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G = C4×C13⋊C9order 468 = 22·32·13

Direct product of C4 and C13⋊C9

direct product, metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary

Aliases: C4×C13⋊C9, C52⋊C9, C134C36, 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

C1C13 — C4×C13⋊C9
C1C13C39C78C2×C13⋊C9 — C4×C13⋊C9
C13 — C4×C13⋊C9
C1C12

Generators and relations for C4×C13⋊C9
 G = < a,b,c | a4=b13=c9=1, ab=ba, ac=ca, cbc-1=b9 >

13C9
13C18
13C36

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)(79 364 130 322)(80 352 118 323)(81 353 119 324)(82 354 120 325)(83 355 121 313)(84 356 122 314)(85 357 123 315)(86 358 124 316)(87 359 125 317)(88 360 126 318)(89 361 127 319)(90 362 128 320)(91 363 129 321)(92 370 135 328)(93 371 136 329)(94 372 137 330)(95 373 138 331)(96 374 139 332)(97 375 140 333)(98 376 141 334)(99 377 142 335)(100 365 143 336)(101 366 131 337)(102 367 132 338)(103 368 133 326)(104 369 134 327)(105 385 148 350)(106 386 149 351)(107 387 150 339)(108 388 151 340)(109 389 152 341)(110 390 153 342)(111 378 154 343)(112 379 155 344)(113 380 156 345)(114 381 144 346)(115 382 145 347)(116 383 146 348)(117 384 147 349)(157 439 200 397)(158 440 201 398)(159 441 202 399)(160 442 203 400)(161 430 204 401)(162 431 205 402)(163 432 206 403)(164 433 207 391)(165 434 208 392)(166 435 196 393)(167 436 197 394)(168 437 198 395)(169 438 199 396)(170 449 214 413)(171 450 215 414)(172 451 216 415)(173 452 217 416)(174 453 218 404)(175 454 219 405)(176 455 220 406)(177 443 221 407)(178 444 209 408)(179 445 210 409)(180 446 211 410)(181 447 212 411)(182 448 213 412)(183 459 230 419)(184 460 231 420)(185 461 232 421)(186 462 233 422)(187 463 234 423)(188 464 222 424)(189 465 223 425)(190 466 224 426)(191 467 225 427)(192 468 226 428)(193 456 227 429)(194 457 228 417)(195 458 229 418)
(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)
(1 186 114 27 175 101 14 168 79)(2 189 110 28 178 97 15 158 88)(3 192 106 29 181 93 16 161 84)(4 195 115 30 171 102 17 164 80)(5 185 111 31 174 98 18 167 89)(6 188 107 32 177 94 19 157 85)(7 191 116 33 180 103 20 160 81)(8 194 112 34 170 99 21 163 90)(9 184 108 35 173 95 22 166 86)(10 187 117 36 176 104 23 169 82)(11 190 113 37 179 100 24 159 91)(12 193 109 38 182 96 25 162 87)(13 183 105 39 172 92 26 165 83)(40 233 144 66 219 131 53 198 130)(41 223 153 67 209 140 54 201 126)(42 226 149 68 212 136 55 204 122)(43 229 145 69 215 132 56 207 118)(44 232 154 70 218 141 57 197 127)(45 222 150 71 221 137 58 200 123)(46 225 146 72 211 133 59 203 119)(47 228 155 73 214 142 60 206 128)(48 231 151 74 217 138 61 196 124)(49 234 147 75 220 134 62 199 120)(50 224 156 76 210 143 63 202 129)(51 227 152 77 213 139 64 205 125)(52 230 148 78 216 135 65 208 121)(235 422 346 261 405 337 248 395 322)(236 425 342 262 408 333 249 398 318)(237 428 351 263 411 329 250 401 314)(238 418 347 264 414 338 251 391 323)(239 421 343 265 404 334 252 394 319)(240 424 339 266 407 330 253 397 315)(241 427 348 267 410 326 254 400 324)(242 417 344 268 413 335 255 403 320)(243 420 340 269 416 331 256 393 316)(244 423 349 270 406 327 257 396 325)(245 426 345 271 409 336 258 399 321)(246 429 341 272 412 332 259 402 317)(247 419 350 273 415 328 260 392 313)(274 462 381 300 454 366 287 437 364)(275 465 390 301 444 375 288 440 360)(276 468 386 302 447 371 289 430 356)(277 458 382 303 450 367 290 433 352)(278 461 378 304 453 376 291 436 361)(279 464 387 305 443 372 292 439 357)(280 467 383 306 446 368 293 442 353)(281 457 379 307 449 377 294 432 362)(282 460 388 308 452 373 295 435 358)(283 463 384 309 455 369 296 438 354)(284 466 380 310 445 365 297 441 363)(285 456 389 311 448 374 298 431 359)(286 459 385 312 451 370 299 434 355)

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)(79,364,130,322)(80,352,118,323)(81,353,119,324)(82,354,120,325)(83,355,121,313)(84,356,122,314)(85,357,123,315)(86,358,124,316)(87,359,125,317)(88,360,126,318)(89,361,127,319)(90,362,128,320)(91,363,129,321)(92,370,135,328)(93,371,136,329)(94,372,137,330)(95,373,138,331)(96,374,139,332)(97,375,140,333)(98,376,141,334)(99,377,142,335)(100,365,143,336)(101,366,131,337)(102,367,132,338)(103,368,133,326)(104,369,134,327)(105,385,148,350)(106,386,149,351)(107,387,150,339)(108,388,151,340)(109,389,152,341)(110,390,153,342)(111,378,154,343)(112,379,155,344)(113,380,156,345)(114,381,144,346)(115,382,145,347)(116,383,146,348)(117,384,147,349)(157,439,200,397)(158,440,201,398)(159,441,202,399)(160,442,203,400)(161,430,204,401)(162,431,205,402)(163,432,206,403)(164,433,207,391)(165,434,208,392)(166,435,196,393)(167,436,197,394)(168,437,198,395)(169,438,199,396)(170,449,214,413)(171,450,215,414)(172,451,216,415)(173,452,217,416)(174,453,218,404)(175,454,219,405)(176,455,220,406)(177,443,221,407)(178,444,209,408)(179,445,210,409)(180,446,211,410)(181,447,212,411)(182,448,213,412)(183,459,230,419)(184,460,231,420)(185,461,232,421)(186,462,233,422)(187,463,234,423)(188,464,222,424)(189,465,223,425)(190,466,224,426)(191,467,225,427)(192,468,226,428)(193,456,227,429)(194,457,228,417)(195,458,229,418), (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), (1,186,114,27,175,101,14,168,79)(2,189,110,28,178,97,15,158,88)(3,192,106,29,181,93,16,161,84)(4,195,115,30,171,102,17,164,80)(5,185,111,31,174,98,18,167,89)(6,188,107,32,177,94,19,157,85)(7,191,116,33,180,103,20,160,81)(8,194,112,34,170,99,21,163,90)(9,184,108,35,173,95,22,166,86)(10,187,117,36,176,104,23,169,82)(11,190,113,37,179,100,24,159,91)(12,193,109,38,182,96,25,162,87)(13,183,105,39,172,92,26,165,83)(40,233,144,66,219,131,53,198,130)(41,223,153,67,209,140,54,201,126)(42,226,149,68,212,136,55,204,122)(43,229,145,69,215,132,56,207,118)(44,232,154,70,218,141,57,197,127)(45,222,150,71,221,137,58,200,123)(46,225,146,72,211,133,59,203,119)(47,228,155,73,214,142,60,206,128)(48,231,151,74,217,138,61,196,124)(49,234,147,75,220,134,62,199,120)(50,224,156,76,210,143,63,202,129)(51,227,152,77,213,139,64,205,125)(52,230,148,78,216,135,65,208,121)(235,422,346,261,405,337,248,395,322)(236,425,342,262,408,333,249,398,318)(237,428,351,263,411,329,250,401,314)(238,418,347,264,414,338,251,391,323)(239,421,343,265,404,334,252,394,319)(240,424,339,266,407,330,253,397,315)(241,427,348,267,410,326,254,400,324)(242,417,344,268,413,335,255,403,320)(243,420,340,269,416,331,256,393,316)(244,423,349,270,406,327,257,396,325)(245,426,345,271,409,336,258,399,321)(246,429,341,272,412,332,259,402,317)(247,419,350,273,415,328,260,392,313)(274,462,381,300,454,366,287,437,364)(275,465,390,301,444,375,288,440,360)(276,468,386,302,447,371,289,430,356)(277,458,382,303,450,367,290,433,352)(278,461,378,304,453,376,291,436,361)(279,464,387,305,443,372,292,439,357)(280,467,383,306,446,368,293,442,353)(281,457,379,307,449,377,294,432,362)(282,460,388,308,452,373,295,435,358)(283,463,384,309,455,369,296,438,354)(284,466,380,310,445,365,297,441,363)(285,456,389,311,448,374,298,431,359)(286,459,385,312,451,370,299,434,355)>;

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)(79,364,130,322)(80,352,118,323)(81,353,119,324)(82,354,120,325)(83,355,121,313)(84,356,122,314)(85,357,123,315)(86,358,124,316)(87,359,125,317)(88,360,126,318)(89,361,127,319)(90,362,128,320)(91,363,129,321)(92,370,135,328)(93,371,136,329)(94,372,137,330)(95,373,138,331)(96,374,139,332)(97,375,140,333)(98,376,141,334)(99,377,142,335)(100,365,143,336)(101,366,131,337)(102,367,132,338)(103,368,133,326)(104,369,134,327)(105,385,148,350)(106,386,149,351)(107,387,150,339)(108,388,151,340)(109,389,152,341)(110,390,153,342)(111,378,154,343)(112,379,155,344)(113,380,156,345)(114,381,144,346)(115,382,145,347)(116,383,146,348)(117,384,147,349)(157,439,200,397)(158,440,201,398)(159,441,202,399)(160,442,203,400)(161,430,204,401)(162,431,205,402)(163,432,206,403)(164,433,207,391)(165,434,208,392)(166,435,196,393)(167,436,197,394)(168,437,198,395)(169,438,199,396)(170,449,214,413)(171,450,215,414)(172,451,216,415)(173,452,217,416)(174,453,218,404)(175,454,219,405)(176,455,220,406)(177,443,221,407)(178,444,209,408)(179,445,210,409)(180,446,211,410)(181,447,212,411)(182,448,213,412)(183,459,230,419)(184,460,231,420)(185,461,232,421)(186,462,233,422)(187,463,234,423)(188,464,222,424)(189,465,223,425)(190,466,224,426)(191,467,225,427)(192,468,226,428)(193,456,227,429)(194,457,228,417)(195,458,229,418), (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), (1,186,114,27,175,101,14,168,79)(2,189,110,28,178,97,15,158,88)(3,192,106,29,181,93,16,161,84)(4,195,115,30,171,102,17,164,80)(5,185,111,31,174,98,18,167,89)(6,188,107,32,177,94,19,157,85)(7,191,116,33,180,103,20,160,81)(8,194,112,34,170,99,21,163,90)(9,184,108,35,173,95,22,166,86)(10,187,117,36,176,104,23,169,82)(11,190,113,37,179,100,24,159,91)(12,193,109,38,182,96,25,162,87)(13,183,105,39,172,92,26,165,83)(40,233,144,66,219,131,53,198,130)(41,223,153,67,209,140,54,201,126)(42,226,149,68,212,136,55,204,122)(43,229,145,69,215,132,56,207,118)(44,232,154,70,218,141,57,197,127)(45,222,150,71,221,137,58,200,123)(46,225,146,72,211,133,59,203,119)(47,228,155,73,214,142,60,206,128)(48,231,151,74,217,138,61,196,124)(49,234,147,75,220,134,62,199,120)(50,224,156,76,210,143,63,202,129)(51,227,152,77,213,139,64,205,125)(52,230,148,78,216,135,65,208,121)(235,422,346,261,405,337,248,395,322)(236,425,342,262,408,333,249,398,318)(237,428,351,263,411,329,250,401,314)(238,418,347,264,414,338,251,391,323)(239,421,343,265,404,334,252,394,319)(240,424,339,266,407,330,253,397,315)(241,427,348,267,410,326,254,400,324)(242,417,344,268,413,335,255,403,320)(243,420,340,269,416,331,256,393,316)(244,423,349,270,406,327,257,396,325)(245,426,345,271,409,336,258,399,321)(246,429,341,272,412,332,259,402,317)(247,419,350,273,415,328,260,392,313)(274,462,381,300,454,366,287,437,364)(275,465,390,301,444,375,288,440,360)(276,468,386,302,447,371,289,430,356)(277,458,382,303,450,367,290,433,352)(278,461,378,304,453,376,291,436,361)(279,464,387,305,443,372,292,439,357)(280,467,383,306,446,368,293,442,353)(281,457,379,307,449,377,294,432,362)(282,460,388,308,452,373,295,435,358)(283,463,384,309,455,369,296,438,354)(284,466,380,310,445,365,297,441,363)(285,456,389,311,448,374,298,431,359)(286,459,385,312,451,370,299,434,355) );

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),(79,364,130,322),(80,352,118,323),(81,353,119,324),(82,354,120,325),(83,355,121,313),(84,356,122,314),(85,357,123,315),(86,358,124,316),(87,359,125,317),(88,360,126,318),(89,361,127,319),(90,362,128,320),(91,363,129,321),(92,370,135,328),(93,371,136,329),(94,372,137,330),(95,373,138,331),(96,374,139,332),(97,375,140,333),(98,376,141,334),(99,377,142,335),(100,365,143,336),(101,366,131,337),(102,367,132,338),(103,368,133,326),(104,369,134,327),(105,385,148,350),(106,386,149,351),(107,387,150,339),(108,388,151,340),(109,389,152,341),(110,390,153,342),(111,378,154,343),(112,379,155,344),(113,380,156,345),(114,381,144,346),(115,382,145,347),(116,383,146,348),(117,384,147,349),(157,439,200,397),(158,440,201,398),(159,441,202,399),(160,442,203,400),(161,430,204,401),(162,431,205,402),(163,432,206,403),(164,433,207,391),(165,434,208,392),(166,435,196,393),(167,436,197,394),(168,437,198,395),(169,438,199,396),(170,449,214,413),(171,450,215,414),(172,451,216,415),(173,452,217,416),(174,453,218,404),(175,454,219,405),(176,455,220,406),(177,443,221,407),(178,444,209,408),(179,445,210,409),(180,446,211,410),(181,447,212,411),(182,448,213,412),(183,459,230,419),(184,460,231,420),(185,461,232,421),(186,462,233,422),(187,463,234,423),(188,464,222,424),(189,465,223,425),(190,466,224,426),(191,467,225,427),(192,468,226,428),(193,456,227,429),(194,457,228,417),(195,458,229,418)], [(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)], [(1,186,114,27,175,101,14,168,79),(2,189,110,28,178,97,15,158,88),(3,192,106,29,181,93,16,161,84),(4,195,115,30,171,102,17,164,80),(5,185,111,31,174,98,18,167,89),(6,188,107,32,177,94,19,157,85),(7,191,116,33,180,103,20,160,81),(8,194,112,34,170,99,21,163,90),(9,184,108,35,173,95,22,166,86),(10,187,117,36,176,104,23,169,82),(11,190,113,37,179,100,24,159,91),(12,193,109,38,182,96,25,162,87),(13,183,105,39,172,92,26,165,83),(40,233,144,66,219,131,53,198,130),(41,223,153,67,209,140,54,201,126),(42,226,149,68,212,136,55,204,122),(43,229,145,69,215,132,56,207,118),(44,232,154,70,218,141,57,197,127),(45,222,150,71,221,137,58,200,123),(46,225,146,72,211,133,59,203,119),(47,228,155,73,214,142,60,206,128),(48,231,151,74,217,138,61,196,124),(49,234,147,75,220,134,62,199,120),(50,224,156,76,210,143,63,202,129),(51,227,152,77,213,139,64,205,125),(52,230,148,78,216,135,65,208,121),(235,422,346,261,405,337,248,395,322),(236,425,342,262,408,333,249,398,318),(237,428,351,263,411,329,250,401,314),(238,418,347,264,414,338,251,391,323),(239,421,343,265,404,334,252,394,319),(240,424,339,266,407,330,253,397,315),(241,427,348,267,410,326,254,400,324),(242,417,344,268,413,335,255,403,320),(243,420,340,269,416,331,256,393,316),(244,423,349,270,406,327,257,396,325),(245,426,345,271,409,336,258,399,321),(246,429,341,272,412,332,259,402,317),(247,419,350,273,415,328,260,392,313),(274,462,381,300,454,366,287,437,364),(275,465,390,301,444,375,288,440,360),(276,468,386,302,447,371,289,430,356),(277,458,382,303,450,367,290,433,352),(278,461,378,304,453,376,291,436,361),(279,464,387,305,443,372,292,439,357),(280,467,383,306,446,368,293,442,353),(281,457,379,307,449,377,294,432,362),(282,460,388,308,452,373,295,435,358),(283,463,384,309,455,369,296,438,354),(284,466,380,310,445,365,297,441,363),(285,456,389,311,448,374,298,431,359),(286,459,385,312,451,370,299,434,355)])

84 conjugacy classes

class 1  2 3A3B4A4B6A6B9A···9F12A12B12C12D13A13B13C13D18A···18F26A26B26C26D36A···36L39A···39H52A···52H78A···78H156A···156P
order123344669···9121212121313131318···182626262636···3639···3952···5278···78156···156
size1111111113···131111333313···13333313···133···33···33···33···3

84 irreducible representations

dim111111111333333
type++
imageC1C2C3C4C6C9C12C18C36C13⋊C3C2×C13⋊C3C13⋊C9C4×C13⋊C3C2×C13⋊C9C4×C13⋊C9
kernelC4×C13⋊C9C2×C13⋊C9C156C13⋊C9C78C52C39C26C13C12C6C4C3C2C1
# reps11222646124488816

Matrix representation of C4×C13⋊C9 in GL3(𝔽937) generated by

74100
07410
00741
,
7134381
100
010
,
210914249
105809230
843288855
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

Export

Subgroup lattice of C4×C13⋊C9 in TeX

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