direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C3×Dic41, C82.C6, C41⋊2C12, C123⋊4C4, C6.2D41, C246.2C2, C2.(C3×D41), SmallGroup(492,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C41 — C3×Dic41 |
Generators and relations for C3×Dic41
G = < a,b,c | a3=b82=1, c2=b41, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C3×Dic41
►Regular action on 492 points
Generators in S492
(1 198 127)(2 199 128)(3 200 129)(4 201 130)(5 202 131)(6 203 132)(7 204 133)(8 205 134)(9 206 135)(10 207 136)(11 208 137)(12 209 138)(13 210 139)(14 211 140)(15 212 141)(16 213 142)(17 214 143)(18 215 144)(19 216 145)(20 217 146)(21 218 147)(22 219 148)(23 220 149)(24 221 150)(25 222 151)(26 223 152)(27 224 153)(28 225 154)(29 226 155)(30 227 156)(31 228 157)(32 229 158)(33 230 159)(34 231 160)(35 232 161)(36 233 162)(37 234 163)(38 235 164)(39 236 83)(40 237 84)(41 238 85)(42 239 86)(43 240 87)(44 241 88)(45 242 89)(46 243 90)(47 244 91)(48 245 92)(49 246 93)(50 165 94)(51 166 95)(52 167 96)(53 168 97)(54 169 98)(55 170 99)(56 171 100)(57 172 101)(58 173 102)(59 174 103)(60 175 104)(61 176 105)(62 177 106)(63 178 107)(64 179 108)(65 180 109)(66 181 110)(67 182 111)(68 183 112)(69 184 113)(70 185 114)(71 186 115)(72 187 116)(73 188 117)(74 189 118)(75 190 119)(76 191 120)(77 192 121)(78 193 122)(79 194 123)(80 195 124)(81 196 125)(82 197 126)(247 411 370)(248 412 371)(249 413 372)(250 414 373)(251 415 374)(252 416 375)(253 417 376)(254 418 377)(255 419 378)(256 420 379)(257 421 380)(258 422 381)(259 423 382)(260 424 383)(261 425 384)(262 426 385)(263 427 386)(264 428 387)(265 429 388)(266 430 389)(267 431 390)(268 432 391)(269 433 392)(270 434 393)(271 435 394)(272 436 395)(273 437 396)(274 438 397)(275 439 398)(276 440 399)(277 441 400)(278 442 401)(279 443 402)(280 444 403)(281 445 404)(282 446 405)(283 447 406)(284 448 407)(285 449 408)(286 450 409)(287 451 410)(288 452 329)(289 453 330)(290 454 331)(291 455 332)(292 456 333)(293 457 334)(294 458 335)(295 459 336)(296 460 337)(297 461 338)(298 462 339)(299 463 340)(300 464 341)(301 465 342)(302 466 343)(303 467 344)(304 468 345)(305 469 346)(306 470 347)(307 471 348)(308 472 349)(309 473 350)(310 474 351)(311 475 352)(312 476 353)(313 477 354)(314 478 355)(315 479 356)(316 480 357)(317 481 358)(318 482 359)(319 483 360)(320 484 361)(321 485 362)(322 486 363)(323 487 364)(324 488 365)(325 489 366)(326 490 367)(327 491 368)(328 492 369)
(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)(411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492)
(1 288 42 247)(2 287 43 328)(3 286 44 327)(4 285 45 326)(5 284 46 325)(6 283 47 324)(7 282 48 323)(8 281 49 322)(9 280 50 321)(10 279 51 320)(11 278 52 319)(12 277 53 318)(13 276 54 317)(14 275 55 316)(15 274 56 315)(16 273 57 314)(17 272 58 313)(18 271 59 312)(19 270 60 311)(20 269 61 310)(21 268 62 309)(22 267 63 308)(23 266 64 307)(24 265 65 306)(25 264 66 305)(26 263 67 304)(27 262 68 303)(28 261 69 302)(29 260 70 301)(30 259 71 300)(31 258 72 299)(32 257 73 298)(33 256 74 297)(34 255 75 296)(35 254 76 295)(36 253 77 294)(37 252 78 293)(38 251 79 292)(39 250 80 291)(40 249 81 290)(41 248 82 289)(83 373 124 332)(84 372 125 331)(85 371 126 330)(86 370 127 329)(87 369 128 410)(88 368 129 409)(89 367 130 408)(90 366 131 407)(91 365 132 406)(92 364 133 405)(93 363 134 404)(94 362 135 403)(95 361 136 402)(96 360 137 401)(97 359 138 400)(98 358 139 399)(99 357 140 398)(100 356 141 397)(101 355 142 396)(102 354 143 395)(103 353 144 394)(104 352 145 393)(105 351 146 392)(106 350 147 391)(107 349 148 390)(108 348 149 389)(109 347 150 388)(110 346 151 387)(111 345 152 386)(112 344 153 385)(113 343 154 384)(114 342 155 383)(115 341 156 382)(116 340 157 381)(117 339 158 380)(118 338 159 379)(119 337 160 378)(120 336 161 377)(121 335 162 376)(122 334 163 375)(123 333 164 374)(165 485 206 444)(166 484 207 443)(167 483 208 442)(168 482 209 441)(169 481 210 440)(170 480 211 439)(171 479 212 438)(172 478 213 437)(173 477 214 436)(174 476 215 435)(175 475 216 434)(176 474 217 433)(177 473 218 432)(178 472 219 431)(179 471 220 430)(180 470 221 429)(181 469 222 428)(182 468 223 427)(183 467 224 426)(184 466 225 425)(185 465 226 424)(186 464 227 423)(187 463 228 422)(188 462 229 421)(189 461 230 420)(190 460 231 419)(191 459 232 418)(192 458 233 417)(193 457 234 416)(194 456 235 415)(195 455 236 414)(196 454 237 413)(197 453 238 412)(198 452 239 411)(199 451 240 492)(200 450 241 491)(201 449 242 490)(202 448 243 489)(203 447 244 488)(204 446 245 487)(205 445 246 486)
G:=sub<Sym(492)| (1,198,127)(2,199,128)(3,200,129)(4,201,130)(5,202,131)(6,203,132)(7,204,133)(8,205,134)(9,206,135)(10,207,136)(11,208,137)(12,209,138)(13,210,139)(14,211,140)(15,212,141)(16,213,142)(17,214,143)(18,215,144)(19,216,145)(20,217,146)(21,218,147)(22,219,148)(23,220,149)(24,221,150)(25,222,151)(26,223,152)(27,224,153)(28,225,154)(29,226,155)(30,227,156)(31,228,157)(32,229,158)(33,230,159)(34,231,160)(35,232,161)(36,233,162)(37,234,163)(38,235,164)(39,236,83)(40,237,84)(41,238,85)(42,239,86)(43,240,87)(44,241,88)(45,242,89)(46,243,90)(47,244,91)(48,245,92)(49,246,93)(50,165,94)(51,166,95)(52,167,96)(53,168,97)(54,169,98)(55,170,99)(56,171,100)(57,172,101)(58,173,102)(59,174,103)(60,175,104)(61,176,105)(62,177,106)(63,178,107)(64,179,108)(65,180,109)(66,181,110)(67,182,111)(68,183,112)(69,184,113)(70,185,114)(71,186,115)(72,187,116)(73,188,117)(74,189,118)(75,190,119)(76,191,120)(77,192,121)(78,193,122)(79,194,123)(80,195,124)(81,196,125)(82,197,126)(247,411,370)(248,412,371)(249,413,372)(250,414,373)(251,415,374)(252,416,375)(253,417,376)(254,418,377)(255,419,378)(256,420,379)(257,421,380)(258,422,381)(259,423,382)(260,424,383)(261,425,384)(262,426,385)(263,427,386)(264,428,387)(265,429,388)(266,430,389)(267,431,390)(268,432,391)(269,433,392)(270,434,393)(271,435,394)(272,436,395)(273,437,396)(274,438,397)(275,439,398)(276,440,399)(277,441,400)(278,442,401)(279,443,402)(280,444,403)(281,445,404)(282,446,405)(283,447,406)(284,448,407)(285,449,408)(286,450,409)(287,451,410)(288,452,329)(289,453,330)(290,454,331)(291,455,332)(292,456,333)(293,457,334)(294,458,335)(295,459,336)(296,460,337)(297,461,338)(298,462,339)(299,463,340)(300,464,341)(301,465,342)(302,466,343)(303,467,344)(304,468,345)(305,469,346)(306,470,347)(307,471,348)(308,472,349)(309,473,350)(310,474,351)(311,475,352)(312,476,353)(313,477,354)(314,478,355)(315,479,356)(316,480,357)(317,481,358)(318,482,359)(319,483,360)(320,484,361)(321,485,362)(322,486,363)(323,487,364)(324,488,365)(325,489,366)(326,490,367)(327,491,368)(328,492,369), (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)(411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492), (1,288,42,247)(2,287,43,328)(3,286,44,327)(4,285,45,326)(5,284,46,325)(6,283,47,324)(7,282,48,323)(8,281,49,322)(9,280,50,321)(10,279,51,320)(11,278,52,319)(12,277,53,318)(13,276,54,317)(14,275,55,316)(15,274,56,315)(16,273,57,314)(17,272,58,313)(18,271,59,312)(19,270,60,311)(20,269,61,310)(21,268,62,309)(22,267,63,308)(23,266,64,307)(24,265,65,306)(25,264,66,305)(26,263,67,304)(27,262,68,303)(28,261,69,302)(29,260,70,301)(30,259,71,300)(31,258,72,299)(32,257,73,298)(33,256,74,297)(34,255,75,296)(35,254,76,295)(36,253,77,294)(37,252,78,293)(38,251,79,292)(39,250,80,291)(40,249,81,290)(41,248,82,289)(83,373,124,332)(84,372,125,331)(85,371,126,330)(86,370,127,329)(87,369,128,410)(88,368,129,409)(89,367,130,408)(90,366,131,407)(91,365,132,406)(92,364,133,405)(93,363,134,404)(94,362,135,403)(95,361,136,402)(96,360,137,401)(97,359,138,400)(98,358,139,399)(99,357,140,398)(100,356,141,397)(101,355,142,396)(102,354,143,395)(103,353,144,394)(104,352,145,393)(105,351,146,392)(106,350,147,391)(107,349,148,390)(108,348,149,389)(109,347,150,388)(110,346,151,387)(111,345,152,386)(112,344,153,385)(113,343,154,384)(114,342,155,383)(115,341,156,382)(116,340,157,381)(117,339,158,380)(118,338,159,379)(119,337,160,378)(120,336,161,377)(121,335,162,376)(122,334,163,375)(123,333,164,374)(165,485,206,444)(166,484,207,443)(167,483,208,442)(168,482,209,441)(169,481,210,440)(170,480,211,439)(171,479,212,438)(172,478,213,437)(173,477,214,436)(174,476,215,435)(175,475,216,434)(176,474,217,433)(177,473,218,432)(178,472,219,431)(179,471,220,430)(180,470,221,429)(181,469,222,428)(182,468,223,427)(183,467,224,426)(184,466,225,425)(185,465,226,424)(186,464,227,423)(187,463,228,422)(188,462,229,421)(189,461,230,420)(190,460,231,419)(191,459,232,418)(192,458,233,417)(193,457,234,416)(194,456,235,415)(195,455,236,414)(196,454,237,413)(197,453,238,412)(198,452,239,411)(199,451,240,492)(200,450,241,491)(201,449,242,490)(202,448,243,489)(203,447,244,488)(204,446,245,487)(205,445,246,486)>;
G:=Group( (1,198,127)(2,199,128)(3,200,129)(4,201,130)(5,202,131)(6,203,132)(7,204,133)(8,205,134)(9,206,135)(10,207,136)(11,208,137)(12,209,138)(13,210,139)(14,211,140)(15,212,141)(16,213,142)(17,214,143)(18,215,144)(19,216,145)(20,217,146)(21,218,147)(22,219,148)(23,220,149)(24,221,150)(25,222,151)(26,223,152)(27,224,153)(28,225,154)(29,226,155)(30,227,156)(31,228,157)(32,229,158)(33,230,159)(34,231,160)(35,232,161)(36,233,162)(37,234,163)(38,235,164)(39,236,83)(40,237,84)(41,238,85)(42,239,86)(43,240,87)(44,241,88)(45,242,89)(46,243,90)(47,244,91)(48,245,92)(49,246,93)(50,165,94)(51,166,95)(52,167,96)(53,168,97)(54,169,98)(55,170,99)(56,171,100)(57,172,101)(58,173,102)(59,174,103)(60,175,104)(61,176,105)(62,177,106)(63,178,107)(64,179,108)(65,180,109)(66,181,110)(67,182,111)(68,183,112)(69,184,113)(70,185,114)(71,186,115)(72,187,116)(73,188,117)(74,189,118)(75,190,119)(76,191,120)(77,192,121)(78,193,122)(79,194,123)(80,195,124)(81,196,125)(82,197,126)(247,411,370)(248,412,371)(249,413,372)(250,414,373)(251,415,374)(252,416,375)(253,417,376)(254,418,377)(255,419,378)(256,420,379)(257,421,380)(258,422,381)(259,423,382)(260,424,383)(261,425,384)(262,426,385)(263,427,386)(264,428,387)(265,429,388)(266,430,389)(267,431,390)(268,432,391)(269,433,392)(270,434,393)(271,435,394)(272,436,395)(273,437,396)(274,438,397)(275,439,398)(276,440,399)(277,441,400)(278,442,401)(279,443,402)(280,444,403)(281,445,404)(282,446,405)(283,447,406)(284,448,407)(285,449,408)(286,450,409)(287,451,410)(288,452,329)(289,453,330)(290,454,331)(291,455,332)(292,456,333)(293,457,334)(294,458,335)(295,459,336)(296,460,337)(297,461,338)(298,462,339)(299,463,340)(300,464,341)(301,465,342)(302,466,343)(303,467,344)(304,468,345)(305,469,346)(306,470,347)(307,471,348)(308,472,349)(309,473,350)(310,474,351)(311,475,352)(312,476,353)(313,477,354)(314,478,355)(315,479,356)(316,480,357)(317,481,358)(318,482,359)(319,483,360)(320,484,361)(321,485,362)(322,486,363)(323,487,364)(324,488,365)(325,489,366)(326,490,367)(327,491,368)(328,492,369), (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)(411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492), (1,288,42,247)(2,287,43,328)(3,286,44,327)(4,285,45,326)(5,284,46,325)(6,283,47,324)(7,282,48,323)(8,281,49,322)(9,280,50,321)(10,279,51,320)(11,278,52,319)(12,277,53,318)(13,276,54,317)(14,275,55,316)(15,274,56,315)(16,273,57,314)(17,272,58,313)(18,271,59,312)(19,270,60,311)(20,269,61,310)(21,268,62,309)(22,267,63,308)(23,266,64,307)(24,265,65,306)(25,264,66,305)(26,263,67,304)(27,262,68,303)(28,261,69,302)(29,260,70,301)(30,259,71,300)(31,258,72,299)(32,257,73,298)(33,256,74,297)(34,255,75,296)(35,254,76,295)(36,253,77,294)(37,252,78,293)(38,251,79,292)(39,250,80,291)(40,249,81,290)(41,248,82,289)(83,373,124,332)(84,372,125,331)(85,371,126,330)(86,370,127,329)(87,369,128,410)(88,368,129,409)(89,367,130,408)(90,366,131,407)(91,365,132,406)(92,364,133,405)(93,363,134,404)(94,362,135,403)(95,361,136,402)(96,360,137,401)(97,359,138,400)(98,358,139,399)(99,357,140,398)(100,356,141,397)(101,355,142,396)(102,354,143,395)(103,353,144,394)(104,352,145,393)(105,351,146,392)(106,350,147,391)(107,349,148,390)(108,348,149,389)(109,347,150,388)(110,346,151,387)(111,345,152,386)(112,344,153,385)(113,343,154,384)(114,342,155,383)(115,341,156,382)(116,340,157,381)(117,339,158,380)(118,338,159,379)(119,337,160,378)(120,336,161,377)(121,335,162,376)(122,334,163,375)(123,333,164,374)(165,485,206,444)(166,484,207,443)(167,483,208,442)(168,482,209,441)(169,481,210,440)(170,480,211,439)(171,479,212,438)(172,478,213,437)(173,477,214,436)(174,476,215,435)(175,475,216,434)(176,474,217,433)(177,473,218,432)(178,472,219,431)(179,471,220,430)(180,470,221,429)(181,469,222,428)(182,468,223,427)(183,467,224,426)(184,466,225,425)(185,465,226,424)(186,464,227,423)(187,463,228,422)(188,462,229,421)(189,461,230,420)(190,460,231,419)(191,459,232,418)(192,458,233,417)(193,457,234,416)(194,456,235,415)(195,455,236,414)(196,454,237,413)(197,453,238,412)(198,452,239,411)(199,451,240,492)(200,450,241,491)(201,449,242,490)(202,448,243,489)(203,447,244,488)(204,446,245,487)(205,445,246,486) );
G=PermutationGroup([[(1,198,127),(2,199,128),(3,200,129),(4,201,130),(5,202,131),(6,203,132),(7,204,133),(8,205,134),(9,206,135),(10,207,136),(11,208,137),(12,209,138),(13,210,139),(14,211,140),(15,212,141),(16,213,142),(17,214,143),(18,215,144),(19,216,145),(20,217,146),(21,218,147),(22,219,148),(23,220,149),(24,221,150),(25,222,151),(26,223,152),(27,224,153),(28,225,154),(29,226,155),(30,227,156),(31,228,157),(32,229,158),(33,230,159),(34,231,160),(35,232,161),(36,233,162),(37,234,163),(38,235,164),(39,236,83),(40,237,84),(41,238,85),(42,239,86),(43,240,87),(44,241,88),(45,242,89),(46,243,90),(47,244,91),(48,245,92),(49,246,93),(50,165,94),(51,166,95),(52,167,96),(53,168,97),(54,169,98),(55,170,99),(56,171,100),(57,172,101),(58,173,102),(59,174,103),(60,175,104),(61,176,105),(62,177,106),(63,178,107),(64,179,108),(65,180,109),(66,181,110),(67,182,111),(68,183,112),(69,184,113),(70,185,114),(71,186,115),(72,187,116),(73,188,117),(74,189,118),(75,190,119),(76,191,120),(77,192,121),(78,193,122),(79,194,123),(80,195,124),(81,196,125),(82,197,126),(247,411,370),(248,412,371),(249,413,372),(250,414,373),(251,415,374),(252,416,375),(253,417,376),(254,418,377),(255,419,378),(256,420,379),(257,421,380),(258,422,381),(259,423,382),(260,424,383),(261,425,384),(262,426,385),(263,427,386),(264,428,387),(265,429,388),(266,430,389),(267,431,390),(268,432,391),(269,433,392),(270,434,393),(271,435,394),(272,436,395),(273,437,396),(274,438,397),(275,439,398),(276,440,399),(277,441,400),(278,442,401),(279,443,402),(280,444,403),(281,445,404),(282,446,405),(283,447,406),(284,448,407),(285,449,408),(286,450,409),(287,451,410),(288,452,329),(289,453,330),(290,454,331),(291,455,332),(292,456,333),(293,457,334),(294,458,335),(295,459,336),(296,460,337),(297,461,338),(298,462,339),(299,463,340),(300,464,341),(301,465,342),(302,466,343),(303,467,344),(304,468,345),(305,469,346),(306,470,347),(307,471,348),(308,472,349),(309,473,350),(310,474,351),(311,475,352),(312,476,353),(313,477,354),(314,478,355),(315,479,356),(316,480,357),(317,481,358),(318,482,359),(319,483,360),(320,484,361),(321,485,362),(322,486,363),(323,487,364),(324,488,365),(325,489,366),(326,490,367),(327,491,368),(328,492,369)], [(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),(411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492)], [(1,288,42,247),(2,287,43,328),(3,286,44,327),(4,285,45,326),(5,284,46,325),(6,283,47,324),(7,282,48,323),(8,281,49,322),(9,280,50,321),(10,279,51,320),(11,278,52,319),(12,277,53,318),(13,276,54,317),(14,275,55,316),(15,274,56,315),(16,273,57,314),(17,272,58,313),(18,271,59,312),(19,270,60,311),(20,269,61,310),(21,268,62,309),(22,267,63,308),(23,266,64,307),(24,265,65,306),(25,264,66,305),(26,263,67,304),(27,262,68,303),(28,261,69,302),(29,260,70,301),(30,259,71,300),(31,258,72,299),(32,257,73,298),(33,256,74,297),(34,255,75,296),(35,254,76,295),(36,253,77,294),(37,252,78,293),(38,251,79,292),(39,250,80,291),(40,249,81,290),(41,248,82,289),(83,373,124,332),(84,372,125,331),(85,371,126,330),(86,370,127,329),(87,369,128,410),(88,368,129,409),(89,367,130,408),(90,366,131,407),(91,365,132,406),(92,364,133,405),(93,363,134,404),(94,362,135,403),(95,361,136,402),(96,360,137,401),(97,359,138,400),(98,358,139,399),(99,357,140,398),(100,356,141,397),(101,355,142,396),(102,354,143,395),(103,353,144,394),(104,352,145,393),(105,351,146,392),(106,350,147,391),(107,349,148,390),(108,348,149,389),(109,347,150,388),(110,346,151,387),(111,345,152,386),(112,344,153,385),(113,343,154,384),(114,342,155,383),(115,341,156,382),(116,340,157,381),(117,339,158,380),(118,338,159,379),(119,337,160,378),(120,336,161,377),(121,335,162,376),(122,334,163,375),(123,333,164,374),(165,485,206,444),(166,484,207,443),(167,483,208,442),(168,482,209,441),(169,481,210,440),(170,480,211,439),(171,479,212,438),(172,478,213,437),(173,477,214,436),(174,476,215,435),(175,475,216,434),(176,474,217,433),(177,473,218,432),(178,472,219,431),(179,471,220,430),(180,470,221,429),(181,469,222,428),(182,468,223,427),(183,467,224,426),(184,466,225,425),(185,465,226,424),(186,464,227,423),(187,463,228,422),(188,462,229,421),(189,461,230,420),(190,460,231,419),(191,459,232,418),(192,458,233,417),(193,457,234,416),(194,456,235,415),(195,455,236,414),(196,454,237,413),(197,453,238,412),(198,452,239,411),(199,451,240,492),(200,450,241,491),(201,449,242,490),(202,448,243,489),(203,447,244,488),(204,446,245,487),(205,445,246,486)]])
132 conjugacy classes
| class | 1 | 2 | 3A | 3B | 4A | 4B | 6A | 6B | 12A | 12B | 12C | 12D | 41A | ··· | 41T | 82A | ··· | 82T | 123A | ··· | 123AN | 246A | ··· | 246AN |
| order | 1 | 2 | 3 | 3 | 4 | 4 | 6 | 6 | 12 | 12 | 12 | 12 | 41 | ··· | 41 | 82 | ··· | 82 | 123 | ··· | 123 | 246 | ··· | 246 |
| size | 1 | 1 | 1 | 1 | 41 | 41 | 1 | 1 | 41 | 41 | 41 | 41 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
132 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||
| image | C1 | C2 | C3 | C4 | C6 | C12 | D41 | Dic41 | C3×D41 | C3×Dic41 |
| kernel | C3×Dic41 | C246 | Dic41 | C123 | C82 | C41 | C6 | C3 | C2 | C1 |
| # reps | 1 | 1 | 2 | 2 | 2 | 4 | 20 | 20 | 40 | 40 |
Matrix representation of C3×Dic41 ►in GL3(𝔽2953) generated by
| 1 | 0 | 0 |
| 0 | 800 | 0 |
| 0 | 0 | 800 |
| 2952 | 0 | 0 |
| 0 | 0 | 1 |
| 0 | 2952 | 1431 |
| 1727 | 0 | 0 |
| 0 | 949 | 1551 |
| 0 | 1190 | 2004 |
G:=sub<GL(3,GF(2953))| [1,0,0,0,800,0,0,0,800],[2952,0,0,0,0,2952,0,1,1431],[1727,0,0,0,949,1190,0,1551,2004] >;
C3×Dic41 in GAP, Magma, Sage, TeX
C_3\times {\rm Dic}_{41} % in TeX
G:=Group("C3xDic41"); // GroupNames label
G:=SmallGroup(492,2);
// by ID
G=gap.SmallGroup(492,2);
# by ID
G:=PCGroup([4,-2,-3,-2,-41,24,7683]);
// Polycyclic
G:=Group<a,b,c|a^3=b^82=1,c^2=b^41,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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