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