Graph forms
for C4 [ 272, 24 ] = PL(Br(8,17;4))
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On this page are computer-accessible forms for the graph C4[ 272, 24 ] =
PL(Br(8,17;4)).
(I) Following is a form readable by MAGMA:
g:=Graph<272|{ {128, 193}, {128, 200}, {129, 201}, {128, 201}, {128, 208}, {129,
209}, {129, 208}, {130, 209}, {129, 216}, {130, 216}, {131, 217}, {130, 217},
{130, 224}, {131, 225}, {131, 224}, {132, 225}, {131, 232}, {132, 232}, {133,
233}, {132, 233}, {132, 240}, {133, 241}, {133, 240}, {134, 241}, {133, 248},
{134, 248}, {135, 249}, {134, 249}, {19, 147}, {119, 247}, {85, 213}, {19, 146},
{50, 179}, {84, 213}, {49, 179}, {84, 214}, {85, 214}, {98, 230}, {107, 239},
{49, 180}, {106, 239}, {98, 231}, {72, 205}, {20, 146}, {110, 232}, {97, 231},
{59, 189}, {58, 188}, {50, 180}, {72, 206}, {20, 147}, {111, 232}, {97, 230},
{59, 188}, {58, 189}, {1, 137}, {111, 231}, {95, 215}, {36, 172}, {2, 138}, {37,
172}, {110, 231}, {95, 214}, {71, 206}, {76, 197}, {41, 163}, {71, 205}, {76,
198}, {1, 138}, {116, 255}, {40, 163}, {2, 137}, {40, 164}, {115, 255}, {99,
239}, {98, 238}, {57, 181}, {81, 221}, {41, 164}, {99, 238}, {98, 239}, {57,
180}, {75, 198}, {80, 221}, {20, 154}, {58, 180}, {37, 171}, {21, 155}, {75,
197}, {80, 222}, {20, 155}, {119, 248}, {58, 181}, {36, 171}, {21, 154}, {81,
222}, {10, 154}, {103, 247}, {95, 207}, {94, 206}, {11, 154}, {95, 206}, {94,
207}, {45, 188}, {11, 153}, {114, 224}, {100, 246}, {55, 165}, {46, 188}, {10,
153}, {115, 224}, {100, 247}, {55, 164}, {56, 172}, {99, 247}, {57, 173}, {46,
187}, {99, 246}, {57, 172}, {56, 173}, {45, 187}, {18, 138}, {19, 139}, {94,
198}, {18, 139}, {94, 199}, {19, 138}, {93, 199}, {106, 240}, {101, 255}, {100,
254}, {93, 198}, {107, 240}, {101, 254}, {100, 255}, {14, 146}, {56, 164}, {15,
146}, {56, 165}, {15, 145}, {14, 145}, {103, 248}, {53, 149}, {119, 215}, {85,
245}, {16, 177}, {118, 215}, {53, 148}, {16, 178}, {54, 148}, {49, 147}, {25,
187}, {24, 186}, {24, 187}, {54, 149}, {48, 147}, {25, 186}, {85, 246}, {6,
162}, {64, 228}, {48, 148}, {23, 179}, {73, 237}, {7, 162}, {109, 200}, {106,
207}, {64, 229}, {49, 148}, {23, 178}, {72, 237}, {7, 161}, {110, 200}, {105,
207}, {72, 238}, {6, 161}, {73, 238}, {2, 170}, {36, 140}, {35, 139}, {77, 229},
{3, 170}, {110, 199}, {76, 229}, {3, 169}, {109, 199}, {55, 157}, {54, 156},
{24, 178}, {76, 230}, {2, 169}, {55, 156}, {54, 157}, {24, 179}, {77, 230}, {64,
236}, {115, 223}, {65, 237}, {81, 253}, {82, 254}, {64, 237}, {114, 223}, {65,
236}, {118, 216}, {35, 140}, {119, 216}, {36, 139}, {81, 254}, {82, 253}, {44,
156}, {69, 245}, {11, 186}, {113, 192}, {45, 156}, {11, 185}, {114, 192}, {69,
246}, {22, 162}, {65, 245}, {12, 185}, {22, 163}, {65, 244}, {12, 186}, {96,
214}, {45, 155}, {21, 163}, {66, 244}, {21, 162}, {127, 200}, {96, 215}, {44,
155}, {66, 245}, {52, 140}, {53, 141}, {52, 141}, {105, 208}, {53, 140}, {106,
208}, {22, 170}, {23, 171}, {15, 178}, {23, 170}, {22, 171}, {15, 177}, {127,
193}, {126, 192}, {97, 223}, {96, 222}, {66, 252}, {67, 253}, {66, 253}, {127,
192}, {97, 222}, {96, 223}, {67, 252}, {17, 209}, {51, 243}, {87, 151}, {16,
209}, {118, 183}, {87, 150}, {16, 210}, {117, 183}, {17, 210}, {82, 150}, {108,
168}, {7, 194}, {125, 184}, {109, 168}, {83, 150}, {7, 193}, {127, 185}, {126,
184}, {105, 175}, {29, 219}, {28, 218}, {83, 149}, {88, 158}, {89, 159}, {28,
219}, {126, 185}, {104, 175}, {51, 244}, {29, 218}, {82, 149}, {88, 159}, {89,
158}, {27, 211}, {43, 227}, {69, 141}, {70, 142}, {3, 202}, {42, 227}, {27,
210}, {8, 193}, {3, 201}, {109, 167}, {38, 236}, {8, 194}, {39, 236}, {108,
167}, {48, 251}, {69, 142}, {70, 141}, {39, 235}, {125, 177}, {124, 176}, {48,
252}, {4, 201}, {125, 176}, {117, 184}, {114, 191}, {38, 235}, {4, 202}, {118,
184}, {113, 191}, {42, 228}, {28, 210}, {88, 150}, {28, 211}, {126, 177}, {43,
228}, {88, 151}, {26, 202}, {112, 160}, {35, 243}, {27, 203}, {78, 158}, {26,
203}, {113, 160}, {27, 202}, {79, 158}, {32, 242}, {79, 157}, {32, 243}, {123,
168}, {47, 252}, {78, 157}, {13, 217}, {125, 169}, {124, 168}, {47, 251}, {12,
217}, {124, 169}, {12, 218}, {13, 218}, {35, 244}, {26, 194}, {104, 176}, {86,
142}, {87, 143}, {26, 195}, {105, 176}, {86, 143}, {87, 142}, {25, 195}, {123,
161}, {122, 160}, {63, 229}, {33, 251}, {32, 250}, {25, 194}, {123, 160}, {63,
228}, {33, 250}, {32, 251}, {124, 161}, {17, 241}, {51, 211}, {50, 211}, {121,
152}, {84, 181}, {62, 220}, {123, 153}, {122, 152}, {117, 151}, {63, 221}, {84,
182}, {92, 190}, {93, 191}, {17, 242}, {122, 153}, {116, 151}, {63, 220}, {62,
221}, {92, 191}, {93, 190}, {83, 182}, {50, 212}, {83, 181}, {51, 212}, {104,
143}, {9, 225}, {121, 145}, {120, 144}, {103, 143}, {61, 213}, {70, 174}, {8,
225}, {121, 144}, {61, 212}, {42, 195}, {37, 204}, {71, 174}, {8, 226}, {62,
212}, {41, 195}, {38, 204}, {71, 173}, {92, 182}, {9, 226}, {122, 145}, {62,
213}, {70, 173}, {92, 183}, {5, 233}, {116, 152}, {31, 243}, {74, 166}, {91,
183}, {4, 233}, {117, 152}, {41, 196}, {38, 203}, {31, 242}, {75, 166}, {80,
189}, {91, 182}, {4, 234}, {113, 159}, {42, 196}, {37, 203}, {75, 165}, {80,
190}, {5, 234}, {112, 159}, {74, 165}, {1, 241}, {121, 137}, {61, 205}, {60,
204}, {60, 205}, {120, 137}, {61, 204}, {79, 190}, {46, 220}, {79, 189}, {1,
242}, {47, 220}, {13, 249}, {47, 219}, {31, 235}, {30, 234}, {14, 250}, {90,
174}, {91, 175}, {30, 235}, {46, 219}, {31, 234}, {90, 175}, {91, 174}, {13,
250}, {103, 144}, {14, 249}, {60, 196}, {104, 144}, {60, 197}, {30, 226}, {90,
166}, {30, 227}, {90, 167}, {29, 227}, {59, 197}, {89, 167}, {29, 226}, {59,
196}, {89, 166}, {9, 257}, {10, 258}, {9, 258}, {10, 257}, {5, 265}, {6, 266},
{5, 266}, {6, 265}, {18, 266}, {18, 267}, {34, 258}, {34, 259}, {33, 259}, {33,
258}, {40, 267}, {40, 268}, {34, 266}, {44, 260}, {43, 259}, {34, 267}, {39,
268}, {39, 267}, {43, 260}, {44, 259}, {52, 268}, {52, 269}, {68, 260}, {68,
261}, {73, 269}, {74, 270}, {67, 261}, {67, 260}, {73, 270}, {74, 269}, {68,
268}, {77, 261}, {78, 262}, {68, 269}, {77, 262}, {78, 261}, {86, 270}, {86,
271}, {102, 262}, {102, 263}, {101, 263}, {101, 262}, {108, 271}, {107, 271},
{111, 264}, {102, 270}, {120, 272}, {111, 263}, {102, 271}, {120, 265}, {115,
256}, {116, 256}, {112, 263}, {112, 264}, {107, 272}, {108, 272}, {136, 264},
{136, 265}, {134, 256}, {135, 257}, {135, 256}, {136, 257}, {135, 264}, {136,
272} }>;
(II) A more general form is to represent the graph as the orbit of {128, 193}
under the group generated by the following permutations:
a: (1, 2)(3, 17)(4, 16)(5, 15)(6, 14)(7, 13)(8, 12)(9, 11)(18, 19)(20, 34)(21,
33)(22, 32)(23, 31)(24, 30)(25, 29)(26, 28)(35, 36)(37, 51)(38, 50)(39, 49)(40,
48)(41, 47)(42, 46)(43, 45)(52, 53)(54, 68)(55, 67)(56, 66)(57, 65)(58, 64)(59,
63)(60, 62)(69, 70)(71, 85)(72, 84)(73, 83)(74, 82)(75, 81)(76, 80)(77, 79)(86,
87)(88, 102)(89, 101)(90, 100)(91, 99)(92, 98)(93, 97)(94, 96)(103, 104)(105,
119)(106, 118)(107, 117)(108, 116)(109, 115)(110, 114)(111, 113)(120, 121)(122,
136)(123, 135)(124, 134)(125, 133)(126, 132)(127, 131)(128, 130)(145, 265)(146,
266)(147, 267)(148, 268)(149, 269)(150, 270)(151, 271)(152, 272)(153, 257)(154,
258)(155, 259)(156, 260)(157, 261)(158, 262)(159, 263)(160, 264)(161, 249)(162,
250)(163, 251)(164, 252)(165, 253)(166, 254)(167, 255)(168, 256)(169, 241)(170,
242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 233)(178,
234)(179, 235)(180, 236)(181, 237)(182, 238)(183, 239)(184, 240)(185, 225)(186,
226)(187, 227)(188, 228)(189, 229)(190, 230)(191, 231)(192, 232)(193, 217)(194,
218)(195, 219)(196, 220)(197, 221)(198, 222)(199, 223)(200, 224)(201, 209)(202,
210)(203, 211)(204, 212)(205, 213)(206, 214)(207, 215)(208, 216) (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, 18, 36, 53, 69, 86, 104, 121)(2, 19, 35, 52, 70, 87, 103, 120)(3, 20, 51,
68, 71, 88, 119, 136)(4, 21, 50, 67, 72, 89, 118, 135)(5, 22, 49, 66, 73, 90,
117, 134)(6, 23, 48, 65, 74, 91, 116, 133)(7, 24, 47, 64, 75, 92, 115, 132)(8,
25, 46, 63, 76, 93, 114, 131)(9, 26, 45, 62, 77, 94, 113, 130)(10, 27, 44, 61,
78, 95, 112, 129)(11, 28, 43, 60, 79, 96, 111, 128)(12, 29, 42, 59, 80, 97, 110,
127)(13, 30, 41, 58, 81, 98, 109, 126)(14, 31, 40, 57, 82, 99, 108, 125)(15, 32,
39, 56, 83, 100, 107, 124)(16, 33, 38, 55, 84, 101, 106, 123)(17, 34, 37, 54,
85, 102, 105, 122)(137, 138, 139, 140, 141, 142, 143, 144)(145, 242, 267, 172,
149, 246, 271, 176)(146, 243, 268, 173, 150, 247, 272, 169)(147, 244, 269, 174,
151, 248, 265, 170)(148, 245, 270, 175, 152, 241, 266, 171)(153, 210, 259, 204,
157, 214, 263, 208)(154, 211, 260, 205, 158, 215, 264, 201)(155, 212, 261, 206,
159, 216, 257, 202)(156, 213, 262, 207, 160, 209, 258, 203)(161, 178, 251, 236,
165, 182, 255, 240)(162, 179, 252, 237, 166, 183, 256, 233)(163, 180, 253, 238,
167, 184, 249, 234)(164, 181, 254, 239, 168, 177, 250, 235)(185, 218, 227, 196,
189, 222, 231, 200)(186, 219, 228, 197, 190, 223, 232, 193)(187, 220, 229, 198,
191, 224, 225, 194)(188, 221, 230, 199, 192, 217, 226, 195)
c: (18, 120)(19, 121)(20, 122)(21, 123)(22, 124)(23, 125)(24, 126)(25, 127)(26,
128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 134)(33, 135)(34, 136)(35,
103)(36, 104)(37, 105)(38, 106)(39, 107)(40, 108)(41, 109)(42, 110)(43, 111)(44,
112)(45, 113)(46, 114)(47, 115)(48, 116)(49, 117)(50, 118)(51, 119)(52, 86)(53,
87)(54, 88)(55, 89)(56, 90)(57, 91)(58, 92)(59, 93)(60, 94)(61, 95)(62, 96)(63,
97)(64, 98)(65, 99)(66, 100)(67, 101)(68, 102)(137, 138)(139, 144)(140,
143)(141, 142)(145, 146)(147, 152)(148, 151)(149, 150)(153, 154)(155, 160)(156,
159)(157, 158)(161, 162)(163, 168)(164, 167)(165, 166)(169, 170)(171, 176)(172,
175)(173, 174)(177, 178)(179, 184)(180, 183)(181, 182)(185, 186)(187, 192)(188,
191)(189, 190)(193, 194)(195, 200)(196, 199)(197, 198)(201, 202)(203, 208)(204,
207)(205, 206)(209, 210)(211, 216)(212, 215)(213, 214)(217, 218)(219, 224)(220,
223)(221, 222)(225, 226)(227, 232)(228, 231)(229, 230)(233, 234)(235, 240)(236,
239)(237, 238)(241, 242)(243, 248)(244, 247)(245, 246)(249, 250)(251, 256)(252,
255)(253, 254)(257, 258)(259, 264)(260, 263)(261, 262)(265, 266)(267, 272)(268,
271)(269, 270)
d: (2, 17)(3, 16)(4, 15)(5, 14)(6, 13)(7, 12)(8, 11)(9, 10)(18, 32)(19, 31)(20,
30)(21, 29)(22, 28)(23, 27)(24, 26)(33, 34)(36, 51)(37, 50)(38, 49)(39, 48)(40,
47)(41, 46)(42, 45)(43, 44)(52, 66)(53, 65)(54, 64)(55, 63)(56, 62)(57, 61)(58,
60)(67, 68)(70, 85)(71, 84)(72, 83)(73, 82)(74, 81)(75, 80)(76, 79)(77, 78)(86,
100)(87, 99)(88, 98)(89, 97)(90, 96)(91, 95)(92, 94)(101, 102)(104, 119)(105,
118)(106, 117)(107, 116)(108, 115)(109, 114)(110, 113)(111, 112)(120, 134)(121,
133)(122, 132)(123, 131)(124, 130)(125, 129)(126, 128)(135, 136)(137, 241)(138,
242)(139, 243)(140, 244)(141, 245)(142, 246)(143, 247)(144, 248)(145, 233)(146,
234)(147, 235)(148, 236)(149, 237)(150, 238)(151, 239)(152, 240)(153, 225)(154,
226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 217)(162,
218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)(169, 209)(170,
210)(171, 211)(172, 212)(173, 213)(174, 214)(175, 215)(176, 216)(177, 201)(178,
202)(179, 203)(180, 204)(181, 205)(182, 206)(183, 207)(184, 208)(185, 193)(186,
194)(187, 195)(188, 196)(189, 197)(190, 198)(191, 199)(192, 200)(249, 265)(250,
266)(251, 267)(252, 268)(253, 269)(254, 270)(255, 271)(256, 272)
C4[ 272, 24 ]
272
-1 242 137 138 241
-2 169 137 170 138
-3 201 169 202 170
-4 233 201 234 202
-5 265 233 266 234
-6 265 266 161 162
-7 193 161 194 162
-8 225 193 226 194
-9 257 225 258 226
-10 154 257 258 153
-11 154 185 153 186
-12 217 185 218 186
-13 249 217 250 218
-14 145 146 249 250
-15 177 145 178 146
-16 209 177 210 178
-17 209 242 210 241
-18 266 267 138 139
-19 146 147 138 139
-20 154 155 146 147
-21 154 155 162 163
-22 170 171 162 163
-23 178 179 170 171
-24 187 178 179 186
-25 187 194 195 186
-26 202 203 194 195
-27 210 211 202 203
-28 210 211 218 219
-29 226 227 218 219
-30 234 235 226 227
-31 242 243 234 235
-32 242 243 250 251
-33 258 259 250 251
-34 266 267 258 259
-35 243 244 139 140
-36 171 139 172 140
-37 203 171 204 172
-38 235 203 236 204
-39 267 235 268 236
-40 267 268 163 164
-41 195 163 196 164
-42 227 195 228 196
-43 259 227 260 228
-44 155 156 259 260
-45 187 155 188 156
-46 187 220 188 219
-47 220 251 219 252
-48 147 148 251 252
-49 179 147 180 148
-50 211 179 212 180
-51 243 211 244 212
-52 268 269 140 141
-53 148 149 140 141
-54 156 157 148 149
-55 165 156 157 164
-56 165 172 173 164
-57 180 181 172 173
-58 188 189 180 181
-59 188 189 196 197
-60 204 205 196 197
-61 212 213 204 205
-62 220 221 212 213
-63 220 221 228 229
-64 236 237 228 229
-65 244 245 236 237
-66 253 244 245 252
-67 253 260 261 252
-68 268 269 260 261
-69 245 246 141 142
-70 173 141 174 142
-71 205 173 206 174
-72 237 205 238 206
-73 269 237 270 238
-74 165 166 269 270
-75 165 198 166 197
-76 198 229 197 230
-77 261 229 262 230
-78 157 158 261 262
-79 189 157 190 158
-80 221 189 222 190
-81 253 221 254 222
-82 253 254 149 150
-83 181 149 182 150
-84 213 181 214 182
-85 245 213 246 214
-86 143 270 271 142
-87 143 150 151 142
-88 158 159 150 151
-89 166 167 158 159
-90 166 167 174 175
-91 182 183 174 175
-92 190 191 182 183
-93 198 199 190 191
-94 198 199 206 207
-95 214 215 206 207
-96 222 223 214 215
-97 231 222 223 230
-98 231 238 239 230
-99 246 247 238 239
-100 254 255 246 247
-101 254 255 262 263
-102 270 271 262 263
-103 143 144 247 248
-104 143 176 144 175
-105 176 207 175 208
-106 239 207 240 208
-107 271 239 272 240
-108 167 168 271 272
-109 199 167 200 168
-110 231 199 232 200
-111 231 264 232 263
-112 264 159 160 263
-113 191 159 192 160
-114 223 191 224 192
-115 255 223 256 224
-116 255 256 151 152
-117 183 151 184 152
-118 215 183 216 184
-119 247 215 248 216
-120 144 265 137 272
-121 144 145 137 152
-122 145 160 152 153
-123 168 160 161 153
-124 176 168 169 161
-125 176 177 169 184
-126 177 192 184 185
-127 200 192 193 185
-128 200 201 193 208
-129 209 201 216 208
-130 209 224 216 217
-131 232 224 225 217
-132 232 233 225 240
-133 233 248 240 241
-134 256 248 249 241
-135 264 256 257 249
-136 264 265 257 272
-137 121 1 2 120
-138 1 2 18 19
-139 35 36 18 19
-140 35 36 52 53
-141 69 70 52 53
-142 69 70 86 87
-143 103 104 86 87
-144 121 103 104 120
-145 121 122 14 15
-146 14 15 19 20
-147 48 49 19 20
-148 48 49 53 54
-149 82 83 53 54
-150 88 82 83 87
-151 88 116 117 87
-152 121 122 116 117
-153 11 122 123 10
-154 11 20 10 21
-155 44 45 20 21
-156 44 55 45 54
-157 55 78 79 54
-158 88 78 89 79
-159 88 89 112 113
-160 122 112 123 113
-161 123 124 6 7
-162 22 6 7 21
-163 22 40 41 21
-164 55 56 40 41
-165 55 56 74 75
-166 89 90 74 75
-167 89 90 108 109
-168 123 124 108 109
-169 2 3 124 125
-170 22 23 2 3
-171 22 23 36 37
-172 56 57 36 37
-173 56 57 70 71
-174 90 91 70 71
-175 90 91 104 105
-176 124 125 104 105
-177 15 125 16 126
-178 23 24 15 16
-179 23 24 49 50
-180 57 58 49 50
-181 57 58 83 84
-182 91 92 83 84
-183 91 92 117 118
-184 125 126 117 118
-185 11 12 126 127
-186 11 12 24 25
-187 45 24 46 25
-188 45 46 58 59
-189 79 58 80 59
-190 79 80 92 93
-191 113 92 114 93
-192 113 114 126 127
-193 127 7 128 8
-194 25 26 7 8
-195 25 26 41 42
-196 59 60 41 42
-197 59 60 75 76
-198 93 94 75 76
-199 110 93 94 109
-200 110 127 128 109
-201 3 4 128 129
-202 3 4 26 27
-203 26 37 27 38
-204 37 38 60 61
-205 60 71 61 72
-206 71 72 94 95
-207 94 105 95 106
-208 105 106 128 129
-209 16 17 129 130
-210 16 27 17 28
-211 27 28 50 51
-212 50 61 51 62
-213 61 62 84 85
-214 84 95 85 96
-215 95 96 118 119
-216 118 129 119 130
-217 12 13 130 131
-218 12 13 28 29
-219 46 47 28 29
-220 46 47 62 63
-221 80 81 62 63
-222 80 81 96 97
-223 114 115 96 97
-224 114 115 130 131
-225 132 8 9 131
-226 29 8 30 9
-227 29 30 42 43
-228 63 42 64 43
-229 77 63 64 76
-230 77 97 76 98
-231 110 111 97 98
-232 110 132 111 131
-233 132 133 4 5
-234 4 5 30 31
-235 38 39 30 31
-236 38 39 64 65
-237 72 73 64 65
-238 99 72 73 98
-239 99 106 107 98
-240 132 133 106 107
-241 1 133 134 17
-242 1 17 31 32
-243 35 51 31 32
-244 66 35 51 65
-245 66 69 85 65
-246 99 100 69 85
-247 99 100 103 119
-248 133 134 103 119
-249 13 134 14 135
-250 33 13 14 32
-251 33 47 48 32
-252 66 67 47 48
-253 66 67 81 82
-254 100 101 81 82
-255 100 101 115 116
-256 134 135 115 116
-257 135 136 9 10
-258 33 34 9 10
-259 33 44 34 43
-260 44 67 68 43
-261 77 67 78 68
-262 77 78 101 102
-263 111 101 112 102
-264 111 112 135 136
-265 136 5 6 120
-266 34 5 6 18
-267 34 39 18 40
-268 68 39 40 52
-269 68 73 52 74
-270 102 73 74 86
-271 102 107 86 108
-272 136 107 108 120
0