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On this page are computer-accessible forms for the graph C4[ 168, 28 ] = PL(WH_28(2,0,5,9),[3^28,14^6]).

(I) Following is a form readable by MAGMA:

g:=Graph<168|{ {84, 94}, {75, 90}, {74, 89}, {78, 93}, {74, 93}, {65, 88}, {65, 92}, {71, 103}, {81, 113}, {80, 114}, {84, 118}, {82, 112}, {81, 115}, {72, 108}, {77, 104}, {84, 113}, {70, 96}, {79, 104}, {71, 111}, {79, 103}, {75, 98}, {72, 98}, {76, 102}, {73, 99}, {68, 104}, {64, 109}, {67, 110}, {80, 127}, {66, 114}, {72, 122}, {67, 112}, {83, 96}, {82, 102}, {83, 102}, {72, 127}, {69, 125}, {68, 126}, {80, 108}, {74, 119}, {64, 127}, {24, 89}, {35, 97}, {43, 111}, {57, 124}, {62, 123}, {16, 86}, {34, 100}, {63, 120}, {38, 110}, {40, 96}, {45, 101}, {29, 87}, {34, 104}, {56, 114}, {59, 113}, {16, 91}, {33, 106}, {23, 92}, {17, 93}, {61, 113}, {32, 108}, {50, 126}, {18, 95}, {21, 88}, {47, 98}, {53, 120}, {55, 121}, {44, 99}, {52, 123}, {14, 94}, {38, 118}, {4, 85}, {43, 122}, {5, 86}, {6, 85}, {1, 85}, {39, 115}, {53, 97}, {3, 86}, {40, 125}, {14, 91}, {41, 124}, {60, 105}, {1, 87}, {51, 101}, {58, 108}, {2, 85}, {34, 117}, {5, 93}, {63, 102}, {12, 86}, {42, 112}, {45, 119}, {55, 109}, {45, 118}, {53, 110}, {6, 90}, {35, 127}, {42, 119}, {46, 115}, {9, 87}, {63, 97}, {44, 114}, {3, 92}, {54, 105}, {11, 107}, {30, 124}, {7, 99}, {15, 107}, {16, 118}, {13, 106}, {26, 125}, {12, 100}, {20, 124}, {48, 88}, {20, 126}, {51, 89}, {9, 101}, {21, 121}, {48, 92}, {6, 107}, {23, 122}, {19, 126}, {7, 106}, {23, 121}, {27, 117}, {49, 95}, {2, 109}, {15, 96}, {4, 107}, {55, 88}, {5, 117}, {9, 120}, {43, 90}, {21, 103}, {8, 123}, {42, 89}, {45, 94}, {16, 100}, {35, 87}, {27, 111}, {1, 116}, {23, 98}, {8, 125}, {47, 90}, {2, 116}, {28, 106}, {13, 123}, {3, 117}, {30, 105}, {31, 103}, {39, 95}, {1, 120}, {22, 111}, {10, 115}, {3, 121}, {37, 95}, {36, 94}, {25, 99}, {11, 112}, {22, 109}, {18, 105}, {15, 116}, {6, 122}, {29, 97}, {24, 101}, {38, 91}, {9, 119}, {11, 116}, {36, 91}, {27, 100}, {17, 110}, {4, 132}, {33, 161}, {26, 154}, {13, 140}, {37, 164}, {25, 152}, {14, 140}, {28, 158}, {5, 134}, {24, 155}, {8, 140}, {36, 160}, {34, 166}, {7, 130}, {20, 145}, {10, 140}, {33, 167}, {7, 128}, {12, 139}, {8, 143}, {2, 138}, {46, 165}, {27, 151}, {19, 158}, {37, 168}, {28, 145}, {13, 130}, {30, 142}, {57, 168}, {51, 161}, {10, 153}, {18, 129}, {54, 165}, {11, 159}, {48, 164}, {54, 162}, {18, 135}, {19, 134}, {49, 164}, {14, 153}, {63, 168}, {26, 141}, {25, 142}, {17, 134}, {17, 137}, {62, 166}, {12, 149}, {31, 134}, {20, 142}, {22, 138}, {61, 161}, {24, 132}, {29, 128}, {22, 136}, {60, 162}, {58, 164}, {4, 155}, {30, 129}, {10, 149}, {39, 135}, {61, 157}, {41, 137}, {57, 152}, {59, 154}, {52, 151}, {60, 159}, {53, 150}, {56, 155}, {36, 128}, {47, 139}, {54, 144}, {56, 158}, {59, 157}, {40, 143}, {62, 153}, {44, 132}, {56, 145}, {15, 165}, {57, 147}, {49, 154}, {55, 156}, {33, 141}, {62, 146}, {39, 139}, {44, 128}, {50, 158}, {50, 159}, {52, 153}, {32, 142}, {58, 148}, {19, 163}, {38, 150}, {41, 152}, {50, 131}, {51, 130}, {21, 167}, {32, 148}, {59, 143}, {42, 159}, {37, 147}, {35, 148}, {48, 135}, {31, 167}, {40, 144}, {32, 152}, {25, 160}, {47, 149}, {46, 149}, {31, 163}, {43, 151}, {52, 136}, {26, 167}, {29, 160}, {28, 161}, {58, 135}, {46, 144}, {49, 143}, {41, 150}, {61, 130}, {60, 131}, {67, 131}, {83, 147}, {82, 147}, {79, 141}, {66, 129}, {83, 144}, {65, 133}, {77, 137}, {76, 138}, {67, 137}, {75, 129}, {71, 141}, {78, 133}, {70, 136}, {69, 138}, {71, 136}, {76, 156}, {70, 151}, {84, 133}, {82, 131}, {78, 157}, {64, 148}, {81, 133}, {80, 132}, {68, 145}, {68, 146}, {66, 155}, {69, 156}, {81, 139}, {73, 146}, {77, 150}, {64, 156}, {65, 157}, {79, 146}, {69, 154}, {66, 162}, {70, 165}, {76, 168}, {73, 160}, {75, 162}, {74, 163}, {77, 166}, {78, 163}, {73, 166} }>;

(II) A more general form is to represent the graph as the orbit of {84, 94} under the group generated by the following permutations:

a: (2, 9)(3, 13)(4, 35)(5, 8)(6, 29)(7, 23)(10, 34)(11, 63)(12, 62)(14, 27)(15, 53)(16, 52)(17, 40)(18, 20)(19, 49)(21, 61)(22, 45)(24, 64)(25, 75)(26, 78)(28, 48)(31, 59)(32, 66)(33, 65)(36, 43)(37, 50)(38, 70)(39, 68)(41, 54)(42, 76)(44, 72)(46, 77)(47, 73)(51, 55)(56, 58)(57, 60)(67, 83)(69, 74)(71, 84)(79, 81)(85, 87)(86, 123)(88, 161)(89, 156)(90, 160)(91, 151)(92, 106)(93, 125)(94, 111)(95, 126)(96, 110)(97, 107)(98, 99)(100, 153)(101, 109)(102, 112)(103, 113)(104, 115)(105, 124)(108, 114)(116, 120)(117, 140)(118, 136)(119, 138)(121, 130)(122, 128)(127, 132)(129, 142)(131, 147)(133, 141)(134, 143)(135, 145)(137, 144)(139, 146)(148, 155)(149, 166)(150, 165)(152, 162)(154, 163)(157, 167)(158, 164)(159, 168)
b: (1, 3, 9, 23, 45, 72, 84, 80, 81, 44, 39, 7, 18, 13, 30, 8, 20, 40, 68, 83, 79, 82, 71, 67, 22, 17, 2, 5)(4, 12, 29, 48, 51, 75, 14, 32, 59, 56, 46, 73, 37, 33, 60, 52, 41, 69, 19, 15, 34, 63, 21, 42, 43, 38, 64, 78)(6, 16, 35, 65, 24, 47, 36, 58, 61, 66, 10, 25, 49, 28, 54, 62, 57, 26, 50, 70, 77, 76, 31, 11, 27, 53, 55, 74)(85, 86, 87, 92, 101, 98, 94, 108, 113, 114, 115, 99, 95, 106, 105, 123, 124, 125, 126, 96, 104, 102, 103, 112, 111, 110, 109, 93)(88, 89, 90, 91, 148, 157, 155, 149, 160, 164, 161, 162, 153, 152, 154, 158, 165, 166, 168, 167, 159, 151, 150, 156, 163, 107, 100, 97)(116, 117, 120, 121, 119, 122, 118, 127, 133, 132, 139, 128, 135, 130, 129, 140, 142, 143, 145, 144, 146, 147, 141, 131, 136, 137, 138, 134)
c: (1, 4, 80, 35)(2, 24, 72, 29)(3, 14, 71, 61)(5, 10, 79, 59)(6, 44, 64, 9)(7, 55, 45, 43)(8, 31, 81, 34)(11, 66, 32, 63)(12, 62, 26, 78)(13, 21, 84, 27)(15, 56, 58, 53)(16, 52, 33, 65)(17, 46, 68, 49)(18, 41, 83, 50)(19, 39, 77, 40)(20, 37, 67, 54)(22, 51, 23, 36)(25, 76, 42, 75)(28, 48, 38, 70)(30, 57, 82, 60)(47, 73, 69, 74)(85, 132, 127, 87)(86, 153, 141, 157)(88, 118, 151, 106)(89, 98, 160, 138)(90, 99, 156, 119)(91, 136, 161, 92)(93, 149, 146, 154)(94, 111, 130, 121)(95, 137, 144, 126)(96, 158, 135, 150)(97, 116, 155, 108)(100, 123, 167, 133)(101, 122, 128, 109)(102, 159, 129, 152)(103, 113, 117, 140)(104, 143, 134, 115)(105, 124, 147, 131)(107, 114, 148, 120)(110, 165, 145, 164)(112, 162, 142, 168)(125, 163, 139, 166)
d: (3, 8)(4, 11)(5, 13)(6, 15)(7, 17)(10, 12)(14, 16)(19, 28)(21, 26)(23, 40)(24, 42)(25, 41)(27, 52)(29, 53)(31, 33)(32, 57)(34, 62)(35, 63)(36, 38)(37, 58)(43, 70)(44, 67)(46, 47)(48, 49)(50, 56)(51, 74)(54, 75)(55, 69)(59, 65)(60, 66)(61, 78)(64, 76)(72, 83)(73, 77)(80, 82)(85, 116)(86, 140)(87, 120)(88, 154)(90, 165)(92, 143)(93, 130)(94, 118)(95, 135)(96, 122)(98, 144)(99, 137)(100, 153)(101, 119)(102, 127)(103, 141)(104, 146)(105, 129)(106, 134)(108, 147)(109, 138)(110, 128)(111, 136)(112, 132)(113, 133)(114, 131)(115, 139)(117, 123)(121, 125)(124, 142)(126, 145)(148, 168)(150, 160)(155, 159)(161, 163)
e: (1, 2, 22, 71, 79, 68, 20, 30, 18, 39, 81, 84, 45, 9)(3, 5, 17, 67, 82, 83, 40, 8, 13, 7, 44, 80, 72, 23)(4, 64, 43, 21, 34, 19, 41, 60, 37, 46, 59, 14, 51, 29)(6, 55, 27, 31, 77, 50, 57, 54, 49, 10, 61, 36, 24, 35)(11, 76, 70, 26, 62, 28, 25, 66, 58, 47, 65, 16, 74, 53)(12, 78, 38, 42, 63, 15, 69, 52, 33, 73, 56, 32, 75, 48)(85, 109, 111, 103, 104, 126, 124, 105, 95, 115, 113, 94, 101, 87)(86, 93, 110, 112, 102, 96, 125, 123, 106, 99, 114, 108, 98, 92)(88, 100, 163, 150, 159, 168, 165, 154, 153, 161, 160, 155, 148, 90)(89, 97, 107, 156, 151, 167, 166, 158, 152, 162, 164, 149, 157, 91)(116, 138, 136, 141, 146, 145, 142, 129, 135, 139, 133, 118, 119, 120)(117, 134, 137, 131, 147, 144, 143, 140, 130, 128, 132, 127, 122, 121)

(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[ 168, 28 ]
168
-1 116 85 87 120
-2 116 138 85 109
-3 121 92 117 86
-4 132 155 85 107
-5 134 93 117 86
-6 122 90 85 107
-7 99 106 128 130
-8 143 123 125 140
-9 101 119 87 120
-10 115 149 140 153
-11 112 159 116 107
-12 100 149 139 86
-13 123 106 140 130
-14 91 94 140 153
-15 165 116 96 107
-16 100 91 118 86
-17 110 134 93 137
-18 135 105 95 129
-19 134 158 126 163
-20 145 124 126 142
-21 88 121 167 103
-22 111 136 138 109
-23 121 122 92 98
-24 132 89 155 101
-25 99 160 152 142
-26 154 167 125 141
-27 100 111 117 151
-28 145 158 106 161
-29 160 128 97 87
-30 124 105 129 142
-31 134 167 103 163
-32 148 108 152 142
-33 167 106 161 141
-34 100 166 104 117
-35 148 127 97 87
-36 91 94 160 128
-37 168 147 95 164
-38 110 91 150 118
-39 135 115 95 139
-40 143 144 125 96
-41 124 137 150 152
-42 89 112 159 119
-43 111 122 90 151
-44 99 132 114 128
-45 101 94 118 119
-46 165 144 115 149
-47 90 149 139 98
-48 88 135 92 164
-49 143 154 95 164
-50 158 126 159 131
-51 89 101 161 130
-52 123 136 151 153
-53 110 150 97 120
-54 165 144 105 162
-55 88 121 156 109
-56 155 145 114 158
-57 124 168 147 152
-58 135 148 108 164
-59 143 154 113 157
-60 159 105 162 131
-61 113 157 161 130
-62 166 123 146 153
-63 102 168 97 120
-64 156 148 127 109
-65 88 133 157 92
-66 155 114 129 162
-67 110 112 137 131
-68 145 146 104 126
-69 154 156 125 138
-70 165 136 96 151
-71 111 103 136 141
-72 122 127 108 98
-73 99 166 146 160
-74 89 93 119 163
-75 90 129 162 98
-76 156 102 168 138
-77 166 104 137 150
-78 133 157 93 163
-79 146 103 104 141
-80 132 114 127 108
-81 133 113 115 139
-82 112 102 147 131
-83 144 102 147 96
-84 133 113 94 118
-85 1 2 4 6
-86 12 3 5 16
-87 1 35 29 9
-88 55 48 21 65
-89 24 51 74 42
-90 47 6 75 43
-91 14 36 16 38
-92 23 3 48 65
-93 78 5 17 74
-94 45 14 36 84
-95 37 49 39 18
-96 15 70 83 40
-97 35 29 63 53
-98 23 47 72 75
-99 44 25 7 73
-100 12 34 16 27
-101 45 24 51 9
-102 82 83 63 76
-103 79 71 31 21
-104 77 34 68 79
-105 60 18 30 54
-106 33 13 28 7
-107 11 4 15 6
-108 58 80 72 32
-109 22 55 2 64
-110 67 38 17 53
-111 22 27 71 43
-112 11 67 82 42
-113 59 81 61 84
-114 44 66 56 80
-115 46 81 39 10
-116 11 1 2 15
-117 34 3 5 27
-118 45 16 38 84
-119 45 74 9 42
-120 1 63 9 53
-121 55 23 3 21
-122 23 6 72 43
-123 13 62 8 52
-124 57 30 41 20
-125 69 26 40 8
-126 68 50 19 20
-127 35 80 72 64
-128 44 36 7 29
-129 66 18 30 75
-130 13 61 7 51
-131 67 60 82 50
-132 44 24 80 4
-133 78 81 84 65
-134 5 17 19 31
-135 58 48 39 18
-136 22 70 71 52
-137 77 67 17 41
-138 22 2 69 76
-139 12 47 81 39
-140 13 14 8 10
-141 33 79 26 71
-142 25 30 20 32
-143 59 49 40 8
-144 46 83 40 54
-145 56 68 28 20
-146 68 79 62 73
-147 57 37 82 83
-148 35 58 64 32
-149 12 46 47 10
-150 77 38 41 53
-151 70 27 52 43
-152 57 25 41 32
-153 14 62 52 10
-154 69 26 59 49
-155 66 56 24 4
-156 55 69 64 76
-157 78 59 61 65
-158 56 28 50 19
-159 11 60 50 42
-160 25 36 29 73
-161 33 28 61 51
-162 66 60 75 54
-163 78 19 74 31
-164 58 37 48 49
-165 46 15 70 54
-166 77 34 62 73
-167 33 26 31 21
-168 57 37 63 76
0

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