direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic7.Q8, C4⋊C4.259D14, Dic7.1(C2×Q8), C22.31(Q8×D7), (C2×C14).42C24, (C2×Dic7).20Q8, C14⋊2(C42.C2), C14.22(C22×Q8), (C2×C28).133C23, (C22×C4).174D14, C22.80(C23×D7), C22.75(C4○D28), C4⋊Dic7.291C22, C23.322(C22×D7), C22.71(D4⋊2D7), Dic7⋊C4.103C22, (C22×C28).356C22, (C22×C14).391C23, (C4×Dic7).290C22, (C2×Dic7).182C23, (C22×Dic7).207C22, C2.6(C2×Q8×D7), C7⋊2(C2×C42.C2), (C2×C4⋊C4).25D7, (C14×C4⋊C4).18C2, C14.18(C2×C4○D4), C2.20(C2×C4○D28), (C2×C14).91(C2×Q8), (C2×C4×Dic7).41C2, C2.13(C2×D4⋊2D7), (C2×C4⋊Dic7).26C2, (C7×C4⋊C4).291C22, (C2×Dic7⋊C4).29C2, (C2×C4).138(C22×D7), (C2×C14).105(C4○D4), SmallGroup(448,951)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Dic7.Q8
G = < a,b,c,d,e | a2=b14=d4=1, c2=b7, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=ebe-1=b-1, bd=db, dcd-1=b7c, ce=ec, ede-1=b7d-1 >
Subgroups: 772 in 226 conjugacy classes, 119 normal (31 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C23, C14, C14, C42, C4⋊C4, C4⋊C4, C22×C4, C22×C4, Dic7, Dic7, C28, C2×C14, C2×C14, C2×C42, C2×C4⋊C4, C2×C4⋊C4, C42.C2, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C2×C42.C2, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C7×C4⋊C4, C22×Dic7, C22×C28, Dic7.Q8, C2×C4×Dic7, C2×Dic7⋊C4, C2×C4⋊Dic7, C14×C4⋊C4, C2×Dic7.Q8
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C4○D4, C24, D14, C42.C2, C22×Q8, C2×C4○D4, C22×D7, C2×C42.C2, C4○D28, D4⋊2D7, Q8×D7, C23×D7, Dic7.Q8, C2×C4○D28, C2×D4⋊2D7, C2×Q8×D7, C2×Dic7.Q8
►Regular action on 448 points
Generators in S448
(1 164)(2 165)(3 166)(4 167)(5 168)(6 155)(7 156)(8 157)(9 158)(10 159)(11 160)(12 161)(13 162)(14 163)(15 322)(16 309)(17 310)(18 311)(19 312)(20 313)(21 314)(22 315)(23 316)(24 317)(25 318)(26 319)(27 320)(28 321)(29 430)(30 431)(31 432)(32 433)(33 434)(34 421)(35 422)(36 423)(37 424)(38 425)(39 426)(40 427)(41 428)(42 429)(43 59)(44 60)(45 61)(46 62)(47 63)(48 64)(49 65)(50 66)(51 67)(52 68)(53 69)(54 70)(55 57)(56 58)(71 185)(72 186)(73 187)(74 188)(75 189)(76 190)(77 191)(78 192)(79 193)(80 194)(81 195)(82 196)(83 183)(84 184)(85 435)(86 436)(87 437)(88 438)(89 439)(90 440)(91 441)(92 442)(93 443)(94 444)(95 445)(96 446)(97 447)(98 448)(99 406)(100 393)(101 394)(102 395)(103 396)(104 397)(105 398)(106 399)(107 400)(108 401)(109 402)(110 403)(111 404)(112 405)(113 132)(114 133)(115 134)(116 135)(117 136)(118 137)(119 138)(120 139)(121 140)(122 127)(123 128)(124 129)(125 130)(126 131)(141 252)(142 239)(143 240)(144 241)(145 242)(146 243)(147 244)(148 245)(149 246)(150 247)(151 248)(152 249)(153 250)(154 251)(169 280)(170 267)(171 268)(172 269)(173 270)(174 271)(175 272)(176 273)(177 274)(178 275)(179 276)(180 277)(181 278)(182 279)(197 234)(198 235)(199 236)(200 237)(201 238)(202 225)(203 226)(204 227)(205 228)(206 229)(207 230)(208 231)(209 232)(210 233)(211 301)(212 302)(213 303)(214 304)(215 305)(216 306)(217 307)(218 308)(219 295)(220 296)(221 297)(222 298)(223 299)(224 300)(253 358)(254 359)(255 360)(256 361)(257 362)(258 363)(259 364)(260 351)(261 352)(262 353)(263 354)(264 355)(265 356)(266 357)(281 334)(282 335)(283 336)(284 323)(285 324)(286 325)(287 326)(288 327)(289 328)(290 329)(291 330)(292 331)(293 332)(294 333)(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)(379 413)(380 414)(381 415)(382 416)(383 417)(384 418)(385 419)(386 420)(387 407)(388 408)(389 409)(390 410)(391 411)(392 412)
(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 15 8 22)(2 28 9 21)(3 27 10 20)(4 26 11 19)(5 25 12 18)(6 24 13 17)(7 23 14 16)(29 329 36 336)(30 328 37 335)(31 327 38 334)(32 326 39 333)(33 325 40 332)(34 324 41 331)(35 323 42 330)(43 178 50 171)(44 177 51 170)(45 176 52 169)(46 175 53 182)(47 174 54 181)(48 173 55 180)(49 172 56 179)(57 277 64 270)(58 276 65 269)(59 275 66 268)(60 274 67 267)(61 273 68 280)(62 272 69 279)(63 271 70 278)(71 212 78 219)(72 211 79 218)(73 224 80 217)(74 223 81 216)(75 222 82 215)(76 221 83 214)(77 220 84 213)(85 375 92 368)(86 374 93 367)(87 373 94 366)(88 372 95 365)(89 371 96 378)(90 370 97 377)(91 369 98 376)(99 203 106 210)(100 202 107 209)(101 201 108 208)(102 200 109 207)(103 199 110 206)(104 198 111 205)(105 197 112 204)(113 360 120 353)(114 359 121 352)(115 358 122 351)(116 357 123 364)(117 356 124 363)(118 355 125 362)(119 354 126 361)(127 260 134 253)(128 259 135 266)(129 258 136 265)(130 257 137 264)(131 256 138 263)(132 255 139 262)(133 254 140 261)(141 391 148 384)(142 390 149 383)(143 389 150 382)(144 388 151 381)(145 387 152 380)(146 386 153 379)(147 385 154 392)(155 317 162 310)(156 316 163 309)(157 315 164 322)(158 314 165 321)(159 313 166 320)(160 312 167 319)(161 311 168 318)(183 304 190 297)(184 303 191 296)(185 302 192 295)(186 301 193 308)(187 300 194 307)(188 299 195 306)(189 298 196 305)(225 400 232 393)(226 399 233 406)(227 398 234 405)(228 397 235 404)(229 396 236 403)(230 395 237 402)(231 394 238 401)(239 410 246 417)(240 409 247 416)(241 408 248 415)(242 407 249 414)(243 420 250 413)(244 419 251 412)(245 418 252 411)(281 432 288 425)(282 431 289 424)(283 430 290 423)(284 429 291 422)(285 428 292 421)(286 427 293 434)(287 426 294 433)(337 446 344 439)(338 445 345 438)(339 444 346 437)(340 443 347 436)(341 442 348 435)(342 441 349 448)(343 440 350 447)
(1 280 287 396)(2 267 288 397)(3 268 289 398)(4 269 290 399)(5 270 291 400)(6 271 292 401)(7 272 293 402)(8 273 294 403)(9 274 281 404)(10 275 282 405)(11 276 283 406)(12 277 284 393)(13 278 285 394)(14 279 286 395)(15 68 426 229)(16 69 427 230)(17 70 428 231)(18 57 429 232)(19 58 430 233)(20 59 431 234)(21 60 432 235)(22 61 433 236)(23 62 434 237)(24 63 421 238)(25 64 422 225)(26 65 423 226)(27 66 424 227)(28 67 425 228)(29 210 312 56)(30 197 313 43)(31 198 314 44)(32 199 315 45)(33 200 316 46)(34 201 317 47)(35 202 318 48)(36 203 319 49)(37 204 320 50)(38 205 321 51)(39 206 322 52)(40 207 309 53)(41 208 310 54)(42 209 311 55)(71 381 439 131)(72 382 440 132)(73 383 441 133)(74 384 442 134)(75 385 443 135)(76 386 444 136)(77 387 445 137)(78 388 446 138)(79 389 447 139)(80 390 448 140)(81 391 435 127)(82 392 436 128)(83 379 437 129)(84 380 438 130)(85 122 195 411)(86 123 196 412)(87 124 183 413)(88 125 184 414)(89 126 185 415)(90 113 186 416)(91 114 187 417)(92 115 188 418)(93 116 189 419)(94 117 190 420)(95 118 191 407)(96 119 192 408)(97 120 193 409)(98 121 194 410)(99 160 179 336)(100 161 180 323)(101 162 181 324)(102 163 182 325)(103 164 169 326)(104 165 170 327)(105 166 171 328)(106 167 172 329)(107 168 173 330)(108 155 174 331)(109 156 175 332)(110 157 176 333)(111 158 177 334)(112 159 178 335)(141 341 253 216)(142 342 254 217)(143 343 255 218)(144 344 256 219)(145 345 257 220)(146 346 258 221)(147 347 259 222)(148 348 260 223)(149 349 261 224)(150 350 262 211)(151 337 263 212)(152 338 264 213)(153 339 265 214)(154 340 266 215)(239 376 359 307)(240 377 360 308)(241 378 361 295)(242 365 362 296)(243 366 363 297)(244 367 364 298)(245 368 351 299)(246 369 352 300)(247 370 353 301)(248 371 354 302)(249 372 355 303)(250 373 356 304)(251 374 357 305)(252 375 358 306)
(1 364 287 244)(2 363 288 243)(3 362 289 242)(4 361 290 241)(5 360 291 240)(6 359 292 239)(7 358 293 252)(8 357 294 251)(9 356 281 250)(10 355 282 249)(11 354 283 248)(12 353 284 247)(13 352 285 246)(14 351 286 245)(15 116 426 419)(16 115 427 418)(17 114 428 417)(18 113 429 416)(19 126 430 415)(20 125 431 414)(21 124 432 413)(22 123 433 412)(23 122 434 411)(24 121 421 410)(25 120 422 409)(26 119 423 408)(27 118 424 407)(28 117 425 420)(29 381 312 131)(30 380 313 130)(31 379 314 129)(32 392 315 128)(33 391 316 127)(34 390 317 140)(35 389 318 139)(36 388 319 138)(37 387 320 137)(38 386 321 136)(39 385 322 135)(40 384 309 134)(41 383 310 133)(42 382 311 132)(43 445 197 77)(44 444 198 76)(45 443 199 75)(46 442 200 74)(47 441 201 73)(48 440 202 72)(49 439 203 71)(50 438 204 84)(51 437 205 83)(52 436 206 82)(53 435 207 81)(54 448 208 80)(55 447 209 79)(56 446 210 78)(57 97 232 193)(58 96 233 192)(59 95 234 191)(60 94 235 190)(61 93 236 189)(62 92 237 188)(63 91 238 187)(64 90 225 186)(65 89 226 185)(66 88 227 184)(67 87 228 183)(68 86 229 196)(69 85 230 195)(70 98 231 194)(99 219 179 344)(100 218 180 343)(101 217 181 342)(102 216 182 341)(103 215 169 340)(104 214 170 339)(105 213 171 338)(106 212 172 337)(107 211 173 350)(108 224 174 349)(109 223 175 348)(110 222 176 347)(111 221 177 346)(112 220 178 345)(141 156 253 332)(142 155 254 331)(143 168 255 330)(144 167 256 329)(145 166 257 328)(146 165 258 327)(147 164 259 326)(148 163 260 325)(149 162 261 324)(150 161 262 323)(151 160 263 336)(152 159 264 335)(153 158 265 334)(154 157 266 333)(267 373 397 304)(268 372 398 303)(269 371 399 302)(270 370 400 301)(271 369 401 300)(272 368 402 299)(273 367 403 298)(274 366 404 297)(275 365 405 296)(276 378 406 295)(277 377 393 308)(278 376 394 307)(279 375 395 306)(280 374 396 305)
G:=sub<Sym(448)| (1,164)(2,165)(3,166)(4,167)(5,168)(6,155)(7,156)(8,157)(9,158)(10,159)(11,160)(12,161)(13,162)(14,163)(15,322)(16,309)(17,310)(18,311)(19,312)(20,313)(21,314)(22,315)(23,316)(24,317)(25,318)(26,319)(27,320)(28,321)(29,430)(30,431)(31,432)(32,433)(33,434)(34,421)(35,422)(36,423)(37,424)(38,425)(39,426)(40,427)(41,428)(42,429)(43,59)(44,60)(45,61)(46,62)(47,63)(48,64)(49,65)(50,66)(51,67)(52,68)(53,69)(54,70)(55,57)(56,58)(71,185)(72,186)(73,187)(74,188)(75,189)(76,190)(77,191)(78,192)(79,193)(80,194)(81,195)(82,196)(83,183)(84,184)(85,435)(86,436)(87,437)(88,438)(89,439)(90,440)(91,441)(92,442)(93,443)(94,444)(95,445)(96,446)(97,447)(98,448)(99,406)(100,393)(101,394)(102,395)(103,396)(104,397)(105,398)(106,399)(107,400)(108,401)(109,402)(110,403)(111,404)(112,405)(113,132)(114,133)(115,134)(116,135)(117,136)(118,137)(119,138)(120,139)(121,140)(122,127)(123,128)(124,129)(125,130)(126,131)(141,252)(142,239)(143,240)(144,241)(145,242)(146,243)(147,244)(148,245)(149,246)(150,247)(151,248)(152,249)(153,250)(154,251)(169,280)(170,267)(171,268)(172,269)(173,270)(174,271)(175,272)(176,273)(177,274)(178,275)(179,276)(180,277)(181,278)(182,279)(197,234)(198,235)(199,236)(200,237)(201,238)(202,225)(203,226)(204,227)(205,228)(206,229)(207,230)(208,231)(209,232)(210,233)(211,301)(212,302)(213,303)(214,304)(215,305)(216,306)(217,307)(218,308)(219,295)(220,296)(221,297)(222,298)(223,299)(224,300)(253,358)(254,359)(255,360)(256,361)(257,362)(258,363)(259,364)(260,351)(261,352)(262,353)(263,354)(264,355)(265,356)(266,357)(281,334)(282,335)(283,336)(284,323)(285,324)(286,325)(287,326)(288,327)(289,328)(290,329)(291,330)(292,331)(293,332)(294,333)(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)(379,413)(380,414)(381,415)(382,416)(383,417)(384,418)(385,419)(386,420)(387,407)(388,408)(389,409)(390,410)(391,411)(392,412), (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), (1,15,8,22)(2,28,9,21)(3,27,10,20)(4,26,11,19)(5,25,12,18)(6,24,13,17)(7,23,14,16)(29,329,36,336)(30,328,37,335)(31,327,38,334)(32,326,39,333)(33,325,40,332)(34,324,41,331)(35,323,42,330)(43,178,50,171)(44,177,51,170)(45,176,52,169)(46,175,53,182)(47,174,54,181)(48,173,55,180)(49,172,56,179)(57,277,64,270)(58,276,65,269)(59,275,66,268)(60,274,67,267)(61,273,68,280)(62,272,69,279)(63,271,70,278)(71,212,78,219)(72,211,79,218)(73,224,80,217)(74,223,81,216)(75,222,82,215)(76,221,83,214)(77,220,84,213)(85,375,92,368)(86,374,93,367)(87,373,94,366)(88,372,95,365)(89,371,96,378)(90,370,97,377)(91,369,98,376)(99,203,106,210)(100,202,107,209)(101,201,108,208)(102,200,109,207)(103,199,110,206)(104,198,111,205)(105,197,112,204)(113,360,120,353)(114,359,121,352)(115,358,122,351)(116,357,123,364)(117,356,124,363)(118,355,125,362)(119,354,126,361)(127,260,134,253)(128,259,135,266)(129,258,136,265)(130,257,137,264)(131,256,138,263)(132,255,139,262)(133,254,140,261)(141,391,148,384)(142,390,149,383)(143,389,150,382)(144,388,151,381)(145,387,152,380)(146,386,153,379)(147,385,154,392)(155,317,162,310)(156,316,163,309)(157,315,164,322)(158,314,165,321)(159,313,166,320)(160,312,167,319)(161,311,168,318)(183,304,190,297)(184,303,191,296)(185,302,192,295)(186,301,193,308)(187,300,194,307)(188,299,195,306)(189,298,196,305)(225,400,232,393)(226,399,233,406)(227,398,234,405)(228,397,235,404)(229,396,236,403)(230,395,237,402)(231,394,238,401)(239,410,246,417)(240,409,247,416)(241,408,248,415)(242,407,249,414)(243,420,250,413)(244,419,251,412)(245,418,252,411)(281,432,288,425)(282,431,289,424)(283,430,290,423)(284,429,291,422)(285,428,292,421)(286,427,293,434)(287,426,294,433)(337,446,344,439)(338,445,345,438)(339,444,346,437)(340,443,347,436)(341,442,348,435)(342,441,349,448)(343,440,350,447), (1,280,287,396)(2,267,288,397)(3,268,289,398)(4,269,290,399)(5,270,291,400)(6,271,292,401)(7,272,293,402)(8,273,294,403)(9,274,281,404)(10,275,282,405)(11,276,283,406)(12,277,284,393)(13,278,285,394)(14,279,286,395)(15,68,426,229)(16,69,427,230)(17,70,428,231)(18,57,429,232)(19,58,430,233)(20,59,431,234)(21,60,432,235)(22,61,433,236)(23,62,434,237)(24,63,421,238)(25,64,422,225)(26,65,423,226)(27,66,424,227)(28,67,425,228)(29,210,312,56)(30,197,313,43)(31,198,314,44)(32,199,315,45)(33,200,316,46)(34,201,317,47)(35,202,318,48)(36,203,319,49)(37,204,320,50)(38,205,321,51)(39,206,322,52)(40,207,309,53)(41,208,310,54)(42,209,311,55)(71,381,439,131)(72,382,440,132)(73,383,441,133)(74,384,442,134)(75,385,443,135)(76,386,444,136)(77,387,445,137)(78,388,446,138)(79,389,447,139)(80,390,448,140)(81,391,435,127)(82,392,436,128)(83,379,437,129)(84,380,438,130)(85,122,195,411)(86,123,196,412)(87,124,183,413)(88,125,184,414)(89,126,185,415)(90,113,186,416)(91,114,187,417)(92,115,188,418)(93,116,189,419)(94,117,190,420)(95,118,191,407)(96,119,192,408)(97,120,193,409)(98,121,194,410)(99,160,179,336)(100,161,180,323)(101,162,181,324)(102,163,182,325)(103,164,169,326)(104,165,170,327)(105,166,171,328)(106,167,172,329)(107,168,173,330)(108,155,174,331)(109,156,175,332)(110,157,176,333)(111,158,177,334)(112,159,178,335)(141,341,253,216)(142,342,254,217)(143,343,255,218)(144,344,256,219)(145,345,257,220)(146,346,258,221)(147,347,259,222)(148,348,260,223)(149,349,261,224)(150,350,262,211)(151,337,263,212)(152,338,264,213)(153,339,265,214)(154,340,266,215)(239,376,359,307)(240,377,360,308)(241,378,361,295)(242,365,362,296)(243,366,363,297)(244,367,364,298)(245,368,351,299)(246,369,352,300)(247,370,353,301)(248,371,354,302)(249,372,355,303)(250,373,356,304)(251,374,357,305)(252,375,358,306), (1,364,287,244)(2,363,288,243)(3,362,289,242)(4,361,290,241)(5,360,291,240)(6,359,292,239)(7,358,293,252)(8,357,294,251)(9,356,281,250)(10,355,282,249)(11,354,283,248)(12,353,284,247)(13,352,285,246)(14,351,286,245)(15,116,426,419)(16,115,427,418)(17,114,428,417)(18,113,429,416)(19,126,430,415)(20,125,431,414)(21,124,432,413)(22,123,433,412)(23,122,434,411)(24,121,421,410)(25,120,422,409)(26,119,423,408)(27,118,424,407)(28,117,425,420)(29,381,312,131)(30,380,313,130)(31,379,314,129)(32,392,315,128)(33,391,316,127)(34,390,317,140)(35,389,318,139)(36,388,319,138)(37,387,320,137)(38,386,321,136)(39,385,322,135)(40,384,309,134)(41,383,310,133)(42,382,311,132)(43,445,197,77)(44,444,198,76)(45,443,199,75)(46,442,200,74)(47,441,201,73)(48,440,202,72)(49,439,203,71)(50,438,204,84)(51,437,205,83)(52,436,206,82)(53,435,207,81)(54,448,208,80)(55,447,209,79)(56,446,210,78)(57,97,232,193)(58,96,233,192)(59,95,234,191)(60,94,235,190)(61,93,236,189)(62,92,237,188)(63,91,238,187)(64,90,225,186)(65,89,226,185)(66,88,227,184)(67,87,228,183)(68,86,229,196)(69,85,230,195)(70,98,231,194)(99,219,179,344)(100,218,180,343)(101,217,181,342)(102,216,182,341)(103,215,169,340)(104,214,170,339)(105,213,171,338)(106,212,172,337)(107,211,173,350)(108,224,174,349)(109,223,175,348)(110,222,176,347)(111,221,177,346)(112,220,178,345)(141,156,253,332)(142,155,254,331)(143,168,255,330)(144,167,256,329)(145,166,257,328)(146,165,258,327)(147,164,259,326)(148,163,260,325)(149,162,261,324)(150,161,262,323)(151,160,263,336)(152,159,264,335)(153,158,265,334)(154,157,266,333)(267,373,397,304)(268,372,398,303)(269,371,399,302)(270,370,400,301)(271,369,401,300)(272,368,402,299)(273,367,403,298)(274,366,404,297)(275,365,405,296)(276,378,406,295)(277,377,393,308)(278,376,394,307)(279,375,395,306)(280,374,396,305)>;
G:=Group( (1,164)(2,165)(3,166)(4,167)(5,168)(6,155)(7,156)(8,157)(9,158)(10,159)(11,160)(12,161)(13,162)(14,163)(15,322)(16,309)(17,310)(18,311)(19,312)(20,313)(21,314)(22,315)(23,316)(24,317)(25,318)(26,319)(27,320)(28,321)(29,430)(30,431)(31,432)(32,433)(33,434)(34,421)(35,422)(36,423)(37,424)(38,425)(39,426)(40,427)(41,428)(42,429)(43,59)(44,60)(45,61)(46,62)(47,63)(48,64)(49,65)(50,66)(51,67)(52,68)(53,69)(54,70)(55,57)(56,58)(71,185)(72,186)(73,187)(74,188)(75,189)(76,190)(77,191)(78,192)(79,193)(80,194)(81,195)(82,196)(83,183)(84,184)(85,435)(86,436)(87,437)(88,438)(89,439)(90,440)(91,441)(92,442)(93,443)(94,444)(95,445)(96,446)(97,447)(98,448)(99,406)(100,393)(101,394)(102,395)(103,396)(104,397)(105,398)(106,399)(107,400)(108,401)(109,402)(110,403)(111,404)(112,405)(113,132)(114,133)(115,134)(116,135)(117,136)(118,137)(119,138)(120,139)(121,140)(122,127)(123,128)(124,129)(125,130)(126,131)(141,252)(142,239)(143,240)(144,241)(145,242)(146,243)(147,244)(148,245)(149,246)(150,247)(151,248)(152,249)(153,250)(154,251)(169,280)(170,267)(171,268)(172,269)(173,270)(174,271)(175,272)(176,273)(177,274)(178,275)(179,276)(180,277)(181,278)(182,279)(197,234)(198,235)(199,236)(200,237)(201,238)(202,225)(203,226)(204,227)(205,228)(206,229)(207,230)(208,231)(209,232)(210,233)(211,301)(212,302)(213,303)(214,304)(215,305)(216,306)(217,307)(218,308)(219,295)(220,296)(221,297)(222,298)(223,299)(224,300)(253,358)(254,359)(255,360)(256,361)(257,362)(258,363)(259,364)(260,351)(261,352)(262,353)(263,354)(264,355)(265,356)(266,357)(281,334)(282,335)(283,336)(284,323)(285,324)(286,325)(287,326)(288,327)(289,328)(290,329)(291,330)(292,331)(293,332)(294,333)(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)(379,413)(380,414)(381,415)(382,416)(383,417)(384,418)(385,419)(386,420)(387,407)(388,408)(389,409)(390,410)(391,411)(392,412), (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), (1,15,8,22)(2,28,9,21)(3,27,10,20)(4,26,11,19)(5,25,12,18)(6,24,13,17)(7,23,14,16)(29,329,36,336)(30,328,37,335)(31,327,38,334)(32,326,39,333)(33,325,40,332)(34,324,41,331)(35,323,42,330)(43,178,50,171)(44,177,51,170)(45,176,52,169)(46,175,53,182)(47,174,54,181)(48,173,55,180)(49,172,56,179)(57,277,64,270)(58,276,65,269)(59,275,66,268)(60,274,67,267)(61,273,68,280)(62,272,69,279)(63,271,70,278)(71,212,78,219)(72,211,79,218)(73,224,80,217)(74,223,81,216)(75,222,82,215)(76,221,83,214)(77,220,84,213)(85,375,92,368)(86,374,93,367)(87,373,94,366)(88,372,95,365)(89,371,96,378)(90,370,97,377)(91,369,98,376)(99,203,106,210)(100,202,107,209)(101,201,108,208)(102,200,109,207)(103,199,110,206)(104,198,111,205)(105,197,112,204)(113,360,120,353)(114,359,121,352)(115,358,122,351)(116,357,123,364)(117,356,124,363)(118,355,125,362)(119,354,126,361)(127,260,134,253)(128,259,135,266)(129,258,136,265)(130,257,137,264)(131,256,138,263)(132,255,139,262)(133,254,140,261)(141,391,148,384)(142,390,149,383)(143,389,150,382)(144,388,151,381)(145,387,152,380)(146,386,153,379)(147,385,154,392)(155,317,162,310)(156,316,163,309)(157,315,164,322)(158,314,165,321)(159,313,166,320)(160,312,167,319)(161,311,168,318)(183,304,190,297)(184,303,191,296)(185,302,192,295)(186,301,193,308)(187,300,194,307)(188,299,195,306)(189,298,196,305)(225,400,232,393)(226,399,233,406)(227,398,234,405)(228,397,235,404)(229,396,236,403)(230,395,237,402)(231,394,238,401)(239,410,246,417)(240,409,247,416)(241,408,248,415)(242,407,249,414)(243,420,250,413)(244,419,251,412)(245,418,252,411)(281,432,288,425)(282,431,289,424)(283,430,290,423)(284,429,291,422)(285,428,292,421)(286,427,293,434)(287,426,294,433)(337,446,344,439)(338,445,345,438)(339,444,346,437)(340,443,347,436)(341,442,348,435)(342,441,349,448)(343,440,350,447), (1,280,287,396)(2,267,288,397)(3,268,289,398)(4,269,290,399)(5,270,291,400)(6,271,292,401)(7,272,293,402)(8,273,294,403)(9,274,281,404)(10,275,282,405)(11,276,283,406)(12,277,284,393)(13,278,285,394)(14,279,286,395)(15,68,426,229)(16,69,427,230)(17,70,428,231)(18,57,429,232)(19,58,430,233)(20,59,431,234)(21,60,432,235)(22,61,433,236)(23,62,434,237)(24,63,421,238)(25,64,422,225)(26,65,423,226)(27,66,424,227)(28,67,425,228)(29,210,312,56)(30,197,313,43)(31,198,314,44)(32,199,315,45)(33,200,316,46)(34,201,317,47)(35,202,318,48)(36,203,319,49)(37,204,320,50)(38,205,321,51)(39,206,322,52)(40,207,309,53)(41,208,310,54)(42,209,311,55)(71,381,439,131)(72,382,440,132)(73,383,441,133)(74,384,442,134)(75,385,443,135)(76,386,444,136)(77,387,445,137)(78,388,446,138)(79,389,447,139)(80,390,448,140)(81,391,435,127)(82,392,436,128)(83,379,437,129)(84,380,438,130)(85,122,195,411)(86,123,196,412)(87,124,183,413)(88,125,184,414)(89,126,185,415)(90,113,186,416)(91,114,187,417)(92,115,188,418)(93,116,189,419)(94,117,190,420)(95,118,191,407)(96,119,192,408)(97,120,193,409)(98,121,194,410)(99,160,179,336)(100,161,180,323)(101,162,181,324)(102,163,182,325)(103,164,169,326)(104,165,170,327)(105,166,171,328)(106,167,172,329)(107,168,173,330)(108,155,174,331)(109,156,175,332)(110,157,176,333)(111,158,177,334)(112,159,178,335)(141,341,253,216)(142,342,254,217)(143,343,255,218)(144,344,256,219)(145,345,257,220)(146,346,258,221)(147,347,259,222)(148,348,260,223)(149,349,261,224)(150,350,262,211)(151,337,263,212)(152,338,264,213)(153,339,265,214)(154,340,266,215)(239,376,359,307)(240,377,360,308)(241,378,361,295)(242,365,362,296)(243,366,363,297)(244,367,364,298)(245,368,351,299)(246,369,352,300)(247,370,353,301)(248,371,354,302)(249,372,355,303)(250,373,356,304)(251,374,357,305)(252,375,358,306), (1,364,287,244)(2,363,288,243)(3,362,289,242)(4,361,290,241)(5,360,291,240)(6,359,292,239)(7,358,293,252)(8,357,294,251)(9,356,281,250)(10,355,282,249)(11,354,283,248)(12,353,284,247)(13,352,285,246)(14,351,286,245)(15,116,426,419)(16,115,427,418)(17,114,428,417)(18,113,429,416)(19,126,430,415)(20,125,431,414)(21,124,432,413)(22,123,433,412)(23,122,434,411)(24,121,421,410)(25,120,422,409)(26,119,423,408)(27,118,424,407)(28,117,425,420)(29,381,312,131)(30,380,313,130)(31,379,314,129)(32,392,315,128)(33,391,316,127)(34,390,317,140)(35,389,318,139)(36,388,319,138)(37,387,320,137)(38,386,321,136)(39,385,322,135)(40,384,309,134)(41,383,310,133)(42,382,311,132)(43,445,197,77)(44,444,198,76)(45,443,199,75)(46,442,200,74)(47,441,201,73)(48,440,202,72)(49,439,203,71)(50,438,204,84)(51,437,205,83)(52,436,206,82)(53,435,207,81)(54,448,208,80)(55,447,209,79)(56,446,210,78)(57,97,232,193)(58,96,233,192)(59,95,234,191)(60,94,235,190)(61,93,236,189)(62,92,237,188)(63,91,238,187)(64,90,225,186)(65,89,226,185)(66,88,227,184)(67,87,228,183)(68,86,229,196)(69,85,230,195)(70,98,231,194)(99,219,179,344)(100,218,180,343)(101,217,181,342)(102,216,182,341)(103,215,169,340)(104,214,170,339)(105,213,171,338)(106,212,172,337)(107,211,173,350)(108,224,174,349)(109,223,175,348)(110,222,176,347)(111,221,177,346)(112,220,178,345)(141,156,253,332)(142,155,254,331)(143,168,255,330)(144,167,256,329)(145,166,257,328)(146,165,258,327)(147,164,259,326)(148,163,260,325)(149,162,261,324)(150,161,262,323)(151,160,263,336)(152,159,264,335)(153,158,265,334)(154,157,266,333)(267,373,397,304)(268,372,398,303)(269,371,399,302)(270,370,400,301)(271,369,401,300)(272,368,402,299)(273,367,403,298)(274,366,404,297)(275,365,405,296)(276,378,406,295)(277,377,393,308)(278,376,394,307)(279,375,395,306)(280,374,396,305) );
G=PermutationGroup([[(1,164),(2,165),(3,166),(4,167),(5,168),(6,155),(7,156),(8,157),(9,158),(10,159),(11,160),(12,161),(13,162),(14,163),(15,322),(16,309),(17,310),(18,311),(19,312),(20,313),(21,314),(22,315),(23,316),(24,317),(25,318),(26,319),(27,320),(28,321),(29,430),(30,431),(31,432),(32,433),(33,434),(34,421),(35,422),(36,423),(37,424),(38,425),(39,426),(40,427),(41,428),(42,429),(43,59),(44,60),(45,61),(46,62),(47,63),(48,64),(49,65),(50,66),(51,67),(52,68),(53,69),(54,70),(55,57),(56,58),(71,185),(72,186),(73,187),(74,188),(75,189),(76,190),(77,191),(78,192),(79,193),(80,194),(81,195),(82,196),(83,183),(84,184),(85,435),(86,436),(87,437),(88,438),(89,439),(90,440),(91,441),(92,442),(93,443),(94,444),(95,445),(96,446),(97,447),(98,448),(99,406),(100,393),(101,394),(102,395),(103,396),(104,397),(105,398),(106,399),(107,400),(108,401),(109,402),(110,403),(111,404),(112,405),(113,132),(114,133),(115,134),(116,135),(117,136),(118,137),(119,138),(120,139),(121,140),(122,127),(123,128),(124,129),(125,130),(126,131),(141,252),(142,239),(143,240),(144,241),(145,242),(146,243),(147,244),(148,245),(149,246),(150,247),(151,248),(152,249),(153,250),(154,251),(169,280),(170,267),(171,268),(172,269),(173,270),(174,271),(175,272),(176,273),(177,274),(178,275),(179,276),(180,277),(181,278),(182,279),(197,234),(198,235),(199,236),(200,237),(201,238),(202,225),(203,226),(204,227),(205,228),(206,229),(207,230),(208,231),(209,232),(210,233),(211,301),(212,302),(213,303),(214,304),(215,305),(216,306),(217,307),(218,308),(219,295),(220,296),(221,297),(222,298),(223,299),(224,300),(253,358),(254,359),(255,360),(256,361),(257,362),(258,363),(259,364),(260,351),(261,352),(262,353),(263,354),(264,355),(265,356),(266,357),(281,334),(282,335),(283,336),(284,323),(285,324),(286,325),(287,326),(288,327),(289,328),(290,329),(291,330),(292,331),(293,332),(294,333),(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),(379,413),(380,414),(381,415),(382,416),(383,417),(384,418),(385,419),(386,420),(387,407),(388,408),(389,409),(390,410),(391,411),(392,412)], [(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)], [(1,15,8,22),(2,28,9,21),(3,27,10,20),(4,26,11,19),(5,25,12,18),(6,24,13,17),(7,23,14,16),(29,329,36,336),(30,328,37,335),(31,327,38,334),(32,326,39,333),(33,325,40,332),(34,324,41,331),(35,323,42,330),(43,178,50,171),(44,177,51,170),(45,176,52,169),(46,175,53,182),(47,174,54,181),(48,173,55,180),(49,172,56,179),(57,277,64,270),(58,276,65,269),(59,275,66,268),(60,274,67,267),(61,273,68,280),(62,272,69,279),(63,271,70,278),(71,212,78,219),(72,211,79,218),(73,224,80,217),(74,223,81,216),(75,222,82,215),(76,221,83,214),(77,220,84,213),(85,375,92,368),(86,374,93,367),(87,373,94,366),(88,372,95,365),(89,371,96,378),(90,370,97,377),(91,369,98,376),(99,203,106,210),(100,202,107,209),(101,201,108,208),(102,200,109,207),(103,199,110,206),(104,198,111,205),(105,197,112,204),(113,360,120,353),(114,359,121,352),(115,358,122,351),(116,357,123,364),(117,356,124,363),(118,355,125,362),(119,354,126,361),(127,260,134,253),(128,259,135,266),(129,258,136,265),(130,257,137,264),(131,256,138,263),(132,255,139,262),(133,254,140,261),(141,391,148,384),(142,390,149,383),(143,389,150,382),(144,388,151,381),(145,387,152,380),(146,386,153,379),(147,385,154,392),(155,317,162,310),(156,316,163,309),(157,315,164,322),(158,314,165,321),(159,313,166,320),(160,312,167,319),(161,311,168,318),(183,304,190,297),(184,303,191,296),(185,302,192,295),(186,301,193,308),(187,300,194,307),(188,299,195,306),(189,298,196,305),(225,400,232,393),(226,399,233,406),(227,398,234,405),(228,397,235,404),(229,396,236,403),(230,395,237,402),(231,394,238,401),(239,410,246,417),(240,409,247,416),(241,408,248,415),(242,407,249,414),(243,420,250,413),(244,419,251,412),(245,418,252,411),(281,432,288,425),(282,431,289,424),(283,430,290,423),(284,429,291,422),(285,428,292,421),(286,427,293,434),(287,426,294,433),(337,446,344,439),(338,445,345,438),(339,444,346,437),(340,443,347,436),(341,442,348,435),(342,441,349,448),(343,440,350,447)], [(1,280,287,396),(2,267,288,397),(3,268,289,398),(4,269,290,399),(5,270,291,400),(6,271,292,401),(7,272,293,402),(8,273,294,403),(9,274,281,404),(10,275,282,405),(11,276,283,406),(12,277,284,393),(13,278,285,394),(14,279,286,395),(15,68,426,229),(16,69,427,230),(17,70,428,231),(18,57,429,232),(19,58,430,233),(20,59,431,234),(21,60,432,235),(22,61,433,236),(23,62,434,237),(24,63,421,238),(25,64,422,225),(26,65,423,226),(27,66,424,227),(28,67,425,228),(29,210,312,56),(30,197,313,43),(31,198,314,44),(32,199,315,45),(33,200,316,46),(34,201,317,47),(35,202,318,48),(36,203,319,49),(37,204,320,50),(38,205,321,51),(39,206,322,52),(40,207,309,53),(41,208,310,54),(42,209,311,55),(71,381,439,131),(72,382,440,132),(73,383,441,133),(74,384,442,134),(75,385,443,135),(76,386,444,136),(77,387,445,137),(78,388,446,138),(79,389,447,139),(80,390,448,140),(81,391,435,127),(82,392,436,128),(83,379,437,129),(84,380,438,130),(85,122,195,411),(86,123,196,412),(87,124,183,413),(88,125,184,414),(89,126,185,415),(90,113,186,416),(91,114,187,417),(92,115,188,418),(93,116,189,419),(94,117,190,420),(95,118,191,407),(96,119,192,408),(97,120,193,409),(98,121,194,410),(99,160,179,336),(100,161,180,323),(101,162,181,324),(102,163,182,325),(103,164,169,326),(104,165,170,327),(105,166,171,328),(106,167,172,329),(107,168,173,330),(108,155,174,331),(109,156,175,332),(110,157,176,333),(111,158,177,334),(112,159,178,335),(141,341,253,216),(142,342,254,217),(143,343,255,218),(144,344,256,219),(145,345,257,220),(146,346,258,221),(147,347,259,222),(148,348,260,223),(149,349,261,224),(150,350,262,211),(151,337,263,212),(152,338,264,213),(153,339,265,214),(154,340,266,215),(239,376,359,307),(240,377,360,308),(241,378,361,295),(242,365,362,296),(243,366,363,297),(244,367,364,298),(245,368,351,299),(246,369,352,300),(247,370,353,301),(248,371,354,302),(249,372,355,303),(250,373,356,304),(251,374,357,305),(252,375,358,306)], [(1,364,287,244),(2,363,288,243),(3,362,289,242),(4,361,290,241),(5,360,291,240),(6,359,292,239),(7,358,293,252),(8,357,294,251),(9,356,281,250),(10,355,282,249),(11,354,283,248),(12,353,284,247),(13,352,285,246),(14,351,286,245),(15,116,426,419),(16,115,427,418),(17,114,428,417),(18,113,429,416),(19,126,430,415),(20,125,431,414),(21,124,432,413),(22,123,433,412),(23,122,434,411),(24,121,421,410),(25,120,422,409),(26,119,423,408),(27,118,424,407),(28,117,425,420),(29,381,312,131),(30,380,313,130),(31,379,314,129),(32,392,315,128),(33,391,316,127),(34,390,317,140),(35,389,318,139),(36,388,319,138),(37,387,320,137),(38,386,321,136),(39,385,322,135),(40,384,309,134),(41,383,310,133),(42,382,311,132),(43,445,197,77),(44,444,198,76),(45,443,199,75),(46,442,200,74),(47,441,201,73),(48,440,202,72),(49,439,203,71),(50,438,204,84),(51,437,205,83),(52,436,206,82),(53,435,207,81),(54,448,208,80),(55,447,209,79),(56,446,210,78),(57,97,232,193),(58,96,233,192),(59,95,234,191),(60,94,235,190),(61,93,236,189),(62,92,237,188),(63,91,238,187),(64,90,225,186),(65,89,226,185),(66,88,227,184),(67,87,228,183),(68,86,229,196),(69,85,230,195),(70,98,231,194),(99,219,179,344),(100,218,180,343),(101,217,181,342),(102,216,182,341),(103,215,169,340),(104,214,170,339),(105,213,171,338),(106,212,172,337),(107,211,173,350),(108,224,174,349),(109,223,175,348),(110,222,176,347),(111,221,177,346),(112,220,178,345),(141,156,253,332),(142,155,254,331),(143,168,255,330),(144,167,256,329),(145,166,257,328),(146,165,258,327),(147,164,259,326),(148,163,260,325),(149,162,261,324),(150,161,262,323),(151,160,263,336),(152,159,264,335),(153,158,265,334),(154,157,266,333),(267,373,397,304),(268,372,398,303),(269,371,399,302),(270,370,400,301),(271,369,401,300),(272,368,402,299),(273,367,403,298),(274,366,404,297),(275,365,405,296),(276,378,406,295),(277,377,393,308),(278,376,394,307),(279,375,395,306),(280,374,396,305)]])
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 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | - | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | C4○D4 | D14 | D14 | C4○D28 | D4⋊2D7 | Q8×D7 |
| kernel | C2×Dic7.Q8 | Dic7.Q8 | C2×C4×Dic7 | C2×Dic7⋊C4 | C2×C4⋊Dic7 | C14×C4⋊C4 | C2×Dic7 | C2×C4⋊C4 | C2×C14 | C4⋊C4 | C22×C4 | C22 | C22 | C22 |
| # reps | 1 | 8 | 1 | 4 | 1 | 1 | 4 | 3 | 8 | 12 | 9 | 24 | 6 | 6 |
Matrix representation of C2×Dic7.Q8 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 20 | 0 | 0 | 0 | 0 | 0 |
| 12 | 16 | 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 |
| 25 | 11 | 0 | 0 | 0 | 0 |
| 25 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 14 | 20 | 0 | 0 |
| 0 | 0 | 9 | 15 | 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 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 21 | 12 |
| 4 | 18 | 0 | 0 | 0 | 0 |
| 4 | 25 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 21 | 0 | 0 |
| 0 | 0 | 8 | 23 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 1 |
| 0 | 0 | 0 | 0 | 15 | 10 |
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],[20,12,0,0,0,0,0,16,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[25,25,0,0,0,0,11,4,0,0,0,0,0,0,14,9,0,0,0,0,20,15,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,17,21,0,0,0,0,0,12],[4,4,0,0,0,0,18,25,0,0,0,0,0,0,6,8,0,0,0,0,21,23,0,0,0,0,0,0,19,15,0,0,0,0,1,10] >;
C2×Dic7.Q8 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_7.Q_8 % in TeX
G:=Group("C2xDic7.Q8"); // GroupNames label
G:=SmallGroup(448,951);
// by ID
G=gap.SmallGroup(448,951);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,100,675,297,136,18822]);
// 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=e*b*e^-1=b^-1,b*d=d*b,d*c*d^-1=b^7*c,c*e=e*c,e*d*e^-1=b^7*d^-1>;
// generators/relations