C2^4xDic7 - GroupNames

G = C₂⁴×Dic₇ order 448 = 2⁶·7

Direct product of C₂⁴ and Dic₇

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

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

Generators and relations for C₂⁴×Dic₇
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 >

Subgroups: 3204 in 1362 conjugacy classes, 1055 normal (7 characteristic)
C₁, C₂, C₂, C₄, C₂², C₇, C₂×C₄, C₂³, C₁₄, C₁₄, C₂²×C₄, C₂⁴, Dic₇, C₂×C₁₄, C₂³×C₄, C₂⁵, C₂×Dic₇, C₂²×C₁₄, C₂⁴×C₄, C₂²×Dic₇, C₂³×C₁₄, C₂³×Dic₇, C₂⁴×C₁₄, C₂⁴×Dic₇
Quotients: C₁, C₂, C₄, C₂², C₂×C₄, C₂³, D₇, C₂²×C₄, C₂⁴, Dic₇, D₁₄, C₂³×C₄, C₂⁵, C₂×Dic₇, C₂²×D₇, C₂⁴×C₄, C₂²×Dic₇, C₂³×D₇, C₂³×Dic₇, D₇×C₂⁴, C₂⁴×Dic₇

Smallest permutation representation of C₂⁴×Dic₇
►Regular action on 448 points

Generators in S₄₄₈

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

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

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

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

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

Matrix representation of C₂⁴×Dic₇ ►in 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] >;

C₂⁴×Dic₇ in GAP, Magma, Sage, TeX

C_2^4\times {\rm 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