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On this page are computer-accessible forms for the graph C4[ 144, 56 ] = PL(CS(W(9,2)[9^4],1)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {68, 95} under the group generated by the following permutations:

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

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

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