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G = C3×Dic41order 492 = 22·3·41

Direct product of C3 and Dic41

direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: C3×Dic41, C82.C6, C412C12, C1234C4, C6.2D41, C246.2C2, C2.(C3×D41), SmallGroup(492,2)

Series: Derived Chief Lower central Upper central

C1C41 — C3×Dic41
C1C41C82C246 — C3×Dic41
C41 — C3×Dic41
C1C6

Generators and relations for C3×Dic41
 G = < a,b,c | a3=b82=1, c2=b41, ab=ba, ac=ca, cbc-1=b-1 >

41C4
41C12

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

G:=sub<Sym(492)| (1,186,91)(2,187,92)(3,188,93)(4,189,94)(5,190,95)(6,191,96)(7,192,97)(8,193,98)(9,194,99)(10,195,100)(11,196,101)(12,197,102)(13,198,103)(14,199,104)(15,200,105)(16,201,106)(17,202,107)(18,203,108)(19,204,109)(20,205,110)(21,206,111)(22,207,112)(23,208,113)(24,209,114)(25,210,115)(26,211,116)(27,212,117)(28,213,118)(29,214,119)(30,215,120)(31,216,121)(32,217,122)(33,218,123)(34,219,124)(35,220,125)(36,221,126)(37,222,127)(38,223,128)(39,224,129)(40,225,130)(41,226,131)(42,227,132)(43,228,133)(44,229,134)(45,230,135)(46,231,136)(47,232,137)(48,233,138)(49,234,139)(50,235,140)(51,236,141)(52,237,142)(53,238,143)(54,239,144)(55,240,145)(56,241,146)(57,242,147)(58,243,148)(59,244,149)(60,245,150)(61,246,151)(62,165,152)(63,166,153)(64,167,154)(65,168,155)(66,169,156)(67,170,157)(68,171,158)(69,172,159)(70,173,160)(71,174,161)(72,175,162)(73,176,163)(74,177,164)(75,178,83)(76,179,84)(77,180,85)(78,181,86)(79,182,87)(80,183,88)(81,184,89)(82,185,90)(247,452,329)(248,453,330)(249,454,331)(250,455,332)(251,456,333)(252,457,334)(253,458,335)(254,459,336)(255,460,337)(256,461,338)(257,462,339)(258,463,340)(259,464,341)(260,465,342)(261,466,343)(262,467,344)(263,468,345)(264,469,346)(265,470,347)(266,471,348)(267,472,349)(268,473,350)(269,474,351)(270,475,352)(271,476,353)(272,477,354)(273,478,355)(274,479,356)(275,480,357)(276,481,358)(277,482,359)(278,483,360)(279,484,361)(280,485,362)(281,486,363)(282,487,364)(283,488,365)(284,489,366)(285,490,367)(286,491,368)(287,492,369)(288,411,370)(289,412,371)(290,413,372)(291,414,373)(292,415,374)(293,416,375)(294,417,376)(295,418,377)(296,419,378)(297,420,379)(298,421,380)(299,422,381)(300,423,382)(301,424,383)(302,425,384)(303,426,385)(304,427,386)(305,428,387)(306,429,388)(307,430,389)(308,431,390)(309,432,391)(310,433,392)(311,434,393)(312,435,394)(313,436,395)(314,437,396)(315,438,397)(316,439,398)(317,440,399)(318,441,400)(319,442,401)(320,443,402)(321,444,403)(322,445,404)(323,446,405)(324,447,406)(325,448,407)(326,449,408)(327,450,409)(328,451,410), (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)(83,378,124,337)(84,377,125,336)(85,376,126,335)(86,375,127,334)(87,374,128,333)(88,373,129,332)(89,372,130,331)(90,371,131,330)(91,370,132,329)(92,369,133,410)(93,368,134,409)(94,367,135,408)(95,366,136,407)(96,365,137,406)(97,364,138,405)(98,363,139,404)(99,362,140,403)(100,361,141,402)(101,360,142,401)(102,359,143,400)(103,358,144,399)(104,357,145,398)(105,356,146,397)(106,355,147,396)(107,354,148,395)(108,353,149,394)(109,352,150,393)(110,351,151,392)(111,350,152,391)(112,349,153,390)(113,348,154,389)(114,347,155,388)(115,346,156,387)(116,345,157,386)(117,344,158,385)(118,343,159,384)(119,342,160,383)(120,341,161,382)(121,340,162,381)(122,339,163,380)(123,338,164,379)(165,432,206,473)(166,431,207,472)(167,430,208,471)(168,429,209,470)(169,428,210,469)(170,427,211,468)(171,426,212,467)(172,425,213,466)(173,424,214,465)(174,423,215,464)(175,422,216,463)(176,421,217,462)(177,420,218,461)(178,419,219,460)(179,418,220,459)(180,417,221,458)(181,416,222,457)(182,415,223,456)(183,414,224,455)(184,413,225,454)(185,412,226,453)(186,411,227,452)(187,492,228,451)(188,491,229,450)(189,490,230,449)(190,489,231,448)(191,488,232,447)(192,487,233,446)(193,486,234,445)(194,485,235,444)(195,484,236,443)(196,483,237,442)(197,482,238,441)(198,481,239,440)(199,480,240,439)(200,479,241,438)(201,478,242,437)(202,477,243,436)(203,476,244,435)(204,475,245,434)(205,474,246,433)>;

G:=Group( (1,186,91)(2,187,92)(3,188,93)(4,189,94)(5,190,95)(6,191,96)(7,192,97)(8,193,98)(9,194,99)(10,195,100)(11,196,101)(12,197,102)(13,198,103)(14,199,104)(15,200,105)(16,201,106)(17,202,107)(18,203,108)(19,204,109)(20,205,110)(21,206,111)(22,207,112)(23,208,113)(24,209,114)(25,210,115)(26,211,116)(27,212,117)(28,213,118)(29,214,119)(30,215,120)(31,216,121)(32,217,122)(33,218,123)(34,219,124)(35,220,125)(36,221,126)(37,222,127)(38,223,128)(39,224,129)(40,225,130)(41,226,131)(42,227,132)(43,228,133)(44,229,134)(45,230,135)(46,231,136)(47,232,137)(48,233,138)(49,234,139)(50,235,140)(51,236,141)(52,237,142)(53,238,143)(54,239,144)(55,240,145)(56,241,146)(57,242,147)(58,243,148)(59,244,149)(60,245,150)(61,246,151)(62,165,152)(63,166,153)(64,167,154)(65,168,155)(66,169,156)(67,170,157)(68,171,158)(69,172,159)(70,173,160)(71,174,161)(72,175,162)(73,176,163)(74,177,164)(75,178,83)(76,179,84)(77,180,85)(78,181,86)(79,182,87)(80,183,88)(81,184,89)(82,185,90)(247,452,329)(248,453,330)(249,454,331)(250,455,332)(251,456,333)(252,457,334)(253,458,335)(254,459,336)(255,460,337)(256,461,338)(257,462,339)(258,463,340)(259,464,341)(260,465,342)(261,466,343)(262,467,344)(263,468,345)(264,469,346)(265,470,347)(266,471,348)(267,472,349)(268,473,350)(269,474,351)(270,475,352)(271,476,353)(272,477,354)(273,478,355)(274,479,356)(275,480,357)(276,481,358)(277,482,359)(278,483,360)(279,484,361)(280,485,362)(281,486,363)(282,487,364)(283,488,365)(284,489,366)(285,490,367)(286,491,368)(287,492,369)(288,411,370)(289,412,371)(290,413,372)(291,414,373)(292,415,374)(293,416,375)(294,417,376)(295,418,377)(296,419,378)(297,420,379)(298,421,380)(299,422,381)(300,423,382)(301,424,383)(302,425,384)(303,426,385)(304,427,386)(305,428,387)(306,429,388)(307,430,389)(308,431,390)(309,432,391)(310,433,392)(311,434,393)(312,435,394)(313,436,395)(314,437,396)(315,438,397)(316,439,398)(317,440,399)(318,441,400)(319,442,401)(320,443,402)(321,444,403)(322,445,404)(323,446,405)(324,447,406)(325,448,407)(326,449,408)(327,450,409)(328,451,410), (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)(83,378,124,337)(84,377,125,336)(85,376,126,335)(86,375,127,334)(87,374,128,333)(88,373,129,332)(89,372,130,331)(90,371,131,330)(91,370,132,329)(92,369,133,410)(93,368,134,409)(94,367,135,408)(95,366,136,407)(96,365,137,406)(97,364,138,405)(98,363,139,404)(99,362,140,403)(100,361,141,402)(101,360,142,401)(102,359,143,400)(103,358,144,399)(104,357,145,398)(105,356,146,397)(106,355,147,396)(107,354,148,395)(108,353,149,394)(109,352,150,393)(110,351,151,392)(111,350,152,391)(112,349,153,390)(113,348,154,389)(114,347,155,388)(115,346,156,387)(116,345,157,386)(117,344,158,385)(118,343,159,384)(119,342,160,383)(120,341,161,382)(121,340,162,381)(122,339,163,380)(123,338,164,379)(165,432,206,473)(166,431,207,472)(167,430,208,471)(168,429,209,470)(169,428,210,469)(170,427,211,468)(171,426,212,467)(172,425,213,466)(173,424,214,465)(174,423,215,464)(175,422,216,463)(176,421,217,462)(177,420,218,461)(178,419,219,460)(179,418,220,459)(180,417,221,458)(181,416,222,457)(182,415,223,456)(183,414,224,455)(184,413,225,454)(185,412,226,453)(186,411,227,452)(187,492,228,451)(188,491,229,450)(189,490,230,449)(190,489,231,448)(191,488,232,447)(192,487,233,446)(193,486,234,445)(194,485,235,444)(195,484,236,443)(196,483,237,442)(197,482,238,441)(198,481,239,440)(199,480,240,439)(200,479,241,438)(201,478,242,437)(202,477,243,436)(203,476,244,435)(204,475,245,434)(205,474,246,433) );

G=PermutationGroup([(1,186,91),(2,187,92),(3,188,93),(4,189,94),(5,190,95),(6,191,96),(7,192,97),(8,193,98),(9,194,99),(10,195,100),(11,196,101),(12,197,102),(13,198,103),(14,199,104),(15,200,105),(16,201,106),(17,202,107),(18,203,108),(19,204,109),(20,205,110),(21,206,111),(22,207,112),(23,208,113),(24,209,114),(25,210,115),(26,211,116),(27,212,117),(28,213,118),(29,214,119),(30,215,120),(31,216,121),(32,217,122),(33,218,123),(34,219,124),(35,220,125),(36,221,126),(37,222,127),(38,223,128),(39,224,129),(40,225,130),(41,226,131),(42,227,132),(43,228,133),(44,229,134),(45,230,135),(46,231,136),(47,232,137),(48,233,138),(49,234,139),(50,235,140),(51,236,141),(52,237,142),(53,238,143),(54,239,144),(55,240,145),(56,241,146),(57,242,147),(58,243,148),(59,244,149),(60,245,150),(61,246,151),(62,165,152),(63,166,153),(64,167,154),(65,168,155),(66,169,156),(67,170,157),(68,171,158),(69,172,159),(70,173,160),(71,174,161),(72,175,162),(73,176,163),(74,177,164),(75,178,83),(76,179,84),(77,180,85),(78,181,86),(79,182,87),(80,183,88),(81,184,89),(82,185,90),(247,452,329),(248,453,330),(249,454,331),(250,455,332),(251,456,333),(252,457,334),(253,458,335),(254,459,336),(255,460,337),(256,461,338),(257,462,339),(258,463,340),(259,464,341),(260,465,342),(261,466,343),(262,467,344),(263,468,345),(264,469,346),(265,470,347),(266,471,348),(267,472,349),(268,473,350),(269,474,351),(270,475,352),(271,476,353),(272,477,354),(273,478,355),(274,479,356),(275,480,357),(276,481,358),(277,482,359),(278,483,360),(279,484,361),(280,485,362),(281,486,363),(282,487,364),(283,488,365),(284,489,366),(285,490,367),(286,491,368),(287,492,369),(288,411,370),(289,412,371),(290,413,372),(291,414,373),(292,415,374),(293,416,375),(294,417,376),(295,418,377),(296,419,378),(297,420,379),(298,421,380),(299,422,381),(300,423,382),(301,424,383),(302,425,384),(303,426,385),(304,427,386),(305,428,387),(306,429,388),(307,430,389),(308,431,390),(309,432,391),(310,433,392),(311,434,393),(312,435,394),(313,436,395),(314,437,396),(315,438,397),(316,439,398),(317,440,399),(318,441,400),(319,442,401),(320,443,402),(321,444,403),(322,445,404),(323,446,405),(324,447,406),(325,448,407),(326,449,408),(327,450,409),(328,451,410)], [(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),(83,378,124,337),(84,377,125,336),(85,376,126,335),(86,375,127,334),(87,374,128,333),(88,373,129,332),(89,372,130,331),(90,371,131,330),(91,370,132,329),(92,369,133,410),(93,368,134,409),(94,367,135,408),(95,366,136,407),(96,365,137,406),(97,364,138,405),(98,363,139,404),(99,362,140,403),(100,361,141,402),(101,360,142,401),(102,359,143,400),(103,358,144,399),(104,357,145,398),(105,356,146,397),(106,355,147,396),(107,354,148,395),(108,353,149,394),(109,352,150,393),(110,351,151,392),(111,350,152,391),(112,349,153,390),(113,348,154,389),(114,347,155,388),(115,346,156,387),(116,345,157,386),(117,344,158,385),(118,343,159,384),(119,342,160,383),(120,341,161,382),(121,340,162,381),(122,339,163,380),(123,338,164,379),(165,432,206,473),(166,431,207,472),(167,430,208,471),(168,429,209,470),(169,428,210,469),(170,427,211,468),(171,426,212,467),(172,425,213,466),(173,424,214,465),(174,423,215,464),(175,422,216,463),(176,421,217,462),(177,420,218,461),(178,419,219,460),(179,418,220,459),(180,417,221,458),(181,416,222,457),(182,415,223,456),(183,414,224,455),(184,413,225,454),(185,412,226,453),(186,411,227,452),(187,492,228,451),(188,491,229,450),(189,490,230,449),(190,489,231,448),(191,488,232,447),(192,487,233,446),(193,486,234,445),(194,485,235,444),(195,484,236,443),(196,483,237,442),(197,482,238,441),(198,481,239,440),(199,480,240,439),(200,479,241,438),(201,478,242,437),(202,477,243,436),(203,476,244,435),(204,475,245,434),(205,474,246,433)])

132 conjugacy classes

class 1  2 3A3B4A4B6A6B12A12B12C12D41A···41T82A···82T123A···123AN246A···246AN
order123344661212121241···4182···82123···123246···246
size1111414111414141412···22···22···22···2

132 irreducible representations

dim1111112222
type+++-
imageC1C2C3C4C6C12D41Dic41C3×D41C3×Dic41
kernelC3×Dic41C246Dic41C123C82C41C6C3C2C1
# reps11222420204040

Matrix representation of C3×Dic41 in GL3(𝔽2953) generated by

100
08000
00800
,
295200
001
029521431
,
172700
09491551
011902004
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

Export

Subgroup lattice of C3×Dic41 in TeX

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