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