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