metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×Dic7).2Q8, (C2×Dic7).9D4, C22.40(Q8×D7), C22.152(D4×D7), (C22×C4).11D14, C2.9(D14⋊Q8), C2.4(C42⋊2D7), C2.9(Dic7.Q8), C14.22(C22⋊Q8), (C22×C28).8C22, C2.C42.4D7, C14.1(C42⋊2C2), C2.9(D14.D4), C14.16(C4.4D4), C22.85(C4○D28), C14.C42.6C2, C14.12(C42.C2), C23.354(C22×D7), C22.83(D4⋊2D7), (C22×C14).283C23, C7⋊1(C23.83C23), C2.8(Dic7.D4), C14.5(C22.D4), C2.8(C23.D14), (C22×Dic7).8C22, (C2×C14).64(C2×Q8), (C2×C14).195(C2×D4), (C2×Dic7⋊C4).7C2, (C2×C14).127(C4○D4), (C7×C2.C42).1C2, SmallGroup(448,192)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×Dic7).Q8
G = < a,b,c,d,e | a2=b14=d4=1, c2=b7, e2=b7d2, ab=ba, ece-1=ac=ca, ad=da, ae=ea, cbc-1=dbd-1=b-1, be=eb, dcd-1=ab7c, ede-1=ad-1 >
Subgroups: 572 in 134 conjugacy classes, 55 normal (51 characteristic)
C1, C2, C4, C22, C7, C2×C4, C23, C14, C4⋊C4, C22×C4, C22×C4, Dic7, C28, C2×C14, C2.C42, C2.C42, C2×C4⋊C4, C2×Dic7, C2×Dic7, C2×C28, C22×C14, C23.83C23, Dic7⋊C4, C22×Dic7, C22×C28, C14.C42, C7×C2.C42, C2×Dic7⋊C4, (C2×Dic7).Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C4○D4, D14, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, C22×D7, C23.83C23, C4○D28, D4×D7, D4⋊2D7, Q8×D7, C42⋊2D7, C23.D14, D14.D4, Dic7.D4, Dic7.Q8, D14⋊Q8, (C2×Dic7).Q8
►Regular action on 448 points
Generators in S448
(1 50)(2 51)(3 52)(4 53)(5 54)(6 55)(7 56)(8 43)(9 44)(10 45)(11 46)(12 47)(13 48)(14 49)(15 326)(16 327)(17 328)(18 329)(19 330)(20 331)(21 332)(22 333)(23 334)(24 335)(25 336)(26 323)(27 324)(28 325)(29 248)(30 249)(31 250)(32 251)(33 252)(34 239)(35 240)(36 241)(37 242)(38 243)(39 244)(40 245)(41 246)(42 247)(57 292)(58 293)(59 294)(60 281)(61 282)(62 283)(63 284)(64 285)(65 286)(66 287)(67 288)(68 289)(69 290)(70 291)(71 174)(72 175)(73 176)(74 177)(75 178)(76 179)(77 180)(78 181)(79 182)(80 169)(81 170)(82 171)(83 172)(84 173)(85 363)(86 364)(87 351)(88 352)(89 353)(90 354)(91 355)(92 356)(93 357)(94 358)(95 359)(96 360)(97 361)(98 362)(99 372)(100 373)(101 374)(102 375)(103 376)(104 377)(105 378)(106 365)(107 366)(108 367)(109 368)(110 369)(111 370)(112 371)(113 296)(114 297)(115 298)(116 299)(117 300)(118 301)(119 302)(120 303)(121 304)(122 305)(123 306)(124 307)(125 308)(126 295)(127 145)(128 146)(129 147)(130 148)(131 149)(132 150)(133 151)(134 152)(135 153)(136 154)(137 141)(138 142)(139 143)(140 144)(155 277)(156 278)(157 279)(158 280)(159 267)(160 268)(161 269)(162 270)(163 271)(164 272)(165 273)(166 274)(167 275)(168 276)(183 440)(184 441)(185 442)(186 443)(187 444)(188 445)(189 446)(190 447)(191 448)(192 435)(193 436)(194 437)(195 438)(196 439)(197 315)(198 316)(199 317)(200 318)(201 319)(202 320)(203 321)(204 322)(205 309)(206 310)(207 311)(208 312)(209 313)(210 314)(211 227)(212 228)(213 229)(214 230)(215 231)(216 232)(217 233)(218 234)(219 235)(220 236)(221 237)(222 238)(223 225)(224 226)(253 415)(254 416)(255 417)(256 418)(257 419)(258 420)(259 407)(260 408)(261 409)(262 410)(263 411)(264 412)(265 413)(266 414)(337 389)(338 390)(339 391)(340 392)(341 379)(342 380)(343 381)(344 382)(345 383)(346 384)(347 385)(348 386)(349 387)(350 388)(393 422)(394 423)(395 424)(396 425)(397 426)(398 427)(399 428)(400 429)(401 430)(402 431)(403 432)(404 433)(405 434)(406 421)
(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)
(1 179 8 172)(2 178 9 171)(3 177 10 170)(4 176 11 169)(5 175 12 182)(6 174 13 181)(7 173 14 180)(15 348 22 341)(16 347 23 340)(17 346 24 339)(18 345 25 338)(19 344 26 337)(20 343 27 350)(21 342 28 349)(29 311 36 318)(30 310 37 317)(31 309 38 316)(32 322 39 315)(33 321 40 314)(34 320 41 313)(35 319 42 312)(43 83 50 76)(44 82 51 75)(45 81 52 74)(46 80 53 73)(47 79 54 72)(48 78 55 71)(49 77 56 84)(57 95 64 88)(58 94 65 87)(59 93 66 86)(60 92 67 85)(61 91 68 98)(62 90 69 97)(63 89 70 96)(99 149 106 142)(100 148 107 141)(101 147 108 154)(102 146 109 153)(103 145 110 152)(104 144 111 151)(105 143 112 150)(113 267 120 274)(114 280 121 273)(115 279 122 272)(116 278 123 271)(117 277 124 270)(118 276 125 269)(119 275 126 268)(127 369 134 376)(128 368 135 375)(129 367 136 374)(130 366 137 373)(131 365 138 372)(132 378 139 371)(133 377 140 370)(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)(183 433 190 426)(184 432 191 425)(185 431 192 424)(186 430 193 423)(187 429 194 422)(188 428 195 421)(189 427 196 434)(197 251 204 244)(198 250 205 243)(199 249 206 242)(200 248 207 241)(201 247 208 240)(202 246 209 239)(203 245 210 252)(211 263 218 256)(212 262 219 255)(213 261 220 254)(214 260 221 253)(215 259 222 266)(216 258 223 265)(217 257 224 264)(225 413 232 420)(226 412 233 419)(227 411 234 418)(228 410 235 417)(229 409 236 416)(230 408 237 415)(231 407 238 414)(281 356 288 363)(282 355 289 362)(283 354 290 361)(284 353 291 360)(285 352 292 359)(286 351 293 358)(287 364 294 357)(323 389 330 382)(324 388 331 381)(325 387 332 380)(326 386 333 379)(327 385 334 392)(328 384 335 391)(329 383 336 390)(393 444 400 437)(394 443 401 436)(395 442 402 435)(396 441 403 448)(397 440 404 447)(398 439 405 446)(399 438 406 445)
(1 226 324 97)(2 225 325 96)(3 238 326 95)(4 237 327 94)(5 236 328 93)(6 235 329 92)(7 234 330 91)(8 233 331 90)(9 232 332 89)(10 231 333 88)(11 230 334 87)(12 229 335 86)(13 228 336 85)(14 227 323 98)(15 359 52 222)(16 358 53 221)(17 357 54 220)(18 356 55 219)(19 355 56 218)(20 354 43 217)(21 353 44 216)(22 352 45 215)(23 351 46 214)(24 364 47 213)(25 363 48 212)(26 362 49 211)(27 361 50 224)(28 360 51 223)(29 102 155 188)(30 101 156 187)(31 100 157 186)(32 99 158 185)(33 112 159 184)(34 111 160 183)(35 110 161 196)(36 109 162 195)(37 108 163 194)(38 107 164 193)(39 106 165 192)(40 105 166 191)(41 104 167 190)(42 103 168 189)(57 74 407 348)(58 73 408 347)(59 72 409 346)(60 71 410 345)(61 84 411 344)(62 83 412 343)(63 82 413 342)(64 81 414 341)(65 80 415 340)(66 79 416 339)(67 78 417 338)(68 77 418 337)(69 76 419 350)(70 75 420 349)(113 432 210 150)(114 431 197 149)(115 430 198 148)(116 429 199 147)(117 428 200 146)(118 427 201 145)(119 426 202 144)(120 425 203 143)(121 424 204 142)(122 423 205 141)(123 422 206 154)(124 421 207 153)(125 434 208 152)(126 433 209 151)(127 301 398 319)(128 300 399 318)(129 299 400 317)(130 298 401 316)(131 297 402 315)(132 296 403 314)(133 295 404 313)(134 308 405 312)(135 307 406 311)(136 306 393 310)(137 305 394 309)(138 304 395 322)(139 303 396 321)(140 302 397 320)(169 253 392 286)(170 266 379 285)(171 265 380 284)(172 264 381 283)(173 263 382 282)(174 262 383 281)(175 261 384 294)(176 260 385 293)(177 259 386 292)(178 258 387 291)(179 257 388 290)(180 256 389 289)(181 255 390 288)(182 254 391 287)(239 370 268 440)(240 369 269 439)(241 368 270 438)(242 367 271 437)(243 366 272 436)(244 365 273 435)(245 378 274 448)(246 377 275 447)(247 376 276 446)(248 375 277 445)(249 374 278 444)(250 373 279 443)(251 372 280 442)(252 371 267 441)
(1 272 331 250)(2 273 332 251)(3 274 333 252)(4 275 334 239)(5 276 335 240)(6 277 336 241)(7 278 323 242)(8 279 324 243)(9 280 325 244)(10 267 326 245)(11 268 327 246)(12 269 328 247)(13 270 329 248)(14 271 330 249)(15 40 45 159)(16 41 46 160)(17 42 47 161)(18 29 48 162)(19 30 49 163)(20 31 50 164)(21 32 51 165)(22 33 52 166)(23 34 53 167)(24 35 54 168)(25 36 55 155)(26 37 56 156)(27 38 43 157)(28 39 44 158)(57 403 414 139)(58 404 415 140)(59 405 416 127)(60 406 417 128)(61 393 418 129)(62 394 419 130)(63 395 420 131)(64 396 407 132)(65 397 408 133)(66 398 409 134)(67 399 410 135)(68 400 411 136)(69 401 412 137)(70 402 413 138)(71 124 338 200)(72 125 339 201)(73 126 340 202)(74 113 341 203)(75 114 342 204)(76 115 343 205)(77 116 344 206)(78 117 345 207)(79 118 346 208)(80 119 347 209)(81 120 348 210)(82 121 349 197)(83 122 350 198)(84 123 337 199)(85 195 235 102)(86 196 236 103)(87 183 237 104)(88 184 238 105)(89 185 225 106)(90 186 226 107)(91 187 227 108)(92 188 228 109)(93 189 229 110)(94 190 230 111)(95 191 231 112)(96 192 232 99)(97 193 233 100)(98 194 234 101)(141 290 430 264)(142 291 431 265)(143 292 432 266)(144 293 433 253)(145 294 434 254)(146 281 421 255)(147 282 422 256)(148 283 423 257)(149 284 424 258)(150 285 425 259)(151 286 426 260)(152 287 427 261)(153 288 428 262)(154 289 429 263)(169 302 385 313)(170 303 386 314)(171 304 387 315)(172 305 388 316)(173 306 389 317)(174 307 390 318)(175 308 391 319)(176 295 392 320)(177 296 379 321)(178 297 380 322)(179 298 381 309)(180 299 382 310)(181 300 383 311)(182 301 384 312)(211 367 355 444)(212 368 356 445)(213 369 357 446)(214 370 358 447)(215 371 359 448)(216 372 360 435)(217 373 361 436)(218 374 362 437)(219 375 363 438)(220 376 364 439)(221 377 351 440)(222 378 352 441)(223 365 353 442)(224 366 354 443)
G:=sub<Sym(448)| (1,50)(2,51)(3,52)(4,53)(5,54)(6,55)(7,56)(8,43)(9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,326)(16,327)(17,328)(18,329)(19,330)(20,331)(21,332)(22,333)(23,334)(24,335)(25,336)(26,323)(27,324)(28,325)(29,248)(30,249)(31,250)(32,251)(33,252)(34,239)(35,240)(36,241)(37,242)(38,243)(39,244)(40,245)(41,246)(42,247)(57,292)(58,293)(59,294)(60,281)(61,282)(62,283)(63,284)(64,285)(65,286)(66,287)(67,288)(68,289)(69,290)(70,291)(71,174)(72,175)(73,176)(74,177)(75,178)(76,179)(77,180)(78,181)(79,182)(80,169)(81,170)(82,171)(83,172)(84,173)(85,363)(86,364)(87,351)(88,352)(89,353)(90,354)(91,355)(92,356)(93,357)(94,358)(95,359)(96,360)(97,361)(98,362)(99,372)(100,373)(101,374)(102,375)(103,376)(104,377)(105,378)(106,365)(107,366)(108,367)(109,368)(110,369)(111,370)(112,371)(113,296)(114,297)(115,298)(116,299)(117,300)(118,301)(119,302)(120,303)(121,304)(122,305)(123,306)(124,307)(125,308)(126,295)(127,145)(128,146)(129,147)(130,148)(131,149)(132,150)(133,151)(134,152)(135,153)(136,154)(137,141)(138,142)(139,143)(140,144)(155,277)(156,278)(157,279)(158,280)(159,267)(160,268)(161,269)(162,270)(163,271)(164,272)(165,273)(166,274)(167,275)(168,276)(183,440)(184,441)(185,442)(186,443)(187,444)(188,445)(189,446)(190,447)(191,448)(192,435)(193,436)(194,437)(195,438)(196,439)(197,315)(198,316)(199,317)(200,318)(201,319)(202,320)(203,321)(204,322)(205,309)(206,310)(207,311)(208,312)(209,313)(210,314)(211,227)(212,228)(213,229)(214,230)(215,231)(216,232)(217,233)(218,234)(219,235)(220,236)(221,237)(222,238)(223,225)(224,226)(253,415)(254,416)(255,417)(256,418)(257,419)(258,420)(259,407)(260,408)(261,409)(262,410)(263,411)(264,412)(265,413)(266,414)(337,389)(338,390)(339,391)(340,392)(341,379)(342,380)(343,381)(344,382)(345,383)(346,384)(347,385)(348,386)(349,387)(350,388)(393,422)(394,423)(395,424)(396,425)(397,426)(398,427)(399,428)(400,429)(401,430)(402,431)(403,432)(404,433)(405,434)(406,421), (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), (1,179,8,172)(2,178,9,171)(3,177,10,170)(4,176,11,169)(5,175,12,182)(6,174,13,181)(7,173,14,180)(15,348,22,341)(16,347,23,340)(17,346,24,339)(18,345,25,338)(19,344,26,337)(20,343,27,350)(21,342,28,349)(29,311,36,318)(30,310,37,317)(31,309,38,316)(32,322,39,315)(33,321,40,314)(34,320,41,313)(35,319,42,312)(43,83,50,76)(44,82,51,75)(45,81,52,74)(46,80,53,73)(47,79,54,72)(48,78,55,71)(49,77,56,84)(57,95,64,88)(58,94,65,87)(59,93,66,86)(60,92,67,85)(61,91,68,98)(62,90,69,97)(63,89,70,96)(99,149,106,142)(100,148,107,141)(101,147,108,154)(102,146,109,153)(103,145,110,152)(104,144,111,151)(105,143,112,150)(113,267,120,274)(114,280,121,273)(115,279,122,272)(116,278,123,271)(117,277,124,270)(118,276,125,269)(119,275,126,268)(127,369,134,376)(128,368,135,375)(129,367,136,374)(130,366,137,373)(131,365,138,372)(132,378,139,371)(133,377,140,370)(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)(183,433,190,426)(184,432,191,425)(185,431,192,424)(186,430,193,423)(187,429,194,422)(188,428,195,421)(189,427,196,434)(197,251,204,244)(198,250,205,243)(199,249,206,242)(200,248,207,241)(201,247,208,240)(202,246,209,239)(203,245,210,252)(211,263,218,256)(212,262,219,255)(213,261,220,254)(214,260,221,253)(215,259,222,266)(216,258,223,265)(217,257,224,264)(225,413,232,420)(226,412,233,419)(227,411,234,418)(228,410,235,417)(229,409,236,416)(230,408,237,415)(231,407,238,414)(281,356,288,363)(282,355,289,362)(283,354,290,361)(284,353,291,360)(285,352,292,359)(286,351,293,358)(287,364,294,357)(323,389,330,382)(324,388,331,381)(325,387,332,380)(326,386,333,379)(327,385,334,392)(328,384,335,391)(329,383,336,390)(393,444,400,437)(394,443,401,436)(395,442,402,435)(396,441,403,448)(397,440,404,447)(398,439,405,446)(399,438,406,445), (1,226,324,97)(2,225,325,96)(3,238,326,95)(4,237,327,94)(5,236,328,93)(6,235,329,92)(7,234,330,91)(8,233,331,90)(9,232,332,89)(10,231,333,88)(11,230,334,87)(12,229,335,86)(13,228,336,85)(14,227,323,98)(15,359,52,222)(16,358,53,221)(17,357,54,220)(18,356,55,219)(19,355,56,218)(20,354,43,217)(21,353,44,216)(22,352,45,215)(23,351,46,214)(24,364,47,213)(25,363,48,212)(26,362,49,211)(27,361,50,224)(28,360,51,223)(29,102,155,188)(30,101,156,187)(31,100,157,186)(32,99,158,185)(33,112,159,184)(34,111,160,183)(35,110,161,196)(36,109,162,195)(37,108,163,194)(38,107,164,193)(39,106,165,192)(40,105,166,191)(41,104,167,190)(42,103,168,189)(57,74,407,348)(58,73,408,347)(59,72,409,346)(60,71,410,345)(61,84,411,344)(62,83,412,343)(63,82,413,342)(64,81,414,341)(65,80,415,340)(66,79,416,339)(67,78,417,338)(68,77,418,337)(69,76,419,350)(70,75,420,349)(113,432,210,150)(114,431,197,149)(115,430,198,148)(116,429,199,147)(117,428,200,146)(118,427,201,145)(119,426,202,144)(120,425,203,143)(121,424,204,142)(122,423,205,141)(123,422,206,154)(124,421,207,153)(125,434,208,152)(126,433,209,151)(127,301,398,319)(128,300,399,318)(129,299,400,317)(130,298,401,316)(131,297,402,315)(132,296,403,314)(133,295,404,313)(134,308,405,312)(135,307,406,311)(136,306,393,310)(137,305,394,309)(138,304,395,322)(139,303,396,321)(140,302,397,320)(169,253,392,286)(170,266,379,285)(171,265,380,284)(172,264,381,283)(173,263,382,282)(174,262,383,281)(175,261,384,294)(176,260,385,293)(177,259,386,292)(178,258,387,291)(179,257,388,290)(180,256,389,289)(181,255,390,288)(182,254,391,287)(239,370,268,440)(240,369,269,439)(241,368,270,438)(242,367,271,437)(243,366,272,436)(244,365,273,435)(245,378,274,448)(246,377,275,447)(247,376,276,446)(248,375,277,445)(249,374,278,444)(250,373,279,443)(251,372,280,442)(252,371,267,441), (1,272,331,250)(2,273,332,251)(3,274,333,252)(4,275,334,239)(5,276,335,240)(6,277,336,241)(7,278,323,242)(8,279,324,243)(9,280,325,244)(10,267,326,245)(11,268,327,246)(12,269,328,247)(13,270,329,248)(14,271,330,249)(15,40,45,159)(16,41,46,160)(17,42,47,161)(18,29,48,162)(19,30,49,163)(20,31,50,164)(21,32,51,165)(22,33,52,166)(23,34,53,167)(24,35,54,168)(25,36,55,155)(26,37,56,156)(27,38,43,157)(28,39,44,158)(57,403,414,139)(58,404,415,140)(59,405,416,127)(60,406,417,128)(61,393,418,129)(62,394,419,130)(63,395,420,131)(64,396,407,132)(65,397,408,133)(66,398,409,134)(67,399,410,135)(68,400,411,136)(69,401,412,137)(70,402,413,138)(71,124,338,200)(72,125,339,201)(73,126,340,202)(74,113,341,203)(75,114,342,204)(76,115,343,205)(77,116,344,206)(78,117,345,207)(79,118,346,208)(80,119,347,209)(81,120,348,210)(82,121,349,197)(83,122,350,198)(84,123,337,199)(85,195,235,102)(86,196,236,103)(87,183,237,104)(88,184,238,105)(89,185,225,106)(90,186,226,107)(91,187,227,108)(92,188,228,109)(93,189,229,110)(94,190,230,111)(95,191,231,112)(96,192,232,99)(97,193,233,100)(98,194,234,101)(141,290,430,264)(142,291,431,265)(143,292,432,266)(144,293,433,253)(145,294,434,254)(146,281,421,255)(147,282,422,256)(148,283,423,257)(149,284,424,258)(150,285,425,259)(151,286,426,260)(152,287,427,261)(153,288,428,262)(154,289,429,263)(169,302,385,313)(170,303,386,314)(171,304,387,315)(172,305,388,316)(173,306,389,317)(174,307,390,318)(175,308,391,319)(176,295,392,320)(177,296,379,321)(178,297,380,322)(179,298,381,309)(180,299,382,310)(181,300,383,311)(182,301,384,312)(211,367,355,444)(212,368,356,445)(213,369,357,446)(214,370,358,447)(215,371,359,448)(216,372,360,435)(217,373,361,436)(218,374,362,437)(219,375,363,438)(220,376,364,439)(221,377,351,440)(222,378,352,441)(223,365,353,442)(224,366,354,443)>;
G:=Group( (1,50)(2,51)(3,52)(4,53)(5,54)(6,55)(7,56)(8,43)(9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,326)(16,327)(17,328)(18,329)(19,330)(20,331)(21,332)(22,333)(23,334)(24,335)(25,336)(26,323)(27,324)(28,325)(29,248)(30,249)(31,250)(32,251)(33,252)(34,239)(35,240)(36,241)(37,242)(38,243)(39,244)(40,245)(41,246)(42,247)(57,292)(58,293)(59,294)(60,281)(61,282)(62,283)(63,284)(64,285)(65,286)(66,287)(67,288)(68,289)(69,290)(70,291)(71,174)(72,175)(73,176)(74,177)(75,178)(76,179)(77,180)(78,181)(79,182)(80,169)(81,170)(82,171)(83,172)(84,173)(85,363)(86,364)(87,351)(88,352)(89,353)(90,354)(91,355)(92,356)(93,357)(94,358)(95,359)(96,360)(97,361)(98,362)(99,372)(100,373)(101,374)(102,375)(103,376)(104,377)(105,378)(106,365)(107,366)(108,367)(109,368)(110,369)(111,370)(112,371)(113,296)(114,297)(115,298)(116,299)(117,300)(118,301)(119,302)(120,303)(121,304)(122,305)(123,306)(124,307)(125,308)(126,295)(127,145)(128,146)(129,147)(130,148)(131,149)(132,150)(133,151)(134,152)(135,153)(136,154)(137,141)(138,142)(139,143)(140,144)(155,277)(156,278)(157,279)(158,280)(159,267)(160,268)(161,269)(162,270)(163,271)(164,272)(165,273)(166,274)(167,275)(168,276)(183,440)(184,441)(185,442)(186,443)(187,444)(188,445)(189,446)(190,447)(191,448)(192,435)(193,436)(194,437)(195,438)(196,439)(197,315)(198,316)(199,317)(200,318)(201,319)(202,320)(203,321)(204,322)(205,309)(206,310)(207,311)(208,312)(209,313)(210,314)(211,227)(212,228)(213,229)(214,230)(215,231)(216,232)(217,233)(218,234)(219,235)(220,236)(221,237)(222,238)(223,225)(224,226)(253,415)(254,416)(255,417)(256,418)(257,419)(258,420)(259,407)(260,408)(261,409)(262,410)(263,411)(264,412)(265,413)(266,414)(337,389)(338,390)(339,391)(340,392)(341,379)(342,380)(343,381)(344,382)(345,383)(346,384)(347,385)(348,386)(349,387)(350,388)(393,422)(394,423)(395,424)(396,425)(397,426)(398,427)(399,428)(400,429)(401,430)(402,431)(403,432)(404,433)(405,434)(406,421), (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), (1,179,8,172)(2,178,9,171)(3,177,10,170)(4,176,11,169)(5,175,12,182)(6,174,13,181)(7,173,14,180)(15,348,22,341)(16,347,23,340)(17,346,24,339)(18,345,25,338)(19,344,26,337)(20,343,27,350)(21,342,28,349)(29,311,36,318)(30,310,37,317)(31,309,38,316)(32,322,39,315)(33,321,40,314)(34,320,41,313)(35,319,42,312)(43,83,50,76)(44,82,51,75)(45,81,52,74)(46,80,53,73)(47,79,54,72)(48,78,55,71)(49,77,56,84)(57,95,64,88)(58,94,65,87)(59,93,66,86)(60,92,67,85)(61,91,68,98)(62,90,69,97)(63,89,70,96)(99,149,106,142)(100,148,107,141)(101,147,108,154)(102,146,109,153)(103,145,110,152)(104,144,111,151)(105,143,112,150)(113,267,120,274)(114,280,121,273)(115,279,122,272)(116,278,123,271)(117,277,124,270)(118,276,125,269)(119,275,126,268)(127,369,134,376)(128,368,135,375)(129,367,136,374)(130,366,137,373)(131,365,138,372)(132,378,139,371)(133,377,140,370)(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)(183,433,190,426)(184,432,191,425)(185,431,192,424)(186,430,193,423)(187,429,194,422)(188,428,195,421)(189,427,196,434)(197,251,204,244)(198,250,205,243)(199,249,206,242)(200,248,207,241)(201,247,208,240)(202,246,209,239)(203,245,210,252)(211,263,218,256)(212,262,219,255)(213,261,220,254)(214,260,221,253)(215,259,222,266)(216,258,223,265)(217,257,224,264)(225,413,232,420)(226,412,233,419)(227,411,234,418)(228,410,235,417)(229,409,236,416)(230,408,237,415)(231,407,238,414)(281,356,288,363)(282,355,289,362)(283,354,290,361)(284,353,291,360)(285,352,292,359)(286,351,293,358)(287,364,294,357)(323,389,330,382)(324,388,331,381)(325,387,332,380)(326,386,333,379)(327,385,334,392)(328,384,335,391)(329,383,336,390)(393,444,400,437)(394,443,401,436)(395,442,402,435)(396,441,403,448)(397,440,404,447)(398,439,405,446)(399,438,406,445), (1,226,324,97)(2,225,325,96)(3,238,326,95)(4,237,327,94)(5,236,328,93)(6,235,329,92)(7,234,330,91)(8,233,331,90)(9,232,332,89)(10,231,333,88)(11,230,334,87)(12,229,335,86)(13,228,336,85)(14,227,323,98)(15,359,52,222)(16,358,53,221)(17,357,54,220)(18,356,55,219)(19,355,56,218)(20,354,43,217)(21,353,44,216)(22,352,45,215)(23,351,46,214)(24,364,47,213)(25,363,48,212)(26,362,49,211)(27,361,50,224)(28,360,51,223)(29,102,155,188)(30,101,156,187)(31,100,157,186)(32,99,158,185)(33,112,159,184)(34,111,160,183)(35,110,161,196)(36,109,162,195)(37,108,163,194)(38,107,164,193)(39,106,165,192)(40,105,166,191)(41,104,167,190)(42,103,168,189)(57,74,407,348)(58,73,408,347)(59,72,409,346)(60,71,410,345)(61,84,411,344)(62,83,412,343)(63,82,413,342)(64,81,414,341)(65,80,415,340)(66,79,416,339)(67,78,417,338)(68,77,418,337)(69,76,419,350)(70,75,420,349)(113,432,210,150)(114,431,197,149)(115,430,198,148)(116,429,199,147)(117,428,200,146)(118,427,201,145)(119,426,202,144)(120,425,203,143)(121,424,204,142)(122,423,205,141)(123,422,206,154)(124,421,207,153)(125,434,208,152)(126,433,209,151)(127,301,398,319)(128,300,399,318)(129,299,400,317)(130,298,401,316)(131,297,402,315)(132,296,403,314)(133,295,404,313)(134,308,405,312)(135,307,406,311)(136,306,393,310)(137,305,394,309)(138,304,395,322)(139,303,396,321)(140,302,397,320)(169,253,392,286)(170,266,379,285)(171,265,380,284)(172,264,381,283)(173,263,382,282)(174,262,383,281)(175,261,384,294)(176,260,385,293)(177,259,386,292)(178,258,387,291)(179,257,388,290)(180,256,389,289)(181,255,390,288)(182,254,391,287)(239,370,268,440)(240,369,269,439)(241,368,270,438)(242,367,271,437)(243,366,272,436)(244,365,273,435)(245,378,274,448)(246,377,275,447)(247,376,276,446)(248,375,277,445)(249,374,278,444)(250,373,279,443)(251,372,280,442)(252,371,267,441), (1,272,331,250)(2,273,332,251)(3,274,333,252)(4,275,334,239)(5,276,335,240)(6,277,336,241)(7,278,323,242)(8,279,324,243)(9,280,325,244)(10,267,326,245)(11,268,327,246)(12,269,328,247)(13,270,329,248)(14,271,330,249)(15,40,45,159)(16,41,46,160)(17,42,47,161)(18,29,48,162)(19,30,49,163)(20,31,50,164)(21,32,51,165)(22,33,52,166)(23,34,53,167)(24,35,54,168)(25,36,55,155)(26,37,56,156)(27,38,43,157)(28,39,44,158)(57,403,414,139)(58,404,415,140)(59,405,416,127)(60,406,417,128)(61,393,418,129)(62,394,419,130)(63,395,420,131)(64,396,407,132)(65,397,408,133)(66,398,409,134)(67,399,410,135)(68,400,411,136)(69,401,412,137)(70,402,413,138)(71,124,338,200)(72,125,339,201)(73,126,340,202)(74,113,341,203)(75,114,342,204)(76,115,343,205)(77,116,344,206)(78,117,345,207)(79,118,346,208)(80,119,347,209)(81,120,348,210)(82,121,349,197)(83,122,350,198)(84,123,337,199)(85,195,235,102)(86,196,236,103)(87,183,237,104)(88,184,238,105)(89,185,225,106)(90,186,226,107)(91,187,227,108)(92,188,228,109)(93,189,229,110)(94,190,230,111)(95,191,231,112)(96,192,232,99)(97,193,233,100)(98,194,234,101)(141,290,430,264)(142,291,431,265)(143,292,432,266)(144,293,433,253)(145,294,434,254)(146,281,421,255)(147,282,422,256)(148,283,423,257)(149,284,424,258)(150,285,425,259)(151,286,426,260)(152,287,427,261)(153,288,428,262)(154,289,429,263)(169,302,385,313)(170,303,386,314)(171,304,387,315)(172,305,388,316)(173,306,389,317)(174,307,390,318)(175,308,391,319)(176,295,392,320)(177,296,379,321)(178,297,380,322)(179,298,381,309)(180,299,382,310)(181,300,383,311)(182,301,384,312)(211,367,355,444)(212,368,356,445)(213,369,357,446)(214,370,358,447)(215,371,359,448)(216,372,360,435)(217,373,361,436)(218,374,362,437)(219,375,363,438)(220,376,364,439)(221,377,351,440)(222,378,352,441)(223,365,353,442)(224,366,354,443) );
G=PermutationGroup([[(1,50),(2,51),(3,52),(4,53),(5,54),(6,55),(7,56),(8,43),(9,44),(10,45),(11,46),(12,47),(13,48),(14,49),(15,326),(16,327),(17,328),(18,329),(19,330),(20,331),(21,332),(22,333),(23,334),(24,335),(25,336),(26,323),(27,324),(28,325),(29,248),(30,249),(31,250),(32,251),(33,252),(34,239),(35,240),(36,241),(37,242),(38,243),(39,244),(40,245),(41,246),(42,247),(57,292),(58,293),(59,294),(60,281),(61,282),(62,283),(63,284),(64,285),(65,286),(66,287),(67,288),(68,289),(69,290),(70,291),(71,174),(72,175),(73,176),(74,177),(75,178),(76,179),(77,180),(78,181),(79,182),(80,169),(81,170),(82,171),(83,172),(84,173),(85,363),(86,364),(87,351),(88,352),(89,353),(90,354),(91,355),(92,356),(93,357),(94,358),(95,359),(96,360),(97,361),(98,362),(99,372),(100,373),(101,374),(102,375),(103,376),(104,377),(105,378),(106,365),(107,366),(108,367),(109,368),(110,369),(111,370),(112,371),(113,296),(114,297),(115,298),(116,299),(117,300),(118,301),(119,302),(120,303),(121,304),(122,305),(123,306),(124,307),(125,308),(126,295),(127,145),(128,146),(129,147),(130,148),(131,149),(132,150),(133,151),(134,152),(135,153),(136,154),(137,141),(138,142),(139,143),(140,144),(155,277),(156,278),(157,279),(158,280),(159,267),(160,268),(161,269),(162,270),(163,271),(164,272),(165,273),(166,274),(167,275),(168,276),(183,440),(184,441),(185,442),(186,443),(187,444),(188,445),(189,446),(190,447),(191,448),(192,435),(193,436),(194,437),(195,438),(196,439),(197,315),(198,316),(199,317),(200,318),(201,319),(202,320),(203,321),(204,322),(205,309),(206,310),(207,311),(208,312),(209,313),(210,314),(211,227),(212,228),(213,229),(214,230),(215,231),(216,232),(217,233),(218,234),(219,235),(220,236),(221,237),(222,238),(223,225),(224,226),(253,415),(254,416),(255,417),(256,418),(257,419),(258,420),(259,407),(260,408),(261,409),(262,410),(263,411),(264,412),(265,413),(266,414),(337,389),(338,390),(339,391),(340,392),(341,379),(342,380),(343,381),(344,382),(345,383),(346,384),(347,385),(348,386),(349,387),(350,388),(393,422),(394,423),(395,424),(396,425),(397,426),(398,427),(399,428),(400,429),(401,430),(402,431),(403,432),(404,433),(405,434),(406,421)], [(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)], [(1,179,8,172),(2,178,9,171),(3,177,10,170),(4,176,11,169),(5,175,12,182),(6,174,13,181),(7,173,14,180),(15,348,22,341),(16,347,23,340),(17,346,24,339),(18,345,25,338),(19,344,26,337),(20,343,27,350),(21,342,28,349),(29,311,36,318),(30,310,37,317),(31,309,38,316),(32,322,39,315),(33,321,40,314),(34,320,41,313),(35,319,42,312),(43,83,50,76),(44,82,51,75),(45,81,52,74),(46,80,53,73),(47,79,54,72),(48,78,55,71),(49,77,56,84),(57,95,64,88),(58,94,65,87),(59,93,66,86),(60,92,67,85),(61,91,68,98),(62,90,69,97),(63,89,70,96),(99,149,106,142),(100,148,107,141),(101,147,108,154),(102,146,109,153),(103,145,110,152),(104,144,111,151),(105,143,112,150),(113,267,120,274),(114,280,121,273),(115,279,122,272),(116,278,123,271),(117,277,124,270),(118,276,125,269),(119,275,126,268),(127,369,134,376),(128,368,135,375),(129,367,136,374),(130,366,137,373),(131,365,138,372),(132,378,139,371),(133,377,140,370),(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),(183,433,190,426),(184,432,191,425),(185,431,192,424),(186,430,193,423),(187,429,194,422),(188,428,195,421),(189,427,196,434),(197,251,204,244),(198,250,205,243),(199,249,206,242),(200,248,207,241),(201,247,208,240),(202,246,209,239),(203,245,210,252),(211,263,218,256),(212,262,219,255),(213,261,220,254),(214,260,221,253),(215,259,222,266),(216,258,223,265),(217,257,224,264),(225,413,232,420),(226,412,233,419),(227,411,234,418),(228,410,235,417),(229,409,236,416),(230,408,237,415),(231,407,238,414),(281,356,288,363),(282,355,289,362),(283,354,290,361),(284,353,291,360),(285,352,292,359),(286,351,293,358),(287,364,294,357),(323,389,330,382),(324,388,331,381),(325,387,332,380),(326,386,333,379),(327,385,334,392),(328,384,335,391),(329,383,336,390),(393,444,400,437),(394,443,401,436),(395,442,402,435),(396,441,403,448),(397,440,404,447),(398,439,405,446),(399,438,406,445)], [(1,226,324,97),(2,225,325,96),(3,238,326,95),(4,237,327,94),(5,236,328,93),(6,235,329,92),(7,234,330,91),(8,233,331,90),(9,232,332,89),(10,231,333,88),(11,230,334,87),(12,229,335,86),(13,228,336,85),(14,227,323,98),(15,359,52,222),(16,358,53,221),(17,357,54,220),(18,356,55,219),(19,355,56,218),(20,354,43,217),(21,353,44,216),(22,352,45,215),(23,351,46,214),(24,364,47,213),(25,363,48,212),(26,362,49,211),(27,361,50,224),(28,360,51,223),(29,102,155,188),(30,101,156,187),(31,100,157,186),(32,99,158,185),(33,112,159,184),(34,111,160,183),(35,110,161,196),(36,109,162,195),(37,108,163,194),(38,107,164,193),(39,106,165,192),(40,105,166,191),(41,104,167,190),(42,103,168,189),(57,74,407,348),(58,73,408,347),(59,72,409,346),(60,71,410,345),(61,84,411,344),(62,83,412,343),(63,82,413,342),(64,81,414,341),(65,80,415,340),(66,79,416,339),(67,78,417,338),(68,77,418,337),(69,76,419,350),(70,75,420,349),(113,432,210,150),(114,431,197,149),(115,430,198,148),(116,429,199,147),(117,428,200,146),(118,427,201,145),(119,426,202,144),(120,425,203,143),(121,424,204,142),(122,423,205,141),(123,422,206,154),(124,421,207,153),(125,434,208,152),(126,433,209,151),(127,301,398,319),(128,300,399,318),(129,299,400,317),(130,298,401,316),(131,297,402,315),(132,296,403,314),(133,295,404,313),(134,308,405,312),(135,307,406,311),(136,306,393,310),(137,305,394,309),(138,304,395,322),(139,303,396,321),(140,302,397,320),(169,253,392,286),(170,266,379,285),(171,265,380,284),(172,264,381,283),(173,263,382,282),(174,262,383,281),(175,261,384,294),(176,260,385,293),(177,259,386,292),(178,258,387,291),(179,257,388,290),(180,256,389,289),(181,255,390,288),(182,254,391,287),(239,370,268,440),(240,369,269,439),(241,368,270,438),(242,367,271,437),(243,366,272,436),(244,365,273,435),(245,378,274,448),(246,377,275,447),(247,376,276,446),(248,375,277,445),(249,374,278,444),(250,373,279,443),(251,372,280,442),(252,371,267,441)], [(1,272,331,250),(2,273,332,251),(3,274,333,252),(4,275,334,239),(5,276,335,240),(6,277,336,241),(7,278,323,242),(8,279,324,243),(9,280,325,244),(10,267,326,245),(11,268,327,246),(12,269,328,247),(13,270,329,248),(14,271,330,249),(15,40,45,159),(16,41,46,160),(17,42,47,161),(18,29,48,162),(19,30,49,163),(20,31,50,164),(21,32,51,165),(22,33,52,166),(23,34,53,167),(24,35,54,168),(25,36,55,155),(26,37,56,156),(27,38,43,157),(28,39,44,158),(57,403,414,139),(58,404,415,140),(59,405,416,127),(60,406,417,128),(61,393,418,129),(62,394,419,130),(63,395,420,131),(64,396,407,132),(65,397,408,133),(66,398,409,134),(67,399,410,135),(68,400,411,136),(69,401,412,137),(70,402,413,138),(71,124,338,200),(72,125,339,201),(73,126,340,202),(74,113,341,203),(75,114,342,204),(76,115,343,205),(77,116,344,206),(78,117,345,207),(79,118,346,208),(80,119,347,209),(81,120,348,210),(82,121,349,197),(83,122,350,198),(84,123,337,199),(85,195,235,102),(86,196,236,103),(87,183,237,104),(88,184,238,105),(89,185,225,106),(90,186,226,107),(91,187,227,108),(92,188,228,109),(93,189,229,110),(94,190,230,111),(95,191,231,112),(96,192,232,99),(97,193,233,100),(98,194,234,101),(141,290,430,264),(142,291,431,265),(143,292,432,266),(144,293,433,253),(145,294,434,254),(146,281,421,255),(147,282,422,256),(148,283,423,257),(149,284,424,258),(150,285,425,259),(151,286,426,260),(152,287,427,261),(153,288,428,262),(154,289,429,263),(169,302,385,313),(170,303,386,314),(171,304,387,315),(172,305,388,316),(173,306,389,317),(174,307,390,318),(175,308,391,319),(176,295,392,320),(177,296,379,321),(178,297,380,322),(179,298,381,309),(180,299,382,310),(181,300,383,311),(182,301,384,312),(211,367,355,444),(212,368,356,445),(213,369,357,446),(214,370,358,447),(215,371,359,448),(216,372,360,435),(217,373,361,436),(218,374,362,437),(219,375,363,438),(220,376,364,439),(221,377,351,440),(222,378,352,441),(223,365,353,442),(224,366,354,443)]])
82 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4F | 4G | ··· | 4N | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 4 | ··· | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | - | + | + | + | - | - | ||
| image | C1 | C2 | C2 | C2 | D4 | Q8 | D7 | C4○D4 | D14 | C4○D28 | D4×D7 | D4⋊2D7 | Q8×D7 |
| kernel | (C2×Dic7).Q8 | C14.C42 | C7×C2.C42 | C2×Dic7⋊C4 | C2×Dic7 | C2×Dic7 | C2.C42 | C2×C14 | C22×C4 | C22 | C22 | C22 | C22 |
| # reps | 1 | 4 | 1 | 2 | 2 | 2 | 3 | 10 | 9 | 36 | 3 | 6 | 3 |
Matrix representation of (C2×Dic7).Q8 ►in GL6(𝔽29)
| 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 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 4 | 1 | 0 | 0 | 0 | 0 |
| 27 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 3 | 27 | 0 | 0 | 0 | 0 |
| 5 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 10 | 0 | 0 |
| 0 | 0 | 11 | 23 | 0 | 0 |
| 0 | 0 | 0 | 0 | 26 | 5 |
| 0 | 0 | 0 | 0 | 27 | 3 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 3 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 7 | 0 | 0 |
| 0 | 0 | 5 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 | 26 |
| 0 | 0 | 0 | 0 | 18 | 13 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 5 | 0 | 0 |
| 0 | 0 | 12 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 27 |
| 0 | 0 | 0 | 0 | 24 | 22 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[4,27,0,0,0,0,1,7,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[3,5,0,0,0,0,27,26,0,0,0,0,0,0,6,11,0,0,0,0,10,23,0,0,0,0,0,0,26,27,0,0,0,0,5,3],[1,3,0,0,0,0,0,28,0,0,0,0,0,0,16,5,0,0,0,0,7,13,0,0,0,0,0,0,16,18,0,0,0,0,26,13],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,12,0,0,0,0,5,17,0,0,0,0,0,0,7,24,0,0,0,0,27,22] >;
(C2×Dic7).Q8 in GAP, Magma, Sage, TeX
(C_2\times {\rm Dic}_7).Q_8 % in TeX
G:=Group("(C2xDic7).Q8"); // GroupNames label
G:=SmallGroup(448,192);
// by ID
G=gap.SmallGroup(448,192);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,64,590,387,100,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^14=d^4=1,c^2=b^7,e^2=b^7*d^2,a*b=b*a,e*c*e^-1=a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=d*b*d^-1=b^-1,b*e=e*b,d*c*d^-1=a*b^7*c,e*d*e^-1=a*d^-1>;
// generators/relations