Graph forms
for C4 [ 231, 5 ] = PS(3,77;10)
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On this page are computer-accessible forms for the graph C4[ 231, 5 ] =
PS(3,77;10).
(I) Following is a form readable by MAGMA:
g:=Graph<231|{ {77, 78}, {145, 155}, {149, 159}, {148, 158}, {146, 156}, {147,
157}, {150, 160}, {151, 161}, {152, 162}, {153, 163}, {154, 164}, {128, 195},
{152, 219}, {148, 215}, {144, 211}, {140, 207}, {136, 203}, {132, 199}, {129,
196}, {153, 220}, {147, 214}, {145, 212}, {139, 206}, {137, 204}, {131, 198},
{130, 197}, {154, 221}, {146, 213}, {138, 205}, {2, 78}, {51, 127}, {50, 126},
{49, 125}, {48, 124}, {35, 111}, {34, 110}, {33, 109}, {3, 79}, {16, 92}, {17,
93}, {18, 94}, {19, 95}, {32, 108}, {133, 200}, {151, 218}, {149, 216}, {135,
202}, {1, 79}, {49, 127}, {48, 126}, {33, 111}, {16, 94}, {17, 95}, {32, 110},
{134, 201}, {150, 217}, {2, 80}, {47, 125}, {46, 124}, {43, 121}, {42, 120},
{39, 117}, {38, 116}, {35, 113}, {34, 112}, {3, 81}, {6, 84}, {7, 85}, {10, 88},
{11, 89}, {14, 92}, {15, 93}, {4, 80}, {47, 123}, {46, 122}, {45, 121}, {44,
120}, {39, 115}, {38, 114}, {37, 113}, {36, 112}, {5, 81}, {6, 82}, {7, 83},
{12, 88}, {13, 89}, {14, 90}, {15, 91}, {4, 82}, {45, 123}, {44, 122}, {37,
115}, {36, 114}, {5, 83}, {12, 90}, {13, 91}, {128, 215}, {136, 223}, {129,
216}, {135, 222}, {133, 220}, {131, 218}, {130, 217}, {134, 221}, {8, 84}, {43,
119}, {42, 118}, {41, 117}, {40, 116}, {9, 85}, {10, 86}, {11, 87}, {141, 208},
{143, 210}, {8, 86}, {41, 119}, {40, 118}, {9, 87}, {132, 219}, {142, 209},
{137, 224}, {143, 230}, {141, 228}, {139, 226}, {138, 225}, {142, 229}, {140,
227}, {18, 96}, {19, 97}, {22, 100}, {23, 101}, {26, 104}, {27, 105}, {30, 108},
{31, 109}, {20, 96}, {21, 97}, {22, 98}, {23, 99}, {28, 104}, {29, 105}, {30,
106}, {31, 107}, {20, 98}, {21, 99}, {28, 106}, {29, 107}, {144, 231}, {24,
100}, {25, 101}, {26, 102}, {27, 103}, {24, 102}, {25, 103}, {24, 155}, {52,
183}, {48, 179}, {44, 175}, {40, 171}, {36, 167}, {32, 163}, {28, 159}, {56,
187}, {60, 191}, {64, 195}, {68, 199}, {72, 203}, {76, 207}, {25, 156}, {51,
182}, {49, 180}, {43, 174}, {41, 172}, {35, 166}, {33, 164}, {27, 158}, {57,
188}, {59, 190}, {65, 196}, {67, 198}, {73, 204}, {75, 206}, {26, 157}, {50,
181}, {42, 173}, {34, 165}, {58, 189}, {66, 197}, {74, 205}, {37, 168}, {53,
184}, {39, 170}, {55, 186}, {69, 200}, {71, 202}, {38, 169}, {54, 185}, {70,
201}, {78, 222}, {79, 223}, {1, 154}, {60, 160}, {61, 161}, {62, 162}, {63,
163}, {45, 176}, {47, 178}, {77, 208}, {46, 177}, {56, 156}, {57, 157}, {58,
158}, {59, 159}, {105, 192}, {127, 214}, {125, 212}, {123, 210}, {121, 208},
{107, 194}, {109, 196}, {111, 198}, {106, 193}, {126, 213}, {122, 209}, {110,
197}, {55, 155}, {108, 195}, {124, 211}, {80, 224}, {81, 225}, {82, 226}, {83,
227}, {84, 228}, {85, 229}, {86, 230}, {87, 231}, {2, 179}, {4, 181}, {6, 183},
{8, 185}, {10, 187}, {12, 189}, {14, 191}, {50, 128}, {54, 132}, {51, 129}, {55,
133}, {58, 136}, {59, 137}, {62, 140}, {63, 141}, {1, 178}, {5, 182}, {9, 186},
{13, 190}, {52, 128}, {54, 130}, {53, 129}, {55, 131}, {60, 136}, {61, 137},
{62, 138}, {63, 139}, {52, 130}, {53, 131}, {60, 138}, {61, 139}, {3, 180},
{120, 207}, {11, 188}, {112, 199}, {113, 200}, {119, 206}, {117, 204}, {115,
202}, {114, 201}, {118, 205}, {56, 132}, {57, 133}, {58, 134}, {59, 135}, {29,
160}, {127, 194}, {125, 192}, {31, 162}, {56, 134}, {57, 135}, {7, 184}, {126,
193}, {116, 203}, {30, 161}, {88, 155}, {124, 191}, {120, 187}, {116, 183}, {92,
159}, {96, 163}, {100, 167}, {104, 171}, {108, 175}, {112, 179}, {89, 156},
{123, 190}, {121, 188}, {91, 158}, {97, 164}, {99, 166}, {105, 172}, {107, 174},
{113, 180}, {115, 182}, {90, 157}, {122, 189}, {98, 165}, {106, 173}, {114,
181}, {64, 140}, {65, 141}, {66, 142}, {67, 143}, {101, 168}, {119, 186}, {117,
184}, {103, 170}, {64, 142}, {65, 143}, {15, 192}, {118, 185}, {47, 224}, {31,
208}, {102, 169}, {1, 209}, {2, 210}, {3, 211}, {4, 212}, {5, 213}, {6, 214},
{7, 215}, {8, 216}, {9, 217}, {10, 218}, {11, 219}, {12, 220}, {13, 221}, {14,
222}, {15, 223}, {16, 193}, {52, 229}, {50, 227}, {48, 225}, {18, 195}, {20,
197}, {22, 199}, {24, 201}, {26, 203}, {28, 205}, {30, 207}, {54, 231}, {66,
144}, {67, 145}, {70, 148}, {71, 149}, {74, 152}, {75, 153}, {17, 194}, {53,
230}, {49, 226}, {21, 198}, {25, 202}, {29, 206}, {68, 144}, {69, 145}, {70,
146}, {71, 147}, {76, 152}, {77, 153}, {68, 146}, {69, 147}, {76, 154}, {19,
196}, {51, 228}, {27, 204}, {96, 183}, {104, 191}, {97, 184}, {99, 186}, {101,
188}, {103, 190}, {98, 185}, {102, 189}, {72, 148}, {73, 149}, {74, 150}, {75,
151}, {109, 176}, {111, 178}, {72, 150}, {73, 151}, {23, 200}, {100, 187}, {110,
177}, {64, 164}, {65, 165}, {66, 166}, {67, 167}, {72, 172}, {73, 173}, {74,
174}, {75, 175}, {79, 166}, {89, 176}, {91, 178}, {93, 180}, {95, 182}, {78,
165}, {90, 177}, {94, 181}, {68, 168}, {69, 169}, {70, 170}, {71, 171}, {92,
179}, {16, 224}, {17, 225}, {18, 226}, {19, 227}, {20, 228}, {21, 229}, {22,
230}, {23, 231}, {32, 209}, {46, 223}, {44, 221}, {42, 219}, {40, 217}, {38,
215}, {36, 213}, {34, 211}, {33, 210}, {45, 222}, {41, 218}, {37, 214}, {35,
212}, {43, 220}, {80, 167}, {88, 175}, {81, 168}, {83, 170}, {85, 172}, {87,
174}, {82, 169}, {86, 173}, {76, 176}, {77, 177}, {61, 192}, {63, 194}, {93,
160}, {95, 162}, {39, 216}, {62, 193}, {84, 171}, {94, 161} }>;
(II) A more general form is to represent the graph as the orbit of {77, 78}
under the group generated by the following permutations:
a: (2, 77)(3, 76)(4, 75)(5, 74)(6, 73)(7, 72)(8, 71)(9, 70)(10, 69)(11, 68)(12,
67)(13, 66)(14, 65)(15, 64)(16, 63)(17, 62)(18, 61)(19, 60)(20, 59)(21, 58)(22,
57)(23, 56)(24, 55)(25, 54)(26, 53)(27, 52)(28, 51)(29, 50)(30, 49)(31, 48)(32,
47)(33, 46)(34, 45)(35, 44)(36, 43)(37, 42)(38, 41)(39, 40)(79, 154)(80,
153)(81, 152)(82, 151)(83, 150)(84, 149)(85, 148)(86, 147)(87, 146)(88, 145)(89,
144)(90, 143)(91, 142)(92, 141)(93, 140)(94, 139)(95, 138)(96, 137)(97, 136)(98,
135)(99, 134)(100, 133)(101, 132)(102, 131)(103, 130)(104, 129)(105, 128)(106,
127)(107, 126)(108, 125)(109, 124)(110, 123)(111, 122)(112, 121)(113, 120)(114,
119)(115, 118)(116, 117)(156, 231)(157, 230)(158, 229)(159, 228)(160, 227)(161,
226)(162, 225)(163, 224)(164, 223)(165, 222)(166, 221)(167, 220)(168, 219)(169,
218)(170, 217)(171, 216)(172, 215)(173, 214)(174, 213)(175, 212)(176, 211)(177,
210)(178, 209)(179, 208)(180, 207)(181, 206)(182, 205)(183, 204)(184, 203)(185,
202)(186, 201)(187, 200)(188, 199)(189, 198)(190, 197)(191, 196)(192, 195)(193,
194) (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.
**************
&Graph **************
b: (1, 78, 155)(2, 145, 178)(3, 135, 201)(4, 125, 224)(5, 115, 170)(6, 105,
193)(7, 95, 216)(8, 85, 162)(9, 152, 185)(10, 142, 208)(11, 132, 231)(12, 122,
177)(13, 112, 200)(14, 102, 223)(15, 92, 169)(16, 82, 192)(17, 149, 215)(18,
139, 161)(19, 129, 184)(20, 119, 207)(21, 109, 230)(22, 99, 176)(23, 89,
199)(24, 79, 222)(25, 146, 168)(26, 136, 191)(27, 126, 214)(28, 116, 160)(29,
106, 183)(30, 96, 206)(31, 86, 229)(32, 153, 175)(33, 143, 198)(34, 133,
221)(35, 123, 167)(36, 113, 190)(37, 103, 213)(38, 93, 159)(39, 83, 182)(40,
150, 205)(41, 140, 228)(42, 130, 174)(43, 120, 197)(44, 110, 220)(45, 100,
166)(46, 90, 189)(47, 80, 212)(48, 147, 158)(49, 137, 181)(50, 127, 204)(51,
117, 227)(52, 107, 173)(53, 97, 196)(54, 87, 219)(55, 154, 165)(56, 144,
188)(57, 134, 211)(58, 124, 157)(59, 114, 180)(60, 104, 203)(61, 94, 226)(62,
84, 172)(63, 151, 195)(64, 141, 218)(65, 131, 164)(66, 121, 187)(67, 111,
210)(68, 101, 156)(69, 91, 179)(70, 81, 202)(71, 148, 225)(72, 138, 171)(73,
128, 194)(74, 118, 217)(75, 108, 163)(76, 98, 186)(77, 88, 209)
c: (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, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196,
197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212,
213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228,
229, 230, 231)
C4[ 231, 5 ]
231
-1 154 209 79 178
-2 78 210 80 179
-3 79 211 81 180
-4 80 212 82 181
-5 81 213 83 182
-6 82 214 84 183
-7 83 215 85 184
-8 84 216 86 185
-9 85 217 87 186
-10 88 187 86 218
-11 89 188 87 219
-12 88 220 90 189
-13 89 221 91 190
-14 90 222 92 191
-15 91 223 93 192
-16 92 224 94 193
-17 93 225 95 194
-18 94 226 96 195
-19 95 227 97 196
-20 96 228 98 197
-21 99 198 97 229
-22 100 199 98 230
-23 99 231 101 200
-24 100 155 102 201
-25 101 156 103 202
-26 102 157 104 203
-27 103 158 105 204
-28 104 159 106 205
-29 105 160 107 206
-30 106 161 108 207
-31 107 162 109 208
-32 110 209 108 163
-33 111 210 109 164
-34 110 165 112 211
-35 111 166 113 212
-36 112 167 114 213
-37 113 168 115 214
-38 114 169 116 215
-39 115 170 117 216
-40 116 171 118 217
-41 117 172 119 218
-42 118 173 120 219
-43 121 220 119 174
-44 122 221 120 175
-45 121 176 123 222
-46 122 177 124 223
-47 123 178 125 224
-48 124 179 126 225
-49 125 180 127 226
-50 126 181 128 227
-51 127 182 129 228
-52 128 183 130 229
-53 129 184 131 230
-54 132 231 130 185
-55 133 155 131 186
-56 132 187 134 156
-57 133 188 135 157
-58 134 189 136 158
-59 135 190 137 159
-60 136 191 138 160
-61 137 192 139 161
-62 138 193 140 162
-63 139 194 141 163
-64 140 195 142 164
-65 143 165 141 196
-66 144 166 142 197
-67 143 198 145 167
-68 144 199 146 168
-69 145 200 147 169
-70 146 201 148 170
-71 147 202 149 171
-72 148 203 150 172
-73 149 204 151 173
-74 150 205 152 174
-75 151 206 153 175
-76 154 176 152 207
-77 78 177 153 208
-78 77 165 2 222
-79 1 166 3 223
-80 2 167 4 224
-81 3 168 5 225
-82 4 169 6 226
-83 5 170 7 227
-84 6 171 8 228
-85 7 172 9 229
-86 8 173 10 230
-87 11 231 9 174
-88 12 155 10 175
-89 11 176 13 156
-90 12 177 14 157
-91 13 178 15 158
-92 14 179 16 159
-93 15 180 17 160
-94 16 181 18 161
-95 17 182 19 162
-96 18 183 20 163
-97 19 184 21 164
-98 22 165 20 185
-99 23 166 21 186
-100 22 187 24 167
-101 23 188 25 168
-102 24 189 26 169
-103 25 190 27 170
-104 26 191 28 171
-105 27 192 29 172
-106 28 193 30 173
-107 29 194 31 174
-108 30 195 32 175
-109 33 176 31 196
-110 34 177 32 197
-111 33 198 35 178
-112 34 199 36 179
-113 35 200 37 180
-114 36 201 38 181
-115 37 202 39 182
-116 38 203 40 183
-117 39 204 41 184
-118 40 205 42 185
-119 41 206 43 186
-120 44 187 42 207
-121 45 188 43 208
-122 44 209 46 189
-123 45 210 47 190
-124 46 211 48 191
-125 47 212 49 192
-126 48 213 50 193
-127 49 214 51 194
-128 50 215 52 195
-129 51 216 53 196
-130 52 217 54 197
-131 55 198 53 218
-132 56 199 54 219
-133 55 220 57 200
-134 56 221 58 201
-135 57 222 59 202
-136 58 223 60 203
-137 59 224 61 204
-138 60 225 62 205
-139 61 226 63 206
-140 62 227 64 207
-141 63 228 65 208
-142 66 209 64 229
-143 67 210 65 230
-144 66 231 68 211
-145 67 155 69 212
-146 68 156 70 213
-147 69 157 71 214
-148 70 158 72 215
-149 71 159 73 216
-150 72 160 74 217
-151 73 161 75 218
-152 74 162 76 219
-153 77 220 75 163
-154 1 221 76 164
-155 55 88 24 145
-156 56 89 25 146
-157 57 90 26 147
-158 58 91 27 148
-159 59 92 28 149
-160 60 93 29 150
-161 61 94 30 151
-162 62 95 31 152
-163 63 96 32 153
-164 33 154 64 97
-165 34 78 65 98
-166 66 99 35 79
-167 67 100 36 80
-168 68 101 37 81
-169 69 102 38 82
-170 70 103 39 83
-171 71 104 40 84
-172 72 105 41 85
-173 73 106 42 86
-174 74 107 43 87
-175 44 88 75 108
-176 45 89 76 109
-177 77 110 46 90
-178 1 111 47 91
-179 2 112 48 92
-180 3 113 49 93
-181 4 114 50 94
-182 5 115 51 95
-183 6 116 52 96
-184 7 117 53 97
-185 8 118 54 98
-186 55 99 9 119
-187 56 100 10 120
-188 11 121 57 101
-189 12 122 58 102
-190 13 123 59 103
-191 14 124 60 104
-192 15 125 61 105
-193 16 126 62 106
-194 17 127 63 107
-195 18 128 64 108
-196 19 129 65 109
-197 66 110 20 130
-198 67 111 21 131
-199 22 132 68 112
-200 23 133 69 113
-201 24 134 70 114
-202 25 135 71 115
-203 26 136 72 116
-204 27 137 73 117
-205 28 138 74 118
-206 29 139 75 119
-207 30 140 76 120
-208 77 121 31 141
-209 1 122 32 142
-210 33 143 2 123
-211 34 144 3 124
-212 35 145 4 125
-213 36 146 5 126
-214 37 147 6 127
-215 38 148 7 128
-216 39 149 8 129
-217 40 150 9 130
-218 41 151 10 131
-219 11 132 42 152
-220 12 133 43 153
-221 44 154 13 134
-222 45 78 14 135
-223 46 79 15 136
-224 47 80 16 137
-225 48 81 17 138
-226 49 82 18 139
-227 50 83 19 140
-228 51 84 20 141
-229 52 85 21 142
-230 22 143 53 86
-231 23 144 54 87
0