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