direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C7×C22.7C42, (C2×C8)⋊3C28, (C2×C56)⋊7C4, (C2×C4)⋊2C56, (C2×C28)⋊4C8, C2.2(C4×C56), C14.11(C4×C8), C14.13(C4⋊C8), C28.66(C4⋊C4), (C2×C28).81Q8, (C2×C28).532D4, (C22×C4).7C28, C22.7(C2×C56), (C2×C42).1C14, (C22×C56).4C2, C22.7(C4×C28), (C22×C8).1C14, C14.8(C8⋊C4), (C22×C28).14C4, C23.35(C2×C28), (C2×C14).29C42, C14.24(C22⋊C8), (C2×C14).28M4(2), C28.109(C22⋊C4), C22.7(C7×M4(2)), (C22×C28).606C22, C14.20(C2.C42), C2.1(C7×C4⋊C8), (C2×C4×C28).1C2, C4.17(C7×C4⋊C4), C2.2(C7×C8⋊C4), C2.1(C7×C22⋊C8), (C2×C4).23(C7×Q8), (C2×C4).81(C2×C28), (C2×C14).38(C2×C8), (C2×C4).141(C7×D4), C4.24(C7×C22⋊C4), C22.15(C7×C4⋊C4), (C2×C14).58(C4⋊C4), (C2×C28).343(C2×C4), C22.27(C7×C22⋊C4), C2.1(C7×C2.C42), (C22×C4).133(C2×C14), (C22×C14).144(C2×C4), (C2×C14).129(C22⋊C4), SmallGroup(448,140)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×C22.7C42
G = < a,b,c,d,e | a7=b2=c2=e4=1, d4=c, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, ede-1=bd=db, be=eb, cd=dc, ce=ec >
Subgroups: 154 in 118 conjugacy classes, 82 normal (26 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, C23, C14, C14, C42, C2×C8, C2×C8, C22×C4, C22×C4, C28, C28, C2×C14, C2×C14, C2×C42, C22×C8, C56, C2×C28, C2×C28, C2×C28, C22×C14, C22.7C42, C4×C28, C2×C56, C2×C56, C22×C28, C22×C28, C2×C4×C28, C22×C56, C7×C22.7C42
Quotients: C1, C2, C4, C22, C7, C8, C2×C4, D4, Q8, C14, C42, C22⋊C4, C4⋊C4, C2×C8, M4(2), C28, C2×C14, C2.C42, C4×C8, C8⋊C4, C22⋊C8, C4⋊C8, C56, C2×C28, C7×D4, C7×Q8, C22.7C42, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×C56, C7×M4(2), C7×C2.C42, C4×C56, C7×C8⋊C4, C7×C22⋊C8, C7×C4⋊C8, C7×C22.7C42
►Regular action on 448 points
Generators in S448
(1 281 273 265 257 249 241)(2 282 274 266 258 250 242)(3 283 275 267 259 251 243)(4 284 276 268 260 252 244)(5 285 277 269 261 253 245)(6 286 278 270 262 254 246)(7 287 279 271 263 255 247)(8 288 280 272 264 256 248)(9 336 328 320 312 304 296)(10 329 321 313 305 297 289)(11 330 322 314 306 298 290)(12 331 323 315 307 299 291)(13 332 324 316 308 300 292)(14 333 325 317 309 301 293)(15 334 326 318 310 302 294)(16 335 327 319 311 303 295)(17 65 57 49 41 33 25)(18 66 58 50 42 34 26)(19 67 59 51 43 35 27)(20 68 60 52 44 36 28)(21 69 61 53 45 37 29)(22 70 62 54 46 38 30)(23 71 63 55 47 39 31)(24 72 64 56 48 40 32)(73 239 113 105 97 89 81)(74 240 114 106 98 90 82)(75 233 115 107 99 91 83)(76 234 116 108 100 92 84)(77 235 117 109 101 93 85)(78 236 118 110 102 94 86)(79 237 119 111 103 95 87)(80 238 120 112 104 96 88)(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)(177 231 217 209 201 193 185)(178 232 218 210 202 194 186)(179 225 219 211 203 195 187)(180 226 220 212 204 196 188)(181 227 221 213 205 197 189)(182 228 222 214 206 198 190)(183 229 223 215 207 199 191)(184 230 224 216 208 200 192)(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 17)(2 18)(3 19)(4 20)(5 21)(6 22)(7 23)(8 24)(9 238)(10 239)(11 240)(12 233)(13 234)(14 235)(15 236)(16 237)(25 241)(26 242)(27 243)(28 244)(29 245)(30 246)(31 247)(32 248)(33 249)(34 250)(35 251)(36 252)(37 253)(38 254)(39 255)(40 256)(41 257)(42 258)(43 259)(44 260)(45 261)(46 262)(47 263)(48 264)(49 265)(50 266)(51 267)(52 268)(53 269)(54 270)(55 271)(56 272)(57 273)(58 274)(59 275)(60 276)(61 277)(62 278)(63 279)(64 280)(65 281)(66 282)(67 283)(68 284)(69 285)(70 286)(71 287)(72 288)(73 289)(74 290)(75 291)(76 292)(77 293)(78 294)(79 295)(80 296)(81 297)(82 298)(83 299)(84 300)(85 301)(86 302)(87 303)(88 304)(89 305)(90 306)(91 307)(92 308)(93 309)(94 310)(95 311)(96 312)(97 313)(98 314)(99 315)(100 316)(101 317)(102 318)(103 319)(104 320)(105 321)(106 322)(107 323)(108 324)(109 325)(110 326)(111 327)(112 328)(113 329)(114 330)(115 331)(116 332)(117 333)(118 334)(119 335)(120 336)(121 337)(122 338)(123 339)(124 340)(125 341)(126 342)(127 343)(128 344)(129 345)(130 346)(131 347)(132 348)(133 349)(134 350)(135 351)(136 352)(137 353)(138 354)(139 355)(140 356)(141 357)(142 358)(143 359)(144 360)(145 361)(146 362)(147 363)(148 364)(149 365)(150 366)(151 367)(152 368)(153 369)(154 370)(155 371)(156 372)(157 373)(158 374)(159 375)(160 376)(161 377)(162 378)(163 379)(164 380)(165 381)(166 382)(167 383)(168 384)(169 385)(170 386)(171 387)(172 388)(173 389)(174 390)(175 391)(176 392)(177 393)(178 394)(179 395)(180 396)(181 397)(182 398)(183 399)(184 400)(185 401)(186 402)(187 403)(188 404)(189 405)(190 406)(191 407)(192 408)(193 409)(194 410)(195 411)(196 412)(197 413)(198 414)(199 415)(200 416)(201 417)(202 418)(203 419)(204 420)(205 421)(206 422)(207 423)(208 424)(209 425)(210 426)(211 427)(212 428)(213 429)(214 430)(215 431)(216 432)(217 433)(218 434)(219 435)(220 436)(221 437)(222 438)(223 439)(224 440)(225 443)(226 444)(227 445)(228 446)(229 447)(230 448)(231 441)(232 442)
(1 5)(2 6)(3 7)(4 8)(9 13)(10 14)(11 15)(12 16)(17 21)(18 22)(19 23)(20 24)(25 29)(26 30)(27 31)(28 32)(33 37)(34 38)(35 39)(36 40)(41 45)(42 46)(43 47)(44 48)(49 53)(50 54)(51 55)(52 56)(57 61)(58 62)(59 63)(60 64)(65 69)(66 70)(67 71)(68 72)(73 77)(74 78)(75 79)(76 80)(81 85)(82 86)(83 87)(84 88)(89 93)(90 94)(91 95)(92 96)(97 101)(98 102)(99 103)(100 104)(105 109)(106 110)(107 111)(108 112)(113 117)(114 118)(115 119)(116 120)(121 125)(122 126)(123 127)(124 128)(129 133)(130 134)(131 135)(132 136)(137 141)(138 142)(139 143)(140 144)(145 149)(146 150)(147 151)(148 152)(153 157)(154 158)(155 159)(156 160)(161 165)(162 166)(163 167)(164 168)(169 173)(170 174)(171 175)(172 176)(177 181)(178 182)(179 183)(180 184)(185 189)(186 190)(187 191)(188 192)(193 197)(194 198)(195 199)(196 200)(201 205)(202 206)(203 207)(204 208)(209 213)(210 214)(211 215)(212 216)(217 221)(218 222)(219 223)(220 224)(225 229)(226 230)(227 231)(228 232)(233 237)(234 238)(235 239)(236 240)(241 245)(242 246)(243 247)(244 248)(249 253)(250 254)(251 255)(252 256)(257 261)(258 262)(259 263)(260 264)(265 269)(266 270)(267 271)(268 272)(273 277)(274 278)(275 279)(276 280)(281 285)(282 286)(283 287)(284 288)(289 293)(290 294)(291 295)(292 296)(297 301)(298 302)(299 303)(300 304)(305 309)(306 310)(307 311)(308 312)(313 317)(314 318)(315 319)(316 320)(321 325)(322 326)(323 327)(324 328)(329 333)(330 334)(331 335)(332 336)(337 341)(338 342)(339 343)(340 344)(345 349)(346 350)(347 351)(348 352)(353 357)(354 358)(355 359)(356 360)(361 365)(362 366)(363 367)(364 368)(369 373)(370 374)(371 375)(372 376)(377 381)(378 382)(379 383)(380 384)(385 389)(386 390)(387 391)(388 392)(393 397)(394 398)(395 399)(396 400)(401 405)(402 406)(403 407)(404 408)(409 413)(410 414)(411 415)(412 416)(417 421)(418 422)(419 423)(420 424)(425 429)(426 430)(427 431)(428 432)(433 437)(434 438)(435 439)(436 440)(441 445)(442 446)(443 447)(444 448)
(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)
(1 399 343 289)(2 184 344 74)(3 393 337 291)(4 178 338 76)(5 395 339 293)(6 180 340 78)(7 397 341 295)(8 182 342 80)(9 72 446 174)(10 281 447 391)(11 66 448 176)(12 283 441 385)(13 68 442 170)(14 285 443 387)(15 70 444 172)(16 287 445 389)(17 183 127 73)(18 400 128 290)(19 177 121 75)(20 394 122 292)(21 179 123 77)(22 396 124 294)(23 181 125 79)(24 398 126 296)(25 191 135 81)(26 408 136 298)(27 185 129 83)(28 402 130 300)(29 187 131 85)(30 404 132 302)(31 189 133 87)(32 406 134 304)(33 199 143 89)(34 416 144 306)(35 193 137 91)(36 410 138 308)(37 195 139 93)(38 412 140 310)(39 197 141 95)(40 414 142 312)(41 207 151 97)(42 424 152 314)(43 201 145 99)(44 418 146 316)(45 203 147 101)(46 420 148 318)(47 205 149 103)(48 422 150 320)(49 215 159 105)(50 432 160 322)(51 209 153 107)(52 426 154 324)(53 211 155 109)(54 428 156 326)(55 213 157 111)(56 430 158 328)(57 223 167 113)(58 440 168 330)(59 217 161 115)(60 434 162 332)(61 219 163 117)(62 436 164 334)(63 221 165 119)(64 438 166 336)(65 229 175 239)(67 231 169 233)(69 225 171 235)(71 227 173 237)(82 242 192 352)(84 244 186 346)(86 246 188 348)(88 248 190 350)(90 250 200 360)(92 252 194 354)(94 254 196 356)(96 256 198 358)(98 258 208 368)(100 260 202 362)(102 262 204 364)(104 264 206 366)(106 266 216 376)(108 268 210 370)(110 270 212 372)(112 272 214 374)(114 274 224 384)(116 276 218 378)(118 278 220 380)(120 280 222 382)(226 388 236 286)(228 390 238 288)(230 392 240 282)(232 386 234 284)(241 407 351 297)(243 401 345 299)(245 403 347 301)(247 405 349 303)(249 415 359 305)(251 409 353 307)(253 411 355 309)(255 413 357 311)(257 423 367 313)(259 417 361 315)(261 419 363 317)(263 421 365 319)(265 431 375 321)(267 425 369 323)(269 427 371 325)(271 429 373 327)(273 439 383 329)(275 433 377 331)(277 435 379 333)(279 437 381 335)
G:=sub<Sym(448)| (1,281,273,265,257,249,241)(2,282,274,266,258,250,242)(3,283,275,267,259,251,243)(4,284,276,268,260,252,244)(5,285,277,269,261,253,245)(6,286,278,270,262,254,246)(7,287,279,271,263,255,247)(8,288,280,272,264,256,248)(9,336,328,320,312,304,296)(10,329,321,313,305,297,289)(11,330,322,314,306,298,290)(12,331,323,315,307,299,291)(13,332,324,316,308,300,292)(14,333,325,317,309,301,293)(15,334,326,318,310,302,294)(16,335,327,319,311,303,295)(17,65,57,49,41,33,25)(18,66,58,50,42,34,26)(19,67,59,51,43,35,27)(20,68,60,52,44,36,28)(21,69,61,53,45,37,29)(22,70,62,54,46,38,30)(23,71,63,55,47,39,31)(24,72,64,56,48,40,32)(73,239,113,105,97,89,81)(74,240,114,106,98,90,82)(75,233,115,107,99,91,83)(76,234,116,108,100,92,84)(77,235,117,109,101,93,85)(78,236,118,110,102,94,86)(79,237,119,111,103,95,87)(80,238,120,112,104,96,88)(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)(177,231,217,209,201,193,185)(178,232,218,210,202,194,186)(179,225,219,211,203,195,187)(180,226,220,212,204,196,188)(181,227,221,213,205,197,189)(182,228,222,214,206,198,190)(183,229,223,215,207,199,191)(184,230,224,216,208,200,192)(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), (1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,238)(10,239)(11,240)(12,233)(13,234)(14,235)(15,236)(16,237)(25,241)(26,242)(27,243)(28,244)(29,245)(30,246)(31,247)(32,248)(33,249)(34,250)(35,251)(36,252)(37,253)(38,254)(39,255)(40,256)(41,257)(42,258)(43,259)(44,260)(45,261)(46,262)(47,263)(48,264)(49,265)(50,266)(51,267)(52,268)(53,269)(54,270)(55,271)(56,272)(57,273)(58,274)(59,275)(60,276)(61,277)(62,278)(63,279)(64,280)(65,281)(66,282)(67,283)(68,284)(69,285)(70,286)(71,287)(72,288)(73,289)(74,290)(75,291)(76,292)(77,293)(78,294)(79,295)(80,296)(81,297)(82,298)(83,299)(84,300)(85,301)(86,302)(87,303)(88,304)(89,305)(90,306)(91,307)(92,308)(93,309)(94,310)(95,311)(96,312)(97,313)(98,314)(99,315)(100,316)(101,317)(102,318)(103,319)(104,320)(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)(112,328)(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)(120,336)(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)(128,344)(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)(136,352)(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)(144,360)(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)(152,368)(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)(160,376)(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)(168,384)(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)(176,392)(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)(184,400)(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)(192,408)(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)(200,416)(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)(208,424)(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)(216,432)(217,433)(218,434)(219,435)(220,436)(221,437)(222,438)(223,439)(224,440)(225,443)(226,444)(227,445)(228,446)(229,447)(230,448)(231,441)(232,442), (1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)(33,37)(34,38)(35,39)(36,40)(41,45)(42,46)(43,47)(44,48)(49,53)(50,54)(51,55)(52,56)(57,61)(58,62)(59,63)(60,64)(65,69)(66,70)(67,71)(68,72)(73,77)(74,78)(75,79)(76,80)(81,85)(82,86)(83,87)(84,88)(89,93)(90,94)(91,95)(92,96)(97,101)(98,102)(99,103)(100,104)(105,109)(106,110)(107,111)(108,112)(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160)(161,165)(162,166)(163,167)(164,168)(169,173)(170,174)(171,175)(172,176)(177,181)(178,182)(179,183)(180,184)(185,189)(186,190)(187,191)(188,192)(193,197)(194,198)(195,199)(196,200)(201,205)(202,206)(203,207)(204,208)(209,213)(210,214)(211,215)(212,216)(217,221)(218,222)(219,223)(220,224)(225,229)(226,230)(227,231)(228,232)(233,237)(234,238)(235,239)(236,240)(241,245)(242,246)(243,247)(244,248)(249,253)(250,254)(251,255)(252,256)(257,261)(258,262)(259,263)(260,264)(265,269)(266,270)(267,271)(268,272)(273,277)(274,278)(275,279)(276,280)(281,285)(282,286)(283,287)(284,288)(289,293)(290,294)(291,295)(292,296)(297,301)(298,302)(299,303)(300,304)(305,309)(306,310)(307,311)(308,312)(313,317)(314,318)(315,319)(316,320)(321,325)(322,326)(323,327)(324,328)(329,333)(330,334)(331,335)(332,336)(337,341)(338,342)(339,343)(340,344)(345,349)(346,350)(347,351)(348,352)(353,357)(354,358)(355,359)(356,360)(361,365)(362,366)(363,367)(364,368)(369,373)(370,374)(371,375)(372,376)(377,381)(378,382)(379,383)(380,384)(385,389)(386,390)(387,391)(388,392)(393,397)(394,398)(395,399)(396,400)(401,405)(402,406)(403,407)(404,408)(409,413)(410,414)(411,415)(412,416)(417,421)(418,422)(419,423)(420,424)(425,429)(426,430)(427,431)(428,432)(433,437)(434,438)(435,439)(436,440)(441,445)(442,446)(443,447)(444,448), (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), (1,399,343,289)(2,184,344,74)(3,393,337,291)(4,178,338,76)(5,395,339,293)(6,180,340,78)(7,397,341,295)(8,182,342,80)(9,72,446,174)(10,281,447,391)(11,66,448,176)(12,283,441,385)(13,68,442,170)(14,285,443,387)(15,70,444,172)(16,287,445,389)(17,183,127,73)(18,400,128,290)(19,177,121,75)(20,394,122,292)(21,179,123,77)(22,396,124,294)(23,181,125,79)(24,398,126,296)(25,191,135,81)(26,408,136,298)(27,185,129,83)(28,402,130,300)(29,187,131,85)(30,404,132,302)(31,189,133,87)(32,406,134,304)(33,199,143,89)(34,416,144,306)(35,193,137,91)(36,410,138,308)(37,195,139,93)(38,412,140,310)(39,197,141,95)(40,414,142,312)(41,207,151,97)(42,424,152,314)(43,201,145,99)(44,418,146,316)(45,203,147,101)(46,420,148,318)(47,205,149,103)(48,422,150,320)(49,215,159,105)(50,432,160,322)(51,209,153,107)(52,426,154,324)(53,211,155,109)(54,428,156,326)(55,213,157,111)(56,430,158,328)(57,223,167,113)(58,440,168,330)(59,217,161,115)(60,434,162,332)(61,219,163,117)(62,436,164,334)(63,221,165,119)(64,438,166,336)(65,229,175,239)(67,231,169,233)(69,225,171,235)(71,227,173,237)(82,242,192,352)(84,244,186,346)(86,246,188,348)(88,248,190,350)(90,250,200,360)(92,252,194,354)(94,254,196,356)(96,256,198,358)(98,258,208,368)(100,260,202,362)(102,262,204,364)(104,264,206,366)(106,266,216,376)(108,268,210,370)(110,270,212,372)(112,272,214,374)(114,274,224,384)(116,276,218,378)(118,278,220,380)(120,280,222,382)(226,388,236,286)(228,390,238,288)(230,392,240,282)(232,386,234,284)(241,407,351,297)(243,401,345,299)(245,403,347,301)(247,405,349,303)(249,415,359,305)(251,409,353,307)(253,411,355,309)(255,413,357,311)(257,423,367,313)(259,417,361,315)(261,419,363,317)(263,421,365,319)(265,431,375,321)(267,425,369,323)(269,427,371,325)(271,429,373,327)(273,439,383,329)(275,433,377,331)(277,435,379,333)(279,437,381,335)>;
G:=Group( (1,281,273,265,257,249,241)(2,282,274,266,258,250,242)(3,283,275,267,259,251,243)(4,284,276,268,260,252,244)(5,285,277,269,261,253,245)(6,286,278,270,262,254,246)(7,287,279,271,263,255,247)(8,288,280,272,264,256,248)(9,336,328,320,312,304,296)(10,329,321,313,305,297,289)(11,330,322,314,306,298,290)(12,331,323,315,307,299,291)(13,332,324,316,308,300,292)(14,333,325,317,309,301,293)(15,334,326,318,310,302,294)(16,335,327,319,311,303,295)(17,65,57,49,41,33,25)(18,66,58,50,42,34,26)(19,67,59,51,43,35,27)(20,68,60,52,44,36,28)(21,69,61,53,45,37,29)(22,70,62,54,46,38,30)(23,71,63,55,47,39,31)(24,72,64,56,48,40,32)(73,239,113,105,97,89,81)(74,240,114,106,98,90,82)(75,233,115,107,99,91,83)(76,234,116,108,100,92,84)(77,235,117,109,101,93,85)(78,236,118,110,102,94,86)(79,237,119,111,103,95,87)(80,238,120,112,104,96,88)(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)(177,231,217,209,201,193,185)(178,232,218,210,202,194,186)(179,225,219,211,203,195,187)(180,226,220,212,204,196,188)(181,227,221,213,205,197,189)(182,228,222,214,206,198,190)(183,229,223,215,207,199,191)(184,230,224,216,208,200,192)(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), (1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,238)(10,239)(11,240)(12,233)(13,234)(14,235)(15,236)(16,237)(25,241)(26,242)(27,243)(28,244)(29,245)(30,246)(31,247)(32,248)(33,249)(34,250)(35,251)(36,252)(37,253)(38,254)(39,255)(40,256)(41,257)(42,258)(43,259)(44,260)(45,261)(46,262)(47,263)(48,264)(49,265)(50,266)(51,267)(52,268)(53,269)(54,270)(55,271)(56,272)(57,273)(58,274)(59,275)(60,276)(61,277)(62,278)(63,279)(64,280)(65,281)(66,282)(67,283)(68,284)(69,285)(70,286)(71,287)(72,288)(73,289)(74,290)(75,291)(76,292)(77,293)(78,294)(79,295)(80,296)(81,297)(82,298)(83,299)(84,300)(85,301)(86,302)(87,303)(88,304)(89,305)(90,306)(91,307)(92,308)(93,309)(94,310)(95,311)(96,312)(97,313)(98,314)(99,315)(100,316)(101,317)(102,318)(103,319)(104,320)(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)(112,328)(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)(120,336)(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)(128,344)(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)(136,352)(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)(144,360)(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)(152,368)(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)(160,376)(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)(168,384)(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)(176,392)(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)(184,400)(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)(192,408)(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)(200,416)(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)(208,424)(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)(216,432)(217,433)(218,434)(219,435)(220,436)(221,437)(222,438)(223,439)(224,440)(225,443)(226,444)(227,445)(228,446)(229,447)(230,448)(231,441)(232,442), 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(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), (1,399,343,289)(2,184,344,74)(3,393,337,291)(4,178,338,76)(5,395,339,293)(6,180,340,78)(7,397,341,295)(8,182,342,80)(9,72,446,174)(10,281,447,391)(11,66,448,176)(12,283,441,385)(13,68,442,170)(14,285,443,387)(15,70,444,172)(16,287,445,389)(17,183,127,73)(18,400,128,290)(19,177,121,75)(20,394,122,292)(21,179,123,77)(22,396,124,294)(23,181,125,79)(24,398,126,296)(25,191,135,81)(26,408,136,298)(27,185,129,83)(28,402,130,300)(29,187,131,85)(30,404,132,302)(31,189,133,87)(32,406,134,304)(33,199,143,89)(34,416,144,306)(35,193,137,91)(36,410,138,308)(37,195,139,93)(38,412,140,310)(39,197,141,95)(40,414,142,312)(41,207,151,97)(42,424,152,314)(43,201,145,99)(44,418,146,316)(45,203,147,101)(46,420,148,318)(47,205,149,103)(48,422,150,320)(49,215,159,105)(50,432,160,322)(51,209,153,107)(52,426,154,324)(53,211,155,109)(54,428,156,326)(55,213,157,111)(56,430,158,328)(57,223,167,113)(58,440,168,330)(59,217,161,115)(60,434,162,332)(61,219,163,117)(62,436,164,334)(63,221,165,119)(64,438,166,336)(65,229,175,239)(67,231,169,233)(69,225,171,235)(71,227,173,237)(82,242,192,352)(84,244,186,346)(86,246,188,348)(88,248,190,350)(90,250,200,360)(92,252,194,354)(94,254,196,356)(96,256,198,358)(98,258,208,368)(100,260,202,362)(102,262,204,364)(104,264,206,366)(106,266,216,376)(108,268,210,370)(110,270,212,372)(112,272,214,374)(114,274,224,384)(116,276,218,378)(118,278,220,380)(120,280,222,382)(226,388,236,286)(228,390,238,288)(230,392,240,282)(232,386,234,284)(241,407,351,297)(243,401,345,299)(245,403,347,301)(247,405,349,303)(249,415,359,305)(251,409,353,307)(253,411,355,309)(255,413,357,311)(257,423,367,313)(259,417,361,315)(261,419,363,317)(263,421,365,319)(265,431,375,321)(267,425,369,323)(269,427,371,325)(271,429,373,327)(273,439,383,329)(275,433,377,331)(277,435,379,333)(279,437,381,335) );
G=PermutationGroup([[(1,281,273,265,257,249,241),(2,282,274,266,258,250,242),(3,283,275,267,259,251,243),(4,284,276,268,260,252,244),(5,285,277,269,261,253,245),(6,286,278,270,262,254,246),(7,287,279,271,263,255,247),(8,288,280,272,264,256,248),(9,336,328,320,312,304,296),(10,329,321,313,305,297,289),(11,330,322,314,306,298,290),(12,331,323,315,307,299,291),(13,332,324,316,308,300,292),(14,333,325,317,309,301,293),(15,334,326,318,310,302,294),(16,335,327,319,311,303,295),(17,65,57,49,41,33,25),(18,66,58,50,42,34,26),(19,67,59,51,43,35,27),(20,68,60,52,44,36,28),(21,69,61,53,45,37,29),(22,70,62,54,46,38,30),(23,71,63,55,47,39,31),(24,72,64,56,48,40,32),(73,239,113,105,97,89,81),(74,240,114,106,98,90,82),(75,233,115,107,99,91,83),(76,234,116,108,100,92,84),(77,235,117,109,101,93,85),(78,236,118,110,102,94,86),(79,237,119,111,103,95,87),(80,238,120,112,104,96,88),(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),(177,231,217,209,201,193,185),(178,232,218,210,202,194,186),(179,225,219,211,203,195,187),(180,226,220,212,204,196,188),(181,227,221,213,205,197,189),(182,228,222,214,206,198,190),(183,229,223,215,207,199,191),(184,230,224,216,208,200,192),(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)], [(1,17),(2,18),(3,19),(4,20),(5,21),(6,22),(7,23),(8,24),(9,238),(10,239),(11,240),(12,233),(13,234),(14,235),(15,236),(16,237),(25,241),(26,242),(27,243),(28,244),(29,245),(30,246),(31,247),(32,248),(33,249),(34,250),(35,251),(36,252),(37,253),(38,254),(39,255),(40,256),(41,257),(42,258),(43,259),(44,260),(45,261),(46,262),(47,263),(48,264),(49,265),(50,266),(51,267),(52,268),(53,269),(54,270),(55,271),(56,272),(57,273),(58,274),(59,275),(60,276),(61,277),(62,278),(63,279),(64,280),(65,281),(66,282),(67,283),(68,284),(69,285),(70,286),(71,287),(72,288),(73,289),(74,290),(75,291),(76,292),(77,293),(78,294),(79,295),(80,296),(81,297),(82,298),(83,299),(84,300),(85,301),(86,302),(87,303),(88,304),(89,305),(90,306),(91,307),(92,308),(93,309),(94,310),(95,311),(96,312),(97,313),(98,314),(99,315),(100,316),(101,317),(102,318),(103,319),(104,320),(105,321),(106,322),(107,323),(108,324),(109,325),(110,326),(111,327),(112,328),(113,329),(114,330),(115,331),(116,332),(117,333),(118,334),(119,335),(120,336),(121,337),(122,338),(123,339),(124,340),(125,341),(126,342),(127,343),(128,344),(129,345),(130,346),(131,347),(132,348),(133,349),(134,350),(135,351),(136,352),(137,353),(138,354),(139,355),(140,356),(141,357),(142,358),(143,359),(144,360),(145,361),(146,362),(147,363),(148,364),(149,365),(150,366),(151,367),(152,368),(153,369),(154,370),(155,371),(156,372),(157,373),(158,374),(159,375),(160,376),(161,377),(162,378),(163,379),(164,380),(165,381),(166,382),(167,383),(168,384),(169,385),(170,386),(171,387),(172,388),(173,389),(174,390),(175,391),(176,392),(177,393),(178,394),(179,395),(180,396),(181,397),(182,398),(183,399),(184,400),(185,401),(186,402),(187,403),(188,404),(189,405),(190,406),(191,407),(192,408),(193,409),(194,410),(195,411),(196,412),(197,413),(198,414),(199,415),(200,416),(201,417),(202,418),(203,419),(204,420),(205,421),(206,422),(207,423),(208,424),(209,425),(210,426),(211,427),(212,428),(213,429),(214,430),(215,431),(216,432),(217,433),(218,434),(219,435),(220,436),(221,437),(222,438),(223,439),(224,440),(225,443),(226,444),(227,445),(228,446),(229,447),(230,448),(231,441),(232,442)], [(1,5),(2,6),(3,7),(4,8),(9,13),(10,14),(11,15),(12,16),(17,21),(18,22),(19,23),(20,24),(25,29),(26,30),(27,31),(28,32),(33,37),(34,38),(35,39),(36,40),(41,45),(42,46),(43,47),(44,48),(49,53),(50,54),(51,55),(52,56),(57,61),(58,62),(59,63),(60,64),(65,69),(66,70),(67,71),(68,72),(73,77),(74,78),(75,79),(76,80),(81,85),(82,86),(83,87),(84,88),(89,93),(90,94),(91,95),(92,96),(97,101),(98,102),(99,103),(100,104),(105,109),(106,110),(107,111),(108,112),(113,117),(114,118),(115,119),(116,120),(121,125),(122,126),(123,127),(124,128),(129,133),(130,134),(131,135),(132,136),(137,141),(138,142),(139,143),(140,144),(145,149),(146,150),(147,151),(148,152),(153,157),(154,158),(155,159),(156,160),(161,165),(162,166),(163,167),(164,168),(169,173),(170,174),(171,175),(172,176),(177,181),(178,182),(179,183),(180,184),(185,189),(186,190),(187,191),(188,192),(193,197),(194,198),(195,199),(196,200),(201,205),(202,206),(203,207),(204,208),(209,213),(210,214),(211,215),(212,216),(217,221),(218,222),(219,223),(220,224),(225,229),(226,230),(227,231),(228,232),(233,237),(234,238),(235,239),(236,240),(241,245),(242,246),(243,247),(244,248),(249,253),(250,254),(251,255),(252,256),(257,261),(258,262),(259,263),(260,264),(265,269),(266,270),(267,271),(268,272),(273,277),(274,278),(275,279),(276,280),(281,285),(282,286),(283,287),(284,288),(289,293),(290,294),(291,295),(292,296),(297,301),(298,302),(299,303),(300,304),(305,309),(306,310),(307,311),(308,312),(313,317),(314,318),(315,319),(316,320),(321,325),(322,326),(323,327),(324,328),(329,333),(330,334),(331,335),(332,336),(337,341),(338,342),(339,343),(340,344),(345,349),(346,350),(347,351),(348,352),(353,357),(354,358),(355,359),(356,360),(361,365),(362,366),(363,367),(364,368),(369,373),(370,374),(371,375),(372,376),(377,381),(378,382),(379,383),(380,384),(385,389),(386,390),(387,391),(388,392),(393,397),(394,398),(395,399),(396,400),(401,405),(402,406),(403,407),(404,408),(409,413),(410,414),(411,415),(412,416),(417,421),(418,422),(419,423),(420,424),(425,429),(426,430),(427,431),(428,432),(433,437),(434,438),(435,439),(436,440),(441,445),(442,446),(443,447),(444,448)], [(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)], [(1,399,343,289),(2,184,344,74),(3,393,337,291),(4,178,338,76),(5,395,339,293),(6,180,340,78),(7,397,341,295),(8,182,342,80),(9,72,446,174),(10,281,447,391),(11,66,448,176),(12,283,441,385),(13,68,442,170),(14,285,443,387),(15,70,444,172),(16,287,445,389),(17,183,127,73),(18,400,128,290),(19,177,121,75),(20,394,122,292),(21,179,123,77),(22,396,124,294),(23,181,125,79),(24,398,126,296),(25,191,135,81),(26,408,136,298),(27,185,129,83),(28,402,130,300),(29,187,131,85),(30,404,132,302),(31,189,133,87),(32,406,134,304),(33,199,143,89),(34,416,144,306),(35,193,137,91),(36,410,138,308),(37,195,139,93),(38,412,140,310),(39,197,141,95),(40,414,142,312),(41,207,151,97),(42,424,152,314),(43,201,145,99),(44,418,146,316),(45,203,147,101),(46,420,148,318),(47,205,149,103),(48,422,150,320),(49,215,159,105),(50,432,160,322),(51,209,153,107),(52,426,154,324),(53,211,155,109),(54,428,156,326),(55,213,157,111),(56,430,158,328),(57,223,167,113),(58,440,168,330),(59,217,161,115),(60,434,162,332),(61,219,163,117),(62,436,164,334),(63,221,165,119),(64,438,166,336),(65,229,175,239),(67,231,169,233),(69,225,171,235),(71,227,173,237),(82,242,192,352),(84,244,186,346),(86,246,188,348),(88,248,190,350),(90,250,200,360),(92,252,194,354),(94,254,196,356),(96,256,198,358),(98,258,208,368),(100,260,202,362),(102,262,204,364),(104,264,206,366),(106,266,216,376),(108,268,210,370),(110,270,212,372),(112,272,214,374),(114,274,224,384),(116,276,218,378),(118,278,220,380),(120,280,222,382),(226,388,236,286),(228,390,238,288),(230,392,240,282),(232,386,234,284),(241,407,351,297),(243,401,345,299),(245,403,347,301),(247,405,349,303),(249,415,359,305),(251,409,353,307),(253,411,355,309),(255,413,357,311),(257,423,367,313),(259,417,361,315),(261,419,363,317),(263,421,365,319),(265,431,375,321),(267,425,369,323),(269,427,371,325),(271,429,373,327),(273,439,383,329),(275,433,377,331),(277,435,379,333),(279,437,381,335)]])
280 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4H | 4I | ··· | 4P | 7A | ··· | 7F | 8A | ··· | 8P | 14A | ··· | 14AP | 28A | ··· | 28AV | 28AW | ··· | 28CR | 56A | ··· | 56CR |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | ··· | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 |
280 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | |||||||||||||
| image | C1 | C2 | C2 | C4 | C4 | C7 | C8 | C14 | C14 | C28 | C28 | C56 | D4 | Q8 | M4(2) | C7×D4 | C7×Q8 | C7×M4(2) |
| kernel | C7×C22.7C42 | C2×C4×C28 | C22×C56 | C2×C56 | C22×C28 | C22.7C42 | C2×C28 | C2×C42 | C22×C8 | C2×C8 | C22×C4 | C2×C4 | C2×C28 | C2×C28 | C2×C14 | C2×C4 | C2×C4 | C22 |
| # reps | 1 | 1 | 2 | 8 | 4 | 6 | 16 | 6 | 12 | 48 | 24 | 96 | 3 | 1 | 4 | 18 | 6 | 24 |
Matrix representation of C7×C22.7C42 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 109 | 0 |
| 0 | 0 | 0 | 109 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 112 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 69 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 111 | 89 |
| 0 | 0 | 89 | 2 |
| 15 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 112 | 0 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,109,0,0,0,0,109],[1,0,0,0,0,1,0,0,0,0,112,0,0,0,0,112],[112,0,0,0,0,1,0,0,0,0,112,0,0,0,0,112],[69,0,0,0,0,1,0,0,0,0,111,89,0,0,89,2],[15,0,0,0,0,98,0,0,0,0,0,112,0,0,1,0] >;
C7×C22.7C42 in GAP, Magma, Sage, TeX
C_7\times C_2^2._7C_4^2
% in TeX
G:=Group("C7xC2^2.7C4^2"); // GroupNames label
G:=SmallGroup(448,140);
// by ID
G=gap.SmallGroup(448,140);
# by ID
G:=PCGroup([7,-2,-2,-7,-2,-2,-2,-2,392,421,792,172]);
// Polycyclic
G:=Group<a,b,c,d,e|a^7=b^2=c^2=e^4=1,d^4=c,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,e*d*e^-1=b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c>;
// generators/relations