direct product, abelian, monomial, 2-elementary
Aliases: C2×C240, SmallGroup(480,212)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C2×C240 |
| C1 — C2×C240 |
| C1 — C2×C240 |
Generators and relations for C2×C240
G = < a,b | a2=b240=1, ab=ba >
Smallest permutation representation of C2×C240
►Regular action on 480 points
Generators in S480
(1 344)(2 345)(3 346)(4 347)(5 348)(6 349)(7 350)(8 351)(9 352)(10 353)(11 354)(12 355)(13 356)(14 357)(15 358)(16 359)(17 360)(18 361)(19 362)(20 363)(21 364)(22 365)(23 366)(24 367)(25 368)(26 369)(27 370)(28 371)(29 372)(30 373)(31 374)(32 375)(33 376)(34 377)(35 378)(36 379)(37 380)(38 381)(39 382)(40 383)(41 384)(42 385)(43 386)(44 387)(45 388)(46 389)(47 390)(48 391)(49 392)(50 393)(51 394)(52 395)(53 396)(54 397)(55 398)(56 399)(57 400)(58 401)(59 402)(60 403)(61 404)(62 405)(63 406)(64 407)(65 408)(66 409)(67 410)(68 411)(69 412)(70 413)(71 414)(72 415)(73 416)(74 417)(75 418)(76 419)(77 420)(78 421)(79 422)(80 423)(81 424)(82 425)(83 426)(84 427)(85 428)(86 429)(87 430)(88 431)(89 432)(90 433)(91 434)(92 435)(93 436)(94 437)(95 438)(96 439)(97 440)(98 441)(99 442)(100 443)(101 444)(102 445)(103 446)(104 447)(105 448)(106 449)(107 450)(108 451)(109 452)(110 453)(111 454)(112 455)(113 456)(114 457)(115 458)(116 459)(117 460)(118 461)(119 462)(120 463)(121 464)(122 465)(123 466)(124 467)(125 468)(126 469)(127 470)(128 471)(129 472)(130 473)(131 474)(132 475)(133 476)(134 477)(135 478)(136 479)(137 480)(138 241)(139 242)(140 243)(141 244)(142 245)(143 246)(144 247)(145 248)(146 249)(147 250)(148 251)(149 252)(150 253)(151 254)(152 255)(153 256)(154 257)(155 258)(156 259)(157 260)(158 261)(159 262)(160 263)(161 264)(162 265)(163 266)(164 267)(165 268)(166 269)(167 270)(168 271)(169 272)(170 273)(171 274)(172 275)(173 276)(174 277)(175 278)(176 279)(177 280)(178 281)(179 282)(180 283)(181 284)(182 285)(183 286)(184 287)(185 288)(186 289)(187 290)(188 291)(189 292)(190 293)(191 294)(192 295)(193 296)(194 297)(195 298)(196 299)(197 300)(198 301)(199 302)(200 303)(201 304)(202 305)(203 306)(204 307)(205 308)(206 309)(207 310)(208 311)(209 312)(210 313)(211 314)(212 315)(213 316)(214 317)(215 318)(216 319)(217 320)(218 321)(219 322)(220 323)(221 324)(222 325)(223 326)(224 327)(225 328)(226 329)(227 330)(228 331)(229 332)(230 333)(231 334)(232 335)(233 336)(234 337)(235 338)(236 339)(237 340)(238 341)(239 342)(240 343)
(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)(241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480)
G:=sub<Sym(480)| (1,344)(2,345)(3,346)(4,347)(5,348)(6,349)(7,350)(8,351)(9,352)(10,353)(11,354)(12,355)(13,356)(14,357)(15,358)(16,359)(17,360)(18,361)(19,362)(20,363)(21,364)(22,365)(23,366)(24,367)(25,368)(26,369)(27,370)(28,371)(29,372)(30,373)(31,374)(32,375)(33,376)(34,377)(35,378)(36,379)(37,380)(38,381)(39,382)(40,383)(41,384)(42,385)(43,386)(44,387)(45,388)(46,389)(47,390)(48,391)(49,392)(50,393)(51,394)(52,395)(53,396)(54,397)(55,398)(56,399)(57,400)(58,401)(59,402)(60,403)(61,404)(62,405)(63,406)(64,407)(65,408)(66,409)(67,410)(68,411)(69,412)(70,413)(71,414)(72,415)(73,416)(74,417)(75,418)(76,419)(77,420)(78,421)(79,422)(80,423)(81,424)(82,425)(83,426)(84,427)(85,428)(86,429)(87,430)(88,431)(89,432)(90,433)(91,434)(92,435)(93,436)(94,437)(95,438)(96,439)(97,440)(98,441)(99,442)(100,443)(101,444)(102,445)(103,446)(104,447)(105,448)(106,449)(107,450)(108,451)(109,452)(110,453)(111,454)(112,455)(113,456)(114,457)(115,458)(116,459)(117,460)(118,461)(119,462)(120,463)(121,464)(122,465)(123,466)(124,467)(125,468)(126,469)(127,470)(128,471)(129,472)(130,473)(131,474)(132,475)(133,476)(134,477)(135,478)(136,479)(137,480)(138,241)(139,242)(140,243)(141,244)(142,245)(143,246)(144,247)(145,248)(146,249)(147,250)(148,251)(149,252)(150,253)(151,254)(152,255)(153,256)(154,257)(155,258)(156,259)(157,260)(158,261)(159,262)(160,263)(161,264)(162,265)(163,266)(164,267)(165,268)(166,269)(167,270)(168,271)(169,272)(170,273)(171,274)(172,275)(173,276)(174,277)(175,278)(176,279)(177,280)(178,281)(179,282)(180,283)(181,284)(182,285)(183,286)(184,287)(185,288)(186,289)(187,290)(188,291)(189,292)(190,293)(191,294)(192,295)(193,296)(194,297)(195,298)(196,299)(197,300)(198,301)(199,302)(200,303)(201,304)(202,305)(203,306)(204,307)(205,308)(206,309)(207,310)(208,311)(209,312)(210,313)(211,314)(212,315)(213,316)(214,317)(215,318)(216,319)(217,320)(218,321)(219,322)(220,323)(221,324)(222,325)(223,326)(224,327)(225,328)(226,329)(227,330)(228,331)(229,332)(230,333)(231,334)(232,335)(233,336)(234,337)(235,338)(236,339)(237,340)(238,341)(239,342)(240,343), (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)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480)>;
G:=Group( (1,344)(2,345)(3,346)(4,347)(5,348)(6,349)(7,350)(8,351)(9,352)(10,353)(11,354)(12,355)(13,356)(14,357)(15,358)(16,359)(17,360)(18,361)(19,362)(20,363)(21,364)(22,365)(23,366)(24,367)(25,368)(26,369)(27,370)(28,371)(29,372)(30,373)(31,374)(32,375)(33,376)(34,377)(35,378)(36,379)(37,380)(38,381)(39,382)(40,383)(41,384)(42,385)(43,386)(44,387)(45,388)(46,389)(47,390)(48,391)(49,392)(50,393)(51,394)(52,395)(53,396)(54,397)(55,398)(56,399)(57,400)(58,401)(59,402)(60,403)(61,404)(62,405)(63,406)(64,407)(65,408)(66,409)(67,410)(68,411)(69,412)(70,413)(71,414)(72,415)(73,416)(74,417)(75,418)(76,419)(77,420)(78,421)(79,422)(80,423)(81,424)(82,425)(83,426)(84,427)(85,428)(86,429)(87,430)(88,431)(89,432)(90,433)(91,434)(92,435)(93,436)(94,437)(95,438)(96,439)(97,440)(98,441)(99,442)(100,443)(101,444)(102,445)(103,446)(104,447)(105,448)(106,449)(107,450)(108,451)(109,452)(110,453)(111,454)(112,455)(113,456)(114,457)(115,458)(116,459)(117,460)(118,461)(119,462)(120,463)(121,464)(122,465)(123,466)(124,467)(125,468)(126,469)(127,470)(128,471)(129,472)(130,473)(131,474)(132,475)(133,476)(134,477)(135,478)(136,479)(137,480)(138,241)(139,242)(140,243)(141,244)(142,245)(143,246)(144,247)(145,248)(146,249)(147,250)(148,251)(149,252)(150,253)(151,254)(152,255)(153,256)(154,257)(155,258)(156,259)(157,260)(158,261)(159,262)(160,263)(161,264)(162,265)(163,266)(164,267)(165,268)(166,269)(167,270)(168,271)(169,272)(170,273)(171,274)(172,275)(173,276)(174,277)(175,278)(176,279)(177,280)(178,281)(179,282)(180,283)(181,284)(182,285)(183,286)(184,287)(185,288)(186,289)(187,290)(188,291)(189,292)(190,293)(191,294)(192,295)(193,296)(194,297)(195,298)(196,299)(197,300)(198,301)(199,302)(200,303)(201,304)(202,305)(203,306)(204,307)(205,308)(206,309)(207,310)(208,311)(209,312)(210,313)(211,314)(212,315)(213,316)(214,317)(215,318)(216,319)(217,320)(218,321)(219,322)(220,323)(221,324)(222,325)(223,326)(224,327)(225,328)(226,329)(227,330)(228,331)(229,332)(230,333)(231,334)(232,335)(233,336)(234,337)(235,338)(236,339)(237,340)(238,341)(239,342)(240,343), (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)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480) );
G=PermutationGroup([[(1,344),(2,345),(3,346),(4,347),(5,348),(6,349),(7,350),(8,351),(9,352),(10,353),(11,354),(12,355),(13,356),(14,357),(15,358),(16,359),(17,360),(18,361),(19,362),(20,363),(21,364),(22,365),(23,366),(24,367),(25,368),(26,369),(27,370),(28,371),(29,372),(30,373),(31,374),(32,375),(33,376),(34,377),(35,378),(36,379),(37,380),(38,381),(39,382),(40,383),(41,384),(42,385),(43,386),(44,387),(45,388),(46,389),(47,390),(48,391),(49,392),(50,393),(51,394),(52,395),(53,396),(54,397),(55,398),(56,399),(57,400),(58,401),(59,402),(60,403),(61,404),(62,405),(63,406),(64,407),(65,408),(66,409),(67,410),(68,411),(69,412),(70,413),(71,414),(72,415),(73,416),(74,417),(75,418),(76,419),(77,420),(78,421),(79,422),(80,423),(81,424),(82,425),(83,426),(84,427),(85,428),(86,429),(87,430),(88,431),(89,432),(90,433),(91,434),(92,435),(93,436),(94,437),(95,438),(96,439),(97,440),(98,441),(99,442),(100,443),(101,444),(102,445),(103,446),(104,447),(105,448),(106,449),(107,450),(108,451),(109,452),(110,453),(111,454),(112,455),(113,456),(114,457),(115,458),(116,459),(117,460),(118,461),(119,462),(120,463),(121,464),(122,465),(123,466),(124,467),(125,468),(126,469),(127,470),(128,471),(129,472),(130,473),(131,474),(132,475),(133,476),(134,477),(135,478),(136,479),(137,480),(138,241),(139,242),(140,243),(141,244),(142,245),(143,246),(144,247),(145,248),(146,249),(147,250),(148,251),(149,252),(150,253),(151,254),(152,255),(153,256),(154,257),(155,258),(156,259),(157,260),(158,261),(159,262),(160,263),(161,264),(162,265),(163,266),(164,267),(165,268),(166,269),(167,270),(168,271),(169,272),(170,273),(171,274),(172,275),(173,276),(174,277),(175,278),(176,279),(177,280),(178,281),(179,282),(180,283),(181,284),(182,285),(183,286),(184,287),(185,288),(186,289),(187,290),(188,291),(189,292),(190,293),(191,294),(192,295),(193,296),(194,297),(195,298),(196,299),(197,300),(198,301),(199,302),(200,303),(201,304),(202,305),(203,306),(204,307),(205,308),(206,309),(207,310),(208,311),(209,312),(210,313),(211,314),(212,315),(213,316),(214,317),(215,318),(216,319),(217,320),(218,321),(219,322),(220,323),(221,324),(222,325),(223,326),(224,327),(225,328),(226,329),(227,330),(228,331),(229,332),(230,333),(231,334),(232,335),(233,336),(234,337),(235,338),(236,339),(237,340),(238,341),(239,342),(240,343)], [(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),(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480)]])
480 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | 4B | 4C | 4D | 5A | 5B | 5C | 5D | 6A | ··· | 6F | 8A | ··· | 8H | 10A | ··· | 10L | 12A | ··· | 12H | 15A | ··· | 15H | 16A | ··· | 16P | 20A | ··· | 20P | 24A | ··· | 24P | 30A | ··· | 30X | 40A | ··· | 40AF | 48A | ··· | 48AF | 60A | ··· | 60AF | 80A | ··· | 80BL | 120A | ··· | 120BL | 240A | ··· | 240DX |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | ··· | 6 | 8 | ··· | 8 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | ··· | 15 | 16 | ··· | 16 | 20 | ··· | 20 | 24 | ··· | 24 | 30 | ··· | 30 | 40 | ··· | 40 | 48 | ··· | 48 | 60 | ··· | 60 | 80 | ··· | 80 | 120 | ··· | 120 | 240 | ··· | 240 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
480 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | + | |||||||||||||||||||||||||||||
| image | C1 | C2 | C2 | C3 | C4 | C4 | C5 | C6 | C6 | C8 | C8 | C10 | C10 | C12 | C12 | C15 | C16 | C20 | C20 | C24 | C24 | C30 | C30 | C40 | C40 | C48 | C60 | C60 | C80 | C120 | C120 | C240 |
| kernel | C2×C240 | C240 | C2×C120 | C2×C80 | C120 | C2×C60 | C2×C48 | C80 | C2×C40 | C60 | C2×C30 | C48 | C2×C24 | C40 | C2×C20 | C2×C16 | C30 | C24 | C2×C12 | C20 | C2×C10 | C16 | C2×C8 | C12 | C2×C6 | C10 | C8 | C2×C4 | C6 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 4 | 2 | 4 | 4 | 8 | 4 | 4 | 4 | 8 | 16 | 8 | 8 | 8 | 8 | 16 | 8 | 16 | 16 | 32 | 16 | 16 | 64 | 32 | 32 | 128 |
Matrix representation of C2×C240 ►in GL2(𝔽241) generated by
| 240 | 0 |
| 0 | 1 |
| 106 | 0 |
| 0 | 172 |
G:=sub<GL(2,GF(241))| [240,0,0,1],[106,0,0,172] >;
C2×C240 in GAP, Magma, Sage, TeX
C_2\times C_{240} % in TeX
G:=Group("C2xC240"); // GroupNames label
G:=SmallGroup(480,212);
// by ID
G=gap.SmallGroup(480,212);
# by ID
G:=PCGroup([7,-2,-2,-3,-5,-2,-2,-2,420,102,124]);
// Polycyclic
G:=Group<a,b|a^2=b^240=1,a*b=b*a>;
// generators/relations
Export