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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

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

Generators and relations
 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 >

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

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

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

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

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

Matrix representation ►G ⊆ 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] >;
 

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

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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