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G = C2×Q8×Dic7  order 448 = 26·7

Direct product of C2, Q8 and Dic7

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

Aliases: C2×Q8×Dic7, C14⋊3(C4×Q8), (Q8×C14)⋊11C4, C22.36(Q8×D7), C14.46(C23×C4), C28.95(C22×C4), (C2×Q8).206D14, (C22×Q8).10D7, C14.52(C22×Q8), C2.8(C23×Dic7), (C2×C14).303C24, (C2×C28).550C23, (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), (C4×Dic7).260C22, (C2×Dic7).287C23, 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), C2.4(C2×Q8⋊2D7), (C2×C14).97(C2×Q8), (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

Derived series
C1 — C14 — C2×Q8×Dic7
Chief series
C1 — C7 — C14 — C2×C14 — C2×Dic7 — C22×Dic7 — C2×C4×Dic7 — C2×Q8×Dic7
Lower central
C7 — C14 — C2×Q8×Dic7
Upper central
C1 — C23 — C22×Q8

Generators and relations for C2×Q8×Dic7
 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 >

Subgroups: 820 in 298 conjugacy classes, 215 normal (16 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, Q8, C23, C14, C14, C42, C4⋊C4, C22×C4, C22×C4, C2×Q8, Dic7, Dic7, C28, C2×C14, C2×C14, C2×C42, C2×C4⋊C4, C4×Q8, C22×Q8, C2×Dic7, C2×Dic7, C2×C28, C7×Q8, C22×C14, C2×C4×Q8, C4×Dic7, C4⋊Dic7, C22×Dic7, C22×Dic7, C22×C28, Q8×C14, C2×C4×Dic7, C2×C4⋊Dic7, Q8×Dic7, Q8×C2×C14, C2×Q8×Dic7
Quotients: C1, C2, C4, C22, C2×C4, Q8, C23, D7, C22×C4, C2×Q8, C4○D4, C24, Dic7, D14, C4×Q8, C23×C4, C22×Q8, C2×C4○D4, C2×Dic7, C22×D7, C2×C4×Q8, Q8×D7, Q8⋊2D7, C22×Dic7, C23×D7, Q8×Dic7, C2×Q8×D7, C2×Q8⋊2D7, C23×Dic7, C2×Q8×Dic7

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

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

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

(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)

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

100 conjugacy classes

class 1 2A···2G4A···4L4M···4T4U···4AF7A7B7C14A···14U28A···28AJ
order12···24···44···44···477714···1428···28
size11···12···27···714···142222···24···4

100 irreducible representations

dim11111122222244
type+++++-++-+-+
imageC1C2C2C2C2C4Q8D7C4○D4D14Dic7D14Q8×D7Q8⋊2D7
kernelC2×Q8×Dic7C2×C4×Dic7C2×C4⋊Dic7Q8×Dic7Q8×C2×C14Q8×C14C2×Dic7C22×Q8C2×C14C22×C4C2×Q8C2×Q8C22C22
# reps13381164349241266

Matrix representation of C2×Q8×Dic7 ►in GL6(𝔽29)

2800000
0280000
0028000
0002800
000010
000001
,
100000
010000
0028000
0002800
000012
00002828
,
100000
010000
0028000
0002800
0000613
00001523
,
0280000
1260000
007100
0028000
000010
000001
,
7200000
12220000
0021600
004800
000010
000001

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] >;
 

C2×Q8×Dic7 in GAP, Magma, Sage, TeX 

C_2\times Q_8\times {\rm 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
 

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