direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22×C4⋊Dic7, C23.63D28, C24.77D14, C23.19Dic14, C28⋊8(C22×C4), (C22×C28)⋊15C4, (C22×C4)⋊9Dic7, C4⋊2(C22×Dic7), (C23×C4).11D7, C2.2(C22×D28), C14.42(C23×C4), (C23×C28).13C2, C14.31(C22×D4), C22.75(C2×D28), C14.20(C22×Q8), (C22×C14).28Q8, C2.4(C23×Dic7), (C2×C28).789C23, (C2×C14).283C24, (C22×C14).148D4, (C22×C4).447D14, C23.45(C2×Dic7), C2.3(C22×Dic14), C22.40(C23×D7), (C23×Dic7).10C2, C22.39(C2×Dic14), C23.334(C22×D7), (C22×C28).529C22, (C22×C14).412C23, (C23×C14).105C22, (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
Generators and relations for C22×C4⋊Dic7
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 >
Subgroups: 1284 in 418 conjugacy classes, 287 normal (15 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C23, C14, C14, C4⋊C4, C22×C4, C22×C4, C24, Dic7, C28, C2×C14, C2×C14, C2×C4⋊C4, C23×C4, C23×C4, C2×Dic7, C2×Dic7, C2×C28, C22×C14, C22×C4⋊C4, C4⋊Dic7, C22×Dic7, C22×Dic7, C22×C28, C23×C14, C2×C4⋊Dic7, C23×Dic7, C23×C28, C22×C4⋊Dic7
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C4⋊C4, C22×C4, C2×D4, C2×Q8, C24, Dic7, D14, C2×C4⋊C4, C23×C4, C22×D4, C22×Q8, Dic14, D28, C2×Dic7, C22×D7, C22×C4⋊C4, C4⋊Dic7, C2×Dic14, C2×D28, C22×Dic7, C23×D7, C2×C4⋊Dic7, C22×Dic14, C22×D28, C23×Dic7, C22×C4⋊Dic7
►Regular action on 448 points
Generators in S448
(1 99)(2 100)(3 101)(4 102)(5 103)(6 104)(7 105)(8 106)(9 107)(10 108)(11 109)(12 110)(13 111)(14 112)(15 259)(16 260)(17 261)(18 262)(19 263)(20 264)(21 265)(22 266)(23 253)(24 254)(25 255)(26 256)(27 257)(28 258)(29 118)(30 119)(31 120)(32 121)(33 122)(34 123)(35 124)(36 125)(37 126)(38 113)(39 114)(40 115)(41 116)(42 117)(43 243)(44 244)(45 245)(46 246)(47 247)(48 248)(49 249)(50 250)(51 251)(52 252)(53 239)(54 240)(55 241)(56 242)(57 390)(58 391)(59 392)(60 379)(61 380)(62 381)(63 382)(64 383)(65 384)(66 385)(67 386)(68 387)(69 388)(70 389)(71 221)(72 222)(73 223)(74 224)(75 211)(76 212)(77 213)(78 214)(79 215)(80 216)(81 217)(82 218)(83 219)(84 220)(85 439)(86 440)(87 441)(88 442)(89 443)(90 444)(91 445)(92 446)(93 447)(94 448)(95 435)(96 436)(97 437)(98 438)(127 280)(128 267)(129 268)(130 269)(131 270)(132 271)(133 272)(134 273)(135 274)(136 275)(137 276)(138 277)(139 278)(140 279)(141 227)(142 228)(143 229)(144 230)(145 231)(146 232)(147 233)(148 234)(149 235)(150 236)(151 237)(152 238)(153 225)(154 226)(155 292)(156 293)(157 294)(158 281)(159 282)(160 283)(161 284)(162 285)(163 286)(164 287)(165 288)(166 289)(167 290)(168 291)(169 332)(170 333)(171 334)(172 335)(173 336)(174 323)(175 324)(176 325)(177 326)(178 327)(179 328)(180 329)(181 330)(182 331)(183 349)(184 350)(185 337)(186 338)(187 339)(188 340)(189 341)(190 342)(191 343)(192 344)(193 345)(194 346)(195 347)(196 348)(197 304)(198 305)(199 306)(200 307)(201 308)(202 295)(203 296)(204 297)(205 298)(206 299)(207 300)(208 301)(209 302)(210 303)(309 429)(310 430)(311 431)(312 432)(313 433)(314 434)(315 421)(316 422)(317 423)(318 424)(319 425)(320 426)(321 427)(322 428)(351 368)(352 369)(353 370)(354 371)(355 372)(356 373)(357 374)(358 375)(359 376)(360 377)(361 378)(362 365)(363 366)(364 367)(393 419)(394 420)(395 407)(396 408)(397 409)(398 410)(399 411)(400 412)(401 413)(402 414)(403 415)(404 416)(405 417)(406 418)
(1 260)(2 261)(3 262)(4 263)(5 264)(6 265)(7 266)(8 253)(9 254)(10 255)(11 256)(12 257)(13 258)(14 259)(15 112)(16 99)(17 100)(18 101)(19 102)(20 103)(21 104)(22 105)(23 106)(24 107)(25 108)(26 109)(27 110)(28 111)(29 64)(30 65)(31 66)(32 67)(33 68)(34 69)(35 70)(36 57)(37 58)(38 59)(39 60)(40 61)(41 62)(42 63)(43 302)(44 303)(45 304)(46 305)(47 306)(48 307)(49 308)(50 295)(51 296)(52 297)(53 298)(54 299)(55 300)(56 301)(71 327)(72 328)(73 329)(74 330)(75 331)(76 332)(77 333)(78 334)(79 335)(80 336)(81 323)(82 324)(83 325)(84 326)(85 309)(86 310)(87 311)(88 312)(89 313)(90 314)(91 315)(92 316)(93 317)(94 318)(95 319)(96 320)(97 321)(98 322)(113 392)(114 379)(115 380)(116 381)(117 382)(118 383)(119 384)(120 385)(121 386)(122 387)(123 388)(124 389)(125 390)(126 391)(127 349)(128 350)(129 337)(130 338)(131 339)(132 340)(133 341)(134 342)(135 343)(136 344)(137 345)(138 346)(139 347)(140 348)(141 373)(142 374)(143 375)(144 376)(145 377)(146 378)(147 365)(148 366)(149 367)(150 368)(151 369)(152 370)(153 371)(154 372)(155 410)(156 411)(157 412)(158 413)(159 414)(160 415)(161 416)(162 417)(163 418)(164 419)(165 420)(166 407)(167 408)(168 409)(169 212)(170 213)(171 214)(172 215)(173 216)(174 217)(175 218)(176 219)(177 220)(178 221)(179 222)(180 223)(181 224)(182 211)(183 280)(184 267)(185 268)(186 269)(187 270)(188 271)(189 272)(190 273)(191 274)(192 275)(193 276)(194 277)(195 278)(196 279)(197 245)(198 246)(199 247)(200 248)(201 249)(202 250)(203 251)(204 252)(205 239)(206 240)(207 241)(208 242)(209 243)(210 244)(225 354)(226 355)(227 356)(228 357)(229 358)(230 359)(231 360)(232 361)(233 362)(234 363)(235 364)(236 351)(237 352)(238 353)(281 401)(282 402)(283 403)(284 404)(285 405)(286 406)(287 393)(288 394)(289 395)(290 396)(291 397)(292 398)(293 399)(294 400)(421 445)(422 446)(423 447)(424 448)(425 435)(426 436)(427 437)(428 438)(429 439)(430 440)(431 441)(432 442)(433 443)(434 444)
(1 338 403 386)(2 339 404 387)(3 340 405 388)(4 341 406 389)(5 342 393 390)(6 343 394 391)(7 344 395 392)(8 345 396 379)(9 346 397 380)(10 347 398 381)(11 348 399 382)(12 349 400 383)(13 350 401 384)(14 337 402 385)(15 268 159 31)(16 269 160 32)(17 270 161 33)(18 271 162 34)(19 272 163 35)(20 273 164 36)(21 274 165 37)(22 275 166 38)(23 276 167 39)(24 277 168 40)(25 278 155 41)(26 279 156 42)(27 280 157 29)(28 267 158 30)(43 154 336 427)(44 141 323 428)(45 142 324 429)(46 143 325 430)(47 144 326 431)(48 145 327 432)(49 146 328 433)(50 147 329 434)(51 148 330 421)(52 149 331 422)(53 150 332 423)(54 151 333 424)(55 152 334 425)(56 153 335 426)(57 103 190 419)(58 104 191 420)(59 105 192 407)(60 106 193 408)(61 107 194 409)(62 108 195 410)(63 109 196 411)(64 110 183 412)(65 111 184 413)(66 112 185 414)(67 99 186 415)(68 100 187 416)(69 101 188 417)(70 102 189 418)(71 442 307 377)(72 443 308 378)(73 444 295 365)(74 445 296 366)(75 446 297 367)(76 447 298 368)(77 448 299 369)(78 435 300 370)(79 436 301 371)(80 437 302 372)(81 438 303 373)(82 439 304 374)(83 440 305 375)(84 441 306 376)(85 197 357 218)(86 198 358 219)(87 199 359 220)(88 200 360 221)(89 201 361 222)(90 202 362 223)(91 203 363 224)(92 204 364 211)(93 205 351 212)(94 206 352 213)(95 207 353 214)(96 208 354 215)(97 209 355 216)(98 210 356 217)(113 266 136 289)(114 253 137 290)(115 254 138 291)(116 255 139 292)(117 256 140 293)(118 257 127 294)(119 258 128 281)(120 259 129 282)(121 260 130 283)(122 261 131 284)(123 262 132 285)(124 263 133 286)(125 264 134 287)(126 265 135 288)(169 317 239 236)(170 318 240 237)(171 319 241 238)(172 320 242 225)(173 321 243 226)(174 322 244 227)(175 309 245 228)(176 310 246 229)(177 311 247 230)(178 312 248 231)(179 313 249 232)(180 314 250 233)(181 315 251 234)(182 316 252 235)
(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)
(1 364 8 357)(2 363 9 356)(3 362 10 355)(4 361 11 354)(5 360 12 353)(6 359 13 352)(7 358 14 351)(15 150 22 143)(16 149 23 142)(17 148 24 141)(18 147 25 154)(19 146 26 153)(20 145 27 152)(21 144 28 151)(29 334 36 327)(30 333 37 326)(31 332 38 325)(32 331 39 324)(33 330 40 323)(34 329 41 336)(35 328 42 335)(43 271 50 278)(44 270 51 277)(45 269 52 276)(46 268 53 275)(47 267 54 274)(48 280 55 273)(49 279 56 272)(57 71 64 78)(58 84 65 77)(59 83 66 76)(60 82 67 75)(61 81 68 74)(62 80 69 73)(63 79 70 72)(85 403 92 396)(86 402 93 395)(87 401 94 394)(88 400 95 393)(89 399 96 406)(90 398 97 405)(91 397 98 404)(99 367 106 374)(100 366 107 373)(101 365 108 372)(102 378 109 371)(103 377 110 370)(104 376 111 369)(105 375 112 368)(113 176 120 169)(114 175 121 182)(115 174 122 181)(116 173 123 180)(117 172 124 179)(118 171 125 178)(119 170 126 177)(127 241 134 248)(128 240 135 247)(129 239 136 246)(130 252 137 245)(131 251 138 244)(132 250 139 243)(133 249 140 242)(155 427 162 434)(156 426 163 433)(157 425 164 432)(158 424 165 431)(159 423 166 430)(160 422 167 429)(161 421 168 428)(183 300 190 307)(184 299 191 306)(185 298 192 305)(186 297 193 304)(187 296 194 303)(188 295 195 302)(189 308 196 301)(197 338 204 345)(198 337 205 344)(199 350 206 343)(200 349 207 342)(201 348 208 341)(202 347 209 340)(203 346 210 339)(211 379 218 386)(212 392 219 385)(213 391 220 384)(214 390 221 383)(215 389 222 382)(216 388 223 381)(217 387 224 380)(225 263 232 256)(226 262 233 255)(227 261 234 254)(228 260 235 253)(229 259 236 266)(230 258 237 265)(231 257 238 264)(281 318 288 311)(282 317 289 310)(283 316 290 309)(284 315 291 322)(285 314 292 321)(286 313 293 320)(287 312 294 319)(407 440 414 447)(408 439 415 446)(409 438 416 445)(410 437 417 444)(411 436 418 443)(412 435 419 442)(413 448 420 441)
G:=sub<Sym(448)| (1,99)(2,100)(3,101)(4,102)(5,103)(6,104)(7,105)(8,106)(9,107)(10,108)(11,109)(12,110)(13,111)(14,112)(15,259)(16,260)(17,261)(18,262)(19,263)(20,264)(21,265)(22,266)(23,253)(24,254)(25,255)(26,256)(27,257)(28,258)(29,118)(30,119)(31,120)(32,121)(33,122)(34,123)(35,124)(36,125)(37,126)(38,113)(39,114)(40,115)(41,116)(42,117)(43,243)(44,244)(45,245)(46,246)(47,247)(48,248)(49,249)(50,250)(51,251)(52,252)(53,239)(54,240)(55,241)(56,242)(57,390)(58,391)(59,392)(60,379)(61,380)(62,381)(63,382)(64,383)(65,384)(66,385)(67,386)(68,387)(69,388)(70,389)(71,221)(72,222)(73,223)(74,224)(75,211)(76,212)(77,213)(78,214)(79,215)(80,216)(81,217)(82,218)(83,219)(84,220)(85,439)(86,440)(87,441)(88,442)(89,443)(90,444)(91,445)(92,446)(93,447)(94,448)(95,435)(96,436)(97,437)(98,438)(127,280)(128,267)(129,268)(130,269)(131,270)(132,271)(133,272)(134,273)(135,274)(136,275)(137,276)(138,277)(139,278)(140,279)(141,227)(142,228)(143,229)(144,230)(145,231)(146,232)(147,233)(148,234)(149,235)(150,236)(151,237)(152,238)(153,225)(154,226)(155,292)(156,293)(157,294)(158,281)(159,282)(160,283)(161,284)(162,285)(163,286)(164,287)(165,288)(166,289)(167,290)(168,291)(169,332)(170,333)(171,334)(172,335)(173,336)(174,323)(175,324)(176,325)(177,326)(178,327)(179,328)(180,329)(181,330)(182,331)(183,349)(184,350)(185,337)(186,338)(187,339)(188,340)(189,341)(190,342)(191,343)(192,344)(193,345)(194,346)(195,347)(196,348)(197,304)(198,305)(199,306)(200,307)(201,308)(202,295)(203,296)(204,297)(205,298)(206,299)(207,300)(208,301)(209,302)(210,303)(309,429)(310,430)(311,431)(312,432)(313,433)(314,434)(315,421)(316,422)(317,423)(318,424)(319,425)(320,426)(321,427)(322,428)(351,368)(352,369)(353,370)(354,371)(355,372)(356,373)(357,374)(358,375)(359,376)(360,377)(361,378)(362,365)(363,366)(364,367)(393,419)(394,420)(395,407)(396,408)(397,409)(398,410)(399,411)(400,412)(401,413)(402,414)(403,415)(404,416)(405,417)(406,418), (1,260)(2,261)(3,262)(4,263)(5,264)(6,265)(7,266)(8,253)(9,254)(10,255)(11,256)(12,257)(13,258)(14,259)(15,112)(16,99)(17,100)(18,101)(19,102)(20,103)(21,104)(22,105)(23,106)(24,107)(25,108)(26,109)(27,110)(28,111)(29,64)(30,65)(31,66)(32,67)(33,68)(34,69)(35,70)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63)(43,302)(44,303)(45,304)(46,305)(47,306)(48,307)(49,308)(50,295)(51,296)(52,297)(53,298)(54,299)(55,300)(56,301)(71,327)(72,328)(73,329)(74,330)(75,331)(76,332)(77,333)(78,334)(79,335)(80,336)(81,323)(82,324)(83,325)(84,326)(85,309)(86,310)(87,311)(88,312)(89,313)(90,314)(91,315)(92,316)(93,317)(94,318)(95,319)(96,320)(97,321)(98,322)(113,392)(114,379)(115,380)(116,381)(117,382)(118,383)(119,384)(120,385)(121,386)(122,387)(123,388)(124,389)(125,390)(126,391)(127,349)(128,350)(129,337)(130,338)(131,339)(132,340)(133,341)(134,342)(135,343)(136,344)(137,345)(138,346)(139,347)(140,348)(141,373)(142,374)(143,375)(144,376)(145,377)(146,378)(147,365)(148,366)(149,367)(150,368)(151,369)(152,370)(153,371)(154,372)(155,410)(156,411)(157,412)(158,413)(159,414)(160,415)(161,416)(162,417)(163,418)(164,419)(165,420)(166,407)(167,408)(168,409)(169,212)(170,213)(171,214)(172,215)(173,216)(174,217)(175,218)(176,219)(177,220)(178,221)(179,222)(180,223)(181,224)(182,211)(183,280)(184,267)(185,268)(186,269)(187,270)(188,271)(189,272)(190,273)(191,274)(192,275)(193,276)(194,277)(195,278)(196,279)(197,245)(198,246)(199,247)(200,248)(201,249)(202,250)(203,251)(204,252)(205,239)(206,240)(207,241)(208,242)(209,243)(210,244)(225,354)(226,355)(227,356)(228,357)(229,358)(230,359)(231,360)(232,361)(233,362)(234,363)(235,364)(236,351)(237,352)(238,353)(281,401)(282,402)(283,403)(284,404)(285,405)(286,406)(287,393)(288,394)(289,395)(290,396)(291,397)(292,398)(293,399)(294,400)(421,445)(422,446)(423,447)(424,448)(425,435)(426,436)(427,437)(428,438)(429,439)(430,440)(431,441)(432,442)(433,443)(434,444), (1,338,403,386)(2,339,404,387)(3,340,405,388)(4,341,406,389)(5,342,393,390)(6,343,394,391)(7,344,395,392)(8,345,396,379)(9,346,397,380)(10,347,398,381)(11,348,399,382)(12,349,400,383)(13,350,401,384)(14,337,402,385)(15,268,159,31)(16,269,160,32)(17,270,161,33)(18,271,162,34)(19,272,163,35)(20,273,164,36)(21,274,165,37)(22,275,166,38)(23,276,167,39)(24,277,168,40)(25,278,155,41)(26,279,156,42)(27,280,157,29)(28,267,158,30)(43,154,336,427)(44,141,323,428)(45,142,324,429)(46,143,325,430)(47,144,326,431)(48,145,327,432)(49,146,328,433)(50,147,329,434)(51,148,330,421)(52,149,331,422)(53,150,332,423)(54,151,333,424)(55,152,334,425)(56,153,335,426)(57,103,190,419)(58,104,191,420)(59,105,192,407)(60,106,193,408)(61,107,194,409)(62,108,195,410)(63,109,196,411)(64,110,183,412)(65,111,184,413)(66,112,185,414)(67,99,186,415)(68,100,187,416)(69,101,188,417)(70,102,189,418)(71,442,307,377)(72,443,308,378)(73,444,295,365)(74,445,296,366)(75,446,297,367)(76,447,298,368)(77,448,299,369)(78,435,300,370)(79,436,301,371)(80,437,302,372)(81,438,303,373)(82,439,304,374)(83,440,305,375)(84,441,306,376)(85,197,357,218)(86,198,358,219)(87,199,359,220)(88,200,360,221)(89,201,361,222)(90,202,362,223)(91,203,363,224)(92,204,364,211)(93,205,351,212)(94,206,352,213)(95,207,353,214)(96,208,354,215)(97,209,355,216)(98,210,356,217)(113,266,136,289)(114,253,137,290)(115,254,138,291)(116,255,139,292)(117,256,140,293)(118,257,127,294)(119,258,128,281)(120,259,129,282)(121,260,130,283)(122,261,131,284)(123,262,132,285)(124,263,133,286)(125,264,134,287)(126,265,135,288)(169,317,239,236)(170,318,240,237)(171,319,241,238)(172,320,242,225)(173,321,243,226)(174,322,244,227)(175,309,245,228)(176,310,246,229)(177,311,247,230)(178,312,248,231)(179,313,249,232)(180,314,250,233)(181,315,251,234)(182,316,252,235), (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), (1,364,8,357)(2,363,9,356)(3,362,10,355)(4,361,11,354)(5,360,12,353)(6,359,13,352)(7,358,14,351)(15,150,22,143)(16,149,23,142)(17,148,24,141)(18,147,25,154)(19,146,26,153)(20,145,27,152)(21,144,28,151)(29,334,36,327)(30,333,37,326)(31,332,38,325)(32,331,39,324)(33,330,40,323)(34,329,41,336)(35,328,42,335)(43,271,50,278)(44,270,51,277)(45,269,52,276)(46,268,53,275)(47,267,54,274)(48,280,55,273)(49,279,56,272)(57,71,64,78)(58,84,65,77)(59,83,66,76)(60,82,67,75)(61,81,68,74)(62,80,69,73)(63,79,70,72)(85,403,92,396)(86,402,93,395)(87,401,94,394)(88,400,95,393)(89,399,96,406)(90,398,97,405)(91,397,98,404)(99,367,106,374)(100,366,107,373)(101,365,108,372)(102,378,109,371)(103,377,110,370)(104,376,111,369)(105,375,112,368)(113,176,120,169)(114,175,121,182)(115,174,122,181)(116,173,123,180)(117,172,124,179)(118,171,125,178)(119,170,126,177)(127,241,134,248)(128,240,135,247)(129,239,136,246)(130,252,137,245)(131,251,138,244)(132,250,139,243)(133,249,140,242)(155,427,162,434)(156,426,163,433)(157,425,164,432)(158,424,165,431)(159,423,166,430)(160,422,167,429)(161,421,168,428)(183,300,190,307)(184,299,191,306)(185,298,192,305)(186,297,193,304)(187,296,194,303)(188,295,195,302)(189,308,196,301)(197,338,204,345)(198,337,205,344)(199,350,206,343)(200,349,207,342)(201,348,208,341)(202,347,209,340)(203,346,210,339)(211,379,218,386)(212,392,219,385)(213,391,220,384)(214,390,221,383)(215,389,222,382)(216,388,223,381)(217,387,224,380)(225,263,232,256)(226,262,233,255)(227,261,234,254)(228,260,235,253)(229,259,236,266)(230,258,237,265)(231,257,238,264)(281,318,288,311)(282,317,289,310)(283,316,290,309)(284,315,291,322)(285,314,292,321)(286,313,293,320)(287,312,294,319)(407,440,414,447)(408,439,415,446)(409,438,416,445)(410,437,417,444)(411,436,418,443)(412,435,419,442)(413,448,420,441)>;
G:=Group( (1,99)(2,100)(3,101)(4,102)(5,103)(6,104)(7,105)(8,106)(9,107)(10,108)(11,109)(12,110)(13,111)(14,112)(15,259)(16,260)(17,261)(18,262)(19,263)(20,264)(21,265)(22,266)(23,253)(24,254)(25,255)(26,256)(27,257)(28,258)(29,118)(30,119)(31,120)(32,121)(33,122)(34,123)(35,124)(36,125)(37,126)(38,113)(39,114)(40,115)(41,116)(42,117)(43,243)(44,244)(45,245)(46,246)(47,247)(48,248)(49,249)(50,250)(51,251)(52,252)(53,239)(54,240)(55,241)(56,242)(57,390)(58,391)(59,392)(60,379)(61,380)(62,381)(63,382)(64,383)(65,384)(66,385)(67,386)(68,387)(69,388)(70,389)(71,221)(72,222)(73,223)(74,224)(75,211)(76,212)(77,213)(78,214)(79,215)(80,216)(81,217)(82,218)(83,219)(84,220)(85,439)(86,440)(87,441)(88,442)(89,443)(90,444)(91,445)(92,446)(93,447)(94,448)(95,435)(96,436)(97,437)(98,438)(127,280)(128,267)(129,268)(130,269)(131,270)(132,271)(133,272)(134,273)(135,274)(136,275)(137,276)(138,277)(139,278)(140,279)(141,227)(142,228)(143,229)(144,230)(145,231)(146,232)(147,233)(148,234)(149,235)(150,236)(151,237)(152,238)(153,225)(154,226)(155,292)(156,293)(157,294)(158,281)(159,282)(160,283)(161,284)(162,285)(163,286)(164,287)(165,288)(166,289)(167,290)(168,291)(169,332)(170,333)(171,334)(172,335)(173,336)(174,323)(175,324)(176,325)(177,326)(178,327)(179,328)(180,329)(181,330)(182,331)(183,349)(184,350)(185,337)(186,338)(187,339)(188,340)(189,341)(190,342)(191,343)(192,344)(193,345)(194,346)(195,347)(196,348)(197,304)(198,305)(199,306)(200,307)(201,308)(202,295)(203,296)(204,297)(205,298)(206,299)(207,300)(208,301)(209,302)(210,303)(309,429)(310,430)(311,431)(312,432)(313,433)(314,434)(315,421)(316,422)(317,423)(318,424)(319,425)(320,426)(321,427)(322,428)(351,368)(352,369)(353,370)(354,371)(355,372)(356,373)(357,374)(358,375)(359,376)(360,377)(361,378)(362,365)(363,366)(364,367)(393,419)(394,420)(395,407)(396,408)(397,409)(398,410)(399,411)(400,412)(401,413)(402,414)(403,415)(404,416)(405,417)(406,418), (1,260)(2,261)(3,262)(4,263)(5,264)(6,265)(7,266)(8,253)(9,254)(10,255)(11,256)(12,257)(13,258)(14,259)(15,112)(16,99)(17,100)(18,101)(19,102)(20,103)(21,104)(22,105)(23,106)(24,107)(25,108)(26,109)(27,110)(28,111)(29,64)(30,65)(31,66)(32,67)(33,68)(34,69)(35,70)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63)(43,302)(44,303)(45,304)(46,305)(47,306)(48,307)(49,308)(50,295)(51,296)(52,297)(53,298)(54,299)(55,300)(56,301)(71,327)(72,328)(73,329)(74,330)(75,331)(76,332)(77,333)(78,334)(79,335)(80,336)(81,323)(82,324)(83,325)(84,326)(85,309)(86,310)(87,311)(88,312)(89,313)(90,314)(91,315)(92,316)(93,317)(94,318)(95,319)(96,320)(97,321)(98,322)(113,392)(114,379)(115,380)(116,381)(117,382)(118,383)(119,384)(120,385)(121,386)(122,387)(123,388)(124,389)(125,390)(126,391)(127,349)(128,350)(129,337)(130,338)(131,339)(132,340)(133,341)(134,342)(135,343)(136,344)(137,345)(138,346)(139,347)(140,348)(141,373)(142,374)(143,375)(144,376)(145,377)(146,378)(147,365)(148,366)(149,367)(150,368)(151,369)(152,370)(153,371)(154,372)(155,410)(156,411)(157,412)(158,413)(159,414)(160,415)(161,416)(162,417)(163,418)(164,419)(165,420)(166,407)(167,408)(168,409)(169,212)(170,213)(171,214)(172,215)(173,216)(174,217)(175,218)(176,219)(177,220)(178,221)(179,222)(180,223)(181,224)(182,211)(183,280)(184,267)(185,268)(186,269)(187,270)(188,271)(189,272)(190,273)(191,274)(192,275)(193,276)(194,277)(195,278)(196,279)(197,245)(198,246)(199,247)(200,248)(201,249)(202,250)(203,251)(204,252)(205,239)(206,240)(207,241)(208,242)(209,243)(210,244)(225,354)(226,355)(227,356)(228,357)(229,358)(230,359)(231,360)(232,361)(233,362)(234,363)(235,364)(236,351)(237,352)(238,353)(281,401)(282,402)(283,403)(284,404)(285,405)(286,406)(287,393)(288,394)(289,395)(290,396)(291,397)(292,398)(293,399)(294,400)(421,445)(422,446)(423,447)(424,448)(425,435)(426,436)(427,437)(428,438)(429,439)(430,440)(431,441)(432,442)(433,443)(434,444), (1,338,403,386)(2,339,404,387)(3,340,405,388)(4,341,406,389)(5,342,393,390)(6,343,394,391)(7,344,395,392)(8,345,396,379)(9,346,397,380)(10,347,398,381)(11,348,399,382)(12,349,400,383)(13,350,401,384)(14,337,402,385)(15,268,159,31)(16,269,160,32)(17,270,161,33)(18,271,162,34)(19,272,163,35)(20,273,164,36)(21,274,165,37)(22,275,166,38)(23,276,167,39)(24,277,168,40)(25,278,155,41)(26,279,156,42)(27,280,157,29)(28,267,158,30)(43,154,336,427)(44,141,323,428)(45,142,324,429)(46,143,325,430)(47,144,326,431)(48,145,327,432)(49,146,328,433)(50,147,329,434)(51,148,330,421)(52,149,331,422)(53,150,332,423)(54,151,333,424)(55,152,334,425)(56,153,335,426)(57,103,190,419)(58,104,191,420)(59,105,192,407)(60,106,193,408)(61,107,194,409)(62,108,195,410)(63,109,196,411)(64,110,183,412)(65,111,184,413)(66,112,185,414)(67,99,186,415)(68,100,187,416)(69,101,188,417)(70,102,189,418)(71,442,307,377)(72,443,308,378)(73,444,295,365)(74,445,296,366)(75,446,297,367)(76,447,298,368)(77,448,299,369)(78,435,300,370)(79,436,301,371)(80,437,302,372)(81,438,303,373)(82,439,304,374)(83,440,305,375)(84,441,306,376)(85,197,357,218)(86,198,358,219)(87,199,359,220)(88,200,360,221)(89,201,361,222)(90,202,362,223)(91,203,363,224)(92,204,364,211)(93,205,351,212)(94,206,352,213)(95,207,353,214)(96,208,354,215)(97,209,355,216)(98,210,356,217)(113,266,136,289)(114,253,137,290)(115,254,138,291)(116,255,139,292)(117,256,140,293)(118,257,127,294)(119,258,128,281)(120,259,129,282)(121,260,130,283)(122,261,131,284)(123,262,132,285)(124,263,133,286)(125,264,134,287)(126,265,135,288)(169,317,239,236)(170,318,240,237)(171,319,241,238)(172,320,242,225)(173,321,243,226)(174,322,244,227)(175,309,245,228)(176,310,246,229)(177,311,247,230)(178,312,248,231)(179,313,249,232)(180,314,250,233)(181,315,251,234)(182,316,252,235), (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), (1,364,8,357)(2,363,9,356)(3,362,10,355)(4,361,11,354)(5,360,12,353)(6,359,13,352)(7,358,14,351)(15,150,22,143)(16,149,23,142)(17,148,24,141)(18,147,25,154)(19,146,26,153)(20,145,27,152)(21,144,28,151)(29,334,36,327)(30,333,37,326)(31,332,38,325)(32,331,39,324)(33,330,40,323)(34,329,41,336)(35,328,42,335)(43,271,50,278)(44,270,51,277)(45,269,52,276)(46,268,53,275)(47,267,54,274)(48,280,55,273)(49,279,56,272)(57,71,64,78)(58,84,65,77)(59,83,66,76)(60,82,67,75)(61,81,68,74)(62,80,69,73)(63,79,70,72)(85,403,92,396)(86,402,93,395)(87,401,94,394)(88,400,95,393)(89,399,96,406)(90,398,97,405)(91,397,98,404)(99,367,106,374)(100,366,107,373)(101,365,108,372)(102,378,109,371)(103,377,110,370)(104,376,111,369)(105,375,112,368)(113,176,120,169)(114,175,121,182)(115,174,122,181)(116,173,123,180)(117,172,124,179)(118,171,125,178)(119,170,126,177)(127,241,134,248)(128,240,135,247)(129,239,136,246)(130,252,137,245)(131,251,138,244)(132,250,139,243)(133,249,140,242)(155,427,162,434)(156,426,163,433)(157,425,164,432)(158,424,165,431)(159,423,166,430)(160,422,167,429)(161,421,168,428)(183,300,190,307)(184,299,191,306)(185,298,192,305)(186,297,193,304)(187,296,194,303)(188,295,195,302)(189,308,196,301)(197,338,204,345)(198,337,205,344)(199,350,206,343)(200,349,207,342)(201,348,208,341)(202,347,209,340)(203,346,210,339)(211,379,218,386)(212,392,219,385)(213,391,220,384)(214,390,221,383)(215,389,222,382)(216,388,223,381)(217,387,224,380)(225,263,232,256)(226,262,233,255)(227,261,234,254)(228,260,235,253)(229,259,236,266)(230,258,237,265)(231,257,238,264)(281,318,288,311)(282,317,289,310)(283,316,290,309)(284,315,291,322)(285,314,292,321)(286,313,293,320)(287,312,294,319)(407,440,414,447)(408,439,415,446)(409,438,416,445)(410,437,417,444)(411,436,418,443)(412,435,419,442)(413,448,420,441) );
G=PermutationGroup([[(1,99),(2,100),(3,101),(4,102),(5,103),(6,104),(7,105),(8,106),(9,107),(10,108),(11,109),(12,110),(13,111),(14,112),(15,259),(16,260),(17,261),(18,262),(19,263),(20,264),(21,265),(22,266),(23,253),(24,254),(25,255),(26,256),(27,257),(28,258),(29,118),(30,119),(31,120),(32,121),(33,122),(34,123),(35,124),(36,125),(37,126),(38,113),(39,114),(40,115),(41,116),(42,117),(43,243),(44,244),(45,245),(46,246),(47,247),(48,248),(49,249),(50,250),(51,251),(52,252),(53,239),(54,240),(55,241),(56,242),(57,390),(58,391),(59,392),(60,379),(61,380),(62,381),(63,382),(64,383),(65,384),(66,385),(67,386),(68,387),(69,388),(70,389),(71,221),(72,222),(73,223),(74,224),(75,211),(76,212),(77,213),(78,214),(79,215),(80,216),(81,217),(82,218),(83,219),(84,220),(85,439),(86,440),(87,441),(88,442),(89,443),(90,444),(91,445),(92,446),(93,447),(94,448),(95,435),(96,436),(97,437),(98,438),(127,280),(128,267),(129,268),(130,269),(131,270),(132,271),(133,272),(134,273),(135,274),(136,275),(137,276),(138,277),(139,278),(140,279),(141,227),(142,228),(143,229),(144,230),(145,231),(146,232),(147,233),(148,234),(149,235),(150,236),(151,237),(152,238),(153,225),(154,226),(155,292),(156,293),(157,294),(158,281),(159,282),(160,283),(161,284),(162,285),(163,286),(164,287),(165,288),(166,289),(167,290),(168,291),(169,332),(170,333),(171,334),(172,335),(173,336),(174,323),(175,324),(176,325),(177,326),(178,327),(179,328),(180,329),(181,330),(182,331),(183,349),(184,350),(185,337),(186,338),(187,339),(188,340),(189,341),(190,342),(191,343),(192,344),(193,345),(194,346),(195,347),(196,348),(197,304),(198,305),(199,306),(200,307),(201,308),(202,295),(203,296),(204,297),(205,298),(206,299),(207,300),(208,301),(209,302),(210,303),(309,429),(310,430),(311,431),(312,432),(313,433),(314,434),(315,421),(316,422),(317,423),(318,424),(319,425),(320,426),(321,427),(322,428),(351,368),(352,369),(353,370),(354,371),(355,372),(356,373),(357,374),(358,375),(359,376),(360,377),(361,378),(362,365),(363,366),(364,367),(393,419),(394,420),(395,407),(396,408),(397,409),(398,410),(399,411),(400,412),(401,413),(402,414),(403,415),(404,416),(405,417),(406,418)], [(1,260),(2,261),(3,262),(4,263),(5,264),(6,265),(7,266),(8,253),(9,254),(10,255),(11,256),(12,257),(13,258),(14,259),(15,112),(16,99),(17,100),(18,101),(19,102),(20,103),(21,104),(22,105),(23,106),(24,107),(25,108),(26,109),(27,110),(28,111),(29,64),(30,65),(31,66),(32,67),(33,68),(34,69),(35,70),(36,57),(37,58),(38,59),(39,60),(40,61),(41,62),(42,63),(43,302),(44,303),(45,304),(46,305),(47,306),(48,307),(49,308),(50,295),(51,296),(52,297),(53,298),(54,299),(55,300),(56,301),(71,327),(72,328),(73,329),(74,330),(75,331),(76,332),(77,333),(78,334),(79,335),(80,336),(81,323),(82,324),(83,325),(84,326),(85,309),(86,310),(87,311),(88,312),(89,313),(90,314),(91,315),(92,316),(93,317),(94,318),(95,319),(96,320),(97,321),(98,322),(113,392),(114,379),(115,380),(116,381),(117,382),(118,383),(119,384),(120,385),(121,386),(122,387),(123,388),(124,389),(125,390),(126,391),(127,349),(128,350),(129,337),(130,338),(131,339),(132,340),(133,341),(134,342),(135,343),(136,344),(137,345),(138,346),(139,347),(140,348),(141,373),(142,374),(143,375),(144,376),(145,377),(146,378),(147,365),(148,366),(149,367),(150,368),(151,369),(152,370),(153,371),(154,372),(155,410),(156,411),(157,412),(158,413),(159,414),(160,415),(161,416),(162,417),(163,418),(164,419),(165,420),(166,407),(167,408),(168,409),(169,212),(170,213),(171,214),(172,215),(173,216),(174,217),(175,218),(176,219),(177,220),(178,221),(179,222),(180,223),(181,224),(182,211),(183,280),(184,267),(185,268),(186,269),(187,270),(188,271),(189,272),(190,273),(191,274),(192,275),(193,276),(194,277),(195,278),(196,279),(197,245),(198,246),(199,247),(200,248),(201,249),(202,250),(203,251),(204,252),(205,239),(206,240),(207,241),(208,242),(209,243),(210,244),(225,354),(226,355),(227,356),(228,357),(229,358),(230,359),(231,360),(232,361),(233,362),(234,363),(235,364),(236,351),(237,352),(238,353),(281,401),(282,402),(283,403),(284,404),(285,405),(286,406),(287,393),(288,394),(289,395),(290,396),(291,397),(292,398),(293,399),(294,400),(421,445),(422,446),(423,447),(424,448),(425,435),(426,436),(427,437),(428,438),(429,439),(430,440),(431,441),(432,442),(433,443),(434,444)], [(1,338,403,386),(2,339,404,387),(3,340,405,388),(4,341,406,389),(5,342,393,390),(6,343,394,391),(7,344,395,392),(8,345,396,379),(9,346,397,380),(10,347,398,381),(11,348,399,382),(12,349,400,383),(13,350,401,384),(14,337,402,385),(15,268,159,31),(16,269,160,32),(17,270,161,33),(18,271,162,34),(19,272,163,35),(20,273,164,36),(21,274,165,37),(22,275,166,38),(23,276,167,39),(24,277,168,40),(25,278,155,41),(26,279,156,42),(27,280,157,29),(28,267,158,30),(43,154,336,427),(44,141,323,428),(45,142,324,429),(46,143,325,430),(47,144,326,431),(48,145,327,432),(49,146,328,433),(50,147,329,434),(51,148,330,421),(52,149,331,422),(53,150,332,423),(54,151,333,424),(55,152,334,425),(56,153,335,426),(57,103,190,419),(58,104,191,420),(59,105,192,407),(60,106,193,408),(61,107,194,409),(62,108,195,410),(63,109,196,411),(64,110,183,412),(65,111,184,413),(66,112,185,414),(67,99,186,415),(68,100,187,416),(69,101,188,417),(70,102,189,418),(71,442,307,377),(72,443,308,378),(73,444,295,365),(74,445,296,366),(75,446,297,367),(76,447,298,368),(77,448,299,369),(78,435,300,370),(79,436,301,371),(80,437,302,372),(81,438,303,373),(82,439,304,374),(83,440,305,375),(84,441,306,376),(85,197,357,218),(86,198,358,219),(87,199,359,220),(88,200,360,221),(89,201,361,222),(90,202,362,223),(91,203,363,224),(92,204,364,211),(93,205,351,212),(94,206,352,213),(95,207,353,214),(96,208,354,215),(97,209,355,216),(98,210,356,217),(113,266,136,289),(114,253,137,290),(115,254,138,291),(116,255,139,292),(117,256,140,293),(118,257,127,294),(119,258,128,281),(120,259,129,282),(121,260,130,283),(122,261,131,284),(123,262,132,285),(124,263,133,286),(125,264,134,287),(126,265,135,288),(169,317,239,236),(170,318,240,237),(171,319,241,238),(172,320,242,225),(173,321,243,226),(174,322,244,227),(175,309,245,228),(176,310,246,229),(177,311,247,230),(178,312,248,231),(179,313,249,232),(180,314,250,233),(181,315,251,234),(182,316,252,235)], [(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)], [(1,364,8,357),(2,363,9,356),(3,362,10,355),(4,361,11,354),(5,360,12,353),(6,359,13,352),(7,358,14,351),(15,150,22,143),(16,149,23,142),(17,148,24,141),(18,147,25,154),(19,146,26,153),(20,145,27,152),(21,144,28,151),(29,334,36,327),(30,333,37,326),(31,332,38,325),(32,331,39,324),(33,330,40,323),(34,329,41,336),(35,328,42,335),(43,271,50,278),(44,270,51,277),(45,269,52,276),(46,268,53,275),(47,267,54,274),(48,280,55,273),(49,279,56,272),(57,71,64,78),(58,84,65,77),(59,83,66,76),(60,82,67,75),(61,81,68,74),(62,80,69,73),(63,79,70,72),(85,403,92,396),(86,402,93,395),(87,401,94,394),(88,400,95,393),(89,399,96,406),(90,398,97,405),(91,397,98,404),(99,367,106,374),(100,366,107,373),(101,365,108,372),(102,378,109,371),(103,377,110,370),(104,376,111,369),(105,375,112,368),(113,176,120,169),(114,175,121,182),(115,174,122,181),(116,173,123,180),(117,172,124,179),(118,171,125,178),(119,170,126,177),(127,241,134,248),(128,240,135,247),(129,239,136,246),(130,252,137,245),(131,251,138,244),(132,250,139,243),(133,249,140,242),(155,427,162,434),(156,426,163,433),(157,425,164,432),(158,424,165,431),(159,423,166,430),(160,422,167,429),(161,421,168,428),(183,300,190,307),(184,299,191,306),(185,298,192,305),(186,297,193,304),(187,296,194,303),(188,295,195,302),(189,308,196,301),(197,338,204,345),(198,337,205,344),(199,350,206,343),(200,349,207,342),(201,348,208,341),(202,347,209,340),(203,346,210,339),(211,379,218,386),(212,392,219,385),(213,391,220,384),(214,390,221,383),(215,389,222,382),(216,388,223,381),(217,387,224,380),(225,263,232,256),(226,262,233,255),(227,261,234,254),(228,260,235,253),(229,259,236,266),(230,258,237,265),(231,257,238,264),(281,318,288,311),(282,317,289,310),(283,316,290,309),(284,315,291,322),(285,314,292,321),(286,313,293,320),(287,312,294,319),(407,440,414,447),(408,439,415,446),(409,438,416,445),(410,437,417,444),(411,436,418,443),(412,435,419,442),(413,448,420,441)]])
136 conjugacy classes
| class | 1 | 2A | ··· | 2O | 4A | ··· | 4H | 4I | ··· | 4X | 7A | 7B | 7C | 14A | ··· | 14AS | 28A | ··· | 28AV |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
136 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | - | + | + | - | + | |
| image | C1 | C2 | C2 | C2 | C4 | D4 | Q8 | D7 | Dic7 | D14 | D14 | Dic14 | D28 |
| kernel | C22×C4⋊Dic7 | C2×C4⋊Dic7 | C23×Dic7 | C23×C28 | C22×C28 | C22×C14 | C22×C14 | C23×C4 | C22×C4 | C22×C4 | C24 | C23 | C23 |
| # reps | 1 | 12 | 2 | 1 | 16 | 4 | 4 | 3 | 24 | 18 | 3 | 24 | 24 |
Matrix representation of C22×C4⋊Dic7 ►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 |
| 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 | 11 |
| 0 | 0 | 0 | 0 | 7 | 3 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 1 | 0 | 0 |
| 0 | 0 | 20 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 28 |
| 0 | 0 | 0 | 0 | 2 | 21 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 26 | 0 | 0 |
| 0 | 0 | 7 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 17 |
| 0 | 0 | 0 | 0 | 23 | 25 |
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] >;
C22×C4⋊Dic7 in GAP, Magma, Sage, TeX
C_2^2\times C_4\rtimes {\rm 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