Copied to
clipboard

## G = C2×C33⋊7C8order 432 = 24·33

### Direct product of C2 and C33⋊7C8

Series: Derived Chief Lower central Upper central

 Derived series C1 — C33 — C2×C33⋊7C8
 Chief series C1 — C3 — C32 — C33 — C32×C6 — C32×C12 — C33⋊7C8 — C2×C33⋊7C8
 Lower central C33 — C2×C33⋊7C8
 Upper central C1 — C2×C4

Generators and relations for C2×C337C8
G = < a,b,c,d,e | a2=b3=c3=d3=e8=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, ebe-1=b-1, cd=dc, ece-1=c-1, ede-1=d-1 >

Subgroups: 776 in 308 conjugacy classes, 227 normal (13 characteristic)
C1, C2, C2, C3, C4, C22, C6, C8, C2×C4, C32, C12, C2×C6, C2×C8, C3×C6, C3⋊C8, C2×C12, C33, C3×C12, C62, C2×C3⋊C8, C32×C6, C32×C6, C324C8, C6×C12, C32×C12, C3×C62, C2×C324C8, C337C8, C3×C6×C12, C2×C337C8
Quotients: C1, C2, C4, C22, S3, C8, C2×C4, Dic3, D6, C2×C8, C3⋊S3, C3⋊C8, C2×Dic3, C3⋊Dic3, C2×C3⋊S3, C2×C3⋊C8, C33⋊C2, C324C8, C2×C3⋊Dic3, C335C4, C2×C33⋊C2, C2×C324C8, C337C8, C2×C335C4, C2×C337C8

Smallest permutation representation of C2×C337C8
Regular action on 432 points
Generators in S432
(1 262)(2 263)(3 264)(4 257)(5 258)(6 259)(7 260)(8 261)(9 104)(10 97)(11 98)(12 99)(13 100)(14 101)(15 102)(16 103)(17 301)(18 302)(19 303)(20 304)(21 297)(22 298)(23 299)(24 300)(25 154)(26 155)(27 156)(28 157)(29 158)(30 159)(31 160)(32 153)(33 279)(34 280)(35 273)(36 274)(37 275)(38 276)(39 277)(40 278)(41 287)(42 288)(43 281)(44 282)(45 283)(46 284)(47 285)(48 286)(49 186)(50 187)(51 188)(52 189)(53 190)(54 191)(55 192)(56 185)(57 243)(58 244)(59 245)(60 246)(61 247)(62 248)(63 241)(64 242)(65 222)(66 223)(67 224)(68 217)(69 218)(70 219)(71 220)(72 221)(73 230)(74 231)(75 232)(76 225)(77 226)(78 227)(79 228)(80 229)(81 210)(82 211)(83 212)(84 213)(85 214)(86 215)(87 216)(88 209)(89 254)(90 255)(91 256)(92 249)(93 250)(94 251)(95 252)(96 253)(105 308)(106 309)(107 310)(108 311)(109 312)(110 305)(111 306)(112 307)(113 334)(114 335)(115 336)(116 329)(117 330)(118 331)(119 332)(120 333)(121 342)(122 343)(123 344)(124 337)(125 338)(126 339)(127 340)(128 341)(129 431)(130 432)(131 425)(132 426)(133 427)(134 428)(135 429)(136 430)(137 366)(138 367)(139 368)(140 361)(141 362)(142 363)(143 364)(144 365)(145 374)(146 375)(147 376)(148 369)(149 370)(150 371)(151 372)(152 373)(161 355)(162 356)(163 357)(164 358)(165 359)(166 360)(167 353)(168 354)(169 390)(170 391)(171 392)(172 385)(173 386)(174 387)(175 388)(176 389)(177 398)(178 399)(179 400)(180 393)(181 394)(182 395)(183 396)(184 397)(193 414)(194 415)(195 416)(196 409)(197 410)(198 411)(199 412)(200 413)(201 422)(202 423)(203 424)(204 417)(205 418)(206 419)(207 420)(208 421)(233 328)(234 321)(235 322)(236 323)(237 324)(238 325)(239 326)(240 327)(265 352)(266 345)(267 346)(268 347)(269 348)(270 349)(271 350)(272 351)(289 384)(290 377)(291 378)(292 379)(293 380)(294 381)(295 382)(296 383)(313 408)(314 401)(315 402)(316 403)(317 404)(318 405)(319 406)(320 407)
(1 81 144)(2 137 82)(3 83 138)(4 139 84)(5 85 140)(6 141 86)(7 87 142)(8 143 88)(9 238 339)(10 340 239)(11 240 341)(12 342 233)(13 234 343)(14 344 235)(15 236 337)(16 338 237)(17 354 134)(18 135 355)(19 356 136)(20 129 357)(21 358 130)(22 131 359)(23 360 132)(24 133 353)(25 171 45)(26 46 172)(27 173 47)(28 48 174)(29 175 41)(30 42 176)(31 169 43)(32 44 170)(33 150 272)(34 265 151)(35 152 266)(36 267 145)(37 146 268)(38 269 147)(39 148 270)(40 271 149)(49 228 118)(50 119 229)(51 230 120)(52 113 231)(53 232 114)(54 115 225)(55 226 116)(56 117 227)(57 307 410)(58 411 308)(59 309 412)(60 413 310)(61 311 414)(62 415 312)(63 305 416)(64 409 306)(65 290 180)(66 181 291)(67 292 182)(68 183 293)(69 294 184)(70 177 295)(71 296 178)(72 179 289)(73 333 188)(74 189 334)(75 335 190)(76 191 336)(77 329 192)(78 185 330)(79 331 186)(80 187 332)(89 202 320)(90 313 203)(91 204 314)(92 315 205)(93 206 316)(94 317 207)(95 208 318)(96 319 201)(97 127 326)(98 327 128)(99 121 328)(100 321 122)(101 123 322)(102 323 124)(103 125 324)(104 325 126)(105 244 198)(106 199 245)(107 246 200)(108 193 247)(109 248 194)(110 195 241)(111 242 196)(112 197 243)(153 282 391)(154 392 283)(155 284 385)(156 386 285)(157 286 387)(158 388 287)(159 288 389)(160 390 281)(161 302 429)(162 430 303)(163 304 431)(164 432 297)(165 298 425)(166 426 299)(167 300 427)(168 428 301)(209 261 364)(210 365 262)(211 263 366)(212 367 264)(213 257 368)(214 361 258)(215 259 362)(216 363 260)(217 396 380)(218 381 397)(219 398 382)(220 383 399)(221 400 384)(222 377 393)(223 394 378)(224 379 395)(249 402 418)(250 419 403)(251 404 420)(252 421 405)(253 406 422)(254 423 407)(255 408 424)(256 417 401)(273 373 345)(274 346 374)(275 375 347)(276 348 376)(277 369 349)(278 350 370)(279 371 351)(280 352 372)
(1 302 398)(2 399 303)(3 304 400)(4 393 297)(5 298 394)(6 395 299)(7 300 396)(8 397 301)(9 315 391)(10 392 316)(11 317 385)(12 386 318)(13 319 387)(14 388 320)(15 313 389)(16 390 314)(17 261 184)(18 177 262)(19 263 178)(20 179 264)(21 257 180)(22 181 258)(23 259 182)(24 183 260)(25 419 326)(26 327 420)(27 421 328)(28 321 422)(29 423 322)(30 323 424)(31 417 324)(32 325 418)(33 58 332)(34 333 59)(35 60 334)(36 335 61)(37 62 336)(38 329 63)(39 64 330)(40 331 57)(41 254 123)(42 124 255)(43 256 125)(44 126 249)(45 250 127)(46 128 251)(47 252 121)(48 122 253)(49 112 350)(50 351 105)(51 106 352)(52 345 107)(53 108 346)(54 347 109)(55 110 348)(56 349 111)(65 358 368)(66 361 359)(67 360 362)(68 363 353)(69 354 364)(70 365 355)(71 356 366)(72 367 357)(73 412 151)(74 152 413)(75 414 145)(76 146 415)(77 416 147)(78 148 409)(79 410 149)(80 150 411)(81 429 382)(82 383 430)(83 431 384)(84 377 432)(85 425 378)(86 379 426)(87 427 380)(88 381 428)(89 344 287)(90 288 337)(91 338 281)(92 282 339)(93 340 283)(94 284 341)(95 342 285)(96 286 343)(97 171 403)(98 404 172)(99 173 405)(100 406 174)(101 175 407)(102 408 176)(103 169 401)(104 402 170)(113 273 246)(114 247 274)(115 275 248)(116 241 276)(117 277 242)(118 243 278)(119 279 244)(120 245 280)(129 289 212)(130 213 290)(131 291 214)(132 215 292)(133 293 216)(134 209 294)(135 295 210)(136 211 296)(137 220 162)(138 163 221)(139 222 164)(140 165 223)(141 224 166)(142 167 217)(143 218 168)(144 161 219)(153 238 205)(154 206 239)(155 240 207)(156 208 233)(157 234 201)(158 202 235)(159 236 203)(160 204 237)(185 270 306)(186 307 271)(187 272 308)(188 309 265)(189 266 310)(190 311 267)(191 268 312)(192 305 269)(193 374 232)(194 225 375)(195 376 226)(196 227 369)(197 370 228)(198 229 371)(199 372 230)(200 231 373)
(1 27 279)(2 280 28)(3 29 273)(4 274 30)(5 31 275)(6 276 32)(7 25 277)(8 278 26)(9 292 77)(10 78 293)(11 294 79)(12 80 295)(13 296 73)(14 74 289)(15 290 75)(16 76 291)(17 57 207)(18 208 58)(19 59 201)(20 202 60)(21 61 203)(22 204 62)(23 63 205)(24 206 64)(33 262 156)(34 157 263)(35 264 158)(36 159 257)(37 258 160)(38 153 259)(39 260 154)(40 155 261)(41 345 138)(42 139 346)(43 347 140)(44 141 348)(45 349 142)(46 143 350)(47 351 144)(48 137 352)(49 128 218)(50 219 121)(51 122 220)(52 221 123)(53 124 222)(54 223 125)(55 126 224)(56 217 127)(65 190 337)(66 338 191)(67 192 339)(68 340 185)(69 186 341)(70 342 187)(71 188 343)(72 344 189)(81 173 371)(82 372 174)(83 175 373)(84 374 176)(85 169 375)(86 376 170)(87 171 369)(88 370 172)(89 310 357)(90 358 311)(91 312 359)(92 360 305)(93 306 353)(94 354 307)(95 308 355)(96 356 309)(97 227 380)(98 381 228)(99 229 382)(100 383 230)(101 231 384)(102 377 232)(103 225 378)(104 379 226)(105 161 252)(106 253 162)(107 163 254)(108 255 164)(109 165 256)(110 249 166)(111 167 250)(112 251 168)(113 400 322)(114 323 393)(115 394 324)(116 325 395)(117 396 326)(118 327 397)(119 398 328)(120 321 399)(129 320 413)(130 414 313)(131 314 415)(132 416 315)(133 316 409)(134 410 317)(135 318 411)(136 412 319)(145 389 213)(146 214 390)(147 391 215)(148 216 392)(149 385 209)(150 210 386)(151 387 211)(152 212 388)(177 233 332)(178 333 234)(179 235 334)(180 335 236)(181 237 336)(182 329 238)(183 239 330)(184 331 240)(193 408 432)(194 425 401)(195 402 426)(196 427 403)(197 404 428)(198 429 405)(199 406 430)(200 431 407)(241 418 299)(242 300 419)(243 420 301)(244 302 421)(245 422 303)(246 304 423)(247 424 297)(248 298 417)(265 286 366)(266 367 287)(267 288 368)(268 361 281)(269 282 362)(270 363 283)(271 284 364)(272 365 285)
(1 2 3 4 5 6 7 8)(9 10 11 12 13 14 15 16)(17 18 19 20 21 22 23 24)(25 26 27 28 29 30 31 32)(33 34 35 36 37 38 39 40)(41 42 43 44 45 46 47 48)(49 50 51 52 53 54 55 56)(57 58 59 60 61 62 63 64)(65 66 67 68 69 70 71 72)(73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88)(89 90 91 92 93 94 95 96)(97 98 99 100 101 102 103 104)(105 106 107 108 109 110 111 112)(113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128)(129 130 131 132 133 134 135 136)(137 138 139 140 141 142 143 144)(145 146 147 148 149 150 151 152)(153 154 155 156 157 158 159 160)(161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176)(177 178 179 180 181 182 183 184)(185 186 187 188 189 190 191 192)(193 194 195 196 197 198 199 200)(201 202 203 204 205 206 207 208)(209 210 211 212 213 214 215 216)(217 218 219 220 221 222 223 224)(225 226 227 228 229 230 231 232)(233 234 235 236 237 238 239 240)(241 242 243 244 245 246 247 248)(249 250 251 252 253 254 255 256)(257 258 259 260 261 262 263 264)(265 266 267 268 269 270 271 272)(273 274 275 276 277 278 279 280)(281 282 283 284 285 286 287 288)(289 290 291 292 293 294 295 296)(297 298 299 300 301 302 303 304)(305 306 307 308 309 310 311 312)(313 314 315 316 317 318 319 320)(321 322 323 324 325 326 327 328)(329 330 331 332 333 334 335 336)(337 338 339 340 341 342 343 344)(345 346 347 348 349 350 351 352)(353 354 355 356 357 358 359 360)(361 362 363 364 365 366 367 368)(369 370 371 372 373 374 375 376)(377 378 379 380 381 382 383 384)(385 386 387 388 389 390 391 392)(393 394 395 396 397 398 399 400)(401 402 403 404 405 406 407 408)(409 410 411 412 413 414 415 416)(417 418 419 420 421 422 423 424)(425 426 427 428 429 430 431 432)

G:=sub<Sym(432)| (1,262)(2,263)(3,264)(4,257)(5,258)(6,259)(7,260)(8,261)(9,104)(10,97)(11,98)(12,99)(13,100)(14,101)(15,102)(16,103)(17,301)(18,302)(19,303)(20,304)(21,297)(22,298)(23,299)(24,300)(25,154)(26,155)(27,156)(28,157)(29,158)(30,159)(31,160)(32,153)(33,279)(34,280)(35,273)(36,274)(37,275)(38,276)(39,277)(40,278)(41,287)(42,288)(43,281)(44,282)(45,283)(46,284)(47,285)(48,286)(49,186)(50,187)(51,188)(52,189)(53,190)(54,191)(55,192)(56,185)(57,243)(58,244)(59,245)(60,246)(61,247)(62,248)(63,241)(64,242)(65,222)(66,223)(67,224)(68,217)(69,218)(70,219)(71,220)(72,221)(73,230)(74,231)(75,232)(76,225)(77,226)(78,227)(79,228)(80,229)(81,210)(82,211)(83,212)(84,213)(85,214)(86,215)(87,216)(88,209)(89,254)(90,255)(91,256)(92,249)(93,250)(94,251)(95,252)(96,253)(105,308)(106,309)(107,310)(108,311)(109,312)(110,305)(111,306)(112,307)(113,334)(114,335)(115,336)(116,329)(117,330)(118,331)(119,332)(120,333)(121,342)(122,343)(123,344)(124,337)(125,338)(126,339)(127,340)(128,341)(129,431)(130,432)(131,425)(132,426)(133,427)(134,428)(135,429)(136,430)(137,366)(138,367)(139,368)(140,361)(141,362)(142,363)(143,364)(144,365)(145,374)(146,375)(147,376)(148,369)(149,370)(150,371)(151,372)(152,373)(161,355)(162,356)(163,357)(164,358)(165,359)(166,360)(167,353)(168,354)(169,390)(170,391)(171,392)(172,385)(173,386)(174,387)(175,388)(176,389)(177,398)(178,399)(179,400)(180,393)(181,394)(182,395)(183,396)(184,397)(193,414)(194,415)(195,416)(196,409)(197,410)(198,411)(199,412)(200,413)(201,422)(202,423)(203,424)(204,417)(205,418)(206,419)(207,420)(208,421)(233,328)(234,321)(235,322)(236,323)(237,324)(238,325)(239,326)(240,327)(265,352)(266,345)(267,346)(268,347)(269,348)(270,349)(271,350)(272,351)(289,384)(290,377)(291,378)(292,379)(293,380)(294,381)(295,382)(296,383)(313,408)(314,401)(315,402)(316,403)(317,404)(318,405)(319,406)(320,407), (1,81,144)(2,137,82)(3,83,138)(4,139,84)(5,85,140)(6,141,86)(7,87,142)(8,143,88)(9,238,339)(10,340,239)(11,240,341)(12,342,233)(13,234,343)(14,344,235)(15,236,337)(16,338,237)(17,354,134)(18,135,355)(19,356,136)(20,129,357)(21,358,130)(22,131,359)(23,360,132)(24,133,353)(25,171,45)(26,46,172)(27,173,47)(28,48,174)(29,175,41)(30,42,176)(31,169,43)(32,44,170)(33,150,272)(34,265,151)(35,152,266)(36,267,145)(37,146,268)(38,269,147)(39,148,270)(40,271,149)(49,228,118)(50,119,229)(51,230,120)(52,113,231)(53,232,114)(54,115,225)(55,226,116)(56,117,227)(57,307,410)(58,411,308)(59,309,412)(60,413,310)(61,311,414)(62,415,312)(63,305,416)(64,409,306)(65,290,180)(66,181,291)(67,292,182)(68,183,293)(69,294,184)(70,177,295)(71,296,178)(72,179,289)(73,333,188)(74,189,334)(75,335,190)(76,191,336)(77,329,192)(78,185,330)(79,331,186)(80,187,332)(89,202,320)(90,313,203)(91,204,314)(92,315,205)(93,206,316)(94,317,207)(95,208,318)(96,319,201)(97,127,326)(98,327,128)(99,121,328)(100,321,122)(101,123,322)(102,323,124)(103,125,324)(104,325,126)(105,244,198)(106,199,245)(107,246,200)(108,193,247)(109,248,194)(110,195,241)(111,242,196)(112,197,243)(153,282,391)(154,392,283)(155,284,385)(156,386,285)(157,286,387)(158,388,287)(159,288,389)(160,390,281)(161,302,429)(162,430,303)(163,304,431)(164,432,297)(165,298,425)(166,426,299)(167,300,427)(168,428,301)(209,261,364)(210,365,262)(211,263,366)(212,367,264)(213,257,368)(214,361,258)(215,259,362)(216,363,260)(217,396,380)(218,381,397)(219,398,382)(220,383,399)(221,400,384)(222,377,393)(223,394,378)(224,379,395)(249,402,418)(250,419,403)(251,404,420)(252,421,405)(253,406,422)(254,423,407)(255,408,424)(256,417,401)(273,373,345)(274,346,374)(275,375,347)(276,348,376)(277,369,349)(278,350,370)(279,371,351)(280,352,372), (1,302,398)(2,399,303)(3,304,400)(4,393,297)(5,298,394)(6,395,299)(7,300,396)(8,397,301)(9,315,391)(10,392,316)(11,317,385)(12,386,318)(13,319,387)(14,388,320)(15,313,389)(16,390,314)(17,261,184)(18,177,262)(19,263,178)(20,179,264)(21,257,180)(22,181,258)(23,259,182)(24,183,260)(25,419,326)(26,327,420)(27,421,328)(28,321,422)(29,423,322)(30,323,424)(31,417,324)(32,325,418)(33,58,332)(34,333,59)(35,60,334)(36,335,61)(37,62,336)(38,329,63)(39,64,330)(40,331,57)(41,254,123)(42,124,255)(43,256,125)(44,126,249)(45,250,127)(46,128,251)(47,252,121)(48,122,253)(49,112,350)(50,351,105)(51,106,352)(52,345,107)(53,108,346)(54,347,109)(55,110,348)(56,349,111)(65,358,368)(66,361,359)(67,360,362)(68,363,353)(69,354,364)(70,365,355)(71,356,366)(72,367,357)(73,412,151)(74,152,413)(75,414,145)(76,146,415)(77,416,147)(78,148,409)(79,410,149)(80,150,411)(81,429,382)(82,383,430)(83,431,384)(84,377,432)(85,425,378)(86,379,426)(87,427,380)(88,381,428)(89,344,287)(90,288,337)(91,338,281)(92,282,339)(93,340,283)(94,284,341)(95,342,285)(96,286,343)(97,171,403)(98,404,172)(99,173,405)(100,406,174)(101,175,407)(102,408,176)(103,169,401)(104,402,170)(113,273,246)(114,247,274)(115,275,248)(116,241,276)(117,277,242)(118,243,278)(119,279,244)(120,245,280)(129,289,212)(130,213,290)(131,291,214)(132,215,292)(133,293,216)(134,209,294)(135,295,210)(136,211,296)(137,220,162)(138,163,221)(139,222,164)(140,165,223)(141,224,166)(142,167,217)(143,218,168)(144,161,219)(153,238,205)(154,206,239)(155,240,207)(156,208,233)(157,234,201)(158,202,235)(159,236,203)(160,204,237)(185,270,306)(186,307,271)(187,272,308)(188,309,265)(189,266,310)(190,311,267)(191,268,312)(192,305,269)(193,374,232)(194,225,375)(195,376,226)(196,227,369)(197,370,228)(198,229,371)(199,372,230)(200,231,373), (1,27,279)(2,280,28)(3,29,273)(4,274,30)(5,31,275)(6,276,32)(7,25,277)(8,278,26)(9,292,77)(10,78,293)(11,294,79)(12,80,295)(13,296,73)(14,74,289)(15,290,75)(16,76,291)(17,57,207)(18,208,58)(19,59,201)(20,202,60)(21,61,203)(22,204,62)(23,63,205)(24,206,64)(33,262,156)(34,157,263)(35,264,158)(36,159,257)(37,258,160)(38,153,259)(39,260,154)(40,155,261)(41,345,138)(42,139,346)(43,347,140)(44,141,348)(45,349,142)(46,143,350)(47,351,144)(48,137,352)(49,128,218)(50,219,121)(51,122,220)(52,221,123)(53,124,222)(54,223,125)(55,126,224)(56,217,127)(65,190,337)(66,338,191)(67,192,339)(68,340,185)(69,186,341)(70,342,187)(71,188,343)(72,344,189)(81,173,371)(82,372,174)(83,175,373)(84,374,176)(85,169,375)(86,376,170)(87,171,369)(88,370,172)(89,310,357)(90,358,311)(91,312,359)(92,360,305)(93,306,353)(94,354,307)(95,308,355)(96,356,309)(97,227,380)(98,381,228)(99,229,382)(100,383,230)(101,231,384)(102,377,232)(103,225,378)(104,379,226)(105,161,252)(106,253,162)(107,163,254)(108,255,164)(109,165,256)(110,249,166)(111,167,250)(112,251,168)(113,400,322)(114,323,393)(115,394,324)(116,325,395)(117,396,326)(118,327,397)(119,398,328)(120,321,399)(129,320,413)(130,414,313)(131,314,415)(132,416,315)(133,316,409)(134,410,317)(135,318,411)(136,412,319)(145,389,213)(146,214,390)(147,391,215)(148,216,392)(149,385,209)(150,210,386)(151,387,211)(152,212,388)(177,233,332)(178,333,234)(179,235,334)(180,335,236)(181,237,336)(182,329,238)(183,239,330)(184,331,240)(193,408,432)(194,425,401)(195,402,426)(196,427,403)(197,404,428)(198,429,405)(199,406,430)(200,431,407)(241,418,299)(242,300,419)(243,420,301)(244,302,421)(245,422,303)(246,304,423)(247,424,297)(248,298,417)(265,286,366)(266,367,287)(267,288,368)(268,361,281)(269,282,362)(270,363,283)(271,284,364)(272,365,285), (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64)(65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104)(105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128)(129,130,131,132,133,134,135,136)(137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152)(153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176)(177,178,179,180,181,182,183,184)(185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224)(225,226,227,228,229,230,231,232)(233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248)(249,250,251,252,253,254,255,256)(257,258,259,260,261,262,263,264)(265,266,267,268,269,270,271,272)(273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288)(289,290,291,292,293,294,295,296)(297,298,299,300,301,302,303,304)(305,306,307,308,309,310,311,312)(313,314,315,316,317,318,319,320)(321,322,323,324,325,326,327,328)(329,330,331,332,333,334,335,336)(337,338,339,340,341,342,343,344)(345,346,347,348,349,350,351,352)(353,354,355,356,357,358,359,360)(361,362,363,364,365,366,367,368)(369,370,371,372,373,374,375,376)(377,378,379,380,381,382,383,384)(385,386,387,388,389,390,391,392)(393,394,395,396,397,398,399,400)(401,402,403,404,405,406,407,408)(409,410,411,412,413,414,415,416)(417,418,419,420,421,422,423,424)(425,426,427,428,429,430,431,432)>;

G:=Group( (1,262)(2,263)(3,264)(4,257)(5,258)(6,259)(7,260)(8,261)(9,104)(10,97)(11,98)(12,99)(13,100)(14,101)(15,102)(16,103)(17,301)(18,302)(19,303)(20,304)(21,297)(22,298)(23,299)(24,300)(25,154)(26,155)(27,156)(28,157)(29,158)(30,159)(31,160)(32,153)(33,279)(34,280)(35,273)(36,274)(37,275)(38,276)(39,277)(40,278)(41,287)(42,288)(43,281)(44,282)(45,283)(46,284)(47,285)(48,286)(49,186)(50,187)(51,188)(52,189)(53,190)(54,191)(55,192)(56,185)(57,243)(58,244)(59,245)(60,246)(61,247)(62,248)(63,241)(64,242)(65,222)(66,223)(67,224)(68,217)(69,218)(70,219)(71,220)(72,221)(73,230)(74,231)(75,232)(76,225)(77,226)(78,227)(79,228)(80,229)(81,210)(82,211)(83,212)(84,213)(85,214)(86,215)(87,216)(88,209)(89,254)(90,255)(91,256)(92,249)(93,250)(94,251)(95,252)(96,253)(105,308)(106,309)(107,310)(108,311)(109,312)(110,305)(111,306)(112,307)(113,334)(114,335)(115,336)(116,329)(117,330)(118,331)(119,332)(120,333)(121,342)(122,343)(123,344)(124,337)(125,338)(126,339)(127,340)(128,341)(129,431)(130,432)(131,425)(132,426)(133,427)(134,428)(135,429)(136,430)(137,366)(138,367)(139,368)(140,361)(141,362)(142,363)(143,364)(144,365)(145,374)(146,375)(147,376)(148,369)(149,370)(150,371)(151,372)(152,373)(161,355)(162,356)(163,357)(164,358)(165,359)(166,360)(167,353)(168,354)(169,390)(170,391)(171,392)(172,385)(173,386)(174,387)(175,388)(176,389)(177,398)(178,399)(179,400)(180,393)(181,394)(182,395)(183,396)(184,397)(193,414)(194,415)(195,416)(196,409)(197,410)(198,411)(199,412)(200,413)(201,422)(202,423)(203,424)(204,417)(205,418)(206,419)(207,420)(208,421)(233,328)(234,321)(235,322)(236,323)(237,324)(238,325)(239,326)(240,327)(265,352)(266,345)(267,346)(268,347)(269,348)(270,349)(271,350)(272,351)(289,384)(290,377)(291,378)(292,379)(293,380)(294,381)(295,382)(296,383)(313,408)(314,401)(315,402)(316,403)(317,404)(318,405)(319,406)(320,407), (1,81,144)(2,137,82)(3,83,138)(4,139,84)(5,85,140)(6,141,86)(7,87,142)(8,143,88)(9,238,339)(10,340,239)(11,240,341)(12,342,233)(13,234,343)(14,344,235)(15,236,337)(16,338,237)(17,354,134)(18,135,355)(19,356,136)(20,129,357)(21,358,130)(22,131,359)(23,360,132)(24,133,353)(25,171,45)(26,46,172)(27,173,47)(28,48,174)(29,175,41)(30,42,176)(31,169,43)(32,44,170)(33,150,272)(34,265,151)(35,152,266)(36,267,145)(37,146,268)(38,269,147)(39,148,270)(40,271,149)(49,228,118)(50,119,229)(51,230,120)(52,113,231)(53,232,114)(54,115,225)(55,226,116)(56,117,227)(57,307,410)(58,411,308)(59,309,412)(60,413,310)(61,311,414)(62,415,312)(63,305,416)(64,409,306)(65,290,180)(66,181,291)(67,292,182)(68,183,293)(69,294,184)(70,177,295)(71,296,178)(72,179,289)(73,333,188)(74,189,334)(75,335,190)(76,191,336)(77,329,192)(78,185,330)(79,331,186)(80,187,332)(89,202,320)(90,313,203)(91,204,314)(92,315,205)(93,206,316)(94,317,207)(95,208,318)(96,319,201)(97,127,326)(98,327,128)(99,121,328)(100,321,122)(101,123,322)(102,323,124)(103,125,324)(104,325,126)(105,244,198)(106,199,245)(107,246,200)(108,193,247)(109,248,194)(110,195,241)(111,242,196)(112,197,243)(153,282,391)(154,392,283)(155,284,385)(156,386,285)(157,286,387)(158,388,287)(159,288,389)(160,390,281)(161,302,429)(162,430,303)(163,304,431)(164,432,297)(165,298,425)(166,426,299)(167,300,427)(168,428,301)(209,261,364)(210,365,262)(211,263,366)(212,367,264)(213,257,368)(214,361,258)(215,259,362)(216,363,260)(217,396,380)(218,381,397)(219,398,382)(220,383,399)(221,400,384)(222,377,393)(223,394,378)(224,379,395)(249,402,418)(250,419,403)(251,404,420)(252,421,405)(253,406,422)(254,423,407)(255,408,424)(256,417,401)(273,373,345)(274,346,374)(275,375,347)(276,348,376)(277,369,349)(278,350,370)(279,371,351)(280,352,372), (1,302,398)(2,399,303)(3,304,400)(4,393,297)(5,298,394)(6,395,299)(7,300,396)(8,397,301)(9,315,391)(10,392,316)(11,317,385)(12,386,318)(13,319,387)(14,388,320)(15,313,389)(16,390,314)(17,261,184)(18,177,262)(19,263,178)(20,179,264)(21,257,180)(22,181,258)(23,259,182)(24,183,260)(25,419,326)(26,327,420)(27,421,328)(28,321,422)(29,423,322)(30,323,424)(31,417,324)(32,325,418)(33,58,332)(34,333,59)(35,60,334)(36,335,61)(37,62,336)(38,329,63)(39,64,330)(40,331,57)(41,254,123)(42,124,255)(43,256,125)(44,126,249)(45,250,127)(46,128,251)(47,252,121)(48,122,253)(49,112,350)(50,351,105)(51,106,352)(52,345,107)(53,108,346)(54,347,109)(55,110,348)(56,349,111)(65,358,368)(66,361,359)(67,360,362)(68,363,353)(69,354,364)(70,365,355)(71,356,366)(72,367,357)(73,412,151)(74,152,413)(75,414,145)(76,146,415)(77,416,147)(78,148,409)(79,410,149)(80,150,411)(81,429,382)(82,383,430)(83,431,384)(84,377,432)(85,425,378)(86,379,426)(87,427,380)(88,381,428)(89,344,287)(90,288,337)(91,338,281)(92,282,339)(93,340,283)(94,284,341)(95,342,285)(96,286,343)(97,171,403)(98,404,172)(99,173,405)(100,406,174)(101,175,407)(102,408,176)(103,169,401)(104,402,170)(113,273,246)(114,247,274)(115,275,248)(116,241,276)(117,277,242)(118,243,278)(119,279,244)(120,245,280)(129,289,212)(130,213,290)(131,291,214)(132,215,292)(133,293,216)(134,209,294)(135,295,210)(136,211,296)(137,220,162)(138,163,221)(139,222,164)(140,165,223)(141,224,166)(142,167,217)(143,218,168)(144,161,219)(153,238,205)(154,206,239)(155,240,207)(156,208,233)(157,234,201)(158,202,235)(159,236,203)(160,204,237)(185,270,306)(186,307,271)(187,272,308)(188,309,265)(189,266,310)(190,311,267)(191,268,312)(192,305,269)(193,374,232)(194,225,375)(195,376,226)(196,227,369)(197,370,228)(198,229,371)(199,372,230)(200,231,373), (1,27,279)(2,280,28)(3,29,273)(4,274,30)(5,31,275)(6,276,32)(7,25,277)(8,278,26)(9,292,77)(10,78,293)(11,294,79)(12,80,295)(13,296,73)(14,74,289)(15,290,75)(16,76,291)(17,57,207)(18,208,58)(19,59,201)(20,202,60)(21,61,203)(22,204,62)(23,63,205)(24,206,64)(33,262,156)(34,157,263)(35,264,158)(36,159,257)(37,258,160)(38,153,259)(39,260,154)(40,155,261)(41,345,138)(42,139,346)(43,347,140)(44,141,348)(45,349,142)(46,143,350)(47,351,144)(48,137,352)(49,128,218)(50,219,121)(51,122,220)(52,221,123)(53,124,222)(54,223,125)(55,126,224)(56,217,127)(65,190,337)(66,338,191)(67,192,339)(68,340,185)(69,186,341)(70,342,187)(71,188,343)(72,344,189)(81,173,371)(82,372,174)(83,175,373)(84,374,176)(85,169,375)(86,376,170)(87,171,369)(88,370,172)(89,310,357)(90,358,311)(91,312,359)(92,360,305)(93,306,353)(94,354,307)(95,308,355)(96,356,309)(97,227,380)(98,381,228)(99,229,382)(100,383,230)(101,231,384)(102,377,232)(103,225,378)(104,379,226)(105,161,252)(106,253,162)(107,163,254)(108,255,164)(109,165,256)(110,249,166)(111,167,250)(112,251,168)(113,400,322)(114,323,393)(115,394,324)(116,325,395)(117,396,326)(118,327,397)(119,398,328)(120,321,399)(129,320,413)(130,414,313)(131,314,415)(132,416,315)(133,316,409)(134,410,317)(135,318,411)(136,412,319)(145,389,213)(146,214,390)(147,391,215)(148,216,392)(149,385,209)(150,210,386)(151,387,211)(152,212,388)(177,233,332)(178,333,234)(179,235,334)(180,335,236)(181,237,336)(182,329,238)(183,239,330)(184,331,240)(193,408,432)(194,425,401)(195,402,426)(196,427,403)(197,404,428)(198,429,405)(199,406,430)(200,431,407)(241,418,299)(242,300,419)(243,420,301)(244,302,421)(245,422,303)(246,304,423)(247,424,297)(248,298,417)(265,286,366)(266,367,287)(267,288,368)(268,361,281)(269,282,362)(270,363,283)(271,284,364)(272,365,285), (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64)(65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104)(105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128)(129,130,131,132,133,134,135,136)(137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152)(153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176)(177,178,179,180,181,182,183,184)(185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224)(225,226,227,228,229,230,231,232)(233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248)(249,250,251,252,253,254,255,256)(257,258,259,260,261,262,263,264)(265,266,267,268,269,270,271,272)(273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288)(289,290,291,292,293,294,295,296)(297,298,299,300,301,302,303,304)(305,306,307,308,309,310,311,312)(313,314,315,316,317,318,319,320)(321,322,323,324,325,326,327,328)(329,330,331,332,333,334,335,336)(337,338,339,340,341,342,343,344)(345,346,347,348,349,350,351,352)(353,354,355,356,357,358,359,360)(361,362,363,364,365,366,367,368)(369,370,371,372,373,374,375,376)(377,378,379,380,381,382,383,384)(385,386,387,388,389,390,391,392)(393,394,395,396,397,398,399,400)(401,402,403,404,405,406,407,408)(409,410,411,412,413,414,415,416)(417,418,419,420,421,422,423,424)(425,426,427,428,429,430,431,432) );

G=PermutationGroup([[(1,262),(2,263),(3,264),(4,257),(5,258),(6,259),(7,260),(8,261),(9,104),(10,97),(11,98),(12,99),(13,100),(14,101),(15,102),(16,103),(17,301),(18,302),(19,303),(20,304),(21,297),(22,298),(23,299),(24,300),(25,154),(26,155),(27,156),(28,157),(29,158),(30,159),(31,160),(32,153),(33,279),(34,280),(35,273),(36,274),(37,275),(38,276),(39,277),(40,278),(41,287),(42,288),(43,281),(44,282),(45,283),(46,284),(47,285),(48,286),(49,186),(50,187),(51,188),(52,189),(53,190),(54,191),(55,192),(56,185),(57,243),(58,244),(59,245),(60,246),(61,247),(62,248),(63,241),(64,242),(65,222),(66,223),(67,224),(68,217),(69,218),(70,219),(71,220),(72,221),(73,230),(74,231),(75,232),(76,225),(77,226),(78,227),(79,228),(80,229),(81,210),(82,211),(83,212),(84,213),(85,214),(86,215),(87,216),(88,209),(89,254),(90,255),(91,256),(92,249),(93,250),(94,251),(95,252),(96,253),(105,308),(106,309),(107,310),(108,311),(109,312),(110,305),(111,306),(112,307),(113,334),(114,335),(115,336),(116,329),(117,330),(118,331),(119,332),(120,333),(121,342),(122,343),(123,344),(124,337),(125,338),(126,339),(127,340),(128,341),(129,431),(130,432),(131,425),(132,426),(133,427),(134,428),(135,429),(136,430),(137,366),(138,367),(139,368),(140,361),(141,362),(142,363),(143,364),(144,365),(145,374),(146,375),(147,376),(148,369),(149,370),(150,371),(151,372),(152,373),(161,355),(162,356),(163,357),(164,358),(165,359),(166,360),(167,353),(168,354),(169,390),(170,391),(171,392),(172,385),(173,386),(174,387),(175,388),(176,389),(177,398),(178,399),(179,400),(180,393),(181,394),(182,395),(183,396),(184,397),(193,414),(194,415),(195,416),(196,409),(197,410),(198,411),(199,412),(200,413),(201,422),(202,423),(203,424),(204,417),(205,418),(206,419),(207,420),(208,421),(233,328),(234,321),(235,322),(236,323),(237,324),(238,325),(239,326),(240,327),(265,352),(266,345),(267,346),(268,347),(269,348),(270,349),(271,350),(272,351),(289,384),(290,377),(291,378),(292,379),(293,380),(294,381),(295,382),(296,383),(313,408),(314,401),(315,402),(316,403),(317,404),(318,405),(319,406),(320,407)], [(1,81,144),(2,137,82),(3,83,138),(4,139,84),(5,85,140),(6,141,86),(7,87,142),(8,143,88),(9,238,339),(10,340,239),(11,240,341),(12,342,233),(13,234,343),(14,344,235),(15,236,337),(16,338,237),(17,354,134),(18,135,355),(19,356,136),(20,129,357),(21,358,130),(22,131,359),(23,360,132),(24,133,353),(25,171,45),(26,46,172),(27,173,47),(28,48,174),(29,175,41),(30,42,176),(31,169,43),(32,44,170),(33,150,272),(34,265,151),(35,152,266),(36,267,145),(37,146,268),(38,269,147),(39,148,270),(40,271,149),(49,228,118),(50,119,229),(51,230,120),(52,113,231),(53,232,114),(54,115,225),(55,226,116),(56,117,227),(57,307,410),(58,411,308),(59,309,412),(60,413,310),(61,311,414),(62,415,312),(63,305,416),(64,409,306),(65,290,180),(66,181,291),(67,292,182),(68,183,293),(69,294,184),(70,177,295),(71,296,178),(72,179,289),(73,333,188),(74,189,334),(75,335,190),(76,191,336),(77,329,192),(78,185,330),(79,331,186),(80,187,332),(89,202,320),(90,313,203),(91,204,314),(92,315,205),(93,206,316),(94,317,207),(95,208,318),(96,319,201),(97,127,326),(98,327,128),(99,121,328),(100,321,122),(101,123,322),(102,323,124),(103,125,324),(104,325,126),(105,244,198),(106,199,245),(107,246,200),(108,193,247),(109,248,194),(110,195,241),(111,242,196),(112,197,243),(153,282,391),(154,392,283),(155,284,385),(156,386,285),(157,286,387),(158,388,287),(159,288,389),(160,390,281),(161,302,429),(162,430,303),(163,304,431),(164,432,297),(165,298,425),(166,426,299),(167,300,427),(168,428,301),(209,261,364),(210,365,262),(211,263,366),(212,367,264),(213,257,368),(214,361,258),(215,259,362),(216,363,260),(217,396,380),(218,381,397),(219,398,382),(220,383,399),(221,400,384),(222,377,393),(223,394,378),(224,379,395),(249,402,418),(250,419,403),(251,404,420),(252,421,405),(253,406,422),(254,423,407),(255,408,424),(256,417,401),(273,373,345),(274,346,374),(275,375,347),(276,348,376),(277,369,349),(278,350,370),(279,371,351),(280,352,372)], [(1,302,398),(2,399,303),(3,304,400),(4,393,297),(5,298,394),(6,395,299),(7,300,396),(8,397,301),(9,315,391),(10,392,316),(11,317,385),(12,386,318),(13,319,387),(14,388,320),(15,313,389),(16,390,314),(17,261,184),(18,177,262),(19,263,178),(20,179,264),(21,257,180),(22,181,258),(23,259,182),(24,183,260),(25,419,326),(26,327,420),(27,421,328),(28,321,422),(29,423,322),(30,323,424),(31,417,324),(32,325,418),(33,58,332),(34,333,59),(35,60,334),(36,335,61),(37,62,336),(38,329,63),(39,64,330),(40,331,57),(41,254,123),(42,124,255),(43,256,125),(44,126,249),(45,250,127),(46,128,251),(47,252,121),(48,122,253),(49,112,350),(50,351,105),(51,106,352),(52,345,107),(53,108,346),(54,347,109),(55,110,348),(56,349,111),(65,358,368),(66,361,359),(67,360,362),(68,363,353),(69,354,364),(70,365,355),(71,356,366),(72,367,357),(73,412,151),(74,152,413),(75,414,145),(76,146,415),(77,416,147),(78,148,409),(79,410,149),(80,150,411),(81,429,382),(82,383,430),(83,431,384),(84,377,432),(85,425,378),(86,379,426),(87,427,380),(88,381,428),(89,344,287),(90,288,337),(91,338,281),(92,282,339),(93,340,283),(94,284,341),(95,342,285),(96,286,343),(97,171,403),(98,404,172),(99,173,405),(100,406,174),(101,175,407),(102,408,176),(103,169,401),(104,402,170),(113,273,246),(114,247,274),(115,275,248),(116,241,276),(117,277,242),(118,243,278),(119,279,244),(120,245,280),(129,289,212),(130,213,290),(131,291,214),(132,215,292),(133,293,216),(134,209,294),(135,295,210),(136,211,296),(137,220,162),(138,163,221),(139,222,164),(140,165,223),(141,224,166),(142,167,217),(143,218,168),(144,161,219),(153,238,205),(154,206,239),(155,240,207),(156,208,233),(157,234,201),(158,202,235),(159,236,203),(160,204,237),(185,270,306),(186,307,271),(187,272,308),(188,309,265),(189,266,310),(190,311,267),(191,268,312),(192,305,269),(193,374,232),(194,225,375),(195,376,226),(196,227,369),(197,370,228),(198,229,371),(199,372,230),(200,231,373)], [(1,27,279),(2,280,28),(3,29,273),(4,274,30),(5,31,275),(6,276,32),(7,25,277),(8,278,26),(9,292,77),(10,78,293),(11,294,79),(12,80,295),(13,296,73),(14,74,289),(15,290,75),(16,76,291),(17,57,207),(18,208,58),(19,59,201),(20,202,60),(21,61,203),(22,204,62),(23,63,205),(24,206,64),(33,262,156),(34,157,263),(35,264,158),(36,159,257),(37,258,160),(38,153,259),(39,260,154),(40,155,261),(41,345,138),(42,139,346),(43,347,140),(44,141,348),(45,349,142),(46,143,350),(47,351,144),(48,137,352),(49,128,218),(50,219,121),(51,122,220),(52,221,123),(53,124,222),(54,223,125),(55,126,224),(56,217,127),(65,190,337),(66,338,191),(67,192,339),(68,340,185),(69,186,341),(70,342,187),(71,188,343),(72,344,189),(81,173,371),(82,372,174),(83,175,373),(84,374,176),(85,169,375),(86,376,170),(87,171,369),(88,370,172),(89,310,357),(90,358,311),(91,312,359),(92,360,305),(93,306,353),(94,354,307),(95,308,355),(96,356,309),(97,227,380),(98,381,228),(99,229,382),(100,383,230),(101,231,384),(102,377,232),(103,225,378),(104,379,226),(105,161,252),(106,253,162),(107,163,254),(108,255,164),(109,165,256),(110,249,166),(111,167,250),(112,251,168),(113,400,322),(114,323,393),(115,394,324),(116,325,395),(117,396,326),(118,327,397),(119,398,328),(120,321,399),(129,320,413),(130,414,313),(131,314,415),(132,416,315),(133,316,409),(134,410,317),(135,318,411),(136,412,319),(145,389,213),(146,214,390),(147,391,215),(148,216,392),(149,385,209),(150,210,386),(151,387,211),(152,212,388),(177,233,332),(178,333,234),(179,235,334),(180,335,236),(181,237,336),(182,329,238),(183,239,330),(184,331,240),(193,408,432),(194,425,401),(195,402,426),(196,427,403),(197,404,428),(198,429,405),(199,406,430),(200,431,407),(241,418,299),(242,300,419),(243,420,301),(244,302,421),(245,422,303),(246,304,423),(247,424,297),(248,298,417),(265,286,366),(266,367,287),(267,288,368),(268,361,281),(269,282,362),(270,363,283),(271,284,364),(272,365,285)], [(1,2,3,4,5,6,7,8),(9,10,11,12,13,14,15,16),(17,18,19,20,21,22,23,24),(25,26,27,28,29,30,31,32),(33,34,35,36,37,38,39,40),(41,42,43,44,45,46,47,48),(49,50,51,52,53,54,55,56),(57,58,59,60,61,62,63,64),(65,66,67,68,69,70,71,72),(73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88),(89,90,91,92,93,94,95,96),(97,98,99,100,101,102,103,104),(105,106,107,108,109,110,111,112),(113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128),(129,130,131,132,133,134,135,136),(137,138,139,140,141,142,143,144),(145,146,147,148,149,150,151,152),(153,154,155,156,157,158,159,160),(161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176),(177,178,179,180,181,182,183,184),(185,186,187,188,189,190,191,192),(193,194,195,196,197,198,199,200),(201,202,203,204,205,206,207,208),(209,210,211,212,213,214,215,216),(217,218,219,220,221,222,223,224),(225,226,227,228,229,230,231,232),(233,234,235,236,237,238,239,240),(241,242,243,244,245,246,247,248),(249,250,251,252,253,254,255,256),(257,258,259,260,261,262,263,264),(265,266,267,268,269,270,271,272),(273,274,275,276,277,278,279,280),(281,282,283,284,285,286,287,288),(289,290,291,292,293,294,295,296),(297,298,299,300,301,302,303,304),(305,306,307,308,309,310,311,312),(313,314,315,316,317,318,319,320),(321,322,323,324,325,326,327,328),(329,330,331,332,333,334,335,336),(337,338,339,340,341,342,343,344),(345,346,347,348,349,350,351,352),(353,354,355,356,357,358,359,360),(361,362,363,364,365,366,367,368),(369,370,371,372,373,374,375,376),(377,378,379,380,381,382,383,384),(385,386,387,388,389,390,391,392),(393,394,395,396,397,398,399,400),(401,402,403,404,405,406,407,408),(409,410,411,412,413,414,415,416),(417,418,419,420,421,422,423,424),(425,426,427,428,429,430,431,432)]])

120 conjugacy classes

 class 1 2A 2B 2C 3A ··· 3M 4A 4B 4C 4D 6A ··· 6AM 8A ··· 8H 12A ··· 12AZ order 1 2 2 2 3 ··· 3 4 4 4 4 6 ··· 6 8 ··· 8 12 ··· 12 size 1 1 1 1 2 ··· 2 1 1 1 1 2 ··· 2 27 ··· 27 2 ··· 2

120 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 2 type + + + + - + - image C1 C2 C2 C4 C4 C8 S3 Dic3 D6 Dic3 C3⋊C8 kernel C2×C33⋊7C8 C33⋊7C8 C3×C6×C12 C32×C12 C3×C62 C32×C6 C6×C12 C3×C12 C3×C12 C62 C3×C6 # reps 1 2 1 2 2 8 13 13 13 13 52

Matrix representation of C2×C337C8 in GL7(𝔽73)

 72 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 72
,
 1 0 0 0 0 0 0 0 72 72 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 72 0 0 0 0 0 1 72 0 0 0 0 0 0 0 0 1 0 0 0 0 0 72 72
,
 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 72 72 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 72 72
,
 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 72 1 0 0 0 0 0 72 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1
,
 72 0 0 0 0 0 0 0 7 32 0 0 0 0 0 25 66 0 0 0 0 0 0 0 70 70 0 0 0 0 0 67 3 0 0 0 0 0 0 0 39 50 0 0 0 0 0 11 34

G:=sub<GL(7,GF(73))| [72,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,72],[1,0,0,0,0,0,0,0,72,1,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,1,72],[1,0,0,0,0,0,0,0,0,72,0,0,0,0,0,1,72,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,72,0,0,0,0,0,1,72],[1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,72,72,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1],[72,0,0,0,0,0,0,0,7,25,0,0,0,0,0,32,66,0,0,0,0,0,0,0,70,67,0,0,0,0,0,70,3,0,0,0,0,0,0,0,39,11,0,0,0,0,0,50,34] >;

C2×C337C8 in GAP, Magma, Sage, TeX

C_2\times C_3^3\rtimes_7C_8
% in TeX

G:=Group("C2xC3^3:7C8");
// GroupNames label

G:=SmallGroup(432,501);
// by ID

G=gap.SmallGroup(432,501);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,28,58,1124,4037,14118]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^3=c^3=d^3=e^8=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,e*b*e^-1=b^-1,c*d=d*c,e*c*e^-1=c^-1,e*d*e^-1=d^-1>;
// generators/relations

׿
×
𝔽