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, (C4×C28).297C22, (C2×C14).384C24, 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
Subgroups: 202 in 172 conjugacy classes, 142 normal (6 characteristic)
C1, C2 [×3], C4 [×15], C22, C7, C2×C4 [×15], C14 [×3], C42 [×5], C4⋊C4 [×30], C28 [×15], C2×C14, C42.C2 [×15], C2×C28 [×15], C22.58C24, C4×C28 [×5], C7×C4⋊C4 [×30], C7×C42.C2 [×15], C7×C22.58C24
Quotients:
C1, C2 [×15], C22 [×35], C7, C23 [×15], C14 [×15], C24, C2×C14 [×35], 2- (1+4) [×3], C22×C14 [×15], C22.58C24, C23×C14, C7×2- (1+4) [×3], C7×C22.58C24
Generators and relations
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 >
►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)(8 443)(9 444)(10 445)(11 446)(12 447)(13 448)(14 442)(15 22)(16 23)(17 24)(18 25)(19 26)(20 27)(21 28)(29 36)(30 37)(31 38)(32 39)(33 40)(34 41)(35 42)(50 74)(51 75)(52 76)(53 77)(54 71)(55 72)(56 73)(57 64)(58 65)(59 66)(60 67)(61 68)(62 69)(63 70)(78 102)(79 103)(80 104)(81 105)(82 99)(83 100)(84 101)(85 92)(86 93)(87 94)(88 95)(89 96)(90 97)(91 98)(106 130)(107 131)(108 132)(109 133)(110 127)(111 128)(112 129)(113 120)(114 121)(115 122)(116 123)(117 124)(118 125)(119 126)(134 158)(135 159)(136 160)(137 161)(138 155)(139 156)(140 157)(141 148)(142 149)(143 150)(144 151)(145 152)(146 153)(147 154)(162 186)(163 187)(164 188)(165 189)(166 183)(167 184)(168 185)(169 176)(170 177)(171 178)(172 179)(173 180)(174 181)(175 182)(190 214)(191 215)(192 216)(193 217)(194 211)(195 212)(196 213)(197 204)(198 205)(199 206)(200 207)(201 208)(202 209)(203 210)(218 242)(219 243)(220 244)(221 245)(222 239)(223 240)(224 241)(225 232)(226 233)(227 234)(228 235)(229 236)(230 237)(231 238)(246 270)(247 271)(248 272)(249 273)(250 267)(251 268)(252 269)(253 260)(254 261)(255 262)(256 263)(257 264)(258 265)(259 266)(274 298)(275 299)(276 300)(277 301)(278 295)(279 296)(280 297)(281 288)(282 289)(283 290)(284 291)(285 292)(286 293)(287 294)(302 326)(303 327)(304 328)(305 329)(306 323)(307 324)(308 325)(309 316)(310 317)(311 318)(312 319)(313 320)(314 321)(315 322)(330 354)(331 355)(332 356)(333 357)(334 351)(335 352)(336 353)(337 344)(338 345)(339 346)(340 347)(341 348)(342 349)(343 350)(358 382)(359 383)(360 384)(361 385)(362 379)(363 380)(364 381)(365 372)(366 373)(367 374)(368 375)(369 376)(370 377)(371 378)(386 410)(387 411)(388 412)(389 413)(390 407)(391 408)(392 409)(393 400)(394 401)(395 402)(396 403)(397 404)(398 405)(399 406)(414 438)(415 439)(416 440)(417 441)(418 435)(419 436)(420 437)(421 428)(422 429)(423 430)(424 431)(425 432)(426 433)(427 434)
(1 35)(2 29)(3 30)(4 31)(5 32)(6 33)(7 34)(8 18)(9 19)(10 20)(11 21)(12 15)(13 16)(14 17)(22 447)(23 448)(24 442)(25 443)(26 444)(27 445)(28 446)(36 48)(37 49)(38 43)(39 44)(40 45)(41 46)(42 47)(50 70)(51 64)(52 65)(53 66)(54 67)(55 68)(56 69)(57 75)(58 76)(59 77)(60 71)(61 72)(62 73)(63 74)(78 98)(79 92)(80 93)(81 94)(82 95)(83 96)(84 97)(85 103)(86 104)(87 105)(88 99)(89 100)(90 101)(91 102)(106 126)(107 120)(108 121)(109 122)(110 123)(111 124)(112 125)(113 131)(114 132)(115 133)(116 127)(117 128)(118 129)(119 130)(134 154)(135 148)(136 149)(137 150)(138 151)(139 152)(140 153)(141 159)(142 160)(143 161)(144 155)(145 156)(146 157)(147 158)(162 182)(163 176)(164 177)(165 178)(166 179)(167 180)(168 181)(169 187)(170 188)(171 189)(172 183)(173 184)(174 185)(175 186)(190 210)(191 204)(192 205)(193 206)(194 207)(195 208)(196 209)(197 215)(198 216)(199 217)(200 211)(201 212)(202 213)(203 214)(218 238)(219 232)(220 233)(221 234)(222 235)(223 236)(224 237)(225 243)(226 244)(227 245)(228 239)(229 240)(230 241)(231 242)(246 266)(247 260)(248 261)(249 262)(250 263)(251 264)(252 265)(253 271)(254 272)(255 273)(256 267)(257 268)(258 269)(259 270)(274 294)(275 288)(276 289)(277 290)(278 291)(279 292)(280 293)(281 299)(282 300)(283 301)(284 295)(285 296)(286 297)(287 298)(302 322)(303 316)(304 317)(305 318)(306 319)(307 320)(308 321)(309 327)(310 328)(311 329)(312 323)(313 324)(314 325)(315 326)(330 350)(331 344)(332 345)(333 346)(334 347)(335 348)(336 349)(337 355)(338 356)(339 357)(340 351)(341 352)(342 353)(343 354)(358 378)(359 372)(360 373)(361 374)(362 375)(363 376)(364 377)(365 383)(366 384)(367 385)(368 379)(369 380)(370 381)(371 382)(386 406)(387 400)(388 401)(389 402)(390 403)(391 404)(392 405)(393 411)(394 412)(395 413)(396 407)(397 408)(398 409)(399 410)(414 434)(415 428)(416 429)(417 430)(418 431)(419 432)(420 433)(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)(8 243 443 219)(9 244 444 220)(10 245 445 221)(11 239 446 222)(12 240 447 223)(13 241 448 224)(14 242 442 218)(15 229 22 236)(16 230 23 237)(17 231 24 238)(18 225 25 232)(19 226 26 233)(20 227 27 234)(21 228 28 235)(29 260 36 253)(30 261 37 254)(31 262 38 255)(32 263 39 256)(33 264 40 257)(34 265 41 258)(35 266 42 259)(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)(57 288 64 281)(58 289 65 282)(59 290 66 283)(60 291 67 284)(61 292 68 285)(62 293 69 286)(63 294 70 287)(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)(85 316 92 309)(86 317 93 310)(87 318 94 311)(88 319 95 312)(89 320 96 313)(90 321 97 314)(91 322 98 315)(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)(113 344 120 337)(114 345 121 338)(115 346 122 339)(116 347 123 340)(117 348 124 341)(118 349 125 342)(119 350 126 343)(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)(141 372 148 365)(142 373 149 366)(143 374 150 367)(144 375 151 368)(145 376 152 369)(146 377 153 370)(147 378 154 371)(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)(169 400 176 393)(170 401 177 394)(171 402 178 395)(172 403 179 396)(173 404 180 397)(174 405 181 398)(175 406 182 399)(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)(197 428 204 421)(198 429 205 422)(199 430 206 423)(200 431 207 424)(201 432 208 425)(202 433 209 426)(203 434 210 427)
(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)(8 331 18 344)(9 332 19 345)(10 333 20 346)(11 334 21 347)(12 335 15 348)(13 336 16 349)(14 330 17 350)(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)(36 135 48 148)(37 136 49 149)(38 137 43 150)(39 138 44 151)(40 139 45 152)(41 140 46 153)(42 134 47 154)(50 182 70 162)(51 176 64 163)(52 177 65 164)(53 178 66 165)(54 179 67 166)(55 180 68 167)(56 181 69 168)(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)(78 210 98 190)(79 204 92 191)(80 205 93 192)(81 206 94 193)(82 207 95 194)(83 208 96 195)(84 209 97 196)(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)(106 238 126 218)(107 232 120 219)(108 233 121 220)(109 234 122 221)(110 235 123 222)(111 236 124 223)(112 237 125 224)(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)(246 371 266 382)(247 365 260 383)(248 366 261 384)(249 367 262 385)(250 368 263 379)(251 369 264 380)(252 370 265 381)(253 359 271 372)(254 360 272 373)(255 361 273 374)(256 362 267 375)(257 363 268 376)(258 364 269 377)(259 358 270 378)(274 399 294 410)(275 393 288 411)(276 394 289 412)(277 395 290 413)(278 396 291 407)(279 397 292 408)(280 398 293 409)(281 387 299 400)(282 388 300 401)(283 389 301 402)(284 390 295 403)(285 391 296 404)(286 392 297 405)(287 386 298 406)(302 427 322 438)(303 421 316 439)(304 422 317 440)(305 423 318 441)(306 424 319 435)(307 425 320 436)(308 426 321 437)(309 415 327 428)(310 416 328 429)(311 417 329 430)(312 418 323 431)(313 419 324 432)(314 420 325 433)(315 414 326 434)
(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)(8 387 18 400)(9 388 19 401)(10 389 20 402)(11 390 21 403)(12 391 15 404)(13 392 16 405)(14 386 17 406)(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 79 48 92)(37 80 49 93)(38 81 43 94)(39 82 44 95)(40 83 45 96)(41 84 46 97)(42 78 47 98)(50 126 70 106)(51 120 64 107)(52 121 65 108)(53 122 66 109)(54 123 67 110)(55 124 68 111)(56 125 69 112)(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)(134 214 154 203)(135 215 148 197)(136 216 149 198)(137 217 150 199)(138 211 151 200)(139 212 152 201)(140 213 153 202)(141 204 159 191)(142 205 160 192)(143 206 161 193)(144 207 155 194)(145 208 156 195)(146 209 157 196)(147 210 158 190)(162 242 182 231)(163 243 176 225)(164 244 177 226)(165 245 178 227)(166 239 179 228)(167 240 180 229)(168 241 181 230)(169 232 187 219)(170 233 188 220)(171 234 189 221)(172 235 183 222)(173 236 184 223)(174 237 185 224)(175 238 186 218)(246 302 266 322)(247 303 260 316)(248 304 261 317)(249 305 262 318)(250 306 263 319)(251 307 264 320)(252 308 265 321)(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)(274 330 294 350)(275 331 288 344)(276 332 289 345)(277 333 290 346)(278 334 291 347)(279 335 292 348)(280 336 293 349)(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)(358 427 378 438)(359 421 372 439)(360 422 373 440)(361 423 374 441)(362 424 375 435)(363 425 376 436)(364 426 377 437)(365 415 383 428)(366 416 384 429)(367 417 385 430)(368 418 379 431)(369 419 380 432)(370 420 381 433)(371 414 382 434)
(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)(8 421 443 428)(9 422 444 429)(10 423 445 430)(11 424 446 431)(12 425 447 432)(13 426 448 433)(14 427 442 434)(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 64 36 57)(30 65 37 58)(31 66 38 59)(32 67 39 60)(33 68 40 61)(34 69 41 62)(35 70 42 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)(85 120 92 113)(86 121 93 114)(87 122 94 115)(88 123 95 116)(89 124 96 117)(90 125 97 118)(91 126 98 119)(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)(141 169 148 176)(142 170 149 177)(143 171 150 178)(144 172 151 179)(145 173 152 180)(146 174 153 181)(147 175 154 182)(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)(197 225 204 232)(198 226 205 233)(199 227 206 234)(200 228 207 235)(201 229 208 236)(202 230 209 237)(203 231 210 238)(246 294 270 287)(247 288 271 281)(248 289 272 282)(249 290 273 283)(250 291 267 284)(251 292 268 285)(252 293 269 286)(253 299 260 275)(254 300 261 276)(255 301 262 277)(256 295 263 278)(257 296 264 279)(258 297 265 280)(259 298 266 274)(302 350 326 343)(303 344 327 337)(304 345 328 338)(305 346 329 339)(306 347 323 340)(307 348 324 341)(308 349 325 342)(309 355 316 331)(310 356 317 332)(311 357 318 333)(312 351 319 334)(313 352 320 335)(314 353 321 336)(315 354 322 330)(358 399 382 406)(359 393 383 400)(360 394 384 401)(361 395 385 402)(362 396 379 403)(363 397 380 404)(364 398 381 405)(365 387 372 411)(366 388 373 412)(367 389 374 413)(368 390 375 407)(369 391 376 408)(370 392 377 409)(371 386 378 410)
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)(8,443)(9,444)(10,445)(11,446)(12,447)(13,448)(14,442)(15,22)(16,23)(17,24)(18,25)(19,26)(20,27)(21,28)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(50,74)(51,75)(52,76)(53,77)(54,71)(55,72)(56,73)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(78,102)(79,103)(80,104)(81,105)(82,99)(83,100)(84,101)(85,92)(86,93)(87,94)(88,95)(89,96)(90,97)(91,98)(106,130)(107,131)(108,132)(109,133)(110,127)(111,128)(112,129)(113,120)(114,121)(115,122)(116,123)(117,124)(118,125)(119,126)(134,158)(135,159)(136,160)(137,161)(138,155)(139,156)(140,157)(141,148)(142,149)(143,150)(144,151)(145,152)(146,153)(147,154)(162,186)(163,187)(164,188)(165,189)(166,183)(167,184)(168,185)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182)(190,214)(191,215)(192,216)(193,217)(194,211)(195,212)(196,213)(197,204)(198,205)(199,206)(200,207)(201,208)(202,209)(203,210)(218,242)(219,243)(220,244)(221,245)(222,239)(223,240)(224,241)(225,232)(226,233)(227,234)(228,235)(229,236)(230,237)(231,238)(246,270)(247,271)(248,272)(249,273)(250,267)(251,268)(252,269)(253,260)(254,261)(255,262)(256,263)(257,264)(258,265)(259,266)(274,298)(275,299)(276,300)(277,301)(278,295)(279,296)(280,297)(281,288)(282,289)(283,290)(284,291)(285,292)(286,293)(287,294)(302,326)(303,327)(304,328)(305,329)(306,323)(307,324)(308,325)(309,316)(310,317)(311,318)(312,319)(313,320)(314,321)(315,322)(330,354)(331,355)(332,356)(333,357)(334,351)(335,352)(336,353)(337,344)(338,345)(339,346)(340,347)(341,348)(342,349)(343,350)(358,382)(359,383)(360,384)(361,385)(362,379)(363,380)(364,381)(365,372)(366,373)(367,374)(368,375)(369,376)(370,377)(371,378)(386,410)(387,411)(388,412)(389,413)(390,407)(391,408)(392,409)(393,400)(394,401)(395,402)(396,403)(397,404)(398,405)(399,406)(414,438)(415,439)(416,440)(417,441)(418,435)(419,436)(420,437)(421,428)(422,429)(423,430)(424,431)(425,432)(426,433)(427,434), (1,35)(2,29)(3,30)(4,31)(5,32)(6,33)(7,34)(8,18)(9,19)(10,20)(11,21)(12,15)(13,16)(14,17)(22,447)(23,448)(24,442)(25,443)(26,444)(27,445)(28,446)(36,48)(37,49)(38,43)(39,44)(40,45)(41,46)(42,47)(50,70)(51,64)(52,65)(53,66)(54,67)(55,68)(56,69)(57,75)(58,76)(59,77)(60,71)(61,72)(62,73)(63,74)(78,98)(79,92)(80,93)(81,94)(82,95)(83,96)(84,97)(85,103)(86,104)(87,105)(88,99)(89,100)(90,101)(91,102)(106,126)(107,120)(108,121)(109,122)(110,123)(111,124)(112,125)(113,131)(114,132)(115,133)(116,127)(117,128)(118,129)(119,130)(134,154)(135,148)(136,149)(137,150)(138,151)(139,152)(140,153)(141,159)(142,160)(143,161)(144,155)(145,156)(146,157)(147,158)(162,182)(163,176)(164,177)(165,178)(166,179)(167,180)(168,181)(169,187)(170,188)(171,189)(172,183)(173,184)(174,185)(175,186)(190,210)(191,204)(192,205)(193,206)(194,207)(195,208)(196,209)(197,215)(198,216)(199,217)(200,211)(201,212)(202,213)(203,214)(218,238)(219,232)(220,233)(221,234)(222,235)(223,236)(224,237)(225,243)(226,244)(227,245)(228,239)(229,240)(230,241)(231,242)(246,266)(247,260)(248,261)(249,262)(250,263)(251,264)(252,265)(253,271)(254,272)(255,273)(256,267)(257,268)(258,269)(259,270)(274,294)(275,288)(276,289)(277,290)(278,291)(279,292)(280,293)(281,299)(282,300)(283,301)(284,295)(285,296)(286,297)(287,298)(302,322)(303,316)(304,317)(305,318)(306,319)(307,320)(308,321)(309,327)(310,328)(311,329)(312,323)(313,324)(314,325)(315,326)(330,350)(331,344)(332,345)(333,346)(334,347)(335,348)(336,349)(337,355)(338,356)(339,357)(340,351)(341,352)(342,353)(343,354)(358,378)(359,372)(360,373)(361,374)(362,375)(363,376)(364,377)(365,383)(366,384)(367,385)(368,379)(369,380)(370,381)(371,382)(386,406)(387,400)(388,401)(389,402)(390,403)(391,404)(392,405)(393,411)(394,412)(395,413)(396,407)(397,408)(398,409)(399,410)(414,434)(415,428)(416,429)(417,430)(418,431)(419,432)(420,433)(421,439)(422,440)(423,441)(424,435)(425,436)(426,437)(427,438), 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(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)(8,243,443,219)(9,244,444,220)(10,245,445,221)(11,239,446,222)(12,240,447,223)(13,241,448,224)(14,242,442,218)(15,229,22,236)(16,230,23,237)(17,231,24,238)(18,225,25,232)(19,226,26,233)(20,227,27,234)(21,228,28,235)(29,260,36,253)(30,261,37,254)(31,262,38,255)(32,263,39,256)(33,264,40,257)(34,265,41,258)(35,266,42,259)(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)(57,288,64,281)(58,289,65,282)(59,290,66,283)(60,291,67,284)(61,292,68,285)(62,293,69,286)(63,294,70,287)(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)(85,316,92,309)(86,317,93,310)(87,318,94,311)(88,319,95,312)(89,320,96,313)(90,321,97,314)(91,322,98,315)(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)(113,344,120,337)(114,345,121,338)(115,346,122,339)(116,347,123,340)(117,348,124,341)(118,349,125,342)(119,350,126,343)(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)(141,372,148,365)(142,373,149,366)(143,374,150,367)(144,375,151,368)(145,376,152,369)(146,377,153,370)(147,378,154,371)(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)(169,400,176,393)(170,401,177,394)(171,402,178,395)(172,403,179,396)(173,404,180,397)(174,405,181,398)(175,406,182,399)(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)(197,428,204,421)(198,429,205,422)(199,430,206,423)(200,431,207,424)(201,432,208,425)(202,433,209,426)(203,434,210,427), (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)(8,331,18,344)(9,332,19,345)(10,333,20,346)(11,334,21,347)(12,335,15,348)(13,336,16,349)(14,330,17,350)(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)(36,135,48,148)(37,136,49,149)(38,137,43,150)(39,138,44,151)(40,139,45,152)(41,140,46,153)(42,134,47,154)(50,182,70,162)(51,176,64,163)(52,177,65,164)(53,178,66,165)(54,179,67,166)(55,180,68,167)(56,181,69,168)(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)(78,210,98,190)(79,204,92,191)(80,205,93,192)(81,206,94,193)(82,207,95,194)(83,208,96,195)(84,209,97,196)(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)(106,238,126,218)(107,232,120,219)(108,233,121,220)(109,234,122,221)(110,235,123,222)(111,236,124,223)(112,237,125,224)(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)(246,371,266,382)(247,365,260,383)(248,366,261,384)(249,367,262,385)(250,368,263,379)(251,369,264,380)(252,370,265,381)(253,359,271,372)(254,360,272,373)(255,361,273,374)(256,362,267,375)(257,363,268,376)(258,364,269,377)(259,358,270,378)(274,399,294,410)(275,393,288,411)(276,394,289,412)(277,395,290,413)(278,396,291,407)(279,397,292,408)(280,398,293,409)(281,387,299,400)(282,388,300,401)(283,389,301,402)(284,390,295,403)(285,391,296,404)(286,392,297,405)(287,386,298,406)(302,427,322,438)(303,421,316,439)(304,422,317,440)(305,423,318,441)(306,424,319,435)(307,425,320,436)(308,426,321,437)(309,415,327,428)(310,416,328,429)(311,417,329,430)(312,418,323,431)(313,419,324,432)(314,420,325,433)(315,414,326,434), (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)(8,387,18,400)(9,388,19,401)(10,389,20,402)(11,390,21,403)(12,391,15,404)(13,392,16,405)(14,386,17,406)(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)(36,79,48,92)(37,80,49,93)(38,81,43,94)(39,82,44,95)(40,83,45,96)(41,84,46,97)(42,78,47,98)(50,126,70,106)(51,120,64,107)(52,121,65,108)(53,122,66,109)(54,123,67,110)(55,124,68,111)(56,125,69,112)(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)(134,214,154,203)(135,215,148,197)(136,216,149,198)(137,217,150,199)(138,211,151,200)(139,212,152,201)(140,213,153,202)(141,204,159,191)(142,205,160,192)(143,206,161,193)(144,207,155,194)(145,208,156,195)(146,209,157,196)(147,210,158,190)(162,242,182,231)(163,243,176,225)(164,244,177,226)(165,245,178,227)(166,239,179,228)(167,240,180,229)(168,241,181,230)(169,232,187,219)(170,233,188,220)(171,234,189,221)(172,235,183,222)(173,236,184,223)(174,237,185,224)(175,238,186,218)(246,302,266,322)(247,303,260,316)(248,304,261,317)(249,305,262,318)(250,306,263,319)(251,307,264,320)(252,308,265,321)(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)(274,330,294,350)(275,331,288,344)(276,332,289,345)(277,333,290,346)(278,334,291,347)(279,335,292,348)(280,336,293,349)(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)(358,427,378,438)(359,421,372,439)(360,422,373,440)(361,423,374,441)(362,424,375,435)(363,425,376,436)(364,426,377,437)(365,415,383,428)(366,416,384,429)(367,417,385,430)(368,418,379,431)(369,419,380,432)(370,420,381,433)(371,414,382,434), (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)(8,421,443,428)(9,422,444,429)(10,423,445,430)(11,424,446,431)(12,425,447,432)(13,426,448,433)(14,427,442,434)(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)(29,64,36,57)(30,65,37,58)(31,66,38,59)(32,67,39,60)(33,68,40,61)(34,69,41,62)(35,70,42,63)(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)(85,120,92,113)(86,121,93,114)(87,122,94,115)(88,123,95,116)(89,124,96,117)(90,125,97,118)(91,126,98,119)(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)(141,169,148,176)(142,170,149,177)(143,171,150,178)(144,172,151,179)(145,173,152,180)(146,174,153,181)(147,175,154,182)(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)(197,225,204,232)(198,226,205,233)(199,227,206,234)(200,228,207,235)(201,229,208,236)(202,230,209,237)(203,231,210,238)(246,294,270,287)(247,288,271,281)(248,289,272,282)(249,290,273,283)(250,291,267,284)(251,292,268,285)(252,293,269,286)(253,299,260,275)(254,300,261,276)(255,301,262,277)(256,295,263,278)(257,296,264,279)(258,297,265,280)(259,298,266,274)(302,350,326,343)(303,344,327,337)(304,345,328,338)(305,346,329,339)(306,347,323,340)(307,348,324,341)(308,349,325,342)(309,355,316,331)(310,356,317,332)(311,357,318,333)(312,351,319,334)(313,352,320,335)(314,353,321,336)(315,354,322,330)(358,399,382,406)(359,393,383,400)(360,394,384,401)(361,395,385,402)(362,396,379,403)(363,397,380,404)(364,398,381,405)(365,387,372,411)(366,388,373,412)(367,389,374,413)(368,390,375,407)(369,391,376,408)(370,392,377,409)(371,386,378,410) );
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),(8,443),(9,444),(10,445),(11,446),(12,447),(13,448),(14,442),(15,22),(16,23),(17,24),(18,25),(19,26),(20,27),(21,28),(29,36),(30,37),(31,38),(32,39),(33,40),(34,41),(35,42),(50,74),(51,75),(52,76),(53,77),(54,71),(55,72),(56,73),(57,64),(58,65),(59,66),(60,67),(61,68),(62,69),(63,70),(78,102),(79,103),(80,104),(81,105),(82,99),(83,100),(84,101),(85,92),(86,93),(87,94),(88,95),(89,96),(90,97),(91,98),(106,130),(107,131),(108,132),(109,133),(110,127),(111,128),(112,129),(113,120),(114,121),(115,122),(116,123),(117,124),(118,125),(119,126),(134,158),(135,159),(136,160),(137,161),(138,155),(139,156),(140,157),(141,148),(142,149),(143,150),(144,151),(145,152),(146,153),(147,154),(162,186),(163,187),(164,188),(165,189),(166,183),(167,184),(168,185),(169,176),(170,177),(171,178),(172,179),(173,180),(174,181),(175,182),(190,214),(191,215),(192,216),(193,217),(194,211),(195,212),(196,213),(197,204),(198,205),(199,206),(200,207),(201,208),(202,209),(203,210),(218,242),(219,243),(220,244),(221,245),(222,239),(223,240),(224,241),(225,232),(226,233),(227,234),(228,235),(229,236),(230,237),(231,238),(246,270),(247,271),(248,272),(249,273),(250,267),(251,268),(252,269),(253,260),(254,261),(255,262),(256,263),(257,264),(258,265),(259,266),(274,298),(275,299),(276,300),(277,301),(278,295),(279,296),(280,297),(281,288),(282,289),(283,290),(284,291),(285,292),(286,293),(287,294),(302,326),(303,327),(304,328),(305,329),(306,323),(307,324),(308,325),(309,316),(310,317),(311,318),(312,319),(313,320),(314,321),(315,322),(330,354),(331,355),(332,356),(333,357),(334,351),(335,352),(336,353),(337,344),(338,345),(339,346),(340,347),(341,348),(342,349),(343,350),(358,382),(359,383),(360,384),(361,385),(362,379),(363,380),(364,381),(365,372),(366,373),(367,374),(368,375),(369,376),(370,377),(371,378),(386,410),(387,411),(388,412),(389,413),(390,407),(391,408),(392,409),(393,400),(394,401),(395,402),(396,403),(397,404),(398,405),(399,406),(414,438),(415,439),(416,440),(417,441),(418,435),(419,436),(420,437),(421,428),(422,429),(423,430),(424,431),(425,432),(426,433),(427,434)], [(1,35),(2,29),(3,30),(4,31),(5,32),(6,33),(7,34),(8,18),(9,19),(10,20),(11,21),(12,15),(13,16),(14,17),(22,447),(23,448),(24,442),(25,443),(26,444),(27,445),(28,446),(36,48),(37,49),(38,43),(39,44),(40,45),(41,46),(42,47),(50,70),(51,64),(52,65),(53,66),(54,67),(55,68),(56,69),(57,75),(58,76),(59,77),(60,71),(61,72),(62,73),(63,74),(78,98),(79,92),(80,93),(81,94),(82,95),(83,96),(84,97),(85,103),(86,104),(87,105),(88,99),(89,100),(90,101),(91,102),(106,126),(107,120),(108,121),(109,122),(110,123),(111,124),(112,125),(113,131),(114,132),(115,133),(116,127),(117,128),(118,129),(119,130),(134,154),(135,148),(136,149),(137,150),(138,151),(139,152),(140,153),(141,159),(142,160),(143,161),(144,155),(145,156),(146,157),(147,158),(162,182),(163,176),(164,177),(165,178),(166,179),(167,180),(168,181),(169,187),(170,188),(171,189),(172,183),(173,184),(174,185),(175,186),(190,210),(191,204),(192,205),(193,206),(194,207),(195,208),(196,209),(197,215),(198,216),(199,217),(200,211),(201,212),(202,213),(203,214),(218,238),(219,232),(220,233),(221,234),(222,235),(223,236),(224,237),(225,243),(226,244),(227,245),(228,239),(229,240),(230,241),(231,242),(246,266),(247,260),(248,261),(249,262),(250,263),(251,264),(252,265),(253,271),(254,272),(255,273),(256,267),(257,268),(258,269),(259,270),(274,294),(275,288),(276,289),(277,290),(278,291),(279,292),(280,293),(281,299),(282,300),(283,301),(284,295),(285,296),(286,297),(287,298),(302,322),(303,316),(304,317),(305,318),(306,319),(307,320),(308,321),(309,327),(310,328),(311,329),(312,323),(313,324),(314,325),(315,326),(330,350),(331,344),(332,345),(333,346),(334,347),(335,348),(336,349),(337,355),(338,356),(339,357),(340,351),(341,352),(342,353),(343,354),(358,378),(359,372),(360,373),(361,374),(362,375),(363,376),(364,377),(365,383),(366,384),(367,385),(368,379),(369,380),(370,381),(371,382),(386,406),(387,400),(388,401),(389,402),(390,403),(391,404),(392,405),(393,411),(394,412),(395,413),(396,407),(397,408),(398,409),(399,410),(414,434),(415,428),(416,429),(417,430),(418,431),(419,432),(420,433),(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),(8,243,443,219),(9,244,444,220),(10,245,445,221),(11,239,446,222),(12,240,447,223),(13,241,448,224),(14,242,442,218),(15,229,22,236),(16,230,23,237),(17,231,24,238),(18,225,25,232),(19,226,26,233),(20,227,27,234),(21,228,28,235),(29,260,36,253),(30,261,37,254),(31,262,38,255),(32,263,39,256),(33,264,40,257),(34,265,41,258),(35,266,42,259),(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),(57,288,64,281),(58,289,65,282),(59,290,66,283),(60,291,67,284),(61,292,68,285),(62,293,69,286),(63,294,70,287),(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),(85,316,92,309),(86,317,93,310),(87,318,94,311),(88,319,95,312),(89,320,96,313),(90,321,97,314),(91,322,98,315),(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),(113,344,120,337),(114,345,121,338),(115,346,122,339),(116,347,123,340),(117,348,124,341),(118,349,125,342),(119,350,126,343),(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),(141,372,148,365),(142,373,149,366),(143,374,150,367),(144,375,151,368),(145,376,152,369),(146,377,153,370),(147,378,154,371),(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),(169,400,176,393),(170,401,177,394),(171,402,178,395),(172,403,179,396),(173,404,180,397),(174,405,181,398),(175,406,182,399),(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),(197,428,204,421),(198,429,205,422),(199,430,206,423),(200,431,207,424),(201,432,208,425),(202,433,209,426),(203,434,210,427)], [(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),(8,331,18,344),(9,332,19,345),(10,333,20,346),(11,334,21,347),(12,335,15,348),(13,336,16,349),(14,330,17,350),(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),(36,135,48,148),(37,136,49,149),(38,137,43,150),(39,138,44,151),(40,139,45,152),(41,140,46,153),(42,134,47,154),(50,182,70,162),(51,176,64,163),(52,177,65,164),(53,178,66,165),(54,179,67,166),(55,180,68,167),(56,181,69,168),(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),(78,210,98,190),(79,204,92,191),(80,205,93,192),(81,206,94,193),(82,207,95,194),(83,208,96,195),(84,209,97,196),(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),(106,238,126,218),(107,232,120,219),(108,233,121,220),(109,234,122,221),(110,235,123,222),(111,236,124,223),(112,237,125,224),(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),(246,371,266,382),(247,365,260,383),(248,366,261,384),(249,367,262,385),(250,368,263,379),(251,369,264,380),(252,370,265,381),(253,359,271,372),(254,360,272,373),(255,361,273,374),(256,362,267,375),(257,363,268,376),(258,364,269,377),(259,358,270,378),(274,399,294,410),(275,393,288,411),(276,394,289,412),(277,395,290,413),(278,396,291,407),(279,397,292,408),(280,398,293,409),(281,387,299,400),(282,388,300,401),(283,389,301,402),(284,390,295,403),(285,391,296,404),(286,392,297,405),(287,386,298,406),(302,427,322,438),(303,421,316,439),(304,422,317,440),(305,423,318,441),(306,424,319,435),(307,425,320,436),(308,426,321,437),(309,415,327,428),(310,416,328,429),(311,417,329,430),(312,418,323,431),(313,419,324,432),(314,420,325,433),(315,414,326,434)], [(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),(8,387,18,400),(9,388,19,401),(10,389,20,402),(11,390,21,403),(12,391,15,404),(13,392,16,405),(14,386,17,406),(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),(36,79,48,92),(37,80,49,93),(38,81,43,94),(39,82,44,95),(40,83,45,96),(41,84,46,97),(42,78,47,98),(50,126,70,106),(51,120,64,107),(52,121,65,108),(53,122,66,109),(54,123,67,110),(55,124,68,111),(56,125,69,112),(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),(134,214,154,203),(135,215,148,197),(136,216,149,198),(137,217,150,199),(138,211,151,200),(139,212,152,201),(140,213,153,202),(141,204,159,191),(142,205,160,192),(143,206,161,193),(144,207,155,194),(145,208,156,195),(146,209,157,196),(147,210,158,190),(162,242,182,231),(163,243,176,225),(164,244,177,226),(165,245,178,227),(166,239,179,228),(167,240,180,229),(168,241,181,230),(169,232,187,219),(170,233,188,220),(171,234,189,221),(172,235,183,222),(173,236,184,223),(174,237,185,224),(175,238,186,218),(246,302,266,322),(247,303,260,316),(248,304,261,317),(249,305,262,318),(250,306,263,319),(251,307,264,320),(252,308,265,321),(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),(274,330,294,350),(275,331,288,344),(276,332,289,345),(277,333,290,346),(278,334,291,347),(279,335,292,348),(280,336,293,349),(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),(358,427,378,438),(359,421,372,439),(360,422,373,440),(361,423,374,441),(362,424,375,435),(363,425,376,436),(364,426,377,437),(365,415,383,428),(366,416,384,429),(367,417,385,430),(368,418,379,431),(369,419,380,432),(370,420,381,433),(371,414,382,434)], [(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),(8,421,443,428),(9,422,444,429),(10,423,445,430),(11,424,446,431),(12,425,447,432),(13,426,448,433),(14,427,442,434),(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),(29,64,36,57),(30,65,37,58),(31,66,38,59),(32,67,39,60),(33,68,40,61),(34,69,41,62),(35,70,42,63),(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),(85,120,92,113),(86,121,93,114),(87,122,94,115),(88,123,95,116),(89,124,96,117),(90,125,97,118),(91,126,98,119),(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),(141,169,148,176),(142,170,149,177),(143,171,150,178),(144,172,151,179),(145,173,152,180),(146,174,153,181),(147,175,154,182),(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),(197,225,204,232),(198,226,205,233),(199,227,206,234),(200,228,207,235),(201,229,208,236),(202,230,209,237),(203,231,210,238),(246,294,270,287),(247,288,271,281),(248,289,272,282),(249,290,273,283),(250,291,267,284),(251,292,268,285),(252,293,269,286),(253,299,260,275),(254,300,261,276),(255,301,262,277),(256,295,263,278),(257,296,264,279),(258,297,265,280),(259,298,266,274),(302,350,326,343),(303,344,327,337),(304,345,328,338),(305,346,329,339),(306,347,323,340),(307,348,324,341),(308,349,325,342),(309,355,316,331),(310,356,317,332),(311,357,318,333),(312,351,319,334),(313,352,320,335),(314,353,321,336),(315,354,322,330),(358,399,382,406),(359,393,383,400),(360,394,384,401),(361,395,385,402),(362,396,379,403),(363,397,380,404),(364,398,381,405),(365,387,372,411),(366,388,373,412),(367,389,374,413),(368,390,375,407),(369,391,376,408),(370,392,377,409),(371,386,378,410)])
Matrix representation ►G ⊆ GL8(𝔽29)
| 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 | 21 | 11 | 24 | 0 | 0 | 0 | 0 |
| 27 | 14 | 23 | 17 | 0 | 0 | 0 | 0 |
| 19 | 21 | 25 | 21 | 0 | 0 | 0 | 0 |
| 2 | 0 | 27 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 26 | 16 | 3 |
| 0 | 0 | 0 | 0 | 3 | 16 | 26 | 13 |
| 0 | 0 | 0 | 0 | 16 | 3 | 16 | 3 |
| 0 | 0 | 0 | 0 | 26 | 13 | 26 | 13 |
| 11 | 25 | 16 | 27 | 0 | 0 | 0 | 0 |
| 10 | 2 | 15 | 1 | 0 | 0 | 0 | 0 |
| 9 | 4 | 22 | 19 | 0 | 0 | 0 | 0 |
| 25 | 6 | 2 | 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 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 28 | 1 | 1 | 27 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 28 | 1 | 1 | 27 | 0 | 0 | 0 | 0 |
| 28 | 0 | 1 | 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 |
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] >;
133 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | ··· | 4O | 7A | ··· | 7F | 14A | ··· | 14R | 28A | ··· | 28CL |
| order | 1 | 2 | 2 | 2 | 4 | ··· | 4 | 7 | ··· | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | ··· | 4 | 1 | ··· | 1 | 1 | ··· | 1 | 4 | ··· | 4 |
133 irreducible representations
| dim | 1 | 1 | 1 | 1 | 4 | 4 |
| type | + | + | - | |||
| image | C1 | C2 | C7 | C14 | 2- (1+4) | C7×2- (1+4) |
| kernel | C7×C22.58C24 | C7×C42.C2 | C22.58C24 | C42.C2 | C14 | C2 |
| # reps | 1 | 15 | 6 | 90 | 3 | 18 |
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
×
⋊
ℤ
𝔽
○
≀