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On this page are computer-accessible forms for the graph C4[ 144, 67 ] = BGCG(AMC(8,3,[0.1:1.2]);K1;{3,6}).

(I) Following is a form readable by MAGMA:

g:=Graph<144|{ {70, 87}, {71, 84}, {64, 87}, {69, 82}, {65, 91}, {72, 82}, {64, 92}, {72, 84}, {67, 92}, {68, 91}, {66, 97}, {69, 97}, {66, 103}, {65, 103}, {66, 101}, {72, 101}, {64, 110}, {65, 110}, {70, 126}, {71, 124}, {65, 124}, {67, 126}, {14, 78}, {26, 90}, {45, 109}, {44, 109}, {48, 113}, {50, 115}, {19, 81}, {59, 121}, {57, 123}, {34, 96}, {46, 108}, {47, 109}, {62, 125}, {53, 113}, {38, 99}, {56, 125}, {37, 99}, {45, 107}, {12, 75}, {62, 121}, {60, 123}, {52, 115}, {18, 90}, {49, 121}, {34, 107}, {45, 100}, {52, 125}, {27, 81}, {42, 96}, {49, 123}, {18, 89}, {17, 93}, {63, 115}, {35, 111}, {44, 96}, {23, 90}, {38, 107}, {34, 111}, {30, 83}, {48, 125}, {31, 81}, {52, 122}, {43, 100}, {60, 115}, {54, 121}, {26, 74}, {62, 110}, {32, 112}, {31, 79}, {40, 120}, {12, 93}, {28, 77}, {26, 75}, {24, 73}, {39, 118}, {40, 122}, {49, 99}, {28, 79}, {63, 108}, {33, 114}, {30, 77}, {41, 122}, {25, 77}, {58, 110}, {47, 123}, {48, 100}, {2, 87}, {57, 108}, {35, 118}, {27, 78}, {24, 77}, {7, 82}, {47, 122}, {49, 100}, {24, 78}, {36, 114}, {53, 99}, {5, 82}, {14, 89}, {13, 90}, {5, 93}, {63, 103}, {41, 113}, {5, 92}, {33, 120}, {21, 76}, {43, 114}, {53, 108}, {1, 91}, {22, 76}, {3, 89}, {2, 89}, {16, 75}, {6, 93}, {41, 114}, {42, 113}, {59, 103}, {6, 91}, {20, 73}, {43, 118}, {9, 87}, {38, 120}, {16, 78}, {51, 109}, {3, 92}, {21, 74}, {20, 75}, {2, 98}, {10, 106}, {53, 85}, {54, 86}, {21, 116}, {30, 127}, {8, 106}, {29, 127}, {1, 98}, {11, 104}, {10, 105}, {2, 97}, {51, 80}, {1, 101}, {27, 127}, {20, 112}, {14, 106}, {4, 97}, {15, 105}, {30, 120}, {41, 79}, {51, 85}, {16, 119}, {18, 117}, {14, 102}, {61, 85}, {60, 84}, {36, 76}, {23, 127}, {39, 79}, {56, 80}, {25, 112}, {12, 102}, {35, 73}, {32, 74}, {50, 88}, {52, 94}, {29, 118}, {59, 80}, {33, 74}, {4, 104}, {24, 116}, {56, 84}, {5, 104}, {36, 73}, {8, 101}, {7, 106}, {51, 94}, {34, 76}, {54, 88}, {13, 98}, {58, 85}, {31, 112}, {22, 102}, {33, 81}, {4, 117}, {45, 95}, {6, 117}, {17, 98}, {3, 119}, {19, 102}, {1, 119}, {37, 83}, {8, 126}, {28, 107}, {36, 83}, {40, 95}, {6, 126}, {23, 111}, {16, 104}, {15, 119}, {46, 86}, {13, 116}, {39, 94}, {7, 124}, {37, 94}, {19, 111}, {35, 95}, {42, 86}, {20, 105}, {23, 105}, {38, 88}, {40, 86}, {46, 80}, {3, 124}, {32, 95}, {31, 96}, {11, 116}, {10, 117}, {39, 88}, {44, 83}, {10, 138}, {4, 134}, {11, 136}, {7, 128}, {9, 128}, {15, 133}, {9, 133}, {12, 128}, {8, 133}, {15, 130}, {13, 128}, {11, 133}, {9, 134}, {25, 136}, {27, 138}, {29, 143}, {17, 130}, {22, 130}, {22, 131}, {26, 131}, {18, 136}, {17, 138}, {25, 130}, {19, 136}, {29, 131}, {21, 138}, {28, 131}, {48, 144}, {50, 144}, {42, 143}, {55, 144}, {44, 132}, {47, 135}, {37, 143}, {58, 144}, {46, 132}, {32, 143}, {43, 132}, {55, 135}, {61, 141}, {57, 137}, {54, 135}, {61, 140}, {60, 141}, {57, 139}, {58, 137}, {56, 140}, {59, 142}, {62, 139}, {50, 132}, {55, 129}, {55, 142}, {61, 135}, {63, 129}, {71, 134}, {72, 137}, {67, 129}, {68, 134}, {69, 129}, {68, 140}, {70, 142}, {71, 142}, {64, 141}, {69, 139}, {66, 141}, {70, 137}, {68, 139}, {67, 140} }>;

(II) A more general form is to represent the graph as the orbit of {70, 87} under the group generated by the following permutations:

a: (1, 10, 19, 28, 37, 46, 55, 64)(2, 17, 27, 31, 39, 51, 59, 70)(3, 15, 23, 34, 38, 53, 63, 67)(4, 12, 24, 32, 43, 47, 62, 72)(5, 16, 20, 35, 45, 49, 57, 69)(6, 14, 25, 29, 44, 54, 58, 66)(7, 11, 26, 36, 40, 48, 60, 68)(8, 18, 22, 30, 42, 50, 61, 65)(9, 13, 21, 33, 41, 52, 56, 71)(73, 95, 100, 123, 139, 82, 104, 75)(74, 114, 122, 125, 84, 134, 128, 116)(76, 120, 113, 115, 140, 124, 133, 90)(77, 143, 132, 135, 110, 101, 117, 102)(78, 112, 118, 109, 121, 137, 97, 93)(79, 94, 80, 142, 87, 98, 138, 81)(83, 86, 144, 141, 91, 106, 136, 131)(85, 103, 126, 89, 130, 127, 96, 88)(92, 119, 105, 111, 107, 99, 108, 129)
b: (1, 2, 4, 6)(3, 9, 5, 8)(10, 65, 13, 69)(11, 67, 15, 64)(12, 72, 14, 71)(16, 70)(17, 66, 18, 68)(19, 56, 22, 60)(20, 58, 24, 55)(21, 63, 23, 62)(25, 61)(26, 57, 27, 59)(28, 47, 31, 51)(29, 49, 33, 46)(30, 54, 32, 53)(34, 52)(35, 48, 36, 50)(37, 38, 40, 42)(39, 45, 41, 44)(73, 144)(74, 108, 127, 121)(75, 137, 78, 142)(76, 115, 111, 125)(77, 135, 112, 85)(79, 109)(80, 131, 123, 81)(82, 106, 124, 128)(83, 88, 95, 113)(84, 102)(86, 143, 99, 120)(87, 104, 126, 119)(89, 134, 93, 101)(90, 139, 138, 103)(91, 98, 97, 117)(92, 133)(94, 107, 122, 96)(100, 114, 132, 118)(105, 110, 116, 129)(130, 141, 136, 140)
c: (2, 8, 3, 6)(4, 9, 7, 5)(10, 64)(11, 71, 12, 69)(13, 72, 16, 68)(14, 67, 18, 70)(15, 65, 17, 66)(19, 55)(20, 62, 21, 60)(22, 63, 25, 59)(23, 58, 27, 61)(24, 56, 26, 57)(28, 46)(29, 53, 30, 51)(31, 54, 34, 50)(32, 49, 36, 52)(33, 47, 35, 48)(38, 44, 39, 42)(40, 45, 43, 41)(73, 125, 74, 123)(75, 139, 116, 84)(76, 115, 112, 121)(77, 80, 131, 108)(78, 140, 90, 137)(79, 86, 107, 132)(81, 135, 111, 144)(82, 104, 134, 128)(83, 94, 143, 99)(85, 127)(87, 106, 92, 117)(88, 96)(89, 126)(91, 98, 101, 119)(93, 97, 133, 124)(95, 100, 114, 122)(102, 129, 136, 142)(103, 130)(105, 110, 138, 141)(109, 118, 113, 120)

(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[ 144, 67 ]
144
-1 101 91 119 98
-2 89 97 87 98
-3 89 124 92 119
-4 134 104 117 97
-5 92 82 93 104
-6 91 93 126 117
-7 124 82 106 128
-8 133 101 126 106
-9 133 134 128 87
-10 105 138 106 117
-11 133 136 104 116
-12 102 93 128 75
-13 90 116 128 98
-14 78 89 102 106
-15 133 105 119 130
-16 78 104 75 119
-17 93 138 130 98
-18 89 90 136 117
-19 111 102 81 136
-20 112 105 73 75
-21 116 138 74 76
-22 102 130 76 131
-23 111 90 105 127
-24 77 78 116 73
-25 77 112 136 130
-26 90 74 75 131
-27 78 81 127 138
-28 77 79 107 131
-29 143 127 118 131
-30 77 83 127 120
-31 79 112 81 96
-32 143 112 95 74
-33 81 114 74 120
-34 111 96 107 76
-35 111 73 95 118
-36 114 83 73 76
-37 99 143 83 94
-38 88 99 107 120
-39 88 79 94 118
-40 122 95 86 120
-41 122 79 113 114
-42 143 113 96 86
-43 132 100 114 118
-44 132 83 96 109
-45 100 95 107 109
-46 132 80 86 108
-47 122 123 135 109
-48 100 144 113 125
-49 99 121 100 123
-50 88 132 144 115
-51 80 94 85 109
-52 122 125 115 94
-53 99 113 85 108
-54 88 121 135 86
-55 144 135 129 142
-56 80 125 84 140
-57 123 137 139 108
-58 110 144 137 85
-59 121 80 103 142
-60 123 115 84 141
-61 135 85 140 141
-62 110 121 125 139
-63 103 115 129 108
-64 110 92 141 87
-65 110 91 124 103
-66 101 103 97 141
-67 92 126 129 140
-68 134 91 139 140
-69 82 139 129 97
-70 126 137 87 142
-71 134 124 84 142
-72 101 82 137 84
-73 24 35 36 20
-74 33 26 21 32
-75 12 26 16 20
-76 22 34 36 21
-77 24 25 28 30
-78 24 14 16 27
-79 28 39 41 31
-80 56 46 59 51
-81 33 27 19 31
-82 69 5 72 7
-83 44 36 37 30
-84 56 60 71 72
-85 58 61 51 53
-86 46 40 42 54
-87 2 70 9 64
-88 38 39 50 54
-89 2 3 14 18
-90 23 13 26 18
-91 1 68 6 65
-92 67 3 5 64
-93 12 5 6 17
-94 37 39 51 52
-95 45 35 40 32
-96 44 34 31 42
-97 66 2 69 4
-98 1 2 13 17
-99 37 38 49 53
-100 45 48 49 43
-101 66 1 72 8
-102 22 12 14 19
-103 66 59 63 65
-104 11 4 5 16
-105 23 15 20 10
-106 14 7 8 10
-107 34 45 38 28
-108 46 57 63 53
-109 44 45 47 51
-110 58 62 64 65
-111 23 34 35 19
-112 25 20 31 32
-113 48 41 42 53
-114 33 36 41 43
-115 60 50 52 63
-116 11 13 24 21
-117 4 6 18 10
-118 35 39 29 43
-119 1 3 15 16
-120 33 38 40 30
-121 59 49 62 54
-122 47 40 41 52
-123 57 47 49 60
-124 3 71 7 65
-125 56 48 62 52
-126 67 70 6 8
-127 23 27 29 30
-128 12 13 7 9
-129 55 67 69 63
-130 22 25 15 17
-131 22 26 28 29
-132 44 46 50 43
-133 11 15 8 9
-134 68 4 71 9
-135 55 47 61 54
-136 11 25 18 19
-137 57 58 70 72
-138 27 17 10 21
-139 57 68 69 62
-140 56 67 68 61
-141 66 60 61 64
-142 55 59 70 71
-143 37 29 42 32
-144 55 58 48 50
0

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