direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: C7×C42.2C22, C4⋊C4.1C28, C14.25C4≀C2, C8⋊C4.3C14, (C2×C28).446D4, C42.2(C2×C14), C42.C2.1C14, (C4×C28).242C22, C14.11(C4.10D4), C2.7(C7×C4≀C2), (C7×C4⋊C4).3C4, (C2×C4).98(C7×D4), (C7×C8⋊C4).8C2, (C2×C4).10(C2×C28), (C2×C28).177(C2×C4), C2.3(C7×C4.10D4), (C7×C42.C2).8C2, C22.38(C7×C22⋊C4), (C2×C14).125(C22⋊C4), SmallGroup(448,134)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×C42.2C22
G = < a,b,c,d,e | a7=b4=c4=1, d2=c, e2=c2, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, dbd-1=bc2, ebe-1=b-1, cd=dc, ece-1=b2c-1, ede-1=b-1c2d >
Subgroups: 98 in 60 conjugacy classes, 30 normal (14 characteristic)
C1, C2, C2, C4, C22, C7, C8, C2×C4, C2×C4, C2×C4, C14, C14, C42, C4⋊C4, C4⋊C4, C2×C8, C28, C2×C14, C8⋊C4, C42.C2, C56, C2×C28, C2×C28, C2×C28, C42.2C22, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×C56, C7×C8⋊C4, C7×C42.C2, C7×C42.2C22
Quotients: C1, C2, C4, C22, C7, C2×C4, D4, C14, C22⋊C4, C28, C2×C14, C4.10D4, C4≀C2, C2×C28, C7×D4, C42.2C22, C7×C22⋊C4, C7×C4.10D4, C7×C4≀C2, C7×C42.2C22
►Regular action on 448 points
Generators in S448
(1 63 55 47 39 31 23)(2 64 56 48 40 32 24)(3 57 49 41 33 25 17)(4 58 50 42 34 26 18)(5 59 51 43 35 27 19)(6 60 52 44 36 28 20)(7 61 53 45 37 29 21)(8 62 54 46 38 30 22)(9 329 321 313 305 297 289)(10 330 322 314 306 298 290)(11 331 323 315 307 299 291)(12 332 324 316 308 300 292)(13 333 325 317 309 301 293)(14 334 326 318 310 302 294)(15 335 327 319 311 303 295)(16 336 328 320 312 304 296)(65 113 105 97 89 81 73)(66 114 106 98 90 82 74)(67 115 107 99 91 83 75)(68 116 108 100 92 84 76)(69 117 109 101 93 85 77)(70 118 110 102 94 86 78)(71 119 111 103 95 87 79)(72 120 112 104 96 88 80)(121 169 161 153 145 137 129)(122 170 162 154 146 138 130)(123 171 163 155 147 139 131)(124 172 164 156 148 140 132)(125 173 165 157 149 141 133)(126 174 166 158 150 142 134)(127 175 167 159 151 143 135)(128 176 168 160 152 144 136)(177 232 217 209 201 193 185)(178 225 218 210 202 194 186)(179 226 219 211 203 195 187)(180 227 220 212 204 196 188)(181 228 221 213 205 197 189)(182 229 222 214 206 198 190)(183 230 223 215 207 199 191)(184 231 224 216 208 200 192)(233 281 273 265 257 249 241)(234 282 274 266 258 250 242)(235 283 275 267 259 251 243)(236 284 276 268 260 252 244)(237 285 277 269 261 253 245)(238 286 278 270 262 254 246)(239 287 279 271 263 255 247)(240 288 280 272 264 256 248)(337 385 377 369 361 353 345)(338 386 378 370 362 354 346)(339 387 379 371 363 355 347)(340 388 380 372 364 356 348)(341 389 381 373 365 357 349)(342 390 382 374 366 358 350)(343 391 383 375 367 359 351)(344 392 384 376 368 360 352)(393 441 433 425 417 409 401)(394 442 434 426 418 410 402)(395 443 435 427 419 411 403)(396 444 436 428 420 412 404)(397 445 437 429 421 413 405)(398 446 438 430 422 414 406)(399 447 439 431 423 415 407)(400 448 440 432 424 416 408)
(1 127 343 239)(2 124 344 236)(3 121 337 233)(4 126 338 238)(5 123 339 235)(6 128 340 240)(7 125 341 237)(8 122 342 234)(9 441 232 113)(10 446 225 118)(11 443 226 115)(12 448 227 120)(13 445 228 117)(14 442 229 114)(15 447 230 119)(16 444 231 116)(17 129 345 241)(18 134 346 246)(19 131 347 243)(20 136 348 248)(21 133 349 245)(22 130 350 242)(23 135 351 247)(24 132 352 244)(25 137 353 249)(26 142 354 254)(27 139 355 251)(28 144 356 256)(29 141 357 253)(30 138 358 250)(31 143 359 255)(32 140 360 252)(33 145 361 257)(34 150 362 262)(35 147 363 259)(36 152 364 264)(37 149 365 261)(38 146 366 258)(39 151 367 263)(40 148 368 260)(41 153 369 265)(42 158 370 270)(43 155 371 267)(44 160 372 272)(45 157 373 269)(46 154 374 266)(47 159 375 271)(48 156 376 268)(49 161 377 273)(50 166 378 278)(51 163 379 275)(52 168 380 280)(53 165 381 277)(54 162 382 274)(55 167 383 279)(56 164 384 276)(57 169 385 281)(58 174 386 286)(59 171 387 283)(60 176 388 288)(61 173 389 285)(62 170 390 282)(63 175 391 287)(64 172 392 284)(65 289 393 177)(66 294 394 182)(67 291 395 179)(68 296 396 184)(69 293 397 181)(70 290 398 178)(71 295 399 183)(72 292 400 180)(73 297 401 185)(74 302 402 190)(75 299 403 187)(76 304 404 192)(77 301 405 189)(78 298 406 186)(79 303 407 191)(80 300 408 188)(81 305 409 193)(82 310 410 198)(83 307 411 195)(84 312 412 200)(85 309 413 197)(86 306 414 194)(87 311 415 199)(88 308 416 196)(89 313 417 201)(90 318 418 206)(91 315 419 203)(92 320 420 208)(93 317 421 205)(94 314 422 202)(95 319 423 207)(96 316 424 204)(97 321 425 209)(98 326 426 214)(99 323 427 211)(100 328 428 216)(101 325 429 213)(102 322 430 210)(103 327 431 215)(104 324 432 212)(105 329 433 217)(106 334 434 222)(107 331 435 219)(108 336 436 224)(109 333 437 221)(110 330 438 218)(111 335 439 223)(112 332 440 220)
(1 3 5 7)(2 4 6 8)(9 11 13 15)(10 12 14 16)(17 19 21 23)(18 20 22 24)(25 27 29 31)(26 28 30 32)(33 35 37 39)(34 36 38 40)(41 43 45 47)(42 44 46 48)(49 51 53 55)(50 52 54 56)(57 59 61 63)(58 60 62 64)(65 67 69 71)(66 68 70 72)(73 75 77 79)(74 76 78 80)(81 83 85 87)(82 84 86 88)(89 91 93 95)(90 92 94 96)(97 99 101 103)(98 100 102 104)(105 107 109 111)(106 108 110 112)(113 115 117 119)(114 116 118 120)(121 123 125 127)(122 124 126 128)(129 131 133 135)(130 132 134 136)(137 139 141 143)(138 140 142 144)(145 147 149 151)(146 148 150 152)(153 155 157 159)(154 156 158 160)(161 163 165 167)(162 164 166 168)(169 171 173 175)(170 172 174 176)(177 179 181 183)(178 180 182 184)(185 187 189 191)(186 188 190 192)(193 195 197 199)(194 196 198 200)(201 203 205 207)(202 204 206 208)(209 211 213 215)(210 212 214 216)(217 219 221 223)(218 220 222 224)(225 227 229 231)(226 228 230 232)(233 235 237 239)(234 236 238 240)(241 243 245 247)(242 244 246 248)(249 251 253 255)(250 252 254 256)(257 259 261 263)(258 260 262 264)(265 267 269 271)(266 268 270 272)(273 275 277 279)(274 276 278 280)(281 283 285 287)(282 284 286 288)(289 291 293 295)(290 292 294 296)(297 299 301 303)(298 300 302 304)(305 307 309 311)(306 308 310 312)(313 315 317 319)(314 316 318 320)(321 323 325 327)(322 324 326 328)(329 331 333 335)(330 332 334 336)(337 339 341 343)(338 340 342 344)(345 347 349 351)(346 348 350 352)(353 355 357 359)(354 356 358 360)(361 363 365 367)(362 364 366 368)(369 371 373 375)(370 372 374 376)(377 379 381 383)(378 380 382 384)(385 387 389 391)(386 388 390 392)(393 395 397 399)(394 396 398 400)(401 403 405 407)(402 404 406 408)(409 411 413 415)(410 412 414 416)(417 419 421 423)(418 420 422 424)(425 427 429 431)(426 428 430 432)(433 435 437 439)(434 436 438 440)(441 443 445 447)(442 444 446 448)
(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)
(1 399 5 395)(2 292 6 296)(3 69 7 65)(4 178 8 182)(9 281 13 285)(10 390 14 386)(11 175 15 171)(12 60 16 64)(17 77 21 73)(18 186 22 190)(19 403 23 407)(20 304 24 300)(25 85 29 81)(26 194 30 198)(27 411 31 415)(28 312 32 308)(33 93 37 89)(34 202 38 206)(35 419 39 423)(36 320 40 316)(41 101 45 97)(42 210 46 214)(43 427 47 431)(44 328 48 324)(49 109 53 105)(50 218 54 222)(51 435 55 439)(52 336 56 332)(57 117 61 113)(58 225 62 229)(59 443 63 447)(66 238 70 234)(67 343 71 339)(68 124 72 128)(74 246 78 242)(75 351 79 347)(76 132 80 136)(82 254 86 250)(83 359 87 355)(84 140 88 144)(90 262 94 258)(91 367 95 363)(92 148 96 152)(98 270 102 266)(99 375 103 371)(100 156 104 160)(106 278 110 274)(107 383 111 379)(108 164 112 168)(114 286 118 282)(115 391 119 387)(116 172 120 176)(121 181 125 177)(122 394 126 398)(123 291 127 295)(129 189 133 185)(130 402 134 406)(131 299 135 303)(137 197 141 193)(138 410 142 414)(139 307 143 311)(145 205 149 201)(146 418 150 422)(147 315 151 319)(153 213 157 209)(154 426 158 430)(155 323 159 327)(161 221 165 217)(162 434 166 438)(163 331 167 335)(169 228 173 232)(170 442 174 446)(179 239 183 235)(180 340 184 344)(187 247 191 243)(188 348 192 352)(195 255 199 251)(196 356 200 360)(203 263 207 259)(204 364 208 368)(211 271 215 267)(212 372 216 376)(219 279 223 275)(220 380 224 384)(226 287 230 283)(227 388 231 392)(233 293 237 289)(236 400 240 396)(241 301 245 297)(244 408 248 404)(249 309 253 305)(252 416 256 412)(257 317 261 313)(260 424 264 420)(265 325 269 321)(268 432 272 428)(273 333 277 329)(276 440 280 436)(284 448 288 444)(290 342 294 338)(298 350 302 346)(306 358 310 354)(314 366 318 362)(322 374 326 370)(330 382 334 378)(337 397 341 393)(345 405 349 401)(353 413 357 409)(361 421 365 417)(369 429 373 425)(377 437 381 433)(385 445 389 441)
G:=sub<Sym(448)| (1,63,55,47,39,31,23)(2,64,56,48,40,32,24)(3,57,49,41,33,25,17)(4,58,50,42,34,26,18)(5,59,51,43,35,27,19)(6,60,52,44,36,28,20)(7,61,53,45,37,29,21)(8,62,54,46,38,30,22)(9,329,321,313,305,297,289)(10,330,322,314,306,298,290)(11,331,323,315,307,299,291)(12,332,324,316,308,300,292)(13,333,325,317,309,301,293)(14,334,326,318,310,302,294)(15,335,327,319,311,303,295)(16,336,328,320,312,304,296)(65,113,105,97,89,81,73)(66,114,106,98,90,82,74)(67,115,107,99,91,83,75)(68,116,108,100,92,84,76)(69,117,109,101,93,85,77)(70,118,110,102,94,86,78)(71,119,111,103,95,87,79)(72,120,112,104,96,88,80)(121,169,161,153,145,137,129)(122,170,162,154,146,138,130)(123,171,163,155,147,139,131)(124,172,164,156,148,140,132)(125,173,165,157,149,141,133)(126,174,166,158,150,142,134)(127,175,167,159,151,143,135)(128,176,168,160,152,144,136)(177,232,217,209,201,193,185)(178,225,218,210,202,194,186)(179,226,219,211,203,195,187)(180,227,220,212,204,196,188)(181,228,221,213,205,197,189)(182,229,222,214,206,198,190)(183,230,223,215,207,199,191)(184,231,224,216,208,200,192)(233,281,273,265,257,249,241)(234,282,274,266,258,250,242)(235,283,275,267,259,251,243)(236,284,276,268,260,252,244)(237,285,277,269,261,253,245)(238,286,278,270,262,254,246)(239,287,279,271,263,255,247)(240,288,280,272,264,256,248)(337,385,377,369,361,353,345)(338,386,378,370,362,354,346)(339,387,379,371,363,355,347)(340,388,380,372,364,356,348)(341,389,381,373,365,357,349)(342,390,382,374,366,358,350)(343,391,383,375,367,359,351)(344,392,384,376,368,360,352)(393,441,433,425,417,409,401)(394,442,434,426,418,410,402)(395,443,435,427,419,411,403)(396,444,436,428,420,412,404)(397,445,437,429,421,413,405)(398,446,438,430,422,414,406)(399,447,439,431,423,415,407)(400,448,440,432,424,416,408), (1,127,343,239)(2,124,344,236)(3,121,337,233)(4,126,338,238)(5,123,339,235)(6,128,340,240)(7,125,341,237)(8,122,342,234)(9,441,232,113)(10,446,225,118)(11,443,226,115)(12,448,227,120)(13,445,228,117)(14,442,229,114)(15,447,230,119)(16,444,231,116)(17,129,345,241)(18,134,346,246)(19,131,347,243)(20,136,348,248)(21,133,349,245)(22,130,350,242)(23,135,351,247)(24,132,352,244)(25,137,353,249)(26,142,354,254)(27,139,355,251)(28,144,356,256)(29,141,357,253)(30,138,358,250)(31,143,359,255)(32,140,360,252)(33,145,361,257)(34,150,362,262)(35,147,363,259)(36,152,364,264)(37,149,365,261)(38,146,366,258)(39,151,367,263)(40,148,368,260)(41,153,369,265)(42,158,370,270)(43,155,371,267)(44,160,372,272)(45,157,373,269)(46,154,374,266)(47,159,375,271)(48,156,376,268)(49,161,377,273)(50,166,378,278)(51,163,379,275)(52,168,380,280)(53,165,381,277)(54,162,382,274)(55,167,383,279)(56,164,384,276)(57,169,385,281)(58,174,386,286)(59,171,387,283)(60,176,388,288)(61,173,389,285)(62,170,390,282)(63,175,391,287)(64,172,392,284)(65,289,393,177)(66,294,394,182)(67,291,395,179)(68,296,396,184)(69,293,397,181)(70,290,398,178)(71,295,399,183)(72,292,400,180)(73,297,401,185)(74,302,402,190)(75,299,403,187)(76,304,404,192)(77,301,405,189)(78,298,406,186)(79,303,407,191)(80,300,408,188)(81,305,409,193)(82,310,410,198)(83,307,411,195)(84,312,412,200)(85,309,413,197)(86,306,414,194)(87,311,415,199)(88,308,416,196)(89,313,417,201)(90,318,418,206)(91,315,419,203)(92,320,420,208)(93,317,421,205)(94,314,422,202)(95,319,423,207)(96,316,424,204)(97,321,425,209)(98,326,426,214)(99,323,427,211)(100,328,428,216)(101,325,429,213)(102,322,430,210)(103,327,431,215)(104,324,432,212)(105,329,433,217)(106,334,434,222)(107,331,435,219)(108,336,436,224)(109,333,437,221)(110,330,438,218)(111,335,439,223)(112,332,440,220), (1,3,5,7)(2,4,6,8)(9,11,13,15)(10,12,14,16)(17,19,21,23)(18,20,22,24)(25,27,29,31)(26,28,30,32)(33,35,37,39)(34,36,38,40)(41,43,45,47)(42,44,46,48)(49,51,53,55)(50,52,54,56)(57,59,61,63)(58,60,62,64)(65,67,69,71)(66,68,70,72)(73,75,77,79)(74,76,78,80)(81,83,85,87)(82,84,86,88)(89,91,93,95)(90,92,94,96)(97,99,101,103)(98,100,102,104)(105,107,109,111)(106,108,110,112)(113,115,117,119)(114,116,118,120)(121,123,125,127)(122,124,126,128)(129,131,133,135)(130,132,134,136)(137,139,141,143)(138,140,142,144)(145,147,149,151)(146,148,150,152)(153,155,157,159)(154,156,158,160)(161,163,165,167)(162,164,166,168)(169,171,173,175)(170,172,174,176)(177,179,181,183)(178,180,182,184)(185,187,189,191)(186,188,190,192)(193,195,197,199)(194,196,198,200)(201,203,205,207)(202,204,206,208)(209,211,213,215)(210,212,214,216)(217,219,221,223)(218,220,222,224)(225,227,229,231)(226,228,230,232)(233,235,237,239)(234,236,238,240)(241,243,245,247)(242,244,246,248)(249,251,253,255)(250,252,254,256)(257,259,261,263)(258,260,262,264)(265,267,269,271)(266,268,270,272)(273,275,277,279)(274,276,278,280)(281,283,285,287)(282,284,286,288)(289,291,293,295)(290,292,294,296)(297,299,301,303)(298,300,302,304)(305,307,309,311)(306,308,310,312)(313,315,317,319)(314,316,318,320)(321,323,325,327)(322,324,326,328)(329,331,333,335)(330,332,334,336)(337,339,341,343)(338,340,342,344)(345,347,349,351)(346,348,350,352)(353,355,357,359)(354,356,358,360)(361,363,365,367)(362,364,366,368)(369,371,373,375)(370,372,374,376)(377,379,381,383)(378,380,382,384)(385,387,389,391)(386,388,390,392)(393,395,397,399)(394,396,398,400)(401,403,405,407)(402,404,406,408)(409,411,413,415)(410,412,414,416)(417,419,421,423)(418,420,422,424)(425,427,429,431)(426,428,430,432)(433,435,437,439)(434,436,438,440)(441,443,445,447)(442,444,446,448), (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), (1,399,5,395)(2,292,6,296)(3,69,7,65)(4,178,8,182)(9,281,13,285)(10,390,14,386)(11,175,15,171)(12,60,16,64)(17,77,21,73)(18,186,22,190)(19,403,23,407)(20,304,24,300)(25,85,29,81)(26,194,30,198)(27,411,31,415)(28,312,32,308)(33,93,37,89)(34,202,38,206)(35,419,39,423)(36,320,40,316)(41,101,45,97)(42,210,46,214)(43,427,47,431)(44,328,48,324)(49,109,53,105)(50,218,54,222)(51,435,55,439)(52,336,56,332)(57,117,61,113)(58,225,62,229)(59,443,63,447)(66,238,70,234)(67,343,71,339)(68,124,72,128)(74,246,78,242)(75,351,79,347)(76,132,80,136)(82,254,86,250)(83,359,87,355)(84,140,88,144)(90,262,94,258)(91,367,95,363)(92,148,96,152)(98,270,102,266)(99,375,103,371)(100,156,104,160)(106,278,110,274)(107,383,111,379)(108,164,112,168)(114,286,118,282)(115,391,119,387)(116,172,120,176)(121,181,125,177)(122,394,126,398)(123,291,127,295)(129,189,133,185)(130,402,134,406)(131,299,135,303)(137,197,141,193)(138,410,142,414)(139,307,143,311)(145,205,149,201)(146,418,150,422)(147,315,151,319)(153,213,157,209)(154,426,158,430)(155,323,159,327)(161,221,165,217)(162,434,166,438)(163,331,167,335)(169,228,173,232)(170,442,174,446)(179,239,183,235)(180,340,184,344)(187,247,191,243)(188,348,192,352)(195,255,199,251)(196,356,200,360)(203,263,207,259)(204,364,208,368)(211,271,215,267)(212,372,216,376)(219,279,223,275)(220,380,224,384)(226,287,230,283)(227,388,231,392)(233,293,237,289)(236,400,240,396)(241,301,245,297)(244,408,248,404)(249,309,253,305)(252,416,256,412)(257,317,261,313)(260,424,264,420)(265,325,269,321)(268,432,272,428)(273,333,277,329)(276,440,280,436)(284,448,288,444)(290,342,294,338)(298,350,302,346)(306,358,310,354)(314,366,318,362)(322,374,326,370)(330,382,334,378)(337,397,341,393)(345,405,349,401)(353,413,357,409)(361,421,365,417)(369,429,373,425)(377,437,381,433)(385,445,389,441)>;
G:=Group( (1,63,55,47,39,31,23)(2,64,56,48,40,32,24)(3,57,49,41,33,25,17)(4,58,50,42,34,26,18)(5,59,51,43,35,27,19)(6,60,52,44,36,28,20)(7,61,53,45,37,29,21)(8,62,54,46,38,30,22)(9,329,321,313,305,297,289)(10,330,322,314,306,298,290)(11,331,323,315,307,299,291)(12,332,324,316,308,300,292)(13,333,325,317,309,301,293)(14,334,326,318,310,302,294)(15,335,327,319,311,303,295)(16,336,328,320,312,304,296)(65,113,105,97,89,81,73)(66,114,106,98,90,82,74)(67,115,107,99,91,83,75)(68,116,108,100,92,84,76)(69,117,109,101,93,85,77)(70,118,110,102,94,86,78)(71,119,111,103,95,87,79)(72,120,112,104,96,88,80)(121,169,161,153,145,137,129)(122,170,162,154,146,138,130)(123,171,163,155,147,139,131)(124,172,164,156,148,140,132)(125,173,165,157,149,141,133)(126,174,166,158,150,142,134)(127,175,167,159,151,143,135)(128,176,168,160,152,144,136)(177,232,217,209,201,193,185)(178,225,218,210,202,194,186)(179,226,219,211,203,195,187)(180,227,220,212,204,196,188)(181,228,221,213,205,197,189)(182,229,222,214,206,198,190)(183,230,223,215,207,199,191)(184,231,224,216,208,200,192)(233,281,273,265,257,249,241)(234,282,274,266,258,250,242)(235,283,275,267,259,251,243)(236,284,276,268,260,252,244)(237,285,277,269,261,253,245)(238,286,278,270,262,254,246)(239,287,279,271,263,255,247)(240,288,280,272,264,256,248)(337,385,377,369,361,353,345)(338,386,378,370,362,354,346)(339,387,379,371,363,355,347)(340,388,380,372,364,356,348)(341,389,381,373,365,357,349)(342,390,382,374,366,358,350)(343,391,383,375,367,359,351)(344,392,384,376,368,360,352)(393,441,433,425,417,409,401)(394,442,434,426,418,410,402)(395,443,435,427,419,411,403)(396,444,436,428,420,412,404)(397,445,437,429,421,413,405)(398,446,438,430,422,414,406)(399,447,439,431,423,415,407)(400,448,440,432,424,416,408), (1,127,343,239)(2,124,344,236)(3,121,337,233)(4,126,338,238)(5,123,339,235)(6,128,340,240)(7,125,341,237)(8,122,342,234)(9,441,232,113)(10,446,225,118)(11,443,226,115)(12,448,227,120)(13,445,228,117)(14,442,229,114)(15,447,230,119)(16,444,231,116)(17,129,345,241)(18,134,346,246)(19,131,347,243)(20,136,348,248)(21,133,349,245)(22,130,350,242)(23,135,351,247)(24,132,352,244)(25,137,353,249)(26,142,354,254)(27,139,355,251)(28,144,356,256)(29,141,357,253)(30,138,358,250)(31,143,359,255)(32,140,360,252)(33,145,361,257)(34,150,362,262)(35,147,363,259)(36,152,364,264)(37,149,365,261)(38,146,366,258)(39,151,367,263)(40,148,368,260)(41,153,369,265)(42,158,370,270)(43,155,371,267)(44,160,372,272)(45,157,373,269)(46,154,374,266)(47,159,375,271)(48,156,376,268)(49,161,377,273)(50,166,378,278)(51,163,379,275)(52,168,380,280)(53,165,381,277)(54,162,382,274)(55,167,383,279)(56,164,384,276)(57,169,385,281)(58,174,386,286)(59,171,387,283)(60,176,388,288)(61,173,389,285)(62,170,390,282)(63,175,391,287)(64,172,392,284)(65,289,393,177)(66,294,394,182)(67,291,395,179)(68,296,396,184)(69,293,397,181)(70,290,398,178)(71,295,399,183)(72,292,400,180)(73,297,401,185)(74,302,402,190)(75,299,403,187)(76,304,404,192)(77,301,405,189)(78,298,406,186)(79,303,407,191)(80,300,408,188)(81,305,409,193)(82,310,410,198)(83,307,411,195)(84,312,412,200)(85,309,413,197)(86,306,414,194)(87,311,415,199)(88,308,416,196)(89,313,417,201)(90,318,418,206)(91,315,419,203)(92,320,420,208)(93,317,421,205)(94,314,422,202)(95,319,423,207)(96,316,424,204)(97,321,425,209)(98,326,426,214)(99,323,427,211)(100,328,428,216)(101,325,429,213)(102,322,430,210)(103,327,431,215)(104,324,432,212)(105,329,433,217)(106,334,434,222)(107,331,435,219)(108,336,436,224)(109,333,437,221)(110,330,438,218)(111,335,439,223)(112,332,440,220), (1,3,5,7)(2,4,6,8)(9,11,13,15)(10,12,14,16)(17,19,21,23)(18,20,22,24)(25,27,29,31)(26,28,30,32)(33,35,37,39)(34,36,38,40)(41,43,45,47)(42,44,46,48)(49,51,53,55)(50,52,54,56)(57,59,61,63)(58,60,62,64)(65,67,69,71)(66,68,70,72)(73,75,77,79)(74,76,78,80)(81,83,85,87)(82,84,86,88)(89,91,93,95)(90,92,94,96)(97,99,101,103)(98,100,102,104)(105,107,109,111)(106,108,110,112)(113,115,117,119)(114,116,118,120)(121,123,125,127)(122,124,126,128)(129,131,133,135)(130,132,134,136)(137,139,141,143)(138,140,142,144)(145,147,149,151)(146,148,150,152)(153,155,157,159)(154,156,158,160)(161,163,165,167)(162,164,166,168)(169,171,173,175)(170,172,174,176)(177,179,181,183)(178,180,182,184)(185,187,189,191)(186,188,190,192)(193,195,197,199)(194,196,198,200)(201,203,205,207)(202,204,206,208)(209,211,213,215)(210,212,214,216)(217,219,221,223)(218,220,222,224)(225,227,229,231)(226,228,230,232)(233,235,237,239)(234,236,238,240)(241,243,245,247)(242,244,246,248)(249,251,253,255)(250,252,254,256)(257,259,261,263)(258,260,262,264)(265,267,269,271)(266,268,270,272)(273,275,277,279)(274,276,278,280)(281,283,285,287)(282,284,286,288)(289,291,293,295)(290,292,294,296)(297,299,301,303)(298,300,302,304)(305,307,309,311)(306,308,310,312)(313,315,317,319)(314,316,318,320)(321,323,325,327)(322,324,326,328)(329,331,333,335)(330,332,334,336)(337,339,341,343)(338,340,342,344)(345,347,349,351)(346,348,350,352)(353,355,357,359)(354,356,358,360)(361,363,365,367)(362,364,366,368)(369,371,373,375)(370,372,374,376)(377,379,381,383)(378,380,382,384)(385,387,389,391)(386,388,390,392)(393,395,397,399)(394,396,398,400)(401,403,405,407)(402,404,406,408)(409,411,413,415)(410,412,414,416)(417,419,421,423)(418,420,422,424)(425,427,429,431)(426,428,430,432)(433,435,437,439)(434,436,438,440)(441,443,445,447)(442,444,446,448), (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), (1,399,5,395)(2,292,6,296)(3,69,7,65)(4,178,8,182)(9,281,13,285)(10,390,14,386)(11,175,15,171)(12,60,16,64)(17,77,21,73)(18,186,22,190)(19,403,23,407)(20,304,24,300)(25,85,29,81)(26,194,30,198)(27,411,31,415)(28,312,32,308)(33,93,37,89)(34,202,38,206)(35,419,39,423)(36,320,40,316)(41,101,45,97)(42,210,46,214)(43,427,47,431)(44,328,48,324)(49,109,53,105)(50,218,54,222)(51,435,55,439)(52,336,56,332)(57,117,61,113)(58,225,62,229)(59,443,63,447)(66,238,70,234)(67,343,71,339)(68,124,72,128)(74,246,78,242)(75,351,79,347)(76,132,80,136)(82,254,86,250)(83,359,87,355)(84,140,88,144)(90,262,94,258)(91,367,95,363)(92,148,96,152)(98,270,102,266)(99,375,103,371)(100,156,104,160)(106,278,110,274)(107,383,111,379)(108,164,112,168)(114,286,118,282)(115,391,119,387)(116,172,120,176)(121,181,125,177)(122,394,126,398)(123,291,127,295)(129,189,133,185)(130,402,134,406)(131,299,135,303)(137,197,141,193)(138,410,142,414)(139,307,143,311)(145,205,149,201)(146,418,150,422)(147,315,151,319)(153,213,157,209)(154,426,158,430)(155,323,159,327)(161,221,165,217)(162,434,166,438)(163,331,167,335)(169,228,173,232)(170,442,174,446)(179,239,183,235)(180,340,184,344)(187,247,191,243)(188,348,192,352)(195,255,199,251)(196,356,200,360)(203,263,207,259)(204,364,208,368)(211,271,215,267)(212,372,216,376)(219,279,223,275)(220,380,224,384)(226,287,230,283)(227,388,231,392)(233,293,237,289)(236,400,240,396)(241,301,245,297)(244,408,248,404)(249,309,253,305)(252,416,256,412)(257,317,261,313)(260,424,264,420)(265,325,269,321)(268,432,272,428)(273,333,277,329)(276,440,280,436)(284,448,288,444)(290,342,294,338)(298,350,302,346)(306,358,310,354)(314,366,318,362)(322,374,326,370)(330,382,334,378)(337,397,341,393)(345,405,349,401)(353,413,357,409)(361,421,365,417)(369,429,373,425)(377,437,381,433)(385,445,389,441) );
G=PermutationGroup([[(1,63,55,47,39,31,23),(2,64,56,48,40,32,24),(3,57,49,41,33,25,17),(4,58,50,42,34,26,18),(5,59,51,43,35,27,19),(6,60,52,44,36,28,20),(7,61,53,45,37,29,21),(8,62,54,46,38,30,22),(9,329,321,313,305,297,289),(10,330,322,314,306,298,290),(11,331,323,315,307,299,291),(12,332,324,316,308,300,292),(13,333,325,317,309,301,293),(14,334,326,318,310,302,294),(15,335,327,319,311,303,295),(16,336,328,320,312,304,296),(65,113,105,97,89,81,73),(66,114,106,98,90,82,74),(67,115,107,99,91,83,75),(68,116,108,100,92,84,76),(69,117,109,101,93,85,77),(70,118,110,102,94,86,78),(71,119,111,103,95,87,79),(72,120,112,104,96,88,80),(121,169,161,153,145,137,129),(122,170,162,154,146,138,130),(123,171,163,155,147,139,131),(124,172,164,156,148,140,132),(125,173,165,157,149,141,133),(126,174,166,158,150,142,134),(127,175,167,159,151,143,135),(128,176,168,160,152,144,136),(177,232,217,209,201,193,185),(178,225,218,210,202,194,186),(179,226,219,211,203,195,187),(180,227,220,212,204,196,188),(181,228,221,213,205,197,189),(182,229,222,214,206,198,190),(183,230,223,215,207,199,191),(184,231,224,216,208,200,192),(233,281,273,265,257,249,241),(234,282,274,266,258,250,242),(235,283,275,267,259,251,243),(236,284,276,268,260,252,244),(237,285,277,269,261,253,245),(238,286,278,270,262,254,246),(239,287,279,271,263,255,247),(240,288,280,272,264,256,248),(337,385,377,369,361,353,345),(338,386,378,370,362,354,346),(339,387,379,371,363,355,347),(340,388,380,372,364,356,348),(341,389,381,373,365,357,349),(342,390,382,374,366,358,350),(343,391,383,375,367,359,351),(344,392,384,376,368,360,352),(393,441,433,425,417,409,401),(394,442,434,426,418,410,402),(395,443,435,427,419,411,403),(396,444,436,428,420,412,404),(397,445,437,429,421,413,405),(398,446,438,430,422,414,406),(399,447,439,431,423,415,407),(400,448,440,432,424,416,408)], [(1,127,343,239),(2,124,344,236),(3,121,337,233),(4,126,338,238),(5,123,339,235),(6,128,340,240),(7,125,341,237),(8,122,342,234),(9,441,232,113),(10,446,225,118),(11,443,226,115),(12,448,227,120),(13,445,228,117),(14,442,229,114),(15,447,230,119),(16,444,231,116),(17,129,345,241),(18,134,346,246),(19,131,347,243),(20,136,348,248),(21,133,349,245),(22,130,350,242),(23,135,351,247),(24,132,352,244),(25,137,353,249),(26,142,354,254),(27,139,355,251),(28,144,356,256),(29,141,357,253),(30,138,358,250),(31,143,359,255),(32,140,360,252),(33,145,361,257),(34,150,362,262),(35,147,363,259),(36,152,364,264),(37,149,365,261),(38,146,366,258),(39,151,367,263),(40,148,368,260),(41,153,369,265),(42,158,370,270),(43,155,371,267),(44,160,372,272),(45,157,373,269),(46,154,374,266),(47,159,375,271),(48,156,376,268),(49,161,377,273),(50,166,378,278),(51,163,379,275),(52,168,380,280),(53,165,381,277),(54,162,382,274),(55,167,383,279),(56,164,384,276),(57,169,385,281),(58,174,386,286),(59,171,387,283),(60,176,388,288),(61,173,389,285),(62,170,390,282),(63,175,391,287),(64,172,392,284),(65,289,393,177),(66,294,394,182),(67,291,395,179),(68,296,396,184),(69,293,397,181),(70,290,398,178),(71,295,399,183),(72,292,400,180),(73,297,401,185),(74,302,402,190),(75,299,403,187),(76,304,404,192),(77,301,405,189),(78,298,406,186),(79,303,407,191),(80,300,408,188),(81,305,409,193),(82,310,410,198),(83,307,411,195),(84,312,412,200),(85,309,413,197),(86,306,414,194),(87,311,415,199),(88,308,416,196),(89,313,417,201),(90,318,418,206),(91,315,419,203),(92,320,420,208),(93,317,421,205),(94,314,422,202),(95,319,423,207),(96,316,424,204),(97,321,425,209),(98,326,426,214),(99,323,427,211),(100,328,428,216),(101,325,429,213),(102,322,430,210),(103,327,431,215),(104,324,432,212),(105,329,433,217),(106,334,434,222),(107,331,435,219),(108,336,436,224),(109,333,437,221),(110,330,438,218),(111,335,439,223),(112,332,440,220)], [(1,3,5,7),(2,4,6,8),(9,11,13,15),(10,12,14,16),(17,19,21,23),(18,20,22,24),(25,27,29,31),(26,28,30,32),(33,35,37,39),(34,36,38,40),(41,43,45,47),(42,44,46,48),(49,51,53,55),(50,52,54,56),(57,59,61,63),(58,60,62,64),(65,67,69,71),(66,68,70,72),(73,75,77,79),(74,76,78,80),(81,83,85,87),(82,84,86,88),(89,91,93,95),(90,92,94,96),(97,99,101,103),(98,100,102,104),(105,107,109,111),(106,108,110,112),(113,115,117,119),(114,116,118,120),(121,123,125,127),(122,124,126,128),(129,131,133,135),(130,132,134,136),(137,139,141,143),(138,140,142,144),(145,147,149,151),(146,148,150,152),(153,155,157,159),(154,156,158,160),(161,163,165,167),(162,164,166,168),(169,171,173,175),(170,172,174,176),(177,179,181,183),(178,180,182,184),(185,187,189,191),(186,188,190,192),(193,195,197,199),(194,196,198,200),(201,203,205,207),(202,204,206,208),(209,211,213,215),(210,212,214,216),(217,219,221,223),(218,220,222,224),(225,227,229,231),(226,228,230,232),(233,235,237,239),(234,236,238,240),(241,243,245,247),(242,244,246,248),(249,251,253,255),(250,252,254,256),(257,259,261,263),(258,260,262,264),(265,267,269,271),(266,268,270,272),(273,275,277,279),(274,276,278,280),(281,283,285,287),(282,284,286,288),(289,291,293,295),(290,292,294,296),(297,299,301,303),(298,300,302,304),(305,307,309,311),(306,308,310,312),(313,315,317,319),(314,316,318,320),(321,323,325,327),(322,324,326,328),(329,331,333,335),(330,332,334,336),(337,339,341,343),(338,340,342,344),(345,347,349,351),(346,348,350,352),(353,355,357,359),(354,356,358,360),(361,363,365,367),(362,364,366,368),(369,371,373,375),(370,372,374,376),(377,379,381,383),(378,380,382,384),(385,387,389,391),(386,388,390,392),(393,395,397,399),(394,396,398,400),(401,403,405,407),(402,404,406,408),(409,411,413,415),(410,412,414,416),(417,419,421,423),(418,420,422,424),(425,427,429,431),(426,428,430,432),(433,435,437,439),(434,436,438,440),(441,443,445,447),(442,444,446,448)], [(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)], [(1,399,5,395),(2,292,6,296),(3,69,7,65),(4,178,8,182),(9,281,13,285),(10,390,14,386),(11,175,15,171),(12,60,16,64),(17,77,21,73),(18,186,22,190),(19,403,23,407),(20,304,24,300),(25,85,29,81),(26,194,30,198),(27,411,31,415),(28,312,32,308),(33,93,37,89),(34,202,38,206),(35,419,39,423),(36,320,40,316),(41,101,45,97),(42,210,46,214),(43,427,47,431),(44,328,48,324),(49,109,53,105),(50,218,54,222),(51,435,55,439),(52,336,56,332),(57,117,61,113),(58,225,62,229),(59,443,63,447),(66,238,70,234),(67,343,71,339),(68,124,72,128),(74,246,78,242),(75,351,79,347),(76,132,80,136),(82,254,86,250),(83,359,87,355),(84,140,88,144),(90,262,94,258),(91,367,95,363),(92,148,96,152),(98,270,102,266),(99,375,103,371),(100,156,104,160),(106,278,110,274),(107,383,111,379),(108,164,112,168),(114,286,118,282),(115,391,119,387),(116,172,120,176),(121,181,125,177),(122,394,126,398),(123,291,127,295),(129,189,133,185),(130,402,134,406),(131,299,135,303),(137,197,141,193),(138,410,142,414),(139,307,143,311),(145,205,149,201),(146,418,150,422),(147,315,151,319),(153,213,157,209),(154,426,158,430),(155,323,159,327),(161,221,165,217),(162,434,166,438),(163,331,167,335),(169,228,173,232),(170,442,174,446),(179,239,183,235),(180,340,184,344),(187,247,191,243),(188,348,192,352),(195,255,199,251),(196,356,200,360),(203,263,207,259),(204,364,208,368),(211,271,215,267),(212,372,216,376),(219,279,223,275),(220,380,224,384),(226,287,230,283),(227,388,231,392),(233,293,237,289),(236,400,240,396),(241,301,245,297),(244,408,248,404),(249,309,253,305),(252,416,256,412),(257,317,261,313),(260,424,264,420),(265,325,269,321),(268,432,272,428),(273,333,277,329),(276,440,280,436),(284,448,288,444),(290,342,294,338),(298,350,302,346),(306,358,310,354),(314,366,318,362),(322,374,326,370),(330,382,334,378),(337,397,341,393),(345,405,349,401),(353,413,357,409),(361,421,365,417),(369,429,373,425),(377,437,381,433),(385,445,389,441)]])
133 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 7A | ··· | 7F | 8A | ··· | 8H | 14A | ··· | 14R | 28A | ··· | 28X | 28Y | ··· | 28AD | 28AE | ··· | 28AP | 56A | ··· | 56AV |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | ··· | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 8 | 8 | 1 | ··· | 1 | 4 | ··· | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
133 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | - | |||||||||
| image | C1 | C2 | C2 | C4 | C7 | C14 | C14 | C28 | D4 | C4≀C2 | C7×D4 | C7×C4≀C2 | C4.10D4 | C7×C4.10D4 |
| kernel | C7×C42.2C22 | C7×C8⋊C4 | C7×C42.C2 | C7×C4⋊C4 | C42.2C22 | C8⋊C4 | C42.C2 | C4⋊C4 | C2×C28 | C14 | C2×C4 | C2 | C14 | C2 |
| # reps | 1 | 2 | 1 | 4 | 6 | 12 | 6 | 24 | 2 | 8 | 12 | 48 | 1 | 6 |
Matrix representation of C7×C42.2C22 ►in GL4(𝔽113) generated by
| 106 | 0 | 0 | 0 |
| 0 | 106 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 15 | 0 | 0 |
| 15 | 0 | 0 | 0 |
| 0 | 0 | 112 | 111 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 15 |
| 106 | 8 | 0 | 0 |
| 8 | 106 | 0 | 0 |
| 0 | 0 | 74 | 15 |
| 0 | 0 | 103 | 39 |
| 98 | 87 | 0 | 0 |
| 26 | 15 | 0 | 0 |
| 0 | 0 | 106 | 40 |
| 0 | 0 | 27 | 7 |
G:=sub<GL(4,GF(113))| [106,0,0,0,0,106,0,0,0,0,1,0,0,0,0,1],[0,15,0,0,15,0,0,0,0,0,112,1,0,0,111,1],[0,1,0,0,1,0,0,0,0,0,15,0,0,0,0,15],[106,8,0,0,8,106,0,0,0,0,74,103,0,0,15,39],[98,26,0,0,87,15,0,0,0,0,106,27,0,0,40,7] >;
C7×C42.2C22 in GAP, Magma, Sage, TeX
C_7\times C_4^2._2C_2^2
% in TeX
G:=Group("C7xC4^2.2C2^2"); // GroupNames label
G:=SmallGroup(448,134);
// by ID
G=gap.SmallGroup(448,134);
# by ID
G:=PCGroup([7,-2,-2,-7,-2,-2,-2,-2,392,421,792,3923,3538,248,6871,102]);
// Polycyclic
G:=Group<a,b,c,d,e|a^7=b^4=c^4=1,d^2=c,e^2=c^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,d*b*d^-1=b*c^2,e*b*e^-1=b^-1,c*d=d*c,e*c*e^-1=b^2*c^-1,e*d*e^-1=b^-1*c^2*d>;
// generators/relations