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