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On this page are computer-accessible forms for the graph C4[ 144, 21 ] = PL(MC3(6,12,1,7,5,0,1),[4^18,6^12]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {70, 76} under the group generated by the following permutations:

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

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

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