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G = C3×C129order 387 = 32·43

Abelian group of type [3,129]

direct product, abelian, monomial, 3-elementary

Aliases: C3×C129, SmallGroup(387,4)

Series: Derived Chief Lower central Upper central

C1 — C3×C129
C1C43C129 — C3×C129
C1 — C3×C129
C1 — C3×C129

Generators and relations for C3×C129
 G = < a,b | a3=b129=1, ab=ba >


Smallest permutation representation of C3×C129
Regular action on 387 points
Generators in S387
(1 263 159)(2 264 160)(3 265 161)(4 266 162)(5 267 163)(6 268 164)(7 269 165)(8 270 166)(9 271 167)(10 272 168)(11 273 169)(12 274 170)(13 275 171)(14 276 172)(15 277 173)(16 278 174)(17 279 175)(18 280 176)(19 281 177)(20 282 178)(21 283 179)(22 284 180)(23 285 181)(24 286 182)(25 287 183)(26 288 184)(27 289 185)(28 290 186)(29 291 187)(30 292 188)(31 293 189)(32 294 190)(33 295 191)(34 296 192)(35 297 193)(36 298 194)(37 299 195)(38 300 196)(39 301 197)(40 302 198)(41 303 199)(42 304 200)(43 305 201)(44 306 202)(45 307 203)(46 308 204)(47 309 205)(48 310 206)(49 311 207)(50 312 208)(51 313 209)(52 314 210)(53 315 211)(54 316 212)(55 317 213)(56 318 214)(57 319 215)(58 320 216)(59 321 217)(60 322 218)(61 323 219)(62 324 220)(63 325 221)(64 326 222)(65 327 223)(66 328 224)(67 329 225)(68 330 226)(69 331 227)(70 332 228)(71 333 229)(72 334 230)(73 335 231)(74 336 232)(75 337 233)(76 338 234)(77 339 235)(78 340 236)(79 341 237)(80 342 238)(81 343 239)(82 344 240)(83 345 241)(84 346 242)(85 347 243)(86 348 244)(87 349 245)(88 350 246)(89 351 247)(90 352 248)(91 353 249)(92 354 250)(93 355 251)(94 356 252)(95 357 253)(96 358 254)(97 359 255)(98 360 256)(99 361 257)(100 362 258)(101 363 130)(102 364 131)(103 365 132)(104 366 133)(105 367 134)(106 368 135)(107 369 136)(108 370 137)(109 371 138)(110 372 139)(111 373 140)(112 374 141)(113 375 142)(114 376 143)(115 377 144)(116 378 145)(117 379 146)(118 380 147)(119 381 148)(120 382 149)(121 383 150)(122 384 151)(123 385 152)(124 386 153)(125 387 154)(126 259 155)(127 260 156)(128 261 157)(129 262 158)
(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)

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

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

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

387 conjugacy classes

class 1 3A···3H43A···43AP129A···129LX
order13···343···43129···129
size11···11···11···1

387 irreducible representations

dim1111
type+
imageC1C3C43C129
kernelC3×C129C129C32C3
# reps1842336

Matrix representation of C3×C129 in GL2(𝔽1033) generated by

1950
0195
,
5780
072
G:=sub<GL(2,GF(1033))| [195,0,0,195],[578,0,0,72] >;

C3×C129 in GAP, Magma, Sage, TeX

C_3\times C_{129}
% in TeX

G:=Group("C3xC129");
// GroupNames label

G:=SmallGroup(387,4);
// by ID

G=gap.SmallGroup(387,4);
# by ID

G:=PCGroup([3,-3,-3,-43]);
// Polycyclic

G:=Group<a,b|a^3=b^129=1,a*b=b*a>;
// generators/relations

Export

Subgroup lattice of C3×C129 in TeX

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