direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22×C7⋊Q16, C28.32C24, Dic14.28C23, (C2×C14)⋊9Q16, C14⋊3(C2×Q16), C7⋊3(C22×Q16), C7⋊C8.29C23, C28.256(C2×D4), (C2×C28).212D4, C4.32(C23×D7), (C22×Q8).7D7, (C2×Q8).185D14, (C7×Q8).21C23, Q8.21(C22×D7), (C2×C28).549C23, (C22×C4).382D14, C14.151(C22×D4), (C22×C14).211D4, C23.107(C7⋊D4), (Q8×C14).230C22, (C22×C28).281C22, (C22×Dic14).18C2, (C2×Dic14).306C22, (Q8×C2×C14).6C2, C4.26(C2×C7⋊D4), (C22×C7⋊C8).14C2, (C2×C14).586(C2×D4), (C2×C7⋊C8).287C22, C2.24(C22×C7⋊D4), (C2×C4).155(C7⋊D4), (C2×C4).630(C22×D7), C22.114(C2×C7⋊D4), SmallGroup(448,1262)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C22×C7⋊Q16
G = < a,b,c,d,e | a2=b2=c7=d8=1, e2=d4, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd-1=c-1, ce=ec, ede-1=d-1 >
Subgroups: 884 in 258 conjugacy classes, 127 normal (15 characteristic)
C1, C2, C2, C4, C4, C4, C22, C7, C8, C2×C4, C2×C4, Q8, Q8, C23, C14, C14, C2×C8, Q16, C22×C4, C22×C4, C2×Q8, C2×Q8, Dic7, C28, C28, C28, C2×C14, C22×C8, C2×Q16, C22×Q8, C22×Q8, C7⋊C8, Dic14, Dic14, C2×Dic7, C2×C28, C2×C28, C7×Q8, C7×Q8, C22×C14, C22×Q16, C2×C7⋊C8, C7⋊Q16, C2×Dic14, C2×Dic14, C22×Dic7, C22×C28, C22×C28, Q8×C14, Q8×C14, C22×C7⋊C8, C2×C7⋊Q16, C22×Dic14, Q8×C2×C14, C22×C7⋊Q16
Quotients: C1, C2, C22, D4, C23, D7, Q16, C2×D4, C24, D14, C2×Q16, C22×D4, C7⋊D4, C22×D7, C22×Q16, C7⋊Q16, C2×C7⋊D4, C23×D7, C2×C7⋊Q16, C22×C7⋊D4, C22×C7⋊Q16
►Regular action on 448 points
Generators in S448
(1 280)(2 273)(3 274)(4 275)(5 276)(6 277)(7 278)(8 279)(9 155)(10 156)(11 157)(12 158)(13 159)(14 160)(15 153)(16 154)(17 394)(18 395)(19 396)(20 397)(21 398)(22 399)(23 400)(24 393)(25 249)(26 250)(27 251)(28 252)(29 253)(30 254)(31 255)(32 256)(33 93)(34 94)(35 95)(36 96)(37 89)(38 90)(39 91)(40 92)(41 101)(42 102)(43 103)(44 104)(45 97)(46 98)(47 99)(48 100)(49 109)(50 110)(51 111)(52 112)(53 105)(54 106)(55 107)(56 108)(57 352)(58 345)(59 346)(60 347)(61 348)(62 349)(63 350)(64 351)(65 205)(66 206)(67 207)(68 208)(69 201)(70 202)(71 203)(72 204)(73 220)(74 221)(75 222)(76 223)(77 224)(78 217)(79 218)(80 219)(81 353)(82 354)(83 355)(84 356)(85 357)(86 358)(87 359)(88 360)(113 173)(114 174)(115 175)(116 176)(117 169)(118 170)(119 171)(120 172)(121 181)(122 182)(123 183)(124 184)(125 177)(126 178)(127 179)(128 180)(129 189)(130 190)(131 191)(132 192)(133 185)(134 186)(135 187)(136 188)(137 197)(138 198)(139 199)(140 200)(141 193)(142 194)(143 195)(144 196)(145 308)(146 309)(147 310)(148 311)(149 312)(150 305)(151 306)(152 307)(161 331)(162 332)(163 333)(164 334)(165 335)(166 336)(167 329)(168 330)(209 259)(210 260)(211 261)(212 262)(213 263)(214 264)(215 257)(216 258)(225 285)(226 286)(227 287)(228 288)(229 281)(230 282)(231 283)(232 284)(233 293)(234 294)(235 295)(236 296)(237 289)(238 290)(239 291)(240 292)(241 301)(242 302)(243 303)(244 304)(245 297)(246 298)(247 299)(248 300)(265 342)(266 343)(267 344)(268 337)(269 338)(270 339)(271 340)(272 341)(313 403)(314 404)(315 405)(316 406)(317 407)(318 408)(319 401)(320 402)(321 410)(322 411)(323 412)(324 413)(325 414)(326 415)(327 416)(328 409)(361 421)(362 422)(363 423)(364 424)(365 417)(366 418)(367 419)(368 420)(369 429)(370 430)(371 431)(372 432)(373 425)(374 426)(375 427)(376 428)(377 437)(378 438)(379 439)(380 440)(381 433)(382 434)(383 435)(384 436)(385 445)(386 446)(387 447)(388 448)(389 441)(390 442)(391 443)(392 444)
(1 252)(2 253)(3 254)(4 255)(5 256)(6 249)(7 250)(8 251)(9 429)(10 430)(11 431)(12 432)(13 425)(14 426)(15 427)(16 428)(17 437)(18 438)(19 439)(20 440)(21 433)(22 434)(23 435)(24 436)(25 277)(26 278)(27 279)(28 280)(29 273)(30 274)(31 275)(32 276)(33 201)(34 202)(35 203)(36 204)(37 205)(38 206)(39 207)(40 208)(41 209)(42 210)(43 211)(44 212)(45 213)(46 214)(47 215)(48 216)(49 217)(50 218)(51 219)(52 220)(53 221)(54 222)(55 223)(56 224)(57 236)(58 237)(59 238)(60 239)(61 240)(62 233)(63 234)(64 235)(65 89)(66 90)(67 91)(68 92)(69 93)(70 94)(71 95)(72 96)(73 112)(74 105)(75 106)(76 107)(77 108)(78 109)(79 110)(80 111)(81 245)(82 246)(83 247)(84 248)(85 241)(86 242)(87 243)(88 244)(97 263)(98 264)(99 257)(100 258)(101 259)(102 260)(103 261)(104 262)(113 318)(114 319)(115 320)(116 313)(117 314)(118 315)(119 316)(120 317)(121 312)(122 305)(123 306)(124 307)(125 308)(126 309)(127 310)(128 311)(129 334)(130 335)(131 336)(132 329)(133 330)(134 331)(135 332)(136 333)(137 328)(138 321)(139 322)(140 323)(141 324)(142 325)(143 326)(144 327)(145 177)(146 178)(147 179)(148 180)(149 181)(150 182)(151 183)(152 184)(153 375)(154 376)(155 369)(156 370)(157 371)(158 372)(159 373)(160 374)(161 186)(162 187)(163 188)(164 189)(165 190)(166 191)(167 192)(168 185)(169 404)(170 405)(171 406)(172 407)(173 408)(174 401)(175 402)(176 403)(193 413)(194 414)(195 415)(196 416)(197 409)(198 410)(199 411)(200 412)(225 272)(226 265)(227 266)(228 267)(229 268)(230 269)(231 270)(232 271)(281 337)(282 338)(283 339)(284 340)(285 341)(286 342)(287 343)(288 344)(289 345)(290 346)(291 347)(292 348)(293 349)(294 350)(295 351)(296 352)(297 353)(298 354)(299 355)(300 356)(301 357)(302 358)(303 359)(304 360)(361 385)(362 386)(363 387)(364 388)(365 389)(366 390)(367 391)(368 392)(377 394)(378 395)(379 396)(380 397)(381 398)(382 399)(383 400)(384 393)(417 441)(418 442)(419 443)(420 444)(421 445)(422 446)(423 447)(424 448)
(1 92 229 165 407 156 411)(2 412 157 408 166 230 93)(3 94 231 167 401 158 413)(4 414 159 402 168 232 95)(5 96 225 161 403 160 415)(6 416 153 404 162 226 89)(7 90 227 163 405 154 409)(8 410 155 406 164 228 91)(9 316 334 288 39 279 321)(10 322 280 40 281 335 317)(11 318 336 282 33 273 323)(12 324 274 34 283 329 319)(13 320 330 284 35 275 325)(14 326 276 36 285 331 313)(15 314 332 286 37 277 327)(16 328 278 38 287 333 315)(17 52 294 47 302 441 308)(18 309 442 303 48 295 53)(19 54 296 41 304 443 310)(20 311 444 297 42 289 55)(21 56 290 43 298 445 312)(22 305 446 299 44 291 49)(23 50 292 45 300 447 306)(24 307 448 301 46 293 51)(25 144 427 117 135 342 205)(26 206 343 136 118 428 137)(27 138 429 119 129 344 207)(28 208 337 130 120 430 139)(29 140 431 113 131 338 201)(30 202 339 132 114 432 141)(31 142 425 115 133 340 203)(32 204 341 134 116 426 143)(57 259 88 367 179 379 75)(58 76 380 180 368 81 260)(59 261 82 361 181 381 77)(60 78 382 182 362 83 262)(61 263 84 363 183 383 79)(62 80 384 184 364 85 264)(63 257 86 365 177 377 73)(64 74 378 178 366 87 258)(65 249 196 375 169 187 265)(66 266 188 170 376 197 250)(67 251 198 369 171 189 267)(68 268 190 172 370 199 252)(69 253 200 371 173 191 269)(70 270 192 174 372 193 254)(71 255 194 373 175 185 271)(72 272 186 176 374 195 256)(97 248 387 151 400 110 240)(98 233 111 393 152 388 241)(99 242 389 145 394 112 234)(100 235 105 395 146 390 243)(101 244 391 147 396 106 236)(102 237 107 397 148 392 245)(103 246 385 149 398 108 238)(104 239 109 399 150 386 247)(121 433 224 346 211 354 421)(122 422 355 212 347 217 434)(123 435 218 348 213 356 423)(124 424 357 214 349 219 436)(125 437 220 350 215 358 417)(126 418 359 216 351 221 438)(127 439 222 352 209 360 419)(128 420 353 210 345 223 440)
(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)
(1 421 5 417)(2 420 6 424)(3 419 7 423)(4 418 8 422)(9 262 13 258)(10 261 14 257)(11 260 15 264)(12 259 16 263)(17 268 21 272)(18 267 22 271)(19 266 23 270)(20 265 24 269)(25 388 29 392)(26 387 30 391)(27 386 31 390)(28 385 32 389)(33 180 37 184)(34 179 38 183)(35 178 39 182)(36 177 40 181)(41 376 45 372)(42 375 46 371)(43 374 47 370)(44 373 48 369)(49 185 53 189)(50 192 54 188)(51 191 55 187)(52 190 56 186)(57 315 61 319)(58 314 62 318)(59 313 63 317)(60 320 64 316)(65 307 69 311)(66 306 70 310)(67 305 71 309)(68 312 72 308)(73 335 77 331)(74 334 78 330)(75 333 79 329)(76 332 80 336)(81 327 85 323)(82 326 86 322)(83 325 87 321)(84 324 88 328)(89 124 93 128)(90 123 94 127)(91 122 95 126)(92 121 96 125)(97 432 101 428)(98 431 102 427)(99 430 103 426)(100 429 104 425)(105 129 109 133)(106 136 110 132)(107 135 111 131)(108 134 112 130)(113 237 117 233)(114 236 118 240)(115 235 119 239)(116 234 120 238)(137 248 141 244)(138 247 142 243)(139 246 143 242)(140 245 144 241)(145 208 149 204)(146 207 150 203)(147 206 151 202)(148 205 152 201)(153 214 157 210)(154 213 158 209)(155 212 159 216)(156 211 160 215)(161 220 165 224)(162 219 166 223)(163 218 167 222)(164 217 168 221)(169 293 173 289)(170 292 174 296)(171 291 175 295)(172 290 176 294)(193 304 197 300)(194 303 198 299)(195 302 199 298)(196 301 200 297)(225 437 229 433)(226 436 230 440)(227 435 231 439)(228 434 232 438)(249 448 253 444)(250 447 254 443)(251 446 255 442)(252 445 256 441)(273 368 277 364)(274 367 278 363)(275 366 279 362)(276 365 280 361)(281 381 285 377)(282 380 286 384)(283 379 287 383)(284 378 288 382)(337 398 341 394)(338 397 342 393)(339 396 343 400)(340 395 344 399)(345 404 349 408)(346 403 350 407)(347 402 351 406)(348 401 352 405)(353 416 357 412)(354 415 358 411)(355 414 359 410)(356 413 360 409)
G:=sub<Sym(448)| (1,280)(2,273)(3,274)(4,275)(5,276)(6,277)(7,278)(8,279)(9,155)(10,156)(11,157)(12,158)(13,159)(14,160)(15,153)(16,154)(17,394)(18,395)(19,396)(20,397)(21,398)(22,399)(23,400)(24,393)(25,249)(26,250)(27,251)(28,252)(29,253)(30,254)(31,255)(32,256)(33,93)(34,94)(35,95)(36,96)(37,89)(38,90)(39,91)(40,92)(41,101)(42,102)(43,103)(44,104)(45,97)(46,98)(47,99)(48,100)(49,109)(50,110)(51,111)(52,112)(53,105)(54,106)(55,107)(56,108)(57,352)(58,345)(59,346)(60,347)(61,348)(62,349)(63,350)(64,351)(65,205)(66,206)(67,207)(68,208)(69,201)(70,202)(71,203)(72,204)(73,220)(74,221)(75,222)(76,223)(77,224)(78,217)(79,218)(80,219)(81,353)(82,354)(83,355)(84,356)(85,357)(86,358)(87,359)(88,360)(113,173)(114,174)(115,175)(116,176)(117,169)(118,170)(119,171)(120,172)(121,181)(122,182)(123,183)(124,184)(125,177)(126,178)(127,179)(128,180)(129,189)(130,190)(131,191)(132,192)(133,185)(134,186)(135,187)(136,188)(137,197)(138,198)(139,199)(140,200)(141,193)(142,194)(143,195)(144,196)(145,308)(146,309)(147,310)(148,311)(149,312)(150,305)(151,306)(152,307)(161,331)(162,332)(163,333)(164,334)(165,335)(166,336)(167,329)(168,330)(209,259)(210,260)(211,261)(212,262)(213,263)(214,264)(215,257)(216,258)(225,285)(226,286)(227,287)(228,288)(229,281)(230,282)(231,283)(232,284)(233,293)(234,294)(235,295)(236,296)(237,289)(238,290)(239,291)(240,292)(241,301)(242,302)(243,303)(244,304)(245,297)(246,298)(247,299)(248,300)(265,342)(266,343)(267,344)(268,337)(269,338)(270,339)(271,340)(272,341)(313,403)(314,404)(315,405)(316,406)(317,407)(318,408)(319,401)(320,402)(321,410)(322,411)(323,412)(324,413)(325,414)(326,415)(327,416)(328,409)(361,421)(362,422)(363,423)(364,424)(365,417)(366,418)(367,419)(368,420)(369,429)(370,430)(371,431)(372,432)(373,425)(374,426)(375,427)(376,428)(377,437)(378,438)(379,439)(380,440)(381,433)(382,434)(383,435)(384,436)(385,445)(386,446)(387,447)(388,448)(389,441)(390,442)(391,443)(392,444), (1,252)(2,253)(3,254)(4,255)(5,256)(6,249)(7,250)(8,251)(9,429)(10,430)(11,431)(12,432)(13,425)(14,426)(15,427)(16,428)(17,437)(18,438)(19,439)(20,440)(21,433)(22,434)(23,435)(24,436)(25,277)(26,278)(27,279)(28,280)(29,273)(30,274)(31,275)(32,276)(33,201)(34,202)(35,203)(36,204)(37,205)(38,206)(39,207)(40,208)(41,209)(42,210)(43,211)(44,212)(45,213)(46,214)(47,215)(48,216)(49,217)(50,218)(51,219)(52,220)(53,221)(54,222)(55,223)(56,224)(57,236)(58,237)(59,238)(60,239)(61,240)(62,233)(63,234)(64,235)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96)(73,112)(74,105)(75,106)(76,107)(77,108)(78,109)(79,110)(80,111)(81,245)(82,246)(83,247)(84,248)(85,241)(86,242)(87,243)(88,244)(97,263)(98,264)(99,257)(100,258)(101,259)(102,260)(103,261)(104,262)(113,318)(114,319)(115,320)(116,313)(117,314)(118,315)(119,316)(120,317)(121,312)(122,305)(123,306)(124,307)(125,308)(126,309)(127,310)(128,311)(129,334)(130,335)(131,336)(132,329)(133,330)(134,331)(135,332)(136,333)(137,328)(138,321)(139,322)(140,323)(141,324)(142,325)(143,326)(144,327)(145,177)(146,178)(147,179)(148,180)(149,181)(150,182)(151,183)(152,184)(153,375)(154,376)(155,369)(156,370)(157,371)(158,372)(159,373)(160,374)(161,186)(162,187)(163,188)(164,189)(165,190)(166,191)(167,192)(168,185)(169,404)(170,405)(171,406)(172,407)(173,408)(174,401)(175,402)(176,403)(193,413)(194,414)(195,415)(196,416)(197,409)(198,410)(199,411)(200,412)(225,272)(226,265)(227,266)(228,267)(229,268)(230,269)(231,270)(232,271)(281,337)(282,338)(283,339)(284,340)(285,341)(286,342)(287,343)(288,344)(289,345)(290,346)(291,347)(292,348)(293,349)(294,350)(295,351)(296,352)(297,353)(298,354)(299,355)(300,356)(301,357)(302,358)(303,359)(304,360)(361,385)(362,386)(363,387)(364,388)(365,389)(366,390)(367,391)(368,392)(377,394)(378,395)(379,396)(380,397)(381,398)(382,399)(383,400)(384,393)(417,441)(418,442)(419,443)(420,444)(421,445)(422,446)(423,447)(424,448), (1,92,229,165,407,156,411)(2,412,157,408,166,230,93)(3,94,231,167,401,158,413)(4,414,159,402,168,232,95)(5,96,225,161,403,160,415)(6,416,153,404,162,226,89)(7,90,227,163,405,154,409)(8,410,155,406,164,228,91)(9,316,334,288,39,279,321)(10,322,280,40,281,335,317)(11,318,336,282,33,273,323)(12,324,274,34,283,329,319)(13,320,330,284,35,275,325)(14,326,276,36,285,331,313)(15,314,332,286,37,277,327)(16,328,278,38,287,333,315)(17,52,294,47,302,441,308)(18,309,442,303,48,295,53)(19,54,296,41,304,443,310)(20,311,444,297,42,289,55)(21,56,290,43,298,445,312)(22,305,446,299,44,291,49)(23,50,292,45,300,447,306)(24,307,448,301,46,293,51)(25,144,427,117,135,342,205)(26,206,343,136,118,428,137)(27,138,429,119,129,344,207)(28,208,337,130,120,430,139)(29,140,431,113,131,338,201)(30,202,339,132,114,432,141)(31,142,425,115,133,340,203)(32,204,341,134,116,426,143)(57,259,88,367,179,379,75)(58,76,380,180,368,81,260)(59,261,82,361,181,381,77)(60,78,382,182,362,83,262)(61,263,84,363,183,383,79)(62,80,384,184,364,85,264)(63,257,86,365,177,377,73)(64,74,378,178,366,87,258)(65,249,196,375,169,187,265)(66,266,188,170,376,197,250)(67,251,198,369,171,189,267)(68,268,190,172,370,199,252)(69,253,200,371,173,191,269)(70,270,192,174,372,193,254)(71,255,194,373,175,185,271)(72,272,186,176,374,195,256)(97,248,387,151,400,110,240)(98,233,111,393,152,388,241)(99,242,389,145,394,112,234)(100,235,105,395,146,390,243)(101,244,391,147,396,106,236)(102,237,107,397,148,392,245)(103,246,385,149,398,108,238)(104,239,109,399,150,386,247)(121,433,224,346,211,354,421)(122,422,355,212,347,217,434)(123,435,218,348,213,356,423)(124,424,357,214,349,219,436)(125,437,220,350,215,358,417)(126,418,359,216,351,221,438)(127,439,222,352,209,360,419)(128,420,353,210,345,223,440), (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), (1,421,5,417)(2,420,6,424)(3,419,7,423)(4,418,8,422)(9,262,13,258)(10,261,14,257)(11,260,15,264)(12,259,16,263)(17,268,21,272)(18,267,22,271)(19,266,23,270)(20,265,24,269)(25,388,29,392)(26,387,30,391)(27,386,31,390)(28,385,32,389)(33,180,37,184)(34,179,38,183)(35,178,39,182)(36,177,40,181)(41,376,45,372)(42,375,46,371)(43,374,47,370)(44,373,48,369)(49,185,53,189)(50,192,54,188)(51,191,55,187)(52,190,56,186)(57,315,61,319)(58,314,62,318)(59,313,63,317)(60,320,64,316)(65,307,69,311)(66,306,70,310)(67,305,71,309)(68,312,72,308)(73,335,77,331)(74,334,78,330)(75,333,79,329)(76,332,80,336)(81,327,85,323)(82,326,86,322)(83,325,87,321)(84,324,88,328)(89,124,93,128)(90,123,94,127)(91,122,95,126)(92,121,96,125)(97,432,101,428)(98,431,102,427)(99,430,103,426)(100,429,104,425)(105,129,109,133)(106,136,110,132)(107,135,111,131)(108,134,112,130)(113,237,117,233)(114,236,118,240)(115,235,119,239)(116,234,120,238)(137,248,141,244)(138,247,142,243)(139,246,143,242)(140,245,144,241)(145,208,149,204)(146,207,150,203)(147,206,151,202)(148,205,152,201)(153,214,157,210)(154,213,158,209)(155,212,159,216)(156,211,160,215)(161,220,165,224)(162,219,166,223)(163,218,167,222)(164,217,168,221)(169,293,173,289)(170,292,174,296)(171,291,175,295)(172,290,176,294)(193,304,197,300)(194,303,198,299)(195,302,199,298)(196,301,200,297)(225,437,229,433)(226,436,230,440)(227,435,231,439)(228,434,232,438)(249,448,253,444)(250,447,254,443)(251,446,255,442)(252,445,256,441)(273,368,277,364)(274,367,278,363)(275,366,279,362)(276,365,280,361)(281,381,285,377)(282,380,286,384)(283,379,287,383)(284,378,288,382)(337,398,341,394)(338,397,342,393)(339,396,343,400)(340,395,344,399)(345,404,349,408)(346,403,350,407)(347,402,351,406)(348,401,352,405)(353,416,357,412)(354,415,358,411)(355,414,359,410)(356,413,360,409)>;
G:=Group( (1,280)(2,273)(3,274)(4,275)(5,276)(6,277)(7,278)(8,279)(9,155)(10,156)(11,157)(12,158)(13,159)(14,160)(15,153)(16,154)(17,394)(18,395)(19,396)(20,397)(21,398)(22,399)(23,400)(24,393)(25,249)(26,250)(27,251)(28,252)(29,253)(30,254)(31,255)(32,256)(33,93)(34,94)(35,95)(36,96)(37,89)(38,90)(39,91)(40,92)(41,101)(42,102)(43,103)(44,104)(45,97)(46,98)(47,99)(48,100)(49,109)(50,110)(51,111)(52,112)(53,105)(54,106)(55,107)(56,108)(57,352)(58,345)(59,346)(60,347)(61,348)(62,349)(63,350)(64,351)(65,205)(66,206)(67,207)(68,208)(69,201)(70,202)(71,203)(72,204)(73,220)(74,221)(75,222)(76,223)(77,224)(78,217)(79,218)(80,219)(81,353)(82,354)(83,355)(84,356)(85,357)(86,358)(87,359)(88,360)(113,173)(114,174)(115,175)(116,176)(117,169)(118,170)(119,171)(120,172)(121,181)(122,182)(123,183)(124,184)(125,177)(126,178)(127,179)(128,180)(129,189)(130,190)(131,191)(132,192)(133,185)(134,186)(135,187)(136,188)(137,197)(138,198)(139,199)(140,200)(141,193)(142,194)(143,195)(144,196)(145,308)(146,309)(147,310)(148,311)(149,312)(150,305)(151,306)(152,307)(161,331)(162,332)(163,333)(164,334)(165,335)(166,336)(167,329)(168,330)(209,259)(210,260)(211,261)(212,262)(213,263)(214,264)(215,257)(216,258)(225,285)(226,286)(227,287)(228,288)(229,281)(230,282)(231,283)(232,284)(233,293)(234,294)(235,295)(236,296)(237,289)(238,290)(239,291)(240,292)(241,301)(242,302)(243,303)(244,304)(245,297)(246,298)(247,299)(248,300)(265,342)(266,343)(267,344)(268,337)(269,338)(270,339)(271,340)(272,341)(313,403)(314,404)(315,405)(316,406)(317,407)(318,408)(319,401)(320,402)(321,410)(322,411)(323,412)(324,413)(325,414)(326,415)(327,416)(328,409)(361,421)(362,422)(363,423)(364,424)(365,417)(366,418)(367,419)(368,420)(369,429)(370,430)(371,431)(372,432)(373,425)(374,426)(375,427)(376,428)(377,437)(378,438)(379,439)(380,440)(381,433)(382,434)(383,435)(384,436)(385,445)(386,446)(387,447)(388,448)(389,441)(390,442)(391,443)(392,444), (1,252)(2,253)(3,254)(4,255)(5,256)(6,249)(7,250)(8,251)(9,429)(10,430)(11,431)(12,432)(13,425)(14,426)(15,427)(16,428)(17,437)(18,438)(19,439)(20,440)(21,433)(22,434)(23,435)(24,436)(25,277)(26,278)(27,279)(28,280)(29,273)(30,274)(31,275)(32,276)(33,201)(34,202)(35,203)(36,204)(37,205)(38,206)(39,207)(40,208)(41,209)(42,210)(43,211)(44,212)(45,213)(46,214)(47,215)(48,216)(49,217)(50,218)(51,219)(52,220)(53,221)(54,222)(55,223)(56,224)(57,236)(58,237)(59,238)(60,239)(61,240)(62,233)(63,234)(64,235)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96)(73,112)(74,105)(75,106)(76,107)(77,108)(78,109)(79,110)(80,111)(81,245)(82,246)(83,247)(84,248)(85,241)(86,242)(87,243)(88,244)(97,263)(98,264)(99,257)(100,258)(101,259)(102,260)(103,261)(104,262)(113,318)(114,319)(115,320)(116,313)(117,314)(118,315)(119,316)(120,317)(121,312)(122,305)(123,306)(124,307)(125,308)(126,309)(127,310)(128,311)(129,334)(130,335)(131,336)(132,329)(133,330)(134,331)(135,332)(136,333)(137,328)(138,321)(139,322)(140,323)(141,324)(142,325)(143,326)(144,327)(145,177)(146,178)(147,179)(148,180)(149,181)(150,182)(151,183)(152,184)(153,375)(154,376)(155,369)(156,370)(157,371)(158,372)(159,373)(160,374)(161,186)(162,187)(163,188)(164,189)(165,190)(166,191)(167,192)(168,185)(169,404)(170,405)(171,406)(172,407)(173,408)(174,401)(175,402)(176,403)(193,413)(194,414)(195,415)(196,416)(197,409)(198,410)(199,411)(200,412)(225,272)(226,265)(227,266)(228,267)(229,268)(230,269)(231,270)(232,271)(281,337)(282,338)(283,339)(284,340)(285,341)(286,342)(287,343)(288,344)(289,345)(290,346)(291,347)(292,348)(293,349)(294,350)(295,351)(296,352)(297,353)(298,354)(299,355)(300,356)(301,357)(302,358)(303,359)(304,360)(361,385)(362,386)(363,387)(364,388)(365,389)(366,390)(367,391)(368,392)(377,394)(378,395)(379,396)(380,397)(381,398)(382,399)(383,400)(384,393)(417,441)(418,442)(419,443)(420,444)(421,445)(422,446)(423,447)(424,448), (1,92,229,165,407,156,411)(2,412,157,408,166,230,93)(3,94,231,167,401,158,413)(4,414,159,402,168,232,95)(5,96,225,161,403,160,415)(6,416,153,404,162,226,89)(7,90,227,163,405,154,409)(8,410,155,406,164,228,91)(9,316,334,288,39,279,321)(10,322,280,40,281,335,317)(11,318,336,282,33,273,323)(12,324,274,34,283,329,319)(13,320,330,284,35,275,325)(14,326,276,36,285,331,313)(15,314,332,286,37,277,327)(16,328,278,38,287,333,315)(17,52,294,47,302,441,308)(18,309,442,303,48,295,53)(19,54,296,41,304,443,310)(20,311,444,297,42,289,55)(21,56,290,43,298,445,312)(22,305,446,299,44,291,49)(23,50,292,45,300,447,306)(24,307,448,301,46,293,51)(25,144,427,117,135,342,205)(26,206,343,136,118,428,137)(27,138,429,119,129,344,207)(28,208,337,130,120,430,139)(29,140,431,113,131,338,201)(30,202,339,132,114,432,141)(31,142,425,115,133,340,203)(32,204,341,134,116,426,143)(57,259,88,367,179,379,75)(58,76,380,180,368,81,260)(59,261,82,361,181,381,77)(60,78,382,182,362,83,262)(61,263,84,363,183,383,79)(62,80,384,184,364,85,264)(63,257,86,365,177,377,73)(64,74,378,178,366,87,258)(65,249,196,375,169,187,265)(66,266,188,170,376,197,250)(67,251,198,369,171,189,267)(68,268,190,172,370,199,252)(69,253,200,371,173,191,269)(70,270,192,174,372,193,254)(71,255,194,373,175,185,271)(72,272,186,176,374,195,256)(97,248,387,151,400,110,240)(98,233,111,393,152,388,241)(99,242,389,145,394,112,234)(100,235,105,395,146,390,243)(101,244,391,147,396,106,236)(102,237,107,397,148,392,245)(103,246,385,149,398,108,238)(104,239,109,399,150,386,247)(121,433,224,346,211,354,421)(122,422,355,212,347,217,434)(123,435,218,348,213,356,423)(124,424,357,214,349,219,436)(125,437,220,350,215,358,417)(126,418,359,216,351,221,438)(127,439,222,352,209,360,419)(128,420,353,210,345,223,440), (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), (1,421,5,417)(2,420,6,424)(3,419,7,423)(4,418,8,422)(9,262,13,258)(10,261,14,257)(11,260,15,264)(12,259,16,263)(17,268,21,272)(18,267,22,271)(19,266,23,270)(20,265,24,269)(25,388,29,392)(26,387,30,391)(27,386,31,390)(28,385,32,389)(33,180,37,184)(34,179,38,183)(35,178,39,182)(36,177,40,181)(41,376,45,372)(42,375,46,371)(43,374,47,370)(44,373,48,369)(49,185,53,189)(50,192,54,188)(51,191,55,187)(52,190,56,186)(57,315,61,319)(58,314,62,318)(59,313,63,317)(60,320,64,316)(65,307,69,311)(66,306,70,310)(67,305,71,309)(68,312,72,308)(73,335,77,331)(74,334,78,330)(75,333,79,329)(76,332,80,336)(81,327,85,323)(82,326,86,322)(83,325,87,321)(84,324,88,328)(89,124,93,128)(90,123,94,127)(91,122,95,126)(92,121,96,125)(97,432,101,428)(98,431,102,427)(99,430,103,426)(100,429,104,425)(105,129,109,133)(106,136,110,132)(107,135,111,131)(108,134,112,130)(113,237,117,233)(114,236,118,240)(115,235,119,239)(116,234,120,238)(137,248,141,244)(138,247,142,243)(139,246,143,242)(140,245,144,241)(145,208,149,204)(146,207,150,203)(147,206,151,202)(148,205,152,201)(153,214,157,210)(154,213,158,209)(155,212,159,216)(156,211,160,215)(161,220,165,224)(162,219,166,223)(163,218,167,222)(164,217,168,221)(169,293,173,289)(170,292,174,296)(171,291,175,295)(172,290,176,294)(193,304,197,300)(194,303,198,299)(195,302,199,298)(196,301,200,297)(225,437,229,433)(226,436,230,440)(227,435,231,439)(228,434,232,438)(249,448,253,444)(250,447,254,443)(251,446,255,442)(252,445,256,441)(273,368,277,364)(274,367,278,363)(275,366,279,362)(276,365,280,361)(281,381,285,377)(282,380,286,384)(283,379,287,383)(284,378,288,382)(337,398,341,394)(338,397,342,393)(339,396,343,400)(340,395,344,399)(345,404,349,408)(346,403,350,407)(347,402,351,406)(348,401,352,405)(353,416,357,412)(354,415,358,411)(355,414,359,410)(356,413,360,409) );
G=PermutationGroup([[(1,280),(2,273),(3,274),(4,275),(5,276),(6,277),(7,278),(8,279),(9,155),(10,156),(11,157),(12,158),(13,159),(14,160),(15,153),(16,154),(17,394),(18,395),(19,396),(20,397),(21,398),(22,399),(23,400),(24,393),(25,249),(26,250),(27,251),(28,252),(29,253),(30,254),(31,255),(32,256),(33,93),(34,94),(35,95),(36,96),(37,89),(38,90),(39,91),(40,92),(41,101),(42,102),(43,103),(44,104),(45,97),(46,98),(47,99),(48,100),(49,109),(50,110),(51,111),(52,112),(53,105),(54,106),(55,107),(56,108),(57,352),(58,345),(59,346),(60,347),(61,348),(62,349),(63,350),(64,351),(65,205),(66,206),(67,207),(68,208),(69,201),(70,202),(71,203),(72,204),(73,220),(74,221),(75,222),(76,223),(77,224),(78,217),(79,218),(80,219),(81,353),(82,354),(83,355),(84,356),(85,357),(86,358),(87,359),(88,360),(113,173),(114,174),(115,175),(116,176),(117,169),(118,170),(119,171),(120,172),(121,181),(122,182),(123,183),(124,184),(125,177),(126,178),(127,179),(128,180),(129,189),(130,190),(131,191),(132,192),(133,185),(134,186),(135,187),(136,188),(137,197),(138,198),(139,199),(140,200),(141,193),(142,194),(143,195),(144,196),(145,308),(146,309),(147,310),(148,311),(149,312),(150,305),(151,306),(152,307),(161,331),(162,332),(163,333),(164,334),(165,335),(166,336),(167,329),(168,330),(209,259),(210,260),(211,261),(212,262),(213,263),(214,264),(215,257),(216,258),(225,285),(226,286),(227,287),(228,288),(229,281),(230,282),(231,283),(232,284),(233,293),(234,294),(235,295),(236,296),(237,289),(238,290),(239,291),(240,292),(241,301),(242,302),(243,303),(244,304),(245,297),(246,298),(247,299),(248,300),(265,342),(266,343),(267,344),(268,337),(269,338),(270,339),(271,340),(272,341),(313,403),(314,404),(315,405),(316,406),(317,407),(318,408),(319,401),(320,402),(321,410),(322,411),(323,412),(324,413),(325,414),(326,415),(327,416),(328,409),(361,421),(362,422),(363,423),(364,424),(365,417),(366,418),(367,419),(368,420),(369,429),(370,430),(371,431),(372,432),(373,425),(374,426),(375,427),(376,428),(377,437),(378,438),(379,439),(380,440),(381,433),(382,434),(383,435),(384,436),(385,445),(386,446),(387,447),(388,448),(389,441),(390,442),(391,443),(392,444)], [(1,252),(2,253),(3,254),(4,255),(5,256),(6,249),(7,250),(8,251),(9,429),(10,430),(11,431),(12,432),(13,425),(14,426),(15,427),(16,428),(17,437),(18,438),(19,439),(20,440),(21,433),(22,434),(23,435),(24,436),(25,277),(26,278),(27,279),(28,280),(29,273),(30,274),(31,275),(32,276),(33,201),(34,202),(35,203),(36,204),(37,205),(38,206),(39,207),(40,208),(41,209),(42,210),(43,211),(44,212),(45,213),(46,214),(47,215),(48,216),(49,217),(50,218),(51,219),(52,220),(53,221),(54,222),(55,223),(56,224),(57,236),(58,237),(59,238),(60,239),(61,240),(62,233),(63,234),(64,235),(65,89),(66,90),(67,91),(68,92),(69,93),(70,94),(71,95),(72,96),(73,112),(74,105),(75,106),(76,107),(77,108),(78,109),(79,110),(80,111),(81,245),(82,246),(83,247),(84,248),(85,241),(86,242),(87,243),(88,244),(97,263),(98,264),(99,257),(100,258),(101,259),(102,260),(103,261),(104,262),(113,318),(114,319),(115,320),(116,313),(117,314),(118,315),(119,316),(120,317),(121,312),(122,305),(123,306),(124,307),(125,308),(126,309),(127,310),(128,311),(129,334),(130,335),(131,336),(132,329),(133,330),(134,331),(135,332),(136,333),(137,328),(138,321),(139,322),(140,323),(141,324),(142,325),(143,326),(144,327),(145,177),(146,178),(147,179),(148,180),(149,181),(150,182),(151,183),(152,184),(153,375),(154,376),(155,369),(156,370),(157,371),(158,372),(159,373),(160,374),(161,186),(162,187),(163,188),(164,189),(165,190),(166,191),(167,192),(168,185),(169,404),(170,405),(171,406),(172,407),(173,408),(174,401),(175,402),(176,403),(193,413),(194,414),(195,415),(196,416),(197,409),(198,410),(199,411),(200,412),(225,272),(226,265),(227,266),(228,267),(229,268),(230,269),(231,270),(232,271),(281,337),(282,338),(283,339),(284,340),(285,341),(286,342),(287,343),(288,344),(289,345),(290,346),(291,347),(292,348),(293,349),(294,350),(295,351),(296,352),(297,353),(298,354),(299,355),(300,356),(301,357),(302,358),(303,359),(304,360),(361,385),(362,386),(363,387),(364,388),(365,389),(366,390),(367,391),(368,392),(377,394),(378,395),(379,396),(380,397),(381,398),(382,399),(383,400),(384,393),(417,441),(418,442),(419,443),(420,444),(421,445),(422,446),(423,447),(424,448)], [(1,92,229,165,407,156,411),(2,412,157,408,166,230,93),(3,94,231,167,401,158,413),(4,414,159,402,168,232,95),(5,96,225,161,403,160,415),(6,416,153,404,162,226,89),(7,90,227,163,405,154,409),(8,410,155,406,164,228,91),(9,316,334,288,39,279,321),(10,322,280,40,281,335,317),(11,318,336,282,33,273,323),(12,324,274,34,283,329,319),(13,320,330,284,35,275,325),(14,326,276,36,285,331,313),(15,314,332,286,37,277,327),(16,328,278,38,287,333,315),(17,52,294,47,302,441,308),(18,309,442,303,48,295,53),(19,54,296,41,304,443,310),(20,311,444,297,42,289,55),(21,56,290,43,298,445,312),(22,305,446,299,44,291,49),(23,50,292,45,300,447,306),(24,307,448,301,46,293,51),(25,144,427,117,135,342,205),(26,206,343,136,118,428,137),(27,138,429,119,129,344,207),(28,208,337,130,120,430,139),(29,140,431,113,131,338,201),(30,202,339,132,114,432,141),(31,142,425,115,133,340,203),(32,204,341,134,116,426,143),(57,259,88,367,179,379,75),(58,76,380,180,368,81,260),(59,261,82,361,181,381,77),(60,78,382,182,362,83,262),(61,263,84,363,183,383,79),(62,80,384,184,364,85,264),(63,257,86,365,177,377,73),(64,74,378,178,366,87,258),(65,249,196,375,169,187,265),(66,266,188,170,376,197,250),(67,251,198,369,171,189,267),(68,268,190,172,370,199,252),(69,253,200,371,173,191,269),(70,270,192,174,372,193,254),(71,255,194,373,175,185,271),(72,272,186,176,374,195,256),(97,248,387,151,400,110,240),(98,233,111,393,152,388,241),(99,242,389,145,394,112,234),(100,235,105,395,146,390,243),(101,244,391,147,396,106,236),(102,237,107,397,148,392,245),(103,246,385,149,398,108,238),(104,239,109,399,150,386,247),(121,433,224,346,211,354,421),(122,422,355,212,347,217,434),(123,435,218,348,213,356,423),(124,424,357,214,349,219,436),(125,437,220,350,215,358,417),(126,418,359,216,351,221,438),(127,439,222,352,209,360,419),(128,420,353,210,345,223,440)], [(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)], [(1,421,5,417),(2,420,6,424),(3,419,7,423),(4,418,8,422),(9,262,13,258),(10,261,14,257),(11,260,15,264),(12,259,16,263),(17,268,21,272),(18,267,22,271),(19,266,23,270),(20,265,24,269),(25,388,29,392),(26,387,30,391),(27,386,31,390),(28,385,32,389),(33,180,37,184),(34,179,38,183),(35,178,39,182),(36,177,40,181),(41,376,45,372),(42,375,46,371),(43,374,47,370),(44,373,48,369),(49,185,53,189),(50,192,54,188),(51,191,55,187),(52,190,56,186),(57,315,61,319),(58,314,62,318),(59,313,63,317),(60,320,64,316),(65,307,69,311),(66,306,70,310),(67,305,71,309),(68,312,72,308),(73,335,77,331),(74,334,78,330),(75,333,79,329),(76,332,80,336),(81,327,85,323),(82,326,86,322),(83,325,87,321),(84,324,88,328),(89,124,93,128),(90,123,94,127),(91,122,95,126),(92,121,96,125),(97,432,101,428),(98,431,102,427),(99,430,103,426),(100,429,104,425),(105,129,109,133),(106,136,110,132),(107,135,111,131),(108,134,112,130),(113,237,117,233),(114,236,118,240),(115,235,119,239),(116,234,120,238),(137,248,141,244),(138,247,142,243),(139,246,143,242),(140,245,144,241),(145,208,149,204),(146,207,150,203),(147,206,151,202),(148,205,152,201),(153,214,157,210),(154,213,158,209),(155,212,159,216),(156,211,160,215),(161,220,165,224),(162,219,166,223),(163,218,167,222),(164,217,168,221),(169,293,173,289),(170,292,174,296),(171,291,175,295),(172,290,176,294),(193,304,197,300),(194,303,198,299),(195,302,199,298),(196,301,200,297),(225,437,229,433),(226,436,230,440),(227,435,231,439),(228,434,232,438),(249,448,253,444),(250,447,254,443),(251,446,255,442),(252,445,256,441),(273,368,277,364),(274,367,278,363),(275,366,279,362),(276,365,280,361),(281,381,285,377),(282,380,286,384),(283,379,287,383),(284,378,288,382),(337,398,341,394),(338,397,342,393),(339,396,343,400),(340,395,344,399),(345,404,349,408),(346,403,350,407),(347,402,351,406),(348,401,352,405),(353,416,357,412),(354,415,358,411),(355,414,359,410),(356,413,360,409)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | Q16 | D14 | D14 | C7⋊D4 | C7⋊D4 | C7⋊Q16 |
| kernel | C22×C7⋊Q16 | C22×C7⋊C8 | C2×C7⋊Q16 | C22×Dic14 | Q8×C2×C14 | C2×C28 | C22×C14 | C22×Q8 | C2×C14 | C22×C4 | C2×Q8 | C2×C4 | C23 | C22 |
| # reps | 1 | 1 | 12 | 1 | 1 | 3 | 1 | 3 | 8 | 3 | 18 | 18 | 6 | 12 |
Matrix representation of C22×C7⋊Q16 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 24 | 112 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 112 | 0 | 0 |
| 0 | 0 | 11 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 52 | 64 | 0 | 0 | 0 | 0 |
| 69 | 61 | 0 | 0 | 0 | 0 |
| 0 | 0 | 47 | 22 | 0 | 0 |
| 0 | 0 | 64 | 66 | 0 | 0 |
| 0 | 0 | 0 | 0 | 31 | 82 |
| 0 | 0 | 0 | 0 | 31 | 31 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 44 |
| 0 | 0 | 0 | 0 | 44 | 53 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[24,1,0,0,0,0,112,0,0,0,0,0,0,0,112,11,0,0,0,0,112,10,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[52,69,0,0,0,0,64,61,0,0,0,0,0,0,47,64,0,0,0,0,22,66,0,0,0,0,0,0,31,31,0,0,0,0,82,31],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,60,44,0,0,0,0,44,53] >;
C22×C7⋊Q16 in GAP, Magma, Sage, TeX
C_2^2\times C_7\rtimes Q_{16} % in TeX
G:=Group("C2^2xC7:Q16"); // GroupNames label
G:=SmallGroup(448,1262);
// by ID
G=gap.SmallGroup(448,1262);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,675,136,1684,235,102,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^7=d^8=1,e^2=d^4,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,d*c*d^-1=c^-1,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations