direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C15⋊C16, C30⋊1C16, C60.3C8, C6⋊(C5⋊C16), C10⋊(C3⋊C16), C15⋊8(C2×C16), C20.3(C3⋊C8), C12.3(C5⋊C8), (C2×C30).1C8, C60.56(C2×C4), C30.34(C2×C8), (C2×C60).13C4, C5⋊2C8.42D6, (C2×C12).13F5, C12.58(C2×F5), C4.3(C15⋊C8), (C2×C20).9Dic3, C5⋊2C8.5Dic3, C20.18(C2×Dic3), C22.2(C15⋊C8), C5⋊2(C2×C3⋊C16), C3⋊2(C2×C5⋊C16), C6.6(C2×C5⋊C8), C10.6(C2×C3⋊C8), C4.17(C2×C3⋊F5), (C2×C6).2(C5⋊C8), (C2×C4).9(C3⋊F5), (C3×C5⋊2C8).8C4, C2.1(C2×C15⋊C8), (C2×C10).1(C3⋊C8), (C6×C5⋊2C8).24C2, (C2×C5⋊2C8).12S3, (C3×C5⋊2C8).55C22, SmallGroup(480,302)
Series: Derived ►Chief ►Lower central ►Upper central
| C15 — C2×C15⋊C16 |
Generators and relations for C2×C15⋊C16
G = < a,b,c | a2=b15=c16=1, ab=ba, ac=ca, cbc-1=b2 >
Smallest permutation representation of C2×C15⋊C16
►Regular action on 480 points
Generators in S480
(1 159)(2 160)(3 145)(4 146)(5 147)(6 148)(7 149)(8 150)(9 151)(10 152)(11 153)(12 154)(13 155)(14 156)(15 157)(16 158)(17 435)(18 436)(19 437)(20 438)(21 439)(22 440)(23 441)(24 442)(25 443)(26 444)(27 445)(28 446)(29 447)(30 448)(31 433)(32 434)(33 294)(34 295)(35 296)(36 297)(37 298)(38 299)(39 300)(40 301)(41 302)(42 303)(43 304)(44 289)(45 290)(46 291)(47 292)(48 293)(49 311)(50 312)(51 313)(52 314)(53 315)(54 316)(55 317)(56 318)(57 319)(58 320)(59 305)(60 306)(61 307)(62 308)(63 309)(64 310)(65 212)(66 213)(67 214)(68 215)(69 216)(70 217)(71 218)(72 219)(73 220)(74 221)(75 222)(76 223)(77 224)(78 209)(79 210)(80 211)(81 451)(82 452)(83 453)(84 454)(85 455)(86 456)(87 457)(88 458)(89 459)(90 460)(91 461)(92 462)(93 463)(94 464)(95 449)(96 450)(97 359)(98 360)(99 361)(100 362)(101 363)(102 364)(103 365)(104 366)(105 367)(106 368)(107 353)(108 354)(109 355)(110 356)(111 357)(112 358)(113 347)(114 348)(115 349)(116 350)(117 351)(118 352)(119 337)(120 338)(121 339)(122 340)(123 341)(124 342)(125 343)(126 344)(127 345)(128 346)(129 247)(130 248)(131 249)(132 250)(133 251)(134 252)(135 253)(136 254)(137 255)(138 256)(139 241)(140 242)(141 243)(142 244)(143 245)(144 246)(161 260)(162 261)(163 262)(164 263)(165 264)(166 265)(167 266)(168 267)(169 268)(170 269)(171 270)(172 271)(173 272)(174 257)(175 258)(176 259)(177 428)(178 429)(179 430)(180 431)(181 432)(182 417)(183 418)(184 419)(185 420)(186 421)(187 422)(188 423)(189 424)(190 425)(191 426)(192 427)(193 415)(194 416)(195 401)(196 402)(197 403)(198 404)(199 405)(200 406)(201 407)(202 408)(203 409)(204 410)(205 411)(206 412)(207 413)(208 414)(225 283)(226 284)(227 285)(228 286)(229 287)(230 288)(231 273)(232 274)(233 275)(234 276)(235 277)(236 278)(237 279)(238 280)(239 281)(240 282)(321 393)(322 394)(323 395)(324 396)(325 397)(326 398)(327 399)(328 400)(329 385)(330 386)(331 387)(332 388)(333 389)(334 390)(335 391)(336 392)(369 465)(370 466)(371 467)(372 468)(373 469)(374 470)(375 471)(376 472)(377 473)(378 474)(379 475)(380 476)(381 477)(382 478)(383 479)(384 480)
(1 221 327 383 401 169 185 304 82 236 355 29 337 252 313)(2 328 402 186 83 356 338 314 222 384 170 289 237 30 253)(3 403 84 339 223 171 238 254 329 187 357 315 369 290 31)(4 85 224 239 330 358 370 32 404 340 172 255 188 316 291)(5 209 331 371 405 173 189 292 86 240 359 17 341 256 317)(6 332 406 190 87 360 342 318 210 372 174 293 225 18 241)(7 407 88 343 211 175 226 242 333 191 361 319 373 294 19)(8 89 212 227 334 362 374 20 408 344 176 243 192 320 295)(9 213 335 375 409 161 177 296 90 228 363 21 345 244 305)(10 336 410 178 91 364 346 306 214 376 162 297 229 22 245)(11 411 92 347 215 163 230 246 321 179 365 307 377 298 23)(12 93 216 231 322 366 378 24 412 348 164 247 180 308 299)(13 217 323 379 413 165 181 300 94 232 367 25 349 248 309)(14 324 414 182 95 368 350 310 218 380 166 301 233 26 249)(15 415 96 351 219 167 234 250 325 183 353 311 381 302 27)(16 81 220 235 326 354 382 28 416 352 168 251 184 312 303)(33 437 149 201 458 125 80 258 284 140 389 426 99 57 469)(34 150 459 65 285 390 100 470 438 202 126 259 141 427 58)(35 460 286 101 439 127 142 59 151 66 391 471 203 260 428)(36 287 440 143 152 392 204 429 461 102 128 60 67 472 261)(37 441 153 205 462 113 68 262 288 144 393 430 103 61 473)(38 154 463 69 273 394 104 474 442 206 114 263 129 431 62)(39 464 274 105 443 115 130 63 155 70 395 475 207 264 432)(40 275 444 131 156 396 208 417 449 106 116 64 71 476 265)(41 445 157 193 450 117 72 266 276 132 397 418 107 49 477)(42 158 451 73 277 398 108 478 446 194 118 267 133 419 50)(43 452 278 109 447 119 134 51 159 74 399 479 195 268 420)(44 279 448 135 160 400 196 421 453 110 120 52 75 480 269)(45 433 145 197 454 121 76 270 280 136 385 422 111 53 465)(46 146 455 77 281 386 112 466 434 198 122 271 137 423 54)(47 456 282 97 435 123 138 55 147 78 387 467 199 272 424)(48 283 436 139 148 388 200 425 457 98 124 56 79 468 257)
(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)| (1,159)(2,160)(3,145)(4,146)(5,147)(6,148)(7,149)(8,150)(9,151)(10,152)(11,153)(12,154)(13,155)(14,156)(15,157)(16,158)(17,435)(18,436)(19,437)(20,438)(21,439)(22,440)(23,441)(24,442)(25,443)(26,444)(27,445)(28,446)(29,447)(30,448)(31,433)(32,434)(33,294)(34,295)(35,296)(36,297)(37,298)(38,299)(39,300)(40,301)(41,302)(42,303)(43,304)(44,289)(45,290)(46,291)(47,292)(48,293)(49,311)(50,312)(51,313)(52,314)(53,315)(54,316)(55,317)(56,318)(57,319)(58,320)(59,305)(60,306)(61,307)(62,308)(63,309)(64,310)(65,212)(66,213)(67,214)(68,215)(69,216)(70,217)(71,218)(72,219)(73,220)(74,221)(75,222)(76,223)(77,224)(78,209)(79,210)(80,211)(81,451)(82,452)(83,453)(84,454)(85,455)(86,456)(87,457)(88,458)(89,459)(90,460)(91,461)(92,462)(93,463)(94,464)(95,449)(96,450)(97,359)(98,360)(99,361)(100,362)(101,363)(102,364)(103,365)(104,366)(105,367)(106,368)(107,353)(108,354)(109,355)(110,356)(111,357)(112,358)(113,347)(114,348)(115,349)(116,350)(117,351)(118,352)(119,337)(120,338)(121,339)(122,340)(123,341)(124,342)(125,343)(126,344)(127,345)(128,346)(129,247)(130,248)(131,249)(132,250)(133,251)(134,252)(135,253)(136,254)(137,255)(138,256)(139,241)(140,242)(141,243)(142,244)(143,245)(144,246)(161,260)(162,261)(163,262)(164,263)(165,264)(166,265)(167,266)(168,267)(169,268)(170,269)(171,270)(172,271)(173,272)(174,257)(175,258)(176,259)(177,428)(178,429)(179,430)(180,431)(181,432)(182,417)(183,418)(184,419)(185,420)(186,421)(187,422)(188,423)(189,424)(190,425)(191,426)(192,427)(193,415)(194,416)(195,401)(196,402)(197,403)(198,404)(199,405)(200,406)(201,407)(202,408)(203,409)(204,410)(205,411)(206,412)(207,413)(208,414)(225,283)(226,284)(227,285)(228,286)(229,287)(230,288)(231,273)(232,274)(233,275)(234,276)(235,277)(236,278)(237,279)(238,280)(239,281)(240,282)(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)(328,400)(329,385)(330,386)(331,387)(332,388)(333,389)(334,390)(335,391)(336,392)(369,465)(370,466)(371,467)(372,468)(373,469)(374,470)(375,471)(376,472)(377,473)(378,474)(379,475)(380,476)(381,477)(382,478)(383,479)(384,480), (1,221,327,383,401,169,185,304,82,236,355,29,337,252,313)(2,328,402,186,83,356,338,314,222,384,170,289,237,30,253)(3,403,84,339,223,171,238,254,329,187,357,315,369,290,31)(4,85,224,239,330,358,370,32,404,340,172,255,188,316,291)(5,209,331,371,405,173,189,292,86,240,359,17,341,256,317)(6,332,406,190,87,360,342,318,210,372,174,293,225,18,241)(7,407,88,343,211,175,226,242,333,191,361,319,373,294,19)(8,89,212,227,334,362,374,20,408,344,176,243,192,320,295)(9,213,335,375,409,161,177,296,90,228,363,21,345,244,305)(10,336,410,178,91,364,346,306,214,376,162,297,229,22,245)(11,411,92,347,215,163,230,246,321,179,365,307,377,298,23)(12,93,216,231,322,366,378,24,412,348,164,247,180,308,299)(13,217,323,379,413,165,181,300,94,232,367,25,349,248,309)(14,324,414,182,95,368,350,310,218,380,166,301,233,26,249)(15,415,96,351,219,167,234,250,325,183,353,311,381,302,27)(16,81,220,235,326,354,382,28,416,352,168,251,184,312,303)(33,437,149,201,458,125,80,258,284,140,389,426,99,57,469)(34,150,459,65,285,390,100,470,438,202,126,259,141,427,58)(35,460,286,101,439,127,142,59,151,66,391,471,203,260,428)(36,287,440,143,152,392,204,429,461,102,128,60,67,472,261)(37,441,153,205,462,113,68,262,288,144,393,430,103,61,473)(38,154,463,69,273,394,104,474,442,206,114,263,129,431,62)(39,464,274,105,443,115,130,63,155,70,395,475,207,264,432)(40,275,444,131,156,396,208,417,449,106,116,64,71,476,265)(41,445,157,193,450,117,72,266,276,132,397,418,107,49,477)(42,158,451,73,277,398,108,478,446,194,118,267,133,419,50)(43,452,278,109,447,119,134,51,159,74,399,479,195,268,420)(44,279,448,135,160,400,196,421,453,110,120,52,75,480,269)(45,433,145,197,454,121,76,270,280,136,385,422,111,53,465)(46,146,455,77,281,386,112,466,434,198,122,271,137,423,54)(47,456,282,97,435,123,138,55,147,78,387,467,199,272,424)(48,283,436,139,148,388,200,425,457,98,124,56,79,468,257), (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( (1,159)(2,160)(3,145)(4,146)(5,147)(6,148)(7,149)(8,150)(9,151)(10,152)(11,153)(12,154)(13,155)(14,156)(15,157)(16,158)(17,435)(18,436)(19,437)(20,438)(21,439)(22,440)(23,441)(24,442)(25,443)(26,444)(27,445)(28,446)(29,447)(30,448)(31,433)(32,434)(33,294)(34,295)(35,296)(36,297)(37,298)(38,299)(39,300)(40,301)(41,302)(42,303)(43,304)(44,289)(45,290)(46,291)(47,292)(48,293)(49,311)(50,312)(51,313)(52,314)(53,315)(54,316)(55,317)(56,318)(57,319)(58,320)(59,305)(60,306)(61,307)(62,308)(63,309)(64,310)(65,212)(66,213)(67,214)(68,215)(69,216)(70,217)(71,218)(72,219)(73,220)(74,221)(75,222)(76,223)(77,224)(78,209)(79,210)(80,211)(81,451)(82,452)(83,453)(84,454)(85,455)(86,456)(87,457)(88,458)(89,459)(90,460)(91,461)(92,462)(93,463)(94,464)(95,449)(96,450)(97,359)(98,360)(99,361)(100,362)(101,363)(102,364)(103,365)(104,366)(105,367)(106,368)(107,353)(108,354)(109,355)(110,356)(111,357)(112,358)(113,347)(114,348)(115,349)(116,350)(117,351)(118,352)(119,337)(120,338)(121,339)(122,340)(123,341)(124,342)(125,343)(126,344)(127,345)(128,346)(129,247)(130,248)(131,249)(132,250)(133,251)(134,252)(135,253)(136,254)(137,255)(138,256)(139,241)(140,242)(141,243)(142,244)(143,245)(144,246)(161,260)(162,261)(163,262)(164,263)(165,264)(166,265)(167,266)(168,267)(169,268)(170,269)(171,270)(172,271)(173,272)(174,257)(175,258)(176,259)(177,428)(178,429)(179,430)(180,431)(181,432)(182,417)(183,418)(184,419)(185,420)(186,421)(187,422)(188,423)(189,424)(190,425)(191,426)(192,427)(193,415)(194,416)(195,401)(196,402)(197,403)(198,404)(199,405)(200,406)(201,407)(202,408)(203,409)(204,410)(205,411)(206,412)(207,413)(208,414)(225,283)(226,284)(227,285)(228,286)(229,287)(230,288)(231,273)(232,274)(233,275)(234,276)(235,277)(236,278)(237,279)(238,280)(239,281)(240,282)(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)(328,400)(329,385)(330,386)(331,387)(332,388)(333,389)(334,390)(335,391)(336,392)(369,465)(370,466)(371,467)(372,468)(373,469)(374,470)(375,471)(376,472)(377,473)(378,474)(379,475)(380,476)(381,477)(382,478)(383,479)(384,480), (1,221,327,383,401,169,185,304,82,236,355,29,337,252,313)(2,328,402,186,83,356,338,314,222,384,170,289,237,30,253)(3,403,84,339,223,171,238,254,329,187,357,315,369,290,31)(4,85,224,239,330,358,370,32,404,340,172,255,188,316,291)(5,209,331,371,405,173,189,292,86,240,359,17,341,256,317)(6,332,406,190,87,360,342,318,210,372,174,293,225,18,241)(7,407,88,343,211,175,226,242,333,191,361,319,373,294,19)(8,89,212,227,334,362,374,20,408,344,176,243,192,320,295)(9,213,335,375,409,161,177,296,90,228,363,21,345,244,305)(10,336,410,178,91,364,346,306,214,376,162,297,229,22,245)(11,411,92,347,215,163,230,246,321,179,365,307,377,298,23)(12,93,216,231,322,366,378,24,412,348,164,247,180,308,299)(13,217,323,379,413,165,181,300,94,232,367,25,349,248,309)(14,324,414,182,95,368,350,310,218,380,166,301,233,26,249)(15,415,96,351,219,167,234,250,325,183,353,311,381,302,27)(16,81,220,235,326,354,382,28,416,352,168,251,184,312,303)(33,437,149,201,458,125,80,258,284,140,389,426,99,57,469)(34,150,459,65,285,390,100,470,438,202,126,259,141,427,58)(35,460,286,101,439,127,142,59,151,66,391,471,203,260,428)(36,287,440,143,152,392,204,429,461,102,128,60,67,472,261)(37,441,153,205,462,113,68,262,288,144,393,430,103,61,473)(38,154,463,69,273,394,104,474,442,206,114,263,129,431,62)(39,464,274,105,443,115,130,63,155,70,395,475,207,264,432)(40,275,444,131,156,396,208,417,449,106,116,64,71,476,265)(41,445,157,193,450,117,72,266,276,132,397,418,107,49,477)(42,158,451,73,277,398,108,478,446,194,118,267,133,419,50)(43,452,278,109,447,119,134,51,159,74,399,479,195,268,420)(44,279,448,135,160,400,196,421,453,110,120,52,75,480,269)(45,433,145,197,454,121,76,270,280,136,385,422,111,53,465)(46,146,455,77,281,386,112,466,434,198,122,271,137,423,54)(47,456,282,97,435,123,138,55,147,78,387,467,199,272,424)(48,283,436,139,148,388,200,425,457,98,124,56,79,468,257), (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([[(1,159),(2,160),(3,145),(4,146),(5,147),(6,148),(7,149),(8,150),(9,151),(10,152),(11,153),(12,154),(13,155),(14,156),(15,157),(16,158),(17,435),(18,436),(19,437),(20,438),(21,439),(22,440),(23,441),(24,442),(25,443),(26,444),(27,445),(28,446),(29,447),(30,448),(31,433),(32,434),(33,294),(34,295),(35,296),(36,297),(37,298),(38,299),(39,300),(40,301),(41,302),(42,303),(43,304),(44,289),(45,290),(46,291),(47,292),(48,293),(49,311),(50,312),(51,313),(52,314),(53,315),(54,316),(55,317),(56,318),(57,319),(58,320),(59,305),(60,306),(61,307),(62,308),(63,309),(64,310),(65,212),(66,213),(67,214),(68,215),(69,216),(70,217),(71,218),(72,219),(73,220),(74,221),(75,222),(76,223),(77,224),(78,209),(79,210),(80,211),(81,451),(82,452),(83,453),(84,454),(85,455),(86,456),(87,457),(88,458),(89,459),(90,460),(91,461),(92,462),(93,463),(94,464),(95,449),(96,450),(97,359),(98,360),(99,361),(100,362),(101,363),(102,364),(103,365),(104,366),(105,367),(106,368),(107,353),(108,354),(109,355),(110,356),(111,357),(112,358),(113,347),(114,348),(115,349),(116,350),(117,351),(118,352),(119,337),(120,338),(121,339),(122,340),(123,341),(124,342),(125,343),(126,344),(127,345),(128,346),(129,247),(130,248),(131,249),(132,250),(133,251),(134,252),(135,253),(136,254),(137,255),(138,256),(139,241),(140,242),(141,243),(142,244),(143,245),(144,246),(161,260),(162,261),(163,262),(164,263),(165,264),(166,265),(167,266),(168,267),(169,268),(170,269),(171,270),(172,271),(173,272),(174,257),(175,258),(176,259),(177,428),(178,429),(179,430),(180,431),(181,432),(182,417),(183,418),(184,419),(185,420),(186,421),(187,422),(188,423),(189,424),(190,425),(191,426),(192,427),(193,415),(194,416),(195,401),(196,402),(197,403),(198,404),(199,405),(200,406),(201,407),(202,408),(203,409),(204,410),(205,411),(206,412),(207,413),(208,414),(225,283),(226,284),(227,285),(228,286),(229,287),(230,288),(231,273),(232,274),(233,275),(234,276),(235,277),(236,278),(237,279),(238,280),(239,281),(240,282),(321,393),(322,394),(323,395),(324,396),(325,397),(326,398),(327,399),(328,400),(329,385),(330,386),(331,387),(332,388),(333,389),(334,390),(335,391),(336,392),(369,465),(370,466),(371,467),(372,468),(373,469),(374,470),(375,471),(376,472),(377,473),(378,474),(379,475),(380,476),(381,477),(382,478),(383,479),(384,480)], [(1,221,327,383,401,169,185,304,82,236,355,29,337,252,313),(2,328,402,186,83,356,338,314,222,384,170,289,237,30,253),(3,403,84,339,223,171,238,254,329,187,357,315,369,290,31),(4,85,224,239,330,358,370,32,404,340,172,255,188,316,291),(5,209,331,371,405,173,189,292,86,240,359,17,341,256,317),(6,332,406,190,87,360,342,318,210,372,174,293,225,18,241),(7,407,88,343,211,175,226,242,333,191,361,319,373,294,19),(8,89,212,227,334,362,374,20,408,344,176,243,192,320,295),(9,213,335,375,409,161,177,296,90,228,363,21,345,244,305),(10,336,410,178,91,364,346,306,214,376,162,297,229,22,245),(11,411,92,347,215,163,230,246,321,179,365,307,377,298,23),(12,93,216,231,322,366,378,24,412,348,164,247,180,308,299),(13,217,323,379,413,165,181,300,94,232,367,25,349,248,309),(14,324,414,182,95,368,350,310,218,380,166,301,233,26,249),(15,415,96,351,219,167,234,250,325,183,353,311,381,302,27),(16,81,220,235,326,354,382,28,416,352,168,251,184,312,303),(33,437,149,201,458,125,80,258,284,140,389,426,99,57,469),(34,150,459,65,285,390,100,470,438,202,126,259,141,427,58),(35,460,286,101,439,127,142,59,151,66,391,471,203,260,428),(36,287,440,143,152,392,204,429,461,102,128,60,67,472,261),(37,441,153,205,462,113,68,262,288,144,393,430,103,61,473),(38,154,463,69,273,394,104,474,442,206,114,263,129,431,62),(39,464,274,105,443,115,130,63,155,70,395,475,207,264,432),(40,275,444,131,156,396,208,417,449,106,116,64,71,476,265),(41,445,157,193,450,117,72,266,276,132,397,418,107,49,477),(42,158,451,73,277,398,108,478,446,194,118,267,133,419,50),(43,452,278,109,447,119,134,51,159,74,399,479,195,268,420),(44,279,448,135,160,400,196,421,453,110,120,52,75,480,269),(45,433,145,197,454,121,76,270,280,136,385,422,111,53,465),(46,146,455,77,281,386,112,466,434,198,122,271,137,423,54),(47,456,282,97,435,123,138,55,147,78,387,467,199,272,424),(48,283,436,139,148,388,200,425,457,98,124,56,79,468,257)], [(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)]])
72 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 5 | 6A | 6B | 6C | 8A | ··· | 8H | 10A | 10B | 10C | 12A | 12B | 12C | 12D | 15A | 15B | 16A | ··· | 16P | 20A | 20B | 20C | 20D | 24A | ··· | 24H | 30A | ··· | 30F | 60A | ··· | 60H |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 5 | 6 | 6 | 6 | 8 | ··· | 8 | 10 | 10 | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 16 | ··· | 16 | 20 | 20 | 20 | 20 | 24 | ··· | 24 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 4 | 2 | 2 | 2 | 5 | ··· | 5 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | 4 | 15 | ··· | 15 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 4 | ··· | 4 | 4 | ··· | 4 |
72 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | - | + | - | + | - | + | - | ||||||||||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | C8 | C16 | S3 | Dic3 | D6 | Dic3 | C3⋊C8 | C3⋊C8 | C3⋊C16 | F5 | C5⋊C8 | C2×F5 | C5⋊C8 | C3⋊F5 | C5⋊C16 | C15⋊C8 | C2×C3⋊F5 | C15⋊C8 | C15⋊C16 |
| kernel | C2×C15⋊C16 | C15⋊C16 | C6×C5⋊2C8 | C3×C5⋊2C8 | C2×C60 | C60 | C2×C30 | C30 | C2×C5⋊2C8 | C5⋊2C8 | C5⋊2C8 | C2×C20 | C20 | C2×C10 | C10 | C2×C12 | C12 | C12 | C2×C6 | C2×C4 | C6 | C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 4 | 4 | 16 | 1 | 1 | 1 | 1 | 2 | 2 | 8 | 1 | 1 | 1 | 1 | 2 | 4 | 2 | 2 | 2 | 8 |
Matrix representation of C2×C15⋊C16 ►in GL6(𝔽241)
| 240 | 0 | 0 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 240 | 0 | 0 | 0 | 0 |
| 1 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 240 | 240 | 240 | 240 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 186 | 73 | 0 | 0 | 0 | 0 |
| 18 | 55 | 0 | 0 | 0 | 0 |
| 0 | 0 | 71 | 160 | 96 | 18 |
| 0 | 0 | 163 | 145 | 216 | 64 |
| 0 | 0 | 89 | 25 | 188 | 170 |
| 0 | 0 | 223 | 53 | 142 | 78 |
G:=sub<GL(6,GF(241))| [240,0,0,0,0,0,0,240,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,240,240,0,0,0,0,0,0,0,240,1,0,0,0,0,240,0,1,0,0,0,240,0,0,0,0,1,240,0,0],[186,18,0,0,0,0,73,55,0,0,0,0,0,0,71,163,89,223,0,0,160,145,25,53,0,0,96,216,188,142,0,0,18,64,170,78] >;
C2×C15⋊C16 in GAP, Magma, Sage, TeX
C_2\times C_{15}\rtimes C_{16} % in TeX
G:=Group("C2xC15:C16"); // GroupNames label
G:=SmallGroup(480,302);
// by ID
G=gap.SmallGroup(480,302);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,28,58,80,2693,14118,4724]);
// Polycyclic
G:=Group<a,b,c|a^2=b^15=c^16=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^2>;
// generators/relations
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