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