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