direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C15⋊3C16, C30⋊3C16, C60.9C8, C8.21D30, C40.72D6, C120.13C4, C24.77D10, C24.4Dic5, C8.4Dic15, C40.8Dic3, C120.90C22, C6⋊(C5⋊2C16), C10⋊2(C3⋊C16), C15⋊13(C2×C16), C20.6(C3⋊C8), (C2×C30).6C8, (C2×C40).9S3, (C2×C8).9D15, C30.60(C2×C8), (C2×C60).40C4, (C2×C24).12D5, C4.3(C15⋊3C8), C12.3(C5⋊2C8), C60.234(C2×C4), (C2×C120).16C2, (C2×C4).8Dic15, C4.9(C2×Dic15), C12.39(C2×Dic5), C20.60(C2×Dic3), (C2×C12).11Dic5, (C2×C20).22Dic3, C22.2(C15⋊3C8), C5⋊4(C2×C3⋊C16), C3⋊2(C2×C5⋊2C16), C10.17(C2×C3⋊C8), C6.8(C2×C5⋊2C8), C2.2(C2×C15⋊3C8), (C2×C10).4(C3⋊C8), (C2×C6).2(C5⋊2C8), SmallGroup(480,171)
Series: Derived ►Chief ►Lower central ►Upper central
| C15 — C2×C15⋊3C16 |
Generators and relations for C2×C15⋊3C16
G = < a,b,c | a2=b15=c16=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×C15⋊3C16
►Regular action on 480 points
Generators in S480
(1 45)(2 46)(3 47)(4 48)(5 33)(6 34)(7 35)(8 36)(9 37)(10 38)(11 39)(12 40)(13 41)(14 42)(15 43)(16 44)(17 450)(18 451)(19 452)(20 453)(21 454)(22 455)(23 456)(24 457)(25 458)(26 459)(27 460)(28 461)(29 462)(30 463)(31 464)(32 449)(49 220)(50 221)(51 222)(52 223)(53 224)(54 209)(55 210)(56 211)(57 212)(58 213)(59 214)(60 215)(61 216)(62 217)(63 218)(64 219)(65 400)(66 385)(67 386)(68 387)(69 388)(70 389)(71 390)(72 391)(73 392)(74 393)(75 394)(76 395)(77 396)(78 397)(79 398)(80 399)(81 379)(82 380)(83 381)(84 382)(85 383)(86 384)(87 369)(88 370)(89 371)(90 372)(91 373)(92 374)(93 375)(94 376)(95 377)(96 378)(97 341)(98 342)(99 343)(100 344)(101 345)(102 346)(103 347)(104 348)(105 349)(106 350)(107 351)(108 352)(109 337)(110 338)(111 339)(112 340)(113 192)(114 177)(115 178)(116 179)(117 180)(118 181)(119 182)(120 183)(121 184)(122 185)(123 186)(124 187)(125 188)(126 189)(127 190)(128 191)(129 273)(130 274)(131 275)(132 276)(133 277)(134 278)(135 279)(136 280)(137 281)(138 282)(139 283)(140 284)(141 285)(142 286)(143 287)(144 288)(145 362)(146 363)(147 364)(148 365)(149 366)(150 367)(151 368)(152 353)(153 354)(154 355)(155 356)(156 357)(157 358)(158 359)(159 360)(160 361)(161 271)(162 272)(163 257)(164 258)(165 259)(166 260)(167 261)(168 262)(169 263)(170 264)(171 265)(172 266)(173 267)(174 268)(175 269)(176 270)(193 256)(194 241)(195 242)(196 243)(197 244)(198 245)(199 246)(200 247)(201 248)(202 249)(203 250)(204 251)(205 252)(206 253)(207 254)(208 255)(225 328)(226 329)(227 330)(228 331)(229 332)(230 333)(231 334)(232 335)(233 336)(234 321)(235 322)(236 323)(237 324)(238 325)(239 326)(240 327)(289 477)(290 478)(291 479)(292 480)(293 465)(294 466)(295 467)(296 468)(297 469)(298 470)(299 471)(300 472)(301 473)(302 474)(303 475)(304 476)(305 429)(306 430)(307 431)(308 432)(309 417)(310 418)(311 419)(312 420)(313 421)(314 422)(315 423)(316 424)(317 425)(318 426)(319 427)(320 428)(401 440)(402 441)(403 442)(404 443)(405 444)(406 445)(407 446)(408 447)(409 448)(410 433)(411 434)(412 435)(413 436)(414 437)(415 438)(416 439)
(1 281 181 295 306 324 110 261 85 21 246 71 412 367 52)(2 53 368 413 72 247 22 86 262 111 325 307 296 182 282)(3 283 183 297 308 326 112 263 87 23 248 73 414 353 54)(4 55 354 415 74 249 24 88 264 97 327 309 298 184 284)(5 285 185 299 310 328 98 265 89 25 250 75 416 355 56)(6 57 356 401 76 251 26 90 266 99 329 311 300 186 286)(7 287 187 301 312 330 100 267 91 27 252 77 402 357 58)(8 59 358 403 78 253 28 92 268 101 331 313 302 188 288)(9 273 189 303 314 332 102 269 93 29 254 79 404 359 60)(10 61 360 405 80 255 30 94 270 103 333 315 304 190 274)(11 275 191 289 316 334 104 271 95 31 256 65 406 361 62)(12 63 362 407 66 241 32 96 272 105 335 317 290 192 276)(13 277 177 291 318 336 106 257 81 17 242 67 408 363 64)(14 49 364 409 68 243 18 82 258 107 321 319 292 178 278)(15 279 179 293 320 322 108 259 83 19 244 69 410 365 50)(16 51 366 411 70 245 20 84 260 109 323 305 294 180 280)(33 141 122 471 418 225 342 171 371 458 203 394 439 154 211)(34 212 155 440 395 204 459 372 172 343 226 419 472 123 142)(35 143 124 473 420 227 344 173 373 460 205 396 441 156 213)(36 214 157 442 397 206 461 374 174 345 228 421 474 125 144)(37 129 126 475 422 229 346 175 375 462 207 398 443 158 215)(38 216 159 444 399 208 463 376 176 347 230 423 476 127 130)(39 131 128 477 424 231 348 161 377 464 193 400 445 160 217)(40 218 145 446 385 194 449 378 162 349 232 425 478 113 132)(41 133 114 479 426 233 350 163 379 450 195 386 447 146 219)(42 220 147 448 387 196 451 380 164 351 234 427 480 115 134)(43 135 116 465 428 235 352 165 381 452 197 388 433 148 221)(44 222 149 434 389 198 453 382 166 337 236 429 466 117 136)(45 137 118 467 430 237 338 167 383 454 199 390 435 150 223)(46 224 151 436 391 200 455 384 168 339 238 431 468 119 138)(47 139 120 469 432 239 340 169 369 456 201 392 437 152 209)(48 210 153 438 393 202 457 370 170 341 240 417 470 121 140)
(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)| (1,45)(2,46)(3,47)(4,48)(5,33)(6,34)(7,35)(8,36)(9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,450)(18,451)(19,452)(20,453)(21,454)(22,455)(23,456)(24,457)(25,458)(26,459)(27,460)(28,461)(29,462)(30,463)(31,464)(32,449)(49,220)(50,221)(51,222)(52,223)(53,224)(54,209)(55,210)(56,211)(57,212)(58,213)(59,214)(60,215)(61,216)(62,217)(63,218)(64,219)(65,400)(66,385)(67,386)(68,387)(69,388)(70,389)(71,390)(72,391)(73,392)(74,393)(75,394)(76,395)(77,396)(78,397)(79,398)(80,399)(81,379)(82,380)(83,381)(84,382)(85,383)(86,384)(87,369)(88,370)(89,371)(90,372)(91,373)(92,374)(93,375)(94,376)(95,377)(96,378)(97,341)(98,342)(99,343)(100,344)(101,345)(102,346)(103,347)(104,348)(105,349)(106,350)(107,351)(108,352)(109,337)(110,338)(111,339)(112,340)(113,192)(114,177)(115,178)(116,179)(117,180)(118,181)(119,182)(120,183)(121,184)(122,185)(123,186)(124,187)(125,188)(126,189)(127,190)(128,191)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)(145,362)(146,363)(147,364)(148,365)(149,366)(150,367)(151,368)(152,353)(153,354)(154,355)(155,356)(156,357)(157,358)(158,359)(159,360)(160,361)(161,271)(162,272)(163,257)(164,258)(165,259)(166,260)(167,261)(168,262)(169,263)(170,264)(171,265)(172,266)(173,267)(174,268)(175,269)(176,270)(193,256)(194,241)(195,242)(196,243)(197,244)(198,245)(199,246)(200,247)(201,248)(202,249)(203,250)(204,251)(205,252)(206,253)(207,254)(208,255)(225,328)(226,329)(227,330)(228,331)(229,332)(230,333)(231,334)(232,335)(233,336)(234,321)(235,322)(236,323)(237,324)(238,325)(239,326)(240,327)(289,477)(290,478)(291,479)(292,480)(293,465)(294,466)(295,467)(296,468)(297,469)(298,470)(299,471)(300,472)(301,473)(302,474)(303,475)(304,476)(305,429)(306,430)(307,431)(308,432)(309,417)(310,418)(311,419)(312,420)(313,421)(314,422)(315,423)(316,424)(317,425)(318,426)(319,427)(320,428)(401,440)(402,441)(403,442)(404,443)(405,444)(406,445)(407,446)(408,447)(409,448)(410,433)(411,434)(412,435)(413,436)(414,437)(415,438)(416,439), (1,281,181,295,306,324,110,261,85,21,246,71,412,367,52)(2,53,368,413,72,247,22,86,262,111,325,307,296,182,282)(3,283,183,297,308,326,112,263,87,23,248,73,414,353,54)(4,55,354,415,74,249,24,88,264,97,327,309,298,184,284)(5,285,185,299,310,328,98,265,89,25,250,75,416,355,56)(6,57,356,401,76,251,26,90,266,99,329,311,300,186,286)(7,287,187,301,312,330,100,267,91,27,252,77,402,357,58)(8,59,358,403,78,253,28,92,268,101,331,313,302,188,288)(9,273,189,303,314,332,102,269,93,29,254,79,404,359,60)(10,61,360,405,80,255,30,94,270,103,333,315,304,190,274)(11,275,191,289,316,334,104,271,95,31,256,65,406,361,62)(12,63,362,407,66,241,32,96,272,105,335,317,290,192,276)(13,277,177,291,318,336,106,257,81,17,242,67,408,363,64)(14,49,364,409,68,243,18,82,258,107,321,319,292,178,278)(15,279,179,293,320,322,108,259,83,19,244,69,410,365,50)(16,51,366,411,70,245,20,84,260,109,323,305,294,180,280)(33,141,122,471,418,225,342,171,371,458,203,394,439,154,211)(34,212,155,440,395,204,459,372,172,343,226,419,472,123,142)(35,143,124,473,420,227,344,173,373,460,205,396,441,156,213)(36,214,157,442,397,206,461,374,174,345,228,421,474,125,144)(37,129,126,475,422,229,346,175,375,462,207,398,443,158,215)(38,216,159,444,399,208,463,376,176,347,230,423,476,127,130)(39,131,128,477,424,231,348,161,377,464,193,400,445,160,217)(40,218,145,446,385,194,449,378,162,349,232,425,478,113,132)(41,133,114,479,426,233,350,163,379,450,195,386,447,146,219)(42,220,147,448,387,196,451,380,164,351,234,427,480,115,134)(43,135,116,465,428,235,352,165,381,452,197,388,433,148,221)(44,222,149,434,389,198,453,382,166,337,236,429,466,117,136)(45,137,118,467,430,237,338,167,383,454,199,390,435,150,223)(46,224,151,436,391,200,455,384,168,339,238,431,468,119,138)(47,139,120,469,432,239,340,169,369,456,201,392,437,152,209)(48,210,153,438,393,202,457,370,170,341,240,417,470,121,140), (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( (1,45)(2,46)(3,47)(4,48)(5,33)(6,34)(7,35)(8,36)(9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,450)(18,451)(19,452)(20,453)(21,454)(22,455)(23,456)(24,457)(25,458)(26,459)(27,460)(28,461)(29,462)(30,463)(31,464)(32,449)(49,220)(50,221)(51,222)(52,223)(53,224)(54,209)(55,210)(56,211)(57,212)(58,213)(59,214)(60,215)(61,216)(62,217)(63,218)(64,219)(65,400)(66,385)(67,386)(68,387)(69,388)(70,389)(71,390)(72,391)(73,392)(74,393)(75,394)(76,395)(77,396)(78,397)(79,398)(80,399)(81,379)(82,380)(83,381)(84,382)(85,383)(86,384)(87,369)(88,370)(89,371)(90,372)(91,373)(92,374)(93,375)(94,376)(95,377)(96,378)(97,341)(98,342)(99,343)(100,344)(101,345)(102,346)(103,347)(104,348)(105,349)(106,350)(107,351)(108,352)(109,337)(110,338)(111,339)(112,340)(113,192)(114,177)(115,178)(116,179)(117,180)(118,181)(119,182)(120,183)(121,184)(122,185)(123,186)(124,187)(125,188)(126,189)(127,190)(128,191)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)(145,362)(146,363)(147,364)(148,365)(149,366)(150,367)(151,368)(152,353)(153,354)(154,355)(155,356)(156,357)(157,358)(158,359)(159,360)(160,361)(161,271)(162,272)(163,257)(164,258)(165,259)(166,260)(167,261)(168,262)(169,263)(170,264)(171,265)(172,266)(173,267)(174,268)(175,269)(176,270)(193,256)(194,241)(195,242)(196,243)(197,244)(198,245)(199,246)(200,247)(201,248)(202,249)(203,250)(204,251)(205,252)(206,253)(207,254)(208,255)(225,328)(226,329)(227,330)(228,331)(229,332)(230,333)(231,334)(232,335)(233,336)(234,321)(235,322)(236,323)(237,324)(238,325)(239,326)(240,327)(289,477)(290,478)(291,479)(292,480)(293,465)(294,466)(295,467)(296,468)(297,469)(298,470)(299,471)(300,472)(301,473)(302,474)(303,475)(304,476)(305,429)(306,430)(307,431)(308,432)(309,417)(310,418)(311,419)(312,420)(313,421)(314,422)(315,423)(316,424)(317,425)(318,426)(319,427)(320,428)(401,440)(402,441)(403,442)(404,443)(405,444)(406,445)(407,446)(408,447)(409,448)(410,433)(411,434)(412,435)(413,436)(414,437)(415,438)(416,439), (1,281,181,295,306,324,110,261,85,21,246,71,412,367,52)(2,53,368,413,72,247,22,86,262,111,325,307,296,182,282)(3,283,183,297,308,326,112,263,87,23,248,73,414,353,54)(4,55,354,415,74,249,24,88,264,97,327,309,298,184,284)(5,285,185,299,310,328,98,265,89,25,250,75,416,355,56)(6,57,356,401,76,251,26,90,266,99,329,311,300,186,286)(7,287,187,301,312,330,100,267,91,27,252,77,402,357,58)(8,59,358,403,78,253,28,92,268,101,331,313,302,188,288)(9,273,189,303,314,332,102,269,93,29,254,79,404,359,60)(10,61,360,405,80,255,30,94,270,103,333,315,304,190,274)(11,275,191,289,316,334,104,271,95,31,256,65,406,361,62)(12,63,362,407,66,241,32,96,272,105,335,317,290,192,276)(13,277,177,291,318,336,106,257,81,17,242,67,408,363,64)(14,49,364,409,68,243,18,82,258,107,321,319,292,178,278)(15,279,179,293,320,322,108,259,83,19,244,69,410,365,50)(16,51,366,411,70,245,20,84,260,109,323,305,294,180,280)(33,141,122,471,418,225,342,171,371,458,203,394,439,154,211)(34,212,155,440,395,204,459,372,172,343,226,419,472,123,142)(35,143,124,473,420,227,344,173,373,460,205,396,441,156,213)(36,214,157,442,397,206,461,374,174,345,228,421,474,125,144)(37,129,126,475,422,229,346,175,375,462,207,398,443,158,215)(38,216,159,444,399,208,463,376,176,347,230,423,476,127,130)(39,131,128,477,424,231,348,161,377,464,193,400,445,160,217)(40,218,145,446,385,194,449,378,162,349,232,425,478,113,132)(41,133,114,479,426,233,350,163,379,450,195,386,447,146,219)(42,220,147,448,387,196,451,380,164,351,234,427,480,115,134)(43,135,116,465,428,235,352,165,381,452,197,388,433,148,221)(44,222,149,434,389,198,453,382,166,337,236,429,466,117,136)(45,137,118,467,430,237,338,167,383,454,199,390,435,150,223)(46,224,151,436,391,200,455,384,168,339,238,431,468,119,138)(47,139,120,469,432,239,340,169,369,456,201,392,437,152,209)(48,210,153,438,393,202,457,370,170,341,240,417,470,121,140), (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([[(1,45),(2,46),(3,47),(4,48),(5,33),(6,34),(7,35),(8,36),(9,37),(10,38),(11,39),(12,40),(13,41),(14,42),(15,43),(16,44),(17,450),(18,451),(19,452),(20,453),(21,454),(22,455),(23,456),(24,457),(25,458),(26,459),(27,460),(28,461),(29,462),(30,463),(31,464),(32,449),(49,220),(50,221),(51,222),(52,223),(53,224),(54,209),(55,210),(56,211),(57,212),(58,213),(59,214),(60,215),(61,216),(62,217),(63,218),(64,219),(65,400),(66,385),(67,386),(68,387),(69,388),(70,389),(71,390),(72,391),(73,392),(74,393),(75,394),(76,395),(77,396),(78,397),(79,398),(80,399),(81,379),(82,380),(83,381),(84,382),(85,383),(86,384),(87,369),(88,370),(89,371),(90,372),(91,373),(92,374),(93,375),(94,376),(95,377),(96,378),(97,341),(98,342),(99,343),(100,344),(101,345),(102,346),(103,347),(104,348),(105,349),(106,350),(107,351),(108,352),(109,337),(110,338),(111,339),(112,340),(113,192),(114,177),(115,178),(116,179),(117,180),(118,181),(119,182),(120,183),(121,184),(122,185),(123,186),(124,187),(125,188),(126,189),(127,190),(128,191),(129,273),(130,274),(131,275),(132,276),(133,277),(134,278),(135,279),(136,280),(137,281),(138,282),(139,283),(140,284),(141,285),(142,286),(143,287),(144,288),(145,362),(146,363),(147,364),(148,365),(149,366),(150,367),(151,368),(152,353),(153,354),(154,355),(155,356),(156,357),(157,358),(158,359),(159,360),(160,361),(161,271),(162,272),(163,257),(164,258),(165,259),(166,260),(167,261),(168,262),(169,263),(170,264),(171,265),(172,266),(173,267),(174,268),(175,269),(176,270),(193,256),(194,241),(195,242),(196,243),(197,244),(198,245),(199,246),(200,247),(201,248),(202,249),(203,250),(204,251),(205,252),(206,253),(207,254),(208,255),(225,328),(226,329),(227,330),(228,331),(229,332),(230,333),(231,334),(232,335),(233,336),(234,321),(235,322),(236,323),(237,324),(238,325),(239,326),(240,327),(289,477),(290,478),(291,479),(292,480),(293,465),(294,466),(295,467),(296,468),(297,469),(298,470),(299,471),(300,472),(301,473),(302,474),(303,475),(304,476),(305,429),(306,430),(307,431),(308,432),(309,417),(310,418),(311,419),(312,420),(313,421),(314,422),(315,423),(316,424),(317,425),(318,426),(319,427),(320,428),(401,440),(402,441),(403,442),(404,443),(405,444),(406,445),(407,446),(408,447),(409,448),(410,433),(411,434),(412,435),(413,436),(414,437),(415,438),(416,439)], [(1,281,181,295,306,324,110,261,85,21,246,71,412,367,52),(2,53,368,413,72,247,22,86,262,111,325,307,296,182,282),(3,283,183,297,308,326,112,263,87,23,248,73,414,353,54),(4,55,354,415,74,249,24,88,264,97,327,309,298,184,284),(5,285,185,299,310,328,98,265,89,25,250,75,416,355,56),(6,57,356,401,76,251,26,90,266,99,329,311,300,186,286),(7,287,187,301,312,330,100,267,91,27,252,77,402,357,58),(8,59,358,403,78,253,28,92,268,101,331,313,302,188,288),(9,273,189,303,314,332,102,269,93,29,254,79,404,359,60),(10,61,360,405,80,255,30,94,270,103,333,315,304,190,274),(11,275,191,289,316,334,104,271,95,31,256,65,406,361,62),(12,63,362,407,66,241,32,96,272,105,335,317,290,192,276),(13,277,177,291,318,336,106,257,81,17,242,67,408,363,64),(14,49,364,409,68,243,18,82,258,107,321,319,292,178,278),(15,279,179,293,320,322,108,259,83,19,244,69,410,365,50),(16,51,366,411,70,245,20,84,260,109,323,305,294,180,280),(33,141,122,471,418,225,342,171,371,458,203,394,439,154,211),(34,212,155,440,395,204,459,372,172,343,226,419,472,123,142),(35,143,124,473,420,227,344,173,373,460,205,396,441,156,213),(36,214,157,442,397,206,461,374,174,345,228,421,474,125,144),(37,129,126,475,422,229,346,175,375,462,207,398,443,158,215),(38,216,159,444,399,208,463,376,176,347,230,423,476,127,130),(39,131,128,477,424,231,348,161,377,464,193,400,445,160,217),(40,218,145,446,385,194,449,378,162,349,232,425,478,113,132),(41,133,114,479,426,233,350,163,379,450,195,386,447,146,219),(42,220,147,448,387,196,451,380,164,351,234,427,480,115,134),(43,135,116,465,428,235,352,165,381,452,197,388,433,148,221),(44,222,149,434,389,198,453,382,166,337,236,429,466,117,136),(45,137,118,467,430,237,338,167,383,454,199,390,435,150,223),(46,224,151,436,391,200,455,384,168,339,238,431,468,119,138),(47,139,120,469,432,239,340,169,369,456,201,392,437,152,209),(48,210,153,438,393,202,457,370,170,341,240,417,470,121,140)], [(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)]])
144 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 5A | 5B | 6A | 6B | 6C | 8A | ··· | 8H | 10A | ··· | 10F | 12A | 12B | 12C | 12D | 15A | 15B | 15C | 15D | 16A | ··· | 16P | 20A | ··· | 20H | 24A | ··· | 24H | 30A | ··· | 30L | 40A | ··· | 40P | 60A | ··· | 60P | 120A | ··· | 120AF |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 8 | ··· | 8 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 15 | 15 | 16 | ··· | 16 | 20 | ··· | 20 | 24 | ··· | 24 | 30 | ··· | 30 | 40 | ··· | 40 | 60 | ··· | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 15 | ··· | 15 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
144 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | - | - | + | - | + | - | + | - | ||||||||||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | C8 | C16 | S3 | D5 | Dic3 | D6 | Dic3 | Dic5 | D10 | Dic5 | C3⋊C8 | C3⋊C8 | D15 | C5⋊2C8 | C5⋊2C8 | C3⋊C16 | Dic15 | D30 | Dic15 | C5⋊2C16 | C15⋊3C8 | C15⋊3C8 | C15⋊3C16 |
| kernel | C2×C15⋊3C16 | C15⋊3C16 | C2×C120 | C120 | C2×C60 | C60 | C2×C30 | C30 | C2×C40 | C2×C24 | C40 | C40 | C2×C20 | C24 | C24 | C2×C12 | C20 | C2×C10 | C2×C8 | C12 | C2×C6 | C10 | C8 | C8 | C2×C4 | C6 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 4 | 4 | 16 | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 8 | 4 | 4 | 4 | 16 | 8 | 8 | 32 |
Matrix representation of C2×C15⋊3C16 ►in GL5(𝔽241)
| 240 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 52 | 52 | 0 | 0 |
| 0 | 189 | 240 | 0 | 0 |
| 0 | 0 | 0 | 225 | 131 |
| 0 | 0 | 0 | 46 | 30 |
| 76 | 0 | 0 | 0 | 0 |
| 0 | 60 | 11 | 0 | 0 |
| 0 | 24 | 181 | 0 | 0 |
| 0 | 0 | 0 | 43 | 62 |
| 0 | 0 | 0 | 43 | 198 |
G:=sub<GL(5,GF(241))| [240,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,52,189,0,0,0,52,240,0,0,0,0,0,225,46,0,0,0,131,30],[76,0,0,0,0,0,60,24,0,0,0,11,181,0,0,0,0,0,43,43,0,0,0,62,198] >;
C2×C15⋊3C16 in GAP, Magma, Sage, TeX
C_2\times C_{15}\rtimes_3C_{16} % in TeX
G:=Group("C2xC15:3C16"); // GroupNames label
G:=SmallGroup(480,171);
// by ID
G=gap.SmallGroup(480,171);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,28,58,80,2693,18822]);
// 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^-1>;
// generators/relations
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