Graph forms
for C4 [ 253, 3 ] = PS(11,23;3)
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On this page are computer-accessible forms for the graph C4[ 253, 3 ] =
PS(11,23;3).
(I) Following is a form readable by MAGMA:
g:=Graph<253|{ {184, 186}, {44, 47}, {89, 93}, {90, 94}, {91, 95}, {226, 231},
{160, 167}, {64, 73}, {161, 168}, {68, 77}, {66, 75}, {129, 139}, {132, 142},
{133, 143}, {65, 74}, {227, 232}, {69, 78}, {112, 123}, {112, 124}, {113, 125},
{114, 126}, {115, 127}, {113, 124}, {230, 235}, {228, 233}, {115, 126}, {128,
141}, {130, 143}, {64, 78}, {183, 185}, {65, 79}, {130, 140}, {131, 141}, {23,
24}, {229, 234}, {67, 76}, {114, 125}, {129, 142}, {160, 176}, {161, 177}, {192,
209}, {206, 223}, {204, 221}, {202, 219}, {200, 217}, {198, 215}, {196, 213},
{194, 211}, {66, 80}, {229, 247}, {228, 246}, {225, 243}, {224, 242}, {67, 81},
{76, 95}, {205, 222}, {201, 218}, {197, 214}, {193, 210}, {131, 144}, {135,
148}, {32, 52}, {43, 63}, {42, 62}, {41, 61}, {40, 60}, {35, 55}, {34, 54}, {33,
53}, {108, 120}, {109, 121}, {110, 122}, {111, 123}, {75, 94}, {170, 191}, {168,
189}, {109, 120}, {111, 122}, {132, 145}, {134, 147}, {8, 30}, {227, 245}, {226,
244}, {69, 83}, {68, 82}, {9, 31}, {134, 144}, {135, 145}, {74, 93}, {203, 220},
{195, 212}, {169, 190}, {110, 121}, {133, 146}, {1, 25}, {7, 31}, {6, 30}, {5,
29}, {4, 28}, {3, 27}, {2, 26}, {162, 187}, {166, 191}, {164, 189}, {2, 24},
{207, 213}, {206, 212}, {203, 209}, {202, 208}, {37, 63}, {36, 62}, {33, 59},
{32, 58}, {7, 29}, {6, 28}, {3, 25}, {136, 146}, {137, 147}, {108, 119}, {167,
188}, {165, 190}, {36, 56}, {225, 253}, {224, 252}, {39, 59}, {38, 58}, {37,
57}, {104, 116}, {105, 117}, {106, 118}, {107, 119}, {45, 48}, {194, 223}, {192,
221}, {166, 187}, {164, 185}, {138, 151}, {105, 116}, {107, 118}, {136, 149},
{4, 26}, {230, 248}, {205, 211}, {204, 210}, {138, 148}, {35, 61}, {34, 60}, {5,
27}, {46, 49}, {199, 216}, {193, 222}, {165, 186}, {163, 188}, {106, 117}, {137,
150}, {128, 161}, {93, 127}, {154, 184}, {151, 181}, {150, 180}, {147, 177},
{146, 176}, {143, 173}, {142, 172}, {139, 169}, {195, 224}, {199, 228}, {212,
240}, {223, 251}, {222, 250}, {221, 249}, {220, 248}, {215, 243}, {214, 242},
{213, 241}, {71, 98}, {198, 227}, {196, 225}, {77, 104}, {79, 106}, {85, 112},
{87, 114}, {30, 56}, {149, 179}, {148, 178}, {141, 171}, {140, 170}, {31, 57},
{70, 97}, {197, 226}, {144, 183}, {78, 105}, {86, 113}, {8, 32}, {15, 39}, {14,
38}, {13, 37}, {12, 36}, {11, 35}, {10, 34}, {9, 33}, {145, 184}, {212, 253},
{210, 251}, {208, 249}, {10, 32}, {29, 55}, {28, 54}, {25, 51}, {24, 50}, {15,
37}, {14, 36}, {11, 33}, {72, 99}, {209, 250}, {76, 103}, {88, 115}, {28, 48},
{219, 247}, {218, 246}, {217, 245}, {216, 244}, {31, 51}, {30, 50}, {29, 49},
{73, 100}, {200, 229}, {75, 102}, {77, 96}, {79, 98}, {12, 34}, {223, 241},
{222, 240}, {153, 183}, {152, 182}, {27, 53}, {26, 52}, {13, 35}, {1, 46}, {211,
252}, {207, 224}, {201, 230}, {74, 101}, {78, 97}, {146, 162}, {159, 175}, {158,
174}, {157, 173}, {156, 172}, {155, 171}, {154, 170}, {153, 169}, {152, 168},
{151, 167}, {150, 166}, {149, 165}, {148, 164}, {147, 163}, {213, 231}, {221,
239}, {220, 238}, {217, 235}, {216, 234}, {80, 99}, {84, 103}, {88, 107}, {92,
111}, {27, 47}, {81, 100}, {83, 102}, {89, 108}, {91, 110}, {16, 38}, {219,
237}, {218, 236}, {71, 113}, {70, 112}, {17, 39}, {82, 101}, {90, 109}, {16,
40}, {22, 46}, {21, 45}, {20, 44}, {19, 43}, {18, 42}, {17, 41}, {139, 178},
{159, 166}, {157, 164}, {155, 162}, {143, 182}, {141, 180}, {18, 40}, {23, 45},
{22, 44}, {19, 41}, {72, 114}, {73, 115}, {80, 107}, {158, 165}, {142, 181},
{84, 111}, {92, 96}, {211, 239}, {210, 238}, {209, 237}, {208, 236}, {81, 108},
{83, 110}, {85, 104}, {87, 106}, {20, 42}, {215, 233}, {214, 232}, {145, 175},
{144, 174}, {21, 43}, {82, 109}, {156, 163}, {140, 179}, {86, 105}, {185, 225},
{190, 230}, {189, 229}, {188, 228}, {187, 227}, {186, 226}, {24, 67}, {25, 68},
{26, 69}, {47, 79}, {60, 92}, {59, 91}, {58, 90}, {57, 89}, {56, 88}, {55, 87},
{54, 86}, {53, 85}, {52, 84}, {51, 83}, {50, 82}, {49, 81}, {48, 80}, {187,
216}, {191, 220}, {48, 85}, {190, 219}, {188, 217}, {50, 87}, {38, 64}, {39,
65}, {49, 86}, {189, 218}, {175, 200}, {167, 192}, {168, 193}, {174, 199}, {172,
197}, {170, 195}, {40, 66}, {41, 67}, {51, 88}, {175, 196}, {173, 198}, {171,
192}, {169, 194}, {55, 92}, {44, 64}, {163, 207}, {162, 206}, {46, 66}, {45,
65}, {52, 89}, {186, 215}, {174, 195}, {172, 193}, {54, 91}, {42, 68}, {43, 69},
{53, 90}, {191, 208}, {185, 214}, {173, 194}, {171, 196}, {58, 72}, {63, 77},
{62, 76}, {59, 73}, {176, 197}, {184, 205}, {178, 199}, {60, 74}, {61, 75}, {63,
72}, {177, 198}, {62, 71}, {182, 207}, {180, 205}, {178, 203}, {176, 201}, {47,
84}, {183, 204}, {181, 206}, {179, 200}, {177, 202}, {61, 70}, {180, 201}, {182,
203}, {56, 70}, {57, 71}, {179, 204}, {181, 202}, {124, 160}, {125, 161}, {93,
128}, {95, 130}, {94, 128}, {95, 129}, {94, 129}, {127, 160}, {116, 149}, {118,
151}, {120, 153}, {122, 155}, {124, 157}, {126, 159}, {10, 232}, {23, 245}, {22,
244}, {19, 241}, {18, 240}, {15, 237}, {14, 236}, {11, 233}, {96, 130}, {97,
131}, {100, 134}, {101, 135}, {104, 138}, {96, 131}, {100, 135}, {117, 150},
{121, 154}, {125, 158}, {120, 156}, {121, 157}, {122, 158}, {123, 159}, {97,
132}, {99, 134}, {12, 234}, {21, 243}, {20, 242}, {13, 235}, {98, 132}, {99,
133}, {98, 133}, {123, 156}, {116, 152}, {117, 153}, {118, 154}, {119, 155},
{101, 136}, {103, 138}, {1, 239}, {9, 231}, {102, 136}, {103, 137}, {102, 137},
{119, 152}, {2, 240}, {15, 253}, {14, 252}, {11, 249}, {10, 248}, {7, 245}, {6,
244}, {3, 241}, {127, 140}, {2, 247}, {8, 253}, {126, 139}, {4, 242}, {13, 251},
{12, 250}, {5, 243}, {1, 246}, {16, 231}, {17, 232}, {23, 238}, {21, 236}, {19,
234}, {3, 248}, {22, 237}, {18, 233}, {7, 252}, {4, 249}, {6, 251}, {8, 246},
{17, 239}, {16, 238}, {9, 247}, {5, 250}, {20, 235} }>;
(II) A more general form is to represent the graph as the orbit of {184, 186}
under the group generated by the following permutations:
a: (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, 244,
245, 246, 247, 248, 249, 250, 251, 252, 253) (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, 24, 47, 70, 93, 116, 139, 162, 185, 208, 231)(2, 27, 56, 74, 105, 129,
155, 164, 191, 226, 239)(3, 30, 65, 78, 94, 119, 148, 166, 197, 221, 247)(4, 33,
51, 82, 106, 132, 141, 168, 203, 216, 232)(5, 36, 60, 86, 95, 122, 157, 170,
186, 211, 240)(6, 39, 69, 90, 107, 135, 150, 172, 192, 229, 248)(7, 42, 55, 71,
96, 125, 143, 174, 198, 224, 233)(8, 45, 64, 75, 108, 138, 159, 176, 204, 219,
241)(9, 25, 50, 79, 97, 128, 152, 178, 187, 214, 249)(10, 28, 59, 83, 109, 118,
145, 180, 193, 209, 234)(11, 31, 68, 87, 98, 131, 161, 182, 199, 227, 242)(12,
34, 54, 91, 110, 121, 154, 184, 205, 222, 250)(13, 37, 63, 72, 99, 134, 147,
163, 188, 217, 235)(14, 40, 49, 76, 111, 124, 140, 165, 194, 212, 243)(15, 43,
58, 80, 100, 137, 156, 167, 200, 230, 251)(16, 46, 67, 84, 112, 127, 149, 169,
206, 225, 236)(17, 26, 53, 88, 101, 117, 142, 171, 189, 220, 244)(18, 29, 62,
92, 113, 130, 158, 173, 195, 215, 252)(19, 32, 48, 73, 102, 120, 151, 175, 201,
210, 237)(20, 35, 57, 77, 114, 133, 144, 177, 207, 228, 245)(21, 38, 66, 81,
103, 123, 160, 179, 190, 223, 253)(22, 41, 52, 85, 115, 136, 153, 181, 196, 218,
238)(23, 44, 61, 89, 104, 126, 146, 183, 202, 213, 246)
c: (2, 23)(3, 22)(4, 21)(5, 20)(6, 19)(7, 18)(8, 17)(9, 16)(10, 15)(11, 14)(12,
13)(25, 46)(26, 45)(27, 44)(28, 43)(29, 42)(30, 41)(31, 40)(32, 39)(33, 38)(34,
37)(35, 36)(48, 69)(49, 68)(50, 67)(51, 66)(52, 65)(53, 64)(54, 63)(55, 62)(56,
61)(57, 60)(58, 59)(71, 92)(72, 91)(73, 90)(74, 89)(75, 88)(76, 87)(77, 86)(78,
85)(79, 84)(80, 83)(81, 82)(94, 115)(95, 114)(96, 113)(97, 112)(98, 111)(99,
110)(100, 109)(101, 108)(102, 107)(103, 106)(104, 105)(117, 138)(118, 137)(119,
136)(120, 135)(121, 134)(122, 133)(123, 132)(124, 131)(125, 130)(126, 129)(127,
128)(140, 161)(141, 160)(142, 159)(143, 158)(144, 157)(145, 156)(146, 155)(147,
154)(148, 153)(149, 152)(150, 151)(163, 184)(164, 183)(165, 182)(166, 181)(167,
180)(168, 179)(169, 178)(170, 177)(171, 176)(172, 175)(173, 174)(186, 207)(187,
206)(188, 205)(189, 204)(190, 203)(191, 202)(192, 201)(193, 200)(194, 199)(195,
198)(196, 197)(209, 230)(210, 229)(211, 228)(212, 227)(213, 226)(214, 225)(215,
224)(216, 223)(217, 222)(218, 221)(219, 220)(232, 253)(233, 252)(234, 251)(235,
250)(236, 249)(237, 248)(238, 247)(239, 246)(240, 245)(241, 244)(242, 243)
C4[ 253, 3 ]
253
-1 46 25 246 239
-2 24 26 247 240
-3 25 27 248 241
-4 242 26 28 249
-5 243 27 29 250
-6 244 28 30 251
-7 245 29 31 252
-8 253 246 30 32
-9 33 231 247 31
-10 34 232 248 32
-11 33 35 233 249
-12 34 36 234 250
-13 35 37 235 251
-14 36 38 236 252
-15 253 37 39 237
-16 231 38 40 238
-17 232 39 41 239
-18 233 40 42 240
-19 234 41 43 241
-20 44 242 235 42
-21 45 243 236 43
-22 44 46 244 237
-23 45 24 245 238
-24 23 67 2 50
-25 1 68 3 51
-26 2 69 4 52
-27 3 47 5 53
-28 4 48 6 54
-29 55 5 49 7
-30 56 6 50 8
-31 57 7 51 9
-32 58 8 52 10
-33 11 59 9 53
-34 12 60 10 54
-35 11 55 13 61
-36 12 56 14 62
-37 13 57 15 63
-38 14 58 16 64
-39 15 59 17 65
-40 66 16 60 18
-41 67 17 61 19
-42 68 18 62 20
-43 69 19 63 21
-44 22 47 20 64
-45 23 48 21 65
-46 22 66 1 49
-47 44 79 27 84
-48 45 80 28 85
-49 46 81 29 86
-50 24 82 30 87
-51 88 25 83 31
-52 89 26 84 32
-53 33 90 27 85
-54 34 91 28 86
-55 35 92 29 87
-56 88 36 70 30
-57 89 37 71 31
-58 90 38 72 32
-59 33 91 39 73
-60 34 92 40 74
-61 35 70 41 75
-62 36 71 42 76
-63 77 37 72 43
-64 44 78 38 73
-65 45 79 39 74
-66 46 80 40 75
-67 24 81 41 76
-68 77 25 82 42
-69 78 26 83 43
-70 56 112 61 97
-71 57 113 62 98
-72 99 58 114 63
-73 100 59 115 64
-74 101 60 93 65
-75 66 102 61 94
-76 67 103 62 95
-77 68 104 63 96
-78 69 105 64 97
-79 47 106 65 98
-80 66 99 48 107
-81 67 100 49 108
-82 68 101 50 109
-83 110 69 102 51
-84 111 47 103 52
-85 112 48 104 53
-86 113 49 105 54
-87 55 114 50 106
-88 56 115 51 107
-89 57 93 52 108
-90 58 94 53 109
-91 110 59 95 54
-92 55 111 60 96
-93 89 127 128 74
-94 90 128 129 75
-95 91 129 130 76
-96 77 92 130 131
-97 132 78 70 131
-98 132 133 79 71
-99 133 134 80 72
-100 134 135 81 73
-101 135 136 82 74
-102 136 137 83 75
-103 137 138 84 76
-104 77 116 138 85
-105 78 116 117 86
-106 79 117 118 87
-107 88 80 118 119
-108 89 81 119 120
-109 121 90 82 120
-110 121 122 91 83
-111 122 123 92 84
-112 123 124 70 85
-113 124 125 71 86
-114 125 126 72 87
-115 88 126 127 73
-116 104 105 149 152
-117 105 106 150 153
-118 154 106 107 151
-119 155 107 108 152
-120 156 108 109 153
-121 110 154 157 109
-122 110 111 155 158
-123 111 112 156 159
-124 112 113 157 160
-125 113 114 158 161
-126 114 115 159 139
-127 93 115 160 140
-128 93 94 161 141
-129 94 95 139 142
-130 143 95 96 140
-131 144 96 97 141
-132 145 97 98 142
-133 99 143 146 98
-134 99 100 144 147
-135 100 101 145 148
-136 101 102 146 149
-137 102 103 147 150
-138 103 104 148 151
-139 178 169 126 129
-140 179 170 127 130
-141 180 171 128 131
-142 132 181 172 129
-143 133 182 173 130
-144 134 183 174 131
-145 132 135 184 175
-146 176 133 136 162
-147 177 134 137 163
-148 178 135 138 164
-149 165 179 136 116
-150 166 180 137 117
-151 167 181 138 118
-152 168 116 182 119
-153 169 117 183 120
-154 121 170 118 184
-155 122 171 162 119
-156 123 172 163 120
-157 121 124 173 164
-158 165 122 125 174
-159 166 123 126 175
-160 176 167 124 127
-161 177 168 125 128
-162 187 155 146 206
-163 188 156 147 207
-164 189 157 148 185
-165 190 158 149 186
-166 187 191 159 150
-167 188 192 160 151
-168 189 193 161 152
-169 190 139 194 153
-170 154 191 140 195
-171 155 192 141 196
-172 156 193 142 197
-173 143 198 157 194
-174 144 199 158 195
-175 145 200 159 196
-176 146 201 160 197
-177 198 147 202 161
-178 199 148 203 139
-179 200 149 204 140
-180 201 150 205 141
-181 202 151 206 142
-182 143 203 152 207
-183 144 204 185 153
-184 154 145 205 186
-185 214 225 183 164
-186 165 215 226 184
-187 166 216 227 162
-188 167 217 228 163
-189 168 218 229 164
-190 165 169 219 230
-191 220 166 170 208
-192 209 221 167 171
-193 210 222 168 172
-194 211 223 169 173
-195 212 224 170 174
-196 213 225 171 175
-197 176 214 226 172
-198 177 215 227 173
-199 178 216 228 174
-200 179 217 229 175
-201 176 180 218 230
-202 177 181 208 219
-203 209 220 178 182
-204 210 221 179 183
-205 211 222 180 184
-206 212 223 181 162
-207 213 224 182 163
-208 191 202 236 249
-209 192 203 237 250
-210 193 204 238 251
-211 194 205 239 252
-212 253 195 206 240
-213 231 196 207 241
-214 242 232 185 197
-215 198 243 233 186
-216 187 199 244 234
-217 188 200 245 235
-218 189 201 246 236
-219 190 202 247 237
-220 191 203 248 238
-221 192 204 249 239
-222 193 205 250 240
-223 194 206 251 241
-224 242 195 207 252
-225 253 243 185 196
-226 231 244 186 197
-227 187 198 232 245
-228 188 199 233 246
-229 189 200 234 247
-230 190 201 235 248
-231 213 16 226 9
-232 214 17 227 10
-233 11 215 18 228
-234 12 216 19 229
-235 13 217 20 230
-236 14 218 21 208
-237 22 209 15 219
-238 220 23 210 16
-239 1 221 211 17
-240 2 222 212 18
-241 3 223 213 19
-242 4 224 214 20
-243 5 225 215 21
-244 22 6 226 216
-245 23 7 227 217
-246 1 8 228 218
-247 2 9 229 219
-248 220 3 10 230
-249 11 221 4 208
-250 209 12 222 5
-251 210 13 223 6
-252 211 14 224 7
-253 212 15 225 8
0