direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Q8×Dic7, C14⋊3(C4×Q8), (Q8×C14)⋊11C4, C22.36(Q8×D7), C28.95(C22×C4), C14.46(C23×C4), (C2×Q8).206D14, (C22×Q8).10D7, C14.52(C22×Q8), C2.8(C23×Dic7), (C2×C28).550C23, (C2×C14).303C24, (C22×C4).383D14, C4.18(C22×Dic7), C22.46(C23×D7), C4⋊Dic7.388C22, (Q8×C14).232C22, C23.340(C22×D7), (C22×C28).283C22, (C22×C14).421C23, C22.38(Q8⋊2D7), (C2×Dic7).287C23, (C4×Dic7).260C22, C22.32(C22×Dic7), (C22×Dic7).245C22, C7⋊4(C2×C4×Q8), C2.4(C2×Q8×D7), (Q8×C2×C14).8C2, (C7×Q8)⋊18(C2×C4), (C2×C14).97(C2×Q8), C2.4(C2×Q8⋊2D7), (C2×C4×Dic7).17C2, (C2×C28).133(C2×C4), C14.126(C2×C4○D4), (C2×C4⋊Dic7).45C2, (C2×C4).55(C2×Dic7), (C2×C4).631(C22×D7), (C2×C14).199(C4○D4), (C2×C14).209(C22×C4), SmallGroup(448,1264)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 820 in 298 conjugacy classes, 215 normal (16 characteristic)
C1, C2 [×3], C2 [×4], C4 [×12], C4 [×10], C22, C22 [×6], C7, C2×C4 [×18], C2×C4 [×18], Q8 [×16], C23, C14 [×3], C14 [×4], C42 [×12], C4⋊C4 [×12], C22×C4 [×3], C22×C4 [×4], C2×Q8 [×12], Dic7 [×4], Dic7 [×6], C28 [×12], C2×C14, C2×C14 [×6], C2×C42 [×3], C2×C4⋊C4 [×3], C4×Q8 [×8], C22×Q8, C2×Dic7 [×12], C2×Dic7 [×6], C2×C28 [×18], C7×Q8 [×16], C22×C14, C2×C4×Q8, C4×Dic7 [×12], C4⋊Dic7 [×12], C22×Dic7, C22×Dic7 [×3], C22×C28 [×3], Q8×C14 [×12], C2×C4×Dic7 [×3], C2×C4⋊Dic7 [×3], Q8×Dic7 [×8], Q8×C2×C14, C2×Q8×Dic7
Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], Q8 [×4], C23 [×15], D7, C22×C4 [×14], C2×Q8 [×6], C4○D4 [×2], C24, Dic7 [×8], D14 [×7], C4×Q8 [×4], C23×C4, C22×Q8, C2×C4○D4, C2×Dic7 [×28], C22×D7 [×7], C2×C4×Q8, Q8×D7 [×2], Q8⋊2D7 [×2], C22×Dic7 [×14], C23×D7, Q8×Dic7 [×4], C2×Q8×D7, C2×Q8⋊2D7, C23×Dic7, C2×Q8×Dic7
Generators and relations
G = < a,b,c,d,e | a2=b4=d14=1, c2=b2, e2=d7, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >
►Regular action on 448 points
Generators in S448
(1 290)(2 291)(3 292)(4 293)(5 294)(6 281)(7 282)(8 283)(9 284)(10 285)(11 286)(12 287)(13 288)(14 289)(15 207)(16 208)(17 209)(18 210)(19 197)(20 198)(21 199)(22 200)(23 201)(24 202)(25 203)(26 204)(27 205)(28 206)(29 357)(30 358)(31 359)(32 360)(33 361)(34 362)(35 363)(36 364)(37 351)(38 352)(39 353)(40 354)(41 355)(42 356)(43 97)(44 98)(45 85)(46 86)(47 87)(48 88)(49 89)(50 90)(51 91)(52 92)(53 93)(54 94)(55 95)(56 96)(57 434)(58 421)(59 422)(60 423)(61 424)(62 425)(63 426)(64 427)(65 428)(66 429)(67 430)(68 431)(69 432)(70 433)(71 242)(72 243)(73 244)(74 245)(75 246)(76 247)(77 248)(78 249)(79 250)(80 251)(81 252)(82 239)(83 240)(84 241)(99 295)(100 296)(101 297)(102 298)(103 299)(104 300)(105 301)(106 302)(107 303)(108 304)(109 305)(110 306)(111 307)(112 308)(113 378)(114 365)(115 366)(116 367)(117 368)(118 369)(119 370)(120 371)(121 372)(122 373)(123 374)(124 375)(125 376)(126 377)(127 177)(128 178)(129 179)(130 180)(131 181)(132 182)(133 169)(134 170)(135 171)(136 172)(137 173)(138 174)(139 175)(140 176)(141 230)(142 231)(143 232)(144 233)(145 234)(146 235)(147 236)(148 237)(149 238)(150 225)(151 226)(152 227)(153 228)(154 229)(155 258)(156 259)(157 260)(158 261)(159 262)(160 263)(161 264)(162 265)(163 266)(164 253)(165 254)(166 255)(167 256)(168 257)(183 387)(184 388)(185 389)(186 390)(187 391)(188 392)(189 379)(190 380)(191 381)(192 382)(193 383)(194 384)(195 385)(196 386)(211 419)(212 420)(213 407)(214 408)(215 409)(216 410)(217 411)(218 412)(219 413)(220 414)(221 415)(222 416)(223 417)(224 418)(267 444)(268 445)(269 446)(270 447)(271 448)(272 435)(273 436)(274 437)(275 438)(276 439)(277 440)(278 441)(279 442)(280 443)(309 398)(310 399)(311 400)(312 401)(313 402)(314 403)(315 404)(316 405)(317 406)(318 393)(319 394)(320 395)(321 396)(322 397)(323 340)(324 341)(325 342)(326 343)(327 344)(328 345)(329 346)(330 347)(331 348)(332 349)(333 350)(334 337)(335 338)(336 339)
(1 40 195 21)(2 41 196 22)(3 42 183 23)(4 29 184 24)(5 30 185 25)(6 31 186 26)(7 32 187 27)(8 33 188 28)(9 34 189 15)(10 35 190 16)(11 36 191 17)(12 37 192 18)(13 38 193 19)(14 39 194 20)(43 370 224 256)(44 371 211 257)(45 372 212 258)(46 373 213 259)(47 374 214 260)(48 375 215 261)(49 376 216 262)(50 377 217 263)(51 378 218 264)(52 365 219 265)(53 366 220 266)(54 367 221 253)(55 368 222 254)(56 369 223 255)(57 105 127 235)(58 106 128 236)(59 107 129 237)(60 108 130 238)(61 109 131 225)(62 110 132 226)(63 111 133 227)(64 112 134 228)(65 99 135 229)(66 100 136 230)(67 101 137 231)(68 102 138 232)(69 103 139 233)(70 104 140 234)(71 333 404 443)(72 334 405 444)(73 335 406 445)(74 336 393 446)(75 323 394 447)(76 324 395 448)(77 325 396 435)(78 326 397 436)(79 327 398 437)(80 328 399 438)(81 329 400 439)(82 330 401 440)(83 331 402 441)(84 332 403 442)(85 121 420 155)(86 122 407 156)(87 123 408 157)(88 124 409 158)(89 125 410 159)(90 126 411 160)(91 113 412 161)(92 114 413 162)(93 115 414 163)(94 116 415 164)(95 117 416 165)(96 118 417 166)(97 119 418 167)(98 120 419 168)(141 429 296 172)(142 430 297 173)(143 431 298 174)(144 432 299 175)(145 433 300 176)(146 434 301 177)(147 421 302 178)(148 422 303 179)(149 423 304 180)(150 424 305 181)(151 425 306 182)(152 426 307 169)(153 427 308 170)(154 428 295 171)(197 288 352 383)(198 289 353 384)(199 290 354 385)(200 291 355 386)(201 292 356 387)(202 293 357 388)(203 294 358 389)(204 281 359 390)(205 282 360 391)(206 283 361 392)(207 284 362 379)(208 285 363 380)(209 286 364 381)(210 287 351 382)(239 347 312 277)(240 348 313 278)(241 349 314 279)(242 350 315 280)(243 337 316 267)(244 338 317 268)(245 339 318 269)(246 340 319 270)(247 341 320 271)(248 342 321 272)(249 343 322 273)(250 344 309 274)(251 345 310 275)(252 346 311 276)
(1 112 195 228)(2 99 196 229)(3 100 183 230)(4 101 184 231)(5 102 185 232)(6 103 186 233)(7 104 187 234)(8 105 188 235)(9 106 189 236)(10 107 190 237)(11 108 191 238)(12 109 192 225)(13 110 193 226)(14 111 194 227)(15 128 34 58)(16 129 35 59)(17 130 36 60)(18 131 37 61)(19 132 38 62)(20 133 39 63)(21 134 40 64)(22 135 41 65)(23 136 42 66)(24 137 29 67)(25 138 30 68)(26 139 31 69)(27 140 32 70)(28 127 33 57)(43 271 224 341)(44 272 211 342)(45 273 212 343)(46 274 213 344)(47 275 214 345)(48 276 215 346)(49 277 216 347)(50 278 217 348)(51 279 218 349)(52 280 219 350)(53 267 220 337)(54 268 221 338)(55 269 222 339)(56 270 223 340)(71 114 404 162)(72 115 405 163)(73 116 406 164)(74 117 393 165)(75 118 394 166)(76 119 395 167)(77 120 396 168)(78 121 397 155)(79 122 398 156)(80 123 399 157)(81 124 400 158)(82 125 401 159)(83 126 402 160)(84 113 403 161)(85 436 420 326)(86 437 407 327)(87 438 408 328)(88 439 409 329)(89 440 410 330)(90 441 411 331)(91 442 412 332)(92 443 413 333)(93 444 414 334)(94 445 415 335)(95 446 416 336)(96 447 417 323)(97 448 418 324)(98 435 419 325)(141 292 296 387)(142 293 297 388)(143 294 298 389)(144 281 299 390)(145 282 300 391)(146 283 301 392)(147 284 302 379)(148 285 303 380)(149 286 304 381)(150 287 305 382)(151 288 306 383)(152 289 307 384)(153 290 308 385)(154 291 295 386)(169 353 426 198)(170 354 427 199)(171 355 428 200)(172 356 429 201)(173 357 430 202)(174 358 431 203)(175 359 432 204)(176 360 433 205)(177 361 434 206)(178 362 421 207)(179 363 422 208)(180 364 423 209)(181 351 424 210)(182 352 425 197)(239 376 312 262)(240 377 313 263)(241 378 314 264)(242 365 315 265)(243 366 316 266)(244 367 317 253)(245 368 318 254)(246 369 319 255)(247 370 320 256)(248 371 321 257)(249 372 322 258)(250 373 309 259)(251 374 310 260)(252 375 311 261)
(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)
(1 314 8 321)(2 313 9 320)(3 312 10 319)(4 311 11 318)(5 310 12 317)(6 309 13 316)(7 322 14 315)(15 341 22 348)(16 340 23 347)(17 339 24 346)(18 338 25 345)(19 337 26 344)(20 350 27 343)(21 349 28 342)(29 276 36 269)(30 275 37 268)(31 274 38 267)(32 273 39 280)(33 272 40 279)(34 271 41 278)(35 270 42 277)(43 135 50 128)(44 134 51 127)(45 133 52 140)(46 132 53 139)(47 131 54 138)(48 130 55 137)(49 129 56 136)(57 211 64 218)(58 224 65 217)(59 223 66 216)(60 222 67 215)(61 221 68 214)(62 220 69 213)(63 219 70 212)(71 391 78 384)(72 390 79 383)(73 389 80 382)(74 388 81 381)(75 387 82 380)(76 386 83 379)(77 385 84 392)(85 169 92 176)(86 182 93 175)(87 181 94 174)(88 180 95 173)(89 179 96 172)(90 178 97 171)(91 177 98 170)(99 263 106 256)(100 262 107 255)(101 261 108 254)(102 260 109 253)(103 259 110 266)(104 258 111 265)(105 257 112 264)(113 146 120 153)(114 145 121 152)(115 144 122 151)(116 143 123 150)(117 142 124 149)(118 141 125 148)(119 154 126 147)(155 307 162 300)(156 306 163 299)(157 305 164 298)(158 304 165 297)(159 303 166 296)(160 302 167 295)(161 301 168 308)(183 239 190 246)(184 252 191 245)(185 251 192 244)(186 250 193 243)(187 249 194 242)(188 248 195 241)(189 247 196 240)(197 334 204 327)(198 333 205 326)(199 332 206 325)(200 331 207 324)(201 330 208 323)(202 329 209 336)(203 328 210 335)(225 367 232 374)(226 366 233 373)(227 365 234 372)(228 378 235 371)(229 377 236 370)(230 376 237 369)(231 375 238 368)(281 398 288 405)(282 397 289 404)(283 396 290 403)(284 395 291 402)(285 394 292 401)(286 393 293 400)(287 406 294 399)(351 445 358 438)(352 444 359 437)(353 443 360 436)(354 442 361 435)(355 441 362 448)(356 440 363 447)(357 439 364 446)(407 425 414 432)(408 424 415 431)(409 423 416 430)(410 422 417 429)(411 421 418 428)(412 434 419 427)(413 433 420 426)
G:=sub<Sym(448)| (1,290)(2,291)(3,292)(4,293)(5,294)(6,281)(7,282)(8,283)(9,284)(10,285)(11,286)(12,287)(13,288)(14,289)(15,207)(16,208)(17,209)(18,210)(19,197)(20,198)(21,199)(22,200)(23,201)(24,202)(25,203)(26,204)(27,205)(28,206)(29,357)(30,358)(31,359)(32,360)(33,361)(34,362)(35,363)(36,364)(37,351)(38,352)(39,353)(40,354)(41,355)(42,356)(43,97)(44,98)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(51,91)(52,92)(53,93)(54,94)(55,95)(56,96)(57,434)(58,421)(59,422)(60,423)(61,424)(62,425)(63,426)(64,427)(65,428)(66,429)(67,430)(68,431)(69,432)(70,433)(71,242)(72,243)(73,244)(74,245)(75,246)(76,247)(77,248)(78,249)(79,250)(80,251)(81,252)(82,239)(83,240)(84,241)(99,295)(100,296)(101,297)(102,298)(103,299)(104,300)(105,301)(106,302)(107,303)(108,304)(109,305)(110,306)(111,307)(112,308)(113,378)(114,365)(115,366)(116,367)(117,368)(118,369)(119,370)(120,371)(121,372)(122,373)(123,374)(124,375)(125,376)(126,377)(127,177)(128,178)(129,179)(130,180)(131,181)(132,182)(133,169)(134,170)(135,171)(136,172)(137,173)(138,174)(139,175)(140,176)(141,230)(142,231)(143,232)(144,233)(145,234)(146,235)(147,236)(148,237)(149,238)(150,225)(151,226)(152,227)(153,228)(154,229)(155,258)(156,259)(157,260)(158,261)(159,262)(160,263)(161,264)(162,265)(163,266)(164,253)(165,254)(166,255)(167,256)(168,257)(183,387)(184,388)(185,389)(186,390)(187,391)(188,392)(189,379)(190,380)(191,381)(192,382)(193,383)(194,384)(195,385)(196,386)(211,419)(212,420)(213,407)(214,408)(215,409)(216,410)(217,411)(218,412)(219,413)(220,414)(221,415)(222,416)(223,417)(224,418)(267,444)(268,445)(269,446)(270,447)(271,448)(272,435)(273,436)(274,437)(275,438)(276,439)(277,440)(278,441)(279,442)(280,443)(309,398)(310,399)(311,400)(312,401)(313,402)(314,403)(315,404)(316,405)(317,406)(318,393)(319,394)(320,395)(321,396)(322,397)(323,340)(324,341)(325,342)(326,343)(327,344)(328,345)(329,346)(330,347)(331,348)(332,349)(333,350)(334,337)(335,338)(336,339), (1,40,195,21)(2,41,196,22)(3,42,183,23)(4,29,184,24)(5,30,185,25)(6,31,186,26)(7,32,187,27)(8,33,188,28)(9,34,189,15)(10,35,190,16)(11,36,191,17)(12,37,192,18)(13,38,193,19)(14,39,194,20)(43,370,224,256)(44,371,211,257)(45,372,212,258)(46,373,213,259)(47,374,214,260)(48,375,215,261)(49,376,216,262)(50,377,217,263)(51,378,218,264)(52,365,219,265)(53,366,220,266)(54,367,221,253)(55,368,222,254)(56,369,223,255)(57,105,127,235)(58,106,128,236)(59,107,129,237)(60,108,130,238)(61,109,131,225)(62,110,132,226)(63,111,133,227)(64,112,134,228)(65,99,135,229)(66,100,136,230)(67,101,137,231)(68,102,138,232)(69,103,139,233)(70,104,140,234)(71,333,404,443)(72,334,405,444)(73,335,406,445)(74,336,393,446)(75,323,394,447)(76,324,395,448)(77,325,396,435)(78,326,397,436)(79,327,398,437)(80,328,399,438)(81,329,400,439)(82,330,401,440)(83,331,402,441)(84,332,403,442)(85,121,420,155)(86,122,407,156)(87,123,408,157)(88,124,409,158)(89,125,410,159)(90,126,411,160)(91,113,412,161)(92,114,413,162)(93,115,414,163)(94,116,415,164)(95,117,416,165)(96,118,417,166)(97,119,418,167)(98,120,419,168)(141,429,296,172)(142,430,297,173)(143,431,298,174)(144,432,299,175)(145,433,300,176)(146,434,301,177)(147,421,302,178)(148,422,303,179)(149,423,304,180)(150,424,305,181)(151,425,306,182)(152,426,307,169)(153,427,308,170)(154,428,295,171)(197,288,352,383)(198,289,353,384)(199,290,354,385)(200,291,355,386)(201,292,356,387)(202,293,357,388)(203,294,358,389)(204,281,359,390)(205,282,360,391)(206,283,361,392)(207,284,362,379)(208,285,363,380)(209,286,364,381)(210,287,351,382)(239,347,312,277)(240,348,313,278)(241,349,314,279)(242,350,315,280)(243,337,316,267)(244,338,317,268)(245,339,318,269)(246,340,319,270)(247,341,320,271)(248,342,321,272)(249,343,322,273)(250,344,309,274)(251,345,310,275)(252,346,311,276), (1,112,195,228)(2,99,196,229)(3,100,183,230)(4,101,184,231)(5,102,185,232)(6,103,186,233)(7,104,187,234)(8,105,188,235)(9,106,189,236)(10,107,190,237)(11,108,191,238)(12,109,192,225)(13,110,193,226)(14,111,194,227)(15,128,34,58)(16,129,35,59)(17,130,36,60)(18,131,37,61)(19,132,38,62)(20,133,39,63)(21,134,40,64)(22,135,41,65)(23,136,42,66)(24,137,29,67)(25,138,30,68)(26,139,31,69)(27,140,32,70)(28,127,33,57)(43,271,224,341)(44,272,211,342)(45,273,212,343)(46,274,213,344)(47,275,214,345)(48,276,215,346)(49,277,216,347)(50,278,217,348)(51,279,218,349)(52,280,219,350)(53,267,220,337)(54,268,221,338)(55,269,222,339)(56,270,223,340)(71,114,404,162)(72,115,405,163)(73,116,406,164)(74,117,393,165)(75,118,394,166)(76,119,395,167)(77,120,396,168)(78,121,397,155)(79,122,398,156)(80,123,399,157)(81,124,400,158)(82,125,401,159)(83,126,402,160)(84,113,403,161)(85,436,420,326)(86,437,407,327)(87,438,408,328)(88,439,409,329)(89,440,410,330)(90,441,411,331)(91,442,412,332)(92,443,413,333)(93,444,414,334)(94,445,415,335)(95,446,416,336)(96,447,417,323)(97,448,418,324)(98,435,419,325)(141,292,296,387)(142,293,297,388)(143,294,298,389)(144,281,299,390)(145,282,300,391)(146,283,301,392)(147,284,302,379)(148,285,303,380)(149,286,304,381)(150,287,305,382)(151,288,306,383)(152,289,307,384)(153,290,308,385)(154,291,295,386)(169,353,426,198)(170,354,427,199)(171,355,428,200)(172,356,429,201)(173,357,430,202)(174,358,431,203)(175,359,432,204)(176,360,433,205)(177,361,434,206)(178,362,421,207)(179,363,422,208)(180,364,423,209)(181,351,424,210)(182,352,425,197)(239,376,312,262)(240,377,313,263)(241,378,314,264)(242,365,315,265)(243,366,316,266)(244,367,317,253)(245,368,318,254)(246,369,319,255)(247,370,320,256)(248,371,321,257)(249,372,322,258)(250,373,309,259)(251,374,310,260)(252,375,311,261), (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), (1,314,8,321)(2,313,9,320)(3,312,10,319)(4,311,11,318)(5,310,12,317)(6,309,13,316)(7,322,14,315)(15,341,22,348)(16,340,23,347)(17,339,24,346)(18,338,25,345)(19,337,26,344)(20,350,27,343)(21,349,28,342)(29,276,36,269)(30,275,37,268)(31,274,38,267)(32,273,39,280)(33,272,40,279)(34,271,41,278)(35,270,42,277)(43,135,50,128)(44,134,51,127)(45,133,52,140)(46,132,53,139)(47,131,54,138)(48,130,55,137)(49,129,56,136)(57,211,64,218)(58,224,65,217)(59,223,66,216)(60,222,67,215)(61,221,68,214)(62,220,69,213)(63,219,70,212)(71,391,78,384)(72,390,79,383)(73,389,80,382)(74,388,81,381)(75,387,82,380)(76,386,83,379)(77,385,84,392)(85,169,92,176)(86,182,93,175)(87,181,94,174)(88,180,95,173)(89,179,96,172)(90,178,97,171)(91,177,98,170)(99,263,106,256)(100,262,107,255)(101,261,108,254)(102,260,109,253)(103,259,110,266)(104,258,111,265)(105,257,112,264)(113,146,120,153)(114,145,121,152)(115,144,122,151)(116,143,123,150)(117,142,124,149)(118,141,125,148)(119,154,126,147)(155,307,162,300)(156,306,163,299)(157,305,164,298)(158,304,165,297)(159,303,166,296)(160,302,167,295)(161,301,168,308)(183,239,190,246)(184,252,191,245)(185,251,192,244)(186,250,193,243)(187,249,194,242)(188,248,195,241)(189,247,196,240)(197,334,204,327)(198,333,205,326)(199,332,206,325)(200,331,207,324)(201,330,208,323)(202,329,209,336)(203,328,210,335)(225,367,232,374)(226,366,233,373)(227,365,234,372)(228,378,235,371)(229,377,236,370)(230,376,237,369)(231,375,238,368)(281,398,288,405)(282,397,289,404)(283,396,290,403)(284,395,291,402)(285,394,292,401)(286,393,293,400)(287,406,294,399)(351,445,358,438)(352,444,359,437)(353,443,360,436)(354,442,361,435)(355,441,362,448)(356,440,363,447)(357,439,364,446)(407,425,414,432)(408,424,415,431)(409,423,416,430)(410,422,417,429)(411,421,418,428)(412,434,419,427)(413,433,420,426)>;
G:=Group( (1,290)(2,291)(3,292)(4,293)(5,294)(6,281)(7,282)(8,283)(9,284)(10,285)(11,286)(12,287)(13,288)(14,289)(15,207)(16,208)(17,209)(18,210)(19,197)(20,198)(21,199)(22,200)(23,201)(24,202)(25,203)(26,204)(27,205)(28,206)(29,357)(30,358)(31,359)(32,360)(33,361)(34,362)(35,363)(36,364)(37,351)(38,352)(39,353)(40,354)(41,355)(42,356)(43,97)(44,98)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(51,91)(52,92)(53,93)(54,94)(55,95)(56,96)(57,434)(58,421)(59,422)(60,423)(61,424)(62,425)(63,426)(64,427)(65,428)(66,429)(67,430)(68,431)(69,432)(70,433)(71,242)(72,243)(73,244)(74,245)(75,246)(76,247)(77,248)(78,249)(79,250)(80,251)(81,252)(82,239)(83,240)(84,241)(99,295)(100,296)(101,297)(102,298)(103,299)(104,300)(105,301)(106,302)(107,303)(108,304)(109,305)(110,306)(111,307)(112,308)(113,378)(114,365)(115,366)(116,367)(117,368)(118,369)(119,370)(120,371)(121,372)(122,373)(123,374)(124,375)(125,376)(126,377)(127,177)(128,178)(129,179)(130,180)(131,181)(132,182)(133,169)(134,170)(135,171)(136,172)(137,173)(138,174)(139,175)(140,176)(141,230)(142,231)(143,232)(144,233)(145,234)(146,235)(147,236)(148,237)(149,238)(150,225)(151,226)(152,227)(153,228)(154,229)(155,258)(156,259)(157,260)(158,261)(159,262)(160,263)(161,264)(162,265)(163,266)(164,253)(165,254)(166,255)(167,256)(168,257)(183,387)(184,388)(185,389)(186,390)(187,391)(188,392)(189,379)(190,380)(191,381)(192,382)(193,383)(194,384)(195,385)(196,386)(211,419)(212,420)(213,407)(214,408)(215,409)(216,410)(217,411)(218,412)(219,413)(220,414)(221,415)(222,416)(223,417)(224,418)(267,444)(268,445)(269,446)(270,447)(271,448)(272,435)(273,436)(274,437)(275,438)(276,439)(277,440)(278,441)(279,442)(280,443)(309,398)(310,399)(311,400)(312,401)(313,402)(314,403)(315,404)(316,405)(317,406)(318,393)(319,394)(320,395)(321,396)(322,397)(323,340)(324,341)(325,342)(326,343)(327,344)(328,345)(329,346)(330,347)(331,348)(332,349)(333,350)(334,337)(335,338)(336,339), (1,40,195,21)(2,41,196,22)(3,42,183,23)(4,29,184,24)(5,30,185,25)(6,31,186,26)(7,32,187,27)(8,33,188,28)(9,34,189,15)(10,35,190,16)(11,36,191,17)(12,37,192,18)(13,38,193,19)(14,39,194,20)(43,370,224,256)(44,371,211,257)(45,372,212,258)(46,373,213,259)(47,374,214,260)(48,375,215,261)(49,376,216,262)(50,377,217,263)(51,378,218,264)(52,365,219,265)(53,366,220,266)(54,367,221,253)(55,368,222,254)(56,369,223,255)(57,105,127,235)(58,106,128,236)(59,107,129,237)(60,108,130,238)(61,109,131,225)(62,110,132,226)(63,111,133,227)(64,112,134,228)(65,99,135,229)(66,100,136,230)(67,101,137,231)(68,102,138,232)(69,103,139,233)(70,104,140,234)(71,333,404,443)(72,334,405,444)(73,335,406,445)(74,336,393,446)(75,323,394,447)(76,324,395,448)(77,325,396,435)(78,326,397,436)(79,327,398,437)(80,328,399,438)(81,329,400,439)(82,330,401,440)(83,331,402,441)(84,332,403,442)(85,121,420,155)(86,122,407,156)(87,123,408,157)(88,124,409,158)(89,125,410,159)(90,126,411,160)(91,113,412,161)(92,114,413,162)(93,115,414,163)(94,116,415,164)(95,117,416,165)(96,118,417,166)(97,119,418,167)(98,120,419,168)(141,429,296,172)(142,430,297,173)(143,431,298,174)(144,432,299,175)(145,433,300,176)(146,434,301,177)(147,421,302,178)(148,422,303,179)(149,423,304,180)(150,424,305,181)(151,425,306,182)(152,426,307,169)(153,427,308,170)(154,428,295,171)(197,288,352,383)(198,289,353,384)(199,290,354,385)(200,291,355,386)(201,292,356,387)(202,293,357,388)(203,294,358,389)(204,281,359,390)(205,282,360,391)(206,283,361,392)(207,284,362,379)(208,285,363,380)(209,286,364,381)(210,287,351,382)(239,347,312,277)(240,348,313,278)(241,349,314,279)(242,350,315,280)(243,337,316,267)(244,338,317,268)(245,339,318,269)(246,340,319,270)(247,341,320,271)(248,342,321,272)(249,343,322,273)(250,344,309,274)(251,345,310,275)(252,346,311,276), (1,112,195,228)(2,99,196,229)(3,100,183,230)(4,101,184,231)(5,102,185,232)(6,103,186,233)(7,104,187,234)(8,105,188,235)(9,106,189,236)(10,107,190,237)(11,108,191,238)(12,109,192,225)(13,110,193,226)(14,111,194,227)(15,128,34,58)(16,129,35,59)(17,130,36,60)(18,131,37,61)(19,132,38,62)(20,133,39,63)(21,134,40,64)(22,135,41,65)(23,136,42,66)(24,137,29,67)(25,138,30,68)(26,139,31,69)(27,140,32,70)(28,127,33,57)(43,271,224,341)(44,272,211,342)(45,273,212,343)(46,274,213,344)(47,275,214,345)(48,276,215,346)(49,277,216,347)(50,278,217,348)(51,279,218,349)(52,280,219,350)(53,267,220,337)(54,268,221,338)(55,269,222,339)(56,270,223,340)(71,114,404,162)(72,115,405,163)(73,116,406,164)(74,117,393,165)(75,118,394,166)(76,119,395,167)(77,120,396,168)(78,121,397,155)(79,122,398,156)(80,123,399,157)(81,124,400,158)(82,125,401,159)(83,126,402,160)(84,113,403,161)(85,436,420,326)(86,437,407,327)(87,438,408,328)(88,439,409,329)(89,440,410,330)(90,441,411,331)(91,442,412,332)(92,443,413,333)(93,444,414,334)(94,445,415,335)(95,446,416,336)(96,447,417,323)(97,448,418,324)(98,435,419,325)(141,292,296,387)(142,293,297,388)(143,294,298,389)(144,281,299,390)(145,282,300,391)(146,283,301,392)(147,284,302,379)(148,285,303,380)(149,286,304,381)(150,287,305,382)(151,288,306,383)(152,289,307,384)(153,290,308,385)(154,291,295,386)(169,353,426,198)(170,354,427,199)(171,355,428,200)(172,356,429,201)(173,357,430,202)(174,358,431,203)(175,359,432,204)(176,360,433,205)(177,361,434,206)(178,362,421,207)(179,363,422,208)(180,364,423,209)(181,351,424,210)(182,352,425,197)(239,376,312,262)(240,377,313,263)(241,378,314,264)(242,365,315,265)(243,366,316,266)(244,367,317,253)(245,368,318,254)(246,369,319,255)(247,370,320,256)(248,371,321,257)(249,372,322,258)(250,373,309,259)(251,374,310,260)(252,375,311,261), (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), (1,314,8,321)(2,313,9,320)(3,312,10,319)(4,311,11,318)(5,310,12,317)(6,309,13,316)(7,322,14,315)(15,341,22,348)(16,340,23,347)(17,339,24,346)(18,338,25,345)(19,337,26,344)(20,350,27,343)(21,349,28,342)(29,276,36,269)(30,275,37,268)(31,274,38,267)(32,273,39,280)(33,272,40,279)(34,271,41,278)(35,270,42,277)(43,135,50,128)(44,134,51,127)(45,133,52,140)(46,132,53,139)(47,131,54,138)(48,130,55,137)(49,129,56,136)(57,211,64,218)(58,224,65,217)(59,223,66,216)(60,222,67,215)(61,221,68,214)(62,220,69,213)(63,219,70,212)(71,391,78,384)(72,390,79,383)(73,389,80,382)(74,388,81,381)(75,387,82,380)(76,386,83,379)(77,385,84,392)(85,169,92,176)(86,182,93,175)(87,181,94,174)(88,180,95,173)(89,179,96,172)(90,178,97,171)(91,177,98,170)(99,263,106,256)(100,262,107,255)(101,261,108,254)(102,260,109,253)(103,259,110,266)(104,258,111,265)(105,257,112,264)(113,146,120,153)(114,145,121,152)(115,144,122,151)(116,143,123,150)(117,142,124,149)(118,141,125,148)(119,154,126,147)(155,307,162,300)(156,306,163,299)(157,305,164,298)(158,304,165,297)(159,303,166,296)(160,302,167,295)(161,301,168,308)(183,239,190,246)(184,252,191,245)(185,251,192,244)(186,250,193,243)(187,249,194,242)(188,248,195,241)(189,247,196,240)(197,334,204,327)(198,333,205,326)(199,332,206,325)(200,331,207,324)(201,330,208,323)(202,329,209,336)(203,328,210,335)(225,367,232,374)(226,366,233,373)(227,365,234,372)(228,378,235,371)(229,377,236,370)(230,376,237,369)(231,375,238,368)(281,398,288,405)(282,397,289,404)(283,396,290,403)(284,395,291,402)(285,394,292,401)(286,393,293,400)(287,406,294,399)(351,445,358,438)(352,444,359,437)(353,443,360,436)(354,442,361,435)(355,441,362,448)(356,440,363,447)(357,439,364,446)(407,425,414,432)(408,424,415,431)(409,423,416,430)(410,422,417,429)(411,421,418,428)(412,434,419,427)(413,433,420,426) );
G=PermutationGroup([(1,290),(2,291),(3,292),(4,293),(5,294),(6,281),(7,282),(8,283),(9,284),(10,285),(11,286),(12,287),(13,288),(14,289),(15,207),(16,208),(17,209),(18,210),(19,197),(20,198),(21,199),(22,200),(23,201),(24,202),(25,203),(26,204),(27,205),(28,206),(29,357),(30,358),(31,359),(32,360),(33,361),(34,362),(35,363),(36,364),(37,351),(38,352),(39,353),(40,354),(41,355),(42,356),(43,97),(44,98),(45,85),(46,86),(47,87),(48,88),(49,89),(50,90),(51,91),(52,92),(53,93),(54,94),(55,95),(56,96),(57,434),(58,421),(59,422),(60,423),(61,424),(62,425),(63,426),(64,427),(65,428),(66,429),(67,430),(68,431),(69,432),(70,433),(71,242),(72,243),(73,244),(74,245),(75,246),(76,247),(77,248),(78,249),(79,250),(80,251),(81,252),(82,239),(83,240),(84,241),(99,295),(100,296),(101,297),(102,298),(103,299),(104,300),(105,301),(106,302),(107,303),(108,304),(109,305),(110,306),(111,307),(112,308),(113,378),(114,365),(115,366),(116,367),(117,368),(118,369),(119,370),(120,371),(121,372),(122,373),(123,374),(124,375),(125,376),(126,377),(127,177),(128,178),(129,179),(130,180),(131,181),(132,182),(133,169),(134,170),(135,171),(136,172),(137,173),(138,174),(139,175),(140,176),(141,230),(142,231),(143,232),(144,233),(145,234),(146,235),(147,236),(148,237),(149,238),(150,225),(151,226),(152,227),(153,228),(154,229),(155,258),(156,259),(157,260),(158,261),(159,262),(160,263),(161,264),(162,265),(163,266),(164,253),(165,254),(166,255),(167,256),(168,257),(183,387),(184,388),(185,389),(186,390),(187,391),(188,392),(189,379),(190,380),(191,381),(192,382),(193,383),(194,384),(195,385),(196,386),(211,419),(212,420),(213,407),(214,408),(215,409),(216,410),(217,411),(218,412),(219,413),(220,414),(221,415),(222,416),(223,417),(224,418),(267,444),(268,445),(269,446),(270,447),(271,448),(272,435),(273,436),(274,437),(275,438),(276,439),(277,440),(278,441),(279,442),(280,443),(309,398),(310,399),(311,400),(312,401),(313,402),(314,403),(315,404),(316,405),(317,406),(318,393),(319,394),(320,395),(321,396),(322,397),(323,340),(324,341),(325,342),(326,343),(327,344),(328,345),(329,346),(330,347),(331,348),(332,349),(333,350),(334,337),(335,338),(336,339)], [(1,40,195,21),(2,41,196,22),(3,42,183,23),(4,29,184,24),(5,30,185,25),(6,31,186,26),(7,32,187,27),(8,33,188,28),(9,34,189,15),(10,35,190,16),(11,36,191,17),(12,37,192,18),(13,38,193,19),(14,39,194,20),(43,370,224,256),(44,371,211,257),(45,372,212,258),(46,373,213,259),(47,374,214,260),(48,375,215,261),(49,376,216,262),(50,377,217,263),(51,378,218,264),(52,365,219,265),(53,366,220,266),(54,367,221,253),(55,368,222,254),(56,369,223,255),(57,105,127,235),(58,106,128,236),(59,107,129,237),(60,108,130,238),(61,109,131,225),(62,110,132,226),(63,111,133,227),(64,112,134,228),(65,99,135,229),(66,100,136,230),(67,101,137,231),(68,102,138,232),(69,103,139,233),(70,104,140,234),(71,333,404,443),(72,334,405,444),(73,335,406,445),(74,336,393,446),(75,323,394,447),(76,324,395,448),(77,325,396,435),(78,326,397,436),(79,327,398,437),(80,328,399,438),(81,329,400,439),(82,330,401,440),(83,331,402,441),(84,332,403,442),(85,121,420,155),(86,122,407,156),(87,123,408,157),(88,124,409,158),(89,125,410,159),(90,126,411,160),(91,113,412,161),(92,114,413,162),(93,115,414,163),(94,116,415,164),(95,117,416,165),(96,118,417,166),(97,119,418,167),(98,120,419,168),(141,429,296,172),(142,430,297,173),(143,431,298,174),(144,432,299,175),(145,433,300,176),(146,434,301,177),(147,421,302,178),(148,422,303,179),(149,423,304,180),(150,424,305,181),(151,425,306,182),(152,426,307,169),(153,427,308,170),(154,428,295,171),(197,288,352,383),(198,289,353,384),(199,290,354,385),(200,291,355,386),(201,292,356,387),(202,293,357,388),(203,294,358,389),(204,281,359,390),(205,282,360,391),(206,283,361,392),(207,284,362,379),(208,285,363,380),(209,286,364,381),(210,287,351,382),(239,347,312,277),(240,348,313,278),(241,349,314,279),(242,350,315,280),(243,337,316,267),(244,338,317,268),(245,339,318,269),(246,340,319,270),(247,341,320,271),(248,342,321,272),(249,343,322,273),(250,344,309,274),(251,345,310,275),(252,346,311,276)], [(1,112,195,228),(2,99,196,229),(3,100,183,230),(4,101,184,231),(5,102,185,232),(6,103,186,233),(7,104,187,234),(8,105,188,235),(9,106,189,236),(10,107,190,237),(11,108,191,238),(12,109,192,225),(13,110,193,226),(14,111,194,227),(15,128,34,58),(16,129,35,59),(17,130,36,60),(18,131,37,61),(19,132,38,62),(20,133,39,63),(21,134,40,64),(22,135,41,65),(23,136,42,66),(24,137,29,67),(25,138,30,68),(26,139,31,69),(27,140,32,70),(28,127,33,57),(43,271,224,341),(44,272,211,342),(45,273,212,343),(46,274,213,344),(47,275,214,345),(48,276,215,346),(49,277,216,347),(50,278,217,348),(51,279,218,349),(52,280,219,350),(53,267,220,337),(54,268,221,338),(55,269,222,339),(56,270,223,340),(71,114,404,162),(72,115,405,163),(73,116,406,164),(74,117,393,165),(75,118,394,166),(76,119,395,167),(77,120,396,168),(78,121,397,155),(79,122,398,156),(80,123,399,157),(81,124,400,158),(82,125,401,159),(83,126,402,160),(84,113,403,161),(85,436,420,326),(86,437,407,327),(87,438,408,328),(88,439,409,329),(89,440,410,330),(90,441,411,331),(91,442,412,332),(92,443,413,333),(93,444,414,334),(94,445,415,335),(95,446,416,336),(96,447,417,323),(97,448,418,324),(98,435,419,325),(141,292,296,387),(142,293,297,388),(143,294,298,389),(144,281,299,390),(145,282,300,391),(146,283,301,392),(147,284,302,379),(148,285,303,380),(149,286,304,381),(150,287,305,382),(151,288,306,383),(152,289,307,384),(153,290,308,385),(154,291,295,386),(169,353,426,198),(170,354,427,199),(171,355,428,200),(172,356,429,201),(173,357,430,202),(174,358,431,203),(175,359,432,204),(176,360,433,205),(177,361,434,206),(178,362,421,207),(179,363,422,208),(180,364,423,209),(181,351,424,210),(182,352,425,197),(239,376,312,262),(240,377,313,263),(241,378,314,264),(242,365,315,265),(243,366,316,266),(244,367,317,253),(245,368,318,254),(246,369,319,255),(247,370,320,256),(248,371,321,257),(249,372,322,258),(250,373,309,259),(251,374,310,260),(252,375,311,261)], [(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)], [(1,314,8,321),(2,313,9,320),(3,312,10,319),(4,311,11,318),(5,310,12,317),(6,309,13,316),(7,322,14,315),(15,341,22,348),(16,340,23,347),(17,339,24,346),(18,338,25,345),(19,337,26,344),(20,350,27,343),(21,349,28,342),(29,276,36,269),(30,275,37,268),(31,274,38,267),(32,273,39,280),(33,272,40,279),(34,271,41,278),(35,270,42,277),(43,135,50,128),(44,134,51,127),(45,133,52,140),(46,132,53,139),(47,131,54,138),(48,130,55,137),(49,129,56,136),(57,211,64,218),(58,224,65,217),(59,223,66,216),(60,222,67,215),(61,221,68,214),(62,220,69,213),(63,219,70,212),(71,391,78,384),(72,390,79,383),(73,389,80,382),(74,388,81,381),(75,387,82,380),(76,386,83,379),(77,385,84,392),(85,169,92,176),(86,182,93,175),(87,181,94,174),(88,180,95,173),(89,179,96,172),(90,178,97,171),(91,177,98,170),(99,263,106,256),(100,262,107,255),(101,261,108,254),(102,260,109,253),(103,259,110,266),(104,258,111,265),(105,257,112,264),(113,146,120,153),(114,145,121,152),(115,144,122,151),(116,143,123,150),(117,142,124,149),(118,141,125,148),(119,154,126,147),(155,307,162,300),(156,306,163,299),(157,305,164,298),(158,304,165,297),(159,303,166,296),(160,302,167,295),(161,301,168,308),(183,239,190,246),(184,252,191,245),(185,251,192,244),(186,250,193,243),(187,249,194,242),(188,248,195,241),(189,247,196,240),(197,334,204,327),(198,333,205,326),(199,332,206,325),(200,331,207,324),(201,330,208,323),(202,329,209,336),(203,328,210,335),(225,367,232,374),(226,366,233,373),(227,365,234,372),(228,378,235,371),(229,377,236,370),(230,376,237,369),(231,375,238,368),(281,398,288,405),(282,397,289,404),(283,396,290,403),(284,395,291,402),(285,394,292,401),(286,393,293,400),(287,406,294,399),(351,445,358,438),(352,444,359,437),(353,443,360,436),(354,442,361,435),(355,441,362,448),(356,440,363,447),(357,439,364,446),(407,425,414,432),(408,424,415,431),(409,423,416,430),(410,422,417,429),(411,421,418,428),(412,434,419,427),(413,433,420,426)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 2 |
| 0 | 0 | 0 | 0 | 28 | 28 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 13 |
| 0 | 0 | 0 | 0 | 15 | 23 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 1 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 1 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 7 | 20 | 0 | 0 | 0 | 0 |
| 12 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 6 | 0 | 0 |
| 0 | 0 | 4 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,28,0,0,0,0,2,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,6,15,0,0,0,0,13,23],[0,1,0,0,0,0,28,26,0,0,0,0,0,0,7,28,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[7,12,0,0,0,0,20,22,0,0,0,0,0,0,21,4,0,0,0,0,6,8,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
100 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4L | 4M | ··· | 4T | 4U | ··· | 4AF | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 7 | ··· | 7 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
100 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | - | + | + | - | + | - | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C4 | Q8 | D7 | C4○D4 | D14 | Dic7 | D14 | Q8×D7 | Q8⋊2D7 |
| kernel | C2×Q8×Dic7 | C2×C4×Dic7 | C2×C4⋊Dic7 | Q8×Dic7 | Q8×C2×C14 | Q8×C14 | C2×Dic7 | C22×Q8 | C2×C14 | C22×C4 | C2×Q8 | C2×Q8 | C22 | C22 |
| # reps | 1 | 3 | 3 | 8 | 1 | 16 | 4 | 3 | 4 | 9 | 24 | 12 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_2\times Q_8\times Dic_7
% in TeX
G:=Group("C2xQ8xDic7"); // GroupNames label
G:=SmallGroup(448,1264);
// by ID
G=gap.SmallGroup(448,1264);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,184,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=d^14=1,c^2=b^2,e^2=d^7,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀