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G = C23×C7⋊C8  order 448 = 26·7

Direct product of C23 and C7⋊C8

direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: C23×C7⋊C8, C28.73C24, C24.6Dic7, C7⋊2(C23×C8), (C22×C14)⋊5C8, C14⋊2(C22×C8), (C23×C4).14D7, C4.72(C23×D7), C14.40(C23×C4), (C22×C28).34C4, (C23×C14).10C4, (C23×C28).20C2, C2.1(C23×Dic7), C28.179(C22×C4), (C2×C28).883C23, (C22×C4).471D14, C4.37(C22×Dic7), (C22×C4).21Dic7, C23.43(C2×Dic7), (C22×C28).568C22, C22.27(C22×Dic7), (C2×C14)⋊9(C2×C8), (C2×C28).321(C2×C4), (C2×C4).105(C2×Dic7), (C2×C4).826(C22×D7), (C2×C14).204(C22×C4), (C22×C14).139(C2×C4), SmallGroup(448,1233)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C7 — C23×C7⋊C8
Chief series
C1 — C7 — C14 — C28 — C7⋊C8 — C2×C7⋊C8 — C22×C7⋊C8 — C23×C7⋊C8
Lower central
C7 — C23×C7⋊C8
Upper central
C1 — C23×C4

Generators and relations for C23×C7⋊C8
 G = < a,b,c,d,e | a2=b2=c2=d7=e8=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

Subgroups: 644 in 338 conjugacy classes, 287 normal (11 characteristic)
C1, C2, C2, C4, C4, C22, C7, C8, C2×C4, C23, C14, C14, C2×C8, C22×C4, C24, C28, C28, C2×C14, C22×C8, C23×C4, C7⋊C8, C2×C28, C22×C14, C23×C8, C2×C7⋊C8, C22×C28, C23×C14, C22×C7⋊C8, C23×C28, C23×C7⋊C8
Quotients: C1, C2, C4, C22, C8, C2×C4, C23, D7, C2×C8, C22×C4, C24, Dic7, D14, C22×C8, C23×C4, C7⋊C8, C2×Dic7, C22×D7, C23×C8, C2×C7⋊C8, C22×Dic7, C23×D7, C22×C7⋊C8, C23×Dic7, C23×C7⋊C8

Smallest permutation representation of C23×C7⋊C8
►Regular action on 448 points
Generators in S448
(1 225)(2 226)(3 227)(4 228)(5 229)(6 230)(7 231)(8 232)(9 238)(10 239)(11 240)(12 233)(13 234)(14 235)(15 236)(16 237)(17 75)(18 76)(19 77)(20 78)(21 79)(22 80)(23 73)(24 74)(25 135)(26 136)(27 129)(28 130)(29 131)(30 132)(31 133)(32 134)(33 393)(34 394)(35 395)(36 396)(37 397)(38 398)(39 399)(40 400)(41 401)(42 402)(43 403)(44 404)(45 405)(46 406)(47 407)(48 408)(49 161)(50 162)(51 163)(52 164)(53 165)(54 166)(55 167)(56 168)(57 298)(58 299)(59 300)(60 301)(61 302)(62 303)(63 304)(64 297)(65 294)(66 295)(67 296)(68 289)(69 290)(70 291)(71 292)(72 293)(81 124)(82 125)(83 126)(84 127)(85 128)(86 121)(87 122)(88 123)(89 446)(90 447)(91 448)(92 441)(93 442)(94 443)(95 444)(96 445)(97 421)(98 422)(99 423)(100 424)(101 417)(102 418)(103 419)(104 420)(105 139)(106 140)(107 141)(108 142)(109 143)(110 144)(111 137)(112 138)(113 315)(114 316)(115 317)(116 318)(117 319)(118 320)(119 313)(120 314)(145 257)(146 258)(147 259)(148 260)(149 261)(150 262)(151 263)(152 264)(153 265)(154 266)(155 267)(156 268)(157 269)(158 270)(159 271)(160 272)(169 284)(170 285)(171 286)(172 287)(173 288)(174 281)(175 282)(176 283)(177 365)(178 366)(179 367)(180 368)(181 361)(182 362)(183 363)(184 364)(185 195)(186 196)(187 197)(188 198)(189 199)(190 200)(191 193)(192 194)(201 337)(202 338)(203 339)(204 340)(205 341)(206 342)(207 343)(208 344)(209 345)(210 346)(211 347)(212 348)(213 349)(214 350)(215 351)(216 352)(217 359)(218 360)(219 353)(220 354)(221 355)(222 356)(223 357)(224 358)(241 411)(242 412)(243 413)(244 414)(245 415)(246 416)(247 409)(248 410)(249 433)(250 434)(251 435)(252 436)(253 437)(254 438)(255 439)(256 440)(273 426)(274 427)(275 428)(276 429)(277 430)(278 431)(279 432)(280 425)(305 370)(306 371)(307 372)(308 373)(309 374)(310 375)(311 376)(312 369)(321 385)(322 386)(323 387)(324 388)(325 389)(326 390)(327 391)(328 392)(329 377)(330 378)(331 379)(332 380)(333 381)(334 382)(335 383)(336 384)

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

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

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

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

160 conjugacy classes

class 1 2A···2O4A···4P7A7B7C8A···8AF14A···14AS28A···28AV
order12···24···47778···814···1428···28
size11···11···12227···72···22···2

160 irreducible representations

dim11111122222
type++++-+-
imageC1C2C2C4C4C8D7Dic7D14Dic7C7⋊C8
kernelC23×C7⋊C8C22×C7⋊C8C23×C28C22×C28C23×C14C22×C14C23×C4C22×C4C22×C4C24C23
# reps11411423232121348

Matrix representation of C23×C7⋊C8 ►in GL5(𝔽113)

1120000
0112000
0011200
00010
00001
,
1120000
01000
0011200
0001120
0000112
,
10000
0112000
0011200
0001120
0000112
,
10000
01000
00100
00080112
00081112
,
150000
0112000
00100
0002064
0002493

G:=sub<GL(5,GF(113))| [112,0,0,0,0,0,112,0,0,0,0,0,112,0,0,0,0,0,1,0,0,0,0,0,1],[112,0,0,0,0,0,1,0,0,0,0,0,112,0,0,0,0,0,112,0,0,0,0,0,112],[1,0,0,0,0,0,112,0,0,0,0,0,112,0,0,0,0,0,112,0,0,0,0,0,112],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,80,81,0,0,0,112,112],[15,0,0,0,0,0,112,0,0,0,0,0,1,0,0,0,0,0,20,24,0,0,0,64,93] >;
 

C23×C7⋊C8 in GAP, Magma, Sage, TeX 

C_2^3\times C_7\rtimes C_8
 
% in TeX
 
G:=Group("C2^3xC7:C8");
 
// GroupNames label
 
G:=SmallGroup(448,1233);
 
// by ID
 
G=gap.SmallGroup(448,1233);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,102,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^7=e^8=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
 
// generators/relations
 

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