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G = Dic3×C41order 492 = 22·3·41

Direct product of C41 and Dic3

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

Aliases: Dic3×C41, C3⋊C164, C6.C82, C1235C4, C82.2S3, C246.3C2, C2.(S3×C41), SmallGroup(492,1)

Series: Derived Chief Lower central Upper central

C1C3 — Dic3×C41
C1C3C6C246 — Dic3×C41
C3 — Dic3×C41
C1C82

Generators and relations for Dic3×C41
 G = < a,b,c | a41=b6=1, c2=b3, ab=ba, ac=ca, cbc-1=b-1 >

3C4
3C164

Smallest permutation representation of Dic3×C41
Regular action on 492 points
Generators in S492
(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)
(1 164 294 342 280 119)(2 124 295 343 281 120)(3 125 296 344 282 121)(4 126 297 345 283 122)(5 127 298 346 284 123)(6 128 299 347 285 83)(7 129 300 348 286 84)(8 130 301 349 287 85)(9 131 302 350 247 86)(10 132 303 351 248 87)(11 133 304 352 249 88)(12 134 305 353 250 89)(13 135 306 354 251 90)(14 136 307 355 252 91)(15 137 308 356 253 92)(16 138 309 357 254 93)(17 139 310 358 255 94)(18 140 311 359 256 95)(19 141 312 360 257 96)(20 142 313 361 258 97)(21 143 314 362 259 98)(22 144 315 363 260 99)(23 145 316 364 261 100)(24 146 317 365 262 101)(25 147 318 366 263 102)(26 148 319 367 264 103)(27 149 320 368 265 104)(28 150 321 369 266 105)(29 151 322 329 267 106)(30 152 323 330 268 107)(31 153 324 331 269 108)(32 154 325 332 270 109)(33 155 326 333 271 110)(34 156 327 334 272 111)(35 157 328 335 273 112)(36 158 288 336 274 113)(37 159 289 337 275 114)(38 160 290 338 276 115)(39 161 291 339 277 116)(40 162 292 340 278 117)(41 163 293 341 279 118)(42 486 186 371 429 243)(43 487 187 372 430 244)(44 488 188 373 431 245)(45 489 189 374 432 246)(46 490 190 375 433 206)(47 491 191 376 434 207)(48 492 192 377 435 208)(49 452 193 378 436 209)(50 453 194 379 437 210)(51 454 195 380 438 211)(52 455 196 381 439 212)(53 456 197 382 440 213)(54 457 198 383 441 214)(55 458 199 384 442 215)(56 459 200 385 443 216)(57 460 201 386 444 217)(58 461 202 387 445 218)(59 462 203 388 446 219)(60 463 204 389 447 220)(61 464 205 390 448 221)(62 465 165 391 449 222)(63 466 166 392 450 223)(64 467 167 393 451 224)(65 468 168 394 411 225)(66 469 169 395 412 226)(67 470 170 396 413 227)(68 471 171 397 414 228)(69 472 172 398 415 229)(70 473 173 399 416 230)(71 474 174 400 417 231)(72 475 175 401 418 232)(73 476 176 402 419 233)(74 477 177 403 420 234)(75 478 178 404 421 235)(76 479 179 405 422 236)(77 480 180 406 423 237)(78 481 181 407 424 238)(79 482 182 408 425 239)(80 483 183 409 426 240)(81 484 184 410 427 241)(82 485 185 370 428 242)
(1 208 342 192)(2 209 343 193)(3 210 344 194)(4 211 345 195)(5 212 346 196)(6 213 347 197)(7 214 348 198)(8 215 349 199)(9 216 350 200)(10 217 351 201)(11 218 352 202)(12 219 353 203)(13 220 354 204)(14 221 355 205)(15 222 356 165)(16 223 357 166)(17 224 358 167)(18 225 359 168)(19 226 360 169)(20 227 361 170)(21 228 362 171)(22 229 363 172)(23 230 364 173)(24 231 365 174)(25 232 366 175)(26 233 367 176)(27 234 368 177)(28 235 369 178)(29 236 329 179)(30 237 330 180)(31 238 331 181)(32 239 332 182)(33 240 333 183)(34 241 334 184)(35 242 335 185)(36 243 336 186)(37 244 337 187)(38 245 338 188)(39 246 339 189)(40 206 340 190)(41 207 341 191)(42 288 371 113)(43 289 372 114)(44 290 373 115)(45 291 374 116)(46 292 375 117)(47 293 376 118)(48 294 377 119)(49 295 378 120)(50 296 379 121)(51 297 380 122)(52 298 381 123)(53 299 382 83)(54 300 383 84)(55 301 384 85)(56 302 385 86)(57 303 386 87)(58 304 387 88)(59 305 388 89)(60 306 389 90)(61 307 390 91)(62 308 391 92)(63 309 392 93)(64 310 393 94)(65 311 394 95)(66 312 395 96)(67 313 396 97)(68 314 397 98)(69 315 398 99)(70 316 399 100)(71 317 400 101)(72 318 401 102)(73 319 402 103)(74 320 403 104)(75 321 404 105)(76 322 405 106)(77 323 406 107)(78 324 407 108)(79 325 408 109)(80 326 409 110)(81 327 410 111)(82 328 370 112)(124 436 281 452)(125 437 282 453)(126 438 283 454)(127 439 284 455)(128 440 285 456)(129 441 286 457)(130 442 287 458)(131 443 247 459)(132 444 248 460)(133 445 249 461)(134 446 250 462)(135 447 251 463)(136 448 252 464)(137 449 253 465)(138 450 254 466)(139 451 255 467)(140 411 256 468)(141 412 257 469)(142 413 258 470)(143 414 259 471)(144 415 260 472)(145 416 261 473)(146 417 262 474)(147 418 263 475)(148 419 264 476)(149 420 265 477)(150 421 266 478)(151 422 267 479)(152 423 268 480)(153 424 269 481)(154 425 270 482)(155 426 271 483)(156 427 272 484)(157 428 273 485)(158 429 274 486)(159 430 275 487)(160 431 276 488)(161 432 277 489)(162 433 278 490)(163 434 279 491)(164 435 280 492)

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

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

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

246 conjugacy classes

class 1  2  3 4A4B 6 41A···41AN82A···82AN123A···123AN164A···164CB246A···246AN
order12344641···4182···82123···123164···164246···246
size1123321···11···12···23···32···2

246 irreducible representations

dim1111112222
type+++-
imageC1C2C4C41C82C164S3Dic3S3×C41Dic3×C41
kernelDic3×C41C246C123Dic3C6C3C82C41C2C1
# reps112404080114040

Matrix representation of Dic3×C41 in GL2(𝔽2953) generated by

12770
01277
,
02952
11
,
4012629
22282552
G:=sub<GL(2,GF(2953))| [1277,0,0,1277],[0,1,2952,1],[401,2228,2629,2552] >;

Dic3×C41 in GAP, Magma, Sage, TeX

{\rm Dic}_3\times C_{41}
% in TeX

G:=Group("Dic3xC41");
// GroupNames label

G:=SmallGroup(492,1);
// by ID

G=gap.SmallGroup(492,1);
# by ID

G:=PCGroup([4,-2,-41,-2,-3,328,5251]);
// Polycyclic

G:=Group<a,b,c|a^41=b^6=1,c^2=b^3,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of Dic3×C41 in TeX

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