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G = C24×C26  order 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

Derived series
C1 — C24×C26
Chief series
C1 — C13 — C26 — C2×C26 — C22×C26 — C23×C26 — C24×C26
Lower central
C1 — C24×C26
Upper central
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, C22, C23, C13, C24, C26, C25, C2×C26, C22×C26, C23×C26, C24×C26
Quotients: C1, C2, C22, C23, C13, C24, C26, C25, C2×C26, C22×C26, C23×C26, C24×C26

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

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

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

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

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

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