direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic7⋊Q8, C14⋊3(C4⋊Q8), Dic7⋊3(C2×Q8), (C2×Dic7)⋊10Q8, C28.257(C2×D4), (C2×C28).213D4, (C22×Q8).8D7, C22.35(Q8×D7), (C2×Q8).186D14, C14.51(C22×Q8), (C2×C28).645C23, (C2×C14).302C24, (C22×C4).275D14, C14.152(C22×D4), (Q8×C14).231C22, C23.339(C22×D7), C22.315(C23×D7), Dic7⋊C4.170C22, (C22×C28).282C22, (C22×C14).420C23, (C2×Dic7).156C23, (C4×Dic7).259C22, (C22×Dic14).19C2, (C2×Dic14).307C22, (C22×Dic7).233C22, C7⋊4(C2×C4⋊Q8), C2.34(C2×Q8×D7), (Q8×C2×C14).7C2, C4.27(C2×C7⋊D4), (C2×C14).96(C2×Q8), (C2×C4×Dic7).16C2, (C2×C14).587(C2×D4), C2.25(C22×C7⋊D4), (C2×C4).156(C7⋊D4), (C2×Dic7⋊C4).34C2, (C2×C4).241(C22×D7), C22.115(C2×C7⋊D4), SmallGroup(448,1263)
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=d2, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, dcd-1=b7c, ce=ec, ede-1=d-1 >
Subgroups: 1012 in 290 conjugacy classes, 143 normal (15 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, Q8, C23, C14, C14, C42, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×Q8, C2×Q8, Dic7, Dic7, C28, C28, C2×C14, C2×C14, C2×C42, C2×C4⋊C4, C4⋊Q8, C22×Q8, C22×Q8, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×C14, C2×C4⋊Q8, C4×Dic7, Dic7⋊C4, C2×Dic14, C2×Dic14, C22×Dic7, C22×C28, C22×C28, Q8×C14, Q8×C14, C2×C4×Dic7, C2×Dic7⋊C4, Dic7⋊Q8, C22×Dic14, Q8×C2×C14, C2×Dic7⋊Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C24, D14, C4⋊Q8, C22×D4, C22×Q8, C7⋊D4, C22×D7, C2×C4⋊Q8, Q8×D7, C2×C7⋊D4, C23×D7, Dic7⋊Q8, C2×Q8×D7, C22×C7⋊D4, C2×Dic7⋊Q8
►Regular action on 448 points
Generators in S448
(1 120)(2 121)(3 122)(4 123)(5 124)(6 125)(7 126)(8 113)(9 114)(10 115)(11 116)(12 117)(13 118)(14 119)(15 134)(16 135)(17 136)(18 137)(19 138)(20 139)(21 140)(22 127)(23 128)(24 129)(25 130)(26 131)(27 132)(28 133)(29 148)(30 149)(31 150)(32 151)(33 152)(34 153)(35 154)(36 141)(37 142)(38 143)(39 144)(40 145)(41 146)(42 147)(43 162)(44 163)(45 164)(46 165)(47 166)(48 167)(49 168)(50 155)(51 156)(52 157)(53 158)(54 159)(55 160)(56 161)(57 169)(58 170)(59 171)(60 172)(61 173)(62 174)(63 175)(64 176)(65 177)(66 178)(67 179)(68 180)(69 181)(70 182)(71 183)(72 184)(73 185)(74 186)(75 187)(76 188)(77 189)(78 190)(79 191)(80 192)(81 193)(82 194)(83 195)(84 196)(85 204)(86 205)(87 206)(88 207)(89 208)(90 209)(91 210)(92 197)(93 198)(94 199)(95 200)(96 201)(97 202)(98 203)(99 218)(100 219)(101 220)(102 221)(103 222)(104 223)(105 224)(106 211)(107 212)(108 213)(109 214)(110 215)(111 216)(112 217)(225 344)(226 345)(227 346)(228 347)(229 348)(230 349)(231 350)(232 337)(233 338)(234 339)(235 340)(236 341)(237 342)(238 343)(239 358)(240 359)(241 360)(242 361)(243 362)(244 363)(245 364)(246 351)(247 352)(248 353)(249 354)(250 355)(251 356)(252 357)(253 378)(254 365)(255 366)(256 367)(257 368)(258 369)(259 370)(260 371)(261 372)(262 373)(263 374)(264 375)(265 376)(266 377)(267 382)(268 383)(269 384)(270 385)(271 386)(272 387)(273 388)(274 389)(275 390)(276 391)(277 392)(278 379)(279 380)(280 381)(281 400)(282 401)(283 402)(284 403)(285 404)(286 405)(287 406)(288 393)(289 394)(290 395)(291 396)(292 397)(293 398)(294 399)(295 409)(296 410)(297 411)(298 412)(299 413)(300 414)(301 415)(302 416)(303 417)(304 418)(305 419)(306 420)(307 407)(308 408)(309 434)(310 421)(311 422)(312 423)(313 424)(314 425)(315 426)(316 427)(317 428)(318 429)(319 430)(320 431)(321 432)(322 433)(323 447)(324 448)(325 435)(326 436)(327 437)(328 438)(329 439)(330 440)(331 441)(332 442)(333 443)(334 444)(335 445)(336 446)
(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)
(1 357 8 364)(2 356 9 363)(3 355 10 362)(4 354 11 361)(5 353 12 360)(6 352 13 359)(7 351 14 358)(15 343 22 350)(16 342 23 349)(17 341 24 348)(18 340 25 347)(19 339 26 346)(20 338 27 345)(21 337 28 344)(29 381 36 388)(30 380 37 387)(31 379 38 386)(32 392 39 385)(33 391 40 384)(34 390 41 383)(35 389 42 382)(43 369 50 376)(44 368 51 375)(45 367 52 374)(46 366 53 373)(47 365 54 372)(48 378 55 371)(49 377 56 370)(57 408 64 415)(58 407 65 414)(59 420 66 413)(60 419 67 412)(61 418 68 411)(62 417 69 410)(63 416 70 409)(71 403 78 396)(72 402 79 395)(73 401 80 394)(74 400 81 393)(75 399 82 406)(76 398 83 405)(77 397 84 404)(85 436 92 443)(86 435 93 442)(87 448 94 441)(88 447 95 440)(89 446 96 439)(90 445 97 438)(91 444 98 437)(99 428 106 421)(100 427 107 434)(101 426 108 433)(102 425 109 432)(103 424 110 431)(104 423 111 430)(105 422 112 429)(113 245 120 252)(114 244 121 251)(115 243 122 250)(116 242 123 249)(117 241 124 248)(118 240 125 247)(119 239 126 246)(127 231 134 238)(128 230 135 237)(129 229 136 236)(130 228 137 235)(131 227 138 234)(132 226 139 233)(133 225 140 232)(141 273 148 280)(142 272 149 279)(143 271 150 278)(144 270 151 277)(145 269 152 276)(146 268 153 275)(147 267 154 274)(155 265 162 258)(156 264 163 257)(157 263 164 256)(158 262 165 255)(159 261 166 254)(160 260 167 253)(161 259 168 266)(169 308 176 301)(170 307 177 300)(171 306 178 299)(172 305 179 298)(173 304 180 297)(174 303 181 296)(175 302 182 295)(183 284 190 291)(184 283 191 290)(185 282 192 289)(186 281 193 288)(187 294 194 287)(188 293 195 286)(189 292 196 285)(197 333 204 326)(198 332 205 325)(199 331 206 324)(200 330 207 323)(201 329 208 336)(202 328 209 335)(203 327 210 334)(211 310 218 317)(212 309 219 316)(213 322 220 315)(214 321 221 314)(215 320 222 313)(216 319 223 312)(217 318 224 311)
(1 218 15 204)(2 219 16 205)(3 220 17 206)(4 221 18 207)(5 222 19 208)(6 223 20 209)(7 224 21 210)(8 211 22 197)(9 212 23 198)(10 213 24 199)(11 214 25 200)(12 215 26 201)(13 216 27 202)(14 217 28 203)(29 169 50 183)(30 170 51 184)(31 171 52 185)(32 172 53 186)(33 173 54 187)(34 174 55 188)(35 175 56 189)(36 176 43 190)(37 177 44 191)(38 178 45 192)(39 179 46 193)(40 180 47 194)(41 181 48 195)(42 182 49 196)(57 155 71 148)(58 156 72 149)(59 157 73 150)(60 158 74 151)(61 159 75 152)(62 160 76 153)(63 161 77 154)(64 162 78 141)(65 163 79 142)(66 164 80 143)(67 165 81 144)(68 166 82 145)(69 167 83 146)(70 168 84 147)(85 120 99 134)(86 121 100 135)(87 122 101 136)(88 123 102 137)(89 124 103 138)(90 125 104 139)(91 126 105 140)(92 113 106 127)(93 114 107 128)(94 115 108 129)(95 116 109 130)(96 117 110 131)(97 118 111 132)(98 119 112 133)(225 444 239 422)(226 445 240 423)(227 446 241 424)(228 447 242 425)(229 448 243 426)(230 435 244 427)(231 436 245 428)(232 437 246 429)(233 438 247 430)(234 439 248 431)(235 440 249 432)(236 441 250 433)(237 442 251 434)(238 443 252 421)(253 398 268 417)(254 399 269 418)(255 400 270 419)(256 401 271 420)(257 402 272 407)(258 403 273 408)(259 404 274 409)(260 405 275 410)(261 406 276 411)(262 393 277 412)(263 394 278 413)(264 395 279 414)(265 396 280 415)(266 397 267 416)(281 385 305 366)(282 386 306 367)(283 387 307 368)(284 388 308 369)(285 389 295 370)(286 390 296 371)(287 391 297 372)(288 392 298 373)(289 379 299 374)(290 380 300 375)(291 381 301 376)(292 382 302 377)(293 383 303 378)(294 384 304 365)(309 342 332 356)(310 343 333 357)(311 344 334 358)(312 345 335 359)(313 346 336 360)(314 347 323 361)(315 348 324 362)(316 349 325 363)(317 350 326 364)(318 337 327 351)(319 338 328 352)(320 339 329 353)(321 340 330 354)(322 341 331 355)
(1 71 15 57)(2 72 16 58)(3 73 17 59)(4 74 18 60)(5 75 19 61)(6 76 20 62)(7 77 21 63)(8 78 22 64)(9 79 23 65)(10 80 24 66)(11 81 25 67)(12 82 26 68)(13 83 27 69)(14 84 28 70)(29 99 50 85)(30 100 51 86)(31 101 52 87)(32 102 53 88)(33 103 54 89)(34 104 55 90)(35 105 56 91)(36 106 43 92)(37 107 44 93)(38 108 45 94)(39 109 46 95)(40 110 47 96)(41 111 48 97)(42 112 49 98)(113 190 127 176)(114 191 128 177)(115 192 129 178)(116 193 130 179)(117 194 131 180)(118 195 132 181)(119 196 133 182)(120 183 134 169)(121 184 135 170)(122 185 136 171)(123 186 137 172)(124 187 138 173)(125 188 139 174)(126 189 140 175)(141 211 162 197)(142 212 163 198)(143 213 164 199)(144 214 165 200)(145 215 166 201)(146 216 167 202)(147 217 168 203)(148 218 155 204)(149 219 156 205)(150 220 157 206)(151 221 158 207)(152 222 159 208)(153 223 160 209)(154 224 161 210)(225 295 239 285)(226 296 240 286)(227 297 241 287)(228 298 242 288)(229 299 243 289)(230 300 244 290)(231 301 245 291)(232 302 246 292)(233 303 247 293)(234 304 248 294)(235 305 249 281)(236 306 250 282)(237 307 251 283)(238 308 252 284)(253 328 268 319)(254 329 269 320)(255 330 270 321)(256 331 271 322)(257 332 272 309)(258 333 273 310)(259 334 274 311)(260 335 275 312)(261 336 276 313)(262 323 277 314)(263 324 278 315)(264 325 279 316)(265 326 280 317)(266 327 267 318)(337 416 351 397)(338 417 352 398)(339 418 353 399)(340 419 354 400)(341 420 355 401)(342 407 356 402)(343 408 357 403)(344 409 358 404)(345 410 359 405)(346 411 360 406)(347 412 361 393)(348 413 362 394)(349 414 363 395)(350 415 364 396)(365 439 384 431)(366 440 385 432)(367 441 386 433)(368 442 387 434)(369 443 388 421)(370 444 389 422)(371 445 390 423)(372 446 391 424)(373 447 392 425)(374 448 379 426)(375 435 380 427)(376 436 381 428)(377 437 382 429)(378 438 383 430)
G:=sub<Sym(448)| (1,120)(2,121)(3,122)(4,123)(5,124)(6,125)(7,126)(8,113)(9,114)(10,115)(11,116)(12,117)(13,118)(14,119)(15,134)(16,135)(17,136)(18,137)(19,138)(20,139)(21,140)(22,127)(23,128)(24,129)(25,130)(26,131)(27,132)(28,133)(29,148)(30,149)(31,150)(32,151)(33,152)(34,153)(35,154)(36,141)(37,142)(38,143)(39,144)(40,145)(41,146)(42,147)(43,162)(44,163)(45,164)(46,165)(47,166)(48,167)(49,168)(50,155)(51,156)(52,157)(53,158)(54,159)(55,160)(56,161)(57,169)(58,170)(59,171)(60,172)(61,173)(62,174)(63,175)(64,176)(65,177)(66,178)(67,179)(68,180)(69,181)(70,182)(71,183)(72,184)(73,185)(74,186)(75,187)(76,188)(77,189)(78,190)(79,191)(80,192)(81,193)(82,194)(83,195)(84,196)(85,204)(86,205)(87,206)(88,207)(89,208)(90,209)(91,210)(92,197)(93,198)(94,199)(95,200)(96,201)(97,202)(98,203)(99,218)(100,219)(101,220)(102,221)(103,222)(104,223)(105,224)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)(112,217)(225,344)(226,345)(227,346)(228,347)(229,348)(230,349)(231,350)(232,337)(233,338)(234,339)(235,340)(236,341)(237,342)(238,343)(239,358)(240,359)(241,360)(242,361)(243,362)(244,363)(245,364)(246,351)(247,352)(248,353)(249,354)(250,355)(251,356)(252,357)(253,378)(254,365)(255,366)(256,367)(257,368)(258,369)(259,370)(260,371)(261,372)(262,373)(263,374)(264,375)(265,376)(266,377)(267,382)(268,383)(269,384)(270,385)(271,386)(272,387)(273,388)(274,389)(275,390)(276,391)(277,392)(278,379)(279,380)(280,381)(281,400)(282,401)(283,402)(284,403)(285,404)(286,405)(287,406)(288,393)(289,394)(290,395)(291,396)(292,397)(293,398)(294,399)(295,409)(296,410)(297,411)(298,412)(299,413)(300,414)(301,415)(302,416)(303,417)(304,418)(305,419)(306,420)(307,407)(308,408)(309,434)(310,421)(311,422)(312,423)(313,424)(314,425)(315,426)(316,427)(317,428)(318,429)(319,430)(320,431)(321,432)(322,433)(323,447)(324,448)(325,435)(326,436)(327,437)(328,438)(329,439)(330,440)(331,441)(332,442)(333,443)(334,444)(335,445)(336,446), (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), (1,357,8,364)(2,356,9,363)(3,355,10,362)(4,354,11,361)(5,353,12,360)(6,352,13,359)(7,351,14,358)(15,343,22,350)(16,342,23,349)(17,341,24,348)(18,340,25,347)(19,339,26,346)(20,338,27,345)(21,337,28,344)(29,381,36,388)(30,380,37,387)(31,379,38,386)(32,392,39,385)(33,391,40,384)(34,390,41,383)(35,389,42,382)(43,369,50,376)(44,368,51,375)(45,367,52,374)(46,366,53,373)(47,365,54,372)(48,378,55,371)(49,377,56,370)(57,408,64,415)(58,407,65,414)(59,420,66,413)(60,419,67,412)(61,418,68,411)(62,417,69,410)(63,416,70,409)(71,403,78,396)(72,402,79,395)(73,401,80,394)(74,400,81,393)(75,399,82,406)(76,398,83,405)(77,397,84,404)(85,436,92,443)(86,435,93,442)(87,448,94,441)(88,447,95,440)(89,446,96,439)(90,445,97,438)(91,444,98,437)(99,428,106,421)(100,427,107,434)(101,426,108,433)(102,425,109,432)(103,424,110,431)(104,423,111,430)(105,422,112,429)(113,245,120,252)(114,244,121,251)(115,243,122,250)(116,242,123,249)(117,241,124,248)(118,240,125,247)(119,239,126,246)(127,231,134,238)(128,230,135,237)(129,229,136,236)(130,228,137,235)(131,227,138,234)(132,226,139,233)(133,225,140,232)(141,273,148,280)(142,272,149,279)(143,271,150,278)(144,270,151,277)(145,269,152,276)(146,268,153,275)(147,267,154,274)(155,265,162,258)(156,264,163,257)(157,263,164,256)(158,262,165,255)(159,261,166,254)(160,260,167,253)(161,259,168,266)(169,308,176,301)(170,307,177,300)(171,306,178,299)(172,305,179,298)(173,304,180,297)(174,303,181,296)(175,302,182,295)(183,284,190,291)(184,283,191,290)(185,282,192,289)(186,281,193,288)(187,294,194,287)(188,293,195,286)(189,292,196,285)(197,333,204,326)(198,332,205,325)(199,331,206,324)(200,330,207,323)(201,329,208,336)(202,328,209,335)(203,327,210,334)(211,310,218,317)(212,309,219,316)(213,322,220,315)(214,321,221,314)(215,320,222,313)(216,319,223,312)(217,318,224,311), (1,218,15,204)(2,219,16,205)(3,220,17,206)(4,221,18,207)(5,222,19,208)(6,223,20,209)(7,224,21,210)(8,211,22,197)(9,212,23,198)(10,213,24,199)(11,214,25,200)(12,215,26,201)(13,216,27,202)(14,217,28,203)(29,169,50,183)(30,170,51,184)(31,171,52,185)(32,172,53,186)(33,173,54,187)(34,174,55,188)(35,175,56,189)(36,176,43,190)(37,177,44,191)(38,178,45,192)(39,179,46,193)(40,180,47,194)(41,181,48,195)(42,182,49,196)(57,155,71,148)(58,156,72,149)(59,157,73,150)(60,158,74,151)(61,159,75,152)(62,160,76,153)(63,161,77,154)(64,162,78,141)(65,163,79,142)(66,164,80,143)(67,165,81,144)(68,166,82,145)(69,167,83,146)(70,168,84,147)(85,120,99,134)(86,121,100,135)(87,122,101,136)(88,123,102,137)(89,124,103,138)(90,125,104,139)(91,126,105,140)(92,113,106,127)(93,114,107,128)(94,115,108,129)(95,116,109,130)(96,117,110,131)(97,118,111,132)(98,119,112,133)(225,444,239,422)(226,445,240,423)(227,446,241,424)(228,447,242,425)(229,448,243,426)(230,435,244,427)(231,436,245,428)(232,437,246,429)(233,438,247,430)(234,439,248,431)(235,440,249,432)(236,441,250,433)(237,442,251,434)(238,443,252,421)(253,398,268,417)(254,399,269,418)(255,400,270,419)(256,401,271,420)(257,402,272,407)(258,403,273,408)(259,404,274,409)(260,405,275,410)(261,406,276,411)(262,393,277,412)(263,394,278,413)(264,395,279,414)(265,396,280,415)(266,397,267,416)(281,385,305,366)(282,386,306,367)(283,387,307,368)(284,388,308,369)(285,389,295,370)(286,390,296,371)(287,391,297,372)(288,392,298,373)(289,379,299,374)(290,380,300,375)(291,381,301,376)(292,382,302,377)(293,383,303,378)(294,384,304,365)(309,342,332,356)(310,343,333,357)(311,344,334,358)(312,345,335,359)(313,346,336,360)(314,347,323,361)(315,348,324,362)(316,349,325,363)(317,350,326,364)(318,337,327,351)(319,338,328,352)(320,339,329,353)(321,340,330,354)(322,341,331,355), (1,71,15,57)(2,72,16,58)(3,73,17,59)(4,74,18,60)(5,75,19,61)(6,76,20,62)(7,77,21,63)(8,78,22,64)(9,79,23,65)(10,80,24,66)(11,81,25,67)(12,82,26,68)(13,83,27,69)(14,84,28,70)(29,99,50,85)(30,100,51,86)(31,101,52,87)(32,102,53,88)(33,103,54,89)(34,104,55,90)(35,105,56,91)(36,106,43,92)(37,107,44,93)(38,108,45,94)(39,109,46,95)(40,110,47,96)(41,111,48,97)(42,112,49,98)(113,190,127,176)(114,191,128,177)(115,192,129,178)(116,193,130,179)(117,194,131,180)(118,195,132,181)(119,196,133,182)(120,183,134,169)(121,184,135,170)(122,185,136,171)(123,186,137,172)(124,187,138,173)(125,188,139,174)(126,189,140,175)(141,211,162,197)(142,212,163,198)(143,213,164,199)(144,214,165,200)(145,215,166,201)(146,216,167,202)(147,217,168,203)(148,218,155,204)(149,219,156,205)(150,220,157,206)(151,221,158,207)(152,222,159,208)(153,223,160,209)(154,224,161,210)(225,295,239,285)(226,296,240,286)(227,297,241,287)(228,298,242,288)(229,299,243,289)(230,300,244,290)(231,301,245,291)(232,302,246,292)(233,303,247,293)(234,304,248,294)(235,305,249,281)(236,306,250,282)(237,307,251,283)(238,308,252,284)(253,328,268,319)(254,329,269,320)(255,330,270,321)(256,331,271,322)(257,332,272,309)(258,333,273,310)(259,334,274,311)(260,335,275,312)(261,336,276,313)(262,323,277,314)(263,324,278,315)(264,325,279,316)(265,326,280,317)(266,327,267,318)(337,416,351,397)(338,417,352,398)(339,418,353,399)(340,419,354,400)(341,420,355,401)(342,407,356,402)(343,408,357,403)(344,409,358,404)(345,410,359,405)(346,411,360,406)(347,412,361,393)(348,413,362,394)(349,414,363,395)(350,415,364,396)(365,439,384,431)(366,440,385,432)(367,441,386,433)(368,442,387,434)(369,443,388,421)(370,444,389,422)(371,445,390,423)(372,446,391,424)(373,447,392,425)(374,448,379,426)(375,435,380,427)(376,436,381,428)(377,437,382,429)(378,438,383,430)>;
G:=Group( (1,120)(2,121)(3,122)(4,123)(5,124)(6,125)(7,126)(8,113)(9,114)(10,115)(11,116)(12,117)(13,118)(14,119)(15,134)(16,135)(17,136)(18,137)(19,138)(20,139)(21,140)(22,127)(23,128)(24,129)(25,130)(26,131)(27,132)(28,133)(29,148)(30,149)(31,150)(32,151)(33,152)(34,153)(35,154)(36,141)(37,142)(38,143)(39,144)(40,145)(41,146)(42,147)(43,162)(44,163)(45,164)(46,165)(47,166)(48,167)(49,168)(50,155)(51,156)(52,157)(53,158)(54,159)(55,160)(56,161)(57,169)(58,170)(59,171)(60,172)(61,173)(62,174)(63,175)(64,176)(65,177)(66,178)(67,179)(68,180)(69,181)(70,182)(71,183)(72,184)(73,185)(74,186)(75,187)(76,188)(77,189)(78,190)(79,191)(80,192)(81,193)(82,194)(83,195)(84,196)(85,204)(86,205)(87,206)(88,207)(89,208)(90,209)(91,210)(92,197)(93,198)(94,199)(95,200)(96,201)(97,202)(98,203)(99,218)(100,219)(101,220)(102,221)(103,222)(104,223)(105,224)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)(112,217)(225,344)(226,345)(227,346)(228,347)(229,348)(230,349)(231,350)(232,337)(233,338)(234,339)(235,340)(236,341)(237,342)(238,343)(239,358)(240,359)(241,360)(242,361)(243,362)(244,363)(245,364)(246,351)(247,352)(248,353)(249,354)(250,355)(251,356)(252,357)(253,378)(254,365)(255,366)(256,367)(257,368)(258,369)(259,370)(260,371)(261,372)(262,373)(263,374)(264,375)(265,376)(266,377)(267,382)(268,383)(269,384)(270,385)(271,386)(272,387)(273,388)(274,389)(275,390)(276,391)(277,392)(278,379)(279,380)(280,381)(281,400)(282,401)(283,402)(284,403)(285,404)(286,405)(287,406)(288,393)(289,394)(290,395)(291,396)(292,397)(293,398)(294,399)(295,409)(296,410)(297,411)(298,412)(299,413)(300,414)(301,415)(302,416)(303,417)(304,418)(305,419)(306,420)(307,407)(308,408)(309,434)(310,421)(311,422)(312,423)(313,424)(314,425)(315,426)(316,427)(317,428)(318,429)(319,430)(320,431)(321,432)(322,433)(323,447)(324,448)(325,435)(326,436)(327,437)(328,438)(329,439)(330,440)(331,441)(332,442)(333,443)(334,444)(335,445)(336,446), (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), (1,357,8,364)(2,356,9,363)(3,355,10,362)(4,354,11,361)(5,353,12,360)(6,352,13,359)(7,351,14,358)(15,343,22,350)(16,342,23,349)(17,341,24,348)(18,340,25,347)(19,339,26,346)(20,338,27,345)(21,337,28,344)(29,381,36,388)(30,380,37,387)(31,379,38,386)(32,392,39,385)(33,391,40,384)(34,390,41,383)(35,389,42,382)(43,369,50,376)(44,368,51,375)(45,367,52,374)(46,366,53,373)(47,365,54,372)(48,378,55,371)(49,377,56,370)(57,408,64,415)(58,407,65,414)(59,420,66,413)(60,419,67,412)(61,418,68,411)(62,417,69,410)(63,416,70,409)(71,403,78,396)(72,402,79,395)(73,401,80,394)(74,400,81,393)(75,399,82,406)(76,398,83,405)(77,397,84,404)(85,436,92,443)(86,435,93,442)(87,448,94,441)(88,447,95,440)(89,446,96,439)(90,445,97,438)(91,444,98,437)(99,428,106,421)(100,427,107,434)(101,426,108,433)(102,425,109,432)(103,424,110,431)(104,423,111,430)(105,422,112,429)(113,245,120,252)(114,244,121,251)(115,243,122,250)(116,242,123,249)(117,241,124,248)(118,240,125,247)(119,239,126,246)(127,231,134,238)(128,230,135,237)(129,229,136,236)(130,228,137,235)(131,227,138,234)(132,226,139,233)(133,225,140,232)(141,273,148,280)(142,272,149,279)(143,271,150,278)(144,270,151,277)(145,269,152,276)(146,268,153,275)(147,267,154,274)(155,265,162,258)(156,264,163,257)(157,263,164,256)(158,262,165,255)(159,261,166,254)(160,260,167,253)(161,259,168,266)(169,308,176,301)(170,307,177,300)(171,306,178,299)(172,305,179,298)(173,304,180,297)(174,303,181,296)(175,302,182,295)(183,284,190,291)(184,283,191,290)(185,282,192,289)(186,281,193,288)(187,294,194,287)(188,293,195,286)(189,292,196,285)(197,333,204,326)(198,332,205,325)(199,331,206,324)(200,330,207,323)(201,329,208,336)(202,328,209,335)(203,327,210,334)(211,310,218,317)(212,309,219,316)(213,322,220,315)(214,321,221,314)(215,320,222,313)(216,319,223,312)(217,318,224,311), (1,218,15,204)(2,219,16,205)(3,220,17,206)(4,221,18,207)(5,222,19,208)(6,223,20,209)(7,224,21,210)(8,211,22,197)(9,212,23,198)(10,213,24,199)(11,214,25,200)(12,215,26,201)(13,216,27,202)(14,217,28,203)(29,169,50,183)(30,170,51,184)(31,171,52,185)(32,172,53,186)(33,173,54,187)(34,174,55,188)(35,175,56,189)(36,176,43,190)(37,177,44,191)(38,178,45,192)(39,179,46,193)(40,180,47,194)(41,181,48,195)(42,182,49,196)(57,155,71,148)(58,156,72,149)(59,157,73,150)(60,158,74,151)(61,159,75,152)(62,160,76,153)(63,161,77,154)(64,162,78,141)(65,163,79,142)(66,164,80,143)(67,165,81,144)(68,166,82,145)(69,167,83,146)(70,168,84,147)(85,120,99,134)(86,121,100,135)(87,122,101,136)(88,123,102,137)(89,124,103,138)(90,125,104,139)(91,126,105,140)(92,113,106,127)(93,114,107,128)(94,115,108,129)(95,116,109,130)(96,117,110,131)(97,118,111,132)(98,119,112,133)(225,444,239,422)(226,445,240,423)(227,446,241,424)(228,447,242,425)(229,448,243,426)(230,435,244,427)(231,436,245,428)(232,437,246,429)(233,438,247,430)(234,439,248,431)(235,440,249,432)(236,441,250,433)(237,442,251,434)(238,443,252,421)(253,398,268,417)(254,399,269,418)(255,400,270,419)(256,401,271,420)(257,402,272,407)(258,403,273,408)(259,404,274,409)(260,405,275,410)(261,406,276,411)(262,393,277,412)(263,394,278,413)(264,395,279,414)(265,396,280,415)(266,397,267,416)(281,385,305,366)(282,386,306,367)(283,387,307,368)(284,388,308,369)(285,389,295,370)(286,390,296,371)(287,391,297,372)(288,392,298,373)(289,379,299,374)(290,380,300,375)(291,381,301,376)(292,382,302,377)(293,383,303,378)(294,384,304,365)(309,342,332,356)(310,343,333,357)(311,344,334,358)(312,345,335,359)(313,346,336,360)(314,347,323,361)(315,348,324,362)(316,349,325,363)(317,350,326,364)(318,337,327,351)(319,338,328,352)(320,339,329,353)(321,340,330,354)(322,341,331,355), (1,71,15,57)(2,72,16,58)(3,73,17,59)(4,74,18,60)(5,75,19,61)(6,76,20,62)(7,77,21,63)(8,78,22,64)(9,79,23,65)(10,80,24,66)(11,81,25,67)(12,82,26,68)(13,83,27,69)(14,84,28,70)(29,99,50,85)(30,100,51,86)(31,101,52,87)(32,102,53,88)(33,103,54,89)(34,104,55,90)(35,105,56,91)(36,106,43,92)(37,107,44,93)(38,108,45,94)(39,109,46,95)(40,110,47,96)(41,111,48,97)(42,112,49,98)(113,190,127,176)(114,191,128,177)(115,192,129,178)(116,193,130,179)(117,194,131,180)(118,195,132,181)(119,196,133,182)(120,183,134,169)(121,184,135,170)(122,185,136,171)(123,186,137,172)(124,187,138,173)(125,188,139,174)(126,189,140,175)(141,211,162,197)(142,212,163,198)(143,213,164,199)(144,214,165,200)(145,215,166,201)(146,216,167,202)(147,217,168,203)(148,218,155,204)(149,219,156,205)(150,220,157,206)(151,221,158,207)(152,222,159,208)(153,223,160,209)(154,224,161,210)(225,295,239,285)(226,296,240,286)(227,297,241,287)(228,298,242,288)(229,299,243,289)(230,300,244,290)(231,301,245,291)(232,302,246,292)(233,303,247,293)(234,304,248,294)(235,305,249,281)(236,306,250,282)(237,307,251,283)(238,308,252,284)(253,328,268,319)(254,329,269,320)(255,330,270,321)(256,331,271,322)(257,332,272,309)(258,333,273,310)(259,334,274,311)(260,335,275,312)(261,336,276,313)(262,323,277,314)(263,324,278,315)(264,325,279,316)(265,326,280,317)(266,327,267,318)(337,416,351,397)(338,417,352,398)(339,418,353,399)(340,419,354,400)(341,420,355,401)(342,407,356,402)(343,408,357,403)(344,409,358,404)(345,410,359,405)(346,411,360,406)(347,412,361,393)(348,413,362,394)(349,414,363,395)(350,415,364,396)(365,439,384,431)(366,440,385,432)(367,441,386,433)(368,442,387,434)(369,443,388,421)(370,444,389,422)(371,445,390,423)(372,446,391,424)(373,447,392,425)(374,448,379,426)(375,435,380,427)(376,436,381,428)(377,437,382,429)(378,438,383,430) );
G=PermutationGroup([[(1,120),(2,121),(3,122),(4,123),(5,124),(6,125),(7,126),(8,113),(9,114),(10,115),(11,116),(12,117),(13,118),(14,119),(15,134),(16,135),(17,136),(18,137),(19,138),(20,139),(21,140),(22,127),(23,128),(24,129),(25,130),(26,131),(27,132),(28,133),(29,148),(30,149),(31,150),(32,151),(33,152),(34,153),(35,154),(36,141),(37,142),(38,143),(39,144),(40,145),(41,146),(42,147),(43,162),(44,163),(45,164),(46,165),(47,166),(48,167),(49,168),(50,155),(51,156),(52,157),(53,158),(54,159),(55,160),(56,161),(57,169),(58,170),(59,171),(60,172),(61,173),(62,174),(63,175),(64,176),(65,177),(66,178),(67,179),(68,180),(69,181),(70,182),(71,183),(72,184),(73,185),(74,186),(75,187),(76,188),(77,189),(78,190),(79,191),(80,192),(81,193),(82,194),(83,195),(84,196),(85,204),(86,205),(87,206),(88,207),(89,208),(90,209),(91,210),(92,197),(93,198),(94,199),(95,200),(96,201),(97,202),(98,203),(99,218),(100,219),(101,220),(102,221),(103,222),(104,223),(105,224),(106,211),(107,212),(108,213),(109,214),(110,215),(111,216),(112,217),(225,344),(226,345),(227,346),(228,347),(229,348),(230,349),(231,350),(232,337),(233,338),(234,339),(235,340),(236,341),(237,342),(238,343),(239,358),(240,359),(241,360),(242,361),(243,362),(244,363),(245,364),(246,351),(247,352),(248,353),(249,354),(250,355),(251,356),(252,357),(253,378),(254,365),(255,366),(256,367),(257,368),(258,369),(259,370),(260,371),(261,372),(262,373),(263,374),(264,375),(265,376),(266,377),(267,382),(268,383),(269,384),(270,385),(271,386),(272,387),(273,388),(274,389),(275,390),(276,391),(277,392),(278,379),(279,380),(280,381),(281,400),(282,401),(283,402),(284,403),(285,404),(286,405),(287,406),(288,393),(289,394),(290,395),(291,396),(292,397),(293,398),(294,399),(295,409),(296,410),(297,411),(298,412),(299,413),(300,414),(301,415),(302,416),(303,417),(304,418),(305,419),(306,420),(307,407),(308,408),(309,434),(310,421),(311,422),(312,423),(313,424),(314,425),(315,426),(316,427),(317,428),(318,429),(319,430),(320,431),(321,432),(322,433),(323,447),(324,448),(325,435),(326,436),(327,437),(328,438),(329,439),(330,440),(331,441),(332,442),(333,443),(334,444),(335,445),(336,446)], [(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)], [(1,357,8,364),(2,356,9,363),(3,355,10,362),(4,354,11,361),(5,353,12,360),(6,352,13,359),(7,351,14,358),(15,343,22,350),(16,342,23,349),(17,341,24,348),(18,340,25,347),(19,339,26,346),(20,338,27,345),(21,337,28,344),(29,381,36,388),(30,380,37,387),(31,379,38,386),(32,392,39,385),(33,391,40,384),(34,390,41,383),(35,389,42,382),(43,369,50,376),(44,368,51,375),(45,367,52,374),(46,366,53,373),(47,365,54,372),(48,378,55,371),(49,377,56,370),(57,408,64,415),(58,407,65,414),(59,420,66,413),(60,419,67,412),(61,418,68,411),(62,417,69,410),(63,416,70,409),(71,403,78,396),(72,402,79,395),(73,401,80,394),(74,400,81,393),(75,399,82,406),(76,398,83,405),(77,397,84,404),(85,436,92,443),(86,435,93,442),(87,448,94,441),(88,447,95,440),(89,446,96,439),(90,445,97,438),(91,444,98,437),(99,428,106,421),(100,427,107,434),(101,426,108,433),(102,425,109,432),(103,424,110,431),(104,423,111,430),(105,422,112,429),(113,245,120,252),(114,244,121,251),(115,243,122,250),(116,242,123,249),(117,241,124,248),(118,240,125,247),(119,239,126,246),(127,231,134,238),(128,230,135,237),(129,229,136,236),(130,228,137,235),(131,227,138,234),(132,226,139,233),(133,225,140,232),(141,273,148,280),(142,272,149,279),(143,271,150,278),(144,270,151,277),(145,269,152,276),(146,268,153,275),(147,267,154,274),(155,265,162,258),(156,264,163,257),(157,263,164,256),(158,262,165,255),(159,261,166,254),(160,260,167,253),(161,259,168,266),(169,308,176,301),(170,307,177,300),(171,306,178,299),(172,305,179,298),(173,304,180,297),(174,303,181,296),(175,302,182,295),(183,284,190,291),(184,283,191,290),(185,282,192,289),(186,281,193,288),(187,294,194,287),(188,293,195,286),(189,292,196,285),(197,333,204,326),(198,332,205,325),(199,331,206,324),(200,330,207,323),(201,329,208,336),(202,328,209,335),(203,327,210,334),(211,310,218,317),(212,309,219,316),(213,322,220,315),(214,321,221,314),(215,320,222,313),(216,319,223,312),(217,318,224,311)], [(1,218,15,204),(2,219,16,205),(3,220,17,206),(4,221,18,207),(5,222,19,208),(6,223,20,209),(7,224,21,210),(8,211,22,197),(9,212,23,198),(10,213,24,199),(11,214,25,200),(12,215,26,201),(13,216,27,202),(14,217,28,203),(29,169,50,183),(30,170,51,184),(31,171,52,185),(32,172,53,186),(33,173,54,187),(34,174,55,188),(35,175,56,189),(36,176,43,190),(37,177,44,191),(38,178,45,192),(39,179,46,193),(40,180,47,194),(41,181,48,195),(42,182,49,196),(57,155,71,148),(58,156,72,149),(59,157,73,150),(60,158,74,151),(61,159,75,152),(62,160,76,153),(63,161,77,154),(64,162,78,141),(65,163,79,142),(66,164,80,143),(67,165,81,144),(68,166,82,145),(69,167,83,146),(70,168,84,147),(85,120,99,134),(86,121,100,135),(87,122,101,136),(88,123,102,137),(89,124,103,138),(90,125,104,139),(91,126,105,140),(92,113,106,127),(93,114,107,128),(94,115,108,129),(95,116,109,130),(96,117,110,131),(97,118,111,132),(98,119,112,133),(225,444,239,422),(226,445,240,423),(227,446,241,424),(228,447,242,425),(229,448,243,426),(230,435,244,427),(231,436,245,428),(232,437,246,429),(233,438,247,430),(234,439,248,431),(235,440,249,432),(236,441,250,433),(237,442,251,434),(238,443,252,421),(253,398,268,417),(254,399,269,418),(255,400,270,419),(256,401,271,420),(257,402,272,407),(258,403,273,408),(259,404,274,409),(260,405,275,410),(261,406,276,411),(262,393,277,412),(263,394,278,413),(264,395,279,414),(265,396,280,415),(266,397,267,416),(281,385,305,366),(282,386,306,367),(283,387,307,368),(284,388,308,369),(285,389,295,370),(286,390,296,371),(287,391,297,372),(288,392,298,373),(289,379,299,374),(290,380,300,375),(291,381,301,376),(292,382,302,377),(293,383,303,378),(294,384,304,365),(309,342,332,356),(310,343,333,357),(311,344,334,358),(312,345,335,359),(313,346,336,360),(314,347,323,361),(315,348,324,362),(316,349,325,363),(317,350,326,364),(318,337,327,351),(319,338,328,352),(320,339,329,353),(321,340,330,354),(322,341,331,355)], [(1,71,15,57),(2,72,16,58),(3,73,17,59),(4,74,18,60),(5,75,19,61),(6,76,20,62),(7,77,21,63),(8,78,22,64),(9,79,23,65),(10,80,24,66),(11,81,25,67),(12,82,26,68),(13,83,27,69),(14,84,28,70),(29,99,50,85),(30,100,51,86),(31,101,52,87),(32,102,53,88),(33,103,54,89),(34,104,55,90),(35,105,56,91),(36,106,43,92),(37,107,44,93),(38,108,45,94),(39,109,46,95),(40,110,47,96),(41,111,48,97),(42,112,49,98),(113,190,127,176),(114,191,128,177),(115,192,129,178),(116,193,130,179),(117,194,131,180),(118,195,132,181),(119,196,133,182),(120,183,134,169),(121,184,135,170),(122,185,136,171),(123,186,137,172),(124,187,138,173),(125,188,139,174),(126,189,140,175),(141,211,162,197),(142,212,163,198),(143,213,164,199),(144,214,165,200),(145,215,166,201),(146,216,167,202),(147,217,168,203),(148,218,155,204),(149,219,156,205),(150,220,157,206),(151,221,158,207),(152,222,159,208),(153,223,160,209),(154,224,161,210),(225,295,239,285),(226,296,240,286),(227,297,241,287),(228,298,242,288),(229,299,243,289),(230,300,244,290),(231,301,245,291),(232,302,246,292),(233,303,247,293),(234,304,248,294),(235,305,249,281),(236,306,250,282),(237,307,251,283),(238,308,252,284),(253,328,268,319),(254,329,269,320),(255,330,270,321),(256,331,271,322),(257,332,272,309),(258,333,273,310),(259,334,274,311),(260,335,275,312),(261,336,276,313),(262,323,277,314),(263,324,278,315),(264,325,279,316),(265,326,280,317),(266,327,267,318),(337,416,351,397),(338,417,352,398),(339,418,353,399),(340,419,354,400),(341,420,355,401),(342,407,356,402),(343,408,357,403),(344,409,358,404),(345,410,359,405),(346,411,360,406),(347,412,361,393),(348,413,362,394),(349,414,363,395),(350,415,364,396),(365,439,384,431),(366,440,385,432),(367,441,386,433),(368,442,387,434),(369,443,388,421),(370,444,389,422),(371,445,390,423),(372,446,391,424),(373,447,392,425),(374,448,379,426),(375,435,380,427),(376,436,381,428),(377,437,382,429),(378,438,383,430)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 4Q | 4R | 4S | 4T | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | Q8 | D4 | D7 | D14 | D14 | C7⋊D4 | Q8×D7 |
| kernel | C2×Dic7⋊Q8 | C2×C4×Dic7 | C2×Dic7⋊C4 | Dic7⋊Q8 | C22×Dic14 | Q8×C2×C14 | C2×Dic7 | C2×C28 | C22×Q8 | C22×C4 | C2×Q8 | C2×C4 | C22 |
| # reps | 1 | 1 | 4 | 8 | 1 | 1 | 8 | 4 | 3 | 9 | 12 | 24 | 12 |
Matrix representation of C2×Dic7⋊Q8 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 28 | 0 | 0 |
| 0 | 0 | 20 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 4 | 0 | 0 |
| 0 | 0 | 17 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 27 |
| 0 | 0 | 0 | 0 | 3 | 11 |
| 11 | 20 | 0 | 0 | 0 | 0 |
| 20 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 2 |
| 0 | 0 | 0 | 0 | 27 | 18 |
| 20 | 18 | 0 | 0 | 0 | 0 |
| 18 | 9 | 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 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,19,20,0,0,0,0,28,28,0,0,0,0,0,0,11,28,0,0,0,0,1,0],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,7,17,0,0,0,0,4,22,0,0,0,0,0,0,18,3,0,0,0,0,27,11],[11,20,0,0,0,0,20,18,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,11,27,0,0,0,0,2,18],[20,18,0,0,0,0,18,9,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
C2×Dic7⋊Q8 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_7\rtimes Q_8 % in TeX
G:=Group("C2xDic7:Q8"); // GroupNames label
G:=SmallGroup(448,1263);
// by ID
G=gap.SmallGroup(448,1263);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,100,1123,185,80,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^14=d^4=1,c^2=b^7,e^2=d^2,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,d*c*d^-1=b^7*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations