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G = Q8×C22×C14  order 448 = 26·7

Direct product of C22×C14 and Q8

direct product, metabelian, nilpotent (class 2), monomial, 2-elementary

Aliases: Q8×C22×C14, C14.22C25, C28.88C24, C2.2(C24×C14), C24.40(C2×C14), (C23×C4).14C14, C4.11(C23×C14), (C23×C28).27C2, (C2×C28).977C23, (C2×C14).385C24, C23.74(C22×C14), C22.14(C23×C14), (C23×C14).120C22, (C22×C28).605C22, (C22×C14).471C23, (C2×C4).145(C22×C14), (C22×C4).132(C2×C14), SmallGroup(448,1387)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2 — Q8×C22×C14
Chief series
C1 — C2 — C14 — C28 — C7×Q8 — Q8×C14 — Q8×C2×C14 — Q8×C22×C14
Lower central
C1 — C2 — Q8×C22×C14
Upper central
C1 — C23×C14 — Q8×C22×C14

Subgroups: 850, all normal (8 characteristic)
C1, C2, C2 [×14], C4 [×24], C22 [×35], C7, C2×C4 [×84], Q8 [×64], C23 [×15], C14, C14 [×14], C22×C4 [×42], C2×Q8 [×112], C24, C28 [×24], C2×C14 [×35], C23×C4 [×3], C22×Q8 [×28], C2×C28 [×84], C7×Q8 [×64], C22×C14 [×15], Q8×C23, C22×C28 [×42], Q8×C14 [×112], C23×C14, C23×C28 [×3], Q8×C2×C14 [×28], Q8×C22×C14

Quotients:
C1, C2 [×31], C22 [×155], C7, Q8 [×8], C23 [×155], C14 [×31], C2×Q8 [×28], C24 [×31], C2×C14 [×155], C22×Q8 [×14], C25, C7×Q8 [×8], C22×C14 [×155], Q8×C23, Q8×C14 [×28], C23×C14 [×31], Q8×C2×C14 [×14], C24×C14, Q8×C22×C14

Generators and relations
 G = < a,b,c,d,e | a2=b2=c14=d4=1, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

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

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

(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)

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

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

Matrix representation ►G ⊆ GL5(𝔽29)

280000
01000
00100
00010
00001
,
10000
028000
00100
00010
00001
,
280000
01000
002800
000240
000024
,
280000
028000
002800
000028
00010
,
280000
028000
00100
000213
0001327

G:=sub<GL(5,GF(29))| [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],[1,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[28,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,24,0,0,0,0,0,24],[28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,28,0],[28,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,2,13,0,0,0,13,27] >;
 

280 conjugacy classes

class 1 2A···2O4A···4X7A···7F14A···14CL28A···28EN
order12···24···47···714···1428···28
size11···12···21···11···12···2

280 irreducible representations

dim11111122
type+++-
imageC1C2C2C7C14C14Q8C7×Q8
kernelQ8×C22×C14C23×C28Q8×C2×C14Q8×C23C23×C4C22×Q8C22×C14C23
# reps1328618168848

In GAP, Magma, Sage, TeX 

Q_8\times C_2^2\times C_{14}
 
% in TeX
 
G:=Group("Q8xC2^2xC14");
 
// GroupNames label
 
G:=SmallGroup(448,1387);
 
// by ID
 
G=gap.SmallGroup(448,1387);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-7,-2,1568,3165,1576]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^14=d^4=1,e^2=d^2,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,e*d*e^-1=d^-1>;
 
// generators/relations
 

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