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