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