Graph forms
for C4 [ 288, 67 ] = UG(ATD[288,13])
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On this page are computer-accessible forms for the graph C4[ 288, 67 ] =
UG(ATD[288,13]).
(I) Following is a form readable by MAGMA:
g:=Graph<288|{ {206, 207}, {230, 231}, {228, 229}, {41, 43}, {1, 2}, {109, 110},
{61, 62}, {121, 122}, {153, 154}, {156, 159}, {265, 269}, {2, 7}, {145, 148},
{155, 158}, {42, 44}, {256, 262}, {115, 117}, {1, 6}, {251, 252}, {40, 47},
{144, 151}, {161, 166}, {274, 282}, {145, 152}, {246, 255}, {244, 253}, {197,
204}, {97, 107}, {193, 203}, {3, 8}, {243, 248}, {227, 232}, {116, 127}, {98,
110}, {192, 204}, {146, 158}, {4, 9}, {256, 270}, {5, 10}, {177, 190}, {38, 41},
{104, 120}, {110, 126}, {12, 29}, {14, 31}, {142, 159}, {163, 178}, {4, 22}, {9,
27}, {8, 26}, {5, 23}, {13, 30}, {263, 276}, {37, 54}, {198, 210}, {129, 148},
{2, 20}, {10, 28}, {3, 21}, {78, 89}, {233, 254}, {99, 116}, {11, 19}, {105,
113}, {142, 150}, {70, 95}, {198, 223}, {172, 181}, {106, 112}, {258, 280},
{200, 210}, {38, 61}, {238, 245}, {202, 209}, {43, 48}, {66, 94}, {162, 190},
{136, 149}, {6, 24}, {7, 25}, {163, 189}, {173, 179}, {5, 39}, {65, 98}, {16,
52}, {82, 118}, {14, 43}, {212, 241}, {147, 182}, {130, 164}, {213, 243}, {83,
116}, {88, 127}, {19, 59}, {136, 160}, {130, 171}, {128, 171}, {143, 164}, {222,
242}, {80, 125}, {205, 224}, {25, 55}, {143, 161}, {15, 32}, {93, 114}, {155,
180}, {195, 243}, {16, 33}, {209, 224}, {18, 35}, {208, 226}, {15, 60}, {79,
124}, {73, 122}, {17, 34}, {142, 189}, {26, 46}, {147, 167}, {89, 111}, {13,
58}, {19, 36}, {159, 168}, {6, 62}, {199, 255}, {7, 63}, {128, 185}, {200, 241},
{135, 190}, {92, 102}, {158, 164}, {18, 47}, {196, 249}, {157, 160}, {223, 225},
{85, 106}, {56, 120}, {59, 123}, {156, 222}, {186, 249}, {145, 213}, {147, 215},
{49, 116}, {181, 240}, {143, 202}, {152, 221}, {153, 220}, {137, 207}, {187,
253}, {57, 126}, {154, 221}, {155, 220}, {8, 64}, {40, 96}, {12, 68}, {11, 67},
{10, 66}, {9, 65}, {141, 197}, {136, 193}, {157, 215}, {14, 69}, {183, 252},
{148, 216}, {149, 217}, {150, 218}, {151, 219}, {53, 120}, {146, 223}, {30, 80},
{31, 81}, {128, 207}, {174, 225}, {45, 125}, {129, 209}, {169, 249}, {28, 78},
{186, 232}, {182, 228}, {176, 226}, {29, 79}, {131, 208}, {177, 226}, {24, 76},
{133, 209}, {134, 210}, {135, 211}, {165, 241}, {166, 242}, {18, 71}, {55, 98},
{53, 96}, {27, 77}, {17, 70}, {54, 97}, {46, 121}, {58, 99}, {43, 113}, {61,
103}, {60, 102}, {56, 99}, {60, 103}, {141, 214}, {171, 240}, {20, 72}, {23,
75}, {22, 74}, {21, 73}, {57, 100}, {137, 212}, {59, 101}, {185, 231}, {17, 78},
{138, 213}, {11, 107}, {5, 100}, {138, 235}, {144, 241}, {170, 203}, {13, 111},
{169, 202}, {172, 200}, {169, 207}, {176, 217}, {177, 216}, {48, 91}, {189,
214}, {63, 84}, {52, 95}, {168, 195}, {174, 197}, {1, 109}, {49, 92}, {51, 94},
{9, 103}, {139, 229}, {50, 93}, {149, 250}, {165, 213}, {166, 214}, {135, 246},
{188, 205}, {172, 221}, {32, 82}, {36, 86}, {33, 83}, {156, 238}, {37, 86}, {39,
84}, {140, 255}, {154, 233}, {167, 212}, {3, 119}, {139, 255}, {175, 219}, {45,
88}, {47, 90}, {175, 218}, {34, 84}, {35, 85}, {128, 246}, {46, 89}, {146, 229},
{174, 217}, {141, 244}, {150, 239}, {138, 240}, {44, 87}, {55, 76}, {134, 253},
{150, 237}, {16, 108}, {147, 238}, {151, 234}, {12, 114}, {137, 247}, {15, 112},
{57, 70}, {117, 245}, {48, 178}, {49, 179}, {121, 251}, {111, 236}, {37, 162},
{40, 175}, {34, 170}, {79, 199}, {37, 173}, {36, 172}, {35, 171}, {22, 159},
{39, 174}, {32, 169}, {119, 254}, {123, 242}, {40, 162}, {109, 231}, {101, 239},
{72, 194}, {60, 182}, {127, 245}, {21, 158}, {33, 170}, {56, 180}, {57, 181},
{20, 153}, {112, 254}, {101, 245}, {50, 160}, {53, 167}, {83, 192}, {118, 229},
{85, 193}, {87, 194}, {85, 194}, {41, 176}, {100, 254}, {105, 243}, {42, 177},
{88, 195}, {119, 236}, {102, 251}, {105, 244}, {123, 230}, {90, 196}, {91, 197},
{98, 253}, {124, 227}, {58, 154}, {76, 236}, {102, 199}, {38, 132}, {99, 198},
{44, 138}, {75, 237}, {54, 145}, {96, 199}, {69, 237}, {50, 152}, {61, 151},
{67, 232}, {104, 196}, {111, 195}, {24, 181}, {17, 191}, {74, 250}, {123, 203},
{124, 204}, {125, 205}, {126, 206}, {91, 234}, {115, 194}, {35, 144}, {121,
202}, {122, 201}, {125, 201}, {4, 179}, {31, 168}, {23, 160}, {62, 134}, {24,
161}, {55, 142}, {30, 167}, {28, 165}, {26, 163}, {34, 152}, {25, 162}, {84,
239}, {51, 136}, {29, 166}, {4, 185}, {89, 228}, {52, 137}, {45, 144}, {28,
161}, {117, 200}, {27, 164}, {118, 201}, {31, 221}, {63, 252}, {45, 233}, {51,
247}, {120, 188}, {18, 215}, {93, 155}, {20, 211}, {62, 246}, {107, 163}, {16,
217}, {92, 149}, {22, 220}, {77, 135}, {19, 216}, {110, 165}, {64, 139}, {126,
178}, {65, 140}, {27, 212}, {54, 230}, {26, 203}, {124, 173}, {29, 206}, {86,
133}, {25, 205}, {82, 134}, {80, 132}, {122, 175}, {13, 219}, {91, 140}, {95,
133}, {1, 218}, {21, 206}, {2, 222}, {95, 131}, {94, 130}, {81, 141}, {80, 140},
{36, 248}, {101, 132}, {106, 139}, {49, 211}, {3, 224}, {96, 131}, {83, 183},
{42, 204}, {86, 187}, {12, 226}, {108, 130}, {48, 222}, {39, 201}, {30, 240},
{15, 225}, {23, 248}, {38, 214}, {105, 153}, {73, 187}, {51, 192}, {53, 193},
{75, 191}, {74, 190}, {72, 189}, {33, 215}, {107, 157}, {106, 156}, {50, 196},
{64, 183}, {79, 184}, {42, 210}, {66, 184}, {67, 185}, {71, 188}, {32, 220},
{74, 183}, {68, 186}, {72, 182}, {69, 187}, {71, 184}, {11, 266}, {8, 271}, {41,
288}, {7, 265}, {10, 260}, {6, 276}, {14, 276}, {58, 283}, {52, 280}, {44, 282},
{63, 264}, {47, 279}, {56, 262}, {46, 273}, {59, 260}, {66, 258}, {64, 257},
{75, 265}, {90, 280}, {70, 261}, {93, 281}, {78, 267}, {65, 263}, {76, 266},
{71, 257}, {77, 266}, {68, 271}, {73, 258}, {68, 264}, {87, 283}, {82, 256},
{92, 271}, {90, 270}, {88, 270}, {118, 288}, {94, 262}, {67, 282}, {81, 267},
{87, 269}, {69, 281}, {81, 268}, {77, 275}, {108, 268}, {114, 274}, {115, 275},
{113, 272}, {114, 275}, {104, 266}, {113, 274}, {97, 261}, {103, 257}, {117,
284}, {97, 269}, {100, 272}, {119, 259}, {127, 265}, {104, 273}, {112, 267},
{108, 272}, {109, 273}, {115, 268}, {132, 261}, {133, 262}, {131, 260}, {129,
264}, {146, 287}, {129, 276}, {148, 258}, {143, 277}, {157, 259}, {191, 288},
{188, 285}, {191, 286}, {180, 278}, {180, 279}, {178, 277}, {176, 284}, {186,
278}, {179, 285}, {173, 284}, {168, 287}, {170, 278}, {184, 261}, {208, 277},
{219, 286}, {216, 285}, {218, 285}, {211, 287}, {208, 257}, {223, 263}, {198,
280}, {192, 288}, {250, 283}, {237, 271}, {232, 268}, {247, 274}, {252, 281},
{249, 287}, {234, 269}, {235, 256}, {235, 263}, {234, 260}, {248, 278}, {231,
279}, {242, 259}, {228, 272}, {250, 270}, {239, 283}, {238, 282}, {230, 275},
{227, 277}, {235, 284}, {233, 273}, {251, 259}, {227, 281}, {236, 279}, {244,
264}, {247, 267}, {224, 286}, {225, 286} }>;
(II) A more general form is to represent the graph as the orbit of {206, 207}
under the group generated by the following permutations:
a: (2, 6)(5, 17)(7, 24)(8, 21)(9, 22)(10, 34)(11, 37)(13, 45)(14, 48)(16,
51)(18, 56)(19, 54)(20, 62)(23, 70)(25, 76)(26, 73)(27, 74)(28, 84)(29, 68)(30,
88)(31, 91)(32, 60)(33, 94)(35, 99)(36, 97)(38, 105)(39, 78)(40, 104)(41,
113)(42, 115)(44, 117)(46, 122)(47, 120)(49, 128)(50, 131)(52, 136)(53, 90)(57,
75)(58, 144)(59, 145)(61, 153)(63, 161)(64, 158)(65, 159)(66, 170)(67, 173)(69,
178)(71, 180)(72, 134)(77, 190)(79, 186)(80, 195)(81, 197)(82, 182)(83, 130)(85,
198)(86, 107)(87, 200)(89, 201)(92, 207)(93, 208)(95, 160)(96, 196)(98,
142)(100, 191)(101, 213)(102, 169)(103, 220)(106, 223)(108, 192)(109, 218)(110,
150)(111, 125)(112, 225)(114, 226)(116, 171)(118, 228)(119, 224)(123, 148)(124,
232)(126, 237)(127, 240)(129, 242)(132, 243)(133, 157)(137, 149)(138, 245)(139,
146)(140, 168)(143, 252)(147, 256)(151, 154)(152, 260)(155, 257)(156, 263)(162,
266)(163, 187)(164, 183)(165, 239)(166, 264)(167, 270)(172, 269)(174, 267)(175,
273)(176, 274)(177, 275)(179, 185)(181, 265)(184, 278)(188, 279)(189, 253)(193,
280)(194, 210)(199, 249)(202, 251)(203, 258)(204, 268)(205, 236)(206, 271)(209,
259)(211, 246)(212, 250)(214, 244)(215, 262)(216, 230)(217, 247)(219, 233)(221,
234)(222, 276)(231, 285)(235, 238)(241, 283)(248, 261)(254, 286)(255, 287)(272,
288)(277, 281)(282, 284) (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, 7, 25, 55, 142, 150, 218)(3, 11, 38, 58, 121, 230, 91, 88)(4, 14, 49,
129, 135, 244, 74, 187)(5, 18, 57, 147, 17, 53, 28, 85)(6, 20, 63, 162, 98, 159,
237, 285)(8, 19, 61, 154, 251, 54, 140, 195)(9, 31, 92, 148, 246, 105, 183,
86)(10, 35, 100, 215, 70, 167, 78, 193)(12, 42, 82, 155, 227, 284, 223, 249)(13,
46, 123, 234, 45, 119, 107, 132)(15, 50, 79, 138, 229, 278, 208, 200)(16, 52,
137, 247, 51, 94, 130, 108)(21, 67, 41, 99, 202, 275, 197, 270)(22, 69, 179,
276, 211, 264, 190, 253)(23, 71, 181, 182, 34, 96, 165, 106)(24, 72, 84, 40,
110, 156, 75, 188)(26, 59, 151, 233, 259, 97, 80, 111)(27, 81, 149, 258, 128,
113, 83, 133)(29, 44, 118, 180, 277, 117, 225, 196)(30, 89, 203, 260, 144, 254,
157, 261)(32, 93, 124, 235, 146, 186, 226, 210)(33, 95, 212, 267, 136, 66, 171,
272)(36, 103, 221, 102, 145, 255, 243, 64)(37, 65, 168, 271, 216, 62, 153,
252)(39, 47, 126, 238, 191, 120, 161, 194)(43, 116, 209, 77, 141, 250, 73,
185)(48, 127, 224, 266, 214, 283, 122, 231)(56, 143, 115, 174, 90, 206, 282,
288)(60, 152, 199, 213, 139, 248, 257, 172)(68, 177, 134, 220, 281, 173, 263,
287)(76, 189, 239, 175, 109, 222, 265, 205)(87, 201, 279, 178, 245, 286, 104,
166)(101, 219, 273, 242, 269, 125, 236, 163)(112, 160, 184, 240, 228, 170, 131,
241)(114, 204, 256, 158, 232, 176, 198, 169)(164, 268, 217, 280, 207, 274, 192,
262)
C4[ 288, 67 ]
288
-1 2 6 218 109
-2 1 222 7 20
-3 224 8 119 21
-4 22 179 9 185
-5 23 100 39 10
-6 1 276 24 62
-7 265 2 25 63
-8 3 26 271 64
-9 4 103 27 65
-10 66 5 28 260
-11 67 266 19 107
-12 68 114 226 29
-13 111 58 30 219
-14 276 69 31 43
-15 112 60 225 32
-16 33 52 217 108
-17 34 78 70 191
-18 35 47 71 215
-19 11 36 59 216
-20 2 211 72 153
-21 3 158 73 206
-22 220 4 159 74
-23 5 160 248 75
-24 181 6 161 76
-25 55 7 205 162
-26 46 203 8 163
-27 77 212 9 164
-28 165 78 161 10
-29 12 166 79 206
-30 13 167 80 240
-31 221 14 168 81
-32 220 15 169 82
-33 16 170 83 215
-34 170 17 84 152
-35 144 171 18 85
-36 248 172 19 86
-37 162 173 86 54
-38 132 214 61 41
-39 201 5 84 174
-40 47 96 162 175
-41 176 288 38 43
-42 44 177 210 204
-43 14 113 48 41
-44 138 282 42 87
-45 88 144 233 125
-46 121 89 26 273
-47 90 279 18 40
-48 178 222 91 43
-49 211 179 92 116
-50 93 160 152 196
-51 136 192 247 94
-52 16 137 280 95
-53 167 193 96 120
-54 145 37 97 230
-55 25 76 98 142
-56 99 180 262 120
-57 100 70 126 181
-58 99 154 13 283
-59 101 123 260 19
-60 102 15 103 182
-61 103 38 62 151
-62 134 246 6 61
-63 264 7 84 252
-64 257 139 183 8
-65 140 9 98 263
-66 258 94 184 10
-67 11 232 282 185
-68 264 12 271 186
-69 187 14 237 281
-70 57 17 95 261
-71 188 257 18 184
-72 189 182 194 20
-73 187 122 258 21
-74 22 190 183 250
-75 23 265 191 237
-76 55 24 266 236
-77 275 266 135 27
-78 89 267 17 28
-79 199 124 29 184
-80 132 125 30 140
-81 267 268 31 141
-82 134 256 118 32
-83 33 192 116 183
-84 34 39 63 239
-85 35 193 106 194
-86 187 133 36 37
-87 44 269 194 283
-88 45 127 270 195
-89 78 111 46 228
-90 47 280 270 196
-91 234 48 140 197
-92 102 49 149 271
-93 155 114 50 281
-94 66 51 130 262
-95 133 70 52 131
-96 199 40 53 131
-97 269 107 261 54
-98 55 110 253 65
-99 198 56 58 116
-100 254 57 5 272
-101 132 245 59 239
-102 199 92 60 251
-103 257 60 61 9
-104 266 196 273 120
-105 243 244 113 153
-106 112 156 139 85
-107 11 157 97 163
-108 268 16 272 130
-109 110 231 1 273
-110 165 126 98 109
-111 89 13 236 195
-112 254 267 15 106
-113 105 272 43 274
-114 275 12 93 274
-115 275 268 117 194
-116 99 49 83 127
-117 200 245 115 284
-118 288 201 82 229
-119 254 3 236 259
-120 56 188 104 53
-121 122 46 202 251
-122 121 201 73 175
-123 242 59 203 230
-124 79 204 227 173
-125 45 80 201 205
-126 110 57 178 206
-127 88 265 245 116
-128 246 171 185 207
-129 209 264 276 148
-130 94 171 108 164
-131 95 260 96 208
-132 101 80 38 261
-133 209 95 86 262
-134 253 210 82 62
-135 77 211 190 246
-136 149 160 193 51
-137 212 247 52 207
-138 44 213 235 240
-139 255 106 64 229
-140 255 80 91 65
-141 244 81 214 197
-142 55 189 159 150
-143 277 202 161 164
-144 45 35 151 241
-145 213 148 152 54
-146 287 223 158 229
-147 167 182 215 238
-148 145 258 216 129
-149 92 136 217 250
-150 237 239 218 142
-151 144 234 61 219
-152 34 221 145 50
-153 154 220 105 20
-154 221 233 58 153
-155 220 158 180 93
-156 222 159 106 238
-157 160 215 259 107
-158 155 146 21 164
-159 22 156 168 142
-160 23 157 136 50
-161 143 166 24 28
-162 25 190 37 40
-163 178 189 26 107
-164 143 158 27 130
-165 110 213 28 241
-166 242 214 29 161
-167 212 147 30 53
-168 287 159 195 31
-169 202 249 207 32
-170 33 34 278 203
-171 35 128 130 240
-172 221 200 36 181
-173 124 179 37 284
-174 225 39 217 197
-175 122 40 218 219
-176 226 41 217 284
-177 190 226 216 42
-178 277 48 126 163
-179 4 49 173 285
-180 56 155 278 279
-181 24 57 172 240
-182 147 60 72 228
-183 83 74 64 252
-184 66 79 71 261
-185 231 67 4 128
-186 232 68 278 249
-187 253 69 73 86
-188 71 205 120 285
-189 214 72 163 142
-190 177 135 74 162
-191 286 288 17 75
-192 288 83 204 51
-193 136 203 85 53
-194 115 72 85 87
-195 88 111 243 168
-196 90 104 50 249
-197 91 204 141 174
-198 99 210 223 280
-199 79 255 102 96
-200 210 117 172 241
-201 122 125 39 118
-202 121 143 209 169
-203 123 26 170 193
-204 124 192 42 197
-205 188 25 125 224
-206 126 29 207 21
-207 169 137 128 206
-208 277 257 226 131
-209 133 202 224 129
-210 198 134 200 42
-211 287 135 49 20
-212 167 27 137 241
-213 165 243 145 138
-214 166 189 38 141
-215 33 157 147 18
-216 177 148 19 285
-217 176 16 149 174
-218 1 150 175 285
-219 286 13 151 175
-220 22 155 32 153
-221 154 172 31 152
-222 242 2 156 48
-223 198 146 225 263
-224 209 286 3 205
-225 286 223 15 174
-226 176 12 177 208
-227 232 277 124 281
-228 89 182 272 229
-229 146 139 118 228
-230 231 275 123 54
-231 279 185 109 230
-232 67 268 227 186
-233 154 45 254 273
-234 91 269 260 151
-235 256 138 284 263
-236 111 279 119 76
-237 69 150 271 75
-238 156 245 147 282
-239 101 84 150 283
-240 181 138 171 30
-241 165 144 200 212
-242 166 123 222 259
-243 213 105 248 195
-244 253 264 105 141
-245 101 127 117 238
-246 255 135 62 128
-247 267 137 51 274
-248 23 243 36 278
-249 287 169 196 186
-250 149 270 74 283
-251 121 102 259 252
-252 281 183 63 251
-253 187 134 244 98
-254 100 112 233 119
-255 199 246 139 140
-256 235 82 270 262
-257 103 71 64 208
-258 66 148 280 73
-259 242 157 119 251
-260 234 59 10 131
-261 132 70 184 97
-262 56 133 256 94
-263 276 223 235 65
-264 68 244 63 129
-265 269 127 7 75
-266 11 77 104 76
-267 78 112 81 247
-268 232 81 115 108
-269 265 234 97 87
-270 88 90 256 250
-271 68 92 237 8
-272 100 113 228 108
-273 46 233 104 109
-274 113 114 247 282
-275 77 114 115 230
-276 14 6 129 263
-277 143 178 227 208
-278 180 170 248 186
-279 231 47 180 236
-280 198 90 258 52
-281 69 93 227 252
-282 44 67 238 274
-283 58 239 250 87
-284 176 235 117 173
-285 188 179 216 218
-286 191 224 225 219
-287 211 146 168 249
-288 191 192 41 118
0