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