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