direct product, metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary
Aliases: C4×C13⋊C9, C52⋊C9, C13⋊4C36, C156.C3, C78.6C6, C39.4C12, C26.2C18, C12.(C13⋊C3), C2.(C2×C13⋊C9), C3.(C4×C13⋊C3), C6.2(C2×C13⋊C3), (C2×C13⋊C9).2C2, SmallGroup(468,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C13 — C4×C13⋊C9 |
Generators and relations for C4×C13⋊C9
G = < a,b,c | a4=b13=c9=1, ab=ba, ac=ca, cbc-1=b9 >
Smallest permutation representation of C4×C13⋊C9
►Regular action on 468 points
Generators in S468
(1 274 40 235)(2 275 41 236)(3 276 42 237)(4 277 43 238)(5 278 44 239)(6 279 45 240)(7 280 46 241)(8 281 47 242)(9 282 48 243)(10 283 49 244)(11 284 50 245)(12 285 51 246)(13 286 52 247)(14 287 53 248)(15 288 54 249)(16 289 55 250)(17 290 56 251)(18 291 57 252)(19 292 58 253)(20 293 59 254)(21 294 60 255)(22 295 61 256)(23 296 62 257)(24 297 63 258)(25 298 64 259)(26 299 65 260)(27 300 66 261)(28 301 67 262)(29 302 68 263)(30 303 69 264)(31 304 70 265)(32 305 71 266)(33 306 72 267)(34 307 73 268)(35 308 74 269)(36 309 75 270)(37 310 76 271)(38 311 77 272)(39 312 78 273)(79 357 118 314)(80 358 119 315)(81 359 120 316)(82 360 121 317)(83 361 122 318)(84 362 123 319)(85 363 124 320)(86 364 125 321)(87 352 126 322)(88 353 127 323)(89 354 128 324)(90 355 129 325)(91 356 130 313)(92 377 143 330)(93 365 131 331)(94 366 132 332)(95 367 133 333)(96 368 134 334)(97 369 135 335)(98 370 136 336)(99 371 137 337)(100 372 138 338)(101 373 139 326)(102 374 140 327)(103 375 141 328)(104 376 142 329)(105 384 144 346)(106 385 145 347)(107 386 146 348)(108 387 147 349)(109 388 148 350)(110 389 149 351)(111 390 150 339)(112 378 151 340)(113 379 152 341)(114 380 153 342)(115 381 154 343)(116 382 155 344)(117 383 156 345)(157 438 200 401)(158 439 201 402)(159 440 202 403)(160 441 203 391)(161 442 204 392)(162 430 205 393)(163 431 206 394)(164 432 207 395)(165 433 208 396)(166 434 196 397)(167 435 197 398)(168 436 198 399)(169 437 199 400)(170 445 219 406)(171 446 220 407)(172 447 221 408)(173 448 209 409)(174 449 210 410)(175 450 211 411)(176 451 212 412)(177 452 213 413)(178 453 214 414)(179 454 215 415)(180 455 216 416)(181 443 217 404)(182 444 218 405)(183 456 226 426)(184 457 227 427)(185 458 228 428)(186 459 229 429)(187 460 230 417)(188 461 231 418)(189 462 232 419)(190 463 233 420)(191 464 234 421)(192 465 222 422)(193 466 223 423)(194 467 224 424)(195 468 225 425)
(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)
(1 187 116 27 175 92 14 167 82)(2 190 112 28 178 101 15 157 91)(3 193 108 29 181 97 16 160 87)(4 183 117 30 171 93 17 163 83)(5 186 113 31 174 102 18 166 79)(6 189 109 32 177 98 19 169 88)(7 192 105 33 180 94 20 159 84)(8 195 114 34 170 103 21 162 80)(9 185 110 35 173 99 22 165 89)(10 188 106 36 176 95 23 168 85)(11 191 115 37 179 104 24 158 81)(12 194 111 38 182 100 25 161 90)(13 184 107 39 172 96 26 164 86)(40 230 155 66 211 143 53 197 121)(41 233 151 67 214 139 54 200 130)(42 223 147 68 217 135 55 203 126)(43 226 156 69 220 131 56 206 122)(44 229 152 70 210 140 57 196 118)(45 232 148 71 213 136 58 199 127)(46 222 144 72 216 132 59 202 123)(47 225 153 73 219 141 60 205 119)(48 228 149 74 209 137 61 208 128)(49 231 145 75 212 133 62 198 124)(50 234 154 76 215 142 63 201 120)(51 224 150 77 218 138 64 204 129)(52 227 146 78 221 134 65 207 125)(235 417 344 261 411 330 248 398 317)(236 420 340 262 414 326 249 401 313)(237 423 349 263 404 335 250 391 322)(238 426 345 264 407 331 251 394 318)(239 429 341 265 410 327 252 397 314)(240 419 350 266 413 336 253 400 323)(241 422 346 267 416 332 254 403 319)(242 425 342 268 406 328 255 393 315)(243 428 351 269 409 337 256 396 324)(244 418 347 270 412 333 257 399 320)(245 421 343 271 415 329 258 402 316)(246 424 339 272 405 338 259 392 325)(247 427 348 273 408 334 260 395 321)(274 460 382 300 450 377 287 435 360)(275 463 378 301 453 373 288 438 356)(276 466 387 302 443 369 289 441 352)(277 456 383 303 446 365 290 431 361)(278 459 379 304 449 374 291 434 357)(279 462 388 305 452 370 292 437 353)(280 465 384 306 455 366 293 440 362)(281 468 380 307 445 375 294 430 358)(282 458 389 308 448 371 295 433 354)(283 461 385 309 451 367 296 436 363)(284 464 381 310 454 376 297 439 359)(285 467 390 311 444 372 298 442 355)(286 457 386 312 447 368 299 432 364)
G:=sub<Sym(468)| (1,274,40,235)(2,275,41,236)(3,276,42,237)(4,277,43,238)(5,278,44,239)(6,279,45,240)(7,280,46,241)(8,281,47,242)(9,282,48,243)(10,283,49,244)(11,284,50,245)(12,285,51,246)(13,286,52,247)(14,287,53,248)(15,288,54,249)(16,289,55,250)(17,290,56,251)(18,291,57,252)(19,292,58,253)(20,293,59,254)(21,294,60,255)(22,295,61,256)(23,296,62,257)(24,297,63,258)(25,298,64,259)(26,299,65,260)(27,300,66,261)(28,301,67,262)(29,302,68,263)(30,303,69,264)(31,304,70,265)(32,305,71,266)(33,306,72,267)(34,307,73,268)(35,308,74,269)(36,309,75,270)(37,310,76,271)(38,311,77,272)(39,312,78,273)(79,357,118,314)(80,358,119,315)(81,359,120,316)(82,360,121,317)(83,361,122,318)(84,362,123,319)(85,363,124,320)(86,364,125,321)(87,352,126,322)(88,353,127,323)(89,354,128,324)(90,355,129,325)(91,356,130,313)(92,377,143,330)(93,365,131,331)(94,366,132,332)(95,367,133,333)(96,368,134,334)(97,369,135,335)(98,370,136,336)(99,371,137,337)(100,372,138,338)(101,373,139,326)(102,374,140,327)(103,375,141,328)(104,376,142,329)(105,384,144,346)(106,385,145,347)(107,386,146,348)(108,387,147,349)(109,388,148,350)(110,389,149,351)(111,390,150,339)(112,378,151,340)(113,379,152,341)(114,380,153,342)(115,381,154,343)(116,382,155,344)(117,383,156,345)(157,438,200,401)(158,439,201,402)(159,440,202,403)(160,441,203,391)(161,442,204,392)(162,430,205,393)(163,431,206,394)(164,432,207,395)(165,433,208,396)(166,434,196,397)(167,435,197,398)(168,436,198,399)(169,437,199,400)(170,445,219,406)(171,446,220,407)(172,447,221,408)(173,448,209,409)(174,449,210,410)(175,450,211,411)(176,451,212,412)(177,452,213,413)(178,453,214,414)(179,454,215,415)(180,455,216,416)(181,443,217,404)(182,444,218,405)(183,456,226,426)(184,457,227,427)(185,458,228,428)(186,459,229,429)(187,460,230,417)(188,461,231,418)(189,462,232,419)(190,463,233,420)(191,464,234,421)(192,465,222,422)(193,466,223,423)(194,467,224,424)(195,468,225,425), (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), (1,187,116,27,175,92,14,167,82)(2,190,112,28,178,101,15,157,91)(3,193,108,29,181,97,16,160,87)(4,183,117,30,171,93,17,163,83)(5,186,113,31,174,102,18,166,79)(6,189,109,32,177,98,19,169,88)(7,192,105,33,180,94,20,159,84)(8,195,114,34,170,103,21,162,80)(9,185,110,35,173,99,22,165,89)(10,188,106,36,176,95,23,168,85)(11,191,115,37,179,104,24,158,81)(12,194,111,38,182,100,25,161,90)(13,184,107,39,172,96,26,164,86)(40,230,155,66,211,143,53,197,121)(41,233,151,67,214,139,54,200,130)(42,223,147,68,217,135,55,203,126)(43,226,156,69,220,131,56,206,122)(44,229,152,70,210,140,57,196,118)(45,232,148,71,213,136,58,199,127)(46,222,144,72,216,132,59,202,123)(47,225,153,73,219,141,60,205,119)(48,228,149,74,209,137,61,208,128)(49,231,145,75,212,133,62,198,124)(50,234,154,76,215,142,63,201,120)(51,224,150,77,218,138,64,204,129)(52,227,146,78,221,134,65,207,125)(235,417,344,261,411,330,248,398,317)(236,420,340,262,414,326,249,401,313)(237,423,349,263,404,335,250,391,322)(238,426,345,264,407,331,251,394,318)(239,429,341,265,410,327,252,397,314)(240,419,350,266,413,336,253,400,323)(241,422,346,267,416,332,254,403,319)(242,425,342,268,406,328,255,393,315)(243,428,351,269,409,337,256,396,324)(244,418,347,270,412,333,257,399,320)(245,421,343,271,415,329,258,402,316)(246,424,339,272,405,338,259,392,325)(247,427,348,273,408,334,260,395,321)(274,460,382,300,450,377,287,435,360)(275,463,378,301,453,373,288,438,356)(276,466,387,302,443,369,289,441,352)(277,456,383,303,446,365,290,431,361)(278,459,379,304,449,374,291,434,357)(279,462,388,305,452,370,292,437,353)(280,465,384,306,455,366,293,440,362)(281,468,380,307,445,375,294,430,358)(282,458,389,308,448,371,295,433,354)(283,461,385,309,451,367,296,436,363)(284,464,381,310,454,376,297,439,359)(285,467,390,311,444,372,298,442,355)(286,457,386,312,447,368,299,432,364)>;
G:=Group( (1,274,40,235)(2,275,41,236)(3,276,42,237)(4,277,43,238)(5,278,44,239)(6,279,45,240)(7,280,46,241)(8,281,47,242)(9,282,48,243)(10,283,49,244)(11,284,50,245)(12,285,51,246)(13,286,52,247)(14,287,53,248)(15,288,54,249)(16,289,55,250)(17,290,56,251)(18,291,57,252)(19,292,58,253)(20,293,59,254)(21,294,60,255)(22,295,61,256)(23,296,62,257)(24,297,63,258)(25,298,64,259)(26,299,65,260)(27,300,66,261)(28,301,67,262)(29,302,68,263)(30,303,69,264)(31,304,70,265)(32,305,71,266)(33,306,72,267)(34,307,73,268)(35,308,74,269)(36,309,75,270)(37,310,76,271)(38,311,77,272)(39,312,78,273)(79,357,118,314)(80,358,119,315)(81,359,120,316)(82,360,121,317)(83,361,122,318)(84,362,123,319)(85,363,124,320)(86,364,125,321)(87,352,126,322)(88,353,127,323)(89,354,128,324)(90,355,129,325)(91,356,130,313)(92,377,143,330)(93,365,131,331)(94,366,132,332)(95,367,133,333)(96,368,134,334)(97,369,135,335)(98,370,136,336)(99,371,137,337)(100,372,138,338)(101,373,139,326)(102,374,140,327)(103,375,141,328)(104,376,142,329)(105,384,144,346)(106,385,145,347)(107,386,146,348)(108,387,147,349)(109,388,148,350)(110,389,149,351)(111,390,150,339)(112,378,151,340)(113,379,152,341)(114,380,153,342)(115,381,154,343)(116,382,155,344)(117,383,156,345)(157,438,200,401)(158,439,201,402)(159,440,202,403)(160,441,203,391)(161,442,204,392)(162,430,205,393)(163,431,206,394)(164,432,207,395)(165,433,208,396)(166,434,196,397)(167,435,197,398)(168,436,198,399)(169,437,199,400)(170,445,219,406)(171,446,220,407)(172,447,221,408)(173,448,209,409)(174,449,210,410)(175,450,211,411)(176,451,212,412)(177,452,213,413)(178,453,214,414)(179,454,215,415)(180,455,216,416)(181,443,217,404)(182,444,218,405)(183,456,226,426)(184,457,227,427)(185,458,228,428)(186,459,229,429)(187,460,230,417)(188,461,231,418)(189,462,232,419)(190,463,233,420)(191,464,234,421)(192,465,222,422)(193,466,223,423)(194,467,224,424)(195,468,225,425), (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), (1,187,116,27,175,92,14,167,82)(2,190,112,28,178,101,15,157,91)(3,193,108,29,181,97,16,160,87)(4,183,117,30,171,93,17,163,83)(5,186,113,31,174,102,18,166,79)(6,189,109,32,177,98,19,169,88)(7,192,105,33,180,94,20,159,84)(8,195,114,34,170,103,21,162,80)(9,185,110,35,173,99,22,165,89)(10,188,106,36,176,95,23,168,85)(11,191,115,37,179,104,24,158,81)(12,194,111,38,182,100,25,161,90)(13,184,107,39,172,96,26,164,86)(40,230,155,66,211,143,53,197,121)(41,233,151,67,214,139,54,200,130)(42,223,147,68,217,135,55,203,126)(43,226,156,69,220,131,56,206,122)(44,229,152,70,210,140,57,196,118)(45,232,148,71,213,136,58,199,127)(46,222,144,72,216,132,59,202,123)(47,225,153,73,219,141,60,205,119)(48,228,149,74,209,137,61,208,128)(49,231,145,75,212,133,62,198,124)(50,234,154,76,215,142,63,201,120)(51,224,150,77,218,138,64,204,129)(52,227,146,78,221,134,65,207,125)(235,417,344,261,411,330,248,398,317)(236,420,340,262,414,326,249,401,313)(237,423,349,263,404,335,250,391,322)(238,426,345,264,407,331,251,394,318)(239,429,341,265,410,327,252,397,314)(240,419,350,266,413,336,253,400,323)(241,422,346,267,416,332,254,403,319)(242,425,342,268,406,328,255,393,315)(243,428,351,269,409,337,256,396,324)(244,418,347,270,412,333,257,399,320)(245,421,343,271,415,329,258,402,316)(246,424,339,272,405,338,259,392,325)(247,427,348,273,408,334,260,395,321)(274,460,382,300,450,377,287,435,360)(275,463,378,301,453,373,288,438,356)(276,466,387,302,443,369,289,441,352)(277,456,383,303,446,365,290,431,361)(278,459,379,304,449,374,291,434,357)(279,462,388,305,452,370,292,437,353)(280,465,384,306,455,366,293,440,362)(281,468,380,307,445,375,294,430,358)(282,458,389,308,448,371,295,433,354)(283,461,385,309,451,367,296,436,363)(284,464,381,310,454,376,297,439,359)(285,467,390,311,444,372,298,442,355)(286,457,386,312,447,368,299,432,364) );
G=PermutationGroup([[(1,274,40,235),(2,275,41,236),(3,276,42,237),(4,277,43,238),(5,278,44,239),(6,279,45,240),(7,280,46,241),(8,281,47,242),(9,282,48,243),(10,283,49,244),(11,284,50,245),(12,285,51,246),(13,286,52,247),(14,287,53,248),(15,288,54,249),(16,289,55,250),(17,290,56,251),(18,291,57,252),(19,292,58,253),(20,293,59,254),(21,294,60,255),(22,295,61,256),(23,296,62,257),(24,297,63,258),(25,298,64,259),(26,299,65,260),(27,300,66,261),(28,301,67,262),(29,302,68,263),(30,303,69,264),(31,304,70,265),(32,305,71,266),(33,306,72,267),(34,307,73,268),(35,308,74,269),(36,309,75,270),(37,310,76,271),(38,311,77,272),(39,312,78,273),(79,357,118,314),(80,358,119,315),(81,359,120,316),(82,360,121,317),(83,361,122,318),(84,362,123,319),(85,363,124,320),(86,364,125,321),(87,352,126,322),(88,353,127,323),(89,354,128,324),(90,355,129,325),(91,356,130,313),(92,377,143,330),(93,365,131,331),(94,366,132,332),(95,367,133,333),(96,368,134,334),(97,369,135,335),(98,370,136,336),(99,371,137,337),(100,372,138,338),(101,373,139,326),(102,374,140,327),(103,375,141,328),(104,376,142,329),(105,384,144,346),(106,385,145,347),(107,386,146,348),(108,387,147,349),(109,388,148,350),(110,389,149,351),(111,390,150,339),(112,378,151,340),(113,379,152,341),(114,380,153,342),(115,381,154,343),(116,382,155,344),(117,383,156,345),(157,438,200,401),(158,439,201,402),(159,440,202,403),(160,441,203,391),(161,442,204,392),(162,430,205,393),(163,431,206,394),(164,432,207,395),(165,433,208,396),(166,434,196,397),(167,435,197,398),(168,436,198,399),(169,437,199,400),(170,445,219,406),(171,446,220,407),(172,447,221,408),(173,448,209,409),(174,449,210,410),(175,450,211,411),(176,451,212,412),(177,452,213,413),(178,453,214,414),(179,454,215,415),(180,455,216,416),(181,443,217,404),(182,444,218,405),(183,456,226,426),(184,457,227,427),(185,458,228,428),(186,459,229,429),(187,460,230,417),(188,461,231,418),(189,462,232,419),(190,463,233,420),(191,464,234,421),(192,465,222,422),(193,466,223,423),(194,467,224,424),(195,468,225,425)], [(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)], [(1,187,116,27,175,92,14,167,82),(2,190,112,28,178,101,15,157,91),(3,193,108,29,181,97,16,160,87),(4,183,117,30,171,93,17,163,83),(5,186,113,31,174,102,18,166,79),(6,189,109,32,177,98,19,169,88),(7,192,105,33,180,94,20,159,84),(8,195,114,34,170,103,21,162,80),(9,185,110,35,173,99,22,165,89),(10,188,106,36,176,95,23,168,85),(11,191,115,37,179,104,24,158,81),(12,194,111,38,182,100,25,161,90),(13,184,107,39,172,96,26,164,86),(40,230,155,66,211,143,53,197,121),(41,233,151,67,214,139,54,200,130),(42,223,147,68,217,135,55,203,126),(43,226,156,69,220,131,56,206,122),(44,229,152,70,210,140,57,196,118),(45,232,148,71,213,136,58,199,127),(46,222,144,72,216,132,59,202,123),(47,225,153,73,219,141,60,205,119),(48,228,149,74,209,137,61,208,128),(49,231,145,75,212,133,62,198,124),(50,234,154,76,215,142,63,201,120),(51,224,150,77,218,138,64,204,129),(52,227,146,78,221,134,65,207,125),(235,417,344,261,411,330,248,398,317),(236,420,340,262,414,326,249,401,313),(237,423,349,263,404,335,250,391,322),(238,426,345,264,407,331,251,394,318),(239,429,341,265,410,327,252,397,314),(240,419,350,266,413,336,253,400,323),(241,422,346,267,416,332,254,403,319),(242,425,342,268,406,328,255,393,315),(243,428,351,269,409,337,256,396,324),(244,418,347,270,412,333,257,399,320),(245,421,343,271,415,329,258,402,316),(246,424,339,272,405,338,259,392,325),(247,427,348,273,408,334,260,395,321),(274,460,382,300,450,377,287,435,360),(275,463,378,301,453,373,288,438,356),(276,466,387,302,443,369,289,441,352),(277,456,383,303,446,365,290,431,361),(278,459,379,304,449,374,291,434,357),(279,462,388,305,452,370,292,437,353),(280,465,384,306,455,366,293,440,362),(281,468,380,307,445,375,294,430,358),(282,458,389,308,448,371,295,433,354),(283,461,385,309,451,367,296,436,363),(284,464,381,310,454,376,297,439,359),(285,467,390,311,444,372,298,442,355),(286,457,386,312,447,368,299,432,364)]])
84 conjugacy classes
| class | 1 | 2 | 3A | 3B | 4A | 4B | 6A | 6B | 9A | ··· | 9F | 12A | 12B | 12C | 12D | 13A | 13B | 13C | 13D | 18A | ··· | 18F | 26A | 26B | 26C | 26D | 36A | ··· | 36L | 39A | ··· | 39H | 52A | ··· | 52H | 78A | ··· | 78H | 156A | ··· | 156P |
| order | 1 | 2 | 3 | 3 | 4 | 4 | 6 | 6 | 9 | ··· | 9 | 12 | 12 | 12 | 12 | 13 | 13 | 13 | 13 | 18 | ··· | 18 | 26 | 26 | 26 | 26 | 36 | ··· | 36 | 39 | ··· | 39 | 52 | ··· | 52 | 78 | ··· | 78 | 156 | ··· | 156 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 13 | ··· | 13 | 1 | 1 | 1 | 1 | 3 | 3 | 3 | 3 | 13 | ··· | 13 | 3 | 3 | 3 | 3 | 13 | ··· | 13 | 3 | ··· | 3 | 3 | ··· | 3 | 3 | ··· | 3 | 3 | ··· | 3 |
84 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 3 | 3 | 3 | 3 | 3 |
| type | + | + | |||||||||||||
| image | C1 | C2 | C3 | C4 | C6 | C9 | C12 | C18 | C36 | C13⋊C3 | C2×C13⋊C3 | C13⋊C9 | C4×C13⋊C3 | C2×C13⋊C9 | C4×C13⋊C9 |
| kernel | C4×C13⋊C9 | C2×C13⋊C9 | C156 | C13⋊C9 | C78 | C52 | C39 | C26 | C13 | C12 | C6 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 2 | 2 | 2 | 6 | 4 | 6 | 12 | 4 | 4 | 8 | 8 | 8 | 16 |
Matrix representation of C4×C13⋊C9 ►in GL3(𝔽937) generated by
| 741 | 0 | 0 |
| 0 | 741 | 0 |
| 0 | 0 | 741 |
| 713 | 438 | 1 |
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 210 | 914 | 249 |
| 105 | 809 | 230 |
| 843 | 288 | 855 |
G:=sub<GL(3,GF(937))| [741,0,0,0,741,0,0,0,741],[713,1,0,438,0,1,1,0,0],[210,105,843,914,809,288,249,230,855] >;
C4×C13⋊C9 in GAP, Magma, Sage, TeX
C_4\times C_{13}\rtimes C_9 % in TeX
G:=Group("C4xC13:C9"); // GroupNames label
G:=SmallGroup(468,2);
// by ID
G=gap.SmallGroup(468,2);
# by ID
G:=PCGroup([5,-2,-3,-2,-3,-13,30,66,1359]);
// Polycyclic
G:=Group<a,b,c|a^4=b^13=c^9=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^9>;
// generators/relations
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