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G = C24×C28  order 448 = 26·7

Abelian group of type [2,2,2,2,28]

direct product, abelian, monomial, 2-elementary

Aliases: C24×C28, SmallGroup(448,1385)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C24×C28
Chief series
C1 — C2 — C14 — C28 — C2×C28 — C22×C28 — C23×C28 — C24×C28
Lower central
C1 — C24×C28
Upper central
C1 — C24×C28

Generators and relations for C24×C28
 G = < a,b,c,d,e | a2=b2=c2=d2=e28=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, de=ed >

Subgroups: 1362, all normal (8 characteristic)
C1, C2, C2, C4, C22, C7, C2×C4, C23, C14, C14, C22×C4, C24, C28, C2×C14, C23×C4, C25, C2×C28, C22×C14, C24×C4, C22×C28, C23×C14, C23×C28, C24×C14, C24×C28
Quotients: C1, C2, C4, C22, C7, C2×C4, C23, C14, C22×C4, C24, C28, C2×C14, C23×C4, C25, C2×C28, C22×C14, C24×C4, C22×C28, C23×C14, C23×C28, C24×C14, C24×C28

Smallest permutation representation of C24×C28
►Regular action on 448 points
Generators in S448
(1 276)(2 277)(3 278)(4 279)(5 280)(6 253)(7 254)(8 255)(9 256)(10 257)(11 258)(12 259)(13 260)(14 261)(15 262)(16 263)(17 264)(18 265)(19 266)(20 267)(21 268)(22 269)(23 270)(24 271)(25 272)(26 273)(27 274)(28 275)(29 154)(30 155)(31 156)(32 157)(33 158)(34 159)(35 160)(36 161)(37 162)(38 163)(39 164)(40 165)(41 166)(42 167)(43 168)(44 141)(45 142)(46 143)(47 144)(48 145)(49 146)(50 147)(51 148)(52 149)(53 150)(54 151)(55 152)(56 153)(57 220)(58 221)(59 222)(60 223)(61 224)(62 197)(63 198)(64 199)(65 200)(66 201)(67 202)(68 203)(69 204)(70 205)(71 206)(72 207)(73 208)(74 209)(75 210)(76 211)(77 212)(78 213)(79 214)(80 215)(81 216)(82 217)(83 218)(84 219)(85 290)(86 291)(87 292)(88 293)(89 294)(90 295)(91 296)(92 297)(93 298)(94 299)(95 300)(96 301)(97 302)(98 303)(99 304)(100 305)(101 306)(102 307)(103 308)(104 281)(105 282)(106 283)(107 284)(108 285)(109 286)(110 287)(111 288)(112 289)(113 411)(114 412)(115 413)(116 414)(117 415)(118 416)(119 417)(120 418)(121 419)(122 420)(123 393)(124 394)(125 395)(126 396)(127 397)(128 398)(129 399)(130 400)(131 401)(132 402)(133 403)(134 404)(135 405)(136 406)(137 407)(138 408)(139 409)(140 410)(169 321)(170 322)(171 323)(172 324)(173 325)(174 326)(175 327)(176 328)(177 329)(178 330)(179 331)(180 332)(181 333)(182 334)(183 335)(184 336)(185 309)(186 310)(187 311)(188 312)(189 313)(190 314)(191 315)(192 316)(193 317)(194 318)(195 319)(196 320)(225 340)(226 341)(227 342)(228 343)(229 344)(230 345)(231 346)(232 347)(233 348)(234 349)(235 350)(236 351)(237 352)(238 353)(239 354)(240 355)(241 356)(242 357)(243 358)(244 359)(245 360)(246 361)(247 362)(248 363)(249 364)(250 337)(251 338)(252 339)(365 422)(366 423)(367 424)(368 425)(369 426)(370 427)(371 428)(372 429)(373 430)(374 431)(375 432)(376 433)(377 434)(378 435)(379 436)(380 437)(381 438)(382 439)(383 440)(384 441)(385 442)(386 443)(387 444)(388 445)(389 446)(390 447)(391 448)(392 421)

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

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

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

(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)| (1,276)(2,277)(3,278)(4,279)(5,280)(6,253)(7,254)(8,255)(9,256)(10,257)(11,258)(12,259)(13,260)(14,261)(15,262)(16,263)(17,264)(18,265)(19,266)(20,267)(21,268)(22,269)(23,270)(24,271)(25,272)(26,273)(27,274)(28,275)(29,154)(30,155)(31,156)(32,157)(33,158)(34,159)(35,160)(36,161)(37,162)(38,163)(39,164)(40,165)(41,166)(42,167)(43,168)(44,141)(45,142)(46,143)(47,144)(48,145)(49,146)(50,147)(51,148)(52,149)(53,150)(54,151)(55,152)(56,153)(57,220)(58,221)(59,222)(60,223)(61,224)(62,197)(63,198)(64,199)(65,200)(66,201)(67,202)(68,203)(69,204)(70,205)(71,206)(72,207)(73,208)(74,209)(75,210)(76,211)(77,212)(78,213)(79,214)(80,215)(81,216)(82,217)(83,218)(84,219)(85,290)(86,291)(87,292)(88,293)(89,294)(90,295)(91,296)(92,297)(93,298)(94,299)(95,300)(96,301)(97,302)(98,303)(99,304)(100,305)(101,306)(102,307)(103,308)(104,281)(105,282)(106,283)(107,284)(108,285)(109,286)(110,287)(111,288)(112,289)(113,411)(114,412)(115,413)(116,414)(117,415)(118,416)(119,417)(120,418)(121,419)(122,420)(123,393)(124,394)(125,395)(126,396)(127,397)(128,398)(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)(136,406)(137,407)(138,408)(139,409)(140,410)(169,321)(170,322)(171,323)(172,324)(173,325)(174,326)(175,327)(176,328)(177,329)(178,330)(179,331)(180,332)(181,333)(182,334)(183,335)(184,336)(185,309)(186,310)(187,311)(188,312)(189,313)(190,314)(191,315)(192,316)(193,317)(194,318)(195,319)(196,320)(225,340)(226,341)(227,342)(228,343)(229,344)(230,345)(231,346)(232,347)(233,348)(234,349)(235,350)(236,351)(237,352)(238,353)(239,354)(240,355)(241,356)(242,357)(243,358)(244,359)(245,360)(246,361)(247,362)(248,363)(249,364)(250,337)(251,338)(252,339)(365,422)(366,423)(367,424)(368,425)(369,426)(370,427)(371,428)(372,429)(373,430)(374,431)(375,432)(376,433)(377,434)(378,435)(379,436)(380,437)(381,438)(382,439)(383,440)(384,441)(385,442)(386,443)(387,444)(388,445)(389,446)(390,447)(391,448)(392,421), (1,414)(2,415)(3,416)(4,417)(5,418)(6,419)(7,420)(8,393)(9,394)(10,395)(11,396)(12,397)(13,398)(14,399)(15,400)(16,401)(17,402)(18,403)(19,404)(20,405)(21,406)(22,407)(23,408)(24,409)(25,410)(26,411)(27,412)(28,413)(29,337)(30,338)(31,339)(32,340)(33,341)(34,342)(35,343)(36,344)(37,345)(38,346)(39,347)(40,348)(41,349)(42,350)(43,351)(44,352)(45,353)(46,354)(47,355)(48,356)(49,357)(50,358)(51,359)(52,360)(53,361)(54,362)(55,363)(56,364)(57,301)(58,302)(59,303)(60,304)(61,305)(62,306)(63,307)(64,308)(65,281)(66,282)(67,283)(68,284)(69,285)(70,286)(71,287)(72,288)(73,289)(74,290)(75,291)(76,292)(77,293)(78,294)(79,295)(80,296)(81,297)(82,298)(83,299)(84,300)(85,209)(86,210)(87,211)(88,212)(89,213)(90,214)(91,215)(92,216)(93,217)(94,218)(95,219)(96,220)(97,221)(98,222)(99,223)(100,224)(101,197)(102,198)(103,199)(104,200)(105,201)(106,202)(107,203)(108,204)(109,205)(110,206)(111,207)(112,208)(113,273)(114,274)(115,275)(116,276)(117,277)(118,278)(119,279)(120,280)(121,253)(122,254)(123,255)(124,256)(125,257)(126,258)(127,259)(128,260)(129,261)(130,262)(131,263)(132,264)(133,265)(134,266)(135,267)(136,268)(137,269)(138,270)(139,271)(140,272)(141,237)(142,238)(143,239)(144,240)(145,241)(146,242)(147,243)(148,244)(149,245)(150,246)(151,247)(152,248)(153,249)(154,250)(155,251)(156,252)(157,225)(158,226)(159,227)(160,228)(161,229)(162,230)(163,231)(164,232)(165,233)(166,234)(167,235)(168,236)(169,391)(170,392)(171,365)(172,366)(173,367)(174,368)(175,369)(176,370)(177,371)(178,372)(179,373)(180,374)(181,375)(182,376)(183,377)(184,378)(185,379)(186,380)(187,381)(188,382)(189,383)(190,384)(191,385)(192,386)(193,387)(194,388)(195,389)(196,390)(309,436)(310,437)(311,438)(312,439)(313,440)(314,441)(315,442)(316,443)(317,444)(318,445)(319,446)(320,447)(321,448)(322,421)(323,422)(324,423)(325,424)(326,425)(327,426)(328,427)(329,428)(330,429)(331,430)(332,431)(333,432)(334,433)(335,434)(336,435), (1,425)(2,426)(3,427)(4,428)(5,429)(6,430)(7,431)(8,432)(9,433)(10,434)(11,435)(12,436)(13,437)(14,438)(15,439)(16,440)(17,441)(18,442)(19,443)(20,444)(21,445)(22,446)(23,447)(24,448)(25,421)(26,422)(27,423)(28,424)(29,216)(30,217)(31,218)(32,219)(33,220)(34,221)(35,222)(36,223)(37,224)(38,197)(39,198)(40,199)(41,200)(42,201)(43,202)(44,203)(45,204)(46,205)(47,206)(48,207)(49,208)(50,209)(51,210)(52,211)(53,212)(54,213)(55,214)(56,215)(57,158)(58,159)(59,160)(60,161)(61,162)(62,163)(63,164)(64,165)(65,166)(66,167)(67,168)(68,141)(69,142)(70,143)(71,144)(72,145)(73,146)(74,147)(75,148)(76,149)(77,150)(78,151)(79,152)(80,153)(81,154)(82,155)(83,156)(84,157)(85,358)(86,359)(87,360)(88,361)(89,362)(90,363)(91,364)(92,337)(93,338)(94,339)(95,340)(96,341)(97,342)(98,343)(99,344)(100,345)(101,346)(102,347)(103,348)(104,349)(105,350)(106,351)(107,352)(108,353)(109,354)(110,355)(111,356)(112,357)(113,171)(114,172)(115,173)(116,174)(117,175)(118,176)(119,177)(120,178)(121,179)(122,180)(123,181)(124,182)(125,183)(126,184)(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)(136,194)(137,195)(138,196)(139,169)(140,170)(225,300)(226,301)(227,302)(228,303)(229,304)(230,305)(231,306)(232,307)(233,308)(234,281)(235,282)(236,283)(237,284)(238,285)(239,286)(240,287)(241,288)(242,289)(243,290)(244,291)(245,292)(246,293)(247,294)(248,295)(249,296)(250,297)(251,298)(252,299)(253,373)(254,374)(255,375)(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)(273,365)(274,366)(275,367)(276,368)(277,369)(278,370)(279,371)(280,372)(309,397)(310,398)(311,399)(312,400)(313,401)(314,402)(315,403)(316,404)(317,405)(318,406)(319,407)(320,408)(321,409)(322,410)(323,411)(324,412)(325,413)(326,414)(327,415)(328,416)(329,417)(330,418)(331,419)(332,420)(333,393)(334,394)(335,395)(336,396), (1,87)(2,88)(3,89)(4,90)(5,91)(6,92)(7,93)(8,94)(9,95)(10,96)(11,97)(12,98)(13,99)(14,100)(15,101)(16,102)(17,103)(18,104)(19,105)(20,106)(21,107)(22,108)(23,109)(24,110)(25,111)(26,112)(27,85)(28,86)(29,331)(30,332)(31,333)(32,334)(33,335)(34,336)(35,309)(36,310)(37,311)(38,312)(39,313)(40,314)(41,315)(42,316)(43,317)(44,318)(45,319)(46,320)(47,321)(48,322)(49,323)(50,324)(51,325)(52,326)(53,327)(54,328)(55,329)(56,330)(57,125)(58,126)(59,127)(60,128)(61,129)(62,130)(63,131)(64,132)(65,133)(66,134)(67,135)(68,136)(69,137)(70,138)(71,139)(72,140)(73,113)(74,114)(75,115)(76,116)(77,117)(78,118)(79,119)(80,120)(81,121)(82,122)(83,123)(84,124)(141,194)(142,195)(143,196)(144,169)(145,170)(146,171)(147,172)(148,173)(149,174)(150,175)(151,176)(152,177)(153,178)(154,179)(155,180)(156,181)(157,182)(158,183)(159,184)(160,185)(161,186)(162,187)(163,188)(164,189)(165,190)(166,191)(167,192)(168,193)(197,400)(198,401)(199,402)(200,403)(201,404)(202,405)(203,406)(204,407)(205,408)(206,409)(207,410)(208,411)(209,412)(210,413)(211,414)(212,415)(213,416)(214,417)(215,418)(216,419)(217,420)(218,393)(219,394)(220,395)(221,396)(222,397)(223,398)(224,399)(225,376)(226,377)(227,378)(228,379)(229,380)(230,381)(231,382)(232,383)(233,384)(234,385)(235,386)(236,387)(237,388)(238,389)(239,390)(240,391)(241,392)(242,365)(243,366)(244,367)(245,368)(246,369)(247,370)(248,371)(249,372)(250,373)(251,374)(252,375)(253,297)(254,298)(255,299)(256,300)(257,301)(258,302)(259,303)(260,304)(261,305)(262,306)(263,307)(264,308)(265,281)(266,282)(267,283)(268,284)(269,285)(270,286)(271,287)(272,288)(273,289)(274,290)(275,291)(276,292)(277,293)(278,294)(279,295)(280,296)(337,430)(338,431)(339,432)(340,433)(341,434)(342,435)(343,436)(344,437)(345,438)(346,439)(347,440)(348,441)(349,442)(350,443)(351,444)(352,445)(353,446)(354,447)(355,448)(356,421)(357,422)(358,423)(359,424)(360,425)(361,426)(362,427)(363,428)(364,429), (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:=Group( (1,276)(2,277)(3,278)(4,279)(5,280)(6,253)(7,254)(8,255)(9,256)(10,257)(11,258)(12,259)(13,260)(14,261)(15,262)(16,263)(17,264)(18,265)(19,266)(20,267)(21,268)(22,269)(23,270)(24,271)(25,272)(26,273)(27,274)(28,275)(29,154)(30,155)(31,156)(32,157)(33,158)(34,159)(35,160)(36,161)(37,162)(38,163)(39,164)(40,165)(41,166)(42,167)(43,168)(44,141)(45,142)(46,143)(47,144)(48,145)(49,146)(50,147)(51,148)(52,149)(53,150)(54,151)(55,152)(56,153)(57,220)(58,221)(59,222)(60,223)(61,224)(62,197)(63,198)(64,199)(65,200)(66,201)(67,202)(68,203)(69,204)(70,205)(71,206)(72,207)(73,208)(74,209)(75,210)(76,211)(77,212)(78,213)(79,214)(80,215)(81,216)(82,217)(83,218)(84,219)(85,290)(86,291)(87,292)(88,293)(89,294)(90,295)(91,296)(92,297)(93,298)(94,299)(95,300)(96,301)(97,302)(98,303)(99,304)(100,305)(101,306)(102,307)(103,308)(104,281)(105,282)(106,283)(107,284)(108,285)(109,286)(110,287)(111,288)(112,289)(113,411)(114,412)(115,413)(116,414)(117,415)(118,416)(119,417)(120,418)(121,419)(122,420)(123,393)(124,394)(125,395)(126,396)(127,397)(128,398)(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)(136,406)(137,407)(138,408)(139,409)(140,410)(169,321)(170,322)(171,323)(172,324)(173,325)(174,326)(175,327)(176,328)(177,329)(178,330)(179,331)(180,332)(181,333)(182,334)(183,335)(184,336)(185,309)(186,310)(187,311)(188,312)(189,313)(190,314)(191,315)(192,316)(193,317)(194,318)(195,319)(196,320)(225,340)(226,341)(227,342)(228,343)(229,344)(230,345)(231,346)(232,347)(233,348)(234,349)(235,350)(236,351)(237,352)(238,353)(239,354)(240,355)(241,356)(242,357)(243,358)(244,359)(245,360)(246,361)(247,362)(248,363)(249,364)(250,337)(251,338)(252,339)(365,422)(366,423)(367,424)(368,425)(369,426)(370,427)(371,428)(372,429)(373,430)(374,431)(375,432)(376,433)(377,434)(378,435)(379,436)(380,437)(381,438)(382,439)(383,440)(384,441)(385,442)(386,443)(387,444)(388,445)(389,446)(390,447)(391,448)(392,421), (1,414)(2,415)(3,416)(4,417)(5,418)(6,419)(7,420)(8,393)(9,394)(10,395)(11,396)(12,397)(13,398)(14,399)(15,400)(16,401)(17,402)(18,403)(19,404)(20,405)(21,406)(22,407)(23,408)(24,409)(25,410)(26,411)(27,412)(28,413)(29,337)(30,338)(31,339)(32,340)(33,341)(34,342)(35,343)(36,344)(37,345)(38,346)(39,347)(40,348)(41,349)(42,350)(43,351)(44,352)(45,353)(46,354)(47,355)(48,356)(49,357)(50,358)(51,359)(52,360)(53,361)(54,362)(55,363)(56,364)(57,301)(58,302)(59,303)(60,304)(61,305)(62,306)(63,307)(64,308)(65,281)(66,282)(67,283)(68,284)(69,285)(70,286)(71,287)(72,288)(73,289)(74,290)(75,291)(76,292)(77,293)(78,294)(79,295)(80,296)(81,297)(82,298)(83,299)(84,300)(85,209)(86,210)(87,211)(88,212)(89,213)(90,214)(91,215)(92,216)(93,217)(94,218)(95,219)(96,220)(97,221)(98,222)(99,223)(100,224)(101,197)(102,198)(103,199)(104,200)(105,201)(106,202)(107,203)(108,204)(109,205)(110,206)(111,207)(112,208)(113,273)(114,274)(115,275)(116,276)(117,277)(118,278)(119,279)(120,280)(121,253)(122,254)(123,255)(124,256)(125,257)(126,258)(127,259)(128,260)(129,261)(130,262)(131,263)(132,264)(133,265)(134,266)(135,267)(136,268)(137,269)(138,270)(139,271)(140,272)(141,237)(142,238)(143,239)(144,240)(145,241)(146,242)(147,243)(148,244)(149,245)(150,246)(151,247)(152,248)(153,249)(154,250)(155,251)(156,252)(157,225)(158,226)(159,227)(160,228)(161,229)(162,230)(163,231)(164,232)(165,233)(166,234)(167,235)(168,236)(169,391)(170,392)(171,365)(172,366)(173,367)(174,368)(175,369)(176,370)(177,371)(178,372)(179,373)(180,374)(181,375)(182,376)(183,377)(184,378)(185,379)(186,380)(187,381)(188,382)(189,383)(190,384)(191,385)(192,386)(193,387)(194,388)(195,389)(196,390)(309,436)(310,437)(311,438)(312,439)(313,440)(314,441)(315,442)(316,443)(317,444)(318,445)(319,446)(320,447)(321,448)(322,421)(323,422)(324,423)(325,424)(326,425)(327,426)(328,427)(329,428)(330,429)(331,430)(332,431)(333,432)(334,433)(335,434)(336,435), (1,425)(2,426)(3,427)(4,428)(5,429)(6,430)(7,431)(8,432)(9,433)(10,434)(11,435)(12,436)(13,437)(14,438)(15,439)(16,440)(17,441)(18,442)(19,443)(20,444)(21,445)(22,446)(23,447)(24,448)(25,421)(26,422)(27,423)(28,424)(29,216)(30,217)(31,218)(32,219)(33,220)(34,221)(35,222)(36,223)(37,224)(38,197)(39,198)(40,199)(41,200)(42,201)(43,202)(44,203)(45,204)(46,205)(47,206)(48,207)(49,208)(50,209)(51,210)(52,211)(53,212)(54,213)(55,214)(56,215)(57,158)(58,159)(59,160)(60,161)(61,162)(62,163)(63,164)(64,165)(65,166)(66,167)(67,168)(68,141)(69,142)(70,143)(71,144)(72,145)(73,146)(74,147)(75,148)(76,149)(77,150)(78,151)(79,152)(80,153)(81,154)(82,155)(83,156)(84,157)(85,358)(86,359)(87,360)(88,361)(89,362)(90,363)(91,364)(92,337)(93,338)(94,339)(95,340)(96,341)(97,342)(98,343)(99,344)(100,345)(101,346)(102,347)(103,348)(104,349)(105,350)(106,351)(107,352)(108,353)(109,354)(110,355)(111,356)(112,357)(113,171)(114,172)(115,173)(116,174)(117,175)(118,176)(119,177)(120,178)(121,179)(122,180)(123,181)(124,182)(125,183)(126,184)(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)(136,194)(137,195)(138,196)(139,169)(140,170)(225,300)(226,301)(227,302)(228,303)(229,304)(230,305)(231,306)(232,307)(233,308)(234,281)(235,282)(236,283)(237,284)(238,285)(239,286)(240,287)(241,288)(242,289)(243,290)(244,291)(245,292)(246,293)(247,294)(248,295)(249,296)(250,297)(251,298)(252,299)(253,373)(254,374)(255,375)(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)(273,365)(274,366)(275,367)(276,368)(277,369)(278,370)(279,371)(280,372)(309,397)(310,398)(311,399)(312,400)(313,401)(314,402)(315,403)(316,404)(317,405)(318,406)(319,407)(320,408)(321,409)(322,410)(323,411)(324,412)(325,413)(326,414)(327,415)(328,416)(329,417)(330,418)(331,419)(332,420)(333,393)(334,394)(335,395)(336,396), (1,87)(2,88)(3,89)(4,90)(5,91)(6,92)(7,93)(8,94)(9,95)(10,96)(11,97)(12,98)(13,99)(14,100)(15,101)(16,102)(17,103)(18,104)(19,105)(20,106)(21,107)(22,108)(23,109)(24,110)(25,111)(26,112)(27,85)(28,86)(29,331)(30,332)(31,333)(32,334)(33,335)(34,336)(35,309)(36,310)(37,311)(38,312)(39,313)(40,314)(41,315)(42,316)(43,317)(44,318)(45,319)(46,320)(47,321)(48,322)(49,323)(50,324)(51,325)(52,326)(53,327)(54,328)(55,329)(56,330)(57,125)(58,126)(59,127)(60,128)(61,129)(62,130)(63,131)(64,132)(65,133)(66,134)(67,135)(68,136)(69,137)(70,138)(71,139)(72,140)(73,113)(74,114)(75,115)(76,116)(77,117)(78,118)(79,119)(80,120)(81,121)(82,122)(83,123)(84,124)(141,194)(142,195)(143,196)(144,169)(145,170)(146,171)(147,172)(148,173)(149,174)(150,175)(151,176)(152,177)(153,178)(154,179)(155,180)(156,181)(157,182)(158,183)(159,184)(160,185)(161,186)(162,187)(163,188)(164,189)(165,190)(166,191)(167,192)(168,193)(197,400)(198,401)(199,402)(200,403)(201,404)(202,405)(203,406)(204,407)(205,408)(206,409)(207,410)(208,411)(209,412)(210,413)(211,414)(212,415)(213,416)(214,417)(215,418)(216,419)(217,420)(218,393)(219,394)(220,395)(221,396)(222,397)(223,398)(224,399)(225,376)(226,377)(227,378)(228,379)(229,380)(230,381)(231,382)(232,383)(233,384)(234,385)(235,386)(236,387)(237,388)(238,389)(239,390)(240,391)(241,392)(242,365)(243,366)(244,367)(245,368)(246,369)(247,370)(248,371)(249,372)(250,373)(251,374)(252,375)(253,297)(254,298)(255,299)(256,300)(257,301)(258,302)(259,303)(260,304)(261,305)(262,306)(263,307)(264,308)(265,281)(266,282)(267,283)(268,284)(269,285)(270,286)(271,287)(272,288)(273,289)(274,290)(275,291)(276,292)(277,293)(278,294)(279,295)(280,296)(337,430)(338,431)(339,432)(340,433)(341,434)(342,435)(343,436)(344,437)(345,438)(346,439)(347,440)(348,441)(349,442)(350,443)(351,444)(352,445)(353,446)(354,447)(355,448)(356,421)(357,422)(358,423)(359,424)(360,425)(361,426)(362,427)(363,428)(364,429), (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([[(1,276),(2,277),(3,278),(4,279),(5,280),(6,253),(7,254),(8,255),(9,256),(10,257),(11,258),(12,259),(13,260),(14,261),(15,262),(16,263),(17,264),(18,265),(19,266),(20,267),(21,268),(22,269),(23,270),(24,271),(25,272),(26,273),(27,274),(28,275),(29,154),(30,155),(31,156),(32,157),(33,158),(34,159),(35,160),(36,161),(37,162),(38,163),(39,164),(40,165),(41,166),(42,167),(43,168),(44,141),(45,142),(46,143),(47,144),(48,145),(49,146),(50,147),(51,148),(52,149),(53,150),(54,151),(55,152),(56,153),(57,220),(58,221),(59,222),(60,223),(61,224),(62,197),(63,198),(64,199),(65,200),(66,201),(67,202),(68,203),(69,204),(70,205),(71,206),(72,207),(73,208),(74,209),(75,210),(76,211),(77,212),(78,213),(79,214),(80,215),(81,216),(82,217),(83,218),(84,219),(85,290),(86,291),(87,292),(88,293),(89,294),(90,295),(91,296),(92,297),(93,298),(94,299),(95,300),(96,301),(97,302),(98,303),(99,304),(100,305),(101,306),(102,307),(103,308),(104,281),(105,282),(106,283),(107,284),(108,285),(109,286),(110,287),(111,288),(112,289),(113,411),(114,412),(115,413),(116,414),(117,415),(118,416),(119,417),(120,418),(121,419),(122,420),(123,393),(124,394),(125,395),(126,396),(127,397),(128,398),(129,399),(130,400),(131,401),(132,402),(133,403),(134,404),(135,405),(136,406),(137,407),(138,408),(139,409),(140,410),(169,321),(170,322),(171,323),(172,324),(173,325),(174,326),(175,327),(176,328),(177,329),(178,330),(179,331),(180,332),(181,333),(182,334),(183,335),(184,336),(185,309),(186,310),(187,311),(188,312),(189,313),(190,314),(191,315),(192,316),(193,317),(194,318),(195,319),(196,320),(225,340),(226,341),(227,342),(228,343),(229,344),(230,345),(231,346),(232,347),(233,348),(234,349),(235,350),(236,351),(237,352),(238,353),(239,354),(240,355),(241,356),(242,357),(243,358),(244,359),(245,360),(246,361),(247,362),(248,363),(249,364),(250,337),(251,338),(252,339),(365,422),(366,423),(367,424),(368,425),(369,426),(370,427),(371,428),(372,429),(373,430),(374,431),(375,432),(376,433),(377,434),(378,435),(379,436),(380,437),(381,438),(382,439),(383,440),(384,441),(385,442),(386,443),(387,444),(388,445),(389,446),(390,447),(391,448),(392,421)], [(1,414),(2,415),(3,416),(4,417),(5,418),(6,419),(7,420),(8,393),(9,394),(10,395),(11,396),(12,397),(13,398),(14,399),(15,400),(16,401),(17,402),(18,403),(19,404),(20,405),(21,406),(22,407),(23,408),(24,409),(25,410),(26,411),(27,412),(28,413),(29,337),(30,338),(31,339),(32,340),(33,341),(34,342),(35,343),(36,344),(37,345),(38,346),(39,347),(40,348),(41,349),(42,350),(43,351),(44,352),(45,353),(46,354),(47,355),(48,356),(49,357),(50,358),(51,359),(52,360),(53,361),(54,362),(55,363),(56,364),(57,301),(58,302),(59,303),(60,304),(61,305),(62,306),(63,307),(64,308),(65,281),(66,282),(67,283),(68,284),(69,285),(70,286),(71,287),(72,288),(73,289),(74,290),(75,291),(76,292),(77,293),(78,294),(79,295),(80,296),(81,297),(82,298),(83,299),(84,300),(85,209),(86,210),(87,211),(88,212),(89,213),(90,214),(91,215),(92,216),(93,217),(94,218),(95,219),(96,220),(97,221),(98,222),(99,223),(100,224),(101,197),(102,198),(103,199),(104,200),(105,201),(106,202),(107,203),(108,204),(109,205),(110,206),(111,207),(112,208),(113,273),(114,274),(115,275),(116,276),(117,277),(118,278),(119,279),(120,280),(121,253),(122,254),(123,255),(124,256),(125,257),(126,258),(127,259),(128,260),(129,261),(130,262),(131,263),(132,264),(133,265),(134,266),(135,267),(136,268),(137,269),(138,270),(139,271),(140,272),(141,237),(142,238),(143,239),(144,240),(145,241),(146,242),(147,243),(148,244),(149,245),(150,246),(151,247),(152,248),(153,249),(154,250),(155,251),(156,252),(157,225),(158,226),(159,227),(160,228),(161,229),(162,230),(163,231),(164,232),(165,233),(166,234),(167,235),(168,236),(169,391),(170,392),(171,365),(172,366),(173,367),(174,368),(175,369),(176,370),(177,371),(178,372),(179,373),(180,374),(181,375),(182,376),(183,377),(184,378),(185,379),(186,380),(187,381),(188,382),(189,383),(190,384),(191,385),(192,386),(193,387),(194,388),(195,389),(196,390),(309,436),(310,437),(311,438),(312,439),(313,440),(314,441),(315,442),(316,443),(317,444),(318,445),(319,446),(320,447),(321,448),(322,421),(323,422),(324,423),(325,424),(326,425),(327,426),(328,427),(329,428),(330,429),(331,430),(332,431),(333,432),(334,433),(335,434),(336,435)], [(1,425),(2,426),(3,427),(4,428),(5,429),(6,430),(7,431),(8,432),(9,433),(10,434),(11,435),(12,436),(13,437),(14,438),(15,439),(16,440),(17,441),(18,442),(19,443),(20,444),(21,445),(22,446),(23,447),(24,448),(25,421),(26,422),(27,423),(28,424),(29,216),(30,217),(31,218),(32,219),(33,220),(34,221),(35,222),(36,223),(37,224),(38,197),(39,198),(40,199),(41,200),(42,201),(43,202),(44,203),(45,204),(46,205),(47,206),(48,207),(49,208),(50,209),(51,210),(52,211),(53,212),(54,213),(55,214),(56,215),(57,158),(58,159),(59,160),(60,161),(61,162),(62,163),(63,164),(64,165),(65,166),(66,167),(67,168),(68,141),(69,142),(70,143),(71,144),(72,145),(73,146),(74,147),(75,148),(76,149),(77,150),(78,151),(79,152),(80,153),(81,154),(82,155),(83,156),(84,157),(85,358),(86,359),(87,360),(88,361),(89,362),(90,363),(91,364),(92,337),(93,338),(94,339),(95,340),(96,341),(97,342),(98,343),(99,344),(100,345),(101,346),(102,347),(103,348),(104,349),(105,350),(106,351),(107,352),(108,353),(109,354),(110,355),(111,356),(112,357),(113,171),(114,172),(115,173),(116,174),(117,175),(118,176),(119,177),(120,178),(121,179),(122,180),(123,181),(124,182),(125,183),(126,184),(127,185),(128,186),(129,187),(130,188),(131,189),(132,190),(133,191),(134,192),(135,193),(136,194),(137,195),(138,196),(139,169),(140,170),(225,300),(226,301),(227,302),(228,303),(229,304),(230,305),(231,306),(232,307),(233,308),(234,281),(235,282),(236,283),(237,284),(238,285),(239,286),(240,287),(241,288),(242,289),(243,290),(244,291),(245,292),(246,293),(247,294),(248,295),(249,296),(250,297),(251,298),(252,299),(253,373),(254,374),(255,375),(256,376),(257,377),(258,378),(259,379),(260,380),(261,381),(262,382),(263,383),(264,384),(265,385),(266,386),(267,387),(268,388),(269,389),(270,390),(271,391),(272,392),(273,365),(274,366),(275,367),(276,368),(277,369),(278,370),(279,371),(280,372),(309,397),(310,398),(311,399),(312,400),(313,401),(314,402),(315,403),(316,404),(317,405),(318,406),(319,407),(320,408),(321,409),(322,410),(323,411),(324,412),(325,413),(326,414),(327,415),(328,416),(329,417),(330,418),(331,419),(332,420),(333,393),(334,394),(335,395),(336,396)], [(1,87),(2,88),(3,89),(4,90),(5,91),(6,92),(7,93),(8,94),(9,95),(10,96),(11,97),(12,98),(13,99),(14,100),(15,101),(16,102),(17,103),(18,104),(19,105),(20,106),(21,107),(22,108),(23,109),(24,110),(25,111),(26,112),(27,85),(28,86),(29,331),(30,332),(31,333),(32,334),(33,335),(34,336),(35,309),(36,310),(37,311),(38,312),(39,313),(40,314),(41,315),(42,316),(43,317),(44,318),(45,319),(46,320),(47,321),(48,322),(49,323),(50,324),(51,325),(52,326),(53,327),(54,328),(55,329),(56,330),(57,125),(58,126),(59,127),(60,128),(61,129),(62,130),(63,131),(64,132),(65,133),(66,134),(67,135),(68,136),(69,137),(70,138),(71,139),(72,140),(73,113),(74,114),(75,115),(76,116),(77,117),(78,118),(79,119),(80,120),(81,121),(82,122),(83,123),(84,124),(141,194),(142,195),(143,196),(144,169),(145,170),(146,171),(147,172),(148,173),(149,174),(150,175),(151,176),(152,177),(153,178),(154,179),(155,180),(156,181),(157,182),(158,183),(159,184),(160,185),(161,186),(162,187),(163,188),(164,189),(165,190),(166,191),(167,192),(168,193),(197,400),(198,401),(199,402),(200,403),(201,404),(202,405),(203,406),(204,407),(205,408),(206,409),(207,410),(208,411),(209,412),(210,413),(211,414),(212,415),(213,416),(214,417),(215,418),(216,419),(217,420),(218,393),(219,394),(220,395),(221,396),(222,397),(223,398),(224,399),(225,376),(226,377),(227,378),(228,379),(229,380),(230,381),(231,382),(232,383),(233,384),(234,385),(235,386),(236,387),(237,388),(238,389),(239,390),(240,391),(241,392),(242,365),(243,366),(244,367),(245,368),(246,369),(247,370),(248,371),(249,372),(250,373),(251,374),(252,375),(253,297),(254,298),(255,299),(256,300),(257,301),(258,302),(259,303),(260,304),(261,305),(262,306),(263,307),(264,308),(265,281),(266,282),(267,283),(268,284),(269,285),(270,286),(271,287),(272,288),(273,289),(274,290),(275,291),(276,292),(277,293),(278,294),(279,295),(280,296),(337,430),(338,431),(339,432),(340,433),(341,434),(342,435),(343,436),(344,437),(345,438),(346,439),(347,440),(348,441),(349,442),(350,443),(351,444),(352,445),(353,446),(354,447),(355,448),(356,421),(357,422),(358,423),(359,424),(360,425),(361,426),(362,427),(363,428),(364,429)], [(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···2AE4A···4AF7A···7F14A···14GD28A···28GJ
order12···24···47···714···1428···28
size11···11···11···11···11···1

448 irreducible representations

dim11111111
type+++
imageC1C2C2C4C7C14C14C28
kernelC24×C28C23×C28C24×C14C23×C14C24×C4C23×C4C25C24
# reps13013261806192

Matrix representation of C24×C28 ►in GL5(𝔽29)

280000
01000
00100
000280
000028
,
280000
01000
00100
00010
00001
,
280000
028000
002800
000280
00001
,
280000
028000
00100
000280
00001
,
100000
017000
002800
000170
000017

G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,28],[28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,1],[28,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,1],[10,0,0,0,0,0,17,0,0,0,0,0,28,0,0,0,0,0,17,0,0,0,0,0,17] >;
 

C24×C28 in GAP, Magma, Sage, TeX 

C_2^4\times C_{28}
 
% in TeX
 
G:=Group("C2^4xC28");
 
// GroupNames label
 
G:=SmallGroup(448,1385);
 
// by ID
 
G=gap.SmallGroup(448,1385);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-7,-2,1568]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^2=e^28=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,d*e=e*d>;
 
// generators/relations
 

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