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G = C22×C4×Dic7  order 448 = 26·7

Direct product of C22×C4 and Dic7

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

Aliases: C22×C4×Dic7, C24.75D14, (C2×C14)⋊4C42, C28⋊9(C22×C4), C14⋊2(C2×C42), C7⋊2(C22×C42), (C22×C28)⋊18C4, C23.67(C4×D7), (C23×C4).15D7, (C23×C28).21C2, C14.36(C23×C4), C2.2(C23×Dic7), (C2×C28).884C23, (C2×C14).280C24, (C22×C4).473D14, C23.44(C2×Dic7), C22.38(C23×D7), (C23×Dic7).12C2, C23.332(C22×D7), (C22×C14).409C23, (C22×C28).569C22, (C23×C14).102C22, (C2×Dic7).314C23, C22.29(C22×Dic7), (C22×Dic7).244C22, (C2×C28)⋊38(C2×C4), C2.3(D7×C22×C4), C22.77(C2×C4×D7), (C2×C4).828(C22×D7), (C22×C14).141(C2×C4), (C2×C14).206(C22×C4), SmallGroup(448,1235)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C7 — C22×C4×Dic7
Chief series
C1 — C7 — C14 — C2×C14 — C2×Dic7 — C22×Dic7 — C23×Dic7 — C22×C4×Dic7
Lower central
C7 — C22×C4×Dic7

Subgroups: 1284 in 498 conjugacy classes, 367 normal (11 characteristic)
C1, C2, C2 [×14], C4 [×8], C4 [×16], C22, C22 [×34], C7, C2×C4 [×28], C2×C4 [×56], C23 [×15], C14, C14 [×14], C42 [×16], C22×C4 [×14], C22×C4 [×28], C24, Dic7 [×16], C28 [×8], C2×C14, C2×C14 [×34], C2×C42 [×12], C23×C4, C23×C4 [×2], C2×Dic7 [×56], C2×C28 [×28], C22×C14 [×15], C22×C42, C4×Dic7 [×16], C22×Dic7 [×28], C22×C28 [×14], C23×C14, C2×C4×Dic7 [×12], C23×Dic7 [×2], C23×C28, C22×C4×Dic7

Quotients:
C1, C2 [×15], C4 [×24], C22 [×35], C2×C4 [×84], C23 [×15], D7, C42 [×16], C22×C4 [×42], C24, Dic7 [×8], D14 [×7], C2×C42 [×12], C23×C4 [×3], C4×D7 [×8], C2×Dic7 [×28], C22×D7 [×7], C22×C42, C4×Dic7 [×16], C2×C4×D7 [×12], C22×Dic7 [×14], C23×D7, C2×C4×Dic7 [×12], D7×C22×C4 [×2], C23×Dic7, C22×C4×Dic7

Generators and relations
 G = < a,b,c,d,e | a2=b2=c4=d14=1, e2=d7, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

Smallest permutation representation
►Regular action on 448 points
Generators in S448
(1 307)(2 308)(3 295)(4 296)(5 297)(6 298)(7 299)(8 300)(9 301)(10 302)(11 303)(12 304)(13 305)(14 306)(15 190)(16 191)(17 192)(18 193)(19 194)(20 195)(21 196)(22 183)(23 184)(24 185)(25 186)(26 187)(27 188)(28 189)(29 358)(30 359)(31 360)(32 361)(33 362)(34 363)(35 364)(36 351)(37 352)(38 353)(39 354)(40 355)(41 356)(42 357)(43 309)(44 310)(45 311)(46 312)(47 313)(48 314)(49 315)(50 316)(51 317)(52 318)(53 319)(54 320)(55 321)(56 322)(57 204)(58 205)(59 206)(60 207)(61 208)(62 209)(63 210)(64 197)(65 198)(66 199)(67 200)(68 201)(69 202)(70 203)(71 233)(72 234)(73 235)(74 236)(75 237)(76 238)(77 225)(78 226)(79 227)(80 228)(81 229)(82 230)(83 231)(84 232)(85 140)(86 127)(87 128)(88 129)(89 130)(90 131)(91 132)(92 133)(93 134)(94 135)(95 136)(96 137)(97 138)(98 139)(99 239)(100 240)(101 241)(102 242)(103 243)(104 244)(105 245)(106 246)(107 247)(108 248)(109 249)(110 250)(111 251)(112 252)(113 334)(114 335)(115 336)(116 323)(117 324)(118 325)(119 326)(120 327)(121 328)(122 329)(123 330)(124 331)(125 332)(126 333)(141 224)(142 211)(143 212)(144 213)(145 214)(146 215)(147 216)(148 217)(149 218)(150 219)(151 220)(152 221)(153 222)(154 223)(155 268)(156 269)(157 270)(158 271)(159 272)(160 273)(161 274)(162 275)(163 276)(164 277)(165 278)(166 279)(167 280)(168 267)(169 392)(170 379)(171 380)(172 381)(173 382)(174 383)(175 384)(176 385)(177 386)(178 387)(179 388)(180 389)(181 390)(182 391)(253 405)(254 406)(255 393)(256 394)(257 395)(258 396)(259 397)(260 398)(261 399)(262 400)(263 401)(264 402)(265 403)(266 404)(281 366)(282 367)(283 368)(284 369)(285 370)(286 371)(287 372)(288 373)(289 374)(290 375)(291 376)(292 377)(293 378)(294 365)(337 410)(338 411)(339 412)(340 413)(341 414)(342 415)(343 416)(344 417)(345 418)(346 419)(347 420)(348 407)(349 408)(350 409)(421 442)(422 443)(423 444)(424 445)(425 446)(426 447)(427 448)(428 435)(429 436)(430 437)(431 438)(432 439)(433 440)(434 441)

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

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

(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)

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

Matrix representation ►G ⊆ GL5(𝔽29)

10000
01000
002800
00010
00001
,
280000
028000
002800
000280
000028
,
280000
028000
002800
000120
000012
,
280000
01000
00100
000128
000525
,
170000
01000
00100
0001217
000017

G:=sub<GL(5,GF(29))| [1,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,1,0,0,0,0,0,1],[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],[28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,12,0,0,0,0,0,12],[28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,5,0,0,0,28,25],[17,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,12,0,0,0,0,17,17] >;
 

160 conjugacy classes

class 1 2A···2O4A···4P4Q···4AV7A7B7C14A···14AS28A···28AV
order12···24···44···477714···1428···28
size11···11···17···72222···22···2

160 irreducible representations

dim11111122222
type+++++-++
imageC1C2C2C2C4C4D7Dic7D14D14C4×D7
kernelC22×C4×Dic7C2×C4×Dic7C23×Dic7C23×C28C22×Dic7C22×C28C23×C4C22×C4C22×C4C24C23
# reps11221321632418348

In GAP, Magma, Sage, TeX 

C_2^2\times C_4\times Dic_7
 
% in TeX
 
G:=Group("C2^2xC4xDic7");
 
// GroupNames label
 
G:=SmallGroup(448,1235);
 
// by ID
 
G=gap.SmallGroup(448,1235);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,136,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^4=d^14=1,e^2=d^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,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
 
// generators/relations
 

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