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On this page are computer-accessible forms for the graph C4[ 126, 6 ] = PS(6,21;4).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {84, 85} under the group generated by the following permutations:

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

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

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