direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Q8⋊Dic7, (Q8×C14)⋊5C4, (C2×Q8)⋊3Dic7, Q8⋊3(C2×Dic7), C28.207(C2×D4), (C2×C28).192D4, (C2×C14).18Q16, C14.46(C2×Q16), C14⋊3(Q8⋊C4), (C22×Q8).1D7, C28.81(C22×C4), (C2×Q8).165D14, (C2×C14).42SD16, C14.79(C2×SD16), C28.33(C22⋊C4), (C2×C28).474C23, (C22×C4).354D14, (C22×C14).198D4, C22.12(Q8⋊D7), C4.10(C23.D7), C4.11(C22×Dic7), C22.9(C7⋊Q16), C23.101(C7⋊D4), C4⋊Dic7.352C22, (Q8×C14).200C22, (C22×C28).200C22, C22.35(C23.D7), C7⋊4(C2×Q8⋊C4), C2.4(C2×Q8⋊D7), (Q8×C2×C14).1C2, (C7×Q8)⋊15(C2×C4), C4.91(C2×C7⋊D4), C2.4(C2×C7⋊Q16), (C22×C7⋊C8).13C2, (C2×C28).119(C2×C4), (C2×C14).558(C2×D4), C14.77(C2×C22⋊C4), (C2×C7⋊C8).281C22, (C2×C4⋊Dic7).40C2, (C2×C4).51(C2×Dic7), C22.93(C2×C7⋊D4), C2.13(C2×C23.D7), (C2×C4).149(C7⋊D4), (C2×C4).560(C22×D7), (C2×C14).114(C22⋊C4), SmallGroup(448,758)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Q8⋊Dic7
G = < a,b,c,d,e | a2=b4=d14=1, c2=b2, e2=d7, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=ebe-1=b-1, bd=db, cd=dc, ece-1=b-1c, ede-1=d-1 >
Subgroups: 500 in 162 conjugacy classes, 87 normal (27 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, Q8, Q8, C23, C14, C14, C4⋊C4, C2×C8, C22×C4, C22×C4, C2×Q8, C2×Q8, Dic7, C28, C28, C28, C2×C14, C2×C14, Q8⋊C4, C2×C4⋊C4, C22×C8, C22×Q8, C7⋊C8, C2×Dic7, C2×C28, C2×C28, C2×C28, C7×Q8, C7×Q8, C22×C14, C2×Q8⋊C4, C2×C7⋊C8, C2×C7⋊C8, C4⋊Dic7, C4⋊Dic7, C22×Dic7, C22×C28, C22×C28, Q8×C14, Q8×C14, Q8⋊Dic7, C22×C7⋊C8, C2×C4⋊Dic7, Q8×C2×C14, C2×Q8⋊Dic7
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, SD16, Q16, C22×C4, C2×D4, Dic7, D14, Q8⋊C4, C2×C22⋊C4, C2×SD16, C2×Q16, C2×Dic7, C7⋊D4, C22×D7, C2×Q8⋊C4, Q8⋊D7, C7⋊Q16, C23.D7, C22×Dic7, C2×C7⋊D4, Q8⋊Dic7, C2×Q8⋊D7, C2×C7⋊Q16, C2×C23.D7, C2×Q8⋊Dic7
►Regular action on 448 points
Generators in S448
(1 306)(2 307)(3 308)(4 295)(5 296)(6 297)(7 298)(8 299)(9 300)(10 301)(11 302)(12 303)(13 304)(14 305)(15 172)(16 173)(17 174)(18 175)(19 176)(20 177)(21 178)(22 179)(23 180)(24 181)(25 182)(26 169)(27 170)(28 171)(29 149)(30 150)(31 151)(32 152)(33 153)(34 154)(35 141)(36 142)(37 143)(38 144)(39 145)(40 146)(41 147)(42 148)(43 95)(44 96)(45 97)(46 98)(47 85)(48 86)(49 87)(50 88)(51 89)(52 90)(53 91)(54 92)(55 93)(56 94)(57 429)(58 430)(59 431)(60 432)(61 433)(62 434)(63 421)(64 422)(65 423)(66 424)(67 425)(68 426)(69 427)(70 428)(71 116)(72 117)(73 118)(74 119)(75 120)(76 121)(77 122)(78 123)(79 124)(80 125)(81 126)(82 113)(83 114)(84 115)(99 442)(100 443)(101 444)(102 445)(103 446)(104 447)(105 448)(106 435)(107 436)(108 437)(109 438)(110 439)(111 440)(112 441)(127 193)(128 194)(129 195)(130 196)(131 183)(132 184)(133 185)(134 186)(135 187)(136 188)(137 189)(138 190)(139 191)(140 192)(155 254)(156 255)(157 256)(158 257)(159 258)(160 259)(161 260)(162 261)(163 262)(164 263)(165 264)(166 265)(167 266)(168 253)(197 367)(198 368)(199 369)(200 370)(201 371)(202 372)(203 373)(204 374)(205 375)(206 376)(207 377)(208 378)(209 365)(210 366)(211 321)(212 322)(213 309)(214 310)(215 311)(216 312)(217 313)(218 314)(219 315)(220 316)(221 317)(222 318)(223 319)(224 320)(225 351)(226 352)(227 353)(228 354)(229 355)(230 356)(231 357)(232 358)(233 359)(234 360)(235 361)(236 362)(237 363)(238 364)(239 331)(240 332)(241 333)(242 334)(243 335)(244 336)(245 323)(246 324)(247 325)(248 326)(249 327)(250 328)(251 329)(252 330)(267 342)(268 343)(269 344)(270 345)(271 346)(272 347)(273 348)(274 349)(275 350)(276 337)(277 338)(278 339)(279 340)(280 341)(281 398)(282 399)(283 400)(284 401)(285 402)(286 403)(287 404)(288 405)(289 406)(290 393)(291 394)(292 395)(293 396)(294 397)(379 409)(380 410)(381 411)(382 412)(383 413)(384 414)(385 415)(386 416)(387 417)(388 418)(389 419)(390 420)(391 407)(392 408)
(1 216 252 43)(2 217 239 44)(3 218 240 45)(4 219 241 46)(5 220 242 47)(6 221 243 48)(7 222 244 49)(8 223 245 50)(9 224 246 51)(10 211 247 52)(11 212 248 53)(12 213 249 54)(13 214 250 55)(14 215 251 56)(15 202 187 430)(16 203 188 431)(17 204 189 432)(18 205 190 433)(19 206 191 434)(20 207 192 421)(21 208 193 422)(22 209 194 423)(23 210 195 424)(24 197 196 425)(25 198 183 426)(26 199 184 427)(27 200 185 428)(28 201 186 429)(29 384 257 77)(30 385 258 78)(31 386 259 79)(32 387 260 80)(33 388 261 81)(34 389 262 82)(35 390 263 83)(36 391 264 84)(37 392 265 71)(38 379 266 72)(39 380 253 73)(40 381 254 74)(41 382 255 75)(42 383 256 76)(57 171 371 134)(58 172 372 135)(59 173 373 136)(60 174 374 137)(61 175 375 138)(62 176 376 139)(63 177 377 140)(64 178 378 127)(65 179 365 128)(66 180 366 129)(67 181 367 130)(68 182 368 131)(69 169 369 132)(70 170 370 133)(85 296 316 334)(86 297 317 335)(87 298 318 336)(88 299 319 323)(89 300 320 324)(90 301 321 325)(91 302 322 326)(92 303 309 327)(93 304 310 328)(94 305 311 329)(95 306 312 330)(96 307 313 331)(97 308 314 332)(98 295 315 333)(99 285 232 342)(100 286 233 343)(101 287 234 344)(102 288 235 345)(103 289 236 346)(104 290 237 347)(105 291 238 348)(106 292 225 349)(107 293 226 350)(108 294 227 337)(109 281 228 338)(110 282 229 339)(111 283 230 340)(112 284 231 341)(113 154 419 163)(114 141 420 164)(115 142 407 165)(116 143 408 166)(117 144 409 167)(118 145 410 168)(119 146 411 155)(120 147 412 156)(121 148 413 157)(122 149 414 158)(123 150 415 159)(124 151 416 160)(125 152 417 161)(126 153 418 162)(267 442 402 358)(268 443 403 359)(269 444 404 360)(270 445 405 361)(271 446 406 362)(272 447 393 363)(273 448 394 364)(274 435 395 351)(275 436 396 352)(276 437 397 353)(277 438 398 354)(278 439 399 355)(279 440 400 356)(280 441 401 357)
(1 374 252 60)(2 375 239 61)(3 376 240 62)(4 377 241 63)(5 378 242 64)(6 365 243 65)(7 366 244 66)(8 367 245 67)(9 368 246 68)(10 369 247 69)(11 370 248 70)(12 371 249 57)(13 372 250 58)(14 373 251 59)(15 93 187 310)(16 94 188 311)(17 95 189 312)(18 96 190 313)(19 97 191 314)(20 98 192 315)(21 85 193 316)(22 86 194 317)(23 87 195 318)(24 88 196 319)(25 89 183 320)(26 90 184 321)(27 91 185 322)(28 92 186 309)(29 440 257 356)(30 441 258 357)(31 442 259 358)(32 443 260 359)(33 444 261 360)(34 445 262 361)(35 446 263 362)(36 447 264 363)(37 448 265 364)(38 435 266 351)(39 436 253 352)(40 437 254 353)(41 438 255 354)(42 439 256 355)(43 137 216 174)(44 138 217 175)(45 139 218 176)(46 140 219 177)(47 127 220 178)(48 128 221 179)(49 129 222 180)(50 130 223 181)(51 131 224 182)(52 132 211 169)(53 133 212 170)(54 134 213 171)(55 135 214 172)(56 136 215 173)(71 394 392 273)(72 395 379 274)(73 396 380 275)(74 397 381 276)(75 398 382 277)(76 399 383 278)(77 400 384 279)(78 401 385 280)(79 402 386 267)(80 403 387 268)(81 404 388 269)(82 405 389 270)(83 406 390 271)(84 393 391 272)(99 160 232 151)(100 161 233 152)(101 162 234 153)(102 163 235 154)(103 164 236 141)(104 165 237 142)(105 166 238 143)(106 167 225 144)(107 168 226 145)(108 155 227 146)(109 156 228 147)(110 157 229 148)(111 158 230 149)(112 159 231 150)(113 288 419 345)(114 289 420 346)(115 290 407 347)(116 291 408 348)(117 292 409 349)(118 293 410 350)(119 294 411 337)(120 281 412 338)(121 282 413 339)(122 283 414 340)(123 284 415 341)(124 285 416 342)(125 286 417 343)(126 287 418 344)(197 323 425 299)(198 324 426 300)(199 325 427 301)(200 326 428 302)(201 327 429 303)(202 328 430 304)(203 329 431 305)(204 330 432 306)(205 331 433 307)(206 332 434 308)(207 333 421 295)(208 334 422 296)(209 335 423 297)(210 336 424 298)
(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)
(1 118 8 125)(2 117 9 124)(3 116 10 123)(4 115 11 122)(5 114 12 121)(6 113 13 120)(7 126 14 119)(15 277 22 270)(16 276 23 269)(17 275 24 268)(18 274 25 267)(19 273 26 280)(20 272 27 279)(21 271 28 278)(29 98 36 91)(30 97 37 90)(31 96 38 89)(32 95 39 88)(33 94 40 87)(34 93 41 86)(35 92 42 85)(43 145 50 152)(44 144 51 151)(45 143 52 150)(46 142 53 149)(47 141 54 148)(48 154 55 147)(49 153 56 146)(57 110 64 103)(58 109 65 102)(59 108 66 101)(60 107 67 100)(61 106 68 99)(62 105 69 112)(63 104 70 111)(71 301 78 308)(72 300 79 307)(73 299 80 306)(74 298 81 305)(75 297 82 304)(76 296 83 303)(77 295 84 302)(127 289 134 282)(128 288 135 281)(129 287 136 294)(130 286 137 293)(131 285 138 292)(132 284 139 291)(133 283 140 290)(155 222 162 215)(156 221 163 214)(157 220 164 213)(158 219 165 212)(159 218 166 211)(160 217 167 224)(161 216 168 223)(169 341 176 348)(170 340 177 347)(171 339 178 346)(172 338 179 345)(173 337 180 344)(174 350 181 343)(175 349 182 342)(183 402 190 395)(184 401 191 394)(185 400 192 393)(186 399 193 406)(187 398 194 405)(188 397 195 404)(189 396 196 403)(197 359 204 352)(198 358 205 351)(199 357 206 364)(200 356 207 363)(201 355 208 362)(202 354 209 361)(203 353 210 360)(225 368 232 375)(226 367 233 374)(227 366 234 373)(228 365 235 372)(229 378 236 371)(230 377 237 370)(231 376 238 369)(239 409 246 416)(240 408 247 415)(241 407 248 414)(242 420 249 413)(243 419 250 412)(244 418 251 411)(245 417 252 410)(253 319 260 312)(254 318 261 311)(255 317 262 310)(256 316 263 309)(257 315 264 322)(258 314 265 321)(259 313 266 320)(323 387 330 380)(324 386 331 379)(325 385 332 392)(326 384 333 391)(327 383 334 390)(328 382 335 389)(329 381 336 388)(421 447 428 440)(422 446 429 439)(423 445 430 438)(424 444 431 437)(425 443 432 436)(426 442 433 435)(427 441 434 448)
G:=sub<Sym(448)| (1,306)(2,307)(3,308)(4,295)(5,296)(6,297)(7,298)(8,299)(9,300)(10,301)(11,302)(12,303)(13,304)(14,305)(15,172)(16,173)(17,174)(18,175)(19,176)(20,177)(21,178)(22,179)(23,180)(24,181)(25,182)(26,169)(27,170)(28,171)(29,149)(30,150)(31,151)(32,152)(33,153)(34,154)(35,141)(36,142)(37,143)(38,144)(39,145)(40,146)(41,147)(42,148)(43,95)(44,96)(45,97)(46,98)(47,85)(48,86)(49,87)(50,88)(51,89)(52,90)(53,91)(54,92)(55,93)(56,94)(57,429)(58,430)(59,431)(60,432)(61,433)(62,434)(63,421)(64,422)(65,423)(66,424)(67,425)(68,426)(69,427)(70,428)(71,116)(72,117)(73,118)(74,119)(75,120)(76,121)(77,122)(78,123)(79,124)(80,125)(81,126)(82,113)(83,114)(84,115)(99,442)(100,443)(101,444)(102,445)(103,446)(104,447)(105,448)(106,435)(107,436)(108,437)(109,438)(110,439)(111,440)(112,441)(127,193)(128,194)(129,195)(130,196)(131,183)(132,184)(133,185)(134,186)(135,187)(136,188)(137,189)(138,190)(139,191)(140,192)(155,254)(156,255)(157,256)(158,257)(159,258)(160,259)(161,260)(162,261)(163,262)(164,263)(165,264)(166,265)(167,266)(168,253)(197,367)(198,368)(199,369)(200,370)(201,371)(202,372)(203,373)(204,374)(205,375)(206,376)(207,377)(208,378)(209,365)(210,366)(211,321)(212,322)(213,309)(214,310)(215,311)(216,312)(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)(224,320)(225,351)(226,352)(227,353)(228,354)(229,355)(230,356)(231,357)(232,358)(233,359)(234,360)(235,361)(236,362)(237,363)(238,364)(239,331)(240,332)(241,333)(242,334)(243,335)(244,336)(245,323)(246,324)(247,325)(248,326)(249,327)(250,328)(251,329)(252,330)(267,342)(268,343)(269,344)(270,345)(271,346)(272,347)(273,348)(274,349)(275,350)(276,337)(277,338)(278,339)(279,340)(280,341)(281,398)(282,399)(283,400)(284,401)(285,402)(286,403)(287,404)(288,405)(289,406)(290,393)(291,394)(292,395)(293,396)(294,397)(379,409)(380,410)(381,411)(382,412)(383,413)(384,414)(385,415)(386,416)(387,417)(388,418)(389,419)(390,420)(391,407)(392,408), (1,216,252,43)(2,217,239,44)(3,218,240,45)(4,219,241,46)(5,220,242,47)(6,221,243,48)(7,222,244,49)(8,223,245,50)(9,224,246,51)(10,211,247,52)(11,212,248,53)(12,213,249,54)(13,214,250,55)(14,215,251,56)(15,202,187,430)(16,203,188,431)(17,204,189,432)(18,205,190,433)(19,206,191,434)(20,207,192,421)(21,208,193,422)(22,209,194,423)(23,210,195,424)(24,197,196,425)(25,198,183,426)(26,199,184,427)(27,200,185,428)(28,201,186,429)(29,384,257,77)(30,385,258,78)(31,386,259,79)(32,387,260,80)(33,388,261,81)(34,389,262,82)(35,390,263,83)(36,391,264,84)(37,392,265,71)(38,379,266,72)(39,380,253,73)(40,381,254,74)(41,382,255,75)(42,383,256,76)(57,171,371,134)(58,172,372,135)(59,173,373,136)(60,174,374,137)(61,175,375,138)(62,176,376,139)(63,177,377,140)(64,178,378,127)(65,179,365,128)(66,180,366,129)(67,181,367,130)(68,182,368,131)(69,169,369,132)(70,170,370,133)(85,296,316,334)(86,297,317,335)(87,298,318,336)(88,299,319,323)(89,300,320,324)(90,301,321,325)(91,302,322,326)(92,303,309,327)(93,304,310,328)(94,305,311,329)(95,306,312,330)(96,307,313,331)(97,308,314,332)(98,295,315,333)(99,285,232,342)(100,286,233,343)(101,287,234,344)(102,288,235,345)(103,289,236,346)(104,290,237,347)(105,291,238,348)(106,292,225,349)(107,293,226,350)(108,294,227,337)(109,281,228,338)(110,282,229,339)(111,283,230,340)(112,284,231,341)(113,154,419,163)(114,141,420,164)(115,142,407,165)(116,143,408,166)(117,144,409,167)(118,145,410,168)(119,146,411,155)(120,147,412,156)(121,148,413,157)(122,149,414,158)(123,150,415,159)(124,151,416,160)(125,152,417,161)(126,153,418,162)(267,442,402,358)(268,443,403,359)(269,444,404,360)(270,445,405,361)(271,446,406,362)(272,447,393,363)(273,448,394,364)(274,435,395,351)(275,436,396,352)(276,437,397,353)(277,438,398,354)(278,439,399,355)(279,440,400,356)(280,441,401,357), (1,374,252,60)(2,375,239,61)(3,376,240,62)(4,377,241,63)(5,378,242,64)(6,365,243,65)(7,366,244,66)(8,367,245,67)(9,368,246,68)(10,369,247,69)(11,370,248,70)(12,371,249,57)(13,372,250,58)(14,373,251,59)(15,93,187,310)(16,94,188,311)(17,95,189,312)(18,96,190,313)(19,97,191,314)(20,98,192,315)(21,85,193,316)(22,86,194,317)(23,87,195,318)(24,88,196,319)(25,89,183,320)(26,90,184,321)(27,91,185,322)(28,92,186,309)(29,440,257,356)(30,441,258,357)(31,442,259,358)(32,443,260,359)(33,444,261,360)(34,445,262,361)(35,446,263,362)(36,447,264,363)(37,448,265,364)(38,435,266,351)(39,436,253,352)(40,437,254,353)(41,438,255,354)(42,439,256,355)(43,137,216,174)(44,138,217,175)(45,139,218,176)(46,140,219,177)(47,127,220,178)(48,128,221,179)(49,129,222,180)(50,130,223,181)(51,131,224,182)(52,132,211,169)(53,133,212,170)(54,134,213,171)(55,135,214,172)(56,136,215,173)(71,394,392,273)(72,395,379,274)(73,396,380,275)(74,397,381,276)(75,398,382,277)(76,399,383,278)(77,400,384,279)(78,401,385,280)(79,402,386,267)(80,403,387,268)(81,404,388,269)(82,405,389,270)(83,406,390,271)(84,393,391,272)(99,160,232,151)(100,161,233,152)(101,162,234,153)(102,163,235,154)(103,164,236,141)(104,165,237,142)(105,166,238,143)(106,167,225,144)(107,168,226,145)(108,155,227,146)(109,156,228,147)(110,157,229,148)(111,158,230,149)(112,159,231,150)(113,288,419,345)(114,289,420,346)(115,290,407,347)(116,291,408,348)(117,292,409,349)(118,293,410,350)(119,294,411,337)(120,281,412,338)(121,282,413,339)(122,283,414,340)(123,284,415,341)(124,285,416,342)(125,286,417,343)(126,287,418,344)(197,323,425,299)(198,324,426,300)(199,325,427,301)(200,326,428,302)(201,327,429,303)(202,328,430,304)(203,329,431,305)(204,330,432,306)(205,331,433,307)(206,332,434,308)(207,333,421,295)(208,334,422,296)(209,335,423,297)(210,336,424,298), (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), (1,118,8,125)(2,117,9,124)(3,116,10,123)(4,115,11,122)(5,114,12,121)(6,113,13,120)(7,126,14,119)(15,277,22,270)(16,276,23,269)(17,275,24,268)(18,274,25,267)(19,273,26,280)(20,272,27,279)(21,271,28,278)(29,98,36,91)(30,97,37,90)(31,96,38,89)(32,95,39,88)(33,94,40,87)(34,93,41,86)(35,92,42,85)(43,145,50,152)(44,144,51,151)(45,143,52,150)(46,142,53,149)(47,141,54,148)(48,154,55,147)(49,153,56,146)(57,110,64,103)(58,109,65,102)(59,108,66,101)(60,107,67,100)(61,106,68,99)(62,105,69,112)(63,104,70,111)(71,301,78,308)(72,300,79,307)(73,299,80,306)(74,298,81,305)(75,297,82,304)(76,296,83,303)(77,295,84,302)(127,289,134,282)(128,288,135,281)(129,287,136,294)(130,286,137,293)(131,285,138,292)(132,284,139,291)(133,283,140,290)(155,222,162,215)(156,221,163,214)(157,220,164,213)(158,219,165,212)(159,218,166,211)(160,217,167,224)(161,216,168,223)(169,341,176,348)(170,340,177,347)(171,339,178,346)(172,338,179,345)(173,337,180,344)(174,350,181,343)(175,349,182,342)(183,402,190,395)(184,401,191,394)(185,400,192,393)(186,399,193,406)(187,398,194,405)(188,397,195,404)(189,396,196,403)(197,359,204,352)(198,358,205,351)(199,357,206,364)(200,356,207,363)(201,355,208,362)(202,354,209,361)(203,353,210,360)(225,368,232,375)(226,367,233,374)(227,366,234,373)(228,365,235,372)(229,378,236,371)(230,377,237,370)(231,376,238,369)(239,409,246,416)(240,408,247,415)(241,407,248,414)(242,420,249,413)(243,419,250,412)(244,418,251,411)(245,417,252,410)(253,319,260,312)(254,318,261,311)(255,317,262,310)(256,316,263,309)(257,315,264,322)(258,314,265,321)(259,313,266,320)(323,387,330,380)(324,386,331,379)(325,385,332,392)(326,384,333,391)(327,383,334,390)(328,382,335,389)(329,381,336,388)(421,447,428,440)(422,446,429,439)(423,445,430,438)(424,444,431,437)(425,443,432,436)(426,442,433,435)(427,441,434,448)>;
G:=Group( (1,306)(2,307)(3,308)(4,295)(5,296)(6,297)(7,298)(8,299)(9,300)(10,301)(11,302)(12,303)(13,304)(14,305)(15,172)(16,173)(17,174)(18,175)(19,176)(20,177)(21,178)(22,179)(23,180)(24,181)(25,182)(26,169)(27,170)(28,171)(29,149)(30,150)(31,151)(32,152)(33,153)(34,154)(35,141)(36,142)(37,143)(38,144)(39,145)(40,146)(41,147)(42,148)(43,95)(44,96)(45,97)(46,98)(47,85)(48,86)(49,87)(50,88)(51,89)(52,90)(53,91)(54,92)(55,93)(56,94)(57,429)(58,430)(59,431)(60,432)(61,433)(62,434)(63,421)(64,422)(65,423)(66,424)(67,425)(68,426)(69,427)(70,428)(71,116)(72,117)(73,118)(74,119)(75,120)(76,121)(77,122)(78,123)(79,124)(80,125)(81,126)(82,113)(83,114)(84,115)(99,442)(100,443)(101,444)(102,445)(103,446)(104,447)(105,448)(106,435)(107,436)(108,437)(109,438)(110,439)(111,440)(112,441)(127,193)(128,194)(129,195)(130,196)(131,183)(132,184)(133,185)(134,186)(135,187)(136,188)(137,189)(138,190)(139,191)(140,192)(155,254)(156,255)(157,256)(158,257)(159,258)(160,259)(161,260)(162,261)(163,262)(164,263)(165,264)(166,265)(167,266)(168,253)(197,367)(198,368)(199,369)(200,370)(201,371)(202,372)(203,373)(204,374)(205,375)(206,376)(207,377)(208,378)(209,365)(210,366)(211,321)(212,322)(213,309)(214,310)(215,311)(216,312)(217,313)(218,314)(219,315)(220,316)(221,317)(222,318)(223,319)(224,320)(225,351)(226,352)(227,353)(228,354)(229,355)(230,356)(231,357)(232,358)(233,359)(234,360)(235,361)(236,362)(237,363)(238,364)(239,331)(240,332)(241,333)(242,334)(243,335)(244,336)(245,323)(246,324)(247,325)(248,326)(249,327)(250,328)(251,329)(252,330)(267,342)(268,343)(269,344)(270,345)(271,346)(272,347)(273,348)(274,349)(275,350)(276,337)(277,338)(278,339)(279,340)(280,341)(281,398)(282,399)(283,400)(284,401)(285,402)(286,403)(287,404)(288,405)(289,406)(290,393)(291,394)(292,395)(293,396)(294,397)(379,409)(380,410)(381,411)(382,412)(383,413)(384,414)(385,415)(386,416)(387,417)(388,418)(389,419)(390,420)(391,407)(392,408), (1,216,252,43)(2,217,239,44)(3,218,240,45)(4,219,241,46)(5,220,242,47)(6,221,243,48)(7,222,244,49)(8,223,245,50)(9,224,246,51)(10,211,247,52)(11,212,248,53)(12,213,249,54)(13,214,250,55)(14,215,251,56)(15,202,187,430)(16,203,188,431)(17,204,189,432)(18,205,190,433)(19,206,191,434)(20,207,192,421)(21,208,193,422)(22,209,194,423)(23,210,195,424)(24,197,196,425)(25,198,183,426)(26,199,184,427)(27,200,185,428)(28,201,186,429)(29,384,257,77)(30,385,258,78)(31,386,259,79)(32,387,260,80)(33,388,261,81)(34,389,262,82)(35,390,263,83)(36,391,264,84)(37,392,265,71)(38,379,266,72)(39,380,253,73)(40,381,254,74)(41,382,255,75)(42,383,256,76)(57,171,371,134)(58,172,372,135)(59,173,373,136)(60,174,374,137)(61,175,375,138)(62,176,376,139)(63,177,377,140)(64,178,378,127)(65,179,365,128)(66,180,366,129)(67,181,367,130)(68,182,368,131)(69,169,369,132)(70,170,370,133)(85,296,316,334)(86,297,317,335)(87,298,318,336)(88,299,319,323)(89,300,320,324)(90,301,321,325)(91,302,322,326)(92,303,309,327)(93,304,310,328)(94,305,311,329)(95,306,312,330)(96,307,313,331)(97,308,314,332)(98,295,315,333)(99,285,232,342)(100,286,233,343)(101,287,234,344)(102,288,235,345)(103,289,236,346)(104,290,237,347)(105,291,238,348)(106,292,225,349)(107,293,226,350)(108,294,227,337)(109,281,228,338)(110,282,229,339)(111,283,230,340)(112,284,231,341)(113,154,419,163)(114,141,420,164)(115,142,407,165)(116,143,408,166)(117,144,409,167)(118,145,410,168)(119,146,411,155)(120,147,412,156)(121,148,413,157)(122,149,414,158)(123,150,415,159)(124,151,416,160)(125,152,417,161)(126,153,418,162)(267,442,402,358)(268,443,403,359)(269,444,404,360)(270,445,405,361)(271,446,406,362)(272,447,393,363)(273,448,394,364)(274,435,395,351)(275,436,396,352)(276,437,397,353)(277,438,398,354)(278,439,399,355)(279,440,400,356)(280,441,401,357), (1,374,252,60)(2,375,239,61)(3,376,240,62)(4,377,241,63)(5,378,242,64)(6,365,243,65)(7,366,244,66)(8,367,245,67)(9,368,246,68)(10,369,247,69)(11,370,248,70)(12,371,249,57)(13,372,250,58)(14,373,251,59)(15,93,187,310)(16,94,188,311)(17,95,189,312)(18,96,190,313)(19,97,191,314)(20,98,192,315)(21,85,193,316)(22,86,194,317)(23,87,195,318)(24,88,196,319)(25,89,183,320)(26,90,184,321)(27,91,185,322)(28,92,186,309)(29,440,257,356)(30,441,258,357)(31,442,259,358)(32,443,260,359)(33,444,261,360)(34,445,262,361)(35,446,263,362)(36,447,264,363)(37,448,265,364)(38,435,266,351)(39,436,253,352)(40,437,254,353)(41,438,255,354)(42,439,256,355)(43,137,216,174)(44,138,217,175)(45,139,218,176)(46,140,219,177)(47,127,220,178)(48,128,221,179)(49,129,222,180)(50,130,223,181)(51,131,224,182)(52,132,211,169)(53,133,212,170)(54,134,213,171)(55,135,214,172)(56,136,215,173)(71,394,392,273)(72,395,379,274)(73,396,380,275)(74,397,381,276)(75,398,382,277)(76,399,383,278)(77,400,384,279)(78,401,385,280)(79,402,386,267)(80,403,387,268)(81,404,388,269)(82,405,389,270)(83,406,390,271)(84,393,391,272)(99,160,232,151)(100,161,233,152)(101,162,234,153)(102,163,235,154)(103,164,236,141)(104,165,237,142)(105,166,238,143)(106,167,225,144)(107,168,226,145)(108,155,227,146)(109,156,228,147)(110,157,229,148)(111,158,230,149)(112,159,231,150)(113,288,419,345)(114,289,420,346)(115,290,407,347)(116,291,408,348)(117,292,409,349)(118,293,410,350)(119,294,411,337)(120,281,412,338)(121,282,413,339)(122,283,414,340)(123,284,415,341)(124,285,416,342)(125,286,417,343)(126,287,418,344)(197,323,425,299)(198,324,426,300)(199,325,427,301)(200,326,428,302)(201,327,429,303)(202,328,430,304)(203,329,431,305)(204,330,432,306)(205,331,433,307)(206,332,434,308)(207,333,421,295)(208,334,422,296)(209,335,423,297)(210,336,424,298), (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), (1,118,8,125)(2,117,9,124)(3,116,10,123)(4,115,11,122)(5,114,12,121)(6,113,13,120)(7,126,14,119)(15,277,22,270)(16,276,23,269)(17,275,24,268)(18,274,25,267)(19,273,26,280)(20,272,27,279)(21,271,28,278)(29,98,36,91)(30,97,37,90)(31,96,38,89)(32,95,39,88)(33,94,40,87)(34,93,41,86)(35,92,42,85)(43,145,50,152)(44,144,51,151)(45,143,52,150)(46,142,53,149)(47,141,54,148)(48,154,55,147)(49,153,56,146)(57,110,64,103)(58,109,65,102)(59,108,66,101)(60,107,67,100)(61,106,68,99)(62,105,69,112)(63,104,70,111)(71,301,78,308)(72,300,79,307)(73,299,80,306)(74,298,81,305)(75,297,82,304)(76,296,83,303)(77,295,84,302)(127,289,134,282)(128,288,135,281)(129,287,136,294)(130,286,137,293)(131,285,138,292)(132,284,139,291)(133,283,140,290)(155,222,162,215)(156,221,163,214)(157,220,164,213)(158,219,165,212)(159,218,166,211)(160,217,167,224)(161,216,168,223)(169,341,176,348)(170,340,177,347)(171,339,178,346)(172,338,179,345)(173,337,180,344)(174,350,181,343)(175,349,182,342)(183,402,190,395)(184,401,191,394)(185,400,192,393)(186,399,193,406)(187,398,194,405)(188,397,195,404)(189,396,196,403)(197,359,204,352)(198,358,205,351)(199,357,206,364)(200,356,207,363)(201,355,208,362)(202,354,209,361)(203,353,210,360)(225,368,232,375)(226,367,233,374)(227,366,234,373)(228,365,235,372)(229,378,236,371)(230,377,237,370)(231,376,238,369)(239,409,246,416)(240,408,247,415)(241,407,248,414)(242,420,249,413)(243,419,250,412)(244,418,251,411)(245,417,252,410)(253,319,260,312)(254,318,261,311)(255,317,262,310)(256,316,263,309)(257,315,264,322)(258,314,265,321)(259,313,266,320)(323,387,330,380)(324,386,331,379)(325,385,332,392)(326,384,333,391)(327,383,334,390)(328,382,335,389)(329,381,336,388)(421,447,428,440)(422,446,429,439)(423,445,430,438)(424,444,431,437)(425,443,432,436)(426,442,433,435)(427,441,434,448) );
G=PermutationGroup([[(1,306),(2,307),(3,308),(4,295),(5,296),(6,297),(7,298),(8,299),(9,300),(10,301),(11,302),(12,303),(13,304),(14,305),(15,172),(16,173),(17,174),(18,175),(19,176),(20,177),(21,178),(22,179),(23,180),(24,181),(25,182),(26,169),(27,170),(28,171),(29,149),(30,150),(31,151),(32,152),(33,153),(34,154),(35,141),(36,142),(37,143),(38,144),(39,145),(40,146),(41,147),(42,148),(43,95),(44,96),(45,97),(46,98),(47,85),(48,86),(49,87),(50,88),(51,89),(52,90),(53,91),(54,92),(55,93),(56,94),(57,429),(58,430),(59,431),(60,432),(61,433),(62,434),(63,421),(64,422),(65,423),(66,424),(67,425),(68,426),(69,427),(70,428),(71,116),(72,117),(73,118),(74,119),(75,120),(76,121),(77,122),(78,123),(79,124),(80,125),(81,126),(82,113),(83,114),(84,115),(99,442),(100,443),(101,444),(102,445),(103,446),(104,447),(105,448),(106,435),(107,436),(108,437),(109,438),(110,439),(111,440),(112,441),(127,193),(128,194),(129,195),(130,196),(131,183),(132,184),(133,185),(134,186),(135,187),(136,188),(137,189),(138,190),(139,191),(140,192),(155,254),(156,255),(157,256),(158,257),(159,258),(160,259),(161,260),(162,261),(163,262),(164,263),(165,264),(166,265),(167,266),(168,253),(197,367),(198,368),(199,369),(200,370),(201,371),(202,372),(203,373),(204,374),(205,375),(206,376),(207,377),(208,378),(209,365),(210,366),(211,321),(212,322),(213,309),(214,310),(215,311),(216,312),(217,313),(218,314),(219,315),(220,316),(221,317),(222,318),(223,319),(224,320),(225,351),(226,352),(227,353),(228,354),(229,355),(230,356),(231,357),(232,358),(233,359),(234,360),(235,361),(236,362),(237,363),(238,364),(239,331),(240,332),(241,333),(242,334),(243,335),(244,336),(245,323),(246,324),(247,325),(248,326),(249,327),(250,328),(251,329),(252,330),(267,342),(268,343),(269,344),(270,345),(271,346),(272,347),(273,348),(274,349),(275,350),(276,337),(277,338),(278,339),(279,340),(280,341),(281,398),(282,399),(283,400),(284,401),(285,402),(286,403),(287,404),(288,405),(289,406),(290,393),(291,394),(292,395),(293,396),(294,397),(379,409),(380,410),(381,411),(382,412),(383,413),(384,414),(385,415),(386,416),(387,417),(388,418),(389,419),(390,420),(391,407),(392,408)], [(1,216,252,43),(2,217,239,44),(3,218,240,45),(4,219,241,46),(5,220,242,47),(6,221,243,48),(7,222,244,49),(8,223,245,50),(9,224,246,51),(10,211,247,52),(11,212,248,53),(12,213,249,54),(13,214,250,55),(14,215,251,56),(15,202,187,430),(16,203,188,431),(17,204,189,432),(18,205,190,433),(19,206,191,434),(20,207,192,421),(21,208,193,422),(22,209,194,423),(23,210,195,424),(24,197,196,425),(25,198,183,426),(26,199,184,427),(27,200,185,428),(28,201,186,429),(29,384,257,77),(30,385,258,78),(31,386,259,79),(32,387,260,80),(33,388,261,81),(34,389,262,82),(35,390,263,83),(36,391,264,84),(37,392,265,71),(38,379,266,72),(39,380,253,73),(40,381,254,74),(41,382,255,75),(42,383,256,76),(57,171,371,134),(58,172,372,135),(59,173,373,136),(60,174,374,137),(61,175,375,138),(62,176,376,139),(63,177,377,140),(64,178,378,127),(65,179,365,128),(66,180,366,129),(67,181,367,130),(68,182,368,131),(69,169,369,132),(70,170,370,133),(85,296,316,334),(86,297,317,335),(87,298,318,336),(88,299,319,323),(89,300,320,324),(90,301,321,325),(91,302,322,326),(92,303,309,327),(93,304,310,328),(94,305,311,329),(95,306,312,330),(96,307,313,331),(97,308,314,332),(98,295,315,333),(99,285,232,342),(100,286,233,343),(101,287,234,344),(102,288,235,345),(103,289,236,346),(104,290,237,347),(105,291,238,348),(106,292,225,349),(107,293,226,350),(108,294,227,337),(109,281,228,338),(110,282,229,339),(111,283,230,340),(112,284,231,341),(113,154,419,163),(114,141,420,164),(115,142,407,165),(116,143,408,166),(117,144,409,167),(118,145,410,168),(119,146,411,155),(120,147,412,156),(121,148,413,157),(122,149,414,158),(123,150,415,159),(124,151,416,160),(125,152,417,161),(126,153,418,162),(267,442,402,358),(268,443,403,359),(269,444,404,360),(270,445,405,361),(271,446,406,362),(272,447,393,363),(273,448,394,364),(274,435,395,351),(275,436,396,352),(276,437,397,353),(277,438,398,354),(278,439,399,355),(279,440,400,356),(280,441,401,357)], [(1,374,252,60),(2,375,239,61),(3,376,240,62),(4,377,241,63),(5,378,242,64),(6,365,243,65),(7,366,244,66),(8,367,245,67),(9,368,246,68),(10,369,247,69),(11,370,248,70),(12,371,249,57),(13,372,250,58),(14,373,251,59),(15,93,187,310),(16,94,188,311),(17,95,189,312),(18,96,190,313),(19,97,191,314),(20,98,192,315),(21,85,193,316),(22,86,194,317),(23,87,195,318),(24,88,196,319),(25,89,183,320),(26,90,184,321),(27,91,185,322),(28,92,186,309),(29,440,257,356),(30,441,258,357),(31,442,259,358),(32,443,260,359),(33,444,261,360),(34,445,262,361),(35,446,263,362),(36,447,264,363),(37,448,265,364),(38,435,266,351),(39,436,253,352),(40,437,254,353),(41,438,255,354),(42,439,256,355),(43,137,216,174),(44,138,217,175),(45,139,218,176),(46,140,219,177),(47,127,220,178),(48,128,221,179),(49,129,222,180),(50,130,223,181),(51,131,224,182),(52,132,211,169),(53,133,212,170),(54,134,213,171),(55,135,214,172),(56,136,215,173),(71,394,392,273),(72,395,379,274),(73,396,380,275),(74,397,381,276),(75,398,382,277),(76,399,383,278),(77,400,384,279),(78,401,385,280),(79,402,386,267),(80,403,387,268),(81,404,388,269),(82,405,389,270),(83,406,390,271),(84,393,391,272),(99,160,232,151),(100,161,233,152),(101,162,234,153),(102,163,235,154),(103,164,236,141),(104,165,237,142),(105,166,238,143),(106,167,225,144),(107,168,226,145),(108,155,227,146),(109,156,228,147),(110,157,229,148),(111,158,230,149),(112,159,231,150),(113,288,419,345),(114,289,420,346),(115,290,407,347),(116,291,408,348),(117,292,409,349),(118,293,410,350),(119,294,411,337),(120,281,412,338),(121,282,413,339),(122,283,414,340),(123,284,415,341),(124,285,416,342),(125,286,417,343),(126,287,418,344),(197,323,425,299),(198,324,426,300),(199,325,427,301),(200,326,428,302),(201,327,429,303),(202,328,430,304),(203,329,431,305),(204,330,432,306),(205,331,433,307),(206,332,434,308),(207,333,421,295),(208,334,422,296),(209,335,423,297),(210,336,424,298)], [(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)], [(1,118,8,125),(2,117,9,124),(3,116,10,123),(4,115,11,122),(5,114,12,121),(6,113,13,120),(7,126,14,119),(15,277,22,270),(16,276,23,269),(17,275,24,268),(18,274,25,267),(19,273,26,280),(20,272,27,279),(21,271,28,278),(29,98,36,91),(30,97,37,90),(31,96,38,89),(32,95,39,88),(33,94,40,87),(34,93,41,86),(35,92,42,85),(43,145,50,152),(44,144,51,151),(45,143,52,150),(46,142,53,149),(47,141,54,148),(48,154,55,147),(49,153,56,146),(57,110,64,103),(58,109,65,102),(59,108,66,101),(60,107,67,100),(61,106,68,99),(62,105,69,112),(63,104,70,111),(71,301,78,308),(72,300,79,307),(73,299,80,306),(74,298,81,305),(75,297,82,304),(76,296,83,303),(77,295,84,302),(127,289,134,282),(128,288,135,281),(129,287,136,294),(130,286,137,293),(131,285,138,292),(132,284,139,291),(133,283,140,290),(155,222,162,215),(156,221,163,214),(157,220,164,213),(158,219,165,212),(159,218,166,211),(160,217,167,224),(161,216,168,223),(169,341,176,348),(170,340,177,347),(171,339,178,346),(172,338,179,345),(173,337,180,344),(174,350,181,343),(175,349,182,342),(183,402,190,395),(184,401,191,394),(185,400,192,393),(186,399,193,406),(187,398,194,405),(188,397,195,404),(189,396,196,403),(197,359,204,352),(198,358,205,351),(199,357,206,364),(200,356,207,363),(201,355,208,362),(202,354,209,361),(203,353,210,360),(225,368,232,375),(226,367,233,374),(227,366,234,373),(228,365,235,372),(229,378,236,371),(230,377,237,370),(231,376,238,369),(239,409,246,416),(240,408,247,415),(241,407,248,414),(242,420,249,413),(243,419,250,412),(244,418,251,411),(245,417,252,410),(253,319,260,312),(254,318,261,311),(255,317,262,310),(256,316,263,309),(257,315,264,322),(258,314,265,321),(259,313,266,320),(323,387,330,380),(324,386,331,379),(325,385,332,392),(326,384,333,391),(327,383,334,390),(328,382,335,389),(329,381,336,388),(421,447,428,440),(422,446,429,439),(423,445,430,438),(424,444,431,437),(425,443,432,436),(426,442,433,435),(427,441,434,448)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | - | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D7 | SD16 | Q16 | D14 | Dic7 | D14 | C7⋊D4 | C7⋊D4 | Q8⋊D7 | C7⋊Q16 |
| kernel | C2×Q8⋊Dic7 | Q8⋊Dic7 | C22×C7⋊C8 | C2×C4⋊Dic7 | Q8×C2×C14 | Q8×C14 | C2×C28 | C22×C14 | C22×Q8 | C2×C14 | C2×C14 | C22×C4 | C2×Q8 | C2×Q8 | C2×C4 | C23 | C22 | C22 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 3 | 1 | 3 | 4 | 4 | 3 | 12 | 6 | 18 | 6 | 6 | 6 |
Matrix representation of C2×Q8⋊Dic7 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 69 |
| 0 | 0 | 0 | 0 | 36 | 112 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 35 | 109 |
| 0 | 0 | 0 | 0 | 24 | 78 |
| 88 | 112 | 0 | 0 | 0 | 0 |
| 2 | 104 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 112 | 89 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 42 | 19 | 0 | 0 | 0 | 0 |
| 44 | 71 | 0 | 0 | 0 | 0 |
| 0 | 0 | 100 | 17 | 0 | 0 |
| 0 | 0 | 103 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 64 | 28 |
| 0 | 0 | 0 | 0 | 108 | 49 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,36,0,0,0,0,69,112],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,35,24,0,0,0,0,109,78],[88,2,0,0,0,0,112,104,0,0,0,0,0,0,0,112,0,0,0,0,1,89,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[42,44,0,0,0,0,19,71,0,0,0,0,0,0,100,103,0,0,0,0,17,13,0,0,0,0,0,0,64,108,0,0,0,0,28,49] >;
C2×Q8⋊Dic7 in GAP, Magma, Sage, TeX
C_2\times Q_8\rtimes {\rm Dic}_7 % in TeX
G:=Group("C2xQ8:Dic7"); // GroupNames label
G:=SmallGroup(448,758);
// by ID
G=gap.SmallGroup(448,758);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,422,184,1684,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=d^14=1,c^2=b^2,e^2=d^7,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=e*b*e^-1=b^-1,b*d=d*b,c*d=d*c,e*c*e^-1=b^-1*c,e*d*e^-1=d^-1>;
// generators/relations