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