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