18, 150)(19, 186)(20, 189)(21, 191)(22, 193)(23, 195)(24, 152)(25, 199)(26, 153)(27, 201)(28, 160)(29, 204)(30, 206)(31, 155)(32, 203)(33, 157)(34, 205)(35, 158)(36, 202)(37, 159)(38, 207)(39, 200)(40, 208)(41, 162)(42, 209)(43, 163)(44, 211)(45, 168)(46, 213)(47, 215)(48, 165)(49, 214)(50, 166)(51, 212)(52, 167)(53, 216)(54, 210)(55, 183)(56, 170)(57, 181)(58, 171)(59, 177)(60, 179)(61, 173)(62, 182)(63, 175)(64, 185)(65, 198)(66, 187)(67, 196)(68, 188)(69, 194)(70, 190)(71, 197)(72, 192)(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) :: { ( 12, 12 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E16.1005 Graph:: simple bipartite v = 90 e = 144 f = 24 degree seq :: [ 2^72, 8^18 ] E16.1007 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y3^2 * Y1^-1 * Y3^-1, Y1^6, (Y3, Y1^-1)^2, (Y3 * Y1^-3)^2, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^-1)^6 ] Map:: polytopal R = (1, 73, 2, 74, 6, 78, 17, 89, 13, 85, 4, 76)(3, 75, 9, 81, 25, 97, 41, 113, 30, 102, 11, 83)(5, 77, 15, 87, 38, 110, 40, 112, 39, 111, 16, 88)(7, 79, 20, 92, 47, 119, 35, 107, 51, 123, 22, 94)(8, 80, 23, 95, 53, 125, 34, 106, 54, 126, 24, 96)(10, 82, 28, 100, 59, 131, 64, 136, 43, 115, 21, 93)(12, 84, 32, 104, 46, 118, 19, 91, 45, 117, 33, 105)(14, 86, 36, 108, 44, 116, 18, 90, 42, 114, 37, 109)(26, 98, 50, 122, 65, 137, 62, 134, 70, 142, 57, 129)(27, 99, 58, 130, 69, 141, 61, 133, 66, 138, 52, 124)(29, 101, 48, 120, 67, 139, 56, 128, 72, 144, 60, 132)(31, 103, 63, 135, 71, 143, 55, 127, 68, 140, 49, 121)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 162)(7, 165)(8, 146)(9, 170)(10, 149)(11, 173)(12, 172)(13, 178)(14, 148)(15, 175)(16, 171)(17, 184)(18, 187)(19, 150)(20, 192)(21, 152)(22, 194)(23, 196)(24, 193)(25, 199)(26, 160)(27, 153)(28, 158)(29, 159)(30, 205)(31, 155)(32, 204)(33, 201)(34, 203)(35, 157)(36, 202)(37, 207)(38, 206)(39, 200)(40, 208)(41, 161)(42, 209)(43, 163)(44, 211)(45, 212)(46, 210)(47, 213)(48, 168)(49, 164)(50, 167)(51, 215)(52, 166)(53, 216)(54, 214)(55, 183)(56, 169)(57, 180)(58, 177)(59, 179)(60, 181)(61, 182)(62, 174)(63, 176)(64, 185)(65, 190)(66, 186)(67, 189)(68, 188)(69, 198)(70, 191)(71, 197)(72, 195)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.1004 Graph:: simple bipartite v = 84 e = 144 f = 30 degree seq :: [ 2^72, 12^12 ] E16.1008 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 6}) Quotient :: dipole Aut^+ = (S3 x S3) : C2 (small group id <72, 40>) Aut = C2 x ((S3 x S3) : C2) (small group id <144, 186>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y1^6, (Y3^-1 * Y1^-2 * Y3^-1)^2, Y3 * Y1 * Y3^-2 * Y1 * Y3 * Y1^-2, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^-1)^6 ] Map:: polytopal R = (1, 73, 2, 74, 6, 78, 15, 87, 12, 84, 4, 76)(3, 75, 9, 81, 21, 93, 41, 113, 20, 92, 8, 80)(5, 77, 11, 83, 25, 97, 48, 120, 30, 102, 14, 86)(7, 79, 18, 90, 37, 109, 60, 132, 36, 108, 17, 89)(10, 82, 24, 96, 46, 118, 59, 131, 35, 107, 23, 95)(13, 85, 27, 99, 47, 119, 66, 138, 51, 123, 29, 101)(16, 88, 34, 106, 57, 129, 69, 141, 56, 128, 33, 105)(19, 91, 40, 112, 26, 98, 49, 121, 55, 127, 39, 111)(22, 94, 45, 117, 58, 130, 53, 125, 31, 103, 44, 116)(28, 100, 32, 104, 54, 126, 68, 140, 67, 139, 50, 122)(38, 110, 63, 135, 52, 124, 64, 136, 42, 114, 62, 134)(43, 115, 65, 137, 71, 143, 72, 144, 70, 142, 61, 133)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 154)(4, 155)(5, 145)(6, 160)(7, 163)(8, 146)(9, 166)(10, 149)(11, 170)(12, 171)(13, 148)(14, 168)(15, 176)(16, 179)(17, 150)(18, 182)(19, 152)(20, 184)(21, 187)(22, 180)(23, 153)(24, 191)(25, 186)(26, 157)(27, 190)(28, 156)(29, 193)(30, 188)(31, 158)(32, 199)(33, 159)(34, 202)(35, 161)(36, 167)(37, 205)(38, 200)(39, 162)(40, 169)(41, 206)(42, 164)(43, 174)(44, 165)(45, 201)(46, 172)(47, 175)(48, 209)(49, 198)(50, 203)(51, 208)(52, 173)(53, 210)(54, 196)(55, 177)(56, 183)(57, 214)(58, 194)(59, 178)(60, 189)(61, 185)(62, 181)(63, 212)(64, 192)(65, 195)(66, 215)(67, 197)(68, 216)(69, 207)(70, 204)(71, 211)(72, 213)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.1003 Graph:: simple bipartite v = 84 e = 144 f = 30 degree seq :: [ 2^72, 12^12 ] E16.1009 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 8, 8}) Quotient :: edge Aut^+ = (C3 x C3) : C8 (small group id <72, 19>) Aut = ((C3 x C3) : C8) : C2 (small group id <144, 117>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-2 * T1^-1 * T2, T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1, T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1, T2^8 ] Map:: non-degenerate R = (1, 3, 9, 25, 49, 35, 15, 5)(2, 6, 17, 38, 59, 43, 21, 7)(4, 11, 24, 47, 65, 54, 32, 12)(8, 22, 45, 63, 56, 34, 14, 23)(10, 26, 48, 66, 55, 33, 13, 27)(16, 36, 57, 69, 61, 42, 20, 37)(18, 39, 58, 70, 60, 41, 19, 40)(28, 44, 62, 71, 68, 53, 31, 46)(29, 50, 64, 72, 67, 52, 30, 51)(73, 74, 76)(75, 80, 82)(77, 85, 86)(78, 88, 90)(79, 91, 92)(81, 96, 89)(83, 100, 101)(84, 102, 103)(87, 104, 93)(94, 116, 108)(95, 109, 118)(97, 120, 117)(98, 122, 111)(99, 112, 123)(105, 124, 113)(106, 125, 114)(107, 128, 127)(110, 130, 129)(115, 133, 132)(119, 136, 134)(121, 131, 137)(126, 140, 139)(135, 141, 143)(138, 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) :: { ( 16^3 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E16.1010 Transitivity :: ET+ Graph:: simple bipartite v = 33 e = 72 f = 9 degree seq :: [ 3^24, 8^9 ] E16.1010 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 8, 8}) Quotient :: loop Aut^+ = (C3 x C3) : C8 (small group id <72, 19>) Aut = ((C3 x C3) : C8) : C2 (small group id <144, 117>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-2 * T1^-1 * T2, T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1, T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1, T2^8 ] Map:: non-degenerate R = (1, 73, 3, 75, 9, 81, 25, 97, 49, 121, 35, 107, 15, 87, 5, 77)(2, 74, 6, 78, 17, 89, 38, 110, 59, 131, 43, 115, 21, 93, 7, 79)(4, 76, 11, 83, 24, 96, 47, 119, 65, 137, 54, 126, 32, 104, 12, 84)(8, 80, 22, 94, 45, 117, 63, 135, 56, 128, 34, 106, 14, 86, 23, 95)(10, 82, 26, 98, 48, 120, 66, 138, 55, 127, 33, 105, 13, 85, 27, 99)(16, 88, 36, 108, 57, 129, 69, 141, 61, 133, 42, 114, 20, 92, 37, 109)(18, 90, 39, 111, 58, 130, 70, 142, 60, 132, 41, 113, 19, 91, 40, 112)(28, 100, 44, 116, 62, 134, 71, 143, 68, 140, 53, 125, 31, 103, 46, 118)(29, 101, 50, 122, 64, 136, 72, 144, 67, 139, 52, 124, 30, 102, 51, 123) L = (1, 74)(2, 76)(3, 80)(4, 73)(5, 85)(6, 88)(7, 91)(8, 82)(9, 96)(10, 75)(11, 100)(12, 102)(13, 86)(14, 77)(15, 104)(16, 90)(17, 81)(18, 78)(19, 92)(20, 79)(21, 87)(22, 116)(23, 109)(24, 89)(25, 120)(26, 122)(27, 112)(28, 101)(29, 83)(30, 103)(31, 84)(32, 93)(33, 124)(34, 125)(35, 128)(36, 94)(37, 118)(38, 130)(39, 98)(40, 123)(41, 105)(42, 106)(43, 133)(44, 108)(45, 97)(46, 95)(47, 136)(48, 117)(49, 131)(50, 111)(51, 99)(52, 113)(53, 114)(54, 140)(55, 107)(56, 127)(57, 110)(58, 129)(59, 137)(60, 115)(61, 132)(62, 119)(63, 141)(64, 134)(65, 121)(66, 142)(67, 126)(68, 139)(69, 143)(70, 144)(71, 135)(72, 138) local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8 ) } Outer automorphisms :: reflexible Dual of E16.1009 Transitivity :: ET+ VT+ AT Graph:: v = 9 e = 72 f = 33 degree seq :: [ 16^9 ] E16.1011 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 8, 8}) Quotient :: dipole Aut^+ = (C3 x C3) : C8 (small group id <72, 19>) Aut = ((C3 x C3) : C8) : C2 (small group id <144, 117>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2^2 * Y3^-1, Y2^-1 * Y3^-1 * Y2^2 * Y1 * Y2^-1, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, Y2^8, Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^8 ] 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, 17, 89)(11, 83, 28, 100, 29, 101)(12, 84, 30, 102, 31, 103)(15, 87, 32, 104, 21, 93)(22, 94, 44, 116, 36, 108)(23, 95, 37, 109, 46, 118)(25, 97, 48, 120, 45, 117)(26, 98, 50, 122, 39, 111)(27, 99, 40, 112, 51, 123)(33, 105, 52, 124, 41, 113)(34, 106, 53, 125, 42, 114)(35, 107, 56, 128, 55, 127)(38, 110, 58, 130, 57, 129)(43, 115, 61, 133, 60, 132)(47, 119, 64, 136, 62, 134)(49, 121, 59, 131, 65, 137)(54, 126, 68, 140, 67, 139)(63, 135, 69, 141, 71, 143)(66, 138, 70, 142, 72, 144)(145, 217, 147, 219, 153, 225, 169, 241, 193, 265, 179, 251, 159, 231, 149, 221)(146, 218, 150, 222, 161, 233, 182, 254, 203, 275, 187, 259, 165, 237, 151, 223)(148, 220, 155, 227, 168, 240, 191, 263, 209, 281, 198, 270, 176, 248, 156, 228)(152, 224, 166, 238, 189, 261, 207, 279, 200, 272, 178, 250, 158, 230, 167, 239)(154, 226, 170, 242, 192, 264, 210, 282, 199, 271, 177, 249, 157, 229, 171, 243)(160, 232, 180, 252, 201, 273, 213, 285, 205, 277, 186, 258, 164, 236, 181, 253)(162, 234, 183, 255, 202, 274, 214, 286, 204, 276, 185, 257, 163, 235, 184, 256)(172, 244, 188, 260, 206, 278, 215, 287, 212, 284, 197, 269, 175, 247, 190, 262)(173, 245, 194, 266, 208, 280, 216, 288, 211, 283, 196, 268, 174, 246, 195, 267) L = (1, 148)(2, 145)(3, 154)(4, 146)(5, 158)(6, 162)(7, 164)(8, 147)(9, 161)(10, 152)(11, 173)(12, 175)(13, 149)(14, 157)(15, 165)(16, 150)(17, 168)(18, 160)(19, 151)(20, 163)(21, 176)(22, 180)(23, 190)(24, 153)(25, 189)(26, 183)(27, 195)(28, 155)(29, 172)(30, 156)(31, 174)(32, 159)(33, 185)(34, 186)(35, 199)(36, 188)(37, 167)(38, 201)(39, 194)(40, 171)(41, 196)(42, 197)(43, 204)(44, 166)(45, 192)(46, 181)(47, 206)(48, 169)(49, 209)(50, 170)(51, 184)(52, 177)(53, 178)(54, 211)(55, 200)(56, 179)(57, 202)(58, 182)(59, 193)(60, 205)(61, 187)(62, 208)(63, 215)(64, 191)(65, 203)(66, 216)(67, 212)(68, 198)(69, 207)(70, 210)(71, 213)(72, 214)(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, 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 E16.1012 Graph:: bipartite v = 33 e = 144 f = 81 degree seq :: [ 6^24, 16^9 ] E16.1012 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 8, 8}) Quotient :: dipole Aut^+ = (C3 x C3) : C8 (small group id <72, 19>) Aut = ((C3 x C3) : C8) : C2 (small group id <144, 117>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3 * Y1^-2 * Y3 * Y1, (Y3 * Y2^-1)^3, Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1^8, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 73, 2, 74, 6, 78, 16, 88, 36, 108, 30, 102, 12, 84, 4, 76)(3, 75, 9, 81, 18, 90, 40, 112, 57, 129, 50, 122, 26, 98, 10, 82)(5, 77, 14, 86, 17, 89, 39, 111, 58, 130, 54, 126, 29, 101, 15, 87)(7, 79, 19, 91, 38, 110, 60, 132, 55, 127, 31, 103, 13, 85, 20, 92)(8, 80, 21, 93, 37, 109, 59, 131, 53, 125, 28, 100, 11, 83, 22, 94)(23, 95, 42, 114, 64, 136, 71, 143, 66, 138, 51, 123, 27, 99, 43, 115)(24, 96, 46, 118, 63, 135, 69, 141, 65, 137, 49, 121, 25, 97, 47, 119)(32, 104, 41, 113, 62, 134, 72, 144, 68, 140, 56, 128, 35, 107, 44, 116)(33, 105, 45, 117, 61, 133, 70, 142, 67, 139, 52, 124, 34, 106, 48, 120)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 149)(4, 155)(5, 145)(6, 161)(7, 152)(8, 146)(9, 167)(10, 169)(11, 157)(12, 173)(13, 148)(14, 176)(15, 178)(16, 181)(17, 162)(18, 150)(19, 185)(20, 187)(21, 189)(22, 191)(23, 168)(24, 153)(25, 171)(26, 156)(27, 154)(28, 196)(29, 170)(30, 199)(31, 200)(32, 177)(33, 158)(34, 179)(35, 159)(36, 201)(37, 182)(38, 160)(39, 205)(40, 207)(41, 186)(42, 163)(43, 188)(44, 164)(45, 190)(46, 165)(47, 192)(48, 166)(49, 172)(50, 210)(51, 175)(52, 193)(53, 174)(54, 212)(55, 197)(56, 195)(57, 202)(58, 180)(59, 213)(60, 215)(61, 206)(62, 183)(63, 208)(64, 184)(65, 194)(66, 209)(67, 198)(68, 211)(69, 214)(70, 203)(71, 216)(72, 204)(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, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E16.1011 Graph:: simple bipartite v = 81 e = 144 f = 33 degree seq :: [ 2^72, 16^9 ] E16.1013 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 8, 8}) Quotient :: edge Aut^+ = (C3 x C3) : C8 (small group id <72, 39>) Aut = (C3 x C3) : C8 (small group id <72, 39>) |r| :: 1 Presentation :: [ X1^3, X2^-1 * X1 * X2^2 * X1^-1 * X2^-1 * X1, X2 * X1^-1 * X2^-2 * X1 * X2 * X1, X1 * X2 * X1^-1 * X2 * X1^-1 * X2^-1 * X1^-1 * X2^-1, X2^8, (X1^-1 * X2^-2)^4 ] Map:: polytopal non-degenerate R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 16, 18)(7, 19, 20)(9, 24, 26)(11, 29, 31)(12, 32, 33)(15, 39, 40)(17, 43, 27)(21, 48, 36)(22, 45, 30)(23, 42, 35)(25, 52, 54)(28, 37, 47)(34, 38, 46)(41, 63, 64)(44, 55, 50)(49, 60, 62)(51, 57, 56)(53, 69, 65)(58, 61, 59)(66, 70, 67)(68, 72, 71)(73, 75, 81, 97, 125, 113, 87, 77)(74, 78, 89, 116, 137, 121, 93, 79)(76, 83, 102, 129, 141, 130, 106, 84)(80, 94, 122, 138, 136, 118, 91, 95)(82, 99, 128, 144, 135, 120, 105, 100)(85, 107, 101, 115, 126, 142, 131, 108)(86, 109, 90, 117, 124, 140, 132, 110)(88, 96, 123, 139, 134, 112, 104, 114)(92, 119, 103, 98, 127, 143, 133, 111) 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) :: { ( 16^3 ), ( 16^8 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 33 e = 72 f = 9 degree seq :: [ 3^24, 8^9 ] E16.1014 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 8, 8}) Quotient :: loop Aut^+ = (C3 x C3) : C8 (small group id <72, 39>) Aut = (C3 x C3) : C8 (small group id <72, 39>) |r| :: 1 Presentation :: [ (X1^-1 * X2^-1)^3, X2 * X1^-2 * X2^-2 * X1, X2^-1 * X1 * X2^2 * X1 * X2^-1 * X1^-2, X1^-1 * X2 * X1 * X2^-1 * X1^-1 * X2^-2 * X1^-1, (X2^3 * X1^-1)^2, X2^-1 * X1^-1 * X2 * X1 * X2^-2 * X1^-2, X2^8, X1^8, (X2 * X1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74, 6, 78, 18, 90, 46, 118, 38, 110, 13, 85, 4, 76)(3, 75, 9, 81, 27, 99, 63, 135, 26, 98, 48, 120, 33, 105, 11, 83)(5, 77, 15, 87, 41, 113, 61, 133, 32, 104, 56, 128, 43, 115, 16, 88)(7, 79, 21, 93, 54, 126, 70, 142, 53, 125, 31, 103, 10, 82, 23, 95)(8, 80, 24, 96, 60, 132, 37, 109, 58, 130, 34, 106, 62, 134, 25, 97)(12, 84, 35, 107, 59, 131, 44, 116, 17, 89, 20, 92, 52, 124, 36, 108)(14, 86, 40, 112, 55, 127, 42, 114, 64, 136, 30, 102, 65, 137, 28, 100)(19, 91, 49, 121, 69, 141, 72, 144, 68, 140, 57, 129, 22, 94, 51, 123)(29, 101, 47, 119, 45, 117, 67, 139, 71, 143, 66, 138, 39, 111, 50, 122) L = (1, 75)(2, 79)(3, 82)(4, 84)(5, 73)(6, 91)(7, 94)(8, 74)(9, 100)(10, 102)(11, 104)(12, 105)(13, 109)(14, 76)(15, 99)(16, 111)(17, 77)(18, 119)(19, 122)(20, 78)(21, 88)(22, 128)(23, 130)(24, 126)(25, 86)(26, 80)(27, 123)(28, 129)(29, 81)(30, 132)(31, 118)(32, 125)(33, 139)(34, 83)(35, 138)(36, 136)(37, 124)(38, 133)(39, 85)(40, 131)(41, 121)(42, 87)(43, 137)(44, 134)(45, 89)(46, 114)(47, 112)(48, 90)(49, 97)(50, 106)(51, 107)(52, 141)(53, 92)(54, 101)(55, 93)(56, 108)(57, 110)(58, 140)(59, 95)(60, 117)(61, 96)(62, 115)(63, 116)(64, 98)(65, 143)(66, 103)(67, 113)(68, 120)(69, 127)(70, 135)(71, 144)(72, 142) local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 9 e = 72 f = 33 degree seq :: [ 16^9 ] E16.1015 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {3, 8, 8}) Quotient :: loop Aut^+ = (C3 x C3) : C8 (small group id <72, 39>) Aut = C2 x ((C3 x C3) : C8) (small group id <144, 185>) |r| :: 2 Presentation :: [ F^2, F * T1 * F * T2, (T1^-1 * T2^-1)^3, T2 * T1^-2 * T2^-2 * T1, T1^-1 * T2^-1 * T1^-1 * T2 * T1 * T2^-2 * T1^-1, (T2^3 * T1^-1)^2, T2 * T1 * T2^-1 * T1^-2 * T2^-1 * T1 * T2, T1^8, T2^8, (T2 * T1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 3, 10, 30, 60, 45, 17, 5)(2, 7, 22, 56, 36, 64, 26, 8)(4, 12, 33, 67, 41, 49, 25, 14)(6, 19, 50, 34, 11, 32, 53, 20)(9, 28, 57, 38, 61, 24, 54, 29)(13, 37, 52, 69, 55, 21, 16, 39)(15, 27, 51, 35, 66, 31, 46, 42)(18, 47, 40, 59, 23, 58, 68, 48)(43, 65, 71, 72, 70, 63, 44, 62)(73, 74, 78, 90, 118, 110, 85, 76)(75, 81, 99, 135, 98, 120, 105, 83)(77, 87, 113, 133, 104, 128, 115, 88)(79, 93, 126, 142, 125, 103, 82, 95)(80, 96, 132, 109, 130, 106, 134, 97)(84, 107, 131, 116, 89, 92, 124, 108)(86, 112, 127, 114, 136, 102, 137, 100)(91, 121, 141, 144, 140, 129, 94, 123)(101, 119, 117, 139, 143, 138, 111, 122) 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) :: { ( 6^8 ) } Outer automorphisms :: reflexible Dual of E16.1016 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 18 e = 72 f = 24 degree seq :: [ 8^18 ] E16.1016 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {3, 8, 8}) Quotient :: edge Aut^+ = (C3 x C3) : C8 (small group id <72, 39>) Aut = C2 x ((C3 x C3) : C8) (small group id <144, 185>) |r| :: 2 Presentation :: [ F^2, T2^3, (T2^-1 * F)^2, F * T1 * T2 * F * T1^-1, T1^-1 * T2 * T1^-1 * T2 * T1^2 * T2^-1, T1^2 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T1 * F * T1^-2 * T2^-1 * F * T1 * T2^-1, T1^8, (T2^-1 * T1^-2)^4 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 5, 77)(2, 74, 7, 79, 8, 80)(4, 76, 11, 83, 13, 85)(6, 78, 17, 89, 18, 90)(9, 81, 24, 96, 25, 97)(10, 82, 26, 98, 28, 100)(12, 84, 31, 103, 33, 105)(14, 86, 37, 109, 38, 110)(15, 87, 39, 111, 41, 113)(16, 88, 43, 115, 44, 116)(19, 91, 48, 120, 36, 108)(20, 92, 49, 121, 29, 101)(21, 93, 23, 95, 51, 123)(22, 94, 34, 106, 52, 124)(27, 99, 55, 127, 30, 102)(32, 104, 59, 131, 60, 132)(35, 107, 54, 126, 40, 112)(42, 114, 65, 137, 66, 138)(45, 117, 63, 135, 50, 122)(46, 118, 47, 119, 53, 125)(56, 128, 62, 134, 61, 133)(57, 129, 64, 136, 58, 130)(67, 139, 72, 144, 70, 142)(68, 140, 69, 141, 71, 143) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 86)(6, 88)(7, 91)(8, 93)(9, 95)(10, 75)(11, 101)(12, 76)(13, 106)(14, 108)(15, 77)(16, 114)(17, 117)(18, 118)(19, 119)(20, 79)(21, 122)(22, 80)(23, 125)(24, 89)(25, 120)(26, 92)(27, 82)(28, 124)(29, 109)(30, 83)(31, 100)(32, 84)(33, 111)(34, 97)(35, 85)(36, 135)(37, 123)(38, 90)(39, 121)(40, 87)(41, 94)(42, 104)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 115)(49, 96)(50, 144)(51, 116)(52, 110)(53, 138)(54, 98)(55, 113)(56, 99)(57, 102)(58, 103)(59, 127)(60, 126)(61, 105)(62, 107)(63, 137)(64, 112)(65, 136)(66, 128)(67, 134)(68, 129)(69, 133)(70, 130)(71, 132)(72, 131) local type(s) :: { ( 8^6 ) } Outer automorphisms :: reflexible Dual of E16.1015 Transitivity :: ET+ VT+ Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 6^24 ] E16.1017 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 8, 8}) Quotient :: edge^2 Aut^+ = (C3 x C3) : C8 (small group id <72, 39>) Aut = C2 x ((C3 x C3) : C8) (small group id <144, 185>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, (Y1^-1 * Y2^-1)^3, Y2 * Y1^-2 * Y2^-2 * Y1, Y2^-1 * Y1 * Y2 * Y1^2 * Y2^2 * Y1^-1, Y1^2 * Y2^2 * Y1 * Y2 * Y1^-1 * Y2^-1, (Y2^3 * Y1^-1)^2, (Y2 * Y1^-1)^4, Y1^8, Y2^8, (Y1^-1 * Y3^-1 * Y2^-1)^3 ] 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, 146, 150, 162, 190, 182, 157, 148)(147, 153, 171, 207, 170, 192, 177, 155)(149, 159, 185, 205, 176, 200, 187, 160)(151, 165, 198, 214, 197, 175, 154, 167)(152, 168, 204, 181, 202, 178, 206, 169)(156, 179, 203, 188, 161, 164, 196, 180)(158, 184, 199, 186, 208, 174, 209, 172)(163, 193, 213, 216, 212, 201, 166, 195)(173, 191, 189, 211, 215, 210, 183, 194)(217, 219, 226, 246, 276, 261, 233, 221)(218, 223, 238, 272, 252, 280, 242, 224)(220, 228, 249, 283, 257, 265, 241, 230)(222, 235, 266, 250, 227, 248, 269, 236)(225, 244, 273, 254, 277, 240, 270, 245)(229, 253, 268, 285, 271, 237, 232, 255)(231, 243, 267, 251, 282, 247, 262, 258)(234, 263, 256, 275, 239, 274, 284, 264)(259, 281, 287, 288, 286, 279, 260, 278) 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) :: { ( 12, 12 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E16.1020 Graph:: simple bipartite v = 90 e = 144 f = 24 degree seq :: [ 2^72, 8^18 ] E16.1018 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 8, 8}) Quotient :: edge^2 Aut^+ = (C3 x C3) : C8 (small group id <72, 39>) Aut = C2 x ((C3 x C3) : C8) (small group id <144, 185>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^-1 * Y3^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y2^2 * Y1^2 * Y3, Y2^-1 * Y3 * Y2 * Y1 * Y3^-1 * Y1^-1, Y1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1, Y2 * Y1^-1 * Y2 * Y1^3 * Y3^-1, Y1 * Y2^-2 * Y3 * Y2 * Y1^-1 * Y2, Y1^8, Y2^8 ] Map:: polyhedral non-degenerate R = (1, 73, 4, 76, 7, 79)(2, 74, 9, 81, 11, 83)(3, 75, 5, 77, 15, 87)(6, 78, 23, 95, 25, 97)(8, 80, 24, 96, 30, 102)(10, 82, 34, 106, 36, 108)(12, 84, 37, 109, 38, 110)(13, 85, 14, 86, 42, 114)(16, 88, 17, 89, 45, 117)(18, 90, 50, 122, 39, 111)(19, 91, 20, 92, 48, 120)(21, 93, 31, 103, 56, 128)(22, 94, 51, 123, 32, 104)(26, 98, 27, 99, 52, 124)(28, 100, 35, 107, 58, 130)(29, 101, 63, 135, 65, 137)(33, 105, 57, 129, 59, 131)(40, 112, 41, 113, 69, 141)(43, 115, 44, 116, 53, 125)(46, 118, 47, 119, 49, 121)(54, 126, 55, 127, 70, 142)(60, 132, 64, 136, 67, 139)(61, 133, 72, 144, 71, 143)(62, 134, 66, 138, 68, 140)(145, 146, 152, 172, 204, 199, 164, 149)(147, 156, 169, 178, 179, 205, 188, 158)(148, 150, 166, 201, 211, 187, 193, 161)(151, 162, 180, 207, 208, 185, 157, 171)(153, 154, 177, 210, 198, 186, 189, 175)(155, 176, 209, 216, 214, 190, 170, 182)(159, 165, 194, 195, 202, 212, 184, 191)(160, 181, 183, 174, 203, 215, 213, 192)(163, 196, 200, 167, 168, 173, 206, 197)(217, 219, 229, 256, 282, 275, 240, 222)(218, 223, 242, 265, 269, 284, 251, 226)(220, 232, 236, 270, 278, 281, 267, 234)(221, 235, 260, 287, 273, 248, 225, 237)(224, 227, 253, 261, 230, 259, 280, 245)(228, 231, 262, 271, 283, 249, 252, 255)(233, 263, 285, 288, 279, 250, 239, 247)(238, 241, 254, 268, 264, 257, 276, 274)(243, 258, 286, 277, 244, 246, 266, 272) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 4^6 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.1019 Graph:: simple bipartite v = 42 e = 144 f = 72 degree seq :: [ 6^24, 8^18 ] E16.1019 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 8, 8}) Quotient :: loop^2 Aut^+ = (C3 x C3) : C8 (small group id <72, 39>) Aut = C2 x ((C3 x C3) : C8) (small group id <144, 185>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, (Y1^-1 * Y2^-1)^3, Y2 * Y1^-2 * Y2^-2 * Y1, Y2^-1 * Y1 * Y2 * Y1^2 * Y2^2 * Y1^-1, Y1^2 * Y2^2 * Y1 * Y2 * Y1^-1 * Y2^-1, (Y2^3 * Y1^-1)^2, (Y2 * Y1^-1)^4, Y1^8, Y2^8, (Y1^-1 * Y3^-1 * Y2^-1)^3 ] Map:: polyhedral non-degenerate R = (1, 73, 145, 217)(2, 74, 146, 218)(3, 75, 147, 219)(4, 76, 148, 220)(5, 77, 149, 221)(6, 78, 150, 222)(7, 79, 151, 223)(8, 80, 152, 224)(9, 81, 153, 225)(10, 82, 154, 226)(11, 83, 155, 227)(12, 84, 156, 228)(13, 85, 157, 229)(14, 86, 158, 230)(15, 87, 159, 231)(16, 88, 160, 232)(17, 89, 161, 233)(18, 90, 162, 234)(19, 91, 163, 235)(20, 92, 164, 236)(21, 93, 165, 237)(22, 94, 166, 238)(23, 95, 167, 239)(24, 96, 168, 240)(25, 97, 169, 241)(26, 98, 170, 242)(27, 99, 171, 243)(28, 100, 172, 244)(29, 101, 173, 245)(30, 102, 174, 246)(31, 103, 175, 247)(32, 104, 176, 248)(33, 105, 177, 249)(34, 106, 178, 250)(35, 107, 179, 251)(36, 108, 180, 252)(37, 109, 181, 253)(38, 110, 182, 254)(39, 111, 183, 255)(40, 112, 184, 256)(41, 113, 185, 257)(42, 114, 186, 258)(43, 115, 187, 259)(44, 116, 188, 260)(45, 117, 189, 261)(46, 118, 190, 262)(47, 119, 191, 263)(48, 120, 192, 264)(49, 121, 193, 265)(50, 122, 194, 266)(51, 123, 195, 267)(52, 124, 196, 268)(53, 125, 197, 269)(54, 126, 198, 270)(55, 127, 199, 271)(56, 128, 200, 272)(57, 129, 201, 273)(58, 130, 202, 274)(59, 131, 203, 275)(60, 132, 204, 276)(61, 133, 205, 277)(62, 134, 206, 278)(63, 135, 207, 279)(64, 136, 208, 280)(65, 137, 209, 281)(66, 138, 210, 282)(67, 139, 211, 283)(68, 140, 212, 284)(69, 141, 213, 285)(70, 142, 214, 286)(71, 143, 215, 287)(72, 144, 216, 288) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 90)(7, 93)(8, 96)(9, 99)(10, 95)(11, 75)(12, 107)(13, 76)(14, 112)(15, 113)(16, 77)(17, 92)(18, 118)(19, 121)(20, 124)(21, 126)(22, 123)(23, 79)(24, 132)(25, 80)(26, 120)(27, 135)(28, 86)(29, 119)(30, 137)(31, 82)(32, 128)(33, 83)(34, 134)(35, 131)(36, 84)(37, 130)(38, 85)(39, 122)(40, 127)(41, 133)(42, 136)(43, 88)(44, 89)(45, 139)(46, 110)(47, 117)(48, 105)(49, 141)(50, 101)(51, 91)(52, 108)(53, 103)(54, 142)(55, 114)(56, 115)(57, 94)(58, 106)(59, 116)(60, 109)(61, 104)(62, 97)(63, 98)(64, 102)(65, 100)(66, 111)(67, 143)(68, 129)(69, 144)(70, 125)(71, 138)(72, 140)(145, 219)(146, 223)(147, 226)(148, 228)(149, 217)(150, 235)(151, 238)(152, 218)(153, 244)(154, 246)(155, 248)(156, 249)(157, 253)(158, 220)(159, 243)(160, 255)(161, 221)(162, 263)(163, 266)(164, 222)(165, 232)(166, 272)(167, 274)(168, 270)(169, 230)(170, 224)(171, 267)(172, 273)(173, 225)(174, 276)(175, 262)(176, 269)(177, 283)(178, 227)(179, 282)(180, 280)(181, 268)(182, 277)(183, 229)(184, 275)(185, 265)(186, 231)(187, 281)(188, 278)(189, 233)(190, 258)(191, 256)(192, 234)(193, 241)(194, 250)(195, 251)(196, 285)(197, 236)(198, 245)(199, 237)(200, 252)(201, 254)(202, 284)(203, 239)(204, 261)(205, 240)(206, 259)(207, 260)(208, 242)(209, 287)(210, 247)(211, 257)(212, 264)(213, 271)(214, 279)(215, 288)(216, 286) local type(s) :: { ( 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E16.1018 Transitivity :: VT+ Graph:: simple bipartite v = 72 e = 144 f = 42 degree seq :: [ 4^72 ] E16.1020 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 8, 8}) Quotient :: loop^2 Aut^+ = (C3 x C3) : C8 (small group id <72, 39>) Aut = C2 x ((C3 x C3) : C8) (small group id <144, 185>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^-1 * Y3^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y2^2 * Y1^2 * Y3, Y2^-1 * Y3 * Y2 * Y1 * Y3^-1 * Y1^-1, Y1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1, Y2 * Y1^-1 * Y2 * Y1^3 * Y3^-1, Y1 * Y2^-2 * Y3 * Y2 * Y1^-1 * Y2, Y1^8, Y2^8 ] Map:: R = (1, 73, 145, 217, 4, 76, 148, 220, 7, 79, 151, 223)(2, 74, 146, 218, 9, 81, 153, 225, 11, 83, 155, 227)(3, 75, 147, 219, 5, 77, 149, 221, 15, 87, 159, 231)(6, 78, 150, 222, 23, 95, 167, 239, 25, 97, 169, 241)(8, 80, 152, 224, 24, 96, 168, 240, 30, 102, 174, 246)(10, 82, 154, 226, 34, 106, 178, 250, 36, 108, 180, 252)(12, 84, 156, 228, 37, 109, 181, 253, 38, 110, 182, 254)(13, 85, 157, 229, 14, 86, 158, 230, 42, 114, 186, 258)(16, 88, 160, 232, 17, 89, 161, 233, 45, 117, 189, 261)(18, 90, 162, 234, 50, 122, 194, 266, 39, 111, 183, 255)(19, 91, 163, 235, 20, 92, 164, 236, 48, 120, 192, 264)(21, 93, 165, 237, 31, 103, 175, 247, 56, 128, 200, 272)(22, 94, 166, 238, 51, 123, 195, 267, 32, 104, 176, 248)(26, 98, 170, 242, 27, 99, 171, 243, 52, 124, 196, 268)(28, 100, 172, 244, 35, 107, 179, 251, 58, 130, 202, 274)(29, 101, 173, 245, 63, 135, 207, 279, 65, 137, 209, 281)(33, 105, 177, 249, 57, 129, 201, 273, 59, 131, 203, 275)(40, 112, 184, 256, 41, 113, 185, 257, 69, 141, 213, 285)(43, 115, 187, 259, 44, 116, 188, 260, 53, 125, 197, 269)(46, 118, 190, 262, 47, 119, 191, 263, 49, 121, 193, 265)(54, 126, 198, 270, 55, 127, 199, 271, 70, 142, 214, 286)(60, 132, 204, 276, 64, 136, 208, 280, 67, 139, 211, 283)(61, 133, 205, 277, 72, 144, 216, 288, 71, 143, 215, 287)(62, 134, 206, 278, 66, 138, 210, 282, 68, 140, 212, 284) L = (1, 74)(2, 80)(3, 84)(4, 78)(5, 73)(6, 94)(7, 90)(8, 100)(9, 82)(10, 105)(11, 104)(12, 97)(13, 99)(14, 75)(15, 93)(16, 109)(17, 76)(18, 108)(19, 124)(20, 77)(21, 122)(22, 129)(23, 96)(24, 101)(25, 106)(26, 110)(27, 79)(28, 132)(29, 134)(30, 131)(31, 81)(32, 137)(33, 138)(34, 107)(35, 133)(36, 135)(37, 111)(38, 83)(39, 102)(40, 119)(41, 85)(42, 117)(43, 121)(44, 86)(45, 103)(46, 98)(47, 87)(48, 88)(49, 89)(50, 123)(51, 130)(52, 128)(53, 91)(54, 114)(55, 92)(56, 95)(57, 139)(58, 140)(59, 143)(60, 127)(61, 116)(62, 125)(63, 136)(64, 113)(65, 144)(66, 126)(67, 115)(68, 112)(69, 120)(70, 118)(71, 141)(72, 142)(145, 219)(146, 223)(147, 229)(148, 232)(149, 235)(150, 217)(151, 242)(152, 227)(153, 237)(154, 218)(155, 253)(156, 231)(157, 256)(158, 259)(159, 262)(160, 236)(161, 263)(162, 220)(163, 260)(164, 270)(165, 221)(166, 241)(167, 247)(168, 222)(169, 254)(170, 265)(171, 258)(172, 246)(173, 224)(174, 266)(175, 233)(176, 225)(177, 252)(178, 239)(179, 226)(180, 255)(181, 261)(182, 268)(183, 228)(184, 282)(185, 276)(186, 286)(187, 280)(188, 287)(189, 230)(190, 271)(191, 285)(192, 257)(193, 269)(194, 272)(195, 234)(196, 264)(197, 284)(198, 278)(199, 283)(200, 243)(201, 248)(202, 238)(203, 240)(204, 274)(205, 244)(206, 281)(207, 250)(208, 245)(209, 267)(210, 275)(211, 249)(212, 251)(213, 288)(214, 277)(215, 273)(216, 279) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E16.1017 Transitivity :: VT+ Graph:: bipartite v = 24 e = 144 f = 90 degree seq :: [ 12^24 ] E16.1021 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 6, 12}) 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 * T1^-1)^3, T2^6, T2^-3 * T1 * T2^-3 * T1^-1, T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 ] Map:: non-degenerate R = (1, 3, 9, 25, 15, 5)(2, 6, 17, 42, 21, 7)(4, 11, 29, 57, 33, 12)(8, 22, 50, 37, 54, 23)(10, 19, 45, 38, 41, 27)(13, 34, 56, 24, 55, 30)(14, 35, 58, 26, 52, 36)(16, 39, 67, 48, 68, 40)(18, 31, 53, 49, 62, 44)(20, 46, 69, 43, 66, 47)(28, 51, 59, 65, 71, 61)(32, 60, 72, 63, 70, 64)(73, 74, 76)(75, 80, 82)(77, 85, 86)(78, 88, 90)(79, 91, 92)(81, 96, 98)(83, 100, 102)(84, 103, 104)(87, 109, 110)(89, 113, 115)(93, 120, 121)(94, 111, 123)(95, 124, 125)(97, 114, 129)(99, 131, 132)(101, 134, 135)(105, 137, 128)(106, 112, 138)(107, 116, 122)(108, 119, 136)(117, 133, 142)(118, 127, 139)(126, 140, 143)(130, 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) :: { ( 24^3 ), ( 24^6 ) } Outer automorphisms :: reflexible Dual of E16.1025 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 72 f = 6 degree seq :: [ 3^24, 6^12 ] E16.1022 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 6, 12}) 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, (F * T1)^2, (F * T2)^2, T1^6, (T2^-1 * T1^-1)^3, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2, T1^-1 * T2^-1 * T1^-3 * T2 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 30, 63, 46, 18, 45, 72, 44, 17, 5)(2, 7, 22, 54, 70, 38, 13, 37, 66, 58, 26, 8)(4, 12, 31, 65, 51, 20, 6, 19, 48, 61, 40, 14)(9, 28, 60, 36, 43, 67, 33, 50, 71, 42, 15, 29)(11, 32, 64, 55, 41, 59, 27, 24, 53, 21, 16, 34)(23, 39, 69, 35, 57, 62, 52, 49, 68, 47, 25, 56)(73, 74, 78, 90, 85, 76)(75, 81, 99, 117, 105, 83)(77, 87, 113, 118, 115, 88)(79, 93, 124, 109, 127, 95)(80, 96, 129, 110, 104, 97)(82, 94, 120, 144, 138, 103)(84, 107, 114, 91, 119, 108)(86, 111, 122, 92, 121, 100)(89, 98, 123, 135, 142, 112)(101, 133, 128, 139, 137, 134)(102, 132, 125, 116, 143, 136)(106, 140, 130, 131, 141, 126) 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) :: { ( 6^6 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E16.1026 Transitivity :: ET+ Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.1023 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 6, 12}) 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, T2^3, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2^-1)^3, T1 * T2 * T1^-2 * T2^-1 * T1, T1^12, (T2^-1 * T1^-1)^6 ] Map:: non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 11, 13)(6, 17, 18)(9, 23, 24)(10, 21, 26)(12, 25, 29)(14, 31, 27)(15, 32, 33)(16, 35, 36)(19, 39, 40)(20, 38, 41)(22, 42, 43)(28, 47, 49)(30, 51, 52)(34, 57, 58)(37, 60, 54)(44, 56, 63)(45, 64, 50)(46, 59, 65)(48, 62, 67)(53, 70, 68)(55, 71, 66)(61, 72, 69)(73, 74, 78, 88, 106, 128, 144, 138, 120, 100, 84, 76)(75, 81, 89, 109, 129, 142, 141, 124, 134, 115, 97, 82)(77, 86, 90, 110, 130, 111, 133, 137, 139, 122, 101, 87)(79, 91, 107, 131, 135, 136, 127, 105, 119, 99, 83, 92)(80, 93, 108, 95, 116, 132, 143, 140, 121, 102, 85, 94)(96, 104, 126, 103, 125, 113, 123, 112, 114, 118, 98, 117) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^3 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E16.1024 Transitivity :: ET+ Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 3^24, 12^6 ] E16.1024 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 6, 12}) 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, (F * T2)^2, (F * T1)^2, (T2 * T1^-1)^3, T2^6, T2^-3 * T1 * T2^-3 * T1^-1, T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 ] Map:: non-degenerate R = (1, 73, 3, 75, 9, 81, 25, 97, 15, 87, 5, 77)(2, 74, 6, 78, 17, 89, 42, 114, 21, 93, 7, 79)(4, 76, 11, 83, 29, 101, 57, 129, 33, 105, 12, 84)(8, 80, 22, 94, 50, 122, 37, 109, 54, 126, 23, 95)(10, 82, 19, 91, 45, 117, 38, 110, 41, 113, 27, 99)(13, 85, 34, 106, 56, 128, 24, 96, 55, 127, 30, 102)(14, 86, 35, 107, 58, 130, 26, 98, 52, 124, 36, 108)(16, 88, 39, 111, 67, 139, 48, 120, 68, 140, 40, 112)(18, 90, 31, 103, 53, 125, 49, 121, 62, 134, 44, 116)(20, 92, 46, 118, 69, 141, 43, 115, 66, 138, 47, 119)(28, 100, 51, 123, 59, 131, 65, 137, 71, 143, 61, 133)(32, 104, 60, 132, 72, 144, 63, 135, 70, 142, 64, 136) L = (1, 74)(2, 76)(3, 80)(4, 73)(5, 85)(6, 88)(7, 91)(8, 82)(9, 96)(10, 75)(11, 100)(12, 103)(13, 86)(14, 77)(15, 109)(16, 90)(17, 113)(18, 78)(19, 92)(20, 79)(21, 120)(22, 111)(23, 124)(24, 98)(25, 114)(26, 81)(27, 131)(28, 102)(29, 134)(30, 83)(31, 104)(32, 84)(33, 137)(34, 112)(35, 116)(36, 119)(37, 110)(38, 87)(39, 123)(40, 138)(41, 115)(42, 129)(43, 89)(44, 122)(45, 133)(46, 127)(47, 136)(48, 121)(49, 93)(50, 107)(51, 94)(52, 125)(53, 95)(54, 140)(55, 139)(56, 105)(57, 97)(58, 141)(59, 132)(60, 99)(61, 142)(62, 135)(63, 101)(64, 108)(65, 128)(66, 106)(67, 118)(68, 143)(69, 144)(70, 117)(71, 126)(72, 130) local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12 ) } Outer automorphisms :: reflexible Dual of E16.1023 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.1025 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 6, 12}) 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, (F * T1)^2, (F * T2)^2, T1^6, (T2^-1 * T1^-1)^3, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2, T1^-1 * T2^-1 * T1^-3 * T2 * T1^-2 ] Map:: non-degenerate R = (1, 73, 3, 75, 10, 82, 30, 102, 63, 135, 46, 118, 18, 90, 45, 117, 72, 144, 44, 116, 17, 89, 5, 77)(2, 74, 7, 79, 22, 94, 54, 126, 70, 142, 38, 110, 13, 85, 37, 109, 66, 138, 58, 130, 26, 98, 8, 80)(4, 76, 12, 84, 31, 103, 65, 137, 51, 123, 20, 92, 6, 78, 19, 91, 48, 120, 61, 133, 40, 112, 14, 86)(9, 81, 28, 100, 60, 132, 36, 108, 43, 115, 67, 139, 33, 105, 50, 122, 71, 143, 42, 114, 15, 87, 29, 101)(11, 83, 32, 104, 64, 136, 55, 127, 41, 113, 59, 131, 27, 99, 24, 96, 53, 125, 21, 93, 16, 88, 34, 106)(23, 95, 39, 111, 69, 141, 35, 107, 57, 129, 62, 134, 52, 124, 49, 121, 68, 140, 47, 119, 25, 97, 56, 128) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 90)(7, 93)(8, 96)(9, 99)(10, 94)(11, 75)(12, 107)(13, 76)(14, 111)(15, 113)(16, 77)(17, 98)(18, 85)(19, 119)(20, 121)(21, 124)(22, 120)(23, 79)(24, 129)(25, 80)(26, 123)(27, 117)(28, 86)(29, 133)(30, 132)(31, 82)(32, 97)(33, 83)(34, 140)(35, 114)(36, 84)(37, 127)(38, 104)(39, 122)(40, 89)(41, 118)(42, 91)(43, 88)(44, 143)(45, 105)(46, 115)(47, 108)(48, 144)(49, 100)(50, 92)(51, 135)(52, 109)(53, 116)(54, 106)(55, 95)(56, 139)(57, 110)(58, 131)(59, 141)(60, 125)(61, 128)(62, 101)(63, 142)(64, 102)(65, 134)(66, 103)(67, 137)(68, 130)(69, 126)(70, 112)(71, 136)(72, 138) local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: reflexible Dual of E16.1021 Transitivity :: ET+ VT+ AT Graph:: v = 6 e = 72 f = 36 degree seq :: [ 24^6 ] E16.1026 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 6, 12}) 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, T2^3, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2^-1)^3, T1 * T2 * T1^-2 * T2^-1 * T1, T1^12, (T2^-1 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 5, 77)(2, 74, 7, 79, 8, 80)(4, 76, 11, 83, 13, 85)(6, 78, 17, 89, 18, 90)(9, 81, 23, 95, 24, 96)(10, 82, 21, 93, 26, 98)(12, 84, 25, 97, 29, 101)(14, 86, 31, 103, 27, 99)(15, 87, 32, 104, 33, 105)(16, 88, 35, 107, 36, 108)(19, 91, 39, 111, 40, 112)(20, 92, 38, 110, 41, 113)(22, 94, 42, 114, 43, 115)(28, 100, 47, 119, 49, 121)(30, 102, 51, 123, 52, 124)(34, 106, 57, 129, 58, 130)(37, 109, 60, 132, 54, 126)(44, 116, 56, 128, 63, 135)(45, 117, 64, 136, 50, 122)(46, 118, 59, 131, 65, 137)(48, 120, 62, 134, 67, 139)(53, 125, 70, 142, 68, 140)(55, 127, 71, 143, 66, 138)(61, 133, 72, 144, 69, 141) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 86)(6, 88)(7, 91)(8, 93)(9, 89)(10, 75)(11, 92)(12, 76)(13, 94)(14, 90)(15, 77)(16, 106)(17, 109)(18, 110)(19, 107)(20, 79)(21, 108)(22, 80)(23, 116)(24, 104)(25, 82)(26, 117)(27, 83)(28, 84)(29, 87)(30, 85)(31, 125)(32, 126)(33, 119)(34, 128)(35, 131)(36, 95)(37, 129)(38, 130)(39, 133)(40, 114)(41, 123)(42, 118)(43, 97)(44, 132)(45, 96)(46, 98)(47, 99)(48, 100)(49, 102)(50, 101)(51, 112)(52, 134)(53, 113)(54, 103)(55, 105)(56, 144)(57, 142)(58, 111)(59, 135)(60, 143)(61, 137)(62, 115)(63, 136)(64, 127)(65, 139)(66, 120)(67, 122)(68, 121)(69, 124)(70, 141)(71, 140)(72, 138) local type(s) :: { ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.1022 Transitivity :: ET+ VT+ AT Graph:: simple v = 24 e = 72 f = 18 degree seq :: [ 6^24 ] E16.1027 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) 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, Y1 * Y3, Y1^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2^6, Y1 * Y2^-3 * Y1^-1 * Y2^-3, Y3 * Y2^-3 * Y3^-1 * Y2^-3, Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-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, 28, 100, 30, 102)(12, 84, 31, 103, 32, 104)(15, 87, 37, 109, 38, 110)(17, 89, 41, 113, 43, 115)(21, 93, 48, 120, 49, 121)(22, 94, 39, 111, 51, 123)(23, 95, 52, 124, 53, 125)(25, 97, 42, 114, 57, 129)(27, 99, 59, 131, 60, 132)(29, 101, 62, 134, 63, 135)(33, 105, 65, 137, 56, 128)(34, 106, 40, 112, 66, 138)(35, 107, 44, 116, 50, 122)(36, 108, 47, 119, 64, 136)(45, 117, 61, 133, 70, 142)(46, 118, 55, 127, 67, 139)(54, 126, 68, 140, 71, 143)(58, 130, 69, 141, 72, 144)(145, 217, 147, 219, 153, 225, 169, 241, 159, 231, 149, 221)(146, 218, 150, 222, 161, 233, 186, 258, 165, 237, 151, 223)(148, 220, 155, 227, 173, 245, 201, 273, 177, 249, 156, 228)(152, 224, 166, 238, 194, 266, 181, 253, 198, 270, 167, 239)(154, 226, 163, 235, 189, 261, 182, 254, 185, 257, 171, 243)(157, 229, 178, 250, 200, 272, 168, 240, 199, 271, 174, 246)(158, 230, 179, 251, 202, 274, 170, 242, 196, 268, 180, 252)(160, 232, 183, 255, 211, 283, 192, 264, 212, 284, 184, 256)(162, 234, 175, 247, 197, 269, 193, 265, 206, 278, 188, 260)(164, 236, 190, 262, 213, 285, 187, 259, 210, 282, 191, 263)(172, 244, 195, 267, 203, 275, 209, 281, 215, 287, 205, 277)(176, 248, 204, 276, 216, 288, 207, 279, 214, 286, 208, 280) L = (1, 148)(2, 145)(3, 154)(4, 146)(5, 158)(6, 162)(7, 164)(8, 147)(9, 170)(10, 152)(11, 174)(12, 176)(13, 149)(14, 157)(15, 182)(16, 150)(17, 187)(18, 160)(19, 151)(20, 163)(21, 193)(22, 195)(23, 197)(24, 153)(25, 201)(26, 168)(27, 204)(28, 155)(29, 207)(30, 172)(31, 156)(32, 175)(33, 200)(34, 210)(35, 194)(36, 208)(37, 159)(38, 181)(39, 166)(40, 178)(41, 161)(42, 169)(43, 185)(44, 179)(45, 214)(46, 211)(47, 180)(48, 165)(49, 192)(50, 188)(51, 183)(52, 167)(53, 196)(54, 215)(55, 190)(56, 209)(57, 186)(58, 216)(59, 171)(60, 203)(61, 189)(62, 173)(63, 206)(64, 191)(65, 177)(66, 184)(67, 199)(68, 198)(69, 202)(70, 205)(71, 212)(72, 213)(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, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E16.1030 Graph:: bipartite v = 36 e = 144 f = 78 degree seq :: [ 6^24, 12^12 ] E16.1028 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) 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, (R * Y1)^2, (R * Y3)^2, Y1^6, Y1^-1 * Y2^2 * Y1 * Y2^-2, (Y3^-1 * Y1^-1)^3, Y1^2 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2, Y2 * Y1 * Y2 * Y1^-2 * Y2 * Y1^-2, Y1^-3 * Y2^6 ] Map:: R = (1, 73, 2, 74, 6, 78, 18, 90, 13, 85, 4, 76)(3, 75, 9, 81, 27, 99, 45, 117, 33, 105, 11, 83)(5, 77, 15, 87, 41, 113, 46, 118, 43, 115, 16, 88)(7, 79, 21, 93, 52, 124, 37, 109, 55, 127, 23, 95)(8, 80, 24, 96, 57, 129, 38, 110, 32, 104, 25, 97)(10, 82, 22, 94, 48, 120, 72, 144, 66, 138, 31, 103)(12, 84, 35, 107, 42, 114, 19, 91, 47, 119, 36, 108)(14, 86, 39, 111, 50, 122, 20, 92, 49, 121, 28, 100)(17, 89, 26, 98, 51, 123, 63, 135, 70, 142, 40, 112)(29, 101, 61, 133, 56, 128, 67, 139, 65, 137, 62, 134)(30, 102, 60, 132, 53, 125, 44, 116, 71, 143, 64, 136)(34, 106, 68, 140, 58, 130, 59, 131, 69, 141, 54, 126)(145, 217, 147, 219, 154, 226, 174, 246, 207, 279, 190, 262, 162, 234, 189, 261, 216, 288, 188, 260, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 198, 270, 214, 286, 182, 254, 157, 229, 181, 253, 210, 282, 202, 274, 170, 242, 152, 224)(148, 220, 156, 228, 175, 247, 209, 281, 195, 267, 164, 236, 150, 222, 163, 235, 192, 264, 205, 277, 184, 256, 158, 230)(153, 225, 172, 244, 204, 276, 180, 252, 187, 259, 211, 283, 177, 249, 194, 266, 215, 287, 186, 258, 159, 231, 173, 245)(155, 227, 176, 248, 208, 280, 199, 271, 185, 257, 203, 275, 171, 243, 168, 240, 197, 269, 165, 237, 160, 232, 178, 250)(167, 239, 183, 255, 213, 285, 179, 251, 201, 273, 206, 278, 196, 268, 193, 265, 212, 284, 191, 263, 169, 241, 200, 272) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 172)(10, 174)(11, 176)(12, 175)(13, 181)(14, 148)(15, 173)(16, 178)(17, 149)(18, 189)(19, 192)(20, 150)(21, 160)(22, 198)(23, 183)(24, 197)(25, 200)(26, 152)(27, 168)(28, 204)(29, 153)(30, 207)(31, 209)(32, 208)(33, 194)(34, 155)(35, 201)(36, 187)(37, 210)(38, 157)(39, 213)(40, 158)(41, 203)(42, 159)(43, 211)(44, 161)(45, 216)(46, 162)(47, 169)(48, 205)(49, 212)(50, 215)(51, 164)(52, 193)(53, 165)(54, 214)(55, 185)(56, 167)(57, 206)(58, 170)(59, 171)(60, 180)(61, 184)(62, 196)(63, 190)(64, 199)(65, 195)(66, 202)(67, 177)(68, 191)(69, 179)(70, 182)(71, 186)(72, 188)(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, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E16.1029 Graph:: bipartite v = 18 e = 144 f = 96 degree seq :: [ 12^12, 24^6 ] E16.1029 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) 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 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y2^-1)^3, Y3^-2 * Y2 * Y3^2 * Y2^-1, Y3^3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, (Y3 * Y2^-1)^6, (Y3^-1 * Y1^-1)^12 ] 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, 161, 233, 169, 241)(155, 227, 172, 244, 173, 245)(156, 228, 174, 246, 166, 238)(159, 231, 165, 237, 175, 247)(167, 239, 185, 257, 186, 258)(168, 240, 184, 256, 188, 260)(170, 242, 190, 262, 191, 263)(171, 243, 192, 264, 179, 251)(176, 248, 196, 268, 197, 269)(177, 249, 198, 270, 178, 250)(180, 252, 201, 273, 202, 274)(181, 253, 203, 275, 189, 261)(182, 254, 204, 276, 205, 277)(183, 255, 206, 278, 193, 265)(187, 259, 200, 272, 210, 282)(194, 266, 213, 285, 209, 281)(195, 267, 214, 286, 211, 283)(199, 271, 207, 279, 208, 280)(212, 284, 215, 287, 216, 288) L = (1, 147)(2, 150)(3, 153)(4, 155)(5, 145)(6, 161)(7, 146)(8, 166)(9, 168)(10, 170)(11, 169)(12, 148)(13, 167)(14, 171)(15, 149)(16, 158)(17, 179)(18, 180)(19, 178)(20, 181)(21, 151)(22, 184)(23, 152)(24, 187)(25, 189)(26, 188)(27, 154)(28, 164)(29, 194)(30, 193)(31, 156)(32, 157)(33, 159)(34, 160)(35, 200)(36, 192)(37, 162)(38, 163)(39, 165)(40, 173)(41, 175)(42, 195)(43, 209)(44, 211)(45, 210)(46, 186)(47, 212)(48, 197)(49, 172)(50, 203)(51, 174)(52, 208)(53, 190)(54, 176)(55, 177)(56, 191)(57, 198)(58, 215)(59, 205)(60, 199)(61, 201)(62, 182)(63, 183)(64, 185)(65, 216)(66, 202)(67, 213)(68, 214)(69, 206)(70, 207)(71, 196)(72, 204)(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) :: { ( 12, 24 ), ( 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E16.1028 Graph:: simple bipartite v = 96 e = 144 f = 18 degree seq :: [ 2^72, 6^24 ] E16.1030 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) 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 :: [ Y2, R^2, Y3^3, Y3^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y1^2 * Y3 * Y1^-1, (Y3 * Y1^-1)^3, (Y3 * Y2^-1)^3, (Y3^-1 * Y1^-1)^6, Y1^12 ] Map:: R = (1, 73, 2, 74, 6, 78, 16, 88, 34, 106, 56, 128, 72, 144, 66, 138, 48, 120, 28, 100, 12, 84, 4, 76)(3, 75, 9, 81, 17, 89, 37, 109, 57, 129, 70, 142, 69, 141, 52, 124, 62, 134, 43, 115, 25, 97, 10, 82)(5, 77, 14, 86, 18, 90, 38, 110, 58, 130, 39, 111, 61, 133, 65, 137, 67, 139, 50, 122, 29, 101, 15, 87)(7, 79, 19, 91, 35, 107, 59, 131, 63, 135, 64, 136, 55, 127, 33, 105, 47, 119, 27, 99, 11, 83, 20, 92)(8, 80, 21, 93, 36, 108, 23, 95, 44, 116, 60, 132, 71, 143, 68, 140, 49, 121, 30, 102, 13, 85, 22, 94)(24, 96, 32, 104, 54, 126, 31, 103, 53, 125, 41, 113, 51, 123, 40, 112, 42, 114, 46, 118, 26, 98, 45, 117)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 149)(4, 155)(5, 145)(6, 161)(7, 152)(8, 146)(9, 167)(10, 165)(11, 157)(12, 169)(13, 148)(14, 175)(15, 176)(16, 179)(17, 162)(18, 150)(19, 183)(20, 182)(21, 170)(22, 186)(23, 168)(24, 153)(25, 173)(26, 154)(27, 158)(28, 191)(29, 156)(30, 195)(31, 171)(32, 177)(33, 159)(34, 201)(35, 180)(36, 160)(37, 204)(38, 185)(39, 184)(40, 163)(41, 164)(42, 187)(43, 166)(44, 200)(45, 208)(46, 203)(47, 193)(48, 206)(49, 172)(50, 189)(51, 196)(52, 174)(53, 214)(54, 181)(55, 215)(56, 207)(57, 202)(58, 178)(59, 209)(60, 198)(61, 216)(62, 211)(63, 188)(64, 194)(65, 190)(66, 199)(67, 192)(68, 197)(69, 205)(70, 212)(71, 210)(72, 213)(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, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.1027 Graph:: simple bipartite v = 78 e = 144 f = 36 degree seq :: [ 2^72, 24^6 ] E16.1031 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) 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, Y1^-1 * Y3^-1, Y3 * Y1^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-1, Y2^-2 * Y1 * Y2^2 * Y1^-1, Y2^-2 * Y3 * Y2^2 * Y3^-1, Y2^3 * Y1 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2^-3 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1, Y2^12, (Y3 * Y2^-1)^6 ] 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, 17, 89, 25, 97)(11, 83, 27, 99, 28, 100)(12, 84, 29, 101, 30, 102)(15, 87, 21, 93, 31, 103)(22, 94, 40, 112, 42, 114)(23, 95, 43, 115, 44, 116)(24, 96, 41, 113, 35, 107)(26, 98, 46, 118, 39, 111)(32, 104, 52, 124, 53, 125)(33, 105, 49, 121, 54, 126)(34, 106, 56, 128, 58, 130)(36, 108, 57, 129, 48, 120)(37, 109, 60, 132, 51, 123)(38, 110, 61, 133, 62, 134)(45, 117, 59, 131, 65, 137)(47, 119, 66, 138, 67, 139)(50, 122, 68, 140, 69, 141)(55, 127, 63, 135, 70, 142)(64, 136, 72, 144, 71, 143)(145, 217, 147, 219, 153, 225, 168, 240, 189, 261, 200, 272, 216, 288, 213, 285, 199, 271, 177, 249, 159, 231, 149, 221)(146, 218, 150, 222, 161, 233, 180, 252, 203, 275, 210, 282, 215, 287, 197, 269, 207, 279, 183, 255, 165, 237, 151, 223)(148, 220, 155, 227, 169, 241, 187, 259, 209, 281, 184, 256, 208, 280, 206, 278, 214, 286, 195, 267, 175, 247, 156, 228)(152, 224, 166, 238, 185, 257, 205, 277, 202, 274, 204, 276, 194, 266, 174, 246, 193, 265, 172, 244, 157, 229, 167, 239)(154, 226, 163, 235, 179, 251, 160, 232, 178, 250, 201, 273, 212, 284, 211, 283, 198, 270, 176, 248, 158, 230, 170, 242)(162, 234, 173, 245, 192, 264, 171, 243, 191, 263, 188, 260, 196, 268, 186, 258, 190, 262, 182, 254, 164, 236, 181, 253) L = (1, 148)(2, 145)(3, 154)(4, 146)(5, 158)(6, 162)(7, 164)(8, 147)(9, 169)(10, 152)(11, 172)(12, 174)(13, 149)(14, 157)(15, 175)(16, 150)(17, 153)(18, 160)(19, 151)(20, 163)(21, 159)(22, 186)(23, 188)(24, 179)(25, 161)(26, 183)(27, 155)(28, 171)(29, 156)(30, 173)(31, 165)(32, 197)(33, 198)(34, 202)(35, 185)(36, 192)(37, 195)(38, 206)(39, 190)(40, 166)(41, 168)(42, 184)(43, 167)(44, 187)(45, 209)(46, 170)(47, 211)(48, 201)(49, 177)(50, 213)(51, 204)(52, 176)(53, 196)(54, 193)(55, 214)(56, 178)(57, 180)(58, 200)(59, 189)(60, 181)(61, 182)(62, 205)(63, 199)(64, 215)(65, 203)(66, 191)(67, 210)(68, 194)(69, 212)(70, 207)(71, 216)(72, 208)(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, 12, 2, 12, 2, 12 ), ( 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 E16.1032 Graph:: bipartite v = 30 e = 144 f = 84 degree seq :: [ 6^24, 24^6 ] E16.1032 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) 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 :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^6, Y3^-1 * Y1 * Y3^2 * Y1^-1 * Y3^-1, (Y3^-1 * Y1^-1)^3, Y1^2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3, Y1^-1 * Y3^-1 * Y1^-3 * Y3 * Y1^-2, Y3 * Y1^3 * Y3^5, (Y3 * Y2^-1)^12 ] Map:: R = (1, 73, 2, 74, 6, 78, 18, 90, 13, 85, 4, 76)(3, 75, 9, 81, 27, 99, 45, 117, 33, 105, 11, 83)(5, 77, 15, 87, 41, 113, 46, 118, 43, 115, 16, 88)(7, 79, 21, 93, 52, 124, 37, 109, 55, 127, 23, 95)(8, 80, 24, 96, 57, 129, 38, 110, 32, 104, 25, 97)(10, 82, 22, 94, 48, 120, 72, 144, 66, 138, 31, 103)(12, 84, 35, 107, 42, 114, 19, 91, 47, 119, 36, 108)(14, 86, 39, 111, 50, 122, 20, 92, 49, 121, 28, 100)(17, 89, 26, 98, 51, 123, 63, 135, 70, 142, 40, 112)(29, 101, 61, 133, 56, 128, 67, 139, 65, 137, 62, 134)(30, 102, 60, 132, 53, 125, 44, 116, 71, 143, 64, 136)(34, 106, 68, 140, 58, 130, 59, 131, 69, 141, 54, 126)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 172)(10, 174)(11, 176)(12, 175)(13, 181)(14, 148)(15, 173)(16, 178)(17, 149)(18, 189)(19, 192)(20, 150)(21, 160)(22, 198)(23, 183)(24, 197)(25, 200)(26, 152)(27, 168)(28, 204)(29, 153)(30, 207)(31, 209)(32, 208)(33, 194)(34, 155)(35, 201)(36, 187)(37, 210)(38, 157)(39, 213)(40, 158)(41, 203)(42, 159)(43, 211)(44, 161)(45, 216)(46, 162)(47, 169)(48, 205)(49, 212)(50, 215)(51, 164)(52, 193)(53, 165)(54, 214)(55, 185)(56, 167)(57, 206)(58, 170)(59, 171)(60, 180)(61, 184)(62, 196)(63, 190)(64, 199)(65, 195)(66, 202)(67, 177)(68, 191)(69, 179)(70, 182)(71, 186)(72, 188)(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, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E16.1031 Graph:: simple bipartite v = 84 e = 144 f = 30 degree seq :: [ 2^72, 12^12 ] E16.1033 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 6, 12}) Quotient :: edge Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1^-1, T2^6, (T2 * T1^-1 * T2^-1 * T1^-1)^2, T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 24, 15, 5)(2, 6, 17, 37, 21, 7)(4, 11, 25, 48, 32, 12)(8, 22, 43, 33, 13, 23)(10, 26, 47, 34, 14, 27)(16, 35, 57, 40, 19, 36)(18, 38, 58, 41, 20, 39)(28, 51, 66, 53, 30, 52)(29, 42, 62, 54, 31, 45)(44, 63, 55, 65, 46, 64)(49, 67, 56, 69, 50, 68)(59, 70, 61, 72, 60, 71)(73, 74, 76)(75, 80, 82)(77, 85, 86)(78, 88, 90)(79, 91, 92)(81, 89, 97)(83, 100, 101)(84, 102, 103)(87, 93, 104)(94, 114, 116)(95, 117, 118)(96, 115, 119)(98, 121, 107)(99, 122, 108)(105, 126, 127)(106, 128, 112)(109, 129, 130)(110, 131, 123)(111, 132, 124)(113, 133, 125)(120, 138, 134)(135, 142, 139)(136, 143, 140)(137, 144, 141) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 24^3 ), ( 24^6 ) } Outer automorphisms :: reflexible Dual of E16.1042 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 72 f = 6 degree seq :: [ 3^24, 6^12 ] E16.1034 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 6, 12}) Quotient :: edge Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-2 * T1 * T2, T2^6, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, (T2 * T1^-1)^4, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 24, 15, 5)(2, 6, 17, 37, 21, 7)(4, 11, 25, 48, 32, 12)(8, 22, 43, 33, 13, 23)(10, 26, 47, 34, 14, 27)(16, 35, 57, 40, 19, 36)(18, 38, 58, 41, 20, 39)(28, 51, 66, 54, 30, 52)(29, 53, 64, 45, 31, 42)(44, 62, 55, 65, 46, 63)(49, 67, 56, 69, 50, 68)(59, 70, 61, 72, 60, 71)(73, 74, 76)(75, 80, 82)(77, 85, 86)(78, 88, 90)(79, 91, 92)(81, 89, 97)(83, 100, 101)(84, 102, 103)(87, 93, 104)(94, 114, 116)(95, 117, 118)(96, 115, 119)(98, 121, 112)(99, 122, 107)(105, 125, 127)(106, 128, 108)(109, 129, 130)(110, 131, 126)(111, 132, 123)(113, 133, 124)(120, 138, 136)(134, 142, 141)(135, 143, 139)(137, 144, 140) 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) :: { ( 24^3 ), ( 24^6 ) } Outer automorphisms :: reflexible Dual of E16.1041 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 72 f = 6 degree seq :: [ 3^24, 6^12 ] E16.1035 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 6, 12}) Quotient :: edge Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-2 * T2^-3, (T2^-1 * T1^-1)^3, T1^6, T1^-2 * T2 * T1^2 * T2^-1, (T2 * T1^-1)^3, T2 * T1^-2 * T2^3 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 30, 13, 32, 43, 20, 6, 19, 17, 5)(2, 7, 22, 14, 4, 12, 34, 40, 18, 39, 26, 8)(9, 27, 51, 33, 11, 24, 48, 59, 41, 25, 49, 28)(15, 36, 44, 21, 16, 37, 47, 23, 42, 60, 57, 35)(29, 54, 69, 56, 31, 52, 67, 58, 38, 53, 68, 55)(45, 63, 72, 65, 46, 61, 70, 66, 50, 62, 71, 64)(73, 74, 78, 90, 85, 76)(75, 81, 91, 113, 104, 83)(77, 87, 92, 114, 102, 88)(79, 93, 111, 107, 84, 95)(80, 96, 112, 99, 86, 97)(82, 101, 89, 110, 115, 103)(94, 117, 98, 122, 106, 118)(100, 124, 131, 126, 105, 125)(108, 127, 132, 130, 109, 128)(116, 133, 129, 135, 119, 134)(120, 136, 123, 138, 121, 137)(139, 142, 141, 144, 140, 143) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6^6 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E16.1044 Transitivity :: ET+ Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.1036 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 6, 12}) Quotient :: edge Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^3 * T1^-2 * T2, (T2^-1 * T1^-1)^3, T1^6, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, (T2 * T1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 3, 10, 20, 6, 19, 42, 34, 13, 31, 17, 5)(2, 7, 22, 40, 18, 39, 35, 14, 4, 12, 26, 8)(9, 27, 51, 59, 41, 25, 49, 32, 11, 24, 48, 28)(15, 36, 47, 23, 43, 60, 44, 21, 16, 37, 57, 33)(29, 54, 69, 58, 38, 53, 68, 56, 30, 52, 67, 55)(45, 63, 72, 66, 50, 62, 71, 65, 46, 61, 70, 64)(73, 74, 78, 90, 85, 76)(75, 81, 91, 113, 103, 83)(77, 87, 92, 115, 106, 88)(79, 93, 111, 105, 84, 95)(80, 96, 112, 99, 86, 97)(82, 101, 114, 110, 89, 102)(94, 117, 107, 122, 98, 118)(100, 124, 131, 126, 104, 125)(108, 130, 132, 128, 109, 127)(116, 133, 129, 135, 119, 134)(120, 138, 123, 137, 121, 136)(139, 142, 141, 144, 140, 143) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6^6 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E16.1043 Transitivity :: ET+ Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 6^12, 12^6 ] E16.1037 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 6, 12}) Quotient :: edge Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2 * T1 * T2^-1, T1^2 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1, (T2 * T1 * T2 * T1^-1)^2, T1^-4 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-3)^2, T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-2 ] Map:: non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 11, 13)(6, 17, 18)(9, 24, 25)(10, 26, 28)(12, 31, 33)(14, 37, 38)(15, 39, 41)(16, 43, 44)(19, 49, 50)(20, 51, 52)(21, 36, 54)(22, 29, 56)(23, 58, 59)(27, 30, 63)(32, 66, 45)(34, 60, 61)(35, 64, 42)(40, 62, 68)(46, 69, 65)(47, 53, 70)(48, 57, 71)(55, 72, 67)(73, 74, 78, 88, 114, 113, 128, 96, 121, 104, 84, 76)(75, 81, 95, 129, 107, 85, 106, 109, 122, 116, 99, 82)(77, 86, 108, 138, 136, 100, 92, 79, 91, 120, 112, 87)(80, 93, 125, 103, 111, 124, 118, 89, 117, 140, 127, 94)(83, 101, 137, 130, 115, 105, 139, 132, 97, 90, 119, 102)(98, 133, 141, 126, 143, 135, 144, 123, 110, 131, 142, 134) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^3 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E16.1039 Transitivity :: ET+ Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 3^24, 12^6 ] E16.1038 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 6, 12}) Quotient :: edge Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1^3 * T2^-1, T2 * T1 * T2^-2 * T1^-3, (T1 * T2^-1)^4, (T1 * T2^-1)^4, (T1^2 * T2)^3, T1^12 ] Map:: non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 11, 13)(6, 17, 18)(9, 16, 24)(10, 25, 27)(12, 22, 30)(14, 32, 33)(15, 34, 29)(19, 36, 41)(20, 42, 43)(21, 44, 45)(23, 47, 48)(26, 50, 51)(28, 53, 55)(31, 52, 56)(35, 59, 61)(37, 62, 63)(38, 64, 54)(39, 65, 66)(40, 58, 67)(46, 69, 70)(49, 71, 60)(57, 68, 72)(73, 74, 78, 88, 108, 134, 143, 144, 128, 101, 84, 76)(75, 81, 95, 104, 113, 140, 127, 130, 103, 85, 98, 82)(77, 86, 92, 79, 91, 112, 116, 135, 124, 99, 107, 87)(80, 93, 110, 89, 109, 133, 137, 132, 106, 115, 118, 94)(83, 90, 111, 122, 96, 121, 142, 119, 129, 102, 126, 100)(97, 120, 136, 131, 105, 125, 138, 114, 139, 123, 141, 117) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^3 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E16.1040 Transitivity :: ET+ Graph:: simple bipartite v = 30 e = 72 f = 12 degree seq :: [ 3^24, 12^6 ] E16.1039 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 6, 12}) Quotient :: loop Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1^-1, T2^6, (T2 * T1^-1 * T2^-1 * T1^-1)^2, T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 73, 3, 75, 9, 81, 24, 96, 15, 87, 5, 77)(2, 74, 6, 78, 17, 89, 37, 109, 21, 93, 7, 79)(4, 76, 11, 83, 25, 97, 48, 120, 32, 104, 12, 84)(8, 80, 22, 94, 43, 115, 33, 105, 13, 85, 23, 95)(10, 82, 26, 98, 47, 119, 34, 106, 14, 86, 27, 99)(16, 88, 35, 107, 57, 129, 40, 112, 19, 91, 36, 108)(18, 90, 38, 110, 58, 130, 41, 113, 20, 92, 39, 111)(28, 100, 51, 123, 66, 138, 53, 125, 30, 102, 52, 124)(29, 101, 42, 114, 62, 134, 54, 126, 31, 103, 45, 117)(44, 116, 63, 135, 55, 127, 65, 137, 46, 118, 64, 136)(49, 121, 67, 139, 56, 128, 69, 141, 50, 122, 68, 140)(59, 131, 70, 142, 61, 133, 72, 144, 60, 132, 71, 143) L = (1, 74)(2, 76)(3, 80)(4, 73)(5, 85)(6, 88)(7, 91)(8, 82)(9, 89)(10, 75)(11, 100)(12, 102)(13, 86)(14, 77)(15, 93)(16, 90)(17, 97)(18, 78)(19, 92)(20, 79)(21, 104)(22, 114)(23, 117)(24, 115)(25, 81)(26, 121)(27, 122)(28, 101)(29, 83)(30, 103)(31, 84)(32, 87)(33, 126)(34, 128)(35, 98)(36, 99)(37, 129)(38, 131)(39, 132)(40, 106)(41, 133)(42, 116)(43, 119)(44, 94)(45, 118)(46, 95)(47, 96)(48, 138)(49, 107)(50, 108)(51, 110)(52, 111)(53, 113)(54, 127)(55, 105)(56, 112)(57, 130)(58, 109)(59, 123)(60, 124)(61, 125)(62, 120)(63, 142)(64, 143)(65, 144)(66, 134)(67, 135)(68, 136)(69, 137)(70, 139)(71, 140)(72, 141) local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12 ) } Outer automorphisms :: reflexible Dual of E16.1037 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.1040 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 6, 12}) Quotient :: loop Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-2 * T1 * T2, T2^6, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, (T2 * T1^-1)^4, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 73, 3, 75, 9, 81, 24, 96, 15, 87, 5, 77)(2, 74, 6, 78, 17, 89, 37, 109, 21, 93, 7, 79)(4, 76, 11, 83, 25, 97, 48, 120, 32, 104, 12, 84)(8, 80, 22, 94, 43, 115, 33, 105, 13, 85, 23, 95)(10, 82, 26, 98, 47, 119, 34, 106, 14, 86, 27, 99)(16, 88, 35, 107, 57, 129, 40, 112, 19, 91, 36, 108)(18, 90, 38, 110, 58, 130, 41, 113, 20, 92, 39, 111)(28, 100, 51, 123, 66, 138, 54, 126, 30, 102, 52, 124)(29, 101, 53, 125, 64, 136, 45, 117, 31, 103, 42, 114)(44, 116, 62, 134, 55, 127, 65, 137, 46, 118, 63, 135)(49, 121, 67, 139, 56, 128, 69, 141, 50, 122, 68, 140)(59, 131, 70, 142, 61, 133, 72, 144, 60, 132, 71, 143) L = (1, 74)(2, 76)(3, 80)(4, 73)(5, 85)(6, 88)(7, 91)(8, 82)(9, 89)(10, 75)(11, 100)(12, 102)(13, 86)(14, 77)(15, 93)(16, 90)(17, 97)(18, 78)(19, 92)(20, 79)(21, 104)(22, 114)(23, 117)(24, 115)(25, 81)(26, 121)(27, 122)(28, 101)(29, 83)(30, 103)(31, 84)(32, 87)(33, 125)(34, 128)(35, 99)(36, 106)(37, 129)(38, 131)(39, 132)(40, 98)(41, 133)(42, 116)(43, 119)(44, 94)(45, 118)(46, 95)(47, 96)(48, 138)(49, 112)(50, 107)(51, 111)(52, 113)(53, 127)(54, 110)(55, 105)(56, 108)(57, 130)(58, 109)(59, 126)(60, 123)(61, 124)(62, 142)(63, 143)(64, 120)(65, 144)(66, 136)(67, 135)(68, 137)(69, 134)(70, 141)(71, 139)(72, 140) local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12 ) } Outer automorphisms :: reflexible Dual of E16.1038 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 72 f = 30 degree seq :: [ 12^12 ] E16.1041 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 6, 12}) Quotient :: loop Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-2 * T2^-3, (T2^-1 * T1^-1)^3, T1^6, T1^-2 * T2 * T1^2 * T2^-1, (T2 * T1^-1)^3, T2 * T1^-2 * T2^3 * T1^-2 ] Map:: non-degenerate R = (1, 73, 3, 75, 10, 82, 30, 102, 13, 85, 32, 104, 43, 115, 20, 92, 6, 78, 19, 91, 17, 89, 5, 77)(2, 74, 7, 79, 22, 94, 14, 86, 4, 76, 12, 84, 34, 106, 40, 112, 18, 90, 39, 111, 26, 98, 8, 80)(9, 81, 27, 99, 51, 123, 33, 105, 11, 83, 24, 96, 48, 120, 59, 131, 41, 113, 25, 97, 49, 121, 28, 100)(15, 87, 36, 108, 44, 116, 21, 93, 16, 88, 37, 109, 47, 119, 23, 95, 42, 114, 60, 132, 57, 129, 35, 107)(29, 101, 54, 126, 69, 141, 56, 128, 31, 103, 52, 124, 67, 139, 58, 130, 38, 110, 53, 125, 68, 140, 55, 127)(45, 117, 63, 135, 72, 144, 65, 137, 46, 118, 61, 133, 70, 142, 66, 138, 50, 122, 62, 134, 71, 143, 64, 136) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 90)(7, 93)(8, 96)(9, 91)(10, 101)(11, 75)(12, 95)(13, 76)(14, 97)(15, 92)(16, 77)(17, 110)(18, 85)(19, 113)(20, 114)(21, 111)(22, 117)(23, 79)(24, 112)(25, 80)(26, 122)(27, 86)(28, 124)(29, 89)(30, 88)(31, 82)(32, 83)(33, 125)(34, 118)(35, 84)(36, 127)(37, 128)(38, 115)(39, 107)(40, 99)(41, 104)(42, 102)(43, 103)(44, 133)(45, 98)(46, 94)(47, 134)(48, 136)(49, 137)(50, 106)(51, 138)(52, 131)(53, 100)(54, 105)(55, 132)(56, 108)(57, 135)(58, 109)(59, 126)(60, 130)(61, 129)(62, 116)(63, 119)(64, 123)(65, 120)(66, 121)(67, 142)(68, 143)(69, 144)(70, 141)(71, 139)(72, 140) local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: reflexible Dual of E16.1034 Transitivity :: ET+ VT+ AT Graph:: v = 6 e = 72 f = 36 degree seq :: [ 24^6 ] E16.1042 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 6, 12}) Quotient :: loop Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^3 * T1^-2 * T2, (T2^-1 * T1^-1)^3, T1^6, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, (T2 * T1^-1)^3 ] Map:: non-degenerate R = (1, 73, 3, 75, 10, 82, 20, 92, 6, 78, 19, 91, 42, 114, 34, 106, 13, 85, 31, 103, 17, 89, 5, 77)(2, 74, 7, 79, 22, 94, 40, 112, 18, 90, 39, 111, 35, 107, 14, 86, 4, 76, 12, 84, 26, 98, 8, 80)(9, 81, 27, 99, 51, 123, 59, 131, 41, 113, 25, 97, 49, 121, 32, 104, 11, 83, 24, 96, 48, 120, 28, 100)(15, 87, 36, 108, 47, 119, 23, 95, 43, 115, 60, 132, 44, 116, 21, 93, 16, 88, 37, 109, 57, 129, 33, 105)(29, 101, 54, 126, 69, 141, 58, 130, 38, 110, 53, 125, 68, 140, 56, 128, 30, 102, 52, 124, 67, 139, 55, 127)(45, 117, 63, 135, 72, 144, 66, 138, 50, 122, 62, 134, 71, 143, 65, 137, 46, 118, 61, 133, 70, 142, 64, 136) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 90)(7, 93)(8, 96)(9, 91)(10, 101)(11, 75)(12, 95)(13, 76)(14, 97)(15, 92)(16, 77)(17, 102)(18, 85)(19, 113)(20, 115)(21, 111)(22, 117)(23, 79)(24, 112)(25, 80)(26, 118)(27, 86)(28, 124)(29, 114)(30, 82)(31, 83)(32, 125)(33, 84)(34, 88)(35, 122)(36, 130)(37, 127)(38, 89)(39, 105)(40, 99)(41, 103)(42, 110)(43, 106)(44, 133)(45, 107)(46, 94)(47, 134)(48, 138)(49, 136)(50, 98)(51, 137)(52, 131)(53, 100)(54, 104)(55, 108)(56, 109)(57, 135)(58, 132)(59, 126)(60, 128)(61, 129)(62, 116)(63, 119)(64, 120)(65, 121)(66, 123)(67, 142)(68, 143)(69, 144)(70, 141)(71, 139)(72, 140) local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: reflexible Dual of E16.1033 Transitivity :: ET+ VT+ AT Graph:: v = 6 e = 72 f = 36 degree seq :: [ 24^6 ] E16.1043 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 6, 12}) Quotient :: loop Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2 * T1 * T2^-1, T1^2 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1, (T2 * T1 * T2 * T1^-1)^2, T1^-4 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-3)^2, T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 5, 77)(2, 74, 7, 79, 8, 80)(4, 76, 11, 83, 13, 85)(6, 78, 17, 89, 18, 90)(9, 81, 24, 96, 25, 97)(10, 82, 26, 98, 28, 100)(12, 84, 31, 103, 33, 105)(14, 86, 37, 109, 38, 110)(15, 87, 39, 111, 41, 113)(16, 88, 43, 115, 44, 116)(19, 91, 49, 121, 50, 122)(20, 92, 51, 123, 52, 124)(21, 93, 36, 108, 54, 126)(22, 94, 29, 101, 56, 128)(23, 95, 58, 130, 59, 131)(27, 99, 30, 102, 63, 135)(32, 104, 66, 138, 45, 117)(34, 106, 60, 132, 61, 133)(35, 107, 64, 136, 42, 114)(40, 112, 62, 134, 68, 140)(46, 118, 69, 141, 65, 137)(47, 119, 53, 125, 70, 142)(48, 120, 57, 129, 71, 143)(55, 127, 72, 144, 67, 139) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 86)(6, 88)(7, 91)(8, 93)(9, 95)(10, 75)(11, 101)(12, 76)(13, 106)(14, 108)(15, 77)(16, 114)(17, 117)(18, 119)(19, 120)(20, 79)(21, 125)(22, 80)(23, 129)(24, 121)(25, 90)(26, 133)(27, 82)(28, 92)(29, 137)(30, 83)(31, 111)(32, 84)(33, 139)(34, 109)(35, 85)(36, 138)(37, 122)(38, 131)(39, 124)(40, 87)(41, 128)(42, 113)(43, 105)(44, 99)(45, 140)(46, 89)(47, 102)(48, 112)(49, 104)(50, 116)(51, 110)(52, 118)(53, 103)(54, 143)(55, 94)(56, 96)(57, 107)(58, 115)(59, 142)(60, 97)(61, 141)(62, 98)(63, 144)(64, 100)(65, 130)(66, 136)(67, 132)(68, 127)(69, 126)(70, 134)(71, 135)(72, 123) local type(s) :: { ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.1036 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 6^24 ] E16.1044 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 6, 12}) Quotient :: loop Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1^3 * T2^-1, T2 * T1 * T2^-2 * T1^-3, (T1 * T2^-1)^4, (T1 * T2^-1)^4, (T1^2 * T2)^3, T1^12 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 5, 77)(2, 74, 7, 79, 8, 80)(4, 76, 11, 83, 13, 85)(6, 78, 17, 89, 18, 90)(9, 81, 16, 88, 24, 96)(10, 82, 25, 97, 27, 99)(12, 84, 22, 94, 30, 102)(14, 86, 32, 104, 33, 105)(15, 87, 34, 106, 29, 101)(19, 91, 36, 108, 41, 113)(20, 92, 42, 114, 43, 115)(21, 93, 44, 116, 45, 117)(23, 95, 47, 119, 48, 120)(26, 98, 50, 122, 51, 123)(28, 100, 53, 125, 55, 127)(31, 103, 52, 124, 56, 128)(35, 107, 59, 131, 61, 133)(37, 109, 62, 134, 63, 135)(38, 110, 64, 136, 54, 126)(39, 111, 65, 137, 66, 138)(40, 112, 58, 130, 67, 139)(46, 118, 69, 141, 70, 142)(49, 121, 71, 143, 60, 132)(57, 129, 68, 140, 72, 144) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 86)(6, 88)(7, 91)(8, 93)(9, 95)(10, 75)(11, 90)(12, 76)(13, 98)(14, 92)(15, 77)(16, 108)(17, 109)(18, 111)(19, 112)(20, 79)(21, 110)(22, 80)(23, 104)(24, 121)(25, 120)(26, 82)(27, 107)(28, 83)(29, 84)(30, 126)(31, 85)(32, 113)(33, 125)(34, 115)(35, 87)(36, 134)(37, 133)(38, 89)(39, 122)(40, 116)(41, 140)(42, 139)(43, 118)(44, 135)(45, 97)(46, 94)(47, 129)(48, 136)(49, 142)(50, 96)(51, 141)(52, 99)(53, 138)(54, 100)(55, 130)(56, 101)(57, 102)(58, 103)(59, 105)(60, 106)(61, 137)(62, 143)(63, 124)(64, 131)(65, 132)(66, 114)(67, 123)(68, 127)(69, 117)(70, 119)(71, 144)(72, 128) local type(s) :: { ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.1035 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 6^24 ] E16.1045 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) Quotient :: dipole Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1^-1, (R * Y2^2)^2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, Y2^6, Y3 * Y2^-1 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-2 * Y3 * Y2^-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, 17, 89, 25, 97)(11, 83, 28, 100, 29, 101)(12, 84, 30, 102, 31, 103)(15, 87, 21, 93, 32, 104)(22, 94, 42, 114, 44, 116)(23, 95, 45, 117, 46, 118)(24, 96, 43, 115, 47, 119)(26, 98, 49, 121, 35, 107)(27, 99, 50, 122, 36, 108)(33, 105, 54, 126, 55, 127)(34, 106, 56, 128, 40, 112)(37, 109, 57, 129, 58, 130)(38, 110, 59, 131, 51, 123)(39, 111, 60, 132, 52, 124)(41, 113, 61, 133, 53, 125)(48, 120, 66, 138, 62, 134)(63, 135, 70, 142, 67, 139)(64, 136, 71, 143, 68, 140)(65, 137, 72, 144, 69, 141)(145, 217, 147, 219, 153, 225, 168, 240, 159, 231, 149, 221)(146, 218, 150, 222, 161, 233, 181, 253, 165, 237, 151, 223)(148, 220, 155, 227, 169, 241, 192, 264, 176, 248, 156, 228)(152, 224, 166, 238, 187, 259, 177, 249, 157, 229, 167, 239)(154, 226, 170, 242, 191, 263, 178, 250, 158, 230, 171, 243)(160, 232, 179, 251, 201, 273, 184, 256, 163, 235, 180, 252)(162, 234, 182, 254, 202, 274, 185, 257, 164, 236, 183, 255)(172, 244, 195, 267, 210, 282, 197, 269, 174, 246, 196, 268)(173, 245, 186, 258, 206, 278, 198, 270, 175, 247, 189, 261)(188, 260, 207, 279, 199, 271, 209, 281, 190, 262, 208, 280)(193, 265, 211, 283, 200, 272, 213, 285, 194, 266, 212, 284)(203, 275, 214, 286, 205, 277, 216, 288, 204, 276, 215, 287) L = (1, 148)(2, 145)(3, 154)(4, 146)(5, 158)(6, 162)(7, 164)(8, 147)(9, 169)(10, 152)(11, 173)(12, 175)(13, 149)(14, 157)(15, 176)(16, 150)(17, 153)(18, 160)(19, 151)(20, 163)(21, 159)(22, 188)(23, 190)(24, 191)(25, 161)(26, 179)(27, 180)(28, 155)(29, 172)(30, 156)(31, 174)(32, 165)(33, 199)(34, 184)(35, 193)(36, 194)(37, 202)(38, 195)(39, 196)(40, 200)(41, 197)(42, 166)(43, 168)(44, 186)(45, 167)(46, 189)(47, 187)(48, 206)(49, 170)(50, 171)(51, 203)(52, 204)(53, 205)(54, 177)(55, 198)(56, 178)(57, 181)(58, 201)(59, 182)(60, 183)(61, 185)(62, 210)(63, 211)(64, 212)(65, 213)(66, 192)(67, 214)(68, 215)(69, 216)(70, 207)(71, 208)(72, 209)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E16.1051 Graph:: bipartite v = 36 e = 144 f = 78 degree seq :: [ 6^24, 12^12 ] E16.1046 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) Quotient :: dipole Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^-2 * Y3^-1 * Y2, Y2^-1 * Y1^-1 * Y2^2 * Y1 * Y2^-1, (R * Y2^2)^2, Y2^6, Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y2^-1 * Y1)^4, Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y3^-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, 17, 89, 25, 97)(11, 83, 28, 100, 29, 101)(12, 84, 30, 102, 31, 103)(15, 87, 21, 93, 32, 104)(22, 94, 42, 114, 44, 116)(23, 95, 45, 117, 46, 118)(24, 96, 43, 115, 47, 119)(26, 98, 49, 121, 40, 112)(27, 99, 50, 122, 35, 107)(33, 105, 53, 125, 55, 127)(34, 106, 56, 128, 36, 108)(37, 109, 57, 129, 58, 130)(38, 110, 59, 131, 54, 126)(39, 111, 60, 132, 51, 123)(41, 113, 61, 133, 52, 124)(48, 120, 66, 138, 64, 136)(62, 134, 70, 142, 69, 141)(63, 135, 71, 143, 67, 139)(65, 137, 72, 144, 68, 140)(145, 217, 147, 219, 153, 225, 168, 240, 159, 231, 149, 221)(146, 218, 150, 222, 161, 233, 181, 253, 165, 237, 151, 223)(148, 220, 155, 227, 169, 241, 192, 264, 176, 248, 156, 228)(152, 224, 166, 238, 187, 259, 177, 249, 157, 229, 167, 239)(154, 226, 170, 242, 191, 263, 178, 250, 158, 230, 171, 243)(160, 232, 179, 251, 201, 273, 184, 256, 163, 235, 180, 252)(162, 234, 182, 254, 202, 274, 185, 257, 164, 236, 183, 255)(172, 244, 195, 267, 210, 282, 198, 270, 174, 246, 196, 268)(173, 245, 197, 269, 208, 280, 189, 261, 175, 247, 186, 258)(188, 260, 206, 278, 199, 271, 209, 281, 190, 262, 207, 279)(193, 265, 211, 283, 200, 272, 213, 285, 194, 266, 212, 284)(203, 275, 214, 286, 205, 277, 216, 288, 204, 276, 215, 287) L = (1, 148)(2, 145)(3, 154)(4, 146)(5, 158)(6, 162)(7, 164)(8, 147)(9, 169)(10, 152)(11, 173)(12, 175)(13, 149)(14, 157)(15, 176)(16, 150)(17, 153)(18, 160)(19, 151)(20, 163)(21, 159)(22, 188)(23, 190)(24, 191)(25, 161)(26, 184)(27, 179)(28, 155)(29, 172)(30, 156)(31, 174)(32, 165)(33, 199)(34, 180)(35, 194)(36, 200)(37, 202)(38, 198)(39, 195)(40, 193)(41, 196)(42, 166)(43, 168)(44, 186)(45, 167)(46, 189)(47, 187)(48, 208)(49, 170)(50, 171)(51, 204)(52, 205)(53, 177)(54, 203)(55, 197)(56, 178)(57, 181)(58, 201)(59, 182)(60, 183)(61, 185)(62, 213)(63, 211)(64, 210)(65, 212)(66, 192)(67, 215)(68, 216)(69, 214)(70, 206)(71, 207)(72, 209)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E16.1052 Graph:: bipartite v = 36 e = 144 f = 78 degree seq :: [ 6^24, 12^12 ] E16.1047 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) Quotient :: dipole Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1^-2 * Y2^-3, (Y2^-1 * Y1^-1)^3, Y2 * Y1^2 * Y2^-1 * Y1^-2, (Y3^-1 * Y1^-1)^3, Y1^6, (Y2 * Y1^-1)^3, Y2 * Y1^-2 * Y2^3 * Y1^-2 ] Map:: R = (1, 73, 2, 74, 6, 78, 18, 90, 13, 85, 4, 76)(3, 75, 9, 81, 19, 91, 41, 113, 32, 104, 11, 83)(5, 77, 15, 87, 20, 92, 42, 114, 30, 102, 16, 88)(7, 79, 21, 93, 39, 111, 35, 107, 12, 84, 23, 95)(8, 80, 24, 96, 40, 112, 27, 99, 14, 86, 25, 97)(10, 82, 29, 101, 17, 89, 38, 110, 43, 115, 31, 103)(22, 94, 45, 117, 26, 98, 50, 122, 34, 106, 46, 118)(28, 100, 52, 124, 59, 131, 54, 126, 33, 105, 53, 125)(36, 108, 55, 127, 60, 132, 58, 130, 37, 109, 56, 128)(44, 116, 61, 133, 57, 129, 63, 135, 47, 119, 62, 134)(48, 120, 64, 136, 51, 123, 66, 138, 49, 121, 65, 137)(67, 139, 70, 142, 69, 141, 72, 144, 68, 140, 71, 143)(145, 217, 147, 219, 154, 226, 174, 246, 157, 229, 176, 248, 187, 259, 164, 236, 150, 222, 163, 235, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 158, 230, 148, 220, 156, 228, 178, 250, 184, 256, 162, 234, 183, 255, 170, 242, 152, 224)(153, 225, 171, 243, 195, 267, 177, 249, 155, 227, 168, 240, 192, 264, 203, 275, 185, 257, 169, 241, 193, 265, 172, 244)(159, 231, 180, 252, 188, 260, 165, 237, 160, 232, 181, 253, 191, 263, 167, 239, 186, 258, 204, 276, 201, 273, 179, 251)(173, 245, 198, 270, 213, 285, 200, 272, 175, 247, 196, 268, 211, 283, 202, 274, 182, 254, 197, 269, 212, 284, 199, 271)(189, 261, 207, 279, 216, 288, 209, 281, 190, 262, 205, 277, 214, 286, 210, 282, 194, 266, 206, 278, 215, 287, 208, 280) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 171)(10, 174)(11, 168)(12, 178)(13, 176)(14, 148)(15, 180)(16, 181)(17, 149)(18, 183)(19, 161)(20, 150)(21, 160)(22, 158)(23, 186)(24, 192)(25, 193)(26, 152)(27, 195)(28, 153)(29, 198)(30, 157)(31, 196)(32, 187)(33, 155)(34, 184)(35, 159)(36, 188)(37, 191)(38, 197)(39, 170)(40, 162)(41, 169)(42, 204)(43, 164)(44, 165)(45, 207)(46, 205)(47, 167)(48, 203)(49, 172)(50, 206)(51, 177)(52, 211)(53, 212)(54, 213)(55, 173)(56, 175)(57, 179)(58, 182)(59, 185)(60, 201)(61, 214)(62, 215)(63, 216)(64, 189)(65, 190)(66, 194)(67, 202)(68, 199)(69, 200)(70, 210)(71, 208)(72, 209)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ), ( 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 E16.1050 Graph:: bipartite v = 18 e = 144 f = 96 degree seq :: [ 12^12, 24^6 ] E16.1048 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) Quotient :: dipole Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1^2 * Y2 * Y1^-2, Y2^4 * Y1^-2, Y1^6, (Y3^-1 * Y1^-1)^3, (Y2 * Y1^-1)^3 ] Map:: R = (1, 73, 2, 74, 6, 78, 18, 90, 13, 85, 4, 76)(3, 75, 9, 81, 19, 91, 41, 113, 31, 103, 11, 83)(5, 77, 15, 87, 20, 92, 43, 115, 34, 106, 16, 88)(7, 79, 21, 93, 39, 111, 33, 105, 12, 84, 23, 95)(8, 80, 24, 96, 40, 112, 27, 99, 14, 86, 25, 97)(10, 82, 29, 101, 42, 114, 38, 110, 17, 89, 30, 102)(22, 94, 45, 117, 35, 107, 50, 122, 26, 98, 46, 118)(28, 100, 52, 124, 59, 131, 54, 126, 32, 104, 53, 125)(36, 108, 58, 130, 60, 132, 56, 128, 37, 109, 55, 127)(44, 116, 61, 133, 57, 129, 63, 135, 47, 119, 62, 134)(48, 120, 66, 138, 51, 123, 65, 137, 49, 121, 64, 136)(67, 139, 70, 142, 69, 141, 72, 144, 68, 140, 71, 143)(145, 217, 147, 219, 154, 226, 164, 236, 150, 222, 163, 235, 186, 258, 178, 250, 157, 229, 175, 247, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 184, 256, 162, 234, 183, 255, 179, 251, 158, 230, 148, 220, 156, 228, 170, 242, 152, 224)(153, 225, 171, 243, 195, 267, 203, 275, 185, 257, 169, 241, 193, 265, 176, 248, 155, 227, 168, 240, 192, 264, 172, 244)(159, 231, 180, 252, 191, 263, 167, 239, 187, 259, 204, 276, 188, 260, 165, 237, 160, 232, 181, 253, 201, 273, 177, 249)(173, 245, 198, 270, 213, 285, 202, 274, 182, 254, 197, 269, 212, 284, 200, 272, 174, 246, 196, 268, 211, 283, 199, 271)(189, 261, 207, 279, 216, 288, 210, 282, 194, 266, 206, 278, 215, 287, 209, 281, 190, 262, 205, 277, 214, 286, 208, 280) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 171)(10, 164)(11, 168)(12, 170)(13, 175)(14, 148)(15, 180)(16, 181)(17, 149)(18, 183)(19, 186)(20, 150)(21, 160)(22, 184)(23, 187)(24, 192)(25, 193)(26, 152)(27, 195)(28, 153)(29, 198)(30, 196)(31, 161)(32, 155)(33, 159)(34, 157)(35, 158)(36, 191)(37, 201)(38, 197)(39, 179)(40, 162)(41, 169)(42, 178)(43, 204)(44, 165)(45, 207)(46, 205)(47, 167)(48, 172)(49, 176)(50, 206)(51, 203)(52, 211)(53, 212)(54, 213)(55, 173)(56, 174)(57, 177)(58, 182)(59, 185)(60, 188)(61, 214)(62, 215)(63, 216)(64, 189)(65, 190)(66, 194)(67, 199)(68, 200)(69, 202)(70, 208)(71, 209)(72, 210)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ), ( 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 E16.1049 Graph:: bipartite v = 18 e = 144 f = 96 degree seq :: [ 12^12, 24^6 ] E16.1049 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) Quotient :: dipole Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3 * Y2^-1 * Y3^-2 * Y2^-1, Y3 * Y2^-1 * Y3^-2 * Y2^-1 * Y3 * Y2, Y3^4 * Y2^-1 * Y3 * Y2^-1 * Y3, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2, (Y2^-1 * Y3^-3)^2, (Y3^-1 * Y1^-1)^12 ] 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, 173, 245, 175, 247)(156, 228, 176, 248, 177, 249)(159, 231, 183, 255, 184, 256)(161, 233, 166, 238, 189, 261)(165, 237, 194, 266, 195, 267)(167, 239, 191, 263, 181, 253)(169, 241, 200, 272, 201, 273)(171, 243, 190, 262, 204, 276)(172, 244, 193, 265, 187, 259)(174, 246, 186, 258, 207, 279)(178, 250, 210, 282, 182, 254)(179, 251, 209, 281, 205, 277)(180, 252, 192, 264, 208, 280)(185, 257, 202, 274, 188, 260)(196, 268, 215, 287, 206, 278)(197, 269, 199, 271, 213, 285)(198, 270, 212, 284, 214, 286)(203, 275, 211, 283, 216, 288) 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, 179)(14, 181)(15, 149)(16, 186)(17, 188)(18, 190)(19, 191)(20, 193)(21, 151)(22, 197)(23, 152)(24, 199)(25, 192)(26, 202)(27, 196)(28, 154)(29, 168)(30, 206)(31, 204)(32, 172)(33, 209)(34, 156)(35, 162)(36, 157)(37, 211)(38, 158)(39, 212)(40, 164)(41, 159)(42, 213)(43, 160)(44, 208)(45, 215)(46, 200)(47, 175)(48, 163)(49, 203)(50, 198)(51, 177)(52, 165)(53, 184)(54, 167)(55, 182)(56, 178)(57, 183)(58, 194)(59, 170)(60, 185)(61, 173)(62, 180)(63, 201)(64, 176)(65, 216)(66, 214)(67, 207)(68, 205)(69, 195)(70, 187)(71, 210)(72, 189)(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) :: { ( 12, 24 ), ( 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E16.1048 Graph:: simple bipartite v = 96 e = 144 f = 18 degree seq :: [ 2^72, 6^24 ] E16.1050 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) Quotient :: dipole Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y2 * Y3^-1 * Y2 * Y3, (Y3 * Y2)^4, (Y2^-1 * Y3^2)^3, (Y3^-1 * Y1^-1)^12 ] 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, 169, 241)(156, 228, 174, 246, 175, 247)(159, 231, 179, 251, 167, 239)(161, 233, 182, 254, 183, 255)(165, 237, 187, 259, 181, 253)(166, 238, 188, 260, 190, 262)(171, 243, 184, 256, 193, 265)(173, 245, 198, 270, 199, 271)(176, 248, 201, 273, 197, 269)(177, 249, 185, 257, 200, 272)(178, 250, 203, 275, 180, 252)(186, 258, 211, 283, 196, 268)(189, 261, 204, 276, 207, 279)(191, 263, 215, 287, 213, 285)(192, 264, 206, 278, 212, 284)(194, 266, 214, 286, 216, 288)(195, 267, 208, 280, 202, 274)(205, 277, 210, 282, 209, 281) L = (1, 147)(2, 150)(3, 153)(4, 155)(5, 145)(6, 161)(7, 146)(8, 166)(9, 169)(10, 171)(11, 173)(12, 148)(13, 176)(14, 168)(15, 149)(16, 180)(17, 154)(18, 184)(19, 159)(20, 182)(21, 151)(22, 189)(23, 152)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 162)(30, 165)(31, 198)(32, 156)(33, 157)(34, 158)(35, 204)(36, 206)(37, 160)(38, 191)(39, 208)(40, 209)(41, 163)(42, 164)(43, 212)(44, 175)(45, 170)(46, 214)(47, 167)(48, 197)(49, 216)(50, 187)(51, 190)(52, 215)(53, 172)(54, 207)(55, 205)(56, 174)(57, 213)(58, 177)(59, 202)(60, 178)(61, 179)(62, 183)(63, 181)(64, 201)(65, 203)(66, 185)(67, 210)(68, 186)(69, 188)(70, 200)(71, 199)(72, 211)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 12, 24 ), ( 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E16.1047 Graph:: simple bipartite v = 96 e = 144 f = 18 degree seq :: [ 2^72, 6^24 ] E16.1051 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) Quotient :: dipole Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^2 * Y3^-1, Y1^2 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, Y1^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-3, (Y3 * Y1^-3)^2, Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-2 ] Map:: R = (1, 73, 2, 74, 6, 78, 16, 88, 42, 114, 41, 113, 56, 128, 24, 96, 49, 121, 32, 104, 12, 84, 4, 76)(3, 75, 9, 81, 23, 95, 57, 129, 35, 107, 13, 85, 34, 106, 37, 109, 50, 122, 44, 116, 27, 99, 10, 82)(5, 77, 14, 86, 36, 108, 66, 138, 64, 136, 28, 100, 20, 92, 7, 79, 19, 91, 48, 120, 40, 112, 15, 87)(8, 80, 21, 93, 53, 125, 31, 103, 39, 111, 52, 124, 46, 118, 17, 89, 45, 117, 68, 140, 55, 127, 22, 94)(11, 83, 29, 101, 65, 137, 58, 130, 43, 115, 33, 105, 67, 139, 60, 132, 25, 97, 18, 90, 47, 119, 30, 102)(26, 98, 61, 133, 69, 141, 54, 126, 71, 143, 63, 135, 72, 144, 51, 123, 38, 110, 59, 131, 70, 142, 62, 134)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 149)(4, 155)(5, 145)(6, 161)(7, 152)(8, 146)(9, 168)(10, 170)(11, 157)(12, 175)(13, 148)(14, 181)(15, 183)(16, 187)(17, 162)(18, 150)(19, 193)(20, 195)(21, 180)(22, 173)(23, 202)(24, 169)(25, 153)(26, 172)(27, 174)(28, 154)(29, 200)(30, 207)(31, 177)(32, 210)(33, 156)(34, 204)(35, 208)(36, 198)(37, 182)(38, 158)(39, 185)(40, 206)(41, 159)(42, 179)(43, 188)(44, 160)(45, 176)(46, 213)(47, 197)(48, 201)(49, 194)(50, 163)(51, 196)(52, 164)(53, 214)(54, 165)(55, 216)(56, 166)(57, 215)(58, 203)(59, 167)(60, 205)(61, 178)(62, 212)(63, 171)(64, 186)(65, 190)(66, 189)(67, 199)(68, 184)(69, 209)(70, 191)(71, 192)(72, 211)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.1045 Graph:: simple bipartite v = 78 e = 144 f = 36 degree seq :: [ 2^72, 24^6 ] E16.1052 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) Quotient :: dipole Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^3, (Y3 * Y2^-1)^3, (Y3 * Y1^-1)^4, (Y1^2 * Y3)^3, (Y3 * Y1 * Y3^-1 * Y1^2)^2, Y3 * Y1 * Y3 * Y1^9 ] Map:: R = (1, 73, 2, 74, 6, 78, 16, 88, 36, 108, 62, 134, 71, 143, 72, 144, 56, 128, 29, 101, 12, 84, 4, 76)(3, 75, 9, 81, 23, 95, 32, 104, 41, 113, 68, 140, 55, 127, 58, 130, 31, 103, 13, 85, 26, 98, 10, 82)(5, 77, 14, 86, 20, 92, 7, 79, 19, 91, 40, 112, 44, 116, 63, 135, 52, 124, 27, 99, 35, 107, 15, 87)(8, 80, 21, 93, 38, 110, 17, 89, 37, 109, 61, 133, 65, 137, 60, 132, 34, 106, 43, 115, 46, 118, 22, 94)(11, 83, 18, 90, 39, 111, 50, 122, 24, 96, 49, 121, 70, 142, 47, 119, 57, 129, 30, 102, 54, 126, 28, 100)(25, 97, 48, 120, 64, 136, 59, 131, 33, 105, 53, 125, 66, 138, 42, 114, 67, 139, 51, 123, 69, 141, 45, 117)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 149)(4, 155)(5, 145)(6, 161)(7, 152)(8, 146)(9, 160)(10, 169)(11, 157)(12, 166)(13, 148)(14, 176)(15, 178)(16, 168)(17, 162)(18, 150)(19, 180)(20, 186)(21, 188)(22, 174)(23, 191)(24, 153)(25, 171)(26, 194)(27, 154)(28, 197)(29, 159)(30, 156)(31, 196)(32, 177)(33, 158)(34, 173)(35, 203)(36, 185)(37, 206)(38, 208)(39, 209)(40, 202)(41, 163)(42, 187)(43, 164)(44, 189)(45, 165)(46, 213)(47, 192)(48, 167)(49, 215)(50, 195)(51, 170)(52, 200)(53, 199)(54, 182)(55, 172)(56, 175)(57, 212)(58, 211)(59, 205)(60, 193)(61, 179)(62, 207)(63, 181)(64, 198)(65, 210)(66, 183)(67, 184)(68, 216)(69, 214)(70, 190)(71, 204)(72, 201)(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, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.1046 Graph:: simple bipartite v = 78 e = 144 f = 36 degree seq :: [ 2^72, 24^6 ] E16.1053 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) Quotient :: dipole Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y3^2 * Y1^-1, Y3 * Y1^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^2 * Y1^-1, Y2^2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y3, Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2, Y2^-5 * Y3 * Y2^-1 * Y1^-1, Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y2^3 * Y3 * Y2^3 * Y1^-1, Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * R * Y2^3 * R * Y2^-2, Y2^2 * Y1 * Y2^2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^6 ] 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, 33, 105)(15, 87, 39, 111, 40, 112)(17, 89, 44, 116, 46, 118)(21, 93, 36, 108, 51, 123)(22, 94, 42, 114, 54, 126)(23, 95, 55, 127, 56, 128)(25, 97, 59, 131, 52, 124)(27, 99, 30, 102, 63, 135)(28, 100, 35, 107, 43, 115)(34, 106, 49, 121, 66, 138)(37, 109, 47, 119, 48, 120)(38, 110, 50, 122, 60, 132)(41, 113, 65, 137, 57, 129)(45, 117, 69, 141, 53, 125)(58, 130, 71, 143, 67, 139)(61, 133, 62, 134, 70, 142)(64, 136, 72, 144, 68, 140)(145, 217, 147, 219, 153, 225, 169, 241, 204, 276, 177, 249, 187, 259, 160, 232, 186, 258, 185, 257, 159, 231, 149, 221)(146, 218, 150, 222, 161, 233, 189, 261, 182, 254, 158, 230, 181, 253, 173, 245, 198, 270, 196, 268, 165, 237, 151, 223)(148, 220, 155, 227, 174, 246, 209, 281, 194, 266, 164, 236, 167, 239, 152, 224, 166, 238, 197, 269, 178, 250, 156, 228)(154, 226, 171, 243, 206, 278, 183, 255, 176, 248, 200, 272, 202, 274, 168, 240, 201, 273, 210, 282, 208, 280, 172, 244)(157, 229, 179, 251, 211, 283, 188, 260, 203, 275, 184, 256, 212, 284, 191, 263, 162, 234, 170, 242, 205, 277, 180, 252)(163, 235, 192, 264, 215, 287, 207, 279, 213, 285, 195, 267, 216, 288, 199, 271, 175, 247, 190, 262, 214, 286, 193, 265) L = (1, 148)(2, 145)(3, 154)(4, 146)(5, 158)(6, 162)(7, 164)(8, 147)(9, 170)(10, 152)(11, 175)(12, 177)(13, 149)(14, 157)(15, 184)(16, 150)(17, 190)(18, 160)(19, 151)(20, 163)(21, 195)(22, 198)(23, 200)(24, 153)(25, 196)(26, 168)(27, 207)(28, 187)(29, 155)(30, 171)(31, 173)(32, 156)(33, 176)(34, 210)(35, 172)(36, 165)(37, 192)(38, 204)(39, 159)(40, 183)(41, 201)(42, 166)(43, 179)(44, 161)(45, 197)(46, 188)(47, 181)(48, 191)(49, 178)(50, 182)(51, 180)(52, 203)(53, 213)(54, 186)(55, 167)(56, 199)(57, 209)(58, 211)(59, 169)(60, 194)(61, 214)(62, 205)(63, 174)(64, 212)(65, 185)(66, 193)(67, 215)(68, 216)(69, 189)(70, 206)(71, 202)(72, 208)(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, 12, 2, 12, 2, 12 ), ( 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 E16.1056 Graph:: bipartite v = 30 e = 144 f = 84 degree seq :: [ 6^24, 24^6 ] E16.1054 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) Quotient :: dipole Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y1^-1, Y1^2 * Y3^-1, (R * Y3^-1)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-3 * Y3^-1, Y2^-1 * Y3 * Y2^3 * Y1^-1, Y2^-1 * Y1 * Y2 * Y1 * Y2^-2, R * Y2^-1 * R * Y3 * Y2^-1 * Y3^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2 * Y1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y1 * Y2^2 * Y1 * Y2^2 * Y3^-1 * Y2^2, Y1 * Y2 * Y3^-1 * Y2^9, (Y3 * Y2^-1)^6 ] 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, 25, 97)(11, 83, 28, 100, 29, 101)(12, 84, 30, 102, 31, 103)(15, 87, 27, 99, 35, 107)(17, 89, 37, 109, 38, 110)(21, 93, 40, 112, 43, 115)(22, 94, 36, 108, 45, 117)(23, 95, 46, 118, 47, 119)(26, 98, 51, 123, 41, 113)(32, 104, 54, 126, 57, 129)(33, 105, 53, 125, 58, 130)(34, 106, 42, 114, 56, 128)(39, 111, 65, 137, 55, 127)(44, 116, 60, 132, 68, 140)(48, 120, 62, 134, 67, 139)(49, 121, 64, 136, 59, 131)(50, 122, 71, 143, 70, 142)(52, 124, 66, 138, 63, 135)(61, 133, 69, 141, 72, 144)(145, 217, 147, 219, 153, 225, 160, 232, 180, 252, 206, 278, 209, 281, 216, 288, 200, 272, 175, 247, 159, 231, 149, 221)(146, 218, 150, 222, 161, 233, 172, 244, 189, 261, 213, 285, 202, 274, 204, 276, 178, 250, 158, 230, 165, 237, 151, 223)(148, 220, 155, 227, 167, 239, 152, 224, 166, 238, 188, 260, 195, 267, 211, 283, 186, 258, 164, 236, 176, 248, 156, 228)(154, 226, 170, 242, 193, 265, 168, 240, 192, 264, 201, 273, 215, 287, 199, 271, 174, 246, 191, 263, 196, 268, 171, 243)(157, 229, 169, 241, 194, 266, 184, 256, 162, 234, 183, 255, 207, 279, 181, 253, 205, 277, 179, 251, 203, 275, 177, 249)(163, 235, 182, 254, 208, 280, 198, 270, 173, 245, 197, 269, 214, 286, 190, 262, 212, 284, 187, 259, 210, 282, 185, 257) L = (1, 148)(2, 145)(3, 154)(4, 146)(5, 158)(6, 162)(7, 164)(8, 147)(9, 169)(10, 152)(11, 173)(12, 175)(13, 149)(14, 157)(15, 179)(16, 150)(17, 182)(18, 160)(19, 151)(20, 163)(21, 187)(22, 189)(23, 191)(24, 153)(25, 168)(26, 185)(27, 159)(28, 155)(29, 172)(30, 156)(31, 174)(32, 201)(33, 202)(34, 200)(35, 171)(36, 166)(37, 161)(38, 181)(39, 199)(40, 165)(41, 195)(42, 178)(43, 184)(44, 212)(45, 180)(46, 167)(47, 190)(48, 211)(49, 203)(50, 214)(51, 170)(52, 207)(53, 177)(54, 176)(55, 209)(56, 186)(57, 198)(58, 197)(59, 208)(60, 188)(61, 216)(62, 192)(63, 210)(64, 193)(65, 183)(66, 196)(67, 206)(68, 204)(69, 205)(70, 215)(71, 194)(72, 213)(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, 12, 2, 12, 2, 12 ), ( 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 E16.1055 Graph:: bipartite v = 30 e = 144 f = 84 degree seq :: [ 6^24, 24^6 ] E16.1055 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) Quotient :: dipole Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-3 * Y1^-2 * Y3^-1, Y1^6, Y1^-1 * Y3 * Y1^2 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^3, (Y3 * Y1^-1)^3, Y3 * Y1^-2 * Y3^3 * Y1^-2, (Y3 * Y2^-1)^12 ] Map:: R = (1, 73, 2, 74, 6, 78, 18, 90, 13, 85, 4, 76)(3, 75, 9, 81, 19, 91, 41, 113, 32, 104, 11, 83)(5, 77, 15, 87, 20, 92, 42, 114, 30, 102, 16, 88)(7, 79, 21, 93, 39, 111, 35, 107, 12, 84, 23, 95)(8, 80, 24, 96, 40, 112, 27, 99, 14, 86, 25, 97)(10, 82, 29, 101, 17, 89, 38, 110, 43, 115, 31, 103)(22, 94, 45, 117, 26, 98, 50, 122, 34, 106, 46, 118)(28, 100, 52, 124, 59, 131, 54, 126, 33, 105, 53, 125)(36, 108, 55, 127, 60, 132, 58, 130, 37, 109, 56, 128)(44, 116, 61, 133, 57, 129, 63, 135, 47, 119, 62, 134)(48, 120, 64, 136, 51, 123, 66, 138, 49, 121, 65, 137)(67, 139, 70, 142, 69, 141, 72, 144, 68, 140, 71, 143)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 171)(10, 174)(11, 168)(12, 178)(13, 176)(14, 148)(15, 180)(16, 181)(17, 149)(18, 183)(19, 161)(20, 150)(21, 160)(22, 158)(23, 186)(24, 192)(25, 193)(26, 152)(27, 195)(28, 153)(29, 198)(30, 157)(31, 196)(32, 187)(33, 155)(34, 184)(35, 159)(36, 188)(37, 191)(38, 197)(39, 170)(40, 162)(41, 169)(42, 204)(43, 164)(44, 165)(45, 207)(46, 205)(47, 167)(48, 203)(49, 172)(50, 206)(51, 177)(52, 211)(53, 212)(54, 213)(55, 173)(56, 175)(57, 179)(58, 182)(59, 185)(60, 201)(61, 214)(62, 215)(63, 216)(64, 189)(65, 190)(66, 194)(67, 202)(68, 199)(69, 200)(70, 210)(71, 208)(72, 209)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E16.1054 Graph:: simple bipartite v = 84 e = 144 f = 30 degree seq :: [ 2^72, 12^12 ] E16.1056 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 12}) Quotient :: dipole Aut^+ = C3 x S4 (small group id <72, 42>) Aut = S3 x S4 (small group id <144, 183>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^3 * Y1^-2 * Y3, Y1^6, (Y3 * Y1^-1)^3, (Y3^-1 * Y1^-1)^3, Y3 * Y1^2 * Y3^-1 * Y1^-2, (Y3 * Y2^-1)^12 ] Map:: R = (1, 73, 2, 74, 6, 78, 18, 90, 13, 85, 4, 76)(3, 75, 9, 81, 19, 91, 41, 113, 31, 103, 11, 83)(5, 77, 15, 87, 20, 92, 43, 115, 34, 106, 16, 88)(7, 79, 21, 93, 39, 111, 33, 105, 12, 84, 23, 95)(8, 80, 24, 96, 40, 112, 27, 99, 14, 86, 25, 97)(10, 82, 29, 101, 42, 114, 38, 110, 17, 89, 30, 102)(22, 94, 45, 117, 35, 107, 50, 122, 26, 98, 46, 118)(28, 100, 52, 124, 59, 131, 54, 126, 32, 104, 53, 125)(36, 108, 58, 130, 60, 132, 56, 128, 37, 109, 55, 127)(44, 116, 61, 133, 57, 129, 63, 135, 47, 119, 62, 134)(48, 120, 66, 138, 51, 123, 65, 137, 49, 121, 64, 136)(67, 139, 70, 142, 69, 141, 72, 144, 68, 140, 71, 143)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 171)(10, 164)(11, 168)(12, 170)(13, 175)(14, 148)(15, 180)(16, 181)(17, 149)(18, 183)(19, 186)(20, 150)(21, 160)(22, 184)(23, 187)(24, 192)(25, 193)(26, 152)(27, 195)(28, 153)(29, 198)(30, 196)(31, 161)(32, 155)(33, 159)(34, 157)(35, 158)(36, 191)(37, 201)(38, 197)(39, 179)(40, 162)(41, 169)(42, 178)(43, 204)(44, 165)(45, 207)(46, 205)(47, 167)(48, 172)(49, 176)(50, 206)(51, 203)(52, 211)(53, 212)(54, 213)(55, 173)(56, 174)(57, 177)(58, 182)(59, 185)(60, 188)(61, 214)(62, 215)(63, 216)(64, 189)(65, 190)(66, 194)(67, 199)(68, 200)(69, 202)(70, 208)(71, 209)(72, 210)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E16.1053 Graph:: simple bipartite v = 84 e = 144 f = 30 degree seq :: [ 2^72, 12^12 ] E16.1057 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 18, 36}) Quotient :: regular Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2 * T1, (T1 * T2 * T1^-1 * T2)^2, T1^-3 * T2 * T1^6 * T2 * T1^-3, T1^-2 * T2 * T1^-15 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 69, 65, 57, 49, 41, 33, 25, 16, 24, 15, 23, 32, 40, 48, 56, 64, 72, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 12, 22, 30, 39, 46, 55, 62, 71, 67, 59, 51, 43, 35, 27, 18, 9, 14, 6, 13, 21, 31, 38, 47, 54, 63, 70, 66, 58, 50, 42, 34, 26, 17, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 25)(19, 27)(20, 30)(22, 32)(26, 33)(28, 34)(29, 38)(31, 40)(35, 41)(36, 43)(37, 46)(39, 48)(42, 49)(44, 50)(45, 54)(47, 56)(51, 57)(52, 59)(53, 62)(55, 64)(58, 65)(60, 66)(61, 70)(63, 72)(67, 69)(68, 71) local type(s) :: { ( 18^36 ) } Outer automorphisms :: reflexible Dual of E16.1058 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 36 f = 4 degree seq :: [ 36^2 ] E16.1058 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 18, 36}) Quotient :: regular Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2 * T1, (T1 * T2 * T1^-1 * T2)^2, T1^18, (T2 * T1^-3)^12 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 12, 22, 30, 39, 46, 55, 62, 69, 66, 58, 50, 42, 34, 26, 17, 8)(6, 13, 21, 31, 38, 47, 54, 63, 68, 67, 59, 51, 43, 35, 27, 18, 9, 14)(15, 23, 32, 40, 48, 56, 64, 70, 72, 71, 65, 57, 49, 41, 33, 25, 16, 24) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 25)(19, 27)(20, 30)(22, 32)(26, 33)(28, 34)(29, 38)(31, 40)(35, 41)(36, 43)(37, 46)(39, 48)(42, 49)(44, 50)(45, 54)(47, 56)(51, 57)(52, 59)(53, 62)(55, 64)(58, 65)(60, 66)(61, 68)(63, 70)(67, 71)(69, 72) local type(s) :: { ( 36^18 ) } Outer automorphisms :: reflexible Dual of E16.1057 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 36 f = 2 degree seq :: [ 18^4 ] E16.1059 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 18, 36}) Quotient :: edge Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, (T2 * T1 * T2^-1 * T1)^2, T2^18, (T1 * T2^-3)^12 ] Map:: R = (1, 3, 8, 17, 26, 34, 42, 50, 58, 66, 60, 52, 44, 36, 28, 19, 10, 4)(2, 5, 12, 22, 30, 38, 46, 54, 62, 69, 64, 56, 48, 40, 32, 24, 14, 6)(7, 15, 25, 33, 41, 49, 57, 65, 71, 67, 59, 51, 43, 35, 27, 18, 9, 16)(11, 20, 29, 37, 45, 53, 61, 68, 72, 70, 63, 55, 47, 39, 31, 23, 13, 21)(73, 74)(75, 79)(76, 81)(77, 83)(78, 85)(80, 84)(82, 86)(87, 92)(88, 93)(89, 97)(90, 95)(91, 99)(94, 101)(96, 103)(98, 102)(100, 104)(105, 109)(106, 113)(107, 111)(108, 115)(110, 117)(112, 119)(114, 118)(116, 120)(121, 125)(122, 129)(123, 127)(124, 131)(126, 133)(128, 135)(130, 134)(132, 136)(137, 140)(138, 143)(139, 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) :: { ( 72, 72 ), ( 72^18 ) } Outer automorphisms :: reflexible Dual of E16.1063 Transitivity :: ET+ Graph:: simple bipartite v = 40 e = 72 f = 2 degree seq :: [ 2^36, 18^4 ] E16.1060 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 18, 36}) Quotient :: edge Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-2 * T2^-1 * T1 * T2^-1 * T1^-1, T1^-1 * T2 * T1^-1 * T2^-3, T2^16 * T1^-2, T1^-1 * T2 * T1^-1 * T2^6 * T1^-1 * T2 * T1^-7 ] Map:: polytopal non-degenerate R = (1, 3, 10, 24, 33, 41, 49, 57, 65, 71, 64, 54, 45, 39, 32, 18, 6, 17, 30, 20, 13, 27, 36, 44, 52, 60, 68, 70, 61, 55, 48, 38, 28, 21, 15, 5)(2, 7, 19, 11, 26, 34, 43, 50, 59, 66, 72, 62, 53, 47, 40, 29, 16, 14, 23, 9, 4, 12, 25, 35, 42, 51, 58, 67, 69, 63, 56, 46, 37, 31, 22, 8)(73, 74, 78, 88, 100, 109, 117, 125, 133, 141, 137, 131, 124, 114, 105, 98, 85, 76)(75, 81, 89, 80, 93, 101, 111, 118, 127, 134, 143, 139, 132, 122, 113, 107, 99, 83)(77, 86, 90, 103, 110, 119, 126, 135, 142, 138, 129, 123, 116, 106, 96, 84, 92, 79)(82, 91, 102, 95, 87, 94, 104, 112, 120, 128, 136, 144, 140, 130, 121, 115, 108, 97) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4^18 ), ( 4^36 ) } Outer automorphisms :: reflexible Dual of E16.1064 Transitivity :: ET+ Graph:: bipartite v = 6 e = 72 f = 36 degree seq :: [ 18^4, 36^2 ] E16.1061 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 18, 36}) Quotient :: edge Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2 * T1, (T1 * T2 * T1^-1 * T2)^2, T1^-3 * T2 * T1^6 * T2 * T1^-3, T1^-2 * T2 * T1^-15 * T2 * T1^-1 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 25)(19, 27)(20, 30)(22, 32)(26, 33)(28, 34)(29, 38)(31, 40)(35, 41)(36, 43)(37, 46)(39, 48)(42, 49)(44, 50)(45, 54)(47, 56)(51, 57)(52, 59)(53, 62)(55, 64)(58, 65)(60, 66)(61, 70)(63, 72)(67, 69)(68, 71)(73, 74, 77, 83, 92, 101, 109, 117, 125, 133, 141, 137, 129, 121, 113, 105, 97, 88, 96, 87, 95, 104, 112, 120, 128, 136, 144, 140, 132, 124, 116, 108, 100, 91, 82, 76)(75, 79, 84, 94, 102, 111, 118, 127, 134, 143, 139, 131, 123, 115, 107, 99, 90, 81, 86, 78, 85, 93, 103, 110, 119, 126, 135, 142, 138, 130, 122, 114, 106, 98, 89, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 36, 36 ), ( 36^36 ) } Outer automorphisms :: reflexible Dual of E16.1062 Transitivity :: ET+ Graph:: simple bipartite v = 38 e = 72 f = 4 degree seq :: [ 2^36, 36^2 ] E16.1062 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 18, 36}) Quotient :: loop Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, (T2 * T1 * T2^-1 * T1)^2, T2^18, (T1 * T2^-3)^12 ] Map:: R = (1, 73, 3, 75, 8, 80, 17, 89, 26, 98, 34, 106, 42, 114, 50, 122, 58, 130, 66, 138, 60, 132, 52, 124, 44, 116, 36, 108, 28, 100, 19, 91, 10, 82, 4, 76)(2, 74, 5, 77, 12, 84, 22, 94, 30, 102, 38, 110, 46, 118, 54, 126, 62, 134, 69, 141, 64, 136, 56, 128, 48, 120, 40, 112, 32, 104, 24, 96, 14, 86, 6, 78)(7, 79, 15, 87, 25, 97, 33, 105, 41, 113, 49, 121, 57, 129, 65, 137, 71, 143, 67, 139, 59, 131, 51, 123, 43, 115, 35, 107, 27, 99, 18, 90, 9, 81, 16, 88)(11, 83, 20, 92, 29, 101, 37, 109, 45, 117, 53, 125, 61, 133, 68, 140, 72, 144, 70, 142, 63, 135, 55, 127, 47, 119, 39, 111, 31, 103, 23, 95, 13, 85, 21, 93) L = (1, 74)(2, 73)(3, 79)(4, 81)(5, 83)(6, 85)(7, 75)(8, 84)(9, 76)(10, 86)(11, 77)(12, 80)(13, 78)(14, 82)(15, 92)(16, 93)(17, 97)(18, 95)(19, 99)(20, 87)(21, 88)(22, 101)(23, 90)(24, 103)(25, 89)(26, 102)(27, 91)(28, 104)(29, 94)(30, 98)(31, 96)(32, 100)(33, 109)(34, 113)(35, 111)(36, 115)(37, 105)(38, 117)(39, 107)(40, 119)(41, 106)(42, 118)(43, 108)(44, 120)(45, 110)(46, 114)(47, 112)(48, 116)(49, 125)(50, 129)(51, 127)(52, 131)(53, 121)(54, 133)(55, 123)(56, 135)(57, 122)(58, 134)(59, 124)(60, 136)(61, 126)(62, 130)(63, 128)(64, 132)(65, 140)(66, 143)(67, 142)(68, 137)(69, 144)(70, 139)(71, 138)(72, 141) local type(s) :: { ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.1061 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 72 f = 38 degree seq :: [ 36^4 ] E16.1063 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 18, 36}) Quotient :: loop Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-2 * T2^-1 * T1 * T2^-1 * T1^-1, T1^-1 * T2 * T1^-1 * T2^-3, T2^16 * T1^-2, T1^-1 * T2 * T1^-1 * T2^6 * T1^-1 * T2 * T1^-7 ] Map:: R = (1, 73, 3, 75, 10, 82, 24, 96, 33, 105, 41, 113, 49, 121, 57, 129, 65, 137, 71, 143, 64, 136, 54, 126, 45, 117, 39, 111, 32, 104, 18, 90, 6, 78, 17, 89, 30, 102, 20, 92, 13, 85, 27, 99, 36, 108, 44, 116, 52, 124, 60, 132, 68, 140, 70, 142, 61, 133, 55, 127, 48, 120, 38, 110, 28, 100, 21, 93, 15, 87, 5, 77)(2, 74, 7, 79, 19, 91, 11, 83, 26, 98, 34, 106, 43, 115, 50, 122, 59, 131, 66, 138, 72, 144, 62, 134, 53, 125, 47, 119, 40, 112, 29, 101, 16, 88, 14, 86, 23, 95, 9, 81, 4, 76, 12, 84, 25, 97, 35, 107, 42, 114, 51, 123, 58, 130, 67, 139, 69, 141, 63, 135, 56, 128, 46, 118, 37, 109, 31, 103, 22, 94, 8, 80) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 86)(6, 88)(7, 77)(8, 93)(9, 89)(10, 91)(11, 75)(12, 92)(13, 76)(14, 90)(15, 94)(16, 100)(17, 80)(18, 103)(19, 102)(20, 79)(21, 101)(22, 104)(23, 87)(24, 84)(25, 82)(26, 85)(27, 83)(28, 109)(29, 111)(30, 95)(31, 110)(32, 112)(33, 98)(34, 96)(35, 99)(36, 97)(37, 117)(38, 119)(39, 118)(40, 120)(41, 107)(42, 105)(43, 108)(44, 106)(45, 125)(46, 127)(47, 126)(48, 128)(49, 115)(50, 113)(51, 116)(52, 114)(53, 133)(54, 135)(55, 134)(56, 136)(57, 123)(58, 121)(59, 124)(60, 122)(61, 141)(62, 143)(63, 142)(64, 144)(65, 131)(66, 129)(67, 132)(68, 130)(69, 137)(70, 138)(71, 139)(72, 140) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E16.1059 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 72 f = 40 degree seq :: [ 72^2 ] E16.1064 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 18, 36}) Quotient :: loop Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2 * T1, (T1 * T2 * T1^-1 * T2)^2, T1^-3 * T2 * T1^6 * T2 * T1^-3, T1^-2 * T2 * T1^-15 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75)(2, 74, 6, 78)(4, 76, 9, 81)(5, 77, 12, 84)(7, 79, 15, 87)(8, 80, 16, 88)(10, 82, 17, 89)(11, 83, 21, 93)(13, 85, 23, 95)(14, 86, 24, 96)(18, 90, 25, 97)(19, 91, 27, 99)(20, 92, 30, 102)(22, 94, 32, 104)(26, 98, 33, 105)(28, 100, 34, 106)(29, 101, 38, 110)(31, 103, 40, 112)(35, 107, 41, 113)(36, 108, 43, 115)(37, 109, 46, 118)(39, 111, 48, 120)(42, 114, 49, 121)(44, 116, 50, 122)(45, 117, 54, 126)(47, 119, 56, 128)(51, 123, 57, 129)(52, 124, 59, 131)(53, 125, 62, 134)(55, 127, 64, 136)(58, 130, 65, 137)(60, 132, 66, 138)(61, 133, 70, 142)(63, 135, 72, 144)(67, 139, 69, 141)(68, 140, 71, 143) L = (1, 74)(2, 77)(3, 79)(4, 73)(5, 83)(6, 85)(7, 84)(8, 75)(9, 86)(10, 76)(11, 92)(12, 94)(13, 93)(14, 78)(15, 95)(16, 96)(17, 80)(18, 81)(19, 82)(20, 101)(21, 103)(22, 102)(23, 104)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 109)(30, 111)(31, 110)(32, 112)(33, 97)(34, 98)(35, 99)(36, 100)(37, 117)(38, 119)(39, 118)(40, 120)(41, 105)(42, 106)(43, 107)(44, 108)(45, 125)(46, 127)(47, 126)(48, 128)(49, 113)(50, 114)(51, 115)(52, 116)(53, 133)(54, 135)(55, 134)(56, 136)(57, 121)(58, 122)(59, 123)(60, 124)(61, 141)(62, 143)(63, 142)(64, 144)(65, 129)(66, 130)(67, 131)(68, 132)(69, 137)(70, 138)(71, 139)(72, 140) local type(s) :: { ( 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E16.1060 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 36 e = 72 f = 6 degree seq :: [ 4^36 ] E16.1065 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 36}) Quotient :: dipole Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1, (Y2^-1 * R * Y2^-1)^2, (Y2 * Y1 * Y2^-1 * Y1)^2, Y2^18, (Y3 * Y2^-1)^36 ] Map:: R = (1, 73, 2, 74)(3, 75, 7, 79)(4, 76, 9, 81)(5, 77, 11, 83)(6, 78, 13, 85)(8, 80, 12, 84)(10, 82, 14, 86)(15, 87, 20, 92)(16, 88, 21, 93)(17, 89, 25, 97)(18, 90, 23, 95)(19, 91, 27, 99)(22, 94, 29, 101)(24, 96, 31, 103)(26, 98, 30, 102)(28, 100, 32, 104)(33, 105, 37, 109)(34, 106, 41, 113)(35, 107, 39, 111)(36, 108, 43, 115)(38, 110, 45, 117)(40, 112, 47, 119)(42, 114, 46, 118)(44, 116, 48, 120)(49, 121, 53, 125)(50, 122, 57, 129)(51, 123, 55, 127)(52, 124, 59, 131)(54, 126, 61, 133)(56, 128, 63, 135)(58, 130, 62, 134)(60, 132, 64, 136)(65, 137, 68, 140)(66, 138, 71, 143)(67, 139, 70, 142)(69, 141, 72, 144)(145, 217, 147, 219, 152, 224, 161, 233, 170, 242, 178, 250, 186, 258, 194, 266, 202, 274, 210, 282, 204, 276, 196, 268, 188, 260, 180, 252, 172, 244, 163, 235, 154, 226, 148, 220)(146, 218, 149, 221, 156, 228, 166, 238, 174, 246, 182, 254, 190, 262, 198, 270, 206, 278, 213, 285, 208, 280, 200, 272, 192, 264, 184, 256, 176, 248, 168, 240, 158, 230, 150, 222)(151, 223, 159, 231, 169, 241, 177, 249, 185, 257, 193, 265, 201, 273, 209, 281, 215, 287, 211, 283, 203, 275, 195, 267, 187, 259, 179, 251, 171, 243, 162, 234, 153, 225, 160, 232)(155, 227, 164, 236, 173, 245, 181, 253, 189, 261, 197, 269, 205, 277, 212, 284, 216, 288, 214, 286, 207, 279, 199, 271, 191, 263, 183, 255, 175, 247, 167, 239, 157, 229, 165, 237) L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 155)(6, 157)(7, 147)(8, 156)(9, 148)(10, 158)(11, 149)(12, 152)(13, 150)(14, 154)(15, 164)(16, 165)(17, 169)(18, 167)(19, 171)(20, 159)(21, 160)(22, 173)(23, 162)(24, 175)(25, 161)(26, 174)(27, 163)(28, 176)(29, 166)(30, 170)(31, 168)(32, 172)(33, 181)(34, 185)(35, 183)(36, 187)(37, 177)(38, 189)(39, 179)(40, 191)(41, 178)(42, 190)(43, 180)(44, 192)(45, 182)(46, 186)(47, 184)(48, 188)(49, 197)(50, 201)(51, 199)(52, 203)(53, 193)(54, 205)(55, 195)(56, 207)(57, 194)(58, 206)(59, 196)(60, 208)(61, 198)(62, 202)(63, 200)(64, 204)(65, 212)(66, 215)(67, 214)(68, 209)(69, 216)(70, 211)(71, 210)(72, 213)(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, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) } Outer automorphisms :: reflexible Dual of E16.1068 Graph:: bipartite v = 40 e = 144 f = 74 degree seq :: [ 4^36, 36^4 ] E16.1066 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 36}) Quotient :: dipole Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y3^-1 * Y1^-1)^2, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2^7 * Y1^-1 * Y2^3 * Y1^-7, Y1^18, Y2^36 ] Map:: R = (1, 73, 2, 74, 6, 78, 16, 88, 28, 100, 37, 109, 45, 117, 53, 125, 61, 133, 69, 141, 65, 137, 59, 131, 52, 124, 42, 114, 33, 105, 26, 98, 13, 85, 4, 76)(3, 75, 9, 81, 17, 89, 8, 80, 21, 93, 29, 101, 39, 111, 46, 118, 55, 127, 62, 134, 71, 143, 67, 139, 60, 132, 50, 122, 41, 113, 35, 107, 27, 99, 11, 83)(5, 77, 14, 86, 18, 90, 31, 103, 38, 110, 47, 119, 54, 126, 63, 135, 70, 142, 66, 138, 57, 129, 51, 123, 44, 116, 34, 106, 24, 96, 12, 84, 20, 92, 7, 79)(10, 82, 19, 91, 30, 102, 23, 95, 15, 87, 22, 94, 32, 104, 40, 112, 48, 120, 56, 128, 64, 136, 72, 144, 68, 140, 58, 130, 49, 121, 43, 115, 36, 108, 25, 97)(145, 217, 147, 219, 154, 226, 168, 240, 177, 249, 185, 257, 193, 265, 201, 273, 209, 281, 215, 287, 208, 280, 198, 270, 189, 261, 183, 255, 176, 248, 162, 234, 150, 222, 161, 233, 174, 246, 164, 236, 157, 229, 171, 243, 180, 252, 188, 260, 196, 268, 204, 276, 212, 284, 214, 286, 205, 277, 199, 271, 192, 264, 182, 254, 172, 244, 165, 237, 159, 231, 149, 221)(146, 218, 151, 223, 163, 235, 155, 227, 170, 242, 178, 250, 187, 259, 194, 266, 203, 275, 210, 282, 216, 288, 206, 278, 197, 269, 191, 263, 184, 256, 173, 245, 160, 232, 158, 230, 167, 239, 153, 225, 148, 220, 156, 228, 169, 241, 179, 251, 186, 258, 195, 267, 202, 274, 211, 283, 213, 285, 207, 279, 200, 272, 190, 262, 181, 253, 175, 247, 166, 238, 152, 224) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 161)(7, 163)(8, 146)(9, 148)(10, 168)(11, 170)(12, 169)(13, 171)(14, 167)(15, 149)(16, 158)(17, 174)(18, 150)(19, 155)(20, 157)(21, 159)(22, 152)(23, 153)(24, 177)(25, 179)(26, 178)(27, 180)(28, 165)(29, 160)(30, 164)(31, 166)(32, 162)(33, 185)(34, 187)(35, 186)(36, 188)(37, 175)(38, 172)(39, 176)(40, 173)(41, 193)(42, 195)(43, 194)(44, 196)(45, 183)(46, 181)(47, 184)(48, 182)(49, 201)(50, 203)(51, 202)(52, 204)(53, 191)(54, 189)(55, 192)(56, 190)(57, 209)(58, 211)(59, 210)(60, 212)(61, 199)(62, 197)(63, 200)(64, 198)(65, 215)(66, 216)(67, 213)(68, 214)(69, 207)(70, 205)(71, 208)(72, 206)(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, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E16.1067 Graph:: bipartite v = 6 e = 144 f = 108 degree seq :: [ 36^4, 72^2 ] E16.1067 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 36}) Quotient :: dipole Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1, (Y3^-1 * Y2 * Y3 * Y2)^2, Y3^17 * Y2 * Y3 * Y2, (Y2 * Y3^3)^6, (Y3^-1 * Y1^-1)^36 ] 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)(147, 219, 151, 223)(148, 220, 153, 225)(149, 221, 155, 227)(150, 222, 157, 229)(152, 224, 156, 228)(154, 226, 158, 230)(159, 231, 164, 236)(160, 232, 165, 237)(161, 233, 169, 241)(162, 234, 167, 239)(163, 235, 171, 243)(166, 238, 173, 245)(168, 240, 175, 247)(170, 242, 174, 246)(172, 244, 176, 248)(177, 249, 181, 253)(178, 250, 185, 257)(179, 251, 183, 255)(180, 252, 187, 259)(182, 254, 189, 261)(184, 256, 191, 263)(186, 258, 190, 262)(188, 260, 192, 264)(193, 265, 197, 269)(194, 266, 201, 273)(195, 267, 199, 271)(196, 268, 203, 275)(198, 270, 205, 277)(200, 272, 207, 279)(202, 274, 206, 278)(204, 276, 208, 280)(209, 281, 213, 285)(210, 282, 216, 288)(211, 283, 215, 287)(212, 284, 214, 286) L = (1, 147)(2, 149)(3, 152)(4, 145)(5, 156)(6, 146)(7, 159)(8, 161)(9, 160)(10, 148)(11, 164)(12, 166)(13, 165)(14, 150)(15, 169)(16, 151)(17, 170)(18, 153)(19, 154)(20, 173)(21, 155)(22, 174)(23, 157)(24, 158)(25, 177)(26, 178)(27, 162)(28, 163)(29, 181)(30, 182)(31, 167)(32, 168)(33, 185)(34, 186)(35, 171)(36, 172)(37, 189)(38, 190)(39, 175)(40, 176)(41, 193)(42, 194)(43, 179)(44, 180)(45, 197)(46, 198)(47, 183)(48, 184)(49, 201)(50, 202)(51, 187)(52, 188)(53, 205)(54, 206)(55, 191)(56, 192)(57, 209)(58, 210)(59, 195)(60, 196)(61, 213)(62, 214)(63, 199)(64, 200)(65, 216)(66, 215)(67, 203)(68, 204)(69, 212)(70, 211)(71, 207)(72, 208)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 36, 72 ), ( 36, 72, 36, 72 ) } Outer automorphisms :: reflexible Dual of E16.1066 Graph:: simple bipartite v = 108 e = 144 f = 6 degree seq :: [ 2^72, 4^36 ] E16.1068 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 36}) Quotient :: dipole Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3^2 * Y1^-1 * Y3^2 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1^-2 * Y3 * Y1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-16, Y1^-4 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 73, 2, 74, 5, 77, 11, 83, 20, 92, 29, 101, 37, 109, 45, 117, 53, 125, 61, 133, 69, 141, 65, 137, 57, 129, 49, 121, 41, 113, 33, 105, 25, 97, 16, 88, 24, 96, 15, 87, 23, 95, 32, 104, 40, 112, 48, 120, 56, 128, 64, 136, 72, 144, 68, 140, 60, 132, 52, 124, 44, 116, 36, 108, 28, 100, 19, 91, 10, 82, 4, 76)(3, 75, 7, 79, 12, 84, 22, 94, 30, 102, 39, 111, 46, 118, 55, 127, 62, 134, 71, 143, 67, 139, 59, 131, 51, 123, 43, 115, 35, 107, 27, 99, 18, 90, 9, 81, 14, 86, 6, 78, 13, 85, 21, 93, 31, 103, 38, 110, 47, 119, 54, 126, 63, 135, 70, 142, 66, 138, 58, 130, 50, 122, 42, 114, 34, 106, 26, 98, 17, 89, 8, 80)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 150)(3, 145)(4, 153)(5, 156)(6, 146)(7, 159)(8, 160)(9, 148)(10, 161)(11, 165)(12, 149)(13, 167)(14, 168)(15, 151)(16, 152)(17, 154)(18, 169)(19, 171)(20, 174)(21, 155)(22, 176)(23, 157)(24, 158)(25, 162)(26, 177)(27, 163)(28, 178)(29, 182)(30, 164)(31, 184)(32, 166)(33, 170)(34, 172)(35, 185)(36, 187)(37, 190)(38, 173)(39, 192)(40, 175)(41, 179)(42, 193)(43, 180)(44, 194)(45, 198)(46, 181)(47, 200)(48, 183)(49, 186)(50, 188)(51, 201)(52, 203)(53, 206)(54, 189)(55, 208)(56, 191)(57, 195)(58, 209)(59, 196)(60, 210)(61, 214)(62, 197)(63, 216)(64, 199)(65, 202)(66, 204)(67, 213)(68, 215)(69, 211)(70, 205)(71, 212)(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) :: { ( 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E16.1065 Graph:: simple bipartite v = 74 e = 144 f = 40 degree seq :: [ 2^72, 72^2 ] E16.1069 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 36}) Quotient :: dipole Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1, (Y2^-1 * R * Y2^-1)^2, (Y2 * Y1 * Y2^-1 * Y1)^2, Y2^17 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^18 ] Map:: R = (1, 73, 2, 74)(3, 75, 7, 79)(4, 76, 9, 81)(5, 77, 11, 83)(6, 78, 13, 85)(8, 80, 12, 84)(10, 82, 14, 86)(15, 87, 20, 92)(16, 88, 21, 93)(17, 89, 25, 97)(18, 90, 23, 95)(19, 91, 27, 99)(22, 94, 29, 101)(24, 96, 31, 103)(26, 98, 30, 102)(28, 100, 32, 104)(33, 105, 37, 109)(34, 106, 41, 113)(35, 107, 39, 111)(36, 108, 43, 115)(38, 110, 45, 117)(40, 112, 47, 119)(42, 114, 46, 118)(44, 116, 48, 120)(49, 121, 53, 125)(50, 122, 57, 129)(51, 123, 55, 127)(52, 124, 59, 131)(54, 126, 61, 133)(56, 128, 63, 135)(58, 130, 62, 134)(60, 132, 64, 136)(65, 137, 69, 141)(66, 138, 72, 144)(67, 139, 71, 143)(68, 140, 70, 142)(145, 217, 147, 219, 152, 224, 161, 233, 170, 242, 178, 250, 186, 258, 194, 266, 202, 274, 210, 282, 215, 287, 207, 279, 199, 271, 191, 263, 183, 255, 175, 247, 167, 239, 157, 229, 165, 237, 155, 227, 164, 236, 173, 245, 181, 253, 189, 261, 197, 269, 205, 277, 213, 285, 212, 284, 204, 276, 196, 268, 188, 260, 180, 252, 172, 244, 163, 235, 154, 226, 148, 220)(146, 218, 149, 221, 156, 228, 166, 238, 174, 246, 182, 254, 190, 262, 198, 270, 206, 278, 214, 286, 211, 283, 203, 275, 195, 267, 187, 259, 179, 251, 171, 243, 162, 234, 153, 225, 160, 232, 151, 223, 159, 231, 169, 241, 177, 249, 185, 257, 193, 265, 201, 273, 209, 281, 216, 288, 208, 280, 200, 272, 192, 264, 184, 256, 176, 248, 168, 240, 158, 230, 150, 222) L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 155)(6, 157)(7, 147)(8, 156)(9, 148)(10, 158)(11, 149)(12, 152)(13, 150)(14, 154)(15, 164)(16, 165)(17, 169)(18, 167)(19, 171)(20, 159)(21, 160)(22, 173)(23, 162)(24, 175)(25, 161)(26, 174)(27, 163)(28, 176)(29, 166)(30, 170)(31, 168)(32, 172)(33, 181)(34, 185)(35, 183)(36, 187)(37, 177)(38, 189)(39, 179)(40, 191)(41, 178)(42, 190)(43, 180)(44, 192)(45, 182)(46, 186)(47, 184)(48, 188)(49, 197)(50, 201)(51, 199)(52, 203)(53, 193)(54, 205)(55, 195)(56, 207)(57, 194)(58, 206)(59, 196)(60, 208)(61, 198)(62, 202)(63, 200)(64, 204)(65, 213)(66, 216)(67, 215)(68, 214)(69, 209)(70, 212)(71, 211)(72, 210)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.1070 Graph:: bipartite v = 38 e = 144 f = 76 degree seq :: [ 4^36, 72^2 ] E16.1070 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 36}) Quotient :: dipole Aut^+ = C9 x D8 (small group id <72, 10>) Aut = D8 x D18 (small group id <144, 41>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-2, Y3 * Y1^-1 * Y3^-3 * Y1^-1, Y1^-1 * Y3 * Y1^-1 * Y3^6 * Y1^-1 * Y3 * Y1^-7, (Y3 * Y2^-1)^36 ] Map:: R = (1, 73, 2, 74, 6, 78, 16, 88, 28, 100, 37, 109, 45, 117, 53, 125, 61, 133, 69, 141, 65, 137, 59, 131, 52, 124, 42, 114, 33, 105, 26, 98, 13, 85, 4, 76)(3, 75, 9, 81, 17, 89, 8, 80, 21, 93, 29, 101, 39, 111, 46, 118, 55, 127, 62, 134, 71, 143, 67, 139, 60, 132, 50, 122, 41, 113, 35, 107, 27, 99, 11, 83)(5, 77, 14, 86, 18, 90, 31, 103, 38, 110, 47, 119, 54, 126, 63, 135, 70, 142, 66, 138, 57, 129, 51, 123, 44, 116, 34, 106, 24, 96, 12, 84, 20, 92, 7, 79)(10, 82, 19, 91, 30, 102, 23, 95, 15, 87, 22, 94, 32, 104, 40, 112, 48, 120, 56, 128, 64, 136, 72, 144, 68, 140, 58, 130, 49, 121, 43, 115, 36, 108, 25, 97)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 161)(7, 163)(8, 146)(9, 148)(10, 168)(11, 170)(12, 169)(13, 171)(14, 167)(15, 149)(16, 158)(17, 174)(18, 150)(19, 155)(20, 157)(21, 159)(22, 152)(23, 153)(24, 177)(25, 179)(26, 178)(27, 180)(28, 165)(29, 160)(30, 164)(31, 166)(32, 162)(33, 185)(34, 187)(35, 186)(36, 188)(37, 175)(38, 172)(39, 176)(40, 173)(41, 193)(42, 195)(43, 194)(44, 196)(45, 183)(46, 181)(47, 184)(48, 182)(49, 201)(50, 203)(51, 202)(52, 204)(53, 191)(54, 189)(55, 192)(56, 190)(57, 209)(58, 211)(59, 210)(60, 212)(61, 199)(62, 197)(63, 200)(64, 198)(65, 215)(66, 216)(67, 213)(68, 214)(69, 207)(70, 205)(71, 208)(72, 206)(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, 72 ), ( 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72 ) } Outer automorphisms :: reflexible Dual of E16.1069 Graph:: simple bipartite v = 76 e = 144 f = 38 degree seq :: [ 2^72, 36^4 ] E16.1071 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 10, 40}) Quotient :: regular Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1 * T2 * T1^-2 * T2 * T1^-1 * T2 * T1^2, T2 * T1^4 * T2 * T1^-4, (T1^-1 * T2 * T1^-4)^2, (T2 * T1^-2 * T2 * T1^2)^2 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 43, 66, 58, 34, 17, 29, 49, 71, 55, 75, 80, 77, 59, 35, 53, 74, 56, 32, 52, 73, 79, 78, 60, 76, 57, 33, 16, 28, 48, 70, 65, 42, 22, 10, 4)(3, 7, 15, 31, 44, 68, 62, 38, 20, 9, 19, 37, 46, 24, 45, 69, 63, 40, 21, 39, 50, 26, 12, 25, 47, 72, 64, 41, 54, 30, 14, 6, 13, 27, 51, 67, 61, 36, 18, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 55)(36, 60)(37, 56)(38, 59)(39, 57)(40, 58)(42, 61)(43, 67)(45, 70)(46, 71)(47, 73)(50, 74)(51, 75)(54, 76)(62, 78)(63, 77)(64, 66)(65, 68)(69, 79)(72, 80) local type(s) :: { ( 10^40 ) } Outer automorphisms :: reflexible Dual of E16.1072 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 40 f = 8 degree seq :: [ 40^2 ] E16.1072 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 10, 40}) Quotient :: regular Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^10, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, (T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3)^8 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 32, 31, 19, 10, 4)(3, 7, 12, 22, 33, 47, 43, 28, 17, 8)(6, 13, 21, 34, 46, 45, 30, 18, 9, 14)(15, 25, 35, 49, 60, 57, 42, 27, 16, 26)(23, 36, 48, 61, 59, 44, 29, 38, 24, 37)(39, 53, 62, 74, 71, 56, 41, 55, 40, 54)(50, 63, 73, 72, 58, 66, 52, 65, 51, 64)(67, 75, 80, 79, 70, 78, 69, 77, 68, 76) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 33)(22, 35)(25, 39)(26, 40)(27, 41)(28, 42)(31, 43)(32, 46)(34, 48)(36, 50)(37, 51)(38, 52)(44, 58)(45, 59)(47, 60)(49, 62)(53, 67)(54, 68)(55, 69)(56, 70)(57, 71)(61, 73)(63, 75)(64, 76)(65, 77)(66, 78)(72, 79)(74, 80) local type(s) :: { ( 40^10 ) } Outer automorphisms :: reflexible Dual of E16.1071 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 8 e = 40 f = 2 degree seq :: [ 10^8 ] E16.1073 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 40}) Quotient :: edge Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^10, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3)^8 ] Map:: R = (1, 3, 8, 17, 28, 43, 31, 19, 10, 4)(2, 5, 12, 22, 35, 50, 38, 24, 14, 6)(7, 15, 26, 41, 56, 45, 30, 18, 9, 16)(11, 20, 33, 48, 63, 52, 37, 23, 13, 21)(25, 39, 54, 69, 59, 44, 29, 42, 27, 40)(32, 46, 61, 75, 66, 51, 36, 49, 34, 47)(53, 67, 79, 72, 58, 71, 57, 70, 55, 68)(60, 73, 80, 78, 65, 77, 64, 76, 62, 74)(81, 82)(83, 87)(84, 89)(85, 91)(86, 93)(88, 92)(90, 94)(95, 105)(96, 107)(97, 106)(98, 109)(99, 110)(100, 112)(101, 114)(102, 113)(103, 116)(104, 117)(108, 115)(111, 118)(119, 133)(120, 135)(121, 134)(122, 137)(123, 136)(124, 138)(125, 139)(126, 140)(127, 142)(128, 141)(129, 144)(130, 143)(131, 145)(132, 146)(147, 153)(148, 154)(149, 159)(150, 156)(151, 157)(152, 158)(155, 160) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 80, 80 ), ( 80^10 ) } Outer automorphisms :: reflexible Dual of E16.1077 Transitivity :: ET+ Graph:: simple bipartite v = 48 e = 80 f = 2 degree seq :: [ 2^40, 10^8 ] E16.1074 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 40}) Quotient :: edge Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ F^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-3 * T2^-1 * T1, T1^2 * T2 * T1^-1 * T2 * T1, T2^-1 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-1 * T1, T2^-1 * T1 * T2 * T1^-3 * T2 * T1 * T2^-1 * T1, T1^-1 * T2 * T1^-1 * T2 * T1^-6, T2^3 * T1^-1 * T2^-5 * T1^-1, T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 48, 66, 38, 18, 6, 17, 36, 64, 78, 70, 55, 61, 34, 21, 42, 71, 80, 68, 41, 30, 53, 62, 43, 72, 79, 67, 39, 20, 13, 28, 51, 73, 59, 33, 15, 5)(2, 7, 19, 40, 69, 49, 63, 35, 16, 14, 31, 56, 77, 47, 26, 50, 60, 37, 32, 57, 76, 46, 24, 11, 27, 52, 65, 58, 75, 45, 23, 9, 4, 12, 29, 54, 74, 44, 22, 8)(81, 82, 86, 96, 114, 140, 133, 107, 93, 84)(83, 89, 97, 88, 101, 115, 142, 130, 108, 91)(85, 94, 98, 117, 141, 132, 110, 92, 100, 87)(90, 104, 116, 103, 122, 102, 123, 143, 131, 106)(95, 112, 118, 145, 135, 109, 121, 99, 119, 111)(105, 127, 144, 126, 151, 125, 152, 124, 153, 129)(113, 138, 146, 134, 150, 120, 148, 136, 147, 137)(128, 149, 158, 157, 160, 156, 159, 155, 139, 154) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4^10 ), ( 4^40 ) } Outer automorphisms :: reflexible Dual of E16.1078 Transitivity :: ET+ Graph:: bipartite v = 10 e = 80 f = 40 degree seq :: [ 10^8, 40^2 ] E16.1075 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 40}) Quotient :: edge Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-4 * T2 * T1^4, (T1^-1 * T2 * T1^-4)^2, (T2 * T1^-2 * T2 * T1^2)^2 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 55)(36, 60)(37, 56)(38, 59)(39, 57)(40, 58)(42, 61)(43, 67)(45, 70)(46, 71)(47, 73)(50, 74)(51, 75)(54, 76)(62, 78)(63, 77)(64, 66)(65, 68)(69, 79)(72, 80)(81, 82, 85, 91, 103, 123, 146, 138, 114, 97, 109, 129, 151, 135, 155, 160, 157, 139, 115, 133, 154, 136, 112, 132, 153, 159, 158, 140, 156, 137, 113, 96, 108, 128, 150, 145, 122, 102, 90, 84)(83, 87, 95, 111, 124, 148, 142, 118, 100, 89, 99, 117, 126, 104, 125, 149, 143, 120, 101, 119, 130, 106, 92, 105, 127, 152, 144, 121, 134, 110, 94, 86, 93, 107, 131, 147, 141, 116, 98, 88) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 20 ), ( 20^40 ) } Outer automorphisms :: reflexible Dual of E16.1076 Transitivity :: ET+ Graph:: simple bipartite v = 42 e = 80 f = 8 degree seq :: [ 2^40, 40^2 ] E16.1076 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 40}) Quotient :: loop Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^10, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3)^8 ] Map:: R = (1, 81, 3, 83, 8, 88, 17, 97, 28, 108, 43, 123, 31, 111, 19, 99, 10, 90, 4, 84)(2, 82, 5, 85, 12, 92, 22, 102, 35, 115, 50, 130, 38, 118, 24, 104, 14, 94, 6, 86)(7, 87, 15, 95, 26, 106, 41, 121, 56, 136, 45, 125, 30, 110, 18, 98, 9, 89, 16, 96)(11, 91, 20, 100, 33, 113, 48, 128, 63, 143, 52, 132, 37, 117, 23, 103, 13, 93, 21, 101)(25, 105, 39, 119, 54, 134, 69, 149, 59, 139, 44, 124, 29, 109, 42, 122, 27, 107, 40, 120)(32, 112, 46, 126, 61, 141, 75, 155, 66, 146, 51, 131, 36, 116, 49, 129, 34, 114, 47, 127)(53, 133, 67, 147, 79, 159, 72, 152, 58, 138, 71, 151, 57, 137, 70, 150, 55, 135, 68, 148)(60, 140, 73, 153, 80, 160, 78, 158, 65, 145, 77, 157, 64, 144, 76, 156, 62, 142, 74, 154) L = (1, 82)(2, 81)(3, 87)(4, 89)(5, 91)(6, 93)(7, 83)(8, 92)(9, 84)(10, 94)(11, 85)(12, 88)(13, 86)(14, 90)(15, 105)(16, 107)(17, 106)(18, 109)(19, 110)(20, 112)(21, 114)(22, 113)(23, 116)(24, 117)(25, 95)(26, 97)(27, 96)(28, 115)(29, 98)(30, 99)(31, 118)(32, 100)(33, 102)(34, 101)(35, 108)(36, 103)(37, 104)(38, 111)(39, 133)(40, 135)(41, 134)(42, 137)(43, 136)(44, 138)(45, 139)(46, 140)(47, 142)(48, 141)(49, 144)(50, 143)(51, 145)(52, 146)(53, 119)(54, 121)(55, 120)(56, 123)(57, 122)(58, 124)(59, 125)(60, 126)(61, 128)(62, 127)(63, 130)(64, 129)(65, 131)(66, 132)(67, 153)(68, 154)(69, 159)(70, 156)(71, 157)(72, 158)(73, 147)(74, 148)(75, 160)(76, 150)(77, 151)(78, 152)(79, 149)(80, 155) local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) } Outer automorphisms :: reflexible Dual of E16.1075 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 80 f = 42 degree seq :: [ 20^8 ] E16.1077 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 40}) Quotient :: loop Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ F^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-3 * T2^-1 * T1, T1^2 * T2 * T1^-1 * T2 * T1, T2^-1 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-1 * T1, T2^-1 * T1 * T2 * T1^-3 * T2 * T1 * T2^-1 * T1, T1^-1 * T2 * T1^-1 * T2 * T1^-6, T2^3 * T1^-1 * T2^-5 * T1^-1, T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-2 ] Map:: R = (1, 81, 3, 83, 10, 90, 25, 105, 48, 128, 66, 146, 38, 118, 18, 98, 6, 86, 17, 97, 36, 116, 64, 144, 78, 158, 70, 150, 55, 135, 61, 141, 34, 114, 21, 101, 42, 122, 71, 151, 80, 160, 68, 148, 41, 121, 30, 110, 53, 133, 62, 142, 43, 123, 72, 152, 79, 159, 67, 147, 39, 119, 20, 100, 13, 93, 28, 108, 51, 131, 73, 153, 59, 139, 33, 113, 15, 95, 5, 85)(2, 82, 7, 87, 19, 99, 40, 120, 69, 149, 49, 129, 63, 143, 35, 115, 16, 96, 14, 94, 31, 111, 56, 136, 77, 157, 47, 127, 26, 106, 50, 130, 60, 140, 37, 117, 32, 112, 57, 137, 76, 156, 46, 126, 24, 104, 11, 91, 27, 107, 52, 132, 65, 145, 58, 138, 75, 155, 45, 125, 23, 103, 9, 89, 4, 84, 12, 92, 29, 109, 54, 134, 74, 154, 44, 124, 22, 102, 8, 88) L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 94)(6, 96)(7, 85)(8, 101)(9, 97)(10, 104)(11, 83)(12, 100)(13, 84)(14, 98)(15, 112)(16, 114)(17, 88)(18, 117)(19, 119)(20, 87)(21, 115)(22, 123)(23, 122)(24, 116)(25, 127)(26, 90)(27, 93)(28, 91)(29, 121)(30, 92)(31, 95)(32, 118)(33, 138)(34, 140)(35, 142)(36, 103)(37, 141)(38, 145)(39, 111)(40, 148)(41, 99)(42, 102)(43, 143)(44, 153)(45, 152)(46, 151)(47, 144)(48, 149)(49, 105)(50, 108)(51, 106)(52, 110)(53, 107)(54, 150)(55, 109)(56, 147)(57, 113)(58, 146)(59, 154)(60, 133)(61, 132)(62, 130)(63, 131)(64, 126)(65, 135)(66, 134)(67, 137)(68, 136)(69, 158)(70, 120)(71, 125)(72, 124)(73, 129)(74, 128)(75, 139)(76, 159)(77, 160)(78, 157)(79, 155)(80, 156) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.1073 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 80 f = 48 degree seq :: [ 80^2 ] E16.1078 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 40}) Quotient :: loop Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-4 * T2 * T1^4, (T1^-1 * T2 * T1^-4)^2, (T2 * T1^-2 * T2 * T1^2)^2 ] Map:: polytopal non-degenerate R = (1, 81, 3, 83)(2, 82, 6, 86)(4, 84, 9, 89)(5, 85, 12, 92)(7, 87, 16, 96)(8, 88, 17, 97)(10, 90, 21, 101)(11, 91, 24, 104)(13, 93, 28, 108)(14, 94, 29, 109)(15, 95, 32, 112)(18, 98, 35, 115)(19, 99, 33, 113)(20, 100, 34, 114)(22, 102, 41, 121)(23, 103, 44, 124)(25, 105, 48, 128)(26, 106, 49, 129)(27, 107, 52, 132)(30, 110, 53, 133)(31, 111, 55, 135)(36, 116, 60, 140)(37, 117, 56, 136)(38, 118, 59, 139)(39, 119, 57, 137)(40, 120, 58, 138)(42, 122, 61, 141)(43, 123, 67, 147)(45, 125, 70, 150)(46, 126, 71, 151)(47, 127, 73, 153)(50, 130, 74, 154)(51, 131, 75, 155)(54, 134, 76, 156)(62, 142, 78, 158)(63, 143, 77, 157)(64, 144, 66, 146)(65, 145, 68, 148)(69, 149, 79, 159)(72, 152, 80, 160) L = (1, 82)(2, 85)(3, 87)(4, 81)(5, 91)(6, 93)(7, 95)(8, 83)(9, 99)(10, 84)(11, 103)(12, 105)(13, 107)(14, 86)(15, 111)(16, 108)(17, 109)(18, 88)(19, 117)(20, 89)(21, 119)(22, 90)(23, 123)(24, 125)(25, 127)(26, 92)(27, 131)(28, 128)(29, 129)(30, 94)(31, 124)(32, 132)(33, 96)(34, 97)(35, 133)(36, 98)(37, 126)(38, 100)(39, 130)(40, 101)(41, 134)(42, 102)(43, 146)(44, 148)(45, 149)(46, 104)(47, 152)(48, 150)(49, 151)(50, 106)(51, 147)(52, 153)(53, 154)(54, 110)(55, 155)(56, 112)(57, 113)(58, 114)(59, 115)(60, 156)(61, 116)(62, 118)(63, 120)(64, 121)(65, 122)(66, 138)(67, 141)(68, 142)(69, 143)(70, 145)(71, 135)(72, 144)(73, 159)(74, 136)(75, 160)(76, 137)(77, 139)(78, 140)(79, 158)(80, 157) local type(s) :: { ( 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E16.1074 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 40 e = 80 f = 10 degree seq :: [ 4^40 ] E16.1079 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 40}) Quotient :: dipole Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1, Y2^10, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^40 ] Map:: R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 9, 89)(5, 85, 11, 91)(6, 86, 13, 93)(8, 88, 12, 92)(10, 90, 14, 94)(15, 95, 25, 105)(16, 96, 27, 107)(17, 97, 26, 106)(18, 98, 29, 109)(19, 99, 30, 110)(20, 100, 32, 112)(21, 101, 34, 114)(22, 102, 33, 113)(23, 103, 36, 116)(24, 104, 37, 117)(28, 108, 35, 115)(31, 111, 38, 118)(39, 119, 53, 133)(40, 120, 55, 135)(41, 121, 54, 134)(42, 122, 57, 137)(43, 123, 56, 136)(44, 124, 58, 138)(45, 125, 59, 139)(46, 126, 60, 140)(47, 127, 62, 142)(48, 128, 61, 141)(49, 129, 64, 144)(50, 130, 63, 143)(51, 131, 65, 145)(52, 132, 66, 146)(67, 147, 73, 153)(68, 148, 74, 154)(69, 149, 79, 159)(70, 150, 76, 156)(71, 151, 77, 157)(72, 152, 78, 158)(75, 155, 80, 160)(161, 241, 163, 243, 168, 248, 177, 257, 188, 268, 203, 283, 191, 271, 179, 259, 170, 250, 164, 244)(162, 242, 165, 245, 172, 252, 182, 262, 195, 275, 210, 290, 198, 278, 184, 264, 174, 254, 166, 246)(167, 247, 175, 255, 186, 266, 201, 281, 216, 296, 205, 285, 190, 270, 178, 258, 169, 249, 176, 256)(171, 251, 180, 260, 193, 273, 208, 288, 223, 303, 212, 292, 197, 277, 183, 263, 173, 253, 181, 261)(185, 265, 199, 279, 214, 294, 229, 309, 219, 299, 204, 284, 189, 269, 202, 282, 187, 267, 200, 280)(192, 272, 206, 286, 221, 301, 235, 315, 226, 306, 211, 291, 196, 276, 209, 289, 194, 274, 207, 287)(213, 293, 227, 307, 239, 319, 232, 312, 218, 298, 231, 311, 217, 297, 230, 310, 215, 295, 228, 308)(220, 300, 233, 313, 240, 320, 238, 318, 225, 305, 237, 317, 224, 304, 236, 316, 222, 302, 234, 314) L = (1, 162)(2, 161)(3, 167)(4, 169)(5, 171)(6, 173)(7, 163)(8, 172)(9, 164)(10, 174)(11, 165)(12, 168)(13, 166)(14, 170)(15, 185)(16, 187)(17, 186)(18, 189)(19, 190)(20, 192)(21, 194)(22, 193)(23, 196)(24, 197)(25, 175)(26, 177)(27, 176)(28, 195)(29, 178)(30, 179)(31, 198)(32, 180)(33, 182)(34, 181)(35, 188)(36, 183)(37, 184)(38, 191)(39, 213)(40, 215)(41, 214)(42, 217)(43, 216)(44, 218)(45, 219)(46, 220)(47, 222)(48, 221)(49, 224)(50, 223)(51, 225)(52, 226)(53, 199)(54, 201)(55, 200)(56, 203)(57, 202)(58, 204)(59, 205)(60, 206)(61, 208)(62, 207)(63, 210)(64, 209)(65, 211)(66, 212)(67, 233)(68, 234)(69, 239)(70, 236)(71, 237)(72, 238)(73, 227)(74, 228)(75, 240)(76, 230)(77, 231)(78, 232)(79, 229)(80, 235)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 80, 2, 80 ), ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ) } Outer automorphisms :: reflexible Dual of E16.1082 Graph:: bipartite v = 48 e = 160 f = 82 degree seq :: [ 4^40, 20^8 ] E16.1080 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 40}) Quotient :: dipole Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y1^-1 * Y2^-1)^2, (Y2 * Y1)^2, R * Y2 * R * Y3, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y2^-1 * Y1^-3 * Y2^-1 * Y1, Y1^-2 * Y2 * Y1^2 * Y2^-1, Y2^7 * Y1^-2 * Y2, Y2^3 * Y1^-3 * Y2^3 * Y1^-1, Y1^10 ] Map:: R = (1, 81, 2, 82, 6, 86, 16, 96, 34, 114, 60, 140, 53, 133, 27, 107, 13, 93, 4, 84)(3, 83, 9, 89, 17, 97, 8, 88, 21, 101, 35, 115, 62, 142, 50, 130, 28, 108, 11, 91)(5, 85, 14, 94, 18, 98, 37, 117, 61, 141, 52, 132, 30, 110, 12, 92, 20, 100, 7, 87)(10, 90, 24, 104, 36, 116, 23, 103, 42, 122, 22, 102, 43, 123, 63, 143, 51, 131, 26, 106)(15, 95, 32, 112, 38, 118, 65, 145, 55, 135, 29, 109, 41, 121, 19, 99, 39, 119, 31, 111)(25, 105, 47, 127, 64, 144, 46, 126, 71, 151, 45, 125, 72, 152, 44, 124, 73, 153, 49, 129)(33, 113, 58, 138, 66, 146, 54, 134, 70, 150, 40, 120, 68, 148, 56, 136, 67, 147, 57, 137)(48, 128, 69, 149, 78, 158, 77, 157, 80, 160, 76, 156, 79, 159, 75, 155, 59, 139, 74, 154)(161, 241, 163, 243, 170, 250, 185, 265, 208, 288, 226, 306, 198, 278, 178, 258, 166, 246, 177, 257, 196, 276, 224, 304, 238, 318, 230, 310, 215, 295, 221, 301, 194, 274, 181, 261, 202, 282, 231, 311, 240, 320, 228, 308, 201, 281, 190, 270, 213, 293, 222, 302, 203, 283, 232, 312, 239, 319, 227, 307, 199, 279, 180, 260, 173, 253, 188, 268, 211, 291, 233, 313, 219, 299, 193, 273, 175, 255, 165, 245)(162, 242, 167, 247, 179, 259, 200, 280, 229, 309, 209, 289, 223, 303, 195, 275, 176, 256, 174, 254, 191, 271, 216, 296, 237, 317, 207, 287, 186, 266, 210, 290, 220, 300, 197, 277, 192, 272, 217, 297, 236, 316, 206, 286, 184, 264, 171, 251, 187, 267, 212, 292, 225, 305, 218, 298, 235, 315, 205, 285, 183, 263, 169, 249, 164, 244, 172, 252, 189, 269, 214, 294, 234, 314, 204, 284, 182, 262, 168, 248) L = (1, 163)(2, 167)(3, 170)(4, 172)(5, 161)(6, 177)(7, 179)(8, 162)(9, 164)(10, 185)(11, 187)(12, 189)(13, 188)(14, 191)(15, 165)(16, 174)(17, 196)(18, 166)(19, 200)(20, 173)(21, 202)(22, 168)(23, 169)(24, 171)(25, 208)(26, 210)(27, 212)(28, 211)(29, 214)(30, 213)(31, 216)(32, 217)(33, 175)(34, 181)(35, 176)(36, 224)(37, 192)(38, 178)(39, 180)(40, 229)(41, 190)(42, 231)(43, 232)(44, 182)(45, 183)(46, 184)(47, 186)(48, 226)(49, 223)(50, 220)(51, 233)(52, 225)(53, 222)(54, 234)(55, 221)(56, 237)(57, 236)(58, 235)(59, 193)(60, 197)(61, 194)(62, 203)(63, 195)(64, 238)(65, 218)(66, 198)(67, 199)(68, 201)(69, 209)(70, 215)(71, 240)(72, 239)(73, 219)(74, 204)(75, 205)(76, 206)(77, 207)(78, 230)(79, 227)(80, 228)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E16.1081 Graph:: bipartite v = 10 e = 160 f = 120 degree seq :: [ 20^8, 80^2 ] E16.1081 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 40}) Quotient :: dipole Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1, Y3^-2 * Y2 * Y3^4 * Y2 * Y3^-2, Y3^-6 * Y2 * Y3^-1 * Y2 * Y3^-3, (Y3^-2 * Y2 * Y3^2 * Y2)^2, (Y3^-1 * Y1^-1)^40 ] Map:: polytopal R = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)(161, 241, 162, 242)(163, 243, 167, 247)(164, 244, 169, 249)(165, 245, 171, 251)(166, 246, 173, 253)(168, 248, 177, 257)(170, 250, 181, 261)(172, 252, 185, 265)(174, 254, 189, 269)(175, 255, 183, 263)(176, 256, 187, 267)(178, 258, 195, 275)(179, 259, 184, 264)(180, 260, 188, 268)(182, 262, 201, 281)(186, 266, 207, 287)(190, 270, 213, 293)(191, 271, 205, 285)(192, 272, 211, 291)(193, 273, 203, 283)(194, 274, 209, 289)(196, 276, 208, 288)(197, 277, 206, 286)(198, 278, 212, 292)(199, 279, 204, 284)(200, 280, 210, 290)(202, 282, 214, 294)(215, 295, 230, 310)(216, 296, 227, 307)(217, 297, 228, 308)(218, 298, 229, 309)(219, 299, 226, 306)(220, 300, 231, 311)(221, 301, 236, 316)(222, 302, 235, 315)(223, 303, 234, 314)(224, 304, 233, 313)(225, 305, 232, 312)(237, 317, 240, 320)(238, 318, 239, 319) L = (1, 163)(2, 165)(3, 168)(4, 161)(5, 172)(6, 162)(7, 175)(8, 178)(9, 179)(10, 164)(11, 183)(12, 186)(13, 187)(14, 166)(15, 191)(16, 167)(17, 193)(18, 196)(19, 197)(20, 169)(21, 199)(22, 170)(23, 203)(24, 171)(25, 205)(26, 208)(27, 209)(28, 173)(29, 211)(30, 174)(31, 215)(32, 176)(33, 217)(34, 177)(35, 219)(36, 221)(37, 220)(38, 180)(39, 218)(40, 181)(41, 216)(42, 182)(43, 226)(44, 184)(45, 228)(46, 185)(47, 230)(48, 232)(49, 231)(50, 188)(51, 229)(52, 189)(53, 227)(54, 190)(55, 236)(56, 192)(57, 237)(58, 194)(59, 238)(60, 195)(61, 233)(62, 198)(63, 200)(64, 201)(65, 202)(66, 225)(67, 204)(68, 239)(69, 206)(70, 240)(71, 207)(72, 222)(73, 210)(74, 212)(75, 213)(76, 214)(77, 224)(78, 223)(79, 235)(80, 234)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 20, 80 ), ( 20, 80, 20, 80 ) } Outer automorphisms :: reflexible Dual of E16.1080 Graph:: simple bipartite v = 120 e = 160 f = 10 degree seq :: [ 2^80, 4^40 ] E16.1082 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 40}) Quotient :: dipole Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1^-4 * Y3 * Y1^4, (Y3 * Y1^-2 * Y3 * Y1^2)^2, (Y1^-1 * Y3 * Y1^-4)^2 ] Map:: R = (1, 81, 2, 82, 5, 85, 11, 91, 23, 103, 43, 123, 66, 146, 58, 138, 34, 114, 17, 97, 29, 109, 49, 129, 71, 151, 55, 135, 75, 155, 80, 160, 77, 157, 59, 139, 35, 115, 53, 133, 74, 154, 56, 136, 32, 112, 52, 132, 73, 153, 79, 159, 78, 158, 60, 140, 76, 156, 57, 137, 33, 113, 16, 96, 28, 108, 48, 128, 70, 150, 65, 145, 42, 122, 22, 102, 10, 90, 4, 84)(3, 83, 7, 87, 15, 95, 31, 111, 44, 124, 68, 148, 62, 142, 38, 118, 20, 100, 9, 89, 19, 99, 37, 117, 46, 126, 24, 104, 45, 125, 69, 149, 63, 143, 40, 120, 21, 101, 39, 119, 50, 130, 26, 106, 12, 92, 25, 105, 47, 127, 72, 152, 64, 144, 41, 121, 54, 134, 30, 110, 14, 94, 6, 86, 13, 93, 27, 107, 51, 131, 67, 147, 61, 141, 36, 116, 18, 98, 8, 88)(161, 241)(162, 242)(163, 243)(164, 244)(165, 245)(166, 246)(167, 247)(168, 248)(169, 249)(170, 250)(171, 251)(172, 252)(173, 253)(174, 254)(175, 255)(176, 256)(177, 257)(178, 258)(179, 259)(180, 260)(181, 261)(182, 262)(183, 263)(184, 264)(185, 265)(186, 266)(187, 267)(188, 268)(189, 269)(190, 270)(191, 271)(192, 272)(193, 273)(194, 274)(195, 275)(196, 276)(197, 277)(198, 278)(199, 279)(200, 280)(201, 281)(202, 282)(203, 283)(204, 284)(205, 285)(206, 286)(207, 287)(208, 288)(209, 289)(210, 290)(211, 291)(212, 292)(213, 293)(214, 294)(215, 295)(216, 296)(217, 297)(218, 298)(219, 299)(220, 300)(221, 301)(222, 302)(223, 303)(224, 304)(225, 305)(226, 306)(227, 307)(228, 308)(229, 309)(230, 310)(231, 311)(232, 312)(233, 313)(234, 314)(235, 315)(236, 316)(237, 317)(238, 318)(239, 319)(240, 320) L = (1, 163)(2, 166)(3, 161)(4, 169)(5, 172)(6, 162)(7, 176)(8, 177)(9, 164)(10, 181)(11, 184)(12, 165)(13, 188)(14, 189)(15, 192)(16, 167)(17, 168)(18, 195)(19, 193)(20, 194)(21, 170)(22, 201)(23, 204)(24, 171)(25, 208)(26, 209)(27, 212)(28, 173)(29, 174)(30, 213)(31, 215)(32, 175)(33, 179)(34, 180)(35, 178)(36, 220)(37, 216)(38, 219)(39, 217)(40, 218)(41, 182)(42, 221)(43, 227)(44, 183)(45, 230)(46, 231)(47, 233)(48, 185)(49, 186)(50, 234)(51, 235)(52, 187)(53, 190)(54, 236)(55, 191)(56, 197)(57, 199)(58, 200)(59, 198)(60, 196)(61, 202)(62, 238)(63, 237)(64, 226)(65, 228)(66, 224)(67, 203)(68, 225)(69, 239)(70, 205)(71, 206)(72, 240)(73, 207)(74, 210)(75, 211)(76, 214)(77, 223)(78, 222)(79, 229)(80, 232)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E16.1079 Graph:: simple bipartite v = 82 e = 160 f = 48 degree seq :: [ 2^80, 80^2 ] E16.1083 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 40}) Quotient :: dipole Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y2^-3 * R * Y2^-1)^2, Y2^4 * Y1 * Y2^-4 * Y1, Y2^3 * Y1 * Y2 * Y1 * Y2^6, (Y2^-2 * Y1 * Y2^2 * Y1)^2, (Y3 * Y2^-1)^10 ] Map:: R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 9, 89)(5, 85, 11, 91)(6, 86, 13, 93)(8, 88, 17, 97)(10, 90, 21, 101)(12, 92, 25, 105)(14, 94, 29, 109)(15, 95, 23, 103)(16, 96, 27, 107)(18, 98, 35, 115)(19, 99, 24, 104)(20, 100, 28, 108)(22, 102, 41, 121)(26, 106, 47, 127)(30, 110, 53, 133)(31, 111, 45, 125)(32, 112, 51, 131)(33, 113, 43, 123)(34, 114, 49, 129)(36, 116, 48, 128)(37, 117, 46, 126)(38, 118, 52, 132)(39, 119, 44, 124)(40, 120, 50, 130)(42, 122, 54, 134)(55, 135, 70, 150)(56, 136, 67, 147)(57, 137, 68, 148)(58, 138, 69, 149)(59, 139, 66, 146)(60, 140, 71, 151)(61, 141, 76, 156)(62, 142, 75, 155)(63, 143, 74, 154)(64, 144, 73, 153)(65, 145, 72, 152)(77, 157, 80, 160)(78, 158, 79, 159)(161, 241, 163, 243, 168, 248, 178, 258, 196, 276, 221, 301, 233, 313, 210, 290, 188, 268, 173, 253, 187, 267, 209, 289, 231, 311, 207, 287, 230, 310, 240, 320, 234, 314, 212, 292, 189, 269, 211, 291, 229, 309, 206, 286, 185, 265, 205, 285, 228, 308, 239, 319, 235, 315, 213, 293, 227, 307, 204, 284, 184, 264, 171, 251, 183, 263, 203, 283, 226, 306, 225, 305, 202, 282, 182, 262, 170, 250, 164, 244)(162, 242, 165, 245, 172, 252, 186, 266, 208, 288, 232, 312, 222, 302, 198, 278, 180, 260, 169, 249, 179, 259, 197, 277, 220, 300, 195, 275, 219, 299, 238, 318, 223, 303, 200, 280, 181, 261, 199, 279, 218, 298, 194, 274, 177, 257, 193, 273, 217, 297, 237, 317, 224, 304, 201, 281, 216, 296, 192, 272, 176, 256, 167, 247, 175, 255, 191, 271, 215, 295, 236, 316, 214, 294, 190, 270, 174, 254, 166, 246) L = (1, 162)(2, 161)(3, 167)(4, 169)(5, 171)(6, 173)(7, 163)(8, 177)(9, 164)(10, 181)(11, 165)(12, 185)(13, 166)(14, 189)(15, 183)(16, 187)(17, 168)(18, 195)(19, 184)(20, 188)(21, 170)(22, 201)(23, 175)(24, 179)(25, 172)(26, 207)(27, 176)(28, 180)(29, 174)(30, 213)(31, 205)(32, 211)(33, 203)(34, 209)(35, 178)(36, 208)(37, 206)(38, 212)(39, 204)(40, 210)(41, 182)(42, 214)(43, 193)(44, 199)(45, 191)(46, 197)(47, 186)(48, 196)(49, 194)(50, 200)(51, 192)(52, 198)(53, 190)(54, 202)(55, 230)(56, 227)(57, 228)(58, 229)(59, 226)(60, 231)(61, 236)(62, 235)(63, 234)(64, 233)(65, 232)(66, 219)(67, 216)(68, 217)(69, 218)(70, 215)(71, 220)(72, 225)(73, 224)(74, 223)(75, 222)(76, 221)(77, 240)(78, 239)(79, 238)(80, 237)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E16.1084 Graph:: bipartite v = 42 e = 160 f = 88 degree seq :: [ 4^40, 80^2 ] E16.1084 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 40}) Quotient :: dipole Aut^+ = C5 x D16 (small group id <80, 25>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3 * Y1)^2, (Y1^-1 * Y3^-1)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^-3 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-3 * Y3^-1 * Y1, Y3^-1 * Y1 * Y3^-1 * Y1^7, Y3^3 * Y1^-3 * Y3^3 * Y1^-1, Y3^8 * Y1^-2, (Y3 * Y2^-1)^40 ] Map:: R = (1, 81, 2, 82, 6, 86, 16, 96, 34, 114, 60, 140, 53, 133, 27, 107, 13, 93, 4, 84)(3, 83, 9, 89, 17, 97, 8, 88, 21, 101, 35, 115, 62, 142, 50, 130, 28, 108, 11, 91)(5, 85, 14, 94, 18, 98, 37, 117, 61, 141, 52, 132, 30, 110, 12, 92, 20, 100, 7, 87)(10, 90, 24, 104, 36, 116, 23, 103, 42, 122, 22, 102, 43, 123, 63, 143, 51, 131, 26, 106)(15, 95, 32, 112, 38, 118, 65, 145, 55, 135, 29, 109, 41, 121, 19, 99, 39, 119, 31, 111)(25, 105, 47, 127, 64, 144, 46, 126, 71, 151, 45, 125, 72, 152, 44, 124, 73, 153, 49, 129)(33, 113, 58, 138, 66, 146, 54, 134, 70, 150, 40, 120, 68, 148, 56, 136, 67, 147, 57, 137)(48, 128, 69, 149, 78, 158, 77, 157, 80, 160, 76, 156, 79, 159, 75, 155, 59, 139, 74, 154)(161, 241)(162, 242)(163, 243)(164, 244)(165, 245)(166, 246)(167, 247)(168, 248)(169, 249)(170, 250)(171, 251)(172, 252)(173, 253)(174, 254)(175, 255)(176, 256)(177, 257)(178, 258)(179, 259)(180, 260)(181, 261)(182, 262)(183, 263)(184, 264)(185, 265)(186, 266)(187, 267)(188, 268)(189, 269)(190, 270)(191, 271)(192, 272)(193, 273)(194, 274)(195, 275)(196, 276)(197, 277)(198, 278)(199, 279)(200, 280)(201, 281)(202, 282)(203, 283)(204, 284)(205, 285)(206, 286)(207, 287)(208, 288)(209, 289)(210, 290)(211, 291)(212, 292)(213, 293)(214, 294)(215, 295)(216, 296)(217, 297)(218, 298)(219, 299)(220, 300)(221, 301)(222, 302)(223, 303)(224, 304)(225, 305)(226, 306)(227, 307)(228, 308)(229, 309)(230, 310)(231, 311)(232, 312)(233, 313)(234, 314)(235, 315)(236, 316)(237, 317)(238, 318)(239, 319)(240, 320) L = (1, 163)(2, 167)(3, 170)(4, 172)(5, 161)(6, 177)(7, 179)(8, 162)(9, 164)(10, 185)(11, 187)(12, 189)(13, 188)(14, 191)(15, 165)(16, 174)(17, 196)(18, 166)(19, 200)(20, 173)(21, 202)(22, 168)(23, 169)(24, 171)(25, 208)(26, 210)(27, 212)(28, 211)(29, 214)(30, 213)(31, 216)(32, 217)(33, 175)(34, 181)(35, 176)(36, 224)(37, 192)(38, 178)(39, 180)(40, 229)(41, 190)(42, 231)(43, 232)(44, 182)(45, 183)(46, 184)(47, 186)(48, 226)(49, 223)(50, 220)(51, 233)(52, 225)(53, 222)(54, 234)(55, 221)(56, 237)(57, 236)(58, 235)(59, 193)(60, 197)(61, 194)(62, 203)(63, 195)(64, 238)(65, 218)(66, 198)(67, 199)(68, 201)(69, 209)(70, 215)(71, 240)(72, 239)(73, 219)(74, 204)(75, 205)(76, 206)(77, 207)(78, 230)(79, 227)(80, 228)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 4, 80 ), ( 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80 ) } Outer automorphisms :: reflexible Dual of E16.1083 Graph:: simple bipartite v = 88 e = 160 f = 42 degree seq :: [ 2^80, 20^8 ] E16.1085 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 48}) Quotient :: regular Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^3 * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-3 * T2 * T1^5 * T2 * T1^-8 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 39, 53, 65, 77, 89, 84, 72, 61, 48, 32, 45, 34, 17, 29, 43, 56, 68, 80, 92, 96, 95, 85, 73, 60, 49, 33, 16, 28, 42, 35, 46, 58, 70, 82, 94, 88, 76, 64, 52, 38, 22, 10, 4)(3, 7, 15, 31, 47, 59, 71, 83, 90, 81, 67, 54, 44, 26, 12, 25, 20, 9, 19, 36, 50, 62, 74, 86, 91, 78, 69, 55, 40, 30, 14, 6, 13, 27, 21, 37, 51, 63, 75, 87, 93, 79, 66, 57, 41, 24, 18, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 31)(23, 40)(25, 42)(26, 43)(27, 45)(30, 46)(36, 48)(37, 49)(38, 50)(39, 54)(41, 56)(44, 58)(47, 60)(51, 61)(52, 63)(53, 66)(55, 68)(57, 70)(59, 72)(62, 73)(64, 71)(65, 78)(67, 80)(69, 82)(74, 84)(75, 85)(76, 86)(77, 90)(79, 92)(81, 94)(83, 95)(87, 89)(88, 93)(91, 96) local type(s) :: { ( 6^48 ) } Outer automorphisms :: reflexible Dual of E16.1086 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 48 f = 16 degree seq :: [ 48^2 ] E16.1086 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 48}) Quotient :: regular Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^6, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 ] Map:: non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 12, 20, 17, 8)(6, 13, 19, 18, 9, 14)(15, 23, 27, 25, 16, 24)(21, 28, 26, 30, 22, 29)(31, 37, 33, 39, 32, 38)(34, 40, 36, 42, 35, 41)(43, 49, 45, 51, 44, 50)(46, 52, 48, 54, 47, 53)(55, 61, 57, 63, 56, 62)(58, 64, 60, 66, 59, 65)(67, 73, 69, 75, 68, 74)(70, 76, 72, 78, 71, 77)(79, 85, 81, 87, 80, 86)(82, 88, 84, 90, 83, 89)(91, 94, 93, 96, 92, 95) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 19)(13, 21)(14, 22)(18, 26)(20, 27)(23, 31)(24, 32)(25, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72)(73, 79)(74, 80)(75, 81)(76, 82)(77, 83)(78, 84)(85, 91)(86, 92)(87, 93)(88, 94)(89, 95)(90, 96) local type(s) :: { ( 48^6 ) } Outer automorphisms :: reflexible Dual of E16.1085 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 16 e = 48 f = 2 degree seq :: [ 6^16 ] E16.1087 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 48}) Quotient :: edge Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 ] Map:: R = (1, 3, 8, 17, 10, 4)(2, 5, 12, 21, 14, 6)(7, 15, 24, 18, 9, 16)(11, 19, 28, 22, 13, 20)(23, 31, 26, 33, 25, 32)(27, 34, 30, 36, 29, 35)(37, 43, 39, 45, 38, 44)(40, 46, 42, 48, 41, 47)(49, 55, 51, 57, 50, 56)(52, 58, 54, 60, 53, 59)(61, 67, 63, 69, 62, 68)(64, 70, 66, 72, 65, 71)(73, 79, 75, 81, 74, 80)(76, 82, 78, 84, 77, 83)(85, 91, 87, 93, 86, 92)(88, 94, 90, 96, 89, 95)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 108)(106, 110)(111, 119)(112, 121)(113, 120)(114, 122)(115, 123)(116, 125)(117, 124)(118, 126)(127, 133)(128, 134)(129, 135)(130, 136)(131, 137)(132, 138)(139, 145)(140, 146)(141, 147)(142, 148)(143, 149)(144, 150)(151, 157)(152, 158)(153, 159)(154, 160)(155, 161)(156, 162)(163, 169)(164, 170)(165, 171)(166, 172)(167, 173)(168, 174)(175, 181)(176, 182)(177, 183)(178, 184)(179, 185)(180, 186)(187, 190)(188, 191)(189, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^6 ) } Outer automorphisms :: reflexible Dual of E16.1091 Transitivity :: ET+ Graph:: simple bipartite v = 64 e = 96 f = 2 degree seq :: [ 2^48, 6^16 ] E16.1088 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 48}) Quotient :: edge Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, (T2^2 * T1^-1)^2, T2^-1 * T1 * T2^-1 * T1^-3, T1^6, (T2^2 * T1^-1)^2, T2^14 * T1 * T2^-2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 37, 49, 61, 73, 85, 90, 78, 66, 54, 42, 30, 18, 6, 17, 29, 41, 53, 65, 77, 89, 96, 91, 79, 67, 55, 43, 31, 20, 13, 21, 33, 45, 57, 69, 81, 93, 88, 76, 64, 52, 40, 28, 15, 5)(2, 7, 19, 32, 44, 56, 68, 80, 92, 84, 72, 60, 48, 36, 24, 11, 16, 14, 27, 39, 51, 63, 75, 87, 95, 83, 71, 59, 47, 35, 23, 9, 4, 12, 26, 38, 50, 62, 74, 86, 94, 82, 70, 58, 46, 34, 22, 8)(97, 98, 102, 112, 109, 100)(99, 105, 113, 104, 117, 107)(101, 110, 114, 108, 116, 103)(106, 120, 125, 119, 129, 118)(111, 122, 126, 115, 127, 123)(121, 130, 137, 132, 141, 131)(124, 128, 138, 135, 139, 134)(133, 143, 149, 142, 153, 144)(136, 147, 150, 146, 151, 140)(145, 156, 161, 155, 165, 154)(148, 158, 162, 152, 163, 159)(157, 166, 173, 168, 177, 167)(160, 164, 174, 171, 175, 170)(169, 179, 185, 178, 189, 180)(172, 183, 186, 182, 187, 176)(181, 188, 192, 191, 184, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^6 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E16.1092 Transitivity :: ET+ Graph:: bipartite v = 18 e = 96 f = 48 degree seq :: [ 6^16, 48^2 ] E16.1089 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 48}) Quotient :: edge Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^3 * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-3 * T2 * T1^5 * T2 * T1^-8 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 31)(23, 40)(25, 42)(26, 43)(27, 45)(30, 46)(36, 48)(37, 49)(38, 50)(39, 54)(41, 56)(44, 58)(47, 60)(51, 61)(52, 63)(53, 66)(55, 68)(57, 70)(59, 72)(62, 73)(64, 71)(65, 78)(67, 80)(69, 82)(74, 84)(75, 85)(76, 86)(77, 90)(79, 92)(81, 94)(83, 95)(87, 89)(88, 93)(91, 96)(97, 98, 101, 107, 119, 135, 149, 161, 173, 185, 180, 168, 157, 144, 128, 141, 130, 113, 125, 139, 152, 164, 176, 188, 192, 191, 181, 169, 156, 145, 129, 112, 124, 138, 131, 142, 154, 166, 178, 190, 184, 172, 160, 148, 134, 118, 106, 100)(99, 103, 111, 127, 143, 155, 167, 179, 186, 177, 163, 150, 140, 122, 108, 121, 116, 105, 115, 132, 146, 158, 170, 182, 187, 174, 165, 151, 136, 126, 110, 102, 109, 123, 117, 133, 147, 159, 171, 183, 189, 175, 162, 153, 137, 120, 114, 104) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12, 12 ), ( 12^48 ) } Outer automorphisms :: reflexible Dual of E16.1090 Transitivity :: ET+ Graph:: simple bipartite v = 50 e = 96 f = 16 degree seq :: [ 2^48, 48^2 ] E16.1090 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 48}) Quotient :: loop Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 ] Map:: R = (1, 97, 3, 99, 8, 104, 17, 113, 10, 106, 4, 100)(2, 98, 5, 101, 12, 108, 21, 117, 14, 110, 6, 102)(7, 103, 15, 111, 24, 120, 18, 114, 9, 105, 16, 112)(11, 107, 19, 115, 28, 124, 22, 118, 13, 109, 20, 116)(23, 119, 31, 127, 26, 122, 33, 129, 25, 121, 32, 128)(27, 123, 34, 130, 30, 126, 36, 132, 29, 125, 35, 131)(37, 133, 43, 139, 39, 135, 45, 141, 38, 134, 44, 140)(40, 136, 46, 142, 42, 138, 48, 144, 41, 137, 47, 143)(49, 145, 55, 151, 51, 147, 57, 153, 50, 146, 56, 152)(52, 148, 58, 154, 54, 150, 60, 156, 53, 149, 59, 155)(61, 157, 67, 163, 63, 159, 69, 165, 62, 158, 68, 164)(64, 160, 70, 166, 66, 162, 72, 168, 65, 161, 71, 167)(73, 169, 79, 175, 75, 171, 81, 177, 74, 170, 80, 176)(76, 172, 82, 178, 78, 174, 84, 180, 77, 173, 83, 179)(85, 181, 91, 187, 87, 183, 93, 189, 86, 182, 92, 188)(88, 184, 94, 190, 90, 186, 96, 192, 89, 185, 95, 191) L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 108)(9, 100)(10, 110)(11, 101)(12, 104)(13, 102)(14, 106)(15, 119)(16, 121)(17, 120)(18, 122)(19, 123)(20, 125)(21, 124)(22, 126)(23, 111)(24, 113)(25, 112)(26, 114)(27, 115)(28, 117)(29, 116)(30, 118)(31, 133)(32, 134)(33, 135)(34, 136)(35, 137)(36, 138)(37, 127)(38, 128)(39, 129)(40, 130)(41, 131)(42, 132)(43, 145)(44, 146)(45, 147)(46, 148)(47, 149)(48, 150)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 157)(56, 158)(57, 159)(58, 160)(59, 161)(60, 162)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 169)(68, 170)(69, 171)(70, 172)(71, 173)(72, 174)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 181)(80, 182)(81, 183)(82, 184)(83, 185)(84, 186)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180)(91, 190)(92, 191)(93, 192)(94, 187)(95, 188)(96, 189) local type(s) :: { ( 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48 ) } Outer automorphisms :: reflexible Dual of E16.1089 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 96 f = 50 degree seq :: [ 12^16 ] E16.1091 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 48}) Quotient :: loop Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, (T2^2 * T1^-1)^2, T2^-1 * T1 * T2^-1 * T1^-3, T1^6, (T2^2 * T1^-1)^2, T2^14 * T1 * T2^-2 * T1^-1 ] Map:: R = (1, 97, 3, 99, 10, 106, 25, 121, 37, 133, 49, 145, 61, 157, 73, 169, 85, 181, 90, 186, 78, 174, 66, 162, 54, 150, 42, 138, 30, 126, 18, 114, 6, 102, 17, 113, 29, 125, 41, 137, 53, 149, 65, 161, 77, 173, 89, 185, 96, 192, 91, 187, 79, 175, 67, 163, 55, 151, 43, 139, 31, 127, 20, 116, 13, 109, 21, 117, 33, 129, 45, 141, 57, 153, 69, 165, 81, 177, 93, 189, 88, 184, 76, 172, 64, 160, 52, 148, 40, 136, 28, 124, 15, 111, 5, 101)(2, 98, 7, 103, 19, 115, 32, 128, 44, 140, 56, 152, 68, 164, 80, 176, 92, 188, 84, 180, 72, 168, 60, 156, 48, 144, 36, 132, 24, 120, 11, 107, 16, 112, 14, 110, 27, 123, 39, 135, 51, 147, 63, 159, 75, 171, 87, 183, 95, 191, 83, 179, 71, 167, 59, 155, 47, 143, 35, 131, 23, 119, 9, 105, 4, 100, 12, 108, 26, 122, 38, 134, 50, 146, 62, 158, 74, 170, 86, 182, 94, 190, 82, 178, 70, 166, 58, 154, 46, 142, 34, 130, 22, 118, 8, 104) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 112)(7, 101)(8, 117)(9, 113)(10, 120)(11, 99)(12, 116)(13, 100)(14, 114)(15, 122)(16, 109)(17, 104)(18, 108)(19, 127)(20, 103)(21, 107)(22, 106)(23, 129)(24, 125)(25, 130)(26, 126)(27, 111)(28, 128)(29, 119)(30, 115)(31, 123)(32, 138)(33, 118)(34, 137)(35, 121)(36, 141)(37, 143)(38, 124)(39, 139)(40, 147)(41, 132)(42, 135)(43, 134)(44, 136)(45, 131)(46, 153)(47, 149)(48, 133)(49, 156)(50, 151)(51, 150)(52, 158)(53, 142)(54, 146)(55, 140)(56, 163)(57, 144)(58, 145)(59, 165)(60, 161)(61, 166)(62, 162)(63, 148)(64, 164)(65, 155)(66, 152)(67, 159)(68, 174)(69, 154)(70, 173)(71, 157)(72, 177)(73, 179)(74, 160)(75, 175)(76, 183)(77, 168)(78, 171)(79, 170)(80, 172)(81, 167)(82, 189)(83, 185)(84, 169)(85, 188)(86, 187)(87, 186)(88, 190)(89, 178)(90, 182)(91, 176)(92, 192)(93, 180)(94, 181)(95, 184)(96, 191) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 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 E16.1087 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 96 f = 64 degree seq :: [ 96^2 ] E16.1092 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 48}) Quotient :: loop Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^3 * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-3 * T2 * T1^5 * T2 * T1^-8 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99)(2, 98, 6, 102)(4, 100, 9, 105)(5, 101, 12, 108)(7, 103, 16, 112)(8, 104, 17, 113)(10, 106, 21, 117)(11, 107, 24, 120)(13, 109, 28, 124)(14, 110, 29, 125)(15, 111, 32, 128)(18, 114, 35, 131)(19, 115, 33, 129)(20, 116, 34, 130)(22, 118, 31, 127)(23, 119, 40, 136)(25, 121, 42, 138)(26, 122, 43, 139)(27, 123, 45, 141)(30, 126, 46, 142)(36, 132, 48, 144)(37, 133, 49, 145)(38, 134, 50, 146)(39, 135, 54, 150)(41, 137, 56, 152)(44, 140, 58, 154)(47, 143, 60, 156)(51, 147, 61, 157)(52, 148, 63, 159)(53, 149, 66, 162)(55, 151, 68, 164)(57, 153, 70, 166)(59, 155, 72, 168)(62, 158, 73, 169)(64, 160, 71, 167)(65, 161, 78, 174)(67, 163, 80, 176)(69, 165, 82, 178)(74, 170, 84, 180)(75, 171, 85, 181)(76, 172, 86, 182)(77, 173, 90, 186)(79, 175, 92, 188)(81, 177, 94, 190)(83, 179, 95, 191)(87, 183, 89, 185)(88, 184, 93, 189)(91, 187, 96, 192) L = (1, 98)(2, 101)(3, 103)(4, 97)(5, 107)(6, 109)(7, 111)(8, 99)(9, 115)(10, 100)(11, 119)(12, 121)(13, 123)(14, 102)(15, 127)(16, 124)(17, 125)(18, 104)(19, 132)(20, 105)(21, 133)(22, 106)(23, 135)(24, 114)(25, 116)(26, 108)(27, 117)(28, 138)(29, 139)(30, 110)(31, 143)(32, 141)(33, 112)(34, 113)(35, 142)(36, 146)(37, 147)(38, 118)(39, 149)(40, 126)(41, 120)(42, 131)(43, 152)(44, 122)(45, 130)(46, 154)(47, 155)(48, 128)(49, 129)(50, 158)(51, 159)(52, 134)(53, 161)(54, 140)(55, 136)(56, 164)(57, 137)(58, 166)(59, 167)(60, 145)(61, 144)(62, 170)(63, 171)(64, 148)(65, 173)(66, 153)(67, 150)(68, 176)(69, 151)(70, 178)(71, 179)(72, 157)(73, 156)(74, 182)(75, 183)(76, 160)(77, 185)(78, 165)(79, 162)(80, 188)(81, 163)(82, 190)(83, 186)(84, 168)(85, 169)(86, 187)(87, 189)(88, 172)(89, 180)(90, 177)(91, 174)(92, 192)(93, 175)(94, 184)(95, 181)(96, 191) local type(s) :: { ( 6, 48, 6, 48 ) } Outer automorphisms :: reflexible Dual of E16.1088 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 48 e = 96 f = 18 degree seq :: [ 4^48 ] E16.1093 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 48}) Quotient :: dipole Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2^6, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^48 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 12, 108)(10, 106, 14, 110)(15, 111, 23, 119)(16, 112, 25, 121)(17, 113, 24, 120)(18, 114, 26, 122)(19, 115, 27, 123)(20, 116, 29, 125)(21, 117, 28, 124)(22, 118, 30, 126)(31, 127, 37, 133)(32, 128, 38, 134)(33, 129, 39, 135)(34, 130, 40, 136)(35, 131, 41, 137)(36, 132, 42, 138)(43, 139, 49, 145)(44, 140, 50, 146)(45, 141, 51, 147)(46, 142, 52, 148)(47, 143, 53, 149)(48, 144, 54, 150)(55, 151, 61, 157)(56, 152, 62, 158)(57, 153, 63, 159)(58, 154, 64, 160)(59, 155, 65, 161)(60, 156, 66, 162)(67, 163, 73, 169)(68, 164, 74, 170)(69, 165, 75, 171)(70, 166, 76, 172)(71, 167, 77, 173)(72, 168, 78, 174)(79, 175, 85, 181)(80, 176, 86, 182)(81, 177, 87, 183)(82, 178, 88, 184)(83, 179, 89, 185)(84, 180, 90, 186)(91, 187, 94, 190)(92, 188, 95, 191)(93, 189, 96, 192)(193, 289, 195, 291, 200, 296, 209, 305, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 213, 309, 206, 302, 198, 294)(199, 295, 207, 303, 216, 312, 210, 306, 201, 297, 208, 304)(203, 299, 211, 307, 220, 316, 214, 310, 205, 301, 212, 308)(215, 311, 223, 319, 218, 314, 225, 321, 217, 313, 224, 320)(219, 315, 226, 322, 222, 318, 228, 324, 221, 317, 227, 323)(229, 325, 235, 331, 231, 327, 237, 333, 230, 326, 236, 332)(232, 328, 238, 334, 234, 330, 240, 336, 233, 329, 239, 335)(241, 337, 247, 343, 243, 339, 249, 345, 242, 338, 248, 344)(244, 340, 250, 346, 246, 342, 252, 348, 245, 341, 251, 347)(253, 349, 259, 355, 255, 351, 261, 357, 254, 350, 260, 356)(256, 352, 262, 358, 258, 354, 264, 360, 257, 353, 263, 359)(265, 361, 271, 367, 267, 363, 273, 369, 266, 362, 272, 368)(268, 364, 274, 370, 270, 366, 276, 372, 269, 365, 275, 371)(277, 373, 283, 379, 279, 375, 285, 381, 278, 374, 284, 380)(280, 376, 286, 382, 282, 378, 288, 384, 281, 377, 287, 383) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 204)(9, 196)(10, 206)(11, 197)(12, 200)(13, 198)(14, 202)(15, 215)(16, 217)(17, 216)(18, 218)(19, 219)(20, 221)(21, 220)(22, 222)(23, 207)(24, 209)(25, 208)(26, 210)(27, 211)(28, 213)(29, 212)(30, 214)(31, 229)(32, 230)(33, 231)(34, 232)(35, 233)(36, 234)(37, 223)(38, 224)(39, 225)(40, 226)(41, 227)(42, 228)(43, 241)(44, 242)(45, 243)(46, 244)(47, 245)(48, 246)(49, 235)(50, 236)(51, 237)(52, 238)(53, 239)(54, 240)(55, 253)(56, 254)(57, 255)(58, 256)(59, 257)(60, 258)(61, 247)(62, 248)(63, 249)(64, 250)(65, 251)(66, 252)(67, 265)(68, 266)(69, 267)(70, 268)(71, 269)(72, 270)(73, 259)(74, 260)(75, 261)(76, 262)(77, 263)(78, 264)(79, 277)(80, 278)(81, 279)(82, 280)(83, 281)(84, 282)(85, 271)(86, 272)(87, 273)(88, 274)(89, 275)(90, 276)(91, 286)(92, 287)(93, 288)(94, 283)(95, 284)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 96, 2, 96 ), ( 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96 ) } Outer automorphisms :: reflexible Dual of E16.1096 Graph:: bipartite v = 64 e = 192 f = 98 degree seq :: [ 4^48, 12^16 ] E16.1094 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 48}) Quotient :: dipole Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y2^-1 * Y1^-1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-2, Y2^-1 * Y1^3 * Y2^-1 * Y1, Y1^6, (Y1^-1 * Y2^5)^2, Y2^15 * Y1 * Y2^-1 * Y1 ] Map:: R = (1, 97, 2, 98, 6, 102, 16, 112, 13, 109, 4, 100)(3, 99, 9, 105, 17, 113, 8, 104, 21, 117, 11, 107)(5, 101, 14, 110, 18, 114, 12, 108, 20, 116, 7, 103)(10, 106, 24, 120, 29, 125, 23, 119, 33, 129, 22, 118)(15, 111, 26, 122, 30, 126, 19, 115, 31, 127, 27, 123)(25, 121, 34, 130, 41, 137, 36, 132, 45, 141, 35, 131)(28, 124, 32, 128, 42, 138, 39, 135, 43, 139, 38, 134)(37, 133, 47, 143, 53, 149, 46, 142, 57, 153, 48, 144)(40, 136, 51, 147, 54, 150, 50, 146, 55, 151, 44, 140)(49, 145, 60, 156, 65, 161, 59, 155, 69, 165, 58, 154)(52, 148, 62, 158, 66, 162, 56, 152, 67, 163, 63, 159)(61, 157, 70, 166, 77, 173, 72, 168, 81, 177, 71, 167)(64, 160, 68, 164, 78, 174, 75, 171, 79, 175, 74, 170)(73, 169, 83, 179, 89, 185, 82, 178, 93, 189, 84, 180)(76, 172, 87, 183, 90, 186, 86, 182, 91, 187, 80, 176)(85, 181, 92, 188, 96, 192, 95, 191, 88, 184, 94, 190)(193, 289, 195, 291, 202, 298, 217, 313, 229, 325, 241, 337, 253, 349, 265, 361, 277, 373, 282, 378, 270, 366, 258, 354, 246, 342, 234, 330, 222, 318, 210, 306, 198, 294, 209, 305, 221, 317, 233, 329, 245, 341, 257, 353, 269, 365, 281, 377, 288, 384, 283, 379, 271, 367, 259, 355, 247, 343, 235, 331, 223, 319, 212, 308, 205, 301, 213, 309, 225, 321, 237, 333, 249, 345, 261, 357, 273, 369, 285, 381, 280, 376, 268, 364, 256, 352, 244, 340, 232, 328, 220, 316, 207, 303, 197, 293)(194, 290, 199, 295, 211, 307, 224, 320, 236, 332, 248, 344, 260, 356, 272, 368, 284, 380, 276, 372, 264, 360, 252, 348, 240, 336, 228, 324, 216, 312, 203, 299, 208, 304, 206, 302, 219, 315, 231, 327, 243, 339, 255, 351, 267, 363, 279, 375, 287, 383, 275, 371, 263, 359, 251, 347, 239, 335, 227, 323, 215, 311, 201, 297, 196, 292, 204, 300, 218, 314, 230, 326, 242, 338, 254, 350, 266, 362, 278, 374, 286, 382, 274, 370, 262, 358, 250, 346, 238, 334, 226, 322, 214, 310, 200, 296) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 211)(8, 194)(9, 196)(10, 217)(11, 208)(12, 218)(13, 213)(14, 219)(15, 197)(16, 206)(17, 221)(18, 198)(19, 224)(20, 205)(21, 225)(22, 200)(23, 201)(24, 203)(25, 229)(26, 230)(27, 231)(28, 207)(29, 233)(30, 210)(31, 212)(32, 236)(33, 237)(34, 214)(35, 215)(36, 216)(37, 241)(38, 242)(39, 243)(40, 220)(41, 245)(42, 222)(43, 223)(44, 248)(45, 249)(46, 226)(47, 227)(48, 228)(49, 253)(50, 254)(51, 255)(52, 232)(53, 257)(54, 234)(55, 235)(56, 260)(57, 261)(58, 238)(59, 239)(60, 240)(61, 265)(62, 266)(63, 267)(64, 244)(65, 269)(66, 246)(67, 247)(68, 272)(69, 273)(70, 250)(71, 251)(72, 252)(73, 277)(74, 278)(75, 279)(76, 256)(77, 281)(78, 258)(79, 259)(80, 284)(81, 285)(82, 262)(83, 263)(84, 264)(85, 282)(86, 286)(87, 287)(88, 268)(89, 288)(90, 270)(91, 271)(92, 276)(93, 280)(94, 274)(95, 275)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E16.1095 Graph:: bipartite v = 18 e = 192 f = 144 degree seq :: [ 12^16, 96^2 ] E16.1095 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 48}) Quotient :: dipole Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^3 * Y2)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y3^2 * Y2 * Y3^-14 * Y2, (Y3^-1 * Y1^-1)^48 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290)(195, 291, 199, 295)(196, 292, 201, 297)(197, 293, 203, 299)(198, 294, 205, 301)(200, 296, 209, 305)(202, 298, 213, 309)(204, 300, 217, 313)(206, 302, 221, 317)(207, 303, 215, 311)(208, 304, 219, 315)(210, 306, 222, 318)(211, 307, 216, 312)(212, 308, 220, 316)(214, 310, 218, 314)(223, 319, 233, 329)(224, 320, 237, 333)(225, 321, 231, 327)(226, 322, 236, 332)(227, 323, 239, 335)(228, 324, 234, 330)(229, 325, 232, 328)(230, 326, 242, 338)(235, 331, 245, 341)(238, 334, 248, 344)(240, 336, 249, 345)(241, 337, 252, 348)(243, 339, 246, 342)(244, 340, 255, 351)(247, 343, 258, 354)(250, 346, 261, 357)(251, 347, 260, 356)(253, 349, 262, 358)(254, 350, 257, 353)(256, 352, 259, 355)(263, 359, 273, 369)(264, 360, 272, 368)(265, 361, 275, 371)(266, 362, 270, 366)(267, 363, 269, 365)(268, 364, 278, 374)(271, 367, 281, 377)(274, 370, 284, 380)(276, 372, 285, 381)(277, 373, 283, 379)(279, 375, 282, 378)(280, 376, 286, 382)(287, 383, 288, 384) L = (1, 195)(2, 197)(3, 200)(4, 193)(5, 204)(6, 194)(7, 207)(8, 210)(9, 211)(10, 196)(11, 215)(12, 218)(13, 219)(14, 198)(15, 223)(16, 199)(17, 225)(18, 227)(19, 228)(20, 201)(21, 229)(22, 202)(23, 231)(24, 203)(25, 233)(26, 235)(27, 236)(28, 205)(29, 237)(30, 206)(31, 213)(32, 208)(33, 212)(34, 209)(35, 241)(36, 242)(37, 243)(38, 214)(39, 221)(40, 216)(41, 220)(42, 217)(43, 247)(44, 248)(45, 249)(46, 222)(47, 224)(48, 226)(49, 253)(50, 254)(51, 255)(52, 230)(53, 232)(54, 234)(55, 259)(56, 260)(57, 261)(58, 238)(59, 239)(60, 240)(61, 265)(62, 266)(63, 267)(64, 244)(65, 245)(66, 246)(67, 271)(68, 272)(69, 273)(70, 250)(71, 251)(72, 252)(73, 277)(74, 278)(75, 279)(76, 256)(77, 257)(78, 258)(79, 283)(80, 284)(81, 285)(82, 262)(83, 263)(84, 264)(85, 282)(86, 287)(87, 286)(88, 268)(89, 269)(90, 270)(91, 276)(92, 288)(93, 280)(94, 274)(95, 275)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 12, 96 ), ( 12, 96, 12, 96 ) } Outer automorphisms :: reflexible Dual of E16.1094 Graph:: simple bipartite v = 144 e = 192 f = 18 degree seq :: [ 2^96, 4^48 ] E16.1096 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 48}) Quotient :: dipole Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3, (Y3 * Y1^-3)^2, Y1^-3 * Y3 * Y1^5 * Y3 * Y1^-8 ] Map:: R = (1, 97, 2, 98, 5, 101, 11, 107, 23, 119, 39, 135, 53, 149, 65, 161, 77, 173, 89, 185, 84, 180, 72, 168, 61, 157, 48, 144, 32, 128, 45, 141, 34, 130, 17, 113, 29, 125, 43, 139, 56, 152, 68, 164, 80, 176, 92, 188, 96, 192, 95, 191, 85, 181, 73, 169, 60, 156, 49, 145, 33, 129, 16, 112, 28, 124, 42, 138, 35, 131, 46, 142, 58, 154, 70, 166, 82, 178, 94, 190, 88, 184, 76, 172, 64, 160, 52, 148, 38, 134, 22, 118, 10, 106, 4, 100)(3, 99, 7, 103, 15, 111, 31, 127, 47, 143, 59, 155, 71, 167, 83, 179, 90, 186, 81, 177, 67, 163, 54, 150, 44, 140, 26, 122, 12, 108, 25, 121, 20, 116, 9, 105, 19, 115, 36, 132, 50, 146, 62, 158, 74, 170, 86, 182, 91, 187, 78, 174, 69, 165, 55, 151, 40, 136, 30, 126, 14, 110, 6, 102, 13, 109, 27, 123, 21, 117, 37, 133, 51, 147, 63, 159, 75, 171, 87, 183, 93, 189, 79, 175, 66, 162, 57, 153, 41, 137, 24, 120, 18, 114, 8, 104)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 198)(3, 193)(4, 201)(5, 204)(6, 194)(7, 208)(8, 209)(9, 196)(10, 213)(11, 216)(12, 197)(13, 220)(14, 221)(15, 224)(16, 199)(17, 200)(18, 227)(19, 225)(20, 226)(21, 202)(22, 223)(23, 232)(24, 203)(25, 234)(26, 235)(27, 237)(28, 205)(29, 206)(30, 238)(31, 214)(32, 207)(33, 211)(34, 212)(35, 210)(36, 240)(37, 241)(38, 242)(39, 246)(40, 215)(41, 248)(42, 217)(43, 218)(44, 250)(45, 219)(46, 222)(47, 252)(48, 228)(49, 229)(50, 230)(51, 253)(52, 255)(53, 258)(54, 231)(55, 260)(56, 233)(57, 262)(58, 236)(59, 264)(60, 239)(61, 243)(62, 265)(63, 244)(64, 263)(65, 270)(66, 245)(67, 272)(68, 247)(69, 274)(70, 249)(71, 256)(72, 251)(73, 254)(74, 276)(75, 277)(76, 278)(77, 282)(78, 257)(79, 284)(80, 259)(81, 286)(82, 261)(83, 287)(84, 266)(85, 267)(86, 268)(87, 281)(88, 285)(89, 279)(90, 269)(91, 288)(92, 271)(93, 280)(94, 273)(95, 275)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 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 E16.1093 Graph:: simple bipartite v = 98 e = 192 f = 64 degree seq :: [ 2^96, 96^2 ] E16.1097 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 48}) Quotient :: dipole Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^3 * Y1)^2, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^6, Y2^-11 * Y1 * Y2^5 * Y1, (Y2^-1 * R * Y2^-7)^2 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 17, 113)(10, 106, 21, 117)(12, 108, 25, 121)(14, 110, 29, 125)(15, 111, 23, 119)(16, 112, 27, 123)(18, 114, 30, 126)(19, 115, 24, 120)(20, 116, 28, 124)(22, 118, 26, 122)(31, 127, 41, 137)(32, 128, 45, 141)(33, 129, 39, 135)(34, 130, 44, 140)(35, 131, 47, 143)(36, 132, 42, 138)(37, 133, 40, 136)(38, 134, 50, 146)(43, 139, 53, 149)(46, 142, 56, 152)(48, 144, 57, 153)(49, 145, 60, 156)(51, 147, 54, 150)(52, 148, 63, 159)(55, 151, 66, 162)(58, 154, 69, 165)(59, 155, 68, 164)(61, 157, 70, 166)(62, 158, 65, 161)(64, 160, 67, 163)(71, 167, 81, 177)(72, 168, 80, 176)(73, 169, 83, 179)(74, 170, 78, 174)(75, 171, 77, 173)(76, 172, 86, 182)(79, 175, 89, 185)(82, 178, 92, 188)(84, 180, 93, 189)(85, 181, 91, 187)(87, 183, 90, 186)(88, 184, 94, 190)(95, 191, 96, 192)(193, 289, 195, 291, 200, 296, 210, 306, 227, 323, 241, 337, 253, 349, 265, 361, 277, 373, 282, 378, 270, 366, 258, 354, 246, 342, 234, 330, 217, 313, 233, 329, 220, 316, 205, 301, 219, 315, 236, 332, 248, 344, 260, 356, 272, 368, 284, 380, 288, 384, 281, 377, 269, 365, 257, 353, 245, 341, 232, 328, 216, 312, 203, 299, 215, 311, 231, 327, 221, 317, 237, 333, 249, 345, 261, 357, 273, 369, 285, 381, 280, 376, 268, 364, 256, 352, 244, 340, 230, 326, 214, 310, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 218, 314, 235, 331, 247, 343, 259, 355, 271, 367, 283, 379, 276, 372, 264, 360, 252, 348, 240, 336, 226, 322, 209, 305, 225, 321, 212, 308, 201, 297, 211, 307, 228, 324, 242, 338, 254, 350, 266, 362, 278, 374, 287, 383, 275, 371, 263, 359, 251, 347, 239, 335, 224, 320, 208, 304, 199, 295, 207, 303, 223, 319, 213, 309, 229, 325, 243, 339, 255, 351, 267, 363, 279, 375, 286, 382, 274, 370, 262, 358, 250, 346, 238, 334, 222, 318, 206, 302, 198, 294) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 209)(9, 196)(10, 213)(11, 197)(12, 217)(13, 198)(14, 221)(15, 215)(16, 219)(17, 200)(18, 222)(19, 216)(20, 220)(21, 202)(22, 218)(23, 207)(24, 211)(25, 204)(26, 214)(27, 208)(28, 212)(29, 206)(30, 210)(31, 233)(32, 237)(33, 231)(34, 236)(35, 239)(36, 234)(37, 232)(38, 242)(39, 225)(40, 229)(41, 223)(42, 228)(43, 245)(44, 226)(45, 224)(46, 248)(47, 227)(48, 249)(49, 252)(50, 230)(51, 246)(52, 255)(53, 235)(54, 243)(55, 258)(56, 238)(57, 240)(58, 261)(59, 260)(60, 241)(61, 262)(62, 257)(63, 244)(64, 259)(65, 254)(66, 247)(67, 256)(68, 251)(69, 250)(70, 253)(71, 273)(72, 272)(73, 275)(74, 270)(75, 269)(76, 278)(77, 267)(78, 266)(79, 281)(80, 264)(81, 263)(82, 284)(83, 265)(84, 285)(85, 283)(86, 268)(87, 282)(88, 286)(89, 271)(90, 279)(91, 277)(92, 274)(93, 276)(94, 280)(95, 288)(96, 287)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E16.1098 Graph:: bipartite v = 50 e = 192 f = 112 degree seq :: [ 4^48, 96^2 ] E16.1098 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 48}) Quotient :: dipole Aut^+ = C3 x D32 (small group id <96, 61>) Aut = $<192, 469>$ (small group id <192, 469>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^3 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1^-3 * Y3 * Y1^-1, Y1 * Y3^-16 * Y1, (Y3 * Y2^-1)^48 ] Map:: R = (1, 97, 2, 98, 6, 102, 16, 112, 13, 109, 4, 100)(3, 99, 9, 105, 17, 113, 8, 104, 21, 117, 11, 107)(5, 101, 14, 110, 18, 114, 12, 108, 20, 116, 7, 103)(10, 106, 24, 120, 29, 125, 23, 119, 33, 129, 22, 118)(15, 111, 26, 122, 30, 126, 19, 115, 31, 127, 27, 123)(25, 121, 34, 130, 41, 137, 36, 132, 45, 141, 35, 131)(28, 124, 32, 128, 42, 138, 39, 135, 43, 139, 38, 134)(37, 133, 47, 143, 53, 149, 46, 142, 57, 153, 48, 144)(40, 136, 51, 147, 54, 150, 50, 146, 55, 151, 44, 140)(49, 145, 60, 156, 65, 161, 59, 155, 69, 165, 58, 154)(52, 148, 62, 158, 66, 162, 56, 152, 67, 163, 63, 159)(61, 157, 70, 166, 77, 173, 72, 168, 81, 177, 71, 167)(64, 160, 68, 164, 78, 174, 75, 171, 79, 175, 74, 170)(73, 169, 83, 179, 89, 185, 82, 178, 93, 189, 84, 180)(76, 172, 87, 183, 90, 186, 86, 182, 91, 187, 80, 176)(85, 181, 92, 188, 96, 192, 95, 191, 88, 184, 94, 190)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 211)(8, 194)(9, 196)(10, 217)(11, 208)(12, 218)(13, 213)(14, 219)(15, 197)(16, 206)(17, 221)(18, 198)(19, 224)(20, 205)(21, 225)(22, 200)(23, 201)(24, 203)(25, 229)(26, 230)(27, 231)(28, 207)(29, 233)(30, 210)(31, 212)(32, 236)(33, 237)(34, 214)(35, 215)(36, 216)(37, 241)(38, 242)(39, 243)(40, 220)(41, 245)(42, 222)(43, 223)(44, 248)(45, 249)(46, 226)(47, 227)(48, 228)(49, 253)(50, 254)(51, 255)(52, 232)(53, 257)(54, 234)(55, 235)(56, 260)(57, 261)(58, 238)(59, 239)(60, 240)(61, 265)(62, 266)(63, 267)(64, 244)(65, 269)(66, 246)(67, 247)(68, 272)(69, 273)(70, 250)(71, 251)(72, 252)(73, 277)(74, 278)(75, 279)(76, 256)(77, 281)(78, 258)(79, 259)(80, 284)(81, 285)(82, 262)(83, 263)(84, 264)(85, 282)(86, 286)(87, 287)(88, 268)(89, 288)(90, 270)(91, 271)(92, 276)(93, 280)(94, 274)(95, 275)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 96 ), ( 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96 ) } Outer automorphisms :: reflexible Dual of E16.1097 Graph:: simple bipartite v = 112 e = 192 f = 50 degree seq :: [ 2^96, 12^16 ] E16.1099 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 5}) Quotient :: dipole Aut^+ = D10 x D10 (small group id <100, 13>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2, (Y1 * Y3 * Y2 * Y1 * Y2)^2, (Y3 * Y1)^5 ] Map:: polytopal non-degenerate R = (1, 101, 2, 102)(3, 103, 7, 107)(4, 104, 9, 109)(5, 105, 10, 110)(6, 106, 12, 112)(8, 108, 15, 115)(11, 111, 20, 120)(13, 113, 23, 123)(14, 114, 25, 125)(16, 116, 28, 128)(17, 117, 30, 130)(18, 118, 31, 131)(19, 119, 33, 133)(21, 121, 36, 136)(22, 122, 38, 138)(24, 124, 34, 134)(26, 126, 32, 132)(27, 127, 44, 144)(29, 129, 45, 145)(35, 135, 52, 152)(37, 137, 53, 153)(39, 139, 55, 155)(40, 140, 56, 156)(41, 141, 57, 157)(42, 142, 59, 159)(43, 143, 60, 160)(46, 146, 63, 163)(47, 147, 64, 164)(48, 148, 65, 165)(49, 149, 66, 166)(50, 150, 68, 168)(51, 151, 69, 169)(54, 154, 72, 172)(58, 158, 70, 170)(61, 161, 67, 167)(62, 162, 79, 179)(71, 171, 86, 186)(73, 173, 87, 187)(74, 174, 88, 188)(75, 175, 89, 189)(76, 176, 85, 185)(77, 177, 90, 190)(78, 178, 83, 183)(80, 180, 91, 191)(81, 181, 92, 192)(82, 182, 93, 193)(84, 184, 94, 194)(95, 195, 98, 198)(96, 196, 100, 200)(97, 197, 99, 199)(201, 301, 203, 303)(202, 302, 205, 305)(204, 304, 208, 308)(206, 306, 211, 311)(207, 307, 213, 313)(209, 309, 216, 316)(210, 310, 218, 318)(212, 312, 221, 321)(214, 314, 224, 324)(215, 315, 226, 326)(217, 317, 229, 329)(219, 319, 232, 332)(220, 320, 234, 334)(222, 322, 237, 337)(223, 323, 239, 339)(225, 325, 241, 341)(227, 327, 243, 343)(228, 328, 240, 340)(230, 330, 246, 346)(231, 331, 247, 347)(233, 333, 249, 349)(235, 335, 251, 351)(236, 336, 248, 348)(238, 338, 254, 354)(242, 342, 258, 358)(244, 344, 261, 361)(245, 345, 260, 360)(250, 350, 267, 367)(252, 352, 270, 370)(253, 353, 269, 369)(255, 355, 273, 373)(256, 356, 275, 375)(257, 357, 274, 374)(259, 359, 277, 377)(262, 362, 278, 378)(263, 363, 276, 376)(264, 364, 280, 380)(265, 365, 282, 382)(266, 366, 281, 381)(268, 368, 284, 384)(271, 371, 285, 385)(272, 372, 283, 383)(279, 379, 290, 390)(286, 386, 294, 394)(287, 387, 295, 395)(288, 388, 297, 397)(289, 389, 296, 396)(291, 391, 298, 398)(292, 392, 300, 400)(293, 393, 299, 399) L = (1, 204)(2, 206)(3, 208)(4, 201)(5, 211)(6, 202)(7, 214)(8, 203)(9, 217)(10, 219)(11, 205)(12, 222)(13, 224)(14, 207)(15, 227)(16, 229)(17, 209)(18, 232)(19, 210)(20, 235)(21, 237)(22, 212)(23, 240)(24, 213)(25, 242)(26, 243)(27, 215)(28, 239)(29, 216)(30, 238)(31, 248)(32, 218)(33, 250)(34, 251)(35, 220)(36, 247)(37, 221)(38, 230)(39, 228)(40, 223)(41, 258)(42, 225)(43, 226)(44, 259)(45, 262)(46, 254)(47, 236)(48, 231)(49, 267)(50, 233)(51, 234)(52, 268)(53, 271)(54, 246)(55, 274)(56, 276)(57, 273)(58, 241)(59, 244)(60, 278)(61, 277)(62, 245)(63, 275)(64, 281)(65, 283)(66, 280)(67, 249)(68, 252)(69, 285)(70, 284)(71, 253)(72, 282)(73, 257)(74, 255)(75, 263)(76, 256)(77, 261)(78, 260)(79, 288)(80, 266)(81, 264)(82, 272)(83, 265)(84, 270)(85, 269)(86, 292)(87, 296)(88, 279)(89, 295)(90, 297)(91, 299)(92, 286)(93, 298)(94, 300)(95, 289)(96, 287)(97, 290)(98, 293)(99, 291)(100, 294)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.1100 Graph:: simple bipartite v = 100 e = 200 f = 70 degree seq :: [ 4^100 ] E16.1100 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 5}) Quotient :: dipole Aut^+ = D10 x D10 (small group id <100, 13>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y1)^2, (Y3 * Y2)^2, (Y1^-1 * Y3)^2, (R * Y3)^2, Y1^5, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y1^-2 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 * Y1^-2 * Y2 ] Map:: polytopal non-degenerate R = (1, 101, 2, 102, 6, 106, 14, 114, 5, 105)(3, 103, 9, 109, 20, 120, 25, 125, 11, 111)(4, 104, 12, 112, 26, 126, 16, 116, 8, 108)(7, 107, 17, 117, 34, 134, 39, 139, 19, 119)(10, 110, 23, 123, 44, 144, 41, 141, 22, 122)(13, 113, 28, 128, 51, 151, 52, 152, 29, 129)(15, 115, 31, 131, 55, 155, 60, 160, 33, 133)(18, 118, 37, 137, 64, 164, 62, 162, 36, 136)(21, 121, 35, 135, 56, 156, 70, 170, 43, 143)(24, 124, 38, 138, 59, 159, 73, 173, 46, 146)(27, 127, 49, 149, 77, 177, 78, 178, 50, 150)(30, 130, 53, 153, 79, 179, 80, 180, 54, 154)(32, 132, 58, 158, 84, 184, 82, 182, 57, 157)(40, 140, 61, 161, 81, 181, 90, 190, 68, 168)(42, 142, 69, 169, 91, 191, 83, 183, 63, 163)(45, 145, 72, 172, 93, 193, 85, 185, 65, 165)(47, 147, 66, 166, 86, 186, 94, 194, 74, 174)(48, 148, 75, 175, 95, 195, 96, 196, 76, 176)(67, 167, 89, 189, 99, 199, 97, 197, 87, 187)(71, 171, 92, 192, 100, 200, 98, 198, 88, 188)(201, 301, 203, 303)(202, 302, 207, 307)(204, 304, 210, 310)(205, 305, 213, 313)(206, 306, 215, 315)(208, 308, 218, 318)(209, 309, 221, 321)(211, 311, 224, 324)(212, 312, 227, 327)(214, 314, 230, 330)(216, 316, 232, 332)(217, 317, 235, 335)(219, 319, 238, 338)(220, 320, 240, 340)(222, 322, 242, 342)(223, 323, 245, 345)(225, 325, 247, 347)(226, 326, 248, 348)(228, 328, 243, 343)(229, 329, 246, 346)(231, 331, 256, 356)(233, 333, 259, 359)(234, 334, 261, 361)(236, 336, 263, 363)(237, 337, 265, 365)(239, 339, 266, 366)(241, 341, 267, 367)(244, 344, 271, 371)(249, 349, 272, 372)(250, 350, 269, 369)(251, 351, 268, 368)(252, 352, 274, 374)(253, 353, 270, 370)(254, 354, 273, 373)(255, 355, 281, 381)(257, 357, 283, 383)(258, 358, 285, 385)(260, 360, 286, 386)(262, 362, 287, 387)(264, 364, 288, 388)(275, 375, 293, 393)(276, 376, 291, 391)(277, 377, 292, 392)(278, 378, 289, 389)(279, 379, 290, 390)(280, 380, 294, 394)(282, 382, 297, 397)(284, 384, 298, 398)(295, 395, 300, 400)(296, 396, 299, 399) L = (1, 204)(2, 208)(3, 210)(4, 201)(5, 212)(6, 216)(7, 218)(8, 202)(9, 222)(10, 203)(11, 223)(12, 205)(13, 227)(14, 226)(15, 232)(16, 206)(17, 236)(18, 207)(19, 237)(20, 241)(21, 242)(22, 209)(23, 211)(24, 245)(25, 244)(26, 214)(27, 213)(28, 250)(29, 249)(30, 248)(31, 257)(32, 215)(33, 258)(34, 262)(35, 263)(36, 217)(37, 219)(38, 265)(39, 264)(40, 267)(41, 220)(42, 221)(43, 269)(44, 225)(45, 224)(46, 272)(47, 271)(48, 230)(49, 229)(50, 228)(51, 278)(52, 277)(53, 276)(54, 275)(55, 282)(56, 283)(57, 231)(58, 233)(59, 285)(60, 284)(61, 287)(62, 234)(63, 235)(64, 239)(65, 238)(66, 288)(67, 240)(68, 289)(69, 243)(70, 291)(71, 247)(72, 246)(73, 293)(74, 292)(75, 254)(76, 253)(77, 252)(78, 251)(79, 296)(80, 295)(81, 297)(82, 255)(83, 256)(84, 260)(85, 259)(86, 298)(87, 261)(88, 266)(89, 268)(90, 299)(91, 270)(92, 274)(93, 273)(94, 300)(95, 280)(96, 279)(97, 281)(98, 286)(99, 290)(100, 294)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 4^4 ), ( 4^10 ) } Outer automorphisms :: reflexible Dual of E16.1099 Graph:: simple bipartite v = 70 e = 200 f = 100 degree seq :: [ 4^50, 10^20 ] E16.1101 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {4, 4, 5}) Quotient :: edge Aut^+ = (C5 x C5) : C4 (small group id <100, 10>) Aut = (C5 x C5) : C4 (small group id <100, 10>) |r| :: 1 Presentation :: [ X1^4, X2^5, X1 * X2 * X1^-2 * X2^-2 * X1 * X2^-1, X2 * X1^-1 * X2^-1 * X1^-1 * X2^-2 * X1^2, (X2, X1^-1, X2^-1), (X2 * X1^-1)^4, (X2^-1 * X1^-1)^4, X2^-1 * X1^-1 * X2 * X1^-2 * X2^2 * X1^-1 * X2^-1 ] Map:: polyhedral non-degenerate R = (1, 2, 6, 4)(3, 9, 25, 11)(5, 14, 38, 15)(7, 19, 51, 21)(8, 22, 58, 23)(10, 28, 59, 29)(12, 32, 77, 34)(13, 35, 80, 36)(16, 43, 53, 44)(17, 45, 89, 47)(18, 48, 92, 49)(20, 54, 73, 55)(24, 63, 87, 64)(26, 67, 93, 56)(27, 69, 37, 61)(30, 74, 94, 60)(31, 75, 83, 46)(33, 57, 39, 79)(40, 66, 90, 62)(41, 78, 70, 50)(42, 81, 91, 52)(65, 85, 97, 86)(68, 98, 88, 96)(71, 82, 76, 99)(72, 100, 84, 95)(101, 103, 110, 116, 105)(102, 107, 120, 124, 108)(104, 112, 133, 137, 113)(106, 117, 146, 150, 118)(109, 126, 168, 170, 127)(111, 130, 151, 176, 131)(114, 139, 183, 184, 140)(115, 141, 185, 158, 142)(119, 152, 195, 169, 153)(121, 156, 189, 197, 157)(122, 159, 179, 198, 160)(123, 161, 199, 192, 162)(125, 165, 154, 134, 166)(128, 147, 191, 177, 171)(129, 172, 193, 148, 173)(132, 174, 200, 164, 178)(135, 175, 155, 196, 181)(136, 163, 182, 138, 167)(143, 186, 180, 194, 149)(144, 187, 145, 190, 188) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 8^4 ), ( 8^5 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 45 e = 100 f = 25 degree seq :: [ 4^25, 5^20 ] E16.1102 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {4, 4, 5}) Quotient :: loop Aut^+ = (C5 x C5) : C4 (small group id <100, 10>) Aut = (C5 x C5) : C4 (small group id <100, 10>) |r| :: 1 Presentation :: [ X2^4, X1^4, X2^-2 * X1^-1 * X2 * X1^2 * X2 * X1^-1, X2^-2 * X1 * X2 * X1^-2 * X2^-1 * X1^-1, X2^-1 * X1 * X2^-1 * X1^-1 * X2 * X1 * X2^-1 * X1^-1 * X2 * X1^-1, X2 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2^-1 * X1^-1 * X2 * X1 ] Map:: polyhedral non-degenerate R = (1, 101, 2, 102, 6, 106, 4, 104)(3, 103, 9, 109, 23, 123, 11, 111)(5, 105, 14, 114, 35, 135, 15, 115)(7, 107, 18, 118, 45, 145, 20, 120)(8, 108, 21, 121, 52, 152, 22, 122)(10, 110, 26, 126, 63, 163, 27, 127)(12, 112, 30, 130, 64, 164, 32, 132)(13, 113, 33, 133, 73, 173, 34, 134)(16, 116, 40, 140, 77, 177, 42, 142)(17, 117, 43, 143, 82, 182, 44, 144)(19, 119, 48, 148, 88, 188, 49, 149)(24, 124, 58, 158, 36, 136, 60, 160)(25, 125, 61, 161, 38, 138, 62, 162)(28, 128, 66, 166, 37, 137, 67, 167)(29, 129, 68, 168, 78, 178, 69, 169)(31, 131, 57, 157, 94, 194, 72, 172)(39, 139, 75, 175, 79, 179, 76, 176)(41, 141, 80, 180, 74, 174, 81, 181)(46, 146, 83, 183, 53, 153, 85, 185)(47, 147, 86, 186, 55, 155, 87, 187)(50, 150, 90, 190, 54, 154, 91, 191)(51, 151, 92, 192, 70, 170, 93, 193)(56, 156, 95, 195, 71, 171, 96, 196)(59, 159, 89, 189, 99, 199, 97, 197)(65, 165, 84, 184, 100, 200, 98, 198) L = (1, 103)(2, 107)(3, 110)(4, 112)(5, 101)(6, 116)(7, 119)(8, 102)(9, 124)(10, 105)(11, 128)(12, 131)(13, 104)(14, 136)(15, 138)(16, 141)(17, 106)(18, 146)(19, 108)(20, 150)(21, 153)(22, 155)(23, 148)(24, 159)(25, 109)(26, 145)(27, 152)(28, 143)(29, 111)(30, 170)(31, 113)(32, 154)(33, 151)(34, 156)(35, 174)(36, 142)(37, 114)(38, 144)(39, 115)(40, 178)(41, 117)(42, 137)(43, 129)(44, 139)(45, 180)(46, 184)(47, 118)(48, 177)(49, 182)(50, 133)(51, 120)(52, 194)(53, 132)(54, 121)(55, 134)(56, 122)(57, 123)(58, 186)(59, 125)(60, 192)(61, 187)(62, 190)(63, 189)(64, 126)(65, 127)(66, 183)(67, 193)(68, 185)(69, 196)(70, 198)(71, 130)(72, 135)(73, 188)(74, 197)(75, 191)(76, 195)(77, 157)(78, 199)(79, 140)(80, 164)(81, 173)(82, 163)(83, 176)(84, 147)(85, 160)(86, 175)(87, 167)(88, 200)(89, 149)(90, 169)(91, 158)(92, 168)(93, 161)(94, 165)(95, 166)(96, 162)(97, 172)(98, 171)(99, 179)(100, 181) local type(s) :: { ( 4, 5, 4, 5, 4, 5, 4, 5 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: simple v = 25 e = 100 f = 45 degree seq :: [ 8^25 ] E16.1103 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {4, 4, 5}) Quotient :: loop Aut^+ = (C5 x C5) : C4 (small group id <100, 10>) Aut = D10 x (C5 : C4) (small group id <200, 41>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, T2^4, F * T1 * F * T2, T2 * T1 * T2^2 * T1^-1 * T2^-1 * T1^-2, T2^-2 * T1^-1 * T2 * T1^-2 * T2 * T1^-1, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 3, 10, 5)(2, 7, 19, 8)(4, 12, 31, 13)(6, 16, 41, 17)(9, 24, 40, 25)(11, 28, 43, 29)(14, 36, 42, 37)(15, 38, 76, 39)(18, 46, 30, 47)(20, 50, 33, 51)(21, 53, 32, 54)(22, 55, 96, 56)(23, 48, 89, 57)(26, 63, 88, 64)(27, 52, 79, 65)(34, 72, 98, 73)(35, 49, 80, 71)(44, 81, 100, 82)(45, 78, 99, 83)(58, 94, 66, 87)(59, 84, 68, 90)(60, 92, 67, 85)(61, 86, 74, 91)(62, 77, 70, 97)(69, 95, 75, 93)(101, 102, 106, 104)(103, 109, 123, 111)(105, 114, 135, 115)(107, 118, 145, 120)(108, 121, 152, 122)(110, 126, 162, 127)(112, 130, 164, 132)(113, 133, 165, 134)(116, 140, 177, 142)(117, 143, 180, 144)(119, 148, 188, 149)(124, 158, 181, 159)(125, 160, 138, 161)(128, 166, 137, 167)(129, 168, 139, 169)(131, 170, 183, 171)(136, 174, 182, 175)(141, 178, 157, 179)(146, 184, 172, 185)(147, 186, 155, 187)(150, 190, 154, 191)(151, 192, 156, 193)(153, 194, 173, 195)(163, 196, 199, 198)(176, 189, 200, 197) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 10^4 ) } Outer automorphisms :: reflexible Dual of E16.1104 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 50 e = 100 f = 20 degree seq :: [ 4^50 ] E16.1104 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {4, 4, 5}) Quotient :: edge Aut^+ = (C5 x C5) : C4 (small group id <100, 10>) Aut = D10 x (C5 : C4) (small group id <200, 41>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, F * T1 * T2 * F * T1^-1, T2^5, T1^-1 * T2 * T1^-1 * T2^-1 * T1^2 * T2^2, T2 * T1^2 * T2^-2 * T1^-1 * T2^-1 * T1^-1, T2^-1 * F * T1^2 * T2^-1 * F * T1^-2, (T2 * T1 * F * T1^-1)^2, T1^-1 * T2^2 * T1^2 * T2 * T1^-1 * T2^-2 ] Map:: polytopal non-degenerate R = (1, 101, 3, 103, 10, 110, 16, 116, 5, 105)(2, 102, 7, 107, 20, 120, 24, 124, 8, 108)(4, 104, 12, 112, 33, 133, 37, 137, 13, 113)(6, 106, 17, 117, 46, 146, 50, 150, 18, 118)(9, 109, 26, 126, 67, 167, 68, 168, 27, 127)(11, 111, 30, 130, 74, 174, 75, 175, 31, 131)(14, 114, 39, 139, 83, 183, 79, 179, 40, 140)(15, 115, 41, 141, 84, 184, 85, 185, 42, 142)(19, 119, 52, 152, 25, 125, 65, 165, 53, 153)(21, 121, 56, 156, 97, 197, 81, 181, 57, 157)(22, 122, 59, 159, 82, 182, 38, 138, 60, 160)(23, 123, 61, 161, 76, 176, 98, 198, 62, 162)(28, 128, 70, 170, 94, 194, 49, 149, 71, 171)(29, 129, 45, 145, 90, 190, 51, 151, 72, 172)(32, 132, 73, 173, 89, 189, 96, 196, 55, 155)(34, 134, 77, 177, 99, 199, 63, 163, 78, 178)(35, 135, 64, 164, 100, 200, 92, 192, 80, 180)(36, 136, 69, 169, 54, 154, 95, 195, 66, 166)(43, 143, 86, 186, 47, 147, 91, 191, 87, 187)(44, 144, 88, 188, 58, 158, 93, 193, 48, 148) L = (1, 102)(2, 106)(3, 109)(4, 101)(5, 114)(6, 104)(7, 119)(8, 122)(9, 125)(10, 128)(11, 103)(12, 132)(13, 135)(14, 138)(15, 105)(16, 143)(17, 145)(18, 148)(19, 151)(20, 154)(21, 107)(22, 158)(23, 108)(24, 163)(25, 111)(26, 166)(27, 146)(28, 169)(29, 110)(30, 173)(31, 164)(32, 167)(33, 176)(34, 112)(35, 179)(36, 113)(37, 181)(38, 115)(39, 150)(40, 177)(41, 155)(42, 180)(43, 178)(44, 116)(45, 189)(46, 184)(47, 117)(48, 192)(49, 118)(50, 175)(51, 121)(52, 142)(53, 133)(54, 141)(55, 120)(56, 126)(57, 139)(58, 123)(59, 137)(60, 130)(61, 127)(62, 140)(63, 131)(64, 124)(65, 188)(66, 193)(67, 134)(68, 182)(69, 129)(70, 199)(71, 153)(72, 200)(73, 194)(74, 198)(75, 157)(76, 171)(77, 190)(78, 144)(79, 136)(80, 191)(81, 186)(82, 172)(83, 165)(84, 161)(85, 197)(86, 159)(87, 195)(88, 196)(89, 147)(90, 162)(91, 152)(92, 149)(93, 156)(94, 160)(95, 174)(96, 183)(97, 170)(98, 187)(99, 185)(100, 168) local type(s) :: { ( 4^10 ) } Outer automorphisms :: reflexible Dual of E16.1103 Transitivity :: ET+ VT+ Graph:: simple bipartite v = 20 e = 100 f = 50 degree seq :: [ 10^20 ] E16.1105 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 5}) Quotient :: edge^2 Aut^+ = (C5 x C5) : C4 (small group id <100, 10>) Aut = D10 x (C5 : C4) (small group id <200, 41>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y2^-1, Y1^4, Y1^4, Y2^4, (R * Y3)^2, R * Y2 * R * Y1, Y3^5, Y3^2 * Y2^-1 * Y1^-1 * Y3^2, Y2 * Y1 * Y2^-1 * Y3^2 * Y1^-1, Y3 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1 * Y3 * Y1^-1 * Y2^-1 * Y3^-1, Y3^2 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y3^2 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y1^-2 * Y3^2 * Y1^-1 * Y3 * Y2 ] Map:: polyhedral non-degenerate R = (1, 101, 4, 104, 17, 117, 29, 129, 7, 107)(2, 102, 9, 109, 33, 133, 42, 142, 11, 111)(3, 103, 5, 105, 21, 121, 53, 153, 15, 115)(6, 106, 24, 124, 70, 170, 77, 177, 25, 125)(8, 108, 30, 130, 75, 175, 66, 166, 20, 120)(10, 110, 37, 137, 23, 123, 72, 172, 38, 138)(12, 112, 44, 144, 92, 192, 98, 198, 45, 145)(13, 113, 14, 114, 49, 149, 35, 135, 47, 147)(16, 116, 18, 118, 59, 159, 90, 190, 56, 156)(19, 119, 61, 161, 64, 164, 65, 165, 62, 162)(22, 122, 60, 160, 88, 188, 91, 191, 71, 171)(26, 126, 79, 179, 48, 148, 43, 143, 80, 180)(27, 127, 28, 128, 83, 183, 87, 187, 81, 181)(31, 131, 89, 189, 36, 136, 57, 157, 50, 150)(32, 132, 34, 134, 74, 174, 100, 200, 51, 151)(39, 139, 52, 152, 82, 182, 78, 178, 95, 195)(40, 140, 41, 141, 76, 176, 69, 169, 96, 196)(46, 146, 63, 163, 84, 184, 73, 173, 94, 194)(54, 154, 55, 155, 67, 167, 68, 168, 97, 197)(58, 158, 85, 185, 86, 186, 93, 193, 99, 199)(201, 202, 208, 205)(203, 212, 243, 214)(204, 206, 223, 218)(207, 226, 278, 228)(209, 210, 236, 234)(211, 239, 294, 241)(213, 246, 274, 224)(215, 251, 285, 252)(216, 244, 242, 255)(217, 219, 249, 250)(220, 263, 298, 265)(221, 222, 270, 268)(225, 275, 287, 276)(227, 245, 293, 237)(229, 258, 267, 284)(230, 231, 288, 286)(232, 279, 266, 256)(233, 235, 283, 271)(238, 253, 269, 262)(240, 280, 297, 289)(247, 290, 296, 299)(248, 272, 273, 291)(254, 281, 300, 261)(257, 292, 277, 282)(259, 260, 264, 295)(301, 303, 313, 306)(302, 307, 327, 310)(304, 316, 354, 319)(305, 320, 364, 322)(308, 311, 340, 331)(309, 332, 390, 335)(312, 315, 339, 342)(314, 348, 388, 350)(317, 357, 352, 358)(318, 337, 386, 360)(321, 367, 399, 369)(323, 325, 341, 373)(324, 334, 389, 368)(326, 329, 363, 366)(328, 382, 370, 371)(330, 385, 400, 387)(333, 391, 384, 355)(336, 338, 365, 392)(343, 345, 381, 397)(344, 356, 375, 377)(346, 347, 393, 398)(349, 362, 376, 383)(351, 353, 372, 379)(359, 378, 380, 396)(361, 374, 394, 395) L = (1, 201)(2, 202)(3, 203)(4, 204)(5, 205)(6, 206)(7, 207)(8, 208)(9, 209)(10, 210)(11, 211)(12, 212)(13, 213)(14, 214)(15, 215)(16, 216)(17, 217)(18, 218)(19, 219)(20, 220)(21, 221)(22, 222)(23, 223)(24, 224)(25, 225)(26, 226)(27, 227)(28, 228)(29, 229)(30, 230)(31, 231)(32, 232)(33, 233)(34, 234)(35, 235)(36, 236)(37, 237)(38, 238)(39, 239)(40, 240)(41, 241)(42, 242)(43, 243)(44, 244)(45, 245)(46, 246)(47, 247)(48, 248)(49, 249)(50, 250)(51, 251)(52, 252)(53, 253)(54, 254)(55, 255)(56, 256)(57, 257)(58, 258)(59, 259)(60, 260)(61, 261)(62, 262)(63, 263)(64, 264)(65, 265)(66, 266)(67, 267)(68, 268)(69, 269)(70, 270)(71, 271)(72, 272)(73, 273)(74, 274)(75, 275)(76, 276)(77, 277)(78, 278)(79, 279)(80, 280)(81, 281)(82, 282)(83, 283)(84, 284)(85, 285)(86, 286)(87, 287)(88, 288)(89, 289)(90, 290)(91, 291)(92, 292)(93, 293)(94, 294)(95, 295)(96, 296)(97, 297)(98, 298)(99, 299)(100, 300)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 4^4 ), ( 4^10 ) } Outer automorphisms :: reflexible Dual of E16.1108 Graph:: simple bipartite v = 70 e = 200 f = 100 degree seq :: [ 4^50, 10^20 ] E16.1106 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 5}) Quotient :: edge^2 Aut^+ = (C5 x C5) : C4 (small group id <100, 10>) Aut = D10 x (C5 : C4) (small group id <200, 41>) |r| :: 2 Presentation :: [ Y3, R^2, Y1^4, Y1^4, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y2 * Y1^-2 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, Y2 * Y1 * Y2^2 * Y1^-1 * Y2^-1 * Y1^-2, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^5 ] Map:: polytopal R = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200)(201, 202, 206, 204)(203, 209, 223, 211)(205, 214, 235, 215)(207, 218, 245, 220)(208, 221, 252, 222)(210, 226, 262, 227)(212, 230, 264, 232)(213, 233, 265, 234)(216, 240, 277, 242)(217, 243, 280, 244)(219, 248, 288, 249)(224, 258, 281, 259)(225, 260, 238, 261)(228, 266, 237, 267)(229, 268, 239, 269)(231, 270, 283, 271)(236, 274, 282, 275)(241, 278, 257, 279)(246, 284, 272, 285)(247, 286, 255, 287)(250, 290, 254, 291)(251, 292, 256, 293)(253, 294, 273, 295)(263, 296, 299, 298)(276, 289, 300, 297)(301, 303, 310, 305)(302, 307, 319, 308)(304, 312, 331, 313)(306, 316, 341, 317)(309, 324, 340, 325)(311, 328, 343, 329)(314, 336, 342, 337)(315, 338, 376, 339)(318, 346, 330, 347)(320, 350, 333, 351)(321, 353, 332, 354)(322, 355, 396, 356)(323, 348, 389, 357)(326, 363, 388, 364)(327, 352, 379, 365)(334, 372, 398, 373)(335, 349, 380, 371)(344, 381, 400, 382)(345, 378, 399, 383)(358, 394, 366, 387)(359, 384, 368, 390)(360, 392, 367, 385)(361, 386, 374, 391)(362, 377, 370, 397)(369, 395, 375, 393) L = (1, 201)(2, 202)(3, 203)(4, 204)(5, 205)(6, 206)(7, 207)(8, 208)(9, 209)(10, 210)(11, 211)(12, 212)(13, 213)(14, 214)(15, 215)(16, 216)(17, 217)(18, 218)(19, 219)(20, 220)(21, 221)(22, 222)(23, 223)(24, 224)(25, 225)(26, 226)(27, 227)(28, 228)(29, 229)(30, 230)(31, 231)(32, 232)(33, 233)(34, 234)(35, 235)(36, 236)(37, 237)(38, 238)(39, 239)(40, 240)(41, 241)(42, 242)(43, 243)(44, 244)(45, 245)(46, 246)(47, 247)(48, 248)(49, 249)(50, 250)(51, 251)(52, 252)(53, 253)(54, 254)(55, 255)(56, 256)(57, 257)(58, 258)(59, 259)(60, 260)(61, 261)(62, 262)(63, 263)(64, 264)(65, 265)(66, 266)(67, 267)(68, 268)(69, 269)(70, 270)(71, 271)(72, 272)(73, 273)(74, 274)(75, 275)(76, 276)(77, 277)(78, 278)(79, 279)(80, 280)(81, 281)(82, 282)(83, 283)(84, 284)(85, 285)(86, 286)(87, 287)(88, 288)(89, 289)(90, 290)(91, 291)(92, 292)(93, 293)(94, 294)(95, 295)(96, 296)(97, 297)(98, 298)(99, 299)(100, 300)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 20, 20 ), ( 20^4 ) } Outer automorphisms :: reflexible Dual of E16.1107 Graph:: simple bipartite v = 150 e = 200 f = 20 degree seq :: [ 2^100, 4^50 ] E16.1107 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 5}) Quotient :: loop^2 Aut^+ = (C5 x C5) : C4 (small group id <100, 10>) Aut = D10 x (C5 : C4) (small group id <200, 41>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y2^-1, Y1^4, Y1^4, Y2^4, (R * Y3)^2, R * Y2 * R * Y1, Y3^5, Y3^2 * Y2^-1 * Y1^-1 * Y3^2, Y2 * Y1 * Y2^-1 * Y3^2 * Y1^-1, Y3 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1 * Y3 * Y1^-1 * Y2^-1 * Y3^-1, Y3^2 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y3^2 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y1^-2 * Y3^2 * Y1^-1 * Y3 * Y2 ] Map:: R = (1, 101, 201, 301, 4, 104, 204, 304, 17, 117, 217, 317, 29, 129, 229, 329, 7, 107, 207, 307)(2, 102, 202, 302, 9, 109, 209, 309, 33, 133, 233, 333, 42, 142, 242, 342, 11, 111, 211, 311)(3, 103, 203, 303, 5, 105, 205, 305, 21, 121, 221, 321, 53, 153, 253, 353, 15, 115, 215, 315)(6, 106, 206, 306, 24, 124, 224, 324, 70, 170, 270, 370, 77, 177, 277, 377, 25, 125, 225, 325)(8, 108, 208, 308, 30, 130, 230, 330, 75, 175, 275, 375, 66, 166, 266, 366, 20, 120, 220, 320)(10, 110, 210, 310, 37, 137, 237, 337, 23, 123, 223, 323, 72, 172, 272, 372, 38, 138, 238, 338)(12, 112, 212, 312, 44, 144, 244, 344, 92, 192, 292, 392, 98, 198, 298, 398, 45, 145, 245, 345)(13, 113, 213, 313, 14, 114, 214, 314, 49, 149, 249, 349, 35, 135, 235, 335, 47, 147, 247, 347)(16, 116, 216, 316, 18, 118, 218, 318, 59, 159, 259, 359, 90, 190, 290, 390, 56, 156, 256, 356)(19, 119, 219, 319, 61, 161, 261, 361, 64, 164, 264, 364, 65, 165, 265, 365, 62, 162, 262, 362)(22, 122, 222, 322, 60, 160, 260, 360, 88, 188, 288, 388, 91, 191, 291, 391, 71, 171, 271, 371)(26, 126, 226, 326, 79, 179, 279, 379, 48, 148, 248, 348, 43, 143, 243, 343, 80, 180, 280, 380)(27, 127, 227, 327, 28, 128, 228, 328, 83, 183, 283, 383, 87, 187, 287, 387, 81, 181, 281, 381)(31, 131, 231, 331, 89, 189, 289, 389, 36, 136, 236, 336, 57, 157, 257, 357, 50, 150, 250, 350)(32, 132, 232, 332, 34, 134, 234, 334, 74, 174, 274, 374, 100, 200, 300, 400, 51, 151, 251, 351)(39, 139, 239, 339, 52, 152, 252, 352, 82, 182, 282, 382, 78, 178, 278, 378, 95, 195, 295, 395)(40, 140, 240, 340, 41, 141, 241, 341, 76, 176, 276, 376, 69, 169, 269, 369, 96, 196, 296, 396)(46, 146, 246, 346, 63, 163, 263, 363, 84, 184, 284, 384, 73, 173, 273, 373, 94, 194, 294, 394)(54, 154, 254, 354, 55, 155, 255, 355, 67, 167, 267, 367, 68, 168, 268, 368, 97, 197, 297, 397)(58, 158, 258, 358, 85, 185, 285, 385, 86, 186, 286, 386, 93, 193, 293, 393, 99, 199, 299, 399) L = (1, 102)(2, 108)(3, 112)(4, 106)(5, 101)(6, 123)(7, 126)(8, 105)(9, 110)(10, 136)(11, 139)(12, 143)(13, 146)(14, 103)(15, 151)(16, 144)(17, 119)(18, 104)(19, 149)(20, 163)(21, 122)(22, 170)(23, 118)(24, 113)(25, 175)(26, 178)(27, 145)(28, 107)(29, 158)(30, 131)(31, 188)(32, 179)(33, 135)(34, 109)(35, 183)(36, 134)(37, 127)(38, 153)(39, 194)(40, 180)(41, 111)(42, 155)(43, 114)(44, 142)(45, 193)(46, 174)(47, 190)(48, 172)(49, 150)(50, 117)(51, 185)(52, 115)(53, 169)(54, 181)(55, 116)(56, 132)(57, 192)(58, 167)(59, 160)(60, 164)(61, 154)(62, 138)(63, 198)(64, 195)(65, 120)(66, 156)(67, 184)(68, 121)(69, 162)(70, 168)(71, 133)(72, 173)(73, 191)(74, 124)(75, 187)(76, 125)(77, 182)(78, 128)(79, 166)(80, 197)(81, 200)(82, 157)(83, 171)(84, 129)(85, 152)(86, 130)(87, 176)(88, 186)(89, 140)(90, 196)(91, 148)(92, 177)(93, 137)(94, 141)(95, 159)(96, 199)(97, 189)(98, 165)(99, 147)(100, 161)(201, 303)(202, 307)(203, 313)(204, 316)(205, 320)(206, 301)(207, 327)(208, 311)(209, 332)(210, 302)(211, 340)(212, 315)(213, 306)(214, 348)(215, 339)(216, 354)(217, 357)(218, 337)(219, 304)(220, 364)(221, 367)(222, 305)(223, 325)(224, 334)(225, 341)(226, 329)(227, 310)(228, 382)(229, 363)(230, 385)(231, 308)(232, 390)(233, 391)(234, 389)(235, 309)(236, 338)(237, 386)(238, 365)(239, 342)(240, 331)(241, 373)(242, 312)(243, 345)(244, 356)(245, 381)(246, 347)(247, 393)(248, 388)(249, 362)(250, 314)(251, 353)(252, 358)(253, 372)(254, 319)(255, 333)(256, 375)(257, 352)(258, 317)(259, 378)(260, 318)(261, 374)(262, 376)(263, 366)(264, 322)(265, 392)(266, 326)(267, 399)(268, 324)(269, 321)(270, 371)(271, 328)(272, 379)(273, 323)(274, 394)(275, 377)(276, 383)(277, 344)(278, 380)(279, 351)(280, 396)(281, 397)(282, 370)(283, 349)(284, 355)(285, 400)(286, 360)(287, 330)(288, 350)(289, 368)(290, 335)(291, 384)(292, 336)(293, 398)(294, 395)(295, 361)(296, 359)(297, 343)(298, 346)(299, 369)(300, 387) 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 E16.1106 Transitivity :: VT+ Graph:: bipartite v = 20 e = 200 f = 150 degree seq :: [ 20^20 ] E16.1108 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 5}) Quotient :: loop^2 Aut^+ = (C5 x C5) : C4 (small group id <100, 10>) Aut = D10 x (C5 : C4) (small group id <200, 41>) |r| :: 2 Presentation :: [ Y3, R^2, Y1^4, Y1^4, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y2 * Y1^-2 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, Y2 * Y1 * Y2^2 * Y1^-1 * Y2^-1 * Y1^-2, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^5 ] Map:: polyhedral non-degenerate R = (1, 101, 201, 301)(2, 102, 202, 302)(3, 103, 203, 303)(4, 104, 204, 304)(5, 105, 205, 305)(6, 106, 206, 306)(7, 107, 207, 307)(8, 108, 208, 308)(9, 109, 209, 309)(10, 110, 210, 310)(11, 111, 211, 311)(12, 112, 212, 312)(13, 113, 213, 313)(14, 114, 214, 314)(15, 115, 215, 315)(16, 116, 216, 316)(17, 117, 217, 317)(18, 118, 218, 318)(19, 119, 219, 319)(20, 120, 220, 320)(21, 121, 221, 321)(22, 122, 222, 322)(23, 123, 223, 323)(24, 124, 224, 324)(25, 125, 225, 325)(26, 126, 226, 326)(27, 127, 227, 327)(28, 128, 228, 328)(29, 129, 229, 329)(30, 130, 230, 330)(31, 131, 231, 331)(32, 132, 232, 332)(33, 133, 233, 333)(34, 134, 234, 334)(35, 135, 235, 335)(36, 136, 236, 336)(37, 137, 237, 337)(38, 138, 238, 338)(39, 139, 239, 339)(40, 140, 240, 340)(41, 141, 241, 341)(42, 142, 242, 342)(43, 143, 243, 343)(44, 144, 244, 344)(45, 145, 245, 345)(46, 146, 246, 346)(47, 147, 247, 347)(48, 148, 248, 348)(49, 149, 249, 349)(50, 150, 250, 350)(51, 151, 251, 351)(52, 152, 252, 352)(53, 153, 253, 353)(54, 154, 254, 354)(55, 155, 255, 355)(56, 156, 256, 356)(57, 157, 257, 357)(58, 158, 258, 358)(59, 159, 259, 359)(60, 160, 260, 360)(61, 161, 261, 361)(62, 162, 262, 362)(63, 163, 263, 363)(64, 164, 264, 364)(65, 165, 265, 365)(66, 166, 266, 366)(67, 167, 267, 367)(68, 168, 268, 368)(69, 169, 269, 369)(70, 170, 270, 370)(71, 171, 271, 371)(72, 172, 272, 372)(73, 173, 273, 373)(74, 174, 274, 374)(75, 175, 275, 375)(76, 176, 276, 376)(77, 177, 277, 377)(78, 178, 278, 378)(79, 179, 279, 379)(80, 180, 280, 380)(81, 181, 281, 381)(82, 182, 282, 382)(83, 183, 283, 383)(84, 184, 284, 384)(85, 185, 285, 385)(86, 186, 286, 386)(87, 187, 287, 387)(88, 188, 288, 388)(89, 189, 289, 389)(90, 190, 290, 390)(91, 191, 291, 391)(92, 192, 292, 392)(93, 193, 293, 393)(94, 194, 294, 394)(95, 195, 295, 395)(96, 196, 296, 396)(97, 197, 297, 397)(98, 198, 298, 398)(99, 199, 299, 399)(100, 200, 300, 400) L = (1, 102)(2, 106)(3, 109)(4, 101)(5, 114)(6, 104)(7, 118)(8, 121)(9, 123)(10, 126)(11, 103)(12, 130)(13, 133)(14, 135)(15, 105)(16, 140)(17, 143)(18, 145)(19, 148)(20, 107)(21, 152)(22, 108)(23, 111)(24, 158)(25, 160)(26, 162)(27, 110)(28, 166)(29, 168)(30, 164)(31, 170)(32, 112)(33, 165)(34, 113)(35, 115)(36, 174)(37, 167)(38, 161)(39, 169)(40, 177)(41, 178)(42, 116)(43, 180)(44, 117)(45, 120)(46, 184)(47, 186)(48, 188)(49, 119)(50, 190)(51, 192)(52, 122)(53, 194)(54, 191)(55, 187)(56, 193)(57, 179)(58, 181)(59, 124)(60, 138)(61, 125)(62, 127)(63, 196)(64, 132)(65, 134)(66, 137)(67, 128)(68, 139)(69, 129)(70, 183)(71, 131)(72, 185)(73, 195)(74, 182)(75, 136)(76, 189)(77, 142)(78, 157)(79, 141)(80, 144)(81, 159)(82, 175)(83, 171)(84, 172)(85, 146)(86, 155)(87, 147)(88, 149)(89, 200)(90, 154)(91, 150)(92, 156)(93, 151)(94, 173)(95, 153)(96, 199)(97, 176)(98, 163)(99, 198)(100, 197)(201, 303)(202, 307)(203, 310)(204, 312)(205, 301)(206, 316)(207, 319)(208, 302)(209, 324)(210, 305)(211, 328)(212, 331)(213, 304)(214, 336)(215, 338)(216, 341)(217, 306)(218, 346)(219, 308)(220, 350)(221, 353)(222, 355)(223, 348)(224, 340)(225, 309)(226, 363)(227, 352)(228, 343)(229, 311)(230, 347)(231, 313)(232, 354)(233, 351)(234, 372)(235, 349)(236, 342)(237, 314)(238, 376)(239, 315)(240, 325)(241, 317)(242, 337)(243, 329)(244, 381)(245, 378)(246, 330)(247, 318)(248, 389)(249, 380)(250, 333)(251, 320)(252, 379)(253, 332)(254, 321)(255, 396)(256, 322)(257, 323)(258, 394)(259, 384)(260, 392)(261, 386)(262, 377)(263, 388)(264, 326)(265, 327)(266, 387)(267, 385)(268, 390)(269, 395)(270, 397)(271, 335)(272, 398)(273, 334)(274, 391)(275, 393)(276, 339)(277, 370)(278, 399)(279, 365)(280, 371)(281, 400)(282, 344)(283, 345)(284, 368)(285, 360)(286, 374)(287, 358)(288, 364)(289, 357)(290, 359)(291, 361)(292, 367)(293, 369)(294, 366)(295, 375)(296, 356)(297, 362)(298, 373)(299, 383)(300, 382) local type(s) :: { ( 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.1105 Transitivity :: VT+ Graph:: simple bipartite v = 100 e = 200 f = 70 degree seq :: [ 4^100 ] E16.1109 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 5}) Quotient :: edge Aut^+ = (C5 x C5) : C4 (small group id <100, 12>) Aut = (D10 x D10) : C2 (small group id <200, 43>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^4, T2^5, (T1 * T2 * T1)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 3, 10, 16, 5)(2, 7, 20, 24, 8)(4, 12, 31, 32, 13)(6, 17, 39, 40, 18)(9, 25, 53, 54, 26)(11, 29, 59, 60, 30)(14, 33, 61, 62, 34)(15, 35, 63, 64, 36)(19, 41, 69, 70, 42)(21, 45, 75, 76, 46)(22, 47, 77, 78, 48)(23, 49, 79, 80, 50)(27, 55, 85, 86, 56)(28, 57, 87, 88, 58)(37, 65, 89, 90, 66)(38, 67, 91, 92, 68)(43, 71, 93, 94, 72)(44, 73, 95, 96, 74)(51, 81, 97, 98, 82)(52, 83, 99, 100, 84)(101, 102, 106, 104)(103, 109, 118, 111)(105, 114, 117, 115)(107, 119, 113, 121)(108, 122, 112, 123)(110, 127, 140, 128)(116, 137, 139, 138)(120, 143, 132, 144)(124, 151, 131, 152)(125, 142, 130, 145)(126, 148, 129, 149)(133, 141, 136, 146)(134, 147, 135, 150)(153, 172, 160, 173)(154, 182, 159, 183)(155, 170, 158, 175)(156, 178, 157, 179)(161, 171, 164, 174)(162, 181, 163, 184)(165, 169, 168, 176)(166, 177, 167, 180)(185, 194, 188, 195)(186, 198, 187, 199)(189, 193, 192, 196)(190, 197, 191, 200) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 8^4 ), ( 8^5 ) } Outer automorphisms :: reflexible Dual of E16.1110 Transitivity :: ET+ Graph:: simple bipartite v = 45 e = 100 f = 25 degree seq :: [ 4^25, 5^20 ] E16.1110 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 5}) Quotient :: loop Aut^+ = (C5 x C5) : C4 (small group id <100, 12>) Aut = (D10 x D10) : C2 (small group id <200, 43>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T2^4, (T2 * T1^-1)^2, T1^4, (T2^-1 * T1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 101, 3, 103, 10, 110, 5, 105)(2, 102, 7, 107, 17, 117, 8, 108)(4, 104, 11, 111, 23, 123, 12, 112)(6, 106, 14, 114, 27, 127, 15, 115)(9, 109, 19, 119, 34, 134, 20, 120)(13, 113, 21, 121, 36, 136, 25, 125)(16, 116, 29, 129, 47, 147, 30, 130)(18, 118, 31, 131, 49, 149, 32, 132)(22, 122, 37, 137, 57, 157, 38, 138)(24, 124, 39, 139, 59, 159, 40, 140)(26, 126, 42, 142, 61, 161, 43, 143)(28, 128, 44, 144, 63, 163, 45, 145)(33, 133, 51, 151, 69, 169, 52, 152)(35, 135, 53, 153, 71, 171, 54, 154)(41, 141, 55, 155, 65, 165, 46, 146)(48, 148, 66, 166, 81, 181, 67, 167)(50, 150, 68, 168, 76, 176, 60, 160)(56, 156, 64, 164, 79, 179, 73, 173)(58, 158, 74, 174, 87, 187, 75, 175)(62, 162, 77, 177, 89, 189, 78, 178)(70, 170, 83, 183, 93, 193, 84, 184)(72, 172, 85, 185, 91, 191, 80, 180)(82, 182, 92, 192, 96, 196, 88, 188)(86, 186, 90, 190, 97, 197, 95, 195)(94, 194, 99, 199, 100, 200, 98, 198) L = (1, 102)(2, 106)(3, 109)(4, 101)(5, 111)(6, 104)(7, 116)(8, 103)(9, 118)(10, 121)(11, 122)(12, 114)(13, 105)(14, 126)(15, 107)(16, 128)(17, 131)(18, 108)(19, 133)(20, 110)(21, 135)(22, 113)(23, 139)(24, 112)(25, 137)(26, 124)(27, 144)(28, 115)(29, 146)(30, 117)(31, 148)(32, 119)(33, 150)(34, 153)(35, 120)(36, 155)(37, 156)(38, 123)(39, 158)(40, 142)(41, 125)(42, 160)(43, 127)(44, 162)(45, 129)(46, 164)(47, 166)(48, 130)(49, 168)(50, 132)(51, 140)(52, 134)(53, 170)(54, 136)(55, 172)(56, 141)(57, 174)(58, 138)(59, 169)(60, 151)(61, 177)(62, 143)(63, 179)(64, 145)(65, 147)(66, 180)(67, 149)(68, 182)(69, 183)(70, 152)(71, 185)(72, 154)(73, 157)(74, 186)(75, 159)(76, 161)(77, 188)(78, 163)(79, 190)(80, 165)(81, 192)(82, 167)(83, 175)(84, 171)(85, 194)(86, 173)(87, 193)(88, 176)(89, 197)(90, 178)(91, 181)(92, 198)(93, 199)(94, 184)(95, 187)(96, 189)(97, 200)(98, 191)(99, 195)(100, 196) local type(s) :: { ( 4, 5, 4, 5, 4, 5, 4, 5 ) } Outer automorphisms :: reflexible Dual of E16.1109 Transitivity :: ET+ VT+ AT Graph:: v = 25 e = 100 f = 45 degree seq :: [ 8^25 ] E16.1111 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 5}) Quotient :: dipole Aut^+ = (C5 x C5) : C4 (small group id <100, 12>) Aut = (D10 x D10) : C2 (small group id <200, 43>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2^5, (Y1 * Y2 * Y1)^2, (Y3^-1 * Y1^-1)^4, Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, (Y2^2 * Y1^-1 * Y2^-1 * Y1^-1)^2, Y2^2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2 * Y1^-1 ] Map:: R = (1, 101, 2, 102, 6, 106, 4, 104)(3, 103, 9, 109, 18, 118, 11, 111)(5, 105, 14, 114, 17, 117, 15, 115)(7, 107, 19, 119, 13, 113, 21, 121)(8, 108, 22, 122, 12, 112, 23, 123)(10, 110, 27, 127, 40, 140, 28, 128)(16, 116, 37, 137, 39, 139, 38, 138)(20, 120, 43, 143, 32, 132, 44, 144)(24, 124, 51, 151, 31, 131, 52, 152)(25, 125, 42, 142, 30, 130, 45, 145)(26, 126, 48, 148, 29, 129, 49, 149)(33, 133, 41, 141, 36, 136, 46, 146)(34, 134, 47, 147, 35, 135, 50, 150)(53, 153, 72, 172, 60, 160, 73, 173)(54, 154, 82, 182, 59, 159, 83, 183)(55, 155, 70, 170, 58, 158, 75, 175)(56, 156, 78, 178, 57, 157, 79, 179)(61, 161, 71, 171, 64, 164, 74, 174)(62, 162, 81, 181, 63, 163, 84, 184)(65, 165, 69, 169, 68, 168, 76, 176)(66, 166, 77, 177, 67, 167, 80, 180)(85, 185, 94, 194, 88, 188, 95, 195)(86, 186, 98, 198, 87, 187, 99, 199)(89, 189, 93, 193, 92, 192, 96, 196)(90, 190, 97, 197, 91, 191, 100, 200)(201, 301, 203, 303, 210, 310, 216, 316, 205, 305)(202, 302, 207, 307, 220, 320, 224, 324, 208, 308)(204, 304, 212, 312, 231, 331, 232, 332, 213, 313)(206, 306, 217, 317, 239, 339, 240, 340, 218, 318)(209, 309, 225, 325, 253, 353, 254, 354, 226, 326)(211, 311, 229, 329, 259, 359, 260, 360, 230, 330)(214, 314, 233, 333, 261, 361, 262, 362, 234, 334)(215, 315, 235, 335, 263, 363, 264, 364, 236, 336)(219, 319, 241, 341, 269, 369, 270, 370, 242, 342)(221, 321, 245, 345, 275, 375, 276, 376, 246, 346)(222, 322, 247, 347, 277, 377, 278, 378, 248, 348)(223, 323, 249, 349, 279, 379, 280, 380, 250, 350)(227, 327, 255, 355, 285, 385, 286, 386, 256, 356)(228, 328, 257, 357, 287, 387, 288, 388, 258, 358)(237, 337, 265, 365, 289, 389, 290, 390, 266, 366)(238, 338, 267, 367, 291, 391, 292, 392, 268, 368)(243, 343, 271, 371, 293, 393, 294, 394, 272, 372)(244, 344, 273, 373, 295, 395, 296, 396, 274, 374)(251, 351, 281, 381, 297, 397, 298, 398, 282, 382)(252, 352, 283, 383, 299, 399, 300, 400, 284, 384) L = (1, 203)(2, 207)(3, 210)(4, 212)(5, 201)(6, 217)(7, 220)(8, 202)(9, 225)(10, 216)(11, 229)(12, 231)(13, 204)(14, 233)(15, 235)(16, 205)(17, 239)(18, 206)(19, 241)(20, 224)(21, 245)(22, 247)(23, 249)(24, 208)(25, 253)(26, 209)(27, 255)(28, 257)(29, 259)(30, 211)(31, 232)(32, 213)(33, 261)(34, 214)(35, 263)(36, 215)(37, 265)(38, 267)(39, 240)(40, 218)(41, 269)(42, 219)(43, 271)(44, 273)(45, 275)(46, 221)(47, 277)(48, 222)(49, 279)(50, 223)(51, 281)(52, 283)(53, 254)(54, 226)(55, 285)(56, 227)(57, 287)(58, 228)(59, 260)(60, 230)(61, 262)(62, 234)(63, 264)(64, 236)(65, 289)(66, 237)(67, 291)(68, 238)(69, 270)(70, 242)(71, 293)(72, 243)(73, 295)(74, 244)(75, 276)(76, 246)(77, 278)(78, 248)(79, 280)(80, 250)(81, 297)(82, 251)(83, 299)(84, 252)(85, 286)(86, 256)(87, 288)(88, 258)(89, 290)(90, 266)(91, 292)(92, 268)(93, 294)(94, 272)(95, 296)(96, 274)(97, 298)(98, 282)(99, 300)(100, 284)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) 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 E16.1112 Graph:: bipartite v = 45 e = 200 f = 125 degree seq :: [ 8^25, 10^20 ] E16.1112 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 5}) Quotient :: dipole Aut^+ = (C5 x C5) : C4 (small group id <100, 12>) Aut = (D10 x D10) : C2 (small group id <200, 43>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-2)^2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2, (Y3 * Y2)^4, (Y3^-1 * Y1^-1)^5, Y3^2 * Y2 * Y3^-2 * Y2 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 ] Map:: polytopal R = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200)(201, 301, 202, 302, 206, 306, 204, 304)(203, 303, 209, 309, 218, 318, 211, 311)(205, 305, 214, 314, 217, 317, 215, 315)(207, 307, 219, 319, 213, 313, 221, 321)(208, 308, 222, 322, 212, 312, 223, 323)(210, 310, 227, 327, 240, 340, 228, 328)(216, 316, 237, 337, 239, 339, 238, 338)(220, 320, 243, 343, 232, 332, 244, 344)(224, 324, 251, 351, 231, 331, 252, 352)(225, 325, 242, 342, 230, 330, 245, 345)(226, 326, 248, 348, 229, 329, 249, 349)(233, 333, 241, 341, 236, 336, 246, 346)(234, 334, 247, 347, 235, 335, 250, 350)(253, 353, 272, 372, 260, 360, 273, 373)(254, 354, 282, 382, 259, 359, 283, 383)(255, 355, 270, 370, 258, 358, 275, 375)(256, 356, 278, 378, 257, 357, 279, 379)(261, 361, 271, 371, 264, 364, 274, 374)(262, 362, 281, 381, 263, 363, 284, 384)(265, 365, 269, 369, 268, 368, 276, 376)(266, 366, 277, 377, 267, 367, 280, 380)(285, 385, 294, 394, 288, 388, 295, 395)(286, 386, 298, 398, 287, 387, 299, 399)(289, 389, 293, 393, 292, 392, 296, 396)(290, 390, 297, 397, 291, 391, 300, 400) L = (1, 203)(2, 207)(3, 210)(4, 212)(5, 201)(6, 217)(7, 220)(8, 202)(9, 225)(10, 216)(11, 229)(12, 231)(13, 204)(14, 233)(15, 235)(16, 205)(17, 239)(18, 206)(19, 241)(20, 224)(21, 245)(22, 247)(23, 249)(24, 208)(25, 253)(26, 209)(27, 255)(28, 257)(29, 259)(30, 211)(31, 232)(32, 213)(33, 261)(34, 214)(35, 263)(36, 215)(37, 265)(38, 267)(39, 240)(40, 218)(41, 269)(42, 219)(43, 271)(44, 273)(45, 275)(46, 221)(47, 277)(48, 222)(49, 279)(50, 223)(51, 281)(52, 283)(53, 254)(54, 226)(55, 285)(56, 227)(57, 287)(58, 228)(59, 260)(60, 230)(61, 262)(62, 234)(63, 264)(64, 236)(65, 289)(66, 237)(67, 291)(68, 238)(69, 270)(70, 242)(71, 293)(72, 243)(73, 295)(74, 244)(75, 276)(76, 246)(77, 278)(78, 248)(79, 280)(80, 250)(81, 297)(82, 251)(83, 299)(84, 252)(85, 286)(86, 256)(87, 288)(88, 258)(89, 290)(90, 266)(91, 292)(92, 268)(93, 294)(94, 272)(95, 296)(96, 274)(97, 298)(98, 282)(99, 300)(100, 284)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E16.1111 Graph:: simple bipartite v = 125 e = 200 f = 45 degree seq :: [ 2^100, 8^25 ] E16.1113 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 10, 10}) Quotient :: regular Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^10, (T2 * T1^-5)^2, T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 43, 42, 22, 10, 4)(3, 7, 15, 31, 55, 70, 62, 36, 18, 8)(6, 13, 27, 51, 81, 69, 84, 54, 30, 14)(9, 19, 37, 63, 72, 44, 71, 64, 38, 20)(12, 25, 47, 77, 68, 41, 67, 80, 50, 26)(16, 28, 48, 74, 93, 92, 100, 88, 58, 33)(17, 29, 49, 75, 94, 85, 99, 89, 59, 34)(21, 39, 65, 76, 46, 24, 45, 73, 66, 40)(32, 52, 78, 95, 91, 61, 83, 98, 87, 57)(35, 53, 79, 96, 86, 56, 82, 97, 90, 60) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 69)(43, 70)(45, 74)(46, 75)(47, 78)(50, 79)(51, 82)(54, 83)(55, 85)(62, 92)(63, 86)(64, 91)(65, 87)(66, 90)(67, 88)(68, 89)(71, 93)(72, 94)(73, 95)(76, 96)(77, 97)(80, 98)(81, 99)(84, 100) local type(s) :: { ( 10^10 ) } Outer automorphisms :: reflexible Dual of E16.1114 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 10 e = 50 f = 10 degree seq :: [ 10^10 ] E16.1114 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 10, 10}) Quotient :: regular Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^10, (T1^-1 * T2)^10 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 32, 31, 19, 10, 4)(3, 7, 12, 22, 33, 47, 43, 28, 17, 8)(6, 13, 21, 34, 46, 45, 30, 18, 9, 14)(15, 25, 35, 49, 60, 57, 42, 27, 16, 26)(23, 36, 48, 61, 59, 44, 29, 38, 24, 37)(39, 53, 62, 74, 71, 56, 41, 55, 40, 54)(50, 63, 73, 72, 58, 66, 52, 65, 51, 64)(67, 79, 85, 83, 70, 82, 69, 81, 68, 80)(75, 86, 84, 90, 78, 89, 77, 88, 76, 87)(91, 96, 95, 100, 94, 99, 93, 98, 92, 97) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 33)(22, 35)(25, 39)(26, 40)(27, 41)(28, 42)(31, 43)(32, 46)(34, 48)(36, 50)(37, 51)(38, 52)(44, 58)(45, 59)(47, 60)(49, 62)(53, 67)(54, 68)(55, 69)(56, 70)(57, 71)(61, 73)(63, 75)(64, 76)(65, 77)(66, 78)(72, 84)(74, 85)(79, 91)(80, 92)(81, 93)(82, 94)(83, 95)(86, 96)(87, 97)(88, 98)(89, 99)(90, 100) local type(s) :: { ( 10^10 ) } Outer automorphisms :: reflexible Dual of E16.1113 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 10 e = 50 f = 10 degree seq :: [ 10^10 ] E16.1115 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 10, 10}) Quotient :: regular Aut^+ = D10 x D10 (small group id <100, 13>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^10, T1 * T2 * T1^-6 * T2 * T1^3, (T1 * T2)^10 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 32, 31, 19, 10, 4)(3, 7, 15, 25, 39, 47, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 46, 34, 21, 14)(16, 26, 17, 28, 35, 49, 60, 53, 40, 27)(23, 36, 24, 38, 48, 61, 58, 45, 30, 37)(41, 54, 42, 56, 67, 74, 62, 57, 43, 55)(50, 63, 51, 65, 59, 72, 73, 66, 52, 64)(68, 79, 69, 81, 71, 83, 85, 82, 70, 80)(75, 86, 76, 88, 78, 90, 84, 89, 77, 87)(91, 97, 92, 99, 94, 100, 95, 98, 93, 96) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 46)(34, 48)(36, 50)(37, 51)(38, 52)(44, 58)(45, 59)(47, 60)(49, 62)(53, 67)(54, 68)(55, 69)(56, 70)(57, 71)(61, 73)(63, 75)(64, 76)(65, 77)(66, 78)(72, 84)(74, 85)(79, 91)(80, 92)(81, 93)(82, 94)(83, 95)(86, 96)(87, 97)(88, 98)(89, 99)(90, 100) local type(s) :: { ( 10^10 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 10 e = 50 f = 10 degree seq :: [ 10^10 ] E16.1116 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 10}) Quotient :: edge Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1, T2^10, (T2^-4 * T1 * T2^-1)^2, T2^2 * T1 * T2^2 * T1 * T2^-2 * T1 * T2^-2 * T1 ] Map:: polytopal R = (1, 3, 8, 18, 36, 62, 42, 22, 10, 4)(2, 5, 12, 26, 48, 77, 54, 30, 14, 6)(7, 15, 31, 55, 85, 69, 86, 56, 32, 16)(9, 19, 37, 63, 92, 61, 91, 64, 38, 20)(11, 23, 43, 70, 93, 84, 94, 71, 44, 24)(13, 27, 49, 78, 100, 76, 99, 79, 50, 28)(17, 33, 57, 87, 68, 41, 67, 88, 58, 34)(21, 39, 65, 90, 60, 35, 59, 89, 66, 40)(25, 45, 72, 95, 83, 53, 82, 96, 73, 46)(29, 51, 80, 98, 75, 47, 74, 97, 81, 52)(101, 102)(103, 107)(104, 109)(105, 111)(106, 113)(108, 117)(110, 121)(112, 125)(114, 129)(115, 123)(116, 127)(118, 135)(119, 124)(120, 128)(122, 141)(126, 147)(130, 153)(131, 145)(132, 151)(133, 143)(134, 149)(136, 161)(137, 146)(138, 152)(139, 144)(140, 150)(142, 169)(148, 176)(154, 184)(155, 174)(156, 182)(157, 172)(158, 180)(159, 170)(160, 178)(162, 177)(163, 175)(164, 183)(165, 173)(166, 181)(167, 171)(168, 179)(185, 199)(186, 194)(187, 197)(188, 196)(189, 195)(190, 198)(191, 193)(192, 200) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 20, 20 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E16.1121 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 100 f = 10 degree seq :: [ 2^50, 10^10 ] E16.1117 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 10}) Quotient :: edge Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^10, (T2^-1 * T1)^10 ] Map:: polytopal R = (1, 3, 8, 17, 28, 43, 31, 19, 10, 4)(2, 5, 12, 22, 35, 50, 38, 24, 14, 6)(7, 15, 26, 41, 56, 45, 30, 18, 9, 16)(11, 20, 33, 48, 63, 52, 37, 23, 13, 21)(25, 39, 54, 69, 59, 44, 29, 42, 27, 40)(32, 46, 61, 75, 66, 51, 36, 49, 34, 47)(53, 67, 80, 72, 58, 71, 57, 70, 55, 68)(60, 73, 86, 78, 65, 77, 64, 76, 62, 74)(79, 91, 84, 95, 83, 94, 82, 93, 81, 92)(85, 96, 90, 100, 89, 99, 88, 98, 87, 97)(101, 102)(103, 107)(104, 109)(105, 111)(106, 113)(108, 112)(110, 114)(115, 125)(116, 127)(117, 126)(118, 129)(119, 130)(120, 132)(121, 134)(122, 133)(123, 136)(124, 137)(128, 135)(131, 138)(139, 153)(140, 155)(141, 154)(142, 157)(143, 156)(144, 158)(145, 159)(146, 160)(147, 162)(148, 161)(149, 164)(150, 163)(151, 165)(152, 166)(167, 179)(168, 181)(169, 180)(170, 182)(171, 183)(172, 184)(173, 185)(174, 187)(175, 186)(176, 188)(177, 189)(178, 190)(191, 196)(192, 197)(193, 198)(194, 199)(195, 200) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 20, 20 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E16.1120 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 100 f = 10 degree seq :: [ 2^50, 10^10 ] E16.1118 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 10}) Quotient :: edge Aut^+ = D10 x D10 (small group id <100, 13>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^2 * T1)^2, T2^10, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: polytopal R = (1, 3, 8, 17, 28, 43, 31, 19, 10, 4)(2, 5, 12, 22, 35, 50, 38, 24, 14, 6)(7, 15, 9, 18, 30, 45, 57, 42, 27, 16)(11, 20, 13, 23, 37, 52, 64, 49, 34, 21)(25, 39, 26, 41, 56, 71, 59, 44, 29, 40)(32, 46, 33, 48, 63, 77, 66, 51, 36, 47)(53, 67, 54, 69, 58, 72, 83, 70, 55, 68)(60, 73, 61, 75, 65, 78, 89, 76, 62, 74)(79, 91, 80, 93, 82, 95, 84, 94, 81, 92)(85, 96, 86, 98, 88, 100, 90, 99, 87, 97)(101, 102)(103, 107)(104, 109)(105, 111)(106, 113)(108, 114)(110, 112)(115, 125)(116, 126)(117, 127)(118, 129)(119, 130)(120, 132)(121, 133)(122, 134)(123, 136)(124, 137)(128, 138)(131, 135)(139, 153)(140, 154)(141, 155)(142, 156)(143, 157)(144, 158)(145, 159)(146, 160)(147, 161)(148, 162)(149, 163)(150, 164)(151, 165)(152, 166)(167, 179)(168, 180)(169, 181)(170, 182)(171, 183)(172, 184)(173, 185)(174, 186)(175, 187)(176, 188)(177, 189)(178, 190)(191, 197)(192, 196)(193, 199)(194, 198)(195, 200) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 20, 20 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E16.1122 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 100 f = 10 degree seq :: [ 2^50, 10^10 ] E16.1119 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 10}) Quotient :: edge Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-3 * T1^-1 * T2, T2 * T1^-1 * T2^-3 * T1^-1, (T1^-1 * T2 * T1^-3)^2, T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^2 * T2^-1 * T1, T1^-1 * T2 * T1^-2 * T2^5 * T1^-1, T1^10 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 48, 69, 44, 21, 15, 5)(2, 7, 19, 11, 27, 49, 70, 39, 22, 8)(4, 12, 26, 50, 74, 43, 33, 14, 24, 9)(6, 17, 37, 20, 41, 28, 52, 65, 40, 18)(13, 30, 51, 73, 59, 32, 47, 23, 46, 29)(16, 35, 63, 38, 67, 42, 71, 53, 66, 36)(31, 56, 79, 58, 77, 45, 76, 54, 78, 55)(34, 61, 86, 64, 89, 68, 91, 72, 88, 62)(57, 83, 94, 75, 93, 80, 95, 81, 96, 82)(60, 84, 97, 87, 99, 90, 100, 92, 98, 85)(101, 102, 106, 116, 134, 160, 157, 131, 113, 104)(103, 109, 123, 145, 175, 184, 162, 153, 128, 111)(105, 114, 132, 158, 183, 185, 172, 142, 120, 107)(108, 121, 143, 173, 156, 182, 192, 168, 138, 117)(110, 119, 137, 163, 186, 197, 194, 179, 151, 126)(112, 129, 154, 180, 187, 161, 136, 165, 149, 125)(115, 122, 140, 166, 188, 198, 196, 178, 146, 124)(118, 139, 169, 150, 130, 155, 181, 190, 164, 135)(127, 141, 167, 189, 199, 193, 177, 159, 174, 148)(133, 144, 170, 152, 171, 191, 200, 195, 176, 147) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4^10 ) } Outer automorphisms :: reflexible Dual of E16.1123 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 100 f = 50 degree seq :: [ 10^20 ] E16.1120 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 10}) Quotient :: loop Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1, T2^10, (T2^-4 * T1 * T2^-1)^2, T2^2 * T1 * T2^2 * T1 * T2^-2 * T1 * T2^-2 * T1 ] Map:: R = (1, 101, 3, 103, 8, 108, 18, 118, 36, 136, 62, 162, 42, 142, 22, 122, 10, 110, 4, 104)(2, 102, 5, 105, 12, 112, 26, 126, 48, 148, 77, 177, 54, 154, 30, 130, 14, 114, 6, 106)(7, 107, 15, 115, 31, 131, 55, 155, 85, 185, 69, 169, 86, 186, 56, 156, 32, 132, 16, 116)(9, 109, 19, 119, 37, 137, 63, 163, 92, 192, 61, 161, 91, 191, 64, 164, 38, 138, 20, 120)(11, 111, 23, 123, 43, 143, 70, 170, 93, 193, 84, 184, 94, 194, 71, 171, 44, 144, 24, 124)(13, 113, 27, 127, 49, 149, 78, 178, 100, 200, 76, 176, 99, 199, 79, 179, 50, 150, 28, 128)(17, 117, 33, 133, 57, 157, 87, 187, 68, 168, 41, 141, 67, 167, 88, 188, 58, 158, 34, 134)(21, 121, 39, 139, 65, 165, 90, 190, 60, 160, 35, 135, 59, 159, 89, 189, 66, 166, 40, 140)(25, 125, 45, 145, 72, 172, 95, 195, 83, 183, 53, 153, 82, 182, 96, 196, 73, 173, 46, 146)(29, 129, 51, 151, 80, 180, 98, 198, 75, 175, 47, 147, 74, 174, 97, 197, 81, 181, 52, 152) L = (1, 102)(2, 101)(3, 107)(4, 109)(5, 111)(6, 113)(7, 103)(8, 117)(9, 104)(10, 121)(11, 105)(12, 125)(13, 106)(14, 129)(15, 123)(16, 127)(17, 108)(18, 135)(19, 124)(20, 128)(21, 110)(22, 141)(23, 115)(24, 119)(25, 112)(26, 147)(27, 116)(28, 120)(29, 114)(30, 153)(31, 145)(32, 151)(33, 143)(34, 149)(35, 118)(36, 161)(37, 146)(38, 152)(39, 144)(40, 150)(41, 122)(42, 169)(43, 133)(44, 139)(45, 131)(46, 137)(47, 126)(48, 176)(49, 134)(50, 140)(51, 132)(52, 138)(53, 130)(54, 184)(55, 174)(56, 182)(57, 172)(58, 180)(59, 170)(60, 178)(61, 136)(62, 177)(63, 175)(64, 183)(65, 173)(66, 181)(67, 171)(68, 179)(69, 142)(70, 159)(71, 167)(72, 157)(73, 165)(74, 155)(75, 163)(76, 148)(77, 162)(78, 160)(79, 168)(80, 158)(81, 166)(82, 156)(83, 164)(84, 154)(85, 199)(86, 194)(87, 197)(88, 196)(89, 195)(90, 198)(91, 193)(92, 200)(93, 191)(94, 186)(95, 189)(96, 188)(97, 187)(98, 190)(99, 185)(100, 192) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.1117 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 100 f = 60 degree seq :: [ 20^10 ] E16.1121 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 10}) Quotient :: loop Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^10, (T2^-1 * T1)^10 ] Map:: R = (1, 101, 3, 103, 8, 108, 17, 117, 28, 128, 43, 143, 31, 131, 19, 119, 10, 110, 4, 104)(2, 102, 5, 105, 12, 112, 22, 122, 35, 135, 50, 150, 38, 138, 24, 124, 14, 114, 6, 106)(7, 107, 15, 115, 26, 126, 41, 141, 56, 156, 45, 145, 30, 130, 18, 118, 9, 109, 16, 116)(11, 111, 20, 120, 33, 133, 48, 148, 63, 163, 52, 152, 37, 137, 23, 123, 13, 113, 21, 121)(25, 125, 39, 139, 54, 154, 69, 169, 59, 159, 44, 144, 29, 129, 42, 142, 27, 127, 40, 140)(32, 132, 46, 146, 61, 161, 75, 175, 66, 166, 51, 151, 36, 136, 49, 149, 34, 134, 47, 147)(53, 153, 67, 167, 80, 180, 72, 172, 58, 158, 71, 171, 57, 157, 70, 170, 55, 155, 68, 168)(60, 160, 73, 173, 86, 186, 78, 178, 65, 165, 77, 177, 64, 164, 76, 176, 62, 162, 74, 174)(79, 179, 91, 191, 84, 184, 95, 195, 83, 183, 94, 194, 82, 182, 93, 193, 81, 181, 92, 192)(85, 185, 96, 196, 90, 190, 100, 200, 89, 189, 99, 199, 88, 188, 98, 198, 87, 187, 97, 197) L = (1, 102)(2, 101)(3, 107)(4, 109)(5, 111)(6, 113)(7, 103)(8, 112)(9, 104)(10, 114)(11, 105)(12, 108)(13, 106)(14, 110)(15, 125)(16, 127)(17, 126)(18, 129)(19, 130)(20, 132)(21, 134)(22, 133)(23, 136)(24, 137)(25, 115)(26, 117)(27, 116)(28, 135)(29, 118)(30, 119)(31, 138)(32, 120)(33, 122)(34, 121)(35, 128)(36, 123)(37, 124)(38, 131)(39, 153)(40, 155)(41, 154)(42, 157)(43, 156)(44, 158)(45, 159)(46, 160)(47, 162)(48, 161)(49, 164)(50, 163)(51, 165)(52, 166)(53, 139)(54, 141)(55, 140)(56, 143)(57, 142)(58, 144)(59, 145)(60, 146)(61, 148)(62, 147)(63, 150)(64, 149)(65, 151)(66, 152)(67, 179)(68, 181)(69, 180)(70, 182)(71, 183)(72, 184)(73, 185)(74, 187)(75, 186)(76, 188)(77, 189)(78, 190)(79, 167)(80, 169)(81, 168)(82, 170)(83, 171)(84, 172)(85, 173)(86, 175)(87, 174)(88, 176)(89, 177)(90, 178)(91, 196)(92, 197)(93, 198)(94, 199)(95, 200)(96, 191)(97, 192)(98, 193)(99, 194)(100, 195) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.1116 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 100 f = 60 degree seq :: [ 20^10 ] E16.1122 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 10}) Quotient :: loop Aut^+ = D10 x D10 (small group id <100, 13>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^2 * T1)^2, T2^10, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 101, 3, 103, 8, 108, 17, 117, 28, 128, 43, 143, 31, 131, 19, 119, 10, 110, 4, 104)(2, 102, 5, 105, 12, 112, 22, 122, 35, 135, 50, 150, 38, 138, 24, 124, 14, 114, 6, 106)(7, 107, 15, 115, 9, 109, 18, 118, 30, 130, 45, 145, 57, 157, 42, 142, 27, 127, 16, 116)(11, 111, 20, 120, 13, 113, 23, 123, 37, 137, 52, 152, 64, 164, 49, 149, 34, 134, 21, 121)(25, 125, 39, 139, 26, 126, 41, 141, 56, 156, 71, 171, 59, 159, 44, 144, 29, 129, 40, 140)(32, 132, 46, 146, 33, 133, 48, 148, 63, 163, 77, 177, 66, 166, 51, 151, 36, 136, 47, 147)(53, 153, 67, 167, 54, 154, 69, 169, 58, 158, 72, 172, 83, 183, 70, 170, 55, 155, 68, 168)(60, 160, 73, 173, 61, 161, 75, 175, 65, 165, 78, 178, 89, 189, 76, 176, 62, 162, 74, 174)(79, 179, 91, 191, 80, 180, 93, 193, 82, 182, 95, 195, 84, 184, 94, 194, 81, 181, 92, 192)(85, 185, 96, 196, 86, 186, 98, 198, 88, 188, 100, 200, 90, 190, 99, 199, 87, 187, 97, 197) L = (1, 102)(2, 101)(3, 107)(4, 109)(5, 111)(6, 113)(7, 103)(8, 114)(9, 104)(10, 112)(11, 105)(12, 110)(13, 106)(14, 108)(15, 125)(16, 126)(17, 127)(18, 129)(19, 130)(20, 132)(21, 133)(22, 134)(23, 136)(24, 137)(25, 115)(26, 116)(27, 117)(28, 138)(29, 118)(30, 119)(31, 135)(32, 120)(33, 121)(34, 122)(35, 131)(36, 123)(37, 124)(38, 128)(39, 153)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 159)(46, 160)(47, 161)(48, 162)(49, 163)(50, 164)(51, 165)(52, 166)(53, 139)(54, 140)(55, 141)(56, 142)(57, 143)(58, 144)(59, 145)(60, 146)(61, 147)(62, 148)(63, 149)(64, 150)(65, 151)(66, 152)(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, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176)(89, 177)(90, 178)(91, 197)(92, 196)(93, 199)(94, 198)(95, 200)(96, 192)(97, 191)(98, 194)(99, 193)(100, 195) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.1118 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 100 f = 60 degree seq :: [ 20^10 ] E16.1123 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 10}) Quotient :: loop Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^10, (T2 * T1^-5)^2, T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 ] Map:: polytopal non-degenerate R = (1, 101, 3, 103)(2, 102, 6, 106)(4, 104, 9, 109)(5, 105, 12, 112)(7, 107, 16, 116)(8, 108, 17, 117)(10, 110, 21, 121)(11, 111, 24, 124)(13, 113, 28, 128)(14, 114, 29, 129)(15, 115, 32, 132)(18, 118, 35, 135)(19, 119, 33, 133)(20, 120, 34, 134)(22, 122, 41, 141)(23, 123, 44, 144)(25, 125, 48, 148)(26, 126, 49, 149)(27, 127, 52, 152)(30, 130, 53, 153)(31, 131, 56, 156)(36, 136, 61, 161)(37, 137, 57, 157)(38, 138, 60, 160)(39, 139, 58, 158)(40, 140, 59, 159)(42, 142, 69, 169)(43, 143, 70, 170)(45, 145, 74, 174)(46, 146, 75, 175)(47, 147, 78, 178)(50, 150, 79, 179)(51, 151, 82, 182)(54, 154, 83, 183)(55, 155, 85, 185)(62, 162, 92, 192)(63, 163, 86, 186)(64, 164, 91, 191)(65, 165, 87, 187)(66, 166, 90, 190)(67, 167, 88, 188)(68, 168, 89, 189)(71, 171, 93, 193)(72, 172, 94, 194)(73, 173, 95, 195)(76, 176, 96, 196)(77, 177, 97, 197)(80, 180, 98, 198)(81, 181, 99, 199)(84, 184, 100, 200) L = (1, 102)(2, 105)(3, 107)(4, 101)(5, 111)(6, 113)(7, 115)(8, 103)(9, 119)(10, 104)(11, 123)(12, 125)(13, 127)(14, 106)(15, 131)(16, 128)(17, 129)(18, 108)(19, 137)(20, 109)(21, 139)(22, 110)(23, 143)(24, 145)(25, 147)(26, 112)(27, 151)(28, 148)(29, 149)(30, 114)(31, 155)(32, 152)(33, 116)(34, 117)(35, 153)(36, 118)(37, 163)(38, 120)(39, 165)(40, 121)(41, 167)(42, 122)(43, 142)(44, 171)(45, 173)(46, 124)(47, 177)(48, 174)(49, 175)(50, 126)(51, 181)(52, 178)(53, 179)(54, 130)(55, 170)(56, 182)(57, 132)(58, 133)(59, 134)(60, 135)(61, 183)(62, 136)(63, 172)(64, 138)(65, 176)(66, 140)(67, 180)(68, 141)(69, 184)(70, 162)(71, 164)(72, 144)(73, 166)(74, 193)(75, 194)(76, 146)(77, 168)(78, 195)(79, 196)(80, 150)(81, 169)(82, 197)(83, 198)(84, 154)(85, 199)(86, 156)(87, 157)(88, 158)(89, 159)(90, 160)(91, 161)(92, 200)(93, 192)(94, 185)(95, 191)(96, 186)(97, 190)(98, 187)(99, 189)(100, 188) local type(s) :: { ( 10^4 ) } Outer automorphisms :: reflexible Dual of E16.1119 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 50 e = 100 f = 20 degree seq :: [ 4^50 ] E16.1124 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 10}) Quotient :: dipole Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, Y2^10, (Y2^-4 * Y1 * Y2^-1)^2, Y2^2 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1, (Y3 * Y2^-1)^10 ] Map:: R = (1, 101, 2, 102)(3, 103, 7, 107)(4, 104, 9, 109)(5, 105, 11, 111)(6, 106, 13, 113)(8, 108, 17, 117)(10, 110, 21, 121)(12, 112, 25, 125)(14, 114, 29, 129)(15, 115, 23, 123)(16, 116, 27, 127)(18, 118, 35, 135)(19, 119, 24, 124)(20, 120, 28, 128)(22, 122, 41, 141)(26, 126, 47, 147)(30, 130, 53, 153)(31, 131, 45, 145)(32, 132, 51, 151)(33, 133, 43, 143)(34, 134, 49, 149)(36, 136, 61, 161)(37, 137, 46, 146)(38, 138, 52, 152)(39, 139, 44, 144)(40, 140, 50, 150)(42, 142, 69, 169)(48, 148, 76, 176)(54, 154, 84, 184)(55, 155, 74, 174)(56, 156, 82, 182)(57, 157, 72, 172)(58, 158, 80, 180)(59, 159, 70, 170)(60, 160, 78, 178)(62, 162, 77, 177)(63, 163, 75, 175)(64, 164, 83, 183)(65, 165, 73, 173)(66, 166, 81, 181)(67, 167, 71, 171)(68, 168, 79, 179)(85, 185, 99, 199)(86, 186, 94, 194)(87, 187, 97, 197)(88, 188, 96, 196)(89, 189, 95, 195)(90, 190, 98, 198)(91, 191, 93, 193)(92, 192, 100, 200)(201, 301, 203, 303, 208, 308, 218, 318, 236, 336, 262, 362, 242, 342, 222, 322, 210, 310, 204, 304)(202, 302, 205, 305, 212, 312, 226, 326, 248, 348, 277, 377, 254, 354, 230, 330, 214, 314, 206, 306)(207, 307, 215, 315, 231, 331, 255, 355, 285, 385, 269, 369, 286, 386, 256, 356, 232, 332, 216, 316)(209, 309, 219, 319, 237, 337, 263, 363, 292, 392, 261, 361, 291, 391, 264, 364, 238, 338, 220, 320)(211, 311, 223, 323, 243, 343, 270, 370, 293, 393, 284, 384, 294, 394, 271, 371, 244, 344, 224, 324)(213, 313, 227, 327, 249, 349, 278, 378, 300, 400, 276, 376, 299, 399, 279, 379, 250, 350, 228, 328)(217, 317, 233, 333, 257, 357, 287, 387, 268, 368, 241, 341, 267, 367, 288, 388, 258, 358, 234, 334)(221, 321, 239, 339, 265, 365, 290, 390, 260, 360, 235, 335, 259, 359, 289, 389, 266, 366, 240, 340)(225, 325, 245, 345, 272, 372, 295, 395, 283, 383, 253, 353, 282, 382, 296, 396, 273, 373, 246, 346)(229, 329, 251, 351, 280, 380, 298, 398, 275, 375, 247, 347, 274, 374, 297, 397, 281, 381, 252, 352) L = (1, 202)(2, 201)(3, 207)(4, 209)(5, 211)(6, 213)(7, 203)(8, 217)(9, 204)(10, 221)(11, 205)(12, 225)(13, 206)(14, 229)(15, 223)(16, 227)(17, 208)(18, 235)(19, 224)(20, 228)(21, 210)(22, 241)(23, 215)(24, 219)(25, 212)(26, 247)(27, 216)(28, 220)(29, 214)(30, 253)(31, 245)(32, 251)(33, 243)(34, 249)(35, 218)(36, 261)(37, 246)(38, 252)(39, 244)(40, 250)(41, 222)(42, 269)(43, 233)(44, 239)(45, 231)(46, 237)(47, 226)(48, 276)(49, 234)(50, 240)(51, 232)(52, 238)(53, 230)(54, 284)(55, 274)(56, 282)(57, 272)(58, 280)(59, 270)(60, 278)(61, 236)(62, 277)(63, 275)(64, 283)(65, 273)(66, 281)(67, 271)(68, 279)(69, 242)(70, 259)(71, 267)(72, 257)(73, 265)(74, 255)(75, 263)(76, 248)(77, 262)(78, 260)(79, 268)(80, 258)(81, 266)(82, 256)(83, 264)(84, 254)(85, 299)(86, 294)(87, 297)(88, 296)(89, 295)(90, 298)(91, 293)(92, 300)(93, 291)(94, 286)(95, 289)(96, 288)(97, 287)(98, 290)(99, 285)(100, 292)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E16.1129 Graph:: bipartite v = 60 e = 200 f = 110 degree seq :: [ 4^50, 20^10 ] E16.1125 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 10}) Quotient :: dipole Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, Y2^10, (Y3 * Y2^-1)^10 ] Map:: R = (1, 101, 2, 102)(3, 103, 7, 107)(4, 104, 9, 109)(5, 105, 11, 111)(6, 106, 13, 113)(8, 108, 12, 112)(10, 110, 14, 114)(15, 115, 25, 125)(16, 116, 27, 127)(17, 117, 26, 126)(18, 118, 29, 129)(19, 119, 30, 130)(20, 120, 32, 132)(21, 121, 34, 134)(22, 122, 33, 133)(23, 123, 36, 136)(24, 124, 37, 137)(28, 128, 35, 135)(31, 131, 38, 138)(39, 139, 53, 153)(40, 140, 55, 155)(41, 141, 54, 154)(42, 142, 57, 157)(43, 143, 56, 156)(44, 144, 58, 158)(45, 145, 59, 159)(46, 146, 60, 160)(47, 147, 62, 162)(48, 148, 61, 161)(49, 149, 64, 164)(50, 150, 63, 163)(51, 151, 65, 165)(52, 152, 66, 166)(67, 167, 79, 179)(68, 168, 81, 181)(69, 169, 80, 180)(70, 170, 82, 182)(71, 171, 83, 183)(72, 172, 84, 184)(73, 173, 85, 185)(74, 174, 87, 187)(75, 175, 86, 186)(76, 176, 88, 188)(77, 177, 89, 189)(78, 178, 90, 190)(91, 191, 96, 196)(92, 192, 97, 197)(93, 193, 98, 198)(94, 194, 99, 199)(95, 195, 100, 200)(201, 301, 203, 303, 208, 308, 217, 317, 228, 328, 243, 343, 231, 331, 219, 319, 210, 310, 204, 304)(202, 302, 205, 305, 212, 312, 222, 322, 235, 335, 250, 350, 238, 338, 224, 324, 214, 314, 206, 306)(207, 307, 215, 315, 226, 326, 241, 341, 256, 356, 245, 345, 230, 330, 218, 318, 209, 309, 216, 316)(211, 311, 220, 320, 233, 333, 248, 348, 263, 363, 252, 352, 237, 337, 223, 323, 213, 313, 221, 321)(225, 325, 239, 339, 254, 354, 269, 369, 259, 359, 244, 344, 229, 329, 242, 342, 227, 327, 240, 340)(232, 332, 246, 346, 261, 361, 275, 375, 266, 366, 251, 351, 236, 336, 249, 349, 234, 334, 247, 347)(253, 353, 267, 367, 280, 380, 272, 372, 258, 358, 271, 371, 257, 357, 270, 370, 255, 355, 268, 368)(260, 360, 273, 373, 286, 386, 278, 378, 265, 365, 277, 377, 264, 364, 276, 376, 262, 362, 274, 374)(279, 379, 291, 391, 284, 384, 295, 395, 283, 383, 294, 394, 282, 382, 293, 393, 281, 381, 292, 392)(285, 385, 296, 396, 290, 390, 300, 400, 289, 389, 299, 399, 288, 388, 298, 398, 287, 387, 297, 397) L = (1, 202)(2, 201)(3, 207)(4, 209)(5, 211)(6, 213)(7, 203)(8, 212)(9, 204)(10, 214)(11, 205)(12, 208)(13, 206)(14, 210)(15, 225)(16, 227)(17, 226)(18, 229)(19, 230)(20, 232)(21, 234)(22, 233)(23, 236)(24, 237)(25, 215)(26, 217)(27, 216)(28, 235)(29, 218)(30, 219)(31, 238)(32, 220)(33, 222)(34, 221)(35, 228)(36, 223)(37, 224)(38, 231)(39, 253)(40, 255)(41, 254)(42, 257)(43, 256)(44, 258)(45, 259)(46, 260)(47, 262)(48, 261)(49, 264)(50, 263)(51, 265)(52, 266)(53, 239)(54, 241)(55, 240)(56, 243)(57, 242)(58, 244)(59, 245)(60, 246)(61, 248)(62, 247)(63, 250)(64, 249)(65, 251)(66, 252)(67, 279)(68, 281)(69, 280)(70, 282)(71, 283)(72, 284)(73, 285)(74, 287)(75, 286)(76, 288)(77, 289)(78, 290)(79, 267)(80, 269)(81, 268)(82, 270)(83, 271)(84, 272)(85, 273)(86, 275)(87, 274)(88, 276)(89, 277)(90, 278)(91, 296)(92, 297)(93, 298)(94, 299)(95, 300)(96, 291)(97, 292)(98, 293)(99, 294)(100, 295)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E16.1130 Graph:: bipartite v = 60 e = 200 f = 110 degree seq :: [ 4^50, 20^10 ] E16.1126 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 10}) Quotient :: dipole Aut^+ = D10 x D10 (small group id <100, 13>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1)^2, Y2^10, (Y3 * Y2^-1)^10 ] Map:: R = (1, 101, 2, 102)(3, 103, 7, 107)(4, 104, 9, 109)(5, 105, 11, 111)(6, 106, 13, 113)(8, 108, 14, 114)(10, 110, 12, 112)(15, 115, 25, 125)(16, 116, 26, 126)(17, 117, 27, 127)(18, 118, 29, 129)(19, 119, 30, 130)(20, 120, 32, 132)(21, 121, 33, 133)(22, 122, 34, 134)(23, 123, 36, 136)(24, 124, 37, 137)(28, 128, 38, 138)(31, 131, 35, 135)(39, 139, 53, 153)(40, 140, 54, 154)(41, 141, 55, 155)(42, 142, 56, 156)(43, 143, 57, 157)(44, 144, 58, 158)(45, 145, 59, 159)(46, 146, 60, 160)(47, 147, 61, 161)(48, 148, 62, 162)(49, 149, 63, 163)(50, 150, 64, 164)(51, 151, 65, 165)(52, 152, 66, 166)(67, 167, 79, 179)(68, 168, 80, 180)(69, 169, 81, 181)(70, 170, 82, 182)(71, 171, 83, 183)(72, 172, 84, 184)(73, 173, 85, 185)(74, 174, 86, 186)(75, 175, 87, 187)(76, 176, 88, 188)(77, 177, 89, 189)(78, 178, 90, 190)(91, 191, 97, 197)(92, 192, 96, 196)(93, 193, 99, 199)(94, 194, 98, 198)(95, 195, 100, 200)(201, 301, 203, 303, 208, 308, 217, 317, 228, 328, 243, 343, 231, 331, 219, 319, 210, 310, 204, 304)(202, 302, 205, 305, 212, 312, 222, 322, 235, 335, 250, 350, 238, 338, 224, 324, 214, 314, 206, 306)(207, 307, 215, 315, 209, 309, 218, 318, 230, 330, 245, 345, 257, 357, 242, 342, 227, 327, 216, 316)(211, 311, 220, 320, 213, 313, 223, 323, 237, 337, 252, 352, 264, 364, 249, 349, 234, 334, 221, 321)(225, 325, 239, 339, 226, 326, 241, 341, 256, 356, 271, 371, 259, 359, 244, 344, 229, 329, 240, 340)(232, 332, 246, 346, 233, 333, 248, 348, 263, 363, 277, 377, 266, 366, 251, 351, 236, 336, 247, 347)(253, 353, 267, 367, 254, 354, 269, 369, 258, 358, 272, 372, 283, 383, 270, 370, 255, 355, 268, 368)(260, 360, 273, 373, 261, 361, 275, 375, 265, 365, 278, 378, 289, 389, 276, 376, 262, 362, 274, 374)(279, 379, 291, 391, 280, 380, 293, 393, 282, 382, 295, 395, 284, 384, 294, 394, 281, 381, 292, 392)(285, 385, 296, 396, 286, 386, 298, 398, 288, 388, 300, 400, 290, 390, 299, 399, 287, 387, 297, 397) L = (1, 202)(2, 201)(3, 207)(4, 209)(5, 211)(6, 213)(7, 203)(8, 214)(9, 204)(10, 212)(11, 205)(12, 210)(13, 206)(14, 208)(15, 225)(16, 226)(17, 227)(18, 229)(19, 230)(20, 232)(21, 233)(22, 234)(23, 236)(24, 237)(25, 215)(26, 216)(27, 217)(28, 238)(29, 218)(30, 219)(31, 235)(32, 220)(33, 221)(34, 222)(35, 231)(36, 223)(37, 224)(38, 228)(39, 253)(40, 254)(41, 255)(42, 256)(43, 257)(44, 258)(45, 259)(46, 260)(47, 261)(48, 262)(49, 263)(50, 264)(51, 265)(52, 266)(53, 239)(54, 240)(55, 241)(56, 242)(57, 243)(58, 244)(59, 245)(60, 246)(61, 247)(62, 248)(63, 249)(64, 250)(65, 251)(66, 252)(67, 279)(68, 280)(69, 281)(70, 282)(71, 283)(72, 284)(73, 285)(74, 286)(75, 287)(76, 288)(77, 289)(78, 290)(79, 267)(80, 268)(81, 269)(82, 270)(83, 271)(84, 272)(85, 273)(86, 274)(87, 275)(88, 276)(89, 277)(90, 278)(91, 297)(92, 296)(93, 299)(94, 298)(95, 300)(96, 292)(97, 291)(98, 294)(99, 293)(100, 295)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E16.1131 Graph:: bipartite v = 60 e = 200 f = 110 degree seq :: [ 4^50, 20^10 ] E16.1127 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 10}) Quotient :: dipole Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y3^-1 * Y1^-1)^2, Y1^2 * Y2 * Y1^-1 * Y2 * Y1, Y2^3 * Y1^-3 * Y2^3 * Y1^-1, Y2^-1 * Y1 * Y2 * Y1^-3 * Y2 * Y1 * Y2^-1 * Y1, Y2^10 ] Map:: R = (1, 101, 2, 102, 6, 106, 16, 116, 34, 134, 60, 160, 53, 153, 27, 127, 13, 113, 4, 104)(3, 103, 9, 109, 17, 117, 8, 108, 21, 121, 35, 135, 62, 162, 50, 150, 28, 128, 11, 111)(5, 105, 14, 114, 18, 118, 37, 137, 61, 161, 52, 152, 30, 130, 12, 112, 20, 120, 7, 107)(10, 110, 24, 124, 36, 136, 23, 123, 42, 142, 22, 122, 43, 143, 63, 163, 51, 151, 26, 126)(15, 115, 32, 132, 38, 138, 65, 165, 55, 155, 29, 129, 41, 141, 19, 119, 39, 139, 31, 131)(25, 125, 47, 147, 64, 164, 46, 146, 71, 171, 45, 145, 72, 172, 44, 144, 73, 173, 49, 149)(33, 133, 58, 158, 66, 166, 54, 154, 70, 170, 40, 140, 68, 168, 56, 156, 67, 167, 57, 157)(48, 148, 78, 178, 84, 184, 77, 177, 90, 190, 76, 176, 91, 191, 75, 175, 92, 192, 74, 174)(59, 159, 80, 180, 85, 185, 69, 169, 88, 188, 81, 181, 87, 187, 82, 182, 86, 186, 83, 183)(79, 179, 89, 189, 97, 197, 96, 196, 100, 200, 95, 195, 99, 199, 94, 194, 98, 198, 93, 193)(201, 301, 203, 303, 210, 310, 225, 325, 248, 348, 279, 379, 259, 359, 233, 333, 215, 315, 205, 305)(202, 302, 207, 307, 219, 319, 240, 340, 269, 369, 289, 389, 274, 374, 244, 344, 222, 322, 208, 308)(204, 304, 212, 312, 229, 329, 254, 354, 280, 380, 293, 393, 275, 375, 245, 345, 223, 323, 209, 309)(206, 306, 217, 317, 236, 336, 264, 364, 284, 384, 297, 397, 285, 385, 266, 366, 238, 338, 218, 318)(211, 311, 227, 327, 252, 352, 265, 365, 258, 358, 283, 383, 294, 394, 276, 376, 246, 346, 224, 324)(213, 313, 228, 328, 251, 351, 273, 373, 292, 392, 298, 398, 286, 386, 267, 367, 239, 339, 220, 320)(214, 314, 231, 331, 256, 356, 281, 381, 296, 396, 278, 378, 249, 349, 263, 363, 235, 335, 216, 316)(221, 321, 242, 342, 271, 371, 290, 390, 300, 400, 288, 388, 270, 370, 255, 355, 261, 361, 234, 334)(226, 326, 250, 350, 260, 360, 237, 337, 232, 332, 257, 357, 282, 382, 295, 395, 277, 377, 247, 347)(230, 330, 253, 353, 262, 362, 243, 343, 272, 372, 291, 391, 299, 399, 287, 387, 268, 368, 241, 341) L = (1, 203)(2, 207)(3, 210)(4, 212)(5, 201)(6, 217)(7, 219)(8, 202)(9, 204)(10, 225)(11, 227)(12, 229)(13, 228)(14, 231)(15, 205)(16, 214)(17, 236)(18, 206)(19, 240)(20, 213)(21, 242)(22, 208)(23, 209)(24, 211)(25, 248)(26, 250)(27, 252)(28, 251)(29, 254)(30, 253)(31, 256)(32, 257)(33, 215)(34, 221)(35, 216)(36, 264)(37, 232)(38, 218)(39, 220)(40, 269)(41, 230)(42, 271)(43, 272)(44, 222)(45, 223)(46, 224)(47, 226)(48, 279)(49, 263)(50, 260)(51, 273)(52, 265)(53, 262)(54, 280)(55, 261)(56, 281)(57, 282)(58, 283)(59, 233)(60, 237)(61, 234)(62, 243)(63, 235)(64, 284)(65, 258)(66, 238)(67, 239)(68, 241)(69, 289)(70, 255)(71, 290)(72, 291)(73, 292)(74, 244)(75, 245)(76, 246)(77, 247)(78, 249)(79, 259)(80, 293)(81, 296)(82, 295)(83, 294)(84, 297)(85, 266)(86, 267)(87, 268)(88, 270)(89, 274)(90, 300)(91, 299)(92, 298)(93, 275)(94, 276)(95, 277)(96, 278)(97, 285)(98, 286)(99, 287)(100, 288)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) 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 E16.1128 Graph:: bipartite v = 20 e = 200 f = 150 degree seq :: [ 20^20 ] E16.1128 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 10}) Quotient :: dipole Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y3^10, (Y3^-4 * Y2 * Y3^-1)^2, Y3^2 * Y2 * Y3^2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2, (Y3^-1 * Y1^-1)^10 ] Map:: polytopal R = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200)(201, 301, 202, 302)(203, 303, 207, 307)(204, 304, 209, 309)(205, 305, 211, 311)(206, 306, 213, 313)(208, 308, 217, 317)(210, 310, 221, 321)(212, 312, 225, 325)(214, 314, 229, 329)(215, 315, 223, 323)(216, 316, 227, 327)(218, 318, 235, 335)(219, 319, 224, 324)(220, 320, 228, 328)(222, 322, 241, 341)(226, 326, 247, 347)(230, 330, 253, 353)(231, 331, 245, 345)(232, 332, 251, 351)(233, 333, 243, 343)(234, 334, 249, 349)(236, 336, 261, 361)(237, 337, 246, 346)(238, 338, 252, 352)(239, 339, 244, 344)(240, 340, 250, 350)(242, 342, 269, 369)(248, 348, 276, 376)(254, 354, 284, 384)(255, 355, 274, 374)(256, 356, 282, 382)(257, 357, 272, 372)(258, 358, 280, 380)(259, 359, 270, 370)(260, 360, 278, 378)(262, 362, 277, 377)(263, 363, 275, 375)(264, 364, 283, 383)(265, 365, 273, 373)(266, 366, 281, 381)(267, 367, 271, 371)(268, 368, 279, 379)(285, 385, 299, 399)(286, 386, 294, 394)(287, 387, 297, 397)(288, 388, 296, 396)(289, 389, 295, 395)(290, 390, 298, 398)(291, 391, 293, 393)(292, 392, 300, 400) L = (1, 203)(2, 205)(3, 208)(4, 201)(5, 212)(6, 202)(7, 215)(8, 218)(9, 219)(10, 204)(11, 223)(12, 226)(13, 227)(14, 206)(15, 231)(16, 207)(17, 233)(18, 236)(19, 237)(20, 209)(21, 239)(22, 210)(23, 243)(24, 211)(25, 245)(26, 248)(27, 249)(28, 213)(29, 251)(30, 214)(31, 255)(32, 216)(33, 257)(34, 217)(35, 259)(36, 262)(37, 263)(38, 220)(39, 265)(40, 221)(41, 267)(42, 222)(43, 270)(44, 224)(45, 272)(46, 225)(47, 274)(48, 277)(49, 278)(50, 228)(51, 280)(52, 229)(53, 282)(54, 230)(55, 285)(56, 232)(57, 287)(58, 234)(59, 289)(60, 235)(61, 291)(62, 242)(63, 292)(64, 238)(65, 290)(66, 240)(67, 288)(68, 241)(69, 286)(70, 293)(71, 244)(72, 295)(73, 246)(74, 297)(75, 247)(76, 299)(77, 254)(78, 300)(79, 250)(80, 298)(81, 252)(82, 296)(83, 253)(84, 294)(85, 269)(86, 256)(87, 268)(88, 258)(89, 266)(90, 260)(91, 264)(92, 261)(93, 284)(94, 271)(95, 283)(96, 273)(97, 281)(98, 275)(99, 279)(100, 276)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 20, 20 ), ( 20^4 ) } Outer automorphisms :: reflexible Dual of E16.1127 Graph:: simple bipartite v = 150 e = 200 f = 20 degree seq :: [ 2^100, 4^50 ] E16.1129 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 10}) Quotient :: dipole Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^2 * Y3^-1 * Y1^-2, Y1^10, (Y3^-1 * Y1^-1)^10 ] Map:: polytopal R = (1, 101, 2, 102, 5, 105, 11, 111, 20, 120, 32, 132, 31, 131, 19, 119, 10, 110, 4, 104)(3, 103, 7, 107, 12, 112, 22, 122, 33, 133, 47, 147, 43, 143, 28, 128, 17, 117, 8, 108)(6, 106, 13, 113, 21, 121, 34, 134, 46, 146, 45, 145, 30, 130, 18, 118, 9, 109, 14, 114)(15, 115, 25, 125, 35, 135, 49, 149, 60, 160, 57, 157, 42, 142, 27, 127, 16, 116, 26, 126)(23, 123, 36, 136, 48, 148, 61, 161, 59, 159, 44, 144, 29, 129, 38, 138, 24, 124, 37, 137)(39, 139, 53, 153, 62, 162, 74, 174, 71, 171, 56, 156, 41, 141, 55, 155, 40, 140, 54, 154)(50, 150, 63, 163, 73, 173, 72, 172, 58, 158, 66, 166, 52, 152, 65, 165, 51, 151, 64, 164)(67, 167, 79, 179, 85, 185, 83, 183, 70, 170, 82, 182, 69, 169, 81, 181, 68, 168, 80, 180)(75, 175, 86, 186, 84, 184, 90, 190, 78, 178, 89, 189, 77, 177, 88, 188, 76, 176, 87, 187)(91, 191, 96, 196, 95, 195, 100, 200, 94, 194, 99, 199, 93, 193, 98, 198, 92, 192, 97, 197)(201, 301)(202, 302)(203, 303)(204, 304)(205, 305)(206, 306)(207, 307)(208, 308)(209, 309)(210, 310)(211, 311)(212, 312)(213, 313)(214, 314)(215, 315)(216, 316)(217, 317)(218, 318)(219, 319)(220, 320)(221, 321)(222, 322)(223, 323)(224, 324)(225, 325)(226, 326)(227, 327)(228, 328)(229, 329)(230, 330)(231, 331)(232, 332)(233, 333)(234, 334)(235, 335)(236, 336)(237, 337)(238, 338)(239, 339)(240, 340)(241, 341)(242, 342)(243, 343)(244, 344)(245, 345)(246, 346)(247, 347)(248, 348)(249, 349)(250, 350)(251, 351)(252, 352)(253, 353)(254, 354)(255, 355)(256, 356)(257, 357)(258, 358)(259, 359)(260, 360)(261, 361)(262, 362)(263, 363)(264, 364)(265, 365)(266, 366)(267, 367)(268, 368)(269, 369)(270, 370)(271, 371)(272, 372)(273, 373)(274, 374)(275, 375)(276, 376)(277, 377)(278, 378)(279, 379)(280, 380)(281, 381)(282, 382)(283, 383)(284, 384)(285, 385)(286, 386)(287, 387)(288, 388)(289, 389)(290, 390)(291, 391)(292, 392)(293, 393)(294, 394)(295, 395)(296, 396)(297, 397)(298, 398)(299, 399)(300, 400) L = (1, 203)(2, 206)(3, 201)(4, 209)(5, 212)(6, 202)(7, 215)(8, 216)(9, 204)(10, 217)(11, 221)(12, 205)(13, 223)(14, 224)(15, 207)(16, 208)(17, 210)(18, 229)(19, 230)(20, 233)(21, 211)(22, 235)(23, 213)(24, 214)(25, 239)(26, 240)(27, 241)(28, 242)(29, 218)(30, 219)(31, 243)(32, 246)(33, 220)(34, 248)(35, 222)(36, 250)(37, 251)(38, 252)(39, 225)(40, 226)(41, 227)(42, 228)(43, 231)(44, 258)(45, 259)(46, 232)(47, 260)(48, 234)(49, 262)(50, 236)(51, 237)(52, 238)(53, 267)(54, 268)(55, 269)(56, 270)(57, 271)(58, 244)(59, 245)(60, 247)(61, 273)(62, 249)(63, 275)(64, 276)(65, 277)(66, 278)(67, 253)(68, 254)(69, 255)(70, 256)(71, 257)(72, 284)(73, 261)(74, 285)(75, 263)(76, 264)(77, 265)(78, 266)(79, 291)(80, 292)(81, 293)(82, 294)(83, 295)(84, 272)(85, 274)(86, 296)(87, 297)(88, 298)(89, 299)(90, 300)(91, 279)(92, 280)(93, 281)(94, 282)(95, 283)(96, 286)(97, 287)(98, 288)(99, 289)(100, 290)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E16.1124 Graph:: simple bipartite v = 110 e = 200 f = 60 degree seq :: [ 2^100, 20^10 ] E16.1130 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 10}) Quotient :: dipole Aut^+ = C10 x D10 (small group id <100, 14>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3, Y1^10, Y1^-1 * Y3 * Y1^-5 * Y3^-1 * Y1^-4, Y1^-2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3^-1 * Y1^-2 * Y3^-1, Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: polytopal R = (1, 101, 2, 102, 5, 105, 11, 111, 23, 123, 43, 143, 42, 142, 22, 122, 10, 110, 4, 104)(3, 103, 7, 107, 15, 115, 31, 131, 55, 155, 70, 170, 62, 162, 36, 136, 18, 118, 8, 108)(6, 106, 13, 113, 27, 127, 51, 151, 81, 181, 69, 169, 84, 184, 54, 154, 30, 130, 14, 114)(9, 109, 19, 119, 37, 137, 63, 163, 72, 172, 44, 144, 71, 171, 64, 164, 38, 138, 20, 120)(12, 112, 25, 125, 47, 147, 77, 177, 68, 168, 41, 141, 67, 167, 80, 180, 50, 150, 26, 126)(16, 116, 28, 128, 48, 148, 74, 174, 93, 193, 92, 192, 100, 200, 88, 188, 58, 158, 33, 133)(17, 117, 29, 129, 49, 149, 75, 175, 94, 194, 85, 185, 99, 199, 89, 189, 59, 159, 34, 134)(21, 121, 39, 139, 65, 165, 76, 176, 46, 146, 24, 124, 45, 145, 73, 173, 66, 166, 40, 140)(32, 132, 52, 152, 78, 178, 95, 195, 91, 191, 61, 161, 83, 183, 98, 198, 87, 187, 57, 157)(35, 135, 53, 153, 79, 179, 96, 196, 86, 186, 56, 156, 82, 182, 97, 197, 90, 190, 60, 160)(201, 301)(202, 302)(203, 303)(204, 304)(205, 305)(206, 306)(207, 307)(208, 308)(209, 309)(210, 310)(211, 311)(212, 312)(213, 313)(214, 314)(215, 315)(216, 316)(217, 317)(218, 318)(219, 319)(220, 320)(221, 321)(222, 322)(223, 323)(224, 324)(225, 325)(226, 326)(227, 327)(228, 328)(229, 329)(230, 330)(231, 331)(232, 332)(233, 333)(234, 334)(235, 335)(236, 336)(237, 337)(238, 338)(239, 339)(240, 340)(241, 341)(242, 342)(243, 343)(244, 344)(245, 345)(246, 346)(247, 347)(248, 348)(249, 349)(250, 350)(251, 351)(252, 352)(253, 353)(254, 354)(255, 355)(256, 356)(257, 357)(258, 358)(259, 359)(260, 360)(261, 361)(262, 362)(263, 363)(264, 364)(265, 365)(266, 366)(267, 367)(268, 368)(269, 369)(270, 370)(271, 371)(272, 372)(273, 373)(274, 374)(275, 375)(276, 376)(277, 377)(278, 378)(279, 379)(280, 380)(281, 381)(282, 382)(283, 383)(284, 384)(285, 385)(286, 386)(287, 387)(288, 388)(289, 389)(290, 390)(291, 391)(292, 392)(293, 393)(294, 394)(295, 395)(296, 396)(297, 397)(298, 398)(299, 399)(300, 400) L = (1, 203)(2, 206)(3, 201)(4, 209)(5, 212)(6, 202)(7, 216)(8, 217)(9, 204)(10, 221)(11, 224)(12, 205)(13, 228)(14, 229)(15, 232)(16, 207)(17, 208)(18, 235)(19, 233)(20, 234)(21, 210)(22, 241)(23, 244)(24, 211)(25, 248)(26, 249)(27, 252)(28, 213)(29, 214)(30, 253)(31, 256)(32, 215)(33, 219)(34, 220)(35, 218)(36, 261)(37, 257)(38, 260)(39, 258)(40, 259)(41, 222)(42, 269)(43, 270)(44, 223)(45, 274)(46, 275)(47, 278)(48, 225)(49, 226)(50, 279)(51, 282)(52, 227)(53, 230)(54, 283)(55, 285)(56, 231)(57, 237)(58, 239)(59, 240)(60, 238)(61, 236)(62, 292)(63, 286)(64, 291)(65, 287)(66, 290)(67, 288)(68, 289)(69, 242)(70, 243)(71, 293)(72, 294)(73, 295)(74, 245)(75, 246)(76, 296)(77, 297)(78, 247)(79, 250)(80, 298)(81, 299)(82, 251)(83, 254)(84, 300)(85, 255)(86, 263)(87, 265)(88, 267)(89, 268)(90, 266)(91, 264)(92, 262)(93, 271)(94, 272)(95, 273)(96, 276)(97, 277)(98, 280)(99, 281)(100, 284)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E16.1125 Graph:: simple bipartite v = 110 e = 200 f = 60 degree seq :: [ 2^100, 20^10 ] E16.1131 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 10}) Quotient :: dipole Aut^+ = D10 x D10 (small group id <100, 13>) Aut = C2 x D10 x D10 (small group id <200, 49>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, Y1^10, Y1 * Y3 * Y1^-6 * Y3^-1 * Y1^3, (Y3^-1 * Y1)^10 ] Map:: polytopal R = (1, 101, 2, 102, 5, 105, 11, 111, 20, 120, 32, 132, 31, 131, 19, 119, 10, 110, 4, 104)(3, 103, 7, 107, 15, 115, 25, 125, 39, 139, 47, 147, 33, 133, 22, 122, 12, 112, 8, 108)(6, 106, 13, 113, 9, 109, 18, 118, 29, 129, 44, 144, 46, 146, 34, 134, 21, 121, 14, 114)(16, 116, 26, 126, 17, 117, 28, 128, 35, 135, 49, 149, 60, 160, 53, 153, 40, 140, 27, 127)(23, 123, 36, 136, 24, 124, 38, 138, 48, 148, 61, 161, 58, 158, 45, 145, 30, 130, 37, 137)(41, 141, 54, 154, 42, 142, 56, 156, 67, 167, 74, 174, 62, 162, 57, 157, 43, 143, 55, 155)(50, 150, 63, 163, 51, 151, 65, 165, 59, 159, 72, 172, 73, 173, 66, 166, 52, 152, 64, 164)(68, 168, 79, 179, 69, 169, 81, 181, 71, 171, 83, 183, 85, 185, 82, 182, 70, 170, 80, 180)(75, 175, 86, 186, 76, 176, 88, 188, 78, 178, 90, 190, 84, 184, 89, 189, 77, 177, 87, 187)(91, 191, 97, 197, 92, 192, 99, 199, 94, 194, 100, 200, 95, 195, 98, 198, 93, 193, 96, 196)(201, 301)(202, 302)(203, 303)(204, 304)(205, 305)(206, 306)(207, 307)(208, 308)(209, 309)(210, 310)(211, 311)(212, 312)(213, 313)(214, 314)(215, 315)(216, 316)(217, 317)(218, 318)(219, 319)(220, 320)(221, 321)(222, 322)(223, 323)(224, 324)(225, 325)(226, 326)(227, 327)(228, 328)(229, 329)(230, 330)(231, 331)(232, 332)(233, 333)(234, 334)(235, 335)(236, 336)(237, 337)(238, 338)(239, 339)(240, 340)(241, 341)(242, 342)(243, 343)(244, 344)(245, 345)(246, 346)(247, 347)(248, 348)(249, 349)(250, 350)(251, 351)(252, 352)(253, 353)(254, 354)(255, 355)(256, 356)(257, 357)(258, 358)(259, 359)(260, 360)(261, 361)(262, 362)(263, 363)(264, 364)(265, 365)(266, 366)(267, 367)(268, 368)(269, 369)(270, 370)(271, 371)(272, 372)(273, 373)(274, 374)(275, 375)(276, 376)(277, 377)(278, 378)(279, 379)(280, 380)(281, 381)(282, 382)(283, 383)(284, 384)(285, 385)(286, 386)(287, 387)(288, 388)(289, 389)(290, 390)(291, 391)(292, 392)(293, 393)(294, 394)(295, 395)(296, 396)(297, 397)(298, 398)(299, 399)(300, 400) L = (1, 203)(2, 206)(3, 201)(4, 209)(5, 212)(6, 202)(7, 216)(8, 217)(9, 204)(10, 215)(11, 221)(12, 205)(13, 223)(14, 224)(15, 210)(16, 207)(17, 208)(18, 230)(19, 229)(20, 233)(21, 211)(22, 235)(23, 213)(24, 214)(25, 240)(26, 241)(27, 242)(28, 243)(29, 219)(30, 218)(31, 239)(32, 246)(33, 220)(34, 248)(35, 222)(36, 250)(37, 251)(38, 252)(39, 231)(40, 225)(41, 226)(42, 227)(43, 228)(44, 258)(45, 259)(46, 232)(47, 260)(48, 234)(49, 262)(50, 236)(51, 237)(52, 238)(53, 267)(54, 268)(55, 269)(56, 270)(57, 271)(58, 244)(59, 245)(60, 247)(61, 273)(62, 249)(63, 275)(64, 276)(65, 277)(66, 278)(67, 253)(68, 254)(69, 255)(70, 256)(71, 257)(72, 284)(73, 261)(74, 285)(75, 263)(76, 264)(77, 265)(78, 266)(79, 291)(80, 292)(81, 293)(82, 294)(83, 295)(84, 272)(85, 274)(86, 296)(87, 297)(88, 298)(89, 299)(90, 300)(91, 279)(92, 280)(93, 281)(94, 282)(95, 283)(96, 286)(97, 287)(98, 288)(99, 289)(100, 290)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E16.1126 Graph:: simple bipartite v = 110 e = 200 f = 60 degree seq :: [ 2^100, 20^10 ] E16.1132 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 18}) Quotient :: regular Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |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, T1^18 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 39, 53, 65, 77, 89, 88, 76, 64, 52, 38, 22, 10, 4)(3, 7, 15, 31, 47, 59, 71, 83, 95, 100, 93, 79, 66, 57, 41, 24, 18, 8)(6, 13, 27, 21, 37, 51, 63, 75, 87, 99, 103, 91, 78, 69, 55, 40, 30, 14)(9, 19, 36, 50, 62, 74, 86, 98, 101, 90, 81, 67, 54, 44, 26, 12, 25, 20)(16, 28, 42, 35, 46, 58, 70, 82, 94, 104, 108, 106, 96, 85, 73, 60, 49, 33)(17, 29, 43, 56, 68, 80, 92, 102, 107, 105, 97, 84, 72, 61, 48, 32, 45, 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, 40)(25, 42)(26, 43)(27, 45)(30, 46)(36, 48)(37, 49)(38, 50)(39, 54)(41, 56)(44, 58)(47, 60)(51, 61)(52, 63)(53, 66)(55, 68)(57, 70)(59, 72)(62, 73)(64, 71)(65, 78)(67, 80)(69, 82)(74, 84)(75, 85)(76, 86)(77, 90)(79, 92)(81, 94)(83, 96)(87, 97)(88, 99)(89, 100)(91, 102)(93, 104)(95, 105)(98, 106)(101, 107)(103, 108) local type(s) :: { ( 6^18 ) } Outer automorphisms :: reflexible Dual of E16.1134 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 6 e = 54 f = 18 degree seq :: [ 18^6 ] E16.1133 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 18}) Quotient :: regular Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^6, T1^18 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 61, 73, 85, 84, 72, 60, 46, 31, 19, 10, 4)(3, 7, 15, 25, 39, 55, 67, 79, 91, 97, 86, 75, 62, 49, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 58, 70, 82, 94, 96, 87, 74, 63, 48, 34, 21, 14)(16, 26, 17, 28, 35, 51, 64, 77, 88, 99, 104, 101, 92, 80, 68, 56, 40, 27)(23, 36, 24, 38, 50, 65, 76, 89, 98, 105, 103, 95, 83, 71, 59, 45, 30, 37)(41, 53, 42, 57, 69, 81, 93, 102, 107, 108, 106, 100, 90, 78, 66, 54, 43, 52) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 59)(45, 57)(46, 58)(47, 62)(49, 64)(51, 66)(55, 68)(56, 69)(60, 67)(61, 74)(63, 76)(65, 78)(70, 83)(71, 81)(72, 82)(73, 86)(75, 88)(77, 90)(79, 92)(80, 93)(84, 91)(85, 96)(87, 98)(89, 100)(94, 103)(95, 102)(97, 104)(99, 106)(101, 107)(105, 108) local type(s) :: { ( 6^18 ) } Outer automorphisms :: reflexible Dual of E16.1135 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 6 e = 54 f = 18 degree seq :: [ 18^6 ] E16.1134 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 18}) Quotient :: regular Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^6, (T1^-1 * T2)^18 ] 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, 88, 48, 90, 47, 89)(52, 92, 56, 91, 61, 93)(53, 95, 62, 94, 55, 96)(54, 86, 63, 85, 68, 87)(57, 82, 70, 84, 60, 83)(58, 100, 71, 102, 59, 101)(64, 103, 69, 105, 65, 104)(66, 72, 78, 77, 67, 73)(74, 106, 76, 108, 75, 107)(79, 99, 81, 98, 80, 97) 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, 97)(50, 98)(51, 99)(52, 83)(53, 86)(54, 73)(55, 87)(56, 82)(57, 66)(58, 92)(59, 93)(60, 67)(61, 84)(62, 85)(63, 72)(64, 95)(65, 96)(68, 77)(69, 94)(70, 78)(71, 91)(74, 100)(75, 101)(76, 102)(79, 103)(80, 104)(81, 105)(88, 106)(89, 107)(90, 108) local type(s) :: { ( 18^6 ) } Outer automorphisms :: reflexible Dual of E16.1132 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 18 e = 54 f = 6 degree seq :: [ 6^18 ] E16.1135 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 18}) Quotient :: regular Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1)^2, T1^6, T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 20, 12, 8)(6, 13, 9, 18, 19, 14)(16, 23, 17, 25, 27, 24)(21, 28, 22, 30, 26, 29)(31, 37, 32, 39, 33, 38)(34, 40, 35, 42, 36, 41)(43, 49, 44, 51, 45, 50)(46, 82, 47, 83, 48, 84)(52, 88, 56, 97, 61, 90)(53, 91, 62, 96, 55, 93)(54, 94, 66, 92, 63, 95)(57, 99, 60, 98, 68, 89)(58, 100, 69, 102, 59, 101)(64, 103, 67, 105, 65, 104)(70, 106, 72, 108, 71, 107)(73, 87, 75, 86, 74, 85)(76, 81, 78, 80, 77, 79) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 19)(13, 21)(14, 22)(18, 26)(20, 27)(23, 31)(24, 32)(25, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)(49, 57)(50, 60)(51, 68)(52, 89)(53, 92)(54, 84)(55, 95)(56, 98)(58, 97)(59, 90)(61, 99)(62, 94)(63, 82)(64, 96)(65, 93)(66, 83)(67, 91)(69, 88)(70, 102)(71, 101)(72, 100)(73, 105)(74, 104)(75, 103)(76, 108)(77, 107)(78, 106)(79, 86)(80, 85)(81, 87) local type(s) :: { ( 18^6 ) } Outer automorphisms :: reflexible Dual of E16.1133 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 18 e = 54 f = 6 degree seq :: [ 6^18 ] E16.1136 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 18}) Quotient :: edge Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |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)^18 ] 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, 55, 51, 57, 50, 52)(53, 76, 59, 78, 61, 77)(54, 85, 63, 87, 56, 82)(58, 89, 67, 91, 60, 83)(62, 93, 65, 86, 64, 84)(66, 97, 69, 90, 68, 88)(70, 95, 72, 94, 71, 92)(73, 99, 75, 98, 74, 96)(79, 102, 81, 101, 80, 100)(103, 106, 105, 108, 104, 107)(109, 110)(111, 115)(112, 117)(113, 119)(114, 121)(116, 120)(118, 122)(123, 131)(124, 133)(125, 132)(126, 134)(127, 135)(128, 137)(129, 136)(130, 138)(139, 145)(140, 146)(141, 147)(142, 148)(143, 149)(144, 150)(151, 157)(152, 158)(153, 159)(154, 184)(155, 185)(156, 186)(160, 190)(161, 191)(162, 192)(163, 193)(164, 194)(165, 195)(166, 196)(167, 197)(168, 198)(169, 199)(170, 200)(171, 201)(172, 202)(173, 203)(174, 204)(175, 205)(176, 206)(177, 207)(178, 208)(179, 209)(180, 210)(181, 211)(182, 212)(183, 213)(187, 214)(188, 215)(189, 216) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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) :: { ( 36, 36 ), ( 36^6 ) } Outer automorphisms :: reflexible Dual of E16.1144 Transitivity :: ET+ Graph:: simple bipartite v = 72 e = 108 f = 6 degree seq :: [ 2^54, 6^18 ] E16.1137 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 18}) Quotient :: edge Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^6, (T2 * T1)^18 ] Map:: polytopal R = (1, 3, 8, 17, 10, 4)(2, 5, 12, 21, 14, 6)(7, 15, 9, 18, 25, 16)(11, 19, 13, 22, 29, 20)(23, 31, 24, 33, 26, 32)(27, 34, 28, 36, 30, 35)(37, 43, 38, 45, 39, 44)(40, 46, 41, 48, 42, 47)(49, 52, 50, 55, 51, 57)(53, 77, 59, 78, 61, 76)(54, 85, 56, 86, 64, 82)(58, 89, 60, 90, 68, 83)(62, 93, 63, 87, 65, 84)(66, 97, 67, 91, 69, 88)(70, 95, 71, 94, 72, 92)(73, 99, 74, 98, 75, 96)(79, 102, 80, 101, 81, 100)(103, 106, 105, 108, 104, 107)(109, 110)(111, 115)(112, 117)(113, 119)(114, 121)(116, 122)(118, 120)(123, 131)(124, 132)(125, 133)(126, 134)(127, 135)(128, 136)(129, 137)(130, 138)(139, 145)(140, 146)(141, 147)(142, 148)(143, 149)(144, 150)(151, 157)(152, 158)(153, 159)(154, 184)(155, 185)(156, 186)(160, 190)(161, 191)(162, 192)(163, 194)(164, 195)(165, 193)(166, 196)(167, 198)(168, 199)(169, 197)(170, 200)(171, 202)(172, 201)(173, 203)(174, 204)(175, 206)(176, 205)(177, 207)(178, 208)(179, 209)(180, 210)(181, 211)(182, 212)(183, 213)(187, 215)(188, 216)(189, 214) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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) :: { ( 36, 36 ), ( 36^6 ) } Outer automorphisms :: reflexible Dual of E16.1145 Transitivity :: ET+ Graph:: simple bipartite v = 72 e = 108 f = 6 degree seq :: [ 2^54, 6^18 ] E16.1138 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 18}) Quotient :: edge Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T1^-2 * T2^-1 * T1 * T2^-1 * T1^-1, T2 * T1^-3 * T2 * T1^-1, T1^6, T2^18 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 37, 49, 61, 73, 85, 97, 88, 76, 64, 52, 40, 28, 15, 5)(2, 7, 19, 32, 44, 56, 68, 80, 92, 103, 94, 82, 70, 58, 46, 34, 22, 8)(4, 12, 26, 38, 50, 62, 74, 86, 98, 105, 95, 83, 71, 59, 47, 35, 23, 9)(6, 17, 29, 41, 53, 65, 77, 89, 100, 107, 101, 90, 78, 66, 54, 42, 30, 18)(11, 16, 14, 27, 39, 51, 63, 75, 87, 99, 106, 96, 84, 72, 60, 48, 36, 24)(13, 21, 33, 45, 57, 69, 81, 93, 104, 108, 102, 91, 79, 67, 55, 43, 31, 20)(109, 110, 114, 124, 121, 112)(111, 117, 125, 116, 129, 119)(113, 122, 126, 120, 128, 115)(118, 132, 137, 131, 141, 130)(123, 134, 138, 127, 139, 135)(133, 142, 149, 144, 153, 143)(136, 140, 150, 147, 151, 146)(145, 155, 161, 154, 165, 156)(148, 159, 162, 158, 163, 152)(157, 168, 173, 167, 177, 166)(160, 170, 174, 164, 175, 171)(169, 178, 185, 180, 189, 179)(172, 176, 186, 183, 187, 182)(181, 191, 197, 190, 201, 192)(184, 195, 198, 194, 199, 188)(193, 204, 208, 203, 212, 202)(196, 206, 209, 200, 210, 207)(205, 211, 215, 214, 216, 213) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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) :: { ( 4^6 ), ( 4^18 ) } Outer automorphisms :: reflexible Dual of E16.1146 Transitivity :: ET+ Graph:: simple bipartite v = 24 e = 108 f = 54 degree seq :: [ 6^18, 18^6 ] E16.1139 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 18}) Quotient :: edge Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^6, T2^18 ] Map:: polytopal non-degenerate R = (1, 3, 10, 21, 33, 45, 57, 69, 81, 93, 84, 72, 60, 48, 36, 24, 13, 5)(2, 7, 17, 29, 41, 53, 65, 77, 89, 100, 90, 78, 66, 54, 42, 30, 18, 8)(4, 11, 23, 35, 47, 59, 71, 83, 95, 102, 92, 80, 68, 56, 44, 32, 20, 9)(6, 15, 27, 39, 51, 63, 75, 87, 98, 106, 99, 88, 76, 64, 52, 40, 28, 16)(12, 19, 31, 43, 55, 67, 79, 91, 101, 107, 103, 94, 82, 70, 58, 46, 34, 22)(14, 25, 37, 49, 61, 73, 85, 96, 104, 108, 105, 97, 86, 74, 62, 50, 38, 26)(109, 110, 114, 122, 120, 112)(111, 117, 127, 134, 123, 116)(113, 119, 130, 133, 124, 115)(118, 126, 135, 146, 139, 128)(121, 125, 136, 145, 142, 131)(129, 140, 151, 158, 147, 138)(132, 143, 154, 157, 148, 137)(141, 150, 159, 170, 163, 152)(144, 149, 160, 169, 166, 155)(153, 164, 175, 182, 171, 162)(156, 167, 178, 181, 172, 161)(165, 174, 183, 194, 187, 176)(168, 173, 184, 193, 190, 179)(177, 188, 199, 205, 195, 186)(180, 191, 202, 204, 196, 185)(189, 198, 206, 213, 209, 200)(192, 197, 207, 212, 211, 203)(201, 210, 215, 216, 214, 208) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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) :: { ( 4^6 ), ( 4^18 ) } Outer automorphisms :: reflexible Dual of E16.1147 Transitivity :: ET+ Graph:: simple bipartite v = 24 e = 108 f = 54 degree seq :: [ 6^18, 18^6 ] E16.1140 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 18}) Quotient :: edge Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |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, T1^18 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 31)(23, 40)(25, 42)(26, 43)(27, 45)(30, 46)(36, 48)(37, 49)(38, 50)(39, 54)(41, 56)(44, 58)(47, 60)(51, 61)(52, 63)(53, 66)(55, 68)(57, 70)(59, 72)(62, 73)(64, 71)(65, 78)(67, 80)(69, 82)(74, 84)(75, 85)(76, 86)(77, 90)(79, 92)(81, 94)(83, 96)(87, 97)(88, 99)(89, 100)(91, 102)(93, 104)(95, 105)(98, 106)(101, 107)(103, 108)(109, 110, 113, 119, 131, 147, 161, 173, 185, 197, 196, 184, 172, 160, 146, 130, 118, 112)(111, 115, 123, 139, 155, 167, 179, 191, 203, 208, 201, 187, 174, 165, 149, 132, 126, 116)(114, 121, 135, 129, 145, 159, 171, 183, 195, 207, 211, 199, 186, 177, 163, 148, 138, 122)(117, 127, 144, 158, 170, 182, 194, 206, 209, 198, 189, 175, 162, 152, 134, 120, 133, 128)(124, 136, 150, 143, 154, 166, 178, 190, 202, 212, 216, 214, 204, 193, 181, 168, 157, 141)(125, 137, 151, 164, 176, 188, 200, 210, 215, 213, 205, 192, 180, 169, 156, 140, 153, 142) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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, 12 ), ( 12^18 ) } Outer automorphisms :: reflexible Dual of E16.1142 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 108 f = 18 degree seq :: [ 2^54, 18^6 ] E16.1141 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 18}) Quotient :: edge Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, (T2 * T1)^6, T1^18 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 59)(45, 57)(46, 58)(47, 62)(49, 64)(51, 66)(55, 68)(56, 69)(60, 67)(61, 74)(63, 76)(65, 78)(70, 83)(71, 81)(72, 82)(73, 86)(75, 88)(77, 90)(79, 92)(80, 93)(84, 91)(85, 96)(87, 98)(89, 100)(94, 103)(95, 102)(97, 104)(99, 106)(101, 107)(105, 108)(109, 110, 113, 119, 128, 140, 155, 169, 181, 193, 192, 180, 168, 154, 139, 127, 118, 112)(111, 115, 123, 133, 147, 163, 175, 187, 199, 205, 194, 183, 170, 157, 141, 130, 120, 116)(114, 121, 117, 126, 137, 152, 166, 178, 190, 202, 204, 195, 182, 171, 156, 142, 129, 122)(124, 134, 125, 136, 143, 159, 172, 185, 196, 207, 212, 209, 200, 188, 176, 164, 148, 135)(131, 144, 132, 146, 158, 173, 184, 197, 206, 213, 211, 203, 191, 179, 167, 153, 138, 145)(149, 161, 150, 165, 177, 189, 201, 210, 215, 216, 214, 208, 198, 186, 174, 162, 151, 160) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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, 12 ), ( 12^18 ) } Outer automorphisms :: reflexible Dual of E16.1143 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 108 f = 18 degree seq :: [ 2^54, 18^6 ] E16.1142 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 18}) Quotient :: loop Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |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)^18 ] Map:: R = (1, 109, 3, 111, 8, 116, 17, 125, 10, 118, 4, 112)(2, 110, 5, 113, 12, 120, 21, 129, 14, 122, 6, 114)(7, 115, 15, 123, 24, 132, 18, 126, 9, 117, 16, 124)(11, 119, 19, 127, 28, 136, 22, 130, 13, 121, 20, 128)(23, 131, 31, 139, 26, 134, 33, 141, 25, 133, 32, 140)(27, 135, 34, 142, 30, 138, 36, 144, 29, 137, 35, 143)(37, 145, 43, 151, 39, 147, 45, 153, 38, 146, 44, 152)(40, 148, 46, 154, 42, 150, 48, 156, 41, 149, 47, 155)(49, 157, 79, 187, 51, 159, 81, 189, 50, 158, 80, 188)(52, 160, 82, 190, 57, 165, 90, 198, 58, 166, 83, 191)(53, 161, 84, 192, 61, 169, 86, 194, 54, 162, 85, 193)(55, 163, 87, 195, 65, 173, 89, 197, 56, 164, 88, 196)(59, 167, 91, 199, 62, 170, 93, 201, 60, 168, 92, 200)(63, 171, 94, 202, 66, 174, 96, 204, 64, 172, 95, 203)(67, 175, 97, 205, 69, 177, 99, 207, 68, 176, 98, 206)(70, 178, 100, 208, 72, 180, 102, 210, 71, 179, 101, 209)(73, 181, 103, 211, 75, 183, 105, 213, 74, 182, 104, 212)(76, 184, 106, 214, 78, 186, 108, 216, 77, 185, 107, 215) 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, 166)(48, 165)(49, 151)(50, 152)(51, 153)(52, 154)(53, 187)(54, 188)(55, 190)(56, 191)(57, 156)(58, 155)(59, 192)(60, 193)(61, 189)(62, 194)(63, 195)(64, 196)(65, 198)(66, 197)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 161)(80, 162)(81, 169)(82, 163)(83, 164)(84, 167)(85, 168)(86, 170)(87, 171)(88, 172)(89, 174)(90, 173)(91, 175)(92, 176)(93, 177)(94, 178)(95, 179)(96, 180)(97, 181)(98, 182)(99, 183)(100, 184)(101, 185)(102, 186)(103, 214)(104, 215)(105, 216)(106, 211)(107, 212)(108, 213) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E16.1140 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 18 e = 108 f = 60 degree seq :: [ 12^18 ] E16.1143 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 18}) Quotient :: loop Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^6, (T2 * T1)^18 ] Map:: R = (1, 109, 3, 111, 8, 116, 17, 125, 10, 118, 4, 112)(2, 110, 5, 113, 12, 120, 21, 129, 14, 122, 6, 114)(7, 115, 15, 123, 9, 117, 18, 126, 25, 133, 16, 124)(11, 119, 19, 127, 13, 121, 22, 130, 29, 137, 20, 128)(23, 131, 31, 139, 24, 132, 33, 141, 26, 134, 32, 140)(27, 135, 34, 142, 28, 136, 36, 144, 30, 138, 35, 143)(37, 145, 43, 151, 38, 146, 45, 153, 39, 147, 44, 152)(40, 148, 46, 154, 41, 149, 48, 156, 42, 150, 47, 155)(49, 157, 55, 163, 50, 158, 57, 165, 51, 159, 52, 160)(53, 161, 76, 184, 59, 167, 77, 185, 61, 169, 78, 186)(54, 162, 85, 193, 56, 164, 82, 190, 64, 172, 86, 194)(58, 166, 89, 197, 60, 168, 83, 191, 68, 176, 90, 198)(62, 170, 87, 195, 63, 171, 84, 192, 65, 173, 93, 201)(66, 174, 91, 199, 67, 175, 88, 196, 69, 177, 97, 205)(70, 178, 94, 202, 71, 179, 92, 200, 72, 180, 95, 203)(73, 181, 98, 206, 74, 182, 96, 204, 75, 183, 99, 207)(79, 187, 101, 209, 80, 188, 100, 208, 81, 189, 102, 210)(103, 211, 108, 216, 105, 213, 106, 214, 104, 212, 107, 215) L = (1, 110)(2, 109)(3, 115)(4, 117)(5, 119)(6, 121)(7, 111)(8, 122)(9, 112)(10, 120)(11, 113)(12, 118)(13, 114)(14, 116)(15, 131)(16, 132)(17, 133)(18, 134)(19, 135)(20, 136)(21, 137)(22, 138)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(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, 184)(47, 185)(48, 186)(49, 151)(50, 152)(51, 153)(52, 190)(53, 191)(54, 192)(55, 193)(56, 195)(57, 194)(58, 196)(59, 197)(60, 199)(61, 198)(62, 200)(63, 202)(64, 201)(65, 203)(66, 204)(67, 206)(68, 205)(69, 207)(70, 208)(71, 209)(72, 210)(73, 211)(74, 212)(75, 213)(76, 154)(77, 155)(78, 156)(79, 215)(80, 214)(81, 216)(82, 160)(83, 161)(84, 162)(85, 163)(86, 165)(87, 164)(88, 166)(89, 167)(90, 169)(91, 168)(92, 170)(93, 172)(94, 171)(95, 173)(96, 174)(97, 176)(98, 175)(99, 177)(100, 178)(101, 179)(102, 180)(103, 181)(104, 182)(105, 183)(106, 188)(107, 187)(108, 189) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E16.1141 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 18 e = 108 f = 60 degree seq :: [ 12^18 ] E16.1144 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 18}) Quotient :: loop Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T1^-2 * T2^-1 * T1 * T2^-1 * T1^-1, T2 * T1^-3 * T2 * T1^-1, T1^6, T2^18 ] Map:: R = (1, 109, 3, 111, 10, 118, 25, 133, 37, 145, 49, 157, 61, 169, 73, 181, 85, 193, 97, 205, 88, 196, 76, 184, 64, 172, 52, 160, 40, 148, 28, 136, 15, 123, 5, 113)(2, 110, 7, 115, 19, 127, 32, 140, 44, 152, 56, 164, 68, 176, 80, 188, 92, 200, 103, 211, 94, 202, 82, 190, 70, 178, 58, 166, 46, 154, 34, 142, 22, 130, 8, 116)(4, 112, 12, 120, 26, 134, 38, 146, 50, 158, 62, 170, 74, 182, 86, 194, 98, 206, 105, 213, 95, 203, 83, 191, 71, 179, 59, 167, 47, 155, 35, 143, 23, 131, 9, 117)(6, 114, 17, 125, 29, 137, 41, 149, 53, 161, 65, 173, 77, 185, 89, 197, 100, 208, 107, 215, 101, 209, 90, 198, 78, 186, 66, 174, 54, 162, 42, 150, 30, 138, 18, 126)(11, 119, 16, 124, 14, 122, 27, 135, 39, 147, 51, 159, 63, 171, 75, 183, 87, 195, 99, 207, 106, 214, 96, 204, 84, 192, 72, 180, 60, 168, 48, 156, 36, 144, 24, 132)(13, 121, 21, 129, 33, 141, 45, 153, 57, 165, 69, 177, 81, 189, 93, 201, 104, 212, 108, 216, 102, 210, 91, 199, 79, 187, 67, 175, 55, 163, 43, 151, 31, 139, 20, 128) L = (1, 110)(2, 114)(3, 117)(4, 109)(5, 122)(6, 124)(7, 113)(8, 129)(9, 125)(10, 132)(11, 111)(12, 128)(13, 112)(14, 126)(15, 134)(16, 121)(17, 116)(18, 120)(19, 139)(20, 115)(21, 119)(22, 118)(23, 141)(24, 137)(25, 142)(26, 138)(27, 123)(28, 140)(29, 131)(30, 127)(31, 135)(32, 150)(33, 130)(34, 149)(35, 133)(36, 153)(37, 155)(38, 136)(39, 151)(40, 159)(41, 144)(42, 147)(43, 146)(44, 148)(45, 143)(46, 165)(47, 161)(48, 145)(49, 168)(50, 163)(51, 162)(52, 170)(53, 154)(54, 158)(55, 152)(56, 175)(57, 156)(58, 157)(59, 177)(60, 173)(61, 178)(62, 174)(63, 160)(64, 176)(65, 167)(66, 164)(67, 171)(68, 186)(69, 166)(70, 185)(71, 169)(72, 189)(73, 191)(74, 172)(75, 187)(76, 195)(77, 180)(78, 183)(79, 182)(80, 184)(81, 179)(82, 201)(83, 197)(84, 181)(85, 204)(86, 199)(87, 198)(88, 206)(89, 190)(90, 194)(91, 188)(92, 210)(93, 192)(94, 193)(95, 212)(96, 208)(97, 211)(98, 209)(99, 196)(100, 203)(101, 200)(102, 207)(103, 215)(104, 202)(105, 205)(106, 216)(107, 214)(108, 213) 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 ) } Outer automorphisms :: reflexible Dual of E16.1136 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 108 f = 72 degree seq :: [ 36^6 ] E16.1145 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 18}) Quotient :: loop Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^6, T2^18 ] Map:: R = (1, 109, 3, 111, 10, 118, 21, 129, 33, 141, 45, 153, 57, 165, 69, 177, 81, 189, 93, 201, 84, 192, 72, 180, 60, 168, 48, 156, 36, 144, 24, 132, 13, 121, 5, 113)(2, 110, 7, 115, 17, 125, 29, 137, 41, 149, 53, 161, 65, 173, 77, 185, 89, 197, 100, 208, 90, 198, 78, 186, 66, 174, 54, 162, 42, 150, 30, 138, 18, 126, 8, 116)(4, 112, 11, 119, 23, 131, 35, 143, 47, 155, 59, 167, 71, 179, 83, 191, 95, 203, 102, 210, 92, 200, 80, 188, 68, 176, 56, 164, 44, 152, 32, 140, 20, 128, 9, 117)(6, 114, 15, 123, 27, 135, 39, 147, 51, 159, 63, 171, 75, 183, 87, 195, 98, 206, 106, 214, 99, 207, 88, 196, 76, 184, 64, 172, 52, 160, 40, 148, 28, 136, 16, 124)(12, 120, 19, 127, 31, 139, 43, 151, 55, 163, 67, 175, 79, 187, 91, 199, 101, 209, 107, 215, 103, 211, 94, 202, 82, 190, 70, 178, 58, 166, 46, 154, 34, 142, 22, 130)(14, 122, 25, 133, 37, 145, 49, 157, 61, 169, 73, 181, 85, 193, 96, 204, 104, 212, 108, 216, 105, 213, 97, 205, 86, 194, 74, 182, 62, 170, 50, 158, 38, 146, 26, 134) L = (1, 110)(2, 114)(3, 117)(4, 109)(5, 119)(6, 122)(7, 113)(8, 111)(9, 127)(10, 126)(11, 130)(12, 112)(13, 125)(14, 120)(15, 116)(16, 115)(17, 136)(18, 135)(19, 134)(20, 118)(21, 140)(22, 133)(23, 121)(24, 143)(25, 124)(26, 123)(27, 146)(28, 145)(29, 132)(30, 129)(31, 128)(32, 151)(33, 150)(34, 131)(35, 154)(36, 149)(37, 142)(38, 139)(39, 138)(40, 137)(41, 160)(42, 159)(43, 158)(44, 141)(45, 164)(46, 157)(47, 144)(48, 167)(49, 148)(50, 147)(51, 170)(52, 169)(53, 156)(54, 153)(55, 152)(56, 175)(57, 174)(58, 155)(59, 178)(60, 173)(61, 166)(62, 163)(63, 162)(64, 161)(65, 184)(66, 183)(67, 182)(68, 165)(69, 188)(70, 181)(71, 168)(72, 191)(73, 172)(74, 171)(75, 194)(76, 193)(77, 180)(78, 177)(79, 176)(80, 199)(81, 198)(82, 179)(83, 202)(84, 197)(85, 190)(86, 187)(87, 186)(88, 185)(89, 207)(90, 206)(91, 205)(92, 189)(93, 210)(94, 204)(95, 192)(96, 196)(97, 195)(98, 213)(99, 212)(100, 201)(101, 200)(102, 215)(103, 203)(104, 211)(105, 209)(106, 208)(107, 216)(108, 214) 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 ) } Outer automorphisms :: reflexible Dual of E16.1137 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 108 f = 72 degree seq :: [ 36^6 ] E16.1146 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 18}) Quotient :: loop Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |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, T1^18 ] Map:: polytopal non-degenerate R = (1, 109, 3, 111)(2, 110, 6, 114)(4, 112, 9, 117)(5, 113, 12, 120)(7, 115, 16, 124)(8, 116, 17, 125)(10, 118, 21, 129)(11, 119, 24, 132)(13, 121, 28, 136)(14, 122, 29, 137)(15, 123, 32, 140)(18, 126, 35, 143)(19, 127, 33, 141)(20, 128, 34, 142)(22, 130, 31, 139)(23, 131, 40, 148)(25, 133, 42, 150)(26, 134, 43, 151)(27, 135, 45, 153)(30, 138, 46, 154)(36, 144, 48, 156)(37, 145, 49, 157)(38, 146, 50, 158)(39, 147, 54, 162)(41, 149, 56, 164)(44, 152, 58, 166)(47, 155, 60, 168)(51, 159, 61, 169)(52, 160, 63, 171)(53, 161, 66, 174)(55, 163, 68, 176)(57, 165, 70, 178)(59, 167, 72, 180)(62, 170, 73, 181)(64, 172, 71, 179)(65, 173, 78, 186)(67, 175, 80, 188)(69, 177, 82, 190)(74, 182, 84, 192)(75, 183, 85, 193)(76, 184, 86, 194)(77, 185, 90, 198)(79, 187, 92, 200)(81, 189, 94, 202)(83, 191, 96, 204)(87, 195, 97, 205)(88, 196, 99, 207)(89, 197, 100, 208)(91, 199, 102, 210)(93, 201, 104, 212)(95, 203, 105, 213)(98, 206, 106, 214)(101, 209, 107, 215)(103, 211, 108, 216) L = (1, 110)(2, 113)(3, 115)(4, 109)(5, 119)(6, 121)(7, 123)(8, 111)(9, 127)(10, 112)(11, 131)(12, 133)(13, 135)(14, 114)(15, 139)(16, 136)(17, 137)(18, 116)(19, 144)(20, 117)(21, 145)(22, 118)(23, 147)(24, 126)(25, 128)(26, 120)(27, 129)(28, 150)(29, 151)(30, 122)(31, 155)(32, 153)(33, 124)(34, 125)(35, 154)(36, 158)(37, 159)(38, 130)(39, 161)(40, 138)(41, 132)(42, 143)(43, 164)(44, 134)(45, 142)(46, 166)(47, 167)(48, 140)(49, 141)(50, 170)(51, 171)(52, 146)(53, 173)(54, 152)(55, 148)(56, 176)(57, 149)(58, 178)(59, 179)(60, 157)(61, 156)(62, 182)(63, 183)(64, 160)(65, 185)(66, 165)(67, 162)(68, 188)(69, 163)(70, 190)(71, 191)(72, 169)(73, 168)(74, 194)(75, 195)(76, 172)(77, 197)(78, 177)(79, 174)(80, 200)(81, 175)(82, 202)(83, 203)(84, 180)(85, 181)(86, 206)(87, 207)(88, 184)(89, 196)(90, 189)(91, 186)(92, 210)(93, 187)(94, 212)(95, 208)(96, 193)(97, 192)(98, 209)(99, 211)(100, 201)(101, 198)(102, 215)(103, 199)(104, 216)(105, 205)(106, 204)(107, 213)(108, 214) local type(s) :: { ( 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E16.1138 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 54 e = 108 f = 24 degree seq :: [ 4^54 ] E16.1147 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 18}) Quotient :: loop Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, (T2 * T1)^6, T1^18 ] Map:: polytopal non-degenerate R = (1, 109, 3, 111)(2, 110, 6, 114)(4, 112, 9, 117)(5, 113, 12, 120)(7, 115, 16, 124)(8, 116, 17, 125)(10, 118, 15, 123)(11, 119, 21, 129)(13, 121, 23, 131)(14, 122, 24, 132)(18, 126, 30, 138)(19, 127, 29, 137)(20, 128, 33, 141)(22, 130, 35, 143)(25, 133, 40, 148)(26, 134, 41, 149)(27, 135, 42, 150)(28, 136, 43, 151)(31, 139, 39, 147)(32, 140, 48, 156)(34, 142, 50, 158)(36, 144, 52, 160)(37, 145, 53, 161)(38, 146, 54, 162)(44, 152, 59, 167)(45, 153, 57, 165)(46, 154, 58, 166)(47, 155, 62, 170)(49, 157, 64, 172)(51, 159, 66, 174)(55, 163, 68, 176)(56, 164, 69, 177)(60, 168, 67, 175)(61, 169, 74, 182)(63, 171, 76, 184)(65, 173, 78, 186)(70, 178, 83, 191)(71, 179, 81, 189)(72, 180, 82, 190)(73, 181, 86, 194)(75, 183, 88, 196)(77, 185, 90, 198)(79, 187, 92, 200)(80, 188, 93, 201)(84, 192, 91, 199)(85, 193, 96, 204)(87, 195, 98, 206)(89, 197, 100, 208)(94, 202, 103, 211)(95, 203, 102, 210)(97, 205, 104, 212)(99, 207, 106, 214)(101, 209, 107, 215)(105, 213, 108, 216) L = (1, 110)(2, 113)(3, 115)(4, 109)(5, 119)(6, 121)(7, 123)(8, 111)(9, 126)(10, 112)(11, 128)(12, 116)(13, 117)(14, 114)(15, 133)(16, 134)(17, 136)(18, 137)(19, 118)(20, 140)(21, 122)(22, 120)(23, 144)(24, 146)(25, 147)(26, 125)(27, 124)(28, 143)(29, 152)(30, 145)(31, 127)(32, 155)(33, 130)(34, 129)(35, 159)(36, 132)(37, 131)(38, 158)(39, 163)(40, 135)(41, 161)(42, 165)(43, 160)(44, 166)(45, 138)(46, 139)(47, 169)(48, 142)(49, 141)(50, 173)(51, 172)(52, 149)(53, 150)(54, 151)(55, 175)(56, 148)(57, 177)(58, 178)(59, 153)(60, 154)(61, 181)(62, 157)(63, 156)(64, 185)(65, 184)(66, 162)(67, 187)(68, 164)(69, 189)(70, 190)(71, 167)(72, 168)(73, 193)(74, 171)(75, 170)(76, 197)(77, 196)(78, 174)(79, 199)(80, 176)(81, 201)(82, 202)(83, 179)(84, 180)(85, 192)(86, 183)(87, 182)(88, 207)(89, 206)(90, 186)(91, 205)(92, 188)(93, 210)(94, 204)(95, 191)(96, 195)(97, 194)(98, 213)(99, 212)(100, 198)(101, 200)(102, 215)(103, 203)(104, 209)(105, 211)(106, 208)(107, 216)(108, 214) local type(s) :: { ( 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E16.1139 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 54 e = 108 f = 24 degree seq :: [ 4^54 ] E16.1148 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18}) Quotient :: dipole Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, Y2^6, (Y3 * Y2^-1)^18 ] Map:: R = (1, 109, 2, 110)(3, 111, 7, 115)(4, 112, 9, 117)(5, 113, 11, 119)(6, 114, 13, 121)(8, 116, 12, 120)(10, 118, 14, 122)(15, 123, 23, 131)(16, 124, 25, 133)(17, 125, 24, 132)(18, 126, 26, 134)(19, 127, 27, 135)(20, 128, 29, 137)(21, 129, 28, 136)(22, 130, 30, 138)(31, 139, 37, 145)(32, 140, 38, 146)(33, 141, 39, 147)(34, 142, 40, 148)(35, 143, 41, 149)(36, 144, 42, 150)(43, 151, 49, 157)(44, 152, 50, 158)(45, 153, 51, 159)(46, 154, 79, 187)(47, 155, 81, 189)(48, 156, 83, 191)(52, 160, 85, 193)(53, 161, 87, 195)(54, 162, 89, 197)(55, 163, 92, 200)(56, 164, 95, 203)(57, 165, 98, 206)(58, 166, 96, 204)(59, 167, 100, 208)(60, 168, 90, 198)(61, 169, 94, 202)(62, 170, 97, 205)(63, 171, 99, 207)(64, 172, 105, 213)(65, 173, 108, 216)(66, 174, 91, 199)(67, 175, 93, 201)(68, 176, 106, 214)(69, 177, 107, 215)(70, 178, 101, 209)(71, 179, 86, 194)(72, 180, 102, 210)(73, 181, 103, 211)(74, 182, 88, 196)(75, 183, 104, 212)(76, 184, 80, 188)(77, 185, 82, 190)(78, 186, 84, 192)(217, 325, 219, 327, 224, 332, 233, 341, 226, 334, 220, 328)(218, 326, 221, 329, 228, 336, 237, 345, 230, 338, 222, 330)(223, 331, 231, 339, 240, 348, 234, 342, 225, 333, 232, 340)(227, 335, 235, 343, 244, 352, 238, 346, 229, 337, 236, 344)(239, 347, 247, 355, 242, 350, 249, 357, 241, 349, 248, 356)(243, 351, 250, 358, 246, 354, 252, 360, 245, 353, 251, 359)(253, 361, 259, 367, 255, 363, 261, 369, 254, 362, 260, 368)(256, 364, 262, 370, 258, 366, 264, 372, 257, 365, 263, 371)(265, 373, 277, 385, 267, 375, 269, 377, 266, 374, 276, 384)(268, 376, 297, 405, 274, 382, 295, 403, 275, 383, 299, 407)(270, 378, 306, 414, 280, 388, 310, 418, 271, 379, 303, 411)(272, 380, 312, 420, 284, 392, 316, 424, 273, 381, 301, 409)(278, 386, 321, 429, 281, 389, 308, 416, 279, 387, 305, 413)(282, 390, 322, 430, 285, 393, 314, 422, 283, 391, 311, 419)(286, 394, 324, 432, 288, 396, 315, 423, 287, 395, 313, 421)(289, 397, 323, 431, 291, 399, 309, 417, 290, 398, 307, 415)(292, 400, 318, 426, 294, 402, 302, 410, 293, 401, 317, 425)(296, 404, 320, 428, 300, 408, 304, 412, 298, 406, 319, 427) L = (1, 218)(2, 217)(3, 223)(4, 225)(5, 227)(6, 229)(7, 219)(8, 228)(9, 220)(10, 230)(11, 221)(12, 224)(13, 222)(14, 226)(15, 239)(16, 241)(17, 240)(18, 242)(19, 243)(20, 245)(21, 244)(22, 246)(23, 231)(24, 233)(25, 232)(26, 234)(27, 235)(28, 237)(29, 236)(30, 238)(31, 253)(32, 254)(33, 255)(34, 256)(35, 257)(36, 258)(37, 247)(38, 248)(39, 249)(40, 250)(41, 251)(42, 252)(43, 265)(44, 266)(45, 267)(46, 295)(47, 297)(48, 299)(49, 259)(50, 260)(51, 261)(52, 301)(53, 303)(54, 305)(55, 308)(56, 311)(57, 314)(58, 312)(59, 316)(60, 306)(61, 310)(62, 313)(63, 315)(64, 321)(65, 324)(66, 307)(67, 309)(68, 322)(69, 323)(70, 317)(71, 302)(72, 318)(73, 319)(74, 304)(75, 320)(76, 296)(77, 298)(78, 300)(79, 262)(80, 292)(81, 263)(82, 293)(83, 264)(84, 294)(85, 268)(86, 287)(87, 269)(88, 290)(89, 270)(90, 276)(91, 282)(92, 271)(93, 283)(94, 277)(95, 272)(96, 274)(97, 278)(98, 273)(99, 279)(100, 275)(101, 286)(102, 288)(103, 289)(104, 291)(105, 280)(106, 284)(107, 285)(108, 281)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432) local type(s) :: { ( 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.1154 Graph:: bipartite v = 72 e = 216 f = 114 degree seq :: [ 4^54, 12^18 ] E16.1149 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18}) Quotient :: dipole Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2^6, (Y3 * Y2^-1)^18 ] Map:: R = (1, 109, 2, 110)(3, 111, 7, 115)(4, 112, 9, 117)(5, 113, 11, 119)(6, 114, 13, 121)(8, 116, 14, 122)(10, 118, 12, 120)(15, 123, 23, 131)(16, 124, 24, 132)(17, 125, 25, 133)(18, 126, 26, 134)(19, 127, 27, 135)(20, 128, 28, 136)(21, 129, 29, 137)(22, 130, 30, 138)(31, 139, 37, 145)(32, 140, 38, 146)(33, 141, 39, 147)(34, 142, 40, 148)(35, 143, 41, 149)(36, 144, 42, 150)(43, 151, 49, 157)(44, 152, 50, 158)(45, 153, 51, 159)(46, 154, 97, 205)(47, 155, 99, 207)(48, 156, 101, 209)(52, 160, 65, 173)(53, 161, 61, 169)(54, 162, 76, 184)(55, 163, 58, 166)(56, 164, 80, 188)(57, 165, 62, 170)(59, 167, 63, 171)(60, 168, 68, 176)(64, 172, 72, 180)(66, 174, 77, 185)(67, 175, 74, 182)(69, 177, 75, 183)(70, 178, 81, 189)(71, 179, 78, 186)(73, 181, 79, 187)(82, 190, 90, 198)(83, 191, 88, 196)(84, 192, 89, 197)(85, 193, 93, 201)(86, 194, 91, 199)(87, 195, 92, 200)(94, 202, 108, 216)(95, 203, 104, 212)(96, 204, 106, 214)(98, 206, 103, 211)(100, 208, 107, 215)(102, 210, 105, 213)(217, 325, 219, 327, 224, 332, 233, 341, 226, 334, 220, 328)(218, 326, 221, 329, 228, 336, 237, 345, 230, 338, 222, 330)(223, 331, 231, 339, 225, 333, 234, 342, 241, 349, 232, 340)(227, 335, 235, 343, 229, 337, 238, 346, 245, 353, 236, 344)(239, 347, 247, 355, 240, 348, 249, 357, 242, 350, 248, 356)(243, 351, 250, 358, 244, 352, 252, 360, 246, 354, 251, 359)(253, 361, 259, 367, 254, 362, 261, 369, 255, 363, 260, 368)(256, 364, 262, 370, 257, 365, 264, 372, 258, 366, 263, 371)(265, 373, 319, 427, 266, 374, 321, 429, 267, 375, 323, 431)(268, 376, 271, 379, 277, 385, 284, 392, 275, 383, 270, 378)(269, 377, 273, 381, 281, 389, 288, 396, 279, 387, 272, 380)(274, 382, 283, 391, 292, 400, 285, 393, 276, 384, 282, 390)(278, 386, 287, 395, 296, 404, 289, 397, 280, 388, 286, 394)(290, 398, 299, 407, 293, 401, 300, 408, 291, 399, 298, 406)(294, 402, 302, 410, 297, 405, 303, 411, 295, 403, 301, 409)(304, 412, 311, 419, 306, 414, 312, 420, 305, 413, 310, 418)(307, 415, 316, 424, 309, 417, 318, 426, 308, 416, 314, 422)(313, 421, 324, 432, 315, 423, 322, 430, 317, 425, 320, 428) L = (1, 218)(2, 217)(3, 223)(4, 225)(5, 227)(6, 229)(7, 219)(8, 230)(9, 220)(10, 228)(11, 221)(12, 226)(13, 222)(14, 224)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 253)(32, 254)(33, 255)(34, 256)(35, 257)(36, 258)(37, 247)(38, 248)(39, 249)(40, 250)(41, 251)(42, 252)(43, 265)(44, 266)(45, 267)(46, 313)(47, 315)(48, 317)(49, 259)(50, 260)(51, 261)(52, 281)(53, 277)(54, 292)(55, 274)(56, 296)(57, 278)(58, 271)(59, 279)(60, 284)(61, 269)(62, 273)(63, 275)(64, 288)(65, 268)(66, 293)(67, 290)(68, 276)(69, 291)(70, 297)(71, 294)(72, 280)(73, 295)(74, 283)(75, 285)(76, 270)(77, 282)(78, 287)(79, 289)(80, 272)(81, 286)(82, 306)(83, 304)(84, 305)(85, 309)(86, 307)(87, 308)(88, 299)(89, 300)(90, 298)(91, 302)(92, 303)(93, 301)(94, 324)(95, 320)(96, 322)(97, 262)(98, 319)(99, 263)(100, 323)(101, 264)(102, 321)(103, 314)(104, 311)(105, 318)(106, 312)(107, 316)(108, 310)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432) local type(s) :: { ( 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E16.1155 Graph:: bipartite v = 72 e = 216 f = 114 degree seq :: [ 4^54, 12^18 ] E16.1150 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18}) Quotient :: dipole Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y2^-1 * Y1^-1)^2, Y2^-1 * Y1^-3 * Y2^-1 * Y1, Y2 * Y1^-1 * Y2 * Y1^-3, Y2^18 ] Map:: R = (1, 109, 2, 110, 6, 114, 16, 124, 13, 121, 4, 112)(3, 111, 9, 117, 17, 125, 8, 116, 21, 129, 11, 119)(5, 113, 14, 122, 18, 126, 12, 120, 20, 128, 7, 115)(10, 118, 24, 132, 29, 137, 23, 131, 33, 141, 22, 130)(15, 123, 26, 134, 30, 138, 19, 127, 31, 139, 27, 135)(25, 133, 34, 142, 41, 149, 36, 144, 45, 153, 35, 143)(28, 136, 32, 140, 42, 150, 39, 147, 43, 151, 38, 146)(37, 145, 47, 155, 53, 161, 46, 154, 57, 165, 48, 156)(40, 148, 51, 159, 54, 162, 50, 158, 55, 163, 44, 152)(49, 157, 60, 168, 65, 173, 59, 167, 69, 177, 58, 166)(52, 160, 62, 170, 66, 174, 56, 164, 67, 175, 63, 171)(61, 169, 70, 178, 77, 185, 72, 180, 81, 189, 71, 179)(64, 172, 68, 176, 78, 186, 75, 183, 79, 187, 74, 182)(73, 181, 83, 191, 89, 197, 82, 190, 93, 201, 84, 192)(76, 184, 87, 195, 90, 198, 86, 194, 91, 199, 80, 188)(85, 193, 96, 204, 100, 208, 95, 203, 104, 212, 94, 202)(88, 196, 98, 206, 101, 209, 92, 200, 102, 210, 99, 207)(97, 205, 103, 211, 107, 215, 106, 214, 108, 216, 105, 213)(217, 325, 219, 327, 226, 334, 241, 349, 253, 361, 265, 373, 277, 385, 289, 397, 301, 409, 313, 421, 304, 412, 292, 400, 280, 388, 268, 376, 256, 364, 244, 352, 231, 339, 221, 329)(218, 326, 223, 331, 235, 343, 248, 356, 260, 368, 272, 380, 284, 392, 296, 404, 308, 416, 319, 427, 310, 418, 298, 406, 286, 394, 274, 382, 262, 370, 250, 358, 238, 346, 224, 332)(220, 328, 228, 336, 242, 350, 254, 362, 266, 374, 278, 386, 290, 398, 302, 410, 314, 422, 321, 429, 311, 419, 299, 407, 287, 395, 275, 383, 263, 371, 251, 359, 239, 347, 225, 333)(222, 330, 233, 341, 245, 353, 257, 365, 269, 377, 281, 389, 293, 401, 305, 413, 316, 424, 323, 431, 317, 425, 306, 414, 294, 402, 282, 390, 270, 378, 258, 366, 246, 354, 234, 342)(227, 335, 232, 340, 230, 338, 243, 351, 255, 363, 267, 375, 279, 387, 291, 399, 303, 411, 315, 423, 322, 430, 312, 420, 300, 408, 288, 396, 276, 384, 264, 372, 252, 360, 240, 348)(229, 337, 237, 345, 249, 357, 261, 369, 273, 381, 285, 393, 297, 405, 309, 417, 320, 428, 324, 432, 318, 426, 307, 415, 295, 403, 283, 391, 271, 379, 259, 367, 247, 355, 236, 344) L = (1, 219)(2, 223)(3, 226)(4, 228)(5, 217)(6, 233)(7, 235)(8, 218)(9, 220)(10, 241)(11, 232)(12, 242)(13, 237)(14, 243)(15, 221)(16, 230)(17, 245)(18, 222)(19, 248)(20, 229)(21, 249)(22, 224)(23, 225)(24, 227)(25, 253)(26, 254)(27, 255)(28, 231)(29, 257)(30, 234)(31, 236)(32, 260)(33, 261)(34, 238)(35, 239)(36, 240)(37, 265)(38, 266)(39, 267)(40, 244)(41, 269)(42, 246)(43, 247)(44, 272)(45, 273)(46, 250)(47, 251)(48, 252)(49, 277)(50, 278)(51, 279)(52, 256)(53, 281)(54, 258)(55, 259)(56, 284)(57, 285)(58, 262)(59, 263)(60, 264)(61, 289)(62, 290)(63, 291)(64, 268)(65, 293)(66, 270)(67, 271)(68, 296)(69, 297)(70, 274)(71, 275)(72, 276)(73, 301)(74, 302)(75, 303)(76, 280)(77, 305)(78, 282)(79, 283)(80, 308)(81, 309)(82, 286)(83, 287)(84, 288)(85, 313)(86, 314)(87, 315)(88, 292)(89, 316)(90, 294)(91, 295)(92, 319)(93, 320)(94, 298)(95, 299)(96, 300)(97, 304)(98, 321)(99, 322)(100, 323)(101, 306)(102, 307)(103, 310)(104, 324)(105, 311)(106, 312)(107, 317)(108, 318)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432) 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 ) } Outer automorphisms :: reflexible Dual of E16.1152 Graph:: bipartite v = 24 e = 216 f = 162 degree seq :: [ 12^18, 36^6 ] E16.1151 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18}) Quotient :: dipole Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^6, Y2^18 ] Map:: R = (1, 109, 2, 110, 6, 114, 14, 122, 12, 120, 4, 112)(3, 111, 9, 117, 19, 127, 26, 134, 15, 123, 8, 116)(5, 113, 11, 119, 22, 130, 25, 133, 16, 124, 7, 115)(10, 118, 18, 126, 27, 135, 38, 146, 31, 139, 20, 128)(13, 121, 17, 125, 28, 136, 37, 145, 34, 142, 23, 131)(21, 129, 32, 140, 43, 151, 50, 158, 39, 147, 30, 138)(24, 132, 35, 143, 46, 154, 49, 157, 40, 148, 29, 137)(33, 141, 42, 150, 51, 159, 62, 170, 55, 163, 44, 152)(36, 144, 41, 149, 52, 160, 61, 169, 58, 166, 47, 155)(45, 153, 56, 164, 67, 175, 74, 182, 63, 171, 54, 162)(48, 156, 59, 167, 70, 178, 73, 181, 64, 172, 53, 161)(57, 165, 66, 174, 75, 183, 86, 194, 79, 187, 68, 176)(60, 168, 65, 173, 76, 184, 85, 193, 82, 190, 71, 179)(69, 177, 80, 188, 91, 199, 97, 205, 87, 195, 78, 186)(72, 180, 83, 191, 94, 202, 96, 204, 88, 196, 77, 185)(81, 189, 90, 198, 98, 206, 105, 213, 101, 209, 92, 200)(84, 192, 89, 197, 99, 207, 104, 212, 103, 211, 95, 203)(93, 201, 102, 210, 107, 215, 108, 216, 106, 214, 100, 208)(217, 325, 219, 327, 226, 334, 237, 345, 249, 357, 261, 369, 273, 381, 285, 393, 297, 405, 309, 417, 300, 408, 288, 396, 276, 384, 264, 372, 252, 360, 240, 348, 229, 337, 221, 329)(218, 326, 223, 331, 233, 341, 245, 353, 257, 365, 269, 377, 281, 389, 293, 401, 305, 413, 316, 424, 306, 414, 294, 402, 282, 390, 270, 378, 258, 366, 246, 354, 234, 342, 224, 332)(220, 328, 227, 335, 239, 347, 251, 359, 263, 371, 275, 383, 287, 395, 299, 407, 311, 419, 318, 426, 308, 416, 296, 404, 284, 392, 272, 380, 260, 368, 248, 356, 236, 344, 225, 333)(222, 330, 231, 339, 243, 351, 255, 363, 267, 375, 279, 387, 291, 399, 303, 411, 314, 422, 322, 430, 315, 423, 304, 412, 292, 400, 280, 388, 268, 376, 256, 364, 244, 352, 232, 340)(228, 336, 235, 343, 247, 355, 259, 367, 271, 379, 283, 391, 295, 403, 307, 415, 317, 425, 323, 431, 319, 427, 310, 418, 298, 406, 286, 394, 274, 382, 262, 370, 250, 358, 238, 346)(230, 338, 241, 349, 253, 361, 265, 373, 277, 385, 289, 397, 301, 409, 312, 420, 320, 428, 324, 432, 321, 429, 313, 421, 302, 410, 290, 398, 278, 386, 266, 374, 254, 362, 242, 350) L = (1, 219)(2, 223)(3, 226)(4, 227)(5, 217)(6, 231)(7, 233)(8, 218)(9, 220)(10, 237)(11, 239)(12, 235)(13, 221)(14, 241)(15, 243)(16, 222)(17, 245)(18, 224)(19, 247)(20, 225)(21, 249)(22, 228)(23, 251)(24, 229)(25, 253)(26, 230)(27, 255)(28, 232)(29, 257)(30, 234)(31, 259)(32, 236)(33, 261)(34, 238)(35, 263)(36, 240)(37, 265)(38, 242)(39, 267)(40, 244)(41, 269)(42, 246)(43, 271)(44, 248)(45, 273)(46, 250)(47, 275)(48, 252)(49, 277)(50, 254)(51, 279)(52, 256)(53, 281)(54, 258)(55, 283)(56, 260)(57, 285)(58, 262)(59, 287)(60, 264)(61, 289)(62, 266)(63, 291)(64, 268)(65, 293)(66, 270)(67, 295)(68, 272)(69, 297)(70, 274)(71, 299)(72, 276)(73, 301)(74, 278)(75, 303)(76, 280)(77, 305)(78, 282)(79, 307)(80, 284)(81, 309)(82, 286)(83, 311)(84, 288)(85, 312)(86, 290)(87, 314)(88, 292)(89, 316)(90, 294)(91, 317)(92, 296)(93, 300)(94, 298)(95, 318)(96, 320)(97, 302)(98, 322)(99, 304)(100, 306)(101, 323)(102, 308)(103, 310)(104, 324)(105, 313)(106, 315)(107, 319)(108, 321)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432) 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 ) } Outer automorphisms :: reflexible Dual of E16.1153 Graph:: bipartite v = 24 e = 216 f = 162 degree seq :: [ 12^18, 36^6 ] E16.1152 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18}) Quotient :: dipole Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |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^-5 * Y2 * Y3^12 * Y2 * Y3^-1, (Y3^-1 * Y1^-1)^18 ] Map:: polytopal R = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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)(217, 325, 218, 326)(219, 327, 223, 331)(220, 328, 225, 333)(221, 329, 227, 335)(222, 330, 229, 337)(224, 332, 233, 341)(226, 334, 237, 345)(228, 336, 241, 349)(230, 338, 245, 353)(231, 339, 239, 347)(232, 340, 243, 351)(234, 342, 246, 354)(235, 343, 240, 348)(236, 344, 244, 352)(238, 346, 242, 350)(247, 355, 257, 365)(248, 356, 261, 369)(249, 357, 255, 363)(250, 358, 260, 368)(251, 359, 263, 371)(252, 360, 258, 366)(253, 361, 256, 364)(254, 362, 266, 374)(259, 367, 269, 377)(262, 370, 272, 380)(264, 372, 273, 381)(265, 373, 276, 384)(267, 375, 270, 378)(268, 376, 279, 387)(271, 379, 282, 390)(274, 382, 285, 393)(275, 383, 284, 392)(277, 385, 286, 394)(278, 386, 281, 389)(280, 388, 283, 391)(287, 395, 297, 405)(288, 396, 296, 404)(289, 397, 299, 407)(290, 398, 294, 402)(291, 399, 293, 401)(292, 400, 302, 410)(295, 403, 305, 413)(298, 406, 308, 416)(300, 408, 309, 417)(301, 409, 312, 420)(303, 411, 306, 414)(304, 412, 315, 423)(307, 415, 317, 425)(310, 418, 320, 428)(311, 419, 319, 427)(313, 421, 318, 426)(314, 422, 316, 424)(321, 429, 323, 431)(322, 430, 324, 432) L = (1, 219)(2, 221)(3, 224)(4, 217)(5, 228)(6, 218)(7, 231)(8, 234)(9, 235)(10, 220)(11, 239)(12, 242)(13, 243)(14, 222)(15, 247)(16, 223)(17, 249)(18, 251)(19, 252)(20, 225)(21, 253)(22, 226)(23, 255)(24, 227)(25, 257)(26, 259)(27, 260)(28, 229)(29, 261)(30, 230)(31, 237)(32, 232)(33, 236)(34, 233)(35, 265)(36, 266)(37, 267)(38, 238)(39, 245)(40, 240)(41, 244)(42, 241)(43, 271)(44, 272)(45, 273)(46, 246)(47, 248)(48, 250)(49, 277)(50, 278)(51, 279)(52, 254)(53, 256)(54, 258)(55, 283)(56, 284)(57, 285)(58, 262)(59, 263)(60, 264)(61, 289)(62, 290)(63, 291)(64, 268)(65, 269)(66, 270)(67, 295)(68, 296)(69, 297)(70, 274)(71, 275)(72, 276)(73, 301)(74, 302)(75, 303)(76, 280)(77, 281)(78, 282)(79, 307)(80, 308)(81, 309)(82, 286)(83, 287)(84, 288)(85, 313)(86, 314)(87, 315)(88, 292)(89, 293)(90, 294)(91, 318)(92, 319)(93, 320)(94, 298)(95, 299)(96, 300)(97, 304)(98, 322)(99, 321)(100, 305)(101, 306)(102, 310)(103, 324)(104, 323)(105, 311)(106, 312)(107, 316)(108, 317)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432) local type(s) :: { ( 12, 36 ), ( 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E16.1150 Graph:: simple bipartite v = 162 e = 216 f = 24 degree seq :: [ 2^108, 4^54 ] E16.1153 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18}) Quotient :: dipole Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^18 ] Map:: polytopal R = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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)(217, 325, 218, 326)(219, 327, 223, 331)(220, 328, 225, 333)(221, 329, 227, 335)(222, 330, 229, 337)(224, 332, 230, 338)(226, 334, 228, 336)(231, 339, 241, 349)(232, 340, 242, 350)(233, 341, 243, 351)(234, 342, 245, 353)(235, 343, 246, 354)(236, 344, 248, 356)(237, 345, 249, 357)(238, 346, 250, 358)(239, 347, 252, 360)(240, 348, 253, 361)(244, 352, 254, 362)(247, 355, 251, 359)(255, 363, 264, 372)(256, 364, 263, 371)(257, 365, 268, 376)(258, 366, 271, 379)(259, 367, 272, 380)(260, 368, 265, 373)(261, 369, 274, 382)(262, 370, 275, 383)(266, 374, 277, 385)(267, 375, 278, 386)(269, 377, 280, 388)(270, 378, 281, 389)(273, 381, 282, 390)(276, 384, 279, 387)(283, 391, 292, 400)(284, 392, 295, 403)(285, 393, 296, 404)(286, 394, 289, 397)(287, 395, 298, 406)(288, 396, 299, 407)(290, 398, 301, 409)(291, 399, 302, 410)(293, 401, 304, 412)(294, 402, 305, 413)(297, 405, 306, 414)(300, 408, 303, 411)(307, 415, 315, 423)(308, 416, 317, 425)(309, 417, 318, 426)(310, 418, 312, 420)(311, 419, 319, 427)(313, 421, 320, 428)(314, 422, 321, 429)(316, 424, 322, 430)(323, 431, 324, 432) L = (1, 219)(2, 221)(3, 224)(4, 217)(5, 228)(6, 218)(7, 231)(8, 233)(9, 234)(10, 220)(11, 236)(12, 238)(13, 239)(14, 222)(15, 225)(16, 223)(17, 244)(18, 246)(19, 226)(20, 229)(21, 227)(22, 251)(23, 253)(24, 230)(25, 255)(26, 257)(27, 232)(28, 259)(29, 256)(30, 261)(31, 235)(32, 263)(33, 265)(34, 237)(35, 267)(36, 264)(37, 269)(38, 240)(39, 242)(40, 241)(41, 271)(42, 243)(43, 273)(44, 245)(45, 275)(46, 247)(47, 249)(48, 248)(49, 277)(50, 250)(51, 279)(52, 252)(53, 281)(54, 254)(55, 283)(56, 258)(57, 285)(58, 260)(59, 287)(60, 262)(61, 289)(62, 266)(63, 291)(64, 268)(65, 293)(66, 270)(67, 295)(68, 272)(69, 297)(70, 274)(71, 299)(72, 276)(73, 301)(74, 278)(75, 303)(76, 280)(77, 305)(78, 282)(79, 307)(80, 284)(81, 309)(82, 286)(83, 311)(84, 288)(85, 312)(86, 290)(87, 314)(88, 292)(89, 316)(90, 294)(91, 317)(92, 296)(93, 300)(94, 298)(95, 318)(96, 320)(97, 302)(98, 306)(99, 304)(100, 321)(101, 323)(102, 308)(103, 310)(104, 324)(105, 313)(106, 315)(107, 319)(108, 322)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432) local type(s) :: { ( 12, 36 ), ( 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E16.1151 Graph:: simple bipartite v = 162 e = 216 f = 24 degree seq :: [ 2^108, 4^54 ] E16.1154 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18}) Quotient :: dipole Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^-2 * Y1 * Y3, Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1, Y3 * Y1^-3 * Y3^-1 * Y1^-3, (Y3^-1 * Y1^-1)^6, Y1^18 ] Map:: polytopal R = (1, 109, 2, 110, 5, 113, 11, 119, 23, 131, 39, 147, 53, 161, 65, 173, 77, 185, 89, 197, 88, 196, 76, 184, 64, 172, 52, 160, 38, 146, 22, 130, 10, 118, 4, 112)(3, 111, 7, 115, 15, 123, 31, 139, 47, 155, 59, 167, 71, 179, 83, 191, 95, 203, 100, 208, 93, 201, 79, 187, 66, 174, 57, 165, 41, 149, 24, 132, 18, 126, 8, 116)(6, 114, 13, 121, 27, 135, 21, 129, 37, 145, 51, 159, 63, 171, 75, 183, 87, 195, 99, 207, 103, 211, 91, 199, 78, 186, 69, 177, 55, 163, 40, 148, 30, 138, 14, 122)(9, 117, 19, 127, 36, 144, 50, 158, 62, 170, 74, 182, 86, 194, 98, 206, 101, 209, 90, 198, 81, 189, 67, 175, 54, 162, 44, 152, 26, 134, 12, 120, 25, 133, 20, 128)(16, 124, 28, 136, 42, 150, 35, 143, 46, 154, 58, 166, 70, 178, 82, 190, 94, 202, 104, 212, 108, 216, 106, 214, 96, 204, 85, 193, 73, 181, 60, 168, 49, 157, 33, 141)(17, 125, 29, 137, 43, 151, 56, 164, 68, 176, 80, 188, 92, 200, 102, 210, 107, 215, 105, 213, 97, 205, 84, 192, 72, 180, 61, 169, 48, 156, 32, 140, 45, 153, 34, 142)(217, 325)(218, 326)(219, 327)(220, 328)(221, 329)(222, 330)(223, 331)(224, 332)(225, 333)(226, 334)(227, 335)(228, 336)(229, 337)(230, 338)(231, 339)(232, 340)(233, 341)(234, 342)(235, 343)(236, 344)(237, 345)(238, 346)(239, 347)(240, 348)(241, 349)(242, 350)(243, 351)(244, 352)(245, 353)(246, 354)(247, 355)(248, 356)(249, 357)(250, 358)(251, 359)(252, 360)(253, 361)(254, 362)(255, 363)(256, 364)(257, 365)(258, 366)(259, 367)(260, 368)(261, 369)(262, 370)(263, 371)(264, 372)(265, 373)(266, 374)(267, 375)(268, 376)(269, 377)(270, 378)(271, 379)(272, 380)(273, 381)(274, 382)(275, 383)(276, 384)(277, 385)(278, 386)(279, 387)(280, 388)(281, 389)(282, 390)(283, 391)(284, 392)(285, 393)(286, 394)(287, 395)(288, 396)(289, 397)(290, 398)(291, 399)(292, 400)(293, 401)(294, 402)(295, 403)(296, 404)(297, 405)(298, 406)(299, 407)(300, 408)(301, 409)(302, 410)(303, 411)(304, 412)(305, 413)(306, 414)(307, 415)(308, 416)(309, 417)(310, 418)(311, 419)(312, 420)(313, 421)(314, 422)(315, 423)(316, 424)(317, 425)(318, 426)(319, 427)(320, 428)(321, 429)(322, 430)(323, 431)(324, 432) L = (1, 219)(2, 222)(3, 217)(4, 225)(5, 228)(6, 218)(7, 232)(8, 233)(9, 220)(10, 237)(11, 240)(12, 221)(13, 244)(14, 245)(15, 248)(16, 223)(17, 224)(18, 251)(19, 249)(20, 250)(21, 226)(22, 247)(23, 256)(24, 227)(25, 258)(26, 259)(27, 261)(28, 229)(29, 230)(30, 262)(31, 238)(32, 231)(33, 235)(34, 236)(35, 234)(36, 264)(37, 265)(38, 266)(39, 270)(40, 239)(41, 272)(42, 241)(43, 242)(44, 274)(45, 243)(46, 246)(47, 276)(48, 252)(49, 253)(50, 254)(51, 277)(52, 279)(53, 282)(54, 255)(55, 284)(56, 257)(57, 286)(58, 260)(59, 288)(60, 263)(61, 267)(62, 289)(63, 268)(64, 287)(65, 294)(66, 269)(67, 296)(68, 271)(69, 298)(70, 273)(71, 280)(72, 275)(73, 278)(74, 300)(75, 301)(76, 302)(77, 306)(78, 281)(79, 308)(80, 283)(81, 310)(82, 285)(83, 312)(84, 290)(85, 291)(86, 292)(87, 313)(88, 315)(89, 316)(90, 293)(91, 318)(92, 295)(93, 320)(94, 297)(95, 321)(96, 299)(97, 303)(98, 322)(99, 304)(100, 305)(101, 323)(102, 307)(103, 324)(104, 309)(105, 311)(106, 314)(107, 317)(108, 319)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432) 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 ) } Outer automorphisms :: reflexible Dual of E16.1148 Graph:: simple bipartite v = 114 e = 216 f = 72 degree seq :: [ 2^108, 36^6 ] E16.1155 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18}) Quotient :: dipole Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1)^6, Y1^18 ] Map:: polytopal R = (1, 109, 2, 110, 5, 113, 11, 119, 20, 128, 32, 140, 47, 155, 61, 169, 73, 181, 85, 193, 84, 192, 72, 180, 60, 168, 46, 154, 31, 139, 19, 127, 10, 118, 4, 112)(3, 111, 7, 115, 15, 123, 25, 133, 39, 147, 55, 163, 67, 175, 79, 187, 91, 199, 97, 205, 86, 194, 75, 183, 62, 170, 49, 157, 33, 141, 22, 130, 12, 120, 8, 116)(6, 114, 13, 121, 9, 117, 18, 126, 29, 137, 44, 152, 58, 166, 70, 178, 82, 190, 94, 202, 96, 204, 87, 195, 74, 182, 63, 171, 48, 156, 34, 142, 21, 129, 14, 122)(16, 124, 26, 134, 17, 125, 28, 136, 35, 143, 51, 159, 64, 172, 77, 185, 88, 196, 99, 207, 104, 212, 101, 209, 92, 200, 80, 188, 68, 176, 56, 164, 40, 148, 27, 135)(23, 131, 36, 144, 24, 132, 38, 146, 50, 158, 65, 173, 76, 184, 89, 197, 98, 206, 105, 213, 103, 211, 95, 203, 83, 191, 71, 179, 59, 167, 45, 153, 30, 138, 37, 145)(41, 149, 53, 161, 42, 150, 57, 165, 69, 177, 81, 189, 93, 201, 102, 210, 107, 215, 108, 216, 106, 214, 100, 208, 90, 198, 78, 186, 66, 174, 54, 162, 43, 151, 52, 160)(217, 325)(218, 326)(219, 327)(220, 328)(221, 329)(222, 330)(223, 331)(224, 332)(225, 333)(226, 334)(227, 335)(228, 336)(229, 337)(230, 338)(231, 339)(232, 340)(233, 341)(234, 342)(235, 343)(236, 344)(237, 345)(238, 346)(239, 347)(240, 348)(241, 349)(242, 350)(243, 351)(244, 352)(245, 353)(246, 354)(247, 355)(248, 356)(249, 357)(250, 358)(251, 359)(252, 360)(253, 361)(254, 362)(255, 363)(256, 364)(257, 365)(258, 366)(259, 367)(260, 368)(261, 369)(262, 370)(263, 371)(264, 372)(265, 373)(266, 374)(267, 375)(268, 376)(269, 377)(270, 378)(271, 379)(272, 380)(273, 381)(274, 382)(275, 383)(276, 384)(277, 385)(278, 386)(279, 387)(280, 388)(281, 389)(282, 390)(283, 391)(284, 392)(285, 393)(286, 394)(287, 395)(288, 396)(289, 397)(290, 398)(291, 399)(292, 400)(293, 401)(294, 402)(295, 403)(296, 404)(297, 405)(298, 406)(299, 407)(300, 408)(301, 409)(302, 410)(303, 411)(304, 412)(305, 413)(306, 414)(307, 415)(308, 416)(309, 417)(310, 418)(311, 419)(312, 420)(313, 421)(314, 422)(315, 423)(316, 424)(317, 425)(318, 426)(319, 427)(320, 428)(321, 429)(322, 430)(323, 431)(324, 432) L = (1, 219)(2, 222)(3, 217)(4, 225)(5, 228)(6, 218)(7, 232)(8, 233)(9, 220)(10, 231)(11, 237)(12, 221)(13, 239)(14, 240)(15, 226)(16, 223)(17, 224)(18, 246)(19, 245)(20, 249)(21, 227)(22, 251)(23, 229)(24, 230)(25, 256)(26, 257)(27, 258)(28, 259)(29, 235)(30, 234)(31, 255)(32, 264)(33, 236)(34, 266)(35, 238)(36, 268)(37, 269)(38, 270)(39, 247)(40, 241)(41, 242)(42, 243)(43, 244)(44, 275)(45, 273)(46, 274)(47, 278)(48, 248)(49, 280)(50, 250)(51, 282)(52, 252)(53, 253)(54, 254)(55, 284)(56, 285)(57, 261)(58, 262)(59, 260)(60, 283)(61, 290)(62, 263)(63, 292)(64, 265)(65, 294)(66, 267)(67, 276)(68, 271)(69, 272)(70, 299)(71, 297)(72, 298)(73, 302)(74, 277)(75, 304)(76, 279)(77, 306)(78, 281)(79, 308)(80, 309)(81, 287)(82, 288)(83, 286)(84, 307)(85, 312)(86, 289)(87, 314)(88, 291)(89, 316)(90, 293)(91, 300)(92, 295)(93, 296)(94, 319)(95, 318)(96, 301)(97, 320)(98, 303)(99, 322)(100, 305)(101, 323)(102, 311)(103, 310)(104, 313)(105, 324)(106, 315)(107, 317)(108, 321)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432) 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 ) } Outer automorphisms :: reflexible Dual of E16.1149 Graph:: simple bipartite v = 114 e = 216 f = 72 degree seq :: [ 2^108, 36^6 ] E16.1156 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18}) Quotient :: dipole Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1 * Y2^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^6, Y2^18 ] Map:: R = (1, 109, 2, 110)(3, 111, 7, 115)(4, 112, 9, 117)(5, 113, 11, 119)(6, 114, 13, 121)(8, 116, 17, 125)(10, 118, 21, 129)(12, 120, 25, 133)(14, 122, 29, 137)(15, 123, 23, 131)(16, 124, 27, 135)(18, 126, 30, 138)(19, 127, 24, 132)(20, 128, 28, 136)(22, 130, 26, 134)(31, 139, 41, 149)(32, 140, 45, 153)(33, 141, 39, 147)(34, 142, 44, 152)(35, 143, 47, 155)(36, 144, 42, 150)(37, 145, 40, 148)(38, 146, 50, 158)(43, 151, 53, 161)(46, 154, 56, 164)(48, 156, 57, 165)(49, 157, 60, 168)(51, 159, 54, 162)(52, 160, 63, 171)(55, 163, 66, 174)(58, 166, 69, 177)(59, 167, 68, 176)(61, 169, 70, 178)(62, 170, 65, 173)(64, 172, 67, 175)(71, 179, 81, 189)(72, 180, 80, 188)(73, 181, 83, 191)(74, 182, 78, 186)(75, 183, 77, 185)(76, 184, 86, 194)(79, 187, 89, 197)(82, 190, 92, 200)(84, 192, 93, 201)(85, 193, 96, 204)(87, 195, 90, 198)(88, 196, 99, 207)(91, 199, 101, 209)(94, 202, 104, 212)(95, 203, 103, 211)(97, 205, 102, 210)(98, 206, 100, 208)(105, 213, 107, 215)(106, 214, 108, 216)(217, 325, 219, 327, 224, 332, 234, 342, 251, 359, 265, 373, 277, 385, 289, 397, 301, 409, 313, 421, 304, 412, 292, 400, 280, 388, 268, 376, 254, 362, 238, 346, 226, 334, 220, 328)(218, 326, 221, 329, 228, 336, 242, 350, 259, 367, 271, 379, 283, 391, 295, 403, 307, 415, 318, 426, 310, 418, 298, 406, 286, 394, 274, 382, 262, 370, 246, 354, 230, 338, 222, 330)(223, 331, 231, 339, 247, 355, 237, 345, 253, 361, 267, 375, 279, 387, 291, 399, 303, 411, 315, 423, 321, 429, 311, 419, 299, 407, 287, 395, 275, 383, 263, 371, 248, 356, 232, 340)(225, 333, 235, 343, 252, 360, 266, 374, 278, 386, 290, 398, 302, 410, 314, 422, 322, 430, 312, 420, 300, 408, 288, 396, 276, 384, 264, 372, 250, 358, 233, 341, 249, 357, 236, 344)(227, 335, 239, 347, 255, 363, 245, 353, 261, 369, 273, 381, 285, 393, 297, 405, 309, 417, 320, 428, 323, 431, 316, 424, 305, 413, 293, 401, 281, 389, 269, 377, 256, 364, 240, 348)(229, 337, 243, 351, 260, 368, 272, 380, 284, 392, 296, 404, 308, 416, 319, 427, 324, 432, 317, 425, 306, 414, 294, 402, 282, 390, 270, 378, 258, 366, 241, 349, 257, 365, 244, 352) L = (1, 218)(2, 217)(3, 223)(4, 225)(5, 227)(6, 229)(7, 219)(8, 233)(9, 220)(10, 237)(11, 221)(12, 241)(13, 222)(14, 245)(15, 239)(16, 243)(17, 224)(18, 246)(19, 240)(20, 244)(21, 226)(22, 242)(23, 231)(24, 235)(25, 228)(26, 238)(27, 232)(28, 236)(29, 230)(30, 234)(31, 257)(32, 261)(33, 255)(34, 260)(35, 263)(36, 258)(37, 256)(38, 266)(39, 249)(40, 253)(41, 247)(42, 252)(43, 269)(44, 250)(45, 248)(46, 272)(47, 251)(48, 273)(49, 276)(50, 254)(51, 270)(52, 279)(53, 259)(54, 267)(55, 282)(56, 262)(57, 264)(58, 285)(59, 284)(60, 265)(61, 286)(62, 281)(63, 268)(64, 283)(65, 278)(66, 271)(67, 280)(68, 275)(69, 274)(70, 277)(71, 297)(72, 296)(73, 299)(74, 294)(75, 293)(76, 302)(77, 291)(78, 290)(79, 305)(80, 288)(81, 287)(82, 308)(83, 289)(84, 309)(85, 312)(86, 292)(87, 306)(88, 315)(89, 295)(90, 303)(91, 317)(92, 298)(93, 300)(94, 320)(95, 319)(96, 301)(97, 318)(98, 316)(99, 304)(100, 314)(101, 307)(102, 313)(103, 311)(104, 310)(105, 323)(106, 324)(107, 321)(108, 322)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E16.1158 Graph:: bipartite v = 60 e = 216 f = 126 degree seq :: [ 4^54, 36^6 ] E16.1157 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18}) Quotient :: dipole Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^6, Y2^18 ] Map:: R = (1, 109, 2, 110)(3, 111, 7, 115)(4, 112, 9, 117)(5, 113, 11, 119)(6, 114, 13, 121)(8, 116, 14, 122)(10, 118, 12, 120)(15, 123, 25, 133)(16, 124, 26, 134)(17, 125, 27, 135)(18, 126, 29, 137)(19, 127, 30, 138)(20, 128, 32, 140)(21, 129, 33, 141)(22, 130, 34, 142)(23, 131, 36, 144)(24, 132, 37, 145)(28, 136, 38, 146)(31, 139, 35, 143)(39, 147, 48, 156)(40, 148, 47, 155)(41, 149, 52, 160)(42, 150, 55, 163)(43, 151, 56, 164)(44, 152, 49, 157)(45, 153, 58, 166)(46, 154, 59, 167)(50, 158, 61, 169)(51, 159, 62, 170)(53, 161, 64, 172)(54, 162, 65, 173)(57, 165, 66, 174)(60, 168, 63, 171)(67, 175, 76, 184)(68, 176, 79, 187)(69, 177, 80, 188)(70, 178, 73, 181)(71, 179, 82, 190)(72, 180, 83, 191)(74, 182, 85, 193)(75, 183, 86, 194)(77, 185, 88, 196)(78, 186, 89, 197)(81, 189, 90, 198)(84, 192, 87, 195)(91, 199, 99, 207)(92, 200, 101, 209)(93, 201, 102, 210)(94, 202, 96, 204)(95, 203, 103, 211)(97, 205, 104, 212)(98, 206, 105, 213)(100, 208, 106, 214)(107, 215, 108, 216)(217, 325, 219, 327, 224, 332, 233, 341, 244, 352, 259, 367, 273, 381, 285, 393, 297, 405, 309, 417, 300, 408, 288, 396, 276, 384, 262, 370, 247, 355, 235, 343, 226, 334, 220, 328)(218, 326, 221, 329, 228, 336, 238, 346, 251, 359, 267, 375, 279, 387, 291, 399, 303, 411, 314, 422, 306, 414, 294, 402, 282, 390, 270, 378, 254, 362, 240, 348, 230, 338, 222, 330)(223, 331, 231, 339, 225, 333, 234, 342, 246, 354, 261, 369, 275, 383, 287, 395, 299, 407, 311, 419, 318, 426, 308, 416, 296, 404, 284, 392, 272, 380, 258, 366, 243, 351, 232, 340)(227, 335, 236, 344, 229, 337, 239, 347, 253, 361, 269, 377, 281, 389, 293, 401, 305, 413, 316, 424, 321, 429, 313, 421, 302, 410, 290, 398, 278, 386, 266, 374, 250, 358, 237, 345)(241, 349, 255, 363, 242, 350, 257, 365, 271, 379, 283, 391, 295, 403, 307, 415, 317, 425, 323, 431, 319, 427, 310, 418, 298, 406, 286, 394, 274, 382, 260, 368, 245, 353, 256, 364)(248, 356, 263, 371, 249, 357, 265, 373, 277, 385, 289, 397, 301, 409, 312, 420, 320, 428, 324, 432, 322, 430, 315, 423, 304, 412, 292, 400, 280, 388, 268, 376, 252, 360, 264, 372) L = (1, 218)(2, 217)(3, 223)(4, 225)(5, 227)(6, 229)(7, 219)(8, 230)(9, 220)(10, 228)(11, 221)(12, 226)(13, 222)(14, 224)(15, 241)(16, 242)(17, 243)(18, 245)(19, 246)(20, 248)(21, 249)(22, 250)(23, 252)(24, 253)(25, 231)(26, 232)(27, 233)(28, 254)(29, 234)(30, 235)(31, 251)(32, 236)(33, 237)(34, 238)(35, 247)(36, 239)(37, 240)(38, 244)(39, 264)(40, 263)(41, 268)(42, 271)(43, 272)(44, 265)(45, 274)(46, 275)(47, 256)(48, 255)(49, 260)(50, 277)(51, 278)(52, 257)(53, 280)(54, 281)(55, 258)(56, 259)(57, 282)(58, 261)(59, 262)(60, 279)(61, 266)(62, 267)(63, 276)(64, 269)(65, 270)(66, 273)(67, 292)(68, 295)(69, 296)(70, 289)(71, 298)(72, 299)(73, 286)(74, 301)(75, 302)(76, 283)(77, 304)(78, 305)(79, 284)(80, 285)(81, 306)(82, 287)(83, 288)(84, 303)(85, 290)(86, 291)(87, 300)(88, 293)(89, 294)(90, 297)(91, 315)(92, 317)(93, 318)(94, 312)(95, 319)(96, 310)(97, 320)(98, 321)(99, 307)(100, 322)(101, 308)(102, 309)(103, 311)(104, 313)(105, 314)(106, 316)(107, 324)(108, 323)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E16.1159 Graph:: bipartite v = 60 e = 216 f = 126 degree seq :: [ 4^54, 36^6 ] E16.1158 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18}) Quotient :: dipole Aut^+ = C6 x D18 (small group id <108, 23>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-2, Y3 * Y1^-1 * Y3 * Y1^3, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y1)^2, (Y3 * Y2^-1)^18 ] Map:: polytopal R = (1, 109, 2, 110, 6, 114, 16, 124, 13, 121, 4, 112)(3, 111, 9, 117, 17, 125, 8, 116, 21, 129, 11, 119)(5, 113, 14, 122, 18, 126, 12, 120, 20, 128, 7, 115)(10, 118, 24, 132, 29, 137, 23, 131, 33, 141, 22, 130)(15, 123, 26, 134, 30, 138, 19, 127, 31, 139, 27, 135)(25, 133, 34, 142, 41, 149, 36, 144, 45, 153, 35, 143)(28, 136, 32, 140, 42, 150, 39, 147, 43, 151, 38, 146)(37, 145, 47, 155, 53, 161, 46, 154, 57, 165, 48, 156)(40, 148, 51, 159, 54, 162, 50, 158, 55, 163, 44, 152)(49, 157, 60, 168, 65, 173, 59, 167, 69, 177, 58, 166)(52, 160, 62, 170, 66, 174, 56, 164, 67, 175, 63, 171)(61, 169, 70, 178, 77, 185, 72, 180, 81, 189, 71, 179)(64, 172, 68, 176, 78, 186, 75, 183, 79, 187, 74, 182)(73, 181, 83, 191, 89, 197, 82, 190, 93, 201, 84, 192)(76, 184, 87, 195, 90, 198, 86, 194, 91, 199, 80, 188)(85, 193, 96, 204, 100, 208, 95, 203, 104, 212, 94, 202)(88, 196, 98, 206, 101, 209, 92, 200, 102, 210, 99, 207)(97, 205, 103, 211, 107, 215, 106, 214, 108, 216, 105, 213)(217, 325)(218, 326)(219, 327)(220, 328)(221, 329)(222, 330)(223, 331)(224, 332)(225, 333)(226, 334)(227, 335)(228, 336)(229, 337)(230, 338)(231, 339)(232, 340)(233, 341)(234, 342)(235, 343)(236, 344)(237, 345)(238, 346)(239, 347)(240, 348)(241, 349)(242, 350)(243, 351)(244, 352)(245, 353)(246, 354)(247, 355)(248, 356)(249, 357)(250, 358)(251, 359)(252, 360)(253, 361)(254, 362)(255, 363)(256, 364)(257, 365)(258, 366)(259, 367)(260, 368)(261, 369)(262, 370)(263, 371)(264, 372)(265, 373)(266, 374)(267, 375)(268, 376)(269, 377)(270, 378)(271, 379)(272, 380)(273, 381)(274, 382)(275, 383)(276, 384)(277, 385)(278, 386)(279, 387)(280, 388)(281, 389)(282, 390)(283, 391)(284, 392)(285, 393)(286, 394)(287, 395)(288, 396)(289, 397)(290, 398)(291, 399)(292, 400)(293, 401)(294, 402)(295, 403)(296, 404)(297, 405)(298, 406)(299, 407)(300, 408)(301, 409)(302, 410)(303, 411)(304, 412)(305, 413)(306, 414)(307, 415)(308, 416)(309, 417)(310, 418)(311, 419)(312, 420)(313, 421)(314, 422)(315, 423)(316, 424)(317, 425)(318, 426)(319, 427)(320, 428)(321, 429)(322, 430)(323, 431)(324, 432) L = (1, 219)(2, 223)(3, 226)(4, 228)(5, 217)(6, 233)(7, 235)(8, 218)(9, 220)(10, 241)(11, 232)(12, 242)(13, 237)(14, 243)(15, 221)(16, 230)(17, 245)(18, 222)(19, 248)(20, 229)(21, 249)(22, 224)(23, 225)(24, 227)(25, 253)(26, 254)(27, 255)(28, 231)(29, 257)(30, 234)(31, 236)(32, 260)(33, 261)(34, 238)(35, 239)(36, 240)(37, 265)(38, 266)(39, 267)(40, 244)(41, 269)(42, 246)(43, 247)(44, 272)(45, 273)(46, 250)(47, 251)(48, 252)(49, 277)(50, 278)(51, 279)(52, 256)(53, 281)(54, 258)(55, 259)(56, 284)(57, 285)(58, 262)(59, 263)(60, 264)(61, 289)(62, 290)(63, 291)(64, 268)(65, 293)(66, 270)(67, 271)(68, 296)(69, 297)(70, 274)(71, 275)(72, 276)(73, 301)(74, 302)(75, 303)(76, 280)(77, 305)(78, 282)(79, 283)(80, 308)(81, 309)(82, 286)(83, 287)(84, 288)(85, 313)(86, 314)(87, 315)(88, 292)(89, 316)(90, 294)(91, 295)(92, 319)(93, 320)(94, 298)(95, 299)(96, 300)(97, 304)(98, 321)(99, 322)(100, 323)(101, 306)(102, 307)(103, 310)(104, 324)(105, 311)(106, 312)(107, 317)(108, 318)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432) local type(s) :: { ( 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E16.1156 Graph:: simple bipartite v = 126 e = 216 f = 60 degree seq :: [ 2^108, 12^18 ] E16.1159 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18}) Quotient :: dipole Aut^+ = S3 x D18 (small group id <108, 16>) Aut = C2 x S3 x D18 (small group id <216, 101>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^6, (Y3 * Y2^-1)^18 ] Map:: polytopal R = (1, 109, 2, 110, 6, 114, 14, 122, 12, 120, 4, 112)(3, 111, 9, 117, 19, 127, 26, 134, 15, 123, 8, 116)(5, 113, 11, 119, 22, 130, 25, 133, 16, 124, 7, 115)(10, 118, 18, 126, 27, 135, 38, 146, 31, 139, 20, 128)(13, 121, 17, 125, 28, 136, 37, 145, 34, 142, 23, 131)(21, 129, 32, 140, 43, 151, 50, 158, 39, 147, 30, 138)(24, 132, 35, 143, 46, 154, 49, 157, 40, 148, 29, 137)(33, 141, 42, 150, 51, 159, 62, 170, 55, 163, 44, 152)(36, 144, 41, 149, 52, 160, 61, 169, 58, 166, 47, 155)(45, 153, 56, 164, 67, 175, 74, 182, 63, 171, 54, 162)(48, 156, 59, 167, 70, 178, 73, 181, 64, 172, 53, 161)(57, 165, 66, 174, 75, 183, 86, 194, 79, 187, 68, 176)(60, 168, 65, 173, 76, 184, 85, 193, 82, 190, 71, 179)(69, 177, 80, 188, 91, 199, 97, 205, 87, 195, 78, 186)(72, 180, 83, 191, 94, 202, 96, 204, 88, 196, 77, 185)(81, 189, 90, 198, 98, 206, 105, 213, 101, 209, 92, 200)(84, 192, 89, 197, 99, 207, 104, 212, 103, 211, 95, 203)(93, 201, 102, 210, 107, 215, 108, 216, 106, 214, 100, 208)(217, 325)(218, 326)(219, 327)(220, 328)(221, 329)(222, 330)(223, 331)(224, 332)(225, 333)(226, 334)(227, 335)(228, 336)(229, 337)(230, 338)(231, 339)(232, 340)(233, 341)(234, 342)(235, 343)(236, 344)(237, 345)(238, 346)(239, 347)(240, 348)(241, 349)(242, 350)(243, 351)(244, 352)(245, 353)(246, 354)(247, 355)(248, 356)(249, 357)(250, 358)(251, 359)(252, 360)(253, 361)(254, 362)(255, 363)(256, 364)(257, 365)(258, 366)(259, 367)(260, 368)(261, 369)(262, 370)(263, 371)(264, 372)(265, 373)(266, 374)(267, 375)(268, 376)(269, 377)(270, 378)(271, 379)(272, 380)(273, 381)(274, 382)(275, 383)(276, 384)(277, 385)(278, 386)(279, 387)(280, 388)(281, 389)(282, 390)(283, 391)(284, 392)(285, 393)(286, 394)(287, 395)(288, 396)(289, 397)(290, 398)(291, 399)(292, 400)(293, 401)(294, 402)(295, 403)(296, 404)(297, 405)(298, 406)(299, 407)(300, 408)(301, 409)(302, 410)(303, 411)(304, 412)(305, 413)(306, 414)(307, 415)(308, 416)(309, 417)(310, 418)(311, 419)(312, 420)(313, 421)(314, 422)(315, 423)(316, 424)(317, 425)(318, 426)(319, 427)(320, 428)(321, 429)(322, 430)(323, 431)(324, 432) L = (1, 219)(2, 223)(3, 226)(4, 227)(5, 217)(6, 231)(7, 233)(8, 218)(9, 220)(10, 237)(11, 239)(12, 235)(13, 221)(14, 241)(15, 243)(16, 222)(17, 245)(18, 224)(19, 247)(20, 225)(21, 249)(22, 228)(23, 251)(24, 229)(25, 253)(26, 230)(27, 255)(28, 232)(29, 257)(30, 234)(31, 259)(32, 236)(33, 261)(34, 238)(35, 263)(36, 240)(37, 265)(38, 242)(39, 267)(40, 244)(41, 269)(42, 246)(43, 271)(44, 248)(45, 273)(46, 250)(47, 275)(48, 252)(49, 277)(50, 254)(51, 279)(52, 256)(53, 281)(54, 258)(55, 283)(56, 260)(57, 285)(58, 262)(59, 287)(60, 264)(61, 289)(62, 266)(63, 291)(64, 268)(65, 293)(66, 270)(67, 295)(68, 272)(69, 297)(70, 274)(71, 299)(72, 276)(73, 301)(74, 278)(75, 303)(76, 280)(77, 305)(78, 282)(79, 307)(80, 284)(81, 309)(82, 286)(83, 311)(84, 288)(85, 312)(86, 290)(87, 314)(88, 292)(89, 316)(90, 294)(91, 317)(92, 296)(93, 300)(94, 298)(95, 318)(96, 320)(97, 302)(98, 322)(99, 304)(100, 306)(101, 323)(102, 308)(103, 310)(104, 324)(105, 313)(106, 315)(107, 319)(108, 321)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432) local type(s) :: { ( 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E16.1157 Graph:: simple bipartite v = 126 e = 216 f = 60 degree seq :: [ 2^108, 12^18 ] E16.1160 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 6, 18}) Quotient :: halfedge Aut^+ = C2 x ((C9 : C3) : C2) (small group id <108, 26>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 1 Presentation :: [ X2^2, (X1^-1 * X2 * X1^-2)^2, X2 * X1^-1 * X2 * X1 * X2 * X1^-2 * X2 * X1^2, (X1^-1 * X2)^6, X1^18 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 43, 70, 94, 105, 108, 107, 104, 93, 69, 42, 22, 10, 4)(3, 7, 15, 31, 55, 85, 102, 82, 101, 106, 96, 84, 95, 74, 45, 24, 18, 8)(6, 13, 27, 21, 41, 61, 91, 97, 86, 103, 92, 98, 88, 58, 72, 44, 30, 14)(9, 19, 38, 64, 87, 99, 90, 59, 89, 100, 81, 62, 71, 48, 26, 12, 25, 20)(16, 33, 57, 37, 63, 39, 65, 76, 46, 75, 68, 78, 51, 28, 50, 80, 54, 34)(17, 35, 60, 73, 49, 79, 53, 29, 52, 83, 67, 40, 66, 77, 47, 32, 56, 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, 44)(25, 46)(26, 47)(27, 49)(30, 54)(33, 58)(34, 59)(35, 61)(36, 62)(38, 52)(41, 68)(42, 64)(43, 71)(45, 73)(48, 78)(50, 81)(51, 82)(53, 84)(55, 80)(56, 86)(57, 87)(60, 89)(63, 92)(65, 74)(66, 85)(67, 72)(69, 91)(70, 95)(75, 96)(76, 97)(77, 98)(79, 99)(83, 101)(88, 94)(90, 104)(93, 102)(100, 105)(103, 107)(106, 108) local type(s) :: { ( 6^18 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 6 e = 54 f = 18 degree seq :: [ 18^6 ] E16.1161 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 6, 18}) Quotient :: halfedge Aut^+ = C2 x ((C9 : C3) : C2) (small group id <108, 26>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 1 Presentation :: [ X2^2, X1^6, (X2 * X1^-1 * X2 * X1^-2)^2, X1^-1 * X2 * X1^-2 * X2 * X1 * X2 * X1^-2 * X2 * X1^-2, X2 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1 * X2 * X1 * X2 * X1^-1, X1^3 * X2 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 29, 18, 8)(6, 13, 25, 48, 28, 14)(9, 19, 36, 66, 39, 20)(12, 23, 44, 78, 47, 24)(16, 31, 58, 94, 61, 32)(17, 33, 62, 80, 45, 34)(21, 40, 71, 97, 73, 41)(22, 42, 74, 100, 77, 43)(26, 50, 38, 70, 88, 51)(27, 52, 89, 101, 75, 53)(30, 56, 79, 54, 92, 57)(35, 65, 83, 67, 85, 49)(37, 68, 76, 102, 84, 69)(46, 81, 55, 93, 72, 82)(59, 95, 64, 99, 105, 87)(60, 96, 103, 86, 106, 91)(63, 90, 104, 108, 107, 98) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 30)(18, 35)(19, 37)(20, 38)(23, 45)(24, 46)(25, 49)(28, 54)(29, 55)(31, 59)(32, 60)(33, 63)(34, 64)(36, 67)(39, 56)(40, 72)(41, 58)(42, 75)(43, 76)(44, 79)(47, 83)(48, 84)(50, 86)(51, 87)(52, 90)(53, 91)(57, 77)(61, 78)(62, 97)(65, 74)(66, 89)(68, 96)(69, 99)(70, 98)(71, 92)(73, 85)(80, 103)(81, 104)(82, 105)(88, 100)(93, 106)(94, 107)(95, 101)(102, 108) local type(s) :: { ( 18^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 18 e = 54 f = 6 degree seq :: [ 6^18 ] E16.1162 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 6, 18}) Quotient :: edge Aut^+ = C2 x ((C9 : C3) : C2) (small group id <108, 26>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 1 Presentation :: [ X1^2, X2^6, (X1 * X2 * X1 * X2^2)^2, X2^-1 * X1 * X2 * X1 * X2^-2 * X1 * X2^3 * X1 * X2^-1, X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1 * X2^-1 * X1, X1 * X2^2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-2 ] Map:: polytopal R = (1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 21)(12, 24)(14, 28)(15, 29)(16, 31)(18, 35)(19, 36)(20, 38)(22, 42)(23, 44)(25, 48)(26, 49)(27, 51)(30, 54)(32, 60)(33, 52)(34, 62)(37, 68)(39, 46)(40, 71)(41, 43)(45, 79)(47, 81)(50, 87)(53, 90)(55, 93)(56, 75)(57, 95)(58, 85)(59, 78)(61, 80)(63, 91)(64, 97)(65, 99)(66, 77)(67, 89)(69, 96)(70, 86)(72, 82)(73, 92)(74, 100)(76, 102)(83, 104)(84, 106)(88, 103)(94, 105)(98, 101)(107, 108)(109, 111, 116, 126, 118, 112)(110, 113, 120, 133, 122, 114)(115, 123, 138, 165, 140, 124)(117, 127, 145, 177, 147, 128)(119, 130, 151, 184, 153, 131)(121, 134, 158, 196, 160, 135)(125, 141, 169, 187, 171, 142)(129, 148, 180, 195, 181, 149)(132, 154, 188, 168, 190, 155)(136, 161, 199, 176, 200, 162)(137, 163, 146, 178, 202, 164)(139, 166, 204, 208, 205, 167)(143, 172, 198, 213, 189, 173)(144, 174, 207, 215, 203, 175)(150, 182, 159, 197, 209, 183)(152, 185, 211, 201, 212, 186)(156, 191, 179, 206, 170, 192)(157, 193, 214, 216, 210, 194) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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) :: { ( 36, 36 ), ( 36^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 72 e = 108 f = 6 degree seq :: [ 2^54, 6^18 ] E16.1163 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 6, 18}) Quotient :: edge Aut^+ = C2 x ((C9 : C3) : C2) (small group id <108, 26>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 1 Presentation :: [ (X2 * X1)^2, (X1^-1 * X2^2)^2, X1^6, X2 * X1^-1 * X2^-1 * X1^-2 * X2^2 * X1^-1, X1^-1 * X2^-1 * X1 * X2^2 * X1^-1 * X2^-3 * X1^-1, X1^-1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1^-2 * X2 * X1^-1, X2^18 ] Map:: polytopal non-degenerate R = (1, 2, 6, 16, 13, 4)(3, 9, 23, 49, 28, 11)(5, 14, 33, 45, 20, 7)(8, 21, 46, 77, 39, 17)(10, 25, 54, 89, 47, 22)(12, 29, 60, 96, 64, 31)(15, 30, 62, 98, 68, 34)(18, 40, 78, 102, 71, 36)(19, 42, 81, 56, 79, 41)(24, 52, 92, 106, 87, 50)(26, 48, 75, 67, 93, 53)(27, 57, 76, 105, 97, 58)(32, 37, 72, 103, 95, 65)(35, 43, 80, 100, 88, 63)(38, 74, 59, 83, 69, 73)(44, 84, 101, 91, 51, 85)(55, 82, 104, 108, 107, 94)(61, 70, 99, 86, 66, 90)(109, 111, 118, 134, 164, 204, 213, 185, 214, 216, 207, 179, 209, 180, 177, 143, 123, 113)(110, 115, 127, 151, 191, 157, 199, 210, 206, 215, 200, 173, 205, 168, 198, 156, 130, 116)(112, 120, 138, 171, 197, 211, 192, 153, 194, 212, 182, 147, 184, 148, 187, 161, 132, 117)(114, 125, 146, 183, 174, 141, 166, 203, 162, 202, 170, 139, 159, 131, 158, 188, 149, 126)(119, 135, 122, 142, 175, 181, 145, 124, 144, 178, 208, 195, 154, 193, 172, 189, 163, 133)(121, 140, 160, 201, 176, 186, 165, 136, 167, 190, 150, 128, 152, 129, 155, 196, 169, 137) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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) :: { ( 4^6 ), ( 4^18 ) } Outer automorphisms :: chiral Dual of E16.1165 Transitivity :: ET+ Graph:: simple bipartite v = 24 e = 108 f = 54 degree seq :: [ 6^18, 18^6 ] E16.1164 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 6, 18}) Quotient :: edge Aut^+ = C2 x ((C9 : C3) : C2) (small group id <108, 26>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 1 Presentation :: [ X2^2, (X1^-1 * X2 * X1^-2)^2, X2 * X1^-1 * X2 * X1 * X2 * X1^-2 * X2 * X1^2, (X2 * X1^-1)^6, X1^18 ] Map:: polytopal R = (1, 2, 5, 11, 23, 43, 70, 94, 105, 108, 107, 104, 93, 69, 42, 22, 10, 4)(3, 7, 15, 31, 55, 85, 102, 82, 101, 106, 96, 84, 95, 74, 45, 24, 18, 8)(6, 13, 27, 21, 41, 61, 91, 97, 86, 103, 92, 98, 88, 58, 72, 44, 30, 14)(9, 19, 38, 64, 87, 99, 90, 59, 89, 100, 81, 62, 71, 48, 26, 12, 25, 20)(16, 33, 57, 37, 63, 39, 65, 76, 46, 75, 68, 78, 51, 28, 50, 80, 54, 34)(17, 35, 60, 73, 49, 79, 53, 29, 52, 83, 67, 40, 66, 77, 47, 32, 56, 36)(109, 111)(110, 114)(112, 117)(113, 120)(115, 124)(116, 125)(118, 129)(119, 132)(121, 136)(122, 137)(123, 140)(126, 145)(127, 147)(128, 148)(130, 139)(131, 152)(133, 154)(134, 155)(135, 157)(138, 162)(141, 166)(142, 167)(143, 169)(144, 170)(146, 160)(149, 176)(150, 172)(151, 179)(153, 181)(156, 186)(158, 189)(159, 190)(161, 192)(163, 188)(164, 194)(165, 195)(168, 197)(171, 200)(173, 182)(174, 193)(175, 180)(177, 199)(178, 203)(183, 204)(184, 205)(185, 206)(187, 207)(191, 209)(196, 202)(198, 212)(201, 210)(208, 213)(211, 215)(214, 216) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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, 12 ), ( 12^18 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 108 f = 18 degree seq :: [ 2^54, 18^6 ] E16.1165 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 6, 18}) Quotient :: loop Aut^+ = C2 x ((C9 : C3) : C2) (small group id <108, 26>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 1 Presentation :: [ X1^2, X2^6, (X1 * X2 * X1 * X2^2)^2, X2^-1 * X1 * X2 * X1 * X2^-2 * X1 * X2^3 * X1 * X2^-1, X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1 * X2^-1 * X1, X1 * X2^2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-2 ] Map:: polytopal non-degenerate R = (1, 109, 2, 110)(3, 111, 7, 115)(4, 112, 9, 117)(5, 113, 11, 119)(6, 114, 13, 121)(8, 116, 17, 125)(10, 118, 21, 129)(12, 120, 24, 132)(14, 122, 28, 136)(15, 123, 29, 137)(16, 124, 31, 139)(18, 126, 35, 143)(19, 127, 36, 144)(20, 128, 38, 146)(22, 130, 42, 150)(23, 131, 44, 152)(25, 133, 48, 156)(26, 134, 49, 157)(27, 135, 51, 159)(30, 138, 54, 162)(32, 140, 60, 168)(33, 141, 52, 160)(34, 142, 62, 170)(37, 145, 68, 176)(39, 147, 46, 154)(40, 148, 71, 179)(41, 149, 43, 151)(45, 153, 79, 187)(47, 155, 81, 189)(50, 158, 87, 195)(53, 161, 90, 198)(55, 163, 93, 201)(56, 164, 75, 183)(57, 165, 95, 203)(58, 166, 85, 193)(59, 167, 78, 186)(61, 169, 80, 188)(63, 171, 91, 199)(64, 172, 97, 205)(65, 173, 99, 207)(66, 174, 77, 185)(67, 175, 89, 197)(69, 177, 96, 204)(70, 178, 86, 194)(72, 180, 82, 190)(73, 181, 92, 200)(74, 182, 100, 208)(76, 184, 102, 210)(83, 191, 104, 212)(84, 192, 106, 214)(88, 196, 103, 211)(94, 202, 105, 213)(98, 206, 101, 209)(107, 215, 108, 216) L = (1, 111)(2, 113)(3, 116)(4, 109)(5, 120)(6, 110)(7, 123)(8, 126)(9, 127)(10, 112)(11, 130)(12, 133)(13, 134)(14, 114)(15, 138)(16, 115)(17, 141)(18, 118)(19, 145)(20, 117)(21, 148)(22, 151)(23, 119)(24, 154)(25, 122)(26, 158)(27, 121)(28, 161)(29, 163)(30, 165)(31, 166)(32, 124)(33, 169)(34, 125)(35, 172)(36, 174)(37, 177)(38, 178)(39, 128)(40, 180)(41, 129)(42, 182)(43, 184)(44, 185)(45, 131)(46, 188)(47, 132)(48, 191)(49, 193)(50, 196)(51, 197)(52, 135)(53, 199)(54, 136)(55, 146)(56, 137)(57, 140)(58, 204)(59, 139)(60, 190)(61, 187)(62, 192)(63, 142)(64, 198)(65, 143)(66, 207)(67, 144)(68, 200)(69, 147)(70, 202)(71, 206)(72, 195)(73, 149)(74, 159)(75, 150)(76, 153)(77, 211)(78, 152)(79, 171)(80, 168)(81, 173)(82, 155)(83, 179)(84, 156)(85, 214)(86, 157)(87, 181)(88, 160)(89, 209)(90, 213)(91, 176)(92, 162)(93, 212)(94, 164)(95, 175)(96, 208)(97, 167)(98, 170)(99, 215)(100, 205)(101, 183)(102, 194)(103, 201)(104, 186)(105, 189)(106, 216)(107, 203)(108, 210) local type(s) :: { ( 6, 18, 6, 18 ) } Outer automorphisms :: chiral Dual of E16.1163 Transitivity :: ET+ VT+ Graph:: simple bipartite v = 54 e = 108 f = 24 degree seq :: [ 4^54 ] E16.1166 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 6, 18}) Quotient :: loop Aut^+ = C2 x ((C9 : C3) : C2) (small group id <108, 26>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 1 Presentation :: [ (X2 * X1)^2, (X1^-1 * X2^2)^2, X1^6, X2 * X1^-1 * X2^-1 * X1^-2 * X2^2 * X1^-1, X1^-1 * X2^-1 * X1 * X2^2 * X1^-1 * X2^-3 * X1^-1, X1^-1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1^-2 * X2 * X1^-1, X2^18 ] Map:: R = (1, 109, 2, 110, 6, 114, 16, 124, 13, 121, 4, 112)(3, 111, 9, 117, 23, 131, 49, 157, 28, 136, 11, 119)(5, 113, 14, 122, 33, 141, 45, 153, 20, 128, 7, 115)(8, 116, 21, 129, 46, 154, 77, 185, 39, 147, 17, 125)(10, 118, 25, 133, 54, 162, 89, 197, 47, 155, 22, 130)(12, 120, 29, 137, 60, 168, 96, 204, 64, 172, 31, 139)(15, 123, 30, 138, 62, 170, 98, 206, 68, 176, 34, 142)(18, 126, 40, 148, 78, 186, 102, 210, 71, 179, 36, 144)(19, 127, 42, 150, 81, 189, 56, 164, 79, 187, 41, 149)(24, 132, 52, 160, 92, 200, 106, 214, 87, 195, 50, 158)(26, 134, 48, 156, 75, 183, 67, 175, 93, 201, 53, 161)(27, 135, 57, 165, 76, 184, 105, 213, 97, 205, 58, 166)(32, 140, 37, 145, 72, 180, 103, 211, 95, 203, 65, 173)(35, 143, 43, 151, 80, 188, 100, 208, 88, 196, 63, 171)(38, 146, 74, 182, 59, 167, 83, 191, 69, 177, 73, 181)(44, 152, 84, 192, 101, 209, 91, 199, 51, 159, 85, 193)(55, 163, 82, 190, 104, 212, 108, 216, 107, 215, 94, 202)(61, 169, 70, 178, 99, 207, 86, 194, 66, 174, 90, 198) L = (1, 111)(2, 115)(3, 118)(4, 120)(5, 109)(6, 125)(7, 127)(8, 110)(9, 112)(10, 134)(11, 135)(12, 138)(13, 140)(14, 142)(15, 113)(16, 144)(17, 146)(18, 114)(19, 151)(20, 152)(21, 155)(22, 116)(23, 158)(24, 117)(25, 119)(26, 164)(27, 122)(28, 167)(29, 121)(30, 171)(31, 159)(32, 160)(33, 166)(34, 175)(35, 123)(36, 178)(37, 124)(38, 183)(39, 184)(40, 187)(41, 126)(42, 128)(43, 191)(44, 129)(45, 194)(46, 193)(47, 196)(48, 130)(49, 199)(50, 188)(51, 131)(52, 201)(53, 132)(54, 202)(55, 133)(56, 204)(57, 136)(58, 203)(59, 190)(60, 198)(61, 137)(62, 139)(63, 197)(64, 189)(65, 205)(66, 141)(67, 181)(68, 186)(69, 143)(70, 208)(71, 209)(72, 177)(73, 145)(74, 147)(75, 174)(76, 148)(77, 214)(78, 165)(79, 161)(80, 149)(81, 163)(82, 150)(83, 157)(84, 153)(85, 172)(86, 212)(87, 154)(88, 169)(89, 211)(90, 156)(91, 210)(92, 173)(93, 176)(94, 170)(95, 162)(96, 213)(97, 168)(98, 215)(99, 179)(100, 195)(101, 180)(102, 206)(103, 192)(104, 182)(105, 185)(106, 216)(107, 200)(108, 207) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: bipartite v = 18 e = 108 f = 60 degree seq :: [ 12^18 ] E16.1167 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 6, 18}) Quotient :: loop Aut^+ = C2 x ((C9 : C3) : C2) (small group id <108, 26>) Aut = C2 x ((C9 : C3) : C2) (small group id <108, 26>) |r| :: 1 Presentation :: [ X2^2, (X1^-1 * X2 * X1^-2)^2, X2 * X1^-1 * X2 * X1 * X2 * X1^-2 * X2 * X1^2, (X2 * X1^-1)^6, X1^18 ] Map:: R = (1, 109, 2, 110, 5, 113, 11, 119, 23, 131, 43, 151, 70, 178, 94, 202, 105, 213, 108, 216, 107, 215, 104, 212, 93, 201, 69, 177, 42, 150, 22, 130, 10, 118, 4, 112)(3, 111, 7, 115, 15, 123, 31, 139, 55, 163, 85, 193, 102, 210, 82, 190, 101, 209, 106, 214, 96, 204, 84, 192, 95, 203, 74, 182, 45, 153, 24, 132, 18, 126, 8, 116)(6, 114, 13, 121, 27, 135, 21, 129, 41, 149, 61, 169, 91, 199, 97, 205, 86, 194, 103, 211, 92, 200, 98, 206, 88, 196, 58, 166, 72, 180, 44, 152, 30, 138, 14, 122)(9, 117, 19, 127, 38, 146, 64, 172, 87, 195, 99, 207, 90, 198, 59, 167, 89, 197, 100, 208, 81, 189, 62, 170, 71, 179, 48, 156, 26, 134, 12, 120, 25, 133, 20, 128)(16, 124, 33, 141, 57, 165, 37, 145, 63, 171, 39, 147, 65, 173, 76, 184, 46, 154, 75, 183, 68, 176, 78, 186, 51, 159, 28, 136, 50, 158, 80, 188, 54, 162, 34, 142)(17, 125, 35, 143, 60, 168, 73, 181, 49, 157, 79, 187, 53, 161, 29, 137, 52, 160, 83, 191, 67, 175, 40, 148, 66, 174, 77, 185, 47, 155, 32, 140, 56, 164, 36, 144) 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, 145)(19, 147)(20, 148)(21, 118)(22, 139)(23, 152)(24, 119)(25, 154)(26, 155)(27, 157)(28, 121)(29, 122)(30, 162)(31, 130)(32, 123)(33, 166)(34, 167)(35, 169)(36, 170)(37, 126)(38, 160)(39, 127)(40, 128)(41, 176)(42, 172)(43, 179)(44, 131)(45, 181)(46, 133)(47, 134)(48, 186)(49, 135)(50, 189)(51, 190)(52, 146)(53, 192)(54, 138)(55, 188)(56, 194)(57, 195)(58, 141)(59, 142)(60, 197)(61, 143)(62, 144)(63, 200)(64, 150)(65, 182)(66, 193)(67, 180)(68, 149)(69, 199)(70, 203)(71, 151)(72, 175)(73, 153)(74, 173)(75, 204)(76, 205)(77, 206)(78, 156)(79, 207)(80, 163)(81, 158)(82, 159)(83, 209)(84, 161)(85, 174)(86, 164)(87, 165)(88, 202)(89, 168)(90, 212)(91, 177)(92, 171)(93, 210)(94, 196)(95, 178)(96, 183)(97, 184)(98, 185)(99, 187)(100, 213)(101, 191)(102, 201)(103, 215)(104, 198)(105, 208)(106, 216)(107, 211)(108, 214) 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 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: bipartite v = 6 e = 108 f = 72 degree seq :: [ 36^6 ] E16.1168 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y3 * R * Y2, (R * Y1)^2, (Y3 * Y2)^3, (Y1 * Y2)^4, (Y3 * Y1)^4, Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 ] Map:: polyhedral non-degenerate R = (1, 122, 2, 121)(3, 127, 7, 123)(4, 129, 9, 124)(5, 131, 11, 125)(6, 133, 13, 126)(8, 137, 17, 128)(10, 141, 21, 130)(12, 144, 24, 132)(14, 148, 28, 134)(15, 142, 22, 135)(16, 150, 30, 136)(18, 154, 34, 138)(19, 155, 35, 139)(20, 147, 27, 140)(23, 161, 41, 143)(25, 165, 45, 145)(26, 166, 46, 146)(29, 171, 51, 149)(31, 175, 55, 151)(32, 176, 56, 152)(33, 174, 54, 153)(36, 183, 63, 156)(37, 185, 65, 157)(38, 181, 61, 158)(39, 187, 67, 159)(40, 189, 69, 160)(42, 180, 60, 162)(43, 184, 64, 163)(44, 191, 71, 164)(47, 179, 59, 167)(48, 196, 76, 168)(49, 194, 74, 169)(50, 172, 52, 170)(53, 201, 81, 173)(57, 198, 78, 177)(58, 204, 84, 178)(62, 207, 87, 182)(66, 211, 91, 186)(68, 192, 72, 188)(70, 215, 95, 190)(73, 217, 97, 193)(75, 218, 98, 195)(77, 221, 101, 197)(79, 203, 83, 199)(80, 214, 94, 200)(82, 225, 105, 202)(85, 230, 110, 205)(86, 223, 103, 206)(88, 233, 113, 208)(89, 219, 99, 209)(90, 212, 92, 210)(93, 216, 96, 213)(100, 222, 102, 220)(104, 238, 118, 224)(106, 235, 115, 226)(107, 237, 117, 227)(108, 232, 112, 228)(109, 231, 111, 229)(114, 236, 116, 234)(119, 240, 120, 239) L = (1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 18)(9, 19)(11, 22)(12, 25)(13, 26)(16, 31)(17, 32)(20, 37)(21, 38)(23, 42)(24, 43)(27, 48)(28, 49)(29, 52)(30, 53)(33, 58)(34, 59)(35, 61)(36, 64)(39, 68)(40, 67)(41, 70)(44, 73)(45, 63)(46, 74)(47, 56)(50, 78)(51, 79)(54, 62)(55, 82)(57, 83)(60, 86)(65, 89)(66, 92)(69, 93)(71, 75)(72, 96)(76, 99)(77, 102)(80, 104)(81, 105)(84, 108)(85, 111)(87, 112)(88, 107)(90, 110)(91, 109)(94, 106)(95, 103)(97, 116)(98, 114)(100, 113)(101, 117)(115, 119)(118, 120)(121, 124)(122, 126)(123, 128)(125, 132)(127, 136)(129, 140)(130, 138)(131, 143)(133, 147)(134, 145)(135, 149)(137, 153)(139, 156)(141, 159)(142, 160)(144, 164)(146, 167)(148, 170)(150, 174)(151, 172)(152, 177)(154, 180)(155, 182)(157, 184)(158, 186)(161, 191)(162, 187)(163, 192)(165, 175)(166, 195)(168, 176)(169, 197)(171, 200)(173, 181)(178, 203)(179, 205)(183, 208)(185, 210)(188, 212)(189, 214)(190, 194)(193, 216)(196, 220)(198, 222)(199, 223)(201, 226)(202, 227)(204, 229)(206, 231)(207, 233)(209, 234)(211, 235)(213, 225)(215, 224)(217, 237)(218, 230)(219, 232)(221, 238)(228, 239)(236, 240) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E16.1169 Transitivity :: VT+ AT Graph:: simple v = 60 e = 120 f = 30 degree seq :: [ 4^60 ] E16.1169 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, Y1^4, (R * Y1)^2, (Y1 * Y3 * Y2)^2, (Y3 * Y2)^3, Y1 * Y3 * Y1^-2 * Y3 * Y1^-1 * Y3, Y1 * Y2 * Y1^-1 * Y2 * Y1^2 * Y2, Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1 ] Map:: polyhedral non-degenerate R = (1, 122, 2, 126, 6, 125, 5, 121)(3, 129, 9, 145, 25, 131, 11, 123)(4, 132, 12, 152, 32, 134, 14, 124)(7, 139, 19, 167, 47, 141, 21, 127)(8, 142, 22, 154, 34, 144, 24, 128)(10, 148, 28, 174, 54, 143, 23, 130)(13, 155, 35, 191, 71, 156, 36, 133)(15, 158, 38, 150, 30, 159, 39, 135)(16, 160, 40, 196, 76, 162, 42, 136)(17, 146, 26, 176, 56, 164, 44, 137)(18, 165, 45, 173, 53, 157, 37, 138)(20, 169, 49, 203, 83, 166, 46, 140)(27, 178, 58, 181, 61, 179, 59, 147)(29, 182, 62, 219, 99, 183, 63, 149)(31, 184, 64, 221, 101, 186, 66, 151)(33, 188, 68, 225, 105, 190, 70, 153)(41, 163, 43, 199, 79, 198, 78, 161)(48, 205, 85, 208, 88, 206, 86, 168)(50, 175, 55, 213, 93, 209, 89, 170)(51, 210, 90, 223, 103, 185, 65, 171)(52, 212, 92, 218, 98, 180, 60, 172)(57, 216, 96, 236, 116, 214, 94, 177)(67, 192, 72, 215, 95, 224, 104, 187)(69, 226, 106, 234, 114, 197, 77, 189)(73, 229, 109, 231, 111, 195, 75, 193)(74, 220, 100, 228, 108, 230, 110, 194)(80, 204, 84, 237, 117, 232, 112, 200)(81, 235, 115, 240, 120, 211, 91, 201)(82, 233, 113, 238, 118, 207, 87, 202)(97, 227, 107, 239, 119, 222, 102, 217) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 17)(8, 23)(9, 26)(10, 29)(11, 30)(12, 33)(14, 27)(16, 41)(18, 46)(19, 38)(20, 50)(21, 25)(22, 52)(24, 48)(28, 60)(31, 65)(32, 67)(34, 63)(35, 72)(36, 61)(37, 57)(39, 56)(40, 77)(42, 74)(43, 80)(44, 47)(45, 82)(49, 87)(51, 91)(53, 89)(54, 88)(55, 94)(58, 68)(59, 95)(62, 86)(64, 102)(66, 75)(69, 100)(70, 71)(73, 97)(76, 112)(78, 108)(79, 114)(81, 111)(83, 116)(84, 110)(85, 92)(90, 119)(93, 118)(96, 113)(98, 99)(101, 120)(103, 109)(104, 105)(106, 117)(107, 115)(121, 124)(122, 128)(123, 130)(125, 136)(126, 138)(127, 140)(129, 147)(131, 151)(132, 154)(133, 149)(134, 157)(135, 155)(137, 163)(139, 168)(141, 171)(142, 173)(143, 170)(144, 162)(145, 175)(146, 177)(148, 181)(150, 182)(152, 160)(153, 189)(156, 193)(158, 194)(159, 195)(161, 192)(164, 201)(165, 196)(166, 200)(167, 204)(169, 208)(172, 188)(174, 184)(176, 215)(178, 209)(179, 186)(180, 217)(183, 220)(185, 206)(187, 216)(190, 227)(191, 228)(197, 233)(198, 235)(199, 236)(202, 212)(203, 210)(205, 232)(207, 222)(211, 214)(213, 221)(218, 226)(219, 229)(223, 237)(224, 240)(225, 238)(230, 231)(234, 239) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.1168 Transitivity :: VT+ AT Graph:: simple v = 30 e = 120 f = 60 degree seq :: [ 8^30 ] E16.1170 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y1 * Y2)^3, (Y3 * Y1)^4, (Y3 * Y2)^4, Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 ] Map:: polytopal R = (1, 121, 4, 124)(2, 122, 6, 126)(3, 123, 8, 128)(5, 125, 12, 132)(7, 127, 15, 135)(9, 129, 19, 139)(10, 130, 21, 141)(11, 131, 22, 142)(13, 133, 26, 146)(14, 134, 28, 148)(16, 136, 32, 152)(17, 137, 34, 154)(18, 138, 36, 156)(20, 140, 38, 158)(23, 143, 43, 163)(24, 144, 45, 165)(25, 145, 47, 167)(27, 147, 49, 169)(29, 149, 52, 172)(30, 150, 54, 174)(31, 151, 56, 176)(33, 153, 58, 178)(35, 155, 60, 180)(37, 157, 64, 184)(39, 159, 68, 188)(40, 160, 67, 187)(41, 161, 63, 183)(42, 162, 72, 192)(44, 164, 73, 193)(46, 166, 66, 186)(48, 168, 76, 196)(50, 170, 78, 198)(51, 171, 80, 200)(53, 173, 81, 201)(55, 175, 61, 181)(57, 177, 83, 203)(59, 179, 86, 206)(62, 182, 88, 208)(65, 185, 91, 211)(69, 189, 94, 214)(70, 190, 95, 215)(71, 191, 74, 194)(75, 195, 100, 220)(77, 197, 103, 223)(79, 199, 85, 205)(82, 202, 107, 227)(84, 204, 110, 230)(87, 207, 112, 232)(89, 209, 113, 233)(90, 210, 114, 234)(92, 212, 115, 235)(93, 213, 98, 218)(96, 216, 111, 231)(97, 217, 108, 228)(99, 219, 117, 237)(101, 221, 106, 226)(102, 222, 118, 238)(104, 224, 105, 225)(109, 229, 119, 239)(116, 236, 120, 240)(241, 242)(243, 247)(244, 249)(245, 251)(246, 253)(248, 256)(250, 260)(252, 263)(254, 267)(255, 269)(257, 273)(258, 275)(259, 266)(261, 279)(262, 280)(264, 284)(265, 286)(268, 290)(270, 293)(271, 295)(272, 292)(274, 299)(276, 301)(277, 303)(278, 305)(281, 310)(282, 311)(283, 307)(285, 297)(287, 314)(288, 294)(289, 317)(291, 319)(296, 300)(298, 324)(302, 327)(304, 329)(306, 312)(308, 331)(309, 333)(313, 337)(315, 339)(316, 341)(318, 343)(320, 338)(321, 346)(322, 342)(323, 348)(325, 334)(326, 350)(328, 332)(330, 336)(335, 353)(340, 344)(345, 356)(347, 351)(349, 355)(352, 359)(354, 358)(357, 360)(361, 363)(362, 365)(364, 370)(366, 374)(367, 371)(368, 377)(369, 378)(372, 384)(373, 385)(375, 390)(376, 391)(379, 397)(380, 395)(381, 394)(382, 401)(383, 402)(386, 408)(387, 406)(388, 405)(389, 411)(392, 417)(393, 415)(396, 422)(398, 426)(399, 427)(400, 429)(403, 419)(404, 431)(407, 435)(409, 420)(410, 412)(413, 439)(414, 423)(416, 442)(418, 445)(421, 441)(424, 448)(425, 450)(428, 452)(430, 453)(432, 456)(433, 458)(434, 455)(436, 460)(437, 462)(438, 464)(440, 465)(443, 467)(444, 469)(446, 471)(447, 466)(449, 451)(454, 475)(457, 476)(459, 473)(461, 463)(468, 470)(472, 478)(474, 477)(479, 480) L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 16, 16 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E16.1173 Graph:: simple bipartite v = 180 e = 240 f = 30 degree seq :: [ 2^120, 4^60 ] E16.1171 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1)^3, (Y3 * Y1 * Y2)^2, Y1 * Y3 * Y1 * Y3^2 * Y1 * Y3^-1, Y2 * Y3^-1 * Y2 * Y3^-2 * Y2 * Y3, Y2 * Y3^-1 * Y2 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3^-1 ] Map:: polytopal R = (1, 121, 4, 124, 14, 134, 5, 125)(2, 122, 7, 127, 22, 142, 8, 128)(3, 123, 10, 130, 28, 148, 11, 131)(6, 126, 18, 138, 46, 166, 19, 139)(9, 129, 25, 145, 58, 178, 26, 146)(12, 132, 31, 151, 20, 140, 32, 152)(13, 133, 34, 154, 69, 189, 35, 155)(15, 135, 39, 159, 76, 196, 40, 160)(16, 136, 41, 161, 30, 150, 42, 162)(17, 137, 43, 163, 80, 200, 44, 164)(21, 141, 50, 170, 87, 207, 51, 171)(23, 143, 36, 156, 71, 191, 54, 174)(24, 144, 55, 175, 48, 168, 56, 176)(27, 147, 60, 180, 73, 193, 37, 157)(29, 149, 63, 183, 98, 218, 64, 184)(33, 153, 67, 187, 102, 222, 68, 188)(38, 158, 72, 192, 108, 228, 74, 194)(45, 165, 82, 202, 90, 210, 52, 172)(47, 167, 85, 205, 115, 235, 78, 198)(49, 169, 86, 206, 112, 232, 75, 195)(53, 173, 89, 209, 119, 239, 91, 211)(57, 177, 65, 185, 99, 219, 93, 213)(59, 179, 61, 181, 95, 215, 92, 212)(62, 182, 70, 190, 106, 226, 96, 216)(66, 186, 100, 220, 94, 214, 79, 199)(77, 197, 81, 201, 83, 203, 114, 234)(84, 204, 88, 208, 118, 238, 97, 217)(101, 221, 107, 227, 111, 231, 117, 237)(103, 223, 104, 224, 116, 236, 113, 233)(105, 225, 109, 229, 110, 230, 120, 240)(241, 242)(243, 249)(244, 252)(245, 255)(246, 257)(247, 260)(248, 263)(250, 264)(251, 269)(253, 273)(254, 276)(256, 258)(259, 287)(261, 289)(262, 279)(265, 288)(266, 299)(267, 293)(268, 301)(270, 283)(271, 294)(272, 280)(274, 306)(275, 310)(277, 312)(278, 285)(281, 317)(282, 318)(284, 321)(286, 323)(290, 305)(291, 328)(292, 329)(295, 332)(296, 304)(297, 324)(298, 303)(300, 322)(302, 319)(307, 334)(308, 343)(309, 344)(311, 316)(313, 349)(314, 350)(315, 351)(320, 325)(326, 333)(327, 357)(330, 360)(331, 345)(335, 338)(336, 356)(337, 341)(339, 347)(340, 353)(342, 346)(348, 359)(352, 358)(354, 355)(361, 363)(362, 366)(364, 373)(365, 376)(367, 381)(368, 384)(369, 377)(370, 387)(371, 390)(372, 386)(374, 397)(375, 398)(378, 405)(379, 408)(380, 404)(382, 412)(383, 413)(385, 417)(388, 395)(389, 422)(391, 425)(392, 426)(393, 419)(394, 401)(396, 428)(399, 435)(400, 437)(402, 420)(403, 439)(406, 411)(407, 444)(409, 441)(410, 415)(414, 452)(416, 442)(418, 454)(421, 451)(423, 457)(424, 438)(427, 461)(429, 433)(430, 465)(431, 467)(432, 463)(434, 443)(436, 473)(440, 453)(445, 456)(446, 476)(447, 450)(448, 470)(449, 471)(455, 477)(458, 480)(459, 460)(462, 479)(464, 474)(466, 478)(468, 472)(469, 475) L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 8, 8 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E16.1172 Graph:: simple bipartite v = 150 e = 240 f = 60 degree seq :: [ 2^120, 8^30 ] E16.1172 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y1 * Y2)^3, (Y3 * Y1)^4, (Y3 * Y2)^4, Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 ] Map:: R = (1, 121, 241, 361, 4, 124, 244, 364)(2, 122, 242, 362, 6, 126, 246, 366)(3, 123, 243, 363, 8, 128, 248, 368)(5, 125, 245, 365, 12, 132, 252, 372)(7, 127, 247, 367, 15, 135, 255, 375)(9, 129, 249, 369, 19, 139, 259, 379)(10, 130, 250, 370, 21, 141, 261, 381)(11, 131, 251, 371, 22, 142, 262, 382)(13, 133, 253, 373, 26, 146, 266, 386)(14, 134, 254, 374, 28, 148, 268, 388)(16, 136, 256, 376, 32, 152, 272, 392)(17, 137, 257, 377, 34, 154, 274, 394)(18, 138, 258, 378, 36, 156, 276, 396)(20, 140, 260, 380, 38, 158, 278, 398)(23, 143, 263, 383, 43, 163, 283, 403)(24, 144, 264, 384, 45, 165, 285, 405)(25, 145, 265, 385, 47, 167, 287, 407)(27, 147, 267, 387, 49, 169, 289, 409)(29, 149, 269, 389, 52, 172, 292, 412)(30, 150, 270, 390, 54, 174, 294, 414)(31, 151, 271, 391, 56, 176, 296, 416)(33, 153, 273, 393, 58, 178, 298, 418)(35, 155, 275, 395, 60, 180, 300, 420)(37, 157, 277, 397, 64, 184, 304, 424)(39, 159, 279, 399, 68, 188, 308, 428)(40, 160, 280, 400, 67, 187, 307, 427)(41, 161, 281, 401, 63, 183, 303, 423)(42, 162, 282, 402, 72, 192, 312, 432)(44, 164, 284, 404, 73, 193, 313, 433)(46, 166, 286, 406, 66, 186, 306, 426)(48, 168, 288, 408, 76, 196, 316, 436)(50, 170, 290, 410, 78, 198, 318, 438)(51, 171, 291, 411, 80, 200, 320, 440)(53, 173, 293, 413, 81, 201, 321, 441)(55, 175, 295, 415, 61, 181, 301, 421)(57, 177, 297, 417, 83, 203, 323, 443)(59, 179, 299, 419, 86, 206, 326, 446)(62, 182, 302, 422, 88, 208, 328, 448)(65, 185, 305, 425, 91, 211, 331, 451)(69, 189, 309, 429, 94, 214, 334, 454)(70, 190, 310, 430, 95, 215, 335, 455)(71, 191, 311, 431, 74, 194, 314, 434)(75, 195, 315, 435, 100, 220, 340, 460)(77, 197, 317, 437, 103, 223, 343, 463)(79, 199, 319, 439, 85, 205, 325, 445)(82, 202, 322, 442, 107, 227, 347, 467)(84, 204, 324, 444, 110, 230, 350, 470)(87, 207, 327, 447, 112, 232, 352, 472)(89, 209, 329, 449, 113, 233, 353, 473)(90, 210, 330, 450, 114, 234, 354, 474)(92, 212, 332, 452, 115, 235, 355, 475)(93, 213, 333, 453, 98, 218, 338, 458)(96, 216, 336, 456, 111, 231, 351, 471)(97, 217, 337, 457, 108, 228, 348, 468)(99, 219, 339, 459, 117, 237, 357, 477)(101, 221, 341, 461, 106, 226, 346, 466)(102, 222, 342, 462, 118, 238, 358, 478)(104, 224, 344, 464, 105, 225, 345, 465)(109, 229, 349, 469, 119, 239, 359, 479)(116, 236, 356, 476, 120, 240, 360, 480) L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 131)(6, 133)(7, 123)(8, 136)(9, 124)(10, 140)(11, 125)(12, 143)(13, 126)(14, 147)(15, 149)(16, 128)(17, 153)(18, 155)(19, 146)(20, 130)(21, 159)(22, 160)(23, 132)(24, 164)(25, 166)(26, 139)(27, 134)(28, 170)(29, 135)(30, 173)(31, 175)(32, 172)(33, 137)(34, 179)(35, 138)(36, 181)(37, 183)(38, 185)(39, 141)(40, 142)(41, 190)(42, 191)(43, 187)(44, 144)(45, 177)(46, 145)(47, 194)(48, 174)(49, 197)(50, 148)(51, 199)(52, 152)(53, 150)(54, 168)(55, 151)(56, 180)(57, 165)(58, 204)(59, 154)(60, 176)(61, 156)(62, 207)(63, 157)(64, 209)(65, 158)(66, 192)(67, 163)(68, 211)(69, 213)(70, 161)(71, 162)(72, 186)(73, 217)(74, 167)(75, 219)(76, 221)(77, 169)(78, 223)(79, 171)(80, 218)(81, 226)(82, 222)(83, 228)(84, 178)(85, 214)(86, 230)(87, 182)(88, 212)(89, 184)(90, 216)(91, 188)(92, 208)(93, 189)(94, 205)(95, 233)(96, 210)(97, 193)(98, 200)(99, 195)(100, 224)(101, 196)(102, 202)(103, 198)(104, 220)(105, 236)(106, 201)(107, 231)(108, 203)(109, 235)(110, 206)(111, 227)(112, 239)(113, 215)(114, 238)(115, 229)(116, 225)(117, 240)(118, 234)(119, 232)(120, 237)(241, 363)(242, 365)(243, 361)(244, 370)(245, 362)(246, 374)(247, 371)(248, 377)(249, 378)(250, 364)(251, 367)(252, 384)(253, 385)(254, 366)(255, 390)(256, 391)(257, 368)(258, 369)(259, 397)(260, 395)(261, 394)(262, 401)(263, 402)(264, 372)(265, 373)(266, 408)(267, 406)(268, 405)(269, 411)(270, 375)(271, 376)(272, 417)(273, 415)(274, 381)(275, 380)(276, 422)(277, 379)(278, 426)(279, 427)(280, 429)(281, 382)(282, 383)(283, 419)(284, 431)(285, 388)(286, 387)(287, 435)(288, 386)(289, 420)(290, 412)(291, 389)(292, 410)(293, 439)(294, 423)(295, 393)(296, 442)(297, 392)(298, 445)(299, 403)(300, 409)(301, 441)(302, 396)(303, 414)(304, 448)(305, 450)(306, 398)(307, 399)(308, 452)(309, 400)(310, 453)(311, 404)(312, 456)(313, 458)(314, 455)(315, 407)(316, 460)(317, 462)(318, 464)(319, 413)(320, 465)(321, 421)(322, 416)(323, 467)(324, 469)(325, 418)(326, 471)(327, 466)(328, 424)(329, 451)(330, 425)(331, 449)(332, 428)(333, 430)(334, 475)(335, 434)(336, 432)(337, 476)(338, 433)(339, 473)(340, 436)(341, 463)(342, 437)(343, 461)(344, 438)(345, 440)(346, 447)(347, 443)(348, 470)(349, 444)(350, 468)(351, 446)(352, 478)(353, 459)(354, 477)(355, 454)(356, 457)(357, 474)(358, 472)(359, 480)(360, 479) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E16.1171 Transitivity :: VT+ Graph:: v = 60 e = 240 f = 150 degree seq :: [ 8^60 ] E16.1173 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1)^3, (Y3 * Y1 * Y2)^2, Y1 * Y3 * Y1 * Y3^2 * Y1 * Y3^-1, Y2 * Y3^-1 * Y2 * Y3^-2 * Y2 * Y3, Y2 * Y3^-1 * Y2 * Y1 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3^-1 ] Map:: R = (1, 121, 241, 361, 4, 124, 244, 364, 14, 134, 254, 374, 5, 125, 245, 365)(2, 122, 242, 362, 7, 127, 247, 367, 22, 142, 262, 382, 8, 128, 248, 368)(3, 123, 243, 363, 10, 130, 250, 370, 28, 148, 268, 388, 11, 131, 251, 371)(6, 126, 246, 366, 18, 138, 258, 378, 46, 166, 286, 406, 19, 139, 259, 379)(9, 129, 249, 369, 25, 145, 265, 385, 58, 178, 298, 418, 26, 146, 266, 386)(12, 132, 252, 372, 31, 151, 271, 391, 20, 140, 260, 380, 32, 152, 272, 392)(13, 133, 253, 373, 34, 154, 274, 394, 69, 189, 309, 429, 35, 155, 275, 395)(15, 135, 255, 375, 39, 159, 279, 399, 76, 196, 316, 436, 40, 160, 280, 400)(16, 136, 256, 376, 41, 161, 281, 401, 30, 150, 270, 390, 42, 162, 282, 402)(17, 137, 257, 377, 43, 163, 283, 403, 80, 200, 320, 440, 44, 164, 284, 404)(21, 141, 261, 381, 50, 170, 290, 410, 87, 207, 327, 447, 51, 171, 291, 411)(23, 143, 263, 383, 36, 156, 276, 396, 71, 191, 311, 431, 54, 174, 294, 414)(24, 144, 264, 384, 55, 175, 295, 415, 48, 168, 288, 408, 56, 176, 296, 416)(27, 147, 267, 387, 60, 180, 300, 420, 73, 193, 313, 433, 37, 157, 277, 397)(29, 149, 269, 389, 63, 183, 303, 423, 98, 218, 338, 458, 64, 184, 304, 424)(33, 153, 273, 393, 67, 187, 307, 427, 102, 222, 342, 462, 68, 188, 308, 428)(38, 158, 278, 398, 72, 192, 312, 432, 108, 228, 348, 468, 74, 194, 314, 434)(45, 165, 285, 405, 82, 202, 322, 442, 90, 210, 330, 450, 52, 172, 292, 412)(47, 167, 287, 407, 85, 205, 325, 445, 115, 235, 355, 475, 78, 198, 318, 438)(49, 169, 289, 409, 86, 206, 326, 446, 112, 232, 352, 472, 75, 195, 315, 435)(53, 173, 293, 413, 89, 209, 329, 449, 119, 239, 359, 479, 91, 211, 331, 451)(57, 177, 297, 417, 65, 185, 305, 425, 99, 219, 339, 459, 93, 213, 333, 453)(59, 179, 299, 419, 61, 181, 301, 421, 95, 215, 335, 455, 92, 212, 332, 452)(62, 182, 302, 422, 70, 190, 310, 430, 106, 226, 346, 466, 96, 216, 336, 456)(66, 186, 306, 426, 100, 220, 340, 460, 94, 214, 334, 454, 79, 199, 319, 439)(77, 197, 317, 437, 81, 201, 321, 441, 83, 203, 323, 443, 114, 234, 354, 474)(84, 204, 324, 444, 88, 208, 328, 448, 118, 238, 358, 478, 97, 217, 337, 457)(101, 221, 341, 461, 107, 227, 347, 467, 111, 231, 351, 471, 117, 237, 357, 477)(103, 223, 343, 463, 104, 224, 344, 464, 116, 236, 356, 476, 113, 233, 353, 473)(105, 225, 345, 465, 109, 229, 349, 469, 110, 230, 350, 470, 120, 240, 360, 480) L = (1, 122)(2, 121)(3, 129)(4, 132)(5, 135)(6, 137)(7, 140)(8, 143)(9, 123)(10, 144)(11, 149)(12, 124)(13, 153)(14, 156)(15, 125)(16, 138)(17, 126)(18, 136)(19, 167)(20, 127)(21, 169)(22, 159)(23, 128)(24, 130)(25, 168)(26, 179)(27, 173)(28, 181)(29, 131)(30, 163)(31, 174)(32, 160)(33, 133)(34, 186)(35, 190)(36, 134)(37, 192)(38, 165)(39, 142)(40, 152)(41, 197)(42, 198)(43, 150)(44, 201)(45, 158)(46, 203)(47, 139)(48, 145)(49, 141)(50, 185)(51, 208)(52, 209)(53, 147)(54, 151)(55, 212)(56, 184)(57, 204)(58, 183)(59, 146)(60, 202)(61, 148)(62, 199)(63, 178)(64, 176)(65, 170)(66, 154)(67, 214)(68, 223)(69, 224)(70, 155)(71, 196)(72, 157)(73, 229)(74, 230)(75, 231)(76, 191)(77, 161)(78, 162)(79, 182)(80, 205)(81, 164)(82, 180)(83, 166)(84, 177)(85, 200)(86, 213)(87, 237)(88, 171)(89, 172)(90, 240)(91, 225)(92, 175)(93, 206)(94, 187)(95, 218)(96, 236)(97, 221)(98, 215)(99, 227)(100, 233)(101, 217)(102, 226)(103, 188)(104, 189)(105, 211)(106, 222)(107, 219)(108, 239)(109, 193)(110, 194)(111, 195)(112, 238)(113, 220)(114, 235)(115, 234)(116, 216)(117, 207)(118, 232)(119, 228)(120, 210)(241, 363)(242, 366)(243, 361)(244, 373)(245, 376)(246, 362)(247, 381)(248, 384)(249, 377)(250, 387)(251, 390)(252, 386)(253, 364)(254, 397)(255, 398)(256, 365)(257, 369)(258, 405)(259, 408)(260, 404)(261, 367)(262, 412)(263, 413)(264, 368)(265, 417)(266, 372)(267, 370)(268, 395)(269, 422)(270, 371)(271, 425)(272, 426)(273, 419)(274, 401)(275, 388)(276, 428)(277, 374)(278, 375)(279, 435)(280, 437)(281, 394)(282, 420)(283, 439)(284, 380)(285, 378)(286, 411)(287, 444)(288, 379)(289, 441)(290, 415)(291, 406)(292, 382)(293, 383)(294, 452)(295, 410)(296, 442)(297, 385)(298, 454)(299, 393)(300, 402)(301, 451)(302, 389)(303, 457)(304, 438)(305, 391)(306, 392)(307, 461)(308, 396)(309, 433)(310, 465)(311, 467)(312, 463)(313, 429)(314, 443)(315, 399)(316, 473)(317, 400)(318, 424)(319, 403)(320, 453)(321, 409)(322, 416)(323, 434)(324, 407)(325, 456)(326, 476)(327, 450)(328, 470)(329, 471)(330, 447)(331, 421)(332, 414)(333, 440)(334, 418)(335, 477)(336, 445)(337, 423)(338, 480)(339, 460)(340, 459)(341, 427)(342, 479)(343, 432)(344, 474)(345, 430)(346, 478)(347, 431)(348, 472)(349, 475)(350, 448)(351, 449)(352, 468)(353, 436)(354, 464)(355, 469)(356, 446)(357, 455)(358, 466)(359, 462)(360, 458) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E16.1170 Transitivity :: VT+ Graph:: v = 30 e = 240 f = 180 degree seq :: [ 16^30 ] E16.1174 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y3)^4, (Y1 * Y2)^6, (Y1 * Y2 * Y1 * Y3)^3, (Y1 * Y3 * Y2)^5, Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2 * Y1 * Y2 ] Map:: polytopal non-degenerate R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 10, 130)(6, 126, 12, 132)(8, 128, 15, 135)(11, 131, 20, 140)(13, 133, 23, 143)(14, 134, 25, 145)(16, 136, 28, 148)(17, 137, 22, 142)(18, 138, 30, 150)(19, 139, 32, 152)(21, 141, 35, 155)(24, 144, 39, 159)(26, 146, 42, 162)(27, 147, 41, 161)(29, 149, 46, 166)(31, 151, 49, 169)(33, 153, 52, 172)(34, 154, 51, 171)(36, 156, 56, 176)(37, 157, 47, 167)(38, 158, 58, 178)(40, 160, 55, 175)(43, 163, 64, 184)(44, 164, 65, 185)(45, 165, 50, 170)(48, 168, 70, 190)(53, 173, 76, 196)(54, 174, 77, 197)(57, 177, 81, 201)(59, 179, 84, 204)(60, 180, 83, 203)(61, 181, 80, 200)(62, 182, 86, 206)(63, 183, 82, 202)(66, 186, 91, 211)(67, 187, 92, 212)(68, 188, 73, 193)(69, 189, 94, 214)(71, 191, 97, 217)(72, 192, 96, 216)(74, 194, 99, 219)(75, 195, 95, 215)(78, 198, 102, 222)(79, 199, 103, 223)(85, 205, 93, 213)(87, 207, 111, 231)(88, 208, 112, 232)(89, 209, 107, 227)(90, 210, 113, 233)(98, 218, 104, 224)(100, 220, 110, 230)(101, 221, 120, 240)(105, 225, 119, 239)(106, 226, 116, 236)(108, 228, 115, 235)(109, 229, 117, 237)(114, 234, 118, 238)(241, 361, 243, 363)(242, 362, 245, 365)(244, 364, 248, 368)(246, 366, 251, 371)(247, 367, 253, 373)(249, 369, 256, 376)(250, 370, 258, 378)(252, 372, 261, 381)(254, 374, 264, 384)(255, 375, 266, 386)(257, 377, 269, 389)(259, 379, 271, 391)(260, 380, 273, 393)(262, 382, 276, 396)(263, 383, 277, 397)(265, 385, 280, 400)(267, 387, 283, 403)(268, 388, 284, 404)(270, 390, 287, 407)(272, 392, 290, 410)(274, 394, 293, 413)(275, 395, 294, 414)(278, 398, 297, 417)(279, 399, 299, 419)(281, 401, 301, 421)(282, 402, 302, 422)(285, 405, 306, 426)(286, 406, 307, 427)(288, 408, 309, 429)(289, 409, 311, 431)(291, 411, 313, 433)(292, 412, 314, 434)(295, 415, 318, 438)(296, 416, 319, 439)(298, 418, 322, 442)(300, 420, 325, 445)(303, 423, 327, 447)(304, 424, 328, 448)(305, 425, 326, 446)(308, 428, 333, 453)(310, 430, 335, 455)(312, 432, 338, 458)(315, 435, 340, 460)(316, 436, 329, 449)(317, 437, 339, 459)(320, 440, 344, 464)(321, 441, 345, 465)(323, 443, 347, 467)(324, 444, 348, 468)(330, 450, 350, 470)(331, 451, 354, 474)(332, 452, 356, 476)(334, 454, 357, 477)(336, 456, 352, 472)(337, 457, 358, 478)(341, 461, 351, 471)(342, 462, 355, 475)(343, 463, 346, 466)(349, 469, 353, 473)(359, 479, 360, 480) L = (1, 244)(2, 246)(3, 248)(4, 241)(5, 251)(6, 242)(7, 254)(8, 243)(9, 257)(10, 259)(11, 245)(12, 262)(13, 264)(14, 247)(15, 267)(16, 269)(17, 249)(18, 271)(19, 250)(20, 274)(21, 276)(22, 252)(23, 278)(24, 253)(25, 281)(26, 283)(27, 255)(28, 285)(29, 256)(30, 288)(31, 258)(32, 291)(33, 293)(34, 260)(35, 295)(36, 261)(37, 297)(38, 263)(39, 300)(40, 301)(41, 265)(42, 303)(43, 266)(44, 306)(45, 268)(46, 308)(47, 309)(48, 270)(49, 312)(50, 313)(51, 272)(52, 315)(53, 273)(54, 318)(55, 275)(56, 320)(57, 277)(58, 323)(59, 325)(60, 279)(61, 280)(62, 327)(63, 282)(64, 329)(65, 330)(66, 284)(67, 333)(68, 286)(69, 287)(70, 336)(71, 338)(72, 289)(73, 290)(74, 340)(75, 292)(76, 328)(77, 341)(78, 294)(79, 344)(80, 296)(81, 346)(82, 347)(83, 298)(84, 349)(85, 299)(86, 350)(87, 302)(88, 316)(89, 304)(90, 305)(91, 355)(92, 357)(93, 307)(94, 356)(95, 352)(96, 310)(97, 359)(98, 311)(99, 351)(100, 314)(101, 317)(102, 354)(103, 345)(104, 319)(105, 343)(106, 321)(107, 322)(108, 353)(109, 324)(110, 326)(111, 339)(112, 335)(113, 348)(114, 342)(115, 331)(116, 334)(117, 332)(118, 360)(119, 337)(120, 358)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.1178 Graph:: simple bipartite v = 120 e = 240 f = 90 degree seq :: [ 4^120 ] E16.1175 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^6, (R * Y2 * Y3^-1)^2, (Y1 * Y2 * Y3^2)^2, (Y3 * Y1 * Y3^-1 * Y2)^2, (Y2 * Y1)^4, (Y3^-1 * Y1)^4, Y3 * Y1 * Y2 * Y1 * Y2 * Y3^-2 * Y1 * Y3, (Y1 * Y3 * Y2)^3, R * Y2 * Y1 * Y2 * R * Y1 * Y2 * Y1 * Y2, (Y1 * Y3^2)^3, (Y1 * Y3^-2)^3, Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 ] Map:: polyhedral non-degenerate R = (1, 121, 2, 122)(3, 123, 9, 129)(4, 124, 12, 132)(5, 125, 14, 134)(6, 126, 16, 136)(7, 127, 19, 139)(8, 128, 21, 141)(10, 130, 26, 146)(11, 131, 28, 148)(13, 133, 33, 153)(15, 135, 38, 158)(17, 137, 42, 162)(18, 138, 44, 164)(20, 140, 49, 169)(22, 142, 54, 174)(23, 143, 39, 159)(24, 144, 57, 177)(25, 145, 59, 179)(27, 147, 43, 163)(29, 149, 68, 188)(30, 150, 69, 189)(31, 151, 53, 173)(32, 152, 72, 192)(34, 154, 74, 194)(35, 155, 75, 195)(36, 156, 78, 198)(37, 157, 47, 167)(40, 160, 85, 205)(41, 161, 86, 206)(45, 165, 60, 180)(46, 166, 92, 212)(48, 168, 95, 215)(50, 170, 96, 216)(51, 171, 97, 217)(52, 172, 100, 220)(55, 175, 93, 213)(56, 176, 77, 197)(58, 178, 81, 201)(61, 181, 91, 211)(62, 182, 106, 226)(63, 183, 108, 228)(64, 184, 109, 229)(65, 185, 79, 199)(66, 186, 101, 221)(67, 187, 87, 207)(70, 190, 84, 204)(71, 191, 80, 200)(73, 193, 115, 235)(76, 196, 104, 224)(82, 202, 99, 219)(83, 203, 113, 233)(88, 208, 114, 234)(89, 209, 112, 232)(90, 210, 119, 239)(94, 214, 102, 222)(98, 218, 105, 225)(103, 223, 117, 237)(107, 227, 110, 230)(111, 231, 120, 240)(116, 236, 118, 238)(241, 361, 243, 363)(242, 362, 246, 366)(244, 364, 251, 371)(245, 365, 250, 370)(247, 367, 258, 378)(248, 368, 257, 377)(249, 369, 263, 383)(252, 372, 270, 390)(253, 373, 269, 389)(254, 374, 275, 395)(255, 375, 267, 387)(256, 376, 279, 399)(259, 379, 286, 406)(260, 380, 285, 405)(261, 381, 291, 411)(262, 382, 283, 403)(264, 384, 296, 416)(265, 385, 295, 415)(266, 386, 301, 421)(268, 388, 305, 425)(271, 391, 310, 430)(272, 392, 303, 423)(273, 393, 300, 420)(274, 394, 304, 424)(276, 396, 317, 437)(277, 397, 316, 436)(278, 398, 321, 441)(280, 400, 322, 442)(281, 401, 324, 444)(282, 402, 327, 447)(284, 404, 306, 426)(287, 407, 333, 453)(288, 408, 329, 449)(289, 409, 308, 428)(290, 410, 330, 450)(292, 412, 339, 459)(293, 413, 338, 458)(294, 414, 298, 418)(297, 417, 328, 448)(299, 419, 344, 464)(302, 422, 325, 445)(307, 427, 337, 457)(309, 429, 319, 439)(311, 431, 347, 467)(312, 432, 353, 473)(313, 433, 343, 463)(314, 434, 350, 470)(315, 435, 331, 451)(318, 438, 354, 474)(320, 440, 349, 469)(323, 443, 351, 471)(326, 446, 345, 465)(332, 452, 341, 461)(334, 454, 358, 478)(335, 455, 355, 475)(336, 456, 356, 476)(340, 460, 346, 466)(342, 462, 359, 479)(348, 468, 360, 480)(352, 472, 357, 477) L = (1, 244)(2, 247)(3, 250)(4, 253)(5, 241)(6, 257)(7, 260)(8, 242)(9, 264)(10, 267)(11, 243)(12, 271)(13, 274)(14, 276)(15, 245)(16, 280)(17, 283)(18, 246)(19, 287)(20, 290)(21, 292)(22, 248)(23, 295)(24, 298)(25, 249)(26, 302)(27, 304)(28, 306)(29, 251)(30, 303)(31, 311)(32, 252)(33, 313)(34, 255)(35, 316)(36, 319)(37, 254)(38, 322)(39, 324)(40, 321)(41, 256)(42, 328)(43, 330)(44, 305)(45, 258)(46, 329)(47, 334)(48, 259)(49, 323)(50, 262)(51, 338)(52, 341)(53, 261)(54, 296)(55, 273)(56, 263)(57, 327)(58, 343)(59, 345)(60, 265)(61, 272)(62, 347)(63, 266)(64, 269)(65, 337)(66, 315)(67, 268)(68, 281)(69, 317)(70, 270)(71, 325)(72, 354)(73, 294)(74, 356)(75, 336)(76, 349)(77, 275)(78, 353)(79, 357)(80, 277)(81, 351)(82, 279)(83, 278)(84, 289)(85, 301)(86, 344)(87, 288)(88, 358)(89, 282)(90, 285)(91, 284)(92, 339)(93, 286)(94, 297)(95, 346)(96, 350)(97, 314)(98, 359)(99, 291)(100, 355)(101, 360)(102, 293)(103, 300)(104, 340)(105, 318)(106, 299)(107, 310)(108, 332)(109, 352)(110, 307)(111, 308)(112, 309)(113, 335)(114, 326)(115, 312)(116, 331)(117, 320)(118, 333)(119, 348)(120, 342)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.1179 Graph:: simple bipartite v = 120 e = 240 f = 90 degree seq :: [ 4^120 ] E16.1176 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, (Y1 * Y3)^4, (Y1 * Y2)^5, Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1, (Y3 * Y2 * Y1)^6 ] Map:: polytopal non-degenerate R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 10, 130)(6, 126, 12, 132)(8, 128, 15, 135)(11, 131, 20, 140)(13, 133, 23, 143)(14, 134, 25, 145)(16, 136, 28, 148)(17, 137, 22, 142)(18, 138, 30, 150)(19, 139, 32, 152)(21, 141, 35, 155)(24, 144, 38, 158)(26, 146, 41, 161)(27, 147, 40, 160)(29, 149, 45, 165)(31, 151, 47, 167)(33, 153, 50, 170)(34, 154, 49, 169)(36, 156, 54, 174)(37, 157, 55, 175)(39, 159, 58, 178)(42, 162, 62, 182)(43, 163, 60, 180)(44, 164, 64, 184)(46, 166, 67, 187)(48, 168, 66, 186)(51, 171, 72, 192)(52, 172, 70, 190)(53, 173, 59, 179)(56, 176, 77, 197)(57, 177, 76, 196)(61, 181, 81, 201)(63, 183, 84, 204)(65, 185, 85, 205)(68, 188, 89, 209)(69, 189, 88, 208)(71, 191, 92, 212)(73, 193, 95, 215)(74, 194, 96, 216)(75, 195, 83, 203)(78, 198, 99, 219)(79, 199, 97, 217)(80, 200, 100, 220)(82, 202, 101, 221)(86, 206, 106, 226)(87, 207, 94, 214)(90, 210, 98, 218)(91, 211, 107, 227)(93, 213, 103, 223)(102, 222, 108, 228)(104, 224, 114, 234)(105, 225, 117, 237)(109, 229, 119, 239)(110, 230, 120, 240)(111, 231, 118, 238)(112, 232, 113, 233)(115, 235, 116, 236)(241, 361, 243, 363)(242, 362, 245, 365)(244, 364, 248, 368)(246, 366, 251, 371)(247, 367, 253, 373)(249, 369, 256, 376)(250, 370, 258, 378)(252, 372, 261, 381)(254, 374, 264, 384)(255, 375, 266, 386)(257, 377, 269, 389)(259, 379, 271, 391)(260, 380, 273, 393)(262, 382, 276, 396)(263, 383, 270, 390)(265, 385, 279, 399)(267, 387, 282, 402)(268, 388, 283, 403)(272, 392, 288, 408)(274, 394, 291, 411)(275, 395, 292, 412)(277, 397, 286, 406)(278, 398, 296, 416)(280, 400, 299, 419)(281, 401, 300, 420)(284, 404, 303, 423)(285, 405, 305, 425)(287, 407, 308, 428)(289, 409, 304, 424)(290, 410, 310, 430)(293, 413, 313, 433)(294, 414, 314, 434)(295, 415, 315, 435)(297, 417, 318, 438)(298, 418, 319, 439)(301, 421, 320, 440)(302, 422, 322, 442)(306, 426, 326, 446)(307, 427, 327, 447)(309, 429, 330, 450)(311, 431, 331, 451)(312, 432, 333, 453)(316, 436, 321, 441)(317, 437, 337, 457)(323, 443, 342, 462)(324, 444, 343, 463)(325, 445, 336, 456)(328, 448, 332, 452)(329, 449, 346, 466)(334, 454, 348, 468)(335, 455, 341, 461)(338, 458, 351, 471)(339, 459, 352, 472)(340, 460, 353, 473)(344, 464, 356, 476)(345, 465, 350, 470)(347, 467, 358, 478)(349, 469, 355, 475)(354, 474, 357, 477)(359, 479, 360, 480) L = (1, 244)(2, 246)(3, 248)(4, 241)(5, 251)(6, 242)(7, 254)(8, 243)(9, 257)(10, 259)(11, 245)(12, 262)(13, 264)(14, 247)(15, 267)(16, 269)(17, 249)(18, 271)(19, 250)(20, 274)(21, 276)(22, 252)(23, 277)(24, 253)(25, 280)(26, 282)(27, 255)(28, 284)(29, 256)(30, 286)(31, 258)(32, 289)(33, 291)(34, 260)(35, 293)(36, 261)(37, 263)(38, 297)(39, 299)(40, 265)(41, 301)(42, 266)(43, 303)(44, 268)(45, 306)(46, 270)(47, 309)(48, 304)(49, 272)(50, 311)(51, 273)(52, 313)(53, 275)(54, 298)(55, 316)(56, 318)(57, 278)(58, 294)(59, 279)(60, 320)(61, 281)(62, 323)(63, 283)(64, 288)(65, 326)(66, 285)(67, 328)(68, 330)(69, 287)(70, 331)(71, 290)(72, 334)(73, 292)(74, 319)(75, 321)(76, 295)(77, 338)(78, 296)(79, 314)(80, 300)(81, 315)(82, 342)(83, 302)(84, 344)(85, 345)(86, 305)(87, 332)(88, 307)(89, 339)(90, 308)(91, 310)(92, 327)(93, 348)(94, 312)(95, 349)(96, 350)(97, 351)(98, 317)(99, 329)(100, 354)(101, 355)(102, 322)(103, 356)(104, 324)(105, 325)(106, 352)(107, 359)(108, 333)(109, 335)(110, 336)(111, 337)(112, 346)(113, 357)(114, 340)(115, 341)(116, 343)(117, 353)(118, 360)(119, 347)(120, 358)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.1177 Graph:: simple bipartite v = 120 e = 240 f = 90 degree seq :: [ 4^120 ] E16.1177 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, Y2 * Y1^-2 * Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y1^-2, (Y2 * Y1)^5, (Y2 * Y1 * Y2 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 121, 2, 122, 6, 126, 5, 125)(3, 123, 9, 129, 19, 139, 11, 131)(4, 124, 12, 132, 15, 135, 8, 128)(7, 127, 16, 136, 30, 150, 18, 138)(10, 130, 22, 142, 36, 156, 21, 141)(13, 133, 25, 145, 45, 165, 26, 146)(14, 134, 27, 147, 48, 168, 29, 149)(17, 137, 33, 153, 54, 174, 32, 152)(20, 140, 37, 157, 61, 181, 39, 159)(23, 143, 41, 161, 68, 188, 42, 162)(24, 144, 43, 163, 53, 173, 44, 164)(28, 148, 51, 171, 35, 155, 50, 170)(31, 151, 55, 175, 81, 201, 57, 177)(34, 154, 59, 179, 87, 207, 60, 180)(38, 158, 64, 184, 90, 210, 63, 183)(40, 160, 66, 186, 89, 209, 67, 187)(46, 166, 72, 192, 101, 221, 73, 193)(47, 167, 74, 194, 92, 212, 62, 182)(49, 169, 75, 195, 103, 223, 77, 197)(52, 172, 79, 199, 109, 229, 80, 200)(56, 176, 83, 203, 112, 232, 82, 202)(58, 178, 85, 205, 111, 231, 86, 206)(65, 185, 88, 208, 116, 236, 94, 214)(69, 189, 96, 216, 113, 233, 97, 217)(70, 190, 91, 211, 117, 237, 98, 218)(71, 191, 99, 219, 118, 238, 100, 220)(76, 196, 105, 225, 120, 240, 104, 224)(78, 198, 107, 227, 119, 239, 108, 228)(84, 204, 110, 230, 95, 215, 114, 234)(93, 213, 106, 226, 102, 222, 115, 235)(241, 361, 243, 363)(242, 362, 247, 367)(244, 364, 250, 370)(245, 365, 253, 373)(246, 366, 254, 374)(248, 368, 257, 377)(249, 369, 260, 380)(251, 371, 263, 383)(252, 372, 264, 384)(255, 375, 268, 388)(256, 376, 271, 391)(258, 378, 274, 394)(259, 379, 275, 395)(261, 381, 278, 398)(262, 382, 280, 400)(265, 385, 286, 406)(266, 386, 287, 407)(267, 387, 289, 409)(269, 389, 292, 412)(270, 390, 293, 413)(272, 392, 296, 416)(273, 393, 298, 418)(276, 396, 288, 408)(277, 397, 302, 422)(279, 399, 305, 425)(281, 401, 309, 429)(282, 402, 295, 415)(283, 403, 310, 430)(284, 404, 311, 431)(285, 405, 294, 414)(290, 410, 316, 436)(291, 411, 318, 438)(297, 417, 324, 444)(299, 419, 328, 448)(300, 420, 315, 435)(301, 421, 329, 449)(303, 423, 331, 451)(304, 424, 333, 453)(306, 426, 322, 442)(307, 427, 335, 455)(308, 428, 330, 450)(312, 432, 320, 440)(313, 433, 337, 457)(314, 434, 342, 462)(317, 437, 346, 466)(319, 439, 350, 470)(321, 441, 351, 471)(323, 443, 353, 473)(325, 445, 344, 464)(326, 446, 355, 475)(327, 447, 352, 472)(332, 452, 358, 478)(334, 454, 345, 465)(336, 456, 348, 468)(338, 458, 356, 476)(339, 459, 354, 474)(340, 460, 347, 467)(341, 461, 357, 477)(343, 463, 359, 479)(349, 469, 360, 480) L = (1, 244)(2, 248)(3, 250)(4, 241)(5, 252)(6, 255)(7, 257)(8, 242)(9, 261)(10, 243)(11, 262)(12, 245)(13, 264)(14, 268)(15, 246)(16, 272)(17, 247)(18, 273)(19, 276)(20, 278)(21, 249)(22, 251)(23, 280)(24, 253)(25, 284)(26, 283)(27, 290)(28, 254)(29, 291)(30, 294)(31, 296)(32, 256)(33, 258)(34, 298)(35, 288)(36, 259)(37, 303)(38, 260)(39, 304)(40, 263)(41, 307)(42, 306)(43, 266)(44, 265)(45, 293)(46, 311)(47, 310)(48, 275)(49, 316)(50, 267)(51, 269)(52, 318)(53, 285)(54, 270)(55, 322)(56, 271)(57, 323)(58, 274)(59, 326)(60, 325)(61, 330)(62, 331)(63, 277)(64, 279)(65, 333)(66, 282)(67, 281)(68, 329)(69, 335)(70, 287)(71, 286)(72, 340)(73, 339)(74, 338)(75, 344)(76, 289)(77, 345)(78, 292)(79, 348)(80, 347)(81, 352)(82, 295)(83, 297)(84, 353)(85, 300)(86, 299)(87, 351)(88, 355)(89, 308)(90, 301)(91, 302)(92, 357)(93, 305)(94, 346)(95, 309)(96, 350)(97, 354)(98, 314)(99, 313)(100, 312)(101, 358)(102, 356)(103, 360)(104, 315)(105, 317)(106, 334)(107, 320)(108, 319)(109, 359)(110, 336)(111, 327)(112, 321)(113, 324)(114, 337)(115, 328)(116, 342)(117, 332)(118, 341)(119, 349)(120, 343)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.1176 Graph:: simple bipartite v = 90 e = 240 f = 120 degree seq :: [ 4^60, 8^30 ] E16.1178 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1^-1 * Y3)^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, Y1 * Y2 * Y1^-2 * Y2 * Y1^-2 * Y2 * Y1, Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1, (Y2 * Y1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 121, 2, 122, 6, 126, 5, 125)(3, 123, 9, 129, 19, 139, 11, 131)(4, 124, 12, 132, 15, 135, 8, 128)(7, 127, 16, 136, 30, 150, 18, 138)(10, 130, 22, 142, 36, 156, 21, 141)(13, 133, 25, 145, 45, 165, 26, 146)(14, 134, 27, 147, 35, 155, 29, 149)(17, 137, 33, 153, 52, 172, 32, 152)(20, 140, 37, 157, 60, 180, 39, 159)(23, 143, 41, 161, 67, 187, 42, 162)(24, 144, 43, 163, 70, 190, 44, 164)(28, 148, 50, 170, 59, 179, 49, 169)(31, 151, 53, 173, 83, 203, 55, 175)(34, 154, 57, 177, 89, 209, 58, 178)(38, 158, 63, 183, 91, 211, 62, 182)(40, 160, 65, 185, 96, 216, 66, 186)(46, 166, 73, 193, 103, 223, 74, 194)(47, 167, 75, 195, 105, 225, 76, 196)(48, 168, 77, 197, 107, 227, 79, 199)(51, 171, 81, 201, 111, 231, 82, 202)(54, 174, 86, 206, 113, 233, 85, 205)(56, 176, 88, 208, 95, 215, 64, 184)(61, 181, 92, 212, 117, 237, 94, 214)(68, 188, 98, 218, 102, 222, 72, 192)(69, 189, 99, 219, 115, 235, 84, 204)(71, 191, 100, 220, 119, 239, 101, 221)(78, 198, 106, 226, 120, 240, 109, 229)(80, 200, 110, 230, 116, 236, 87, 207)(90, 210, 118, 238, 93, 213, 108, 228)(97, 217, 114, 234, 104, 224, 112, 232)(241, 361, 243, 363)(242, 362, 247, 367)(244, 364, 250, 370)(245, 365, 253, 373)(246, 366, 254, 374)(248, 368, 257, 377)(249, 369, 260, 380)(251, 371, 263, 383)(252, 372, 264, 384)(255, 375, 268, 388)(256, 376, 271, 391)(258, 378, 274, 394)(259, 379, 275, 395)(261, 381, 278, 398)(262, 382, 280, 400)(265, 385, 286, 406)(266, 386, 287, 407)(267, 387, 288, 408)(269, 389, 291, 411)(270, 390, 285, 405)(272, 392, 294, 414)(273, 393, 296, 416)(276, 396, 299, 419)(277, 397, 301, 421)(279, 399, 304, 424)(281, 401, 308, 428)(282, 402, 309, 429)(283, 403, 311, 431)(284, 404, 312, 432)(289, 409, 318, 438)(290, 410, 320, 440)(292, 412, 310, 430)(293, 413, 324, 444)(295, 415, 327, 447)(297, 417, 303, 423)(298, 418, 330, 450)(300, 420, 307, 427)(302, 422, 333, 453)(305, 425, 337, 457)(306, 426, 314, 434)(313, 433, 344, 464)(315, 435, 346, 466)(316, 436, 332, 452)(317, 437, 348, 468)(319, 439, 341, 461)(321, 441, 326, 446)(322, 442, 352, 472)(323, 443, 329, 449)(325, 445, 354, 474)(328, 448, 357, 477)(331, 451, 336, 456)(334, 454, 349, 469)(335, 455, 353, 473)(338, 458, 359, 479)(339, 459, 350, 470)(340, 460, 358, 478)(342, 462, 355, 475)(343, 463, 345, 465)(347, 467, 351, 471)(356, 476, 360, 480) L = (1, 244)(2, 248)(3, 250)(4, 241)(5, 252)(6, 255)(7, 257)(8, 242)(9, 261)(10, 243)(11, 262)(12, 245)(13, 264)(14, 268)(15, 246)(16, 272)(17, 247)(18, 273)(19, 276)(20, 278)(21, 249)(22, 251)(23, 280)(24, 253)(25, 284)(26, 283)(27, 289)(28, 254)(29, 290)(30, 292)(31, 294)(32, 256)(33, 258)(34, 296)(35, 299)(36, 259)(37, 302)(38, 260)(39, 303)(40, 263)(41, 306)(42, 305)(43, 266)(44, 265)(45, 310)(46, 312)(47, 311)(48, 318)(49, 267)(50, 269)(51, 320)(52, 270)(53, 325)(54, 271)(55, 326)(56, 274)(57, 304)(58, 328)(59, 275)(60, 331)(61, 333)(62, 277)(63, 279)(64, 297)(65, 282)(66, 281)(67, 336)(68, 314)(69, 337)(70, 285)(71, 287)(72, 286)(73, 342)(74, 308)(75, 341)(76, 340)(77, 349)(78, 288)(79, 346)(80, 291)(81, 327)(82, 350)(83, 353)(84, 354)(85, 293)(86, 295)(87, 321)(88, 298)(89, 335)(90, 357)(91, 300)(92, 358)(93, 301)(94, 348)(95, 329)(96, 307)(97, 309)(98, 343)(99, 352)(100, 316)(101, 315)(102, 313)(103, 338)(104, 355)(105, 359)(106, 319)(107, 360)(108, 334)(109, 317)(110, 322)(111, 356)(112, 339)(113, 323)(114, 324)(115, 344)(116, 351)(117, 330)(118, 332)(119, 345)(120, 347)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.1174 Graph:: simple bipartite v = 90 e = 240 f = 120 degree seq :: [ 4^60, 8^30 ] E16.1179 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, Y1^4, (R * Y3)^2, (Y1 * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2 * Y1^-1 * Y2 * Y1, (Y1 * Y2 * Y1 * Y3)^2, Y3 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y3^-1 * Y1 * Y2 ] Map:: polyhedral non-degenerate R = (1, 121, 2, 122, 7, 127, 5, 125)(3, 123, 11, 131, 29, 149, 13, 133)(4, 124, 15, 135, 38, 158, 16, 136)(6, 126, 19, 139, 27, 147, 9, 129)(8, 128, 23, 143, 30, 150, 25, 145)(10, 130, 28, 148, 50, 170, 21, 141)(12, 132, 33, 153, 68, 188, 34, 154)(14, 134, 37, 157, 66, 186, 31, 151)(17, 137, 42, 162, 82, 202, 43, 163)(18, 138, 22, 142, 51, 171, 45, 165)(20, 140, 47, 167, 52, 172, 35, 155)(24, 144, 55, 175, 100, 220, 56, 176)(26, 146, 58, 178, 98, 218, 53, 173)(32, 152, 67, 187, 108, 228, 62, 182)(36, 156, 63, 183, 96, 216, 73, 193)(39, 159, 77, 197, 74, 194, 78, 198)(40, 160, 79, 199, 114, 234, 80, 200)(41, 161, 76, 196, 95, 215, 60, 180)(44, 164, 86, 206, 117, 237, 83, 203)(46, 166, 88, 208, 69, 189, 89, 209)(48, 168, 72, 192, 113, 233, 92, 212)(49, 169, 93, 213, 115, 235, 90, 210)(54, 174, 99, 219, 109, 229, 64, 184)(57, 177, 65, 185, 75, 195, 103, 223)(59, 179, 104, 224, 112, 232, 70, 190)(61, 181, 106, 226, 85, 205, 107, 227)(71, 191, 101, 221, 94, 214, 110, 230)(81, 201, 97, 217, 91, 211, 111, 231)(84, 204, 118, 238, 105, 225, 116, 236)(87, 207, 119, 239, 102, 222, 120, 240)(241, 361, 243, 363)(242, 362, 248, 368)(244, 364, 254, 374)(245, 365, 257, 377)(246, 366, 252, 372)(247, 367, 260, 380)(249, 369, 266, 386)(250, 370, 264, 384)(251, 371, 270, 390)(253, 373, 275, 395)(255, 375, 279, 399)(256, 376, 280, 400)(258, 378, 284, 404)(259, 379, 286, 406)(261, 381, 289, 409)(262, 382, 288, 408)(263, 383, 292, 412)(265, 385, 283, 403)(267, 387, 299, 419)(268, 388, 301, 421)(269, 389, 282, 402)(271, 391, 305, 425)(272, 392, 304, 424)(273, 393, 309, 429)(274, 394, 310, 430)(276, 396, 312, 432)(277, 397, 314, 434)(278, 398, 315, 435)(281, 401, 321, 441)(285, 405, 327, 447)(287, 407, 322, 442)(290, 410, 334, 454)(291, 411, 336, 456)(293, 413, 329, 449)(294, 414, 337, 457)(295, 415, 325, 445)(296, 416, 341, 461)(297, 417, 317, 437)(298, 418, 308, 428)(300, 420, 345, 465)(302, 422, 324, 444)(303, 423, 323, 443)(306, 426, 319, 439)(307, 427, 351, 471)(311, 431, 346, 466)(313, 433, 342, 462)(316, 436, 349, 469)(318, 438, 320, 440)(326, 446, 353, 473)(328, 448, 352, 472)(330, 450, 347, 467)(331, 451, 356, 476)(332, 452, 360, 480)(333, 453, 340, 460)(335, 455, 348, 468)(338, 458, 344, 464)(339, 459, 358, 478)(343, 463, 354, 474)(350, 470, 355, 475)(357, 477, 359, 479) L = (1, 244)(2, 249)(3, 252)(4, 246)(5, 258)(6, 241)(7, 261)(8, 264)(9, 250)(10, 242)(11, 271)(12, 254)(13, 276)(14, 243)(15, 245)(16, 281)(17, 279)(18, 255)(19, 256)(20, 288)(21, 262)(22, 247)(23, 293)(24, 266)(25, 297)(26, 248)(27, 300)(28, 267)(29, 302)(30, 304)(31, 272)(32, 251)(33, 253)(34, 311)(35, 309)(36, 273)(37, 274)(38, 285)(39, 284)(40, 286)(41, 259)(42, 323)(43, 325)(44, 257)(45, 316)(46, 321)(47, 330)(48, 289)(49, 260)(50, 335)(51, 290)(52, 337)(53, 294)(54, 263)(55, 265)(56, 342)(57, 295)(58, 296)(59, 301)(60, 268)(61, 345)(62, 303)(63, 269)(64, 305)(65, 270)(66, 350)(67, 306)(68, 313)(69, 312)(70, 314)(71, 277)(72, 275)(73, 341)(74, 346)(75, 349)(76, 278)(77, 283)(78, 352)(79, 351)(80, 353)(81, 280)(82, 356)(83, 324)(84, 282)(85, 317)(86, 318)(87, 315)(88, 320)(89, 292)(90, 331)(91, 287)(92, 354)(93, 332)(94, 336)(95, 291)(96, 348)(97, 329)(98, 359)(99, 338)(100, 343)(101, 308)(102, 298)(103, 360)(104, 358)(105, 299)(106, 310)(107, 322)(108, 334)(109, 327)(110, 307)(111, 355)(112, 326)(113, 328)(114, 333)(115, 319)(116, 347)(117, 344)(118, 357)(119, 339)(120, 340)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.1175 Graph:: simple bipartite v = 90 e = 240 f = 120 degree seq :: [ 4^60, 8^30 ] E16.1180 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = D10 x S4 (small group id <240, 194>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y3)^3, Y2 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1, Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1, (Y1 * Y2 * Y3)^4 ] Map:: polytopal non-degenerate R = (1, 122, 2, 121)(3, 127, 7, 123)(4, 129, 9, 124)(5, 131, 11, 125)(6, 133, 13, 126)(8, 137, 17, 128)(10, 141, 21, 130)(12, 144, 24, 132)(14, 148, 28, 134)(15, 149, 29, 135)(16, 151, 31, 136)(18, 155, 35, 138)(19, 156, 36, 139)(20, 158, 38, 140)(22, 162, 42, 142)(23, 164, 44, 143)(25, 168, 48, 145)(26, 169, 49, 146)(27, 171, 51, 147)(30, 167, 47, 150)(32, 180, 60, 152)(33, 181, 61, 153)(34, 163, 43, 154)(37, 188, 68, 157)(39, 173, 53, 159)(40, 172, 52, 160)(41, 192, 72, 161)(45, 199, 79, 165)(46, 200, 80, 166)(50, 207, 87, 170)(54, 211, 91, 174)(55, 213, 93, 175)(56, 208, 88, 176)(57, 209, 89, 177)(58, 215, 95, 178)(59, 203, 83, 179)(62, 212, 92, 182)(63, 216, 96, 183)(64, 198, 78, 184)(65, 205, 85, 185)(66, 204, 84, 186)(67, 219, 99, 187)(69, 195, 75, 189)(70, 196, 76, 190)(71, 223, 103, 191)(73, 201, 81, 193)(74, 225, 105, 194)(77, 227, 107, 197)(82, 228, 108, 202)(86, 231, 111, 206)(90, 235, 115, 210)(94, 230, 110, 214)(97, 229, 109, 217)(98, 226, 106, 218)(100, 234, 114, 220)(101, 236, 116, 221)(102, 232, 112, 222)(104, 233, 113, 224)(117, 240, 120, 237)(118, 239, 119, 238) L = (1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 18)(9, 19)(11, 22)(12, 25)(13, 26)(16, 32)(17, 33)(20, 39)(21, 40)(23, 45)(24, 46)(27, 52)(28, 53)(29, 55)(30, 57)(31, 58)(34, 63)(35, 64)(36, 66)(37, 69)(38, 70)(41, 73)(42, 74)(43, 76)(44, 77)(47, 82)(48, 83)(49, 85)(50, 88)(51, 89)(54, 92)(56, 94)(59, 78)(60, 96)(61, 98)(62, 100)(65, 102)(67, 86)(68, 97)(71, 104)(72, 95)(75, 106)(79, 108)(80, 110)(81, 112)(84, 114)(87, 109)(90, 116)(91, 107)(93, 113)(99, 117)(101, 105)(103, 118)(111, 119)(115, 120)(121, 124)(122, 126)(123, 128)(125, 132)(127, 136)(129, 140)(130, 138)(131, 143)(133, 147)(134, 145)(135, 150)(137, 154)(139, 157)(141, 161)(142, 163)(144, 167)(146, 170)(148, 174)(149, 176)(151, 179)(152, 177)(153, 182)(155, 185)(156, 187)(158, 175)(159, 189)(160, 191)(162, 195)(164, 198)(165, 196)(166, 201)(168, 204)(169, 206)(171, 194)(172, 208)(173, 210)(178, 197)(180, 217)(181, 219)(183, 220)(184, 221)(186, 205)(188, 223)(190, 214)(192, 218)(193, 224)(199, 229)(200, 231)(202, 232)(203, 233)(207, 235)(209, 226)(211, 230)(212, 236)(213, 234)(215, 237)(216, 238)(222, 225)(227, 239)(228, 240) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E16.1182 Transitivity :: VT+ AT Graph:: simple v = 60 e = 120 f = 30 degree seq :: [ 4^60 ] E16.1181 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = C2 x ((C5 x A4) : C2) (small group id <240, 197>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (Y3 * Y2)^2, (R * Y1)^2, R * Y3 * R * Y2, Y3 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y2, (Y2 * Y1)^15 ] Map:: polytopal non-degenerate R = (1, 122, 2, 121)(3, 127, 7, 123)(4, 129, 9, 124)(5, 130, 10, 125)(6, 132, 12, 126)(8, 135, 15, 128)(11, 140, 20, 131)(13, 143, 23, 133)(14, 145, 25, 134)(16, 148, 28, 136)(17, 150, 30, 137)(18, 151, 31, 138)(19, 153, 33, 139)(21, 156, 36, 141)(22, 158, 38, 142)(24, 155, 35, 144)(26, 157, 37, 146)(27, 152, 32, 147)(29, 154, 34, 149)(39, 169, 49, 159)(40, 170, 50, 160)(41, 171, 51, 161)(42, 172, 52, 162)(43, 168, 48, 163)(44, 173, 53, 164)(45, 174, 54, 165)(46, 175, 55, 166)(47, 176, 56, 167)(57, 185, 65, 177)(58, 186, 66, 178)(59, 187, 67, 179)(60, 188, 68, 180)(61, 189, 69, 181)(62, 190, 70, 182)(63, 191, 71, 183)(64, 192, 72, 184)(73, 201, 81, 193)(74, 202, 82, 194)(75, 203, 83, 195)(76, 204, 84, 196)(77, 205, 85, 197)(78, 206, 86, 198)(79, 207, 87, 199)(80, 208, 88, 200)(89, 217, 97, 209)(90, 218, 98, 210)(91, 219, 99, 211)(92, 220, 100, 212)(93, 221, 101, 213)(94, 222, 102, 214)(95, 223, 103, 215)(96, 224, 104, 216)(105, 233, 113, 225)(106, 234, 114, 226)(107, 235, 115, 227)(108, 236, 116, 228)(109, 237, 117, 229)(110, 238, 118, 230)(111, 239, 119, 231)(112, 240, 120, 232) 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, 57)(50, 59)(51, 60)(52, 58)(53, 61)(54, 63)(55, 64)(56, 62)(65, 73)(66, 75)(67, 76)(68, 74)(69, 77)(70, 79)(71, 80)(72, 78)(81, 89)(82, 91)(83, 92)(84, 90)(85, 93)(86, 95)(87, 96)(88, 94)(97, 105)(98, 107)(99, 108)(100, 106)(101, 109)(102, 111)(103, 112)(104, 110)(113, 117)(114, 119)(115, 118)(116, 120)(121, 124)(122, 126)(123, 128)(125, 131)(127, 134)(129, 137)(130, 139)(132, 142)(133, 144)(135, 147)(136, 149)(138, 152)(140, 155)(141, 157)(143, 160)(145, 162)(146, 163)(148, 161)(150, 159)(151, 165)(153, 167)(154, 168)(156, 166)(158, 164)(169, 178)(170, 180)(171, 179)(172, 177)(173, 182)(174, 184)(175, 183)(176, 181)(185, 194)(186, 196)(187, 195)(188, 193)(189, 198)(190, 200)(191, 199)(192, 197)(201, 210)(202, 212)(203, 211)(204, 209)(205, 214)(206, 216)(207, 215)(208, 213)(217, 226)(218, 228)(219, 227)(220, 225)(221, 230)(222, 232)(223, 231)(224, 229)(233, 240)(234, 238)(235, 239)(236, 237) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E16.1183 Transitivity :: VT+ AT Graph:: simple v = 60 e = 120 f = 30 degree seq :: [ 4^60 ] E16.1182 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = D10 x S4 (small group id <240, 194>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^4, Y1^4, R * Y3 * R * Y2, Y1^4, (R * Y1)^2, (Y3 * Y1^-1 * Y2)^2, (Y3 * Y2)^3, Y1 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y1, Y3 * Y1^-1 * Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1, Y2 * Y3 * Y1^2 * Y3 * Y1^-2 * Y2 * Y1^-2, (Y2 * Y1^-2 * Y2 * Y1^-1)^2, (Y3 * Y2 * Y3 * Y1^-2)^2, Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 122, 2, 126, 6, 125, 5, 121)(3, 129, 9, 145, 25, 131, 11, 123)(4, 132, 12, 152, 32, 134, 14, 124)(7, 139, 19, 169, 49, 141, 21, 127)(8, 142, 22, 176, 56, 144, 24, 128)(10, 148, 28, 179, 59, 143, 23, 130)(13, 155, 35, 199, 79, 156, 36, 133)(15, 158, 38, 203, 83, 159, 39, 135)(16, 160, 40, 188, 68, 162, 42, 136)(17, 163, 43, 209, 89, 165, 45, 137)(18, 166, 46, 215, 95, 168, 48, 138)(20, 172, 52, 217, 97, 167, 47, 140)(26, 183, 63, 214, 94, 185, 65, 146)(27, 186, 66, 211, 91, 187, 67, 147)(29, 190, 70, 213, 93, 191, 71, 149)(30, 192, 72, 210, 90, 193, 73, 150)(31, 194, 74, 153, 33, 195, 75, 151)(34, 197, 77, 218, 98, 198, 78, 154)(37, 201, 81, 216, 96, 202, 82, 157)(41, 164, 44, 212, 92, 182, 62, 161)(50, 220, 100, 206, 86, 222, 102, 170)(51, 223, 103, 205, 85, 224, 104, 171)(53, 226, 106, 200, 80, 227, 107, 173)(54, 228, 108, 204, 84, 229, 109, 174)(55, 230, 110, 177, 57, 231, 111, 175)(58, 233, 113, 208, 88, 234, 114, 178)(60, 235, 115, 207, 87, 236, 116, 180)(61, 232, 112, 196, 76, 219, 99, 181)(64, 225, 105, 239, 119, 237, 117, 184)(69, 221, 101, 240, 120, 238, 118, 189) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 17)(8, 23)(9, 26)(10, 29)(11, 30)(12, 33)(14, 27)(16, 41)(18, 47)(19, 50)(20, 53)(21, 54)(22, 57)(24, 51)(25, 61)(28, 68)(31, 46)(32, 52)(34, 71)(35, 80)(36, 69)(37, 64)(38, 84)(39, 86)(40, 55)(42, 85)(43, 90)(44, 93)(45, 94)(48, 91)(49, 99)(56, 92)(58, 107)(59, 105)(60, 101)(62, 117)(63, 111)(65, 104)(66, 102)(67, 108)(70, 96)(72, 103)(73, 110)(74, 100)(75, 109)(76, 89)(77, 114)(78, 116)(79, 95)(81, 113)(82, 115)(83, 112)(87, 106)(88, 118)(97, 120)(98, 119)(121, 124)(122, 128)(123, 130)(125, 136)(126, 138)(127, 140)(129, 147)(131, 151)(132, 154)(133, 149)(134, 157)(135, 155)(137, 164)(139, 171)(141, 175)(142, 178)(143, 173)(144, 180)(145, 182)(146, 184)(148, 189)(150, 190)(152, 196)(153, 165)(156, 169)(158, 205)(159, 177)(160, 207)(161, 200)(162, 208)(163, 211)(166, 216)(167, 213)(168, 218)(170, 221)(172, 225)(174, 226)(176, 232)(179, 209)(181, 215)(183, 228)(185, 220)(186, 235)(187, 234)(188, 219)(191, 214)(192, 229)(193, 222)(194, 233)(195, 236)(197, 231)(198, 223)(199, 237)(201, 224)(202, 230)(203, 217)(204, 238)(206, 227)(210, 239)(212, 240) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.1180 Transitivity :: VT+ AT Graph:: simple v = 30 e = 120 f = 60 degree seq :: [ 8^30 ] E16.1183 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = C2 x ((C5 x A4) : C2) (small group id <240, 197>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y3)^2, R * Y3 * R * Y2, (R * Y1)^2, Y1^4, (Y2 * Y1^-1 * Y3)^2, Y1^-1 * Y3 * Y1^-2 * Y2 * Y1^-1, Y2 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 122, 2, 126, 6, 125, 5, 121)(3, 129, 9, 137, 17, 131, 11, 123)(4, 132, 12, 136, 16, 133, 13, 124)(7, 138, 18, 135, 15, 140, 20, 127)(8, 141, 21, 134, 14, 142, 22, 128)(10, 145, 25, 148, 28, 139, 19, 130)(23, 153, 33, 147, 27, 154, 34, 143)(24, 155, 35, 146, 26, 156, 36, 144)(29, 157, 37, 152, 32, 158, 38, 149)(30, 159, 39, 151, 31, 160, 40, 150)(41, 169, 49, 164, 44, 170, 50, 161)(42, 171, 51, 163, 43, 172, 52, 162)(45, 173, 53, 168, 48, 174, 54, 165)(46, 175, 55, 167, 47, 176, 56, 166)(57, 185, 65, 180, 60, 186, 66, 177)(58, 187, 67, 179, 59, 188, 68, 178)(61, 189, 69, 184, 64, 190, 70, 181)(62, 191, 71, 183, 63, 192, 72, 182)(73, 201, 81, 196, 76, 202, 82, 193)(74, 203, 83, 195, 75, 204, 84, 194)(77, 205, 85, 200, 80, 206, 86, 197)(78, 207, 87, 199, 79, 208, 88, 198)(89, 217, 97, 212, 92, 218, 98, 209)(90, 219, 99, 211, 91, 220, 100, 210)(93, 221, 101, 216, 96, 222, 102, 213)(94, 223, 103, 215, 95, 224, 104, 214)(105, 233, 113, 228, 108, 234, 114, 225)(106, 235, 115, 227, 107, 236, 116, 226)(109, 237, 117, 232, 112, 238, 118, 229)(110, 239, 119, 231, 111, 240, 120, 230) 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, 57)(50, 59)(51, 60)(52, 58)(53, 61)(54, 63)(55, 64)(56, 62)(65, 73)(66, 75)(67, 76)(68, 74)(69, 77)(70, 79)(71, 80)(72, 78)(81, 89)(82, 91)(83, 92)(84, 90)(85, 93)(86, 95)(87, 96)(88, 94)(97, 105)(98, 107)(99, 108)(100, 106)(101, 109)(102, 111)(103, 112)(104, 110)(113, 119)(114, 117)(115, 120)(116, 118)(121, 124)(122, 128)(123, 130)(125, 135)(126, 137)(127, 139)(129, 144)(131, 147)(132, 146)(133, 143)(134, 145)(136, 148)(138, 150)(140, 152)(141, 151)(142, 149)(153, 162)(154, 164)(155, 163)(156, 161)(157, 166)(158, 168)(159, 167)(160, 165)(169, 178)(170, 180)(171, 179)(172, 177)(173, 182)(174, 184)(175, 183)(176, 181)(185, 194)(186, 196)(187, 195)(188, 193)(189, 198)(190, 200)(191, 199)(192, 197)(201, 210)(202, 212)(203, 211)(204, 209)(205, 214)(206, 216)(207, 215)(208, 213)(217, 226)(218, 228)(219, 227)(220, 225)(221, 230)(222, 232)(223, 231)(224, 229)(233, 238)(234, 240)(235, 237)(236, 239) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.1181 Transitivity :: VT+ AT Graph:: v = 30 e = 120 f = 60 degree seq :: [ 8^30 ] E16.1184 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = D10 x S4 (small group id <240, 194>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y1 * Y2)^3, Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y1, Y1 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2, (Y1 * Y3 * Y2)^4 ] Map:: polytopal R = (1, 121, 4, 124)(2, 122, 6, 126)(3, 123, 8, 128)(5, 125, 12, 132)(7, 127, 15, 135)(9, 129, 19, 139)(10, 130, 21, 141)(11, 131, 22, 142)(13, 133, 26, 146)(14, 134, 28, 148)(16, 136, 32, 152)(17, 137, 34, 154)(18, 138, 36, 156)(20, 140, 39, 159)(23, 143, 45, 165)(24, 144, 47, 167)(25, 145, 49, 169)(27, 147, 52, 172)(29, 149, 56, 176)(30, 150, 58, 178)(31, 151, 60, 180)(33, 153, 63, 183)(35, 155, 65, 185)(37, 157, 67, 187)(38, 158, 69, 189)(40, 160, 72, 192)(41, 161, 73, 193)(42, 162, 75, 195)(43, 163, 77, 197)(44, 164, 79, 199)(46, 166, 82, 202)(48, 168, 84, 204)(50, 170, 86, 206)(51, 171, 88, 208)(53, 173, 91, 211)(54, 174, 92, 212)(55, 175, 94, 214)(57, 177, 95, 215)(59, 179, 96, 216)(61, 181, 97, 217)(62, 182, 81, 201)(64, 184, 83, 203)(66, 186, 100, 220)(68, 188, 102, 222)(70, 190, 103, 223)(71, 191, 104, 224)(74, 194, 106, 226)(76, 196, 107, 227)(78, 198, 108, 228)(80, 200, 109, 229)(85, 205, 112, 232)(87, 207, 114, 234)(89, 209, 115, 235)(90, 210, 116, 236)(93, 213, 113, 233)(98, 218, 117, 237)(99, 219, 118, 238)(101, 221, 105, 225)(110, 230, 119, 239)(111, 231, 120, 240)(241, 242)(243, 247)(244, 249)(245, 251)(246, 253)(248, 256)(250, 260)(252, 263)(254, 267)(255, 269)(257, 273)(258, 275)(259, 277)(261, 280)(262, 282)(264, 286)(265, 288)(266, 290)(268, 293)(270, 297)(271, 299)(272, 301)(274, 304)(276, 306)(278, 308)(279, 303)(281, 296)(283, 316)(284, 318)(285, 320)(287, 323)(289, 325)(291, 327)(292, 322)(294, 315)(295, 333)(298, 331)(300, 329)(302, 338)(305, 332)(307, 341)(309, 330)(310, 319)(311, 328)(312, 317)(313, 324)(314, 345)(321, 350)(326, 353)(334, 351)(335, 347)(336, 349)(337, 348)(339, 346)(340, 354)(342, 352)(343, 356)(344, 355)(357, 360)(358, 359)(361, 363)(362, 365)(364, 370)(366, 374)(367, 371)(368, 377)(369, 378)(372, 384)(373, 385)(375, 390)(376, 391)(379, 398)(380, 395)(381, 401)(382, 403)(383, 404)(386, 411)(387, 408)(388, 414)(389, 415)(392, 422)(393, 419)(394, 410)(396, 409)(397, 407)(399, 430)(400, 431)(402, 434)(405, 441)(406, 438)(412, 449)(413, 450)(416, 448)(417, 453)(418, 440)(420, 454)(421, 437)(423, 459)(424, 447)(425, 457)(426, 455)(427, 456)(428, 443)(429, 435)(432, 458)(433, 461)(436, 465)(439, 466)(442, 471)(444, 469)(445, 467)(446, 468)(451, 470)(452, 473)(460, 477)(462, 475)(463, 474)(464, 478)(472, 479)(476, 480) L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 16, 16 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E16.1190 Graph:: simple bipartite v = 180 e = 240 f = 30 degree seq :: [ 2^120, 4^60 ] E16.1185 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = C2 x ((C5 x A4) : C2) (small group id <240, 197>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (Y2 * Y1)^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y3 * Y1, (Y3 * Y1)^15 ] Map:: polytopal R = (1, 121, 4, 124)(2, 122, 6, 126)(3, 123, 7, 127)(5, 125, 10, 130)(8, 128, 16, 136)(9, 129, 17, 137)(11, 131, 21, 141)(12, 132, 22, 142)(13, 133, 24, 144)(14, 134, 25, 145)(15, 135, 26, 146)(18, 138, 32, 152)(19, 139, 33, 153)(20, 140, 34, 154)(23, 143, 39, 159)(27, 147, 40, 160)(28, 148, 41, 161)(29, 149, 42, 162)(30, 150, 43, 163)(31, 151, 44, 164)(35, 155, 45, 165)(36, 156, 46, 166)(37, 157, 47, 167)(38, 158, 48, 168)(49, 169, 57, 177)(50, 170, 58, 178)(51, 171, 59, 179)(52, 172, 60, 180)(53, 173, 61, 181)(54, 174, 62, 182)(55, 175, 63, 183)(56, 176, 64, 184)(65, 185, 73, 193)(66, 186, 74, 194)(67, 187, 75, 195)(68, 188, 76, 196)(69, 189, 77, 197)(70, 190, 78, 198)(71, 191, 79, 199)(72, 192, 80, 200)(81, 201, 89, 209)(82, 202, 90, 210)(83, 203, 91, 211)(84, 204, 92, 212)(85, 205, 93, 213)(86, 206, 94, 214)(87, 207, 95, 215)(88, 208, 96, 216)(97, 217, 105, 225)(98, 218, 106, 226)(99, 219, 107, 227)(100, 220, 108, 228)(101, 221, 109, 229)(102, 222, 110, 230)(103, 223, 111, 231)(104, 224, 112, 232)(113, 233, 117, 237)(114, 234, 120, 240)(115, 235, 119, 239)(116, 236, 118, 238)(241, 242)(243, 245)(244, 248)(246, 251)(247, 253)(249, 255)(250, 258)(252, 260)(254, 263)(256, 267)(257, 269)(259, 271)(261, 275)(262, 277)(264, 278)(265, 276)(266, 279)(268, 273)(270, 272)(274, 284)(280, 289)(281, 291)(282, 292)(283, 290)(285, 293)(286, 295)(287, 296)(288, 294)(297, 305)(298, 307)(299, 308)(300, 306)(301, 309)(302, 311)(303, 312)(304, 310)(313, 321)(314, 323)(315, 324)(316, 322)(317, 325)(318, 327)(319, 328)(320, 326)(329, 337)(330, 339)(331, 340)(332, 338)(333, 341)(334, 343)(335, 344)(336, 342)(345, 353)(346, 355)(347, 356)(348, 354)(349, 357)(350, 359)(351, 360)(352, 358)(361, 363)(362, 365)(364, 369)(366, 372)(367, 374)(368, 375)(370, 379)(371, 380)(373, 383)(376, 388)(377, 390)(378, 391)(381, 396)(382, 398)(384, 397)(385, 395)(386, 394)(387, 393)(389, 392)(399, 404)(400, 410)(401, 412)(402, 411)(403, 409)(405, 414)(406, 416)(407, 415)(408, 413)(417, 426)(418, 428)(419, 427)(420, 425)(421, 430)(422, 432)(423, 431)(424, 429)(433, 442)(434, 444)(435, 443)(436, 441)(437, 446)(438, 448)(439, 447)(440, 445)(449, 458)(450, 460)(451, 459)(452, 457)(453, 462)(454, 464)(455, 463)(456, 461)(465, 474)(466, 476)(467, 475)(468, 473)(469, 478)(470, 480)(471, 479)(472, 477) L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 16, 16 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E16.1191 Graph:: simple bipartite v = 180 e = 240 f = 30 degree seq :: [ 2^120, 4^60 ] E16.1186 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = D10 x S4 (small group id <240, 194>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1)^3, (Y2 * Y3 * Y1)^2, Y3^-1 * Y1 * Y3^-2 * Y2 * Y3^-1 * Y1 * Y2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^-2 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3^-1 * Y1, (Y3 * Y1 * Y3^-2 * Y1)^2 ] Map:: polytopal R = (1, 121, 4, 124, 14, 134, 5, 125)(2, 122, 7, 127, 22, 142, 8, 128)(3, 123, 10, 130, 28, 148, 11, 131)(6, 126, 18, 138, 46, 166, 19, 139)(9, 129, 25, 145, 62, 182, 26, 146)(12, 132, 31, 151, 73, 193, 32, 152)(13, 133, 34, 154, 47, 167, 35, 155)(15, 135, 39, 159, 61, 181, 40, 160)(16, 136, 41, 161, 87, 207, 42, 162)(17, 137, 43, 163, 90, 210, 44, 164)(20, 140, 49, 169, 101, 221, 50, 170)(21, 141, 52, 172, 29, 149, 53, 173)(23, 143, 57, 177, 89, 209, 58, 178)(24, 144, 59, 179, 115, 235, 60, 180)(27, 147, 64, 184, 91, 211, 65, 185)(30, 150, 69, 189, 118, 238, 70, 190)(33, 153, 55, 175, 110, 230, 76, 196)(36, 156, 68, 188, 95, 215, 80, 200)(37, 157, 82, 202, 104, 224, 51, 171)(38, 158, 81, 201, 117, 237, 66, 186)(45, 165, 92, 212, 63, 183, 93, 213)(48, 168, 97, 217, 120, 240, 98, 218)(54, 174, 96, 216, 67, 187, 108, 228)(56, 176, 109, 229, 119, 239, 94, 214)(71, 191, 106, 226, 84, 204, 100, 220)(72, 192, 99, 219, 78, 198, 112, 232)(74, 194, 113, 233, 83, 203, 103, 223)(75, 195, 102, 222, 85, 205, 111, 231)(77, 197, 107, 227, 88, 208, 114, 234)(79, 199, 116, 236, 86, 206, 105, 225)(241, 242)(243, 249)(244, 252)(245, 255)(246, 257)(247, 260)(248, 263)(250, 264)(251, 269)(253, 273)(254, 276)(256, 258)(259, 287)(261, 291)(262, 294)(265, 288)(266, 303)(267, 296)(268, 306)(270, 283)(271, 311)(272, 314)(274, 315)(275, 318)(277, 321)(278, 285)(279, 323)(280, 324)(281, 325)(282, 312)(284, 331)(286, 334)(289, 339)(290, 342)(292, 343)(293, 346)(295, 349)(297, 351)(298, 352)(299, 353)(300, 340)(301, 336)(302, 344)(304, 356)(305, 347)(307, 335)(308, 329)(309, 345)(310, 354)(313, 348)(316, 330)(317, 337)(319, 333)(320, 341)(322, 355)(326, 338)(327, 350)(328, 332)(357, 360)(358, 359)(361, 363)(362, 366)(364, 373)(365, 376)(367, 381)(368, 384)(369, 377)(370, 387)(371, 390)(372, 386)(374, 397)(375, 398)(378, 405)(379, 408)(380, 404)(382, 415)(383, 416)(385, 421)(388, 427)(389, 428)(391, 432)(392, 435)(393, 423)(394, 437)(395, 439)(396, 436)(399, 438)(400, 445)(401, 446)(402, 448)(403, 449)(406, 455)(407, 456)(409, 460)(410, 463)(411, 451)(412, 465)(413, 467)(414, 464)(417, 466)(418, 473)(419, 474)(420, 476)(422, 469)(424, 459)(425, 471)(426, 454)(429, 462)(430, 472)(431, 452)(433, 477)(434, 457)(440, 475)(441, 450)(442, 478)(443, 453)(444, 458)(447, 468)(461, 479)(470, 480) L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 8, 8 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E16.1188 Graph:: simple bipartite v = 150 e = 240 f = 60 degree seq :: [ 2^120, 8^30 ] E16.1187 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = C2 x ((C5 x A4) : C2) (small group id <240, 197>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3^-2 * Y1 * Y3^-1, (Y3 * Y1 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: polytopal R = (1, 121, 4, 124, 13, 133, 5, 125)(2, 122, 7, 127, 20, 140, 8, 128)(3, 123, 9, 129, 23, 143, 10, 130)(6, 126, 16, 136, 28, 148, 17, 137)(11, 131, 24, 144, 15, 135, 25, 145)(12, 132, 26, 146, 14, 134, 27, 147)(18, 138, 29, 149, 22, 142, 30, 150)(19, 139, 31, 151, 21, 141, 32, 152)(33, 153, 41, 161, 36, 156, 42, 162)(34, 154, 43, 163, 35, 155, 44, 164)(37, 157, 45, 165, 40, 160, 46, 166)(38, 158, 47, 167, 39, 159, 48, 168)(49, 169, 57, 177, 52, 172, 58, 178)(50, 170, 59, 179, 51, 171, 60, 180)(53, 173, 61, 181, 56, 176, 62, 182)(54, 174, 63, 183, 55, 175, 64, 184)(65, 185, 73, 193, 68, 188, 74, 194)(66, 186, 75, 195, 67, 187, 76, 196)(69, 189, 77, 197, 72, 192, 78, 198)(70, 190, 79, 199, 71, 191, 80, 200)(81, 201, 89, 209, 84, 204, 90, 210)(82, 202, 91, 211, 83, 203, 92, 212)(85, 205, 93, 213, 88, 208, 94, 214)(86, 206, 95, 215, 87, 207, 96, 216)(97, 217, 105, 225, 100, 220, 106, 226)(98, 218, 107, 227, 99, 219, 108, 228)(101, 221, 109, 229, 104, 224, 110, 230)(102, 222, 111, 231, 103, 223, 112, 232)(113, 233, 119, 239, 116, 236, 118, 238)(114, 234, 117, 237, 115, 235, 120, 240)(241, 242)(243, 246)(244, 251)(245, 254)(247, 258)(248, 261)(249, 262)(250, 259)(252, 257)(253, 263)(255, 256)(260, 268)(264, 273)(265, 275)(266, 276)(267, 274)(269, 277)(270, 279)(271, 280)(272, 278)(281, 289)(282, 291)(283, 292)(284, 290)(285, 293)(286, 295)(287, 296)(288, 294)(297, 305)(298, 307)(299, 308)(300, 306)(301, 309)(302, 311)(303, 312)(304, 310)(313, 321)(314, 323)(315, 324)(316, 322)(317, 325)(318, 327)(319, 328)(320, 326)(329, 337)(330, 339)(331, 340)(332, 338)(333, 341)(334, 343)(335, 344)(336, 342)(345, 353)(346, 355)(347, 356)(348, 354)(349, 357)(350, 359)(351, 360)(352, 358)(361, 363)(362, 366)(364, 372)(365, 375)(367, 379)(368, 382)(369, 381)(370, 378)(371, 377)(373, 380)(374, 376)(383, 388)(384, 394)(385, 396)(386, 395)(387, 393)(389, 398)(390, 400)(391, 399)(392, 397)(401, 410)(402, 412)(403, 411)(404, 409)(405, 414)(406, 416)(407, 415)(408, 413)(417, 426)(418, 428)(419, 427)(420, 425)(421, 430)(422, 432)(423, 431)(424, 429)(433, 442)(434, 444)(435, 443)(436, 441)(437, 446)(438, 448)(439, 447)(440, 445)(449, 458)(450, 460)(451, 459)(452, 457)(453, 462)(454, 464)(455, 463)(456, 461)(465, 474)(466, 476)(467, 475)(468, 473)(469, 478)(470, 480)(471, 479)(472, 477) L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 8, 8 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E16.1189 Graph:: simple bipartite v = 150 e = 240 f = 60 degree seq :: [ 2^120, 8^30 ] E16.1188 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = D10 x S4 (small group id <240, 194>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y1 * Y2)^3, Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y1, Y1 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2, (Y1 * Y3 * Y2)^4 ] Map:: R = (1, 121, 241, 361, 4, 124, 244, 364)(2, 122, 242, 362, 6, 126, 246, 366)(3, 123, 243, 363, 8, 128, 248, 368)(5, 125, 245, 365, 12, 132, 252, 372)(7, 127, 247, 367, 15, 135, 255, 375)(9, 129, 249, 369, 19, 139, 259, 379)(10, 130, 250, 370, 21, 141, 261, 381)(11, 131, 251, 371, 22, 142, 262, 382)(13, 133, 253, 373, 26, 146, 266, 386)(14, 134, 254, 374, 28, 148, 268, 388)(16, 136, 256, 376, 32, 152, 272, 392)(17, 137, 257, 377, 34, 154, 274, 394)(18, 138, 258, 378, 36, 156, 276, 396)(20, 140, 260, 380, 39, 159, 279, 399)(23, 143, 263, 383, 45, 165, 285, 405)(24, 144, 264, 384, 47, 167, 287, 407)(25, 145, 265, 385, 49, 169, 289, 409)(27, 147, 267, 387, 52, 172, 292, 412)(29, 149, 269, 389, 56, 176, 296, 416)(30, 150, 270, 390, 58, 178, 298, 418)(31, 151, 271, 391, 60, 180, 300, 420)(33, 153, 273, 393, 63, 183, 303, 423)(35, 155, 275, 395, 65, 185, 305, 425)(37, 157, 277, 397, 67, 187, 307, 427)(38, 158, 278, 398, 69, 189, 309, 429)(40, 160, 280, 400, 72, 192, 312, 432)(41, 161, 281, 401, 73, 193, 313, 433)(42, 162, 282, 402, 75, 195, 315, 435)(43, 163, 283, 403, 77, 197, 317, 437)(44, 164, 284, 404, 79, 199, 319, 439)(46, 166, 286, 406, 82, 202, 322, 442)(48, 168, 288, 408, 84, 204, 324, 444)(50, 170, 290, 410, 86, 206, 326, 446)(51, 171, 291, 411, 88, 208, 328, 448)(53, 173, 293, 413, 91, 211, 331, 451)(54, 174, 294, 414, 92, 212, 332, 452)(55, 175, 295, 415, 94, 214, 334, 454)(57, 177, 297, 417, 95, 215, 335, 455)(59, 179, 299, 419, 96, 216, 336, 456)(61, 181, 301, 421, 97, 217, 337, 457)(62, 182, 302, 422, 81, 201, 321, 441)(64, 184, 304, 424, 83, 203, 323, 443)(66, 186, 306, 426, 100, 220, 340, 460)(68, 188, 308, 428, 102, 222, 342, 462)(70, 190, 310, 430, 103, 223, 343, 463)(71, 191, 311, 431, 104, 224, 344, 464)(74, 194, 314, 434, 106, 226, 346, 466)(76, 196, 316, 436, 107, 227, 347, 467)(78, 198, 318, 438, 108, 228, 348, 468)(80, 200, 320, 440, 109, 229, 349, 469)(85, 205, 325, 445, 112, 232, 352, 472)(87, 207, 327, 447, 114, 234, 354, 474)(89, 209, 329, 449, 115, 235, 355, 475)(90, 210, 330, 450, 116, 236, 356, 476)(93, 213, 333, 453, 113, 233, 353, 473)(98, 218, 338, 458, 117, 237, 357, 477)(99, 219, 339, 459, 118, 238, 358, 478)(101, 221, 341, 461, 105, 225, 345, 465)(110, 230, 350, 470, 119, 239, 359, 479)(111, 231, 351, 471, 120, 240, 360, 480) L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 131)(6, 133)(7, 123)(8, 136)(9, 124)(10, 140)(11, 125)(12, 143)(13, 126)(14, 147)(15, 149)(16, 128)(17, 153)(18, 155)(19, 157)(20, 130)(21, 160)(22, 162)(23, 132)(24, 166)(25, 168)(26, 170)(27, 134)(28, 173)(29, 135)(30, 177)(31, 179)(32, 181)(33, 137)(34, 184)(35, 138)(36, 186)(37, 139)(38, 188)(39, 183)(40, 141)(41, 176)(42, 142)(43, 196)(44, 198)(45, 200)(46, 144)(47, 203)(48, 145)(49, 205)(50, 146)(51, 207)(52, 202)(53, 148)(54, 195)(55, 213)(56, 161)(57, 150)(58, 211)(59, 151)(60, 209)(61, 152)(62, 218)(63, 159)(64, 154)(65, 212)(66, 156)(67, 221)(68, 158)(69, 210)(70, 199)(71, 208)(72, 197)(73, 204)(74, 225)(75, 174)(76, 163)(77, 192)(78, 164)(79, 190)(80, 165)(81, 230)(82, 172)(83, 167)(84, 193)(85, 169)(86, 233)(87, 171)(88, 191)(89, 180)(90, 189)(91, 178)(92, 185)(93, 175)(94, 231)(95, 227)(96, 229)(97, 228)(98, 182)(99, 226)(100, 234)(101, 187)(102, 232)(103, 236)(104, 235)(105, 194)(106, 219)(107, 215)(108, 217)(109, 216)(110, 201)(111, 214)(112, 222)(113, 206)(114, 220)(115, 224)(116, 223)(117, 240)(118, 239)(119, 238)(120, 237)(241, 363)(242, 365)(243, 361)(244, 370)(245, 362)(246, 374)(247, 371)(248, 377)(249, 378)(250, 364)(251, 367)(252, 384)(253, 385)(254, 366)(255, 390)(256, 391)(257, 368)(258, 369)(259, 398)(260, 395)(261, 401)(262, 403)(263, 404)(264, 372)(265, 373)(266, 411)(267, 408)(268, 414)(269, 415)(270, 375)(271, 376)(272, 422)(273, 419)(274, 410)(275, 380)(276, 409)(277, 407)(278, 379)(279, 430)(280, 431)(281, 381)(282, 434)(283, 382)(284, 383)(285, 441)(286, 438)(287, 397)(288, 387)(289, 396)(290, 394)(291, 386)(292, 449)(293, 450)(294, 388)(295, 389)(296, 448)(297, 453)(298, 440)(299, 393)(300, 454)(301, 437)(302, 392)(303, 459)(304, 447)(305, 457)(306, 455)(307, 456)(308, 443)(309, 435)(310, 399)(311, 400)(312, 458)(313, 461)(314, 402)(315, 429)(316, 465)(317, 421)(318, 406)(319, 466)(320, 418)(321, 405)(322, 471)(323, 428)(324, 469)(325, 467)(326, 468)(327, 424)(328, 416)(329, 412)(330, 413)(331, 470)(332, 473)(333, 417)(334, 420)(335, 426)(336, 427)(337, 425)(338, 432)(339, 423)(340, 477)(341, 433)(342, 475)(343, 474)(344, 478)(345, 436)(346, 439)(347, 445)(348, 446)(349, 444)(350, 451)(351, 442)(352, 479)(353, 452)(354, 463)(355, 462)(356, 480)(357, 460)(358, 464)(359, 472)(360, 476) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E16.1186 Transitivity :: VT+ Graph:: v = 60 e = 240 f = 150 degree seq :: [ 8^60 ] E16.1189 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = C2 x ((C5 x A4) : C2) (small group id <240, 197>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (Y2 * Y1)^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y3 * Y1, (Y3 * Y1)^15 ] Map:: R = (1, 121, 241, 361, 4, 124, 244, 364)(2, 122, 242, 362, 6, 126, 246, 366)(3, 123, 243, 363, 7, 127, 247, 367)(5, 125, 245, 365, 10, 130, 250, 370)(8, 128, 248, 368, 16, 136, 256, 376)(9, 129, 249, 369, 17, 137, 257, 377)(11, 131, 251, 371, 21, 141, 261, 381)(12, 132, 252, 372, 22, 142, 262, 382)(13, 133, 253, 373, 24, 144, 264, 384)(14, 134, 254, 374, 25, 145, 265, 385)(15, 135, 255, 375, 26, 146, 266, 386)(18, 138, 258, 378, 32, 152, 272, 392)(19, 139, 259, 379, 33, 153, 273, 393)(20, 140, 260, 380, 34, 154, 274, 394)(23, 143, 263, 383, 39, 159, 279, 399)(27, 147, 267, 387, 40, 160, 280, 400)(28, 148, 268, 388, 41, 161, 281, 401)(29, 149, 269, 389, 42, 162, 282, 402)(30, 150, 270, 390, 43, 163, 283, 403)(31, 151, 271, 391, 44, 164, 284, 404)(35, 155, 275, 395, 45, 165, 285, 405)(36, 156, 276, 396, 46, 166, 286, 406)(37, 157, 277, 397, 47, 167, 287, 407)(38, 158, 278, 398, 48, 168, 288, 408)(49, 169, 289, 409, 57, 177, 297, 417)(50, 170, 290, 410, 58, 178, 298, 418)(51, 171, 291, 411, 59, 179, 299, 419)(52, 172, 292, 412, 60, 180, 300, 420)(53, 173, 293, 413, 61, 181, 301, 421)(54, 174, 294, 414, 62, 182, 302, 422)(55, 175, 295, 415, 63, 183, 303, 423)(56, 176, 296, 416, 64, 184, 304, 424)(65, 185, 305, 425, 73, 193, 313, 433)(66, 186, 306, 426, 74, 194, 314, 434)(67, 187, 307, 427, 75, 195, 315, 435)(68, 188, 308, 428, 76, 196, 316, 436)(69, 189, 309, 429, 77, 197, 317, 437)(70, 190, 310, 430, 78, 198, 318, 438)(71, 191, 311, 431, 79, 199, 319, 439)(72, 192, 312, 432, 80, 200, 320, 440)(81, 201, 321, 441, 89, 209, 329, 449)(82, 202, 322, 442, 90, 210, 330, 450)(83, 203, 323, 443, 91, 211, 331, 451)(84, 204, 324, 444, 92, 212, 332, 452)(85, 205, 325, 445, 93, 213, 333, 453)(86, 206, 326, 446, 94, 214, 334, 454)(87, 207, 327, 447, 95, 215, 335, 455)(88, 208, 328, 448, 96, 216, 336, 456)(97, 217, 337, 457, 105, 225, 345, 465)(98, 218, 338, 458, 106, 226, 346, 466)(99, 219, 339, 459, 107, 227, 347, 467)(100, 220, 340, 460, 108, 228, 348, 468)(101, 221, 341, 461, 109, 229, 349, 469)(102, 222, 342, 462, 110, 230, 350, 470)(103, 223, 343, 463, 111, 231, 351, 471)(104, 224, 344, 464, 112, 232, 352, 472)(113, 233, 353, 473, 117, 237, 357, 477)(114, 234, 354, 474, 120, 240, 360, 480)(115, 235, 355, 475, 119, 239, 359, 479)(116, 236, 356, 476, 118, 238, 358, 478) L = (1, 122)(2, 121)(3, 125)(4, 128)(5, 123)(6, 131)(7, 133)(8, 124)(9, 135)(10, 138)(11, 126)(12, 140)(13, 127)(14, 143)(15, 129)(16, 147)(17, 149)(18, 130)(19, 151)(20, 132)(21, 155)(22, 157)(23, 134)(24, 158)(25, 156)(26, 159)(27, 136)(28, 153)(29, 137)(30, 152)(31, 139)(32, 150)(33, 148)(34, 164)(35, 141)(36, 145)(37, 142)(38, 144)(39, 146)(40, 169)(41, 171)(42, 172)(43, 170)(44, 154)(45, 173)(46, 175)(47, 176)(48, 174)(49, 160)(50, 163)(51, 161)(52, 162)(53, 165)(54, 168)(55, 166)(56, 167)(57, 185)(58, 187)(59, 188)(60, 186)(61, 189)(62, 191)(63, 192)(64, 190)(65, 177)(66, 180)(67, 178)(68, 179)(69, 181)(70, 184)(71, 182)(72, 183)(73, 201)(74, 203)(75, 204)(76, 202)(77, 205)(78, 207)(79, 208)(80, 206)(81, 193)(82, 196)(83, 194)(84, 195)(85, 197)(86, 200)(87, 198)(88, 199)(89, 217)(90, 219)(91, 220)(92, 218)(93, 221)(94, 223)(95, 224)(96, 222)(97, 209)(98, 212)(99, 210)(100, 211)(101, 213)(102, 216)(103, 214)(104, 215)(105, 233)(106, 235)(107, 236)(108, 234)(109, 237)(110, 239)(111, 240)(112, 238)(113, 225)(114, 228)(115, 226)(116, 227)(117, 229)(118, 232)(119, 230)(120, 231)(241, 363)(242, 365)(243, 361)(244, 369)(245, 362)(246, 372)(247, 374)(248, 375)(249, 364)(250, 379)(251, 380)(252, 366)(253, 383)(254, 367)(255, 368)(256, 388)(257, 390)(258, 391)(259, 370)(260, 371)(261, 396)(262, 398)(263, 373)(264, 397)(265, 395)(266, 394)(267, 393)(268, 376)(269, 392)(270, 377)(271, 378)(272, 389)(273, 387)(274, 386)(275, 385)(276, 381)(277, 384)(278, 382)(279, 404)(280, 410)(281, 412)(282, 411)(283, 409)(284, 399)(285, 414)(286, 416)(287, 415)(288, 413)(289, 403)(290, 400)(291, 402)(292, 401)(293, 408)(294, 405)(295, 407)(296, 406)(297, 426)(298, 428)(299, 427)(300, 425)(301, 430)(302, 432)(303, 431)(304, 429)(305, 420)(306, 417)(307, 419)(308, 418)(309, 424)(310, 421)(311, 423)(312, 422)(313, 442)(314, 444)(315, 443)(316, 441)(317, 446)(318, 448)(319, 447)(320, 445)(321, 436)(322, 433)(323, 435)(324, 434)(325, 440)(326, 437)(327, 439)(328, 438)(329, 458)(330, 460)(331, 459)(332, 457)(333, 462)(334, 464)(335, 463)(336, 461)(337, 452)(338, 449)(339, 451)(340, 450)(341, 456)(342, 453)(343, 455)(344, 454)(345, 474)(346, 476)(347, 475)(348, 473)(349, 478)(350, 480)(351, 479)(352, 477)(353, 468)(354, 465)(355, 467)(356, 466)(357, 472)(358, 469)(359, 471)(360, 470) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E16.1187 Transitivity :: VT+ Graph:: v = 60 e = 240 f = 150 degree seq :: [ 8^60 ] E16.1190 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = D10 x S4 (small group id <240, 194>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1)^3, (Y2 * Y3 * Y1)^2, Y3^-1 * Y1 * Y3^-2 * Y2 * Y3^-1 * Y1 * Y2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^-2 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3^-1 * Y1, (Y3 * Y1 * Y3^-2 * Y1)^2 ] Map:: R = (1, 121, 241, 361, 4, 124, 244, 364, 14, 134, 254, 374, 5, 125, 245, 365)(2, 122, 242, 362, 7, 127, 247, 367, 22, 142, 262, 382, 8, 128, 248, 368)(3, 123, 243, 363, 10, 130, 250, 370, 28, 148, 268, 388, 11, 131, 251, 371)(6, 126, 246, 366, 18, 138, 258, 378, 46, 166, 286, 406, 19, 139, 259, 379)(9, 129, 249, 369, 25, 145, 265, 385, 62, 182, 302, 422, 26, 146, 266, 386)(12, 132, 252, 372, 31, 151, 271, 391, 73, 193, 313, 433, 32, 152, 272, 392)(13, 133, 253, 373, 34, 154, 274, 394, 47, 167, 287, 407, 35, 155, 275, 395)(15, 135, 255, 375, 39, 159, 279, 399, 61, 181, 301, 421, 40, 160, 280, 400)(16, 136, 256, 376, 41, 161, 281, 401, 87, 207, 327, 447, 42, 162, 282, 402)(17, 137, 257, 377, 43, 163, 283, 403, 90, 210, 330, 450, 44, 164, 284, 404)(20, 140, 260, 380, 49, 169, 289, 409, 101, 221, 341, 461, 50, 170, 290, 410)(21, 141, 261, 381, 52, 172, 292, 412, 29, 149, 269, 389, 53, 173, 293, 413)(23, 143, 263, 383, 57, 177, 297, 417, 89, 209, 329, 449, 58, 178, 298, 418)(24, 144, 264, 384, 59, 179, 299, 419, 115, 235, 355, 475, 60, 180, 300, 420)(27, 147, 267, 387, 64, 184, 304, 424, 91, 211, 331, 451, 65, 185, 305, 425)(30, 150, 270, 390, 69, 189, 309, 429, 118, 238, 358, 478, 70, 190, 310, 430)(33, 153, 273, 393, 55, 175, 295, 415, 110, 230, 350, 470, 76, 196, 316, 436)(36, 156, 276, 396, 68, 188, 308, 428, 95, 215, 335, 455, 80, 200, 320, 440)(37, 157, 277, 397, 82, 202, 322, 442, 104, 224, 344, 464, 51, 171, 291, 411)(38, 158, 278, 398, 81, 201, 321, 441, 117, 237, 357, 477, 66, 186, 306, 426)(45, 165, 285, 405, 92, 212, 332, 452, 63, 183, 303, 423, 93, 213, 333, 453)(48, 168, 288, 408, 97, 217, 337, 457, 120, 240, 360, 480, 98, 218, 338, 458)(54, 174, 294, 414, 96, 216, 336, 456, 67, 187, 307, 427, 108, 228, 348, 468)(56, 176, 296, 416, 109, 229, 349, 469, 119, 239, 359, 479, 94, 214, 334, 454)(71, 191, 311, 431, 106, 226, 346, 466, 84, 204, 324, 444, 100, 220, 340, 460)(72, 192, 312, 432, 99, 219, 339, 459, 78, 198, 318, 438, 112, 232, 352, 472)(74, 194, 314, 434, 113, 233, 353, 473, 83, 203, 323, 443, 103, 223, 343, 463)(75, 195, 315, 435, 102, 222, 342, 462, 85, 205, 325, 445, 111, 231, 351, 471)(77, 197, 317, 437, 107, 227, 347, 467, 88, 208, 328, 448, 114, 234, 354, 474)(79, 199, 319, 439, 116, 236, 356, 476, 86, 206, 326, 446, 105, 225, 345, 465) L = (1, 122)(2, 121)(3, 129)(4, 132)(5, 135)(6, 137)(7, 140)(8, 143)(9, 123)(10, 144)(11, 149)(12, 124)(13, 153)(14, 156)(15, 125)(16, 138)(17, 126)(18, 136)(19, 167)(20, 127)(21, 171)(22, 174)(23, 128)(24, 130)(25, 168)(26, 183)(27, 176)(28, 186)(29, 131)(30, 163)(31, 191)(32, 194)(33, 133)(34, 195)(35, 198)(36, 134)(37, 201)(38, 165)(39, 203)(40, 204)(41, 205)(42, 192)(43, 150)(44, 211)(45, 158)(46, 214)(47, 139)(48, 145)(49, 219)(50, 222)(51, 141)(52, 223)(53, 226)(54, 142)(55, 229)(56, 147)(57, 231)(58, 232)(59, 233)(60, 220)(61, 216)(62, 224)(63, 146)(64, 236)(65, 227)(66, 148)(67, 215)(68, 209)(69, 225)(70, 234)(71, 151)(72, 162)(73, 228)(74, 152)(75, 154)(76, 210)(77, 217)(78, 155)(79, 213)(80, 221)(81, 157)(82, 235)(83, 159)(84, 160)(85, 161)(86, 218)(87, 230)(88, 212)(89, 188)(90, 196)(91, 164)(92, 208)(93, 199)(94, 166)(95, 187)(96, 181)(97, 197)(98, 206)(99, 169)(100, 180)(101, 200)(102, 170)(103, 172)(104, 182)(105, 189)(106, 173)(107, 185)(108, 193)(109, 175)(110, 207)(111, 177)(112, 178)(113, 179)(114, 190)(115, 202)(116, 184)(117, 240)(118, 239)(119, 238)(120, 237)(241, 363)(242, 366)(243, 361)(244, 373)(245, 376)(246, 362)(247, 381)(248, 384)(249, 377)(250, 387)(251, 390)(252, 386)(253, 364)(254, 397)(255, 398)(256, 365)(257, 369)(258, 405)(259, 408)(260, 404)(261, 367)(262, 415)(263, 416)(264, 368)(265, 421)(266, 372)(267, 370)(268, 427)(269, 428)(270, 371)(271, 432)(272, 435)(273, 423)(274, 437)(275, 439)(276, 436)(277, 374)(278, 375)(279, 438)(280, 445)(281, 446)(282, 448)(283, 449)(284, 380)(285, 378)(286, 455)(287, 456)(288, 379)(289, 460)(290, 463)(291, 451)(292, 465)(293, 467)(294, 464)(295, 382)(296, 383)(297, 466)(298, 473)(299, 474)(300, 476)(301, 385)(302, 469)(303, 393)(304, 459)(305, 471)(306, 454)(307, 388)(308, 389)(309, 462)(310, 472)(311, 452)(312, 391)(313, 477)(314, 457)(315, 392)(316, 396)(317, 394)(318, 399)(319, 395)(320, 475)(321, 450)(322, 478)(323, 453)(324, 458)(325, 400)(326, 401)(327, 468)(328, 402)(329, 403)(330, 441)(331, 411)(332, 431)(333, 443)(334, 426)(335, 406)(336, 407)(337, 434)(338, 444)(339, 424)(340, 409)(341, 479)(342, 429)(343, 410)(344, 414)(345, 412)(346, 417)(347, 413)(348, 447)(349, 422)(350, 480)(351, 425)(352, 430)(353, 418)(354, 419)(355, 440)(356, 420)(357, 433)(358, 442)(359, 461)(360, 470) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E16.1184 Transitivity :: VT+ Graph:: v = 30 e = 240 f = 180 degree seq :: [ 16^30 ] E16.1191 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = C2 x ((C5 x A4) : C2) (small group id <240, 197>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3^-2 * Y1 * Y3^-1, (Y3 * Y1 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 121, 241, 361, 4, 124, 244, 364, 13, 133, 253, 373, 5, 125, 245, 365)(2, 122, 242, 362, 7, 127, 247, 367, 20, 140, 260, 380, 8, 128, 248, 368)(3, 123, 243, 363, 9, 129, 249, 369, 23, 143, 263, 383, 10, 130, 250, 370)(6, 126, 246, 366, 16, 136, 256, 376, 28, 148, 268, 388, 17, 137, 257, 377)(11, 131, 251, 371, 24, 144, 264, 384, 15, 135, 255, 375, 25, 145, 265, 385)(12, 132, 252, 372, 26, 146, 266, 386, 14, 134, 254, 374, 27, 147, 267, 387)(18, 138, 258, 378, 29, 149, 269, 389, 22, 142, 262, 382, 30, 150, 270, 390)(19, 139, 259, 379, 31, 151, 271, 391, 21, 141, 261, 381, 32, 152, 272, 392)(33, 153, 273, 393, 41, 161, 281, 401, 36, 156, 276, 396, 42, 162, 282, 402)(34, 154, 274, 394, 43, 163, 283, 403, 35, 155, 275, 395, 44, 164, 284, 404)(37, 157, 277, 397, 45, 165, 285, 405, 40, 160, 280, 400, 46, 166, 286, 406)(38, 158, 278, 398, 47, 167, 287, 407, 39, 159, 279, 399, 48, 168, 288, 408)(49, 169, 289, 409, 57, 177, 297, 417, 52, 172, 292, 412, 58, 178, 298, 418)(50, 170, 290, 410, 59, 179, 299, 419, 51, 171, 291, 411, 60, 180, 300, 420)(53, 173, 293, 413, 61, 181, 301, 421, 56, 176, 296, 416, 62, 182, 302, 422)(54, 174, 294, 414, 63, 183, 303, 423, 55, 175, 295, 415, 64, 184, 304, 424)(65, 185, 305, 425, 73, 193, 313, 433, 68, 188, 308, 428, 74, 194, 314, 434)(66, 186, 306, 426, 75, 195, 315, 435, 67, 187, 307, 427, 76, 196, 316, 436)(69, 189, 309, 429, 77, 197, 317, 437, 72, 192, 312, 432, 78, 198, 318, 438)(70, 190, 310, 430, 79, 199, 319, 439, 71, 191, 311, 431, 80, 200, 320, 440)(81, 201, 321, 441, 89, 209, 329, 449, 84, 204, 324, 444, 90, 210, 330, 450)(82, 202, 322, 442, 91, 211, 331, 451, 83, 203, 323, 443, 92, 212, 332, 452)(85, 205, 325, 445, 93, 213, 333, 453, 88, 208, 328, 448, 94, 214, 334, 454)(86, 206, 326, 446, 95, 215, 335, 455, 87, 207, 327, 447, 96, 216, 336, 456)(97, 217, 337, 457, 105, 225, 345, 465, 100, 220, 340, 460, 106, 226, 346, 466)(98, 218, 338, 458, 107, 227, 347, 467, 99, 219, 339, 459, 108, 228, 348, 468)(101, 221, 341, 461, 109, 229, 349, 469, 104, 224, 344, 464, 110, 230, 350, 470)(102, 222, 342, 462, 111, 231, 351, 471, 103, 223, 343, 463, 112, 232, 352, 472)(113, 233, 353, 473, 119, 239, 359, 479, 116, 236, 356, 476, 118, 238, 358, 478)(114, 234, 354, 474, 117, 237, 357, 477, 115, 235, 355, 475, 120, 240, 360, 480) L = (1, 122)(2, 121)(3, 126)(4, 131)(5, 134)(6, 123)(7, 138)(8, 141)(9, 142)(10, 139)(11, 124)(12, 137)(13, 143)(14, 125)(15, 136)(16, 135)(17, 132)(18, 127)(19, 130)(20, 148)(21, 128)(22, 129)(23, 133)(24, 153)(25, 155)(26, 156)(27, 154)(28, 140)(29, 157)(30, 159)(31, 160)(32, 158)(33, 144)(34, 147)(35, 145)(36, 146)(37, 149)(38, 152)(39, 150)(40, 151)(41, 169)(42, 171)(43, 172)(44, 170)(45, 173)(46, 175)(47, 176)(48, 174)(49, 161)(50, 164)(51, 162)(52, 163)(53, 165)(54, 168)(55, 166)(56, 167)(57, 185)(58, 187)(59, 188)(60, 186)(61, 189)(62, 191)(63, 192)(64, 190)(65, 177)(66, 180)(67, 178)(68, 179)(69, 181)(70, 184)(71, 182)(72, 183)(73, 201)(74, 203)(75, 204)(76, 202)(77, 205)(78, 207)(79, 208)(80, 206)(81, 193)(82, 196)(83, 194)(84, 195)(85, 197)(86, 200)(87, 198)(88, 199)(89, 217)(90, 219)(91, 220)(92, 218)(93, 221)(94, 223)(95, 224)(96, 222)(97, 209)(98, 212)(99, 210)(100, 211)(101, 213)(102, 216)(103, 214)(104, 215)(105, 233)(106, 235)(107, 236)(108, 234)(109, 237)(110, 239)(111, 240)(112, 238)(113, 225)(114, 228)(115, 226)(116, 227)(117, 229)(118, 232)(119, 230)(120, 231)(241, 363)(242, 366)(243, 361)(244, 372)(245, 375)(246, 362)(247, 379)(248, 382)(249, 381)(250, 378)(251, 377)(252, 364)(253, 380)(254, 376)(255, 365)(256, 374)(257, 371)(258, 370)(259, 367)(260, 373)(261, 369)(262, 368)(263, 388)(264, 394)(265, 396)(266, 395)(267, 393)(268, 383)(269, 398)(270, 400)(271, 399)(272, 397)(273, 387)(274, 384)(275, 386)(276, 385)(277, 392)(278, 389)(279, 391)(280, 390)(281, 410)(282, 412)(283, 411)(284, 409)(285, 414)(286, 416)(287, 415)(288, 413)(289, 404)(290, 401)(291, 403)(292, 402)(293, 408)(294, 405)(295, 407)(296, 406)(297, 426)(298, 428)(299, 427)(300, 425)(301, 430)(302, 432)(303, 431)(304, 429)(305, 420)(306, 417)(307, 419)(308, 418)(309, 424)(310, 421)(311, 423)(312, 422)(313, 442)(314, 444)(315, 443)(316, 441)(317, 446)(318, 448)(319, 447)(320, 445)(321, 436)(322, 433)(323, 435)(324, 434)(325, 440)(326, 437)(327, 439)(328, 438)(329, 458)(330, 460)(331, 459)(332, 457)(333, 462)(334, 464)(335, 463)(336, 461)(337, 452)(338, 449)(339, 451)(340, 450)(341, 456)(342, 453)(343, 455)(344, 454)(345, 474)(346, 476)(347, 475)(348, 473)(349, 478)(350, 480)(351, 479)(352, 477)(353, 468)(354, 465)(355, 467)(356, 466)(357, 472)(358, 469)(359, 471)(360, 470) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E16.1185 Transitivity :: VT+ Graph:: v = 30 e = 240 f = 180 degree seq :: [ 16^30 ] E16.1192 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = D10 x S4 (small group id <240, 194>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (Y3^-1 * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y3)^4, Y3^-1 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 121, 2, 122)(3, 123, 9, 129)(4, 124, 12, 132)(5, 125, 13, 133)(6, 126, 14, 134)(7, 127, 17, 137)(8, 128, 18, 138)(10, 130, 22, 142)(11, 131, 23, 143)(15, 135, 33, 153)(16, 136, 34, 154)(19, 139, 41, 161)(20, 140, 44, 164)(21, 141, 45, 165)(24, 144, 52, 172)(25, 145, 40, 160)(26, 146, 55, 175)(27, 147, 56, 176)(28, 148, 59, 179)(29, 149, 36, 156)(30, 150, 60, 180)(31, 151, 53, 173)(32, 152, 63, 183)(35, 155, 69, 189)(37, 157, 71, 191)(38, 158, 48, 168)(39, 159, 74, 194)(42, 162, 78, 198)(43, 163, 79, 199)(46, 166, 82, 202)(47, 167, 81, 201)(49, 169, 85, 205)(50, 170, 73, 193)(51, 171, 70, 190)(54, 174, 68, 188)(57, 177, 89, 209)(58, 178, 67, 187)(61, 181, 96, 216)(62, 182, 97, 217)(64, 184, 100, 220)(65, 185, 99, 219)(66, 186, 102, 222)(72, 192, 106, 226)(75, 195, 104, 224)(76, 196, 83, 203)(77, 197, 105, 225)(80, 200, 107, 227)(84, 204, 112, 232)(86, 206, 114, 234)(87, 207, 93, 213)(88, 208, 95, 215)(90, 210, 98, 218)(91, 211, 108, 228)(92, 212, 94, 214)(101, 221, 109, 229)(103, 223, 113, 233)(110, 230, 117, 237)(111, 231, 120, 240)(115, 235, 119, 239)(116, 236, 118, 238)(241, 361, 243, 363)(242, 362, 246, 366)(244, 364, 251, 371)(245, 365, 250, 370)(247, 367, 256, 376)(248, 368, 255, 375)(249, 369, 259, 379)(252, 372, 264, 384)(253, 373, 267, 387)(254, 374, 270, 390)(257, 377, 275, 395)(258, 378, 278, 398)(260, 380, 283, 403)(261, 381, 282, 402)(262, 382, 286, 406)(263, 383, 289, 409)(265, 385, 294, 414)(266, 386, 293, 413)(268, 388, 298, 418)(269, 389, 297, 417)(271, 391, 302, 422)(272, 392, 301, 421)(273, 393, 304, 424)(274, 394, 306, 426)(276, 396, 310, 430)(277, 397, 284, 404)(279, 399, 313, 433)(280, 400, 312, 432)(281, 401, 315, 435)(285, 405, 295, 415)(287, 407, 324, 444)(288, 408, 323, 443)(290, 410, 327, 447)(291, 411, 326, 446)(292, 412, 328, 448)(296, 416, 332, 452)(299, 419, 320, 440)(300, 420, 333, 453)(303, 423, 311, 431)(305, 425, 341, 461)(307, 427, 344, 464)(308, 428, 343, 463)(309, 429, 345, 465)(314, 434, 338, 458)(316, 436, 337, 457)(317, 437, 349, 469)(318, 438, 350, 470)(319, 439, 334, 454)(321, 441, 331, 451)(322, 442, 353, 473)(325, 445, 342, 462)(329, 449, 357, 477)(330, 450, 356, 476)(335, 455, 352, 472)(336, 456, 351, 471)(339, 459, 348, 468)(340, 460, 354, 474)(346, 466, 360, 480)(347, 467, 359, 479)(355, 475, 358, 478) L = (1, 244)(2, 247)(3, 250)(4, 245)(5, 241)(6, 255)(7, 248)(8, 242)(9, 260)(10, 251)(11, 243)(12, 265)(13, 268)(14, 271)(15, 256)(16, 246)(17, 276)(18, 279)(19, 282)(20, 261)(21, 249)(22, 287)(23, 290)(24, 293)(25, 266)(26, 252)(27, 297)(28, 269)(29, 253)(30, 301)(31, 272)(32, 254)(33, 305)(34, 307)(35, 284)(36, 277)(37, 257)(38, 312)(39, 280)(40, 258)(41, 316)(42, 283)(43, 259)(44, 310)(45, 320)(46, 323)(47, 288)(48, 262)(49, 326)(50, 291)(51, 263)(52, 329)(53, 294)(54, 264)(55, 331)(56, 273)(57, 298)(58, 267)(59, 295)(60, 334)(61, 302)(62, 270)(63, 338)(64, 332)(65, 296)(66, 343)(67, 308)(68, 274)(69, 346)(70, 275)(71, 348)(72, 313)(73, 278)(74, 311)(75, 349)(76, 317)(77, 281)(78, 351)(79, 333)(80, 321)(81, 285)(82, 354)(83, 324)(84, 286)(85, 318)(86, 327)(87, 289)(88, 356)(89, 330)(90, 292)(91, 299)(92, 341)(93, 352)(94, 335)(95, 300)(96, 350)(97, 315)(98, 339)(99, 303)(100, 353)(101, 304)(102, 336)(103, 344)(104, 306)(105, 359)(106, 347)(107, 309)(108, 314)(109, 337)(110, 342)(111, 325)(112, 319)(113, 358)(114, 355)(115, 322)(116, 357)(117, 328)(118, 340)(119, 360)(120, 345)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.1194 Graph:: simple bipartite v = 120 e = 240 f = 90 degree seq :: [ 4^120 ] E16.1193 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = C2 x ((C5 x A4) : C2) (small group id <240, 197>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y2 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3 * Y1)^4, Y3 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1, (Y2 * Y1)^15 ] Map:: polytopal non-degenerate R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 10, 130)(6, 126, 12, 132)(8, 128, 15, 135)(11, 131, 20, 140)(13, 133, 23, 143)(14, 134, 25, 145)(16, 136, 28, 148)(17, 137, 22, 142)(18, 138, 30, 150)(19, 139, 29, 149)(21, 141, 27, 147)(24, 144, 35, 155)(26, 146, 36, 156)(31, 151, 41, 161)(32, 152, 42, 162)(33, 153, 43, 163)(34, 154, 37, 157)(38, 158, 40, 160)(39, 159, 47, 167)(44, 164, 53, 173)(45, 165, 54, 174)(46, 166, 52, 172)(48, 168, 57, 177)(49, 169, 58, 178)(50, 170, 56, 176)(51, 171, 59, 179)(55, 175, 63, 183)(60, 180, 69, 189)(61, 181, 70, 190)(62, 182, 68, 188)(64, 184, 73, 193)(65, 185, 74, 194)(66, 186, 72, 192)(67, 187, 75, 195)(71, 191, 79, 199)(76, 196, 85, 205)(77, 197, 86, 206)(78, 198, 84, 204)(80, 200, 89, 209)(81, 201, 90, 210)(82, 202, 88, 208)(83, 203, 91, 211)(87, 207, 95, 215)(92, 212, 101, 221)(93, 213, 102, 222)(94, 214, 100, 220)(96, 216, 105, 225)(97, 217, 106, 226)(98, 218, 104, 224)(99, 219, 107, 227)(103, 223, 111, 231)(108, 228, 116, 236)(109, 229, 117, 237)(110, 230, 115, 235)(112, 232, 119, 239)(113, 233, 120, 240)(114, 234, 118, 238)(241, 361, 243, 363)(242, 362, 245, 365)(244, 364, 248, 368)(246, 366, 251, 371)(247, 367, 253, 373)(249, 369, 256, 376)(250, 370, 258, 378)(252, 372, 261, 381)(254, 374, 264, 384)(255, 375, 266, 386)(257, 377, 269, 389)(259, 379, 271, 391)(260, 380, 272, 392)(262, 382, 265, 385)(263, 383, 273, 393)(267, 387, 277, 397)(268, 388, 278, 398)(270, 390, 279, 399)(274, 394, 284, 404)(275, 395, 285, 405)(276, 396, 286, 406)(280, 400, 288, 408)(281, 401, 289, 409)(282, 402, 290, 410)(283, 403, 291, 411)(287, 407, 295, 415)(292, 412, 300, 420)(293, 413, 301, 421)(294, 414, 302, 422)(296, 416, 304, 424)(297, 417, 305, 425)(298, 418, 306, 426)(299, 419, 307, 427)(303, 423, 311, 431)(308, 428, 316, 436)(309, 429, 317, 437)(310, 430, 318, 438)(312, 432, 320, 440)(313, 433, 321, 441)(314, 434, 322, 442)(315, 435, 323, 443)(319, 439, 327, 447)(324, 444, 332, 452)(325, 445, 333, 453)(326, 446, 334, 454)(328, 448, 336, 456)(329, 449, 337, 457)(330, 450, 338, 458)(331, 451, 339, 459)(335, 455, 343, 463)(340, 460, 348, 468)(341, 461, 349, 469)(342, 462, 350, 470)(344, 464, 352, 472)(345, 465, 353, 473)(346, 466, 354, 474)(347, 467, 351, 471)(355, 475, 358, 478)(356, 476, 360, 480)(357, 477, 359, 479) L = (1, 244)(2, 246)(3, 248)(4, 241)(5, 251)(6, 242)(7, 254)(8, 243)(9, 257)(10, 259)(11, 245)(12, 262)(13, 264)(14, 247)(15, 267)(16, 269)(17, 249)(18, 271)(19, 250)(20, 268)(21, 265)(22, 252)(23, 274)(24, 253)(25, 261)(26, 277)(27, 255)(28, 260)(29, 256)(30, 280)(31, 258)(32, 278)(33, 284)(34, 263)(35, 276)(36, 275)(37, 266)(38, 272)(39, 288)(40, 270)(41, 282)(42, 281)(43, 292)(44, 273)(45, 286)(46, 285)(47, 296)(48, 279)(49, 290)(50, 289)(51, 300)(52, 283)(53, 294)(54, 293)(55, 304)(56, 287)(57, 298)(58, 297)(59, 308)(60, 291)(61, 302)(62, 301)(63, 312)(64, 295)(65, 306)(66, 305)(67, 316)(68, 299)(69, 310)(70, 309)(71, 320)(72, 303)(73, 314)(74, 313)(75, 324)(76, 307)(77, 318)(78, 317)(79, 328)(80, 311)(81, 322)(82, 321)(83, 332)(84, 315)(85, 326)(86, 325)(87, 336)(88, 319)(89, 330)(90, 329)(91, 340)(92, 323)(93, 334)(94, 333)(95, 344)(96, 327)(97, 338)(98, 337)(99, 348)(100, 331)(101, 342)(102, 341)(103, 352)(104, 335)(105, 346)(106, 345)(107, 355)(108, 339)(109, 350)(110, 349)(111, 358)(112, 343)(113, 354)(114, 353)(115, 347)(116, 357)(117, 356)(118, 351)(119, 360)(120, 359)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.1195 Graph:: simple bipartite v = 120 e = 240 f = 90 degree seq :: [ 4^120 ] E16.1194 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = D10 x S4 (small group id <240, 194>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, (Y3 * Y1)^2, (R * Y1)^2, (Y3 * Y2)^2, Y1^4, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1 * Y3 * Y1^2 * Y3, Y1^-1 * Y2 * Y3^-1 * Y1^-2 * Y3 * Y2 * Y1^-1, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1^-1 * Y2 ] Map:: polytopal non-degenerate R = (1, 121, 2, 122, 7, 127, 5, 125)(3, 123, 11, 131, 29, 149, 13, 133)(4, 124, 15, 135, 38, 158, 16, 136)(6, 126, 19, 139, 27, 147, 9, 129)(8, 128, 23, 143, 53, 173, 25, 145)(10, 130, 28, 148, 51, 171, 21, 141)(12, 132, 33, 153, 69, 189, 34, 154)(14, 134, 37, 157, 50, 170, 31, 151)(17, 137, 42, 162, 79, 199, 43, 163)(18, 138, 22, 142, 52, 172, 45, 165)(20, 140, 47, 167, 83, 203, 49, 169)(24, 144, 57, 177, 40, 160, 58, 178)(26, 146, 61, 181, 44, 164, 55, 175)(30, 150, 65, 185, 86, 206, 67, 187)(32, 152, 48, 168, 85, 205, 62, 182)(35, 155, 72, 192, 84, 204, 73, 193)(36, 156, 64, 184, 87, 207, 75, 195)(39, 159, 78, 198, 88, 208, 56, 176)(41, 161, 77, 197, 89, 209, 63, 183)(46, 166, 60, 180, 90, 210, 82, 202)(54, 174, 91, 211, 81, 201, 93, 213)(59, 179, 97, 217, 80, 200, 98, 218)(66, 186, 104, 224, 71, 191, 105, 225)(68, 188, 108, 228, 74, 194, 102, 222)(70, 190, 109, 229, 115, 235, 103, 223)(76, 196, 107, 227, 116, 236, 112, 232)(92, 212, 101, 221, 96, 216, 111, 231)(94, 214, 119, 239, 99, 219, 117, 237)(95, 215, 106, 226, 113, 233, 110, 230)(100, 220, 118, 238, 114, 234, 120, 240)(241, 361, 243, 363)(242, 362, 248, 368)(244, 364, 254, 374)(245, 365, 257, 377)(246, 366, 252, 372)(247, 367, 260, 380)(249, 369, 266, 386)(250, 370, 264, 384)(251, 371, 270, 390)(253, 373, 275, 395)(255, 375, 279, 399)(256, 376, 280, 400)(258, 378, 284, 404)(259, 379, 286, 406)(261, 381, 290, 410)(262, 382, 288, 408)(263, 383, 294, 414)(265, 385, 299, 419)(267, 387, 302, 422)(268, 388, 304, 424)(269, 389, 303, 423)(271, 391, 308, 428)(272, 392, 306, 426)(273, 393, 310, 430)(274, 394, 311, 431)(276, 396, 314, 434)(277, 397, 316, 436)(278, 398, 315, 435)(281, 401, 319, 439)(282, 402, 320, 440)(283, 403, 321, 441)(285, 405, 309, 429)(287, 407, 324, 444)(289, 409, 326, 446)(291, 411, 328, 448)(292, 412, 330, 450)(293, 413, 329, 449)(295, 415, 334, 454)(296, 416, 332, 452)(297, 417, 335, 455)(298, 418, 336, 456)(300, 420, 339, 459)(301, 421, 340, 460)(305, 425, 341, 461)(307, 427, 346, 466)(312, 432, 350, 470)(313, 433, 351, 471)(317, 437, 323, 443)(318, 438, 353, 473)(322, 442, 354, 474)(325, 445, 355, 475)(327, 447, 356, 476)(331, 451, 345, 465)(333, 453, 343, 463)(337, 457, 349, 469)(338, 458, 344, 464)(342, 462, 358, 478)(347, 467, 360, 480)(348, 468, 357, 477)(352, 472, 359, 479) L = (1, 244)(2, 249)(3, 252)(4, 246)(5, 258)(6, 241)(7, 261)(8, 264)(9, 250)(10, 242)(11, 271)(12, 254)(13, 276)(14, 243)(15, 245)(16, 281)(17, 279)(18, 255)(19, 256)(20, 288)(21, 262)(22, 247)(23, 295)(24, 266)(25, 300)(26, 248)(27, 303)(28, 267)(29, 302)(30, 306)(31, 272)(32, 251)(33, 253)(34, 287)(35, 310)(36, 273)(37, 274)(38, 285)(39, 284)(40, 286)(41, 259)(42, 301)(43, 322)(44, 257)(45, 317)(46, 319)(47, 277)(48, 290)(49, 327)(50, 260)(51, 329)(52, 291)(53, 328)(54, 332)(55, 296)(56, 263)(57, 265)(58, 282)(59, 335)(60, 297)(61, 298)(62, 304)(63, 268)(64, 269)(65, 342)(66, 308)(67, 347)(68, 270)(69, 315)(70, 314)(71, 316)(72, 348)(73, 352)(74, 275)(75, 323)(76, 324)(77, 278)(78, 283)(79, 280)(80, 336)(81, 353)(82, 318)(83, 309)(84, 311)(85, 289)(86, 355)(87, 325)(88, 330)(89, 292)(90, 293)(91, 357)(92, 334)(93, 358)(94, 294)(95, 339)(96, 340)(97, 359)(98, 360)(99, 299)(100, 320)(101, 333)(102, 343)(103, 305)(104, 307)(105, 312)(106, 338)(107, 344)(108, 345)(109, 313)(110, 331)(111, 337)(112, 349)(113, 354)(114, 321)(115, 356)(116, 326)(117, 350)(118, 341)(119, 351)(120, 346)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.1192 Graph:: simple bipartite v = 90 e = 240 f = 120 degree seq :: [ 4^60, 8^30 ] E16.1195 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = (C5 x A4) : C2 (small group id <120, 38>) Aut = C2 x ((C5 x A4) : C2) (small group id <240, 197>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, (R * Y2)^2, Y1^4, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y1^-2 * Y2 * Y1^-1 * Y3, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 121, 2, 122, 6, 126, 5, 125)(3, 123, 9, 129, 19, 139, 11, 131)(4, 124, 12, 132, 15, 135, 8, 128)(7, 127, 16, 136, 24, 144, 18, 138)(10, 130, 22, 142, 14, 134, 21, 141)(13, 133, 25, 145, 17, 137, 26, 146)(20, 140, 29, 149, 32, 152, 31, 151)(23, 143, 33, 153, 30, 150, 34, 154)(27, 147, 37, 157, 36, 156, 38, 158)(28, 148, 39, 159, 35, 155, 40, 160)(41, 161, 49, 169, 44, 164, 50, 170)(42, 162, 51, 171, 43, 163, 52, 172)(45, 165, 53, 173, 48, 168, 54, 174)(46, 166, 55, 175, 47, 167, 56, 176)(57, 177, 65, 185, 60, 180, 66, 186)(58, 178, 67, 187, 59, 179, 68, 188)(61, 181, 69, 189, 64, 184, 70, 190)(62, 182, 71, 191, 63, 183, 72, 192)(73, 193, 81, 201, 76, 196, 82, 202)(74, 194, 83, 203, 75, 195, 84, 204)(77, 197, 85, 205, 80, 200, 86, 206)(78, 198, 87, 207, 79, 199, 88, 208)(89, 209, 97, 217, 92, 212, 98, 218)(90, 210, 99, 219, 91, 211, 100, 220)(93, 213, 101, 221, 96, 216, 102, 222)(94, 214, 103, 223, 95, 215, 104, 224)(105, 225, 113, 233, 108, 228, 114, 234)(106, 226, 115, 235, 107, 227, 116, 236)(109, 229, 117, 237, 112, 232, 118, 238)(110, 230, 119, 239, 111, 231, 120, 240)(241, 361, 243, 363)(242, 362, 247, 367)(244, 364, 250, 370)(245, 365, 253, 373)(246, 366, 254, 374)(248, 368, 257, 377)(249, 369, 260, 380)(251, 371, 263, 383)(252, 372, 264, 384)(255, 375, 259, 379)(256, 376, 267, 387)(258, 378, 268, 388)(261, 381, 270, 390)(262, 382, 272, 392)(265, 385, 275, 395)(266, 386, 276, 396)(269, 389, 281, 401)(271, 391, 282, 402)(273, 393, 283, 403)(274, 394, 284, 404)(277, 397, 285, 405)(278, 398, 286, 406)(279, 399, 287, 407)(280, 400, 288, 408)(289, 409, 297, 417)(290, 410, 298, 418)(291, 411, 299, 419)(292, 412, 300, 420)(293, 413, 301, 421)(294, 414, 302, 422)(295, 415, 303, 423)(296, 416, 304, 424)(305, 425, 313, 433)(306, 426, 314, 434)(307, 427, 315, 435)(308, 428, 316, 436)(309, 429, 317, 437)(310, 430, 318, 438)(311, 431, 319, 439)(312, 432, 320, 440)(321, 441, 329, 449)(322, 442, 330, 450)(323, 443, 331, 451)(324, 444, 332, 452)(325, 445, 333, 453)(326, 446, 334, 454)(327, 447, 335, 455)(328, 448, 336, 456)(337, 457, 345, 465)(338, 458, 346, 466)(339, 459, 347, 467)(340, 460, 348, 468)(341, 461, 349, 469)(342, 462, 350, 470)(343, 463, 351, 471)(344, 464, 352, 472)(353, 473, 360, 480)(354, 474, 357, 477)(355, 475, 358, 478)(356, 476, 359, 479) L = (1, 244)(2, 248)(3, 250)(4, 241)(5, 252)(6, 255)(7, 257)(8, 242)(9, 261)(10, 243)(11, 262)(12, 245)(13, 264)(14, 259)(15, 246)(16, 265)(17, 247)(18, 266)(19, 254)(20, 270)(21, 249)(22, 251)(23, 272)(24, 253)(25, 256)(26, 258)(27, 275)(28, 276)(29, 273)(30, 260)(31, 274)(32, 263)(33, 269)(34, 271)(35, 267)(36, 268)(37, 279)(38, 280)(39, 277)(40, 278)(41, 283)(42, 284)(43, 281)(44, 282)(45, 287)(46, 288)(47, 285)(48, 286)(49, 291)(50, 292)(51, 289)(52, 290)(53, 295)(54, 296)(55, 293)(56, 294)(57, 299)(58, 300)(59, 297)(60, 298)(61, 303)(62, 304)(63, 301)(64, 302)(65, 307)(66, 308)(67, 305)(68, 306)(69, 311)(70, 312)(71, 309)(72, 310)(73, 315)(74, 316)(75, 313)(76, 314)(77, 319)(78, 320)(79, 317)(80, 318)(81, 323)(82, 324)(83, 321)(84, 322)(85, 327)(86, 328)(87, 325)(88, 326)(89, 331)(90, 332)(91, 329)(92, 330)(93, 335)(94, 336)(95, 333)(96, 334)(97, 339)(98, 340)(99, 337)(100, 338)(101, 343)(102, 344)(103, 341)(104, 342)(105, 347)(106, 348)(107, 345)(108, 346)(109, 351)(110, 352)(111, 349)(112, 350)(113, 355)(114, 356)(115, 353)(116, 354)(117, 359)(118, 360)(119, 357)(120, 358)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.1193 Graph:: simple bipartite v = 90 e = 240 f = 120 degree seq :: [ 4^60, 8^30 ] E16.1196 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 6}) Quotient :: edge Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^4, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 3, 9, 5)(2, 6, 16, 7)(4, 11, 22, 12)(8, 20, 14, 21)(10, 23, 13, 24)(15, 29, 19, 30)(17, 31, 18, 32)(25, 41, 28, 42)(26, 43, 27, 44)(33, 53, 36, 54)(34, 55, 35, 56)(37, 57, 40, 58)(38, 59, 39, 60)(45, 69, 48, 70)(46, 71, 47, 72)(49, 73, 52, 74)(50, 75, 51, 76)(61, 89, 64, 90)(62, 80, 63, 77)(65, 91, 68, 92)(66, 85, 67, 84)(78, 97, 79, 98)(81, 99, 82, 100)(83, 101, 86, 102)(87, 103, 88, 104)(93, 105, 94, 106)(95, 107, 96, 108)(109, 115, 110, 116)(111, 117, 112, 118)(113, 119, 114, 120)(121, 122, 124)(123, 128, 130)(125, 133, 134)(126, 135, 137)(127, 138, 139)(129, 142, 136)(131, 145, 146)(132, 147, 148)(140, 153, 154)(141, 155, 156)(143, 157, 158)(144, 159, 160)(149, 165, 166)(150, 167, 168)(151, 169, 170)(152, 171, 172)(161, 181, 182)(162, 183, 184)(163, 185, 186)(164, 187, 188)(173, 197, 198)(174, 199, 200)(175, 190, 201)(176, 202, 189)(177, 203, 204)(178, 205, 206)(179, 207, 194)(180, 193, 208)(191, 210, 213)(192, 214, 209)(195, 215, 212)(196, 211, 216)(217, 222, 229)(218, 230, 221)(219, 231, 224)(220, 223, 232)(225, 233, 228)(226, 227, 234)(235, 240, 238)(236, 237, 239) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 12^3 ), ( 12^4 ) } Outer automorphisms :: reflexible Dual of E16.1205 Transitivity :: ET+ Graph:: simple bipartite v = 70 e = 120 f = 20 degree seq :: [ 3^40, 4^30 ] E16.1197 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 6}) Quotient :: edge Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^4, (F * T1)^2, (F * T2)^2, (T1 * T2^-1)^4, (T2, T1^-1)^2, (T2^-2 * T1^-1 * T2^-1 * T1^-1)^2, T2^2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-2 * T1^-1, T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1, (T2 * T1 * T2 * T1 * T2 * T1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 3, 9, 5)(2, 6, 16, 7)(4, 11, 27, 12)(8, 20, 46, 21)(10, 24, 54, 25)(13, 31, 67, 32)(14, 33, 69, 34)(15, 35, 74, 36)(17, 39, 82, 40)(18, 41, 84, 42)(19, 43, 85, 44)(22, 49, 86, 50)(23, 51, 98, 52)(26, 57, 103, 55)(28, 60, 109, 61)(29, 62, 101, 63)(30, 64, 94, 65)(37, 77, 110, 78)(38, 79, 47, 80)(45, 88, 72, 89)(48, 92, 83, 93)(53, 100, 119, 99)(56, 104, 66, 105)(58, 107, 71, 97)(59, 108, 75, 90)(68, 95, 118, 91)(70, 96, 76, 113)(73, 114, 87, 102)(81, 116, 120, 115)(106, 117, 111, 112)(121, 122, 124)(123, 128, 130)(125, 133, 134)(126, 135, 137)(127, 138, 139)(129, 142, 143)(131, 146, 148)(132, 149, 150)(136, 157, 158)(140, 165, 167)(141, 168, 160)(144, 173, 162)(145, 175, 176)(147, 178, 179)(151, 186, 163)(152, 180, 188)(153, 182, 190)(154, 191, 192)(155, 193, 195)(156, 196, 181)(159, 201, 183)(161, 203, 184)(164, 206, 207)(166, 210, 211)(169, 214, 215)(170, 216, 199)(171, 217, 213)(172, 219, 194)(174, 221, 222)(177, 226, 218)(185, 230, 231)(187, 232, 202)(189, 220, 197)(198, 225, 228)(200, 235, 223)(204, 209, 229)(205, 236, 227)(208, 237, 234)(212, 233, 224)(238, 240, 239) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 12^3 ), ( 12^4 ) } Outer automorphisms :: reflexible Dual of E16.1204 Transitivity :: ET+ Graph:: simple bipartite v = 70 e = 120 f = 20 degree seq :: [ 3^40, 4^30 ] E16.1198 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 6}) Quotient :: edge Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1)^3, (T2^-2 * T1)^2, T2^6, (T2^-1, T1)^2, T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2 * T1 * T2^2 * T1^-1 * T2^-1 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 29, 16, 5)(2, 7, 20, 50, 24, 8)(4, 12, 33, 72, 36, 13)(6, 17, 42, 84, 46, 18)(9, 26, 59, 99, 62, 27)(11, 30, 14, 38, 69, 31)(15, 39, 65, 94, 48, 19)(21, 51, 22, 54, 100, 52)(23, 55, 97, 66, 82, 41)(25, 57, 102, 53, 101, 58)(28, 63, 108, 79, 40, 64)(32, 45, 89, 67, 98, 68)(34, 73, 35, 75, 110, 74)(37, 77, 93, 70, 109, 78)(43, 85, 44, 88, 115, 86)(47, 91, 116, 87, 80, 92)(49, 95, 118, 103, 56, 96)(60, 104, 61, 81, 112, 107)(71, 106, 119, 111, 76, 105)(83, 113, 120, 117, 90, 114)(121, 122, 126, 124)(123, 129, 145, 131)(125, 134, 157, 135)(127, 139, 167, 141)(128, 142, 173, 143)(130, 148, 176, 144)(132, 152, 190, 154)(133, 155, 180, 146)(136, 153, 191, 160)(137, 161, 201, 163)(138, 164, 207, 165)(140, 169, 210, 166)(147, 181, 215, 172)(149, 185, 205, 182)(150, 186, 204, 187)(151, 188, 212, 183)(156, 162, 203, 196)(158, 199, 224, 175)(159, 195, 231, 200)(168, 213, 233, 206)(170, 217, 193, 214)(171, 218, 192, 219)(174, 223, 197, 209)(177, 220, 236, 225)(178, 226, 194, 202)(179, 208, 237, 221)(184, 211, 235, 227)(189, 222, 234, 229)(198, 216, 232, 230)(228, 239, 240, 238) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 6^4 ), ( 6^6 ) } Outer automorphisms :: reflexible Dual of E16.1207 Transitivity :: ET+ Graph:: simple bipartite v = 50 e = 120 f = 40 degree seq :: [ 4^30, 6^20 ] E16.1199 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 6}) Quotient :: edge Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2 * T1^-1)^2, T2^6, (T1^-1 * T2^-1)^3, T2^-2 * T1^-1 * T2 * T1^2 * T2 * T1^-1 * T2^-2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 24, 14, 5)(2, 7, 18, 36, 20, 8)(4, 11, 26, 46, 27, 12)(6, 15, 31, 52, 33, 16)(9, 21, 39, 62, 41, 22)(13, 28, 49, 56, 34, 17)(19, 37, 60, 73, 50, 30)(23, 38, 58, 79, 66, 42)(25, 32, 53, 77, 68, 44)(29, 43, 64, 84, 69, 45)(35, 54, 75, 93, 81, 57)(40, 63, 86, 100, 82, 59)(47, 70, 89, 95, 74, 51)(48, 67, 88, 106, 91, 71)(55, 78, 98, 110, 96, 76)(61, 72, 92, 108, 102, 83)(65, 87, 104, 114, 103, 85)(80, 99, 112, 118, 111, 97)(90, 101, 113, 119, 115, 105)(94, 109, 117, 120, 116, 107)(121, 122, 126, 124)(123, 129, 139, 128)(125, 131, 145, 133)(127, 137, 152, 136)(130, 143, 160, 142)(132, 135, 150, 141)(134, 148, 168, 149)(138, 155, 175, 154)(140, 157, 179, 158)(144, 163, 185, 162)(146, 165, 187, 164)(147, 159, 181, 167)(151, 171, 192, 170)(153, 173, 196, 174)(156, 178, 200, 177)(161, 183, 205, 184)(166, 190, 210, 189)(169, 186, 207, 191)(172, 195, 214, 194)(176, 198, 217, 199)(180, 201, 219, 202)(182, 204, 221, 203)(188, 208, 225, 209)(193, 212, 227, 213)(197, 215, 229, 216)(206, 222, 233, 223)(211, 224, 231, 218)(220, 232, 236, 228)(226, 230, 237, 235)(234, 239, 240, 238) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 6^4 ), ( 6^6 ) } Outer automorphisms :: reflexible Dual of E16.1206 Transitivity :: ET+ Graph:: simple bipartite v = 50 e = 120 f = 40 degree seq :: [ 4^30, 6^20 ] E16.1200 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 6}) Quotient :: edge Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1)^2, T1^6, (T2 * T1 * T2^-1 * T1)^2, (T1^2 * T2^-1)^3 ] 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, 23)(14, 34, 35)(15, 36, 37)(16, 38, 39)(19, 43, 44)(20, 45, 47)(21, 49, 50)(22, 51, 52)(27, 59, 33)(29, 56, 61)(30, 62, 55)(32, 54, 65)(40, 71, 72)(41, 73, 74)(42, 75, 76)(46, 63, 48)(53, 83, 84)(57, 68, 87)(58, 88, 67)(60, 66, 90)(64, 94, 91)(69, 97, 98)(70, 99, 100)(77, 82, 92)(78, 105, 81)(79, 80, 96)(85, 89, 86)(93, 109, 95)(101, 117, 104)(102, 103, 106)(107, 111, 110)(108, 112, 119)(113, 120, 116)(114, 115, 118)(121, 122, 126, 136, 132, 124)(123, 129, 143, 173, 147, 130)(125, 134, 153, 160, 137, 135)(127, 139, 133, 152, 166, 140)(128, 141, 168, 189, 158, 142)(131, 149, 159, 190, 183, 150)(138, 161, 179, 184, 151, 162)(144, 164, 148, 180, 205, 174)(145, 175, 206, 227, 203, 176)(146, 177, 204, 228, 209, 178)(154, 163, 157, 167, 199, 186)(155, 187, 216, 221, 191, 188)(156, 172, 192, 222, 200, 169)(165, 197, 185, 215, 210, 198)(170, 201, 226, 233, 217, 202)(171, 196, 218, 234, 223, 193)(181, 211, 230, 235, 219, 195)(182, 212, 220, 236, 231, 213)(194, 224, 238, 232, 214, 207)(208, 229, 239, 240, 237, 225) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 8^3 ), ( 8^6 ) } Outer automorphisms :: reflexible Dual of E16.1202 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 120 f = 30 degree seq :: [ 3^40, 6^20 ] E16.1201 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 6}) Quotient :: edge Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1^6, T1^6, (T2 * T1^-3)^2, (T1^-1, T2^-1)^2, (T2^-1 * T1^-1)^4, (T1 * T2^-1)^4, T2 * T1 * T2 * T1^-2 * T2^-1 * T1 * T2^-1 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 11, 13)(6, 17, 18)(9, 24, 25)(10, 26, 28)(12, 31, 32)(14, 36, 37)(15, 38, 40)(16, 41, 42)(19, 48, 49)(20, 50, 52)(21, 54, 55)(22, 56, 58)(23, 59, 60)(27, 65, 66)(29, 69, 67)(30, 70, 71)(33, 72, 73)(34, 74, 61)(35, 75, 76)(39, 80, 81)(43, 83, 84)(44, 85, 86)(45, 87, 88)(46, 89, 90)(47, 91, 92)(51, 96, 97)(53, 99, 100)(57, 104, 105)(62, 109, 78)(63, 110, 79)(64, 111, 82)(68, 112, 77)(93, 117, 102)(94, 107, 103)(95, 118, 106)(98, 114, 101)(108, 113, 119)(115, 120, 116)(121, 122, 126, 136, 132, 124)(123, 129, 143, 162, 147, 130)(125, 134, 155, 161, 159, 135)(127, 139, 167, 152, 171, 140)(128, 141, 173, 151, 177, 142)(131, 149, 166, 138, 165, 150)(133, 153, 164, 137, 163, 154)(144, 181, 228, 186, 205, 182)(145, 183, 211, 185, 218, 172)(146, 184, 224, 180, 222, 175)(148, 187, 227, 179, 207, 188)(156, 197, 220, 201, 223, 176)(157, 190, 233, 200, 210, 198)(158, 192, 234, 196, 204, 199)(160, 202, 217, 195, 213, 168)(169, 214, 194, 216, 232, 206)(170, 215, 189, 212, 236, 208)(174, 221, 191, 225, 230, 209)(178, 226, 193, 219, 235, 203)(229, 238, 231, 239, 240, 237) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 8^3 ), ( 8^6 ) } Outer automorphisms :: reflexible Dual of E16.1203 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 120 f = 30 degree seq :: [ 3^40, 6^20 ] E16.1202 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 6}) Quotient :: loop Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^4, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123, 9, 129, 5, 125)(2, 122, 6, 126, 16, 136, 7, 127)(4, 124, 11, 131, 22, 142, 12, 132)(8, 128, 20, 140, 14, 134, 21, 141)(10, 130, 23, 143, 13, 133, 24, 144)(15, 135, 29, 149, 19, 139, 30, 150)(17, 137, 31, 151, 18, 138, 32, 152)(25, 145, 41, 161, 28, 148, 42, 162)(26, 146, 43, 163, 27, 147, 44, 164)(33, 153, 53, 173, 36, 156, 54, 174)(34, 154, 55, 175, 35, 155, 56, 176)(37, 157, 57, 177, 40, 160, 58, 178)(38, 158, 59, 179, 39, 159, 60, 180)(45, 165, 69, 189, 48, 168, 70, 190)(46, 166, 71, 191, 47, 167, 72, 192)(49, 169, 73, 193, 52, 172, 74, 194)(50, 170, 75, 195, 51, 171, 76, 196)(61, 181, 89, 209, 64, 184, 90, 210)(62, 182, 80, 200, 63, 183, 77, 197)(65, 185, 91, 211, 68, 188, 92, 212)(66, 186, 85, 205, 67, 187, 84, 204)(78, 198, 97, 217, 79, 199, 98, 218)(81, 201, 99, 219, 82, 202, 100, 220)(83, 203, 101, 221, 86, 206, 102, 222)(87, 207, 103, 223, 88, 208, 104, 224)(93, 213, 105, 225, 94, 214, 106, 226)(95, 215, 107, 227, 96, 216, 108, 228)(109, 229, 115, 235, 110, 230, 116, 236)(111, 231, 117, 237, 112, 232, 118, 238)(113, 233, 119, 239, 114, 234, 120, 240) L = (1, 122)(2, 124)(3, 128)(4, 121)(5, 133)(6, 135)(7, 138)(8, 130)(9, 142)(10, 123)(11, 145)(12, 147)(13, 134)(14, 125)(15, 137)(16, 129)(17, 126)(18, 139)(19, 127)(20, 153)(21, 155)(22, 136)(23, 157)(24, 159)(25, 146)(26, 131)(27, 148)(28, 132)(29, 165)(30, 167)(31, 169)(32, 171)(33, 154)(34, 140)(35, 156)(36, 141)(37, 158)(38, 143)(39, 160)(40, 144)(41, 181)(42, 183)(43, 185)(44, 187)(45, 166)(46, 149)(47, 168)(48, 150)(49, 170)(50, 151)(51, 172)(52, 152)(53, 197)(54, 199)(55, 190)(56, 202)(57, 203)(58, 205)(59, 207)(60, 193)(61, 182)(62, 161)(63, 184)(64, 162)(65, 186)(66, 163)(67, 188)(68, 164)(69, 176)(70, 201)(71, 210)(72, 214)(73, 208)(74, 179)(75, 215)(76, 211)(77, 198)(78, 173)(79, 200)(80, 174)(81, 175)(82, 189)(83, 204)(84, 177)(85, 206)(86, 178)(87, 194)(88, 180)(89, 192)(90, 213)(91, 216)(92, 195)(93, 191)(94, 209)(95, 212)(96, 196)(97, 222)(98, 230)(99, 231)(100, 223)(101, 218)(102, 229)(103, 232)(104, 219)(105, 233)(106, 227)(107, 234)(108, 225)(109, 217)(110, 221)(111, 224)(112, 220)(113, 228)(114, 226)(115, 240)(116, 237)(117, 239)(118, 235)(119, 236)(120, 238) local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: reflexible Dual of E16.1200 Transitivity :: ET+ VT+ AT Graph:: v = 30 e = 120 f = 60 degree seq :: [ 8^30 ] E16.1203 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 6}) Quotient :: loop Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^4, (F * T1)^2, (F * T2)^2, (T1 * T2^-1)^4, (T2, T1^-1)^2, (T2^-2 * T1^-1 * T2^-1 * T1^-1)^2, T2^2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-2 * T1^-1, T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1, (T2 * T1 * T2 * T1 * T2 * T1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123, 9, 129, 5, 125)(2, 122, 6, 126, 16, 136, 7, 127)(4, 124, 11, 131, 27, 147, 12, 132)(8, 128, 20, 140, 46, 166, 21, 141)(10, 130, 24, 144, 54, 174, 25, 145)(13, 133, 31, 151, 67, 187, 32, 152)(14, 134, 33, 153, 69, 189, 34, 154)(15, 135, 35, 155, 74, 194, 36, 156)(17, 137, 39, 159, 82, 202, 40, 160)(18, 138, 41, 161, 84, 204, 42, 162)(19, 139, 43, 163, 85, 205, 44, 164)(22, 142, 49, 169, 86, 206, 50, 170)(23, 143, 51, 171, 98, 218, 52, 172)(26, 146, 57, 177, 103, 223, 55, 175)(28, 148, 60, 180, 109, 229, 61, 181)(29, 149, 62, 182, 101, 221, 63, 183)(30, 150, 64, 184, 94, 214, 65, 185)(37, 157, 77, 197, 110, 230, 78, 198)(38, 158, 79, 199, 47, 167, 80, 200)(45, 165, 88, 208, 72, 192, 89, 209)(48, 168, 92, 212, 83, 203, 93, 213)(53, 173, 100, 220, 119, 239, 99, 219)(56, 176, 104, 224, 66, 186, 105, 225)(58, 178, 107, 227, 71, 191, 97, 217)(59, 179, 108, 228, 75, 195, 90, 210)(68, 188, 95, 215, 118, 238, 91, 211)(70, 190, 96, 216, 76, 196, 113, 233)(73, 193, 114, 234, 87, 207, 102, 222)(81, 201, 116, 236, 120, 240, 115, 235)(106, 226, 117, 237, 111, 231, 112, 232) L = (1, 122)(2, 124)(3, 128)(4, 121)(5, 133)(6, 135)(7, 138)(8, 130)(9, 142)(10, 123)(11, 146)(12, 149)(13, 134)(14, 125)(15, 137)(16, 157)(17, 126)(18, 139)(19, 127)(20, 165)(21, 168)(22, 143)(23, 129)(24, 173)(25, 175)(26, 148)(27, 178)(28, 131)(29, 150)(30, 132)(31, 186)(32, 180)(33, 182)(34, 191)(35, 193)(36, 196)(37, 158)(38, 136)(39, 201)(40, 141)(41, 203)(42, 144)(43, 151)(44, 206)(45, 167)(46, 210)(47, 140)(48, 160)(49, 214)(50, 216)(51, 217)(52, 219)(53, 162)(54, 221)(55, 176)(56, 145)(57, 226)(58, 179)(59, 147)(60, 188)(61, 156)(62, 190)(63, 159)(64, 161)(65, 230)(66, 163)(67, 232)(68, 152)(69, 220)(70, 153)(71, 192)(72, 154)(73, 195)(74, 172)(75, 155)(76, 181)(77, 189)(78, 225)(79, 170)(80, 235)(81, 183)(82, 187)(83, 184)(84, 209)(85, 236)(86, 207)(87, 164)(88, 237)(89, 229)(90, 211)(91, 166)(92, 233)(93, 171)(94, 215)(95, 169)(96, 199)(97, 213)(98, 177)(99, 194)(100, 197)(101, 222)(102, 174)(103, 200)(104, 212)(105, 228)(106, 218)(107, 205)(108, 198)(109, 204)(110, 231)(111, 185)(112, 202)(113, 224)(114, 208)(115, 223)(116, 227)(117, 234)(118, 240)(119, 238)(120, 239) local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: reflexible Dual of E16.1201 Transitivity :: ET+ VT+ AT Graph:: simple v = 30 e = 120 f = 60 degree seq :: [ 8^30 ] E16.1204 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 6}) Quotient :: loop Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1)^3, (T2^-2 * T1)^2, T2^6, (T2^-1, T1)^2, T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2 * T1 * T2^2 * T1^-1 * T2^-1 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123, 10, 130, 29, 149, 16, 136, 5, 125)(2, 122, 7, 127, 20, 140, 50, 170, 24, 144, 8, 128)(4, 124, 12, 132, 33, 153, 72, 192, 36, 156, 13, 133)(6, 126, 17, 137, 42, 162, 84, 204, 46, 166, 18, 138)(9, 129, 26, 146, 59, 179, 99, 219, 62, 182, 27, 147)(11, 131, 30, 150, 14, 134, 38, 158, 69, 189, 31, 151)(15, 135, 39, 159, 65, 185, 94, 214, 48, 168, 19, 139)(21, 141, 51, 171, 22, 142, 54, 174, 100, 220, 52, 172)(23, 143, 55, 175, 97, 217, 66, 186, 82, 202, 41, 161)(25, 145, 57, 177, 102, 222, 53, 173, 101, 221, 58, 178)(28, 148, 63, 183, 108, 228, 79, 199, 40, 160, 64, 184)(32, 152, 45, 165, 89, 209, 67, 187, 98, 218, 68, 188)(34, 154, 73, 193, 35, 155, 75, 195, 110, 230, 74, 194)(37, 157, 77, 197, 93, 213, 70, 190, 109, 229, 78, 198)(43, 163, 85, 205, 44, 164, 88, 208, 115, 235, 86, 206)(47, 167, 91, 211, 116, 236, 87, 207, 80, 200, 92, 212)(49, 169, 95, 215, 118, 238, 103, 223, 56, 176, 96, 216)(60, 180, 104, 224, 61, 181, 81, 201, 112, 232, 107, 227)(71, 191, 106, 226, 119, 239, 111, 231, 76, 196, 105, 225)(83, 203, 113, 233, 120, 240, 117, 237, 90, 210, 114, 234) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 134)(6, 124)(7, 139)(8, 142)(9, 145)(10, 148)(11, 123)(12, 152)(13, 155)(14, 157)(15, 125)(16, 153)(17, 161)(18, 164)(19, 167)(20, 169)(21, 127)(22, 173)(23, 128)(24, 130)(25, 131)(26, 133)(27, 181)(28, 176)(29, 185)(30, 186)(31, 188)(32, 190)(33, 191)(34, 132)(35, 180)(36, 162)(37, 135)(38, 199)(39, 195)(40, 136)(41, 201)(42, 203)(43, 137)(44, 207)(45, 138)(46, 140)(47, 141)(48, 213)(49, 210)(50, 217)(51, 218)(52, 147)(53, 143)(54, 223)(55, 158)(56, 144)(57, 220)(58, 226)(59, 208)(60, 146)(61, 215)(62, 149)(63, 151)(64, 211)(65, 205)(66, 204)(67, 150)(68, 212)(69, 222)(70, 154)(71, 160)(72, 219)(73, 214)(74, 202)(75, 231)(76, 156)(77, 209)(78, 216)(79, 224)(80, 159)(81, 163)(82, 178)(83, 196)(84, 187)(85, 182)(86, 168)(87, 165)(88, 237)(89, 174)(90, 166)(91, 235)(92, 183)(93, 233)(94, 170)(95, 172)(96, 232)(97, 193)(98, 192)(99, 171)(100, 236)(101, 179)(102, 234)(103, 197)(104, 175)(105, 177)(106, 194)(107, 184)(108, 239)(109, 189)(110, 198)(111, 200)(112, 230)(113, 206)(114, 229)(115, 227)(116, 225)(117, 221)(118, 228)(119, 240)(120, 238) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E16.1197 Transitivity :: ET+ VT+ AT Graph:: v = 20 e = 120 f = 70 degree seq :: [ 12^20 ] E16.1205 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 6}) Quotient :: loop Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2 * T1^-1)^2, T2^6, (T1^-1 * T2^-1)^3, T2^-2 * T1^-1 * T2 * T1^2 * T2 * T1^-1 * T2^-2 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123, 10, 130, 24, 144, 14, 134, 5, 125)(2, 122, 7, 127, 18, 138, 36, 156, 20, 140, 8, 128)(4, 124, 11, 131, 26, 146, 46, 166, 27, 147, 12, 132)(6, 126, 15, 135, 31, 151, 52, 172, 33, 153, 16, 136)(9, 129, 21, 141, 39, 159, 62, 182, 41, 161, 22, 142)(13, 133, 28, 148, 49, 169, 56, 176, 34, 154, 17, 137)(19, 139, 37, 157, 60, 180, 73, 193, 50, 170, 30, 150)(23, 143, 38, 158, 58, 178, 79, 199, 66, 186, 42, 162)(25, 145, 32, 152, 53, 173, 77, 197, 68, 188, 44, 164)(29, 149, 43, 163, 64, 184, 84, 204, 69, 189, 45, 165)(35, 155, 54, 174, 75, 195, 93, 213, 81, 201, 57, 177)(40, 160, 63, 183, 86, 206, 100, 220, 82, 202, 59, 179)(47, 167, 70, 190, 89, 209, 95, 215, 74, 194, 51, 171)(48, 168, 67, 187, 88, 208, 106, 226, 91, 211, 71, 191)(55, 175, 78, 198, 98, 218, 110, 230, 96, 216, 76, 196)(61, 181, 72, 192, 92, 212, 108, 228, 102, 222, 83, 203)(65, 185, 87, 207, 104, 224, 114, 234, 103, 223, 85, 205)(80, 200, 99, 219, 112, 232, 118, 238, 111, 231, 97, 217)(90, 210, 101, 221, 113, 233, 119, 239, 115, 235, 105, 225)(94, 214, 109, 229, 117, 237, 120, 240, 116, 236, 107, 227) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 131)(6, 124)(7, 137)(8, 123)(9, 139)(10, 143)(11, 145)(12, 135)(13, 125)(14, 148)(15, 150)(16, 127)(17, 152)(18, 155)(19, 128)(20, 157)(21, 132)(22, 130)(23, 160)(24, 163)(25, 133)(26, 165)(27, 159)(28, 168)(29, 134)(30, 141)(31, 171)(32, 136)(33, 173)(34, 138)(35, 175)(36, 178)(37, 179)(38, 140)(39, 181)(40, 142)(41, 183)(42, 144)(43, 185)(44, 146)(45, 187)(46, 190)(47, 147)(48, 149)(49, 186)(50, 151)(51, 192)(52, 195)(53, 196)(54, 153)(55, 154)(56, 198)(57, 156)(58, 200)(59, 158)(60, 201)(61, 167)(62, 204)(63, 205)(64, 161)(65, 162)(66, 207)(67, 164)(68, 208)(69, 166)(70, 210)(71, 169)(72, 170)(73, 212)(74, 172)(75, 214)(76, 174)(77, 215)(78, 217)(79, 176)(80, 177)(81, 219)(82, 180)(83, 182)(84, 221)(85, 184)(86, 222)(87, 191)(88, 225)(89, 188)(90, 189)(91, 224)(92, 227)(93, 193)(94, 194)(95, 229)(96, 197)(97, 199)(98, 211)(99, 202)(100, 232)(101, 203)(102, 233)(103, 206)(104, 231)(105, 209)(106, 230)(107, 213)(108, 220)(109, 216)(110, 237)(111, 218)(112, 236)(113, 223)(114, 239)(115, 226)(116, 228)(117, 235)(118, 234)(119, 240)(120, 238) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E16.1196 Transitivity :: ET+ VT+ AT Graph:: v = 20 e = 120 f = 70 degree seq :: [ 12^20 ] E16.1206 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 6}) Quotient :: loop Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1)^2, T1^6, (T2 * T1 * T2^-1 * T1)^2, (T1^2 * T2^-1)^3 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123, 5, 125)(2, 122, 7, 127, 8, 128)(4, 124, 11, 131, 13, 133)(6, 126, 17, 137, 18, 138)(9, 129, 24, 144, 25, 145)(10, 130, 26, 146, 28, 148)(12, 132, 31, 151, 23, 143)(14, 134, 34, 154, 35, 155)(15, 135, 36, 156, 37, 157)(16, 136, 38, 158, 39, 159)(19, 139, 43, 163, 44, 164)(20, 140, 45, 165, 47, 167)(21, 141, 49, 169, 50, 170)(22, 142, 51, 171, 52, 172)(27, 147, 59, 179, 33, 153)(29, 149, 56, 176, 61, 181)(30, 150, 62, 182, 55, 175)(32, 152, 54, 174, 65, 185)(40, 160, 71, 191, 72, 192)(41, 161, 73, 193, 74, 194)(42, 162, 75, 195, 76, 196)(46, 166, 63, 183, 48, 168)(53, 173, 83, 203, 84, 204)(57, 177, 68, 188, 87, 207)(58, 178, 88, 208, 67, 187)(60, 180, 66, 186, 90, 210)(64, 184, 94, 214, 91, 211)(69, 189, 97, 217, 98, 218)(70, 190, 99, 219, 100, 220)(77, 197, 82, 202, 92, 212)(78, 198, 105, 225, 81, 201)(79, 199, 80, 200, 96, 216)(85, 205, 89, 209, 86, 206)(93, 213, 109, 229, 95, 215)(101, 221, 117, 237, 104, 224)(102, 222, 103, 223, 106, 226)(107, 227, 111, 231, 110, 230)(108, 228, 112, 232, 119, 239)(113, 233, 120, 240, 116, 236)(114, 234, 115, 235, 118, 238) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 134)(6, 136)(7, 139)(8, 141)(9, 143)(10, 123)(11, 149)(12, 124)(13, 152)(14, 153)(15, 125)(16, 132)(17, 135)(18, 161)(19, 133)(20, 127)(21, 168)(22, 128)(23, 173)(24, 164)(25, 175)(26, 177)(27, 130)(28, 180)(29, 159)(30, 131)(31, 162)(32, 166)(33, 160)(34, 163)(35, 187)(36, 172)(37, 167)(38, 142)(39, 190)(40, 137)(41, 179)(42, 138)(43, 157)(44, 148)(45, 197)(46, 140)(47, 199)(48, 189)(49, 156)(50, 201)(51, 196)(52, 192)(53, 147)(54, 144)(55, 206)(56, 145)(57, 204)(58, 146)(59, 184)(60, 205)(61, 211)(62, 212)(63, 150)(64, 151)(65, 215)(66, 154)(67, 216)(68, 155)(69, 158)(70, 183)(71, 188)(72, 222)(73, 171)(74, 224)(75, 181)(76, 218)(77, 185)(78, 165)(79, 186)(80, 169)(81, 226)(82, 170)(83, 176)(84, 228)(85, 174)(86, 227)(87, 194)(88, 229)(89, 178)(90, 198)(91, 230)(92, 220)(93, 182)(94, 207)(95, 210)(96, 221)(97, 202)(98, 234)(99, 195)(100, 236)(101, 191)(102, 200)(103, 193)(104, 238)(105, 208)(106, 233)(107, 203)(108, 209)(109, 239)(110, 235)(111, 213)(112, 214)(113, 217)(114, 223)(115, 219)(116, 231)(117, 225)(118, 232)(119, 240)(120, 237) local type(s) :: { ( 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.1199 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 40 e = 120 f = 50 degree seq :: [ 6^40 ] E16.1207 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 6}) Quotient :: loop Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1^6, T1^6, (T2 * T1^-3)^2, (T1^-1, T2^-1)^2, (T2^-1 * T1^-1)^4, (T1 * T2^-1)^4, T2 * T1 * T2 * T1^-2 * T2^-1 * T1 * T2^-1 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123, 5, 125)(2, 122, 7, 127, 8, 128)(4, 124, 11, 131, 13, 133)(6, 126, 17, 137, 18, 138)(9, 129, 24, 144, 25, 145)(10, 130, 26, 146, 28, 148)(12, 132, 31, 151, 32, 152)(14, 134, 36, 156, 37, 157)(15, 135, 38, 158, 40, 160)(16, 136, 41, 161, 42, 162)(19, 139, 48, 168, 49, 169)(20, 140, 50, 170, 52, 172)(21, 141, 54, 174, 55, 175)(22, 142, 56, 176, 58, 178)(23, 143, 59, 179, 60, 180)(27, 147, 65, 185, 66, 186)(29, 149, 69, 189, 67, 187)(30, 150, 70, 190, 71, 191)(33, 153, 72, 192, 73, 193)(34, 154, 74, 194, 61, 181)(35, 155, 75, 195, 76, 196)(39, 159, 80, 200, 81, 201)(43, 163, 83, 203, 84, 204)(44, 164, 85, 205, 86, 206)(45, 165, 87, 207, 88, 208)(46, 166, 89, 209, 90, 210)(47, 167, 91, 211, 92, 212)(51, 171, 96, 216, 97, 217)(53, 173, 99, 219, 100, 220)(57, 177, 104, 224, 105, 225)(62, 182, 109, 229, 78, 198)(63, 183, 110, 230, 79, 199)(64, 184, 111, 231, 82, 202)(68, 188, 112, 232, 77, 197)(93, 213, 117, 237, 102, 222)(94, 214, 107, 227, 103, 223)(95, 215, 118, 238, 106, 226)(98, 218, 114, 234, 101, 221)(108, 228, 113, 233, 119, 239)(115, 235, 120, 240, 116, 236) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 134)(6, 136)(7, 139)(8, 141)(9, 143)(10, 123)(11, 149)(12, 124)(13, 153)(14, 155)(15, 125)(16, 132)(17, 163)(18, 165)(19, 167)(20, 127)(21, 173)(22, 128)(23, 162)(24, 181)(25, 183)(26, 184)(27, 130)(28, 187)(29, 166)(30, 131)(31, 177)(32, 171)(33, 164)(34, 133)(35, 161)(36, 197)(37, 190)(38, 192)(39, 135)(40, 202)(41, 159)(42, 147)(43, 154)(44, 137)(45, 150)(46, 138)(47, 152)(48, 160)(49, 214)(50, 215)(51, 140)(52, 145)(53, 151)(54, 221)(55, 146)(56, 156)(57, 142)(58, 226)(59, 207)(60, 222)(61, 228)(62, 144)(63, 211)(64, 224)(65, 218)(66, 205)(67, 227)(68, 148)(69, 212)(70, 233)(71, 225)(72, 234)(73, 219)(74, 216)(75, 213)(76, 204)(77, 220)(78, 157)(79, 158)(80, 210)(81, 223)(82, 217)(83, 178)(84, 199)(85, 182)(86, 169)(87, 188)(88, 170)(89, 174)(90, 198)(91, 185)(92, 236)(93, 168)(94, 194)(95, 189)(96, 232)(97, 195)(98, 172)(99, 235)(100, 201)(101, 191)(102, 175)(103, 176)(104, 180)(105, 230)(106, 193)(107, 179)(108, 186)(109, 238)(110, 209)(111, 239)(112, 206)(113, 200)(114, 196)(115, 203)(116, 208)(117, 229)(118, 231)(119, 240)(120, 237) local type(s) :: { ( 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E16.1198 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 40 e = 120 f = 50 degree seq :: [ 6^40 ] E16.1208 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, Y2^4, (R * Y1)^2, (R * Y3)^2, (Y2 * Y3 * Y2)^2, Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-1, Y3 * Y2^-2 * Y1^-1 * Y2^-2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 121, 2, 122, 4, 124)(3, 123, 8, 128, 10, 130)(5, 125, 13, 133, 14, 134)(6, 126, 15, 135, 17, 137)(7, 127, 18, 138, 19, 139)(9, 129, 22, 142, 16, 136)(11, 131, 25, 145, 26, 146)(12, 132, 27, 147, 28, 148)(20, 140, 33, 153, 34, 154)(21, 141, 35, 155, 36, 156)(23, 143, 37, 157, 38, 158)(24, 144, 39, 159, 40, 160)(29, 149, 45, 165, 46, 166)(30, 150, 47, 167, 48, 168)(31, 151, 49, 169, 50, 170)(32, 152, 51, 171, 52, 172)(41, 161, 61, 181, 62, 182)(42, 162, 63, 183, 64, 184)(43, 163, 65, 185, 66, 186)(44, 164, 67, 187, 68, 188)(53, 173, 77, 197, 78, 198)(54, 174, 79, 199, 80, 200)(55, 175, 70, 190, 81, 201)(56, 176, 82, 202, 69, 189)(57, 177, 83, 203, 84, 204)(58, 178, 85, 205, 86, 206)(59, 179, 87, 207, 74, 194)(60, 180, 73, 193, 88, 208)(71, 191, 90, 210, 93, 213)(72, 192, 94, 214, 89, 209)(75, 195, 95, 215, 92, 212)(76, 196, 91, 211, 96, 216)(97, 217, 102, 222, 109, 229)(98, 218, 110, 230, 101, 221)(99, 219, 111, 231, 104, 224)(100, 220, 103, 223, 112, 232)(105, 225, 113, 233, 108, 228)(106, 226, 107, 227, 114, 234)(115, 235, 120, 240, 118, 238)(116, 236, 117, 237, 119, 239)(241, 361, 243, 363, 249, 369, 245, 365)(242, 362, 246, 366, 256, 376, 247, 367)(244, 364, 251, 371, 262, 382, 252, 372)(248, 368, 260, 380, 254, 374, 261, 381)(250, 370, 263, 383, 253, 373, 264, 384)(255, 375, 269, 389, 259, 379, 270, 390)(257, 377, 271, 391, 258, 378, 272, 392)(265, 385, 281, 401, 268, 388, 282, 402)(266, 386, 283, 403, 267, 387, 284, 404)(273, 393, 293, 413, 276, 396, 294, 414)(274, 394, 295, 415, 275, 395, 296, 416)(277, 397, 297, 417, 280, 400, 298, 418)(278, 398, 299, 419, 279, 399, 300, 420)(285, 405, 309, 429, 288, 408, 310, 430)(286, 406, 311, 431, 287, 407, 312, 432)(289, 409, 313, 433, 292, 412, 314, 434)(290, 410, 315, 435, 291, 411, 316, 436)(301, 421, 329, 449, 304, 424, 330, 450)(302, 422, 320, 440, 303, 423, 317, 437)(305, 425, 331, 451, 308, 428, 332, 452)(306, 426, 325, 445, 307, 427, 324, 444)(318, 438, 337, 457, 319, 439, 338, 458)(321, 441, 339, 459, 322, 442, 340, 460)(323, 443, 341, 461, 326, 446, 342, 462)(327, 447, 343, 463, 328, 448, 344, 464)(333, 453, 345, 465, 334, 454, 346, 466)(335, 455, 347, 467, 336, 456, 348, 468)(349, 469, 355, 475, 350, 470, 356, 476)(351, 471, 357, 477, 352, 472, 358, 478)(353, 473, 359, 479, 354, 474, 360, 480) L = (1, 244)(2, 241)(3, 250)(4, 242)(5, 254)(6, 257)(7, 259)(8, 243)(9, 256)(10, 248)(11, 266)(12, 268)(13, 245)(14, 253)(15, 246)(16, 262)(17, 255)(18, 247)(19, 258)(20, 274)(21, 276)(22, 249)(23, 278)(24, 280)(25, 251)(26, 265)(27, 252)(28, 267)(29, 286)(30, 288)(31, 290)(32, 292)(33, 260)(34, 273)(35, 261)(36, 275)(37, 263)(38, 277)(39, 264)(40, 279)(41, 302)(42, 304)(43, 306)(44, 308)(45, 269)(46, 285)(47, 270)(48, 287)(49, 271)(50, 289)(51, 272)(52, 291)(53, 318)(54, 320)(55, 321)(56, 309)(57, 324)(58, 326)(59, 314)(60, 328)(61, 281)(62, 301)(63, 282)(64, 303)(65, 283)(66, 305)(67, 284)(68, 307)(69, 322)(70, 295)(71, 333)(72, 329)(73, 300)(74, 327)(75, 332)(76, 336)(77, 293)(78, 317)(79, 294)(80, 319)(81, 310)(82, 296)(83, 297)(84, 323)(85, 298)(86, 325)(87, 299)(88, 313)(89, 334)(90, 311)(91, 316)(92, 335)(93, 330)(94, 312)(95, 315)(96, 331)(97, 349)(98, 341)(99, 344)(100, 352)(101, 350)(102, 337)(103, 340)(104, 351)(105, 348)(106, 354)(107, 346)(108, 353)(109, 342)(110, 338)(111, 339)(112, 343)(113, 345)(114, 347)(115, 358)(116, 359)(117, 356)(118, 360)(119, 357)(120, 355)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E16.1214 Graph:: bipartite v = 70 e = 240 f = 140 degree seq :: [ 6^40, 8^30 ] E16.1209 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3, Y2^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1, Y1^-1 * Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2, Y3 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3 * Y2, Y2^-1 * Y3 * Y2^-2 * Y3 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, Y2^-1 * Y1 * Y2 * Y1 * Y2^-2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2^-2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-2, Y3 * Y2^-2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-2, Y3^-1 * Y2^2 * Y3 * Y2^-2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y2^-2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-2 * Y1^-1, Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2^2 * Y3^-1 * Y2^-1, (Y3 * Y2 * Y1 * Y2 * Y1 * Y2)^2 ] Map:: R = (1, 121, 2, 122, 4, 124)(3, 123, 8, 128, 10, 130)(5, 125, 13, 133, 14, 134)(6, 126, 15, 135, 17, 137)(7, 127, 18, 138, 19, 139)(9, 129, 22, 142, 23, 143)(11, 131, 26, 146, 28, 148)(12, 132, 29, 149, 30, 150)(16, 136, 37, 157, 38, 158)(20, 140, 45, 165, 47, 167)(21, 141, 48, 168, 40, 160)(24, 144, 53, 173, 42, 162)(25, 145, 55, 175, 56, 176)(27, 147, 58, 178, 59, 179)(31, 151, 66, 186, 43, 163)(32, 152, 60, 180, 68, 188)(33, 153, 62, 182, 70, 190)(34, 154, 71, 191, 72, 192)(35, 155, 73, 193, 75, 195)(36, 156, 76, 196, 61, 181)(39, 159, 81, 201, 63, 183)(41, 161, 83, 203, 64, 184)(44, 164, 86, 206, 87, 207)(46, 166, 90, 210, 91, 211)(49, 169, 94, 214, 95, 215)(50, 170, 96, 216, 79, 199)(51, 171, 97, 217, 93, 213)(52, 172, 99, 219, 74, 194)(54, 174, 101, 221, 102, 222)(57, 177, 106, 226, 98, 218)(65, 185, 110, 230, 111, 231)(67, 187, 112, 232, 82, 202)(69, 189, 100, 220, 77, 197)(78, 198, 105, 225, 108, 228)(80, 200, 115, 235, 103, 223)(84, 204, 89, 209, 109, 229)(85, 205, 116, 236, 107, 227)(88, 208, 117, 237, 114, 234)(92, 212, 113, 233, 104, 224)(118, 238, 120, 240, 119, 239)(241, 361, 243, 363, 249, 369, 245, 365)(242, 362, 246, 366, 256, 376, 247, 367)(244, 364, 251, 371, 267, 387, 252, 372)(248, 368, 260, 380, 286, 406, 261, 381)(250, 370, 264, 384, 294, 414, 265, 385)(253, 373, 271, 391, 307, 427, 272, 392)(254, 374, 273, 393, 309, 429, 274, 394)(255, 375, 275, 395, 314, 434, 276, 396)(257, 377, 279, 399, 322, 442, 280, 400)(258, 378, 281, 401, 324, 444, 282, 402)(259, 379, 283, 403, 325, 445, 284, 404)(262, 382, 289, 409, 326, 446, 290, 410)(263, 383, 291, 411, 338, 458, 292, 412)(266, 386, 297, 417, 343, 463, 295, 415)(268, 388, 300, 420, 349, 469, 301, 421)(269, 389, 302, 422, 341, 461, 303, 423)(270, 390, 304, 424, 334, 454, 305, 425)(277, 397, 317, 437, 350, 470, 318, 438)(278, 398, 319, 439, 287, 407, 320, 440)(285, 405, 328, 448, 312, 432, 329, 449)(288, 408, 332, 452, 323, 443, 333, 453)(293, 413, 340, 460, 359, 479, 339, 459)(296, 416, 344, 464, 306, 426, 345, 465)(298, 418, 347, 467, 311, 431, 337, 457)(299, 419, 348, 468, 315, 435, 330, 450)(308, 428, 335, 455, 358, 478, 331, 451)(310, 430, 336, 456, 316, 436, 353, 473)(313, 433, 354, 474, 327, 447, 342, 462)(321, 441, 356, 476, 360, 480, 355, 475)(346, 466, 357, 477, 351, 471, 352, 472) L = (1, 244)(2, 241)(3, 250)(4, 242)(5, 254)(6, 257)(7, 259)(8, 243)(9, 263)(10, 248)(11, 268)(12, 270)(13, 245)(14, 253)(15, 246)(16, 278)(17, 255)(18, 247)(19, 258)(20, 287)(21, 280)(22, 249)(23, 262)(24, 282)(25, 296)(26, 251)(27, 299)(28, 266)(29, 252)(30, 269)(31, 283)(32, 308)(33, 310)(34, 312)(35, 315)(36, 301)(37, 256)(38, 277)(39, 303)(40, 288)(41, 304)(42, 293)(43, 306)(44, 327)(45, 260)(46, 331)(47, 285)(48, 261)(49, 335)(50, 319)(51, 333)(52, 314)(53, 264)(54, 342)(55, 265)(56, 295)(57, 338)(58, 267)(59, 298)(60, 272)(61, 316)(62, 273)(63, 321)(64, 323)(65, 351)(66, 271)(67, 322)(68, 300)(69, 317)(70, 302)(71, 274)(72, 311)(73, 275)(74, 339)(75, 313)(76, 276)(77, 340)(78, 348)(79, 336)(80, 343)(81, 279)(82, 352)(83, 281)(84, 349)(85, 347)(86, 284)(87, 326)(88, 354)(89, 324)(90, 286)(91, 330)(92, 344)(93, 337)(94, 289)(95, 334)(96, 290)(97, 291)(98, 346)(99, 292)(100, 309)(101, 294)(102, 341)(103, 355)(104, 353)(105, 318)(106, 297)(107, 356)(108, 345)(109, 329)(110, 305)(111, 350)(112, 307)(113, 332)(114, 357)(115, 320)(116, 325)(117, 328)(118, 359)(119, 360)(120, 358)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E16.1215 Graph:: bipartite v = 70 e = 240 f = 140 degree seq :: [ 6^40, 8^30 ] E16.1210 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^3, (Y2^-1 * Y1 * Y2^-1)^2, Y2^6, (Y3^-1 * Y1^-1)^3, Y2 * Y1^-1 * Y2^-4 * Y1^-1 * Y2, Y2^-1 * Y1^-1 * Y2^-1 * Y1^3 * Y2^-1 * Y1^-1, (Y2^-1, Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1 * Y2^2 * Y1^-1 * Y2^-1 * Y1^-2 ] Map:: R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 25, 145, 11, 131)(5, 125, 14, 134, 37, 157, 15, 135)(7, 127, 19, 139, 47, 167, 21, 141)(8, 128, 22, 142, 53, 173, 23, 143)(10, 130, 28, 148, 56, 176, 24, 144)(12, 132, 32, 152, 70, 190, 34, 154)(13, 133, 35, 155, 60, 180, 26, 146)(16, 136, 33, 153, 71, 191, 40, 160)(17, 137, 41, 161, 81, 201, 43, 163)(18, 138, 44, 164, 87, 207, 45, 165)(20, 140, 49, 169, 90, 210, 46, 166)(27, 147, 61, 181, 95, 215, 52, 172)(29, 149, 65, 185, 85, 205, 62, 182)(30, 150, 66, 186, 84, 204, 67, 187)(31, 151, 68, 188, 92, 212, 63, 183)(36, 156, 42, 162, 83, 203, 76, 196)(38, 158, 79, 199, 104, 224, 55, 175)(39, 159, 75, 195, 111, 231, 80, 200)(48, 168, 93, 213, 113, 233, 86, 206)(50, 170, 97, 217, 73, 193, 94, 214)(51, 171, 98, 218, 72, 192, 99, 219)(54, 174, 103, 223, 77, 197, 89, 209)(57, 177, 100, 220, 116, 236, 105, 225)(58, 178, 106, 226, 74, 194, 82, 202)(59, 179, 88, 208, 117, 237, 101, 221)(64, 184, 91, 211, 115, 235, 107, 227)(69, 189, 102, 222, 114, 234, 109, 229)(78, 198, 96, 216, 112, 232, 110, 230)(108, 228, 119, 239, 120, 240, 118, 238)(241, 361, 243, 363, 250, 370, 269, 389, 256, 376, 245, 365)(242, 362, 247, 367, 260, 380, 290, 410, 264, 384, 248, 368)(244, 364, 252, 372, 273, 393, 312, 432, 276, 396, 253, 373)(246, 366, 257, 377, 282, 402, 324, 444, 286, 406, 258, 378)(249, 369, 266, 386, 299, 419, 339, 459, 302, 422, 267, 387)(251, 371, 270, 390, 254, 374, 278, 398, 309, 429, 271, 391)(255, 375, 279, 399, 305, 425, 334, 454, 288, 408, 259, 379)(261, 381, 291, 411, 262, 382, 294, 414, 340, 460, 292, 412)(263, 383, 295, 415, 337, 457, 306, 426, 322, 442, 281, 401)(265, 385, 297, 417, 342, 462, 293, 413, 341, 461, 298, 418)(268, 388, 303, 423, 348, 468, 319, 439, 280, 400, 304, 424)(272, 392, 285, 405, 329, 449, 307, 427, 338, 458, 308, 428)(274, 394, 313, 433, 275, 395, 315, 435, 350, 470, 314, 434)(277, 397, 317, 437, 333, 453, 310, 430, 349, 469, 318, 438)(283, 403, 325, 445, 284, 404, 328, 448, 355, 475, 326, 446)(287, 407, 331, 451, 356, 476, 327, 447, 320, 440, 332, 452)(289, 409, 335, 455, 358, 478, 343, 463, 296, 416, 336, 456)(300, 420, 344, 464, 301, 421, 321, 441, 352, 472, 347, 467)(311, 431, 346, 466, 359, 479, 351, 471, 316, 436, 345, 465)(323, 443, 353, 473, 360, 480, 357, 477, 330, 450, 354, 474) L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 257)(7, 260)(8, 242)(9, 266)(10, 269)(11, 270)(12, 273)(13, 244)(14, 278)(15, 279)(16, 245)(17, 282)(18, 246)(19, 255)(20, 290)(21, 291)(22, 294)(23, 295)(24, 248)(25, 297)(26, 299)(27, 249)(28, 303)(29, 256)(30, 254)(31, 251)(32, 285)(33, 312)(34, 313)(35, 315)(36, 253)(37, 317)(38, 309)(39, 305)(40, 304)(41, 263)(42, 324)(43, 325)(44, 328)(45, 329)(46, 258)(47, 331)(48, 259)(49, 335)(50, 264)(51, 262)(52, 261)(53, 341)(54, 340)(55, 337)(56, 336)(57, 342)(58, 265)(59, 339)(60, 344)(61, 321)(62, 267)(63, 348)(64, 268)(65, 334)(66, 322)(67, 338)(68, 272)(69, 271)(70, 349)(71, 346)(72, 276)(73, 275)(74, 274)(75, 350)(76, 345)(77, 333)(78, 277)(79, 280)(80, 332)(81, 352)(82, 281)(83, 353)(84, 286)(85, 284)(86, 283)(87, 320)(88, 355)(89, 307)(90, 354)(91, 356)(92, 287)(93, 310)(94, 288)(95, 358)(96, 289)(97, 306)(98, 308)(99, 302)(100, 292)(101, 298)(102, 293)(103, 296)(104, 301)(105, 311)(106, 359)(107, 300)(108, 319)(109, 318)(110, 314)(111, 316)(112, 347)(113, 360)(114, 323)(115, 326)(116, 327)(117, 330)(118, 343)(119, 351)(120, 357)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E16.1213 Graph:: bipartite v = 50 e = 240 f = 160 degree seq :: [ 8^30, 12^20 ] E16.1211 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, (Y2^-1 * Y1)^2, Y2^6, (Y3^-1 * Y1^-1)^3, (Y1^-1 * Y2^-1)^3, Y2^-2 * Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1 * Y2^-2 ] Map:: R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 19, 139, 8, 128)(5, 125, 11, 131, 25, 145, 13, 133)(7, 127, 17, 137, 32, 152, 16, 136)(10, 130, 23, 143, 40, 160, 22, 142)(12, 132, 15, 135, 30, 150, 21, 141)(14, 134, 28, 148, 48, 168, 29, 149)(18, 138, 35, 155, 55, 175, 34, 154)(20, 140, 37, 157, 59, 179, 38, 158)(24, 144, 43, 163, 65, 185, 42, 162)(26, 146, 45, 165, 67, 187, 44, 164)(27, 147, 39, 159, 61, 181, 47, 167)(31, 151, 51, 171, 72, 192, 50, 170)(33, 153, 53, 173, 76, 196, 54, 174)(36, 156, 58, 178, 80, 200, 57, 177)(41, 161, 63, 183, 85, 205, 64, 184)(46, 166, 70, 190, 90, 210, 69, 189)(49, 169, 66, 186, 87, 207, 71, 191)(52, 172, 75, 195, 94, 214, 74, 194)(56, 176, 78, 198, 97, 217, 79, 199)(60, 180, 81, 201, 99, 219, 82, 202)(62, 182, 84, 204, 101, 221, 83, 203)(68, 188, 88, 208, 105, 225, 89, 209)(73, 193, 92, 212, 107, 227, 93, 213)(77, 197, 95, 215, 109, 229, 96, 216)(86, 206, 102, 222, 113, 233, 103, 223)(91, 211, 104, 224, 111, 231, 98, 218)(100, 220, 112, 232, 116, 236, 108, 228)(106, 226, 110, 230, 117, 237, 115, 235)(114, 234, 119, 239, 120, 240, 118, 238)(241, 361, 243, 363, 250, 370, 264, 384, 254, 374, 245, 365)(242, 362, 247, 367, 258, 378, 276, 396, 260, 380, 248, 368)(244, 364, 251, 371, 266, 386, 286, 406, 267, 387, 252, 372)(246, 366, 255, 375, 271, 391, 292, 412, 273, 393, 256, 376)(249, 369, 261, 381, 279, 399, 302, 422, 281, 401, 262, 382)(253, 373, 268, 388, 289, 409, 296, 416, 274, 394, 257, 377)(259, 379, 277, 397, 300, 420, 313, 433, 290, 410, 270, 390)(263, 383, 278, 398, 298, 418, 319, 439, 306, 426, 282, 402)(265, 385, 272, 392, 293, 413, 317, 437, 308, 428, 284, 404)(269, 389, 283, 403, 304, 424, 324, 444, 309, 429, 285, 405)(275, 395, 294, 414, 315, 435, 333, 453, 321, 441, 297, 417)(280, 400, 303, 423, 326, 446, 340, 460, 322, 442, 299, 419)(287, 407, 310, 430, 329, 449, 335, 455, 314, 434, 291, 411)(288, 408, 307, 427, 328, 448, 346, 466, 331, 451, 311, 431)(295, 415, 318, 438, 338, 458, 350, 470, 336, 456, 316, 436)(301, 421, 312, 432, 332, 452, 348, 468, 342, 462, 323, 443)(305, 425, 327, 447, 344, 464, 354, 474, 343, 463, 325, 445)(320, 440, 339, 459, 352, 472, 358, 478, 351, 471, 337, 457)(330, 450, 341, 461, 353, 473, 359, 479, 355, 475, 345, 465)(334, 454, 349, 469, 357, 477, 360, 480, 356, 476, 347, 467) L = (1, 243)(2, 247)(3, 250)(4, 251)(5, 241)(6, 255)(7, 258)(8, 242)(9, 261)(10, 264)(11, 266)(12, 244)(13, 268)(14, 245)(15, 271)(16, 246)(17, 253)(18, 276)(19, 277)(20, 248)(21, 279)(22, 249)(23, 278)(24, 254)(25, 272)(26, 286)(27, 252)(28, 289)(29, 283)(30, 259)(31, 292)(32, 293)(33, 256)(34, 257)(35, 294)(36, 260)(37, 300)(38, 298)(39, 302)(40, 303)(41, 262)(42, 263)(43, 304)(44, 265)(45, 269)(46, 267)(47, 310)(48, 307)(49, 296)(50, 270)(51, 287)(52, 273)(53, 317)(54, 315)(55, 318)(56, 274)(57, 275)(58, 319)(59, 280)(60, 313)(61, 312)(62, 281)(63, 326)(64, 324)(65, 327)(66, 282)(67, 328)(68, 284)(69, 285)(70, 329)(71, 288)(72, 332)(73, 290)(74, 291)(75, 333)(76, 295)(77, 308)(78, 338)(79, 306)(80, 339)(81, 297)(82, 299)(83, 301)(84, 309)(85, 305)(86, 340)(87, 344)(88, 346)(89, 335)(90, 341)(91, 311)(92, 348)(93, 321)(94, 349)(95, 314)(96, 316)(97, 320)(98, 350)(99, 352)(100, 322)(101, 353)(102, 323)(103, 325)(104, 354)(105, 330)(106, 331)(107, 334)(108, 342)(109, 357)(110, 336)(111, 337)(112, 358)(113, 359)(114, 343)(115, 345)(116, 347)(117, 360)(118, 351)(119, 355)(120, 356)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 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 E16.1212 Graph:: bipartite v = 50 e = 240 f = 160 degree seq :: [ 8^30, 12^20 ] E16.1212 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y2 * Y3^-1)^2, (R * Y2 * Y3^-1)^2, Y3^6, Y3^2 * Y2^-1 * Y3^-4 * Y2^-1, Y2^-1 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3, (Y3 * Y2 * Y3)^3, (Y3^-1 * Y1^-1)^6, Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: polytopal R = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(241, 361, 242, 362, 244, 364)(243, 363, 248, 368, 250, 370)(245, 365, 253, 373, 254, 374)(246, 366, 256, 376, 258, 378)(247, 367, 259, 379, 260, 380)(249, 369, 264, 384, 261, 381)(251, 371, 268, 388, 270, 390)(252, 372, 271, 391, 272, 392)(255, 375, 269, 389, 277, 397)(257, 377, 280, 400, 273, 393)(262, 382, 287, 407, 286, 406)(263, 383, 285, 405, 289, 409)(265, 385, 293, 413, 290, 410)(266, 386, 294, 414, 282, 402)(267, 387, 284, 404, 295, 415)(274, 394, 304, 424, 300, 420)(275, 395, 305, 425, 298, 418)(276, 396, 297, 417, 306, 426)(278, 398, 309, 429, 303, 423)(279, 399, 302, 422, 311, 431)(281, 401, 313, 433, 312, 432)(283, 403, 301, 421, 314, 434)(288, 408, 307, 427, 296, 416)(291, 411, 322, 442, 321, 441)(292, 412, 320, 440, 323, 443)(299, 419, 329, 449, 328, 448)(308, 428, 333, 453, 336, 456)(310, 430, 316, 436, 315, 435)(317, 437, 338, 458, 326, 446)(318, 438, 325, 445, 334, 454)(319, 439, 343, 463, 342, 462)(324, 444, 347, 467, 346, 466)(327, 447, 331, 451, 330, 450)(332, 452, 337, 457, 335, 455)(339, 459, 345, 465, 354, 474)(340, 460, 341, 461, 344, 464)(348, 468, 350, 470, 351, 471)(349, 469, 353, 473, 352, 472)(355, 475, 359, 479, 360, 480)(356, 476, 357, 477, 358, 478) L = (1, 243)(2, 246)(3, 249)(4, 251)(5, 241)(6, 257)(7, 242)(8, 262)(9, 265)(10, 266)(11, 269)(12, 244)(13, 274)(14, 275)(15, 245)(16, 278)(17, 281)(18, 282)(19, 284)(20, 285)(21, 247)(22, 288)(23, 248)(24, 291)(25, 255)(26, 253)(27, 250)(28, 297)(29, 299)(30, 294)(31, 301)(32, 302)(33, 252)(34, 296)(35, 293)(36, 254)(37, 292)(38, 310)(39, 256)(40, 308)(41, 261)(42, 259)(43, 258)(44, 315)(45, 313)(46, 260)(47, 317)(48, 319)(49, 320)(50, 263)(51, 280)(52, 264)(53, 324)(54, 271)(55, 325)(56, 267)(57, 327)(58, 268)(59, 273)(60, 270)(61, 330)(62, 329)(63, 272)(64, 332)(65, 333)(66, 334)(67, 276)(68, 277)(69, 337)(70, 339)(71, 322)(72, 279)(73, 340)(74, 326)(75, 283)(76, 286)(77, 341)(78, 287)(79, 290)(80, 343)(81, 289)(82, 345)(83, 305)(84, 307)(85, 304)(86, 295)(87, 348)(88, 298)(89, 349)(90, 300)(91, 303)(92, 314)(93, 350)(94, 347)(95, 306)(96, 311)(97, 353)(98, 309)(99, 312)(100, 316)(101, 355)(102, 318)(103, 356)(104, 321)(105, 357)(106, 323)(107, 359)(108, 328)(109, 331)(110, 358)(111, 335)(112, 336)(113, 360)(114, 338)(115, 342)(116, 344)(117, 352)(118, 346)(119, 351)(120, 354)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.1211 Graph:: simple bipartite v = 160 e = 240 f = 50 degree seq :: [ 2^120, 6^40 ] E16.1213 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^6, Y2 * Y3^3 * Y2 * Y3^-3, (Y2^-1 * Y3^-3)^2, (Y3^-1 * Y2^-1)^4, (Y3 * Y2^-1)^4, (Y3^-1, Y2^-1)^2, Y3 * Y2^-1 * Y3^-2 * Y2 * Y3 * Y2 * Y3^-2 * Y2^-1, (Y3^-1 * Y1^-1)^6 ] Map:: polytopal R = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(241, 361, 242, 362, 244, 364)(243, 363, 248, 368, 250, 370)(245, 365, 253, 373, 254, 374)(246, 366, 256, 376, 258, 378)(247, 367, 259, 379, 260, 380)(249, 369, 264, 384, 266, 386)(251, 371, 269, 389, 271, 391)(252, 372, 272, 392, 273, 393)(255, 375, 279, 399, 280, 400)(257, 377, 283, 403, 285, 405)(261, 381, 292, 412, 293, 413)(262, 382, 294, 414, 296, 416)(263, 383, 297, 417, 287, 407)(265, 385, 301, 421, 284, 404)(267, 387, 304, 424, 289, 409)(268, 388, 306, 426, 307, 427)(270, 390, 310, 430, 311, 431)(274, 394, 317, 437, 318, 438)(275, 395, 319, 439, 290, 410)(276, 396, 312, 432, 320, 440)(277, 397, 314, 434, 321, 441)(278, 398, 322, 442, 281, 401)(282, 402, 324, 444, 313, 433)(286, 406, 330, 450, 315, 435)(288, 408, 333, 453, 316, 436)(291, 411, 334, 454, 309, 429)(295, 415, 331, 451, 336, 456)(298, 418, 341, 461, 342, 462)(299, 419, 343, 463, 344, 464)(300, 420, 325, 445, 338, 458)(302, 422, 326, 446, 340, 460)(303, 423, 345, 465, 346, 466)(305, 425, 348, 468, 349, 469)(308, 428, 329, 449, 352, 472)(323, 443, 354, 474, 355, 475)(327, 447, 350, 470, 337, 457)(328, 448, 335, 455, 357, 477)(332, 452, 353, 473, 347, 467)(339, 459, 356, 476, 351, 471)(358, 478, 359, 479, 360, 480) L = (1, 243)(2, 246)(3, 249)(4, 251)(5, 241)(6, 257)(7, 242)(8, 262)(9, 265)(10, 267)(11, 270)(12, 244)(13, 275)(14, 277)(15, 245)(16, 281)(17, 284)(18, 286)(19, 288)(20, 290)(21, 247)(22, 295)(23, 248)(24, 299)(25, 255)(26, 302)(27, 305)(28, 250)(29, 309)(30, 301)(31, 312)(32, 314)(33, 316)(34, 252)(35, 303)(36, 253)(37, 300)(38, 254)(39, 308)(40, 298)(41, 323)(42, 256)(43, 326)(44, 261)(45, 328)(46, 331)(47, 258)(48, 329)(49, 259)(50, 327)(51, 260)(52, 332)(53, 325)(54, 273)(55, 280)(56, 337)(57, 339)(58, 263)(59, 278)(60, 264)(61, 274)(62, 276)(63, 266)(64, 347)(65, 279)(66, 269)(67, 351)(68, 268)(69, 349)(70, 335)(71, 344)(72, 354)(73, 271)(74, 353)(75, 272)(76, 342)(77, 346)(78, 350)(79, 336)(80, 352)(81, 348)(82, 341)(83, 293)(84, 356)(85, 282)(86, 291)(87, 283)(88, 289)(89, 285)(90, 345)(91, 292)(92, 287)(93, 355)(94, 338)(95, 294)(96, 358)(97, 322)(98, 296)(99, 319)(100, 297)(101, 334)(102, 310)(103, 307)(104, 315)(105, 304)(106, 313)(107, 320)(108, 359)(109, 318)(110, 306)(111, 321)(112, 330)(113, 311)(114, 317)(115, 360)(116, 333)(117, 324)(118, 340)(119, 343)(120, 357)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E16.1210 Graph:: simple bipartite v = 160 e = 240 f = 50 degree seq :: [ 2^120, 6^40 ] E16.1214 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1 * Y1^-1)^2, (Y3 * Y2^-1)^3, Y1^6, (Y3 * Y1 * Y3^-1 * Y1)^2, (Y1^2 * Y3^-1)^3 ] Map:: polytopal R = (1, 121, 2, 122, 6, 126, 16, 136, 12, 132, 4, 124)(3, 123, 9, 129, 23, 143, 53, 173, 27, 147, 10, 130)(5, 125, 14, 134, 33, 153, 40, 160, 17, 137, 15, 135)(7, 127, 19, 139, 13, 133, 32, 152, 46, 166, 20, 140)(8, 128, 21, 141, 48, 168, 69, 189, 38, 158, 22, 142)(11, 131, 29, 149, 39, 159, 70, 190, 63, 183, 30, 150)(18, 138, 41, 161, 59, 179, 64, 184, 31, 151, 42, 162)(24, 144, 44, 164, 28, 148, 60, 180, 85, 205, 54, 174)(25, 145, 55, 175, 86, 206, 107, 227, 83, 203, 56, 176)(26, 146, 57, 177, 84, 204, 108, 228, 89, 209, 58, 178)(34, 154, 43, 163, 37, 157, 47, 167, 79, 199, 66, 186)(35, 155, 67, 187, 96, 216, 101, 221, 71, 191, 68, 188)(36, 156, 52, 172, 72, 192, 102, 222, 80, 200, 49, 169)(45, 165, 77, 197, 65, 185, 95, 215, 90, 210, 78, 198)(50, 170, 81, 201, 106, 226, 113, 233, 97, 217, 82, 202)(51, 171, 76, 196, 98, 218, 114, 234, 103, 223, 73, 193)(61, 181, 91, 211, 110, 230, 115, 235, 99, 219, 75, 195)(62, 182, 92, 212, 100, 220, 116, 236, 111, 231, 93, 213)(74, 194, 104, 224, 118, 238, 112, 232, 94, 214, 87, 207)(88, 208, 109, 229, 119, 239, 120, 240, 117, 237, 105, 225)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 247)(3, 245)(4, 251)(5, 241)(6, 257)(7, 248)(8, 242)(9, 264)(10, 266)(11, 253)(12, 271)(13, 244)(14, 274)(15, 276)(16, 278)(17, 258)(18, 246)(19, 283)(20, 285)(21, 289)(22, 291)(23, 252)(24, 265)(25, 249)(26, 268)(27, 299)(28, 250)(29, 296)(30, 302)(31, 263)(32, 294)(33, 267)(34, 275)(35, 254)(36, 277)(37, 255)(38, 279)(39, 256)(40, 311)(41, 313)(42, 315)(43, 284)(44, 259)(45, 287)(46, 303)(47, 260)(48, 286)(49, 290)(50, 261)(51, 292)(52, 262)(53, 323)(54, 305)(55, 270)(56, 301)(57, 308)(58, 328)(59, 273)(60, 306)(61, 269)(62, 295)(63, 288)(64, 334)(65, 272)(66, 330)(67, 298)(68, 327)(69, 337)(70, 339)(71, 312)(72, 280)(73, 314)(74, 281)(75, 316)(76, 282)(77, 322)(78, 345)(79, 320)(80, 336)(81, 318)(82, 332)(83, 324)(84, 293)(85, 329)(86, 325)(87, 297)(88, 307)(89, 326)(90, 300)(91, 304)(92, 317)(93, 349)(94, 331)(95, 333)(96, 319)(97, 338)(98, 309)(99, 340)(100, 310)(101, 357)(102, 343)(103, 346)(104, 341)(105, 321)(106, 342)(107, 351)(108, 352)(109, 335)(110, 347)(111, 350)(112, 359)(113, 360)(114, 355)(115, 358)(116, 353)(117, 344)(118, 354)(119, 348)(120, 356)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E16.1208 Graph:: simple bipartite v = 140 e = 240 f = 70 degree seq :: [ 2^120, 12^20 ] E16.1215 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, Y1^6, (R * Y2 * Y3^-1)^2, Y1^6, (Y3 * Y2^-1)^3, (Y3^-1, Y1^-1)^2, (Y3^-1 * Y1^-1)^4, (Y3 * Y1^-1)^4, (Y3 * Y1^-3)^2, Y3 * Y1 * Y3 * Y1^-2 * Y3^-1 * Y1 * Y3^-1 * Y1^-2 ] Map:: polytopal R = (1, 121, 2, 122, 6, 126, 16, 136, 12, 132, 4, 124)(3, 123, 9, 129, 23, 143, 42, 162, 27, 147, 10, 130)(5, 125, 14, 134, 35, 155, 41, 161, 39, 159, 15, 135)(7, 127, 19, 139, 47, 167, 32, 152, 51, 171, 20, 140)(8, 128, 21, 141, 53, 173, 31, 151, 57, 177, 22, 142)(11, 131, 29, 149, 46, 166, 18, 138, 45, 165, 30, 150)(13, 133, 33, 153, 44, 164, 17, 137, 43, 163, 34, 154)(24, 144, 61, 181, 108, 228, 66, 186, 85, 205, 62, 182)(25, 145, 63, 183, 91, 211, 65, 185, 98, 218, 52, 172)(26, 146, 64, 184, 104, 224, 60, 180, 102, 222, 55, 175)(28, 148, 67, 187, 107, 227, 59, 179, 87, 207, 68, 188)(36, 156, 77, 197, 100, 220, 81, 201, 103, 223, 56, 176)(37, 157, 70, 190, 113, 233, 80, 200, 90, 210, 78, 198)(38, 158, 72, 192, 114, 234, 76, 196, 84, 204, 79, 199)(40, 160, 82, 202, 97, 217, 75, 195, 93, 213, 48, 168)(49, 169, 94, 214, 74, 194, 96, 216, 112, 232, 86, 206)(50, 170, 95, 215, 69, 189, 92, 212, 116, 236, 88, 208)(54, 174, 101, 221, 71, 191, 105, 225, 110, 230, 89, 209)(58, 178, 106, 226, 73, 193, 99, 219, 115, 235, 83, 203)(109, 229, 118, 238, 111, 231, 119, 239, 120, 240, 117, 237)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 247)(3, 245)(4, 251)(5, 241)(6, 257)(7, 248)(8, 242)(9, 264)(10, 266)(11, 253)(12, 271)(13, 244)(14, 276)(15, 278)(16, 281)(17, 258)(18, 246)(19, 288)(20, 290)(21, 294)(22, 296)(23, 299)(24, 265)(25, 249)(26, 268)(27, 305)(28, 250)(29, 309)(30, 310)(31, 272)(32, 252)(33, 312)(34, 314)(35, 315)(36, 277)(37, 254)(38, 280)(39, 320)(40, 255)(41, 282)(42, 256)(43, 323)(44, 325)(45, 327)(46, 329)(47, 331)(48, 289)(49, 259)(50, 292)(51, 336)(52, 260)(53, 339)(54, 295)(55, 261)(56, 298)(57, 344)(58, 262)(59, 300)(60, 263)(61, 274)(62, 349)(63, 350)(64, 351)(65, 306)(66, 267)(67, 269)(68, 352)(69, 307)(70, 311)(71, 270)(72, 313)(73, 273)(74, 301)(75, 316)(76, 275)(77, 308)(78, 302)(79, 303)(80, 321)(81, 279)(82, 304)(83, 324)(84, 283)(85, 326)(86, 284)(87, 328)(88, 285)(89, 330)(90, 286)(91, 332)(92, 287)(93, 357)(94, 347)(95, 358)(96, 337)(97, 291)(98, 354)(99, 340)(100, 293)(101, 338)(102, 333)(103, 334)(104, 345)(105, 297)(106, 335)(107, 343)(108, 353)(109, 318)(110, 319)(111, 322)(112, 317)(113, 359)(114, 341)(115, 360)(116, 355)(117, 342)(118, 346)(119, 348)(120, 356)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E16.1209 Graph:: simple bipartite v = 140 e = 240 f = 70 degree seq :: [ 2^120, 12^20 ] E16.1216 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y1^-1 * Y3^-1, Y1^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2^-2 * Y1^-1 * Y2^-1, Y2^6, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y1^-1 * Y2, Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^-1 * Y2^-2 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1 ] Map:: R = (1, 121, 2, 122, 4, 124)(3, 123, 8, 128, 10, 130)(5, 125, 13, 133, 14, 134)(6, 126, 16, 136, 18, 138)(7, 127, 19, 139, 20, 140)(9, 129, 24, 144, 26, 146)(11, 131, 29, 149, 31, 151)(12, 132, 32, 152, 33, 153)(15, 135, 37, 157, 17, 137)(21, 141, 46, 166, 30, 150)(22, 142, 47, 167, 38, 158)(23, 143, 48, 168, 49, 169)(25, 145, 52, 172, 53, 173)(27, 147, 56, 176, 58, 178)(28, 148, 59, 179, 60, 180)(34, 154, 42, 162, 64, 184)(35, 155, 65, 185, 41, 161)(36, 156, 39, 159, 67, 187)(40, 160, 70, 190, 71, 191)(43, 163, 63, 183, 73, 193)(44, 164, 74, 194, 62, 182)(45, 165, 61, 181, 76, 196)(50, 170, 66, 186, 57, 177)(51, 171, 80, 200, 81, 201)(54, 174, 84, 204, 85, 205)(55, 175, 86, 206, 87, 207)(68, 188, 96, 216, 92, 212)(69, 189, 75, 195, 72, 192)(77, 197, 90, 210, 93, 213)(78, 198, 100, 220, 89, 209)(79, 199, 88, 208, 91, 211)(82, 202, 103, 223, 104, 224)(83, 203, 105, 225, 106, 226)(94, 214, 99, 219, 95, 215)(97, 217, 111, 231, 110, 230)(98, 218, 112, 232, 113, 233)(101, 221, 114, 234, 108, 228)(102, 222, 107, 227, 109, 229)(115, 235, 120, 240, 118, 238)(116, 236, 117, 237, 119, 239)(241, 361, 243, 363, 249, 369, 265, 385, 255, 375, 245, 365)(242, 362, 246, 366, 257, 377, 280, 400, 261, 381, 247, 367)(244, 364, 251, 371, 270, 390, 291, 411, 264, 384, 252, 372)(248, 368, 262, 382, 254, 374, 276, 396, 290, 410, 263, 383)(250, 370, 267, 387, 297, 417, 322, 442, 292, 412, 268, 388)(253, 373, 274, 394, 293, 413, 323, 443, 306, 426, 275, 395)(256, 376, 278, 398, 260, 380, 285, 405, 309, 429, 279, 399)(258, 378, 281, 401, 312, 432, 337, 457, 310, 430, 282, 402)(259, 379, 283, 403, 311, 431, 338, 458, 315, 435, 284, 404)(266, 386, 294, 414, 286, 406, 308, 428, 277, 397, 295, 415)(269, 389, 287, 407, 273, 393, 289, 409, 319, 439, 301, 421)(271, 391, 302, 422, 331, 451, 341, 461, 320, 440, 303, 423)(272, 392, 300, 420, 321, 441, 342, 462, 328, 448, 296, 416)(288, 408, 317, 437, 307, 427, 335, 455, 316, 436, 318, 438)(298, 418, 329, 449, 349, 469, 355, 475, 343, 463, 330, 450)(299, 419, 327, 447, 344, 464, 356, 476, 347, 467, 324, 444)(304, 424, 332, 452, 350, 470, 357, 477, 345, 465, 326, 446)(305, 425, 333, 453, 346, 466, 358, 478, 351, 471, 334, 454)(313, 433, 325, 445, 348, 468, 359, 479, 352, 472, 336, 456)(314, 434, 339, 459, 353, 473, 360, 480, 354, 474, 340, 460) L = (1, 244)(2, 241)(3, 250)(4, 242)(5, 254)(6, 258)(7, 260)(8, 243)(9, 266)(10, 248)(11, 271)(12, 273)(13, 245)(14, 253)(15, 257)(16, 246)(17, 277)(18, 256)(19, 247)(20, 259)(21, 270)(22, 278)(23, 289)(24, 249)(25, 293)(26, 264)(27, 298)(28, 300)(29, 251)(30, 286)(31, 269)(32, 252)(33, 272)(34, 304)(35, 281)(36, 307)(37, 255)(38, 287)(39, 276)(40, 311)(41, 305)(42, 274)(43, 313)(44, 302)(45, 316)(46, 261)(47, 262)(48, 263)(49, 288)(50, 297)(51, 321)(52, 265)(53, 292)(54, 325)(55, 327)(56, 267)(57, 306)(58, 296)(59, 268)(60, 299)(61, 285)(62, 314)(63, 283)(64, 282)(65, 275)(66, 290)(67, 279)(68, 332)(69, 312)(70, 280)(71, 310)(72, 315)(73, 303)(74, 284)(75, 309)(76, 301)(77, 333)(78, 329)(79, 331)(80, 291)(81, 320)(82, 344)(83, 346)(84, 294)(85, 324)(86, 295)(87, 326)(88, 319)(89, 340)(90, 317)(91, 328)(92, 336)(93, 330)(94, 335)(95, 339)(96, 308)(97, 350)(98, 353)(99, 334)(100, 318)(101, 348)(102, 349)(103, 322)(104, 343)(105, 323)(106, 345)(107, 342)(108, 354)(109, 347)(110, 351)(111, 337)(112, 338)(113, 352)(114, 341)(115, 358)(116, 359)(117, 356)(118, 360)(119, 357)(120, 355)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E16.1219 Graph:: bipartite v = 60 e = 240 f = 150 degree seq :: [ 6^40, 12^20 ] E16.1217 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^6, Y3 * Y2^-3 * Y1^-1 * Y2^-3, Y2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y2^-1 * Y3, (Y3 * Y2^-1)^4, Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2^2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y3 * Y2^-2 * Y3^-1 * Y2 * Y3^-1 * Y2^-2, Y3 * Y2^2 * Y1 * Y2^-1 * Y3^-1 * Y2^2 * Y1^-1 * Y2^-1 ] Map:: R = (1, 121, 2, 122, 4, 124)(3, 123, 8, 128, 10, 130)(5, 125, 13, 133, 14, 134)(6, 126, 16, 136, 18, 138)(7, 127, 19, 139, 20, 140)(9, 129, 24, 144, 26, 146)(11, 131, 29, 149, 31, 151)(12, 132, 32, 152, 33, 153)(15, 135, 39, 159, 40, 160)(17, 137, 43, 163, 45, 165)(21, 141, 52, 172, 53, 173)(22, 142, 54, 174, 56, 176)(23, 143, 57, 177, 47, 167)(25, 145, 61, 181, 44, 164)(27, 147, 64, 184, 49, 169)(28, 148, 66, 186, 67, 187)(30, 150, 70, 190, 71, 191)(34, 154, 77, 197, 78, 198)(35, 155, 79, 199, 50, 170)(36, 156, 72, 192, 80, 200)(37, 157, 74, 194, 81, 201)(38, 158, 82, 202, 41, 161)(42, 162, 84, 204, 73, 193)(46, 166, 90, 210, 75, 195)(48, 168, 93, 213, 76, 196)(51, 171, 94, 214, 69, 189)(55, 175, 91, 211, 96, 216)(58, 178, 101, 221, 102, 222)(59, 179, 103, 223, 104, 224)(60, 180, 85, 205, 98, 218)(62, 182, 86, 206, 100, 220)(63, 183, 105, 225, 106, 226)(65, 185, 108, 228, 109, 229)(68, 188, 89, 209, 112, 232)(83, 203, 114, 234, 115, 235)(87, 207, 110, 230, 97, 217)(88, 208, 95, 215, 117, 237)(92, 212, 113, 233, 107, 227)(99, 219, 116, 236, 111, 231)(118, 238, 119, 239, 120, 240)(241, 361, 243, 363, 249, 369, 265, 385, 255, 375, 245, 365)(242, 362, 246, 366, 257, 377, 284, 404, 261, 381, 247, 367)(244, 364, 251, 371, 270, 390, 301, 421, 274, 394, 252, 372)(248, 368, 262, 382, 295, 415, 280, 400, 298, 418, 263, 383)(250, 370, 267, 387, 305, 425, 279, 399, 308, 428, 268, 388)(253, 373, 275, 395, 303, 423, 266, 386, 302, 422, 276, 396)(254, 374, 277, 397, 300, 420, 264, 384, 299, 419, 278, 398)(256, 376, 281, 401, 323, 443, 293, 413, 325, 445, 282, 402)(258, 378, 286, 406, 331, 451, 292, 412, 332, 452, 287, 407)(259, 379, 288, 408, 329, 449, 285, 405, 328, 448, 289, 409)(260, 380, 290, 410, 327, 447, 283, 403, 326, 446, 291, 411)(269, 389, 309, 429, 349, 469, 318, 438, 350, 470, 306, 426)(271, 391, 312, 432, 354, 474, 317, 437, 346, 466, 313, 433)(272, 392, 314, 434, 353, 473, 311, 431, 344, 464, 315, 435)(273, 393, 316, 436, 342, 462, 310, 430, 335, 455, 294, 414)(296, 416, 337, 457, 322, 442, 341, 461, 334, 454, 338, 458)(297, 417, 339, 459, 319, 439, 336, 456, 358, 478, 340, 460)(304, 424, 347, 467, 320, 440, 352, 472, 330, 450, 345, 465)(307, 427, 351, 471, 321, 441, 348, 468, 359, 479, 343, 463)(324, 444, 356, 476, 333, 453, 355, 475, 360, 480, 357, 477) L = (1, 244)(2, 241)(3, 250)(4, 242)(5, 254)(6, 258)(7, 260)(8, 243)(9, 266)(10, 248)(11, 271)(12, 273)(13, 245)(14, 253)(15, 280)(16, 246)(17, 285)(18, 256)(19, 247)(20, 259)(21, 293)(22, 296)(23, 287)(24, 249)(25, 284)(26, 264)(27, 289)(28, 307)(29, 251)(30, 311)(31, 269)(32, 252)(33, 272)(34, 318)(35, 290)(36, 320)(37, 321)(38, 281)(39, 255)(40, 279)(41, 322)(42, 313)(43, 257)(44, 301)(45, 283)(46, 315)(47, 297)(48, 316)(49, 304)(50, 319)(51, 309)(52, 261)(53, 292)(54, 262)(55, 336)(56, 294)(57, 263)(58, 342)(59, 344)(60, 338)(61, 265)(62, 340)(63, 346)(64, 267)(65, 349)(66, 268)(67, 306)(68, 352)(69, 334)(70, 270)(71, 310)(72, 276)(73, 324)(74, 277)(75, 330)(76, 333)(77, 274)(78, 317)(79, 275)(80, 312)(81, 314)(82, 278)(83, 355)(84, 282)(85, 300)(86, 302)(87, 337)(88, 357)(89, 308)(90, 286)(91, 295)(92, 347)(93, 288)(94, 291)(95, 328)(96, 331)(97, 350)(98, 325)(99, 351)(100, 326)(101, 298)(102, 341)(103, 299)(104, 343)(105, 303)(106, 345)(107, 353)(108, 305)(109, 348)(110, 327)(111, 356)(112, 329)(113, 332)(114, 323)(115, 354)(116, 339)(117, 335)(118, 360)(119, 358)(120, 359)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E16.1218 Graph:: bipartite v = 60 e = 240 f = 150 degree seq :: [ 6^40, 12^20 ] E16.1218 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^4, (R * Y3)^2, (R * Y1)^2, Y3^6, (R * Y2 * Y3^-1)^2, (Y3 * Y1)^3, (Y3^-1 * Y1 * Y3^-1)^2, Y3 * Y1^-1 * Y3^-4 * Y1^-1 * Y3, Y3^-1 * Y1^-1 * Y3^-1 * Y1^3 * Y3^-1 * Y1^-1, (Y3, Y1)^2, Y3 * Y1^-1 * Y3 * Y1 * Y3^2 * Y1^-1 * Y3^-1 * Y1^-2, (Y3 * Y2^-1)^6 ] Map:: polytopal R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 25, 145, 11, 131)(5, 125, 14, 134, 37, 157, 15, 135)(7, 127, 19, 139, 47, 167, 21, 141)(8, 128, 22, 142, 53, 173, 23, 143)(10, 130, 28, 148, 56, 176, 24, 144)(12, 132, 32, 152, 70, 190, 34, 154)(13, 133, 35, 155, 60, 180, 26, 146)(16, 136, 33, 153, 71, 191, 40, 160)(17, 137, 41, 161, 81, 201, 43, 163)(18, 138, 44, 164, 87, 207, 45, 165)(20, 140, 49, 169, 90, 210, 46, 166)(27, 147, 61, 181, 95, 215, 52, 172)(29, 149, 65, 185, 85, 205, 62, 182)(30, 150, 66, 186, 84, 204, 67, 187)(31, 151, 68, 188, 92, 212, 63, 183)(36, 156, 42, 162, 83, 203, 76, 196)(38, 158, 79, 199, 104, 224, 55, 175)(39, 159, 75, 195, 111, 231, 80, 200)(48, 168, 93, 213, 113, 233, 86, 206)(50, 170, 97, 217, 73, 193, 94, 214)(51, 171, 98, 218, 72, 192, 99, 219)(54, 174, 103, 223, 77, 197, 89, 209)(57, 177, 100, 220, 116, 236, 105, 225)(58, 178, 106, 226, 74, 194, 82, 202)(59, 179, 88, 208, 117, 237, 101, 221)(64, 184, 91, 211, 115, 235, 107, 227)(69, 189, 102, 222, 114, 234, 109, 229)(78, 198, 96, 216, 112, 232, 110, 230)(108, 228, 119, 239, 120, 240, 118, 238)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 257)(7, 260)(8, 242)(9, 266)(10, 269)(11, 270)(12, 273)(13, 244)(14, 278)(15, 279)(16, 245)(17, 282)(18, 246)(19, 255)(20, 290)(21, 291)(22, 294)(23, 295)(24, 248)(25, 297)(26, 299)(27, 249)(28, 303)(29, 256)(30, 254)(31, 251)(32, 285)(33, 312)(34, 313)(35, 315)(36, 253)(37, 317)(38, 309)(39, 305)(40, 304)(41, 263)(42, 324)(43, 325)(44, 328)(45, 329)(46, 258)(47, 331)(48, 259)(49, 335)(50, 264)(51, 262)(52, 261)(53, 341)(54, 340)(55, 337)(56, 336)(57, 342)(58, 265)(59, 339)(60, 344)(61, 321)(62, 267)(63, 348)(64, 268)(65, 334)(66, 322)(67, 338)(68, 272)(69, 271)(70, 349)(71, 346)(72, 276)(73, 275)(74, 274)(75, 350)(76, 345)(77, 333)(78, 277)(79, 280)(80, 332)(81, 352)(82, 281)(83, 353)(84, 286)(85, 284)(86, 283)(87, 320)(88, 355)(89, 307)(90, 354)(91, 356)(92, 287)(93, 310)(94, 288)(95, 358)(96, 289)(97, 306)(98, 308)(99, 302)(100, 292)(101, 298)(102, 293)(103, 296)(104, 301)(105, 311)(106, 359)(107, 300)(108, 319)(109, 318)(110, 314)(111, 316)(112, 347)(113, 360)(114, 323)(115, 326)(116, 327)(117, 330)(118, 343)(119, 351)(120, 357)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.1217 Graph:: simple bipartite v = 150 e = 240 f = 60 degree seq :: [ 2^120, 8^30 ] E16.1219 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6}) Quotient :: dipole Aut^+ = S5 (small group id <120, 34>) Aut = C2 x S5 (small group id <240, 189>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y3^6, (Y1^-1 * Y3^-1)^3, Y3^-2 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1 * Y3^-2, (Y3 * Y2^-1)^6 ] Map:: polytopal R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 19, 139, 8, 128)(5, 125, 11, 131, 25, 145, 13, 133)(7, 127, 17, 137, 32, 152, 16, 136)(10, 130, 23, 143, 40, 160, 22, 142)(12, 132, 15, 135, 30, 150, 21, 141)(14, 134, 28, 148, 48, 168, 29, 149)(18, 138, 35, 155, 55, 175, 34, 154)(20, 140, 37, 157, 59, 179, 38, 158)(24, 144, 43, 163, 65, 185, 42, 162)(26, 146, 45, 165, 67, 187, 44, 164)(27, 147, 39, 159, 61, 181, 47, 167)(31, 151, 51, 171, 72, 192, 50, 170)(33, 153, 53, 173, 76, 196, 54, 174)(36, 156, 58, 178, 80, 200, 57, 177)(41, 161, 63, 183, 85, 205, 64, 184)(46, 166, 70, 190, 90, 210, 69, 189)(49, 169, 66, 186, 87, 207, 71, 191)(52, 172, 75, 195, 94, 214, 74, 194)(56, 176, 78, 198, 97, 217, 79, 199)(60, 180, 81, 201, 99, 219, 82, 202)(62, 182, 84, 204, 101, 221, 83, 203)(68, 188, 88, 208, 105, 225, 89, 209)(73, 193, 92, 212, 107, 227, 93, 213)(77, 197, 95, 215, 109, 229, 96, 216)(86, 206, 102, 222, 113, 233, 103, 223)(91, 211, 104, 224, 111, 231, 98, 218)(100, 220, 112, 232, 116, 236, 108, 228)(106, 226, 110, 230, 117, 237, 115, 235)(114, 234, 119, 239, 120, 240, 118, 238)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 247)(3, 250)(4, 251)(5, 241)(6, 255)(7, 258)(8, 242)(9, 261)(10, 264)(11, 266)(12, 244)(13, 268)(14, 245)(15, 271)(16, 246)(17, 253)(18, 276)(19, 277)(20, 248)(21, 279)(22, 249)(23, 278)(24, 254)(25, 272)(26, 286)(27, 252)(28, 289)(29, 283)(30, 259)(31, 292)(32, 293)(33, 256)(34, 257)(35, 294)(36, 260)(37, 300)(38, 298)(39, 302)(40, 303)(41, 262)(42, 263)(43, 304)(44, 265)(45, 269)(46, 267)(47, 310)(48, 307)(49, 296)(50, 270)(51, 287)(52, 273)(53, 317)(54, 315)(55, 318)(56, 274)(57, 275)(58, 319)(59, 280)(60, 313)(61, 312)(62, 281)(63, 326)(64, 324)(65, 327)(66, 282)(67, 328)(68, 284)(69, 285)(70, 329)(71, 288)(72, 332)(73, 290)(74, 291)(75, 333)(76, 295)(77, 308)(78, 338)(79, 306)(80, 339)(81, 297)(82, 299)(83, 301)(84, 309)(85, 305)(86, 340)(87, 344)(88, 346)(89, 335)(90, 341)(91, 311)(92, 348)(93, 321)(94, 349)(95, 314)(96, 316)(97, 320)(98, 350)(99, 352)(100, 322)(101, 353)(102, 323)(103, 325)(104, 354)(105, 330)(106, 331)(107, 334)(108, 342)(109, 357)(110, 336)(111, 337)(112, 358)(113, 359)(114, 343)(115, 345)(116, 347)(117, 360)(118, 351)(119, 355)(120, 356)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E16.1216 Graph:: simple bipartite v = 150 e = 240 f = 60 degree seq :: [ 2^120, 8^30 ] E16.1220 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 64}) Quotient :: regular Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T1 * T2)^4, T2 * T1^-1 * T2 * T1^31, T1^-2 * T2 * T1^15 * T2 * T1^-15 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 117, 125, 122, 114, 106, 98, 90, 82, 74, 66, 58, 50, 42, 34, 26, 16, 23, 17, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 124, 116, 108, 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97, 105, 113, 121, 127, 118, 111, 102, 95, 86, 79, 70, 63, 54, 47, 38, 31, 21, 14, 6, 13, 9, 18, 27, 35, 43, 51, 59, 67, 75, 83, 91, 99, 107, 115, 123, 126, 119, 110, 103, 94, 87, 78, 71, 62, 55, 46, 39, 30, 22, 12, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 70)(63, 72)(67, 74)(68, 75)(69, 78)(71, 80)(73, 82)(76, 81)(77, 86)(79, 88)(83, 90)(84, 91)(85, 94)(87, 96)(89, 98)(92, 97)(93, 102)(95, 104)(99, 106)(100, 107)(101, 110)(103, 112)(105, 114)(108, 113)(109, 118)(111, 120)(115, 122)(116, 123)(117, 126)(119, 128)(121, 125)(124, 127) local type(s) :: { ( 4^64 ) } Outer automorphisms :: reflexible Dual of E16.1221 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 64 f = 32 degree seq :: [ 64^2 ] E16.1221 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 64}) Quotient :: regular Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^4, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 2, 5, 4)(3, 7, 10, 8)(6, 11, 9, 12)(13, 17, 14, 18)(15, 19, 16, 20)(21, 25, 22, 26)(23, 27, 24, 28)(29, 33, 30, 34)(31, 35, 32, 36)(37, 42, 38, 39)(40, 57, 41, 59)(43, 67, 44, 61)(45, 65, 46, 63)(47, 71, 48, 69)(49, 75, 50, 73)(51, 79, 52, 77)(53, 83, 54, 81)(55, 87, 56, 85)(58, 91, 60, 89)(62, 93, 68, 95)(64, 98, 66, 97)(70, 101, 72, 102)(74, 104, 76, 105)(78, 109, 80, 110)(82, 113, 84, 114)(86, 117, 88, 118)(90, 121, 92, 122)(94, 125, 96, 126)(99, 128, 100, 127)(103, 123, 108, 124)(106, 120, 107, 119)(111, 116, 112, 115) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 57)(36, 59)(39, 61)(40, 63)(41, 65)(42, 67)(43, 69)(44, 71)(45, 73)(46, 75)(47, 77)(48, 79)(49, 81)(50, 83)(51, 85)(52, 87)(53, 89)(54, 91)(55, 93)(56, 95)(58, 98)(60, 97)(62, 102)(64, 105)(66, 104)(68, 101)(70, 110)(72, 109)(74, 114)(76, 113)(78, 118)(80, 117)(82, 122)(84, 121)(86, 126)(88, 125)(90, 127)(92, 128)(94, 123)(96, 124)(99, 120)(100, 119)(103, 115)(106, 112)(107, 111)(108, 116) local type(s) :: { ( 64^4 ) } Outer automorphisms :: reflexible Dual of E16.1220 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 32 e = 64 f = 2 degree seq :: [ 4^32 ] E16.1222 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 64}) Quotient :: edge Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 9, 14)(10, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)(33, 37, 34, 38)(35, 52, 36, 51)(39, 68, 46, 69)(40, 71, 49, 72)(41, 73, 42, 74)(43, 66, 44, 65)(45, 76, 47, 67)(48, 79, 50, 70)(53, 77, 54, 75)(55, 80, 56, 78)(57, 82, 58, 81)(59, 84, 60, 83)(61, 86, 62, 85)(63, 88, 64, 87)(89, 93, 90, 94)(91, 104, 92, 103)(95, 123, 96, 124)(97, 122, 98, 121)(99, 125, 100, 126)(101, 127, 102, 128)(105, 119, 106, 120)(107, 117, 108, 118)(109, 116, 110, 115)(111, 114, 112, 113)(129, 130)(131, 135)(132, 137)(133, 138)(134, 140)(136, 139)(141, 145)(142, 146)(143, 147)(144, 148)(149, 153)(150, 154)(151, 155)(152, 156)(157, 161)(158, 162)(159, 163)(160, 164)(165, 193)(166, 194)(167, 195)(168, 198)(169, 199)(170, 200)(171, 196)(172, 197)(173, 203)(174, 204)(175, 205)(176, 206)(177, 207)(178, 208)(179, 201)(180, 202)(181, 209)(182, 210)(183, 211)(184, 212)(185, 213)(186, 214)(187, 215)(188, 216)(189, 217)(190, 218)(191, 219)(192, 220)(221, 249)(222, 250)(223, 248)(224, 247)(225, 251)(226, 252)(227, 246)(228, 245)(229, 253)(230, 254)(231, 255)(232, 256)(233, 243)(234, 244)(235, 241)(236, 242)(237, 240)(238, 239) L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 128, 128 ), ( 128^4 ) } Outer automorphisms :: reflexible Dual of E16.1226 Transitivity :: ET+ Graph:: simple bipartite v = 96 e = 128 f = 2 degree seq :: [ 2^64, 4^32 ] E16.1223 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 64}) Quotient :: edge Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1^-1)^2, (T2^-1 * T1^-1)^2, T2^31 * T1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 114, 122, 126, 118, 110, 102, 94, 86, 78, 70, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 117, 125, 124, 116, 108, 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 111, 119, 127, 121, 113, 105, 97, 89, 81, 73, 65, 57, 49, 41, 33, 25, 17, 9, 4, 11, 19, 27, 35, 43, 51, 59, 67, 75, 83, 91, 99, 107, 115, 123, 128, 120, 112, 104, 96, 88, 80, 72, 64, 56, 48, 40, 32, 24, 16, 8)(129, 130, 134, 132)(131, 137, 141, 136)(133, 139, 142, 135)(138, 144, 149, 145)(140, 143, 150, 147)(146, 153, 157, 152)(148, 155, 158, 151)(154, 160, 165, 161)(156, 159, 166, 163)(162, 169, 173, 168)(164, 171, 174, 167)(170, 176, 181, 177)(172, 175, 182, 179)(178, 185, 189, 184)(180, 187, 190, 183)(186, 192, 197, 193)(188, 191, 198, 195)(194, 201, 205, 200)(196, 203, 206, 199)(202, 208, 213, 209)(204, 207, 214, 211)(210, 217, 221, 216)(212, 219, 222, 215)(218, 224, 229, 225)(220, 223, 230, 227)(226, 233, 237, 232)(228, 235, 238, 231)(234, 240, 245, 241)(236, 239, 246, 243)(242, 249, 253, 248)(244, 251, 254, 247)(250, 256, 252, 255) L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^4 ), ( 4^64 ) } Outer automorphisms :: reflexible Dual of E16.1227 Transitivity :: ET+ Graph:: bipartite v = 34 e = 128 f = 64 degree seq :: [ 4^32, 64^2 ] E16.1224 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 64}) Quotient :: edge Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, T2 * T1^-1 * T2 * T1^31, T1^-2 * T2 * T1^15 * T2 * T1^-15 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 70)(63, 72)(67, 74)(68, 75)(69, 78)(71, 80)(73, 82)(76, 81)(77, 86)(79, 88)(83, 90)(84, 91)(85, 94)(87, 96)(89, 98)(92, 97)(93, 102)(95, 104)(99, 106)(100, 107)(101, 110)(103, 112)(105, 114)(108, 113)(109, 118)(111, 120)(115, 122)(116, 123)(117, 126)(119, 128)(121, 125)(124, 127)(129, 130, 133, 139, 148, 157, 165, 173, 181, 189, 197, 205, 213, 221, 229, 237, 245, 253, 250, 242, 234, 226, 218, 210, 202, 194, 186, 178, 170, 162, 154, 144, 151, 145, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 252, 244, 236, 228, 220, 212, 204, 196, 188, 180, 172, 164, 156, 147, 138, 132)(131, 135, 143, 153, 161, 169, 177, 185, 193, 201, 209, 217, 225, 233, 241, 249, 255, 246, 239, 230, 223, 214, 207, 198, 191, 182, 175, 166, 159, 149, 142, 134, 141, 137, 146, 155, 163, 171, 179, 187, 195, 203, 211, 219, 227, 235, 243, 251, 254, 247, 238, 231, 222, 215, 206, 199, 190, 183, 174, 167, 158, 150, 140, 136) L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 8 ), ( 8^64 ) } Outer automorphisms :: reflexible Dual of E16.1225 Transitivity :: ET+ Graph:: simple bipartite v = 66 e = 128 f = 32 degree seq :: [ 2^64, 64^2 ] E16.1225 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 64}) Quotient :: loop Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 129, 3, 131, 8, 136, 4, 132)(2, 130, 5, 133, 11, 139, 6, 134)(7, 135, 13, 141, 9, 137, 14, 142)(10, 138, 15, 143, 12, 140, 16, 144)(17, 145, 21, 149, 18, 146, 22, 150)(19, 147, 23, 151, 20, 148, 24, 152)(25, 153, 29, 157, 26, 154, 30, 158)(27, 155, 31, 159, 28, 156, 32, 160)(33, 161, 37, 165, 34, 162, 38, 166)(35, 163, 47, 175, 36, 164, 45, 173)(39, 167, 66, 194, 46, 174, 68, 196)(40, 168, 63, 191, 48, 176, 61, 189)(41, 169, 72, 200, 42, 170, 69, 197)(43, 171, 77, 205, 44, 172, 65, 193)(49, 177, 74, 202, 50, 178, 71, 199)(51, 179, 79, 207, 52, 180, 76, 204)(53, 181, 87, 215, 54, 182, 85, 213)(55, 183, 91, 219, 56, 184, 89, 217)(57, 185, 95, 223, 58, 186, 93, 221)(59, 187, 99, 227, 60, 188, 97, 225)(62, 190, 103, 231, 64, 192, 101, 229)(67, 195, 114, 242, 82, 210, 116, 244)(70, 198, 111, 239, 84, 212, 109, 237)(73, 201, 120, 248, 75, 203, 117, 245)(78, 206, 124, 252, 80, 208, 113, 241)(81, 209, 105, 233, 83, 211, 107, 235)(86, 214, 122, 250, 88, 216, 119, 247)(90, 218, 123, 251, 92, 220, 121, 249)(94, 222, 115, 243, 96, 224, 126, 254)(98, 226, 118, 246, 100, 228, 128, 256)(102, 230, 125, 253, 104, 232, 127, 255)(106, 234, 112, 240, 108, 236, 110, 238) 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, 189)(38, 191)(39, 193)(40, 197)(41, 199)(42, 202)(43, 204)(44, 207)(45, 194)(46, 205)(47, 196)(48, 200)(49, 213)(50, 215)(51, 217)(52, 219)(53, 221)(54, 223)(55, 225)(56, 227)(57, 229)(58, 231)(59, 233)(60, 235)(61, 165)(62, 237)(63, 166)(64, 239)(65, 167)(66, 173)(67, 241)(68, 175)(69, 168)(70, 245)(71, 169)(72, 176)(73, 247)(74, 170)(75, 250)(76, 171)(77, 174)(78, 249)(79, 172)(80, 251)(81, 242)(82, 252)(83, 244)(84, 248)(85, 177)(86, 254)(87, 178)(88, 243)(89, 179)(90, 256)(91, 180)(92, 246)(93, 181)(94, 255)(95, 182)(96, 253)(97, 183)(98, 238)(99, 184)(100, 240)(101, 185)(102, 236)(103, 186)(104, 234)(105, 187)(106, 232)(107, 188)(108, 230)(109, 190)(110, 226)(111, 192)(112, 228)(113, 195)(114, 209)(115, 216)(116, 211)(117, 198)(118, 220)(119, 201)(120, 212)(121, 206)(122, 203)(123, 208)(124, 210)(125, 224)(126, 214)(127, 222)(128, 218) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64 ) } Outer automorphisms :: reflexible Dual of E16.1224 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 32 e = 128 f = 66 degree seq :: [ 8^32 ] E16.1226 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 64}) Quotient :: loop Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1^-1)^2, (T2^-1 * T1^-1)^2, T2^31 * T1 * T2^-1 * T1^-1 ] Map:: R = (1, 129, 3, 131, 10, 138, 18, 146, 26, 154, 34, 162, 42, 170, 50, 178, 58, 186, 66, 194, 74, 202, 82, 210, 90, 218, 98, 226, 106, 234, 114, 242, 122, 250, 126, 254, 118, 246, 110, 238, 102, 230, 94, 222, 86, 214, 78, 206, 70, 198, 62, 190, 54, 182, 46, 174, 38, 166, 30, 158, 22, 150, 14, 142, 6, 134, 13, 141, 21, 149, 29, 157, 37, 165, 45, 173, 53, 181, 61, 189, 69, 197, 77, 205, 85, 213, 93, 221, 101, 229, 109, 237, 117, 245, 125, 253, 124, 252, 116, 244, 108, 236, 100, 228, 92, 220, 84, 212, 76, 204, 68, 196, 60, 188, 52, 180, 44, 172, 36, 164, 28, 156, 20, 148, 12, 140, 5, 133)(2, 130, 7, 135, 15, 143, 23, 151, 31, 159, 39, 167, 47, 175, 55, 183, 63, 191, 71, 199, 79, 207, 87, 215, 95, 223, 103, 231, 111, 239, 119, 247, 127, 255, 121, 249, 113, 241, 105, 233, 97, 225, 89, 217, 81, 209, 73, 201, 65, 193, 57, 185, 49, 177, 41, 169, 33, 161, 25, 153, 17, 145, 9, 137, 4, 132, 11, 139, 19, 147, 27, 155, 35, 163, 43, 171, 51, 179, 59, 187, 67, 195, 75, 203, 83, 211, 91, 219, 99, 227, 107, 235, 115, 243, 123, 251, 128, 256, 120, 248, 112, 240, 104, 232, 96, 224, 88, 216, 80, 208, 72, 200, 64, 192, 56, 184, 48, 176, 40, 168, 32, 160, 24, 152, 16, 144, 8, 136) L = (1, 130)(2, 134)(3, 137)(4, 129)(5, 139)(6, 132)(7, 133)(8, 131)(9, 141)(10, 144)(11, 142)(12, 143)(13, 136)(14, 135)(15, 150)(16, 149)(17, 138)(18, 153)(19, 140)(20, 155)(21, 145)(22, 147)(23, 148)(24, 146)(25, 157)(26, 160)(27, 158)(28, 159)(29, 152)(30, 151)(31, 166)(32, 165)(33, 154)(34, 169)(35, 156)(36, 171)(37, 161)(38, 163)(39, 164)(40, 162)(41, 173)(42, 176)(43, 174)(44, 175)(45, 168)(46, 167)(47, 182)(48, 181)(49, 170)(50, 185)(51, 172)(52, 187)(53, 177)(54, 179)(55, 180)(56, 178)(57, 189)(58, 192)(59, 190)(60, 191)(61, 184)(62, 183)(63, 198)(64, 197)(65, 186)(66, 201)(67, 188)(68, 203)(69, 193)(70, 195)(71, 196)(72, 194)(73, 205)(74, 208)(75, 206)(76, 207)(77, 200)(78, 199)(79, 214)(80, 213)(81, 202)(82, 217)(83, 204)(84, 219)(85, 209)(86, 211)(87, 212)(88, 210)(89, 221)(90, 224)(91, 222)(92, 223)(93, 216)(94, 215)(95, 230)(96, 229)(97, 218)(98, 233)(99, 220)(100, 235)(101, 225)(102, 227)(103, 228)(104, 226)(105, 237)(106, 240)(107, 238)(108, 239)(109, 232)(110, 231)(111, 246)(112, 245)(113, 234)(114, 249)(115, 236)(116, 251)(117, 241)(118, 243)(119, 244)(120, 242)(121, 253)(122, 256)(123, 254)(124, 255)(125, 248)(126, 247)(127, 250)(128, 252) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E16.1222 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 128 f = 96 degree seq :: [ 128^2 ] E16.1227 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 64}) Quotient :: loop Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, T2 * T1^-1 * T2 * T1^31, T1^-2 * T2 * T1^15 * T2 * T1^-15 ] Map:: polytopal non-degenerate R = (1, 129, 3, 131)(2, 130, 6, 134)(4, 132, 9, 137)(5, 133, 12, 140)(7, 135, 16, 144)(8, 136, 17, 145)(10, 138, 15, 143)(11, 139, 21, 149)(13, 141, 23, 151)(14, 142, 24, 152)(18, 146, 26, 154)(19, 147, 27, 155)(20, 148, 30, 158)(22, 150, 32, 160)(25, 153, 34, 162)(28, 156, 33, 161)(29, 157, 38, 166)(31, 159, 40, 168)(35, 163, 42, 170)(36, 164, 43, 171)(37, 165, 46, 174)(39, 167, 48, 176)(41, 169, 50, 178)(44, 172, 49, 177)(45, 173, 54, 182)(47, 175, 56, 184)(51, 179, 58, 186)(52, 180, 59, 187)(53, 181, 62, 190)(55, 183, 64, 192)(57, 185, 66, 194)(60, 188, 65, 193)(61, 189, 70, 198)(63, 191, 72, 200)(67, 195, 74, 202)(68, 196, 75, 203)(69, 197, 78, 206)(71, 199, 80, 208)(73, 201, 82, 210)(76, 204, 81, 209)(77, 205, 86, 214)(79, 207, 88, 216)(83, 211, 90, 218)(84, 212, 91, 219)(85, 213, 94, 222)(87, 215, 96, 224)(89, 217, 98, 226)(92, 220, 97, 225)(93, 221, 102, 230)(95, 223, 104, 232)(99, 227, 106, 234)(100, 228, 107, 235)(101, 229, 110, 238)(103, 231, 112, 240)(105, 233, 114, 242)(108, 236, 113, 241)(109, 237, 118, 246)(111, 239, 120, 248)(115, 243, 122, 250)(116, 244, 123, 251)(117, 245, 126, 254)(119, 247, 128, 256)(121, 249, 125, 253)(124, 252, 127, 255) L = (1, 130)(2, 133)(3, 135)(4, 129)(5, 139)(6, 141)(7, 143)(8, 131)(9, 146)(10, 132)(11, 148)(12, 136)(13, 137)(14, 134)(15, 153)(16, 151)(17, 152)(18, 155)(19, 138)(20, 157)(21, 142)(22, 140)(23, 145)(24, 160)(25, 161)(26, 144)(27, 163)(28, 147)(29, 165)(30, 150)(31, 149)(32, 168)(33, 169)(34, 154)(35, 171)(36, 156)(37, 173)(38, 159)(39, 158)(40, 176)(41, 177)(42, 162)(43, 179)(44, 164)(45, 181)(46, 167)(47, 166)(48, 184)(49, 185)(50, 170)(51, 187)(52, 172)(53, 189)(54, 175)(55, 174)(56, 192)(57, 193)(58, 178)(59, 195)(60, 180)(61, 197)(62, 183)(63, 182)(64, 200)(65, 201)(66, 186)(67, 203)(68, 188)(69, 205)(70, 191)(71, 190)(72, 208)(73, 209)(74, 194)(75, 211)(76, 196)(77, 213)(78, 199)(79, 198)(80, 216)(81, 217)(82, 202)(83, 219)(84, 204)(85, 221)(86, 207)(87, 206)(88, 224)(89, 225)(90, 210)(91, 227)(92, 212)(93, 229)(94, 215)(95, 214)(96, 232)(97, 233)(98, 218)(99, 235)(100, 220)(101, 237)(102, 223)(103, 222)(104, 240)(105, 241)(106, 226)(107, 243)(108, 228)(109, 245)(110, 231)(111, 230)(112, 248)(113, 249)(114, 234)(115, 251)(116, 236)(117, 253)(118, 239)(119, 238)(120, 256)(121, 255)(122, 242)(123, 254)(124, 244)(125, 250)(126, 247)(127, 246)(128, 252) local type(s) :: { ( 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E16.1223 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 64 e = 128 f = 34 degree seq :: [ 4^64 ] E16.1228 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 64}) Quotient :: dipole Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^64 ] Map:: R = (1, 129, 2, 130)(3, 131, 7, 135)(4, 132, 9, 137)(5, 133, 10, 138)(6, 134, 12, 140)(8, 136, 11, 139)(13, 141, 17, 145)(14, 142, 18, 146)(15, 143, 19, 147)(16, 144, 20, 148)(21, 149, 25, 153)(22, 150, 26, 154)(23, 151, 27, 155)(24, 152, 28, 156)(29, 157, 33, 161)(30, 158, 34, 162)(31, 159, 35, 163)(32, 160, 36, 164)(37, 165, 61, 189)(38, 166, 62, 190)(39, 167, 63, 191)(40, 168, 64, 192)(41, 169, 65, 193)(42, 170, 66, 194)(43, 171, 67, 195)(44, 172, 68, 196)(45, 173, 69, 197)(46, 174, 70, 198)(47, 175, 71, 199)(48, 176, 72, 200)(49, 177, 73, 201)(50, 178, 74, 202)(51, 179, 75, 203)(52, 180, 76, 204)(53, 181, 77, 205)(54, 182, 78, 206)(55, 183, 79, 207)(56, 184, 80, 208)(57, 185, 81, 209)(58, 186, 82, 210)(59, 187, 83, 211)(60, 188, 84, 212)(85, 213, 109, 237)(86, 214, 110, 238)(87, 215, 111, 239)(88, 216, 112, 240)(89, 217, 113, 241)(90, 218, 114, 242)(91, 219, 115, 243)(92, 220, 116, 244)(93, 221, 117, 245)(94, 222, 118, 246)(95, 223, 119, 247)(96, 224, 120, 248)(97, 225, 121, 249)(98, 226, 122, 250)(99, 227, 123, 251)(100, 228, 124, 252)(101, 229, 125, 253)(102, 230, 126, 254)(103, 231, 127, 255)(104, 232, 128, 256)(105, 233, 108, 236)(106, 234, 107, 235)(257, 385, 259, 387, 264, 392, 260, 388)(258, 386, 261, 389, 267, 395, 262, 390)(263, 391, 269, 397, 265, 393, 270, 398)(266, 394, 271, 399, 268, 396, 272, 400)(273, 401, 277, 405, 274, 402, 278, 406)(275, 403, 279, 407, 276, 404, 280, 408)(281, 409, 285, 413, 282, 410, 286, 414)(283, 411, 287, 415, 284, 412, 288, 416)(289, 417, 293, 421, 290, 418, 294, 422)(291, 419, 297, 425, 292, 420, 298, 426)(295, 423, 317, 445, 300, 428, 318, 446)(296, 424, 321, 449, 303, 431, 322, 450)(299, 427, 324, 452, 301, 429, 319, 447)(302, 430, 327, 455, 304, 432, 320, 448)(305, 433, 325, 453, 306, 434, 323, 451)(307, 435, 328, 456, 308, 436, 326, 454)(309, 437, 330, 458, 310, 438, 329, 457)(311, 439, 332, 460, 312, 440, 331, 459)(313, 441, 334, 462, 314, 442, 333, 461)(315, 443, 336, 464, 316, 444, 335, 463)(337, 465, 341, 469, 338, 466, 342, 470)(339, 467, 345, 473, 340, 468, 346, 474)(343, 471, 365, 493, 348, 476, 366, 494)(344, 472, 369, 497, 351, 479, 370, 498)(347, 475, 372, 500, 349, 477, 367, 495)(350, 478, 375, 503, 352, 480, 368, 496)(353, 481, 373, 501, 354, 482, 371, 499)(355, 483, 376, 504, 356, 484, 374, 502)(357, 485, 378, 506, 358, 486, 377, 505)(359, 487, 380, 508, 360, 488, 379, 507)(361, 489, 382, 510, 362, 490, 381, 509)(363, 491, 384, 512, 364, 492, 383, 511) L = (1, 258)(2, 257)(3, 263)(4, 265)(5, 266)(6, 268)(7, 259)(8, 267)(9, 260)(10, 261)(11, 264)(12, 262)(13, 273)(14, 274)(15, 275)(16, 276)(17, 269)(18, 270)(19, 271)(20, 272)(21, 281)(22, 282)(23, 283)(24, 284)(25, 277)(26, 278)(27, 279)(28, 280)(29, 289)(30, 290)(31, 291)(32, 292)(33, 285)(34, 286)(35, 287)(36, 288)(37, 317)(38, 318)(39, 319)(40, 320)(41, 321)(42, 322)(43, 323)(44, 324)(45, 325)(46, 326)(47, 327)(48, 328)(49, 329)(50, 330)(51, 331)(52, 332)(53, 333)(54, 334)(55, 335)(56, 336)(57, 337)(58, 338)(59, 339)(60, 340)(61, 293)(62, 294)(63, 295)(64, 296)(65, 297)(66, 298)(67, 299)(68, 300)(69, 301)(70, 302)(71, 303)(72, 304)(73, 305)(74, 306)(75, 307)(76, 308)(77, 309)(78, 310)(79, 311)(80, 312)(81, 313)(82, 314)(83, 315)(84, 316)(85, 365)(86, 366)(87, 367)(88, 368)(89, 369)(90, 370)(91, 371)(92, 372)(93, 373)(94, 374)(95, 375)(96, 376)(97, 377)(98, 378)(99, 379)(100, 380)(101, 381)(102, 382)(103, 383)(104, 384)(105, 364)(106, 363)(107, 362)(108, 361)(109, 341)(110, 342)(111, 343)(112, 344)(113, 345)(114, 346)(115, 347)(116, 348)(117, 349)(118, 350)(119, 351)(120, 352)(121, 353)(122, 354)(123, 355)(124, 356)(125, 357)(126, 358)(127, 359)(128, 360)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 2, 128, 2, 128 ), ( 2, 128, 2, 128, 2, 128, 2, 128 ) } Outer automorphisms :: reflexible Dual of E16.1231 Graph:: bipartite v = 96 e = 256 f = 130 degree seq :: [ 4^64, 8^32 ] E16.1229 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 64}) Quotient :: dipole Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1)^2, Y1^4, Y1^-1 * Y2^-32 * Y1^-1 ] Map:: R = (1, 129, 2, 130, 6, 134, 4, 132)(3, 131, 9, 137, 13, 141, 8, 136)(5, 133, 11, 139, 14, 142, 7, 135)(10, 138, 16, 144, 21, 149, 17, 145)(12, 140, 15, 143, 22, 150, 19, 147)(18, 146, 25, 153, 29, 157, 24, 152)(20, 148, 27, 155, 30, 158, 23, 151)(26, 154, 32, 160, 37, 165, 33, 161)(28, 156, 31, 159, 38, 166, 35, 163)(34, 162, 41, 169, 45, 173, 40, 168)(36, 164, 43, 171, 46, 174, 39, 167)(42, 170, 48, 176, 53, 181, 49, 177)(44, 172, 47, 175, 54, 182, 51, 179)(50, 178, 57, 185, 61, 189, 56, 184)(52, 180, 59, 187, 62, 190, 55, 183)(58, 186, 64, 192, 69, 197, 65, 193)(60, 188, 63, 191, 70, 198, 67, 195)(66, 194, 73, 201, 77, 205, 72, 200)(68, 196, 75, 203, 78, 206, 71, 199)(74, 202, 80, 208, 85, 213, 81, 209)(76, 204, 79, 207, 86, 214, 83, 211)(82, 210, 89, 217, 93, 221, 88, 216)(84, 212, 91, 219, 94, 222, 87, 215)(90, 218, 96, 224, 101, 229, 97, 225)(92, 220, 95, 223, 102, 230, 99, 227)(98, 226, 105, 233, 109, 237, 104, 232)(100, 228, 107, 235, 110, 238, 103, 231)(106, 234, 112, 240, 117, 245, 113, 241)(108, 236, 111, 239, 118, 246, 115, 243)(114, 242, 121, 249, 125, 253, 120, 248)(116, 244, 123, 251, 126, 254, 119, 247)(122, 250, 128, 256, 124, 252, 127, 255)(257, 385, 259, 387, 266, 394, 274, 402, 282, 410, 290, 418, 298, 426, 306, 434, 314, 442, 322, 450, 330, 458, 338, 466, 346, 474, 354, 482, 362, 490, 370, 498, 378, 506, 382, 510, 374, 502, 366, 494, 358, 486, 350, 478, 342, 470, 334, 462, 326, 454, 318, 446, 310, 438, 302, 430, 294, 422, 286, 414, 278, 406, 270, 398, 262, 390, 269, 397, 277, 405, 285, 413, 293, 421, 301, 429, 309, 437, 317, 445, 325, 453, 333, 461, 341, 469, 349, 477, 357, 485, 365, 493, 373, 501, 381, 509, 380, 508, 372, 500, 364, 492, 356, 484, 348, 476, 340, 468, 332, 460, 324, 452, 316, 444, 308, 436, 300, 428, 292, 420, 284, 412, 276, 404, 268, 396, 261, 389)(258, 386, 263, 391, 271, 399, 279, 407, 287, 415, 295, 423, 303, 431, 311, 439, 319, 447, 327, 455, 335, 463, 343, 471, 351, 479, 359, 487, 367, 495, 375, 503, 383, 511, 377, 505, 369, 497, 361, 489, 353, 481, 345, 473, 337, 465, 329, 457, 321, 449, 313, 441, 305, 433, 297, 425, 289, 417, 281, 409, 273, 401, 265, 393, 260, 388, 267, 395, 275, 403, 283, 411, 291, 419, 299, 427, 307, 435, 315, 443, 323, 451, 331, 459, 339, 467, 347, 475, 355, 483, 363, 491, 371, 499, 379, 507, 384, 512, 376, 504, 368, 496, 360, 488, 352, 480, 344, 472, 336, 464, 328, 456, 320, 448, 312, 440, 304, 432, 296, 424, 288, 416, 280, 408, 272, 400, 264, 392) L = (1, 259)(2, 263)(3, 266)(4, 267)(5, 257)(6, 269)(7, 271)(8, 258)(9, 260)(10, 274)(11, 275)(12, 261)(13, 277)(14, 262)(15, 279)(16, 264)(17, 265)(18, 282)(19, 283)(20, 268)(21, 285)(22, 270)(23, 287)(24, 272)(25, 273)(26, 290)(27, 291)(28, 276)(29, 293)(30, 278)(31, 295)(32, 280)(33, 281)(34, 298)(35, 299)(36, 284)(37, 301)(38, 286)(39, 303)(40, 288)(41, 289)(42, 306)(43, 307)(44, 292)(45, 309)(46, 294)(47, 311)(48, 296)(49, 297)(50, 314)(51, 315)(52, 300)(53, 317)(54, 302)(55, 319)(56, 304)(57, 305)(58, 322)(59, 323)(60, 308)(61, 325)(62, 310)(63, 327)(64, 312)(65, 313)(66, 330)(67, 331)(68, 316)(69, 333)(70, 318)(71, 335)(72, 320)(73, 321)(74, 338)(75, 339)(76, 324)(77, 341)(78, 326)(79, 343)(80, 328)(81, 329)(82, 346)(83, 347)(84, 332)(85, 349)(86, 334)(87, 351)(88, 336)(89, 337)(90, 354)(91, 355)(92, 340)(93, 357)(94, 342)(95, 359)(96, 344)(97, 345)(98, 362)(99, 363)(100, 348)(101, 365)(102, 350)(103, 367)(104, 352)(105, 353)(106, 370)(107, 371)(108, 356)(109, 373)(110, 358)(111, 375)(112, 360)(113, 361)(114, 378)(115, 379)(116, 364)(117, 381)(118, 366)(119, 383)(120, 368)(121, 369)(122, 382)(123, 384)(124, 372)(125, 380)(126, 374)(127, 377)(128, 376)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E16.1230 Graph:: bipartite v = 34 e = 256 f = 192 degree seq :: [ 8^32, 128^2 ] E16.1230 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 64}) Quotient :: dipole Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |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, Y3^29 * Y2 * Y3^-3 * Y2, (Y3^-1 * Y1^-1)^64 ] Map:: polytopal R = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)(257, 385, 258, 386)(259, 387, 263, 391)(260, 388, 265, 393)(261, 389, 267, 395)(262, 390, 269, 397)(264, 392, 270, 398)(266, 394, 268, 396)(271, 399, 276, 404)(272, 400, 279, 407)(273, 401, 281, 409)(274, 402, 277, 405)(275, 403, 283, 411)(278, 406, 285, 413)(280, 408, 287, 415)(282, 410, 288, 416)(284, 412, 286, 414)(289, 417, 295, 423)(290, 418, 297, 425)(291, 419, 293, 421)(292, 420, 299, 427)(294, 422, 301, 429)(296, 424, 303, 431)(298, 426, 304, 432)(300, 428, 302, 430)(305, 433, 311, 439)(306, 434, 313, 441)(307, 435, 309, 437)(308, 436, 315, 443)(310, 438, 317, 445)(312, 440, 319, 447)(314, 442, 320, 448)(316, 444, 318, 446)(321, 449, 327, 455)(322, 450, 329, 457)(323, 451, 325, 453)(324, 452, 331, 459)(326, 454, 333, 461)(328, 456, 335, 463)(330, 458, 336, 464)(332, 460, 334, 462)(337, 465, 343, 471)(338, 466, 345, 473)(339, 467, 341, 469)(340, 468, 347, 475)(342, 470, 349, 477)(344, 472, 351, 479)(346, 474, 352, 480)(348, 476, 350, 478)(353, 481, 359, 487)(354, 482, 361, 489)(355, 483, 357, 485)(356, 484, 363, 491)(358, 486, 365, 493)(360, 488, 367, 495)(362, 490, 368, 496)(364, 492, 366, 494)(369, 497, 375, 503)(370, 498, 377, 505)(371, 499, 373, 501)(372, 500, 379, 507)(374, 502, 381, 509)(376, 504, 383, 511)(378, 506, 384, 512)(380, 508, 382, 510) L = (1, 259)(2, 261)(3, 264)(4, 257)(5, 268)(6, 258)(7, 271)(8, 273)(9, 274)(10, 260)(11, 276)(12, 278)(13, 279)(14, 262)(15, 265)(16, 263)(17, 282)(18, 283)(19, 266)(20, 269)(21, 267)(22, 286)(23, 287)(24, 270)(25, 272)(26, 290)(27, 291)(28, 275)(29, 277)(30, 294)(31, 295)(32, 280)(33, 281)(34, 298)(35, 299)(36, 284)(37, 285)(38, 302)(39, 303)(40, 288)(41, 289)(42, 306)(43, 307)(44, 292)(45, 293)(46, 310)(47, 311)(48, 296)(49, 297)(50, 314)(51, 315)(52, 300)(53, 301)(54, 318)(55, 319)(56, 304)(57, 305)(58, 322)(59, 323)(60, 308)(61, 309)(62, 326)(63, 327)(64, 312)(65, 313)(66, 330)(67, 331)(68, 316)(69, 317)(70, 334)(71, 335)(72, 320)(73, 321)(74, 338)(75, 339)(76, 324)(77, 325)(78, 342)(79, 343)(80, 328)(81, 329)(82, 346)(83, 347)(84, 332)(85, 333)(86, 350)(87, 351)(88, 336)(89, 337)(90, 354)(91, 355)(92, 340)(93, 341)(94, 358)(95, 359)(96, 344)(97, 345)(98, 362)(99, 363)(100, 348)(101, 349)(102, 366)(103, 367)(104, 352)(105, 353)(106, 370)(107, 371)(108, 356)(109, 357)(110, 374)(111, 375)(112, 360)(113, 361)(114, 378)(115, 379)(116, 364)(117, 365)(118, 382)(119, 383)(120, 368)(121, 369)(122, 381)(123, 384)(124, 372)(125, 373)(126, 377)(127, 380)(128, 376)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 8, 128 ), ( 8, 128, 8, 128 ) } Outer automorphisms :: reflexible Dual of E16.1229 Graph:: simple bipartite v = 192 e = 256 f = 34 degree seq :: [ 2^128, 4^64 ] E16.1231 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 64}) Quotient :: dipole Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y3 * Y1^-2)^2, (Y3 * Y1)^4, Y3 * Y1^-1 * Y3 * Y1^31, Y1^-2 * Y3 * Y1^15 * Y3 * Y1^-15 ] Map:: R = (1, 129, 2, 130, 5, 133, 11, 139, 20, 148, 29, 157, 37, 165, 45, 173, 53, 181, 61, 189, 69, 197, 77, 205, 85, 213, 93, 221, 101, 229, 109, 237, 117, 245, 125, 253, 122, 250, 114, 242, 106, 234, 98, 226, 90, 218, 82, 210, 74, 202, 66, 194, 58, 186, 50, 178, 42, 170, 34, 162, 26, 154, 16, 144, 23, 151, 17, 145, 24, 152, 32, 160, 40, 168, 48, 176, 56, 184, 64, 192, 72, 200, 80, 208, 88, 216, 96, 224, 104, 232, 112, 240, 120, 248, 128, 256, 124, 252, 116, 244, 108, 236, 100, 228, 92, 220, 84, 212, 76, 204, 68, 196, 60, 188, 52, 180, 44, 172, 36, 164, 28, 156, 19, 147, 10, 138, 4, 132)(3, 131, 7, 135, 15, 143, 25, 153, 33, 161, 41, 169, 49, 177, 57, 185, 65, 193, 73, 201, 81, 209, 89, 217, 97, 225, 105, 233, 113, 241, 121, 249, 127, 255, 118, 246, 111, 239, 102, 230, 95, 223, 86, 214, 79, 207, 70, 198, 63, 191, 54, 182, 47, 175, 38, 166, 31, 159, 21, 149, 14, 142, 6, 134, 13, 141, 9, 137, 18, 146, 27, 155, 35, 163, 43, 171, 51, 179, 59, 187, 67, 195, 75, 203, 83, 211, 91, 219, 99, 227, 107, 235, 115, 243, 123, 251, 126, 254, 119, 247, 110, 238, 103, 231, 94, 222, 87, 215, 78, 206, 71, 199, 62, 190, 55, 183, 46, 174, 39, 167, 30, 158, 22, 150, 12, 140, 8, 136)(257, 385)(258, 386)(259, 387)(260, 388)(261, 389)(262, 390)(263, 391)(264, 392)(265, 393)(266, 394)(267, 395)(268, 396)(269, 397)(270, 398)(271, 399)(272, 400)(273, 401)(274, 402)(275, 403)(276, 404)(277, 405)(278, 406)(279, 407)(280, 408)(281, 409)(282, 410)(283, 411)(284, 412)(285, 413)(286, 414)(287, 415)(288, 416)(289, 417)(290, 418)(291, 419)(292, 420)(293, 421)(294, 422)(295, 423)(296, 424)(297, 425)(298, 426)(299, 427)(300, 428)(301, 429)(302, 430)(303, 431)(304, 432)(305, 433)(306, 434)(307, 435)(308, 436)(309, 437)(310, 438)(311, 439)(312, 440)(313, 441)(314, 442)(315, 443)(316, 444)(317, 445)(318, 446)(319, 447)(320, 448)(321, 449)(322, 450)(323, 451)(324, 452)(325, 453)(326, 454)(327, 455)(328, 456)(329, 457)(330, 458)(331, 459)(332, 460)(333, 461)(334, 462)(335, 463)(336, 464)(337, 465)(338, 466)(339, 467)(340, 468)(341, 469)(342, 470)(343, 471)(344, 472)(345, 473)(346, 474)(347, 475)(348, 476)(349, 477)(350, 478)(351, 479)(352, 480)(353, 481)(354, 482)(355, 483)(356, 484)(357, 485)(358, 486)(359, 487)(360, 488)(361, 489)(362, 490)(363, 491)(364, 492)(365, 493)(366, 494)(367, 495)(368, 496)(369, 497)(370, 498)(371, 499)(372, 500)(373, 501)(374, 502)(375, 503)(376, 504)(377, 505)(378, 506)(379, 507)(380, 508)(381, 509)(382, 510)(383, 511)(384, 512) L = (1, 259)(2, 262)(3, 257)(4, 265)(5, 268)(6, 258)(7, 272)(8, 273)(9, 260)(10, 271)(11, 277)(12, 261)(13, 279)(14, 280)(15, 266)(16, 263)(17, 264)(18, 282)(19, 283)(20, 286)(21, 267)(22, 288)(23, 269)(24, 270)(25, 290)(26, 274)(27, 275)(28, 289)(29, 294)(30, 276)(31, 296)(32, 278)(33, 284)(34, 281)(35, 298)(36, 299)(37, 302)(38, 285)(39, 304)(40, 287)(41, 306)(42, 291)(43, 292)(44, 305)(45, 310)(46, 293)(47, 312)(48, 295)(49, 300)(50, 297)(51, 314)(52, 315)(53, 318)(54, 301)(55, 320)(56, 303)(57, 322)(58, 307)(59, 308)(60, 321)(61, 326)(62, 309)(63, 328)(64, 311)(65, 316)(66, 313)(67, 330)(68, 331)(69, 334)(70, 317)(71, 336)(72, 319)(73, 338)(74, 323)(75, 324)(76, 337)(77, 342)(78, 325)(79, 344)(80, 327)(81, 332)(82, 329)(83, 346)(84, 347)(85, 350)(86, 333)(87, 352)(88, 335)(89, 354)(90, 339)(91, 340)(92, 353)(93, 358)(94, 341)(95, 360)(96, 343)(97, 348)(98, 345)(99, 362)(100, 363)(101, 366)(102, 349)(103, 368)(104, 351)(105, 370)(106, 355)(107, 356)(108, 369)(109, 374)(110, 357)(111, 376)(112, 359)(113, 364)(114, 361)(115, 378)(116, 379)(117, 382)(118, 365)(119, 384)(120, 367)(121, 381)(122, 371)(123, 372)(124, 383)(125, 377)(126, 373)(127, 380)(128, 375)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E16.1228 Graph:: simple bipartite v = 130 e = 256 f = 96 degree seq :: [ 2^128, 128^2 ] E16.1232 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 64}) Quotient :: dipole Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^4, Y2^3 * Y1 * Y2^-29 * Y1 ] Map:: R = (1, 129, 2, 130)(3, 131, 7, 135)(4, 132, 9, 137)(5, 133, 11, 139)(6, 134, 13, 141)(8, 136, 14, 142)(10, 138, 12, 140)(15, 143, 20, 148)(16, 144, 23, 151)(17, 145, 25, 153)(18, 146, 21, 149)(19, 147, 27, 155)(22, 150, 29, 157)(24, 152, 31, 159)(26, 154, 32, 160)(28, 156, 30, 158)(33, 161, 39, 167)(34, 162, 41, 169)(35, 163, 37, 165)(36, 164, 43, 171)(38, 166, 45, 173)(40, 168, 47, 175)(42, 170, 48, 176)(44, 172, 46, 174)(49, 177, 55, 183)(50, 178, 57, 185)(51, 179, 53, 181)(52, 180, 59, 187)(54, 182, 61, 189)(56, 184, 63, 191)(58, 186, 64, 192)(60, 188, 62, 190)(65, 193, 71, 199)(66, 194, 73, 201)(67, 195, 69, 197)(68, 196, 75, 203)(70, 198, 77, 205)(72, 200, 79, 207)(74, 202, 80, 208)(76, 204, 78, 206)(81, 209, 87, 215)(82, 210, 89, 217)(83, 211, 85, 213)(84, 212, 91, 219)(86, 214, 93, 221)(88, 216, 95, 223)(90, 218, 96, 224)(92, 220, 94, 222)(97, 225, 103, 231)(98, 226, 105, 233)(99, 227, 101, 229)(100, 228, 107, 235)(102, 230, 109, 237)(104, 232, 111, 239)(106, 234, 112, 240)(108, 236, 110, 238)(113, 241, 119, 247)(114, 242, 121, 249)(115, 243, 117, 245)(116, 244, 123, 251)(118, 246, 125, 253)(120, 248, 127, 255)(122, 250, 128, 256)(124, 252, 126, 254)(257, 385, 259, 387, 264, 392, 273, 401, 282, 410, 290, 418, 298, 426, 306, 434, 314, 442, 322, 450, 330, 458, 338, 466, 346, 474, 354, 482, 362, 490, 370, 498, 378, 506, 381, 509, 373, 501, 365, 493, 357, 485, 349, 477, 341, 469, 333, 461, 325, 453, 317, 445, 309, 437, 301, 429, 293, 421, 285, 413, 277, 405, 267, 395, 276, 404, 269, 397, 279, 407, 287, 415, 295, 423, 303, 431, 311, 439, 319, 447, 327, 455, 335, 463, 343, 471, 351, 479, 359, 487, 367, 495, 375, 503, 383, 511, 380, 508, 372, 500, 364, 492, 356, 484, 348, 476, 340, 468, 332, 460, 324, 452, 316, 444, 308, 436, 300, 428, 292, 420, 284, 412, 275, 403, 266, 394, 260, 388)(258, 386, 261, 389, 268, 396, 278, 406, 286, 414, 294, 422, 302, 430, 310, 438, 318, 446, 326, 454, 334, 462, 342, 470, 350, 478, 358, 486, 366, 494, 374, 502, 382, 510, 377, 505, 369, 497, 361, 489, 353, 481, 345, 473, 337, 465, 329, 457, 321, 449, 313, 441, 305, 433, 297, 425, 289, 417, 281, 409, 272, 400, 263, 391, 271, 399, 265, 393, 274, 402, 283, 411, 291, 419, 299, 427, 307, 435, 315, 443, 323, 451, 331, 459, 339, 467, 347, 475, 355, 483, 363, 491, 371, 499, 379, 507, 384, 512, 376, 504, 368, 496, 360, 488, 352, 480, 344, 472, 336, 464, 328, 456, 320, 448, 312, 440, 304, 432, 296, 424, 288, 416, 280, 408, 270, 398, 262, 390) L = (1, 258)(2, 257)(3, 263)(4, 265)(5, 267)(6, 269)(7, 259)(8, 270)(9, 260)(10, 268)(11, 261)(12, 266)(13, 262)(14, 264)(15, 276)(16, 279)(17, 281)(18, 277)(19, 283)(20, 271)(21, 274)(22, 285)(23, 272)(24, 287)(25, 273)(26, 288)(27, 275)(28, 286)(29, 278)(30, 284)(31, 280)(32, 282)(33, 295)(34, 297)(35, 293)(36, 299)(37, 291)(38, 301)(39, 289)(40, 303)(41, 290)(42, 304)(43, 292)(44, 302)(45, 294)(46, 300)(47, 296)(48, 298)(49, 311)(50, 313)(51, 309)(52, 315)(53, 307)(54, 317)(55, 305)(56, 319)(57, 306)(58, 320)(59, 308)(60, 318)(61, 310)(62, 316)(63, 312)(64, 314)(65, 327)(66, 329)(67, 325)(68, 331)(69, 323)(70, 333)(71, 321)(72, 335)(73, 322)(74, 336)(75, 324)(76, 334)(77, 326)(78, 332)(79, 328)(80, 330)(81, 343)(82, 345)(83, 341)(84, 347)(85, 339)(86, 349)(87, 337)(88, 351)(89, 338)(90, 352)(91, 340)(92, 350)(93, 342)(94, 348)(95, 344)(96, 346)(97, 359)(98, 361)(99, 357)(100, 363)(101, 355)(102, 365)(103, 353)(104, 367)(105, 354)(106, 368)(107, 356)(108, 366)(109, 358)(110, 364)(111, 360)(112, 362)(113, 375)(114, 377)(115, 373)(116, 379)(117, 371)(118, 381)(119, 369)(120, 383)(121, 370)(122, 384)(123, 372)(124, 382)(125, 374)(126, 380)(127, 376)(128, 378)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E16.1233 Graph:: bipartite v = 66 e = 256 f = 160 degree seq :: [ 4^64, 128^2 ] E16.1233 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 64}) Quotient :: dipole Aut^+ = $<128, 162>$ (small group id <128, 162>) Aut = $<256, 6730>$ (small group id <256, 6730>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-32 * Y1^-1, (Y3 * Y2^-1)^64 ] Map:: R = (1, 129, 2, 130, 6, 134, 4, 132)(3, 131, 9, 137, 13, 141, 8, 136)(5, 133, 11, 139, 14, 142, 7, 135)(10, 138, 16, 144, 21, 149, 17, 145)(12, 140, 15, 143, 22, 150, 19, 147)(18, 146, 25, 153, 29, 157, 24, 152)(20, 148, 27, 155, 30, 158, 23, 151)(26, 154, 32, 160, 37, 165, 33, 161)(28, 156, 31, 159, 38, 166, 35, 163)(34, 162, 41, 169, 45, 173, 40, 168)(36, 164, 43, 171, 46, 174, 39, 167)(42, 170, 48, 176, 53, 181, 49, 177)(44, 172, 47, 175, 54, 182, 51, 179)(50, 178, 57, 185, 61, 189, 56, 184)(52, 180, 59, 187, 62, 190, 55, 183)(58, 186, 64, 192, 69, 197, 65, 193)(60, 188, 63, 191, 70, 198, 67, 195)(66, 194, 73, 201, 77, 205, 72, 200)(68, 196, 75, 203, 78, 206, 71, 199)(74, 202, 80, 208, 85, 213, 81, 209)(76, 204, 79, 207, 86, 214, 83, 211)(82, 210, 89, 217, 93, 221, 88, 216)(84, 212, 91, 219, 94, 222, 87, 215)(90, 218, 96, 224, 101, 229, 97, 225)(92, 220, 95, 223, 102, 230, 99, 227)(98, 226, 105, 233, 109, 237, 104, 232)(100, 228, 107, 235, 110, 238, 103, 231)(106, 234, 112, 240, 117, 245, 113, 241)(108, 236, 111, 239, 118, 246, 115, 243)(114, 242, 121, 249, 125, 253, 120, 248)(116, 244, 123, 251, 126, 254, 119, 247)(122, 250, 128, 256, 124, 252, 127, 255)(257, 385)(258, 386)(259, 387)(260, 388)(261, 389)(262, 390)(263, 391)(264, 392)(265, 393)(266, 394)(267, 395)(268, 396)(269, 397)(270, 398)(271, 399)(272, 400)(273, 401)(274, 402)(275, 403)(276, 404)(277, 405)(278, 406)(279, 407)(280, 408)(281, 409)(282, 410)(283, 411)(284, 412)(285, 413)(286, 414)(287, 415)(288, 416)(289, 417)(290, 418)(291, 419)(292, 420)(293, 421)(294, 422)(295, 423)(296, 424)(297, 425)(298, 426)(299, 427)(300, 428)(301, 429)(302, 430)(303, 431)(304, 432)(305, 433)(306, 434)(307, 435)(308, 436)(309, 437)(310, 438)(311, 439)(312, 440)(313, 441)(314, 442)(315, 443)(316, 444)(317, 445)(318, 446)(319, 447)(320, 448)(321, 449)(322, 450)(323, 451)(324, 452)(325, 453)(326, 454)(327, 455)(328, 456)(329, 457)(330, 458)(331, 459)(332, 460)(333, 461)(334, 462)(335, 463)(336, 464)(337, 465)(338, 466)(339, 467)(340, 468)(341, 469)(342, 470)(343, 471)(344, 472)(345, 473)(346, 474)(347, 475)(348, 476)(349, 477)(350, 478)(351, 479)(352, 480)(353, 481)(354, 482)(355, 483)(356, 484)(357, 485)(358, 486)(359, 487)(360, 488)(361, 489)(362, 490)(363, 491)(364, 492)(365, 493)(366, 494)(367, 495)(368, 496)(369, 497)(370, 498)(371, 499)(372, 500)(373, 501)(374, 502)(375, 503)(376, 504)(377, 505)(378, 506)(379, 507)(380, 508)(381, 509)(382, 510)(383, 511)(384, 512) L = (1, 259)(2, 263)(3, 266)(4, 267)(5, 257)(6, 269)(7, 271)(8, 258)(9, 260)(10, 274)(11, 275)(12, 261)(13, 277)(14, 262)(15, 279)(16, 264)(17, 265)(18, 282)(19, 283)(20, 268)(21, 285)(22, 270)(23, 287)(24, 272)(25, 273)(26, 290)(27, 291)(28, 276)(29, 293)(30, 278)(31, 295)(32, 280)(33, 281)(34, 298)(35, 299)(36, 284)(37, 301)(38, 286)(39, 303)(40, 288)(41, 289)(42, 306)(43, 307)(44, 292)(45, 309)(46, 294)(47, 311)(48, 296)(49, 297)(50, 314)(51, 315)(52, 300)(53, 317)(54, 302)(55, 319)(56, 304)(57, 305)(58, 322)(59, 323)(60, 308)(61, 325)(62, 310)(63, 327)(64, 312)(65, 313)(66, 330)(67, 331)(68, 316)(69, 333)(70, 318)(71, 335)(72, 320)(73, 321)(74, 338)(75, 339)(76, 324)(77, 341)(78, 326)(79, 343)(80, 328)(81, 329)(82, 346)(83, 347)(84, 332)(85, 349)(86, 334)(87, 351)(88, 336)(89, 337)(90, 354)(91, 355)(92, 340)(93, 357)(94, 342)(95, 359)(96, 344)(97, 345)(98, 362)(99, 363)(100, 348)(101, 365)(102, 350)(103, 367)(104, 352)(105, 353)(106, 370)(107, 371)(108, 356)(109, 373)(110, 358)(111, 375)(112, 360)(113, 361)(114, 378)(115, 379)(116, 364)(117, 381)(118, 366)(119, 383)(120, 368)(121, 369)(122, 382)(123, 384)(124, 372)(125, 380)(126, 374)(127, 377)(128, 376)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 4, 128 ), ( 4, 128, 4, 128, 4, 128, 4, 128 ) } Outer automorphisms :: reflexible Dual of E16.1232 Graph:: simple bipartite v = 160 e = 256 f = 66 degree seq :: [ 2^128, 8^32 ] E16.1234 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 34}) Quotient :: regular Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T1^34 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 105, 118, 126, 117, 114, 112, 104, 100, 96, 92, 88, 82, 76, 71, 69, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 65, 109, 113, 131, 125, 123, 115, 121, 106, 102, 97, 94, 89, 84, 77, 74, 70, 73, 62, 55, 46, 39, 30, 22, 12, 8)(6, 13, 9, 18, 27, 35, 43, 51, 59, 67, 111, 134, 116, 130, 119, 128, 124, 108, 101, 98, 93, 90, 83, 79, 72, 78, 75, 63, 54, 47, 38, 31, 21, 14)(16, 23, 17, 24, 32, 40, 48, 56, 64, 107, 120, 127, 122, 129, 132, 135, 133, 136, 110, 103, 99, 95, 91, 87, 80, 85, 81, 86, 66, 58, 50, 42, 34, 26) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 75)(63, 107)(67, 86)(68, 111)(69, 113)(70, 105)(71, 116)(72, 118)(73, 120)(74, 122)(76, 125)(77, 126)(78, 127)(79, 129)(80, 131)(81, 109)(82, 119)(83, 117)(84, 132)(85, 134)(87, 130)(88, 115)(89, 114)(90, 135)(91, 123)(92, 124)(93, 112)(94, 133)(95, 128)(96, 106)(97, 104)(98, 136)(99, 121)(100, 101)(102, 110)(103, 108) local type(s) :: { ( 4^34 ) } Outer automorphisms :: reflexible Dual of E16.1235 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 68 f = 34 degree seq :: [ 34^4 ] E16.1235 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 34}) Quotient :: regular Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^34 ] 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, 42, 38, 39)(40, 57, 41, 59)(43, 67, 44, 61)(45, 65, 46, 63)(47, 71, 48, 69)(49, 75, 50, 73)(51, 79, 52, 77)(53, 83, 54, 81)(55, 87, 56, 85)(58, 91, 60, 89)(62, 93, 68, 95)(64, 98, 66, 97)(70, 101, 72, 102)(74, 104, 76, 105)(78, 109, 80, 110)(82, 113, 84, 114)(86, 117, 88, 118)(90, 121, 92, 122)(94, 125, 96, 126)(99, 129, 100, 130)(103, 134, 108, 133)(106, 135, 107, 136)(111, 131, 112, 132)(115, 128, 116, 127)(119, 124, 120, 123) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 57)(36, 59)(39, 61)(40, 63)(41, 65)(42, 67)(43, 69)(44, 71)(45, 73)(46, 75)(47, 77)(48, 79)(49, 81)(50, 83)(51, 85)(52, 87)(53, 89)(54, 91)(55, 93)(56, 95)(58, 98)(60, 97)(62, 102)(64, 105)(66, 104)(68, 101)(70, 110)(72, 109)(74, 114)(76, 113)(78, 118)(80, 117)(82, 122)(84, 121)(86, 126)(88, 125)(90, 130)(92, 129)(94, 134)(96, 133)(99, 135)(100, 136)(103, 132)(106, 127)(107, 128)(108, 131)(111, 123)(112, 124)(115, 120)(116, 119) local type(s) :: { ( 34^4 ) } Outer automorphisms :: reflexible Dual of E16.1234 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 34 e = 68 f = 4 degree seq :: [ 4^34 ] E16.1236 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 34}) Quotient :: edge Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^34 ] 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, 60, 36, 59)(39, 72, 46, 73)(40, 75, 49, 76)(41, 77, 42, 78)(43, 79, 44, 80)(45, 82, 47, 71)(48, 85, 50, 74)(51, 87, 52, 88)(53, 70, 54, 69)(55, 83, 56, 81)(57, 86, 58, 84)(61, 90, 62, 89)(63, 92, 64, 91)(65, 94, 66, 93)(67, 96, 68, 95)(97, 101, 98, 102)(99, 120, 100, 119)(103, 127, 114, 128)(104, 131, 105, 132)(106, 125, 117, 126)(107, 129, 108, 130)(109, 135, 110, 136)(111, 134, 112, 133)(113, 124, 115, 123)(116, 122, 118, 121)(137, 138)(139, 143)(140, 145)(141, 146)(142, 148)(144, 147)(149, 153)(150, 154)(151, 155)(152, 156)(157, 161)(158, 162)(159, 163)(160, 164)(165, 169)(166, 170)(167, 171)(168, 172)(173, 205)(174, 206)(175, 207)(176, 210)(177, 211)(178, 212)(179, 208)(180, 209)(181, 217)(182, 218)(183, 219)(184, 220)(185, 221)(186, 222)(187, 213)(188, 214)(189, 215)(190, 216)(191, 225)(192, 226)(193, 227)(194, 228)(195, 223)(196, 224)(197, 229)(198, 230)(199, 231)(200, 232)(201, 233)(202, 234)(203, 235)(204, 236)(237, 269)(238, 270)(239, 259)(240, 263)(241, 264)(242, 257)(243, 261)(244, 262)(245, 265)(246, 266)(247, 267)(248, 268)(249, 254)(250, 260)(251, 252)(253, 258)(255, 271)(256, 272) L = (1, 137)(2, 138)(3, 139)(4, 140)(5, 141)(6, 142)(7, 143)(8, 144)(9, 145)(10, 146)(11, 147)(12, 148)(13, 149)(14, 150)(15, 151)(16, 152)(17, 153)(18, 154)(19, 155)(20, 156)(21, 157)(22, 158)(23, 159)(24, 160)(25, 161)(26, 162)(27, 163)(28, 164)(29, 165)(30, 166)(31, 167)(32, 168)(33, 169)(34, 170)(35, 171)(36, 172)(37, 173)(38, 174)(39, 175)(40, 176)(41, 177)(42, 178)(43, 179)(44, 180)(45, 181)(46, 182)(47, 183)(48, 184)(49, 185)(50, 186)(51, 187)(52, 188)(53, 189)(54, 190)(55, 191)(56, 192)(57, 193)(58, 194)(59, 195)(60, 196)(61, 197)(62, 198)(63, 199)(64, 200)(65, 201)(66, 202)(67, 203)(68, 204)(69, 205)(70, 206)(71, 207)(72, 208)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 257)(122, 258)(123, 259)(124, 260)(125, 261)(126, 262)(127, 263)(128, 264)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272) local type(s) :: { ( 68, 68 ), ( 68^4 ) } Outer automorphisms :: reflexible Dual of E16.1240 Transitivity :: ET+ Graph:: simple bipartite v = 102 e = 136 f = 4 degree seq :: [ 2^68, 4^34 ] E16.1237 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 34}) Quotient :: edge Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^34 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 106, 126, 132, 129, 121, 115, 109, 112, 102, 97, 93, 89, 85, 81, 77, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 103, 116, 120, 130, 133, 125, 117, 111, 105, 99, 95, 91, 87, 83, 79, 75, 72, 64, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 59, 67, 107, 114, 122, 128, 135, 127, 119, 113, 104, 98, 94, 90, 86, 82, 78, 74, 70, 65, 57, 49, 41, 33, 25, 17, 9)(6, 13, 21, 29, 37, 45, 53, 61, 101, 110, 118, 124, 134, 136, 131, 123, 108, 100, 96, 92, 88, 84, 80, 76, 73, 69, 71, 62, 54, 46, 38, 30, 22, 14)(137, 138, 142, 140)(139, 145, 149, 144)(141, 147, 150, 143)(146, 152, 157, 153)(148, 151, 158, 155)(154, 161, 165, 160)(156, 163, 166, 159)(162, 168, 173, 169)(164, 167, 174, 171)(170, 177, 181, 176)(172, 179, 182, 175)(178, 184, 189, 185)(180, 183, 190, 187)(186, 193, 197, 192)(188, 195, 198, 191)(194, 200, 237, 201)(196, 199, 207, 203)(202, 206, 246, 208)(204, 243, 205, 239)(209, 250, 213, 252)(210, 242, 211, 254)(212, 256, 217, 258)(214, 260, 215, 262)(216, 264, 221, 266)(218, 268, 219, 270)(220, 269, 225, 271)(222, 272, 223, 265)(224, 263, 229, 261)(226, 257, 227, 267)(228, 253, 233, 255)(230, 259, 231, 251)(232, 249, 238, 247)(234, 245, 235, 244)(236, 241, 248, 240) L = (1, 137)(2, 138)(3, 139)(4, 140)(5, 141)(6, 142)(7, 143)(8, 144)(9, 145)(10, 146)(11, 147)(12, 148)(13, 149)(14, 150)(15, 151)(16, 152)(17, 153)(18, 154)(19, 155)(20, 156)(21, 157)(22, 158)(23, 159)(24, 160)(25, 161)(26, 162)(27, 163)(28, 164)(29, 165)(30, 166)(31, 167)(32, 168)(33, 169)(34, 170)(35, 171)(36, 172)(37, 173)(38, 174)(39, 175)(40, 176)(41, 177)(42, 178)(43, 179)(44, 180)(45, 181)(46, 182)(47, 183)(48, 184)(49, 185)(50, 186)(51, 187)(52, 188)(53, 189)(54, 190)(55, 191)(56, 192)(57, 193)(58, 194)(59, 195)(60, 196)(61, 197)(62, 198)(63, 199)(64, 200)(65, 201)(66, 202)(67, 203)(68, 204)(69, 205)(70, 206)(71, 207)(72, 208)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 257)(122, 258)(123, 259)(124, 260)(125, 261)(126, 262)(127, 263)(128, 264)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272) local type(s) :: { ( 4^4 ), ( 4^34 ) } Outer automorphisms :: reflexible Dual of E16.1241 Transitivity :: ET+ Graph:: simple bipartite v = 38 e = 136 f = 68 degree seq :: [ 4^34, 34^4 ] E16.1238 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 34}) Quotient :: edge Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^34 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 101)(63, 72)(67, 105)(68, 71)(69, 107)(70, 109)(73, 113)(74, 115)(75, 117)(76, 119)(77, 121)(78, 123)(79, 125)(80, 127)(81, 129)(82, 131)(83, 133)(84, 130)(85, 128)(86, 135)(87, 120)(88, 136)(89, 116)(90, 134)(91, 132)(92, 114)(93, 122)(94, 124)(95, 110)(96, 126)(97, 106)(98, 118)(99, 102)(100, 108)(103, 111)(104, 112)(137, 138, 141, 147, 156, 165, 173, 181, 189, 197, 215, 218, 222, 226, 230, 234, 239, 248, 244, 246, 250, 256, 266, 259, 253, 204, 196, 188, 180, 172, 164, 155, 146, 140)(139, 143, 151, 161, 169, 177, 185, 193, 201, 213, 211, 216, 220, 224, 228, 232, 236, 242, 247, 252, 260, 265, 271, 249, 261, 243, 198, 191, 182, 175, 166, 158, 148, 144)(142, 149, 145, 154, 163, 171, 179, 187, 195, 203, 207, 210, 214, 219, 223, 227, 231, 235, 240, 258, 254, 264, 270, 255, 267, 245, 237, 199, 190, 183, 174, 167, 157, 150)(152, 159, 153, 160, 168, 176, 184, 192, 200, 208, 205, 206, 209, 212, 217, 221, 225, 229, 233, 238, 262, 268, 272, 269, 263, 251, 257, 241, 202, 194, 186, 178, 170, 162) L = (1, 137)(2, 138)(3, 139)(4, 140)(5, 141)(6, 142)(7, 143)(8, 144)(9, 145)(10, 146)(11, 147)(12, 148)(13, 149)(14, 150)(15, 151)(16, 152)(17, 153)(18, 154)(19, 155)(20, 156)(21, 157)(22, 158)(23, 159)(24, 160)(25, 161)(26, 162)(27, 163)(28, 164)(29, 165)(30, 166)(31, 167)(32, 168)(33, 169)(34, 170)(35, 171)(36, 172)(37, 173)(38, 174)(39, 175)(40, 176)(41, 177)(42, 178)(43, 179)(44, 180)(45, 181)(46, 182)(47, 183)(48, 184)(49, 185)(50, 186)(51, 187)(52, 188)(53, 189)(54, 190)(55, 191)(56, 192)(57, 193)(58, 194)(59, 195)(60, 196)(61, 197)(62, 198)(63, 199)(64, 200)(65, 201)(66, 202)(67, 203)(68, 204)(69, 205)(70, 206)(71, 207)(72, 208)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 257)(122, 258)(123, 259)(124, 260)(125, 261)(126, 262)(127, 263)(128, 264)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272) local type(s) :: { ( 8, 8 ), ( 8^34 ) } Outer automorphisms :: reflexible Dual of E16.1239 Transitivity :: ET+ Graph:: simple bipartite v = 72 e = 136 f = 34 degree seq :: [ 2^68, 34^4 ] E16.1239 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 34}) Quotient :: loop Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^34 ] Map:: R = (1, 137, 3, 139, 8, 144, 4, 140)(2, 138, 5, 141, 11, 147, 6, 142)(7, 143, 13, 149, 9, 145, 14, 150)(10, 146, 15, 151, 12, 148, 16, 152)(17, 153, 21, 157, 18, 154, 22, 158)(19, 155, 23, 159, 20, 156, 24, 160)(25, 161, 29, 165, 26, 162, 30, 166)(27, 163, 31, 167, 28, 164, 32, 168)(33, 169, 37, 173, 34, 170, 38, 174)(35, 171, 60, 196, 36, 172, 59, 195)(39, 175, 72, 208, 46, 182, 73, 209)(40, 176, 75, 211, 49, 185, 76, 212)(41, 177, 77, 213, 42, 178, 78, 214)(43, 179, 79, 215, 44, 180, 80, 216)(45, 181, 82, 218, 47, 183, 71, 207)(48, 184, 85, 221, 50, 186, 74, 210)(51, 187, 87, 223, 52, 188, 88, 224)(53, 189, 70, 206, 54, 190, 69, 205)(55, 191, 83, 219, 56, 192, 81, 217)(57, 193, 86, 222, 58, 194, 84, 220)(61, 197, 90, 226, 62, 198, 89, 225)(63, 199, 92, 228, 64, 200, 91, 227)(65, 201, 94, 230, 66, 202, 93, 229)(67, 203, 96, 232, 68, 204, 95, 231)(97, 233, 101, 237, 98, 234, 102, 238)(99, 235, 120, 256, 100, 236, 119, 255)(103, 239, 127, 263, 114, 250, 128, 264)(104, 240, 131, 267, 105, 241, 132, 268)(106, 242, 125, 261, 117, 253, 126, 262)(107, 243, 129, 265, 108, 244, 130, 266)(109, 245, 135, 271, 110, 246, 136, 272)(111, 247, 134, 270, 112, 248, 133, 269)(113, 249, 124, 260, 115, 251, 123, 259)(116, 252, 122, 258, 118, 254, 121, 257) L = (1, 138)(2, 137)(3, 143)(4, 145)(5, 146)(6, 148)(7, 139)(8, 147)(9, 140)(10, 141)(11, 144)(12, 142)(13, 153)(14, 154)(15, 155)(16, 156)(17, 149)(18, 150)(19, 151)(20, 152)(21, 161)(22, 162)(23, 163)(24, 164)(25, 157)(26, 158)(27, 159)(28, 160)(29, 169)(30, 170)(31, 171)(32, 172)(33, 165)(34, 166)(35, 167)(36, 168)(37, 205)(38, 206)(39, 207)(40, 210)(41, 211)(42, 212)(43, 208)(44, 209)(45, 217)(46, 218)(47, 219)(48, 220)(49, 221)(50, 222)(51, 213)(52, 214)(53, 215)(54, 216)(55, 225)(56, 226)(57, 227)(58, 228)(59, 223)(60, 224)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 173)(70, 174)(71, 175)(72, 179)(73, 180)(74, 176)(75, 177)(76, 178)(77, 187)(78, 188)(79, 189)(80, 190)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 195)(88, 196)(89, 191)(90, 192)(91, 193)(92, 194)(93, 197)(94, 198)(95, 199)(96, 200)(97, 201)(98, 202)(99, 203)(100, 204)(101, 269)(102, 270)(103, 259)(104, 263)(105, 264)(106, 257)(107, 261)(108, 262)(109, 265)(110, 266)(111, 267)(112, 268)(113, 254)(114, 260)(115, 252)(116, 251)(117, 258)(118, 249)(119, 271)(120, 272)(121, 242)(122, 253)(123, 239)(124, 250)(125, 243)(126, 244)(127, 240)(128, 241)(129, 245)(130, 246)(131, 247)(132, 248)(133, 237)(134, 238)(135, 255)(136, 256) local type(s) :: { ( 2, 34, 2, 34, 2, 34, 2, 34 ) } Outer automorphisms :: reflexible Dual of E16.1238 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 34 e = 136 f = 72 degree seq :: [ 8^34 ] E16.1240 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 34}) Quotient :: loop Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^34 ] Map:: R = (1, 137, 3, 139, 10, 146, 18, 154, 26, 162, 34, 170, 42, 178, 50, 186, 58, 194, 66, 202, 77, 213, 81, 217, 85, 221, 89, 225, 93, 229, 97, 233, 103, 239, 105, 241, 109, 245, 116, 252, 124, 260, 132, 268, 128, 264, 122, 258, 112, 248, 68, 204, 60, 196, 52, 188, 44, 180, 36, 172, 28, 164, 20, 156, 12, 148, 5, 141)(2, 138, 7, 143, 15, 151, 23, 159, 31, 167, 39, 175, 47, 183, 55, 191, 63, 199, 73, 209, 76, 212, 80, 216, 84, 220, 88, 224, 92, 228, 96, 232, 102, 238, 107, 243, 113, 249, 121, 257, 129, 265, 131, 267, 125, 261, 115, 251, 110, 246, 104, 240, 64, 200, 56, 192, 48, 184, 40, 176, 32, 168, 24, 160, 16, 152, 8, 144)(4, 140, 11, 147, 19, 155, 27, 163, 35, 171, 43, 179, 51, 187, 59, 195, 67, 203, 71, 207, 74, 210, 78, 214, 82, 218, 86, 222, 90, 226, 94, 230, 99, 235, 111, 247, 118, 254, 126, 262, 134, 270, 133, 269, 123, 259, 117, 253, 108, 244, 100, 236, 65, 201, 57, 193, 49, 185, 41, 177, 33, 169, 25, 161, 17, 153, 9, 145)(6, 142, 13, 149, 21, 157, 29, 165, 37, 173, 45, 181, 53, 189, 61, 197, 69, 205, 70, 206, 72, 208, 75, 211, 79, 215, 83, 219, 87, 223, 91, 227, 95, 231, 101, 237, 119, 255, 127, 263, 135, 271, 136, 272, 130, 266, 120, 256, 114, 250, 106, 242, 98, 234, 62, 198, 54, 190, 46, 182, 38, 174, 30, 166, 22, 158, 14, 150) L = (1, 138)(2, 142)(3, 145)(4, 137)(5, 147)(6, 140)(7, 141)(8, 139)(9, 149)(10, 152)(11, 150)(12, 151)(13, 144)(14, 143)(15, 158)(16, 157)(17, 146)(18, 161)(19, 148)(20, 163)(21, 153)(22, 155)(23, 156)(24, 154)(25, 165)(26, 168)(27, 166)(28, 167)(29, 160)(30, 159)(31, 174)(32, 173)(33, 162)(34, 177)(35, 164)(36, 179)(37, 169)(38, 171)(39, 172)(40, 170)(41, 181)(42, 184)(43, 182)(44, 183)(45, 176)(46, 175)(47, 190)(48, 189)(49, 178)(50, 193)(51, 180)(52, 195)(53, 185)(54, 187)(55, 188)(56, 186)(57, 197)(58, 200)(59, 198)(60, 199)(61, 192)(62, 191)(63, 234)(64, 205)(65, 194)(66, 236)(67, 196)(68, 207)(69, 201)(70, 240)(71, 242)(72, 244)(73, 204)(74, 248)(75, 251)(76, 250)(77, 246)(78, 256)(79, 259)(80, 258)(81, 253)(82, 264)(83, 267)(84, 266)(85, 261)(86, 272)(87, 270)(88, 268)(89, 269)(90, 260)(91, 257)(92, 271)(93, 265)(94, 263)(95, 254)(96, 252)(97, 262)(98, 203)(99, 245)(100, 206)(101, 243)(102, 255)(103, 249)(104, 202)(105, 247)(106, 209)(107, 241)(108, 213)(109, 238)(110, 208)(111, 237)(112, 212)(113, 231)(114, 210)(115, 217)(116, 230)(117, 211)(118, 239)(119, 235)(120, 216)(121, 233)(122, 214)(123, 221)(124, 228)(125, 215)(126, 227)(127, 232)(128, 220)(129, 223)(130, 218)(131, 225)(132, 222)(133, 219)(134, 229)(135, 226)(136, 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, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E16.1236 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 136 f = 102 degree seq :: [ 68^4 ] E16.1241 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 34}) Quotient :: loop Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^34 ] Map:: polytopal non-degenerate R = (1, 137, 3, 139)(2, 138, 6, 142)(4, 140, 9, 145)(5, 141, 12, 148)(7, 143, 16, 152)(8, 144, 17, 153)(10, 146, 15, 151)(11, 147, 21, 157)(13, 149, 23, 159)(14, 150, 24, 160)(18, 154, 26, 162)(19, 155, 27, 163)(20, 156, 30, 166)(22, 158, 32, 168)(25, 161, 34, 170)(28, 164, 33, 169)(29, 165, 38, 174)(31, 167, 40, 176)(35, 171, 42, 178)(36, 172, 43, 179)(37, 173, 46, 182)(39, 175, 48, 184)(41, 177, 50, 186)(44, 180, 49, 185)(45, 181, 54, 190)(47, 183, 56, 192)(51, 187, 58, 194)(52, 188, 59, 195)(53, 189, 62, 198)(55, 191, 64, 200)(57, 193, 66, 202)(60, 196, 65, 201)(61, 197, 109, 245)(63, 199, 123, 259)(67, 203, 118, 254)(68, 204, 127, 263)(69, 205, 111, 247)(70, 206, 116, 252)(71, 207, 110, 246)(72, 208, 104, 240)(73, 209, 122, 258)(74, 210, 103, 239)(75, 211, 126, 262)(76, 212, 114, 250)(77, 213, 115, 251)(78, 214, 97, 233)(79, 215, 129, 265)(80, 216, 96, 232)(81, 217, 119, 255)(82, 218, 108, 244)(83, 219, 120, 256)(84, 220, 105, 241)(85, 221, 117, 253)(86, 222, 130, 266)(87, 223, 89, 225)(88, 224, 131, 267)(90, 226, 101, 237)(91, 227, 112, 248)(92, 228, 124, 260)(93, 229, 132, 268)(94, 230, 98, 234)(95, 231, 128, 264)(99, 235, 133, 269)(100, 236, 121, 257)(102, 238, 135, 271)(106, 242, 136, 272)(107, 243, 134, 270)(113, 249, 125, 261) L = (1, 138)(2, 141)(3, 143)(4, 137)(5, 147)(6, 149)(7, 151)(8, 139)(9, 154)(10, 140)(11, 156)(12, 144)(13, 145)(14, 142)(15, 161)(16, 159)(17, 160)(18, 163)(19, 146)(20, 165)(21, 150)(22, 148)(23, 153)(24, 168)(25, 169)(26, 152)(27, 171)(28, 155)(29, 173)(30, 158)(31, 157)(32, 176)(33, 177)(34, 162)(35, 179)(36, 164)(37, 181)(38, 167)(39, 166)(40, 184)(41, 185)(42, 170)(43, 187)(44, 172)(45, 189)(46, 175)(47, 174)(48, 192)(49, 193)(50, 178)(51, 195)(52, 180)(53, 197)(54, 183)(55, 182)(56, 200)(57, 201)(58, 186)(59, 203)(60, 188)(61, 257)(62, 191)(63, 190)(64, 259)(65, 261)(66, 194)(67, 263)(68, 196)(69, 206)(70, 209)(71, 211)(72, 205)(73, 215)(74, 217)(75, 219)(76, 207)(77, 222)(78, 208)(79, 224)(80, 212)(81, 213)(82, 210)(83, 229)(84, 227)(85, 228)(86, 231)(87, 214)(88, 204)(89, 218)(90, 216)(91, 221)(92, 235)(93, 236)(94, 220)(95, 238)(96, 223)(97, 226)(98, 225)(99, 242)(100, 243)(101, 230)(102, 245)(103, 232)(104, 234)(105, 233)(106, 249)(107, 198)(108, 237)(109, 199)(110, 239)(111, 241)(112, 240)(113, 254)(114, 244)(115, 246)(116, 248)(117, 247)(118, 202)(119, 250)(120, 251)(121, 264)(122, 253)(123, 270)(124, 252)(125, 267)(126, 255)(127, 272)(128, 256)(129, 260)(130, 262)(131, 269)(132, 266)(133, 258)(134, 271)(135, 268)(136, 265) local type(s) :: { ( 4, 34, 4, 34 ) } Outer automorphisms :: reflexible Dual of E16.1237 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 68 e = 136 f = 38 degree seq :: [ 4^68 ] E16.1242 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 34}) Quotient :: dipole Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^34 ] Map:: R = (1, 137, 2, 138)(3, 139, 7, 143)(4, 140, 9, 145)(5, 141, 10, 146)(6, 142, 12, 148)(8, 144, 11, 147)(13, 149, 17, 153)(14, 150, 18, 154)(15, 151, 19, 155)(16, 152, 20, 156)(21, 157, 25, 161)(22, 158, 26, 162)(23, 159, 27, 163)(24, 160, 28, 164)(29, 165, 33, 169)(30, 166, 34, 170)(31, 167, 35, 171)(32, 168, 36, 172)(37, 173, 54, 190)(38, 174, 53, 189)(39, 175, 69, 205)(40, 176, 73, 209)(41, 177, 77, 213)(42, 178, 80, 216)(43, 179, 82, 218)(44, 180, 85, 221)(45, 181, 70, 206)(46, 182, 83, 219)(47, 183, 72, 208)(48, 184, 74, 210)(49, 185, 78, 214)(50, 186, 76, 212)(51, 187, 67, 203)(52, 188, 65, 201)(55, 191, 87, 223)(56, 192, 89, 225)(57, 193, 92, 228)(58, 194, 94, 230)(59, 195, 101, 237)(60, 196, 103, 239)(61, 197, 105, 241)(62, 198, 107, 243)(63, 199, 109, 245)(64, 200, 111, 247)(66, 202, 113, 249)(68, 204, 115, 251)(71, 207, 127, 263)(75, 211, 132, 268)(79, 215, 135, 271)(81, 217, 129, 265)(84, 220, 136, 272)(86, 222, 134, 270)(88, 224, 128, 264)(90, 226, 125, 261)(91, 227, 126, 262)(93, 229, 133, 269)(95, 231, 130, 266)(96, 232, 131, 267)(97, 233, 121, 257)(98, 234, 122, 258)(99, 235, 119, 255)(100, 236, 117, 253)(102, 238, 123, 259)(104, 240, 124, 260)(106, 242, 118, 254)(108, 244, 120, 256)(110, 246, 116, 252)(112, 248, 114, 250)(273, 409, 275, 411, 280, 416, 276, 412)(274, 410, 277, 413, 283, 419, 278, 414)(279, 415, 285, 421, 281, 417, 286, 422)(282, 418, 287, 423, 284, 420, 288, 424)(289, 425, 293, 429, 290, 426, 294, 430)(291, 427, 295, 431, 292, 428, 296, 432)(297, 433, 301, 437, 298, 434, 302, 438)(299, 435, 303, 439, 300, 436, 304, 440)(305, 441, 309, 445, 306, 442, 310, 446)(307, 443, 337, 473, 308, 444, 339, 475)(311, 447, 342, 478, 318, 454, 344, 480)(312, 448, 346, 482, 321, 457, 348, 484)(313, 449, 350, 486, 314, 450, 345, 481)(315, 451, 355, 491, 316, 452, 341, 477)(317, 453, 359, 495, 319, 455, 361, 497)(320, 456, 364, 500, 322, 458, 366, 502)(323, 459, 352, 488, 324, 460, 349, 485)(325, 461, 357, 493, 326, 462, 354, 490)(327, 463, 373, 509, 328, 464, 375, 511)(329, 465, 377, 513, 330, 466, 379, 515)(331, 467, 381, 517, 332, 468, 383, 519)(333, 469, 385, 521, 334, 470, 387, 523)(335, 471, 389, 525, 336, 472, 391, 527)(338, 474, 394, 530, 340, 476, 393, 529)(343, 479, 400, 536, 362, 498, 398, 534)(347, 483, 405, 541, 367, 503, 403, 539)(351, 487, 402, 538, 353, 489, 404, 540)(356, 492, 397, 533, 358, 494, 399, 535)(360, 496, 395, 531, 363, 499, 396, 532)(365, 501, 390, 526, 368, 504, 392, 528)(369, 505, 401, 537, 370, 506, 407, 543)(371, 507, 406, 542, 372, 508, 408, 544)(374, 510, 388, 524, 376, 512, 386, 522)(378, 514, 384, 520, 380, 516, 382, 518) L = (1, 274)(2, 273)(3, 279)(4, 281)(5, 282)(6, 284)(7, 275)(8, 283)(9, 276)(10, 277)(11, 280)(12, 278)(13, 289)(14, 290)(15, 291)(16, 292)(17, 285)(18, 286)(19, 287)(20, 288)(21, 297)(22, 298)(23, 299)(24, 300)(25, 293)(26, 294)(27, 295)(28, 296)(29, 305)(30, 306)(31, 307)(32, 308)(33, 301)(34, 302)(35, 303)(36, 304)(37, 326)(38, 325)(39, 341)(40, 345)(41, 349)(42, 352)(43, 354)(44, 357)(45, 342)(46, 355)(47, 344)(48, 346)(49, 350)(50, 348)(51, 339)(52, 337)(53, 310)(54, 309)(55, 359)(56, 361)(57, 364)(58, 366)(59, 373)(60, 375)(61, 377)(62, 379)(63, 381)(64, 383)(65, 324)(66, 385)(67, 323)(68, 387)(69, 311)(70, 317)(71, 399)(72, 319)(73, 312)(74, 320)(75, 404)(76, 322)(77, 313)(78, 321)(79, 407)(80, 314)(81, 401)(82, 315)(83, 318)(84, 408)(85, 316)(86, 406)(87, 327)(88, 400)(89, 328)(90, 397)(91, 398)(92, 329)(93, 405)(94, 330)(95, 402)(96, 403)(97, 393)(98, 394)(99, 391)(100, 389)(101, 331)(102, 395)(103, 332)(104, 396)(105, 333)(106, 390)(107, 334)(108, 392)(109, 335)(110, 388)(111, 336)(112, 386)(113, 338)(114, 384)(115, 340)(116, 382)(117, 372)(118, 378)(119, 371)(120, 380)(121, 369)(122, 370)(123, 374)(124, 376)(125, 362)(126, 363)(127, 343)(128, 360)(129, 353)(130, 367)(131, 368)(132, 347)(133, 365)(134, 358)(135, 351)(136, 356)(137, 409)(138, 410)(139, 411)(140, 412)(141, 413)(142, 414)(143, 415)(144, 416)(145, 417)(146, 418)(147, 419)(148, 420)(149, 421)(150, 422)(151, 423)(152, 424)(153, 425)(154, 426)(155, 427)(156, 428)(157, 429)(158, 430)(159, 431)(160, 432)(161, 433)(162, 434)(163, 435)(164, 436)(165, 437)(166, 438)(167, 439)(168, 440)(169, 441)(170, 442)(171, 443)(172, 444)(173, 445)(174, 446)(175, 447)(176, 448)(177, 449)(178, 450)(179, 451)(180, 452)(181, 453)(182, 454)(183, 455)(184, 456)(185, 457)(186, 458)(187, 459)(188, 460)(189, 461)(190, 462)(191, 463)(192, 464)(193, 465)(194, 466)(195, 467)(196, 468)(197, 469)(198, 470)(199, 471)(200, 472)(201, 473)(202, 474)(203, 475)(204, 476)(205, 477)(206, 478)(207, 479)(208, 480)(209, 481)(210, 482)(211, 483)(212, 484)(213, 485)(214, 486)(215, 487)(216, 488)(217, 489)(218, 490)(219, 491)(220, 492)(221, 493)(222, 494)(223, 495)(224, 496)(225, 497)(226, 498)(227, 499)(228, 500)(229, 501)(230, 502)(231, 503)(232, 504)(233, 505)(234, 506)(235, 507)(236, 508)(237, 509)(238, 510)(239, 511)(240, 512)(241, 513)(242, 514)(243, 515)(244, 516)(245, 517)(246, 518)(247, 519)(248, 520)(249, 521)(250, 522)(251, 523)(252, 524)(253, 525)(254, 526)(255, 527)(256, 528)(257, 529)(258, 530)(259, 531)(260, 532)(261, 533)(262, 534)(263, 535)(264, 536)(265, 537)(266, 538)(267, 539)(268, 540)(269, 541)(270, 542)(271, 543)(272, 544) local type(s) :: { ( 2, 68, 2, 68 ), ( 2, 68, 2, 68, 2, 68, 2, 68 ) } Outer automorphisms :: reflexible Dual of E16.1245 Graph:: bipartite v = 102 e = 272 f = 140 degree seq :: [ 4^68, 8^34 ] E16.1243 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 34}) Quotient :: dipole Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1)^2, Y1^4, Y2^34 ] Map:: R = (1, 137, 2, 138, 6, 142, 4, 140)(3, 139, 9, 145, 13, 149, 8, 144)(5, 141, 11, 147, 14, 150, 7, 143)(10, 146, 16, 152, 21, 157, 17, 153)(12, 148, 15, 151, 22, 158, 19, 155)(18, 154, 25, 161, 29, 165, 24, 160)(20, 156, 27, 163, 30, 166, 23, 159)(26, 162, 32, 168, 37, 173, 33, 169)(28, 164, 31, 167, 38, 174, 35, 171)(34, 170, 41, 177, 45, 181, 40, 176)(36, 172, 43, 179, 46, 182, 39, 175)(42, 178, 48, 184, 53, 189, 49, 185)(44, 180, 47, 183, 54, 190, 51, 187)(50, 186, 57, 193, 61, 197, 56, 192)(52, 188, 59, 195, 62, 198, 55, 191)(58, 194, 64, 200, 121, 257, 65, 201)(60, 196, 63, 199, 114, 250, 67, 203)(66, 202, 104, 240, 136, 272, 112, 248)(68, 204, 127, 263, 108, 244, 123, 259)(69, 205, 113, 249, 74, 210, 116, 252)(70, 206, 117, 253, 72, 208, 109, 245)(71, 207, 110, 246, 81, 217, 107, 243)(73, 209, 120, 256, 82, 218, 118, 254)(75, 211, 102, 238, 79, 215, 111, 247)(76, 212, 115, 251, 77, 213, 122, 258)(78, 214, 99, 235, 89, 225, 103, 239)(80, 216, 124, 260, 90, 226, 128, 264)(83, 219, 105, 241, 87, 223, 94, 230)(84, 220, 129, 265, 85, 221, 119, 255)(86, 222, 95, 231, 97, 233, 91, 227)(88, 224, 130, 266, 98, 234, 131, 267)(92, 228, 126, 262, 93, 229, 132, 268)(96, 232, 133, 269, 106, 242, 125, 261)(100, 236, 134, 270, 101, 237, 135, 271)(273, 409, 275, 411, 282, 418, 290, 426, 298, 434, 306, 442, 314, 450, 322, 458, 330, 466, 338, 474, 397, 533, 403, 539, 400, 536, 390, 526, 388, 524, 379, 515, 375, 511, 363, 499, 359, 495, 347, 483, 344, 480, 348, 484, 357, 493, 364, 500, 373, 509, 340, 476, 332, 468, 324, 460, 316, 452, 308, 444, 300, 436, 292, 428, 284, 420, 277, 413)(274, 410, 279, 415, 287, 423, 295, 431, 303, 439, 311, 447, 319, 455, 327, 463, 335, 471, 395, 531, 407, 543, 404, 540, 391, 527, 394, 530, 381, 517, 383, 519, 366, 502, 369, 505, 350, 486, 353, 489, 341, 477, 354, 490, 352, 488, 370, 506, 368, 504, 384, 520, 336, 472, 328, 464, 320, 456, 312, 448, 304, 440, 296, 432, 288, 424, 280, 416)(276, 412, 283, 419, 291, 427, 299, 435, 307, 443, 315, 451, 323, 459, 331, 467, 339, 475, 399, 535, 406, 542, 398, 534, 401, 537, 387, 523, 389, 525, 374, 510, 377, 513, 358, 494, 361, 497, 343, 479, 346, 482, 345, 481, 362, 498, 360, 496, 378, 514, 376, 512, 337, 473, 329, 465, 321, 457, 313, 449, 305, 441, 297, 433, 289, 425, 281, 417)(278, 414, 285, 421, 293, 429, 301, 437, 309, 445, 317, 453, 325, 461, 333, 469, 393, 529, 408, 544, 405, 541, 402, 538, 396, 532, 392, 528, 385, 521, 382, 518, 371, 507, 367, 503, 355, 491, 351, 487, 342, 478, 349, 485, 356, 492, 365, 501, 372, 508, 380, 516, 386, 522, 334, 470, 326, 462, 318, 454, 310, 446, 302, 438, 294, 430, 286, 422) L = (1, 275)(2, 279)(3, 282)(4, 283)(5, 273)(6, 285)(7, 287)(8, 274)(9, 276)(10, 290)(11, 291)(12, 277)(13, 293)(14, 278)(15, 295)(16, 280)(17, 281)(18, 298)(19, 299)(20, 284)(21, 301)(22, 286)(23, 303)(24, 288)(25, 289)(26, 306)(27, 307)(28, 292)(29, 309)(30, 294)(31, 311)(32, 296)(33, 297)(34, 314)(35, 315)(36, 300)(37, 317)(38, 302)(39, 319)(40, 304)(41, 305)(42, 322)(43, 323)(44, 308)(45, 325)(46, 310)(47, 327)(48, 312)(49, 313)(50, 330)(51, 331)(52, 316)(53, 333)(54, 318)(55, 335)(56, 320)(57, 321)(58, 338)(59, 339)(60, 324)(61, 393)(62, 326)(63, 395)(64, 328)(65, 329)(66, 397)(67, 399)(68, 332)(69, 354)(70, 349)(71, 346)(72, 348)(73, 362)(74, 345)(75, 344)(76, 357)(77, 356)(78, 353)(79, 342)(80, 370)(81, 341)(82, 352)(83, 351)(84, 365)(85, 364)(86, 361)(87, 347)(88, 378)(89, 343)(90, 360)(91, 359)(92, 373)(93, 372)(94, 369)(95, 355)(96, 384)(97, 350)(98, 368)(99, 367)(100, 380)(101, 340)(102, 377)(103, 363)(104, 337)(105, 358)(106, 376)(107, 375)(108, 386)(109, 383)(110, 371)(111, 366)(112, 336)(113, 382)(114, 334)(115, 389)(116, 379)(117, 374)(118, 388)(119, 394)(120, 385)(121, 408)(122, 381)(123, 407)(124, 392)(125, 403)(126, 401)(127, 406)(128, 390)(129, 387)(130, 396)(131, 400)(132, 391)(133, 402)(134, 398)(135, 404)(136, 405)(137, 409)(138, 410)(139, 411)(140, 412)(141, 413)(142, 414)(143, 415)(144, 416)(145, 417)(146, 418)(147, 419)(148, 420)(149, 421)(150, 422)(151, 423)(152, 424)(153, 425)(154, 426)(155, 427)(156, 428)(157, 429)(158, 430)(159, 431)(160, 432)(161, 433)(162, 434)(163, 435)(164, 436)(165, 437)(166, 438)(167, 439)(168, 440)(169, 441)(170, 442)(171, 443)(172, 444)(173, 445)(174, 446)(175, 447)(176, 448)(177, 449)(178, 450)(179, 451)(180, 452)(181, 453)(182, 454)(183, 455)(184, 456)(185, 457)(186, 458)(187, 459)(188, 460)(189, 461)(190, 462)(191, 463)(192, 464)(193, 465)(194, 466)(195, 467)(196, 468)(197, 469)(198, 470)(199, 471)(200, 472)(201, 473)(202, 474)(203, 475)(204, 476)(205, 477)(206, 478)(207, 479)(208, 480)(209, 481)(210, 482)(211, 483)(212, 484)(213, 485)(214, 486)(215, 487)(216, 488)(217, 489)(218, 490)(219, 491)(220, 492)(221, 493)(222, 494)(223, 495)(224, 496)(225, 497)(226, 498)(227, 499)(228, 500)(229, 501)(230, 502)(231, 503)(232, 504)(233, 505)(234, 506)(235, 507)(236, 508)(237, 509)(238, 510)(239, 511)(240, 512)(241, 513)(242, 514)(243, 515)(244, 516)(245, 517)(246, 518)(247, 519)(248, 520)(249, 521)(250, 522)(251, 523)(252, 524)(253, 525)(254, 526)(255, 527)(256, 528)(257, 529)(258, 530)(259, 531)(260, 532)(261, 533)(262, 534)(263, 535)(264, 536)(265, 537)(266, 538)(267, 539)(268, 540)(269, 541)(270, 542)(271, 543)(272, 544) 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 ) } Outer automorphisms :: reflexible Dual of E16.1244 Graph:: bipartite v = 38 e = 272 f = 204 degree seq :: [ 8^34, 68^4 ] E16.1244 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 34}) Quotient :: dipole Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^34 ] Map:: polytopal R = (1, 137)(2, 138)(3, 139)(4, 140)(5, 141)(6, 142)(7, 143)(8, 144)(9, 145)(10, 146)(11, 147)(12, 148)(13, 149)(14, 150)(15, 151)(16, 152)(17, 153)(18, 154)(19, 155)(20, 156)(21, 157)(22, 158)(23, 159)(24, 160)(25, 161)(26, 162)(27, 163)(28, 164)(29, 165)(30, 166)(31, 167)(32, 168)(33, 169)(34, 170)(35, 171)(36, 172)(37, 173)(38, 174)(39, 175)(40, 176)(41, 177)(42, 178)(43, 179)(44, 180)(45, 181)(46, 182)(47, 183)(48, 184)(49, 185)(50, 186)(51, 187)(52, 188)(53, 189)(54, 190)(55, 191)(56, 192)(57, 193)(58, 194)(59, 195)(60, 196)(61, 197)(62, 198)(63, 199)(64, 200)(65, 201)(66, 202)(67, 203)(68, 204)(69, 205)(70, 206)(71, 207)(72, 208)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 257)(122, 258)(123, 259)(124, 260)(125, 261)(126, 262)(127, 263)(128, 264)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272)(273, 409, 274, 410)(275, 411, 279, 415)(276, 412, 281, 417)(277, 413, 283, 419)(278, 414, 285, 421)(280, 416, 286, 422)(282, 418, 284, 420)(287, 423, 292, 428)(288, 424, 295, 431)(289, 425, 297, 433)(290, 426, 293, 429)(291, 427, 299, 435)(294, 430, 301, 437)(296, 432, 303, 439)(298, 434, 304, 440)(300, 436, 302, 438)(305, 441, 311, 447)(306, 442, 313, 449)(307, 443, 309, 445)(308, 444, 315, 451)(310, 446, 317, 453)(312, 448, 319, 455)(314, 450, 320, 456)(316, 452, 318, 454)(321, 457, 327, 463)(322, 458, 329, 465)(323, 459, 325, 461)(324, 460, 331, 467)(326, 462, 333, 469)(328, 464, 335, 471)(330, 466, 336, 472)(332, 468, 334, 470)(337, 473, 375, 511)(338, 474, 352, 488)(339, 475, 344, 480)(340, 476, 379, 515)(341, 477, 381, 517)(342, 478, 382, 518)(343, 479, 383, 519)(345, 481, 384, 520)(346, 482, 385, 521)(347, 483, 386, 522)(348, 484, 377, 513)(349, 485, 373, 509)(350, 486, 387, 523)(351, 487, 388, 524)(353, 489, 389, 525)(354, 490, 390, 526)(355, 491, 391, 527)(356, 492, 392, 528)(357, 493, 393, 529)(358, 494, 394, 530)(359, 495, 395, 531)(360, 496, 396, 532)(361, 497, 397, 533)(362, 498, 398, 534)(363, 499, 399, 535)(364, 500, 400, 536)(365, 501, 401, 537)(366, 502, 402, 538)(367, 503, 403, 539)(368, 504, 405, 541)(369, 505, 378, 514)(370, 506, 406, 542)(371, 507, 380, 516)(372, 508, 407, 543)(374, 510, 404, 540)(376, 512, 408, 544) L = (1, 275)(2, 277)(3, 280)(4, 273)(5, 284)(6, 274)(7, 287)(8, 289)(9, 290)(10, 276)(11, 292)(12, 294)(13, 295)(14, 278)(15, 281)(16, 279)(17, 298)(18, 299)(19, 282)(20, 285)(21, 283)(22, 302)(23, 303)(24, 286)(25, 288)(26, 306)(27, 307)(28, 291)(29, 293)(30, 310)(31, 311)(32, 296)(33, 297)(34, 314)(35, 315)(36, 300)(37, 301)(38, 318)(39, 319)(40, 304)(41, 305)(42, 322)(43, 323)(44, 308)(45, 309)(46, 326)(47, 327)(48, 312)(49, 313)(50, 330)(51, 331)(52, 316)(53, 317)(54, 334)(55, 335)(56, 320)(57, 321)(58, 338)(59, 339)(60, 324)(61, 325)(62, 373)(63, 375)(64, 328)(65, 329)(66, 377)(67, 379)(68, 332)(69, 336)(70, 352)(71, 349)(72, 333)(73, 348)(74, 340)(75, 346)(76, 341)(77, 344)(78, 354)(79, 343)(80, 337)(81, 351)(82, 342)(83, 358)(84, 347)(85, 356)(86, 345)(87, 362)(88, 353)(89, 360)(90, 350)(91, 366)(92, 357)(93, 364)(94, 355)(95, 370)(96, 361)(97, 368)(98, 359)(99, 376)(100, 365)(101, 385)(102, 372)(103, 381)(104, 363)(105, 390)(106, 404)(107, 383)(108, 369)(109, 382)(110, 384)(111, 386)(112, 387)(113, 388)(114, 389)(115, 391)(116, 392)(117, 393)(118, 394)(119, 395)(120, 396)(121, 397)(122, 398)(123, 399)(124, 400)(125, 401)(126, 402)(127, 403)(128, 405)(129, 378)(130, 406)(131, 380)(132, 367)(133, 407)(134, 408)(135, 371)(136, 374)(137, 409)(138, 410)(139, 411)(140, 412)(141, 413)(142, 414)(143, 415)(144, 416)(145, 417)(146, 418)(147, 419)(148, 420)(149, 421)(150, 422)(151, 423)(152, 424)(153, 425)(154, 426)(155, 427)(156, 428)(157, 429)(158, 430)(159, 431)(160, 432)(161, 433)(162, 434)(163, 435)(164, 436)(165, 437)(166, 438)(167, 439)(168, 440)(169, 441)(170, 442)(171, 443)(172, 444)(173, 445)(174, 446)(175, 447)(176, 448)(177, 449)(178, 450)(179, 451)(180, 452)(181, 453)(182, 454)(183, 455)(184, 456)(185, 457)(186, 458)(187, 459)(188, 460)(189, 461)(190, 462)(191, 463)(192, 464)(193, 465)(194, 466)(195, 467)(196, 468)(197, 469)(198, 470)(199, 471)(200, 472)(201, 473)(202, 474)(203, 475)(204, 476)(205, 477)(206, 478)(207, 479)(208, 480)(209, 481)(210, 482)(211, 483)(212, 484)(213, 485)(214, 486)(215, 487)(216, 488)(217, 489)(218, 490)(219, 491)(220, 492)(221, 493)(222, 494)(223, 495)(224, 496)(225, 497)(226, 498)(227, 499)(228, 500)(229, 501)(230, 502)(231, 503)(232, 504)(233, 505)(234, 506)(235, 507)(236, 508)(237, 509)(238, 510)(239, 511)(240, 512)(241, 513)(242, 514)(243, 515)(244, 516)(245, 517)(246, 518)(247, 519)(248, 520)(249, 521)(250, 522)(251, 523)(252, 524)(253, 525)(254, 526)(255, 527)(256, 528)(257, 529)(258, 530)(259, 531)(260, 532)(261, 533)(262, 534)(263, 535)(264, 536)(265, 537)(266, 538)(267, 539)(268, 540)(269, 541)(270, 542)(271, 543)(272, 544) local type(s) :: { ( 8, 68 ), ( 8, 68, 8, 68 ) } Outer automorphisms :: reflexible Dual of E16.1243 Graph:: simple bipartite v = 204 e = 272 f = 38 degree seq :: [ 2^136, 4^68 ] E16.1245 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 34}) Quotient :: dipole Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1)^4, Y1^34 ] Map:: polytopal R = (1, 137, 2, 138, 5, 141, 11, 147, 20, 156, 29, 165, 37, 173, 45, 181, 53, 189, 61, 197, 71, 207, 75, 211, 80, 216, 85, 221, 89, 225, 93, 229, 97, 233, 102, 238, 136, 272, 135, 271, 131, 267, 127, 263, 123, 259, 119, 255, 115, 251, 68, 204, 60, 196, 52, 188, 44, 180, 36, 172, 28, 164, 19, 155, 10, 146, 4, 140)(3, 139, 7, 143, 15, 151, 25, 161, 33, 169, 41, 177, 49, 185, 57, 193, 65, 201, 69, 205, 78, 214, 74, 210, 87, 223, 84, 220, 95, 231, 92, 228, 104, 240, 100, 236, 134, 270, 130, 266, 125, 261, 122, 258, 117, 253, 114, 250, 109, 245, 113, 249, 62, 198, 55, 191, 46, 182, 39, 175, 30, 166, 22, 158, 12, 148, 8, 144)(6, 142, 13, 149, 9, 145, 18, 154, 27, 163, 35, 171, 43, 179, 51, 187, 59, 195, 67, 203, 82, 218, 70, 206, 83, 219, 79, 215, 91, 227, 88, 224, 99, 235, 96, 232, 132, 268, 106, 242, 129, 265, 126, 262, 121, 257, 118, 254, 112, 248, 110, 246, 101, 237, 63, 199, 54, 190, 47, 183, 38, 174, 31, 167, 21, 157, 14, 150)(16, 152, 23, 159, 17, 153, 24, 160, 32, 168, 40, 176, 48, 184, 56, 192, 64, 200, 72, 208, 76, 212, 73, 209, 77, 213, 81, 217, 86, 222, 90, 226, 94, 230, 98, 234, 103, 239, 133, 269, 128, 264, 124, 260, 120, 256, 116, 252, 111, 247, 108, 244, 107, 243, 105, 241, 66, 202, 58, 194, 50, 186, 42, 178, 34, 170, 26, 162)(273, 409)(274, 410)(275, 411)(276, 412)(277, 413)(278, 414)(279, 415)(280, 416)(281, 417)(282, 418)(283, 419)(284, 420)(285, 421)(286, 422)(287, 423)(288, 424)(289, 425)(290, 426)(291, 427)(292, 428)(293, 429)(294, 430)(295, 431)(296, 432)(297, 433)(298, 434)(299, 435)(300, 436)(301, 437)(302, 438)(303, 439)(304, 440)(305, 441)(306, 442)(307, 443)(308, 444)(309, 445)(310, 446)(311, 447)(312, 448)(313, 449)(314, 450)(315, 451)(316, 452)(317, 453)(318, 454)(319, 455)(320, 456)(321, 457)(322, 458)(323, 459)(324, 460)(325, 461)(326, 462)(327, 463)(328, 464)(329, 465)(330, 466)(331, 467)(332, 468)(333, 469)(334, 470)(335, 471)(336, 472)(337, 473)(338, 474)(339, 475)(340, 476)(341, 477)(342, 478)(343, 479)(344, 480)(345, 481)(346, 482)(347, 483)(348, 484)(349, 485)(350, 486)(351, 487)(352, 488)(353, 489)(354, 490)(355, 491)(356, 492)(357, 493)(358, 494)(359, 495)(360, 496)(361, 497)(362, 498)(363, 499)(364, 500)(365, 501)(366, 502)(367, 503)(368, 504)(369, 505)(370, 506)(371, 507)(372, 508)(373, 509)(374, 510)(375, 511)(376, 512)(377, 513)(378, 514)(379, 515)(380, 516)(381, 517)(382, 518)(383, 519)(384, 520)(385, 521)(386, 522)(387, 523)(388, 524)(389, 525)(390, 526)(391, 527)(392, 528)(393, 529)(394, 530)(395, 531)(396, 532)(397, 533)(398, 534)(399, 535)(400, 536)(401, 537)(402, 538)(403, 539)(404, 540)(405, 541)(406, 542)(407, 543)(408, 544) L = (1, 275)(2, 278)(3, 273)(4, 281)(5, 284)(6, 274)(7, 288)(8, 289)(9, 276)(10, 287)(11, 293)(12, 277)(13, 295)(14, 296)(15, 282)(16, 279)(17, 280)(18, 298)(19, 299)(20, 302)(21, 283)(22, 304)(23, 285)(24, 286)(25, 306)(26, 290)(27, 291)(28, 305)(29, 310)(30, 292)(31, 312)(32, 294)(33, 300)(34, 297)(35, 314)(36, 315)(37, 318)(38, 301)(39, 320)(40, 303)(41, 322)(42, 307)(43, 308)(44, 321)(45, 326)(46, 309)(47, 328)(48, 311)(49, 316)(50, 313)(51, 330)(52, 331)(53, 334)(54, 317)(55, 336)(56, 319)(57, 338)(58, 323)(59, 324)(60, 337)(61, 373)(62, 325)(63, 344)(64, 327)(65, 332)(66, 329)(67, 377)(68, 354)(69, 379)(70, 380)(71, 381)(72, 335)(73, 382)(74, 383)(75, 384)(76, 385)(77, 386)(78, 387)(79, 388)(80, 389)(81, 390)(82, 340)(83, 391)(84, 392)(85, 393)(86, 394)(87, 395)(88, 396)(89, 397)(90, 398)(91, 399)(92, 400)(93, 401)(94, 402)(95, 403)(96, 405)(97, 406)(98, 378)(99, 407)(100, 375)(101, 333)(102, 404)(103, 372)(104, 408)(105, 339)(106, 370)(107, 341)(108, 342)(109, 343)(110, 345)(111, 346)(112, 347)(113, 348)(114, 349)(115, 350)(116, 351)(117, 352)(118, 353)(119, 355)(120, 356)(121, 357)(122, 358)(123, 359)(124, 360)(125, 361)(126, 362)(127, 363)(128, 364)(129, 365)(130, 366)(131, 367)(132, 374)(133, 368)(134, 369)(135, 371)(136, 376)(137, 409)(138, 410)(139, 411)(140, 412)(141, 413)(142, 414)(143, 415)(144, 416)(145, 417)(146, 418)(147, 419)(148, 420)(149, 421)(150, 422)(151, 423)(152, 424)(153, 425)(154, 426)(155, 427)(156, 428)(157, 429)(158, 430)(159, 431)(160, 432)(161, 433)(162, 434)(163, 435)(164, 436)(165, 437)(166, 438)(167, 439)(168, 440)(169, 441)(170, 442)(171, 443)(172, 444)(173, 445)(174, 446)(175, 447)(176, 448)(177, 449)(178, 450)(179, 451)(180, 452)(181, 453)(182, 454)(183, 455)(184, 456)(185, 457)(186, 458)(187, 459)(188, 460)(189, 461)(190, 462)(191, 463)(192, 464)(193, 465)(194, 466)(195, 467)(196, 468)(197, 469)(198, 470)(199, 471)(200, 472)(201, 473)(202, 474)(203, 475)(204, 476)(205, 477)(206, 478)(207, 479)(208, 480)(209, 481)(210, 482)(211, 483)(212, 484)(213, 485)(214, 486)(215, 487)(216, 488)(217, 489)(218, 490)(219, 491)(220, 492)(221, 493)(222, 494)(223, 495)(224, 496)(225, 497)(226, 498)(227, 499)(228, 500)(229, 501)(230, 502)(231, 503)(232, 504)(233, 505)(234, 506)(235, 507)(236, 508)(237, 509)(238, 510)(239, 511)(240, 512)(241, 513)(242, 514)(243, 515)(244, 516)(245, 517)(246, 518)(247, 519)(248, 520)(249, 521)(250, 522)(251, 523)(252, 524)(253, 525)(254, 526)(255, 527)(256, 528)(257, 529)(258, 530)(259, 531)(260, 532)(261, 533)(262, 534)(263, 535)(264, 536)(265, 537)(266, 538)(267, 539)(268, 540)(269, 541)(270, 542)(271, 543)(272, 544) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.1242 Graph:: simple bipartite v = 140 e = 272 f = 102 degree seq :: [ 2^136, 68^4 ] E16.1246 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 34}) Quotient :: dipole Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^34 ] Map:: R = (1, 137, 2, 138)(3, 139, 7, 143)(4, 140, 9, 145)(5, 141, 11, 147)(6, 142, 13, 149)(8, 144, 14, 150)(10, 146, 12, 148)(15, 151, 20, 156)(16, 152, 23, 159)(17, 153, 25, 161)(18, 154, 21, 157)(19, 155, 27, 163)(22, 158, 29, 165)(24, 160, 31, 167)(26, 162, 32, 168)(28, 164, 30, 166)(33, 169, 39, 175)(34, 170, 41, 177)(35, 171, 37, 173)(36, 172, 43, 179)(38, 174, 45, 181)(40, 176, 47, 183)(42, 178, 48, 184)(44, 180, 46, 182)(49, 185, 55, 191)(50, 186, 57, 193)(51, 187, 53, 189)(52, 188, 59, 195)(54, 190, 61, 197)(56, 192, 63, 199)(58, 194, 64, 200)(60, 196, 62, 198)(65, 201, 71, 207)(66, 202, 104, 240)(67, 203, 105, 241)(68, 204, 80, 216)(69, 205, 107, 243)(70, 206, 108, 244)(72, 208, 109, 245)(73, 209, 110, 246)(74, 210, 111, 247)(75, 211, 112, 248)(76, 212, 113, 249)(77, 213, 114, 250)(78, 214, 115, 251)(79, 215, 116, 252)(81, 217, 117, 253)(82, 218, 118, 254)(83, 219, 119, 255)(84, 220, 120, 256)(85, 221, 121, 257)(86, 222, 122, 258)(87, 223, 123, 259)(88, 224, 124, 260)(89, 225, 125, 261)(90, 226, 126, 262)(91, 227, 127, 263)(92, 228, 128, 264)(93, 229, 129, 265)(94, 230, 130, 266)(95, 231, 131, 267)(96, 232, 132, 268)(97, 233, 134, 270)(98, 234, 106, 242)(99, 235, 135, 271)(100, 236, 103, 239)(101, 237, 136, 272)(102, 238, 133, 269)(273, 409, 275, 411, 280, 416, 289, 425, 298, 434, 306, 442, 314, 450, 322, 458, 330, 466, 338, 474, 345, 481, 348, 484, 355, 491, 358, 494, 363, 499, 366, 502, 371, 507, 374, 510, 408, 544, 406, 542, 401, 537, 397, 533, 393, 529, 389, 525, 384, 520, 340, 476, 332, 468, 324, 460, 316, 452, 308, 444, 300, 436, 291, 427, 282, 418, 276, 412)(274, 410, 277, 413, 284, 420, 294, 430, 302, 438, 310, 446, 318, 454, 326, 462, 334, 470, 341, 477, 347, 483, 346, 482, 357, 493, 356, 492, 365, 501, 364, 500, 373, 509, 372, 508, 407, 543, 403, 539, 399, 535, 395, 531, 391, 527, 387, 523, 382, 518, 386, 522, 336, 472, 328, 464, 320, 456, 312, 448, 304, 440, 296, 432, 286, 422, 278, 414)(279, 415, 287, 423, 281, 417, 290, 426, 299, 435, 307, 443, 315, 451, 323, 459, 331, 467, 339, 475, 352, 488, 342, 478, 353, 489, 351, 487, 361, 497, 360, 496, 369, 505, 368, 504, 405, 541, 378, 514, 402, 538, 398, 534, 394, 530, 390, 526, 385, 521, 381, 517, 376, 512, 337, 473, 329, 465, 321, 457, 313, 449, 305, 441, 297, 433, 288, 424)(283, 419, 292, 428, 285, 421, 295, 431, 303, 439, 311, 447, 319, 455, 327, 463, 335, 471, 343, 479, 349, 485, 344, 480, 350, 486, 354, 490, 359, 495, 362, 498, 367, 503, 370, 506, 375, 511, 404, 540, 400, 536, 396, 532, 392, 528, 388, 524, 383, 519, 380, 516, 379, 515, 377, 513, 333, 469, 325, 461, 317, 453, 309, 445, 301, 437, 293, 429) L = (1, 274)(2, 273)(3, 279)(4, 281)(5, 283)(6, 285)(7, 275)(8, 286)(9, 276)(10, 284)(11, 277)(12, 282)(13, 278)(14, 280)(15, 292)(16, 295)(17, 297)(18, 293)(19, 299)(20, 287)(21, 290)(22, 301)(23, 288)(24, 303)(25, 289)(26, 304)(27, 291)(28, 302)(29, 294)(30, 300)(31, 296)(32, 298)(33, 311)(34, 313)(35, 309)(36, 315)(37, 307)(38, 317)(39, 305)(40, 319)(41, 306)(42, 320)(43, 308)(44, 318)(45, 310)(46, 316)(47, 312)(48, 314)(49, 327)(50, 329)(51, 325)(52, 331)(53, 323)(54, 333)(55, 321)(56, 335)(57, 322)(58, 336)(59, 324)(60, 334)(61, 326)(62, 332)(63, 328)(64, 330)(65, 343)(66, 376)(67, 377)(68, 352)(69, 379)(70, 380)(71, 337)(72, 381)(73, 382)(74, 383)(75, 384)(76, 385)(77, 386)(78, 387)(79, 388)(80, 340)(81, 389)(82, 390)(83, 391)(84, 392)(85, 393)(86, 394)(87, 395)(88, 396)(89, 397)(90, 398)(91, 399)(92, 400)(93, 401)(94, 402)(95, 403)(96, 404)(97, 406)(98, 378)(99, 407)(100, 375)(101, 408)(102, 405)(103, 372)(104, 338)(105, 339)(106, 370)(107, 341)(108, 342)(109, 344)(110, 345)(111, 346)(112, 347)(113, 348)(114, 349)(115, 350)(116, 351)(117, 353)(118, 354)(119, 355)(120, 356)(121, 357)(122, 358)(123, 359)(124, 360)(125, 361)(126, 362)(127, 363)(128, 364)(129, 365)(130, 366)(131, 367)(132, 368)(133, 374)(134, 369)(135, 371)(136, 373)(137, 409)(138, 410)(139, 411)(140, 412)(141, 413)(142, 414)(143, 415)(144, 416)(145, 417)(146, 418)(147, 419)(148, 420)(149, 421)(150, 422)(151, 423)(152, 424)(153, 425)(154, 426)(155, 427)(156, 428)(157, 429)(158, 430)(159, 431)(160, 432)(161, 433)(162, 434)(163, 435)(164, 436)(165, 437)(166, 438)(167, 439)(168, 440)(169, 441)(170, 442)(171, 443)(172, 444)(173, 445)(174, 446)(175, 447)(176, 448)(177, 449)(178, 450)(179, 451)(180, 452)(181, 453)(182, 454)(183, 455)(184, 456)(185, 457)(186, 458)(187, 459)(188, 460)(189, 461)(190, 462)(191, 463)(192, 464)(193, 465)(194, 466)(195, 467)(196, 468)(197, 469)(198, 470)(199, 471)(200, 472)(201, 473)(202, 474)(203, 475)(204, 476)(205, 477)(206, 478)(207, 479)(208, 480)(209, 481)(210, 482)(211, 483)(212, 484)(213, 485)(214, 486)(215, 487)(216, 488)(217, 489)(218, 490)(219, 491)(220, 492)(221, 493)(222, 494)(223, 495)(224, 496)(225, 497)(226, 498)(227, 499)(228, 500)(229, 501)(230, 502)(231, 503)(232, 504)(233, 505)(234, 506)(235, 507)(236, 508)(237, 509)(238, 510)(239, 511)(240, 512)(241, 513)(242, 514)(243, 515)(244, 516)(245, 517)(246, 518)(247, 519)(248, 520)(249, 521)(250, 522)(251, 523)(252, 524)(253, 525)(254, 526)(255, 527)(256, 528)(257, 529)(258, 530)(259, 531)(260, 532)(261, 533)(262, 534)(263, 535)(264, 536)(265, 537)(266, 538)(267, 539)(268, 540)(269, 541)(270, 542)(271, 543)(272, 544) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E16.1247 Graph:: bipartite v = 72 e = 272 f = 170 degree seq :: [ 4^68, 68^4 ] E16.1247 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 34}) Quotient :: dipole Aut^+ = (C34 x C2) : C2 (small group id <136, 8>) Aut = D8 x D34 (small group id <272, 40>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^34 ] Map:: polytopal R = (1, 137, 2, 138, 6, 142, 4, 140)(3, 139, 9, 145, 13, 149, 8, 144)(5, 141, 11, 147, 14, 150, 7, 143)(10, 146, 16, 152, 21, 157, 17, 153)(12, 148, 15, 151, 22, 158, 19, 155)(18, 154, 25, 161, 29, 165, 24, 160)(20, 156, 27, 163, 30, 166, 23, 159)(26, 162, 32, 168, 37, 173, 33, 169)(28, 164, 31, 167, 38, 174, 35, 171)(34, 170, 41, 177, 45, 181, 40, 176)(36, 172, 43, 179, 46, 182, 39, 175)(42, 178, 48, 184, 53, 189, 49, 185)(44, 180, 47, 183, 54, 190, 51, 187)(50, 186, 57, 193, 61, 197, 56, 192)(52, 188, 59, 195, 62, 198, 55, 191)(58, 194, 64, 200, 101, 237, 65, 201)(60, 196, 63, 199, 71, 207, 67, 203)(66, 202, 70, 206, 110, 246, 72, 208)(68, 204, 107, 243, 69, 205, 103, 239)(73, 209, 114, 250, 77, 213, 116, 252)(74, 210, 106, 242, 75, 211, 118, 254)(76, 212, 120, 256, 81, 217, 122, 258)(78, 214, 124, 260, 79, 215, 126, 262)(80, 216, 128, 264, 85, 221, 130, 266)(82, 218, 132, 268, 83, 219, 134, 270)(84, 220, 133, 269, 89, 225, 135, 271)(86, 222, 136, 272, 87, 223, 129, 265)(88, 224, 127, 263, 93, 229, 125, 261)(90, 226, 121, 257, 91, 227, 131, 267)(92, 228, 117, 253, 97, 233, 119, 255)(94, 230, 123, 259, 95, 231, 115, 251)(96, 232, 113, 249, 102, 238, 111, 247)(98, 234, 109, 245, 99, 235, 108, 244)(100, 236, 105, 241, 112, 248, 104, 240)(273, 409)(274, 410)(275, 411)(276, 412)(277, 413)(278, 414)(279, 415)(280, 416)(281, 417)(282, 418)(283, 419)(284, 420)(285, 421)(286, 422)(287, 423)(288, 424)(289, 425)(290, 426)(291, 427)(292, 428)(293, 429)(294, 430)(295, 431)(296, 432)(297, 433)(298, 434)(299, 435)(300, 436)(301, 437)(302, 438)(303, 439)(304, 440)(305, 441)(306, 442)(307, 443)(308, 444)(309, 445)(310, 446)(311, 447)(312, 448)(313, 449)(314, 450)(315, 451)(316, 452)(317, 453)(318, 454)(319, 455)(320, 456)(321, 457)(322, 458)(323, 459)(324, 460)(325, 461)(326, 462)(327, 463)(328, 464)(329, 465)(330, 466)(331, 467)(332, 468)(333, 469)(334, 470)(335, 471)(336, 472)(337, 473)(338, 474)(339, 475)(340, 476)(341, 477)(342, 478)(343, 479)(344, 480)(345, 481)(346, 482)(347, 483)(348, 484)(349, 485)(350, 486)(351, 487)(352, 488)(353, 489)(354, 490)(355, 491)(356, 492)(357, 493)(358, 494)(359, 495)(360, 496)(361, 497)(362, 498)(363, 499)(364, 500)(365, 501)(366, 502)(367, 503)(368, 504)(369, 505)(370, 506)(371, 507)(372, 508)(373, 509)(374, 510)(375, 511)(376, 512)(377, 513)(378, 514)(379, 515)(380, 516)(381, 517)(382, 518)(383, 519)(384, 520)(385, 521)(386, 522)(387, 523)(388, 524)(389, 525)(390, 526)(391, 527)(392, 528)(393, 529)(394, 530)(395, 531)(396, 532)(397, 533)(398, 534)(399, 535)(400, 536)(401, 537)(402, 538)(403, 539)(404, 540)(405, 541)(406, 542)(407, 543)(408, 544) L = (1, 275)(2, 279)(3, 282)(4, 283)(5, 273)(6, 285)(7, 287)(8, 274)(9, 276)(10, 290)(11, 291)(12, 277)(13, 293)(14, 278)(15, 295)(16, 280)(17, 281)(18, 298)(19, 299)(20, 284)(21, 301)(22, 286)(23, 303)(24, 288)(25, 289)(26, 306)(27, 307)(28, 292)(29, 309)(30, 294)(31, 311)(32, 296)(33, 297)(34, 314)(35, 315)(36, 300)(37, 317)(38, 302)(39, 319)(40, 304)(41, 305)(42, 322)(43, 323)(44, 308)(45, 325)(46, 310)(47, 327)(48, 312)(49, 313)(50, 330)(51, 331)(52, 316)(53, 333)(54, 318)(55, 335)(56, 320)(57, 321)(58, 338)(59, 339)(60, 324)(61, 373)(62, 326)(63, 375)(64, 328)(65, 329)(66, 378)(67, 379)(68, 332)(69, 343)(70, 337)(71, 334)(72, 336)(73, 341)(74, 342)(75, 344)(76, 345)(77, 340)(78, 346)(79, 347)(80, 348)(81, 349)(82, 350)(83, 351)(84, 352)(85, 353)(86, 354)(87, 355)(88, 356)(89, 357)(90, 358)(91, 359)(92, 360)(93, 361)(94, 362)(95, 363)(96, 364)(97, 365)(98, 366)(99, 367)(100, 368)(101, 382)(102, 369)(103, 388)(104, 370)(105, 371)(106, 398)(107, 386)(108, 372)(109, 384)(110, 390)(111, 377)(112, 374)(113, 376)(114, 394)(115, 381)(116, 392)(117, 383)(118, 396)(119, 385)(120, 402)(121, 387)(122, 400)(123, 380)(124, 406)(125, 389)(126, 404)(127, 391)(128, 407)(129, 393)(130, 405)(131, 395)(132, 401)(133, 397)(134, 408)(135, 399)(136, 403)(137, 409)(138, 410)(139, 411)(140, 412)(141, 413)(142, 414)(143, 415)(144, 416)(145, 417)(146, 418)(147, 419)(148, 420)(149, 421)(150, 422)(151, 423)(152, 424)(153, 425)(154, 426)(155, 427)(156, 428)(157, 429)(158, 430)(159, 431)(160, 432)(161, 433)(162, 434)(163, 435)(164, 436)(165, 437)(166, 438)(167, 439)(168, 440)(169, 441)(170, 442)(171, 443)(172, 444)(173, 445)(174, 446)(175, 447)(176, 448)(177, 449)(178, 450)(179, 451)(180, 452)(181, 453)(182, 454)(183, 455)(184, 456)(185, 457)(186, 458)(187, 459)(188, 460)(189, 461)(190, 462)(191, 463)(192, 464)(193, 465)(194, 466)(195, 467)(196, 468)(197, 469)(198, 470)(199, 471)(200, 472)(201, 473)(202, 474)(203, 475)(204, 476)(205, 477)(206, 478)(207, 479)(208, 480)(209, 481)(210, 482)(211, 483)(212, 484)(213, 485)(214, 486)(215, 487)(216, 488)(217, 489)(218, 490)(219, 491)(220, 492)(221, 493)(222, 494)(223, 495)(224, 496)(225, 497)(226, 498)(227, 499)(228, 500)(229, 501)(230, 502)(231, 503)(232, 504)(233, 505)(234, 506)(235, 507)(236, 508)(237, 509)(238, 510)(239, 511)(240, 512)(241, 513)(242, 514)(243, 515)(244, 516)(245, 517)(246, 518)(247, 519)(248, 520)(249, 521)(250, 522)(251, 523)(252, 524)(253, 525)(254, 526)(255, 527)(256, 528)(257, 529)(258, 530)(259, 531)(260, 532)(261, 533)(262, 534)(263, 535)(264, 536)(265, 537)(266, 538)(267, 539)(268, 540)(269, 541)(270, 542)(271, 543)(272, 544) local type(s) :: { ( 4, 68 ), ( 4, 68, 4, 68, 4, 68, 4, 68 ) } Outer automorphisms :: reflexible Dual of E16.1246 Graph:: simple bipartite v = 170 e = 272 f = 72 degree seq :: [ 2^136, 8^34 ] E16.1248 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 8}) Quotient :: regular Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^8, T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-2, (T1^-1 * T2)^6 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 22, 10, 4)(3, 7, 15, 31, 46, 38, 18, 8)(6, 13, 27, 53, 45, 60, 30, 14)(9, 19, 39, 48, 24, 47, 42, 20)(12, 25, 49, 44, 21, 43, 52, 26)(16, 33, 58, 29, 57, 85, 65, 34)(17, 35, 66, 89, 61, 40, 68, 36)(28, 55, 79, 51, 78, 109, 84, 56)(32, 62, 90, 70, 37, 69, 93, 63)(41, 50, 77, 105, 75, 74, 102, 72)(54, 81, 113, 88, 59, 87, 116, 82)(64, 94, 123, 92, 119, 131, 125, 95)(67, 91, 115, 137, 121, 99, 117, 83)(71, 100, 129, 104, 73, 103, 130, 101)(76, 106, 132, 112, 80, 111, 135, 107)(86, 114, 134, 126, 96, 120, 136, 108)(97, 110, 133, 128, 98, 118, 138, 127)(122, 141, 144, 140, 124, 142, 143, 139) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 37)(19, 40)(20, 41)(22, 45)(23, 46)(25, 50)(26, 51)(27, 54)(30, 59)(31, 61)(33, 64)(34, 53)(35, 47)(36, 67)(38, 57)(39, 71)(42, 73)(43, 74)(44, 56)(48, 75)(49, 76)(52, 80)(55, 83)(58, 86)(60, 78)(62, 91)(63, 92)(65, 96)(66, 97)(68, 98)(69, 99)(70, 95)(72, 94)(77, 108)(79, 110)(81, 114)(82, 115)(84, 118)(85, 119)(87, 120)(88, 117)(89, 121)(90, 122)(93, 124)(100, 123)(101, 127)(102, 126)(103, 125)(104, 128)(105, 131)(106, 133)(107, 134)(109, 137)(111, 138)(112, 136)(113, 139)(116, 140)(129, 141)(130, 142)(132, 143)(135, 144) local type(s) :: { ( 6^8 ) } Outer automorphisms :: reflexible Dual of E16.1249 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 18 e = 72 f = 24 degree seq :: [ 8^18 ] E16.1249 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 8}) Quotient :: regular Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, T1^-1 * T2 * T1^-1 * T2 * T1^-2 * T2 * T1 * T2 * T1^-1, T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 29, 18, 8)(6, 13, 25, 48, 28, 14)(9, 19, 36, 64, 39, 20)(12, 23, 44, 73, 47, 24)(16, 31, 57, 75, 45, 32)(17, 33, 60, 76, 46, 34)(21, 40, 67, 96, 68, 41)(22, 42, 69, 97, 72, 43)(26, 50, 37, 65, 70, 51)(27, 52, 38, 66, 71, 53)(30, 54, 74, 99, 85, 56)(35, 49, 77, 98, 92, 63)(55, 83, 111, 125, 100, 84)(58, 86, 61, 90, 112, 87)(59, 88, 62, 91, 113, 89)(78, 103, 93, 120, 124, 104)(79, 105, 81, 109, 129, 106)(80, 107, 82, 110, 130, 108)(94, 121, 95, 123, 140, 122)(101, 126, 102, 128, 141, 127)(114, 131, 116, 133, 142, 137)(115, 135, 117, 136, 143, 138)(118, 132, 119, 134, 144, 139) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 30)(18, 35)(19, 37)(20, 38)(23, 45)(24, 46)(25, 49)(28, 54)(29, 55)(31, 58)(32, 59)(33, 61)(34, 62)(36, 63)(39, 56)(40, 57)(41, 60)(42, 70)(43, 71)(44, 74)(47, 77)(48, 78)(50, 79)(51, 80)(52, 81)(53, 82)(64, 93)(65, 94)(66, 95)(67, 85)(68, 92)(69, 98)(72, 99)(73, 100)(75, 101)(76, 102)(83, 112)(84, 113)(86, 114)(87, 115)(88, 116)(89, 117)(90, 118)(91, 119)(96, 111)(97, 124)(103, 129)(104, 130)(105, 131)(106, 132)(107, 133)(108, 134)(109, 135)(110, 136)(120, 140)(121, 137)(122, 139)(123, 138)(125, 141)(126, 142)(127, 143)(128, 144) local type(s) :: { ( 8^6 ) } Outer automorphisms :: reflexible Dual of E16.1248 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 24 e = 72 f = 18 degree seq :: [ 6^24 ] E16.1250 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 8}) Quotient :: edge Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^6, T2^-1 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2 * T1 * T2^-1, T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: polytopal R = (1, 3, 8, 18, 10, 4)(2, 5, 12, 25, 14, 6)(7, 15, 30, 57, 32, 16)(9, 19, 37, 65, 39, 20)(11, 22, 43, 71, 45, 23)(13, 26, 50, 79, 52, 27)(17, 33, 60, 90, 61, 34)(21, 40, 67, 96, 68, 41)(24, 46, 74, 104, 75, 47)(28, 53, 81, 110, 82, 54)(29, 55, 36, 64, 85, 56)(31, 58, 38, 66, 89, 59)(35, 62, 91, 119, 92, 63)(42, 69, 49, 78, 99, 70)(44, 72, 51, 80, 103, 73)(48, 76, 105, 132, 106, 77)(83, 111, 87, 117, 137, 112)(84, 113, 88, 118, 138, 114)(86, 115, 94, 122, 139, 116)(93, 120, 95, 123, 140, 121)(97, 124, 101, 130, 141, 125)(98, 126, 102, 131, 142, 127)(100, 128, 108, 135, 143, 129)(107, 133, 109, 136, 144, 134)(145, 146)(147, 151)(148, 153)(149, 155)(150, 157)(152, 161)(154, 165)(156, 168)(158, 172)(159, 173)(160, 175)(162, 179)(163, 180)(164, 182)(166, 186)(167, 188)(169, 192)(170, 193)(171, 195)(174, 197)(176, 190)(177, 189)(178, 196)(181, 198)(183, 191)(184, 187)(185, 194)(199, 227)(200, 228)(201, 230)(202, 231)(203, 232)(204, 218)(205, 225)(206, 229)(207, 233)(208, 237)(209, 238)(210, 239)(211, 219)(212, 226)(213, 241)(214, 242)(215, 244)(216, 245)(217, 246)(220, 243)(221, 247)(222, 251)(223, 252)(224, 253)(234, 250)(235, 254)(236, 248)(240, 249)(255, 268)(256, 277)(257, 274)(258, 280)(259, 281)(260, 282)(261, 270)(262, 275)(263, 283)(264, 269)(265, 278)(266, 284)(267, 271)(272, 285)(273, 286)(276, 287)(279, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 16, 16 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E16.1254 Transitivity :: ET+ Graph:: simple bipartite v = 96 e = 144 f = 18 degree seq :: [ 2^72, 6^24 ] E16.1251 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 8}) Quotient :: edge Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T1^6, T2 * T1^-1 * T2^2 * T1^-2 * T2^-1 * T1, T2^8, (T2 * T1^-2 * T2 * T1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 26, 61, 38, 15, 5)(2, 7, 19, 46, 89, 54, 22, 8)(4, 12, 31, 68, 100, 57, 24, 9)(6, 17, 41, 80, 117, 86, 44, 18)(11, 28, 63, 37, 75, 102, 59, 25)(13, 33, 58, 99, 130, 107, 66, 30)(14, 35, 73, 104, 60, 27, 42, 36)(16, 39, 76, 112, 136, 115, 79, 40)(20, 48, 23, 53, 96, 122, 87, 45)(21, 51, 94, 124, 88, 47, 77, 52)(29, 65, 103, 132, 110, 72, 34, 62)(32, 69, 78, 56, 98, 129, 108, 67)(43, 84, 120, 140, 116, 81, 71, 85)(49, 92, 123, 143, 125, 93, 50, 90)(55, 91, 70, 109, 121, 142, 128, 97)(64, 106, 127, 101, 131, 141, 134, 105)(74, 82, 118, 139, 133, 111, 119, 83)(95, 113, 137, 135, 144, 126, 138, 114)(145, 146, 150, 160, 157, 148)(147, 153, 167, 199, 173, 155)(149, 158, 178, 193, 164, 151)(152, 165, 194, 226, 186, 161)(154, 169, 202, 225, 185, 171)(156, 174, 207, 249, 214, 176)(159, 181, 210, 228, 188, 179)(162, 187, 227, 257, 221, 183)(163, 189, 175, 211, 220, 191)(166, 197, 168, 200, 223, 195)(170, 204, 247, 269, 240, 198)(172, 206, 180, 218, 229, 208)(177, 184, 222, 258, 250, 215)(182, 212, 231, 265, 254, 219)(190, 232, 267, 255, 217, 230)(192, 234, 196, 239, 213, 235)(201, 243, 203, 245, 272, 242)(205, 233, 261, 280, 274, 244)(209, 241, 271, 282, 262, 237)(216, 253, 278, 281, 263, 236)(224, 260, 283, 270, 238, 259)(246, 276, 248, 277, 284, 275)(251, 256, 252, 279, 285, 264)(266, 287, 268, 288, 273, 286) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 4^6 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.1255 Transitivity :: ET+ Graph:: simple bipartite v = 42 e = 144 f = 72 degree seq :: [ 6^24, 8^18 ] E16.1252 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 8}) Quotient :: edge Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^8, T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-2, (T2 * T1^-1)^6 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 37)(19, 40)(20, 41)(22, 45)(23, 46)(25, 50)(26, 51)(27, 54)(30, 59)(31, 61)(33, 64)(34, 53)(35, 47)(36, 67)(38, 57)(39, 71)(42, 73)(43, 74)(44, 56)(48, 75)(49, 76)(52, 80)(55, 83)(58, 86)(60, 78)(62, 91)(63, 92)(65, 96)(66, 97)(68, 98)(69, 99)(70, 95)(72, 94)(77, 108)(79, 110)(81, 114)(82, 115)(84, 118)(85, 119)(87, 120)(88, 117)(89, 121)(90, 122)(93, 124)(100, 123)(101, 127)(102, 126)(103, 125)(104, 128)(105, 131)(106, 133)(107, 134)(109, 137)(111, 138)(112, 136)(113, 139)(116, 140)(129, 141)(130, 142)(132, 143)(135, 144)(145, 146, 149, 155, 167, 166, 154, 148)(147, 151, 159, 175, 190, 182, 162, 152)(150, 157, 171, 197, 189, 204, 174, 158)(153, 163, 183, 192, 168, 191, 186, 164)(156, 169, 193, 188, 165, 187, 196, 170)(160, 177, 202, 173, 201, 229, 209, 178)(161, 179, 210, 233, 205, 184, 212, 180)(172, 199, 223, 195, 222, 253, 228, 200)(176, 206, 234, 214, 181, 213, 237, 207)(185, 194, 221, 249, 219, 218, 246, 216)(198, 225, 257, 232, 203, 231, 260, 226)(208, 238, 267, 236, 263, 275, 269, 239)(211, 235, 259, 281, 265, 243, 261, 227)(215, 244, 273, 248, 217, 247, 274, 245)(220, 250, 276, 256, 224, 255, 279, 251)(230, 258, 278, 270, 240, 264, 280, 252)(241, 254, 277, 272, 242, 262, 282, 271)(266, 285, 288, 284, 268, 286, 287, 283) 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) :: { ( 12, 12 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E16.1253 Transitivity :: ET+ Graph:: simple bipartite v = 90 e = 144 f = 24 degree seq :: [ 2^72, 8^18 ] E16.1253 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 8}) Quotient :: loop Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^6, T2^-1 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2 * T1 * T2^-1, T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 145, 3, 147, 8, 152, 18, 162, 10, 154, 4, 148)(2, 146, 5, 149, 12, 156, 25, 169, 14, 158, 6, 150)(7, 151, 15, 159, 30, 174, 57, 201, 32, 176, 16, 160)(9, 153, 19, 163, 37, 181, 65, 209, 39, 183, 20, 164)(11, 155, 22, 166, 43, 187, 71, 215, 45, 189, 23, 167)(13, 157, 26, 170, 50, 194, 79, 223, 52, 196, 27, 171)(17, 161, 33, 177, 60, 204, 90, 234, 61, 205, 34, 178)(21, 165, 40, 184, 67, 211, 96, 240, 68, 212, 41, 185)(24, 168, 46, 190, 74, 218, 104, 248, 75, 219, 47, 191)(28, 172, 53, 197, 81, 225, 110, 254, 82, 226, 54, 198)(29, 173, 55, 199, 36, 180, 64, 208, 85, 229, 56, 200)(31, 175, 58, 202, 38, 182, 66, 210, 89, 233, 59, 203)(35, 179, 62, 206, 91, 235, 119, 263, 92, 236, 63, 207)(42, 186, 69, 213, 49, 193, 78, 222, 99, 243, 70, 214)(44, 188, 72, 216, 51, 195, 80, 224, 103, 247, 73, 217)(48, 192, 76, 220, 105, 249, 132, 276, 106, 250, 77, 221)(83, 227, 111, 255, 87, 231, 117, 261, 137, 281, 112, 256)(84, 228, 113, 257, 88, 232, 118, 262, 138, 282, 114, 258)(86, 230, 115, 259, 94, 238, 122, 266, 139, 283, 116, 260)(93, 237, 120, 264, 95, 239, 123, 267, 140, 284, 121, 265)(97, 241, 124, 268, 101, 245, 130, 274, 141, 285, 125, 269)(98, 242, 126, 270, 102, 246, 131, 275, 142, 286, 127, 271)(100, 244, 128, 272, 108, 252, 135, 279, 143, 287, 129, 273)(107, 251, 133, 277, 109, 253, 136, 280, 144, 288, 134, 278) L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 155)(6, 157)(7, 147)(8, 161)(9, 148)(10, 165)(11, 149)(12, 168)(13, 150)(14, 172)(15, 173)(16, 175)(17, 152)(18, 179)(19, 180)(20, 182)(21, 154)(22, 186)(23, 188)(24, 156)(25, 192)(26, 193)(27, 195)(28, 158)(29, 159)(30, 197)(31, 160)(32, 190)(33, 189)(34, 196)(35, 162)(36, 163)(37, 198)(38, 164)(39, 191)(40, 187)(41, 194)(42, 166)(43, 184)(44, 167)(45, 177)(46, 176)(47, 183)(48, 169)(49, 170)(50, 185)(51, 171)(52, 178)(53, 174)(54, 181)(55, 227)(56, 228)(57, 230)(58, 231)(59, 232)(60, 218)(61, 225)(62, 229)(63, 233)(64, 237)(65, 238)(66, 239)(67, 219)(68, 226)(69, 241)(70, 242)(71, 244)(72, 245)(73, 246)(74, 204)(75, 211)(76, 243)(77, 247)(78, 251)(79, 252)(80, 253)(81, 205)(82, 212)(83, 199)(84, 200)(85, 206)(86, 201)(87, 202)(88, 203)(89, 207)(90, 250)(91, 254)(92, 248)(93, 208)(94, 209)(95, 210)(96, 249)(97, 213)(98, 214)(99, 220)(100, 215)(101, 216)(102, 217)(103, 221)(104, 236)(105, 240)(106, 234)(107, 222)(108, 223)(109, 224)(110, 235)(111, 268)(112, 277)(113, 274)(114, 280)(115, 281)(116, 282)(117, 270)(118, 275)(119, 283)(120, 269)(121, 278)(122, 284)(123, 271)(124, 255)(125, 264)(126, 261)(127, 267)(128, 285)(129, 286)(130, 257)(131, 262)(132, 287)(133, 256)(134, 265)(135, 288)(136, 258)(137, 259)(138, 260)(139, 263)(140, 266)(141, 272)(142, 273)(143, 276)(144, 279) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E16.1252 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 24 e = 144 f = 90 degree seq :: [ 12^24 ] E16.1254 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 8}) Quotient :: loop Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T1^6, T2 * T1^-1 * T2^2 * T1^-2 * T2^-1 * T1, T2^8, (T2 * T1^-2 * T2 * T1^-1)^2 ] Map:: R = (1, 145, 3, 147, 10, 154, 26, 170, 61, 205, 38, 182, 15, 159, 5, 149)(2, 146, 7, 151, 19, 163, 46, 190, 89, 233, 54, 198, 22, 166, 8, 152)(4, 148, 12, 156, 31, 175, 68, 212, 100, 244, 57, 201, 24, 168, 9, 153)(6, 150, 17, 161, 41, 185, 80, 224, 117, 261, 86, 230, 44, 188, 18, 162)(11, 155, 28, 172, 63, 207, 37, 181, 75, 219, 102, 246, 59, 203, 25, 169)(13, 157, 33, 177, 58, 202, 99, 243, 130, 274, 107, 251, 66, 210, 30, 174)(14, 158, 35, 179, 73, 217, 104, 248, 60, 204, 27, 171, 42, 186, 36, 180)(16, 160, 39, 183, 76, 220, 112, 256, 136, 280, 115, 259, 79, 223, 40, 184)(20, 164, 48, 192, 23, 167, 53, 197, 96, 240, 122, 266, 87, 231, 45, 189)(21, 165, 51, 195, 94, 238, 124, 268, 88, 232, 47, 191, 77, 221, 52, 196)(29, 173, 65, 209, 103, 247, 132, 276, 110, 254, 72, 216, 34, 178, 62, 206)(32, 176, 69, 213, 78, 222, 56, 200, 98, 242, 129, 273, 108, 252, 67, 211)(43, 187, 84, 228, 120, 264, 140, 284, 116, 260, 81, 225, 71, 215, 85, 229)(49, 193, 92, 236, 123, 267, 143, 287, 125, 269, 93, 237, 50, 194, 90, 234)(55, 199, 91, 235, 70, 214, 109, 253, 121, 265, 142, 286, 128, 272, 97, 241)(64, 208, 106, 250, 127, 271, 101, 245, 131, 275, 141, 285, 134, 278, 105, 249)(74, 218, 82, 226, 118, 262, 139, 283, 133, 277, 111, 255, 119, 263, 83, 227)(95, 239, 113, 257, 137, 281, 135, 279, 144, 288, 126, 270, 138, 282, 114, 258) L = (1, 146)(2, 150)(3, 153)(4, 145)(5, 158)(6, 160)(7, 149)(8, 165)(9, 167)(10, 169)(11, 147)(12, 174)(13, 148)(14, 178)(15, 181)(16, 157)(17, 152)(18, 187)(19, 189)(20, 151)(21, 194)(22, 197)(23, 199)(24, 200)(25, 202)(26, 204)(27, 154)(28, 206)(29, 155)(30, 207)(31, 211)(32, 156)(33, 184)(34, 193)(35, 159)(36, 218)(37, 210)(38, 212)(39, 162)(40, 222)(41, 171)(42, 161)(43, 227)(44, 179)(45, 175)(46, 232)(47, 163)(48, 234)(49, 164)(50, 226)(51, 166)(52, 239)(53, 168)(54, 170)(55, 173)(56, 223)(57, 243)(58, 225)(59, 245)(60, 247)(61, 233)(62, 180)(63, 249)(64, 172)(65, 241)(66, 228)(67, 220)(68, 231)(69, 235)(70, 176)(71, 177)(72, 253)(73, 230)(74, 229)(75, 182)(76, 191)(77, 183)(78, 258)(79, 195)(80, 260)(81, 185)(82, 186)(83, 257)(84, 188)(85, 208)(86, 190)(87, 265)(88, 267)(89, 261)(90, 196)(91, 192)(92, 216)(93, 209)(94, 259)(95, 213)(96, 198)(97, 271)(98, 201)(99, 203)(100, 205)(101, 272)(102, 276)(103, 269)(104, 277)(105, 214)(106, 215)(107, 256)(108, 279)(109, 278)(110, 219)(111, 217)(112, 252)(113, 221)(114, 250)(115, 224)(116, 283)(117, 280)(118, 237)(119, 236)(120, 251)(121, 254)(122, 287)(123, 255)(124, 288)(125, 240)(126, 238)(127, 282)(128, 242)(129, 286)(130, 244)(131, 246)(132, 248)(133, 284)(134, 281)(135, 285)(136, 274)(137, 263)(138, 262)(139, 270)(140, 275)(141, 264)(142, 266)(143, 268)(144, 273) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E16.1250 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 18 e = 144 f = 96 degree seq :: [ 16^18 ] E16.1255 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 8}) Quotient :: loop Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^8, T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-2, (T2 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 145, 3, 147)(2, 146, 6, 150)(4, 148, 9, 153)(5, 149, 12, 156)(7, 151, 16, 160)(8, 152, 17, 161)(10, 154, 21, 165)(11, 155, 24, 168)(13, 157, 28, 172)(14, 158, 29, 173)(15, 159, 32, 176)(18, 162, 37, 181)(19, 163, 40, 184)(20, 164, 41, 185)(22, 166, 45, 189)(23, 167, 46, 190)(25, 169, 50, 194)(26, 170, 51, 195)(27, 171, 54, 198)(30, 174, 59, 203)(31, 175, 61, 205)(33, 177, 64, 208)(34, 178, 53, 197)(35, 179, 47, 191)(36, 180, 67, 211)(38, 182, 57, 201)(39, 183, 71, 215)(42, 186, 73, 217)(43, 187, 74, 218)(44, 188, 56, 200)(48, 192, 75, 219)(49, 193, 76, 220)(52, 196, 80, 224)(55, 199, 83, 227)(58, 202, 86, 230)(60, 204, 78, 222)(62, 206, 91, 235)(63, 207, 92, 236)(65, 209, 96, 240)(66, 210, 97, 241)(68, 212, 98, 242)(69, 213, 99, 243)(70, 214, 95, 239)(72, 216, 94, 238)(77, 221, 108, 252)(79, 223, 110, 254)(81, 225, 114, 258)(82, 226, 115, 259)(84, 228, 118, 262)(85, 229, 119, 263)(87, 231, 120, 264)(88, 232, 117, 261)(89, 233, 121, 265)(90, 234, 122, 266)(93, 237, 124, 268)(100, 244, 123, 267)(101, 245, 127, 271)(102, 246, 126, 270)(103, 247, 125, 269)(104, 248, 128, 272)(105, 249, 131, 275)(106, 250, 133, 277)(107, 251, 134, 278)(109, 253, 137, 281)(111, 255, 138, 282)(112, 256, 136, 280)(113, 257, 139, 283)(116, 260, 140, 284)(129, 273, 141, 285)(130, 274, 142, 286)(132, 276, 143, 287)(135, 279, 144, 288) L = (1, 146)(2, 149)(3, 151)(4, 145)(5, 155)(6, 157)(7, 159)(8, 147)(9, 163)(10, 148)(11, 167)(12, 169)(13, 171)(14, 150)(15, 175)(16, 177)(17, 179)(18, 152)(19, 183)(20, 153)(21, 187)(22, 154)(23, 166)(24, 191)(25, 193)(26, 156)(27, 197)(28, 199)(29, 201)(30, 158)(31, 190)(32, 206)(33, 202)(34, 160)(35, 210)(36, 161)(37, 213)(38, 162)(39, 192)(40, 212)(41, 194)(42, 164)(43, 196)(44, 165)(45, 204)(46, 182)(47, 186)(48, 168)(49, 188)(50, 221)(51, 222)(52, 170)(53, 189)(54, 225)(55, 223)(56, 172)(57, 229)(58, 173)(59, 231)(60, 174)(61, 184)(62, 234)(63, 176)(64, 238)(65, 178)(66, 233)(67, 235)(68, 180)(69, 237)(70, 181)(71, 244)(72, 185)(73, 247)(74, 246)(75, 218)(76, 250)(77, 249)(78, 253)(79, 195)(80, 255)(81, 257)(82, 198)(83, 211)(84, 200)(85, 209)(86, 258)(87, 260)(88, 203)(89, 205)(90, 214)(91, 259)(92, 263)(93, 207)(94, 267)(95, 208)(96, 264)(97, 254)(98, 262)(99, 261)(100, 273)(101, 215)(102, 216)(103, 274)(104, 217)(105, 219)(106, 276)(107, 220)(108, 230)(109, 228)(110, 277)(111, 279)(112, 224)(113, 232)(114, 278)(115, 281)(116, 226)(117, 227)(118, 282)(119, 275)(120, 280)(121, 243)(122, 285)(123, 236)(124, 286)(125, 239)(126, 240)(127, 241)(128, 242)(129, 248)(130, 245)(131, 269)(132, 256)(133, 272)(134, 270)(135, 251)(136, 252)(137, 265)(138, 271)(139, 266)(140, 268)(141, 288)(142, 287)(143, 283)(144, 284) local type(s) :: { ( 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E16.1251 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 72 e = 144 f = 42 degree seq :: [ 4^72 ] E16.1256 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8}) Quotient :: dipole Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^6, (R * Y2^2 * Y1)^2, Y2^2 * Y1 * Y2 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 11, 155)(6, 150, 13, 157)(8, 152, 17, 161)(10, 154, 21, 165)(12, 156, 24, 168)(14, 158, 28, 172)(15, 159, 29, 173)(16, 160, 31, 175)(18, 162, 35, 179)(19, 163, 36, 180)(20, 164, 38, 182)(22, 166, 42, 186)(23, 167, 44, 188)(25, 169, 48, 192)(26, 170, 49, 193)(27, 171, 51, 195)(30, 174, 53, 197)(32, 176, 46, 190)(33, 177, 45, 189)(34, 178, 52, 196)(37, 181, 54, 198)(39, 183, 47, 191)(40, 184, 43, 187)(41, 185, 50, 194)(55, 199, 83, 227)(56, 200, 84, 228)(57, 201, 86, 230)(58, 202, 87, 231)(59, 203, 88, 232)(60, 204, 74, 218)(61, 205, 81, 225)(62, 206, 85, 229)(63, 207, 89, 233)(64, 208, 93, 237)(65, 209, 94, 238)(66, 210, 95, 239)(67, 211, 75, 219)(68, 212, 82, 226)(69, 213, 97, 241)(70, 214, 98, 242)(71, 215, 100, 244)(72, 216, 101, 245)(73, 217, 102, 246)(76, 220, 99, 243)(77, 221, 103, 247)(78, 222, 107, 251)(79, 223, 108, 252)(80, 224, 109, 253)(90, 234, 106, 250)(91, 235, 110, 254)(92, 236, 104, 248)(96, 240, 105, 249)(111, 255, 124, 268)(112, 256, 133, 277)(113, 257, 130, 274)(114, 258, 136, 280)(115, 259, 137, 281)(116, 260, 138, 282)(117, 261, 126, 270)(118, 262, 131, 275)(119, 263, 139, 283)(120, 264, 125, 269)(121, 265, 134, 278)(122, 266, 140, 284)(123, 267, 127, 271)(128, 272, 141, 285)(129, 273, 142, 286)(132, 276, 143, 287)(135, 279, 144, 288)(289, 433, 291, 435, 296, 440, 306, 450, 298, 442, 292, 436)(290, 434, 293, 437, 300, 444, 313, 457, 302, 446, 294, 438)(295, 439, 303, 447, 318, 462, 345, 489, 320, 464, 304, 448)(297, 441, 307, 451, 325, 469, 353, 497, 327, 471, 308, 452)(299, 443, 310, 454, 331, 475, 359, 503, 333, 477, 311, 455)(301, 445, 314, 458, 338, 482, 367, 511, 340, 484, 315, 459)(305, 449, 321, 465, 348, 492, 378, 522, 349, 493, 322, 466)(309, 453, 328, 472, 355, 499, 384, 528, 356, 500, 329, 473)(312, 456, 334, 478, 362, 506, 392, 536, 363, 507, 335, 479)(316, 460, 341, 485, 369, 513, 398, 542, 370, 514, 342, 486)(317, 461, 343, 487, 324, 468, 352, 496, 373, 517, 344, 488)(319, 463, 346, 490, 326, 470, 354, 498, 377, 521, 347, 491)(323, 467, 350, 494, 379, 523, 407, 551, 380, 524, 351, 495)(330, 474, 357, 501, 337, 481, 366, 510, 387, 531, 358, 502)(332, 476, 360, 504, 339, 483, 368, 512, 391, 535, 361, 505)(336, 480, 364, 508, 393, 537, 420, 564, 394, 538, 365, 509)(371, 515, 399, 543, 375, 519, 405, 549, 425, 569, 400, 544)(372, 516, 401, 545, 376, 520, 406, 550, 426, 570, 402, 546)(374, 518, 403, 547, 382, 526, 410, 554, 427, 571, 404, 548)(381, 525, 408, 552, 383, 527, 411, 555, 428, 572, 409, 553)(385, 529, 412, 556, 389, 533, 418, 562, 429, 573, 413, 557)(386, 530, 414, 558, 390, 534, 419, 563, 430, 574, 415, 559)(388, 532, 416, 560, 396, 540, 423, 567, 431, 575, 417, 561)(395, 539, 421, 565, 397, 541, 424, 568, 432, 576, 422, 566) L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 299)(6, 301)(7, 291)(8, 305)(9, 292)(10, 309)(11, 293)(12, 312)(13, 294)(14, 316)(15, 317)(16, 319)(17, 296)(18, 323)(19, 324)(20, 326)(21, 298)(22, 330)(23, 332)(24, 300)(25, 336)(26, 337)(27, 339)(28, 302)(29, 303)(30, 341)(31, 304)(32, 334)(33, 333)(34, 340)(35, 306)(36, 307)(37, 342)(38, 308)(39, 335)(40, 331)(41, 338)(42, 310)(43, 328)(44, 311)(45, 321)(46, 320)(47, 327)(48, 313)(49, 314)(50, 329)(51, 315)(52, 322)(53, 318)(54, 325)(55, 371)(56, 372)(57, 374)(58, 375)(59, 376)(60, 362)(61, 369)(62, 373)(63, 377)(64, 381)(65, 382)(66, 383)(67, 363)(68, 370)(69, 385)(70, 386)(71, 388)(72, 389)(73, 390)(74, 348)(75, 355)(76, 387)(77, 391)(78, 395)(79, 396)(80, 397)(81, 349)(82, 356)(83, 343)(84, 344)(85, 350)(86, 345)(87, 346)(88, 347)(89, 351)(90, 394)(91, 398)(92, 392)(93, 352)(94, 353)(95, 354)(96, 393)(97, 357)(98, 358)(99, 364)(100, 359)(101, 360)(102, 361)(103, 365)(104, 380)(105, 384)(106, 378)(107, 366)(108, 367)(109, 368)(110, 379)(111, 412)(112, 421)(113, 418)(114, 424)(115, 425)(116, 426)(117, 414)(118, 419)(119, 427)(120, 413)(121, 422)(122, 428)(123, 415)(124, 399)(125, 408)(126, 405)(127, 411)(128, 429)(129, 430)(130, 401)(131, 406)(132, 431)(133, 400)(134, 409)(135, 432)(136, 402)(137, 403)(138, 404)(139, 407)(140, 410)(141, 416)(142, 417)(143, 420)(144, 423)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E16.1259 Graph:: bipartite v = 96 e = 288 f = 162 degree seq :: [ 4^72, 12^24 ] E16.1257 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8}) Quotient :: dipole Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^6, Y1^-1 * Y2^-1 * Y1 * Y2^-2 * Y1 * Y2^-1 * Y1^-1, (Y2^3 * Y1^-1)^2, Y2^8, (Y2 * Y1^-2 * Y2 * Y1^-1)^2 ] Map:: R = (1, 145, 2, 146, 6, 150, 16, 160, 13, 157, 4, 148)(3, 147, 9, 153, 23, 167, 55, 199, 29, 173, 11, 155)(5, 149, 14, 158, 34, 178, 49, 193, 20, 164, 7, 151)(8, 152, 21, 165, 50, 194, 82, 226, 42, 186, 17, 161)(10, 154, 25, 169, 58, 202, 81, 225, 41, 185, 27, 171)(12, 156, 30, 174, 63, 207, 105, 249, 70, 214, 32, 176)(15, 159, 37, 181, 66, 210, 84, 228, 44, 188, 35, 179)(18, 162, 43, 187, 83, 227, 113, 257, 77, 221, 39, 183)(19, 163, 45, 189, 31, 175, 67, 211, 76, 220, 47, 191)(22, 166, 53, 197, 24, 168, 56, 200, 79, 223, 51, 195)(26, 170, 60, 204, 103, 247, 125, 269, 96, 240, 54, 198)(28, 172, 62, 206, 36, 180, 74, 218, 85, 229, 64, 208)(33, 177, 40, 184, 78, 222, 114, 258, 106, 250, 71, 215)(38, 182, 68, 212, 87, 231, 121, 265, 110, 254, 75, 219)(46, 190, 88, 232, 123, 267, 111, 255, 73, 217, 86, 230)(48, 192, 90, 234, 52, 196, 95, 239, 69, 213, 91, 235)(57, 201, 99, 243, 59, 203, 101, 245, 128, 272, 98, 242)(61, 205, 89, 233, 117, 261, 136, 280, 130, 274, 100, 244)(65, 209, 97, 241, 127, 271, 138, 282, 118, 262, 93, 237)(72, 216, 109, 253, 134, 278, 137, 281, 119, 263, 92, 236)(80, 224, 116, 260, 139, 283, 126, 270, 94, 238, 115, 259)(102, 246, 132, 276, 104, 248, 133, 277, 140, 284, 131, 275)(107, 251, 112, 256, 108, 252, 135, 279, 141, 285, 120, 264)(122, 266, 143, 287, 124, 268, 144, 288, 129, 273, 142, 286)(289, 433, 291, 435, 298, 442, 314, 458, 349, 493, 326, 470, 303, 447, 293, 437)(290, 434, 295, 439, 307, 451, 334, 478, 377, 521, 342, 486, 310, 454, 296, 440)(292, 436, 300, 444, 319, 463, 356, 500, 388, 532, 345, 489, 312, 456, 297, 441)(294, 438, 305, 449, 329, 473, 368, 512, 405, 549, 374, 518, 332, 476, 306, 450)(299, 443, 316, 460, 351, 495, 325, 469, 363, 507, 390, 534, 347, 491, 313, 457)(301, 445, 321, 465, 346, 490, 387, 531, 418, 562, 395, 539, 354, 498, 318, 462)(302, 446, 323, 467, 361, 505, 392, 536, 348, 492, 315, 459, 330, 474, 324, 468)(304, 448, 327, 471, 364, 508, 400, 544, 424, 568, 403, 547, 367, 511, 328, 472)(308, 452, 336, 480, 311, 455, 341, 485, 384, 528, 410, 554, 375, 519, 333, 477)(309, 453, 339, 483, 382, 526, 412, 556, 376, 520, 335, 479, 365, 509, 340, 484)(317, 461, 353, 497, 391, 535, 420, 564, 398, 542, 360, 504, 322, 466, 350, 494)(320, 464, 357, 501, 366, 510, 344, 488, 386, 530, 417, 561, 396, 540, 355, 499)(331, 475, 372, 516, 408, 552, 428, 572, 404, 548, 369, 513, 359, 503, 373, 517)(337, 481, 380, 524, 411, 555, 431, 575, 413, 557, 381, 525, 338, 482, 378, 522)(343, 487, 379, 523, 358, 502, 397, 541, 409, 553, 430, 574, 416, 560, 385, 529)(352, 496, 394, 538, 415, 559, 389, 533, 419, 563, 429, 573, 422, 566, 393, 537)(362, 506, 370, 514, 406, 550, 427, 571, 421, 565, 399, 543, 407, 551, 371, 515)(383, 527, 401, 545, 425, 569, 423, 567, 432, 576, 414, 558, 426, 570, 402, 546) L = (1, 291)(2, 295)(3, 298)(4, 300)(5, 289)(6, 305)(7, 307)(8, 290)(9, 292)(10, 314)(11, 316)(12, 319)(13, 321)(14, 323)(15, 293)(16, 327)(17, 329)(18, 294)(19, 334)(20, 336)(21, 339)(22, 296)(23, 341)(24, 297)(25, 299)(26, 349)(27, 330)(28, 351)(29, 353)(30, 301)(31, 356)(32, 357)(33, 346)(34, 350)(35, 361)(36, 302)(37, 363)(38, 303)(39, 364)(40, 304)(41, 368)(42, 324)(43, 372)(44, 306)(45, 308)(46, 377)(47, 365)(48, 311)(49, 380)(50, 378)(51, 382)(52, 309)(53, 384)(54, 310)(55, 379)(56, 386)(57, 312)(58, 387)(59, 313)(60, 315)(61, 326)(62, 317)(63, 325)(64, 394)(65, 391)(66, 318)(67, 320)(68, 388)(69, 366)(70, 397)(71, 373)(72, 322)(73, 392)(74, 370)(75, 390)(76, 400)(77, 340)(78, 344)(79, 328)(80, 405)(81, 359)(82, 406)(83, 362)(84, 408)(85, 331)(86, 332)(87, 333)(88, 335)(89, 342)(90, 337)(91, 358)(92, 411)(93, 338)(94, 412)(95, 401)(96, 410)(97, 343)(98, 417)(99, 418)(100, 345)(101, 419)(102, 347)(103, 420)(104, 348)(105, 352)(106, 415)(107, 354)(108, 355)(109, 409)(110, 360)(111, 407)(112, 424)(113, 425)(114, 383)(115, 367)(116, 369)(117, 374)(118, 427)(119, 371)(120, 428)(121, 430)(122, 375)(123, 431)(124, 376)(125, 381)(126, 426)(127, 389)(128, 385)(129, 396)(130, 395)(131, 429)(132, 398)(133, 399)(134, 393)(135, 432)(136, 403)(137, 423)(138, 402)(139, 421)(140, 404)(141, 422)(142, 416)(143, 413)(144, 414)(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 ) } Outer automorphisms :: reflexible Dual of E16.1258 Graph:: bipartite v = 42 e = 288 f = 216 degree seq :: [ 12^24, 16^18 ] E16.1258 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8}) Quotient :: dipole Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1, Y3^-2 * Y2 * Y3^4 * Y2 * Y3^-2, (Y3 * Y2)^6, (Y3^-1 * Y1^-1)^8 ] Map:: polytopal R = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)(289, 433, 290, 434)(291, 435, 295, 439)(292, 436, 297, 441)(293, 437, 299, 443)(294, 438, 301, 445)(296, 440, 305, 449)(298, 442, 309, 453)(300, 444, 313, 457)(302, 446, 317, 461)(303, 447, 319, 463)(304, 448, 321, 465)(306, 450, 325, 469)(307, 451, 327, 471)(308, 452, 329, 473)(310, 454, 333, 477)(311, 455, 334, 478)(312, 456, 336, 480)(314, 458, 340, 484)(315, 459, 342, 486)(316, 460, 344, 488)(318, 462, 348, 492)(320, 464, 351, 495)(322, 466, 352, 496)(323, 467, 354, 498)(324, 468, 356, 500)(326, 470, 341, 485)(328, 472, 359, 503)(330, 474, 361, 505)(331, 475, 362, 506)(332, 476, 350, 494)(335, 479, 365, 509)(337, 481, 366, 510)(338, 482, 368, 512)(339, 483, 370, 514)(343, 487, 373, 517)(345, 489, 375, 519)(346, 490, 376, 520)(347, 491, 364, 508)(349, 493, 374, 518)(353, 497, 383, 527)(355, 499, 385, 529)(357, 501, 386, 530)(358, 502, 387, 531)(360, 504, 363, 507)(367, 511, 399, 543)(369, 513, 401, 545)(371, 515, 402, 546)(372, 516, 403, 547)(377, 521, 404, 548)(378, 522, 407, 551)(379, 523, 395, 539)(380, 524, 400, 544)(381, 525, 397, 541)(382, 526, 406, 550)(384, 528, 396, 540)(388, 532, 393, 537)(389, 533, 405, 549)(390, 534, 398, 542)(391, 535, 394, 538)(392, 536, 408, 552)(409, 553, 422, 566)(410, 554, 424, 568)(411, 555, 426, 570)(412, 556, 419, 563)(413, 557, 427, 571)(414, 558, 420, 564)(415, 559, 428, 572)(416, 560, 421, 565)(417, 561, 423, 567)(418, 562, 425, 569)(429, 573, 432, 576)(430, 574, 431, 575) L = (1, 291)(2, 293)(3, 296)(4, 289)(5, 300)(6, 290)(7, 303)(8, 306)(9, 307)(10, 292)(11, 311)(12, 314)(13, 315)(14, 294)(15, 320)(16, 295)(17, 323)(18, 326)(19, 328)(20, 297)(21, 331)(22, 298)(23, 335)(24, 299)(25, 338)(26, 341)(27, 343)(28, 301)(29, 346)(30, 302)(31, 349)(32, 336)(33, 348)(34, 304)(35, 355)(36, 305)(37, 342)(38, 310)(39, 345)(40, 358)(41, 354)(42, 308)(43, 357)(44, 309)(45, 353)(46, 363)(47, 321)(48, 333)(49, 312)(50, 369)(51, 313)(52, 327)(53, 318)(54, 330)(55, 372)(56, 368)(57, 316)(58, 371)(59, 317)(60, 367)(61, 377)(62, 319)(63, 379)(64, 381)(65, 322)(66, 384)(67, 332)(68, 383)(69, 324)(70, 325)(71, 388)(72, 329)(73, 391)(74, 390)(75, 393)(76, 334)(77, 395)(78, 397)(79, 337)(80, 400)(81, 347)(82, 399)(83, 339)(84, 340)(85, 404)(86, 344)(87, 407)(88, 406)(89, 356)(90, 350)(91, 410)(92, 351)(93, 411)(94, 352)(95, 409)(96, 412)(97, 413)(98, 415)(99, 362)(100, 417)(101, 359)(102, 360)(103, 418)(104, 361)(105, 370)(106, 364)(107, 420)(108, 365)(109, 421)(110, 366)(111, 419)(112, 422)(113, 423)(114, 425)(115, 376)(116, 427)(117, 373)(118, 374)(119, 428)(120, 375)(121, 378)(122, 382)(123, 380)(124, 387)(125, 429)(126, 385)(127, 430)(128, 386)(129, 392)(130, 389)(131, 394)(132, 398)(133, 396)(134, 403)(135, 431)(136, 401)(137, 432)(138, 402)(139, 408)(140, 405)(141, 416)(142, 414)(143, 426)(144, 424)(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) :: { ( 12, 16 ), ( 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E16.1257 Graph:: simple bipartite v = 216 e = 288 f = 42 degree seq :: [ 2^144, 4^72 ] E16.1259 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8}) Quotient :: dipole Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1^8, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-3, (Y3 * Y1^-1)^6 ] Map:: polytopal R = (1, 145, 2, 146, 5, 149, 11, 155, 23, 167, 22, 166, 10, 154, 4, 148)(3, 147, 7, 151, 15, 159, 31, 175, 46, 190, 38, 182, 18, 162, 8, 152)(6, 150, 13, 157, 27, 171, 53, 197, 45, 189, 60, 204, 30, 174, 14, 158)(9, 153, 19, 163, 39, 183, 48, 192, 24, 168, 47, 191, 42, 186, 20, 164)(12, 156, 25, 169, 49, 193, 44, 188, 21, 165, 43, 187, 52, 196, 26, 170)(16, 160, 33, 177, 58, 202, 29, 173, 57, 201, 85, 229, 65, 209, 34, 178)(17, 161, 35, 179, 66, 210, 89, 233, 61, 205, 40, 184, 68, 212, 36, 180)(28, 172, 55, 199, 79, 223, 51, 195, 78, 222, 109, 253, 84, 228, 56, 200)(32, 176, 62, 206, 90, 234, 70, 214, 37, 181, 69, 213, 93, 237, 63, 207)(41, 185, 50, 194, 77, 221, 105, 249, 75, 219, 74, 218, 102, 246, 72, 216)(54, 198, 81, 225, 113, 257, 88, 232, 59, 203, 87, 231, 116, 260, 82, 226)(64, 208, 94, 238, 123, 267, 92, 236, 119, 263, 131, 275, 125, 269, 95, 239)(67, 211, 91, 235, 115, 259, 137, 281, 121, 265, 99, 243, 117, 261, 83, 227)(71, 215, 100, 244, 129, 273, 104, 248, 73, 217, 103, 247, 130, 274, 101, 245)(76, 220, 106, 250, 132, 276, 112, 256, 80, 224, 111, 255, 135, 279, 107, 251)(86, 230, 114, 258, 134, 278, 126, 270, 96, 240, 120, 264, 136, 280, 108, 252)(97, 241, 110, 254, 133, 277, 128, 272, 98, 242, 118, 262, 138, 282, 127, 271)(122, 266, 141, 285, 144, 288, 140, 284, 124, 268, 142, 286, 143, 287, 139, 283)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576) L = (1, 291)(2, 294)(3, 289)(4, 297)(5, 300)(6, 290)(7, 304)(8, 305)(9, 292)(10, 309)(11, 312)(12, 293)(13, 316)(14, 317)(15, 320)(16, 295)(17, 296)(18, 325)(19, 328)(20, 329)(21, 298)(22, 333)(23, 334)(24, 299)(25, 338)(26, 339)(27, 342)(28, 301)(29, 302)(30, 347)(31, 349)(32, 303)(33, 352)(34, 341)(35, 335)(36, 355)(37, 306)(38, 345)(39, 359)(40, 307)(41, 308)(42, 361)(43, 362)(44, 344)(45, 310)(46, 311)(47, 323)(48, 363)(49, 364)(50, 313)(51, 314)(52, 368)(53, 322)(54, 315)(55, 371)(56, 332)(57, 326)(58, 374)(59, 318)(60, 366)(61, 319)(62, 379)(63, 380)(64, 321)(65, 384)(66, 385)(67, 324)(68, 386)(69, 387)(70, 383)(71, 327)(72, 382)(73, 330)(74, 331)(75, 336)(76, 337)(77, 396)(78, 348)(79, 398)(80, 340)(81, 402)(82, 403)(83, 343)(84, 406)(85, 407)(86, 346)(87, 408)(88, 405)(89, 409)(90, 410)(91, 350)(92, 351)(93, 412)(94, 360)(95, 358)(96, 353)(97, 354)(98, 356)(99, 357)(100, 411)(101, 415)(102, 414)(103, 413)(104, 416)(105, 419)(106, 421)(107, 422)(108, 365)(109, 425)(110, 367)(111, 426)(112, 424)(113, 427)(114, 369)(115, 370)(116, 428)(117, 376)(118, 372)(119, 373)(120, 375)(121, 377)(122, 378)(123, 388)(124, 381)(125, 391)(126, 390)(127, 389)(128, 392)(129, 429)(130, 430)(131, 393)(132, 431)(133, 394)(134, 395)(135, 432)(136, 400)(137, 397)(138, 399)(139, 401)(140, 404)(141, 417)(142, 418)(143, 420)(144, 423)(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, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E16.1256 Graph:: simple bipartite v = 162 e = 288 f = 96 degree seq :: [ 2^144, 16^18 ] E16.1260 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8}) Quotient :: dipole Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^8, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-2, (Y3 * Y2^-1)^6 ] Map:: R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 11, 155)(6, 150, 13, 157)(8, 152, 17, 161)(10, 154, 21, 165)(12, 156, 25, 169)(14, 158, 29, 173)(15, 159, 31, 175)(16, 160, 33, 177)(18, 162, 37, 181)(19, 163, 39, 183)(20, 164, 41, 185)(22, 166, 45, 189)(23, 167, 46, 190)(24, 168, 48, 192)(26, 170, 52, 196)(27, 171, 54, 198)(28, 172, 56, 200)(30, 174, 60, 204)(32, 176, 63, 207)(34, 178, 64, 208)(35, 179, 66, 210)(36, 180, 68, 212)(38, 182, 53, 197)(40, 184, 71, 215)(42, 186, 73, 217)(43, 187, 74, 218)(44, 188, 62, 206)(47, 191, 77, 221)(49, 193, 78, 222)(50, 194, 80, 224)(51, 195, 82, 226)(55, 199, 85, 229)(57, 201, 87, 231)(58, 202, 88, 232)(59, 203, 76, 220)(61, 205, 86, 230)(65, 209, 95, 239)(67, 211, 97, 241)(69, 213, 98, 242)(70, 214, 99, 243)(72, 216, 75, 219)(79, 223, 111, 255)(81, 225, 113, 257)(83, 227, 114, 258)(84, 228, 115, 259)(89, 233, 116, 260)(90, 234, 119, 263)(91, 235, 107, 251)(92, 236, 112, 256)(93, 237, 109, 253)(94, 238, 118, 262)(96, 240, 108, 252)(100, 244, 105, 249)(101, 245, 117, 261)(102, 246, 110, 254)(103, 247, 106, 250)(104, 248, 120, 264)(121, 265, 134, 278)(122, 266, 136, 280)(123, 267, 138, 282)(124, 268, 131, 275)(125, 269, 139, 283)(126, 270, 132, 276)(127, 271, 140, 284)(128, 272, 133, 277)(129, 273, 135, 279)(130, 274, 137, 281)(141, 285, 144, 288)(142, 286, 143, 287)(289, 433, 291, 435, 296, 440, 306, 450, 326, 470, 310, 454, 298, 442, 292, 436)(290, 434, 293, 437, 300, 444, 314, 458, 341, 485, 318, 462, 302, 446, 294, 438)(295, 439, 303, 447, 320, 464, 336, 480, 333, 477, 353, 497, 322, 466, 304, 448)(297, 441, 307, 451, 328, 472, 358, 502, 325, 469, 342, 486, 330, 474, 308, 452)(299, 443, 311, 455, 335, 479, 321, 465, 348, 492, 367, 511, 337, 481, 312, 456)(301, 445, 315, 459, 343, 487, 372, 516, 340, 484, 327, 471, 345, 489, 316, 460)(305, 449, 323, 467, 355, 499, 332, 476, 309, 453, 331, 475, 357, 501, 324, 468)(313, 457, 338, 482, 369, 513, 347, 491, 317, 461, 346, 490, 371, 515, 339, 483)(319, 463, 349, 493, 377, 521, 356, 500, 383, 527, 409, 553, 378, 522, 350, 494)(329, 473, 354, 498, 384, 528, 412, 556, 387, 531, 362, 506, 390, 534, 360, 504)(334, 478, 363, 507, 393, 537, 370, 514, 399, 543, 419, 563, 394, 538, 364, 508)(344, 488, 368, 512, 400, 544, 422, 566, 403, 547, 376, 520, 406, 550, 374, 518)(351, 495, 379, 523, 410, 554, 382, 526, 352, 496, 381, 525, 411, 555, 380, 524)(359, 503, 388, 532, 417, 561, 392, 536, 361, 505, 391, 535, 418, 562, 389, 533)(365, 509, 395, 539, 420, 564, 398, 542, 366, 510, 397, 541, 421, 565, 396, 540)(373, 517, 404, 548, 427, 571, 408, 552, 375, 519, 407, 551, 428, 572, 405, 549)(385, 529, 413, 557, 429, 573, 416, 560, 386, 530, 415, 559, 430, 574, 414, 558)(401, 545, 423, 567, 431, 575, 426, 570, 402, 546, 425, 569, 432, 576, 424, 568) L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 299)(6, 301)(7, 291)(8, 305)(9, 292)(10, 309)(11, 293)(12, 313)(13, 294)(14, 317)(15, 319)(16, 321)(17, 296)(18, 325)(19, 327)(20, 329)(21, 298)(22, 333)(23, 334)(24, 336)(25, 300)(26, 340)(27, 342)(28, 344)(29, 302)(30, 348)(31, 303)(32, 351)(33, 304)(34, 352)(35, 354)(36, 356)(37, 306)(38, 341)(39, 307)(40, 359)(41, 308)(42, 361)(43, 362)(44, 350)(45, 310)(46, 311)(47, 365)(48, 312)(49, 366)(50, 368)(51, 370)(52, 314)(53, 326)(54, 315)(55, 373)(56, 316)(57, 375)(58, 376)(59, 364)(60, 318)(61, 374)(62, 332)(63, 320)(64, 322)(65, 383)(66, 323)(67, 385)(68, 324)(69, 386)(70, 387)(71, 328)(72, 363)(73, 330)(74, 331)(75, 360)(76, 347)(77, 335)(78, 337)(79, 399)(80, 338)(81, 401)(82, 339)(83, 402)(84, 403)(85, 343)(86, 349)(87, 345)(88, 346)(89, 404)(90, 407)(91, 395)(92, 400)(93, 397)(94, 406)(95, 353)(96, 396)(97, 355)(98, 357)(99, 358)(100, 393)(101, 405)(102, 398)(103, 394)(104, 408)(105, 388)(106, 391)(107, 379)(108, 384)(109, 381)(110, 390)(111, 367)(112, 380)(113, 369)(114, 371)(115, 372)(116, 377)(117, 389)(118, 382)(119, 378)(120, 392)(121, 422)(122, 424)(123, 426)(124, 419)(125, 427)(126, 420)(127, 428)(128, 421)(129, 423)(130, 425)(131, 412)(132, 414)(133, 416)(134, 409)(135, 417)(136, 410)(137, 418)(138, 411)(139, 413)(140, 415)(141, 432)(142, 431)(143, 430)(144, 429)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E16.1261 Graph:: bipartite v = 90 e = 288 f = 168 degree seq :: [ 4^72, 16^18 ] E16.1261 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8}) Quotient :: dipole Aut^+ = ((C3 x C3) : C8) : C2 (small group id <144, 117>) Aut = $<288, 873>$ (small group id <288, 873>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^6, Y3 * Y1^-1 * Y3^2 * Y1^-2 * Y3^-1 * Y1, (Y3 * Y1^-1 * Y3 * Y1^-2)^2, (Y3 * Y2^-1)^8 ] Map:: polytopal R = (1, 145, 2, 146, 6, 150, 16, 160, 13, 157, 4, 148)(3, 147, 9, 153, 23, 167, 55, 199, 29, 173, 11, 155)(5, 149, 14, 158, 34, 178, 49, 193, 20, 164, 7, 151)(8, 152, 21, 165, 50, 194, 82, 226, 42, 186, 17, 161)(10, 154, 25, 169, 58, 202, 81, 225, 41, 185, 27, 171)(12, 156, 30, 174, 63, 207, 105, 249, 70, 214, 32, 176)(15, 159, 37, 181, 66, 210, 84, 228, 44, 188, 35, 179)(18, 162, 43, 187, 83, 227, 113, 257, 77, 221, 39, 183)(19, 163, 45, 189, 31, 175, 67, 211, 76, 220, 47, 191)(22, 166, 53, 197, 24, 168, 56, 200, 79, 223, 51, 195)(26, 170, 60, 204, 103, 247, 125, 269, 96, 240, 54, 198)(28, 172, 62, 206, 36, 180, 74, 218, 85, 229, 64, 208)(33, 177, 40, 184, 78, 222, 114, 258, 106, 250, 71, 215)(38, 182, 68, 212, 87, 231, 121, 265, 110, 254, 75, 219)(46, 190, 88, 232, 123, 267, 111, 255, 73, 217, 86, 230)(48, 192, 90, 234, 52, 196, 95, 239, 69, 213, 91, 235)(57, 201, 99, 243, 59, 203, 101, 245, 128, 272, 98, 242)(61, 205, 89, 233, 117, 261, 136, 280, 130, 274, 100, 244)(65, 209, 97, 241, 127, 271, 138, 282, 118, 262, 93, 237)(72, 216, 109, 253, 134, 278, 137, 281, 119, 263, 92, 236)(80, 224, 116, 260, 139, 283, 126, 270, 94, 238, 115, 259)(102, 246, 132, 276, 104, 248, 133, 277, 140, 284, 131, 275)(107, 251, 112, 256, 108, 252, 135, 279, 141, 285, 120, 264)(122, 266, 143, 287, 124, 268, 144, 288, 129, 273, 142, 286)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576) L = (1, 291)(2, 295)(3, 298)(4, 300)(5, 289)(6, 305)(7, 307)(8, 290)(9, 292)(10, 314)(11, 316)(12, 319)(13, 321)(14, 323)(15, 293)(16, 327)(17, 329)(18, 294)(19, 334)(20, 336)(21, 339)(22, 296)(23, 341)(24, 297)(25, 299)(26, 349)(27, 330)(28, 351)(29, 353)(30, 301)(31, 356)(32, 357)(33, 346)(34, 350)(35, 361)(36, 302)(37, 363)(38, 303)(39, 364)(40, 304)(41, 368)(42, 324)(43, 372)(44, 306)(45, 308)(46, 377)(47, 365)(48, 311)(49, 380)(50, 378)(51, 382)(52, 309)(53, 384)(54, 310)(55, 379)(56, 386)(57, 312)(58, 387)(59, 313)(60, 315)(61, 326)(62, 317)(63, 325)(64, 394)(65, 391)(66, 318)(67, 320)(68, 388)(69, 366)(70, 397)(71, 373)(72, 322)(73, 392)(74, 370)(75, 390)(76, 400)(77, 340)(78, 344)(79, 328)(80, 405)(81, 359)(82, 406)(83, 362)(84, 408)(85, 331)(86, 332)(87, 333)(88, 335)(89, 342)(90, 337)(91, 358)(92, 411)(93, 338)(94, 412)(95, 401)(96, 410)(97, 343)(98, 417)(99, 418)(100, 345)(101, 419)(102, 347)(103, 420)(104, 348)(105, 352)(106, 415)(107, 354)(108, 355)(109, 409)(110, 360)(111, 407)(112, 424)(113, 425)(114, 383)(115, 367)(116, 369)(117, 374)(118, 427)(119, 371)(120, 428)(121, 430)(122, 375)(123, 431)(124, 376)(125, 381)(126, 426)(127, 389)(128, 385)(129, 396)(130, 395)(131, 429)(132, 398)(133, 399)(134, 393)(135, 432)(136, 403)(137, 423)(138, 402)(139, 421)(140, 404)(141, 422)(142, 416)(143, 413)(144, 414)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E16.1260 Graph:: simple bipartite v = 168 e = 288 f = 90 degree seq :: [ 2^144, 12^24 ] E16.1262 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 10}) Quotient :: regular Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^4, (T2 * T1 * T2 * T1^-1)^2, T1^10, T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2, (T1^-3 * T2 * T1^3 * T2)^2, T1^-4 * T2 * T1^-4 * T2 * T1^4 * T2 * T1^4 * T2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 43, 42, 22, 10, 4)(3, 7, 15, 31, 55, 85, 62, 36, 18, 8)(6, 13, 27, 51, 81, 116, 84, 54, 30, 14)(9, 19, 37, 63, 94, 128, 95, 64, 38, 20)(12, 25, 47, 77, 112, 147, 115, 80, 50, 26)(16, 33, 58, 89, 123, 137, 105, 75, 48, 29)(17, 34, 59, 90, 124, 136, 106, 74, 49, 28)(21, 39, 65, 96, 129, 158, 130, 97, 66, 40)(24, 45, 73, 108, 143, 171, 146, 111, 76, 46)(32, 53, 78, 110, 140, 165, 154, 122, 88, 57)(35, 52, 79, 109, 141, 164, 155, 125, 91, 60)(41, 67, 98, 131, 159, 180, 160, 132, 99, 68)(44, 71, 104, 139, 167, 187, 170, 142, 107, 72)(56, 87, 121, 153, 177, 185, 168, 145, 113, 83)(61, 92, 126, 156, 178, 184, 169, 144, 114, 82)(69, 100, 133, 161, 181, 194, 182, 162, 134, 101)(70, 102, 135, 163, 183, 195, 186, 166, 138, 103)(86, 118, 148, 173, 188, 197, 192, 176, 152, 120)(93, 117, 149, 172, 189, 196, 193, 179, 157, 127)(119, 151, 175, 191, 199, 200, 198, 190, 174, 150) 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, 34)(20, 33)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 60)(38, 57)(39, 58)(40, 59)(42, 69)(43, 70)(45, 74)(46, 75)(47, 78)(50, 79)(51, 82)(54, 83)(55, 86)(62, 93)(63, 92)(64, 87)(65, 88)(66, 91)(67, 90)(68, 89)(71, 105)(72, 106)(73, 109)(76, 110)(77, 113)(80, 114)(81, 117)(84, 118)(85, 119)(94, 127)(95, 120)(96, 121)(97, 126)(98, 125)(99, 122)(100, 123)(101, 124)(102, 136)(103, 137)(104, 140)(107, 141)(108, 144)(111, 145)(112, 148)(115, 149)(116, 150)(128, 151)(129, 152)(130, 157)(131, 156)(132, 153)(133, 154)(134, 155)(135, 164)(138, 165)(139, 168)(142, 169)(143, 172)(146, 173)(147, 174)(158, 175)(159, 179)(160, 176)(161, 177)(162, 178)(163, 184)(166, 185)(167, 188)(170, 189)(171, 190)(180, 191)(181, 192)(182, 193)(183, 196)(186, 197)(187, 198)(194, 199)(195, 200) local type(s) :: { ( 4^10 ) } Outer automorphisms :: reflexible Dual of E16.1263 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 20 e = 100 f = 50 degree seq :: [ 10^20 ] E16.1263 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 10}) Quotient :: regular Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1^-1 * T2 * T1)^2, (T1^-1 * T2)^10 ] Map:: polytopal non-degenerate R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 27, 17)(10, 18, 29, 19)(14, 24, 34, 22)(15, 25, 38, 26)(21, 33, 44, 31)(23, 35, 49, 36)(28, 30, 43, 41)(32, 45, 62, 46)(37, 52, 69, 51)(39, 50, 68, 54)(40, 55, 74, 56)(42, 58, 77, 59)(47, 65, 84, 64)(48, 63, 83, 66)(53, 71, 92, 72)(57, 75, 96, 76)(60, 80, 100, 79)(61, 78, 99, 81)(67, 87, 109, 88)(70, 91, 108, 86)(73, 93, 116, 94)(82, 103, 128, 104)(85, 107, 127, 102)(89, 112, 137, 111)(90, 110, 136, 113)(95, 118, 144, 119)(97, 101, 126, 121)(98, 122, 147, 123)(105, 131, 156, 130)(106, 129, 155, 132)(114, 140, 163, 139)(115, 141, 164, 142)(117, 138, 158, 133)(120, 146, 167, 145)(124, 150, 170, 149)(125, 148, 169, 151)(134, 157, 172, 152)(135, 159, 177, 160)(143, 153, 171, 165)(154, 173, 188, 174)(161, 180, 192, 179)(162, 178, 190, 175)(166, 182, 194, 183)(168, 184, 195, 185)(176, 189, 197, 186)(181, 187, 196, 193)(191, 199, 200, 198) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 25)(17, 28)(18, 30)(19, 31)(20, 32)(24, 37)(26, 39)(27, 40)(29, 42)(33, 47)(34, 48)(35, 50)(36, 51)(38, 53)(41, 57)(43, 60)(44, 61)(45, 63)(46, 64)(49, 67)(52, 70)(54, 73)(55, 75)(56, 72)(58, 78)(59, 79)(62, 82)(65, 85)(66, 86)(68, 89)(69, 90)(71, 93)(74, 95)(76, 97)(77, 98)(80, 101)(81, 102)(83, 105)(84, 106)(87, 110)(88, 111)(91, 114)(92, 115)(94, 117)(96, 120)(99, 124)(100, 125)(103, 129)(104, 130)(107, 133)(108, 134)(109, 135)(112, 138)(113, 139)(116, 143)(118, 141)(119, 145)(121, 140)(122, 148)(123, 149)(126, 152)(127, 153)(128, 154)(131, 157)(132, 158)(136, 161)(137, 162)(142, 165)(144, 166)(146, 163)(147, 168)(150, 171)(151, 172)(155, 175)(156, 176)(159, 178)(160, 179)(164, 181)(167, 180)(169, 186)(170, 187)(173, 189)(174, 190)(177, 191)(182, 192)(183, 193)(184, 196)(185, 197)(188, 198)(194, 199)(195, 200) local type(s) :: { ( 10^4 ) } Outer automorphisms :: reflexible Dual of E16.1262 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 50 e = 100 f = 20 degree seq :: [ 4^50 ] E16.1264 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 10}) Quotient :: edge Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T2)^2, (F * T1)^2, (T1 * T2^-1 * T1 * T2)^2, (T2^-1 * T1)^10 ] Map:: polytopal R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 24, 14)(9, 16, 27, 17)(10, 18, 30, 19)(12, 21, 33, 22)(15, 25, 39, 26)(20, 31, 46, 32)(23, 35, 50, 36)(28, 38, 53, 41)(29, 42, 59, 43)(34, 45, 62, 48)(37, 51, 70, 52)(40, 55, 75, 56)(44, 60, 80, 61)(47, 64, 85, 65)(49, 67, 88, 68)(54, 72, 94, 73)(57, 74, 95, 76)(58, 77, 99, 78)(63, 82, 105, 83)(66, 84, 106, 86)(69, 89, 112, 90)(71, 92, 116, 93)(79, 100, 125, 101)(81, 103, 129, 104)(87, 109, 135, 110)(91, 113, 139, 114)(96, 119, 146, 120)(97, 115, 140, 121)(98, 122, 147, 123)(102, 126, 151, 127)(107, 132, 158, 133)(108, 128, 152, 134)(111, 136, 159, 137)(117, 142, 165, 143)(118, 144, 166, 145)(124, 148, 168, 149)(130, 154, 174, 155)(131, 156, 175, 157)(138, 160, 177, 161)(141, 163, 180, 164)(150, 169, 184, 170)(153, 172, 187, 173)(162, 178, 191, 179)(167, 182, 194, 183)(171, 185, 195, 186)(176, 189, 198, 190)(181, 192, 199, 193)(188, 196, 200, 197)(201, 202)(203, 207)(204, 209)(205, 210)(206, 212)(208, 215)(211, 220)(213, 223)(214, 219)(216, 221)(217, 228)(218, 229)(222, 234)(224, 237)(225, 238)(226, 236)(227, 240)(230, 244)(231, 245)(232, 243)(233, 247)(235, 249)(239, 254)(241, 257)(242, 258)(246, 263)(248, 266)(250, 269)(251, 260)(252, 268)(253, 271)(255, 274)(256, 265)(259, 279)(261, 278)(262, 281)(264, 284)(267, 287)(270, 291)(272, 289)(273, 293)(275, 296)(276, 297)(277, 298)(280, 302)(282, 300)(283, 304)(285, 307)(286, 308)(288, 311)(290, 310)(292, 315)(294, 317)(295, 318)(299, 324)(301, 323)(303, 328)(305, 330)(306, 331)(309, 334)(312, 338)(313, 336)(314, 327)(316, 341)(319, 332)(320, 345)(321, 322)(325, 350)(326, 348)(329, 353)(333, 357)(335, 356)(337, 352)(339, 362)(340, 349)(342, 363)(343, 361)(344, 347)(346, 367)(351, 371)(354, 372)(355, 370)(358, 376)(359, 373)(360, 375)(364, 368)(365, 381)(366, 369)(374, 388)(377, 389)(378, 385)(379, 387)(380, 386)(382, 384)(383, 390)(391, 397)(392, 398)(393, 395)(394, 396)(399, 400) L = (1, 201)(2, 202)(3, 203)(4, 204)(5, 205)(6, 206)(7, 207)(8, 208)(9, 209)(10, 210)(11, 211)(12, 212)(13, 213)(14, 214)(15, 215)(16, 216)(17, 217)(18, 218)(19, 219)(20, 220)(21, 221)(22, 222)(23, 223)(24, 224)(25, 225)(26, 226)(27, 227)(28, 228)(29, 229)(30, 230)(31, 231)(32, 232)(33, 233)(34, 234)(35, 235)(36, 236)(37, 237)(38, 238)(39, 239)(40, 240)(41, 241)(42, 242)(43, 243)(44, 244)(45, 245)(46, 246)(47, 247)(48, 248)(49, 249)(50, 250)(51, 251)(52, 252)(53, 253)(54, 254)(55, 255)(56, 256)(57, 257)(58, 258)(59, 259)(60, 260)(61, 261)(62, 262)(63, 263)(64, 264)(65, 265)(66, 266)(67, 267)(68, 268)(69, 269)(70, 270)(71, 271)(72, 272)(73, 273)(74, 274)(75, 275)(76, 276)(77, 277)(78, 278)(79, 279)(80, 280)(81, 281)(82, 282)(83, 283)(84, 284)(85, 285)(86, 286)(87, 287)(88, 288)(89, 289)(90, 290)(91, 291)(92, 292)(93, 293)(94, 294)(95, 295)(96, 296)(97, 297)(98, 298)(99, 299)(100, 300)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 20, 20 ), ( 20^4 ) } Outer automorphisms :: reflexible Dual of E16.1268 Transitivity :: ET+ Graph:: simple bipartite v = 150 e = 200 f = 20 degree seq :: [ 2^100, 4^50 ] E16.1265 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 10}) Quotient :: edge Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ F^2, T1^4, (T2 * T1)^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2^-2 * T1^-2 * T2^-2 * T1, T2^10, (T2^4 * T1^-1 * T2 * T1^-1)^2 ] Map:: polyhedral non-degenerate R = (1, 3, 10, 24, 48, 82, 60, 32, 14, 5)(2, 7, 17, 38, 66, 105, 76, 44, 20, 8)(4, 12, 27, 53, 89, 118, 80, 46, 22, 9)(6, 15, 33, 61, 96, 134, 103, 64, 36, 16)(11, 26, 51, 87, 126, 139, 101, 63, 35, 23)(13, 29, 34, 62, 98, 136, 132, 92, 56, 30)(18, 40, 69, 108, 146, 116, 78, 45, 21, 37)(19, 41, 28, 54, 86, 125, 151, 111, 72, 42)(25, 50, 85, 124, 159, 176, 154, 115, 77, 47)(31, 57, 70, 109, 145, 171, 149, 110, 71, 58)(39, 68, 52, 88, 123, 158, 130, 91, 55, 65)(43, 73, 99, 137, 165, 185, 168, 138, 100, 74)(49, 84, 122, 157, 179, 187, 167, 140, 102, 81)(59, 93, 97, 135, 164, 184, 183, 162, 129, 94)(67, 107, 144, 170, 189, 175, 153, 117, 79, 104)(75, 112, 90, 128, 160, 181, 192, 173, 148, 113)(83, 121, 156, 178, 194, 199, 193, 177, 155, 119)(95, 120, 147, 172, 190, 198, 191, 174, 150, 133)(106, 143, 127, 161, 180, 195, 182, 163, 131, 141)(114, 142, 166, 186, 196, 200, 197, 188, 169, 152)(201, 202, 206, 204)(203, 209, 221, 211)(205, 213, 218, 207)(208, 219, 234, 215)(210, 223, 236, 225)(212, 216, 235, 228)(214, 231, 233, 229)(217, 237, 222, 239)(220, 243, 227, 241)(224, 247, 278, 249)(226, 245, 277, 252)(230, 255, 270, 240)(232, 259, 269, 257)(238, 265, 256, 267)(242, 271, 299, 262)(244, 275, 298, 273)(246, 279, 251, 268)(248, 281, 303, 283)(250, 264, 302, 286)(253, 274, 301, 290)(254, 263, 300, 285)(258, 272, 297, 261)(260, 295, 296, 293)(266, 304, 280, 306)(276, 314, 289, 312)(282, 319, 346, 320)(284, 316, 355, 323)(287, 317, 354, 327)(288, 315, 353, 322)(291, 329, 344, 309)(292, 331, 345, 307)(294, 330, 347, 308)(305, 341, 332, 342)(310, 348, 364, 337)(311, 350, 365, 335)(313, 349, 366, 336)(318, 352, 326, 343)(321, 334, 333, 351)(324, 338, 367, 360)(325, 340, 368, 356)(328, 339, 369, 359)(357, 375, 393, 380)(358, 377, 389, 372)(361, 376, 388, 379)(362, 382, 390, 370)(363, 383, 386, 371)(373, 391, 396, 384)(374, 392, 378, 385)(381, 387, 397, 394)(395, 399, 400, 398) L = (1, 201)(2, 202)(3, 203)(4, 204)(5, 205)(6, 206)(7, 207)(8, 208)(9, 209)(10, 210)(11, 211)(12, 212)(13, 213)(14, 214)(15, 215)(16, 216)(17, 217)(18, 218)(19, 219)(20, 220)(21, 221)(22, 222)(23, 223)(24, 224)(25, 225)(26, 226)(27, 227)(28, 228)(29, 229)(30, 230)(31, 231)(32, 232)(33, 233)(34, 234)(35, 235)(36, 236)(37, 237)(38, 238)(39, 239)(40, 240)(41, 241)(42, 242)(43, 243)(44, 244)(45, 245)(46, 246)(47, 247)(48, 248)(49, 249)(50, 250)(51, 251)(52, 252)(53, 253)(54, 254)(55, 255)(56, 256)(57, 257)(58, 258)(59, 259)(60, 260)(61, 261)(62, 262)(63, 263)(64, 264)(65, 265)(66, 266)(67, 267)(68, 268)(69, 269)(70, 270)(71, 271)(72, 272)(73, 273)(74, 274)(75, 275)(76, 276)(77, 277)(78, 278)(79, 279)(80, 280)(81, 281)(82, 282)(83, 283)(84, 284)(85, 285)(86, 286)(87, 287)(88, 288)(89, 289)(90, 290)(91, 291)(92, 292)(93, 293)(94, 294)(95, 295)(96, 296)(97, 297)(98, 298)(99, 299)(100, 300)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 4^4 ), ( 4^10 ) } Outer automorphisms :: reflexible Dual of E16.1269 Transitivity :: ET+ Graph:: simple bipartite v = 70 e = 200 f = 100 degree seq :: [ 4^50, 10^20 ] E16.1266 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 10}) Quotient :: edge Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, (T2 * T1 * T2 * T1^-1)^2, T1^10, T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2, (T1^-3 * T2 * T1^3 * T2)^2, T1^-4 * T2 * T1^-4 * T2 * T1^4 * T2 * T1^4 * T2 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 34)(20, 33)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 60)(38, 57)(39, 58)(40, 59)(42, 69)(43, 70)(45, 74)(46, 75)(47, 78)(50, 79)(51, 82)(54, 83)(55, 86)(62, 93)(63, 92)(64, 87)(65, 88)(66, 91)(67, 90)(68, 89)(71, 105)(72, 106)(73, 109)(76, 110)(77, 113)(80, 114)(81, 117)(84, 118)(85, 119)(94, 127)(95, 120)(96, 121)(97, 126)(98, 125)(99, 122)(100, 123)(101, 124)(102, 136)(103, 137)(104, 140)(107, 141)(108, 144)(111, 145)(112, 148)(115, 149)(116, 150)(128, 151)(129, 152)(130, 157)(131, 156)(132, 153)(133, 154)(134, 155)(135, 164)(138, 165)(139, 168)(142, 169)(143, 172)(146, 173)(147, 174)(158, 175)(159, 179)(160, 176)(161, 177)(162, 178)(163, 184)(166, 185)(167, 188)(170, 189)(171, 190)(180, 191)(181, 192)(182, 193)(183, 196)(186, 197)(187, 198)(194, 199)(195, 200)(201, 202, 205, 211, 223, 243, 242, 222, 210, 204)(203, 207, 215, 231, 255, 285, 262, 236, 218, 208)(206, 213, 227, 251, 281, 316, 284, 254, 230, 214)(209, 219, 237, 263, 294, 328, 295, 264, 238, 220)(212, 225, 247, 277, 312, 347, 315, 280, 250, 226)(216, 233, 258, 289, 323, 337, 305, 275, 248, 229)(217, 234, 259, 290, 324, 336, 306, 274, 249, 228)(221, 239, 265, 296, 329, 358, 330, 297, 266, 240)(224, 245, 273, 308, 343, 371, 346, 311, 276, 246)(232, 253, 278, 310, 340, 365, 354, 322, 288, 257)(235, 252, 279, 309, 341, 364, 355, 325, 291, 260)(241, 267, 298, 331, 359, 380, 360, 332, 299, 268)(244, 271, 304, 339, 367, 387, 370, 342, 307, 272)(256, 287, 321, 353, 377, 385, 368, 345, 313, 283)(261, 292, 326, 356, 378, 384, 369, 344, 314, 282)(269, 300, 333, 361, 381, 394, 382, 362, 334, 301)(270, 302, 335, 363, 383, 395, 386, 366, 338, 303)(286, 318, 348, 373, 388, 397, 392, 376, 352, 320)(293, 317, 349, 372, 389, 396, 393, 379, 357, 327)(319, 351, 375, 391, 399, 400, 398, 390, 374, 350) L = (1, 201)(2, 202)(3, 203)(4, 204)(5, 205)(6, 206)(7, 207)(8, 208)(9, 209)(10, 210)(11, 211)(12, 212)(13, 213)(14, 214)(15, 215)(16, 216)(17, 217)(18, 218)(19, 219)(20, 220)(21, 221)(22, 222)(23, 223)(24, 224)(25, 225)(26, 226)(27, 227)(28, 228)(29, 229)(30, 230)(31, 231)(32, 232)(33, 233)(34, 234)(35, 235)(36, 236)(37, 237)(38, 238)(39, 239)(40, 240)(41, 241)(42, 242)(43, 243)(44, 244)(45, 245)(46, 246)(47, 247)(48, 248)(49, 249)(50, 250)(51, 251)(52, 252)(53, 253)(54, 254)(55, 255)(56, 256)(57, 257)(58, 258)(59, 259)(60, 260)(61, 261)(62, 262)(63, 263)(64, 264)(65, 265)(66, 266)(67, 267)(68, 268)(69, 269)(70, 270)(71, 271)(72, 272)(73, 273)(74, 274)(75, 275)(76, 276)(77, 277)(78, 278)(79, 279)(80, 280)(81, 281)(82, 282)(83, 283)(84, 284)(85, 285)(86, 286)(87, 287)(88, 288)(89, 289)(90, 290)(91, 291)(92, 292)(93, 293)(94, 294)(95, 295)(96, 296)(97, 297)(98, 298)(99, 299)(100, 300)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400) local type(s) :: { ( 8, 8 ), ( 8^10 ) } Outer automorphisms :: reflexible Dual of E16.1267 Transitivity :: ET+ Graph:: simple bipartite v = 120 e = 200 f = 50 degree seq :: [ 2^100, 10^20 ] E16.1267 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 10}) Quotient :: loop Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T2)^2, (F * T1)^2, (T1 * T2^-1 * T1 * T2)^2, (T2^-1 * T1)^10 ] Map:: R = (1, 201, 3, 203, 8, 208, 4, 204)(2, 202, 5, 205, 11, 211, 6, 206)(7, 207, 13, 213, 24, 224, 14, 214)(9, 209, 16, 216, 27, 227, 17, 217)(10, 210, 18, 218, 30, 230, 19, 219)(12, 212, 21, 221, 33, 233, 22, 222)(15, 215, 25, 225, 39, 239, 26, 226)(20, 220, 31, 231, 46, 246, 32, 232)(23, 223, 35, 235, 50, 250, 36, 236)(28, 228, 38, 238, 53, 253, 41, 241)(29, 229, 42, 242, 59, 259, 43, 243)(34, 234, 45, 245, 62, 262, 48, 248)(37, 237, 51, 251, 70, 270, 52, 252)(40, 240, 55, 255, 75, 275, 56, 256)(44, 244, 60, 260, 80, 280, 61, 261)(47, 247, 64, 264, 85, 285, 65, 265)(49, 249, 67, 267, 88, 288, 68, 268)(54, 254, 72, 272, 94, 294, 73, 273)(57, 257, 74, 274, 95, 295, 76, 276)(58, 258, 77, 277, 99, 299, 78, 278)(63, 263, 82, 282, 105, 305, 83, 283)(66, 266, 84, 284, 106, 306, 86, 286)(69, 269, 89, 289, 112, 312, 90, 290)(71, 271, 92, 292, 116, 316, 93, 293)(79, 279, 100, 300, 125, 325, 101, 301)(81, 281, 103, 303, 129, 329, 104, 304)(87, 287, 109, 309, 135, 335, 110, 310)(91, 291, 113, 313, 139, 339, 114, 314)(96, 296, 119, 319, 146, 346, 120, 320)(97, 297, 115, 315, 140, 340, 121, 321)(98, 298, 122, 322, 147, 347, 123, 323)(102, 302, 126, 326, 151, 351, 127, 327)(107, 307, 132, 332, 158, 358, 133, 333)(108, 308, 128, 328, 152, 352, 134, 334)(111, 311, 136, 336, 159, 359, 137, 337)(117, 317, 142, 342, 165, 365, 143, 343)(118, 318, 144, 344, 166, 366, 145, 345)(124, 324, 148, 348, 168, 368, 149, 349)(130, 330, 154, 354, 174, 374, 155, 355)(131, 331, 156, 356, 175, 375, 157, 357)(138, 338, 160, 360, 177, 377, 161, 361)(141, 341, 163, 363, 180, 380, 164, 364)(150, 350, 169, 369, 184, 384, 170, 370)(153, 353, 172, 372, 187, 387, 173, 373)(162, 362, 178, 378, 191, 391, 179, 379)(167, 367, 182, 382, 194, 394, 183, 383)(171, 371, 185, 385, 195, 395, 186, 386)(176, 376, 189, 389, 198, 398, 190, 390)(181, 381, 192, 392, 199, 399, 193, 393)(188, 388, 196, 396, 200, 400, 197, 397) L = (1, 202)(2, 201)(3, 207)(4, 209)(5, 210)(6, 212)(7, 203)(8, 215)(9, 204)(10, 205)(11, 220)(12, 206)(13, 223)(14, 219)(15, 208)(16, 221)(17, 228)(18, 229)(19, 214)(20, 211)(21, 216)(22, 234)(23, 213)(24, 237)(25, 238)(26, 236)(27, 240)(28, 217)(29, 218)(30, 244)(31, 245)(32, 243)(33, 247)(34, 222)(35, 249)(36, 226)(37, 224)(38, 225)(39, 254)(40, 227)(41, 257)(42, 258)(43, 232)(44, 230)(45, 231)(46, 263)(47, 233)(48, 266)(49, 235)(50, 269)(51, 260)(52, 268)(53, 271)(54, 239)(55, 274)(56, 265)(57, 241)(58, 242)(59, 279)(60, 251)(61, 278)(62, 281)(63, 246)(64, 284)(65, 256)(66, 248)(67, 287)(68, 252)(69, 250)(70, 291)(71, 253)(72, 289)(73, 293)(74, 255)(75, 296)(76, 297)(77, 298)(78, 261)(79, 259)(80, 302)(81, 262)(82, 300)(83, 304)(84, 264)(85, 307)(86, 308)(87, 267)(88, 311)(89, 272)(90, 310)(91, 270)(92, 315)(93, 273)(94, 317)(95, 318)(96, 275)(97, 276)(98, 277)(99, 324)(100, 282)(101, 323)(102, 280)(103, 328)(104, 283)(105, 330)(106, 331)(107, 285)(108, 286)(109, 334)(110, 290)(111, 288)(112, 338)(113, 336)(114, 327)(115, 292)(116, 341)(117, 294)(118, 295)(119, 332)(120, 345)(121, 322)(122, 321)(123, 301)(124, 299)(125, 350)(126, 348)(127, 314)(128, 303)(129, 353)(130, 305)(131, 306)(132, 319)(133, 357)(134, 309)(135, 356)(136, 313)(137, 352)(138, 312)(139, 362)(140, 349)(141, 316)(142, 363)(143, 361)(144, 347)(145, 320)(146, 367)(147, 344)(148, 326)(149, 340)(150, 325)(151, 371)(152, 337)(153, 329)(154, 372)(155, 370)(156, 335)(157, 333)(158, 376)(159, 373)(160, 375)(161, 343)(162, 339)(163, 342)(164, 368)(165, 381)(166, 369)(167, 346)(168, 364)(169, 366)(170, 355)(171, 351)(172, 354)(173, 359)(174, 388)(175, 360)(176, 358)(177, 389)(178, 385)(179, 387)(180, 386)(181, 365)(182, 384)(183, 390)(184, 382)(185, 378)(186, 380)(187, 379)(188, 374)(189, 377)(190, 383)(191, 397)(192, 398)(193, 395)(194, 396)(195, 393)(196, 394)(197, 391)(198, 392)(199, 400)(200, 399) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.1266 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 50 e = 200 f = 120 degree seq :: [ 8^50 ] E16.1268 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 10}) Quotient :: loop Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ F^2, T1^4, (T2 * T1)^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2^-2 * T1^-2 * T2^-2 * T1, T2^10, (T2^4 * T1^-1 * T2 * T1^-1)^2 ] Map:: R = (1, 201, 3, 203, 10, 210, 24, 224, 48, 248, 82, 282, 60, 260, 32, 232, 14, 214, 5, 205)(2, 202, 7, 207, 17, 217, 38, 238, 66, 266, 105, 305, 76, 276, 44, 244, 20, 220, 8, 208)(4, 204, 12, 212, 27, 227, 53, 253, 89, 289, 118, 318, 80, 280, 46, 246, 22, 222, 9, 209)(6, 206, 15, 215, 33, 233, 61, 261, 96, 296, 134, 334, 103, 303, 64, 264, 36, 236, 16, 216)(11, 211, 26, 226, 51, 251, 87, 287, 126, 326, 139, 339, 101, 301, 63, 263, 35, 235, 23, 223)(13, 213, 29, 229, 34, 234, 62, 262, 98, 298, 136, 336, 132, 332, 92, 292, 56, 256, 30, 230)(18, 218, 40, 240, 69, 269, 108, 308, 146, 346, 116, 316, 78, 278, 45, 245, 21, 221, 37, 237)(19, 219, 41, 241, 28, 228, 54, 254, 86, 286, 125, 325, 151, 351, 111, 311, 72, 272, 42, 242)(25, 225, 50, 250, 85, 285, 124, 324, 159, 359, 176, 376, 154, 354, 115, 315, 77, 277, 47, 247)(31, 231, 57, 257, 70, 270, 109, 309, 145, 345, 171, 371, 149, 349, 110, 310, 71, 271, 58, 258)(39, 239, 68, 268, 52, 252, 88, 288, 123, 323, 158, 358, 130, 330, 91, 291, 55, 255, 65, 265)(43, 243, 73, 273, 99, 299, 137, 337, 165, 365, 185, 385, 168, 368, 138, 338, 100, 300, 74, 274)(49, 249, 84, 284, 122, 322, 157, 357, 179, 379, 187, 387, 167, 367, 140, 340, 102, 302, 81, 281)(59, 259, 93, 293, 97, 297, 135, 335, 164, 364, 184, 384, 183, 383, 162, 362, 129, 329, 94, 294)(67, 267, 107, 307, 144, 344, 170, 370, 189, 389, 175, 375, 153, 353, 117, 317, 79, 279, 104, 304)(75, 275, 112, 312, 90, 290, 128, 328, 160, 360, 181, 381, 192, 392, 173, 373, 148, 348, 113, 313)(83, 283, 121, 321, 156, 356, 178, 378, 194, 394, 199, 399, 193, 393, 177, 377, 155, 355, 119, 319)(95, 295, 120, 320, 147, 347, 172, 372, 190, 390, 198, 398, 191, 391, 174, 374, 150, 350, 133, 333)(106, 306, 143, 343, 127, 327, 161, 361, 180, 380, 195, 395, 182, 382, 163, 363, 131, 331, 141, 341)(114, 314, 142, 342, 166, 366, 186, 386, 196, 396, 200, 400, 197, 397, 188, 388, 169, 369, 152, 352) L = (1, 202)(2, 206)(3, 209)(4, 201)(5, 213)(6, 204)(7, 205)(8, 219)(9, 221)(10, 223)(11, 203)(12, 216)(13, 218)(14, 231)(15, 208)(16, 235)(17, 237)(18, 207)(19, 234)(20, 243)(21, 211)(22, 239)(23, 236)(24, 247)(25, 210)(26, 245)(27, 241)(28, 212)(29, 214)(30, 255)(31, 233)(32, 259)(33, 229)(34, 215)(35, 228)(36, 225)(37, 222)(38, 265)(39, 217)(40, 230)(41, 220)(42, 271)(43, 227)(44, 275)(45, 277)(46, 279)(47, 278)(48, 281)(49, 224)(50, 264)(51, 268)(52, 226)(53, 274)(54, 263)(55, 270)(56, 267)(57, 232)(58, 272)(59, 269)(60, 295)(61, 258)(62, 242)(63, 300)(64, 302)(65, 256)(66, 304)(67, 238)(68, 246)(69, 257)(70, 240)(71, 299)(72, 297)(73, 244)(74, 301)(75, 298)(76, 314)(77, 252)(78, 249)(79, 251)(80, 306)(81, 303)(82, 319)(83, 248)(84, 316)(85, 254)(86, 250)(87, 317)(88, 315)(89, 312)(90, 253)(91, 329)(92, 331)(93, 260)(94, 330)(95, 296)(96, 293)(97, 261)(98, 273)(99, 262)(100, 285)(101, 290)(102, 286)(103, 283)(104, 280)(105, 341)(106, 266)(107, 292)(108, 294)(109, 291)(110, 348)(111, 350)(112, 276)(113, 349)(114, 289)(115, 353)(116, 355)(117, 354)(118, 352)(119, 346)(120, 282)(121, 334)(122, 288)(123, 284)(124, 338)(125, 340)(126, 343)(127, 287)(128, 339)(129, 344)(130, 347)(131, 345)(132, 342)(133, 351)(134, 333)(135, 311)(136, 313)(137, 310)(138, 367)(139, 369)(140, 368)(141, 332)(142, 305)(143, 318)(144, 309)(145, 307)(146, 320)(147, 308)(148, 364)(149, 366)(150, 365)(151, 321)(152, 326)(153, 322)(154, 327)(155, 323)(156, 325)(157, 375)(158, 377)(159, 328)(160, 324)(161, 376)(162, 382)(163, 383)(164, 337)(165, 335)(166, 336)(167, 360)(168, 356)(169, 359)(170, 362)(171, 363)(172, 358)(173, 391)(174, 392)(175, 393)(176, 388)(177, 389)(178, 385)(179, 361)(180, 357)(181, 387)(182, 390)(183, 386)(184, 373)(185, 374)(186, 371)(187, 397)(188, 379)(189, 372)(190, 370)(191, 396)(192, 378)(193, 380)(194, 381)(195, 399)(196, 384)(197, 394)(198, 395)(199, 400)(200, 398) 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 E16.1264 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 20 e = 200 f = 150 degree seq :: [ 20^20 ] E16.1269 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 10}) Quotient :: loop Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, (T2 * T1 * T2 * T1^-1)^2, T1^10, T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2, (T1^-3 * T2 * T1^3 * T2)^2, T1^-4 * T2 * T1^-4 * T2 * T1^4 * T2 * T1^4 * T2 ] Map:: polyhedral non-degenerate R = (1, 201, 3, 203)(2, 202, 6, 206)(4, 204, 9, 209)(5, 205, 12, 212)(7, 207, 16, 216)(8, 208, 17, 217)(10, 210, 21, 221)(11, 211, 24, 224)(13, 213, 28, 228)(14, 214, 29, 229)(15, 215, 32, 232)(18, 218, 35, 235)(19, 219, 34, 234)(20, 220, 33, 233)(22, 222, 41, 241)(23, 223, 44, 244)(25, 225, 48, 248)(26, 226, 49, 249)(27, 227, 52, 252)(30, 230, 53, 253)(31, 231, 56, 256)(36, 236, 61, 261)(37, 237, 60, 260)(38, 238, 57, 257)(39, 239, 58, 258)(40, 240, 59, 259)(42, 242, 69, 269)(43, 243, 70, 270)(45, 245, 74, 274)(46, 246, 75, 275)(47, 247, 78, 278)(50, 250, 79, 279)(51, 251, 82, 282)(54, 254, 83, 283)(55, 255, 86, 286)(62, 262, 93, 293)(63, 263, 92, 292)(64, 264, 87, 287)(65, 265, 88, 288)(66, 266, 91, 291)(67, 267, 90, 290)(68, 268, 89, 289)(71, 271, 105, 305)(72, 272, 106, 306)(73, 273, 109, 309)(76, 276, 110, 310)(77, 277, 113, 313)(80, 280, 114, 314)(81, 281, 117, 317)(84, 284, 118, 318)(85, 285, 119, 319)(94, 294, 127, 327)(95, 295, 120, 320)(96, 296, 121, 321)(97, 297, 126, 326)(98, 298, 125, 325)(99, 299, 122, 322)(100, 300, 123, 323)(101, 301, 124, 324)(102, 302, 136, 336)(103, 303, 137, 337)(104, 304, 140, 340)(107, 307, 141, 341)(108, 308, 144, 344)(111, 311, 145, 345)(112, 312, 148, 348)(115, 315, 149, 349)(116, 316, 150, 350)(128, 328, 151, 351)(129, 329, 152, 352)(130, 330, 157, 357)(131, 331, 156, 356)(132, 332, 153, 353)(133, 333, 154, 354)(134, 334, 155, 355)(135, 335, 164, 364)(138, 338, 165, 365)(139, 339, 168, 368)(142, 342, 169, 369)(143, 343, 172, 372)(146, 346, 173, 373)(147, 347, 174, 374)(158, 358, 175, 375)(159, 359, 179, 379)(160, 360, 176, 376)(161, 361, 177, 377)(162, 362, 178, 378)(163, 363, 184, 384)(166, 366, 185, 385)(167, 367, 188, 388)(170, 370, 189, 389)(171, 371, 190, 390)(180, 380, 191, 391)(181, 381, 192, 392)(182, 382, 193, 393)(183, 383, 196, 396)(186, 386, 197, 397)(187, 387, 198, 398)(194, 394, 199, 399)(195, 395, 200, 400) L = (1, 202)(2, 205)(3, 207)(4, 201)(5, 211)(6, 213)(7, 215)(8, 203)(9, 219)(10, 204)(11, 223)(12, 225)(13, 227)(14, 206)(15, 231)(16, 233)(17, 234)(18, 208)(19, 237)(20, 209)(21, 239)(22, 210)(23, 243)(24, 245)(25, 247)(26, 212)(27, 251)(28, 217)(29, 216)(30, 214)(31, 255)(32, 253)(33, 258)(34, 259)(35, 252)(36, 218)(37, 263)(38, 220)(39, 265)(40, 221)(41, 267)(42, 222)(43, 242)(44, 271)(45, 273)(46, 224)(47, 277)(48, 229)(49, 228)(50, 226)(51, 281)(52, 279)(53, 278)(54, 230)(55, 285)(56, 287)(57, 232)(58, 289)(59, 290)(60, 235)(61, 292)(62, 236)(63, 294)(64, 238)(65, 296)(66, 240)(67, 298)(68, 241)(69, 300)(70, 302)(71, 304)(72, 244)(73, 308)(74, 249)(75, 248)(76, 246)(77, 312)(78, 310)(79, 309)(80, 250)(81, 316)(82, 261)(83, 256)(84, 254)(85, 262)(86, 318)(87, 321)(88, 257)(89, 323)(90, 324)(91, 260)(92, 326)(93, 317)(94, 328)(95, 264)(96, 329)(97, 266)(98, 331)(99, 268)(100, 333)(101, 269)(102, 335)(103, 270)(104, 339)(105, 275)(106, 274)(107, 272)(108, 343)(109, 341)(110, 340)(111, 276)(112, 347)(113, 283)(114, 282)(115, 280)(116, 284)(117, 349)(118, 348)(119, 351)(120, 286)(121, 353)(122, 288)(123, 337)(124, 336)(125, 291)(126, 356)(127, 293)(128, 295)(129, 358)(130, 297)(131, 359)(132, 299)(133, 361)(134, 301)(135, 363)(136, 306)(137, 305)(138, 303)(139, 367)(140, 365)(141, 364)(142, 307)(143, 371)(144, 314)(145, 313)(146, 311)(147, 315)(148, 373)(149, 372)(150, 319)(151, 375)(152, 320)(153, 377)(154, 322)(155, 325)(156, 378)(157, 327)(158, 330)(159, 380)(160, 332)(161, 381)(162, 334)(163, 383)(164, 355)(165, 354)(166, 338)(167, 387)(168, 345)(169, 344)(170, 342)(171, 346)(172, 389)(173, 388)(174, 350)(175, 391)(176, 352)(177, 385)(178, 384)(179, 357)(180, 360)(181, 394)(182, 362)(183, 395)(184, 369)(185, 368)(186, 366)(187, 370)(188, 397)(189, 396)(190, 374)(191, 399)(192, 376)(193, 379)(194, 382)(195, 386)(196, 393)(197, 392)(198, 390)(199, 400)(200, 398) local type(s) :: { ( 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.1265 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 100 e = 200 f = 70 degree seq :: [ 4^100 ] E16.1270 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10}) Quotient :: dipole Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^10 ] Map:: R = (1, 201, 2, 202)(3, 203, 7, 207)(4, 204, 9, 209)(5, 205, 10, 210)(6, 206, 12, 212)(8, 208, 15, 215)(11, 211, 20, 220)(13, 213, 23, 223)(14, 214, 19, 219)(16, 216, 21, 221)(17, 217, 28, 228)(18, 218, 29, 229)(22, 222, 34, 234)(24, 224, 37, 237)(25, 225, 38, 238)(26, 226, 36, 236)(27, 227, 40, 240)(30, 230, 44, 244)(31, 231, 45, 245)(32, 232, 43, 243)(33, 233, 47, 247)(35, 235, 49, 249)(39, 239, 54, 254)(41, 241, 57, 257)(42, 242, 58, 258)(46, 246, 63, 263)(48, 248, 66, 266)(50, 250, 69, 269)(51, 251, 60, 260)(52, 252, 68, 268)(53, 253, 71, 271)(55, 255, 74, 274)(56, 256, 65, 265)(59, 259, 79, 279)(61, 261, 78, 278)(62, 262, 81, 281)(64, 264, 84, 284)(67, 267, 87, 287)(70, 270, 91, 291)(72, 272, 89, 289)(73, 273, 93, 293)(75, 275, 96, 296)(76, 276, 97, 297)(77, 277, 98, 298)(80, 280, 102, 302)(82, 282, 100, 300)(83, 283, 104, 304)(85, 285, 107, 307)(86, 286, 108, 308)(88, 288, 111, 311)(90, 290, 110, 310)(92, 292, 115, 315)(94, 294, 117, 317)(95, 295, 118, 318)(99, 299, 124, 324)(101, 301, 123, 323)(103, 303, 128, 328)(105, 305, 130, 330)(106, 306, 131, 331)(109, 309, 134, 334)(112, 312, 138, 338)(113, 313, 136, 336)(114, 314, 127, 327)(116, 316, 141, 341)(119, 319, 132, 332)(120, 320, 145, 345)(121, 321, 122, 322)(125, 325, 150, 350)(126, 326, 148, 348)(129, 329, 153, 353)(133, 333, 157, 357)(135, 335, 156, 356)(137, 337, 152, 352)(139, 339, 162, 362)(140, 340, 149, 349)(142, 342, 163, 363)(143, 343, 161, 361)(144, 344, 147, 347)(146, 346, 167, 367)(151, 351, 171, 371)(154, 354, 172, 372)(155, 355, 170, 370)(158, 358, 176, 376)(159, 359, 173, 373)(160, 360, 175, 375)(164, 364, 168, 368)(165, 365, 181, 381)(166, 366, 169, 369)(174, 374, 188, 388)(177, 377, 189, 389)(178, 378, 185, 385)(179, 379, 187, 387)(180, 380, 186, 386)(182, 382, 184, 384)(183, 383, 190, 390)(191, 391, 197, 397)(192, 392, 198, 398)(193, 393, 195, 395)(194, 394, 196, 396)(199, 399, 200, 400)(401, 601, 403, 603, 408, 608, 404, 604)(402, 602, 405, 605, 411, 611, 406, 606)(407, 607, 413, 613, 424, 624, 414, 614)(409, 609, 416, 616, 427, 627, 417, 617)(410, 610, 418, 618, 430, 630, 419, 619)(412, 612, 421, 621, 433, 633, 422, 622)(415, 615, 425, 625, 439, 639, 426, 626)(420, 620, 431, 631, 446, 646, 432, 632)(423, 623, 435, 635, 450, 650, 436, 636)(428, 628, 438, 638, 453, 653, 441, 641)(429, 629, 442, 642, 459, 659, 443, 643)(434, 634, 445, 645, 462, 662, 448, 648)(437, 637, 451, 651, 470, 670, 452, 652)(440, 640, 455, 655, 475, 675, 456, 656)(444, 644, 460, 660, 480, 680, 461, 661)(447, 647, 464, 664, 485, 685, 465, 665)(449, 649, 467, 667, 488, 688, 468, 668)(454, 654, 472, 672, 494, 694, 473, 673)(457, 657, 474, 674, 495, 695, 476, 676)(458, 658, 477, 677, 499, 699, 478, 678)(463, 663, 482, 682, 505, 705, 483, 683)(466, 666, 484, 684, 506, 706, 486, 686)(469, 669, 489, 689, 512, 712, 490, 690)(471, 671, 492, 692, 516, 716, 493, 693)(479, 679, 500, 700, 525, 725, 501, 701)(481, 681, 503, 703, 529, 729, 504, 704)(487, 687, 509, 709, 535, 735, 510, 710)(491, 691, 513, 713, 539, 739, 514, 714)(496, 696, 519, 719, 546, 746, 520, 720)(497, 697, 515, 715, 540, 740, 521, 721)(498, 698, 522, 722, 547, 747, 523, 723)(502, 702, 526, 726, 551, 751, 527, 727)(507, 707, 532, 732, 558, 758, 533, 733)(508, 708, 528, 728, 552, 752, 534, 734)(511, 711, 536, 736, 559, 759, 537, 737)(517, 717, 542, 742, 565, 765, 543, 743)(518, 718, 544, 744, 566, 766, 545, 745)(524, 724, 548, 748, 568, 768, 549, 749)(530, 730, 554, 754, 574, 774, 555, 755)(531, 731, 556, 756, 575, 775, 557, 757)(538, 738, 560, 760, 577, 777, 561, 761)(541, 741, 563, 763, 580, 780, 564, 764)(550, 750, 569, 769, 584, 784, 570, 770)(553, 753, 572, 772, 587, 787, 573, 773)(562, 762, 578, 778, 591, 791, 579, 779)(567, 767, 582, 782, 594, 794, 583, 783)(571, 771, 585, 785, 595, 795, 586, 786)(576, 776, 589, 789, 598, 798, 590, 790)(581, 781, 592, 792, 599, 799, 593, 793)(588, 788, 596, 796, 600, 800, 597, 797) L = (1, 402)(2, 401)(3, 407)(4, 409)(5, 410)(6, 412)(7, 403)(8, 415)(9, 404)(10, 405)(11, 420)(12, 406)(13, 423)(14, 419)(15, 408)(16, 421)(17, 428)(18, 429)(19, 414)(20, 411)(21, 416)(22, 434)(23, 413)(24, 437)(25, 438)(26, 436)(27, 440)(28, 417)(29, 418)(30, 444)(31, 445)(32, 443)(33, 447)(34, 422)(35, 449)(36, 426)(37, 424)(38, 425)(39, 454)(40, 427)(41, 457)(42, 458)(43, 432)(44, 430)(45, 431)(46, 463)(47, 433)(48, 466)(49, 435)(50, 469)(51, 460)(52, 468)(53, 471)(54, 439)(55, 474)(56, 465)(57, 441)(58, 442)(59, 479)(60, 451)(61, 478)(62, 481)(63, 446)(64, 484)(65, 456)(66, 448)(67, 487)(68, 452)(69, 450)(70, 491)(71, 453)(72, 489)(73, 493)(74, 455)(75, 496)(76, 497)(77, 498)(78, 461)(79, 459)(80, 502)(81, 462)(82, 500)(83, 504)(84, 464)(85, 507)(86, 508)(87, 467)(88, 511)(89, 472)(90, 510)(91, 470)(92, 515)(93, 473)(94, 517)(95, 518)(96, 475)(97, 476)(98, 477)(99, 524)(100, 482)(101, 523)(102, 480)(103, 528)(104, 483)(105, 530)(106, 531)(107, 485)(108, 486)(109, 534)(110, 490)(111, 488)(112, 538)(113, 536)(114, 527)(115, 492)(116, 541)(117, 494)(118, 495)(119, 532)(120, 545)(121, 522)(122, 521)(123, 501)(124, 499)(125, 550)(126, 548)(127, 514)(128, 503)(129, 553)(130, 505)(131, 506)(132, 519)(133, 557)(134, 509)(135, 556)(136, 513)(137, 552)(138, 512)(139, 562)(140, 549)(141, 516)(142, 563)(143, 561)(144, 547)(145, 520)(146, 567)(147, 544)(148, 526)(149, 540)(150, 525)(151, 571)(152, 537)(153, 529)(154, 572)(155, 570)(156, 535)(157, 533)(158, 576)(159, 573)(160, 575)(161, 543)(162, 539)(163, 542)(164, 568)(165, 581)(166, 569)(167, 546)(168, 564)(169, 566)(170, 555)(171, 551)(172, 554)(173, 559)(174, 588)(175, 560)(176, 558)(177, 589)(178, 585)(179, 587)(180, 586)(181, 565)(182, 584)(183, 590)(184, 582)(185, 578)(186, 580)(187, 579)(188, 574)(189, 577)(190, 583)(191, 597)(192, 598)(193, 595)(194, 596)(195, 593)(196, 594)(197, 591)(198, 592)(199, 600)(200, 599)(201, 601)(202, 602)(203, 603)(204, 604)(205, 605)(206, 606)(207, 607)(208, 608)(209, 609)(210, 610)(211, 611)(212, 612)(213, 613)(214, 614)(215, 615)(216, 616)(217, 617)(218, 618)(219, 619)(220, 620)(221, 621)(222, 622)(223, 623)(224, 624)(225, 625)(226, 626)(227, 627)(228, 628)(229, 629)(230, 630)(231, 631)(232, 632)(233, 633)(234, 634)(235, 635)(236, 636)(237, 637)(238, 638)(239, 639)(240, 640)(241, 641)(242, 642)(243, 643)(244, 644)(245, 645)(246, 646)(247, 647)(248, 648)(249, 649)(250, 650)(251, 651)(252, 652)(253, 653)(254, 654)(255, 655)(256, 656)(257, 657)(258, 658)(259, 659)(260, 660)(261, 661)(262, 662)(263, 663)(264, 664)(265, 665)(266, 666)(267, 667)(268, 668)(269, 669)(270, 670)(271, 671)(272, 672)(273, 673)(274, 674)(275, 675)(276, 676)(277, 677)(278, 678)(279, 679)(280, 680)(281, 681)(282, 682)(283, 683)(284, 684)(285, 685)(286, 686)(287, 687)(288, 688)(289, 689)(290, 690)(291, 691)(292, 692)(293, 693)(294, 694)(295, 695)(296, 696)(297, 697)(298, 698)(299, 699)(300, 700)(301, 701)(302, 702)(303, 703)(304, 704)(305, 705)(306, 706)(307, 707)(308, 708)(309, 709)(310, 710)(311, 711)(312, 712)(313, 713)(314, 714)(315, 715)(316, 716)(317, 717)(318, 718)(319, 719)(320, 720)(321, 721)(322, 722)(323, 723)(324, 724)(325, 725)(326, 726)(327, 727)(328, 728)(329, 729)(330, 730)(331, 731)(332, 732)(333, 733)(334, 734)(335, 735)(336, 736)(337, 737)(338, 738)(339, 739)(340, 740)(341, 741)(342, 742)(343, 743)(344, 744)(345, 745)(346, 746)(347, 747)(348, 748)(349, 749)(350, 750)(351, 751)(352, 752)(353, 753)(354, 754)(355, 755)(356, 756)(357, 757)(358, 758)(359, 759)(360, 760)(361, 761)(362, 762)(363, 763)(364, 764)(365, 765)(366, 766)(367, 767)(368, 768)(369, 769)(370, 770)(371, 771)(372, 772)(373, 773)(374, 774)(375, 775)(376, 776)(377, 777)(378, 778)(379, 779)(380, 780)(381, 781)(382, 782)(383, 783)(384, 784)(385, 785)(386, 786)(387, 787)(388, 788)(389, 789)(390, 790)(391, 791)(392, 792)(393, 793)(394, 794)(395, 795)(396, 796)(397, 797)(398, 798)(399, 799)(400, 800) local type(s) :: { ( 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E16.1273 Graph:: bipartite v = 150 e = 400 f = 220 degree seq :: [ 4^100, 8^50 ] E16.1271 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10}) Quotient :: dipole Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (Y2 * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y2 * Y1^-2 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, Y2^10, Y1^-1 * Y2^3 * Y1^-1 * Y2^-1 * Y1 * Y2^4 * Y1^-1, (Y2^4 * Y1^-1 * Y2 * Y1^-1)^2 ] Map:: R = (1, 201, 2, 202, 6, 206, 4, 204)(3, 203, 9, 209, 21, 221, 11, 211)(5, 205, 13, 213, 18, 218, 7, 207)(8, 208, 19, 219, 34, 234, 15, 215)(10, 210, 23, 223, 36, 236, 25, 225)(12, 212, 16, 216, 35, 235, 28, 228)(14, 214, 31, 231, 33, 233, 29, 229)(17, 217, 37, 237, 22, 222, 39, 239)(20, 220, 43, 243, 27, 227, 41, 241)(24, 224, 47, 247, 78, 278, 49, 249)(26, 226, 45, 245, 77, 277, 52, 252)(30, 230, 55, 255, 70, 270, 40, 240)(32, 232, 59, 259, 69, 269, 57, 257)(38, 238, 65, 265, 56, 256, 67, 267)(42, 242, 71, 271, 99, 299, 62, 262)(44, 244, 75, 275, 98, 298, 73, 273)(46, 246, 79, 279, 51, 251, 68, 268)(48, 248, 81, 281, 103, 303, 83, 283)(50, 250, 64, 264, 102, 302, 86, 286)(53, 253, 74, 274, 101, 301, 90, 290)(54, 254, 63, 263, 100, 300, 85, 285)(58, 258, 72, 272, 97, 297, 61, 261)(60, 260, 95, 295, 96, 296, 93, 293)(66, 266, 104, 304, 80, 280, 106, 306)(76, 276, 114, 314, 89, 289, 112, 312)(82, 282, 119, 319, 146, 346, 120, 320)(84, 284, 116, 316, 155, 355, 123, 323)(87, 287, 117, 317, 154, 354, 127, 327)(88, 288, 115, 315, 153, 353, 122, 322)(91, 291, 129, 329, 144, 344, 109, 309)(92, 292, 131, 331, 145, 345, 107, 307)(94, 294, 130, 330, 147, 347, 108, 308)(105, 305, 141, 341, 132, 332, 142, 342)(110, 310, 148, 348, 164, 364, 137, 337)(111, 311, 150, 350, 165, 365, 135, 335)(113, 313, 149, 349, 166, 366, 136, 336)(118, 318, 152, 352, 126, 326, 143, 343)(121, 321, 134, 334, 133, 333, 151, 351)(124, 324, 138, 338, 167, 367, 160, 360)(125, 325, 140, 340, 168, 368, 156, 356)(128, 328, 139, 339, 169, 369, 159, 359)(157, 357, 175, 375, 193, 393, 180, 380)(158, 358, 177, 377, 189, 389, 172, 372)(161, 361, 176, 376, 188, 388, 179, 379)(162, 362, 182, 382, 190, 390, 170, 370)(163, 363, 183, 383, 186, 386, 171, 371)(173, 373, 191, 391, 196, 396, 184, 384)(174, 374, 192, 392, 178, 378, 185, 385)(181, 381, 187, 387, 197, 397, 194, 394)(195, 395, 199, 399, 200, 400, 198, 398)(401, 601, 403, 603, 410, 610, 424, 624, 448, 648, 482, 682, 460, 660, 432, 632, 414, 614, 405, 605)(402, 602, 407, 607, 417, 617, 438, 638, 466, 666, 505, 705, 476, 676, 444, 644, 420, 620, 408, 608)(404, 604, 412, 612, 427, 627, 453, 653, 489, 689, 518, 718, 480, 680, 446, 646, 422, 622, 409, 609)(406, 606, 415, 615, 433, 633, 461, 661, 496, 696, 534, 734, 503, 703, 464, 664, 436, 636, 416, 616)(411, 611, 426, 626, 451, 651, 487, 687, 526, 726, 539, 739, 501, 701, 463, 663, 435, 635, 423, 623)(413, 613, 429, 629, 434, 634, 462, 662, 498, 698, 536, 736, 532, 732, 492, 692, 456, 656, 430, 630)(418, 618, 440, 640, 469, 669, 508, 708, 546, 746, 516, 716, 478, 678, 445, 645, 421, 621, 437, 637)(419, 619, 441, 641, 428, 628, 454, 654, 486, 686, 525, 725, 551, 751, 511, 711, 472, 672, 442, 642)(425, 625, 450, 650, 485, 685, 524, 724, 559, 759, 576, 776, 554, 754, 515, 715, 477, 677, 447, 647)(431, 631, 457, 657, 470, 670, 509, 709, 545, 745, 571, 771, 549, 749, 510, 710, 471, 671, 458, 658)(439, 639, 468, 668, 452, 652, 488, 688, 523, 723, 558, 758, 530, 730, 491, 691, 455, 655, 465, 665)(443, 643, 473, 673, 499, 699, 537, 737, 565, 765, 585, 785, 568, 768, 538, 738, 500, 700, 474, 674)(449, 649, 484, 684, 522, 722, 557, 757, 579, 779, 587, 787, 567, 767, 540, 740, 502, 702, 481, 681)(459, 659, 493, 693, 497, 697, 535, 735, 564, 764, 584, 784, 583, 783, 562, 762, 529, 729, 494, 694)(467, 667, 507, 707, 544, 744, 570, 770, 589, 789, 575, 775, 553, 753, 517, 717, 479, 679, 504, 704)(475, 675, 512, 712, 490, 690, 528, 728, 560, 760, 581, 781, 592, 792, 573, 773, 548, 748, 513, 713)(483, 683, 521, 721, 556, 756, 578, 778, 594, 794, 599, 799, 593, 793, 577, 777, 555, 755, 519, 719)(495, 695, 520, 720, 547, 747, 572, 772, 590, 790, 598, 798, 591, 791, 574, 774, 550, 750, 533, 733)(506, 706, 543, 743, 527, 727, 561, 761, 580, 780, 595, 795, 582, 782, 563, 763, 531, 731, 541, 741)(514, 714, 542, 742, 566, 766, 586, 786, 596, 796, 600, 800, 597, 797, 588, 788, 569, 769, 552, 752) L = (1, 403)(2, 407)(3, 410)(4, 412)(5, 401)(6, 415)(7, 417)(8, 402)(9, 404)(10, 424)(11, 426)(12, 427)(13, 429)(14, 405)(15, 433)(16, 406)(17, 438)(18, 440)(19, 441)(20, 408)(21, 437)(22, 409)(23, 411)(24, 448)(25, 450)(26, 451)(27, 453)(28, 454)(29, 434)(30, 413)(31, 457)(32, 414)(33, 461)(34, 462)(35, 423)(36, 416)(37, 418)(38, 466)(39, 468)(40, 469)(41, 428)(42, 419)(43, 473)(44, 420)(45, 421)(46, 422)(47, 425)(48, 482)(49, 484)(50, 485)(51, 487)(52, 488)(53, 489)(54, 486)(55, 465)(56, 430)(57, 470)(58, 431)(59, 493)(60, 432)(61, 496)(62, 498)(63, 435)(64, 436)(65, 439)(66, 505)(67, 507)(68, 452)(69, 508)(70, 509)(71, 458)(72, 442)(73, 499)(74, 443)(75, 512)(76, 444)(77, 447)(78, 445)(79, 504)(80, 446)(81, 449)(82, 460)(83, 521)(84, 522)(85, 524)(86, 525)(87, 526)(88, 523)(89, 518)(90, 528)(91, 455)(92, 456)(93, 497)(94, 459)(95, 520)(96, 534)(97, 535)(98, 536)(99, 537)(100, 474)(101, 463)(102, 481)(103, 464)(104, 467)(105, 476)(106, 543)(107, 544)(108, 546)(109, 545)(110, 471)(111, 472)(112, 490)(113, 475)(114, 542)(115, 477)(116, 478)(117, 479)(118, 480)(119, 483)(120, 547)(121, 556)(122, 557)(123, 558)(124, 559)(125, 551)(126, 539)(127, 561)(128, 560)(129, 494)(130, 491)(131, 541)(132, 492)(133, 495)(134, 503)(135, 564)(136, 532)(137, 565)(138, 500)(139, 501)(140, 502)(141, 506)(142, 566)(143, 527)(144, 570)(145, 571)(146, 516)(147, 572)(148, 513)(149, 510)(150, 533)(151, 511)(152, 514)(153, 517)(154, 515)(155, 519)(156, 578)(157, 579)(158, 530)(159, 576)(160, 581)(161, 580)(162, 529)(163, 531)(164, 584)(165, 585)(166, 586)(167, 540)(168, 538)(169, 552)(170, 589)(171, 549)(172, 590)(173, 548)(174, 550)(175, 553)(176, 554)(177, 555)(178, 594)(179, 587)(180, 595)(181, 592)(182, 563)(183, 562)(184, 583)(185, 568)(186, 596)(187, 567)(188, 569)(189, 575)(190, 598)(191, 574)(192, 573)(193, 577)(194, 599)(195, 582)(196, 600)(197, 588)(198, 591)(199, 593)(200, 597)(201, 601)(202, 602)(203, 603)(204, 604)(205, 605)(206, 606)(207, 607)(208, 608)(209, 609)(210, 610)(211, 611)(212, 612)(213, 613)(214, 614)(215, 615)(216, 616)(217, 617)(218, 618)(219, 619)(220, 620)(221, 621)(222, 622)(223, 623)(224, 624)(225, 625)(226, 626)(227, 627)(228, 628)(229, 629)(230, 630)(231, 631)(232, 632)(233, 633)(234, 634)(235, 635)(236, 636)(237, 637)(238, 638)(239, 639)(240, 640)(241, 641)(242, 642)(243, 643)(244, 644)(245, 645)(246, 646)(247, 647)(248, 648)(249, 649)(250, 650)(251, 651)(252, 652)(253, 653)(254, 654)(255, 655)(256, 656)(257, 657)(258, 658)(259, 659)(260, 660)(261, 661)(262, 662)(263, 663)(264, 664)(265, 665)(266, 666)(267, 667)(268, 668)(269, 669)(270, 670)(271, 671)(272, 672)(273, 673)(274, 674)(275, 675)(276, 676)(277, 677)(278, 678)(279, 679)(280, 680)(281, 681)(282, 682)(283, 683)(284, 684)(285, 685)(286, 686)(287, 687)(288, 688)(289, 689)(290, 690)(291, 691)(292, 692)(293, 693)(294, 694)(295, 695)(296, 696)(297, 697)(298, 698)(299, 699)(300, 700)(301, 701)(302, 702)(303, 703)(304, 704)(305, 705)(306, 706)(307, 707)(308, 708)(309, 709)(310, 710)(311, 711)(312, 712)(313, 713)(314, 714)(315, 715)(316, 716)(317, 717)(318, 718)(319, 719)(320, 720)(321, 721)(322, 722)(323, 723)(324, 724)(325, 725)(326, 726)(327, 727)(328, 728)(329, 729)(330, 730)(331, 731)(332, 732)(333, 733)(334, 734)(335, 735)(336, 736)(337, 737)(338, 738)(339, 739)(340, 740)(341, 741)(342, 742)(343, 743)(344, 744)(345, 745)(346, 746)(347, 747)(348, 748)(349, 749)(350, 750)(351, 751)(352, 752)(353, 753)(354, 754)(355, 755)(356, 756)(357, 757)(358, 758)(359, 759)(360, 760)(361, 761)(362, 762)(363, 763)(364, 764)(365, 765)(366, 766)(367, 767)(368, 768)(369, 769)(370, 770)(371, 771)(372, 772)(373, 773)(374, 774)(375, 775)(376, 776)(377, 777)(378, 778)(379, 779)(380, 780)(381, 781)(382, 782)(383, 783)(384, 784)(385, 785)(386, 786)(387, 787)(388, 788)(389, 789)(390, 790)(391, 791)(392, 792)(393, 793)(394, 794)(395, 795)(396, 796)(397, 797)(398, 798)(399, 799)(400, 800) 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 ) } Outer automorphisms :: reflexible Dual of E16.1272 Graph:: bipartite v = 70 e = 400 f = 300 degree seq :: [ 8^50, 20^20 ] E16.1272 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10}) Quotient :: dipole Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^4, (Y3 * Y2 * Y3^-1 * Y2)^2, Y3^2 * Y2 * Y3^2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2, (Y3^3 * Y2 * Y3^-3 * Y2)^2, Y3^4 * Y2 * Y3^4 * Y2 * Y3^-4 * Y2 * Y3^-4 * Y2, (Y3^-1 * Y1^-1)^10 ] Map:: polytopal R = (1, 201)(2, 202)(3, 203)(4, 204)(5, 205)(6, 206)(7, 207)(8, 208)(9, 209)(10, 210)(11, 211)(12, 212)(13, 213)(14, 214)(15, 215)(16, 216)(17, 217)(18, 218)(19, 219)(20, 220)(21, 221)(22, 222)(23, 223)(24, 224)(25, 225)(26, 226)(27, 227)(28, 228)(29, 229)(30, 230)(31, 231)(32, 232)(33, 233)(34, 234)(35, 235)(36, 236)(37, 237)(38, 238)(39, 239)(40, 240)(41, 241)(42, 242)(43, 243)(44, 244)(45, 245)(46, 246)(47, 247)(48, 248)(49, 249)(50, 250)(51, 251)(52, 252)(53, 253)(54, 254)(55, 255)(56, 256)(57, 257)(58, 258)(59, 259)(60, 260)(61, 261)(62, 262)(63, 263)(64, 264)(65, 265)(66, 266)(67, 267)(68, 268)(69, 269)(70, 270)(71, 271)(72, 272)(73, 273)(74, 274)(75, 275)(76, 276)(77, 277)(78, 278)(79, 279)(80, 280)(81, 281)(82, 282)(83, 283)(84, 284)(85, 285)(86, 286)(87, 287)(88, 288)(89, 289)(90, 290)(91, 291)(92, 292)(93, 293)(94, 294)(95, 295)(96, 296)(97, 297)(98, 298)(99, 299)(100, 300)(101, 301)(102, 302)(103, 303)(104, 304)(105, 305)(106, 306)(107, 307)(108, 308)(109, 309)(110, 310)(111, 311)(112, 312)(113, 313)(114, 314)(115, 315)(116, 316)(117, 317)(118, 318)(119, 319)(120, 320)(121, 321)(122, 322)(123, 323)(124, 324)(125, 325)(126, 326)(127, 327)(128, 328)(129, 329)(130, 330)(131, 331)(132, 332)(133, 333)(134, 334)(135, 335)(136, 336)(137, 337)(138, 338)(139, 339)(140, 340)(141, 341)(142, 342)(143, 343)(144, 344)(145, 345)(146, 346)(147, 347)(148, 348)(149, 349)(150, 350)(151, 351)(152, 352)(153, 353)(154, 354)(155, 355)(156, 356)(157, 357)(158, 358)(159, 359)(160, 360)(161, 361)(162, 362)(163, 363)(164, 364)(165, 365)(166, 366)(167, 367)(168, 368)(169, 369)(170, 370)(171, 371)(172, 372)(173, 373)(174, 374)(175, 375)(176, 376)(177, 377)(178, 378)(179, 379)(180, 380)(181, 381)(182, 382)(183, 383)(184, 384)(185, 385)(186, 386)(187, 387)(188, 388)(189, 389)(190, 390)(191, 391)(192, 392)(193, 393)(194, 394)(195, 395)(196, 396)(197, 397)(198, 398)(199, 399)(200, 400)(401, 601, 402, 602)(403, 603, 407, 607)(404, 604, 409, 609)(405, 605, 411, 611)(406, 606, 413, 613)(408, 608, 417, 617)(410, 610, 421, 621)(412, 612, 425, 625)(414, 614, 429, 629)(415, 615, 428, 628)(416, 616, 424, 624)(418, 618, 435, 635)(419, 619, 427, 627)(420, 620, 423, 623)(422, 622, 441, 641)(426, 626, 447, 647)(430, 630, 453, 653)(431, 631, 451, 651)(432, 632, 445, 645)(433, 633, 444, 644)(434, 634, 450, 650)(436, 636, 461, 661)(437, 637, 452, 652)(438, 638, 446, 646)(439, 639, 443, 643)(440, 640, 449, 649)(442, 642, 469, 669)(448, 648, 476, 676)(454, 654, 484, 684)(455, 655, 483, 683)(456, 656, 475, 675)(457, 657, 472, 672)(458, 658, 480, 680)(459, 659, 479, 679)(460, 660, 471, 671)(462, 662, 493, 693)(463, 663, 482, 682)(464, 664, 474, 674)(465, 665, 473, 673)(466, 666, 481, 681)(467, 667, 478, 678)(468, 668, 470, 670)(477, 677, 510, 710)(485, 685, 517, 717)(486, 686, 508, 708)(487, 687, 507, 707)(488, 688, 516, 716)(489, 689, 513, 713)(490, 690, 504, 704)(491, 691, 503, 703)(492, 692, 512, 712)(494, 694, 518, 718)(495, 695, 509, 709)(496, 696, 506, 706)(497, 697, 515, 715)(498, 698, 514, 714)(499, 699, 505, 705)(500, 700, 502, 702)(501, 701, 511, 711)(519, 719, 543, 743)(520, 720, 540, 740)(521, 721, 549, 749)(522, 722, 548, 748)(523, 723, 539, 739)(524, 724, 536, 736)(525, 725, 545, 745)(526, 726, 544, 744)(527, 727, 535, 735)(528, 728, 542, 742)(529, 729, 541, 741)(530, 730, 550, 750)(531, 731, 547, 747)(532, 732, 538, 738)(533, 733, 537, 737)(534, 734, 546, 746)(551, 751, 569, 769)(552, 752, 573, 773)(553, 753, 566, 766)(554, 754, 565, 765)(555, 755, 572, 772)(556, 756, 570, 770)(557, 757, 563, 763)(558, 758, 568, 768)(559, 759, 574, 774)(560, 760, 567, 767)(561, 761, 564, 764)(562, 762, 571, 771)(575, 775, 587, 787)(576, 776, 584, 784)(577, 777, 589, 789)(578, 778, 588, 788)(579, 779, 583, 783)(580, 780, 586, 786)(581, 781, 585, 785)(582, 782, 590, 790)(591, 791, 597, 797)(592, 792, 598, 798)(593, 793, 595, 795)(594, 794, 596, 796)(599, 799, 600, 800) L = (1, 403)(2, 405)(3, 408)(4, 401)(5, 412)(6, 402)(7, 415)(8, 418)(9, 419)(10, 404)(11, 423)(12, 426)(13, 427)(14, 406)(15, 431)(16, 407)(17, 433)(18, 436)(19, 437)(20, 409)(21, 439)(22, 410)(23, 443)(24, 411)(25, 445)(26, 448)(27, 449)(28, 413)(29, 451)(30, 414)(31, 455)(32, 416)(33, 457)(34, 417)(35, 459)(36, 462)(37, 463)(38, 420)(39, 465)(40, 421)(41, 467)(42, 422)(43, 470)(44, 424)(45, 472)(46, 425)(47, 474)(48, 477)(49, 478)(50, 428)(51, 480)(52, 429)(53, 482)(54, 430)(55, 485)(56, 432)(57, 487)(58, 434)(59, 489)(60, 435)(61, 491)(62, 442)(63, 494)(64, 438)(65, 496)(66, 440)(67, 498)(68, 441)(69, 500)(70, 502)(71, 444)(72, 504)(73, 446)(74, 506)(75, 447)(76, 508)(77, 454)(78, 511)(79, 450)(80, 513)(81, 452)(82, 515)(83, 453)(84, 517)(85, 519)(86, 456)(87, 520)(88, 458)(89, 522)(90, 460)(91, 524)(92, 461)(93, 526)(94, 528)(95, 464)(96, 529)(97, 466)(98, 531)(99, 468)(100, 533)(101, 469)(102, 535)(103, 471)(104, 536)(105, 473)(106, 538)(107, 475)(108, 540)(109, 476)(110, 542)(111, 544)(112, 479)(113, 545)(114, 481)(115, 547)(116, 483)(117, 549)(118, 484)(119, 486)(120, 551)(121, 488)(122, 552)(123, 490)(124, 554)(125, 492)(126, 556)(127, 493)(128, 495)(129, 558)(130, 497)(131, 559)(132, 499)(133, 561)(134, 501)(135, 503)(136, 563)(137, 505)(138, 564)(139, 507)(140, 566)(141, 509)(142, 568)(143, 510)(144, 512)(145, 570)(146, 514)(147, 571)(148, 516)(149, 573)(150, 518)(151, 521)(152, 575)(153, 523)(154, 576)(155, 525)(156, 578)(157, 527)(158, 530)(159, 580)(160, 532)(161, 581)(162, 534)(163, 537)(164, 583)(165, 539)(166, 584)(167, 541)(168, 586)(169, 543)(170, 546)(171, 588)(172, 548)(173, 589)(174, 550)(175, 553)(176, 591)(177, 555)(178, 592)(179, 557)(180, 560)(181, 594)(182, 562)(183, 565)(184, 595)(185, 567)(186, 596)(187, 569)(188, 572)(189, 598)(190, 574)(191, 577)(192, 599)(193, 579)(194, 582)(195, 585)(196, 600)(197, 587)(198, 590)(199, 593)(200, 597)(201, 601)(202, 602)(203, 603)(204, 604)(205, 605)(206, 606)(207, 607)(208, 608)(209, 609)(210, 610)(211, 611)(212, 612)(213, 613)(214, 614)(215, 615)(216, 616)(217, 617)(218, 618)(219, 619)(220, 620)(221, 621)(222, 622)(223, 623)(224, 624)(225, 625)(226, 626)(227, 627)(228, 628)(229, 629)(230, 630)(231, 631)(232, 632)(233, 633)(234, 634)(235, 635)(236, 636)(237, 637)(238, 638)(239, 639)(240, 640)(241, 641)(242, 642)(243, 643)(244, 644)(245, 645)(246, 646)(247, 647)(248, 648)(249, 649)(250, 650)(251, 651)(252, 652)(253, 653)(254, 654)(255, 655)(256, 656)(257, 657)(258, 658)(259, 659)(260, 660)(261, 661)(262, 662)(263, 663)(264, 664)(265, 665)(266, 666)(267, 667)(268, 668)(269, 669)(270, 670)(271, 671)(272, 672)(273, 673)(274, 674)(275, 675)(276, 676)(277, 677)(278, 678)(279, 679)(280, 680)(281, 681)(282, 682)(283, 683)(284, 684)(285, 685)(286, 686)(287, 687)(288, 688)(289, 689)(290, 690)(291, 691)(292, 692)(293, 693)(294, 694)(295, 695)(296, 696)(297, 697)(298, 698)(299, 699)(300, 700)(301, 701)(302, 702)(303, 703)(304, 704)(305, 705)(306, 706)(307, 707)(308, 708)(309, 709)(310, 710)(311, 711)(312, 712)(313, 713)(314, 714)(315, 715)(316, 716)(317, 717)(318, 718)(319, 719)(320, 720)(321, 721)(322, 722)(323, 723)(324, 724)(325, 725)(326, 726)(327, 727)(328, 728)(329, 729)(330, 730)(331, 731)(332, 732)(333, 733)(334, 734)(335, 735)(336, 736)(337, 737)(338, 738)(339, 739)(340, 740)(341, 741)(342, 742)(343, 743)(344, 744)(345, 745)(346, 746)(347, 747)(348, 748)(349, 749)(350, 750)(351, 751)(352, 752)(353, 753)(354, 754)(355, 755)(356, 756)(357, 757)(358, 758)(359, 759)(360, 760)(361, 761)(362, 762)(363, 763)(364, 764)(365, 765)(366, 766)(367, 767)(368, 768)(369, 769)(370, 770)(371, 771)(372, 772)(373, 773)(374, 774)(375, 775)(376, 776)(377, 777)(378, 778)(379, 779)(380, 780)(381, 781)(382, 782)(383, 783)(384, 784)(385, 785)(386, 786)(387, 787)(388, 788)(389, 789)(390, 790)(391, 791)(392, 792)(393, 793)(394, 794)(395, 795)(396, 796)(397, 797)(398, 798)(399, 799)(400, 800) local type(s) :: { ( 8, 20 ), ( 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E16.1271 Graph:: simple bipartite v = 300 e = 400 f = 70 degree seq :: [ 2^200, 4^100 ] E16.1273 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10}) Quotient :: dipole Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, Y3^4, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, Y3^-2 * Y1 * Y3^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1 * Y3^-1 * Y1^-1)^2, (Y3 * Y1^-1)^4, (Y3 * Y1^-1 * Y3^-1 * Y1^-1)^2, Y1^10, Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1, Y1^-2 * Y3 * Y1^3 * Y3 * Y1^-2 * Y3^-1 * Y1^-3 * Y3^-1, Y1^-3 * Y3 * Y1^-4 * Y3 * Y1^3 * Y3^-1 * Y1^-4 * Y3^-1 ] Map:: polytopal R = (1, 201, 2, 202, 5, 205, 11, 211, 23, 223, 43, 243, 42, 242, 22, 222, 10, 210, 4, 204)(3, 203, 7, 207, 15, 215, 31, 231, 55, 255, 85, 285, 62, 262, 36, 236, 18, 218, 8, 208)(6, 206, 13, 213, 27, 227, 51, 251, 81, 281, 116, 316, 84, 284, 54, 254, 30, 230, 14, 214)(9, 209, 19, 219, 37, 237, 63, 263, 94, 294, 128, 328, 95, 295, 64, 264, 38, 238, 20, 220)(12, 212, 25, 225, 47, 247, 77, 277, 112, 312, 147, 347, 115, 315, 80, 280, 50, 250, 26, 226)(16, 216, 33, 233, 58, 258, 89, 289, 123, 323, 137, 337, 105, 305, 75, 275, 48, 248, 29, 229)(17, 217, 34, 234, 59, 259, 90, 290, 124, 324, 136, 336, 106, 306, 74, 274, 49, 249, 28, 228)(21, 221, 39, 239, 65, 265, 96, 296, 129, 329, 158, 358, 130, 330, 97, 297, 66, 266, 40, 240)(24, 224, 45, 245, 73, 273, 108, 308, 143, 343, 171, 371, 146, 346, 111, 311, 76, 276, 46, 246)(32, 232, 53, 253, 78, 278, 110, 310, 140, 340, 165, 365, 154, 354, 122, 322, 88, 288, 57, 257)(35, 235, 52, 252, 79, 279, 109, 309, 141, 341, 164, 364, 155, 355, 125, 325, 91, 291, 60, 260)(41, 241, 67, 267, 98, 298, 131, 331, 159, 359, 180, 380, 160, 360, 132, 332, 99, 299, 68, 268)(44, 244, 71, 271, 104, 304, 139, 339, 167, 367, 187, 387, 170, 370, 142, 342, 107, 307, 72, 272)(56, 256, 87, 287, 121, 321, 153, 353, 177, 377, 185, 385, 168, 368, 145, 345, 113, 313, 83, 283)(61, 261, 92, 292, 126, 326, 156, 356, 178, 378, 184, 384, 169, 369, 144, 344, 114, 314, 82, 282)(69, 269, 100, 300, 133, 333, 161, 361, 181, 381, 194, 394, 182, 382, 162, 362, 134, 334, 101, 301)(70, 270, 102, 302, 135, 335, 163, 363, 183, 383, 195, 395, 186, 386, 166, 366, 138, 338, 103, 303)(86, 286, 118, 318, 148, 348, 173, 373, 188, 388, 197, 397, 192, 392, 176, 376, 152, 352, 120, 320)(93, 293, 117, 317, 149, 349, 172, 372, 189, 389, 196, 396, 193, 393, 179, 379, 157, 357, 127, 327)(119, 319, 151, 351, 175, 375, 191, 391, 199, 399, 200, 400, 198, 398, 190, 390, 174, 374, 150, 350)(401, 601)(402, 602)(403, 603)(404, 604)(405, 605)(406, 606)(407, 607)(408, 608)(409, 609)(410, 610)(411, 611)(412, 612)(413, 613)(414, 614)(415, 615)(416, 616)(417, 617)(418, 618)(419, 619)(420, 620)(421, 621)(422, 622)(423, 623)(424, 624)(425, 625)(426, 626)(427, 627)(428, 628)(429, 629)(430, 630)(431, 631)(432, 632)(433, 633)(434, 634)(435, 635)(436, 636)(437, 637)(438, 638)(439, 639)(440, 640)(441, 641)(442, 642)(443, 643)(444, 644)(445, 645)(446, 646)(447, 647)(448, 648)(449, 649)(450, 650)(451, 651)(452, 652)(453, 653)(454, 654)(455, 655)(456, 656)(457, 657)(458, 658)(459, 659)(460, 660)(461, 661)(462, 662)(463, 663)(464, 664)(465, 665)(466, 666)(467, 667)(468, 668)(469, 669)(470, 670)(471, 671)(472, 672)(473, 673)(474, 674)(475, 675)(476, 676)(477, 677)(478, 678)(479, 679)(480, 680)(481, 681)(482, 682)(483, 683)(484, 684)(485, 685)(486, 686)(487, 687)(488, 688)(489, 689)(490, 690)(491, 691)(492, 692)(493, 693)(494, 694)(495, 695)(496, 696)(497, 697)(498, 698)(499, 699)(500, 700)(501, 701)(502, 702)(503, 703)(504, 704)(505, 705)(506, 706)(507, 707)(508, 708)(509, 709)(510, 710)(511, 711)(512, 712)(513, 713)(514, 714)(515, 715)(516, 716)(517, 717)(518, 718)(519, 719)(520, 720)(521, 721)(522, 722)(523, 723)(524, 724)(525, 725)(526, 726)(527, 727)(528, 728)(529, 729)(530, 730)(531, 731)(532, 732)(533, 733)(534, 734)(535, 735)(536, 736)(537, 737)(538, 738)(539, 739)(540, 740)(541, 741)(542, 742)(543, 743)(544, 744)(545, 745)(546, 746)(547, 747)(548, 748)(549, 749)(550, 750)(551, 751)(552, 752)(553, 753)(554, 754)(555, 755)(556, 756)(557, 757)(558, 758)(559, 759)(560, 760)(561, 761)(562, 762)(563, 763)(564, 764)(565, 765)(566, 766)(567, 767)(568, 768)(569, 769)(570, 770)(571, 771)(572, 772)(573, 773)(574, 774)(575, 775)(576, 776)(577, 777)(578, 778)(579, 779)(580, 780)(581, 781)(582, 782)(583, 783)(584, 784)(585, 785)(586, 786)(587, 787)(588, 788)(589, 789)(590, 790)(591, 791)(592, 792)(593, 793)(594, 794)(595, 795)(596, 796)(597, 797)(598, 798)(599, 799)(600, 800) L = (1, 403)(2, 406)(3, 401)(4, 409)(5, 412)(6, 402)(7, 416)(8, 417)(9, 404)(10, 421)(11, 424)(12, 405)(13, 428)(14, 429)(15, 432)(16, 407)(17, 408)(18, 435)(19, 434)(20, 433)(21, 410)(22, 441)(23, 444)(24, 411)(25, 448)(26, 449)(27, 452)(28, 413)(29, 414)(30, 453)(31, 456)(32, 415)(33, 420)(34, 419)(35, 418)(36, 461)(37, 460)(38, 457)(39, 458)(40, 459)(41, 422)(42, 469)(43, 470)(44, 423)(45, 474)(46, 475)(47, 478)(48, 425)(49, 426)(50, 479)(51, 482)(52, 427)(53, 430)(54, 483)(55, 486)(56, 431)(57, 438)(58, 439)(59, 440)(60, 437)(61, 436)(62, 493)(63, 492)(64, 487)(65, 488)(66, 491)(67, 490)(68, 489)(69, 442)(70, 443)(71, 505)(72, 506)(73, 509)(74, 445)(75, 446)(76, 510)(77, 513)(78, 447)(79, 450)(80, 514)(81, 517)(82, 451)(83, 454)(84, 518)(85, 519)(86, 455)(87, 464)(88, 465)(89, 468)(90, 467)(91, 466)(92, 463)(93, 462)(94, 527)(95, 520)(96, 521)(97, 526)(98, 525)(99, 522)(100, 523)(101, 524)(102, 536)(103, 537)(104, 540)(105, 471)(106, 472)(107, 541)(108, 544)(109, 473)(110, 476)(111, 545)(112, 548)(113, 477)(114, 480)(115, 549)(116, 550)(117, 481)(118, 484)(119, 485)(120, 495)(121, 496)(122, 499)(123, 500)(124, 501)(125, 498)(126, 497)(127, 494)(128, 551)(129, 552)(130, 557)(131, 556)(132, 553)(133, 554)(134, 555)(135, 564)(136, 502)(137, 503)(138, 565)(139, 568)(140, 504)(141, 507)(142, 569)(143, 572)(144, 508)(145, 511)(146, 573)(147, 574)(148, 512)(149, 515)(150, 516)(151, 528)(152, 529)(153, 532)(154, 533)(155, 534)(156, 531)(157, 530)(158, 575)(159, 579)(160, 576)(161, 577)(162, 578)(163, 584)(164, 535)(165, 538)(166, 585)(167, 588)(168, 539)(169, 542)(170, 589)(171, 590)(172, 543)(173, 546)(174, 547)(175, 558)(176, 560)(177, 561)(178, 562)(179, 559)(180, 591)(181, 592)(182, 593)(183, 596)(184, 563)(185, 566)(186, 597)(187, 598)(188, 567)(189, 570)(190, 571)(191, 580)(192, 581)(193, 582)(194, 599)(195, 600)(196, 583)(197, 586)(198, 587)(199, 594)(200, 595)(201, 601)(202, 602)(203, 603)(204, 604)(205, 605)(206, 606)(207, 607)(208, 608)(209, 609)(210, 610)(211, 611)(212, 612)(213, 613)(214, 614)(215, 615)(216, 616)(217, 617)(218, 618)(219, 619)(220, 620)(221, 621)(222, 622)(223, 623)(224, 624)(225, 625)(226, 626)(227, 627)(228, 628)(229, 629)(230, 630)(231, 631)(232, 632)(233, 633)(234, 634)(235, 635)(236, 636)(237, 637)(238, 638)(239, 639)(240, 640)(241, 641)(242, 642)(243, 643)(244, 644)(245, 645)(246, 646)(247, 647)(248, 648)(249, 649)(250, 650)(251, 651)(252, 652)(253, 653)(254, 654)(255, 655)(256, 656)(257, 657)(258, 658)(259, 659)(260, 660)(261, 661)(262, 662)(263, 663)(264, 664)(265, 665)(266, 666)(267, 667)(268, 668)(269, 669)(270, 670)(271, 671)(272, 672)(273, 673)(274, 674)(275, 675)(276, 676)(277, 677)(278, 678)(279, 679)(280, 680)(281, 681)(282, 682)(283, 683)(284, 684)(285, 685)(286, 686)(287, 687)(288, 688)(289, 689)(290, 690)(291, 691)(292, 692)(293, 693)(294, 694)(295, 695)(296, 696)(297, 697)(298, 698)(299, 699)(300, 700)(301, 701)(302, 702)(303, 703)(304, 704)(305, 705)(306, 706)(307, 707)(308, 708)(309, 709)(310, 710)(311, 711)(312, 712)(313, 713)(314, 714)(315, 715)(316, 716)(317, 717)(318, 718)(319, 719)(320, 720)(321, 721)(322, 722)(323, 723)(324, 724)(325, 725)(326, 726)(327, 727)(328, 728)(329, 729)(330, 730)(331, 731)(332, 732)(333, 733)(334, 734)(335, 735)(336, 736)(337, 737)(338, 738)(339, 739)(340, 740)(341, 741)(342, 742)(343, 743)(344, 744)(345, 745)(346, 746)(347, 747)(348, 748)(349, 749)(350, 750)(351, 751)(352, 752)(353, 753)(354, 754)(355, 755)(356, 756)(357, 757)(358, 758)(359, 759)(360, 760)(361, 761)(362, 762)(363, 763)(364, 764)(365, 765)(366, 766)(367, 767)(368, 768)(369, 769)(370, 770)(371, 771)(372, 772)(373, 773)(374, 774)(375, 775)(376, 776)(377, 777)(378, 778)(379, 779)(380, 780)(381, 781)(382, 782)(383, 783)(384, 784)(385, 785)(386, 786)(387, 787)(388, 788)(389, 789)(390, 790)(391, 791)(392, 792)(393, 793)(394, 794)(395, 795)(396, 796)(397, 797)(398, 798)(399, 799)(400, 800) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.1270 Graph:: simple bipartite v = 220 e = 400 f = 150 degree seq :: [ 2^200, 20^20 ] E16.1274 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10}) Quotient :: dipole Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^4, (Y3 * Y2^-1)^4, (Y2^-1 * Y1 * Y2 * Y1)^2, Y2^10, Y2^2 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1, (Y2^3 * Y1 * Y2^-3 * Y1)^2, Y2^4 * Y1 * Y2^4 * Y1 * Y2^-4 * Y1 * Y2^-4 * Y1 ] Map:: R = (1, 201, 2, 202)(3, 203, 7, 207)(4, 204, 9, 209)(5, 205, 11, 211)(6, 206, 13, 213)(8, 208, 17, 217)(10, 210, 21, 221)(12, 212, 25, 225)(14, 214, 29, 229)(15, 215, 28, 228)(16, 216, 24, 224)(18, 218, 35, 235)(19, 219, 27, 227)(20, 220, 23, 223)(22, 222, 41, 241)(26, 226, 47, 247)(30, 230, 53, 253)(31, 231, 51, 251)(32, 232, 45, 245)(33, 233, 44, 244)(34, 234, 50, 250)(36, 236, 61, 261)(37, 237, 52, 252)(38, 238, 46, 246)(39, 239, 43, 243)(40, 240, 49, 249)(42, 242, 69, 269)(48, 248, 76, 276)(54, 254, 84, 284)(55, 255, 83, 283)(56, 256, 75, 275)(57, 257, 72, 272)(58, 258, 80, 280)(59, 259, 79, 279)(60, 260, 71, 271)(62, 262, 93, 293)(63, 263, 82, 282)(64, 264, 74, 274)(65, 265, 73, 273)(66, 266, 81, 281)(67, 267, 78, 278)(68, 268, 70, 270)(77, 277, 110, 310)(85, 285, 117, 317)(86, 286, 108, 308)(87, 287, 107, 307)(88, 288, 116, 316)(89, 289, 113, 313)(90, 290, 104, 304)(91, 291, 103, 303)(92, 292, 112, 312)(94, 294, 118, 318)(95, 295, 109, 309)(96, 296, 106, 306)(97, 297, 115, 315)(98, 298, 114, 314)(99, 299, 105, 305)(100, 300, 102, 302)(101, 301, 111, 311)(119, 319, 143, 343)(120, 320, 140, 340)(121, 321, 149, 349)(122, 322, 148, 348)(123, 323, 139, 339)(124, 324, 136, 336)(125, 325, 145, 345)(126, 326, 144, 344)(127, 327, 135, 335)(128, 328, 142, 342)(129, 329, 141, 341)(130, 330, 150, 350)(131, 331, 147, 347)(132, 332, 138, 338)(133, 333, 137, 337)(134, 334, 146, 346)(151, 351, 169, 369)(152, 352, 173, 373)(153, 353, 166, 366)(154, 354, 165, 365)(155, 355, 172, 372)(156, 356, 170, 370)(157, 357, 163, 363)(158, 358, 168, 368)(159, 359, 174, 374)(160, 360, 167, 367)(161, 361, 164, 364)(162, 362, 171, 371)(175, 375, 187, 387)(176, 376, 184, 384)(177, 377, 189, 389)(178, 378, 188, 388)(179, 379, 183, 383)(180, 380, 186, 386)(181, 381, 185, 385)(182, 382, 190, 390)(191, 391, 197, 397)(192, 392, 198, 398)(193, 393, 195, 395)(194, 394, 196, 396)(199, 399, 200, 400)(401, 601, 403, 603, 408, 608, 418, 618, 436, 636, 462, 662, 442, 642, 422, 622, 410, 610, 404, 604)(402, 602, 405, 605, 412, 612, 426, 626, 448, 648, 477, 677, 454, 654, 430, 630, 414, 614, 406, 606)(407, 607, 415, 615, 431, 631, 455, 655, 485, 685, 519, 719, 486, 686, 456, 656, 432, 632, 416, 616)(409, 609, 419, 619, 437, 637, 463, 663, 494, 694, 528, 728, 495, 695, 464, 664, 438, 638, 420, 620)(411, 611, 423, 623, 443, 643, 470, 670, 502, 702, 535, 735, 503, 703, 471, 671, 444, 644, 424, 624)(413, 613, 427, 627, 449, 649, 478, 678, 511, 711, 544, 744, 512, 712, 479, 679, 450, 650, 428, 628)(417, 617, 433, 633, 457, 657, 487, 687, 520, 720, 551, 751, 521, 721, 488, 688, 458, 658, 434, 634)(421, 621, 439, 639, 465, 665, 496, 696, 529, 729, 558, 758, 530, 730, 497, 697, 466, 666, 440, 640)(425, 625, 445, 645, 472, 672, 504, 704, 536, 736, 563, 763, 537, 737, 505, 705, 473, 673, 446, 646)(429, 629, 451, 651, 480, 680, 513, 713, 545, 745, 570, 770, 546, 746, 514, 714, 481, 681, 452, 652)(435, 635, 459, 659, 489, 689, 522, 722, 552, 752, 575, 775, 553, 753, 523, 723, 490, 690, 460, 660)(441, 641, 467, 667, 498, 698, 531, 731, 559, 759, 580, 780, 560, 760, 532, 732, 499, 699, 468, 668)(447, 647, 474, 674, 506, 706, 538, 738, 564, 764, 583, 783, 565, 765, 539, 739, 507, 707, 475, 675)(453, 653, 482, 682, 515, 715, 547, 747, 571, 771, 588, 788, 572, 772, 548, 748, 516, 716, 483, 683)(461, 661, 491, 691, 524, 724, 554, 754, 576, 776, 591, 791, 577, 777, 555, 755, 525, 725, 492, 692)(469, 669, 500, 700, 533, 733, 561, 761, 581, 781, 594, 794, 582, 782, 562, 762, 534, 734, 501, 701)(476, 676, 508, 708, 540, 740, 566, 766, 584, 784, 595, 795, 585, 785, 567, 767, 541, 741, 509, 709)(484, 684, 517, 717, 549, 749, 573, 773, 589, 789, 598, 798, 590, 790, 574, 774, 550, 750, 518, 718)(493, 693, 526, 726, 556, 756, 578, 778, 592, 792, 599, 799, 593, 793, 579, 779, 557, 757, 527, 727)(510, 710, 542, 742, 568, 768, 586, 786, 596, 796, 600, 800, 597, 797, 587, 787, 569, 769, 543, 743) L = (1, 402)(2, 401)(3, 407)(4, 409)(5, 411)(6, 413)(7, 403)(8, 417)(9, 404)(10, 421)(11, 405)(12, 425)(13, 406)(14, 429)(15, 428)(16, 424)(17, 408)(18, 435)(19, 427)(20, 423)(21, 410)(22, 441)(23, 420)(24, 416)(25, 412)(26, 447)(27, 419)(28, 415)(29, 414)(30, 453)(31, 451)(32, 445)(33, 444)(34, 450)(35, 418)(36, 461)(37, 452)(38, 446)(39, 443)(40, 449)(41, 422)(42, 469)(43, 439)(44, 433)(45, 432)(46, 438)(47, 426)(48, 476)(49, 440)(50, 434)(51, 431)(52, 437)(53, 430)(54, 484)(55, 483)(56, 475)(57, 472)(58, 480)(59, 479)(60, 471)(61, 436)(62, 493)(63, 482)(64, 474)(65, 473)(66, 481)(67, 478)(68, 470)(69, 442)(70, 468)(71, 460)(72, 457)(73, 465)(74, 464)(75, 456)(76, 448)(77, 510)(78, 467)(79, 459)(80, 458)(81, 466)(82, 463)(83, 455)(84, 454)(85, 517)(86, 508)(87, 507)(88, 516)(89, 513)(90, 504)(91, 503)(92, 512)(93, 462)(94, 518)(95, 509)(96, 506)(97, 515)(98, 514)(99, 505)(100, 502)(101, 511)(102, 500)(103, 491)(104, 490)(105, 499)(106, 496)(107, 487)(108, 486)(109, 495)(110, 477)(111, 501)(112, 492)(113, 489)(114, 498)(115, 497)(116, 488)(117, 485)(118, 494)(119, 543)(120, 540)(121, 549)(122, 548)(123, 539)(124, 536)(125, 545)(126, 544)(127, 535)(128, 542)(129, 541)(130, 550)(131, 547)(132, 538)(133, 537)(134, 546)(135, 527)(136, 524)(137, 533)(138, 532)(139, 523)(140, 520)(141, 529)(142, 528)(143, 519)(144, 526)(145, 525)(146, 534)(147, 531)(148, 522)(149, 521)(150, 530)(151, 569)(152, 573)(153, 566)(154, 565)(155, 572)(156, 570)(157, 563)(158, 568)(159, 574)(160, 567)(161, 564)(162, 571)(163, 557)(164, 561)(165, 554)(166, 553)(167, 560)(168, 558)(169, 551)(170, 556)(171, 562)(172, 555)(173, 552)(174, 559)(175, 587)(176, 584)(177, 589)(178, 588)(179, 583)(180, 586)(181, 585)(182, 590)(183, 579)(184, 576)(185, 581)(186, 580)(187, 575)(188, 578)(189, 577)(190, 582)(191, 597)(192, 598)(193, 595)(194, 596)(195, 593)(196, 594)(197, 591)(198, 592)(199, 600)(200, 599)(201, 601)(202, 602)(203, 603)(204, 604)(205, 605)(206, 606)(207, 607)(208, 608)(209, 609)(210, 610)(211, 611)(212, 612)(213, 613)(214, 614)(215, 615)(216, 616)(217, 617)(218, 618)(219, 619)(220, 620)(221, 621)(222, 622)(223, 623)(224, 624)(225, 625)(226, 626)(227, 627)(228, 628)(229, 629)(230, 630)(231, 631)(232, 632)(233, 633)(234, 634)(235, 635)(236, 636)(237, 637)(238, 638)(239, 639)(240, 640)(241, 641)(242, 642)(243, 643)(244, 644)(245, 645)(246, 646)(247, 647)(248, 648)(249, 649)(250, 650)(251, 651)(252, 652)(253, 653)(254, 654)(255, 655)(256, 656)(257, 657)(258, 658)(259, 659)(260, 660)(261, 661)(262, 662)(263, 663)(264, 664)(265, 665)(266, 666)(267, 667)(268, 668)(269, 669)(270, 670)(271, 671)(272, 672)(273, 673)(274, 674)(275, 675)(276, 676)(277, 677)(278, 678)(279, 679)(280, 680)(281, 681)(282, 682)(283, 683)(284, 684)(285, 685)(286, 686)(287, 687)(288, 688)(289, 689)(290, 690)(291, 691)(292, 692)(293, 693)(294, 694)(295, 695)(296, 696)(297, 697)(298, 698)(299, 699)(300, 700)(301, 701)(302, 702)(303, 703)(304, 704)(305, 705)(306, 706)(307, 707)(308, 708)(309, 709)(310, 710)(311, 711)(312, 712)(313, 713)(314, 714)(315, 715)(316, 716)(317, 717)(318, 718)(319, 719)(320, 720)(321, 721)(322, 722)(323, 723)(324, 724)(325, 725)(326, 726)(327, 727)(328, 728)(329, 729)(330, 730)(331, 731)(332, 732)(333, 733)(334, 734)(335, 735)(336, 736)(337, 737)(338, 738)(339, 739)(340, 740)(341, 741)(342, 742)(343, 743)(344, 744)(345, 745)(346, 746)(347, 747)(348, 748)(349, 749)(350, 750)(351, 751)(352, 752)(353, 753)(354, 754)(355, 755)(356, 756)(357, 757)(358, 758)(359, 759)(360, 760)(361, 761)(362, 762)(363, 763)(364, 764)(365, 765)(366, 766)(367, 767)(368, 768)(369, 769)(370, 770)(371, 771)(372, 772)(373, 773)(374, 774)(375, 775)(376, 776)(377, 777)(378, 778)(379, 779)(380, 780)(381, 781)(382, 782)(383, 783)(384, 784)(385, 785)(386, 786)(387, 787)(388, 788)(389, 789)(390, 790)(391, 791)(392, 792)(393, 793)(394, 794)(395, 795)(396, 796)(397, 797)(398, 798)(399, 799)(400, 800) 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 E16.1275 Graph:: bipartite v = 120 e = 400 f = 250 degree seq :: [ 4^100, 20^20 ] E16.1275 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10}) Quotient :: dipole Aut^+ = (D10 x D10) : C2 (small group id <200, 43>) Aut = C2 x ((D10 x D10) : C2) (small group id <400, 211>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^4, (Y1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-2, Y1^-2 * Y3^3 * Y1^-1 * Y3^-2 * Y1 * Y3^-2 * Y1^2 * Y3, Y3^3 * Y1^-2 * Y3^-6 * Y1 * Y3^-1 * Y1^-1, (Y3^4 * Y1^-1 * Y3 * Y1^-1)^2, (Y3 * Y2^-1)^10 ] Map:: polytopal R = (1, 201, 2, 202, 6, 206, 4, 204)(3, 203, 9, 209, 21, 221, 11, 211)(5, 205, 13, 213, 18, 218, 7, 207)(8, 208, 19, 219, 34, 234, 15, 215)(10, 210, 23, 223, 36, 236, 25, 225)(12, 212, 16, 216, 35, 235, 28, 228)(14, 214, 31, 231, 33, 233, 29, 229)(17, 217, 37, 237, 22, 222, 39, 239)(20, 220, 43, 243, 27, 227, 41, 241)(24, 224, 47, 247, 78, 278, 49, 249)(26, 226, 45, 245, 77, 277, 52, 252)(30, 230, 55, 255, 70, 270, 40, 240)(32, 232, 59, 259, 69, 269, 57, 257)(38, 238, 65, 265, 56, 256, 67, 267)(42, 242, 71, 271, 99, 299, 62, 262)(44, 244, 75, 275, 98, 298, 73, 273)(46, 246, 79, 279, 51, 251, 68, 268)(48, 248, 81, 281, 103, 303, 83, 283)(50, 250, 64, 264, 102, 302, 86, 286)(53, 253, 74, 274, 101, 301, 90, 290)(54, 254, 63, 263, 100, 300, 85, 285)(58, 258, 72, 272, 97, 297, 61, 261)(60, 260, 95, 295, 96, 296, 93, 293)(66, 266, 104, 304, 80, 280, 106, 306)(76, 276, 114, 314, 89, 289, 112, 312)(82, 282, 119, 319, 146, 346, 120, 320)(84, 284, 116, 316, 155, 355, 123, 323)(87, 287, 117, 317, 154, 354, 127, 327)(88, 288, 115, 315, 153, 353, 122, 322)(91, 291, 129, 329, 144, 344, 109, 309)(92, 292, 131, 331, 145, 345, 107, 307)(94, 294, 130, 330, 147, 347, 108, 308)(105, 305, 141, 341, 132, 332, 142, 342)(110, 310, 148, 348, 164, 364, 137, 337)(111, 311, 150, 350, 165, 365, 135, 335)(113, 313, 149, 349, 166, 366, 136, 336)(118, 318, 152, 352, 126, 326, 143, 343)(121, 321, 134, 334, 133, 333, 151, 351)(124, 324, 138, 338, 167, 367, 160, 360)(125, 325, 140, 340, 168, 368, 156, 356)(128, 328, 139, 339, 169, 369, 159, 359)(157, 357, 175, 375, 193, 393, 180, 380)(158, 358, 177, 377, 189, 389, 172, 372)(161, 361, 176, 376, 188, 388, 179, 379)(162, 362, 182, 382, 190, 390, 170, 370)(163, 363, 183, 383, 186, 386, 171, 371)(173, 373, 191, 391, 196, 396, 184, 384)(174, 374, 192, 392, 178, 378, 185, 385)(181, 381, 187, 387, 197, 397, 194, 394)(195, 395, 199, 399, 200, 400, 198, 398)(401, 601)(402, 602)(403, 603)(404, 604)(405, 605)(406, 606)(407, 607)(408, 608)(409, 609)(410, 610)(411, 611)(412, 612)(413, 613)(414, 614)(415, 615)(416, 616)(417, 617)(418, 618)(419, 619)(420, 620)(421, 621)(422, 622)(423, 623)(424, 624)(425, 625)(426, 626)(427, 627)(428, 628)(429, 629)(430, 630)(431, 631)(432, 632)(433, 633)(434, 634)(435, 635)(436, 636)(437, 637)(438, 638)(439, 639)(440, 640)(441, 641)(442, 642)(443, 643)(444, 644)(445, 645)(446, 646)(447, 647)(448, 648)(449, 649)(450, 650)(451, 651)(452, 652)(453, 653)(454, 654)(455, 655)(456, 656)(457, 657)(458, 658)(459, 659)(460, 660)(461, 661)(462, 662)(463, 663)(464, 664)(465, 665)(466, 666)(467, 667)(468, 668)(469, 669)(470, 670)(471, 671)(472, 672)(473, 673)(474, 674)(475, 675)(476, 676)(477, 677)(478, 678)(479, 679)(480, 680)(481, 681)(482, 682)(483, 683)(484, 684)(485, 685)(486, 686)(487, 687)(488, 688)(489, 689)(490, 690)(491, 691)(492, 692)(493, 693)(494, 694)(495, 695)(496, 696)(497, 697)(498, 698)(499, 699)(500, 700)(501, 701)(502, 702)(503, 703)(504, 704)(505, 705)(506, 706)(507, 707)(508, 708)(509, 709)(510, 710)(511, 711)(512, 712)(513, 713)(514, 714)(515, 715)(516, 716)(517, 717)(518, 718)(519, 719)(520, 720)(521, 721)(522, 722)(523, 723)(524, 724)(525, 725)(526, 726)(527, 727)(528, 728)(529, 729)(530, 730)(531, 731)(532, 732)(533, 733)(534, 734)(535, 735)(536, 736)(537, 737)(538, 738)(539, 739)(540, 740)(541, 741)(542, 742)(543, 743)(544, 744)(545, 745)(546, 746)(547, 747)(548, 748)(549, 749)(550, 750)(551, 751)(552, 752)(553, 753)(554, 754)(555, 755)(556, 756)(557, 757)(558, 758)(559, 759)(560, 760)(561, 761)(562, 762)(563, 763)(564, 764)(565, 765)(566, 766)(567, 767)(568, 768)(569, 769)(570, 770)(571, 771)(572, 772)(573, 773)(574, 774)(575, 775)(576, 776)(577, 777)(578, 778)(579, 779)(580, 780)(581, 781)(582, 782)(583, 783)(584, 784)(585, 785)(586, 786)(587, 787)(588, 788)(589, 789)(590, 790)(591, 791)(592, 792)(593, 793)(594, 794)(595, 795)(596, 796)(597, 797)(598, 798)(599, 799)(600, 800) L = (1, 403)(2, 407)(3, 410)(4, 412)(5, 401)(6, 415)(7, 417)(8, 402)(9, 404)(10, 424)(11, 426)(12, 427)(13, 429)(14, 405)(15, 433)(16, 406)(17, 438)(18, 440)(19, 441)(20, 408)(21, 437)(22, 409)(23, 411)(24, 448)(25, 450)(26, 451)(27, 453)(28, 454)(29, 434)(30, 413)(31, 457)(32, 414)(33, 461)(34, 462)(35, 423)(36, 416)(37, 418)(38, 466)(39, 468)(40, 469)(41, 428)(42, 419)(43, 473)(44, 420)(45, 421)(46, 422)(47, 425)(48, 482)(49, 484)(50, 485)(51, 487)(52, 488)(53, 489)(54, 486)(55, 465)(56, 430)(57, 470)(58, 431)(59, 493)(60, 432)(61, 496)(62, 498)(63, 435)(64, 436)(65, 439)(66, 505)(67, 507)(68, 452)(69, 508)(70, 509)(71, 458)(72, 442)(73, 499)(74, 443)(75, 512)(76, 444)(77, 447)(78, 445)(79, 504)(80, 446)(81, 449)(82, 460)(83, 521)(84, 522)(85, 524)(86, 525)(87, 526)(88, 523)(89, 518)(90, 528)(91, 455)(92, 456)(93, 497)(94, 459)(95, 520)(96, 534)(97, 535)(98, 536)(99, 537)(100, 474)(101, 463)(102, 481)(103, 464)(104, 467)(105, 476)(106, 543)(107, 544)(108, 546)(109, 545)(110, 471)(111, 472)(112, 490)(113, 475)(114, 542)(115, 477)(116, 478)(117, 479)(118, 480)(119, 483)(120, 547)(121, 556)(122, 557)(123, 558)(124, 559)(125, 551)(126, 539)(127, 561)(128, 560)(129, 494)(130, 491)(131, 541)(132, 492)(133, 495)(134, 503)(135, 564)(136, 532)(137, 565)(138, 500)(139, 501)(140, 502)(141, 506)(142, 566)(143, 527)(144, 570)(145, 571)(146, 516)(147, 572)(148, 513)(149, 510)(150, 533)(151, 511)(152, 514)(153, 517)(154, 515)(155, 519)(156, 578)(157, 579)(158, 530)(159, 576)(160, 581)(161, 580)(162, 529)(163, 531)(164, 584)(165, 585)(166, 586)(167, 540)(168, 538)(169, 552)(170, 589)(171, 549)(172, 590)(173, 548)(174, 550)(175, 553)(176, 554)(177, 555)(178, 594)(179, 587)(180, 595)(181, 592)(182, 563)(183, 562)(184, 583)(185, 568)(186, 596)(187, 567)(188, 569)(189, 575)(190, 598)(191, 574)(192, 573)(193, 577)(194, 599)(195, 582)(196, 600)(197, 588)(198, 591)(199, 593)(200, 597)(201, 601)(202, 602)(203, 603)(204, 604)(205, 605)(206, 606)(207, 607)(208, 608)(209, 609)(210, 610)(211, 611)(212, 612)(213, 613)(214, 614)(215, 615)(216, 616)(217, 617)(218, 618)(219, 619)(220, 620)(221, 621)(222, 622)(223, 623)(224, 624)(225, 625)(226, 626)(227, 627)(228, 628)(229, 629)(230, 630)(231, 631)(232, 632)(233, 633)(234, 634)(235, 635)(236, 636)(237, 637)(238, 638)(239, 639)(240, 640)(241, 641)(242, 642)(243, 643)(244, 644)(245, 645)(246, 646)(247, 647)(248, 648)(249, 649)(250, 650)(251, 651)(252, 652)(253, 653)(254, 654)(255, 655)(256, 656)(257, 657)(258, 658)(259, 659)(260, 660)(261, 661)(262, 662)(263, 663)(264, 664)(265, 665)(266, 666)(267, 667)(268, 668)(269, 669)(270, 670)(271, 671)(272, 672)(273, 673)(274, 674)(275, 675)(276, 676)(277, 677)(278, 678)(279, 679)(280, 680)(281, 681)(282, 682)(283, 683)(284, 684)(285, 685)(286, 686)(287, 687)(288, 688)(289, 689)(290, 690)(291, 691)(292, 692)(293, 693)(294, 694)(295, 695)(296, 696)(297, 697)(298, 698)(299, 699)(300, 700)(301, 701)(302, 702)(303, 703)(304, 704)(305, 705)(306, 706)(307, 707)(308, 708)(309, 709)(310, 710)(311, 711)(312, 712)(313, 713)(314, 714)(315, 715)(316, 716)(317, 717)(318, 718)(319, 719)(320, 720)(321, 721)(322, 722)(323, 723)(324, 724)(325, 725)(326, 726)(327, 727)(328, 728)(329, 729)(330, 730)(331, 731)(332, 732)(333, 733)(334, 734)(335, 735)(336, 736)(337, 737)(338, 738)(339, 739)(340, 740)(341, 741)(342, 742)(343, 743)(344, 744)(345, 745)(346, 746)(347, 747)(348, 748)(349, 749)(350, 750)(351, 751)(352, 752)(353, 753)(354, 754)(355, 755)(356, 756)(357, 757)(358, 758)(359, 759)(360, 760)(361, 761)(362, 762)(363, 763)(364, 764)(365, 765)(366, 766)(367, 767)(368, 768)(369, 769)(370, 770)(371, 771)(372, 772)(373, 773)(374, 774)(375, 775)(376, 776)(377, 777)(378, 778)(379, 779)(380, 780)(381, 781)(382, 782)(383, 783)(384, 784)(385, 785)(386, 786)(387, 787)(388, 788)(389, 789)(390, 790)(391, 791)(392, 792)(393, 793)(394, 794)(395, 795)(396, 796)(397, 797)(398, 798)(399, 799)(400, 800) local type(s) :: { ( 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E16.1274 Graph:: simple bipartite v = 250 e = 400 f = 120 degree seq :: [ 2^200, 8^50 ] E16.1276 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 5, 5}) Quotient :: regular Aut^+ = C5 x A5 (small group id <300, 22>) Aut = $<600, 146>$ (small group id <600, 146>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^5, (T2 * T1^-1)^5, (T2 * T1 * T2 * T1^-1)^3, T2 * T1 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^-2 * T2 * T1^-2, T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-2 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 10, 4)(3, 7, 14, 17, 8)(6, 12, 23, 26, 13)(9, 18, 33, 36, 19)(11, 21, 39, 42, 22)(15, 28, 51, 54, 29)(16, 30, 55, 57, 31)(20, 37, 65, 68, 38)(24, 44, 77, 79, 45)(25, 46, 80, 82, 47)(27, 49, 85, 88, 50)(32, 58, 97, 100, 59)(34, 61, 103, 105, 62)(35, 63, 106, 90, 52)(40, 70, 117, 119, 71)(41, 72, 120, 122, 73)(43, 75, 125, 128, 76)(48, 83, 135, 138, 84)(53, 81, 133, 148, 91)(56, 94, 153, 155, 95)(60, 101, 163, 166, 102)(64, 108, 173, 176, 109)(66, 111, 179, 180, 112)(67, 113, 181, 168, 104)(69, 115, 185, 188, 116)(74, 123, 195, 198, 124)(78, 121, 193, 207, 130)(86, 140, 221, 223, 141)(87, 142, 224, 226, 143)(89, 145, 186, 231, 146)(92, 149, 234, 236, 150)(93, 151, 187, 239, 152)(96, 156, 243, 245, 157)(98, 159, 191, 248, 160)(99, 161, 194, 241, 154)(107, 171, 259, 261, 172)(110, 177, 263, 266, 178)(114, 183, 269, 270, 184)(118, 182, 268, 274, 190)(126, 200, 255, 167, 201)(127, 202, 258, 170, 203)(129, 205, 264, 283, 206)(131, 208, 230, 174, 209)(132, 210, 265, 286, 211)(134, 213, 260, 175, 214)(136, 216, 267, 290, 217)(137, 218, 256, 287, 212)(139, 199, 271, 291, 220)(144, 227, 288, 293, 228)(147, 225, 276, 197, 232)(158, 246, 272, 280, 247)(162, 219, 279, 298, 250)(164, 242, 273, 189, 251)(165, 252, 275, 192, 253)(169, 257, 278, 196, 237)(204, 222, 249, 262, 281)(215, 240, 294, 229, 289)(233, 254, 282, 244, 277)(235, 284, 297, 300, 295)(238, 285, 299, 292, 296) L = (1, 3)(2, 6)(4, 9)(5, 11)(7, 15)(8, 16)(10, 20)(12, 24)(13, 25)(14, 27)(17, 32)(18, 34)(19, 35)(21, 40)(22, 41)(23, 43)(26, 48)(28, 52)(29, 53)(30, 56)(31, 44)(33, 60)(36, 64)(37, 66)(38, 67)(39, 69)(42, 74)(45, 78)(46, 81)(47, 70)(49, 86)(50, 87)(51, 89)(54, 92)(55, 93)(57, 96)(58, 98)(59, 99)(61, 104)(62, 95)(63, 107)(65, 110)(68, 114)(71, 118)(72, 121)(73, 111)(75, 126)(76, 127)(77, 129)(79, 131)(80, 132)(82, 134)(83, 136)(84, 137)(85, 139)(88, 144)(90, 147)(91, 140)(94, 154)(97, 158)(100, 162)(101, 164)(102, 165)(103, 167)(105, 169)(106, 170)(108, 174)(109, 175)(112, 172)(113, 182)(115, 186)(116, 187)(117, 189)(119, 191)(120, 192)(122, 194)(123, 196)(124, 197)(125, 199)(128, 204)(130, 200)(133, 212)(135, 215)(138, 219)(141, 222)(142, 225)(143, 159)(145, 229)(146, 230)(148, 233)(149, 235)(150, 210)(151, 237)(152, 238)(153, 240)(155, 242)(156, 202)(157, 244)(160, 206)(161, 249)(163, 220)(166, 254)(168, 256)(171, 260)(173, 262)(176, 250)(177, 264)(178, 265)(179, 223)(180, 267)(181, 226)(183, 236)(184, 245)(185, 271)(188, 272)(190, 231)(193, 276)(195, 277)(198, 279)(201, 280)(203, 216)(205, 282)(207, 228)(208, 284)(209, 253)(211, 285)(213, 239)(214, 288)(217, 273)(218, 247)(221, 278)(224, 292)(227, 251)(232, 289)(234, 255)(241, 286)(243, 268)(246, 259)(248, 297)(252, 287)(257, 295)(258, 296)(261, 283)(263, 291)(266, 294)(269, 293)(270, 298)(274, 281)(275, 299)(290, 300) local type(s) :: { ( 5^5 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 60 e = 150 f = 60 degree seq :: [ 5^60 ] E16.1277 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 5, 5}) Quotient :: edge Aut^+ = C5 x A5 (small group id <300, 22>) Aut = $<600, 146>$ (small group id <600, 146>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^5, (T1 * T2)^5, (T1 * T2 * T1 * T2^-1)^3, T2^-1 * T1 * T2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1, T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-2 * T1 * T2 * T1 * T2^-1 ] Map:: polytopal R = (1, 3, 8, 10, 4)(2, 5, 12, 14, 6)(7, 15, 28, 30, 16)(9, 18, 34, 36, 19)(11, 21, 40, 42, 22)(13, 24, 46, 48, 25)(17, 31, 57, 59, 32)(20, 37, 66, 68, 38)(23, 43, 75, 77, 44)(26, 49, 84, 86, 50)(27, 47, 81, 88, 51)(29, 53, 91, 93, 54)(33, 60, 102, 103, 61)(35, 63, 107, 69, 39)(41, 71, 118, 120, 72)(45, 78, 129, 130, 79)(52, 89, 145, 147, 90)(55, 94, 152, 154, 95)(56, 92, 149, 156, 96)(58, 98, 159, 160, 99)(62, 104, 167, 169, 105)(64, 108, 174, 176, 109)(65, 110, 177, 178, 111)(67, 113, 182, 163, 101)(70, 116, 188, 190, 117)(73, 121, 195, 197, 122)(74, 119, 192, 199, 123)(76, 125, 202, 203, 126)(80, 131, 210, 212, 132)(82, 134, 216, 218, 135)(83, 136, 219, 220, 137)(85, 139, 224, 206, 128)(87, 141, 227, 229, 142)(97, 157, 244, 245, 158)(100, 161, 248, 250, 162)(106, 170, 259, 260, 171)(112, 179, 265, 267, 180)(114, 183, 269, 270, 184)(115, 185, 271, 249, 186)(124, 200, 279, 280, 201)(127, 204, 282, 283, 205)(133, 213, 264, 289, 214)(138, 221, 291, 292, 222)(140, 225, 293, 294, 226)(143, 230, 189, 173, 231)(144, 228, 252, 164, 232)(146, 215, 261, 172, 233)(148, 196, 266, 284, 235)(150, 237, 258, 175, 238)(151, 239, 263, 296, 240)(153, 242, 251, 274, 191)(155, 181, 268, 297, 243)(165, 253, 275, 247, 209)(166, 208, 285, 236, 254)(168, 255, 298, 246, 256)(187, 272, 241, 207, 273)(193, 257, 288, 217, 276)(194, 277, 290, 299, 278)(198, 223, 262, 295, 234)(211, 286, 300, 281, 287)(301, 302)(303, 307)(304, 309)(305, 311)(306, 313)(308, 317)(310, 320)(312, 323)(314, 326)(315, 327)(316, 329)(318, 333)(319, 335)(321, 339)(322, 341)(324, 345)(325, 347)(328, 352)(330, 355)(331, 356)(332, 358)(334, 362)(336, 364)(337, 365)(338, 367)(340, 370)(342, 373)(343, 374)(344, 376)(346, 380)(348, 382)(349, 383)(350, 385)(351, 387)(353, 371)(354, 392)(357, 397)(359, 400)(360, 401)(361, 379)(363, 406)(366, 412)(368, 414)(369, 415)(372, 419)(375, 424)(377, 427)(378, 428)(381, 433)(384, 438)(386, 440)(388, 443)(389, 444)(390, 446)(391, 448)(393, 450)(394, 451)(395, 453)(396, 455)(398, 441)(399, 410)(402, 464)(403, 465)(404, 466)(405, 468)(407, 472)(408, 473)(409, 475)(411, 471)(413, 481)(416, 487)(417, 489)(418, 491)(420, 493)(421, 494)(422, 496)(423, 498)(425, 485)(426, 436)(429, 507)(430, 508)(431, 509)(432, 511)(434, 515)(435, 517)(437, 514)(439, 523)(442, 528)(445, 500)(447, 534)(449, 536)(452, 541)(454, 525)(456, 519)(457, 488)(458, 510)(459, 546)(460, 524)(461, 547)(462, 549)(463, 551)(467, 501)(469, 557)(470, 558)(474, 562)(476, 526)(477, 499)(478, 563)(479, 564)(480, 566)(482, 503)(483, 497)(484, 518)(486, 572)(490, 543)(492, 575)(495, 552)(502, 581)(504, 554)(505, 529)(506, 584)(512, 537)(513, 588)(516, 568)(520, 590)(521, 559)(522, 542)(527, 571)(530, 577)(531, 556)(532, 592)(533, 539)(535, 586)(538, 582)(540, 585)(544, 579)(545, 591)(548, 576)(550, 593)(553, 578)(555, 574)(560, 589)(561, 587)(565, 580)(567, 573)(569, 583)(570, 594)(595, 597)(596, 599)(598, 600) L = (1, 301)(2, 302)(3, 303)(4, 304)(5, 305)(6, 306)(7, 307)(8, 308)(9, 309)(10, 310)(11, 311)(12, 312)(13, 313)(14, 314)(15, 315)(16, 316)(17, 317)(18, 318)(19, 319)(20, 320)(21, 321)(22, 322)(23, 323)(24, 324)(25, 325)(26, 326)(27, 327)(28, 328)(29, 329)(30, 330)(31, 331)(32, 332)(33, 333)(34, 334)(35, 335)(36, 336)(37, 337)(38, 338)(39, 339)(40, 340)(41, 341)(42, 342)(43, 343)(44, 344)(45, 345)(46, 346)(47, 347)(48, 348)(49, 349)(50, 350)(51, 351)(52, 352)(53, 353)(54, 354)(55, 355)(56, 356)(57, 357)(58, 358)(59, 359)(60, 360)(61, 361)(62, 362)(63, 363)(64, 364)(65, 365)(66, 366)(67, 367)(68, 368)(69, 369)(70, 370)(71, 371)(72, 372)(73, 373)(74, 374)(75, 375)(76, 376)(77, 377)(78, 378)(79, 379)(80, 380)(81, 381)(82, 382)(83, 383)(84, 384)(85, 385)(86, 386)(87, 387)(88, 388)(89, 389)(90, 390)(91, 391)(92, 392)(93, 393)(94, 394)(95, 395)(96, 396)(97, 397)(98, 398)(99, 399)(100, 400)(101, 401)(102, 402)(103, 403)(104, 404)(105, 405)(106, 406)(107, 407)(108, 408)(109, 409)(110, 410)(111, 411)(112, 412)(113, 413)(114, 414)(115, 415)(116, 416)(117, 417)(118, 418)(119, 419)(120, 420)(121, 421)(122, 422)(123, 423)(124, 424)(125, 425)(126, 426)(127, 427)(128, 428)(129, 429)(130, 430)(131, 431)(132, 432)(133, 433)(134, 434)(135, 435)(136, 436)(137, 437)(138, 438)(139, 439)(140, 440)(141, 441)(142, 442)(143, 443)(144, 444)(145, 445)(146, 446)(147, 447)(148, 448)(149, 449)(150, 450)(151, 451)(152, 452)(153, 453)(154, 454)(155, 455)(156, 456)(157, 457)(158, 458)(159, 459)(160, 460)(161, 461)(162, 462)(163, 463)(164, 464)(165, 465)(166, 466)(167, 467)(168, 468)(169, 469)(170, 470)(171, 471)(172, 472)(173, 473)(174, 474)(175, 475)(176, 476)(177, 477)(178, 478)(179, 479)(180, 480)(181, 481)(182, 482)(183, 483)(184, 484)(185, 485)(186, 486)(187, 487)(188, 488)(189, 489)(190, 490)(191, 491)(192, 492)(193, 493)(194, 494)(195, 495)(196, 496)(197, 497)(198, 498)(199, 499)(200, 500)(201, 501)(202, 502)(203, 503)(204, 504)(205, 505)(206, 506)(207, 507)(208, 508)(209, 509)(210, 510)(211, 511)(212, 512)(213, 513)(214, 514)(215, 515)(216, 516)(217, 517)(218, 518)(219, 519)(220, 520)(221, 521)(222, 522)(223, 523)(224, 524)(225, 525)(226, 526)(227, 527)(228, 528)(229, 529)(230, 530)(231, 531)(232, 532)(233, 533)(234, 534)(235, 535)(236, 536)(237, 537)(238, 538)(239, 539)(240, 540)(241, 541)(242, 542)(243, 543)(244, 544)(245, 545)(246, 546)(247, 547)(248, 548)(249, 549)(250, 550)(251, 551)(252, 552)(253, 553)(254, 554)(255, 555)(256, 556)(257, 557)(258, 558)(259, 559)(260, 560)(261, 561)(262, 562)(263, 563)(264, 564)(265, 565)(266, 566)(267, 567)(268, 568)(269, 569)(270, 570)(271, 571)(272, 572)(273, 573)(274, 574)(275, 575)(276, 576)(277, 577)(278, 578)(279, 579)(280, 580)(281, 581)(282, 582)(283, 583)(284, 584)(285, 585)(286, 586)(287, 587)(288, 588)(289, 589)(290, 590)(291, 591)(292, 592)(293, 593)(294, 594)(295, 595)(296, 596)(297, 597)(298, 598)(299, 599)(300, 600) local type(s) :: { ( 10, 10 ), ( 10^5 ) } Outer automorphisms :: reflexible Dual of E16.1278 Transitivity :: ET+ Graph:: simple bipartite v = 210 e = 300 f = 60 degree seq :: [ 2^150, 5^60 ] E16.1278 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 5, 5}) Quotient :: loop Aut^+ = C5 x A5 (small group id <300, 22>) Aut = $<600, 146>$ (small group id <600, 146>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^5, (T1 * T2)^5, (T1 * T2 * T1 * T2^-1)^3, T2^-1 * T1 * T2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1, T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-2 * T1 * T2 * T1 * T2^-1 ] Map:: R = (1, 301, 3, 303, 8, 308, 10, 310, 4, 304)(2, 302, 5, 305, 12, 312, 14, 314, 6, 306)(7, 307, 15, 315, 28, 328, 30, 330, 16, 316)(9, 309, 18, 318, 34, 334, 36, 336, 19, 319)(11, 311, 21, 321, 40, 340, 42, 342, 22, 322)(13, 313, 24, 324, 46, 346, 48, 348, 25, 325)(17, 317, 31, 331, 57, 357, 59, 359, 32, 332)(20, 320, 37, 337, 66, 366, 68, 368, 38, 338)(23, 323, 43, 343, 75, 375, 77, 377, 44, 344)(26, 326, 49, 349, 84, 384, 86, 386, 50, 350)(27, 327, 47, 347, 81, 381, 88, 388, 51, 351)(29, 329, 53, 353, 91, 391, 93, 393, 54, 354)(33, 333, 60, 360, 102, 402, 103, 403, 61, 361)(35, 335, 63, 363, 107, 407, 69, 369, 39, 339)(41, 341, 71, 371, 118, 418, 120, 420, 72, 372)(45, 345, 78, 378, 129, 429, 130, 430, 79, 379)(52, 352, 89, 389, 145, 445, 147, 447, 90, 390)(55, 355, 94, 394, 152, 452, 154, 454, 95, 395)(56, 356, 92, 392, 149, 449, 156, 456, 96, 396)(58, 358, 98, 398, 159, 459, 160, 460, 99, 399)(62, 362, 104, 404, 167, 467, 169, 469, 105, 405)(64, 364, 108, 408, 174, 474, 176, 476, 109, 409)(65, 365, 110, 410, 177, 477, 178, 478, 111, 411)(67, 367, 113, 413, 182, 482, 163, 463, 101, 401)(70, 370, 116, 416, 188, 488, 190, 490, 117, 417)(73, 373, 121, 421, 195, 495, 197, 497, 122, 422)(74, 374, 119, 419, 192, 492, 199, 499, 123, 423)(76, 376, 125, 425, 202, 502, 203, 503, 126, 426)(80, 380, 131, 431, 210, 510, 212, 512, 132, 432)(82, 382, 134, 434, 216, 516, 218, 518, 135, 435)(83, 383, 136, 436, 219, 519, 220, 520, 137, 437)(85, 385, 139, 439, 224, 524, 206, 506, 128, 428)(87, 387, 141, 441, 227, 527, 229, 529, 142, 442)(97, 397, 157, 457, 244, 544, 245, 545, 158, 458)(100, 400, 161, 461, 248, 548, 250, 550, 162, 462)(106, 406, 170, 470, 259, 559, 260, 560, 171, 471)(112, 412, 179, 479, 265, 565, 267, 567, 180, 480)(114, 414, 183, 483, 269, 569, 270, 570, 184, 484)(115, 415, 185, 485, 271, 571, 249, 549, 186, 486)(124, 424, 200, 500, 279, 579, 280, 580, 201, 501)(127, 427, 204, 504, 282, 582, 283, 583, 205, 505)(133, 433, 213, 513, 264, 564, 289, 589, 214, 514)(138, 438, 221, 521, 291, 591, 292, 592, 222, 522)(140, 440, 225, 525, 293, 593, 294, 594, 226, 526)(143, 443, 230, 530, 189, 489, 173, 473, 231, 531)(144, 444, 228, 528, 252, 552, 164, 464, 232, 532)(146, 446, 215, 515, 261, 561, 172, 472, 233, 533)(148, 448, 196, 496, 266, 566, 284, 584, 235, 535)(150, 450, 237, 537, 258, 558, 175, 475, 238, 538)(151, 451, 239, 539, 263, 563, 296, 596, 240, 540)(153, 453, 242, 542, 251, 551, 274, 574, 191, 491)(155, 455, 181, 481, 268, 568, 297, 597, 243, 543)(165, 465, 253, 553, 275, 575, 247, 547, 209, 509)(166, 466, 208, 508, 285, 585, 236, 536, 254, 554)(168, 468, 255, 555, 298, 598, 246, 546, 256, 556)(187, 487, 272, 572, 241, 541, 207, 507, 273, 573)(193, 493, 257, 557, 288, 588, 217, 517, 276, 576)(194, 494, 277, 577, 290, 590, 299, 599, 278, 578)(198, 498, 223, 523, 262, 562, 295, 595, 234, 534)(211, 511, 286, 586, 300, 600, 281, 581, 287, 587) L = (1, 302)(2, 301)(3, 307)(4, 309)(5, 311)(6, 313)(7, 303)(8, 317)(9, 304)(10, 320)(11, 305)(12, 323)(13, 306)(14, 326)(15, 327)(16, 329)(17, 308)(18, 333)(19, 335)(20, 310)(21, 339)(22, 341)(23, 312)(24, 345)(25, 347)(26, 314)(27, 315)(28, 352)(29, 316)(30, 355)(31, 356)(32, 358)(33, 318)(34, 362)(35, 319)(36, 364)(37, 365)(38, 367)(39, 321)(40, 370)(41, 322)(42, 373)(43, 374)(44, 376)(45, 324)(46, 380)(47, 325)(48, 382)(49, 383)(50, 385)(51, 387)(52, 328)(53, 371)(54, 392)(55, 330)(56, 331)(57, 397)(58, 332)(59, 400)(60, 401)(61, 379)(62, 334)(63, 406)(64, 336)(65, 337)(66, 412)(67, 338)(68, 414)(69, 415)(70, 340)(71, 353)(72, 419)(73, 342)(74, 343)(75, 424)(76, 344)(77, 427)(78, 428)(79, 361)(80, 346)(81, 433)(82, 348)(83, 349)(84, 438)(85, 350)(86, 440)(87, 351)(88, 443)(89, 444)(90, 446)(91, 448)(92, 354)(93, 450)(94, 451)(95, 453)(96, 455)(97, 357)(98, 441)(99, 410)(100, 359)(101, 360)(102, 464)(103, 465)(104, 466)(105, 468)(106, 363)(107, 472)(108, 473)(109, 475)(110, 399)(111, 471)(112, 366)(113, 481)(114, 368)(115, 369)(116, 487)(117, 489)(118, 491)(119, 372)(120, 493)(121, 494)(122, 496)(123, 498)(124, 375)(125, 485)(126, 436)(127, 377)(128, 378)(129, 507)(130, 508)(131, 509)(132, 511)(133, 381)(134, 515)(135, 517)(136, 426)(137, 514)(138, 384)(139, 523)(140, 386)(141, 398)(142, 528)(143, 388)(144, 389)(145, 500)(146, 390)(147, 534)(148, 391)(149, 536)(150, 393)(151, 394)(152, 541)(153, 395)(154, 525)(155, 396)(156, 519)(157, 488)(158, 510)(159, 546)(160, 524)(161, 547)(162, 549)(163, 551)(164, 402)(165, 403)(166, 404)(167, 501)(168, 405)(169, 557)(170, 558)(171, 411)(172, 407)(173, 408)(174, 562)(175, 409)(176, 526)(177, 499)(178, 563)(179, 564)(180, 566)(181, 413)(182, 503)(183, 497)(184, 518)(185, 425)(186, 572)(187, 416)(188, 457)(189, 417)(190, 543)(191, 418)(192, 575)(193, 420)(194, 421)(195, 552)(196, 422)(197, 483)(198, 423)(199, 477)(200, 445)(201, 467)(202, 581)(203, 482)(204, 554)(205, 529)(206, 584)(207, 429)(208, 430)(209, 431)(210, 458)(211, 432)(212, 537)(213, 588)(214, 437)(215, 434)(216, 568)(217, 435)(218, 484)(219, 456)(220, 590)(221, 559)(222, 542)(223, 439)(224, 460)(225, 454)(226, 476)(227, 571)(228, 442)(229, 505)(230, 577)(231, 556)(232, 592)(233, 539)(234, 447)(235, 586)(236, 449)(237, 512)(238, 582)(239, 533)(240, 585)(241, 452)(242, 522)(243, 490)(244, 579)(245, 591)(246, 459)(247, 461)(248, 576)(249, 462)(250, 593)(251, 463)(252, 495)(253, 578)(254, 504)(255, 574)(256, 531)(257, 469)(258, 470)(259, 521)(260, 589)(261, 587)(262, 474)(263, 478)(264, 479)(265, 580)(266, 480)(267, 573)(268, 516)(269, 583)(270, 594)(271, 527)(272, 486)(273, 567)(274, 555)(275, 492)(276, 548)(277, 530)(278, 553)(279, 544)(280, 565)(281, 502)(282, 538)(283, 569)(284, 506)(285, 540)(286, 535)(287, 561)(288, 513)(289, 560)(290, 520)(291, 545)(292, 532)(293, 550)(294, 570)(295, 597)(296, 599)(297, 595)(298, 600)(299, 596)(300, 598) local type(s) :: { ( 2, 5, 2, 5, 2, 5, 2, 5, 2, 5 ) } Outer automorphisms :: reflexible Dual of E16.1277 Transitivity :: ET+ VT+ AT Graph:: v = 60 e = 300 f = 210 degree seq :: [ 10^60 ] E16.1279 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 5, 5}) Quotient :: dipole Aut^+ = C5 x A5 (small group id <300, 22>) Aut = $<600, 146>$ (small group id <600, 146>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^5, (R * Y2 * Y3^-1)^2, (R * Y2^-2 * Y1)^2, (Y1 * Y2^-1)^5, (Y3 * Y2^-1)^5, (Y2 * Y1 * Y2^-1 * Y1)^3, Y2^-1 * Y1 * Y2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^-2 * Y1 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-2 * Y1 * Y2 * Y1 * Y2^-1 ] Map:: R = (1, 301, 2, 302)(3, 303, 7, 307)(4, 304, 9, 309)(5, 305, 11, 311)(6, 306, 13, 313)(8, 308, 17, 317)(10, 310, 20, 320)(12, 312, 23, 323)(14, 314, 26, 326)(15, 315, 27, 327)(16, 316, 29, 329)(18, 318, 33, 333)(19, 319, 35, 335)(21, 321, 39, 339)(22, 322, 41, 341)(24, 324, 45, 345)(25, 325, 47, 347)(28, 328, 52, 352)(30, 330, 55, 355)(31, 331, 56, 356)(32, 332, 58, 358)(34, 334, 62, 362)(36, 336, 64, 364)(37, 337, 65, 365)(38, 338, 67, 367)(40, 340, 70, 370)(42, 342, 73, 373)(43, 343, 74, 374)(44, 344, 76, 376)(46, 346, 80, 380)(48, 348, 82, 382)(49, 349, 83, 383)(50, 350, 85, 385)(51, 351, 87, 387)(53, 353, 71, 371)(54, 354, 92, 392)(57, 357, 97, 397)(59, 359, 100, 400)(60, 360, 101, 401)(61, 361, 79, 379)(63, 363, 106, 406)(66, 366, 112, 412)(68, 368, 114, 414)(69, 369, 115, 415)(72, 372, 119, 419)(75, 375, 124, 424)(77, 377, 127, 427)(78, 378, 128, 428)(81, 381, 133, 433)(84, 384, 138, 438)(86, 386, 140, 440)(88, 388, 143, 443)(89, 389, 144, 444)(90, 390, 146, 446)(91, 391, 148, 448)(93, 393, 150, 450)(94, 394, 151, 451)(95, 395, 153, 453)(96, 396, 155, 455)(98, 398, 141, 441)(99, 399, 110, 410)(102, 402, 164, 464)(103, 403, 165, 465)(104, 404, 166, 466)(105, 405, 168, 468)(107, 407, 172, 472)(108, 408, 173, 473)(109, 409, 175, 475)(111, 411, 171, 471)(113, 413, 181, 481)(116, 416, 187, 487)(117, 417, 189, 489)(118, 418, 191, 491)(120, 420, 193, 493)(121, 421, 194, 494)(122, 422, 196, 496)(123, 423, 198, 498)(125, 425, 185, 485)(126, 426, 136, 436)(129, 429, 207, 507)(130, 430, 208, 508)(131, 431, 209, 509)(132, 432, 211, 511)(134, 434, 215, 515)(135, 435, 217, 517)(137, 437, 214, 514)(139, 439, 223, 523)(142, 442, 228, 528)(145, 445, 200, 500)(147, 447, 234, 534)(149, 449, 236, 536)(152, 452, 241, 541)(154, 454, 225, 525)(156, 456, 219, 519)(157, 457, 188, 488)(158, 458, 210, 510)(159, 459, 246, 546)(160, 460, 224, 524)(161, 461, 247, 547)(162, 462, 249, 549)(163, 463, 251, 551)(167, 467, 201, 501)(169, 469, 257, 557)(170, 470, 258, 558)(174, 474, 262, 562)(176, 476, 226, 526)(177, 477, 199, 499)(178, 478, 263, 563)(179, 479, 264, 564)(180, 480, 266, 566)(182, 482, 203, 503)(183, 483, 197, 497)(184, 484, 218, 518)(186, 486, 272, 572)(190, 490, 243, 543)(192, 492, 275, 575)(195, 495, 252, 552)(202, 502, 281, 581)(204, 504, 254, 554)(205, 505, 229, 529)(206, 506, 284, 584)(212, 512, 237, 537)(213, 513, 288, 588)(216, 516, 268, 568)(220, 520, 290, 590)(221, 521, 259, 559)(222, 522, 242, 542)(227, 527, 271, 571)(230, 530, 277, 577)(231, 531, 256, 556)(232, 532, 292, 592)(233, 533, 239, 539)(235, 535, 286, 586)(238, 538, 282, 582)(240, 540, 285, 585)(244, 544, 279, 579)(245, 545, 291, 591)(248, 548, 276, 576)(250, 550, 293, 593)(253, 553, 278, 578)(255, 555, 274, 574)(260, 560, 289, 589)(261, 561, 287, 587)(265, 565, 280, 580)(267, 567, 273, 573)(269, 569, 283, 583)(270, 570, 294, 594)(295, 595, 297, 597)(296, 596, 299, 599)(298, 598, 300, 600)(601, 901, 603, 903, 608, 908, 610, 910, 604, 904)(602, 902, 605, 905, 612, 912, 614, 914, 606, 906)(607, 907, 615, 915, 628, 928, 630, 930, 616, 916)(609, 909, 618, 918, 634, 934, 636, 936, 619, 919)(611, 911, 621, 921, 640, 940, 642, 942, 622, 922)(613, 913, 624, 924, 646, 946, 648, 948, 625, 925)(617, 917, 631, 931, 657, 957, 659, 959, 632, 932)(620, 920, 637, 937, 666, 966, 668, 968, 638, 938)(623, 923, 643, 943, 675, 975, 677, 977, 644, 944)(626, 926, 649, 949, 684, 984, 686, 986, 650, 950)(627, 927, 647, 947, 681, 981, 688, 988, 651, 951)(629, 929, 653, 953, 691, 991, 693, 993, 654, 954)(633, 933, 660, 960, 702, 1002, 703, 1003, 661, 961)(635, 935, 663, 963, 707, 1007, 669, 969, 639, 939)(641, 941, 671, 971, 718, 1018, 720, 1020, 672, 972)(645, 945, 678, 978, 729, 1029, 730, 1030, 679, 979)(652, 952, 689, 989, 745, 1045, 747, 1047, 690, 990)(655, 955, 694, 994, 752, 1052, 754, 1054, 695, 995)(656, 956, 692, 992, 749, 1049, 756, 1056, 696, 996)(658, 958, 698, 998, 759, 1059, 760, 1060, 699, 999)(662, 962, 704, 1004, 767, 1067, 769, 1069, 705, 1005)(664, 964, 708, 1008, 774, 1074, 776, 1076, 709, 1009)(665, 965, 710, 1010, 777, 1077, 778, 1078, 711, 1011)(667, 967, 713, 1013, 782, 1082, 763, 1063, 701, 1001)(670, 970, 716, 1016, 788, 1088, 790, 1090, 717, 1017)(673, 973, 721, 1021, 795, 1095, 797, 1097, 722, 1022)(674, 974, 719, 1019, 792, 1092, 799, 1099, 723, 1023)(676, 976, 725, 1025, 802, 1102, 803, 1103, 726, 1026)(680, 980, 731, 1031, 810, 1110, 812, 1112, 732, 1032)(682, 982, 734, 1034, 816, 1116, 818, 1118, 735, 1035)(683, 983, 736, 1036, 819, 1119, 820, 1120, 737, 1037)(685, 985, 739, 1039, 824, 1124, 806, 1106, 728, 1028)(687, 987, 741, 1041, 827, 1127, 829, 1129, 742, 1042)(697, 997, 757, 1057, 844, 1144, 845, 1145, 758, 1058)(700, 1000, 761, 1061, 848, 1148, 850, 1150, 762, 1062)(706, 1006, 770, 1070, 859, 1159, 860, 1160, 771, 1071)(712, 1012, 779, 1079, 865, 1165, 867, 1167, 780, 1080)(714, 1014, 783, 1083, 869, 1169, 870, 1170, 784, 1084)(715, 1015, 785, 1085, 871, 1171, 849, 1149, 786, 1086)(724, 1024, 800, 1100, 879, 1179, 880, 1180, 801, 1101)(727, 1027, 804, 1104, 882, 1182, 883, 1183, 805, 1105)(733, 1033, 813, 1113, 864, 1164, 889, 1189, 814, 1114)(738, 1038, 821, 1121, 891, 1191, 892, 1192, 822, 1122)(740, 1040, 825, 1125, 893, 1193, 894, 1194, 826, 1126)(743, 1043, 830, 1130, 789, 1089, 773, 1073, 831, 1131)(744, 1044, 828, 1128, 852, 1152, 764, 1064, 832, 1132)(746, 1046, 815, 1115, 861, 1161, 772, 1072, 833, 1133)(748, 1048, 796, 1096, 866, 1166, 884, 1184, 835, 1135)(750, 1050, 837, 1137, 858, 1158, 775, 1075, 838, 1138)(751, 1051, 839, 1139, 863, 1163, 896, 1196, 840, 1140)(753, 1053, 842, 1142, 851, 1151, 874, 1174, 791, 1091)(755, 1055, 781, 1081, 868, 1168, 897, 1197, 843, 1143)(765, 1065, 853, 1153, 875, 1175, 847, 1147, 809, 1109)(766, 1066, 808, 1108, 885, 1185, 836, 1136, 854, 1154)(768, 1068, 855, 1155, 898, 1198, 846, 1146, 856, 1156)(787, 1087, 872, 1172, 841, 1141, 807, 1107, 873, 1173)(793, 1093, 857, 1157, 888, 1188, 817, 1117, 876, 1176)(794, 1094, 877, 1177, 890, 1190, 899, 1199, 878, 1178)(798, 1098, 823, 1123, 862, 1162, 895, 1195, 834, 1134)(811, 1111, 886, 1186, 900, 1200, 881, 1181, 887, 1187) L = (1, 602)(2, 601)(3, 607)(4, 609)(5, 611)(6, 613)(7, 603)(8, 617)(9, 604)(10, 620)(11, 605)(12, 623)(13, 606)(14, 626)(15, 627)(16, 629)(17, 608)(18, 633)(19, 635)(20, 610)(21, 639)(22, 641)(23, 612)(24, 645)(25, 647)(26, 614)(27, 615)(28, 652)(29, 616)(30, 655)(31, 656)(32, 658)(33, 618)(34, 662)(35, 619)(36, 664)(37, 665)(38, 667)(39, 621)(40, 670)(41, 622)(42, 673)(43, 674)(44, 676)(45, 624)(46, 680)(47, 625)(48, 682)(49, 683)(50, 685)(51, 687)(52, 628)(53, 671)(54, 692)(55, 630)(56, 631)(57, 697)(58, 632)(59, 700)(60, 701)(61, 679)(62, 634)(63, 706)(64, 636)(65, 637)(66, 712)(67, 638)(68, 714)(69, 715)(70, 640)(71, 653)(72, 719)(73, 642)(74, 643)(75, 724)(76, 644)(77, 727)(78, 728)(79, 661)(80, 646)(81, 733)(82, 648)(83, 649)(84, 738)(85, 650)(86, 740)(87, 651)(88, 743)(89, 744)(90, 746)(91, 748)(92, 654)(93, 750)(94, 751)(95, 753)(96, 755)(97, 657)(98, 741)(99, 710)(100, 659)(101, 660)(102, 764)(103, 765)(104, 766)(105, 768)(106, 663)(107, 772)(108, 773)(109, 775)(110, 699)(111, 771)(112, 666)(113, 781)(114, 668)(115, 669)(116, 787)(117, 789)(118, 791)(119, 672)(120, 793)(121, 794)(122, 796)(123, 798)(124, 675)(125, 785)(126, 736)(127, 677)(128, 678)(129, 807)(130, 808)(131, 809)(132, 811)(133, 681)(134, 815)(135, 817)(136, 726)(137, 814)(138, 684)(139, 823)(140, 686)(141, 698)(142, 828)(143, 688)(144, 689)(145, 800)(146, 690)(147, 834)(148, 691)(149, 836)(150, 693)(151, 694)(152, 841)(153, 695)(154, 825)(155, 696)(156, 819)(157, 788)(158, 810)(159, 846)(160, 824)(161, 847)(162, 849)(163, 851)(164, 702)(165, 703)(166, 704)(167, 801)(168, 705)(169, 857)(170, 858)(171, 711)(172, 707)(173, 708)(174, 862)(175, 709)(176, 826)(177, 799)(178, 863)(179, 864)(180, 866)(181, 713)(182, 803)(183, 797)(184, 818)(185, 725)(186, 872)(187, 716)(188, 757)(189, 717)(190, 843)(191, 718)(192, 875)(193, 720)(194, 721)(195, 852)(196, 722)(197, 783)(198, 723)(199, 777)(200, 745)(201, 767)(202, 881)(203, 782)(204, 854)(205, 829)(206, 884)(207, 729)(208, 730)(209, 731)(210, 758)(211, 732)(212, 837)(213, 888)(214, 737)(215, 734)(216, 868)(217, 735)(218, 784)(219, 756)(220, 890)(221, 859)(222, 842)(223, 739)(224, 760)(225, 754)(226, 776)(227, 871)(228, 742)(229, 805)(230, 877)(231, 856)(232, 892)(233, 839)(234, 747)(235, 886)(236, 749)(237, 812)(238, 882)(239, 833)(240, 885)(241, 752)(242, 822)(243, 790)(244, 879)(245, 891)(246, 759)(247, 761)(248, 876)(249, 762)(250, 893)(251, 763)(252, 795)(253, 878)(254, 804)(255, 874)(256, 831)(257, 769)(258, 770)(259, 821)(260, 889)(261, 887)(262, 774)(263, 778)(264, 779)(265, 880)(266, 780)(267, 873)(268, 816)(269, 883)(270, 894)(271, 827)(272, 786)(273, 867)(274, 855)(275, 792)(276, 848)(277, 830)(278, 853)(279, 844)(280, 865)(281, 802)(282, 838)(283, 869)(284, 806)(285, 840)(286, 835)(287, 861)(288, 813)(289, 860)(290, 820)(291, 845)(292, 832)(293, 850)(294, 870)(295, 897)(296, 899)(297, 895)(298, 900)(299, 896)(300, 898)(301, 901)(302, 902)(303, 903)(304, 904)(305, 905)(306, 906)(307, 907)(308, 908)(309, 909)(310, 910)(311, 911)(312, 912)(313, 913)(314, 914)(315, 915)(316, 916)(317, 917)(318, 918)(319, 919)(320, 920)(321, 921)(322, 922)(323, 923)(324, 924)(325, 925)(326, 926)(327, 927)(328, 928)(329, 929)(330, 930)(331, 931)(332, 932)(333, 933)(334, 934)(335, 935)(336, 936)(337, 937)(338, 938)(339, 939)(340, 940)(341, 941)(342, 942)(343, 943)(344, 944)(345, 945)(346, 946)(347, 947)(348, 948)(349, 949)(350, 950)(351, 951)(352, 952)(353, 953)(354, 954)(355, 955)(356, 956)(357, 957)(358, 958)(359, 959)(360, 960)(361, 961)(362, 962)(363, 963)(364, 964)(365, 965)(366, 966)(367, 967)(368, 968)(369, 969)(370, 970)(371, 971)(372, 972)(373, 973)(374, 974)(375, 975)(376, 976)(377, 977)(378, 978)(379, 979)(380, 980)(381, 981)(382, 982)(383, 983)(384, 984)(385, 985)(386, 986)(387, 987)(388, 988)(389, 989)(390, 990)(391, 991)(392, 992)(393, 993)(394, 994)(395, 995)(396, 996)(397, 997)(398, 998)(399, 999)(400, 1000)(401, 1001)(402, 1002)(403, 1003)(404, 1004)(405, 1005)(406, 1006)(407, 1007)(408, 1008)(409, 1009)(410, 1010)(411, 1011)(412, 1012)(413, 1013)(414, 1014)(415, 1015)(416, 1016)(417, 1017)(418, 1018)(419, 1019)(420, 1020)(421, 1021)(422, 1022)(423, 1023)(424, 1024)(425, 1025)(426, 1026)(427, 1027)(428, 1028)(429, 1029)(430, 1030)(431, 1031)(432, 1032)(433, 1033)(434, 1034)(435, 1035)(436, 1036)(437, 1037)(438, 1038)(439, 1039)(440, 1040)(441, 1041)(442, 1042)(443, 1043)(444, 1044)(445, 1045)(446, 1046)(447, 1047)(448, 1048)(449, 1049)(450, 1050)(451, 1051)(452, 1052)(453, 1053)(454, 1054)(455, 1055)(456, 1056)(457, 1057)(458, 1058)(459, 1059)(460, 1060)(461, 1061)(462, 1062)(463, 1063)(464, 1064)(465, 1065)(466, 1066)(467, 1067)(468, 1068)(469, 1069)(470, 1070)(471, 1071)(472, 1072)(473, 1073)(474, 1074)(475, 1075)(476, 1076)(477, 1077)(478, 1078)(479, 1079)(480, 1080)(481, 1081)(482, 1082)(483, 1083)(484, 1084)(485, 1085)(486, 1086)(487, 1087)(488, 1088)(489, 1089)(490, 1090)(491, 1091)(492, 1092)(493, 1093)(494, 1094)(495, 1095)(496, 1096)(497, 1097)(498, 1098)(499, 1099)(500, 1100)(501, 1101)(502, 1102)(503, 1103)(504, 1104)(505, 1105)(506, 1106)(507, 1107)(508, 1108)(509, 1109)(510, 1110)(511, 1111)(512, 1112)(513, 1113)(514, 1114)(515, 1115)(516, 1116)(517, 1117)(518, 1118)(519, 1119)(520, 1120)(521, 1121)(522, 1122)(523, 1123)(524, 1124)(525, 1125)(526, 1126)(527, 1127)(528, 1128)(529, 1129)(530, 1130)(531, 1131)(532, 1132)(533, 1133)(534, 1134)(535, 1135)(536, 1136)(537, 1137)(538, 1138)(539, 1139)(540, 1140)(541, 1141)(542, 1142)(543, 1143)(544, 1144)(545, 1145)(546, 1146)(547, 1147)(548, 1148)(549, 1149)(550, 1150)(551, 1151)(552, 1152)(553, 1153)(554, 1154)(555, 1155)(556, 1156)(557, 1157)(558, 1158)(559, 1159)(560, 1160)(561, 1161)(562, 1162)(563, 1163)(564, 1164)(565, 1165)(566, 1166)(567, 1167)(568, 1168)(569, 1169)(570, 1170)(571, 1171)(572, 1172)(573, 1173)(574, 1174)(575, 1175)(576, 1176)(577, 1177)(578, 1178)(579, 1179)(580, 1180)(581, 1181)(582, 1182)(583, 1183)(584, 1184)(585, 1185)(586, 1186)(587, 1187)(588, 1188)(589, 1189)(590, 1190)(591, 1191)(592, 1192)(593, 1193)(594, 1194)(595, 1195)(596, 1196)(597, 1197)(598, 1198)(599, 1199)(600, 1200) local type(s) :: { ( 2, 10, 2, 10 ), ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.1280 Graph:: bipartite v = 210 e = 600 f = 360 degree seq :: [ 4^150, 10^60 ] E16.1280 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 5, 5}) Quotient :: dipole Aut^+ = C5 x A5 (small group id <300, 22>) Aut = $<600, 146>$ (small group id <600, 146>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, Y1^5, (Y3 * Y1^-1)^5, (Y3 * Y1 * Y3 * Y1^-1)^3, Y3 * Y1^-2 * Y3 * Y1 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1^-2, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-2 ] Map:: polytopal R = (1, 301, 2, 302, 5, 305, 10, 310, 4, 304)(3, 303, 7, 307, 14, 314, 17, 317, 8, 308)(6, 306, 12, 312, 23, 323, 26, 326, 13, 313)(9, 309, 18, 318, 33, 333, 36, 336, 19, 319)(11, 311, 21, 321, 39, 339, 42, 342, 22, 322)(15, 315, 28, 328, 51, 351, 54, 354, 29, 329)(16, 316, 30, 330, 55, 355, 57, 357, 31, 331)(20, 320, 37, 337, 65, 365, 68, 368, 38, 338)(24, 324, 44, 344, 77, 377, 79, 379, 45, 345)(25, 325, 46, 346, 80, 380, 82, 382, 47, 347)(27, 327, 49, 349, 85, 385, 88, 388, 50, 350)(32, 332, 58, 358, 97, 397, 100, 400, 59, 359)(34, 334, 61, 361, 103, 403, 105, 405, 62, 362)(35, 335, 63, 363, 106, 406, 90, 390, 52, 352)(40, 340, 70, 370, 117, 417, 119, 419, 71, 371)(41, 341, 72, 372, 120, 420, 122, 422, 73, 373)(43, 343, 75, 375, 125, 425, 128, 428, 76, 376)(48, 348, 83, 383, 135, 435, 138, 438, 84, 384)(53, 353, 81, 381, 133, 433, 148, 448, 91, 391)(56, 356, 94, 394, 153, 453, 155, 455, 95, 395)(60, 360, 101, 401, 163, 463, 166, 466, 102, 402)(64, 364, 108, 408, 173, 473, 176, 476, 109, 409)(66, 366, 111, 411, 179, 479, 180, 480, 112, 412)(67, 367, 113, 413, 181, 481, 168, 468, 104, 404)(69, 369, 115, 415, 185, 485, 188, 488, 116, 416)(74, 374, 123, 423, 195, 495, 198, 498, 124, 424)(78, 378, 121, 421, 193, 493, 207, 507, 130, 430)(86, 386, 140, 440, 221, 521, 223, 523, 141, 441)(87, 387, 142, 442, 224, 524, 226, 526, 143, 443)(89, 389, 145, 445, 186, 486, 231, 531, 146, 446)(92, 392, 149, 449, 234, 534, 236, 536, 150, 450)(93, 393, 151, 451, 187, 487, 239, 539, 152, 452)(96, 396, 156, 456, 243, 543, 245, 545, 157, 457)(98, 398, 159, 459, 191, 491, 248, 548, 160, 460)(99, 399, 161, 461, 194, 494, 241, 541, 154, 454)(107, 407, 171, 471, 259, 559, 261, 561, 172, 472)(110, 410, 177, 477, 263, 563, 266, 566, 178, 478)(114, 414, 183, 483, 269, 569, 270, 570, 184, 484)(118, 418, 182, 482, 268, 568, 274, 574, 190, 490)(126, 426, 200, 500, 255, 555, 167, 467, 201, 501)(127, 427, 202, 502, 258, 558, 170, 470, 203, 503)(129, 429, 205, 505, 264, 564, 283, 583, 206, 506)(131, 431, 208, 508, 230, 530, 174, 474, 209, 509)(132, 432, 210, 510, 265, 565, 286, 586, 211, 511)(134, 434, 213, 513, 260, 560, 175, 475, 214, 514)(136, 436, 216, 516, 267, 567, 290, 590, 217, 517)(137, 437, 218, 518, 256, 556, 287, 587, 212, 512)(139, 439, 199, 499, 271, 571, 291, 591, 220, 520)(144, 444, 227, 527, 288, 588, 293, 593, 228, 528)(147, 447, 225, 525, 276, 576, 197, 497, 232, 532)(158, 458, 246, 546, 272, 572, 280, 580, 247, 547)(162, 462, 219, 519, 279, 579, 298, 598, 250, 550)(164, 464, 242, 542, 273, 573, 189, 489, 251, 551)(165, 465, 252, 552, 275, 575, 192, 492, 253, 553)(169, 469, 257, 557, 278, 578, 196, 496, 237, 537)(204, 504, 222, 522, 249, 549, 262, 562, 281, 581)(215, 515, 240, 540, 294, 594, 229, 529, 289, 589)(233, 533, 254, 554, 282, 582, 244, 544, 277, 577)(235, 535, 284, 584, 297, 597, 300, 600, 295, 595)(238, 538, 285, 585, 299, 599, 292, 592, 296, 596)(601, 901)(602, 902)(603, 903)(604, 904)(605, 905)(606, 906)(607, 907)(608, 908)(609, 909)(610, 910)(611, 911)(612, 912)(613, 913)(614, 914)(615, 915)(616, 916)(617, 917)(618, 918)(619, 919)(620, 920)(621, 921)(622, 922)(623, 923)(624, 924)(625, 925)(626, 926)(627, 927)(628, 928)(629, 929)(630, 930)(631, 931)(632, 932)(633, 933)(634, 934)(635, 935)(636, 936)(637, 937)(638, 938)(639, 939)(640, 940)(641, 941)(642, 942)(643, 943)(644, 944)(645, 945)(646, 946)(647, 947)(648, 948)(649, 949)(650, 950)(651, 951)(652, 952)(653, 953)(654, 954)(655, 955)(656, 956)(657, 957)(658, 958)(659, 959)(660, 960)(661, 961)(662, 962)(663, 963)(664, 964)(665, 965)(666, 966)(667, 967)(668, 968)(669, 969)(670, 970)(671, 971)(672, 972)(673, 973)(674, 974)(675, 975)(676, 976)(677, 977)(678, 978)(679, 979)(680, 980)(681, 981)(682, 982)(683, 983)(684, 984)(685, 985)(686, 986)(687, 987)(688, 988)(689, 989)(690, 990)(691, 991)(692, 992)(693, 993)(694, 994)(695, 995)(696, 996)(697, 997)(698, 998)(699, 999)(700, 1000)(701, 1001)(702, 1002)(703, 1003)(704, 1004)(705, 1005)(706, 1006)(707, 1007)(708, 1008)(709, 1009)(710, 1010)(711, 1011)(712, 1012)(713, 1013)(714, 1014)(715, 1015)(716, 1016)(717, 1017)(718, 1018)(719, 1019)(720, 1020)(721, 1021)(722, 1022)(723, 1023)(724, 1024)(725, 1025)(726, 1026)(727, 1027)(728, 1028)(729, 1029)(730, 1030)(731, 1031)(732, 1032)(733, 1033)(734, 1034)(735, 1035)(736, 1036)(737, 1037)(738, 1038)(739, 1039)(740, 1040)(741, 1041)(742, 1042)(743, 1043)(744, 1044)(745, 1045)(746, 1046)(747, 1047)(748, 1048)(749, 1049)(750, 1050)(751, 1051)(752, 1052)(753, 1053)(754, 1054)(755, 1055)(756, 1056)(757, 1057)(758, 1058)(759, 1059)(760, 1060)(761, 1061)(762, 1062)(763, 1063)(764, 1064)(765, 1065)(766, 1066)(767, 1067)(768, 1068)(769, 1069)(770, 1070)(771, 1071)(772, 1072)(773, 1073)(774, 1074)(775, 1075)(776, 1076)(777, 1077)(778, 1078)(779, 1079)(780, 1080)(781, 1081)(782, 1082)(783, 1083)(784, 1084)(785, 1085)(786, 1086)(787, 1087)(788, 1088)(789, 1089)(790, 1090)(791, 1091)(792, 1092)(793, 1093)(794, 1094)(795, 1095)(796, 1096)(797, 1097)(798, 1098)(799, 1099)(800, 1100)(801, 1101)(802, 1102)(803, 1103)(804, 1104)(805, 1105)(806, 1106)(807, 1107)(808, 1108)(809, 1109)(810, 1110)(811, 1111)(812, 1112)(813, 1113)(814, 1114)(815, 1115)(816, 1116)(817, 1117)(818, 1118)(819, 1119)(820, 1120)(821, 1121)(822, 1122)(823, 1123)(824, 1124)(825, 1125)(826, 1126)(827, 1127)(828, 1128)(829, 1129)(830, 1130)(831, 1131)(832, 1132)(833, 1133)(834, 1134)(835, 1135)(836, 1136)(837, 1137)(838, 1138)(839, 1139)(840, 1140)(841, 1141)(842, 1142)(843, 1143)(844, 1144)(845, 1145)(846, 1146)(847, 1147)(848, 1148)(849, 1149)(850, 1150)(851, 1151)(852, 1152)(853, 1153)(854, 1154)(855, 1155)(856, 1156)(857, 1157)(858, 1158)(859, 1159)(860, 1160)(861, 1161)(862, 1162)(863, 1163)(864, 1164)(865, 1165)(866, 1166)(867, 1167)(868, 1168)(869, 1169)(870, 1170)(871, 1171)(872, 1172)(873, 1173)(874, 1174)(875, 1175)(876, 1176)(877, 1177)(878, 1178)(879, 1179)(880, 1180)(881, 1181)(882, 1182)(883, 1183)(884, 1184)(885, 1185)(886, 1186)(887, 1187)(888, 1188)(889, 1189)(890, 1190)(891, 1191)(892, 1192)(893, 1193)(894, 1194)(895, 1195)(896, 1196)(897, 1197)(898, 1198)(899, 1199)(900, 1200) L = (1, 603)(2, 606)(3, 601)(4, 609)(5, 611)(6, 602)(7, 615)(8, 616)(9, 604)(10, 620)(11, 605)(12, 624)(13, 625)(14, 627)(15, 607)(16, 608)(17, 632)(18, 634)(19, 635)(20, 610)(21, 640)(22, 641)(23, 643)(24, 612)(25, 613)(26, 648)(27, 614)(28, 652)(29, 653)(30, 656)(31, 644)(32, 617)(33, 660)(34, 618)(35, 619)(36, 664)(37, 666)(38, 667)(39, 669)(40, 621)(41, 622)(42, 674)(43, 623)(44, 631)(45, 678)(46, 681)(47, 670)(48, 626)(49, 686)(50, 687)(51, 689)(52, 628)(53, 629)(54, 692)(55, 693)(56, 630)(57, 696)(58, 698)(59, 699)(60, 633)(61, 704)(62, 695)(63, 707)(64, 636)(65, 710)(66, 637)(67, 638)(68, 714)(69, 639)(70, 647)(71, 718)(72, 721)(73, 711)(74, 642)(75, 726)(76, 727)(77, 729)(78, 645)(79, 731)(80, 732)(81, 646)(82, 734)(83, 736)(84, 737)(85, 739)(86, 649)(87, 650)(88, 744)(89, 651)(90, 747)(91, 740)(92, 654)(93, 655)(94, 754)(95, 662)(96, 657)(97, 758)(98, 658)(99, 659)(100, 762)(101, 764)(102, 765)(103, 767)(104, 661)(105, 769)(106, 770)(107, 663)(108, 774)(109, 775)(110, 665)(111, 673)(112, 772)(113, 782)(114, 668)(115, 786)(116, 787)(117, 789)(118, 671)(119, 791)(120, 792)(121, 672)(122, 794)(123, 796)(124, 797)(125, 799)(126, 675)(127, 676)(128, 804)(129, 677)(130, 800)(131, 679)(132, 680)(133, 812)(134, 682)(135, 815)(136, 683)(137, 684)(138, 819)(139, 685)(140, 691)(141, 822)(142, 825)(143, 759)(144, 688)(145, 829)(146, 830)(147, 690)(148, 833)(149, 835)(150, 810)(151, 837)(152, 838)(153, 840)(154, 694)(155, 842)(156, 802)(157, 844)(158, 697)(159, 743)(160, 806)(161, 849)(162, 700)(163, 820)(164, 701)(165, 702)(166, 854)(167, 703)(168, 856)(169, 705)(170, 706)(171, 860)(172, 712)(173, 862)(174, 708)(175, 709)(176, 850)(177, 864)(178, 865)(179, 823)(180, 867)(181, 826)(182, 713)(183, 836)(184, 845)(185, 871)(186, 715)(187, 716)(188, 872)(189, 717)(190, 831)(191, 719)(192, 720)(193, 876)(194, 722)(195, 877)(196, 723)(197, 724)(198, 879)(199, 725)(200, 730)(201, 880)(202, 756)(203, 816)(204, 728)(205, 882)(206, 760)(207, 828)(208, 884)(209, 853)(210, 750)(211, 885)(212, 733)(213, 839)(214, 888)(215, 735)(216, 803)(217, 873)(218, 847)(219, 738)(220, 763)(221, 878)(222, 741)(223, 779)(224, 892)(225, 742)(226, 781)(227, 851)(228, 807)(229, 745)(230, 746)(231, 790)(232, 889)(233, 748)(234, 855)(235, 749)(236, 783)(237, 751)(238, 752)(239, 813)(240, 753)(241, 886)(242, 755)(243, 868)(244, 757)(245, 784)(246, 859)(247, 818)(248, 897)(249, 761)(250, 776)(251, 827)(252, 887)(253, 809)(254, 766)(255, 834)(256, 768)(257, 895)(258, 896)(259, 846)(260, 771)(261, 883)(262, 773)(263, 891)(264, 777)(265, 778)(266, 894)(267, 780)(268, 843)(269, 893)(270, 898)(271, 785)(272, 788)(273, 817)(274, 881)(275, 899)(276, 793)(277, 795)(278, 821)(279, 798)(280, 801)(281, 874)(282, 805)(283, 861)(284, 808)(285, 811)(286, 841)(287, 852)(288, 814)(289, 832)(290, 900)(291, 863)(292, 824)(293, 869)(294, 866)(295, 857)(296, 858)(297, 848)(298, 870)(299, 875)(300, 890)(301, 901)(302, 902)(303, 903)(304, 904)(305, 905)(306, 906)(307, 907)(308, 908)(309, 909)(310, 910)(311, 911)(312, 912)(313, 913)(314, 914)(315, 915)(316, 916)(317, 917)(318, 918)(319, 919)(320, 920)(321, 921)(322, 922)(323, 923)(324, 924)(325, 925)(326, 926)(327, 927)(328, 928)(329, 929)(330, 930)(331, 931)(332, 932)(333, 933)(334, 934)(335, 935)(336, 936)(337, 937)(338, 938)(339, 939)(340, 940)(341, 941)(342, 942)(343, 943)(344, 944)(345, 945)(346, 946)(347, 947)(348, 948)(349, 949)(350, 950)(351, 951)(352, 952)(353, 953)(354, 954)(355, 955)(356, 956)(357, 957)(358, 958)(359, 959)(360, 960)(361, 961)(362, 962)(363, 963)(364, 964)(365, 965)(366, 966)(367, 967)(368, 968)(369, 969)(370, 970)(371, 971)(372, 972)(373, 973)(374, 974)(375, 975)(376, 976)(377, 977)(378, 978)(379, 979)(380, 980)(381, 981)(382, 982)(383, 983)(384, 984)(385, 985)(386, 986)(387, 987)(388, 988)(389, 989)(390, 990)(391, 991)(392, 992)(393, 993)(394, 994)(395, 995)(396, 996)(397, 997)(398, 998)(399, 999)(400, 1000)(401, 1001)(402, 1002)(403, 1003)(404, 1004)(405, 1005)(406, 1006)(407, 1007)(408, 1008)(409, 1009)(410, 1010)(411, 1011)(412, 1012)(413, 1013)(414, 1014)(415, 1015)(416, 1016)(417, 1017)(418, 1018)(419, 1019)(420, 1020)(421, 1021)(422, 1022)(423, 1023)(424, 1024)(425, 1025)(426, 1026)(427, 1027)(428, 1028)(429, 1029)(430, 1030)(431, 1031)(432, 1032)(433, 1033)(434, 1034)(435, 1035)(436, 1036)(437, 1037)(438, 1038)(439, 1039)(440, 1040)(441, 1041)(442, 1042)(443, 1043)(444, 1044)(445, 1045)(446, 1046)(447, 1047)(448, 1048)(449, 1049)(450, 1050)(451, 1051)(452, 1052)(453, 1053)(454, 1054)(455, 1055)(456, 1056)(457, 1057)(458, 1058)(459, 1059)(460, 1060)(461, 1061)(462, 1062)(463, 1063)(464, 1064)(465, 1065)(466, 1066)(467, 1067)(468, 1068)(469, 1069)(470, 1070)(471, 1071)(472, 1072)(473, 1073)(474, 1074)(475, 1075)(476, 1076)(477, 1077)(478, 1078)(479, 1079)(480, 1080)(481, 1081)(482, 1082)(483, 1083)(484, 1084)(485, 1085)(486, 1086)(487, 1087)(488, 1088)(489, 1089)(490, 1090)(491, 1091)(492, 1092)(493, 1093)(494, 1094)(495, 1095)(496, 1096)(497, 1097)(498, 1098)(499, 1099)(500, 1100)(501, 1101)(502, 1102)(503, 1103)(504, 1104)(505, 1105)(506, 1106)(507, 1107)(508, 1108)(509, 1109)(510, 1110)(511, 1111)(512, 1112)(513, 1113)(514, 1114)(515, 1115)(516, 1116)(517, 1117)(518, 1118)(519, 1119)(520, 1120)(521, 1121)(522, 1122)(523, 1123)(524, 1124)(525, 1125)(526, 1126)(527, 1127)(528, 1128)(529, 1129)(530, 1130)(531, 1131)(532, 1132)(533, 1133)(534, 1134)(535, 1135)(536, 1136)(537, 1137)(538, 1138)(539, 1139)(540, 1140)(541, 1141)(542, 1142)(543, 1143)(544, 1144)(545, 1145)(546, 1146)(547, 1147)(548, 1148)(549, 1149)(550, 1150)(551, 1151)(552, 1152)(553, 1153)(554, 1154)(555, 1155)(556, 1156)(557, 1157)(558, 1158)(559, 1159)(560, 1160)(561, 1161)(562, 1162)(563, 1163)(564, 1164)(565, 1165)(566, 1166)(567, 1167)(568, 1168)(569, 1169)(570, 1170)(571, 1171)(572, 1172)(573, 1173)(574, 1174)(575, 1175)(576, 1176)(577, 1177)(578, 1178)(579, 1179)(580, 1180)(581, 1181)(582, 1182)(583, 1183)(584, 1184)(585, 1185)(586, 1186)(587, 1187)(588, 1188)(589, 1189)(590, 1190)(591, 1191)(592, 1192)(593, 1193)(594, 1194)(595, 1195)(596, 1196)(597, 1197)(598, 1198)(599, 1199)(600, 1200) local type(s) :: { ( 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.1279 Graph:: simple bipartite v = 360 e = 600 f = 210 degree seq :: [ 2^300, 10^60 ] E16.1281 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 3, 4}) Quotient :: edge Aut^+ = A6 (small group id <360, 118>) Aut = C2 x A6 (small group id <720, 766>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1^-1)^3, (T1 * T2)^3, (T1 * T2^-1)^5, (T2^-2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1)^2, (T2 * T1 * T2^-1 * T1 * T2^-2 * T1^-1)^2 ] Map:: polyhedral non-degenerate R = (1, 3, 9, 5)(2, 6, 16, 7)(4, 11, 27, 12)(8, 20, 41, 21)(10, 24, 49, 25)(13, 30, 59, 31)(14, 32, 33, 15)(17, 36, 72, 37)(18, 38, 75, 39)(19, 40, 52, 26)(22, 44, 86, 45)(23, 46, 90, 47)(28, 55, 105, 56)(29, 57, 108, 58)(34, 67, 124, 68)(35, 69, 128, 70)(42, 83, 148, 84)(43, 85, 92, 48)(50, 77, 140, 95)(51, 96, 169, 97)(53, 100, 176, 101)(54, 102, 180, 103)(60, 114, 198, 115)(61, 116, 185, 106)(62, 117, 118, 63)(64, 119, 205, 120)(65, 121, 207, 122)(66, 123, 130, 71)(73, 110, 191, 133)(74, 134, 227, 135)(76, 138, 234, 139)(78, 141, 142, 79)(80, 143, 240, 144)(81, 111, 192, 145)(82, 146, 245, 147)(87, 156, 258, 157)(88, 158, 159, 89)(91, 150, 250, 162)(93, 164, 267, 165)(94, 166, 270, 167)(98, 173, 264, 174)(99, 175, 182, 104)(107, 186, 260, 187)(109, 171, 276, 190)(112, 193, 300, 194)(113, 195, 303, 196)(125, 214, 315, 215)(126, 216, 217, 127)(129, 208, 309, 220)(131, 222, 269, 223)(132, 224, 321, 225)(136, 229, 326, 230)(137, 231, 328, 232)(149, 248, 201, 249)(151, 251, 252, 152)(153, 253, 200, 254)(154, 172, 277, 255)(155, 256, 343, 257)(160, 261, 344, 262)(161, 263, 212, 197)(163, 265, 206, 266)(168, 272, 202, 273)(170, 199, 305, 275)(177, 284, 334, 246)(178, 285, 286, 179)(181, 278, 338, 288)(183, 289, 320, 268)(184, 290, 346, 291)(188, 294, 345, 295)(189, 296, 302, 297)(203, 306, 259, 204)(209, 274, 310, 210)(211, 311, 236, 312)(213, 313, 336, 314)(218, 247, 335, 301)(219, 317, 282, 233)(221, 318, 241, 319)(226, 322, 237, 323)(228, 235, 329, 325)(238, 330, 316, 239)(242, 331, 292, 332)(243, 333, 304, 244)(271, 347, 307, 283)(279, 324, 350, 280)(281, 351, 299, 337)(287, 308, 342, 327)(293, 298, 352, 339)(340, 358, 353, 341)(348, 349, 359, 354)(355, 356, 360, 357)(361, 362, 364)(363, 368, 370)(365, 373, 374)(366, 375, 377)(367, 378, 379)(369, 382, 383)(371, 386, 388)(372, 389, 380)(376, 394, 395)(381, 402, 403)(384, 408, 410)(385, 411, 404)(387, 413, 414)(390, 407, 420)(391, 421, 422)(392, 423, 424)(393, 425, 426)(396, 431, 433)(397, 434, 427)(398, 430, 436)(399, 437, 438)(400, 439, 440)(401, 441, 442)(405, 447, 448)(406, 449, 451)(409, 453, 454)(412, 458, 459)(415, 464, 466)(416, 467, 460)(417, 463, 469)(418, 470, 471)(419, 472, 473)(428, 485, 486)(429, 487, 489)(432, 491, 492)(435, 496, 497)(443, 507, 509)(444, 510, 511)(445, 512, 513)(446, 514, 515)(450, 520, 521)(452, 523, 501)(455, 528, 524)(456, 527, 530)(457, 531, 532)(461, 537, 538)(462, 539, 541)(465, 543, 544)(468, 548, 549)(474, 557, 495)(475, 559, 553)(476, 556, 560)(477, 542, 561)(478, 562, 563)(479, 564, 517)(480, 566, 481)(482, 568, 569)(483, 570, 571)(484, 572, 573)(488, 578, 579)(490, 581, 552)(493, 586, 582)(494, 585, 588)(498, 593, 547)(499, 595, 589)(500, 592, 596)(502, 597, 598)(503, 599, 575)(504, 601, 533)(505, 602, 603)(506, 604, 606)(508, 607, 580)(516, 617, 600)(518, 619, 594)(519, 620, 611)(522, 624, 621)(525, 628, 583)(526, 629, 631)(529, 634, 577)(534, 638, 639)(535, 640, 641)(536, 642, 643)(540, 647, 637)(545, 652, 649)(546, 651, 653)(550, 658, 654)(551, 657, 659)(554, 661, 662)(555, 656, 591)(558, 645, 664)(565, 644, 667)(567, 668, 648)(574, 674, 605)(576, 676, 636)(584, 680, 616)(587, 684, 646)(590, 687, 663)(608, 696, 633)(609, 697, 695)(610, 669, 698)(612, 699, 700)(613, 701, 692)(614, 702, 625)(615, 686, 681)(618, 675, 694)(622, 688, 655)(623, 705, 706)(626, 707, 683)(627, 673, 650)(630, 677, 660)(632, 671, 708)(635, 709, 670)(665, 693, 713)(666, 714, 689)(672, 704, 678)(679, 703, 691)(682, 711, 715)(685, 716, 710)(690, 717, 712)(718, 720, 719) L = (1, 361)(2, 362)(3, 363)(4, 364)(5, 365)(6, 366)(7, 367)(8, 368)(9, 369)(10, 370)(11, 371)(12, 372)(13, 373)(14, 374)(15, 375)(16, 376)(17, 377)(18, 378)(19, 379)(20, 380)(21, 381)(22, 382)(23, 383)(24, 384)(25, 385)(26, 386)(27, 387)(28, 388)(29, 389)(30, 390)(31, 391)(32, 392)(33, 393)(34, 394)(35, 395)(36, 396)(37, 397)(38, 398)(39, 399)(40, 400)(41, 401)(42, 402)(43, 403)(44, 404)(45, 405)(46, 406)(47, 407)(48, 408)(49, 409)(50, 410)(51, 411)(52, 412)(53, 413)(54, 414)(55, 415)(56, 416)(57, 417)(58, 418)(59, 419)(60, 420)(61, 421)(62, 422)(63, 423)(64, 424)(65, 425)(66, 426)(67, 427)(68, 428)(69, 429)(70, 430)(71, 431)(72, 432)(73, 433)(74, 434)(75, 435)(76, 436)(77, 437)(78, 438)(79, 439)(80, 440)(81, 441)(82, 442)(83, 443)(84, 444)(85, 445)(86, 446)(87, 447)(88, 448)(89, 449)(90, 450)(91, 451)(92, 452)(93, 453)(94, 454)(95, 455)(96, 456)(97, 457)(98, 458)(99, 459)(100, 460)(101, 461)(102, 462)(103, 463)(104, 464)(105, 465)(106, 466)(107, 467)(108, 468)(109, 469)(110, 470)(111, 471)(112, 472)(113, 473)(114, 474)(115, 475)(116, 476)(117, 477)(118, 478)(119, 479)(120, 480)(121, 481)(122, 482)(123, 483)(124, 484)(125, 485)(126, 486)(127, 487)(128, 488)(129, 489)(130, 490)(131, 491)(132, 492)(133, 493)(134, 494)(135, 495)(136, 496)(137, 497)(138, 498)(139, 499)(140, 500)(141, 501)(142, 502)(143, 503)(144, 504)(145, 505)(146, 506)(147, 507)(148, 508)(149, 509)(150, 510)(151, 511)(152, 512)(153, 513)(154, 514)(155, 515)(156, 516)(157, 517)(158, 518)(159, 519)(160, 520)(161, 521)(162, 522)(163, 523)(164, 524)(165, 525)(166, 526)(167, 527)(168, 528)(169, 529)(170, 530)(171, 531)(172, 532)(173, 533)(174, 534)(175, 535)(176, 536)(177, 537)(178, 538)(179, 539)(180, 540)(181, 541)(182, 542)(183, 543)(184, 544)(185, 545)(186, 546)(187, 547)(188, 548)(189, 549)(190, 550)(191, 551)(192, 552)(193, 553)(194, 554)(195, 555)(196, 556)(197, 557)(198, 558)(199, 559)(200, 560)(201, 561)(202, 562)(203, 563)(204, 564)(205, 565)(206, 566)(207, 567)(208, 568)(209, 569)(210, 570)(211, 571)(212, 572)(213, 573)(214, 574)(215, 575)(216, 576)(217, 577)(218, 578)(219, 579)(220, 580)(221, 581)(222, 582)(223, 583)(224, 584)(225, 585)(226, 586)(227, 587)(228, 588)(229, 589)(230, 590)(231, 591)(232, 592)(233, 593)(234, 594)(235, 595)(236, 596)(237, 597)(238, 598)(239, 599)(240, 600)(241, 601)(242, 602)(243, 603)(244, 604)(245, 605)(246, 606)(247, 607)(248, 608)(249, 609)(250, 610)(251, 611)(252, 612)(253, 613)(254, 614)(255, 615)(256, 616)(257, 617)(258, 618)(259, 619)(260, 620)(261, 621)(262, 622)(263, 623)(264, 624)(265, 625)(266, 626)(267, 627)(268, 628)(269, 629)(270, 630)(271, 631)(272, 632)(273, 633)(274, 634)(275, 635)(276, 636)(277, 637)(278, 638)(279, 639)(280, 640)(281, 641)(282, 642)(283, 643)(284, 644)(285, 645)(286, 646)(287, 647)(288, 648)(289, 649)(290, 650)(291, 651)(292, 652)(293, 653)(294, 654)(295, 655)(296, 656)(297, 657)(298, 658)(299, 659)(300, 660)(301, 661)(302, 662)(303, 663)(304, 664)(305, 665)(306, 666)(307, 667)(308, 668)(309, 669)(310, 670)(311, 671)(312, 672)(313, 673)(314, 674)(315, 675)(316, 676)(317, 677)(318, 678)(319, 679)(320, 680)(321, 681)(322, 682)(323, 683)(324, 684)(325, 685)(326, 686)(327, 687)(328, 688)(329, 689)(330, 690)(331, 691)(332, 692)(333, 693)(334, 694)(335, 695)(336, 696)(337, 697)(338, 698)(339, 699)(340, 700)(341, 701)(342, 702)(343, 703)(344, 704)(345, 705)(346, 706)(347, 707)(348, 708)(349, 709)(350, 710)(351, 711)(352, 712)(353, 713)(354, 714)(355, 715)(356, 716)(357, 717)(358, 718)(359, 719)(360, 720) local type(s) :: { ( 6^3 ), ( 6^4 ) } Outer automorphisms :: reflexible Dual of E16.1282 Transitivity :: ET+ Graph:: simple bipartite v = 210 e = 360 f = 120 degree seq :: [ 3^120, 4^90 ] E16.1282 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 3, 4}) Quotient :: loop Aut^+ = A6 (small group id <360, 118>) Aut = C2 x A6 (small group id <720, 766>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^4, (T1 * T2^-1)^5, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1, T2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2 * T1^-1, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1, T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 361, 3, 363, 5, 365)(2, 362, 6, 366, 7, 367)(4, 364, 10, 370, 11, 371)(8, 368, 18, 378, 19, 379)(9, 369, 20, 380, 21, 381)(12, 372, 26, 386, 27, 387)(13, 373, 28, 388, 29, 389)(14, 374, 30, 390, 31, 391)(15, 375, 32, 392, 33, 393)(16, 376, 34, 394, 35, 395)(17, 377, 36, 396, 37, 397)(22, 382, 46, 406, 47, 407)(23, 383, 48, 408, 49, 409)(24, 384, 50, 410, 51, 411)(25, 385, 52, 412, 38, 398)(39, 399, 73, 433, 74, 434)(40, 400, 75, 435, 76, 436)(41, 401, 77, 437, 78, 438)(42, 402, 79, 439, 80, 440)(43, 403, 68, 428, 81, 441)(44, 404, 82, 442, 83, 443)(45, 405, 84, 444, 53, 413)(54, 414, 97, 457, 98, 458)(55, 415, 99, 459, 88, 448)(56, 416, 100, 460, 101, 461)(57, 417, 102, 462, 103, 463)(58, 418, 104, 464, 105, 465)(59, 419, 106, 466, 107, 467)(60, 420, 108, 468, 109, 469)(61, 421, 110, 470, 111, 471)(62, 422, 112, 472, 113, 473)(63, 423, 93, 453, 114, 474)(64, 424, 115, 475, 116, 476)(65, 425, 117, 477, 66, 426)(67, 427, 118, 478, 119, 479)(69, 429, 120, 480, 121, 481)(70, 430, 122, 482, 123, 483)(71, 431, 124, 484, 125, 485)(72, 432, 126, 486, 127, 487)(85, 445, 148, 508, 149, 509)(86, 446, 150, 510, 151, 511)(87, 447, 152, 512, 153, 513)(89, 449, 154, 514, 155, 515)(90, 450, 156, 516, 91, 451)(92, 452, 157, 517, 158, 518)(94, 454, 159, 519, 160, 520)(95, 455, 161, 521, 162, 522)(96, 456, 163, 523, 164, 524)(128, 488, 213, 573, 214, 574)(129, 489, 144, 504, 215, 575)(130, 490, 216, 576, 217, 577)(131, 491, 218, 578, 132, 492)(133, 493, 219, 579, 220, 580)(134, 494, 221, 581, 222, 582)(135, 495, 223, 583, 224, 584)(136, 496, 225, 585, 226, 586)(137, 497, 227, 587, 228, 588)(138, 498, 229, 589, 230, 590)(139, 499, 231, 591, 202, 562)(140, 500, 201, 561, 232, 592)(141, 501, 233, 593, 142, 502)(143, 503, 234, 594, 235, 595)(145, 505, 236, 596, 237, 597)(146, 506, 238, 598, 239, 599)(147, 507, 240, 600, 241, 601)(165, 525, 264, 624, 265, 625)(166, 526, 180, 540, 266, 626)(167, 527, 267, 627, 268, 628)(168, 528, 269, 629, 169, 529)(170, 530, 270, 630, 250, 610)(171, 531, 249, 609, 271, 631)(172, 532, 272, 632, 273, 633)(173, 533, 274, 634, 275, 635)(174, 534, 276, 636, 186, 546)(175, 535, 277, 637, 278, 638)(176, 536, 279, 639, 280, 640)(177, 537, 281, 641, 178, 538)(179, 539, 194, 554, 282, 642)(181, 541, 283, 643, 182, 542)(183, 543, 284, 644, 285, 645)(184, 544, 286, 646, 287, 647)(185, 545, 288, 648, 289, 649)(187, 547, 290, 650, 291, 651)(188, 548, 292, 652, 293, 653)(189, 549, 294, 654, 259, 619)(190, 550, 258, 618, 295, 655)(191, 551, 296, 656, 192, 552)(193, 553, 297, 657, 298, 658)(195, 555, 299, 659, 300, 660)(196, 556, 301, 661, 302, 662)(197, 557, 303, 663, 304, 664)(198, 558, 305, 665, 306, 666)(199, 559, 211, 571, 307, 667)(200, 560, 308, 668, 309, 669)(203, 563, 310, 670, 311, 671)(204, 564, 312, 672, 313, 673)(205, 565, 314, 674, 246, 606)(206, 566, 315, 675, 316, 676)(207, 567, 317, 677, 318, 678)(208, 568, 319, 679, 209, 569)(210, 570, 252, 612, 320, 680)(212, 572, 321, 681, 242, 602)(243, 603, 327, 687, 336, 696)(244, 604, 337, 697, 338, 698)(245, 605, 339, 699, 340, 700)(247, 607, 322, 682, 326, 686)(248, 608, 325, 685, 330, 690)(251, 611, 329, 689, 323, 683)(253, 613, 335, 695, 341, 701)(254, 614, 342, 702, 332, 692)(255, 615, 331, 691, 343, 703)(256, 616, 344, 704, 345, 705)(257, 617, 346, 706, 328, 688)(260, 620, 333, 693, 347, 707)(261, 621, 348, 708, 349, 709)(262, 622, 350, 710, 351, 711)(263, 623, 352, 712, 353, 713)(324, 684, 358, 718, 354, 714)(334, 694, 359, 719, 355, 715)(356, 716, 360, 720, 357, 717) L = (1, 362)(2, 364)(3, 368)(4, 361)(5, 372)(6, 374)(7, 376)(8, 369)(9, 363)(10, 382)(11, 384)(12, 373)(13, 365)(14, 375)(15, 366)(16, 377)(17, 367)(18, 398)(19, 400)(20, 402)(21, 404)(22, 383)(23, 370)(24, 385)(25, 371)(26, 413)(27, 415)(28, 417)(29, 419)(30, 389)(31, 420)(32, 422)(33, 424)(34, 426)(35, 428)(36, 430)(37, 432)(38, 399)(39, 378)(40, 401)(41, 379)(42, 403)(43, 380)(44, 405)(45, 381)(46, 397)(47, 445)(48, 447)(49, 449)(50, 451)(51, 453)(52, 455)(53, 414)(54, 386)(55, 416)(56, 387)(57, 418)(58, 388)(59, 390)(60, 421)(61, 391)(62, 423)(63, 392)(64, 425)(65, 393)(66, 427)(67, 394)(68, 429)(69, 395)(70, 431)(71, 396)(72, 406)(73, 488)(74, 490)(75, 492)(76, 464)(77, 495)(78, 497)(79, 438)(80, 498)(81, 500)(82, 502)(83, 504)(84, 506)(85, 446)(86, 407)(87, 448)(88, 408)(89, 450)(90, 409)(91, 452)(92, 410)(93, 454)(94, 411)(95, 456)(96, 412)(97, 525)(98, 527)(99, 529)(100, 531)(101, 533)(102, 461)(103, 534)(104, 494)(105, 536)(106, 538)(107, 540)(108, 542)(109, 484)(110, 545)(111, 547)(112, 471)(113, 548)(114, 550)(115, 552)(116, 554)(117, 556)(118, 558)(119, 560)(120, 562)(121, 564)(122, 481)(123, 565)(124, 544)(125, 567)(126, 569)(127, 571)(128, 489)(129, 433)(130, 491)(131, 434)(132, 493)(133, 435)(134, 436)(135, 496)(136, 437)(137, 439)(138, 499)(139, 440)(140, 501)(141, 441)(142, 503)(143, 442)(144, 505)(145, 443)(146, 507)(147, 444)(148, 602)(149, 523)(150, 605)(151, 607)(152, 511)(153, 608)(154, 610)(155, 612)(156, 614)(157, 616)(158, 617)(159, 619)(160, 621)(161, 520)(162, 585)(163, 604)(164, 623)(165, 526)(166, 457)(167, 528)(168, 458)(169, 530)(170, 459)(171, 532)(172, 460)(173, 462)(174, 535)(175, 463)(176, 537)(177, 465)(178, 539)(179, 466)(180, 541)(181, 467)(182, 543)(183, 468)(184, 469)(185, 546)(186, 470)(187, 472)(188, 549)(189, 473)(190, 551)(191, 474)(192, 553)(193, 475)(194, 555)(195, 476)(196, 557)(197, 477)(198, 559)(199, 478)(200, 561)(201, 479)(202, 563)(203, 480)(204, 482)(205, 566)(206, 483)(207, 568)(208, 485)(209, 570)(210, 486)(211, 572)(212, 487)(213, 524)(214, 661)(215, 648)(216, 646)(217, 517)(218, 665)(219, 652)(220, 674)(221, 638)(222, 680)(223, 582)(224, 683)(225, 622)(226, 677)(227, 644)(228, 686)(229, 650)(230, 600)(231, 688)(232, 690)(233, 692)(234, 654)(235, 694)(236, 659)(237, 679)(238, 597)(239, 632)(240, 655)(241, 681)(242, 603)(243, 508)(244, 509)(245, 606)(246, 510)(247, 512)(248, 609)(249, 513)(250, 611)(251, 514)(252, 613)(253, 515)(254, 615)(255, 516)(256, 577)(257, 618)(258, 518)(259, 620)(260, 519)(261, 521)(262, 522)(263, 573)(264, 601)(265, 666)(266, 697)(267, 710)(268, 594)(269, 653)(270, 662)(271, 669)(272, 656)(273, 678)(274, 708)(275, 671)(276, 712)(277, 715)(278, 667)(279, 580)(280, 673)(281, 702)(282, 699)(283, 704)(284, 685)(285, 586)(286, 676)(287, 575)(288, 647)(289, 595)(290, 687)(291, 588)(292, 682)(293, 663)(294, 628)(295, 590)(296, 599)(297, 631)(298, 716)(299, 695)(300, 574)(301, 660)(302, 670)(303, 629)(304, 578)(305, 664)(306, 705)(307, 581)(308, 637)(309, 657)(310, 630)(311, 713)(312, 634)(313, 707)(314, 639)(315, 717)(316, 576)(317, 645)(318, 709)(319, 598)(320, 583)(321, 624)(322, 579)(323, 684)(324, 584)(325, 587)(326, 651)(327, 589)(328, 689)(329, 591)(330, 691)(331, 592)(332, 693)(333, 593)(334, 649)(335, 596)(336, 636)(337, 711)(338, 642)(339, 698)(340, 658)(341, 641)(342, 701)(343, 643)(344, 703)(345, 625)(346, 675)(347, 640)(348, 672)(349, 633)(350, 714)(351, 626)(352, 696)(353, 635)(354, 627)(355, 668)(356, 700)(357, 706)(358, 720)(359, 718)(360, 719) local type(s) :: { ( 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E16.1281 Transitivity :: ET+ VT+ AT Graph:: simple v = 120 e = 360 f = 210 degree seq :: [ 6^120 ] E16.1283 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4}) Quotient :: dipole Aut^+ = A6 (small group id <360, 118>) Aut = C2 x A6 (small group id <720, 766>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, Y2^4, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y1^-1)^3, (Y1 * Y2)^3, (Y3^-1 * Y1^-1)^3, (Y1^-1 * Y2)^5, (Y2^-2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1)^2, (Y2 * Y1 * Y2^-1 * Y1 * Y2^-2 * Y1^-1)^2 ] Map:: R = (1, 361, 2, 362, 4, 364)(3, 363, 8, 368, 10, 370)(5, 365, 13, 373, 14, 374)(6, 366, 15, 375, 17, 377)(7, 367, 18, 378, 19, 379)(9, 369, 22, 382, 23, 383)(11, 371, 26, 386, 28, 388)(12, 372, 29, 389, 20, 380)(16, 376, 34, 394, 35, 395)(21, 381, 42, 402, 43, 403)(24, 384, 48, 408, 50, 410)(25, 385, 51, 411, 44, 404)(27, 387, 53, 413, 54, 414)(30, 390, 47, 407, 60, 420)(31, 391, 61, 421, 62, 422)(32, 392, 63, 423, 64, 424)(33, 393, 65, 425, 66, 426)(36, 396, 71, 431, 73, 433)(37, 397, 74, 434, 67, 427)(38, 398, 70, 430, 76, 436)(39, 399, 77, 437, 78, 438)(40, 400, 79, 439, 80, 440)(41, 401, 81, 441, 82, 442)(45, 405, 87, 447, 88, 448)(46, 406, 89, 449, 91, 451)(49, 409, 93, 453, 94, 454)(52, 412, 98, 458, 99, 459)(55, 415, 104, 464, 106, 466)(56, 416, 107, 467, 100, 460)(57, 417, 103, 463, 109, 469)(58, 418, 110, 470, 111, 471)(59, 419, 112, 472, 113, 473)(68, 428, 125, 485, 126, 486)(69, 429, 127, 487, 129, 489)(72, 432, 131, 491, 132, 492)(75, 435, 136, 496, 137, 497)(83, 443, 147, 507, 149, 509)(84, 444, 150, 510, 151, 511)(85, 445, 152, 512, 153, 513)(86, 446, 154, 514, 155, 515)(90, 450, 160, 520, 161, 521)(92, 452, 163, 523, 141, 501)(95, 455, 168, 528, 164, 524)(96, 456, 167, 527, 170, 530)(97, 457, 171, 531, 172, 532)(101, 461, 177, 537, 178, 538)(102, 462, 179, 539, 181, 541)(105, 465, 183, 543, 184, 544)(108, 468, 188, 548, 189, 549)(114, 474, 197, 557, 135, 495)(115, 475, 199, 559, 193, 553)(116, 476, 196, 556, 200, 560)(117, 477, 182, 542, 201, 561)(118, 478, 202, 562, 203, 563)(119, 479, 204, 564, 157, 517)(120, 480, 206, 566, 121, 481)(122, 482, 208, 568, 209, 569)(123, 483, 210, 570, 211, 571)(124, 484, 212, 572, 213, 573)(128, 488, 218, 578, 219, 579)(130, 490, 221, 581, 192, 552)(133, 493, 226, 586, 222, 582)(134, 494, 225, 585, 228, 588)(138, 498, 233, 593, 187, 547)(139, 499, 235, 595, 229, 589)(140, 500, 232, 592, 236, 596)(142, 502, 237, 597, 238, 598)(143, 503, 239, 599, 215, 575)(144, 504, 241, 601, 173, 533)(145, 505, 242, 602, 243, 603)(146, 506, 244, 604, 246, 606)(148, 508, 247, 607, 220, 580)(156, 516, 257, 617, 240, 600)(158, 518, 259, 619, 234, 594)(159, 519, 260, 620, 251, 611)(162, 522, 264, 624, 261, 621)(165, 525, 268, 628, 223, 583)(166, 526, 269, 629, 271, 631)(169, 529, 274, 634, 217, 577)(174, 534, 278, 638, 279, 639)(175, 535, 280, 640, 281, 641)(176, 536, 282, 642, 283, 643)(180, 540, 287, 647, 277, 637)(185, 545, 292, 652, 289, 649)(186, 546, 291, 651, 293, 653)(190, 550, 298, 658, 294, 654)(191, 551, 297, 657, 299, 659)(194, 554, 301, 661, 302, 662)(195, 555, 296, 656, 231, 591)(198, 558, 285, 645, 304, 664)(205, 565, 284, 644, 307, 667)(207, 567, 308, 668, 288, 648)(214, 574, 314, 674, 245, 605)(216, 576, 316, 676, 276, 636)(224, 584, 320, 680, 256, 616)(227, 587, 324, 684, 286, 646)(230, 590, 327, 687, 303, 663)(248, 608, 336, 696, 273, 633)(249, 609, 337, 697, 335, 695)(250, 610, 309, 669, 338, 698)(252, 612, 339, 699, 340, 700)(253, 613, 341, 701, 332, 692)(254, 614, 342, 702, 265, 625)(255, 615, 326, 686, 321, 681)(258, 618, 315, 675, 334, 694)(262, 622, 328, 688, 295, 655)(263, 623, 345, 705, 346, 706)(266, 626, 347, 707, 323, 683)(267, 627, 313, 673, 290, 650)(270, 630, 317, 677, 300, 660)(272, 632, 311, 671, 348, 708)(275, 635, 349, 709, 310, 670)(305, 665, 333, 693, 353, 713)(306, 666, 354, 714, 329, 689)(312, 672, 344, 704, 318, 678)(319, 679, 343, 703, 331, 691)(322, 682, 351, 711, 355, 715)(325, 685, 356, 716, 350, 710)(330, 690, 357, 717, 352, 712)(358, 718, 360, 720, 359, 719)(721, 1081, 723, 1083, 729, 1089, 725, 1085)(722, 1082, 726, 1086, 736, 1096, 727, 1087)(724, 1084, 731, 1091, 747, 1107, 732, 1092)(728, 1088, 740, 1100, 761, 1121, 741, 1101)(730, 1090, 744, 1104, 769, 1129, 745, 1105)(733, 1093, 750, 1110, 779, 1139, 751, 1111)(734, 1094, 752, 1112, 753, 1113, 735, 1095)(737, 1097, 756, 1116, 792, 1152, 757, 1117)(738, 1098, 758, 1118, 795, 1155, 759, 1119)(739, 1099, 760, 1120, 772, 1132, 746, 1106)(742, 1102, 764, 1124, 806, 1166, 765, 1125)(743, 1103, 766, 1126, 810, 1170, 767, 1127)(748, 1108, 775, 1135, 825, 1185, 776, 1136)(749, 1109, 777, 1137, 828, 1188, 778, 1138)(754, 1114, 787, 1147, 844, 1204, 788, 1148)(755, 1115, 789, 1149, 848, 1208, 790, 1150)(762, 1122, 803, 1163, 868, 1228, 804, 1164)(763, 1123, 805, 1165, 812, 1172, 768, 1128)(770, 1130, 797, 1157, 860, 1220, 815, 1175)(771, 1131, 816, 1176, 889, 1249, 817, 1177)(773, 1133, 820, 1180, 896, 1256, 821, 1181)(774, 1134, 822, 1182, 900, 1260, 823, 1183)(780, 1140, 834, 1194, 918, 1278, 835, 1195)(781, 1141, 836, 1196, 905, 1265, 826, 1186)(782, 1142, 837, 1197, 838, 1198, 783, 1143)(784, 1144, 839, 1199, 925, 1285, 840, 1200)(785, 1145, 841, 1201, 927, 1287, 842, 1202)(786, 1146, 843, 1203, 850, 1210, 791, 1151)(793, 1153, 830, 1190, 911, 1271, 853, 1213)(794, 1154, 854, 1214, 947, 1307, 855, 1215)(796, 1156, 858, 1218, 954, 1314, 859, 1219)(798, 1158, 861, 1221, 862, 1222, 799, 1159)(800, 1160, 863, 1223, 960, 1320, 864, 1224)(801, 1161, 831, 1191, 912, 1272, 865, 1225)(802, 1162, 866, 1226, 965, 1325, 867, 1227)(807, 1167, 876, 1236, 978, 1338, 877, 1237)(808, 1168, 878, 1238, 879, 1239, 809, 1169)(811, 1171, 870, 1230, 970, 1330, 882, 1242)(813, 1173, 884, 1244, 987, 1347, 885, 1245)(814, 1174, 886, 1246, 990, 1350, 887, 1247)(818, 1178, 893, 1253, 984, 1344, 894, 1254)(819, 1179, 895, 1255, 902, 1262, 824, 1184)(827, 1187, 906, 1266, 980, 1340, 907, 1267)(829, 1189, 891, 1251, 996, 1356, 910, 1270)(832, 1192, 913, 1273, 1020, 1380, 914, 1274)(833, 1193, 915, 1275, 1023, 1383, 916, 1276)(845, 1205, 934, 1294, 1035, 1395, 935, 1295)(846, 1206, 936, 1296, 937, 1297, 847, 1207)(849, 1209, 928, 1288, 1029, 1389, 940, 1300)(851, 1211, 942, 1302, 989, 1349, 943, 1303)(852, 1212, 944, 1304, 1041, 1401, 945, 1305)(856, 1216, 949, 1309, 1046, 1406, 950, 1310)(857, 1217, 951, 1311, 1048, 1408, 952, 1312)(869, 1229, 968, 1328, 921, 1281, 969, 1329)(871, 1231, 971, 1331, 972, 1332, 872, 1232)(873, 1233, 973, 1333, 920, 1280, 974, 1334)(874, 1234, 892, 1252, 997, 1357, 975, 1335)(875, 1235, 976, 1336, 1063, 1423, 977, 1337)(880, 1240, 981, 1341, 1064, 1424, 982, 1342)(881, 1241, 983, 1343, 932, 1292, 917, 1277)(883, 1243, 985, 1345, 926, 1286, 986, 1346)(888, 1248, 992, 1352, 922, 1282, 993, 1353)(890, 1250, 919, 1279, 1025, 1385, 995, 1355)(897, 1257, 1004, 1364, 1054, 1414, 966, 1326)(898, 1258, 1005, 1365, 1006, 1366, 899, 1259)(901, 1261, 998, 1358, 1058, 1418, 1008, 1368)(903, 1263, 1009, 1369, 1040, 1400, 988, 1348)(904, 1264, 1010, 1370, 1066, 1426, 1011, 1371)(908, 1268, 1014, 1374, 1065, 1425, 1015, 1375)(909, 1269, 1016, 1376, 1022, 1382, 1017, 1377)(923, 1283, 1026, 1386, 979, 1339, 924, 1284)(929, 1289, 994, 1354, 1030, 1390, 930, 1290)(931, 1291, 1031, 1391, 956, 1316, 1032, 1392)(933, 1293, 1033, 1393, 1056, 1416, 1034, 1394)(938, 1298, 967, 1327, 1055, 1415, 1021, 1381)(939, 1299, 1037, 1397, 1002, 1362, 953, 1313)(941, 1301, 1038, 1398, 961, 1321, 1039, 1399)(946, 1306, 1042, 1402, 957, 1317, 1043, 1403)(948, 1308, 955, 1315, 1049, 1409, 1045, 1405)(958, 1318, 1050, 1410, 1036, 1396, 959, 1319)(962, 1322, 1051, 1411, 1012, 1372, 1052, 1412)(963, 1323, 1053, 1413, 1024, 1384, 964, 1324)(991, 1351, 1067, 1427, 1027, 1387, 1003, 1363)(999, 1359, 1044, 1404, 1070, 1430, 1000, 1360)(1001, 1361, 1071, 1431, 1019, 1379, 1057, 1417)(1007, 1367, 1028, 1388, 1062, 1422, 1047, 1407)(1013, 1373, 1018, 1378, 1072, 1432, 1059, 1419)(1060, 1420, 1078, 1438, 1073, 1433, 1061, 1421)(1068, 1428, 1069, 1429, 1079, 1439, 1074, 1434)(1075, 1435, 1076, 1436, 1080, 1440, 1077, 1437) L = (1, 723)(2, 726)(3, 729)(4, 731)(5, 721)(6, 736)(7, 722)(8, 740)(9, 725)(10, 744)(11, 747)(12, 724)(13, 750)(14, 752)(15, 734)(16, 727)(17, 756)(18, 758)(19, 760)(20, 761)(21, 728)(22, 764)(23, 766)(24, 769)(25, 730)(26, 739)(27, 732)(28, 775)(29, 777)(30, 779)(31, 733)(32, 753)(33, 735)(34, 787)(35, 789)(36, 792)(37, 737)(38, 795)(39, 738)(40, 772)(41, 741)(42, 803)(43, 805)(44, 806)(45, 742)(46, 810)(47, 743)(48, 763)(49, 745)(50, 797)(51, 816)(52, 746)(53, 820)(54, 822)(55, 825)(56, 748)(57, 828)(58, 749)(59, 751)(60, 834)(61, 836)(62, 837)(63, 782)(64, 839)(65, 841)(66, 843)(67, 844)(68, 754)(69, 848)(70, 755)(71, 786)(72, 757)(73, 830)(74, 854)(75, 759)(76, 858)(77, 860)(78, 861)(79, 798)(80, 863)(81, 831)(82, 866)(83, 868)(84, 762)(85, 812)(86, 765)(87, 876)(88, 878)(89, 808)(90, 767)(91, 870)(92, 768)(93, 884)(94, 886)(95, 770)(96, 889)(97, 771)(98, 893)(99, 895)(100, 896)(101, 773)(102, 900)(103, 774)(104, 819)(105, 776)(106, 781)(107, 906)(108, 778)(109, 891)(110, 911)(111, 912)(112, 913)(113, 915)(114, 918)(115, 780)(116, 905)(117, 838)(118, 783)(119, 925)(120, 784)(121, 927)(122, 785)(123, 850)(124, 788)(125, 934)(126, 936)(127, 846)(128, 790)(129, 928)(130, 791)(131, 942)(132, 944)(133, 793)(134, 947)(135, 794)(136, 949)(137, 951)(138, 954)(139, 796)(140, 815)(141, 862)(142, 799)(143, 960)(144, 800)(145, 801)(146, 965)(147, 802)(148, 804)(149, 968)(150, 970)(151, 971)(152, 871)(153, 973)(154, 892)(155, 976)(156, 978)(157, 807)(158, 879)(159, 809)(160, 981)(161, 983)(162, 811)(163, 985)(164, 987)(165, 813)(166, 990)(167, 814)(168, 992)(169, 817)(170, 919)(171, 996)(172, 997)(173, 984)(174, 818)(175, 902)(176, 821)(177, 1004)(178, 1005)(179, 898)(180, 823)(181, 998)(182, 824)(183, 1009)(184, 1010)(185, 826)(186, 980)(187, 827)(188, 1014)(189, 1016)(190, 829)(191, 853)(192, 865)(193, 1020)(194, 832)(195, 1023)(196, 833)(197, 881)(198, 835)(199, 1025)(200, 974)(201, 969)(202, 993)(203, 1026)(204, 923)(205, 840)(206, 986)(207, 842)(208, 1029)(209, 994)(210, 929)(211, 1031)(212, 917)(213, 1033)(214, 1035)(215, 845)(216, 937)(217, 847)(218, 967)(219, 1037)(220, 849)(221, 1038)(222, 989)(223, 851)(224, 1041)(225, 852)(226, 1042)(227, 855)(228, 955)(229, 1046)(230, 856)(231, 1048)(232, 857)(233, 939)(234, 859)(235, 1049)(236, 1032)(237, 1043)(238, 1050)(239, 958)(240, 864)(241, 1039)(242, 1051)(243, 1053)(244, 963)(245, 867)(246, 897)(247, 1055)(248, 921)(249, 869)(250, 882)(251, 972)(252, 872)(253, 920)(254, 873)(255, 874)(256, 1063)(257, 875)(258, 877)(259, 924)(260, 907)(261, 1064)(262, 880)(263, 932)(264, 894)(265, 926)(266, 883)(267, 885)(268, 903)(269, 943)(270, 887)(271, 1067)(272, 922)(273, 888)(274, 1030)(275, 890)(276, 910)(277, 975)(278, 1058)(279, 1044)(280, 999)(281, 1071)(282, 953)(283, 991)(284, 1054)(285, 1006)(286, 899)(287, 1028)(288, 901)(289, 1040)(290, 1066)(291, 904)(292, 1052)(293, 1018)(294, 1065)(295, 908)(296, 1022)(297, 909)(298, 1072)(299, 1057)(300, 914)(301, 938)(302, 1017)(303, 916)(304, 964)(305, 995)(306, 979)(307, 1003)(308, 1062)(309, 940)(310, 930)(311, 956)(312, 931)(313, 1056)(314, 933)(315, 935)(316, 959)(317, 1002)(318, 961)(319, 941)(320, 988)(321, 945)(322, 957)(323, 946)(324, 1070)(325, 948)(326, 950)(327, 1007)(328, 952)(329, 1045)(330, 1036)(331, 1012)(332, 962)(333, 1024)(334, 966)(335, 1021)(336, 1034)(337, 1001)(338, 1008)(339, 1013)(340, 1078)(341, 1060)(342, 1047)(343, 977)(344, 982)(345, 1015)(346, 1011)(347, 1027)(348, 1069)(349, 1079)(350, 1000)(351, 1019)(352, 1059)(353, 1061)(354, 1068)(355, 1076)(356, 1080)(357, 1075)(358, 1073)(359, 1074)(360, 1077)(361, 1081)(362, 1082)(363, 1083)(364, 1084)(365, 1085)(366, 1086)(367, 1087)(368, 1088)(369, 1089)(370, 1090)(371, 1091)(372, 1092)(373, 1093)(374, 1094)(375, 1095)(376, 1096)(377, 1097)(378, 1098)(379, 1099)(380, 1100)(381, 1101)(382, 1102)(383, 1103)(384, 1104)(385, 1105)(386, 1106)(387, 1107)(388, 1108)(389, 1109)(390, 1110)(391, 1111)(392, 1112)(393, 1113)(394, 1114)(395, 1115)(396, 1116)(397, 1117)(398, 1118)(399, 1119)(400, 1120)(401, 1121)(402, 1122)(403, 1123)(404, 1124)(405, 1125)(406, 1126)(407, 1127)(408, 1128)(409, 1129)(410, 1130)(411, 1131)(412, 1132)(413, 1133)(414, 1134)(415, 1135)(416, 1136)(417, 1137)(418, 1138)(419, 1139)(420, 1140)(421, 1141)(422, 1142)(423, 1143)(424, 1144)(425, 1145)(426, 1146)(427, 1147)(428, 1148)(429, 1149)(430, 1150)(431, 1151)(432, 1152)(433, 1153)(434, 1154)(435, 1155)(436, 1156)(437, 1157)(438, 1158)(439, 1159)(440, 1160)(441, 1161)(442, 1162)(443, 1163)(444, 1164)(445, 1165)(446, 1166)(447, 1167)(448, 1168)(449, 1169)(450, 1170)(451, 1171)(452, 1172)(453, 1173)(454, 1174)(455, 1175)(456, 1176)(457, 1177)(458, 1178)(459, 1179)(460, 1180)(461, 1181)(462, 1182)(463, 1183)(464, 1184)(465, 1185)(466, 1186)(467, 1187)(468, 1188)(469, 1189)(470, 1190)(471, 1191)(472, 1192)(473, 1193)(474, 1194)(475, 1195)(476, 1196)(477, 1197)(478, 1198)(479, 1199)(480, 1200)(481, 1201)(482, 1202)(483, 1203)(484, 1204)(485, 1205)(486, 1206)(487, 1207)(488, 1208)(489, 1209)(490, 1210)(491, 1211)(492, 1212)(493, 1213)(494, 1214)(495, 1215)(496, 1216)(497, 1217)(498, 1218)(499, 1219)(500, 1220)(501, 1221)(502, 1222)(503, 1223)(504, 1224)(505, 1225)(506, 1226)(507, 1227)(508, 1228)(509, 1229)(510, 1230)(511, 1231)(512, 1232)(513, 1233)(514, 1234)(515, 1235)(516, 1236)(517, 1237)(518, 1238)(519, 1239)(520, 1240)(521, 1241)(522, 1242)(523, 1243)(524, 1244)(525, 1245)(526, 1246)(527, 1247)(528, 1248)(529, 1249)(530, 1250)(531, 1251)(532, 1252)(533, 1253)(534, 1254)(535, 1255)(536, 1256)(537, 1257)(538, 1258)(539, 1259)(540, 1260)(541, 1261)(542, 1262)(543, 1263)(544, 1264)(545, 1265)(546, 1266)(547, 1267)(548, 1268)(549, 1269)(550, 1270)(551, 1271)(552, 1272)(553, 1273)(554, 1274)(555, 1275)(556, 1276)(557, 1277)(558, 1278)(559, 1279)(560, 1280)(561, 1281)(562, 1282)(563, 1283)(564, 1284)(565, 1285)(566, 1286)(567, 1287)(568, 1288)(569, 1289)(570, 1290)(571, 1291)(572, 1292)(573, 1293)(574, 1294)(575, 1295)(576, 1296)(577, 1297)(578, 1298)(579, 1299)(580, 1300)(581, 1301)(582, 1302)(583, 1303)(584, 1304)(585, 1305)(586, 1306)(587, 1307)(588, 1308)(589, 1309)(590, 1310)(591, 1311)(592, 1312)(593, 1313)(594, 1314)(595, 1315)(596, 1316)(597, 1317)(598, 1318)(599, 1319)(600, 1320)(601, 1321)(602, 1322)(603, 1323)(604, 1324)(605, 1325)(606, 1326)(607, 1327)(608, 1328)(609, 1329)(610, 1330)(611, 1331)(612, 1332)(613, 1333)(614, 1334)(615, 1335)(616, 1336)(617, 1337)(618, 1338)(619, 1339)(620, 1340)(621, 1341)(622, 1342)(623, 1343)(624, 1344)(625, 1345)(626, 1346)(627, 1347)(628, 1348)(629, 1349)(630, 1350)(631, 1351)(632, 1352)(633, 1353)(634, 1354)(635, 1355)(636, 1356)(637, 1357)(638, 1358)(639, 1359)(640, 1360)(641, 1361)(642, 1362)(643, 1363)(644, 1364)(645, 1365)(646, 1366)(647, 1367)(648, 1368)(649, 1369)(650, 1370)(651, 1371)(652, 1372)(653, 1373)(654, 1374)(655, 1375)(656, 1376)(657, 1377)(658, 1378)(659, 1379)(660, 1380)(661, 1381)(662, 1382)(663, 1383)(664, 1384)(665, 1385)(666, 1386)(667, 1387)(668, 1388)(669, 1389)(670, 1390)(671, 1391)(672, 1392)(673, 1393)(674, 1394)(675, 1395)(676, 1396)(677, 1397)(678, 1398)(679, 1399)(680, 1400)(681, 1401)(682, 1402)(683, 1403)(684, 1404)(685, 1405)(686, 1406)(687, 1407)(688, 1408)(689, 1409)(690, 1410)(691, 1411)(692, 1412)(693, 1413)(694, 1414)(695, 1415)(696, 1416)(697, 1417)(698, 1418)(699, 1419)(700, 1420)(701, 1421)(702, 1422)(703, 1423)(704, 1424)(705, 1425)(706, 1426)(707, 1427)(708, 1428)(709, 1429)(710, 1430)(711, 1431)(712, 1432)(713, 1433)(714, 1434)(715, 1435)(716, 1436)(717, 1437)(718, 1438)(719, 1439)(720, 1440) local type(s) :: { ( 2, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E16.1284 Graph:: bipartite v = 210 e = 720 f = 480 degree seq :: [ 6^120, 8^90 ] E16.1284 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4}) Quotient :: dipole Aut^+ = A6 (small group id <360, 118>) Aut = C2 x A6 (small group id <720, 766>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, Y3^4, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y2)^3, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, (Y3^-1 * Y1^-1)^4, (Y3^-1 * Y2^-1)^5, (Y3^-2 * Y2 * Y3 * Y2 * Y3^-1 * Y2^-1)^2, (Y3 * Y2 * Y3^-2 * Y2^-1 * Y3^-1 * Y2^-1)^2 ] Map:: polytopal R = (1, 361)(2, 362)(3, 363)(4, 364)(5, 365)(6, 366)(7, 367)(8, 368)(9, 369)(10, 370)(11, 371)(12, 372)(13, 373)(14, 374)(15, 375)(16, 376)(17, 377)(18, 378)(19, 379)(20, 380)(21, 381)(22, 382)(23, 383)(24, 384)(25, 385)(26, 386)(27, 387)(28, 388)(29, 389)(30, 390)(31, 391)(32, 392)(33, 393)(34, 394)(35, 395)(36, 396)(37, 397)(38, 398)(39, 399)(40, 400)(41, 401)(42, 402)(43, 403)(44, 404)(45, 405)(46, 406)(47, 407)(48, 408)(49, 409)(50, 410)(51, 411)(52, 412)(53, 413)(54, 414)(55, 415)(56, 416)(57, 417)(58, 418)(59, 419)(60, 420)(61, 421)(62, 422)(63, 423)(64, 424)(65, 425)(66, 426)(67, 427)(68, 428)(69, 429)(70, 430)(71, 431)(72, 432)(73, 433)(74, 434)(75, 435)(76, 436)(77, 437)(78, 438)(79, 439)(80, 440)(81, 441)(82, 442)(83, 443)(84, 444)(85, 445)(86, 446)(87, 447)(88, 448)(89, 449)(90, 450)(91, 451)(92, 452)(93, 453)(94, 454)(95, 455)(96, 456)(97, 457)(98, 458)(99, 459)(100, 460)(101, 461)(102, 462)(103, 463)(104, 464)(105, 465)(106, 466)(107, 467)(108, 468)(109, 469)(110, 470)(111, 471)(112, 472)(113, 473)(114, 474)(115, 475)(116, 476)(117, 477)(118, 478)(119, 479)(120, 480)(121, 481)(122, 482)(123, 483)(124, 484)(125, 485)(126, 486)(127, 487)(128, 488)(129, 489)(130, 490)(131, 491)(132, 492)(133, 493)(134, 494)(135, 495)(136, 496)(137, 497)(138, 498)(139, 499)(140, 500)(141, 501)(142, 502)(143, 503)(144, 504)(145, 505)(146, 506)(147, 507)(148, 508)(149, 509)(150, 510)(151, 511)(152, 512)(153, 513)(154, 514)(155, 515)(156, 516)(157, 517)(158, 518)(159, 519)(160, 520)(161, 521)(162, 522)(163, 523)(164, 524)(165, 525)(166, 526)(167, 527)(168, 528)(169, 529)(170, 530)(171, 531)(172, 532)(173, 533)(174, 534)(175, 535)(176, 536)(177, 537)(178, 538)(179, 539)(180, 540)(181, 541)(182, 542)(183, 543)(184, 544)(185, 545)(186, 546)(187, 547)(188, 548)(189, 549)(190, 550)(191, 551)(192, 552)(193, 553)(194, 554)(195, 555)(196, 556)(197, 557)(198, 558)(199, 559)(200, 560)(201, 561)(202, 562)(203, 563)(204, 564)(205, 565)(206, 566)(207, 567)(208, 568)(209, 569)(210, 570)(211, 571)(212, 572)(213, 573)(214, 574)(215, 575)(216, 576)(217, 577)(218, 578)(219, 579)(220, 580)(221, 581)(222, 582)(223, 583)(224, 584)(225, 585)(226, 586)(227, 587)(228, 588)(229, 589)(230, 590)(231, 591)(232, 592)(233, 593)(234, 594)(235, 595)(236, 596)(237, 597)(238, 598)(239, 599)(240, 600)(241, 601)(242, 602)(243, 603)(244, 604)(245, 605)(246, 606)(247, 607)(248, 608)(249, 609)(250, 610)(251, 611)(252, 612)(253, 613)(254, 614)(255, 615)(256, 616)(257, 617)(258, 618)(259, 619)(260, 620)(261, 621)(262, 622)(263, 623)(264, 624)(265, 625)(266, 626)(267, 627)(268, 628)(269, 629)(270, 630)(271, 631)(272, 632)(273, 633)(274, 634)(275, 635)(276, 636)(277, 637)(278, 638)(279, 639)(280, 640)(281, 641)(282, 642)(283, 643)(284, 644)(285, 645)(286, 646)(287, 647)(288, 648)(289, 649)(290, 650)(291, 651)(292, 652)(293, 653)(294, 654)(295, 655)(296, 656)(297, 657)(298, 658)(299, 659)(300, 660)(301, 661)(302, 662)(303, 663)(304, 664)(305, 665)(306, 666)(307, 667)(308, 668)(309, 669)(310, 670)(311, 671)(312, 672)(313, 673)(314, 674)(315, 675)(316, 676)(317, 677)(318, 678)(319, 679)(320, 680)(321, 681)(322, 682)(323, 683)(324, 684)(325, 685)(326, 686)(327, 687)(328, 688)(329, 689)(330, 690)(331, 691)(332, 692)(333, 693)(334, 694)(335, 695)(336, 696)(337, 697)(338, 698)(339, 699)(340, 700)(341, 701)(342, 702)(343, 703)(344, 704)(345, 705)(346, 706)(347, 707)(348, 708)(349, 709)(350, 710)(351, 711)(352, 712)(353, 713)(354, 714)(355, 715)(356, 716)(357, 717)(358, 718)(359, 719)(360, 720)(721, 1081, 722, 1082, 724, 1084)(723, 1083, 728, 1088, 730, 1090)(725, 1085, 733, 1093, 734, 1094)(726, 1086, 735, 1095, 737, 1097)(727, 1087, 738, 1098, 739, 1099)(729, 1089, 742, 1102, 743, 1103)(731, 1091, 745, 1105, 747, 1107)(732, 1092, 748, 1108, 749, 1109)(736, 1096, 755, 1115, 756, 1116)(740, 1100, 761, 1121, 763, 1123)(741, 1101, 764, 1124, 765, 1125)(744, 1104, 769, 1129, 770, 1130)(746, 1106, 773, 1133, 774, 1134)(750, 1110, 779, 1139, 780, 1140)(751, 1111, 781, 1141, 767, 1127)(752, 1112, 783, 1143, 784, 1144)(753, 1113, 785, 1145, 787, 1147)(754, 1114, 788, 1148, 789, 1149)(757, 1117, 793, 1153, 794, 1154)(758, 1118, 795, 1155, 796, 1156)(759, 1119, 797, 1157, 791, 1151)(760, 1120, 799, 1159, 800, 1160)(762, 1122, 803, 1163, 804, 1164)(766, 1126, 809, 1169, 811, 1171)(768, 1128, 812, 1172, 813, 1173)(771, 1131, 817, 1177, 819, 1179)(772, 1132, 820, 1180, 821, 1181)(775, 1135, 825, 1185, 826, 1186)(776, 1136, 827, 1187, 828, 1188)(777, 1137, 829, 1189, 823, 1183)(778, 1138, 831, 1191, 801, 1161)(782, 1142, 837, 1197, 838, 1198)(786, 1146, 842, 1202, 843, 1203)(790, 1150, 848, 1208, 850, 1210)(792, 1152, 851, 1211, 852, 1212)(798, 1158, 861, 1221, 862, 1222)(802, 1162, 866, 1226, 867, 1227)(805, 1165, 871, 1231, 872, 1232)(806, 1166, 873, 1233, 874, 1234)(807, 1167, 875, 1235, 869, 1229)(808, 1168, 877, 1237, 859, 1219)(810, 1170, 880, 1240, 881, 1241)(814, 1174, 886, 1246, 887, 1247)(815, 1175, 888, 1248, 857, 1217)(816, 1176, 890, 1250, 878, 1238)(818, 1178, 892, 1252, 893, 1253)(822, 1182, 898, 1258, 900, 1260)(824, 1184, 901, 1261, 902, 1262)(830, 1190, 911, 1271, 912, 1272)(832, 1192, 885, 1245, 914, 1274)(833, 1193, 904, 1264, 915, 1275)(834, 1194, 916, 1276, 917, 1277)(835, 1195, 897, 1257, 919, 1279)(836, 1196, 920, 1280, 921, 1281)(839, 1199, 925, 1285, 844, 1204)(840, 1200, 926, 1286, 923, 1283)(841, 1201, 927, 1287, 928, 1288)(845, 1205, 932, 1292, 933, 1293)(846, 1206, 934, 1294, 930, 1290)(847, 1207, 936, 1296, 909, 1269)(849, 1209, 939, 1299, 940, 1300)(853, 1213, 945, 1305, 946, 1306)(854, 1214, 947, 1307, 907, 1267)(855, 1215, 949, 1309, 937, 1297)(856, 1216, 944, 1304, 951, 1311)(858, 1218, 952, 1312, 953, 1313)(860, 1220, 955, 1315, 956, 1316)(863, 1223, 960, 1320, 894, 1254)(864, 1224, 961, 1321, 958, 1318)(865, 1225, 962, 1322, 963, 1323)(868, 1228, 967, 1327, 969, 1329)(870, 1230, 970, 1330, 931, 1291)(876, 1236, 977, 1337, 978, 1338)(879, 1239, 980, 1340, 948, 1308)(882, 1242, 983, 1343, 935, 1295)(883, 1243, 984, 1344, 985, 1345)(884, 1244, 986, 1346, 974, 1334)(889, 1249, 993, 1353, 994, 1354)(891, 1251, 995, 1355, 996, 1356)(895, 1255, 999, 1359, 1000, 1360)(896, 1256, 1001, 1361, 998, 1358)(899, 1259, 1004, 1364, 1005, 1365)(903, 1263, 1009, 1369, 1010, 1370)(905, 1265, 1012, 1372, 1003, 1363)(906, 1266, 1008, 1368, 1013, 1373)(908, 1268, 1014, 1374, 1015, 1375)(910, 1270, 1016, 1376, 1017, 1377)(913, 1273, 1020, 1380, 943, 1303)(918, 1278, 1022, 1382, 942, 1302)(922, 1282, 1018, 1378, 957, 1317)(924, 1284, 1026, 1386, 1027, 1387)(929, 1289, 1031, 1391, 964, 1324)(938, 1298, 1036, 1396, 1011, 1371)(941, 1301, 1038, 1398, 1002, 1362)(950, 1310, 1045, 1405, 1007, 1367)(954, 1314, 1047, 1407, 1006, 1366)(959, 1319, 1050, 1410, 982, 1342)(965, 1325, 1053, 1413, 1052, 1412)(966, 1326, 1054, 1414, 991, 1351)(968, 1328, 1023, 1383, 1033, 1393)(971, 1331, 1056, 1416, 989, 1349)(972, 1332, 1057, 1417, 1055, 1415)(973, 1333, 1028, 1388, 997, 1357)(975, 1335, 1059, 1419, 1060, 1420)(976, 1336, 1061, 1421, 1062, 1422)(979, 1339, 1035, 1395, 1063, 1423)(981, 1341, 1032, 1392, 1048, 1408)(987, 1347, 1039, 1399, 1065, 1425)(988, 1348, 1029, 1389, 1066, 1426)(990, 1350, 1067, 1427, 1034, 1394)(992, 1352, 1068, 1428, 1041, 1401)(1019, 1379, 1025, 1385, 1037, 1397)(1021, 1381, 1072, 1432, 1073, 1433)(1024, 1384, 1074, 1434, 1046, 1406)(1030, 1390, 1058, 1418, 1043, 1403)(1040, 1400, 1069, 1429, 1075, 1435)(1042, 1402, 1076, 1436, 1070, 1430)(1044, 1404, 1064, 1424, 1051, 1411)(1049, 1409, 1077, 1437, 1071, 1431)(1078, 1438, 1080, 1440, 1079, 1439) L = (1, 723)(2, 726)(3, 729)(4, 731)(5, 721)(6, 736)(7, 722)(8, 740)(9, 725)(10, 738)(11, 746)(12, 724)(13, 750)(14, 751)(15, 753)(16, 727)(17, 748)(18, 758)(19, 759)(20, 762)(21, 728)(22, 766)(23, 764)(24, 730)(25, 771)(26, 732)(27, 733)(28, 776)(29, 777)(30, 775)(31, 782)(32, 734)(33, 786)(34, 735)(35, 790)(36, 788)(37, 737)(38, 744)(39, 798)(40, 739)(41, 801)(42, 741)(43, 769)(44, 806)(45, 807)(46, 810)(47, 742)(48, 743)(49, 814)(50, 815)(51, 818)(52, 745)(53, 822)(54, 820)(55, 747)(56, 757)(57, 830)(58, 749)(59, 832)(60, 783)(61, 835)(62, 752)(63, 839)(64, 840)(65, 784)(66, 754)(67, 793)(68, 845)(69, 846)(70, 849)(71, 755)(72, 756)(73, 853)(74, 854)(75, 856)(76, 799)(77, 859)(78, 760)(79, 863)(80, 864)(81, 865)(82, 761)(83, 868)(84, 866)(85, 763)(86, 768)(87, 876)(88, 765)(89, 878)(90, 767)(91, 812)(92, 883)(93, 884)(94, 805)(95, 889)(96, 770)(97, 800)(98, 772)(99, 825)(100, 895)(101, 896)(102, 899)(103, 773)(104, 774)(105, 903)(106, 904)(107, 906)(108, 831)(109, 909)(110, 778)(111, 871)(112, 913)(113, 779)(114, 780)(115, 918)(116, 781)(117, 922)(118, 920)(119, 834)(120, 841)(121, 785)(122, 929)(123, 927)(124, 787)(125, 792)(126, 935)(127, 789)(128, 937)(129, 791)(130, 851)(131, 942)(132, 943)(133, 844)(134, 948)(135, 794)(136, 950)(137, 795)(138, 796)(139, 954)(140, 797)(141, 957)(142, 955)(143, 858)(144, 891)(145, 802)(146, 964)(147, 965)(148, 968)(149, 803)(150, 804)(151, 908)(152, 971)(153, 973)(154, 877)(155, 921)(156, 808)(157, 939)(158, 979)(159, 809)(160, 981)(161, 980)(162, 811)(163, 882)(164, 987)(165, 813)(166, 988)(167, 890)(168, 991)(169, 816)(170, 983)(171, 817)(172, 997)(173, 995)(174, 819)(175, 824)(176, 1002)(177, 821)(178, 1003)(179, 823)(180, 901)(181, 1006)(182, 1007)(183, 894)(184, 1011)(185, 826)(186, 986)(187, 827)(188, 828)(189, 984)(190, 829)(191, 1018)(192, 1016)(193, 833)(194, 916)(195, 972)(196, 1021)(197, 966)(198, 836)(199, 880)(200, 1023)(201, 1024)(202, 1025)(203, 837)(204, 838)(205, 992)(206, 989)(207, 1028)(208, 1029)(209, 1032)(210, 842)(211, 843)(212, 967)(213, 936)(214, 956)(215, 847)(216, 1004)(217, 1035)(218, 848)(219, 975)(220, 1036)(221, 850)(222, 941)(223, 1039)(224, 852)(225, 1040)(226, 949)(227, 1043)(228, 855)(229, 1038)(230, 857)(231, 952)(232, 1046)(233, 1030)(234, 860)(235, 1048)(236, 1049)(237, 1026)(238, 861)(239, 862)(240, 1044)(241, 1041)(242, 1051)(243, 911)(244, 870)(245, 917)(246, 867)(247, 1055)(248, 869)(249, 970)(250, 893)(251, 915)(252, 872)(253, 1058)(254, 873)(255, 874)(256, 875)(257, 900)(258, 1061)(259, 879)(260, 1064)(261, 1000)(262, 881)(263, 990)(264, 910)(265, 914)(266, 907)(267, 885)(268, 926)(269, 886)(270, 887)(271, 925)(272, 888)(273, 898)(274, 1068)(275, 969)(276, 1069)(277, 1059)(278, 892)(279, 1031)(280, 919)(281, 1017)(282, 897)(283, 1063)(284, 1033)(285, 994)(286, 977)(287, 1065)(288, 902)(289, 1052)(290, 1012)(291, 905)(292, 978)(293, 1014)(294, 1071)(295, 1057)(296, 1060)(297, 1072)(298, 1050)(299, 912)(300, 932)(301, 985)(302, 951)(303, 924)(304, 976)(305, 923)(306, 958)(307, 1005)(308, 931)(309, 953)(310, 928)(311, 1054)(312, 930)(313, 933)(314, 934)(315, 938)(316, 1056)(317, 940)(318, 1042)(319, 944)(320, 961)(321, 945)(322, 946)(323, 960)(324, 947)(325, 999)(326, 1022)(327, 1013)(328, 959)(329, 1034)(330, 963)(331, 1009)(332, 962)(333, 1062)(334, 1045)(335, 1020)(336, 1037)(337, 996)(338, 974)(339, 998)(340, 1019)(341, 1010)(342, 1078)(343, 993)(344, 982)(345, 1008)(346, 1067)(347, 1079)(348, 1027)(349, 1015)(350, 1001)(351, 1047)(352, 1070)(353, 1053)(354, 1066)(355, 1076)(356, 1080)(357, 1075)(358, 1073)(359, 1074)(360, 1077)(361, 1081)(362, 1082)(363, 1083)(364, 1084)(365, 1085)(366, 1086)(367, 1087)(368, 1088)(369, 1089)(370, 1090)(371, 1091)(372, 1092)(373, 1093)(374, 1094)(375, 1095)(376, 1096)(377, 1097)(378, 1098)(379, 1099)(380, 1100)(381, 1101)(382, 1102)(383, 1103)(384, 1104)(385, 1105)(386, 1106)(387, 1107)(388, 1108)(389, 1109)(390, 1110)(391, 1111)(392, 1112)(393, 1113)(394, 1114)(395, 1115)(396, 1116)(397, 1117)(398, 1118)(399, 1119)(400, 1120)(401, 1121)(402, 1122)(403, 1123)(404, 1124)(405, 1125)(406, 1126)(407, 1127)(408, 1128)(409, 1129)(410, 1130)(411, 1131)(412, 1132)(413, 1133)(414, 1134)(415, 1135)(416, 1136)(417, 1137)(418, 1138)(419, 1139)(420, 1140)(421, 1141)(422, 1142)(423, 1143)(424, 1144)(425, 1145)(426, 1146)(427, 1147)(428, 1148)(429, 1149)(430, 1150)(431, 1151)(432, 1152)(433, 1153)(434, 1154)(435, 1155)(436, 1156)(437, 1157)(438, 1158)(439, 1159)(440, 1160)(441, 1161)(442, 1162)(443, 1163)(444, 1164)(445, 1165)(446, 1166)(447, 1167)(448, 1168)(449, 1169)(450, 1170)(451, 1171)(452, 1172)(453, 1173)(454, 1174)(455, 1175)(456, 1176)(457, 1177)(458, 1178)(459, 1179)(460, 1180)(461, 1181)(462, 1182)(463, 1183)(464, 1184)(465, 1185)(466, 1186)(467, 1187)(468, 1188)(469, 1189)(470, 1190)(471, 1191)(472, 1192)(473, 1193)(474, 1194)(475, 1195)(476, 1196)(477, 1197)(478, 1198)(479, 1199)(480, 1200)(481, 1201)(482, 1202)(483, 1203)(484, 1204)(485, 1205)(486, 1206)(487, 1207)(488, 1208)(489, 1209)(490, 1210)(491, 1211)(492, 1212)(493, 1213)(494, 1214)(495, 1215)(496, 1216)(497, 1217)(498, 1218)(499, 1219)(500, 1220)(501, 1221)(502, 1222)(503, 1223)(504, 1224)(505, 1225)(506, 1226)(507, 1227)(508, 1228)(509, 1229)(510, 1230)(511, 1231)(512, 1232)(513, 1233)(514, 1234)(515, 1235)(516, 1236)(517, 1237)(518, 1238)(519, 1239)(520, 1240)(521, 1241)(522, 1242)(523, 1243)(524, 1244)(525, 1245)(526, 1246)(527, 1247)(528, 1248)(529, 1249)(530, 1250)(531, 1251)(532, 1252)(533, 1253)(534, 1254)(535, 1255)(536, 1256)(537, 1257)(538, 1258)(539, 1259)(540, 1260)(541, 1261)(542, 1262)(543, 1263)(544, 1264)(545, 1265)(546, 1266)(547, 1267)(548, 1268)(549, 1269)(550, 1270)(551, 1271)(552, 1272)(553, 1273)(554, 1274)(555, 1275)(556, 1276)(557, 1277)(558, 1278)(559, 1279)(560, 1280)(561, 1281)(562, 1282)(563, 1283)(564, 1284)(565, 1285)(566, 1286)(567, 1287)(568, 1288)(569, 1289)(570, 1290)(571, 1291)(572, 1292)(573, 1293)(574, 1294)(575, 1295)(576, 1296)(577, 1297)(578, 1298)(579, 1299)(580, 1300)(581, 1301)(582, 1302)(583, 1303)(584, 1304)(585, 1305)(586, 1306)(587, 1307)(588, 1308)(589, 1309)(590, 1310)(591, 1311)(592, 1312)(593, 1313)(594, 1314)(595, 1315)(596, 1316)(597, 1317)(598, 1318)(599, 1319)(600, 1320)(601, 1321)(602, 1322)(603, 1323)(604, 1324)(605, 1325)(606, 1326)(607, 1327)(608, 1328)(609, 1329)(610, 1330)(611, 1331)(612, 1332)(613, 1333)(614, 1334)(615, 1335)(616, 1336)(617, 1337)(618, 1338)(619, 1339)(620, 1340)(621, 1341)(622, 1342)(623, 1343)(624, 1344)(625, 1345)(626, 1346)(627, 1347)(628, 1348)(629, 1349)(630, 1350)(631, 1351)(632, 1352)(633, 1353)(634, 1354)(635, 1355)(636, 1356)(637, 1357)(638, 1358)(639, 1359)(640, 1360)(641, 1361)(642, 1362)(643, 1363)(644, 1364)(645, 1365)(646, 1366)(647, 1367)(648, 1368)(649, 1369)(650, 1370)(651, 1371)(652, 1372)(653, 1373)(654, 1374)(655, 1375)(656, 1376)(657, 1377)(658, 1378)(659, 1379)(660, 1380)(661, 1381)(662, 1382)(663, 1383)(664, 1384)(665, 1385)(666, 1386)(667, 1387)(668, 1388)(669, 1389)(670, 1390)(671, 1391)(672, 1392)(673, 1393)(674, 1394)(675, 1395)(676, 1396)(677, 1397)(678, 1398)(679, 1399)(680, 1400)(681, 1401)(682, 1402)(683, 1403)(684, 1404)(685, 1405)(686, 1406)(687, 1407)(688, 1408)(689, 1409)(690, 1410)(691, 1411)(692, 1412)(693, 1413)(694, 1414)(695, 1415)(696, 1416)(697, 1417)(698, 1418)(699, 1419)(700, 1420)(701, 1421)(702, 1422)(703, 1423)(704, 1424)(705, 1425)(706, 1426)(707, 1427)(708, 1428)(709, 1429)(710, 1430)(711, 1431)(712, 1432)(713, 1433)(714, 1434)(715, 1435)(716, 1436)(717, 1437)(718, 1438)(719, 1439)(720, 1440) local type(s) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E16.1283 Graph:: simple bipartite v = 480 e = 720 f = 210 degree seq :: [ 2^360, 6^120 ] E16.1285 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 5}) Quotient :: regular Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^5, (T1 * T2)^4, (T2 * T1^-2)^6, T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 10, 4)(3, 7, 14, 17, 8)(6, 12, 23, 26, 13)(9, 18, 32, 34, 19)(11, 21, 37, 40, 22)(15, 28, 47, 49, 29)(16, 30, 50, 42, 24)(20, 35, 58, 60, 36)(25, 43, 68, 62, 38)(27, 45, 72, 75, 46)(31, 52, 82, 84, 53)(33, 55, 87, 89, 56)(39, 63, 98, 93, 59)(41, 65, 102, 105, 66)(44, 70, 110, 112, 71)(48, 77, 119, 114, 73)(51, 80, 125, 127, 81)(54, 85, 131, 134, 86)(57, 90, 138, 140, 91)(61, 95, 146, 149, 96)(64, 100, 154, 156, 101)(67, 106, 161, 158, 103)(69, 108, 165, 167, 109)(74, 115, 174, 129, 83)(76, 117, 178, 180, 118)(78, 121, 184, 186, 122)(79, 123, 187, 190, 124)(88, 136, 205, 200, 132)(92, 141, 212, 215, 142)(94, 144, 217, 219, 145)(97, 150, 224, 221, 147)(99, 152, 228, 230, 153)(104, 159, 237, 169, 111)(107, 163, 243, 246, 164)(113, 171, 255, 258, 172)(116, 176, 263, 265, 177)(120, 182, 271, 273, 183)(126, 192, 283, 278, 188)(128, 194, 287, 290, 195)(130, 197, 292, 220, 198)(133, 201, 297, 210, 139)(135, 203, 301, 303, 204)(137, 207, 307, 309, 208)(143, 216, 318, 315, 213)(148, 222, 323, 232, 155)(151, 226, 329, 332, 227)(157, 234, 211, 313, 235)(160, 239, 346, 348, 240)(162, 189, 279, 352, 242)(166, 248, 359, 354, 244)(168, 250, 363, 366, 251)(170, 253, 368, 314, 254)(173, 259, 372, 370, 256)(175, 261, 376, 378, 262)(179, 267, 383, 275, 185)(181, 269, 324, 389, 270)(191, 281, 322, 404, 282)(193, 285, 408, 410, 286)(196, 291, 335, 412, 288)(199, 294, 233, 339, 295)(202, 299, 423, 425, 300)(206, 305, 429, 431, 306)(209, 310, 434, 437, 311)(214, 316, 440, 321, 218)(223, 325, 448, 450, 326)(225, 245, 355, 453, 328)(229, 334, 459, 455, 330)(231, 336, 461, 464, 337)(236, 342, 382, 266, 340)(238, 344, 428, 304, 345)(241, 349, 441, 473, 350)(247, 357, 439, 481, 358)(249, 361, 435, 312, 362)(252, 367, 427, 487, 364)(257, 353, 476, 380, 264)(260, 374, 493, 496, 375)(268, 385, 462, 338, 386)(272, 391, 509, 505, 387)(274, 393, 512, 514, 394)(276, 369, 365, 411, 396)(277, 397, 381, 424, 398)(280, 401, 463, 486, 402)(284, 406, 523, 482, 407)(289, 413, 527, 417, 293)(296, 419, 458, 333, 418)(298, 421, 451, 327, 422)(302, 426, 533, 433, 308)(317, 442, 542, 543, 443)(319, 331, 456, 544, 444)(320, 445, 545, 546, 446)(341, 454, 554, 470, 347)(343, 466, 564, 567, 467)(351, 474, 392, 511, 471)(356, 371, 490, 561, 479)(360, 483, 577, 559, 484)(373, 388, 506, 555, 492)(377, 498, 583, 553, 494)(379, 469, 549, 584, 499)(384, 502, 522, 405, 503)(390, 507, 526, 558, 508)(395, 515, 521, 551, 513)(399, 517, 576, 497, 516)(400, 518, 580, 491, 519)(403, 520, 556, 525, 409)(414, 488, 562, 593, 528)(415, 495, 582, 560, 460)(416, 432, 538, 550, 449)(420, 530, 591, 581, 531)(430, 537, 594, 565, 468)(436, 540, 557, 457, 438)(447, 547, 595, 590, 548)(452, 552, 475, 570, 532)(465, 472, 568, 539, 563)(477, 572, 529, 535, 571)(478, 573, 504, 500, 574)(480, 575, 536, 579, 485)(489, 566, 501, 585, 534)(510, 569, 596, 599, 588)(524, 578, 597, 600, 586)(541, 589, 587, 598, 592) L = (1, 3)(2, 6)(4, 9)(5, 11)(7, 15)(8, 16)(10, 20)(12, 24)(13, 25)(14, 27)(17, 31)(18, 33)(19, 28)(21, 38)(22, 39)(23, 41)(26, 44)(29, 48)(30, 51)(32, 54)(34, 57)(35, 59)(36, 55)(37, 61)(40, 64)(42, 67)(43, 69)(45, 73)(46, 74)(47, 76)(49, 78)(50, 79)(52, 83)(53, 80)(56, 88)(58, 92)(60, 94)(62, 97)(63, 99)(65, 103)(66, 104)(68, 107)(70, 111)(71, 108)(72, 113)(75, 116)(77, 120)(81, 126)(82, 128)(84, 130)(85, 132)(86, 133)(87, 135)(89, 137)(90, 139)(91, 117)(93, 143)(95, 147)(96, 148)(98, 151)(100, 155)(101, 152)(102, 157)(105, 160)(106, 162)(109, 166)(110, 168)(112, 170)(114, 173)(115, 175)(118, 179)(119, 181)(121, 185)(122, 182)(123, 188)(124, 189)(125, 191)(127, 193)(129, 196)(131, 199)(134, 202)(136, 206)(138, 209)(140, 211)(141, 213)(142, 214)(144, 218)(145, 203)(146, 220)(149, 223)(150, 225)(153, 229)(154, 231)(156, 233)(158, 236)(159, 238)(161, 241)(163, 244)(164, 245)(165, 247)(167, 249)(169, 252)(171, 256)(172, 257)(174, 260)(176, 264)(177, 261)(178, 266)(180, 268)(183, 272)(184, 274)(186, 276)(187, 277)(190, 280)(192, 284)(194, 288)(195, 289)(197, 293)(198, 281)(200, 296)(201, 298)(204, 302)(205, 304)(207, 308)(208, 305)(210, 312)(212, 314)(215, 317)(216, 319)(217, 320)(219, 255)(221, 322)(222, 324)(224, 327)(226, 330)(227, 331)(228, 333)(230, 335)(232, 338)(234, 340)(235, 341)(237, 343)(239, 347)(240, 344)(242, 351)(243, 353)(246, 356)(248, 360)(250, 364)(251, 365)(253, 369)(254, 357)(258, 371)(259, 373)(262, 377)(263, 379)(265, 381)(267, 384)(269, 387)(270, 388)(271, 390)(273, 392)(275, 395)(278, 399)(279, 400)(282, 403)(283, 405)(285, 409)(286, 406)(287, 411)(290, 414)(291, 415)(292, 416)(294, 418)(295, 398)(297, 420)(299, 424)(300, 421)(301, 370)(303, 427)(306, 430)(307, 432)(309, 417)(310, 435)(311, 436)(313, 438)(315, 439)(316, 441)(318, 378)(321, 410)(323, 447)(325, 449)(326, 389)(328, 452)(329, 454)(332, 457)(334, 460)(336, 462)(337, 463)(339, 401)(342, 465)(345, 468)(346, 469)(348, 380)(349, 471)(350, 472)(352, 475)(354, 477)(355, 478)(358, 480)(359, 482)(361, 485)(362, 483)(363, 486)(366, 488)(367, 489)(368, 394)(372, 491)(374, 494)(375, 495)(376, 497)(382, 500)(383, 501)(385, 504)(386, 502)(391, 510)(393, 513)(396, 507)(397, 516)(402, 518)(404, 521)(407, 524)(408, 445)(412, 526)(413, 434)(419, 529)(422, 532)(423, 499)(425, 512)(426, 534)(428, 535)(429, 536)(431, 509)(433, 539)(437, 528)(440, 541)(442, 514)(443, 473)(444, 498)(446, 490)(448, 549)(450, 470)(451, 551)(453, 553)(455, 555)(456, 556)(458, 558)(459, 559)(461, 561)(464, 562)(466, 565)(467, 566)(474, 569)(476, 571)(479, 573)(481, 576)(484, 578)(487, 580)(492, 581)(493, 574)(496, 563)(503, 586)(505, 547)(506, 554)(508, 587)(511, 589)(515, 567)(517, 590)(519, 591)(520, 564)(522, 548)(523, 592)(525, 557)(527, 579)(530, 570)(531, 577)(533, 582)(537, 588)(538, 568)(540, 545)(542, 584)(543, 550)(544, 594)(546, 593)(552, 596)(560, 597)(572, 598)(575, 595)(583, 599)(585, 600) local type(s) :: { ( 4^5 ) } Outer automorphisms :: reflexible Dual of E16.1286 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 120 e = 300 f = 150 degree seq :: [ 5^120 ] E16.1286 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 5}) Quotient :: regular Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^4, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^5, (T1^-1 * T2 * T1^-1)^6, T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-2 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 41, 25)(15, 26, 44, 27)(21, 35, 57, 36)(22, 37, 59, 38)(23, 39, 61, 40)(29, 47, 73, 48)(30, 49, 65, 42)(32, 51, 78, 52)(33, 53, 80, 54)(34, 55, 82, 56)(43, 66, 99, 67)(45, 69, 103, 70)(46, 71, 105, 72)(50, 76, 113, 77)(58, 86, 129, 87)(60, 89, 133, 90)(62, 92, 137, 93)(63, 94, 139, 95)(64, 96, 141, 97)(68, 101, 149, 102)(74, 109, 162, 110)(75, 111, 164, 112)(79, 117, 173, 118)(81, 120, 177, 121)(83, 123, 181, 124)(84, 125, 183, 126)(85, 127, 185, 128)(88, 131, 191, 132)(91, 135, 166, 136)(98, 144, 210, 145)(100, 147, 214, 148)(104, 153, 222, 154)(106, 156, 224, 157)(107, 158, 226, 159)(108, 160, 228, 161)(114, 167, 237, 168)(115, 169, 239, 170)(116, 171, 241, 172)(119, 175, 247, 176)(122, 179, 155, 180)(130, 189, 267, 190)(134, 195, 275, 196)(138, 200, 283, 201)(140, 203, 287, 204)(142, 206, 291, 207)(143, 208, 293, 209)(146, 212, 298, 213)(150, 217, 304, 218)(151, 219, 262, 186)(152, 220, 307, 221)(163, 232, 325, 233)(165, 235, 329, 236)(174, 245, 343, 246)(178, 251, 351, 252)(182, 256, 359, 257)(184, 259, 363, 260)(187, 263, 368, 264)(188, 265, 370, 266)(192, 270, 376, 271)(193, 272, 338, 242)(194, 273, 379, 274)(197, 277, 385, 278)(198, 279, 386, 280)(199, 281, 387, 282)(202, 285, 393, 286)(205, 289, 216, 290)(211, 296, 407, 297)(215, 302, 352, 303)(223, 311, 344, 312)(225, 314, 427, 315)(227, 317, 431, 318)(229, 249, 348, 320)(230, 321, 432, 322)(231, 323, 434, 324)(234, 327, 409, 328)(238, 332, 441, 333)(240, 335, 445, 336)(243, 339, 450, 340)(244, 341, 452, 342)(248, 346, 456, 347)(250, 349, 459, 350)(253, 353, 463, 354)(254, 355, 464, 356)(255, 357, 465, 358)(258, 361, 470, 362)(261, 365, 269, 366)(268, 374, 330, 375)(276, 383, 326, 384)(284, 391, 499, 392)(288, 382, 491, 397)(292, 380, 472, 401)(294, 403, 457, 404)(295, 405, 319, 406)(299, 410, 461, 411)(300, 378, 488, 388)(301, 360, 469, 412)(305, 415, 451, 416)(306, 417, 521, 418)(308, 395, 502, 419)(309, 420, 453, 421)(310, 422, 523, 423)(313, 425, 525, 426)(316, 429, 528, 430)(331, 439, 531, 440)(334, 443, 536, 444)(337, 447, 345, 448)(364, 462, 548, 474)(367, 460, 538, 477)(369, 479, 408, 480)(371, 481, 437, 482)(372, 458, 547, 466)(373, 442, 535, 483)(377, 486, 433, 487)(381, 489, 435, 490)(389, 496, 544, 497)(390, 498, 552, 467)(394, 501, 546, 473)(396, 503, 565, 485)(398, 504, 574, 505)(399, 506, 542, 507)(400, 508, 532, 454)(402, 509, 533, 468)(413, 516, 424, 517)(414, 518, 537, 519)(428, 527, 545, 455)(436, 529, 543, 449)(438, 530, 540, 446)(471, 554, 513, 539)(475, 555, 586, 556)(476, 557, 511, 558)(478, 559, 526, 534)(484, 563, 492, 564)(493, 551, 585, 553)(494, 569, 589, 570)(495, 571, 500, 550)(510, 568, 587, 562)(512, 573, 591, 575)(514, 567, 522, 561)(515, 566, 524, 576)(520, 578, 588, 572)(541, 581, 594, 582)(549, 579, 593, 580)(560, 584, 577, 583)(590, 596, 599, 598)(592, 595, 600, 597) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 32)(19, 33)(20, 34)(24, 42)(25, 43)(26, 45)(27, 35)(28, 46)(31, 50)(36, 58)(37, 60)(38, 51)(39, 62)(40, 63)(41, 64)(44, 68)(47, 54)(48, 74)(49, 75)(52, 79)(53, 81)(55, 83)(56, 84)(57, 85)(59, 88)(61, 91)(65, 98)(66, 100)(67, 92)(69, 95)(70, 104)(71, 106)(72, 107)(73, 108)(76, 114)(77, 115)(78, 116)(80, 119)(82, 122)(86, 130)(87, 123)(89, 126)(90, 134)(93, 138)(94, 140)(96, 142)(97, 143)(99, 146)(101, 150)(102, 151)(103, 152)(105, 155)(109, 163)(110, 156)(111, 159)(112, 165)(113, 166)(117, 174)(118, 167)(120, 170)(121, 178)(124, 182)(125, 184)(127, 186)(128, 187)(129, 188)(131, 192)(132, 193)(133, 194)(135, 197)(136, 198)(137, 199)(139, 202)(141, 205)(144, 211)(145, 206)(147, 209)(148, 215)(149, 216)(153, 223)(154, 217)(157, 225)(158, 227)(160, 229)(161, 230)(162, 231)(164, 234)(168, 238)(169, 240)(171, 242)(172, 243)(173, 244)(175, 248)(176, 249)(177, 250)(179, 253)(180, 254)(181, 255)(183, 258)(185, 261)(189, 264)(190, 268)(191, 269)(195, 276)(196, 270)(200, 284)(201, 277)(203, 280)(204, 288)(207, 292)(208, 294)(210, 295)(212, 299)(213, 300)(214, 301)(218, 305)(219, 306)(220, 308)(221, 309)(222, 310)(224, 313)(226, 316)(228, 319)(232, 322)(233, 326)(235, 330)(236, 296)(237, 331)(239, 334)(241, 337)(245, 340)(246, 344)(247, 345)(251, 352)(252, 346)(256, 360)(257, 353)(259, 356)(260, 364)(262, 367)(263, 369)(265, 371)(266, 372)(267, 373)(271, 377)(272, 378)(273, 380)(274, 381)(275, 382)(278, 335)(279, 333)(281, 388)(282, 389)(283, 390)(285, 394)(286, 395)(287, 396)(289, 398)(290, 399)(291, 400)(293, 402)(297, 408)(298, 409)(302, 413)(303, 410)(304, 414)(307, 370)(311, 421)(312, 424)(314, 428)(315, 355)(317, 354)(318, 423)(320, 419)(321, 433)(323, 435)(324, 418)(325, 392)(327, 436)(328, 437)(329, 438)(332, 442)(336, 446)(338, 449)(339, 451)(341, 453)(342, 454)(343, 455)(347, 457)(348, 458)(349, 460)(350, 461)(351, 462)(357, 466)(358, 467)(359, 468)(361, 471)(362, 472)(363, 473)(365, 475)(366, 476)(368, 478)(374, 484)(375, 481)(376, 485)(379, 452)(383, 490)(384, 492)(385, 493)(386, 494)(387, 495)(391, 497)(393, 500)(397, 501)(401, 504)(403, 507)(404, 510)(405, 511)(406, 512)(407, 513)(411, 514)(412, 515)(415, 520)(416, 506)(417, 505)(420, 522)(422, 524)(425, 521)(426, 526)(427, 496)(429, 503)(430, 529)(431, 518)(432, 498)(434, 459)(439, 532)(440, 533)(441, 534)(443, 537)(444, 538)(445, 539)(447, 541)(448, 542)(450, 544)(456, 546)(463, 549)(464, 550)(465, 551)(469, 552)(470, 553)(474, 554)(477, 555)(479, 558)(480, 560)(482, 561)(483, 562)(486, 566)(487, 557)(488, 556)(489, 567)(491, 568)(499, 572)(502, 573)(508, 575)(509, 535)(516, 576)(517, 577)(519, 540)(523, 565)(525, 569)(527, 559)(528, 570)(530, 578)(531, 579)(536, 580)(543, 581)(545, 583)(547, 582)(548, 584)(563, 587)(564, 588)(571, 590)(574, 592)(585, 595)(586, 596)(589, 597)(591, 598)(593, 599)(594, 600) local type(s) :: { ( 5^4 ) } Outer automorphisms :: reflexible Dual of E16.1285 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 150 e = 300 f = 120 degree seq :: [ 4^150 ] E16.1287 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 5}) Quotient :: edge Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T2)^2, (F * T1)^2, (T2 * T1)^5, T2^-1 * T1 * T2^-2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-1, T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1, T2 * T1 * T2^-2 * T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1 * T2^2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1, T1 * T2 * T1 * T2^-2 * T1 * T2 * T1 * T2^-2 * T1 * T2^2 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2^2 ] 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, 44, 27)(20, 34, 55, 35)(23, 38, 60, 39)(25, 41, 65, 42)(28, 46, 71, 47)(30, 49, 50, 31)(33, 52, 80, 53)(36, 57, 86, 58)(40, 62, 94, 63)(43, 66, 99, 67)(45, 69, 104, 70)(48, 73, 109, 74)(51, 77, 116, 78)(54, 81, 121, 82)(56, 84, 126, 85)(59, 88, 131, 89)(61, 91, 136, 92)(64, 96, 142, 97)(68, 101, 150, 102)(72, 106, 158, 107)(75, 111, 164, 112)(76, 113, 167, 114)(79, 118, 173, 119)(83, 123, 181, 124)(87, 128, 189, 129)(90, 133, 195, 134)(93, 137, 200, 138)(95, 140, 205, 141)(98, 144, 210, 145)(100, 147, 215, 148)(103, 152, 220, 153)(105, 155, 225, 156)(108, 159, 230, 160)(110, 162, 233, 163)(115, 168, 240, 169)(117, 171, 245, 172)(120, 175, 250, 176)(122, 178, 255, 179)(125, 183, 260, 184)(127, 186, 265, 187)(130, 190, 270, 191)(132, 193, 273, 194)(135, 197, 277, 198)(139, 202, 161, 203)(143, 207, 292, 208)(146, 212, 298, 213)(149, 216, 303, 217)(151, 218, 306, 219)(154, 222, 311, 223)(157, 227, 317, 228)(165, 235, 330, 236)(166, 237, 331, 238)(170, 242, 192, 243)(174, 247, 346, 248)(177, 252, 352, 253)(180, 256, 357, 257)(182, 258, 360, 259)(185, 262, 365, 263)(188, 267, 371, 268)(196, 275, 384, 276)(199, 279, 368, 280)(201, 282, 392, 283)(204, 286, 397, 287)(206, 289, 401, 290)(209, 293, 405, 294)(211, 296, 407, 297)(214, 300, 411, 301)(221, 308, 420, 309)(224, 312, 424, 313)(226, 315, 426, 316)(229, 319, 428, 320)(231, 322, 432, 323)(232, 324, 433, 325)(234, 327, 349, 328)(239, 333, 314, 334)(241, 336, 446, 337)(244, 340, 451, 341)(246, 343, 455, 344)(249, 347, 459, 348)(251, 350, 461, 351)(254, 354, 465, 355)(261, 362, 474, 363)(264, 366, 478, 367)(266, 369, 480, 370)(269, 373, 482, 374)(271, 376, 486, 377)(272, 378, 487, 379)(274, 381, 295, 382)(278, 386, 329, 387)(281, 390, 500, 391)(284, 393, 501, 394)(285, 395, 502, 396)(288, 399, 506, 400)(291, 403, 318, 404)(299, 409, 516, 410)(302, 412, 507, 413)(304, 415, 470, 359)(305, 358, 469, 416)(307, 418, 523, 419)(310, 421, 524, 422)(321, 429, 525, 430)(326, 434, 528, 435)(332, 440, 383, 441)(335, 444, 538, 445)(338, 447, 539, 448)(339, 449, 540, 450)(342, 453, 544, 454)(345, 457, 372, 458)(353, 463, 554, 464)(356, 466, 545, 467)(361, 472, 561, 473)(364, 475, 562, 476)(375, 483, 563, 484)(380, 488, 566, 489)(385, 493, 543, 494)(388, 496, 437, 497)(389, 498, 571, 499)(398, 503, 573, 504)(402, 508, 427, 509)(406, 511, 425, 512)(408, 514, 423, 515)(414, 518, 577, 519)(417, 521, 578, 522)(431, 527, 576, 517)(436, 529, 574, 513)(438, 530, 564, 520)(439, 531, 505, 532)(442, 534, 491, 535)(443, 536, 581, 537)(452, 541, 583, 542)(456, 546, 481, 547)(460, 549, 479, 550)(462, 552, 477, 553)(468, 556, 587, 557)(471, 559, 588, 560)(485, 565, 586, 555)(490, 567, 584, 551)(492, 568, 526, 558)(495, 569, 510, 570)(533, 579, 548, 580)(572, 590, 598, 591)(575, 592, 597, 589)(582, 594, 600, 595)(585, 596, 599, 593)(601, 602)(603, 607)(604, 609)(605, 610)(606, 612)(608, 615)(611, 620)(613, 623)(614, 625)(616, 628)(617, 630)(618, 631)(619, 633)(621, 636)(622, 638)(624, 640)(626, 643)(627, 645)(629, 648)(632, 651)(634, 654)(635, 656)(637, 659)(639, 661)(641, 664)(642, 666)(644, 668)(646, 670)(647, 672)(649, 675)(650, 676)(652, 679)(653, 681)(655, 683)(657, 685)(658, 687)(660, 690)(662, 693)(663, 695)(665, 698)(667, 700)(669, 703)(671, 705)(673, 708)(674, 710)(677, 715)(678, 717)(680, 720)(682, 722)(684, 725)(686, 727)(688, 730)(689, 732)(691, 735)(692, 737)(694, 739)(696, 741)(697, 743)(699, 746)(701, 749)(702, 751)(704, 754)(706, 757)(707, 759)(709, 761)(711, 763)(712, 765)(713, 766)(714, 768)(716, 770)(718, 772)(719, 774)(721, 777)(723, 780)(724, 782)(726, 785)(728, 788)(729, 790)(731, 792)(733, 794)(734, 796)(736, 799)(738, 801)(740, 804)(742, 806)(744, 809)(745, 811)(747, 814)(748, 816)(750, 781)(752, 819)(753, 821)(755, 824)(756, 826)(758, 829)(760, 831)(762, 832)(764, 834)(767, 839)(769, 841)(771, 844)(773, 846)(775, 849)(776, 851)(778, 854)(779, 856)(783, 859)(784, 861)(786, 864)(787, 866)(789, 869)(791, 871)(793, 872)(795, 874)(797, 876)(798, 878)(800, 881)(802, 884)(803, 885)(805, 888)(807, 891)(808, 893)(810, 895)(812, 897)(813, 899)(815, 902)(817, 904)(818, 905)(820, 907)(822, 910)(823, 912)(825, 914)(827, 916)(828, 918)(830, 921)(833, 926)(835, 929)(836, 837)(838, 932)(840, 935)(842, 938)(843, 939)(845, 942)(847, 945)(848, 947)(850, 949)(852, 951)(853, 953)(855, 956)(857, 958)(858, 959)(860, 961)(862, 964)(863, 966)(865, 968)(867, 970)(868, 972)(870, 975)(873, 980)(875, 983)(877, 985)(879, 988)(880, 989)(882, 943)(883, 993)(886, 996)(887, 998)(889, 936)(890, 1002)(892, 962)(894, 1006)(896, 950)(898, 1008)(900, 1010)(901, 971)(903, 1014)(906, 1017)(908, 946)(909, 1021)(911, 1023)(913, 967)(915, 1025)(917, 955)(919, 1027)(920, 979)(922, 1031)(923, 995)(924, 994)(925, 974)(927, 1036)(928, 1037)(930, 1038)(931, 1039)(933, 1042)(934, 1043)(937, 1047)(940, 1050)(941, 1052)(944, 1056)(948, 1060)(952, 1062)(954, 1064)(957, 1068)(960, 1071)(963, 1075)(965, 1077)(969, 1079)(973, 1081)(976, 1085)(977, 1049)(978, 1048)(981, 1090)(982, 1091)(984, 1092)(986, 1095)(987, 1096)(990, 1099)(991, 1067)(992, 1054)(997, 1076)(999, 1105)(1000, 1046)(1001, 1107)(1003, 1109)(1004, 1110)(1005, 1073)(1007, 1113)(1009, 1086)(1011, 1117)(1012, 1080)(1013, 1045)(1015, 1093)(1016, 1120)(1018, 1088)(1019, 1059)(1020, 1103)(1022, 1051)(1024, 1098)(1026, 1066)(1028, 1123)(1029, 1087)(1030, 1126)(1032, 1063)(1033, 1083)(1034, 1072)(1035, 1129)(1040, 1133)(1041, 1134)(1044, 1137)(1053, 1143)(1055, 1145)(1057, 1147)(1058, 1148)(1061, 1151)(1065, 1155)(1069, 1131)(1070, 1158)(1074, 1141)(1078, 1136)(1082, 1161)(1084, 1164)(1089, 1167)(1094, 1142)(1097, 1150)(1100, 1156)(1101, 1172)(1102, 1153)(1104, 1132)(1106, 1157)(1108, 1149)(1111, 1146)(1112, 1135)(1114, 1175)(1115, 1140)(1116, 1154)(1118, 1138)(1119, 1144)(1121, 1163)(1122, 1166)(1124, 1162)(1125, 1159)(1127, 1168)(1128, 1160)(1130, 1165)(1139, 1182)(1152, 1185)(1169, 1183)(1170, 1186)(1171, 1189)(1173, 1179)(1174, 1192)(1176, 1180)(1177, 1190)(1178, 1191)(1181, 1193)(1184, 1196)(1187, 1194)(1188, 1195)(1197, 1200)(1198, 1199) L = (1, 601)(2, 602)(3, 603)(4, 604)(5, 605)(6, 606)(7, 607)(8, 608)(9, 609)(10, 610)(11, 611)(12, 612)(13, 613)(14, 614)(15, 615)(16, 616)(17, 617)(18, 618)(19, 619)(20, 620)(21, 621)(22, 622)(23, 623)(24, 624)(25, 625)(26, 626)(27, 627)(28, 628)(29, 629)(30, 630)(31, 631)(32, 632)(33, 633)(34, 634)(35, 635)(36, 636)(37, 637)(38, 638)(39, 639)(40, 640)(41, 641)(42, 642)(43, 643)(44, 644)(45, 645)(46, 646)(47, 647)(48, 648)(49, 649)(50, 650)(51, 651)(52, 652)(53, 653)(54, 654)(55, 655)(56, 656)(57, 657)(58, 658)(59, 659)(60, 660)(61, 661)(62, 662)(63, 663)(64, 664)(65, 665)(66, 666)(67, 667)(68, 668)(69, 669)(70, 670)(71, 671)(72, 672)(73, 673)(74, 674)(75, 675)(76, 676)(77, 677)(78, 678)(79, 679)(80, 680)(81, 681)(82, 682)(83, 683)(84, 684)(85, 685)(86, 686)(87, 687)(88, 688)(89, 689)(90, 690)(91, 691)(92, 692)(93, 693)(94, 694)(95, 695)(96, 696)(97, 697)(98, 698)(99, 699)(100, 700)(101, 701)(102, 702)(103, 703)(104, 704)(105, 705)(106, 706)(107, 707)(108, 708)(109, 709)(110, 710)(111, 711)(112, 712)(113, 713)(114, 714)(115, 715)(116, 716)(117, 717)(118, 718)(119, 719)(120, 720)(121, 721)(122, 722)(123, 723)(124, 724)(125, 725)(126, 726)(127, 727)(128, 728)(129, 729)(130, 730)(131, 731)(132, 732)(133, 733)(134, 734)(135, 735)(136, 736)(137, 737)(138, 738)(139, 739)(140, 740)(141, 741)(142, 742)(143, 743)(144, 744)(145, 745)(146, 746)(147, 747)(148, 748)(149, 749)(150, 750)(151, 751)(152, 752)(153, 753)(154, 754)(155, 755)(156, 756)(157, 757)(158, 758)(159, 759)(160, 760)(161, 761)(162, 762)(163, 763)(164, 764)(165, 765)(166, 766)(167, 767)(168, 768)(169, 769)(170, 770)(171, 771)(172, 772)(173, 773)(174, 774)(175, 775)(176, 776)(177, 777)(178, 778)(179, 779)(180, 780)(181, 781)(182, 782)(183, 783)(184, 784)(185, 785)(186, 786)(187, 787)(188, 788)(189, 789)(190, 790)(191, 791)(192, 792)(193, 793)(194, 794)(195, 795)(196, 796)(197, 797)(198, 798)(199, 799)(200, 800)(201, 801)(202, 802)(203, 803)(204, 804)(205, 805)(206, 806)(207, 807)(208, 808)(209, 809)(210, 810)(211, 811)(212, 812)(213, 813)(214, 814)(215, 815)(216, 816)(217, 817)(218, 818)(219, 819)(220, 820)(221, 821)(222, 822)(223, 823)(224, 824)(225, 825)(226, 826)(227, 827)(228, 828)(229, 829)(230, 830)(231, 831)(232, 832)(233, 833)(234, 834)(235, 835)(236, 836)(237, 837)(238, 838)(239, 839)(240, 840)(241, 841)(242, 842)(243, 843)(244, 844)(245, 845)(246, 846)(247, 847)(248, 848)(249, 849)(250, 850)(251, 851)(252, 852)(253, 853)(254, 854)(255, 855)(256, 856)(257, 857)(258, 858)(259, 859)(260, 860)(261, 861)(262, 862)(263, 863)(264, 864)(265, 865)(266, 866)(267, 867)(268, 868)(269, 869)(270, 870)(271, 871)(272, 872)(273, 873)(274, 874)(275, 875)(276, 876)(277, 877)(278, 878)(279, 879)(280, 880)(281, 881)(282, 882)(283, 883)(284, 884)(285, 885)(286, 886)(287, 887)(288, 888)(289, 889)(290, 890)(291, 891)(292, 892)(293, 893)(294, 894)(295, 895)(296, 896)(297, 897)(298, 898)(299, 899)(300, 900)(301, 901)(302, 902)(303, 903)(304, 904)(305, 905)(306, 906)(307, 907)(308, 908)(309, 909)(310, 910)(311, 911)(312, 912)(313, 913)(314, 914)(315, 915)(316, 916)(317, 917)(318, 918)(319, 919)(320, 920)(321, 921)(322, 922)(323, 923)(324, 924)(325, 925)(326, 926)(327, 927)(328, 928)(329, 929)(330, 930)(331, 931)(332, 932)(333, 933)(334, 934)(335, 935)(336, 936)(337, 937)(338, 938)(339, 939)(340, 940)(341, 941)(342, 942)(343, 943)(344, 944)(345, 945)(346, 946)(347, 947)(348, 948)(349, 949)(350, 950)(351, 951)(352, 952)(353, 953)(354, 954)(355, 955)(356, 956)(357, 957)(358, 958)(359, 959)(360, 960)(361, 961)(362, 962)(363, 963)(364, 964)(365, 965)(366, 966)(367, 967)(368, 968)(369, 969)(370, 970)(371, 971)(372, 972)(373, 973)(374, 974)(375, 975)(376, 976)(377, 977)(378, 978)(379, 979)(380, 980)(381, 981)(382, 982)(383, 983)(384, 984)(385, 985)(386, 986)(387, 987)(388, 988)(389, 989)(390, 990)(391, 991)(392, 992)(393, 993)(394, 994)(395, 995)(396, 996)(397, 997)(398, 998)(399, 999)(400, 1000)(401, 1001)(402, 1002)(403, 1003)(404, 1004)(405, 1005)(406, 1006)(407, 1007)(408, 1008)(409, 1009)(410, 1010)(411, 1011)(412, 1012)(413, 1013)(414, 1014)(415, 1015)(416, 1016)(417, 1017)(418, 1018)(419, 1019)(420, 1020)(421, 1021)(422, 1022)(423, 1023)(424, 1024)(425, 1025)(426, 1026)(427, 1027)(428, 1028)(429, 1029)(430, 1030)(431, 1031)(432, 1032)(433, 1033)(434, 1034)(435, 1035)(436, 1036)(437, 1037)(438, 1038)(439, 1039)(440, 1040)(441, 1041)(442, 1042)(443, 1043)(444, 1044)(445, 1045)(446, 1046)(447, 1047)(448, 1048)(449, 1049)(450, 1050)(451, 1051)(452, 1052)(453, 1053)(454, 1054)(455, 1055)(456, 1056)(457, 1057)(458, 1058)(459, 1059)(460, 1060)(461, 1061)(462, 1062)(463, 1063)(464, 1064)(465, 1065)(466, 1066)(467, 1067)(468, 1068)(469, 1069)(470, 1070)(471, 1071)(472, 1072)(473, 1073)(474, 1074)(475, 1075)(476, 1076)(477, 1077)(478, 1078)(479, 1079)(480, 1080)(481, 1081)(482, 1082)(483, 1083)(484, 1084)(485, 1085)(486, 1086)(487, 1087)(488, 1088)(489, 1089)(490, 1090)(491, 1091)(492, 1092)(493, 1093)(494, 1094)(495, 1095)(496, 1096)(497, 1097)(498, 1098)(499, 1099)(500, 1100)(501, 1101)(502, 1102)(503, 1103)(504, 1104)(505, 1105)(506, 1106)(507, 1107)(508, 1108)(509, 1109)(510, 1110)(511, 1111)(512, 1112)(513, 1113)(514, 1114)(515, 1115)(516, 1116)(517, 1117)(518, 1118)(519, 1119)(520, 1120)(521, 1121)(522, 1122)(523, 1123)(524, 1124)(525, 1125)(526, 1126)(527, 1127)(528, 1128)(529, 1129)(530, 1130)(531, 1131)(532, 1132)(533, 1133)(534, 1134)(535, 1135)(536, 1136)(537, 1137)(538, 1138)(539, 1139)(540, 1140)(541, 1141)(542, 1142)(543, 1143)(544, 1144)(545, 1145)(546, 1146)(547, 1147)(548, 1148)(549, 1149)(550, 1150)(551, 1151)(552, 1152)(553, 1153)(554, 1154)(555, 1155)(556, 1156)(557, 1157)(558, 1158)(559, 1159)(560, 1160)(561, 1161)(562, 1162)(563, 1163)(564, 1164)(565, 1165)(566, 1166)(567, 1167)(568, 1168)(569, 1169)(570, 1170)(571, 1171)(572, 1172)(573, 1173)(574, 1174)(575, 1175)(576, 1176)(577, 1177)(578, 1178)(579, 1179)(580, 1180)(581, 1181)(582, 1182)(583, 1183)(584, 1184)(585, 1185)(586, 1186)(587, 1187)(588, 1188)(589, 1189)(590, 1190)(591, 1191)(592, 1192)(593, 1193)(594, 1194)(595, 1195)(596, 1196)(597, 1197)(598, 1198)(599, 1199)(600, 1200) local type(s) :: { ( 10, 10 ), ( 10^4 ) } Outer automorphisms :: reflexible Dual of E16.1291 Transitivity :: ET+ Graph:: simple bipartite v = 450 e = 600 f = 120 degree seq :: [ 2^300, 4^150 ] E16.1288 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 5}) Quotient :: edge Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, T2^5, T2^-2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^6, T2 * T1^-1 * T2^-2 * T1 * T2^-1 * T1 * T2^2 * T1^-2 * T2^-2 * T1 * T2^-2 * T1^-2, T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1, T1^-1 * T2^-2 * T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1^-1, T2 * T1^-1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1 * T2^-2 * T1^-2 * T2^-2 * T1^-1 * T2 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 3, 10, 14, 5)(2, 7, 17, 20, 8)(4, 12, 26, 22, 9)(6, 15, 31, 34, 16)(11, 25, 47, 45, 23)(13, 28, 52, 55, 29)(18, 37, 66, 64, 35)(19, 38, 68, 71, 39)(21, 41, 73, 76, 42)(24, 46, 81, 56, 30)(27, 51, 89, 87, 49)(32, 59, 101, 99, 57)(33, 60, 103, 106, 61)(36, 65, 111, 72, 40)(43, 50, 88, 130, 77)(44, 78, 131, 134, 79)(48, 85, 142, 140, 83)(53, 93, 153, 151, 91)(54, 94, 155, 157, 95)(58, 100, 163, 107, 62)(63, 108, 175, 178, 109)(67, 115, 186, 184, 113)(69, 118, 190, 188, 116)(70, 119, 192, 194, 120)(74, 125, 200, 198, 123)(75, 126, 202, 204, 127)(80, 84, 141, 216, 135)(82, 138, 220, 218, 136)(86, 143, 226, 229, 144)(90, 149, 235, 233, 147)(92, 152, 239, 158, 96)(97, 137, 219, 249, 159)(98, 160, 250, 253, 161)(102, 167, 261, 259, 165)(104, 170, 265, 263, 168)(105, 171, 267, 269, 172)(110, 114, 185, 279, 179)(112, 182, 283, 281, 180)(117, 189, 292, 195, 121)(122, 181, 282, 302, 196)(124, 199, 306, 205, 128)(129, 206, 316, 318, 207)(132, 211, 323, 321, 209)(133, 212, 325, 327, 213)(139, 221, 336, 339, 222)(145, 148, 234, 350, 230)(146, 231, 351, 319, 208)(150, 236, 357, 360, 237)(154, 243, 367, 365, 241)(156, 246, 371, 369, 244)(162, 166, 260, 383, 254)(164, 257, 387, 385, 255)(169, 264, 396, 270, 173)(174, 256, 386, 406, 271)(176, 274, 410, 408, 272)(177, 275, 412, 414, 276)(183, 284, 423, 426, 285)(187, 289, 430, 433, 290)(191, 296, 440, 438, 294)(193, 299, 444, 442, 297)(197, 303, 449, 452, 304)(201, 310, 457, 455, 308)(203, 313, 461, 459, 311)(210, 322, 468, 328, 214)(215, 329, 384, 362, 240)(217, 331, 397, 382, 332)(223, 225, 342, 479, 340)(224, 341, 480, 474, 330)(227, 345, 485, 483, 343)(228, 346, 487, 489, 347)(232, 352, 469, 478, 353)(238, 242, 366, 441, 361)(245, 370, 445, 373, 247)(248, 363, 496, 501, 374)(251, 378, 506, 504, 376)(252, 379, 508, 510, 380)(258, 388, 512, 515, 389)(262, 393, 519, 522, 394)(266, 400, 527, 525, 398)(268, 403, 531, 529, 401)(273, 409, 337, 415, 277)(278, 416, 317, 435, 293)(280, 418, 307, 349, 419)(286, 288, 429, 338, 427)(287, 428, 543, 465, 417)(291, 295, 439, 528, 434)(298, 443, 532, 446, 300)(301, 436, 491, 551, 447)(305, 309, 456, 368, 453)(312, 460, 372, 463, 314)(315, 420, 422, 540, 464)(320, 466, 558, 560, 467)(324, 359, 495, 561, 470)(326, 472, 563, 562, 471)(333, 335, 475, 534, 405)(334, 391, 517, 502, 375)(344, 484, 513, 490, 348)(354, 356, 492, 514, 473)(355, 481, 552, 448, 421)(358, 494, 570, 569, 493)(364, 497, 571, 572, 498)(377, 505, 424, 511, 381)(390, 392, 518, 425, 516)(395, 399, 526, 458, 523)(402, 530, 462, 533, 404)(407, 535, 582, 583, 536)(411, 432, 546, 584, 537)(413, 539, 559, 585, 538)(431, 545, 588, 587, 544)(437, 547, 589, 557, 548)(450, 554, 592, 591, 553)(451, 555, 593, 567, 486)(454, 556, 590, 549, 550)(476, 564, 577, 509, 477)(482, 565, 595, 594, 566)(488, 542, 541, 586, 568)(499, 500, 524, 581, 573)(503, 574, 596, 597, 575)(507, 521, 580, 598, 576)(520, 579, 600, 599, 578)(601, 602, 606, 604)(603, 609, 621, 611)(605, 613, 618, 607)(608, 619, 632, 615)(610, 623, 644, 624)(612, 616, 633, 627)(614, 630, 653, 628)(617, 635, 663, 636)(620, 640, 669, 638)(622, 643, 674, 641)(625, 642, 675, 648)(626, 649, 686, 650)(629, 654, 667, 637)(631, 657, 698, 658)(634, 662, 704, 660)(639, 670, 702, 659)(645, 680, 732, 678)(646, 679, 733, 682)(647, 683, 739, 684)(651, 661, 705, 690)(652, 691, 750, 692)(655, 696, 756, 694)(656, 697, 754, 693)(664, 710, 776, 708)(665, 709, 777, 712)(666, 713, 783, 714)(668, 716, 787, 717)(671, 721, 793, 719)(672, 722, 791, 718)(673, 723, 797, 724)(676, 728, 803, 726)(677, 729, 801, 725)(681, 736, 817, 737)(685, 727, 767, 720)(687, 745, 827, 743)(688, 744, 828, 746)(689, 747, 832, 748)(695, 749, 772, 715)(699, 762, 851, 760)(700, 761, 852, 764)(701, 765, 858, 766)(703, 768, 862, 769)(706, 773, 868, 771)(707, 774, 866, 770)(711, 780, 880, 781)(730, 808, 917, 806)(731, 809, 920, 810)(734, 814, 926, 812)(735, 815, 924, 811)(738, 813, 910, 807)(740, 823, 937, 821)(741, 822, 938, 824)(742, 794, 900, 825)(751, 838, 958, 836)(752, 837, 959, 840)(753, 841, 964, 842)(755, 844, 968, 845)(757, 847, 956, 835)(758, 848, 972, 846)(759, 782, 876, 843)(763, 855, 984, 856)(775, 872, 1007, 873)(778, 877, 1013, 875)(779, 878, 1011, 874)(784, 886, 1024, 884)(785, 885, 1025, 887)(786, 869, 1004, 888)(788, 891, 1031, 889)(789, 890, 1032, 893)(790, 894, 1037, 895)(792, 897, 1041, 898)(795, 901, 1045, 899)(796, 857, 980, 896)(798, 905, 1050, 903)(799, 904, 1051, 907)(800, 908, 1054, 909)(802, 911, 1058, 912)(804, 914, 992, 861)(805, 915, 1062, 913)(816, 930, 986, 929)(818, 933, 996, 931)(819, 932, 983, 934)(820, 918, 1065, 935)(826, 943, 1082, 944)(829, 948, 1088, 946)(830, 949, 1086, 945)(831, 947, 1000, 871)(833, 954, 1068, 952)(834, 953, 1079, 955)(839, 962, 985, 963)(849, 975, 1022, 883)(850, 976, 1103, 977)(853, 981, 1109, 979)(854, 982, 1107, 978)(859, 990, 1113, 988)(860, 989, 1114, 991)(863, 995, 1120, 993)(864, 994, 1121, 997)(865, 998, 1124, 999)(867, 1001, 1128, 1002)(870, 1005, 1132, 1003)(879, 1017, 916, 1016)(881, 1020, 906, 1018)(882, 1019, 950, 1021)(892, 1035, 919, 1036)(902, 1048, 1096, 987)(921, 1030, 1144, 1066)(922, 1067, 1159, 1069)(923, 1070, 1146, 1033)(925, 1071, 1147, 1038)(927, 1040, 1110, 1057)(928, 1073, 1115, 1072)(936, 1009, 1136, 1076)(939, 1077, 1111, 1027)(940, 1078, 1139, 1015)(941, 1029, 1133, 1064)(942, 1046, 1134, 1081)(951, 1006, 1074, 1091)(957, 1093, 1165, 1083)(960, 1085, 1167, 1095)(961, 1042, 1149, 1094)(965, 1087, 1168, 1097)(966, 1098, 1131, 1043)(967, 1014, 1127, 1089)(969, 1099, 1154, 1053)(970, 1056, 1150, 1044)(971, 1060, 1126, 1100)(973, 1047, 1117, 1092)(974, 1028, 1118, 1063)(1008, 1119, 1178, 1135)(1010, 1137, 1180, 1122)(1012, 1138, 1181, 1125)(1023, 1105, 1175, 1141)(1026, 1142, 1090, 1116)(1034, 1129, 1172, 1145)(1039, 1148, 1061, 1130)(1049, 1153, 1174, 1104)(1052, 1106, 1176, 1155)(1055, 1108, 1177, 1156)(1059, 1157, 1179, 1123)(1075, 1143, 1101, 1152)(1080, 1140, 1102, 1151)(1084, 1166, 1163, 1112)(1158, 1187, 1196, 1191)(1160, 1192, 1173, 1185)(1161, 1193, 1198, 1184)(1162, 1194, 1200, 1189)(1164, 1183, 1170, 1190)(1169, 1182, 1199, 1195)(1171, 1186, 1197, 1188) L = (1, 601)(2, 602)(3, 603)(4, 604)(5, 605)(6, 606)(7, 607)(8, 608)(9, 609)(10, 610)(11, 611)(12, 612)(13, 613)(14, 614)(15, 615)(16, 616)(17, 617)(18, 618)(19, 619)(20, 620)(21, 621)(22, 622)(23, 623)(24, 624)(25, 625)(26, 626)(27, 627)(28, 628)(29, 629)(30, 630)(31, 631)(32, 632)(33, 633)(34, 634)(35, 635)(36, 636)(37, 637)(38, 638)(39, 639)(40, 640)(41, 641)(42, 642)(43, 643)(44, 644)(45, 645)(46, 646)(47, 647)(48, 648)(49, 649)(50, 650)(51, 651)(52, 652)(53, 653)(54, 654)(55, 655)(56, 656)(57, 657)(58, 658)(59, 659)(60, 660)(61, 661)(62, 662)(63, 663)(64, 664)(65, 665)(66, 666)(67, 667)(68, 668)(69, 669)(70, 670)(71, 671)(72, 672)(73, 673)(74, 674)(75, 675)(76, 676)(77, 677)(78, 678)(79, 679)(80, 680)(81, 681)(82, 682)(83, 683)(84, 684)(85, 685)(86, 686)(87, 687)(88, 688)(89, 689)(90, 690)(91, 691)(92, 692)(93, 693)(94, 694)(95, 695)(96, 696)(97, 697)(98, 698)(99, 699)(100, 700)(101, 701)(102, 702)(103, 703)(104, 704)(105, 705)(106, 706)(107, 707)(108, 708)(109, 709)(110, 710)(111, 711)(112, 712)(113, 713)(114, 714)(115, 715)(116, 716)(117, 717)(118, 718)(119, 719)(120, 720)(121, 721)(122, 722)(123, 723)(124, 724)(125, 725)(126, 726)(127, 727)(128, 728)(129, 729)(130, 730)(131, 731)(132, 732)(133, 733)(134, 734)(135, 735)(136, 736)(137, 737)(138, 738)(139, 739)(140, 740)(141, 741)(142, 742)(143, 743)(144, 744)(145, 745)(146, 746)(147, 747)(148, 748)(149, 749)(150, 750)(151, 751)(152, 752)(153, 753)(154, 754)(155, 755)(156, 756)(157, 757)(158, 758)(159, 759)(160, 760)(161, 761)(162, 762)(163, 763)(164, 764)(165, 765)(166, 766)(167, 767)(168, 768)(169, 769)(170, 770)(171, 771)(172, 772)(173, 773)(174, 774)(175, 775)(176, 776)(177, 777)(178, 778)(179, 779)(180, 780)(181, 781)(182, 782)(183, 783)(184, 784)(185, 785)(186, 786)(187, 787)(188, 788)(189, 789)(190, 790)(191, 791)(192, 792)(193, 793)(194, 794)(195, 795)(196, 796)(197, 797)(198, 798)(199, 799)(200, 800)(201, 801)(202, 802)(203, 803)(204, 804)(205, 805)(206, 806)(207, 807)(208, 808)(209, 809)(210, 810)(211, 811)(212, 812)(213, 813)(214, 814)(215, 815)(216, 816)(217, 817)(218, 818)(219, 819)(220, 820)(221, 821)(222, 822)(223, 823)(224, 824)(225, 825)(226, 826)(227, 827)(228, 828)(229, 829)(230, 830)(231, 831)(232, 832)(233, 833)(234, 834)(235, 835)(236, 836)(237, 837)(238, 838)(239, 839)(240, 840)(241, 841)(242, 842)(243, 843)(244, 844)(245, 845)(246, 846)(247, 847)(248, 848)(249, 849)(250, 850)(251, 851)(252, 852)(253, 853)(254, 854)(255, 855)(256, 856)(257, 857)(258, 858)(259, 859)(260, 860)(261, 861)(262, 862)(263, 863)(264, 864)(265, 865)(266, 866)(267, 867)(268, 868)(269, 869)(270, 870)(271, 871)(272, 872)(273, 873)(274, 874)(275, 875)(276, 876)(277, 877)(278, 878)(279, 879)(280, 880)(281, 881)(282, 882)(283, 883)(284, 884)(285, 885)(286, 886)(287, 887)(288, 888)(289, 889)(290, 890)(291, 891)(292, 892)(293, 893)(294, 894)(295, 895)(296, 896)(297, 897)(298, 898)(299, 899)(300, 900)(301, 901)(302, 902)(303, 903)(304, 904)(305, 905)(306, 906)(307, 907)(308, 908)(309, 909)(310, 910)(311, 911)(312, 912)(313, 913)(314, 914)(315, 915)(316, 916)(317, 917)(318, 918)(319, 919)(320, 920)(321, 921)(322, 922)(323, 923)(324, 924)(325, 925)(326, 926)(327, 927)(328, 928)(329, 929)(330, 930)(331, 931)(332, 932)(333, 933)(334, 934)(335, 935)(336, 936)(337, 937)(338, 938)(339, 939)(340, 940)(341, 941)(342, 942)(343, 943)(344, 944)(345, 945)(346, 946)(347, 947)(348, 948)(349, 949)(350, 950)(351, 951)(352, 952)(353, 953)(354, 954)(355, 955)(356, 956)(357, 957)(358, 958)(359, 959)(360, 960)(361, 961)(362, 962)(363, 963)(364, 964)(365, 965)(366, 966)(367, 967)(368, 968)(369, 969)(370, 970)(371, 971)(372, 972)(373, 973)(374, 974)(375, 975)(376, 976)(377, 977)(378, 978)(379, 979)(380, 980)(381, 981)(382, 982)(383, 983)(384, 984)(385, 985)(386, 986)(387, 987)(388, 988)(389, 989)(390, 990)(391, 991)(392, 992)(393, 993)(394, 994)(395, 995)(396, 996)(397, 997)(398, 998)(399, 999)(400, 1000)(401, 1001)(402, 1002)(403, 1003)(404, 1004)(405, 1005)(406, 1006)(407, 1007)(408, 1008)(409, 1009)(410, 1010)(411, 1011)(412, 1012)(413, 1013)(414, 1014)(415, 1015)(416, 1016)(417, 1017)(418, 1018)(419, 1019)(420, 1020)(421, 1021)(422, 1022)(423, 1023)(424, 1024)(425, 1025)(426, 1026)(427, 1027)(428, 1028)(429, 1029)(430, 1030)(431, 1031)(432, 1032)(433, 1033)(434, 1034)(435, 1035)(436, 1036)(437, 1037)(438, 1038)(439, 1039)(440, 1040)(441, 1041)(442, 1042)(443, 1043)(444, 1044)(445, 1045)(446, 1046)(447, 1047)(448, 1048)(449, 1049)(450, 1050)(451, 1051)(452, 1052)(453, 1053)(454, 1054)(455, 1055)(456, 1056)(457, 1057)(458, 1058)(459, 1059)(460, 1060)(461, 1061)(462, 1062)(463, 1063)(464, 1064)(465, 1065)(466, 1066)(467, 1067)(468, 1068)(469, 1069)(470, 1070)(471, 1071)(472, 1072)(473, 1073)(474, 1074)(475, 1075)(476, 1076)(477, 1077)(478, 1078)(479, 1079)(480, 1080)(481, 1081)(482, 1082)(483, 1083)(484, 1084)(485, 1085)(486, 1086)(487, 1087)(488, 1088)(489, 1089)(490, 1090)(491, 1091)(492, 1092)(493, 1093)(494, 1094)(495, 1095)(496, 1096)(497, 1097)(498, 1098)(499, 1099)(500, 1100)(501, 1101)(502, 1102)(503, 1103)(504, 1104)(505, 1105)(506, 1106)(507, 1107)(508, 1108)(509, 1109)(510, 1110)(511, 1111)(512, 1112)(513, 1113)(514, 1114)(515, 1115)(516, 1116)(517, 1117)(518, 1118)(519, 1119)(520, 1120)(521, 1121)(522, 1122)(523, 1123)(524, 1124)(525, 1125)(526, 1126)(527, 1127)(528, 1128)(529, 1129)(530, 1130)(531, 1131)(532, 1132)(533, 1133)(534, 1134)(535, 1135)(536, 1136)(537, 1137)(538, 1138)(539, 1139)(540, 1140)(541, 1141)(542, 1142)(543, 1143)(544, 1144)(545, 1145)(546, 1146)(547, 1147)(548, 1148)(549, 1149)(550, 1150)(551, 1151)(552, 1152)(553, 1153)(554, 1154)(555, 1155)(556, 1156)(557, 1157)(558, 1158)(559, 1159)(560, 1160)(561, 1161)(562, 1162)(563, 1163)(564, 1164)(565, 1165)(566, 1166)(567, 1167)(568, 1168)(569, 1169)(570, 1170)(571, 1171)(572, 1172)(573, 1173)(574, 1174)(575, 1175)(576, 1176)(577, 1177)(578, 1178)(579, 1179)(580, 1180)(581, 1181)(582, 1182)(583, 1183)(584, 1184)(585, 1185)(586, 1186)(587, 1187)(588, 1188)(589, 1189)(590, 1190)(591, 1191)(592, 1192)(593, 1193)(594, 1194)(595, 1195)(596, 1196)(597, 1197)(598, 1198)(599, 1199)(600, 1200) local type(s) :: { ( 4^4 ), ( 4^5 ) } Outer automorphisms :: reflexible Dual of E16.1292 Transitivity :: ET+ Graph:: simple bipartite v = 270 e = 600 f = 300 degree seq :: [ 4^150, 5^120 ] E16.1289 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 5}) Quotient :: edge Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^5, (T1 * T2)^4, (T2 * T1^-2)^6, T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-1 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 11)(7, 15)(8, 16)(10, 20)(12, 24)(13, 25)(14, 27)(17, 31)(18, 33)(19, 28)(21, 38)(22, 39)(23, 41)(26, 44)(29, 48)(30, 51)(32, 54)(34, 57)(35, 59)(36, 55)(37, 61)(40, 64)(42, 67)(43, 69)(45, 73)(46, 74)(47, 76)(49, 78)(50, 79)(52, 83)(53, 80)(56, 88)(58, 92)(60, 94)(62, 97)(63, 99)(65, 103)(66, 104)(68, 107)(70, 111)(71, 108)(72, 113)(75, 116)(77, 120)(81, 126)(82, 128)(84, 130)(85, 132)(86, 133)(87, 135)(89, 137)(90, 139)(91, 117)(93, 143)(95, 147)(96, 148)(98, 151)(100, 155)(101, 152)(102, 157)(105, 160)(106, 162)(109, 166)(110, 168)(112, 170)(114, 173)(115, 175)(118, 179)(119, 181)(121, 185)(122, 182)(123, 188)(124, 189)(125, 191)(127, 193)(129, 196)(131, 199)(134, 202)(136, 206)(138, 209)(140, 211)(141, 213)(142, 214)(144, 218)(145, 203)(146, 220)(149, 223)(150, 225)(153, 229)(154, 231)(156, 233)(158, 236)(159, 238)(161, 241)(163, 244)(164, 245)(165, 247)(167, 249)(169, 252)(171, 256)(172, 257)(174, 260)(176, 264)(177, 261)(178, 266)(180, 268)(183, 272)(184, 274)(186, 276)(187, 277)(190, 280)(192, 284)(194, 288)(195, 289)(197, 293)(198, 281)(200, 296)(201, 298)(204, 302)(205, 304)(207, 308)(208, 305)(210, 312)(212, 314)(215, 317)(216, 319)(217, 320)(219, 255)(221, 322)(222, 324)(224, 327)(226, 330)(227, 331)(228, 333)(230, 335)(232, 338)(234, 340)(235, 341)(237, 343)(239, 347)(240, 344)(242, 351)(243, 353)(246, 356)(248, 360)(250, 364)(251, 365)(253, 369)(254, 357)(258, 371)(259, 373)(262, 377)(263, 379)(265, 381)(267, 384)(269, 387)(270, 388)(271, 390)(273, 392)(275, 395)(278, 399)(279, 400)(282, 403)(283, 405)(285, 409)(286, 406)(287, 411)(290, 414)(291, 415)(292, 416)(294, 418)(295, 398)(297, 420)(299, 424)(300, 421)(301, 370)(303, 427)(306, 430)(307, 432)(309, 417)(310, 435)(311, 436)(313, 438)(315, 439)(316, 441)(318, 378)(321, 410)(323, 447)(325, 449)(326, 389)(328, 452)(329, 454)(332, 457)(334, 460)(336, 462)(337, 463)(339, 401)(342, 465)(345, 468)(346, 469)(348, 380)(349, 471)(350, 472)(352, 475)(354, 477)(355, 478)(358, 480)(359, 482)(361, 485)(362, 483)(363, 486)(366, 488)(367, 489)(368, 394)(372, 491)(374, 494)(375, 495)(376, 497)(382, 500)(383, 501)(385, 504)(386, 502)(391, 510)(393, 513)(396, 507)(397, 516)(402, 518)(404, 521)(407, 524)(408, 445)(412, 526)(413, 434)(419, 529)(422, 532)(423, 499)(425, 512)(426, 534)(428, 535)(429, 536)(431, 509)(433, 539)(437, 528)(440, 541)(442, 514)(443, 473)(444, 498)(446, 490)(448, 549)(450, 470)(451, 551)(453, 553)(455, 555)(456, 556)(458, 558)(459, 559)(461, 561)(464, 562)(466, 565)(467, 566)(474, 569)(476, 571)(479, 573)(481, 576)(484, 578)(487, 580)(492, 581)(493, 574)(496, 563)(503, 586)(505, 547)(506, 554)(508, 587)(511, 589)(515, 567)(517, 590)(519, 591)(520, 564)(522, 548)(523, 592)(525, 557)(527, 579)(530, 570)(531, 577)(533, 582)(537, 588)(538, 568)(540, 545)(542, 584)(543, 550)(544, 594)(546, 593)(552, 596)(560, 597)(572, 598)(575, 595)(583, 599)(585, 600)(601, 602, 605, 610, 604)(603, 607, 614, 617, 608)(606, 612, 623, 626, 613)(609, 618, 632, 634, 619)(611, 621, 637, 640, 622)(615, 628, 647, 649, 629)(616, 630, 650, 642, 624)(620, 635, 658, 660, 636)(625, 643, 668, 662, 638)(627, 645, 672, 675, 646)(631, 652, 682, 684, 653)(633, 655, 687, 689, 656)(639, 663, 698, 693, 659)(641, 665, 702, 705, 666)(644, 670, 710, 712, 671)(648, 677, 719, 714, 673)(651, 680, 725, 727, 681)(654, 685, 731, 734, 686)(657, 690, 738, 740, 691)(661, 695, 746, 749, 696)(664, 700, 754, 756, 701)(667, 706, 761, 758, 703)(669, 708, 765, 767, 709)(674, 715, 774, 729, 683)(676, 717, 778, 780, 718)(678, 721, 784, 786, 722)(679, 723, 787, 790, 724)(688, 736, 805, 800, 732)(692, 741, 812, 815, 742)(694, 744, 817, 819, 745)(697, 750, 824, 821, 747)(699, 752, 828, 830, 753)(704, 759, 837, 769, 711)(707, 763, 843, 846, 764)(713, 771, 855, 858, 772)(716, 776, 863, 865, 777)(720, 782, 871, 873, 783)(726, 792, 883, 878, 788)(728, 794, 887, 890, 795)(730, 797, 892, 820, 798)(733, 801, 897, 810, 739)(735, 803, 901, 903, 804)(737, 807, 907, 909, 808)(743, 816, 918, 915, 813)(748, 822, 923, 832, 755)(751, 826, 929, 932, 827)(757, 834, 811, 913, 835)(760, 839, 946, 948, 840)(762, 789, 879, 952, 842)(766, 848, 959, 954, 844)(768, 850, 963, 966, 851)(770, 853, 968, 914, 854)(773, 859, 972, 970, 856)(775, 861, 976, 978, 862)(779, 867, 983, 875, 785)(781, 869, 924, 989, 870)(791, 881, 922, 1004, 882)(793, 885, 1008, 1010, 886)(796, 891, 935, 1012, 888)(799, 894, 833, 939, 895)(802, 899, 1023, 1025, 900)(806, 905, 1029, 1031, 906)(809, 910, 1034, 1037, 911)(814, 916, 1040, 921, 818)(823, 925, 1048, 1050, 926)(825, 845, 955, 1053, 928)(829, 934, 1059, 1055, 930)(831, 936, 1061, 1064, 937)(836, 942, 982, 866, 940)(838, 944, 1028, 904, 945)(841, 949, 1041, 1073, 950)(847, 957, 1039, 1081, 958)(849, 961, 1035, 912, 962)(852, 967, 1027, 1087, 964)(857, 953, 1076, 980, 864)(860, 974, 1093, 1096, 975)(868, 985, 1062, 938, 986)(872, 991, 1109, 1105, 987)(874, 993, 1112, 1114, 994)(876, 969, 965, 1011, 996)(877, 997, 981, 1024, 998)(880, 1001, 1063, 1086, 1002)(884, 1006, 1123, 1082, 1007)(889, 1013, 1127, 1017, 893)(896, 1019, 1058, 933, 1018)(898, 1021, 1051, 927, 1022)(902, 1026, 1133, 1033, 908)(917, 1042, 1142, 1143, 1043)(919, 931, 1056, 1144, 1044)(920, 1045, 1145, 1146, 1046)(941, 1054, 1154, 1070, 947)(943, 1066, 1164, 1167, 1067)(951, 1074, 992, 1111, 1071)(956, 971, 1090, 1161, 1079)(960, 1083, 1177, 1159, 1084)(973, 988, 1106, 1155, 1092)(977, 1098, 1183, 1153, 1094)(979, 1069, 1149, 1184, 1099)(984, 1102, 1122, 1005, 1103)(990, 1107, 1126, 1158, 1108)(995, 1115, 1121, 1151, 1113)(999, 1117, 1176, 1097, 1116)(1000, 1118, 1180, 1091, 1119)(1003, 1120, 1156, 1125, 1009)(1014, 1088, 1162, 1193, 1128)(1015, 1095, 1182, 1160, 1060)(1016, 1032, 1138, 1150, 1049)(1020, 1130, 1191, 1181, 1131)(1030, 1137, 1194, 1165, 1068)(1036, 1140, 1157, 1057, 1038)(1047, 1147, 1195, 1190, 1148)(1052, 1152, 1075, 1170, 1132)(1065, 1072, 1168, 1139, 1163)(1077, 1172, 1129, 1135, 1171)(1078, 1173, 1104, 1100, 1174)(1080, 1175, 1136, 1179, 1085)(1089, 1166, 1101, 1185, 1134)(1110, 1169, 1196, 1199, 1188)(1124, 1178, 1197, 1200, 1186)(1141, 1189, 1187, 1198, 1192) L = (1, 601)(2, 602)(3, 603)(4, 604)(5, 605)(6, 606)(7, 607)(8, 608)(9, 609)(10, 610)(11, 611)(12, 612)(13, 613)(14, 614)(15, 615)(16, 616)(17, 617)(18, 618)(19, 619)(20, 620)(21, 621)(22, 622)(23, 623)(24, 624)(25, 625)(26, 626)(27, 627)(28, 628)(29, 629)(30, 630)(31, 631)(32, 632)(33, 633)(34, 634)(35, 635)(36, 636)(37, 637)(38, 638)(39, 639)(40, 640)(41, 641)(42, 642)(43, 643)(44, 644)(45, 645)(46, 646)(47, 647)(48, 648)(49, 649)(50, 650)(51, 651)(52, 652)(53, 653)(54, 654)(55, 655)(56, 656)(57, 657)(58, 658)(59, 659)(60, 660)(61, 661)(62, 662)(63, 663)(64, 664)(65, 665)(66, 666)(67, 667)(68, 668)(69, 669)(70, 670)(71, 671)(72, 672)(73, 673)(74, 674)(75, 675)(76, 676)(77, 677)(78, 678)(79, 679)(80, 680)(81, 681)(82, 682)(83, 683)(84, 684)(85, 685)(86, 686)(87, 687)(88, 688)(89, 689)(90, 690)(91, 691)(92, 692)(93, 693)(94, 694)(95, 695)(96, 696)(97, 697)(98, 698)(99, 699)(100, 700)(101, 701)(102, 702)(103, 703)(104, 704)(105, 705)(106, 706)(107, 707)(108, 708)(109, 709)(110, 710)(111, 711)(112, 712)(113, 713)(114, 714)(115, 715)(116, 716)(117, 717)(118, 718)(119, 719)(120, 720)(121, 721)(122, 722)(123, 723)(124, 724)(125, 725)(126, 726)(127, 727)(128, 728)(129, 729)(130, 730)(131, 731)(132, 732)(133, 733)(134, 734)(135, 735)(136, 736)(137, 737)(138, 738)(139, 739)(140, 740)(141, 741)(142, 742)(143, 743)(144, 744)(145, 745)(146, 746)(147, 747)(148, 748)(149, 749)(150, 750)(151, 751)(152, 752)(153, 753)(154, 754)(155, 755)(156, 756)(157, 757)(158, 758)(159, 759)(160, 760)(161, 761)(162, 762)(163, 763)(164, 764)(165, 765)(166, 766)(167, 767)(168, 768)(169, 769)(170, 770)(171, 771)(172, 772)(173, 773)(174, 774)(175, 775)(176, 776)(177, 777)(178, 778)(179, 779)(180, 780)(181, 781)(182, 782)(183, 783)(184, 784)(185, 785)(186, 786)(187, 787)(188, 788)(189, 789)(190, 790)(191, 791)(192, 792)(193, 793)(194, 794)(195, 795)(196, 796)(197, 797)(198, 798)(199, 799)(200, 800)(201, 801)(202, 802)(203, 803)(204, 804)(205, 805)(206, 806)(207, 807)(208, 808)(209, 809)(210, 810)(211, 811)(212, 812)(213, 813)(214, 814)(215, 815)(216, 816)(217, 817)(218, 818)(219, 819)(220, 820)(221, 821)(222, 822)(223, 823)(224, 824)(225, 825)(226, 826)(227, 827)(228, 828)(229, 829)(230, 830)(231, 831)(232, 832)(233, 833)(234, 834)(235, 835)(236, 836)(237, 837)(238, 838)(239, 839)(240, 840)(241, 841)(242, 842)(243, 843)(244, 844)(245, 845)(246, 846)(247, 847)(248, 848)(249, 849)(250, 850)(251, 851)(252, 852)(253, 853)(254, 854)(255, 855)(256, 856)(257, 857)(258, 858)(259, 859)(260, 860)(261, 861)(262, 862)(263, 863)(264, 864)(265, 865)(266, 866)(267, 867)(268, 868)(269, 869)(270, 870)(271, 871)(272, 872)(273, 873)(274, 874)(275, 875)(276, 876)(277, 877)(278, 878)(279, 879)(280, 880)(281, 881)(282, 882)(283, 883)(284, 884)(285, 885)(286, 886)(287, 887)(288, 888)(289, 889)(290, 890)(291, 891)(292, 892)(293, 893)(294, 894)(295, 895)(296, 896)(297, 897)(298, 898)(299, 899)(300, 900)(301, 901)(302, 902)(303, 903)(304, 904)(305, 905)(306, 906)(307, 907)(308, 908)(309, 909)(310, 910)(311, 911)(312, 912)(313, 913)(314, 914)(315, 915)(316, 916)(317, 917)(318, 918)(319, 919)(320, 920)(321, 921)(322, 922)(323, 923)(324, 924)(325, 925)(326, 926)(327, 927)(328, 928)(329, 929)(330, 930)(331, 931)(332, 932)(333, 933)(334, 934)(335, 935)(336, 936)(337, 937)(338, 938)(339, 939)(340, 940)(341, 941)(342, 942)(343, 943)(344, 944)(345, 945)(346, 946)(347, 947)(348, 948)(349, 949)(350, 950)(351, 951)(352, 952)(353, 953)(354, 954)(355, 955)(356, 956)(357, 957)(358, 958)(359, 959)(360, 960)(361, 961)(362, 962)(363, 963)(364, 964)(365, 965)(366, 966)(367, 967)(368, 968)(369, 969)(370, 970)(371, 971)(372, 972)(373, 973)(374, 974)(375, 975)(376, 976)(377, 977)(378, 978)(379, 979)(380, 980)(381, 981)(382, 982)(383, 983)(384, 984)(385, 985)(386, 986)(387, 987)(388, 988)(389, 989)(390, 990)(391, 991)(392, 992)(393, 993)(394, 994)(395, 995)(396, 996)(397, 997)(398, 998)(399, 999)(400, 1000)(401, 1001)(402, 1002)(403, 1003)(404, 1004)(405, 1005)(406, 1006)(407, 1007)(408, 1008)(409, 1009)(410, 1010)(411, 1011)(412, 1012)(413, 1013)(414, 1014)(415, 1015)(416, 1016)(417, 1017)(418, 1018)(419, 1019)(420, 1020)(421, 1021)(422, 1022)(423, 1023)(424, 1024)(425, 1025)(426, 1026)(427, 1027)(428, 1028)(429, 1029)(430, 1030)(431, 1031)(432, 1032)(433, 1033)(434, 1034)(435, 1035)(436, 1036)(437, 1037)(438, 1038)(439, 1039)(440, 1040)(441, 1041)(442, 1042)(443, 1043)(444, 1044)(445, 1045)(446, 1046)(447, 1047)(448, 1048)(449, 1049)(450, 1050)(451, 1051)(452, 1052)(453, 1053)(454, 1054)(455, 1055)(456, 1056)(457, 1057)(458, 1058)(459, 1059)(460, 1060)(461, 1061)(462, 1062)(463, 1063)(464, 1064)(465, 1065)(466, 1066)(467, 1067)(468, 1068)(469, 1069)(470, 1070)(471, 1071)(472, 1072)(473, 1073)(474, 1074)(475, 1075)(476, 1076)(477, 1077)(478, 1078)(479, 1079)(480, 1080)(481, 1081)(482, 1082)(483, 1083)(484, 1084)(485, 1085)(486, 1086)(487, 1087)(488, 1088)(489, 1089)(490, 1090)(491, 1091)(492, 1092)(493, 1093)(494, 1094)(495, 1095)(496, 1096)(497, 1097)(498, 1098)(499, 1099)(500, 1100)(501, 1101)(502, 1102)(503, 1103)(504, 1104)(505, 1105)(506, 1106)(507, 1107)(508, 1108)(509, 1109)(510, 1110)(511, 1111)(512, 1112)(513, 1113)(514, 1114)(515, 1115)(516, 1116)(517, 1117)(518, 1118)(519, 1119)(520, 1120)(521, 1121)(522, 1122)(523, 1123)(524, 1124)(525, 1125)(526, 1126)(527, 1127)(528, 1128)(529, 1129)(530, 1130)(531, 1131)(532, 1132)(533, 1133)(534, 1134)(535, 1135)(536, 1136)(537, 1137)(538, 1138)(539, 1139)(540, 1140)(541, 1141)(542, 1142)(543, 1143)(544, 1144)(545, 1145)(546, 1146)(547, 1147)(548, 1148)(549, 1149)(550, 1150)(551, 1151)(552, 1152)(553, 1153)(554, 1154)(555, 1155)(556, 1156)(557, 1157)(558, 1158)(559, 1159)(560, 1160)(561, 1161)(562, 1162)(563, 1163)(564, 1164)(565, 1165)(566, 1166)(567, 1167)(568, 1168)(569, 1169)(570, 1170)(571, 1171)(572, 1172)(573, 1173)(574, 1174)(575, 1175)(576, 1176)(577, 1177)(578, 1178)(579, 1179)(580, 1180)(581, 1181)(582, 1182)(583, 1183)(584, 1184)(585, 1185)(586, 1186)(587, 1187)(588, 1188)(589, 1189)(590, 1190)(591, 1191)(592, 1192)(593, 1193)(594, 1194)(595, 1195)(596, 1196)(597, 1197)(598, 1198)(599, 1199)(600, 1200) local type(s) :: { ( 8, 8 ), ( 8^5 ) } Outer automorphisms :: reflexible Dual of E16.1290 Transitivity :: ET+ Graph:: simple bipartite v = 420 e = 600 f = 150 degree seq :: [ 2^300, 5^120 ] E16.1290 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 5}) Quotient :: loop Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T2)^2, (F * T1)^2, (T2 * T1)^5, T2^-1 * T1 * T2^-2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-1, T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1, T2 * T1 * T2^-2 * T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1 * T2^2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1, T1 * T2 * T1 * T2^-2 * T1 * T2 * T1 * T2^-2 * T1 * T2^2 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2^2 ] Map:: R = (1, 601, 3, 603, 8, 608, 4, 604)(2, 602, 5, 605, 11, 611, 6, 606)(7, 607, 13, 613, 24, 624, 14, 614)(9, 609, 16, 616, 29, 629, 17, 617)(10, 610, 18, 618, 32, 632, 19, 619)(12, 612, 21, 621, 37, 637, 22, 622)(15, 615, 26, 626, 44, 644, 27, 627)(20, 620, 34, 634, 55, 655, 35, 635)(23, 623, 38, 638, 60, 660, 39, 639)(25, 625, 41, 641, 65, 665, 42, 642)(28, 628, 46, 646, 71, 671, 47, 647)(30, 630, 49, 649, 50, 650, 31, 631)(33, 633, 52, 652, 80, 680, 53, 653)(36, 636, 57, 657, 86, 686, 58, 658)(40, 640, 62, 662, 94, 694, 63, 663)(43, 643, 66, 666, 99, 699, 67, 667)(45, 645, 69, 669, 104, 704, 70, 670)(48, 648, 73, 673, 109, 709, 74, 674)(51, 651, 77, 677, 116, 716, 78, 678)(54, 654, 81, 681, 121, 721, 82, 682)(56, 656, 84, 684, 126, 726, 85, 685)(59, 659, 88, 688, 131, 731, 89, 689)(61, 661, 91, 691, 136, 736, 92, 692)(64, 664, 96, 696, 142, 742, 97, 697)(68, 668, 101, 701, 150, 750, 102, 702)(72, 672, 106, 706, 158, 758, 107, 707)(75, 675, 111, 711, 164, 764, 112, 712)(76, 676, 113, 713, 167, 767, 114, 714)(79, 679, 118, 718, 173, 773, 119, 719)(83, 683, 123, 723, 181, 781, 124, 724)(87, 687, 128, 728, 189, 789, 129, 729)(90, 690, 133, 733, 195, 795, 134, 734)(93, 693, 137, 737, 200, 800, 138, 738)(95, 695, 140, 740, 205, 805, 141, 741)(98, 698, 144, 744, 210, 810, 145, 745)(100, 700, 147, 747, 215, 815, 148, 748)(103, 703, 152, 752, 220, 820, 153, 753)(105, 705, 155, 755, 225, 825, 156, 756)(108, 708, 159, 759, 230, 830, 160, 760)(110, 710, 162, 762, 233, 833, 163, 763)(115, 715, 168, 768, 240, 840, 169, 769)(117, 717, 171, 771, 245, 845, 172, 772)(120, 720, 175, 775, 250, 850, 176, 776)(122, 722, 178, 778, 255, 855, 179, 779)(125, 725, 183, 783, 260, 860, 184, 784)(127, 727, 186, 786, 265, 865, 187, 787)(130, 730, 190, 790, 270, 870, 191, 791)(132, 732, 193, 793, 273, 873, 194, 794)(135, 735, 197, 797, 277, 877, 198, 798)(139, 739, 202, 802, 161, 761, 203, 803)(143, 743, 207, 807, 292, 892, 208, 808)(146, 746, 212, 812, 298, 898, 213, 813)(149, 749, 216, 816, 303, 903, 217, 817)(151, 751, 218, 818, 306, 906, 219, 819)(154, 754, 222, 822, 311, 911, 223, 823)(157, 757, 227, 827, 317, 917, 228, 828)(165, 765, 235, 835, 330, 930, 236, 836)(166, 766, 237, 837, 331, 931, 238, 838)(170, 770, 242, 842, 192, 792, 243, 843)(174, 774, 247, 847, 346, 946, 248, 848)(177, 777, 252, 852, 352, 952, 253, 853)(180, 780, 256, 856, 357, 957, 257, 857)(182, 782, 258, 858, 360, 960, 259, 859)(185, 785, 262, 862, 365, 965, 263, 863)(188, 788, 267, 867, 371, 971, 268, 868)(196, 796, 275, 875, 384, 984, 276, 876)(199, 799, 279, 879, 368, 968, 280, 880)(201, 801, 282, 882, 392, 992, 283, 883)(204, 804, 286, 886, 397, 997, 287, 887)(206, 806, 289, 889, 401, 1001, 290, 890)(209, 809, 293, 893, 405, 1005, 294, 894)(211, 811, 296, 896, 407, 1007, 297, 897)(214, 814, 300, 900, 411, 1011, 301, 901)(221, 821, 308, 908, 420, 1020, 309, 909)(224, 824, 312, 912, 424, 1024, 313, 913)(226, 826, 315, 915, 426, 1026, 316, 916)(229, 829, 319, 919, 428, 1028, 320, 920)(231, 831, 322, 922, 432, 1032, 323, 923)(232, 832, 324, 924, 433, 1033, 325, 925)(234, 834, 327, 927, 349, 949, 328, 928)(239, 839, 333, 933, 314, 914, 334, 934)(241, 841, 336, 936, 446, 1046, 337, 937)(244, 844, 340, 940, 451, 1051, 341, 941)(246, 846, 343, 943, 455, 1055, 344, 944)(249, 849, 347, 947, 459, 1059, 348, 948)(251, 851, 350, 950, 461, 1061, 351, 951)(254, 854, 354, 954, 465, 1065, 355, 955)(261, 861, 362, 962, 474, 1074, 363, 963)(264, 864, 366, 966, 478, 1078, 367, 967)(266, 866, 369, 969, 480, 1080, 370, 970)(269, 869, 373, 973, 482, 1082, 374, 974)(271, 871, 376, 976, 486, 1086, 377, 977)(272, 872, 378, 978, 487, 1087, 379, 979)(274, 874, 381, 981, 295, 895, 382, 982)(278, 878, 386, 986, 329, 929, 387, 987)(281, 881, 390, 990, 500, 1100, 391, 991)(284, 884, 393, 993, 501, 1101, 394, 994)(285, 885, 395, 995, 502, 1102, 396, 996)(288, 888, 399, 999, 506, 1106, 400, 1000)(291, 891, 403, 1003, 318, 918, 404, 1004)(299, 899, 409, 1009, 516, 1116, 410, 1010)(302, 902, 412, 1012, 507, 1107, 413, 1013)(304, 904, 415, 1015, 470, 1070, 359, 959)(305, 905, 358, 958, 469, 1069, 416, 1016)(307, 907, 418, 1018, 523, 1123, 419, 1019)(310, 910, 421, 1021, 524, 1124, 422, 1022)(321, 921, 429, 1029, 525, 1125, 430, 1030)(326, 926, 434, 1034, 528, 1128, 435, 1035)(332, 932, 440, 1040, 383, 983, 441, 1041)(335, 935, 444, 1044, 538, 1138, 445, 1045)(338, 938, 447, 1047, 539, 1139, 448, 1048)(339, 939, 449, 1049, 540, 1140, 450, 1050)(342, 942, 453, 1053, 544, 1144, 454, 1054)(345, 945, 457, 1057, 372, 972, 458, 1058)(353, 953, 463, 1063, 554, 1154, 464, 1064)(356, 956, 466, 1066, 545, 1145, 467, 1067)(361, 961, 472, 1072, 561, 1161, 473, 1073)(364, 964, 475, 1075, 562, 1162, 476, 1076)(375, 975, 483, 1083, 563, 1163, 484, 1084)(380, 980, 488, 1088, 566, 1166, 489, 1089)(385, 985, 493, 1093, 543, 1143, 494, 1094)(388, 988, 496, 1096, 437, 1037, 497, 1097)(389, 989, 498, 1098, 571, 1171, 499, 1099)(398, 998, 503, 1103, 573, 1173, 504, 1104)(402, 1002, 508, 1108, 427, 1027, 509, 1109)(406, 1006, 511, 1111, 425, 1025, 512, 1112)(408, 1008, 514, 1114, 423, 1023, 515, 1115)(414, 1014, 518, 1118, 577, 1177, 519, 1119)(417, 1017, 521, 1121, 578, 1178, 522, 1122)(431, 1031, 527, 1127, 576, 1176, 517, 1117)(436, 1036, 529, 1129, 574, 1174, 513, 1113)(438, 1038, 530, 1130, 564, 1164, 520, 1120)(439, 1039, 531, 1131, 505, 1105, 532, 1132)(442, 1042, 534, 1134, 491, 1091, 535, 1135)(443, 1043, 536, 1136, 581, 1181, 537, 1137)(452, 1052, 541, 1141, 583, 1183, 542, 1142)(456, 1056, 546, 1146, 481, 1081, 547, 1147)(460, 1060, 549, 1149, 479, 1079, 550, 1150)(462, 1062, 552, 1152, 477, 1077, 553, 1153)(468, 1068, 556, 1156, 587, 1187, 557, 1157)(471, 1071, 559, 1159, 588, 1188, 560, 1160)(485, 1085, 565, 1165, 586, 1186, 555, 1155)(490, 1090, 567, 1167, 584, 1184, 551, 1151)(492, 1092, 568, 1168, 526, 1126, 558, 1158)(495, 1095, 569, 1169, 510, 1110, 570, 1170)(533, 1133, 579, 1179, 548, 1148, 580, 1180)(572, 1172, 590, 1190, 598, 1198, 591, 1191)(575, 1175, 592, 1192, 597, 1197, 589, 1189)(582, 1182, 594, 1194, 600, 1200, 595, 1195)(585, 1185, 596, 1196, 599, 1199, 593, 1193) L = (1, 602)(2, 601)(3, 607)(4, 609)(5, 610)(6, 612)(7, 603)(8, 615)(9, 604)(10, 605)(11, 620)(12, 606)(13, 623)(14, 625)(15, 608)(16, 628)(17, 630)(18, 631)(19, 633)(20, 611)(21, 636)(22, 638)(23, 613)(24, 640)(25, 614)(26, 643)(27, 645)(28, 616)(29, 648)(30, 617)(31, 618)(32, 651)(33, 619)(34, 654)(35, 656)(36, 621)(37, 659)(38, 622)(39, 661)(40, 624)(41, 664)(42, 666)(43, 626)(44, 668)(45, 627)(46, 670)(47, 672)(48, 629)(49, 675)(50, 676)(51, 632)(52, 679)(53, 681)(54, 634)(55, 683)(56, 635)(57, 685)(58, 687)(59, 637)(60, 690)(61, 639)(62, 693)(63, 695)(64, 641)(65, 698)(66, 642)(67, 700)(68, 644)(69, 703)(70, 646)(71, 705)(72, 647)(73, 708)(74, 710)(75, 649)(76, 650)(77, 715)(78, 717)(79, 652)(80, 720)(81, 653)(82, 722)(83, 655)(84, 725)(85, 657)(86, 727)(87, 658)(88, 730)(89, 732)(90, 660)(91, 735)(92, 737)(93, 662)(94, 739)(95, 663)(96, 741)(97, 743)(98, 665)(99, 746)(100, 667)(101, 749)(102, 751)(103, 669)(104, 754)(105, 671)(106, 757)(107, 759)(108, 673)(109, 761)(110, 674)(111, 763)(112, 765)(113, 766)(114, 768)(115, 677)(116, 770)(117, 678)(118, 772)(119, 774)(120, 680)(121, 777)(122, 682)(123, 780)(124, 782)(125, 684)(126, 785)(127, 686)(128, 788)(129, 790)(130, 688)(131, 792)(132, 689)(133, 794)(134, 796)(135, 691)(136, 799)(137, 692)(138, 801)(139, 694)(140, 804)(141, 696)(142, 806)(143, 697)(144, 809)(145, 811)(146, 699)(147, 814)(148, 816)(149, 701)(150, 781)(151, 702)(152, 819)(153, 821)(154, 704)(155, 824)(156, 826)(157, 706)(158, 829)(159, 707)(160, 831)(161, 709)(162, 832)(163, 711)(164, 834)(165, 712)(166, 713)(167, 839)(168, 714)(169, 841)(170, 716)(171, 844)(172, 718)(173, 846)(174, 719)(175, 849)(176, 851)(177, 721)(178, 854)(179, 856)(180, 723)(181, 750)(182, 724)(183, 859)(184, 861)(185, 726)(186, 864)(187, 866)(188, 728)(189, 869)(190, 729)(191, 871)(192, 731)(193, 872)(194, 733)(195, 874)(196, 734)(197, 876)(198, 878)(199, 736)(200, 881)(201, 738)(202, 884)(203, 885)(204, 740)(205, 888)(206, 742)(207, 891)(208, 893)(209, 744)(210, 895)(211, 745)(212, 897)(213, 899)(214, 747)(215, 902)(216, 748)(217, 904)(218, 905)(219, 752)(220, 907)(221, 753)(222, 910)(223, 912)(224, 755)(225, 914)(226, 756)(227, 916)(228, 918)(229, 758)(230, 921)(231, 760)(232, 762)(233, 926)(234, 764)(235, 929)(236, 837)(237, 836)(238, 932)(239, 767)(240, 935)(241, 769)(242, 938)(243, 939)(244, 771)(245, 942)(246, 773)(247, 945)(248, 947)(249, 775)(250, 949)(251, 776)(252, 951)(253, 953)(254, 778)(255, 956)(256, 779)(257, 958)(258, 959)(259, 783)(260, 961)(261, 784)(262, 964)(263, 966)(264, 786)(265, 968)(266, 787)(267, 970)(268, 972)(269, 789)(270, 975)(271, 791)(272, 793)(273, 980)(274, 795)(275, 983)(276, 797)(277, 985)(278, 798)(279, 988)(280, 989)(281, 800)(282, 943)(283, 993)(284, 802)(285, 803)(286, 996)(287, 998)(288, 805)(289, 936)(290, 1002)(291, 807)(292, 962)(293, 808)(294, 1006)(295, 810)(296, 950)(297, 812)(298, 1008)(299, 813)(300, 1010)(301, 971)(302, 815)(303, 1014)(304, 817)(305, 818)(306, 1017)(307, 820)(308, 946)(309, 1021)(310, 822)(311, 1023)(312, 823)(313, 967)(314, 825)(315, 1025)(316, 827)(317, 955)(318, 828)(319, 1027)(320, 979)(321, 830)(322, 1031)(323, 995)(324, 994)(325, 974)(326, 833)(327, 1036)(328, 1037)(329, 835)(330, 1038)(331, 1039)(332, 838)(333, 1042)(334, 1043)(335, 840)(336, 889)(337, 1047)(338, 842)(339, 843)(340, 1050)(341, 1052)(342, 845)(343, 882)(344, 1056)(345, 847)(346, 908)(347, 848)(348, 1060)(349, 850)(350, 896)(351, 852)(352, 1062)(353, 853)(354, 1064)(355, 917)(356, 855)(357, 1068)(358, 857)(359, 858)(360, 1071)(361, 860)(362, 892)(363, 1075)(364, 862)(365, 1077)(366, 863)(367, 913)(368, 865)(369, 1079)(370, 867)(371, 901)(372, 868)(373, 1081)(374, 925)(375, 870)(376, 1085)(377, 1049)(378, 1048)(379, 920)(380, 873)(381, 1090)(382, 1091)(383, 875)(384, 1092)(385, 877)(386, 1095)(387, 1096)(388, 879)(389, 880)(390, 1099)(391, 1067)(392, 1054)(393, 883)(394, 924)(395, 923)(396, 886)(397, 1076)(398, 887)(399, 1105)(400, 1046)(401, 1107)(402, 890)(403, 1109)(404, 1110)(405, 1073)(406, 894)(407, 1113)(408, 898)(409, 1086)(410, 900)(411, 1117)(412, 1080)(413, 1045)(414, 903)(415, 1093)(416, 1120)(417, 906)(418, 1088)(419, 1059)(420, 1103)(421, 909)(422, 1051)(423, 911)(424, 1098)(425, 915)(426, 1066)(427, 919)(428, 1123)(429, 1087)(430, 1126)(431, 922)(432, 1063)(433, 1083)(434, 1072)(435, 1129)(436, 927)(437, 928)(438, 930)(439, 931)(440, 1133)(441, 1134)(442, 933)(443, 934)(444, 1137)(445, 1013)(446, 1000)(447, 937)(448, 978)(449, 977)(450, 940)(451, 1022)(452, 941)(453, 1143)(454, 992)(455, 1145)(456, 944)(457, 1147)(458, 1148)(459, 1019)(460, 948)(461, 1151)(462, 952)(463, 1032)(464, 954)(465, 1155)(466, 1026)(467, 991)(468, 957)(469, 1131)(470, 1158)(471, 960)(472, 1034)(473, 1005)(474, 1141)(475, 963)(476, 997)(477, 965)(478, 1136)(479, 969)(480, 1012)(481, 973)(482, 1161)(483, 1033)(484, 1164)(485, 976)(486, 1009)(487, 1029)(488, 1018)(489, 1167)(490, 981)(491, 982)(492, 984)(493, 1015)(494, 1142)(495, 986)(496, 987)(497, 1150)(498, 1024)(499, 990)(500, 1156)(501, 1172)(502, 1153)(503, 1020)(504, 1132)(505, 999)(506, 1157)(507, 1001)(508, 1149)(509, 1003)(510, 1004)(511, 1146)(512, 1135)(513, 1007)(514, 1175)(515, 1140)(516, 1154)(517, 1011)(518, 1138)(519, 1144)(520, 1016)(521, 1163)(522, 1166)(523, 1028)(524, 1162)(525, 1159)(526, 1030)(527, 1168)(528, 1160)(529, 1035)(530, 1165)(531, 1069)(532, 1104)(533, 1040)(534, 1041)(535, 1112)(536, 1078)(537, 1044)(538, 1118)(539, 1182)(540, 1115)(541, 1074)(542, 1094)(543, 1053)(544, 1119)(545, 1055)(546, 1111)(547, 1057)(548, 1058)(549, 1108)(550, 1097)(551, 1061)(552, 1185)(553, 1102)(554, 1116)(555, 1065)(556, 1100)(557, 1106)(558, 1070)(559, 1125)(560, 1128)(561, 1082)(562, 1124)(563, 1121)(564, 1084)(565, 1130)(566, 1122)(567, 1089)(568, 1127)(569, 1183)(570, 1186)(571, 1189)(572, 1101)(573, 1179)(574, 1192)(575, 1114)(576, 1180)(577, 1190)(578, 1191)(579, 1173)(580, 1176)(581, 1193)(582, 1139)(583, 1169)(584, 1196)(585, 1152)(586, 1170)(587, 1194)(588, 1195)(589, 1171)(590, 1177)(591, 1178)(592, 1174)(593, 1181)(594, 1187)(595, 1188)(596, 1184)(597, 1200)(598, 1199)(599, 1198)(600, 1197) local type(s) :: { ( 2, 5, 2, 5, 2, 5, 2, 5 ) } Outer automorphisms :: reflexible Dual of E16.1289 Transitivity :: ET+ VT+ AT Graph:: v = 150 e = 600 f = 420 degree seq :: [ 8^150 ] E16.1291 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 5}) Quotient :: loop Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, T2^5, T2^-2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^6, T2 * T1^-1 * T2^-2 * T1 * T2^-1 * T1 * T2^2 * T1^-2 * T2^-2 * T1 * T2^-2 * T1^-2, T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1, T1^-1 * T2^-2 * T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1^-1, T2 * T1^-1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1 * T2^-2 * T1^-2 * T2^-2 * T1^-1 * T2 * T1^-1 ] Map:: R = (1, 601, 3, 603, 10, 610, 14, 614, 5, 605)(2, 602, 7, 607, 17, 617, 20, 620, 8, 608)(4, 604, 12, 612, 26, 626, 22, 622, 9, 609)(6, 606, 15, 615, 31, 631, 34, 634, 16, 616)(11, 611, 25, 625, 47, 647, 45, 645, 23, 623)(13, 613, 28, 628, 52, 652, 55, 655, 29, 629)(18, 618, 37, 637, 66, 666, 64, 664, 35, 635)(19, 619, 38, 638, 68, 668, 71, 671, 39, 639)(21, 621, 41, 641, 73, 673, 76, 676, 42, 642)(24, 624, 46, 646, 81, 681, 56, 656, 30, 630)(27, 627, 51, 651, 89, 689, 87, 687, 49, 649)(32, 632, 59, 659, 101, 701, 99, 699, 57, 657)(33, 633, 60, 660, 103, 703, 106, 706, 61, 661)(36, 636, 65, 665, 111, 711, 72, 672, 40, 640)(43, 643, 50, 650, 88, 688, 130, 730, 77, 677)(44, 644, 78, 678, 131, 731, 134, 734, 79, 679)(48, 648, 85, 685, 142, 742, 140, 740, 83, 683)(53, 653, 93, 693, 153, 753, 151, 751, 91, 691)(54, 654, 94, 694, 155, 755, 157, 757, 95, 695)(58, 658, 100, 700, 163, 763, 107, 707, 62, 662)(63, 663, 108, 708, 175, 775, 178, 778, 109, 709)(67, 667, 115, 715, 186, 786, 184, 784, 113, 713)(69, 669, 118, 718, 190, 790, 188, 788, 116, 716)(70, 670, 119, 719, 192, 792, 194, 794, 120, 720)(74, 674, 125, 725, 200, 800, 198, 798, 123, 723)(75, 675, 126, 726, 202, 802, 204, 804, 127, 727)(80, 680, 84, 684, 141, 741, 216, 816, 135, 735)(82, 682, 138, 738, 220, 820, 218, 818, 136, 736)(86, 686, 143, 743, 226, 826, 229, 829, 144, 744)(90, 690, 149, 749, 235, 835, 233, 833, 147, 747)(92, 692, 152, 752, 239, 839, 158, 758, 96, 696)(97, 697, 137, 737, 219, 819, 249, 849, 159, 759)(98, 698, 160, 760, 250, 850, 253, 853, 161, 761)(102, 702, 167, 767, 261, 861, 259, 859, 165, 765)(104, 704, 170, 770, 265, 865, 263, 863, 168, 768)(105, 705, 171, 771, 267, 867, 269, 869, 172, 772)(110, 710, 114, 714, 185, 785, 279, 879, 179, 779)(112, 712, 182, 782, 283, 883, 281, 881, 180, 780)(117, 717, 189, 789, 292, 892, 195, 795, 121, 721)(122, 722, 181, 781, 282, 882, 302, 902, 196, 796)(124, 724, 199, 799, 306, 906, 205, 805, 128, 728)(129, 729, 206, 806, 316, 916, 318, 918, 207, 807)(132, 732, 211, 811, 323, 923, 321, 921, 209, 809)(133, 733, 212, 812, 325, 925, 327, 927, 213, 813)(139, 739, 221, 821, 336, 936, 339, 939, 222, 822)(145, 745, 148, 748, 234, 834, 350, 950, 230, 830)(146, 746, 231, 831, 351, 951, 319, 919, 208, 808)(150, 750, 236, 836, 357, 957, 360, 960, 237, 837)(154, 754, 243, 843, 367, 967, 365, 965, 241, 841)(156, 756, 246, 846, 371, 971, 369, 969, 244, 844)(162, 762, 166, 766, 260, 860, 383, 983, 254, 854)(164, 764, 257, 857, 387, 987, 385, 985, 255, 855)(169, 769, 264, 864, 396, 996, 270, 870, 173, 773)(174, 774, 256, 856, 386, 986, 406, 1006, 271, 871)(176, 776, 274, 874, 410, 1010, 408, 1008, 272, 872)(177, 777, 275, 875, 412, 1012, 414, 1014, 276, 876)(183, 783, 284, 884, 423, 1023, 426, 1026, 285, 885)(187, 787, 289, 889, 430, 1030, 433, 1033, 290, 890)(191, 791, 296, 896, 440, 1040, 438, 1038, 294, 894)(193, 793, 299, 899, 444, 1044, 442, 1042, 297, 897)(197, 797, 303, 903, 449, 1049, 452, 1052, 304, 904)(201, 801, 310, 910, 457, 1057, 455, 1055, 308, 908)(203, 803, 313, 913, 461, 1061, 459, 1059, 311, 911)(210, 810, 322, 922, 468, 1068, 328, 928, 214, 814)(215, 815, 329, 929, 384, 984, 362, 962, 240, 840)(217, 817, 331, 931, 397, 997, 382, 982, 332, 932)(223, 823, 225, 825, 342, 942, 479, 1079, 340, 940)(224, 824, 341, 941, 480, 1080, 474, 1074, 330, 930)(227, 827, 345, 945, 485, 1085, 483, 1083, 343, 943)(228, 828, 346, 946, 487, 1087, 489, 1089, 347, 947)(232, 832, 352, 952, 469, 1069, 478, 1078, 353, 953)(238, 838, 242, 842, 366, 966, 441, 1041, 361, 961)(245, 845, 370, 970, 445, 1045, 373, 973, 247, 847)(248, 848, 363, 963, 496, 1096, 501, 1101, 374, 974)(251, 851, 378, 978, 506, 1106, 504, 1104, 376, 976)(252, 852, 379, 979, 508, 1108, 510, 1110, 380, 980)(258, 858, 388, 988, 512, 1112, 515, 1115, 389, 989)(262, 862, 393, 993, 519, 1119, 522, 1122, 394, 994)(266, 866, 400, 1000, 527, 1127, 525, 1125, 398, 998)(268, 868, 403, 1003, 531, 1131, 529, 1129, 401, 1001)(273, 873, 409, 1009, 337, 937, 415, 1015, 277, 877)(278, 878, 416, 1016, 317, 917, 435, 1035, 293, 893)(280, 880, 418, 1018, 307, 907, 349, 949, 419, 1019)(286, 886, 288, 888, 429, 1029, 338, 938, 427, 1027)(287, 887, 428, 1028, 543, 1143, 465, 1065, 417, 1017)(291, 891, 295, 895, 439, 1039, 528, 1128, 434, 1034)(298, 898, 443, 1043, 532, 1132, 446, 1046, 300, 900)(301, 901, 436, 1036, 491, 1091, 551, 1151, 447, 1047)(305, 905, 309, 909, 456, 1056, 368, 968, 453, 1053)(312, 912, 460, 1060, 372, 972, 463, 1063, 314, 914)(315, 915, 420, 1020, 422, 1022, 540, 1140, 464, 1064)(320, 920, 466, 1066, 558, 1158, 560, 1160, 467, 1067)(324, 924, 359, 959, 495, 1095, 561, 1161, 470, 1070)(326, 926, 472, 1072, 563, 1163, 562, 1162, 471, 1071)(333, 933, 335, 935, 475, 1075, 534, 1134, 405, 1005)(334, 934, 391, 991, 517, 1117, 502, 1102, 375, 975)(344, 944, 484, 1084, 513, 1113, 490, 1090, 348, 948)(354, 954, 356, 956, 492, 1092, 514, 1114, 473, 1073)(355, 955, 481, 1081, 552, 1152, 448, 1048, 421, 1021)(358, 958, 494, 1094, 570, 1170, 569, 1169, 493, 1093)(364, 964, 497, 1097, 571, 1171, 572, 1172, 498, 1098)(377, 977, 505, 1105, 424, 1024, 511, 1111, 381, 981)(390, 990, 392, 992, 518, 1118, 425, 1025, 516, 1116)(395, 995, 399, 999, 526, 1126, 458, 1058, 523, 1123)(402, 1002, 530, 1130, 462, 1062, 533, 1133, 404, 1004)(407, 1007, 535, 1135, 582, 1182, 583, 1183, 536, 1136)(411, 1011, 432, 1032, 546, 1146, 584, 1184, 537, 1137)(413, 1013, 539, 1139, 559, 1159, 585, 1185, 538, 1138)(431, 1031, 545, 1145, 588, 1188, 587, 1187, 544, 1144)(437, 1037, 547, 1147, 589, 1189, 557, 1157, 548, 1148)(450, 1050, 554, 1154, 592, 1192, 591, 1191, 553, 1153)(451, 1051, 555, 1155, 593, 1193, 567, 1167, 486, 1086)(454, 1054, 556, 1156, 590, 1190, 549, 1149, 550, 1150)(476, 1076, 564, 1164, 577, 1177, 509, 1109, 477, 1077)(482, 1082, 565, 1165, 595, 1195, 594, 1194, 566, 1166)(488, 1088, 542, 1142, 541, 1141, 586, 1186, 568, 1168)(499, 1099, 500, 1100, 524, 1124, 581, 1181, 573, 1173)(503, 1103, 574, 1174, 596, 1196, 597, 1197, 575, 1175)(507, 1107, 521, 1121, 580, 1180, 598, 1198, 576, 1176)(520, 1120, 579, 1179, 600, 1200, 599, 1199, 578, 1178) L = (1, 602)(2, 606)(3, 609)(4, 601)(5, 613)(6, 604)(7, 605)(8, 619)(9, 621)(10, 623)(11, 603)(12, 616)(13, 618)(14, 630)(15, 608)(16, 633)(17, 635)(18, 607)(19, 632)(20, 640)(21, 611)(22, 643)(23, 644)(24, 610)(25, 642)(26, 649)(27, 612)(28, 614)(29, 654)(30, 653)(31, 657)(32, 615)(33, 627)(34, 662)(35, 663)(36, 617)(37, 629)(38, 620)(39, 670)(40, 669)(41, 622)(42, 675)(43, 674)(44, 624)(45, 680)(46, 679)(47, 683)(48, 625)(49, 686)(50, 626)(51, 661)(52, 691)(53, 628)(54, 667)(55, 696)(56, 697)(57, 698)(58, 631)(59, 639)(60, 634)(61, 705)(62, 704)(63, 636)(64, 710)(65, 709)(66, 713)(67, 637)(68, 716)(69, 638)(70, 702)(71, 721)(72, 722)(73, 723)(74, 641)(75, 648)(76, 728)(77, 729)(78, 645)(79, 733)(80, 732)(81, 736)(82, 646)(83, 739)(84, 647)(85, 727)(86, 650)(87, 745)(88, 744)(89, 747)(90, 651)(91, 750)(92, 652)(93, 656)(94, 655)(95, 749)(96, 756)(97, 754)(98, 658)(99, 762)(100, 761)(101, 765)(102, 659)(103, 768)(104, 660)(105, 690)(106, 773)(107, 774)(108, 664)(109, 777)(110, 776)(111, 780)(112, 665)(113, 783)(114, 666)(115, 695)(116, 787)(117, 668)(118, 672)(119, 671)(120, 685)(121, 793)(122, 791)(123, 797)(124, 673)(125, 677)(126, 676)(127, 767)(128, 803)(129, 801)(130, 808)(131, 809)(132, 678)(133, 682)(134, 814)(135, 815)(136, 817)(137, 681)(138, 813)(139, 684)(140, 823)(141, 822)(142, 794)(143, 687)(144, 828)(145, 827)(146, 688)(147, 832)(148, 689)(149, 772)(150, 692)(151, 838)(152, 837)(153, 841)(154, 693)(155, 844)(156, 694)(157, 847)(158, 848)(159, 782)(160, 699)(161, 852)(162, 851)(163, 855)(164, 700)(165, 858)(166, 701)(167, 720)(168, 862)(169, 703)(170, 707)(171, 706)(172, 715)(173, 868)(174, 866)(175, 872)(176, 708)(177, 712)(178, 877)(179, 878)(180, 880)(181, 711)(182, 876)(183, 714)(184, 886)(185, 885)(186, 869)(187, 717)(188, 891)(189, 890)(190, 894)(191, 718)(192, 897)(193, 719)(194, 900)(195, 901)(196, 857)(197, 724)(198, 905)(199, 904)(200, 908)(201, 725)(202, 911)(203, 726)(204, 914)(205, 915)(206, 730)(207, 738)(208, 917)(209, 920)(210, 731)(211, 735)(212, 734)(213, 910)(214, 926)(215, 924)(216, 930)(217, 737)(218, 933)(219, 932)(220, 918)(221, 740)(222, 938)(223, 937)(224, 741)(225, 742)(226, 943)(227, 743)(228, 746)(229, 948)(230, 949)(231, 947)(232, 748)(233, 954)(234, 953)(235, 757)(236, 751)(237, 959)(238, 958)(239, 962)(240, 752)(241, 964)(242, 753)(243, 759)(244, 968)(245, 755)(246, 758)(247, 956)(248, 972)(249, 975)(250, 976)(251, 760)(252, 764)(253, 981)(254, 982)(255, 984)(256, 763)(257, 980)(258, 766)(259, 990)(260, 989)(261, 804)(262, 769)(263, 995)(264, 994)(265, 998)(266, 770)(267, 1001)(268, 771)(269, 1004)(270, 1005)(271, 831)(272, 1007)(273, 775)(274, 779)(275, 778)(276, 843)(277, 1013)(278, 1011)(279, 1017)(280, 781)(281, 1020)(282, 1019)(283, 849)(284, 784)(285, 1025)(286, 1024)(287, 785)(288, 786)(289, 788)(290, 1032)(291, 1031)(292, 1035)(293, 789)(294, 1037)(295, 790)(296, 796)(297, 1041)(298, 792)(299, 795)(300, 825)(301, 1045)(302, 1048)(303, 798)(304, 1051)(305, 1050)(306, 1018)(307, 799)(308, 1054)(309, 800)(310, 807)(311, 1058)(312, 802)(313, 805)(314, 992)(315, 1062)(316, 1016)(317, 806)(318, 1065)(319, 1036)(320, 810)(321, 1030)(322, 1067)(323, 1070)(324, 811)(325, 1071)(326, 812)(327, 1040)(328, 1073)(329, 816)(330, 986)(331, 818)(332, 983)(333, 996)(334, 819)(335, 820)(336, 1009)(337, 821)(338, 824)(339, 1077)(340, 1078)(341, 1029)(342, 1046)(343, 1082)(344, 826)(345, 830)(346, 829)(347, 1000)(348, 1088)(349, 1086)(350, 1021)(351, 1006)(352, 833)(353, 1079)(354, 1068)(355, 834)(356, 835)(357, 1093)(358, 836)(359, 840)(360, 1085)(361, 1042)(362, 985)(363, 839)(364, 842)(365, 1087)(366, 1098)(367, 1014)(368, 845)(369, 1099)(370, 1056)(371, 1060)(372, 846)(373, 1047)(374, 1028)(375, 1022)(376, 1103)(377, 850)(378, 854)(379, 853)(380, 896)(381, 1109)(382, 1107)(383, 934)(384, 856)(385, 963)(386, 929)(387, 902)(388, 859)(389, 1114)(390, 1113)(391, 860)(392, 861)(393, 863)(394, 1121)(395, 1120)(396, 931)(397, 864)(398, 1124)(399, 865)(400, 871)(401, 1128)(402, 867)(403, 870)(404, 888)(405, 1132)(406, 1074)(407, 873)(408, 1119)(409, 1136)(410, 1137)(411, 874)(412, 1138)(413, 875)(414, 1127)(415, 940)(416, 879)(417, 916)(418, 881)(419, 950)(420, 906)(421, 882)(422, 883)(423, 1105)(424, 884)(425, 887)(426, 1142)(427, 939)(428, 1118)(429, 1133)(430, 1144)(431, 889)(432, 893)(433, 923)(434, 1129)(435, 919)(436, 892)(437, 895)(438, 925)(439, 1148)(440, 1110)(441, 898)(442, 1149)(443, 966)(444, 970)(445, 899)(446, 1134)(447, 1117)(448, 1096)(449, 1153)(450, 903)(451, 907)(452, 1106)(453, 969)(454, 909)(455, 1108)(456, 1150)(457, 927)(458, 912)(459, 1157)(460, 1126)(461, 1130)(462, 913)(463, 974)(464, 941)(465, 935)(466, 921)(467, 1159)(468, 952)(469, 922)(470, 1146)(471, 1147)(472, 928)(473, 1115)(474, 1091)(475, 1143)(476, 936)(477, 1111)(478, 1139)(479, 955)(480, 1140)(481, 942)(482, 944)(483, 957)(484, 1166)(485, 1167)(486, 945)(487, 1168)(488, 946)(489, 967)(490, 1116)(491, 951)(492, 973)(493, 1165)(494, 961)(495, 960)(496, 987)(497, 965)(498, 1131)(499, 1154)(500, 971)(501, 1152)(502, 1151)(503, 977)(504, 1049)(505, 1175)(506, 1176)(507, 978)(508, 1177)(509, 979)(510, 1057)(511, 1027)(512, 1084)(513, 988)(514, 991)(515, 1072)(516, 1026)(517, 1092)(518, 1063)(519, 1178)(520, 993)(521, 997)(522, 1010)(523, 1059)(524, 999)(525, 1012)(526, 1100)(527, 1089)(528, 1002)(529, 1172)(530, 1039)(531, 1043)(532, 1003)(533, 1064)(534, 1081)(535, 1008)(536, 1076)(537, 1180)(538, 1181)(539, 1015)(540, 1102)(541, 1023)(542, 1090)(543, 1101)(544, 1066)(545, 1034)(546, 1033)(547, 1038)(548, 1061)(549, 1094)(550, 1044)(551, 1080)(552, 1075)(553, 1174)(554, 1053)(555, 1052)(556, 1055)(557, 1179)(558, 1187)(559, 1069)(560, 1192)(561, 1193)(562, 1194)(563, 1112)(564, 1183)(565, 1083)(566, 1163)(567, 1095)(568, 1097)(569, 1182)(570, 1190)(571, 1186)(572, 1145)(573, 1185)(574, 1104)(575, 1141)(576, 1155)(577, 1156)(578, 1135)(579, 1123)(580, 1122)(581, 1125)(582, 1199)(583, 1170)(584, 1161)(585, 1160)(586, 1197)(587, 1196)(588, 1171)(589, 1162)(590, 1164)(591, 1158)(592, 1173)(593, 1198)(594, 1200)(595, 1169)(596, 1191)(597, 1188)(598, 1184)(599, 1195)(600, 1189) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E16.1287 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 120 e = 600 f = 450 degree seq :: [ 10^120 ] E16.1292 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 5}) Quotient :: loop Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^5, (T1 * T2)^4, (T2 * T1^-2)^6, T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 601, 3, 603)(2, 602, 6, 606)(4, 604, 9, 609)(5, 605, 11, 611)(7, 607, 15, 615)(8, 608, 16, 616)(10, 610, 20, 620)(12, 612, 24, 624)(13, 613, 25, 625)(14, 614, 27, 627)(17, 617, 31, 631)(18, 618, 33, 633)(19, 619, 28, 628)(21, 621, 38, 638)(22, 622, 39, 639)(23, 623, 41, 641)(26, 626, 44, 644)(29, 629, 48, 648)(30, 630, 51, 651)(32, 632, 54, 654)(34, 634, 57, 657)(35, 635, 59, 659)(36, 636, 55, 655)(37, 637, 61, 661)(40, 640, 64, 664)(42, 642, 67, 667)(43, 643, 69, 669)(45, 645, 73, 673)(46, 646, 74, 674)(47, 647, 76, 676)(49, 649, 78, 678)(50, 650, 79, 679)(52, 652, 83, 683)(53, 653, 80, 680)(56, 656, 88, 688)(58, 658, 92, 692)(60, 660, 94, 694)(62, 662, 97, 697)(63, 663, 99, 699)(65, 665, 103, 703)(66, 666, 104, 704)(68, 668, 107, 707)(70, 670, 111, 711)(71, 671, 108, 708)(72, 672, 113, 713)(75, 675, 116, 716)(77, 677, 120, 720)(81, 681, 126, 726)(82, 682, 128, 728)(84, 684, 130, 730)(85, 685, 132, 732)(86, 686, 133, 733)(87, 687, 135, 735)(89, 689, 137, 737)(90, 690, 139, 739)(91, 691, 117, 717)(93, 693, 143, 743)(95, 695, 147, 747)(96, 696, 148, 748)(98, 698, 151, 751)(100, 700, 155, 755)(101, 701, 152, 752)(102, 702, 157, 757)(105, 705, 160, 760)(106, 706, 162, 762)(109, 709, 166, 766)(110, 710, 168, 768)(112, 712, 170, 770)(114, 714, 173, 773)(115, 715, 175, 775)(118, 718, 179, 779)(119, 719, 181, 781)(121, 721, 185, 785)(122, 722, 182, 782)(123, 723, 188, 788)(124, 724, 189, 789)(125, 725, 191, 791)(127, 727, 193, 793)(129, 729, 196, 796)(131, 731, 199, 799)(134, 734, 202, 802)(136, 736, 206, 806)(138, 738, 209, 809)(140, 740, 211, 811)(141, 741, 213, 813)(142, 742, 214, 814)(144, 744, 218, 818)(145, 745, 203, 803)(146, 746, 220, 820)(149, 749, 223, 823)(150, 750, 225, 825)(153, 753, 229, 829)(154, 754, 231, 831)(156, 756, 233, 833)(158, 758, 236, 836)(159, 759, 238, 838)(161, 761, 241, 841)(163, 763, 244, 844)(164, 764, 245, 845)(165, 765, 247, 847)(167, 767, 249, 849)(169, 769, 252, 852)(171, 771, 256, 856)(172, 772, 257, 857)(174, 774, 260, 860)(176, 776, 264, 864)(177, 777, 261, 861)(178, 778, 266, 866)(180, 780, 268, 868)(183, 783, 272, 872)(184, 784, 274, 874)(186, 786, 276, 876)(187, 787, 277, 877)(190, 790, 280, 880)(192, 792, 284, 884)(194, 794, 288, 888)(195, 795, 289, 889)(197, 797, 293, 893)(198, 798, 281, 881)(200, 800, 296, 896)(201, 801, 298, 898)(204, 804, 302, 902)(205, 805, 304, 904)(207, 807, 308, 908)(208, 808, 305, 905)(210, 810, 312, 912)(212, 812, 314, 914)(215, 815, 317, 917)(216, 816, 319, 919)(217, 817, 320, 920)(219, 819, 255, 855)(221, 821, 322, 922)(222, 822, 324, 924)(224, 824, 327, 927)(226, 826, 330, 930)(227, 827, 331, 931)(228, 828, 333, 933)(230, 830, 335, 935)(232, 832, 338, 938)(234, 834, 340, 940)(235, 835, 341, 941)(237, 837, 343, 943)(239, 839, 347, 947)(240, 840, 344, 944)(242, 842, 351, 951)(243, 843, 353, 953)(246, 846, 356, 956)(248, 848, 360, 960)(250, 850, 364, 964)(251, 851, 365, 965)(253, 853, 369, 969)(254, 854, 357, 957)(258, 858, 371, 971)(259, 859, 373, 973)(262, 862, 377, 977)(263, 863, 379, 979)(265, 865, 381, 981)(267, 867, 384, 984)(269, 869, 387, 987)(270, 870, 388, 988)(271, 871, 390, 990)(273, 873, 392, 992)(275, 875, 395, 995)(278, 878, 399, 999)(279, 879, 400, 1000)(282, 882, 403, 1003)(283, 883, 405, 1005)(285, 885, 409, 1009)(286, 886, 406, 1006)(287, 887, 411, 1011)(290, 890, 414, 1014)(291, 891, 415, 1015)(292, 892, 416, 1016)(294, 894, 418, 1018)(295, 895, 398, 998)(297, 897, 420, 1020)(299, 899, 424, 1024)(300, 900, 421, 1021)(301, 901, 370, 970)(303, 903, 427, 1027)(306, 906, 430, 1030)(307, 907, 432, 1032)(309, 909, 417, 1017)(310, 910, 435, 1035)(311, 911, 436, 1036)(313, 913, 438, 1038)(315, 915, 439, 1039)(316, 916, 441, 1041)(318, 918, 378, 978)(321, 921, 410, 1010)(323, 923, 447, 1047)(325, 925, 449, 1049)(326, 926, 389, 989)(328, 928, 452, 1052)(329, 929, 454, 1054)(332, 932, 457, 1057)(334, 934, 460, 1060)(336, 936, 462, 1062)(337, 937, 463, 1063)(339, 939, 401, 1001)(342, 942, 465, 1065)(345, 945, 468, 1068)(346, 946, 469, 1069)(348, 948, 380, 980)(349, 949, 471, 1071)(350, 950, 472, 1072)(352, 952, 475, 1075)(354, 954, 477, 1077)(355, 955, 478, 1078)(358, 958, 480, 1080)(359, 959, 482, 1082)(361, 961, 485, 1085)(362, 962, 483, 1083)(363, 963, 486, 1086)(366, 966, 488, 1088)(367, 967, 489, 1089)(368, 968, 394, 994)(372, 972, 491, 1091)(374, 974, 494, 1094)(375, 975, 495, 1095)(376, 976, 497, 1097)(382, 982, 500, 1100)(383, 983, 501, 1101)(385, 985, 504, 1104)(386, 986, 502, 1102)(391, 991, 510, 1110)(393, 993, 513, 1113)(396, 996, 507, 1107)(397, 997, 516, 1116)(402, 1002, 518, 1118)(404, 1004, 521, 1121)(407, 1007, 524, 1124)(408, 1008, 445, 1045)(412, 1012, 526, 1126)(413, 1013, 434, 1034)(419, 1019, 529, 1129)(422, 1022, 532, 1132)(423, 1023, 499, 1099)(425, 1025, 512, 1112)(426, 1026, 534, 1134)(428, 1028, 535, 1135)(429, 1029, 536, 1136)(431, 1031, 509, 1109)(433, 1033, 539, 1139)(437, 1037, 528, 1128)(440, 1040, 541, 1141)(442, 1042, 514, 1114)(443, 1043, 473, 1073)(444, 1044, 498, 1098)(446, 1046, 490, 1090)(448, 1048, 549, 1149)(450, 1050, 470, 1070)(451, 1051, 551, 1151)(453, 1053, 553, 1153)(455, 1055, 555, 1155)(456, 1056, 556, 1156)(458, 1058, 558, 1158)(459, 1059, 559, 1159)(461, 1061, 561, 1161)(464, 1064, 562, 1162)(466, 1066, 565, 1165)(467, 1067, 566, 1166)(474, 1074, 569, 1169)(476, 1076, 571, 1171)(479, 1079, 573, 1173)(481, 1081, 576, 1176)(484, 1084, 578, 1178)(487, 1087, 580, 1180)(492, 1092, 581, 1181)(493, 1093, 574, 1174)(496, 1096, 563, 1163)(503, 1103, 586, 1186)(505, 1105, 547, 1147)(506, 1106, 554, 1154)(508, 1108, 587, 1187)(511, 1111, 589, 1189)(515, 1115, 567, 1167)(517, 1117, 590, 1190)(519, 1119, 591, 1191)(520, 1120, 564, 1164)(522, 1122, 548, 1148)(523, 1123, 592, 1192)(525, 1125, 557, 1157)(527, 1127, 579, 1179)(530, 1130, 570, 1170)(531, 1131, 577, 1177)(533, 1133, 582, 1182)(537, 1137, 588, 1188)(538, 1138, 568, 1168)(540, 1140, 545, 1145)(542, 1142, 584, 1184)(543, 1143, 550, 1150)(544, 1144, 594, 1194)(546, 1146, 593, 1193)(552, 1152, 596, 1196)(560, 1160, 597, 1197)(572, 1172, 598, 1198)(575, 1175, 595, 1195)(583, 1183, 599, 1199)(585, 1185, 600, 1200) L = (1, 602)(2, 605)(3, 607)(4, 601)(5, 610)(6, 612)(7, 614)(8, 603)(9, 618)(10, 604)(11, 621)(12, 623)(13, 606)(14, 617)(15, 628)(16, 630)(17, 608)(18, 632)(19, 609)(20, 635)(21, 637)(22, 611)(23, 626)(24, 616)(25, 643)(26, 613)(27, 645)(28, 647)(29, 615)(30, 650)(31, 652)(32, 634)(33, 655)(34, 619)(35, 658)(36, 620)(37, 640)(38, 625)(39, 663)(40, 622)(41, 665)(42, 624)(43, 668)(44, 670)(45, 672)(46, 627)(47, 649)(48, 677)(49, 629)(50, 642)(51, 680)(52, 682)(53, 631)(54, 685)(55, 687)(56, 633)(57, 690)(58, 660)(59, 639)(60, 636)(61, 695)(62, 638)(63, 698)(64, 700)(65, 702)(66, 641)(67, 706)(68, 662)(69, 708)(70, 710)(71, 644)(72, 675)(73, 648)(74, 715)(75, 646)(76, 717)(77, 719)(78, 721)(79, 723)(80, 725)(81, 651)(82, 684)(83, 674)(84, 653)(85, 731)(86, 654)(87, 689)(88, 736)(89, 656)(90, 738)(91, 657)(92, 741)(93, 659)(94, 744)(95, 746)(96, 661)(97, 750)(98, 693)(99, 752)(100, 754)(101, 664)(102, 705)(103, 667)(104, 759)(105, 666)(106, 761)(107, 763)(108, 765)(109, 669)(110, 712)(111, 704)(112, 671)(113, 771)(114, 673)(115, 774)(116, 776)(117, 778)(118, 676)(119, 714)(120, 782)(121, 784)(122, 678)(123, 787)(124, 679)(125, 727)(126, 792)(127, 681)(128, 794)(129, 683)(130, 797)(131, 734)(132, 688)(133, 801)(134, 686)(135, 803)(136, 805)(137, 807)(138, 740)(139, 733)(140, 691)(141, 812)(142, 692)(143, 816)(144, 817)(145, 694)(146, 749)(147, 697)(148, 822)(149, 696)(150, 824)(151, 826)(152, 828)(153, 699)(154, 756)(155, 748)(156, 701)(157, 834)(158, 703)(159, 837)(160, 839)(161, 758)(162, 789)(163, 843)(164, 707)(165, 767)(166, 848)(167, 709)(168, 850)(169, 711)(170, 853)(171, 855)(172, 713)(173, 859)(174, 729)(175, 861)(176, 863)(177, 716)(178, 780)(179, 867)(180, 718)(181, 869)(182, 871)(183, 720)(184, 786)(185, 779)(186, 722)(187, 790)(188, 726)(189, 879)(190, 724)(191, 881)(192, 883)(193, 885)(194, 887)(195, 728)(196, 891)(197, 892)(198, 730)(199, 894)(200, 732)(201, 897)(202, 899)(203, 901)(204, 735)(205, 800)(206, 905)(207, 907)(208, 737)(209, 910)(210, 739)(211, 913)(212, 815)(213, 743)(214, 916)(215, 742)(216, 918)(217, 819)(218, 814)(219, 745)(220, 798)(221, 747)(222, 923)(223, 925)(224, 821)(225, 845)(226, 929)(227, 751)(228, 830)(229, 934)(230, 753)(231, 936)(232, 755)(233, 939)(234, 811)(235, 757)(236, 942)(237, 769)(238, 944)(239, 946)(240, 760)(241, 949)(242, 762)(243, 846)(244, 766)(245, 955)(246, 764)(247, 957)(248, 959)(249, 961)(250, 963)(251, 768)(252, 967)(253, 968)(254, 770)(255, 858)(256, 773)(257, 953)(258, 772)(259, 972)(260, 974)(261, 976)(262, 775)(263, 865)(264, 857)(265, 777)(266, 940)(267, 983)(268, 985)(269, 924)(270, 781)(271, 873)(272, 991)(273, 783)(274, 993)(275, 785)(276, 969)(277, 997)(278, 788)(279, 952)(280, 1001)(281, 922)(282, 791)(283, 878)(284, 1006)(285, 1008)(286, 793)(287, 890)(288, 796)(289, 1013)(290, 795)(291, 935)(292, 820)(293, 889)(294, 833)(295, 799)(296, 1019)(297, 810)(298, 1021)(299, 1023)(300, 802)(301, 903)(302, 1026)(303, 804)(304, 945)(305, 1029)(306, 806)(307, 909)(308, 902)(309, 808)(310, 1034)(311, 809)(312, 962)(313, 835)(314, 854)(315, 813)(316, 1040)(317, 1042)(318, 915)(319, 931)(320, 1045)(321, 818)(322, 1004)(323, 832)(324, 989)(325, 1048)(326, 823)(327, 1022)(328, 825)(329, 932)(330, 829)(331, 1056)(332, 827)(333, 1018)(334, 1059)(335, 1012)(336, 1061)(337, 831)(338, 986)(339, 895)(340, 836)(341, 1054)(342, 982)(343, 1066)(344, 1028)(345, 838)(346, 948)(347, 941)(348, 840)(349, 1041)(350, 841)(351, 1074)(352, 842)(353, 1076)(354, 844)(355, 1053)(356, 971)(357, 1039)(358, 847)(359, 954)(360, 1083)(361, 1035)(362, 849)(363, 966)(364, 852)(365, 1011)(366, 851)(367, 1027)(368, 914)(369, 965)(370, 856)(371, 1090)(372, 970)(373, 988)(374, 1093)(375, 860)(376, 978)(377, 1098)(378, 862)(379, 1069)(380, 864)(381, 1024)(382, 866)(383, 875)(384, 1102)(385, 1062)(386, 868)(387, 872)(388, 1106)(389, 870)(390, 1107)(391, 1109)(392, 1111)(393, 1112)(394, 874)(395, 1115)(396, 876)(397, 981)(398, 877)(399, 1117)(400, 1118)(401, 1063)(402, 880)(403, 1120)(404, 882)(405, 1103)(406, 1123)(407, 884)(408, 1010)(409, 1003)(410, 886)(411, 996)(412, 888)(413, 1127)(414, 1088)(415, 1095)(416, 1032)(417, 893)(418, 896)(419, 1058)(420, 1130)(421, 1051)(422, 898)(423, 1025)(424, 998)(425, 900)(426, 1133)(427, 1087)(428, 904)(429, 1031)(430, 1137)(431, 906)(432, 1138)(433, 908)(434, 1037)(435, 912)(436, 1140)(437, 911)(438, 1036)(439, 1081)(440, 921)(441, 1073)(442, 1142)(443, 917)(444, 919)(445, 1145)(446, 920)(447, 1147)(448, 1050)(449, 1016)(450, 926)(451, 927)(452, 1152)(453, 928)(454, 1154)(455, 930)(456, 1144)(457, 1038)(458, 933)(459, 1055)(460, 1015)(461, 1064)(462, 938)(463, 1086)(464, 937)(465, 1072)(466, 1164)(467, 943)(468, 1030)(469, 1149)(470, 947)(471, 951)(472, 1168)(473, 950)(474, 992)(475, 1170)(476, 980)(477, 1172)(478, 1173)(479, 956)(480, 1175)(481, 958)(482, 1007)(483, 1177)(484, 960)(485, 1080)(486, 1002)(487, 964)(488, 1162)(489, 1166)(490, 1161)(491, 1119)(492, 973)(493, 1096)(494, 977)(495, 1182)(496, 975)(497, 1116)(498, 1183)(499, 979)(500, 1174)(501, 1185)(502, 1122)(503, 984)(504, 1100)(505, 987)(506, 1155)(507, 1126)(508, 990)(509, 1105)(510, 1169)(511, 1071)(512, 1114)(513, 995)(514, 994)(515, 1121)(516, 999)(517, 1176)(518, 1180)(519, 1000)(520, 1156)(521, 1151)(522, 1005)(523, 1082)(524, 1178)(525, 1009)(526, 1158)(527, 1017)(528, 1014)(529, 1135)(530, 1191)(531, 1020)(532, 1052)(533, 1033)(534, 1089)(535, 1171)(536, 1179)(537, 1194)(538, 1150)(539, 1163)(540, 1157)(541, 1189)(542, 1143)(543, 1043)(544, 1044)(545, 1146)(546, 1046)(547, 1195)(548, 1047)(549, 1184)(550, 1049)(551, 1113)(552, 1075)(553, 1094)(554, 1070)(555, 1092)(556, 1125)(557, 1057)(558, 1108)(559, 1084)(560, 1060)(561, 1079)(562, 1193)(563, 1065)(564, 1167)(565, 1068)(566, 1101)(567, 1067)(568, 1139)(569, 1196)(570, 1132)(571, 1077)(572, 1129)(573, 1104)(574, 1078)(575, 1136)(576, 1097)(577, 1159)(578, 1197)(579, 1085)(580, 1091)(581, 1131)(582, 1160)(583, 1153)(584, 1099)(585, 1134)(586, 1124)(587, 1198)(588, 1110)(589, 1187)(590, 1148)(591, 1181)(592, 1141)(593, 1128)(594, 1165)(595, 1190)(596, 1199)(597, 1200)(598, 1192)(599, 1188)(600, 1186) local type(s) :: { ( 4, 5, 4, 5 ) } Outer automorphisms :: reflexible Dual of E16.1288 Transitivity :: ET+ VT+ AT Graph:: simple v = 300 e = 600 f = 270 degree seq :: [ 4^300 ] E16.1293 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5}) Quotient :: dipole Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^5, (Y3 * Y2^-1)^5, (Y2^-1 * Y1 * Y2^-1)^6, Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1, (Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-2 * Y1 * Y2^-1 * Y1)^2, Y2 * Y1 * Y2^-2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1 * Y2 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: R = (1, 601, 2, 602)(3, 603, 7, 607)(4, 604, 9, 609)(5, 605, 10, 610)(6, 606, 12, 612)(8, 608, 15, 615)(11, 611, 20, 620)(13, 613, 23, 623)(14, 614, 25, 625)(16, 616, 28, 628)(17, 617, 30, 630)(18, 618, 31, 631)(19, 619, 33, 633)(21, 621, 36, 636)(22, 622, 38, 638)(24, 624, 40, 640)(26, 626, 43, 643)(27, 627, 45, 645)(29, 629, 48, 648)(32, 632, 51, 651)(34, 634, 54, 654)(35, 635, 56, 656)(37, 637, 59, 659)(39, 639, 61, 661)(41, 641, 64, 664)(42, 642, 66, 666)(44, 644, 68, 668)(46, 646, 70, 670)(47, 647, 72, 672)(49, 649, 75, 675)(50, 650, 76, 676)(52, 652, 79, 679)(53, 653, 81, 681)(55, 655, 83, 683)(57, 657, 85, 685)(58, 658, 87, 687)(60, 660, 90, 690)(62, 662, 93, 693)(63, 663, 95, 695)(65, 665, 98, 698)(67, 667, 100, 700)(69, 669, 103, 703)(71, 671, 105, 705)(73, 673, 108, 708)(74, 674, 110, 710)(77, 677, 115, 715)(78, 678, 117, 717)(80, 680, 120, 720)(82, 682, 122, 722)(84, 684, 125, 725)(86, 686, 127, 727)(88, 688, 130, 730)(89, 689, 132, 732)(91, 691, 135, 735)(92, 692, 137, 737)(94, 694, 139, 739)(96, 696, 141, 741)(97, 697, 143, 743)(99, 699, 146, 746)(101, 701, 149, 749)(102, 702, 151, 751)(104, 704, 154, 754)(106, 706, 157, 757)(107, 707, 159, 759)(109, 709, 161, 761)(111, 711, 163, 763)(112, 712, 165, 765)(113, 713, 166, 766)(114, 714, 168, 768)(116, 716, 170, 770)(118, 718, 172, 772)(119, 719, 174, 774)(121, 721, 177, 777)(123, 723, 180, 780)(124, 724, 182, 782)(126, 726, 185, 785)(128, 728, 188, 788)(129, 729, 190, 790)(131, 731, 192, 792)(133, 733, 194, 794)(134, 734, 196, 796)(136, 736, 199, 799)(138, 738, 201, 801)(140, 740, 204, 804)(142, 742, 206, 806)(144, 744, 209, 809)(145, 745, 211, 811)(147, 747, 214, 814)(148, 748, 216, 816)(150, 750, 181, 781)(152, 752, 219, 819)(153, 753, 221, 821)(155, 755, 224, 824)(156, 756, 226, 826)(158, 758, 229, 829)(160, 760, 231, 831)(162, 762, 232, 832)(164, 764, 234, 834)(167, 767, 239, 839)(169, 769, 241, 841)(171, 771, 244, 844)(173, 773, 246, 846)(175, 775, 249, 849)(176, 776, 251, 851)(178, 778, 254, 854)(179, 779, 256, 856)(183, 783, 259, 859)(184, 784, 261, 861)(186, 786, 264, 864)(187, 787, 266, 866)(189, 789, 269, 869)(191, 791, 271, 871)(193, 793, 272, 872)(195, 795, 274, 874)(197, 797, 276, 876)(198, 798, 278, 878)(200, 800, 281, 881)(202, 802, 284, 884)(203, 803, 285, 885)(205, 805, 288, 888)(207, 807, 291, 891)(208, 808, 293, 893)(210, 810, 295, 895)(212, 812, 297, 897)(213, 813, 299, 899)(215, 815, 302, 902)(217, 817, 304, 904)(218, 818, 305, 905)(220, 820, 307, 907)(222, 822, 310, 910)(223, 823, 312, 912)(225, 825, 314, 914)(227, 827, 316, 916)(228, 828, 318, 918)(230, 830, 321, 921)(233, 833, 326, 926)(235, 835, 329, 929)(236, 836, 237, 837)(238, 838, 332, 932)(240, 840, 335, 935)(242, 842, 338, 938)(243, 843, 339, 939)(245, 845, 342, 942)(247, 847, 345, 945)(248, 848, 347, 947)(250, 850, 349, 949)(252, 852, 351, 951)(253, 853, 353, 953)(255, 855, 356, 956)(257, 857, 358, 958)(258, 858, 359, 959)(260, 860, 361, 961)(262, 862, 364, 964)(263, 863, 366, 966)(265, 865, 368, 968)(267, 867, 370, 970)(268, 868, 372, 972)(270, 870, 375, 975)(273, 873, 380, 980)(275, 875, 383, 983)(277, 877, 385, 985)(279, 879, 388, 988)(280, 880, 389, 989)(282, 882, 343, 943)(283, 883, 393, 993)(286, 886, 396, 996)(287, 887, 398, 998)(289, 889, 336, 936)(290, 890, 402, 1002)(292, 892, 362, 962)(294, 894, 406, 1006)(296, 896, 350, 950)(298, 898, 408, 1008)(300, 900, 410, 1010)(301, 901, 371, 971)(303, 903, 414, 1014)(306, 906, 417, 1017)(308, 908, 346, 946)(309, 909, 421, 1021)(311, 911, 423, 1023)(313, 913, 367, 967)(315, 915, 425, 1025)(317, 917, 355, 955)(319, 919, 427, 1027)(320, 920, 379, 979)(322, 922, 431, 1031)(323, 923, 395, 995)(324, 924, 394, 994)(325, 925, 374, 974)(327, 927, 436, 1036)(328, 928, 437, 1037)(330, 930, 438, 1038)(331, 931, 439, 1039)(333, 933, 442, 1042)(334, 934, 443, 1043)(337, 937, 447, 1047)(340, 940, 450, 1050)(341, 941, 452, 1052)(344, 944, 456, 1056)(348, 948, 460, 1060)(352, 952, 462, 1062)(354, 954, 464, 1064)(357, 957, 468, 1068)(360, 960, 471, 1071)(363, 963, 475, 1075)(365, 965, 477, 1077)(369, 969, 479, 1079)(373, 973, 481, 1081)(376, 976, 485, 1085)(377, 977, 449, 1049)(378, 978, 448, 1048)(381, 981, 490, 1090)(382, 982, 491, 1091)(384, 984, 492, 1092)(386, 986, 495, 1095)(387, 987, 496, 1096)(390, 990, 499, 1099)(391, 991, 467, 1067)(392, 992, 454, 1054)(397, 997, 476, 1076)(399, 999, 505, 1105)(400, 1000, 446, 1046)(401, 1001, 507, 1107)(403, 1003, 509, 1109)(404, 1004, 510, 1110)(405, 1005, 473, 1073)(407, 1007, 513, 1113)(409, 1009, 486, 1086)(411, 1011, 517, 1117)(412, 1012, 480, 1080)(413, 1013, 445, 1045)(415, 1015, 493, 1093)(416, 1016, 520, 1120)(418, 1018, 488, 1088)(419, 1019, 459, 1059)(420, 1020, 503, 1103)(422, 1022, 451, 1051)(424, 1024, 498, 1098)(426, 1026, 466, 1066)(428, 1028, 523, 1123)(429, 1029, 487, 1087)(430, 1030, 526, 1126)(432, 1032, 463, 1063)(433, 1033, 483, 1083)(434, 1034, 472, 1072)(435, 1035, 529, 1129)(440, 1040, 533, 1133)(441, 1041, 534, 1134)(444, 1044, 537, 1137)(453, 1053, 543, 1143)(455, 1055, 545, 1145)(457, 1057, 547, 1147)(458, 1058, 548, 1148)(461, 1061, 551, 1151)(465, 1065, 555, 1155)(469, 1069, 531, 1131)(470, 1070, 558, 1158)(474, 1074, 541, 1141)(478, 1078, 536, 1136)(482, 1082, 561, 1161)(484, 1084, 564, 1164)(489, 1089, 567, 1167)(494, 1094, 542, 1142)(497, 1097, 550, 1150)(500, 1100, 556, 1156)(501, 1101, 572, 1172)(502, 1102, 553, 1153)(504, 1104, 532, 1132)(506, 1106, 557, 1157)(508, 1108, 549, 1149)(511, 1111, 546, 1146)(512, 1112, 535, 1135)(514, 1114, 575, 1175)(515, 1115, 540, 1140)(516, 1116, 554, 1154)(518, 1118, 538, 1138)(519, 1119, 544, 1144)(521, 1121, 563, 1163)(522, 1122, 566, 1166)(524, 1124, 562, 1162)(525, 1125, 559, 1159)(527, 1127, 568, 1168)(528, 1128, 560, 1160)(530, 1130, 565, 1165)(539, 1139, 582, 1182)(552, 1152, 585, 1185)(569, 1169, 583, 1183)(570, 1170, 586, 1186)(571, 1171, 589, 1189)(573, 1173, 579, 1179)(574, 1174, 592, 1192)(576, 1176, 580, 1180)(577, 1177, 590, 1190)(578, 1178, 591, 1191)(581, 1181, 593, 1193)(584, 1184, 596, 1196)(587, 1187, 594, 1194)(588, 1188, 595, 1195)(597, 1197, 600, 1200)(598, 1198, 599, 1199)(1201, 1801, 1203, 1803, 1208, 1808, 1204, 1804)(1202, 1802, 1205, 1805, 1211, 1811, 1206, 1806)(1207, 1807, 1213, 1813, 1224, 1824, 1214, 1814)(1209, 1809, 1216, 1816, 1229, 1829, 1217, 1817)(1210, 1810, 1218, 1818, 1232, 1832, 1219, 1819)(1212, 1812, 1221, 1821, 1237, 1837, 1222, 1822)(1215, 1815, 1226, 1826, 1244, 1844, 1227, 1827)(1220, 1820, 1234, 1834, 1255, 1855, 1235, 1835)(1223, 1823, 1238, 1838, 1260, 1860, 1239, 1839)(1225, 1825, 1241, 1841, 1265, 1865, 1242, 1842)(1228, 1828, 1246, 1846, 1271, 1871, 1247, 1847)(1230, 1830, 1249, 1849, 1250, 1850, 1231, 1831)(1233, 1833, 1252, 1852, 1280, 1880, 1253, 1853)(1236, 1836, 1257, 1857, 1286, 1886, 1258, 1858)(1240, 1840, 1262, 1862, 1294, 1894, 1263, 1863)(1243, 1843, 1266, 1866, 1299, 1899, 1267, 1867)(1245, 1845, 1269, 1869, 1304, 1904, 1270, 1870)(1248, 1848, 1273, 1873, 1309, 1909, 1274, 1874)(1251, 1851, 1277, 1877, 1316, 1916, 1278, 1878)(1254, 1854, 1281, 1881, 1321, 1921, 1282, 1882)(1256, 1856, 1284, 1884, 1326, 1926, 1285, 1885)(1259, 1859, 1288, 1888, 1331, 1931, 1289, 1889)(1261, 1861, 1291, 1891, 1336, 1936, 1292, 1892)(1264, 1864, 1296, 1896, 1342, 1942, 1297, 1897)(1268, 1868, 1301, 1901, 1350, 1950, 1302, 1902)(1272, 1872, 1306, 1906, 1358, 1958, 1307, 1907)(1275, 1875, 1311, 1911, 1364, 1964, 1312, 1912)(1276, 1876, 1313, 1913, 1367, 1967, 1314, 1914)(1279, 1879, 1318, 1918, 1373, 1973, 1319, 1919)(1283, 1883, 1323, 1923, 1381, 1981, 1324, 1924)(1287, 1887, 1328, 1928, 1389, 1989, 1329, 1929)(1290, 1890, 1333, 1933, 1395, 1995, 1334, 1934)(1293, 1893, 1337, 1937, 1400, 2000, 1338, 1938)(1295, 1895, 1340, 1940, 1405, 2005, 1341, 1941)(1298, 1898, 1344, 1944, 1410, 2010, 1345, 1945)(1300, 1900, 1347, 1947, 1415, 2015, 1348, 1948)(1303, 1903, 1352, 1952, 1420, 2020, 1353, 1953)(1305, 1905, 1355, 1955, 1425, 2025, 1356, 1956)(1308, 1908, 1359, 1959, 1430, 2030, 1360, 1960)(1310, 1910, 1362, 1962, 1433, 2033, 1363, 1963)(1315, 1915, 1368, 1968, 1440, 2040, 1369, 1969)(1317, 1917, 1371, 1971, 1445, 2045, 1372, 1972)(1320, 1920, 1375, 1975, 1450, 2050, 1376, 1976)(1322, 1922, 1378, 1978, 1455, 2055, 1379, 1979)(1325, 1925, 1383, 1983, 1460, 2060, 1384, 1984)(1327, 1927, 1386, 1986, 1465, 2065, 1387, 1987)(1330, 1930, 1390, 1990, 1470, 2070, 1391, 1991)(1332, 1932, 1393, 1993, 1473, 2073, 1394, 1994)(1335, 1935, 1397, 1997, 1477, 2077, 1398, 1998)(1339, 1939, 1402, 2002, 1361, 1961, 1403, 2003)(1343, 1943, 1407, 2007, 1492, 2092, 1408, 2008)(1346, 1946, 1412, 2012, 1498, 2098, 1413, 2013)(1349, 1949, 1416, 2016, 1503, 2103, 1417, 2017)(1351, 1951, 1418, 2018, 1506, 2106, 1419, 2019)(1354, 1954, 1422, 2022, 1511, 2111, 1423, 2023)(1357, 1957, 1427, 2027, 1517, 2117, 1428, 2028)(1365, 1965, 1435, 2035, 1530, 2130, 1436, 2036)(1366, 1966, 1437, 2037, 1531, 2131, 1438, 2038)(1370, 1970, 1442, 2042, 1392, 1992, 1443, 2043)(1374, 1974, 1447, 2047, 1546, 2146, 1448, 2048)(1377, 1977, 1452, 2052, 1552, 2152, 1453, 2053)(1380, 1980, 1456, 2056, 1557, 2157, 1457, 2057)(1382, 1982, 1458, 2058, 1560, 2160, 1459, 2059)(1385, 1985, 1462, 2062, 1565, 2165, 1463, 2063)(1388, 1988, 1467, 2067, 1571, 2171, 1468, 2068)(1396, 1996, 1475, 2075, 1584, 2184, 1476, 2076)(1399, 1999, 1479, 2079, 1568, 2168, 1480, 2080)(1401, 2001, 1482, 2082, 1592, 2192, 1483, 2083)(1404, 2004, 1486, 2086, 1597, 2197, 1487, 2087)(1406, 2006, 1489, 2089, 1601, 2201, 1490, 2090)(1409, 2009, 1493, 2093, 1605, 2205, 1494, 2094)(1411, 2011, 1496, 2096, 1607, 2207, 1497, 2097)(1414, 2014, 1500, 2100, 1611, 2211, 1501, 2101)(1421, 2021, 1508, 2108, 1620, 2220, 1509, 2109)(1424, 2024, 1512, 2112, 1624, 2224, 1513, 2113)(1426, 2026, 1515, 2115, 1626, 2226, 1516, 2116)(1429, 2029, 1519, 2119, 1628, 2228, 1520, 2120)(1431, 2031, 1522, 2122, 1632, 2232, 1523, 2123)(1432, 2032, 1524, 2124, 1633, 2233, 1525, 2125)(1434, 2034, 1527, 2127, 1549, 2149, 1528, 2128)(1439, 2039, 1533, 2133, 1514, 2114, 1534, 2134)(1441, 2041, 1536, 2136, 1646, 2246, 1537, 2137)(1444, 2044, 1540, 2140, 1651, 2251, 1541, 2141)(1446, 2046, 1543, 2143, 1655, 2255, 1544, 2144)(1449, 2049, 1547, 2147, 1659, 2259, 1548, 2148)(1451, 2051, 1550, 2150, 1661, 2261, 1551, 2151)(1454, 2054, 1554, 2154, 1665, 2265, 1555, 2155)(1461, 2061, 1562, 2162, 1674, 2274, 1563, 2163)(1464, 2064, 1566, 2166, 1678, 2278, 1567, 2167)(1466, 2066, 1569, 2169, 1680, 2280, 1570, 2170)(1469, 2069, 1573, 2173, 1682, 2282, 1574, 2174)(1471, 2071, 1576, 2176, 1686, 2286, 1577, 2177)(1472, 2072, 1578, 2178, 1687, 2287, 1579, 2179)(1474, 2074, 1581, 2181, 1495, 2095, 1582, 2182)(1478, 2078, 1586, 2186, 1529, 2129, 1587, 2187)(1481, 2081, 1590, 2190, 1700, 2300, 1591, 2191)(1484, 2084, 1593, 2193, 1701, 2301, 1594, 2194)(1485, 2085, 1595, 2195, 1702, 2302, 1596, 2196)(1488, 2088, 1599, 2199, 1706, 2306, 1600, 2200)(1491, 2091, 1603, 2203, 1518, 2118, 1604, 2204)(1499, 2099, 1609, 2209, 1716, 2316, 1610, 2210)(1502, 2102, 1612, 2212, 1707, 2307, 1613, 2213)(1504, 2104, 1615, 2215, 1670, 2270, 1559, 2159)(1505, 2105, 1558, 2158, 1669, 2269, 1616, 2216)(1507, 2107, 1618, 2218, 1723, 2323, 1619, 2219)(1510, 2110, 1621, 2221, 1724, 2324, 1622, 2222)(1521, 2121, 1629, 2229, 1725, 2325, 1630, 2230)(1526, 2126, 1634, 2234, 1728, 2328, 1635, 2235)(1532, 2132, 1640, 2240, 1583, 2183, 1641, 2241)(1535, 2135, 1644, 2244, 1738, 2338, 1645, 2245)(1538, 2138, 1647, 2247, 1739, 2339, 1648, 2248)(1539, 2139, 1649, 2249, 1740, 2340, 1650, 2250)(1542, 2142, 1653, 2253, 1744, 2344, 1654, 2254)(1545, 2145, 1657, 2257, 1572, 2172, 1658, 2258)(1553, 2153, 1663, 2263, 1754, 2354, 1664, 2264)(1556, 2156, 1666, 2266, 1745, 2345, 1667, 2267)(1561, 2161, 1672, 2272, 1761, 2361, 1673, 2273)(1564, 2164, 1675, 2275, 1762, 2362, 1676, 2276)(1575, 2175, 1683, 2283, 1763, 2363, 1684, 2284)(1580, 2180, 1688, 2288, 1766, 2366, 1689, 2289)(1585, 2185, 1693, 2293, 1743, 2343, 1694, 2294)(1588, 2188, 1696, 2296, 1637, 2237, 1697, 2297)(1589, 2189, 1698, 2298, 1771, 2371, 1699, 2299)(1598, 2198, 1703, 2303, 1773, 2373, 1704, 2304)(1602, 2202, 1708, 2308, 1627, 2227, 1709, 2309)(1606, 2206, 1711, 2311, 1625, 2225, 1712, 2312)(1608, 2208, 1714, 2314, 1623, 2223, 1715, 2315)(1614, 2214, 1718, 2318, 1777, 2377, 1719, 2319)(1617, 2217, 1721, 2321, 1778, 2378, 1722, 2322)(1631, 2231, 1727, 2327, 1776, 2376, 1717, 2317)(1636, 2236, 1729, 2329, 1774, 2374, 1713, 2313)(1638, 2238, 1730, 2330, 1764, 2364, 1720, 2320)(1639, 2239, 1731, 2331, 1705, 2305, 1732, 2332)(1642, 2242, 1734, 2334, 1691, 2291, 1735, 2335)(1643, 2243, 1736, 2336, 1781, 2381, 1737, 2337)(1652, 2252, 1741, 2341, 1783, 2383, 1742, 2342)(1656, 2256, 1746, 2346, 1681, 2281, 1747, 2347)(1660, 2260, 1749, 2349, 1679, 2279, 1750, 2350)(1662, 2262, 1752, 2352, 1677, 2277, 1753, 2353)(1668, 2268, 1756, 2356, 1787, 2387, 1757, 2357)(1671, 2271, 1759, 2359, 1788, 2388, 1760, 2360)(1685, 2285, 1765, 2365, 1786, 2386, 1755, 2355)(1690, 2290, 1767, 2367, 1784, 2384, 1751, 2351)(1692, 2292, 1768, 2368, 1726, 2326, 1758, 2358)(1695, 2295, 1769, 2369, 1710, 2310, 1770, 2370)(1733, 2333, 1779, 2379, 1748, 2348, 1780, 2380)(1772, 2372, 1790, 2390, 1798, 2398, 1791, 2391)(1775, 2375, 1792, 2392, 1797, 2397, 1789, 2389)(1782, 2382, 1794, 2394, 1800, 2400, 1795, 2395)(1785, 2385, 1796, 2396, 1799, 2399, 1793, 2393) L = (1, 1202)(2, 1201)(3, 1207)(4, 1209)(5, 1210)(6, 1212)(7, 1203)(8, 1215)(9, 1204)(10, 1205)(11, 1220)(12, 1206)(13, 1223)(14, 1225)(15, 1208)(16, 1228)(17, 1230)(18, 1231)(19, 1233)(20, 1211)(21, 1236)(22, 1238)(23, 1213)(24, 1240)(25, 1214)(26, 1243)(27, 1245)(28, 1216)(29, 1248)(30, 1217)(31, 1218)(32, 1251)(33, 1219)(34, 1254)(35, 1256)(36, 1221)(37, 1259)(38, 1222)(39, 1261)(40, 1224)(41, 1264)(42, 1266)(43, 1226)(44, 1268)(45, 1227)(46, 1270)(47, 1272)(48, 1229)(49, 1275)(50, 1276)(51, 1232)(52, 1279)(53, 1281)(54, 1234)(55, 1283)(56, 1235)(57, 1285)(58, 1287)(59, 1237)(60, 1290)(61, 1239)(62, 1293)(63, 1295)(64, 1241)(65, 1298)(66, 1242)(67, 1300)(68, 1244)(69, 1303)(70, 1246)(71, 1305)(72, 1247)(73, 1308)(74, 1310)(75, 1249)(76, 1250)(77, 1315)(78, 1317)(79, 1252)(80, 1320)(81, 1253)(82, 1322)(83, 1255)(84, 1325)(85, 1257)(86, 1327)(87, 1258)(88, 1330)(89, 1332)(90, 1260)(91, 1335)(92, 1337)(93, 1262)(94, 1339)(95, 1263)(96, 1341)(97, 1343)(98, 1265)(99, 1346)(100, 1267)(101, 1349)(102, 1351)(103, 1269)(104, 1354)(105, 1271)(106, 1357)(107, 1359)(108, 1273)(109, 1361)(110, 1274)(111, 1363)(112, 1365)(113, 1366)(114, 1368)(115, 1277)(116, 1370)(117, 1278)(118, 1372)(119, 1374)(120, 1280)(121, 1377)(122, 1282)(123, 1380)(124, 1382)(125, 1284)(126, 1385)(127, 1286)(128, 1388)(129, 1390)(130, 1288)(131, 1392)(132, 1289)(133, 1394)(134, 1396)(135, 1291)(136, 1399)(137, 1292)(138, 1401)(139, 1294)(140, 1404)(141, 1296)(142, 1406)(143, 1297)(144, 1409)(145, 1411)(146, 1299)(147, 1414)(148, 1416)(149, 1301)(150, 1381)(151, 1302)(152, 1419)(153, 1421)(154, 1304)(155, 1424)(156, 1426)(157, 1306)(158, 1429)(159, 1307)(160, 1431)(161, 1309)(162, 1432)(163, 1311)(164, 1434)(165, 1312)(166, 1313)(167, 1439)(168, 1314)(169, 1441)(170, 1316)(171, 1444)(172, 1318)(173, 1446)(174, 1319)(175, 1449)(176, 1451)(177, 1321)(178, 1454)(179, 1456)(180, 1323)(181, 1350)(182, 1324)(183, 1459)(184, 1461)(185, 1326)(186, 1464)(187, 1466)(188, 1328)(189, 1469)(190, 1329)(191, 1471)(192, 1331)(193, 1472)(194, 1333)(195, 1474)(196, 1334)(197, 1476)(198, 1478)(199, 1336)(200, 1481)(201, 1338)(202, 1484)(203, 1485)(204, 1340)(205, 1488)(206, 1342)(207, 1491)(208, 1493)(209, 1344)(210, 1495)(211, 1345)(212, 1497)(213, 1499)(214, 1347)(215, 1502)(216, 1348)(217, 1504)(218, 1505)(219, 1352)(220, 1507)(221, 1353)(222, 1510)(223, 1512)(224, 1355)(225, 1514)(226, 1356)(227, 1516)(228, 1518)(229, 1358)(230, 1521)(231, 1360)(232, 1362)(233, 1526)(234, 1364)(235, 1529)(236, 1437)(237, 1436)(238, 1532)(239, 1367)(240, 1535)(241, 1369)(242, 1538)(243, 1539)(244, 1371)(245, 1542)(246, 1373)(247, 1545)(248, 1547)(249, 1375)(250, 1549)(251, 1376)(252, 1551)(253, 1553)(254, 1378)(255, 1556)(256, 1379)(257, 1558)(258, 1559)(259, 1383)(260, 1561)(261, 1384)(262, 1564)(263, 1566)(264, 1386)(265, 1568)(266, 1387)(267, 1570)(268, 1572)(269, 1389)(270, 1575)(271, 1391)(272, 1393)(273, 1580)(274, 1395)(275, 1583)(276, 1397)(277, 1585)(278, 1398)(279, 1588)(280, 1589)(281, 1400)(282, 1543)(283, 1593)(284, 1402)(285, 1403)(286, 1596)(287, 1598)(288, 1405)(289, 1536)(290, 1602)(291, 1407)(292, 1562)(293, 1408)(294, 1606)(295, 1410)(296, 1550)(297, 1412)(298, 1608)(299, 1413)(300, 1610)(301, 1571)(302, 1415)(303, 1614)(304, 1417)(305, 1418)(306, 1617)(307, 1420)(308, 1546)(309, 1621)(310, 1422)(311, 1623)(312, 1423)(313, 1567)(314, 1425)(315, 1625)(316, 1427)(317, 1555)(318, 1428)(319, 1627)(320, 1579)(321, 1430)(322, 1631)(323, 1595)(324, 1594)(325, 1574)(326, 1433)(327, 1636)(328, 1637)(329, 1435)(330, 1638)(331, 1639)(332, 1438)(333, 1642)(334, 1643)(335, 1440)(336, 1489)(337, 1647)(338, 1442)(339, 1443)(340, 1650)(341, 1652)(342, 1445)(343, 1482)(344, 1656)(345, 1447)(346, 1508)(347, 1448)(348, 1660)(349, 1450)(350, 1496)(351, 1452)(352, 1662)(353, 1453)(354, 1664)(355, 1517)(356, 1455)(357, 1668)(358, 1457)(359, 1458)(360, 1671)(361, 1460)(362, 1492)(363, 1675)(364, 1462)(365, 1677)(366, 1463)(367, 1513)(368, 1465)(369, 1679)(370, 1467)(371, 1501)(372, 1468)(373, 1681)(374, 1525)(375, 1470)(376, 1685)(377, 1649)(378, 1648)(379, 1520)(380, 1473)(381, 1690)(382, 1691)(383, 1475)(384, 1692)(385, 1477)(386, 1695)(387, 1696)(388, 1479)(389, 1480)(390, 1699)(391, 1667)(392, 1654)(393, 1483)(394, 1524)(395, 1523)(396, 1486)(397, 1676)(398, 1487)(399, 1705)(400, 1646)(401, 1707)(402, 1490)(403, 1709)(404, 1710)(405, 1673)(406, 1494)(407, 1713)(408, 1498)(409, 1686)(410, 1500)(411, 1717)(412, 1680)(413, 1645)(414, 1503)(415, 1693)(416, 1720)(417, 1506)(418, 1688)(419, 1659)(420, 1703)(421, 1509)(422, 1651)(423, 1511)(424, 1698)(425, 1515)(426, 1666)(427, 1519)(428, 1723)(429, 1687)(430, 1726)(431, 1522)(432, 1663)(433, 1683)(434, 1672)(435, 1729)(436, 1527)(437, 1528)(438, 1530)(439, 1531)(440, 1733)(441, 1734)(442, 1533)(443, 1534)(444, 1737)(445, 1613)(446, 1600)(447, 1537)(448, 1578)(449, 1577)(450, 1540)(451, 1622)(452, 1541)(453, 1743)(454, 1592)(455, 1745)(456, 1544)(457, 1747)(458, 1748)(459, 1619)(460, 1548)(461, 1751)(462, 1552)(463, 1632)(464, 1554)(465, 1755)(466, 1626)(467, 1591)(468, 1557)(469, 1731)(470, 1758)(471, 1560)(472, 1634)(473, 1605)(474, 1741)(475, 1563)(476, 1597)(477, 1565)(478, 1736)(479, 1569)(480, 1612)(481, 1573)(482, 1761)(483, 1633)(484, 1764)(485, 1576)(486, 1609)(487, 1629)(488, 1618)(489, 1767)(490, 1581)(491, 1582)(492, 1584)(493, 1615)(494, 1742)(495, 1586)(496, 1587)(497, 1750)(498, 1624)(499, 1590)(500, 1756)(501, 1772)(502, 1753)(503, 1620)(504, 1732)(505, 1599)(506, 1757)(507, 1601)(508, 1749)(509, 1603)(510, 1604)(511, 1746)(512, 1735)(513, 1607)(514, 1775)(515, 1740)(516, 1754)(517, 1611)(518, 1738)(519, 1744)(520, 1616)(521, 1763)(522, 1766)(523, 1628)(524, 1762)(525, 1759)(526, 1630)(527, 1768)(528, 1760)(529, 1635)(530, 1765)(531, 1669)(532, 1704)(533, 1640)(534, 1641)(535, 1712)(536, 1678)(537, 1644)(538, 1718)(539, 1782)(540, 1715)(541, 1674)(542, 1694)(543, 1653)(544, 1719)(545, 1655)(546, 1711)(547, 1657)(548, 1658)(549, 1708)(550, 1697)(551, 1661)(552, 1785)(553, 1702)(554, 1716)(555, 1665)(556, 1700)(557, 1706)(558, 1670)(559, 1725)(560, 1728)(561, 1682)(562, 1724)(563, 1721)(564, 1684)(565, 1730)(566, 1722)(567, 1689)(568, 1727)(569, 1783)(570, 1786)(571, 1789)(572, 1701)(573, 1779)(574, 1792)(575, 1714)(576, 1780)(577, 1790)(578, 1791)(579, 1773)(580, 1776)(581, 1793)(582, 1739)(583, 1769)(584, 1796)(585, 1752)(586, 1770)(587, 1794)(588, 1795)(589, 1771)(590, 1777)(591, 1778)(592, 1774)(593, 1781)(594, 1787)(595, 1788)(596, 1784)(597, 1800)(598, 1799)(599, 1798)(600, 1797)(601, 1801)(602, 1802)(603, 1803)(604, 1804)(605, 1805)(606, 1806)(607, 1807)(608, 1808)(609, 1809)(610, 1810)(611, 1811)(612, 1812)(613, 1813)(614, 1814)(615, 1815)(616, 1816)(617, 1817)(618, 1818)(619, 1819)(620, 1820)(621, 1821)(622, 1822)(623, 1823)(624, 1824)(625, 1825)(626, 1826)(627, 1827)(628, 1828)(629, 1829)(630, 1830)(631, 1831)(632, 1832)(633, 1833)(634, 1834)(635, 1835)(636, 1836)(637, 1837)(638, 1838)(639, 1839)(640, 1840)(641, 1841)(642, 1842)(643, 1843)(644, 1844)(645, 1845)(646, 1846)(647, 1847)(648, 1848)(649, 1849)(650, 1850)(651, 1851)(652, 1852)(653, 1853)(654, 1854)(655, 1855)(656, 1856)(657, 1857)(658, 1858)(659, 1859)(660, 1860)(661, 1861)(662, 1862)(663, 1863)(664, 1864)(665, 1865)(666, 1866)(667, 1867)(668, 1868)(669, 1869)(670, 1870)(671, 1871)(672, 1872)(673, 1873)(674, 1874)(675, 1875)(676, 1876)(677, 1877)(678, 1878)(679, 1879)(680, 1880)(681, 1881)(682, 1882)(683, 1883)(684, 1884)(685, 1885)(686, 1886)(687, 1887)(688, 1888)(689, 1889)(690, 1890)(691, 1891)(692, 1892)(693, 1893)(694, 1894)(695, 1895)(696, 1896)(697, 1897)(698, 1898)(699, 1899)(700, 1900)(701, 1901)(702, 1902)(703, 1903)(704, 1904)(705, 1905)(706, 1906)(707, 1907)(708, 1908)(709, 1909)(710, 1910)(711, 1911)(712, 1912)(713, 1913)(714, 1914)(715, 1915)(716, 1916)(717, 1917)(718, 1918)(719, 1919)(720, 1920)(721, 1921)(722, 1922)(723, 1923)(724, 1924)(725, 1925)(726, 1926)(727, 1927)(728, 1928)(729, 1929)(730, 1930)(731, 1931)(732, 1932)(733, 1933)(734, 1934)(735, 1935)(736, 1936)(737, 1937)(738, 1938)(739, 1939)(740, 1940)(741, 1941)(742, 1942)(743, 1943)(744, 1944)(745, 1945)(746, 1946)(747, 1947)(748, 1948)(749, 1949)(750, 1950)(751, 1951)(752, 1952)(753, 1953)(754, 1954)(755, 1955)(756, 1956)(757, 1957)(758, 1958)(759, 1959)(760, 1960)(761, 1961)(762, 1962)(763, 1963)(764, 1964)(765, 1965)(766, 1966)(767, 1967)(768, 1968)(769, 1969)(770, 1970)(771, 1971)(772, 1972)(773, 1973)(774, 1974)(775, 1975)(776, 1976)(777, 1977)(778, 1978)(779, 1979)(780, 1980)(781, 1981)(782, 1982)(783, 1983)(784, 1984)(785, 1985)(786, 1986)(787, 1987)(788, 1988)(789, 1989)(790, 1990)(791, 1991)(792, 1992)(793, 1993)(794, 1994)(795, 1995)(796, 1996)(797, 1997)(798, 1998)(799, 1999)(800, 2000)(801, 2001)(802, 2002)(803, 2003)(804, 2004)(805, 2005)(806, 2006)(807, 2007)(808, 2008)(809, 2009)(810, 2010)(811, 2011)(812, 2012)(813, 2013)(814, 2014)(815, 2015)(816, 2016)(817, 2017)(818, 2018)(819, 2019)(820, 2020)(821, 2021)(822, 2022)(823, 2023)(824, 2024)(825, 2025)(826, 2026)(827, 2027)(828, 2028)(829, 2029)(830, 2030)(831, 2031)(832, 2032)(833, 2033)(834, 2034)(835, 2035)(836, 2036)(837, 2037)(838, 2038)(839, 2039)(840, 2040)(841, 2041)(842, 2042)(843, 2043)(844, 2044)(845, 2045)(846, 2046)(847, 2047)(848, 2048)(849, 2049)(850, 2050)(851, 2051)(852, 2052)(853, 2053)(854, 2054)(855, 2055)(856, 2056)(857, 2057)(858, 2058)(859, 2059)(860, 2060)(861, 2061)(862, 2062)(863, 2063)(864, 2064)(865, 2065)(866, 2066)(867, 2067)(868, 2068)(869, 2069)(870, 2070)(871, 2071)(872, 2072)(873, 2073)(874, 2074)(875, 2075)(876, 2076)(877, 2077)(878, 2078)(879, 2079)(880, 2080)(881, 2081)(882, 2082)(883, 2083)(884, 2084)(885, 2085)(886, 2086)(887, 2087)(888, 2088)(889, 2089)(890, 2090)(891, 2091)(892, 2092)(893, 2093)(894, 2094)(895, 2095)(896, 2096)(897, 2097)(898, 2098)(899, 2099)(900, 2100)(901, 2101)(902, 2102)(903, 2103)(904, 2104)(905, 2105)(906, 2106)(907, 2107)(908, 2108)(909, 2109)(910, 2110)(911, 2111)(912, 2112)(913, 2113)(914, 2114)(915, 2115)(916, 2116)(917, 2117)(918, 2118)(919, 2119)(920, 2120)(921, 2121)(922, 2122)(923, 2123)(924, 2124)(925, 2125)(926, 2126)(927, 2127)(928, 2128)(929, 2129)(930, 2130)(931, 2131)(932, 2132)(933, 2133)(934, 2134)(935, 2135)(936, 2136)(937, 2137)(938, 2138)(939, 2139)(940, 2140)(941, 2141)(942, 2142)(943, 2143)(944, 2144)(945, 2145)(946, 2146)(947, 2147)(948, 2148)(949, 2149)(950, 2150)(951, 2151)(952, 2152)(953, 2153)(954, 2154)(955, 2155)(956, 2156)(957, 2157)(958, 2158)(959, 2159)(960, 2160)(961, 2161)(962, 2162)(963, 2163)(964, 2164)(965, 2165)(966, 2166)(967, 2167)(968, 2168)(969, 2169)(970, 2170)(971, 2171)(972, 2172)(973, 2173)(974, 2174)(975, 2175)(976, 2176)(977, 2177)(978, 2178)(979, 2179)(980, 2180)(981, 2181)(982, 2182)(983, 2183)(984, 2184)(985, 2185)(986, 2186)(987, 2187)(988, 2188)(989, 2189)(990, 2190)(991, 2191)(992, 2192)(993, 2193)(994, 2194)(995, 2195)(996, 2196)(997, 2197)(998, 2198)(999, 2199)(1000, 2200)(1001, 2201)(1002, 2202)(1003, 2203)(1004, 2204)(1005, 2205)(1006, 2206)(1007, 2207)(1008, 2208)(1009, 2209)(1010, 2210)(1011, 2211)(1012, 2212)(1013, 2213)(1014, 2214)(1015, 2215)(1016, 2216)(1017, 2217)(1018, 2218)(1019, 2219)(1020, 2220)(1021, 2221)(1022, 2222)(1023, 2223)(1024, 2224)(1025, 2225)(1026, 2226)(1027, 2227)(1028, 2228)(1029, 2229)(1030, 2230)(1031, 2231)(1032, 2232)(1033, 2233)(1034, 2234)(1035, 2235)(1036, 2236)(1037, 2237)(1038, 2238)(1039, 2239)(1040, 2240)(1041, 2241)(1042, 2242)(1043, 2243)(1044, 2244)(1045, 2245)(1046, 2246)(1047, 2247)(1048, 2248)(1049, 2249)(1050, 2250)(1051, 2251)(1052, 2252)(1053, 2253)(1054, 2254)(1055, 2255)(1056, 2256)(1057, 2257)(1058, 2258)(1059, 2259)(1060, 2260)(1061, 2261)(1062, 2262)(1063, 2263)(1064, 2264)(1065, 2265)(1066, 2266)(1067, 2267)(1068, 2268)(1069, 2269)(1070, 2270)(1071, 2271)(1072, 2272)(1073, 2273)(1074, 2274)(1075, 2275)(1076, 2276)(1077, 2277)(1078, 2278)(1079, 2279)(1080, 2280)(1081, 2281)(1082, 2282)(1083, 2283)(1084, 2284)(1085, 2285)(1086, 2286)(1087, 2287)(1088, 2288)(1089, 2289)(1090, 2290)(1091, 2291)(1092, 2292)(1093, 2293)(1094, 2294)(1095, 2295)(1096, 2296)(1097, 2297)(1098, 2298)(1099, 2299)(1100, 2300)(1101, 2301)(1102, 2302)(1103, 2303)(1104, 2304)(1105, 2305)(1106, 2306)(1107, 2307)(1108, 2308)(1109, 2309)(1110, 2310)(1111, 2311)(1112, 2312)(1113, 2313)(1114, 2314)(1115, 2315)(1116, 2316)(1117, 2317)(1118, 2318)(1119, 2319)(1120, 2320)(1121, 2321)(1122, 2322)(1123, 2323)(1124, 2324)(1125, 2325)(1126, 2326)(1127, 2327)(1128, 2328)(1129, 2329)(1130, 2330)(1131, 2331)(1132, 2332)(1133, 2333)(1134, 2334)(1135, 2335)(1136, 2336)(1137, 2337)(1138, 2338)(1139, 2339)(1140, 2340)(1141, 2341)(1142, 2342)(1143, 2343)(1144, 2344)(1145, 2345)(1146, 2346)(1147, 2347)(1148, 2348)(1149, 2349)(1150, 2350)(1151, 2351)(1152, 2352)(1153, 2353)(1154, 2354)(1155, 2355)(1156, 2356)(1157, 2357)(1158, 2358)(1159, 2359)(1160, 2360)(1161, 2361)(1162, 2362)(1163, 2363)(1164, 2364)(1165, 2365)(1166, 2366)(1167, 2367)(1168, 2368)(1169, 2369)(1170, 2370)(1171, 2371)(1172, 2372)(1173, 2373)(1174, 2374)(1175, 2375)(1176, 2376)(1177, 2377)(1178, 2378)(1179, 2379)(1180, 2380)(1181, 2381)(1182, 2382)(1183, 2383)(1184, 2384)(1185, 2385)(1186, 2386)(1187, 2387)(1188, 2388)(1189, 2389)(1190, 2390)(1191, 2391)(1192, 2392)(1193, 2393)(1194, 2394)(1195, 2395)(1196, 2396)(1197, 2397)(1198, 2398)(1199, 2399)(1200, 2400) local type(s) :: { ( 2, 10, 2, 10 ), ( 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E16.1296 Graph:: bipartite v = 450 e = 1200 f = 720 degree seq :: [ 4^300, 8^150 ] E16.1294 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5}) Quotient :: dipole Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, Y1^4, (R * Y1)^2, R * Y2 * R * Y3, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y2^5, Y2^-2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y2 * Y1^-1)^6, Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2 * Y1^-1 * Y2^-2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y1^-1 * Y2^-2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, Y2 * Y1^-1 * Y2^-2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1^-2 * Y2^-2 * Y1 * Y2^-2 * Y1^-2, Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^-2 * Y1^-2 * Y2^-2 * Y1^-1 * Y2 * Y1^-1 ] Map:: R = (1, 601, 2, 602, 6, 606, 4, 604)(3, 603, 9, 609, 21, 621, 11, 611)(5, 605, 13, 613, 18, 618, 7, 607)(8, 608, 19, 619, 32, 632, 15, 615)(10, 610, 23, 623, 44, 644, 24, 624)(12, 612, 16, 616, 33, 633, 27, 627)(14, 614, 30, 630, 53, 653, 28, 628)(17, 617, 35, 635, 63, 663, 36, 636)(20, 620, 40, 640, 69, 669, 38, 638)(22, 622, 43, 643, 74, 674, 41, 641)(25, 625, 42, 642, 75, 675, 48, 648)(26, 626, 49, 649, 86, 686, 50, 650)(29, 629, 54, 654, 67, 667, 37, 637)(31, 631, 57, 657, 98, 698, 58, 658)(34, 634, 62, 662, 104, 704, 60, 660)(39, 639, 70, 670, 102, 702, 59, 659)(45, 645, 80, 680, 132, 732, 78, 678)(46, 646, 79, 679, 133, 733, 82, 682)(47, 647, 83, 683, 139, 739, 84, 684)(51, 651, 61, 661, 105, 705, 90, 690)(52, 652, 91, 691, 150, 750, 92, 692)(55, 655, 96, 696, 156, 756, 94, 694)(56, 656, 97, 697, 154, 754, 93, 693)(64, 664, 110, 710, 176, 776, 108, 708)(65, 665, 109, 709, 177, 777, 112, 712)(66, 666, 113, 713, 183, 783, 114, 714)(68, 668, 116, 716, 187, 787, 117, 717)(71, 671, 121, 721, 193, 793, 119, 719)(72, 672, 122, 722, 191, 791, 118, 718)(73, 673, 123, 723, 197, 797, 124, 724)(76, 676, 128, 728, 203, 803, 126, 726)(77, 677, 129, 729, 201, 801, 125, 725)(81, 681, 136, 736, 217, 817, 137, 737)(85, 685, 127, 727, 167, 767, 120, 720)(87, 687, 145, 745, 227, 827, 143, 743)(88, 688, 144, 744, 228, 828, 146, 746)(89, 689, 147, 747, 232, 832, 148, 748)(95, 695, 149, 749, 172, 772, 115, 715)(99, 699, 162, 762, 251, 851, 160, 760)(100, 700, 161, 761, 252, 852, 164, 764)(101, 701, 165, 765, 258, 858, 166, 766)(103, 703, 168, 768, 262, 862, 169, 769)(106, 706, 173, 773, 268, 868, 171, 771)(107, 707, 174, 774, 266, 866, 170, 770)(111, 711, 180, 780, 280, 880, 181, 781)(130, 730, 208, 808, 317, 917, 206, 806)(131, 731, 209, 809, 320, 920, 210, 810)(134, 734, 214, 814, 326, 926, 212, 812)(135, 735, 215, 815, 324, 924, 211, 811)(138, 738, 213, 813, 310, 910, 207, 807)(140, 740, 223, 823, 337, 937, 221, 821)(141, 741, 222, 822, 338, 938, 224, 824)(142, 742, 194, 794, 300, 900, 225, 825)(151, 751, 238, 838, 358, 958, 236, 836)(152, 752, 237, 837, 359, 959, 240, 840)(153, 753, 241, 841, 364, 964, 242, 842)(155, 755, 244, 844, 368, 968, 245, 845)(157, 757, 247, 847, 356, 956, 235, 835)(158, 758, 248, 848, 372, 972, 246, 846)(159, 759, 182, 782, 276, 876, 243, 843)(163, 763, 255, 855, 384, 984, 256, 856)(175, 775, 272, 872, 407, 1007, 273, 873)(178, 778, 277, 877, 413, 1013, 275, 875)(179, 779, 278, 878, 411, 1011, 274, 874)(184, 784, 286, 886, 424, 1024, 284, 884)(185, 785, 285, 885, 425, 1025, 287, 887)(186, 786, 269, 869, 404, 1004, 288, 888)(188, 788, 291, 891, 431, 1031, 289, 889)(189, 789, 290, 890, 432, 1032, 293, 893)(190, 790, 294, 894, 437, 1037, 295, 895)(192, 792, 297, 897, 441, 1041, 298, 898)(195, 795, 301, 901, 445, 1045, 299, 899)(196, 796, 257, 857, 380, 980, 296, 896)(198, 798, 305, 905, 450, 1050, 303, 903)(199, 799, 304, 904, 451, 1051, 307, 907)(200, 800, 308, 908, 454, 1054, 309, 909)(202, 802, 311, 911, 458, 1058, 312, 912)(204, 804, 314, 914, 392, 992, 261, 861)(205, 805, 315, 915, 462, 1062, 313, 913)(216, 816, 330, 930, 386, 986, 329, 929)(218, 818, 333, 933, 396, 996, 331, 931)(219, 819, 332, 932, 383, 983, 334, 934)(220, 820, 318, 918, 465, 1065, 335, 935)(226, 826, 343, 943, 482, 1082, 344, 944)(229, 829, 348, 948, 488, 1088, 346, 946)(230, 830, 349, 949, 486, 1086, 345, 945)(231, 831, 347, 947, 400, 1000, 271, 871)(233, 833, 354, 954, 468, 1068, 352, 952)(234, 834, 353, 953, 479, 1079, 355, 955)(239, 839, 362, 962, 385, 985, 363, 963)(249, 849, 375, 975, 422, 1022, 283, 883)(250, 850, 376, 976, 503, 1103, 377, 977)(253, 853, 381, 981, 509, 1109, 379, 979)(254, 854, 382, 982, 507, 1107, 378, 978)(259, 859, 390, 990, 513, 1113, 388, 988)(260, 860, 389, 989, 514, 1114, 391, 991)(263, 863, 395, 995, 520, 1120, 393, 993)(264, 864, 394, 994, 521, 1121, 397, 997)(265, 865, 398, 998, 524, 1124, 399, 999)(267, 867, 401, 1001, 528, 1128, 402, 1002)(270, 870, 405, 1005, 532, 1132, 403, 1003)(279, 879, 417, 1017, 316, 916, 416, 1016)(281, 881, 420, 1020, 306, 906, 418, 1018)(282, 882, 419, 1019, 350, 950, 421, 1021)(292, 892, 435, 1035, 319, 919, 436, 1036)(302, 902, 448, 1048, 496, 1096, 387, 987)(321, 921, 430, 1030, 544, 1144, 466, 1066)(322, 922, 467, 1067, 559, 1159, 469, 1069)(323, 923, 470, 1070, 546, 1146, 433, 1033)(325, 925, 471, 1071, 547, 1147, 438, 1038)(327, 927, 440, 1040, 510, 1110, 457, 1057)(328, 928, 473, 1073, 515, 1115, 472, 1072)(336, 936, 409, 1009, 536, 1136, 476, 1076)(339, 939, 477, 1077, 511, 1111, 427, 1027)(340, 940, 478, 1078, 539, 1139, 415, 1015)(341, 941, 429, 1029, 533, 1133, 464, 1064)(342, 942, 446, 1046, 534, 1134, 481, 1081)(351, 951, 406, 1006, 474, 1074, 491, 1091)(357, 957, 493, 1093, 565, 1165, 483, 1083)(360, 960, 485, 1085, 567, 1167, 495, 1095)(361, 961, 442, 1042, 549, 1149, 494, 1094)(365, 965, 487, 1087, 568, 1168, 497, 1097)(366, 966, 498, 1098, 531, 1131, 443, 1043)(367, 967, 414, 1014, 527, 1127, 489, 1089)(369, 969, 499, 1099, 554, 1154, 453, 1053)(370, 970, 456, 1056, 550, 1150, 444, 1044)(371, 971, 460, 1060, 526, 1126, 500, 1100)(373, 973, 447, 1047, 517, 1117, 492, 1092)(374, 974, 428, 1028, 518, 1118, 463, 1063)(408, 1008, 519, 1119, 578, 1178, 535, 1135)(410, 1010, 537, 1137, 580, 1180, 522, 1122)(412, 1012, 538, 1138, 581, 1181, 525, 1125)(423, 1023, 505, 1105, 575, 1175, 541, 1141)(426, 1026, 542, 1142, 490, 1090, 516, 1116)(434, 1034, 529, 1129, 572, 1172, 545, 1145)(439, 1039, 548, 1148, 461, 1061, 530, 1130)(449, 1049, 553, 1153, 574, 1174, 504, 1104)(452, 1052, 506, 1106, 576, 1176, 555, 1155)(455, 1055, 508, 1108, 577, 1177, 556, 1156)(459, 1059, 557, 1157, 579, 1179, 523, 1123)(475, 1075, 543, 1143, 501, 1101, 552, 1152)(480, 1080, 540, 1140, 502, 1102, 551, 1151)(484, 1084, 566, 1166, 563, 1163, 512, 1112)(558, 1158, 587, 1187, 596, 1196, 591, 1191)(560, 1160, 592, 1192, 573, 1173, 585, 1185)(561, 1161, 593, 1193, 598, 1198, 584, 1184)(562, 1162, 594, 1194, 600, 1200, 589, 1189)(564, 1164, 583, 1183, 570, 1170, 590, 1190)(569, 1169, 582, 1182, 599, 1199, 595, 1195)(571, 1171, 586, 1186, 597, 1197, 588, 1188)(1201, 1801, 1203, 1803, 1210, 1810, 1214, 1814, 1205, 1805)(1202, 1802, 1207, 1807, 1217, 1817, 1220, 1820, 1208, 1808)(1204, 1804, 1212, 1812, 1226, 1826, 1222, 1822, 1209, 1809)(1206, 1806, 1215, 1815, 1231, 1831, 1234, 1834, 1216, 1816)(1211, 1811, 1225, 1825, 1247, 1847, 1245, 1845, 1223, 1823)(1213, 1813, 1228, 1828, 1252, 1852, 1255, 1855, 1229, 1829)(1218, 1818, 1237, 1837, 1266, 1866, 1264, 1864, 1235, 1835)(1219, 1819, 1238, 1838, 1268, 1868, 1271, 1871, 1239, 1839)(1221, 1821, 1241, 1841, 1273, 1873, 1276, 1876, 1242, 1842)(1224, 1824, 1246, 1846, 1281, 1881, 1256, 1856, 1230, 1830)(1227, 1827, 1251, 1851, 1289, 1889, 1287, 1887, 1249, 1849)(1232, 1832, 1259, 1859, 1301, 1901, 1299, 1899, 1257, 1857)(1233, 1833, 1260, 1860, 1303, 1903, 1306, 1906, 1261, 1861)(1236, 1836, 1265, 1865, 1311, 1911, 1272, 1872, 1240, 1840)(1243, 1843, 1250, 1850, 1288, 1888, 1330, 1930, 1277, 1877)(1244, 1844, 1278, 1878, 1331, 1931, 1334, 1934, 1279, 1879)(1248, 1848, 1285, 1885, 1342, 1942, 1340, 1940, 1283, 1883)(1253, 1853, 1293, 1893, 1353, 1953, 1351, 1951, 1291, 1891)(1254, 1854, 1294, 1894, 1355, 1955, 1357, 1957, 1295, 1895)(1258, 1858, 1300, 1900, 1363, 1963, 1307, 1907, 1262, 1862)(1263, 1863, 1308, 1908, 1375, 1975, 1378, 1978, 1309, 1909)(1267, 1867, 1315, 1915, 1386, 1986, 1384, 1984, 1313, 1913)(1269, 1869, 1318, 1918, 1390, 1990, 1388, 1988, 1316, 1916)(1270, 1870, 1319, 1919, 1392, 1992, 1394, 1994, 1320, 1920)(1274, 1874, 1325, 1925, 1400, 2000, 1398, 1998, 1323, 1923)(1275, 1875, 1326, 1926, 1402, 2002, 1404, 2004, 1327, 1927)(1280, 1880, 1284, 1884, 1341, 1941, 1416, 2016, 1335, 1935)(1282, 1882, 1338, 1938, 1420, 2020, 1418, 2018, 1336, 1936)(1286, 1886, 1343, 1943, 1426, 2026, 1429, 2029, 1344, 1944)(1290, 1890, 1349, 1949, 1435, 2035, 1433, 2033, 1347, 1947)(1292, 1892, 1352, 1952, 1439, 2039, 1358, 1958, 1296, 1896)(1297, 1897, 1337, 1937, 1419, 2019, 1449, 2049, 1359, 1959)(1298, 1898, 1360, 1960, 1450, 2050, 1453, 2053, 1361, 1961)(1302, 1902, 1367, 1967, 1461, 2061, 1459, 2059, 1365, 1965)(1304, 1904, 1370, 1970, 1465, 2065, 1463, 2063, 1368, 1968)(1305, 1905, 1371, 1971, 1467, 2067, 1469, 2069, 1372, 1972)(1310, 1910, 1314, 1914, 1385, 1985, 1479, 2079, 1379, 1979)(1312, 1912, 1382, 1982, 1483, 2083, 1481, 2081, 1380, 1980)(1317, 1917, 1389, 1989, 1492, 2092, 1395, 1995, 1321, 1921)(1322, 1922, 1381, 1981, 1482, 2082, 1502, 2102, 1396, 1996)(1324, 1924, 1399, 1999, 1506, 2106, 1405, 2005, 1328, 1928)(1329, 1929, 1406, 2006, 1516, 2116, 1518, 2118, 1407, 2007)(1332, 1932, 1411, 2011, 1523, 2123, 1521, 2121, 1409, 2009)(1333, 1933, 1412, 2012, 1525, 2125, 1527, 2127, 1413, 2013)(1339, 1939, 1421, 2021, 1536, 2136, 1539, 2139, 1422, 2022)(1345, 1945, 1348, 1948, 1434, 2034, 1550, 2150, 1430, 2030)(1346, 1946, 1431, 2031, 1551, 2151, 1519, 2119, 1408, 2008)(1350, 1950, 1436, 2036, 1557, 2157, 1560, 2160, 1437, 2037)(1354, 1954, 1443, 2043, 1567, 2167, 1565, 2165, 1441, 2041)(1356, 1956, 1446, 2046, 1571, 2171, 1569, 2169, 1444, 2044)(1362, 1962, 1366, 1966, 1460, 2060, 1583, 2183, 1454, 2054)(1364, 1964, 1457, 2057, 1587, 2187, 1585, 2185, 1455, 2055)(1369, 1969, 1464, 2064, 1596, 2196, 1470, 2070, 1373, 1973)(1374, 1974, 1456, 2056, 1586, 2186, 1606, 2206, 1471, 2071)(1376, 1976, 1474, 2074, 1610, 2210, 1608, 2208, 1472, 2072)(1377, 1977, 1475, 2075, 1612, 2212, 1614, 2214, 1476, 2076)(1383, 1983, 1484, 2084, 1623, 2223, 1626, 2226, 1485, 2085)(1387, 1987, 1489, 2089, 1630, 2230, 1633, 2233, 1490, 2090)(1391, 1991, 1496, 2096, 1640, 2240, 1638, 2238, 1494, 2094)(1393, 1993, 1499, 2099, 1644, 2244, 1642, 2242, 1497, 2097)(1397, 1997, 1503, 2103, 1649, 2249, 1652, 2252, 1504, 2104)(1401, 2001, 1510, 2110, 1657, 2257, 1655, 2255, 1508, 2108)(1403, 2003, 1513, 2113, 1661, 2261, 1659, 2259, 1511, 2111)(1410, 2010, 1522, 2122, 1668, 2268, 1528, 2128, 1414, 2014)(1415, 2015, 1529, 2129, 1584, 2184, 1562, 2162, 1440, 2040)(1417, 2017, 1531, 2131, 1597, 2197, 1582, 2182, 1532, 2132)(1423, 2023, 1425, 2025, 1542, 2142, 1679, 2279, 1540, 2140)(1424, 2024, 1541, 2141, 1680, 2280, 1674, 2274, 1530, 2130)(1427, 2027, 1545, 2145, 1685, 2285, 1683, 2283, 1543, 2143)(1428, 2028, 1546, 2146, 1687, 2287, 1689, 2289, 1547, 2147)(1432, 2032, 1552, 2152, 1669, 2269, 1678, 2278, 1553, 2153)(1438, 2038, 1442, 2042, 1566, 2166, 1641, 2241, 1561, 2161)(1445, 2045, 1570, 2170, 1645, 2245, 1573, 2173, 1447, 2047)(1448, 2048, 1563, 2163, 1696, 2296, 1701, 2301, 1574, 2174)(1451, 2051, 1578, 2178, 1706, 2306, 1704, 2304, 1576, 2176)(1452, 2052, 1579, 2179, 1708, 2308, 1710, 2310, 1580, 2180)(1458, 2058, 1588, 2188, 1712, 2312, 1715, 2315, 1589, 2189)(1462, 2062, 1593, 2193, 1719, 2319, 1722, 2322, 1594, 2194)(1466, 2066, 1600, 2200, 1727, 2327, 1725, 2325, 1598, 2198)(1468, 2068, 1603, 2203, 1731, 2331, 1729, 2329, 1601, 2201)(1473, 2073, 1609, 2209, 1537, 2137, 1615, 2215, 1477, 2077)(1478, 2078, 1616, 2216, 1517, 2117, 1635, 2235, 1493, 2093)(1480, 2080, 1618, 2218, 1507, 2107, 1549, 2149, 1619, 2219)(1486, 2086, 1488, 2088, 1629, 2229, 1538, 2138, 1627, 2227)(1487, 2087, 1628, 2228, 1743, 2343, 1665, 2265, 1617, 2217)(1491, 2091, 1495, 2095, 1639, 2239, 1728, 2328, 1634, 2234)(1498, 2098, 1643, 2243, 1732, 2332, 1646, 2246, 1500, 2100)(1501, 2101, 1636, 2236, 1691, 2291, 1751, 2351, 1647, 2247)(1505, 2105, 1509, 2109, 1656, 2256, 1568, 2168, 1653, 2253)(1512, 2112, 1660, 2260, 1572, 2172, 1663, 2263, 1514, 2114)(1515, 2115, 1620, 2220, 1622, 2222, 1740, 2340, 1664, 2264)(1520, 2120, 1666, 2266, 1758, 2358, 1760, 2360, 1667, 2267)(1524, 2124, 1559, 2159, 1695, 2295, 1761, 2361, 1670, 2270)(1526, 2126, 1672, 2272, 1763, 2363, 1762, 2362, 1671, 2271)(1533, 2133, 1535, 2135, 1675, 2275, 1734, 2334, 1605, 2205)(1534, 2134, 1591, 2191, 1717, 2317, 1702, 2302, 1575, 2175)(1544, 2144, 1684, 2284, 1713, 2313, 1690, 2290, 1548, 2148)(1554, 2154, 1556, 2156, 1692, 2292, 1714, 2314, 1673, 2273)(1555, 2155, 1681, 2281, 1752, 2352, 1648, 2248, 1621, 2221)(1558, 2158, 1694, 2294, 1770, 2370, 1769, 2369, 1693, 2293)(1564, 2164, 1697, 2297, 1771, 2371, 1772, 2372, 1698, 2298)(1577, 2177, 1705, 2305, 1624, 2224, 1711, 2311, 1581, 2181)(1590, 2190, 1592, 2192, 1718, 2318, 1625, 2225, 1716, 2316)(1595, 2195, 1599, 2199, 1726, 2326, 1658, 2258, 1723, 2323)(1602, 2202, 1730, 2330, 1662, 2262, 1733, 2333, 1604, 2204)(1607, 2207, 1735, 2335, 1782, 2382, 1783, 2383, 1736, 2336)(1611, 2211, 1632, 2232, 1746, 2346, 1784, 2384, 1737, 2337)(1613, 2213, 1739, 2339, 1759, 2359, 1785, 2385, 1738, 2338)(1631, 2231, 1745, 2345, 1788, 2388, 1787, 2387, 1744, 2344)(1637, 2237, 1747, 2347, 1789, 2389, 1757, 2357, 1748, 2348)(1650, 2250, 1754, 2354, 1792, 2392, 1791, 2391, 1753, 2353)(1651, 2251, 1755, 2355, 1793, 2393, 1767, 2367, 1686, 2286)(1654, 2254, 1756, 2356, 1790, 2390, 1749, 2349, 1750, 2350)(1676, 2276, 1764, 2364, 1777, 2377, 1709, 2309, 1677, 2277)(1682, 2282, 1765, 2365, 1795, 2395, 1794, 2394, 1766, 2366)(1688, 2288, 1742, 2342, 1741, 2341, 1786, 2386, 1768, 2368)(1699, 2299, 1700, 2300, 1724, 2324, 1781, 2381, 1773, 2373)(1703, 2303, 1774, 2374, 1796, 2396, 1797, 2397, 1775, 2375)(1707, 2307, 1721, 2321, 1780, 2380, 1798, 2398, 1776, 2376)(1720, 2320, 1779, 2379, 1800, 2400, 1799, 2399, 1778, 2378) L = (1, 1203)(2, 1207)(3, 1210)(4, 1212)(5, 1201)(6, 1215)(7, 1217)(8, 1202)(9, 1204)(10, 1214)(11, 1225)(12, 1226)(13, 1228)(14, 1205)(15, 1231)(16, 1206)(17, 1220)(18, 1237)(19, 1238)(20, 1208)(21, 1241)(22, 1209)(23, 1211)(24, 1246)(25, 1247)(26, 1222)(27, 1251)(28, 1252)(29, 1213)(30, 1224)(31, 1234)(32, 1259)(33, 1260)(34, 1216)(35, 1218)(36, 1265)(37, 1266)(38, 1268)(39, 1219)(40, 1236)(41, 1273)(42, 1221)(43, 1250)(44, 1278)(45, 1223)(46, 1281)(47, 1245)(48, 1285)(49, 1227)(50, 1288)(51, 1289)(52, 1255)(53, 1293)(54, 1294)(55, 1229)(56, 1230)(57, 1232)(58, 1300)(59, 1301)(60, 1303)(61, 1233)(62, 1258)(63, 1308)(64, 1235)(65, 1311)(66, 1264)(67, 1315)(68, 1271)(69, 1318)(70, 1319)(71, 1239)(72, 1240)(73, 1276)(74, 1325)(75, 1326)(76, 1242)(77, 1243)(78, 1331)(79, 1244)(80, 1284)(81, 1256)(82, 1338)(83, 1248)(84, 1341)(85, 1342)(86, 1343)(87, 1249)(88, 1330)(89, 1287)(90, 1349)(91, 1253)(92, 1352)(93, 1353)(94, 1355)(95, 1254)(96, 1292)(97, 1337)(98, 1360)(99, 1257)(100, 1363)(101, 1299)(102, 1367)(103, 1306)(104, 1370)(105, 1371)(106, 1261)(107, 1262)(108, 1375)(109, 1263)(110, 1314)(111, 1272)(112, 1382)(113, 1267)(114, 1385)(115, 1386)(116, 1269)(117, 1389)(118, 1390)(119, 1392)(120, 1270)(121, 1317)(122, 1381)(123, 1274)(124, 1399)(125, 1400)(126, 1402)(127, 1275)(128, 1324)(129, 1406)(130, 1277)(131, 1334)(132, 1411)(133, 1412)(134, 1279)(135, 1280)(136, 1282)(137, 1419)(138, 1420)(139, 1421)(140, 1283)(141, 1416)(142, 1340)(143, 1426)(144, 1286)(145, 1348)(146, 1431)(147, 1290)(148, 1434)(149, 1435)(150, 1436)(151, 1291)(152, 1439)(153, 1351)(154, 1443)(155, 1357)(156, 1446)(157, 1295)(158, 1296)(159, 1297)(160, 1450)(161, 1298)(162, 1366)(163, 1307)(164, 1457)(165, 1302)(166, 1460)(167, 1461)(168, 1304)(169, 1464)(170, 1465)(171, 1467)(172, 1305)(173, 1369)(174, 1456)(175, 1378)(176, 1474)(177, 1475)(178, 1309)(179, 1310)(180, 1312)(181, 1482)(182, 1483)(183, 1484)(184, 1313)(185, 1479)(186, 1384)(187, 1489)(188, 1316)(189, 1492)(190, 1388)(191, 1496)(192, 1394)(193, 1499)(194, 1320)(195, 1321)(196, 1322)(197, 1503)(198, 1323)(199, 1506)(200, 1398)(201, 1510)(202, 1404)(203, 1513)(204, 1327)(205, 1328)(206, 1516)(207, 1329)(208, 1346)(209, 1332)(210, 1522)(211, 1523)(212, 1525)(213, 1333)(214, 1410)(215, 1529)(216, 1335)(217, 1531)(218, 1336)(219, 1449)(220, 1418)(221, 1536)(222, 1339)(223, 1425)(224, 1541)(225, 1542)(226, 1429)(227, 1545)(228, 1546)(229, 1344)(230, 1345)(231, 1551)(232, 1552)(233, 1347)(234, 1550)(235, 1433)(236, 1557)(237, 1350)(238, 1442)(239, 1358)(240, 1415)(241, 1354)(242, 1566)(243, 1567)(244, 1356)(245, 1570)(246, 1571)(247, 1445)(248, 1563)(249, 1359)(250, 1453)(251, 1578)(252, 1579)(253, 1361)(254, 1362)(255, 1364)(256, 1586)(257, 1587)(258, 1588)(259, 1365)(260, 1583)(261, 1459)(262, 1593)(263, 1368)(264, 1596)(265, 1463)(266, 1600)(267, 1469)(268, 1603)(269, 1372)(270, 1373)(271, 1374)(272, 1376)(273, 1609)(274, 1610)(275, 1612)(276, 1377)(277, 1473)(278, 1616)(279, 1379)(280, 1618)(281, 1380)(282, 1502)(283, 1481)(284, 1623)(285, 1383)(286, 1488)(287, 1628)(288, 1629)(289, 1630)(290, 1387)(291, 1495)(292, 1395)(293, 1478)(294, 1391)(295, 1639)(296, 1640)(297, 1393)(298, 1643)(299, 1644)(300, 1498)(301, 1636)(302, 1396)(303, 1649)(304, 1397)(305, 1509)(306, 1405)(307, 1549)(308, 1401)(309, 1656)(310, 1657)(311, 1403)(312, 1660)(313, 1661)(314, 1512)(315, 1620)(316, 1518)(317, 1635)(318, 1407)(319, 1408)(320, 1666)(321, 1409)(322, 1668)(323, 1521)(324, 1559)(325, 1527)(326, 1672)(327, 1413)(328, 1414)(329, 1584)(330, 1424)(331, 1597)(332, 1417)(333, 1535)(334, 1591)(335, 1675)(336, 1539)(337, 1615)(338, 1627)(339, 1422)(340, 1423)(341, 1680)(342, 1679)(343, 1427)(344, 1684)(345, 1685)(346, 1687)(347, 1428)(348, 1544)(349, 1619)(350, 1430)(351, 1519)(352, 1669)(353, 1432)(354, 1556)(355, 1681)(356, 1692)(357, 1560)(358, 1694)(359, 1695)(360, 1437)(361, 1438)(362, 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2282)(1083, 2283)(1084, 2284)(1085, 2285)(1086, 2286)(1087, 2287)(1088, 2288)(1089, 2289)(1090, 2290)(1091, 2291)(1092, 2292)(1093, 2293)(1094, 2294)(1095, 2295)(1096, 2296)(1097, 2297)(1098, 2298)(1099, 2299)(1100, 2300)(1101, 2301)(1102, 2302)(1103, 2303)(1104, 2304)(1105, 2305)(1106, 2306)(1107, 2307)(1108, 2308)(1109, 2309)(1110, 2310)(1111, 2311)(1112, 2312)(1113, 2313)(1114, 2314)(1115, 2315)(1116, 2316)(1117, 2317)(1118, 2318)(1119, 2319)(1120, 2320)(1121, 2321)(1122, 2322)(1123, 2323)(1124, 2324)(1125, 2325)(1126, 2326)(1127, 2327)(1128, 2328)(1129, 2329)(1130, 2330)(1131, 2331)(1132, 2332)(1133, 2333)(1134, 2334)(1135, 2335)(1136, 2336)(1137, 2337)(1138, 2338)(1139, 2339)(1140, 2340)(1141, 2341)(1142, 2342)(1143, 2343)(1144, 2344)(1145, 2345)(1146, 2346)(1147, 2347)(1148, 2348)(1149, 2349)(1150, 2350)(1151, 2351)(1152, 2352)(1153, 2353)(1154, 2354)(1155, 2355)(1156, 2356)(1157, 2357)(1158, 2358)(1159, 2359)(1160, 2360)(1161, 2361)(1162, 2362)(1163, 2363)(1164, 2364)(1165, 2365)(1166, 2366)(1167, 2367)(1168, 2368)(1169, 2369)(1170, 2370)(1171, 2371)(1172, 2372)(1173, 2373)(1174, 2374)(1175, 2375)(1176, 2376)(1177, 2377)(1178, 2378)(1179, 2379)(1180, 2380)(1181, 2381)(1182, 2382)(1183, 2383)(1184, 2384)(1185, 2385)(1186, 2386)(1187, 2387)(1188, 2388)(1189, 2389)(1190, 2390)(1191, 2391)(1192, 2392)(1193, 2393)(1194, 2394)(1195, 2395)(1196, 2396)(1197, 2397)(1198, 2398)(1199, 2399)(1200, 2400) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E16.1295 Graph:: bipartite v = 270 e = 1200 f = 900 degree seq :: [ 8^150, 10^120 ] E16.1295 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5}) Quotient :: dipole Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^5, (R * Y2 * Y3^-1)^2, (Y2 * Y3^-1)^4, (Y3^-1 * Y1^-1)^5, (Y2 * Y3^-2)^6, Y3^-1 * Y2 * Y3^-2 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1, (Y3 * Y2 * Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-2 * Y2 * Y3^-1 * Y2)^2 ] Map:: polytopal R = (1, 601)(2, 602)(3, 603)(4, 604)(5, 605)(6, 606)(7, 607)(8, 608)(9, 609)(10, 610)(11, 611)(12, 612)(13, 613)(14, 614)(15, 615)(16, 616)(17, 617)(18, 618)(19, 619)(20, 620)(21, 621)(22, 622)(23, 623)(24, 624)(25, 625)(26, 626)(27, 627)(28, 628)(29, 629)(30, 630)(31, 631)(32, 632)(33, 633)(34, 634)(35, 635)(36, 636)(37, 637)(38, 638)(39, 639)(40, 640)(41, 641)(42, 642)(43, 643)(44, 644)(45, 645)(46, 646)(47, 647)(48, 648)(49, 649)(50, 650)(51, 651)(52, 652)(53, 653)(54, 654)(55, 655)(56, 656)(57, 657)(58, 658)(59, 659)(60, 660)(61, 661)(62, 662)(63, 663)(64, 664)(65, 665)(66, 666)(67, 667)(68, 668)(69, 669)(70, 670)(71, 671)(72, 672)(73, 673)(74, 674)(75, 675)(76, 676)(77, 677)(78, 678)(79, 679)(80, 680)(81, 681)(82, 682)(83, 683)(84, 684)(85, 685)(86, 686)(87, 687)(88, 688)(89, 689)(90, 690)(91, 691)(92, 692)(93, 693)(94, 694)(95, 695)(96, 696)(97, 697)(98, 698)(99, 699)(100, 700)(101, 701)(102, 702)(103, 703)(104, 704)(105, 705)(106, 706)(107, 707)(108, 708)(109, 709)(110, 710)(111, 711)(112, 712)(113, 713)(114, 714)(115, 715)(116, 716)(117, 717)(118, 718)(119, 719)(120, 720)(121, 721)(122, 722)(123, 723)(124, 724)(125, 725)(126, 726)(127, 727)(128, 728)(129, 729)(130, 730)(131, 731)(132, 732)(133, 733)(134, 734)(135, 735)(136, 736)(137, 737)(138, 738)(139, 739)(140, 740)(141, 741)(142, 742)(143, 743)(144, 744)(145, 745)(146, 746)(147, 747)(148, 748)(149, 749)(150, 750)(151, 751)(152, 752)(153, 753)(154, 754)(155, 755)(156, 756)(157, 757)(158, 758)(159, 759)(160, 760)(161, 761)(162, 762)(163, 763)(164, 764)(165, 765)(166, 766)(167, 767)(168, 768)(169, 769)(170, 770)(171, 771)(172, 772)(173, 773)(174, 774)(175, 775)(176, 776)(177, 777)(178, 778)(179, 779)(180, 780)(181, 781)(182, 782)(183, 783)(184, 784)(185, 785)(186, 786)(187, 787)(188, 788)(189, 789)(190, 790)(191, 791)(192, 792)(193, 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893)(294, 894)(295, 895)(296, 896)(297, 897)(298, 898)(299, 899)(300, 900)(301, 901)(302, 902)(303, 903)(304, 904)(305, 905)(306, 906)(307, 907)(308, 908)(309, 909)(310, 910)(311, 911)(312, 912)(313, 913)(314, 914)(315, 915)(316, 916)(317, 917)(318, 918)(319, 919)(320, 920)(321, 921)(322, 922)(323, 923)(324, 924)(325, 925)(326, 926)(327, 927)(328, 928)(329, 929)(330, 930)(331, 931)(332, 932)(333, 933)(334, 934)(335, 935)(336, 936)(337, 937)(338, 938)(339, 939)(340, 940)(341, 941)(342, 942)(343, 943)(344, 944)(345, 945)(346, 946)(347, 947)(348, 948)(349, 949)(350, 950)(351, 951)(352, 952)(353, 953)(354, 954)(355, 955)(356, 956)(357, 957)(358, 958)(359, 959)(360, 960)(361, 961)(362, 962)(363, 963)(364, 964)(365, 965)(366, 966)(367, 967)(368, 968)(369, 969)(370, 970)(371, 971)(372, 972)(373, 973)(374, 974)(375, 975)(376, 976)(377, 977)(378, 978)(379, 979)(380, 980)(381, 981)(382, 982)(383, 983)(384, 984)(385, 985)(386, 986)(387, 987)(388, 988)(389, 989)(390, 990)(391, 991)(392, 992)(393, 993)(394, 994)(395, 995)(396, 996)(397, 997)(398, 998)(399, 999)(400, 1000)(401, 1001)(402, 1002)(403, 1003)(404, 1004)(405, 1005)(406, 1006)(407, 1007)(408, 1008)(409, 1009)(410, 1010)(411, 1011)(412, 1012)(413, 1013)(414, 1014)(415, 1015)(416, 1016)(417, 1017)(418, 1018)(419, 1019)(420, 1020)(421, 1021)(422, 1022)(423, 1023)(424, 1024)(425, 1025)(426, 1026)(427, 1027)(428, 1028)(429, 1029)(430, 1030)(431, 1031)(432, 1032)(433, 1033)(434, 1034)(435, 1035)(436, 1036)(437, 1037)(438, 1038)(439, 1039)(440, 1040)(441, 1041)(442, 1042)(443, 1043)(444, 1044)(445, 1045)(446, 1046)(447, 1047)(448, 1048)(449, 1049)(450, 1050)(451, 1051)(452, 1052)(453, 1053)(454, 1054)(455, 1055)(456, 1056)(457, 1057)(458, 1058)(459, 1059)(460, 1060)(461, 1061)(462, 1062)(463, 1063)(464, 1064)(465, 1065)(466, 1066)(467, 1067)(468, 1068)(469, 1069)(470, 1070)(471, 1071)(472, 1072)(473, 1073)(474, 1074)(475, 1075)(476, 1076)(477, 1077)(478, 1078)(479, 1079)(480, 1080)(481, 1081)(482, 1082)(483, 1083)(484, 1084)(485, 1085)(486, 1086)(487, 1087)(488, 1088)(489, 1089)(490, 1090)(491, 1091)(492, 1092)(493, 1093)(494, 1094)(495, 1095)(496, 1096)(497, 1097)(498, 1098)(499, 1099)(500, 1100)(501, 1101)(502, 1102)(503, 1103)(504, 1104)(505, 1105)(506, 1106)(507, 1107)(508, 1108)(509, 1109)(510, 1110)(511, 1111)(512, 1112)(513, 1113)(514, 1114)(515, 1115)(516, 1116)(517, 1117)(518, 1118)(519, 1119)(520, 1120)(521, 1121)(522, 1122)(523, 1123)(524, 1124)(525, 1125)(526, 1126)(527, 1127)(528, 1128)(529, 1129)(530, 1130)(531, 1131)(532, 1132)(533, 1133)(534, 1134)(535, 1135)(536, 1136)(537, 1137)(538, 1138)(539, 1139)(540, 1140)(541, 1141)(542, 1142)(543, 1143)(544, 1144)(545, 1145)(546, 1146)(547, 1147)(548, 1148)(549, 1149)(550, 1150)(551, 1151)(552, 1152)(553, 1153)(554, 1154)(555, 1155)(556, 1156)(557, 1157)(558, 1158)(559, 1159)(560, 1160)(561, 1161)(562, 1162)(563, 1163)(564, 1164)(565, 1165)(566, 1166)(567, 1167)(568, 1168)(569, 1169)(570, 1170)(571, 1171)(572, 1172)(573, 1173)(574, 1174)(575, 1175)(576, 1176)(577, 1177)(578, 1178)(579, 1179)(580, 1180)(581, 1181)(582, 1182)(583, 1183)(584, 1184)(585, 1185)(586, 1186)(587, 1187)(588, 1188)(589, 1189)(590, 1190)(591, 1191)(592, 1192)(593, 1193)(594, 1194)(595, 1195)(596, 1196)(597, 1197)(598, 1198)(599, 1199)(600, 1200)(1201, 1801, 1202, 1802)(1203, 1803, 1207, 1807)(1204, 1804, 1209, 1809)(1205, 1805, 1211, 1811)(1206, 1806, 1213, 1813)(1208, 1808, 1217, 1817)(1210, 1810, 1220, 1820)(1212, 1812, 1223, 1823)(1214, 1814, 1226, 1826)(1215, 1815, 1225, 1825)(1216, 1816, 1228, 1828)(1218, 1818, 1232, 1832)(1219, 1819, 1221, 1821)(1222, 1822, 1238, 1838)(1224, 1824, 1242, 1842)(1227, 1827, 1247, 1847)(1229, 1829, 1250, 1850)(1230, 1830, 1249, 1849)(1231, 1831, 1252, 1852)(1233, 1833, 1256, 1856)(1234, 1834, 1257, 1857)(1235, 1835, 1258, 1858)(1236, 1836, 1254, 1854)(1237, 1837, 1261, 1861)(1239, 1839, 1264, 1864)(1240, 1840, 1263, 1863)(1241, 1841, 1266, 1866)(1243, 1843, 1270, 1870)(1244, 1844, 1271, 1871)(1245, 1845, 1272, 1872)(1246, 1846, 1268, 1868)(1248, 1848, 1277, 1877)(1251, 1851, 1282, 1882)(1253, 1853, 1284, 1884)(1255, 1855, 1286, 1886)(1259, 1859, 1293, 1893)(1260, 1860, 1294, 1894)(1262, 1862, 1297, 1897)(1265, 1865, 1302, 1902)(1267, 1867, 1304, 1904)(1269, 1869, 1306, 1906)(1273, 1873, 1313, 1913)(1274, 1874, 1314, 1914)(1275, 1875, 1311, 1911)(1276, 1876, 1316, 1916)(1278, 1878, 1320, 1920)(1279, 1879, 1321, 1921)(1280, 1880, 1322, 1922)(1281, 1881, 1318, 1918)(1283, 1883, 1327, 1927)(1285, 1885, 1331, 1931)(1287, 1887, 1334, 1934)(1288, 1888, 1333, 1933)(1289, 1889, 1336, 1936)(1290, 1890, 1338, 1938)(1291, 1891, 1295, 1895)(1292, 1892, 1341, 1941)(1296, 1896, 1347, 1947)(1298, 1898, 1351, 1951)(1299, 1899, 1352, 1952)(1300, 1900, 1353, 1953)(1301, 1901, 1349, 1949)(1303, 1903, 1358, 1958)(1305, 1905, 1362, 1962)(1307, 1907, 1365, 1965)(1308, 1908, 1364, 1964)(1309, 1909, 1367, 1967)(1310, 1910, 1369, 1969)(1312, 1912, 1372, 1972)(1315, 1915, 1377, 1977)(1317, 1917, 1379, 1979)(1319, 1919, 1381, 1981)(1323, 1923, 1388, 1988)(1324, 1924, 1389, 1989)(1325, 1925, 1386, 1986)(1326, 1926, 1391, 1991)(1328, 1928, 1395, 1995)(1329, 1929, 1396, 1996)(1330, 1930, 1393, 1993)(1332, 1932, 1401, 2001)(1335, 1935, 1406, 2006)(1337, 1937, 1408, 2008)(1339, 1939, 1410, 2010)(1340, 1940, 1411, 2011)(1342, 1942, 1413, 2013)(1343, 1943, 1415, 2015)(1344, 1944, 1417, 2017)(1345, 1945, 1399, 1999)(1346, 1946, 1420, 2020)(1348, 1948, 1422, 2022)(1350, 1950, 1424, 2024)(1354, 1954, 1431, 2031)(1355, 1955, 1432, 2032)(1356, 1956, 1429, 2029)(1357, 1957, 1434, 2034)(1359, 1959, 1438, 2038)(1360, 1960, 1439, 2039)(1361, 1961, 1436, 2036)(1363, 1963, 1444, 2044)(1366, 1966, 1449, 2049)(1368, 1968, 1451, 2051)(1370, 1970, 1453, 2053)(1371, 1971, 1454, 2054)(1373, 1973, 1456, 2056)(1374, 1974, 1458, 2058)(1375, 1975, 1460, 2060)(1376, 1976, 1442, 2042)(1378, 1978, 1465, 2065)(1380, 1980, 1469, 2069)(1382, 1982, 1472, 2072)(1383, 1983, 1471, 2071)(1384, 1984, 1474, 2074)(1385, 1985, 1476, 2076)(1387, 1987, 1479, 2079)(1390, 1990, 1462, 2062)(1392, 1992, 1485, 2085)(1394, 1994, 1487, 2087)(1397, 1997, 1492, 2092)(1398, 1998, 1493, 2093)(1400, 2000, 1495, 2095)(1402, 2002, 1499, 2099)(1403, 2003, 1500, 2100)(1404, 2004, 1501, 2101)(1405, 2005, 1497, 2097)(1407, 2007, 1506, 2106)(1409, 2009, 1510, 2110)(1412, 2012, 1514, 2114)(1414, 2014, 1517, 2117)(1416, 2016, 1519, 2119)(1418, 2018, 1521, 2121)(1419, 2019, 1433, 2033)(1421, 2021, 1524, 2124)(1423, 2023, 1528, 2128)(1425, 2025, 1531, 2131)(1426, 2026, 1530, 2130)(1427, 2027, 1533, 2133)(1428, 2028, 1535, 2135)(1430, 2030, 1538, 2138)(1435, 2035, 1544, 2144)(1437, 2037, 1546, 2146)(1440, 2040, 1551, 2151)(1441, 2041, 1552, 2152)(1443, 2043, 1554, 2154)(1445, 2045, 1558, 2158)(1446, 2046, 1559, 2159)(1447, 2047, 1560, 2160)(1448, 2048, 1556, 2156)(1450, 2050, 1565, 2165)(1452, 2052, 1569, 2169)(1455, 2055, 1573, 2173)(1457, 2057, 1576, 2176)(1459, 2059, 1578, 2178)(1461, 2061, 1580, 2180)(1463, 2063, 1522, 2122)(1464, 2064, 1581, 2181)(1466, 2066, 1584, 2184)(1467, 2067, 1585, 2185)(1468, 2068, 1582, 2182)(1470, 2070, 1590, 2190)(1473, 2073, 1543, 2143)(1475, 2075, 1596, 2196)(1477, 2077, 1598, 2198)(1478, 2078, 1553, 2153)(1480, 2080, 1600, 2200)(1481, 2081, 1602, 2202)(1482, 2082, 1541, 2141)(1483, 2083, 1588, 2188)(1484, 2084, 1532, 2132)(1486, 2086, 1608, 2208)(1488, 2088, 1574, 2174)(1489, 2089, 1610, 2210)(1490, 2090, 1612, 2212)(1491, 2091, 1614, 2214)(1494, 2094, 1537, 2137)(1496, 2096, 1619, 2219)(1498, 2098, 1621, 2221)(1502, 2102, 1627, 2227)(1503, 2103, 1579, 2179)(1504, 2104, 1625, 2225)(1505, 2105, 1564, 2164)(1507, 2107, 1630, 2230)(1508, 2108, 1631, 2231)(1509, 2109, 1628, 2228)(1511, 2111, 1634, 2234)(1512, 2112, 1636, 2236)(1513, 2113, 1638, 2238)(1515, 2115, 1547, 2147)(1516, 2116, 1640, 2240)(1518, 2118, 1641, 2241)(1520, 2120, 1562, 2162)(1523, 2123, 1647, 2247)(1525, 2125, 1650, 2250)(1526, 2126, 1651, 2251)(1527, 2127, 1648, 2248)(1529, 2129, 1655, 2255)(1534, 2134, 1607, 2207)(1536, 2136, 1662, 2262)(1539, 2139, 1664, 2264)(1540, 2140, 1604, 2204)(1542, 2142, 1653, 2253)(1545, 2145, 1669, 2269)(1548, 2148, 1671, 2271)(1549, 2149, 1673, 2273)(1550, 2150, 1587, 2187)(1555, 2155, 1678, 2278)(1557, 2157, 1680, 2280)(1561, 2161, 1645, 2245)(1563, 2163, 1684, 2284)(1566, 2166, 1688, 2288)(1567, 2167, 1617, 2217)(1568, 2168, 1686, 2286)(1570, 2170, 1691, 2291)(1571, 2171, 1692, 2292)(1572, 2172, 1694, 2294)(1575, 2175, 1696, 2296)(1577, 2177, 1635, 2235)(1583, 2183, 1702, 2302)(1586, 2186, 1675, 2275)(1589, 2189, 1706, 2306)(1591, 2191, 1681, 2281)(1592, 2192, 1710, 2310)(1593, 2193, 1711, 2311)(1594, 2194, 1708, 2308)(1595, 2195, 1712, 2312)(1597, 2197, 1715, 2315)(1599, 2199, 1717, 2317)(1601, 2201, 1690, 2290)(1603, 2203, 1698, 2298)(1605, 2205, 1719, 2319)(1606, 2206, 1700, 2300)(1609, 2209, 1695, 2295)(1611, 2211, 1701, 2301)(1613, 2213, 1726, 2326)(1615, 2215, 1652, 2252)(1616, 2216, 1689, 2289)(1618, 2218, 1729, 2329)(1620, 2220, 1731, 2331)(1622, 2222, 1656, 2256)(1623, 2223, 1733, 2333)(1624, 2224, 1734, 2334)(1626, 2226, 1735, 2335)(1629, 2229, 1737, 2337)(1632, 2232, 1676, 2276)(1633, 2233, 1665, 2265)(1637, 2237, 1699, 2299)(1639, 2239, 1670, 2270)(1642, 2242, 1742, 2342)(1643, 2243, 1666, 2266)(1644, 2244, 1693, 2293)(1646, 2246, 1668, 2268)(1649, 2249, 1748, 2348)(1654, 2254, 1752, 2352)(1657, 2257, 1756, 2356)(1658, 2258, 1757, 2357)(1659, 2259, 1754, 2354)(1660, 2260, 1758, 2358)(1661, 2261, 1760, 2360)(1663, 2263, 1762, 2362)(1667, 2267, 1764, 2364)(1672, 2272, 1747, 2347)(1674, 2274, 1770, 2370)(1677, 2277, 1773, 2373)(1679, 2279, 1775, 2375)(1682, 2282, 1777, 2377)(1683, 2283, 1778, 2378)(1685, 2285, 1779, 2379)(1687, 2287, 1780, 2380)(1697, 2297, 1785, 2385)(1703, 2303, 1789, 2389)(1704, 2304, 1750, 2350)(1705, 2305, 1721, 2321)(1707, 2307, 1766, 2366)(1709, 2309, 1776, 2376)(1713, 2313, 1768, 2368)(1714, 2314, 1751, 2351)(1716, 2316, 1763, 2363)(1718, 2318, 1761, 2361)(1720, 2320, 1771, 2371)(1722, 2322, 1753, 2353)(1723, 2323, 1792, 2392)(1724, 2324, 1759, 2359)(1725, 2325, 1774, 2374)(1727, 2327, 1765, 2365)(1728, 2328, 1786, 2386)(1730, 2330, 1769, 2369)(1732, 2332, 1755, 2355)(1736, 2336, 1783, 2383)(1738, 2338, 1781, 2381)(1739, 2339, 1791, 2391)(1740, 2340, 1745, 2345)(1741, 2341, 1794, 2394)(1743, 2343, 1772, 2372)(1744, 2344, 1788, 2388)(1746, 2346, 1787, 2387)(1749, 2349, 1795, 2395)(1767, 2367, 1798, 2398)(1782, 2382, 1797, 2397)(1784, 2384, 1800, 2400)(1790, 2390, 1799, 2399)(1793, 2393, 1796, 2396) L = (1, 1203)(2, 1205)(3, 1208)(4, 1201)(5, 1212)(6, 1202)(7, 1215)(8, 1210)(9, 1218)(10, 1204)(11, 1221)(12, 1214)(13, 1224)(14, 1206)(15, 1227)(16, 1207)(17, 1230)(18, 1233)(19, 1209)(20, 1235)(21, 1237)(22, 1211)(23, 1240)(24, 1243)(25, 1213)(26, 1245)(27, 1229)(28, 1248)(29, 1216)(30, 1251)(31, 1217)(32, 1254)(33, 1234)(34, 1219)(35, 1259)(36, 1220)(37, 1239)(38, 1262)(39, 1222)(40, 1265)(41, 1223)(42, 1268)(43, 1244)(44, 1225)(45, 1273)(46, 1226)(47, 1275)(48, 1278)(49, 1228)(50, 1280)(51, 1253)(52, 1283)(53, 1231)(54, 1285)(55, 1232)(56, 1288)(57, 1290)(58, 1252)(59, 1260)(60, 1236)(61, 1295)(62, 1298)(63, 1238)(64, 1300)(65, 1267)(66, 1303)(67, 1241)(68, 1305)(69, 1242)(70, 1308)(71, 1310)(72, 1266)(73, 1274)(74, 1246)(75, 1315)(76, 1247)(77, 1318)(78, 1279)(79, 1249)(80, 1323)(81, 1250)(82, 1325)(83, 1328)(84, 1329)(85, 1287)(86, 1332)(87, 1255)(88, 1335)(89, 1256)(90, 1339)(91, 1257)(92, 1258)(93, 1342)(94, 1344)(95, 1346)(96, 1261)(97, 1349)(98, 1299)(99, 1263)(100, 1354)(101, 1264)(102, 1356)(103, 1359)(104, 1360)(105, 1307)(106, 1363)(107, 1269)(108, 1366)(109, 1270)(110, 1370)(111, 1271)(112, 1272)(113, 1373)(114, 1375)(115, 1317)(116, 1378)(117, 1276)(118, 1380)(119, 1277)(120, 1383)(121, 1385)(122, 1316)(123, 1324)(124, 1281)(125, 1390)(126, 1282)(127, 1393)(128, 1292)(129, 1397)(130, 1284)(131, 1399)(132, 1402)(133, 1286)(134, 1404)(135, 1337)(136, 1407)(137, 1289)(138, 1336)(139, 1340)(140, 1291)(141, 1412)(142, 1414)(143, 1293)(144, 1418)(145, 1294)(146, 1348)(147, 1421)(148, 1296)(149, 1423)(150, 1297)(151, 1426)(152, 1428)(153, 1347)(154, 1355)(155, 1301)(156, 1433)(157, 1302)(158, 1436)(159, 1312)(160, 1440)(161, 1304)(162, 1442)(163, 1445)(164, 1306)(165, 1447)(166, 1368)(167, 1450)(168, 1309)(169, 1367)(170, 1371)(171, 1311)(172, 1455)(173, 1457)(174, 1313)(175, 1461)(176, 1314)(177, 1463)(178, 1466)(179, 1467)(180, 1382)(181, 1470)(182, 1319)(183, 1473)(184, 1320)(185, 1477)(186, 1321)(187, 1322)(188, 1480)(189, 1482)(190, 1392)(191, 1484)(192, 1326)(193, 1486)(194, 1327)(195, 1489)(196, 1391)(197, 1398)(198, 1330)(199, 1494)(200, 1331)(201, 1497)(202, 1403)(203, 1333)(204, 1502)(205, 1334)(206, 1504)(207, 1507)(208, 1508)(209, 1338)(210, 1511)(211, 1513)(212, 1515)(213, 1341)(214, 1416)(215, 1518)(216, 1343)(217, 1415)(218, 1419)(219, 1345)(220, 1522)(221, 1525)(222, 1526)(223, 1425)(224, 1529)(225, 1350)(226, 1532)(227, 1351)(228, 1536)(229, 1352)(230, 1353)(231, 1539)(232, 1541)(233, 1435)(234, 1543)(235, 1357)(236, 1545)(237, 1358)(238, 1548)(239, 1434)(240, 1441)(241, 1361)(242, 1553)(243, 1362)(244, 1556)(245, 1446)(246, 1364)(247, 1561)(248, 1365)(249, 1563)(250, 1566)(251, 1567)(252, 1369)(253, 1570)(254, 1572)(255, 1574)(256, 1372)(257, 1459)(258, 1577)(259, 1374)(260, 1458)(261, 1462)(262, 1376)(263, 1411)(264, 1377)(265, 1582)(266, 1387)(267, 1586)(268, 1379)(269, 1588)(270, 1591)(271, 1381)(272, 1593)(273, 1475)(274, 1595)(275, 1384)(276, 1474)(277, 1478)(278, 1386)(279, 1599)(280, 1601)(281, 1388)(282, 1604)(283, 1389)(284, 1605)(285, 1606)(286, 1488)(287, 1609)(288, 1394)(289, 1611)(290, 1395)(291, 1396)(292, 1615)(293, 1617)(294, 1496)(295, 1618)(296, 1400)(297, 1620)(298, 1401)(299, 1583)(300, 1624)(301, 1495)(302, 1503)(303, 1405)(304, 1493)(305, 1406)(306, 1628)(307, 1409)(308, 1632)(309, 1408)(310, 1594)(311, 1635)(312, 1410)(313, 1464)(314, 1612)(315, 1516)(316, 1413)(317, 1483)(318, 1642)(319, 1643)(320, 1417)(321, 1645)(322, 1454)(323, 1420)(324, 1648)(325, 1430)(326, 1652)(327, 1422)(328, 1653)(329, 1656)(330, 1424)(331, 1658)(332, 1534)(333, 1660)(334, 1427)(335, 1533)(336, 1537)(337, 1429)(338, 1663)(339, 1665)(340, 1431)(341, 1602)(342, 1432)(343, 1667)(344, 1668)(345, 1547)(346, 1670)(347, 1437)(348, 1672)(349, 1438)(350, 1439)(351, 1675)(352, 1631)(353, 1555)(354, 1677)(355, 1443)(356, 1679)(357, 1444)(358, 1649)(359, 1683)(360, 1554)(361, 1562)(362, 1448)(363, 1552)(364, 1449)(365, 1686)(366, 1452)(367, 1689)(368, 1451)(369, 1659)(370, 1641)(371, 1453)(372, 1523)(373, 1673)(374, 1575)(375, 1456)(376, 1542)(377, 1697)(378, 1698)(379, 1460)(380, 1627)(381, 1701)(382, 1623)(383, 1465)(384, 1703)(385, 1581)(386, 1587)(387, 1468)(388, 1640)(389, 1469)(390, 1708)(391, 1592)(392, 1471)(393, 1634)(394, 1472)(395, 1713)(396, 1544)(397, 1476)(398, 1629)(399, 1619)(400, 1479)(401, 1603)(402, 1576)(403, 1481)(404, 1517)(405, 1491)(406, 1720)(407, 1485)(408, 1625)(409, 1723)(410, 1487)(411, 1613)(412, 1725)(413, 1490)(414, 1527)(415, 1727)(416, 1492)(417, 1505)(418, 1730)(419, 1718)(420, 1622)(421, 1732)(422, 1498)(423, 1499)(424, 1722)(425, 1500)(426, 1501)(427, 1736)(428, 1716)(429, 1506)(430, 1738)(431, 1564)(432, 1633)(433, 1509)(434, 1510)(435, 1637)(436, 1740)(437, 1512)(438, 1636)(439, 1514)(440, 1707)(441, 1693)(442, 1520)(443, 1743)(444, 1519)(445, 1745)(446, 1521)(447, 1747)(448, 1682)(449, 1524)(450, 1749)(451, 1647)(452, 1614)(453, 1696)(454, 1528)(455, 1754)(456, 1657)(457, 1530)(458, 1691)(459, 1531)(460, 1759)(461, 1535)(462, 1687)(463, 1678)(464, 1538)(465, 1666)(466, 1540)(467, 1550)(468, 1765)(469, 1684)(470, 1767)(471, 1546)(472, 1674)(473, 1769)(474, 1549)(475, 1771)(476, 1551)(477, 1774)(478, 1763)(479, 1681)(480, 1776)(481, 1557)(482, 1558)(483, 1766)(484, 1559)(485, 1560)(486, 1761)(487, 1565)(488, 1781)(489, 1690)(490, 1568)(491, 1569)(492, 1783)(493, 1571)(494, 1692)(495, 1573)(496, 1753)(497, 1579)(498, 1786)(499, 1578)(500, 1580)(501, 1758)(502, 1621)(503, 1773)(504, 1584)(505, 1585)(506, 1790)(507, 1589)(508, 1791)(509, 1590)(510, 1793)(511, 1706)(512, 1751)(513, 1597)(514, 1596)(515, 1782)(516, 1598)(517, 1750)(518, 1600)(519, 1756)(520, 1721)(521, 1607)(522, 1608)(523, 1724)(524, 1610)(525, 1741)(526, 1638)(527, 1728)(528, 1616)(529, 1717)(530, 1626)(531, 1785)(532, 1794)(533, 1764)(534, 1733)(535, 1770)(536, 1788)(537, 1715)(538, 1780)(539, 1630)(540, 1779)(541, 1639)(542, 1757)(543, 1744)(544, 1644)(545, 1746)(546, 1646)(547, 1712)(548, 1680)(549, 1729)(550, 1650)(551, 1651)(552, 1796)(553, 1654)(554, 1797)(555, 1655)(556, 1799)(557, 1752)(558, 1705)(559, 1661)(560, 1739)(561, 1662)(562, 1704)(563, 1664)(564, 1710)(565, 1714)(566, 1669)(567, 1768)(568, 1671)(569, 1784)(570, 1694)(571, 1772)(572, 1676)(573, 1762)(574, 1685)(575, 1742)(576, 1800)(577, 1719)(578, 1777)(579, 1726)(580, 1760)(581, 1737)(582, 1688)(583, 1735)(584, 1695)(585, 1711)(586, 1787)(587, 1699)(588, 1700)(589, 1702)(590, 1731)(591, 1792)(592, 1709)(593, 1734)(594, 1789)(595, 1748)(596, 1775)(597, 1798)(598, 1755)(599, 1778)(600, 1795)(601, 1801)(602, 1802)(603, 1803)(604, 1804)(605, 1805)(606, 1806)(607, 1807)(608, 1808)(609, 1809)(610, 1810)(611, 1811)(612, 1812)(613, 1813)(614, 1814)(615, 1815)(616, 1816)(617, 1817)(618, 1818)(619, 1819)(620, 1820)(621, 1821)(622, 1822)(623, 1823)(624, 1824)(625, 1825)(626, 1826)(627, 1827)(628, 1828)(629, 1829)(630, 1830)(631, 1831)(632, 1832)(633, 1833)(634, 1834)(635, 1835)(636, 1836)(637, 1837)(638, 1838)(639, 1839)(640, 1840)(641, 1841)(642, 1842)(643, 1843)(644, 1844)(645, 1845)(646, 1846)(647, 1847)(648, 1848)(649, 1849)(650, 1850)(651, 1851)(652, 1852)(653, 1853)(654, 1854)(655, 1855)(656, 1856)(657, 1857)(658, 1858)(659, 1859)(660, 1860)(661, 1861)(662, 1862)(663, 1863)(664, 1864)(665, 1865)(666, 1866)(667, 1867)(668, 1868)(669, 1869)(670, 1870)(671, 1871)(672, 1872)(673, 1873)(674, 1874)(675, 1875)(676, 1876)(677, 1877)(678, 1878)(679, 1879)(680, 1880)(681, 1881)(682, 1882)(683, 1883)(684, 1884)(685, 1885)(686, 1886)(687, 1887)(688, 1888)(689, 1889)(690, 1890)(691, 1891)(692, 1892)(693, 1893)(694, 1894)(695, 1895)(696, 1896)(697, 1897)(698, 1898)(699, 1899)(700, 1900)(701, 1901)(702, 1902)(703, 1903)(704, 1904)(705, 1905)(706, 1906)(707, 1907)(708, 1908)(709, 1909)(710, 1910)(711, 1911)(712, 1912)(713, 1913)(714, 1914)(715, 1915)(716, 1916)(717, 1917)(718, 1918)(719, 1919)(720, 1920)(721, 1921)(722, 1922)(723, 1923)(724, 1924)(725, 1925)(726, 1926)(727, 1927)(728, 1928)(729, 1929)(730, 1930)(731, 1931)(732, 1932)(733, 1933)(734, 1934)(735, 1935)(736, 1936)(737, 1937)(738, 1938)(739, 1939)(740, 1940)(741, 1941)(742, 1942)(743, 1943)(744, 1944)(745, 1945)(746, 1946)(747, 1947)(748, 1948)(749, 1949)(750, 1950)(751, 1951)(752, 1952)(753, 1953)(754, 1954)(755, 1955)(756, 1956)(757, 1957)(758, 1958)(759, 1959)(760, 1960)(761, 1961)(762, 1962)(763, 1963)(764, 1964)(765, 1965)(766, 1966)(767, 1967)(768, 1968)(769, 1969)(770, 1970)(771, 1971)(772, 1972)(773, 1973)(774, 1974)(775, 1975)(776, 1976)(777, 1977)(778, 1978)(779, 1979)(780, 1980)(781, 1981)(782, 1982)(783, 1983)(784, 1984)(785, 1985)(786, 1986)(787, 1987)(788, 1988)(789, 1989)(790, 1990)(791, 1991)(792, 1992)(793, 1993)(794, 1994)(795, 1995)(796, 1996)(797, 1997)(798, 1998)(799, 1999)(800, 2000)(801, 2001)(802, 2002)(803, 2003)(804, 2004)(805, 2005)(806, 2006)(807, 2007)(808, 2008)(809, 2009)(810, 2010)(811, 2011)(812, 2012)(813, 2013)(814, 2014)(815, 2015)(816, 2016)(817, 2017)(818, 2018)(819, 2019)(820, 2020)(821, 2021)(822, 2022)(823, 2023)(824, 2024)(825, 2025)(826, 2026)(827, 2027)(828, 2028)(829, 2029)(830, 2030)(831, 2031)(832, 2032)(833, 2033)(834, 2034)(835, 2035)(836, 2036)(837, 2037)(838, 2038)(839, 2039)(840, 2040)(841, 2041)(842, 2042)(843, 2043)(844, 2044)(845, 2045)(846, 2046)(847, 2047)(848, 2048)(849, 2049)(850, 2050)(851, 2051)(852, 2052)(853, 2053)(854, 2054)(855, 2055)(856, 2056)(857, 2057)(858, 2058)(859, 2059)(860, 2060)(861, 2061)(862, 2062)(863, 2063)(864, 2064)(865, 2065)(866, 2066)(867, 2067)(868, 2068)(869, 2069)(870, 2070)(871, 2071)(872, 2072)(873, 2073)(874, 2074)(875, 2075)(876, 2076)(877, 2077)(878, 2078)(879, 2079)(880, 2080)(881, 2081)(882, 2082)(883, 2083)(884, 2084)(885, 2085)(886, 2086)(887, 2087)(888, 2088)(889, 2089)(890, 2090)(891, 2091)(892, 2092)(893, 2093)(894, 2094)(895, 2095)(896, 2096)(897, 2097)(898, 2098)(899, 2099)(900, 2100)(901, 2101)(902, 2102)(903, 2103)(904, 2104)(905, 2105)(906, 2106)(907, 2107)(908, 2108)(909, 2109)(910, 2110)(911, 2111)(912, 2112)(913, 2113)(914, 2114)(915, 2115)(916, 2116)(917, 2117)(918, 2118)(919, 2119)(920, 2120)(921, 2121)(922, 2122)(923, 2123)(924, 2124)(925, 2125)(926, 2126)(927, 2127)(928, 2128)(929, 2129)(930, 2130)(931, 2131)(932, 2132)(933, 2133)(934, 2134)(935, 2135)(936, 2136)(937, 2137)(938, 2138)(939, 2139)(940, 2140)(941, 2141)(942, 2142)(943, 2143)(944, 2144)(945, 2145)(946, 2146)(947, 2147)(948, 2148)(949, 2149)(950, 2150)(951, 2151)(952, 2152)(953, 2153)(954, 2154)(955, 2155)(956, 2156)(957, 2157)(958, 2158)(959, 2159)(960, 2160)(961, 2161)(962, 2162)(963, 2163)(964, 2164)(965, 2165)(966, 2166)(967, 2167)(968, 2168)(969, 2169)(970, 2170)(971, 2171)(972, 2172)(973, 2173)(974, 2174)(975, 2175)(976, 2176)(977, 2177)(978, 2178)(979, 2179)(980, 2180)(981, 2181)(982, 2182)(983, 2183)(984, 2184)(985, 2185)(986, 2186)(987, 2187)(988, 2188)(989, 2189)(990, 2190)(991, 2191)(992, 2192)(993, 2193)(994, 2194)(995, 2195)(996, 2196)(997, 2197)(998, 2198)(999, 2199)(1000, 2200)(1001, 2201)(1002, 2202)(1003, 2203)(1004, 2204)(1005, 2205)(1006, 2206)(1007, 2207)(1008, 2208)(1009, 2209)(1010, 2210)(1011, 2211)(1012, 2212)(1013, 2213)(1014, 2214)(1015, 2215)(1016, 2216)(1017, 2217)(1018, 2218)(1019, 2219)(1020, 2220)(1021, 2221)(1022, 2222)(1023, 2223)(1024, 2224)(1025, 2225)(1026, 2226)(1027, 2227)(1028, 2228)(1029, 2229)(1030, 2230)(1031, 2231)(1032, 2232)(1033, 2233)(1034, 2234)(1035, 2235)(1036, 2236)(1037, 2237)(1038, 2238)(1039, 2239)(1040, 2240)(1041, 2241)(1042, 2242)(1043, 2243)(1044, 2244)(1045, 2245)(1046, 2246)(1047, 2247)(1048, 2248)(1049, 2249)(1050, 2250)(1051, 2251)(1052, 2252)(1053, 2253)(1054, 2254)(1055, 2255)(1056, 2256)(1057, 2257)(1058, 2258)(1059, 2259)(1060, 2260)(1061, 2261)(1062, 2262)(1063, 2263)(1064, 2264)(1065, 2265)(1066, 2266)(1067, 2267)(1068, 2268)(1069, 2269)(1070, 2270)(1071, 2271)(1072, 2272)(1073, 2273)(1074, 2274)(1075, 2275)(1076, 2276)(1077, 2277)(1078, 2278)(1079, 2279)(1080, 2280)(1081, 2281)(1082, 2282)(1083, 2283)(1084, 2284)(1085, 2285)(1086, 2286)(1087, 2287)(1088, 2288)(1089, 2289)(1090, 2290)(1091, 2291)(1092, 2292)(1093, 2293)(1094, 2294)(1095, 2295)(1096, 2296)(1097, 2297)(1098, 2298)(1099, 2299)(1100, 2300)(1101, 2301)(1102, 2302)(1103, 2303)(1104, 2304)(1105, 2305)(1106, 2306)(1107, 2307)(1108, 2308)(1109, 2309)(1110, 2310)(1111, 2311)(1112, 2312)(1113, 2313)(1114, 2314)(1115, 2315)(1116, 2316)(1117, 2317)(1118, 2318)(1119, 2319)(1120, 2320)(1121, 2321)(1122, 2322)(1123, 2323)(1124, 2324)(1125, 2325)(1126, 2326)(1127, 2327)(1128, 2328)(1129, 2329)(1130, 2330)(1131, 2331)(1132, 2332)(1133, 2333)(1134, 2334)(1135, 2335)(1136, 2336)(1137, 2337)(1138, 2338)(1139, 2339)(1140, 2340)(1141, 2341)(1142, 2342)(1143, 2343)(1144, 2344)(1145, 2345)(1146, 2346)(1147, 2347)(1148, 2348)(1149, 2349)(1150, 2350)(1151, 2351)(1152, 2352)(1153, 2353)(1154, 2354)(1155, 2355)(1156, 2356)(1157, 2357)(1158, 2358)(1159, 2359)(1160, 2360)(1161, 2361)(1162, 2362)(1163, 2363)(1164, 2364)(1165, 2365)(1166, 2366)(1167, 2367)(1168, 2368)(1169, 2369)(1170, 2370)(1171, 2371)(1172, 2372)(1173, 2373)(1174, 2374)(1175, 2375)(1176, 2376)(1177, 2377)(1178, 2378)(1179, 2379)(1180, 2380)(1181, 2381)(1182, 2382)(1183, 2383)(1184, 2384)(1185, 2385)(1186, 2386)(1187, 2387)(1188, 2388)(1189, 2389)(1190, 2390)(1191, 2391)(1192, 2392)(1193, 2393)(1194, 2394)(1195, 2395)(1196, 2396)(1197, 2397)(1198, 2398)(1199, 2399)(1200, 2400) local type(s) :: { ( 8, 10 ), ( 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E16.1294 Graph:: simple bipartite v = 900 e = 1200 f = 270 degree seq :: [ 2^600, 4^300 ] E16.1296 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5}) Quotient :: dipole Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (Y3 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1^5, (Y1 * Y3)^4, (Y3 * Y1^-2)^6, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-2 * Y3 * Y1^-2 ] Map:: polytopal R = (1, 601, 2, 602, 5, 605, 10, 610, 4, 604)(3, 603, 7, 607, 14, 614, 17, 617, 8, 608)(6, 606, 12, 612, 23, 623, 26, 626, 13, 613)(9, 609, 18, 618, 32, 632, 34, 634, 19, 619)(11, 611, 21, 621, 37, 637, 40, 640, 22, 622)(15, 615, 28, 628, 47, 647, 49, 649, 29, 629)(16, 616, 30, 630, 50, 650, 42, 642, 24, 624)(20, 620, 35, 635, 58, 658, 60, 660, 36, 636)(25, 625, 43, 643, 68, 668, 62, 662, 38, 638)(27, 627, 45, 645, 72, 672, 75, 675, 46, 646)(31, 631, 52, 652, 82, 682, 84, 684, 53, 653)(33, 633, 55, 655, 87, 687, 89, 689, 56, 656)(39, 639, 63, 663, 98, 698, 93, 693, 59, 659)(41, 641, 65, 665, 102, 702, 105, 705, 66, 666)(44, 644, 70, 670, 110, 710, 112, 712, 71, 671)(48, 648, 77, 677, 119, 719, 114, 714, 73, 673)(51, 651, 80, 680, 125, 725, 127, 727, 81, 681)(54, 654, 85, 685, 131, 731, 134, 734, 86, 686)(57, 657, 90, 690, 138, 738, 140, 740, 91, 691)(61, 661, 95, 695, 146, 746, 149, 749, 96, 696)(64, 664, 100, 700, 154, 754, 156, 756, 101, 701)(67, 667, 106, 706, 161, 761, 158, 758, 103, 703)(69, 669, 108, 708, 165, 765, 167, 767, 109, 709)(74, 674, 115, 715, 174, 774, 129, 729, 83, 683)(76, 676, 117, 717, 178, 778, 180, 780, 118, 718)(78, 678, 121, 721, 184, 784, 186, 786, 122, 722)(79, 679, 123, 723, 187, 787, 190, 790, 124, 724)(88, 688, 136, 736, 205, 805, 200, 800, 132, 732)(92, 692, 141, 741, 212, 812, 215, 815, 142, 742)(94, 694, 144, 744, 217, 817, 219, 819, 145, 745)(97, 697, 150, 750, 224, 824, 221, 821, 147, 747)(99, 699, 152, 752, 228, 828, 230, 830, 153, 753)(104, 704, 159, 759, 237, 837, 169, 769, 111, 711)(107, 707, 163, 763, 243, 843, 246, 846, 164, 764)(113, 713, 171, 771, 255, 855, 258, 858, 172, 772)(116, 716, 176, 776, 263, 863, 265, 865, 177, 777)(120, 720, 182, 782, 271, 871, 273, 873, 183, 783)(126, 726, 192, 792, 283, 883, 278, 878, 188, 788)(128, 728, 194, 794, 287, 887, 290, 890, 195, 795)(130, 730, 197, 797, 292, 892, 220, 820, 198, 798)(133, 733, 201, 801, 297, 897, 210, 810, 139, 739)(135, 735, 203, 803, 301, 901, 303, 903, 204, 804)(137, 737, 207, 807, 307, 907, 309, 909, 208, 808)(143, 743, 216, 816, 318, 918, 315, 915, 213, 813)(148, 748, 222, 822, 323, 923, 232, 832, 155, 755)(151, 751, 226, 826, 329, 929, 332, 932, 227, 827)(157, 757, 234, 834, 211, 811, 313, 913, 235, 835)(160, 760, 239, 839, 346, 946, 348, 948, 240, 840)(162, 762, 189, 789, 279, 879, 352, 952, 242, 842)(166, 766, 248, 848, 359, 959, 354, 954, 244, 844)(168, 768, 250, 850, 363, 963, 366, 966, 251, 851)(170, 770, 253, 853, 368, 968, 314, 914, 254, 854)(173, 773, 259, 859, 372, 972, 370, 970, 256, 856)(175, 775, 261, 861, 376, 976, 378, 978, 262, 862)(179, 779, 267, 867, 383, 983, 275, 875, 185, 785)(181, 781, 269, 869, 324, 924, 389, 989, 270, 870)(191, 791, 281, 881, 322, 922, 404, 1004, 282, 882)(193, 793, 285, 885, 408, 1008, 410, 1010, 286, 886)(196, 796, 291, 891, 335, 935, 412, 1012, 288, 888)(199, 799, 294, 894, 233, 833, 339, 939, 295, 895)(202, 802, 299, 899, 423, 1023, 425, 1025, 300, 900)(206, 806, 305, 905, 429, 1029, 431, 1031, 306, 906)(209, 809, 310, 910, 434, 1034, 437, 1037, 311, 911)(214, 814, 316, 916, 440, 1040, 321, 921, 218, 818)(223, 823, 325, 925, 448, 1048, 450, 1050, 326, 926)(225, 825, 245, 845, 355, 955, 453, 1053, 328, 928)(229, 829, 334, 934, 459, 1059, 455, 1055, 330, 930)(231, 831, 336, 936, 461, 1061, 464, 1064, 337, 937)(236, 836, 342, 942, 382, 982, 266, 866, 340, 940)(238, 838, 344, 944, 428, 1028, 304, 904, 345, 945)(241, 841, 349, 949, 441, 1041, 473, 1073, 350, 950)(247, 847, 357, 957, 439, 1039, 481, 1081, 358, 958)(249, 849, 361, 961, 435, 1035, 312, 912, 362, 962)(252, 852, 367, 967, 427, 1027, 487, 1087, 364, 964)(257, 857, 353, 953, 476, 1076, 380, 980, 264, 864)(260, 860, 374, 974, 493, 1093, 496, 1096, 375, 975)(268, 868, 385, 985, 462, 1062, 338, 938, 386, 986)(272, 872, 391, 991, 509, 1109, 505, 1105, 387, 987)(274, 874, 393, 993, 512, 1112, 514, 1114, 394, 994)(276, 876, 369, 969, 365, 965, 411, 1011, 396, 996)(277, 877, 397, 997, 381, 981, 424, 1024, 398, 998)(280, 880, 401, 1001, 463, 1063, 486, 1086, 402, 1002)(284, 884, 406, 1006, 523, 1123, 482, 1082, 407, 1007)(289, 889, 413, 1013, 527, 1127, 417, 1017, 293, 893)(296, 896, 419, 1019, 458, 1058, 333, 933, 418, 1018)(298, 898, 421, 1021, 451, 1051, 327, 927, 422, 1022)(302, 902, 426, 1026, 533, 1133, 433, 1033, 308, 908)(317, 917, 442, 1042, 542, 1142, 543, 1143, 443, 1043)(319, 919, 331, 931, 456, 1056, 544, 1144, 444, 1044)(320, 920, 445, 1045, 545, 1145, 546, 1146, 446, 1046)(341, 941, 454, 1054, 554, 1154, 470, 1070, 347, 947)(343, 943, 466, 1066, 564, 1164, 567, 1167, 467, 1067)(351, 951, 474, 1074, 392, 992, 511, 1111, 471, 1071)(356, 956, 371, 971, 490, 1090, 561, 1161, 479, 1079)(360, 960, 483, 1083, 577, 1177, 559, 1159, 484, 1084)(373, 973, 388, 988, 506, 1106, 555, 1155, 492, 1092)(377, 977, 498, 1098, 583, 1183, 553, 1153, 494, 1094)(379, 979, 469, 1069, 549, 1149, 584, 1184, 499, 1099)(384, 984, 502, 1102, 522, 1122, 405, 1005, 503, 1103)(390, 990, 507, 1107, 526, 1126, 558, 1158, 508, 1108)(395, 995, 515, 1115, 521, 1121, 551, 1151, 513, 1113)(399, 999, 517, 1117, 576, 1176, 497, 1097, 516, 1116)(400, 1000, 518, 1118, 580, 1180, 491, 1091, 519, 1119)(403, 1003, 520, 1120, 556, 1156, 525, 1125, 409, 1009)(414, 1014, 488, 1088, 562, 1162, 593, 1193, 528, 1128)(415, 1015, 495, 1095, 582, 1182, 560, 1160, 460, 1060)(416, 1016, 432, 1032, 538, 1138, 550, 1150, 449, 1049)(420, 1020, 530, 1130, 591, 1191, 581, 1181, 531, 1131)(430, 1030, 537, 1137, 594, 1194, 565, 1165, 468, 1068)(436, 1036, 540, 1140, 557, 1157, 457, 1057, 438, 1038)(447, 1047, 547, 1147, 595, 1195, 590, 1190, 548, 1148)(452, 1052, 552, 1152, 475, 1075, 570, 1170, 532, 1132)(465, 1065, 472, 1072, 568, 1168, 539, 1139, 563, 1163)(477, 1077, 572, 1172, 529, 1129, 535, 1135, 571, 1171)(478, 1078, 573, 1173, 504, 1104, 500, 1100, 574, 1174)(480, 1080, 575, 1175, 536, 1136, 579, 1179, 485, 1085)(489, 1089, 566, 1166, 501, 1101, 585, 1185, 534, 1134)(510, 1110, 569, 1169, 596, 1196, 599, 1199, 588, 1188)(524, 1124, 578, 1178, 597, 1197, 600, 1200, 586, 1186)(541, 1141, 589, 1189, 587, 1187, 598, 1198, 592, 1192)(1201, 1801)(1202, 1802)(1203, 1803)(1204, 1804)(1205, 1805)(1206, 1806)(1207, 1807)(1208, 1808)(1209, 1809)(1210, 1810)(1211, 1811)(1212, 1812)(1213, 1813)(1214, 1814)(1215, 1815)(1216, 1816)(1217, 1817)(1218, 1818)(1219, 1819)(1220, 1820)(1221, 1821)(1222, 1822)(1223, 1823)(1224, 1824)(1225, 1825)(1226, 1826)(1227, 1827)(1228, 1828)(1229, 1829)(1230, 1830)(1231, 1831)(1232, 1832)(1233, 1833)(1234, 1834)(1235, 1835)(1236, 1836)(1237, 1837)(1238, 1838)(1239, 1839)(1240, 1840)(1241, 1841)(1242, 1842)(1243, 1843)(1244, 1844)(1245, 1845)(1246, 1846)(1247, 1847)(1248, 1848)(1249, 1849)(1250, 1850)(1251, 1851)(1252, 1852)(1253, 1853)(1254, 1854)(1255, 1855)(1256, 1856)(1257, 1857)(1258, 1858)(1259, 1859)(1260, 1860)(1261, 1861)(1262, 1862)(1263, 1863)(1264, 1864)(1265, 1865)(1266, 1866)(1267, 1867)(1268, 1868)(1269, 1869)(1270, 1870)(1271, 1871)(1272, 1872)(1273, 1873)(1274, 1874)(1275, 1875)(1276, 1876)(1277, 1877)(1278, 1878)(1279, 1879)(1280, 1880)(1281, 1881)(1282, 1882)(1283, 1883)(1284, 1884)(1285, 1885)(1286, 1886)(1287, 1887)(1288, 1888)(1289, 1889)(1290, 1890)(1291, 1891)(1292, 1892)(1293, 1893)(1294, 1894)(1295, 1895)(1296, 1896)(1297, 1897)(1298, 1898)(1299, 1899)(1300, 1900)(1301, 1901)(1302, 1902)(1303, 1903)(1304, 1904)(1305, 1905)(1306, 1906)(1307, 1907)(1308, 1908)(1309, 1909)(1310, 1910)(1311, 1911)(1312, 1912)(1313, 1913)(1314, 1914)(1315, 1915)(1316, 1916)(1317, 1917)(1318, 1918)(1319, 1919)(1320, 1920)(1321, 1921)(1322, 1922)(1323, 1923)(1324, 1924)(1325, 1925)(1326, 1926)(1327, 1927)(1328, 1928)(1329, 1929)(1330, 1930)(1331, 1931)(1332, 1932)(1333, 1933)(1334, 1934)(1335, 1935)(1336, 1936)(1337, 1937)(1338, 1938)(1339, 1939)(1340, 1940)(1341, 1941)(1342, 1942)(1343, 1943)(1344, 1944)(1345, 1945)(1346, 1946)(1347, 1947)(1348, 1948)(1349, 1949)(1350, 1950)(1351, 1951)(1352, 1952)(1353, 1953)(1354, 1954)(1355, 1955)(1356, 1956)(1357, 1957)(1358, 1958)(1359, 1959)(1360, 1960)(1361, 1961)(1362, 1962)(1363, 1963)(1364, 1964)(1365, 1965)(1366, 1966)(1367, 1967)(1368, 1968)(1369, 1969)(1370, 1970)(1371, 1971)(1372, 1972)(1373, 1973)(1374, 1974)(1375, 1975)(1376, 1976)(1377, 1977)(1378, 1978)(1379, 1979)(1380, 1980)(1381, 1981)(1382, 1982)(1383, 1983)(1384, 1984)(1385, 1985)(1386, 1986)(1387, 1987)(1388, 1988)(1389, 1989)(1390, 1990)(1391, 1991)(1392, 1992)(1393, 1993)(1394, 1994)(1395, 1995)(1396, 1996)(1397, 1997)(1398, 1998)(1399, 1999)(1400, 2000)(1401, 2001)(1402, 2002)(1403, 2003)(1404, 2004)(1405, 2005)(1406, 2006)(1407, 2007)(1408, 2008)(1409, 2009)(1410, 2010)(1411, 2011)(1412, 2012)(1413, 2013)(1414, 2014)(1415, 2015)(1416, 2016)(1417, 2017)(1418, 2018)(1419, 2019)(1420, 2020)(1421, 2021)(1422, 2022)(1423, 2023)(1424, 2024)(1425, 2025)(1426, 2026)(1427, 2027)(1428, 2028)(1429, 2029)(1430, 2030)(1431, 2031)(1432, 2032)(1433, 2033)(1434, 2034)(1435, 2035)(1436, 2036)(1437, 2037)(1438, 2038)(1439, 2039)(1440, 2040)(1441, 2041)(1442, 2042)(1443, 2043)(1444, 2044)(1445, 2045)(1446, 2046)(1447, 2047)(1448, 2048)(1449, 2049)(1450, 2050)(1451, 2051)(1452, 2052)(1453, 2053)(1454, 2054)(1455, 2055)(1456, 2056)(1457, 2057)(1458, 2058)(1459, 2059)(1460, 2060)(1461, 2061)(1462, 2062)(1463, 2063)(1464, 2064)(1465, 2065)(1466, 2066)(1467, 2067)(1468, 2068)(1469, 2069)(1470, 2070)(1471, 2071)(1472, 2072)(1473, 2073)(1474, 2074)(1475, 2075)(1476, 2076)(1477, 2077)(1478, 2078)(1479, 2079)(1480, 2080)(1481, 2081)(1482, 2082)(1483, 2083)(1484, 2084)(1485, 2085)(1486, 2086)(1487, 2087)(1488, 2088)(1489, 2089)(1490, 2090)(1491, 2091)(1492, 2092)(1493, 2093)(1494, 2094)(1495, 2095)(1496, 2096)(1497, 2097)(1498, 2098)(1499, 2099)(1500, 2100)(1501, 2101)(1502, 2102)(1503, 2103)(1504, 2104)(1505, 2105)(1506, 2106)(1507, 2107)(1508, 2108)(1509, 2109)(1510, 2110)(1511, 2111)(1512, 2112)(1513, 2113)(1514, 2114)(1515, 2115)(1516, 2116)(1517, 2117)(1518, 2118)(1519, 2119)(1520, 2120)(1521, 2121)(1522, 2122)(1523, 2123)(1524, 2124)(1525, 2125)(1526, 2126)(1527, 2127)(1528, 2128)(1529, 2129)(1530, 2130)(1531, 2131)(1532, 2132)(1533, 2133)(1534, 2134)(1535, 2135)(1536, 2136)(1537, 2137)(1538, 2138)(1539, 2139)(1540, 2140)(1541, 2141)(1542, 2142)(1543, 2143)(1544, 2144)(1545, 2145)(1546, 2146)(1547, 2147)(1548, 2148)(1549, 2149)(1550, 2150)(1551, 2151)(1552, 2152)(1553, 2153)(1554, 2154)(1555, 2155)(1556, 2156)(1557, 2157)(1558, 2158)(1559, 2159)(1560, 2160)(1561, 2161)(1562, 2162)(1563, 2163)(1564, 2164)(1565, 2165)(1566, 2166)(1567, 2167)(1568, 2168)(1569, 2169)(1570, 2170)(1571, 2171)(1572, 2172)(1573, 2173)(1574, 2174)(1575, 2175)(1576, 2176)(1577, 2177)(1578, 2178)(1579, 2179)(1580, 2180)(1581, 2181)(1582, 2182)(1583, 2183)(1584, 2184)(1585, 2185)(1586, 2186)(1587, 2187)(1588, 2188)(1589, 2189)(1590, 2190)(1591, 2191)(1592, 2192)(1593, 2193)(1594, 2194)(1595, 2195)(1596, 2196)(1597, 2197)(1598, 2198)(1599, 2199)(1600, 2200)(1601, 2201)(1602, 2202)(1603, 2203)(1604, 2204)(1605, 2205)(1606, 2206)(1607, 2207)(1608, 2208)(1609, 2209)(1610, 2210)(1611, 2211)(1612, 2212)(1613, 2213)(1614, 2214)(1615, 2215)(1616, 2216)(1617, 2217)(1618, 2218)(1619, 2219)(1620, 2220)(1621, 2221)(1622, 2222)(1623, 2223)(1624, 2224)(1625, 2225)(1626, 2226)(1627, 2227)(1628, 2228)(1629, 2229)(1630, 2230)(1631, 2231)(1632, 2232)(1633, 2233)(1634, 2234)(1635, 2235)(1636, 2236)(1637, 2237)(1638, 2238)(1639, 2239)(1640, 2240)(1641, 2241)(1642, 2242)(1643, 2243)(1644, 2244)(1645, 2245)(1646, 2246)(1647, 2247)(1648, 2248)(1649, 2249)(1650, 2250)(1651, 2251)(1652, 2252)(1653, 2253)(1654, 2254)(1655, 2255)(1656, 2256)(1657, 2257)(1658, 2258)(1659, 2259)(1660, 2260)(1661, 2261)(1662, 2262)(1663, 2263)(1664, 2264)(1665, 2265)(1666, 2266)(1667, 2267)(1668, 2268)(1669, 2269)(1670, 2270)(1671, 2271)(1672, 2272)(1673, 2273)(1674, 2274)(1675, 2275)(1676, 2276)(1677, 2277)(1678, 2278)(1679, 2279)(1680, 2280)(1681, 2281)(1682, 2282)(1683, 2283)(1684, 2284)(1685, 2285)(1686, 2286)(1687, 2287)(1688, 2288)(1689, 2289)(1690, 2290)(1691, 2291)(1692, 2292)(1693, 2293)(1694, 2294)(1695, 2295)(1696, 2296)(1697, 2297)(1698, 2298)(1699, 2299)(1700, 2300)(1701, 2301)(1702, 2302)(1703, 2303)(1704, 2304)(1705, 2305)(1706, 2306)(1707, 2307)(1708, 2308)(1709, 2309)(1710, 2310)(1711, 2311)(1712, 2312)(1713, 2313)(1714, 2314)(1715, 2315)(1716, 2316)(1717, 2317)(1718, 2318)(1719, 2319)(1720, 2320)(1721, 2321)(1722, 2322)(1723, 2323)(1724, 2324)(1725, 2325)(1726, 2326)(1727, 2327)(1728, 2328)(1729, 2329)(1730, 2330)(1731, 2331)(1732, 2332)(1733, 2333)(1734, 2334)(1735, 2335)(1736, 2336)(1737, 2337)(1738, 2338)(1739, 2339)(1740, 2340)(1741, 2341)(1742, 2342)(1743, 2343)(1744, 2344)(1745, 2345)(1746, 2346)(1747, 2347)(1748, 2348)(1749, 2349)(1750, 2350)(1751, 2351)(1752, 2352)(1753, 2353)(1754, 2354)(1755, 2355)(1756, 2356)(1757, 2357)(1758, 2358)(1759, 2359)(1760, 2360)(1761, 2361)(1762, 2362)(1763, 2363)(1764, 2364)(1765, 2365)(1766, 2366)(1767, 2367)(1768, 2368)(1769, 2369)(1770, 2370)(1771, 2371)(1772, 2372)(1773, 2373)(1774, 2374)(1775, 2375)(1776, 2376)(1777, 2377)(1778, 2378)(1779, 2379)(1780, 2380)(1781, 2381)(1782, 2382)(1783, 2383)(1784, 2384)(1785, 2385)(1786, 2386)(1787, 2387)(1788, 2388)(1789, 2389)(1790, 2390)(1791, 2391)(1792, 2392)(1793, 2393)(1794, 2394)(1795, 2395)(1796, 2396)(1797, 2397)(1798, 2398)(1799, 2399)(1800, 2400) L = (1, 1203)(2, 1206)(3, 1201)(4, 1209)(5, 1211)(6, 1202)(7, 1215)(8, 1216)(9, 1204)(10, 1220)(11, 1205)(12, 1224)(13, 1225)(14, 1227)(15, 1207)(16, 1208)(17, 1231)(18, 1233)(19, 1228)(20, 1210)(21, 1238)(22, 1239)(23, 1241)(24, 1212)(25, 1213)(26, 1244)(27, 1214)(28, 1219)(29, 1248)(30, 1251)(31, 1217)(32, 1254)(33, 1218)(34, 1257)(35, 1259)(36, 1255)(37, 1261)(38, 1221)(39, 1222)(40, 1264)(41, 1223)(42, 1267)(43, 1269)(44, 1226)(45, 1273)(46, 1274)(47, 1276)(48, 1229)(49, 1278)(50, 1279)(51, 1230)(52, 1283)(53, 1280)(54, 1232)(55, 1236)(56, 1288)(57, 1234)(58, 1292)(59, 1235)(60, 1294)(61, 1237)(62, 1297)(63, 1299)(64, 1240)(65, 1303)(66, 1304)(67, 1242)(68, 1307)(69, 1243)(70, 1311)(71, 1308)(72, 1313)(73, 1245)(74, 1246)(75, 1316)(76, 1247)(77, 1320)(78, 1249)(79, 1250)(80, 1253)(81, 1326)(82, 1328)(83, 1252)(84, 1330)(85, 1332)(86, 1333)(87, 1335)(88, 1256)(89, 1337)(90, 1339)(91, 1317)(92, 1258)(93, 1343)(94, 1260)(95, 1347)(96, 1348)(97, 1262)(98, 1351)(99, 1263)(100, 1355)(101, 1352)(102, 1357)(103, 1265)(104, 1266)(105, 1360)(106, 1362)(107, 1268)(108, 1271)(109, 1366)(110, 1368)(111, 1270)(112, 1370)(113, 1272)(114, 1373)(115, 1375)(116, 1275)(117, 1291)(118, 1379)(119, 1381)(120, 1277)(121, 1385)(122, 1382)(123, 1388)(124, 1389)(125, 1391)(126, 1281)(127, 1393)(128, 1282)(129, 1396)(130, 1284)(131, 1399)(132, 1285)(133, 1286)(134, 1402)(135, 1287)(136, 1406)(137, 1289)(138, 1409)(139, 1290)(140, 1411)(141, 1413)(142, 1414)(143, 1293)(144, 1418)(145, 1403)(146, 1420)(147, 1295)(148, 1296)(149, 1423)(150, 1425)(151, 1298)(152, 1301)(153, 1429)(154, 1431)(155, 1300)(156, 1433)(157, 1302)(158, 1436)(159, 1438)(160, 1305)(161, 1441)(162, 1306)(163, 1444)(164, 1445)(165, 1447)(166, 1309)(167, 1449)(168, 1310)(169, 1452)(170, 1312)(171, 1456)(172, 1457)(173, 1314)(174, 1460)(175, 1315)(176, 1464)(177, 1461)(178, 1466)(179, 1318)(180, 1468)(181, 1319)(182, 1322)(183, 1472)(184, 1474)(185, 1321)(186, 1476)(187, 1477)(188, 1323)(189, 1324)(190, 1480)(191, 1325)(192, 1484)(193, 1327)(194, 1488)(195, 1489)(196, 1329)(197, 1493)(198, 1481)(199, 1331)(200, 1496)(201, 1498)(202, 1334)(203, 1345)(204, 1502)(205, 1504)(206, 1336)(207, 1508)(208, 1505)(209, 1338)(210, 1512)(211, 1340)(212, 1514)(213, 1341)(214, 1342)(215, 1517)(216, 1519)(217, 1520)(218, 1344)(219, 1455)(220, 1346)(221, 1522)(222, 1524)(223, 1349)(224, 1527)(225, 1350)(226, 1530)(227, 1531)(228, 1533)(229, 1353)(230, 1535)(231, 1354)(232, 1538)(233, 1356)(234, 1540)(235, 1541)(236, 1358)(237, 1543)(238, 1359)(239, 1547)(240, 1544)(241, 1361)(242, 1551)(243, 1553)(244, 1363)(245, 1364)(246, 1556)(247, 1365)(248, 1560)(249, 1367)(250, 1564)(251, 1565)(252, 1369)(253, 1569)(254, 1557)(255, 1419)(256, 1371)(257, 1372)(258, 1571)(259, 1573)(260, 1374)(261, 1377)(262, 1577)(263, 1579)(264, 1376)(265, 1581)(266, 1378)(267, 1584)(268, 1380)(269, 1587)(270, 1588)(271, 1590)(272, 1383)(273, 1592)(274, 1384)(275, 1595)(276, 1386)(277, 1387)(278, 1599)(279, 1600)(280, 1390)(281, 1398)(282, 1603)(283, 1605)(284, 1392)(285, 1609)(286, 1606)(287, 1611)(288, 1394)(289, 1395)(290, 1614)(291, 1615)(292, 1616)(293, 1397)(294, 1618)(295, 1598)(296, 1400)(297, 1620)(298, 1401)(299, 1624)(300, 1621)(301, 1570)(302, 1404)(303, 1627)(304, 1405)(305, 1408)(306, 1630)(307, 1632)(308, 1407)(309, 1617)(310, 1635)(311, 1636)(312, 1410)(313, 1638)(314, 1412)(315, 1639)(316, 1641)(317, 1415)(318, 1578)(319, 1416)(320, 1417)(321, 1610)(322, 1421)(323, 1647)(324, 1422)(325, 1649)(326, 1589)(327, 1424)(328, 1652)(329, 1654)(330, 1426)(331, 1427)(332, 1657)(333, 1428)(334, 1660)(335, 1430)(336, 1662)(337, 1663)(338, 1432)(339, 1601)(340, 1434)(341, 1435)(342, 1665)(343, 1437)(344, 1440)(345, 1668)(346, 1669)(347, 1439)(348, 1580)(349, 1671)(350, 1672)(351, 1442)(352, 1675)(353, 1443)(354, 1677)(355, 1678)(356, 1446)(357, 1454)(358, 1680)(359, 1682)(360, 1448)(361, 1685)(362, 1683)(363, 1686)(364, 1450)(365, 1451)(366, 1688)(367, 1689)(368, 1594)(369, 1453)(370, 1501)(371, 1458)(372, 1691)(373, 1459)(374, 1694)(375, 1695)(376, 1697)(377, 1462)(378, 1518)(379, 1463)(380, 1548)(381, 1465)(382, 1700)(383, 1701)(384, 1467)(385, 1704)(386, 1702)(387, 1469)(388, 1470)(389, 1526)(390, 1471)(391, 1710)(392, 1473)(393, 1713)(394, 1568)(395, 1475)(396, 1707)(397, 1716)(398, 1495)(399, 1478)(400, 1479)(401, 1539)(402, 1718)(403, 1482)(404, 1721)(405, 1483)(406, 1486)(407, 1724)(408, 1645)(409, 1485)(410, 1521)(411, 1487)(412, 1726)(413, 1634)(414, 1490)(415, 1491)(416, 1492)(417, 1509)(418, 1494)(419, 1729)(420, 1497)(421, 1500)(422, 1732)(423, 1699)(424, 1499)(425, 1712)(426, 1734)(427, 1503)(428, 1735)(429, 1736)(430, 1506)(431, 1709)(432, 1507)(433, 1739)(434, 1613)(435, 1510)(436, 1511)(437, 1728)(438, 1513)(439, 1515)(440, 1741)(441, 1516)(442, 1714)(443, 1673)(444, 1698)(445, 1608)(446, 1690)(447, 1523)(448, 1749)(449, 1525)(450, 1670)(451, 1751)(452, 1528)(453, 1753)(454, 1529)(455, 1755)(456, 1756)(457, 1532)(458, 1758)(459, 1759)(460, 1534)(461, 1761)(462, 1536)(463, 1537)(464, 1762)(465, 1542)(466, 1765)(467, 1766)(468, 1545)(469, 1546)(470, 1650)(471, 1549)(472, 1550)(473, 1643)(474, 1769)(475, 1552)(476, 1771)(477, 1554)(478, 1555)(479, 1773)(480, 1558)(481, 1776)(482, 1559)(483, 1562)(484, 1778)(485, 1561)(486, 1563)(487, 1780)(488, 1566)(489, 1567)(490, 1646)(491, 1572)(492, 1781)(493, 1774)(494, 1574)(495, 1575)(496, 1763)(497, 1576)(498, 1644)(499, 1623)(500, 1582)(501, 1583)(502, 1586)(503, 1786)(504, 1585)(505, 1747)(506, 1754)(507, 1596)(508, 1787)(509, 1631)(510, 1591)(511, 1789)(512, 1625)(513, 1593)(514, 1642)(515, 1767)(516, 1597)(517, 1790)(518, 1602)(519, 1791)(520, 1764)(521, 1604)(522, 1748)(523, 1792)(524, 1607)(525, 1757)(526, 1612)(527, 1779)(528, 1637)(529, 1619)(530, 1770)(531, 1777)(532, 1622)(533, 1782)(534, 1626)(535, 1628)(536, 1629)(537, 1788)(538, 1768)(539, 1633)(540, 1745)(541, 1640)(542, 1784)(543, 1750)(544, 1794)(545, 1740)(546, 1793)(547, 1705)(548, 1722)(549, 1648)(550, 1743)(551, 1651)(552, 1796)(553, 1653)(554, 1706)(555, 1655)(556, 1656)(557, 1725)(558, 1658)(559, 1659)(560, 1797)(561, 1661)(562, 1664)(563, 1696)(564, 1720)(565, 1666)(566, 1667)(567, 1715)(568, 1738)(569, 1674)(570, 1730)(571, 1676)(572, 1798)(573, 1679)(574, 1693)(575, 1795)(576, 1681)(577, 1731)(578, 1684)(579, 1727)(580, 1687)(581, 1692)(582, 1733)(583, 1799)(584, 1742)(585, 1800)(586, 1703)(587, 1708)(588, 1737)(589, 1711)(590, 1717)(591, 1719)(592, 1723)(593, 1746)(594, 1744)(595, 1775)(596, 1752)(597, 1760)(598, 1772)(599, 1783)(600, 1785)(601, 1801)(602, 1802)(603, 1803)(604, 1804)(605, 1805)(606, 1806)(607, 1807)(608, 1808)(609, 1809)(610, 1810)(611, 1811)(612, 1812)(613, 1813)(614, 1814)(615, 1815)(616, 1816)(617, 1817)(618, 1818)(619, 1819)(620, 1820)(621, 1821)(622, 1822)(623, 1823)(624, 1824)(625, 1825)(626, 1826)(627, 1827)(628, 1828)(629, 1829)(630, 1830)(631, 1831)(632, 1832)(633, 1833)(634, 1834)(635, 1835)(636, 1836)(637, 1837)(638, 1838)(639, 1839)(640, 1840)(641, 1841)(642, 1842)(643, 1843)(644, 1844)(645, 1845)(646, 1846)(647, 1847)(648, 1848)(649, 1849)(650, 1850)(651, 1851)(652, 1852)(653, 1853)(654, 1854)(655, 1855)(656, 1856)(657, 1857)(658, 1858)(659, 1859)(660, 1860)(661, 1861)(662, 1862)(663, 1863)(664, 1864)(665, 1865)(666, 1866)(667, 1867)(668, 1868)(669, 1869)(670, 1870)(671, 1871)(672, 1872)(673, 1873)(674, 1874)(675, 1875)(676, 1876)(677, 1877)(678, 1878)(679, 1879)(680, 1880)(681, 1881)(682, 1882)(683, 1883)(684, 1884)(685, 1885)(686, 1886)(687, 1887)(688, 1888)(689, 1889)(690, 1890)(691, 1891)(692, 1892)(693, 1893)(694, 1894)(695, 1895)(696, 1896)(697, 1897)(698, 1898)(699, 1899)(700, 1900)(701, 1901)(702, 1902)(703, 1903)(704, 1904)(705, 1905)(706, 1906)(707, 1907)(708, 1908)(709, 1909)(710, 1910)(711, 1911)(712, 1912)(713, 1913)(714, 1914)(715, 1915)(716, 1916)(717, 1917)(718, 1918)(719, 1919)(720, 1920)(721, 1921)(722, 1922)(723, 1923)(724, 1924)(725, 1925)(726, 1926)(727, 1927)(728, 1928)(729, 1929)(730, 1930)(731, 1931)(732, 1932)(733, 1933)(734, 1934)(735, 1935)(736, 1936)(737, 1937)(738, 1938)(739, 1939)(740, 1940)(741, 1941)(742, 1942)(743, 1943)(744, 1944)(745, 1945)(746, 1946)(747, 1947)(748, 1948)(749, 1949)(750, 1950)(751, 1951)(752, 1952)(753, 1953)(754, 1954)(755, 1955)(756, 1956)(757, 1957)(758, 1958)(759, 1959)(760, 1960)(761, 1961)(762, 1962)(763, 1963)(764, 1964)(765, 1965)(766, 1966)(767, 1967)(768, 1968)(769, 1969)(770, 1970)(771, 1971)(772, 1972)(773, 1973)(774, 1974)(775, 1975)(776, 1976)(777, 1977)(778, 1978)(779, 1979)(780, 1980)(781, 1981)(782, 1982)(783, 1983)(784, 1984)(785, 1985)(786, 1986)(787, 1987)(788, 1988)(789, 1989)(790, 1990)(791, 1991)(792, 1992)(793, 1993)(794, 1994)(795, 1995)(796, 1996)(797, 1997)(798, 1998)(799, 1999)(800, 2000)(801, 2001)(802, 2002)(803, 2003)(804, 2004)(805, 2005)(806, 2006)(807, 2007)(808, 2008)(809, 2009)(810, 2010)(811, 2011)(812, 2012)(813, 2013)(814, 2014)(815, 2015)(816, 2016)(817, 2017)(818, 2018)(819, 2019)(820, 2020)(821, 2021)(822, 2022)(823, 2023)(824, 2024)(825, 2025)(826, 2026)(827, 2027)(828, 2028)(829, 2029)(830, 2030)(831, 2031)(832, 2032)(833, 2033)(834, 2034)(835, 2035)(836, 2036)(837, 2037)(838, 2038)(839, 2039)(840, 2040)(841, 2041)(842, 2042)(843, 2043)(844, 2044)(845, 2045)(846, 2046)(847, 2047)(848, 2048)(849, 2049)(850, 2050)(851, 2051)(852, 2052)(853, 2053)(854, 2054)(855, 2055)(856, 2056)(857, 2057)(858, 2058)(859, 2059)(860, 2060)(861, 2061)(862, 2062)(863, 2063)(864, 2064)(865, 2065)(866, 2066)(867, 2067)(868, 2068)(869, 2069)(870, 2070)(871, 2071)(872, 2072)(873, 2073)(874, 2074)(875, 2075)(876, 2076)(877, 2077)(878, 2078)(879, 2079)(880, 2080)(881, 2081)(882, 2082)(883, 2083)(884, 2084)(885, 2085)(886, 2086)(887, 2087)(888, 2088)(889, 2089)(890, 2090)(891, 2091)(892, 2092)(893, 2093)(894, 2094)(895, 2095)(896, 2096)(897, 2097)(898, 2098)(899, 2099)(900, 2100)(901, 2101)(902, 2102)(903, 2103)(904, 2104)(905, 2105)(906, 2106)(907, 2107)(908, 2108)(909, 2109)(910, 2110)(911, 2111)(912, 2112)(913, 2113)(914, 2114)(915, 2115)(916, 2116)(917, 2117)(918, 2118)(919, 2119)(920, 2120)(921, 2121)(922, 2122)(923, 2123)(924, 2124)(925, 2125)(926, 2126)(927, 2127)(928, 2128)(929, 2129)(930, 2130)(931, 2131)(932, 2132)(933, 2133)(934, 2134)(935, 2135)(936, 2136)(937, 2137)(938, 2138)(939, 2139)(940, 2140)(941, 2141)(942, 2142)(943, 2143)(944, 2144)(945, 2145)(946, 2146)(947, 2147)(948, 2148)(949, 2149)(950, 2150)(951, 2151)(952, 2152)(953, 2153)(954, 2154)(955, 2155)(956, 2156)(957, 2157)(958, 2158)(959, 2159)(960, 2160)(961, 2161)(962, 2162)(963, 2163)(964, 2164)(965, 2165)(966, 2166)(967, 2167)(968, 2168)(969, 2169)(970, 2170)(971, 2171)(972, 2172)(973, 2173)(974, 2174)(975, 2175)(976, 2176)(977, 2177)(978, 2178)(979, 2179)(980, 2180)(981, 2181)(982, 2182)(983, 2183)(984, 2184)(985, 2185)(986, 2186)(987, 2187)(988, 2188)(989, 2189)(990, 2190)(991, 2191)(992, 2192)(993, 2193)(994, 2194)(995, 2195)(996, 2196)(997, 2197)(998, 2198)(999, 2199)(1000, 2200)(1001, 2201)(1002, 2202)(1003, 2203)(1004, 2204)(1005, 2205)(1006, 2206)(1007, 2207)(1008, 2208)(1009, 2209)(1010, 2210)(1011, 2211)(1012, 2212)(1013, 2213)(1014, 2214)(1015, 2215)(1016, 2216)(1017, 2217)(1018, 2218)(1019, 2219)(1020, 2220)(1021, 2221)(1022, 2222)(1023, 2223)(1024, 2224)(1025, 2225)(1026, 2226)(1027, 2227)(1028, 2228)(1029, 2229)(1030, 2230)(1031, 2231)(1032, 2232)(1033, 2233)(1034, 2234)(1035, 2235)(1036, 2236)(1037, 2237)(1038, 2238)(1039, 2239)(1040, 2240)(1041, 2241)(1042, 2242)(1043, 2243)(1044, 2244)(1045, 2245)(1046, 2246)(1047, 2247)(1048, 2248)(1049, 2249)(1050, 2250)(1051, 2251)(1052, 2252)(1053, 2253)(1054, 2254)(1055, 2255)(1056, 2256)(1057, 2257)(1058, 2258)(1059, 2259)(1060, 2260)(1061, 2261)(1062, 2262)(1063, 2263)(1064, 2264)(1065, 2265)(1066, 2266)(1067, 2267)(1068, 2268)(1069, 2269)(1070, 2270)(1071, 2271)(1072, 2272)(1073, 2273)(1074, 2274)(1075, 2275)(1076, 2276)(1077, 2277)(1078, 2278)(1079, 2279)(1080, 2280)(1081, 2281)(1082, 2282)(1083, 2283)(1084, 2284)(1085, 2285)(1086, 2286)(1087, 2287)(1088, 2288)(1089, 2289)(1090, 2290)(1091, 2291)(1092, 2292)(1093, 2293)(1094, 2294)(1095, 2295)(1096, 2296)(1097, 2297)(1098, 2298)(1099, 2299)(1100, 2300)(1101, 2301)(1102, 2302)(1103, 2303)(1104, 2304)(1105, 2305)(1106, 2306)(1107, 2307)(1108, 2308)(1109, 2309)(1110, 2310)(1111, 2311)(1112, 2312)(1113, 2313)(1114, 2314)(1115, 2315)(1116, 2316)(1117, 2317)(1118, 2318)(1119, 2319)(1120, 2320)(1121, 2321)(1122, 2322)(1123, 2323)(1124, 2324)(1125, 2325)(1126, 2326)(1127, 2327)(1128, 2328)(1129, 2329)(1130, 2330)(1131, 2331)(1132, 2332)(1133, 2333)(1134, 2334)(1135, 2335)(1136, 2336)(1137, 2337)(1138, 2338)(1139, 2339)(1140, 2340)(1141, 2341)(1142, 2342)(1143, 2343)(1144, 2344)(1145, 2345)(1146, 2346)(1147, 2347)(1148, 2348)(1149, 2349)(1150, 2350)(1151, 2351)(1152, 2352)(1153, 2353)(1154, 2354)(1155, 2355)(1156, 2356)(1157, 2357)(1158, 2358)(1159, 2359)(1160, 2360)(1161, 2361)(1162, 2362)(1163, 2363)(1164, 2364)(1165, 2365)(1166, 2366)(1167, 2367)(1168, 2368)(1169, 2369)(1170, 2370)(1171, 2371)(1172, 2372)(1173, 2373)(1174, 2374)(1175, 2375)(1176, 2376)(1177, 2377)(1178, 2378)(1179, 2379)(1180, 2380)(1181, 2381)(1182, 2382)(1183, 2383)(1184, 2384)(1185, 2385)(1186, 2386)(1187, 2387)(1188, 2388)(1189, 2389)(1190, 2390)(1191, 2391)(1192, 2392)(1193, 2393)(1194, 2394)(1195, 2395)(1196, 2396)(1197, 2397)(1198, 2398)(1199, 2399)(1200, 2400) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E16.1293 Graph:: simple bipartite v = 720 e = 1200 f = 450 degree seq :: [ 2^600, 10^120 ] E16.1297 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5}) Quotient :: dipole Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^5, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-1)^4, (Y3 * Y2^-1)^4, (Y1 * Y2^-2)^6, Y2^-1 * Y1 * Y2^-2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1, (Y2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-1 * Y1)^2 ] Map:: R = (1, 601, 2, 602)(3, 603, 7, 607)(4, 604, 9, 609)(5, 605, 11, 611)(6, 606, 13, 613)(8, 608, 17, 617)(10, 610, 20, 620)(12, 612, 23, 623)(14, 614, 26, 626)(15, 615, 25, 625)(16, 616, 28, 628)(18, 618, 32, 632)(19, 619, 21, 621)(22, 622, 38, 638)(24, 624, 42, 642)(27, 627, 47, 647)(29, 629, 50, 650)(30, 630, 49, 649)(31, 631, 52, 652)(33, 633, 56, 656)(34, 634, 57, 657)(35, 635, 58, 658)(36, 636, 54, 654)(37, 637, 61, 661)(39, 639, 64, 664)(40, 640, 63, 663)(41, 641, 66, 666)(43, 643, 70, 670)(44, 644, 71, 671)(45, 645, 72, 672)(46, 646, 68, 668)(48, 648, 77, 677)(51, 651, 82, 682)(53, 653, 84, 684)(55, 655, 86, 686)(59, 659, 93, 693)(60, 660, 94, 694)(62, 662, 97, 697)(65, 665, 102, 702)(67, 667, 104, 704)(69, 669, 106, 706)(73, 673, 113, 713)(74, 674, 114, 714)(75, 675, 111, 711)(76, 676, 116, 716)(78, 678, 120, 720)(79, 679, 121, 721)(80, 680, 122, 722)(81, 681, 118, 718)(83, 683, 127, 727)(85, 685, 131, 731)(87, 687, 134, 734)(88, 688, 133, 733)(89, 689, 136, 736)(90, 690, 138, 738)(91, 691, 95, 695)(92, 692, 141, 741)(96, 696, 147, 747)(98, 698, 151, 751)(99, 699, 152, 752)(100, 700, 153, 753)(101, 701, 149, 749)(103, 703, 158, 758)(105, 705, 162, 762)(107, 707, 165, 765)(108, 708, 164, 764)(109, 709, 167, 767)(110, 710, 169, 769)(112, 712, 172, 772)(115, 715, 177, 777)(117, 717, 179, 779)(119, 719, 181, 781)(123, 723, 188, 788)(124, 724, 189, 789)(125, 725, 186, 786)(126, 726, 191, 791)(128, 728, 195, 795)(129, 729, 196, 796)(130, 730, 193, 793)(132, 732, 201, 801)(135, 735, 206, 806)(137, 737, 208, 808)(139, 739, 210, 810)(140, 740, 211, 811)(142, 742, 213, 813)(143, 743, 215, 815)(144, 744, 217, 817)(145, 745, 199, 799)(146, 746, 220, 820)(148, 748, 222, 822)(150, 750, 224, 824)(154, 754, 231, 831)(155, 755, 232, 832)(156, 756, 229, 829)(157, 757, 234, 834)(159, 759, 238, 838)(160, 760, 239, 839)(161, 761, 236, 836)(163, 763, 244, 844)(166, 766, 249, 849)(168, 768, 251, 851)(170, 770, 253, 853)(171, 771, 254, 854)(173, 773, 256, 856)(174, 774, 258, 858)(175, 775, 260, 860)(176, 776, 242, 842)(178, 778, 265, 865)(180, 780, 269, 869)(182, 782, 272, 872)(183, 783, 271, 871)(184, 784, 274, 874)(185, 785, 276, 876)(187, 787, 279, 879)(190, 790, 262, 862)(192, 792, 285, 885)(194, 794, 287, 887)(197, 797, 292, 892)(198, 798, 293, 893)(200, 800, 295, 895)(202, 802, 299, 899)(203, 803, 300, 900)(204, 804, 301, 901)(205, 805, 297, 897)(207, 807, 306, 906)(209, 809, 310, 910)(212, 812, 314, 914)(214, 814, 317, 917)(216, 816, 319, 919)(218, 818, 321, 921)(219, 819, 233, 833)(221, 821, 324, 924)(223, 823, 328, 928)(225, 825, 331, 931)(226, 826, 330, 930)(227, 827, 333, 933)(228, 828, 335, 935)(230, 830, 338, 938)(235, 835, 344, 944)(237, 837, 346, 946)(240, 840, 351, 951)(241, 841, 352, 952)(243, 843, 354, 954)(245, 845, 358, 958)(246, 846, 359, 959)(247, 847, 360, 960)(248, 848, 356, 956)(250, 850, 365, 965)(252, 852, 369, 969)(255, 855, 373, 973)(257, 857, 376, 976)(259, 859, 378, 978)(261, 861, 380, 980)(263, 863, 322, 922)(264, 864, 381, 981)(266, 866, 384, 984)(267, 867, 385, 985)(268, 868, 382, 982)(270, 870, 390, 990)(273, 873, 343, 943)(275, 875, 396, 996)(277, 877, 398, 998)(278, 878, 353, 953)(280, 880, 400, 1000)(281, 881, 402, 1002)(282, 882, 341, 941)(283, 883, 388, 988)(284, 884, 332, 932)(286, 886, 408, 1008)(288, 888, 374, 974)(289, 889, 410, 1010)(290, 890, 412, 1012)(291, 891, 414, 1014)(294, 894, 337, 937)(296, 896, 419, 1019)(298, 898, 421, 1021)(302, 902, 427, 1027)(303, 903, 379, 979)(304, 904, 425, 1025)(305, 905, 364, 964)(307, 907, 430, 1030)(308, 908, 431, 1031)(309, 909, 428, 1028)(311, 911, 434, 1034)(312, 912, 436, 1036)(313, 913, 438, 1038)(315, 915, 347, 947)(316, 916, 440, 1040)(318, 918, 441, 1041)(320, 920, 362, 962)(323, 923, 447, 1047)(325, 925, 450, 1050)(326, 926, 451, 1051)(327, 927, 448, 1048)(329, 929, 455, 1055)(334, 934, 407, 1007)(336, 936, 462, 1062)(339, 939, 464, 1064)(340, 940, 404, 1004)(342, 942, 453, 1053)(345, 945, 469, 1069)(348, 948, 471, 1071)(349, 949, 473, 1073)(350, 950, 387, 987)(355, 955, 478, 1078)(357, 957, 480, 1080)(361, 961, 445, 1045)(363, 963, 484, 1084)(366, 966, 488, 1088)(367, 967, 417, 1017)(368, 968, 486, 1086)(370, 970, 491, 1091)(371, 971, 492, 1092)(372, 972, 494, 1094)(375, 975, 496, 1096)(377, 977, 435, 1035)(383, 983, 502, 1102)(386, 986, 475, 1075)(389, 989, 506, 1106)(391, 991, 481, 1081)(392, 992, 510, 1110)(393, 993, 511, 1111)(394, 994, 508, 1108)(395, 995, 512, 1112)(397, 997, 515, 1115)(399, 999, 517, 1117)(401, 1001, 490, 1090)(403, 1003, 498, 1098)(405, 1005, 519, 1119)(406, 1006, 500, 1100)(409, 1009, 495, 1095)(411, 1011, 501, 1101)(413, 1013, 526, 1126)(415, 1015, 452, 1052)(416, 1016, 489, 1089)(418, 1018, 529, 1129)(420, 1020, 531, 1131)(422, 1022, 456, 1056)(423, 1023, 533, 1133)(424, 1024, 534, 1134)(426, 1026, 535, 1135)(429, 1029, 537, 1137)(432, 1032, 476, 1076)(433, 1033, 465, 1065)(437, 1037, 499, 1099)(439, 1039, 470, 1070)(442, 1042, 542, 1142)(443, 1043, 466, 1066)(444, 1044, 493, 1093)(446, 1046, 468, 1068)(449, 1049, 548, 1148)(454, 1054, 552, 1152)(457, 1057, 556, 1156)(458, 1058, 557, 1157)(459, 1059, 554, 1154)(460, 1060, 558, 1158)(461, 1061, 560, 1160)(463, 1063, 562, 1162)(467, 1067, 564, 1164)(472, 1072, 547, 1147)(474, 1074, 570, 1170)(477, 1077, 573, 1173)(479, 1079, 575, 1175)(482, 1082, 577, 1177)(483, 1083, 578, 1178)(485, 1085, 579, 1179)(487, 1087, 580, 1180)(497, 1097, 585, 1185)(503, 1103, 589, 1189)(504, 1104, 550, 1150)(505, 1105, 521, 1121)(507, 1107, 566, 1166)(509, 1109, 576, 1176)(513, 1113, 568, 1168)(514, 1114, 551, 1151)(516, 1116, 563, 1163)(518, 1118, 561, 1161)(520, 1120, 571, 1171)(522, 1122, 553, 1153)(523, 1123, 592, 1192)(524, 1124, 559, 1159)(525, 1125, 574, 1174)(527, 1127, 565, 1165)(528, 1128, 586, 1186)(530, 1130, 569, 1169)(532, 1132, 555, 1155)(536, 1136, 583, 1183)(538, 1138, 581, 1181)(539, 1139, 591, 1191)(540, 1140, 545, 1145)(541, 1141, 594, 1194)(543, 1143, 572, 1172)(544, 1144, 588, 1188)(546, 1146, 587, 1187)(549, 1149, 595, 1195)(567, 1167, 598, 1198)(582, 1182, 597, 1197)(584, 1184, 600, 1200)(590, 1190, 599, 1199)(593, 1193, 596, 1196)(1201, 1801, 1203, 1803, 1208, 1808, 1210, 1810, 1204, 1804)(1202, 1802, 1205, 1805, 1212, 1812, 1214, 1814, 1206, 1806)(1207, 1807, 1215, 1815, 1227, 1827, 1229, 1829, 1216, 1816)(1209, 1809, 1218, 1818, 1233, 1833, 1234, 1834, 1219, 1819)(1211, 1811, 1221, 1821, 1237, 1837, 1239, 1839, 1222, 1822)(1213, 1813, 1224, 1824, 1243, 1843, 1244, 1844, 1225, 1825)(1217, 1817, 1230, 1830, 1251, 1851, 1253, 1853, 1231, 1831)(1220, 1820, 1235, 1835, 1259, 1859, 1260, 1860, 1236, 1836)(1223, 1823, 1240, 1840, 1265, 1865, 1267, 1867, 1241, 1841)(1226, 1826, 1245, 1845, 1273, 1873, 1274, 1874, 1246, 1846)(1228, 1828, 1248, 1848, 1278, 1878, 1279, 1879, 1249, 1849)(1232, 1832, 1254, 1854, 1285, 1885, 1287, 1887, 1255, 1855)(1238, 1838, 1262, 1862, 1298, 1898, 1299, 1899, 1263, 1863)(1242, 1842, 1268, 1868, 1305, 1905, 1307, 1907, 1269, 1869)(1247, 1847, 1275, 1875, 1315, 1915, 1317, 1917, 1276, 1876)(1250, 1850, 1280, 1880, 1323, 1923, 1324, 1924, 1281, 1881)(1252, 1852, 1283, 1883, 1328, 1928, 1292, 1892, 1258, 1858)(1256, 1856, 1288, 1888, 1335, 1935, 1337, 1937, 1289, 1889)(1257, 1857, 1290, 1890, 1339, 1939, 1340, 1940, 1291, 1891)(1261, 1861, 1295, 1895, 1346, 1946, 1348, 1948, 1296, 1896)(1264, 1864, 1300, 1900, 1354, 1954, 1355, 1955, 1301, 1901)(1266, 1866, 1303, 1903, 1359, 1959, 1312, 1912, 1272, 1872)(1270, 1870, 1308, 1908, 1366, 1966, 1368, 1968, 1309, 1909)(1271, 1871, 1310, 1910, 1370, 1970, 1371, 1971, 1311, 1911)(1277, 1877, 1318, 1918, 1380, 1980, 1382, 1982, 1319, 1919)(1282, 1882, 1325, 1925, 1390, 1990, 1392, 1992, 1326, 1926)(1284, 1884, 1329, 1929, 1397, 1997, 1398, 1998, 1330, 1930)(1286, 1886, 1332, 1932, 1402, 2002, 1403, 2003, 1333, 1933)(1293, 1893, 1342, 1942, 1414, 2014, 1416, 2016, 1343, 1943)(1294, 1894, 1344, 1944, 1418, 2018, 1419, 2019, 1345, 1945)(1297, 1897, 1349, 1949, 1423, 2023, 1425, 2025, 1350, 1950)(1302, 1902, 1356, 1956, 1433, 2033, 1435, 2035, 1357, 1957)(1304, 1904, 1360, 1960, 1440, 2040, 1441, 2041, 1361, 1961)(1306, 1906, 1363, 1963, 1445, 2045, 1446, 2046, 1364, 1964)(1313, 1913, 1373, 1973, 1457, 2057, 1459, 2059, 1374, 1974)(1314, 1914, 1375, 1975, 1461, 2061, 1462, 2062, 1376, 1976)(1316, 1916, 1378, 1978, 1466, 2066, 1387, 1987, 1322, 1922)(1320, 1920, 1383, 1983, 1473, 2073, 1475, 2075, 1384, 1984)(1321, 1921, 1385, 1985, 1477, 2077, 1478, 2078, 1386, 1986)(1327, 1927, 1393, 1993, 1486, 2086, 1488, 2088, 1394, 1994)(1331, 1931, 1399, 1999, 1494, 2094, 1496, 2096, 1400, 2000)(1334, 1934, 1404, 2004, 1502, 2102, 1503, 2103, 1405, 2005)(1336, 1936, 1407, 2007, 1507, 2107, 1409, 2009, 1338, 1938)(1341, 1941, 1412, 2012, 1515, 2115, 1516, 2116, 1413, 2013)(1347, 1947, 1421, 2021, 1525, 2125, 1430, 2030, 1353, 1953)(1351, 1951, 1426, 2026, 1532, 2132, 1534, 2134, 1427, 2027)(1352, 1952, 1428, 2028, 1536, 2136, 1537, 2137, 1429, 2029)(1358, 1958, 1436, 2036, 1545, 2145, 1547, 2147, 1437, 2037)(1362, 1962, 1442, 2042, 1553, 2153, 1555, 2155, 1443, 2043)(1365, 1965, 1447, 2047, 1561, 2161, 1562, 2162, 1448, 2048)(1367, 1967, 1450, 2050, 1566, 2166, 1452, 2052, 1369, 1969)(1372, 1972, 1455, 2055, 1574, 2174, 1575, 2175, 1456, 2056)(1377, 1977, 1463, 2063, 1411, 2011, 1513, 2113, 1464, 2064)(1379, 1979, 1467, 2067, 1586, 2186, 1587, 2187, 1468, 2068)(1381, 1981, 1470, 2070, 1591, 2191, 1592, 2192, 1471, 2071)(1388, 1988, 1480, 2080, 1601, 2201, 1603, 2203, 1481, 2081)(1389, 1989, 1482, 2082, 1604, 2204, 1517, 2117, 1483, 2083)(1391, 1991, 1484, 2084, 1605, 2205, 1491, 2091, 1396, 1996)(1395, 1995, 1489, 2089, 1611, 2211, 1613, 2213, 1490, 2090)(1401, 2001, 1497, 2097, 1620, 2220, 1622, 2222, 1498, 2098)(1406, 2006, 1504, 2104, 1493, 2093, 1617, 2217, 1505, 2105)(1408, 2008, 1508, 2108, 1632, 2232, 1633, 2233, 1509, 2109)(1410, 2010, 1511, 2111, 1635, 2235, 1637, 2237, 1512, 2112)(1415, 2015, 1518, 2118, 1642, 2242, 1520, 2120, 1417, 2017)(1420, 2020, 1522, 2122, 1454, 2054, 1572, 2172, 1523, 2123)(1422, 2022, 1526, 2126, 1652, 2252, 1614, 2214, 1527, 2127)(1424, 2024, 1529, 2129, 1656, 2256, 1657, 2257, 1530, 2130)(1431, 2031, 1539, 2139, 1665, 2265, 1666, 2266, 1540, 2140)(1432, 2032, 1541, 2141, 1602, 2202, 1576, 2176, 1542, 2142)(1434, 2034, 1543, 2143, 1667, 2267, 1550, 2150, 1439, 2039)(1438, 2038, 1548, 2148, 1672, 2272, 1674, 2274, 1549, 2149)(1444, 2044, 1556, 2156, 1679, 2279, 1681, 2281, 1557, 2157)(1449, 2049, 1563, 2163, 1552, 2152, 1631, 2231, 1564, 2164)(1451, 2051, 1567, 2167, 1689, 2289, 1690, 2290, 1568, 2168)(1453, 2053, 1570, 2170, 1641, 2241, 1693, 2293, 1571, 2171)(1458, 2058, 1577, 2177, 1697, 2297, 1579, 2179, 1460, 2060)(1465, 2065, 1582, 2182, 1623, 2223, 1499, 2099, 1583, 2183)(1469, 2069, 1588, 2188, 1640, 2240, 1707, 2307, 1589, 2189)(1472, 2072, 1593, 2193, 1634, 2234, 1510, 2110, 1594, 2194)(1474, 2074, 1595, 2195, 1713, 2313, 1597, 2197, 1476, 2076)(1479, 2079, 1599, 2199, 1619, 2219, 1718, 2318, 1600, 2200)(1485, 2085, 1606, 2206, 1720, 2320, 1721, 2321, 1607, 2207)(1487, 2087, 1609, 2209, 1723, 2323, 1724, 2324, 1610, 2210)(1492, 2092, 1615, 2215, 1727, 2327, 1728, 2328, 1616, 2216)(1495, 2095, 1618, 2218, 1730, 2330, 1626, 2226, 1501, 2101)(1500, 2100, 1624, 2224, 1722, 2322, 1608, 2208, 1625, 2225)(1506, 2106, 1628, 2228, 1716, 2316, 1598, 2198, 1629, 2229)(1514, 2114, 1612, 2212, 1725, 2325, 1741, 2341, 1639, 2239)(1519, 2119, 1643, 2243, 1743, 2343, 1744, 2344, 1644, 2244)(1521, 2121, 1645, 2245, 1745, 2345, 1746, 2346, 1646, 2246)(1524, 2124, 1648, 2248, 1682, 2282, 1558, 2158, 1649, 2249)(1528, 2128, 1653, 2253, 1696, 2296, 1753, 2353, 1654, 2254)(1531, 2131, 1658, 2258, 1691, 2291, 1569, 2169, 1659, 2259)(1533, 2133, 1660, 2260, 1759, 2359, 1661, 2261, 1535, 2135)(1538, 2138, 1663, 2263, 1678, 2278, 1763, 2363, 1664, 2264)(1544, 2144, 1668, 2268, 1765, 2365, 1714, 2314, 1596, 2196)(1546, 2146, 1670, 2270, 1767, 2367, 1768, 2368, 1671, 2271)(1551, 2151, 1675, 2275, 1771, 2371, 1772, 2372, 1676, 2276)(1554, 2154, 1677, 2277, 1774, 2374, 1685, 2285, 1560, 2160)(1559, 2159, 1683, 2283, 1766, 2366, 1669, 2269, 1684, 2284)(1565, 2165, 1686, 2286, 1761, 2361, 1662, 2262, 1687, 2287)(1573, 2173, 1673, 2273, 1769, 2369, 1784, 2384, 1695, 2295)(1578, 2178, 1698, 2298, 1786, 2386, 1787, 2387, 1699, 2299)(1580, 2180, 1627, 2227, 1736, 2336, 1788, 2388, 1700, 2300)(1581, 2181, 1701, 2301, 1758, 2358, 1705, 2305, 1585, 2185)(1584, 2184, 1703, 2303, 1773, 2373, 1762, 2362, 1704, 2304)(1590, 2190, 1708, 2308, 1791, 2391, 1792, 2392, 1709, 2309)(1621, 2221, 1732, 2332, 1794, 2394, 1789, 2389, 1702, 2302)(1630, 2230, 1738, 2338, 1780, 2380, 1760, 2360, 1739, 2339)(1636, 2236, 1740, 2340, 1779, 2379, 1726, 2326, 1638, 2238)(1647, 2247, 1747, 2347, 1712, 2312, 1751, 2351, 1651, 2251)(1650, 2250, 1749, 2349, 1729, 2329, 1717, 2317, 1750, 2350)(1655, 2255, 1754, 2354, 1797, 2397, 1798, 2398, 1755, 2355)(1680, 2280, 1776, 2376, 1800, 2400, 1795, 2395, 1748, 2348)(1688, 2288, 1781, 2381, 1737, 2337, 1715, 2315, 1782, 2382)(1692, 2292, 1783, 2383, 1735, 2335, 1770, 2370, 1694, 2294)(1706, 2306, 1790, 2390, 1731, 2331, 1785, 2385, 1711, 2311)(1710, 2310, 1793, 2393, 1734, 2334, 1733, 2333, 1764, 2364)(1719, 2319, 1756, 2356, 1799, 2399, 1778, 2378, 1777, 2377)(1742, 2342, 1757, 2357, 1752, 2352, 1796, 2396, 1775, 2375) L = (1, 1202)(2, 1201)(3, 1207)(4, 1209)(5, 1211)(6, 1213)(7, 1203)(8, 1217)(9, 1204)(10, 1220)(11, 1205)(12, 1223)(13, 1206)(14, 1226)(15, 1225)(16, 1228)(17, 1208)(18, 1232)(19, 1221)(20, 1210)(21, 1219)(22, 1238)(23, 1212)(24, 1242)(25, 1215)(26, 1214)(27, 1247)(28, 1216)(29, 1250)(30, 1249)(31, 1252)(32, 1218)(33, 1256)(34, 1257)(35, 1258)(36, 1254)(37, 1261)(38, 1222)(39, 1264)(40, 1263)(41, 1266)(42, 1224)(43, 1270)(44, 1271)(45, 1272)(46, 1268)(47, 1227)(48, 1277)(49, 1230)(50, 1229)(51, 1282)(52, 1231)(53, 1284)(54, 1236)(55, 1286)(56, 1233)(57, 1234)(58, 1235)(59, 1293)(60, 1294)(61, 1237)(62, 1297)(63, 1240)(64, 1239)(65, 1302)(66, 1241)(67, 1304)(68, 1246)(69, 1306)(70, 1243)(71, 1244)(72, 1245)(73, 1313)(74, 1314)(75, 1311)(76, 1316)(77, 1248)(78, 1320)(79, 1321)(80, 1322)(81, 1318)(82, 1251)(83, 1327)(84, 1253)(85, 1331)(86, 1255)(87, 1334)(88, 1333)(89, 1336)(90, 1338)(91, 1295)(92, 1341)(93, 1259)(94, 1260)(95, 1291)(96, 1347)(97, 1262)(98, 1351)(99, 1352)(100, 1353)(101, 1349)(102, 1265)(103, 1358)(104, 1267)(105, 1362)(106, 1269)(107, 1365)(108, 1364)(109, 1367)(110, 1369)(111, 1275)(112, 1372)(113, 1273)(114, 1274)(115, 1377)(116, 1276)(117, 1379)(118, 1281)(119, 1381)(120, 1278)(121, 1279)(122, 1280)(123, 1388)(124, 1389)(125, 1386)(126, 1391)(127, 1283)(128, 1395)(129, 1396)(130, 1393)(131, 1285)(132, 1401)(133, 1288)(134, 1287)(135, 1406)(136, 1289)(137, 1408)(138, 1290)(139, 1410)(140, 1411)(141, 1292)(142, 1413)(143, 1415)(144, 1417)(145, 1399)(146, 1420)(147, 1296)(148, 1422)(149, 1301)(150, 1424)(151, 1298)(152, 1299)(153, 1300)(154, 1431)(155, 1432)(156, 1429)(157, 1434)(158, 1303)(159, 1438)(160, 1439)(161, 1436)(162, 1305)(163, 1444)(164, 1308)(165, 1307)(166, 1449)(167, 1309)(168, 1451)(169, 1310)(170, 1453)(171, 1454)(172, 1312)(173, 1456)(174, 1458)(175, 1460)(176, 1442)(177, 1315)(178, 1465)(179, 1317)(180, 1469)(181, 1319)(182, 1472)(183, 1471)(184, 1474)(185, 1476)(186, 1325)(187, 1479)(188, 1323)(189, 1324)(190, 1462)(191, 1326)(192, 1485)(193, 1330)(194, 1487)(195, 1328)(196, 1329)(197, 1492)(198, 1493)(199, 1345)(200, 1495)(201, 1332)(202, 1499)(203, 1500)(204, 1501)(205, 1497)(206, 1335)(207, 1506)(208, 1337)(209, 1510)(210, 1339)(211, 1340)(212, 1514)(213, 1342)(214, 1517)(215, 1343)(216, 1519)(217, 1344)(218, 1521)(219, 1433)(220, 1346)(221, 1524)(222, 1348)(223, 1528)(224, 1350)(225, 1531)(226, 1530)(227, 1533)(228, 1535)(229, 1356)(230, 1538)(231, 1354)(232, 1355)(233, 1419)(234, 1357)(235, 1544)(236, 1361)(237, 1546)(238, 1359)(239, 1360)(240, 1551)(241, 1552)(242, 1376)(243, 1554)(244, 1363)(245, 1558)(246, 1559)(247, 1560)(248, 1556)(249, 1366)(250, 1565)(251, 1368)(252, 1569)(253, 1370)(254, 1371)(255, 1573)(256, 1373)(257, 1576)(258, 1374)(259, 1578)(260, 1375)(261, 1580)(262, 1390)(263, 1522)(264, 1581)(265, 1378)(266, 1584)(267, 1585)(268, 1582)(269, 1380)(270, 1590)(271, 1383)(272, 1382)(273, 1543)(274, 1384)(275, 1596)(276, 1385)(277, 1598)(278, 1553)(279, 1387)(280, 1600)(281, 1602)(282, 1541)(283, 1588)(284, 1532)(285, 1392)(286, 1608)(287, 1394)(288, 1574)(289, 1610)(290, 1612)(291, 1614)(292, 1397)(293, 1398)(294, 1537)(295, 1400)(296, 1619)(297, 1405)(298, 1621)(299, 1402)(300, 1403)(301, 1404)(302, 1627)(303, 1579)(304, 1625)(305, 1564)(306, 1407)(307, 1630)(308, 1631)(309, 1628)(310, 1409)(311, 1634)(312, 1636)(313, 1638)(314, 1412)(315, 1547)(316, 1640)(317, 1414)(318, 1641)(319, 1416)(320, 1562)(321, 1418)(322, 1463)(323, 1647)(324, 1421)(325, 1650)(326, 1651)(327, 1648)(328, 1423)(329, 1655)(330, 1426)(331, 1425)(332, 1484)(333, 1427)(334, 1607)(335, 1428)(336, 1662)(337, 1494)(338, 1430)(339, 1664)(340, 1604)(341, 1482)(342, 1653)(343, 1473)(344, 1435)(345, 1669)(346, 1437)(347, 1515)(348, 1671)(349, 1673)(350, 1587)(351, 1440)(352, 1441)(353, 1478)(354, 1443)(355, 1678)(356, 1448)(357, 1680)(358, 1445)(359, 1446)(360, 1447)(361, 1645)(362, 1520)(363, 1684)(364, 1505)(365, 1450)(366, 1688)(367, 1617)(368, 1686)(369, 1452)(370, 1691)(371, 1692)(372, 1694)(373, 1455)(374, 1488)(375, 1696)(376, 1457)(377, 1635)(378, 1459)(379, 1503)(380, 1461)(381, 1464)(382, 1468)(383, 1702)(384, 1466)(385, 1467)(386, 1675)(387, 1550)(388, 1483)(389, 1706)(390, 1470)(391, 1681)(392, 1710)(393, 1711)(394, 1708)(395, 1712)(396, 1475)(397, 1715)(398, 1477)(399, 1717)(400, 1480)(401, 1690)(402, 1481)(403, 1698)(404, 1540)(405, 1719)(406, 1700)(407, 1534)(408, 1486)(409, 1695)(410, 1489)(411, 1701)(412, 1490)(413, 1726)(414, 1491)(415, 1652)(416, 1689)(417, 1567)(418, 1729)(419, 1496)(420, 1731)(421, 1498)(422, 1656)(423, 1733)(424, 1734)(425, 1504)(426, 1735)(427, 1502)(428, 1509)(429, 1737)(430, 1507)(431, 1508)(432, 1676)(433, 1665)(434, 1511)(435, 1577)(436, 1512)(437, 1699)(438, 1513)(439, 1670)(440, 1516)(441, 1518)(442, 1742)(443, 1666)(444, 1693)(445, 1561)(446, 1668)(447, 1523)(448, 1527)(449, 1748)(450, 1525)(451, 1526)(452, 1615)(453, 1542)(454, 1752)(455, 1529)(456, 1622)(457, 1756)(458, 1757)(459, 1754)(460, 1758)(461, 1760)(462, 1536)(463, 1762)(464, 1539)(465, 1633)(466, 1643)(467, 1764)(468, 1646)(469, 1545)(470, 1639)(471, 1548)(472, 1747)(473, 1549)(474, 1770)(475, 1586)(476, 1632)(477, 1773)(478, 1555)(479, 1775)(480, 1557)(481, 1591)(482, 1777)(483, 1778)(484, 1563)(485, 1779)(486, 1568)(487, 1780)(488, 1566)(489, 1616)(490, 1601)(491, 1570)(492, 1571)(493, 1644)(494, 1572)(495, 1609)(496, 1575)(497, 1785)(498, 1603)(499, 1637)(500, 1606)(501, 1611)(502, 1583)(503, 1789)(504, 1750)(505, 1721)(506, 1589)(507, 1766)(508, 1594)(509, 1776)(510, 1592)(511, 1593)(512, 1595)(513, 1768)(514, 1751)(515, 1597)(516, 1763)(517, 1599)(518, 1761)(519, 1605)(520, 1771)(521, 1705)(522, 1753)(523, 1792)(524, 1759)(525, 1774)(526, 1613)(527, 1765)(528, 1786)(529, 1618)(530, 1769)(531, 1620)(532, 1755)(533, 1623)(534, 1624)(535, 1626)(536, 1783)(537, 1629)(538, 1781)(539, 1791)(540, 1745)(541, 1794)(542, 1642)(543, 1772)(544, 1788)(545, 1740)(546, 1787)(547, 1672)(548, 1649)(549, 1795)(550, 1704)(551, 1714)(552, 1654)(553, 1722)(554, 1659)(555, 1732)(556, 1657)(557, 1658)(558, 1660)(559, 1724)(560, 1661)(561, 1718)(562, 1663)(563, 1716)(564, 1667)(565, 1727)(566, 1707)(567, 1798)(568, 1713)(569, 1730)(570, 1674)(571, 1720)(572, 1743)(573, 1677)(574, 1725)(575, 1679)(576, 1709)(577, 1682)(578, 1683)(579, 1685)(580, 1687)(581, 1738)(582, 1797)(583, 1736)(584, 1800)(585, 1697)(586, 1728)(587, 1746)(588, 1744)(589, 1703)(590, 1799)(591, 1739)(592, 1723)(593, 1796)(594, 1741)(595, 1749)(596, 1793)(597, 1782)(598, 1767)(599, 1790)(600, 1784)(601, 1801)(602, 1802)(603, 1803)(604, 1804)(605, 1805)(606, 1806)(607, 1807)(608, 1808)(609, 1809)(610, 1810)(611, 1811)(612, 1812)(613, 1813)(614, 1814)(615, 1815)(616, 1816)(617, 1817)(618, 1818)(619, 1819)(620, 1820)(621, 1821)(622, 1822)(623, 1823)(624, 1824)(625, 1825)(626, 1826)(627, 1827)(628, 1828)(629, 1829)(630, 1830)(631, 1831)(632, 1832)(633, 1833)(634, 1834)(635, 1835)(636, 1836)(637, 1837)(638, 1838)(639, 1839)(640, 1840)(641, 1841)(642, 1842)(643, 1843)(644, 1844)(645, 1845)(646, 1846)(647, 1847)(648, 1848)(649, 1849)(650, 1850)(651, 1851)(652, 1852)(653, 1853)(654, 1854)(655, 1855)(656, 1856)(657, 1857)(658, 1858)(659, 1859)(660, 1860)(661, 1861)(662, 1862)(663, 1863)(664, 1864)(665, 1865)(666, 1866)(667, 1867)(668, 1868)(669, 1869)(670, 1870)(671, 1871)(672, 1872)(673, 1873)(674, 1874)(675, 1875)(676, 1876)(677, 1877)(678, 1878)(679, 1879)(680, 1880)(681, 1881)(682, 1882)(683, 1883)(684, 1884)(685, 1885)(686, 1886)(687, 1887)(688, 1888)(689, 1889)(690, 1890)(691, 1891)(692, 1892)(693, 1893)(694, 1894)(695, 1895)(696, 1896)(697, 1897)(698, 1898)(699, 1899)(700, 1900)(701, 1901)(702, 1902)(703, 1903)(704, 1904)(705, 1905)(706, 1906)(707, 1907)(708, 1908)(709, 1909)(710, 1910)(711, 1911)(712, 1912)(713, 1913)(714, 1914)(715, 1915)(716, 1916)(717, 1917)(718, 1918)(719, 1919)(720, 1920)(721, 1921)(722, 1922)(723, 1923)(724, 1924)(725, 1925)(726, 1926)(727, 1927)(728, 1928)(729, 1929)(730, 1930)(731, 1931)(732, 1932)(733, 1933)(734, 1934)(735, 1935)(736, 1936)(737, 1937)(738, 1938)(739, 1939)(740, 1940)(741, 1941)(742, 1942)(743, 1943)(744, 1944)(745, 1945)(746, 1946)(747, 1947)(748, 1948)(749, 1949)(750, 1950)(751, 1951)(752, 1952)(753, 1953)(754, 1954)(755, 1955)(756, 1956)(757, 1957)(758, 1958)(759, 1959)(760, 1960)(761, 1961)(762, 1962)(763, 1963)(764, 1964)(765, 1965)(766, 1966)(767, 1967)(768, 1968)(769, 1969)(770, 1970)(771, 1971)(772, 1972)(773, 1973)(774, 1974)(775, 1975)(776, 1976)(777, 1977)(778, 1978)(779, 1979)(780, 1980)(781, 1981)(782, 1982)(783, 1983)(784, 1984)(785, 1985)(786, 1986)(787, 1987)(788, 1988)(789, 1989)(790, 1990)(791, 1991)(792, 1992)(793, 1993)(794, 1994)(795, 1995)(796, 1996)(797, 1997)(798, 1998)(799, 1999)(800, 2000)(801, 2001)(802, 2002)(803, 2003)(804, 2004)(805, 2005)(806, 2006)(807, 2007)(808, 2008)(809, 2009)(810, 2010)(811, 2011)(812, 2012)(813, 2013)(814, 2014)(815, 2015)(816, 2016)(817, 2017)(818, 2018)(819, 2019)(820, 2020)(821, 2021)(822, 2022)(823, 2023)(824, 2024)(825, 2025)(826, 2026)(827, 2027)(828, 2028)(829, 2029)(830, 2030)(831, 2031)(832, 2032)(833, 2033)(834, 2034)(835, 2035)(836, 2036)(837, 2037)(838, 2038)(839, 2039)(840, 2040)(841, 2041)(842, 2042)(843, 2043)(844, 2044)(845, 2045)(846, 2046)(847, 2047)(848, 2048)(849, 2049)(850, 2050)(851, 2051)(852, 2052)(853, 2053)(854, 2054)(855, 2055)(856, 2056)(857, 2057)(858, 2058)(859, 2059)(860, 2060)(861, 2061)(862, 2062)(863, 2063)(864, 2064)(865, 2065)(866, 2066)(867, 2067)(868, 2068)(869, 2069)(870, 2070)(871, 2071)(872, 2072)(873, 2073)(874, 2074)(875, 2075)(876, 2076)(877, 2077)(878, 2078)(879, 2079)(880, 2080)(881, 2081)(882, 2082)(883, 2083)(884, 2084)(885, 2085)(886, 2086)(887, 2087)(888, 2088)(889, 2089)(890, 2090)(891, 2091)(892, 2092)(893, 2093)(894, 2094)(895, 2095)(896, 2096)(897, 2097)(898, 2098)(899, 2099)(900, 2100)(901, 2101)(902, 2102)(903, 2103)(904, 2104)(905, 2105)(906, 2106)(907, 2107)(908, 2108)(909, 2109)(910, 2110)(911, 2111)(912, 2112)(913, 2113)(914, 2114)(915, 2115)(916, 2116)(917, 2117)(918, 2118)(919, 2119)(920, 2120)(921, 2121)(922, 2122)(923, 2123)(924, 2124)(925, 2125)(926, 2126)(927, 2127)(928, 2128)(929, 2129)(930, 2130)(931, 2131)(932, 2132)(933, 2133)(934, 2134)(935, 2135)(936, 2136)(937, 2137)(938, 2138)(939, 2139)(940, 2140)(941, 2141)(942, 2142)(943, 2143)(944, 2144)(945, 2145)(946, 2146)(947, 2147)(948, 2148)(949, 2149)(950, 2150)(951, 2151)(952, 2152)(953, 2153)(954, 2154)(955, 2155)(956, 2156)(957, 2157)(958, 2158)(959, 2159)(960, 2160)(961, 2161)(962, 2162)(963, 2163)(964, 2164)(965, 2165)(966, 2166)(967, 2167)(968, 2168)(969, 2169)(970, 2170)(971, 2171)(972, 2172)(973, 2173)(974, 2174)(975, 2175)(976, 2176)(977, 2177)(978, 2178)(979, 2179)(980, 2180)(981, 2181)(982, 2182)(983, 2183)(984, 2184)(985, 2185)(986, 2186)(987, 2187)(988, 2188)(989, 2189)(990, 2190)(991, 2191)(992, 2192)(993, 2193)(994, 2194)(995, 2195)(996, 2196)(997, 2197)(998, 2198)(999, 2199)(1000, 2200)(1001, 2201)(1002, 2202)(1003, 2203)(1004, 2204)(1005, 2205)(1006, 2206)(1007, 2207)(1008, 2208)(1009, 2209)(1010, 2210)(1011, 2211)(1012, 2212)(1013, 2213)(1014, 2214)(1015, 2215)(1016, 2216)(1017, 2217)(1018, 2218)(1019, 2219)(1020, 2220)(1021, 2221)(1022, 2222)(1023, 2223)(1024, 2224)(1025, 2225)(1026, 2226)(1027, 2227)(1028, 2228)(1029, 2229)(1030, 2230)(1031, 2231)(1032, 2232)(1033, 2233)(1034, 2234)(1035, 2235)(1036, 2236)(1037, 2237)(1038, 2238)(1039, 2239)(1040, 2240)(1041, 2241)(1042, 2242)(1043, 2243)(1044, 2244)(1045, 2245)(1046, 2246)(1047, 2247)(1048, 2248)(1049, 2249)(1050, 2250)(1051, 2251)(1052, 2252)(1053, 2253)(1054, 2254)(1055, 2255)(1056, 2256)(1057, 2257)(1058, 2258)(1059, 2259)(1060, 2260)(1061, 2261)(1062, 2262)(1063, 2263)(1064, 2264)(1065, 2265)(1066, 2266)(1067, 2267)(1068, 2268)(1069, 2269)(1070, 2270)(1071, 2271)(1072, 2272)(1073, 2273)(1074, 2274)(1075, 2275)(1076, 2276)(1077, 2277)(1078, 2278)(1079, 2279)(1080, 2280)(1081, 2281)(1082, 2282)(1083, 2283)(1084, 2284)(1085, 2285)(1086, 2286)(1087, 2287)(1088, 2288)(1089, 2289)(1090, 2290)(1091, 2291)(1092, 2292)(1093, 2293)(1094, 2294)(1095, 2295)(1096, 2296)(1097, 2297)(1098, 2298)(1099, 2299)(1100, 2300)(1101, 2301)(1102, 2302)(1103, 2303)(1104, 2304)(1105, 2305)(1106, 2306)(1107, 2307)(1108, 2308)(1109, 2309)(1110, 2310)(1111, 2311)(1112, 2312)(1113, 2313)(1114, 2314)(1115, 2315)(1116, 2316)(1117, 2317)(1118, 2318)(1119, 2319)(1120, 2320)(1121, 2321)(1122, 2322)(1123, 2323)(1124, 2324)(1125, 2325)(1126, 2326)(1127, 2327)(1128, 2328)(1129, 2329)(1130, 2330)(1131, 2331)(1132, 2332)(1133, 2333)(1134, 2334)(1135, 2335)(1136, 2336)(1137, 2337)(1138, 2338)(1139, 2339)(1140, 2340)(1141, 2341)(1142, 2342)(1143, 2343)(1144, 2344)(1145, 2345)(1146, 2346)(1147, 2347)(1148, 2348)(1149, 2349)(1150, 2350)(1151, 2351)(1152, 2352)(1153, 2353)(1154, 2354)(1155, 2355)(1156, 2356)(1157, 2357)(1158, 2358)(1159, 2359)(1160, 2360)(1161, 2361)(1162, 2362)(1163, 2363)(1164, 2364)(1165, 2365)(1166, 2366)(1167, 2367)(1168, 2368)(1169, 2369)(1170, 2370)(1171, 2371)(1172, 2372)(1173, 2373)(1174, 2374)(1175, 2375)(1176, 2376)(1177, 2377)(1178, 2378)(1179, 2379)(1180, 2380)(1181, 2381)(1182, 2382)(1183, 2383)(1184, 2384)(1185, 2385)(1186, 2386)(1187, 2387)(1188, 2388)(1189, 2389)(1190, 2390)(1191, 2391)(1192, 2392)(1193, 2393)(1194, 2394)(1195, 2395)(1196, 2396)(1197, 2397)(1198, 2398)(1199, 2399)(1200, 2400) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E16.1298 Graph:: bipartite v = 420 e = 1200 f = 750 degree seq :: [ 4^300, 10^120 ] E16.1298 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5}) Quotient :: dipole Aut^+ = (C5 x A5) : C2 (small group id <600, 145>) Aut = $<1200, 941>$ (small group id <1200, 941>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y3^5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5, (Y3^-1 * Y1)^6, Y3^-1 * Y1 * Y3^-2 * Y1^-1 * Y3 * Y1^-1 * Y3^2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y1^-1 * Y3^-2 * Y1 * Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-2 * Y1^-1, Y1^-1 * Y3^-1 * Y1 * Y3^2 * Y1^-1 * Y3^2 * Y1 * Y3^-1 * Y1^-2 * Y3^-2 * Y1 * Y3^-2 * Y1^-1, Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1 * Y1 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-1 * Y3 * Y1^-1 ] Map:: polytopal R = (1, 601, 2, 602, 6, 606, 4, 604)(3, 603, 9, 609, 21, 621, 11, 611)(5, 605, 13, 613, 18, 618, 7, 607)(8, 608, 19, 619, 32, 632, 15, 615)(10, 610, 23, 623, 44, 644, 24, 624)(12, 612, 16, 616, 33, 633, 27, 627)(14, 614, 30, 630, 53, 653, 28, 628)(17, 617, 35, 635, 63, 663, 36, 636)(20, 620, 40, 640, 69, 669, 38, 638)(22, 622, 43, 643, 74, 674, 41, 641)(25, 625, 42, 642, 75, 675, 48, 648)(26, 626, 49, 649, 86, 686, 50, 650)(29, 629, 54, 654, 67, 667, 37, 637)(31, 631, 57, 657, 98, 698, 58, 658)(34, 634, 62, 662, 104, 704, 60, 660)(39, 639, 70, 670, 102, 702, 59, 659)(45, 645, 80, 680, 132, 732, 78, 678)(46, 646, 79, 679, 133, 733, 82, 682)(47, 647, 83, 683, 139, 739, 84, 684)(51, 651, 61, 661, 105, 705, 90, 690)(52, 652, 91, 691, 150, 750, 92, 692)(55, 655, 96, 696, 156, 756, 94, 694)(56, 656, 97, 697, 154, 754, 93, 693)(64, 664, 110, 710, 176, 776, 108, 708)(65, 665, 109, 709, 177, 777, 112, 712)(66, 666, 113, 713, 183, 783, 114, 714)(68, 668, 116, 716, 187, 787, 117, 717)(71, 671, 121, 721, 193, 793, 119, 719)(72, 672, 122, 722, 191, 791, 118, 718)(73, 673, 123, 723, 197, 797, 124, 724)(76, 676, 128, 728, 203, 803, 126, 726)(77, 677, 129, 729, 201, 801, 125, 725)(81, 681, 136, 736, 217, 817, 137, 737)(85, 685, 127, 727, 167, 767, 120, 720)(87, 687, 145, 745, 227, 827, 143, 743)(88, 688, 144, 744, 228, 828, 146, 746)(89, 689, 147, 747, 232, 832, 148, 748)(95, 695, 149, 749, 172, 772, 115, 715)(99, 699, 162, 762, 251, 851, 160, 760)(100, 700, 161, 761, 252, 852, 164, 764)(101, 701, 165, 765, 258, 858, 166, 766)(103, 703, 168, 768, 262, 862, 169, 769)(106, 706, 173, 773, 268, 868, 171, 771)(107, 707, 174, 774, 266, 866, 170, 770)(111, 711, 180, 780, 280, 880, 181, 781)(130, 730, 208, 808, 317, 917, 206, 806)(131, 731, 209, 809, 320, 920, 210, 810)(134, 734, 214, 814, 326, 926, 212, 812)(135, 735, 215, 815, 324, 924, 211, 811)(138, 738, 213, 813, 310, 910, 207, 807)(140, 740, 223, 823, 337, 937, 221, 821)(141, 741, 222, 822, 338, 938, 224, 824)(142, 742, 194, 794, 300, 900, 225, 825)(151, 751, 238, 838, 358, 958, 236, 836)(152, 752, 237, 837, 359, 959, 240, 840)(153, 753, 241, 841, 364, 964, 242, 842)(155, 755, 244, 844, 368, 968, 245, 845)(157, 757, 247, 847, 356, 956, 235, 835)(158, 758, 248, 848, 372, 972, 246, 846)(159, 759, 182, 782, 276, 876, 243, 843)(163, 763, 255, 855, 384, 984, 256, 856)(175, 775, 272, 872, 407, 1007, 273, 873)(178, 778, 277, 877, 413, 1013, 275, 875)(179, 779, 278, 878, 411, 1011, 274, 874)(184, 784, 286, 886, 424, 1024, 284, 884)(185, 785, 285, 885, 425, 1025, 287, 887)(186, 786, 269, 869, 404, 1004, 288, 888)(188, 788, 291, 891, 431, 1031, 289, 889)(189, 789, 290, 890, 432, 1032, 293, 893)(190, 790, 294, 894, 437, 1037, 295, 895)(192, 792, 297, 897, 441, 1041, 298, 898)(195, 795, 301, 901, 445, 1045, 299, 899)(196, 796, 257, 857, 380, 980, 296, 896)(198, 798, 305, 905, 450, 1050, 303, 903)(199, 799, 304, 904, 451, 1051, 307, 907)(200, 800, 308, 908, 454, 1054, 309, 909)(202, 802, 311, 911, 458, 1058, 312, 912)(204, 804, 314, 914, 392, 992, 261, 861)(205, 805, 315, 915, 462, 1062, 313, 913)(216, 816, 330, 930, 386, 986, 329, 929)(218, 818, 333, 933, 396, 996, 331, 931)(219, 819, 332, 932, 383, 983, 334, 934)(220, 820, 318, 918, 465, 1065, 335, 935)(226, 826, 343, 943, 482, 1082, 344, 944)(229, 829, 348, 948, 488, 1088, 346, 946)(230, 830, 349, 949, 486, 1086, 345, 945)(231, 831, 347, 947, 400, 1000, 271, 871)(233, 833, 354, 954, 468, 1068, 352, 952)(234, 834, 353, 953, 479, 1079, 355, 955)(239, 839, 362, 962, 385, 985, 363, 963)(249, 849, 375, 975, 422, 1022, 283, 883)(250, 850, 376, 976, 503, 1103, 377, 977)(253, 853, 381, 981, 509, 1109, 379, 979)(254, 854, 382, 982, 507, 1107, 378, 978)(259, 859, 390, 990, 513, 1113, 388, 988)(260, 860, 389, 989, 514, 1114, 391, 991)(263, 863, 395, 995, 520, 1120, 393, 993)(264, 864, 394, 994, 521, 1121, 397, 997)(265, 865, 398, 998, 524, 1124, 399, 999)(267, 867, 401, 1001, 528, 1128, 402, 1002)(270, 870, 405, 1005, 532, 1132, 403, 1003)(279, 879, 417, 1017, 316, 916, 416, 1016)(281, 881, 420, 1020, 306, 906, 418, 1018)(282, 882, 419, 1019, 350, 950, 421, 1021)(292, 892, 435, 1035, 319, 919, 436, 1036)(302, 902, 448, 1048, 496, 1096, 387, 987)(321, 921, 430, 1030, 544, 1144, 466, 1066)(322, 922, 467, 1067, 559, 1159, 469, 1069)(323, 923, 470, 1070, 546, 1146, 433, 1033)(325, 925, 471, 1071, 547, 1147, 438, 1038)(327, 927, 440, 1040, 510, 1110, 457, 1057)(328, 928, 473, 1073, 515, 1115, 472, 1072)(336, 936, 409, 1009, 536, 1136, 476, 1076)(339, 939, 477, 1077, 511, 1111, 427, 1027)(340, 940, 478, 1078, 539, 1139, 415, 1015)(341, 941, 429, 1029, 533, 1133, 464, 1064)(342, 942, 446, 1046, 534, 1134, 481, 1081)(351, 951, 406, 1006, 474, 1074, 491, 1091)(357, 957, 493, 1093, 565, 1165, 483, 1083)(360, 960, 485, 1085, 567, 1167, 495, 1095)(361, 961, 442, 1042, 549, 1149, 494, 1094)(365, 965, 487, 1087, 568, 1168, 497, 1097)(366, 966, 498, 1098, 531, 1131, 443, 1043)(367, 967, 414, 1014, 527, 1127, 489, 1089)(369, 969, 499, 1099, 554, 1154, 453, 1053)(370, 970, 456, 1056, 550, 1150, 444, 1044)(371, 971, 460, 1060, 526, 1126, 500, 1100)(373, 973, 447, 1047, 517, 1117, 492, 1092)(374, 974, 428, 1028, 518, 1118, 463, 1063)(408, 1008, 519, 1119, 578, 1178, 535, 1135)(410, 1010, 537, 1137, 580, 1180, 522, 1122)(412, 1012, 538, 1138, 581, 1181, 525, 1125)(423, 1023, 505, 1105, 575, 1175, 541, 1141)(426, 1026, 542, 1142, 490, 1090, 516, 1116)(434, 1034, 529, 1129, 572, 1172, 545, 1145)(439, 1039, 548, 1148, 461, 1061, 530, 1130)(449, 1049, 553, 1153, 574, 1174, 504, 1104)(452, 1052, 506, 1106, 576, 1176, 555, 1155)(455, 1055, 508, 1108, 577, 1177, 556, 1156)(459, 1059, 557, 1157, 579, 1179, 523, 1123)(475, 1075, 543, 1143, 501, 1101, 552, 1152)(480, 1080, 540, 1140, 502, 1102, 551, 1151)(484, 1084, 566, 1166, 563, 1163, 512, 1112)(558, 1158, 587, 1187, 596, 1196, 591, 1191)(560, 1160, 592, 1192, 573, 1173, 585, 1185)(561, 1161, 593, 1193, 598, 1198, 584, 1184)(562, 1162, 594, 1194, 600, 1200, 589, 1189)(564, 1164, 583, 1183, 570, 1170, 590, 1190)(569, 1169, 582, 1182, 599, 1199, 595, 1195)(571, 1171, 586, 1186, 597, 1197, 588, 1188)(1201, 1801)(1202, 1802)(1203, 1803)(1204, 1804)(1205, 1805)(1206, 1806)(1207, 1807)(1208, 1808)(1209, 1809)(1210, 1810)(1211, 1811)(1212, 1812)(1213, 1813)(1214, 1814)(1215, 1815)(1216, 1816)(1217, 1817)(1218, 1818)(1219, 1819)(1220, 1820)(1221, 1821)(1222, 1822)(1223, 1823)(1224, 1824)(1225, 1825)(1226, 1826)(1227, 1827)(1228, 1828)(1229, 1829)(1230, 1830)(1231, 1831)(1232, 1832)(1233, 1833)(1234, 1834)(1235, 1835)(1236, 1836)(1237, 1837)(1238, 1838)(1239, 1839)(1240, 1840)(1241, 1841)(1242, 1842)(1243, 1843)(1244, 1844)(1245, 1845)(1246, 1846)(1247, 1847)(1248, 1848)(1249, 1849)(1250, 1850)(1251, 1851)(1252, 1852)(1253, 1853)(1254, 1854)(1255, 1855)(1256, 1856)(1257, 1857)(1258, 1858)(1259, 1859)(1260, 1860)(1261, 1861)(1262, 1862)(1263, 1863)(1264, 1864)(1265, 1865)(1266, 1866)(1267, 1867)(1268, 1868)(1269, 1869)(1270, 1870)(1271, 1871)(1272, 1872)(1273, 1873)(1274, 1874)(1275, 1875)(1276, 1876)(1277, 1877)(1278, 1878)(1279, 1879)(1280, 1880)(1281, 1881)(1282, 1882)(1283, 1883)(1284, 1884)(1285, 1885)(1286, 1886)(1287, 1887)(1288, 1888)(1289, 1889)(1290, 1890)(1291, 1891)(1292, 1892)(1293, 1893)(1294, 1894)(1295, 1895)(1296, 1896)(1297, 1897)(1298, 1898)(1299, 1899)(1300, 1900)(1301, 1901)(1302, 1902)(1303, 1903)(1304, 1904)(1305, 1905)(1306, 1906)(1307, 1907)(1308, 1908)(1309, 1909)(1310, 1910)(1311, 1911)(1312, 1912)(1313, 1913)(1314, 1914)(1315, 1915)(1316, 1916)(1317, 1917)(1318, 1918)(1319, 1919)(1320, 1920)(1321, 1921)(1322, 1922)(1323, 1923)(1324, 1924)(1325, 1925)(1326, 1926)(1327, 1927)(1328, 1928)(1329, 1929)(1330, 1930)(1331, 1931)(1332, 1932)(1333, 1933)(1334, 1934)(1335, 1935)(1336, 1936)(1337, 1937)(1338, 1938)(1339, 1939)(1340, 1940)(1341, 1941)(1342, 1942)(1343, 1943)(1344, 1944)(1345, 1945)(1346, 1946)(1347, 1947)(1348, 1948)(1349, 1949)(1350, 1950)(1351, 1951)(1352, 1952)(1353, 1953)(1354, 1954)(1355, 1955)(1356, 1956)(1357, 1957)(1358, 1958)(1359, 1959)(1360, 1960)(1361, 1961)(1362, 1962)(1363, 1963)(1364, 1964)(1365, 1965)(1366, 1966)(1367, 1967)(1368, 1968)(1369, 1969)(1370, 1970)(1371, 1971)(1372, 1972)(1373, 1973)(1374, 1974)(1375, 1975)(1376, 1976)(1377, 1977)(1378, 1978)(1379, 1979)(1380, 1980)(1381, 1981)(1382, 1982)(1383, 1983)(1384, 1984)(1385, 1985)(1386, 1986)(1387, 1987)(1388, 1988)(1389, 1989)(1390, 1990)(1391, 1991)(1392, 1992)(1393, 1993)(1394, 1994)(1395, 1995)(1396, 1996)(1397, 1997)(1398, 1998)(1399, 1999)(1400, 2000)(1401, 2001)(1402, 2002)(1403, 2003)(1404, 2004)(1405, 2005)(1406, 2006)(1407, 2007)(1408, 2008)(1409, 2009)(1410, 2010)(1411, 2011)(1412, 2012)(1413, 2013)(1414, 2014)(1415, 2015)(1416, 2016)(1417, 2017)(1418, 2018)(1419, 2019)(1420, 2020)(1421, 2021)(1422, 2022)(1423, 2023)(1424, 2024)(1425, 2025)(1426, 2026)(1427, 2027)(1428, 2028)(1429, 2029)(1430, 2030)(1431, 2031)(1432, 2032)(1433, 2033)(1434, 2034)(1435, 2035)(1436, 2036)(1437, 2037)(1438, 2038)(1439, 2039)(1440, 2040)(1441, 2041)(1442, 2042)(1443, 2043)(1444, 2044)(1445, 2045)(1446, 2046)(1447, 2047)(1448, 2048)(1449, 2049)(1450, 2050)(1451, 2051)(1452, 2052)(1453, 2053)(1454, 2054)(1455, 2055)(1456, 2056)(1457, 2057)(1458, 2058)(1459, 2059)(1460, 2060)(1461, 2061)(1462, 2062)(1463, 2063)(1464, 2064)(1465, 2065)(1466, 2066)(1467, 2067)(1468, 2068)(1469, 2069)(1470, 2070)(1471, 2071)(1472, 2072)(1473, 2073)(1474, 2074)(1475, 2075)(1476, 2076)(1477, 2077)(1478, 2078)(1479, 2079)(1480, 2080)(1481, 2081)(1482, 2082)(1483, 2083)(1484, 2084)(1485, 2085)(1486, 2086)(1487, 2087)(1488, 2088)(1489, 2089)(1490, 2090)(1491, 2091)(1492, 2092)(1493, 2093)(1494, 2094)(1495, 2095)(1496, 2096)(1497, 2097)(1498, 2098)(1499, 2099)(1500, 2100)(1501, 2101)(1502, 2102)(1503, 2103)(1504, 2104)(1505, 2105)(1506, 2106)(1507, 2107)(1508, 2108)(1509, 2109)(1510, 2110)(1511, 2111)(1512, 2112)(1513, 2113)(1514, 2114)(1515, 2115)(1516, 2116)(1517, 2117)(1518, 2118)(1519, 2119)(1520, 2120)(1521, 2121)(1522, 2122)(1523, 2123)(1524, 2124)(1525, 2125)(1526, 2126)(1527, 2127)(1528, 2128)(1529, 2129)(1530, 2130)(1531, 2131)(1532, 2132)(1533, 2133)(1534, 2134)(1535, 2135)(1536, 2136)(1537, 2137)(1538, 2138)(1539, 2139)(1540, 2140)(1541, 2141)(1542, 2142)(1543, 2143)(1544, 2144)(1545, 2145)(1546, 2146)(1547, 2147)(1548, 2148)(1549, 2149)(1550, 2150)(1551, 2151)(1552, 2152)(1553, 2153)(1554, 2154)(1555, 2155)(1556, 2156)(1557, 2157)(1558, 2158)(1559, 2159)(1560, 2160)(1561, 2161)(1562, 2162)(1563, 2163)(1564, 2164)(1565, 2165)(1566, 2166)(1567, 2167)(1568, 2168)(1569, 2169)(1570, 2170)(1571, 2171)(1572, 2172)(1573, 2173)(1574, 2174)(1575, 2175)(1576, 2176)(1577, 2177)(1578, 2178)(1579, 2179)(1580, 2180)(1581, 2181)(1582, 2182)(1583, 2183)(1584, 2184)(1585, 2185)(1586, 2186)(1587, 2187)(1588, 2188)(1589, 2189)(1590, 2190)(1591, 2191)(1592, 2192)(1593, 2193)(1594, 2194)(1595, 2195)(1596, 2196)(1597, 2197)(1598, 2198)(1599, 2199)(1600, 2200)(1601, 2201)(1602, 2202)(1603, 2203)(1604, 2204)(1605, 2205)(1606, 2206)(1607, 2207)(1608, 2208)(1609, 2209)(1610, 2210)(1611, 2211)(1612, 2212)(1613, 2213)(1614, 2214)(1615, 2215)(1616, 2216)(1617, 2217)(1618, 2218)(1619, 2219)(1620, 2220)(1621, 2221)(1622, 2222)(1623, 2223)(1624, 2224)(1625, 2225)(1626, 2226)(1627, 2227)(1628, 2228)(1629, 2229)(1630, 2230)(1631, 2231)(1632, 2232)(1633, 2233)(1634, 2234)(1635, 2235)(1636, 2236)(1637, 2237)(1638, 2238)(1639, 2239)(1640, 2240)(1641, 2241)(1642, 2242)(1643, 2243)(1644, 2244)(1645, 2245)(1646, 2246)(1647, 2247)(1648, 2248)(1649, 2249)(1650, 2250)(1651, 2251)(1652, 2252)(1653, 2253)(1654, 2254)(1655, 2255)(1656, 2256)(1657, 2257)(1658, 2258)(1659, 2259)(1660, 2260)(1661, 2261)(1662, 2262)(1663, 2263)(1664, 2264)(1665, 2265)(1666, 2266)(1667, 2267)(1668, 2268)(1669, 2269)(1670, 2270)(1671, 2271)(1672, 2272)(1673, 2273)(1674, 2274)(1675, 2275)(1676, 2276)(1677, 2277)(1678, 2278)(1679, 2279)(1680, 2280)(1681, 2281)(1682, 2282)(1683, 2283)(1684, 2284)(1685, 2285)(1686, 2286)(1687, 2287)(1688, 2288)(1689, 2289)(1690, 2290)(1691, 2291)(1692, 2292)(1693, 2293)(1694, 2294)(1695, 2295)(1696, 2296)(1697, 2297)(1698, 2298)(1699, 2299)(1700, 2300)(1701, 2301)(1702, 2302)(1703, 2303)(1704, 2304)(1705, 2305)(1706, 2306)(1707, 2307)(1708, 2308)(1709, 2309)(1710, 2310)(1711, 2311)(1712, 2312)(1713, 2313)(1714, 2314)(1715, 2315)(1716, 2316)(1717, 2317)(1718, 2318)(1719, 2319)(1720, 2320)(1721, 2321)(1722, 2322)(1723, 2323)(1724, 2324)(1725, 2325)(1726, 2326)(1727, 2327)(1728, 2328)(1729, 2329)(1730, 2330)(1731, 2331)(1732, 2332)(1733, 2333)(1734, 2334)(1735, 2335)(1736, 2336)(1737, 2337)(1738, 2338)(1739, 2339)(1740, 2340)(1741, 2341)(1742, 2342)(1743, 2343)(1744, 2344)(1745, 2345)(1746, 2346)(1747, 2347)(1748, 2348)(1749, 2349)(1750, 2350)(1751, 2351)(1752, 2352)(1753, 2353)(1754, 2354)(1755, 2355)(1756, 2356)(1757, 2357)(1758, 2358)(1759, 2359)(1760, 2360)(1761, 2361)(1762, 2362)(1763, 2363)(1764, 2364)(1765, 2365)(1766, 2366)(1767, 2367)(1768, 2368)(1769, 2369)(1770, 2370)(1771, 2371)(1772, 2372)(1773, 2373)(1774, 2374)(1775, 2375)(1776, 2376)(1777, 2377)(1778, 2378)(1779, 2379)(1780, 2380)(1781, 2381)(1782, 2382)(1783, 2383)(1784, 2384)(1785, 2385)(1786, 2386)(1787, 2387)(1788, 2388)(1789, 2389)(1790, 2390)(1791, 2391)(1792, 2392)(1793, 2393)(1794, 2394)(1795, 2395)(1796, 2396)(1797, 2397)(1798, 2398)(1799, 2399)(1800, 2400) L = (1, 1203)(2, 1207)(3, 1210)(4, 1212)(5, 1201)(6, 1215)(7, 1217)(8, 1202)(9, 1204)(10, 1214)(11, 1225)(12, 1226)(13, 1228)(14, 1205)(15, 1231)(16, 1206)(17, 1220)(18, 1237)(19, 1238)(20, 1208)(21, 1241)(22, 1209)(23, 1211)(24, 1246)(25, 1247)(26, 1222)(27, 1251)(28, 1252)(29, 1213)(30, 1224)(31, 1234)(32, 1259)(33, 1260)(34, 1216)(35, 1218)(36, 1265)(37, 1266)(38, 1268)(39, 1219)(40, 1236)(41, 1273)(42, 1221)(43, 1250)(44, 1278)(45, 1223)(46, 1281)(47, 1245)(48, 1285)(49, 1227)(50, 1288)(51, 1289)(52, 1255)(53, 1293)(54, 1294)(55, 1229)(56, 1230)(57, 1232)(58, 1300)(59, 1301)(60, 1303)(61, 1233)(62, 1258)(63, 1308)(64, 1235)(65, 1311)(66, 1264)(67, 1315)(68, 1271)(69, 1318)(70, 1319)(71, 1239)(72, 1240)(73, 1276)(74, 1325)(75, 1326)(76, 1242)(77, 1243)(78, 1331)(79, 1244)(80, 1284)(81, 1256)(82, 1338)(83, 1248)(84, 1341)(85, 1342)(86, 1343)(87, 1249)(88, 1330)(89, 1287)(90, 1349)(91, 1253)(92, 1352)(93, 1353)(94, 1355)(95, 1254)(96, 1292)(97, 1337)(98, 1360)(99, 1257)(100, 1363)(101, 1299)(102, 1367)(103, 1306)(104, 1370)(105, 1371)(106, 1261)(107, 1262)(108, 1375)(109, 1263)(110, 1314)(111, 1272)(112, 1382)(113, 1267)(114, 1385)(115, 1386)(116, 1269)(117, 1389)(118, 1390)(119, 1392)(120, 1270)(121, 1317)(122, 1381)(123, 1274)(124, 1399)(125, 1400)(126, 1402)(127, 1275)(128, 1324)(129, 1406)(130, 1277)(131, 1334)(132, 1411)(133, 1412)(134, 1279)(135, 1280)(136, 1282)(137, 1419)(138, 1420)(139, 1421)(140, 1283)(141, 1416)(142, 1340)(143, 1426)(144, 1286)(145, 1348)(146, 1431)(147, 1290)(148, 1434)(149, 1435)(150, 1436)(151, 1291)(152, 1439)(153, 1351)(154, 1443)(155, 1357)(156, 1446)(157, 1295)(158, 1296)(159, 1297)(160, 1450)(161, 1298)(162, 1366)(163, 1307)(164, 1457)(165, 1302)(166, 1460)(167, 1461)(168, 1304)(169, 1464)(170, 1465)(171, 1467)(172, 1305)(173, 1369)(174, 1456)(175, 1378)(176, 1474)(177, 1475)(178, 1309)(179, 1310)(180, 1312)(181, 1482)(182, 1483)(183, 1484)(184, 1313)(185, 1479)(186, 1384)(187, 1489)(188, 1316)(189, 1492)(190, 1388)(191, 1496)(192, 1394)(193, 1499)(194, 1320)(195, 1321)(196, 1322)(197, 1503)(198, 1323)(199, 1506)(200, 1398)(201, 1510)(202, 1404)(203, 1513)(204, 1327)(205, 1328)(206, 1516)(207, 1329)(208, 1346)(209, 1332)(210, 1522)(211, 1523)(212, 1525)(213, 1333)(214, 1410)(215, 1529)(216, 1335)(217, 1531)(218, 1336)(219, 1449)(220, 1418)(221, 1536)(222, 1339)(223, 1425)(224, 1541)(225, 1542)(226, 1429)(227, 1545)(228, 1546)(229, 1344)(230, 1345)(231, 1551)(232, 1552)(233, 1347)(234, 1550)(235, 1433)(236, 1557)(237, 1350)(238, 1442)(239, 1358)(240, 1415)(241, 1354)(242, 1566)(243, 1567)(244, 1356)(245, 1570)(246, 1571)(247, 1445)(248, 1563)(249, 1359)(250, 1453)(251, 1578)(252, 1579)(253, 1361)(254, 1362)(255, 1364)(256, 1586)(257, 1587)(258, 1588)(259, 1365)(260, 1583)(261, 1459)(262, 1593)(263, 1368)(264, 1596)(265, 1463)(266, 1600)(267, 1469)(268, 1603)(269, 1372)(270, 1373)(271, 1374)(272, 1376)(273, 1609)(274, 1610)(275, 1612)(276, 1377)(277, 1473)(278, 1616)(279, 1379)(280, 1618)(281, 1380)(282, 1502)(283, 1481)(284, 1623)(285, 1383)(286, 1488)(287, 1628)(288, 1629)(289, 1630)(290, 1387)(291, 1495)(292, 1395)(293, 1478)(294, 1391)(295, 1639)(296, 1640)(297, 1393)(298, 1643)(299, 1644)(300, 1498)(301, 1636)(302, 1396)(303, 1649)(304, 1397)(305, 1509)(306, 1405)(307, 1549)(308, 1401)(309, 1656)(310, 1657)(311, 1403)(312, 1660)(313, 1661)(314, 1512)(315, 1620)(316, 1518)(317, 1635)(318, 1407)(319, 1408)(320, 1666)(321, 1409)(322, 1668)(323, 1521)(324, 1559)(325, 1527)(326, 1672)(327, 1413)(328, 1414)(329, 1584)(330, 1424)(331, 1597)(332, 1417)(333, 1535)(334, 1591)(335, 1675)(336, 1539)(337, 1615)(338, 1627)(339, 1422)(340, 1423)(341, 1680)(342, 1679)(343, 1427)(344, 1684)(345, 1685)(346, 1687)(347, 1428)(348, 1544)(349, 1619)(350, 1430)(351, 1519)(352, 1669)(353, 1432)(354, 1556)(355, 1681)(356, 1692)(357, 1560)(358, 1694)(359, 1695)(360, 1437)(361, 1438)(362, 1440)(363, 1696)(364, 1697)(365, 1441)(366, 1641)(367, 1565)(368, 1653)(369, 1444)(370, 1645)(371, 1569)(372, 1663)(373, 1447)(374, 1448)(375, 1534)(376, 1451)(377, 1705)(378, 1706)(379, 1708)(380, 1452)(381, 1577)(382, 1532)(383, 1454)(384, 1562)(385, 1455)(386, 1606)(387, 1585)(388, 1712)(389, 1458)(390, 1592)(391, 1717)(392, 1718)(393, 1719)(394, 1462)(395, 1599)(396, 1470)(397, 1582)(398, 1466)(399, 1726)(400, 1727)(401, 1468)(402, 1730)(403, 1731)(404, 1602)(405, 1533)(406, 1471)(407, 1735)(408, 1472)(409, 1537)(410, 1608)(411, 1632)(412, 1614)(413, 1739)(414, 1476)(415, 1477)(416, 1517)(417, 1487)(418, 1507)(419, 1480)(420, 1622)(421, 1555)(422, 1740)(423, 1626)(424, 1711)(425, 1716)(426, 1485)(427, 1486)(428, 1743)(429, 1538)(430, 1633)(431, 1745)(432, 1746)(433, 1490)(434, 1491)(435, 1493)(436, 1691)(437, 1747)(438, 1494)(439, 1728)(440, 1638)(441, 1561)(442, 1497)(443, 1732)(444, 1642)(445, 1573)(446, 1500)(447, 1501)(448, 1621)(449, 1652)(450, 1754)(451, 1755)(452, 1504)(453, 1505)(454, 1756)(455, 1508)(456, 1568)(457, 1655)(458, 1723)(459, 1511)(460, 1572)(461, 1659)(462, 1733)(463, 1514)(464, 1515)(465, 1617)(466, 1758)(467, 1520)(468, 1528)(469, 1678)(470, 1524)(471, 1526)(472, 1763)(473, 1554)(474, 1530)(475, 1734)(476, 1764)(477, 1676)(478, 1553)(479, 1540)(480, 1674)(481, 1752)(482, 1765)(483, 1543)(484, 1713)(485, 1683)(486, 1651)(487, 1689)(488, 1742)(489, 1547)(490, 1548)(491, 1751)(492, 1714)(493, 1558)(494, 1770)(495, 1761)(496, 1701)(497, 1771)(498, 1564)(499, 1700)(500, 1724)(501, 1574)(502, 1575)(503, 1774)(504, 1576)(505, 1624)(506, 1704)(507, 1721)(508, 1710)(509, 1677)(510, 1580)(511, 1581)(512, 1715)(513, 1690)(514, 1673)(515, 1589)(516, 1590)(517, 1702)(518, 1625)(519, 1722)(520, 1779)(521, 1780)(522, 1594)(523, 1595)(524, 1781)(525, 1598)(526, 1658)(527, 1725)(528, 1634)(529, 1601)(530, 1662)(531, 1729)(532, 1646)(533, 1604)(534, 1605)(535, 1782)(536, 1607)(537, 1611)(538, 1613)(539, 1759)(540, 1664)(541, 1786)(542, 1741)(543, 1665)(544, 1631)(545, 1788)(546, 1784)(547, 1789)(548, 1637)(549, 1750)(550, 1654)(551, 1647)(552, 1648)(553, 1650)(554, 1792)(555, 1793)(556, 1790)(557, 1748)(558, 1760)(559, 1785)(560, 1667)(561, 1670)(562, 1671)(563, 1762)(564, 1777)(565, 1795)(566, 1682)(567, 1686)(568, 1688)(569, 1693)(570, 1769)(571, 1772)(572, 1698)(573, 1699)(574, 1796)(575, 1703)(576, 1707)(577, 1709)(578, 1720)(579, 1800)(580, 1798)(581, 1773)(582, 1783)(583, 1736)(584, 1737)(585, 1738)(586, 1768)(587, 1744)(588, 1787)(589, 1757)(590, 1749)(591, 1753)(592, 1791)(593, 1767)(594, 1766)(595, 1794)(596, 1797)(597, 1775)(598, 1776)(599, 1778)(600, 1799)(601, 1801)(602, 1802)(603, 1803)(604, 1804)(605, 1805)(606, 1806)(607, 1807)(608, 1808)(609, 1809)(610, 1810)(611, 1811)(612, 1812)(613, 1813)(614, 1814)(615, 1815)(616, 1816)(617, 1817)(618, 1818)(619, 1819)(620, 1820)(621, 1821)(622, 1822)(623, 1823)(624, 1824)(625, 1825)(626, 1826)(627, 1827)(628, 1828)(629, 1829)(630, 1830)(631, 1831)(632, 1832)(633, 1833)(634, 1834)(635, 1835)(636, 1836)(637, 1837)(638, 1838)(639, 1839)(640, 1840)(641, 1841)(642, 1842)(643, 1843)(644, 1844)(645, 1845)(646, 1846)(647, 1847)(648, 1848)(649, 1849)(650, 1850)(651, 1851)(652, 1852)(653, 1853)(654, 1854)(655, 1855)(656, 1856)(657, 1857)(658, 1858)(659, 1859)(660, 1860)(661, 1861)(662, 1862)(663, 1863)(664, 1864)(665, 1865)(666, 1866)(667, 1867)(668, 1868)(669, 1869)(670, 1870)(671, 1871)(672, 1872)(673, 1873)(674, 1874)(675, 1875)(676, 1876)(677, 1877)(678, 1878)(679, 1879)(680, 1880)(681, 1881)(682, 1882)(683, 1883)(684, 1884)(685, 1885)(686, 1886)(687, 1887)(688, 1888)(689, 1889)(690, 1890)(691, 1891)(692, 1892)(693, 1893)(694, 1894)(695, 1895)(696, 1896)(697, 1897)(698, 1898)(699, 1899)(700, 1900)(701, 1901)(702, 1902)(703, 1903)(704, 1904)(705, 1905)(706, 1906)(707, 1907)(708, 1908)(709, 1909)(710, 1910)(711, 1911)(712, 1912)(713, 1913)(714, 1914)(715, 1915)(716, 1916)(717, 1917)(718, 1918)(719, 1919)(720, 1920)(721, 1921)(722, 1922)(723, 1923)(724, 1924)(725, 1925)(726, 1926)(727, 1927)(728, 1928)(729, 1929)(730, 1930)(731, 1931)(732, 1932)(733, 1933)(734, 1934)(735, 1935)(736, 1936)(737, 1937)(738, 1938)(739, 1939)(740, 1940)(741, 1941)(742, 1942)(743, 1943)(744, 1944)(745, 1945)(746, 1946)(747, 1947)(748, 1948)(749, 1949)(750, 1950)(751, 1951)(752, 1952)(753, 1953)(754, 1954)(755, 1955)(756, 1956)(757, 1957)(758, 1958)(759, 1959)(760, 1960)(761, 1961)(762, 1962)(763, 1963)(764, 1964)(765, 1965)(766, 1966)(767, 1967)(768, 1968)(769, 1969)(770, 1970)(771, 1971)(772, 1972)(773, 1973)(774, 1974)(775, 1975)(776, 1976)(777, 1977)(778, 1978)(779, 1979)(780, 1980)(781, 1981)(782, 1982)(783, 1983)(784, 1984)(785, 1985)(786, 1986)(787, 1987)(788, 1988)(789, 1989)(790, 1990)(791, 1991)(792, 1992)(793, 1993)(794, 1994)(795, 1995)(796, 1996)(797, 1997)(798, 1998)(799, 1999)(800, 2000)(801, 2001)(802, 2002)(803, 2003)(804, 2004)(805, 2005)(806, 2006)(807, 2007)(808, 2008)(809, 2009)(810, 2010)(811, 2011)(812, 2012)(813, 2013)(814, 2014)(815, 2015)(816, 2016)(817, 2017)(818, 2018)(819, 2019)(820, 2020)(821, 2021)(822, 2022)(823, 2023)(824, 2024)(825, 2025)(826, 2026)(827, 2027)(828, 2028)(829, 2029)(830, 2030)(831, 2031)(832, 2032)(833, 2033)(834, 2034)(835, 2035)(836, 2036)(837, 2037)(838, 2038)(839, 2039)(840, 2040)(841, 2041)(842, 2042)(843, 2043)(844, 2044)(845, 2045)(846, 2046)(847, 2047)(848, 2048)(849, 2049)(850, 2050)(851, 2051)(852, 2052)(853, 2053)(854, 2054)(855, 2055)(856, 2056)(857, 2057)(858, 2058)(859, 2059)(860, 2060)(861, 2061)(862, 2062)(863, 2063)(864, 2064)(865, 2065)(866, 2066)(867, 2067)(868, 2068)(869, 2069)(870, 2070)(871, 2071)(872, 2072)(873, 2073)(874, 2074)(875, 2075)(876, 2076)(877, 2077)(878, 2078)(879, 2079)(880, 2080)(881, 2081)(882, 2082)(883, 2083)(884, 2084)(885, 2085)(886, 2086)(887, 2087)(888, 2088)(889, 2089)(890, 2090)(891, 2091)(892, 2092)(893, 2093)(894, 2094)(895, 2095)(896, 2096)(897, 2097)(898, 2098)(899, 2099)(900, 2100)(901, 2101)(902, 2102)(903, 2103)(904, 2104)(905, 2105)(906, 2106)(907, 2107)(908, 2108)(909, 2109)(910, 2110)(911, 2111)(912, 2112)(913, 2113)(914, 2114)(915, 2115)(916, 2116)(917, 2117)(918, 2118)(919, 2119)(920, 2120)(921, 2121)(922, 2122)(923, 2123)(924, 2124)(925, 2125)(926, 2126)(927, 2127)(928, 2128)(929, 2129)(930, 2130)(931, 2131)(932, 2132)(933, 2133)(934, 2134)(935, 2135)(936, 2136)(937, 2137)(938, 2138)(939, 2139)(940, 2140)(941, 2141)(942, 2142)(943, 2143)(944, 2144)(945, 2145)(946, 2146)(947, 2147)(948, 2148)(949, 2149)(950, 2150)(951, 2151)(952, 2152)(953, 2153)(954, 2154)(955, 2155)(956, 2156)(957, 2157)(958, 2158)(959, 2159)(960, 2160)(961, 2161)(962, 2162)(963, 2163)(964, 2164)(965, 2165)(966, 2166)(967, 2167)(968, 2168)(969, 2169)(970, 2170)(971, 2171)(972, 2172)(973, 2173)(974, 2174)(975, 2175)(976, 2176)(977, 2177)(978, 2178)(979, 2179)(980, 2180)(981, 2181)(982, 2182)(983, 2183)(984, 2184)(985, 2185)(986, 2186)(987, 2187)(988, 2188)(989, 2189)(990, 2190)(991, 2191)(992, 2192)(993, 2193)(994, 2194)(995, 2195)(996, 2196)(997, 2197)(998, 2198)(999, 2199)(1000, 2200)(1001, 2201)(1002, 2202)(1003, 2203)(1004, 2204)(1005, 2205)(1006, 2206)(1007, 2207)(1008, 2208)(1009, 2209)(1010, 2210)(1011, 2211)(1012, 2212)(1013, 2213)(1014, 2214)(1015, 2215)(1016, 2216)(1017, 2217)(1018, 2218)(1019, 2219)(1020, 2220)(1021, 2221)(1022, 2222)(1023, 2223)(1024, 2224)(1025, 2225)(1026, 2226)(1027, 2227)(1028, 2228)(1029, 2229)(1030, 2230)(1031, 2231)(1032, 2232)(1033, 2233)(1034, 2234)(1035, 2235)(1036, 2236)(1037, 2237)(1038, 2238)(1039, 2239)(1040, 2240)(1041, 2241)(1042, 2242)(1043, 2243)(1044, 2244)(1045, 2245)(1046, 2246)(1047, 2247)(1048, 2248)(1049, 2249)(1050, 2250)(1051, 2251)(1052, 2252)(1053, 2253)(1054, 2254)(1055, 2255)(1056, 2256)(1057, 2257)(1058, 2258)(1059, 2259)(1060, 2260)(1061, 2261)(1062, 2262)(1063, 2263)(1064, 2264)(1065, 2265)(1066, 2266)(1067, 2267)(1068, 2268)(1069, 2269)(1070, 2270)(1071, 2271)(1072, 2272)(1073, 2273)(1074, 2274)(1075, 2275)(1076, 2276)(1077, 2277)(1078, 2278)(1079, 2279)(1080, 2280)(1081, 2281)(1082, 2282)(1083, 2283)(1084, 2284)(1085, 2285)(1086, 2286)(1087, 2287)(1088, 2288)(1089, 2289)(1090, 2290)(1091, 2291)(1092, 2292)(1093, 2293)(1094, 2294)(1095, 2295)(1096, 2296)(1097, 2297)(1098, 2298)(1099, 2299)(1100, 2300)(1101, 2301)(1102, 2302)(1103, 2303)(1104, 2304)(1105, 2305)(1106, 2306)(1107, 2307)(1108, 2308)(1109, 2309)(1110, 2310)(1111, 2311)(1112, 2312)(1113, 2313)(1114, 2314)(1115, 2315)(1116, 2316)(1117, 2317)(1118, 2318)(1119, 2319)(1120, 2320)(1121, 2321)(1122, 2322)(1123, 2323)(1124, 2324)(1125, 2325)(1126, 2326)(1127, 2327)(1128, 2328)(1129, 2329)(1130, 2330)(1131, 2331)(1132, 2332)(1133, 2333)(1134, 2334)(1135, 2335)(1136, 2336)(1137, 2337)(1138, 2338)(1139, 2339)(1140, 2340)(1141, 2341)(1142, 2342)(1143, 2343)(1144, 2344)(1145, 2345)(1146, 2346)(1147, 2347)(1148, 2348)(1149, 2349)(1150, 2350)(1151, 2351)(1152, 2352)(1153, 2353)(1154, 2354)(1155, 2355)(1156, 2356)(1157, 2357)(1158, 2358)(1159, 2359)(1160, 2360)(1161, 2361)(1162, 2362)(1163, 2363)(1164, 2364)(1165, 2365)(1166, 2366)(1167, 2367)(1168, 2368)(1169, 2369)(1170, 2370)(1171, 2371)(1172, 2372)(1173, 2373)(1174, 2374)(1175, 2375)(1176, 2376)(1177, 2377)(1178, 2378)(1179, 2379)(1180, 2380)(1181, 2381)(1182, 2382)(1183, 2383)(1184, 2384)(1185, 2385)(1186, 2386)(1187, 2387)(1188, 2388)(1189, 2389)(1190, 2390)(1191, 2391)(1192, 2392)(1193, 2393)(1194, 2394)(1195, 2395)(1196, 2396)(1197, 2397)(1198, 2398)(1199, 2399)(1200, 2400) local type(s) :: { ( 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E16.1297 Graph:: simple bipartite v = 750 e = 1200 f = 420 degree seq :: [ 2^600, 8^150 ] E16.1299 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 8}) Quotient :: regular Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2)^3, T1^8, T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-3 * T2 * T1^-2 * T2 * T1^2 * T2 * T1, T2 * T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-3 * T2 * T1^-3, T2 * T1^-4 * T2 * T1^-2 * T2 * T1^3 * T2 * T1^-3 * T2 * T1^2 * T2 * T1^-4 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 11, 21, 20, 10, 4)(3, 7, 15, 27, 45, 31, 17, 8)(6, 13, 25, 41, 66, 44, 26, 14)(9, 18, 32, 52, 77, 49, 29, 16)(12, 23, 39, 62, 95, 65, 40, 24)(19, 34, 55, 85, 126, 84, 54, 33)(22, 37, 60, 91, 137, 94, 61, 38)(28, 47, 74, 111, 165, 114, 75, 48)(30, 50, 78, 117, 154, 103, 68, 42)(35, 57, 88, 131, 192, 130, 87, 56)(36, 58, 89, 133, 195, 136, 90, 59)(43, 69, 104, 155, 212, 145, 97, 63)(46, 72, 109, 161, 235, 164, 110, 73)(51, 80, 120, 177, 256, 176, 119, 79)(53, 82, 123, 181, 263, 184, 124, 83)(64, 98, 146, 213, 294, 203, 139, 92)(67, 101, 151, 219, 317, 222, 152, 102)(70, 106, 158, 229, 330, 228, 157, 105)(71, 107, 159, 231, 333, 234, 160, 108)(76, 115, 170, 247, 348, 243, 167, 112)(81, 121, 179, 259, 368, 262, 180, 122)(86, 128, 189, 273, 386, 276, 190, 129)(93, 140, 204, 295, 401, 285, 197, 134)(96, 143, 209, 301, 422, 304, 210, 144)(99, 148, 216, 311, 433, 310, 215, 147)(100, 149, 217, 313, 436, 316, 218, 150)(113, 168, 244, 349, 469, 341, 237, 162)(116, 172, 250, 357, 489, 356, 249, 171)(118, 174, 253, 293, 410, 362, 254, 175)(125, 185, 268, 378, 442, 318, 265, 182)(127, 187, 271, 382, 521, 385, 272, 188)(132, 135, 198, 286, 402, 395, 281, 194)(138, 201, 291, 255, 363, 409, 292, 202)(141, 206, 298, 416, 556, 415, 297, 205)(142, 207, 299, 418, 559, 421, 300, 208)(153, 223, 322, 446, 374, 264, 319, 220)(156, 226, 327, 400, 539, 453, 328, 227)(163, 238, 342, 470, 540, 462, 335, 232)(166, 241, 302, 211, 305, 425, 347, 242)(169, 246, 352, 482, 537, 481, 351, 245)(173, 251, 359, 492, 544, 495, 360, 252)(178, 233, 336, 463, 541, 503, 367, 258)(183, 266, 375, 511, 542, 403, 370, 260)(186, 270, 381, 519, 639, 518, 380, 269)(191, 277, 389, 468, 340, 236, 339, 274)(193, 279, 392, 432, 575, 532, 393, 280)(196, 283, 398, 329, 454, 538, 399, 284)(199, 288, 405, 543, 505, 369, 404, 287)(200, 289, 406, 545, 659, 548, 407, 290)(214, 308, 430, 394, 533, 574, 431, 309)(221, 320, 443, 589, 534, 583, 438, 314)(224, 324, 449, 597, 531, 596, 448, 323)(225, 325, 450, 599, 528, 602, 451, 326)(230, 315, 439, 584, 524, 610, 458, 332)(239, 344, 473, 618, 658, 617, 472, 343)(240, 345, 474, 558, 417, 547, 475, 346)(248, 354, 486, 554, 412, 553, 487, 355)(257, 365, 500, 626, 657, 640, 501, 366)(261, 371, 506, 551, 411, 552, 491, 358)(267, 377, 514, 546, 408, 549, 513, 376)(275, 387, 525, 555, 414, 296, 413, 383)(278, 391, 530, 653, 704, 652, 529, 390)(282, 396, 535, 655, 708, 656, 536, 397)(303, 423, 565, 526, 388, 527, 561, 419)(306, 427, 570, 520, 384, 522, 569, 426)(307, 428, 571, 517, 379, 516, 572, 429)(312, 420, 562, 510, 373, 509, 579, 435)(321, 445, 592, 688, 615, 687, 591, 444)(331, 456, 607, 692, 654, 698, 608, 457)(334, 460, 612, 488, 631, 682, 576, 461)(337, 465, 613, 665, 582, 437, 581, 464)(338, 466, 614, 660, 646, 670, 563, 467)(350, 479, 624, 502, 641, 702, 625, 480)(353, 484, 628, 662, 550, 663, 629, 485)(361, 496, 634, 696, 604, 471, 616, 493)(364, 499, 638, 677, 601, 694, 637, 498)(372, 508, 580, 667, 557, 666, 643, 507)(424, 567, 674, 648, 515, 647, 673, 566)(434, 577, 683, 650, 523, 611, 459, 578)(440, 586, 504, 642, 669, 560, 668, 585)(441, 587, 685, 627, 483, 620, 661, 588)(447, 594, 690, 609, 478, 623, 691, 595)(452, 603, 695, 714, 681, 590, 686, 600)(455, 606, 490, 632, 679, 649, 697, 605)(476, 621, 700, 635, 497, 636, 699, 619)(477, 622, 693, 598, 494, 633, 671, 564)(512, 644, 703, 630, 664, 709, 706, 645)(568, 675, 711, 684, 593, 689, 712, 676)(573, 680, 713, 707, 651, 672, 710, 678)(701, 718, 720, 716, 705, 717, 719, 715) 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, 36)(24, 37)(25, 42)(26, 43)(27, 46)(29, 47)(31, 51)(32, 53)(34, 56)(38, 58)(39, 63)(40, 64)(41, 67)(44, 70)(45, 71)(48, 72)(49, 76)(50, 79)(52, 81)(54, 82)(55, 86)(57, 59)(60, 92)(61, 93)(62, 96)(65, 99)(66, 100)(68, 101)(69, 105)(73, 107)(74, 112)(75, 113)(77, 116)(78, 118)(80, 108)(83, 121)(84, 125)(85, 127)(87, 128)(88, 132)(89, 134)(90, 135)(91, 138)(94, 141)(95, 142)(97, 143)(98, 147)(102, 149)(103, 153)(104, 156)(106, 150)(109, 162)(110, 163)(111, 166)(114, 169)(115, 171)(117, 173)(119, 174)(120, 178)(122, 172)(123, 182)(124, 183)(126, 186)(129, 187)(130, 191)(131, 193)(133, 196)(136, 199)(137, 200)(139, 201)(140, 205)(144, 207)(145, 211)(146, 214)(148, 208)(151, 220)(152, 221)(154, 224)(155, 225)(157, 226)(158, 230)(159, 232)(160, 233)(161, 236)(164, 239)(165, 240)(167, 241)(168, 245)(170, 248)(175, 251)(176, 255)(177, 257)(179, 260)(180, 261)(181, 264)(184, 267)(185, 269)(188, 270)(189, 274)(190, 275)(192, 278)(194, 279)(195, 282)(197, 283)(198, 287)(202, 289)(203, 293)(204, 296)(206, 290)(209, 302)(210, 303)(212, 306)(213, 307)(215, 308)(216, 312)(217, 314)(218, 315)(219, 318)(222, 321)(223, 323)(227, 325)(228, 329)(229, 331)(231, 334)(234, 337)(235, 338)(237, 339)(238, 343)(242, 345)(243, 301)(244, 350)(246, 346)(247, 353)(249, 354)(250, 358)(252, 324)(253, 291)(254, 361)(256, 364)(258, 365)(259, 369)(262, 372)(263, 373)(265, 319)(266, 376)(268, 379)(271, 383)(272, 384)(273, 341)(276, 388)(277, 390)(280, 391)(281, 394)(284, 396)(285, 400)(286, 403)(288, 397)(292, 408)(294, 411)(295, 412)(297, 413)(298, 417)(299, 419)(300, 420)(304, 424)(305, 426)(309, 428)(310, 432)(311, 434)(313, 437)(316, 440)(317, 441)(320, 444)(322, 447)(326, 427)(327, 398)(328, 452)(330, 455)(332, 456)(333, 459)(335, 460)(336, 464)(340, 466)(342, 471)(344, 467)(347, 476)(348, 477)(349, 478)(351, 479)(352, 483)(355, 484)(356, 488)(357, 490)(359, 493)(360, 494)(362, 497)(363, 498)(366, 499)(367, 502)(368, 504)(370, 404)(371, 507)(374, 509)(375, 512)(377, 510)(378, 515)(380, 516)(381, 520)(382, 415)(385, 523)(386, 524)(387, 526)(389, 528)(392, 430)(393, 531)(395, 534)(399, 537)(401, 540)(402, 541)(405, 544)(406, 546)(407, 547)(409, 550)(410, 551)(414, 553)(416, 557)(418, 560)(421, 563)(422, 564)(423, 566)(425, 568)(429, 552)(431, 573)(433, 576)(435, 577)(436, 580)(438, 581)(439, 585)(442, 587)(443, 590)(445, 588)(446, 593)(448, 594)(449, 598)(450, 600)(451, 601)(453, 604)(454, 605)(457, 606)(458, 609)(461, 578)(462, 554)(463, 583)(465, 611)(468, 615)(469, 610)(470, 539)(472, 616)(473, 559)(474, 619)(475, 620)(480, 623)(481, 626)(482, 535)(485, 622)(486, 612)(487, 630)(489, 608)(491, 632)(492, 617)(495, 536)(496, 635)(500, 624)(501, 639)(503, 542)(505, 642)(506, 636)(508, 586)(511, 641)(513, 644)(514, 646)(517, 647)(518, 649)(519, 638)(521, 613)(522, 650)(525, 651)(527, 584)(529, 602)(530, 597)(532, 654)(533, 589)(538, 657)(543, 658)(545, 660)(548, 661)(549, 662)(555, 664)(556, 665)(558, 666)(561, 668)(562, 670)(565, 672)(567, 671)(569, 675)(570, 677)(571, 678)(572, 679)(574, 681)(575, 682)(579, 684)(582, 667)(591, 686)(592, 659)(595, 689)(596, 692)(599, 687)(603, 696)(607, 690)(614, 688)(618, 669)(621, 676)(625, 701)(627, 655)(628, 703)(629, 704)(631, 698)(633, 656)(634, 705)(637, 663)(640, 697)(643, 699)(645, 702)(648, 685)(652, 694)(653, 693)(673, 710)(674, 708)(680, 714)(683, 711)(691, 715)(695, 716)(700, 717)(706, 718)(707, 709)(712, 719)(713, 720) local type(s) :: { ( 3^8 ) } Outer automorphisms :: reflexible Dual of E16.1300 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 90 e = 360 f = 240 degree seq :: [ 8^90 ] E16.1300 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 8}) Quotient :: regular Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2 * T1)^8, (T2 * T1 * T2 * T1^-1)^5, (T1^-1 * T2 * T1 * T2)^5, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * 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, 67, 68)(48, 69, 70)(49, 71, 72)(50, 73, 74)(59, 83, 84)(60, 85, 86)(61, 87, 88)(62, 89, 90)(63, 91, 92)(64, 93, 94)(65, 95, 96)(66, 97, 75)(76, 105, 106)(77, 107, 108)(78, 109, 110)(79, 111, 112)(80, 113, 114)(81, 115, 116)(82, 117, 98)(99, 132, 133)(100, 134, 135)(101, 136, 137)(102, 138, 139)(103, 140, 141)(104, 142, 143)(118, 157, 158)(119, 159, 160)(120, 161, 162)(121, 163, 164)(122, 152, 165)(123, 166, 167)(124, 168, 125)(126, 169, 170)(127, 171, 172)(128, 173, 174)(129, 175, 176)(130, 177, 178)(131, 179, 180)(144, 192, 193)(145, 194, 195)(146, 196, 197)(147, 188, 198)(148, 199, 200)(149, 201, 150)(151, 202, 203)(153, 204, 205)(154, 206, 207)(155, 208, 209)(156, 210, 211)(181, 235, 236)(182, 237, 238)(183, 239, 240)(184, 241, 242)(185, 243, 186)(187, 244, 245)(189, 246, 247)(190, 248, 249)(191, 250, 251)(212, 413, 665)(213, 366, 636)(214, 368, 593)(215, 231, 431)(216, 415, 666)(217, 416, 218)(219, 380, 260)(220, 305, 554)(221, 420, 408)(222, 422, 671)(223, 352, 375)(224, 423, 600)(225, 291, 529)(226, 293, 534)(227, 427, 673)(228, 429, 229)(230, 430, 281)(232, 364, 351)(233, 434, 681)(234, 398, 655)(252, 457, 458)(253, 459, 461)(254, 402, 462)(255, 463, 418)(256, 374, 465)(257, 466, 468)(258, 388, 354)(259, 471, 473)(261, 349, 476)(262, 477, 479)(263, 360, 339)(264, 321, 483)(265, 484, 486)(266, 487, 489)(267, 329, 323)(268, 333, 491)(269, 492, 494)(270, 495, 497)(271, 345, 296)(272, 304, 452)(273, 363, 500)(274, 501, 428)(275, 503, 505)(276, 317, 308)(277, 283, 370)(278, 391, 508)(279, 387, 509)(280, 510, 511)(282, 513, 449)(284, 518, 379)(285, 520, 493)(286, 295, 307)(287, 292, 403)(288, 439, 525)(289, 526, 527)(290, 405, 460)(294, 535, 502)(297, 540, 538)(298, 541, 542)(299, 315, 544)(300, 545, 546)(301, 547, 548)(302, 453, 464)(303, 550, 399)(306, 555, 485)(309, 559, 557)(310, 561, 562)(311, 327, 564)(312, 565, 566)(313, 567, 568)(314, 569, 467)(316, 573, 519)(318, 574, 575)(319, 576, 470)(320, 578, 474)(322, 581, 472)(324, 584, 523)(325, 586, 587)(326, 343, 589)(328, 592, 521)(330, 594, 595)(331, 421, 475)(332, 597, 480)(334, 599, 478)(335, 601, 558)(336, 456, 443)(337, 358, 445)(338, 604, 605)(340, 607, 506)(341, 609, 610)(342, 367, 441)(344, 614, 536)(346, 615, 616)(347, 617, 481)(348, 618, 469)(350, 577, 583)(353, 622, 623)(355, 625, 490)(356, 627, 628)(357, 400, 362)(359, 632, 440)(361, 386, 634)(365, 619, 488)(369, 451, 401)(371, 455, 392)(372, 384, 407)(373, 442, 404)(376, 596, 539)(377, 409, 393)(378, 412, 395)(381, 644, 498)(382, 646, 647)(383, 450, 390)(385, 620, 648)(389, 438, 651)(394, 653, 654)(396, 579, 496)(397, 560, 570)(406, 436, 454)(410, 482, 661)(411, 448, 662)(414, 549, 606)(417, 660, 670)(419, 664, 652)(424, 635, 507)(425, 672, 667)(426, 641, 668)(432, 678, 516)(433, 679, 680)(435, 512, 624)(437, 580, 682)(444, 685, 686)(446, 598, 504)(447, 585, 582)(499, 629, 621)(514, 531, 707)(515, 669, 551)(517, 659, 711)(522, 675, 626)(524, 611, 603)(528, 643, 602)(530, 552, 709)(532, 658, 712)(533, 689, 710)(537, 692, 645)(543, 588, 563)(553, 639, 713)(556, 676, 608)(571, 702, 708)(572, 719, 705)(590, 696, 704)(591, 715, 674)(612, 699, 706)(613, 717, 703)(630, 693, 700)(631, 684, 642)(633, 656, 688)(637, 657, 683)(638, 649, 687)(640, 677, 694)(650, 690, 720)(663, 691, 697)(695, 701, 698)(714, 716, 718) 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, 98)(68, 99)(69, 100)(70, 101)(71, 102)(72, 103)(73, 104)(74, 83)(84, 118)(85, 119)(86, 120)(87, 121)(88, 122)(89, 123)(90, 124)(91, 125)(92, 126)(93, 127)(94, 128)(95, 129)(96, 130)(97, 131)(105, 144)(106, 145)(107, 146)(108, 147)(109, 148)(110, 149)(111, 150)(112, 151)(113, 152)(114, 153)(115, 154)(116, 155)(117, 156)(132, 181)(133, 182)(134, 183)(135, 172)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(157, 212)(158, 213)(159, 214)(160, 215)(161, 216)(162, 217)(163, 218)(164, 219)(165, 220)(166, 221)(167, 222)(168, 223)(169, 224)(170, 225)(171, 226)(173, 227)(174, 228)(175, 229)(176, 230)(177, 231)(178, 232)(179, 233)(180, 234)(192, 273)(193, 384)(194, 385)(195, 387)(196, 279)(197, 360)(198, 379)(199, 392)(200, 394)(201, 395)(202, 397)(203, 399)(204, 338)(205, 402)(206, 254)(207, 405)(208, 407)(209, 409)(210, 410)(211, 411)(235, 278)(236, 436)(237, 437)(238, 439)(239, 288)(240, 388)(241, 442)(242, 444)(243, 445)(244, 447)(245, 449)(246, 353)(247, 374)(248, 256)(249, 453)(250, 454)(251, 456)(252, 420)(253, 371)(255, 404)(257, 346)(258, 469)(259, 318)(260, 474)(261, 434)(262, 330)(263, 480)(264, 482)(265, 301)(266, 361)(267, 490)(268, 413)(269, 280)(270, 389)(271, 498)(272, 499)(274, 289)(275, 440)(276, 506)(277, 507)(281, 497)(282, 514)(283, 516)(284, 313)(285, 521)(286, 523)(287, 524)(290, 505)(291, 530)(292, 532)(293, 300)(294, 536)(295, 538)(296, 539)(297, 423)(298, 368)(299, 543)(302, 489)(303, 551)(304, 425)(305, 312)(306, 519)(307, 557)(308, 558)(309, 560)(310, 363)(311, 563)(314, 493)(315, 571)(316, 401)(317, 508)(319, 479)(320, 579)(321, 377)(322, 502)(323, 583)(324, 585)(325, 391)(326, 588)(327, 590)(328, 451)(329, 593)(331, 468)(332, 598)(333, 336)(334, 485)(335, 602)(337, 603)(339, 606)(340, 608)(341, 540)(342, 611)(343, 612)(344, 369)(345, 500)(347, 473)(348, 619)(349, 351)(350, 414)(352, 621)(354, 624)(355, 626)(356, 559)(357, 629)(358, 630)(359, 614)(362, 461)(364, 417)(365, 472)(366, 553)(367, 637)(370, 491)(372, 486)(373, 599)(375, 640)(376, 435)(378, 635)(380, 643)(381, 645)(382, 584)(383, 424)(386, 573)(390, 418)(393, 650)(396, 478)(398, 517)(400, 656)(403, 476)(406, 494)(408, 569)(412, 663)(415, 616)(416, 668)(419, 601)(421, 661)(422, 481)(426, 596)(427, 618)(428, 431)(429, 564)(430, 676)(432, 654)(433, 607)(438, 592)(441, 458)(443, 680)(446, 467)(448, 533)(450, 687)(452, 483)(455, 581)(457, 554)(459, 518)(460, 675)(462, 589)(463, 534)(464, 692)(465, 544)(466, 501)(470, 653)(471, 484)(475, 685)(477, 492)(487, 510)(488, 669)(495, 526)(496, 707)(503, 547)(504, 709)(509, 652)(511, 659)(512, 703)(513, 567)(515, 651)(520, 574)(522, 682)(525, 684)(527, 689)(528, 705)(529, 545)(531, 632)(535, 594)(537, 666)(541, 636)(542, 628)(546, 715)(548, 639)(549, 674)(550, 565)(552, 634)(555, 615)(556, 648)(561, 655)(562, 647)(566, 717)(568, 719)(570, 710)(572, 677)(575, 620)(576, 681)(577, 642)(578, 604)(580, 595)(582, 713)(586, 662)(587, 610)(591, 691)(597, 622)(600, 711)(605, 649)(609, 694)(613, 693)(617, 665)(623, 683)(625, 660)(627, 697)(631, 695)(633, 673)(638, 696)(641, 698)(644, 690)(646, 700)(657, 699)(658, 686)(664, 701)(667, 714)(670, 706)(671, 672)(678, 716)(679, 704)(688, 702)(708, 720)(712, 718) local type(s) :: { ( 8^3 ) } Outer automorphisms :: reflexible Dual of E16.1299 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 240 e = 360 f = 90 degree seq :: [ 3^240 ] E16.1301 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 8}) Quotient :: edge Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1)^8, (T1 * T2 * T1 * T2^-1)^5, (T2 * T1 * T2^-1 * T1)^5, T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 ] 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, 119, 120)(92, 121, 122)(93, 123, 124)(94, 125, 126)(95, 127, 128)(96, 129, 130)(97, 131, 98)(99, 132, 133)(100, 134, 135)(101, 136, 137)(102, 138, 139)(103, 140, 141)(104, 142, 143)(105, 144, 145)(106, 146, 147)(107, 148, 149)(108, 150, 151)(109, 152, 153)(110, 154, 155)(111, 156, 112)(113, 157, 158)(114, 159, 160)(115, 161, 162)(116, 163, 164)(117, 165, 166)(118, 167, 168)(169, 215, 216)(170, 217, 218)(171, 219, 220)(172, 188, 221)(173, 222, 223)(174, 224, 175)(176, 225, 226)(177, 227, 228)(178, 229, 230)(179, 231, 232)(180, 233, 234)(181, 235, 236)(182, 237, 238)(183, 239, 240)(184, 241, 242)(185, 243, 186)(187, 244, 245)(189, 246, 247)(190, 248, 249)(191, 250, 251)(192, 273, 304)(193, 383, 375)(194, 384, 645)(195, 211, 334)(196, 386, 446)(197, 388, 198)(199, 391, 649)(200, 393, 651)(201, 336, 364)(202, 395, 294)(203, 305, 535)(204, 259, 353)(205, 397, 654)(206, 398, 656)(207, 400, 659)(208, 401, 209)(210, 404, 660)(212, 407, 663)(213, 292, 309)(214, 410, 331)(252, 451, 453)(253, 411, 421)(254, 455, 402)(255, 457, 459)(256, 449, 376)(257, 461, 463)(258, 435, 444)(260, 465, 466)(261, 361, 332)(262, 468, 470)(263, 428, 369)(264, 472, 474)(265, 347, 325)(266, 476, 478)(267, 479, 389)(268, 481, 483)(269, 454, 484)(270, 464, 485)(271, 452, 487)(272, 418, 488)(274, 317, 313)(275, 490, 492)(276, 493, 495)(277, 496, 392)(278, 340, 299)(279, 497, 499)(280, 500, 502)(281, 503, 505)(282, 306, 300)(283, 506, 508)(284, 509, 511)(285, 430, 371)(286, 354, 295)(287, 512, 443)(288, 514, 516)(289, 489, 518)(290, 456, 520)(291, 441, 521)(293, 458, 523)(296, 460, 525)(297, 486, 526)(298, 462, 528)(301, 529, 531)(302, 532, 534)(303, 450, 378)(307, 537, 539)(308, 540, 542)(310, 543, 420)(311, 545, 547)(312, 475, 549)(314, 550, 552)(315, 553, 555)(316, 556, 405)(318, 557, 559)(319, 560, 561)(320, 562, 564)(321, 565, 567)(322, 467, 569)(323, 519, 570)(324, 469, 572)(326, 471, 574)(327, 522, 575)(328, 473, 577)(329, 524, 434)(330, 477, 581)(333, 480, 584)(335, 527, 586)(337, 482, 424)(338, 589, 408)(339, 382, 548)(341, 592, 593)(342, 580, 594)(343, 595, 597)(344, 598, 600)(345, 601, 603)(346, 409, 517)(348, 605, 607)(349, 608, 609)(350, 396, 583)(351, 440, 380)(352, 366, 568)(355, 415, 439)(356, 571, 613)(357, 614, 616)(358, 448, 618)(359, 619, 423)(360, 381, 504)(362, 622, 414)(363, 624, 625)(365, 373, 573)(367, 491, 630)(368, 433, 632)(370, 494, 606)(372, 432, 417)(374, 498, 637)(377, 501, 558)(379, 576, 640)(385, 507, 646)(387, 578, 628)(390, 510, 623)(394, 536, 647)(399, 513, 658)(403, 515, 538)(406, 588, 635)(412, 666, 413)(416, 669, 671)(419, 673, 675)(422, 676, 445)(425, 591, 678)(426, 680, 427)(429, 664, 438)(431, 681, 682)(436, 685, 437)(442, 648, 690)(447, 604, 692)(530, 617, 546)(533, 636, 667)(541, 579, 686)(544, 679, 670)(551, 599, 566)(554, 657, 699)(563, 701, 708)(582, 712, 705)(585, 709, 674)(587, 693, 683)(590, 652, 696)(596, 661, 715)(602, 718, 698)(610, 706, 717)(611, 633, 694)(612, 668, 650)(615, 639, 688)(620, 672, 689)(621, 702, 662)(626, 641, 695)(627, 687, 719)(629, 634, 642)(631, 716, 700)(638, 707, 644)(643, 653, 665)(655, 684, 710)(677, 703, 714)(691, 697, 720)(704, 713, 711)(721, 722)(723, 727)(724, 728)(725, 729)(726, 730)(731, 739)(732, 740)(733, 741)(734, 742)(735, 743)(736, 744)(737, 745)(738, 746)(747, 763)(748, 764)(749, 765)(750, 766)(751, 767)(752, 768)(753, 769)(754, 770)(755, 771)(756, 772)(757, 773)(758, 774)(759, 775)(760, 776)(761, 777)(762, 778)(779, 810)(780, 811)(781, 812)(782, 813)(783, 814)(784, 815)(785, 816)(786, 817)(787, 818)(788, 819)(789, 820)(790, 821)(791, 822)(792, 823)(793, 824)(794, 795)(796, 825)(797, 826)(798, 827)(799, 828)(800, 829)(801, 830)(802, 831)(803, 832)(804, 833)(805, 834)(806, 835)(807, 836)(808, 837)(809, 838)(839, 889)(840, 890)(841, 891)(842, 892)(843, 893)(844, 894)(845, 895)(846, 896)(847, 872)(848, 897)(849, 898)(850, 899)(851, 900)(852, 901)(853, 902)(854, 903)(855, 880)(856, 904)(857, 905)(858, 906)(859, 907)(860, 908)(861, 909)(862, 910)(863, 911)(864, 912)(865, 913)(866, 914)(867, 915)(868, 916)(869, 917)(870, 918)(871, 919)(873, 920)(874, 921)(875, 922)(876, 923)(877, 924)(878, 925)(879, 926)(881, 927)(882, 928)(883, 929)(884, 930)(885, 931)(886, 932)(887, 933)(888, 934)(935, 1031)(936, 1005)(937, 1101)(938, 1132)(939, 1133)(940, 1134)(941, 1136)(942, 1137)(943, 1138)(944, 1140)(945, 1141)(946, 1143)(947, 1145)(948, 1146)(949, 1147)(950, 1032)(951, 1150)(952, 1083)(953, 1074)(954, 1153)(955, 1008)(956, 1023)(957, 1057)(958, 1156)(959, 1157)(960, 1158)(961, 1160)(962, 1161)(963, 1163)(964, 1164)(965, 1165)(966, 1167)(967, 1168)(968, 1078)(969, 1009)(970, 1170)(971, 1151)(972, 983)(973, 987)(974, 976)(975, 981)(977, 985)(978, 996)(979, 1000)(980, 1004)(982, 994)(984, 998)(986, 1002)(988, 1006)(989, 1022)(990, 1028)(991, 1035)(992, 1039)(993, 1041)(995, 1020)(997, 1024)(999, 1026)(1001, 1029)(1003, 1033)(1007, 1037)(1010, 1058)(1011, 1062)(1012, 1064)(1013, 1065)(1014, 1069)(1015, 1034)(1016, 1071)(1017, 1076)(1018, 1079)(1019, 1021)(1025, 1060)(1027, 1045)(1030, 1067)(1036, 1073)(1038, 1052)(1040, 1081)(1042, 1084)(1043, 1099)(1044, 1142)(1046, 1152)(1047, 1055)(1048, 1117)(1049, 1126)(1050, 1299)(1051, 1302)(1053, 1256)(1054, 1305)(1056, 1307)(1059, 1131)(1061, 1089)(1063, 1148)(1066, 1155)(1068, 1096)(1070, 1169)(1072, 1171)(1075, 1109)(1077, 1199)(1080, 1185)(1082, 1122)(1085, 1175)(1086, 1348)(1087, 1343)(1088, 1351)(1090, 1264)(1091, 1340)(1092, 1353)(1093, 1354)(1094, 1356)(1095, 1358)(1097, 1233)(1098, 1359)(1100, 1361)(1102, 1352)(1103, 1129)(1104, 1364)(1105, 1326)(1106, 1367)(1107, 1368)(1108, 1284)(1110, 1283)(1111, 1173)(1112, 1322)(1113, 1370)(1114, 1372)(1115, 1216)(1116, 1373)(1118, 1375)(1119, 1377)(1120, 1309)(1121, 1219)(1123, 1218)(1124, 1186)(1125, 1381)(1127, 1382)(1128, 1384)(1130, 1276)(1135, 1215)(1139, 1213)(1144, 1174)(1149, 1179)(1154, 1177)(1159, 1222)(1162, 1220)(1166, 1184)(1172, 1297)(1176, 1248)(1178, 1292)(1180, 1243)(1181, 1290)(1182, 1301)(1183, 1346)(1187, 1207)(1188, 1295)(1189, 1350)(1190, 1403)(1191, 1240)(1192, 1246)(1193, 1357)(1194, 1331)(1195, 1204)(1196, 1306)(1197, 1366)(1198, 1400)(1200, 1245)(1201, 1241)(1202, 1378)(1203, 1310)(1205, 1209)(1206, 1379)(1208, 1223)(1210, 1333)(1211, 1337)(1212, 1338)(1214, 1289)(1217, 1360)(1221, 1294)(1224, 1399)(1225, 1274)(1226, 1314)(1227, 1319)(1228, 1320)(1229, 1411)(1230, 1269)(1231, 1312)(1232, 1355)(1234, 1420)(1235, 1304)(1236, 1313)(1237, 1421)(1238, 1253)(1239, 1398)(1242, 1412)(1244, 1388)(1247, 1422)(1249, 1329)(1250, 1271)(1251, 1272)(1252, 1341)(1254, 1325)(1255, 1298)(1257, 1281)(1258, 1286)(1259, 1287)(1260, 1397)(1261, 1380)(1262, 1277)(1263, 1349)(1265, 1425)(1266, 1278)(1267, 1279)(1268, 1426)(1270, 1345)(1273, 1324)(1275, 1342)(1280, 1431)(1282, 1363)(1285, 1402)(1288, 1407)(1291, 1423)(1293, 1430)(1296, 1417)(1300, 1424)(1303, 1405)(1308, 1393)(1311, 1321)(1315, 1385)(1316, 1387)(1317, 1386)(1318, 1383)(1323, 1369)(1327, 1365)(1328, 1433)(1330, 1406)(1332, 1339)(1334, 1362)(1335, 1419)(1336, 1427)(1344, 1434)(1347, 1396)(1371, 1413)(1374, 1404)(1376, 1415)(1389, 1439)(1390, 1438)(1391, 1414)(1392, 1428)(1394, 1416)(1395, 1432)(1401, 1440)(1408, 1435)(1409, 1418)(1410, 1436)(1429, 1437) L = (1, 721)(2, 722)(3, 723)(4, 724)(5, 725)(6, 726)(7, 727)(8, 728)(9, 729)(10, 730)(11, 731)(12, 732)(13, 733)(14, 734)(15, 735)(16, 736)(17, 737)(18, 738)(19, 739)(20, 740)(21, 741)(22, 742)(23, 743)(24, 744)(25, 745)(26, 746)(27, 747)(28, 748)(29, 749)(30, 750)(31, 751)(32, 752)(33, 753)(34, 754)(35, 755)(36, 756)(37, 757)(38, 758)(39, 759)(40, 760)(41, 761)(42, 762)(43, 763)(44, 764)(45, 765)(46, 766)(47, 767)(48, 768)(49, 769)(50, 770)(51, 771)(52, 772)(53, 773)(54, 774)(55, 775)(56, 776)(57, 777)(58, 778)(59, 779)(60, 780)(61, 781)(62, 782)(63, 783)(64, 784)(65, 785)(66, 786)(67, 787)(68, 788)(69, 789)(70, 790)(71, 791)(72, 792)(73, 793)(74, 794)(75, 795)(76, 796)(77, 797)(78, 798)(79, 799)(80, 800)(81, 801)(82, 802)(83, 803)(84, 804)(85, 805)(86, 806)(87, 807)(88, 808)(89, 809)(90, 810)(91, 811)(92, 812)(93, 813)(94, 814)(95, 815)(96, 816)(97, 817)(98, 818)(99, 819)(100, 820)(101, 821)(102, 822)(103, 823)(104, 824)(105, 825)(106, 826)(107, 827)(108, 828)(109, 829)(110, 830)(111, 831)(112, 832)(113, 833)(114, 834)(115, 835)(116, 836)(117, 837)(118, 838)(119, 839)(120, 840)(121, 841)(122, 842)(123, 843)(124, 844)(125, 845)(126, 846)(127, 847)(128, 848)(129, 849)(130, 850)(131, 851)(132, 852)(133, 853)(134, 854)(135, 855)(136, 856)(137, 857)(138, 858)(139, 859)(140, 860)(141, 861)(142, 862)(143, 863)(144, 864)(145, 865)(146, 866)(147, 867)(148, 868)(149, 869)(150, 870)(151, 871)(152, 872)(153, 873)(154, 874)(155, 875)(156, 876)(157, 877)(158, 878)(159, 879)(160, 880)(161, 881)(162, 882)(163, 883)(164, 884)(165, 885)(166, 886)(167, 887)(168, 888)(169, 889)(170, 890)(171, 891)(172, 892)(173, 893)(174, 894)(175, 895)(176, 896)(177, 897)(178, 898)(179, 899)(180, 900)(181, 901)(182, 902)(183, 903)(184, 904)(185, 905)(186, 906)(187, 907)(188, 908)(189, 909)(190, 910)(191, 911)(192, 912)(193, 913)(194, 914)(195, 915)(196, 916)(197, 917)(198, 918)(199, 919)(200, 920)(201, 921)(202, 922)(203, 923)(204, 924)(205, 925)(206, 926)(207, 927)(208, 928)(209, 929)(210, 930)(211, 931)(212, 932)(213, 933)(214, 934)(215, 935)(216, 936)(217, 937)(218, 938)(219, 939)(220, 940)(221, 941)(222, 942)(223, 943)(224, 944)(225, 945)(226, 946)(227, 947)(228, 948)(229, 949)(230, 950)(231, 951)(232, 952)(233, 953)(234, 954)(235, 955)(236, 956)(237, 957)(238, 958)(239, 959)(240, 960)(241, 961)(242, 962)(243, 963)(244, 964)(245, 965)(246, 966)(247, 967)(248, 968)(249, 969)(250, 970)(251, 971)(252, 972)(253, 973)(254, 974)(255, 975)(256, 976)(257, 977)(258, 978)(259, 979)(260, 980)(261, 981)(262, 982)(263, 983)(264, 984)(265, 985)(266, 986)(267, 987)(268, 988)(269, 989)(270, 990)(271, 991)(272, 992)(273, 993)(274, 994)(275, 995)(276, 996)(277, 997)(278, 998)(279, 999)(280, 1000)(281, 1001)(282, 1002)(283, 1003)(284, 1004)(285, 1005)(286, 1006)(287, 1007)(288, 1008)(289, 1009)(290, 1010)(291, 1011)(292, 1012)(293, 1013)(294, 1014)(295, 1015)(296, 1016)(297, 1017)(298, 1018)(299, 1019)(300, 1020)(301, 1021)(302, 1022)(303, 1023)(304, 1024)(305, 1025)(306, 1026)(307, 1027)(308, 1028)(309, 1029)(310, 1030)(311, 1031)(312, 1032)(313, 1033)(314, 1034)(315, 1035)(316, 1036)(317, 1037)(318, 1038)(319, 1039)(320, 1040)(321, 1041)(322, 1042)(323, 1043)(324, 1044)(325, 1045)(326, 1046)(327, 1047)(328, 1048)(329, 1049)(330, 1050)(331, 1051)(332, 1052)(333, 1053)(334, 1054)(335, 1055)(336, 1056)(337, 1057)(338, 1058)(339, 1059)(340, 1060)(341, 1061)(342, 1062)(343, 1063)(344, 1064)(345, 1065)(346, 1066)(347, 1067)(348, 1068)(349, 1069)(350, 1070)(351, 1071)(352, 1072)(353, 1073)(354, 1074)(355, 1075)(356, 1076)(357, 1077)(358, 1078)(359, 1079)(360, 1080)(361, 1081)(362, 1082)(363, 1083)(364, 1084)(365, 1085)(366, 1086)(367, 1087)(368, 1088)(369, 1089)(370, 1090)(371, 1091)(372, 1092)(373, 1093)(374, 1094)(375, 1095)(376, 1096)(377, 1097)(378, 1098)(379, 1099)(380, 1100)(381, 1101)(382, 1102)(383, 1103)(384, 1104)(385, 1105)(386, 1106)(387, 1107)(388, 1108)(389, 1109)(390, 1110)(391, 1111)(392, 1112)(393, 1113)(394, 1114)(395, 1115)(396, 1116)(397, 1117)(398, 1118)(399, 1119)(400, 1120)(401, 1121)(402, 1122)(403, 1123)(404, 1124)(405, 1125)(406, 1126)(407, 1127)(408, 1128)(409, 1129)(410, 1130)(411, 1131)(412, 1132)(413, 1133)(414, 1134)(415, 1135)(416, 1136)(417, 1137)(418, 1138)(419, 1139)(420, 1140)(421, 1141)(422, 1142)(423, 1143)(424, 1144)(425, 1145)(426, 1146)(427, 1147)(428, 1148)(429, 1149)(430, 1150)(431, 1151)(432, 1152)(433, 1153)(434, 1154)(435, 1155)(436, 1156)(437, 1157)(438, 1158)(439, 1159)(440, 1160)(441, 1161)(442, 1162)(443, 1163)(444, 1164)(445, 1165)(446, 1166)(447, 1167)(448, 1168)(449, 1169)(450, 1170)(451, 1171)(452, 1172)(453, 1173)(454, 1174)(455, 1175)(456, 1176)(457, 1177)(458, 1178)(459, 1179)(460, 1180)(461, 1181)(462, 1182)(463, 1183)(464, 1184)(465, 1185)(466, 1186)(467, 1187)(468, 1188)(469, 1189)(470, 1190)(471, 1191)(472, 1192)(473, 1193)(474, 1194)(475, 1195)(476, 1196)(477, 1197)(478, 1198)(479, 1199)(480, 1200)(481, 1201)(482, 1202)(483, 1203)(484, 1204)(485, 1205)(486, 1206)(487, 1207)(488, 1208)(489, 1209)(490, 1210)(491, 1211)(492, 1212)(493, 1213)(494, 1214)(495, 1215)(496, 1216)(497, 1217)(498, 1218)(499, 1219)(500, 1220)(501, 1221)(502, 1222)(503, 1223)(504, 1224)(505, 1225)(506, 1226)(507, 1227)(508, 1228)(509, 1229)(510, 1230)(511, 1231)(512, 1232)(513, 1233)(514, 1234)(515, 1235)(516, 1236)(517, 1237)(518, 1238)(519, 1239)(520, 1240)(521, 1241)(522, 1242)(523, 1243)(524, 1244)(525, 1245)(526, 1246)(527, 1247)(528, 1248)(529, 1249)(530, 1250)(531, 1251)(532, 1252)(533, 1253)(534, 1254)(535, 1255)(536, 1256)(537, 1257)(538, 1258)(539, 1259)(540, 1260)(541, 1261)(542, 1262)(543, 1263)(544, 1264)(545, 1265)(546, 1266)(547, 1267)(548, 1268)(549, 1269)(550, 1270)(551, 1271)(552, 1272)(553, 1273)(554, 1274)(555, 1275)(556, 1276)(557, 1277)(558, 1278)(559, 1279)(560, 1280)(561, 1281)(562, 1282)(563, 1283)(564, 1284)(565, 1285)(566, 1286)(567, 1287)(568, 1288)(569, 1289)(570, 1290)(571, 1291)(572, 1292)(573, 1293)(574, 1294)(575, 1295)(576, 1296)(577, 1297)(578, 1298)(579, 1299)(580, 1300)(581, 1301)(582, 1302)(583, 1303)(584, 1304)(585, 1305)(586, 1306)(587, 1307)(588, 1308)(589, 1309)(590, 1310)(591, 1311)(592, 1312)(593, 1313)(594, 1314)(595, 1315)(596, 1316)(597, 1317)(598, 1318)(599, 1319)(600, 1320)(601, 1321)(602, 1322)(603, 1323)(604, 1324)(605, 1325)(606, 1326)(607, 1327)(608, 1328)(609, 1329)(610, 1330)(611, 1331)(612, 1332)(613, 1333)(614, 1334)(615, 1335)(616, 1336)(617, 1337)(618, 1338)(619, 1339)(620, 1340)(621, 1341)(622, 1342)(623, 1343)(624, 1344)(625, 1345)(626, 1346)(627, 1347)(628, 1348)(629, 1349)(630, 1350)(631, 1351)(632, 1352)(633, 1353)(634, 1354)(635, 1355)(636, 1356)(637, 1357)(638, 1358)(639, 1359)(640, 1360)(641, 1361)(642, 1362)(643, 1363)(644, 1364)(645, 1365)(646, 1366)(647, 1367)(648, 1368)(649, 1369)(650, 1370)(651, 1371)(652, 1372)(653, 1373)(654, 1374)(655, 1375)(656, 1376)(657, 1377)(658, 1378)(659, 1379)(660, 1380)(661, 1381)(662, 1382)(663, 1383)(664, 1384)(665, 1385)(666, 1386)(667, 1387)(668, 1388)(669, 1389)(670, 1390)(671, 1391)(672, 1392)(673, 1393)(674, 1394)(675, 1395)(676, 1396)(677, 1397)(678, 1398)(679, 1399)(680, 1400)(681, 1401)(682, 1402)(683, 1403)(684, 1404)(685, 1405)(686, 1406)(687, 1407)(688, 1408)(689, 1409)(690, 1410)(691, 1411)(692, 1412)(693, 1413)(694, 1414)(695, 1415)(696, 1416)(697, 1417)(698, 1418)(699, 1419)(700, 1420)(701, 1421)(702, 1422)(703, 1423)(704, 1424)(705, 1425)(706, 1426)(707, 1427)(708, 1428)(709, 1429)(710, 1430)(711, 1431)(712, 1432)(713, 1433)(714, 1434)(715, 1435)(716, 1436)(717, 1437)(718, 1438)(719, 1439)(720, 1440) local type(s) :: { ( 16, 16 ), ( 16^3 ) } Outer automorphisms :: reflexible Dual of E16.1305 Transitivity :: ET+ Graph:: simple bipartite v = 600 e = 720 f = 90 degree seq :: [ 2^360, 3^240 ] E16.1302 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 8}) Quotient :: edge Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T2^8, T2^2 * T1 * T2^-7 * T1^-1 * T2 * T1^-2, (T2^2 * T1^-1)^5, T2^2 * T1^-1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1^-1 * T2^2 * T1^-1 * T2^3 * T1^-1, T2^3 * T1^-1 * T2^2 * T1^-1 * T2^-2 * T1 * T2^-4 * T1^-1 * T2^2 * T1^-1 * T2^-3 * T1^-1, T2 * T1^-1 * T2^-3 * T1 * T2^-4 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-4 * T1^-1, T2 * T1^-1 * T2^4 * T1 * T2^-2 * T1 * T2^2 * T1^-1 * T2^3 * T1^-1 * T2^-4 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 3, 9, 19, 37, 26, 13, 5)(2, 6, 14, 27, 49, 32, 16, 7)(4, 11, 22, 41, 60, 34, 17, 8)(10, 21, 40, 68, 100, 62, 35, 18)(12, 23, 43, 73, 115, 76, 44, 24)(15, 29, 52, 85, 134, 88, 53, 30)(20, 39, 67, 106, 160, 102, 63, 36)(25, 45, 77, 121, 186, 124, 78, 46)(28, 51, 84, 131, 197, 127, 80, 48)(31, 54, 89, 140, 215, 143, 90, 55)(33, 57, 92, 145, 223, 148, 93, 58)(38, 66, 105, 164, 247, 162, 103, 64)(42, 72, 113, 175, 262, 173, 111, 70)(47, 65, 104, 163, 248, 193, 125, 79)(50, 83, 130, 201, 295, 199, 128, 81)(56, 82, 129, 200, 296, 221, 144, 91)(59, 94, 149, 228, 330, 231, 150, 95)(61, 97, 152, 233, 338, 235, 153, 98)(69, 110, 171, 258, 369, 256, 169, 108)(71, 112, 174, 263, 336, 232, 151, 96)(74, 117, 181, 272, 385, 268, 177, 114)(75, 118, 182, 273, 393, 275, 183, 119)(86, 136, 210, 307, 431, 303, 206, 133)(87, 137, 211, 308, 438, 310, 212, 138)(99, 154, 236, 342, 478, 345, 237, 155)(101, 157, 239, 347, 486, 349, 240, 158)(107, 168, 142, 218, 317, 364, 253, 166)(109, 170, 257, 370, 484, 346, 238, 156)(116, 180, 271, 389, 534, 387, 269, 178)(120, 179, 270, 388, 535, 397, 276, 184)(122, 188, 281, 403, 548, 399, 277, 185)(123, 189, 282, 404, 380, 265, 176, 190)(126, 194, 287, 409, 563, 411, 288, 195)(132, 205, 147, 226, 327, 426, 300, 203)(135, 209, 306, 435, 590, 433, 304, 207)(139, 208, 305, 434, 591, 442, 311, 213)(141, 217, 316, 448, 603, 444, 312, 214)(146, 225, 326, 458, 618, 454, 322, 222)(159, 241, 350, 490, 650, 492, 351, 242)(161, 244, 353, 494, 608, 496, 354, 245)(165, 252, 230, 333, 466, 502, 361, 250)(167, 254, 365, 507, 653, 493, 352, 243)(172, 259, 373, 517, 655, 519, 374, 260)(187, 280, 402, 552, 613, 550, 400, 278)(191, 279, 401, 551, 604, 558, 406, 283)(192, 284, 407, 559, 423, 298, 202, 285)(196, 289, 412, 566, 501, 568, 413, 290)(198, 292, 415, 570, 489, 572, 416, 293)(204, 301, 427, 582, 491, 569, 414, 291)(216, 315, 447, 607, 630, 605, 445, 313)(219, 314, 446, 606, 619, 611, 450, 318)(220, 319, 451, 612, 523, 378, 264, 320)(224, 325, 457, 622, 560, 620, 455, 323)(227, 324, 456, 621, 549, 625, 460, 328)(229, 332, 465, 629, 553, 626, 461, 329)(234, 340, 475, 639, 672, 635, 471, 337)(246, 355, 497, 594, 679, 537, 390, 356)(249, 360, 344, 481, 644, 600, 499, 358)(251, 362, 503, 656, 693, 589, 498, 357)(255, 366, 509, 662, 547, 664, 510, 367)(261, 375, 520, 661, 577, 673, 521, 376)(266, 381, 526, 657, 567, 652, 522, 377)(267, 382, 527, 675, 602, 654, 495, 383)(274, 395, 543, 648, 487, 649, 540, 392)(286, 359, 500, 592, 694, 610, 561, 408)(294, 417, 573, 515, 669, 593, 436, 418)(297, 422, 396, 544, 645, 482, 575, 420)(299, 424, 578, 508, 646, 483, 574, 419)(302, 428, 584, 691, 617, 687, 571, 429)(309, 440, 598, 685, 564, 686, 595, 437)(321, 421, 576, 479, 642, 624, 614, 452)(331, 464, 441, 599, 682, 545, 627, 462)(334, 463, 628, 536, 678, 557, 631, 467)(335, 468, 632, 538, 668, 514, 371, 469)(339, 474, 638, 554, 405, 556, 636, 472)(341, 473, 637, 532, 386, 531, 640, 476)(343, 480, 643, 530, 391, 539, 641, 477)(348, 488, 398, 546, 683, 703, 647, 485)(363, 504, 658, 529, 384, 528, 659, 505)(368, 511, 665, 674, 525, 555, 666, 512)(372, 516, 670, 588, 432, 587, 667, 513)(379, 524, 651, 583, 677, 533, 633, 470)(394, 542, 660, 506, 449, 609, 681, 541)(410, 565, 443, 601, 697, 708, 684, 562)(425, 579, 688, 586, 430, 585, 689, 580)(439, 597, 690, 581, 459, 623, 696, 596)(453, 615, 698, 711, 701, 671, 518, 616)(634, 699, 712, 718, 714, 705, 663, 700)(676, 704, 680, 702, 713, 719, 715, 706)(692, 709, 695, 707, 716, 720, 717, 710)(721, 722, 724)(723, 728, 730)(725, 732, 726)(727, 735, 731)(729, 738, 740)(733, 745, 743)(734, 744, 748)(736, 751, 749)(737, 753, 741)(739, 756, 758)(742, 750, 762)(746, 767, 765)(747, 768, 770)(752, 776, 774)(754, 779, 777)(755, 781, 759)(757, 784, 785)(760, 778, 789)(761, 790, 791)(763, 766, 794)(764, 795, 771)(769, 801, 802)(772, 775, 806)(773, 807, 792)(780, 816, 814)(782, 819, 817)(783, 821, 786)(787, 818, 827)(788, 828, 829)(793, 834, 836)(796, 840, 838)(797, 799, 842)(798, 843, 837)(800, 846, 803)(804, 839, 852)(805, 853, 855)(808, 859, 857)(809, 811, 861)(810, 862, 856)(812, 815, 866)(813, 867, 830)(820, 876, 874)(822, 879, 877)(823, 881, 824)(825, 878, 885)(826, 886, 887)(831, 892, 832)(833, 858, 896)(835, 898, 899)(841, 905, 907)(844, 911, 909)(845, 912, 908)(847, 916, 914)(848, 918, 849)(850, 915, 922)(851, 923, 924)(854, 927, 928)(860, 934, 936)(863, 939, 938)(864, 940, 937)(865, 942, 944)(868, 947, 946)(869, 871, 949)(870, 950, 945)(872, 875, 954)(873, 930, 888)(880, 963, 961)(882, 966, 964)(883, 965, 969)(884, 970, 971)(889, 975, 890)(891, 925, 903)(893, 981, 979)(894, 980, 984)(895, 985, 986)(897, 987, 900)(901, 910, 932)(902, 904, 994)(906, 998, 999)(913, 1006, 1004)(917, 1011, 1009)(919, 1014, 1012)(920, 1013, 1017)(921, 1018, 1019)(926, 1022, 929)(931, 933, 1029)(935, 1033, 1034)(941, 1041, 1039)(943, 1043, 1044)(948, 1049, 1051)(951, 1054, 1053)(952, 1055, 1052)(953, 1057, 1059)(955, 1061, 1027)(956, 958, 1063)(957, 1064, 1060)(959, 962, 1068)(960, 1046, 972)(967, 1077, 1075)(968, 1078, 1079)(973, 1083, 974)(976, 1088, 1086)(977, 1087, 1091)(978, 995, 1092)(982, 1097, 1095)(983, 1098, 1099)(988, 1104, 1102)(989, 1106, 990)(991, 1103, 1110)(992, 1030, 1111)(993, 1112, 1114)(996, 1116, 1115)(997, 1118, 1000)(1001, 1005, 1008)(1002, 1003, 1125)(1007, 1010, 1130)(1015, 1139, 1137)(1016, 1140, 1141)(1020, 1145, 1021)(1023, 1150, 1148)(1024, 1152, 1025)(1026, 1149, 1156)(1028, 1157, 1159)(1031, 1161, 1160)(1032, 1163, 1035)(1036, 1040, 1094)(1037, 1038, 1169)(1042, 1173, 1045)(1047, 1048, 1179)(1050, 1182, 1183)(1056, 1190, 1188)(1058, 1192, 1193)(1062, 1197, 1199)(1065, 1202, 1201)(1066, 1203, 1200)(1067, 1205, 1207)(1069, 1209, 1178)(1070, 1072, 1211)(1071, 1122, 1208)(1073, 1076, 1215)(1074, 1195, 1080)(1081, 1221, 1082)(1084, 1226, 1224)(1085, 1225, 1228)(1089, 1233, 1231)(1090, 1234, 1235)(1093, 1096, 1238)(1100, 1245, 1101)(1105, 1250, 1248)(1107, 1253, 1251)(1108, 1252, 1256)(1109, 1257, 1258)(1113, 1261, 1236)(1117, 1265, 1264)(1119, 1267, 1266)(1120, 1269, 1121)(1123, 1131, 1273)(1124, 1274, 1275)(1126, 1277, 1276)(1127, 1128, 1280)(1129, 1282, 1284)(1132, 1134, 1287)(1133, 1167, 1285)(1135, 1138, 1291)(1136, 1263, 1142)(1143, 1297, 1144)(1146, 1301, 1299)(1147, 1300, 1303)(1151, 1196, 1305)(1153, 1309, 1307)(1154, 1308, 1312)(1155, 1313, 1314)(1158, 1316, 1259)(1162, 1320, 1319)(1164, 1322, 1321)(1165, 1324, 1166)(1168, 1239, 1328)(1170, 1330, 1329)(1171, 1172, 1333)(1174, 1337, 1335)(1175, 1339, 1176)(1177, 1336, 1241)(1180, 1344, 1343)(1181, 1318, 1184)(1185, 1189, 1230)(1186, 1187, 1350)(1191, 1354, 1194)(1198, 1296, 1295)(1204, 1293, 1294)(1206, 1368, 1292)(1210, 1302, 1371)(1212, 1332, 1272)(1213, 1372, 1289)(1214, 1374, 1323)(1216, 1375, 1359)(1217, 1218, 1310)(1219, 1311, 1220)(1222, 1327, 1288)(1223, 1286, 1377)(1227, 1298, 1381)(1229, 1232, 1383)(1237, 1391, 1392)(1240, 1242, 1373)(1243, 1370, 1244)(1246, 1394, 1376)(1247, 1249, 1396)(1254, 1352, 1353)(1255, 1348, 1347)(1260, 1400, 1262)(1268, 1349, 1384)(1270, 1334, 1345)(1271, 1341, 1326)(1278, 1325, 1351)(1279, 1342, 1393)(1281, 1331, 1340)(1283, 1405, 1346)(1290, 1407, 1338)(1304, 1306, 1412)(1315, 1415, 1317)(1355, 1421, 1419)(1356, 1398, 1357)(1358, 1420, 1386)(1360, 1397, 1409)(1361, 1416, 1362)(1363, 1366, 1379)(1364, 1365, 1402)(1367, 1422, 1369)(1378, 1380, 1424)(1382, 1425, 1403)(1385, 1387, 1413)(1388, 1399, 1389)(1390, 1401, 1414)(1395, 1426, 1417)(1404, 1427, 1406)(1408, 1410, 1429)(1411, 1430, 1418)(1423, 1434, 1433)(1428, 1435, 1436)(1431, 1437, 1432)(1438, 1440, 1439) L = (1, 721)(2, 722)(3, 723)(4, 724)(5, 725)(6, 726)(7, 727)(8, 728)(9, 729)(10, 730)(11, 731)(12, 732)(13, 733)(14, 734)(15, 735)(16, 736)(17, 737)(18, 738)(19, 739)(20, 740)(21, 741)(22, 742)(23, 743)(24, 744)(25, 745)(26, 746)(27, 747)(28, 748)(29, 749)(30, 750)(31, 751)(32, 752)(33, 753)(34, 754)(35, 755)(36, 756)(37, 757)(38, 758)(39, 759)(40, 760)(41, 761)(42, 762)(43, 763)(44, 764)(45, 765)(46, 766)(47, 767)(48, 768)(49, 769)(50, 770)(51, 771)(52, 772)(53, 773)(54, 774)(55, 775)(56, 776)(57, 777)(58, 778)(59, 779)(60, 780)(61, 781)(62, 782)(63, 783)(64, 784)(65, 785)(66, 786)(67, 787)(68, 788)(69, 789)(70, 790)(71, 791)(72, 792)(73, 793)(74, 794)(75, 795)(76, 796)(77, 797)(78, 798)(79, 799)(80, 800)(81, 801)(82, 802)(83, 803)(84, 804)(85, 805)(86, 806)(87, 807)(88, 808)(89, 809)(90, 810)(91, 811)(92, 812)(93, 813)(94, 814)(95, 815)(96, 816)(97, 817)(98, 818)(99, 819)(100, 820)(101, 821)(102, 822)(103, 823)(104, 824)(105, 825)(106, 826)(107, 827)(108, 828)(109, 829)(110, 830)(111, 831)(112, 832)(113, 833)(114, 834)(115, 835)(116, 836)(117, 837)(118, 838)(119, 839)(120, 840)(121, 841)(122, 842)(123, 843)(124, 844)(125, 845)(126, 846)(127, 847)(128, 848)(129, 849)(130, 850)(131, 851)(132, 852)(133, 853)(134, 854)(135, 855)(136, 856)(137, 857)(138, 858)(139, 859)(140, 860)(141, 861)(142, 862)(143, 863)(144, 864)(145, 865)(146, 866)(147, 867)(148, 868)(149, 869)(150, 870)(151, 871)(152, 872)(153, 873)(154, 874)(155, 875)(156, 876)(157, 877)(158, 878)(159, 879)(160, 880)(161, 881)(162, 882)(163, 883)(164, 884)(165, 885)(166, 886)(167, 887)(168, 888)(169, 889)(170, 890)(171, 891)(172, 892)(173, 893)(174, 894)(175, 895)(176, 896)(177, 897)(178, 898)(179, 899)(180, 900)(181, 901)(182, 902)(183, 903)(184, 904)(185, 905)(186, 906)(187, 907)(188, 908)(189, 909)(190, 910)(191, 911)(192, 912)(193, 913)(194, 914)(195, 915)(196, 916)(197, 917)(198, 918)(199, 919)(200, 920)(201, 921)(202, 922)(203, 923)(204, 924)(205, 925)(206, 926)(207, 927)(208, 928)(209, 929)(210, 930)(211, 931)(212, 932)(213, 933)(214, 934)(215, 935)(216, 936)(217, 937)(218, 938)(219, 939)(220, 940)(221, 941)(222, 942)(223, 943)(224, 944)(225, 945)(226, 946)(227, 947)(228, 948)(229, 949)(230, 950)(231, 951)(232, 952)(233, 953)(234, 954)(235, 955)(236, 956)(237, 957)(238, 958)(239, 959)(240, 960)(241, 961)(242, 962)(243, 963)(244, 964)(245, 965)(246, 966)(247, 967)(248, 968)(249, 969)(250, 970)(251, 971)(252, 972)(253, 973)(254, 974)(255, 975)(256, 976)(257, 977)(258, 978)(259, 979)(260, 980)(261, 981)(262, 982)(263, 983)(264, 984)(265, 985)(266, 986)(267, 987)(268, 988)(269, 989)(270, 990)(271, 991)(272, 992)(273, 993)(274, 994)(275, 995)(276, 996)(277, 997)(278, 998)(279, 999)(280, 1000)(281, 1001)(282, 1002)(283, 1003)(284, 1004)(285, 1005)(286, 1006)(287, 1007)(288, 1008)(289, 1009)(290, 1010)(291, 1011)(292, 1012)(293, 1013)(294, 1014)(295, 1015)(296, 1016)(297, 1017)(298, 1018)(299, 1019)(300, 1020)(301, 1021)(302, 1022)(303, 1023)(304, 1024)(305, 1025)(306, 1026)(307, 1027)(308, 1028)(309, 1029)(310, 1030)(311, 1031)(312, 1032)(313, 1033)(314, 1034)(315, 1035)(316, 1036)(317, 1037)(318, 1038)(319, 1039)(320, 1040)(321, 1041)(322, 1042)(323, 1043)(324, 1044)(325, 1045)(326, 1046)(327, 1047)(328, 1048)(329, 1049)(330, 1050)(331, 1051)(332, 1052)(333, 1053)(334, 1054)(335, 1055)(336, 1056)(337, 1057)(338, 1058)(339, 1059)(340, 1060)(341, 1061)(342, 1062)(343, 1063)(344, 1064)(345, 1065)(346, 1066)(347, 1067)(348, 1068)(349, 1069)(350, 1070)(351, 1071)(352, 1072)(353, 1073)(354, 1074)(355, 1075)(356, 1076)(357, 1077)(358, 1078)(359, 1079)(360, 1080)(361, 1081)(362, 1082)(363, 1083)(364, 1084)(365, 1085)(366, 1086)(367, 1087)(368, 1088)(369, 1089)(370, 1090)(371, 1091)(372, 1092)(373, 1093)(374, 1094)(375, 1095)(376, 1096)(377, 1097)(378, 1098)(379, 1099)(380, 1100)(381, 1101)(382, 1102)(383, 1103)(384, 1104)(385, 1105)(386, 1106)(387, 1107)(388, 1108)(389, 1109)(390, 1110)(391, 1111)(392, 1112)(393, 1113)(394, 1114)(395, 1115)(396, 1116)(397, 1117)(398, 1118)(399, 1119)(400, 1120)(401, 1121)(402, 1122)(403, 1123)(404, 1124)(405, 1125)(406, 1126)(407, 1127)(408, 1128)(409, 1129)(410, 1130)(411, 1131)(412, 1132)(413, 1133)(414, 1134)(415, 1135)(416, 1136)(417, 1137)(418, 1138)(419, 1139)(420, 1140)(421, 1141)(422, 1142)(423, 1143)(424, 1144)(425, 1145)(426, 1146)(427, 1147)(428, 1148)(429, 1149)(430, 1150)(431, 1151)(432, 1152)(433, 1153)(434, 1154)(435, 1155)(436, 1156)(437, 1157)(438, 1158)(439, 1159)(440, 1160)(441, 1161)(442, 1162)(443, 1163)(444, 1164)(445, 1165)(446, 1166)(447, 1167)(448, 1168)(449, 1169)(450, 1170)(451, 1171)(452, 1172)(453, 1173)(454, 1174)(455, 1175)(456, 1176)(457, 1177)(458, 1178)(459, 1179)(460, 1180)(461, 1181)(462, 1182)(463, 1183)(464, 1184)(465, 1185)(466, 1186)(467, 1187)(468, 1188)(469, 1189)(470, 1190)(471, 1191)(472, 1192)(473, 1193)(474, 1194)(475, 1195)(476, 1196)(477, 1197)(478, 1198)(479, 1199)(480, 1200)(481, 1201)(482, 1202)(483, 1203)(484, 1204)(485, 1205)(486, 1206)(487, 1207)(488, 1208)(489, 1209)(490, 1210)(491, 1211)(492, 1212)(493, 1213)(494, 1214)(495, 1215)(496, 1216)(497, 1217)(498, 1218)(499, 1219)(500, 1220)(501, 1221)(502, 1222)(503, 1223)(504, 1224)(505, 1225)(506, 1226)(507, 1227)(508, 1228)(509, 1229)(510, 1230)(511, 1231)(512, 1232)(513, 1233)(514, 1234)(515, 1235)(516, 1236)(517, 1237)(518, 1238)(519, 1239)(520, 1240)(521, 1241)(522, 1242)(523, 1243)(524, 1244)(525, 1245)(526, 1246)(527, 1247)(528, 1248)(529, 1249)(530, 1250)(531, 1251)(532, 1252)(533, 1253)(534, 1254)(535, 1255)(536, 1256)(537, 1257)(538, 1258)(539, 1259)(540, 1260)(541, 1261)(542, 1262)(543, 1263)(544, 1264)(545, 1265)(546, 1266)(547, 1267)(548, 1268)(549, 1269)(550, 1270)(551, 1271)(552, 1272)(553, 1273)(554, 1274)(555, 1275)(556, 1276)(557, 1277)(558, 1278)(559, 1279)(560, 1280)(561, 1281)(562, 1282)(563, 1283)(564, 1284)(565, 1285)(566, 1286)(567, 1287)(568, 1288)(569, 1289)(570, 1290)(571, 1291)(572, 1292)(573, 1293)(574, 1294)(575, 1295)(576, 1296)(577, 1297)(578, 1298)(579, 1299)(580, 1300)(581, 1301)(582, 1302)(583, 1303)(584, 1304)(585, 1305)(586, 1306)(587, 1307)(588, 1308)(589, 1309)(590, 1310)(591, 1311)(592, 1312)(593, 1313)(594, 1314)(595, 1315)(596, 1316)(597, 1317)(598, 1318)(599, 1319)(600, 1320)(601, 1321)(602, 1322)(603, 1323)(604, 1324)(605, 1325)(606, 1326)(607, 1327)(608, 1328)(609, 1329)(610, 1330)(611, 1331)(612, 1332)(613, 1333)(614, 1334)(615, 1335)(616, 1336)(617, 1337)(618, 1338)(619, 1339)(620, 1340)(621, 1341)(622, 1342)(623, 1343)(624, 1344)(625, 1345)(626, 1346)(627, 1347)(628, 1348)(629, 1349)(630, 1350)(631, 1351)(632, 1352)(633, 1353)(634, 1354)(635, 1355)(636, 1356)(637, 1357)(638, 1358)(639, 1359)(640, 1360)(641, 1361)(642, 1362)(643, 1363)(644, 1364)(645, 1365)(646, 1366)(647, 1367)(648, 1368)(649, 1369)(650, 1370)(651, 1371)(652, 1372)(653, 1373)(654, 1374)(655, 1375)(656, 1376)(657, 1377)(658, 1378)(659, 1379)(660, 1380)(661, 1381)(662, 1382)(663, 1383)(664, 1384)(665, 1385)(666, 1386)(667, 1387)(668, 1388)(669, 1389)(670, 1390)(671, 1391)(672, 1392)(673, 1393)(674, 1394)(675, 1395)(676, 1396)(677, 1397)(678, 1398)(679, 1399)(680, 1400)(681, 1401)(682, 1402)(683, 1403)(684, 1404)(685, 1405)(686, 1406)(687, 1407)(688, 1408)(689, 1409)(690, 1410)(691, 1411)(692, 1412)(693, 1413)(694, 1414)(695, 1415)(696, 1416)(697, 1417)(698, 1418)(699, 1419)(700, 1420)(701, 1421)(702, 1422)(703, 1423)(704, 1424)(705, 1425)(706, 1426)(707, 1427)(708, 1428)(709, 1429)(710, 1430)(711, 1431)(712, 1432)(713, 1433)(714, 1434)(715, 1435)(716, 1436)(717, 1437)(718, 1438)(719, 1439)(720, 1440) local type(s) :: { ( 4^3 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E16.1306 Transitivity :: ET+ Graph:: simple bipartite v = 330 e = 720 f = 360 degree seq :: [ 3^240, 8^90 ] E16.1303 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 8}) Quotient :: edge Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^8, T1^2 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^3 * T2, T2 * T1^-2 * T2 * T1^2 * T2 * T1^3 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-3, T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^3, T2 * T1^-4 * T2 * T1^-2 * T2 * T1^3 * T2 * T1^-3 * T2 * T1^2 * T2 * T1^-4 ] 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, 36)(24, 37)(25, 42)(26, 43)(27, 46)(29, 47)(31, 51)(32, 53)(34, 56)(38, 58)(39, 63)(40, 64)(41, 67)(44, 70)(45, 71)(48, 72)(49, 76)(50, 79)(52, 81)(54, 82)(55, 86)(57, 59)(60, 92)(61, 93)(62, 96)(65, 99)(66, 100)(68, 101)(69, 105)(73, 107)(74, 112)(75, 113)(77, 116)(78, 118)(80, 108)(83, 121)(84, 125)(85, 127)(87, 128)(88, 132)(89, 134)(90, 135)(91, 138)(94, 141)(95, 142)(97, 143)(98, 147)(102, 149)(103, 153)(104, 156)(106, 150)(109, 162)(110, 163)(111, 166)(114, 169)(115, 171)(117, 173)(119, 174)(120, 178)(122, 172)(123, 182)(124, 183)(126, 186)(129, 187)(130, 191)(131, 193)(133, 196)(136, 199)(137, 200)(139, 201)(140, 205)(144, 207)(145, 211)(146, 214)(148, 208)(151, 220)(152, 221)(154, 224)(155, 225)(157, 226)(158, 230)(159, 232)(160, 233)(161, 236)(164, 239)(165, 240)(167, 241)(168, 245)(170, 248)(175, 251)(176, 255)(177, 257)(179, 260)(180, 261)(181, 264)(184, 267)(185, 269)(188, 270)(189, 274)(190, 275)(192, 278)(194, 279)(195, 282)(197, 283)(198, 287)(202, 289)(203, 293)(204, 296)(206, 290)(209, 302)(210, 303)(212, 306)(213, 307)(215, 308)(216, 312)(217, 314)(218, 315)(219, 318)(222, 321)(223, 323)(227, 325)(228, 329)(229, 331)(231, 334)(234, 337)(235, 338)(237, 339)(238, 343)(242, 345)(243, 301)(244, 350)(246, 346)(247, 353)(249, 354)(250, 358)(252, 324)(253, 291)(254, 361)(256, 364)(258, 365)(259, 369)(262, 372)(263, 373)(265, 319)(266, 376)(268, 379)(271, 383)(272, 384)(273, 341)(276, 388)(277, 390)(280, 391)(281, 394)(284, 396)(285, 400)(286, 403)(288, 397)(292, 408)(294, 411)(295, 412)(297, 413)(298, 417)(299, 419)(300, 420)(304, 424)(305, 426)(309, 428)(310, 432)(311, 434)(313, 437)(316, 440)(317, 441)(320, 444)(322, 447)(326, 427)(327, 398)(328, 452)(330, 455)(332, 456)(333, 459)(335, 460)(336, 464)(340, 466)(342, 471)(344, 467)(347, 476)(348, 477)(349, 478)(351, 479)(352, 483)(355, 484)(356, 488)(357, 490)(359, 493)(360, 494)(362, 497)(363, 498)(366, 499)(367, 502)(368, 504)(370, 404)(371, 507)(374, 509)(375, 512)(377, 510)(378, 515)(380, 516)(381, 520)(382, 415)(385, 523)(386, 524)(387, 526)(389, 528)(392, 430)(393, 531)(395, 534)(399, 537)(401, 540)(402, 541)(405, 544)(406, 546)(407, 547)(409, 550)(410, 551)(414, 553)(416, 557)(418, 560)(421, 563)(422, 564)(423, 566)(425, 568)(429, 552)(431, 573)(433, 576)(435, 577)(436, 580)(438, 581)(439, 585)(442, 587)(443, 590)(445, 588)(446, 593)(448, 594)(449, 598)(450, 600)(451, 601)(453, 604)(454, 605)(457, 606)(458, 609)(461, 578)(462, 554)(463, 583)(465, 611)(468, 615)(469, 610)(470, 539)(472, 616)(473, 559)(474, 619)(475, 620)(480, 623)(481, 626)(482, 535)(485, 622)(486, 612)(487, 630)(489, 608)(491, 632)(492, 617)(495, 536)(496, 635)(500, 624)(501, 639)(503, 542)(505, 642)(506, 636)(508, 586)(511, 641)(513, 644)(514, 646)(517, 647)(518, 649)(519, 638)(521, 613)(522, 650)(525, 651)(527, 584)(529, 602)(530, 597)(532, 654)(533, 589)(538, 657)(543, 658)(545, 660)(548, 661)(549, 662)(555, 664)(556, 665)(558, 666)(561, 668)(562, 670)(565, 672)(567, 671)(569, 675)(570, 677)(571, 678)(572, 679)(574, 681)(575, 682)(579, 684)(582, 667)(591, 686)(592, 659)(595, 689)(596, 692)(599, 687)(603, 696)(607, 690)(614, 688)(618, 669)(621, 676)(625, 701)(627, 655)(628, 703)(629, 704)(631, 698)(633, 656)(634, 705)(637, 663)(640, 697)(643, 699)(645, 702)(648, 685)(652, 694)(653, 693)(673, 710)(674, 708)(680, 714)(683, 711)(691, 715)(695, 716)(700, 717)(706, 718)(707, 709)(712, 719)(713, 720)(721, 722, 725, 731, 741, 740, 730, 724)(723, 727, 735, 747, 765, 751, 737, 728)(726, 733, 745, 761, 786, 764, 746, 734)(729, 738, 752, 772, 797, 769, 749, 736)(732, 743, 759, 782, 815, 785, 760, 744)(739, 754, 775, 805, 846, 804, 774, 753)(742, 757, 780, 811, 857, 814, 781, 758)(748, 767, 794, 831, 885, 834, 795, 768)(750, 770, 798, 837, 874, 823, 788, 762)(755, 777, 808, 851, 912, 850, 807, 776)(756, 778, 809, 853, 915, 856, 810, 779)(763, 789, 824, 875, 932, 865, 817, 783)(766, 792, 829, 881, 955, 884, 830, 793)(771, 800, 840, 897, 976, 896, 839, 799)(773, 802, 843, 901, 983, 904, 844, 803)(784, 818, 866, 933, 1014, 923, 859, 812)(787, 821, 871, 939, 1037, 942, 872, 822)(790, 826, 878, 949, 1050, 948, 877, 825)(791, 827, 879, 951, 1053, 954, 880, 828)(796, 835, 890, 967, 1068, 963, 887, 832)(801, 841, 899, 979, 1088, 982, 900, 842)(806, 848, 909, 993, 1106, 996, 910, 849)(813, 860, 924, 1015, 1121, 1005, 917, 854)(816, 863, 929, 1021, 1142, 1024, 930, 864)(819, 868, 936, 1031, 1153, 1030, 935, 867)(820, 869, 937, 1033, 1156, 1036, 938, 870)(833, 888, 964, 1069, 1189, 1061, 957, 882)(836, 892, 970, 1077, 1209, 1076, 969, 891)(838, 894, 973, 1013, 1130, 1082, 974, 895)(845, 905, 988, 1098, 1162, 1038, 985, 902)(847, 907, 991, 1102, 1241, 1105, 992, 908)(852, 855, 918, 1006, 1122, 1115, 1001, 914)(858, 921, 1011, 975, 1083, 1129, 1012, 922)(861, 926, 1018, 1136, 1276, 1135, 1017, 925)(862, 927, 1019, 1138, 1279, 1141, 1020, 928)(873, 943, 1042, 1166, 1094, 984, 1039, 940)(876, 946, 1047, 1120, 1259, 1173, 1048, 947)(883, 958, 1062, 1190, 1260, 1182, 1055, 952)(886, 961, 1022, 931, 1025, 1145, 1067, 962)(889, 966, 1072, 1202, 1257, 1201, 1071, 965)(893, 971, 1079, 1212, 1264, 1215, 1080, 972)(898, 953, 1056, 1183, 1261, 1223, 1087, 978)(903, 986, 1095, 1231, 1262, 1123, 1090, 980)(906, 990, 1101, 1239, 1359, 1238, 1100, 989)(911, 997, 1109, 1188, 1060, 956, 1059, 994)(913, 999, 1112, 1152, 1295, 1252, 1113, 1000)(916, 1003, 1118, 1049, 1174, 1258, 1119, 1004)(919, 1008, 1125, 1263, 1225, 1089, 1124, 1007)(920, 1009, 1126, 1265, 1379, 1268, 1127, 1010)(934, 1028, 1150, 1114, 1253, 1294, 1151, 1029)(941, 1040, 1163, 1309, 1254, 1303, 1158, 1034)(944, 1044, 1169, 1317, 1251, 1316, 1168, 1043)(945, 1045, 1170, 1319, 1248, 1322, 1171, 1046)(950, 1035, 1159, 1304, 1244, 1330, 1178, 1052)(959, 1064, 1193, 1338, 1378, 1337, 1192, 1063)(960, 1065, 1194, 1278, 1137, 1267, 1195, 1066)(968, 1074, 1206, 1274, 1132, 1273, 1207, 1075)(977, 1085, 1220, 1346, 1377, 1360, 1221, 1086)(981, 1091, 1226, 1271, 1131, 1272, 1211, 1078)(987, 1097, 1234, 1266, 1128, 1269, 1233, 1096)(995, 1107, 1245, 1275, 1134, 1016, 1133, 1103)(998, 1111, 1250, 1373, 1424, 1372, 1249, 1110)(1002, 1116, 1255, 1375, 1428, 1376, 1256, 1117)(1023, 1143, 1285, 1246, 1108, 1247, 1281, 1139)(1026, 1147, 1290, 1240, 1104, 1242, 1289, 1146)(1027, 1148, 1291, 1237, 1099, 1236, 1292, 1149)(1032, 1140, 1282, 1230, 1093, 1229, 1299, 1155)(1041, 1165, 1312, 1408, 1335, 1407, 1311, 1164)(1051, 1176, 1327, 1412, 1374, 1418, 1328, 1177)(1054, 1180, 1332, 1208, 1351, 1402, 1296, 1181)(1057, 1185, 1333, 1385, 1302, 1157, 1301, 1184)(1058, 1186, 1334, 1380, 1366, 1390, 1283, 1187)(1070, 1199, 1344, 1222, 1361, 1422, 1345, 1200)(1073, 1204, 1348, 1382, 1270, 1383, 1349, 1205)(1081, 1216, 1354, 1416, 1324, 1191, 1336, 1213)(1084, 1219, 1358, 1397, 1321, 1414, 1357, 1218)(1092, 1228, 1300, 1387, 1277, 1386, 1363, 1227)(1144, 1287, 1394, 1368, 1235, 1367, 1393, 1286)(1154, 1297, 1403, 1370, 1243, 1331, 1179, 1298)(1160, 1306, 1224, 1362, 1389, 1280, 1388, 1305)(1161, 1307, 1405, 1347, 1203, 1340, 1381, 1308)(1167, 1314, 1410, 1329, 1198, 1343, 1411, 1315)(1172, 1323, 1415, 1434, 1401, 1310, 1406, 1320)(1175, 1326, 1210, 1352, 1399, 1369, 1417, 1325)(1196, 1341, 1420, 1355, 1217, 1356, 1419, 1339)(1197, 1342, 1413, 1318, 1214, 1353, 1391, 1284)(1232, 1364, 1423, 1350, 1384, 1429, 1426, 1365)(1288, 1395, 1431, 1404, 1313, 1409, 1432, 1396)(1293, 1400, 1433, 1427, 1371, 1392, 1430, 1398)(1421, 1438, 1440, 1436, 1425, 1437, 1439, 1435) L = (1, 721)(2, 722)(3, 723)(4, 724)(5, 725)(6, 726)(7, 727)(8, 728)(9, 729)(10, 730)(11, 731)(12, 732)(13, 733)(14, 734)(15, 735)(16, 736)(17, 737)(18, 738)(19, 739)(20, 740)(21, 741)(22, 742)(23, 743)(24, 744)(25, 745)(26, 746)(27, 747)(28, 748)(29, 749)(30, 750)(31, 751)(32, 752)(33, 753)(34, 754)(35, 755)(36, 756)(37, 757)(38, 758)(39, 759)(40, 760)(41, 761)(42, 762)(43, 763)(44, 764)(45, 765)(46, 766)(47, 767)(48, 768)(49, 769)(50, 770)(51, 771)(52, 772)(53, 773)(54, 774)(55, 775)(56, 776)(57, 777)(58, 778)(59, 779)(60, 780)(61, 781)(62, 782)(63, 783)(64, 784)(65, 785)(66, 786)(67, 787)(68, 788)(69, 789)(70, 790)(71, 791)(72, 792)(73, 793)(74, 794)(75, 795)(76, 796)(77, 797)(78, 798)(79, 799)(80, 800)(81, 801)(82, 802)(83, 803)(84, 804)(85, 805)(86, 806)(87, 807)(88, 808)(89, 809)(90, 810)(91, 811)(92, 812)(93, 813)(94, 814)(95, 815)(96, 816)(97, 817)(98, 818)(99, 819)(100, 820)(101, 821)(102, 822)(103, 823)(104, 824)(105, 825)(106, 826)(107, 827)(108, 828)(109, 829)(110, 830)(111, 831)(112, 832)(113, 833)(114, 834)(115, 835)(116, 836)(117, 837)(118, 838)(119, 839)(120, 840)(121, 841)(122, 842)(123, 843)(124, 844)(125, 845)(126, 846)(127, 847)(128, 848)(129, 849)(130, 850)(131, 851)(132, 852)(133, 853)(134, 854)(135, 855)(136, 856)(137, 857)(138, 858)(139, 859)(140, 860)(141, 861)(142, 862)(143, 863)(144, 864)(145, 865)(146, 866)(147, 867)(148, 868)(149, 869)(150, 870)(151, 871)(152, 872)(153, 873)(154, 874)(155, 875)(156, 876)(157, 877)(158, 878)(159, 879)(160, 880)(161, 881)(162, 882)(163, 883)(164, 884)(165, 885)(166, 886)(167, 887)(168, 888)(169, 889)(170, 890)(171, 891)(172, 892)(173, 893)(174, 894)(175, 895)(176, 896)(177, 897)(178, 898)(179, 899)(180, 900)(181, 901)(182, 902)(183, 903)(184, 904)(185, 905)(186, 906)(187, 907)(188, 908)(189, 909)(190, 910)(191, 911)(192, 912)(193, 913)(194, 914)(195, 915)(196, 916)(197, 917)(198, 918)(199, 919)(200, 920)(201, 921)(202, 922)(203, 923)(204, 924)(205, 925)(206, 926)(207, 927)(208, 928)(209, 929)(210, 930)(211, 931)(212, 932)(213, 933)(214, 934)(215, 935)(216, 936)(217, 937)(218, 938)(219, 939)(220, 940)(221, 941)(222, 942)(223, 943)(224, 944)(225, 945)(226, 946)(227, 947)(228, 948)(229, 949)(230, 950)(231, 951)(232, 952)(233, 953)(234, 954)(235, 955)(236, 956)(237, 957)(238, 958)(239, 959)(240, 960)(241, 961)(242, 962)(243, 963)(244, 964)(245, 965)(246, 966)(247, 967)(248, 968)(249, 969)(250, 970)(251, 971)(252, 972)(253, 973)(254, 974)(255, 975)(256, 976)(257, 977)(258, 978)(259, 979)(260, 980)(261, 981)(262, 982)(263, 983)(264, 984)(265, 985)(266, 986)(267, 987)(268, 988)(269, 989)(270, 990)(271, 991)(272, 992)(273, 993)(274, 994)(275, 995)(276, 996)(277, 997)(278, 998)(279, 999)(280, 1000)(281, 1001)(282, 1002)(283, 1003)(284, 1004)(285, 1005)(286, 1006)(287, 1007)(288, 1008)(289, 1009)(290, 1010)(291, 1011)(292, 1012)(293, 1013)(294, 1014)(295, 1015)(296, 1016)(297, 1017)(298, 1018)(299, 1019)(300, 1020)(301, 1021)(302, 1022)(303, 1023)(304, 1024)(305, 1025)(306, 1026)(307, 1027)(308, 1028)(309, 1029)(310, 1030)(311, 1031)(312, 1032)(313, 1033)(314, 1034)(315, 1035)(316, 1036)(317, 1037)(318, 1038)(319, 1039)(320, 1040)(321, 1041)(322, 1042)(323, 1043)(324, 1044)(325, 1045)(326, 1046)(327, 1047)(328, 1048)(329, 1049)(330, 1050)(331, 1051)(332, 1052)(333, 1053)(334, 1054)(335, 1055)(336, 1056)(337, 1057)(338, 1058)(339, 1059)(340, 1060)(341, 1061)(342, 1062)(343, 1063)(344, 1064)(345, 1065)(346, 1066)(347, 1067)(348, 1068)(349, 1069)(350, 1070)(351, 1071)(352, 1072)(353, 1073)(354, 1074)(355, 1075)(356, 1076)(357, 1077)(358, 1078)(359, 1079)(360, 1080)(361, 1081)(362, 1082)(363, 1083)(364, 1084)(365, 1085)(366, 1086)(367, 1087)(368, 1088)(369, 1089)(370, 1090)(371, 1091)(372, 1092)(373, 1093)(374, 1094)(375, 1095)(376, 1096)(377, 1097)(378, 1098)(379, 1099)(380, 1100)(381, 1101)(382, 1102)(383, 1103)(384, 1104)(385, 1105)(386, 1106)(387, 1107)(388, 1108)(389, 1109)(390, 1110)(391, 1111)(392, 1112)(393, 1113)(394, 1114)(395, 1115)(396, 1116)(397, 1117)(398, 1118)(399, 1119)(400, 1120)(401, 1121)(402, 1122)(403, 1123)(404, 1124)(405, 1125)(406, 1126)(407, 1127)(408, 1128)(409, 1129)(410, 1130)(411, 1131)(412, 1132)(413, 1133)(414, 1134)(415, 1135)(416, 1136)(417, 1137)(418, 1138)(419, 1139)(420, 1140)(421, 1141)(422, 1142)(423, 1143)(424, 1144)(425, 1145)(426, 1146)(427, 1147)(428, 1148)(429, 1149)(430, 1150)(431, 1151)(432, 1152)(433, 1153)(434, 1154)(435, 1155)(436, 1156)(437, 1157)(438, 1158)(439, 1159)(440, 1160)(441, 1161)(442, 1162)(443, 1163)(444, 1164)(445, 1165)(446, 1166)(447, 1167)(448, 1168)(449, 1169)(450, 1170)(451, 1171)(452, 1172)(453, 1173)(454, 1174)(455, 1175)(456, 1176)(457, 1177)(458, 1178)(459, 1179)(460, 1180)(461, 1181)(462, 1182)(463, 1183)(464, 1184)(465, 1185)(466, 1186)(467, 1187)(468, 1188)(469, 1189)(470, 1190)(471, 1191)(472, 1192)(473, 1193)(474, 1194)(475, 1195)(476, 1196)(477, 1197)(478, 1198)(479, 1199)(480, 1200)(481, 1201)(482, 1202)(483, 1203)(484, 1204)(485, 1205)(486, 1206)(487, 1207)(488, 1208)(489, 1209)(490, 1210)(491, 1211)(492, 1212)(493, 1213)(494, 1214)(495, 1215)(496, 1216)(497, 1217)(498, 1218)(499, 1219)(500, 1220)(501, 1221)(502, 1222)(503, 1223)(504, 1224)(505, 1225)(506, 1226)(507, 1227)(508, 1228)(509, 1229)(510, 1230)(511, 1231)(512, 1232)(513, 1233)(514, 1234)(515, 1235)(516, 1236)(517, 1237)(518, 1238)(519, 1239)(520, 1240)(521, 1241)(522, 1242)(523, 1243)(524, 1244)(525, 1245)(526, 1246)(527, 1247)(528, 1248)(529, 1249)(530, 1250)(531, 1251)(532, 1252)(533, 1253)(534, 1254)(535, 1255)(536, 1256)(537, 1257)(538, 1258)(539, 1259)(540, 1260)(541, 1261)(542, 1262)(543, 1263)(544, 1264)(545, 1265)(546, 1266)(547, 1267)(548, 1268)(549, 1269)(550, 1270)(551, 1271)(552, 1272)(553, 1273)(554, 1274)(555, 1275)(556, 1276)(557, 1277)(558, 1278)(559, 1279)(560, 1280)(561, 1281)(562, 1282)(563, 1283)(564, 1284)(565, 1285)(566, 1286)(567, 1287)(568, 1288)(569, 1289)(570, 1290)(571, 1291)(572, 1292)(573, 1293)(574, 1294)(575, 1295)(576, 1296)(577, 1297)(578, 1298)(579, 1299)(580, 1300)(581, 1301)(582, 1302)(583, 1303)(584, 1304)(585, 1305)(586, 1306)(587, 1307)(588, 1308)(589, 1309)(590, 1310)(591, 1311)(592, 1312)(593, 1313)(594, 1314)(595, 1315)(596, 1316)(597, 1317)(598, 1318)(599, 1319)(600, 1320)(601, 1321)(602, 1322)(603, 1323)(604, 1324)(605, 1325)(606, 1326)(607, 1327)(608, 1328)(609, 1329)(610, 1330)(611, 1331)(612, 1332)(613, 1333)(614, 1334)(615, 1335)(616, 1336)(617, 1337)(618, 1338)(619, 1339)(620, 1340)(621, 1341)(622, 1342)(623, 1343)(624, 1344)(625, 1345)(626, 1346)(627, 1347)(628, 1348)(629, 1349)(630, 1350)(631, 1351)(632, 1352)(633, 1353)(634, 1354)(635, 1355)(636, 1356)(637, 1357)(638, 1358)(639, 1359)(640, 1360)(641, 1361)(642, 1362)(643, 1363)(644, 1364)(645, 1365)(646, 1366)(647, 1367)(648, 1368)(649, 1369)(650, 1370)(651, 1371)(652, 1372)(653, 1373)(654, 1374)(655, 1375)(656, 1376)(657, 1377)(658, 1378)(659, 1379)(660, 1380)(661, 1381)(662, 1382)(663, 1383)(664, 1384)(665, 1385)(666, 1386)(667, 1387)(668, 1388)(669, 1389)(670, 1390)(671, 1391)(672, 1392)(673, 1393)(674, 1394)(675, 1395)(676, 1396)(677, 1397)(678, 1398)(679, 1399)(680, 1400)(681, 1401)(682, 1402)(683, 1403)(684, 1404)(685, 1405)(686, 1406)(687, 1407)(688, 1408)(689, 1409)(690, 1410)(691, 1411)(692, 1412)(693, 1413)(694, 1414)(695, 1415)(696, 1416)(697, 1417)(698, 1418)(699, 1419)(700, 1420)(701, 1421)(702, 1422)(703, 1423)(704, 1424)(705, 1425)(706, 1426)(707, 1427)(708, 1428)(709, 1429)(710, 1430)(711, 1431)(712, 1432)(713, 1433)(714, 1434)(715, 1435)(716, 1436)(717, 1437)(718, 1438)(719, 1439)(720, 1440) local type(s) :: { ( 6, 6 ), ( 6^8 ) } Outer automorphisms :: reflexible Dual of E16.1304 Transitivity :: ET+ Graph:: simple bipartite v = 450 e = 720 f = 240 degree seq :: [ 2^360, 8^90 ] E16.1304 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 8}) Quotient :: loop Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1)^8, (T1 * T2 * T1 * T2^-1)^5, (T2 * T1 * T2^-1 * T1)^5, T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 721, 3, 723, 4, 724)(2, 722, 5, 725, 6, 726)(7, 727, 11, 731, 12, 732)(8, 728, 13, 733, 14, 734)(9, 729, 15, 735, 16, 736)(10, 730, 17, 737, 18, 738)(19, 739, 27, 747, 28, 748)(20, 740, 29, 749, 30, 750)(21, 741, 31, 751, 32, 752)(22, 742, 33, 753, 34, 754)(23, 743, 35, 755, 36, 756)(24, 744, 37, 757, 38, 758)(25, 745, 39, 759, 40, 760)(26, 746, 41, 761, 42, 762)(43, 763, 59, 779, 60, 780)(44, 764, 61, 781, 62, 782)(45, 765, 63, 783, 64, 784)(46, 766, 65, 785, 66, 786)(47, 767, 67, 787, 68, 788)(48, 768, 69, 789, 70, 790)(49, 769, 71, 791, 72, 792)(50, 770, 73, 793, 74, 794)(51, 771, 75, 795, 76, 796)(52, 772, 77, 797, 78, 798)(53, 773, 79, 799, 80, 800)(54, 774, 81, 801, 82, 802)(55, 775, 83, 803, 84, 804)(56, 776, 85, 805, 86, 806)(57, 777, 87, 807, 88, 808)(58, 778, 89, 809, 90, 810)(91, 811, 119, 839, 120, 840)(92, 812, 121, 841, 122, 842)(93, 813, 123, 843, 124, 844)(94, 814, 125, 845, 126, 846)(95, 815, 127, 847, 128, 848)(96, 816, 129, 849, 130, 850)(97, 817, 131, 851, 98, 818)(99, 819, 132, 852, 133, 853)(100, 820, 134, 854, 135, 855)(101, 821, 136, 856, 137, 857)(102, 822, 138, 858, 139, 859)(103, 823, 140, 860, 141, 861)(104, 824, 142, 862, 143, 863)(105, 825, 144, 864, 145, 865)(106, 826, 146, 866, 147, 867)(107, 827, 148, 868, 149, 869)(108, 828, 150, 870, 151, 871)(109, 829, 152, 872, 153, 873)(110, 830, 154, 874, 155, 875)(111, 831, 156, 876, 112, 832)(113, 833, 157, 877, 158, 878)(114, 834, 159, 879, 160, 880)(115, 835, 161, 881, 162, 882)(116, 836, 163, 883, 164, 884)(117, 837, 165, 885, 166, 886)(118, 838, 167, 887, 168, 888)(169, 889, 215, 935, 216, 936)(170, 890, 217, 937, 218, 938)(171, 891, 219, 939, 220, 940)(172, 892, 188, 908, 221, 941)(173, 893, 222, 942, 223, 943)(174, 894, 224, 944, 175, 895)(176, 896, 225, 945, 226, 946)(177, 897, 227, 947, 228, 948)(178, 898, 229, 949, 230, 950)(179, 899, 231, 951, 232, 952)(180, 900, 233, 953, 234, 954)(181, 901, 235, 955, 236, 956)(182, 902, 237, 957, 238, 958)(183, 903, 239, 959, 240, 960)(184, 904, 241, 961, 242, 962)(185, 905, 243, 963, 186, 906)(187, 907, 244, 964, 245, 965)(189, 909, 246, 966, 247, 967)(190, 910, 248, 968, 249, 969)(191, 911, 250, 970, 251, 971)(192, 912, 398, 1118, 417, 1137)(193, 913, 400, 1120, 607, 1327)(194, 914, 401, 1121, 609, 1329)(195, 915, 211, 931, 421, 1141)(196, 916, 334, 1054, 514, 1234)(197, 917, 404, 1124, 198, 918)(199, 919, 303, 1023, 509, 1229)(200, 920, 408, 1128, 615, 1335)(201, 921, 358, 1078, 570, 1290)(202, 922, 410, 1130, 617, 1337)(203, 923, 411, 1131, 587, 1307)(204, 924, 413, 1133, 336, 1056)(205, 925, 415, 1135, 625, 1345)(206, 926, 416, 1136, 627, 1347)(207, 927, 402, 1122, 557, 1277)(208, 928, 364, 1084, 209, 929)(210, 930, 273, 993, 485, 1205)(212, 932, 422, 1142, 632, 1352)(213, 933, 423, 1143, 633, 1353)(214, 934, 425, 1145, 634, 1354)(252, 972, 353, 1073, 350, 1070)(253, 973, 372, 1092, 369, 1089)(254, 974, 363, 1083, 359, 1079)(255, 975, 324, 1044, 320, 1040)(256, 976, 381, 1101, 377, 1097)(257, 977, 310, 1030, 306, 1026)(258, 978, 431, 1151, 385, 1105)(259, 979, 459, 1179, 453, 1173)(260, 980, 479, 1199, 368, 1088)(261, 981, 480, 1200, 447, 1167)(262, 982, 445, 1165, 441, 1161)(263, 983, 317, 1037, 313, 1033)(264, 984, 472, 1192, 468, 1188)(265, 985, 290, 1010, 286, 1006)(266, 986, 487, 1207, 488, 1208)(267, 987, 331, 1051, 327, 1047)(268, 988, 489, 1209, 490, 1210)(269, 989, 283, 1003, 279, 999)(270, 990, 481, 1201, 329, 1049)(271, 991, 484, 1204, 474, 1194)(272, 992, 482, 1202, 357, 1077)(274, 994, 478, 1198, 315, 1035)(275, 995, 486, 1206, 494, 1214)(276, 996, 483, 1203, 376, 1096)(277, 997, 497, 1217, 498, 1218)(278, 998, 338, 1058, 356, 1076)(280, 1000, 500, 1220, 501, 1221)(281, 1001, 297, 1017, 367, 1087)(282, 1002, 502, 1222, 503, 1223)(284, 1004, 505, 1225, 506, 1226)(285, 1005, 346, 1066, 375, 1095)(287, 1007, 463, 1183, 508, 1228)(288, 1008, 291, 1011, 384, 1104)(289, 1009, 510, 1230, 511, 1231)(292, 1012, 496, 1216, 513, 1233)(293, 1013, 491, 1211, 438, 1158)(294, 1014, 451, 1171, 308, 1028)(295, 1015, 499, 1219, 515, 1235)(296, 1016, 492, 1212, 465, 1185)(298, 1018, 504, 1224, 518, 1238)(299, 1019, 493, 1213, 519, 1239)(300, 1020, 495, 1215, 322, 1042)(301, 1021, 507, 1227, 428, 1148)(302, 1022, 467, 1187, 521, 1241)(304, 1024, 524, 1244, 525, 1245)(305, 1025, 389, 1109, 436, 1156)(307, 1027, 374, 1094, 526, 1246)(309, 1029, 528, 1248, 529, 1249)(311, 1031, 531, 1251, 532, 1252)(312, 1032, 395, 1115, 378, 1098)(314, 1034, 435, 1155, 533, 1253)(316, 1036, 535, 1255, 536, 1256)(318, 1038, 534, 1254, 462, 1182)(319, 1039, 406, 1126, 437, 1157)(321, 1041, 355, 1075, 538, 1258)(323, 1043, 540, 1260, 541, 1261)(325, 1045, 446, 1166, 444, 1164)(326, 1046, 419, 1139, 360, 1080)(328, 1048, 543, 1263, 544, 1264)(330, 1050, 545, 1265, 464, 1184)(332, 1052, 523, 1243, 547, 1267)(333, 1053, 512, 1232, 548, 1268)(335, 1055, 409, 1129, 456, 1176)(337, 1057, 527, 1247, 434, 1154)(339, 1059, 530, 1250, 552, 1272)(340, 1060, 516, 1236, 361, 1081)(341, 1061, 440, 1160, 554, 1274)(342, 1062, 537, 1257, 556, 1276)(343, 1063, 517, 1237, 558, 1278)(344, 1064, 391, 1111, 549, 1269)(345, 1065, 539, 1259, 560, 1280)(347, 1067, 542, 1262, 562, 1282)(348, 1068, 520, 1240, 379, 1099)(349, 1069, 522, 1242, 564, 1284)(351, 1071, 365, 1085, 565, 1285)(352, 1072, 567, 1287, 568, 1288)(354, 1074, 473, 1193, 471, 1191)(362, 1082, 572, 1292, 573, 1293)(366, 1086, 575, 1295, 576, 1296)(370, 1090, 382, 1102, 577, 1297)(371, 1091, 579, 1299, 580, 1300)(373, 1093, 582, 1302, 583, 1303)(380, 1100, 585, 1305, 586, 1306)(383, 1103, 588, 1308, 589, 1309)(386, 1106, 546, 1266, 591, 1311)(387, 1107, 397, 1117, 553, 1273)(388, 1108, 566, 1286, 593, 1313)(390, 1110, 569, 1289, 595, 1315)(392, 1112, 550, 1270, 597, 1317)(393, 1113, 551, 1271, 599, 1319)(394, 1114, 571, 1291, 601, 1321)(396, 1116, 574, 1294, 603, 1323)(399, 1119, 555, 1275, 606, 1326)(403, 1123, 424, 1144, 563, 1283)(405, 1125, 578, 1298, 613, 1333)(407, 1127, 581, 1301, 614, 1334)(412, 1132, 559, 1279, 621, 1341)(414, 1134, 561, 1281, 624, 1344)(418, 1138, 584, 1304, 629, 1349)(420, 1140, 466, 1186, 630, 1350)(426, 1146, 635, 1355, 628, 1348)(427, 1147, 448, 1168, 638, 1358)(429, 1149, 640, 1360, 641, 1361)(430, 1150, 642, 1362, 432, 1152)(433, 1153, 643, 1363, 644, 1364)(439, 1159, 646, 1366, 648, 1368)(442, 1162, 636, 1356, 590, 1310)(443, 1163, 622, 1342, 650, 1370)(449, 1169, 651, 1371, 652, 1372)(450, 1170, 653, 1373, 626, 1346)(452, 1172, 654, 1374, 655, 1375)(454, 1174, 656, 1376, 616, 1336)(455, 1175, 475, 1195, 658, 1378)(457, 1177, 659, 1379, 660, 1380)(458, 1178, 605, 1325, 460, 1180)(461, 1181, 604, 1324, 662, 1382)(469, 1189, 657, 1377, 598, 1318)(470, 1190, 665, 1385, 666, 1386)(476, 1196, 667, 1387, 668, 1388)(477, 1197, 669, 1389, 670, 1390)(592, 1312, 687, 1407, 647, 1367)(594, 1314, 689, 1409, 649, 1369)(596, 1316, 639, 1359, 637, 1357)(600, 1320, 692, 1412, 663, 1383)(602, 1322, 686, 1406, 664, 1384)(608, 1328, 700, 1420, 705, 1425)(610, 1330, 661, 1381, 645, 1365)(611, 1331, 706, 1426, 672, 1392)(612, 1332, 682, 1402, 707, 1427)(618, 1338, 674, 1394, 671, 1391)(619, 1339, 710, 1430, 677, 1397)(620, 1340, 676, 1396, 704, 1424)(623, 1343, 631, 1351, 681, 1401)(673, 1393, 703, 1423, 708, 1428)(675, 1395, 713, 1433, 697, 1417)(678, 1398, 717, 1437, 693, 1413)(679, 1399, 691, 1411, 718, 1438)(680, 1400, 685, 1405, 719, 1439)(683, 1403, 720, 1440, 695, 1415)(684, 1404, 712, 1432, 709, 1429)(688, 1408, 716, 1436, 696, 1416)(690, 1410, 702, 1422, 699, 1419)(694, 1414, 701, 1421, 714, 1434)(698, 1418, 711, 1431, 715, 1435) L = (1, 722)(2, 721)(3, 727)(4, 728)(5, 729)(6, 730)(7, 723)(8, 724)(9, 725)(10, 726)(11, 739)(12, 740)(13, 741)(14, 742)(15, 743)(16, 744)(17, 745)(18, 746)(19, 731)(20, 732)(21, 733)(22, 734)(23, 735)(24, 736)(25, 737)(26, 738)(27, 763)(28, 764)(29, 765)(30, 766)(31, 767)(32, 768)(33, 769)(34, 770)(35, 771)(36, 772)(37, 773)(38, 774)(39, 775)(40, 776)(41, 777)(42, 778)(43, 747)(44, 748)(45, 749)(46, 750)(47, 751)(48, 752)(49, 753)(50, 754)(51, 755)(52, 756)(53, 757)(54, 758)(55, 759)(56, 760)(57, 761)(58, 762)(59, 810)(60, 811)(61, 812)(62, 813)(63, 814)(64, 815)(65, 816)(66, 817)(67, 818)(68, 819)(69, 820)(70, 821)(71, 822)(72, 823)(73, 824)(74, 795)(75, 794)(76, 825)(77, 826)(78, 827)(79, 828)(80, 829)(81, 830)(82, 831)(83, 832)(84, 833)(85, 834)(86, 835)(87, 836)(88, 837)(89, 838)(90, 779)(91, 780)(92, 781)(93, 782)(94, 783)(95, 784)(96, 785)(97, 786)(98, 787)(99, 788)(100, 789)(101, 790)(102, 791)(103, 792)(104, 793)(105, 796)(106, 797)(107, 798)(108, 799)(109, 800)(110, 801)(111, 802)(112, 803)(113, 804)(114, 805)(115, 806)(116, 807)(117, 808)(118, 809)(119, 889)(120, 890)(121, 891)(122, 892)(123, 893)(124, 894)(125, 895)(126, 896)(127, 872)(128, 897)(129, 898)(130, 899)(131, 900)(132, 901)(133, 902)(134, 903)(135, 880)(136, 904)(137, 905)(138, 906)(139, 907)(140, 908)(141, 909)(142, 910)(143, 911)(144, 912)(145, 913)(146, 914)(147, 915)(148, 916)(149, 917)(150, 918)(151, 919)(152, 847)(153, 920)(154, 921)(155, 922)(156, 923)(157, 924)(158, 925)(159, 926)(160, 855)(161, 927)(162, 928)(163, 929)(164, 930)(165, 931)(166, 932)(167, 933)(168, 934)(169, 839)(170, 840)(171, 841)(172, 842)(173, 843)(174, 844)(175, 845)(176, 846)(177, 848)(178, 849)(179, 850)(180, 851)(181, 852)(182, 853)(183, 854)(184, 856)(185, 857)(186, 858)(187, 859)(188, 860)(189, 861)(190, 862)(191, 863)(192, 864)(193, 865)(194, 866)(195, 867)(196, 868)(197, 869)(198, 870)(199, 871)(200, 873)(201, 874)(202, 875)(203, 876)(204, 877)(205, 878)(206, 879)(207, 881)(208, 882)(209, 883)(210, 884)(211, 885)(212, 886)(213, 887)(214, 888)(215, 1146)(216, 1148)(217, 1081)(218, 1150)(219, 1152)(220, 1154)(221, 1048)(222, 1157)(223, 1019)(224, 1159)(225, 1160)(226, 1002)(227, 1162)(228, 1164)(229, 1166)(230, 1167)(231, 1021)(232, 1170)(233, 1172)(234, 1086)(235, 1174)(236, 1176)(237, 1042)(238, 1178)(239, 1180)(240, 1182)(241, 1184)(242, 1053)(243, 1186)(244, 1187)(245, 988)(246, 1189)(247, 1191)(248, 1193)(249, 1194)(250, 1055)(251, 1197)(252, 1151)(253, 1199)(254, 1179)(255, 1092)(256, 1200)(257, 1073)(258, 1201)(259, 1202)(260, 1198)(261, 1203)(262, 1204)(263, 1083)(264, 1205)(265, 1044)(266, 1206)(267, 1101)(268, 965)(269, 1030)(270, 1104)(271, 1211)(272, 1171)(273, 1212)(274, 1087)(275, 1213)(276, 1215)(277, 1216)(278, 1165)(279, 1037)(280, 1219)(281, 1192)(282, 946)(283, 1010)(284, 1224)(285, 1207)(286, 1051)(287, 1227)(288, 1209)(289, 1229)(290, 1003)(291, 1047)(292, 1232)(293, 1234)(294, 1076)(295, 1130)(296, 1236)(297, 1033)(298, 1237)(299, 943)(300, 1095)(301, 951)(302, 1240)(303, 1242)(304, 1243)(305, 1217)(306, 1058)(307, 1129)(308, 1135)(309, 1247)(310, 989)(311, 1250)(312, 1220)(313, 1017)(314, 1141)(315, 1222)(316, 1254)(317, 999)(318, 1257)(319, 1225)(320, 1066)(321, 1111)(322, 957)(323, 1259)(324, 985)(325, 1262)(326, 1183)(327, 1011)(328, 941)(329, 1230)(330, 1244)(331, 1006)(332, 1266)(333, 962)(334, 1156)(335, 970)(336, 1269)(337, 1270)(338, 1026)(339, 1271)(340, 1098)(341, 1273)(342, 1275)(343, 1277)(344, 1145)(345, 1279)(346, 1040)(347, 1281)(348, 1080)(349, 1283)(350, 1109)(351, 1117)(352, 1286)(353, 977)(354, 1289)(355, 1094)(356, 1014)(357, 1248)(358, 1251)(359, 1115)(360, 1068)(361, 937)(362, 1291)(363, 983)(364, 1294)(365, 1155)(366, 954)(367, 994)(368, 1255)(369, 1126)(370, 1144)(371, 1298)(372, 975)(373, 1301)(374, 1075)(375, 1020)(376, 1260)(377, 1139)(378, 1060)(379, 1120)(380, 1304)(381, 987)(382, 1263)(383, 1307)(384, 990)(385, 1265)(386, 1310)(387, 1295)(388, 1312)(389, 1070)(390, 1314)(391, 1041)(392, 1316)(393, 1318)(394, 1320)(395, 1079)(396, 1322)(397, 1071)(398, 1324)(399, 1175)(400, 1099)(401, 1328)(402, 1256)(403, 1308)(404, 1331)(405, 1332)(406, 1089)(407, 1149)(408, 1195)(409, 1027)(410, 1015)(411, 1339)(412, 1340)(413, 1342)(414, 1343)(415, 1028)(416, 1168)(417, 1235)(418, 1190)(419, 1097)(420, 1196)(421, 1034)(422, 1351)(423, 1302)(424, 1090)(425, 1064)(426, 935)(427, 1357)(428, 936)(429, 1127)(430, 938)(431, 972)(432, 939)(433, 1330)(434, 940)(435, 1085)(436, 1054)(437, 942)(438, 1287)(439, 944)(440, 945)(441, 1258)(442, 947)(443, 1349)(444, 948)(445, 998)(446, 949)(447, 950)(448, 1136)(449, 1368)(450, 952)(451, 992)(452, 953)(453, 1290)(454, 955)(455, 1119)(456, 956)(457, 1365)(458, 958)(459, 974)(460, 959)(461, 1333)(462, 960)(463, 1046)(464, 961)(465, 1292)(466, 963)(467, 964)(468, 1285)(469, 966)(470, 1138)(471, 967)(472, 1001)(473, 968)(474, 969)(475, 1128)(476, 1140)(477, 971)(478, 980)(479, 973)(480, 976)(481, 978)(482, 979)(483, 981)(484, 982)(485, 984)(486, 986)(487, 1005)(488, 1246)(489, 1008)(490, 1297)(491, 991)(492, 993)(493, 995)(494, 1353)(495, 996)(496, 997)(497, 1025)(498, 1253)(499, 1000)(500, 1032)(501, 1228)(502, 1035)(503, 1378)(504, 1004)(505, 1039)(506, 1264)(507, 1007)(508, 1221)(509, 1009)(510, 1049)(511, 1356)(512, 1012)(513, 1375)(514, 1013)(515, 1137)(516, 1016)(517, 1018)(518, 1397)(519, 1299)(520, 1022)(521, 1305)(522, 1023)(523, 1024)(524, 1050)(525, 1347)(526, 1208)(527, 1029)(528, 1077)(529, 1377)(530, 1031)(531, 1078)(532, 1335)(533, 1218)(534, 1036)(535, 1088)(536, 1122)(537, 1038)(538, 1161)(539, 1043)(540, 1096)(541, 1401)(542, 1045)(543, 1102)(544, 1226)(545, 1105)(546, 1052)(547, 1402)(548, 1360)(549, 1056)(550, 1057)(551, 1059)(552, 1404)(553, 1061)(554, 1385)(555, 1062)(556, 1407)(557, 1063)(558, 1409)(559, 1065)(560, 1329)(561, 1067)(562, 1410)(563, 1069)(564, 1412)(565, 1188)(566, 1072)(567, 1158)(568, 1414)(569, 1074)(570, 1173)(571, 1082)(572, 1185)(573, 1416)(574, 1084)(575, 1107)(576, 1411)(577, 1210)(578, 1091)(579, 1239)(580, 1418)(581, 1093)(582, 1143)(583, 1352)(584, 1100)(585, 1241)(586, 1415)(587, 1103)(588, 1123)(589, 1405)(590, 1106)(591, 1406)(592, 1108)(593, 1348)(594, 1110)(595, 1419)(596, 1112)(597, 1341)(598, 1113)(599, 1344)(600, 1114)(601, 1336)(602, 1116)(603, 1422)(604, 1118)(605, 1424)(606, 1387)(607, 1420)(608, 1121)(609, 1280)(610, 1153)(611, 1124)(612, 1125)(613, 1181)(614, 1429)(615, 1252)(616, 1321)(617, 1379)(618, 1392)(619, 1131)(620, 1132)(621, 1317)(622, 1133)(623, 1134)(624, 1319)(625, 1358)(626, 1364)(627, 1245)(628, 1313)(629, 1163)(630, 1432)(631, 1142)(632, 1303)(633, 1214)(634, 1423)(635, 1393)(636, 1231)(637, 1147)(638, 1345)(639, 1371)(640, 1268)(641, 1431)(642, 1433)(643, 1374)(644, 1346)(645, 1177)(646, 1427)(647, 1426)(648, 1169)(649, 1421)(650, 1400)(651, 1359)(652, 1398)(653, 1434)(654, 1363)(655, 1233)(656, 1399)(657, 1249)(658, 1223)(659, 1337)(660, 1435)(661, 1430)(662, 1390)(663, 1417)(664, 1408)(665, 1274)(666, 1413)(667, 1326)(668, 1403)(669, 1436)(670, 1382)(671, 1395)(672, 1338)(673, 1355)(674, 1396)(675, 1391)(676, 1394)(677, 1238)(678, 1372)(679, 1376)(680, 1370)(681, 1261)(682, 1267)(683, 1388)(684, 1272)(685, 1309)(686, 1311)(687, 1276)(688, 1384)(689, 1278)(690, 1282)(691, 1296)(692, 1284)(693, 1386)(694, 1288)(695, 1306)(696, 1293)(697, 1383)(698, 1300)(699, 1315)(700, 1327)(701, 1369)(702, 1323)(703, 1354)(704, 1325)(705, 1437)(706, 1367)(707, 1366)(708, 1440)(709, 1334)(710, 1381)(711, 1361)(712, 1350)(713, 1362)(714, 1373)(715, 1380)(716, 1389)(717, 1425)(718, 1439)(719, 1438)(720, 1428) local type(s) :: { ( 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E16.1303 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 240 e = 720 f = 450 degree seq :: [ 6^240 ] E16.1305 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 8}) Quotient :: loop Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T2^8, T2^2 * T1 * T2^-7 * T1^-1 * T2 * T1^-2, (T2^2 * T1^-1)^5, T2^2 * T1^-1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1^-1 * T2^2 * T1^-1 * T2^3 * T1^-1, T2^3 * T1^-1 * T2^2 * T1^-1 * T2^-2 * T1 * T2^-4 * T1^-1 * T2^2 * T1^-1 * T2^-3 * T1^-1, T2 * T1^-1 * T2^-3 * T1 * T2^-4 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-4 * T1^-1, T2 * T1^-1 * T2^4 * T1 * T2^-2 * T1 * T2^2 * T1^-1 * T2^3 * T1^-1 * T2^-4 * T1^-1 ] Map:: R = (1, 721, 3, 723, 9, 729, 19, 739, 37, 757, 26, 746, 13, 733, 5, 725)(2, 722, 6, 726, 14, 734, 27, 747, 49, 769, 32, 752, 16, 736, 7, 727)(4, 724, 11, 731, 22, 742, 41, 761, 60, 780, 34, 754, 17, 737, 8, 728)(10, 730, 21, 741, 40, 760, 68, 788, 100, 820, 62, 782, 35, 755, 18, 738)(12, 732, 23, 743, 43, 763, 73, 793, 115, 835, 76, 796, 44, 764, 24, 744)(15, 735, 29, 749, 52, 772, 85, 805, 134, 854, 88, 808, 53, 773, 30, 750)(20, 740, 39, 759, 67, 787, 106, 826, 160, 880, 102, 822, 63, 783, 36, 756)(25, 745, 45, 765, 77, 797, 121, 841, 186, 906, 124, 844, 78, 798, 46, 766)(28, 748, 51, 771, 84, 804, 131, 851, 197, 917, 127, 847, 80, 800, 48, 768)(31, 751, 54, 774, 89, 809, 140, 860, 215, 935, 143, 863, 90, 810, 55, 775)(33, 753, 57, 777, 92, 812, 145, 865, 223, 943, 148, 868, 93, 813, 58, 778)(38, 758, 66, 786, 105, 825, 164, 884, 247, 967, 162, 882, 103, 823, 64, 784)(42, 762, 72, 792, 113, 833, 175, 895, 262, 982, 173, 893, 111, 831, 70, 790)(47, 767, 65, 785, 104, 824, 163, 883, 248, 968, 193, 913, 125, 845, 79, 799)(50, 770, 83, 803, 130, 850, 201, 921, 295, 1015, 199, 919, 128, 848, 81, 801)(56, 776, 82, 802, 129, 849, 200, 920, 296, 1016, 221, 941, 144, 864, 91, 811)(59, 779, 94, 814, 149, 869, 228, 948, 330, 1050, 231, 951, 150, 870, 95, 815)(61, 781, 97, 817, 152, 872, 233, 953, 338, 1058, 235, 955, 153, 873, 98, 818)(69, 789, 110, 830, 171, 891, 258, 978, 369, 1089, 256, 976, 169, 889, 108, 828)(71, 791, 112, 832, 174, 894, 263, 983, 336, 1056, 232, 952, 151, 871, 96, 816)(74, 794, 117, 837, 181, 901, 272, 992, 385, 1105, 268, 988, 177, 897, 114, 834)(75, 795, 118, 838, 182, 902, 273, 993, 393, 1113, 275, 995, 183, 903, 119, 839)(86, 806, 136, 856, 210, 930, 307, 1027, 431, 1151, 303, 1023, 206, 926, 133, 853)(87, 807, 137, 857, 211, 931, 308, 1028, 438, 1158, 310, 1030, 212, 932, 138, 858)(99, 819, 154, 874, 236, 956, 342, 1062, 478, 1198, 345, 1065, 237, 957, 155, 875)(101, 821, 157, 877, 239, 959, 347, 1067, 486, 1206, 349, 1069, 240, 960, 158, 878)(107, 827, 168, 888, 142, 862, 218, 938, 317, 1037, 364, 1084, 253, 973, 166, 886)(109, 829, 170, 890, 257, 977, 370, 1090, 484, 1204, 346, 1066, 238, 958, 156, 876)(116, 836, 180, 900, 271, 991, 389, 1109, 534, 1254, 387, 1107, 269, 989, 178, 898)(120, 840, 179, 899, 270, 990, 388, 1108, 535, 1255, 397, 1117, 276, 996, 184, 904)(122, 842, 188, 908, 281, 1001, 403, 1123, 548, 1268, 399, 1119, 277, 997, 185, 905)(123, 843, 189, 909, 282, 1002, 404, 1124, 380, 1100, 265, 985, 176, 896, 190, 910)(126, 846, 194, 914, 287, 1007, 409, 1129, 563, 1283, 411, 1131, 288, 1008, 195, 915)(132, 852, 205, 925, 147, 867, 226, 946, 327, 1047, 426, 1146, 300, 1020, 203, 923)(135, 855, 209, 929, 306, 1026, 435, 1155, 590, 1310, 433, 1153, 304, 1024, 207, 927)(139, 859, 208, 928, 305, 1025, 434, 1154, 591, 1311, 442, 1162, 311, 1031, 213, 933)(141, 861, 217, 937, 316, 1036, 448, 1168, 603, 1323, 444, 1164, 312, 1032, 214, 934)(146, 866, 225, 945, 326, 1046, 458, 1178, 618, 1338, 454, 1174, 322, 1042, 222, 942)(159, 879, 241, 961, 350, 1070, 490, 1210, 650, 1370, 492, 1212, 351, 1071, 242, 962)(161, 881, 244, 964, 353, 1073, 494, 1214, 608, 1328, 496, 1216, 354, 1074, 245, 965)(165, 885, 252, 972, 230, 950, 333, 1053, 466, 1186, 502, 1222, 361, 1081, 250, 970)(167, 887, 254, 974, 365, 1085, 507, 1227, 653, 1373, 493, 1213, 352, 1072, 243, 963)(172, 892, 259, 979, 373, 1093, 517, 1237, 655, 1375, 519, 1239, 374, 1094, 260, 980)(187, 907, 280, 1000, 402, 1122, 552, 1272, 613, 1333, 550, 1270, 400, 1120, 278, 998)(191, 911, 279, 999, 401, 1121, 551, 1271, 604, 1324, 558, 1278, 406, 1126, 283, 1003)(192, 912, 284, 1004, 407, 1127, 559, 1279, 423, 1143, 298, 1018, 202, 922, 285, 1005)(196, 916, 289, 1009, 412, 1132, 566, 1286, 501, 1221, 568, 1288, 413, 1133, 290, 1010)(198, 918, 292, 1012, 415, 1135, 570, 1290, 489, 1209, 572, 1292, 416, 1136, 293, 1013)(204, 924, 301, 1021, 427, 1147, 582, 1302, 491, 1211, 569, 1289, 414, 1134, 291, 1011)(216, 936, 315, 1035, 447, 1167, 607, 1327, 630, 1350, 605, 1325, 445, 1165, 313, 1033)(219, 939, 314, 1034, 446, 1166, 606, 1326, 619, 1339, 611, 1331, 450, 1170, 318, 1038)(220, 940, 319, 1039, 451, 1171, 612, 1332, 523, 1243, 378, 1098, 264, 984, 320, 1040)(224, 944, 325, 1045, 457, 1177, 622, 1342, 560, 1280, 620, 1340, 455, 1175, 323, 1043)(227, 947, 324, 1044, 456, 1176, 621, 1341, 549, 1269, 625, 1345, 460, 1180, 328, 1048)(229, 949, 332, 1052, 465, 1185, 629, 1349, 553, 1273, 626, 1346, 461, 1181, 329, 1049)(234, 954, 340, 1060, 475, 1195, 639, 1359, 672, 1392, 635, 1355, 471, 1191, 337, 1057)(246, 966, 355, 1075, 497, 1217, 594, 1314, 679, 1399, 537, 1257, 390, 1110, 356, 1076)(249, 969, 360, 1080, 344, 1064, 481, 1201, 644, 1364, 600, 1320, 499, 1219, 358, 1078)(251, 971, 362, 1082, 503, 1223, 656, 1376, 693, 1413, 589, 1309, 498, 1218, 357, 1077)(255, 975, 366, 1086, 509, 1229, 662, 1382, 547, 1267, 664, 1384, 510, 1230, 367, 1087)(261, 981, 375, 1095, 520, 1240, 661, 1381, 577, 1297, 673, 1393, 521, 1241, 376, 1096)(266, 986, 381, 1101, 526, 1246, 657, 1377, 567, 1287, 652, 1372, 522, 1242, 377, 1097)(267, 987, 382, 1102, 527, 1247, 675, 1395, 602, 1322, 654, 1374, 495, 1215, 383, 1103)(274, 994, 395, 1115, 543, 1263, 648, 1368, 487, 1207, 649, 1369, 540, 1260, 392, 1112)(286, 1006, 359, 1079, 500, 1220, 592, 1312, 694, 1414, 610, 1330, 561, 1281, 408, 1128)(294, 1014, 417, 1137, 573, 1293, 515, 1235, 669, 1389, 593, 1313, 436, 1156, 418, 1138)(297, 1017, 422, 1142, 396, 1116, 544, 1264, 645, 1365, 482, 1202, 575, 1295, 420, 1140)(299, 1019, 424, 1144, 578, 1298, 508, 1228, 646, 1366, 483, 1203, 574, 1294, 419, 1139)(302, 1022, 428, 1148, 584, 1304, 691, 1411, 617, 1337, 687, 1407, 571, 1291, 429, 1149)(309, 1029, 440, 1160, 598, 1318, 685, 1405, 564, 1284, 686, 1406, 595, 1315, 437, 1157)(321, 1041, 421, 1141, 576, 1296, 479, 1199, 642, 1362, 624, 1344, 614, 1334, 452, 1172)(331, 1051, 464, 1184, 441, 1161, 599, 1319, 682, 1402, 545, 1265, 627, 1347, 462, 1182)(334, 1054, 463, 1183, 628, 1348, 536, 1256, 678, 1398, 557, 1277, 631, 1351, 467, 1187)(335, 1055, 468, 1188, 632, 1352, 538, 1258, 668, 1388, 514, 1234, 371, 1091, 469, 1189)(339, 1059, 474, 1194, 638, 1358, 554, 1274, 405, 1125, 556, 1276, 636, 1356, 472, 1192)(341, 1061, 473, 1193, 637, 1357, 532, 1252, 386, 1106, 531, 1251, 640, 1360, 476, 1196)(343, 1063, 480, 1200, 643, 1363, 530, 1250, 391, 1111, 539, 1259, 641, 1361, 477, 1197)(348, 1068, 488, 1208, 398, 1118, 546, 1266, 683, 1403, 703, 1423, 647, 1367, 485, 1205)(363, 1083, 504, 1224, 658, 1378, 529, 1249, 384, 1104, 528, 1248, 659, 1379, 505, 1225)(368, 1088, 511, 1231, 665, 1385, 674, 1394, 525, 1245, 555, 1275, 666, 1386, 512, 1232)(372, 1092, 516, 1236, 670, 1390, 588, 1308, 432, 1152, 587, 1307, 667, 1387, 513, 1233)(379, 1099, 524, 1244, 651, 1371, 583, 1303, 677, 1397, 533, 1253, 633, 1353, 470, 1190)(394, 1114, 542, 1262, 660, 1380, 506, 1226, 449, 1169, 609, 1329, 681, 1401, 541, 1261)(410, 1130, 565, 1285, 443, 1163, 601, 1321, 697, 1417, 708, 1428, 684, 1404, 562, 1282)(425, 1145, 579, 1299, 688, 1408, 586, 1306, 430, 1150, 585, 1305, 689, 1409, 580, 1300)(439, 1159, 597, 1317, 690, 1410, 581, 1301, 459, 1179, 623, 1343, 696, 1416, 596, 1316)(453, 1173, 615, 1335, 698, 1418, 711, 1431, 701, 1421, 671, 1391, 518, 1238, 616, 1336)(634, 1354, 699, 1419, 712, 1432, 718, 1438, 714, 1434, 705, 1425, 663, 1383, 700, 1420)(676, 1396, 704, 1424, 680, 1400, 702, 1422, 713, 1433, 719, 1439, 715, 1435, 706, 1426)(692, 1412, 709, 1429, 695, 1415, 707, 1427, 716, 1436, 720, 1440, 717, 1437, 710, 1430) L = (1, 722)(2, 724)(3, 728)(4, 721)(5, 732)(6, 725)(7, 735)(8, 730)(9, 738)(10, 723)(11, 727)(12, 726)(13, 745)(14, 744)(15, 731)(16, 751)(17, 753)(18, 740)(19, 756)(20, 729)(21, 737)(22, 750)(23, 733)(24, 748)(25, 743)(26, 767)(27, 768)(28, 734)(29, 736)(30, 762)(31, 749)(32, 776)(33, 741)(34, 779)(35, 781)(36, 758)(37, 784)(38, 739)(39, 755)(40, 778)(41, 790)(42, 742)(43, 766)(44, 795)(45, 746)(46, 794)(47, 765)(48, 770)(49, 801)(50, 747)(51, 764)(52, 775)(53, 807)(54, 752)(55, 806)(56, 774)(57, 754)(58, 789)(59, 777)(60, 816)(61, 759)(62, 819)(63, 821)(64, 785)(65, 757)(66, 783)(67, 818)(68, 828)(69, 760)(70, 791)(71, 761)(72, 773)(73, 834)(74, 763)(75, 771)(76, 840)(77, 799)(78, 843)(79, 842)(80, 846)(81, 802)(82, 769)(83, 800)(84, 839)(85, 853)(86, 772)(87, 792)(88, 859)(89, 811)(90, 862)(91, 861)(92, 815)(93, 867)(94, 780)(95, 866)(96, 814)(97, 782)(98, 827)(99, 817)(100, 876)(101, 786)(102, 879)(103, 881)(104, 823)(105, 878)(106, 886)(107, 787)(108, 829)(109, 788)(110, 813)(111, 892)(112, 831)(113, 858)(114, 836)(115, 898)(116, 793)(117, 798)(118, 796)(119, 852)(120, 838)(121, 905)(122, 797)(123, 837)(124, 911)(125, 912)(126, 803)(127, 916)(128, 918)(129, 848)(130, 915)(131, 923)(132, 804)(133, 855)(134, 927)(135, 805)(136, 810)(137, 808)(138, 896)(139, 857)(140, 934)(141, 809)(142, 856)(143, 939)(144, 940)(145, 942)(146, 812)(147, 830)(148, 947)(149, 871)(150, 950)(151, 949)(152, 875)(153, 930)(154, 820)(155, 954)(156, 874)(157, 822)(158, 885)(159, 877)(160, 963)(161, 824)(162, 966)(163, 965)(164, 970)(165, 825)(166, 887)(167, 826)(168, 873)(169, 975)(170, 889)(171, 925)(172, 832)(173, 981)(174, 980)(175, 985)(176, 833)(177, 987)(178, 899)(179, 835)(180, 897)(181, 910)(182, 904)(183, 891)(184, 994)(185, 907)(186, 998)(187, 841)(188, 845)(189, 844)(190, 932)(191, 909)(192, 908)(193, 1006)(194, 847)(195, 922)(196, 914)(197, 1011)(198, 849)(199, 1014)(200, 1013)(201, 1018)(202, 850)(203, 924)(204, 851)(205, 903)(206, 1022)(207, 928)(208, 854)(209, 926)(210, 888)(211, 933)(212, 901)(213, 1029)(214, 936)(215, 1033)(216, 860)(217, 864)(218, 863)(219, 938)(220, 937)(221, 1041)(222, 944)(223, 1043)(224, 865)(225, 870)(226, 868)(227, 946)(228, 1049)(229, 869)(230, 945)(231, 1054)(232, 1055)(233, 1057)(234, 872)(235, 1061)(236, 958)(237, 1064)(238, 1063)(239, 962)(240, 1046)(241, 880)(242, 1068)(243, 961)(244, 882)(245, 969)(246, 964)(247, 1077)(248, 1078)(249, 883)(250, 971)(251, 884)(252, 960)(253, 1083)(254, 973)(255, 890)(256, 1088)(257, 1087)(258, 995)(259, 893)(260, 984)(261, 979)(262, 1097)(263, 1098)(264, 894)(265, 986)(266, 895)(267, 900)(268, 1104)(269, 1106)(270, 989)(271, 1103)(272, 1030)(273, 1112)(274, 902)(275, 1092)(276, 1116)(277, 1118)(278, 999)(279, 906)(280, 997)(281, 1005)(282, 1003)(283, 1125)(284, 913)(285, 1008)(286, 1004)(287, 1010)(288, 1001)(289, 917)(290, 1130)(291, 1009)(292, 919)(293, 1017)(294, 1012)(295, 1139)(296, 1140)(297, 920)(298, 1019)(299, 921)(300, 1145)(301, 1020)(302, 929)(303, 1150)(304, 1152)(305, 1024)(306, 1149)(307, 955)(308, 1157)(309, 931)(310, 1111)(311, 1161)(312, 1163)(313, 1034)(314, 935)(315, 1032)(316, 1040)(317, 1038)(318, 1169)(319, 941)(320, 1094)(321, 1039)(322, 1173)(323, 1044)(324, 943)(325, 1042)(326, 972)(327, 1048)(328, 1179)(329, 1051)(330, 1182)(331, 948)(332, 952)(333, 951)(334, 1053)(335, 1052)(336, 1190)(337, 1059)(338, 1192)(339, 953)(340, 957)(341, 1027)(342, 1197)(343, 956)(344, 1060)(345, 1202)(346, 1203)(347, 1205)(348, 959)(349, 1209)(350, 1072)(351, 1122)(352, 1211)(353, 1076)(354, 1195)(355, 967)(356, 1215)(357, 1075)(358, 1079)(359, 968)(360, 1074)(361, 1221)(362, 1081)(363, 974)(364, 1226)(365, 1225)(366, 976)(367, 1091)(368, 1086)(369, 1233)(370, 1234)(371, 977)(372, 978)(373, 1096)(374, 1036)(375, 982)(376, 1238)(377, 1095)(378, 1099)(379, 983)(380, 1245)(381, 1100)(382, 988)(383, 1110)(384, 1102)(385, 1250)(386, 990)(387, 1253)(388, 1252)(389, 1257)(390, 991)(391, 992)(392, 1114)(393, 1261)(394, 993)(395, 996)(396, 1115)(397, 1265)(398, 1000)(399, 1267)(400, 1269)(401, 1120)(402, 1208)(403, 1131)(404, 1274)(405, 1002)(406, 1277)(407, 1128)(408, 1280)(409, 1282)(410, 1007)(411, 1273)(412, 1134)(413, 1167)(414, 1287)(415, 1138)(416, 1263)(417, 1015)(418, 1291)(419, 1137)(420, 1141)(421, 1016)(422, 1136)(423, 1297)(424, 1143)(425, 1021)(426, 1301)(427, 1300)(428, 1023)(429, 1156)(430, 1148)(431, 1196)(432, 1025)(433, 1309)(434, 1308)(435, 1313)(436, 1026)(437, 1159)(438, 1316)(439, 1028)(440, 1031)(441, 1160)(442, 1320)(443, 1035)(444, 1322)(445, 1324)(446, 1165)(447, 1285)(448, 1239)(449, 1037)(450, 1330)(451, 1172)(452, 1333)(453, 1045)(454, 1337)(455, 1339)(456, 1175)(457, 1336)(458, 1069)(459, 1047)(460, 1344)(461, 1318)(462, 1183)(463, 1050)(464, 1181)(465, 1189)(466, 1187)(467, 1350)(468, 1056)(469, 1230)(470, 1188)(471, 1354)(472, 1193)(473, 1058)(474, 1191)(475, 1080)(476, 1305)(477, 1199)(478, 1296)(479, 1062)(480, 1066)(481, 1065)(482, 1201)(483, 1200)(484, 1293)(485, 1207)(486, 1368)(487, 1067)(488, 1071)(489, 1178)(490, 1302)(491, 1070)(492, 1332)(493, 1372)(494, 1374)(495, 1073)(496, 1375)(497, 1218)(498, 1310)(499, 1311)(500, 1219)(501, 1082)(502, 1327)(503, 1286)(504, 1084)(505, 1228)(506, 1224)(507, 1298)(508, 1085)(509, 1232)(510, 1185)(511, 1089)(512, 1383)(513, 1231)(514, 1235)(515, 1090)(516, 1113)(517, 1391)(518, 1093)(519, 1328)(520, 1242)(521, 1177)(522, 1373)(523, 1370)(524, 1243)(525, 1101)(526, 1394)(527, 1249)(528, 1105)(529, 1396)(530, 1248)(531, 1107)(532, 1256)(533, 1251)(534, 1352)(535, 1348)(536, 1108)(537, 1258)(538, 1109)(539, 1158)(540, 1400)(541, 1236)(542, 1260)(543, 1142)(544, 1117)(545, 1264)(546, 1119)(547, 1266)(548, 1349)(549, 1121)(550, 1334)(551, 1341)(552, 1212)(553, 1123)(554, 1275)(555, 1124)(556, 1126)(557, 1276)(558, 1325)(559, 1342)(560, 1127)(561, 1331)(562, 1284)(563, 1405)(564, 1129)(565, 1133)(566, 1377)(567, 1132)(568, 1222)(569, 1213)(570, 1407)(571, 1135)(572, 1206)(573, 1294)(574, 1204)(575, 1198)(576, 1295)(577, 1144)(578, 1381)(579, 1146)(580, 1303)(581, 1299)(582, 1371)(583, 1147)(584, 1306)(585, 1151)(586, 1412)(587, 1153)(588, 1312)(589, 1307)(590, 1217)(591, 1220)(592, 1154)(593, 1314)(594, 1155)(595, 1415)(596, 1259)(597, 1315)(598, 1184)(599, 1162)(600, 1319)(601, 1164)(602, 1321)(603, 1214)(604, 1166)(605, 1351)(606, 1271)(607, 1288)(608, 1168)(609, 1170)(610, 1329)(611, 1340)(612, 1272)(613, 1171)(614, 1345)(615, 1174)(616, 1241)(617, 1335)(618, 1290)(619, 1176)(620, 1281)(621, 1326)(622, 1393)(623, 1180)(624, 1343)(625, 1270)(626, 1283)(627, 1255)(628, 1347)(629, 1384)(630, 1186)(631, 1278)(632, 1353)(633, 1254)(634, 1194)(635, 1421)(636, 1398)(637, 1356)(638, 1420)(639, 1216)(640, 1397)(641, 1416)(642, 1361)(643, 1366)(644, 1365)(645, 1402)(646, 1379)(647, 1422)(648, 1292)(649, 1367)(650, 1244)(651, 1210)(652, 1289)(653, 1240)(654, 1323)(655, 1359)(656, 1246)(657, 1223)(658, 1380)(659, 1363)(660, 1424)(661, 1227)(662, 1425)(663, 1229)(664, 1268)(665, 1387)(666, 1358)(667, 1413)(668, 1399)(669, 1388)(670, 1401)(671, 1392)(672, 1237)(673, 1279)(674, 1376)(675, 1426)(676, 1247)(677, 1409)(678, 1357)(679, 1389)(680, 1262)(681, 1414)(682, 1364)(683, 1382)(684, 1427)(685, 1346)(686, 1404)(687, 1338)(688, 1410)(689, 1360)(690, 1429)(691, 1430)(692, 1304)(693, 1385)(694, 1390)(695, 1317)(696, 1362)(697, 1395)(698, 1411)(699, 1355)(700, 1386)(701, 1419)(702, 1369)(703, 1434)(704, 1378)(705, 1403)(706, 1417)(707, 1406)(708, 1435)(709, 1408)(710, 1418)(711, 1437)(712, 1431)(713, 1423)(714, 1433)(715, 1436)(716, 1428)(717, 1432)(718, 1440)(719, 1438)(720, 1439) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E16.1301 Transitivity :: ET+ VT+ AT Graph:: v = 90 e = 720 f = 600 degree seq :: [ 16^90 ] E16.1306 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 8}) Quotient :: loop Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^8, T1^2 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^3 * T2, T2 * T1^-2 * T2 * T1^2 * T2 * T1^3 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-3, T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^3, T2 * T1^-4 * T2 * T1^-2 * T2 * T1^3 * T2 * T1^-3 * T2 * T1^2 * T2 * T1^-4 ] Map:: polyhedral non-degenerate R = (1, 721, 3, 723)(2, 722, 6, 726)(4, 724, 9, 729)(5, 725, 12, 732)(7, 727, 16, 736)(8, 728, 13, 733)(10, 730, 19, 739)(11, 731, 22, 742)(14, 734, 23, 743)(15, 735, 28, 748)(17, 737, 30, 750)(18, 738, 33, 753)(20, 740, 35, 755)(21, 741, 36, 756)(24, 744, 37, 757)(25, 745, 42, 762)(26, 746, 43, 763)(27, 747, 46, 766)(29, 749, 47, 767)(31, 751, 51, 771)(32, 752, 53, 773)(34, 754, 56, 776)(38, 758, 58, 778)(39, 759, 63, 783)(40, 760, 64, 784)(41, 761, 67, 787)(44, 764, 70, 790)(45, 765, 71, 791)(48, 768, 72, 792)(49, 769, 76, 796)(50, 770, 79, 799)(52, 772, 81, 801)(54, 774, 82, 802)(55, 775, 86, 806)(57, 777, 59, 779)(60, 780, 92, 812)(61, 781, 93, 813)(62, 782, 96, 816)(65, 785, 99, 819)(66, 786, 100, 820)(68, 788, 101, 821)(69, 789, 105, 825)(73, 793, 107, 827)(74, 794, 112, 832)(75, 795, 113, 833)(77, 797, 116, 836)(78, 798, 118, 838)(80, 800, 108, 828)(83, 803, 121, 841)(84, 804, 125, 845)(85, 805, 127, 847)(87, 807, 128, 848)(88, 808, 132, 852)(89, 809, 134, 854)(90, 810, 135, 855)(91, 811, 138, 858)(94, 814, 141, 861)(95, 815, 142, 862)(97, 817, 143, 863)(98, 818, 147, 867)(102, 822, 149, 869)(103, 823, 153, 873)(104, 824, 156, 876)(106, 826, 150, 870)(109, 829, 162, 882)(110, 830, 163, 883)(111, 831, 166, 886)(114, 834, 169, 889)(115, 835, 171, 891)(117, 837, 173, 893)(119, 839, 174, 894)(120, 840, 178, 898)(122, 842, 172, 892)(123, 843, 182, 902)(124, 844, 183, 903)(126, 846, 186, 906)(129, 849, 187, 907)(130, 850, 191, 911)(131, 851, 193, 913)(133, 853, 196, 916)(136, 856, 199, 919)(137, 857, 200, 920)(139, 859, 201, 921)(140, 860, 205, 925)(144, 864, 207, 927)(145, 865, 211, 931)(146, 866, 214, 934)(148, 868, 208, 928)(151, 871, 220, 940)(152, 872, 221, 941)(154, 874, 224, 944)(155, 875, 225, 945)(157, 877, 226, 946)(158, 878, 230, 950)(159, 879, 232, 952)(160, 880, 233, 953)(161, 881, 236, 956)(164, 884, 239, 959)(165, 885, 240, 960)(167, 887, 241, 961)(168, 888, 245, 965)(170, 890, 248, 968)(175, 895, 251, 971)(176, 896, 255, 975)(177, 897, 257, 977)(179, 899, 260, 980)(180, 900, 261, 981)(181, 901, 264, 984)(184, 904, 267, 987)(185, 905, 269, 989)(188, 908, 270, 990)(189, 909, 274, 994)(190, 910, 275, 995)(192, 912, 278, 998)(194, 914, 279, 999)(195, 915, 282, 1002)(197, 917, 283, 1003)(198, 918, 287, 1007)(202, 922, 289, 1009)(203, 923, 293, 1013)(204, 924, 296, 1016)(206, 926, 290, 1010)(209, 929, 302, 1022)(210, 930, 303, 1023)(212, 932, 306, 1026)(213, 933, 307, 1027)(215, 935, 308, 1028)(216, 936, 312, 1032)(217, 937, 314, 1034)(218, 938, 315, 1035)(219, 939, 318, 1038)(222, 942, 321, 1041)(223, 943, 323, 1043)(227, 947, 325, 1045)(228, 948, 329, 1049)(229, 949, 331, 1051)(231, 951, 334, 1054)(234, 954, 337, 1057)(235, 955, 338, 1058)(237, 957, 339, 1059)(238, 958, 343, 1063)(242, 962, 345, 1065)(243, 963, 301, 1021)(244, 964, 350, 1070)(246, 966, 346, 1066)(247, 967, 353, 1073)(249, 969, 354, 1074)(250, 970, 358, 1078)(252, 972, 324, 1044)(253, 973, 291, 1011)(254, 974, 361, 1081)(256, 976, 364, 1084)(258, 978, 365, 1085)(259, 979, 369, 1089)(262, 982, 372, 1092)(263, 983, 373, 1093)(265, 985, 319, 1039)(266, 986, 376, 1096)(268, 988, 379, 1099)(271, 991, 383, 1103)(272, 992, 384, 1104)(273, 993, 341, 1061)(276, 996, 388, 1108)(277, 997, 390, 1110)(280, 1000, 391, 1111)(281, 1001, 394, 1114)(284, 1004, 396, 1116)(285, 1005, 400, 1120)(286, 1006, 403, 1123)(288, 1008, 397, 1117)(292, 1012, 408, 1128)(294, 1014, 411, 1131)(295, 1015, 412, 1132)(297, 1017, 413, 1133)(298, 1018, 417, 1137)(299, 1019, 419, 1139)(300, 1020, 420, 1140)(304, 1024, 424, 1144)(305, 1025, 426, 1146)(309, 1029, 428, 1148)(310, 1030, 432, 1152)(311, 1031, 434, 1154)(313, 1033, 437, 1157)(316, 1036, 440, 1160)(317, 1037, 441, 1161)(320, 1040, 444, 1164)(322, 1042, 447, 1167)(326, 1046, 427, 1147)(327, 1047, 398, 1118)(328, 1048, 452, 1172)(330, 1050, 455, 1175)(332, 1052, 456, 1176)(333, 1053, 459, 1179)(335, 1055, 460, 1180)(336, 1056, 464, 1184)(340, 1060, 466, 1186)(342, 1062, 471, 1191)(344, 1064, 467, 1187)(347, 1067, 476, 1196)(348, 1068, 477, 1197)(349, 1069, 478, 1198)(351, 1071, 479, 1199)(352, 1072, 483, 1203)(355, 1075, 484, 1204)(356, 1076, 488, 1208)(357, 1077, 490, 1210)(359, 1079, 493, 1213)(360, 1080, 494, 1214)(362, 1082, 497, 1217)(363, 1083, 498, 1218)(366, 1086, 499, 1219)(367, 1087, 502, 1222)(368, 1088, 504, 1224)(370, 1090, 404, 1124)(371, 1091, 507, 1227)(374, 1094, 509, 1229)(375, 1095, 512, 1232)(377, 1097, 510, 1230)(378, 1098, 515, 1235)(380, 1100, 516, 1236)(381, 1101, 520, 1240)(382, 1102, 415, 1135)(385, 1105, 523, 1243)(386, 1106, 524, 1244)(387, 1107, 526, 1246)(389, 1109, 528, 1248)(392, 1112, 430, 1150)(393, 1113, 531, 1251)(395, 1115, 534, 1254)(399, 1119, 537, 1257)(401, 1121, 540, 1260)(402, 1122, 541, 1261)(405, 1125, 544, 1264)(406, 1126, 546, 1266)(407, 1127, 547, 1267)(409, 1129, 550, 1270)(410, 1130, 551, 1271)(414, 1134, 553, 1273)(416, 1136, 557, 1277)(418, 1138, 560, 1280)(421, 1141, 563, 1283)(422, 1142, 564, 1284)(423, 1143, 566, 1286)(425, 1145, 568, 1288)(429, 1149, 552, 1272)(431, 1151, 573, 1293)(433, 1153, 576, 1296)(435, 1155, 577, 1297)(436, 1156, 580, 1300)(438, 1158, 581, 1301)(439, 1159, 585, 1305)(442, 1162, 587, 1307)(443, 1163, 590, 1310)(445, 1165, 588, 1308)(446, 1166, 593, 1313)(448, 1168, 594, 1314)(449, 1169, 598, 1318)(450, 1170, 600, 1320)(451, 1171, 601, 1321)(453, 1173, 604, 1324)(454, 1174, 605, 1325)(457, 1177, 606, 1326)(458, 1178, 609, 1329)(461, 1181, 578, 1298)(462, 1182, 554, 1274)(463, 1183, 583, 1303)(465, 1185, 611, 1331)(468, 1188, 615, 1335)(469, 1189, 610, 1330)(470, 1190, 539, 1259)(472, 1192, 616, 1336)(473, 1193, 559, 1279)(474, 1194, 619, 1339)(475, 1195, 620, 1340)(480, 1200, 623, 1343)(481, 1201, 626, 1346)(482, 1202, 535, 1255)(485, 1205, 622, 1342)(486, 1206, 612, 1332)(487, 1207, 630, 1350)(489, 1209, 608, 1328)(491, 1211, 632, 1352)(492, 1212, 617, 1337)(495, 1215, 536, 1256)(496, 1216, 635, 1355)(500, 1220, 624, 1344)(501, 1221, 639, 1359)(503, 1223, 542, 1262)(505, 1225, 642, 1362)(506, 1226, 636, 1356)(508, 1228, 586, 1306)(511, 1231, 641, 1361)(513, 1233, 644, 1364)(514, 1234, 646, 1366)(517, 1237, 647, 1367)(518, 1238, 649, 1369)(519, 1239, 638, 1358)(521, 1241, 613, 1333)(522, 1242, 650, 1370)(525, 1245, 651, 1371)(527, 1247, 584, 1304)(529, 1249, 602, 1322)(530, 1250, 597, 1317)(532, 1252, 654, 1374)(533, 1253, 589, 1309)(538, 1258, 657, 1377)(543, 1263, 658, 1378)(545, 1265, 660, 1380)(548, 1268, 661, 1381)(549, 1269, 662, 1382)(555, 1275, 664, 1384)(556, 1276, 665, 1385)(558, 1278, 666, 1386)(561, 1281, 668, 1388)(562, 1282, 670, 1390)(565, 1285, 672, 1392)(567, 1287, 671, 1391)(569, 1289, 675, 1395)(570, 1290, 677, 1397)(571, 1291, 678, 1398)(572, 1292, 679, 1399)(574, 1294, 681, 1401)(575, 1295, 682, 1402)(579, 1299, 684, 1404)(582, 1302, 667, 1387)(591, 1311, 686, 1406)(592, 1312, 659, 1379)(595, 1315, 689, 1409)(596, 1316, 692, 1412)(599, 1319, 687, 1407)(603, 1323, 696, 1416)(607, 1327, 690, 1410)(614, 1334, 688, 1408)(618, 1338, 669, 1389)(621, 1341, 676, 1396)(625, 1345, 701, 1421)(627, 1347, 655, 1375)(628, 1348, 703, 1423)(629, 1349, 704, 1424)(631, 1351, 698, 1418)(633, 1353, 656, 1376)(634, 1354, 705, 1425)(637, 1357, 663, 1383)(640, 1360, 697, 1417)(643, 1363, 699, 1419)(645, 1365, 702, 1422)(648, 1368, 685, 1405)(652, 1372, 694, 1414)(653, 1373, 693, 1413)(673, 1393, 710, 1430)(674, 1394, 708, 1428)(680, 1400, 714, 1434)(683, 1403, 711, 1431)(691, 1411, 715, 1435)(695, 1415, 716, 1436)(700, 1420, 717, 1437)(706, 1426, 718, 1438)(707, 1427, 709, 1429)(712, 1432, 719, 1439)(713, 1433, 720, 1440) L = (1, 722)(2, 725)(3, 727)(4, 721)(5, 731)(6, 733)(7, 735)(8, 723)(9, 738)(10, 724)(11, 741)(12, 743)(13, 745)(14, 726)(15, 747)(16, 729)(17, 728)(18, 752)(19, 754)(20, 730)(21, 740)(22, 757)(23, 759)(24, 732)(25, 761)(26, 734)(27, 765)(28, 767)(29, 736)(30, 770)(31, 737)(32, 772)(33, 739)(34, 775)(35, 777)(36, 778)(37, 780)(38, 742)(39, 782)(40, 744)(41, 786)(42, 750)(43, 789)(44, 746)(45, 751)(46, 792)(47, 794)(48, 748)(49, 749)(50, 798)(51, 800)(52, 797)(53, 802)(54, 753)(55, 805)(56, 755)(57, 808)(58, 809)(59, 756)(60, 811)(61, 758)(62, 815)(63, 763)(64, 818)(65, 760)(66, 764)(67, 821)(68, 762)(69, 824)(70, 826)(71, 827)(72, 829)(73, 766)(74, 831)(75, 768)(76, 835)(77, 769)(78, 837)(79, 771)(80, 840)(81, 841)(82, 843)(83, 773)(84, 774)(85, 846)(86, 848)(87, 776)(88, 851)(89, 853)(90, 779)(91, 857)(92, 784)(93, 860)(94, 781)(95, 785)(96, 863)(97, 783)(98, 866)(99, 868)(100, 869)(101, 871)(102, 787)(103, 788)(104, 875)(105, 790)(106, 878)(107, 879)(108, 791)(109, 881)(110, 793)(111, 885)(112, 796)(113, 888)(114, 795)(115, 890)(116, 892)(117, 874)(118, 894)(119, 799)(120, 897)(121, 899)(122, 801)(123, 901)(124, 803)(125, 905)(126, 804)(127, 907)(128, 909)(129, 806)(130, 807)(131, 912)(132, 855)(133, 915)(134, 813)(135, 918)(136, 810)(137, 814)(138, 921)(139, 812)(140, 924)(141, 926)(142, 927)(143, 929)(144, 816)(145, 817)(146, 933)(147, 819)(148, 936)(149, 937)(150, 820)(151, 939)(152, 822)(153, 943)(154, 823)(155, 932)(156, 946)(157, 825)(158, 949)(159, 951)(160, 828)(161, 955)(162, 833)(163, 958)(164, 830)(165, 834)(166, 961)(167, 832)(168, 964)(169, 966)(170, 967)(171, 836)(172, 970)(173, 971)(174, 973)(175, 838)(176, 839)(177, 976)(178, 953)(179, 979)(180, 842)(181, 983)(182, 845)(183, 986)(184, 844)(185, 988)(186, 990)(187, 991)(188, 847)(189, 993)(190, 849)(191, 997)(192, 850)(193, 999)(194, 852)(195, 856)(196, 1003)(197, 854)(198, 1006)(199, 1008)(200, 1009)(201, 1011)(202, 858)(203, 859)(204, 1015)(205, 861)(206, 1018)(207, 1019)(208, 862)(209, 1021)(210, 864)(211, 1025)(212, 865)(213, 1014)(214, 1028)(215, 867)(216, 1031)(217, 1033)(218, 870)(219, 1037)(220, 873)(221, 1040)(222, 872)(223, 1042)(224, 1044)(225, 1045)(226, 1047)(227, 876)(228, 877)(229, 1050)(230, 1035)(231, 1053)(232, 883)(233, 1056)(234, 880)(235, 884)(236, 1059)(237, 882)(238, 1062)(239, 1064)(240, 1065)(241, 1022)(242, 886)(243, 887)(244, 1069)(245, 889)(246, 1072)(247, 1068)(248, 1074)(249, 891)(250, 1077)(251, 1079)(252, 893)(253, 1013)(254, 895)(255, 1083)(256, 896)(257, 1085)(258, 898)(259, 1088)(260, 903)(261, 1091)(262, 900)(263, 904)(264, 1039)(265, 902)(266, 1095)(267, 1097)(268, 1098)(269, 906)(270, 1101)(271, 1102)(272, 908)(273, 1106)(274, 911)(275, 1107)(276, 910)(277, 1109)(278, 1111)(279, 1112)(280, 913)(281, 914)(282, 1116)(283, 1118)(284, 916)(285, 917)(286, 1122)(287, 919)(288, 1125)(289, 1126)(290, 920)(291, 975)(292, 922)(293, 1130)(294, 923)(295, 1121)(296, 1133)(297, 925)(298, 1136)(299, 1138)(300, 928)(301, 1142)(302, 931)(303, 1143)(304, 930)(305, 1145)(306, 1147)(307, 1148)(308, 1150)(309, 934)(310, 935)(311, 1153)(312, 1140)(313, 1156)(314, 941)(315, 1159)(316, 938)(317, 942)(318, 985)(319, 940)(320, 1163)(321, 1165)(322, 1166)(323, 944)(324, 1169)(325, 1170)(326, 945)(327, 1120)(328, 947)(329, 1174)(330, 948)(331, 1176)(332, 950)(333, 954)(334, 1180)(335, 952)(336, 1183)(337, 1185)(338, 1186)(339, 994)(340, 956)(341, 957)(342, 1190)(343, 959)(344, 1193)(345, 1194)(346, 960)(347, 962)(348, 963)(349, 1189)(350, 1199)(351, 965)(352, 1202)(353, 1204)(354, 1206)(355, 968)(356, 969)(357, 1209)(358, 981)(359, 1212)(360, 972)(361, 1216)(362, 974)(363, 1129)(364, 1219)(365, 1220)(366, 977)(367, 978)(368, 982)(369, 1124)(370, 980)(371, 1226)(372, 1228)(373, 1229)(374, 984)(375, 1231)(376, 987)(377, 1234)(378, 1162)(379, 1236)(380, 989)(381, 1239)(382, 1241)(383, 995)(384, 1242)(385, 992)(386, 996)(387, 1245)(388, 1247)(389, 1188)(390, 998)(391, 1250)(392, 1152)(393, 1000)(394, 1253)(395, 1001)(396, 1255)(397, 1002)(398, 1049)(399, 1004)(400, 1259)(401, 1005)(402, 1115)(403, 1090)(404, 1007)(405, 1263)(406, 1265)(407, 1010)(408, 1269)(409, 1012)(410, 1082)(411, 1272)(412, 1273)(413, 1103)(414, 1016)(415, 1017)(416, 1276)(417, 1267)(418, 1279)(419, 1023)(420, 1282)(421, 1020)(422, 1024)(423, 1285)(424, 1287)(425, 1067)(426, 1026)(427, 1290)(428, 1291)(429, 1027)(430, 1114)(431, 1029)(432, 1295)(433, 1030)(434, 1297)(435, 1032)(436, 1036)(437, 1301)(438, 1034)(439, 1304)(440, 1306)(441, 1307)(442, 1038)(443, 1309)(444, 1041)(445, 1312)(446, 1094)(447, 1314)(448, 1043)(449, 1317)(450, 1319)(451, 1046)(452, 1323)(453, 1048)(454, 1258)(455, 1326)(456, 1327)(457, 1051)(458, 1052)(459, 1298)(460, 1332)(461, 1054)(462, 1055)(463, 1261)(464, 1057)(465, 1333)(466, 1334)(467, 1058)(468, 1060)(469, 1061)(470, 1260)(471, 1336)(472, 1063)(473, 1338)(474, 1278)(475, 1066)(476, 1341)(477, 1342)(478, 1343)(479, 1344)(480, 1070)(481, 1071)(482, 1257)(483, 1340)(484, 1348)(485, 1073)(486, 1274)(487, 1075)(488, 1351)(489, 1076)(490, 1352)(491, 1078)(492, 1264)(493, 1081)(494, 1353)(495, 1080)(496, 1354)(497, 1356)(498, 1084)(499, 1358)(500, 1346)(501, 1086)(502, 1361)(503, 1087)(504, 1362)(505, 1089)(506, 1271)(507, 1092)(508, 1300)(509, 1299)(510, 1093)(511, 1262)(512, 1364)(513, 1096)(514, 1266)(515, 1367)(516, 1292)(517, 1099)(518, 1100)(519, 1359)(520, 1104)(521, 1105)(522, 1289)(523, 1331)(524, 1330)(525, 1275)(526, 1108)(527, 1281)(528, 1322)(529, 1110)(530, 1373)(531, 1316)(532, 1113)(533, 1294)(534, 1303)(535, 1375)(536, 1117)(537, 1201)(538, 1119)(539, 1173)(540, 1182)(541, 1223)(542, 1123)(543, 1225)(544, 1215)(545, 1379)(546, 1128)(547, 1195)(548, 1127)(549, 1233)(550, 1383)(551, 1131)(552, 1211)(553, 1207)(554, 1132)(555, 1134)(556, 1135)(557, 1386)(558, 1137)(559, 1141)(560, 1388)(561, 1139)(562, 1230)(563, 1187)(564, 1197)(565, 1246)(566, 1144)(567, 1394)(568, 1395)(569, 1146)(570, 1240)(571, 1237)(572, 1149)(573, 1400)(574, 1151)(575, 1252)(576, 1181)(577, 1403)(578, 1154)(579, 1155)(580, 1387)(581, 1184)(582, 1157)(583, 1158)(584, 1244)(585, 1160)(586, 1224)(587, 1405)(588, 1161)(589, 1254)(590, 1406)(591, 1164)(592, 1408)(593, 1409)(594, 1410)(595, 1167)(596, 1168)(597, 1251)(598, 1214)(599, 1248)(600, 1172)(601, 1414)(602, 1171)(603, 1415)(604, 1191)(605, 1175)(606, 1210)(607, 1412)(608, 1177)(609, 1198)(610, 1178)(611, 1179)(612, 1208)(613, 1385)(614, 1380)(615, 1407)(616, 1213)(617, 1192)(618, 1378)(619, 1196)(620, 1381)(621, 1420)(622, 1413)(623, 1411)(624, 1222)(625, 1200)(626, 1377)(627, 1203)(628, 1382)(629, 1205)(630, 1384)(631, 1402)(632, 1399)(633, 1391)(634, 1416)(635, 1217)(636, 1419)(637, 1218)(638, 1397)(639, 1238)(640, 1221)(641, 1422)(642, 1389)(643, 1227)(644, 1423)(645, 1232)(646, 1390)(647, 1393)(648, 1235)(649, 1417)(650, 1243)(651, 1392)(652, 1249)(653, 1424)(654, 1418)(655, 1428)(656, 1256)(657, 1360)(658, 1337)(659, 1268)(660, 1366)(661, 1308)(662, 1270)(663, 1349)(664, 1429)(665, 1302)(666, 1363)(667, 1277)(668, 1305)(669, 1280)(670, 1283)(671, 1284)(672, 1430)(673, 1286)(674, 1368)(675, 1431)(676, 1288)(677, 1321)(678, 1293)(679, 1369)(680, 1433)(681, 1310)(682, 1296)(683, 1370)(684, 1313)(685, 1347)(686, 1320)(687, 1311)(688, 1335)(689, 1432)(690, 1329)(691, 1315)(692, 1374)(693, 1318)(694, 1357)(695, 1434)(696, 1324)(697, 1325)(698, 1328)(699, 1339)(700, 1355)(701, 1438)(702, 1345)(703, 1350)(704, 1372)(705, 1437)(706, 1365)(707, 1371)(708, 1376)(709, 1426)(710, 1398)(711, 1404)(712, 1396)(713, 1427)(714, 1401)(715, 1421)(716, 1425)(717, 1439)(718, 1440)(719, 1435)(720, 1436) local type(s) :: { ( 3, 8, 3, 8 ) } Outer automorphisms :: reflexible Dual of E16.1302 Transitivity :: ET+ VT+ AT Graph:: simple v = 360 e = 720 f = 330 degree seq :: [ 4^360 ] E16.1307 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8}) Quotient :: dipole Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-1)^8, (Y3 * Y2^-1)^8, (Y2 * Y1 * Y2^-1 * Y1)^5, (Y2 * Y1 * Y2^-1 * Y1)^5, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: R = (1, 721, 2, 722)(3, 723, 7, 727)(4, 724, 8, 728)(5, 725, 9, 729)(6, 726, 10, 730)(11, 731, 19, 739)(12, 732, 20, 740)(13, 733, 21, 741)(14, 734, 22, 742)(15, 735, 23, 743)(16, 736, 24, 744)(17, 737, 25, 745)(18, 738, 26, 746)(27, 747, 43, 763)(28, 748, 44, 764)(29, 749, 45, 765)(30, 750, 46, 766)(31, 751, 47, 767)(32, 752, 48, 768)(33, 753, 49, 769)(34, 754, 50, 770)(35, 755, 51, 771)(36, 756, 52, 772)(37, 757, 53, 773)(38, 758, 54, 774)(39, 759, 55, 775)(40, 760, 56, 776)(41, 761, 57, 777)(42, 762, 58, 778)(59, 779, 90, 810)(60, 780, 91, 811)(61, 781, 92, 812)(62, 782, 93, 813)(63, 783, 94, 814)(64, 784, 95, 815)(65, 785, 96, 816)(66, 786, 97, 817)(67, 787, 98, 818)(68, 788, 99, 819)(69, 789, 100, 820)(70, 790, 101, 821)(71, 791, 102, 822)(72, 792, 103, 823)(73, 793, 104, 824)(74, 794, 75, 795)(76, 796, 105, 825)(77, 797, 106, 826)(78, 798, 107, 827)(79, 799, 108, 828)(80, 800, 109, 829)(81, 801, 110, 830)(82, 802, 111, 831)(83, 803, 112, 832)(84, 804, 113, 833)(85, 805, 114, 834)(86, 806, 115, 835)(87, 807, 116, 836)(88, 808, 117, 837)(89, 809, 118, 838)(119, 839, 169, 889)(120, 840, 170, 890)(121, 841, 171, 891)(122, 842, 172, 892)(123, 843, 173, 893)(124, 844, 174, 894)(125, 845, 175, 895)(126, 846, 176, 896)(127, 847, 152, 872)(128, 848, 177, 897)(129, 849, 178, 898)(130, 850, 179, 899)(131, 851, 180, 900)(132, 852, 181, 901)(133, 853, 182, 902)(134, 854, 183, 903)(135, 855, 160, 880)(136, 856, 184, 904)(137, 857, 185, 905)(138, 858, 186, 906)(139, 859, 187, 907)(140, 860, 188, 908)(141, 861, 189, 909)(142, 862, 190, 910)(143, 863, 191, 911)(144, 864, 192, 912)(145, 865, 193, 913)(146, 866, 194, 914)(147, 867, 195, 915)(148, 868, 196, 916)(149, 869, 197, 917)(150, 870, 198, 918)(151, 871, 199, 919)(153, 873, 200, 920)(154, 874, 201, 921)(155, 875, 202, 922)(156, 876, 203, 923)(157, 877, 204, 924)(158, 878, 205, 925)(159, 879, 206, 926)(161, 881, 207, 927)(162, 882, 208, 928)(163, 883, 209, 929)(164, 884, 210, 930)(165, 885, 211, 931)(166, 886, 212, 932)(167, 887, 213, 933)(168, 888, 214, 934)(215, 935, 373, 1093)(216, 936, 416, 1136)(217, 937, 418, 1138)(218, 938, 419, 1139)(219, 939, 421, 1141)(220, 940, 423, 1143)(221, 941, 327, 1047)(222, 942, 258, 978)(223, 943, 425, 1145)(224, 944, 426, 1146)(225, 945, 371, 1091)(226, 946, 429, 1149)(227, 947, 430, 1150)(228, 948, 361, 1081)(229, 949, 433, 1153)(230, 950, 365, 1085)(231, 951, 436, 1156)(232, 952, 437, 1157)(233, 953, 284, 1004)(234, 954, 440, 1160)(235, 955, 381, 1101)(236, 956, 442, 1162)(237, 957, 444, 1164)(238, 958, 445, 1165)(239, 959, 447, 1167)(240, 960, 352, 1072)(241, 961, 253, 973)(242, 962, 356, 1076)(243, 963, 450, 1170)(244, 964, 380, 1100)(245, 965, 453, 1173)(246, 966, 454, 1174)(247, 967, 357, 1077)(248, 968, 457, 1177)(249, 969, 434, 1154)(250, 970, 459, 1179)(251, 971, 460, 1180)(252, 972, 405, 1125)(254, 974, 466, 1186)(255, 975, 469, 1189)(256, 976, 472, 1192)(257, 977, 475, 1195)(259, 979, 390, 1110)(260, 980, 483, 1203)(261, 981, 486, 1206)(262, 982, 490, 1210)(263, 983, 492, 1212)(264, 984, 424, 1144)(265, 985, 499, 1219)(266, 986, 503, 1223)(267, 987, 506, 1226)(268, 988, 509, 1229)(269, 989, 512, 1232)(270, 990, 514, 1234)(271, 991, 449, 1169)(272, 992, 519, 1239)(273, 993, 523, 1243)(274, 994, 358, 1078)(275, 995, 527, 1247)(276, 996, 531, 1251)(277, 997, 508, 1228)(278, 998, 536, 1256)(279, 999, 540, 1260)(280, 1000, 341, 1061)(281, 1001, 545, 1265)(282, 1002, 547, 1267)(283, 1003, 549, 1269)(285, 1005, 554, 1274)(286, 1006, 556, 1276)(287, 1007, 559, 1279)(288, 1008, 561, 1281)(289, 1009, 400, 1120)(290, 1010, 566, 1286)(291, 1011, 568, 1288)(292, 1012, 435, 1155)(293, 1013, 558, 1278)(294, 1014, 511, 1231)(295, 1015, 575, 1295)(296, 1016, 579, 1299)(297, 1017, 349, 1069)(298, 1018, 584, 1304)(299, 1019, 586, 1306)(300, 1020, 588, 1308)(301, 1021, 482, 1202)(302, 1022, 399, 1119)(303, 1023, 596, 1316)(304, 1024, 316, 1036)(305, 1025, 600, 1320)(306, 1026, 602, 1322)(307, 1027, 605, 1325)(308, 1028, 516, 1236)(309, 1029, 610, 1330)(310, 1030, 368, 1088)(311, 1031, 443, 1163)(312, 1032, 615, 1335)(313, 1033, 480, 1200)(314, 1034, 378, 1098)(315, 1035, 452, 1172)(317, 1037, 624, 1344)(318, 1038, 628, 1348)(319, 1039, 412, 1132)(320, 1040, 633, 1353)(321, 1041, 458, 1178)(322, 1042, 563, 1283)(323, 1043, 635, 1355)(324, 1044, 636, 1356)(325, 1045, 622, 1342)(326, 1046, 366, 1086)(328, 1048, 640, 1360)(329, 1049, 641, 1361)(330, 1050, 572, 1292)(331, 1051, 642, 1362)(332, 1052, 643, 1363)(333, 1053, 598, 1318)(334, 1054, 347, 1067)(335, 1055, 439, 1159)(336, 1056, 353, 1073)(337, 1057, 647, 1367)(338, 1058, 465, 1185)(339, 1059, 386, 1106)(340, 1060, 360, 1080)(342, 1062, 620, 1340)(343, 1063, 350, 1070)(344, 1064, 417, 1137)(345, 1065, 658, 1378)(346, 1066, 660, 1380)(348, 1068, 428, 1148)(351, 1071, 634, 1354)(354, 1074, 663, 1383)(355, 1075, 463, 1183)(359, 1079, 594, 1314)(362, 1082, 674, 1394)(363, 1083, 530, 1250)(364, 1084, 676, 1396)(367, 1087, 528, 1248)(369, 1089, 638, 1358)(370, 1090, 682, 1402)(372, 1092, 683, 1403)(374, 1094, 392, 1112)(375, 1095, 684, 1404)(376, 1096, 685, 1405)(377, 1097, 543, 1263)(379, 1099, 666, 1386)(382, 1102, 609, 1329)(383, 1103, 687, 1407)(384, 1104, 688, 1408)(385, 1105, 582, 1302)(387, 1107, 391, 1111)(388, 1108, 494, 1214)(389, 1109, 394, 1114)(393, 1113, 690, 1410)(395, 1115, 692, 1412)(396, 1116, 525, 1245)(397, 1117, 657, 1377)(398, 1118, 473, 1193)(401, 1121, 406, 1126)(402, 1122, 542, 1262)(403, 1123, 432, 1152)(404, 1124, 410, 1130)(407, 1127, 697, 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2521, 2113, 2833, 1873, 2593)(1802, 2522, 1861, 2581, 1859, 2579)(1804, 2524, 1811, 2531, 2117, 2837)(1805, 2525, 1965, 2685, 2118, 2838)(1806, 2526, 2087, 2807, 1969, 2689)(1807, 2527, 2119, 2839, 2120, 2840)(1817, 2537, 1888, 2608, 2073, 2793)(1818, 2538, 1894, 2614, 1909, 2629)(1819, 2539, 1858, 2578, 1946, 2666)(1820, 2540, 2126, 2846, 1872, 2592)(1836, 2556, 2107, 2827, 2080, 2800)(1839, 2559, 2040, 2760, 1915, 2635)(1843, 2563, 1934, 2654, 1952, 2672)(1844, 2564, 2136, 2856, 2106, 2826)(1856, 2576, 1876, 2596, 2076, 2796)(1857, 2577, 1971, 2691, 2060, 2780)(1860, 2580, 2143, 2863, 2130, 2850)(1863, 2583, 2090, 2810, 2145, 2865)(1865, 2585, 2072, 2792, 1871, 2591)(1866, 2586, 2068, 2788, 2052, 2772)(1874, 2594, 1937, 2657, 2132, 2852)(1875, 2595, 2098, 2818, 1941, 2661)(1878, 2598, 2149, 2869, 2150, 2870)(1882, 2602, 1899, 2619, 2006, 2726)(1883, 2603, 1943, 2663, 2050, 2770)(1886, 2606, 2141, 2861, 2151, 2871)(1890, 2610, 2075, 2795, 2066, 2786)(1898, 2618, 2055, 2775, 1961, 2681)(1901, 2621, 2153, 2873, 2139, 2859)(1913, 2633, 2083, 2803, 2138, 2858)(1917, 2637, 1994, 2714, 2146, 2866)(1924, 2644, 2125, 2845, 2133, 2853)(1926, 2646, 1976, 2696, 1985, 2705)(1928, 2648, 1999, 2719, 2116, 2836)(1931, 2651, 2128, 2848, 2157, 2877)(1932, 2652, 2015, 2735, 2024, 2744)(1939, 2659, 1959, 2679, 1967, 2687)(1978, 2698, 2081, 2801, 2028, 2748)(1988, 2708, 2158, 2878, 2124, 2844)(1989, 2709, 2034, 2754, 2114, 2834)(2017, 2737, 2123, 2843, 2045, 2765)(2027, 2747, 2159, 2879, 2127, 2847)(2043, 2763, 2137, 2857, 2082, 2802)(2079, 2799, 2121, 2841, 2122, 2842)(2111, 2831, 2134, 2854, 2135, 2855)(2115, 2835, 2160, 2880, 2144, 2864)(2147, 2867, 2152, 2872, 2148, 2868)(2154, 2874, 2155, 2875, 2156, 2876) L = (1, 1442)(2, 1441)(3, 1447)(4, 1448)(5, 1449)(6, 1450)(7, 1443)(8, 1444)(9, 1445)(10, 1446)(11, 1459)(12, 1460)(13, 1461)(14, 1462)(15, 1463)(16, 1464)(17, 1465)(18, 1466)(19, 1451)(20, 1452)(21, 1453)(22, 1454)(23, 1455)(24, 1456)(25, 1457)(26, 1458)(27, 1483)(28, 1484)(29, 1485)(30, 1486)(31, 1487)(32, 1488)(33, 1489)(34, 1490)(35, 1491)(36, 1492)(37, 1493)(38, 1494)(39, 1495)(40, 1496)(41, 1497)(42, 1498)(43, 1467)(44, 1468)(45, 1469)(46, 1470)(47, 1471)(48, 1472)(49, 1473)(50, 1474)(51, 1475)(52, 1476)(53, 1477)(54, 1478)(55, 1479)(56, 1480)(57, 1481)(58, 1482)(59, 1530)(60, 1531)(61, 1532)(62, 1533)(63, 1534)(64, 1535)(65, 1536)(66, 1537)(67, 1538)(68, 1539)(69, 1540)(70, 1541)(71, 1542)(72, 1543)(73, 1544)(74, 1515)(75, 1514)(76, 1545)(77, 1546)(78, 1547)(79, 1548)(80, 1549)(81, 1550)(82, 1551)(83, 1552)(84, 1553)(85, 1554)(86, 1555)(87, 1556)(88, 1557)(89, 1558)(90, 1499)(91, 1500)(92, 1501)(93, 1502)(94, 1503)(95, 1504)(96, 1505)(97, 1506)(98, 1507)(99, 1508)(100, 1509)(101, 1510)(102, 1511)(103, 1512)(104, 1513)(105, 1516)(106, 1517)(107, 1518)(108, 1519)(109, 1520)(110, 1521)(111, 1522)(112, 1523)(113, 1524)(114, 1525)(115, 1526)(116, 1527)(117, 1528)(118, 1529)(119, 1609)(120, 1610)(121, 1611)(122, 1612)(123, 1613)(124, 1614)(125, 1615)(126, 1616)(127, 1592)(128, 1617)(129, 1618)(130, 1619)(131, 1620)(132, 1621)(133, 1622)(134, 1623)(135, 1600)(136, 1624)(137, 1625)(138, 1626)(139, 1627)(140, 1628)(141, 1629)(142, 1630)(143, 1631)(144, 1632)(145, 1633)(146, 1634)(147, 1635)(148, 1636)(149, 1637)(150, 1638)(151, 1639)(152, 1567)(153, 1640)(154, 1641)(155, 1642)(156, 1643)(157, 1644)(158, 1645)(159, 1646)(160, 1575)(161, 1647)(162, 1648)(163, 1649)(164, 1650)(165, 1651)(166, 1652)(167, 1653)(168, 1654)(169, 1559)(170, 1560)(171, 1561)(172, 1562)(173, 1563)(174, 1564)(175, 1565)(176, 1566)(177, 1568)(178, 1569)(179, 1570)(180, 1571)(181, 1572)(182, 1573)(183, 1574)(184, 1576)(185, 1577)(186, 1578)(187, 1579)(188, 1580)(189, 1581)(190, 1582)(191, 1583)(192, 1584)(193, 1585)(194, 1586)(195, 1587)(196, 1588)(197, 1589)(198, 1590)(199, 1591)(200, 1593)(201, 1594)(202, 1595)(203, 1596)(204, 1597)(205, 1598)(206, 1599)(207, 1601)(208, 1602)(209, 1603)(210, 1604)(211, 1605)(212, 1606)(213, 1607)(214, 1608)(215, 1813)(216, 1856)(217, 1858)(218, 1859)(219, 1861)(220, 1863)(221, 1767)(222, 1698)(223, 1865)(224, 1866)(225, 1811)(226, 1869)(227, 1870)(228, 1801)(229, 1873)(230, 1805)(231, 1876)(232, 1877)(233, 1724)(234, 1880)(235, 1821)(236, 1882)(237, 1884)(238, 1885)(239, 1887)(240, 1792)(241, 1693)(242, 1796)(243, 1890)(244, 1820)(245, 1893)(246, 1894)(247, 1797)(248, 1897)(249, 1874)(250, 1899)(251, 1900)(252, 1845)(253, 1681)(254, 1906)(255, 1909)(256, 1912)(257, 1915)(258, 1662)(259, 1830)(260, 1923)(261, 1926)(262, 1930)(263, 1932)(264, 1864)(265, 1939)(266, 1943)(267, 1946)(268, 1949)(269, 1952)(270, 1954)(271, 1889)(272, 1959)(273, 1963)(274, 1798)(275, 1967)(276, 1971)(277, 1948)(278, 1976)(279, 1980)(280, 1781)(281, 1985)(282, 1987)(283, 1989)(284, 1673)(285, 1994)(286, 1996)(287, 1999)(288, 2001)(289, 1840)(290, 2006)(291, 2008)(292, 1875)(293, 1998)(294, 1951)(295, 2015)(296, 2019)(297, 1789)(298, 2024)(299, 2026)(300, 2028)(301, 1922)(302, 1839)(303, 2036)(304, 1756)(305, 2040)(306, 2042)(307, 2045)(308, 1956)(309, 2050)(310, 1808)(311, 1883)(312, 2055)(313, 1920)(314, 1818)(315, 1892)(316, 1744)(317, 2064)(318, 2068)(319, 1852)(320, 2073)(321, 1898)(322, 2003)(323, 2075)(324, 2076)(325, 2062)(326, 1806)(327, 1661)(328, 2080)(329, 2081)(330, 2012)(331, 2082)(332, 2083)(333, 2038)(334, 1787)(335, 1879)(336, 1793)(337, 2087)(338, 1905)(339, 1826)(340, 1800)(341, 1720)(342, 2060)(343, 1790)(344, 1857)(345, 2098)(346, 2100)(347, 1774)(348, 1868)(349, 1737)(350, 1783)(351, 2074)(352, 1680)(353, 1776)(354, 2103)(355, 1903)(356, 1682)(357, 1687)(358, 1714)(359, 2034)(360, 1780)(361, 1668)(362, 2114)(363, 1970)(364, 2116)(365, 1670)(366, 1766)(367, 1968)(368, 1750)(369, 2078)(370, 2122)(371, 1665)(372, 2123)(373, 1655)(374, 1832)(375, 2124)(376, 2125)(377, 1983)(378, 1754)(379, 2106)(380, 1684)(381, 1675)(382, 2049)(383, 2127)(384, 2128)(385, 2022)(386, 1779)(387, 1831)(388, 1934)(389, 1834)(390, 1699)(391, 1827)(392, 1814)(393, 2130)(394, 1829)(395, 2132)(396, 1965)(397, 2097)(398, 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2121)(490, 1702)(491, 2077)(492, 1703)(493, 2148)(494, 1828)(495, 2136)(496, 2140)(497, 2079)(498, 1997)(499, 1705)(500, 1878)(501, 2067)(502, 1871)(503, 1706)(504, 2154)(505, 2126)(506, 1707)(507, 2039)(508, 1717)(509, 1708)(510, 1984)(511, 1734)(512, 1709)(513, 2063)(514, 1710)(515, 1966)(516, 1748)(517, 2118)(518, 2002)(519, 1712)(520, 1901)(521, 2095)(522, 1895)(523, 1713)(524, 2155)(525, 1836)(526, 1955)(527, 1715)(528, 1807)(529, 2053)(530, 1803)(531, 1716)(532, 2156)(533, 2117)(534, 2102)(535, 2011)(536, 1718)(537, 2027)(538, 1867)(539, 2041)(540, 1719)(541, 2147)(542, 1842)(543, 1817)(544, 1950)(545, 1721)(546, 2018)(547, 1722)(548, 2033)(549, 1723)(550, 2152)(551, 2099)(552, 2105)(553, 2157)(554, 1725)(555, 2007)(556, 1726)(557, 1938)(558, 1733)(559, 1727)(560, 2071)(561, 1728)(562, 1958)(563, 1762)(564, 2120)(565, 2151)(566, 1730)(567, 1995)(568, 1731)(569, 1925)(570, 1881)(571, 1975)(572, 1770)(573, 2058)(574, 1848)(575, 1735)(576, 2043)(577, 1891)(578, 1986)(579, 1736)(580, 2135)(581, 1914)(582, 1825)(583, 1921)(584, 1738)(585, 2035)(586, 1739)(587, 1977)(588, 1740)(589, 2111)(590, 2057)(591, 1853)(592, 2048)(593, 1988)(594, 1799)(595, 2025)(596, 1743)(597, 2160)(598, 1773)(599, 1947)(600, 1745)(601, 1979)(602, 1746)(603, 2016)(604, 1928)(605, 1747)(606, 2144)(607, 2089)(608, 2032)(609, 1822)(610, 1749)(611, 2066)(612, 2093)(613, 1969)(614, 1919)(615, 1752)(616, 2090)(617, 2030)(618, 2013)(619, 1860)(620, 1782)(621, 2149)(622, 1765)(623, 1953)(624, 1757)(625, 2094)(626, 2051)(627, 1941)(628, 1758)(629, 2150)(630, 2110)(631, 2000)(632, 1924)(633, 1760)(634, 1791)(635, 1763)(636, 1764)(637, 1931)(638, 1809)(639, 1937)(640, 1768)(641, 1769)(642, 1771)(643, 1772)(644, 1886)(645, 2109)(646, 1904)(647, 1777)(648, 2101)(649, 2047)(650, 2056)(651, 2153)(652, 1854)(653, 2052)(654, 2065)(655, 1961)(656, 2143)(657, 1837)(658, 1785)(659, 1991)(660, 1786)(661, 2088)(662, 1974)(663, 1794)(664, 2119)(665, 1992)(666, 1819)(667, 1918)(668, 1902)(669, 2085)(670, 2070)(671, 2029)(672, 2159)(673, 2158)(674, 1802)(675, 1927)(676, 1804)(677, 1973)(678, 1957)(679, 2104)(680, 2004)(681, 1929)(682, 1810)(683, 1812)(684, 1815)(685, 1816)(686, 1945)(687, 1823)(688, 1824)(689, 2138)(690, 1833)(691, 1907)(692, 1835)(693, 2142)(694, 1916)(695, 2020)(696, 1935)(697, 1847)(698, 2129)(699, 1849)(700, 1936)(701, 1851)(702, 2133)(703, 2096)(704, 2046)(705, 1910)(706, 1896)(707, 1981)(708, 1933)(709, 2061)(710, 2069)(711, 2005)(712, 1990)(713, 2091)(714, 1944)(715, 1964)(716, 1972)(717, 1993)(718, 2113)(719, 2112)(720, 2037)(721, 2161)(722, 2162)(723, 2163)(724, 2164)(725, 2165)(726, 2166)(727, 2167)(728, 2168)(729, 2169)(730, 2170)(731, 2171)(732, 2172)(733, 2173)(734, 2174)(735, 2175)(736, 2176)(737, 2177)(738, 2178)(739, 2179)(740, 2180)(741, 2181)(742, 2182)(743, 2183)(744, 2184)(745, 2185)(746, 2186)(747, 2187)(748, 2188)(749, 2189)(750, 2190)(751, 2191)(752, 2192)(753, 2193)(754, 2194)(755, 2195)(756, 2196)(757, 2197)(758, 2198)(759, 2199)(760, 2200)(761, 2201)(762, 2202)(763, 2203)(764, 2204)(765, 2205)(766, 2206)(767, 2207)(768, 2208)(769, 2209)(770, 2210)(771, 2211)(772, 2212)(773, 2213)(774, 2214)(775, 2215)(776, 2216)(777, 2217)(778, 2218)(779, 2219)(780, 2220)(781, 2221)(782, 2222)(783, 2223)(784, 2224)(785, 2225)(786, 2226)(787, 2227)(788, 2228)(789, 2229)(790, 2230)(791, 2231)(792, 2232)(793, 2233)(794, 2234)(795, 2235)(796, 2236)(797, 2237)(798, 2238)(799, 2239)(800, 2240)(801, 2241)(802, 2242)(803, 2243)(804, 2244)(805, 2245)(806, 2246)(807, 2247)(808, 2248)(809, 2249)(810, 2250)(811, 2251)(812, 2252)(813, 2253)(814, 2254)(815, 2255)(816, 2256)(817, 2257)(818, 2258)(819, 2259)(820, 2260)(821, 2261)(822, 2262)(823, 2263)(824, 2264)(825, 2265)(826, 2266)(827, 2267)(828, 2268)(829, 2269)(830, 2270)(831, 2271)(832, 2272)(833, 2273)(834, 2274)(835, 2275)(836, 2276)(837, 2277)(838, 2278)(839, 2279)(840, 2280)(841, 2281)(842, 2282)(843, 2283)(844, 2284)(845, 2285)(846, 2286)(847, 2287)(848, 2288)(849, 2289)(850, 2290)(851, 2291)(852, 2292)(853, 2293)(854, 2294)(855, 2295)(856, 2296)(857, 2297)(858, 2298)(859, 2299)(860, 2300)(861, 2301)(862, 2302)(863, 2303)(864, 2304)(865, 2305)(866, 2306)(867, 2307)(868, 2308)(869, 2309)(870, 2310)(871, 2311)(872, 2312)(873, 2313)(874, 2314)(875, 2315)(876, 2316)(877, 2317)(878, 2318)(879, 2319)(880, 2320)(881, 2321)(882, 2322)(883, 2323)(884, 2324)(885, 2325)(886, 2326)(887, 2327)(888, 2328)(889, 2329)(890, 2330)(891, 2331)(892, 2332)(893, 2333)(894, 2334)(895, 2335)(896, 2336)(897, 2337)(898, 2338)(899, 2339)(900, 2340)(901, 2341)(902, 2342)(903, 2343)(904, 2344)(905, 2345)(906, 2346)(907, 2347)(908, 2348)(909, 2349)(910, 2350)(911, 2351)(912, 2352)(913, 2353)(914, 2354)(915, 2355)(916, 2356)(917, 2357)(918, 2358)(919, 2359)(920, 2360)(921, 2361)(922, 2362)(923, 2363)(924, 2364)(925, 2365)(926, 2366)(927, 2367)(928, 2368)(929, 2369)(930, 2370)(931, 2371)(932, 2372)(933, 2373)(934, 2374)(935, 2375)(936, 2376)(937, 2377)(938, 2378)(939, 2379)(940, 2380)(941, 2381)(942, 2382)(943, 2383)(944, 2384)(945, 2385)(946, 2386)(947, 2387)(948, 2388)(949, 2389)(950, 2390)(951, 2391)(952, 2392)(953, 2393)(954, 2394)(955, 2395)(956, 2396)(957, 2397)(958, 2398)(959, 2399)(960, 2400)(961, 2401)(962, 2402)(963, 2403)(964, 2404)(965, 2405)(966, 2406)(967, 2407)(968, 2408)(969, 2409)(970, 2410)(971, 2411)(972, 2412)(973, 2413)(974, 2414)(975, 2415)(976, 2416)(977, 2417)(978, 2418)(979, 2419)(980, 2420)(981, 2421)(982, 2422)(983, 2423)(984, 2424)(985, 2425)(986, 2426)(987, 2427)(988, 2428)(989, 2429)(990, 2430)(991, 2431)(992, 2432)(993, 2433)(994, 2434)(995, 2435)(996, 2436)(997, 2437)(998, 2438)(999, 2439)(1000, 2440)(1001, 2441)(1002, 2442)(1003, 2443)(1004, 2444)(1005, 2445)(1006, 2446)(1007, 2447)(1008, 2448)(1009, 2449)(1010, 2450)(1011, 2451)(1012, 2452)(1013, 2453)(1014, 2454)(1015, 2455)(1016, 2456)(1017, 2457)(1018, 2458)(1019, 2459)(1020, 2460)(1021, 2461)(1022, 2462)(1023, 2463)(1024, 2464)(1025, 2465)(1026, 2466)(1027, 2467)(1028, 2468)(1029, 2469)(1030, 2470)(1031, 2471)(1032, 2472)(1033, 2473)(1034, 2474)(1035, 2475)(1036, 2476)(1037, 2477)(1038, 2478)(1039, 2479)(1040, 2480)(1041, 2481)(1042, 2482)(1043, 2483)(1044, 2484)(1045, 2485)(1046, 2486)(1047, 2487)(1048, 2488)(1049, 2489)(1050, 2490)(1051, 2491)(1052, 2492)(1053, 2493)(1054, 2494)(1055, 2495)(1056, 2496)(1057, 2497)(1058, 2498)(1059, 2499)(1060, 2500)(1061, 2501)(1062, 2502)(1063, 2503)(1064, 2504)(1065, 2505)(1066, 2506)(1067, 2507)(1068, 2508)(1069, 2509)(1070, 2510)(1071, 2511)(1072, 2512)(1073, 2513)(1074, 2514)(1075, 2515)(1076, 2516)(1077, 2517)(1078, 2518)(1079, 2519)(1080, 2520)(1081, 2521)(1082, 2522)(1083, 2523)(1084, 2524)(1085, 2525)(1086, 2526)(1087, 2527)(1088, 2528)(1089, 2529)(1090, 2530)(1091, 2531)(1092, 2532)(1093, 2533)(1094, 2534)(1095, 2535)(1096, 2536)(1097, 2537)(1098, 2538)(1099, 2539)(1100, 2540)(1101, 2541)(1102, 2542)(1103, 2543)(1104, 2544)(1105, 2545)(1106, 2546)(1107, 2547)(1108, 2548)(1109, 2549)(1110, 2550)(1111, 2551)(1112, 2552)(1113, 2553)(1114, 2554)(1115, 2555)(1116, 2556)(1117, 2557)(1118, 2558)(1119, 2559)(1120, 2560)(1121, 2561)(1122, 2562)(1123, 2563)(1124, 2564)(1125, 2565)(1126, 2566)(1127, 2567)(1128, 2568)(1129, 2569)(1130, 2570)(1131, 2571)(1132, 2572)(1133, 2573)(1134, 2574)(1135, 2575)(1136, 2576)(1137, 2577)(1138, 2578)(1139, 2579)(1140, 2580)(1141, 2581)(1142, 2582)(1143, 2583)(1144, 2584)(1145, 2585)(1146, 2586)(1147, 2587)(1148, 2588)(1149, 2589)(1150, 2590)(1151, 2591)(1152, 2592)(1153, 2593)(1154, 2594)(1155, 2595)(1156, 2596)(1157, 2597)(1158, 2598)(1159, 2599)(1160, 2600)(1161, 2601)(1162, 2602)(1163, 2603)(1164, 2604)(1165, 2605)(1166, 2606)(1167, 2607)(1168, 2608)(1169, 2609)(1170, 2610)(1171, 2611)(1172, 2612)(1173, 2613)(1174, 2614)(1175, 2615)(1176, 2616)(1177, 2617)(1178, 2618)(1179, 2619)(1180, 2620)(1181, 2621)(1182, 2622)(1183, 2623)(1184, 2624)(1185, 2625)(1186, 2626)(1187, 2627)(1188, 2628)(1189, 2629)(1190, 2630)(1191, 2631)(1192, 2632)(1193, 2633)(1194, 2634)(1195, 2635)(1196, 2636)(1197, 2637)(1198, 2638)(1199, 2639)(1200, 2640)(1201, 2641)(1202, 2642)(1203, 2643)(1204, 2644)(1205, 2645)(1206, 2646)(1207, 2647)(1208, 2648)(1209, 2649)(1210, 2650)(1211, 2651)(1212, 2652)(1213, 2653)(1214, 2654)(1215, 2655)(1216, 2656)(1217, 2657)(1218, 2658)(1219, 2659)(1220, 2660)(1221, 2661)(1222, 2662)(1223, 2663)(1224, 2664)(1225, 2665)(1226, 2666)(1227, 2667)(1228, 2668)(1229, 2669)(1230, 2670)(1231, 2671)(1232, 2672)(1233, 2673)(1234, 2674)(1235, 2675)(1236, 2676)(1237, 2677)(1238, 2678)(1239, 2679)(1240, 2680)(1241, 2681)(1242, 2682)(1243, 2683)(1244, 2684)(1245, 2685)(1246, 2686)(1247, 2687)(1248, 2688)(1249, 2689)(1250, 2690)(1251, 2691)(1252, 2692)(1253, 2693)(1254, 2694)(1255, 2695)(1256, 2696)(1257, 2697)(1258, 2698)(1259, 2699)(1260, 2700)(1261, 2701)(1262, 2702)(1263, 2703)(1264, 2704)(1265, 2705)(1266, 2706)(1267, 2707)(1268, 2708)(1269, 2709)(1270, 2710)(1271, 2711)(1272, 2712)(1273, 2713)(1274, 2714)(1275, 2715)(1276, 2716)(1277, 2717)(1278, 2718)(1279, 2719)(1280, 2720)(1281, 2721)(1282, 2722)(1283, 2723)(1284, 2724)(1285, 2725)(1286, 2726)(1287, 2727)(1288, 2728)(1289, 2729)(1290, 2730)(1291, 2731)(1292, 2732)(1293, 2733)(1294, 2734)(1295, 2735)(1296, 2736)(1297, 2737)(1298, 2738)(1299, 2739)(1300, 2740)(1301, 2741)(1302, 2742)(1303, 2743)(1304, 2744)(1305, 2745)(1306, 2746)(1307, 2747)(1308, 2748)(1309, 2749)(1310, 2750)(1311, 2751)(1312, 2752)(1313, 2753)(1314, 2754)(1315, 2755)(1316, 2756)(1317, 2757)(1318, 2758)(1319, 2759)(1320, 2760)(1321, 2761)(1322, 2762)(1323, 2763)(1324, 2764)(1325, 2765)(1326, 2766)(1327, 2767)(1328, 2768)(1329, 2769)(1330, 2770)(1331, 2771)(1332, 2772)(1333, 2773)(1334, 2774)(1335, 2775)(1336, 2776)(1337, 2777)(1338, 2778)(1339, 2779)(1340, 2780)(1341, 2781)(1342, 2782)(1343, 2783)(1344, 2784)(1345, 2785)(1346, 2786)(1347, 2787)(1348, 2788)(1349, 2789)(1350, 2790)(1351, 2791)(1352, 2792)(1353, 2793)(1354, 2794)(1355, 2795)(1356, 2796)(1357, 2797)(1358, 2798)(1359, 2799)(1360, 2800)(1361, 2801)(1362, 2802)(1363, 2803)(1364, 2804)(1365, 2805)(1366, 2806)(1367, 2807)(1368, 2808)(1369, 2809)(1370, 2810)(1371, 2811)(1372, 2812)(1373, 2813)(1374, 2814)(1375, 2815)(1376, 2816)(1377, 2817)(1378, 2818)(1379, 2819)(1380, 2820)(1381, 2821)(1382, 2822)(1383, 2823)(1384, 2824)(1385, 2825)(1386, 2826)(1387, 2827)(1388, 2828)(1389, 2829)(1390, 2830)(1391, 2831)(1392, 2832)(1393, 2833)(1394, 2834)(1395, 2835)(1396, 2836)(1397, 2837)(1398, 2838)(1399, 2839)(1400, 2840)(1401, 2841)(1402, 2842)(1403, 2843)(1404, 2844)(1405, 2845)(1406, 2846)(1407, 2847)(1408, 2848)(1409, 2849)(1410, 2850)(1411, 2851)(1412, 2852)(1413, 2853)(1414, 2854)(1415, 2855)(1416, 2856)(1417, 2857)(1418, 2858)(1419, 2859)(1420, 2860)(1421, 2861)(1422, 2862)(1423, 2863)(1424, 2864)(1425, 2865)(1426, 2866)(1427, 2867)(1428, 2868)(1429, 2869)(1430, 2870)(1431, 2871)(1432, 2872)(1433, 2873)(1434, 2874)(1435, 2875)(1436, 2876)(1437, 2877)(1438, 2878)(1439, 2879)(1440, 2880) local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E16.1310 Graph:: bipartite v = 600 e = 1440 f = 810 degree seq :: [ 4^360, 6^240 ] E16.1308 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8}) Quotient :: dipole Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (Y2^-1 * Y1^-1)^2, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2^8, Y2^8, (Y1 * Y2^-2)^5, Y2^-1 * Y1 * Y2^-3 * Y1 * Y2^3 * Y1^-1 * Y2^-2 * Y1 * Y2^-3 * Y1 * Y2^4 * Y1, Y2^2 * Y1^-1 * Y2^-3 * Y1 * Y2^-3 * Y1 * Y2^-3 * Y1^-1 * Y2^2 * Y1^-1 * Y2^3 * Y1^-1, Y2^-1 * Y1 * Y2^4 * Y1 * Y2^-2 * Y1 * Y2^2 * Y1^-1 * Y2^3 * Y1^-1 * Y2^4 * Y1, Y2^3 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-2 * Y1 * Y2^-4 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-3 * Y1^-1 ] Map:: R = (1, 721, 2, 722, 4, 724)(3, 723, 8, 728, 10, 730)(5, 725, 12, 732, 6, 726)(7, 727, 15, 735, 11, 731)(9, 729, 18, 738, 20, 740)(13, 733, 25, 745, 23, 743)(14, 734, 24, 744, 28, 748)(16, 736, 31, 751, 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2877, 2150, 2870) L = (1, 1443)(2, 1446)(3, 1449)(4, 1451)(5, 1441)(6, 1454)(7, 1442)(8, 1444)(9, 1459)(10, 1461)(11, 1462)(12, 1463)(13, 1445)(14, 1467)(15, 1469)(16, 1447)(17, 1448)(18, 1450)(19, 1477)(20, 1479)(21, 1480)(22, 1481)(23, 1483)(24, 1452)(25, 1485)(26, 1453)(27, 1489)(28, 1491)(29, 1492)(30, 1455)(31, 1494)(32, 1456)(33, 1497)(34, 1457)(35, 1458)(36, 1460)(37, 1466)(38, 1506)(39, 1507)(40, 1508)(41, 1500)(42, 1512)(43, 1513)(44, 1464)(45, 1517)(46, 1465)(47, 1505)(48, 1468)(49, 1472)(50, 1523)(51, 1524)(52, 1525)(53, 1470)(54, 1529)(55, 1471)(56, 1522)(57, 1532)(58, 1473)(59, 1534)(60, 1474)(61, 1537)(62, 1475)(63, 1476)(64, 1478)(65, 1544)(66, 1545)(67, 1546)(68, 1540)(69, 1550)(70, 1482)(71, 1552)(72, 1553)(73, 1555)(74, 1557)(75, 1558)(76, 1484)(77, 1561)(78, 1486)(79, 1487)(80, 1488)(81, 1490)(82, 1569)(83, 1570)(84, 1571)(85, 1574)(86, 1576)(87, 1577)(88, 1493)(89, 1580)(90, 1495)(91, 1496)(92, 1585)(93, 1498)(94, 1589)(95, 1499)(96, 1511)(97, 1592)(98, 1501)(99, 1594)(100, 1502)(101, 1597)(102, 1503)(103, 1504)(104, 1603)(105, 1604)(106, 1600)(107, 1608)(108, 1509)(109, 1610)(110, 1611)(111, 1510)(112, 1614)(113, 1615)(114, 1514)(115, 1516)(116, 1620)(117, 1621)(118, 1622)(119, 1515)(120, 1619)(121, 1626)(122, 1628)(123, 1629)(124, 1518)(125, 1519)(126, 1634)(127, 1520)(128, 1521)(129, 1640)(130, 1641)(131, 1637)(132, 1645)(133, 1526)(134, 1528)(135, 1649)(136, 1650)(137, 1651)(138, 1527)(139, 1648)(140, 1655)(141, 1657)(142, 1658)(143, 1530)(144, 1531)(145, 1663)(146, 1665)(147, 1666)(148, 1533)(149, 1668)(150, 1535)(151, 1536)(152, 1673)(153, 1538)(154, 1676)(155, 1539)(156, 1549)(157, 1679)(158, 1541)(159, 1681)(160, 1542)(161, 1684)(162, 1543)(163, 1688)(164, 1687)(165, 1692)(166, 1547)(167, 1694)(168, 1582)(169, 1548)(170, 1697)(171, 1698)(172, 1699)(173, 1551)(174, 1703)(175, 1702)(176, 1630)(177, 1554)(178, 1556)(179, 1710)(180, 1711)(181, 1712)(182, 1713)(183, 1559)(184, 1560)(185, 1562)(186, 1564)(187, 1720)(188, 1721)(189, 1722)(190, 1563)(191, 1719)(192, 1724)(193, 1565)(194, 1727)(195, 1566)(196, 1729)(197, 1567)(198, 1732)(199, 1568)(200, 1736)(201, 1735)(202, 1725)(203, 1572)(204, 1741)(205, 1587)(206, 1573)(207, 1575)(208, 1745)(209, 1746)(210, 1747)(211, 1748)(212, 1578)(213, 1579)(214, 1581)(215, 1583)(216, 1755)(217, 1756)(218, 1757)(219, 1754)(220, 1759)(221, 1584)(222, 1586)(223, 1588)(224, 1765)(225, 1766)(226, 1767)(227, 1764)(228, 1770)(229, 1772)(230, 1773)(231, 1590)(232, 1591)(233, 1778)(234, 1780)(235, 1593)(236, 1782)(237, 1595)(238, 1596)(239, 1787)(240, 1598)(241, 1790)(242, 1599)(243, 1607)(244, 1793)(245, 1601)(246, 1795)(247, 1602)(248, 1633)(249, 1800)(250, 1605)(251, 1802)(252, 1670)(253, 1606)(254, 1805)(255, 1806)(256, 1609)(257, 1810)(258, 1809)(259, 1813)(260, 1612)(261, 1815)(262, 1613)(263, 1776)(264, 1760)(265, 1616)(266, 1821)(267, 1822)(268, 1617)(269, 1618)(270, 1828)(271, 1829)(272, 1825)(273, 1833)(274, 1835)(275, 1623)(276, 1624)(277, 1625)(278, 1627)(279, 1841)(280, 1842)(281, 1843)(282, 1844)(283, 1631)(284, 1847)(285, 1632)(286, 1799)(287, 1849)(288, 1635)(289, 1852)(290, 1636)(291, 1644)(292, 1855)(293, 1638)(294, 1857)(295, 1639)(296, 1661)(297, 1862)(298, 1642)(299, 1864)(300, 1643)(301, 1867)(302, 1868)(303, 1646)(304, 1647)(305, 1874)(306, 1875)(307, 1871)(308, 1878)(309, 1880)(310, 1652)(311, 1653)(312, 1654)(313, 1656)(314, 1886)(315, 1887)(316, 1888)(317, 1804)(318, 1659)(319, 1891)(320, 1660)(321, 1861)(322, 1662)(323, 1664)(324, 1896)(325, 1897)(326, 1898)(327, 1866)(328, 1667)(329, 1669)(330, 1671)(331, 1904)(332, 1905)(333, 1906)(334, 1903)(335, 1908)(336, 1672)(337, 1674)(338, 1675)(339, 1914)(340, 1915)(341, 1913)(342, 1918)(343, 1920)(344, 1921)(345, 1677)(346, 1678)(347, 1926)(348, 1928)(349, 1680)(350, 1930)(351, 1682)(352, 1683)(353, 1934)(354, 1685)(355, 1937)(356, 1686)(357, 1691)(358, 1689)(359, 1940)(360, 1784)(361, 1690)(362, 1943)(363, 1944)(364, 1693)(365, 1947)(366, 1949)(367, 1695)(368, 1951)(369, 1696)(370, 1924)(371, 1909)(372, 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2068)(464, 1881)(465, 2069)(466, 1942)(467, 1774)(468, 2072)(469, 1775)(470, 1819)(471, 1777)(472, 1779)(473, 2077)(474, 2078)(475, 2079)(476, 1781)(477, 1783)(478, 1785)(479, 2082)(480, 2083)(481, 2084)(482, 2015)(483, 2014)(484, 1786)(485, 1788)(486, 1789)(487, 2089)(488, 1838)(489, 2012)(490, 2090)(491, 2009)(492, 1791)(493, 1792)(494, 2048)(495, 1823)(496, 1794)(497, 2034)(498, 1797)(499, 1798)(500, 2032)(501, 2008)(502, 1801)(503, 2096)(504, 2098)(505, 1803)(506, 1889)(507, 2093)(508, 2086)(509, 2102)(510, 1807)(511, 2105)(512, 1808)(513, 1812)(514, 1811)(515, 2109)(516, 2110)(517, 2095)(518, 2056)(519, 1814)(520, 2101)(521, 1816)(522, 1817)(523, 1818)(524, 2091)(525, 1995)(526, 2097)(527, 2115)(528, 2099)(529, 1824)(530, 1831)(531, 2080)(532, 1826)(533, 2073)(534, 1827)(535, 1837)(536, 2118)(537, 1830)(538, 2108)(539, 2081)(540, 1832)(541, 1834)(542, 2100)(543, 2088)(544, 2085)(545, 2067)(546, 2123)(547, 2104)(548, 1839)(549, 2065)(550, 1840)(551, 2044)(552, 2053)(553, 2066)(554, 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2176)(737, 2177)(738, 2178)(739, 2179)(740, 2180)(741, 2181)(742, 2182)(743, 2183)(744, 2184)(745, 2185)(746, 2186)(747, 2187)(748, 2188)(749, 2189)(750, 2190)(751, 2191)(752, 2192)(753, 2193)(754, 2194)(755, 2195)(756, 2196)(757, 2197)(758, 2198)(759, 2199)(760, 2200)(761, 2201)(762, 2202)(763, 2203)(764, 2204)(765, 2205)(766, 2206)(767, 2207)(768, 2208)(769, 2209)(770, 2210)(771, 2211)(772, 2212)(773, 2213)(774, 2214)(775, 2215)(776, 2216)(777, 2217)(778, 2218)(779, 2219)(780, 2220)(781, 2221)(782, 2222)(783, 2223)(784, 2224)(785, 2225)(786, 2226)(787, 2227)(788, 2228)(789, 2229)(790, 2230)(791, 2231)(792, 2232)(793, 2233)(794, 2234)(795, 2235)(796, 2236)(797, 2237)(798, 2238)(799, 2239)(800, 2240)(801, 2241)(802, 2242)(803, 2243)(804, 2244)(805, 2245)(806, 2246)(807, 2247)(808, 2248)(809, 2249)(810, 2250)(811, 2251)(812, 2252)(813, 2253)(814, 2254)(815, 2255)(816, 2256)(817, 2257)(818, 2258)(819, 2259)(820, 2260)(821, 2261)(822, 2262)(823, 2263)(824, 2264)(825, 2265)(826, 2266)(827, 2267)(828, 2268)(829, 2269)(830, 2270)(831, 2271)(832, 2272)(833, 2273)(834, 2274)(835, 2275)(836, 2276)(837, 2277)(838, 2278)(839, 2279)(840, 2280)(841, 2281)(842, 2282)(843, 2283)(844, 2284)(845, 2285)(846, 2286)(847, 2287)(848, 2288)(849, 2289)(850, 2290)(851, 2291)(852, 2292)(853, 2293)(854, 2294)(855, 2295)(856, 2296)(857, 2297)(858, 2298)(859, 2299)(860, 2300)(861, 2301)(862, 2302)(863, 2303)(864, 2304)(865, 2305)(866, 2306)(867, 2307)(868, 2308)(869, 2309)(870, 2310)(871, 2311)(872, 2312)(873, 2313)(874, 2314)(875, 2315)(876, 2316)(877, 2317)(878, 2318)(879, 2319)(880, 2320)(881, 2321)(882, 2322)(883, 2323)(884, 2324)(885, 2325)(886, 2326)(887, 2327)(888, 2328)(889, 2329)(890, 2330)(891, 2331)(892, 2332)(893, 2333)(894, 2334)(895, 2335)(896, 2336)(897, 2337)(898, 2338)(899, 2339)(900, 2340)(901, 2341)(902, 2342)(903, 2343)(904, 2344)(905, 2345)(906, 2346)(907, 2347)(908, 2348)(909, 2349)(910, 2350)(911, 2351)(912, 2352)(913, 2353)(914, 2354)(915, 2355)(916, 2356)(917, 2357)(918, 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2780)(1341, 2781)(1342, 2782)(1343, 2783)(1344, 2784)(1345, 2785)(1346, 2786)(1347, 2787)(1348, 2788)(1349, 2789)(1350, 2790)(1351, 2791)(1352, 2792)(1353, 2793)(1354, 2794)(1355, 2795)(1356, 2796)(1357, 2797)(1358, 2798)(1359, 2799)(1360, 2800)(1361, 2801)(1362, 2802)(1363, 2803)(1364, 2804)(1365, 2805)(1366, 2806)(1367, 2807)(1368, 2808)(1369, 2809)(1370, 2810)(1371, 2811)(1372, 2812)(1373, 2813)(1374, 2814)(1375, 2815)(1376, 2816)(1377, 2817)(1378, 2818)(1379, 2819)(1380, 2820)(1381, 2821)(1382, 2822)(1383, 2823)(1384, 2824)(1385, 2825)(1386, 2826)(1387, 2827)(1388, 2828)(1389, 2829)(1390, 2830)(1391, 2831)(1392, 2832)(1393, 2833)(1394, 2834)(1395, 2835)(1396, 2836)(1397, 2837)(1398, 2838)(1399, 2839)(1400, 2840)(1401, 2841)(1402, 2842)(1403, 2843)(1404, 2844)(1405, 2845)(1406, 2846)(1407, 2847)(1408, 2848)(1409, 2849)(1410, 2850)(1411, 2851)(1412, 2852)(1413, 2853)(1414, 2854)(1415, 2855)(1416, 2856)(1417, 2857)(1418, 2858)(1419, 2859)(1420, 2860)(1421, 2861)(1422, 2862)(1423, 2863)(1424, 2864)(1425, 2865)(1426, 2866)(1427, 2867)(1428, 2868)(1429, 2869)(1430, 2870)(1431, 2871)(1432, 2872)(1433, 2873)(1434, 2874)(1435, 2875)(1436, 2876)(1437, 2877)(1438, 2878)(1439, 2879)(1440, 2880) 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 ) } Outer automorphisms :: reflexible Dual of E16.1309 Graph:: bipartite v = 330 e = 1440 f = 1080 degree seq :: [ 6^240, 16^90 ] E16.1309 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8}) Quotient :: dipole Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y3)^3, Y3^8, (Y3^-1 * Y1^-1)^8, Y2 * Y3^-2 * Y2 * Y3^2 * Y2 * Y3^3 * Y2 * Y3^2 * Y2 * Y3^-2 * Y2 * Y3^-3, Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1, Y3^2 * Y2 * Y3^-2 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2 * Y3^3 * Y2 * Y3^-2 * Y2 * Y3^3 * Y2 * Y3^2 ] Map:: polytopal R = (1, 721)(2, 722)(3, 723)(4, 724)(5, 725)(6, 726)(7, 727)(8, 728)(9, 729)(10, 730)(11, 731)(12, 732)(13, 733)(14, 734)(15, 735)(16, 736)(17, 737)(18, 738)(19, 739)(20, 740)(21, 741)(22, 742)(23, 743)(24, 744)(25, 745)(26, 746)(27, 747)(28, 748)(29, 749)(30, 750)(31, 751)(32, 752)(33, 753)(34, 754)(35, 755)(36, 756)(37, 757)(38, 758)(39, 759)(40, 760)(41, 761)(42, 762)(43, 763)(44, 764)(45, 765)(46, 766)(47, 767)(48, 768)(49, 769)(50, 770)(51, 771)(52, 772)(53, 773)(54, 774)(55, 775)(56, 776)(57, 777)(58, 778)(59, 779)(60, 780)(61, 781)(62, 782)(63, 783)(64, 784)(65, 785)(66, 786)(67, 787)(68, 788)(69, 789)(70, 790)(71, 791)(72, 792)(73, 793)(74, 794)(75, 795)(76, 796)(77, 797)(78, 798)(79, 799)(80, 800)(81, 801)(82, 802)(83, 803)(84, 804)(85, 805)(86, 806)(87, 807)(88, 808)(89, 809)(90, 810)(91, 811)(92, 812)(93, 813)(94, 814)(95, 815)(96, 816)(97, 817)(98, 818)(99, 819)(100, 820)(101, 821)(102, 822)(103, 823)(104, 824)(105, 825)(106, 826)(107, 827)(108, 828)(109, 829)(110, 830)(111, 831)(112, 832)(113, 833)(114, 834)(115, 835)(116, 836)(117, 837)(118, 838)(119, 839)(120, 840)(121, 841)(122, 842)(123, 843)(124, 844)(125, 845)(126, 846)(127, 847)(128, 848)(129, 849)(130, 850)(131, 851)(132, 852)(133, 853)(134, 854)(135, 855)(136, 856)(137, 857)(138, 858)(139, 859)(140, 860)(141, 861)(142, 862)(143, 863)(144, 864)(145, 865)(146, 866)(147, 867)(148, 868)(149, 869)(150, 870)(151, 871)(152, 872)(153, 873)(154, 874)(155, 875)(156, 876)(157, 877)(158, 878)(159, 879)(160, 880)(161, 881)(162, 882)(163, 883)(164, 884)(165, 885)(166, 886)(167, 887)(168, 888)(169, 889)(170, 890)(171, 891)(172, 892)(173, 893)(174, 894)(175, 895)(176, 896)(177, 897)(178, 898)(179, 899)(180, 900)(181, 901)(182, 902)(183, 903)(184, 904)(185, 905)(186, 906)(187, 907)(188, 908)(189, 909)(190, 910)(191, 911)(192, 912)(193, 913)(194, 914)(195, 915)(196, 916)(197, 917)(198, 918)(199, 919)(200, 920)(201, 921)(202, 922)(203, 923)(204, 924)(205, 925)(206, 926)(207, 927)(208, 928)(209, 929)(210, 930)(211, 931)(212, 932)(213, 933)(214, 934)(215, 935)(216, 936)(217, 937)(218, 938)(219, 939)(220, 940)(221, 941)(222, 942)(223, 943)(224, 944)(225, 945)(226, 946)(227, 947)(228, 948)(229, 949)(230, 950)(231, 951)(232, 952)(233, 953)(234, 954)(235, 955)(236, 956)(237, 957)(238, 958)(239, 959)(240, 960)(241, 961)(242, 962)(243, 963)(244, 964)(245, 965)(246, 966)(247, 967)(248, 968)(249, 969)(250, 970)(251, 971)(252, 972)(253, 973)(254, 974)(255, 975)(256, 976)(257, 977)(258, 978)(259, 979)(260, 980)(261, 981)(262, 982)(263, 983)(264, 984)(265, 985)(266, 986)(267, 987)(268, 988)(269, 989)(270, 990)(271, 991)(272, 992)(273, 993)(274, 994)(275, 995)(276, 996)(277, 997)(278, 998)(279, 999)(280, 1000)(281, 1001)(282, 1002)(283, 1003)(284, 1004)(285, 1005)(286, 1006)(287, 1007)(288, 1008)(289, 1009)(290, 1010)(291, 1011)(292, 1012)(293, 1013)(294, 1014)(295, 1015)(296, 1016)(297, 1017)(298, 1018)(299, 1019)(300, 1020)(301, 1021)(302, 1022)(303, 1023)(304, 1024)(305, 1025)(306, 1026)(307, 1027)(308, 1028)(309, 1029)(310, 1030)(311, 1031)(312, 1032)(313, 1033)(314, 1034)(315, 1035)(316, 1036)(317, 1037)(318, 1038)(319, 1039)(320, 1040)(321, 1041)(322, 1042)(323, 1043)(324, 1044)(325, 1045)(326, 1046)(327, 1047)(328, 1048)(329, 1049)(330, 1050)(331, 1051)(332, 1052)(333, 1053)(334, 1054)(335, 1055)(336, 1056)(337, 1057)(338, 1058)(339, 1059)(340, 1060)(341, 1061)(342, 1062)(343, 1063)(344, 1064)(345, 1065)(346, 1066)(347, 1067)(348, 1068)(349, 1069)(350, 1070)(351, 1071)(352, 1072)(353, 1073)(354, 1074)(355, 1075)(356, 1076)(357, 1077)(358, 1078)(359, 1079)(360, 1080)(361, 1081)(362, 1082)(363, 1083)(364, 1084)(365, 1085)(366, 1086)(367, 1087)(368, 1088)(369, 1089)(370, 1090)(371, 1091)(372, 1092)(373, 1093)(374, 1094)(375, 1095)(376, 1096)(377, 1097)(378, 1098)(379, 1099)(380, 1100)(381, 1101)(382, 1102)(383, 1103)(384, 1104)(385, 1105)(386, 1106)(387, 1107)(388, 1108)(389, 1109)(390, 1110)(391, 1111)(392, 1112)(393, 1113)(394, 1114)(395, 1115)(396, 1116)(397, 1117)(398, 1118)(399, 1119)(400, 1120)(401, 1121)(402, 1122)(403, 1123)(404, 1124)(405, 1125)(406, 1126)(407, 1127)(408, 1128)(409, 1129)(410, 1130)(411, 1131)(412, 1132)(413, 1133)(414, 1134)(415, 1135)(416, 1136)(417, 1137)(418, 1138)(419, 1139)(420, 1140)(421, 1141)(422, 1142)(423, 1143)(424, 1144)(425, 1145)(426, 1146)(427, 1147)(428, 1148)(429, 1149)(430, 1150)(431, 1151)(432, 1152)(433, 1153)(434, 1154)(435, 1155)(436, 1156)(437, 1157)(438, 1158)(439, 1159)(440, 1160)(441, 1161)(442, 1162)(443, 1163)(444, 1164)(445, 1165)(446, 1166)(447, 1167)(448, 1168)(449, 1169)(450, 1170)(451, 1171)(452, 1172)(453, 1173)(454, 1174)(455, 1175)(456, 1176)(457, 1177)(458, 1178)(459, 1179)(460, 1180)(461, 1181)(462, 1182)(463, 1183)(464, 1184)(465, 1185)(466, 1186)(467, 1187)(468, 1188)(469, 1189)(470, 1190)(471, 1191)(472, 1192)(473, 1193)(474, 1194)(475, 1195)(476, 1196)(477, 1197)(478, 1198)(479, 1199)(480, 1200)(481, 1201)(482, 1202)(483, 1203)(484, 1204)(485, 1205)(486, 1206)(487, 1207)(488, 1208)(489, 1209)(490, 1210)(491, 1211)(492, 1212)(493, 1213)(494, 1214)(495, 1215)(496, 1216)(497, 1217)(498, 1218)(499, 1219)(500, 1220)(501, 1221)(502, 1222)(503, 1223)(504, 1224)(505, 1225)(506, 1226)(507, 1227)(508, 1228)(509, 1229)(510, 1230)(511, 1231)(512, 1232)(513, 1233)(514, 1234)(515, 1235)(516, 1236)(517, 1237)(518, 1238)(519, 1239)(520, 1240)(521, 1241)(522, 1242)(523, 1243)(524, 1244)(525, 1245)(526, 1246)(527, 1247)(528, 1248)(529, 1249)(530, 1250)(531, 1251)(532, 1252)(533, 1253)(534, 1254)(535, 1255)(536, 1256)(537, 1257)(538, 1258)(539, 1259)(540, 1260)(541, 1261)(542, 1262)(543, 1263)(544, 1264)(545, 1265)(546, 1266)(547, 1267)(548, 1268)(549, 1269)(550, 1270)(551, 1271)(552, 1272)(553, 1273)(554, 1274)(555, 1275)(556, 1276)(557, 1277)(558, 1278)(559, 1279)(560, 1280)(561, 1281)(562, 1282)(563, 1283)(564, 1284)(565, 1285)(566, 1286)(567, 1287)(568, 1288)(569, 1289)(570, 1290)(571, 1291)(572, 1292)(573, 1293)(574, 1294)(575, 1295)(576, 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1387)(668, 1388)(669, 1389)(670, 1390)(671, 1391)(672, 1392)(673, 1393)(674, 1394)(675, 1395)(676, 1396)(677, 1397)(678, 1398)(679, 1399)(680, 1400)(681, 1401)(682, 1402)(683, 1403)(684, 1404)(685, 1405)(686, 1406)(687, 1407)(688, 1408)(689, 1409)(690, 1410)(691, 1411)(692, 1412)(693, 1413)(694, 1414)(695, 1415)(696, 1416)(697, 1417)(698, 1418)(699, 1419)(700, 1420)(701, 1421)(702, 1422)(703, 1423)(704, 1424)(705, 1425)(706, 1426)(707, 1427)(708, 1428)(709, 1429)(710, 1430)(711, 1431)(712, 1432)(713, 1433)(714, 1434)(715, 1435)(716, 1436)(717, 1437)(718, 1438)(719, 1439)(720, 1440)(1441, 2161, 1442, 2162)(1443, 2163, 1447, 2167)(1444, 2164, 1449, 2169)(1445, 2165, 1451, 2171)(1446, 2166, 1453, 2173)(1448, 2168, 1456, 2176)(1450, 2170, 1459, 2179)(1452, 2172, 1462, 2182)(1454, 2174, 1465, 2185)(1455, 2175, 1467, 2187)(1457, 2177, 1470, 2190)(1458, 2178, 1472, 2192)(1460, 2180, 1475, 2195)(1461, 2181, 1476, 2196)(1463, 2183, 1479, 2199)(1464, 2184, 1481, 2201)(1466, 2186, 1484, 2204)(1468, 2188, 1486, 2206)(1469, 2189, 1488, 2208)(1471, 2191, 1491, 2211)(1473, 2193, 1493, 2213)(1474, 2194, 1495, 2215)(1477, 2197, 1499, 2219)(1478, 2198, 1501, 2221)(1480, 2200, 1504, 2224)(1482, 2202, 1506, 2226)(1483, 2203, 1508, 2228)(1485, 2205, 1511, 2231)(1487, 2207, 1514, 2234)(1489, 2209, 1516, 2236)(1490, 2210, 1518, 2238)(1492, 2212, 1521, 2241)(1494, 2214, 1524, 2244)(1496, 2216, 1526, 2246)(1497, 2217, 1520, 2240)(1498, 2218, 1529, 2249)(1500, 2220, 1532, 2252)(1502, 2222, 1534, 2254)(1503, 2223, 1536, 2256)(1505, 2225, 1539, 2259)(1507, 2227, 1542, 2262)(1509, 2229, 1544, 2264)(1510, 2230, 1538, 2258)(1512, 2232, 1548, 2268)(1513, 2233, 1550, 2270)(1515, 2235, 1553, 2273)(1517, 2237, 1556, 2276)(1519, 2239, 1558, 2278)(1522, 2242, 1562, 2282)(1523, 2243, 1564, 2284)(1525, 2245, 1567, 2287)(1527, 2247, 1570, 2290)(1528, 2248, 1571, 2291)(1530, 2250, 1574, 2294)(1531, 2251, 1576, 2296)(1533, 2253, 1579, 2299)(1535, 2255, 1582, 2302)(1537, 2257, 1584, 2304)(1540, 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2598)(1758, 2478, 1880, 2600)(1761, 2481, 1884, 2604)(1764, 2484, 1886, 2606)(1766, 2486, 1889, 2609)(1768, 2488, 1892, 2612)(1769, 2489, 1893, 2613)(1771, 2491, 1896, 2616)(1772, 2492, 1888, 2608)(1773, 2493, 1899, 2619)(1775, 2495, 1901, 2621)(1777, 2497, 1904, 2624)(1778, 2498, 1905, 2625)(1779, 2499, 1907, 2627)(1781, 2501, 1910, 2630)(1783, 2503, 1912, 2632)(1784, 2504, 1900, 2620)(1785, 2505, 1915, 2635)(1787, 2507, 1918, 2638)(1789, 2509, 1920, 2640)(1792, 2512, 1923, 2643)(1793, 2513, 1925, 2645)(1796, 2516, 1929, 2649)(1798, 2518, 1908, 2628)(1799, 2519, 1931, 2651)(1801, 2521, 1934, 2654)(1803, 2523, 1937, 2657)(1804, 2524, 1938, 2658)(1806, 2526, 1941, 2661)(1807, 2527, 1933, 2653)(1808, 2528, 1944, 2664)(1810, 2530, 1946, 2666)(1812, 2532, 1949, 2669)(1813, 2533, 1950, 2670)(1814, 2534, 1940, 2660)(1816, 2536, 1953, 2673)(1818, 2538, 1955, 2675)(1819, 2539, 1945, 2665)(1820, 2540, 1958, 2678)(1822, 2542, 1961, 2681)(1824, 2544, 1963, 2683)(1827, 2547, 1935, 2655)(1828, 2548, 1966, 2686)(1831, 2551, 1970, 2690)(1832, 2552, 1922, 2642)(1834, 2554, 1972, 2692)(1835, 2555, 1973, 2693)(1836, 2556, 1975, 2695)(1838, 2558, 1977, 2697)(1840, 2560, 1980, 2700)(1841, 2561, 1981, 2701)(1842, 2562, 1983, 2703)(1844, 2564, 1986, 2706)(1846, 2566, 1988, 2708)(1847, 2567, 1976, 2696)(1848, 2568, 1991, 2711)(1850, 2570, 1994, 2714)(1852, 2572, 1996, 2716)(1855, 2575, 1999, 2719)(1856, 2576, 2001, 2721)(1859, 2579, 2005, 2725)(1861, 2581, 1984, 2704)(1862, 2582, 2007, 2727)(1864, 2584, 2010, 2730)(1866, 2586, 2013, 2733)(1867, 2587, 2014, 2734)(1869, 2589, 2017, 2737)(1870, 2590, 2009, 2729)(1871, 2591, 2020, 2740)(1873, 2593, 2022, 2742)(1875, 2595, 2025, 2745)(1876, 2596, 2026, 2746)(1877, 2597, 2016, 2736)(1879, 2599, 2029, 2749)(1881, 2601, 2031, 2751)(1882, 2602, 2021, 2741)(1883, 2603, 2034, 2754)(1885, 2605, 2037, 2757)(1887, 2607, 2039, 2759)(1890, 2610, 2011, 2731)(1891, 2611, 2042, 2762)(1894, 2614, 2046, 2766)(1895, 2615, 1998, 2718)(1897, 2617, 2048, 2768)(1898, 2618, 2049, 2769)(1902, 2622, 2054, 2774)(1903, 2623, 2055, 2775)(1906, 2626, 1997, 2717)(1909, 2629, 2059, 2779)(1911, 2631, 2061, 2781)(1913, 2633, 2012, 2732)(1914, 2634, 2064, 2784)(1916, 2636, 2003, 2723)(1917, 2637, 1993, 2713)(1919, 2639, 2067, 2787)(1921, 2641, 1982, 2702)(1924, 2644, 2008, 2728)(1926, 2646, 2073, 2793)(1927, 2647, 1992, 2712)(1928, 2648, 2076, 2796)(1930, 2650, 2006, 2726)(1932, 2652, 2000, 2720)(1936, 2656, 1989, 2709)(1939, 2659, 2080, 2800)(1942, 2662, 2018, 2738)(1943, 2663, 2041, 2761)(1947, 2667, 2082, 2802)(1948, 2668, 2083, 2803)(1951, 2671, 2040, 2760)(1952, 2672, 2085, 2805)(1954, 2674, 2086, 2806)(1956, 2676, 2047, 2767)(1957, 2677, 2088, 2808)(1959, 2679, 2044, 2764)(1960, 2680, 2036, 2756)(1962, 2682, 2065, 2785)(1964, 2684, 2027, 2747)(1965, 2685, 2019, 2739)(1967, 2687, 2092, 2812)(1968, 2688, 2035, 2755)(1969, 2689, 2093, 2813)(1971, 2691, 2032, 2752)(1974, 2694, 2094, 2814)(1978, 2698, 2098, 2818)(1979, 2699, 2099, 2819)(1985, 2705, 2103, 2823)(1987, 2707, 2105, 2825)(1990, 2710, 2108, 2828)(1995, 2715, 2111, 2831)(2002, 2722, 2117, 2837)(2004, 2724, 2120, 2840)(2015, 2735, 2124, 2844)(2023, 2743, 2126, 2846)(2024, 2744, 2127, 2847)(2028, 2748, 2129, 2849)(2030, 2750, 2130, 2850)(2033, 2753, 2132, 2852)(2038, 2758, 2109, 2829)(2043, 2763, 2136, 2856)(2045, 2765, 2137, 2857)(2050, 2770, 2138, 2858)(2051, 2771, 2101, 2821)(2052, 2772, 2135, 2855)(2053, 2773, 2133, 2853)(2056, 2776, 2140, 2860)(2057, 2777, 2095, 2815)(2058, 2778, 2114, 2834)(2060, 2780, 2115, 2835)(2062, 2782, 2113, 2833)(2063, 2783, 2123, 2843)(2066, 2786, 2119, 2839)(2068, 2788, 2112, 2832)(2069, 2789, 2106, 2826)(2070, 2790, 2102, 2822)(2071, 2791, 2104, 2824)(2072, 2792, 2143, 2863)(2074, 2794, 2131, 2851)(2075, 2795, 2110, 2830)(2077, 2797, 2128, 2848)(2078, 2798, 2125, 2845)(2079, 2799, 2107, 2827)(2081, 2801, 2122, 2842)(2084, 2804, 2121, 2841)(2087, 2807, 2118, 2838)(2089, 2809, 2097, 2817)(2090, 2810, 2134, 2854)(2091, 2811, 2096, 2816)(2100, 2820, 2149, 2869)(2116, 2836, 2152, 2872)(2139, 2859, 2157, 2877)(2141, 2861, 2154, 2874)(2142, 2862, 2156, 2876)(2144, 2864, 2155, 2875)(2145, 2865, 2150, 2870)(2146, 2866, 2153, 2873)(2147, 2867, 2151, 2871)(2148, 2868, 2159, 2879)(2158, 2878, 2160, 2880) L = (1, 1443)(2, 1445)(3, 1448)(4, 1441)(5, 1452)(6, 1442)(7, 1453)(8, 1457)(9, 1458)(10, 1444)(11, 1449)(12, 1463)(13, 1464)(14, 1446)(15, 1447)(16, 1467)(17, 1471)(18, 1473)(19, 1474)(20, 1450)(21, 1451)(22, 1476)(23, 1480)(24, 1482)(25, 1483)(26, 1454)(27, 1485)(28, 1455)(29, 1456)(30, 1488)(31, 1460)(32, 1459)(33, 1494)(34, 1496)(35, 1497)(36, 1498)(37, 1461)(38, 1462)(39, 1501)(40, 1466)(41, 1465)(42, 1507)(43, 1509)(44, 1510)(45, 1512)(46, 1513)(47, 1468)(48, 1515)(49, 1469)(50, 1470)(51, 1518)(52, 1472)(53, 1521)(54, 1500)(55, 1475)(56, 1527)(57, 1528)(58, 1530)(59, 1531)(60, 1477)(61, 1533)(62, 1478)(63, 1479)(64, 1536)(65, 1481)(66, 1539)(67, 1487)(68, 1484)(69, 1545)(70, 1546)(71, 1486)(72, 1549)(73, 1551)(74, 1552)(75, 1554)(76, 1555)(77, 1489)(78, 1557)(79, 1490)(80, 1491)(81, 1561)(82, 1492)(83, 1493)(84, 1564)(85, 1495)(86, 1567)(87, 1563)(88, 1572)(89, 1499)(90, 1575)(91, 1577)(92, 1578)(93, 1580)(94, 1581)(95, 1502)(96, 1583)(97, 1503)(98, 1504)(99, 1587)(100, 1505)(101, 1506)(102, 1590)(103, 1508)(104, 1593)(105, 1589)(106, 1598)(107, 1511)(108, 1599)(109, 1517)(110, 1514)(111, 1605)(112, 1606)(113, 1516)(114, 1609)(115, 1611)(116, 1612)(117, 1614)(118, 1615)(119, 1519)(120, 1520)(121, 1620)(122, 1621)(123, 1522)(124, 1623)(125, 1523)(126, 1524)(127, 1627)(128, 1525)(129, 1526)(130, 1630)(131, 1617)(132, 1629)(133, 1529)(134, 1635)(135, 1535)(136, 1532)(137, 1641)(138, 1642)(139, 1534)(140, 1645)(141, 1647)(142, 1648)(143, 1650)(144, 1651)(145, 1537)(146, 1538)(147, 1656)(148, 1657)(149, 1540)(150, 1659)(151, 1541)(152, 1542)(153, 1663)(154, 1543)(155, 1544)(156, 1666)(157, 1653)(158, 1665)(159, 1671)(160, 1547)(161, 1548)(162, 1674)(163, 1550)(164, 1677)(165, 1673)(166, 1682)(167, 1553)(168, 1683)(169, 1559)(170, 1556)(171, 1689)(172, 1690)(173, 1558)(174, 1693)(175, 1695)(176, 1696)(177, 1697)(178, 1560)(179, 1562)(180, 1701)(181, 1703)(182, 1704)(183, 1706)(184, 1707)(185, 1565)(186, 1566)(187, 1712)(188, 1713)(189, 1568)(190, 1715)(191, 1569)(192, 1570)(193, 1571)(194, 1719)(195, 1722)(196, 1573)(197, 1574)(198, 1725)(199, 1576)(200, 1728)(201, 1724)(202, 1733)(203, 1579)(204, 1734)(205, 1585)(206, 1582)(207, 1740)(208, 1741)(209, 1584)(210, 1744)(211, 1746)(212, 1747)(213, 1748)(214, 1586)(215, 1588)(216, 1752)(217, 1754)(218, 1755)(219, 1757)(220, 1758)(221, 1591)(222, 1592)(223, 1763)(224, 1764)(225, 1594)(226, 1766)(227, 1595)(228, 1596)(229, 1597)(230, 1770)(231, 1723)(232, 1773)(233, 1600)(234, 1775)(235, 1601)(236, 1602)(237, 1779)(238, 1603)(239, 1604)(240, 1782)(241, 1760)(242, 1781)(243, 1762)(244, 1607)(245, 1608)(246, 1788)(247, 1610)(248, 1791)(249, 1787)(250, 1796)(251, 1613)(252, 1797)(253, 1618)(254, 1616)(255, 1803)(256, 1804)(257, 1806)(258, 1807)(259, 1619)(260, 1750)(261, 1625)(262, 1622)(263, 1812)(264, 1813)(265, 1624)(266, 1816)(267, 1818)(268, 1819)(269, 1820)(270, 1626)(271, 1628)(272, 1822)(273, 1824)(274, 1825)(275, 1827)(276, 1828)(277, 1631)(278, 1632)(279, 1832)(280, 1633)(281, 1634)(282, 1672)(283, 1836)(284, 1636)(285, 1838)(286, 1637)(287, 1638)(288, 1842)(289, 1639)(290, 1640)(291, 1845)(292, 1709)(293, 1844)(294, 1711)(295, 1643)(296, 1644)(297, 1851)(298, 1646)(299, 1854)(300, 1850)(301, 1859)(302, 1649)(303, 1860)(304, 1654)(305, 1652)(306, 1866)(307, 1867)(308, 1869)(309, 1870)(310, 1655)(311, 1699)(312, 1661)(313, 1658)(314, 1875)(315, 1876)(316, 1660)(317, 1879)(318, 1881)(319, 1882)(320, 1883)(321, 1662)(322, 1664)(323, 1885)(324, 1887)(325, 1888)(326, 1890)(327, 1891)(328, 1667)(329, 1668)(330, 1895)(331, 1669)(332, 1670)(333, 1840)(334, 1900)(335, 1902)(336, 1903)(337, 1675)(338, 1676)(339, 1908)(340, 1909)(341, 1678)(342, 1911)(343, 1679)(344, 1680)(345, 1681)(346, 1915)(347, 1684)(348, 1919)(349, 1685)(350, 1686)(351, 1922)(352, 1687)(353, 1688)(354, 1925)(355, 1905)(356, 1924)(357, 1907)(358, 1691)(359, 1692)(360, 1931)(361, 1694)(362, 1934)(363, 1930)(364, 1939)(365, 1698)(366, 1942)(367, 1943)(368, 1700)(369, 1944)(370, 1702)(371, 1946)(372, 1871)(373, 1951)(374, 1705)(375, 1940)(376, 1710)(377, 1708)(378, 1956)(379, 1957)(380, 1959)(381, 1960)(382, 1717)(383, 1714)(384, 1852)(385, 1964)(386, 1716)(387, 1965)(388, 1967)(389, 1968)(390, 1969)(391, 1718)(392, 1923)(393, 1971)(394, 1720)(395, 1721)(396, 1777)(397, 1976)(398, 1978)(399, 1979)(400, 1726)(401, 1727)(402, 1984)(403, 1985)(404, 1729)(405, 1987)(406, 1730)(407, 1731)(408, 1732)(409, 1991)(410, 1735)(411, 1995)(412, 1736)(413, 1737)(414, 1998)(415, 1738)(416, 1739)(417, 2001)(418, 1981)(419, 2000)(420, 1983)(421, 1742)(422, 1743)(423, 2007)(424, 1745)(425, 2010)(426, 2006)(427, 2015)(428, 1749)(429, 2018)(430, 2019)(431, 1751)(432, 2020)(433, 1753)(434, 2022)(435, 1808)(436, 2027)(437, 1756)(438, 2016)(439, 1761)(440, 1759)(441, 2032)(442, 2033)(443, 2035)(444, 2036)(445, 1768)(446, 1765)(447, 1789)(448, 2040)(449, 1767)(450, 2041)(451, 2043)(452, 2044)(453, 2045)(454, 1769)(455, 1999)(456, 2047)(457, 1771)(458, 1772)(459, 1774)(460, 2052)(461, 1776)(462, 2014)(463, 2056)(464, 2057)(465, 2058)(466, 1778)(467, 1780)(468, 2013)(469, 2060)(470, 1993)(471, 2062)(472, 2063)(473, 1783)(474, 1784)(475, 2066)(476, 1785)(477, 1786)(478, 1992)(479, 2068)(480, 2069)(481, 1790)(482, 1833)(483, 2071)(484, 1792)(485, 2072)(486, 1793)(487, 1794)(488, 1795)(489, 2076)(490, 1798)(491, 2005)(492, 1799)(493, 1800)(494, 1826)(495, 1801)(496, 1802)(497, 1989)(498, 1982)(499, 2078)(500, 1805)(501, 1814)(502, 1834)(503, 2081)(504, 2077)(505, 1809)(506, 2075)(507, 1810)(508, 1811)(509, 2083)(510, 1830)(511, 2049)(512, 1815)(513, 2085)(514, 1817)(515, 2086)(516, 2048)(517, 2067)(518, 1821)(519, 2037)(520, 2029)(521, 1994)(522, 1823)(523, 2065)(524, 2091)(525, 1831)(526, 1829)(527, 2079)(528, 2053)(529, 2051)(530, 2009)(531, 2074)(532, 2017)(533, 2023)(534, 1835)(535, 1837)(536, 2096)(537, 1839)(538, 1938)(539, 2100)(540, 2101)(541, 2102)(542, 1841)(543, 1843)(544, 1937)(545, 2104)(546, 1917)(547, 2106)(548, 2107)(549, 1846)(550, 1847)(551, 2110)(552, 1848)(553, 1849)(554, 1916)(555, 2112)(556, 2113)(557, 1853)(558, 1896)(559, 2115)(560, 1855)(561, 2116)(562, 1856)(563, 1857)(564, 1858)(565, 2120)(566, 1861)(567, 1929)(568, 1862)(569, 1863)(570, 1889)(571, 1864)(572, 1865)(573, 1913)(574, 1906)(575, 2122)(576, 1868)(577, 1877)(578, 1897)(579, 2125)(580, 2121)(581, 1872)(582, 2119)(583, 1873)(584, 1874)(585, 2127)(586, 1893)(587, 1973)(588, 1878)(589, 2129)(590, 1880)(591, 2130)(592, 1972)(593, 2111)(594, 1884)(595, 1961)(596, 1953)(597, 1918)(598, 1886)(599, 2109)(600, 2135)(601, 1894)(602, 1892)(603, 2123)(604, 2097)(605, 2095)(606, 1933)(607, 2118)(608, 1941)(609, 1947)(610, 1898)(611, 1899)(612, 1950)(613, 1901)(614, 2133)(615, 1904)(616, 1966)(617, 2141)(618, 1945)(619, 1910)(620, 1932)(621, 1912)(622, 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2160)(714, 2137)(715, 2131)(716, 2136)(717, 2143)(718, 2147)(719, 2152)(720, 2156)(721, 2161)(722, 2162)(723, 2163)(724, 2164)(725, 2165)(726, 2166)(727, 2167)(728, 2168)(729, 2169)(730, 2170)(731, 2171)(732, 2172)(733, 2173)(734, 2174)(735, 2175)(736, 2176)(737, 2177)(738, 2178)(739, 2179)(740, 2180)(741, 2181)(742, 2182)(743, 2183)(744, 2184)(745, 2185)(746, 2186)(747, 2187)(748, 2188)(749, 2189)(750, 2190)(751, 2191)(752, 2192)(753, 2193)(754, 2194)(755, 2195)(756, 2196)(757, 2197)(758, 2198)(759, 2199)(760, 2200)(761, 2201)(762, 2202)(763, 2203)(764, 2204)(765, 2205)(766, 2206)(767, 2207)(768, 2208)(769, 2209)(770, 2210)(771, 2211)(772, 2212)(773, 2213)(774, 2214)(775, 2215)(776, 2216)(777, 2217)(778, 2218)(779, 2219)(780, 2220)(781, 2221)(782, 2222)(783, 2223)(784, 2224)(785, 2225)(786, 2226)(787, 2227)(788, 2228)(789, 2229)(790, 2230)(791, 2231)(792, 2232)(793, 2233)(794, 2234)(795, 2235)(796, 2236)(797, 2237)(798, 2238)(799, 2239)(800, 2240)(801, 2241)(802, 2242)(803, 2243)(804, 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2426)(987, 2427)(988, 2428)(989, 2429)(990, 2430)(991, 2431)(992, 2432)(993, 2433)(994, 2434)(995, 2435)(996, 2436)(997, 2437)(998, 2438)(999, 2439)(1000, 2440)(1001, 2441)(1002, 2442)(1003, 2443)(1004, 2444)(1005, 2445)(1006, 2446)(1007, 2447)(1008, 2448)(1009, 2449)(1010, 2450)(1011, 2451)(1012, 2452)(1013, 2453)(1014, 2454)(1015, 2455)(1016, 2456)(1017, 2457)(1018, 2458)(1019, 2459)(1020, 2460)(1021, 2461)(1022, 2462)(1023, 2463)(1024, 2464)(1025, 2465)(1026, 2466)(1027, 2467)(1028, 2468)(1029, 2469)(1030, 2470)(1031, 2471)(1032, 2472)(1033, 2473)(1034, 2474)(1035, 2475)(1036, 2476)(1037, 2477)(1038, 2478)(1039, 2479)(1040, 2480)(1041, 2481)(1042, 2482)(1043, 2483)(1044, 2484)(1045, 2485)(1046, 2486)(1047, 2487)(1048, 2488)(1049, 2489)(1050, 2490)(1051, 2491)(1052, 2492)(1053, 2493)(1054, 2494)(1055, 2495)(1056, 2496)(1057, 2497)(1058, 2498)(1059, 2499)(1060, 2500)(1061, 2501)(1062, 2502)(1063, 2503)(1064, 2504)(1065, 2505)(1066, 2506)(1067, 2507)(1068, 2508)(1069, 2509)(1070, 2510)(1071, 2511)(1072, 2512)(1073, 2513)(1074, 2514)(1075, 2515)(1076, 2516)(1077, 2517)(1078, 2518)(1079, 2519)(1080, 2520)(1081, 2521)(1082, 2522)(1083, 2523)(1084, 2524)(1085, 2525)(1086, 2526)(1087, 2527)(1088, 2528)(1089, 2529)(1090, 2530)(1091, 2531)(1092, 2532)(1093, 2533)(1094, 2534)(1095, 2535)(1096, 2536)(1097, 2537)(1098, 2538)(1099, 2539)(1100, 2540)(1101, 2541)(1102, 2542)(1103, 2543)(1104, 2544)(1105, 2545)(1106, 2546)(1107, 2547)(1108, 2548)(1109, 2549)(1110, 2550)(1111, 2551)(1112, 2552)(1113, 2553)(1114, 2554)(1115, 2555)(1116, 2556)(1117, 2557)(1118, 2558)(1119, 2559)(1120, 2560)(1121, 2561)(1122, 2562)(1123, 2563)(1124, 2564)(1125, 2565)(1126, 2566)(1127, 2567)(1128, 2568)(1129, 2569)(1130, 2570)(1131, 2571)(1132, 2572)(1133, 2573)(1134, 2574)(1135, 2575)(1136, 2576)(1137, 2577)(1138, 2578)(1139, 2579)(1140, 2580)(1141, 2581)(1142, 2582)(1143, 2583)(1144, 2584)(1145, 2585)(1146, 2586)(1147, 2587)(1148, 2588)(1149, 2589)(1150, 2590)(1151, 2591)(1152, 2592)(1153, 2593)(1154, 2594)(1155, 2595)(1156, 2596)(1157, 2597)(1158, 2598)(1159, 2599)(1160, 2600)(1161, 2601)(1162, 2602)(1163, 2603)(1164, 2604)(1165, 2605)(1166, 2606)(1167, 2607)(1168, 2608)(1169, 2609)(1170, 2610)(1171, 2611)(1172, 2612)(1173, 2613)(1174, 2614)(1175, 2615)(1176, 2616)(1177, 2617)(1178, 2618)(1179, 2619)(1180, 2620)(1181, 2621)(1182, 2622)(1183, 2623)(1184, 2624)(1185, 2625)(1186, 2626)(1187, 2627)(1188, 2628)(1189, 2629)(1190, 2630)(1191, 2631)(1192, 2632)(1193, 2633)(1194, 2634)(1195, 2635)(1196, 2636)(1197, 2637)(1198, 2638)(1199, 2639)(1200, 2640)(1201, 2641)(1202, 2642)(1203, 2643)(1204, 2644)(1205, 2645)(1206, 2646)(1207, 2647)(1208, 2648)(1209, 2649)(1210, 2650)(1211, 2651)(1212, 2652)(1213, 2653)(1214, 2654)(1215, 2655)(1216, 2656)(1217, 2657)(1218, 2658)(1219, 2659)(1220, 2660)(1221, 2661)(1222, 2662)(1223, 2663)(1224, 2664)(1225, 2665)(1226, 2666)(1227, 2667)(1228, 2668)(1229, 2669)(1230, 2670)(1231, 2671)(1232, 2672)(1233, 2673)(1234, 2674)(1235, 2675)(1236, 2676)(1237, 2677)(1238, 2678)(1239, 2679)(1240, 2680)(1241, 2681)(1242, 2682)(1243, 2683)(1244, 2684)(1245, 2685)(1246, 2686)(1247, 2687)(1248, 2688)(1249, 2689)(1250, 2690)(1251, 2691)(1252, 2692)(1253, 2693)(1254, 2694)(1255, 2695)(1256, 2696)(1257, 2697)(1258, 2698)(1259, 2699)(1260, 2700)(1261, 2701)(1262, 2702)(1263, 2703)(1264, 2704)(1265, 2705)(1266, 2706)(1267, 2707)(1268, 2708)(1269, 2709)(1270, 2710)(1271, 2711)(1272, 2712)(1273, 2713)(1274, 2714)(1275, 2715)(1276, 2716)(1277, 2717)(1278, 2718)(1279, 2719)(1280, 2720)(1281, 2721)(1282, 2722)(1283, 2723)(1284, 2724)(1285, 2725)(1286, 2726)(1287, 2727)(1288, 2728)(1289, 2729)(1290, 2730)(1291, 2731)(1292, 2732)(1293, 2733)(1294, 2734)(1295, 2735)(1296, 2736)(1297, 2737)(1298, 2738)(1299, 2739)(1300, 2740)(1301, 2741)(1302, 2742)(1303, 2743)(1304, 2744)(1305, 2745)(1306, 2746)(1307, 2747)(1308, 2748)(1309, 2749)(1310, 2750)(1311, 2751)(1312, 2752)(1313, 2753)(1314, 2754)(1315, 2755)(1316, 2756)(1317, 2757)(1318, 2758)(1319, 2759)(1320, 2760)(1321, 2761)(1322, 2762)(1323, 2763)(1324, 2764)(1325, 2765)(1326, 2766)(1327, 2767)(1328, 2768)(1329, 2769)(1330, 2770)(1331, 2771)(1332, 2772)(1333, 2773)(1334, 2774)(1335, 2775)(1336, 2776)(1337, 2777)(1338, 2778)(1339, 2779)(1340, 2780)(1341, 2781)(1342, 2782)(1343, 2783)(1344, 2784)(1345, 2785)(1346, 2786)(1347, 2787)(1348, 2788)(1349, 2789)(1350, 2790)(1351, 2791)(1352, 2792)(1353, 2793)(1354, 2794)(1355, 2795)(1356, 2796)(1357, 2797)(1358, 2798)(1359, 2799)(1360, 2800)(1361, 2801)(1362, 2802)(1363, 2803)(1364, 2804)(1365, 2805)(1366, 2806)(1367, 2807)(1368, 2808)(1369, 2809)(1370, 2810)(1371, 2811)(1372, 2812)(1373, 2813)(1374, 2814)(1375, 2815)(1376, 2816)(1377, 2817)(1378, 2818)(1379, 2819)(1380, 2820)(1381, 2821)(1382, 2822)(1383, 2823)(1384, 2824)(1385, 2825)(1386, 2826)(1387, 2827)(1388, 2828)(1389, 2829)(1390, 2830)(1391, 2831)(1392, 2832)(1393, 2833)(1394, 2834)(1395, 2835)(1396, 2836)(1397, 2837)(1398, 2838)(1399, 2839)(1400, 2840)(1401, 2841)(1402, 2842)(1403, 2843)(1404, 2844)(1405, 2845)(1406, 2846)(1407, 2847)(1408, 2848)(1409, 2849)(1410, 2850)(1411, 2851)(1412, 2852)(1413, 2853)(1414, 2854)(1415, 2855)(1416, 2856)(1417, 2857)(1418, 2858)(1419, 2859)(1420, 2860)(1421, 2861)(1422, 2862)(1423, 2863)(1424, 2864)(1425, 2865)(1426, 2866)(1427, 2867)(1428, 2868)(1429, 2869)(1430, 2870)(1431, 2871)(1432, 2872)(1433, 2873)(1434, 2874)(1435, 2875)(1436, 2876)(1437, 2877)(1438, 2878)(1439, 2879)(1440, 2880) local type(s) :: { ( 6, 16 ), ( 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E16.1308 Graph:: simple bipartite v = 1080 e = 1440 f = 330 degree seq :: [ 2^720, 4^360 ] E16.1310 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8}) Quotient :: dipole Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |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)^3, Y1^8, Y1^-3 * Y3 * Y1^-2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-2 * Y3, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-2 * Y3 * Y1^-3 * Y3 * Y1^-2, Y3 * Y1^3 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-3 * Y3 * Y1^3 * Y3 * Y1^-2 ] Map:: polytopal R = (1, 721, 2, 722, 5, 725, 11, 731, 21, 741, 20, 740, 10, 730, 4, 724)(3, 723, 7, 727, 15, 735, 27, 747, 45, 765, 31, 751, 17, 737, 8, 728)(6, 726, 13, 733, 25, 745, 41, 761, 66, 786, 44, 764, 26, 746, 14, 734)(9, 729, 18, 738, 32, 752, 52, 772, 77, 797, 49, 769, 29, 749, 16, 736)(12, 732, 23, 743, 39, 759, 62, 782, 95, 815, 65, 785, 40, 760, 24, 744)(19, 739, 34, 754, 55, 775, 85, 805, 126, 846, 84, 804, 54, 774, 33, 753)(22, 742, 37, 757, 60, 780, 91, 811, 137, 857, 94, 814, 61, 781, 38, 758)(28, 748, 47, 767, 74, 794, 111, 831, 165, 885, 114, 834, 75, 795, 48, 768)(30, 750, 50, 770, 78, 798, 117, 837, 154, 874, 103, 823, 68, 788, 42, 762)(35, 755, 57, 777, 88, 808, 131, 851, 192, 912, 130, 850, 87, 807, 56, 776)(36, 756, 58, 778, 89, 809, 133, 853, 195, 915, 136, 856, 90, 810, 59, 779)(43, 763, 69, 789, 104, 824, 155, 875, 212, 932, 145, 865, 97, 817, 63, 783)(46, 766, 72, 792, 109, 829, 161, 881, 235, 955, 164, 884, 110, 830, 73, 793)(51, 771, 80, 800, 120, 840, 177, 897, 256, 976, 176, 896, 119, 839, 79, 799)(53, 773, 82, 802, 123, 843, 181, 901, 263, 983, 184, 904, 124, 844, 83, 803)(64, 784, 98, 818, 146, 866, 213, 933, 294, 1014, 203, 923, 139, 859, 92, 812)(67, 787, 101, 821, 151, 871, 219, 939, 317, 1037, 222, 942, 152, 872, 102, 822)(70, 790, 106, 826, 158, 878, 229, 949, 330, 1050, 228, 948, 157, 877, 105, 825)(71, 791, 107, 827, 159, 879, 231, 951, 333, 1053, 234, 954, 160, 880, 108, 828)(76, 796, 115, 835, 170, 890, 247, 967, 348, 1068, 243, 963, 167, 887, 112, 832)(81, 801, 121, 841, 179, 899, 259, 979, 368, 1088, 262, 982, 180, 900, 122, 842)(86, 806, 128, 848, 189, 909, 273, 993, 386, 1106, 276, 996, 190, 910, 129, 849)(93, 813, 140, 860, 204, 924, 295, 1015, 401, 1121, 285, 1005, 197, 917, 134, 854)(96, 816, 143, 863, 209, 929, 301, 1021, 422, 1142, 304, 1024, 210, 930, 144, 864)(99, 819, 148, 868, 216, 936, 311, 1031, 433, 1153, 310, 1030, 215, 935, 147, 867)(100, 820, 149, 869, 217, 937, 313, 1033, 436, 1156, 316, 1036, 218, 938, 150, 870)(113, 833, 168, 888, 244, 964, 349, 1069, 469, 1189, 341, 1061, 237, 957, 162, 882)(116, 836, 172, 892, 250, 970, 357, 1077, 489, 1209, 356, 1076, 249, 969, 171, 891)(118, 838, 174, 894, 253, 973, 293, 1013, 410, 1130, 362, 1082, 254, 974, 175, 895)(125, 845, 185, 905, 268, 988, 378, 1098, 442, 1162, 318, 1038, 265, 985, 182, 902)(127, 847, 187, 907, 271, 991, 382, 1102, 521, 1241, 385, 1105, 272, 992, 188, 908)(132, 852, 135, 855, 198, 918, 286, 1006, 402, 1122, 395, 1115, 281, 1001, 194, 914)(138, 858, 201, 921, 291, 1011, 255, 975, 363, 1083, 409, 1129, 292, 1012, 202, 922)(141, 861, 206, 926, 298, 1018, 416, 1136, 556, 1276, 415, 1135, 297, 1017, 205, 925)(142, 862, 207, 927, 299, 1019, 418, 1138, 559, 1279, 421, 1141, 300, 1020, 208, 928)(153, 873, 223, 943, 322, 1042, 446, 1166, 374, 1094, 264, 984, 319, 1039, 220, 940)(156, 876, 226, 946, 327, 1047, 400, 1120, 539, 1259, 453, 1173, 328, 1048, 227, 947)(163, 883, 238, 958, 342, 1062, 470, 1190, 540, 1260, 462, 1182, 335, 1055, 232, 952)(166, 886, 241, 961, 302, 1022, 211, 931, 305, 1025, 425, 1145, 347, 1067, 242, 962)(169, 889, 246, 966, 352, 1072, 482, 1202, 537, 1257, 481, 1201, 351, 1071, 245, 965)(173, 893, 251, 971, 359, 1079, 492, 1212, 544, 1264, 495, 1215, 360, 1080, 252, 972)(178, 898, 233, 953, 336, 1056, 463, 1183, 541, 1261, 503, 1223, 367, 1087, 258, 978)(183, 903, 266, 986, 375, 1095, 511, 1231, 542, 1262, 403, 1123, 370, 1090, 260, 980)(186, 906, 270, 990, 381, 1101, 519, 1239, 639, 1359, 518, 1238, 380, 1100, 269, 989)(191, 911, 277, 997, 389, 1109, 468, 1188, 340, 1060, 236, 956, 339, 1059, 274, 994)(193, 913, 279, 999, 392, 1112, 432, 1152, 575, 1295, 532, 1252, 393, 1113, 280, 1000)(196, 916, 283, 1003, 398, 1118, 329, 1049, 454, 1174, 538, 1258, 399, 1119, 284, 1004)(199, 919, 288, 1008, 405, 1125, 543, 1263, 505, 1225, 369, 1089, 404, 1124, 287, 1007)(200, 920, 289, 1009, 406, 1126, 545, 1265, 659, 1379, 548, 1268, 407, 1127, 290, 1010)(214, 934, 308, 1028, 430, 1150, 394, 1114, 533, 1253, 574, 1294, 431, 1151, 309, 1029)(221, 941, 320, 1040, 443, 1163, 589, 1309, 534, 1254, 583, 1303, 438, 1158, 314, 1034)(224, 944, 324, 1044, 449, 1169, 597, 1317, 531, 1251, 596, 1316, 448, 1168, 323, 1043)(225, 945, 325, 1045, 450, 1170, 599, 1319, 528, 1248, 602, 1322, 451, 1171, 326, 1046)(230, 950, 315, 1035, 439, 1159, 584, 1304, 524, 1244, 610, 1330, 458, 1178, 332, 1052)(239, 959, 344, 1064, 473, 1193, 618, 1338, 658, 1378, 617, 1337, 472, 1192, 343, 1063)(240, 960, 345, 1065, 474, 1194, 558, 1278, 417, 1137, 547, 1267, 475, 1195, 346, 1066)(248, 968, 354, 1074, 486, 1206, 554, 1274, 412, 1132, 553, 1273, 487, 1207, 355, 1075)(257, 977, 365, 1085, 500, 1220, 626, 1346, 657, 1377, 640, 1360, 501, 1221, 366, 1086)(261, 981, 371, 1091, 506, 1226, 551, 1271, 411, 1131, 552, 1272, 491, 1211, 358, 1078)(267, 987, 377, 1097, 514, 1234, 546, 1266, 408, 1128, 549, 1269, 513, 1233, 376, 1096)(275, 995, 387, 1107, 525, 1245, 555, 1275, 414, 1134, 296, 1016, 413, 1133, 383, 1103)(278, 998, 391, 1111, 530, 1250, 653, 1373, 704, 1424, 652, 1372, 529, 1249, 390, 1110)(282, 1002, 396, 1116, 535, 1255, 655, 1375, 708, 1428, 656, 1376, 536, 1256, 397, 1117)(303, 1023, 423, 1143, 565, 1285, 526, 1246, 388, 1108, 527, 1247, 561, 1281, 419, 1139)(306, 1026, 427, 1147, 570, 1290, 520, 1240, 384, 1104, 522, 1242, 569, 1289, 426, 1146)(307, 1027, 428, 1148, 571, 1291, 517, 1237, 379, 1099, 516, 1236, 572, 1292, 429, 1149)(312, 1032, 420, 1140, 562, 1282, 510, 1230, 373, 1093, 509, 1229, 579, 1299, 435, 1155)(321, 1041, 445, 1165, 592, 1312, 688, 1408, 615, 1335, 687, 1407, 591, 1311, 444, 1164)(331, 1051, 456, 1176, 607, 1327, 692, 1412, 654, 1374, 698, 1418, 608, 1328, 457, 1177)(334, 1054, 460, 1180, 612, 1332, 488, 1208, 631, 1351, 682, 1402, 576, 1296, 461, 1181)(337, 1057, 465, 1185, 613, 1333, 665, 1385, 582, 1302, 437, 1157, 581, 1301, 464, 1184)(338, 1058, 466, 1186, 614, 1334, 660, 1380, 646, 1366, 670, 1390, 563, 1283, 467, 1187)(350, 1070, 479, 1199, 624, 1344, 502, 1222, 641, 1361, 702, 1422, 625, 1345, 480, 1200)(353, 1073, 484, 1204, 628, 1348, 662, 1382, 550, 1270, 663, 1383, 629, 1349, 485, 1205)(361, 1081, 496, 1216, 634, 1354, 696, 1416, 604, 1324, 471, 1191, 616, 1336, 493, 1213)(364, 1084, 499, 1219, 638, 1358, 677, 1397, 601, 1321, 694, 1414, 637, 1357, 498, 1218)(372, 1092, 508, 1228, 580, 1300, 667, 1387, 557, 1277, 666, 1386, 643, 1363, 507, 1227)(424, 1144, 567, 1287, 674, 1394, 648, 1368, 515, 1235, 647, 1367, 673, 1393, 566, 1286)(434, 1154, 577, 1297, 683, 1403, 650, 1370, 523, 1243, 611, 1331, 459, 1179, 578, 1298)(440, 1160, 586, 1306, 504, 1224, 642, 1362, 669, 1389, 560, 1280, 668, 1388, 585, 1305)(441, 1161, 587, 1307, 685, 1405, 627, 1347, 483, 1203, 620, 1340, 661, 1381, 588, 1308)(447, 1167, 594, 1314, 690, 1410, 609, 1329, 478, 1198, 623, 1343, 691, 1411, 595, 1315)(452, 1172, 603, 1323, 695, 1415, 714, 1434, 681, 1401, 590, 1310, 686, 1406, 600, 1320)(455, 1175, 606, 1326, 490, 1210, 632, 1352, 679, 1399, 649, 1369, 697, 1417, 605, 1325)(476, 1196, 621, 1341, 700, 1420, 635, 1355, 497, 1217, 636, 1356, 699, 1419, 619, 1339)(477, 1197, 622, 1342, 693, 1413, 598, 1318, 494, 1214, 633, 1353, 671, 1391, 564, 1284)(512, 1232, 644, 1364, 703, 1423, 630, 1350, 664, 1384, 709, 1429, 706, 1426, 645, 1365)(568, 1288, 675, 1395, 711, 1431, 684, 1404, 593, 1313, 689, 1409, 712, 1432, 676, 1396)(573, 1293, 680, 1400, 713, 1433, 707, 1427, 651, 1371, 672, 1392, 710, 1430, 678, 1398)(701, 1421, 718, 1438, 720, 1440, 716, 1436, 705, 1425, 717, 1437, 719, 1439, 715, 1435)(1441, 2161)(1442, 2162)(1443, 2163)(1444, 2164)(1445, 2165)(1446, 2166)(1447, 2167)(1448, 2168)(1449, 2169)(1450, 2170)(1451, 2171)(1452, 2172)(1453, 2173)(1454, 2174)(1455, 2175)(1456, 2176)(1457, 2177)(1458, 2178)(1459, 2179)(1460, 2180)(1461, 2181)(1462, 2182)(1463, 2183)(1464, 2184)(1465, 2185)(1466, 2186)(1467, 2187)(1468, 2188)(1469, 2189)(1470, 2190)(1471, 2191)(1472, 2192)(1473, 2193)(1474, 2194)(1475, 2195)(1476, 2196)(1477, 2197)(1478, 2198)(1479, 2199)(1480, 2200)(1481, 2201)(1482, 2202)(1483, 2203)(1484, 2204)(1485, 2205)(1486, 2206)(1487, 2207)(1488, 2208)(1489, 2209)(1490, 2210)(1491, 2211)(1492, 2212)(1493, 2213)(1494, 2214)(1495, 2215)(1496, 2216)(1497, 2217)(1498, 2218)(1499, 2219)(1500, 2220)(1501, 2221)(1502, 2222)(1503, 2223)(1504, 2224)(1505, 2225)(1506, 2226)(1507, 2227)(1508, 2228)(1509, 2229)(1510, 2230)(1511, 2231)(1512, 2232)(1513, 2233)(1514, 2234)(1515, 2235)(1516, 2236)(1517, 2237)(1518, 2238)(1519, 2239)(1520, 2240)(1521, 2241)(1522, 2242)(1523, 2243)(1524, 2244)(1525, 2245)(1526, 2246)(1527, 2247)(1528, 2248)(1529, 2249)(1530, 2250)(1531, 2251)(1532, 2252)(1533, 2253)(1534, 2254)(1535, 2255)(1536, 2256)(1537, 2257)(1538, 2258)(1539, 2259)(1540, 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2426)(1707, 2427)(1708, 2428)(1709, 2429)(1710, 2430)(1711, 2431)(1712, 2432)(1713, 2433)(1714, 2434)(1715, 2435)(1716, 2436)(1717, 2437)(1718, 2438)(1719, 2439)(1720, 2440)(1721, 2441)(1722, 2442)(1723, 2443)(1724, 2444)(1725, 2445)(1726, 2446)(1727, 2447)(1728, 2448)(1729, 2449)(1730, 2450)(1731, 2451)(1732, 2452)(1733, 2453)(1734, 2454)(1735, 2455)(1736, 2456)(1737, 2457)(1738, 2458)(1739, 2459)(1740, 2460)(1741, 2461)(1742, 2462)(1743, 2463)(1744, 2464)(1745, 2465)(1746, 2466)(1747, 2467)(1748, 2468)(1749, 2469)(1750, 2470)(1751, 2471)(1752, 2472)(1753, 2473)(1754, 2474)(1755, 2475)(1756, 2476)(1757, 2477)(1758, 2478)(1759, 2479)(1760, 2480)(1761, 2481)(1762, 2482)(1763, 2483)(1764, 2484)(1765, 2485)(1766, 2486)(1767, 2487)(1768, 2488)(1769, 2489)(1770, 2490)(1771, 2491)(1772, 2492)(1773, 2493)(1774, 2494)(1775, 2495)(1776, 2496)(1777, 2497)(1778, 2498)(1779, 2499)(1780, 2500)(1781, 2501)(1782, 2502)(1783, 2503)(1784, 2504)(1785, 2505)(1786, 2506)(1787, 2507)(1788, 2508)(1789, 2509)(1790, 2510)(1791, 2511)(1792, 2512)(1793, 2513)(1794, 2514)(1795, 2515)(1796, 2516)(1797, 2517)(1798, 2518)(1799, 2519)(1800, 2520)(1801, 2521)(1802, 2522)(1803, 2523)(1804, 2524)(1805, 2525)(1806, 2526)(1807, 2527)(1808, 2528)(1809, 2529)(1810, 2530)(1811, 2531)(1812, 2532)(1813, 2533)(1814, 2534)(1815, 2535)(1816, 2536)(1817, 2537)(1818, 2538)(1819, 2539)(1820, 2540)(1821, 2541)(1822, 2542)(1823, 2543)(1824, 2544)(1825, 2545)(1826, 2546)(1827, 2547)(1828, 2548)(1829, 2549)(1830, 2550)(1831, 2551)(1832, 2552)(1833, 2553)(1834, 2554)(1835, 2555)(1836, 2556)(1837, 2557)(1838, 2558)(1839, 2559)(1840, 2560)(1841, 2561)(1842, 2562)(1843, 2563)(1844, 2564)(1845, 2565)(1846, 2566)(1847, 2567)(1848, 2568)(1849, 2569)(1850, 2570)(1851, 2571)(1852, 2572)(1853, 2573)(1854, 2574)(1855, 2575)(1856, 2576)(1857, 2577)(1858, 2578)(1859, 2579)(1860, 2580)(1861, 2581)(1862, 2582)(1863, 2583)(1864, 2584)(1865, 2585)(1866, 2586)(1867, 2587)(1868, 2588)(1869, 2589)(1870, 2590)(1871, 2591)(1872, 2592)(1873, 2593)(1874, 2594)(1875, 2595)(1876, 2596)(1877, 2597)(1878, 2598)(1879, 2599)(1880, 2600)(1881, 2601)(1882, 2602)(1883, 2603)(1884, 2604)(1885, 2605)(1886, 2606)(1887, 2607)(1888, 2608)(1889, 2609)(1890, 2610)(1891, 2611)(1892, 2612)(1893, 2613)(1894, 2614)(1895, 2615)(1896, 2616)(1897, 2617)(1898, 2618)(1899, 2619)(1900, 2620)(1901, 2621)(1902, 2622)(1903, 2623)(1904, 2624)(1905, 2625)(1906, 2626)(1907, 2627)(1908, 2628)(1909, 2629)(1910, 2630)(1911, 2631)(1912, 2632)(1913, 2633)(1914, 2634)(1915, 2635)(1916, 2636)(1917, 2637)(1918, 2638)(1919, 2639)(1920, 2640)(1921, 2641)(1922, 2642)(1923, 2643)(1924, 2644)(1925, 2645)(1926, 2646)(1927, 2647)(1928, 2648)(1929, 2649)(1930, 2650)(1931, 2651)(1932, 2652)(1933, 2653)(1934, 2654)(1935, 2655)(1936, 2656)(1937, 2657)(1938, 2658)(1939, 2659)(1940, 2660)(1941, 2661)(1942, 2662)(1943, 2663)(1944, 2664)(1945, 2665)(1946, 2666)(1947, 2667)(1948, 2668)(1949, 2669)(1950, 2670)(1951, 2671)(1952, 2672)(1953, 2673)(1954, 2674)(1955, 2675)(1956, 2676)(1957, 2677)(1958, 2678)(1959, 2679)(1960, 2680)(1961, 2681)(1962, 2682)(1963, 2683)(1964, 2684)(1965, 2685)(1966, 2686)(1967, 2687)(1968, 2688)(1969, 2689)(1970, 2690)(1971, 2691)(1972, 2692)(1973, 2693)(1974, 2694)(1975, 2695)(1976, 2696)(1977, 2697)(1978, 2698)(1979, 2699)(1980, 2700)(1981, 2701)(1982, 2702)(1983, 2703)(1984, 2704)(1985, 2705)(1986, 2706)(1987, 2707)(1988, 2708)(1989, 2709)(1990, 2710)(1991, 2711)(1992, 2712)(1993, 2713)(1994, 2714)(1995, 2715)(1996, 2716)(1997, 2717)(1998, 2718)(1999, 2719)(2000, 2720)(2001, 2721)(2002, 2722)(2003, 2723)(2004, 2724)(2005, 2725)(2006, 2726)(2007, 2727)(2008, 2728)(2009, 2729)(2010, 2730)(2011, 2731)(2012, 2732)(2013, 2733)(2014, 2734)(2015, 2735)(2016, 2736)(2017, 2737)(2018, 2738)(2019, 2739)(2020, 2740)(2021, 2741)(2022, 2742)(2023, 2743)(2024, 2744)(2025, 2745)(2026, 2746)(2027, 2747)(2028, 2748)(2029, 2749)(2030, 2750)(2031, 2751)(2032, 2752)(2033, 2753)(2034, 2754)(2035, 2755)(2036, 2756)(2037, 2757)(2038, 2758)(2039, 2759)(2040, 2760)(2041, 2761)(2042, 2762)(2043, 2763)(2044, 2764)(2045, 2765)(2046, 2766)(2047, 2767)(2048, 2768)(2049, 2769)(2050, 2770)(2051, 2771)(2052, 2772)(2053, 2773)(2054, 2774)(2055, 2775)(2056, 2776)(2057, 2777)(2058, 2778)(2059, 2779)(2060, 2780)(2061, 2781)(2062, 2782)(2063, 2783)(2064, 2784)(2065, 2785)(2066, 2786)(2067, 2787)(2068, 2788)(2069, 2789)(2070, 2790)(2071, 2791)(2072, 2792)(2073, 2793)(2074, 2794)(2075, 2795)(2076, 2796)(2077, 2797)(2078, 2798)(2079, 2799)(2080, 2800)(2081, 2801)(2082, 2802)(2083, 2803)(2084, 2804)(2085, 2805)(2086, 2806)(2087, 2807)(2088, 2808)(2089, 2809)(2090, 2810)(2091, 2811)(2092, 2812)(2093, 2813)(2094, 2814)(2095, 2815)(2096, 2816)(2097, 2817)(2098, 2818)(2099, 2819)(2100, 2820)(2101, 2821)(2102, 2822)(2103, 2823)(2104, 2824)(2105, 2825)(2106, 2826)(2107, 2827)(2108, 2828)(2109, 2829)(2110, 2830)(2111, 2831)(2112, 2832)(2113, 2833)(2114, 2834)(2115, 2835)(2116, 2836)(2117, 2837)(2118, 2838)(2119, 2839)(2120, 2840)(2121, 2841)(2122, 2842)(2123, 2843)(2124, 2844)(2125, 2845)(2126, 2846)(2127, 2847)(2128, 2848)(2129, 2849)(2130, 2850)(2131, 2851)(2132, 2852)(2133, 2853)(2134, 2854)(2135, 2855)(2136, 2856)(2137, 2857)(2138, 2858)(2139, 2859)(2140, 2860)(2141, 2861)(2142, 2862)(2143, 2863)(2144, 2864)(2145, 2865)(2146, 2866)(2147, 2867)(2148, 2868)(2149, 2869)(2150, 2870)(2151, 2871)(2152, 2872)(2153, 2873)(2154, 2874)(2155, 2875)(2156, 2876)(2157, 2877)(2158, 2878)(2159, 2879)(2160, 2880) L = (1, 1443)(2, 1446)(3, 1441)(4, 1449)(5, 1452)(6, 1442)(7, 1456)(8, 1453)(9, 1444)(10, 1459)(11, 1462)(12, 1445)(13, 1448)(14, 1463)(15, 1468)(16, 1447)(17, 1470)(18, 1473)(19, 1450)(20, 1475)(21, 1476)(22, 1451)(23, 1454)(24, 1477)(25, 1482)(26, 1483)(27, 1486)(28, 1455)(29, 1487)(30, 1457)(31, 1491)(32, 1493)(33, 1458)(34, 1496)(35, 1460)(36, 1461)(37, 1464)(38, 1498)(39, 1503)(40, 1504)(41, 1507)(42, 1465)(43, 1466)(44, 1510)(45, 1511)(46, 1467)(47, 1469)(48, 1512)(49, 1516)(50, 1519)(51, 1471)(52, 1521)(53, 1472)(54, 1522)(55, 1526)(56, 1474)(57, 1499)(58, 1478)(59, 1497)(60, 1532)(61, 1533)(62, 1536)(63, 1479)(64, 1480)(65, 1539)(66, 1540)(67, 1481)(68, 1541)(69, 1545)(70, 1484)(71, 1485)(72, 1488)(73, 1547)(74, 1552)(75, 1553)(76, 1489)(77, 1556)(78, 1558)(79, 1490)(80, 1548)(81, 1492)(82, 1494)(83, 1561)(84, 1565)(85, 1567)(86, 1495)(87, 1568)(88, 1572)(89, 1574)(90, 1575)(91, 1578)(92, 1500)(93, 1501)(94, 1581)(95, 1582)(96, 1502)(97, 1583)(98, 1587)(99, 1505)(100, 1506)(101, 1508)(102, 1589)(103, 1593)(104, 1596)(105, 1509)(106, 1590)(107, 1513)(108, 1520)(109, 1602)(110, 1603)(111, 1606)(112, 1514)(113, 1515)(114, 1609)(115, 1611)(116, 1517)(117, 1613)(118, 1518)(119, 1614)(120, 1618)(121, 1523)(122, 1612)(123, 1622)(124, 1623)(125, 1524)(126, 1626)(127, 1525)(128, 1527)(129, 1627)(130, 1631)(131, 1633)(132, 1528)(133, 1636)(134, 1529)(135, 1530)(136, 1639)(137, 1640)(138, 1531)(139, 1641)(140, 1645)(141, 1534)(142, 1535)(143, 1537)(144, 1647)(145, 1651)(146, 1654)(147, 1538)(148, 1648)(149, 1542)(150, 1546)(151, 1660)(152, 1661)(153, 1543)(154, 1664)(155, 1665)(156, 1544)(157, 1666)(158, 1670)(159, 1672)(160, 1673)(161, 1676)(162, 1549)(163, 1550)(164, 1679)(165, 1680)(166, 1551)(167, 1681)(168, 1685)(169, 1554)(170, 1688)(171, 1555)(172, 1562)(173, 1557)(174, 1559)(175, 1691)(176, 1695)(177, 1697)(178, 1560)(179, 1700)(180, 1701)(181, 1704)(182, 1563)(183, 1564)(184, 1707)(185, 1709)(186, 1566)(187, 1569)(188, 1710)(189, 1714)(190, 1715)(191, 1570)(192, 1718)(193, 1571)(194, 1719)(195, 1722)(196, 1573)(197, 1723)(198, 1727)(199, 1576)(200, 1577)(201, 1579)(202, 1729)(203, 1733)(204, 1736)(205, 1580)(206, 1730)(207, 1584)(208, 1588)(209, 1742)(210, 1743)(211, 1585)(212, 1746)(213, 1747)(214, 1586)(215, 1748)(216, 1752)(217, 1754)(218, 1755)(219, 1758)(220, 1591)(221, 1592)(222, 1761)(223, 1763)(224, 1594)(225, 1595)(226, 1597)(227, 1765)(228, 1769)(229, 1771)(230, 1598)(231, 1774)(232, 1599)(233, 1600)(234, 1777)(235, 1778)(236, 1601)(237, 1779)(238, 1783)(239, 1604)(240, 1605)(241, 1607)(242, 1785)(243, 1741)(244, 1790)(245, 1608)(246, 1786)(247, 1793)(248, 1610)(249, 1794)(250, 1798)(251, 1615)(252, 1764)(253, 1731)(254, 1801)(255, 1616)(256, 1804)(257, 1617)(258, 1805)(259, 1809)(260, 1619)(261, 1620)(262, 1812)(263, 1813)(264, 1621)(265, 1759)(266, 1816)(267, 1624)(268, 1819)(269, 1625)(270, 1628)(271, 1823)(272, 1824)(273, 1781)(274, 1629)(275, 1630)(276, 1828)(277, 1830)(278, 1632)(279, 1634)(280, 1831)(281, 1834)(282, 1635)(283, 1637)(284, 1836)(285, 1840)(286, 1843)(287, 1638)(288, 1837)(289, 1642)(290, 1646)(291, 1693)(292, 1848)(293, 1643)(294, 1851)(295, 1852)(296, 1644)(297, 1853)(298, 1857)(299, 1859)(300, 1860)(301, 1683)(302, 1649)(303, 1650)(304, 1864)(305, 1866)(306, 1652)(307, 1653)(308, 1655)(309, 1868)(310, 1872)(311, 1874)(312, 1656)(313, 1877)(314, 1657)(315, 1658)(316, 1880)(317, 1881)(318, 1659)(319, 1705)(320, 1884)(321, 1662)(322, 1887)(323, 1663)(324, 1692)(325, 1667)(326, 1867)(327, 1838)(328, 1892)(329, 1668)(330, 1895)(331, 1669)(332, 1896)(333, 1899)(334, 1671)(335, 1900)(336, 1904)(337, 1674)(338, 1675)(339, 1677)(340, 1906)(341, 1713)(342, 1911)(343, 1678)(344, 1907)(345, 1682)(346, 1686)(347, 1916)(348, 1917)(349, 1918)(350, 1684)(351, 1919)(352, 1923)(353, 1687)(354, 1689)(355, 1924)(356, 1928)(357, 1930)(358, 1690)(359, 1933)(360, 1934)(361, 1694)(362, 1937)(363, 1938)(364, 1696)(365, 1698)(366, 1939)(367, 1942)(368, 1944)(369, 1699)(370, 1844)(371, 1947)(372, 1702)(373, 1703)(374, 1949)(375, 1952)(376, 1706)(377, 1950)(378, 1955)(379, 1708)(380, 1956)(381, 1960)(382, 1855)(383, 1711)(384, 1712)(385, 1963)(386, 1964)(387, 1966)(388, 1716)(389, 1968)(390, 1717)(391, 1720)(392, 1870)(393, 1971)(394, 1721)(395, 1974)(396, 1724)(397, 1728)(398, 1767)(399, 1977)(400, 1725)(401, 1980)(402, 1981)(403, 1726)(404, 1810)(405, 1984)(406, 1986)(407, 1987)(408, 1732)(409, 1990)(410, 1991)(411, 1734)(412, 1735)(413, 1737)(414, 1993)(415, 1822)(416, 1997)(417, 1738)(418, 2000)(419, 1739)(420, 1740)(421, 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2225)(786, 2226)(787, 2227)(788, 2228)(789, 2229)(790, 2230)(791, 2231)(792, 2232)(793, 2233)(794, 2234)(795, 2235)(796, 2236)(797, 2237)(798, 2238)(799, 2239)(800, 2240)(801, 2241)(802, 2242)(803, 2243)(804, 2244)(805, 2245)(806, 2246)(807, 2247)(808, 2248)(809, 2249)(810, 2250)(811, 2251)(812, 2252)(813, 2253)(814, 2254)(815, 2255)(816, 2256)(817, 2257)(818, 2258)(819, 2259)(820, 2260)(821, 2261)(822, 2262)(823, 2263)(824, 2264)(825, 2265)(826, 2266)(827, 2267)(828, 2268)(829, 2269)(830, 2270)(831, 2271)(832, 2272)(833, 2273)(834, 2274)(835, 2275)(836, 2276)(837, 2277)(838, 2278)(839, 2279)(840, 2280)(841, 2281)(842, 2282)(843, 2283)(844, 2284)(845, 2285)(846, 2286)(847, 2287)(848, 2288)(849, 2289)(850, 2290)(851, 2291)(852, 2292)(853, 2293)(854, 2294)(855, 2295)(856, 2296)(857, 2297)(858, 2298)(859, 2299)(860, 2300)(861, 2301)(862, 2302)(863, 2303)(864, 2304)(865, 2305)(866, 2306)(867, 2307)(868, 2308)(869, 2309)(870, 2310)(871, 2311)(872, 2312)(873, 2313)(874, 2314)(875, 2315)(876, 2316)(877, 2317)(878, 2318)(879, 2319)(880, 2320)(881, 2321)(882, 2322)(883, 2323)(884, 2324)(885, 2325)(886, 2326)(887, 2327)(888, 2328)(889, 2329)(890, 2330)(891, 2331)(892, 2332)(893, 2333)(894, 2334)(895, 2335)(896, 2336)(897, 2337)(898, 2338)(899, 2339)(900, 2340)(901, 2341)(902, 2342)(903, 2343)(904, 2344)(905, 2345)(906, 2346)(907, 2347)(908, 2348)(909, 2349)(910, 2350)(911, 2351)(912, 2352)(913, 2353)(914, 2354)(915, 2355)(916, 2356)(917, 2357)(918, 2358)(919, 2359)(920, 2360)(921, 2361)(922, 2362)(923, 2363)(924, 2364)(925, 2365)(926, 2366)(927, 2367)(928, 2368)(929, 2369)(930, 2370)(931, 2371)(932, 2372)(933, 2373)(934, 2374)(935, 2375)(936, 2376)(937, 2377)(938, 2378)(939, 2379)(940, 2380)(941, 2381)(942, 2382)(943, 2383)(944, 2384)(945, 2385)(946, 2386)(947, 2387)(948, 2388)(949, 2389)(950, 2390)(951, 2391)(952, 2392)(953, 2393)(954, 2394)(955, 2395)(956, 2396)(957, 2397)(958, 2398)(959, 2399)(960, 2400)(961, 2401)(962, 2402)(963, 2403)(964, 2404)(965, 2405)(966, 2406)(967, 2407)(968, 2408)(969, 2409)(970, 2410)(971, 2411)(972, 2412)(973, 2413)(974, 2414)(975, 2415)(976, 2416)(977, 2417)(978, 2418)(979, 2419)(980, 2420)(981, 2421)(982, 2422)(983, 2423)(984, 2424)(985, 2425)(986, 2426)(987, 2427)(988, 2428)(989, 2429)(990, 2430)(991, 2431)(992, 2432)(993, 2433)(994, 2434)(995, 2435)(996, 2436)(997, 2437)(998, 2438)(999, 2439)(1000, 2440)(1001, 2441)(1002, 2442)(1003, 2443)(1004, 2444)(1005, 2445)(1006, 2446)(1007, 2447)(1008, 2448)(1009, 2449)(1010, 2450)(1011, 2451)(1012, 2452)(1013, 2453)(1014, 2454)(1015, 2455)(1016, 2456)(1017, 2457)(1018, 2458)(1019, 2459)(1020, 2460)(1021, 2461)(1022, 2462)(1023, 2463)(1024, 2464)(1025, 2465)(1026, 2466)(1027, 2467)(1028, 2468)(1029, 2469)(1030, 2470)(1031, 2471)(1032, 2472)(1033, 2473)(1034, 2474)(1035, 2475)(1036, 2476)(1037, 2477)(1038, 2478)(1039, 2479)(1040, 2480)(1041, 2481)(1042, 2482)(1043, 2483)(1044, 2484)(1045, 2485)(1046, 2486)(1047, 2487)(1048, 2488)(1049, 2489)(1050, 2490)(1051, 2491)(1052, 2492)(1053, 2493)(1054, 2494)(1055, 2495)(1056, 2496)(1057, 2497)(1058, 2498)(1059, 2499)(1060, 2500)(1061, 2501)(1062, 2502)(1063, 2503)(1064, 2504)(1065, 2505)(1066, 2506)(1067, 2507)(1068, 2508)(1069, 2509)(1070, 2510)(1071, 2511)(1072, 2512)(1073, 2513)(1074, 2514)(1075, 2515)(1076, 2516)(1077, 2517)(1078, 2518)(1079, 2519)(1080, 2520)(1081, 2521)(1082, 2522)(1083, 2523)(1084, 2524)(1085, 2525)(1086, 2526)(1087, 2527)(1088, 2528)(1089, 2529)(1090, 2530)(1091, 2531)(1092, 2532)(1093, 2533)(1094, 2534)(1095, 2535)(1096, 2536)(1097, 2537)(1098, 2538)(1099, 2539)(1100, 2540)(1101, 2541)(1102, 2542)(1103, 2543)(1104, 2544)(1105, 2545)(1106, 2546)(1107, 2547)(1108, 2548)(1109, 2549)(1110, 2550)(1111, 2551)(1112, 2552)(1113, 2553)(1114, 2554)(1115, 2555)(1116, 2556)(1117, 2557)(1118, 2558)(1119, 2559)(1120, 2560)(1121, 2561)(1122, 2562)(1123, 2563)(1124, 2564)(1125, 2565)(1126, 2566)(1127, 2567)(1128, 2568)(1129, 2569)(1130, 2570)(1131, 2571)(1132, 2572)(1133, 2573)(1134, 2574)(1135, 2575)(1136, 2576)(1137, 2577)(1138, 2578)(1139, 2579)(1140, 2580)(1141, 2581)(1142, 2582)(1143, 2583)(1144, 2584)(1145, 2585)(1146, 2586)(1147, 2587)(1148, 2588)(1149, 2589)(1150, 2590)(1151, 2591)(1152, 2592)(1153, 2593)(1154, 2594)(1155, 2595)(1156, 2596)(1157, 2597)(1158, 2598)(1159, 2599)(1160, 2600)(1161, 2601)(1162, 2602)(1163, 2603)(1164, 2604)(1165, 2605)(1166, 2606)(1167, 2607)(1168, 2608)(1169, 2609)(1170, 2610)(1171, 2611)(1172, 2612)(1173, 2613)(1174, 2614)(1175, 2615)(1176, 2616)(1177, 2617)(1178, 2618)(1179, 2619)(1180, 2620)(1181, 2621)(1182, 2622)(1183, 2623)(1184, 2624)(1185, 2625)(1186, 2626)(1187, 2627)(1188, 2628)(1189, 2629)(1190, 2630)(1191, 2631)(1192, 2632)(1193, 2633)(1194, 2634)(1195, 2635)(1196, 2636)(1197, 2637)(1198, 2638)(1199, 2639)(1200, 2640)(1201, 2641)(1202, 2642)(1203, 2643)(1204, 2644)(1205, 2645)(1206, 2646)(1207, 2647)(1208, 2648)(1209, 2649)(1210, 2650)(1211, 2651)(1212, 2652)(1213, 2653)(1214, 2654)(1215, 2655)(1216, 2656)(1217, 2657)(1218, 2658)(1219, 2659)(1220, 2660)(1221, 2661)(1222, 2662)(1223, 2663)(1224, 2664)(1225, 2665)(1226, 2666)(1227, 2667)(1228, 2668)(1229, 2669)(1230, 2670)(1231, 2671)(1232, 2672)(1233, 2673)(1234, 2674)(1235, 2675)(1236, 2676)(1237, 2677)(1238, 2678)(1239, 2679)(1240, 2680)(1241, 2681)(1242, 2682)(1243, 2683)(1244, 2684)(1245, 2685)(1246, 2686)(1247, 2687)(1248, 2688)(1249, 2689)(1250, 2690)(1251, 2691)(1252, 2692)(1253, 2693)(1254, 2694)(1255, 2695)(1256, 2696)(1257, 2697)(1258, 2698)(1259, 2699)(1260, 2700)(1261, 2701)(1262, 2702)(1263, 2703)(1264, 2704)(1265, 2705)(1266, 2706)(1267, 2707)(1268, 2708)(1269, 2709)(1270, 2710)(1271, 2711)(1272, 2712)(1273, 2713)(1274, 2714)(1275, 2715)(1276, 2716)(1277, 2717)(1278, 2718)(1279, 2719)(1280, 2720)(1281, 2721)(1282, 2722)(1283, 2723)(1284, 2724)(1285, 2725)(1286, 2726)(1287, 2727)(1288, 2728)(1289, 2729)(1290, 2730)(1291, 2731)(1292, 2732)(1293, 2733)(1294, 2734)(1295, 2735)(1296, 2736)(1297, 2737)(1298, 2738)(1299, 2739)(1300, 2740)(1301, 2741)(1302, 2742)(1303, 2743)(1304, 2744)(1305, 2745)(1306, 2746)(1307, 2747)(1308, 2748)(1309, 2749)(1310, 2750)(1311, 2751)(1312, 2752)(1313, 2753)(1314, 2754)(1315, 2755)(1316, 2756)(1317, 2757)(1318, 2758)(1319, 2759)(1320, 2760)(1321, 2761)(1322, 2762)(1323, 2763)(1324, 2764)(1325, 2765)(1326, 2766)(1327, 2767)(1328, 2768)(1329, 2769)(1330, 2770)(1331, 2771)(1332, 2772)(1333, 2773)(1334, 2774)(1335, 2775)(1336, 2776)(1337, 2777)(1338, 2778)(1339, 2779)(1340, 2780)(1341, 2781)(1342, 2782)(1343, 2783)(1344, 2784)(1345, 2785)(1346, 2786)(1347, 2787)(1348, 2788)(1349, 2789)(1350, 2790)(1351, 2791)(1352, 2792)(1353, 2793)(1354, 2794)(1355, 2795)(1356, 2796)(1357, 2797)(1358, 2798)(1359, 2799)(1360, 2800)(1361, 2801)(1362, 2802)(1363, 2803)(1364, 2804)(1365, 2805)(1366, 2806)(1367, 2807)(1368, 2808)(1369, 2809)(1370, 2810)(1371, 2811)(1372, 2812)(1373, 2813)(1374, 2814)(1375, 2815)(1376, 2816)(1377, 2817)(1378, 2818)(1379, 2819)(1380, 2820)(1381, 2821)(1382, 2822)(1383, 2823)(1384, 2824)(1385, 2825)(1386, 2826)(1387, 2827)(1388, 2828)(1389, 2829)(1390, 2830)(1391, 2831)(1392, 2832)(1393, 2833)(1394, 2834)(1395, 2835)(1396, 2836)(1397, 2837)(1398, 2838)(1399, 2839)(1400, 2840)(1401, 2841)(1402, 2842)(1403, 2843)(1404, 2844)(1405, 2845)(1406, 2846)(1407, 2847)(1408, 2848)(1409, 2849)(1410, 2850)(1411, 2851)(1412, 2852)(1413, 2853)(1414, 2854)(1415, 2855)(1416, 2856)(1417, 2857)(1418, 2858)(1419, 2859)(1420, 2860)(1421, 2861)(1422, 2862)(1423, 2863)(1424, 2864)(1425, 2865)(1426, 2866)(1427, 2867)(1428, 2868)(1429, 2869)(1430, 2870)(1431, 2871)(1432, 2872)(1433, 2873)(1434, 2874)(1435, 2875)(1436, 2876)(1437, 2877)(1438, 2878)(1439, 2879)(1440, 2880) 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 E16.1307 Graph:: simple bipartite v = 810 e = 1440 f = 600 degree seq :: [ 2^720, 16^90 ] E16.1311 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8}) Quotient :: dipole Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-1)^3, (Y3 * Y2^-1)^3, Y2^8, Y1 * Y2^-2 * Y1 * Y2^2 * Y1 * Y2^3 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-3, (Y1 * Y2^3)^5, Y2^2 * Y1 * Y2^-2 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^3 * Y1 * Y2^-2 * Y1 * Y2^3 * Y1 * Y2^2 ] Map:: R = (1, 721, 2, 722)(3, 723, 7, 727)(4, 724, 9, 729)(5, 725, 11, 731)(6, 726, 13, 733)(8, 728, 16, 736)(10, 730, 19, 739)(12, 732, 22, 742)(14, 734, 25, 745)(15, 735, 27, 747)(17, 737, 30, 750)(18, 738, 32, 752)(20, 740, 35, 755)(21, 741, 36, 756)(23, 743, 39, 759)(24, 744, 41, 761)(26, 746, 44, 764)(28, 748, 46, 766)(29, 749, 48, 768)(31, 751, 51, 771)(33, 753, 53, 773)(34, 754, 55, 775)(37, 757, 59, 779)(38, 758, 61, 781)(40, 760, 64, 784)(42, 762, 66, 786)(43, 763, 68, 788)(45, 765, 71, 791)(47, 767, 74, 794)(49, 769, 76, 796)(50, 770, 78, 798)(52, 772, 81, 801)(54, 774, 84, 804)(56, 776, 86, 806)(57, 777, 80, 800)(58, 778, 89, 809)(60, 780, 92, 812)(62, 782, 94, 814)(63, 783, 96, 816)(65, 785, 99, 819)(67, 787, 102, 822)(69, 789, 104, 824)(70, 790, 98, 818)(72, 792, 108, 828)(73, 793, 110, 830)(75, 795, 113, 833)(77, 797, 116, 836)(79, 799, 118, 838)(82, 802, 122, 842)(83, 803, 124, 844)(85, 805, 127, 847)(87, 807, 130, 850)(88, 808, 131, 851)(90, 810, 134, 854)(91, 811, 136, 856)(93, 813, 139, 859)(95, 815, 142, 862)(97, 817, 144, 864)(100, 820, 148, 868)(101, 821, 150, 870)(103, 823, 153, 873)(105, 825, 156, 876)(106, 826, 157, 877)(107, 827, 159, 879)(109, 829, 162, 882)(111, 831, 164, 884)(112, 832, 152, 872)(114, 834, 168, 888)(115, 835, 170, 890)(117, 837, 173, 893)(119, 839, 176, 896)(120, 840, 177, 897)(121, 841, 179, 899)(123, 843, 182, 902)(125, 845, 184, 904)(126, 846, 138, 858)(128, 848, 188, 908)(129, 849, 190, 910)(132, 852, 194, 914)(133, 853, 195, 915)(135, 855, 198, 918)(137, 857, 200, 920)(140, 860, 204, 924)(141, 861, 206, 926)(143, 863, 209, 929)(145, 865, 212, 932)(146, 866, 213, 933)(147, 867, 215, 935)(149, 869, 218, 938)(151, 871, 220, 940)(154, 874, 224, 944)(155, 875, 226, 946)(158, 878, 230, 950)(160, 880, 232, 952)(161, 881, 234, 954)(163, 883, 237, 957)(165, 885, 240, 960)(166, 886, 241, 961)(167, 887, 243, 963)(169, 889, 246, 966)(171, 891, 248, 968)(172, 892, 236, 956)(174, 894, 252, 972)(175, 895, 254, 974)(178, 898, 258, 978)(180, 900, 260, 980)(181, 901, 262, 982)(183, 903, 265, 985)(185, 905, 268, 988)(186, 906, 269, 989)(187, 907, 271, 991)(189, 909, 274, 994)(191, 911, 276, 996)(192, 912, 264, 984)(193, 913, 279, 999)(196, 916, 283, 1003)(197, 917, 285, 1005)(199, 919, 288, 1008)(201, 921, 291, 1011)(202, 922, 292, 1012)(203, 923, 294, 1014)(205, 925, 297, 1017)(207, 927, 299, 1019)(208, 928, 287, 1007)(210, 930, 303, 1023)(211, 931, 305, 1025)(214, 934, 309, 1029)(216, 936, 311, 1031)(217, 937, 313, 1033)(219, 939, 316, 1036)(221, 941, 319, 1039)(222, 942, 320, 1040)(223, 943, 322, 1042)(225, 945, 325, 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2805, 2124, 2844, 2054, 2774, 2133, 2853, 2034, 2754)(1904, 2624, 2057, 2777, 2141, 2861, 2084, 2804, 1949, 2669, 2083, 2803, 2139, 2859, 2055, 2775)(1912, 2632, 2063, 2783, 2142, 2862, 2155, 2875, 2131, 2851, 2031, 2751, 2130, 2850, 2061, 2781)(1955, 2675, 2086, 2806, 2105, 2825, 1988, 2708, 2107, 2827, 2151, 2871, 2146, 2866, 2087, 2807)(1980, 2700, 2101, 2821, 2150, 2870, 2128, 2848, 2025, 2745, 2127, 2847, 2148, 2868, 2099, 2819)(2073, 2793, 2144, 2864, 2158, 2878, 2147, 2867, 2092, 2812, 2140, 2860, 2157, 2877, 2143, 2863)(2117, 2837, 2153, 2873, 2160, 2880, 2156, 2876, 2136, 2856, 2149, 2869, 2159, 2879, 2152, 2872) L = (1, 1442)(2, 1441)(3, 1447)(4, 1449)(5, 1451)(6, 1453)(7, 1443)(8, 1456)(9, 1444)(10, 1459)(11, 1445)(12, 1462)(13, 1446)(14, 1465)(15, 1467)(16, 1448)(17, 1470)(18, 1472)(19, 1450)(20, 1475)(21, 1476)(22, 1452)(23, 1479)(24, 1481)(25, 1454)(26, 1484)(27, 1455)(28, 1486)(29, 1488)(30, 1457)(31, 1491)(32, 1458)(33, 1493)(34, 1495)(35, 1460)(36, 1461)(37, 1499)(38, 1501)(39, 1463)(40, 1504)(41, 1464)(42, 1506)(43, 1508)(44, 1466)(45, 1511)(46, 1468)(47, 1514)(48, 1469)(49, 1516)(50, 1518)(51, 1471)(52, 1521)(53, 1473)(54, 1524)(55, 1474)(56, 1526)(57, 1520)(58, 1529)(59, 1477)(60, 1532)(61, 1478)(62, 1534)(63, 1536)(64, 1480)(65, 1539)(66, 1482)(67, 1542)(68, 1483)(69, 1544)(70, 1538)(71, 1485)(72, 1548)(73, 1550)(74, 1487)(75, 1553)(76, 1489)(77, 1556)(78, 1490)(79, 1558)(80, 1497)(81, 1492)(82, 1562)(83, 1564)(84, 1494)(85, 1567)(86, 1496)(87, 1570)(88, 1571)(89, 1498)(90, 1574)(91, 1576)(92, 1500)(93, 1579)(94, 1502)(95, 1582)(96, 1503)(97, 1584)(98, 1510)(99, 1505)(100, 1588)(101, 1590)(102, 1507)(103, 1593)(104, 1509)(105, 1596)(106, 1597)(107, 1599)(108, 1512)(109, 1602)(110, 1513)(111, 1604)(112, 1592)(113, 1515)(114, 1608)(115, 1610)(116, 1517)(117, 1613)(118, 1519)(119, 1616)(120, 1617)(121, 1619)(122, 1522)(123, 1622)(124, 1523)(125, 1624)(126, 1578)(127, 1525)(128, 1628)(129, 1630)(130, 1527)(131, 1528)(132, 1634)(133, 1635)(134, 1530)(135, 1638)(136, 1531)(137, 1640)(138, 1566)(139, 1533)(140, 1644)(141, 1646)(142, 1535)(143, 1649)(144, 1537)(145, 1652)(146, 1653)(147, 1655)(148, 1540)(149, 1658)(150, 1541)(151, 1660)(152, 1552)(153, 1543)(154, 1664)(155, 1666)(156, 1545)(157, 1546)(158, 1670)(159, 1547)(160, 1672)(161, 1674)(162, 1549)(163, 1677)(164, 1551)(165, 1680)(166, 1681)(167, 1683)(168, 1554)(169, 1686)(170, 1555)(171, 1688)(172, 1676)(173, 1557)(174, 1692)(175, 1694)(176, 1559)(177, 1560)(178, 1698)(179, 1561)(180, 1700)(181, 1702)(182, 1563)(183, 1705)(184, 1565)(185, 1708)(186, 1709)(187, 1711)(188, 1568)(189, 1714)(190, 1569)(191, 1716)(192, 1704)(193, 1719)(194, 1572)(195, 1573)(196, 1723)(197, 1725)(198, 1575)(199, 1728)(200, 1577)(201, 1731)(202, 1732)(203, 1734)(204, 1580)(205, 1737)(206, 1581)(207, 1739)(208, 1727)(209, 1583)(210, 1743)(211, 1745)(212, 1585)(213, 1586)(214, 1749)(215, 1587)(216, 1751)(217, 1753)(218, 1589)(219, 1756)(220, 1591)(221, 1759)(222, 1760)(223, 1762)(224, 1594)(225, 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1804)(499, 2080)(500, 1814)(501, 1806)(502, 2018)(503, 2041)(504, 1808)(505, 1819)(506, 1810)(507, 2082)(508, 2083)(509, 1812)(510, 1813)(511, 2040)(512, 2085)(513, 1816)(514, 2086)(515, 1818)(516, 2047)(517, 2088)(518, 1820)(519, 2044)(520, 2036)(521, 1822)(522, 2065)(523, 1824)(524, 2027)(525, 2019)(526, 1828)(527, 2092)(528, 2035)(529, 2093)(530, 1831)(531, 2032)(532, 1834)(533, 1835)(534, 2094)(535, 1836)(536, 1847)(537, 1838)(538, 2098)(539, 2099)(540, 1840)(541, 1841)(542, 1921)(543, 1842)(544, 1861)(545, 2103)(546, 1844)(547, 2105)(548, 1846)(549, 1936)(550, 2108)(551, 1848)(552, 1927)(553, 1917)(554, 1850)(555, 2111)(556, 1852)(557, 1906)(558, 1895)(559, 1855)(560, 1932)(561, 1856)(562, 2117)(563, 1916)(564, 2120)(565, 1859)(566, 1930)(567, 1862)(568, 1924)(569, 1870)(570, 1864)(571, 1890)(572, 1913)(573, 1866)(574, 1867)(575, 2124)(576, 1877)(577, 1869)(578, 1942)(579, 1965)(580, 1871)(581, 1882)(582, 1873)(583, 2126)(584, 2127)(585, 1875)(586, 1876)(587, 1964)(588, 2129)(589, 1879)(590, 2130)(591, 1881)(592, 1971)(593, 2132)(594, 1883)(595, 1968)(596, 1960)(597, 1885)(598, 2109)(599, 1887)(600, 1951)(601, 1943)(602, 1891)(603, 2136)(604, 1959)(605, 2137)(606, 1894)(607, 1956)(608, 1897)(609, 1898)(610, 2138)(611, 2101)(612, 2135)(613, 2133)(614, 1902)(615, 1903)(616, 2140)(617, 2095)(618, 2114)(619, 1909)(620, 2115)(621, 1911)(622, 2113)(623, 2123)(624, 1914)(625, 1962)(626, 2119)(627, 1919)(628, 2112)(629, 2106)(630, 2102)(631, 2104)(632, 2143)(633, 1926)(634, 2131)(635, 2110)(636, 1928)(637, 2128)(638, 2125)(639, 2107)(640, 1939)(641, 2122)(642, 1947)(643, 1948)(644, 2121)(645, 1952)(646, 1954)(647, 2118)(648, 1957)(649, 2097)(650, 2134)(651, 2096)(652, 1967)(653, 1969)(654, 1974)(655, 2057)(656, 2091)(657, 2089)(658, 1978)(659, 1979)(660, 2149)(661, 2051)(662, 2070)(663, 1985)(664, 2071)(665, 1987)(666, 2069)(667, 2079)(668, 1990)(669, 2038)(670, 2075)(671, 1995)(672, 2068)(673, 2062)(674, 2058)(675, 2060)(676, 2152)(677, 2002)(678, 2087)(679, 2066)(680, 2004)(681, 2084)(682, 2081)(683, 2063)(684, 2015)(685, 2078)(686, 2023)(687, 2024)(688, 2077)(689, 2028)(690, 2030)(691, 2074)(692, 2033)(693, 2053)(694, 2090)(695, 2052)(696, 2043)(697, 2045)(698, 2050)(699, 2157)(700, 2056)(701, 2154)(702, 2156)(703, 2072)(704, 2155)(705, 2150)(706, 2153)(707, 2151)(708, 2159)(709, 2100)(710, 2145)(711, 2147)(712, 2116)(713, 2146)(714, 2141)(715, 2144)(716, 2142)(717, 2139)(718, 2160)(719, 2148)(720, 2158)(721, 2161)(722, 2162)(723, 2163)(724, 2164)(725, 2165)(726, 2166)(727, 2167)(728, 2168)(729, 2169)(730, 2170)(731, 2171)(732, 2172)(733, 2173)(734, 2174)(735, 2175)(736, 2176)(737, 2177)(738, 2178)(739, 2179)(740, 2180)(741, 2181)(742, 2182)(743, 2183)(744, 2184)(745, 2185)(746, 2186)(747, 2187)(748, 2188)(749, 2189)(750, 2190)(751, 2191)(752, 2192)(753, 2193)(754, 2194)(755, 2195)(756, 2196)(757, 2197)(758, 2198)(759, 2199)(760, 2200)(761, 2201)(762, 2202)(763, 2203)(764, 2204)(765, 2205)(766, 2206)(767, 2207)(768, 2208)(769, 2209)(770, 2210)(771, 2211)(772, 2212)(773, 2213)(774, 2214)(775, 2215)(776, 2216)(777, 2217)(778, 2218)(779, 2219)(780, 2220)(781, 2221)(782, 2222)(783, 2223)(784, 2224)(785, 2225)(786, 2226)(787, 2227)(788, 2228)(789, 2229)(790, 2230)(791, 2231)(792, 2232)(793, 2233)(794, 2234)(795, 2235)(796, 2236)(797, 2237)(798, 2238)(799, 2239)(800, 2240)(801, 2241)(802, 2242)(803, 2243)(804, 2244)(805, 2245)(806, 2246)(807, 2247)(808, 2248)(809, 2249)(810, 2250)(811, 2251)(812, 2252)(813, 2253)(814, 2254)(815, 2255)(816, 2256)(817, 2257)(818, 2258)(819, 2259)(820, 2260)(821, 2261)(822, 2262)(823, 2263)(824, 2264)(825, 2265)(826, 2266)(827, 2267)(828, 2268)(829, 2269)(830, 2270)(831, 2271)(832, 2272)(833, 2273)(834, 2274)(835, 2275)(836, 2276)(837, 2277)(838, 2278)(839, 2279)(840, 2280)(841, 2281)(842, 2282)(843, 2283)(844, 2284)(845, 2285)(846, 2286)(847, 2287)(848, 2288)(849, 2289)(850, 2290)(851, 2291)(852, 2292)(853, 2293)(854, 2294)(855, 2295)(856, 2296)(857, 2297)(858, 2298)(859, 2299)(860, 2300)(861, 2301)(862, 2302)(863, 2303)(864, 2304)(865, 2305)(866, 2306)(867, 2307)(868, 2308)(869, 2309)(870, 2310)(871, 2311)(872, 2312)(873, 2313)(874, 2314)(875, 2315)(876, 2316)(877, 2317)(878, 2318)(879, 2319)(880, 2320)(881, 2321)(882, 2322)(883, 2323)(884, 2324)(885, 2325)(886, 2326)(887, 2327)(888, 2328)(889, 2329)(890, 2330)(891, 2331)(892, 2332)(893, 2333)(894, 2334)(895, 2335)(896, 2336)(897, 2337)(898, 2338)(899, 2339)(900, 2340)(901, 2341)(902, 2342)(903, 2343)(904, 2344)(905, 2345)(906, 2346)(907, 2347)(908, 2348)(909, 2349)(910, 2350)(911, 2351)(912, 2352)(913, 2353)(914, 2354)(915, 2355)(916, 2356)(917, 2357)(918, 2358)(919, 2359)(920, 2360)(921, 2361)(922, 2362)(923, 2363)(924, 2364)(925, 2365)(926, 2366)(927, 2367)(928, 2368)(929, 2369)(930, 2370)(931, 2371)(932, 2372)(933, 2373)(934, 2374)(935, 2375)(936, 2376)(937, 2377)(938, 2378)(939, 2379)(940, 2380)(941, 2381)(942, 2382)(943, 2383)(944, 2384)(945, 2385)(946, 2386)(947, 2387)(948, 2388)(949, 2389)(950, 2390)(951, 2391)(952, 2392)(953, 2393)(954, 2394)(955, 2395)(956, 2396)(957, 2397)(958, 2398)(959, 2399)(960, 2400)(961, 2401)(962, 2402)(963, 2403)(964, 2404)(965, 2405)(966, 2406)(967, 2407)(968, 2408)(969, 2409)(970, 2410)(971, 2411)(972, 2412)(973, 2413)(974, 2414)(975, 2415)(976, 2416)(977, 2417)(978, 2418)(979, 2419)(980, 2420)(981, 2421)(982, 2422)(983, 2423)(984, 2424)(985, 2425)(986, 2426)(987, 2427)(988, 2428)(989, 2429)(990, 2430)(991, 2431)(992, 2432)(993, 2433)(994, 2434)(995, 2435)(996, 2436)(997, 2437)(998, 2438)(999, 2439)(1000, 2440)(1001, 2441)(1002, 2442)(1003, 2443)(1004, 2444)(1005, 2445)(1006, 2446)(1007, 2447)(1008, 2448)(1009, 2449)(1010, 2450)(1011, 2451)(1012, 2452)(1013, 2453)(1014, 2454)(1015, 2455)(1016, 2456)(1017, 2457)(1018, 2458)(1019, 2459)(1020, 2460)(1021, 2461)(1022, 2462)(1023, 2463)(1024, 2464)(1025, 2465)(1026, 2466)(1027, 2467)(1028, 2468)(1029, 2469)(1030, 2470)(1031, 2471)(1032, 2472)(1033, 2473)(1034, 2474)(1035, 2475)(1036, 2476)(1037, 2477)(1038, 2478)(1039, 2479)(1040, 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2646)(1207, 2647)(1208, 2648)(1209, 2649)(1210, 2650)(1211, 2651)(1212, 2652)(1213, 2653)(1214, 2654)(1215, 2655)(1216, 2656)(1217, 2657)(1218, 2658)(1219, 2659)(1220, 2660)(1221, 2661)(1222, 2662)(1223, 2663)(1224, 2664)(1225, 2665)(1226, 2666)(1227, 2667)(1228, 2668)(1229, 2669)(1230, 2670)(1231, 2671)(1232, 2672)(1233, 2673)(1234, 2674)(1235, 2675)(1236, 2676)(1237, 2677)(1238, 2678)(1239, 2679)(1240, 2680)(1241, 2681)(1242, 2682)(1243, 2683)(1244, 2684)(1245, 2685)(1246, 2686)(1247, 2687)(1248, 2688)(1249, 2689)(1250, 2690)(1251, 2691)(1252, 2692)(1253, 2693)(1254, 2694)(1255, 2695)(1256, 2696)(1257, 2697)(1258, 2698)(1259, 2699)(1260, 2700)(1261, 2701)(1262, 2702)(1263, 2703)(1264, 2704)(1265, 2705)(1266, 2706)(1267, 2707)(1268, 2708)(1269, 2709)(1270, 2710)(1271, 2711)(1272, 2712)(1273, 2713)(1274, 2714)(1275, 2715)(1276, 2716)(1277, 2717)(1278, 2718)(1279, 2719)(1280, 2720)(1281, 2721)(1282, 2722)(1283, 2723)(1284, 2724)(1285, 2725)(1286, 2726)(1287, 2727)(1288, 2728)(1289, 2729)(1290, 2730)(1291, 2731)(1292, 2732)(1293, 2733)(1294, 2734)(1295, 2735)(1296, 2736)(1297, 2737)(1298, 2738)(1299, 2739)(1300, 2740)(1301, 2741)(1302, 2742)(1303, 2743)(1304, 2744)(1305, 2745)(1306, 2746)(1307, 2747)(1308, 2748)(1309, 2749)(1310, 2750)(1311, 2751)(1312, 2752)(1313, 2753)(1314, 2754)(1315, 2755)(1316, 2756)(1317, 2757)(1318, 2758)(1319, 2759)(1320, 2760)(1321, 2761)(1322, 2762)(1323, 2763)(1324, 2764)(1325, 2765)(1326, 2766)(1327, 2767)(1328, 2768)(1329, 2769)(1330, 2770)(1331, 2771)(1332, 2772)(1333, 2773)(1334, 2774)(1335, 2775)(1336, 2776)(1337, 2777)(1338, 2778)(1339, 2779)(1340, 2780)(1341, 2781)(1342, 2782)(1343, 2783)(1344, 2784)(1345, 2785)(1346, 2786)(1347, 2787)(1348, 2788)(1349, 2789)(1350, 2790)(1351, 2791)(1352, 2792)(1353, 2793)(1354, 2794)(1355, 2795)(1356, 2796)(1357, 2797)(1358, 2798)(1359, 2799)(1360, 2800)(1361, 2801)(1362, 2802)(1363, 2803)(1364, 2804)(1365, 2805)(1366, 2806)(1367, 2807)(1368, 2808)(1369, 2809)(1370, 2810)(1371, 2811)(1372, 2812)(1373, 2813)(1374, 2814)(1375, 2815)(1376, 2816)(1377, 2817)(1378, 2818)(1379, 2819)(1380, 2820)(1381, 2821)(1382, 2822)(1383, 2823)(1384, 2824)(1385, 2825)(1386, 2826)(1387, 2827)(1388, 2828)(1389, 2829)(1390, 2830)(1391, 2831)(1392, 2832)(1393, 2833)(1394, 2834)(1395, 2835)(1396, 2836)(1397, 2837)(1398, 2838)(1399, 2839)(1400, 2840)(1401, 2841)(1402, 2842)(1403, 2843)(1404, 2844)(1405, 2845)(1406, 2846)(1407, 2847)(1408, 2848)(1409, 2849)(1410, 2850)(1411, 2851)(1412, 2852)(1413, 2853)(1414, 2854)(1415, 2855)(1416, 2856)(1417, 2857)(1418, 2858)(1419, 2859)(1420, 2860)(1421, 2861)(1422, 2862)(1423, 2863)(1424, 2864)(1425, 2865)(1426, 2866)(1427, 2867)(1428, 2868)(1429, 2869)(1430, 2870)(1431, 2871)(1432, 2872)(1433, 2873)(1434, 2874)(1435, 2875)(1436, 2876)(1437, 2877)(1438, 2878)(1439, 2879)(1440, 2880) 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 E16.1312 Graph:: bipartite v = 450 e = 1440 f = 960 degree seq :: [ 4^360, 16^90 ] E16.1312 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8}) Quotient :: dipole Aut^+ = A6 : C2 (small group id <720, 764>) Aut = $<1440, 5843>$ (small group id <1440, 5843>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^3, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^8, Y3 * Y1^-2 * Y3^2 * Y1 * Y3^-7 * Y1^-1, (Y3^-2 * Y1)^5, (Y3 * Y2^-1)^8, Y3^3 * Y1^-1 * Y3^2 * Y1^-1 * Y3^-2 * Y1 * Y3^-4 * Y1^-1 * Y3^2 * Y1^-1 * Y3^-3 * Y1^-1, Y3^2 * Y1^-1 * Y3^-3 * Y1 * Y3^-3 * Y1 * Y3^-3 * Y1^-1 * Y3^2 * Y1^-1 * Y3^3 * Y1^-1, Y3 * Y1^-1 * Y3^-3 * Y1 * Y3^-4 * Y1 * Y3^-1 * Y1 * Y3^-3 * Y1 * Y3^-4 * Y1^-1, Y3^2 * Y1^-1 * Y3^-3 * Y1 * Y3^3 * Y1 * Y3^-3 * Y1 * Y3^-3 * Y1 * Y3^-2 * Y1^-1 ] Map:: polytopal R = (1, 721, 2, 722, 4, 724)(3, 723, 8, 728, 10, 730)(5, 725, 12, 732, 6, 726)(7, 727, 15, 735, 11, 731)(9, 729, 18, 738, 20, 740)(13, 733, 25, 745, 23, 743)(14, 734, 24, 744, 28, 748)(16, 736, 31, 751, 29, 749)(17, 737, 33, 753, 21, 741)(19, 739, 36, 756, 38, 758)(22, 742, 30, 750, 42, 762)(26, 746, 47, 767, 45, 765)(27, 747, 48, 768, 50, 770)(32, 752, 56, 776, 54, 774)(34, 754, 59, 779, 57, 777)(35, 755, 61, 781, 39, 759)(37, 757, 64, 784, 65, 785)(40, 760, 58, 778, 69, 789)(41, 761, 70, 790, 71, 791)(43, 763, 46, 766, 74, 794)(44, 764, 75, 795, 51, 771)(49, 769, 81, 801, 82, 802)(52, 772, 55, 775, 86, 806)(53, 773, 87, 807, 72, 792)(60, 780, 96, 816, 94, 814)(62, 782, 99, 819, 97, 817)(63, 783, 101, 821, 66, 786)(67, 787, 98, 818, 107, 827)(68, 788, 108, 828, 109, 829)(73, 793, 114, 834, 116, 836)(76, 796, 120, 840, 118, 838)(77, 797, 79, 799, 122, 842)(78, 798, 123, 843, 117, 837)(80, 800, 126, 846, 83, 803)(84, 804, 119, 839, 132, 852)(85, 805, 133, 853, 135, 855)(88, 808, 139, 859, 137, 857)(89, 809, 91, 811, 141, 861)(90, 810, 142, 862, 136, 856)(92, 812, 95, 815, 146, 866)(93, 813, 147, 867, 110, 830)(100, 820, 156, 876, 154, 874)(102, 822, 159, 879, 157, 877)(103, 823, 161, 881, 104, 824)(105, 825, 158, 878, 165, 885)(106, 826, 166, 886, 167, 887)(111, 831, 172, 892, 112, 832)(113, 833, 138, 858, 176, 896)(115, 835, 178, 898, 179, 899)(121, 841, 185, 905, 187, 907)(124, 844, 191, 911, 189, 909)(125, 845, 192, 912, 188, 908)(127, 847, 196, 916, 194, 914)(128, 848, 198, 918, 129, 849)(130, 850, 195, 915, 202, 922)(131, 851, 203, 923, 204, 924)(134, 854, 207, 927, 208, 928)(140, 860, 214, 934, 216, 936)(143, 863, 219, 939, 218, 938)(144, 864, 220, 940, 217, 937)(145, 865, 222, 942, 224, 944)(148, 868, 227, 947, 226, 946)(149, 869, 151, 871, 229, 949)(150, 870, 230, 950, 225, 945)(152, 872, 155, 875, 234, 954)(153, 873, 210, 930, 168, 888)(160, 880, 243, 963, 241, 961)(162, 882, 246, 966, 244, 964)(163, 883, 245, 965, 249, 969)(164, 884, 250, 970, 251, 971)(169, 889, 255, 975, 170, 890)(171, 891, 205, 925, 183, 903)(173, 893, 261, 981, 259, 979)(174, 894, 260, 980, 264, 984)(175, 895, 265, 985, 266, 986)(177, 897, 267, 987, 180, 900)(181, 901, 190, 910, 212, 932)(182, 902, 184, 904, 274, 994)(186, 906, 278, 998, 279, 999)(193, 913, 286, 1006, 284, 1004)(197, 917, 291, 1011, 289, 1009)(199, 919, 294, 1014, 292, 1012)(200, 920, 293, 1013, 297, 1017)(201, 921, 298, 1018, 299, 1019)(206, 926, 302, 1022, 209, 929)(211, 931, 213, 933, 309, 1029)(215, 935, 313, 1033, 314, 1034)(221, 941, 321, 1041, 319, 1039)(223, 943, 323, 1043, 324, 1044)(228, 948, 329, 1049, 331, 1051)(231, 951, 334, 1054, 333, 1053)(232, 952, 335, 1055, 332, 1052)(233, 953, 337, 1057, 339, 1059)(235, 955, 341, 1061, 307, 1027)(236, 956, 238, 958, 343, 1063)(237, 957, 344, 1064, 340, 1060)(239, 959, 242, 962, 348, 1068)(240, 960, 326, 1046, 252, 972)(247, 967, 357, 1077, 355, 1075)(248, 968, 358, 1078, 359, 1079)(253, 973, 363, 1083, 254, 974)(256, 976, 368, 1088, 366, 1086)(257, 977, 367, 1087, 371, 1091)(258, 978, 275, 995, 372, 1092)(262, 982, 377, 1097, 375, 1095)(263, 983, 378, 1098, 379, 1099)(268, 988, 384, 1104, 382, 1102)(269, 989, 386, 1106, 270, 990)(271, 991, 383, 1103, 390, 1110)(272, 992, 310, 1030, 391, 1111)(273, 993, 392, 1112, 394, 1114)(276, 996, 396, 1116, 395, 1115)(277, 997, 398, 1118, 280, 1000)(281, 1001, 285, 1005, 288, 1008)(282, 1002, 283, 1003, 405, 1125)(287, 1007, 290, 1010, 410, 1130)(295, 1015, 419, 1139, 417, 1137)(296, 1016, 420, 1140, 421, 1141)(300, 1020, 425, 1145, 301, 1021)(303, 1023, 430, 1150, 428, 1148)(304, 1024, 432, 1152, 305, 1025)(306, 1026, 429, 1149, 436, 1156)(308, 1028, 437, 1157, 439, 1159)(311, 1031, 441, 1161, 440, 1160)(312, 1032, 443, 1163, 315, 1035)(316, 1036, 320, 1040, 374, 1094)(317, 1037, 318, 1038, 449, 1169)(322, 1042, 453, 1173, 325, 1045)(327, 1047, 328, 1048, 459, 1179)(330, 1050, 462, 1182, 463, 1183)(336, 1056, 470, 1190, 468, 1188)(338, 1058, 472, 1192, 473, 1193)(342, 1062, 477, 1197, 479, 1199)(345, 1065, 482, 1202, 481, 1201)(346, 1066, 483, 1203, 480, 1200)(347, 1067, 485, 1205, 487, 1207)(349, 1069, 489, 1209, 458, 1178)(350, 1070, 352, 1072, 491, 1211)(351, 1071, 402, 1122, 488, 1208)(353, 1073, 356, 1076, 495, 1215)(354, 1074, 475, 1195, 360, 1080)(361, 1081, 501, 1221, 362, 1082)(364, 1084, 506, 1226, 504, 1224)(365, 1085, 505, 1225, 508, 1228)(369, 1089, 513, 1233, 511, 1231)(370, 1090, 514, 1234, 515, 1235)(373, 1093, 376, 1096, 518, 1238)(380, 1100, 525, 1245, 381, 1101)(385, 1105, 530, 1250, 528, 1248)(387, 1107, 533, 1253, 531, 1251)(388, 1108, 532, 1252, 536, 1256)(389, 1109, 537, 1257, 538, 1258)(393, 1113, 541, 1261, 516, 1236)(397, 1117, 545, 1265, 544, 1264)(399, 1119, 547, 1267, 546, 1266)(400, 1120, 549, 1269, 401, 1121)(403, 1123, 411, 1131, 553, 1273)(404, 1124, 554, 1274, 555, 1275)(406, 1126, 557, 1277, 556, 1276)(407, 1127, 408, 1128, 560, 1280)(409, 1129, 562, 1282, 564, 1284)(412, 1132, 414, 1134, 567, 1287)(413, 1133, 447, 1167, 565, 1285)(415, 1135, 418, 1138, 571, 1291)(416, 1136, 543, 1263, 422, 1142)(423, 1143, 577, 1297, 424, 1144)(426, 1146, 581, 1301, 579, 1299)(427, 1147, 580, 1300, 583, 1303)(431, 1151, 476, 1196, 585, 1305)(433, 1153, 589, 1309, 587, 1307)(434, 1154, 588, 1308, 592, 1312)(435, 1155, 593, 1313, 594, 1314)(438, 1158, 596, 1316, 539, 1259)(442, 1162, 600, 1320, 599, 1319)(444, 1164, 602, 1322, 601, 1321)(445, 1165, 604, 1324, 446, 1166)(448, 1168, 519, 1239, 608, 1328)(450, 1170, 610, 1330, 609, 1329)(451, 1171, 452, 1172, 613, 1333)(454, 1174, 617, 1337, 615, 1335)(455, 1175, 619, 1339, 456, 1176)(457, 1177, 616, 1336, 521, 1241)(460, 1180, 624, 1344, 623, 1343)(461, 1181, 598, 1318, 464, 1184)(465, 1185, 469, 1189, 510, 1230)(466, 1186, 467, 1187, 630, 1350)(471, 1191, 634, 1354, 474, 1194)(478, 1198, 576, 1296, 575, 1295)(484, 1204, 573, 1293, 574, 1294)(486, 1206, 648, 1368, 572, 1292)(490, 1210, 582, 1302, 651, 1371)(492, 1212, 612, 1332, 552, 1272)(493, 1213, 652, 1372, 569, 1289)(494, 1214, 654, 1374, 603, 1323)(496, 1216, 655, 1375, 639, 1359)(497, 1217, 498, 1218, 590, 1310)(499, 1219, 591, 1311, 500, 1220)(502, 1222, 607, 1327, 568, 1288)(503, 1223, 566, 1286, 657, 1377)(507, 1227, 578, 1298, 661, 1381)(509, 1229, 512, 1232, 663, 1383)(517, 1237, 671, 1391, 672, 1392)(520, 1240, 522, 1242, 653, 1373)(523, 1243, 650, 1370, 524, 1244)(526, 1246, 674, 1394, 656, 1376)(527, 1247, 529, 1249, 676, 1396)(534, 1254, 632, 1352, 633, 1353)(535, 1255, 628, 1348, 627, 1347)(540, 1260, 680, 1400, 542, 1262)(548, 1268, 629, 1349, 664, 1384)(550, 1270, 614, 1334, 625, 1345)(551, 1271, 621, 1341, 606, 1326)(558, 1278, 605, 1325, 631, 1351)(559, 1279, 622, 1342, 673, 1393)(561, 1281, 611, 1331, 620, 1340)(563, 1283, 685, 1405, 626, 1346)(570, 1290, 687, 1407, 618, 1338)(584, 1304, 586, 1306, 692, 1412)(595, 1315, 695, 1415, 597, 1317)(635, 1355, 701, 1421, 699, 1419)(636, 1356, 678, 1398, 637, 1357)(638, 1358, 700, 1420, 666, 1386)(640, 1360, 677, 1397, 689, 1409)(641, 1361, 696, 1416, 642, 1362)(643, 1363, 646, 1366, 659, 1379)(644, 1364, 645, 1365, 682, 1402)(647, 1367, 702, 1422, 649, 1369)(658, 1378, 660, 1380, 704, 1424)(662, 1382, 705, 1425, 683, 1403)(665, 1385, 667, 1387, 693, 1413)(668, 1388, 679, 1399, 669, 1389)(670, 1390, 681, 1401, 694, 1414)(675, 1395, 706, 1426, 697, 1417)(684, 1404, 707, 1427, 686, 1406)(688, 1408, 690, 1410, 709, 1429)(691, 1411, 710, 1430, 698, 1418)(703, 1423, 714, 1434, 713, 1433)(708, 1428, 715, 1435, 716, 1436)(711, 1431, 717, 1437, 712, 1432)(718, 1438, 720, 1440, 719, 1439)(1441, 2161)(1442, 2162)(1443, 2163)(1444, 2164)(1445, 2165)(1446, 2166)(1447, 2167)(1448, 2168)(1449, 2169)(1450, 2170)(1451, 2171)(1452, 2172)(1453, 2173)(1454, 2174)(1455, 2175)(1456, 2176)(1457, 2177)(1458, 2178)(1459, 2179)(1460, 2180)(1461, 2181)(1462, 2182)(1463, 2183)(1464, 2184)(1465, 2185)(1466, 2186)(1467, 2187)(1468, 2188)(1469, 2189)(1470, 2190)(1471, 2191)(1472, 2192)(1473, 2193)(1474, 2194)(1475, 2195)(1476, 2196)(1477, 2197)(1478, 2198)(1479, 2199)(1480, 2200)(1481, 2201)(1482, 2202)(1483, 2203)(1484, 2204)(1485, 2205)(1486, 2206)(1487, 2207)(1488, 2208)(1489, 2209)(1490, 2210)(1491, 2211)(1492, 2212)(1493, 2213)(1494, 2214)(1495, 2215)(1496, 2216)(1497, 2217)(1498, 2218)(1499, 2219)(1500, 2220)(1501, 2221)(1502, 2222)(1503, 2223)(1504, 2224)(1505, 2225)(1506, 2226)(1507, 2227)(1508, 2228)(1509, 2229)(1510, 2230)(1511, 2231)(1512, 2232)(1513, 2233)(1514, 2234)(1515, 2235)(1516, 2236)(1517, 2237)(1518, 2238)(1519, 2239)(1520, 2240)(1521, 2241)(1522, 2242)(1523, 2243)(1524, 2244)(1525, 2245)(1526, 2246)(1527, 2247)(1528, 2248)(1529, 2249)(1530, 2250)(1531, 2251)(1532, 2252)(1533, 2253)(1534, 2254)(1535, 2255)(1536, 2256)(1537, 2257)(1538, 2258)(1539, 2259)(1540, 2260)(1541, 2261)(1542, 2262)(1543, 2263)(1544, 2264)(1545, 2265)(1546, 2266)(1547, 2267)(1548, 2268)(1549, 2269)(1550, 2270)(1551, 2271)(1552, 2272)(1553, 2273)(1554, 2274)(1555, 2275)(1556, 2276)(1557, 2277)(1558, 2278)(1559, 2279)(1560, 2280)(1561, 2281)(1562, 2282)(1563, 2283)(1564, 2284)(1565, 2285)(1566, 2286)(1567, 2287)(1568, 2288)(1569, 2289)(1570, 2290)(1571, 2291)(1572, 2292)(1573, 2293)(1574, 2294)(1575, 2295)(1576, 2296)(1577, 2297)(1578, 2298)(1579, 2299)(1580, 2300)(1581, 2301)(1582, 2302)(1583, 2303)(1584, 2304)(1585, 2305)(1586, 2306)(1587, 2307)(1588, 2308)(1589, 2309)(1590, 2310)(1591, 2311)(1592, 2312)(1593, 2313)(1594, 2314)(1595, 2315)(1596, 2316)(1597, 2317)(1598, 2318)(1599, 2319)(1600, 2320)(1601, 2321)(1602, 2322)(1603, 2323)(1604, 2324)(1605, 2325)(1606, 2326)(1607, 2327)(1608, 2328)(1609, 2329)(1610, 2330)(1611, 2331)(1612, 2332)(1613, 2333)(1614, 2334)(1615, 2335)(1616, 2336)(1617, 2337)(1618, 2338)(1619, 2339)(1620, 2340)(1621, 2341)(1622, 2342)(1623, 2343)(1624, 2344)(1625, 2345)(1626, 2346)(1627, 2347)(1628, 2348)(1629, 2349)(1630, 2350)(1631, 2351)(1632, 2352)(1633, 2353)(1634, 2354)(1635, 2355)(1636, 2356)(1637, 2357)(1638, 2358)(1639, 2359)(1640, 2360)(1641, 2361)(1642, 2362)(1643, 2363)(1644, 2364)(1645, 2365)(1646, 2366)(1647, 2367)(1648, 2368)(1649, 2369)(1650, 2370)(1651, 2371)(1652, 2372)(1653, 2373)(1654, 2374)(1655, 2375)(1656, 2376)(1657, 2377)(1658, 2378)(1659, 2379)(1660, 2380)(1661, 2381)(1662, 2382)(1663, 2383)(1664, 2384)(1665, 2385)(1666, 2386)(1667, 2387)(1668, 2388)(1669, 2389)(1670, 2390)(1671, 2391)(1672, 2392)(1673, 2393)(1674, 2394)(1675, 2395)(1676, 2396)(1677, 2397)(1678, 2398)(1679, 2399)(1680, 2400)(1681, 2401)(1682, 2402)(1683, 2403)(1684, 2404)(1685, 2405)(1686, 2406)(1687, 2407)(1688, 2408)(1689, 2409)(1690, 2410)(1691, 2411)(1692, 2412)(1693, 2413)(1694, 2414)(1695, 2415)(1696, 2416)(1697, 2417)(1698, 2418)(1699, 2419)(1700, 2420)(1701, 2421)(1702, 2422)(1703, 2423)(1704, 2424)(1705, 2425)(1706, 2426)(1707, 2427)(1708, 2428)(1709, 2429)(1710, 2430)(1711, 2431)(1712, 2432)(1713, 2433)(1714, 2434)(1715, 2435)(1716, 2436)(1717, 2437)(1718, 2438)(1719, 2439)(1720, 2440)(1721, 2441)(1722, 2442)(1723, 2443)(1724, 2444)(1725, 2445)(1726, 2446)(1727, 2447)(1728, 2448)(1729, 2449)(1730, 2450)(1731, 2451)(1732, 2452)(1733, 2453)(1734, 2454)(1735, 2455)(1736, 2456)(1737, 2457)(1738, 2458)(1739, 2459)(1740, 2460)(1741, 2461)(1742, 2462)(1743, 2463)(1744, 2464)(1745, 2465)(1746, 2466)(1747, 2467)(1748, 2468)(1749, 2469)(1750, 2470)(1751, 2471)(1752, 2472)(1753, 2473)(1754, 2474)(1755, 2475)(1756, 2476)(1757, 2477)(1758, 2478)(1759, 2479)(1760, 2480)(1761, 2481)(1762, 2482)(1763, 2483)(1764, 2484)(1765, 2485)(1766, 2486)(1767, 2487)(1768, 2488)(1769, 2489)(1770, 2490)(1771, 2491)(1772, 2492)(1773, 2493)(1774, 2494)(1775, 2495)(1776, 2496)(1777, 2497)(1778, 2498)(1779, 2499)(1780, 2500)(1781, 2501)(1782, 2502)(1783, 2503)(1784, 2504)(1785, 2505)(1786, 2506)(1787, 2507)(1788, 2508)(1789, 2509)(1790, 2510)(1791, 2511)(1792, 2512)(1793, 2513)(1794, 2514)(1795, 2515)(1796, 2516)(1797, 2517)(1798, 2518)(1799, 2519)(1800, 2520)(1801, 2521)(1802, 2522)(1803, 2523)(1804, 2524)(1805, 2525)(1806, 2526)(1807, 2527)(1808, 2528)(1809, 2529)(1810, 2530)(1811, 2531)(1812, 2532)(1813, 2533)(1814, 2534)(1815, 2535)(1816, 2536)(1817, 2537)(1818, 2538)(1819, 2539)(1820, 2540)(1821, 2541)(1822, 2542)(1823, 2543)(1824, 2544)(1825, 2545)(1826, 2546)(1827, 2547)(1828, 2548)(1829, 2549)(1830, 2550)(1831, 2551)(1832, 2552)(1833, 2553)(1834, 2554)(1835, 2555)(1836, 2556)(1837, 2557)(1838, 2558)(1839, 2559)(1840, 2560)(1841, 2561)(1842, 2562)(1843, 2563)(1844, 2564)(1845, 2565)(1846, 2566)(1847, 2567)(1848, 2568)(1849, 2569)(1850, 2570)(1851, 2571)(1852, 2572)(1853, 2573)(1854, 2574)(1855, 2575)(1856, 2576)(1857, 2577)(1858, 2578)(1859, 2579)(1860, 2580)(1861, 2581)(1862, 2582)(1863, 2583)(1864, 2584)(1865, 2585)(1866, 2586)(1867, 2587)(1868, 2588)(1869, 2589)(1870, 2590)(1871, 2591)(1872, 2592)(1873, 2593)(1874, 2594)(1875, 2595)(1876, 2596)(1877, 2597)(1878, 2598)(1879, 2599)(1880, 2600)(1881, 2601)(1882, 2602)(1883, 2603)(1884, 2604)(1885, 2605)(1886, 2606)(1887, 2607)(1888, 2608)(1889, 2609)(1890, 2610)(1891, 2611)(1892, 2612)(1893, 2613)(1894, 2614)(1895, 2615)(1896, 2616)(1897, 2617)(1898, 2618)(1899, 2619)(1900, 2620)(1901, 2621)(1902, 2622)(1903, 2623)(1904, 2624)(1905, 2625)(1906, 2626)(1907, 2627)(1908, 2628)(1909, 2629)(1910, 2630)(1911, 2631)(1912, 2632)(1913, 2633)(1914, 2634)(1915, 2635)(1916, 2636)(1917, 2637)(1918, 2638)(1919, 2639)(1920, 2640)(1921, 2641)(1922, 2642)(1923, 2643)(1924, 2644)(1925, 2645)(1926, 2646)(1927, 2647)(1928, 2648)(1929, 2649)(1930, 2650)(1931, 2651)(1932, 2652)(1933, 2653)(1934, 2654)(1935, 2655)(1936, 2656)(1937, 2657)(1938, 2658)(1939, 2659)(1940, 2660)(1941, 2661)(1942, 2662)(1943, 2663)(1944, 2664)(1945, 2665)(1946, 2666)(1947, 2667)(1948, 2668)(1949, 2669)(1950, 2670)(1951, 2671)(1952, 2672)(1953, 2673)(1954, 2674)(1955, 2675)(1956, 2676)(1957, 2677)(1958, 2678)(1959, 2679)(1960, 2680)(1961, 2681)(1962, 2682)(1963, 2683)(1964, 2684)(1965, 2685)(1966, 2686)(1967, 2687)(1968, 2688)(1969, 2689)(1970, 2690)(1971, 2691)(1972, 2692)(1973, 2693)(1974, 2694)(1975, 2695)(1976, 2696)(1977, 2697)(1978, 2698)(1979, 2699)(1980, 2700)(1981, 2701)(1982, 2702)(1983, 2703)(1984, 2704)(1985, 2705)(1986, 2706)(1987, 2707)(1988, 2708)(1989, 2709)(1990, 2710)(1991, 2711)(1992, 2712)(1993, 2713)(1994, 2714)(1995, 2715)(1996, 2716)(1997, 2717)(1998, 2718)(1999, 2719)(2000, 2720)(2001, 2721)(2002, 2722)(2003, 2723)(2004, 2724)(2005, 2725)(2006, 2726)(2007, 2727)(2008, 2728)(2009, 2729)(2010, 2730)(2011, 2731)(2012, 2732)(2013, 2733)(2014, 2734)(2015, 2735)(2016, 2736)(2017, 2737)(2018, 2738)(2019, 2739)(2020, 2740)(2021, 2741)(2022, 2742)(2023, 2743)(2024, 2744)(2025, 2745)(2026, 2746)(2027, 2747)(2028, 2748)(2029, 2749)(2030, 2750)(2031, 2751)(2032, 2752)(2033, 2753)(2034, 2754)(2035, 2755)(2036, 2756)(2037, 2757)(2038, 2758)(2039, 2759)(2040, 2760)(2041, 2761)(2042, 2762)(2043, 2763)(2044, 2764)(2045, 2765)(2046, 2766)(2047, 2767)(2048, 2768)(2049, 2769)(2050, 2770)(2051, 2771)(2052, 2772)(2053, 2773)(2054, 2774)(2055, 2775)(2056, 2776)(2057, 2777)(2058, 2778)(2059, 2779)(2060, 2780)(2061, 2781)(2062, 2782)(2063, 2783)(2064, 2784)(2065, 2785)(2066, 2786)(2067, 2787)(2068, 2788)(2069, 2789)(2070, 2790)(2071, 2791)(2072, 2792)(2073, 2793)(2074, 2794)(2075, 2795)(2076, 2796)(2077, 2797)(2078, 2798)(2079, 2799)(2080, 2800)(2081, 2801)(2082, 2802)(2083, 2803)(2084, 2804)(2085, 2805)(2086, 2806)(2087, 2807)(2088, 2808)(2089, 2809)(2090, 2810)(2091, 2811)(2092, 2812)(2093, 2813)(2094, 2814)(2095, 2815)(2096, 2816)(2097, 2817)(2098, 2818)(2099, 2819)(2100, 2820)(2101, 2821)(2102, 2822)(2103, 2823)(2104, 2824)(2105, 2825)(2106, 2826)(2107, 2827)(2108, 2828)(2109, 2829)(2110, 2830)(2111, 2831)(2112, 2832)(2113, 2833)(2114, 2834)(2115, 2835)(2116, 2836)(2117, 2837)(2118, 2838)(2119, 2839)(2120, 2840)(2121, 2841)(2122, 2842)(2123, 2843)(2124, 2844)(2125, 2845)(2126, 2846)(2127, 2847)(2128, 2848)(2129, 2849)(2130, 2850)(2131, 2851)(2132, 2852)(2133, 2853)(2134, 2854)(2135, 2855)(2136, 2856)(2137, 2857)(2138, 2858)(2139, 2859)(2140, 2860)(2141, 2861)(2142, 2862)(2143, 2863)(2144, 2864)(2145, 2865)(2146, 2866)(2147, 2867)(2148, 2868)(2149, 2869)(2150, 2870)(2151, 2871)(2152, 2872)(2153, 2873)(2154, 2874)(2155, 2875)(2156, 2876)(2157, 2877)(2158, 2878)(2159, 2879)(2160, 2880) L = (1, 1443)(2, 1446)(3, 1449)(4, 1451)(5, 1441)(6, 1454)(7, 1442)(8, 1444)(9, 1459)(10, 1461)(11, 1462)(12, 1463)(13, 1445)(14, 1467)(15, 1469)(16, 1447)(17, 1448)(18, 1450)(19, 1477)(20, 1479)(21, 1480)(22, 1481)(23, 1483)(24, 1452)(25, 1485)(26, 1453)(27, 1489)(28, 1491)(29, 1492)(30, 1455)(31, 1494)(32, 1456)(33, 1497)(34, 1457)(35, 1458)(36, 1460)(37, 1466)(38, 1506)(39, 1507)(40, 1508)(41, 1500)(42, 1512)(43, 1513)(44, 1464)(45, 1517)(46, 1465)(47, 1505)(48, 1468)(49, 1472)(50, 1523)(51, 1524)(52, 1525)(53, 1470)(54, 1529)(55, 1471)(56, 1522)(57, 1532)(58, 1473)(59, 1534)(60, 1474)(61, 1537)(62, 1475)(63, 1476)(64, 1478)(65, 1544)(66, 1545)(67, 1546)(68, 1540)(69, 1550)(70, 1482)(71, 1552)(72, 1553)(73, 1555)(74, 1557)(75, 1558)(76, 1484)(77, 1561)(78, 1486)(79, 1487)(80, 1488)(81, 1490)(82, 1569)(83, 1570)(84, 1571)(85, 1574)(86, 1576)(87, 1577)(88, 1493)(89, 1580)(90, 1495)(91, 1496)(92, 1585)(93, 1498)(94, 1589)(95, 1499)(96, 1511)(97, 1592)(98, 1501)(99, 1594)(100, 1502)(101, 1597)(102, 1503)(103, 1504)(104, 1603)(105, 1604)(106, 1600)(107, 1608)(108, 1509)(109, 1610)(110, 1611)(111, 1510)(112, 1614)(113, 1615)(114, 1514)(115, 1516)(116, 1620)(117, 1621)(118, 1622)(119, 1515)(120, 1619)(121, 1626)(122, 1628)(123, 1629)(124, 1518)(125, 1519)(126, 1634)(127, 1520)(128, 1521)(129, 1640)(130, 1641)(131, 1637)(132, 1645)(133, 1526)(134, 1528)(135, 1649)(136, 1650)(137, 1651)(138, 1527)(139, 1648)(140, 1655)(141, 1657)(142, 1658)(143, 1530)(144, 1531)(145, 1663)(146, 1665)(147, 1666)(148, 1533)(149, 1668)(150, 1535)(151, 1536)(152, 1673)(153, 1538)(154, 1676)(155, 1539)(156, 1549)(157, 1679)(158, 1541)(159, 1681)(160, 1542)(161, 1684)(162, 1543)(163, 1688)(164, 1687)(165, 1692)(166, 1547)(167, 1694)(168, 1582)(169, 1548)(170, 1697)(171, 1698)(172, 1699)(173, 1551)(174, 1703)(175, 1702)(176, 1630)(177, 1554)(178, 1556)(179, 1710)(180, 1711)(181, 1712)(182, 1713)(183, 1559)(184, 1560)(185, 1562)(186, 1564)(187, 1720)(188, 1721)(189, 1722)(190, 1563)(191, 1719)(192, 1724)(193, 1565)(194, 1727)(195, 1566)(196, 1729)(197, 1567)(198, 1732)(199, 1568)(200, 1736)(201, 1735)(202, 1725)(203, 1572)(204, 1741)(205, 1587)(206, 1573)(207, 1575)(208, 1745)(209, 1746)(210, 1747)(211, 1748)(212, 1578)(213, 1579)(214, 1581)(215, 1583)(216, 1755)(217, 1756)(218, 1757)(219, 1754)(220, 1759)(221, 1584)(222, 1586)(223, 1588)(224, 1765)(225, 1766)(226, 1767)(227, 1764)(228, 1770)(229, 1772)(230, 1773)(231, 1590)(232, 1591)(233, 1778)(234, 1780)(235, 1593)(236, 1782)(237, 1595)(238, 1596)(239, 1787)(240, 1598)(241, 1790)(242, 1599)(243, 1607)(244, 1793)(245, 1601)(246, 1795)(247, 1602)(248, 1633)(249, 1800)(250, 1605)(251, 1802)(252, 1670)(253, 1606)(254, 1805)(255, 1806)(256, 1609)(257, 1810)(258, 1809)(259, 1813)(260, 1612)(261, 1815)(262, 1613)(263, 1776)(264, 1760)(265, 1616)(266, 1821)(267, 1822)(268, 1617)(269, 1618)(270, 1828)(271, 1829)(272, 1825)(273, 1833)(274, 1835)(275, 1623)(276, 1624)(277, 1625)(278, 1627)(279, 1841)(280, 1842)(281, 1843)(282, 1844)(283, 1631)(284, 1847)(285, 1632)(286, 1799)(287, 1849)(288, 1635)(289, 1852)(290, 1636)(291, 1644)(292, 1855)(293, 1638)(294, 1857)(295, 1639)(296, 1661)(297, 1862)(298, 1642)(299, 1864)(300, 1643)(301, 1867)(302, 1868)(303, 1646)(304, 1647)(305, 1874)(306, 1875)(307, 1871)(308, 1878)(309, 1880)(310, 1652)(311, 1653)(312, 1654)(313, 1656)(314, 1886)(315, 1887)(316, 1888)(317, 1804)(318, 1659)(319, 1891)(320, 1660)(321, 1861)(322, 1662)(323, 1664)(324, 1896)(325, 1897)(326, 1898)(327, 1866)(328, 1667)(329, 1669)(330, 1671)(331, 1904)(332, 1905)(333, 1906)(334, 1903)(335, 1908)(336, 1672)(337, 1674)(338, 1675)(339, 1914)(340, 1915)(341, 1913)(342, 1918)(343, 1920)(344, 1921)(345, 1677)(346, 1678)(347, 1926)(348, 1928)(349, 1680)(350, 1930)(351, 1682)(352, 1683)(353, 1934)(354, 1685)(355, 1937)(356, 1686)(357, 1691)(358, 1689)(359, 1940)(360, 1784)(361, 1690)(362, 1943)(363, 1944)(364, 1693)(365, 1947)(366, 1949)(367, 1695)(368, 1951)(369, 1696)(370, 1924)(371, 1909)(372, 1956)(373, 1957)(374, 1700)(375, 1960)(376, 1701)(377, 1706)(378, 1704)(379, 1964)(380, 1705)(381, 1966)(382, 1967)(383, 1707)(384, 1968)(385, 1708)(386, 1971)(387, 1709)(388, 1975)(389, 1974)(390, 1796)(391, 1979)(392, 1714)(393, 1715)(394, 1982)(395, 1983)(396, 1984)(397, 1716)(398, 1986)(399, 1717)(400, 1718)(401, 1991)(402, 1992)(403, 1988)(404, 1820)(405, 1996)(406, 1723)(407, 1999)(408, 1726)(409, 2003)(410, 2005)(411, 1728)(412, 2006)(413, 1730)(414, 1731)(415, 2010)(416, 1733)(417, 2013)(418, 1734)(419, 1739)(420, 1737)(421, 2016)(422, 1836)(423, 1738)(424, 2018)(425, 2019)(426, 1740)(427, 2022)(428, 2024)(429, 1742)(430, 2025)(431, 1743)(432, 2027)(433, 1744)(434, 2031)(435, 2030)(436, 1858)(437, 1749)(438, 1750)(439, 2037)(440, 2038)(441, 2039)(442, 1751)(443, 2041)(444, 1752)(445, 1753)(446, 2046)(447, 2047)(448, 2043)(449, 2049)(450, 1758)(451, 2052)(452, 1761)(453, 2055)(454, 1762)(455, 1763)(456, 2061)(457, 2062)(458, 2058)(459, 2063)(460, 1768)(461, 1769)(462, 1771)(463, 2068)(464, 1881)(465, 2069)(466, 1942)(467, 1774)(468, 2072)(469, 1775)(470, 1819)(471, 1777)(472, 1779)(473, 2077)(474, 2078)(475, 2079)(476, 1781)(477, 1783)(478, 1785)(479, 2082)(480, 2083)(481, 2084)(482, 2015)(483, 2014)(484, 1786)(485, 1788)(486, 1789)(487, 2089)(488, 1838)(489, 2012)(490, 2090)(491, 2009)(492, 1791)(493, 1792)(494, 2048)(495, 1823)(496, 1794)(497, 2034)(498, 1797)(499, 1798)(500, 2032)(501, 2008)(502, 1801)(503, 2096)(504, 2098)(505, 1803)(506, 1889)(507, 2093)(508, 2086)(509, 2102)(510, 1807)(511, 2105)(512, 1808)(513, 1812)(514, 1811)(515, 2109)(516, 2110)(517, 2095)(518, 2056)(519, 1814)(520, 2101)(521, 1816)(522, 1817)(523, 1818)(524, 2091)(525, 1995)(526, 2097)(527, 2115)(528, 2099)(529, 1824)(530, 1831)(531, 2080)(532, 1826)(533, 2073)(534, 1827)(535, 1837)(536, 2118)(537, 1830)(538, 2108)(539, 2081)(540, 1832)(541, 1834)(542, 2100)(543, 2088)(544, 2085)(545, 2067)(546, 2123)(547, 2104)(548, 1839)(549, 2065)(550, 1840)(551, 2044)(552, 2053)(553, 2066)(554, 1845)(555, 2106)(556, 2076)(557, 2071)(558, 1846)(559, 1863)(560, 2060)(561, 1848)(562, 1850)(563, 1851)(564, 2126)(565, 1883)(566, 1941)(567, 2092)(568, 1853)(569, 1854)(570, 1929)(571, 1869)(572, 1856)(573, 1955)(574, 1859)(575, 1860)(576, 1919)(577, 2113)(578, 1948)(579, 2128)(580, 1865)(581, 1899)(582, 1931)(583, 2117)(584, 2131)(585, 2129)(586, 1870)(587, 2107)(588, 1872)(589, 1938)(590, 1873)(591, 1882)(592, 2134)(593, 1876)(594, 2119)(595, 1877)(596, 1879)(597, 2130)(598, 2125)(599, 2122)(600, 1939)(601, 2137)(602, 2094)(603, 1884)(604, 1998)(605, 1885)(606, 2059)(607, 2070)(608, 1936)(609, 2121)(610, 2001)(611, 1890)(612, 1963)(613, 1990)(614, 1892)(615, 2138)(616, 1893)(617, 2127)(618, 1894)(619, 2051)(620, 1895)(621, 1989)(622, 2000)(623, 2136)(624, 2054)(625, 1900)(626, 1901)(627, 1902)(628, 1976)(629, 1993)(630, 2045)(631, 1907)(632, 1978)(633, 1910)(634, 2139)(635, 1911)(636, 1912)(637, 1972)(638, 1994)(639, 2112)(640, 1916)(641, 1917)(642, 2064)(643, 1970)(644, 2040)(645, 1922)(646, 1923)(647, 1925)(648, 1927)(649, 1980)(650, 1932)(651, 2023)(652, 1962)(653, 1933)(654, 1935)(655, 1959)(656, 2133)(657, 2007)(658, 1969)(659, 1945)(660, 1946)(661, 2017)(662, 1987)(663, 2140)(664, 1950)(665, 2114)(666, 1952)(667, 1953)(668, 1954)(669, 2033)(670, 2028)(671, 1958)(672, 2075)(673, 1961)(674, 1965)(675, 2042)(676, 2144)(677, 1973)(678, 1997)(679, 1977)(680, 2142)(681, 1981)(682, 1985)(683, 2143)(684, 2002)(685, 2004)(686, 2035)(687, 2011)(688, 2026)(689, 2020)(690, 2021)(691, 2057)(692, 2149)(693, 2029)(694, 2050)(695, 2147)(696, 2036)(697, 2148)(698, 2151)(699, 2152)(700, 2074)(701, 2111)(702, 2153)(703, 2087)(704, 2120)(705, 2103)(706, 2116)(707, 2156)(708, 2124)(709, 2135)(710, 2132)(711, 2141)(712, 2158)(713, 2159)(714, 2145)(715, 2146)(716, 2160)(717, 2150)(718, 2154)(719, 2155)(720, 2157)(721, 2161)(722, 2162)(723, 2163)(724, 2164)(725, 2165)(726, 2166)(727, 2167)(728, 2168)(729, 2169)(730, 2170)(731, 2171)(732, 2172)(733, 2173)(734, 2174)(735, 2175)(736, 2176)(737, 2177)(738, 2178)(739, 2179)(740, 2180)(741, 2181)(742, 2182)(743, 2183)(744, 2184)(745, 2185)(746, 2186)(747, 2187)(748, 2188)(749, 2189)(750, 2190)(751, 2191)(752, 2192)(753, 2193)(754, 2194)(755, 2195)(756, 2196)(757, 2197)(758, 2198)(759, 2199)(760, 2200)(761, 2201)(762, 2202)(763, 2203)(764, 2204)(765, 2205)(766, 2206)(767, 2207)(768, 2208)(769, 2209)(770, 2210)(771, 2211)(772, 2212)(773, 2213)(774, 2214)(775, 2215)(776, 2216)(777, 2217)(778, 2218)(779, 2219)(780, 2220)(781, 2221)(782, 2222)(783, 2223)(784, 2224)(785, 2225)(786, 2226)(787, 2227)(788, 2228)(789, 2229)(790, 2230)(791, 2231)(792, 2232)(793, 2233)(794, 2234)(795, 2235)(796, 2236)(797, 2237)(798, 2238)(799, 2239)(800, 2240)(801, 2241)(802, 2242)(803, 2243)(804, 2244)(805, 2245)(806, 2246)(807, 2247)(808, 2248)(809, 2249)(810, 2250)(811, 2251)(812, 2252)(813, 2253)(814, 2254)(815, 2255)(816, 2256)(817, 2257)(818, 2258)(819, 2259)(820, 2260)(821, 2261)(822, 2262)(823, 2263)(824, 2264)(825, 2265)(826, 2266)(827, 2267)(828, 2268)(829, 2269)(830, 2270)(831, 2271)(832, 2272)(833, 2273)(834, 2274)(835, 2275)(836, 2276)(837, 2277)(838, 2278)(839, 2279)(840, 2280)(841, 2281)(842, 2282)(843, 2283)(844, 2284)(845, 2285)(846, 2286)(847, 2287)(848, 2288)(849, 2289)(850, 2290)(851, 2291)(852, 2292)(853, 2293)(854, 2294)(855, 2295)(856, 2296)(857, 2297)(858, 2298)(859, 2299)(860, 2300)(861, 2301)(862, 2302)(863, 2303)(864, 2304)(865, 2305)(866, 2306)(867, 2307)(868, 2308)(869, 2309)(870, 2310)(871, 2311)(872, 2312)(873, 2313)(874, 2314)(875, 2315)(876, 2316)(877, 2317)(878, 2318)(879, 2319)(880, 2320)(881, 2321)(882, 2322)(883, 2323)(884, 2324)(885, 2325)(886, 2326)(887, 2327)(888, 2328)(889, 2329)(890, 2330)(891, 2331)(892, 2332)(893, 2333)(894, 2334)(895, 2335)(896, 2336)(897, 2337)(898, 2338)(899, 2339)(900, 2340)(901, 2341)(902, 2342)(903, 2343)(904, 2344)(905, 2345)(906, 2346)(907, 2347)(908, 2348)(909, 2349)(910, 2350)(911, 2351)(912, 2352)(913, 2353)(914, 2354)(915, 2355)(916, 2356)(917, 2357)(918, 2358)(919, 2359)(920, 2360)(921, 2361)(922, 2362)(923, 2363)(924, 2364)(925, 2365)(926, 2366)(927, 2367)(928, 2368)(929, 2369)(930, 2370)(931, 2371)(932, 2372)(933, 2373)(934, 2374)(935, 2375)(936, 2376)(937, 2377)(938, 2378)(939, 2379)(940, 2380)(941, 2381)(942, 2382)(943, 2383)(944, 2384)(945, 2385)(946, 2386)(947, 2387)(948, 2388)(949, 2389)(950, 2390)(951, 2391)(952, 2392)(953, 2393)(954, 2394)(955, 2395)(956, 2396)(957, 2397)(958, 2398)(959, 2399)(960, 2400)(961, 2401)(962, 2402)(963, 2403)(964, 2404)(965, 2405)(966, 2406)(967, 2407)(968, 2408)(969, 2409)(970, 2410)(971, 2411)(972, 2412)(973, 2413)(974, 2414)(975, 2415)(976, 2416)(977, 2417)(978, 2418)(979, 2419)(980, 2420)(981, 2421)(982, 2422)(983, 2423)(984, 2424)(985, 2425)(986, 2426)(987, 2427)(988, 2428)(989, 2429)(990, 2430)(991, 2431)(992, 2432)(993, 2433)(994, 2434)(995, 2435)(996, 2436)(997, 2437)(998, 2438)(999, 2439)(1000, 2440)(1001, 2441)(1002, 2442)(1003, 2443)(1004, 2444)(1005, 2445)(1006, 2446)(1007, 2447)(1008, 2448)(1009, 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2864)(1425, 2865)(1426, 2866)(1427, 2867)(1428, 2868)(1429, 2869)(1430, 2870)(1431, 2871)(1432, 2872)(1433, 2873)(1434, 2874)(1435, 2875)(1436, 2876)(1437, 2877)(1438, 2878)(1439, 2879)(1440, 2880) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E16.1311 Graph:: simple bipartite v = 960 e = 1440 f = 450 degree seq :: [ 2^720, 6^240 ] ## Checksum: 1312 records. ## Written on: Sun Oct 20 06:23:32 CEST 2019