Copied to
clipboard

G = C15⋊Q32order 480 = 25·3·5

1st semidirect product of C15 and Q32 acting via Q32/C8=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C151Q32, C60.75D4, C30.10D8, C40.10D6, C24.10D10, Dic12.2D5, Dic20.2S3, C120.35C22, C8.28(S3×D5), C32(C5⋊Q32), C52(C3⋊Q32), C153C16.2C2, C6.11(D4⋊D5), C4.4(C15⋊D4), C2.7(C15⋊D8), C12.4(C5⋊D4), C20.4(C3⋊D4), C10.11(D4⋊S3), (C5×Dic12).2C2, (C3×Dic20).3C2, SmallGroup(480,22)

Series: Derived Chief Lower central Upper central

C1C120 — C15⋊Q32
C1C5C15C30C60C120C3×Dic20 — C15⋊Q32
C15C30C60C120 — C15⋊Q32
C1C2C4C8

Generators and relations for C15⋊Q32
 G = < a,b,c | a15=b16=1, c2=b8, bab-1=a-1, cac-1=a11, cbc-1=b-1 >

12C4
20C4
6Q8
10Q8
4Dic3
20C12
4Dic5
12C20
3Q16
5Q16
15C16
2Dic6
10C3×Q8
2Dic10
6C5×Q8
4C5×Dic3
4C3×Dic5
15Q32
5C3×Q16
5C3⋊C16
3C52C16
3C5×Q16
2C3×Dic10
2C5×Dic6
5C3⋊Q32
3C5⋊Q32

Smallest permutation representation of C15⋊Q32
Regular action on 480 points
Generators in S480
(1 94 148 29 277 408 125 141 328 368 197 395 71 214 308)(2 309 215 72 396 198 353 329 142 126 409 278 30 149 95)(3 96 150 31 279 410 127 143 330 354 199 397 73 216 310)(4 311 217 74 398 200 355 331 144 128 411 280 32 151 81)(5 82 152 17 281 412 113 129 332 356 201 399 75 218 312)(6 313 219 76 400 202 357 333 130 114 413 282 18 153 83)(7 84 154 19 283 414 115 131 334 358 203 385 77 220 314)(8 315 221 78 386 204 359 335 132 116 415 284 20 155 85)(9 86 156 21 285 416 117 133 336 360 205 387 79 222 316)(10 317 223 80 388 206 361 321 134 118 401 286 22 157 87)(11 88 158 23 287 402 119 135 322 362 207 389 65 224 318)(12 319 209 66 390 208 363 323 136 120 403 288 24 159 89)(13 90 160 25 273 404 121 137 324 364 193 391 67 210 320)(14 305 211 68 392 194 365 325 138 122 405 274 26 145 91)(15 92 146 27 275 406 123 139 326 366 195 393 69 212 306)(16 307 213 70 394 196 367 327 140 124 407 276 28 147 93)(33 106 169 183 293 462 233 350 379 50 247 265 438 477 430)(34 431 478 439 266 248 51 380 351 234 463 294 184 170 107)(35 108 171 185 295 464 235 352 381 52 249 267 440 479 432)(36 417 480 441 268 250 53 382 337 236 449 296 186 172 109)(37 110 173 187 297 450 237 338 383 54 251 269 442 465 418)(38 419 466 443 270 252 55 384 339 238 451 298 188 174 111)(39 112 175 189 299 452 239 340 369 56 253 271 444 467 420)(40 421 468 445 272 254 57 370 341 240 453 300 190 176 97)(41 98 161 191 301 454 225 342 371 58 255 257 446 469 422)(42 423 470 447 258 256 59 372 343 226 455 302 192 162 99)(43 100 163 177 303 456 227 344 373 60 241 259 448 471 424)(44 425 472 433 260 242 61 374 345 228 457 304 178 164 101)(45 102 165 179 289 458 229 346 375 62 243 261 434 473 426)(46 427 474 435 262 244 63 376 347 230 459 290 180 166 103)(47 104 167 181 291 460 231 348 377 64 245 263 436 475 428)(48 429 476 437 264 246 49 378 349 232 461 292 182 168 105)
(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)
(1 440 9 448)(2 439 10 447)(3 438 11 446)(4 437 12 445)(5 436 13 444)(6 435 14 443)(7 434 15 442)(8 433 16 441)(17 47 25 39)(18 46 26 38)(19 45 27 37)(20 44 28 36)(21 43 29 35)(22 42 30 34)(23 41 31 33)(24 40 32 48)(49 66 57 74)(50 65 58 73)(51 80 59 72)(52 79 60 71)(53 78 61 70)(54 77 62 69)(55 76 63 68)(56 75 64 67)(81 378 89 370)(82 377 90 369)(83 376 91 384)(84 375 92 383)(85 374 93 382)(86 373 94 381)(87 372 95 380)(88 371 96 379)(97 311 105 319)(98 310 106 318)(99 309 107 317)(100 308 108 316)(101 307 109 315)(102 306 110 314)(103 305 111 313)(104 320 112 312)(113 181 121 189)(114 180 122 188)(115 179 123 187)(116 178 124 186)(117 177 125 185)(118 192 126 184)(119 191 127 183)(120 190 128 182)(129 428 137 420)(130 427 138 419)(131 426 139 418)(132 425 140 417)(133 424 141 432)(134 423 142 431)(135 422 143 430)(136 421 144 429)(145 298 153 290)(146 297 154 289)(147 296 155 304)(148 295 156 303)(149 294 157 302)(150 293 158 301)(151 292 159 300)(152 291 160 299)(161 199 169 207)(162 198 170 206)(163 197 171 205)(164 196 172 204)(165 195 173 203)(166 194 174 202)(167 193 175 201)(168 208 176 200)(209 453 217 461)(210 452 218 460)(211 451 219 459)(212 450 220 458)(213 449 221 457)(214 464 222 456)(215 463 223 455)(216 462 224 454)(225 354 233 362)(226 353 234 361)(227 368 235 360)(228 367 236 359)(229 366 237 358)(230 365 238 357)(231 364 239 356)(232 363 240 355)(241 328 249 336)(242 327 250 335)(243 326 251 334)(244 325 252 333)(245 324 253 332)(246 323 254 331)(247 322 255 330)(248 321 256 329)(257 279 265 287)(258 278 266 286)(259 277 267 285)(260 276 268 284)(261 275 269 283)(262 274 270 282)(263 273 271 281)(264 288 272 280)(337 415 345 407)(338 414 346 406)(339 413 347 405)(340 412 348 404)(341 411 349 403)(342 410 350 402)(343 409 351 401)(344 408 352 416)(385 473 393 465)(386 472 394 480)(387 471 395 479)(388 470 396 478)(389 469 397 477)(390 468 398 476)(391 467 399 475)(392 466 400 474)

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

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

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

48 conjugacy classes

class 1  2  3 4A4B4C5A5B 6 8A8B10A10B12A12B12C15A15B16A16B16C16D20A20B20C20D20E20F24A24B30A30B40A40B40C40D60A60B60C60D120A···120H
order123444556881010121212151516161616202020202020242430304040404060606060120···120
size11222440222222244040443030303044242424244444444444444···4

48 irreducible representations

dim111122222222244444444
type++++++++++-+++---
imageC1C2C2C2S3D4D5D6D8D10C3⋊D4Q32C5⋊D4D4⋊S3S3×D5D4⋊D5C3⋊Q32C15⋊D4C5⋊Q32C15⋊D8C15⋊Q32
kernelC15⋊Q32C153C16C3×Dic20C5×Dic12Dic20C60Dic12C40C30C24C20C15C12C10C8C6C5C4C3C2C1
# reps111111212224412222448

Matrix representation of C15⋊Q32 in GL6(𝔽241)

100000
010000
005118900
0051000
00002401
00002400
,
1291700000
156580000
00887900
008515300
0000136232
0000127105
,
173940000
220680000
0016510300
00897600
0000136232
0000127105

G:=sub<GL(6,GF(241))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,51,51,0,0,0,0,189,0,0,0,0,0,0,0,240,240,0,0,0,0,1,0],[129,156,0,0,0,0,170,58,0,0,0,0,0,0,88,85,0,0,0,0,79,153,0,0,0,0,0,0,136,127,0,0,0,0,232,105],[173,220,0,0,0,0,94,68,0,0,0,0,0,0,165,89,0,0,0,0,103,76,0,0,0,0,0,0,136,127,0,0,0,0,232,105] >;

C15⋊Q32 in GAP, Magma, Sage, TeX

C_{15}\rtimes Q_{32}
% in TeX

G:=Group("C15:Q32");
// GroupNames label

G:=SmallGroup(480,22);
// by ID

G=gap.SmallGroup(480,22);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,85,120,254,135,142,675,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c|a^15=b^16=1,c^2=b^8,b*a*b^-1=a^-1,c*a*c^-1=a^11,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C15⋊Q32 in TeX

׿
×
𝔽