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G = C24×C28order 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

C1 — C24×C28
C1C2C14C28C2×C28C22×C28C23×C28 — C24×C28
C1 — C24×C28
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 [×30], C4 [×16], C22 [×155], C7, C2×C4 [×120], C23 [×155], C14, C14 [×30], C22×C4 [×140], C24 [×31], C28 [×16], C2×C14 [×155], C23×C4 [×30], C25, C2×C28 [×120], C22×C14 [×155], C24×C4, C22×C28 [×140], C23×C14 [×31], C23×C28 [×30], C24×C14, C24×C28
Quotients: C1, C2 [×31], C4 [×16], C22 [×155], C7, C2×C4 [×120], C23 [×155], C14 [×31], C22×C4 [×140], C24 [×31], C28 [×16], C2×C14 [×155], C23×C4 [×30], C25, C2×C28 [×120], C22×C14 [×155], C24×C4, C22×C28 [×140], C23×C14 [×31], C23×C28 [×30], C24×C14, C24×C28

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

׿
×
𝔽