Graph forms
for C4 [ 231, 3 ] = C_231(1,76)
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On this page are computer-accessible forms for the graph C4[ 231, 3 ] =
C_231(1,76).
(I) Following is a form readable by MAGMA:
g:=Graph<231|{ {2, 3}, {230, 231}, {228, 229}, {226, 227}, {224, 225}, {222,
223}, {220, 221}, {218, 219}, {216, 217}, {214, 215}, {212, 213}, {210, 211},
{208, 209}, {206, 207}, {204, 205}, {202, 203}, {200, 201}, {198, 199}, {196,
197}, {194, 195}, {192, 193}, {190, 191}, {188, 189}, {186, 187}, {184, 185},
{182, 183}, {180, 181}, {178, 179}, {176, 177}, {174, 175}, {172, 173}, {170,
171}, {168, 169}, {166, 167}, {164, 165}, {162, 163}, {160, 161}, {158, 159},
{156, 157}, {154, 155}, {152, 153}, {150, 151}, {148, 149}, {146, 147}, {144,
145}, {142, 143}, {140, 141}, {138, 139}, {136, 137}, {70, 71}, {68, 69}, {66,
67}, {64, 65}, {62, 63}, {60, 61}, {58, 59}, {56, 57}, {54, 55}, {52, 53}, {50,
51}, {48, 49}, {46, 47}, {44, 45}, {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}, {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}, {1, 2}, {229, 230}, {225, 226}, {221, 222}, {217,
218}, {213, 214}, {209, 210}, {205, 206}, {201, 202}, {197, 198}, {193, 194},
{189, 190}, {185, 186}, {181, 182}, {177, 178}, {173, 174}, {169, 170}, {165,
166}, {161, 162}, {157, 158}, {153, 154}, {149, 150}, {145, 146}, {141, 142},
{137, 138}, {69, 70}, {65, 66}, {61, 62}, {57, 58}, {53, 54}, {49, 50}, {45,
46}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33,
34}, {37, 38}, {41, 42}, {73, 74}, {77, 78}, {81, 82}, {85, 86}, {89, 90}, {93,
94}, {97, 98}, {101, 102}, {105, 106}, {109, 110}, {113, 114}, {117, 118}, {121,
122}, {125, 126}, {129, 130}, {133, 134}, {3, 4}, {227, 228}, {219, 220}, {211,
212}, {203, 204}, {195, 196}, {187, 188}, {179, 180}, {171, 172}, {163, 164},
{155, 156}, {147, 148}, {139, 140}, {67, 68}, {59, 60}, {51, 52}, {43, 44}, {11,
12}, {19, 20}, {27, 28}, {35, 36}, {75, 76}, {83, 84}, {91, 92}, {99, 100},
{107, 108}, {115, 116}, {123, 124}, {131, 132}, {7, 8}, {215, 216}, {199, 200},
{183, 184}, {167, 168}, {151, 152}, {55, 56}, {23, 24}, {39, 40}, {71, 72}, {87,
88}, {103, 104}, {119, 120}, {135, 136}, {15, 16}, {207, 208}, {175, 176}, {143,
144}, {47, 48}, {79, 80}, {111, 112}, {31, 32}, {223, 224}, {159, 160}, {95,
96}, {1, 77}, {147, 223}, {146, 222}, {145, 221}, {144, 220}, {51, 127}, {50,
126}, {49, 125}, {48, 124}, {2, 78}, {3, 79}, {16, 92}, {17, 93}, {18, 94}, {19,
95}, {32, 108}, {33, 109}, {34, 110}, {35, 111}, {128, 204}, {129, 205}, {130,
206}, {131, 207}, {4, 80}, {143, 219}, {142, 218}, {141, 217}, {140, 216}, {47,
123}, {46, 122}, {45, 121}, {44, 120}, {5, 81}, {6, 82}, {7, 83}, {12, 88}, {13,
89}, {14, 90}, {15, 91}, {36, 112}, {37, 113}, {38, 114}, {39, 115}, {132, 208},
{133, 209}, {134, 210}, {135, 211}, {8, 84}, {139, 215}, {138, 214}, {137, 213},
{136, 212}, {43, 119}, {42, 118}, {9, 85}, {10, 86}, {11, 87}, {40, 116}, {41,
117}, {20, 96}, {151, 227}, {150, 226}, {149, 225}, {148, 224}, {21, 97}, {22,
98}, {23, 99}, {28, 104}, {29, 105}, {30, 106}, {31, 107}, {24, 100}, {155,
231}, {154, 230}, {153, 229}, {152, 228}, {25, 101}, {26, 102}, {27, 103}, {63,
64}, {191, 192}, {4, 159}, {68, 223}, {64, 219}, {32, 187}, {36, 191}, {1, 156},
{67, 222}, {65, 220}, {3, 158}, {33, 188}, {35, 190}, {2, 157}, {66, 221}, {34,
189}, {5, 160}, {69, 224}, {7, 162}, {13, 168}, {15, 170}, {21, 176}, {23, 178},
{29, 184}, {31, 186}, {71, 226}, {6, 161}, {70, 225}, {14, 169}, {22, 177}, {30,
185}, {8, 163}, {12, 167}, {24, 179}, {28, 183}, {72, 227}, {76, 231}, {9, 164},
{11, 166}, {25, 180}, {27, 182}, {73, 228}, {75, 230}, {10, 165}, {26, 181},
{74, 229}, {52, 128}, {63, 139}, {62, 138}, {61, 137}, {60, 136}, {55, 131},
{54, 130}, {53, 129}, {116, 192}, {117, 193}, {118, 194}, {119, 195}, {124,
200}, {125, 201}, {126, 202}, {127, 203}, {16, 171}, {20, 175}, {56, 132}, {59,
135}, {58, 134}, {57, 133}, {120, 196}, {121, 197}, {122, 198}, {123, 199}, {17,
172}, {19, 174}, {18, 173}, {64, 140}, {67, 143}, {66, 142}, {65, 141}, {80,
156}, {81, 157}, {82, 158}, {83, 159}, {96, 172}, {97, 173}, {98, 174}, {99,
175}, {112, 188}, {113, 189}, {114, 190}, {115, 191}, {68, 144}, {70, 146}, {69,
145}, {71, 147}, {76, 152}, {77, 153}, {78, 154}, {79, 155}, {100, 176}, {101,
177}, {102, 178}, {103, 179}, {108, 184}, {109, 185}, {110, 186}, {111, 187},
{72, 148}, {73, 149}, {74, 150}, {75, 151}, {104, 180}, {105, 181}, {106, 182},
{107, 183}, {37, 192}, {63, 218}, {61, 216}, {55, 210}, {53, 208}, {47, 202},
{45, 200}, {39, 194}, {1, 231}, {38, 193}, {62, 217}, {54, 209}, {46, 201}, {40,
195}, {60, 215}, {56, 211}, {44, 199}, {41, 196}, {59, 214}, {57, 212}, {43,
198}, {42, 197}, {58, 213}, {84, 160}, {85, 161}, {86, 162}, {87, 163}, {92,
168}, {93, 169}, {94, 170}, {95, 171}, {48, 203}, {52, 207}, {88, 164}, {89,
165}, {90, 166}, {91, 167}, {49, 204}, {51, 206}, {50, 205}, {127, 128}
}>;
(II) A more general form is to represent the graph as the orbit of {2, 3}
under the group generated by the following permutations:
a: (2, 156)(3, 80)(5, 159)(6, 83)(8, 162)(9, 86)(11, 165)(12, 89)(14, 168)(15,
92)(17, 171)(18, 95)(20, 174)(21, 98)(23, 177)(24, 101)(26, 180)(27, 104)(29,
183)(30, 107)(32, 186)(33, 110)(35, 189)(36, 113)(38, 192)(39, 116)(41, 195)(42,
119)(44, 198)(45, 122)(47, 201)(48, 125)(50, 204)(51, 128)(53, 207)(54, 131)(56,
210)(57, 134)(59, 213)(60, 137)(62, 216)(63, 140)(65, 219)(66, 143)(68, 222)(69,
146)(71, 225)(72, 149)(74, 228)(75, 152)(77, 231)(78, 155)(81, 158)(84, 161)(87,
164)(90, 167)(93, 170)(96, 173)(99, 176)(102, 179)(105, 182)(108, 185)(111,
188)(114, 191)(117, 194)(120, 197)(123, 200)(126, 203)(129, 206)(132, 209)(135,
212)(138, 215)(141, 218)(144, 221)(147, 224)(150, 227)(153, 230) (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: (2, 77)(3, 153)(4, 229)(5, 74)(6, 150)(7, 226)(8, 71)(9, 147)(10, 223)(11,
68)(12, 144)(13, 220)(14, 65)(15, 141)(16, 217)(17, 62)(18, 138)(19, 214)(20,
59)(21, 135)(22, 211)(23, 56)(24, 132)(25, 208)(26, 53)(27, 129)(28, 205)(29,
50)(30, 126)(31, 202)(32, 47)(33, 123)(34, 199)(35, 44)(36, 120)(37, 196)(38,
41)(39, 117)(40, 193)(42, 114)(43, 190)(45, 111)(46, 187)(48, 108)(49, 184)(51,
105)(52, 181)(54, 102)(55, 178)(57, 99)(58, 175)(60, 96)(61, 172)(63, 93)(64,
169)(66, 90)(67, 166)(69, 87)(70, 163)(72, 84)(73, 160)(75, 81)(76, 157)(79,
154)(80, 230)(82, 151)(83, 227)(85, 148)(86, 224)(88, 145)(89, 221)(91, 142)(92,
218)(94, 139)(95, 215)(97, 136)(98, 212)(100, 133)(101, 209)(103, 130)(104,
206)(106, 127)(107, 203)(109, 124)(110, 200)(112, 121)(113, 197)(115, 118)(116,
194)(119, 191)(122, 188)(125, 185)(128, 182)(131, 179)(134, 176)(137, 173)(140,
170)(143, 167)(146, 164)(149, 161)(152, 158)(156, 231)(159, 228)(162, 225)(165,
222)(168, 219)(171, 216)(174, 213)(177, 210)(180, 207)(183, 204)(186, 201)(189,
198)(192, 195)
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, 3 ]
231
-1 77 231 2 156
-2 1 78 3 157
-3 2 79 4 158
-4 3 80 5 159
-5 4 81 6 160
-6 5 82 7 161
-7 6 83 8 162
-8 7 84 9 163
-9 8 85 10 164
-10 11 165 9 86
-11 12 166 10 87
-12 11 88 13 167
-13 12 89 14 168
-14 13 90 15 169
-15 14 91 16 170
-16 15 92 17 171
-17 16 93 18 172
-18 17 94 19 173
-19 18 95 20 174
-20 19 96 21 175
-21 22 176 20 97
-22 23 177 21 98
-23 22 99 24 178
-24 23 100 25 179
-25 24 101 26 180
-26 25 102 27 181
-27 26 103 28 182
-28 27 104 29 183
-29 28 105 30 184
-30 29 106 31 185
-31 30 107 32 186
-32 33 187 31 108
-33 34 188 32 109
-34 33 110 35 189
-35 34 111 36 190
-36 35 112 37 191
-37 36 113 38 192
-38 37 114 39 193
-39 38 115 40 194
-40 39 116 41 195
-41 40 117 42 196
-42 41 118 43 197
-43 44 198 42 119
-44 45 199 43 120
-45 44 121 46 200
-46 45 122 47 201
-47 46 123 48 202
-48 47 124 49 203
-49 48 125 50 204
-50 49 126 51 205
-51 50 127 52 206
-52 51 128 53 207
-53 52 129 54 208
-54 55 209 53 130
-55 56 210 54 131
-56 55 132 57 211
-57 56 133 58 212
-58 57 134 59 213
-59 58 135 60 214
-60 59 136 61 215
-61 60 137 62 216
-62 61 138 63 217
-63 62 139 64 218
-64 63 140 65 219
-65 66 220 64 141
-66 67 221 65 142
-67 66 143 68 222
-68 67 144 69 223
-69 68 145 70 224
-70 69 146 71 225
-71 70 147 72 226
-72 71 148 73 227
-73 72 149 74 228
-74 73 150 75 229
-75 74 151 76 230
-76 77 231 75 152
-77 1 78 76 153
-78 77 154 2 79
-79 78 155 3 80
-80 79 156 4 81
-81 80 157 5 82
-82 81 158 6 83
-83 82 159 7 84
-84 83 160 8 85
-85 84 161 9 86
-86 85 162 10 87
-87 11 88 86 163
-88 12 89 87 164
-89 88 165 13 90
-90 89 166 14 91
-91 90 167 15 92
-92 91 168 16 93
-93 92 169 17 94
-94 93 170 18 95
-95 94 171 19 96
-96 95 172 20 97
-97 96 173 21 98
-98 22 99 97 174
-99 23 100 98 175
-100 99 176 24 101
-101 100 177 25 102
-102 101 178 26 103
-103 102 179 27 104
-104 103 180 28 105
-105 104 181 29 106
-106 105 182 30 107
-107 106 183 31 108
-108 107 184 32 109
-109 33 110 108 185
-110 34 111 109 186
-111 110 187 35 112
-112 111 188 36 113
-113 112 189 37 114
-114 113 190 38 115
-115 114 191 39 116
-116 115 192 40 117
-117 116 193 41 118
-118 117 194 42 119
-119 118 195 43 120
-120 44 121 119 196
-121 45 122 120 197
-122 121 198 46 123
-123 122 199 47 124
-124 123 200 48 125
-125 124 201 49 126
-126 125 202 50 127
-127 126 203 51 128
-128 127 204 52 129
-129 128 205 53 130
-130 129 206 54 131
-131 55 132 130 207
-132 56 133 131 208
-133 132 209 57 134
-134 133 210 58 135
-135 134 211 59 136
-136 135 212 60 137
-137 136 213 61 138
-138 137 214 62 139
-139 138 215 63 140
-140 139 216 64 141
-141 140 217 65 142
-142 66 143 141 218
-143 67 144 142 219
-144 143 220 68 145
-145 144 221 69 146
-146 145 222 70 147
-147 146 223 71 148
-148 147 224 72 149
-149 148 225 73 150
-150 149 226 74 151
-151 150 227 75 152
-152 151 228 76 153
-153 77 154 152 229
-154 78 155 153 230
-155 154 231 79 156
-156 1 155 80 157
-157 2 156 81 158
-158 3 157 82 159
-159 4 158 83 160
-160 5 159 84 161
-161 6 160 85 162
-162 7 161 86 163
-163 8 162 87 164
-164 88 165 9 163
-165 89 166 10 164
-166 11 165 90 167
-167 12 166 91 168
-168 13 167 92 169
-169 14 168 93 170
-170 15 169 94 171
-171 16 170 95 172
-172 17 171 96 173
-173 18 172 97 174
-174 19 173 98 175
-175 99 176 20 174
-176 100 177 21 175
-177 22 176 101 178
-178 23 177 102 179
-179 24 178 103 180
-180 25 179 104 181
-181 26 180 105 182
-182 27 181 106 183
-183 28 182 107 184
-184 29 183 108 185
-185 30 184 109 186
-186 110 187 31 185
-187 111 188 32 186
-188 33 187 112 189
-189 34 188 113 190
-190 35 189 114 191
-191 36 190 115 192
-192 37 191 116 193
-193 38 192 117 194
-194 39 193 118 195
-195 40 194 119 196
-196 41 195 120 197
-197 121 198 42 196
-198 122 199 43 197
-199 44 198 123 200
-200 45 199 124 201
-201 46 200 125 202
-202 47 201 126 203
-203 48 202 127 204
-204 49 203 128 205
-205 50 204 129 206
-206 51 205 130 207
-207 52 206 131 208
-208 132 209 53 207
-209 133 210 54 208
-210 55 209 134 211
-211 56 210 135 212
-212 57 211 136 213
-213 58 212 137 214
-214 59 213 138 215
-215 60 214 139 216
-216 61 215 140 217
-217 62 216 141 218
-218 63 217 142 219
-219 143 220 64 218
-220 144 221 65 219
-221 66 220 145 222
-222 67 221 146 223
-223 68 222 147 224
-224 69 223 148 225
-225 70 224 149 226
-226 71 225 150 227
-227 72 226 151 228
-228 73 227 152 229
-229 74 228 153 230
-230 154 231 75 229
-231 1 155 76 230
0