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