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On this page are computer-accessible forms for the graph C4[ 144, 22 ] = PL(MC3(6,12,1,7,5,6,1),[4^18,12^6]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {72, 77} under the group generated by the following permutations:

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

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