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