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