direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22×Dic7⋊C4, C24.76D14, C23.18Dic14, (C23×C4).6D7, (C23×C28).9C2, C23.68(C4×D7), C14.37(C23×C4), Dic7⋊5(C22×C4), C14.18(C22×Q8), (C22×C14).27Q8, (C2×C14).281C24, (C2×C28).702C23, (C22×Dic7)⋊11C4, (C22×C14).203D4, (C22×C4).411D14, C14.129(C22×D4), (C23×Dic7).9C2, C2.2(C22×Dic14), C22.39(C23×D7), C23.102(C7⋊D4), C22.38(C2×Dic14), C23.333(C22×D7), (C22×C14).410C23, (C23×C14).103C22, (C22×C28).506C22, (C2×Dic7).276C23, (C22×Dic7).227C22, C14⋊2(C2×C4⋊C4), C7⋊2(C22×C4⋊C4), (C2×C14)⋊8(C4⋊C4), C22.78(C2×C4×D7), C2.37(D7×C22×C4), (C2×C14).53(C2×Q8), C2.1(C22×C7⋊D4), (C2×Dic7)⋊24(C2×C4), (C2×C14).570(C2×D4), C22.99(C2×C7⋊D4), (C2×C4).655(C22×D7), (C22×C14).104(C2×C4), (C2×C14).157(C22×C4), SmallGroup(448,1236)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C22×Dic7⋊C4
G = < a,b,c,d,e | a2=b2=c14=e4=1, d2=c7, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd-1=c-1, ce=ec, ede-1=c7d >
Subgroups: 1284 in 418 conjugacy classes, 247 normal (17 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C23, C14, C14, C4⋊C4, C22×C4, C22×C4, C24, Dic7, Dic7, C28, C2×C14, C2×C14, C2×C4⋊C4, C23×C4, C23×C4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C22×C4⋊C4, Dic7⋊C4, C22×Dic7, C22×Dic7, C22×C28, C22×C28, C23×C14, C2×Dic7⋊C4, C23×Dic7, C23×C28, C22×Dic7⋊C4
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C4⋊C4, C22×C4, C2×D4, C2×Q8, C24, D14, C2×C4⋊C4, C23×C4, C22×D4, C22×Q8, Dic14, C4×D7, C7⋊D4, C22×D7, C22×C4⋊C4, Dic7⋊C4, C2×Dic14, C2×C4×D7, C2×C7⋊D4, C23×D7, C2×Dic7⋊C4, C22×Dic14, D7×C22×C4, C22×C7⋊D4, C22×Dic7⋊C4
►Regular action on 448 points
Generators in S448
(1 134)(2 135)(3 136)(4 137)(5 138)(6 139)(7 140)(8 127)(9 128)(10 129)(11 130)(12 131)(13 132)(14 133)(15 120)(16 121)(17 122)(18 123)(19 124)(20 125)(21 126)(22 113)(23 114)(24 115)(25 116)(26 117)(27 118)(28 119)(29 162)(30 163)(31 164)(32 165)(33 166)(34 167)(35 168)(36 155)(37 156)(38 157)(39 158)(40 159)(41 160)(42 161)(43 141)(44 142)(45 143)(46 144)(47 145)(48 146)(49 147)(50 148)(51 149)(52 150)(53 151)(54 152)(55 153)(56 154)(57 183)(58 184)(59 185)(60 186)(61 187)(62 188)(63 189)(64 190)(65 191)(66 192)(67 193)(68 194)(69 195)(70 196)(71 176)(72 177)(73 178)(74 179)(75 180)(76 181)(77 182)(78 169)(79 170)(80 171)(81 172)(82 173)(83 174)(84 175)(85 211)(86 212)(87 213)(88 214)(89 215)(90 216)(91 217)(92 218)(93 219)(94 220)(95 221)(96 222)(97 223)(98 224)(99 204)(100 205)(101 206)(102 207)(103 208)(104 209)(105 210)(106 197)(107 198)(108 199)(109 200)(110 201)(111 202)(112 203)(225 362)(226 363)(227 364)(228 351)(229 352)(230 353)(231 354)(232 355)(233 356)(234 357)(235 358)(236 359)(237 360)(238 361)(239 345)(240 346)(241 347)(242 348)(243 349)(244 350)(245 337)(246 338)(247 339)(248 340)(249 341)(250 342)(251 343)(252 344)(253 383)(254 384)(255 385)(256 386)(257 387)(258 388)(259 389)(260 390)(261 391)(262 392)(263 379)(264 380)(265 381)(266 382)(267 368)(268 369)(269 370)(270 371)(271 372)(272 373)(273 374)(274 375)(275 376)(276 377)(277 378)(278 365)(279 366)(280 367)(281 418)(282 419)(283 420)(284 407)(285 408)(286 409)(287 410)(288 411)(289 412)(290 413)(291 414)(292 415)(293 416)(294 417)(295 395)(296 396)(297 397)(298 398)(299 399)(300 400)(301 401)(302 402)(303 403)(304 404)(305 405)(306 406)(307 393)(308 394)(309 443)(310 444)(311 445)(312 446)(313 447)(314 448)(315 435)(316 436)(317 437)(318 438)(319 439)(320 440)(321 441)(322 442)(323 424)(324 425)(325 426)(326 427)(327 428)(328 429)(329 430)(330 431)(331 432)(332 433)(333 434)(334 421)(335 422)(336 423)
(1 78)(2 79)(3 80)(4 81)(5 82)(6 83)(7 84)(8 71)(9 72)(10 73)(11 74)(12 75)(13 76)(14 77)(15 57)(16 58)(17 59)(18 60)(19 61)(20 62)(21 63)(22 64)(23 65)(24 66)(25 67)(26 68)(27 69)(28 70)(29 106)(30 107)(31 108)(32 109)(33 110)(34 111)(35 112)(36 99)(37 100)(38 101)(39 102)(40 103)(41 104)(42 105)(43 92)(44 93)(45 94)(46 95)(47 96)(48 97)(49 98)(50 85)(51 86)(52 87)(53 88)(54 89)(55 90)(56 91)(113 190)(114 191)(115 192)(116 193)(117 194)(118 195)(119 196)(120 183)(121 184)(122 185)(123 186)(124 187)(125 188)(126 189)(127 176)(128 177)(129 178)(130 179)(131 180)(132 181)(133 182)(134 169)(135 170)(136 171)(137 172)(138 173)(139 174)(140 175)(141 218)(142 219)(143 220)(144 221)(145 222)(146 223)(147 224)(148 211)(149 212)(150 213)(151 214)(152 215)(153 216)(154 217)(155 204)(156 205)(157 206)(158 207)(159 208)(160 209)(161 210)(162 197)(163 198)(164 199)(165 200)(166 201)(167 202)(168 203)(225 298)(226 299)(227 300)(228 301)(229 302)(230 303)(231 304)(232 305)(233 306)(234 307)(235 308)(236 295)(237 296)(238 297)(239 293)(240 294)(241 281)(242 282)(243 283)(244 284)(245 285)(246 286)(247 287)(248 288)(249 289)(250 290)(251 291)(252 292)(253 326)(254 327)(255 328)(256 329)(257 330)(258 331)(259 332)(260 333)(261 334)(262 335)(263 336)(264 323)(265 324)(266 325)(267 311)(268 312)(269 313)(270 314)(271 315)(272 316)(273 317)(274 318)(275 319)(276 320)(277 321)(278 322)(279 309)(280 310)(337 408)(338 409)(339 410)(340 411)(341 412)(342 413)(343 414)(344 415)(345 416)(346 417)(347 418)(348 419)(349 420)(350 407)(351 401)(352 402)(353 403)(354 404)(355 405)(356 406)(357 393)(358 394)(359 395)(360 396)(361 397)(362 398)(363 399)(364 400)(365 442)(366 443)(367 444)(368 445)(369 446)(370 447)(371 448)(372 435)(373 436)(374 437)(375 438)(376 439)(377 440)(378 441)(379 423)(380 424)(381 425)(382 426)(383 427)(384 428)(385 429)(386 430)(387 431)(388 432)(389 433)(390 434)(391 421)(392 422)
(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)
(1 361 8 354)(2 360 9 353)(3 359 10 352)(4 358 11 351)(5 357 12 364)(6 356 13 363)(7 355 14 362)(15 348 22 341)(16 347 23 340)(17 346 24 339)(18 345 25 338)(19 344 26 337)(20 343 27 350)(21 342 28 349)(29 381 36 388)(30 380 37 387)(31 379 38 386)(32 392 39 385)(33 391 40 384)(34 390 41 383)(35 389 42 382)(43 365 50 372)(44 378 51 371)(45 377 52 370)(46 376 53 369)(47 375 54 368)(48 374 55 367)(49 373 56 366)(57 419 64 412)(58 418 65 411)(59 417 66 410)(60 416 67 409)(61 415 68 408)(62 414 69 407)(63 413 70 420)(71 404 78 397)(72 403 79 396)(73 402 80 395)(74 401 81 394)(75 400 82 393)(76 399 83 406)(77 398 84 405)(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)(99 432 106 425)(100 431 107 424)(101 430 108 423)(102 429 109 422)(103 428 110 421)(104 427 111 434)(105 426 112 433)(113 249 120 242)(114 248 121 241)(115 247 122 240)(116 246 123 239)(117 245 124 252)(118 244 125 251)(119 243 126 250)(127 231 134 238)(128 230 135 237)(129 229 136 236)(130 228 137 235)(131 227 138 234)(132 226 139 233)(133 225 140 232)(141 278 148 271)(142 277 149 270)(143 276 150 269)(144 275 151 268)(145 274 152 267)(146 273 153 280)(147 272 154 279)(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)(169 297 176 304)(170 296 177 303)(171 295 178 302)(172 308 179 301)(173 307 180 300)(174 306 181 299)(175 305 182 298)(183 282 190 289)(184 281 191 288)(185 294 192 287)(186 293 193 286)(187 292 194 285)(188 291 195 284)(189 290 196 283)(197 324 204 331)(198 323 205 330)(199 336 206 329)(200 335 207 328)(201 334 208 327)(202 333 209 326)(203 332 210 325)(211 315 218 322)(212 314 219 321)(213 313 220 320)(214 312 221 319)(215 311 222 318)(216 310 223 317)(217 309 224 316)
(1 211 15 197)(2 212 16 198)(3 213 17 199)(4 214 18 200)(5 215 19 201)(6 216 20 202)(7 217 21 203)(8 218 22 204)(9 219 23 205)(10 220 24 206)(11 221 25 207)(12 222 26 208)(13 223 27 209)(14 224 28 210)(29 169 50 183)(30 170 51 184)(31 171 52 185)(32 172 53 186)(33 173 54 187)(34 174 55 188)(35 175 56 189)(36 176 43 190)(37 177 44 191)(38 178 45 192)(39 179 46 193)(40 180 47 194)(41 181 48 195)(42 182 49 196)(57 162 78 148)(58 163 79 149)(59 164 80 150)(60 165 81 151)(61 166 82 152)(62 167 83 153)(63 168 84 154)(64 155 71 141)(65 156 72 142)(66 157 73 143)(67 158 74 144)(68 159 75 145)(69 160 76 146)(70 161 77 147)(85 120 106 134)(86 121 107 135)(87 122 108 136)(88 123 109 137)(89 124 110 138)(90 125 111 139)(91 126 112 140)(92 113 99 127)(93 114 100 128)(94 115 101 129)(95 116 102 130)(96 117 103 131)(97 118 104 132)(98 119 105 133)(225 443 243 433)(226 444 244 434)(227 445 245 421)(228 446 246 422)(229 447 247 423)(230 448 248 424)(231 435 249 425)(232 436 250 426)(233 437 251 427)(234 438 252 428)(235 439 239 429)(236 440 240 430)(237 441 241 431)(238 442 242 432)(253 406 273 414)(254 393 274 415)(255 394 275 416)(256 395 276 417)(257 396 277 418)(258 397 278 419)(259 398 279 420)(260 399 280 407)(261 400 267 408)(262 401 268 409)(263 402 269 410)(264 403 270 411)(265 404 271 412)(266 405 272 413)(281 387 296 378)(282 388 297 365)(283 389 298 366)(284 390 299 367)(285 391 300 368)(286 392 301 369)(287 379 302 370)(288 380 303 371)(289 381 304 372)(290 382 305 373)(291 383 306 374)(292 384 307 375)(293 385 308 376)(294 386 295 377)(309 349 332 362)(310 350 333 363)(311 337 334 364)(312 338 335 351)(313 339 336 352)(314 340 323 353)(315 341 324 354)(316 342 325 355)(317 343 326 356)(318 344 327 357)(319 345 328 358)(320 346 329 359)(321 347 330 360)(322 348 331 361)
G:=sub<Sym(448)| (1,134)(2,135)(3,136)(4,137)(5,138)(6,139)(7,140)(8,127)(9,128)(10,129)(11,130)(12,131)(13,132)(14,133)(15,120)(16,121)(17,122)(18,123)(19,124)(20,125)(21,126)(22,113)(23,114)(24,115)(25,116)(26,117)(27,118)(28,119)(29,162)(30,163)(31,164)(32,165)(33,166)(34,167)(35,168)(36,155)(37,156)(38,157)(39,158)(40,159)(41,160)(42,161)(43,141)(44,142)(45,143)(46,144)(47,145)(48,146)(49,147)(50,148)(51,149)(52,150)(53,151)(54,152)(55,153)(56,154)(57,183)(58,184)(59,185)(60,186)(61,187)(62,188)(63,189)(64,190)(65,191)(66,192)(67,193)(68,194)(69,195)(70,196)(71,176)(72,177)(73,178)(74,179)(75,180)(76,181)(77,182)(78,169)(79,170)(80,171)(81,172)(82,173)(83,174)(84,175)(85,211)(86,212)(87,213)(88,214)(89,215)(90,216)(91,217)(92,218)(93,219)(94,220)(95,221)(96,222)(97,223)(98,224)(99,204)(100,205)(101,206)(102,207)(103,208)(104,209)(105,210)(106,197)(107,198)(108,199)(109,200)(110,201)(111,202)(112,203)(225,362)(226,363)(227,364)(228,351)(229,352)(230,353)(231,354)(232,355)(233,356)(234,357)(235,358)(236,359)(237,360)(238,361)(239,345)(240,346)(241,347)(242,348)(243,349)(244,350)(245,337)(246,338)(247,339)(248,340)(249,341)(250,342)(251,343)(252,344)(253,383)(254,384)(255,385)(256,386)(257,387)(258,388)(259,389)(260,390)(261,391)(262,392)(263,379)(264,380)(265,381)(266,382)(267,368)(268,369)(269,370)(270,371)(271,372)(272,373)(273,374)(274,375)(275,376)(276,377)(277,378)(278,365)(279,366)(280,367)(281,418)(282,419)(283,420)(284,407)(285,408)(286,409)(287,410)(288,411)(289,412)(290,413)(291,414)(292,415)(293,416)(294,417)(295,395)(296,396)(297,397)(298,398)(299,399)(300,400)(301,401)(302,402)(303,403)(304,404)(305,405)(306,406)(307,393)(308,394)(309,443)(310,444)(311,445)(312,446)(313,447)(314,448)(315,435)(316,436)(317,437)(318,438)(319,439)(320,440)(321,441)(322,442)(323,424)(324,425)(325,426)(326,427)(327,428)(328,429)(329,430)(330,431)(331,432)(332,433)(333,434)(334,421)(335,422)(336,423), (1,78)(2,79)(3,80)(4,81)(5,82)(6,83)(7,84)(8,71)(9,72)(10,73)(11,74)(12,75)(13,76)(14,77)(15,57)(16,58)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)(25,67)(26,68)(27,69)(28,70)(29,106)(30,107)(31,108)(32,109)(33,110)(34,111)(35,112)(36,99)(37,100)(38,101)(39,102)(40,103)(41,104)(42,105)(43,92)(44,93)(45,94)(46,95)(47,96)(48,97)(49,98)(50,85)(51,86)(52,87)(53,88)(54,89)(55,90)(56,91)(113,190)(114,191)(115,192)(116,193)(117,194)(118,195)(119,196)(120,183)(121,184)(122,185)(123,186)(124,187)(125,188)(126,189)(127,176)(128,177)(129,178)(130,179)(131,180)(132,181)(133,182)(134,169)(135,170)(136,171)(137,172)(138,173)(139,174)(140,175)(141,218)(142,219)(143,220)(144,221)(145,222)(146,223)(147,224)(148,211)(149,212)(150,213)(151,214)(152,215)(153,216)(154,217)(155,204)(156,205)(157,206)(158,207)(159,208)(160,209)(161,210)(162,197)(163,198)(164,199)(165,200)(166,201)(167,202)(168,203)(225,298)(226,299)(227,300)(228,301)(229,302)(230,303)(231,304)(232,305)(233,306)(234,307)(235,308)(236,295)(237,296)(238,297)(239,293)(240,294)(241,281)(242,282)(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)(250,290)(251,291)(252,292)(253,326)(254,327)(255,328)(256,329)(257,330)(258,331)(259,332)(260,333)(261,334)(262,335)(263,336)(264,323)(265,324)(266,325)(267,311)(268,312)(269,313)(270,314)(271,315)(272,316)(273,317)(274,318)(275,319)(276,320)(277,321)(278,322)(279,309)(280,310)(337,408)(338,409)(339,410)(340,411)(341,412)(342,413)(343,414)(344,415)(345,416)(346,417)(347,418)(348,419)(349,420)(350,407)(351,401)(352,402)(353,403)(354,404)(355,405)(356,406)(357,393)(358,394)(359,395)(360,396)(361,397)(362,398)(363,399)(364,400)(365,442)(366,443)(367,444)(368,445)(369,446)(370,447)(371,448)(372,435)(373,436)(374,437)(375,438)(376,439)(377,440)(378,441)(379,423)(380,424)(381,425)(382,426)(383,427)(384,428)(385,429)(386,430)(387,431)(388,432)(389,433)(390,434)(391,421)(392,422), (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), (1,361,8,354)(2,360,9,353)(3,359,10,352)(4,358,11,351)(5,357,12,364)(6,356,13,363)(7,355,14,362)(15,348,22,341)(16,347,23,340)(17,346,24,339)(18,345,25,338)(19,344,26,337)(20,343,27,350)(21,342,28,349)(29,381,36,388)(30,380,37,387)(31,379,38,386)(32,392,39,385)(33,391,40,384)(34,390,41,383)(35,389,42,382)(43,365,50,372)(44,378,51,371)(45,377,52,370)(46,376,53,369)(47,375,54,368)(48,374,55,367)(49,373,56,366)(57,419,64,412)(58,418,65,411)(59,417,66,410)(60,416,67,409)(61,415,68,408)(62,414,69,407)(63,413,70,420)(71,404,78,397)(72,403,79,396)(73,402,80,395)(74,401,81,394)(75,400,82,393)(76,399,83,406)(77,398,84,405)(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)(99,432,106,425)(100,431,107,424)(101,430,108,423)(102,429,109,422)(103,428,110,421)(104,427,111,434)(105,426,112,433)(113,249,120,242)(114,248,121,241)(115,247,122,240)(116,246,123,239)(117,245,124,252)(118,244,125,251)(119,243,126,250)(127,231,134,238)(128,230,135,237)(129,229,136,236)(130,228,137,235)(131,227,138,234)(132,226,139,233)(133,225,140,232)(141,278,148,271)(142,277,149,270)(143,276,150,269)(144,275,151,268)(145,274,152,267)(146,273,153,280)(147,272,154,279)(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)(169,297,176,304)(170,296,177,303)(171,295,178,302)(172,308,179,301)(173,307,180,300)(174,306,181,299)(175,305,182,298)(183,282,190,289)(184,281,191,288)(185,294,192,287)(186,293,193,286)(187,292,194,285)(188,291,195,284)(189,290,196,283)(197,324,204,331)(198,323,205,330)(199,336,206,329)(200,335,207,328)(201,334,208,327)(202,333,209,326)(203,332,210,325)(211,315,218,322)(212,314,219,321)(213,313,220,320)(214,312,221,319)(215,311,222,318)(216,310,223,317)(217,309,224,316), (1,211,15,197)(2,212,16,198)(3,213,17,199)(4,214,18,200)(5,215,19,201)(6,216,20,202)(7,217,21,203)(8,218,22,204)(9,219,23,205)(10,220,24,206)(11,221,25,207)(12,222,26,208)(13,223,27,209)(14,224,28,210)(29,169,50,183)(30,170,51,184)(31,171,52,185)(32,172,53,186)(33,173,54,187)(34,174,55,188)(35,175,56,189)(36,176,43,190)(37,177,44,191)(38,178,45,192)(39,179,46,193)(40,180,47,194)(41,181,48,195)(42,182,49,196)(57,162,78,148)(58,163,79,149)(59,164,80,150)(60,165,81,151)(61,166,82,152)(62,167,83,153)(63,168,84,154)(64,155,71,141)(65,156,72,142)(66,157,73,143)(67,158,74,144)(68,159,75,145)(69,160,76,146)(70,161,77,147)(85,120,106,134)(86,121,107,135)(87,122,108,136)(88,123,109,137)(89,124,110,138)(90,125,111,139)(91,126,112,140)(92,113,99,127)(93,114,100,128)(94,115,101,129)(95,116,102,130)(96,117,103,131)(97,118,104,132)(98,119,105,133)(225,443,243,433)(226,444,244,434)(227,445,245,421)(228,446,246,422)(229,447,247,423)(230,448,248,424)(231,435,249,425)(232,436,250,426)(233,437,251,427)(234,438,252,428)(235,439,239,429)(236,440,240,430)(237,441,241,431)(238,442,242,432)(253,406,273,414)(254,393,274,415)(255,394,275,416)(256,395,276,417)(257,396,277,418)(258,397,278,419)(259,398,279,420)(260,399,280,407)(261,400,267,408)(262,401,268,409)(263,402,269,410)(264,403,270,411)(265,404,271,412)(266,405,272,413)(281,387,296,378)(282,388,297,365)(283,389,298,366)(284,390,299,367)(285,391,300,368)(286,392,301,369)(287,379,302,370)(288,380,303,371)(289,381,304,372)(290,382,305,373)(291,383,306,374)(292,384,307,375)(293,385,308,376)(294,386,295,377)(309,349,332,362)(310,350,333,363)(311,337,334,364)(312,338,335,351)(313,339,336,352)(314,340,323,353)(315,341,324,354)(316,342,325,355)(317,343,326,356)(318,344,327,357)(319,345,328,358)(320,346,329,359)(321,347,330,360)(322,348,331,361)>;
G:=Group( (1,134)(2,135)(3,136)(4,137)(5,138)(6,139)(7,140)(8,127)(9,128)(10,129)(11,130)(12,131)(13,132)(14,133)(15,120)(16,121)(17,122)(18,123)(19,124)(20,125)(21,126)(22,113)(23,114)(24,115)(25,116)(26,117)(27,118)(28,119)(29,162)(30,163)(31,164)(32,165)(33,166)(34,167)(35,168)(36,155)(37,156)(38,157)(39,158)(40,159)(41,160)(42,161)(43,141)(44,142)(45,143)(46,144)(47,145)(48,146)(49,147)(50,148)(51,149)(52,150)(53,151)(54,152)(55,153)(56,154)(57,183)(58,184)(59,185)(60,186)(61,187)(62,188)(63,189)(64,190)(65,191)(66,192)(67,193)(68,194)(69,195)(70,196)(71,176)(72,177)(73,178)(74,179)(75,180)(76,181)(77,182)(78,169)(79,170)(80,171)(81,172)(82,173)(83,174)(84,175)(85,211)(86,212)(87,213)(88,214)(89,215)(90,216)(91,217)(92,218)(93,219)(94,220)(95,221)(96,222)(97,223)(98,224)(99,204)(100,205)(101,206)(102,207)(103,208)(104,209)(105,210)(106,197)(107,198)(108,199)(109,200)(110,201)(111,202)(112,203)(225,362)(226,363)(227,364)(228,351)(229,352)(230,353)(231,354)(232,355)(233,356)(234,357)(235,358)(236,359)(237,360)(238,361)(239,345)(240,346)(241,347)(242,348)(243,349)(244,350)(245,337)(246,338)(247,339)(248,340)(249,341)(250,342)(251,343)(252,344)(253,383)(254,384)(255,385)(256,386)(257,387)(258,388)(259,389)(260,390)(261,391)(262,392)(263,379)(264,380)(265,381)(266,382)(267,368)(268,369)(269,370)(270,371)(271,372)(272,373)(273,374)(274,375)(275,376)(276,377)(277,378)(278,365)(279,366)(280,367)(281,418)(282,419)(283,420)(284,407)(285,408)(286,409)(287,410)(288,411)(289,412)(290,413)(291,414)(292,415)(293,416)(294,417)(295,395)(296,396)(297,397)(298,398)(299,399)(300,400)(301,401)(302,402)(303,403)(304,404)(305,405)(306,406)(307,393)(308,394)(309,443)(310,444)(311,445)(312,446)(313,447)(314,448)(315,435)(316,436)(317,437)(318,438)(319,439)(320,440)(321,441)(322,442)(323,424)(324,425)(325,426)(326,427)(327,428)(328,429)(329,430)(330,431)(331,432)(332,433)(333,434)(334,421)(335,422)(336,423), (1,78)(2,79)(3,80)(4,81)(5,82)(6,83)(7,84)(8,71)(9,72)(10,73)(11,74)(12,75)(13,76)(14,77)(15,57)(16,58)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)(25,67)(26,68)(27,69)(28,70)(29,106)(30,107)(31,108)(32,109)(33,110)(34,111)(35,112)(36,99)(37,100)(38,101)(39,102)(40,103)(41,104)(42,105)(43,92)(44,93)(45,94)(46,95)(47,96)(48,97)(49,98)(50,85)(51,86)(52,87)(53,88)(54,89)(55,90)(56,91)(113,190)(114,191)(115,192)(116,193)(117,194)(118,195)(119,196)(120,183)(121,184)(122,185)(123,186)(124,187)(125,188)(126,189)(127,176)(128,177)(129,178)(130,179)(131,180)(132,181)(133,182)(134,169)(135,170)(136,171)(137,172)(138,173)(139,174)(140,175)(141,218)(142,219)(143,220)(144,221)(145,222)(146,223)(147,224)(148,211)(149,212)(150,213)(151,214)(152,215)(153,216)(154,217)(155,204)(156,205)(157,206)(158,207)(159,208)(160,209)(161,210)(162,197)(163,198)(164,199)(165,200)(166,201)(167,202)(168,203)(225,298)(226,299)(227,300)(228,301)(229,302)(230,303)(231,304)(232,305)(233,306)(234,307)(235,308)(236,295)(237,296)(238,297)(239,293)(240,294)(241,281)(242,282)(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)(250,290)(251,291)(252,292)(253,326)(254,327)(255,328)(256,329)(257,330)(258,331)(259,332)(260,333)(261,334)(262,335)(263,336)(264,323)(265,324)(266,325)(267,311)(268,312)(269,313)(270,314)(271,315)(272,316)(273,317)(274,318)(275,319)(276,320)(277,321)(278,322)(279,309)(280,310)(337,408)(338,409)(339,410)(340,411)(341,412)(342,413)(343,414)(344,415)(345,416)(346,417)(347,418)(348,419)(349,420)(350,407)(351,401)(352,402)(353,403)(354,404)(355,405)(356,406)(357,393)(358,394)(359,395)(360,396)(361,397)(362,398)(363,399)(364,400)(365,442)(366,443)(367,444)(368,445)(369,446)(370,447)(371,448)(372,435)(373,436)(374,437)(375,438)(376,439)(377,440)(378,441)(379,423)(380,424)(381,425)(382,426)(383,427)(384,428)(385,429)(386,430)(387,431)(388,432)(389,433)(390,434)(391,421)(392,422), (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), (1,361,8,354)(2,360,9,353)(3,359,10,352)(4,358,11,351)(5,357,12,364)(6,356,13,363)(7,355,14,362)(15,348,22,341)(16,347,23,340)(17,346,24,339)(18,345,25,338)(19,344,26,337)(20,343,27,350)(21,342,28,349)(29,381,36,388)(30,380,37,387)(31,379,38,386)(32,392,39,385)(33,391,40,384)(34,390,41,383)(35,389,42,382)(43,365,50,372)(44,378,51,371)(45,377,52,370)(46,376,53,369)(47,375,54,368)(48,374,55,367)(49,373,56,366)(57,419,64,412)(58,418,65,411)(59,417,66,410)(60,416,67,409)(61,415,68,408)(62,414,69,407)(63,413,70,420)(71,404,78,397)(72,403,79,396)(73,402,80,395)(74,401,81,394)(75,400,82,393)(76,399,83,406)(77,398,84,405)(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)(99,432,106,425)(100,431,107,424)(101,430,108,423)(102,429,109,422)(103,428,110,421)(104,427,111,434)(105,426,112,433)(113,249,120,242)(114,248,121,241)(115,247,122,240)(116,246,123,239)(117,245,124,252)(118,244,125,251)(119,243,126,250)(127,231,134,238)(128,230,135,237)(129,229,136,236)(130,228,137,235)(131,227,138,234)(132,226,139,233)(133,225,140,232)(141,278,148,271)(142,277,149,270)(143,276,150,269)(144,275,151,268)(145,274,152,267)(146,273,153,280)(147,272,154,279)(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)(169,297,176,304)(170,296,177,303)(171,295,178,302)(172,308,179,301)(173,307,180,300)(174,306,181,299)(175,305,182,298)(183,282,190,289)(184,281,191,288)(185,294,192,287)(186,293,193,286)(187,292,194,285)(188,291,195,284)(189,290,196,283)(197,324,204,331)(198,323,205,330)(199,336,206,329)(200,335,207,328)(201,334,208,327)(202,333,209,326)(203,332,210,325)(211,315,218,322)(212,314,219,321)(213,313,220,320)(214,312,221,319)(215,311,222,318)(216,310,223,317)(217,309,224,316), (1,211,15,197)(2,212,16,198)(3,213,17,199)(4,214,18,200)(5,215,19,201)(6,216,20,202)(7,217,21,203)(8,218,22,204)(9,219,23,205)(10,220,24,206)(11,221,25,207)(12,222,26,208)(13,223,27,209)(14,224,28,210)(29,169,50,183)(30,170,51,184)(31,171,52,185)(32,172,53,186)(33,173,54,187)(34,174,55,188)(35,175,56,189)(36,176,43,190)(37,177,44,191)(38,178,45,192)(39,179,46,193)(40,180,47,194)(41,181,48,195)(42,182,49,196)(57,162,78,148)(58,163,79,149)(59,164,80,150)(60,165,81,151)(61,166,82,152)(62,167,83,153)(63,168,84,154)(64,155,71,141)(65,156,72,142)(66,157,73,143)(67,158,74,144)(68,159,75,145)(69,160,76,146)(70,161,77,147)(85,120,106,134)(86,121,107,135)(87,122,108,136)(88,123,109,137)(89,124,110,138)(90,125,111,139)(91,126,112,140)(92,113,99,127)(93,114,100,128)(94,115,101,129)(95,116,102,130)(96,117,103,131)(97,118,104,132)(98,119,105,133)(225,443,243,433)(226,444,244,434)(227,445,245,421)(228,446,246,422)(229,447,247,423)(230,448,248,424)(231,435,249,425)(232,436,250,426)(233,437,251,427)(234,438,252,428)(235,439,239,429)(236,440,240,430)(237,441,241,431)(238,442,242,432)(253,406,273,414)(254,393,274,415)(255,394,275,416)(256,395,276,417)(257,396,277,418)(258,397,278,419)(259,398,279,420)(260,399,280,407)(261,400,267,408)(262,401,268,409)(263,402,269,410)(264,403,270,411)(265,404,271,412)(266,405,272,413)(281,387,296,378)(282,388,297,365)(283,389,298,366)(284,390,299,367)(285,391,300,368)(286,392,301,369)(287,379,302,370)(288,380,303,371)(289,381,304,372)(290,382,305,373)(291,383,306,374)(292,384,307,375)(293,385,308,376)(294,386,295,377)(309,349,332,362)(310,350,333,363)(311,337,334,364)(312,338,335,351)(313,339,336,352)(314,340,323,353)(315,341,324,354)(316,342,325,355)(317,343,326,356)(318,344,327,357)(319,345,328,358)(320,346,329,359)(321,347,330,360)(322,348,331,361) );
G=PermutationGroup([[(1,134),(2,135),(3,136),(4,137),(5,138),(6,139),(7,140),(8,127),(9,128),(10,129),(11,130),(12,131),(13,132),(14,133),(15,120),(16,121),(17,122),(18,123),(19,124),(20,125),(21,126),(22,113),(23,114),(24,115),(25,116),(26,117),(27,118),(28,119),(29,162),(30,163),(31,164),(32,165),(33,166),(34,167),(35,168),(36,155),(37,156),(38,157),(39,158),(40,159),(41,160),(42,161),(43,141),(44,142),(45,143),(46,144),(47,145),(48,146),(49,147),(50,148),(51,149),(52,150),(53,151),(54,152),(55,153),(56,154),(57,183),(58,184),(59,185),(60,186),(61,187),(62,188),(63,189),(64,190),(65,191),(66,192),(67,193),(68,194),(69,195),(70,196),(71,176),(72,177),(73,178),(74,179),(75,180),(76,181),(77,182),(78,169),(79,170),(80,171),(81,172),(82,173),(83,174),(84,175),(85,211),(86,212),(87,213),(88,214),(89,215),(90,216),(91,217),(92,218),(93,219),(94,220),(95,221),(96,222),(97,223),(98,224),(99,204),(100,205),(101,206),(102,207),(103,208),(104,209),(105,210),(106,197),(107,198),(108,199),(109,200),(110,201),(111,202),(112,203),(225,362),(226,363),(227,364),(228,351),(229,352),(230,353),(231,354),(232,355),(233,356),(234,357),(235,358),(236,359),(237,360),(238,361),(239,345),(240,346),(241,347),(242,348),(243,349),(244,350),(245,337),(246,338),(247,339),(248,340),(249,341),(250,342),(251,343),(252,344),(253,383),(254,384),(255,385),(256,386),(257,387),(258,388),(259,389),(260,390),(261,391),(262,392),(263,379),(264,380),(265,381),(266,382),(267,368),(268,369),(269,370),(270,371),(271,372),(272,373),(273,374),(274,375),(275,376),(276,377),(277,378),(278,365),(279,366),(280,367),(281,418),(282,419),(283,420),(284,407),(285,408),(286,409),(287,410),(288,411),(289,412),(290,413),(291,414),(292,415),(293,416),(294,417),(295,395),(296,396),(297,397),(298,398),(299,399),(300,400),(301,401),(302,402),(303,403),(304,404),(305,405),(306,406),(307,393),(308,394),(309,443),(310,444),(311,445),(312,446),(313,447),(314,448),(315,435),(316,436),(317,437),(318,438),(319,439),(320,440),(321,441),(322,442),(323,424),(324,425),(325,426),(326,427),(327,428),(328,429),(329,430),(330,431),(331,432),(332,433),(333,434),(334,421),(335,422),(336,423)], [(1,78),(2,79),(3,80),(4,81),(5,82),(6,83),(7,84),(8,71),(9,72),(10,73),(11,74),(12,75),(13,76),(14,77),(15,57),(16,58),(17,59),(18,60),(19,61),(20,62),(21,63),(22,64),(23,65),(24,66),(25,67),(26,68),(27,69),(28,70),(29,106),(30,107),(31,108),(32,109),(33,110),(34,111),(35,112),(36,99),(37,100),(38,101),(39,102),(40,103),(41,104),(42,105),(43,92),(44,93),(45,94),(46,95),(47,96),(48,97),(49,98),(50,85),(51,86),(52,87),(53,88),(54,89),(55,90),(56,91),(113,190),(114,191),(115,192),(116,193),(117,194),(118,195),(119,196),(120,183),(121,184),(122,185),(123,186),(124,187),(125,188),(126,189),(127,176),(128,177),(129,178),(130,179),(131,180),(132,181),(133,182),(134,169),(135,170),(136,171),(137,172),(138,173),(139,174),(140,175),(141,218),(142,219),(143,220),(144,221),(145,222),(146,223),(147,224),(148,211),(149,212),(150,213),(151,214),(152,215),(153,216),(154,217),(155,204),(156,205),(157,206),(158,207),(159,208),(160,209),(161,210),(162,197),(163,198),(164,199),(165,200),(166,201),(167,202),(168,203),(225,298),(226,299),(227,300),(228,301),(229,302),(230,303),(231,304),(232,305),(233,306),(234,307),(235,308),(236,295),(237,296),(238,297),(239,293),(240,294),(241,281),(242,282),(243,283),(244,284),(245,285),(246,286),(247,287),(248,288),(249,289),(250,290),(251,291),(252,292),(253,326),(254,327),(255,328),(256,329),(257,330),(258,331),(259,332),(260,333),(261,334),(262,335),(263,336),(264,323),(265,324),(266,325),(267,311),(268,312),(269,313),(270,314),(271,315),(272,316),(273,317),(274,318),(275,319),(276,320),(277,321),(278,322),(279,309),(280,310),(337,408),(338,409),(339,410),(340,411),(341,412),(342,413),(343,414),(344,415),(345,416),(346,417),(347,418),(348,419),(349,420),(350,407),(351,401),(352,402),(353,403),(354,404),(355,405),(356,406),(357,393),(358,394),(359,395),(360,396),(361,397),(362,398),(363,399),(364,400),(365,442),(366,443),(367,444),(368,445),(369,446),(370,447),(371,448),(372,435),(373,436),(374,437),(375,438),(376,439),(377,440),(378,441),(379,423),(380,424),(381,425),(382,426),(383,427),(384,428),(385,429),(386,430),(387,431),(388,432),(389,433),(390,434),(391,421),(392,422)], [(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)], [(1,361,8,354),(2,360,9,353),(3,359,10,352),(4,358,11,351),(5,357,12,364),(6,356,13,363),(7,355,14,362),(15,348,22,341),(16,347,23,340),(17,346,24,339),(18,345,25,338),(19,344,26,337),(20,343,27,350),(21,342,28,349),(29,381,36,388),(30,380,37,387),(31,379,38,386),(32,392,39,385),(33,391,40,384),(34,390,41,383),(35,389,42,382),(43,365,50,372),(44,378,51,371),(45,377,52,370),(46,376,53,369),(47,375,54,368),(48,374,55,367),(49,373,56,366),(57,419,64,412),(58,418,65,411),(59,417,66,410),(60,416,67,409),(61,415,68,408),(62,414,69,407),(63,413,70,420),(71,404,78,397),(72,403,79,396),(73,402,80,395),(74,401,81,394),(75,400,82,393),(76,399,83,406),(77,398,84,405),(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),(99,432,106,425),(100,431,107,424),(101,430,108,423),(102,429,109,422),(103,428,110,421),(104,427,111,434),(105,426,112,433),(113,249,120,242),(114,248,121,241),(115,247,122,240),(116,246,123,239),(117,245,124,252),(118,244,125,251),(119,243,126,250),(127,231,134,238),(128,230,135,237),(129,229,136,236),(130,228,137,235),(131,227,138,234),(132,226,139,233),(133,225,140,232),(141,278,148,271),(142,277,149,270),(143,276,150,269),(144,275,151,268),(145,274,152,267),(146,273,153,280),(147,272,154,279),(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),(169,297,176,304),(170,296,177,303),(171,295,178,302),(172,308,179,301),(173,307,180,300),(174,306,181,299),(175,305,182,298),(183,282,190,289),(184,281,191,288),(185,294,192,287),(186,293,193,286),(187,292,194,285),(188,291,195,284),(189,290,196,283),(197,324,204,331),(198,323,205,330),(199,336,206,329),(200,335,207,328),(201,334,208,327),(202,333,209,326),(203,332,210,325),(211,315,218,322),(212,314,219,321),(213,313,220,320),(214,312,221,319),(215,311,222,318),(216,310,223,317),(217,309,224,316)], [(1,211,15,197),(2,212,16,198),(3,213,17,199),(4,214,18,200),(5,215,19,201),(6,216,20,202),(7,217,21,203),(8,218,22,204),(9,219,23,205),(10,220,24,206),(11,221,25,207),(12,222,26,208),(13,223,27,209),(14,224,28,210),(29,169,50,183),(30,170,51,184),(31,171,52,185),(32,172,53,186),(33,173,54,187),(34,174,55,188),(35,175,56,189),(36,176,43,190),(37,177,44,191),(38,178,45,192),(39,179,46,193),(40,180,47,194),(41,181,48,195),(42,182,49,196),(57,162,78,148),(58,163,79,149),(59,164,80,150),(60,165,81,151),(61,166,82,152),(62,167,83,153),(63,168,84,154),(64,155,71,141),(65,156,72,142),(66,157,73,143),(67,158,74,144),(68,159,75,145),(69,160,76,146),(70,161,77,147),(85,120,106,134),(86,121,107,135),(87,122,108,136),(88,123,109,137),(89,124,110,138),(90,125,111,139),(91,126,112,140),(92,113,99,127),(93,114,100,128),(94,115,101,129),(95,116,102,130),(96,117,103,131),(97,118,104,132),(98,119,105,133),(225,443,243,433),(226,444,244,434),(227,445,245,421),(228,446,246,422),(229,447,247,423),(230,448,248,424),(231,435,249,425),(232,436,250,426),(233,437,251,427),(234,438,252,428),(235,439,239,429),(236,440,240,430),(237,441,241,431),(238,442,242,432),(253,406,273,414),(254,393,274,415),(255,394,275,416),(256,395,276,417),(257,396,277,418),(258,397,278,419),(259,398,279,420),(260,399,280,407),(261,400,267,408),(262,401,268,409),(263,402,269,410),(264,403,270,411),(265,404,271,412),(266,405,272,413),(281,387,296,378),(282,388,297,365),(283,389,298,366),(284,390,299,367),(285,391,300,368),(286,392,301,369),(287,379,302,370),(288,380,303,371),(289,381,304,372),(290,382,305,373),(291,383,306,374),(292,384,307,375),(293,385,308,376),(294,386,295,377),(309,349,332,362),(310,350,333,363),(311,337,334,364),(312,338,335,351),(313,339,336,352),(314,340,323,353),(315,341,324,354),(316,342,325,355),(317,343,326,356),(318,344,327,357),(319,345,328,358),(320,346,329,359),(321,347,330,360),(322,348,331,361)]])
136 conjugacy classes
| class | 1 | 2A | ··· | 2O | 4A | ··· | 4H | 4I | ··· | 4X | 7A | 7B | 7C | 14A | ··· | 14AS | 28A | ··· | 28AV |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
136 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C4 | D4 | Q8 | D7 | D14 | D14 | Dic14 | C4×D7 | C7⋊D4 |
| kernel | C22×Dic7⋊C4 | C2×Dic7⋊C4 | C23×Dic7 | C23×C28 | C22×Dic7 | C22×C14 | C22×C14 | C23×C4 | C22×C4 | C24 | C23 | C23 | C23 |
| # reps | 1 | 12 | 2 | 1 | 16 | 4 | 4 | 3 | 18 | 3 | 24 | 24 | 24 |
Matrix representation of C22×Dic7⋊C4 ►in GL5(𝔽29)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 28 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 6 | 0 |
| 0 | 0 | 0 | 0 | 5 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 0 | 1 | 0 |
| 12 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(5,GF(29))| [1,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,28],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,6,0,0,0,0,0,5],[1,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,28,0],[12,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,1] >;
C22×Dic7⋊C4 in GAP, Magma, Sage, TeX
C_2^2\times {\rm Dic}_7\rtimes C_4 % in TeX
G:=Group("C2^2xDic7:C4"); // GroupNames label
G:=SmallGroup(448,1236);
// by ID
G=gap.SmallGroup(448,1236);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,1123,80,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^14=e^4=1,d^2=c^7,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,d*c*d^-1=c^-1,c*e=e*c,e*d*e^-1=c^7*d>;
// generators/relations