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