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G = C3×C159order 477 = 32·53

Abelian group of type [3,159]

direct product, abelian, monomial, 3-elementary

Aliases: C3×C159, SmallGroup(477,2)

Series: Derived Chief Lower central Upper central

C1 — C3×C159
C1C53C159 — C3×C159
C1 — C3×C159
C1 — C3×C159

Generators and relations for C3×C159
 G = < a,b | a3=b159=1, ab=ba >


Smallest permutation representation of C3×C159
Regular action on 477 points
Generators in S477
(1 458 227)(2 459 228)(3 460 229)(4 461 230)(5 462 231)(6 463 232)(7 464 233)(8 465 234)(9 466 235)(10 467 236)(11 468 237)(12 469 238)(13 470 239)(14 471 240)(15 472 241)(16 473 242)(17 474 243)(18 475 244)(19 476 245)(20 477 246)(21 319 247)(22 320 248)(23 321 249)(24 322 250)(25 323 251)(26 324 252)(27 325 253)(28 326 254)(29 327 255)(30 328 256)(31 329 257)(32 330 258)(33 331 259)(34 332 260)(35 333 261)(36 334 262)(37 335 263)(38 336 264)(39 337 265)(40 338 266)(41 339 267)(42 340 268)(43 341 269)(44 342 270)(45 343 271)(46 344 272)(47 345 273)(48 346 274)(49 347 275)(50 348 276)(51 349 277)(52 350 278)(53 351 279)(54 352 280)(55 353 281)(56 354 282)(57 355 283)(58 356 284)(59 357 285)(60 358 286)(61 359 287)(62 360 288)(63 361 289)(64 362 290)(65 363 291)(66 364 292)(67 365 293)(68 366 294)(69 367 295)(70 368 296)(71 369 297)(72 370 298)(73 371 299)(74 372 300)(75 373 301)(76 374 302)(77 375 303)(78 376 304)(79 377 305)(80 378 306)(81 379 307)(82 380 308)(83 381 309)(84 382 310)(85 383 311)(86 384 312)(87 385 313)(88 386 314)(89 387 315)(90 388 316)(91 389 317)(92 390 318)(93 391 160)(94 392 161)(95 393 162)(96 394 163)(97 395 164)(98 396 165)(99 397 166)(100 398 167)(101 399 168)(102 400 169)(103 401 170)(104 402 171)(105 403 172)(106 404 173)(107 405 174)(108 406 175)(109 407 176)(110 408 177)(111 409 178)(112 410 179)(113 411 180)(114 412 181)(115 413 182)(116 414 183)(117 415 184)(118 416 185)(119 417 186)(120 418 187)(121 419 188)(122 420 189)(123 421 190)(124 422 191)(125 423 192)(126 424 193)(127 425 194)(128 426 195)(129 427 196)(130 428 197)(131 429 198)(132 430 199)(133 431 200)(134 432 201)(135 433 202)(136 434 203)(137 435 204)(138 436 205)(139 437 206)(140 438 207)(141 439 208)(142 440 209)(143 441 210)(144 442 211)(145 443 212)(146 444 213)(147 445 214)(148 446 215)(149 447 216)(150 448 217)(151 449 218)(152 450 219)(153 451 220)(154 452 221)(155 453 222)(156 454 223)(157 455 224)(158 456 225)(159 457 226)
(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)(319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477)

G:=sub<Sym(477)| (1,458,227)(2,459,228)(3,460,229)(4,461,230)(5,462,231)(6,463,232)(7,464,233)(8,465,234)(9,466,235)(10,467,236)(11,468,237)(12,469,238)(13,470,239)(14,471,240)(15,472,241)(16,473,242)(17,474,243)(18,475,244)(19,476,245)(20,477,246)(21,319,247)(22,320,248)(23,321,249)(24,322,250)(25,323,251)(26,324,252)(27,325,253)(28,326,254)(29,327,255)(30,328,256)(31,329,257)(32,330,258)(33,331,259)(34,332,260)(35,333,261)(36,334,262)(37,335,263)(38,336,264)(39,337,265)(40,338,266)(41,339,267)(42,340,268)(43,341,269)(44,342,270)(45,343,271)(46,344,272)(47,345,273)(48,346,274)(49,347,275)(50,348,276)(51,349,277)(52,350,278)(53,351,279)(54,352,280)(55,353,281)(56,354,282)(57,355,283)(58,356,284)(59,357,285)(60,358,286)(61,359,287)(62,360,288)(63,361,289)(64,362,290)(65,363,291)(66,364,292)(67,365,293)(68,366,294)(69,367,295)(70,368,296)(71,369,297)(72,370,298)(73,371,299)(74,372,300)(75,373,301)(76,374,302)(77,375,303)(78,376,304)(79,377,305)(80,378,306)(81,379,307)(82,380,308)(83,381,309)(84,382,310)(85,383,311)(86,384,312)(87,385,313)(88,386,314)(89,387,315)(90,388,316)(91,389,317)(92,390,318)(93,391,160)(94,392,161)(95,393,162)(96,394,163)(97,395,164)(98,396,165)(99,397,166)(100,398,167)(101,399,168)(102,400,169)(103,401,170)(104,402,171)(105,403,172)(106,404,173)(107,405,174)(108,406,175)(109,407,176)(110,408,177)(111,409,178)(112,410,179)(113,411,180)(114,412,181)(115,413,182)(116,414,183)(117,415,184)(118,416,185)(119,417,186)(120,418,187)(121,419,188)(122,420,189)(123,421,190)(124,422,191)(125,423,192)(126,424,193)(127,425,194)(128,426,195)(129,427,196)(130,428,197)(131,429,198)(132,430,199)(133,431,200)(134,432,201)(135,433,202)(136,434,203)(137,435,204)(138,436,205)(139,437,206)(140,438,207)(141,439,208)(142,440,209)(143,441,210)(144,442,211)(145,443,212)(146,444,213)(147,445,214)(148,446,215)(149,447,216)(150,448,217)(151,449,218)(152,450,219)(153,451,220)(154,452,221)(155,453,222)(156,454,223)(157,455,224)(158,456,225)(159,457,226), (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)(319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477)>;

G:=Group( (1,458,227)(2,459,228)(3,460,229)(4,461,230)(5,462,231)(6,463,232)(7,464,233)(8,465,234)(9,466,235)(10,467,236)(11,468,237)(12,469,238)(13,470,239)(14,471,240)(15,472,241)(16,473,242)(17,474,243)(18,475,244)(19,476,245)(20,477,246)(21,319,247)(22,320,248)(23,321,249)(24,322,250)(25,323,251)(26,324,252)(27,325,253)(28,326,254)(29,327,255)(30,328,256)(31,329,257)(32,330,258)(33,331,259)(34,332,260)(35,333,261)(36,334,262)(37,335,263)(38,336,264)(39,337,265)(40,338,266)(41,339,267)(42,340,268)(43,341,269)(44,342,270)(45,343,271)(46,344,272)(47,345,273)(48,346,274)(49,347,275)(50,348,276)(51,349,277)(52,350,278)(53,351,279)(54,352,280)(55,353,281)(56,354,282)(57,355,283)(58,356,284)(59,357,285)(60,358,286)(61,359,287)(62,360,288)(63,361,289)(64,362,290)(65,363,291)(66,364,292)(67,365,293)(68,366,294)(69,367,295)(70,368,296)(71,369,297)(72,370,298)(73,371,299)(74,372,300)(75,373,301)(76,374,302)(77,375,303)(78,376,304)(79,377,305)(80,378,306)(81,379,307)(82,380,308)(83,381,309)(84,382,310)(85,383,311)(86,384,312)(87,385,313)(88,386,314)(89,387,315)(90,388,316)(91,389,317)(92,390,318)(93,391,160)(94,392,161)(95,393,162)(96,394,163)(97,395,164)(98,396,165)(99,397,166)(100,398,167)(101,399,168)(102,400,169)(103,401,170)(104,402,171)(105,403,172)(106,404,173)(107,405,174)(108,406,175)(109,407,176)(110,408,177)(111,409,178)(112,410,179)(113,411,180)(114,412,181)(115,413,182)(116,414,183)(117,415,184)(118,416,185)(119,417,186)(120,418,187)(121,419,188)(122,420,189)(123,421,190)(124,422,191)(125,423,192)(126,424,193)(127,425,194)(128,426,195)(129,427,196)(130,428,197)(131,429,198)(132,430,199)(133,431,200)(134,432,201)(135,433,202)(136,434,203)(137,435,204)(138,436,205)(139,437,206)(140,438,207)(141,439,208)(142,440,209)(143,441,210)(144,442,211)(145,443,212)(146,444,213)(147,445,214)(148,446,215)(149,447,216)(150,448,217)(151,449,218)(152,450,219)(153,451,220)(154,452,221)(155,453,222)(156,454,223)(157,455,224)(158,456,225)(159,457,226), (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)(319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477) );

G=PermutationGroup([(1,458,227),(2,459,228),(3,460,229),(4,461,230),(5,462,231),(6,463,232),(7,464,233),(8,465,234),(9,466,235),(10,467,236),(11,468,237),(12,469,238),(13,470,239),(14,471,240),(15,472,241),(16,473,242),(17,474,243),(18,475,244),(19,476,245),(20,477,246),(21,319,247),(22,320,248),(23,321,249),(24,322,250),(25,323,251),(26,324,252),(27,325,253),(28,326,254),(29,327,255),(30,328,256),(31,329,257),(32,330,258),(33,331,259),(34,332,260),(35,333,261),(36,334,262),(37,335,263),(38,336,264),(39,337,265),(40,338,266),(41,339,267),(42,340,268),(43,341,269),(44,342,270),(45,343,271),(46,344,272),(47,345,273),(48,346,274),(49,347,275),(50,348,276),(51,349,277),(52,350,278),(53,351,279),(54,352,280),(55,353,281),(56,354,282),(57,355,283),(58,356,284),(59,357,285),(60,358,286),(61,359,287),(62,360,288),(63,361,289),(64,362,290),(65,363,291),(66,364,292),(67,365,293),(68,366,294),(69,367,295),(70,368,296),(71,369,297),(72,370,298),(73,371,299),(74,372,300),(75,373,301),(76,374,302),(77,375,303),(78,376,304),(79,377,305),(80,378,306),(81,379,307),(82,380,308),(83,381,309),(84,382,310),(85,383,311),(86,384,312),(87,385,313),(88,386,314),(89,387,315),(90,388,316),(91,389,317),(92,390,318),(93,391,160),(94,392,161),(95,393,162),(96,394,163),(97,395,164),(98,396,165),(99,397,166),(100,398,167),(101,399,168),(102,400,169),(103,401,170),(104,402,171),(105,403,172),(106,404,173),(107,405,174),(108,406,175),(109,407,176),(110,408,177),(111,409,178),(112,410,179),(113,411,180),(114,412,181),(115,413,182),(116,414,183),(117,415,184),(118,416,185),(119,417,186),(120,418,187),(121,419,188),(122,420,189),(123,421,190),(124,422,191),(125,423,192),(126,424,193),(127,425,194),(128,426,195),(129,427,196),(130,428,197),(131,429,198),(132,430,199),(133,431,200),(134,432,201),(135,433,202),(136,434,203),(137,435,204),(138,436,205),(139,437,206),(140,438,207),(141,439,208),(142,440,209),(143,441,210),(144,442,211),(145,443,212),(146,444,213),(147,445,214),(148,446,215),(149,447,216),(150,448,217),(151,449,218),(152,450,219),(153,451,220),(154,452,221),(155,453,222),(156,454,223),(157,455,224),(158,456,225),(159,457,226)], [(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),(319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477)])

477 conjugacy classes

class 1 3A···3H53A···53AZ159A···159OZ
order13···353···53159···159
size11···11···11···1

477 irreducible representations

dim1111
type+
imageC1C3C53C159
kernelC3×C159C159C32C3
# reps1852416

Matrix representation of C3×C159 in GL2(𝔽3181) generated by

4400
0440
,
27450
01527
G:=sub<GL(2,GF(3181))| [440,0,0,440],[2745,0,0,1527] >;

C3×C159 in GAP, Magma, Sage, TeX

C_3\times C_{159}
% in TeX

G:=Group("C3xC159");
// GroupNames label

G:=SmallGroup(477,2);
// by ID

G=gap.SmallGroup(477,2);
# by ID

G:=PCGroup([3,-3,-3,-53]);
// Polycyclic

G:=Group<a,b|a^3=b^159=1,a*b=b*a>;
// generators/relations

Export

Subgroup lattice of C3×C159 in TeX

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