direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic7⋊3Q8, C14⋊2(C4×Q8), Dic7⋊6(C2×Q8), C4⋊C4.304D14, (C2×Dic7)⋊11Q8, (C2×Dic14)⋊17C4, Dic14⋊21(C2×C4), C22.29(Q8×D7), C14.10(C23×C4), C28.87(C22×C4), (C2×C14).40C24, C14.21(C22×Q8), (C2×C28).576C23, (C22×C4).315D14, Dic7.4(C22×C4), C22.20(C23×D7), C23.320(C22×D7), C22.70(D4⋊2D7), Dic7⋊C4.128C22, (C22×C28).213C22, (C22×C14).389C23, (C2×Dic7).304C23, (C22×Dic14).16C2, (C4×Dic7).289C22, (C2×Dic14).280C22, (C22×Dic7).205C22, C7⋊2(C2×C4×Q8), C2.1(C2×Q8×D7), C4.56(C2×C4×D7), (C2×C4⋊C4).29D7, (C2×C4).86(C4×D7), (C14×C4⋊C4).16C2, C22.70(C2×C4×D7), C2.12(D7×C22×C4), C14.69(C2×C4○D4), C2.3(C2×D4⋊2D7), (C2×C14).90(C2×Q8), (C2×C4×Dic7).40C2, (C2×C28).127(C2×C4), (C7×C4⋊C4).289C22, (C2×Dic7⋊C4).28C2, (C2×Dic7).70(C2×C4), (C2×C4).263(C22×D7), (C2×C14).169(C4○D4), (C2×C14).149(C22×C4), SmallGroup(448,949)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Dic7⋊3Q8
G = < a,b,c,d,e | a2=b14=d4=1, c2=b7, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=dbd-1=b-1, be=eb, cd=dc, ce=ec, ede-1=d-1 >
Subgroups: 964 in 298 conjugacy classes, 175 normal (21 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, Q8, C23, C14, C14, C42, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×Q8, Dic7, Dic7, C28, C28, C2×C14, C2×C14, C2×C42, C2×C4⋊C4, C2×C4⋊C4, C4×Q8, C22×Q8, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C2×C4×Q8, C4×Dic7, Dic7⋊C4, C7×C4⋊C4, C2×Dic14, C22×Dic7, C22×Dic7, C22×C28, C22×C28, Dic7⋊3Q8, C2×C4×Dic7, C2×C4×Dic7, C2×Dic7⋊C4, C14×C4⋊C4, C22×Dic14, C2×Dic7⋊3Q8
Quotients: C1, C2, C4, C22, C2×C4, Q8, C23, D7, C22×C4, C2×Q8, C4○D4, C24, D14, C4×Q8, C23×C4, C22×Q8, C2×C4○D4, C4×D7, C22×D7, C2×C4×Q8, C2×C4×D7, D4⋊2D7, Q8×D7, C23×D7, Dic7⋊3Q8, D7×C22×C4, C2×D4⋊2D7, C2×Q8×D7, C2×Dic7⋊3Q8
►Regular action on 448 points
Generators in S448
(1 113)(2 114)(3 115)(4 116)(5 117)(6 118)(7 119)(8 120)(9 121)(10 122)(11 123)(12 124)(13 125)(14 126)(15 127)(16 128)(17 129)(18 130)(19 131)(20 132)(21 133)(22 134)(23 135)(24 136)(25 137)(26 138)(27 139)(28 140)(29 148)(30 149)(31 150)(32 151)(33 152)(34 153)(35 154)(36 141)(37 142)(38 143)(39 144)(40 145)(41 146)(42 147)(43 162)(44 163)(45 164)(46 165)(47 166)(48 167)(49 168)(50 155)(51 156)(52 157)(53 158)(54 159)(55 160)(56 161)(57 169)(58 170)(59 171)(60 172)(61 173)(62 174)(63 175)(64 176)(65 177)(66 178)(67 179)(68 180)(69 181)(70 182)(71 190)(72 191)(73 192)(74 193)(75 194)(76 195)(77 196)(78 183)(79 184)(80 185)(81 186)(82 187)(83 188)(84 189)(85 204)(86 205)(87 206)(88 207)(89 208)(90 209)(91 210)(92 197)(93 198)(94 199)(95 200)(96 201)(97 202)(98 203)(99 218)(100 219)(101 220)(102 221)(103 222)(104 223)(105 224)(106 211)(107 212)(108 213)(109 214)(110 215)(111 216)(112 217)(225 339)(226 340)(227 341)(228 342)(229 343)(230 344)(231 345)(232 346)(233 347)(234 348)(235 349)(236 350)(237 337)(238 338)(239 364)(240 351)(241 352)(242 353)(243 354)(244 355)(245 356)(246 357)(247 358)(248 359)(249 360)(250 361)(251 362)(252 363)(253 378)(254 365)(255 366)(256 367)(257 368)(258 369)(259 370)(260 371)(261 372)(262 373)(263 374)(264 375)(265 376)(266 377)(267 390)(268 391)(269 392)(270 379)(271 380)(272 381)(273 382)(274 383)(275 384)(276 385)(277 386)(278 387)(279 388)(280 389)(281 397)(282 398)(283 399)(284 400)(285 401)(286 402)(287 403)(288 404)(289 405)(290 406)(291 393)(292 394)(293 395)(294 396)(295 410)(296 411)(297 412)(298 413)(299 414)(300 415)(301 416)(302 417)(303 418)(304 419)(305 420)(306 407)(307 408)(308 409)(309 432)(310 433)(311 434)(312 421)(313 422)(314 423)(315 424)(316 425)(317 426)(318 427)(319 428)(320 429)(321 430)(322 431)(323 444)(324 445)(325 446)(326 447)(327 448)(328 435)(329 436)(330 437)(331 438)(332 439)(333 440)(334 441)(335 442)(336 443)
(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)
(1 351 8 358)(2 364 9 357)(3 363 10 356)(4 362 11 355)(5 361 12 354)(6 360 13 353)(7 359 14 352)(15 349 22 342)(16 348 23 341)(17 347 24 340)(18 346 25 339)(19 345 26 338)(20 344 27 337)(21 343 28 350)(29 382 36 389)(30 381 37 388)(31 380 38 387)(32 379 39 386)(33 392 40 385)(34 391 41 384)(35 390 42 383)(43 376 50 369)(44 375 51 368)(45 374 52 367)(46 373 53 366)(47 372 54 365)(48 371 55 378)(49 370 56 377)(57 416 64 409)(58 415 65 408)(59 414 66 407)(60 413 67 420)(61 412 68 419)(62 411 69 418)(63 410 70 417)(71 393 78 400)(72 406 79 399)(73 405 80 398)(74 404 81 397)(75 403 82 396)(76 402 83 395)(77 401 84 394)(85 435 92 442)(86 448 93 441)(87 447 94 440)(88 446 95 439)(89 445 96 438)(90 444 97 437)(91 443 98 436)(99 427 106 434)(100 426 107 433)(101 425 108 432)(102 424 109 431)(103 423 110 430)(104 422 111 429)(105 421 112 428)(113 240 120 247)(114 239 121 246)(115 252 122 245)(116 251 123 244)(117 250 124 243)(118 249 125 242)(119 248 126 241)(127 235 134 228)(128 234 135 227)(129 233 136 226)(130 232 137 225)(131 231 138 238)(132 230 139 237)(133 229 140 236)(141 280 148 273)(142 279 149 272)(143 278 150 271)(144 277 151 270)(145 276 152 269)(146 275 153 268)(147 274 154 267)(155 258 162 265)(156 257 163 264)(157 256 164 263)(158 255 165 262)(159 254 166 261)(160 253 167 260)(161 266 168 259)(169 301 176 308)(170 300 177 307)(171 299 178 306)(172 298 179 305)(173 297 180 304)(174 296 181 303)(175 295 182 302)(183 284 190 291)(184 283 191 290)(185 282 192 289)(186 281 193 288)(187 294 194 287)(188 293 195 286)(189 292 196 285)(197 335 204 328)(198 334 205 327)(199 333 206 326)(200 332 207 325)(201 331 208 324)(202 330 209 323)(203 329 210 336)(211 311 218 318)(212 310 219 317)(213 309 220 316)(214 322 221 315)(215 321 222 314)(216 320 223 313)(217 319 224 312)
(1 265 15 280)(2 264 16 279)(3 263 17 278)(4 262 18 277)(5 261 19 276)(6 260 20 275)(7 259 21 274)(8 258 22 273)(9 257 23 272)(10 256 24 271)(11 255 25 270)(12 254 26 269)(13 253 27 268)(14 266 28 267)(29 240 50 235)(30 239 51 234)(31 252 52 233)(32 251 53 232)(33 250 54 231)(34 249 55 230)(35 248 56 229)(36 247 43 228)(37 246 44 227)(38 245 45 226)(39 244 46 225)(40 243 47 238)(41 242 48 237)(42 241 49 236)(57 335 71 318)(58 334 72 317)(59 333 73 316)(60 332 74 315)(61 331 75 314)(62 330 76 313)(63 329 77 312)(64 328 78 311)(65 327 79 310)(66 326 80 309)(67 325 81 322)(68 324 82 321)(69 323 83 320)(70 336 84 319)(85 291 106 301)(86 290 107 300)(87 289 108 299)(88 288 109 298)(89 287 110 297)(90 286 111 296)(91 285 112 295)(92 284 99 308)(93 283 100 307)(94 282 101 306)(95 281 102 305)(96 294 103 304)(97 293 104 303)(98 292 105 302)(113 376 127 389)(114 375 128 388)(115 374 129 387)(116 373 130 386)(117 372 131 385)(118 371 132 384)(119 370 133 383)(120 369 134 382)(121 368 135 381)(122 367 136 380)(123 366 137 379)(124 365 138 392)(125 378 139 391)(126 377 140 390)(141 358 162 342)(142 357 163 341)(143 356 164 340)(144 355 165 339)(145 354 166 338)(146 353 167 337)(147 352 168 350)(148 351 155 349)(149 364 156 348)(150 363 157 347)(151 362 158 346)(152 361 159 345)(153 360 160 344)(154 359 161 343)(169 442 190 427)(170 441 191 426)(171 440 192 425)(172 439 193 424)(173 438 194 423)(174 437 195 422)(175 436 196 421)(176 435 183 434)(177 448 184 433)(178 447 185 432)(179 446 186 431)(180 445 187 430)(181 444 188 429)(182 443 189 428)(197 400 218 409)(198 399 219 408)(199 398 220 407)(200 397 221 420)(201 396 222 419)(202 395 223 418)(203 394 224 417)(204 393 211 416)(205 406 212 415)(206 405 213 414)(207 404 214 413)(208 403 215 412)(209 402 216 411)(210 401 217 410)
(1 78 15 64)(2 79 16 65)(3 80 17 66)(4 81 18 67)(5 82 19 68)(6 83 20 69)(7 84 21 70)(8 71 22 57)(9 72 23 58)(10 73 24 59)(11 74 25 60)(12 75 26 61)(13 76 27 62)(14 77 28 63)(29 99 50 92)(30 100 51 93)(31 101 52 94)(32 102 53 95)(33 103 54 96)(34 104 55 97)(35 105 56 98)(36 106 43 85)(37 107 44 86)(38 108 45 87)(39 109 46 88)(40 110 47 89)(41 111 48 90)(42 112 49 91)(113 183 127 176)(114 184 128 177)(115 185 129 178)(116 186 130 179)(117 187 131 180)(118 188 132 181)(119 189 133 182)(120 190 134 169)(121 191 135 170)(122 192 136 171)(123 193 137 172)(124 194 138 173)(125 195 139 174)(126 196 140 175)(141 211 162 204)(142 212 163 205)(143 213 164 206)(144 214 165 207)(145 215 166 208)(146 216 167 209)(147 217 168 210)(148 218 155 197)(149 219 156 198)(150 220 157 199)(151 221 158 200)(152 222 159 201)(153 223 160 202)(154 224 161 203)(225 298 244 288)(226 299 245 289)(227 300 246 290)(228 301 247 291)(229 302 248 292)(230 303 249 293)(231 304 250 294)(232 305 251 281)(233 306 252 282)(234 307 239 283)(235 308 240 284)(236 295 241 285)(237 296 242 286)(238 297 243 287)(253 330 268 313)(254 331 269 314)(255 332 270 315)(256 333 271 316)(257 334 272 317)(258 335 273 318)(259 336 274 319)(260 323 275 320)(261 324 276 321)(262 325 277 322)(263 326 278 309)(264 327 279 310)(265 328 280 311)(266 329 267 312)(337 411 353 402)(338 412 354 403)(339 413 355 404)(340 414 356 405)(341 415 357 406)(342 416 358 393)(343 417 359 394)(344 418 360 395)(345 419 361 396)(346 420 362 397)(347 407 363 398)(348 408 364 399)(349 409 351 400)(350 410 352 401)(365 438 392 423)(366 439 379 424)(367 440 380 425)(368 441 381 426)(369 442 382 427)(370 443 383 428)(371 444 384 429)(372 445 385 430)(373 446 386 431)(374 447 387 432)(375 448 388 433)(376 435 389 434)(377 436 390 421)(378 437 391 422)
G:=sub<Sym(448)| (1,113)(2,114)(3,115)(4,116)(5,117)(6,118)(7,119)(8,120)(9,121)(10,122)(11,123)(12,124)(13,125)(14,126)(15,127)(16,128)(17,129)(18,130)(19,131)(20,132)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,148)(30,149)(31,150)(32,151)(33,152)(34,153)(35,154)(36,141)(37,142)(38,143)(39,144)(40,145)(41,146)(42,147)(43,162)(44,163)(45,164)(46,165)(47,166)(48,167)(49,168)(50,155)(51,156)(52,157)(53,158)(54,159)(55,160)(56,161)(57,169)(58,170)(59,171)(60,172)(61,173)(62,174)(63,175)(64,176)(65,177)(66,178)(67,179)(68,180)(69,181)(70,182)(71,190)(72,191)(73,192)(74,193)(75,194)(76,195)(77,196)(78,183)(79,184)(80,185)(81,186)(82,187)(83,188)(84,189)(85,204)(86,205)(87,206)(88,207)(89,208)(90,209)(91,210)(92,197)(93,198)(94,199)(95,200)(96,201)(97,202)(98,203)(99,218)(100,219)(101,220)(102,221)(103,222)(104,223)(105,224)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)(112,217)(225,339)(226,340)(227,341)(228,342)(229,343)(230,344)(231,345)(232,346)(233,347)(234,348)(235,349)(236,350)(237,337)(238,338)(239,364)(240,351)(241,352)(242,353)(243,354)(244,355)(245,356)(246,357)(247,358)(248,359)(249,360)(250,361)(251,362)(252,363)(253,378)(254,365)(255,366)(256,367)(257,368)(258,369)(259,370)(260,371)(261,372)(262,373)(263,374)(264,375)(265,376)(266,377)(267,390)(268,391)(269,392)(270,379)(271,380)(272,381)(273,382)(274,383)(275,384)(276,385)(277,386)(278,387)(279,388)(280,389)(281,397)(282,398)(283,399)(284,400)(285,401)(286,402)(287,403)(288,404)(289,405)(290,406)(291,393)(292,394)(293,395)(294,396)(295,410)(296,411)(297,412)(298,413)(299,414)(300,415)(301,416)(302,417)(303,418)(304,419)(305,420)(306,407)(307,408)(308,409)(309,432)(310,433)(311,434)(312,421)(313,422)(314,423)(315,424)(316,425)(317,426)(318,427)(319,428)(320,429)(321,430)(322,431)(323,444)(324,445)(325,446)(326,447)(327,448)(328,435)(329,436)(330,437)(331,438)(332,439)(333,440)(334,441)(335,442)(336,443), (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), (1,351,8,358)(2,364,9,357)(3,363,10,356)(4,362,11,355)(5,361,12,354)(6,360,13,353)(7,359,14,352)(15,349,22,342)(16,348,23,341)(17,347,24,340)(18,346,25,339)(19,345,26,338)(20,344,27,337)(21,343,28,350)(29,382,36,389)(30,381,37,388)(31,380,38,387)(32,379,39,386)(33,392,40,385)(34,391,41,384)(35,390,42,383)(43,376,50,369)(44,375,51,368)(45,374,52,367)(46,373,53,366)(47,372,54,365)(48,371,55,378)(49,370,56,377)(57,416,64,409)(58,415,65,408)(59,414,66,407)(60,413,67,420)(61,412,68,419)(62,411,69,418)(63,410,70,417)(71,393,78,400)(72,406,79,399)(73,405,80,398)(74,404,81,397)(75,403,82,396)(76,402,83,395)(77,401,84,394)(85,435,92,442)(86,448,93,441)(87,447,94,440)(88,446,95,439)(89,445,96,438)(90,444,97,437)(91,443,98,436)(99,427,106,434)(100,426,107,433)(101,425,108,432)(102,424,109,431)(103,423,110,430)(104,422,111,429)(105,421,112,428)(113,240,120,247)(114,239,121,246)(115,252,122,245)(116,251,123,244)(117,250,124,243)(118,249,125,242)(119,248,126,241)(127,235,134,228)(128,234,135,227)(129,233,136,226)(130,232,137,225)(131,231,138,238)(132,230,139,237)(133,229,140,236)(141,280,148,273)(142,279,149,272)(143,278,150,271)(144,277,151,270)(145,276,152,269)(146,275,153,268)(147,274,154,267)(155,258,162,265)(156,257,163,264)(157,256,164,263)(158,255,165,262)(159,254,166,261)(160,253,167,260)(161,266,168,259)(169,301,176,308)(170,300,177,307)(171,299,178,306)(172,298,179,305)(173,297,180,304)(174,296,181,303)(175,295,182,302)(183,284,190,291)(184,283,191,290)(185,282,192,289)(186,281,193,288)(187,294,194,287)(188,293,195,286)(189,292,196,285)(197,335,204,328)(198,334,205,327)(199,333,206,326)(200,332,207,325)(201,331,208,324)(202,330,209,323)(203,329,210,336)(211,311,218,318)(212,310,219,317)(213,309,220,316)(214,322,221,315)(215,321,222,314)(216,320,223,313)(217,319,224,312), (1,265,15,280)(2,264,16,279)(3,263,17,278)(4,262,18,277)(5,261,19,276)(6,260,20,275)(7,259,21,274)(8,258,22,273)(9,257,23,272)(10,256,24,271)(11,255,25,270)(12,254,26,269)(13,253,27,268)(14,266,28,267)(29,240,50,235)(30,239,51,234)(31,252,52,233)(32,251,53,232)(33,250,54,231)(34,249,55,230)(35,248,56,229)(36,247,43,228)(37,246,44,227)(38,245,45,226)(39,244,46,225)(40,243,47,238)(41,242,48,237)(42,241,49,236)(57,335,71,318)(58,334,72,317)(59,333,73,316)(60,332,74,315)(61,331,75,314)(62,330,76,313)(63,329,77,312)(64,328,78,311)(65,327,79,310)(66,326,80,309)(67,325,81,322)(68,324,82,321)(69,323,83,320)(70,336,84,319)(85,291,106,301)(86,290,107,300)(87,289,108,299)(88,288,109,298)(89,287,110,297)(90,286,111,296)(91,285,112,295)(92,284,99,308)(93,283,100,307)(94,282,101,306)(95,281,102,305)(96,294,103,304)(97,293,104,303)(98,292,105,302)(113,376,127,389)(114,375,128,388)(115,374,129,387)(116,373,130,386)(117,372,131,385)(118,371,132,384)(119,370,133,383)(120,369,134,382)(121,368,135,381)(122,367,136,380)(123,366,137,379)(124,365,138,392)(125,378,139,391)(126,377,140,390)(141,358,162,342)(142,357,163,341)(143,356,164,340)(144,355,165,339)(145,354,166,338)(146,353,167,337)(147,352,168,350)(148,351,155,349)(149,364,156,348)(150,363,157,347)(151,362,158,346)(152,361,159,345)(153,360,160,344)(154,359,161,343)(169,442,190,427)(170,441,191,426)(171,440,192,425)(172,439,193,424)(173,438,194,423)(174,437,195,422)(175,436,196,421)(176,435,183,434)(177,448,184,433)(178,447,185,432)(179,446,186,431)(180,445,187,430)(181,444,188,429)(182,443,189,428)(197,400,218,409)(198,399,219,408)(199,398,220,407)(200,397,221,420)(201,396,222,419)(202,395,223,418)(203,394,224,417)(204,393,211,416)(205,406,212,415)(206,405,213,414)(207,404,214,413)(208,403,215,412)(209,402,216,411)(210,401,217,410), (1,78,15,64)(2,79,16,65)(3,80,17,66)(4,81,18,67)(5,82,19,68)(6,83,20,69)(7,84,21,70)(8,71,22,57)(9,72,23,58)(10,73,24,59)(11,74,25,60)(12,75,26,61)(13,76,27,62)(14,77,28,63)(29,99,50,92)(30,100,51,93)(31,101,52,94)(32,102,53,95)(33,103,54,96)(34,104,55,97)(35,105,56,98)(36,106,43,85)(37,107,44,86)(38,108,45,87)(39,109,46,88)(40,110,47,89)(41,111,48,90)(42,112,49,91)(113,183,127,176)(114,184,128,177)(115,185,129,178)(116,186,130,179)(117,187,131,180)(118,188,132,181)(119,189,133,182)(120,190,134,169)(121,191,135,170)(122,192,136,171)(123,193,137,172)(124,194,138,173)(125,195,139,174)(126,196,140,175)(141,211,162,204)(142,212,163,205)(143,213,164,206)(144,214,165,207)(145,215,166,208)(146,216,167,209)(147,217,168,210)(148,218,155,197)(149,219,156,198)(150,220,157,199)(151,221,158,200)(152,222,159,201)(153,223,160,202)(154,224,161,203)(225,298,244,288)(226,299,245,289)(227,300,246,290)(228,301,247,291)(229,302,248,292)(230,303,249,293)(231,304,250,294)(232,305,251,281)(233,306,252,282)(234,307,239,283)(235,308,240,284)(236,295,241,285)(237,296,242,286)(238,297,243,287)(253,330,268,313)(254,331,269,314)(255,332,270,315)(256,333,271,316)(257,334,272,317)(258,335,273,318)(259,336,274,319)(260,323,275,320)(261,324,276,321)(262,325,277,322)(263,326,278,309)(264,327,279,310)(265,328,280,311)(266,329,267,312)(337,411,353,402)(338,412,354,403)(339,413,355,404)(340,414,356,405)(341,415,357,406)(342,416,358,393)(343,417,359,394)(344,418,360,395)(345,419,361,396)(346,420,362,397)(347,407,363,398)(348,408,364,399)(349,409,351,400)(350,410,352,401)(365,438,392,423)(366,439,379,424)(367,440,380,425)(368,441,381,426)(369,442,382,427)(370,443,383,428)(371,444,384,429)(372,445,385,430)(373,446,386,431)(374,447,387,432)(375,448,388,433)(376,435,389,434)(377,436,390,421)(378,437,391,422)>;
G:=Group( (1,113)(2,114)(3,115)(4,116)(5,117)(6,118)(7,119)(8,120)(9,121)(10,122)(11,123)(12,124)(13,125)(14,126)(15,127)(16,128)(17,129)(18,130)(19,131)(20,132)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,148)(30,149)(31,150)(32,151)(33,152)(34,153)(35,154)(36,141)(37,142)(38,143)(39,144)(40,145)(41,146)(42,147)(43,162)(44,163)(45,164)(46,165)(47,166)(48,167)(49,168)(50,155)(51,156)(52,157)(53,158)(54,159)(55,160)(56,161)(57,169)(58,170)(59,171)(60,172)(61,173)(62,174)(63,175)(64,176)(65,177)(66,178)(67,179)(68,180)(69,181)(70,182)(71,190)(72,191)(73,192)(74,193)(75,194)(76,195)(77,196)(78,183)(79,184)(80,185)(81,186)(82,187)(83,188)(84,189)(85,204)(86,205)(87,206)(88,207)(89,208)(90,209)(91,210)(92,197)(93,198)(94,199)(95,200)(96,201)(97,202)(98,203)(99,218)(100,219)(101,220)(102,221)(103,222)(104,223)(105,224)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)(112,217)(225,339)(226,340)(227,341)(228,342)(229,343)(230,344)(231,345)(232,346)(233,347)(234,348)(235,349)(236,350)(237,337)(238,338)(239,364)(240,351)(241,352)(242,353)(243,354)(244,355)(245,356)(246,357)(247,358)(248,359)(249,360)(250,361)(251,362)(252,363)(253,378)(254,365)(255,366)(256,367)(257,368)(258,369)(259,370)(260,371)(261,372)(262,373)(263,374)(264,375)(265,376)(266,377)(267,390)(268,391)(269,392)(270,379)(271,380)(272,381)(273,382)(274,383)(275,384)(276,385)(277,386)(278,387)(279,388)(280,389)(281,397)(282,398)(283,399)(284,400)(285,401)(286,402)(287,403)(288,404)(289,405)(290,406)(291,393)(292,394)(293,395)(294,396)(295,410)(296,411)(297,412)(298,413)(299,414)(300,415)(301,416)(302,417)(303,418)(304,419)(305,420)(306,407)(307,408)(308,409)(309,432)(310,433)(311,434)(312,421)(313,422)(314,423)(315,424)(316,425)(317,426)(318,427)(319,428)(320,429)(321,430)(322,431)(323,444)(324,445)(325,446)(326,447)(327,448)(328,435)(329,436)(330,437)(331,438)(332,439)(333,440)(334,441)(335,442)(336,443), (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), (1,351,8,358)(2,364,9,357)(3,363,10,356)(4,362,11,355)(5,361,12,354)(6,360,13,353)(7,359,14,352)(15,349,22,342)(16,348,23,341)(17,347,24,340)(18,346,25,339)(19,345,26,338)(20,344,27,337)(21,343,28,350)(29,382,36,389)(30,381,37,388)(31,380,38,387)(32,379,39,386)(33,392,40,385)(34,391,41,384)(35,390,42,383)(43,376,50,369)(44,375,51,368)(45,374,52,367)(46,373,53,366)(47,372,54,365)(48,371,55,378)(49,370,56,377)(57,416,64,409)(58,415,65,408)(59,414,66,407)(60,413,67,420)(61,412,68,419)(62,411,69,418)(63,410,70,417)(71,393,78,400)(72,406,79,399)(73,405,80,398)(74,404,81,397)(75,403,82,396)(76,402,83,395)(77,401,84,394)(85,435,92,442)(86,448,93,441)(87,447,94,440)(88,446,95,439)(89,445,96,438)(90,444,97,437)(91,443,98,436)(99,427,106,434)(100,426,107,433)(101,425,108,432)(102,424,109,431)(103,423,110,430)(104,422,111,429)(105,421,112,428)(113,240,120,247)(114,239,121,246)(115,252,122,245)(116,251,123,244)(117,250,124,243)(118,249,125,242)(119,248,126,241)(127,235,134,228)(128,234,135,227)(129,233,136,226)(130,232,137,225)(131,231,138,238)(132,230,139,237)(133,229,140,236)(141,280,148,273)(142,279,149,272)(143,278,150,271)(144,277,151,270)(145,276,152,269)(146,275,153,268)(147,274,154,267)(155,258,162,265)(156,257,163,264)(157,256,164,263)(158,255,165,262)(159,254,166,261)(160,253,167,260)(161,266,168,259)(169,301,176,308)(170,300,177,307)(171,299,178,306)(172,298,179,305)(173,297,180,304)(174,296,181,303)(175,295,182,302)(183,284,190,291)(184,283,191,290)(185,282,192,289)(186,281,193,288)(187,294,194,287)(188,293,195,286)(189,292,196,285)(197,335,204,328)(198,334,205,327)(199,333,206,326)(200,332,207,325)(201,331,208,324)(202,330,209,323)(203,329,210,336)(211,311,218,318)(212,310,219,317)(213,309,220,316)(214,322,221,315)(215,321,222,314)(216,320,223,313)(217,319,224,312), (1,265,15,280)(2,264,16,279)(3,263,17,278)(4,262,18,277)(5,261,19,276)(6,260,20,275)(7,259,21,274)(8,258,22,273)(9,257,23,272)(10,256,24,271)(11,255,25,270)(12,254,26,269)(13,253,27,268)(14,266,28,267)(29,240,50,235)(30,239,51,234)(31,252,52,233)(32,251,53,232)(33,250,54,231)(34,249,55,230)(35,248,56,229)(36,247,43,228)(37,246,44,227)(38,245,45,226)(39,244,46,225)(40,243,47,238)(41,242,48,237)(42,241,49,236)(57,335,71,318)(58,334,72,317)(59,333,73,316)(60,332,74,315)(61,331,75,314)(62,330,76,313)(63,329,77,312)(64,328,78,311)(65,327,79,310)(66,326,80,309)(67,325,81,322)(68,324,82,321)(69,323,83,320)(70,336,84,319)(85,291,106,301)(86,290,107,300)(87,289,108,299)(88,288,109,298)(89,287,110,297)(90,286,111,296)(91,285,112,295)(92,284,99,308)(93,283,100,307)(94,282,101,306)(95,281,102,305)(96,294,103,304)(97,293,104,303)(98,292,105,302)(113,376,127,389)(114,375,128,388)(115,374,129,387)(116,373,130,386)(117,372,131,385)(118,371,132,384)(119,370,133,383)(120,369,134,382)(121,368,135,381)(122,367,136,380)(123,366,137,379)(124,365,138,392)(125,378,139,391)(126,377,140,390)(141,358,162,342)(142,357,163,341)(143,356,164,340)(144,355,165,339)(145,354,166,338)(146,353,167,337)(147,352,168,350)(148,351,155,349)(149,364,156,348)(150,363,157,347)(151,362,158,346)(152,361,159,345)(153,360,160,344)(154,359,161,343)(169,442,190,427)(170,441,191,426)(171,440,192,425)(172,439,193,424)(173,438,194,423)(174,437,195,422)(175,436,196,421)(176,435,183,434)(177,448,184,433)(178,447,185,432)(179,446,186,431)(180,445,187,430)(181,444,188,429)(182,443,189,428)(197,400,218,409)(198,399,219,408)(199,398,220,407)(200,397,221,420)(201,396,222,419)(202,395,223,418)(203,394,224,417)(204,393,211,416)(205,406,212,415)(206,405,213,414)(207,404,214,413)(208,403,215,412)(209,402,216,411)(210,401,217,410), (1,78,15,64)(2,79,16,65)(3,80,17,66)(4,81,18,67)(5,82,19,68)(6,83,20,69)(7,84,21,70)(8,71,22,57)(9,72,23,58)(10,73,24,59)(11,74,25,60)(12,75,26,61)(13,76,27,62)(14,77,28,63)(29,99,50,92)(30,100,51,93)(31,101,52,94)(32,102,53,95)(33,103,54,96)(34,104,55,97)(35,105,56,98)(36,106,43,85)(37,107,44,86)(38,108,45,87)(39,109,46,88)(40,110,47,89)(41,111,48,90)(42,112,49,91)(113,183,127,176)(114,184,128,177)(115,185,129,178)(116,186,130,179)(117,187,131,180)(118,188,132,181)(119,189,133,182)(120,190,134,169)(121,191,135,170)(122,192,136,171)(123,193,137,172)(124,194,138,173)(125,195,139,174)(126,196,140,175)(141,211,162,204)(142,212,163,205)(143,213,164,206)(144,214,165,207)(145,215,166,208)(146,216,167,209)(147,217,168,210)(148,218,155,197)(149,219,156,198)(150,220,157,199)(151,221,158,200)(152,222,159,201)(153,223,160,202)(154,224,161,203)(225,298,244,288)(226,299,245,289)(227,300,246,290)(228,301,247,291)(229,302,248,292)(230,303,249,293)(231,304,250,294)(232,305,251,281)(233,306,252,282)(234,307,239,283)(235,308,240,284)(236,295,241,285)(237,296,242,286)(238,297,243,287)(253,330,268,313)(254,331,269,314)(255,332,270,315)(256,333,271,316)(257,334,272,317)(258,335,273,318)(259,336,274,319)(260,323,275,320)(261,324,276,321)(262,325,277,322)(263,326,278,309)(264,327,279,310)(265,328,280,311)(266,329,267,312)(337,411,353,402)(338,412,354,403)(339,413,355,404)(340,414,356,405)(341,415,357,406)(342,416,358,393)(343,417,359,394)(344,418,360,395)(345,419,361,396)(346,420,362,397)(347,407,363,398)(348,408,364,399)(349,409,351,400)(350,410,352,401)(365,438,392,423)(366,439,379,424)(367,440,380,425)(368,441,381,426)(369,442,382,427)(370,443,383,428)(371,444,384,429)(372,445,385,430)(373,446,386,431)(374,447,387,432)(375,448,388,433)(376,435,389,434)(377,436,390,421)(378,437,391,422) );
G=PermutationGroup([[(1,113),(2,114),(3,115),(4,116),(5,117),(6,118),(7,119),(8,120),(9,121),(10,122),(11,123),(12,124),(13,125),(14,126),(15,127),(16,128),(17,129),(18,130),(19,131),(20,132),(21,133),(22,134),(23,135),(24,136),(25,137),(26,138),(27,139),(28,140),(29,148),(30,149),(31,150),(32,151),(33,152),(34,153),(35,154),(36,141),(37,142),(38,143),(39,144),(40,145),(41,146),(42,147),(43,162),(44,163),(45,164),(46,165),(47,166),(48,167),(49,168),(50,155),(51,156),(52,157),(53,158),(54,159),(55,160),(56,161),(57,169),(58,170),(59,171),(60,172),(61,173),(62,174),(63,175),(64,176),(65,177),(66,178),(67,179),(68,180),(69,181),(70,182),(71,190),(72,191),(73,192),(74,193),(75,194),(76,195),(77,196),(78,183),(79,184),(80,185),(81,186),(82,187),(83,188),(84,189),(85,204),(86,205),(87,206),(88,207),(89,208),(90,209),(91,210),(92,197),(93,198),(94,199),(95,200),(96,201),(97,202),(98,203),(99,218),(100,219),(101,220),(102,221),(103,222),(104,223),(105,224),(106,211),(107,212),(108,213),(109,214),(110,215),(111,216),(112,217),(225,339),(226,340),(227,341),(228,342),(229,343),(230,344),(231,345),(232,346),(233,347),(234,348),(235,349),(236,350),(237,337),(238,338),(239,364),(240,351),(241,352),(242,353),(243,354),(244,355),(245,356),(246,357),(247,358),(248,359),(249,360),(250,361),(251,362),(252,363),(253,378),(254,365),(255,366),(256,367),(257,368),(258,369),(259,370),(260,371),(261,372),(262,373),(263,374),(264,375),(265,376),(266,377),(267,390),(268,391),(269,392),(270,379),(271,380),(272,381),(273,382),(274,383),(275,384),(276,385),(277,386),(278,387),(279,388),(280,389),(281,397),(282,398),(283,399),(284,400),(285,401),(286,402),(287,403),(288,404),(289,405),(290,406),(291,393),(292,394),(293,395),(294,396),(295,410),(296,411),(297,412),(298,413),(299,414),(300,415),(301,416),(302,417),(303,418),(304,419),(305,420),(306,407),(307,408),(308,409),(309,432),(310,433),(311,434),(312,421),(313,422),(314,423),(315,424),(316,425),(317,426),(318,427),(319,428),(320,429),(321,430),(322,431),(323,444),(324,445),(325,446),(326,447),(327,448),(328,435),(329,436),(330,437),(331,438),(332,439),(333,440),(334,441),(335,442),(336,443)], [(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)], [(1,351,8,358),(2,364,9,357),(3,363,10,356),(4,362,11,355),(5,361,12,354),(6,360,13,353),(7,359,14,352),(15,349,22,342),(16,348,23,341),(17,347,24,340),(18,346,25,339),(19,345,26,338),(20,344,27,337),(21,343,28,350),(29,382,36,389),(30,381,37,388),(31,380,38,387),(32,379,39,386),(33,392,40,385),(34,391,41,384),(35,390,42,383),(43,376,50,369),(44,375,51,368),(45,374,52,367),(46,373,53,366),(47,372,54,365),(48,371,55,378),(49,370,56,377),(57,416,64,409),(58,415,65,408),(59,414,66,407),(60,413,67,420),(61,412,68,419),(62,411,69,418),(63,410,70,417),(71,393,78,400),(72,406,79,399),(73,405,80,398),(74,404,81,397),(75,403,82,396),(76,402,83,395),(77,401,84,394),(85,435,92,442),(86,448,93,441),(87,447,94,440),(88,446,95,439),(89,445,96,438),(90,444,97,437),(91,443,98,436),(99,427,106,434),(100,426,107,433),(101,425,108,432),(102,424,109,431),(103,423,110,430),(104,422,111,429),(105,421,112,428),(113,240,120,247),(114,239,121,246),(115,252,122,245),(116,251,123,244),(117,250,124,243),(118,249,125,242),(119,248,126,241),(127,235,134,228),(128,234,135,227),(129,233,136,226),(130,232,137,225),(131,231,138,238),(132,230,139,237),(133,229,140,236),(141,280,148,273),(142,279,149,272),(143,278,150,271),(144,277,151,270),(145,276,152,269),(146,275,153,268),(147,274,154,267),(155,258,162,265),(156,257,163,264),(157,256,164,263),(158,255,165,262),(159,254,166,261),(160,253,167,260),(161,266,168,259),(169,301,176,308),(170,300,177,307),(171,299,178,306),(172,298,179,305),(173,297,180,304),(174,296,181,303),(175,295,182,302),(183,284,190,291),(184,283,191,290),(185,282,192,289),(186,281,193,288),(187,294,194,287),(188,293,195,286),(189,292,196,285),(197,335,204,328),(198,334,205,327),(199,333,206,326),(200,332,207,325),(201,331,208,324),(202,330,209,323),(203,329,210,336),(211,311,218,318),(212,310,219,317),(213,309,220,316),(214,322,221,315),(215,321,222,314),(216,320,223,313),(217,319,224,312)], [(1,265,15,280),(2,264,16,279),(3,263,17,278),(4,262,18,277),(5,261,19,276),(6,260,20,275),(7,259,21,274),(8,258,22,273),(9,257,23,272),(10,256,24,271),(11,255,25,270),(12,254,26,269),(13,253,27,268),(14,266,28,267),(29,240,50,235),(30,239,51,234),(31,252,52,233),(32,251,53,232),(33,250,54,231),(34,249,55,230),(35,248,56,229),(36,247,43,228),(37,246,44,227),(38,245,45,226),(39,244,46,225),(40,243,47,238),(41,242,48,237),(42,241,49,236),(57,335,71,318),(58,334,72,317),(59,333,73,316),(60,332,74,315),(61,331,75,314),(62,330,76,313),(63,329,77,312),(64,328,78,311),(65,327,79,310),(66,326,80,309),(67,325,81,322),(68,324,82,321),(69,323,83,320),(70,336,84,319),(85,291,106,301),(86,290,107,300),(87,289,108,299),(88,288,109,298),(89,287,110,297),(90,286,111,296),(91,285,112,295),(92,284,99,308),(93,283,100,307),(94,282,101,306),(95,281,102,305),(96,294,103,304),(97,293,104,303),(98,292,105,302),(113,376,127,389),(114,375,128,388),(115,374,129,387),(116,373,130,386),(117,372,131,385),(118,371,132,384),(119,370,133,383),(120,369,134,382),(121,368,135,381),(122,367,136,380),(123,366,137,379),(124,365,138,392),(125,378,139,391),(126,377,140,390),(141,358,162,342),(142,357,163,341),(143,356,164,340),(144,355,165,339),(145,354,166,338),(146,353,167,337),(147,352,168,350),(148,351,155,349),(149,364,156,348),(150,363,157,347),(151,362,158,346),(152,361,159,345),(153,360,160,344),(154,359,161,343),(169,442,190,427),(170,441,191,426),(171,440,192,425),(172,439,193,424),(173,438,194,423),(174,437,195,422),(175,436,196,421),(176,435,183,434),(177,448,184,433),(178,447,185,432),(179,446,186,431),(180,445,187,430),(181,444,188,429),(182,443,189,428),(197,400,218,409),(198,399,219,408),(199,398,220,407),(200,397,221,420),(201,396,222,419),(202,395,223,418),(203,394,224,417),(204,393,211,416),(205,406,212,415),(206,405,213,414),(207,404,214,413),(208,403,215,412),(209,402,216,411),(210,401,217,410)], [(1,78,15,64),(2,79,16,65),(3,80,17,66),(4,81,18,67),(5,82,19,68),(6,83,20,69),(7,84,21,70),(8,71,22,57),(9,72,23,58),(10,73,24,59),(11,74,25,60),(12,75,26,61),(13,76,27,62),(14,77,28,63),(29,99,50,92),(30,100,51,93),(31,101,52,94),(32,102,53,95),(33,103,54,96),(34,104,55,97),(35,105,56,98),(36,106,43,85),(37,107,44,86),(38,108,45,87),(39,109,46,88),(40,110,47,89),(41,111,48,90),(42,112,49,91),(113,183,127,176),(114,184,128,177),(115,185,129,178),(116,186,130,179),(117,187,131,180),(118,188,132,181),(119,189,133,182),(120,190,134,169),(121,191,135,170),(122,192,136,171),(123,193,137,172),(124,194,138,173),(125,195,139,174),(126,196,140,175),(141,211,162,204),(142,212,163,205),(143,213,164,206),(144,214,165,207),(145,215,166,208),(146,216,167,209),(147,217,168,210),(148,218,155,197),(149,219,156,198),(150,220,157,199),(151,221,158,200),(152,222,159,201),(153,223,160,202),(154,224,161,203),(225,298,244,288),(226,299,245,289),(227,300,246,290),(228,301,247,291),(229,302,248,292),(230,303,249,293),(231,304,250,294),(232,305,251,281),(233,306,252,282),(234,307,239,283),(235,308,240,284),(236,295,241,285),(237,296,242,286),(238,297,243,287),(253,330,268,313),(254,331,269,314),(255,332,270,315),(256,333,271,316),(257,334,272,317),(258,335,273,318),(259,336,274,319),(260,323,275,320),(261,324,276,321),(262,325,277,322),(263,326,278,309),(264,327,279,310),(265,328,280,311),(266,329,267,312),(337,411,353,402),(338,412,354,403),(339,413,355,404),(340,414,356,405),(341,415,357,406),(342,416,358,393),(343,417,359,394),(344,418,360,395),(345,419,361,396),(346,420,362,397),(347,407,363,398),(348,408,364,399),(349,409,351,400),(350,410,352,401),(365,438,392,423),(366,439,379,424),(367,440,380,425),(368,441,381,426),(369,442,382,427),(370,443,383,428),(371,444,384,429),(372,445,385,430),(373,446,386,431),(374,447,387,432),(375,448,388,433),(376,435,389,434),(377,436,390,421),(378,437,391,422)]])
100 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4L | 4M | ··· | 4T | 4U | ··· | 4AF | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 7 | ··· | 7 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
100 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | Q8 | D7 | C4○D4 | D14 | D14 | C4×D7 | D4⋊2D7 | Q8×D7 |
| kernel | C2×Dic7⋊3Q8 | Dic7⋊3Q8 | C2×C4×Dic7 | C2×Dic7⋊C4 | C14×C4⋊C4 | C22×Dic14 | C2×Dic14 | C2×Dic7 | C2×C4⋊C4 | C2×C14 | C4⋊C4 | C22×C4 | C2×C4 | C22 | C22 |
| # reps | 1 | 8 | 3 | 2 | 1 | 1 | 16 | 4 | 3 | 4 | 12 | 9 | 24 | 6 | 6 |
Matrix representation of C2×Dic7⋊3Q8 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 8 | 28 | 0 | 0 | 0 | 0 |
| 9 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 1 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 3 | 7 | 0 | 0 | 0 | 0 |
| 3 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 17 | 0 | 0 |
| 0 | 0 | 25 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 26 | 22 | 0 | 0 | 0 | 0 |
| 26 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 28 | 0 | 0 |
| 0 | 0 | 19 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 2 |
| 0 | 0 | 0 | 0 | 28 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 24 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[8,9,0,0,0,0,28,28,0,0,0,0,0,0,22,28,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[3,3,0,0,0,0,7,26,0,0,0,0,0,0,26,25,0,0,0,0,17,3,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[26,26,0,0,0,0,22,3,0,0,0,0,0,0,7,19,0,0,0,0,28,22,0,0,0,0,0,0,28,28,0,0,0,0,2,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,24,12] >;
C2×Dic7⋊3Q8 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_7\rtimes_3Q_8 % in TeX
G:=Group("C2xDic7:3Q8"); // GroupNames label
G:=SmallGroup(448,949);
// by ID
G=gap.SmallGroup(448,949);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,100,185,192,18822]);
// 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=d*b*d^-1=b^-1,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations