Graph forms
for C4 [ 264, 17 ] = Pr_88(1,9,13,21)
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On this page are computer-accessible forms for the graph C4[ 264, 17 ] =
Pr_88(1,9,13,21).
(I) Following is a form readable by MAGMA:
g:=Graph<264|{ {2, 3}, {86, 87}, {84, 85}, {82, 83}, {80, 81}, {78, 79}, {76,
77}, {74, 75}, {72, 73}, {70, 71}, {68, 69}, {66, 67}, {64, 65}, {62, 63}, {60,
61}, {58, 59}, {56, 57}, {54, 55}, {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}, {1, 2}, {85, 86}, {81, 82}, {77, 78},
{73, 74}, {69, 70}, {65, 66}, {61, 62}, {57, 58}, {5, 6}, {9, 10}, {13, 14},
{17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37, 38}, {41, 42}, {45, 46},
{49, 50}, {53, 54}, {3, 4}, {83, 84}, {75, 76}, {67, 68}, {59, 60}, {11, 12},
{19, 20}, {27, 28}, {35, 36}, {43, 44}, {51, 52}, {176, 189}, {7, 8}, {87, 88},
{71, 72}, {55, 56}, {23, 24}, {39, 40}, {167, 180}, {171, 184}, {175, 188},
{164, 177}, {234, 255}, {232, 253}, {226, 247}, {224, 245}, {166, 179}, {172,
185}, {174, 187}, {192, 213}, {194, 215}, {200, 221}, {202, 223}, {165, 178},
{233, 254}, {225, 246}, {173, 186}, {193, 214}, {201, 222}, {195, 216}, {231,
252}, {227, 248}, {199, 220}, {168, 181}, {230, 251}, {228, 249}, {170, 183},
{196, 217}, {198, 219}, {15, 16}, {229, 250}, {79, 80}, {47, 48}, {169, 182},
{197, 218}, {203, 224}, {223, 244}, {219, 240}, {207, 228}, {204, 225}, {222,
243}, {220, 241}, {206, 227}, {205, 226}, {221, 242}, {208, 229}, {218, 239},
{216, 237}, {210, 231}, {209, 230}, {217, 238}, {211, 232}, {215, 236}, {212,
233}, {214, 235}, {31, 32}, {213, 234}, {180, 247}, {184, 251}, {188, 255},
{177, 244}, {179, 246}, {185, 252}, {187, 254}, {178, 245}, {186, 253}, {181,
248}, {183, 250}, {16, 95}, {32, 111}, {48, 127}, {182, 249}, {11, 90}, {13,
92}, {15, 94}, {33, 112}, {35, 114}, {37, 116}, {39, 118}, {41, 120}, {43, 122},
{45, 124}, {47, 126}, {10, 89}, {14, 93}, {34, 113}, {38, 117}, {42, 121}, {46,
125}, {12, 91}, {36, 115}, {44, 123}, {1, 89}, {2, 90}, {3, 91}, {4, 92}, {5,
93}, {6, 94}, {7, 95}, {32, 120}, {33, 121}, {34, 122}, {35, 123}, {36, 124},
{37, 125}, {38, 126}, {39, 127}, {128, 216}, {129, 217}, {130, 218}, {131, 219},
{132, 220}, {133, 221}, {134, 222}, {135, 223}, {160, 248}, {161, 249}, {162,
250}, {163, 251}, {164, 252}, {165, 253}, {166, 254}, {167, 255}, {1, 88}, {40,
119}, {128, 229}, {130, 231}, {136, 237}, {138, 239}, {144, 245}, {146, 247},
{152, 253}, {154, 255}, {129, 230}, {137, 238}, {145, 246}, {153, 254}, {8, 96},
{9, 97}, {10, 98}, {11, 99}, {12, 100}, {13, 101}, {14, 102}, {15, 103}, {24,
112}, {25, 113}, {26, 114}, {27, 115}, {28, 116}, {29, 117}, {30, 118}, {31,
119}, {136, 224}, {137, 225}, {138, 226}, {139, 227}, {140, 228}, {141, 229},
{142, 230}, {143, 231}, {152, 240}, {153, 241}, {154, 242}, {155, 243}, {156,
244}, {157, 245}, {158, 246}, {159, 247}, {131, 232}, {135, 236}, {147, 248},
{151, 252}, {187, 208}, {191, 212}, {132, 233}, {134, 235}, {148, 249}, {150,
251}, {188, 209}, {190, 211}, {133, 234}, {149, 250}, {189, 210}, {17, 96}, {19,
98}, {21, 100}, {23, 102}, {25, 104}, {27, 106}, {29, 108}, {31, 110}, {18, 97},
{22, 101}, {26, 105}, {30, 109}, {178, 199}, {184, 205}, {186, 207}, {20, 99},
{28, 107}, {177, 198}, {185, 206}, {16, 104}, {17, 105}, {18, 106}, {19, 107},
{20, 108}, {21, 109}, {22, 110}, {23, 111}, {144, 232}, {145, 233}, {146, 234},
{147, 235}, {148, 236}, {149, 237}, {150, 238}, {151, 239}, {139, 240}, {143,
244}, {179, 200}, {183, 204}, {140, 241}, {142, 243}, {180, 201}, {182, 203},
{24, 103}, {63, 64}, {141, 242}, {181, 202}, {91, 192}, {95, 196}, {123, 224},
{127, 228}, {92, 193}, {94, 195}, {124, 225}, {126, 227}, {93, 194}, {125, 226},
{96, 197}, {98, 199}, {104, 205}, {106, 207}, {112, 213}, {114, 215}, {120,
221}, {122, 223}, {8, 175}, {97, 198}, {105, 206}, {113, 214}, {121, 222}, {40,
128}, {63, 151}, {62, 150}, {61, 149}, {60, 148}, {59, 147}, {58, 146}, {57,
145}, {56, 144}, {41, 129}, {42, 130}, {43, 131}, {44, 132}, {45, 133}, {46,
134}, {47, 135}, {104, 192}, {105, 193}, {106, 194}, {107, 195}, {108, 196},
{109, 197}, {110, 198}, {111, 199}, {120, 208}, {121, 209}, {122, 210}, {123,
211}, {124, 212}, {125, 213}, {126, 214}, {127, 215}, {1, 168}, {3, 170}, {5,
172}, {7, 174}, {2, 169}, {6, 173}, {99, 200}, {103, 204}, {115, 216}, {119,
220}, {100, 201}, {102, 203}, {116, 217}, {118, 219}, {4, 171}, {101, 202},
{117, 218}, {49, 128}, {63, 142}, {61, 140}, {59, 138}, {57, 136}, {55, 134},
{51, 130}, {53, 132}, {50, 129}, {62, 141}, {58, 137}, {54, 133}, {52, 131},
{60, 139}, {48, 136}, {55, 143}, {54, 142}, {53, 141}, {49, 137}, {50, 138},
{51, 139}, {52, 140}, {112, 200}, {113, 201}, {114, 202}, {115, 203}, {116,
204}, {117, 205}, {118, 206}, {119, 207}, {9, 176}, {107, 208}, {111, 212},
{108, 209}, {110, 211}, {56, 135}, {109, 210}, {64, 143}, {80, 159}, {65, 144},
{79, 158}, {77, 156}, {75, 154}, {73, 152}, {71, 150}, {69, 148}, {67, 146},
{66, 145}, {78, 157}, {74, 153}, {70, 149}, {68, 147}, {76, 155}, {64, 152},
{71, 159}, {70, 158}, {69, 157}, {68, 156}, {67, 155}, {66, 154}, {65, 153},
{96, 184}, {97, 185}, {98, 186}, {99, 187}, {100, 188}, {101, 189}, {102, 190},
{103, 191}, {72, 151}, {90, 191}, {89, 190}, {72, 160}, {95, 183}, {94, 182},
{93, 181}, {92, 180}, {91, 179}, {90, 178}, {89, 177}, {88, 176}, {79, 167},
{78, 166}, {77, 165}, {76, 164}, {75, 163}, {74, 162}, {73, 161}, {81, 160},
{87, 166}, {85, 164}, {83, 162}, {82, 161}, {86, 165}, {84, 163}, {80, 168},
{87, 175}, {86, 174}, {85, 173}, {84, 172}, {83, 171}, {82, 170}, {81, 169},
{88, 167}, {155, 256}, {159, 260}, {156, 257}, {158, 259}, {157, 258}, {160,
261}, {162, 263}, {161, 262}, {168, 256}, {169, 257}, {170, 258}, {171, 259},
{172, 260}, {173, 261}, {174, 262}, {175, 263}, {163, 264}, {176, 264}, {189,
256}, {191, 258}, {190, 257}, {192, 259}, {196, 263}, {193, 260}, {195, 262},
{194, 261}, {197, 264}, {235, 256}, {239, 260}, {236, 257}, {238, 259}, {237,
258}, {240, 261}, {242, 263}, {241, 262}, {243, 264} }>;
(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, 168)(3, 181)(4, 93)(6, 172)(7, 185)(8, 97)(10, 176)(11, 189)(12, 101)(14,
92)(15, 193)(16, 105)(18, 96)(19, 197)(20, 109)(22, 100)(23, 201)(24, 113)(26,
104)(27, 205)(28, 117)(30, 108)(31, 209)(32, 121)(34, 112)(35, 213)(36, 125)(38,
116)(39, 217)(40, 129)(42, 120)(43, 221)(44, 133)(46, 124)(47, 225)(48, 137)(50,
128)(51, 229)(52, 141)(54, 132)(55, 233)(56, 145)(58, 136)(59, 237)(60, 149)(62,
140)(63, 241)(64, 153)(66, 144)(67, 245)(68, 157)(70, 148)(71, 249)(72, 161)(74,
152)(75, 253)(76, 165)(78, 156)(79, 257)(80, 169)(82, 160)(83, 261)(84, 173)(86,
164)(87, 177)(88, 89)(90, 256)(91, 202)(94, 260)(95, 206)(98, 264)(99, 210)(102,
180)(103, 214)(106, 184)(107, 218)(110, 188)(111, 222)(114, 192)(115, 226)(118,
196)(119, 230)(122, 200)(123, 234)(126, 204)(127, 238)(130, 208)(131, 242)(134,
212)(135, 246)(138, 216)(139, 250)(142, 220)(143, 254)(146, 224)(147, 258)(150,
228)(151, 262)(154, 232)(155, 178)(158, 236)(159, 182)(162, 240)(163, 186)(166,
244)(167, 190)(170, 248)(171, 194)(174, 252)(175, 198)(179, 223)(183, 227)(187,
231)(191, 235)(195, 239)(199, 243)(203, 247)(207, 251)(211, 255)(215, 259)(219,
263) (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, 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, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244,
245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260,
261, 262, 263, 264)
c: (2, 88)(3, 87)(4, 86)(5, 85)(6, 84)(7, 83)(8, 82)(9, 81)(10, 80)(11, 79)(12,
78)(13, 77)(14, 76)(15, 75)(16, 74)(17, 73)(18, 72)(19, 71)(20, 70)(21, 69)(22,
68)(23, 67)(24, 66)(25, 65)(26, 64)(27, 63)(28, 62)(29, 61)(30, 60)(31, 59)(32,
58)(33, 57)(34, 56)(35, 55)(36, 54)(37, 53)(38, 52)(39, 51)(40, 50)(41, 49)(42,
48)(43, 47)(44, 46)(89, 168)(90, 167)(91, 166)(92, 165)(93, 164)(94, 163)(95,
162)(96, 161)(97, 160)(98, 159)(99, 158)(100, 157)(101, 156)(102, 155)(103,
154)(104, 153)(105, 152)(106, 151)(107, 150)(108, 149)(109, 148)(110, 147)(111,
146)(112, 145)(113, 144)(114, 143)(115, 142)(116, 141)(117, 140)(118, 139)(119,
138)(120, 137)(121, 136)(122, 135)(123, 134)(124, 133)(125, 132)(126, 131)(127,
130)(128, 129)(169, 176)(170, 175)(171, 174)(172, 173)(177, 181)(178, 180)(182,
264)(183, 263)(184, 262)(185, 261)(186, 260)(187, 259)(188, 258)(189, 257)(190,
256)(191, 255)(192, 254)(193, 253)(194, 252)(195, 251)(196, 250)(197, 249)(198,
248)(199, 247)(200, 246)(201, 245)(202, 244)(203, 243)(204, 242)(205, 241)(206,
240)(207, 239)(208, 238)(209, 237)(210, 236)(211, 235)(212, 234)(213, 233)(214,
232)(215, 231)(216, 230)(217, 229)(218, 228)(219, 227)(220, 226)(221, 225)(222,
224)
C4[ 264, 17 ]
264
-1 88 89 2 168
-2 1 90 3 169
-3 2 91 4 170
-4 3 92 5 171
-5 4 93 6 172
-6 5 94 7 173
-7 6 95 8 174
-8 7 96 9 175
-9 176 8 97 10
-10 11 89 9 98
-11 99 12 90 10
-12 11 100 13 91
-13 12 101 14 92
-14 13 102 15 93
-15 14 103 16 94
-16 15 104 17 95
-17 16 105 18 96
-18 17 106 19 97
-19 18 107 20 98
-20 99 19 108 21
-21 22 100 20 109
-22 110 23 101 21
-23 22 111 24 102
-24 23 112 25 103
-25 24 113 26 104
-26 25 114 27 105
-27 26 115 28 106
-28 27 116 29 107
-29 28 117 30 108
-30 29 118 31 109
-31 110 30 119 32
-32 33 111 31 120
-33 121 34 112 32
-34 33 122 35 113
-35 34 123 36 114
-36 35 124 37 115
-37 36 125 38 116
-38 37 126 39 117
-39 38 127 40 118
-40 39 128 41 119
-41 40 129 42 120
-42 121 41 130 43
-43 44 122 42 131
-44 132 45 123 43
-45 44 133 46 124
-46 45 134 47 125
-47 46 135 48 126
-48 47 136 49 127
-49 48 137 50 128
-50 49 138 51 129
-51 50 139 52 130
-52 51 140 53 131
-53 132 52 141 54
-54 55 133 53 142
-55 143 56 134 54
-56 55 144 57 135
-57 56 145 58 136
-58 57 146 59 137
-59 58 147 60 138
-60 59 148 61 139
-61 60 149 62 140
-62 61 150 63 141
-63 62 151 64 142
-64 143 63 152 65
-65 66 144 64 153
-66 154 67 145 65
-67 66 155 68 146
-68 67 156 69 147
-69 68 157 70 148
-70 69 158 71 149
-71 70 159 72 150
-72 71 160 73 151
-73 72 161 74 152
-74 73 162 75 153
-75 154 74 163 76
-76 77 155 75 164
-77 165 78 156 76
-78 77 166 79 157
-79 78 167 80 158
-80 79 168 81 159
-81 80 169 82 160
-82 81 170 83 161
-83 82 171 84 162
-84 83 172 85 163
-85 84 173 86 164
-86 165 85 174 87
-87 88 166 86 175
-88 176 1 167 87
-89 1 177 190 10
-90 11 2 178 191
-91 12 3 179 192
-92 13 4 180 193
-93 14 5 181 194
-94 15 6 182 195
-95 16 7 183 196
-96 17 8 184 197
-97 198 18 9 185
-98 199 19 10 186
-99 11 187 200 20
-100 12 188 201 21
-101 22 13 189 202
-102 23 14 190 203
-103 24 15 191 204
-104 25 16 192 205
-105 26 17 193 206
-106 27 18 194 207
-107 28 19 195 208
-108 209 29 20 196
-109 210 30 21 197
-110 22 198 211 31
-111 23 199 212 32
-112 33 24 200 213
-113 34 25 201 214
-114 35 26 202 215
-115 36 27 203 216
-116 37 28 204 217
-117 38 29 205 218
-118 39 30 206 219
-119 220 40 31 207
-120 221 41 32 208
-121 33 209 222 42
-122 34 210 223 43
-123 44 35 211 224
-124 45 36 212 225
-125 46 37 213 226
-126 47 38 214 227
-127 48 39 215 228
-128 49 40 216 229
-129 50 41 217 230
-130 231 51 42 218
-131 232 52 43 219
-132 44 220 233 53
-133 45 221 234 54
-134 55 46 222 235
-135 56 47 223 236
-136 57 48 224 237
-137 58 49 225 238
-138 59 50 226 239
-139 60 51 227 240
-140 61 52 228 241
-141 242 62 53 229
-142 243 63 54 230
-143 55 231 244 64
-144 56 232 245 65
-145 66 57 233 246
-146 67 58 234 247
-147 68 59 235 248
-148 69 60 236 249
-149 70 61 237 250
-150 71 62 238 251
-151 72 63 239 252
-152 253 73 64 240
-153 254 74 65 241
-154 66 242 255 75
-155 67 243 256 76
-156 77 68 244 257
-157 78 69 245 258
-158 79 70 246 259
-159 80 71 247 260
-160 81 72 248 261
-161 82 73 249 262
-162 83 74 250 263
-163 264 84 75 251
-164 177 85 76 252
-165 77 253 178 86
-166 78 254 179 87
-167 88 79 255 180
-168 1 80 256 181
-169 2 81 257 182
-170 3 82 258 183
-171 4 83 259 184
-172 5 84 260 185
-173 6 85 261 186
-174 187 7 86 262
-175 188 8 87 263
-176 88 264 189 9
-177 198 89 244 164
-178 165 199 90 245
-179 166 200 91 246
-180 167 201 92 247
-181 168 202 93 248
-182 169 203 94 249
-183 170 204 95 250
-184 171 205 96 251
-185 172 206 97 252
-186 253 173 207 98
-187 99 254 174 208
-188 209 100 255 175
-189 176 210 101 256
-190 89 211 102 257
-191 90 212 103 258
-192 91 213 104 259
-193 92 214 105 260
-194 93 215 106 261
-195 94 216 107 262
-196 95 217 108 263
-197 264 96 218 109
-198 110 177 97 219
-199 220 111 178 98
-200 99 221 112 179
-201 100 222 113 180
-202 101 223 114 181
-203 102 224 115 182
-204 103 225 116 183
-205 104 226 117 184
-206 105 227 118 185
-207 106 228 119 186
-208 187 107 229 120
-209 121 188 108 230
-210 231 122 189 109
-211 110 232 123 190
-212 111 233 124 191
-213 112 234 125 192
-214 113 235 126 193
-215 114 236 127 194
-216 115 237 128 195
-217 116 238 129 196
-218 117 239 130 197
-219 198 118 240 131
-220 132 199 119 241
-221 242 133 200 120
-222 121 243 134 201
-223 122 244 135 202
-224 123 245 136 203
-225 124 246 137 204
-226 125 247 138 205
-227 126 248 139 206
-228 127 249 140 207
-229 128 250 141 208
-230 209 129 251 142
-231 143 210 130 252
-232 253 144 211 131
-233 132 254 145 212
-234 133 255 146 213
-235 134 256 147 214
-236 135 257 148 215
-237 136 258 149 216
-238 137 259 150 217
-239 138 260 151 218
-240 139 261 152 219
-241 220 140 262 153
-242 154 221 141 263
-243 264 155 222 142
-244 143 177 156 223
-245 144 178 157 224
-246 145 179 158 225
-247 146 180 159 226
-248 147 181 160 227
-249 148 182 161 228
-250 149 183 162 229
-251 150 184 163 230
-252 231 151 185 164
-253 165 232 152 186
-254 187 166 233 153
-255 154 188 167 234
-256 155 189 168 235
-257 156 190 169 236
-258 157 191 170 237
-259 158 192 171 238
-260 159 193 172 239
-261 160 194 173 240
-262 161 195 174 241
-263 242 162 196 175
-264 176 243 163 197
0