direct product, abelian, monomial, 2-elementary
Aliases: C25×C14, SmallGroup(448,1396)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C25×C14 |
| C1 — C25×C14 |
| C1 — C25×C14 |
Subgroups: 5650, all normal (4 characteristic)
C1, C2 [×63], C22 [×651], C7, C23 [×1395], C14 [×63], C24 [×651], C2×C14 [×651], C25 [×63], C22×C14 [×1395], C26, C23×C14 [×651], C24×C14 [×63], C25×C14
Quotients:
C1, C2 [×63], C22 [×651], C7, C23 [×1395], C14 [×63], C24 [×651], C2×C14 [×651], C25 [×63], C22×C14 [×1395], C26, C23×C14 [×651], C24×C14 [×63], C25×C14
Generators and relations
G = < a,b,c,d,e,f | a2=b2=c2=d2=e2=f14=1, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, ef=fe >
►Regular action on 448 points
Generators in S448
(1 238)(2 225)(3 226)(4 227)(5 228)(6 229)(7 230)(8 231)(9 232)(10 233)(11 234)(12 235)(13 236)(14 237)(15 242)(16 243)(17 244)(18 245)(19 246)(20 247)(21 248)(22 249)(23 250)(24 251)(25 252)(26 239)(27 240)(28 241)(29 263)(30 264)(31 265)(32 266)(33 253)(34 254)(35 255)(36 256)(37 257)(38 258)(39 259)(40 260)(41 261)(42 262)(43 280)(44 267)(45 268)(46 269)(47 270)(48 271)(49 272)(50 273)(51 274)(52 275)(53 276)(54 277)(55 278)(56 279)(57 281)(58 282)(59 283)(60 284)(61 285)(62 286)(63 287)(64 288)(65 289)(66 290)(67 291)(68 292)(69 293)(70 294)(71 304)(72 305)(73 306)(74 307)(75 308)(76 295)(77 296)(78 297)(79 298)(80 299)(81 300)(82 301)(83 302)(84 303)(85 311)(86 312)(87 313)(88 314)(89 315)(90 316)(91 317)(92 318)(93 319)(94 320)(95 321)(96 322)(97 309)(98 310)(99 324)(100 325)(101 326)(102 327)(103 328)(104 329)(105 330)(106 331)(107 332)(108 333)(109 334)(110 335)(111 336)(112 323)(113 348)(114 349)(115 350)(116 337)(117 338)(118 339)(119 340)(120 341)(121 342)(122 343)(123 344)(124 345)(125 346)(126 347)(127 353)(128 354)(129 355)(130 356)(131 357)(132 358)(133 359)(134 360)(135 361)(136 362)(137 363)(138 364)(139 351)(140 352)(141 377)(142 378)(143 365)(144 366)(145 367)(146 368)(147 369)(148 370)(149 371)(150 372)(151 373)(152 374)(153 375)(154 376)(155 384)(156 385)(157 386)(158 387)(159 388)(160 389)(161 390)(162 391)(163 392)(164 379)(165 380)(166 381)(167 382)(168 383)(169 401)(170 402)(171 403)(172 404)(173 405)(174 406)(175 393)(176 394)(177 395)(178 396)(179 397)(180 398)(181 399)(182 400)(183 410)(184 411)(185 412)(186 413)(187 414)(188 415)(189 416)(190 417)(191 418)(192 419)(193 420)(194 407)(195 408)(196 409)(197 421)(198 422)(199 423)(200 424)(201 425)(202 426)(203 427)(204 428)(205 429)(206 430)(207 431)(208 432)(209 433)(210 434)(211 448)(212 435)(213 436)(214 437)(215 438)(216 439)(217 440)(218 441)(219 442)(220 443)(221 444)(222 445)(223 446)(224 447)
(1 126)(2 113)(3 114)(4 115)(5 116)(6 117)(7 118)(8 119)(9 120)(10 121)(11 122)(12 123)(13 124)(14 125)(15 128)(16 129)(17 130)(18 131)(19 132)(20 133)(21 134)(22 135)(23 136)(24 137)(25 138)(26 139)(27 140)(28 127)(29 152)(30 153)(31 154)(32 141)(33 142)(34 143)(35 144)(36 145)(37 146)(38 147)(39 148)(40 149)(41 150)(42 151)(43 164)(44 165)(45 166)(46 167)(47 168)(48 155)(49 156)(50 157)(51 158)(52 159)(53 160)(54 161)(55 162)(56 163)(57 170)(58 171)(59 172)(60 173)(61 174)(62 175)(63 176)(64 177)(65 178)(66 179)(67 180)(68 181)(69 182)(70 169)(71 191)(72 192)(73 193)(74 194)(75 195)(76 196)(77 183)(78 184)(79 185)(80 186)(81 187)(82 188)(83 189)(84 190)(85 208)(86 209)(87 210)(88 197)(89 198)(90 199)(91 200)(92 201)(93 202)(94 203)(95 204)(96 205)(97 206)(98 207)(99 222)(100 223)(101 224)(102 211)(103 212)(104 213)(105 214)(106 215)(107 216)(108 217)(109 218)(110 219)(111 220)(112 221)(225 348)(226 349)(227 350)(228 337)(229 338)(230 339)(231 340)(232 341)(233 342)(234 343)(235 344)(236 345)(237 346)(238 347)(239 351)(240 352)(241 353)(242 354)(243 355)(244 356)(245 357)(246 358)(247 359)(248 360)(249 361)(250 362)(251 363)(252 364)(253 378)(254 365)(255 366)(256 367)(257 368)(258 369)(259 370)(260 371)(261 372)(262 373)(263 374)(264 375)(265 376)(266 377)(267 380)(268 381)(269 382)(270 383)(271 384)(272 385)(273 386)(274 387)(275 388)(276 389)(277 390)(278 391)(279 392)(280 379)(281 402)(282 403)(283 404)(284 405)(285 406)(286 393)(287 394)(288 395)(289 396)(290 397)(291 398)(292 399)(293 400)(294 401)(295 409)(296 410)(297 411)(298 412)(299 413)(300 414)(301 415)(302 416)(303 417)(304 418)(305 419)(306 420)(307 407)(308 408)(309 430)(310 431)(311 432)(312 433)(313 434)(314 421)(315 422)(316 423)(317 424)(318 425)(319 426)(320 427)(321 428)(322 429)(323 444)(324 445)(325 446)(326 447)(327 448)(328 435)(329 436)(330 437)(331 438)(332 439)(333 440)(334 441)(335 442)(336 443)
(1 70)(2 57)(3 58)(4 59)(5 60)(6 61)(7 62)(8 63)(9 64)(10 65)(11 66)(12 67)(13 68)(14 69)(15 74)(16 75)(17 76)(18 77)(19 78)(20 79)(21 80)(22 81)(23 82)(24 83)(25 84)(26 71)(27 72)(28 73)(29 97)(30 98)(31 85)(32 86)(33 87)(34 88)(35 89)(36 90)(37 91)(38 92)(39 93)(40 94)(41 95)(42 96)(43 111)(44 112)(45 99)(46 100)(47 101)(48 102)(49 103)(50 104)(51 105)(52 106)(53 107)(54 108)(55 109)(56 110)(113 170)(114 171)(115 172)(116 173)(117 174)(118 175)(119 176)(120 177)(121 178)(122 179)(123 180)(124 181)(125 182)(126 169)(127 193)(128 194)(129 195)(130 196)(131 183)(132 184)(133 185)(134 186)(135 187)(136 188)(137 189)(138 190)(139 191)(140 192)(141 209)(142 210)(143 197)(144 198)(145 199)(146 200)(147 201)(148 202)(149 203)(150 204)(151 205)(152 206)(153 207)(154 208)(155 211)(156 212)(157 213)(158 214)(159 215)(160 216)(161 217)(162 218)(163 219)(164 220)(165 221)(166 222)(167 223)(168 224)(225 281)(226 282)(227 283)(228 284)(229 285)(230 286)(231 287)(232 288)(233 289)(234 290)(235 291)(236 292)(237 293)(238 294)(239 304)(240 305)(241 306)(242 307)(243 308)(244 295)(245 296)(246 297)(247 298)(248 299)(249 300)(250 301)(251 302)(252 303)(253 313)(254 314)(255 315)(256 316)(257 317)(258 318)(259 319)(260 320)(261 321)(262 322)(263 309)(264 310)(265 311)(266 312)(267 323)(268 324)(269 325)(270 326)(271 327)(272 328)(273 329)(274 330)(275 331)(276 332)(277 333)(278 334)(279 335)(280 336)(337 405)(338 406)(339 393)(340 394)(341 395)(342 396)(343 397)(344 398)(345 399)(346 400)(347 401)(348 402)(349 403)(350 404)(351 418)(352 419)(353 420)(354 407)(355 408)(356 409)(357 410)(358 411)(359 412)(360 413)(361 414)(362 415)(363 416)(364 417)(365 421)(366 422)(367 423)(368 424)(369 425)(370 426)(371 427)(372 428)(373 429)(374 430)(375 431)(376 432)(377 433)(378 434)(379 443)(380 444)(381 445)(382 446)(383 447)(384 448)(385 435)(386 436)(387 437)(388 438)(389 439)(390 440)(391 441)(392 442)
(1 29)(2 30)(3 31)(4 32)(5 33)(6 34)(7 35)(8 36)(9 37)(10 38)(11 39)(12 40)(13 41)(14 42)(15 46)(16 47)(17 48)(18 49)(19 50)(20 51)(21 52)(22 53)(23 54)(24 55)(25 56)(26 43)(27 44)(28 45)(57 98)(58 85)(59 86)(60 87)(61 88)(62 89)(63 90)(64 91)(65 92)(66 93)(67 94)(68 95)(69 96)(70 97)(71 111)(72 112)(73 99)(74 100)(75 101)(76 102)(77 103)(78 104)(79 105)(80 106)(81 107)(82 108)(83 109)(84 110)(113 153)(114 154)(115 141)(116 142)(117 143)(118 144)(119 145)(120 146)(121 147)(122 148)(123 149)(124 150)(125 151)(126 152)(127 166)(128 167)(129 168)(130 155)(131 156)(132 157)(133 158)(134 159)(135 160)(136 161)(137 162)(138 163)(139 164)(140 165)(169 206)(170 207)(171 208)(172 209)(173 210)(174 197)(175 198)(176 199)(177 200)(178 201)(179 202)(180 203)(181 204)(182 205)(183 212)(184 213)(185 214)(186 215)(187 216)(188 217)(189 218)(190 219)(191 220)(192 221)(193 222)(194 223)(195 224)(196 211)(225 264)(226 265)(227 266)(228 253)(229 254)(230 255)(231 256)(232 257)(233 258)(234 259)(235 260)(236 261)(237 262)(238 263)(239 280)(240 267)(241 268)(242 269)(243 270)(244 271)(245 272)(246 273)(247 274)(248 275)(249 276)(250 277)(251 278)(252 279)(281 310)(282 311)(283 312)(284 313)(285 314)(286 315)(287 316)(288 317)(289 318)(290 319)(291 320)(292 321)(293 322)(294 309)(295 327)(296 328)(297 329)(298 330)(299 331)(300 332)(301 333)(302 334)(303 335)(304 336)(305 323)(306 324)(307 325)(308 326)(337 378)(338 365)(339 366)(340 367)(341 368)(342 369)(343 370)(344 371)(345 372)(346 373)(347 374)(348 375)(349 376)(350 377)(351 379)(352 380)(353 381)(354 382)(355 383)(356 384)(357 385)(358 386)(359 387)(360 388)(361 389)(362 390)(363 391)(364 392)(393 422)(394 423)(395 424)(396 425)(397 426)(398 427)(399 428)(400 429)(401 430)(402 431)(403 432)(404 433)(405 434)(406 421)(407 446)(408 447)(409 448)(410 435)(411 436)(412 437)(413 438)(414 439)(415 440)(416 441)(417 442)(418 443)(419 444)(420 445)
(1 26)(2 27)(3 28)(4 15)(5 16)(6 17)(7 18)(8 19)(9 20)(10 21)(11 22)(12 23)(13 24)(14 25)(29 43)(30 44)(31 45)(32 46)(33 47)(34 48)(35 49)(36 50)(37 51)(38 52)(39 53)(40 54)(41 55)(42 56)(57 72)(58 73)(59 74)(60 75)(61 76)(62 77)(63 78)(64 79)(65 80)(66 81)(67 82)(68 83)(69 84)(70 71)(85 99)(86 100)(87 101)(88 102)(89 103)(90 104)(91 105)(92 106)(93 107)(94 108)(95 109)(96 110)(97 111)(98 112)(113 140)(114 127)(115 128)(116 129)(117 130)(118 131)(119 132)(120 133)(121 134)(122 135)(123 136)(124 137)(125 138)(126 139)(141 167)(142 168)(143 155)(144 156)(145 157)(146 158)(147 159)(148 160)(149 161)(150 162)(151 163)(152 164)(153 165)(154 166)(169 191)(170 192)(171 193)(172 194)(173 195)(174 196)(175 183)(176 184)(177 185)(178 186)(179 187)(180 188)(181 189)(182 190)(197 211)(198 212)(199 213)(200 214)(201 215)(202 216)(203 217)(204 218)(205 219)(206 220)(207 221)(208 222)(209 223)(210 224)(225 240)(226 241)(227 242)(228 243)(229 244)(230 245)(231 246)(232 247)(233 248)(234 249)(235 250)(236 251)(237 252)(238 239)(253 270)(254 271)(255 272)(256 273)(257 274)(258 275)(259 276)(260 277)(261 278)(262 279)(263 280)(264 267)(265 268)(266 269)(281 305)(282 306)(283 307)(284 308)(285 295)(286 296)(287 297)(288 298)(289 299)(290 300)(291 301)(292 302)(293 303)(294 304)(309 336)(310 323)(311 324)(312 325)(313 326)(314 327)(315 328)(316 329)(317 330)(318 331)(319 332)(320 333)(321 334)(322 335)(337 355)(338 356)(339 357)(340 358)(341 359)(342 360)(343 361)(344 362)(345 363)(346 364)(347 351)(348 352)(349 353)(350 354)(365 384)(366 385)(367 386)(368 387)(369 388)(370 389)(371 390)(372 391)(373 392)(374 379)(375 380)(376 381)(377 382)(378 383)(393 410)(394 411)(395 412)(396 413)(397 414)(398 415)(399 416)(400 417)(401 418)(402 419)(403 420)(404 407)(405 408)(406 409)(421 448)(422 435)(423 436)(424 437)(425 438)(426 439)(427 440)(428 441)(429 442)(430 443)(431 444)(432 445)(433 446)(434 447)
(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)(421 422 423 424 425 426 427 428 429 430 431 432 433 434)(435 436 437 438 439 440 441 442 443 444 445 446 447 448)
G:=sub<Sym(448)| (1,238)(2,225)(3,226)(4,227)(5,228)(6,229)(7,230)(8,231)(9,232)(10,233)(11,234)(12,235)(13,236)(14,237)(15,242)(16,243)(17,244)(18,245)(19,246)(20,247)(21,248)(22,249)(23,250)(24,251)(25,252)(26,239)(27,240)(28,241)(29,263)(30,264)(31,265)(32,266)(33,253)(34,254)(35,255)(36,256)(37,257)(38,258)(39,259)(40,260)(41,261)(42,262)(43,280)(44,267)(45,268)(46,269)(47,270)(48,271)(49,272)(50,273)(51,274)(52,275)(53,276)(54,277)(55,278)(56,279)(57,281)(58,282)(59,283)(60,284)(61,285)(62,286)(63,287)(64,288)(65,289)(66,290)(67,291)(68,292)(69,293)(70,294)(71,304)(72,305)(73,306)(74,307)(75,308)(76,295)(77,296)(78,297)(79,298)(80,299)(81,300)(82,301)(83,302)(84,303)(85,311)(86,312)(87,313)(88,314)(89,315)(90,316)(91,317)(92,318)(93,319)(94,320)(95,321)(96,322)(97,309)(98,310)(99,324)(100,325)(101,326)(102,327)(103,328)(104,329)(105,330)(106,331)(107,332)(108,333)(109,334)(110,335)(111,336)(112,323)(113,348)(114,349)(115,350)(116,337)(117,338)(118,339)(119,340)(120,341)(121,342)(122,343)(123,344)(124,345)(125,346)(126,347)(127,353)(128,354)(129,355)(130,356)(131,357)(132,358)(133,359)(134,360)(135,361)(136,362)(137,363)(138,364)(139,351)(140,352)(141,377)(142,378)(143,365)(144,366)(145,367)(146,368)(147,369)(148,370)(149,371)(150,372)(151,373)(152,374)(153,375)(154,376)(155,384)(156,385)(157,386)(158,387)(159,388)(160,389)(161,390)(162,391)(163,392)(164,379)(165,380)(166,381)(167,382)(168,383)(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,393)(176,394)(177,395)(178,396)(179,397)(180,398)(181,399)(182,400)(183,410)(184,411)(185,412)(186,413)(187,414)(188,415)(189,416)(190,417)(191,418)(192,419)(193,420)(194,407)(195,408)(196,409)(197,421)(198,422)(199,423)(200,424)(201,425)(202,426)(203,427)(204,428)(205,429)(206,430)(207,431)(208,432)(209,433)(210,434)(211,448)(212,435)(213,436)(214,437)(215,438)(216,439)(217,440)(218,441)(219,442)(220,443)(221,444)(222,445)(223,446)(224,447), (1,126)(2,113)(3,114)(4,115)(5,116)(6,117)(7,118)(8,119)(9,120)(10,121)(11,122)(12,123)(13,124)(14,125)(15,128)(16,129)(17,130)(18,131)(19,132)(20,133)(21,134)(22,135)(23,136)(24,137)(25,138)(26,139)(27,140)(28,127)(29,152)(30,153)(31,154)(32,141)(33,142)(34,143)(35,144)(36,145)(37,146)(38,147)(39,148)(40,149)(41,150)(42,151)(43,164)(44,165)(45,166)(46,167)(47,168)(48,155)(49,156)(50,157)(51,158)(52,159)(53,160)(54,161)(55,162)(56,163)(57,170)(58,171)(59,172)(60,173)(61,174)(62,175)(63,176)(64,177)(65,178)(66,179)(67,180)(68,181)(69,182)(70,169)(71,191)(72,192)(73,193)(74,194)(75,195)(76,196)(77,183)(78,184)(79,185)(80,186)(81,187)(82,188)(83,189)(84,190)(85,208)(86,209)(87,210)(88,197)(89,198)(90,199)(91,200)(92,201)(93,202)(94,203)(95,204)(96,205)(97,206)(98,207)(99,222)(100,223)(101,224)(102,211)(103,212)(104,213)(105,214)(106,215)(107,216)(108,217)(109,218)(110,219)(111,220)(112,221)(225,348)(226,349)(227,350)(228,337)(229,338)(230,339)(231,340)(232,341)(233,342)(234,343)(235,344)(236,345)(237,346)(238,347)(239,351)(240,352)(241,353)(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)(248,360)(249,361)(250,362)(251,363)(252,364)(253,378)(254,365)(255,366)(256,367)(257,368)(258,369)(259,370)(260,371)(261,372)(262,373)(263,374)(264,375)(265,376)(266,377)(267,380)(268,381)(269,382)(270,383)(271,384)(272,385)(273,386)(274,387)(275,388)(276,389)(277,390)(278,391)(279,392)(280,379)(281,402)(282,403)(283,404)(284,405)(285,406)(286,393)(287,394)(288,395)(289,396)(290,397)(291,398)(292,399)(293,400)(294,401)(295,409)(296,410)(297,411)(298,412)(299,413)(300,414)(301,415)(302,416)(303,417)(304,418)(305,419)(306,420)(307,407)(308,408)(309,430)(310,431)(311,432)(312,433)(313,434)(314,421)(315,422)(316,423)(317,424)(318,425)(319,426)(320,427)(321,428)(322,429)(323,444)(324,445)(325,446)(326,447)(327,448)(328,435)(329,436)(330,437)(331,438)(332,439)(333,440)(334,441)(335,442)(336,443), (1,70)(2,57)(3,58)(4,59)(5,60)(6,61)(7,62)(8,63)(9,64)(10,65)(11,66)(12,67)(13,68)(14,69)(15,74)(16,75)(17,76)(18,77)(19,78)(20,79)(21,80)(22,81)(23,82)(24,83)(25,84)(26,71)(27,72)(28,73)(29,97)(30,98)(31,85)(32,86)(33,87)(34,88)(35,89)(36,90)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,111)(44,112)(45,99)(46,100)(47,101)(48,102)(49,103)(50,104)(51,105)(52,106)(53,107)(54,108)(55,109)(56,110)(113,170)(114,171)(115,172)(116,173)(117,174)(118,175)(119,176)(120,177)(121,178)(122,179)(123,180)(124,181)(125,182)(126,169)(127,193)(128,194)(129,195)(130,196)(131,183)(132,184)(133,185)(134,186)(135,187)(136,188)(137,189)(138,190)(139,191)(140,192)(141,209)(142,210)(143,197)(144,198)(145,199)(146,200)(147,201)(148,202)(149,203)(150,204)(151,205)(152,206)(153,207)(154,208)(155,211)(156,212)(157,213)(158,214)(159,215)(160,216)(161,217)(162,218)(163,219)(164,220)(165,221)(166,222)(167,223)(168,224)(225,281)(226,282)(227,283)(228,284)(229,285)(230,286)(231,287)(232,288)(233,289)(234,290)(235,291)(236,292)(237,293)(238,294)(239,304)(240,305)(241,306)(242,307)(243,308)(244,295)(245,296)(246,297)(247,298)(248,299)(249,300)(250,301)(251,302)(252,303)(253,313)(254,314)(255,315)(256,316)(257,317)(258,318)(259,319)(260,320)(261,321)(262,322)(263,309)(264,310)(265,311)(266,312)(267,323)(268,324)(269,325)(270,326)(271,327)(272,328)(273,329)(274,330)(275,331)(276,332)(277,333)(278,334)(279,335)(280,336)(337,405)(338,406)(339,393)(340,394)(341,395)(342,396)(343,397)(344,398)(345,399)(346,400)(347,401)(348,402)(349,403)(350,404)(351,418)(352,419)(353,420)(354,407)(355,408)(356,409)(357,410)(358,411)(359,412)(360,413)(361,414)(362,415)(363,416)(364,417)(365,421)(366,422)(367,423)(368,424)(369,425)(370,426)(371,427)(372,428)(373,429)(374,430)(375,431)(376,432)(377,433)(378,434)(379,443)(380,444)(381,445)(382,446)(383,447)(384,448)(385,435)(386,436)(387,437)(388,438)(389,439)(390,440)(391,441)(392,442), (1,29)(2,30)(3,31)(4,32)(5,33)(6,34)(7,35)(8,36)(9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,46)(16,47)(17,48)(18,49)(19,50)(20,51)(21,52)(22,53)(23,54)(24,55)(25,56)(26,43)(27,44)(28,45)(57,98)(58,85)(59,86)(60,87)(61,88)(62,89)(63,90)(64,91)(65,92)(66,93)(67,94)(68,95)(69,96)(70,97)(71,111)(72,112)(73,99)(74,100)(75,101)(76,102)(77,103)(78,104)(79,105)(80,106)(81,107)(82,108)(83,109)(84,110)(113,153)(114,154)(115,141)(116,142)(117,143)(118,144)(119,145)(120,146)(121,147)(122,148)(123,149)(124,150)(125,151)(126,152)(127,166)(128,167)(129,168)(130,155)(131,156)(132,157)(133,158)(134,159)(135,160)(136,161)(137,162)(138,163)(139,164)(140,165)(169,206)(170,207)(171,208)(172,209)(173,210)(174,197)(175,198)(176,199)(177,200)(178,201)(179,202)(180,203)(181,204)(182,205)(183,212)(184,213)(185,214)(186,215)(187,216)(188,217)(189,218)(190,219)(191,220)(192,221)(193,222)(194,223)(195,224)(196,211)(225,264)(226,265)(227,266)(228,253)(229,254)(230,255)(231,256)(232,257)(233,258)(234,259)(235,260)(236,261)(237,262)(238,263)(239,280)(240,267)(241,268)(242,269)(243,270)(244,271)(245,272)(246,273)(247,274)(248,275)(249,276)(250,277)(251,278)(252,279)(281,310)(282,311)(283,312)(284,313)(285,314)(286,315)(287,316)(288,317)(289,318)(290,319)(291,320)(292,321)(293,322)(294,309)(295,327)(296,328)(297,329)(298,330)(299,331)(300,332)(301,333)(302,334)(303,335)(304,336)(305,323)(306,324)(307,325)(308,326)(337,378)(338,365)(339,366)(340,367)(341,368)(342,369)(343,370)(344,371)(345,372)(346,373)(347,374)(348,375)(349,376)(350,377)(351,379)(352,380)(353,381)(354,382)(355,383)(356,384)(357,385)(358,386)(359,387)(360,388)(361,389)(362,390)(363,391)(364,392)(393,422)(394,423)(395,424)(396,425)(397,426)(398,427)(399,428)(400,429)(401,430)(402,431)(403,432)(404,433)(405,434)(406,421)(407,446)(408,447)(409,448)(410,435)(411,436)(412,437)(413,438)(414,439)(415,440)(416,441)(417,442)(418,443)(419,444)(420,445), 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(1,29)(2,30)(3,31)(4,32)(5,33)(6,34)(7,35)(8,36)(9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,46)(16,47)(17,48)(18,49)(19,50)(20,51)(21,52)(22,53)(23,54)(24,55)(25,56)(26,43)(27,44)(28,45)(57,98)(58,85)(59,86)(60,87)(61,88)(62,89)(63,90)(64,91)(65,92)(66,93)(67,94)(68,95)(69,96)(70,97)(71,111)(72,112)(73,99)(74,100)(75,101)(76,102)(77,103)(78,104)(79,105)(80,106)(81,107)(82,108)(83,109)(84,110)(113,153)(114,154)(115,141)(116,142)(117,143)(118,144)(119,145)(120,146)(121,147)(122,148)(123,149)(124,150)(125,151)(126,152)(127,166)(128,167)(129,168)(130,155)(131,156)(132,157)(133,158)(134,159)(135,160)(136,161)(137,162)(138,163)(139,164)(140,165)(169,206)(170,207)(171,208)(172,209)(173,210)(174,197)(175,198)(176,199)(177,200)(178,201)(179,202)(180,203)(181,204)(182,205)(183,212)(184,213)(185,214)(186,215)(187,216)(188,217)(189,218)(190,219)(191,220)(192,221)(193,222)(194,223)(195,224)(196,211)(225,264)(226,265)(227,266)(228,253)(229,254)(230,255)(231,256)(232,257)(233,258)(234,259)(235,260)(236,261)(237,262)(238,263)(239,280)(240,267)(241,268)(242,269)(243,270)(244,271)(245,272)(246,273)(247,274)(248,275)(249,276)(250,277)(251,278)(252,279)(281,310)(282,311)(283,312)(284,313)(285,314)(286,315)(287,316)(288,317)(289,318)(290,319)(291,320)(292,321)(293,322)(294,309)(295,327)(296,328)(297,329)(298,330)(299,331)(300,332)(301,333)(302,334)(303,335)(304,336)(305,323)(306,324)(307,325)(308,326)(337,378)(338,365)(339,366)(340,367)(341,368)(342,369)(343,370)(344,371)(345,372)(346,373)(347,374)(348,375)(349,376)(350,377)(351,379)(352,380)(353,381)(354,382)(355,383)(356,384)(357,385)(358,386)(359,387)(360,388)(361,389)(362,390)(363,391)(364,392)(393,422)(394,423)(395,424)(396,425)(397,426)(398,427)(399,428)(400,429)(401,430)(402,431)(403,432)(404,433)(405,434)(406,421)(407,446)(408,447)(409,448)(410,435)(411,436)(412,437)(413,438)(414,439)(415,440)(416,441)(417,442)(418,443)(419,444)(420,445), (1,26)(2,27)(3,28)(4,15)(5,16)(6,17)(7,18)(8,19)(9,20)(10,21)(11,22)(12,23)(13,24)(14,25)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,72)(58,73)(59,74)(60,75)(61,76)(62,77)(63,78)(64,79)(65,80)(66,81)(67,82)(68,83)(69,84)(70,71)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(113,140)(114,127)(115,128)(116,129)(117,130)(118,131)(119,132)(120,133)(121,134)(122,135)(123,136)(124,137)(125,138)(126,139)(141,167)(142,168)(143,155)(144,156)(145,157)(146,158)(147,159)(148,160)(149,161)(150,162)(151,163)(152,164)(153,165)(154,166)(169,191)(170,192)(171,193)(172,194)(173,195)(174,196)(175,183)(176,184)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224)(225,240)(226,241)(227,242)(228,243)(229,244)(230,245)(231,246)(232,247)(233,248)(234,249)(235,250)(236,251)(237,252)(238,239)(253,270)(254,271)(255,272)(256,273)(257,274)(258,275)(259,276)(260,277)(261,278)(262,279)(263,280)(264,267)(265,268)(266,269)(281,305)(282,306)(283,307)(284,308)(285,295)(286,296)(287,297)(288,298)(289,299)(290,300)(291,301)(292,302)(293,303)(294,304)(309,336)(310,323)(311,324)(312,325)(313,326)(314,327)(315,328)(316,329)(317,330)(318,331)(319,332)(320,333)(321,334)(322,335)(337,355)(338,356)(339,357)(340,358)(341,359)(342,360)(343,361)(344,362)(345,363)(346,364)(347,351)(348,352)(349,353)(350,354)(365,384)(366,385)(367,386)(368,387)(369,388)(370,389)(371,390)(372,391)(373,392)(374,379)(375,380)(376,381)(377,382)(378,383)(393,410)(394,411)(395,412)(396,413)(397,414)(398,415)(399,416)(400,417)(401,418)(402,419)(403,420)(404,407)(405,408)(406,409)(421,448)(422,435)(423,436)(424,437)(425,438)(426,439)(427,440)(428,441)(429,442)(430,443)(431,444)(432,445)(433,446)(434,447), (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)(421,422,423,424,425,426,427,428,429,430,431,432,433,434)(435,436,437,438,439,440,441,442,443,444,445,446,447,448) );
G=PermutationGroup([(1,238),(2,225),(3,226),(4,227),(5,228),(6,229),(7,230),(8,231),(9,232),(10,233),(11,234),(12,235),(13,236),(14,237),(15,242),(16,243),(17,244),(18,245),(19,246),(20,247),(21,248),(22,249),(23,250),(24,251),(25,252),(26,239),(27,240),(28,241),(29,263),(30,264),(31,265),(32,266),(33,253),(34,254),(35,255),(36,256),(37,257),(38,258),(39,259),(40,260),(41,261),(42,262),(43,280),(44,267),(45,268),(46,269),(47,270),(48,271),(49,272),(50,273),(51,274),(52,275),(53,276),(54,277),(55,278),(56,279),(57,281),(58,282),(59,283),(60,284),(61,285),(62,286),(63,287),(64,288),(65,289),(66,290),(67,291),(68,292),(69,293),(70,294),(71,304),(72,305),(73,306),(74,307),(75,308),(76,295),(77,296),(78,297),(79,298),(80,299),(81,300),(82,301),(83,302),(84,303),(85,311),(86,312),(87,313),(88,314),(89,315),(90,316),(91,317),(92,318),(93,319),(94,320),(95,321),(96,322),(97,309),(98,310),(99,324),(100,325),(101,326),(102,327),(103,328),(104,329),(105,330),(106,331),(107,332),(108,333),(109,334),(110,335),(111,336),(112,323),(113,348),(114,349),(115,350),(116,337),(117,338),(118,339),(119,340),(120,341),(121,342),(122,343),(123,344),(124,345),(125,346),(126,347),(127,353),(128,354),(129,355),(130,356),(131,357),(132,358),(133,359),(134,360),(135,361),(136,362),(137,363),(138,364),(139,351),(140,352),(141,377),(142,378),(143,365),(144,366),(145,367),(146,368),(147,369),(148,370),(149,371),(150,372),(151,373),(152,374),(153,375),(154,376),(155,384),(156,385),(157,386),(158,387),(159,388),(160,389),(161,390),(162,391),(163,392),(164,379),(165,380),(166,381),(167,382),(168,383),(169,401),(170,402),(171,403),(172,404),(173,405),(174,406),(175,393),(176,394),(177,395),(178,396),(179,397),(180,398),(181,399),(182,400),(183,410),(184,411),(185,412),(186,413),(187,414),(188,415),(189,416),(190,417),(191,418),(192,419),(193,420),(194,407),(195,408),(196,409),(197,421),(198,422),(199,423),(200,424),(201,425),(202,426),(203,427),(204,428),(205,429),(206,430),(207,431),(208,432),(209,433),(210,434),(211,448),(212,435),(213,436),(214,437),(215,438),(216,439),(217,440),(218,441),(219,442),(220,443),(221,444),(222,445),(223,446),(224,447)], [(1,126),(2,113),(3,114),(4,115),(5,116),(6,117),(7,118),(8,119),(9,120),(10,121),(11,122),(12,123),(13,124),(14,125),(15,128),(16,129),(17,130),(18,131),(19,132),(20,133),(21,134),(22,135),(23,136),(24,137),(25,138),(26,139),(27,140),(28,127),(29,152),(30,153),(31,154),(32,141),(33,142),(34,143),(35,144),(36,145),(37,146),(38,147),(39,148),(40,149),(41,150),(42,151),(43,164),(44,165),(45,166),(46,167),(47,168),(48,155),(49,156),(50,157),(51,158),(52,159),(53,160),(54,161),(55,162),(56,163),(57,170),(58,171),(59,172),(60,173),(61,174),(62,175),(63,176),(64,177),(65,178),(66,179),(67,180),(68,181),(69,182),(70,169),(71,191),(72,192),(73,193),(74,194),(75,195),(76,196),(77,183),(78,184),(79,185),(80,186),(81,187),(82,188),(83,189),(84,190),(85,208),(86,209),(87,210),(88,197),(89,198),(90,199),(91,200),(92,201),(93,202),(94,203),(95,204),(96,205),(97,206),(98,207),(99,222),(100,223),(101,224),(102,211),(103,212),(104,213),(105,214),(106,215),(107,216),(108,217),(109,218),(110,219),(111,220),(112,221),(225,348),(226,349),(227,350),(228,337),(229,338),(230,339),(231,340),(232,341),(233,342),(234,343),(235,344),(236,345),(237,346),(238,347),(239,351),(240,352),(241,353),(242,354),(243,355),(244,356),(245,357),(246,358),(247,359),(248,360),(249,361),(250,362),(251,363),(252,364),(253,378),(254,365),(255,366),(256,367),(257,368),(258,369),(259,370),(260,371),(261,372),(262,373),(263,374),(264,375),(265,376),(266,377),(267,380),(268,381),(269,382),(270,383),(271,384),(272,385),(273,386),(274,387),(275,388),(276,389),(277,390),(278,391),(279,392),(280,379),(281,402),(282,403),(283,404),(284,405),(285,406),(286,393),(287,394),(288,395),(289,396),(290,397),(291,398),(292,399),(293,400),(294,401),(295,409),(296,410),(297,411),(298,412),(299,413),(300,414),(301,415),(302,416),(303,417),(304,418),(305,419),(306,420),(307,407),(308,408),(309,430),(310,431),(311,432),(312,433),(313,434),(314,421),(315,422),(316,423),(317,424),(318,425),(319,426),(320,427),(321,428),(322,429),(323,444),(324,445),(325,446),(326,447),(327,448),(328,435),(329,436),(330,437),(331,438),(332,439),(333,440),(334,441),(335,442),(336,443)], [(1,70),(2,57),(3,58),(4,59),(5,60),(6,61),(7,62),(8,63),(9,64),(10,65),(11,66),(12,67),(13,68),(14,69),(15,74),(16,75),(17,76),(18,77),(19,78),(20,79),(21,80),(22,81),(23,82),(24,83),(25,84),(26,71),(27,72),(28,73),(29,97),(30,98),(31,85),(32,86),(33,87),(34,88),(35,89),(36,90),(37,91),(38,92),(39,93),(40,94),(41,95),(42,96),(43,111),(44,112),(45,99),(46,100),(47,101),(48,102),(49,103),(50,104),(51,105),(52,106),(53,107),(54,108),(55,109),(56,110),(113,170),(114,171),(115,172),(116,173),(117,174),(118,175),(119,176),(120,177),(121,178),(122,179),(123,180),(124,181),(125,182),(126,169),(127,193),(128,194),(129,195),(130,196),(131,183),(132,184),(133,185),(134,186),(135,187),(136,188),(137,189),(138,190),(139,191),(140,192),(141,209),(142,210),(143,197),(144,198),(145,199),(146,200),(147,201),(148,202),(149,203),(150,204),(151,205),(152,206),(153,207),(154,208),(155,211),(156,212),(157,213),(158,214),(159,215),(160,216),(161,217),(162,218),(163,219),(164,220),(165,221),(166,222),(167,223),(168,224),(225,281),(226,282),(227,283),(228,284),(229,285),(230,286),(231,287),(232,288),(233,289),(234,290),(235,291),(236,292),(237,293),(238,294),(239,304),(240,305),(241,306),(242,307),(243,308),(244,295),(245,296),(246,297),(247,298),(248,299),(249,300),(250,301),(251,302),(252,303),(253,313),(254,314),(255,315),(256,316),(257,317),(258,318),(259,319),(260,320),(261,321),(262,322),(263,309),(264,310),(265,311),(266,312),(267,323),(268,324),(269,325),(270,326),(271,327),(272,328),(273,329),(274,330),(275,331),(276,332),(277,333),(278,334),(279,335),(280,336),(337,405),(338,406),(339,393),(340,394),(341,395),(342,396),(343,397),(344,398),(345,399),(346,400),(347,401),(348,402),(349,403),(350,404),(351,418),(352,419),(353,420),(354,407),(355,408),(356,409),(357,410),(358,411),(359,412),(360,413),(361,414),(362,415),(363,416),(364,417),(365,421),(366,422),(367,423),(368,424),(369,425),(370,426),(371,427),(372,428),(373,429),(374,430),(375,431),(376,432),(377,433),(378,434),(379,443),(380,444),(381,445),(382,446),(383,447),(384,448),(385,435),(386,436),(387,437),(388,438),(389,439),(390,440),(391,441),(392,442)], [(1,29),(2,30),(3,31),(4,32),(5,33),(6,34),(7,35),(8,36),(9,37),(10,38),(11,39),(12,40),(13,41),(14,42),(15,46),(16,47),(17,48),(18,49),(19,50),(20,51),(21,52),(22,53),(23,54),(24,55),(25,56),(26,43),(27,44),(28,45),(57,98),(58,85),(59,86),(60,87),(61,88),(62,89),(63,90),(64,91),(65,92),(66,93),(67,94),(68,95),(69,96),(70,97),(71,111),(72,112),(73,99),(74,100),(75,101),(76,102),(77,103),(78,104),(79,105),(80,106),(81,107),(82,108),(83,109),(84,110),(113,153),(114,154),(115,141),(116,142),(117,143),(118,144),(119,145),(120,146),(121,147),(122,148),(123,149),(124,150),(125,151),(126,152),(127,166),(128,167),(129,168),(130,155),(131,156),(132,157),(133,158),(134,159),(135,160),(136,161),(137,162),(138,163),(139,164),(140,165),(169,206),(170,207),(171,208),(172,209),(173,210),(174,197),(175,198),(176,199),(177,200),(178,201),(179,202),(180,203),(181,204),(182,205),(183,212),(184,213),(185,214),(186,215),(187,216),(188,217),(189,218),(190,219),(191,220),(192,221),(193,222),(194,223),(195,224),(196,211),(225,264),(226,265),(227,266),(228,253),(229,254),(230,255),(231,256),(232,257),(233,258),(234,259),(235,260),(236,261),(237,262),(238,263),(239,280),(240,267),(241,268),(242,269),(243,270),(244,271),(245,272),(246,273),(247,274),(248,275),(249,276),(250,277),(251,278),(252,279),(281,310),(282,311),(283,312),(284,313),(285,314),(286,315),(287,316),(288,317),(289,318),(290,319),(291,320),(292,321),(293,322),(294,309),(295,327),(296,328),(297,329),(298,330),(299,331),(300,332),(301,333),(302,334),(303,335),(304,336),(305,323),(306,324),(307,325),(308,326),(337,378),(338,365),(339,366),(340,367),(341,368),(342,369),(343,370),(344,371),(345,372),(346,373),(347,374),(348,375),(349,376),(350,377),(351,379),(352,380),(353,381),(354,382),(355,383),(356,384),(357,385),(358,386),(359,387),(360,388),(361,389),(362,390),(363,391),(364,392),(393,422),(394,423),(395,424),(396,425),(397,426),(398,427),(399,428),(400,429),(401,430),(402,431),(403,432),(404,433),(405,434),(406,421),(407,446),(408,447),(409,448),(410,435),(411,436),(412,437),(413,438),(414,439),(415,440),(416,441),(417,442),(418,443),(419,444),(420,445)], [(1,26),(2,27),(3,28),(4,15),(5,16),(6,17),(7,18),(8,19),(9,20),(10,21),(11,22),(12,23),(13,24),(14,25),(29,43),(30,44),(31,45),(32,46),(33,47),(34,48),(35,49),(36,50),(37,51),(38,52),(39,53),(40,54),(41,55),(42,56),(57,72),(58,73),(59,74),(60,75),(61,76),(62,77),(63,78),(64,79),(65,80),(66,81),(67,82),(68,83),(69,84),(70,71),(85,99),(86,100),(87,101),(88,102),(89,103),(90,104),(91,105),(92,106),(93,107),(94,108),(95,109),(96,110),(97,111),(98,112),(113,140),(114,127),(115,128),(116,129),(117,130),(118,131),(119,132),(120,133),(121,134),(122,135),(123,136),(124,137),(125,138),(126,139),(141,167),(142,168),(143,155),(144,156),(145,157),(146,158),(147,159),(148,160),(149,161),(150,162),(151,163),(152,164),(153,165),(154,166),(169,191),(170,192),(171,193),(172,194),(173,195),(174,196),(175,183),(176,184),(177,185),(178,186),(179,187),(180,188),(181,189),(182,190),(197,211),(198,212),(199,213),(200,214),(201,215),(202,216),(203,217),(204,218),(205,219),(206,220),(207,221),(208,222),(209,223),(210,224),(225,240),(226,241),(227,242),(228,243),(229,244),(230,245),(231,246),(232,247),(233,248),(234,249),(235,250),(236,251),(237,252),(238,239),(253,270),(254,271),(255,272),(256,273),(257,274),(258,275),(259,276),(260,277),(261,278),(262,279),(263,280),(264,267),(265,268),(266,269),(281,305),(282,306),(283,307),(284,308),(285,295),(286,296),(287,297),(288,298),(289,299),(290,300),(291,301),(292,302),(293,303),(294,304),(309,336),(310,323),(311,324),(312,325),(313,326),(314,327),(315,328),(316,329),(317,330),(318,331),(319,332),(320,333),(321,334),(322,335),(337,355),(338,356),(339,357),(340,358),(341,359),(342,360),(343,361),(344,362),(345,363),(346,364),(347,351),(348,352),(349,353),(350,354),(365,384),(366,385),(367,386),(368,387),(369,388),(370,389),(371,390),(372,391),(373,392),(374,379),(375,380),(376,381),(377,382),(378,383),(393,410),(394,411),(395,412),(396,413),(397,414),(398,415),(399,416),(400,417),(401,418),(402,419),(403,420),(404,407),(405,408),(406,409),(421,448),(422,435),(423,436),(424,437),(425,438),(426,439),(427,440),(428,441),(429,442),(430,443),(431,444),(432,445),(433,446),(434,447)], [(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),(421,422,423,424,425,426,427,428,429,430,431,432,433,434),(435,436,437,438,439,440,441,442,443,444,445,446,447,448)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 5 | 0 | 0 | 0 | 0 | 0 |
| 0 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 0 | 0 | 0 |
| 0 | 0 | 0 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 0 |
| 0 | 0 | 0 | 0 | 0 | 7 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,1],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1],[5,0,0,0,0,0,0,5,0,0,0,0,0,0,5,0,0,0,0,0,0,22,0,0,0,0,0,0,22,0,0,0,0,0,0,7] >;
448 conjugacy classes
| class | 1 | 2A | ··· | 2BK | 7A | ··· | 7F | 14A | ··· | 14NN |
| order | 1 | 2 | ··· | 2 | 7 | ··· | 7 | 14 | ··· | 14 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
448 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C7 | C14 |
| kernel | C25×C14 | C24×C14 | C26 | C25 |
| # reps | 1 | 63 | 6 | 378 |
In GAP, Magma, Sage, TeX
C_2^5\times C_{14} % in TeX
G:=Group("C2^5xC14"); // GroupNames label
G:=SmallGroup(448,1396);
// by ID
G=gap.SmallGroup(448,1396);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^2=f^14=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,e*f=f*e>;
// generators/relations
×
⋊
ℤ
𝔽
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≀