Graph forms
for C4 [ 275, 6 ] = PS(5,55;19)
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On this page are computer-accessible forms for the graph C4[ 275, 6 ] =
PS(5,55;19).
(I) Following is a form readable by MAGMA:
g:=Graph<275|{ {55, 56}, {205, 221}, {206, 222}, {207, 223}, {96, 115}, {100,
119}, {104, 123}, {108, 127}, {97, 116}, {99, 118}, {105, 124}, {107, 126}, {98,
117}, {106, 125}, {160, 184}, {161, 185}, {162, 186}, {163, 187}, {164, 188},
{165, 189}, {101, 120}, {103, 122}, {102, 121}, {160, 191}, {135, 166}, {137,
168}, {139, 170}, {141, 172}, {143, 174}, {145, 176}, {147, 178}, {149, 180},
{151, 182}, {153, 184}, {155, 186}, {157, 188}, {159, 190}, {138, 169}, {142,
173}, {146, 177}, {150, 181}, {154, 185}, {158, 189}, {75, 111}, {91, 127}, {90,
126}, {89, 125}, {88, 124}, {83, 119}, {82, 118}, {81, 117}, {80, 116}, {140,
171}, {216, 255}, {148, 179}, {156, 187}, {192, 231}, {200, 239}, {208, 247},
{142, 166}, {143, 167}, {152, 176}, {153, 177}, {154, 178}, {155, 179}, {156,
180}, {157, 181}, {158, 182}, {159, 183}, {193, 232}, {215, 254}, {213, 252},
{195, 234}, {197, 236}, {199, 238}, {209, 248}, {211, 250}, {194, 233}, {214,
253}, {198, 237}, {210, 249}, {84, 120}, {87, 123}, {86, 122}, {85, 121}, {93,
112}, {95, 114}, {94, 113}, {212, 251}, {136, 167}, {152, 183}, {196, 235},
{208, 224}, {220, 236}, {219, 235}, {218, 234}, {217, 233}, {216, 232}, {215,
231}, {214, 230}, {213, 229}, {212, 228}, {209, 225}, {210, 226}, {211, 227},
{92, 111}, {8, 62}, {9, 63}, {1, 57}, {2, 58}, {3, 59}, {4, 60}, {5, 61}, {6,
62}, {7, 63}, {144, 168}, {145, 169}, {146, 170}, {147, 171}, {148, 172}, {149,
173}, {150, 174}, {151, 175}, {201, 240}, {203, 242}, {205, 244}, {207, 246},
{2, 56}, {3, 57}, {6, 60}, {7, 61}, {202, 241}, {206, 245}, {76, 112}, {79,
115}, {78, 114}, {77, 113}, {4, 58}, {5, 59}, {144, 175}, {204, 243}, {168,
239}, {176, 247}, {184, 255}, {8, 64}, {47, 103}, {46, 102}, {45, 101}, {44,
100}, {9, 65}, {10, 66}, {11, 67}, {12, 68}, {13, 69}, {14, 70}, {15, 71}, {24,
80}, {25, 81}, {26, 82}, {27, 83}, {28, 84}, {29, 85}, {30, 86}, {31, 87}, {40,
96}, {41, 97}, {42, 98}, {43, 99}, {167, 238}, {177, 248}, {179, 250}, {181,
252}, {183, 254}, {10, 64}, {47, 101}, {46, 100}, {11, 65}, {14, 68}, {15, 69},
{26, 80}, {27, 81}, {30, 84}, {31, 85}, {42, 96}, {43, 97}, {166, 237}, {178,
249}, {182, 253}, {12, 66}, {45, 99}, {44, 98}, {13, 67}, {28, 82}, {29, 83},
{128, 207}, {180, 251}, {129, 208}, {131, 210}, {133, 212}, {135, 214}, {137,
216}, {139, 218}, {141, 220}, {130, 209}, {134, 213}, {138, 217}, {16, 70}, {49,
103}, {48, 102}, {17, 71}, {24, 78}, {25, 79}, {128, 214}, {129, 215}, {132,
211}, {140, 219}, {16, 72}, {54, 110}, {53, 109}, {52, 108}, {51, 107}, {50,
106}, {49, 105}, {48, 104}, {17, 73}, {18, 74}, {19, 75}, {20, 76}, {21, 77},
{22, 78}, {23, 79}, {169, 240}, {171, 242}, {173, 244}, {175, 246}, {185, 224},
{187, 226}, {189, 228}, {191, 230}, {18, 72}, {55, 109}, {54, 108}, {51, 105},
{50, 104}, {19, 73}, {22, 76}, {23, 77}, {130, 216}, {131, 217}, {134, 220},
{170, 241}, {174, 245}, {186, 225}, {190, 229}, {20, 74}, {53, 107}, {52, 106},
{21, 75}, {132, 218}, {133, 219}, {136, 215}, {172, 243}, {188, 227}, {161,
192}, {163, 194}, {165, 196}, {162, 193}, {164, 195}, {184, 223}, {183, 222},
{182, 221}, {1, 110}, {32, 86}, {33, 87}, {40, 94}, {41, 95}, {32, 88}, {33,
89}, {34, 90}, {35, 91}, {36, 92}, {37, 93}, {38, 94}, {39, 95}, {34, 88}, {35,
89}, {38, 92}, {39, 93}, {36, 90}, {37, 91}, {61, 152}, {63, 154}, {62, 153},
{111, 197}, {122, 208}, {123, 209}, {126, 212}, {127, 213}, {56, 147}, {60,
151}, {57, 148}, {59, 150}, {124, 210}, {125, 211}, {58, 149}, {113, 192}, {115,
194}, {117, 196}, {119, 198}, {121, 200}, {123, 202}, {125, 204}, {127, 206},
{114, 193}, {118, 197}, {122, 201}, {126, 205}, {62, 136}, {63, 137}, {112,
198}, {113, 199}, {120, 206}, {121, 207}, {116, 195}, {124, 203}, {56, 130},
{61, 135}, {60, 134}, {57, 131}, {114, 200}, {115, 201}, {118, 204}, {119, 205},
{58, 132}, {59, 133}, {116, 202}, {117, 203}, {120, 199}, {31, 222}, {55, 246},
{53, 244}, {51, 242}, {49, 240}, {47, 238}, {45, 236}, {33, 224}, {35, 226},
{37, 228}, {39, 230}, {41, 232}, {43, 234}, {28, 222}, {53, 247}, {52, 246},
{49, 243}, {48, 242}, {45, 239}, {44, 238}, {29, 223}, {32, 226}, {33, 227},
{36, 230}, {37, 231}, {40, 234}, {41, 235}, {30, 221}, {54, 245}, {50, 241},
{46, 237}, {34, 225}, {38, 229}, {42, 233}, {27, 221}, {51, 245}, {50, 244},
{43, 237}, {34, 228}, {35, 229}, {42, 236}, {36, 227}, {52, 243}, {44, 235},
{64, 138}, {85, 159}, {84, 158}, {81, 155}, {80, 154}, {69, 143}, {68, 142},
{65, 139}, {38, 232}, {83, 157}, {82, 156}, {67, 141}, {66, 140}, {55, 249},
{54, 248}, {39, 233}, {40, 231}, {112, 191}, {111, 190}, {70, 144}, {79, 153},
{78, 152}, {71, 145}, {72, 146}, {77, 151}, {76, 150}, {73, 147}, {64, 155},
{68, 159}, {92, 128}, {94, 130}, {93, 129}, {95, 131}, {65, 156}, {67, 158},
{46, 240}, {75, 149}, {74, 148}, {47, 241}, {48, 239}, {66, 157}, {96, 132},
{97, 133}, {98, 134}, {99, 135}, {104, 140}, {105, 141}, {106, 142}, {107, 143},
{69, 160}, {71, 162}, {70, 161}, {72, 163}, {100, 136}, {101, 137}, {102, 138},
{103, 139}, {73, 164}, {109, 128}, {74, 165}, {110, 129}, {1, 247}, {87, 161},
{86, 160}, {8, 254}, {9, 255}, {2, 251}, {4, 253}, {6, 255}, {2, 248}, {89,
163}, {88, 162}, {3, 249}, {6, 252}, {7, 253}, {1, 250}, {5, 254}, {108, 144},
{109, 145}, {110, 146}, {4, 250}, {91, 165}, {90, 164}, {5, 251}, {30, 224},
{31, 225}, {3, 252}, {32, 223}, {7, 256}, {15, 264}, {23, 272}, {8, 257}, {10,
259}, {12, 261}, {14, 263}, {24, 273}, {26, 275}, {10, 256}, {11, 257}, {14,
260}, {15, 261}, {26, 272}, {27, 273}, {9, 258}, {13, 262}, {25, 274}, {12,
258}, {13, 259}, {28, 274}, {29, 275}, {11, 260}, {16, 262}, {17, 263}, {24,
270}, {25, 271}, {16, 265}, {18, 267}, {20, 269}, {22, 271}, {18, 264}, {19,
265}, {22, 268}, {23, 269}, {17, 266}, {21, 270}, {20, 266}, {21, 267}, {19,
268}, {166, 260}, {167, 261}, {170, 264}, {171, 265}, {174, 268}, {175, 269},
{178, 272}, {179, 273}, {172, 266}, {173, 267}, {180, 274}, {181, 275}, {168,
262}, {169, 263}, {185, 256}, {187, 258}, {189, 260}, {191, 262}, {186, 257},
{190, 261}, {176, 270}, {177, 271}, {188, 259}, {192, 263}, {200, 271}, {193,
264}, {195, 266}, {197, 268}, {199, 270}, {194, 265}, {198, 269}, {196, 267},
{201, 272}, {219, 258}, {217, 256}, {203, 274}, {202, 273}, {218, 257}, {204,
275}, {220, 259} }>;
(II) A more general form is to represent the graph as the orbit of {55, 56}
under the group generated by the following permutations:
a: (2, 55)(3, 54)(4, 53)(5, 52)(6, 51)(7, 50)(8, 49)(9, 48)(10, 47)(11, 46)(12,
45)(13, 44)(14, 43)(15, 42)(16, 41)(17, 40)(18, 39)(19, 38)(20, 37)(21, 36)(22,
35)(23, 34)(24, 33)(25, 32)(26, 31)(27, 30)(28, 29)(57, 110)(58, 109)(59,
108)(60, 107)(61, 106)(62, 105)(63, 104)(64, 103)(65, 102)(66, 101)(67, 100)(68,
99)(69, 98)(70, 97)(71, 96)(72, 95)(73, 94)(74, 93)(75, 92)(76, 91)(77, 90)(78,
89)(79, 88)(80, 87)(81, 86)(82, 85)(83, 84)(112, 165)(113, 164)(114, 163)(115,
162)(116, 161)(117, 160)(118, 159)(119, 158)(120, 157)(121, 156)(122, 155)(123,
154)(124, 153)(125, 152)(126, 151)(127, 150)(128, 149)(129, 148)(130, 147)(131,
146)(132, 145)(133, 144)(134, 143)(135, 142)(136, 141)(137, 140)(138, 139)(167,
220)(168, 219)(169, 218)(170, 217)(171, 216)(172, 215)(173, 214)(174, 213)(175,
212)(176, 211)(177, 210)(178, 209)(179, 208)(180, 207)(181, 206)(182, 205)(183,
204)(184, 203)(185, 202)(186, 201)(187, 200)(188, 199)(189, 198)(190, 197)(191,
196)(192, 195)(193, 194)(222, 275)(223, 274)(224, 273)(225, 272)(226, 271)(227,
270)(228, 269)(229, 268)(230, 267)(231, 266)(232, 265)(233, 264)(234, 263)(235,
262)(236, 261)(237, 260)(238, 259)(239, 258)(240, 257)(241, 256)(242, 255)(243,
254)(244, 253)(245, 252)(246, 251)(247, 250)(248, 249) (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, 273, 274, 275)
c: (1, 56, 111, 166, 221)(2, 75, 142, 205, 247, 55, 92, 135, 182, 250)(3, 94,
118, 189, 273, 54, 73, 159, 198, 224)(4, 58, 149, 173, 244, 53, 109, 128, 214,
253)(5, 77, 125, 212, 270, 52, 90, 152, 175, 227)(6, 96, 156, 196, 241, 51, 71,
121, 191, 256)(7, 60, 132, 180, 267, 50, 107, 145, 207, 230)(8, 79, 163, 219,
238, 49, 88, 114, 168, 259)(9, 98, 139, 203, 264, 48, 69, 138, 184, 233)(10, 62,
115, 187, 235, 47, 105, 162, 200, 262)(11, 81, 146, 171, 261, 46, 86, 131, 216,
236)(12, 100, 122, 210, 232, 45, 67, 155, 177, 265)(13, 64, 153, 194, 258, 44,
103, 124, 193, 239)(14, 83, 129, 178, 229, 43, 84, 148, 209, 268)(15, 102, 160,
217, 255, 42, 65, 117, 170, 242)(16, 66, 136, 201, 226, 41, 101, 141, 186,
271)(17, 85, 112, 185, 252, 40, 82, 165, 202, 245)(18, 104, 143, 169, 223, 39,
63, 134, 218, 274)(19, 68, 119, 208, 249, 38, 99, 158, 179, 248)(20, 87, 150,
192, 275, 37, 80, 127, 195, 222)(21, 106, 126, 176, 246, 36, 61, 151, 211,
251)(22, 70, 157, 215, 272, 35, 97, 120, 172, 225)(23, 89, 133, 199, 243, 34,
78, 144, 188, 254)(24, 108, 164, 183, 269, 33, 59, 113, 204, 228)(25, 72, 140,
167, 240, 32, 95, 137, 220, 257)(26, 91, 116, 206, 266, 31, 76, 161, 181,
231)(27, 110, 147, 190, 237, 30, 57, 130, 197, 260)(28, 74, 123, 174, 263, 29,
93, 154, 213, 234)
C4[ 275, 6 ]
275
-1 110 57 247 250
-2 56 58 248 251
-3 57 59 249 252
-4 253 58 60 250
-5 254 59 61 251
-6 255 60 62 252
-7 253 256 61 63
-8 254 257 62 64
-9 255 258 63 65
-10 66 256 259 64
-11 67 257 260 65
-12 66 68 258 261
-13 67 69 259 262
-14 68 70 260 263
-15 264 69 71 261
-16 265 70 72 262
-17 266 71 73 263
-18 264 267 72 74
-19 265 268 73 75
-20 266 269 74 76
-21 77 267 270 75
-22 78 268 271 76
-23 77 79 269 272
-24 78 80 270 273
-25 79 81 271 274
-26 275 80 82 272
-27 221 81 83 273
-28 222 82 84 274
-29 275 223 83 85
-30 221 224 84 86
-31 222 225 85 87
-32 88 223 226 86
-33 89 224 227 87
-34 88 90 225 228
-35 89 91 226 229
-36 90 92 227 230
-37 231 91 93 228
-38 232 92 94 229
-39 233 93 95 230
-40 231 234 94 96
-41 232 235 95 97
-42 233 236 96 98
-43 99 234 237 97
-44 100 235 238 98
-45 99 101 236 239
-46 100 102 237 240
-47 101 103 238 241
-48 242 102 104 239
-49 243 103 105 240
-50 244 104 106 241
-51 242 245 105 107
-52 243 246 106 108
-53 244 247 107 109
-54 110 245 248 108
-55 56 246 249 109
-56 55 2 147 130
-57 1 3 148 131
-58 132 2 4 149
-59 133 3 5 150
-60 134 4 6 151
-61 135 5 7 152
-62 136 6 8 153
-63 154 137 7 9
-64 155 138 8 10
-65 11 156 139 9
-66 12 157 140 10
-67 11 13 158 141
-68 12 14 159 142
-69 143 13 15 160
-70 144 14 16 161
-71 145 15 17 162
-72 146 16 18 163
-73 147 17 19 164
-74 165 148 18 20
-75 111 149 19 21
-76 22 112 150 20
-77 23 113 151 21
-78 22 24 114 152
-79 23 25 115 153
-80 154 24 26 116
-81 155 25 27 117
-82 156 26 28 118
-83 157 27 29 119
-84 158 28 30 120
-85 121 159 29 31
-86 122 160 30 32
-87 33 123 161 31
-88 34 124 162 32
-89 33 35 125 163
-90 34 36 126 164
-91 165 35 37 127
-92 111 36 38 128
-93 112 37 39 129
-94 113 38 40 130
-95 114 39 41 131
-96 132 115 40 42
-97 133 116 41 43
-98 44 134 117 42
-99 45 135 118 43
-100 44 46 136 119
-101 45 47 137 120
-102 121 46 48 138
-103 122 47 49 139
-104 123 48 50 140
-105 124 49 51 141
-106 125 50 52 142
-107 143 126 51 53
-108 144 127 52 54
-109 55 145 128 53
-110 1 146 129 54
-111 190 92 75 197
-112 198 191 93 76
-113 77 199 192 94
-114 78 200 193 95
-115 79 201 194 96
-116 80 202 195 97
-117 81 203 196 98
-118 99 82 204 197
-119 198 100 83 205
-120 199 101 84 206
-121 200 102 85 207
-122 201 103 86 208
-123 209 202 104 87
-124 88 210 203 105
-125 89 211 204 106
-126 90 212 205 107
-127 91 213 206 108
-128 92 214 207 109
-129 110 93 215 208
-130 209 56 94 216
-131 210 57 95 217
-132 211 58 96 218
-133 212 59 97 219
-134 220 213 60 98
-135 99 166 214 61
-136 100 167 215 62
-137 101 168 216 63
-138 102 169 217 64
-139 103 170 218 65
-140 66 104 171 219
-141 220 67 105 172
-142 166 68 106 173
-143 167 69 107 174
-144 168 70 108 175
-145 176 169 71 109
-146 110 177 170 72
-147 56 178 171 73
-148 57 179 172 74
-149 58 180 173 75
-150 59 181 174 76
-151 77 60 182 175
-152 176 78 61 183
-153 177 79 62 184
-154 178 80 63 185
-155 179 81 64 186
-156 187 180 82 65
-157 66 188 181 83
-158 67 189 182 84
-159 68 190 183 85
-160 69 191 184 86
-161 70 192 185 87
-162 88 71 193 186
-163 187 89 72 194
-164 188 90 73 195
-165 189 91 74 196
-166 135 237 260 142
-167 143 136 238 261
-168 144 137 239 262
-169 145 138 240 263
-170 264 146 139 241
-171 242 265 147 140
-172 243 266 148 141
-173 244 267 149 142
-174 143 245 268 150
-175 144 246 269 151
-176 145 247 270 152
-177 146 248 271 153
-178 154 147 249 272
-179 155 148 250 273
-180 156 149 251 274
-181 275 157 150 252
-182 253 221 158 151
-183 254 222 159 152
-184 255 223 160 153
-185 154 256 224 161
-186 155 257 225 162
-187 156 258 226 163
-188 157 259 227 164
-189 165 158 260 228
-190 111 159 261 229
-191 112 160 262 230
-192 231 113 161 263
-193 264 232 114 162
-194 265 233 115 163
-195 266 234 116 164
-196 165 267 235 117
-197 111 268 236 118
-198 112 269 237 119
-199 113 270 238 120
-200 121 114 271 239
-201 122 115 272 240
-202 123 116 273 241
-203 242 124 117 274
-204 275 243 125 118
-205 221 244 126 119
-206 222 245 127 120
-207 121 223 246 128
-208 122 224 247 129
-209 123 225 248 130
-210 124 226 249 131
-211 132 125 227 250
-212 133 126 228 251
-213 134 127 229 252
-214 253 135 128 230
-215 231 254 136 129
-216 232 255 137 130
-217 233 256 138 131
-218 132 234 257 139
-219 133 235 258 140
-220 134 236 259 141
-221 27 182 205 30
-222 28 183 206 31
-223 29 184 207 32
-224 33 30 185 208
-225 209 34 31 186
-226 187 210 35 32
-227 33 188 211 36
-228 34 189 212 37
-229 35 190 213 38
-230 36 191 214 39
-231 37 192 215 40
-232 38 193 216 41
-233 39 194 217 42
-234 40 195 218 43
-235 44 41 196 219
-236 220 45 42 197
-237 198 166 46 43
-238 44 199 167 47
-239 45 200 168 48
-240 46 201 169 49
-241 47 202 170 50
-242 48 203 171 51
-243 49 204 172 52
-244 50 205 173 53
-245 51 206 174 54
-246 55 52 207 175
-247 176 1 53 208
-248 209 177 2 54
-249 55 210 178 3
-250 1 211 179 4
-251 2 212 180 5
-252 3 213 181 6
-253 4 214 182 7
-254 5 215 183 8
-255 6 216 184 9
-256 7 217 185 10
-257 11 8 218 186
-258 187 12 9 219
-259 220 188 13 10
-260 11 166 189 14
-261 12 167 190 15
-262 13 168 191 16
-263 14 169 192 17
-264 15 170 193 18
-265 16 171 194 19
-266 17 172 195 20
-267 18 173 196 21
-268 22 19 174 197
-269 198 23 20 175
-270 176 199 24 21
-271 22 177 200 25
-272 23 178 201 26
-273 24 179 202 27
-274 25 180 203 28
-275 26 181 204 29
0