direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C42.D7, C28.23C42, C42.5Dic7, C42.244D14, (C4×C28).20C4, C14⋊1(C8⋊C4), (C2×C42).2D7, C4.18(C4×Dic7), C14.14(C2×C42), (C22×C28).16C4, (C2×C14).22C42, (C22×C4).9Dic7, C28.134(C22×C4), (C2×C28).839C23, (C4×C28).343C22, (C22×C4).454D14, (C2×C14).24M4(2), C14.34(C2×M4(2)), C23.39(C2×Dic7), C22.19(C4×Dic7), C22.8(C4.Dic7), (C22×C28).551C22, C22.12(C22×Dic7), (C2×C7⋊C8)⋊12C4, C7⋊2(C2×C8⋊C4), C7⋊C8⋊26(C2×C4), (C2×C4×C28).26C2, C4.108(C2×C4×D7), C2.4(C2×C4×Dic7), (C2×C4).178(C4×D7), (C22×C7⋊C8).17C2, (C2×C28).275(C2×C4), C2.1(C2×C4.Dic7), (C2×C7⋊C8).309C22, (C2×C4).96(C2×Dic7), (C2×C4).781(C22×D7), (C22×C14).127(C2×C4), (C2×C14).168(C22×C4), SmallGroup(448,455)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C42.D7
G = < a,b,c,d,e | a2=b4=c4=d7=1, e2=c, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, ebe-1=bc2, cd=dc, ce=ec, ede-1=d-1 >
Subgroups: 324 in 146 conjugacy classes, 103 normal (17 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, C23, C14, C14, C42, C2×C8, C22×C4, C22×C4, C28, C28, C2×C14, C2×C14, C8⋊C4, C2×C42, C22×C8, C7⋊C8, C2×C28, C2×C28, C2×C28, C22×C14, C2×C8⋊C4, C2×C7⋊C8, C4×C28, C22×C28, C22×C28, C42.D7, C22×C7⋊C8, C2×C4×C28, C2×C42.D7
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C42, M4(2), C22×C4, Dic7, D14, C8⋊C4, C2×C42, C2×M4(2), C4×D7, C2×Dic7, C22×D7, C2×C8⋊C4, C4.Dic7, C4×Dic7, C2×C4×D7, C22×Dic7, C42.D7, C2×C4.Dic7, C2×C4×Dic7, C2×C42.D7
►Regular action on 448 points
Generators in S448
(1 287)(2 288)(3 281)(4 282)(5 283)(6 284)(7 285)(8 286)(9 114)(10 115)(11 116)(12 117)(13 118)(14 119)(15 120)(16 113)(17 385)(18 386)(19 387)(20 388)(21 389)(22 390)(23 391)(24 392)(25 427)(26 428)(27 429)(28 430)(29 431)(30 432)(31 425)(32 426)(33 418)(34 419)(35 420)(36 421)(37 422)(38 423)(39 424)(40 417)(41 248)(42 241)(43 242)(44 243)(45 244)(46 245)(47 246)(48 247)(49 363)(50 364)(51 365)(52 366)(53 367)(54 368)(55 361)(56 362)(57 323)(58 324)(59 325)(60 326)(61 327)(62 328)(63 321)(64 322)(65 396)(66 397)(67 398)(68 399)(69 400)(70 393)(71 394)(72 395)(73 142)(74 143)(75 144)(76 137)(77 138)(78 139)(79 140)(80 141)(81 405)(82 406)(83 407)(84 408)(85 401)(86 402)(87 403)(88 404)(89 159)(90 160)(91 153)(92 154)(93 155)(94 156)(95 157)(96 158)(97 439)(98 440)(99 433)(100 434)(101 435)(102 436)(103 437)(104 438)(105 442)(106 443)(107 444)(108 445)(109 446)(110 447)(111 448)(112 441)(121 269)(122 270)(123 271)(124 272)(125 265)(126 266)(127 267)(128 268)(129 277)(130 278)(131 279)(132 280)(133 273)(134 274)(135 275)(136 276)(145 300)(146 301)(147 302)(148 303)(149 304)(150 297)(151 298)(152 299)(161 232)(162 225)(163 226)(164 227)(165 228)(166 229)(167 230)(168 231)(169 190)(170 191)(171 192)(172 185)(173 186)(174 187)(175 188)(176 189)(177 349)(178 350)(179 351)(180 352)(181 345)(182 346)(183 347)(184 348)(193 316)(194 317)(195 318)(196 319)(197 320)(198 313)(199 314)(200 315)(201 354)(202 355)(203 356)(204 357)(205 358)(206 359)(207 360)(208 353)(209 220)(210 221)(211 222)(212 223)(213 224)(214 217)(215 218)(216 219)(233 338)(234 339)(235 340)(236 341)(237 342)(238 343)(239 344)(240 337)(249 294)(250 295)(251 296)(252 289)(253 290)(254 291)(255 292)(256 293)(257 332)(258 333)(259 334)(260 335)(261 336)(262 329)(263 330)(264 331)(305 412)(306 413)(307 414)(308 415)(309 416)(310 409)(311 410)(312 411)(369 384)(370 377)(371 378)(372 379)(373 380)(374 381)(375 382)(376 383)
(1 315 419 126)(2 320 420 123)(3 317 421 128)(4 314 422 125)(5 319 423 122)(6 316 424 127)(7 313 417 124)(8 318 418 121)(9 293 188 75)(10 290 189 80)(11 295 190 77)(12 292 191 74)(13 289 192 79)(14 294 185 76)(15 291 186 73)(16 296 187 78)(17 99 445 381)(18 104 446 378)(19 101 447 383)(20 98 448 380)(21 103 441 377)(22 100 442 382)(23 97 443 379)(24 102 444 384)(25 225 323 216)(26 230 324 213)(27 227 325 210)(28 232 326 215)(29 229 327 212)(30 226 328 209)(31 231 321 214)(32 228 322 211)(33 269 286 195)(34 266 287 200)(35 271 288 197)(36 268 281 194)(37 265 282 199)(38 270 283 196)(39 267 284 193)(40 272 285 198)(41 337 300 66)(42 342 301 71)(43 339 302 68)(44 344 303 65)(45 341 304 70)(46 338 297 67)(47 343 298 72)(48 340 299 69)(49 349 273 85)(50 346 274 82)(51 351 275 87)(52 348 276 84)(53 345 277 81)(54 350 278 86)(55 347 279 83)(56 352 280 88)(57 219 427 162)(58 224 428 167)(59 221 429 164)(60 218 430 161)(61 223 431 166)(62 220 432 163)(63 217 425 168)(64 222 426 165)(89 334 205 311)(90 331 206 308)(91 336 207 305)(92 333 208 310)(93 330 201 307)(94 335 202 312)(95 332 203 309)(96 329 204 306)(105 375 390 434)(106 372 391 439)(107 369 392 436)(108 374 385 433)(109 371 386 438)(110 376 387 435)(111 373 388 440)(112 370 389 437)(113 251 174 139)(114 256 175 144)(115 253 176 141)(116 250 169 138)(117 255 170 143)(118 252 171 140)(119 249 172 137)(120 254 173 142)(129 405 367 181)(130 402 368 178)(131 407 361 183)(132 404 362 180)(133 401 363 177)(134 406 364 182)(135 403 365 179)(136 408 366 184)(145 397 248 240)(146 394 241 237)(147 399 242 234)(148 396 243 239)(149 393 244 236)(150 398 245 233)(151 395 246 238)(152 400 247 235)(153 261 360 412)(154 258 353 409)(155 263 354 414)(156 260 355 411)(157 257 356 416)(158 262 357 413)(159 259 358 410)(160 264 359 415)
(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)
(1 365 255 263 150 427 389)(2 390 428 151 264 256 366)(3 367 249 257 152 429 391)(4 392 430 145 258 250 368)(5 361 251 259 146 431 385)(6 386 432 147 260 252 362)(7 363 253 261 148 425 387)(8 388 426 149 262 254 364)(9 84 271 382 213 343 90)(10 91 344 214 383 272 85)(11 86 265 384 215 337 92)(12 93 338 216 377 266 87)(13 88 267 378 209 339 94)(14 95 340 210 379 268 81)(15 82 269 380 211 341 96)(16 89 342 212 381 270 83)(17 283 55 296 334 301 29)(18 30 302 335 289 56 284)(19 285 49 290 336 303 31)(20 32 304 329 291 50 286)(21 287 51 292 330 297 25)(22 26 298 331 293 52 288)(23 281 53 294 332 299 27)(24 28 300 333 295 54 282)(33 448 322 45 306 73 274)(34 275 74 307 46 323 441)(35 442 324 47 308 75 276)(36 277 76 309 48 325 443)(37 444 326 41 310 77 278)(38 279 78 311 42 327 445)(39 446 328 43 312 79 280)(40 273 80 305 44 321 447)(57 112 419 135 143 414 245)(58 246 415 144 136 420 105)(59 106 421 129 137 416 247)(60 248 409 138 130 422 107)(61 108 423 131 139 410 241)(62 242 411 140 132 424 109)(63 110 417 133 141 412 243)(64 244 413 142 134 418 111)(65 231 101 198 349 189 207)(66 208 190 350 199 102 232)(67 225 103 200 351 191 201)(68 202 192 352 193 104 226)(69 227 97 194 345 185 203)(70 204 186 346 195 98 228)(71 229 99 196 347 187 205)(72 206 188 348 197 100 230)(113 159 237 223 374 122 407)(114 408 123 375 224 238 160)(115 153 239 217 376 124 401)(116 402 125 369 218 240 154)(117 155 233 219 370 126 403)(118 404 127 371 220 234 156)(119 157 235 221 372 128 405)(120 406 121 373 222 236 158)(161 397 353 169 178 314 436)(162 437 315 179 170 354 398)(163 399 355 171 180 316 438)(164 439 317 181 172 356 400)(165 393 357 173 182 318 440)(166 433 319 183 174 358 394)(167 395 359 175 184 320 434)(168 435 313 177 176 360 396)
(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)
G:=sub<Sym(448)| (1,287)(2,288)(3,281)(4,282)(5,283)(6,284)(7,285)(8,286)(9,114)(10,115)(11,116)(12,117)(13,118)(14,119)(15,120)(16,113)(17,385)(18,386)(19,387)(20,388)(21,389)(22,390)(23,391)(24,392)(25,427)(26,428)(27,429)(28,430)(29,431)(30,432)(31,425)(32,426)(33,418)(34,419)(35,420)(36,421)(37,422)(38,423)(39,424)(40,417)(41,248)(42,241)(43,242)(44,243)(45,244)(46,245)(47,246)(48,247)(49,363)(50,364)(51,365)(52,366)(53,367)(54,368)(55,361)(56,362)(57,323)(58,324)(59,325)(60,326)(61,327)(62,328)(63,321)(64,322)(65,396)(66,397)(67,398)(68,399)(69,400)(70,393)(71,394)(72,395)(73,142)(74,143)(75,144)(76,137)(77,138)(78,139)(79,140)(80,141)(81,405)(82,406)(83,407)(84,408)(85,401)(86,402)(87,403)(88,404)(89,159)(90,160)(91,153)(92,154)(93,155)(94,156)(95,157)(96,158)(97,439)(98,440)(99,433)(100,434)(101,435)(102,436)(103,437)(104,438)(105,442)(106,443)(107,444)(108,445)(109,446)(110,447)(111,448)(112,441)(121,269)(122,270)(123,271)(124,272)(125,265)(126,266)(127,267)(128,268)(129,277)(130,278)(131,279)(132,280)(133,273)(134,274)(135,275)(136,276)(145,300)(146,301)(147,302)(148,303)(149,304)(150,297)(151,298)(152,299)(161,232)(162,225)(163,226)(164,227)(165,228)(166,229)(167,230)(168,231)(169,190)(170,191)(171,192)(172,185)(173,186)(174,187)(175,188)(176,189)(177,349)(178,350)(179,351)(180,352)(181,345)(182,346)(183,347)(184,348)(193,316)(194,317)(195,318)(196,319)(197,320)(198,313)(199,314)(200,315)(201,354)(202,355)(203,356)(204,357)(205,358)(206,359)(207,360)(208,353)(209,220)(210,221)(211,222)(212,223)(213,224)(214,217)(215,218)(216,219)(233,338)(234,339)(235,340)(236,341)(237,342)(238,343)(239,344)(240,337)(249,294)(250,295)(251,296)(252,289)(253,290)(254,291)(255,292)(256,293)(257,332)(258,333)(259,334)(260,335)(261,336)(262,329)(263,330)(264,331)(305,412)(306,413)(307,414)(308,415)(309,416)(310,409)(311,410)(312,411)(369,384)(370,377)(371,378)(372,379)(373,380)(374,381)(375,382)(376,383), (1,315,419,126)(2,320,420,123)(3,317,421,128)(4,314,422,125)(5,319,423,122)(6,316,424,127)(7,313,417,124)(8,318,418,121)(9,293,188,75)(10,290,189,80)(11,295,190,77)(12,292,191,74)(13,289,192,79)(14,294,185,76)(15,291,186,73)(16,296,187,78)(17,99,445,381)(18,104,446,378)(19,101,447,383)(20,98,448,380)(21,103,441,377)(22,100,442,382)(23,97,443,379)(24,102,444,384)(25,225,323,216)(26,230,324,213)(27,227,325,210)(28,232,326,215)(29,229,327,212)(30,226,328,209)(31,231,321,214)(32,228,322,211)(33,269,286,195)(34,266,287,200)(35,271,288,197)(36,268,281,194)(37,265,282,199)(38,270,283,196)(39,267,284,193)(40,272,285,198)(41,337,300,66)(42,342,301,71)(43,339,302,68)(44,344,303,65)(45,341,304,70)(46,338,297,67)(47,343,298,72)(48,340,299,69)(49,349,273,85)(50,346,274,82)(51,351,275,87)(52,348,276,84)(53,345,277,81)(54,350,278,86)(55,347,279,83)(56,352,280,88)(57,219,427,162)(58,224,428,167)(59,221,429,164)(60,218,430,161)(61,223,431,166)(62,220,432,163)(63,217,425,168)(64,222,426,165)(89,334,205,311)(90,331,206,308)(91,336,207,305)(92,333,208,310)(93,330,201,307)(94,335,202,312)(95,332,203,309)(96,329,204,306)(105,375,390,434)(106,372,391,439)(107,369,392,436)(108,374,385,433)(109,371,386,438)(110,376,387,435)(111,373,388,440)(112,370,389,437)(113,251,174,139)(114,256,175,144)(115,253,176,141)(116,250,169,138)(117,255,170,143)(118,252,171,140)(119,249,172,137)(120,254,173,142)(129,405,367,181)(130,402,368,178)(131,407,361,183)(132,404,362,180)(133,401,363,177)(134,406,364,182)(135,403,365,179)(136,408,366,184)(145,397,248,240)(146,394,241,237)(147,399,242,234)(148,396,243,239)(149,393,244,236)(150,398,245,233)(151,395,246,238)(152,400,247,235)(153,261,360,412)(154,258,353,409)(155,263,354,414)(156,260,355,411)(157,257,356,416)(158,262,357,413)(159,259,358,410)(160,264,359,415), (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), (1,365,255,263,150,427,389)(2,390,428,151,264,256,366)(3,367,249,257,152,429,391)(4,392,430,145,258,250,368)(5,361,251,259,146,431,385)(6,386,432,147,260,252,362)(7,363,253,261,148,425,387)(8,388,426,149,262,254,364)(9,84,271,382,213,343,90)(10,91,344,214,383,272,85)(11,86,265,384,215,337,92)(12,93,338,216,377,266,87)(13,88,267,378,209,339,94)(14,95,340,210,379,268,81)(15,82,269,380,211,341,96)(16,89,342,212,381,270,83)(17,283,55,296,334,301,29)(18,30,302,335,289,56,284)(19,285,49,290,336,303,31)(20,32,304,329,291,50,286)(21,287,51,292,330,297,25)(22,26,298,331,293,52,288)(23,281,53,294,332,299,27)(24,28,300,333,295,54,282)(33,448,322,45,306,73,274)(34,275,74,307,46,323,441)(35,442,324,47,308,75,276)(36,277,76,309,48,325,443)(37,444,326,41,310,77,278)(38,279,78,311,42,327,445)(39,446,328,43,312,79,280)(40,273,80,305,44,321,447)(57,112,419,135,143,414,245)(58,246,415,144,136,420,105)(59,106,421,129,137,416,247)(60,248,409,138,130,422,107)(61,108,423,131,139,410,241)(62,242,411,140,132,424,109)(63,110,417,133,141,412,243)(64,244,413,142,134,418,111)(65,231,101,198,349,189,207)(66,208,190,350,199,102,232)(67,225,103,200,351,191,201)(68,202,192,352,193,104,226)(69,227,97,194,345,185,203)(70,204,186,346,195,98,228)(71,229,99,196,347,187,205)(72,206,188,348,197,100,230)(113,159,237,223,374,122,407)(114,408,123,375,224,238,160)(115,153,239,217,376,124,401)(116,402,125,369,218,240,154)(117,155,233,219,370,126,403)(118,404,127,371,220,234,156)(119,157,235,221,372,128,405)(120,406,121,373,222,236,158)(161,397,353,169,178,314,436)(162,437,315,179,170,354,398)(163,399,355,171,180,316,438)(164,439,317,181,172,356,400)(165,393,357,173,182,318,440)(166,433,319,183,174,358,394)(167,395,359,175,184,320,434)(168,435,313,177,176,360,396), (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)>;
G:=Group( (1,287)(2,288)(3,281)(4,282)(5,283)(6,284)(7,285)(8,286)(9,114)(10,115)(11,116)(12,117)(13,118)(14,119)(15,120)(16,113)(17,385)(18,386)(19,387)(20,388)(21,389)(22,390)(23,391)(24,392)(25,427)(26,428)(27,429)(28,430)(29,431)(30,432)(31,425)(32,426)(33,418)(34,419)(35,420)(36,421)(37,422)(38,423)(39,424)(40,417)(41,248)(42,241)(43,242)(44,243)(45,244)(46,245)(47,246)(48,247)(49,363)(50,364)(51,365)(52,366)(53,367)(54,368)(55,361)(56,362)(57,323)(58,324)(59,325)(60,326)(61,327)(62,328)(63,321)(64,322)(65,396)(66,397)(67,398)(68,399)(69,400)(70,393)(71,394)(72,395)(73,142)(74,143)(75,144)(76,137)(77,138)(78,139)(79,140)(80,141)(81,405)(82,406)(83,407)(84,408)(85,401)(86,402)(87,403)(88,404)(89,159)(90,160)(91,153)(92,154)(93,155)(94,156)(95,157)(96,158)(97,439)(98,440)(99,433)(100,434)(101,435)(102,436)(103,437)(104,438)(105,442)(106,443)(107,444)(108,445)(109,446)(110,447)(111,448)(112,441)(121,269)(122,270)(123,271)(124,272)(125,265)(126,266)(127,267)(128,268)(129,277)(130,278)(131,279)(132,280)(133,273)(134,274)(135,275)(136,276)(145,300)(146,301)(147,302)(148,303)(149,304)(150,297)(151,298)(152,299)(161,232)(162,225)(163,226)(164,227)(165,228)(166,229)(167,230)(168,231)(169,190)(170,191)(171,192)(172,185)(173,186)(174,187)(175,188)(176,189)(177,349)(178,350)(179,351)(180,352)(181,345)(182,346)(183,347)(184,348)(193,316)(194,317)(195,318)(196,319)(197,320)(198,313)(199,314)(200,315)(201,354)(202,355)(203,356)(204,357)(205,358)(206,359)(207,360)(208,353)(209,220)(210,221)(211,222)(212,223)(213,224)(214,217)(215,218)(216,219)(233,338)(234,339)(235,340)(236,341)(237,342)(238,343)(239,344)(240,337)(249,294)(250,295)(251,296)(252,289)(253,290)(254,291)(255,292)(256,293)(257,332)(258,333)(259,334)(260,335)(261,336)(262,329)(263,330)(264,331)(305,412)(306,413)(307,414)(308,415)(309,416)(310,409)(311,410)(312,411)(369,384)(370,377)(371,378)(372,379)(373,380)(374,381)(375,382)(376,383), (1,315,419,126)(2,320,420,123)(3,317,421,128)(4,314,422,125)(5,319,423,122)(6,316,424,127)(7,313,417,124)(8,318,418,121)(9,293,188,75)(10,290,189,80)(11,295,190,77)(12,292,191,74)(13,289,192,79)(14,294,185,76)(15,291,186,73)(16,296,187,78)(17,99,445,381)(18,104,446,378)(19,101,447,383)(20,98,448,380)(21,103,441,377)(22,100,442,382)(23,97,443,379)(24,102,444,384)(25,225,323,216)(26,230,324,213)(27,227,325,210)(28,232,326,215)(29,229,327,212)(30,226,328,209)(31,231,321,214)(32,228,322,211)(33,269,286,195)(34,266,287,200)(35,271,288,197)(36,268,281,194)(37,265,282,199)(38,270,283,196)(39,267,284,193)(40,272,285,198)(41,337,300,66)(42,342,301,71)(43,339,302,68)(44,344,303,65)(45,341,304,70)(46,338,297,67)(47,343,298,72)(48,340,299,69)(49,349,273,85)(50,346,274,82)(51,351,275,87)(52,348,276,84)(53,345,277,81)(54,350,278,86)(55,347,279,83)(56,352,280,88)(57,219,427,162)(58,224,428,167)(59,221,429,164)(60,218,430,161)(61,223,431,166)(62,220,432,163)(63,217,425,168)(64,222,426,165)(89,334,205,311)(90,331,206,308)(91,336,207,305)(92,333,208,310)(93,330,201,307)(94,335,202,312)(95,332,203,309)(96,329,204,306)(105,375,390,434)(106,372,391,439)(107,369,392,436)(108,374,385,433)(109,371,386,438)(110,376,387,435)(111,373,388,440)(112,370,389,437)(113,251,174,139)(114,256,175,144)(115,253,176,141)(116,250,169,138)(117,255,170,143)(118,252,171,140)(119,249,172,137)(120,254,173,142)(129,405,367,181)(130,402,368,178)(131,407,361,183)(132,404,362,180)(133,401,363,177)(134,406,364,182)(135,403,365,179)(136,408,366,184)(145,397,248,240)(146,394,241,237)(147,399,242,234)(148,396,243,239)(149,393,244,236)(150,398,245,233)(151,395,246,238)(152,400,247,235)(153,261,360,412)(154,258,353,409)(155,263,354,414)(156,260,355,411)(157,257,356,416)(158,262,357,413)(159,259,358,410)(160,264,359,415), (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), (1,365,255,263,150,427,389)(2,390,428,151,264,256,366)(3,367,249,257,152,429,391)(4,392,430,145,258,250,368)(5,361,251,259,146,431,385)(6,386,432,147,260,252,362)(7,363,253,261,148,425,387)(8,388,426,149,262,254,364)(9,84,271,382,213,343,90)(10,91,344,214,383,272,85)(11,86,265,384,215,337,92)(12,93,338,216,377,266,87)(13,88,267,378,209,339,94)(14,95,340,210,379,268,81)(15,82,269,380,211,341,96)(16,89,342,212,381,270,83)(17,283,55,296,334,301,29)(18,30,302,335,289,56,284)(19,285,49,290,336,303,31)(20,32,304,329,291,50,286)(21,287,51,292,330,297,25)(22,26,298,331,293,52,288)(23,281,53,294,332,299,27)(24,28,300,333,295,54,282)(33,448,322,45,306,73,274)(34,275,74,307,46,323,441)(35,442,324,47,308,75,276)(36,277,76,309,48,325,443)(37,444,326,41,310,77,278)(38,279,78,311,42,327,445)(39,446,328,43,312,79,280)(40,273,80,305,44,321,447)(57,112,419,135,143,414,245)(58,246,415,144,136,420,105)(59,106,421,129,137,416,247)(60,248,409,138,130,422,107)(61,108,423,131,139,410,241)(62,242,411,140,132,424,109)(63,110,417,133,141,412,243)(64,244,413,142,134,418,111)(65,231,101,198,349,189,207)(66,208,190,350,199,102,232)(67,225,103,200,351,191,201)(68,202,192,352,193,104,226)(69,227,97,194,345,185,203)(70,204,186,346,195,98,228)(71,229,99,196,347,187,205)(72,206,188,348,197,100,230)(113,159,237,223,374,122,407)(114,408,123,375,224,238,160)(115,153,239,217,376,124,401)(116,402,125,369,218,240,154)(117,155,233,219,370,126,403)(118,404,127,371,220,234,156)(119,157,235,221,372,128,405)(120,406,121,373,222,236,158)(161,397,353,169,178,314,436)(162,437,315,179,170,354,398)(163,399,355,171,180,316,438)(164,439,317,181,172,356,400)(165,393,357,173,182,318,440)(166,433,319,183,174,358,394)(167,395,359,175,184,320,434)(168,435,313,177,176,360,396), (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) );
G=PermutationGroup([[(1,287),(2,288),(3,281),(4,282),(5,283),(6,284),(7,285),(8,286),(9,114),(10,115),(11,116),(12,117),(13,118),(14,119),(15,120),(16,113),(17,385),(18,386),(19,387),(20,388),(21,389),(22,390),(23,391),(24,392),(25,427),(26,428),(27,429),(28,430),(29,431),(30,432),(31,425),(32,426),(33,418),(34,419),(35,420),(36,421),(37,422),(38,423),(39,424),(40,417),(41,248),(42,241),(43,242),(44,243),(45,244),(46,245),(47,246),(48,247),(49,363),(50,364),(51,365),(52,366),(53,367),(54,368),(55,361),(56,362),(57,323),(58,324),(59,325),(60,326),(61,327),(62,328),(63,321),(64,322),(65,396),(66,397),(67,398),(68,399),(69,400),(70,393),(71,394),(72,395),(73,142),(74,143),(75,144),(76,137),(77,138),(78,139),(79,140),(80,141),(81,405),(82,406),(83,407),(84,408),(85,401),(86,402),(87,403),(88,404),(89,159),(90,160),(91,153),(92,154),(93,155),(94,156),(95,157),(96,158),(97,439),(98,440),(99,433),(100,434),(101,435),(102,436),(103,437),(104,438),(105,442),(106,443),(107,444),(108,445),(109,446),(110,447),(111,448),(112,441),(121,269),(122,270),(123,271),(124,272),(125,265),(126,266),(127,267),(128,268),(129,277),(130,278),(131,279),(132,280),(133,273),(134,274),(135,275),(136,276),(145,300),(146,301),(147,302),(148,303),(149,304),(150,297),(151,298),(152,299),(161,232),(162,225),(163,226),(164,227),(165,228),(166,229),(167,230),(168,231),(169,190),(170,191),(171,192),(172,185),(173,186),(174,187),(175,188),(176,189),(177,349),(178,350),(179,351),(180,352),(181,345),(182,346),(183,347),(184,348),(193,316),(194,317),(195,318),(196,319),(197,320),(198,313),(199,314),(200,315),(201,354),(202,355),(203,356),(204,357),(205,358),(206,359),(207,360),(208,353),(209,220),(210,221),(211,222),(212,223),(213,224),(214,217),(215,218),(216,219),(233,338),(234,339),(235,340),(236,341),(237,342),(238,343),(239,344),(240,337),(249,294),(250,295),(251,296),(252,289),(253,290),(254,291),(255,292),(256,293),(257,332),(258,333),(259,334),(260,335),(261,336),(262,329),(263,330),(264,331),(305,412),(306,413),(307,414),(308,415),(309,416),(310,409),(311,410),(312,411),(369,384),(370,377),(371,378),(372,379),(373,380),(374,381),(375,382),(376,383)], [(1,315,419,126),(2,320,420,123),(3,317,421,128),(4,314,422,125),(5,319,423,122),(6,316,424,127),(7,313,417,124),(8,318,418,121),(9,293,188,75),(10,290,189,80),(11,295,190,77),(12,292,191,74),(13,289,192,79),(14,294,185,76),(15,291,186,73),(16,296,187,78),(17,99,445,381),(18,104,446,378),(19,101,447,383),(20,98,448,380),(21,103,441,377),(22,100,442,382),(23,97,443,379),(24,102,444,384),(25,225,323,216),(26,230,324,213),(27,227,325,210),(28,232,326,215),(29,229,327,212),(30,226,328,209),(31,231,321,214),(32,228,322,211),(33,269,286,195),(34,266,287,200),(35,271,288,197),(36,268,281,194),(37,265,282,199),(38,270,283,196),(39,267,284,193),(40,272,285,198),(41,337,300,66),(42,342,301,71),(43,339,302,68),(44,344,303,65),(45,341,304,70),(46,338,297,67),(47,343,298,72),(48,340,299,69),(49,349,273,85),(50,346,274,82),(51,351,275,87),(52,348,276,84),(53,345,277,81),(54,350,278,86),(55,347,279,83),(56,352,280,88),(57,219,427,162),(58,224,428,167),(59,221,429,164),(60,218,430,161),(61,223,431,166),(62,220,432,163),(63,217,425,168),(64,222,426,165),(89,334,205,311),(90,331,206,308),(91,336,207,305),(92,333,208,310),(93,330,201,307),(94,335,202,312),(95,332,203,309),(96,329,204,306),(105,375,390,434),(106,372,391,439),(107,369,392,436),(108,374,385,433),(109,371,386,438),(110,376,387,435),(111,373,388,440),(112,370,389,437),(113,251,174,139),(114,256,175,144),(115,253,176,141),(116,250,169,138),(117,255,170,143),(118,252,171,140),(119,249,172,137),(120,254,173,142),(129,405,367,181),(130,402,368,178),(131,407,361,183),(132,404,362,180),(133,401,363,177),(134,406,364,182),(135,403,365,179),(136,408,366,184),(145,397,248,240),(146,394,241,237),(147,399,242,234),(148,396,243,239),(149,393,244,236),(150,398,245,233),(151,395,246,238),(152,400,247,235),(153,261,360,412),(154,258,353,409),(155,263,354,414),(156,260,355,411),(157,257,356,416),(158,262,357,413),(159,259,358,410),(160,264,359,415)], [(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)], [(1,365,255,263,150,427,389),(2,390,428,151,264,256,366),(3,367,249,257,152,429,391),(4,392,430,145,258,250,368),(5,361,251,259,146,431,385),(6,386,432,147,260,252,362),(7,363,253,261,148,425,387),(8,388,426,149,262,254,364),(9,84,271,382,213,343,90),(10,91,344,214,383,272,85),(11,86,265,384,215,337,92),(12,93,338,216,377,266,87),(13,88,267,378,209,339,94),(14,95,340,210,379,268,81),(15,82,269,380,211,341,96),(16,89,342,212,381,270,83),(17,283,55,296,334,301,29),(18,30,302,335,289,56,284),(19,285,49,290,336,303,31),(20,32,304,329,291,50,286),(21,287,51,292,330,297,25),(22,26,298,331,293,52,288),(23,281,53,294,332,299,27),(24,28,300,333,295,54,282),(33,448,322,45,306,73,274),(34,275,74,307,46,323,441),(35,442,324,47,308,75,276),(36,277,76,309,48,325,443),(37,444,326,41,310,77,278),(38,279,78,311,42,327,445),(39,446,328,43,312,79,280),(40,273,80,305,44,321,447),(57,112,419,135,143,414,245),(58,246,415,144,136,420,105),(59,106,421,129,137,416,247),(60,248,409,138,130,422,107),(61,108,423,131,139,410,241),(62,242,411,140,132,424,109),(63,110,417,133,141,412,243),(64,244,413,142,134,418,111),(65,231,101,198,349,189,207),(66,208,190,350,199,102,232),(67,225,103,200,351,191,201),(68,202,192,352,193,104,226),(69,227,97,194,345,185,203),(70,204,186,346,195,98,228),(71,229,99,196,347,187,205),(72,206,188,348,197,100,230),(113,159,237,223,374,122,407),(114,408,123,375,224,238,160),(115,153,239,217,376,124,401),(116,402,125,369,218,240,154),(117,155,233,219,370,126,403),(118,404,127,371,220,234,156),(119,157,235,221,372,128,405),(120,406,121,373,222,236,158),(161,397,353,169,178,314,436),(162,437,315,179,170,354,398),(163,399,355,171,180,316,438),(164,439,317,181,172,356,400),(165,393,357,173,182,318,440),(166,433,319,183,174,358,394),(167,395,359,175,184,320,434),(168,435,313,177,176,360,396)], [(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)]])
136 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4H | 4I | ··· | 4P | 7A | 7B | 7C | 8A | ··· | 8P | 14A | ··· | 14U | 28A | ··· | 28BT |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 2 | ··· | 2 |
136 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | - | + | ||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C4 | D7 | M4(2) | Dic7 | D14 | Dic7 | D14 | C4×D7 | C4.Dic7 |
| kernel | C2×C42.D7 | C42.D7 | C22×C7⋊C8 | C2×C4×C28 | C2×C7⋊C8 | C4×C28 | C22×C28 | C2×C42 | C2×C14 | C42 | C42 | C22×C4 | C22×C4 | C2×C4 | C22 |
| # reps | 1 | 4 | 2 | 1 | 16 | 4 | 4 | 3 | 8 | 6 | 6 | 6 | 3 | 24 | 48 |
Matrix representation of C2×C42.D7 ►in GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 15 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 55 | 38 |
| 0 | 0 | 75 | 58 |
| 112 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 98 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 9 | 112 |
| 0 | 0 | 1 | 0 |
| 98 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 10 | 89 |
| 0 | 0 | 66 | 103 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,1,0,0,0,0,1],[15,0,0,0,0,1,0,0,0,0,55,75,0,0,38,58],[112,0,0,0,0,1,0,0,0,0,98,0,0,0,0,98],[1,0,0,0,0,1,0,0,0,0,9,1,0,0,112,0],[98,0,0,0,0,1,0,0,0,0,10,66,0,0,89,103] >;
C2×C42.D7 in GAP, Magma, Sage, TeX
C_2\times C_4^2.D_7
% in TeX
G:=Group("C2xC4^2.D7"); // GroupNames label
G:=SmallGroup(448,455);
// by ID
G=gap.SmallGroup(448,455);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,758,100,136,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=c^4=d^7=1,e^2=c,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,e*b*e^-1=b*c^2,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations