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