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