Graph forms
for C4 [ 256, 31 ] =
PL(LoPr_32(1,16,6,16,7),[4^32,32^4])
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On this page are computer-accessible forms for the graph C4[ 256, 31 ] =
PL(LoPr_32(1,16,6,16,7),[4^32,32^4]).
(I) Following is a form readable by MAGMA:
g:=Graph<256|{ {128, 137}, {128, 162}, {128, 203}, {128, 212}, {2, 131}, {96,
225}, {55, 182}, {36, 165}, {1, 131}, {58, 184}, {45, 175}, {31, 157}, {2, 129},
{108, 239}, {93, 222}, {51, 176}, {46, 173}, {11, 136}, {12, 136}, {118, 242},
{10, 143}, {17, 148}, {70, 195}, {5, 131}, {100, 226}, {38, 160}, {37, 163},
{74, 204}, {4, 131}, {103, 224}, {47, 168}, {6, 129}, {60, 187}, {81, 214}, {3,
139}, {22, 158}, {1, 136}, {109, 228}, {95, 214}, {40, 161}, {32, 169}, {23,
158}, {65, 200}, {15, 133}, {113, 251}, {97, 235}, {52, 190}, {38, 172}, {26,
144}, {25, 147}, {20, 158}, {83, 217}, {84, 222}, {3, 136}, {124, 247}, {103,
236}, {99, 232}, {16, 155}, {68, 207}, {7, 139}, {116, 248}, {92, 208}, {55,
187}, {47, 163}, {61, 176}, {125, 240}, {97, 236}, {75, 198}, {87, 218}, {69,
203}, {76, 194}, {48, 191}, {105, 230}, {15, 159}, {114, 226}, {93, 205}, {42,
186}, {71, 215}, {73, 216}, {118, 231}, {25, 139}, {121, 235}, {98, 240}, {45,
191}, {37, 183}, {35, 177}, {29, 143}, {64, 210}, {54, 165}, {89, 202}, {86,
197}, {68, 208}, {104, 252}, {83, 199}, {88, 204}, {26, 143}, {28, 137}, {70,
211}, {63, 169}, {119, 225}, {90, 204}, {79, 217}, {28, 139}, {109, 250}, {54,
161}, {36, 179}, {7, 159}, {107, 243}, {40, 176}, {39, 191}, {26, 130}, {71,
223}, {69, 220}, {24, 130}, {111, 245}, {92, 198}, {50, 168}, {72, 210}, {29,
134}, {108, 247}, {106, 241}, {67, 216}, {18, 143}, {119, 234}, {110, 243},
{101, 248}, {32, 189}, {73, 212}, {75, 214}, {43, 181}, {126, 224}, {59, 165},
{27, 132}, {123, 228}, {117, 234}, {106, 245}, {59, 164}, {67, 220}, {80, 207},
{8, 168}, {116, 212}, {48, 144}, {10, 170}, {88, 248}, {65, 224}, {126, 223},
{30, 188}, {105, 203}, {56, 154}, {62, 156}, {9, 170}, {16, 180}, {33, 133},
{19, 183}, {86, 242}, {14, 171}, {58, 159}, {19, 182}, {22, 176}, {101, 195},
{77, 235}, {111, 200}, {42, 130}, {107, 195}, {57, 145}, {49, 153}, {61, 149},
{74, 226}, {81, 248}, {13, 167}, {100, 206}, {53, 159}, {21, 191}, {77, 230},
{84, 255}, {4, 168}, {127, 211}, {123, 215}, {102, 202}, {45, 129}, {30, 178},
{6, 171}, {122, 215}, {114, 223}, {89, 244}, {39, 138}, {82, 255}, {34, 140},
{44, 130}, {53, 154}, {98, 205}, {91, 244}, {41, 153}, {115, 195}, {90, 234},
{48, 129}, {127, 206}, {115, 194}, {96, 209}, {60, 141}, {66, 240}, {117, 199},
{85, 231}, {14, 189}, {57, 138}, {66, 241}, {72, 251}, {79, 252}, {78, 250},
{124, 200}, {122, 206}, {80, 228}, {64, 245}, {82, 231}, {13, 187}, {94, 232},
{63, 137}, {18, 165}, {125, 202}, {102, 209}, {46, 153}, {41, 158}, {35, 148},
{20, 172}, {112, 200}, {43, 147}, {31, 167}, {34, 155}, {94, 231}, {62, 132},
{110, 212}, {76, 246}, {85, 239}, {99, 216}, {113, 202}, {104, 211}, {8, 180},
{44, 144}, {78, 242}, {11, 182}, {95, 226}, {91, 230}, {33, 156}, {23, 170},
{87, 234}, {5, 187}, {121, 199}, {120, 198}, {52, 138}, {12, 178}, {21, 170},
{120, 199}, {112, 207}, {49, 142}, {44, 147}, {1, 193}, {121, 185}, {74, 138},
{77, 141}, {81, 145}, {88, 152}, {5, 196}, {108, 173}, {42, 235}, {16, 209},
{12, 205}, {8, 201}, {18, 208}, {82, 144}, {2, 193}, {70, 133}, {17, 213}, {99,
167}, {125, 184}, {64, 134}, {25, 222}, {103, 160}, {46, 233}, {41, 238}, {61,
250}, {9, 193}, {59, 243}, {63, 247}, {9, 192}, {119, 190}, {45, 228}, {18,
219}, {13, 196}, {69, 140}, {10, 193}, {35, 232}, {22, 218}, {125, 177}, {121,
181}, {118, 186}, {57, 245}, {50, 255}, {120, 181}, {91, 150}, {62, 243}, {74,
135}, {75, 134}, {19, 221}, {98, 172}, {52, 250}, {29, 210}, {120, 183}, {107,
164}, {96, 175}, {90, 149}, {89, 150}, {48, 255}, {72, 135}, {85, 154}, {33,
241}, {118, 166}, {10, 219}, {127, 174}, {124, 173}, {17, 192}, {112, 162}, {30,
205}, {117, 166}, {98, 177}, {96, 179}, {93, 142}, {60, 239}, {112, 164}, {122,
174}, {66, 151}, {102, 179}, {76, 153}, {11, 221}, {116, 162}, {91, 141}, {19,
197}, {52, 227}, {49, 233}, {119, 175}, {97, 185}, {64, 152}, {68, 156}, {16,
201}, {100, 189}, {95, 134}, {43, 242}, {38, 252}, {104, 178}, {57, 227}, {53,
239}, {39, 253}, {76, 150}, {84, 142}, {32, 251}, {73, 146}, {9, 213}, {100,
184}, {79, 147}, {83, 142}, {56, 230}, {126, 160}, {102, 184}, {41, 246}, {113,
174}, {99, 188}, {62, 225}, {66, 157}, {37, 197}, {123, 155}, {117, 149}, {105,
137}, {101, 133}, {61, 221}, {63, 223}, {13, 236}, {122, 155}, {108, 141}, {87,
182}, {12, 238}, {127, 157}, {95, 189}, {55, 213}, {26, 249}, {65, 162}, {1,
229}, {115, 151}, {94, 186}, {29, 249}, {6, 227}, {116, 145}, {115, 150}, {46,
203}, {27, 254}, {24, 253}, {11, 238}, {3, 229}, {27, 253}, {24, 254}, {5, 237},
{92, 180}, {49, 217}, {21, 253}, {20, 252}, {69, 173}, {4, 237}, {109, 132},
{50, 219}, {60, 213}, {73, 160}, {87, 190}, {3, 233}, {28, 246}, {67, 169}, {75,
161}, {28, 247}, {92, 183}, {39, 204}, {72, 163}, {82, 185}, {85, 185}, {14,
227}, {55, 218}, {7, 233}, {124, 146}, {51, 221}, {40, 198}, {33, 207}, {71,
169}, {25, 246}, {31, 240}, {35, 211}, {68, 180}, {78, 190}, {86, 166}, {8,
249}, {93, 172}, {90, 171}, {20, 229}, {40, 218}, {126, 140}, {110, 156}, {59,
201}, {81, 163}, {7, 244}, {105, 154}, {103, 148}, {54, 197}, {51, 192}, {36,
215}, {34, 209}, {31, 236}, {22, 229}, {88, 171}, {36, 208}, {58, 206}, {47,
219}, {71, 179}, {80, 164}, {14, 251}, {114, 135}, {104, 157}, {97, 148}, {44,
217}, {43, 222}, {83, 166}, {113, 135}, {37, 210}, {111, 152}, {89, 174}, {53,
194}, {51, 196}, {70, 177}, {77, 186}, {86, 161}, {6, 254}, {109, 149}, {58,
194}, {56, 192}, {21, 237}, {17, 232}, {94, 167}, {47, 214}, {23, 238}, {23,
237}, {27, 225}, {15, 244}, {106, 145}, {78, 181}, {2, 254}, {110, 146}, {107,
151}, {56, 196}, {32, 220}, {4, 249}, {111, 146}, {106, 151}, {101, 152}, {65,
188}, {79, 178}, {15, 241}, {114, 140}, {38, 216}, {34, 220}, {30, 224}, {54,
201}, {123, 132}, {67, 188}, {80, 175}, {24, 256}, {42, 256}, {50, 256}, {84,
256} }>;
(II) A more general form is to represent the graph as the orbit of {128, 137}
under the group generated by the following permutations:
a: (1, 2)(3, 6)(4, 5)(7, 14)(8, 13)(9, 10)(11, 48)(12, 45)(15, 32)(16, 31)(17,
18)(19, 82)(20, 27)(21, 23)(22, 24)(25, 90)(26, 51)(28, 88)(29, 56)(30, 80)(33,
67)(34, 66)(35, 36)(37, 85)(38, 62)(39, 41)(40, 42)(43, 117)(44, 61)(46, 57)(47,
60)(49, 52)(50, 55)(53, 72)(54, 97)(58, 113)(59, 103)(63, 101)(64, 105)(65,
112)(68, 99)(69, 106)(70, 71)(73, 110)(74, 76)(75, 77)(78, 83)(79, 109)(81,
108)(84, 87)(86, 121)(89, 100)(91, 95)(92, 94)(93, 119)(96, 98)(102, 125)(104,
123)(107, 126)(111, 128)(114, 115)(116, 124)(118, 120)(122, 127)(129, 136)(130,
176)(132, 252)(133, 169)(134, 230)(135, 194)(137, 152)(138, 153)(139, 171)(140,
151)(141, 214)(142, 190)(143, 192)(144, 221)(145, 173)(146, 212)(147, 149)(148,
165)(150, 226)(154, 210)(155, 157)(156, 216)(158, 253)(159, 251)(160, 243)(161,
235)(162, 200)(163, 239)(164, 224)(166, 181)(167, 180)(168, 187)(172, 225)(174,
206)(175, 205)(177, 179)(178, 228)(182, 255)(183, 231)(184, 202)(185, 197)(186,
198)(188, 207)(189, 244)(191, 238)(195, 223)(196, 249)(199, 242)(201, 236)(203,
245)(204, 246)(208, 232)(209, 240)(211, 215)(213, 219)(217, 250)(218, 256)(220,
241)(222, 234)(227, 233)(229, 254)(247, 248) (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, 3)(4, 20)(5, 22)(6, 7)(8, 38)(9, 11)(10, 12)(13, 40)(14, 15)(16, 73)(17,
19)(18, 30)(21, 41)(24, 49)(25, 48)(26, 79)(27, 46)(28, 45)(29, 104)(31, 75)(32,
33)(34, 110)(35, 37)(36, 65)(39, 76)(42, 83)(43, 82)(47, 98)(50, 93)(51, 55)(52,
53)(54, 103)(56, 87)(57, 58)(59, 126)(60, 61)(62, 69)(63, 80)(64, 127)(66,
95)(67, 68)(70, 72)(71, 112)(74, 115)(77, 117)(78, 85)(81, 125)(86, 97)(88,
89)(90, 91)(92, 99)(94, 120)(96, 128)(100, 106)(101, 113)(102, 116)(105,
119)(107, 114)(108, 109)(111, 122)(118, 121)(123, 124)(129, 139)(130, 217)(131,
229)(132, 173)(133, 251)(134, 157)(135, 195)(136, 193)(137, 175)(138, 194)(140,
243)(141, 149)(142, 256)(143, 178)(144, 147)(145, 184)(146, 155)(148, 197)(150,
204)(151, 226)(152, 174)(153, 253)(154, 190)(156, 220)(158, 237)(159, 227)(160,
201)(161, 236)(162, 179)(163, 177)(164, 223)(165, 224)(166, 235)(167, 198)(168,
172)(169, 207)(170, 238)(171, 244)(176, 187)(180, 216)(181, 231)(182, 192)(183,
232)(185, 242)(186, 199)(188, 208)(189, 241)(191, 246)(196, 218)(200, 215)(202,
248)(203, 225)(205, 219)(206, 245)(209, 212)(210, 211)(213, 221)(214, 240)(222,
255)(228, 247)(230, 234)(233, 254)(239, 250)(249, 252)
c: (1, 4, 29, 95, 114, 63, 105, 77, 118, 117, 119, 80, 33, 66, 104, 20, 23, 10,
47, 72, 32, 69, 108, 85, 121, 78, 109, 62, 107, 70, 98, 12)(2, 8, 64, 100, 126,
28, 56, 42, 86, 90, 96, 112, 15, 31, 79, 22, 21, 18, 81, 113, 67, 46, 60, 82,
120, 52, 123, 110, 115, 35, 93, 11)(3, 5, 26, 75, 74, 71, 128, 91, 94, 83, 87,
45, 68, 106, 127, 38, 41, 9, 50, 37, 14, 34, 124, 53, 97, 43, 61, 27, 59, 101,
125, 30)(6, 16, 111, 58, 103, 25, 51, 24, 54, 88, 102, 65, 7, 13, 44, 40, 39,
36, 116, 89, 99, 49, 55, 48, 92, 57, 122, 73, 76, 17, 84, 19)(129, 180, 245,
206, 160, 246, 192, 256, 197, 171, 209, 200, 159, 236, 147, 176, 253, 165, 248,
202, 188, 233, 187, 144, 198, 138, 215, 212, 150, 232, 142, 182)(130, 161, 204,
179, 162, 244, 167, 217, 218, 191, 208, 145, 174, 216, 153, 213, 255, 183, 227,
155, 146, 194, 148, 222, 221, 254, 201, 152, 184, 224, 139, 196)(131, 249, 134,
226, 223, 137, 230, 186, 166, 234, 175, 207, 241, 157, 252, 158, 170, 219, 163,
251, 220, 173, 239, 185, 181, 250, 132, 243, 195, 177, 205, 136)(133, 240, 178,
229, 237, 143, 214, 135, 169, 203, 141, 231, 199, 190, 228, 156, 151, 211, 172,
238, 193, 168, 210, 189, 140, 247, 154, 235, 242, 149, 225, 164)
d: (26, 50)(29, 47)(44, 84)(51, 55)(56, 60)(61, 87)(64, 81)(79, 93)(96, 123)(98,
104)(102, 122)(105, 108)(109, 119)(111, 116)(124, 128)(125, 127)(130, 256)(132,
225)(134, 214)(137, 247)(141, 230)(142, 217)(143, 219)(144, 255)(145, 245)(146,
212)(147, 222)(149, 234)(152, 248)(154, 239)(155, 209)(157, 240)(162, 200)(163,
210)(168, 249)(172, 252)(173, 203)(174, 202)(175, 228)(176, 218)(177, 211)(178,
205)(179, 215)(182, 221)(184, 206)(187, 196)(190, 250)(192, 213)
e: (4, 10)(5, 9)(8, 18)(13, 17)(16, 36)(25, 49)(26, 50)(28, 46)(29, 47)(31,
35)(34, 71)(43, 83)(44, 84)(51, 55)(52, 90)(56, 60)(57, 88)(61, 87)(63, 69)(64,
81)(66, 70)(78, 117)(79, 93)(96, 123)(98, 104)(101, 106)(102, 122)(105,
108)(109, 119)(111, 116)(124, 128)(125, 127)(130, 256)(131, 193)(132, 225)(133,
241)(134, 214)(137, 173)(138, 204)(139, 233)(140, 223)(141, 230)(142, 147)(143,
168)(144, 255)(145, 152)(146, 212)(148, 236)(149, 190)(151, 195)(153, 246)(154,
239)(155, 179)(157, 177)(162, 200)(163, 210)(165, 201)(166, 242)(167, 232)(169,
220)(170, 237)(171, 227)(172, 252)(174, 202)(175, 228)(176, 218)(178, 205)(180,
208)(181, 199)(182, 221)(184, 206)(187, 192)(196, 213)(203, 247)(209, 215)(211,
240)(217, 222)(219, 249)(234, 250)(245, 248)
C4[ 256, 31 ]
256
-1 136 193 229 131
-2 254 193 129 131
-3 233 136 139 229
-4 168 237 249 131
-5 187 237 196 131
-6 254 171 227 129
-7 233 244 159 139
-8 168 201 180 249
-9 213 170 192 193
-10 143 170 193 219
-11 221 136 182 238
-12 178 136 205 238
-13 187 167 236 196
-14 189 171 227 251
-15 133 244 159 241
-16 209 155 201 180
-17 232 213 148 192
-18 143 165 208 219
-19 221 182 183 197
-20 158 172 229 252
-21 253 191 170 237
-22 176 158 218 229
-23 158 170 237 238
-24 253 254 256 130
-25 222 147 246 139
-26 143 144 249 130
-27 132 253 254 225
-28 246 137 247 139
-29 143 210 134 249
-30 188 178 224 205
-31 167 157 236 240
-32 220 189 169 251
-33 133 156 207 241
-34 209 220 155 140
-35 177 232 211 148
-36 165 179 215 208
-37 210 183 163 197
-38 160 172 216 252
-39 253 191 138 204
-40 176 198 161 218
-41 158 246 238 153
-42 256 235 130 186
-43 242 222 147 181
-44 144 147 217 130
-45 191 129 228 175
-46 233 203 173 153
-47 168 214 163 219
-48 144 255 191 129
-49 233 217 142 153
-50 255 168 256 219
-51 176 221 192 196
-52 190 138 227 250
-53 154 159 194 239
-54 165 201 161 197
-55 187 213 182 218
-56 154 192 196 230
-57 145 245 138 227
-58 159 194 184 206
-59 165 243 201 164
-60 187 213 239 141
-61 176 221 149 250
-62 132 243 156 225
-63 223 169 137 247
-64 210 134 245 152
-65 188 200 224 162
-66 157 151 240 241
-67 220 188 169 216
-68 156 180 207 208
-69 220 203 140 173
-70 133 177 211 195
-71 179 223 169 215
-72 210 135 163 251
-73 146 212 160 216
-74 135 138 204 226
-75 198 134 214 161
-76 246 150 194 153
-77 235 141 186 230
-78 242 190 181 250
-79 178 147 217 252
-80 228 207 164 175
-81 145 214 248 163
-82 231 144 255 185
-83 166 199 217 142
-84 222 255 256 142
-85 154 231 239 185
-86 242 166 161 197
-87 190 234 182 218
-88 171 204 248 152
-89 244 202 150 174
-90 234 149 171 204
-91 244 150 141 230
-92 198 180 183 208
-93 222 172 205 142
-94 231 232 167 186
-95 134 189 214 226
-96 209 179 225 175
-97 235 148 236 185
-98 177 172 205 240
-99 188 232 167 216
-100 189 226 184 206
-101 133 248 195 152
-102 209 179 202 184
-103 224 148 236 160
-104 178 211 157 252
-105 154 137 203 230
-106 145 245 151 241
-107 243 151 195 164
-108 247 173 239 141
-109 132 149 228 250
-110 243 156 146 212
-111 200 146 245 152
-112 200 162 207 164
-113 135 202 174 251
-114 135 223 226 140
-115 150 194 151 195
-116 145 212 248 162
-117 166 199 234 149
-118 231 242 166 186
-119 190 234 225 175
-120 198 199 181 183
-121 199 235 181 185
-122 155 215 206 174
-123 132 155 215 228
-124 200 146 247 173
-125 177 202 184 240
-126 223 224 160 140
-127 211 157 206 174
-128 212 137 203 162
-129 45 2 48 6
-130 44 24 26 42
-131 1 2 4 5
-132 123 27 62 109
-133 33 101 15 70
-134 29 95 64 75
-135 113 114 72 74
-136 11 1 12 3
-137 28 105 128 63
-138 57 39 52 74
-139 3 25 28 7
-140 34 69 114 126
-141 77 91 60 108
-142 49 93 83 84
-143 26 18 29 10
-144 44 26 48 82
-145 57 81 116 106
-146 110 111 124 73
-147 44 79 25 43
-148 35 103 17 97
-149 90 61 117 109
-150 89 91 115 76
-151 66 115 106 107
-152 88 111 101 64
-153 46 49 41 76
-154 56 105 85 53
-155 34 122 123 16
-156 33 110 68 62
-157 66 104 127 31
-158 22 23 41 20
-159 58 15 7 53
-160 103 38 126 73
-161 40 75 86 54
-162 112 116 128 65
-163 47 37 81 72
-164 112 80 59 107
-165 36 59 18 54
-166 83 117 118 86
-167 99 13 94 31
-168 47 4 50 8
-169 67 71 63 32
-170 23 9 10 21
-171 88 90 14 6
-172 38 93 20 98
-173 46 69 124 108
-174 89 122 113 127
-175 45 80 96 119
-176 22 61 40 51
-177 35 70 125 98
-178 12 79 104 30
-179 36 102 71 96
-180 68 92 16 8
-181 121 78 43 120
-182 11 55 19 87
-183 37 92 19 120
-184 100 58 102 125
-185 121 82 85 97
-186 77 94 118 42
-187 55 13 5 60
-188 99 67 30 65
-189 100 14 95 32
-190 78 52 119 87
-191 45 48 39 21
-192 56 17 51 9
-193 1 2 9 10
-194 58 115 53 76
-195 101 70 115 107
-196 56 13 5 51
-197 37 19 86 54
-198 92 40 75 120
-199 121 83 117 120
-200 111 112 124 65
-201 59 16 8 54
-202 89 102 113 125
-203 46 69 105 128
-204 88 90 39 74
-205 12 93 30 98
-206 100 122 58 127
-207 33 68 112 80
-208 68 36 92 18
-209 34 102 16 96
-210 37 72 29 64
-211 35 70 104 127
-212 110 116 73 128
-213 55 60 17 9
-214 47 81 95 75
-215 122 123 36 71
-216 99 67 38 73
-217 44 79 49 83
-218 22 55 40 87
-219 47 50 18 10
-220 34 67 69 32
-221 11 61 51 19
-222 25 93 84 43
-223 114 71 126 63
-224 103 126 30 65
-225 27 62 96 119
-226 100 114 95 74
-227 57 14 6 52
-228 45 123 80 109
-229 22 1 3 20
-230 77 56 91 105
-231 82 94 85 118
-232 99 35 17 94
-233 46 3 49 7
-234 90 117 119 87
-235 77 121 42 97
-236 13 103 31 97
-237 23 4 5 21
-238 11 12 23 41
-239 60 85 53 108
-240 66 125 31 98
-241 33 66 15 106
-242 78 118 86 43
-243 110 59 62 107
-244 89 91 15 7
-245 111 57 106 64
-246 25 28 41 76
-247 124 28 63 108
-248 88 101 81 116
-249 4 26 29 8
-250 78 61 52 109
-251 14 113 72 32
-252 79 38 104 20
-253 24 27 39 21
-254 2 24 27 6
-255 48 82 50 84
-256 24 50 84 42
0