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