direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C15⋊Q16, C30⋊1Q16, C60.86D4, C60.157C23, Dic10.39D6, Dic6.39D10, C15⋊4(C2×Q16), (C2×C30).61D4, C30.93(C2×D4), C6⋊2(C5⋊Q16), C10⋊2(C3⋊Q16), (C2×C20).101D6, C4.8(C15⋊D4), (C2×Dic6).7D5, (C2×C12).102D10, C20.32(C3⋊D4), C12.32(C5⋊D4), C20.98(C22×S3), (C2×Dic10).8S3, (C10×Dic6).7C2, (C6×Dic10).7C2, (C2×C60).190C22, C15⋊3C8.45C22, C12.100(C22×D5), C22.22(C15⋊D4), (C5×Dic6).46C22, (C3×Dic10).46C22, C5⋊3(C2×C3⋊Q16), C3⋊3(C2×C5⋊Q16), C4.130(C2×S3×D5), C6.79(C2×C5⋊D4), (C2×C4).200(S3×D5), C10.80(C2×C3⋊D4), C2.13(C2×C15⋊D4), (C2×C15⋊3C8).15C2, (C2×C6).56(C5⋊D4), (C2×C10).56(C3⋊D4), SmallGroup(480,394)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C15⋊Q16
G = < a,b,c,d | a2=b15=c8=1, d2=c4, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd-1=b11, dcd-1=c-1 >
Subgroups: 444 in 120 conjugacy classes, 52 normal (30 characteristic)
C1, C2, C2, C3, C4, C4, C22, C5, C6, C6, C8, C2×C4, C2×C4, Q8, C10, C10, Dic3, C12, C12, C2×C6, C15, C2×C8, Q16, C2×Q8, Dic5, C20, C20, C2×C10, C3⋊C8, Dic6, Dic6, C2×Dic3, C2×C12, C2×C12, C3×Q8, C30, C30, C2×Q16, C5⋊2C8, Dic10, Dic10, C2×Dic5, C2×C20, C2×C20, C5×Q8, C2×C3⋊C8, C3⋊Q16, C2×Dic6, C6×Q8, C5×Dic3, C3×Dic5, C60, C2×C30, C2×C5⋊2C8, C5⋊Q16, C2×Dic10, Q8×C10, C2×C3⋊Q16, C15⋊3C8, C3×Dic10, C3×Dic10, C6×Dic5, C5×Dic6, C5×Dic6, C10×Dic3, C2×C60, C2×C5⋊Q16, C15⋊Q16, C2×C15⋊3C8, C6×Dic10, C10×Dic6, C2×C15⋊Q16
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, Q16, C2×D4, D10, C3⋊D4, C22×S3, C2×Q16, C5⋊D4, C22×D5, C3⋊Q16, C2×C3⋊D4, S3×D5, C5⋊Q16, C2×C5⋊D4, C2×C3⋊Q16, C15⋊D4, C2×S3×D5, C2×C5⋊Q16, C15⋊Q16, C2×C15⋊D4, C2×C15⋊Q16
►Regular action on 480 points
Generators in S480
(1 62)(2 63)(3 64)(4 65)(5 66)(6 67)(7 68)(8 69)(9 70)(10 71)(11 72)(12 73)(13 74)(14 75)(15 61)(16 90)(17 76)(18 77)(19 78)(20 79)(21 80)(22 81)(23 82)(24 83)(25 84)(26 85)(27 86)(28 87)(29 88)(30 89)(31 100)(32 101)(33 102)(34 103)(35 104)(36 105)(37 91)(38 92)(39 93)(40 94)(41 95)(42 96)(43 97)(44 98)(45 99)(46 115)(47 116)(48 117)(49 118)(50 119)(51 120)(52 106)(53 107)(54 108)(55 109)(56 110)(57 111)(58 112)(59 113)(60 114)(121 194)(122 195)(123 181)(124 182)(125 183)(126 184)(127 185)(128 186)(129 187)(130 188)(131 189)(132 190)(133 191)(134 192)(135 193)(136 202)(137 203)(138 204)(139 205)(140 206)(141 207)(142 208)(143 209)(144 210)(145 196)(146 197)(147 198)(148 199)(149 200)(150 201)(151 217)(152 218)(153 219)(154 220)(155 221)(156 222)(157 223)(158 224)(159 225)(160 211)(161 212)(162 213)(163 214)(164 215)(165 216)(166 235)(167 236)(168 237)(169 238)(170 239)(171 240)(172 226)(173 227)(174 228)(175 229)(176 230)(177 231)(178 232)(179 233)(180 234)(241 312)(242 313)(243 314)(244 315)(245 301)(246 302)(247 303)(248 304)(249 305)(250 306)(251 307)(252 308)(253 309)(254 310)(255 311)(256 326)(257 327)(258 328)(259 329)(260 330)(261 316)(262 317)(263 318)(264 319)(265 320)(266 321)(267 322)(268 323)(269 324)(270 325)(271 345)(272 331)(273 332)(274 333)(275 334)(276 335)(277 336)(278 337)(279 338)(280 339)(281 340)(282 341)(283 342)(284 343)(285 344)(286 349)(287 350)(288 351)(289 352)(290 353)(291 354)(292 355)(293 356)(294 357)(295 358)(296 359)(297 360)(298 346)(299 347)(300 348)(361 428)(362 429)(363 430)(364 431)(365 432)(366 433)(367 434)(368 435)(369 421)(370 422)(371 423)(372 424)(373 425)(374 426)(375 427)(376 436)(377 437)(378 438)(379 439)(380 440)(381 441)(382 442)(383 443)(384 444)(385 445)(386 446)(387 447)(388 448)(389 449)(390 450)(391 465)(392 451)(393 452)(394 453)(395 454)(396 455)(397 456)(398 457)(399 458)(400 459)(401 460)(402 461)(403 462)(404 463)(405 464)(406 466)(407 467)(408 468)(409 469)(410 470)(411 471)(412 472)(413 473)(414 474)(415 475)(416 476)(417 477)(418 478)(419 479)(420 480)
(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)
(1 451 35 437 30 470 50 429)(2 465 36 436 16 469 51 428)(3 464 37 450 17 468 52 427)(4 463 38 449 18 467 53 426)(5 462 39 448 19 466 54 425)(6 461 40 447 20 480 55 424)(7 460 41 446 21 479 56 423)(8 459 42 445 22 478 57 422)(9 458 43 444 23 477 58 421)(10 457 44 443 24 476 59 435)(11 456 45 442 25 475 60 434)(12 455 31 441 26 474 46 433)(13 454 32 440 27 473 47 432)(14 453 33 439 28 472 48 431)(15 452 34 438 29 471 49 430)(61 393 103 378 88 411 118 363)(62 392 104 377 89 410 119 362)(63 391 105 376 90 409 120 361)(64 405 91 390 76 408 106 375)(65 404 92 389 77 407 107 374)(66 403 93 388 78 406 108 373)(67 402 94 387 79 420 109 372)(68 401 95 386 80 419 110 371)(69 400 96 385 81 418 111 370)(70 399 97 384 82 417 112 369)(71 398 98 383 83 416 113 368)(72 397 99 382 84 415 114 367)(73 396 100 381 85 414 115 366)(74 395 101 380 86 413 116 365)(75 394 102 379 87 412 117 364)(121 335 168 305 147 352 160 316)(122 334 169 304 148 351 161 330)(123 333 170 303 149 350 162 329)(124 332 171 302 150 349 163 328)(125 331 172 301 136 348 164 327)(126 345 173 315 137 347 165 326)(127 344 174 314 138 346 151 325)(128 343 175 313 139 360 152 324)(129 342 176 312 140 359 153 323)(130 341 177 311 141 358 154 322)(131 340 178 310 142 357 155 321)(132 339 179 309 143 356 156 320)(133 338 180 308 144 355 157 319)(134 337 166 307 145 354 158 318)(135 336 167 306 146 353 159 317)(181 274 239 247 200 287 213 259)(182 273 240 246 201 286 214 258)(183 272 226 245 202 300 215 257)(184 271 227 244 203 299 216 256)(185 285 228 243 204 298 217 270)(186 284 229 242 205 297 218 269)(187 283 230 241 206 296 219 268)(188 282 231 255 207 295 220 267)(189 281 232 254 208 294 221 266)(190 280 233 253 209 293 222 265)(191 279 234 252 210 292 223 264)(192 278 235 251 196 291 224 263)(193 277 236 250 197 290 225 262)(194 276 237 249 198 289 211 261)(195 275 238 248 199 288 212 260)
(1 145 30 134)(2 141 16 130)(3 137 17 126)(4 148 18 122)(5 144 19 133)(6 140 20 129)(7 136 21 125)(8 147 22 121)(9 143 23 132)(10 139 24 128)(11 150 25 124)(12 146 26 135)(13 142 27 131)(14 138 28 127)(15 149 29 123)(31 167 46 159)(32 178 47 155)(33 174 48 151)(34 170 49 162)(35 166 50 158)(36 177 51 154)(37 173 52 165)(38 169 53 161)(39 180 54 157)(40 176 55 153)(41 172 56 164)(42 168 57 160)(43 179 58 156)(44 175 59 152)(45 171 60 163)(61 200 88 181)(62 196 89 192)(63 207 90 188)(64 203 76 184)(65 199 77 195)(66 210 78 191)(67 206 79 187)(68 202 80 183)(69 198 81 194)(70 209 82 190)(71 205 83 186)(72 201 84 182)(73 197 85 193)(74 208 86 189)(75 204 87 185)(91 227 106 216)(92 238 107 212)(93 234 108 223)(94 230 109 219)(95 226 110 215)(96 237 111 211)(97 233 112 222)(98 229 113 218)(99 240 114 214)(100 236 115 225)(101 232 116 221)(102 228 117 217)(103 239 118 213)(104 235 119 224)(105 231 120 220)(241 420 268 402)(242 416 269 398)(243 412 270 394)(244 408 256 405)(245 419 257 401)(246 415 258 397)(247 411 259 393)(248 407 260 404)(249 418 261 400)(250 414 262 396)(251 410 263 392)(252 406 264 403)(253 417 265 399)(254 413 266 395)(255 409 267 391)(271 375 299 390)(272 371 300 386)(273 367 286 382)(274 363 287 378)(275 374 288 389)(276 370 289 385)(277 366 290 381)(278 362 291 377)(279 373 292 388)(280 369 293 384)(281 365 294 380)(282 361 295 376)(283 372 296 387)(284 368 297 383)(285 364 298 379)(301 479 327 460)(302 475 328 456)(303 471 329 452)(304 467 330 463)(305 478 316 459)(306 474 317 455)(307 470 318 451)(308 466 319 462)(309 477 320 458)(310 473 321 454)(311 469 322 465)(312 480 323 461)(313 476 324 457)(314 472 325 453)(315 468 326 464)(331 423 348 446)(332 434 349 442)(333 430 350 438)(334 426 351 449)(335 422 352 445)(336 433 353 441)(337 429 354 437)(338 425 355 448)(339 421 356 444)(340 432 357 440)(341 428 358 436)(342 424 359 447)(343 435 360 443)(344 431 346 439)(345 427 347 450)
G:=sub<Sym(480)| (1,62)(2,63)(3,64)(4,65)(5,66)(6,67)(7,68)(8,69)(9,70)(10,71)(11,72)(12,73)(13,74)(14,75)(15,61)(16,90)(17,76)(18,77)(19,78)(20,79)(21,80)(22,81)(23,82)(24,83)(25,84)(26,85)(27,86)(28,87)(29,88)(30,89)(31,100)(32,101)(33,102)(34,103)(35,104)(36,105)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,115)(47,116)(48,117)(49,118)(50,119)(51,120)(52,106)(53,107)(54,108)(55,109)(56,110)(57,111)(58,112)(59,113)(60,114)(121,194)(122,195)(123,181)(124,182)(125,183)(126,184)(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)(136,202)(137,203)(138,204)(139,205)(140,206)(141,207)(142,208)(143,209)(144,210)(145,196)(146,197)(147,198)(148,199)(149,200)(150,201)(151,217)(152,218)(153,219)(154,220)(155,221)(156,222)(157,223)(158,224)(159,225)(160,211)(161,212)(162,213)(163,214)(164,215)(165,216)(166,235)(167,236)(168,237)(169,238)(170,239)(171,240)(172,226)(173,227)(174,228)(175,229)(176,230)(177,231)(178,232)(179,233)(180,234)(241,312)(242,313)(243,314)(244,315)(245,301)(246,302)(247,303)(248,304)(249,305)(250,306)(251,307)(252,308)(253,309)(254,310)(255,311)(256,326)(257,327)(258,328)(259,329)(260,330)(261,316)(262,317)(263,318)(264,319)(265,320)(266,321)(267,322)(268,323)(269,324)(270,325)(271,345)(272,331)(273,332)(274,333)(275,334)(276,335)(277,336)(278,337)(279,338)(280,339)(281,340)(282,341)(283,342)(284,343)(285,344)(286,349)(287,350)(288,351)(289,352)(290,353)(291,354)(292,355)(293,356)(294,357)(295,358)(296,359)(297,360)(298,346)(299,347)(300,348)(361,428)(362,429)(363,430)(364,431)(365,432)(366,433)(367,434)(368,435)(369,421)(370,422)(371,423)(372,424)(373,425)(374,426)(375,427)(376,436)(377,437)(378,438)(379,439)(380,440)(381,441)(382,442)(383,443)(384,444)(385,445)(386,446)(387,447)(388,448)(389,449)(390,450)(391,465)(392,451)(393,452)(394,453)(395,454)(396,455)(397,456)(398,457)(399,458)(400,459)(401,460)(402,461)(403,462)(404,463)(405,464)(406,466)(407,467)(408,468)(409,469)(410,470)(411,471)(412,472)(413,473)(414,474)(415,475)(416,476)(417,477)(418,478)(419,479)(420,480), (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), (1,451,35,437,30,470,50,429)(2,465,36,436,16,469,51,428)(3,464,37,450,17,468,52,427)(4,463,38,449,18,467,53,426)(5,462,39,448,19,466,54,425)(6,461,40,447,20,480,55,424)(7,460,41,446,21,479,56,423)(8,459,42,445,22,478,57,422)(9,458,43,444,23,477,58,421)(10,457,44,443,24,476,59,435)(11,456,45,442,25,475,60,434)(12,455,31,441,26,474,46,433)(13,454,32,440,27,473,47,432)(14,453,33,439,28,472,48,431)(15,452,34,438,29,471,49,430)(61,393,103,378,88,411,118,363)(62,392,104,377,89,410,119,362)(63,391,105,376,90,409,120,361)(64,405,91,390,76,408,106,375)(65,404,92,389,77,407,107,374)(66,403,93,388,78,406,108,373)(67,402,94,387,79,420,109,372)(68,401,95,386,80,419,110,371)(69,400,96,385,81,418,111,370)(70,399,97,384,82,417,112,369)(71,398,98,383,83,416,113,368)(72,397,99,382,84,415,114,367)(73,396,100,381,85,414,115,366)(74,395,101,380,86,413,116,365)(75,394,102,379,87,412,117,364)(121,335,168,305,147,352,160,316)(122,334,169,304,148,351,161,330)(123,333,170,303,149,350,162,329)(124,332,171,302,150,349,163,328)(125,331,172,301,136,348,164,327)(126,345,173,315,137,347,165,326)(127,344,174,314,138,346,151,325)(128,343,175,313,139,360,152,324)(129,342,176,312,140,359,153,323)(130,341,177,311,141,358,154,322)(131,340,178,310,142,357,155,321)(132,339,179,309,143,356,156,320)(133,338,180,308,144,355,157,319)(134,337,166,307,145,354,158,318)(135,336,167,306,146,353,159,317)(181,274,239,247,200,287,213,259)(182,273,240,246,201,286,214,258)(183,272,226,245,202,300,215,257)(184,271,227,244,203,299,216,256)(185,285,228,243,204,298,217,270)(186,284,229,242,205,297,218,269)(187,283,230,241,206,296,219,268)(188,282,231,255,207,295,220,267)(189,281,232,254,208,294,221,266)(190,280,233,253,209,293,222,265)(191,279,234,252,210,292,223,264)(192,278,235,251,196,291,224,263)(193,277,236,250,197,290,225,262)(194,276,237,249,198,289,211,261)(195,275,238,248,199,288,212,260), (1,145,30,134)(2,141,16,130)(3,137,17,126)(4,148,18,122)(5,144,19,133)(6,140,20,129)(7,136,21,125)(8,147,22,121)(9,143,23,132)(10,139,24,128)(11,150,25,124)(12,146,26,135)(13,142,27,131)(14,138,28,127)(15,149,29,123)(31,167,46,159)(32,178,47,155)(33,174,48,151)(34,170,49,162)(35,166,50,158)(36,177,51,154)(37,173,52,165)(38,169,53,161)(39,180,54,157)(40,176,55,153)(41,172,56,164)(42,168,57,160)(43,179,58,156)(44,175,59,152)(45,171,60,163)(61,200,88,181)(62,196,89,192)(63,207,90,188)(64,203,76,184)(65,199,77,195)(66,210,78,191)(67,206,79,187)(68,202,80,183)(69,198,81,194)(70,209,82,190)(71,205,83,186)(72,201,84,182)(73,197,85,193)(74,208,86,189)(75,204,87,185)(91,227,106,216)(92,238,107,212)(93,234,108,223)(94,230,109,219)(95,226,110,215)(96,237,111,211)(97,233,112,222)(98,229,113,218)(99,240,114,214)(100,236,115,225)(101,232,116,221)(102,228,117,217)(103,239,118,213)(104,235,119,224)(105,231,120,220)(241,420,268,402)(242,416,269,398)(243,412,270,394)(244,408,256,405)(245,419,257,401)(246,415,258,397)(247,411,259,393)(248,407,260,404)(249,418,261,400)(250,414,262,396)(251,410,263,392)(252,406,264,403)(253,417,265,399)(254,413,266,395)(255,409,267,391)(271,375,299,390)(272,371,300,386)(273,367,286,382)(274,363,287,378)(275,374,288,389)(276,370,289,385)(277,366,290,381)(278,362,291,377)(279,373,292,388)(280,369,293,384)(281,365,294,380)(282,361,295,376)(283,372,296,387)(284,368,297,383)(285,364,298,379)(301,479,327,460)(302,475,328,456)(303,471,329,452)(304,467,330,463)(305,478,316,459)(306,474,317,455)(307,470,318,451)(308,466,319,462)(309,477,320,458)(310,473,321,454)(311,469,322,465)(312,480,323,461)(313,476,324,457)(314,472,325,453)(315,468,326,464)(331,423,348,446)(332,434,349,442)(333,430,350,438)(334,426,351,449)(335,422,352,445)(336,433,353,441)(337,429,354,437)(338,425,355,448)(339,421,356,444)(340,432,357,440)(341,428,358,436)(342,424,359,447)(343,435,360,443)(344,431,346,439)(345,427,347,450)>;
G:=Group( (1,62)(2,63)(3,64)(4,65)(5,66)(6,67)(7,68)(8,69)(9,70)(10,71)(11,72)(12,73)(13,74)(14,75)(15,61)(16,90)(17,76)(18,77)(19,78)(20,79)(21,80)(22,81)(23,82)(24,83)(25,84)(26,85)(27,86)(28,87)(29,88)(30,89)(31,100)(32,101)(33,102)(34,103)(35,104)(36,105)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,115)(47,116)(48,117)(49,118)(50,119)(51,120)(52,106)(53,107)(54,108)(55,109)(56,110)(57,111)(58,112)(59,113)(60,114)(121,194)(122,195)(123,181)(124,182)(125,183)(126,184)(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)(136,202)(137,203)(138,204)(139,205)(140,206)(141,207)(142,208)(143,209)(144,210)(145,196)(146,197)(147,198)(148,199)(149,200)(150,201)(151,217)(152,218)(153,219)(154,220)(155,221)(156,222)(157,223)(158,224)(159,225)(160,211)(161,212)(162,213)(163,214)(164,215)(165,216)(166,235)(167,236)(168,237)(169,238)(170,239)(171,240)(172,226)(173,227)(174,228)(175,229)(176,230)(177,231)(178,232)(179,233)(180,234)(241,312)(242,313)(243,314)(244,315)(245,301)(246,302)(247,303)(248,304)(249,305)(250,306)(251,307)(252,308)(253,309)(254,310)(255,311)(256,326)(257,327)(258,328)(259,329)(260,330)(261,316)(262,317)(263,318)(264,319)(265,320)(266,321)(267,322)(268,323)(269,324)(270,325)(271,345)(272,331)(273,332)(274,333)(275,334)(276,335)(277,336)(278,337)(279,338)(280,339)(281,340)(282,341)(283,342)(284,343)(285,344)(286,349)(287,350)(288,351)(289,352)(290,353)(291,354)(292,355)(293,356)(294,357)(295,358)(296,359)(297,360)(298,346)(299,347)(300,348)(361,428)(362,429)(363,430)(364,431)(365,432)(366,433)(367,434)(368,435)(369,421)(370,422)(371,423)(372,424)(373,425)(374,426)(375,427)(376,436)(377,437)(378,438)(379,439)(380,440)(381,441)(382,442)(383,443)(384,444)(385,445)(386,446)(387,447)(388,448)(389,449)(390,450)(391,465)(392,451)(393,452)(394,453)(395,454)(396,455)(397,456)(398,457)(399,458)(400,459)(401,460)(402,461)(403,462)(404,463)(405,464)(406,466)(407,467)(408,468)(409,469)(410,470)(411,471)(412,472)(413,473)(414,474)(415,475)(416,476)(417,477)(418,478)(419,479)(420,480), (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), (1,451,35,437,30,470,50,429)(2,465,36,436,16,469,51,428)(3,464,37,450,17,468,52,427)(4,463,38,449,18,467,53,426)(5,462,39,448,19,466,54,425)(6,461,40,447,20,480,55,424)(7,460,41,446,21,479,56,423)(8,459,42,445,22,478,57,422)(9,458,43,444,23,477,58,421)(10,457,44,443,24,476,59,435)(11,456,45,442,25,475,60,434)(12,455,31,441,26,474,46,433)(13,454,32,440,27,473,47,432)(14,453,33,439,28,472,48,431)(15,452,34,438,29,471,49,430)(61,393,103,378,88,411,118,363)(62,392,104,377,89,410,119,362)(63,391,105,376,90,409,120,361)(64,405,91,390,76,408,106,375)(65,404,92,389,77,407,107,374)(66,403,93,388,78,406,108,373)(67,402,94,387,79,420,109,372)(68,401,95,386,80,419,110,371)(69,400,96,385,81,418,111,370)(70,399,97,384,82,417,112,369)(71,398,98,383,83,416,113,368)(72,397,99,382,84,415,114,367)(73,396,100,381,85,414,115,366)(74,395,101,380,86,413,116,365)(75,394,102,379,87,412,117,364)(121,335,168,305,147,352,160,316)(122,334,169,304,148,351,161,330)(123,333,170,303,149,350,162,329)(124,332,171,302,150,349,163,328)(125,331,172,301,136,348,164,327)(126,345,173,315,137,347,165,326)(127,344,174,314,138,346,151,325)(128,343,175,313,139,360,152,324)(129,342,176,312,140,359,153,323)(130,341,177,311,141,358,154,322)(131,340,178,310,142,357,155,321)(132,339,179,309,143,356,156,320)(133,338,180,308,144,355,157,319)(134,337,166,307,145,354,158,318)(135,336,167,306,146,353,159,317)(181,274,239,247,200,287,213,259)(182,273,240,246,201,286,214,258)(183,272,226,245,202,300,215,257)(184,271,227,244,203,299,216,256)(185,285,228,243,204,298,217,270)(186,284,229,242,205,297,218,269)(187,283,230,241,206,296,219,268)(188,282,231,255,207,295,220,267)(189,281,232,254,208,294,221,266)(190,280,233,253,209,293,222,265)(191,279,234,252,210,292,223,264)(192,278,235,251,196,291,224,263)(193,277,236,250,197,290,225,262)(194,276,237,249,198,289,211,261)(195,275,238,248,199,288,212,260), (1,145,30,134)(2,141,16,130)(3,137,17,126)(4,148,18,122)(5,144,19,133)(6,140,20,129)(7,136,21,125)(8,147,22,121)(9,143,23,132)(10,139,24,128)(11,150,25,124)(12,146,26,135)(13,142,27,131)(14,138,28,127)(15,149,29,123)(31,167,46,159)(32,178,47,155)(33,174,48,151)(34,170,49,162)(35,166,50,158)(36,177,51,154)(37,173,52,165)(38,169,53,161)(39,180,54,157)(40,176,55,153)(41,172,56,164)(42,168,57,160)(43,179,58,156)(44,175,59,152)(45,171,60,163)(61,200,88,181)(62,196,89,192)(63,207,90,188)(64,203,76,184)(65,199,77,195)(66,210,78,191)(67,206,79,187)(68,202,80,183)(69,198,81,194)(70,209,82,190)(71,205,83,186)(72,201,84,182)(73,197,85,193)(74,208,86,189)(75,204,87,185)(91,227,106,216)(92,238,107,212)(93,234,108,223)(94,230,109,219)(95,226,110,215)(96,237,111,211)(97,233,112,222)(98,229,113,218)(99,240,114,214)(100,236,115,225)(101,232,116,221)(102,228,117,217)(103,239,118,213)(104,235,119,224)(105,231,120,220)(241,420,268,402)(242,416,269,398)(243,412,270,394)(244,408,256,405)(245,419,257,401)(246,415,258,397)(247,411,259,393)(248,407,260,404)(249,418,261,400)(250,414,262,396)(251,410,263,392)(252,406,264,403)(253,417,265,399)(254,413,266,395)(255,409,267,391)(271,375,299,390)(272,371,300,386)(273,367,286,382)(274,363,287,378)(275,374,288,389)(276,370,289,385)(277,366,290,381)(278,362,291,377)(279,373,292,388)(280,369,293,384)(281,365,294,380)(282,361,295,376)(283,372,296,387)(284,368,297,383)(285,364,298,379)(301,479,327,460)(302,475,328,456)(303,471,329,452)(304,467,330,463)(305,478,316,459)(306,474,317,455)(307,470,318,451)(308,466,319,462)(309,477,320,458)(310,473,321,454)(311,469,322,465)(312,480,323,461)(313,476,324,457)(314,472,325,453)(315,468,326,464)(331,423,348,446)(332,434,349,442)(333,430,350,438)(334,426,351,449)(335,422,352,445)(336,433,353,441)(337,429,354,437)(338,425,355,448)(339,421,356,444)(340,432,357,440)(341,428,358,436)(342,424,359,447)(343,435,360,443)(344,431,346,439)(345,427,347,450) );
G=PermutationGroup([[(1,62),(2,63),(3,64),(4,65),(5,66),(6,67),(7,68),(8,69),(9,70),(10,71),(11,72),(12,73),(13,74),(14,75),(15,61),(16,90),(17,76),(18,77),(19,78),(20,79),(21,80),(22,81),(23,82),(24,83),(25,84),(26,85),(27,86),(28,87),(29,88),(30,89),(31,100),(32,101),(33,102),(34,103),(35,104),(36,105),(37,91),(38,92),(39,93),(40,94),(41,95),(42,96),(43,97),(44,98),(45,99),(46,115),(47,116),(48,117),(49,118),(50,119),(51,120),(52,106),(53,107),(54,108),(55,109),(56,110),(57,111),(58,112),(59,113),(60,114),(121,194),(122,195),(123,181),(124,182),(125,183),(126,184),(127,185),(128,186),(129,187),(130,188),(131,189),(132,190),(133,191),(134,192),(135,193),(136,202),(137,203),(138,204),(139,205),(140,206),(141,207),(142,208),(143,209),(144,210),(145,196),(146,197),(147,198),(148,199),(149,200),(150,201),(151,217),(152,218),(153,219),(154,220),(155,221),(156,222),(157,223),(158,224),(159,225),(160,211),(161,212),(162,213),(163,214),(164,215),(165,216),(166,235),(167,236),(168,237),(169,238),(170,239),(171,240),(172,226),(173,227),(174,228),(175,229),(176,230),(177,231),(178,232),(179,233),(180,234),(241,312),(242,313),(243,314),(244,315),(245,301),(246,302),(247,303),(248,304),(249,305),(250,306),(251,307),(252,308),(253,309),(254,310),(255,311),(256,326),(257,327),(258,328),(259,329),(260,330),(261,316),(262,317),(263,318),(264,319),(265,320),(266,321),(267,322),(268,323),(269,324),(270,325),(271,345),(272,331),(273,332),(274,333),(275,334),(276,335),(277,336),(278,337),(279,338),(280,339),(281,340),(282,341),(283,342),(284,343),(285,344),(286,349),(287,350),(288,351),(289,352),(290,353),(291,354),(292,355),(293,356),(294,357),(295,358),(296,359),(297,360),(298,346),(299,347),(300,348),(361,428),(362,429),(363,430),(364,431),(365,432),(366,433),(367,434),(368,435),(369,421),(370,422),(371,423),(372,424),(373,425),(374,426),(375,427),(376,436),(377,437),(378,438),(379,439),(380,440),(381,441),(382,442),(383,443),(384,444),(385,445),(386,446),(387,447),(388,448),(389,449),(390,450),(391,465),(392,451),(393,452),(394,453),(395,454),(396,455),(397,456),(398,457),(399,458),(400,459),(401,460),(402,461),(403,462),(404,463),(405,464),(406,466),(407,467),(408,468),(409,469),(410,470),(411,471),(412,472),(413,473),(414,474),(415,475),(416,476),(417,477),(418,478),(419,479),(420,480)], [(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)], [(1,451,35,437,30,470,50,429),(2,465,36,436,16,469,51,428),(3,464,37,450,17,468,52,427),(4,463,38,449,18,467,53,426),(5,462,39,448,19,466,54,425),(6,461,40,447,20,480,55,424),(7,460,41,446,21,479,56,423),(8,459,42,445,22,478,57,422),(9,458,43,444,23,477,58,421),(10,457,44,443,24,476,59,435),(11,456,45,442,25,475,60,434),(12,455,31,441,26,474,46,433),(13,454,32,440,27,473,47,432),(14,453,33,439,28,472,48,431),(15,452,34,438,29,471,49,430),(61,393,103,378,88,411,118,363),(62,392,104,377,89,410,119,362),(63,391,105,376,90,409,120,361),(64,405,91,390,76,408,106,375),(65,404,92,389,77,407,107,374),(66,403,93,388,78,406,108,373),(67,402,94,387,79,420,109,372),(68,401,95,386,80,419,110,371),(69,400,96,385,81,418,111,370),(70,399,97,384,82,417,112,369),(71,398,98,383,83,416,113,368),(72,397,99,382,84,415,114,367),(73,396,100,381,85,414,115,366),(74,395,101,380,86,413,116,365),(75,394,102,379,87,412,117,364),(121,335,168,305,147,352,160,316),(122,334,169,304,148,351,161,330),(123,333,170,303,149,350,162,329),(124,332,171,302,150,349,163,328),(125,331,172,301,136,348,164,327),(126,345,173,315,137,347,165,326),(127,344,174,314,138,346,151,325),(128,343,175,313,139,360,152,324),(129,342,176,312,140,359,153,323),(130,341,177,311,141,358,154,322),(131,340,178,310,142,357,155,321),(132,339,179,309,143,356,156,320),(133,338,180,308,144,355,157,319),(134,337,166,307,145,354,158,318),(135,336,167,306,146,353,159,317),(181,274,239,247,200,287,213,259),(182,273,240,246,201,286,214,258),(183,272,226,245,202,300,215,257),(184,271,227,244,203,299,216,256),(185,285,228,243,204,298,217,270),(186,284,229,242,205,297,218,269),(187,283,230,241,206,296,219,268),(188,282,231,255,207,295,220,267),(189,281,232,254,208,294,221,266),(190,280,233,253,209,293,222,265),(191,279,234,252,210,292,223,264),(192,278,235,251,196,291,224,263),(193,277,236,250,197,290,225,262),(194,276,237,249,198,289,211,261),(195,275,238,248,199,288,212,260)], [(1,145,30,134),(2,141,16,130),(3,137,17,126),(4,148,18,122),(5,144,19,133),(6,140,20,129),(7,136,21,125),(8,147,22,121),(9,143,23,132),(10,139,24,128),(11,150,25,124),(12,146,26,135),(13,142,27,131),(14,138,28,127),(15,149,29,123),(31,167,46,159),(32,178,47,155),(33,174,48,151),(34,170,49,162),(35,166,50,158),(36,177,51,154),(37,173,52,165),(38,169,53,161),(39,180,54,157),(40,176,55,153),(41,172,56,164),(42,168,57,160),(43,179,58,156),(44,175,59,152),(45,171,60,163),(61,200,88,181),(62,196,89,192),(63,207,90,188),(64,203,76,184),(65,199,77,195),(66,210,78,191),(67,206,79,187),(68,202,80,183),(69,198,81,194),(70,209,82,190),(71,205,83,186),(72,201,84,182),(73,197,85,193),(74,208,86,189),(75,204,87,185),(91,227,106,216),(92,238,107,212),(93,234,108,223),(94,230,109,219),(95,226,110,215),(96,237,111,211),(97,233,112,222),(98,229,113,218),(99,240,114,214),(100,236,115,225),(101,232,116,221),(102,228,117,217),(103,239,118,213),(104,235,119,224),(105,231,120,220),(241,420,268,402),(242,416,269,398),(243,412,270,394),(244,408,256,405),(245,419,257,401),(246,415,258,397),(247,411,259,393),(248,407,260,404),(249,418,261,400),(250,414,262,396),(251,410,263,392),(252,406,264,403),(253,417,265,399),(254,413,266,395),(255,409,267,391),(271,375,299,390),(272,371,300,386),(273,367,286,382),(274,363,287,378),(275,374,288,389),(276,370,289,385),(277,366,290,381),(278,362,291,377),(279,373,292,388),(280,369,293,384),(281,365,294,380),(282,361,295,376),(283,372,296,387),(284,368,297,383),(285,364,298,379),(301,479,327,460),(302,475,328,456),(303,471,329,452),(304,467,330,463),(305,478,316,459),(306,474,317,455),(307,470,318,451),(308,466,319,462),(309,477,320,458),(310,473,321,454),(311,469,322,465),(312,480,323,461),(313,476,324,457),(314,472,325,453),(315,468,326,464),(331,423,348,446),(332,434,349,442),(333,430,350,438),(334,426,351,449),(335,422,352,445),(336,433,353,441),(337,429,354,437),(338,425,355,448),(339,421,356,444),(340,432,357,440),(341,428,358,436),(342,424,359,447),(343,435,360,443),(344,431,346,439),(345,427,347,450)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 5A | 5B | 6A | 6B | 6C | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 12A | 12B | 12C | 12D | 12E | 12F | 15A | 15B | 20A | 20B | 20C | 20D | 20E | ··· | 20L | 30A | ··· | 30F | 60A | ··· | 60H |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 12 | 12 | 20 | 20 | 2 | 2 | 2 | 2 | 2 | 30 | 30 | 30 | 30 | 2 | ··· | 2 | 4 | 4 | 20 | 20 | 20 | 20 | 4 | 4 | 4 | 4 | 4 | 4 | 12 | ··· | 12 | 4 | ··· | 4 | 4 | ··· | 4 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | + | + | - | + | - | - | + | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | S3 | D4 | D4 | D5 | D6 | D6 | Q16 | D10 | D10 | C3⋊D4 | C3⋊D4 | C5⋊D4 | C5⋊D4 | C3⋊Q16 | S3×D5 | C5⋊Q16 | C15⋊D4 | C2×S3×D5 | C15⋊D4 | C15⋊Q16 |
| kernel | C2×C15⋊Q16 | C15⋊Q16 | C2×C15⋊3C8 | C6×Dic10 | C10×Dic6 | C2×Dic10 | C60 | C2×C30 | C2×Dic6 | Dic10 | C2×C20 | C30 | Dic6 | C2×C12 | C20 | C2×C10 | C12 | C2×C6 | C10 | C2×C4 | C6 | C4 | C4 | C22 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 4 | 4 | 2 | 2 | 2 | 4 | 4 | 2 | 2 | 4 | 2 | 2 | 2 | 8 |
Matrix representation of C2×C15⋊Q16 ►in GL6(𝔽241)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 0 | 0 | 0 | 0 | 240 | 0 |
| 0 | 0 | 0 | 0 | 0 | 240 |
| 240 | 240 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 189 | 190 | 0 | 0 |
| 0 | 0 | 52 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 47 | 40 | 0 | 0 | 0 | 0 |
| 234 | 194 | 0 | 0 | 0 | 0 |
| 0 | 0 | 95 | 129 | 0 | 0 |
| 0 | 0 | 115 | 146 | 0 | 0 |
| 0 | 0 | 0 | 0 | 132 | 127 |
| 0 | 0 | 0 | 0 | 176 | 131 |
| 194 | 201 | 0 | 0 | 0 | 0 |
| 7 | 47 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 0 | 0 | 0 | 0 | 150 | 53 |
| 0 | 0 | 0 | 0 | 62 | 91 |
G:=sub<GL(6,GF(241))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,240],[240,1,0,0,0,0,240,0,0,0,0,0,0,0,189,52,0,0,0,0,190,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[47,234,0,0,0,0,40,194,0,0,0,0,0,0,95,115,0,0,0,0,129,146,0,0,0,0,0,0,132,176,0,0,0,0,127,131],[194,7,0,0,0,0,201,47,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,150,62,0,0,0,0,53,91] >;
C2×C15⋊Q16 in GAP, Magma, Sage, TeX
C_2\times C_{15}\rtimes Q_{16} % in TeX
G:=Group("C2xC15:Q16"); // GroupNames label
G:=SmallGroup(480,394);
// by ID
G=gap.SmallGroup(480,394);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,141,120,675,346,80,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^15=c^8=1,d^2=c^4,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d^-1=b^11,d*c*d^-1=c^-1>;
// generators/relations