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G = C7×C22.58C24  order 448 = 26·7

Direct product of C7 and C22.58C24

direct product, metabelian, nilpotent (class 2), monomial, 2-elementary

Aliases: C7×C22.58C24, C14.1252- 1+4, C42.56(C2×C14), C42.C2.7C14, (C2×C28).685C23, (C2×C14).384C24, (C4×C28).297C22, C22.58(C23×C14), C2.17(C7×2- 1+4), C4⋊C4.36(C2×C14), (C7×C4⋊C4).253C22, (C2×C4).44(C22×C14), (C7×C42.C2).14C2, SmallGroup(448,1347)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C22 — C7×C22.58C24
Chief series
C1 — C2 — C22 — C2×C14 — C2×C28 — C7×C4⋊C4 — C7×C42.C2 — C7×C22.58C24
Lower central
C1 — C22 — C7×C22.58C24
Upper central
C1 — C2×C14 — C7×C22.58C24

Generators and relations for C7×C22.58C24
 G = < a,b,c,d,e,f,g | a7=b2=c2=1, d2=g2=b, e2=f2=c, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ag=ga, bc=cb, ede-1=bd=db, geg-1=be=eb, bf=fb, bg=gb, fdf-1=cd=dc, ce=ec, cf=fc, cg=gc, gdg-1=bcd, fef-1=bce, fg=gf >

Subgroups: 202 in 172 conjugacy classes, 142 normal (6 characteristic)
C1, C2, C4, C22, C7, C2×C4, C14, C42, C4⋊C4, C28, C2×C14, C42.C2, C2×C28, C22.58C24, C4×C28, C7×C4⋊C4, C7×C42.C2, C7×C22.58C24
Quotients: C1, C2, C22, C7, C23, C14, C24, C2×C14, 2- 1+4, C22×C14, C22.58C24, C23×C14, C7×2- 1+4, C7×C22.58C24

Smallest permutation representation of C7×C22.58C24
►Regular action on 448 points
Generators in S448
(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 47)(2 48)(3 49)(4 43)(5 44)(6 45)(7 46)(8 446)(9 447)(10 448)(11 442)(12 443)(13 444)(14 445)(15 22)(16 23)(17 24)(18 25)(19 26)(20 27)(21 28)(29 40)(30 41)(31 42)(32 36)(33 37)(34 38)(35 39)(50 74)(51 75)(52 76)(53 77)(54 71)(55 72)(56 73)(57 68)(58 69)(59 70)(60 64)(61 65)(62 66)(63 67)(78 102)(79 103)(80 104)(81 105)(82 99)(83 100)(84 101)(85 96)(86 97)(87 98)(88 92)(89 93)(90 94)(91 95)(106 130)(107 131)(108 132)(109 133)(110 127)(111 128)(112 129)(113 124)(114 125)(115 126)(116 120)(117 121)(118 122)(119 123)(134 158)(135 159)(136 160)(137 161)(138 155)(139 156)(140 157)(141 152)(142 153)(143 154)(144 148)(145 149)(146 150)(147 151)(162 186)(163 187)(164 188)(165 189)(166 183)(167 184)(168 185)(169 180)(170 181)(171 182)(172 176)(173 177)(174 178)(175 179)(190 214)(191 215)(192 216)(193 217)(194 211)(195 212)(196 213)(197 208)(198 209)(199 210)(200 204)(201 205)(202 206)(203 207)(218 242)(219 243)(220 244)(221 245)(222 239)(223 240)(224 241)(225 236)(226 237)(227 238)(228 232)(229 233)(230 234)(231 235)(246 270)(247 271)(248 272)(249 273)(250 267)(251 268)(252 269)(253 264)(254 265)(255 266)(256 260)(257 261)(258 262)(259 263)(274 298)(275 299)(276 300)(277 301)(278 295)(279 296)(280 297)(281 292)(282 293)(283 294)(284 288)(285 289)(286 290)(287 291)(302 326)(303 327)(304 328)(305 329)(306 323)(307 324)(308 325)(309 320)(310 321)(311 322)(312 316)(313 317)(314 318)(315 319)(330 354)(331 355)(332 356)(333 357)(334 351)(335 352)(336 353)(337 348)(338 349)(339 350)(340 344)(341 345)(342 346)(343 347)(358 382)(359 383)(360 384)(361 385)(362 379)(363 380)(364 381)(365 376)(366 377)(367 378)(368 372)(369 373)(370 374)(371 375)(386 410)(387 411)(388 412)(389 413)(390 407)(391 408)(392 409)(393 404)(394 405)(395 406)(396 400)(397 401)(398 402)(399 403)(414 438)(415 439)(416 440)(417 441)(418 435)(419 436)(420 437)(421 432)(422 433)(423 434)(424 428)(425 429)(426 430)(427 431)

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

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

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

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

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

133 conjugacy classes

class 1 2A2B2C4A···4O7A···7F14A···14R28A···28CL
order12224···47···714···1428···28
size11114···41···11···14···4

133 irreducible representations

dim111144
type++-
imageC1C2C7C142- 1+4C7×2- 1+4
kernelC7×C22.58C24C7×C42.C2C22.58C24C42.C2C14C2
# reps115690318

Matrix representation of C7×C22.58C24 ►in GL8(𝔽29)

160000000
016000000
001600000
000160000
000023000
000002300
000000230
000000023
,
280000000
028000000
002800000
000280000
00001000
00000100
00000010
00000001
,
10000000
01000000
00100000
00010000
000028000
000002800
000000280
000000028
,
42111240000
271423170000
192125210000
2027150000
00001326163
00003162613
0000163163
000026132613
,
112516270000
1021510000
9422190000
2562230000
000097207
000079720
00002072022
00007202220
,
00100000
2811270000
10000000
000280000
00000010
00000001
000028000
000002800
,
01000000
280000000
2811270000
2801280000
00000100
00001000
00000001
00000010

G:=sub<GL(8,GF(29))| [16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,23,0,0,0,0,0,0,0,0,23,0,0,0,0,0,0,0,0,23,0,0,0,0,0,0,0,0,23],[28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28],[4,27,19,2,0,0,0,0,21,14,21,0,0,0,0,0,11,23,25,27,0,0,0,0,24,17,21,15,0,0,0,0,0,0,0,0,13,3,16,26,0,0,0,0,26,16,3,13,0,0,0,0,16,26,16,26,0,0,0,0,3,13,3,13],[11,10,9,25,0,0,0,0,25,2,4,6,0,0,0,0,16,15,22,2,0,0,0,0,27,1,19,23,0,0,0,0,0,0,0,0,9,7,20,7,0,0,0,0,7,9,7,20,0,0,0,0,20,7,20,22,0,0,0,0,7,20,22,20],[0,28,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,27,0,28,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[0,28,28,28,0,0,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,27,28,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;
 

C7×C22.58C24 in GAP, Magma, Sage, TeX 

C_7\times C_2^2._{58}C_2^4
 
% in TeX
 
G:=Group("C7xC2^2.58C2^4");
 
// GroupNames label
 
G:=SmallGroup(448,1347);
 
// by ID
 
G=gap.SmallGroup(448,1347);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,784,1597,1576,4790,3579,1192,9635,1690,416]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f,g|a^7=b^2=c^2=1,d^2=g^2=b,e^2=f^2=c,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,a*g=g*a,b*c=c*b,e*d*e^-1=b*d=d*b,g*e*g^-1=b*e=e*b,b*f=f*b,b*g=g*b,f*d*f^-1=c*d=d*c,c*e=e*c,c*f=f*c,c*g=g*c,g*d*g^-1=b*c*d,f*e*f^-1=b*c*e,f*g=g*f>;
 
// generators/relations
 

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