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