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