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