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