metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C28)⋊1Q8, (C2×Dic7)⋊1Q8, (C2×C4)⋊1Dic14, (C2×C4).16D28, (C2×C28).27D4, C2.6(C28⋊Q8), C14.1C22≀C2, C14.11(C4⋊Q8), (C2×Dic7).7D4, C22.38(Q8×D7), C2.4(C28⋊2Q8), (C22×C4).67D14, C22.77(C2×D28), C22.150(D4×D7), C2.6(C22⋊D28), C2.6(D14⋊2Q8), C14.20(C22⋊Q8), (C22×C28).44C22, (C22×Dic14).2C2, C22.40(C2×Dic14), C2.C42.12D7, C23.352(C22×D7), C22.81(D4⋊2D7), C14.C42.24C2, (C22×C14).281C23, C2.8(C22⋊Dic14), C7⋊1(C23.78C23), (C22×Dic7).6C22, (C2×C14).93(C2×D4), (C2×C4⋊Dic7).6C2, (C2×C14).62(C2×Q8), (C2×Dic7⋊C4).18C2, (C2×C14).126(C4○D4), (C7×C2.C42).8C2, SmallGroup(448,190)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×Dic7)⋊Q8
G = < a,b,c,d,e | a2=b14=d4=1, c2=b7, e2=d2, ab=ba, dcd-1=ac=ca, ad=da, ae=ea, cbc-1=dbd-1=b-1, be=eb, ece-1=b7c, ede-1=d-1 >
Subgroups: 828 in 182 conjugacy classes, 69 normal (25 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, Q8, C23, C14, C14, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×Q8, Dic7, 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, C23.78C23, Dic7⋊C4, C4⋊Dic7, C2×Dic14, C22×Dic7, C22×Dic7, C22×C28, C22×C28, C14.C42, C7×C2.C42, C2×Dic7⋊C4, C2×C4⋊Dic7, C22×Dic14, (C2×Dic7)⋊Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C4○D4, D14, C22≀C2, C22⋊Q8, C4⋊Q8, Dic14, D28, C22×D7, C23.78C23, C2×Dic14, C2×D28, D4×D7, D4⋊2D7, Q8×D7, C28⋊2Q8, C22⋊Dic14, C22⋊D28, C28⋊Q8, D14⋊2Q8, (C2×Dic7)⋊Q8
►Regular action on 448 points
Generators in S448
(1 384)(2 385)(3 386)(4 387)(5 388)(6 389)(7 390)(8 391)(9 392)(10 379)(11 380)(12 381)(13 382)(14 383)(15 432)(16 433)(17 434)(18 421)(19 422)(20 423)(21 424)(22 425)(23 426)(24 427)(25 428)(26 429)(27 430)(28 431)(29 61)(30 62)(31 63)(32 64)(33 65)(34 66)(35 67)(36 68)(37 69)(38 70)(39 57)(40 58)(41 59)(42 60)(43 411)(44 412)(45 413)(46 414)(47 415)(48 416)(49 417)(50 418)(51 419)(52 420)(53 407)(54 408)(55 409)(56 410)(71 133)(72 134)(73 135)(74 136)(75 137)(76 138)(77 139)(78 140)(79 127)(80 128)(81 129)(82 130)(83 131)(84 132)(85 313)(86 314)(87 315)(88 316)(89 317)(90 318)(91 319)(92 320)(93 321)(94 322)(95 309)(96 310)(97 311)(98 312)(99 402)(100 403)(101 404)(102 405)(103 406)(104 393)(105 394)(106 395)(107 396)(108 397)(109 398)(110 399)(111 400)(112 401)(113 336)(114 323)(115 324)(116 325)(117 326)(118 327)(119 328)(120 329)(121 330)(122 331)(123 332)(124 333)(125 334)(126 335)(141 180)(142 181)(143 182)(144 169)(145 170)(146 171)(147 172)(148 173)(149 174)(150 175)(151 176)(152 177)(153 178)(154 179)(155 276)(156 277)(157 278)(158 279)(159 280)(160 267)(161 268)(162 269)(163 270)(164 271)(165 272)(166 273)(167 274)(168 275)(183 245)(184 246)(185 247)(186 248)(187 249)(188 250)(189 251)(190 252)(191 239)(192 240)(193 241)(194 242)(195 243)(196 244)(197 436)(198 437)(199 438)(200 439)(201 440)(202 441)(203 442)(204 443)(205 444)(206 445)(207 446)(208 447)(209 448)(210 435)(211 285)(212 286)(213 287)(214 288)(215 289)(216 290)(217 291)(218 292)(219 293)(220 294)(221 281)(222 282)(223 283)(224 284)(225 259)(226 260)(227 261)(228 262)(229 263)(230 264)(231 265)(232 266)(233 253)(234 254)(235 255)(236 256)(237 257)(238 258)(295 355)(296 356)(297 357)(298 358)(299 359)(300 360)(301 361)(302 362)(303 363)(304 364)(305 351)(306 352)(307 353)(308 354)(337 371)(338 372)(339 373)(340 374)(341 375)(342 376)(343 377)(344 378)(345 365)(346 366)(347 367)(348 368)(349 369)(350 370)
(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 92 8 85)(2 91 9 98)(3 90 10 97)(4 89 11 96)(5 88 12 95)(6 87 13 94)(7 86 14 93)(15 51 22 44)(16 50 23 43)(17 49 24 56)(18 48 25 55)(19 47 26 54)(20 46 27 53)(21 45 28 52)(29 357 36 364)(30 356 37 363)(31 355 38 362)(32 354 39 361)(33 353 40 360)(34 352 41 359)(35 351 42 358)(57 301 64 308)(58 300 65 307)(59 299 66 306)(60 298 67 305)(61 297 68 304)(62 296 69 303)(63 295 70 302)(71 369 78 376)(72 368 79 375)(73 367 80 374)(74 366 81 373)(75 365 82 372)(76 378 83 371)(77 377 84 370)(99 180 106 173)(100 179 107 172)(101 178 108 171)(102 177 109 170)(103 176 110 169)(104 175 111 182)(105 174 112 181)(113 278 120 271)(114 277 121 270)(115 276 122 269)(116 275 123 268)(117 274 124 267)(118 273 125 280)(119 272 126 279)(127 341 134 348)(128 340 135 347)(129 339 136 346)(130 338 137 345)(131 337 138 344)(132 350 139 343)(133 349 140 342)(141 395 148 402)(142 394 149 401)(143 393 150 400)(144 406 151 399)(145 405 152 398)(146 404 153 397)(147 403 154 396)(155 331 162 324)(156 330 163 323)(157 329 164 336)(158 328 165 335)(159 327 166 334)(160 326 167 333)(161 325 168 332)(183 291 190 284)(184 290 191 283)(185 289 192 282)(186 288 193 281)(187 287 194 294)(188 286 195 293)(189 285 196 292)(197 258 204 265)(198 257 205 264)(199 256 206 263)(200 255 207 262)(201 254 208 261)(202 253 209 260)(203 266 210 259)(211 244 218 251)(212 243 219 250)(213 242 220 249)(214 241 221 248)(215 240 222 247)(216 239 223 246)(217 252 224 245)(225 442 232 435)(226 441 233 448)(227 440 234 447)(228 439 235 446)(229 438 236 445)(230 437 237 444)(231 436 238 443)(309 388 316 381)(310 387 317 380)(311 386 318 379)(312 385 319 392)(313 384 320 391)(314 383 321 390)(315 382 322 389)(407 423 414 430)(408 422 415 429)(409 421 416 428)(410 434 417 427)(411 433 418 426)(412 432 419 425)(413 431 420 424)
(1 229 60 327)(2 228 61 326)(3 227 62 325)(4 226 63 324)(5 225 64 323)(6 238 65 336)(7 237 66 335)(8 236 67 334)(9 235 68 333)(10 234 69 332)(11 233 70 331)(12 232 57 330)(13 231 58 329)(14 230 59 328)(15 147 339 224)(16 146 340 223)(17 145 341 222)(18 144 342 221)(19 143 343 220)(20 142 344 219)(21 141 345 218)(22 154 346 217)(23 153 347 216)(24 152 348 215)(25 151 349 214)(26 150 350 213)(27 149 337 212)(28 148 338 211)(29 117 385 262)(30 116 386 261)(31 115 387 260)(32 114 388 259)(33 113 389 258)(34 126 390 257)(35 125 391 256)(36 124 392 255)(37 123 379 254)(38 122 380 253)(39 121 381 266)(40 120 382 265)(41 119 383 264)(42 118 384 263)(43 108 128 191)(44 107 129 190)(45 106 130 189)(46 105 131 188)(47 104 132 187)(48 103 133 186)(49 102 134 185)(50 101 135 184)(51 100 136 183)(52 99 137 196)(53 112 138 195)(54 111 139 194)(55 110 140 193)(56 109 127 192)(71 248 416 406)(72 247 417 405)(73 246 418 404)(74 245 419 403)(75 244 420 402)(76 243 407 401)(77 242 408 400)(78 241 409 399)(79 240 410 398)(80 239 411 397)(81 252 412 396)(82 251 413 395)(83 250 414 394)(84 249 415 393)(85 206 305 280)(86 205 306 279)(87 204 307 278)(88 203 308 277)(89 202 295 276)(90 201 296 275)(91 200 297 274)(92 199 298 273)(93 198 299 272)(94 197 300 271)(95 210 301 270)(96 209 302 269)(97 208 303 268)(98 207 304 267)(155 317 441 355)(156 316 442 354)(157 315 443 353)(158 314 444 352)(159 313 445 351)(160 312 446 364)(161 311 447 363)(162 310 448 362)(163 309 435 361)(164 322 436 360)(165 321 437 359)(166 320 438 358)(167 319 439 357)(168 318 440 356)(169 376 281 421)(170 375 282 434)(171 374 283 433)(172 373 284 432)(173 372 285 431)(174 371 286 430)(175 370 287 429)(176 369 288 428)(177 368 289 427)(178 367 290 426)(179 366 291 425)(180 365 292 424)(181 378 293 423)(182 377 294 422)
(1 349 60 25)(2 350 61 26)(3 337 62 27)(4 338 63 28)(5 339 64 15)(6 340 65 16)(7 341 66 17)(8 342 67 18)(9 343 68 19)(10 344 69 20)(11 345 70 21)(12 346 57 22)(13 347 58 23)(14 348 59 24)(29 429 385 370)(30 430 386 371)(31 431 387 372)(32 432 388 373)(33 433 389 374)(34 434 390 375)(35 421 391 376)(36 422 392 377)(37 423 379 378)(38 424 380 365)(39 425 381 366)(40 426 382 367)(41 427 383 368)(42 428 384 369)(43 87 128 307)(44 88 129 308)(45 89 130 295)(46 90 131 296)(47 91 132 297)(48 92 133 298)(49 93 134 299)(50 94 135 300)(51 95 136 301)(52 96 137 302)(53 97 138 303)(54 98 139 304)(55 85 140 305)(56 86 127 306)(71 358 416 320)(72 359 417 321)(73 360 418 322)(74 361 419 309)(75 362 420 310)(76 363 407 311)(77 364 408 312)(78 351 409 313)(79 352 410 314)(80 353 411 315)(81 354 412 316)(82 355 413 317)(83 356 414 318)(84 357 415 319)(99 269 196 209)(100 270 183 210)(101 271 184 197)(102 272 185 198)(103 273 186 199)(104 274 187 200)(105 275 188 201)(106 276 189 202)(107 277 190 203)(108 278 191 204)(109 279 192 205)(110 280 193 206)(111 267 194 207)(112 268 195 208)(113 283 258 171)(114 284 259 172)(115 285 260 173)(116 286 261 174)(117 287 262 175)(118 288 263 176)(119 289 264 177)(120 290 265 178)(121 291 266 179)(122 292 253 180)(123 293 254 181)(124 294 255 182)(125 281 256 169)(126 282 257 170)(141 331 218 233)(142 332 219 234)(143 333 220 235)(144 334 221 236)(145 335 222 237)(146 336 223 238)(147 323 224 225)(148 324 211 226)(149 325 212 227)(150 326 213 228)(151 327 214 229)(152 328 215 230)(153 329 216 231)(154 330 217 232)(155 251 441 395)(156 252 442 396)(157 239 443 397)(158 240 444 398)(159 241 445 399)(160 242 446 400)(161 243 447 401)(162 244 448 402)(163 245 435 403)(164 246 436 404)(165 247 437 405)(166 248 438 406)(167 249 439 393)(168 250 440 394)
G:=sub<Sym(448)| (1,384)(2,385)(3,386)(4,387)(5,388)(6,389)(7,390)(8,391)(9,392)(10,379)(11,380)(12,381)(13,382)(14,383)(15,432)(16,433)(17,434)(18,421)(19,422)(20,423)(21,424)(22,425)(23,426)(24,427)(25,428)(26,429)(27,430)(28,431)(29,61)(30,62)(31,63)(32,64)(33,65)(34,66)(35,67)(36,68)(37,69)(38,70)(39,57)(40,58)(41,59)(42,60)(43,411)(44,412)(45,413)(46,414)(47,415)(48,416)(49,417)(50,418)(51,419)(52,420)(53,407)(54,408)(55,409)(56,410)(71,133)(72,134)(73,135)(74,136)(75,137)(76,138)(77,139)(78,140)(79,127)(80,128)(81,129)(82,130)(83,131)(84,132)(85,313)(86,314)(87,315)(88,316)(89,317)(90,318)(91,319)(92,320)(93,321)(94,322)(95,309)(96,310)(97,311)(98,312)(99,402)(100,403)(101,404)(102,405)(103,406)(104,393)(105,394)(106,395)(107,396)(108,397)(109,398)(110,399)(111,400)(112,401)(113,336)(114,323)(115,324)(116,325)(117,326)(118,327)(119,328)(120,329)(121,330)(122,331)(123,332)(124,333)(125,334)(126,335)(141,180)(142,181)(143,182)(144,169)(145,170)(146,171)(147,172)(148,173)(149,174)(150,175)(151,176)(152,177)(153,178)(154,179)(155,276)(156,277)(157,278)(158,279)(159,280)(160,267)(161,268)(162,269)(163,270)(164,271)(165,272)(166,273)(167,274)(168,275)(183,245)(184,246)(185,247)(186,248)(187,249)(188,250)(189,251)(190,252)(191,239)(192,240)(193,241)(194,242)(195,243)(196,244)(197,436)(198,437)(199,438)(200,439)(201,440)(202,441)(203,442)(204,443)(205,444)(206,445)(207,446)(208,447)(209,448)(210,435)(211,285)(212,286)(213,287)(214,288)(215,289)(216,290)(217,291)(218,292)(219,293)(220,294)(221,281)(222,282)(223,283)(224,284)(225,259)(226,260)(227,261)(228,262)(229,263)(230,264)(231,265)(232,266)(233,253)(234,254)(235,255)(236,256)(237,257)(238,258)(295,355)(296,356)(297,357)(298,358)(299,359)(300,360)(301,361)(302,362)(303,363)(304,364)(305,351)(306,352)(307,353)(308,354)(337,371)(338,372)(339,373)(340,374)(341,375)(342,376)(343,377)(344,378)(345,365)(346,366)(347,367)(348,368)(349,369)(350,370), (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), (1,92,8,85)(2,91,9,98)(3,90,10,97)(4,89,11,96)(5,88,12,95)(6,87,13,94)(7,86,14,93)(15,51,22,44)(16,50,23,43)(17,49,24,56)(18,48,25,55)(19,47,26,54)(20,46,27,53)(21,45,28,52)(29,357,36,364)(30,356,37,363)(31,355,38,362)(32,354,39,361)(33,353,40,360)(34,352,41,359)(35,351,42,358)(57,301,64,308)(58,300,65,307)(59,299,66,306)(60,298,67,305)(61,297,68,304)(62,296,69,303)(63,295,70,302)(71,369,78,376)(72,368,79,375)(73,367,80,374)(74,366,81,373)(75,365,82,372)(76,378,83,371)(77,377,84,370)(99,180,106,173)(100,179,107,172)(101,178,108,171)(102,177,109,170)(103,176,110,169)(104,175,111,182)(105,174,112,181)(113,278,120,271)(114,277,121,270)(115,276,122,269)(116,275,123,268)(117,274,124,267)(118,273,125,280)(119,272,126,279)(127,341,134,348)(128,340,135,347)(129,339,136,346)(130,338,137,345)(131,337,138,344)(132,350,139,343)(133,349,140,342)(141,395,148,402)(142,394,149,401)(143,393,150,400)(144,406,151,399)(145,405,152,398)(146,404,153,397)(147,403,154,396)(155,331,162,324)(156,330,163,323)(157,329,164,336)(158,328,165,335)(159,327,166,334)(160,326,167,333)(161,325,168,332)(183,291,190,284)(184,290,191,283)(185,289,192,282)(186,288,193,281)(187,287,194,294)(188,286,195,293)(189,285,196,292)(197,258,204,265)(198,257,205,264)(199,256,206,263)(200,255,207,262)(201,254,208,261)(202,253,209,260)(203,266,210,259)(211,244,218,251)(212,243,219,250)(213,242,220,249)(214,241,221,248)(215,240,222,247)(216,239,223,246)(217,252,224,245)(225,442,232,435)(226,441,233,448)(227,440,234,447)(228,439,235,446)(229,438,236,445)(230,437,237,444)(231,436,238,443)(309,388,316,381)(310,387,317,380)(311,386,318,379)(312,385,319,392)(313,384,320,391)(314,383,321,390)(315,382,322,389)(407,423,414,430)(408,422,415,429)(409,421,416,428)(410,434,417,427)(411,433,418,426)(412,432,419,425)(413,431,420,424), (1,229,60,327)(2,228,61,326)(3,227,62,325)(4,226,63,324)(5,225,64,323)(6,238,65,336)(7,237,66,335)(8,236,67,334)(9,235,68,333)(10,234,69,332)(11,233,70,331)(12,232,57,330)(13,231,58,329)(14,230,59,328)(15,147,339,224)(16,146,340,223)(17,145,341,222)(18,144,342,221)(19,143,343,220)(20,142,344,219)(21,141,345,218)(22,154,346,217)(23,153,347,216)(24,152,348,215)(25,151,349,214)(26,150,350,213)(27,149,337,212)(28,148,338,211)(29,117,385,262)(30,116,386,261)(31,115,387,260)(32,114,388,259)(33,113,389,258)(34,126,390,257)(35,125,391,256)(36,124,392,255)(37,123,379,254)(38,122,380,253)(39,121,381,266)(40,120,382,265)(41,119,383,264)(42,118,384,263)(43,108,128,191)(44,107,129,190)(45,106,130,189)(46,105,131,188)(47,104,132,187)(48,103,133,186)(49,102,134,185)(50,101,135,184)(51,100,136,183)(52,99,137,196)(53,112,138,195)(54,111,139,194)(55,110,140,193)(56,109,127,192)(71,248,416,406)(72,247,417,405)(73,246,418,404)(74,245,419,403)(75,244,420,402)(76,243,407,401)(77,242,408,400)(78,241,409,399)(79,240,410,398)(80,239,411,397)(81,252,412,396)(82,251,413,395)(83,250,414,394)(84,249,415,393)(85,206,305,280)(86,205,306,279)(87,204,307,278)(88,203,308,277)(89,202,295,276)(90,201,296,275)(91,200,297,274)(92,199,298,273)(93,198,299,272)(94,197,300,271)(95,210,301,270)(96,209,302,269)(97,208,303,268)(98,207,304,267)(155,317,441,355)(156,316,442,354)(157,315,443,353)(158,314,444,352)(159,313,445,351)(160,312,446,364)(161,311,447,363)(162,310,448,362)(163,309,435,361)(164,322,436,360)(165,321,437,359)(166,320,438,358)(167,319,439,357)(168,318,440,356)(169,376,281,421)(170,375,282,434)(171,374,283,433)(172,373,284,432)(173,372,285,431)(174,371,286,430)(175,370,287,429)(176,369,288,428)(177,368,289,427)(178,367,290,426)(179,366,291,425)(180,365,292,424)(181,378,293,423)(182,377,294,422), (1,349,60,25)(2,350,61,26)(3,337,62,27)(4,338,63,28)(5,339,64,15)(6,340,65,16)(7,341,66,17)(8,342,67,18)(9,343,68,19)(10,344,69,20)(11,345,70,21)(12,346,57,22)(13,347,58,23)(14,348,59,24)(29,429,385,370)(30,430,386,371)(31,431,387,372)(32,432,388,373)(33,433,389,374)(34,434,390,375)(35,421,391,376)(36,422,392,377)(37,423,379,378)(38,424,380,365)(39,425,381,366)(40,426,382,367)(41,427,383,368)(42,428,384,369)(43,87,128,307)(44,88,129,308)(45,89,130,295)(46,90,131,296)(47,91,132,297)(48,92,133,298)(49,93,134,299)(50,94,135,300)(51,95,136,301)(52,96,137,302)(53,97,138,303)(54,98,139,304)(55,85,140,305)(56,86,127,306)(71,358,416,320)(72,359,417,321)(73,360,418,322)(74,361,419,309)(75,362,420,310)(76,363,407,311)(77,364,408,312)(78,351,409,313)(79,352,410,314)(80,353,411,315)(81,354,412,316)(82,355,413,317)(83,356,414,318)(84,357,415,319)(99,269,196,209)(100,270,183,210)(101,271,184,197)(102,272,185,198)(103,273,186,199)(104,274,187,200)(105,275,188,201)(106,276,189,202)(107,277,190,203)(108,278,191,204)(109,279,192,205)(110,280,193,206)(111,267,194,207)(112,268,195,208)(113,283,258,171)(114,284,259,172)(115,285,260,173)(116,286,261,174)(117,287,262,175)(118,288,263,176)(119,289,264,177)(120,290,265,178)(121,291,266,179)(122,292,253,180)(123,293,254,181)(124,294,255,182)(125,281,256,169)(126,282,257,170)(141,331,218,233)(142,332,219,234)(143,333,220,235)(144,334,221,236)(145,335,222,237)(146,336,223,238)(147,323,224,225)(148,324,211,226)(149,325,212,227)(150,326,213,228)(151,327,214,229)(152,328,215,230)(153,329,216,231)(154,330,217,232)(155,251,441,395)(156,252,442,396)(157,239,443,397)(158,240,444,398)(159,241,445,399)(160,242,446,400)(161,243,447,401)(162,244,448,402)(163,245,435,403)(164,246,436,404)(165,247,437,405)(166,248,438,406)(167,249,439,393)(168,250,440,394)>;
G:=Group( (1,384)(2,385)(3,386)(4,387)(5,388)(6,389)(7,390)(8,391)(9,392)(10,379)(11,380)(12,381)(13,382)(14,383)(15,432)(16,433)(17,434)(18,421)(19,422)(20,423)(21,424)(22,425)(23,426)(24,427)(25,428)(26,429)(27,430)(28,431)(29,61)(30,62)(31,63)(32,64)(33,65)(34,66)(35,67)(36,68)(37,69)(38,70)(39,57)(40,58)(41,59)(42,60)(43,411)(44,412)(45,413)(46,414)(47,415)(48,416)(49,417)(50,418)(51,419)(52,420)(53,407)(54,408)(55,409)(56,410)(71,133)(72,134)(73,135)(74,136)(75,137)(76,138)(77,139)(78,140)(79,127)(80,128)(81,129)(82,130)(83,131)(84,132)(85,313)(86,314)(87,315)(88,316)(89,317)(90,318)(91,319)(92,320)(93,321)(94,322)(95,309)(96,310)(97,311)(98,312)(99,402)(100,403)(101,404)(102,405)(103,406)(104,393)(105,394)(106,395)(107,396)(108,397)(109,398)(110,399)(111,400)(112,401)(113,336)(114,323)(115,324)(116,325)(117,326)(118,327)(119,328)(120,329)(121,330)(122,331)(123,332)(124,333)(125,334)(126,335)(141,180)(142,181)(143,182)(144,169)(145,170)(146,171)(147,172)(148,173)(149,174)(150,175)(151,176)(152,177)(153,178)(154,179)(155,276)(156,277)(157,278)(158,279)(159,280)(160,267)(161,268)(162,269)(163,270)(164,271)(165,272)(166,273)(167,274)(168,275)(183,245)(184,246)(185,247)(186,248)(187,249)(188,250)(189,251)(190,252)(191,239)(192,240)(193,241)(194,242)(195,243)(196,244)(197,436)(198,437)(199,438)(200,439)(201,440)(202,441)(203,442)(204,443)(205,444)(206,445)(207,446)(208,447)(209,448)(210,435)(211,285)(212,286)(213,287)(214,288)(215,289)(216,290)(217,291)(218,292)(219,293)(220,294)(221,281)(222,282)(223,283)(224,284)(225,259)(226,260)(227,261)(228,262)(229,263)(230,264)(231,265)(232,266)(233,253)(234,254)(235,255)(236,256)(237,257)(238,258)(295,355)(296,356)(297,357)(298,358)(299,359)(300,360)(301,361)(302,362)(303,363)(304,364)(305,351)(306,352)(307,353)(308,354)(337,371)(338,372)(339,373)(340,374)(341,375)(342,376)(343,377)(344,378)(345,365)(346,366)(347,367)(348,368)(349,369)(350,370), (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), (1,92,8,85)(2,91,9,98)(3,90,10,97)(4,89,11,96)(5,88,12,95)(6,87,13,94)(7,86,14,93)(15,51,22,44)(16,50,23,43)(17,49,24,56)(18,48,25,55)(19,47,26,54)(20,46,27,53)(21,45,28,52)(29,357,36,364)(30,356,37,363)(31,355,38,362)(32,354,39,361)(33,353,40,360)(34,352,41,359)(35,351,42,358)(57,301,64,308)(58,300,65,307)(59,299,66,306)(60,298,67,305)(61,297,68,304)(62,296,69,303)(63,295,70,302)(71,369,78,376)(72,368,79,375)(73,367,80,374)(74,366,81,373)(75,365,82,372)(76,378,83,371)(77,377,84,370)(99,180,106,173)(100,179,107,172)(101,178,108,171)(102,177,109,170)(103,176,110,169)(104,175,111,182)(105,174,112,181)(113,278,120,271)(114,277,121,270)(115,276,122,269)(116,275,123,268)(117,274,124,267)(118,273,125,280)(119,272,126,279)(127,341,134,348)(128,340,135,347)(129,339,136,346)(130,338,137,345)(131,337,138,344)(132,350,139,343)(133,349,140,342)(141,395,148,402)(142,394,149,401)(143,393,150,400)(144,406,151,399)(145,405,152,398)(146,404,153,397)(147,403,154,396)(155,331,162,324)(156,330,163,323)(157,329,164,336)(158,328,165,335)(159,327,166,334)(160,326,167,333)(161,325,168,332)(183,291,190,284)(184,290,191,283)(185,289,192,282)(186,288,193,281)(187,287,194,294)(188,286,195,293)(189,285,196,292)(197,258,204,265)(198,257,205,264)(199,256,206,263)(200,255,207,262)(201,254,208,261)(202,253,209,260)(203,266,210,259)(211,244,218,251)(212,243,219,250)(213,242,220,249)(214,241,221,248)(215,240,222,247)(216,239,223,246)(217,252,224,245)(225,442,232,435)(226,441,233,448)(227,440,234,447)(228,439,235,446)(229,438,236,445)(230,437,237,444)(231,436,238,443)(309,388,316,381)(310,387,317,380)(311,386,318,379)(312,385,319,392)(313,384,320,391)(314,383,321,390)(315,382,322,389)(407,423,414,430)(408,422,415,429)(409,421,416,428)(410,434,417,427)(411,433,418,426)(412,432,419,425)(413,431,420,424), (1,229,60,327)(2,228,61,326)(3,227,62,325)(4,226,63,324)(5,225,64,323)(6,238,65,336)(7,237,66,335)(8,236,67,334)(9,235,68,333)(10,234,69,332)(11,233,70,331)(12,232,57,330)(13,231,58,329)(14,230,59,328)(15,147,339,224)(16,146,340,223)(17,145,341,222)(18,144,342,221)(19,143,343,220)(20,142,344,219)(21,141,345,218)(22,154,346,217)(23,153,347,216)(24,152,348,215)(25,151,349,214)(26,150,350,213)(27,149,337,212)(28,148,338,211)(29,117,385,262)(30,116,386,261)(31,115,387,260)(32,114,388,259)(33,113,389,258)(34,126,390,257)(35,125,391,256)(36,124,392,255)(37,123,379,254)(38,122,380,253)(39,121,381,266)(40,120,382,265)(41,119,383,264)(42,118,384,263)(43,108,128,191)(44,107,129,190)(45,106,130,189)(46,105,131,188)(47,104,132,187)(48,103,133,186)(49,102,134,185)(50,101,135,184)(51,100,136,183)(52,99,137,196)(53,112,138,195)(54,111,139,194)(55,110,140,193)(56,109,127,192)(71,248,416,406)(72,247,417,405)(73,246,418,404)(74,245,419,403)(75,244,420,402)(76,243,407,401)(77,242,408,400)(78,241,409,399)(79,240,410,398)(80,239,411,397)(81,252,412,396)(82,251,413,395)(83,250,414,394)(84,249,415,393)(85,206,305,280)(86,205,306,279)(87,204,307,278)(88,203,308,277)(89,202,295,276)(90,201,296,275)(91,200,297,274)(92,199,298,273)(93,198,299,272)(94,197,300,271)(95,210,301,270)(96,209,302,269)(97,208,303,268)(98,207,304,267)(155,317,441,355)(156,316,442,354)(157,315,443,353)(158,314,444,352)(159,313,445,351)(160,312,446,364)(161,311,447,363)(162,310,448,362)(163,309,435,361)(164,322,436,360)(165,321,437,359)(166,320,438,358)(167,319,439,357)(168,318,440,356)(169,376,281,421)(170,375,282,434)(171,374,283,433)(172,373,284,432)(173,372,285,431)(174,371,286,430)(175,370,287,429)(176,369,288,428)(177,368,289,427)(178,367,290,426)(179,366,291,425)(180,365,292,424)(181,378,293,423)(182,377,294,422), (1,349,60,25)(2,350,61,26)(3,337,62,27)(4,338,63,28)(5,339,64,15)(6,340,65,16)(7,341,66,17)(8,342,67,18)(9,343,68,19)(10,344,69,20)(11,345,70,21)(12,346,57,22)(13,347,58,23)(14,348,59,24)(29,429,385,370)(30,430,386,371)(31,431,387,372)(32,432,388,373)(33,433,389,374)(34,434,390,375)(35,421,391,376)(36,422,392,377)(37,423,379,378)(38,424,380,365)(39,425,381,366)(40,426,382,367)(41,427,383,368)(42,428,384,369)(43,87,128,307)(44,88,129,308)(45,89,130,295)(46,90,131,296)(47,91,132,297)(48,92,133,298)(49,93,134,299)(50,94,135,300)(51,95,136,301)(52,96,137,302)(53,97,138,303)(54,98,139,304)(55,85,140,305)(56,86,127,306)(71,358,416,320)(72,359,417,321)(73,360,418,322)(74,361,419,309)(75,362,420,310)(76,363,407,311)(77,364,408,312)(78,351,409,313)(79,352,410,314)(80,353,411,315)(81,354,412,316)(82,355,413,317)(83,356,414,318)(84,357,415,319)(99,269,196,209)(100,270,183,210)(101,271,184,197)(102,272,185,198)(103,273,186,199)(104,274,187,200)(105,275,188,201)(106,276,189,202)(107,277,190,203)(108,278,191,204)(109,279,192,205)(110,280,193,206)(111,267,194,207)(112,268,195,208)(113,283,258,171)(114,284,259,172)(115,285,260,173)(116,286,261,174)(117,287,262,175)(118,288,263,176)(119,289,264,177)(120,290,265,178)(121,291,266,179)(122,292,253,180)(123,293,254,181)(124,294,255,182)(125,281,256,169)(126,282,257,170)(141,331,218,233)(142,332,219,234)(143,333,220,235)(144,334,221,236)(145,335,222,237)(146,336,223,238)(147,323,224,225)(148,324,211,226)(149,325,212,227)(150,326,213,228)(151,327,214,229)(152,328,215,230)(153,329,216,231)(154,330,217,232)(155,251,441,395)(156,252,442,396)(157,239,443,397)(158,240,444,398)(159,241,445,399)(160,242,446,400)(161,243,447,401)(162,244,448,402)(163,245,435,403)(164,246,436,404)(165,247,437,405)(166,248,438,406)(167,249,439,393)(168,250,440,394) );
G=PermutationGroup([[(1,384),(2,385),(3,386),(4,387),(5,388),(6,389),(7,390),(8,391),(9,392),(10,379),(11,380),(12,381),(13,382),(14,383),(15,432),(16,433),(17,434),(18,421),(19,422),(20,423),(21,424),(22,425),(23,426),(24,427),(25,428),(26,429),(27,430),(28,431),(29,61),(30,62),(31,63),(32,64),(33,65),(34,66),(35,67),(36,68),(37,69),(38,70),(39,57),(40,58),(41,59),(42,60),(43,411),(44,412),(45,413),(46,414),(47,415),(48,416),(49,417),(50,418),(51,419),(52,420),(53,407),(54,408),(55,409),(56,410),(71,133),(72,134),(73,135),(74,136),(75,137),(76,138),(77,139),(78,140),(79,127),(80,128),(81,129),(82,130),(83,131),(84,132),(85,313),(86,314),(87,315),(88,316),(89,317),(90,318),(91,319),(92,320),(93,321),(94,322),(95,309),(96,310),(97,311),(98,312),(99,402),(100,403),(101,404),(102,405),(103,406),(104,393),(105,394),(106,395),(107,396),(108,397),(109,398),(110,399),(111,400),(112,401),(113,336),(114,323),(115,324),(116,325),(117,326),(118,327),(119,328),(120,329),(121,330),(122,331),(123,332),(124,333),(125,334),(126,335),(141,180),(142,181),(143,182),(144,169),(145,170),(146,171),(147,172),(148,173),(149,174),(150,175),(151,176),(152,177),(153,178),(154,179),(155,276),(156,277),(157,278),(158,279),(159,280),(160,267),(161,268),(162,269),(163,270),(164,271),(165,272),(166,273),(167,274),(168,275),(183,245),(184,246),(185,247),(186,248),(187,249),(188,250),(189,251),(190,252),(191,239),(192,240),(193,241),(194,242),(195,243),(196,244),(197,436),(198,437),(199,438),(200,439),(201,440),(202,441),(203,442),(204,443),(205,444),(206,445),(207,446),(208,447),(209,448),(210,435),(211,285),(212,286),(213,287),(214,288),(215,289),(216,290),(217,291),(218,292),(219,293),(220,294),(221,281),(222,282),(223,283),(224,284),(225,259),(226,260),(227,261),(228,262),(229,263),(230,264),(231,265),(232,266),(233,253),(234,254),(235,255),(236,256),(237,257),(238,258),(295,355),(296,356),(297,357),(298,358),(299,359),(300,360),(301,361),(302,362),(303,363),(304,364),(305,351),(306,352),(307,353),(308,354),(337,371),(338,372),(339,373),(340,374),(341,375),(342,376),(343,377),(344,378),(345,365),(346,366),(347,367),(348,368),(349,369),(350,370)], [(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)], [(1,92,8,85),(2,91,9,98),(3,90,10,97),(4,89,11,96),(5,88,12,95),(6,87,13,94),(7,86,14,93),(15,51,22,44),(16,50,23,43),(17,49,24,56),(18,48,25,55),(19,47,26,54),(20,46,27,53),(21,45,28,52),(29,357,36,364),(30,356,37,363),(31,355,38,362),(32,354,39,361),(33,353,40,360),(34,352,41,359),(35,351,42,358),(57,301,64,308),(58,300,65,307),(59,299,66,306),(60,298,67,305),(61,297,68,304),(62,296,69,303),(63,295,70,302),(71,369,78,376),(72,368,79,375),(73,367,80,374),(74,366,81,373),(75,365,82,372),(76,378,83,371),(77,377,84,370),(99,180,106,173),(100,179,107,172),(101,178,108,171),(102,177,109,170),(103,176,110,169),(104,175,111,182),(105,174,112,181),(113,278,120,271),(114,277,121,270),(115,276,122,269),(116,275,123,268),(117,274,124,267),(118,273,125,280),(119,272,126,279),(127,341,134,348),(128,340,135,347),(129,339,136,346),(130,338,137,345),(131,337,138,344),(132,350,139,343),(133,349,140,342),(141,395,148,402),(142,394,149,401),(143,393,150,400),(144,406,151,399),(145,405,152,398),(146,404,153,397),(147,403,154,396),(155,331,162,324),(156,330,163,323),(157,329,164,336),(158,328,165,335),(159,327,166,334),(160,326,167,333),(161,325,168,332),(183,291,190,284),(184,290,191,283),(185,289,192,282),(186,288,193,281),(187,287,194,294),(188,286,195,293),(189,285,196,292),(197,258,204,265),(198,257,205,264),(199,256,206,263),(200,255,207,262),(201,254,208,261),(202,253,209,260),(203,266,210,259),(211,244,218,251),(212,243,219,250),(213,242,220,249),(214,241,221,248),(215,240,222,247),(216,239,223,246),(217,252,224,245),(225,442,232,435),(226,441,233,448),(227,440,234,447),(228,439,235,446),(229,438,236,445),(230,437,237,444),(231,436,238,443),(309,388,316,381),(310,387,317,380),(311,386,318,379),(312,385,319,392),(313,384,320,391),(314,383,321,390),(315,382,322,389),(407,423,414,430),(408,422,415,429),(409,421,416,428),(410,434,417,427),(411,433,418,426),(412,432,419,425),(413,431,420,424)], [(1,229,60,327),(2,228,61,326),(3,227,62,325),(4,226,63,324),(5,225,64,323),(6,238,65,336),(7,237,66,335),(8,236,67,334),(9,235,68,333),(10,234,69,332),(11,233,70,331),(12,232,57,330),(13,231,58,329),(14,230,59,328),(15,147,339,224),(16,146,340,223),(17,145,341,222),(18,144,342,221),(19,143,343,220),(20,142,344,219),(21,141,345,218),(22,154,346,217),(23,153,347,216),(24,152,348,215),(25,151,349,214),(26,150,350,213),(27,149,337,212),(28,148,338,211),(29,117,385,262),(30,116,386,261),(31,115,387,260),(32,114,388,259),(33,113,389,258),(34,126,390,257),(35,125,391,256),(36,124,392,255),(37,123,379,254),(38,122,380,253),(39,121,381,266),(40,120,382,265),(41,119,383,264),(42,118,384,263),(43,108,128,191),(44,107,129,190),(45,106,130,189),(46,105,131,188),(47,104,132,187),(48,103,133,186),(49,102,134,185),(50,101,135,184),(51,100,136,183),(52,99,137,196),(53,112,138,195),(54,111,139,194),(55,110,140,193),(56,109,127,192),(71,248,416,406),(72,247,417,405),(73,246,418,404),(74,245,419,403),(75,244,420,402),(76,243,407,401),(77,242,408,400),(78,241,409,399),(79,240,410,398),(80,239,411,397),(81,252,412,396),(82,251,413,395),(83,250,414,394),(84,249,415,393),(85,206,305,280),(86,205,306,279),(87,204,307,278),(88,203,308,277),(89,202,295,276),(90,201,296,275),(91,200,297,274),(92,199,298,273),(93,198,299,272),(94,197,300,271),(95,210,301,270),(96,209,302,269),(97,208,303,268),(98,207,304,267),(155,317,441,355),(156,316,442,354),(157,315,443,353),(158,314,444,352),(159,313,445,351),(160,312,446,364),(161,311,447,363),(162,310,448,362),(163,309,435,361),(164,322,436,360),(165,321,437,359),(166,320,438,358),(167,319,439,357),(168,318,440,356),(169,376,281,421),(170,375,282,434),(171,374,283,433),(172,373,284,432),(173,372,285,431),(174,371,286,430),(175,370,287,429),(176,369,288,428),(177,368,289,427),(178,367,290,426),(179,366,291,425),(180,365,292,424),(181,378,293,423),(182,377,294,422)], [(1,349,60,25),(2,350,61,26),(3,337,62,27),(4,338,63,28),(5,339,64,15),(6,340,65,16),(7,341,66,17),(8,342,67,18),(9,343,68,19),(10,344,69,20),(11,345,70,21),(12,346,57,22),(13,347,58,23),(14,348,59,24),(29,429,385,370),(30,430,386,371),(31,431,387,372),(32,432,388,373),(33,433,389,374),(34,434,390,375),(35,421,391,376),(36,422,392,377),(37,423,379,378),(38,424,380,365),(39,425,381,366),(40,426,382,367),(41,427,383,368),(42,428,384,369),(43,87,128,307),(44,88,129,308),(45,89,130,295),(46,90,131,296),(47,91,132,297),(48,92,133,298),(49,93,134,299),(50,94,135,300),(51,95,136,301),(52,96,137,302),(53,97,138,303),(54,98,139,304),(55,85,140,305),(56,86,127,306),(71,358,416,320),(72,359,417,321),(73,360,418,322),(74,361,419,309),(75,362,420,310),(76,363,407,311),(77,364,408,312),(78,351,409,313),(79,352,410,314),(80,353,411,315),(81,354,412,316),(82,355,413,317),(83,356,414,318),(84,357,415,319),(99,269,196,209),(100,270,183,210),(101,271,184,197),(102,272,185,198),(103,273,186,199),(104,274,187,200),(105,275,188,201),(106,276,189,202),(107,277,190,203),(108,278,191,204),(109,279,192,205),(110,280,193,206),(111,267,194,207),(112,268,195,208),(113,283,258,171),(114,284,259,172),(115,285,260,173),(116,286,261,174),(117,287,262,175),(118,288,263,176),(119,289,264,177),(120,290,265,178),(121,291,266,179),(122,292,253,180),(123,293,254,181),(124,294,255,182),(125,281,256,169),(126,282,257,170),(141,331,218,233),(142,332,219,234),(143,333,220,235),(144,334,221,236),(145,335,222,237),(146,336,223,238),(147,323,224,225),(148,324,211,226),(149,325,212,227),(150,326,213,228),(151,327,214,229),(152,328,215,230),(153,329,216,231),(154,330,217,232),(155,251,441,395),(156,252,442,396),(157,239,443,397),(158,240,444,398),(159,241,445,399),(160,242,446,400),(161,243,447,401),(162,244,448,402),(163,245,435,403),(164,246,436,404),(165,247,437,405),(166,248,438,406),(167,249,439,393),(168,250,440,394)]])
82 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4F | 4G | ··· | 4N | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 4 | ··· | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | - | + | + | - | + | + | - | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | Q8 | D4 | Q8 | D7 | C4○D4 | D14 | Dic14 | D28 | D4×D7 | D4⋊2D7 | Q8×D7 |
| kernel | (C2×Dic7)⋊Q8 | C14.C42 | C7×C2.C42 | C2×Dic7⋊C4 | C2×C4⋊Dic7 | C22×Dic14 | C2×Dic7 | C2×Dic7 | C2×C28 | C2×C28 | C2.C42 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C22 | C22 | C22 |
| # reps | 1 | 2 | 1 | 1 | 2 | 1 | 4 | 2 | 2 | 4 | 3 | 2 | 9 | 24 | 12 | 6 | 3 | 3 |
Matrix representation of (C2×Dic7)⋊Q8 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 26 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 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 |
| 12 | 22 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 7 | 0 | 0 |
| 0 | 0 | 5 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 24 | 2 | 0 | 0 | 0 | 0 |
| 16 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 19 | 0 | 0 |
| 0 | 0 | 18 | 6 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 5 |
| 0 | 0 | 0 | 0 | 7 | 15 |
| 27 | 11 | 0 | 0 | 0 | 0 |
| 18 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 3 |
| 0 | 0 | 0 | 0 | 27 | 18 |
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],[26,28,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[12,0,0,0,0,0,22,17,0,0,0,0,0,0,16,5,0,0,0,0,7,13,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[24,16,0,0,0,0,2,5,0,0,0,0,0,0,23,18,0,0,0,0,19,6,0,0,0,0,0,0,14,7,0,0,0,0,5,15],[27,18,0,0,0,0,11,2,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,11,27,0,0,0,0,3,18] >;
(C2×Dic7)⋊Q8 in GAP, Magma, Sage, TeX
(C_2\times {\rm Dic}_7)\rtimes Q_8 % in TeX
G:=Group("(C2xDic7):Q8"); // GroupNames label
G:=SmallGroup(448,190);
// by ID
G=gap.SmallGroup(448,190);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,253,120,254,387,58,18822]);
// 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,e*c*e^-1=b^7*c,e*d*e^-1=d^-1>;
// generators/relations