C2^4xDic7

direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: C₂⁴×Dic₇, C₂⁵.₃D₇, C₁₄.₁₉C₂⁵, C₂⁴.₈₃D₁₄, C₇⋊₂(C₂⁴×C₄), (C₂³×C₁₄)⋊₉C₄, C₁₄⋊₂(C₂³×C₄), C₂.₂(D₇×C₂⁴), (C₂⁴×C₁₄).₅C₂, (C₂×C₁₄).₃₃₁C₂⁴, C₂².₅₈(C₂³×D₇), C₂³.₃₅₁(C₂²×D₇), (C₂²×C₁₄).₄₃₈C₂³, (C₂³×C₁₄).₁₁₇C₂², (C₂²×C₁₄)⋊₁₈(C₂×C₄), (C₂×C₁₄)⋊₁₀(C₂²×C₄), SmallGroup(448,1383)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₇ — C₂⁴×Dic₇

Chief series

C₁ — C₇ — C₁₄ — Dic₇ — C₂×Dic₇ — C₂²×Dic₇ — C₂³×Dic₇ — C₂⁴×Dic₇

Lower central

C₇ — C₂⁴×Dic₇

Upper central

C₁ — C₂⁵

Subgroups: 3204 in 1362 conjugacy classes, 1055 normal (7 characteristic)
C₁, C₂, C₂^[×30], C₄^[×16], C₂²^[×155], C₇, C₂×C₄^[×120], C₂³^[×155], C₁₄, C₁₄^[×30], C₂²×C₄^[×140], C₂⁴^[×31], Dic₇^[×16], C₂×C₁₄^[×155], C₂³×C₄^[×30], C₂⁵, C₂×Dic₇^[×120], C₂²×C₁₄^[×155], C₂⁴×C₄, C₂²×Dic₇^[×140], C₂³×C₁₄^[×31], C₂³×Dic₇^[×30], C₂⁴×C₁₄, C₂⁴×Dic₇

Quotients:
C₁, C₂^[×31], C₄^[×16], C₂²^[×155], C₂×C₄^[×120], C₂³^[×155], D₇, C₂²×C₄^[×140], C₂⁴^[×31], Dic₇^[×16], D₁₄^[×15], C₂³×C₄^[×30], C₂⁵, C₂×Dic₇^[×120], C₂²×D₇^[×35], C₂⁴×C₄, C₂²×Dic₇^[×140], C₂³×D₇^[×15], C₂³×Dic₇^[×30], D₇×C₂⁴, C₂⁴×Dic₇

Generators and relations
G = < a,b,c,d,e,f | a²=b²=c²=d²=e¹⁴=1, f²=e⁷, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef^-1=e^-1 >

Smallest permutation representation
►Regular action on 448 points

Generators in S₄₄₈

(1 115)(2 116)(3 117)(4 118)(5 119)(6 120)(7 121)(8 122)(9 123)(10 124)(11 125)(12 126)(13 113)(14 114)(15 138)(16 139)(17 140)(18 127)(19 128)(20 129)(21 130)(22 131)(23 132)(24 133)(25 134)(26 135)(27 136)(28 137)(29 147)(30 148)(31 149)(32 150)(33 151)(34 152)(35 153)(36 154)(37 141)(38 142)(39 143)(40 144)(41 145)(42 146)(43 166)(44 167)(45 168)(46 155)(47 156)(48 157)(49 158)(50 159)(51 160)(52 161)(53 162)(54 163)(55 164)(56 165)(57 180)(58 181)(59 182)(60 169)(61 170)(62 171)(63 172)(64 173)(65 174)(66 175)(67 176)(68 177)(69 178)(70 179)(71 196)(72 183)(73 184)(74 185)(75 186)(76 187)(77 188)(78 189)(79 190)(80 191)(81 192)(82 193)(83 194)(84 195)(85 205)(86 206)(87 207)(88 208)(89 209)(90 210)(91 197)(92 198)(93 199)(94 200)(95 201)(96 202)(97 203)(98 204)(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)(225 344)(226 345)(227 346)(228 347)(229 348)(230 349)(231 350)(232 337)(233 338)(234 339)(235 340)(236 341)(237 342)(238 343)(239 351)(240 352)(241 353)(242 354)(243 355)(244 356)(245 357)(246 358)(247 359)(248 360)(249 361)(250 362)(251 363)(252 364)(253 365)(254 366)(255 367)(256 368)(257 369)(258 370)(259 371)(260 372)(261 373)(262 374)(263 375)(264 376)(265 377)(266 378)(267 386)(268 387)(269 388)(270 389)(271 390)(272 391)(273 392)(274 379)(275 380)(276 381)(277 382)(278 383)(279 384)(280 385)(281 393)(282 394)(283 395)(284 396)(285 397)(286 398)(287 399)(288 400)(289 401)(290 402)(291 403)(292 404)(293 405)(294 406)(295 407)(296 408)(297 409)(298 410)(299 411)(300 412)(301 413)(302 414)(303 415)(304 416)(305 417)(306 418)(307 419)(308 420)(309 428)(310 429)(311 430)(312 431)(313 432)(314 433)(315 434)(316 421)(317 422)(318 423)(319 424)(320 425)(321 426)(322 427)(323 435)(324 436)(325 437)(326 438)(327 439)(328 440)(329 441)(330 442)(331 443)(332 444)(333 445)(334 446)(335 447)(336 448)

(1 111)(2 112)(3 99)(4 100)(5 101)(6 102)(7 103)(8 104)(9 105)(10 106)(11 107)(12 108)(13 109)(14 110)(15 89)(16 90)(17 91)(18 92)(19 93)(20 94)(21 95)(22 96)(23 97)(24 98)(25 85)(26 86)(27 87)(28 88)(29 84)(30 71)(31 72)(32 73)(33 74)(34 75)(35 76)(36 77)(37 78)(38 79)(39 80)(40 81)(41 82)(42 83)(43 57)(44 58)(45 59)(46 60)(47 61)(48 62)(49 63)(50 64)(51 65)(52 66)(53 67)(54 68)(55 69)(56 70)(113 214)(114 215)(115 216)(116 217)(117 218)(118 219)(119 220)(120 221)(121 222)(122 223)(123 224)(124 211)(125 212)(126 213)(127 198)(128 199)(129 200)(130 201)(131 202)(132 203)(133 204)(134 205)(135 206)(136 207)(137 208)(138 209)(139 210)(140 197)(141 189)(142 190)(143 191)(144 192)(145 193)(146 194)(147 195)(148 196)(149 183)(150 184)(151 185)(152 186)(153 187)(154 188)(155 169)(156 170)(157 171)(158 172)(159 173)(160 174)(161 175)(162 176)(163 177)(164 178)(165 179)(166 180)(167 181)(168 182)(225 323)(226 324)(227 325)(228 326)(229 327)(230 328)(231 329)(232 330)(233 331)(234 332)(235 333)(236 334)(237 335)(238 336)(239 309)(240 310)(241 311)(242 312)(243 313)(244 314)(245 315)(246 316)(247 317)(248 318)(249 319)(250 320)(251 321)(252 322)(253 302)(254 303)(255 304)(256 305)(257 306)(258 307)(259 308)(260 295)(261 296)(262 297)(263 298)(264 299)(265 300)(266 301)(267 288)(268 289)(269 290)(270 291)(271 292)(272 293)(273 294)(274 281)(275 282)(276 283)(277 284)(278 285)(279 286)(280 287)(337 442)(338 443)(339 444)(340 445)(341 446)(342 447)(343 448)(344 435)(345 436)(346 437)(347 438)(348 439)(349 440)(350 441)(351 428)(352 429)(353 430)(354 431)(355 432)(356 433)(357 434)(358 421)(359 422)(360 423)(361 424)(362 425)(363 426)(364 427)(365 414)(366 415)(367 416)(368 417)(369 418)(370 419)(371 420)(372 407)(373 408)(374 409)(375 410)(376 411)(377 412)(378 413)(379 393)(380 394)(381 395)(382 396)(383 397)(384 398)(385 399)(386 400)(387 401)(388 402)(389 403)(390 404)(391 405)(392 406)

(1 51)(2 52)(3 53)(4 54)(5 55)(6 56)(7 43)(8 44)(9 45)(10 46)(11 47)(12 48)(13 49)(14 50)(15 33)(16 34)(17 35)(18 36)(19 37)(20 38)(21 39)(22 40)(23 41)(24 42)(25 29)(26 30)(27 31)(28 32)(57 103)(58 104)(59 105)(60 106)(61 107)(62 108)(63 109)(64 110)(65 111)(66 112)(67 99)(68 100)(69 101)(70 102)(71 86)(72 87)(73 88)(74 89)(75 90)(76 91)(77 92)(78 93)(79 94)(80 95)(81 96)(82 97)(83 98)(84 85)(113 158)(114 159)(115 160)(116 161)(117 162)(118 163)(119 164)(120 165)(121 166)(122 167)(123 168)(124 155)(125 156)(126 157)(127 154)(128 141)(129 142)(130 143)(131 144)(132 145)(133 146)(134 147)(135 148)(136 149)(137 150)(138 151)(139 152)(140 153)(169 211)(170 212)(171 213)(172 214)(173 215)(174 216)(175 217)(176 218)(177 219)(178 220)(179 221)(180 222)(181 223)(182 224)(183 207)(184 208)(185 209)(186 210)(187 197)(188 198)(189 199)(190 200)(191 201)(192 202)(193 203)(194 204)(195 205)(196 206)(225 267)(226 268)(227 269)(228 270)(229 271)(230 272)(231 273)(232 274)(233 275)(234 276)(235 277)(236 278)(237 279)(238 280)(239 253)(240 254)(241 255)(242 256)(243 257)(244 258)(245 259)(246 260)(247 261)(248 262)(249 263)(250 264)(251 265)(252 266)(281 330)(282 331)(283 332)(284 333)(285 334)(286 335)(287 336)(288 323)(289 324)(290 325)(291 326)(292 327)(293 328)(294 329)(295 316)(296 317)(297 318)(298 319)(299 320)(300 321)(301 322)(302 309)(303 310)(304 311)(305 312)(306 313)(307 314)(308 315)(337 379)(338 380)(339 381)(340 382)(341 383)(342 384)(343 385)(344 386)(345 387)(346 388)(347 389)(348 390)(349 391)(350 392)(351 365)(352 366)(353 367)(354 368)(355 369)(356 370)(357 371)(358 372)(359 373)(360 374)(361 375)(362 376)(363 377)(364 378)(393 442)(394 443)(395 444)(396 445)(397 446)(398 447)(399 448)(400 435)(401 436)(402 437)(403 438)(404 439)(405 440)(406 441)(407 421)(408 422)(409 423)(410 424)(411 425)(412 426)(413 427)(414 428)(415 429)(416 430)(417 431)(418 432)(419 433)(420 434)

(1 17)(2 18)(3 19)(4 20)(5 21)(6 22)(7 23)(8 24)(9 25)(10 26)(11 27)(12 28)(13 15)(14 16)(29 45)(30 46)(31 47)(32 48)(33 49)(34 50)(35 51)(36 52)(37 53)(38 54)(39 55)(40 56)(41 43)(42 44)(57 82)(58 83)(59 84)(60 71)(61 72)(62 73)(63 74)(64 75)(65 76)(66 77)(67 78)(68 79)(69 80)(70 81)(85 105)(86 106)(87 107)(88 108)(89 109)(90 110)(91 111)(92 112)(93 99)(94 100)(95 101)(96 102)(97 103)(98 104)(113 138)(114 139)(115 140)(116 127)(117 128)(118 129)(119 130)(120 131)(121 132)(122 133)(123 134)(124 135)(125 136)(126 137)(141 162)(142 163)(143 164)(144 165)(145 166)(146 167)(147 168)(148 155)(149 156)(150 157)(151 158)(152 159)(153 160)(154 161)(169 196)(170 183)(171 184)(172 185)(173 186)(174 187)(175 188)(176 189)(177 190)(178 191)(179 192)(180 193)(181 194)(182 195)(197 216)(198 217)(199 218)(200 219)(201 220)(202 221)(203 222)(204 223)(205 224)(206 211)(207 212)(208 213)(209 214)(210 215)(225 246)(226 247)(227 248)(228 249)(229 250)(230 251)(231 252)(232 239)(233 240)(234 241)(235 242)(236 243)(237 244)(238 245)(253 274)(254 275)(255 276)(256 277)(257 278)(258 279)(259 280)(260 267)(261 268)(262 269)(263 270)(264 271)(265 272)(266 273)(281 302)(282 303)(283 304)(284 305)(285 306)(286 307)(287 308)(288 295)(289 296)(290 297)(291 298)(292 299)(293 300)(294 301)(309 330)(310 331)(311 332)(312 333)(313 334)(314 335)(315 336)(316 323)(317 324)(318 325)(319 326)(320 327)(321 328)(322 329)(337 351)(338 352)(339 353)(340 354)(341 355)(342 356)(343 357)(344 358)(345 359)(346 360)(347 361)(348 362)(349 363)(350 364)(365 379)(366 380)(367 381)(368 382)(369 383)(370 384)(371 385)(372 386)(373 387)(374 388)(375 389)(376 390)(377 391)(378 392)(393 414)(394 415)(395 416)(396 417)(397 418)(398 419)(399 420)(400 407)(401 408)(402 409)(403 410)(404 411)(405 412)(406 413)(421 435)(422 436)(423 437)(424 438)(425 439)(426 440)(427 441)(428 442)(429 443)(430 444)(431 445)(432 446)(433 447)(434 448)

(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)

(1 281 8 288)(2 294 9 287)(3 293 10 286)(4 292 11 285)(5 291 12 284)(6 290 13 283)(7 289 14 282)(15 304 22 297)(16 303 23 296)(17 302 24 295)(18 301 25 308)(19 300 26 307)(20 299 27 306)(21 298 28 305)(29 315 36 322)(30 314 37 321)(31 313 38 320)(32 312 39 319)(33 311 40 318)(34 310 41 317)(35 309 42 316)(43 324 50 331)(44 323 51 330)(45 336 52 329)(46 335 53 328)(47 334 54 327)(48 333 55 326)(49 332 56 325)(57 226 64 233)(58 225 65 232)(59 238 66 231)(60 237 67 230)(61 236 68 229)(62 235 69 228)(63 234 70 227)(71 244 78 251)(72 243 79 250)(73 242 80 249)(74 241 81 248)(75 240 82 247)(76 239 83 246)(77 252 84 245)(85 259 92 266)(86 258 93 265)(87 257 94 264)(88 256 95 263)(89 255 96 262)(90 254 97 261)(91 253 98 260)(99 272 106 279)(100 271 107 278)(101 270 108 277)(102 269 109 276)(103 268 110 275)(104 267 111 274)(105 280 112 273)(113 395 120 402)(114 394 121 401)(115 393 122 400)(116 406 123 399)(117 405 124 398)(118 404 125 397)(119 403 126 396)(127 413 134 420)(128 412 135 419)(129 411 136 418)(130 410 137 417)(131 409 138 416)(132 408 139 415)(133 407 140 414)(141 426 148 433)(142 425 149 432)(143 424 150 431)(144 423 151 430)(145 422 152 429)(146 421 153 428)(147 434 154 427)(155 447 162 440)(156 446 163 439)(157 445 164 438)(158 444 165 437)(159 443 166 436)(160 442 167 435)(161 441 168 448)(169 342 176 349)(170 341 177 348)(171 340 178 347)(172 339 179 346)(173 338 180 345)(174 337 181 344)(175 350 182 343)(183 355 190 362)(184 354 191 361)(185 353 192 360)(186 352 193 359)(187 351 194 358)(188 364 195 357)(189 363 196 356)(197 365 204 372)(198 378 205 371)(199 377 206 370)(200 376 207 369)(201 375 208 368)(202 374 209 367)(203 373 210 366)(211 384 218 391)(212 383 219 390)(213 382 220 389)(214 381 221 388)(215 380 222 387)(216 379 223 386)(217 392 224 385)

G:=sub<Sym(448)| (1,115)(2,116)(3,117)(4,118)(5,119)(6,120)(7,121)(8,122)(9,123)(10,124)(11,125)(12,126)(13,113)(14,114)(15,138)(16,139)(17,140)(18,127)(19,128)(20,129)(21,130)(22,131)(23,132)(24,133)(25,134)(26,135)(27,136)(28,137)(29,147)(30,148)(31,149)(32,150)(33,151)(34,152)(35,153)(36,154)(37,141)(38,142)(39,143)(40,144)(41,145)(42,146)(43,166)(44,167)(45,168)(46,155)(47,156)(48,157)(49,158)(50,159)(51,160)(52,161)(53,162)(54,163)(55,164)(56,165)(57,180)(58,181)(59,182)(60,169)(61,170)(62,171)(63,172)(64,173)(65,174)(66,175)(67,176)(68,177)(69,178)(70,179)(71,196)(72,183)(73,184)(74,185)(75,186)(76,187)(77,188)(78,189)(79,190)(80,191)(81,192)(82,193)(83,194)(84,195)(85,205)(86,206)(87,207)(88,208)(89,209)(90,210)(91,197)(92,198)(93,199)(94,200)(95,201)(96,202)(97,203)(98,204)(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)(225,344)(226,345)(227,346)(228,347)(229,348)(230,349)(231,350)(232,337)(233,338)(234,339)(235,340)(236,341)(237,342)(238,343)(239,351)(240,352)(241,353)(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)(248,360)(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)(256,368)(257,369)(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)(264,376)(265,377)(266,378)(267,386)(268,387)(269,388)(270,389)(271,390)(272,391)(273,392)(274,379)(275,380)(276,381)(277,382)(278,383)(279,384)(280,385)(281,393)(282,394)(283,395)(284,396)(285,397)(286,398)(287,399)(288,400)(289,401)(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)(296,408)(297,409)(298,410)(299,411)(300,412)(301,413)(302,414)(303,415)(304,416)(305,417)(306,418)(307,419)(308,420)(309,428)(310,429)(311,430)(312,431)(313,432)(314,433)(315,434)(316,421)(317,422)(318,423)(319,424)(320,425)(321,426)(322,427)(323,435)(324,436)(325,437)(326,438)(327,439)(328,440)(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)(336,448), (1,111)(2,112)(3,99)(4,100)(5,101)(6,102)(7,103)(8,104)(9,105)(10,106)(11,107)(12,108)(13,109)(14,110)(15,89)(16,90)(17,91)(18,92)(19,93)(20,94)(21,95)(22,96)(23,97)(24,98)(25,85)(26,86)(27,87)(28,88)(29,84)(30,71)(31,72)(32,73)(33,74)(34,75)(35,76)(36,77)(37,78)(38,79)(39,80)(40,81)(41,82)(42,83)(43,57)(44,58)(45,59)(46,60)(47,61)(48,62)(49,63)(50,64)(51,65)(52,66)(53,67)(54,68)(55,69)(56,70)(113,214)(114,215)(115,216)(116,217)(117,218)(118,219)(119,220)(120,221)(121,222)(122,223)(123,224)(124,211)(125,212)(126,213)(127,198)(128,199)(129,200)(130,201)(131,202)(132,203)(133,204)(134,205)(135,206)(136,207)(137,208)(138,209)(139,210)(140,197)(141,189)(142,190)(143,191)(144,192)(145,193)(146,194)(147,195)(148,196)(149,183)(150,184)(151,185)(152,186)(153,187)(154,188)(155,169)(156,170)(157,171)(158,172)(159,173)(160,174)(161,175)(162,176)(163,177)(164,178)(165,179)(166,180)(167,181)(168,182)(225,323)(226,324)(227,325)(228,326)(229,327)(230,328)(231,329)(232,330)(233,331)(234,332)(235,333)(236,334)(237,335)(238,336)(239,309)(240,310)(241,311)(242,312)(243,313)(244,314)(245,315)(246,316)(247,317)(248,318)(249,319)(250,320)(251,321)(252,322)(253,302)(254,303)(255,304)(256,305)(257,306)(258,307)(259,308)(260,295)(261,296)(262,297)(263,298)(264,299)(265,300)(266,301)(267,288)(268,289)(269,290)(270,291)(271,292)(272,293)(273,294)(274,281)(275,282)(276,283)(277,284)(278,285)(279,286)(280,287)(337,442)(338,443)(339,444)(340,445)(341,446)(342,447)(343,448)(344,435)(345,436)(346,437)(347,438)(348,439)(349,440)(350,441)(351,428)(352,429)(353,430)(354,431)(355,432)(356,433)(357,434)(358,421)(359,422)(360,423)(361,424)(362,425)(363,426)(364,427)(365,414)(366,415)(367,416)(368,417)(369,418)(370,419)(371,420)(372,407)(373,408)(374,409)(375,410)(376,411)(377,412)(378,413)(379,393)(380,394)(381,395)(382,396)(383,397)(384,398)(385,399)(386,400)(387,401)(388,402)(389,403)(390,404)(391,405)(392,406), (1,51)(2,52)(3,53)(4,54)(5,55)(6,56)(7,43)(8,44)(9,45)(10,46)(11,47)(12,48)(13,49)(14,50)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40)(23,41)(24,42)(25,29)(26,30)(27,31)(28,32)(57,103)(58,104)(59,105)(60,106)(61,107)(62,108)(63,109)(64,110)(65,111)(66,112)(67,99)(68,100)(69,101)(70,102)(71,86)(72,87)(73,88)(74,89)(75,90)(76,91)(77,92)(78,93)(79,94)(80,95)(81,96)(82,97)(83,98)(84,85)(113,158)(114,159)(115,160)(116,161)(117,162)(118,163)(119,164)(120,165)(121,166)(122,167)(123,168)(124,155)(125,156)(126,157)(127,154)(128,141)(129,142)(130,143)(131,144)(132,145)(133,146)(134,147)(135,148)(136,149)(137,150)(138,151)(139,152)(140,153)(169,211)(170,212)(171,213)(172,214)(173,215)(174,216)(175,217)(176,218)(177,219)(178,220)(179,221)(180,222)(181,223)(182,224)(183,207)(184,208)(185,209)(186,210)(187,197)(188,198)(189,199)(190,200)(191,201)(192,202)(193,203)(194,204)(195,205)(196,206)(225,267)(226,268)(227,269)(228,270)(229,271)(230,272)(231,273)(232,274)(233,275)(234,276)(235,277)(236,278)(237,279)(238,280)(239,253)(240,254)(241,255)(242,256)(243,257)(244,258)(245,259)(246,260)(247,261)(248,262)(249,263)(250,264)(251,265)(252,266)(281,330)(282,331)(283,332)(284,333)(285,334)(286,335)(287,336)(288,323)(289,324)(290,325)(291,326)(292,327)(293,328)(294,329)(295,316)(296,317)(297,318)(298,319)(299,320)(300,321)(301,322)(302,309)(303,310)(304,311)(305,312)(306,313)(307,314)(308,315)(337,379)(338,380)(339,381)(340,382)(341,383)(342,384)(343,385)(344,386)(345,387)(346,388)(347,389)(348,390)(349,391)(350,392)(351,365)(352,366)(353,367)(354,368)(355,369)(356,370)(357,371)(358,372)(359,373)(360,374)(361,375)(362,376)(363,377)(364,378)(393,442)(394,443)(395,444)(396,445)(397,446)(398,447)(399,448)(400,435)(401,436)(402,437)(403,438)(404,439)(405,440)(406,441)(407,421)(408,422)(409,423)(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)(418,432)(419,433)(420,434), 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G:=Group( 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(1,51)(2,52)(3,53)(4,54)(5,55)(6,56)(7,43)(8,44)(9,45)(10,46)(11,47)(12,48)(13,49)(14,50)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40)(23,41)(24,42)(25,29)(26,30)(27,31)(28,32)(57,103)(58,104)(59,105)(60,106)(61,107)(62,108)(63,109)(64,110)(65,111)(66,112)(67,99)(68,100)(69,101)(70,102)(71,86)(72,87)(73,88)(74,89)(75,90)(76,91)(77,92)(78,93)(79,94)(80,95)(81,96)(82,97)(83,98)(84,85)(113,158)(114,159)(115,160)(116,161)(117,162)(118,163)(119,164)(120,165)(121,166)(122,167)(123,168)(124,155)(125,156)(126,157)(127,154)(128,141)(129,142)(130,143)(131,144)(132,145)(133,146)(134,147)(135,148)(136,149)(137,150)(138,151)(139,152)(140,153)(169,211)(170,212)(171,213)(172,214)(173,215)(174,216)(175,217)(176,218)(177,219)(178,220)(179,221)(180,222)(181,223)(182,224)(183,207)(184,208)(185,209)(186,210)(187,197)(188,198)(189,199)(190,200)(191,201)(192,202)(193,203)(194,204)(195,205)(196,206)(225,267)(226,268)(227,269)(228,270)(229,271)(230,272)(231,273)(232,274)(233,275)(234,276)(235,277)(236,278)(237,279)(238,280)(239,253)(240,254)(241,255)(242,256)(243,257)(244,258)(245,259)(246,260)(247,261)(248,262)(249,263)(250,264)(251,265)(252,266)(281,330)(282,331)(283,332)(284,333)(285,334)(286,335)(287,336)(288,323)(289,324)(290,325)(291,326)(292,327)(293,328)(294,329)(295,316)(296,317)(297,318)(298,319)(299,320)(300,321)(301,322)(302,309)(303,310)(304,311)(305,312)(306,313)(307,314)(308,315)(337,379)(338,380)(339,381)(340,382)(341,383)(342,384)(343,385)(344,386)(345,387)(346,388)(347,389)(348,390)(349,391)(350,392)(351,365)(352,366)(353,367)(354,368)(355,369)(356,370)(357,371)(358,372)(359,373)(360,374)(361,375)(362,376)(363,377)(364,378)(393,442)(394,443)(395,444)(396,445)(397,446)(398,447)(399,448)(400,435)(401,436)(402,437)(403,438)(404,439)(405,440)(406,441)(407,421)(408,422)(409,423)(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)(418,432)(419,433)(420,434), (1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,15)(14,16)(29,45)(30,46)(31,47)(32,48)(33,49)(34,50)(35,51)(36,52)(37,53)(38,54)(39,55)(40,56)(41,43)(42,44)(57,82)(58,83)(59,84)(60,71)(61,72)(62,73)(63,74)(64,75)(65,76)(66,77)(67,78)(68,79)(69,80)(70,81)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,99)(94,100)(95,101)(96,102)(97,103)(98,104)(113,138)(114,139)(115,140)(116,127)(117,128)(118,129)(119,130)(120,131)(121,132)(122,133)(123,134)(124,135)(125,136)(126,137)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168)(148,155)(149,156)(150,157)(151,158)(152,159)(153,160)(154,161)(169,196)(170,183)(171,184)(172,185)(173,186)(174,187)(175,188)(176,189)(177,190)(178,191)(179,192)(180,193)(181,194)(182,195)(197,216)(198,217)(199,218)(200,219)(201,220)(202,221)(203,222)(204,223)(205,224)(206,211)(207,212)(208,213)(209,214)(210,215)(225,246)(226,247)(227,248)(228,249)(229,250)(230,251)(231,252)(232,239)(233,240)(234,241)(235,242)(236,243)(237,244)(238,245)(253,274)(254,275)(255,276)(256,277)(257,278)(258,279)(259,280)(260,267)(261,268)(262,269)(263,270)(264,271)(265,272)(266,273)(281,302)(282,303)(283,304)(284,305)(285,306)(286,307)(287,308)(288,295)(289,296)(290,297)(291,298)(292,299)(293,300)(294,301)(309,330)(310,331)(311,332)(312,333)(313,334)(314,335)(315,336)(316,323)(317,324)(318,325)(319,326)(320,327)(321,328)(322,329)(337,351)(338,352)(339,353)(340,354)(341,355)(342,356)(343,357)(344,358)(345,359)(346,360)(347,361)(348,362)(349,363)(350,364)(365,379)(366,380)(367,381)(368,382)(369,383)(370,384)(371,385)(372,386)(373,387)(374,388)(375,389)(376,390)(377,391)(378,392)(393,414)(394,415)(395,416)(396,417)(397,418)(398,419)(399,420)(400,407)(401,408)(402,409)(403,410)(404,411)(405,412)(406,413)(421,435)(422,436)(423,437)(424,438)(425,439)(426,440)(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)(434,448), (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), (1,281,8,288)(2,294,9,287)(3,293,10,286)(4,292,11,285)(5,291,12,284)(6,290,13,283)(7,289,14,282)(15,304,22,297)(16,303,23,296)(17,302,24,295)(18,301,25,308)(19,300,26,307)(20,299,27,306)(21,298,28,305)(29,315,36,322)(30,314,37,321)(31,313,38,320)(32,312,39,319)(33,311,40,318)(34,310,41,317)(35,309,42,316)(43,324,50,331)(44,323,51,330)(45,336,52,329)(46,335,53,328)(47,334,54,327)(48,333,55,326)(49,332,56,325)(57,226,64,233)(58,225,65,232)(59,238,66,231)(60,237,67,230)(61,236,68,229)(62,235,69,228)(63,234,70,227)(71,244,78,251)(72,243,79,250)(73,242,80,249)(74,241,81,248)(75,240,82,247)(76,239,83,246)(77,252,84,245)(85,259,92,266)(86,258,93,265)(87,257,94,264)(88,256,95,263)(89,255,96,262)(90,254,97,261)(91,253,98,260)(99,272,106,279)(100,271,107,278)(101,270,108,277)(102,269,109,276)(103,268,110,275)(104,267,111,274)(105,280,112,273)(113,395,120,402)(114,394,121,401)(115,393,122,400)(116,406,123,399)(117,405,124,398)(118,404,125,397)(119,403,126,396)(127,413,134,420)(128,412,135,419)(129,411,136,418)(130,410,137,417)(131,409,138,416)(132,408,139,415)(133,407,140,414)(141,426,148,433)(142,425,149,432)(143,424,150,431)(144,423,151,430)(145,422,152,429)(146,421,153,428)(147,434,154,427)(155,447,162,440)(156,446,163,439)(157,445,164,438)(158,444,165,437)(159,443,166,436)(160,442,167,435)(161,441,168,448)(169,342,176,349)(170,341,177,348)(171,340,178,347)(172,339,179,346)(173,338,180,345)(174,337,181,344)(175,350,182,343)(183,355,190,362)(184,354,191,361)(185,353,192,360)(186,352,193,359)(187,351,194,358)(188,364,195,357)(189,363,196,356)(197,365,204,372)(198,378,205,371)(199,377,206,370)(200,376,207,369)(201,375,208,368)(202,374,209,367)(203,373,210,366)(211,384,218,391)(212,383,219,390)(213,382,220,389)(214,381,221,388)(215,380,222,387)(216,379,223,386)(217,392,224,385) );

G=PermutationGroup([(1,115),(2,116),(3,117),(4,118),(5,119),(6,120),(7,121),(8,122),(9,123),(10,124),(11,125),(12,126),(13,113),(14,114),(15,138),(16,139),(17,140),(18,127),(19,128),(20,129),(21,130),(22,131),(23,132),(24,133),(25,134),(26,135),(27,136),(28,137),(29,147),(30,148),(31,149),(32,150),(33,151),(34,152),(35,153),(36,154),(37,141),(38,142),(39,143),(40,144),(41,145),(42,146),(43,166),(44,167),(45,168),(46,155),(47,156),(48,157),(49,158),(50,159),(51,160),(52,161),(53,162),(54,163),(55,164),(56,165),(57,180),(58,181),(59,182),(60,169),(61,170),(62,171),(63,172),(64,173),(65,174),(66,175),(67,176),(68,177),(69,178),(70,179),(71,196),(72,183),(73,184),(74,185),(75,186),(76,187),(77,188),(78,189),(79,190),(80,191),(81,192),(82,193),(83,194),(84,195),(85,205),(86,206),(87,207),(88,208),(89,209),(90,210),(91,197),(92,198),(93,199),(94,200),(95,201),(96,202),(97,203),(98,204),(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),(225,344),(226,345),(227,346),(228,347),(229,348),(230,349),(231,350),(232,337),(233,338),(234,339),(235,340),(236,341),(237,342),(238,343),(239,351),(240,352),(241,353),(242,354),(243,355),(244,356),(245,357),(246,358),(247,359),(248,360),(249,361),(250,362),(251,363),(252,364),(253,365),(254,366),(255,367),(256,368),(257,369),(258,370),(259,371),(260,372),(261,373),(262,374),(263,375),(264,376),(265,377),(266,378),(267,386),(268,387),(269,388),(270,389),(271,390),(272,391),(273,392),(274,379),(275,380),(276,381),(277,382),(278,383),(279,384),(280,385),(281,393),(282,394),(283,395),(284,396),(285,397),(286,398),(287,399),(288,400),(289,401),(290,402),(291,403),(292,404),(293,405),(294,406),(295,407),(296,408),(297,409),(298,410),(299,411),(300,412),(301,413),(302,414),(303,415),(304,416),(305,417),(306,418),(307,419),(308,420),(309,428),(310,429),(311,430),(312,431),(313,432),(314,433),(315,434),(316,421),(317,422),(318,423),(319,424),(320,425),(321,426),(322,427),(323,435),(324,436),(325,437),(326,438),(327,439),(328,440),(329,441),(330,442),(331,443),(332,444),(333,445),(334,446),(335,447),(336,448)], [(1,111),(2,112),(3,99),(4,100),(5,101),(6,102),(7,103),(8,104),(9,105),(10,106),(11,107),(12,108),(13,109),(14,110),(15,89),(16,90),(17,91),(18,92),(19,93),(20,94),(21,95),(22,96),(23,97),(24,98),(25,85),(26,86),(27,87),(28,88),(29,84),(30,71),(31,72),(32,73),(33,74),(34,75),(35,76),(36,77),(37,78),(38,79),(39,80),(40,81),(41,82),(42,83),(43,57),(44,58),(45,59),(46,60),(47,61),(48,62),(49,63),(50,64),(51,65),(52,66),(53,67),(54,68),(55,69),(56,70),(113,214),(114,215),(115,216),(116,217),(117,218),(118,219),(119,220),(120,221),(121,222),(122,223),(123,224),(124,211),(125,212),(126,213),(127,198),(128,199),(129,200),(130,201),(131,202),(132,203),(133,204),(134,205),(135,206),(136,207),(137,208),(138,209),(139,210),(140,197),(141,189),(142,190),(143,191),(144,192),(145,193),(146,194),(147,195),(148,196),(149,183),(150,184),(151,185),(152,186),(153,187),(154,188),(155,169),(156,170),(157,171),(158,172),(159,173),(160,174),(161,175),(162,176),(163,177),(164,178),(165,179),(166,180),(167,181),(168,182),(225,323),(226,324),(227,325),(228,326),(229,327),(230,328),(231,329),(232,330),(233,331),(234,332),(235,333),(236,334),(237,335),(238,336),(239,309),(240,310),(241,311),(242,312),(243,313),(244,314),(245,315),(246,316),(247,317),(248,318),(249,319),(250,320),(251,321),(252,322),(253,302),(254,303),(255,304),(256,305),(257,306),(258,307),(259,308),(260,295),(261,296),(262,297),(263,298),(264,299),(265,300),(266,301),(267,288),(268,289),(269,290),(270,291),(271,292),(272,293),(273,294),(274,281),(275,282),(276,283),(277,284),(278,285),(279,286),(280,287),(337,442),(338,443),(339,444),(340,445),(341,446),(342,447),(343,448),(344,435),(345,436),(346,437),(347,438),(348,439),(349,440),(350,441),(351,428),(352,429),(353,430),(354,431),(355,432),(356,433),(357,434),(358,421),(359,422),(360,423),(361,424),(362,425),(363,426),(364,427),(365,414),(366,415),(367,416),(368,417),(369,418),(370,419),(371,420),(372,407),(373,408),(374,409),(375,410),(376,411),(377,412),(378,413),(379,393),(380,394),(381,395),(382,396),(383,397),(384,398),(385,399),(386,400),(387,401),(388,402),(389,403),(390,404),(391,405),(392,406)], [(1,51),(2,52),(3,53),(4,54),(5,55),(6,56),(7,43),(8,44),(9,45),(10,46),(11,47),(12,48),(13,49),(14,50),(15,33),(16,34),(17,35),(18,36),(19,37),(20,38),(21,39),(22,40),(23,41),(24,42),(25,29),(26,30),(27,31),(28,32),(57,103),(58,104),(59,105),(60,106),(61,107),(62,108),(63,109),(64,110),(65,111),(66,112),(67,99),(68,100),(69,101),(70,102),(71,86),(72,87),(73,88),(74,89),(75,90),(76,91),(77,92),(78,93),(79,94),(80,95),(81,96),(82,97),(83,98),(84,85),(113,158),(114,159),(115,160),(116,161),(117,162),(118,163),(119,164),(120,165),(121,166),(122,167),(123,168),(124,155),(125,156),(126,157),(127,154),(128,141),(129,142),(130,143),(131,144),(132,145),(133,146),(134,147),(135,148),(136,149),(137,150),(138,151),(139,152),(140,153),(169,211),(170,212),(171,213),(172,214),(173,215),(174,216),(175,217),(176,218),(177,219),(178,220),(179,221),(180,222),(181,223),(182,224),(183,207),(184,208),(185,209),(186,210),(187,197),(188,198),(189,199),(190,200),(191,201),(192,202),(193,203),(194,204),(195,205),(196,206),(225,267),(226,268),(227,269),(228,270),(229,271),(230,272),(231,273),(232,274),(233,275),(234,276),(235,277),(236,278),(237,279),(238,280),(239,253),(240,254),(241,255),(242,256),(243,257),(244,258),(245,259),(246,260),(247,261),(248,262),(249,263),(250,264),(251,265),(252,266),(281,330),(282,331),(283,332),(284,333),(285,334),(286,335),(287,336),(288,323),(289,324),(290,325),(291,326),(292,327),(293,328),(294,329),(295,316),(296,317),(297,318),(298,319),(299,320),(300,321),(301,322),(302,309),(303,310),(304,311),(305,312),(306,313),(307,314),(308,315),(337,379),(338,380),(339,381),(340,382),(341,383),(342,384),(343,385),(344,386),(345,387),(346,388),(347,389),(348,390),(349,391),(350,392),(351,365),(352,366),(353,367),(354,368),(355,369),(356,370),(357,371),(358,372),(359,373),(360,374),(361,375),(362,376),(363,377),(364,378),(393,442),(394,443),(395,444),(396,445),(397,446),(398,447),(399,448),(400,435),(401,436),(402,437),(403,438),(404,439),(405,440),(406,441),(407,421),(408,422),(409,423),(410,424),(411,425),(412,426),(413,427),(414,428),(415,429),(416,430),(417,431),(418,432),(419,433),(420,434)], [(1,17),(2,18),(3,19),(4,20),(5,21),(6,22),(7,23),(8,24),(9,25),(10,26),(11,27),(12,28),(13,15),(14,16),(29,45),(30,46),(31,47),(32,48),(33,49),(34,50),(35,51),(36,52),(37,53),(38,54),(39,55),(40,56),(41,43),(42,44),(57,82),(58,83),(59,84),(60,71),(61,72),(62,73),(63,74),(64,75),(65,76),(66,77),(67,78),(68,79),(69,80),(70,81),(85,105),(86,106),(87,107),(88,108),(89,109),(90,110),(91,111),(92,112),(93,99),(94,100),(95,101),(96,102),(97,103),(98,104),(113,138),(114,139),(115,140),(116,127),(117,128),(118,129),(119,130),(120,131),(121,132),(122,133),(123,134),(124,135),(125,136),(126,137),(141,162),(142,163),(143,164),(144,165),(145,166),(146,167),(147,168),(148,155),(149,156),(150,157),(151,158),(152,159),(153,160),(154,161),(169,196),(170,183),(171,184),(172,185),(173,186),(174,187),(175,188),(176,189),(177,190),(178,191),(179,192),(180,193),(181,194),(182,195),(197,216),(198,217),(199,218),(200,219),(201,220),(202,221),(203,222),(204,223),(205,224),(206,211),(207,212),(208,213),(209,214),(210,215),(225,246),(226,247),(227,248),(228,249),(229,250),(230,251),(231,252),(232,239),(233,240),(234,241),(235,242),(236,243),(237,244),(238,245),(253,274),(254,275),(255,276),(256,277),(257,278),(258,279),(259,280),(260,267),(261,268),(262,269),(263,270),(264,271),(265,272),(266,273),(281,302),(282,303),(283,304),(284,305),(285,306),(286,307),(287,308),(288,295),(289,296),(290,297),(291,298),(292,299),(293,300),(294,301),(309,330),(310,331),(311,332),(312,333),(313,334),(314,335),(315,336),(316,323),(317,324),(318,325),(319,326),(320,327),(321,328),(322,329),(337,351),(338,352),(339,353),(340,354),(341,355),(342,356),(343,357),(344,358),(345,359),(346,360),(347,361),(348,362),(349,363),(350,364),(365,379),(366,380),(367,381),(368,382),(369,383),(370,384),(371,385),(372,386),(373,387),(374,388),(375,389),(376,390),(377,391),(378,392),(393,414),(394,415),(395,416),(396,417),(397,418),(398,419),(399,420),(400,407),(401,408),(402,409),(403,410),(404,411),(405,412),(406,413),(421,435),(422,436),(423,437),(424,438),(425,439),(426,440),(427,441),(428,442),(429,443),(430,444),(431,445),(432,446),(433,447),(434,448)], [(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)], [(1,281,8,288),(2,294,9,287),(3,293,10,286),(4,292,11,285),(5,291,12,284),(6,290,13,283),(7,289,14,282),(15,304,22,297),(16,303,23,296),(17,302,24,295),(18,301,25,308),(19,300,26,307),(20,299,27,306),(21,298,28,305),(29,315,36,322),(30,314,37,321),(31,313,38,320),(32,312,39,319),(33,311,40,318),(34,310,41,317),(35,309,42,316),(43,324,50,331),(44,323,51,330),(45,336,52,329),(46,335,53,328),(47,334,54,327),(48,333,55,326),(49,332,56,325),(57,226,64,233),(58,225,65,232),(59,238,66,231),(60,237,67,230),(61,236,68,229),(62,235,69,228),(63,234,70,227),(71,244,78,251),(72,243,79,250),(73,242,80,249),(74,241,81,248),(75,240,82,247),(76,239,83,246),(77,252,84,245),(85,259,92,266),(86,258,93,265),(87,257,94,264),(88,256,95,263),(89,255,96,262),(90,254,97,261),(91,253,98,260),(99,272,106,279),(100,271,107,278),(101,270,108,277),(102,269,109,276),(103,268,110,275),(104,267,111,274),(105,280,112,273),(113,395,120,402),(114,394,121,401),(115,393,122,400),(116,406,123,399),(117,405,124,398),(118,404,125,397),(119,403,126,396),(127,413,134,420),(128,412,135,419),(129,411,136,418),(130,410,137,417),(131,409,138,416),(132,408,139,415),(133,407,140,414),(141,426,148,433),(142,425,149,432),(143,424,150,431),(144,423,151,430),(145,422,152,429),(146,421,153,428),(147,434,154,427),(155,447,162,440),(156,446,163,439),(157,445,164,438),(158,444,165,437),(159,443,166,436),(160,442,167,435),(161,441,168,448),(169,342,176,349),(170,341,177,348),(171,340,178,347),(172,339,179,346),(173,338,180,345),(174,337,181,344),(175,350,182,343),(183,355,190,362),(184,354,191,361),(185,353,192,360),(186,352,193,359),(187,351,194,358),(188,364,195,357),(189,363,196,356),(197,365,204,372),(198,378,205,371),(199,377,206,370),(200,376,207,369),(201,375,208,368),(202,374,209,367),(203,373,210,366),(211,384,218,391),(212,383,219,390),(213,382,220,389),(214,381,221,388),(215,380,222,387),(216,379,223,386),(217,392,224,385)])

Matrix representation ►G ⊆ GL₆(𝔽₂₉)

1	0	0	0	0	0
0	28	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	28

1	0	0	0	0	0
0	28	0	0	0	0
0	0	28	0	0	0
0	0	0	28	0	0
0	0	0	0	1	0
0	0	0	0	0	1

28	0	0	0	0	0
0	28	0	0	0	0
0	0	1	0	0	0
0	0	0	28	0	0
0	0	0	0	1	0
0	0	0	0	0	1

1	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	0
0	0	0	0	0	1

1	0	0	0	0	0
0	1	0	0	0	0
0	0	1	0	0	0
0	0	0	1	0	0
0	0	0	0	0	28
0	0	0	0	1	22

1	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	19	20
0	0	0	0	8	10

G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,28,22],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,19,8,0,0,0,0,20,10] >;

160 conjugacy classes

class	1	2A	···	2AE	4A	···	4AF	7A	7B	7C	14A	···	14CO
order	1	2	···	2	4	···	4	7	7	7	14	···	14
size	1	1	···	1	7	···	7	2	2	2	2	···	2

160 irreducible representations

dim	1	1	1	1	2	2	2
type	+	+	+		+	-	+
image	C₁	C₂	C₂	C₄	D₇	Dic₇	D₁₄
kernel	C₂⁴×Dic₇	C₂³×Dic₇	C₂⁴×C₁₄	C₂³×C₁₄	C₂⁵	C₂⁴	C₂⁴
# reps	1	30	1	32	3	48	45

In GAP, Magma, Sage, TeX

C_2^4\times Dic_7

% in TeX

G:=Group("C2^4xDic7");

// GroupNames label

G:=SmallGroup(448,1383);

// by ID

G=gap.SmallGroup(448,1383);

# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,18822]);

// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^14=1,f^2=e^7,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=e^-1>;

// generators/relations

G = C₂⁴×Dic₇ order 448 = 2⁶·7

Direct product of C₂⁴ and Dic₇

G = C24×Dic7 order 448 = 26·7

Direct product of C24 and Dic7

G = C₂⁴×Dic₇ order 448 = 2⁶·7

Direct product of C₂⁴ and Dic₇