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On this page are computer-accessible forms for the graph C4[ 144, 23 ] = PL(WH_24(3,0,5,11),[3^24,8^9]).

(I) Following is a form readable by MAGMA:

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

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

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

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