direct product, metacyclic, supersoluble, monomial, A-group
Aliases: C22×C13⋊C9, C26⋊2C18, C78.7C6, (C2×C26)⋊3C9, C13⋊2(C2×C18), C39.2(C2×C6), (C2×C78).3C3, C6.3(C2×C13⋊C3), C3.(C22×C13⋊C3), (C2×C6).2(C13⋊C3), SmallGroup(468,12)
Series: Derived ►Chief ►Lower central ►Upper central
| C13 — C22×C13⋊C9 |
Generators and relations for C22×C13⋊C9
G = < a,b,c,d | a2=b2=c13=d9=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c9 >
Smallest permutation representation of C22×C13⋊C9
►Regular action on 468 points
Generators in S468
(1 235)(2 236)(3 237)(4 238)(5 239)(6 240)(7 241)(8 242)(9 243)(10 244)(11 245)(12 246)(13 247)(14 248)(15 249)(16 250)(17 251)(18 252)(19 253)(20 254)(21 255)(22 256)(23 257)(24 258)(25 259)(26 260)(27 261)(28 262)(29 263)(30 264)(31 265)(32 266)(33 267)(34 268)(35 269)(36 270)(37 271)(38 272)(39 273)(40 280)(41 281)(42 282)(43 283)(44 284)(45 285)(46 286)(47 274)(48 275)(49 276)(50 277)(51 278)(52 279)(53 297)(54 298)(55 299)(56 287)(57 288)(58 289)(59 290)(60 291)(61 292)(62 293)(63 294)(64 295)(65 296)(66 312)(67 300)(68 301)(69 302)(70 303)(71 304)(72 305)(73 306)(74 307)(75 308)(76 309)(77 310)(78 311)(79 325)(80 313)(81 314)(82 315)(83 316)(84 317)(85 318)(86 319)(87 320)(88 321)(89 322)(90 323)(91 324)(92 326)(93 327)(94 328)(95 329)(96 330)(97 331)(98 332)(99 333)(100 334)(101 335)(102 336)(103 337)(104 338)(105 343)(106 344)(107 345)(108 346)(109 347)(110 348)(111 349)(112 350)(113 351)(114 339)(115 340)(116 341)(117 342)(118 352)(119 353)(120 354)(121 355)(122 356)(123 357)(124 358)(125 359)(126 360)(127 361)(128 362)(129 363)(130 364)(131 365)(132 366)(133 367)(134 368)(135 369)(136 370)(137 371)(138 372)(139 373)(140 374)(141 375)(142 376)(143 377)(144 378)(145 379)(146 380)(147 381)(148 382)(149 383)(150 384)(151 385)(152 386)(153 387)(154 388)(155 389)(156 390)(157 394)(158 395)(159 396)(160 397)(161 398)(162 399)(163 400)(164 401)(165 402)(166 403)(167 391)(168 392)(169 393)(170 409)(171 410)(172 411)(173 412)(174 413)(175 414)(176 415)(177 416)(178 404)(179 405)(180 406)(181 407)(182 408)(183 419)(184 420)(185 421)(186 422)(187 423)(188 424)(189 425)(190 426)(191 427)(192 428)(193 429)(194 417)(195 418)(196 433)(197 434)(198 435)(199 436)(200 437)(201 438)(202 439)(203 440)(204 441)(205 442)(206 430)(207 431)(208 432)(209 444)(210 445)(211 446)(212 447)(213 448)(214 449)(215 450)(216 451)(217 452)(218 453)(219 454)(220 455)(221 443)(222 456)(223 457)(224 458)(225 459)(226 460)(227 461)(228 462)(229 463)(230 464)(231 465)(232 466)(233 467)(234 468)
(1 118)(2 119)(3 120)(4 121)(5 122)(6 123)(7 124)(8 125)(9 126)(10 127)(11 128)(12 129)(13 130)(14 131)(15 132)(16 133)(17 134)(18 135)(19 136)(20 137)(21 138)(22 139)(23 140)(24 141)(25 142)(26 143)(27 144)(28 145)(29 146)(30 147)(31 148)(32 149)(33 150)(34 151)(35 152)(36 153)(37 154)(38 155)(39 156)(40 166)(41 167)(42 168)(43 169)(44 157)(45 158)(46 159)(47 160)(48 161)(49 162)(50 163)(51 164)(52 165)(53 182)(54 170)(55 171)(56 172)(57 173)(58 174)(59 175)(60 176)(61 177)(62 178)(63 179)(64 180)(65 181)(66 189)(67 190)(68 191)(69 192)(70 193)(71 194)(72 195)(73 183)(74 184)(75 185)(76 186)(77 187)(78 188)(79 207)(80 208)(81 196)(82 197)(83 198)(84 199)(85 200)(86 201)(87 202)(88 203)(89 204)(90 205)(91 206)(92 221)(93 209)(94 210)(95 211)(96 212)(97 213)(98 214)(99 215)(100 216)(101 217)(102 218)(103 219)(104 220)(105 226)(106 227)(107 228)(108 229)(109 230)(110 231)(111 232)(112 233)(113 234)(114 222)(115 223)(116 224)(117 225)(235 352)(236 353)(237 354)(238 355)(239 356)(240 357)(241 358)(242 359)(243 360)(244 361)(245 362)(246 363)(247 364)(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)(261 378)(262 379)(263 380)(264 381)(265 382)(266 383)(267 384)(268 385)(269 386)(270 387)(271 388)(272 389)(273 390)(274 397)(275 398)(276 399)(277 400)(278 401)(279 402)(280 403)(281 391)(282 392)(283 393)(284 394)(285 395)(286 396)(287 411)(288 412)(289 413)(290 414)(291 415)(292 416)(293 404)(294 405)(295 406)(296 407)(297 408)(298 409)(299 410)(300 426)(301 427)(302 428)(303 429)(304 417)(305 418)(306 419)(307 420)(308 421)(309 422)(310 423)(311 424)(312 425)(313 432)(314 433)(315 434)(316 435)(317 436)(318 437)(319 438)(320 439)(321 440)(322 441)(323 442)(324 430)(325 431)(326 443)(327 444)(328 445)(329 446)(330 447)(331 448)(332 449)(333 450)(334 451)(335 452)(336 453)(337 454)(338 455)(339 456)(340 457)(341 458)(342 459)(343 460)(344 461)(345 462)(346 463)(347 464)(348 465)(349 466)(350 467)(351 468)
(1 2 3 4 5 6 7 8 9 10 11 12 13)(14 15 16 17 18 19 20 21 22 23 24 25 26)(27 28 29 30 31 32 33 34 35 36 37 38 39)(40 41 42 43 44 45 46 47 48 49 50 51 52)(53 54 55 56 57 58 59 60 61 62 63 64 65)(66 67 68 69 70 71 72 73 74 75 76 77 78)(79 80 81 82 83 84 85 86 87 88 89 90 91)(92 93 94 95 96 97 98 99 100 101 102 103 104)(105 106 107 108 109 110 111 112 113 114 115 116 117)(118 119 120 121 122 123 124 125 126 127 128 129 130)(131 132 133 134 135 136 137 138 139 140 141 142 143)(144 145 146 147 148 149 150 151 152 153 154 155 156)(157 158 159 160 161 162 163 164 165 166 167 168 169)(170 171 172 173 174 175 176 177 178 179 180 181 182)(183 184 185 186 187 188 189 190 191 192 193 194 195)(196 197 198 199 200 201 202 203 204 205 206 207 208)(209 210 211 212 213 214 215 216 217 218 219 220 221)(222 223 224 225 226 227 228 229 230 231 232 233 234)(235 236 237 238 239 240 241 242 243 244 245 246 247)(248 249 250 251 252 253 254 255 256 257 258 259 260)(261 262 263 264 265 266 267 268 269 270 271 272 273)(274 275 276 277 278 279 280 281 282 283 284 285 286)(287 288 289 290 291 292 293 294 295 296 297 298 299)(300 301 302 303 304 305 306 307 308 309 310 311 312)(313 314 315 316 317 318 319 320 321 322 323 324 325)(326 327 328 329 330 331 332 333 334 335 336 337 338)(339 340 341 342 343 344 345 346 347 348 349 350 351)(352 353 354 355 356 357 358 359 360 361 362 363 364)(365 366 367 368 369 370 371 372 373 374 375 376 377)(378 379 380 381 382 383 384 385 386 387 388 389 390)(391 392 393 394 395 396 397 398 399 400 401 402 403)(404 405 406 407 408 409 410 411 412 413 414 415 416)(417 418 419 420 421 422 423 424 425 426 427 428 429)(430 431 432 433 434 435 436 437 438 439 440 441 442)(443 444 445 446 447 448 449 450 451 452 453 454 455)(456 457 458 459 460 461 462 463 464 465 466 467 468)
(1 116 74 27 93 65 14 91 40)(2 106 70 28 96 61 15 81 49)(3 109 66 29 99 57 16 84 45)(4 112 75 30 102 53 17 87 41)(5 115 71 31 92 62 18 90 50)(6 105 67 32 95 58 19 80 46)(7 108 76 33 98 54 20 83 42)(8 111 72 34 101 63 21 86 51)(9 114 68 35 104 59 22 89 47)(10 117 77 36 94 55 23 79 43)(11 107 73 37 97 64 24 82 52)(12 110 69 38 100 60 25 85 48)(13 113 78 39 103 56 26 88 44)(118 224 184 144 209 181 131 206 166)(119 227 193 145 212 177 132 196 162)(120 230 189 146 215 173 133 199 158)(121 233 185 147 218 182 134 202 167)(122 223 194 148 221 178 135 205 163)(123 226 190 149 211 174 136 208 159)(124 229 186 150 214 170 137 198 168)(125 232 195 151 217 179 138 201 164)(126 222 191 152 220 175 139 204 160)(127 225 187 153 210 171 140 207 169)(128 228 183 154 213 180 141 197 165)(129 231 192 155 216 176 142 200 161)(130 234 188 156 219 172 143 203 157)(235 341 307 261 327 296 248 324 280)(236 344 303 262 330 292 249 314 276)(237 347 312 263 333 288 250 317 285)(238 350 308 264 336 297 251 320 281)(239 340 304 265 326 293 252 323 277)(240 343 300 266 329 289 253 313 286)(241 346 309 267 332 298 254 316 282)(242 349 305 268 335 294 255 319 278)(243 339 301 269 338 290 256 322 274)(244 342 310 270 328 299 257 325 283)(245 345 306 271 331 295 258 315 279)(246 348 302 272 334 291 259 318 275)(247 351 311 273 337 287 260 321 284)(352 458 420 378 444 407 365 430 403)(353 461 429 379 447 416 366 433 399)(354 464 425 380 450 412 367 436 395)(355 467 421 381 453 408 368 439 391)(356 457 417 382 443 404 369 442 400)(357 460 426 383 446 413 370 432 396)(358 463 422 384 449 409 371 435 392)(359 466 418 385 452 405 372 438 401)(360 456 427 386 455 414 373 441 397)(361 459 423 387 445 410 374 431 393)(362 462 419 388 448 406 375 434 402)(363 465 428 389 451 415 376 437 398)(364 468 424 390 454 411 377 440 394)
G:=sub<Sym(468)| (1,235)(2,236)(3,237)(4,238)(5,239)(6,240)(7,241)(8,242)(9,243)(10,244)(11,245)(12,246)(13,247)(14,248)(15,249)(16,250)(17,251)(18,252)(19,253)(20,254)(21,255)(22,256)(23,257)(24,258)(25,259)(26,260)(27,261)(28,262)(29,263)(30,264)(31,265)(32,266)(33,267)(34,268)(35,269)(36,270)(37,271)(38,272)(39,273)(40,280)(41,281)(42,282)(43,283)(44,284)(45,285)(46,286)(47,274)(48,275)(49,276)(50,277)(51,278)(52,279)(53,297)(54,298)(55,299)(56,287)(57,288)(58,289)(59,290)(60,291)(61,292)(62,293)(63,294)(64,295)(65,296)(66,312)(67,300)(68,301)(69,302)(70,303)(71,304)(72,305)(73,306)(74,307)(75,308)(76,309)(77,310)(78,311)(79,325)(80,313)(81,314)(82,315)(83,316)(84,317)(85,318)(86,319)(87,320)(88,321)(89,322)(90,323)(91,324)(92,326)(93,327)(94,328)(95,329)(96,330)(97,331)(98,332)(99,333)(100,334)(101,335)(102,336)(103,337)(104,338)(105,343)(106,344)(107,345)(108,346)(109,347)(110,348)(111,349)(112,350)(113,351)(114,339)(115,340)(116,341)(117,342)(118,352)(119,353)(120,354)(121,355)(122,356)(123,357)(124,358)(125,359)(126,360)(127,361)(128,362)(129,363)(130,364)(131,365)(132,366)(133,367)(134,368)(135,369)(136,370)(137,371)(138,372)(139,373)(140,374)(141,375)(142,376)(143,377)(144,378)(145,379)(146,380)(147,381)(148,382)(149,383)(150,384)(151,385)(152,386)(153,387)(154,388)(155,389)(156,390)(157,394)(158,395)(159,396)(160,397)(161,398)(162,399)(163,400)(164,401)(165,402)(166,403)(167,391)(168,392)(169,393)(170,409)(171,410)(172,411)(173,412)(174,413)(175,414)(176,415)(177,416)(178,404)(179,405)(180,406)(181,407)(182,408)(183,419)(184,420)(185,421)(186,422)(187,423)(188,424)(189,425)(190,426)(191,427)(192,428)(193,429)(194,417)(195,418)(196,433)(197,434)(198,435)(199,436)(200,437)(201,438)(202,439)(203,440)(204,441)(205,442)(206,430)(207,431)(208,432)(209,444)(210,445)(211,446)(212,447)(213,448)(214,449)(215,450)(216,451)(217,452)(218,453)(219,454)(220,455)(221,443)(222,456)(223,457)(224,458)(225,459)(226,460)(227,461)(228,462)(229,463)(230,464)(231,465)(232,466)(233,467)(234,468), (1,118)(2,119)(3,120)(4,121)(5,122)(6,123)(7,124)(8,125)(9,126)(10,127)(11,128)(12,129)(13,130)(14,131)(15,132)(16,133)(17,134)(18,135)(19,136)(20,137)(21,138)(22,139)(23,140)(24,141)(25,142)(26,143)(27,144)(28,145)(29,146)(30,147)(31,148)(32,149)(33,150)(34,151)(35,152)(36,153)(37,154)(38,155)(39,156)(40,166)(41,167)(42,168)(43,169)(44,157)(45,158)(46,159)(47,160)(48,161)(49,162)(50,163)(51,164)(52,165)(53,182)(54,170)(55,171)(56,172)(57,173)(58,174)(59,175)(60,176)(61,177)(62,178)(63,179)(64,180)(65,181)(66,189)(67,190)(68,191)(69,192)(70,193)(71,194)(72,195)(73,183)(74,184)(75,185)(76,186)(77,187)(78,188)(79,207)(80,208)(81,196)(82,197)(83,198)(84,199)(85,200)(86,201)(87,202)(88,203)(89,204)(90,205)(91,206)(92,221)(93,209)(94,210)(95,211)(96,212)(97,213)(98,214)(99,215)(100,216)(101,217)(102,218)(103,219)(104,220)(105,226)(106,227)(107,228)(108,229)(109,230)(110,231)(111,232)(112,233)(113,234)(114,222)(115,223)(116,224)(117,225)(235,352)(236,353)(237,354)(238,355)(239,356)(240,357)(241,358)(242,359)(243,360)(244,361)(245,362)(246,363)(247,364)(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)(261,378)(262,379)(263,380)(264,381)(265,382)(266,383)(267,384)(268,385)(269,386)(270,387)(271,388)(272,389)(273,390)(274,397)(275,398)(276,399)(277,400)(278,401)(279,402)(280,403)(281,391)(282,392)(283,393)(284,394)(285,395)(286,396)(287,411)(288,412)(289,413)(290,414)(291,415)(292,416)(293,404)(294,405)(295,406)(296,407)(297,408)(298,409)(299,410)(300,426)(301,427)(302,428)(303,429)(304,417)(305,418)(306,419)(307,420)(308,421)(309,422)(310,423)(311,424)(312,425)(313,432)(314,433)(315,434)(316,435)(317,436)(318,437)(319,438)(320,439)(321,440)(322,441)(323,442)(324,430)(325,431)(326,443)(327,444)(328,445)(329,446)(330,447)(331,448)(332,449)(333,450)(334,451)(335,452)(336,453)(337,454)(338,455)(339,456)(340,457)(341,458)(342,459)(343,460)(344,461)(345,462)(346,463)(347,464)(348,465)(349,466)(350,467)(351,468), (1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39)(40,41,42,43,44,45,46,47,48,49,50,51,52)(53,54,55,56,57,58,59,60,61,62,63,64,65)(66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91)(92,93,94,95,96,97,98,99,100,101,102,103,104)(105,106,107,108,109,110,111,112,113,114,115,116,117)(118,119,120,121,122,123,124,125,126,127,128,129,130)(131,132,133,134,135,136,137,138,139,140,141,142,143)(144,145,146,147,148,149,150,151,152,153,154,155,156)(157,158,159,160,161,162,163,164,165,166,167,168,169)(170,171,172,173,174,175,176,177,178,179,180,181,182)(183,184,185,186,187,188,189,190,191,192,193,194,195)(196,197,198,199,200,201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216,217,218,219,220,221)(222,223,224,225,226,227,228,229,230,231,232,233,234)(235,236,237,238,239,240,241,242,243,244,245,246,247)(248,249,250,251,252,253,254,255,256,257,258,259,260)(261,262,263,264,265,266,267,268,269,270,271,272,273)(274,275,276,277,278,279,280,281,282,283,284,285,286)(287,288,289,290,291,292,293,294,295,296,297,298,299)(300,301,302,303,304,305,306,307,308,309,310,311,312)(313,314,315,316,317,318,319,320,321,322,323,324,325)(326,327,328,329,330,331,332,333,334,335,336,337,338)(339,340,341,342,343,344,345,346,347,348,349,350,351)(352,353,354,355,356,357,358,359,360,361,362,363,364)(365,366,367,368,369,370,371,372,373,374,375,376,377)(378,379,380,381,382,383,384,385,386,387,388,389,390)(391,392,393,394,395,396,397,398,399,400,401,402,403)(404,405,406,407,408,409,410,411,412,413,414,415,416)(417,418,419,420,421,422,423,424,425,426,427,428,429)(430,431,432,433,434,435,436,437,438,439,440,441,442)(443,444,445,446,447,448,449,450,451,452,453,454,455)(456,457,458,459,460,461,462,463,464,465,466,467,468), (1,116,74,27,93,65,14,91,40)(2,106,70,28,96,61,15,81,49)(3,109,66,29,99,57,16,84,45)(4,112,75,30,102,53,17,87,41)(5,115,71,31,92,62,18,90,50)(6,105,67,32,95,58,19,80,46)(7,108,76,33,98,54,20,83,42)(8,111,72,34,101,63,21,86,51)(9,114,68,35,104,59,22,89,47)(10,117,77,36,94,55,23,79,43)(11,107,73,37,97,64,24,82,52)(12,110,69,38,100,60,25,85,48)(13,113,78,39,103,56,26,88,44)(118,224,184,144,209,181,131,206,166)(119,227,193,145,212,177,132,196,162)(120,230,189,146,215,173,133,199,158)(121,233,185,147,218,182,134,202,167)(122,223,194,148,221,178,135,205,163)(123,226,190,149,211,174,136,208,159)(124,229,186,150,214,170,137,198,168)(125,232,195,151,217,179,138,201,164)(126,222,191,152,220,175,139,204,160)(127,225,187,153,210,171,140,207,169)(128,228,183,154,213,180,141,197,165)(129,231,192,155,216,176,142,200,161)(130,234,188,156,219,172,143,203,157)(235,341,307,261,327,296,248,324,280)(236,344,303,262,330,292,249,314,276)(237,347,312,263,333,288,250,317,285)(238,350,308,264,336,297,251,320,281)(239,340,304,265,326,293,252,323,277)(240,343,300,266,329,289,253,313,286)(241,346,309,267,332,298,254,316,282)(242,349,305,268,335,294,255,319,278)(243,339,301,269,338,290,256,322,274)(244,342,310,270,328,299,257,325,283)(245,345,306,271,331,295,258,315,279)(246,348,302,272,334,291,259,318,275)(247,351,311,273,337,287,260,321,284)(352,458,420,378,444,407,365,430,403)(353,461,429,379,447,416,366,433,399)(354,464,425,380,450,412,367,436,395)(355,467,421,381,453,408,368,439,391)(356,457,417,382,443,404,369,442,400)(357,460,426,383,446,413,370,432,396)(358,463,422,384,449,409,371,435,392)(359,466,418,385,452,405,372,438,401)(360,456,427,386,455,414,373,441,397)(361,459,423,387,445,410,374,431,393)(362,462,419,388,448,406,375,434,402)(363,465,428,389,451,415,376,437,398)(364,468,424,390,454,411,377,440,394)>;
G:=Group( (1,235)(2,236)(3,237)(4,238)(5,239)(6,240)(7,241)(8,242)(9,243)(10,244)(11,245)(12,246)(13,247)(14,248)(15,249)(16,250)(17,251)(18,252)(19,253)(20,254)(21,255)(22,256)(23,257)(24,258)(25,259)(26,260)(27,261)(28,262)(29,263)(30,264)(31,265)(32,266)(33,267)(34,268)(35,269)(36,270)(37,271)(38,272)(39,273)(40,280)(41,281)(42,282)(43,283)(44,284)(45,285)(46,286)(47,274)(48,275)(49,276)(50,277)(51,278)(52,279)(53,297)(54,298)(55,299)(56,287)(57,288)(58,289)(59,290)(60,291)(61,292)(62,293)(63,294)(64,295)(65,296)(66,312)(67,300)(68,301)(69,302)(70,303)(71,304)(72,305)(73,306)(74,307)(75,308)(76,309)(77,310)(78,311)(79,325)(80,313)(81,314)(82,315)(83,316)(84,317)(85,318)(86,319)(87,320)(88,321)(89,322)(90,323)(91,324)(92,326)(93,327)(94,328)(95,329)(96,330)(97,331)(98,332)(99,333)(100,334)(101,335)(102,336)(103,337)(104,338)(105,343)(106,344)(107,345)(108,346)(109,347)(110,348)(111,349)(112,350)(113,351)(114,339)(115,340)(116,341)(117,342)(118,352)(119,353)(120,354)(121,355)(122,356)(123,357)(124,358)(125,359)(126,360)(127,361)(128,362)(129,363)(130,364)(131,365)(132,366)(133,367)(134,368)(135,369)(136,370)(137,371)(138,372)(139,373)(140,374)(141,375)(142,376)(143,377)(144,378)(145,379)(146,380)(147,381)(148,382)(149,383)(150,384)(151,385)(152,386)(153,387)(154,388)(155,389)(156,390)(157,394)(158,395)(159,396)(160,397)(161,398)(162,399)(163,400)(164,401)(165,402)(166,403)(167,391)(168,392)(169,393)(170,409)(171,410)(172,411)(173,412)(174,413)(175,414)(176,415)(177,416)(178,404)(179,405)(180,406)(181,407)(182,408)(183,419)(184,420)(185,421)(186,422)(187,423)(188,424)(189,425)(190,426)(191,427)(192,428)(193,429)(194,417)(195,418)(196,433)(197,434)(198,435)(199,436)(200,437)(201,438)(202,439)(203,440)(204,441)(205,442)(206,430)(207,431)(208,432)(209,444)(210,445)(211,446)(212,447)(213,448)(214,449)(215,450)(216,451)(217,452)(218,453)(219,454)(220,455)(221,443)(222,456)(223,457)(224,458)(225,459)(226,460)(227,461)(228,462)(229,463)(230,464)(231,465)(232,466)(233,467)(234,468), (1,118)(2,119)(3,120)(4,121)(5,122)(6,123)(7,124)(8,125)(9,126)(10,127)(11,128)(12,129)(13,130)(14,131)(15,132)(16,133)(17,134)(18,135)(19,136)(20,137)(21,138)(22,139)(23,140)(24,141)(25,142)(26,143)(27,144)(28,145)(29,146)(30,147)(31,148)(32,149)(33,150)(34,151)(35,152)(36,153)(37,154)(38,155)(39,156)(40,166)(41,167)(42,168)(43,169)(44,157)(45,158)(46,159)(47,160)(48,161)(49,162)(50,163)(51,164)(52,165)(53,182)(54,170)(55,171)(56,172)(57,173)(58,174)(59,175)(60,176)(61,177)(62,178)(63,179)(64,180)(65,181)(66,189)(67,190)(68,191)(69,192)(70,193)(71,194)(72,195)(73,183)(74,184)(75,185)(76,186)(77,187)(78,188)(79,207)(80,208)(81,196)(82,197)(83,198)(84,199)(85,200)(86,201)(87,202)(88,203)(89,204)(90,205)(91,206)(92,221)(93,209)(94,210)(95,211)(96,212)(97,213)(98,214)(99,215)(100,216)(101,217)(102,218)(103,219)(104,220)(105,226)(106,227)(107,228)(108,229)(109,230)(110,231)(111,232)(112,233)(113,234)(114,222)(115,223)(116,224)(117,225)(235,352)(236,353)(237,354)(238,355)(239,356)(240,357)(241,358)(242,359)(243,360)(244,361)(245,362)(246,363)(247,364)(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)(261,378)(262,379)(263,380)(264,381)(265,382)(266,383)(267,384)(268,385)(269,386)(270,387)(271,388)(272,389)(273,390)(274,397)(275,398)(276,399)(277,400)(278,401)(279,402)(280,403)(281,391)(282,392)(283,393)(284,394)(285,395)(286,396)(287,411)(288,412)(289,413)(290,414)(291,415)(292,416)(293,404)(294,405)(295,406)(296,407)(297,408)(298,409)(299,410)(300,426)(301,427)(302,428)(303,429)(304,417)(305,418)(306,419)(307,420)(308,421)(309,422)(310,423)(311,424)(312,425)(313,432)(314,433)(315,434)(316,435)(317,436)(318,437)(319,438)(320,439)(321,440)(322,441)(323,442)(324,430)(325,431)(326,443)(327,444)(328,445)(329,446)(330,447)(331,448)(332,449)(333,450)(334,451)(335,452)(336,453)(337,454)(338,455)(339,456)(340,457)(341,458)(342,459)(343,460)(344,461)(345,462)(346,463)(347,464)(348,465)(349,466)(350,467)(351,468), (1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39)(40,41,42,43,44,45,46,47,48,49,50,51,52)(53,54,55,56,57,58,59,60,61,62,63,64,65)(66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91)(92,93,94,95,96,97,98,99,100,101,102,103,104)(105,106,107,108,109,110,111,112,113,114,115,116,117)(118,119,120,121,122,123,124,125,126,127,128,129,130)(131,132,133,134,135,136,137,138,139,140,141,142,143)(144,145,146,147,148,149,150,151,152,153,154,155,156)(157,158,159,160,161,162,163,164,165,166,167,168,169)(170,171,172,173,174,175,176,177,178,179,180,181,182)(183,184,185,186,187,188,189,190,191,192,193,194,195)(196,197,198,199,200,201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216,217,218,219,220,221)(222,223,224,225,226,227,228,229,230,231,232,233,234)(235,236,237,238,239,240,241,242,243,244,245,246,247)(248,249,250,251,252,253,254,255,256,257,258,259,260)(261,262,263,264,265,266,267,268,269,270,271,272,273)(274,275,276,277,278,279,280,281,282,283,284,285,286)(287,288,289,290,291,292,293,294,295,296,297,298,299)(300,301,302,303,304,305,306,307,308,309,310,311,312)(313,314,315,316,317,318,319,320,321,322,323,324,325)(326,327,328,329,330,331,332,333,334,335,336,337,338)(339,340,341,342,343,344,345,346,347,348,349,350,351)(352,353,354,355,356,357,358,359,360,361,362,363,364)(365,366,367,368,369,370,371,372,373,374,375,376,377)(378,379,380,381,382,383,384,385,386,387,388,389,390)(391,392,393,394,395,396,397,398,399,400,401,402,403)(404,405,406,407,408,409,410,411,412,413,414,415,416)(417,418,419,420,421,422,423,424,425,426,427,428,429)(430,431,432,433,434,435,436,437,438,439,440,441,442)(443,444,445,446,447,448,449,450,451,452,453,454,455)(456,457,458,459,460,461,462,463,464,465,466,467,468), (1,116,74,27,93,65,14,91,40)(2,106,70,28,96,61,15,81,49)(3,109,66,29,99,57,16,84,45)(4,112,75,30,102,53,17,87,41)(5,115,71,31,92,62,18,90,50)(6,105,67,32,95,58,19,80,46)(7,108,76,33,98,54,20,83,42)(8,111,72,34,101,63,21,86,51)(9,114,68,35,104,59,22,89,47)(10,117,77,36,94,55,23,79,43)(11,107,73,37,97,64,24,82,52)(12,110,69,38,100,60,25,85,48)(13,113,78,39,103,56,26,88,44)(118,224,184,144,209,181,131,206,166)(119,227,193,145,212,177,132,196,162)(120,230,189,146,215,173,133,199,158)(121,233,185,147,218,182,134,202,167)(122,223,194,148,221,178,135,205,163)(123,226,190,149,211,174,136,208,159)(124,229,186,150,214,170,137,198,168)(125,232,195,151,217,179,138,201,164)(126,222,191,152,220,175,139,204,160)(127,225,187,153,210,171,140,207,169)(128,228,183,154,213,180,141,197,165)(129,231,192,155,216,176,142,200,161)(130,234,188,156,219,172,143,203,157)(235,341,307,261,327,296,248,324,280)(236,344,303,262,330,292,249,314,276)(237,347,312,263,333,288,250,317,285)(238,350,308,264,336,297,251,320,281)(239,340,304,265,326,293,252,323,277)(240,343,300,266,329,289,253,313,286)(241,346,309,267,332,298,254,316,282)(242,349,305,268,335,294,255,319,278)(243,339,301,269,338,290,256,322,274)(244,342,310,270,328,299,257,325,283)(245,345,306,271,331,295,258,315,279)(246,348,302,272,334,291,259,318,275)(247,351,311,273,337,287,260,321,284)(352,458,420,378,444,407,365,430,403)(353,461,429,379,447,416,366,433,399)(354,464,425,380,450,412,367,436,395)(355,467,421,381,453,408,368,439,391)(356,457,417,382,443,404,369,442,400)(357,460,426,383,446,413,370,432,396)(358,463,422,384,449,409,371,435,392)(359,466,418,385,452,405,372,438,401)(360,456,427,386,455,414,373,441,397)(361,459,423,387,445,410,374,431,393)(362,462,419,388,448,406,375,434,402)(363,465,428,389,451,415,376,437,398)(364,468,424,390,454,411,377,440,394) );
G=PermutationGroup([[(1,235),(2,236),(3,237),(4,238),(5,239),(6,240),(7,241),(8,242),(9,243),(10,244),(11,245),(12,246),(13,247),(14,248),(15,249),(16,250),(17,251),(18,252),(19,253),(20,254),(21,255),(22,256),(23,257),(24,258),(25,259),(26,260),(27,261),(28,262),(29,263),(30,264),(31,265),(32,266),(33,267),(34,268),(35,269),(36,270),(37,271),(38,272),(39,273),(40,280),(41,281),(42,282),(43,283),(44,284),(45,285),(46,286),(47,274),(48,275),(49,276),(50,277),(51,278),(52,279),(53,297),(54,298),(55,299),(56,287),(57,288),(58,289),(59,290),(60,291),(61,292),(62,293),(63,294),(64,295),(65,296),(66,312),(67,300),(68,301),(69,302),(70,303),(71,304),(72,305),(73,306),(74,307),(75,308),(76,309),(77,310),(78,311),(79,325),(80,313),(81,314),(82,315),(83,316),(84,317),(85,318),(86,319),(87,320),(88,321),(89,322),(90,323),(91,324),(92,326),(93,327),(94,328),(95,329),(96,330),(97,331),(98,332),(99,333),(100,334),(101,335),(102,336),(103,337),(104,338),(105,343),(106,344),(107,345),(108,346),(109,347),(110,348),(111,349),(112,350),(113,351),(114,339),(115,340),(116,341),(117,342),(118,352),(119,353),(120,354),(121,355),(122,356),(123,357),(124,358),(125,359),(126,360),(127,361),(128,362),(129,363),(130,364),(131,365),(132,366),(133,367),(134,368),(135,369),(136,370),(137,371),(138,372),(139,373),(140,374),(141,375),(142,376),(143,377),(144,378),(145,379),(146,380),(147,381),(148,382),(149,383),(150,384),(151,385),(152,386),(153,387),(154,388),(155,389),(156,390),(157,394),(158,395),(159,396),(160,397),(161,398),(162,399),(163,400),(164,401),(165,402),(166,403),(167,391),(168,392),(169,393),(170,409),(171,410),(172,411),(173,412),(174,413),(175,414),(176,415),(177,416),(178,404),(179,405),(180,406),(181,407),(182,408),(183,419),(184,420),(185,421),(186,422),(187,423),(188,424),(189,425),(190,426),(191,427),(192,428),(193,429),(194,417),(195,418),(196,433),(197,434),(198,435),(199,436),(200,437),(201,438),(202,439),(203,440),(204,441),(205,442),(206,430),(207,431),(208,432),(209,444),(210,445),(211,446),(212,447),(213,448),(214,449),(215,450),(216,451),(217,452),(218,453),(219,454),(220,455),(221,443),(222,456),(223,457),(224,458),(225,459),(226,460),(227,461),(228,462),(229,463),(230,464),(231,465),(232,466),(233,467),(234,468)], [(1,118),(2,119),(3,120),(4,121),(5,122),(6,123),(7,124),(8,125),(9,126),(10,127),(11,128),(12,129),(13,130),(14,131),(15,132),(16,133),(17,134),(18,135),(19,136),(20,137),(21,138),(22,139),(23,140),(24,141),(25,142),(26,143),(27,144),(28,145),(29,146),(30,147),(31,148),(32,149),(33,150),(34,151),(35,152),(36,153),(37,154),(38,155),(39,156),(40,166),(41,167),(42,168),(43,169),(44,157),(45,158),(46,159),(47,160),(48,161),(49,162),(50,163),(51,164),(52,165),(53,182),(54,170),(55,171),(56,172),(57,173),(58,174),(59,175),(60,176),(61,177),(62,178),(63,179),(64,180),(65,181),(66,189),(67,190),(68,191),(69,192),(70,193),(71,194),(72,195),(73,183),(74,184),(75,185),(76,186),(77,187),(78,188),(79,207),(80,208),(81,196),(82,197),(83,198),(84,199),(85,200),(86,201),(87,202),(88,203),(89,204),(90,205),(91,206),(92,221),(93,209),(94,210),(95,211),(96,212),(97,213),(98,214),(99,215),(100,216),(101,217),(102,218),(103,219),(104,220),(105,226),(106,227),(107,228),(108,229),(109,230),(110,231),(111,232),(112,233),(113,234),(114,222),(115,223),(116,224),(117,225),(235,352),(236,353),(237,354),(238,355),(239,356),(240,357),(241,358),(242,359),(243,360),(244,361),(245,362),(246,363),(247,364),(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),(261,378),(262,379),(263,380),(264,381),(265,382),(266,383),(267,384),(268,385),(269,386),(270,387),(271,388),(272,389),(273,390),(274,397),(275,398),(276,399),(277,400),(278,401),(279,402),(280,403),(281,391),(282,392),(283,393),(284,394),(285,395),(286,396),(287,411),(288,412),(289,413),(290,414),(291,415),(292,416),(293,404),(294,405),(295,406),(296,407),(297,408),(298,409),(299,410),(300,426),(301,427),(302,428),(303,429),(304,417),(305,418),(306,419),(307,420),(308,421),(309,422),(310,423),(311,424),(312,425),(313,432),(314,433),(315,434),(316,435),(317,436),(318,437),(319,438),(320,439),(321,440),(322,441),(323,442),(324,430),(325,431),(326,443),(327,444),(328,445),(329,446),(330,447),(331,448),(332,449),(333,450),(334,451),(335,452),(336,453),(337,454),(338,455),(339,456),(340,457),(341,458),(342,459),(343,460),(344,461),(345,462),(346,463),(347,464),(348,465),(349,466),(350,467),(351,468)], [(1,2,3,4,5,6,7,8,9,10,11,12,13),(14,15,16,17,18,19,20,21,22,23,24,25,26),(27,28,29,30,31,32,33,34,35,36,37,38,39),(40,41,42,43,44,45,46,47,48,49,50,51,52),(53,54,55,56,57,58,59,60,61,62,63,64,65),(66,67,68,69,70,71,72,73,74,75,76,77,78),(79,80,81,82,83,84,85,86,87,88,89,90,91),(92,93,94,95,96,97,98,99,100,101,102,103,104),(105,106,107,108,109,110,111,112,113,114,115,116,117),(118,119,120,121,122,123,124,125,126,127,128,129,130),(131,132,133,134,135,136,137,138,139,140,141,142,143),(144,145,146,147,148,149,150,151,152,153,154,155,156),(157,158,159,160,161,162,163,164,165,166,167,168,169),(170,171,172,173,174,175,176,177,178,179,180,181,182),(183,184,185,186,187,188,189,190,191,192,193,194,195),(196,197,198,199,200,201,202,203,204,205,206,207,208),(209,210,211,212,213,214,215,216,217,218,219,220,221),(222,223,224,225,226,227,228,229,230,231,232,233,234),(235,236,237,238,239,240,241,242,243,244,245,246,247),(248,249,250,251,252,253,254,255,256,257,258,259,260),(261,262,263,264,265,266,267,268,269,270,271,272,273),(274,275,276,277,278,279,280,281,282,283,284,285,286),(287,288,289,290,291,292,293,294,295,296,297,298,299),(300,301,302,303,304,305,306,307,308,309,310,311,312),(313,314,315,316,317,318,319,320,321,322,323,324,325),(326,327,328,329,330,331,332,333,334,335,336,337,338),(339,340,341,342,343,344,345,346,347,348,349,350,351),(352,353,354,355,356,357,358,359,360,361,362,363,364),(365,366,367,368,369,370,371,372,373,374,375,376,377),(378,379,380,381,382,383,384,385,386,387,388,389,390),(391,392,393,394,395,396,397,398,399,400,401,402,403),(404,405,406,407,408,409,410,411,412,413,414,415,416),(417,418,419,420,421,422,423,424,425,426,427,428,429),(430,431,432,433,434,435,436,437,438,439,440,441,442),(443,444,445,446,447,448,449,450,451,452,453,454,455),(456,457,458,459,460,461,462,463,464,465,466,467,468)], [(1,116,74,27,93,65,14,91,40),(2,106,70,28,96,61,15,81,49),(3,109,66,29,99,57,16,84,45),(4,112,75,30,102,53,17,87,41),(5,115,71,31,92,62,18,90,50),(6,105,67,32,95,58,19,80,46),(7,108,76,33,98,54,20,83,42),(8,111,72,34,101,63,21,86,51),(9,114,68,35,104,59,22,89,47),(10,117,77,36,94,55,23,79,43),(11,107,73,37,97,64,24,82,52),(12,110,69,38,100,60,25,85,48),(13,113,78,39,103,56,26,88,44),(118,224,184,144,209,181,131,206,166),(119,227,193,145,212,177,132,196,162),(120,230,189,146,215,173,133,199,158),(121,233,185,147,218,182,134,202,167),(122,223,194,148,221,178,135,205,163),(123,226,190,149,211,174,136,208,159),(124,229,186,150,214,170,137,198,168),(125,232,195,151,217,179,138,201,164),(126,222,191,152,220,175,139,204,160),(127,225,187,153,210,171,140,207,169),(128,228,183,154,213,180,141,197,165),(129,231,192,155,216,176,142,200,161),(130,234,188,156,219,172,143,203,157),(235,341,307,261,327,296,248,324,280),(236,344,303,262,330,292,249,314,276),(237,347,312,263,333,288,250,317,285),(238,350,308,264,336,297,251,320,281),(239,340,304,265,326,293,252,323,277),(240,343,300,266,329,289,253,313,286),(241,346,309,267,332,298,254,316,282),(242,349,305,268,335,294,255,319,278),(243,339,301,269,338,290,256,322,274),(244,342,310,270,328,299,257,325,283),(245,345,306,271,331,295,258,315,279),(246,348,302,272,334,291,259,318,275),(247,351,311,273,337,287,260,321,284),(352,458,420,378,444,407,365,430,403),(353,461,429,379,447,416,366,433,399),(354,464,425,380,450,412,367,436,395),(355,467,421,381,453,408,368,439,391),(356,457,417,382,443,404,369,442,400),(357,460,426,383,446,413,370,432,396),(358,463,422,384,449,409,371,435,392),(359,466,418,385,452,405,372,438,401),(360,456,427,386,455,414,373,441,397),(361,459,423,387,445,410,374,431,393),(362,462,419,388,448,406,375,434,402),(363,465,428,389,451,415,376,437,398),(364,468,424,390,454,411,377,440,394)]])
84 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 6A | ··· | 6F | 9A | ··· | 9F | 13A | 13B | 13C | 13D | 18A | ··· | 18R | 26A | ··· | 26L | 39A | ··· | 39H | 78A | ··· | 78X |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 6 | ··· | 6 | 9 | ··· | 9 | 13 | 13 | 13 | 13 | 18 | ··· | 18 | 26 | ··· | 26 | 39 | ··· | 39 | 78 | ··· | 78 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 13 | ··· | 13 | 3 | 3 | 3 | 3 | 13 | ··· | 13 | 3 | ··· | 3 | 3 | ··· | 3 | 3 | ··· | 3 |
84 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 3 | 3 | 3 |
| type | + | + | ||||||||
| image | C1 | C2 | C3 | C6 | C9 | C18 | C13⋊C3 | C2×C13⋊C3 | C13⋊C9 | C2×C13⋊C9 |
| kernel | C22×C13⋊C9 | C2×C13⋊C9 | C2×C78 | C78 | C2×C26 | C26 | C2×C6 | C6 | C22 | C2 |
| # reps | 1 | 3 | 2 | 6 | 6 | 18 | 4 | 12 | 8 | 24 |
Matrix representation of C22×C13⋊C9 ►in GL5(𝔽937)
| 936 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 936 | 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 | 454 | 730 | 1 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 321 | 862 | 394 |
| 0 | 0 | 7 | 912 | 448 |
| 0 | 0 | 577 | 29 | 641 |
G:=sub<GL(5,GF(937))| [936,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,936,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,454,1,0,0,0,730,0,1,0,0,1,0,0],[1,0,0,0,0,0,1,0,0,0,0,0,321,7,577,0,0,862,912,29,0,0,394,448,641] >;
C22×C13⋊C9 in GAP, Magma, Sage, TeX
C_2^2\times C_{13}\rtimes C_9 % in TeX
G:=Group("C2^2xC13:C9"); // GroupNames label
G:=SmallGroup(468,12);
// by ID
G=gap.SmallGroup(468,12);
# by ID
G:=PCGroup([5,-2,-2,-3,-3,-13,57,689]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^13=d^9=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^9>;
// generators/relations
Export