(C2^2xC4).D14 - GroupNames

G = (C₂²×C₄).D₁₄ order 448 = 2⁶·7

14^th non-split extension by C₂²×C₄ of D₁₄ acting via D₁₄/C₇=C₂²

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: (C₂²×C₄).₁₄D₁₄, C₂.₅(C₄²⋊₂D₇), C₇⋊(C₂³.₈₄C₂³), C₂.C₄².₅D₇, C₂².₈₈(C₄○D₂₈), C₁₄.C₄².₈C₂, (C₂²×C₂₈).₁₁C₂², C₂³.₃₅₈(C₂²×D₇), C₁₄.₁₉(C₄²⋊₂C₂), C₂².₈₇(D₄⋊₂D₇), (C₂²×C₁₄).₂₈₇C₂³, C₂².₄₃(Q₈⋊₂D₇), C₂.₁₁(C₂³.D₁₄), (C₂²×Dic₇).₁₂C₂², C₂.₉(C₄⋊C₄⋊D₇), (C₂×C₁₄).₁₃₀(C₄○D₄), (C₇×C₂.C₄²).₂C₂, SmallGroup(448,196)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₂²×C₁₄ — (C₂²×C₄).D₁₄

Chief series

C₁ — C₇ — C₁₄ — C₂×C₁₄ — C₂²×C₁₄ — C₂²×Dic₇ — C₁₄.C₄² — (C₂²×C₄).D₁₄

Lower central

C₇ — C₂²×C₁₄ — (C₂²×C₄).D₁₄

Upper central

C₁ — C₂³ — C₂.C₄²

Generators and relations for (C₂²×C₄).D₁₄
G = < a,b,c,d,e | a²=b²=c⁴=1, d¹⁴=ba=ab, e²=bc², ac=ca, ad=da, ae=ea, dcd^-1=bc=cb, bd=db, be=eb, ece^-1=abc, ede^-1=abc²d¹³ >

Subgroups: 508 in 118 conjugacy classes, 51 normal (12 characteristic)
C₁, C₂, C₂, C₄, C₂², C₂², C₇, C₂×C₄, C₂³, C₁₄, C₁₄, C₂²×C₄, C₂²×C₄, Dic₇, C₂₈, C₂×C₁₄, C₂×C₁₄, C₂.C₄², C₂.C₄², C₂×Dic₇, C₂×C₂₈, C₂²×C₁₄, C₂³.₈₄C₂³, C₂²×Dic₇, C₂²×Dic₇, C₂²×C₂₈, C₁₄.C₄², C₇×C₂.C₄², (C₂²×C₄).D₁₄
Quotients: C₁, C₂, C₂², C₂³, D₇, C₄○D₄, D₁₄, C₄²⋊₂C₂, C₂²×D₇, C₂³.₈₄C₂³, C₄○D₂₈, D₄⋊₂D₇, Q₈⋊₂D₇, C₄²⋊₂D₇, C₂³.D₁₄, C₄⋊C₄⋊D₇, (C₂²×C₄).D₁₄

Smallest permutation representation of (C₂²×C₄).D₁₄
►Regular action on 448 points

Generators in S₄₄₈

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

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

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

(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)

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

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

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

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

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	2	2	2	2	4	4
type	+	+	+	+		+		-	+
image	C₁	C₂	C₂	D₇	C₄○D₄	D₁₄	C₄○D₂₈	D₄⋊₂D₇	Q₈⋊₂D₇
kernel	(C₂²×C₄).D₁₄	C₁₄.C₄²	C₇×C₂.C₄²	C₂.C₄²	C₂×C₁₄	C₂²×C₄	C₂²	C₂²	C₂²
# reps	1	6	1	3	14	9	36	9	3

Matrix representation of (C₂²×C₄).D₁₄ ►in GL₆(𝔽₂₉)

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

1	0	0	0	0	0
0	1	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

24	13	0	0	0	0
16	5	0	0	0	0
0	0	13	5	0	0
0	0	24	16	0	0
0	0	0	0	13	2
0	0	0	0	2	16

12	17	0	0	0	0
12	5	0	0	0	0
0	0	10	10	0	0
0	0	19	16	0	0
0	0	0	0	0	1
0	0	0	0	28	0

12	5	0	0	0	0
12	17	0	0	0	0
0	0	16	19	0	0
0	0	17	13	0	0
0	0	0	0	0	17
0	0	0	0	12	0

G:=sub<GL(6,GF(29))| [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],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[24,16,0,0,0,0,13,5,0,0,0,0,0,0,13,24,0,0,0,0,5,16,0,0,0,0,0,0,13,2,0,0,0,0,2,16],[12,12,0,0,0,0,17,5,0,0,0,0,0,0,10,19,0,0,0,0,10,16,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[12,12,0,0,0,0,5,17,0,0,0,0,0,0,16,17,0,0,0,0,19,13,0,0,0,0,0,0,0,12,0,0,0,0,17,0] >;

(C₂²×C₄).D₁₄ in GAP, Magma, Sage, TeX

(C_2^2\times C_4).D_{14}

% in TeX

G:=Group("(C2^2xC4).D14");

// GroupNames label

G:=SmallGroup(448,196);

// by ID

G=gap.SmallGroup(448,196);

# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,64,1262,387,268,18822]);

// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^4=1,d^14=b*a=a*b,e^2=b*c^2,a*c=c*a,a*d=d*a,a*e=e*a,d*c*d^-1=b*c=c*b,b*d=d*b,b*e=e*b,e*c*e^-1=a*b*c,e*d*e^-1=a*b*c^2*d^13>;

// generators/relations

G = (C22×C4).D14 order 448 = 26·7

14th non-split extension by C22×C4 of D14 acting via D14/C7=C22

G = (C₂²×C₄).D₁₄ order 448 = 2⁶·7

14^th non-split extension by C₂²×C₄ of D₁₄ acting via D₁₄/C₇=C₂²