C14.C2^2wrC2 - GroupNames

G = C₁₄.C₂²≀C₂ order 448 = 2⁶·7

8^th non-split extension by C₁₄ of C₂²≀C₂ acting via C₂²≀C₂/C₂⁴=C₂

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: (C₂×Dic₇)⋊₃Q₈, (C₂×C₂₈).₃₀₅D₄, C₁₄.₃₃(C₄⋊Q₈), C₁₄.₇₆C₂²≀C₂, (C₂²×Q₈).₅D₇, C₂².₅₂(Q₈×D₇), (C₂²×C₄).₁₅₈D₁₄, C₁₄.₇₉(C₂²⋊Q₈), C₂.₁₆(D₁₄⋊₃Q₈), C₂.₁₀(C₂⁴⋊D₇), C₂³.₃₈₆(C₂²×D₇), C₂.₁₃(Dic₇⋊Q₈), C₁₄.C₄².₃₉C₂, (C₂²×C₁₄).₃₆₉C₂³, (C₂²×C₂₈).₃₉₇C₂², C₇⋊₃(C₂³.₇₈C₂³), C₂².₅₅(Q₈⋊₂D₇), (C₂²×Dic₇).₇₀C₂², (Q₈×C₂×C₁₄).₁₀C₂, (C₂×C₁₄).₈₇(C₂×Q₈), (C₂×C₁₄).₅₆₂(C₂×D₄), (C₂×C₄).₈₈(C₇⋊D₄), (C₂×Dic₇⋊C₄).₃₃C₂, C₂².₂₂₂(C₂×C₇⋊D₄), (C₂×C₁₄).₁₉₃(C₄○D₄), SmallGroup(448,763)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₂²×C₁₄ — C₁₄.C₂²≀C₂

Chief series

C₁ — C₇ — C₁₄ — C₂×C₁₄ — C₂²×C₁₄ — C₂²×Dic₇ — C₂×Dic₇⋊C₄ — C₁₄.C₂²≀C₂

Lower central

C₇ — C₂²×C₁₄ — C₁₄.C₂²≀C₂

Upper central

C₁ — C₂³ — C₂²×Q₈

Generators and relations for C₁₄.C₂²≀C₂
G = < a,b,c,d,e,f | a¹⁴=d²=e²=1, b²=c²=f²=a⁷, ab=ba, ac=ca, ad=da, ae=ea, faf^-1=a^-1, cbc^-1=a⁷b, fbf^-1=bd=db, be=eb, cd=dc, fcf^-1=ce=ec, de=ed, df=fd, ef=fe >

Subgroups: 660 in 182 conjugacy classes, 69 normal (12 characteristic)
C₁, C₂, C₂, C₄, C₂², C₂², C₇, C₂×C₄, C₂×C₄, Q₈, C₂³, C₁₄, C₁₄, C₄⋊C₄, C₂²×C₄, C₂²×C₄, C₂×Q₈, Dic₇, C₂₈, C₂×C₁₄, C₂×C₁₄, C₂.C₄², C₂×C₄⋊C₄, C₂²×Q₈, C₂×Dic₇, C₂×Dic₇, C₂×C₂₈, C₂×C₂₈, C₇×Q₈, C₂²×C₁₄, C₂³.₇₈C₂³, Dic₇⋊C₄, C₂²×Dic₇, C₂²×Dic₇, C₂²×C₂₈, Q₈×C₁₄, C₁₄.C₄², C₂×Dic₇⋊C₄, Q₈×C₂×C₁₄, C₁₄.C₂²≀C₂
Quotients: C₁, C₂, C₂², D₄, Q₈, C₂³, D₇, C₂×D₄, C₂×Q₈, C₄○D₄, D₁₄, C₂²≀C₂, C₂²⋊Q₈, C₄⋊Q₈, C₇⋊D₄, C₂²×D₇, C₂³.₇₈C₂³, Q₈×D₇, Q₈⋊₂D₇, C₂×C₇⋊D₄, Dic₇⋊Q₈, D₁₄⋊₃Q₈, C₂⁴⋊D₇, C₁₄.C₂²≀C₂

Smallest permutation representation of C₁₄.C₂²≀C₂
►Regular action on 448 points

Generators in S₄₄₈

(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)

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

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

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

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

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

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

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

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

82 conjugacy classes

class	1	2A	···	2G	4A	···	4F	4G	···	4N	7A	7B	7C	14A	···	14U	28A	···	28AJ
order	1	2	···	2	4	···	4	4	···	4	7	7	7	14	···	14	28	···	28
size	1	1	···	1	4	···	4	28	···	28	2	2	2	2	···	2	4	···	4

82 irreducible representations

dim	1	1	1	1	2	2	2	2	2	2	4	4
type	+	+	+	+	-	+	+		+		-	+
image	C₁	C₂	C₂	C₂	Q₈	D₄	D₇	C₄○D₄	D₁₄	C₇⋊D₄	Q₈×D₇	Q₈⋊₂D₇
kernel	C₁₄.C₂²≀C₂	C₁₄.C₄²	C₂×Dic₇⋊C₄	Q₈×C₂×C₁₄	C₂×Dic₇	C₂×C₂₈	C₂²×Q₈	C₂×C₁₄	C₂²×C₄	C₂×C₄	C₂²	C₂²
# reps	1	3	3	1	6	6	3	2	9	36	9	3

Matrix representation of C₁₄.C₂²≀C₂ ►in GL₆(𝔽₂₉)

21	10	0	0	0	0
23	11	0	0	0	0
0	0	24	0	0	0
0	0	8	23	0	0
0	0	0	0	28	0
0	0	0	0	0	28

7	14	0	0	0	0
9	22	0	0	0	0
0	0	1	0	0	0
0	0	0	1	0	0
0	0	0	0	13	3
0	0	0	0	11	16

7	14	0	0	0	0
9	22	0	0	0	0
0	0	1	0	0	0
0	0	16	28	0	0
0	0	0	0	3	24
0	0	0	0	2	26

28	0	0	0	0	0
0	28	0	0	0	0
0	0	1	0	0	0
0	0	0	1	0	0
0	0	0	0	28	0
0	0	0	0	0	28

28	0	0	0	0	0
0	28	0	0	0	0
0	0	28	0	0	0
0	0	0	28	0	0
0	0	0	0	1	0
0	0	0	0	0	1

26	1	0	0	0	0
21	3	0	0	0	0
0	0	11	24	0	0
0	0	24	18	0	0
0	0	0	0	26	5
0	0	0	0	27	3

G:=sub<GL(6,GF(29))| [21,23,0,0,0,0,10,11,0,0,0,0,0,0,24,8,0,0,0,0,0,23,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[7,9,0,0,0,0,14,22,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,13,11,0,0,0,0,3,16],[7,9,0,0,0,0,14,22,0,0,0,0,0,0,1,16,0,0,0,0,0,28,0,0,0,0,0,0,3,2,0,0,0,0,24,26],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[26,21,0,0,0,0,1,3,0,0,0,0,0,0,11,24,0,0,0,0,24,18,0,0,0,0,0,0,26,27,0,0,0,0,5,3] >;

C₁₄.C₂²≀C₂ in GAP, Magma, Sage, TeX

C_{14}.C_2^2\wr C_2

% in TeX

G:=Group("C14.C2^2wrC2");

// GroupNames label

G:=SmallGroup(448,763);

// by ID

G=gap.SmallGroup(448,763);

# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,232,254,387,184,18822]);

// Polycyclic

G:=Group<a,b,c,d,e,f|a^14=d^2=e^2=1,b^2=c^2=f^2=a^7,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,f*a*f^-1=a^-1,c*b*c^-1=a^7*b,f*b*f^-1=b*d=d*b,b*e=e*b,c*d=d*c,f*c*f^-1=c*e=e*c,d*e=e*d,d*f=f*d,e*f=f*e>;

// generators/relations

G = C14.C22≀C2 order 448 = 26·7

8th non-split extension by C14 of C22≀C2 acting via C22≀C2/C24=C2

G = C₁₄.C₂²≀C₂ order 448 = 2⁶·7

8^th non-split extension by C₁₄ of C₂²≀C₂ acting via C₂²≀C₂/C₂⁴=C₂