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G = C24×C26order 416 = 25·13

Abelian group of type [2,2,2,2,26]

direct product, abelian, monomial, 2-elementary

Aliases: C24×C26, SmallGroup(416,235)

Series: Derived Chief Lower central Upper central

C1 — C24×C26
C1C13C26C2×C26C22×C26C23×C26 — C24×C26
C1 — C24×C26
C1 — C24×C26

Generators and relations for C24×C26
 G = < a,b,c,d,e | a2=b2=c2=d2=e26=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, de=ed >

Subgroups: 748, all normal (4 characteristic)
C1, C2 [×31], C22 [×155], C23 [×155], C13, C24 [×31], C26 [×31], C25, C2×C26 [×155], C22×C26 [×155], C23×C26 [×31], C24×C26
Quotients: C1, C2 [×31], C22 [×155], C23 [×155], C13, C24 [×31], C26 [×31], C25, C2×C26 [×155], C22×C26 [×155], C23×C26 [×31], C24×C26

Smallest permutation representation of C24×C26
Regular action on 416 points
Generators in S416
(1 227)(2 228)(3 229)(4 230)(5 231)(6 232)(7 233)(8 234)(9 209)(10 210)(11 211)(12 212)(13 213)(14 214)(15 215)(16 216)(17 217)(18 218)(19 219)(20 220)(21 221)(22 222)(23 223)(24 224)(25 225)(26 226)(27 247)(28 248)(29 249)(30 250)(31 251)(32 252)(33 253)(34 254)(35 255)(36 256)(37 257)(38 258)(39 259)(40 260)(41 235)(42 236)(43 237)(44 238)(45 239)(46 240)(47 241)(48 242)(49 243)(50 244)(51 245)(52 246)(53 270)(54 271)(55 272)(56 273)(57 274)(58 275)(59 276)(60 277)(61 278)(62 279)(63 280)(64 281)(65 282)(66 283)(67 284)(68 285)(69 286)(70 261)(71 262)(72 263)(73 264)(74 265)(75 266)(76 267)(77 268)(78 269)(79 308)(80 309)(81 310)(82 311)(83 312)(84 287)(85 288)(86 289)(87 290)(88 291)(89 292)(90 293)(91 294)(92 295)(93 296)(94 297)(95 298)(96 299)(97 300)(98 301)(99 302)(100 303)(101 304)(102 305)(103 306)(104 307)(105 317)(106 318)(107 319)(108 320)(109 321)(110 322)(111 323)(112 324)(113 325)(114 326)(115 327)(116 328)(117 329)(118 330)(119 331)(120 332)(121 333)(122 334)(123 335)(124 336)(125 337)(126 338)(127 313)(128 314)(129 315)(130 316)(131 363)(132 364)(133 339)(134 340)(135 341)(136 342)(137 343)(138 344)(139 345)(140 346)(141 347)(142 348)(143 349)(144 350)(145 351)(146 352)(147 353)(148 354)(149 355)(150 356)(151 357)(152 358)(153 359)(154 360)(155 361)(156 362)(157 366)(158 367)(159 368)(160 369)(161 370)(162 371)(163 372)(164 373)(165 374)(166 375)(167 376)(168 377)(169 378)(170 379)(171 380)(172 381)(173 382)(174 383)(175 384)(176 385)(177 386)(178 387)(179 388)(180 389)(181 390)(182 365)(183 391)(184 392)(185 393)(186 394)(187 395)(188 396)(189 397)(190 398)(191 399)(192 400)(193 401)(194 402)(195 403)(196 404)(197 405)(198 406)(199 407)(200 408)(201 409)(202 410)(203 411)(204 412)(205 413)(206 414)(207 415)(208 416)
(1 127)(2 128)(3 129)(4 130)(5 105)(6 106)(7 107)(8 108)(9 109)(10 110)(11 111)(12 112)(13 113)(14 114)(15 115)(16 116)(17 117)(18 118)(19 119)(20 120)(21 121)(22 122)(23 123)(24 124)(25 125)(26 126)(27 143)(28 144)(29 145)(30 146)(31 147)(32 148)(33 149)(34 150)(35 151)(36 152)(37 153)(38 154)(39 155)(40 156)(41 131)(42 132)(43 133)(44 134)(45 135)(46 136)(47 137)(48 138)(49 139)(50 140)(51 141)(52 142)(53 161)(54 162)(55 163)(56 164)(57 165)(58 166)(59 167)(60 168)(61 169)(62 170)(63 171)(64 172)(65 173)(66 174)(67 175)(68 176)(69 177)(70 178)(71 179)(72 180)(73 181)(74 182)(75 157)(76 158)(77 159)(78 160)(79 203)(80 204)(81 205)(82 206)(83 207)(84 208)(85 183)(86 184)(87 185)(88 186)(89 187)(90 188)(91 189)(92 190)(93 191)(94 192)(95 193)(96 194)(97 195)(98 196)(99 197)(100 198)(101 199)(102 200)(103 201)(104 202)(209 321)(210 322)(211 323)(212 324)(213 325)(214 326)(215 327)(216 328)(217 329)(218 330)(219 331)(220 332)(221 333)(222 334)(223 335)(224 336)(225 337)(226 338)(227 313)(228 314)(229 315)(230 316)(231 317)(232 318)(233 319)(234 320)(235 363)(236 364)(237 339)(238 340)(239 341)(240 342)(241 343)(242 344)(243 345)(244 346)(245 347)(246 348)(247 349)(248 350)(249 351)(250 352)(251 353)(252 354)(253 355)(254 356)(255 357)(256 358)(257 359)(258 360)(259 361)(260 362)(261 387)(262 388)(263 389)(264 390)(265 365)(266 366)(267 367)(268 368)(269 369)(270 370)(271 371)(272 372)(273 373)(274 374)(275 375)(276 376)(277 377)(278 378)(279 379)(280 380)(281 381)(282 382)(283 383)(284 384)(285 385)(286 386)(287 416)(288 391)(289 392)(290 393)(291 394)(292 395)(293 396)(294 397)(295 398)(296 399)(297 400)(298 401)(299 402)(300 403)(301 404)(302 405)(303 406)(304 407)(305 408)(306 409)(307 410)(308 411)(309 412)(310 413)(311 414)(312 415)
(1 69)(2 70)(3 71)(4 72)(5 73)(6 74)(7 75)(8 76)(9 77)(10 78)(11 53)(12 54)(13 55)(14 56)(15 57)(16 58)(17 59)(18 60)(19 61)(20 62)(21 63)(22 64)(23 65)(24 66)(25 67)(26 68)(27 88)(28 89)(29 90)(30 91)(31 92)(32 93)(33 94)(34 95)(35 96)(36 97)(37 98)(38 99)(39 100)(40 101)(41 102)(42 103)(43 104)(44 79)(45 80)(46 81)(47 82)(48 83)(49 84)(50 85)(51 86)(52 87)(105 181)(106 182)(107 157)(108 158)(109 159)(110 160)(111 161)(112 162)(113 163)(114 164)(115 165)(116 166)(117 167)(118 168)(119 169)(120 170)(121 171)(122 172)(123 173)(124 174)(125 175)(126 176)(127 177)(128 178)(129 179)(130 180)(131 200)(132 201)(133 202)(134 203)(135 204)(136 205)(137 206)(138 207)(139 208)(140 183)(141 184)(142 185)(143 186)(144 187)(145 188)(146 189)(147 190)(148 191)(149 192)(150 193)(151 194)(152 195)(153 196)(154 197)(155 198)(156 199)(209 268)(210 269)(211 270)(212 271)(213 272)(214 273)(215 274)(216 275)(217 276)(218 277)(219 278)(220 279)(221 280)(222 281)(223 282)(224 283)(225 284)(226 285)(227 286)(228 261)(229 262)(230 263)(231 264)(232 265)(233 266)(234 267)(235 305)(236 306)(237 307)(238 308)(239 309)(240 310)(241 311)(242 312)(243 287)(244 288)(245 289)(246 290)(247 291)(248 292)(249 293)(250 294)(251 295)(252 296)(253 297)(254 298)(255 299)(256 300)(257 301)(258 302)(259 303)(260 304)(313 386)(314 387)(315 388)(316 389)(317 390)(318 365)(319 366)(320 367)(321 368)(322 369)(323 370)(324 371)(325 372)(326 373)(327 374)(328 375)(329 376)(330 377)(331 378)(332 379)(333 380)(334 381)(335 382)(336 383)(337 384)(338 385)(339 410)(340 411)(341 412)(342 413)(343 414)(344 415)(345 416)(346 391)(347 392)(348 393)(349 394)(350 395)(351 396)(352 397)(353 398)(354 399)(355 400)(356 401)(357 402)(358 403)(359 404)(360 405)(361 406)(362 407)(363 408)(364 409)
(1 41)(2 42)(3 43)(4 44)(5 45)(6 46)(7 47)(8 48)(9 49)(10 50)(11 51)(12 52)(13 27)(14 28)(15 29)(16 30)(17 31)(18 32)(19 33)(20 34)(21 35)(22 36)(23 37)(24 38)(25 39)(26 40)(53 86)(54 87)(55 88)(56 89)(57 90)(58 91)(59 92)(60 93)(61 94)(62 95)(63 96)(64 97)(65 98)(66 99)(67 100)(68 101)(69 102)(70 103)(71 104)(72 79)(73 80)(74 81)(75 82)(76 83)(77 84)(78 85)(105 135)(106 136)(107 137)(108 138)(109 139)(110 140)(111 141)(112 142)(113 143)(114 144)(115 145)(116 146)(117 147)(118 148)(119 149)(120 150)(121 151)(122 152)(123 153)(124 154)(125 155)(126 156)(127 131)(128 132)(129 133)(130 134)(157 206)(158 207)(159 208)(160 183)(161 184)(162 185)(163 186)(164 187)(165 188)(166 189)(167 190)(168 191)(169 192)(170 193)(171 194)(172 195)(173 196)(174 197)(175 198)(176 199)(177 200)(178 201)(179 202)(180 203)(181 204)(182 205)(209 243)(210 244)(211 245)(212 246)(213 247)(214 248)(215 249)(216 250)(217 251)(218 252)(219 253)(220 254)(221 255)(222 256)(223 257)(224 258)(225 259)(226 260)(227 235)(228 236)(229 237)(230 238)(231 239)(232 240)(233 241)(234 242)(261 306)(262 307)(263 308)(264 309)(265 310)(266 311)(267 312)(268 287)(269 288)(270 289)(271 290)(272 291)(273 292)(274 293)(275 294)(276 295)(277 296)(278 297)(279 298)(280 299)(281 300)(282 301)(283 302)(284 303)(285 304)(286 305)(313 363)(314 364)(315 339)(316 340)(317 341)(318 342)(319 343)(320 344)(321 345)(322 346)(323 347)(324 348)(325 349)(326 350)(327 351)(328 352)(329 353)(330 354)(331 355)(332 356)(333 357)(334 358)(335 359)(336 360)(337 361)(338 362)(365 413)(366 414)(367 415)(368 416)(369 391)(370 392)(371 393)(372 394)(373 395)(374 396)(375 397)(376 398)(377 399)(378 400)(379 401)(380 402)(381 403)(382 404)(383 405)(384 406)(385 407)(386 408)(387 409)(388 410)(389 411)(390 412)
(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)

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

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

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

416 conjugacy classes

class 1 2A···2AE13A···13L26A···26NH
order12···213···1326···26
size11···11···11···1

416 irreducible representations

dim1111
type++
imageC1C2C13C26
kernelC24×C26C23×C26C25C24
# reps13112372

Matrix representation of C24×C26 in GL5(𝔽53)

520000
01000
005200
00010
00001
,
10000
052000
00100
00010
00001
,
520000
01000
00100
000520
000052
,
10000
052000
005200
000520
00001
,
160000
037000
001600
000520
000024

G:=sub<GL(5,GF(53))| [52,0,0,0,0,0,1,0,0,0,0,0,52,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,52,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[52,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,52,0,0,0,0,0,52],[1,0,0,0,0,0,52,0,0,0,0,0,52,0,0,0,0,0,52,0,0,0,0,0,1],[16,0,0,0,0,0,37,0,0,0,0,0,16,0,0,0,0,0,52,0,0,0,0,0,24] >;

C24×C26 in GAP, Magma, Sage, TeX

C_2^4\times C_{26}
% in TeX

G:=Group("C2^4xC26");
// GroupNames label

G:=SmallGroup(416,235);
// by ID

G=gap.SmallGroup(416,235);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-13]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^2=e^26=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,d*e=e*d>;
// generators/relations

׿
×
𝔽