Graph forms
for C4 [ 272, 20 ] =
PL(MC3(4,34,1,33,13,0,1),[4^34,34^4])
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On this page are computer-accessible forms for the graph C4[ 272, 20 ] =
PL(MC3(4,34,1,33,13,0,1),[4^34,34^4]).
(I) Following is a form readable by MAGMA:
g:=Graph<272|{ {136, 143}, {134, 140}, {132, 143}, {128, 141}, {134, 148}, {135,
149}, {128, 160}, {136, 168}, {129, 164}, {132, 163}, {134, 161}, {132, 172},
{130, 168}, {133, 174}, {128, 172}, {133, 169}, {129, 175}, {130, 180}, {131,
191}, {136, 180}, {134, 186}, {133, 205}, {131, 200}, {128, 210}, {131, 221},
{133, 229}, {131, 241}, {130, 241}, {132, 242}, {136, 242}, {135, 250}, {129,
255}, {23, 151}, {102, 230}, {58, 186}, {25, 153}, {56, 185}, {121, 248}, {112,
241}, {75, 202}, {108, 238}, {124, 254}, {16, 147}, {63, 188}, {50, 177}, {83,
208}, {96, 227}, {15, 139}, {57, 189}, {22, 147}, {124, 249}, {64, 197}, {28,
155}, {55, 176}, {39, 160}, {35, 164}, {32, 167}, {65, 198}, {70, 193}, {6,
142}, {117, 253}, {64, 200}, {69, 205}, {70, 206}, {27, 146}, {117, 252}, {73,
192}, {23, 157}, {108, 230}, {99, 233}, {21, 158}, {106, 225}, {44, 167}, {68,
207}, {84, 216}, {118, 250}, {67, 206}, {70, 203}, {91, 214}, {48, 190}, {105,
231}, {60, 178}, {76, 194}, {28, 147}, {49, 190}, {55, 167}, {107, 251}, {98,
242}, {64, 208}, {78, 222}, {15, 158}, {52, 165}, {71, 214}, {84, 197}, {58,
169}, {125, 238}, {90, 201}, {6, 146}, {83, 199}, {90, 206}, {27, 142}, {83,
198}, {59, 173}, {107, 253}, {75, 221}, {92, 202}, {63, 168}, {77, 218}, {88,
207}, {3, 155}, {113, 233}, {43, 178}, {103, 254}, {97, 248}, {59, 162}, {65,
216}, {87, 206}, {36, 190}, {123, 225}, {90, 192}, {37, 190}, {126, 229}, {125,
230}, {93, 193}, {122, 230}, {60, 161}, {103, 250}, {98, 255}, {76, 209}, {79,
209}, {4, 155}, {120, 231}, {42, 181}, {15, 144}, {10, 170}, {23, 183}, {95,
255}, {88, 249}, {108, 205}, {64, 226}, {85, 247}, {30, 189}, {72, 235}, {21,
177}, {119, 211}, {96, 196}, {18, 183}, {111, 202}, {106, 207}, {54, 147}, {13,
171}, {114, 212}, {17, 183}, {88, 254}, {13, 170}, {127, 216}, {55, 144}, {49,
153}, {113, 217}, {92, 244}, {2, 171}, {22, 191}, {74, 227}, {81, 248}, {1,
171}, {98, 200}, {27, 177}, {30, 181}, {32, 140}, {58, 150}, {76, 224}, {80,
252}, {7, 170}, {116, 217}, {109, 192}, {54, 155}, {80, 253}, {81, 252}, {69,
235}, {73, 231}, {85, 251}, {16, 191}, {120, 215}, {105, 198}, {24, 183}, {3,
179}, {100, 212}, {61, 141}, {26, 170}, {82, 226}, {26, 171}, {62, 143}, {32,
145}, {83, 226}, {91, 234}, {31, 173}, {111, 221}, {59, 137}, {47, 157}, {89,
235}, {10, 185}, {126, 205}, {36, 151}, {61, 137}, {123, 207}, {62, 138}, {96,
212}, {17, 164}, {109, 216}, {32, 149}, {5, 179}, {6, 176}, {4, 179}, {43, 156},
{92, 235}, {47, 151}, {9, 176}, {44, 149}, {68, 253}, {93, 231}, {99, 217}, {53,
142}, {104, 211}, {66, 249}, {42, 150}, {110, 210}, {55, 139}, {72, 244}, {31,
162}, {120, 197}, {94, 227}, {7, 185}, {127, 193}, {105, 215}, {39, 153}, {15,
177}, {12, 179}, {102, 217}, {68, 251}, {102, 166}, {123, 187}, {122, 186},
{111, 175}, {104, 168}, {13, 204}, {29, 220}, {17, 208}, {16, 210}, {62, 252},
{22, 212}, {95, 157}, {24, 219}, {127, 188}, {61, 254}, {31, 220}, {101, 161},
{114, 182}, {40, 238}, {115, 181}, {62, 248}, {14, 201}, {61, 250}, {50, 245},
{48, 247}, {40, 239}, {38, 225}, {23, 208}, {78, 137}, {90, 146}, {18, 219},
{37, 236}, {20, 222}, {99, 169}, {28, 214}, {82, 152}, {30, 213}, {125, 182},
{111, 164}, {110, 165}, {100, 175}, {48, 251}, {14, 194}, {113, 189}, {89, 148},
{84, 154}, {3, 204}, {39, 232}, {37, 234}, {26, 213}, {10, 218}, {101, 181},
{14, 222}, {4, 213}, {126, 175}, {7, 214}, {69, 148}, {73, 152}, {51, 225},
{105, 187}, {100, 182}, {77, 159}, {78, 156}, {89, 139}, {92, 142}, {12, 223},
{112, 163}, {33, 242}, {11, 223}, {119, 163}, {104, 188}, {35, 247}, {29, 201},
{70, 146}, {66, 151}, {116, 161}, {115, 166}, {75, 157}, {8, 223}, {101, 178},
{20, 195}, {57, 224}, {123, 162}, {67, 154}, {80, 137}, {96, 185}, {1, 219},
{110, 180}, {53, 239}, {41, 243}, {76, 150}, {53, 238}, {114, 169}, {45, 241},
{122, 166}, {114, 174}, {112, 172}, {52, 232}, {49, 237}, {2, 223}, {98, 191},
{63, 226}, {56, 229}, {36, 249}, {30, 195}, {80, 141}, {5, 219}, {115, 173},
{54, 232}, {52, 234}, {33, 255}, {71, 153}, {20, 203}, {29, 194}, {67, 156}, {4,
228}, {116, 148}, {58, 218}, {88, 184}, {93, 188}, {126, 159}, {10, 232}, {120,
154}, {41, 203}, {79, 173}, {3, 224}, {118, 149}, {110, 141}, {91, 184}, {11,
239}, {20, 240}, {8, 237}, {59, 222}, {33, 196}, {75, 174}, {17, 247}, {119,
145}, {33, 199}, {18, 244}, {86, 176}, {11, 236}, {121, 158}, {48, 215}, {38,
193}, {34, 197}, {71, 160}, {42, 194}, {57, 209}, {46, 198}, {37, 204}, {46,
199}, {45, 196}, {79, 166}, {34, 200}, {56, 210}, {45, 199}, {41, 195}, {54,
218}, {87, 187}, {13, 224}, {60, 209}, {38, 203}, {97, 140}, {7, 233}, {113,
159}, {29, 243}, {27, 245}, {74, 165}, {127, 144}, {119, 152}, {101, 138}, {89,
182}, {6, 246}, {106, 154}, {45, 221}, {77, 189}, {97, 145}, {34, 211}, {82,
163}, {86, 167}, {95, 174}, {1, 243}, {2, 240}, {94, 172}, {5, 246}, {51, 192},
{36, 215}, {1, 245}, {25, 237}, {24, 236}, {16, 229}, {109, 152}, {99, 150},
{41, 220}, {28, 233}, {22, 227}, {87, 162}, {5, 243}, {125, 139}, {122, 140},
{106, 156}, {2, 245}, {43, 220}, {24, 239}, {19, 228}, {77, 186}, {19, 234},
{118, 143}, {115, 138}, {104, 145}, {12, 246}, {65, 187}, {57, 195}, {51, 201},
{100, 159}, {8, 244}, {118, 138}, {56, 196}, {12, 240}, {68, 184}, {78, 178},
{25, 228}, {109, 144}, {49, 204}, {46, 211}, {14, 240}, {26, 228}, {74, 180},
{91, 165}, {94, 160}, {9, 246}, {53, 202}, {42, 213}, {19, 236}, {18, 237}, {71,
184}, {97, 158}, {8, 265}, {11, 265}, {9, 256}, {25, 269}, {21, 259}, {31, 263},
{9, 272}, {21, 268}, {19, 269}, {40, 264}, {35, 257}, {50, 272}, {44, 270}, {34,
257}, {51, 272}, {47, 265}, {40, 256}, {35, 265}, {44, 262}, {43, 263}, {39,
266}, {47, 257}, {46, 257}, {63, 270}, {50, 256}, {38, 272}, {60, 260}, {52,
266}, {72, 264}, {67, 258}, {65, 261}, {73, 268}, {74, 271}, {69, 259}, {66,
261}, {72, 256}, {79, 260}, {66, 269}, {85, 261}, {84, 261}, {93, 268}, {94,
271}, {81, 260}, {86, 259}, {87, 258}, {95, 264}, {85, 269}, {81, 267}, {86,
268}, {82, 270}, {102, 262}, {103, 263}, {107, 266}, {103, 271}, {107, 258},
{108, 259}, {116, 262}, {117, 263}, {124, 266}, {121, 270}, {117, 271}, {112,
267}, {124, 258}, {121, 262}, {135, 260}, {129, 264}, {130, 267}, {135, 267}
}>;
(II) A more general form is to represent the graph as the orbit of {136, 143}
under the group generated by the following permutations:
a: (1, 3, 7, 16, 33, 34, 65, 67, 31, 60, 102, 69, 40, 8, 19, 39, 74, 112, 63,
73, 38, 14, 30, 58, 100, 75, 17, 36, 68, 61, 62, 32, 15, 6)(2, 4, 10, 22, 45,
64, 105, 106, 59, 101, 122, 89, 53, 18, 37, 71, 110, 132, 104, 109, 70, 29, 57,
99, 126, 95, 35, 66, 107, 103, 81, 44, 21, 9)(5, 13, 28, 56, 98, 46, 84, 87, 43,
79, 116, 108, 72, 11, 25, 52, 94, 130, 82, 93, 51, 20, 42, 77, 114, 111, 23, 48,
88, 80, 118, 97, 55, 27)(12, 26, 54, 96, 131, 83, 120, 123, 78, 115, 134, 125,
92, 24, 49, 91, 128, 136, 119, 127, 90, 41, 76, 113, 133, 129, 47, 85, 124, 117,
135, 121, 86, 50)(137, 138, 140, 139, 142, 219, 204, 214, 210, 242, 211, 216,
206, 220, 209, 217, 205, 264, 265, 269, 266, 271, 267, 270, 268, 272, 240, 213,
218, 212, 221, 208, 215, 207)(141, 143, 145, 144, 146, 243, 224, 233, 229, 255,
257, 261, 258, 263, 260, 262, 259, 256, 223, 228, 232, 227, 241, 226, 231, 225,
222, 181, 186, 182, 202, 183, 190, 184)(147, 196, 200, 198, 154, 162, 178, 166,
148, 238, 244, 236, 153, 165, 172, 168, 152, 193, 201, 195, 150, 159, 174, 164,
151, 251, 254, 252, 149, 158, 176, 245, 179, 170)(155, 185, 191, 199, 197, 187,
156, 173, 161, 230, 235, 239, 237, 234, 160, 180, 163, 188, 192, 203, 194, 189,
169, 175, 157, 247, 249, 253, 250, 248, 167, 177, 246, 171) (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, 5)(3, 8, 6, 14)(4, 11, 9, 20)(7, 17, 15, 31)(10, 23, 21, 43)(13, 18, 27,
29)(16, 34, 32, 61)(19, 40, 38, 30)(22, 46, 44, 80)(24, 50, 41, 26)(25, 53, 51,
57)(28, 35, 55, 59)(33, 63, 62, 74)(36, 69, 67, 58)(37, 72, 70, 42)(39, 75, 73,
60)(45, 82, 81, 94)(47, 86, 78, 54)(48, 89, 87, 99)(49, 92, 90, 76)(52, 95, 93,
101)(56, 64, 97, 103)(65, 102, 68, 100)(66, 108, 106, 77)(71, 111, 109, 79)(83,
121, 117, 96)(84, 122, 88, 126)(85, 125, 123, 113)(91, 129, 127, 115)(98, 104,
118, 110)(105, 116, 107, 114)(119, 135, 128, 131)(120, 134, 124, 133)(130,
132)(137, 147, 257, 167)(138, 165, 255, 188)(139, 162, 233, 247)(140, 254, 229,
197)(141, 191, 211, 149)(142, 201, 224, 237)(143, 180, 242, 168)(144, 173, 214,
164)(145, 250, 210, 200)(146, 194, 204, 244)(148, 258, 169, 215)(150, 190, 235,
206)(151, 259, 156, 218)(152, 260, 160, 221)(153, 202, 192, 209)(154, 186, 249,
205)(155, 265, 176, 222)(157, 268, 178, 232)(158, 263, 185, 208)(159, 261, 230,
207)(161, 266, 174, 231)(163, 267, 172, 241)(166, 184, 175, 216)(170, 183, 177,
220)(171, 219, 245, 243)(179, 223, 246, 240)(181, 234, 264, 193)(182, 187, 217,
251)(189, 269, 238, 225)(195, 228, 239, 272)(196, 226, 248, 271)(198, 262, 253,
212)(199, 270, 252, 227)(203, 213, 236, 256)
c: (1, 2, 12, 5)(3, 18, 50, 20)(4, 24, 27, 14)(6, 29, 26, 11)(7, 35, 86, 43)(8,
9, 41, 13)(10, 47, 55, 31)(15, 59, 54, 23)(16, 64, 121, 80)(17, 21, 78, 28)(19,
53, 90, 42)(22, 83, 97, 61)(25, 40, 70, 76)(30, 37, 92, 51)(32, 103, 96, 46)(33,
104, 135, 94)(34, 44, 117, 56)(36, 89, 123, 77)(38, 57, 49, 72)(39, 95, 127,
79)(45, 119, 118, 74)(48, 69, 106, 113)(52, 75, 109, 115)(58, 66, 125, 87)(60,
71, 129, 93)(62, 110, 131, 82)(63, 81, 128, 98)(65, 122, 124, 114)(67, 99, 85,
108)(68, 126, 120, 116)(73, 101, 91, 111)(84, 102, 107, 133)(88, 100, 105,
134)(112, 132, 136, 130)(137, 147, 208, 158)(138, 165, 221, 152)(139, 162, 218,
151)(140, 254, 212, 198)(141, 191, 226, 248)(142, 201, 213, 236)(143, 180, 241,
163)(144, 173, 232, 157)(145, 250, 227, 199)(146, 194, 228, 239)(148, 207, 159,
215)(149, 271, 196, 211)(150, 269, 238, 206)(153, 264, 193, 209)(154, 217, 251,
205)(155, 183, 177, 222)(156, 233, 247, 259)(160, 255, 188, 260)(161, 184, 175,
231)(164, 268, 178, 214)(166, 266, 174, 216)(167, 263, 185, 257)(168, 267, 172,
242)(169, 261, 230, 258)(170, 265, 176, 220)(171, 223, 246, 243)(179, 219, 245,
240)(181, 234, 202, 192)(182, 187, 186, 249)(189, 190, 235, 225)(195, 204, 244,
272)(197, 262, 253, 229)(200, 270, 252, 210)(203, 224, 237, 256)
C4[ 272, 20 ]
272
-1 243 245 171 219
-2 223 245 171 240
-3 155 179 224 204
-4 155 179 213 228
-5 243 179 246 219
-6 176 146 246 142
-7 233 170 214 185
-8 265 244 223 237
-9 176 256 246 272
-10 232 170 185 218
-11 265 223 236 239
-12 179 223 246 240
-13 224 170 171 204
-14 222 201 194 240
-15 144 177 158 139
-16 210 147 191 229
-17 247 183 164 208
-18 244 237 183 219
-19 234 236 269 228
-20 222 203 195 240
-21 177 158 268 259
-22 212 147 191 227
-23 157 183 151 208
-24 236 183 239 219
-25 269 237 228 153
-26 213 170 171 228
-27 177 146 245 142
-28 155 233 147 214
-29 220 243 201 194
-30 189 213 181 195
-31 220 162 173 263
-32 145 167 149 140
-33 242 199 255 196
-34 200 211 257 197
-35 265 257 247 164
-36 190 215 249 151
-37 190 234 236 204
-38 203 225 193 272
-39 232 266 160 153
-40 264 256 238 239
-41 220 243 203 195
-42 213 181 150 194
-43 220 156 178 263
-44 167 149 270 262
-45 199 221 196 241
-46 198 199 211 257
-47 265 157 257 151
-48 190 247 215 251
-49 190 204 237 153
-50 177 245 256 272
-51 201 192 225 272
-52 165 232 266 234
-53 202 238 239 142
-54 155 232 147 218
-55 176 144 167 139
-56 210 185 196 229
-57 209 189 224 195
-58 169 150 218 186
-59 222 137 162 173
-60 209 178 161 260
-61 254 137 250 141
-62 143 138 248 252
-63 188 168 226 270
-64 200 226 197 208
-65 187 198 216 261
-66 269 249 151 261
-67 154 156 258 206
-68 253 184 207 251
-69 235 148 259 205
-70 146 203 193 206
-71 214 160 184 153
-72 264 244 256 235
-73 231 268 192 152
-74 165 180 227 271
-75 221 157 202 174
-76 209 224 150 194
-77 189 159 218 186
-78 156 178 222 137
-79 209 166 260 173
-80 253 137 141 252
-81 267 248 260 252
-82 226 270 152 163
-83 198 199 226 208
-84 154 216 261 197
-85 247 269 261 251
-86 176 167 268 259
-87 187 258 162 206
-88 254 249 184 207
-89 235 148 182 139
-90 146 201 192 206
-91 165 234 214 184
-92 244 202 235 142
-93 231 188 268 193
-94 160 172 227 271
-95 264 255 157 174
-96 212 227 185 196
-97 145 158 248 140
-98 242 200 255 191
-99 233 169 150 217
-100 212 159 182 175
-101 178 181 138 161
-102 166 217 262 230
-103 254 271 250 263
-104 188 145 211 168
-105 187 198 231 215
-106 154 156 225 207
-107 253 266 258 251
-108 259 205 238 230
-109 144 192 216 152
-110 165 210 180 141
-111 221 202 164 175
-112 267 172 163 241
-113 189 233 159 217
-114 212 169 182 174
-115 166 181 138 173
-116 148 161 217 262
-117 253 271 252 263
-118 143 138 149 250
-119 145 211 152 163
-120 154 231 215 197
-121 158 248 270 262
-122 166 140 186 230
-123 187 225 162 207
-124 254 266 258 249
-125 182 139 238 230
-126 159 205 229 175
-127 144 188 193 216
-128 210 160 172 141
-129 264 255 164 175
-130 168 267 180 241
-131 221 200 191 241
-132 143 242 172 163
-133 169 205 174 229
-134 148 161 140 186
-135 267 149 260 250
-136 143 242 168 180
-137 78 80 59 61
-138 101 115 62 118
-139 55 89 15 125
-140 122 134 97 32
-141 110 80 61 128
-142 92 27 6 53
-143 132 136 62 118
-144 55 15 127 109
-145 104 97 119 32
-146 90 70 27 6
-147 22 16 28 54
-148 89 134 69 116
-149 44 135 118 32
-150 99 58 42 76
-151 66 23 36 47
-152 82 73 119 109
-153 25 49 71 39
-154 67 84 106 120
-155 3 4 28 54
-156 67 78 106 43
-157 23 47 95 75
-158 121 15 97 21
-159 77 100 113 126
-160 71 39 94 128
-161 101 134 60 116
-162 123 59 31 87
-163 132 112 82 119
-164 111 35 17 129
-165 110 91 52 74
-166 122 79 102 115
-167 44 55 86 32
-168 136 104 63 130
-169 99 133 58 114
-170 13 26 7 10
-171 1 2 13 26
-172 132 112 94 128
-173 79 59 115 31
-174 133 114 95 75
-175 100 111 126 129
-176 55 6 9 86
-177 15 27 50 21
-178 78 101 60 43
-179 12 3 4 5
-180 110 136 74 130
-181 101 115 30 42
-182 89 100 114 125
-183 23 24 17 18
-184 88 68 91 71
-185 56 7 96 10
-186 77 122 134 58
-187 123 105 65 87
-188 93 104 127 63
-189 77 57 113 30
-190 36 37 48 49
-191 22 16 98 131
-192 90 51 73 109
-193 70 38 93 127
-194 14 29 42 76
-195 57 30 41 20
-196 33 45 56 96
-197 34 84 64 120
-198 46 83 105 65
-199 33 45 46 83
-200 34 64 98 131
-201 90 14 29 51
-202 111 92 53 75
-203 70 38 41 20
-204 13 3 37 49
-205 133 69 126 108
-206 67 90 70 87
-207 88 68 123 106
-208 23 17 83 64
-209 57 79 60 76
-210 110 56 16 128
-211 34 46 104 119
-212 22 100 114 96
-213 4 26 30 42
-214 91 71 28 7
-215 36 48 105 120
-216 127 84 65 109
-217 99 102 113 116
-218 77 58 10 54
-219 1 24 5 18
-220 29 41 31 43
-221 45 111 75 131
-222 78 14 59 20
-223 11 12 2 8
-224 13 57 3 76
-225 123 38 51 106
-226 82 83 63 64
-227 22 94 74 96
-228 25 4 26 19
-229 56 133 16 126
-230 122 102 125 108
-231 93 105 73 120
-232 39 52 10 54
-233 99 113 28 7
-234 91 37 19 52
-235 89 69 92 72
-236 11 24 37 19
-237 25 49 18 8
-238 125 40 53 108
-239 11 24 40 53
-240 12 2 14 20
-241 45 112 130 131
-242 33 132 136 98
-243 1 5 29 41
-244 92 72 18 8
-245 1 2 27 50
-246 12 5 6 9
-247 35 48 17 85
-248 121 81 62 97
-249 66 88 36 124
-250 135 103 61 118
-251 68 48 85 107
-252 80 81 62 117
-253 68 80 117 107
-254 88 124 103 61
-255 33 95 129 98
-256 50 72 40 9
-257 34 35 46 47
-258 67 124 107 87
-259 69 86 108 21
-260 79 135 81 60
-261 66 84 85 65
-262 44 121 102 116
-263 103 117 31 43
-264 72 40 95 129
-265 11 35 47 8
-266 124 39 52 107
-267 112 135 81 130
-268 93 73 86 21
-269 66 25 19 85
-270 44 121 82 63
-271 103 94 117 74
-272 38 50 51 9
0