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