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