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G = C3×C141order 423 = 32·47

Abelian group of type [3,141]

direct product, abelian, monomial, 3-elementary

Aliases: C3×C141, SmallGroup(423,2)

Series: Derived Chief Lower central Upper central

C1 — C3×C141
C1C47C141 — 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
(1 348 191)(2 349 192)(3 350 193)(4 351 194)(5 352 195)(6 353 196)(7 354 197)(8 355 198)(9 356 199)(10 357 200)(11 358 201)(12 359 202)(13 360 203)(14 361 204)(15 362 205)(16 363 206)(17 364 207)(18 365 208)(19 366 209)(20 367 210)(21 368 211)(22 369 212)(23 370 213)(24 371 214)(25 372 215)(26 373 216)(27 374 217)(28 375 218)(29 376 219)(30 377 220)(31 378 221)(32 379 222)(33 380 223)(34 381 224)(35 382 225)(36 383 226)(37 384 227)(38 385 228)(39 386 229)(40 387 230)(41 388 231)(42 389 232)(43 390 233)(44 391 234)(45 392 235)(46 393 236)(47 394 237)(48 395 238)(49 396 239)(50 397 240)(51 398 241)(52 399 242)(53 400 243)(54 401 244)(55 402 245)(56 403 246)(57 404 247)(58 405 248)(59 406 249)(60 407 250)(61 408 251)(62 409 252)(63 410 253)(64 411 254)(65 412 255)(66 413 256)(67 414 257)(68 415 258)(69 416 259)(70 417 260)(71 418 261)(72 419 262)(73 420 263)(74 421 264)(75 422 265)(76 423 266)(77 283 267)(78 284 268)(79 285 269)(80 286 270)(81 287 271)(82 288 272)(83 289 273)(84 290 274)(85 291 275)(86 292 276)(87 293 277)(88 294 278)(89 295 279)(90 296 280)(91 297 281)(92 298 282)(93 299 142)(94 300 143)(95 301 144)(96 302 145)(97 303 146)(98 304 147)(99 305 148)(100 306 149)(101 307 150)(102 308 151)(103 309 152)(104 310 153)(105 311 154)(106 312 155)(107 313 156)(108 314 157)(109 315 158)(110 316 159)(111 317 160)(112 318 161)(113 319 162)(114 320 163)(115 321 164)(116 322 165)(117 323 166)(118 324 167)(119 325 168)(120 326 169)(121 327 170)(122 328 171)(123 329 172)(124 330 173)(125 331 174)(126 332 175)(127 333 176)(128 334 177)(129 335 178)(130 336 179)(131 337 180)(132 338 181)(133 339 182)(134 340 183)(135 341 184)(136 342 185)(137 343 186)(138 344 187)(139 345 188)(140 346 189)(141 347 190)
(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)| (1,348,191)(2,349,192)(3,350,193)(4,351,194)(5,352,195)(6,353,196)(7,354,197)(8,355,198)(9,356,199)(10,357,200)(11,358,201)(12,359,202)(13,360,203)(14,361,204)(15,362,205)(16,363,206)(17,364,207)(18,365,208)(19,366,209)(20,367,210)(21,368,211)(22,369,212)(23,370,213)(24,371,214)(25,372,215)(26,373,216)(27,374,217)(28,375,218)(29,376,219)(30,377,220)(31,378,221)(32,379,222)(33,380,223)(34,381,224)(35,382,225)(36,383,226)(37,384,227)(38,385,228)(39,386,229)(40,387,230)(41,388,231)(42,389,232)(43,390,233)(44,391,234)(45,392,235)(46,393,236)(47,394,237)(48,395,238)(49,396,239)(50,397,240)(51,398,241)(52,399,242)(53,400,243)(54,401,244)(55,402,245)(56,403,246)(57,404,247)(58,405,248)(59,406,249)(60,407,250)(61,408,251)(62,409,252)(63,410,253)(64,411,254)(65,412,255)(66,413,256)(67,414,257)(68,415,258)(69,416,259)(70,417,260)(71,418,261)(72,419,262)(73,420,263)(74,421,264)(75,422,265)(76,423,266)(77,283,267)(78,284,268)(79,285,269)(80,286,270)(81,287,271)(82,288,272)(83,289,273)(84,290,274)(85,291,275)(86,292,276)(87,293,277)(88,294,278)(89,295,279)(90,296,280)(91,297,281)(92,298,282)(93,299,142)(94,300,143)(95,301,144)(96,302,145)(97,303,146)(98,304,147)(99,305,148)(100,306,149)(101,307,150)(102,308,151)(103,309,152)(104,310,153)(105,311,154)(106,312,155)(107,313,156)(108,314,157)(109,315,158)(110,316,159)(111,317,160)(112,318,161)(113,319,162)(114,320,163)(115,321,164)(116,322,165)(117,323,166)(118,324,167)(119,325,168)(120,326,169)(121,327,170)(122,328,171)(123,329,172)(124,330,173)(125,331,174)(126,332,175)(127,333,176)(128,334,177)(129,335,178)(130,336,179)(131,337,180)(132,338,181)(133,339,182)(134,340,183)(135,341,184)(136,342,185)(137,343,186)(138,344,187)(139,345,188)(140,346,189)(141,347,190), (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( (1,348,191)(2,349,192)(3,350,193)(4,351,194)(5,352,195)(6,353,196)(7,354,197)(8,355,198)(9,356,199)(10,357,200)(11,358,201)(12,359,202)(13,360,203)(14,361,204)(15,362,205)(16,363,206)(17,364,207)(18,365,208)(19,366,209)(20,367,210)(21,368,211)(22,369,212)(23,370,213)(24,371,214)(25,372,215)(26,373,216)(27,374,217)(28,375,218)(29,376,219)(30,377,220)(31,378,221)(32,379,222)(33,380,223)(34,381,224)(35,382,225)(36,383,226)(37,384,227)(38,385,228)(39,386,229)(40,387,230)(41,388,231)(42,389,232)(43,390,233)(44,391,234)(45,392,235)(46,393,236)(47,394,237)(48,395,238)(49,396,239)(50,397,240)(51,398,241)(52,399,242)(53,400,243)(54,401,244)(55,402,245)(56,403,246)(57,404,247)(58,405,248)(59,406,249)(60,407,250)(61,408,251)(62,409,252)(63,410,253)(64,411,254)(65,412,255)(66,413,256)(67,414,257)(68,415,258)(69,416,259)(70,417,260)(71,418,261)(72,419,262)(73,420,263)(74,421,264)(75,422,265)(76,423,266)(77,283,267)(78,284,268)(79,285,269)(80,286,270)(81,287,271)(82,288,272)(83,289,273)(84,290,274)(85,291,275)(86,292,276)(87,293,277)(88,294,278)(89,295,279)(90,296,280)(91,297,281)(92,298,282)(93,299,142)(94,300,143)(95,301,144)(96,302,145)(97,303,146)(98,304,147)(99,305,148)(100,306,149)(101,307,150)(102,308,151)(103,309,152)(104,310,153)(105,311,154)(106,312,155)(107,313,156)(108,314,157)(109,315,158)(110,316,159)(111,317,160)(112,318,161)(113,319,162)(114,320,163)(115,321,164)(116,322,165)(117,323,166)(118,324,167)(119,325,168)(120,326,169)(121,327,170)(122,328,171)(123,329,172)(124,330,173)(125,331,174)(126,332,175)(127,333,176)(128,334,177)(129,335,178)(130,336,179)(131,337,180)(132,338,181)(133,339,182)(134,340,183)(135,341,184)(136,342,185)(137,343,186)(138,344,187)(139,345,188)(140,346,189)(141,347,190), (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([(1,348,191),(2,349,192),(3,350,193),(4,351,194),(5,352,195),(6,353,196),(7,354,197),(8,355,198),(9,356,199),(10,357,200),(11,358,201),(12,359,202),(13,360,203),(14,361,204),(15,362,205),(16,363,206),(17,364,207),(18,365,208),(19,366,209),(20,367,210),(21,368,211),(22,369,212),(23,370,213),(24,371,214),(25,372,215),(26,373,216),(27,374,217),(28,375,218),(29,376,219),(30,377,220),(31,378,221),(32,379,222),(33,380,223),(34,381,224),(35,382,225),(36,383,226),(37,384,227),(38,385,228),(39,386,229),(40,387,230),(41,388,231),(42,389,232),(43,390,233),(44,391,234),(45,392,235),(46,393,236),(47,394,237),(48,395,238),(49,396,239),(50,397,240),(51,398,241),(52,399,242),(53,400,243),(54,401,244),(55,402,245),(56,403,246),(57,404,247),(58,405,248),(59,406,249),(60,407,250),(61,408,251),(62,409,252),(63,410,253),(64,411,254),(65,412,255),(66,413,256),(67,414,257),(68,415,258),(69,416,259),(70,417,260),(71,418,261),(72,419,262),(73,420,263),(74,421,264),(75,422,265),(76,423,266),(77,283,267),(78,284,268),(79,285,269),(80,286,270),(81,287,271),(82,288,272),(83,289,273),(84,290,274),(85,291,275),(86,292,276),(87,293,277),(88,294,278),(89,295,279),(90,296,280),(91,297,281),(92,298,282),(93,299,142),(94,300,143),(95,301,144),(96,302,145),(97,303,146),(98,304,147),(99,305,148),(100,306,149),(101,307,150),(102,308,151),(103,309,152),(104,310,153),(105,311,154),(106,312,155),(107,313,156),(108,314,157),(109,315,158),(110,316,159),(111,317,160),(112,318,161),(113,319,162),(114,320,163),(115,321,164),(116,322,165),(117,323,166),(118,324,167),(119,325,168),(120,326,169),(121,327,170),(122,328,171),(123,329,172),(124,330,173),(125,331,174),(126,332,175),(127,333,176),(128,334,177),(129,335,178),(130,336,179),(131,337,180),(132,338,181),(133,339,182),(134,340,183),(135,341,184),(136,342,185),(137,343,186),(138,344,187),(139,345,188),(140,346,189),(141,347,190)], [(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···3H47A···47AT141A···141ND
order13···347···47141···141
size11···11···11···1

423 irreducible representations

dim1111
type+
imageC1C3C47C141
kernelC3×C141C141C32C3
# reps1846368

Matrix representation of C3×C141 in GL2(𝔽283) generated by

10
044
,
2270
0158
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

Subgroup lattice of C3×C141 in TeX

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