metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×Dic7)⋊6Q8, C14.21(C4×Q8), C4.9(D14⋊C4), (C2×C28).137D4, (C2×C4).141D28, C14.25(C4⋊Q8), (C2×Dic14)⋊10C4, C22.20(Q8×D7), C22.45(C2×D28), C28.22(C22⋊C4), C2.3(D14⋊2Q8), (C22×C4).332D14, C14.44(C22⋊Q8), C2.2(Dic7⋊Q8), C2.2(C28.17D4), C14.39(C4.4D4), C23.288(C22×D7), C2.11(Dic7⋊3Q8), C22.53(D4⋊2D7), C14.C42.16C2, (C22×C28).141C22, (C22×C14).338C23, C7⋊3(C23.67C23), (C22×Dic14).11C2, (C22×Dic7).50C22, (C2×C4⋊C4).12D7, (C2×C4).78(C4×D7), (C14×C4⋊C4).10C2, (C2×C4×Dic7).4C2, (C2×C28).81(C2×C4), C2.14(C2×D14⋊C4), (C2×C14).74(C2×Q8), C22.132(C2×C4×D7), (C2×C14).150(C2×D4), C14.41(C2×C22⋊C4), C22.62(C2×C7⋊D4), (C2×C4).126(C7⋊D4), (C2×Dic7).29(C2×C4), (C2×C14).150(C4○D4), (C2×C14).114(C22×C4), SmallGroup(448,508)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×Dic7)⋊6Q8
G = < a,b,c,d,e | a2=b14=d4=1, c2=b7, e2=d2, ab=ba, dcd-1=ac=ca, ad=da, ae=ea, cbc-1=dbd-1=b-1, be=eb, ce=ec, ede-1=d-1 >
Subgroups: 772 in 186 conjugacy classes, 83 normal (23 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, Dic7, C28, C28, C2×C14, C2×C14, C2.C42, C2×C42, C2×C4⋊C4, C22×Q8, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C23.67C23, C4×Dic7, C7×C4⋊C4, C2×Dic14, C2×Dic14, C22×Dic7, C22×C28, C22×C28, C14.C42, C2×C4×Dic7, C14×C4⋊C4, C22×Dic14, (C2×Dic7)⋊6Q8
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C22⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, D14, C2×C22⋊C4, C4×Q8, C22⋊Q8, C4.4D4, C4⋊Q8, C4×D7, D28, C7⋊D4, C22×D7, C23.67C23, D14⋊C4, C2×C4×D7, C2×D28, D4⋊2D7, Q8×D7, C2×C7⋊D4, Dic7⋊3Q8, D14⋊2Q8, C2×D14⋊C4, C28.17D4, Dic7⋊Q8, (C2×Dic7)⋊6Q8
►Regular action on 448 points
Generators in S448
(1 36)(2 37)(3 38)(4 39)(5 40)(6 41)(7 42)(8 29)(9 30)(10 31)(11 32)(12 33)(13 34)(14 35)(15 43)(16 44)(17 45)(18 46)(19 47)(20 48)(21 49)(22 50)(23 51)(24 52)(25 53)(26 54)(27 55)(28 56)(57 92)(58 93)(59 94)(60 95)(61 96)(62 97)(63 98)(64 85)(65 86)(66 87)(67 88)(68 89)(69 90)(70 91)(71 106)(72 107)(73 108)(74 109)(75 110)(76 111)(77 112)(78 99)(79 100)(80 101)(81 102)(82 103)(83 104)(84 105)(113 148)(114 149)(115 150)(116 151)(117 152)(118 153)(119 154)(120 141)(121 142)(122 143)(123 144)(124 145)(125 146)(126 147)(127 155)(128 156)(129 157)(130 158)(131 159)(132 160)(133 161)(134 162)(135 163)(136 164)(137 165)(138 166)(139 167)(140 168)(169 197)(170 198)(171 199)(172 200)(173 201)(174 202)(175 203)(176 204)(177 205)(178 206)(179 207)(180 208)(181 209)(182 210)(183 211)(184 212)(185 213)(186 214)(187 215)(188 216)(189 217)(190 218)(191 219)(192 220)(193 221)(194 222)(195 223)(196 224)(225 261)(226 262)(227 263)(228 264)(229 265)(230 266)(231 253)(232 254)(233 255)(234 256)(235 257)(236 258)(237 259)(238 260)(239 270)(240 271)(241 272)(242 273)(243 274)(244 275)(245 276)(246 277)(247 278)(248 279)(249 280)(250 267)(251 268)(252 269)(281 319)(282 320)(283 321)(284 322)(285 309)(286 310)(287 311)(288 312)(289 313)(290 314)(291 315)(292 316)(293 317)(294 318)(295 331)(296 332)(297 333)(298 334)(299 335)(300 336)(301 323)(302 324)(303 325)(304 326)(305 327)(306 328)(307 329)(308 330)(337 374)(338 375)(339 376)(340 377)(341 378)(342 365)(343 366)(344 367)(345 368)(346 369)(347 370)(348 371)(349 372)(350 373)(351 390)(352 391)(353 392)(354 379)(355 380)(356 381)(357 382)(358 383)(359 384)(360 385)(361 386)(362 387)(363 388)(364 389)(393 426)(394 427)(395 428)(396 429)(397 430)(398 431)(399 432)(400 433)(401 434)(402 421)(403 422)(404 423)(405 424)(406 425)(407 445)(408 446)(409 447)(410 448)(411 435)(412 436)(413 437)(414 438)(415 439)(416 440)(417 441)(418 442)(419 443)(420 444)
(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)
(1 236 8 229)(2 235 9 228)(3 234 10 227)(4 233 11 226)(5 232 12 225)(6 231 13 238)(7 230 14 237)(15 241 22 248)(16 240 23 247)(17 239 24 246)(18 252 25 245)(19 251 26 244)(20 250 27 243)(21 249 28 242)(29 265 36 258)(30 264 37 257)(31 263 38 256)(32 262 39 255)(33 261 40 254)(34 260 41 253)(35 259 42 266)(43 272 50 279)(44 271 51 278)(45 270 52 277)(46 269 53 276)(47 268 54 275)(48 267 55 274)(49 280 56 273)(57 285 64 292)(58 284 65 291)(59 283 66 290)(60 282 67 289)(61 281 68 288)(62 294 69 287)(63 293 70 286)(71 295 78 302)(72 308 79 301)(73 307 80 300)(74 306 81 299)(75 305 82 298)(76 304 83 297)(77 303 84 296)(85 316 92 309)(86 315 93 322)(87 314 94 321)(88 313 95 320)(89 312 96 319)(90 311 97 318)(91 310 98 317)(99 324 106 331)(100 323 107 330)(101 336 108 329)(102 335 109 328)(103 334 110 327)(104 333 111 326)(105 332 112 325)(113 344 120 337)(114 343 121 350)(115 342 122 349)(116 341 123 348)(117 340 124 347)(118 339 125 346)(119 338 126 345)(127 356 134 363)(128 355 135 362)(129 354 136 361)(130 353 137 360)(131 352 138 359)(132 351 139 358)(133 364 140 357)(141 374 148 367)(142 373 149 366)(143 372 150 365)(144 371 151 378)(145 370 152 377)(146 369 153 376)(147 368 154 375)(155 381 162 388)(156 380 163 387)(157 379 164 386)(158 392 165 385)(159 391 166 384)(160 390 167 383)(161 389 168 382)(169 398 176 405)(170 397 177 404)(171 396 178 403)(172 395 179 402)(173 394 180 401)(174 393 181 400)(175 406 182 399)(183 410 190 417)(184 409 191 416)(185 408 192 415)(186 407 193 414)(187 420 194 413)(188 419 195 412)(189 418 196 411)(197 431 204 424)(198 430 205 423)(199 429 206 422)(200 428 207 421)(201 427 208 434)(202 426 209 433)(203 425 210 432)(211 448 218 441)(212 447 219 440)(213 446 220 439)(214 445 221 438)(215 444 222 437)(216 443 223 436)(217 442 224 435)
(1 295 15 285)(2 308 16 284)(3 307 17 283)(4 306 18 282)(5 305 19 281)(6 304 20 294)(7 303 21 293)(8 302 22 292)(9 301 23 291)(10 300 24 290)(11 299 25 289)(12 298 26 288)(13 297 27 287)(14 296 28 286)(29 324 50 316)(30 323 51 315)(31 336 52 314)(32 335 53 313)(33 334 54 312)(34 333 55 311)(35 332 56 310)(36 331 43 309)(37 330 44 322)(38 329 45 321)(39 328 46 320)(40 327 47 319)(41 326 48 318)(42 325 49 317)(57 265 71 279)(58 264 72 278)(59 263 73 277)(60 262 74 276)(61 261 75 275)(62 260 76 274)(63 259 77 273)(64 258 78 272)(65 257 79 271)(66 256 80 270)(67 255 81 269)(68 254 82 268)(69 253 83 267)(70 266 84 280)(85 236 99 241)(86 235 100 240)(87 234 101 239)(88 233 102 252)(89 232 103 251)(90 231 104 250)(91 230 105 249)(92 229 106 248)(93 228 107 247)(94 227 108 246)(95 226 109 245)(96 225 110 244)(97 238 111 243)(98 237 112 242)(113 405 127 410)(114 404 128 409)(115 403 129 408)(116 402 130 407)(117 401 131 420)(118 400 132 419)(119 399 133 418)(120 398 134 417)(121 397 135 416)(122 396 136 415)(123 395 137 414)(124 394 138 413)(125 393 139 412)(126 406 140 411)(141 431 162 441)(142 430 163 440)(143 429 164 439)(144 428 165 438)(145 427 166 437)(146 426 167 436)(147 425 168 435)(148 424 155 448)(149 423 156 447)(150 422 157 446)(151 421 158 445)(152 434 159 444)(153 433 160 443)(154 432 161 442)(169 381 190 367)(170 380 191 366)(171 379 192 365)(172 392 193 378)(173 391 194 377)(174 390 195 376)(175 389 196 375)(176 388 183 374)(177 387 184 373)(178 386 185 372)(179 385 186 371)(180 384 187 370)(181 383 188 369)(182 382 189 368)(197 356 218 344)(198 355 219 343)(199 354 220 342)(200 353 221 341)(201 352 222 340)(202 351 223 339)(203 364 224 338)(204 363 211 337)(205 362 212 350)(206 361 213 349)(207 360 214 348)(208 359 215 347)(209 358 216 346)(210 357 217 345)
(1 127 15 113)(2 128 16 114)(3 129 17 115)(4 130 18 116)(5 131 19 117)(6 132 20 118)(7 133 21 119)(8 134 22 120)(9 135 23 121)(10 136 24 122)(11 137 25 123)(12 138 26 124)(13 139 27 125)(14 140 28 126)(29 162 50 141)(30 163 51 142)(31 164 52 143)(32 165 53 144)(33 166 54 145)(34 167 55 146)(35 168 56 147)(36 155 43 148)(37 156 44 149)(38 157 45 150)(39 158 46 151)(40 159 47 152)(41 160 48 153)(42 161 49 154)(57 183 71 176)(58 184 72 177)(59 185 73 178)(60 186 74 179)(61 187 75 180)(62 188 76 181)(63 189 77 182)(64 190 78 169)(65 191 79 170)(66 192 80 171)(67 193 81 172)(68 194 82 173)(69 195 83 174)(70 196 84 175)(85 218 99 197)(86 219 100 198)(87 220 101 199)(88 221 102 200)(89 222 103 201)(90 223 104 202)(91 224 105 203)(92 211 106 204)(93 212 107 205)(94 213 108 206)(95 214 109 207)(96 215 110 208)(97 216 111 209)(98 217 112 210)(225 359 244 347)(226 360 245 348)(227 361 246 349)(228 362 247 350)(229 363 248 337)(230 364 249 338)(231 351 250 339)(232 352 251 340)(233 353 252 341)(234 354 239 342)(235 355 240 343)(236 356 241 344)(237 357 242 345)(238 358 243 346)(253 390 267 376)(254 391 268 377)(255 392 269 378)(256 379 270 365)(257 380 271 366)(258 381 272 367)(259 382 273 368)(260 383 274 369)(261 384 275 370)(262 385 276 371)(263 386 277 372)(264 387 278 373)(265 388 279 374)(266 389 280 375)(281 420 305 401)(282 407 306 402)(283 408 307 403)(284 409 308 404)(285 410 295 405)(286 411 296 406)(287 412 297 393)(288 413 298 394)(289 414 299 395)(290 415 300 396)(291 416 301 397)(292 417 302 398)(293 418 303 399)(294 419 304 400)(309 448 331 424)(310 435 332 425)(311 436 333 426)(312 437 334 427)(313 438 335 428)(314 439 336 429)(315 440 323 430)(316 441 324 431)(317 442 325 432)(318 443 326 433)(319 444 327 434)(320 445 328 421)(321 446 329 422)(322 447 330 423)
G:=sub<Sym(448)| (1,36)(2,37)(3,38)(4,39)(5,40)(6,41)(7,42)(8,29)(9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(57,92)(58,93)(59,94)(60,95)(61,96)(62,97)(63,98)(64,85)(65,86)(66,87)(67,88)(68,89)(69,90)(70,91)(71,106)(72,107)(73,108)(74,109)(75,110)(76,111)(77,112)(78,99)(79,100)(80,101)(81,102)(82,103)(83,104)(84,105)(113,148)(114,149)(115,150)(116,151)(117,152)(118,153)(119,154)(120,141)(121,142)(122,143)(123,144)(124,145)(125,146)(126,147)(127,155)(128,156)(129,157)(130,158)(131,159)(132,160)(133,161)(134,162)(135,163)(136,164)(137,165)(138,166)(139,167)(140,168)(169,197)(170,198)(171,199)(172,200)(173,201)(174,202)(175,203)(176,204)(177,205)(178,206)(179,207)(180,208)(181,209)(182,210)(183,211)(184,212)(185,213)(186,214)(187,215)(188,216)(189,217)(190,218)(191,219)(192,220)(193,221)(194,222)(195,223)(196,224)(225,261)(226,262)(227,263)(228,264)(229,265)(230,266)(231,253)(232,254)(233,255)(234,256)(235,257)(236,258)(237,259)(238,260)(239,270)(240,271)(241,272)(242,273)(243,274)(244,275)(245,276)(246,277)(247,278)(248,279)(249,280)(250,267)(251,268)(252,269)(281,319)(282,320)(283,321)(284,322)(285,309)(286,310)(287,311)(288,312)(289,313)(290,314)(291,315)(292,316)(293,317)(294,318)(295,331)(296,332)(297,333)(298,334)(299,335)(300,336)(301,323)(302,324)(303,325)(304,326)(305,327)(306,328)(307,329)(308,330)(337,374)(338,375)(339,376)(340,377)(341,378)(342,365)(343,366)(344,367)(345,368)(346,369)(347,370)(348,371)(349,372)(350,373)(351,390)(352,391)(353,392)(354,379)(355,380)(356,381)(357,382)(358,383)(359,384)(360,385)(361,386)(362,387)(363,388)(364,389)(393,426)(394,427)(395,428)(396,429)(397,430)(398,431)(399,432)(400,433)(401,434)(402,421)(403,422)(404,423)(405,424)(406,425)(407,445)(408,446)(409,447)(410,448)(411,435)(412,436)(413,437)(414,438)(415,439)(416,440)(417,441)(418,442)(419,443)(420,444), (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), (1,236,8,229)(2,235,9,228)(3,234,10,227)(4,233,11,226)(5,232,12,225)(6,231,13,238)(7,230,14,237)(15,241,22,248)(16,240,23,247)(17,239,24,246)(18,252,25,245)(19,251,26,244)(20,250,27,243)(21,249,28,242)(29,265,36,258)(30,264,37,257)(31,263,38,256)(32,262,39,255)(33,261,40,254)(34,260,41,253)(35,259,42,266)(43,272,50,279)(44,271,51,278)(45,270,52,277)(46,269,53,276)(47,268,54,275)(48,267,55,274)(49,280,56,273)(57,285,64,292)(58,284,65,291)(59,283,66,290)(60,282,67,289)(61,281,68,288)(62,294,69,287)(63,293,70,286)(71,295,78,302)(72,308,79,301)(73,307,80,300)(74,306,81,299)(75,305,82,298)(76,304,83,297)(77,303,84,296)(85,316,92,309)(86,315,93,322)(87,314,94,321)(88,313,95,320)(89,312,96,319)(90,311,97,318)(91,310,98,317)(99,324,106,331)(100,323,107,330)(101,336,108,329)(102,335,109,328)(103,334,110,327)(104,333,111,326)(105,332,112,325)(113,344,120,337)(114,343,121,350)(115,342,122,349)(116,341,123,348)(117,340,124,347)(118,339,125,346)(119,338,126,345)(127,356,134,363)(128,355,135,362)(129,354,136,361)(130,353,137,360)(131,352,138,359)(132,351,139,358)(133,364,140,357)(141,374,148,367)(142,373,149,366)(143,372,150,365)(144,371,151,378)(145,370,152,377)(146,369,153,376)(147,368,154,375)(155,381,162,388)(156,380,163,387)(157,379,164,386)(158,392,165,385)(159,391,166,384)(160,390,167,383)(161,389,168,382)(169,398,176,405)(170,397,177,404)(171,396,178,403)(172,395,179,402)(173,394,180,401)(174,393,181,400)(175,406,182,399)(183,410,190,417)(184,409,191,416)(185,408,192,415)(186,407,193,414)(187,420,194,413)(188,419,195,412)(189,418,196,411)(197,431,204,424)(198,430,205,423)(199,429,206,422)(200,428,207,421)(201,427,208,434)(202,426,209,433)(203,425,210,432)(211,448,218,441)(212,447,219,440)(213,446,220,439)(214,445,221,438)(215,444,222,437)(216,443,223,436)(217,442,224,435), (1,295,15,285)(2,308,16,284)(3,307,17,283)(4,306,18,282)(5,305,19,281)(6,304,20,294)(7,303,21,293)(8,302,22,292)(9,301,23,291)(10,300,24,290)(11,299,25,289)(12,298,26,288)(13,297,27,287)(14,296,28,286)(29,324,50,316)(30,323,51,315)(31,336,52,314)(32,335,53,313)(33,334,54,312)(34,333,55,311)(35,332,56,310)(36,331,43,309)(37,330,44,322)(38,329,45,321)(39,328,46,320)(40,327,47,319)(41,326,48,318)(42,325,49,317)(57,265,71,279)(58,264,72,278)(59,263,73,277)(60,262,74,276)(61,261,75,275)(62,260,76,274)(63,259,77,273)(64,258,78,272)(65,257,79,271)(66,256,80,270)(67,255,81,269)(68,254,82,268)(69,253,83,267)(70,266,84,280)(85,236,99,241)(86,235,100,240)(87,234,101,239)(88,233,102,252)(89,232,103,251)(90,231,104,250)(91,230,105,249)(92,229,106,248)(93,228,107,247)(94,227,108,246)(95,226,109,245)(96,225,110,244)(97,238,111,243)(98,237,112,242)(113,405,127,410)(114,404,128,409)(115,403,129,408)(116,402,130,407)(117,401,131,420)(118,400,132,419)(119,399,133,418)(120,398,134,417)(121,397,135,416)(122,396,136,415)(123,395,137,414)(124,394,138,413)(125,393,139,412)(126,406,140,411)(141,431,162,441)(142,430,163,440)(143,429,164,439)(144,428,165,438)(145,427,166,437)(146,426,167,436)(147,425,168,435)(148,424,155,448)(149,423,156,447)(150,422,157,446)(151,421,158,445)(152,434,159,444)(153,433,160,443)(154,432,161,442)(169,381,190,367)(170,380,191,366)(171,379,192,365)(172,392,193,378)(173,391,194,377)(174,390,195,376)(175,389,196,375)(176,388,183,374)(177,387,184,373)(178,386,185,372)(179,385,186,371)(180,384,187,370)(181,383,188,369)(182,382,189,368)(197,356,218,344)(198,355,219,343)(199,354,220,342)(200,353,221,341)(201,352,222,340)(202,351,223,339)(203,364,224,338)(204,363,211,337)(205,362,212,350)(206,361,213,349)(207,360,214,348)(208,359,215,347)(209,358,216,346)(210,357,217,345), (1,127,15,113)(2,128,16,114)(3,129,17,115)(4,130,18,116)(5,131,19,117)(6,132,20,118)(7,133,21,119)(8,134,22,120)(9,135,23,121)(10,136,24,122)(11,137,25,123)(12,138,26,124)(13,139,27,125)(14,140,28,126)(29,162,50,141)(30,163,51,142)(31,164,52,143)(32,165,53,144)(33,166,54,145)(34,167,55,146)(35,168,56,147)(36,155,43,148)(37,156,44,149)(38,157,45,150)(39,158,46,151)(40,159,47,152)(41,160,48,153)(42,161,49,154)(57,183,71,176)(58,184,72,177)(59,185,73,178)(60,186,74,179)(61,187,75,180)(62,188,76,181)(63,189,77,182)(64,190,78,169)(65,191,79,170)(66,192,80,171)(67,193,81,172)(68,194,82,173)(69,195,83,174)(70,196,84,175)(85,218,99,197)(86,219,100,198)(87,220,101,199)(88,221,102,200)(89,222,103,201)(90,223,104,202)(91,224,105,203)(92,211,106,204)(93,212,107,205)(94,213,108,206)(95,214,109,207)(96,215,110,208)(97,216,111,209)(98,217,112,210)(225,359,244,347)(226,360,245,348)(227,361,246,349)(228,362,247,350)(229,363,248,337)(230,364,249,338)(231,351,250,339)(232,352,251,340)(233,353,252,341)(234,354,239,342)(235,355,240,343)(236,356,241,344)(237,357,242,345)(238,358,243,346)(253,390,267,376)(254,391,268,377)(255,392,269,378)(256,379,270,365)(257,380,271,366)(258,381,272,367)(259,382,273,368)(260,383,274,369)(261,384,275,370)(262,385,276,371)(263,386,277,372)(264,387,278,373)(265,388,279,374)(266,389,280,375)(281,420,305,401)(282,407,306,402)(283,408,307,403)(284,409,308,404)(285,410,295,405)(286,411,296,406)(287,412,297,393)(288,413,298,394)(289,414,299,395)(290,415,300,396)(291,416,301,397)(292,417,302,398)(293,418,303,399)(294,419,304,400)(309,448,331,424)(310,435,332,425)(311,436,333,426)(312,437,334,427)(313,438,335,428)(314,439,336,429)(315,440,323,430)(316,441,324,431)(317,442,325,432)(318,443,326,433)(319,444,327,434)(320,445,328,421)(321,446,329,422)(322,447,330,423)>;
G:=Group( (1,36)(2,37)(3,38)(4,39)(5,40)(6,41)(7,42)(8,29)(9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(57,92)(58,93)(59,94)(60,95)(61,96)(62,97)(63,98)(64,85)(65,86)(66,87)(67,88)(68,89)(69,90)(70,91)(71,106)(72,107)(73,108)(74,109)(75,110)(76,111)(77,112)(78,99)(79,100)(80,101)(81,102)(82,103)(83,104)(84,105)(113,148)(114,149)(115,150)(116,151)(117,152)(118,153)(119,154)(120,141)(121,142)(122,143)(123,144)(124,145)(125,146)(126,147)(127,155)(128,156)(129,157)(130,158)(131,159)(132,160)(133,161)(134,162)(135,163)(136,164)(137,165)(138,166)(139,167)(140,168)(169,197)(170,198)(171,199)(172,200)(173,201)(174,202)(175,203)(176,204)(177,205)(178,206)(179,207)(180,208)(181,209)(182,210)(183,211)(184,212)(185,213)(186,214)(187,215)(188,216)(189,217)(190,218)(191,219)(192,220)(193,221)(194,222)(195,223)(196,224)(225,261)(226,262)(227,263)(228,264)(229,265)(230,266)(231,253)(232,254)(233,255)(234,256)(235,257)(236,258)(237,259)(238,260)(239,270)(240,271)(241,272)(242,273)(243,274)(244,275)(245,276)(246,277)(247,278)(248,279)(249,280)(250,267)(251,268)(252,269)(281,319)(282,320)(283,321)(284,322)(285,309)(286,310)(287,311)(288,312)(289,313)(290,314)(291,315)(292,316)(293,317)(294,318)(295,331)(296,332)(297,333)(298,334)(299,335)(300,336)(301,323)(302,324)(303,325)(304,326)(305,327)(306,328)(307,329)(308,330)(337,374)(338,375)(339,376)(340,377)(341,378)(342,365)(343,366)(344,367)(345,368)(346,369)(347,370)(348,371)(349,372)(350,373)(351,390)(352,391)(353,392)(354,379)(355,380)(356,381)(357,382)(358,383)(359,384)(360,385)(361,386)(362,387)(363,388)(364,389)(393,426)(394,427)(395,428)(396,429)(397,430)(398,431)(399,432)(400,433)(401,434)(402,421)(403,422)(404,423)(405,424)(406,425)(407,445)(408,446)(409,447)(410,448)(411,435)(412,436)(413,437)(414,438)(415,439)(416,440)(417,441)(418,442)(419,443)(420,444), (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), (1,236,8,229)(2,235,9,228)(3,234,10,227)(4,233,11,226)(5,232,12,225)(6,231,13,238)(7,230,14,237)(15,241,22,248)(16,240,23,247)(17,239,24,246)(18,252,25,245)(19,251,26,244)(20,250,27,243)(21,249,28,242)(29,265,36,258)(30,264,37,257)(31,263,38,256)(32,262,39,255)(33,261,40,254)(34,260,41,253)(35,259,42,266)(43,272,50,279)(44,271,51,278)(45,270,52,277)(46,269,53,276)(47,268,54,275)(48,267,55,274)(49,280,56,273)(57,285,64,292)(58,284,65,291)(59,283,66,290)(60,282,67,289)(61,281,68,288)(62,294,69,287)(63,293,70,286)(71,295,78,302)(72,308,79,301)(73,307,80,300)(74,306,81,299)(75,305,82,298)(76,304,83,297)(77,303,84,296)(85,316,92,309)(86,315,93,322)(87,314,94,321)(88,313,95,320)(89,312,96,319)(90,311,97,318)(91,310,98,317)(99,324,106,331)(100,323,107,330)(101,336,108,329)(102,335,109,328)(103,334,110,327)(104,333,111,326)(105,332,112,325)(113,344,120,337)(114,343,121,350)(115,342,122,349)(116,341,123,348)(117,340,124,347)(118,339,125,346)(119,338,126,345)(127,356,134,363)(128,355,135,362)(129,354,136,361)(130,353,137,360)(131,352,138,359)(132,351,139,358)(133,364,140,357)(141,374,148,367)(142,373,149,366)(143,372,150,365)(144,371,151,378)(145,370,152,377)(146,369,153,376)(147,368,154,375)(155,381,162,388)(156,380,163,387)(157,379,164,386)(158,392,165,385)(159,391,166,384)(160,390,167,383)(161,389,168,382)(169,398,176,405)(170,397,177,404)(171,396,178,403)(172,395,179,402)(173,394,180,401)(174,393,181,400)(175,406,182,399)(183,410,190,417)(184,409,191,416)(185,408,192,415)(186,407,193,414)(187,420,194,413)(188,419,195,412)(189,418,196,411)(197,431,204,424)(198,430,205,423)(199,429,206,422)(200,428,207,421)(201,427,208,434)(202,426,209,433)(203,425,210,432)(211,448,218,441)(212,447,219,440)(213,446,220,439)(214,445,221,438)(215,444,222,437)(216,443,223,436)(217,442,224,435), (1,295,15,285)(2,308,16,284)(3,307,17,283)(4,306,18,282)(5,305,19,281)(6,304,20,294)(7,303,21,293)(8,302,22,292)(9,301,23,291)(10,300,24,290)(11,299,25,289)(12,298,26,288)(13,297,27,287)(14,296,28,286)(29,324,50,316)(30,323,51,315)(31,336,52,314)(32,335,53,313)(33,334,54,312)(34,333,55,311)(35,332,56,310)(36,331,43,309)(37,330,44,322)(38,329,45,321)(39,328,46,320)(40,327,47,319)(41,326,48,318)(42,325,49,317)(57,265,71,279)(58,264,72,278)(59,263,73,277)(60,262,74,276)(61,261,75,275)(62,260,76,274)(63,259,77,273)(64,258,78,272)(65,257,79,271)(66,256,80,270)(67,255,81,269)(68,254,82,268)(69,253,83,267)(70,266,84,280)(85,236,99,241)(86,235,100,240)(87,234,101,239)(88,233,102,252)(89,232,103,251)(90,231,104,250)(91,230,105,249)(92,229,106,248)(93,228,107,247)(94,227,108,246)(95,226,109,245)(96,225,110,244)(97,238,111,243)(98,237,112,242)(113,405,127,410)(114,404,128,409)(115,403,129,408)(116,402,130,407)(117,401,131,420)(118,400,132,419)(119,399,133,418)(120,398,134,417)(121,397,135,416)(122,396,136,415)(123,395,137,414)(124,394,138,413)(125,393,139,412)(126,406,140,411)(141,431,162,441)(142,430,163,440)(143,429,164,439)(144,428,165,438)(145,427,166,437)(146,426,167,436)(147,425,168,435)(148,424,155,448)(149,423,156,447)(150,422,157,446)(151,421,158,445)(152,434,159,444)(153,433,160,443)(154,432,161,442)(169,381,190,367)(170,380,191,366)(171,379,192,365)(172,392,193,378)(173,391,194,377)(174,390,195,376)(175,389,196,375)(176,388,183,374)(177,387,184,373)(178,386,185,372)(179,385,186,371)(180,384,187,370)(181,383,188,369)(182,382,189,368)(197,356,218,344)(198,355,219,343)(199,354,220,342)(200,353,221,341)(201,352,222,340)(202,351,223,339)(203,364,224,338)(204,363,211,337)(205,362,212,350)(206,361,213,349)(207,360,214,348)(208,359,215,347)(209,358,216,346)(210,357,217,345), (1,127,15,113)(2,128,16,114)(3,129,17,115)(4,130,18,116)(5,131,19,117)(6,132,20,118)(7,133,21,119)(8,134,22,120)(9,135,23,121)(10,136,24,122)(11,137,25,123)(12,138,26,124)(13,139,27,125)(14,140,28,126)(29,162,50,141)(30,163,51,142)(31,164,52,143)(32,165,53,144)(33,166,54,145)(34,167,55,146)(35,168,56,147)(36,155,43,148)(37,156,44,149)(38,157,45,150)(39,158,46,151)(40,159,47,152)(41,160,48,153)(42,161,49,154)(57,183,71,176)(58,184,72,177)(59,185,73,178)(60,186,74,179)(61,187,75,180)(62,188,76,181)(63,189,77,182)(64,190,78,169)(65,191,79,170)(66,192,80,171)(67,193,81,172)(68,194,82,173)(69,195,83,174)(70,196,84,175)(85,218,99,197)(86,219,100,198)(87,220,101,199)(88,221,102,200)(89,222,103,201)(90,223,104,202)(91,224,105,203)(92,211,106,204)(93,212,107,205)(94,213,108,206)(95,214,109,207)(96,215,110,208)(97,216,111,209)(98,217,112,210)(225,359,244,347)(226,360,245,348)(227,361,246,349)(228,362,247,350)(229,363,248,337)(230,364,249,338)(231,351,250,339)(232,352,251,340)(233,353,252,341)(234,354,239,342)(235,355,240,343)(236,356,241,344)(237,357,242,345)(238,358,243,346)(253,390,267,376)(254,391,268,377)(255,392,269,378)(256,379,270,365)(257,380,271,366)(258,381,272,367)(259,382,273,368)(260,383,274,369)(261,384,275,370)(262,385,276,371)(263,386,277,372)(264,387,278,373)(265,388,279,374)(266,389,280,375)(281,420,305,401)(282,407,306,402)(283,408,307,403)(284,409,308,404)(285,410,295,405)(286,411,296,406)(287,412,297,393)(288,413,298,394)(289,414,299,395)(290,415,300,396)(291,416,301,397)(292,417,302,398)(293,418,303,399)(294,419,304,400)(309,448,331,424)(310,435,332,425)(311,436,333,426)(312,437,334,427)(313,438,335,428)(314,439,336,429)(315,440,323,430)(316,441,324,431)(317,442,325,432)(318,443,326,433)(319,444,327,434)(320,445,328,421)(321,446,329,422)(322,447,330,423) );
G=PermutationGroup([[(1,36),(2,37),(3,38),(4,39),(5,40),(6,41),(7,42),(8,29),(9,30),(10,31),(11,32),(12,33),(13,34),(14,35),(15,43),(16,44),(17,45),(18,46),(19,47),(20,48),(21,49),(22,50),(23,51),(24,52),(25,53),(26,54),(27,55),(28,56),(57,92),(58,93),(59,94),(60,95),(61,96),(62,97),(63,98),(64,85),(65,86),(66,87),(67,88),(68,89),(69,90),(70,91),(71,106),(72,107),(73,108),(74,109),(75,110),(76,111),(77,112),(78,99),(79,100),(80,101),(81,102),(82,103),(83,104),(84,105),(113,148),(114,149),(115,150),(116,151),(117,152),(118,153),(119,154),(120,141),(121,142),(122,143),(123,144),(124,145),(125,146),(126,147),(127,155),(128,156),(129,157),(130,158),(131,159),(132,160),(133,161),(134,162),(135,163),(136,164),(137,165),(138,166),(139,167),(140,168),(169,197),(170,198),(171,199),(172,200),(173,201),(174,202),(175,203),(176,204),(177,205),(178,206),(179,207),(180,208),(181,209),(182,210),(183,211),(184,212),(185,213),(186,214),(187,215),(188,216),(189,217),(190,218),(191,219),(192,220),(193,221),(194,222),(195,223),(196,224),(225,261),(226,262),(227,263),(228,264),(229,265),(230,266),(231,253),(232,254),(233,255),(234,256),(235,257),(236,258),(237,259),(238,260),(239,270),(240,271),(241,272),(242,273),(243,274),(244,275),(245,276),(246,277),(247,278),(248,279),(249,280),(250,267),(251,268),(252,269),(281,319),(282,320),(283,321),(284,322),(285,309),(286,310),(287,311),(288,312),(289,313),(290,314),(291,315),(292,316),(293,317),(294,318),(295,331),(296,332),(297,333),(298,334),(299,335),(300,336),(301,323),(302,324),(303,325),(304,326),(305,327),(306,328),(307,329),(308,330),(337,374),(338,375),(339,376),(340,377),(341,378),(342,365),(343,366),(344,367),(345,368),(346,369),(347,370),(348,371),(349,372),(350,373),(351,390),(352,391),(353,392),(354,379),(355,380),(356,381),(357,382),(358,383),(359,384),(360,385),(361,386),(362,387),(363,388),(364,389),(393,426),(394,427),(395,428),(396,429),(397,430),(398,431),(399,432),(400,433),(401,434),(402,421),(403,422),(404,423),(405,424),(406,425),(407,445),(408,446),(409,447),(410,448),(411,435),(412,436),(413,437),(414,438),(415,439),(416,440),(417,441),(418,442),(419,443),(420,444)], [(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)], [(1,236,8,229),(2,235,9,228),(3,234,10,227),(4,233,11,226),(5,232,12,225),(6,231,13,238),(7,230,14,237),(15,241,22,248),(16,240,23,247),(17,239,24,246),(18,252,25,245),(19,251,26,244),(20,250,27,243),(21,249,28,242),(29,265,36,258),(30,264,37,257),(31,263,38,256),(32,262,39,255),(33,261,40,254),(34,260,41,253),(35,259,42,266),(43,272,50,279),(44,271,51,278),(45,270,52,277),(46,269,53,276),(47,268,54,275),(48,267,55,274),(49,280,56,273),(57,285,64,292),(58,284,65,291),(59,283,66,290),(60,282,67,289),(61,281,68,288),(62,294,69,287),(63,293,70,286),(71,295,78,302),(72,308,79,301),(73,307,80,300),(74,306,81,299),(75,305,82,298),(76,304,83,297),(77,303,84,296),(85,316,92,309),(86,315,93,322),(87,314,94,321),(88,313,95,320),(89,312,96,319),(90,311,97,318),(91,310,98,317),(99,324,106,331),(100,323,107,330),(101,336,108,329),(102,335,109,328),(103,334,110,327),(104,333,111,326),(105,332,112,325),(113,344,120,337),(114,343,121,350),(115,342,122,349),(116,341,123,348),(117,340,124,347),(118,339,125,346),(119,338,126,345),(127,356,134,363),(128,355,135,362),(129,354,136,361),(130,353,137,360),(131,352,138,359),(132,351,139,358),(133,364,140,357),(141,374,148,367),(142,373,149,366),(143,372,150,365),(144,371,151,378),(145,370,152,377),(146,369,153,376),(147,368,154,375),(155,381,162,388),(156,380,163,387),(157,379,164,386),(158,392,165,385),(159,391,166,384),(160,390,167,383),(161,389,168,382),(169,398,176,405),(170,397,177,404),(171,396,178,403),(172,395,179,402),(173,394,180,401),(174,393,181,400),(175,406,182,399),(183,410,190,417),(184,409,191,416),(185,408,192,415),(186,407,193,414),(187,420,194,413),(188,419,195,412),(189,418,196,411),(197,431,204,424),(198,430,205,423),(199,429,206,422),(200,428,207,421),(201,427,208,434),(202,426,209,433),(203,425,210,432),(211,448,218,441),(212,447,219,440),(213,446,220,439),(214,445,221,438),(215,444,222,437),(216,443,223,436),(217,442,224,435)], [(1,295,15,285),(2,308,16,284),(3,307,17,283),(4,306,18,282),(5,305,19,281),(6,304,20,294),(7,303,21,293),(8,302,22,292),(9,301,23,291),(10,300,24,290),(11,299,25,289),(12,298,26,288),(13,297,27,287),(14,296,28,286),(29,324,50,316),(30,323,51,315),(31,336,52,314),(32,335,53,313),(33,334,54,312),(34,333,55,311),(35,332,56,310),(36,331,43,309),(37,330,44,322),(38,329,45,321),(39,328,46,320),(40,327,47,319),(41,326,48,318),(42,325,49,317),(57,265,71,279),(58,264,72,278),(59,263,73,277),(60,262,74,276),(61,261,75,275),(62,260,76,274),(63,259,77,273),(64,258,78,272),(65,257,79,271),(66,256,80,270),(67,255,81,269),(68,254,82,268),(69,253,83,267),(70,266,84,280),(85,236,99,241),(86,235,100,240),(87,234,101,239),(88,233,102,252),(89,232,103,251),(90,231,104,250),(91,230,105,249),(92,229,106,248),(93,228,107,247),(94,227,108,246),(95,226,109,245),(96,225,110,244),(97,238,111,243),(98,237,112,242),(113,405,127,410),(114,404,128,409),(115,403,129,408),(116,402,130,407),(117,401,131,420),(118,400,132,419),(119,399,133,418),(120,398,134,417),(121,397,135,416),(122,396,136,415),(123,395,137,414),(124,394,138,413),(125,393,139,412),(126,406,140,411),(141,431,162,441),(142,430,163,440),(143,429,164,439),(144,428,165,438),(145,427,166,437),(146,426,167,436),(147,425,168,435),(148,424,155,448),(149,423,156,447),(150,422,157,446),(151,421,158,445),(152,434,159,444),(153,433,160,443),(154,432,161,442),(169,381,190,367),(170,380,191,366),(171,379,192,365),(172,392,193,378),(173,391,194,377),(174,390,195,376),(175,389,196,375),(176,388,183,374),(177,387,184,373),(178,386,185,372),(179,385,186,371),(180,384,187,370),(181,383,188,369),(182,382,189,368),(197,356,218,344),(198,355,219,343),(199,354,220,342),(200,353,221,341),(201,352,222,340),(202,351,223,339),(203,364,224,338),(204,363,211,337),(205,362,212,350),(206,361,213,349),(207,360,214,348),(208,359,215,347),(209,358,216,346),(210,357,217,345)], [(1,127,15,113),(2,128,16,114),(3,129,17,115),(4,130,18,116),(5,131,19,117),(6,132,20,118),(7,133,21,119),(8,134,22,120),(9,135,23,121),(10,136,24,122),(11,137,25,123),(12,138,26,124),(13,139,27,125),(14,140,28,126),(29,162,50,141),(30,163,51,142),(31,164,52,143),(32,165,53,144),(33,166,54,145),(34,167,55,146),(35,168,56,147),(36,155,43,148),(37,156,44,149),(38,157,45,150),(39,158,46,151),(40,159,47,152),(41,160,48,153),(42,161,49,154),(57,183,71,176),(58,184,72,177),(59,185,73,178),(60,186,74,179),(61,187,75,180),(62,188,76,181),(63,189,77,182),(64,190,78,169),(65,191,79,170),(66,192,80,171),(67,193,81,172),(68,194,82,173),(69,195,83,174),(70,196,84,175),(85,218,99,197),(86,219,100,198),(87,220,101,199),(88,221,102,200),(89,222,103,201),(90,223,104,202),(91,224,105,203),(92,211,106,204),(93,212,107,205),(94,213,108,206),(95,214,109,207),(96,215,110,208),(97,216,111,209),(98,217,112,210),(225,359,244,347),(226,360,245,348),(227,361,246,349),(228,362,247,350),(229,363,248,337),(230,364,249,338),(231,351,250,339),(232,352,251,340),(233,353,252,341),(234,354,239,342),(235,355,240,343),(236,356,241,344),(237,357,242,345),(238,358,243,346),(253,390,267,376),(254,391,268,377),(255,392,269,378),(256,379,270,365),(257,380,271,366),(258,381,272,367),(259,382,273,368),(260,383,274,369),(261,384,275,370),(262,385,276,371),(263,386,277,372),(264,387,278,373),(265,388,279,374),(266,389,280,375),(281,420,305,401),(282,407,306,402),(283,408,307,403),(284,409,308,404),(285,410,295,405),(286,411,296,406),(287,412,297,393),(288,413,298,394),(289,414,299,395),(290,415,300,396),(291,416,301,397),(292,417,302,398),(293,418,303,399),(294,419,304,400),(309,448,331,424),(310,435,332,425),(311,436,333,426),(312,437,334,427),(313,438,335,428),(314,439,336,429),(315,440,323,430),(316,441,324,431),(317,442,325,432),(318,443,326,433),(319,444,327,434),(320,445,328,421),(321,446,329,422),(322,447,330,423)]])
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 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | - | + | + | + | + | - | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | Q8 | D4 | D7 | C4○D4 | D14 | C4×D7 | D28 | C7⋊D4 | D4⋊2D7 | Q8×D7 |
| kernel | (C2×Dic7)⋊6Q8 | C14.C42 | C2×C4×Dic7 | C14×C4⋊C4 | C22×Dic14 | C2×Dic14 | C2×Dic7 | C2×C28 | C2×C4⋊C4 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C22 | C22 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 4 | 4 | 3 | 4 | 9 | 12 | 12 | 12 | 6 | 6 |
Matrix representation of (C2×Dic7)⋊6Q8 ►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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 5 | 0 | 0 | 0 | 0 | 0 |
| 0 | 6 | 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 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 22 | 0 | 0 |
| 0 | 0 | 9 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 14 | 0 | 0 |
| 0 | 0 | 19 | 5 | 0 | 0 |
| 0 | 0 | 0 | 0 | 23 | 12 |
| 0 | 0 | 0 | 0 | 9 | 6 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 1 |
| 0 | 0 | 0 | 0 | 6 | 15 |
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],[5,0,0,0,0,0,0,6,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,8,9,0,0,0,0,22,21,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[0,28,0,0,0,0,28,0,0,0,0,0,0,0,24,19,0,0,0,0,14,5,0,0,0,0,0,0,23,9,0,0,0,0,12,6],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,14,6,0,0,0,0,1,15] >;
(C2×Dic7)⋊6Q8 in GAP, Magma, Sage, TeX
(C_2\times {\rm Dic}_7)\rtimes_6Q_8 % in TeX
G:=Group("(C2xDic7):6Q8"); // GroupNames label
G:=SmallGroup(448,508);
// by ID
G=gap.SmallGroup(448,508);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,120,254,219,310,18822]);
// 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,d*c*d^-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,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations