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