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G = C25×C14order 448 = 26·7

Abelian group of type [2,2,2,2,2,14]

direct product, abelian, monomial, 2-elementary

Aliases: C25×C14, SmallGroup(448,1396)

Series: Derived Chief Lower central Upper central

C1 — C25×C14
C1C7C14C2×C14C22×C14C23×C14C24×C14 — C25×C14
C1 — C25×C14
C1 — C25×C14

Generators and relations for C25×C14
 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 >

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

Smallest permutation representation of C25×C14
Regular action on 448 points
Generators in S448
(1 233)(2 234)(3 235)(4 236)(5 237)(6 238)(7 225)(8 226)(9 227)(10 228)(11 229)(12 230)(13 231)(14 232)(15 241)(16 242)(17 243)(18 244)(19 245)(20 246)(21 247)(22 248)(23 249)(24 250)(25 251)(26 252)(27 239)(28 240)(29 254)(30 255)(31 256)(32 257)(33 258)(34 259)(35 260)(36 261)(37 262)(38 263)(39 264)(40 265)(41 266)(42 253)(43 269)(44 270)(45 271)(46 272)(47 273)(48 274)(49 275)(50 276)(51 277)(52 278)(53 279)(54 280)(55 267)(56 268)(57 282)(58 283)(59 284)(60 285)(61 286)(62 287)(63 288)(64 289)(65 290)(66 291)(67 292)(68 293)(69 294)(70 281)(71 305)(72 306)(73 307)(74 308)(75 295)(76 296)(77 297)(78 298)(79 299)(80 300)(81 301)(82 302)(83 303)(84 304)(85 310)(86 311)(87 312)(88 313)(89 314)(90 315)(91 316)(92 317)(93 318)(94 319)(95 320)(96 321)(97 322)(98 309)(99 325)(100 326)(101 327)(102 328)(103 329)(104 330)(105 331)(106 332)(107 333)(108 334)(109 335)(110 336)(111 323)(112 324)(113 342)(114 343)(115 344)(116 345)(117 346)(118 347)(119 348)(120 349)(121 350)(122 337)(123 338)(124 339)(125 340)(126 341)(127 361)(128 362)(129 363)(130 364)(131 351)(132 352)(133 353)(134 354)(135 355)(136 356)(137 357)(138 358)(139 359)(140 360)(141 378)(142 365)(143 366)(144 367)(145 368)(146 369)(147 370)(148 371)(149 372)(150 373)(151 374)(152 375)(153 376)(154 377)(155 382)(156 383)(157 384)(158 385)(159 386)(160 387)(161 388)(162 389)(163 390)(164 391)(165 392)(166 379)(167 380)(168 381)(169 394)(170 395)(171 396)(172 397)(173 398)(174 399)(175 400)(176 401)(177 402)(178 403)(179 404)(180 405)(181 406)(182 393)(183 415)(184 416)(185 417)(186 418)(187 419)(188 420)(189 407)(190 408)(191 409)(192 410)(193 411)(194 412)(195 413)(196 414)(197 434)(198 421)(199 422)(200 423)(201 424)(202 425)(203 426)(204 427)(205 428)(206 429)(207 430)(208 431)(209 432)(210 433)(211 447)(212 448)(213 435)(214 436)(215 437)(216 438)(217 439)(218 440)(219 441)(220 442)(221 443)(222 444)(223 445)(224 446)
(1 121)(2 122)(3 123)(4 124)(5 125)(6 126)(7 113)(8 114)(9 115)(10 116)(11 117)(12 118)(13 119)(14 120)(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)(29 141)(30 142)(31 143)(32 144)(33 145)(34 146)(35 147)(36 148)(37 149)(38 150)(39 151)(40 152)(41 153)(42 154)(43 158)(44 159)(45 160)(46 161)(47 162)(48 163)(49 164)(50 165)(51 166)(52 167)(53 168)(54 155)(55 156)(56 157)(57 171)(58 172)(59 173)(60 174)(61 175)(62 176)(63 177)(64 178)(65 179)(66 180)(67 181)(68 182)(69 169)(70 170)(71 183)(72 184)(73 185)(74 186)(75 187)(76 188)(77 189)(78 190)(79 191)(80 192)(81 193)(82 194)(83 195)(84 196)(85 200)(86 201)(87 202)(88 203)(89 204)(90 205)(91 206)(92 207)(93 208)(94 209)(95 210)(96 197)(97 198)(98 199)(99 224)(100 211)(101 212)(102 213)(103 214)(104 215)(105 216)(106 217)(107 218)(108 219)(109 220)(110 221)(111 222)(112 223)(225 342)(226 343)(227 344)(228 345)(229 346)(230 347)(231 348)(232 349)(233 350)(234 337)(235 338)(236 339)(237 340)(238 341)(239 360)(240 361)(241 362)(242 363)(243 364)(244 351)(245 352)(246 353)(247 354)(248 355)(249 356)(250 357)(251 358)(252 359)(253 377)(254 378)(255 365)(256 366)(257 367)(258 368)(259 369)(260 370)(261 371)(262 372)(263 373)(264 374)(265 375)(266 376)(267 383)(268 384)(269 385)(270 386)(271 387)(272 388)(273 389)(274 390)(275 391)(276 392)(277 379)(278 380)(279 381)(280 382)(281 395)(282 396)(283 397)(284 398)(285 399)(286 400)(287 401)(288 402)(289 403)(290 404)(291 405)(292 406)(293 393)(294 394)(295 419)(296 420)(297 407)(298 408)(299 409)(300 410)(301 411)(302 412)(303 413)(304 414)(305 415)(306 416)(307 417)(308 418)(309 422)(310 423)(311 424)(312 425)(313 426)(314 427)(315 428)(316 429)(317 430)(318 431)(319 432)(320 433)(321 434)(322 421)(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 67)(2 68)(3 69)(4 70)(5 57)(6 58)(7 59)(8 60)(9 61)(10 62)(11 63)(12 64)(13 65)(14 66)(15 73)(16 74)(17 75)(18 76)(19 77)(20 78)(21 79)(22 80)(23 81)(24 82)(25 83)(26 84)(27 71)(28 72)(29 85)(30 86)(31 87)(32 88)(33 89)(34 90)(35 91)(36 92)(37 93)(38 94)(39 95)(40 96)(41 97)(42 98)(43 103)(44 104)(45 105)(46 106)(47 107)(48 108)(49 109)(50 110)(51 111)(52 112)(53 99)(54 100)(55 101)(56 102)(113 173)(114 174)(115 175)(116 176)(117 177)(118 178)(119 179)(120 180)(121 181)(122 182)(123 169)(124 170)(125 171)(126 172)(127 184)(128 185)(129 186)(130 187)(131 188)(132 189)(133 190)(134 191)(135 192)(136 193)(137 194)(138 195)(139 196)(140 183)(141 200)(142 201)(143 202)(144 203)(145 204)(146 205)(147 206)(148 207)(149 208)(150 209)(151 210)(152 197)(153 198)(154 199)(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)(225 284)(226 285)(227 286)(228 287)(229 288)(230 289)(231 290)(232 291)(233 292)(234 293)(235 294)(236 281)(237 282)(238 283)(239 305)(240 306)(241 307)(242 308)(243 295)(244 296)(245 297)(246 298)(247 299)(248 300)(249 301)(250 302)(251 303)(252 304)(253 309)(254 310)(255 311)(256 312)(257 313)(258 314)(259 315)(260 316)(261 317)(262 318)(263 319)(264 320)(265 321)(266 322)(267 327)(268 328)(269 329)(270 330)(271 331)(272 332)(273 333)(274 334)(275 335)(276 336)(277 323)(278 324)(279 325)(280 326)(337 393)(338 394)(339 395)(340 396)(341 397)(342 398)(343 399)(344 400)(345 401)(346 402)(347 403)(348 404)(349 405)(350 406)(351 420)(352 407)(353 408)(354 409)(355 410)(356 411)(357 412)(358 413)(359 414)(360 415)(361 416)(362 417)(363 418)(364 419)(365 424)(366 425)(367 426)(368 427)(369 428)(370 429)(371 430)(372 431)(373 432)(374 433)(375 434)(376 421)(377 422)(378 423)(379 444)(380 445)(381 446)(382 447)(383 448)(384 435)(385 436)(386 437)(387 438)(388 439)(389 440)(390 441)(391 442)(392 443)
(1 38)(2 39)(3 40)(4 41)(5 42)(6 29)(7 30)(8 31)(9 32)(10 33)(11 34)(12 35)(13 36)(14 37)(15 53)(16 54)(17 55)(18 56)(19 43)(20 44)(21 45)(22 46)(23 47)(24 48)(25 49)(26 50)(27 51)(28 52)(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)(113 142)(114 143)(115 144)(116 145)(117 146)(118 147)(119 148)(120 149)(121 150)(122 151)(123 152)(124 153)(125 154)(126 141)(127 167)(128 168)(129 155)(130 156)(131 157)(132 158)(133 159)(134 160)(135 161)(136 162)(137 163)(138 164)(139 165)(140 166)(169 197)(170 198)(171 199)(172 200)(173 201)(174 202)(175 203)(176 204)(177 205)(178 206)(179 207)(180 208)(181 209)(182 210)(183 222)(184 223)(185 224)(186 211)(187 212)(188 213)(189 214)(190 215)(191 216)(192 217)(193 218)(194 219)(195 220)(196 221)(225 255)(226 256)(227 257)(228 258)(229 259)(230 260)(231 261)(232 262)(233 263)(234 264)(235 265)(236 266)(237 253)(238 254)(239 277)(240 278)(241 279)(242 280)(243 267)(244 268)(245 269)(246 270)(247 271)(248 272)(249 273)(250 274)(251 275)(252 276)(281 322)(282 309)(283 310)(284 311)(285 312)(286 313)(287 314)(288 315)(289 316)(290 317)(291 318)(292 319)(293 320)(294 321)(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)(337 374)(338 375)(339 376)(340 377)(341 378)(342 365)(343 366)(344 367)(345 368)(346 369)(347 370)(348 371)(349 372)(350 373)(351 384)(352 385)(353 386)(354 387)(355 388)(356 389)(357 390)(358 391)(359 392)(360 379)(361 380)(362 381)(363 382)(364 383)(393 433)(394 434)(395 421)(396 422)(397 423)(398 424)(399 425)(400 426)(401 427)(402 428)(403 429)(404 430)(405 431)(406 432)(407 436)(408 437)(409 438)(410 439)(411 440)(412 441)(413 442)(414 443)(415 444)(416 445)(417 446)(418 447)(419 448)(420 435)
(1 27)(2 28)(3 15)(4 16)(5 17)(6 18)(7 19)(8 20)(9 21)(10 22)(11 23)(12 24)(13 25)(14 26)(29 56)(30 43)(31 44)(32 45)(33 46)(34 47)(35 48)(36 49)(37 50)(38 51)(39 52)(40 53)(41 54)(42 55)(57 75)(58 76)(59 77)(60 78)(61 79)(62 80)(63 81)(64 82)(65 83)(66 84)(67 71)(68 72)(69 73)(70 74)(85 102)(86 103)(87 104)(88 105)(89 106)(90 107)(91 108)(92 109)(93 110)(94 111)(95 112)(96 99)(97 100)(98 101)(113 132)(114 133)(115 134)(116 135)(117 136)(118 137)(119 138)(120 139)(121 140)(122 127)(123 128)(124 129)(125 130)(126 131)(141 157)(142 158)(143 159)(144 160)(145 161)(146 162)(147 163)(148 164)(149 165)(150 166)(151 167)(152 168)(153 155)(154 156)(169 185)(170 186)(171 187)(172 188)(173 189)(174 190)(175 191)(176 192)(177 193)(178 194)(179 195)(180 196)(181 183)(182 184)(197 224)(198 211)(199 212)(200 213)(201 214)(202 215)(203 216)(204 217)(205 218)(206 219)(207 220)(208 221)(209 222)(210 223)(225 245)(226 246)(227 247)(228 248)(229 249)(230 250)(231 251)(232 252)(233 239)(234 240)(235 241)(236 242)(237 243)(238 244)(253 267)(254 268)(255 269)(256 270)(257 271)(258 272)(259 273)(260 274)(261 275)(262 276)(263 277)(264 278)(265 279)(266 280)(281 308)(282 295)(283 296)(284 297)(285 298)(286 299)(287 300)(288 301)(289 302)(290 303)(291 304)(292 305)(293 306)(294 307)(309 327)(310 328)(311 329)(312 330)(313 331)(314 332)(315 333)(316 334)(317 335)(318 336)(319 323)(320 324)(321 325)(322 326)(337 361)(338 362)(339 363)(340 364)(341 351)(342 352)(343 353)(344 354)(345 355)(346 356)(347 357)(348 358)(349 359)(350 360)(365 385)(366 386)(367 387)(368 388)(369 389)(370 390)(371 391)(372 392)(373 379)(374 380)(375 381)(376 382)(377 383)(378 384)(393 416)(394 417)(395 418)(396 419)(397 420)(398 407)(399 408)(400 409)(401 410)(402 411)(403 412)(404 413)(405 414)(406 415)(421 447)(422 448)(423 435)(424 436)(425 437)(426 438)(427 439)(428 440)(429 441)(430 442)(431 443)(432 444)(433 445)(434 446)
(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)| (1,233)(2,234)(3,235)(4,236)(5,237)(6,238)(7,225)(8,226)(9,227)(10,228)(11,229)(12,230)(13,231)(14,232)(15,241)(16,242)(17,243)(18,244)(19,245)(20,246)(21,247)(22,248)(23,249)(24,250)(25,251)(26,252)(27,239)(28,240)(29,254)(30,255)(31,256)(32,257)(33,258)(34,259)(35,260)(36,261)(37,262)(38,263)(39,264)(40,265)(41,266)(42,253)(43,269)(44,270)(45,271)(46,272)(47,273)(48,274)(49,275)(50,276)(51,277)(52,278)(53,279)(54,280)(55,267)(56,268)(57,282)(58,283)(59,284)(60,285)(61,286)(62,287)(63,288)(64,289)(65,290)(66,291)(67,292)(68,293)(69,294)(70,281)(71,305)(72,306)(73,307)(74,308)(75,295)(76,296)(77,297)(78,298)(79,299)(80,300)(81,301)(82,302)(83,303)(84,304)(85,310)(86,311)(87,312)(88,313)(89,314)(90,315)(91,316)(92,317)(93,318)(94,319)(95,320)(96,321)(97,322)(98,309)(99,325)(100,326)(101,327)(102,328)(103,329)(104,330)(105,331)(106,332)(107,333)(108,334)(109,335)(110,336)(111,323)(112,324)(113,342)(114,343)(115,344)(116,345)(117,346)(118,347)(119,348)(120,349)(121,350)(122,337)(123,338)(124,339)(125,340)(126,341)(127,361)(128,362)(129,363)(130,364)(131,351)(132,352)(133,353)(134,354)(135,355)(136,356)(137,357)(138,358)(139,359)(140,360)(141,378)(142,365)(143,366)(144,367)(145,368)(146,369)(147,370)(148,371)(149,372)(150,373)(151,374)(152,375)(153,376)(154,377)(155,382)(156,383)(157,384)(158,385)(159,386)(160,387)(161,388)(162,389)(163,390)(164,391)(165,392)(166,379)(167,380)(168,381)(169,394)(170,395)(171,396)(172,397)(173,398)(174,399)(175,400)(176,401)(177,402)(178,403)(179,404)(180,405)(181,406)(182,393)(183,415)(184,416)(185,417)(186,418)(187,419)(188,420)(189,407)(190,408)(191,409)(192,410)(193,411)(194,412)(195,413)(196,414)(197,434)(198,421)(199,422)(200,423)(201,424)(202,425)(203,426)(204,427)(205,428)(206,429)(207,430)(208,431)(209,432)(210,433)(211,447)(212,448)(213,435)(214,436)(215,437)(216,438)(217,439)(218,440)(219,441)(220,442)(221,443)(222,444)(223,445)(224,446), (1,121)(2,122)(3,123)(4,124)(5,125)(6,126)(7,113)(8,114)(9,115)(10,116)(11,117)(12,118)(13,119)(14,120)(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)(29,141)(30,142)(31,143)(32,144)(33,145)(34,146)(35,147)(36,148)(37,149)(38,150)(39,151)(40,152)(41,153)(42,154)(43,158)(44,159)(45,160)(46,161)(47,162)(48,163)(49,164)(50,165)(51,166)(52,167)(53,168)(54,155)(55,156)(56,157)(57,171)(58,172)(59,173)(60,174)(61,175)(62,176)(63,177)(64,178)(65,179)(66,180)(67,181)(68,182)(69,169)(70,170)(71,183)(72,184)(73,185)(74,186)(75,187)(76,188)(77,189)(78,190)(79,191)(80,192)(81,193)(82,194)(83,195)(84,196)(85,200)(86,201)(87,202)(88,203)(89,204)(90,205)(91,206)(92,207)(93,208)(94,209)(95,210)(96,197)(97,198)(98,199)(99,224)(100,211)(101,212)(102,213)(103,214)(104,215)(105,216)(106,217)(107,218)(108,219)(109,220)(110,221)(111,222)(112,223)(225,342)(226,343)(227,344)(228,345)(229,346)(230,347)(231,348)(232,349)(233,350)(234,337)(235,338)(236,339)(237,340)(238,341)(239,360)(240,361)(241,362)(242,363)(243,364)(244,351)(245,352)(246,353)(247,354)(248,355)(249,356)(250,357)(251,358)(252,359)(253,377)(254,378)(255,365)(256,366)(257,367)(258,368)(259,369)(260,370)(261,371)(262,372)(263,373)(264,374)(265,375)(266,376)(267,383)(268,384)(269,385)(270,386)(271,387)(272,388)(273,389)(274,390)(275,391)(276,392)(277,379)(278,380)(279,381)(280,382)(281,395)(282,396)(283,397)(284,398)(285,399)(286,400)(287,401)(288,402)(289,403)(290,404)(291,405)(292,406)(293,393)(294,394)(295,419)(296,420)(297,407)(298,408)(299,409)(300,410)(301,411)(302,412)(303,413)(304,414)(305,415)(306,416)(307,417)(308,418)(309,422)(310,423)(311,424)(312,425)(313,426)(314,427)(315,428)(316,429)(317,430)(318,431)(319,432)(320,433)(321,434)(322,421)(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), (1,67)(2,68)(3,69)(4,70)(5,57)(6,58)(7,59)(8,60)(9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,73)(16,74)(17,75)(18,76)(19,77)(20,78)(21,79)(22,80)(23,81)(24,82)(25,83)(26,84)(27,71)(28,72)(29,85)(30,86)(31,87)(32,88)(33,89)(34,90)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,97)(42,98)(43,103)(44,104)(45,105)(46,106)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,99)(54,100)(55,101)(56,102)(113,173)(114,174)(115,175)(116,176)(117,177)(118,178)(119,179)(120,180)(121,181)(122,182)(123,169)(124,170)(125,171)(126,172)(127,184)(128,185)(129,186)(130,187)(131,188)(132,189)(133,190)(134,191)(135,192)(136,193)(137,194)(138,195)(139,196)(140,183)(141,200)(142,201)(143,202)(144,203)(145,204)(146,205)(147,206)(148,207)(149,208)(150,209)(151,210)(152,197)(153,198)(154,199)(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)(225,284)(226,285)(227,286)(228,287)(229,288)(230,289)(231,290)(232,291)(233,292)(234,293)(235,294)(236,281)(237,282)(238,283)(239,305)(240,306)(241,307)(242,308)(243,295)(244,296)(245,297)(246,298)(247,299)(248,300)(249,301)(250,302)(251,303)(252,304)(253,309)(254,310)(255,311)(256,312)(257,313)(258,314)(259,315)(260,316)(261,317)(262,318)(263,319)(264,320)(265,321)(266,322)(267,327)(268,328)(269,329)(270,330)(271,331)(272,332)(273,333)(274,334)(275,335)(276,336)(277,323)(278,324)(279,325)(280,326)(337,393)(338,394)(339,395)(340,396)(341,397)(342,398)(343,399)(344,400)(345,401)(346,402)(347,403)(348,404)(349,405)(350,406)(351,420)(352,407)(353,408)(354,409)(355,410)(356,411)(357,412)(358,413)(359,414)(360,415)(361,416)(362,417)(363,418)(364,419)(365,424)(366,425)(367,426)(368,427)(369,428)(370,429)(371,430)(372,431)(373,432)(374,433)(375,434)(376,421)(377,422)(378,423)(379,444)(380,445)(381,446)(382,447)(383,448)(384,435)(385,436)(386,437)(387,438)(388,439)(389,440)(390,441)(391,442)(392,443), (1,38)(2,39)(3,40)(4,41)(5,42)(6,29)(7,30)(8,31)(9,32)(10,33)(11,34)(12,35)(13,36)(14,37)(15,53)(16,54)(17,55)(18,56)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,49)(26,50)(27,51)(28,52)(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)(113,142)(114,143)(115,144)(116,145)(117,146)(118,147)(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,141)(127,167)(128,168)(129,155)(130,156)(131,157)(132,158)(133,159)(134,160)(135,161)(136,162)(137,163)(138,164)(139,165)(140,166)(169,197)(170,198)(171,199)(172,200)(173,201)(174,202)(175,203)(176,204)(177,205)(178,206)(179,207)(180,208)(181,209)(182,210)(183,222)(184,223)(185,224)(186,211)(187,212)(188,213)(189,214)(190,215)(191,216)(192,217)(193,218)(194,219)(195,220)(196,221)(225,255)(226,256)(227,257)(228,258)(229,259)(230,260)(231,261)(232,262)(233,263)(234,264)(235,265)(236,266)(237,253)(238,254)(239,277)(240,278)(241,279)(242,280)(243,267)(244,268)(245,269)(246,270)(247,271)(248,272)(249,273)(250,274)(251,275)(252,276)(281,322)(282,309)(283,310)(284,311)(285,312)(286,313)(287,314)(288,315)(289,316)(290,317)(291,318)(292,319)(293,320)(294,321)(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)(337,374)(338,375)(339,376)(340,377)(341,378)(342,365)(343,366)(344,367)(345,368)(346,369)(347,370)(348,371)(349,372)(350,373)(351,384)(352,385)(353,386)(354,387)(355,388)(356,389)(357,390)(358,391)(359,392)(360,379)(361,380)(362,381)(363,382)(364,383)(393,433)(394,434)(395,421)(396,422)(397,423)(398,424)(399,425)(400,426)(401,427)(402,428)(403,429)(404,430)(405,431)(406,432)(407,436)(408,437)(409,438)(410,439)(411,440)(412,441)(413,442)(414,443)(415,444)(416,445)(417,446)(418,447)(419,448)(420,435), 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G:=Group( 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(1,38)(2,39)(3,40)(4,41)(5,42)(6,29)(7,30)(8,31)(9,32)(10,33)(11,34)(12,35)(13,36)(14,37)(15,53)(16,54)(17,55)(18,56)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,49)(26,50)(27,51)(28,52)(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)(113,142)(114,143)(115,144)(116,145)(117,146)(118,147)(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,141)(127,167)(128,168)(129,155)(130,156)(131,157)(132,158)(133,159)(134,160)(135,161)(136,162)(137,163)(138,164)(139,165)(140,166)(169,197)(170,198)(171,199)(172,200)(173,201)(174,202)(175,203)(176,204)(177,205)(178,206)(179,207)(180,208)(181,209)(182,210)(183,222)(184,223)(185,224)(186,211)(187,212)(188,213)(189,214)(190,215)(191,216)(192,217)(193,218)(194,219)(195,220)(196,221)(225,255)(226,256)(227,257)(228,258)(229,259)(230,260)(231,261)(232,262)(233,263)(234,264)(235,265)(236,266)(237,253)(238,254)(239,277)(240,278)(241,279)(242,280)(243,267)(244,268)(245,269)(246,270)(247,271)(248,272)(249,273)(250,274)(251,275)(252,276)(281,322)(282,309)(283,310)(284,311)(285,312)(286,313)(287,314)(288,315)(289,316)(290,317)(291,318)(292,319)(293,320)(294,321)(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)(337,374)(338,375)(339,376)(340,377)(341,378)(342,365)(343,366)(344,367)(345,368)(346,369)(347,370)(348,371)(349,372)(350,373)(351,384)(352,385)(353,386)(354,387)(355,388)(356,389)(357,390)(358,391)(359,392)(360,379)(361,380)(362,381)(363,382)(364,383)(393,433)(394,434)(395,421)(396,422)(397,423)(398,424)(399,425)(400,426)(401,427)(402,428)(403,429)(404,430)(405,431)(406,432)(407,436)(408,437)(409,438)(410,439)(411,440)(412,441)(413,442)(414,443)(415,444)(416,445)(417,446)(418,447)(419,448)(420,435), (1,27)(2,28)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(29,56)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52)(40,53)(41,54)(42,55)(57,75)(58,76)(59,77)(60,78)(61,79)(62,80)(63,81)(64,82)(65,83)(66,84)(67,71)(68,72)(69,73)(70,74)(85,102)(86,103)(87,104)(88,105)(89,106)(90,107)(91,108)(92,109)(93,110)(94,111)(95,112)(96,99)(97,100)(98,101)(113,132)(114,133)(115,134)(116,135)(117,136)(118,137)(119,138)(120,139)(121,140)(122,127)(123,128)(124,129)(125,130)(126,131)(141,157)(142,158)(143,159)(144,160)(145,161)(146,162)(147,163)(148,164)(149,165)(150,166)(151,167)(152,168)(153,155)(154,156)(169,185)(170,186)(171,187)(172,188)(173,189)(174,190)(175,191)(176,192)(177,193)(178,194)(179,195)(180,196)(181,183)(182,184)(197,224)(198,211)(199,212)(200,213)(201,214)(202,215)(203,216)(204,217)(205,218)(206,219)(207,220)(208,221)(209,222)(210,223)(225,245)(226,246)(227,247)(228,248)(229,249)(230,250)(231,251)(232,252)(233,239)(234,240)(235,241)(236,242)(237,243)(238,244)(253,267)(254,268)(255,269)(256,270)(257,271)(258,272)(259,273)(260,274)(261,275)(262,276)(263,277)(264,278)(265,279)(266,280)(281,308)(282,295)(283,296)(284,297)(285,298)(286,299)(287,300)(288,301)(289,302)(290,303)(291,304)(292,305)(293,306)(294,307)(309,327)(310,328)(311,329)(312,330)(313,331)(314,332)(315,333)(316,334)(317,335)(318,336)(319,323)(320,324)(321,325)(322,326)(337,361)(338,362)(339,363)(340,364)(341,351)(342,352)(343,353)(344,354)(345,355)(346,356)(347,357)(348,358)(349,359)(350,360)(365,385)(366,386)(367,387)(368,388)(369,389)(370,390)(371,391)(372,392)(373,379)(374,380)(375,381)(376,382)(377,383)(378,384)(393,416)(394,417)(395,418)(396,419)(397,420)(398,407)(399,408)(400,409)(401,410)(402,411)(403,412)(404,413)(405,414)(406,415)(421,447)(422,448)(423,435)(424,436)(425,437)(426,438)(427,439)(428,440)(429,441)(430,442)(431,443)(432,444)(433,445)(434,446), (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([(1,233),(2,234),(3,235),(4,236),(5,237),(6,238),(7,225),(8,226),(9,227),(10,228),(11,229),(12,230),(13,231),(14,232),(15,241),(16,242),(17,243),(18,244),(19,245),(20,246),(21,247),(22,248),(23,249),(24,250),(25,251),(26,252),(27,239),(28,240),(29,254),(30,255),(31,256),(32,257),(33,258),(34,259),(35,260),(36,261),(37,262),(38,263),(39,264),(40,265),(41,266),(42,253),(43,269),(44,270),(45,271),(46,272),(47,273),(48,274),(49,275),(50,276),(51,277),(52,278),(53,279),(54,280),(55,267),(56,268),(57,282),(58,283),(59,284),(60,285),(61,286),(62,287),(63,288),(64,289),(65,290),(66,291),(67,292),(68,293),(69,294),(70,281),(71,305),(72,306),(73,307),(74,308),(75,295),(76,296),(77,297),(78,298),(79,299),(80,300),(81,301),(82,302),(83,303),(84,304),(85,310),(86,311),(87,312),(88,313),(89,314),(90,315),(91,316),(92,317),(93,318),(94,319),(95,320),(96,321),(97,322),(98,309),(99,325),(100,326),(101,327),(102,328),(103,329),(104,330),(105,331),(106,332),(107,333),(108,334),(109,335),(110,336),(111,323),(112,324),(113,342),(114,343),(115,344),(116,345),(117,346),(118,347),(119,348),(120,349),(121,350),(122,337),(123,338),(124,339),(125,340),(126,341),(127,361),(128,362),(129,363),(130,364),(131,351),(132,352),(133,353),(134,354),(135,355),(136,356),(137,357),(138,358),(139,359),(140,360),(141,378),(142,365),(143,366),(144,367),(145,368),(146,369),(147,370),(148,371),(149,372),(150,373),(151,374),(152,375),(153,376),(154,377),(155,382),(156,383),(157,384),(158,385),(159,386),(160,387),(161,388),(162,389),(163,390),(164,391),(165,392),(166,379),(167,380),(168,381),(169,394),(170,395),(171,396),(172,397),(173,398),(174,399),(175,400),(176,401),(177,402),(178,403),(179,404),(180,405),(181,406),(182,393),(183,415),(184,416),(185,417),(186,418),(187,419),(188,420),(189,407),(190,408),(191,409),(192,410),(193,411),(194,412),(195,413),(196,414),(197,434),(198,421),(199,422),(200,423),(201,424),(202,425),(203,426),(204,427),(205,428),(206,429),(207,430),(208,431),(209,432),(210,433),(211,447),(212,448),(213,435),(214,436),(215,437),(216,438),(217,439),(218,440),(219,441),(220,442),(221,443),(222,444),(223,445),(224,446)], [(1,121),(2,122),(3,123),(4,124),(5,125),(6,126),(7,113),(8,114),(9,115),(10,116),(11,117),(12,118),(13,119),(14,120),(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),(29,141),(30,142),(31,143),(32,144),(33,145),(34,146),(35,147),(36,148),(37,149),(38,150),(39,151),(40,152),(41,153),(42,154),(43,158),(44,159),(45,160),(46,161),(47,162),(48,163),(49,164),(50,165),(51,166),(52,167),(53,168),(54,155),(55,156),(56,157),(57,171),(58,172),(59,173),(60,174),(61,175),(62,176),(63,177),(64,178),(65,179),(66,180),(67,181),(68,182),(69,169),(70,170),(71,183),(72,184),(73,185),(74,186),(75,187),(76,188),(77,189),(78,190),(79,191),(80,192),(81,193),(82,194),(83,195),(84,196),(85,200),(86,201),(87,202),(88,203),(89,204),(90,205),(91,206),(92,207),(93,208),(94,209),(95,210),(96,197),(97,198),(98,199),(99,224),(100,211),(101,212),(102,213),(103,214),(104,215),(105,216),(106,217),(107,218),(108,219),(109,220),(110,221),(111,222),(112,223),(225,342),(226,343),(227,344),(228,345),(229,346),(230,347),(231,348),(232,349),(233,350),(234,337),(235,338),(236,339),(237,340),(238,341),(239,360),(240,361),(241,362),(242,363),(243,364),(244,351),(245,352),(246,353),(247,354),(248,355),(249,356),(250,357),(251,358),(252,359),(253,377),(254,378),(255,365),(256,366),(257,367),(258,368),(259,369),(260,370),(261,371),(262,372),(263,373),(264,374),(265,375),(266,376),(267,383),(268,384),(269,385),(270,386),(271,387),(272,388),(273,389),(274,390),(275,391),(276,392),(277,379),(278,380),(279,381),(280,382),(281,395),(282,396),(283,397),(284,398),(285,399),(286,400),(287,401),(288,402),(289,403),(290,404),(291,405),(292,406),(293,393),(294,394),(295,419),(296,420),(297,407),(298,408),(299,409),(300,410),(301,411),(302,412),(303,413),(304,414),(305,415),(306,416),(307,417),(308,418),(309,422),(310,423),(311,424),(312,425),(313,426),(314,427),(315,428),(316,429),(317,430),(318,431),(319,432),(320,433),(321,434),(322,421),(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)], [(1,67),(2,68),(3,69),(4,70),(5,57),(6,58),(7,59),(8,60),(9,61),(10,62),(11,63),(12,64),(13,65),(14,66),(15,73),(16,74),(17,75),(18,76),(19,77),(20,78),(21,79),(22,80),(23,81),(24,82),(25,83),(26,84),(27,71),(28,72),(29,85),(30,86),(31,87),(32,88),(33,89),(34,90),(35,91),(36,92),(37,93),(38,94),(39,95),(40,96),(41,97),(42,98),(43,103),(44,104),(45,105),(46,106),(47,107),(48,108),(49,109),(50,110),(51,111),(52,112),(53,99),(54,100),(55,101),(56,102),(113,173),(114,174),(115,175),(116,176),(117,177),(118,178),(119,179),(120,180),(121,181),(122,182),(123,169),(124,170),(125,171),(126,172),(127,184),(128,185),(129,186),(130,187),(131,188),(132,189),(133,190),(134,191),(135,192),(136,193),(137,194),(138,195),(139,196),(140,183),(141,200),(142,201),(143,202),(144,203),(145,204),(146,205),(147,206),(148,207),(149,208),(150,209),(151,210),(152,197),(153,198),(154,199),(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),(225,284),(226,285),(227,286),(228,287),(229,288),(230,289),(231,290),(232,291),(233,292),(234,293),(235,294),(236,281),(237,282),(238,283),(239,305),(240,306),(241,307),(242,308),(243,295),(244,296),(245,297),(246,298),(247,299),(248,300),(249,301),(250,302),(251,303),(252,304),(253,309),(254,310),(255,311),(256,312),(257,313),(258,314),(259,315),(260,316),(261,317),(262,318),(263,319),(264,320),(265,321),(266,322),(267,327),(268,328),(269,329),(270,330),(271,331),(272,332),(273,333),(274,334),(275,335),(276,336),(277,323),(278,324),(279,325),(280,326),(337,393),(338,394),(339,395),(340,396),(341,397),(342,398),(343,399),(344,400),(345,401),(346,402),(347,403),(348,404),(349,405),(350,406),(351,420),(352,407),(353,408),(354,409),(355,410),(356,411),(357,412),(358,413),(359,414),(360,415),(361,416),(362,417),(363,418),(364,419),(365,424),(366,425),(367,426),(368,427),(369,428),(370,429),(371,430),(372,431),(373,432),(374,433),(375,434),(376,421),(377,422),(378,423),(379,444),(380,445),(381,446),(382,447),(383,448),(384,435),(385,436),(386,437),(387,438),(388,439),(389,440),(390,441),(391,442),(392,443)], [(1,38),(2,39),(3,40),(4,41),(5,42),(6,29),(7,30),(8,31),(9,32),(10,33),(11,34),(12,35),(13,36),(14,37),(15,53),(16,54),(17,55),(18,56),(19,43),(20,44),(21,45),(22,46),(23,47),(24,48),(25,49),(26,50),(27,51),(28,52),(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),(113,142),(114,143),(115,144),(116,145),(117,146),(118,147),(119,148),(120,149),(121,150),(122,151),(123,152),(124,153),(125,154),(126,141),(127,167),(128,168),(129,155),(130,156),(131,157),(132,158),(133,159),(134,160),(135,161),(136,162),(137,163),(138,164),(139,165),(140,166),(169,197),(170,198),(171,199),(172,200),(173,201),(174,202),(175,203),(176,204),(177,205),(178,206),(179,207),(180,208),(181,209),(182,210),(183,222),(184,223),(185,224),(186,211),(187,212),(188,213),(189,214),(190,215),(191,216),(192,217),(193,218),(194,219),(195,220),(196,221),(225,255),(226,256),(227,257),(228,258),(229,259),(230,260),(231,261),(232,262),(233,263),(234,264),(235,265),(236,266),(237,253),(238,254),(239,277),(240,278),(241,279),(242,280),(243,267),(244,268),(245,269),(246,270),(247,271),(248,272),(249,273),(250,274),(251,275),(252,276),(281,322),(282,309),(283,310),(284,311),(285,312),(286,313),(287,314),(288,315),(289,316),(290,317),(291,318),(292,319),(293,320),(294,321),(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),(337,374),(338,375),(339,376),(340,377),(341,378),(342,365),(343,366),(344,367),(345,368),(346,369),(347,370),(348,371),(349,372),(350,373),(351,384),(352,385),(353,386),(354,387),(355,388),(356,389),(357,390),(358,391),(359,392),(360,379),(361,380),(362,381),(363,382),(364,383),(393,433),(394,434),(395,421),(396,422),(397,423),(398,424),(399,425),(400,426),(401,427),(402,428),(403,429),(404,430),(405,431),(406,432),(407,436),(408,437),(409,438),(410,439),(411,440),(412,441),(413,442),(414,443),(415,444),(416,445),(417,446),(418,447),(419,448),(420,435)], [(1,27),(2,28),(3,15),(4,16),(5,17),(6,18),(7,19),(8,20),(9,21),(10,22),(11,23),(12,24),(13,25),(14,26),(29,56),(30,43),(31,44),(32,45),(33,46),(34,47),(35,48),(36,49),(37,50),(38,51),(39,52),(40,53),(41,54),(42,55),(57,75),(58,76),(59,77),(60,78),(61,79),(62,80),(63,81),(64,82),(65,83),(66,84),(67,71),(68,72),(69,73),(70,74),(85,102),(86,103),(87,104),(88,105),(89,106),(90,107),(91,108),(92,109),(93,110),(94,111),(95,112),(96,99),(97,100),(98,101),(113,132),(114,133),(115,134),(116,135),(117,136),(118,137),(119,138),(120,139),(121,140),(122,127),(123,128),(124,129),(125,130),(126,131),(141,157),(142,158),(143,159),(144,160),(145,161),(146,162),(147,163),(148,164),(149,165),(150,166),(151,167),(152,168),(153,155),(154,156),(169,185),(170,186),(171,187),(172,188),(173,189),(174,190),(175,191),(176,192),(177,193),(178,194),(179,195),(180,196),(181,183),(182,184),(197,224),(198,211),(199,212),(200,213),(201,214),(202,215),(203,216),(204,217),(205,218),(206,219),(207,220),(208,221),(209,222),(210,223),(225,245),(226,246),(227,247),(228,248),(229,249),(230,250),(231,251),(232,252),(233,239),(234,240),(235,241),(236,242),(237,243),(238,244),(253,267),(254,268),(255,269),(256,270),(257,271),(258,272),(259,273),(260,274),(261,275),(262,276),(263,277),(264,278),(265,279),(266,280),(281,308),(282,295),(283,296),(284,297),(285,298),(286,299),(287,300),(288,301),(289,302),(290,303),(291,304),(292,305),(293,306),(294,307),(309,327),(310,328),(311,329),(312,330),(313,331),(314,332),(315,333),(316,334),(317,335),(318,336),(319,323),(320,324),(321,325),(322,326),(337,361),(338,362),(339,363),(340,364),(341,351),(342,352),(343,353),(344,354),(345,355),(346,356),(347,357),(348,358),(349,359),(350,360),(365,385),(366,386),(367,387),(368,388),(369,389),(370,390),(371,391),(372,392),(373,379),(374,380),(375,381),(376,382),(377,383),(378,384),(393,416),(394,417),(395,418),(396,419),(397,420),(398,407),(399,408),(400,409),(401,410),(402,411),(403,412),(404,413),(405,414),(406,415),(421,447),(422,448),(423,435),(424,436),(425,437),(426,438),(427,439),(428,440),(429,441),(430,442),(431,443),(432,444),(433,445),(434,446)], [(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)])

448 conjugacy classes

class 1 2A···2BK7A···7F14A···14NN
order12···27···714···14
size11···11···11···1

448 irreducible representations

dim1111
type++
imageC1C2C7C14
kernelC25×C14C24×C14C26C25
# reps1636378

Matrix representation of C25×C14 in GL6(𝔽29)

2800000
010000
0028000
000100
0000280
000001
,
2800000
0280000
001000
0002800
0000280
0000028
,
2800000
010000
001000
0002800
000010
000001
,
100000
0280000
0028000
0002800
0000280
0000028
,
100000
0280000
0028000
0002800
0000280
000001
,
500000
050000
005000
0002200
0000220
000007

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] >;

C25×C14 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

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