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On this page are computer-accessible forms for the graph C4[ 126, 7 ] = PS(6,21;8).

(I) Following is a form readable by MAGMA:

g:=Graph<126|{ {21, 22}, {105, 106}, {35, 43}, {39, 47}, {38, 46}, {37, 45}, {36, 44}, {80, 88}, {81, 89}, {82, 90}, {83, 91}, {84, 92}, {32, 45}, {34, 47}, {80, 93}, {82, 95}, {33, 46}, {81, 94}, {35, 48}, {39, 52}, {75, 88}, {79, 92}, {2, 22}, {105, 125}, {104, 124}, {99, 119}, {98, 118}, {97, 117}, {96, 116}, {3, 23}, {8, 28}, {9, 29}, {10, 30}, {11, 31}, {36, 49}, {38, 51}, {76, 89}, {78, 91}, {1, 23}, {104, 126}, {97, 119}, {96, 118}, {8, 30}, {9, 31}, {37, 50}, {77, 90}, {40, 48}, {42, 50}, {41, 49}, {77, 85}, {78, 86}, {79, 87}, {2, 24}, {103, 125}, {102, 124}, {99, 121}, {98, 120}, {3, 25}, {6, 28}, {7, 29}, {4, 24}, {103, 123}, {102, 122}, {101, 121}, {100, 120}, {5, 25}, {6, 26}, {7, 27}, {32, 61}, {42, 55}, {40, 53}, {34, 63}, {64, 93}, {66, 95}, {72, 85}, {74, 87}, {4, 26}, {101, 123}, {100, 122}, {5, 27}, {33, 62}, {41, 54}, {65, 94}, {73, 86}, {24, 58}, {29, 63}, {28, 62}, {25, 59}, {64, 98}, {65, 99}, {68, 102}, {69, 103}, {23, 52}, {31, 60}, {27, 56}, {67, 96}, {71, 100}, {75, 104}, {22, 51}, {30, 59}, {28, 57}, {68, 97}, {70, 99}, {76, 105}, {26, 60}, {27, 61}, {66, 100}, {67, 101}, {29, 58}, {69, 98}, {10, 32}, {95, 117}, {94, 116}, {11, 33}, {14, 36}, {15, 37}, {90, 112}, {91, 113}, {1, 42}, {85, 126}, {12, 32}, {95, 115}, {94, 114}, {93, 113}, {92, 112}, {13, 33}, {14, 34}, {15, 35}, {24, 53}, {26, 55}, {72, 101}, {74, 103}, {12, 34}, {93, 115}, {92, 114}, {23, 57}, {22, 56}, {13, 35}, {70, 104}, {71, 105}, {25, 54}, {73, 102}, {31, 44}, {83, 96}, {16, 36}, {17, 37}, {18, 38}, {19, 39}, {88, 108}, {89, 109}, {90, 110}, {91, 111}, {30, 43}, {84, 97}, {16, 38}, {17, 39}, {88, 110}, {89, 111}, {18, 40}, {19, 41}, {86, 108}, {87, 109}, {20, 40}, {21, 41}, {86, 106}, {87, 107}, {20, 42}, {85, 107}, {10, 107}, {12, 109}, {14, 111}, {16, 113}, {18, 115}, {20, 117}, {9, 106}, {21, 118}, {13, 110}, {17, 114}, {14, 106}, {21, 113}, {15, 107}, {20, 112}, {11, 108}, {19, 116}, {43, 65}, {47, 69}, {46, 68}, {58, 80}, {59, 81}, {62, 84}, {44, 64}, {47, 67}, {46, 66}, {45, 65}, {60, 80}, {61, 81}, {62, 82}, {63, 83}, {44, 66}, {45, 67}, {60, 82}, {61, 83}, {2, 115}, {4, 117}, {6, 119}, {8, 121}, {10, 123}, {12, 125}, {1, 114}, {5, 118}, {9, 122}, {13, 126}, {48, 68}, {51, 71}, {50, 70}, {49, 69}, {56, 76}, {57, 77}, {58, 78}, {59, 79}, {1, 119}, {49, 71}, {48, 70}, {8, 126}, {56, 78}, {57, 79}, {3, 116}, {11, 124}, {2, 120}, {51, 73}, {50, 72}, {3, 121}, {6, 124}, {7, 125}, {54, 76}, {55, 77}, {16, 108}, {53, 73}, {52, 72}, {17, 109}, {18, 110}, {19, 111}, {54, 74}, {55, 75}, {4, 122}, {52, 74}, {5, 123}, {53, 75}, {7, 120}, {43, 84}, {15, 112}, {63, 64} }>;

(II) A more general form is to represent the graph as the orbit of {21, 22} under the group generated by the following permutations:

a: (1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)(64, 85)(65, 86)(66, 87)(67, 88)(68, 89)(69, 90)(70, 91)(71, 92)(72, 93)(73, 94)(74, 95)(75, 96)(76, 97)(77, 98)(78, 99)(79, 100)(80, 101)(81, 102)(82, 103)(83, 104)(84, 105)
b: (2, 49, 9, 91)(3, 97, 17, 55)(4, 19)(5, 46, 12, 88)(6, 94, 20, 52)(7, 16)(8, 43, 15, 85)(10, 13)(11, 61, 18, 103)(14, 58, 21, 100)(22, 71, 106, 78)(23, 119, 114, 42)(24, 41, 122, 111)(25, 68, 109, 75)(26, 116, 117, 39)(27, 38, 125, 108)(28, 65, 112, 72)(29, 113, 120, 36)(30, 35, 107, 126)(31, 83, 115, 69)(32, 110, 123, 33)(34, 80, 118, 66)(37, 77, 121, 84)(40, 74, 124, 81)(44, 63, 93, 98)(45, 90, 101, 62)(47, 60, 96, 95)(48, 87, 104, 59)(50, 57, 99, 92)(51, 105, 86, 56)(53, 54, 102, 89)(67, 82)(70, 79)(73, 76)
c: (1, 2)(3, 21)(4, 20)(5, 19)(6, 18)(7, 17)(8, 16)(9, 15)(10, 14)(11, 13)(22, 23)(24, 42)(25, 41)(26, 40)(27, 39)(28, 38)(29, 37)(30, 36)(31, 35)(32, 34)(43, 44)(45, 63)(46, 62)(47, 61)(48, 60)(49, 59)(50, 58)(51, 57)(52, 56)(53, 55)(64, 65)(66, 84)(67, 83)(68, 82)(69, 81)(70, 80)(71, 79)(72, 78)(73, 77)(74, 76)(85, 86)(87, 105)(88, 104)(89, 103)(90, 102)(91, 101)(92, 100)(93, 99)(94, 98)(95, 97)(106, 107)(108, 126)(109, 125)(110, 124)(111, 123)(112, 122)(113, 121)(114, 120)(115, 119)(116, 118)
d: (2, 14)(3, 6)(4, 19)(5, 11)(7, 16)(9, 21)(10, 13)(12, 18)(17, 20)(22, 106)(23, 119)(24, 111)(25, 124)(26, 116)(27, 108)(28, 121)(29, 113)(30, 126)(31, 118)(32, 110)(33, 123)(34, 115)(35, 107)(36, 120)(37, 112)(38, 125)(39, 117)(40, 109)(41, 122)(42, 114)(43, 85)(44, 98)(45, 90)(46, 103)(47, 95)(48, 87)(49, 100)(50, 92)(51, 105)(52, 97)(53, 89)(54, 102)(55, 94)(56, 86)(57, 99)(58, 91)(59, 104)(60, 96)(61, 88)(62, 101)(63, 93)(65, 77)(66, 69)(67, 82)(68, 74)(70, 79)(72, 84)(73, 76)(75, 81)(80, 83)
e: (2, 9)(3, 17)(5, 12)(6, 20)(8, 15)(11, 18)(14, 21)(22, 106)(23, 114)(24, 122)(25, 109)(26, 117)(27, 125)(28, 112)(29, 120)(30, 107)(31, 115)(32, 123)(33, 110)(34, 118)(35, 126)(36, 113)(37, 121)(38, 108)(39, 116)(40, 124)(41, 111)(42, 119)(43, 85)(44, 93)(45, 101)(46, 88)(47, 96)(48, 104)(49, 91)(50, 99)(51, 86)(52, 94)(53, 102)(54, 89)(55, 97)(56, 105)(57, 92)(58, 100)(59, 87)(60, 95)(61, 103)(62, 90)(63, 98)(65, 72)(66, 80)(68, 75)(69, 83)(71, 78)(74, 81)(77, 84)

(III) Last is Groups&Graphs. Copy everything between (not including) the lines of asterisks into a plain text file and save it as "graph.txt". Then launch G&G (Groups&Graphs) and select Read Text from the File menu.

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&Graph
C4[ 126, 7 ]
126
-1 23 114 42 119
-2 22 24 115 120
-3 121 23 25 116
-4 122 24 26 117
-5 123 25 27 118
-6 124 26 28 119
-7 125 27 29 120
-8 121 126 28 30
-9 122 29 106 31
-10 123 30 107 32
-11 33 124 31 108
-12 34 125 32 109
-13 33 110 35 126
-14 34 111 36 106
-15 35 112 37 107
-16 36 113 38 108
-17 37 114 39 109
-18 110 38 115 40
-19 111 39 116 41
-20 112 40 117 42
-21 22 113 41 118
-22 56 2 51 21
-23 1 57 3 52
-24 2 58 4 53
-25 3 59 5 54
-26 55 4 60 6
-27 56 5 61 7
-28 57 6 62 8
-29 58 7 63 9
-30 59 8 10 43
-31 11 44 60 9
-32 12 45 61 10
-33 11 13 46 62
-34 12 14 47 63
-35 13 15 48 43
-36 44 14 16 49
-37 45 15 17 50
-38 46 16 18 51
-39 47 17 19 52
-40 48 18 20 53
-41 49 19 21 54
-42 55 1 50 20
-43 35 84 30 65
-44 66 36 31 64
-45 67 37 32 65
-46 33 66 68 38
-47 34 67 69 39
-48 35 68 70 40
-49 36 69 71 41
-50 37 70 72 42
-51 22 38 71 73
-52 23 39 72 74
-53 24 40 73 75
-54 25 41 74 76
-55 77 26 42 75
-56 22 78 27 76
-57 77 23 79 28
-58 78 24 80 29
-59 79 25 81 30
-60 80 26 82 31
-61 81 27 83 32
-62 33 82 28 84
-63 34 83 29 64
-64 44 93 63 98
-65 99 45 94 43
-66 44 100 46 95
-67 45 101 47 96
-68 46 102 48 97
-69 47 103 49 98
-70 99 48 104 50
-71 100 49 105 51
-72 101 50 52 85
-73 102 51 53 86
-74 103 52 54 87
-75 55 88 104 53
-76 56 89 105 54
-77 55 57 90 85
-78 56 58 91 86
-79 57 59 92 87
-80 88 58 60 93
-81 89 59 61 94
-82 90 60 62 95
-83 91 61 63 96
-84 92 62 97 43
-85 77 126 72 107
-86 78 73 106 108
-87 79 74 107 109
-88 110 80 75 108
-89 111 81 76 109
-90 77 110 112 82
-91 78 111 113 83
-92 79 112 114 84
-93 80 113 115 64
-94 81 114 116 65
-95 66 82 115 117
-96 67 83 116 118
-97 68 84 117 119
-98 69 118 64 120
-99 121 70 119 65
-100 66 122 71 120
-101 121 67 123 72
-102 122 68 124 73
-103 123 69 125 74
-104 124 70 126 75
-105 125 71 106 76
-106 14 105 9 86
-107 15 85 10 87
-108 11 88 16 86
-109 12 89 17 87
-110 88 13 90 18
-111 89 14 91 19
-112 90 15 92 20
-113 91 16 93 21
-114 1 92 17 94
-115 2 93 18 95
-116 3 94 19 96
-117 4 95 20 97
-118 5 96 21 98
-119 99 1 6 97
-120 100 2 7 98
-121 99 101 3 8
-122 100 102 4 9
-123 101 103 5 10
-124 11 102 104 6
-125 12 103 105 7
-126 13 104 8 85
0

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