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