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