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