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On this page are computer-accessible forms for the graph C4[ 186, 3 ] = PS(6,31;5).

(I) Following is a form readable by MAGMA:

g:=Graph<186|{ {124, 125}, {58, 63}, {154, 159}, {152, 157}, {88, 94}, {89, 95}, {153, 158}, {151, 156}, {70, 95}, {37, 63}, {133, 159}, {132, 158}, {69, 94}, {96, 126}, {131, 157}, {130, 156}, {97, 127}, {1, 33}, {30, 62}, {29, 61}, {28, 60}, {27, 59}, {26, 58}, {25, 57}, {2, 34}, {3, 35}, {4, 36}, {5, 37}, {6, 38}, {7, 39}, {8, 40}, {9, 41}, {10, 42}, {11, 43}, {12, 44}, {13, 45}, {14, 46}, {15, 47}, {16, 48}, {17, 49}, {18, 50}, {19, 51}, {20, 52}, {21, 53}, {22, 54}, {23, 55}, {24, 56}, {94, 126}, {95, 127}, {2, 32}, {31, 61}, {30, 60}, {27, 57}, {26, 56}, {3, 33}, {6, 36}, {7, 37}, {10, 40}, {11, 41}, {14, 44}, {15, 45}, {18, 48}, {19, 49}, {22, 52}, {23, 53}, {95, 125}, {128, 164}, {147, 183}, {146, 182}, {145, 181}, {144, 180}, {139, 175}, {138, 174}, {137, 173}, {136, 172}, {131, 167}, {130, 166}, {129, 165}, {64, 101}, {66, 103}, {72, 109}, {74, 111}, {80, 117}, {82, 119}, {4, 34}, {151, 177}, {150, 176}, {143, 169}, {142, 168}, {135, 161}, {134, 160}, {29, 59}, {28, 58}, {5, 35}, {12, 42}, {13, 43}, {20, 50}, {21, 51}, {65, 102}, {71, 96}, {73, 110}, {79, 104}, {81, 118}, {87, 112}, {72, 97}, {74, 99}, {76, 101}, {78, 103}, {88, 113}, {90, 115}, {92, 117}, {136, 162}, {153, 179}, {152, 178}, {141, 167}, {140, 166}, {137, 163}, {67, 104}, {71, 108}, {73, 98}, {77, 102}, {83, 120}, {87, 124}, {89, 114}, {93, 118}, {132, 168}, {150, 186}, {149, 185}, {148, 184}, {135, 171}, {134, 170}, {133, 169}, {68, 105}, {70, 107}, {84, 121}, {86, 123}, {8, 38}, {155, 181}, {154, 180}, {139, 165}, {138, 164}, {25, 55}, {9, 39}, {24, 54}, {69, 106}, {75, 100}, {85, 122}, {91, 116}, {64, 120}, {65, 121}, {66, 122}, {67, 123}, {68, 124}, {80, 105}, {128, 185}, {82, 107}, {84, 109}, {86, 111}, {90, 96}, {149, 175}, {148, 174}, {145, 171}, {144, 170}, {91, 97}, {75, 112}, {155, 160}, {129, 186}, {79, 116}, {81, 106}, {85, 110}, {140, 176}, {143, 179}, {142, 178}, {141, 177}, {76, 113}, {78, 115}, {16, 46}, {147, 173}, {146, 172}, {17, 47}, {92, 98}, {93, 99}, {1, 62}, {31, 32}, {77, 114}, {83, 108}, {63, 119}, {63, 100}, {32, 68}, {51, 87}, {50, 86}, {49, 85}, {48, 84}, {43, 79}, {42, 78}, {41, 77}, {40, 76}, {35, 71}, {34, 70}, {33, 69}, {56, 92}, {57, 93}, {38, 64}, {47, 73}, {46, 72}, {39, 65}, {54, 80}, {55, 81}, {62, 88}, {40, 66}, {45, 71}, {44, 70}, {41, 67}, {56, 82}, {57, 83}, {60, 86}, {61, 87}, {36, 72}, {52, 88}, {39, 75}, {38, 74}, {37, 73}, {53, 89}, {54, 90}, {55, 91}, {42, 68}, {43, 69}, {58, 84}, {59, 85}, {32, 89}, {36, 93}, {34, 91}, {48, 74}, {53, 79}, {52, 78}, {49, 75}, {33, 90}, {59, 64}, {44, 80}, {47, 83}, {46, 82}, {45, 81}, {60, 65}, {62, 67}, {50, 76}, {51, 77}, {35, 92}, {61, 66}, {28, 158}, {29, 159}, {26, 156}, {27, 157}, {8, 157}, {10, 159}, {9, 158}, {7, 156}, {2, 163}, {4, 165}, {6, 167}, {8, 169}, {10, 171}, {12, 173}, {14, 175}, {16, 177}, {18, 179}, {20, 181}, {22, 183}, {24, 185}, {1, 162}, {25, 186}, {5, 166}, {9, 170}, {13, 174}, {17, 178}, {21, 182}, {3, 164}, {11, 172}, {19, 180}, {11, 160}, {31, 180}, {27, 176}, {15, 164}, {12, 161}, {30, 179}, {28, 177}, {14, 163}, {7, 168}, {29, 178}, {13, 162}, {23, 184}, {1, 181}, {2, 182}, {3, 183}, {16, 165}, {26, 175}, {18, 167}, {24, 173}, {17, 166}, {25, 174}, {19, 168}, {23, 172}, {4, 184}, {5, 185}, {6, 186}, {20, 169}, {22, 171}, {30, 160}, {31, 161}, {15, 176}, {21, 170}, {94, 155}, {127, 184}, {126, 183}, {125, 182}, {125, 161}, {127, 163}, {126, 162}, {96, 128}, {123, 155}, {122, 154}, {121, 153}, {120, 152}, {119, 151}, {118, 150}, {117, 149}, {116, 148}, {97, 129}, {98, 130}, {99, 131}, {100, 132}, {101, 133}, {102, 134}, {103, 135}, {104, 136}, {105, 137}, {106, 138}, {107, 139}, {108, 140}, {109, 141}, {110, 142}, {111, 143}, {112, 144}, {113, 145}, {114, 146}, {115, 147}, {98, 128}, {123, 153}, {122, 152}, {119, 149}, {118, 148}, {99, 129}, {102, 132}, {103, 133}, {106, 136}, {107, 137}, {110, 140}, {111, 141}, {114, 144}, {115, 145}, {100, 130}, {124, 154}, {117, 147}, {116, 146}, {101, 131}, {108, 138}, {109, 139}, {104, 134}, {121, 151}, {120, 150}, {105, 135}, {112, 142}, {113, 143} }>;

(II) A more general form is to represent the graph as the orbit of {124, 125} under the group generated by the following permutations:

a: (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, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186)
b: (1, 32, 63, 94, 125, 156)(2, 37, 88, 95, 130, 181)(3, 42, 82, 96, 135, 175)(4, 47, 76, 97, 140, 169)(5, 52, 70, 98, 145, 163)(6, 57, 64, 99, 150, 157)(7, 62, 89, 100, 155, 182)(8, 36, 83, 101, 129, 176)(9, 41, 77, 102, 134, 170)(10, 46, 71, 103, 139, 164)(11, 51, 65, 104, 144, 158)(12, 56, 90, 105, 149, 183)(13, 61, 84, 106, 154, 177)(14, 35, 78, 107, 128, 171)(15, 40, 72, 108, 133, 165)(16, 45, 66, 109, 138, 159)(17, 50, 91, 110, 143, 184)(18, 55, 85, 111, 148, 178)(19, 60, 79, 112, 153, 172)(20, 34, 73, 113, 127, 166)(21, 39, 67, 114, 132, 160)(22, 44, 92, 115, 137, 185)(23, 49, 86, 116, 142, 179)(24, 54, 80, 117, 147, 173)(25, 59, 74, 118, 152, 167)(26, 33, 68, 119, 126, 161)(27, 38, 93, 120, 131, 186)(28, 43, 87, 121, 136, 180)(29, 48, 81, 122, 141, 174)(30, 53, 75, 123, 146, 168)(31, 58, 69, 124, 151, 162)
c: (2, 31)(3, 30)(4, 29)(5, 28)(6, 27)(7, 26)(8, 25)(9, 24)(10, 23)(11, 22)(12, 21)(13, 20)(14, 19)(15, 18)(16, 17)(33, 62)(34, 61)(35, 60)(36, 59)(37, 58)(38, 57)(39, 56)(40, 55)(41, 54)(42, 53)(43, 52)(44, 51)(45, 50)(46, 49)(47, 48)(64, 93)(65, 92)(66, 91)(67, 90)(68, 89)(69, 88)(70, 87)(71, 86)(72, 85)(73, 84)(74, 83)(75, 82)(76, 81)(77, 80)(78, 79)(95, 124)(96, 123)(97, 122)(98, 121)(99, 120)(100, 119)(101, 118)(102, 117)(103, 116)(104, 115)(105, 114)(106, 113)(107, 112)(108, 111)(109, 110)(126, 155)(127, 154)(128, 153)(129, 152)(130, 151)(131, 150)(132, 149)(133, 148)(134, 147)(135, 146)(136, 145)(137, 144)(138, 143)(139, 142)(140, 141)(157, 186)(158, 185)(159, 184)(160, 183)(161, 182)(162, 181)(163, 180)(164, 179)(165, 178)(166, 177)(167, 176)(168, 175)(169, 174)(170, 173)(171, 172)

(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[ 186, 3 ]
186
-1 33 181 62 162
-2 34 182 163 32
-3 33 35 183 164
-4 165 34 36 184
-5 166 35 37 185
-6 167 36 38 186
-7 156 168 37 39
-8 157 169 38 40
-9 158 170 39 41
-10 159 171 40 42
-11 160 172 41 43
-12 44 161 173 42
-13 45 162 174 43
-14 44 46 163 175
-15 176 45 47 164
-16 165 177 46 48
-17 166 178 47 49
-18 167 179 48 50
-19 168 180 49 51
-20 169 181 50 52
-21 170 182 51 53
-22 171 183 52 54
-23 55 172 184 53
-24 56 173 185 54
-25 55 57 174 186
-26 56 156 58 175
-27 176 57 157 59
-28 177 58 158 60
-29 178 59 159 61
-30 179 60 160 62
-31 180 61 161 32
-32 89 2 68 31
-33 1 90 3 69
-34 2 91 4 70
-35 3 92 5 71
-36 4 93 6 72
-37 5 7 73 63
-38 6 8 74 64
-39 7 9 75 65
-40 66 8 10 76
-41 11 77 67 9
-42 12 78 68 10
-43 11 13 79 69
-44 12 14 80 70
-45 13 15 81 71
-46 14 16 82 72
-47 15 17 83 73
-48 16 18 84 74
-49 17 19 85 75
-50 18 20 86 76
-51 77 19 21 87
-52 22 88 78 20
-53 23 89 79 21
-54 22 24 90 80
-55 23 25 91 81
-56 24 26 92 82
-57 25 27 93 83
-58 26 28 84 63
-59 27 29 85 64
-60 28 30 86 65
-61 66 29 31 87
-62 88 1 67 30
-63 100 58 37 119
-64 101 59 38 120
-65 121 102 60 39
-66 122 103 61 40
-67 123 104 62 41
-68 124 105 42 32
-69 33 94 106 43
-70 44 34 95 107
-71 45 35 96 108
-72 46 36 97 109
-73 110 47 37 98
-74 99 111 48 38
-75 100 112 49 39
-76 101 113 50 40
-77 102 114 51 41
-78 103 115 52 42
-79 104 116 53 43
-80 44 105 117 54
-81 55 45 106 118
-82 56 46 107 119
-83 57 47 108 120
-84 121 58 48 109
-85 110 122 59 49
-86 111 123 60 50
-87 112 124 61 51
-88 113 94 62 52
-89 114 95 53 32
-90 33 115 96 54
-91 55 34 116 97
-92 56 35 117 98
-93 99 57 36 118
-94 88 155 69 126
-95 89 70 125 127
-96 90 71 126 128
-97 91 72 127 129
-98 92 73 128 130
-99 93 74 129 131
-100 132 63 75 130
-101 133 64 76 131
-102 77 132 134 65
-103 66 78 133 135
-104 67 79 134 136
-105 68 80 135 137
-106 69 81 136 138
-107 70 82 137 139
-108 71 83 138 140
-109 72 84 139 141
-110 73 85 140 142
-111 143 74 86 141
-112 144 75 87 142
-113 88 143 145 76
-114 77 89 144 146
-115 78 90 145 147
-116 79 91 146 148
-117 80 92 147 149
-118 81 93 148 150
-119 82 149 63 151
-120 83 150 64 152
-121 84 151 65 153
-122 66 154 85 152
-123 67 155 86 153
-124 154 68 125 87
-125 124 182 95 161
-126 94 183 96 162
-127 95 184 97 163
-128 96 185 98 164
-129 99 165 97 186
-130 100 166 156 98
-131 99 101 167 157
-132 100 102 168 158
-133 101 103 169 159
-134 102 104 170 160
-135 103 105 171 161
-136 104 106 172 162
-137 105 107 173 163
-138 106 108 174 164
-139 165 107 109 175
-140 110 176 166 108
-141 111 177 167 109
-142 110 112 178 168
-143 111 113 179 169
-144 112 114 180 170
-145 113 115 181 171
-146 114 116 182 172
-147 115 117 183 173
-148 116 118 184 174
-149 117 119 185 175
-150 176 118 120 186
-151 121 177 156 119
-152 122 178 157 120
-153 121 123 179 158
-154 122 124 180 159
-155 123 181 94 160
-156 26 7 151 130
-157 27 8 152 131
-158 132 28 9 153
-159 154 133 29 10
-160 11 155 134 30
-161 12 135 125 31
-162 1 13 136 126
-163 2 14 137 127
-164 3 15 138 128
-165 4 16 139 129
-166 5 17 140 130
-167 6 18 141 131
-168 132 7 19 142
-169 143 133 8 20
-170 144 134 9 21
-171 22 145 135 10
-172 11 23 146 136
-173 12 24 147 137
-174 13 25 148 138
-175 14 26 149 139
-176 15 27 150 140
-177 16 28 151 141
-178 17 29 152 142
-179 143 18 30 153
-180 154 144 19 31
-181 1 155 145 20
-182 2 146 125 21
-183 22 3 147 126
-184 23 4 148 127
-185 24 5 149 128
-186 25 6 150 129
0

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