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G = C22×C4⋊Dic7  order 448 = 26·7

Direct product of C22 and C4⋊Dic7

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C22×C4⋊Dic7, C24.77D14, C23.63D28, C23.19Dic14, C28⋊8(C22×C4), (C22×C28)⋊15C4, (C22×C4)⋊9Dic7, C4⋊2(C22×Dic7), (C23×C4).11D7, C2.2(C22×D28), (C23×C28).13C2, C14.42(C23×C4), C22.75(C2×D28), C14.31(C22×D4), C14.20(C22×Q8), (C22×C14).28Q8, C2.4(C23×Dic7), (C2×C14).283C24, (C2×C28).789C23, (C22×C14).148D4, (C22×C4).447D14, C2.3(C22×Dic14), C23.45(C2×Dic7), C22.40(C23×D7), (C23×Dic7).10C2, C22.39(C2×Dic14), C23.334(C22×D7), (C23×C14).105C22, (C22×C14).412C23, (C22×C28).529C22, (C2×Dic7).277C23, C22.30(C22×Dic7), (C22×Dic7).228C22, C14⋊3(C2×C4⋊C4), C7⋊3(C22×C4⋊C4), (C2×C14)⋊9(C4⋊C4), (C2×C28)⋊36(C2×C4), (C2×C4)⋊10(C2×Dic7), (C2×C14).54(C2×Q8), (C2×C14).181(C2×D4), (C2×C4).739(C22×D7), (C22×C14).142(C2×C4), (C2×C14).207(C22×C4), SmallGroup(448,1238)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C14 — C22×C4⋊Dic7
Chief series
C1 — C7 — C14 — C2×C14 — C2×Dic7 — C22×Dic7 — C23×Dic7 — C22×C4⋊Dic7
Lower central
C7 — C14 — C22×C4⋊Dic7

Subgroups: 1284 in 418 conjugacy classes, 287 normal (15 characteristic)
C1, C2 [×3], C2 [×12], C4 [×8], C4 [×8], C22, C22 [×34], C7, C2×C4 [×28], C2×C4 [×32], C23 [×15], C14 [×3], C14 [×12], C4⋊C4 [×16], C22×C4 [×14], C22×C4 [×20], C24, Dic7 [×8], C28 [×8], C2×C14, C2×C14 [×34], C2×C4⋊C4 [×12], C23×C4, C23×C4 [×2], C2×Dic7 [×8], C2×Dic7 [×24], C2×C28 [×28], C22×C14 [×15], C22×C4⋊C4, C4⋊Dic7 [×16], C22×Dic7 [×12], C22×Dic7 [×8], C22×C28 [×14], C23×C14, C2×C4⋊Dic7 [×12], C23×Dic7 [×2], C23×C28, C22×C4⋊Dic7

Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], D4 [×4], Q8 [×4], C23 [×15], D7, C4⋊C4 [×16], C22×C4 [×14], C2×D4 [×6], C2×Q8 [×6], C24, Dic7 [×8], D14 [×7], C2×C4⋊C4 [×12], C23×C4, C22×D4, C22×Q8, Dic14 [×4], D28 [×4], C2×Dic7 [×28], C22×D7 [×7], C22×C4⋊C4, C4⋊Dic7 [×16], C2×Dic14 [×6], C2×D28 [×6], C22×Dic7 [×14], C23×D7, C2×C4⋊Dic7 [×12], C22×Dic14, C22×D28, C23×Dic7, C22×C4⋊Dic7

Generators and relations
 G = < a,b,c,d,e | a2=b2=c4=d14=1, e2=d7, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ece-1=c-1, ede-1=d-1 >

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

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

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

(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)

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

Matrix representation ►G ⊆ GL6(𝔽29)

2800000
0280000
0028000
0002800
000010
000001
,
2800000
010000
001000
000100
000010
000001
,
2800000
0280000
001000
000100
00002611
000073
,
100000
010000
0021100
0020100
00001128
0000221
,
100000
0280000
0072600
0072200
0000417
00002325

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],[28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,26,7,0,0,0,0,11,3],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,21,20,0,0,0,0,1,1,0,0,0,0,0,0,11,2,0,0,0,0,28,21],[1,0,0,0,0,0,0,28,0,0,0,0,0,0,7,7,0,0,0,0,26,22,0,0,0,0,0,0,4,23,0,0,0,0,17,25] >;
 

136 conjugacy classes

class 1 2A···2O4A···4H4I···4X7A7B7C14A···14AS28A···28AV
order12···24···44···477714···1428···28
size11···12···214···142222···22···2

136 irreducible representations

dim1111122222222
type+++++-+-++-+
imageC1C2C2C2C4D4Q8D7Dic7D14D14Dic14D28
kernelC22×C4⋊Dic7C2×C4⋊Dic7C23×Dic7C23×C28C22×C28C22×C14C22×C14C23×C4C22×C4C22×C4C24C23C23
# reps1122116443241832424

In GAP, Magma, Sage, TeX 

C_2^2\times C_4\rtimes Dic_7
 
% in TeX
 
G:=Group("C2^2xC4:Dic7");
 
// GroupNames label
 
G:=SmallGroup(448,1238);
 
// by ID
 
G=gap.SmallGroup(448,1238);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,1123,136,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^4=d^14=1,e^2=d^7,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,e*c*e^-1=c^-1,e*d*e^-1=d^-1>;
 
// generators/relations
 

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