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G = C3×C147order 441 = 32·72

Abelian group of type [3,147]

direct product, abelian, monomial, 3-elementary

Aliases: C3×C147, SmallGroup(441,4)

Series: Derived Chief Lower central Upper central

C1 — C3×C147
C1C7C49C147 — C3×C147
C1 — C3×C147
C1 — C3×C147

Generators and relations for C3×C147
 G = < a,b | a3=b147=1, ab=ba >


Smallest permutation representation of C3×C147
Regular action on 441 points
Generators in S441
(1 409 288)(2 410 289)(3 411 290)(4 412 291)(5 413 292)(6 414 293)(7 415 294)(8 416 148)(9 417 149)(10 418 150)(11 419 151)(12 420 152)(13 421 153)(14 422 154)(15 423 155)(16 424 156)(17 425 157)(18 426 158)(19 427 159)(20 428 160)(21 429 161)(22 430 162)(23 431 163)(24 432 164)(25 433 165)(26 434 166)(27 435 167)(28 436 168)(29 437 169)(30 438 170)(31 439 171)(32 440 172)(33 441 173)(34 295 174)(35 296 175)(36 297 176)(37 298 177)(38 299 178)(39 300 179)(40 301 180)(41 302 181)(42 303 182)(43 304 183)(44 305 184)(45 306 185)(46 307 186)(47 308 187)(48 309 188)(49 310 189)(50 311 190)(51 312 191)(52 313 192)(53 314 193)(54 315 194)(55 316 195)(56 317 196)(57 318 197)(58 319 198)(59 320 199)(60 321 200)(61 322 201)(62 323 202)(63 324 203)(64 325 204)(65 326 205)(66 327 206)(67 328 207)(68 329 208)(69 330 209)(70 331 210)(71 332 211)(72 333 212)(73 334 213)(74 335 214)(75 336 215)(76 337 216)(77 338 217)(78 339 218)(79 340 219)(80 341 220)(81 342 221)(82 343 222)(83 344 223)(84 345 224)(85 346 225)(86 347 226)(87 348 227)(88 349 228)(89 350 229)(90 351 230)(91 352 231)(92 353 232)(93 354 233)(94 355 234)(95 356 235)(96 357 236)(97 358 237)(98 359 238)(99 360 239)(100 361 240)(101 362 241)(102 363 242)(103 364 243)(104 365 244)(105 366 245)(106 367 246)(107 368 247)(108 369 248)(109 370 249)(110 371 250)(111 372 251)(112 373 252)(113 374 253)(114 375 254)(115 376 255)(116 377 256)(117 378 257)(118 379 258)(119 380 259)(120 381 260)(121 382 261)(122 383 262)(123 384 263)(124 385 264)(125 386 265)(126 387 266)(127 388 267)(128 389 268)(129 390 269)(130 391 270)(131 392 271)(132 393 272)(133 394 273)(134 395 274)(135 396 275)(136 397 276)(137 398 277)(138 399 278)(139 400 279)(140 401 280)(141 402 281)(142 403 282)(143 404 283)(144 405 284)(145 406 285)(146 407 286)(147 408 287)
(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)

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

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

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

441 conjugacy classes

class 1 3A···3H7A···7F21A···21AV49A···49AP147A···147LX
order13···37···721···2149···49147···147
size11···11···11···11···11···1

441 irreducible representations

dim111111
type+
imageC1C3C7C21C49C147
kernelC3×C147C147C3×C21C21C32C3
# reps1864842336

Matrix representation of C3×C147 in GL2(𝔽883) generated by

3370
0337
,
4270
0315
G:=sub<GL(2,GF(883))| [337,0,0,337],[427,0,0,315] >;

C3×C147 in GAP, Magma, Sage, TeX

C_3\times C_{147}
% in TeX

G:=Group("C3xC147");
// GroupNames label

G:=SmallGroup(441,4);
// by ID

G=gap.SmallGroup(441,4);
# by ID

G:=PCGroup([4,-3,-3,-7,-7,94]);
// Polycyclic

G:=Group<a,b|a^3=b^147=1,a*b=b*a>;
// generators/relations

Export

Subgroup lattice of C3×C147 in TeX

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