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On this page are computer-accessible forms for the graph C4[ 168, 23 ] = PL(MC3(4,21,1,20,8,0,1),[4^21,42^2]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {82, 86} under the group generated by the following permutations:

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

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

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