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On this page are computer-accessible forms for the graph C4[ 168, 24 ] = PL(MC3(6,14,1,8,3,0,2),[3^28,4^21]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {81, 86} under the group generated by the following permutations:

a: (9, 26)(10, 27)(16, 42)(88, 103)(94, 145)(105, 141)(116, 126)(129, 166)(137, 159)
b: (2, 69)(3, 44)(4, 6)(5, 56)(7, 72)(8, 73)(9, 10)(11, 34)(12, 20)(13, 21)(14, 49)(15, 19)(17, 78)(18, 83)(22, 43)(24, 35)(25, 47)(26, 27)(28, 62)(30, 66)(31, 37)(38, 58)(39, 50)(40, 75)(41, 46)(45, 70)(51, 71)(53, 63)(54, 67)(59, 65)(76, 79)(80, 82)(85, 109)(88, 141)(89, 133)(90, 158)(91, 148)(92, 150)(93, 114)(94, 116)(97, 115)(99, 160)(100, 135)(101, 106)(102, 122)(103, 105)(104, 112)(107, 147)(108, 128)(113, 151)(117, 138)(118, 163)(119, 143)(120, 139)(121, 157)(123, 132)(125, 146)(126, 145)(130, 167)(134, 152)(136, 156)(144, 155)(149, 161)(165, 168)
c: (15, 41)(24, 53)(34, 62)(90, 118)(97, 101)(100, 108)(132, 133)(147, 150)(152, 155)
d: (4, 12)(6, 20)(55, 77)(91, 121)(96, 111)(99, 113)(127, 140)(148, 157)(151, 160)
e: (44, 72)(56, 78)(67, 79)(97, 132)(101, 133)(109, 119)(112, 120)(149, 156)(167, 168)
f: (29, 57)(32, 60)(33, 61)(87, 98)(96, 140)(110, 124)(111, 127)(153, 154)(162, 164)
g: (3, 7)(5, 17)(54, 76)(85, 143)(89, 106)(104, 139)(115, 123)(130, 165)(136, 161)
h: (1, 2, 69)(3, 47, 27, 7, 73, 10)(4, 31, 21)(5, 70, 26, 17, 83, 9)(6, 14, 23)(8, 78, 57)(11, 24, 36)(12, 59, 50)(13, 55, 22)(15, 48, 19)(16, 54, 30, 42, 76, 58)(18, 72, 61)(20, 40, 52)(25, 56, 29)(28, 53, 64)(32, 66, 67)(33, 45, 44)(34, 68, 35)(37, 75, 43, 65, 49, 71)(38, 79, 60)(39, 77, 51)(41, 74, 46)(62, 81, 63)(80, 82, 84)(85, 113, 145, 143, 121, 94)(86, 128, 108)(87, 107, 133)(88, 165, 138, 116, 136, 93)(89, 147, 137, 106, 152, 159)(90, 131, 158)(91, 105, 104, 99, 141, 139)(92, 132, 124)(95, 135, 100)(96, 114, 109)(97, 110, 144)(98, 134, 101)(102, 126, 161, 146, 103, 130)(111, 122, 112)(115, 155, 166, 123, 150, 129)(117, 120, 127)(118, 142, 163)(119, 140, 125)(148, 149, 153)(151, 167, 162)(154, 160, 156)(157, 168, 164)
m: (13, 39)(21, 50)(23, 52)(29, 57)(32, 60)(33, 61)(85, 104)(87, 98)(96, 140)(109, 112)(110, 124)(111, 127)(119, 120)(139, 143)(153, 162)(154, 164)
n1: (36, 64)(48, 74)(68, 81)(86, 95)(87, 124)(98, 110)(129, 137)(131, 142)(159, 166)
a1: (8, 25)(14, 40)(18, 45)(22, 51)(31, 59)(38, 66)(92, 144)(94, 105)(107, 134)(114, 117)(122, 125)(141, 145)(148, 160)(149, 168)(151, 157)(156, 167)
b1: (2, 69)(3, 56, 8, 70)(4, 49, 13, 51)(5, 44, 18, 47)(6, 43, 21, 40)(7, 78, 25, 83)(9, 29, 27, 61)(10, 33, 26, 57)(11, 34, 35, 24)(12, 75, 39, 22)(14, 20, 71, 50)(15, 19)(16, 32, 42, 60)(17, 72, 45, 73)(23, 59, 55, 37)(28, 62, 63, 53)(30, 54, 67, 38)(31, 77, 65, 52)(36, 68)(41, 46)(58, 76, 79, 66)(64, 81)(80, 82)(85, 156, 157, 93)(87, 137, 98, 159)(88, 153, 94, 111)(89, 133, 134, 147)(90, 158)(91, 161, 120, 114)(92, 155, 115, 97)(96, 126, 164, 105)(99, 136, 112, 125)(100, 135)(101, 107, 152, 106)(102, 104, 167, 148)(103, 154, 145, 127)(108, 128)(109, 117, 113, 130)(110, 166, 124, 129)(116, 162, 141, 140)(118, 163)(119, 122, 121, 165)(123, 132, 144, 150)(138, 139, 168, 160)(143, 149, 151, 146)
c1: (2, 69)(3, 47)(4, 21, 12, 50)(5, 70)(6, 13, 20, 39)(7, 73)(8, 44)(11, 24)(14, 51)(15, 19)(17, 83)(18, 56)(22, 40)(23, 77, 52, 55)(25, 72)(28, 53)(29, 61)(30, 54)(31, 59)(32, 60)(33, 57)(34, 35)(38, 67)(41, 46)(43, 49)(45, 78)(58, 76)(62, 63)(66, 79)(71, 75)(80, 82)(85, 99, 104, 113)(87, 98)(89, 147)(90, 158)(91, 139, 121, 143)(92, 97)(93, 130)(94, 105)(96, 164, 111, 153)(100, 135)(101, 107)(102, 136)(106, 152)(108, 128)(109, 148, 112, 157)(110, 124)(114, 149)(115, 155)(117, 167)(118, 163)(119, 160, 120, 151)(122, 168)(123, 150)(125, 156)(127, 154, 140, 162)(132, 144)(133, 134)(138, 161)(141, 145)(146, 165)
d1: (11, 28)(19, 46)(35, 63)(89, 123)(92, 107)(106, 115)(128, 135)(134, 144)(158, 163)
e1: (37, 65)(43, 71)(49, 75)(88, 126)(93, 102)(103, 116)(130, 136)(138, 146)(161, 165)
f1: (1, 3, 47, 84, 7, 73)(2, 5, 30, 80, 17, 58)(4, 48, 21, 12, 74, 50)(6, 36, 13, 20, 64, 39)(8, 42, 72, 25, 16, 44)(9, 67, 38, 26, 79, 66)(10, 56, 18, 27, 78, 45)(11, 43, 41, 28, 71, 15)(14, 22, 31)(19, 49, 53, 46, 75, 24)(23, 77, 81, 52, 55, 68)(29, 61, 32, 57, 33, 60)(34, 35, 37, 62, 63, 65)(40, 51, 59)(54, 70, 82, 76, 83, 69)(85, 99, 131, 139, 121, 86)(87, 154, 140, 110, 164, 111)(88, 132, 144, 116, 101, 107)(89, 138, 108, 115, 93, 90)(91, 95, 104, 113, 142, 143)(92, 126, 133, 134, 103, 97)(94, 167, 125, 145, 168, 114)(96, 124, 162, 127, 98, 153)(100, 106, 102, 118, 123, 146)(105, 156, 117, 141, 149, 122)(109, 148, 159, 120, 151, 129)(112, 157, 166, 119, 160, 137)(128, 130, 152, 158, 161, 150)(135, 136, 155, 163, 165, 147)
g1: (14, 40)(22, 51)(31, 59)(94, 105)(114, 122)(117, 125)(141, 145)(149, 168)(156, 167)
h1: (1, 4, 16, 24, 32, 43, 84, 12, 42, 53, 60, 71)(2, 6, 10, 34, 29, 49, 80, 20, 27, 62, 57, 75)(3, 11, 38, 51, 78, 39, 7, 28, 66, 22, 56, 13)(5, 19, 8, 59, 79, 52, 17, 46, 25, 31, 67, 23)(9, 15, 33, 37, 82, 77, 26, 41, 61, 65, 69, 55)(14, 44, 21, 54, 35, 18, 40, 72, 50, 76, 63, 45)(30, 81, 83, 48, 47, 64, 58, 68, 70, 74, 73, 36)(85, 89, 92, 114, 149, 109, 139, 115, 134, 117, 167, 120)(86, 91, 137, 152, 110, 138, 131, 113, 166, 150, 87, 93)(88, 118, 140, 126, 108, 127, 116, 100, 111, 103, 90, 96)(94, 133, 162, 161, 163, 151, 141, 97, 153, 130, 135, 148)(95, 99, 129, 147, 98, 102, 142, 121, 159, 155, 124, 146)(101, 154, 136, 158, 157, 145, 132, 164, 165, 128, 160, 105)(104, 106, 107, 125, 168, 119, 143, 123, 144, 122, 156, 112)

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

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