direct product, abelian, monomial, 3-elementary
Aliases: C3×C141, SmallGroup(423,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C3×C141 |
| C1 — C3×C141 |
| C1 — C3×C141 |
Generators and relations for C3×C141
G = < a,b | a3=b141=1, ab=ba >
Smallest permutation representation of C3×C141
►Regular action on 423 points
Generators in S423
(1 338 239)(2 339 240)(3 340 241)(4 341 242)(5 342 243)(6 343 244)(7 344 245)(8 345 246)(9 346 247)(10 347 248)(11 348 249)(12 349 250)(13 350 251)(14 351 252)(15 352 253)(16 353 254)(17 354 255)(18 355 256)(19 356 257)(20 357 258)(21 358 259)(22 359 260)(23 360 261)(24 361 262)(25 362 263)(26 363 264)(27 364 265)(28 365 266)(29 366 267)(30 367 268)(31 368 269)(32 369 270)(33 370 271)(34 371 272)(35 372 273)(36 373 274)(37 374 275)(38 375 276)(39 376 277)(40 377 278)(41 378 279)(42 379 280)(43 380 281)(44 381 282)(45 382 142)(46 383 143)(47 384 144)(48 385 145)(49 386 146)(50 387 147)(51 388 148)(52 389 149)(53 390 150)(54 391 151)(55 392 152)(56 393 153)(57 394 154)(58 395 155)(59 396 156)(60 397 157)(61 398 158)(62 399 159)(63 400 160)(64 401 161)(65 402 162)(66 403 163)(67 404 164)(68 405 165)(69 406 166)(70 407 167)(71 408 168)(72 409 169)(73 410 170)(74 411 171)(75 412 172)(76 413 173)(77 414 174)(78 415 175)(79 416 176)(80 417 177)(81 418 178)(82 419 179)(83 420 180)(84 421 181)(85 422 182)(86 423 183)(87 283 184)(88 284 185)(89 285 186)(90 286 187)(91 287 188)(92 288 189)(93 289 190)(94 290 191)(95 291 192)(96 292 193)(97 293 194)(98 294 195)(99 295 196)(100 296 197)(101 297 198)(102 298 199)(103 299 200)(104 300 201)(105 301 202)(106 302 203)(107 303 204)(108 304 205)(109 305 206)(110 306 207)(111 307 208)(112 308 209)(113 309 210)(114 310 211)(115 311 212)(116 312 213)(117 313 214)(118 314 215)(119 315 216)(120 316 217)(121 317 218)(122 318 219)(123 319 220)(124 320 221)(125 321 222)(126 322 223)(127 323 224)(128 324 225)(129 325 226)(130 326 227)(131 327 228)(132 328 229)(133 329 230)(134 330 231)(135 331 232)(136 332 233)(137 333 234)(138 334 235)(139 335 236)(140 336 237)(141 337 238)
(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)
G:=sub<Sym(423)| (1,338,239)(2,339,240)(3,340,241)(4,341,242)(5,342,243)(6,343,244)(7,344,245)(8,345,246)(9,346,247)(10,347,248)(11,348,249)(12,349,250)(13,350,251)(14,351,252)(15,352,253)(16,353,254)(17,354,255)(18,355,256)(19,356,257)(20,357,258)(21,358,259)(22,359,260)(23,360,261)(24,361,262)(25,362,263)(26,363,264)(27,364,265)(28,365,266)(29,366,267)(30,367,268)(31,368,269)(32,369,270)(33,370,271)(34,371,272)(35,372,273)(36,373,274)(37,374,275)(38,375,276)(39,376,277)(40,377,278)(41,378,279)(42,379,280)(43,380,281)(44,381,282)(45,382,142)(46,383,143)(47,384,144)(48,385,145)(49,386,146)(50,387,147)(51,388,148)(52,389,149)(53,390,150)(54,391,151)(55,392,152)(56,393,153)(57,394,154)(58,395,155)(59,396,156)(60,397,157)(61,398,158)(62,399,159)(63,400,160)(64,401,161)(65,402,162)(66,403,163)(67,404,164)(68,405,165)(69,406,166)(70,407,167)(71,408,168)(72,409,169)(73,410,170)(74,411,171)(75,412,172)(76,413,173)(77,414,174)(78,415,175)(79,416,176)(80,417,177)(81,418,178)(82,419,179)(83,420,180)(84,421,181)(85,422,182)(86,423,183)(87,283,184)(88,284,185)(89,285,186)(90,286,187)(91,287,188)(92,288,189)(93,289,190)(94,290,191)(95,291,192)(96,292,193)(97,293,194)(98,294,195)(99,295,196)(100,296,197)(101,297,198)(102,298,199)(103,299,200)(104,300,201)(105,301,202)(106,302,203)(107,303,204)(108,304,205)(109,305,206)(110,306,207)(111,307,208)(112,308,209)(113,309,210)(114,310,211)(115,311,212)(116,312,213)(117,313,214)(118,314,215)(119,315,216)(120,316,217)(121,317,218)(122,318,219)(123,319,220)(124,320,221)(125,321,222)(126,322,223)(127,323,224)(128,324,225)(129,325,226)(130,326,227)(131,327,228)(132,328,229)(133,329,230)(134,330,231)(135,331,232)(136,332,233)(137,333,234)(138,334,235)(139,335,236)(140,336,237)(141,337,238), (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)>;
G:=Group( (1,338,239)(2,339,240)(3,340,241)(4,341,242)(5,342,243)(6,343,244)(7,344,245)(8,345,246)(9,346,247)(10,347,248)(11,348,249)(12,349,250)(13,350,251)(14,351,252)(15,352,253)(16,353,254)(17,354,255)(18,355,256)(19,356,257)(20,357,258)(21,358,259)(22,359,260)(23,360,261)(24,361,262)(25,362,263)(26,363,264)(27,364,265)(28,365,266)(29,366,267)(30,367,268)(31,368,269)(32,369,270)(33,370,271)(34,371,272)(35,372,273)(36,373,274)(37,374,275)(38,375,276)(39,376,277)(40,377,278)(41,378,279)(42,379,280)(43,380,281)(44,381,282)(45,382,142)(46,383,143)(47,384,144)(48,385,145)(49,386,146)(50,387,147)(51,388,148)(52,389,149)(53,390,150)(54,391,151)(55,392,152)(56,393,153)(57,394,154)(58,395,155)(59,396,156)(60,397,157)(61,398,158)(62,399,159)(63,400,160)(64,401,161)(65,402,162)(66,403,163)(67,404,164)(68,405,165)(69,406,166)(70,407,167)(71,408,168)(72,409,169)(73,410,170)(74,411,171)(75,412,172)(76,413,173)(77,414,174)(78,415,175)(79,416,176)(80,417,177)(81,418,178)(82,419,179)(83,420,180)(84,421,181)(85,422,182)(86,423,183)(87,283,184)(88,284,185)(89,285,186)(90,286,187)(91,287,188)(92,288,189)(93,289,190)(94,290,191)(95,291,192)(96,292,193)(97,293,194)(98,294,195)(99,295,196)(100,296,197)(101,297,198)(102,298,199)(103,299,200)(104,300,201)(105,301,202)(106,302,203)(107,303,204)(108,304,205)(109,305,206)(110,306,207)(111,307,208)(112,308,209)(113,309,210)(114,310,211)(115,311,212)(116,312,213)(117,313,214)(118,314,215)(119,315,216)(120,316,217)(121,317,218)(122,318,219)(123,319,220)(124,320,221)(125,321,222)(126,322,223)(127,323,224)(128,324,225)(129,325,226)(130,326,227)(131,327,228)(132,328,229)(133,329,230)(134,330,231)(135,331,232)(136,332,233)(137,333,234)(138,334,235)(139,335,236)(140,336,237)(141,337,238), (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) );
G=PermutationGroup([[(1,338,239),(2,339,240),(3,340,241),(4,341,242),(5,342,243),(6,343,244),(7,344,245),(8,345,246),(9,346,247),(10,347,248),(11,348,249),(12,349,250),(13,350,251),(14,351,252),(15,352,253),(16,353,254),(17,354,255),(18,355,256),(19,356,257),(20,357,258),(21,358,259),(22,359,260),(23,360,261),(24,361,262),(25,362,263),(26,363,264),(27,364,265),(28,365,266),(29,366,267),(30,367,268),(31,368,269),(32,369,270),(33,370,271),(34,371,272),(35,372,273),(36,373,274),(37,374,275),(38,375,276),(39,376,277),(40,377,278),(41,378,279),(42,379,280),(43,380,281),(44,381,282),(45,382,142),(46,383,143),(47,384,144),(48,385,145),(49,386,146),(50,387,147),(51,388,148),(52,389,149),(53,390,150),(54,391,151),(55,392,152),(56,393,153),(57,394,154),(58,395,155),(59,396,156),(60,397,157),(61,398,158),(62,399,159),(63,400,160),(64,401,161),(65,402,162),(66,403,163),(67,404,164),(68,405,165),(69,406,166),(70,407,167),(71,408,168),(72,409,169),(73,410,170),(74,411,171),(75,412,172),(76,413,173),(77,414,174),(78,415,175),(79,416,176),(80,417,177),(81,418,178),(82,419,179),(83,420,180),(84,421,181),(85,422,182),(86,423,183),(87,283,184),(88,284,185),(89,285,186),(90,286,187),(91,287,188),(92,288,189),(93,289,190),(94,290,191),(95,291,192),(96,292,193),(97,293,194),(98,294,195),(99,295,196),(100,296,197),(101,297,198),(102,298,199),(103,299,200),(104,300,201),(105,301,202),(106,302,203),(107,303,204),(108,304,205),(109,305,206),(110,306,207),(111,307,208),(112,308,209),(113,309,210),(114,310,211),(115,311,212),(116,312,213),(117,313,214),(118,314,215),(119,315,216),(120,316,217),(121,317,218),(122,318,219),(123,319,220),(124,320,221),(125,321,222),(126,322,223),(127,323,224),(128,324,225),(129,325,226),(130,326,227),(131,327,228),(132,328,229),(133,329,230),(134,330,231),(135,331,232),(136,332,233),(137,333,234),(138,334,235),(139,335,236),(140,336,237),(141,337,238)], [(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)]])
423 conjugacy classes
| class | 1 | 3A | ··· | 3H | 47A | ··· | 47AT | 141A | ··· | 141ND |
| order | 1 | 3 | ··· | 3 | 47 | ··· | 47 | 141 | ··· | 141 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
423 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | |||
| image | C1 | C3 | C47 | C141 |
| kernel | C3×C141 | C141 | C32 | C3 |
| # reps | 1 | 8 | 46 | 368 |
Matrix representation of C3×C141 ►in GL2(𝔽283) generated by
| 1 | 0 |
| 0 | 44 |
| 227 | 0 |
| 0 | 158 |
G:=sub<GL(2,GF(283))| [1,0,0,44],[227,0,0,158] >;
C3×C141 in GAP, Magma, Sage, TeX
C_3\times C_{141} % in TeX
G:=Group("C3xC141"); // GroupNames label
G:=SmallGroup(423,2);
// by ID
G=gap.SmallGroup(423,2);
# by ID
G:=PCGroup([3,-3,-3,-47]);
// Polycyclic
G:=Group<a,b|a^3=b^141=1,a*b=b*a>;
// generators/relations
Export