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