Graph forms
for C4 [ 272, 15 ] = PS(4,136;13)
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On this page are computer-accessible forms for the graph C4[ 272, 15 ] =
PS(4,136;13).
(I) Following is a form readable by MAGMA:
g:=Graph<272|{ {136, 143}, {131, 138}, {133, 140}, {135, 142}, {130, 137}, {134,
141}, {132, 139}, {192, 208}, {204, 220}, {203, 219}, {202, 218}, {201, 217},
{200, 216}, {199, 215}, {198, 214}, {197, 213}, {196, 212}, {195, 211}, {194,
210}, {193, 209}, {192, 243}, {204, 255}, {200, 251}, {196, 247}, {193, 244},
{203, 254}, {201, 252}, {195, 246}, {194, 245}, {202, 253}, {197, 248}, {199,
250}, {128, 190}, {129, 191}, {198, 249}, {130, 192}, {131, 193}, {134, 196},
{135, 197}, {4, 71}, {60, 127}, {56, 123}, {52, 119}, {48, 115}, {44, 111}, {8,
75}, {12, 79}, {16, 83}, {20, 87}, {24, 91}, {28, 95}, {32, 99}, {36, 103}, {40,
107}, {1, 69}, {59, 127}, {58, 126}, {57, 125}, {56, 124}, {51, 119}, {50, 118},
{49, 117}, {48, 116}, {43, 111}, {42, 110}, {2, 70}, {3, 71}, {8, 76}, {9, 77},
{10, 78}, {11, 79}, {16, 84}, {17, 85}, {18, 86}, {19, 87}, {24, 92}, {25, 93},
{26, 94}, {27, 95}, {32, 100}, {33, 101}, {34, 102}, {35, 103}, {40, 108}, {41,
109}, {3, 70}, {59, 126}, {57, 124}, {51, 118}, {49, 116}, {43, 110}, {9, 76},
{11, 78}, {17, 84}, {19, 86}, {25, 92}, {27, 94}, {33, 100}, {35, 102}, {41,
108}, {132, 194}, {133, 195}, {2, 69}, {58, 125}, {50, 117}, {42, 109}, {10,
77}, {18, 85}, {26, 93}, {34, 101}, {128, 203}, {4, 72}, {55, 123}, {54, 122},
{53, 121}, {52, 120}, {5, 73}, {6, 74}, {7, 75}, {20, 88}, {21, 89}, {22, 90},
{23, 91}, {36, 104}, {37, 105}, {38, 106}, {39, 107}, {5, 72}, {191, 242}, {189,
240}, {55, 122}, {53, 120}, {7, 74}, {21, 88}, {23, 90}, {37, 104}, {39, 106},
{129, 204}, {157, 208}, {159, 210}, {173, 224}, {175, 226}, {136, 198}, {6, 73},
{190, 241}, {54, 121}, {22, 89}, {38, 105}, {158, 209}, {174, 225}, {156, 207},
{188, 239}, {176, 227}, {180, 231}, {184, 235}, {137, 221}, {138, 222}, {139,
223}, {160, 244}, {161, 245}, {162, 246}, {163, 247}, {168, 252}, {169, 253},
{170, 254}, {171, 255}, {155, 206}, {187, 238}, {177, 228}, {179, 230}, {185,
236}, {154, 205}, {186, 237}, {178, 229}, {12, 80}, {47, 115}, {46, 114}, {45,
113}, {44, 112}, {13, 81}, {14, 82}, {15, 83}, {164, 248}, {165, 249}, {166,
250}, {167, 251}, {13, 80}, {47, 114}, {45, 112}, {15, 82}, {181, 232}, {183,
234}, {14, 81}, {46, 113}, {182, 233}, {140, 224}, {141, 225}, {142, 226}, {143,
227}, {156, 240}, {157, 241}, {158, 242}, {159, 243}, {189, 205}, {191, 207},
{190, 206}, {160, 211}, {164, 215}, {168, 219}, {172, 223}, {144, 228}, {145,
229}, {146, 230}, {147, 231}, {152, 236}, {153, 237}, {154, 238}, {155, 239},
{161, 212}, {163, 214}, {169, 220}, {171, 222}, {162, 213}, {170, 221}, {28,
96}, {29, 97}, {30, 98}, {31, 99}, {148, 232}, {149, 233}, {150, 234}, {151,
235}, {29, 96}, {31, 98}, {165, 216}, {167, 218}, {30, 97}, {166, 217}, {69,
199}, {73, 203}, {72, 202}, {74, 204}, {1, 136}, {70, 200}, {71, 201}, {64,
210}, {68, 214}, {65, 211}, {66, 212}, {67, 213}, {117, 192}, {119, 194}, {125,
200}, {127, 202}, {118, 193}, {126, 201}, {120, 195}, {124, 199}, {60, 128},
{63, 131}, {62, 130}, {61, 129}, {61, 128}, {63, 130}, {121, 196}, {123, 198},
{62, 129}, {122, 197}, {12, 205}, {62, 255}, {60, 253}, {58, 251}, {56, 249},
{54, 247}, {52, 245}, {50, 243}, {48, 241}, {46, 239}, {44, 237}, {42, 235},
{14, 207}, {16, 209}, {18, 211}, {20, 213}, {22, 215}, {24, 217}, {26, 219},
{28, 221}, {30, 223}, {32, 225}, {34, 227}, {36, 229}, {38, 231}, {40, 233},
{75, 137}, {78, 140}, {79, 141}, {82, 144}, {83, 145}, {86, 148}, {87, 149},
{90, 152}, {91, 153}, {94, 156}, {95, 157}, {98, 160}, {99, 161}, {102, 164},
{103, 165}, {106, 168}, {107, 169}, {110, 172}, {111, 173}, {114, 176}, {115,
177}, {118, 180}, {119, 181}, {122, 184}, {123, 185}, {126, 188}, {127, 189},
{13, 206}, {68, 135}, {64, 131}, {61, 254}, {57, 250}, {53, 246}, {49, 242},
{45, 238}, {17, 210}, {21, 214}, {25, 218}, {29, 222}, {33, 226}, {37, 230},
{41, 234}, {64, 132}, {67, 135}, {66, 134}, {65, 133}, {65, 132}, {67, 134},
{76, 138}, {77, 139}, {84, 146}, {85, 147}, {92, 154}, {93, 155}, {100, 162},
{101, 163}, {108, 170}, {109, 171}, {116, 178}, {117, 179}, {124, 186}, {125,
187}, {19, 212}, {66, 133}, {59, 252}, {51, 244}, {43, 236}, {27, 220}, {35,
228}, {80, 155}, {84, 159}, {96, 171}, {100, 175}, {112, 187}, {116, 191}, {68,
136}, {81, 156}, {83, 158}, {97, 172}, {99, 174}, {113, 188}, {115, 190}, {88,
150}, {89, 151}, {104, 166}, {105, 167}, {120, 182}, {121, 183}, {23, 216}, {55,
248}, {39, 232}, {82, 157}, {98, 173}, {114, 189}, {69, 144}, {77, 152}, {71,
146}, {79, 154}, {101, 176}, {103, 178}, {109, 184}, {111, 186}, {1, 215}, {8,
222}, {9, 223}, {32, 246}, {33, 247}, {40, 254}, {41, 255}, {70, 145}, {78,
153}, {102, 177}, {110, 185}, {2, 216}, {3, 217}, {6, 220}, {7, 221}, {34, 248},
{35, 249}, {38, 252}, {39, 253}, {72, 147}, {76, 151}, {104, 179}, {108, 183},
{73, 148}, {75, 150}, {105, 180}, {107, 182}, {4, 218}, {5, 219}, {36, 250},
{37, 251}, {80, 142}, {81, 143}, {112, 174}, {113, 175}, {15, 208}, {74, 149},
{47, 240}, {106, 181}, {10, 224}, {11, 225}, {14, 228}, {15, 229}, {26, 240},
{27, 241}, {30, 244}, {31, 245}, {12, 226}, {63, 209}, {62, 208}, {13, 227},
{28, 242}, {29, 243}, {60, 206}, {61, 207}, {85, 160}, {87, 162}, {93, 168},
{95, 170}, {16, 230}, {59, 205}, {17, 231}, {24, 238}, {25, 239}, {86, 161},
{94, 169}, {18, 232}, {19, 233}, {22, 236}, {23, 237}, {88, 163}, {92, 167},
{89, 164}, {91, 166}, {20, 234}, {21, 235}, {96, 158}, {97, 159}, {31, 224},
{90, 165}, {2, 263}, {8, 269}, {10, 271}, {1, 262}, {9, 270}, {3, 264}, {7,
268}, {4, 265}, {6, 267}, {5, 266}, {11, 272}, {42, 256}, {58, 272}, {47, 261},
{46, 260}, {43, 257}, {44, 258}, {45, 259}, {48, 262}, {57, 271}, {56, 270},
{49, 263}, {50, 264}, {55, 269}, {54, 268}, {51, 265}, {52, 266}, {53, 267},
{63, 256}, {64, 257}, {68, 261}, {66, 259}, {65, 258}, {67, 260}, {137, 256},
{139, 258}, {141, 260}, {143, 262}, {153, 272}, {138, 257}, {142, 261}, {140,
259}, {144, 263}, {152, 271}, {145, 264}, {147, 266}, {149, 268}, {151, 270},
{146, 265}, {150, 269}, {148, 267}, {172, 256}, {188, 272}, {173, 257}, {174,
258}, {175, 259}, {176, 260}, {187, 271}, {186, 270}, {177, 261}, {178, 262},
{179, 263}, {184, 268}, {185, 269}, {180, 264}, {181, 265}, {182, 266}, {183,
267} }>;
(II) A more general form is to represent the graph as the orbit of {136, 143}
under the group generated by the following permutations:
a: (2, 68)(3, 67)(4, 66)(5, 65)(6, 64)(7, 63)(8, 62)(9, 61)(10, 60)(11, 59)(12,
58)(13, 57)(14, 56)(15, 55)(16, 54)(17, 53)(18, 52)(19, 51)(20, 50)(21, 49)(22,
48)(23, 47)(24, 46)(25, 45)(26, 44)(27, 43)(28, 42)(29, 41)(30, 40)(31, 39)(32,
38)(33, 37)(34, 36)(69, 136)(70, 135)(71, 134)(72, 133)(73, 132)(74, 131)(75,
130)(76, 129)(77, 128)(78, 127)(79, 126)(80, 125)(81, 124)(82, 123)(83, 122)(84,
121)(85, 120)(86, 119)(87, 118)(88, 117)(89, 116)(90, 115)(91, 114)(92, 113)(93,
112)(94, 111)(95, 110)(96, 109)(97, 108)(98, 107)(99, 106)(100, 105)(101,
104)(102, 103)(138, 204)(139, 203)(140, 202)(141, 201)(142, 200)(143, 199)(144,
198)(145, 197)(146, 196)(147, 195)(148, 194)(149, 193)(150, 192)(151, 191)(152,
190)(153, 189)(154, 188)(155, 187)(156, 186)(157, 185)(158, 184)(159, 183)(160,
182)(161, 181)(162, 180)(163, 179)(164, 178)(165, 177)(166, 176)(167, 175)(168,
174)(169, 173)(170, 172)(205, 272)(206, 271)(207, 270)(208, 269)(209, 268)(210,
267)(211, 266)(212, 265)(213, 264)(214, 263)(215, 262)(216, 261)(217, 260)(218,
259)(219, 258)(220, 257)(221, 256)(222, 255)(223, 254)(224, 253)(225, 252)(226,
251)(227, 250)(228, 249)(229, 248)(230, 247)(231, 246)(232, 245)(233, 244)(234,
243)(235, 242)(236, 241)(237, 240)(238, 239) (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, 244,
245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260,
261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272)
c: (1, 69, 144, 228, 35, 103, 178, 262)(2, 82, 177, 249, 36, 116, 143, 215)(3,
95, 142, 270, 37, 129, 176, 236)(4, 108, 175, 223, 38, 74, 141, 257)(5, 121,
140, 244, 39, 87, 174, 210)(6, 134, 173, 265, 40, 100, 139, 231)(7, 79, 138,
218, 41, 113, 172, 252)(8, 92, 171, 239, 42, 126, 137, 205)(9, 105, 204, 260,
43, 71, 170, 226)(10, 118, 169, 213, 44, 84, 203, 247)(11, 131, 202, 234, 45,
97, 168, 268)(12, 76, 167, 255, 46, 110, 201, 221)(13, 89, 200, 208, 47, 123,
166, 242)(14, 102, 165, 229, 48, 136, 199, 263)(15, 115, 198, 250, 49, 81, 164,
216)(16, 128, 163, 271, 50, 94, 197, 237)(17, 73, 196, 224, 51, 107, 162,
258)(18, 86, 161, 245, 52, 120, 195, 211)(19, 99, 194, 266, 53, 133, 160,
232)(20, 112, 159, 219, 54, 78, 193, 253)(21, 125, 192, 240, 55, 91, 158,
206)(22, 70, 157, 261, 56, 104, 191, 227)(23, 83, 190, 214, 57, 117, 156,
248)(24, 96, 155, 235, 58, 130, 189, 269)(25, 109, 188, 256, 59, 75, 154,
222)(26, 122, 153, 209, 60, 88, 187, 243)(27, 135, 186, 230, 61, 101, 152,
264)(28, 80, 151, 251, 62, 114, 185, 217)(29, 93, 184, 272, 63, 127, 150,
238)(30, 106, 149, 225, 64, 72, 183, 259)(31, 119, 182, 246, 65, 85, 148,
212)(32, 132, 147, 267, 66, 98, 181, 233)(33, 77, 180, 220, 67, 111, 146,
254)(34, 90, 145, 241, 68, 124, 179, 207)
C4[ 272, 15 ]
272
-1 69 136 215 262
-2 69 70 216 263
-3 264 70 71 217
-4 265 71 72 218
-5 266 72 73 219
-6 220 267 73 74
-7 221 268 74 75
-8 222 269 75 76
-9 77 223 270 76
-10 77 78 224 271
-11 78 79 225 272
-12 79 80 226 205
-13 80 81 227 206
-14 81 82 228 207
-15 82 83 229 208
-16 209 83 84 230
-17 231 210 84 85
-18 232 211 85 86
-19 233 212 86 87
-20 88 234 213 87
-21 88 89 235 214
-22 89 90 236 215
-23 90 91 237 216
-24 91 92 238 217
-25 92 93 239 218
-26 93 94 240 219
-27 220 94 95 241
-28 242 221 95 96
-29 243 222 96 97
-30 244 223 97 98
-31 99 245 224 98
-32 99 100 246 225
-33 100 101 247 226
-34 101 102 248 227
-35 102 103 249 228
-36 103 104 250 229
-37 104 105 251 230
-38 231 105 106 252
-39 253 232 106 107
-40 254 233 107 108
-41 255 234 108 109
-42 110 256 235 109
-43 110 111 257 236
-44 111 112 258 237
-45 112 113 259 238
-46 113 114 260 239
-47 114 115 261 240
-48 115 116 262 241
-49 242 116 117 263
-50 264 243 117 118
-51 265 244 118 119
-52 266 245 119 120
-53 121 267 246 120
-54 121 122 268 247
-55 122 123 269 248
-56 123 124 270 249
-57 124 125 271 250
-58 125 126 272 251
-59 126 127 205 252
-60 253 127 128 206
-61 254 128 129 207
-62 255 129 130 208
-63 209 256 130 131
-64 132 210 257 131
-65 132 133 211 258
-66 133 134 212 259
-67 134 135 213 260
-68 135 136 214 261
-69 1 144 199 2
-70 2 145 200 3
-71 3 146 201 4
-72 4 147 202 5
-73 5 148 203 6
-74 6 149 204 7
-75 137 7 150 8
-76 138 8 151 9
-77 139 9 152 10
-78 11 140 10 153
-79 11 154 12 141
-80 12 155 13 142
-81 143 13 156 14
-82 144 14 157 15
-83 145 15 158 16
-84 146 16 159 17
-85 147 17 160 18
-86 148 18 161 19
-87 149 19 162 20
-88 150 20 163 21
-89 22 151 21 164
-90 22 165 23 152
-91 23 166 24 153
-92 154 24 167 25
-93 155 25 168 26
-94 156 26 169 27
-95 157 27 170 28
-96 158 28 171 29
-97 159 29 172 30
-98 160 30 173 31
-99 161 31 174 32
-100 33 162 32 175
-101 33 176 34 163
-102 34 177 35 164
-103 165 35 178 36
-104 166 36 179 37
-105 167 37 180 38
-106 168 38 181 39
-107 169 39 182 40
-108 170 40 183 41
-109 171 41 184 42
-110 172 42 185 43
-111 44 173 43 186
-112 44 187 45 174
-113 45 188 46 175
-114 176 46 189 47
-115 177 47 190 48
-116 178 48 191 49
-117 179 49 192 50
-118 180 50 193 51
-119 181 51 194 52
-120 182 52 195 53
-121 183 53 196 54
-122 55 184 54 197
-123 55 198 56 185
-124 56 199 57 186
-125 187 57 200 58
-126 188 58 201 59
-127 189 59 202 60
-128 190 60 203 61
-129 191 61 204 62
-130 137 192 62 63
-131 138 193 63 64
-132 139 194 64 65
-133 66 140 195 65
-134 66 67 141 196
-135 67 68 142 197
-136 143 198 1 68
-137 221 256 75 130
-138 222 257 76 131
-139 77 132 223 258
-140 78 133 224 259
-141 79 134 225 260
-142 80 135 226 261
-143 81 136 227 262
-144 69 82 228 263
-145 264 70 83 229
-146 265 71 84 230
-147 231 266 72 85
-148 232 267 73 86
-149 233 268 74 87
-150 88 234 269 75
-151 89 235 270 76
-152 77 90 236 271
-153 78 91 237 272
-154 79 92 205 238
-155 80 93 206 239
-156 81 94 207 240
-157 82 95 208 241
-158 209 242 83 96
-159 210 243 84 97
-160 211 244 85 98
-161 99 212 245 86
-162 100 213 246 87
-163 88 101 214 247
-164 89 102 215 248
-165 90 103 216 249
-166 91 104 217 250
-167 92 105 218 251
-168 93 106 219 252
-169 220 253 94 107
-170 221 254 95 108
-171 222 255 96 109
-172 110 223 256 97
-173 111 224 257 98
-174 99 112 225 258
-175 100 113 226 259
-176 101 114 227 260
-177 102 115 228 261
-178 103 116 229 262
-179 104 117 230 263
-180 231 264 105 118
-181 232 265 106 119
-182 233 266 107 120
-183 121 234 267 108
-184 122 235 268 109
-185 110 123 236 269
-186 111 124 237 270
-187 112 125 238 271
-188 113 126 239 272
-189 114 127 205 240
-190 115 128 206 241
-191 242 116 129 207
-192 243 117 130 208
-193 209 244 118 131
-194 132 210 245 119
-195 133 211 246 120
-196 121 134 212 247
-197 122 135 213 248
-198 123 136 214 249
-199 69 124 215 250
-200 70 125 216 251
-201 71 126 217 252
-202 253 72 127 218
-203 254 73 128 219
-204 220 255 74 129
-205 154 12 189 59
-206 155 13 190 60
-207 156 14 191 61
-208 157 15 192 62
-209 158 16 193 63
-210 159 17 194 64
-211 160 18 195 65
-212 66 161 19 196
-213 67 162 20 197
-214 198 68 163 21
-215 22 1 199 164
-216 165 23 2 200
-217 166 24 3 201
-218 167 25 4 202
-219 168 26 5 203
-220 169 27 6 204
-221 137 170 28 7
-222 138 171 29 8
-223 139 172 30 9
-224 140 173 31 10
-225 11 141 174 32
-226 33 12 142 175
-227 143 176 34 13
-228 144 177 35 14
-229 145 178 36 15
-230 146 179 37 16
-231 147 180 38 17
-232 148 181 39 18
-233 149 182 40 19
-234 150 183 41 20
-235 151 184 42 21
-236 22 152 185 43
-237 44 23 153 186
-238 154 187 45 24
-239 155 188 46 25
-240 156 189 47 26
-241 157 190 48 27
-242 158 191 49 28
-243 159 192 50 29
-244 160 193 51 30
-245 161 194 52 31
-246 162 195 53 32
-247 33 163 196 54
-248 55 34 164 197
-249 165 198 56 35
-250 166 199 57 36
-251 167 200 58 37
-252 168 201 59 38
-253 169 202 60 39
-254 170 203 61 40
-255 171 204 62 41
-256 137 172 63 42
-257 138 173 64 43
-258 44 139 174 65
-259 66 45 140 175
-260 176 67 46 141
-261 177 68 47 142
-262 143 1 178 48
-263 144 2 179 49
-264 145 3 180 50
-265 146 4 181 51
-266 147 5 182 52
-267 148 6 183 53
-268 149 7 184 54
-269 55 150 8 185
-270 56 151 9 186
-271 187 57 152 10
-272 11 188 58 153
0