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