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On this page are computer-accessible forms for the graph C4[ 144, 24 ] = PL(WH_24(3,5,11,12),[6^12,8^9]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {72, 78} under the group generated by the following permutations:

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

(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.

**************

&Graph
C4[ 144, 24 ]
144
-1 81 104 117 85
-2 81 125 104 129
-3 126 105 87 131
-4 111 105 84 87
-5 113 95 106 97
-6 121 132 96 118
-7 80 83 106 139
-8 111 113 84 95
-9 121 132 134 124
-10 137 83 128 139
-11 112 135 86 98
-12 143 144 101 131
-13 122 127 119 130
-14 110 93 94 86
-15 101 102 114 108
-16 88 134 119 141
-17 134 124 135 98
-18 144 101 137 128
-19 122 125 129 130
-20 110 102 93 141
-21 102 83 107 108
-22 99 134 141 142
-23 133 96 140 75
-24 136 94 85 118
-25 99 82 115 116
-26 144 135 103 74
-27 133 123 128 120
-28 77 78 113 124
-29 136 137 127 84
-30 133 102 140 141
-31 112 83 107 86
-32 99 94 118 142
-33 82 116 117 85
-34 132 103 139 74
-35 110 100 128 120
-36 78 124 105 76
-37 79 115 137 84
-38 114 82 138 73
-39 79 112 125 75
-40 88 80 126 117
-41 92 95 140 109
-42 111 90 73 98
-43 89 122 91 107
-44 143 129 97 142
-45 132 82 138 139
-46 101 114 96 118
-47 110 100 106 97
-48 105 96 75 76
-49 88 112 75 119
-50 79 80 115 126
-51 133 123 126 131
-52 92 93 87 109
-53 121 89 111 90
-54 99 103 115 109
-55 89 81 92 107
-56 90 129 120 142
-57 77 123 91 116
-58 100 138 130 76
-59 122 144 91 135
-60 91 93 116 87
-61 77 113 94 86
-62 121 143 89 131
-63 103 127 119 109
-64 81 92 114 73
-65 143 136 127 97
-66 80 73 106 98
-67 88 90 117 120
-68 100 104 74 76
-69 78 79 125 108
-70 138 95 140 130
-71 77 123 104 74
-72 78 136 85 108
-73 66 38 42 64
-74 34 68 26 71
-75 23 48 49 39
-76 68 36 58 48
-77 57 71 28 61
-78 36 69 28 72
-79 69 37 39 50
-80 66 50 7 40
-81 55 1 2 64
-82 33 45 25 38
-83 7 31 10 21
-84 4 37 29 8
-85 33 1 24 72
-86 11 14 61 31
-87 3 4 60 52
-88 67 16 49 40
-89 55 62 53 43
-90 56 67 42 53
-91 57 59 60 43
-92 55 41 52 64
-93 14 60 52 20
-94 24 14 61 32
-95 70 5 8 41
-96 23 46 48 6
-97 44 47 5 65
-98 11 66 17 42
-99 22 25 32 54
-100 35 68 47 58
-101 12 46 15 18
-102 15 30 20 21
-103 34 26 63 54
-104 1 2 68 71
-105 3 36 4 48
-106 66 47 5 7
-107 55 31 21 43
-108 69 15 72 21
-109 41 52 63 54
-110 35 14 47 20
-111 4 8 42 53
-112 11 49 39 31
-113 5 28 61 8
-114 46 15 38 64
-115 25 37 50 54
-116 33 57 25 60
-117 33 1 67 40
-118 24 46 6 32
-119 13 16 49 63
-120 56 67 35 27
-121 6 62 9 53
-122 13 59 19 43
-123 57 27 71 51
-124 36 17 28 9
-125 2 69 39 19
-126 3 50 40 51
-127 13 29 63 65
-128 35 27 18 10
-129 44 56 2 19
-130 13 58 70 19
-131 12 3 51 62
-132 34 45 6 9
-133 23 27 51 30
-134 22 16 17 9
-135 11 26 59 17
-136 24 72 29 65
-137 37 18 29 10
-138 45 58 70 38
-139 34 45 7 10
-140 23 70 30 41
-141 22 16 30 20
-142 22 44 56 32
-143 44 12 62 65
-144 12 26 59 18
0

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