Copied to
clipboard

G = C3×Dic40order 480 = 25·3·5

Direct product of C3 and Dic40

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

Aliases: C3×Dic40, C155Q32, C80.1C6, C48.2D5, C240.2C2, C6.15D40, C30.29D8, C60.171D4, C12.41D20, C24.72D10, Dic20.1C6, C120.85C22, C16.(C3×D5), C51(C3×Q32), C8.15(C6×D5), C2.5(C3×D40), C4.3(C3×D20), C10.3(C3×D8), C40.16(C2×C6), C20.26(C3×D4), (C3×Dic20).2C2, SmallGroup(480,79)

Series: Derived Chief Lower central Upper central

C1C40 — C3×Dic40
C1C5C10C20C40C120C3×Dic20 — C3×Dic40
C5C10C20C40 — C3×Dic40
C1C6C12C24C48

Generators and relations for C3×Dic40
 G = < a,b,c | a3=b80=1, c2=b40, ab=ba, ac=ca, cbc-1=b-1 >

20C4
20C4
10Q8
10Q8
20C12
20C12
4Dic5
4Dic5
5Q16
5Q16
10C3×Q8
10C3×Q8
2Dic10
2Dic10
4C3×Dic5
4C3×Dic5
5Q32
5C3×Q16
5C3×Q16
2C3×Dic10
2C3×Dic10
5C3×Q32

Smallest permutation representation of C3×Dic40
Regular action on 480 points
Generators in S480
(1 232 334)(2 233 335)(3 234 336)(4 235 337)(5 236 338)(6 237 339)(7 238 340)(8 239 341)(9 240 342)(10 161 343)(11 162 344)(12 163 345)(13 164 346)(14 165 347)(15 166 348)(16 167 349)(17 168 350)(18 169 351)(19 170 352)(20 171 353)(21 172 354)(22 173 355)(23 174 356)(24 175 357)(25 176 358)(26 177 359)(27 178 360)(28 179 361)(29 180 362)(30 181 363)(31 182 364)(32 183 365)(33 184 366)(34 185 367)(35 186 368)(36 187 369)(37 188 370)(38 189 371)(39 190 372)(40 191 373)(41 192 374)(42 193 375)(43 194 376)(44 195 377)(45 196 378)(46 197 379)(47 198 380)(48 199 381)(49 200 382)(50 201 383)(51 202 384)(52 203 385)(53 204 386)(54 205 387)(55 206 388)(56 207 389)(57 208 390)(58 209 391)(59 210 392)(60 211 393)(61 212 394)(62 213 395)(63 214 396)(64 215 397)(65 216 398)(66 217 399)(67 218 400)(68 219 321)(69 220 322)(70 221 323)(71 222 324)(72 223 325)(73 224 326)(74 225 327)(75 226 328)(76 227 329)(77 228 330)(78 229 331)(79 230 332)(80 231 333)(81 460 263)(82 461 264)(83 462 265)(84 463 266)(85 464 267)(86 465 268)(87 466 269)(88 467 270)(89 468 271)(90 469 272)(91 470 273)(92 471 274)(93 472 275)(94 473 276)(95 474 277)(96 475 278)(97 476 279)(98 477 280)(99 478 281)(100 479 282)(101 480 283)(102 401 284)(103 402 285)(104 403 286)(105 404 287)(106 405 288)(107 406 289)(108 407 290)(109 408 291)(110 409 292)(111 410 293)(112 411 294)(113 412 295)(114 413 296)(115 414 297)(116 415 298)(117 416 299)(118 417 300)(119 418 301)(120 419 302)(121 420 303)(122 421 304)(123 422 305)(124 423 306)(125 424 307)(126 425 308)(127 426 309)(128 427 310)(129 428 311)(130 429 312)(131 430 313)(132 431 314)(133 432 315)(134 433 316)(135 434 317)(136 435 318)(137 436 319)(138 437 320)(139 438 241)(140 439 242)(141 440 243)(142 441 244)(143 442 245)(144 443 246)(145 444 247)(146 445 248)(147 446 249)(148 447 250)(149 448 251)(150 449 252)(151 450 253)(152 451 254)(153 452 255)(154 453 256)(155 454 257)(156 455 258)(157 456 259)(158 457 260)(159 458 261)(160 459 262)
(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)
(1 441 41 401)(2 440 42 480)(3 439 43 479)(4 438 44 478)(5 437 45 477)(6 436 46 476)(7 435 47 475)(8 434 48 474)(9 433 49 473)(10 432 50 472)(11 431 51 471)(12 430 52 470)(13 429 53 469)(14 428 54 468)(15 427 55 467)(16 426 56 466)(17 425 57 465)(18 424 58 464)(19 423 59 463)(20 422 60 462)(21 421 61 461)(22 420 62 460)(23 419 63 459)(24 418 64 458)(25 417 65 457)(26 416 66 456)(27 415 67 455)(28 414 68 454)(29 413 69 453)(30 412 70 452)(31 411 71 451)(32 410 72 450)(33 409 73 449)(34 408 74 448)(35 407 75 447)(36 406 76 446)(37 405 77 445)(38 404 78 444)(39 403 79 443)(40 402 80 442)(81 355 121 395)(82 354 122 394)(83 353 123 393)(84 352 124 392)(85 351 125 391)(86 350 126 390)(87 349 127 389)(88 348 128 388)(89 347 129 387)(90 346 130 386)(91 345 131 385)(92 344 132 384)(93 343 133 383)(94 342 134 382)(95 341 135 381)(96 340 136 380)(97 339 137 379)(98 338 138 378)(99 337 139 377)(100 336 140 376)(101 335 141 375)(102 334 142 374)(103 333 143 373)(104 332 144 372)(105 331 145 371)(106 330 146 370)(107 329 147 369)(108 328 148 368)(109 327 149 367)(110 326 150 366)(111 325 151 365)(112 324 152 364)(113 323 153 363)(114 322 154 362)(115 321 155 361)(116 400 156 360)(117 399 157 359)(118 398 158 358)(119 397 159 357)(120 396 160 356)(161 315 201 275)(162 314 202 274)(163 313 203 273)(164 312 204 272)(165 311 205 271)(166 310 206 270)(167 309 207 269)(168 308 208 268)(169 307 209 267)(170 306 210 266)(171 305 211 265)(172 304 212 264)(173 303 213 263)(174 302 214 262)(175 301 215 261)(176 300 216 260)(177 299 217 259)(178 298 218 258)(179 297 219 257)(180 296 220 256)(181 295 221 255)(182 294 222 254)(183 293 223 253)(184 292 224 252)(185 291 225 251)(186 290 226 250)(187 289 227 249)(188 288 228 248)(189 287 229 247)(190 286 230 246)(191 285 231 245)(192 284 232 244)(193 283 233 243)(194 282 234 242)(195 281 235 241)(196 280 236 320)(197 279 237 319)(198 278 238 318)(199 277 239 317)(200 276 240 316)

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

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

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

129 conjugacy classes

class 1  2 3A3B4A4B4C5A5B6A6B8A8B10A10B12A12B12C12D12E12F15A15B15C15D16A16B16C16D20A20B20C20D24A24B24C24D30A30B30C30D40A···40H48A···48H60A···60H80A···80P120A···120P240A···240AF
order12334445566881010121212121212151515151616161620202020242424243030303040···4048···4860···6080···80120···120240···240
size111124040221122222240404040222222222222222222222···22···22···22···22···22···2

129 irreducible representations

dim1111112222222222222222
type+++++++-++-
imageC1C2C2C3C6C6D4D5D8D10C3×D4C3×D5Q32D20C3×D8C6×D5D40C3×Q32C3×D20Dic40C3×D40C3×Dic40
kernelC3×Dic40C240C3×Dic20Dic40C80Dic20C60C48C30C24C20C16C15C12C10C8C6C5C4C3C2C1
# reps1122241222244444888161632

Matrix representation of C3×Dic40 in GL2(𝔽241) generated by

150
015
,
4984
103152
,
10937
226132
G:=sub<GL(2,GF(241))| [15,0,0,15],[49,103,84,152],[109,226,37,132] >;

C3×Dic40 in GAP, Magma, Sage, TeX

C_3\times {\rm Dic}_{40}
% in TeX

G:=Group("C3xDic40");
// GroupNames label

G:=SmallGroup(480,79);
// by ID

G=gap.SmallGroup(480,79);
# by ID

G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,336,197,260,1011,192,2524,102,18822]);
// Polycyclic

G:=Group<a,b,c|a^3=b^80=1,c^2=b^40,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C3×Dic40 in TeX

׿
×
𝔽