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