C2^5xC14 - GroupNames

G = C₂⁵×C₁₄ order 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

Derived series

C₁ — C₂⁵×C₁₄

Chief series

C₁ — C₇ — C₁₄ — C₂×C₁₄ — C₂²×C₁₄ — C₂³×C₁₄ — C₂⁴×C₁₄ — C₂⁵×C₁₄

Lower central

C₁ — C₂⁵×C₁₄

Upper central

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, C₂², C₇, C₂³, C₁₄, C₂⁴, C₂×C₁₄, C₂⁵, C₂²×C₁₄, C₂⁶, C₂³×C₁₄, C₂⁴×C₁₄, C₂⁵×C₁₄
Quotients: C₁, C₂, C₂², C₇, C₂³, C₁₄, C₂⁴, C₂×C₁₄, C₂⁵, C₂²×C₁₄, C₂⁶, C₂³×C₁₄, C₂⁴×C₁₄, 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)(15 244)(16 245)(17 246)(18 247)(19 248)(20 249)(21 250)(22 251)(23 252)(24 239)(25 240)(26 241)(27 242)(28 243)(29 265)(30 266)(31 253)(32 254)(33 255)(34 256)(35 257)(36 258)(37 259)(38 260)(39 261)(40 262)(41 263)(42 264)(43 268)(44 269)(45 270)(46 271)(47 272)(48 273)(49 274)(50 275)(51 276)(52 277)(53 278)(54 279)(55 280)(56 267)(57 286)(58 287)(59 288)(60 289)(61 290)(62 291)(63 292)(64 293)(65 294)(66 281)(67 282)(68 283)(69 284)(70 285)(71 299)(72 300)(73 301)(74 302)(75 303)(76 304)(77 305)(78 306)(79 307)(80 308)(81 295)(82 296)(83 297)(84 298)(85 315)(86 316)(87 317)(88 318)(89 319)(90 320)(91 321)(92 322)(93 309)(94 310)(95 311)(96 312)(97 313)(98 314)(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)(113 338)(114 339)(115 340)(116 341)(117 342)(118 343)(119 344)(120 345)(121 346)(122 347)(123 348)(124 349)(125 350)(126 337)(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)(141 368)(142 369)(143 370)(144 371)(145 372)(146 373)(147 374)(148 375)(149 376)(150 377)(151 378)(152 365)(153 366)(154 367)(155 390)(156 391)(157 392)(158 379)(159 380)(160 381)(161 382)(162 383)(163 384)(164 385)(165 386)(166 387)(167 388)(168 389)(169 403)(170 404)(171 405)(172 406)(173 393)(174 394)(175 395)(176 396)(177 397)(178 398)(179 399)(180 400)(181 401)(182 402)(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)(197 431)(198 432)(199 433)(200 434)(201 421)(202 422)(203 423)(204 424)(205 425)(206 426)(207 427)(208 428)(209 429)(210 430)(211 435)(212 436)(213 437)(214 438)(215 439)(216 440)(217 441)(218 442)(219 443)(220 444)(221 445)(222 446)(223 447)(224 448)

(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)(15 133)(16 134)(17 135)(18 136)(19 137)(20 138)(21 139)(22 140)(23 127)(24 128)(25 129)(26 130)(27 131)(28 132)(29 154)(30 141)(31 142)(32 143)(33 144)(34 145)(35 146)(36 147)(37 148)(38 149)(39 150)(40 151)(41 152)(42 153)(43 160)(44 161)(45 162)(46 163)(47 164)(48 165)(49 166)(50 167)(51 168)(52 155)(53 156)(54 157)(55 158)(56 159)(57 174)(58 175)(59 176)(60 177)(61 178)(62 179)(63 180)(64 181)(65 182)(66 169)(67 170)(68 171)(69 172)(70 173)(71 186)(72 187)(73 188)(74 189)(75 190)(76 191)(77 192)(78 193)(79 194)(80 195)(81 196)(82 183)(83 184)(84 185)(85 203)(86 204)(87 205)(88 206)(89 207)(90 208)(91 209)(92 210)(93 197)(94 198)(95 199)(96 200)(97 201)(98 202)(99 211)(100 212)(101 213)(102 214)(103 215)(104 216)(105 217)(106 218)(107 219)(108 220)(109 221)(110 222)(111 223)(112 224)(225 338)(226 339)(227 340)(228 341)(229 342)(230 343)(231 344)(232 345)(233 346)(234 347)(235 348)(236 349)(237 350)(238 337)(239 362)(240 363)(241 364)(242 351)(243 352)(244 353)(245 354)(246 355)(247 356)(248 357)(249 358)(250 359)(251 360)(252 361)(253 369)(254 370)(255 371)(256 372)(257 373)(258 374)(259 375)(260 376)(261 377)(262 378)(263 365)(264 366)(265 367)(266 368)(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)(281 403)(282 404)(283 405)(284 406)(285 393)(286 394)(287 395)(288 396)(289 397)(290 398)(291 399)(292 400)(293 401)(294 402)(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)(309 431)(310 432)(311 433)(312 434)(313 421)(314 422)(315 423)(316 424)(317 425)(318 426)(319 427)(320 428)(321 429)(322 430)(323 448)(324 435)(325 436)(326 437)(327 438)(328 439)(329 440)(330 441)(331 442)(332 443)(333 444)(334 445)(335 446)(336 447)

(1 65)(2 66)(3 67)(4 68)(5 69)(6 70)(7 57)(8 58)(9 59)(10 60)(11 61)(12 62)(13 63)(14 64)(15 71)(16 72)(17 73)(18 74)(19 75)(20 76)(21 77)(22 78)(23 79)(24 80)(25 81)(26 82)(27 83)(28 84)(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 99)(44 100)(45 101)(46 102)(47 103)(48 104)(49 105)(50 106)(51 107)(52 108)(53 109)(54 110)(55 111)(56 112)(113 174)(114 175)(115 176)(116 177)(117 178)(118 179)(119 180)(120 181)(121 182)(122 169)(123 170)(124 171)(125 172)(126 173)(127 194)(128 195)(129 196)(130 183)(131 184)(132 185)(133 186)(134 187)(135 188)(136 189)(137 190)(138 191)(139 192)(140 193)(141 202)(142 203)(143 204)(144 205)(145 206)(146 207)(147 208)(148 209)(149 210)(150 197)(151 198)(152 199)(153 200)(154 201)(155 220)(156 221)(157 222)(158 223)(159 224)(160 211)(161 212)(162 213)(163 214)(164 215)(165 216)(166 217)(167 218)(168 219)(225 286)(226 287)(227 288)(228 289)(229 290)(230 291)(231 292)(232 293)(233 294)(234 281)(235 282)(236 283)(237 284)(238 285)(239 308)(240 295)(241 296)(242 297)(243 298)(244 299)(245 300)(246 301)(247 302)(248 303)(249 304)(250 305)(251 306)(252 307)(253 315)(254 316)(255 317)(256 318)(257 319)(258 320)(259 321)(260 322)(261 309)(262 310)(263 311)(264 312)(265 313)(266 314)(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)(337 393)(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)(351 411)(352 412)(353 413)(354 414)(355 415)(356 416)(357 417)(358 418)(359 419)(360 420)(361 407)(362 408)(363 409)(364 410)(365 433)(366 434)(367 421)(368 422)(369 423)(370 424)(371 425)(372 426)(373 427)(374 428)(375 429)(376 430)(377 431)(378 432)(379 447)(380 448)(381 435)(382 436)(383 437)(384 438)(385 439)(386 440)(387 441)(388 442)(389 443)(390 444)(391 445)(392 446)

(1 39)(2 40)(3 41)(4 42)(5 29)(6 30)(7 31)(8 32)(9 33)(10 34)(11 35)(12 36)(13 37)(14 38)(15 44)(16 45)(17 46)(18 47)(19 48)(20 49)(21 50)(22 51)(23 52)(24 53)(25 54)(26 55)(27 56)(28 43)(57 85)(58 86)(59 87)(60 88)(61 89)(62 90)(63 91)(64 92)(65 93)(66 94)(67 95)(68 96)(69 97)(70 98)(71 100)(72 101)(73 102)(74 103)(75 104)(76 105)(77 106)(78 107)(79 108)(80 109)(81 110)(82 111)(83 112)(84 99)(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)(127 155)(128 156)(129 157)(130 158)(131 159)(132 160)(133 161)(134 162)(135 163)(136 164)(137 165)(138 166)(139 167)(140 168)(169 198)(170 199)(171 200)(172 201)(173 202)(174 203)(175 204)(176 205)(177 206)(178 207)(179 208)(180 209)(181 210)(182 197)(183 223)(184 224)(185 211)(186 212)(187 213)(188 214)(189 215)(190 216)(191 217)(192 218)(193 219)(194 220)(195 221)(196 222)(225 253)(226 254)(227 255)(228 256)(229 257)(230 258)(231 259)(232 260)(233 261)(234 262)(235 263)(236 264)(237 265)(238 266)(239 278)(240 279)(241 280)(242 267)(243 268)(244 269)(245 270)(246 271)(247 272)(248 273)(249 274)(250 275)(251 276)(252 277)(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)(295 335)(296 336)(297 323)(298 324)(299 325)(300 326)(301 327)(302 328)(303 329)(304 330)(305 331)(306 332)(307 333)(308 334)(337 368)(338 369)(339 370)(340 371)(341 372)(342 373)(343 374)(344 375)(345 376)(346 377)(347 378)(348 365)(349 366)(350 367)(351 380)(352 381)(353 382)(354 383)(355 384)(356 385)(357 386)(358 387)(359 388)(360 389)(361 390)(362 391)(363 392)(364 379)(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)(407 444)(408 445)(409 446)(410 447)(411 448)(412 435)(413 436)(414 437)(415 438)(416 439)(417 440)(418 441)(419 442)(420 443)

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

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

Matrix representation of C₂⁵×C₁₄ ►in 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] >;

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

G = C25×C14 order 448 = 26·7

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

G = C₂⁵×C₁₄ order 448 = 2⁶·7