C2^3xDic13 - GroupNames

G = C₂³×Dic₁₃ order 416 = 2⁵·13

Direct product of C₂³ and Dic₁₃

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

Aliases: C₂³×Dic₁₃, C₂⁴.₂D₁₃, C₂₆.₁₄C₂⁴, C₂³.₃₆D₂₆, C₁₃⋊₃(C₂³×C₄), C₂₆⋊₃(C₂²×C₄), (C₂²×C₂₆)⋊₈C₄, (C₂³×C₂₆).₃C₂, C₂.₂(C₂³×D₁₃), (C₂×C₂₆).₆₉C₂³, (C₂²×C₂₆).₄₇C₂², C₂².₃₃(C₂²×D₁₃), (C₂×C₂₆)⋊₁₂(C₂×C₄), SmallGroup(416,225)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₁₃ — C₂³×Dic₁₃

Chief series

C₁ — C₁₃ — C₂₆ — Dic₁₃ — C₂×Dic₁₃ — C₂²×Dic₁₃ — C₂³×Dic₁₃

Lower central

C₁₃ — C₂³×Dic₁₃

Upper central

C₁ — C₂⁴

Generators and relations for C₂³×Dic₁₃
G = < a,b,c,d,e | a²=b²=c²=d²⁶=1, e²=d¹³, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede^-1=d^-1 >

Subgroups: 848 in 236 conjugacy classes, 185 normal (7 characteristic)
C₁, C₂, C₂, C₄, C₂², C₂×C₄, C₂³, C₁₃, C₂²×C₄, C₂⁴, C₂₆, C₂₆, C₂³×C₄, Dic₁₃, C₂×C₂₆, C₂×Dic₁₃, C₂²×C₂₆, C₂²×Dic₁₃, C₂³×C₂₆, C₂³×Dic₁₃
Quotients: C₁, C₂, C₄, C₂², C₂×C₄, C₂³, C₂²×C₄, C₂⁴, D₁₃, C₂³×C₄, Dic₁₃, D₂₆, C₂×Dic₁₃, C₂²×D₁₃, C₂²×Dic₁₃, C₂³×D₁₃, C₂³×Dic₁₃

Smallest permutation representation of C₂³×Dic₁₃
►Regular action on 416 points

Generators in S₄₁₆

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

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

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

(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)

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

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

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

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

128 conjugacy classes

class	1	2A	···	2O	4A	···	4P	13A	···	13F	26A	···	26CL
order	1	2	···	2	4	···	4	13	···	13	26	···	26
size	1	1	···	1	13	···	13	2	···	2	2	···	2

128 irreducible representations

dim	1	1	1	1	2	2	2
type	+	+	+		+	-	+
image	C₁	C₂	C₂	C₄	D₁₃	Dic₁₃	D₂₆
kernel	C₂³×Dic₁₃	C₂²×Dic₁₃	C₂³×C₂₆	C₂²×C₂₆	C₂⁴	C₂³	C₂³
# reps	1	14	1	16	6	48	42

Matrix representation of C₂³×Dic₁₃ ►in GL₅(𝔽₅₃)

1	0	0	0	0
0	52	0	0	0
0	0	52	0	0
0	0	0	52	0
0	0	0	0	52

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

1	0	0	0	0
0	1	0	0	0
0	0	1	0	0
0	0	0	1	52
0	0	0	15	39

1	0	0	0	0
0	52	0	0	0
0	0	52	0	0
0	0	0	10	29
0	0	0	2	43

G:=sub<GL(5,GF(53))| [1,0,0,0,0,0,52,0,0,0,0,0,52,0,0,0,0,0,52,0,0,0,0,0,52],[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],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,15,0,0,0,52,39],[1,0,0,0,0,0,52,0,0,0,0,0,52,0,0,0,0,0,10,2,0,0,0,29,43] >;

C₂³×Dic₁₃ in GAP, Magma, Sage, TeX

C_2^3\times {\rm Dic}_{13}

% in TeX

G:=Group("C2^3xDic13");

// GroupNames label

G:=SmallGroup(416,225);

// by ID

G=gap.SmallGroup(416,225);

# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-13,96,13829]);

// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^26=1,e^2=d^13,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

G = C23×Dic13 order 416 = 25·13

Direct product of C23 and Dic13

G = C₂³×Dic₁₃ order 416 = 2⁵·13

Direct product of C₂³ and Dic₁₃