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On this page are computer-accessible forms for the graph C4[ 168, 17 ] = PS(6,56;17).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {81, 85} under the group generated by the following permutations:

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

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

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