direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C6×C5⋊2C16, C30⋊4C16, C10⋊2C48, C20.6C24, C60.13C8, C40.8C12, C120.18C4, C24.82D10, C24.8Dic5, C120.100C22, C5⋊4(C2×C48), C15⋊14(C2×C16), (C2×C30).8C8, (C2×C40).9C6, C8.21(C6×D5), (C2×C60).48C4, C40.21(C2×C6), (C2×C10).4C24, C30.65(C2×C8), (C2×C24).19D5, C8.4(C3×Dic5), C12.6(C5⋊2C8), (C2×C120).25C2, C60.248(C2×C4), C10.17(C2×C24), C20.60(C2×C12), (C2×C20).23C12, C4.10(C6×Dic5), (C2×C12).17Dic5, C12.49(C2×Dic5), C4.3(C3×C5⋊2C8), C2.2(C6×C5⋊2C8), (C2×C8).9(C3×D5), C6.13(C2×C5⋊2C8), (C2×C6).4(C5⋊2C8), C22.2(C3×C5⋊2C8), (C2×C4).8(C3×Dic5), SmallGroup(480,89)
Series: Derived ►Chief ►Lower central ►Upper central
| C5 — C6×C5⋊2C16 |
Generators and relations for C6×C5⋊2C16
G = < a,b,c | a6=b5=c16=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C6×C5⋊2C16
►Regular action on 480 points
Generators in S480
(1 407 37 389 430 62)(2 408 38 390 431 63)(3 409 39 391 432 64)(4 410 40 392 417 49)(5 411 41 393 418 50)(6 412 42 394 419 51)(7 413 43 395 420 52)(8 414 44 396 421 53)(9 415 45 397 422 54)(10 416 46 398 423 55)(11 401 47 399 424 56)(12 402 48 400 425 57)(13 403 33 385 426 58)(14 404 34 386 427 59)(15 405 35 387 428 60)(16 406 36 388 429 61)(17 475 353 323 102 176)(18 476 354 324 103 161)(19 477 355 325 104 162)(20 478 356 326 105 163)(21 479 357 327 106 164)(22 480 358 328 107 165)(23 465 359 329 108 166)(24 466 360 330 109 167)(25 467 361 331 110 168)(26 468 362 332 111 169)(27 469 363 333 112 170)(28 470 364 334 97 171)(29 471 365 335 98 172)(30 472 366 336 99 173)(31 473 367 321 100 174)(32 474 368 322 101 175)(65 141 457 318 267 233)(66 142 458 319 268 234)(67 143 459 320 269 235)(68 144 460 305 270 236)(69 129 461 306 271 237)(70 130 462 307 272 238)(71 131 463 308 257 239)(72 132 464 309 258 240)(73 133 449 310 259 225)(74 134 450 311 260 226)(75 135 451 312 261 227)(76 136 452 313 262 228)(77 137 453 314 263 229)(78 138 454 315 264 230)(79 139 455 316 265 231)(80 140 456 317 266 232)(81 300 205 160 437 341)(82 301 206 145 438 342)(83 302 207 146 439 343)(84 303 208 147 440 344)(85 304 193 148 441 345)(86 289 194 149 442 346)(87 290 195 150 443 347)(88 291 196 151 444 348)(89 292 197 152 445 349)(90 293 198 153 446 350)(91 294 199 154 447 351)(92 295 200 155 448 352)(93 296 201 156 433 337)(94 297 202 157 434 338)(95 298 203 158 435 339)(96 299 204 159 436 340)(113 274 224 375 255 187)(114 275 209 376 256 188)(115 276 210 377 241 189)(116 277 211 378 242 190)(117 278 212 379 243 191)(118 279 213 380 244 192)(119 280 214 381 245 177)(120 281 215 382 246 178)(121 282 216 383 247 179)(122 283 217 384 248 180)(123 284 218 369 249 181)(124 285 219 370 250 182)(125 286 220 371 251 183)(126 287 221 372 252 184)(127 288 222 373 253 185)(128 273 223 374 254 186)
(1 165 369 305 342)(2 343 306 370 166)(3 167 371 307 344)(4 345 308 372 168)(5 169 373 309 346)(6 347 310 374 170)(7 171 375 311 348)(8 349 312 376 172)(9 173 377 313 350)(10 351 314 378 174)(11 175 379 315 352)(12 337 316 380 176)(13 161 381 317 338)(14 339 318 382 162)(15 163 383 319 340)(16 341 320 384 164)(17 402 93 265 244)(18 245 266 94 403)(19 404 95 267 246)(20 247 268 96 405)(21 406 81 269 248)(22 249 270 82 407)(23 408 83 271 250)(24 251 272 84 409)(25 410 85 257 252)(26 253 258 86 411)(27 412 87 259 254)(28 255 260 88 413)(29 414 89 261 256)(30 241 262 90 415)(31 416 91 263 242)(32 243 264 92 401)(33 476 177 232 297)(34 298 233 178 477)(35 478 179 234 299)(36 300 235 180 479)(37 480 181 236 301)(38 302 237 182 465)(39 466 183 238 303)(40 304 239 184 467)(41 468 185 240 289)(42 290 225 186 469)(43 470 187 226 291)(44 292 227 188 471)(45 472 189 228 293)(46 294 229 190 473)(47 474 191 230 295)(48 296 231 192 475)(49 441 463 221 110)(50 111 222 464 442)(51 443 449 223 112)(52 97 224 450 444)(53 445 451 209 98)(54 99 210 452 446)(55 447 453 211 100)(56 101 212 454 448)(57 433 455 213 102)(58 103 214 456 434)(59 435 457 215 104)(60 105 216 458 436)(61 437 459 217 106)(62 107 218 460 438)(63 439 461 219 108)(64 109 220 462 440)(65 120 355 386 203)(66 204 387 356 121)(67 122 357 388 205)(68 206 389 358 123)(69 124 359 390 207)(70 208 391 360 125)(71 126 361 392 193)(72 194 393 362 127)(73 128 363 394 195)(74 196 395 364 113)(75 114 365 396 197)(76 198 397 366 115)(77 116 367 398 199)(78 200 399 368 117)(79 118 353 400 201)(80 202 385 354 119)(129 285 329 431 146)(130 147 432 330 286)(131 287 331 417 148)(132 149 418 332 288)(133 273 333 419 150)(134 151 420 334 274)(135 275 335 421 152)(136 153 422 336 276)(137 277 321 423 154)(138 155 424 322 278)(139 279 323 425 156)(140 157 426 324 280)(141 281 325 427 158)(142 159 428 326 282)(143 283 327 429 160)(144 145 430 328 284)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16)(17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32)(33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48)(49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64)(65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96)(97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112)(113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128)(129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144)(145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160)(161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176)(177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192)(193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208)(209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224)(225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240)(241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256)(257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272)(273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288)(289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304)(305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320)(321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336)(337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352)(353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368)(369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384)(385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400)(401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416)(417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432)(433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448)(449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464)(465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480)
G:=sub<Sym(480)| (1,407,37,389,430,62)(2,408,38,390,431,63)(3,409,39,391,432,64)(4,410,40,392,417,49)(5,411,41,393,418,50)(6,412,42,394,419,51)(7,413,43,395,420,52)(8,414,44,396,421,53)(9,415,45,397,422,54)(10,416,46,398,423,55)(11,401,47,399,424,56)(12,402,48,400,425,57)(13,403,33,385,426,58)(14,404,34,386,427,59)(15,405,35,387,428,60)(16,406,36,388,429,61)(17,475,353,323,102,176)(18,476,354,324,103,161)(19,477,355,325,104,162)(20,478,356,326,105,163)(21,479,357,327,106,164)(22,480,358,328,107,165)(23,465,359,329,108,166)(24,466,360,330,109,167)(25,467,361,331,110,168)(26,468,362,332,111,169)(27,469,363,333,112,170)(28,470,364,334,97,171)(29,471,365,335,98,172)(30,472,366,336,99,173)(31,473,367,321,100,174)(32,474,368,322,101,175)(65,141,457,318,267,233)(66,142,458,319,268,234)(67,143,459,320,269,235)(68,144,460,305,270,236)(69,129,461,306,271,237)(70,130,462,307,272,238)(71,131,463,308,257,239)(72,132,464,309,258,240)(73,133,449,310,259,225)(74,134,450,311,260,226)(75,135,451,312,261,227)(76,136,452,313,262,228)(77,137,453,314,263,229)(78,138,454,315,264,230)(79,139,455,316,265,231)(80,140,456,317,266,232)(81,300,205,160,437,341)(82,301,206,145,438,342)(83,302,207,146,439,343)(84,303,208,147,440,344)(85,304,193,148,441,345)(86,289,194,149,442,346)(87,290,195,150,443,347)(88,291,196,151,444,348)(89,292,197,152,445,349)(90,293,198,153,446,350)(91,294,199,154,447,351)(92,295,200,155,448,352)(93,296,201,156,433,337)(94,297,202,157,434,338)(95,298,203,158,435,339)(96,299,204,159,436,340)(113,274,224,375,255,187)(114,275,209,376,256,188)(115,276,210,377,241,189)(116,277,211,378,242,190)(117,278,212,379,243,191)(118,279,213,380,244,192)(119,280,214,381,245,177)(120,281,215,382,246,178)(121,282,216,383,247,179)(122,283,217,384,248,180)(123,284,218,369,249,181)(124,285,219,370,250,182)(125,286,220,371,251,183)(126,287,221,372,252,184)(127,288,222,373,253,185)(128,273,223,374,254,186), (1,165,369,305,342)(2,343,306,370,166)(3,167,371,307,344)(4,345,308,372,168)(5,169,373,309,346)(6,347,310,374,170)(7,171,375,311,348)(8,349,312,376,172)(9,173,377,313,350)(10,351,314,378,174)(11,175,379,315,352)(12,337,316,380,176)(13,161,381,317,338)(14,339,318,382,162)(15,163,383,319,340)(16,341,320,384,164)(17,402,93,265,244)(18,245,266,94,403)(19,404,95,267,246)(20,247,268,96,405)(21,406,81,269,248)(22,249,270,82,407)(23,408,83,271,250)(24,251,272,84,409)(25,410,85,257,252)(26,253,258,86,411)(27,412,87,259,254)(28,255,260,88,413)(29,414,89,261,256)(30,241,262,90,415)(31,416,91,263,242)(32,243,264,92,401)(33,476,177,232,297)(34,298,233,178,477)(35,478,179,234,299)(36,300,235,180,479)(37,480,181,236,301)(38,302,237,182,465)(39,466,183,238,303)(40,304,239,184,467)(41,468,185,240,289)(42,290,225,186,469)(43,470,187,226,291)(44,292,227,188,471)(45,472,189,228,293)(46,294,229,190,473)(47,474,191,230,295)(48,296,231,192,475)(49,441,463,221,110)(50,111,222,464,442)(51,443,449,223,112)(52,97,224,450,444)(53,445,451,209,98)(54,99,210,452,446)(55,447,453,211,100)(56,101,212,454,448)(57,433,455,213,102)(58,103,214,456,434)(59,435,457,215,104)(60,105,216,458,436)(61,437,459,217,106)(62,107,218,460,438)(63,439,461,219,108)(64,109,220,462,440)(65,120,355,386,203)(66,204,387,356,121)(67,122,357,388,205)(68,206,389,358,123)(69,124,359,390,207)(70,208,391,360,125)(71,126,361,392,193)(72,194,393,362,127)(73,128,363,394,195)(74,196,395,364,113)(75,114,365,396,197)(76,198,397,366,115)(77,116,367,398,199)(78,200,399,368,117)(79,118,353,400,201)(80,202,385,354,119)(129,285,329,431,146)(130,147,432,330,286)(131,287,331,417,148)(132,149,418,332,288)(133,273,333,419,150)(134,151,420,334,274)(135,275,335,421,152)(136,153,422,336,276)(137,277,321,423,154)(138,155,424,322,278)(139,279,323,425,156)(140,157,426,324,280)(141,281,325,427,158)(142,159,428,326,282)(143,283,327,429,160)(144,145,430,328,284), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128)(129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176)(177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224)(225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256)(257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272)(273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288)(289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304)(305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320)(321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336)(337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352)(353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368)(369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384)(385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400)(401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416)(417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432)(433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448)(449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464)(465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480)>;
G:=Group( (1,407,37,389,430,62)(2,408,38,390,431,63)(3,409,39,391,432,64)(4,410,40,392,417,49)(5,411,41,393,418,50)(6,412,42,394,419,51)(7,413,43,395,420,52)(8,414,44,396,421,53)(9,415,45,397,422,54)(10,416,46,398,423,55)(11,401,47,399,424,56)(12,402,48,400,425,57)(13,403,33,385,426,58)(14,404,34,386,427,59)(15,405,35,387,428,60)(16,406,36,388,429,61)(17,475,353,323,102,176)(18,476,354,324,103,161)(19,477,355,325,104,162)(20,478,356,326,105,163)(21,479,357,327,106,164)(22,480,358,328,107,165)(23,465,359,329,108,166)(24,466,360,330,109,167)(25,467,361,331,110,168)(26,468,362,332,111,169)(27,469,363,333,112,170)(28,470,364,334,97,171)(29,471,365,335,98,172)(30,472,366,336,99,173)(31,473,367,321,100,174)(32,474,368,322,101,175)(65,141,457,318,267,233)(66,142,458,319,268,234)(67,143,459,320,269,235)(68,144,460,305,270,236)(69,129,461,306,271,237)(70,130,462,307,272,238)(71,131,463,308,257,239)(72,132,464,309,258,240)(73,133,449,310,259,225)(74,134,450,311,260,226)(75,135,451,312,261,227)(76,136,452,313,262,228)(77,137,453,314,263,229)(78,138,454,315,264,230)(79,139,455,316,265,231)(80,140,456,317,266,232)(81,300,205,160,437,341)(82,301,206,145,438,342)(83,302,207,146,439,343)(84,303,208,147,440,344)(85,304,193,148,441,345)(86,289,194,149,442,346)(87,290,195,150,443,347)(88,291,196,151,444,348)(89,292,197,152,445,349)(90,293,198,153,446,350)(91,294,199,154,447,351)(92,295,200,155,448,352)(93,296,201,156,433,337)(94,297,202,157,434,338)(95,298,203,158,435,339)(96,299,204,159,436,340)(113,274,224,375,255,187)(114,275,209,376,256,188)(115,276,210,377,241,189)(116,277,211,378,242,190)(117,278,212,379,243,191)(118,279,213,380,244,192)(119,280,214,381,245,177)(120,281,215,382,246,178)(121,282,216,383,247,179)(122,283,217,384,248,180)(123,284,218,369,249,181)(124,285,219,370,250,182)(125,286,220,371,251,183)(126,287,221,372,252,184)(127,288,222,373,253,185)(128,273,223,374,254,186), (1,165,369,305,342)(2,343,306,370,166)(3,167,371,307,344)(4,345,308,372,168)(5,169,373,309,346)(6,347,310,374,170)(7,171,375,311,348)(8,349,312,376,172)(9,173,377,313,350)(10,351,314,378,174)(11,175,379,315,352)(12,337,316,380,176)(13,161,381,317,338)(14,339,318,382,162)(15,163,383,319,340)(16,341,320,384,164)(17,402,93,265,244)(18,245,266,94,403)(19,404,95,267,246)(20,247,268,96,405)(21,406,81,269,248)(22,249,270,82,407)(23,408,83,271,250)(24,251,272,84,409)(25,410,85,257,252)(26,253,258,86,411)(27,412,87,259,254)(28,255,260,88,413)(29,414,89,261,256)(30,241,262,90,415)(31,416,91,263,242)(32,243,264,92,401)(33,476,177,232,297)(34,298,233,178,477)(35,478,179,234,299)(36,300,235,180,479)(37,480,181,236,301)(38,302,237,182,465)(39,466,183,238,303)(40,304,239,184,467)(41,468,185,240,289)(42,290,225,186,469)(43,470,187,226,291)(44,292,227,188,471)(45,472,189,228,293)(46,294,229,190,473)(47,474,191,230,295)(48,296,231,192,475)(49,441,463,221,110)(50,111,222,464,442)(51,443,449,223,112)(52,97,224,450,444)(53,445,451,209,98)(54,99,210,452,446)(55,447,453,211,100)(56,101,212,454,448)(57,433,455,213,102)(58,103,214,456,434)(59,435,457,215,104)(60,105,216,458,436)(61,437,459,217,106)(62,107,218,460,438)(63,439,461,219,108)(64,109,220,462,440)(65,120,355,386,203)(66,204,387,356,121)(67,122,357,388,205)(68,206,389,358,123)(69,124,359,390,207)(70,208,391,360,125)(71,126,361,392,193)(72,194,393,362,127)(73,128,363,394,195)(74,196,395,364,113)(75,114,365,396,197)(76,198,397,366,115)(77,116,367,398,199)(78,200,399,368,117)(79,118,353,400,201)(80,202,385,354,119)(129,285,329,431,146)(130,147,432,330,286)(131,287,331,417,148)(132,149,418,332,288)(133,273,333,419,150)(134,151,420,334,274)(135,275,335,421,152)(136,153,422,336,276)(137,277,321,423,154)(138,155,424,322,278)(139,279,323,425,156)(140,157,426,324,280)(141,281,325,427,158)(142,159,428,326,282)(143,283,327,429,160)(144,145,430,328,284), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128)(129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176)(177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224)(225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256)(257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272)(273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288)(289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304)(305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320)(321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336)(337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352)(353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368)(369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384)(385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400)(401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416)(417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432)(433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448)(449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464)(465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480) );
G=PermutationGroup([[(1,407,37,389,430,62),(2,408,38,390,431,63),(3,409,39,391,432,64),(4,410,40,392,417,49),(5,411,41,393,418,50),(6,412,42,394,419,51),(7,413,43,395,420,52),(8,414,44,396,421,53),(9,415,45,397,422,54),(10,416,46,398,423,55),(11,401,47,399,424,56),(12,402,48,400,425,57),(13,403,33,385,426,58),(14,404,34,386,427,59),(15,405,35,387,428,60),(16,406,36,388,429,61),(17,475,353,323,102,176),(18,476,354,324,103,161),(19,477,355,325,104,162),(20,478,356,326,105,163),(21,479,357,327,106,164),(22,480,358,328,107,165),(23,465,359,329,108,166),(24,466,360,330,109,167),(25,467,361,331,110,168),(26,468,362,332,111,169),(27,469,363,333,112,170),(28,470,364,334,97,171),(29,471,365,335,98,172),(30,472,366,336,99,173),(31,473,367,321,100,174),(32,474,368,322,101,175),(65,141,457,318,267,233),(66,142,458,319,268,234),(67,143,459,320,269,235),(68,144,460,305,270,236),(69,129,461,306,271,237),(70,130,462,307,272,238),(71,131,463,308,257,239),(72,132,464,309,258,240),(73,133,449,310,259,225),(74,134,450,311,260,226),(75,135,451,312,261,227),(76,136,452,313,262,228),(77,137,453,314,263,229),(78,138,454,315,264,230),(79,139,455,316,265,231),(80,140,456,317,266,232),(81,300,205,160,437,341),(82,301,206,145,438,342),(83,302,207,146,439,343),(84,303,208,147,440,344),(85,304,193,148,441,345),(86,289,194,149,442,346),(87,290,195,150,443,347),(88,291,196,151,444,348),(89,292,197,152,445,349),(90,293,198,153,446,350),(91,294,199,154,447,351),(92,295,200,155,448,352),(93,296,201,156,433,337),(94,297,202,157,434,338),(95,298,203,158,435,339),(96,299,204,159,436,340),(113,274,224,375,255,187),(114,275,209,376,256,188),(115,276,210,377,241,189),(116,277,211,378,242,190),(117,278,212,379,243,191),(118,279,213,380,244,192),(119,280,214,381,245,177),(120,281,215,382,246,178),(121,282,216,383,247,179),(122,283,217,384,248,180),(123,284,218,369,249,181),(124,285,219,370,250,182),(125,286,220,371,251,183),(126,287,221,372,252,184),(127,288,222,373,253,185),(128,273,223,374,254,186)], [(1,165,369,305,342),(2,343,306,370,166),(3,167,371,307,344),(4,345,308,372,168),(5,169,373,309,346),(6,347,310,374,170),(7,171,375,311,348),(8,349,312,376,172),(9,173,377,313,350),(10,351,314,378,174),(11,175,379,315,352),(12,337,316,380,176),(13,161,381,317,338),(14,339,318,382,162),(15,163,383,319,340),(16,341,320,384,164),(17,402,93,265,244),(18,245,266,94,403),(19,404,95,267,246),(20,247,268,96,405),(21,406,81,269,248),(22,249,270,82,407),(23,408,83,271,250),(24,251,272,84,409),(25,410,85,257,252),(26,253,258,86,411),(27,412,87,259,254),(28,255,260,88,413),(29,414,89,261,256),(30,241,262,90,415),(31,416,91,263,242),(32,243,264,92,401),(33,476,177,232,297),(34,298,233,178,477),(35,478,179,234,299),(36,300,235,180,479),(37,480,181,236,301),(38,302,237,182,465),(39,466,183,238,303),(40,304,239,184,467),(41,468,185,240,289),(42,290,225,186,469),(43,470,187,226,291),(44,292,227,188,471),(45,472,189,228,293),(46,294,229,190,473),(47,474,191,230,295),(48,296,231,192,475),(49,441,463,221,110),(50,111,222,464,442),(51,443,449,223,112),(52,97,224,450,444),(53,445,451,209,98),(54,99,210,452,446),(55,447,453,211,100),(56,101,212,454,448),(57,433,455,213,102),(58,103,214,456,434),(59,435,457,215,104),(60,105,216,458,436),(61,437,459,217,106),(62,107,218,460,438),(63,439,461,219,108),(64,109,220,462,440),(65,120,355,386,203),(66,204,387,356,121),(67,122,357,388,205),(68,206,389,358,123),(69,124,359,390,207),(70,208,391,360,125),(71,126,361,392,193),(72,194,393,362,127),(73,128,363,394,195),(74,196,395,364,113),(75,114,365,396,197),(76,198,397,366,115),(77,116,367,398,199),(78,200,399,368,117),(79,118,353,400,201),(80,202,385,354,119),(129,285,329,431,146),(130,147,432,330,286),(131,287,331,417,148),(132,149,418,332,288),(133,273,333,419,150),(134,151,420,334,274),(135,275,335,421,152),(136,153,422,336,276),(137,277,321,423,154),(138,155,424,322,278),(139,279,323,425,156),(140,157,426,324,280),(141,281,325,427,158),(142,159,428,326,282),(143,283,327,429,160),(144,145,430,328,284)], [(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)]])
192 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | 4B | 4C | 4D | 5A | 5B | 6A | ··· | 6F | 8A | ··· | 8H | 10A | ··· | 10F | 12A | ··· | 12H | 15A | 15B | 15C | 15D | 16A | ··· | 16P | 20A | ··· | 20H | 24A | ··· | 24P | 30A | ··· | 30L | 40A | ··· | 40P | 48A | ··· | 48AF | 60A | ··· | 60P | 120A | ··· | 120AF |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | ··· | 6 | 8 | ··· | 8 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 16 | ··· | 16 | 20 | ··· | 20 | 24 | ··· | 24 | 30 | ··· | 30 | 40 | ··· | 40 | 48 | ··· | 48 | 60 | ··· | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 5 | ··· | 5 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 5 | ··· | 5 | 2 | ··· | 2 | 2 | ··· | 2 |
192 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | |||||||||||||||||||||||
| image | C1 | C2 | C2 | C3 | C4 | C4 | C6 | C6 | C8 | C8 | C12 | C12 | C16 | C24 | C24 | C48 | D5 | Dic5 | D10 | Dic5 | C3×D5 | C5⋊2C8 | C5⋊2C8 | C3×Dic5 | C6×D5 | C3×Dic5 | C5⋊2C16 | C3×C5⋊2C8 | C3×C5⋊2C8 | C3×C5⋊2C16 |
| kernel | C6×C5⋊2C16 | C3×C5⋊2C16 | C2×C120 | C2×C5⋊2C16 | C120 | C2×C60 | C5⋊2C16 | C2×C40 | C60 | C2×C30 | C40 | C2×C20 | C30 | C20 | C2×C10 | C10 | C2×C24 | C24 | C24 | C2×C12 | C2×C8 | C12 | C2×C6 | C8 | C8 | C2×C4 | C6 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 2 | 4 | 4 | 4 | 4 | 16 | 8 | 8 | 32 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 16 | 8 | 8 | 32 |
Matrix representation of C6×C5⋊2C16 ►in GL3(𝔽241) generated by
| 16 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
| 1 | 0 | 0 |
| 0 | 51 | 240 |
| 0 | 1 | 0 |
| 240 | 0 | 0 |
| 0 | 179 | 169 |
| 0 | 140 | 62 |
G:=sub<GL(3,GF(241))| [16,0,0,0,1,0,0,0,1],[1,0,0,0,51,1,0,240,0],[240,0,0,0,179,140,0,169,62] >;
C6×C5⋊2C16 in GAP, Magma, Sage, TeX
C_6\times C_5\rtimes_2C_{16} % in TeX
G:=Group("C6xC5:2C16"); // GroupNames label
G:=SmallGroup(480,89);
// by ID
G=gap.SmallGroup(480,89);
# by ID
G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,84,80,102,18822]);
// Polycyclic
G:=Group<a,b,c|a^6=b^5=c^16=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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