metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic15⋊1Q8, Dic3⋊1Dic10, C15⋊1(C4⋊Q8), C3⋊5(C20⋊Q8), C6.2(Q8×D5), (C2×C20).2D6, C30.4(C2×Q8), (C5×Dic3)⋊1Q8, C30.99(C2×D4), C6.124(D4×D5), C10.20(S3×Q8), C2.6(D15⋊Q8), Dic3⋊C4.7D5, (C3×Dic5).6D4, C2.6(S3×Dic10), C6.2(C2×Dic10), (C2×C12).216D10, C5⋊2(Dic3⋊Q8), (C2×C30).17C23, (C2×Dic5).81D6, (C2×Dic10).4S3, C6.Dic10.2C2, C30.4Q8.6C2, Dic15⋊5C4.2C2, (C2×C60).247C22, (Dic3×Dic5).4C2, (C6×Dic10).13C2, (C2×Dic3).73D10, (C6×Dic5).4C22, Dic5.10(C3⋊D4), (C10×Dic3).4C22, (C2×Dic15).25C22, C2.9(D5×C3⋊D4), (C2×C15⋊Q8).4C2, (C2×C4).20(S3×D5), C10.26(C2×C3⋊D4), C22.114(C2×S3×D5), (C5×Dic3⋊C4).7C2, (C2×C6).29(C22×D5), (C2×C10).29(C22×S3), SmallGroup(480,403)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic15⋊1Q8
G = < a,b,c,d | a30=c4=1, b2=a15, d2=c2, bab-1=a-1, ac=ca, dad-1=a19, cbc-1=a15b, bd=db, dcd-1=c-1 >
Subgroups: 604 in 136 conjugacy classes, 54 normal (44 characteristic)
C1, C2, C3, C4, C22, C5, C6, C2×C4, C2×C4, Q8, C10, Dic3, Dic3, C12, C2×C6, C15, C42, C4⋊C4, C2×Q8, Dic5, Dic5, C20, C2×C10, Dic6, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C3×Q8, C30, C4⋊Q8, Dic10, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C4×Dic3, Dic3⋊C4, Dic3⋊C4, C2×Dic6, C6×Q8, C5×Dic3, C5×Dic3, C3×Dic5, C3×Dic5, Dic15, Dic15, C60, C2×C30, C4×Dic5, C10.D4, C4⋊Dic5, C5×C4⋊C4, C2×Dic10, C2×Dic10, Dic3⋊Q8, C15⋊Q8, C3×Dic10, C6×Dic5, C10×Dic3, C2×Dic15, C2×C60, C20⋊Q8, Dic3×Dic5, Dic15⋊5C4, C6.Dic10, C5×Dic3⋊C4, C30.4Q8, C2×C15⋊Q8, C6×Dic10, Dic15⋊1Q8
Quotients: C1, C2, C22, S3, D4, Q8, C23, D5, D6, C2×D4, C2×Q8, D10, C3⋊D4, C22×S3, C4⋊Q8, Dic10, C22×D5, S3×Q8, C2×C3⋊D4, S3×D5, C2×Dic10, D4×D5, Q8×D5, Dic3⋊Q8, C2×S3×D5, C20⋊Q8, S3×Dic10, D15⋊Q8, D5×C3⋊D4, Dic15⋊1Q8
►Regular action on 480 points
Generators in S480
(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 65 16 80)(2 64 17 79)(3 63 18 78)(4 62 19 77)(5 61 20 76)(6 90 21 75)(7 89 22 74)(8 88 23 73)(9 87 24 72)(10 86 25 71)(11 85 26 70)(12 84 27 69)(13 83 28 68)(14 82 29 67)(15 81 30 66)(31 136 46 121)(32 135 47 150)(33 134 48 149)(34 133 49 148)(35 132 50 147)(36 131 51 146)(37 130 52 145)(38 129 53 144)(39 128 54 143)(40 127 55 142)(41 126 56 141)(42 125 57 140)(43 124 58 139)(44 123 59 138)(45 122 60 137)(91 412 106 397)(92 411 107 396)(93 410 108 395)(94 409 109 394)(95 408 110 393)(96 407 111 392)(97 406 112 391)(98 405 113 420)(99 404 114 419)(100 403 115 418)(101 402 116 417)(102 401 117 416)(103 400 118 415)(104 399 119 414)(105 398 120 413)(151 328 166 313)(152 327 167 312)(153 326 168 311)(154 325 169 310)(155 324 170 309)(156 323 171 308)(157 322 172 307)(158 321 173 306)(159 320 174 305)(160 319 175 304)(161 318 176 303)(162 317 177 302)(163 316 178 301)(164 315 179 330)(165 314 180 329)(181 252 196 267)(182 251 197 266)(183 250 198 265)(184 249 199 264)(185 248 200 263)(186 247 201 262)(187 246 202 261)(188 245 203 260)(189 244 204 259)(190 243 205 258)(191 242 206 257)(192 241 207 256)(193 270 208 255)(194 269 209 254)(195 268 210 253)(211 350 226 335)(212 349 227 334)(213 348 228 333)(214 347 229 332)(215 346 230 331)(216 345 231 360)(217 344 232 359)(218 343 233 358)(219 342 234 357)(220 341 235 356)(221 340 236 355)(222 339 237 354)(223 338 238 353)(224 337 239 352)(225 336 240 351)(271 477 286 462)(272 476 287 461)(273 475 288 460)(274 474 289 459)(275 473 290 458)(276 472 291 457)(277 471 292 456)(278 470 293 455)(279 469 294 454)(280 468 295 453)(281 467 296 452)(282 466 297 451)(283 465 298 480)(284 464 299 479)(285 463 300 478)(361 433 376 448)(362 432 377 447)(363 431 378 446)(364 430 379 445)(365 429 380 444)(366 428 381 443)(367 427 382 442)(368 426 383 441)(369 425 384 440)(370 424 385 439)(371 423 386 438)(372 422 387 437)(373 421 388 436)(374 450 389 435)(375 449 390 434)
(1 344 177 372)(2 345 178 373)(3 346 179 374)(4 347 180 375)(5 348 151 376)(6 349 152 377)(7 350 153 378)(8 351 154 379)(9 352 155 380)(10 353 156 381)(11 354 157 382)(12 355 158 383)(13 356 159 384)(14 357 160 385)(15 358 161 386)(16 359 162 387)(17 360 163 388)(18 331 164 389)(19 332 165 390)(20 333 166 361)(21 334 167 362)(22 335 168 363)(23 336 169 364)(24 337 170 365)(25 338 171 366)(26 339 172 367)(27 340 173 368)(28 341 174 369)(29 342 175 370)(30 343 176 371)(31 477 196 406)(32 478 197 407)(33 479 198 408)(34 480 199 409)(35 451 200 410)(36 452 201 411)(37 453 202 412)(38 454 203 413)(39 455 204 414)(40 456 205 415)(41 457 206 416)(42 458 207 417)(43 459 208 418)(44 460 209 419)(45 461 210 420)(46 462 181 391)(47 463 182 392)(48 464 183 393)(49 465 184 394)(50 466 185 395)(51 467 186 396)(52 468 187 397)(53 469 188 398)(54 470 189 399)(55 471 190 400)(56 472 191 401)(57 473 192 402)(58 474 193 403)(59 475 194 404)(60 476 195 405)(61 213 328 433)(62 214 329 434)(63 215 330 435)(64 216 301 436)(65 217 302 437)(66 218 303 438)(67 219 304 439)(68 220 305 440)(69 221 306 441)(70 222 307 442)(71 223 308 443)(72 224 309 444)(73 225 310 445)(74 226 311 446)(75 227 312 447)(76 228 313 448)(77 229 314 449)(78 230 315 450)(79 231 316 421)(80 232 317 422)(81 233 318 423)(82 234 319 424)(83 235 320 425)(84 236 321 426)(85 237 322 427)(86 238 323 428)(87 239 324 429)(88 240 325 430)(89 211 326 431)(90 212 327 432)(91 130 295 261)(92 131 296 262)(93 132 297 263)(94 133 298 264)(95 134 299 265)(96 135 300 266)(97 136 271 267)(98 137 272 268)(99 138 273 269)(100 139 274 270)(101 140 275 241)(102 141 276 242)(103 142 277 243)(104 143 278 244)(105 144 279 245)(106 145 280 246)(107 146 281 247)(108 147 282 248)(109 148 283 249)(110 149 284 250)(111 150 285 251)(112 121 286 252)(113 122 287 253)(114 123 288 254)(115 124 289 255)(116 125 290 256)(117 126 291 257)(118 127 292 258)(119 128 293 259)(120 129 294 260)
(1 242 177 141)(2 261 178 130)(3 250 179 149)(4 269 180 138)(5 258 151 127)(6 247 152 146)(7 266 153 135)(8 255 154 124)(9 244 155 143)(10 263 156 132)(11 252 157 121)(12 241 158 140)(13 260 159 129)(14 249 160 148)(15 268 161 137)(16 257 162 126)(17 246 163 145)(18 265 164 134)(19 254 165 123)(20 243 166 142)(21 262 167 131)(22 251 168 150)(23 270 169 139)(24 259 170 128)(25 248 171 147)(26 267 172 136)(27 256 173 125)(28 245 174 144)(29 264 175 133)(30 253 176 122)(31 85 196 322)(32 74 197 311)(33 63 198 330)(34 82 199 319)(35 71 200 308)(36 90 201 327)(37 79 202 316)(38 68 203 305)(39 87 204 324)(40 76 205 313)(41 65 206 302)(42 84 207 321)(43 73 208 310)(44 62 209 329)(45 81 210 318)(46 70 181 307)(47 89 182 326)(48 78 183 315)(49 67 184 304)(50 86 185 323)(51 75 186 312)(52 64 187 301)(53 83 188 320)(54 72 189 309)(55 61 190 328)(56 80 191 317)(57 69 192 306)(58 88 193 325)(59 77 194 314)(60 66 195 303)(91 345 295 373)(92 334 296 362)(93 353 297 381)(94 342 298 370)(95 331 299 389)(96 350 300 378)(97 339 271 367)(98 358 272 386)(99 347 273 375)(100 336 274 364)(101 355 275 383)(102 344 276 372)(103 333 277 361)(104 352 278 380)(105 341 279 369)(106 360 280 388)(107 349 281 377)(108 338 282 366)(109 357 283 385)(110 346 284 374)(111 335 285 363)(112 354 286 382)(113 343 287 371)(114 332 288 390)(115 351 289 379)(116 340 290 368)(117 359 291 387)(118 348 292 376)(119 337 293 365)(120 356 294 384)(211 463 431 392)(212 452 432 411)(213 471 433 400)(214 460 434 419)(215 479 435 408)(216 468 436 397)(217 457 437 416)(218 476 438 405)(219 465 439 394)(220 454 440 413)(221 473 441 402)(222 462 442 391)(223 451 443 410)(224 470 444 399)(225 459 445 418)(226 478 446 407)(227 467 447 396)(228 456 448 415)(229 475 449 404)(230 464 450 393)(231 453 421 412)(232 472 422 401)(233 461 423 420)(234 480 424 409)(235 469 425 398)(236 458 426 417)(237 477 427 406)(238 466 428 395)(239 455 429 414)(240 474 430 403)
G:=sub<Sym(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), (1,65,16,80)(2,64,17,79)(3,63,18,78)(4,62,19,77)(5,61,20,76)(6,90,21,75)(7,89,22,74)(8,88,23,73)(9,87,24,72)(10,86,25,71)(11,85,26,70)(12,84,27,69)(13,83,28,68)(14,82,29,67)(15,81,30,66)(31,136,46,121)(32,135,47,150)(33,134,48,149)(34,133,49,148)(35,132,50,147)(36,131,51,146)(37,130,52,145)(38,129,53,144)(39,128,54,143)(40,127,55,142)(41,126,56,141)(42,125,57,140)(43,124,58,139)(44,123,59,138)(45,122,60,137)(91,412,106,397)(92,411,107,396)(93,410,108,395)(94,409,109,394)(95,408,110,393)(96,407,111,392)(97,406,112,391)(98,405,113,420)(99,404,114,419)(100,403,115,418)(101,402,116,417)(102,401,117,416)(103,400,118,415)(104,399,119,414)(105,398,120,413)(151,328,166,313)(152,327,167,312)(153,326,168,311)(154,325,169,310)(155,324,170,309)(156,323,171,308)(157,322,172,307)(158,321,173,306)(159,320,174,305)(160,319,175,304)(161,318,176,303)(162,317,177,302)(163,316,178,301)(164,315,179,330)(165,314,180,329)(181,252,196,267)(182,251,197,266)(183,250,198,265)(184,249,199,264)(185,248,200,263)(186,247,201,262)(187,246,202,261)(188,245,203,260)(189,244,204,259)(190,243,205,258)(191,242,206,257)(192,241,207,256)(193,270,208,255)(194,269,209,254)(195,268,210,253)(211,350,226,335)(212,349,227,334)(213,348,228,333)(214,347,229,332)(215,346,230,331)(216,345,231,360)(217,344,232,359)(218,343,233,358)(219,342,234,357)(220,341,235,356)(221,340,236,355)(222,339,237,354)(223,338,238,353)(224,337,239,352)(225,336,240,351)(271,477,286,462)(272,476,287,461)(273,475,288,460)(274,474,289,459)(275,473,290,458)(276,472,291,457)(277,471,292,456)(278,470,293,455)(279,469,294,454)(280,468,295,453)(281,467,296,452)(282,466,297,451)(283,465,298,480)(284,464,299,479)(285,463,300,478)(361,433,376,448)(362,432,377,447)(363,431,378,446)(364,430,379,445)(365,429,380,444)(366,428,381,443)(367,427,382,442)(368,426,383,441)(369,425,384,440)(370,424,385,439)(371,423,386,438)(372,422,387,437)(373,421,388,436)(374,450,389,435)(375,449,390,434), (1,344,177,372)(2,345,178,373)(3,346,179,374)(4,347,180,375)(5,348,151,376)(6,349,152,377)(7,350,153,378)(8,351,154,379)(9,352,155,380)(10,353,156,381)(11,354,157,382)(12,355,158,383)(13,356,159,384)(14,357,160,385)(15,358,161,386)(16,359,162,387)(17,360,163,388)(18,331,164,389)(19,332,165,390)(20,333,166,361)(21,334,167,362)(22,335,168,363)(23,336,169,364)(24,337,170,365)(25,338,171,366)(26,339,172,367)(27,340,173,368)(28,341,174,369)(29,342,175,370)(30,343,176,371)(31,477,196,406)(32,478,197,407)(33,479,198,408)(34,480,199,409)(35,451,200,410)(36,452,201,411)(37,453,202,412)(38,454,203,413)(39,455,204,414)(40,456,205,415)(41,457,206,416)(42,458,207,417)(43,459,208,418)(44,460,209,419)(45,461,210,420)(46,462,181,391)(47,463,182,392)(48,464,183,393)(49,465,184,394)(50,466,185,395)(51,467,186,396)(52,468,187,397)(53,469,188,398)(54,470,189,399)(55,471,190,400)(56,472,191,401)(57,473,192,402)(58,474,193,403)(59,475,194,404)(60,476,195,405)(61,213,328,433)(62,214,329,434)(63,215,330,435)(64,216,301,436)(65,217,302,437)(66,218,303,438)(67,219,304,439)(68,220,305,440)(69,221,306,441)(70,222,307,442)(71,223,308,443)(72,224,309,444)(73,225,310,445)(74,226,311,446)(75,227,312,447)(76,228,313,448)(77,229,314,449)(78,230,315,450)(79,231,316,421)(80,232,317,422)(81,233,318,423)(82,234,319,424)(83,235,320,425)(84,236,321,426)(85,237,322,427)(86,238,323,428)(87,239,324,429)(88,240,325,430)(89,211,326,431)(90,212,327,432)(91,130,295,261)(92,131,296,262)(93,132,297,263)(94,133,298,264)(95,134,299,265)(96,135,300,266)(97,136,271,267)(98,137,272,268)(99,138,273,269)(100,139,274,270)(101,140,275,241)(102,141,276,242)(103,142,277,243)(104,143,278,244)(105,144,279,245)(106,145,280,246)(107,146,281,247)(108,147,282,248)(109,148,283,249)(110,149,284,250)(111,150,285,251)(112,121,286,252)(113,122,287,253)(114,123,288,254)(115,124,289,255)(116,125,290,256)(117,126,291,257)(118,127,292,258)(119,128,293,259)(120,129,294,260), (1,242,177,141)(2,261,178,130)(3,250,179,149)(4,269,180,138)(5,258,151,127)(6,247,152,146)(7,266,153,135)(8,255,154,124)(9,244,155,143)(10,263,156,132)(11,252,157,121)(12,241,158,140)(13,260,159,129)(14,249,160,148)(15,268,161,137)(16,257,162,126)(17,246,163,145)(18,265,164,134)(19,254,165,123)(20,243,166,142)(21,262,167,131)(22,251,168,150)(23,270,169,139)(24,259,170,128)(25,248,171,147)(26,267,172,136)(27,256,173,125)(28,245,174,144)(29,264,175,133)(30,253,176,122)(31,85,196,322)(32,74,197,311)(33,63,198,330)(34,82,199,319)(35,71,200,308)(36,90,201,327)(37,79,202,316)(38,68,203,305)(39,87,204,324)(40,76,205,313)(41,65,206,302)(42,84,207,321)(43,73,208,310)(44,62,209,329)(45,81,210,318)(46,70,181,307)(47,89,182,326)(48,78,183,315)(49,67,184,304)(50,86,185,323)(51,75,186,312)(52,64,187,301)(53,83,188,320)(54,72,189,309)(55,61,190,328)(56,80,191,317)(57,69,192,306)(58,88,193,325)(59,77,194,314)(60,66,195,303)(91,345,295,373)(92,334,296,362)(93,353,297,381)(94,342,298,370)(95,331,299,389)(96,350,300,378)(97,339,271,367)(98,358,272,386)(99,347,273,375)(100,336,274,364)(101,355,275,383)(102,344,276,372)(103,333,277,361)(104,352,278,380)(105,341,279,369)(106,360,280,388)(107,349,281,377)(108,338,282,366)(109,357,283,385)(110,346,284,374)(111,335,285,363)(112,354,286,382)(113,343,287,371)(114,332,288,390)(115,351,289,379)(116,340,290,368)(117,359,291,387)(118,348,292,376)(119,337,293,365)(120,356,294,384)(211,463,431,392)(212,452,432,411)(213,471,433,400)(214,460,434,419)(215,479,435,408)(216,468,436,397)(217,457,437,416)(218,476,438,405)(219,465,439,394)(220,454,440,413)(221,473,441,402)(222,462,442,391)(223,451,443,410)(224,470,444,399)(225,459,445,418)(226,478,446,407)(227,467,447,396)(228,456,448,415)(229,475,449,404)(230,464,450,393)(231,453,421,412)(232,472,422,401)(233,461,423,420)(234,480,424,409)(235,469,425,398)(236,458,426,417)(237,477,427,406)(238,466,428,395)(239,455,429,414)(240,474,430,403)>;
G:=Group( (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), (1,65,16,80)(2,64,17,79)(3,63,18,78)(4,62,19,77)(5,61,20,76)(6,90,21,75)(7,89,22,74)(8,88,23,73)(9,87,24,72)(10,86,25,71)(11,85,26,70)(12,84,27,69)(13,83,28,68)(14,82,29,67)(15,81,30,66)(31,136,46,121)(32,135,47,150)(33,134,48,149)(34,133,49,148)(35,132,50,147)(36,131,51,146)(37,130,52,145)(38,129,53,144)(39,128,54,143)(40,127,55,142)(41,126,56,141)(42,125,57,140)(43,124,58,139)(44,123,59,138)(45,122,60,137)(91,412,106,397)(92,411,107,396)(93,410,108,395)(94,409,109,394)(95,408,110,393)(96,407,111,392)(97,406,112,391)(98,405,113,420)(99,404,114,419)(100,403,115,418)(101,402,116,417)(102,401,117,416)(103,400,118,415)(104,399,119,414)(105,398,120,413)(151,328,166,313)(152,327,167,312)(153,326,168,311)(154,325,169,310)(155,324,170,309)(156,323,171,308)(157,322,172,307)(158,321,173,306)(159,320,174,305)(160,319,175,304)(161,318,176,303)(162,317,177,302)(163,316,178,301)(164,315,179,330)(165,314,180,329)(181,252,196,267)(182,251,197,266)(183,250,198,265)(184,249,199,264)(185,248,200,263)(186,247,201,262)(187,246,202,261)(188,245,203,260)(189,244,204,259)(190,243,205,258)(191,242,206,257)(192,241,207,256)(193,270,208,255)(194,269,209,254)(195,268,210,253)(211,350,226,335)(212,349,227,334)(213,348,228,333)(214,347,229,332)(215,346,230,331)(216,345,231,360)(217,344,232,359)(218,343,233,358)(219,342,234,357)(220,341,235,356)(221,340,236,355)(222,339,237,354)(223,338,238,353)(224,337,239,352)(225,336,240,351)(271,477,286,462)(272,476,287,461)(273,475,288,460)(274,474,289,459)(275,473,290,458)(276,472,291,457)(277,471,292,456)(278,470,293,455)(279,469,294,454)(280,468,295,453)(281,467,296,452)(282,466,297,451)(283,465,298,480)(284,464,299,479)(285,463,300,478)(361,433,376,448)(362,432,377,447)(363,431,378,446)(364,430,379,445)(365,429,380,444)(366,428,381,443)(367,427,382,442)(368,426,383,441)(369,425,384,440)(370,424,385,439)(371,423,386,438)(372,422,387,437)(373,421,388,436)(374,450,389,435)(375,449,390,434), (1,344,177,372)(2,345,178,373)(3,346,179,374)(4,347,180,375)(5,348,151,376)(6,349,152,377)(7,350,153,378)(8,351,154,379)(9,352,155,380)(10,353,156,381)(11,354,157,382)(12,355,158,383)(13,356,159,384)(14,357,160,385)(15,358,161,386)(16,359,162,387)(17,360,163,388)(18,331,164,389)(19,332,165,390)(20,333,166,361)(21,334,167,362)(22,335,168,363)(23,336,169,364)(24,337,170,365)(25,338,171,366)(26,339,172,367)(27,340,173,368)(28,341,174,369)(29,342,175,370)(30,343,176,371)(31,477,196,406)(32,478,197,407)(33,479,198,408)(34,480,199,409)(35,451,200,410)(36,452,201,411)(37,453,202,412)(38,454,203,413)(39,455,204,414)(40,456,205,415)(41,457,206,416)(42,458,207,417)(43,459,208,418)(44,460,209,419)(45,461,210,420)(46,462,181,391)(47,463,182,392)(48,464,183,393)(49,465,184,394)(50,466,185,395)(51,467,186,396)(52,468,187,397)(53,469,188,398)(54,470,189,399)(55,471,190,400)(56,472,191,401)(57,473,192,402)(58,474,193,403)(59,475,194,404)(60,476,195,405)(61,213,328,433)(62,214,329,434)(63,215,330,435)(64,216,301,436)(65,217,302,437)(66,218,303,438)(67,219,304,439)(68,220,305,440)(69,221,306,441)(70,222,307,442)(71,223,308,443)(72,224,309,444)(73,225,310,445)(74,226,311,446)(75,227,312,447)(76,228,313,448)(77,229,314,449)(78,230,315,450)(79,231,316,421)(80,232,317,422)(81,233,318,423)(82,234,319,424)(83,235,320,425)(84,236,321,426)(85,237,322,427)(86,238,323,428)(87,239,324,429)(88,240,325,430)(89,211,326,431)(90,212,327,432)(91,130,295,261)(92,131,296,262)(93,132,297,263)(94,133,298,264)(95,134,299,265)(96,135,300,266)(97,136,271,267)(98,137,272,268)(99,138,273,269)(100,139,274,270)(101,140,275,241)(102,141,276,242)(103,142,277,243)(104,143,278,244)(105,144,279,245)(106,145,280,246)(107,146,281,247)(108,147,282,248)(109,148,283,249)(110,149,284,250)(111,150,285,251)(112,121,286,252)(113,122,287,253)(114,123,288,254)(115,124,289,255)(116,125,290,256)(117,126,291,257)(118,127,292,258)(119,128,293,259)(120,129,294,260), (1,242,177,141)(2,261,178,130)(3,250,179,149)(4,269,180,138)(5,258,151,127)(6,247,152,146)(7,266,153,135)(8,255,154,124)(9,244,155,143)(10,263,156,132)(11,252,157,121)(12,241,158,140)(13,260,159,129)(14,249,160,148)(15,268,161,137)(16,257,162,126)(17,246,163,145)(18,265,164,134)(19,254,165,123)(20,243,166,142)(21,262,167,131)(22,251,168,150)(23,270,169,139)(24,259,170,128)(25,248,171,147)(26,267,172,136)(27,256,173,125)(28,245,174,144)(29,264,175,133)(30,253,176,122)(31,85,196,322)(32,74,197,311)(33,63,198,330)(34,82,199,319)(35,71,200,308)(36,90,201,327)(37,79,202,316)(38,68,203,305)(39,87,204,324)(40,76,205,313)(41,65,206,302)(42,84,207,321)(43,73,208,310)(44,62,209,329)(45,81,210,318)(46,70,181,307)(47,89,182,326)(48,78,183,315)(49,67,184,304)(50,86,185,323)(51,75,186,312)(52,64,187,301)(53,83,188,320)(54,72,189,309)(55,61,190,328)(56,80,191,317)(57,69,192,306)(58,88,193,325)(59,77,194,314)(60,66,195,303)(91,345,295,373)(92,334,296,362)(93,353,297,381)(94,342,298,370)(95,331,299,389)(96,350,300,378)(97,339,271,367)(98,358,272,386)(99,347,273,375)(100,336,274,364)(101,355,275,383)(102,344,276,372)(103,333,277,361)(104,352,278,380)(105,341,279,369)(106,360,280,388)(107,349,281,377)(108,338,282,366)(109,357,283,385)(110,346,284,374)(111,335,285,363)(112,354,286,382)(113,343,287,371)(114,332,288,390)(115,351,289,379)(116,340,290,368)(117,359,291,387)(118,348,292,376)(119,337,293,365)(120,356,294,384)(211,463,431,392)(212,452,432,411)(213,471,433,400)(214,460,434,419)(215,479,435,408)(216,468,436,397)(217,457,437,416)(218,476,438,405)(219,465,439,394)(220,454,440,413)(221,473,441,402)(222,462,442,391)(223,451,443,410)(224,470,444,399)(225,459,445,418)(226,478,446,407)(227,467,447,396)(228,456,448,415)(229,475,449,404)(230,464,450,393)(231,453,421,412)(232,472,422,401)(233,461,423,420)(234,480,424,409)(235,469,425,398)(236,458,426,417)(237,477,427,406)(238,466,428,395)(239,455,429,414)(240,474,430,403) );
G=PermutationGroup([[(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)], [(1,65,16,80),(2,64,17,79),(3,63,18,78),(4,62,19,77),(5,61,20,76),(6,90,21,75),(7,89,22,74),(8,88,23,73),(9,87,24,72),(10,86,25,71),(11,85,26,70),(12,84,27,69),(13,83,28,68),(14,82,29,67),(15,81,30,66),(31,136,46,121),(32,135,47,150),(33,134,48,149),(34,133,49,148),(35,132,50,147),(36,131,51,146),(37,130,52,145),(38,129,53,144),(39,128,54,143),(40,127,55,142),(41,126,56,141),(42,125,57,140),(43,124,58,139),(44,123,59,138),(45,122,60,137),(91,412,106,397),(92,411,107,396),(93,410,108,395),(94,409,109,394),(95,408,110,393),(96,407,111,392),(97,406,112,391),(98,405,113,420),(99,404,114,419),(100,403,115,418),(101,402,116,417),(102,401,117,416),(103,400,118,415),(104,399,119,414),(105,398,120,413),(151,328,166,313),(152,327,167,312),(153,326,168,311),(154,325,169,310),(155,324,170,309),(156,323,171,308),(157,322,172,307),(158,321,173,306),(159,320,174,305),(160,319,175,304),(161,318,176,303),(162,317,177,302),(163,316,178,301),(164,315,179,330),(165,314,180,329),(181,252,196,267),(182,251,197,266),(183,250,198,265),(184,249,199,264),(185,248,200,263),(186,247,201,262),(187,246,202,261),(188,245,203,260),(189,244,204,259),(190,243,205,258),(191,242,206,257),(192,241,207,256),(193,270,208,255),(194,269,209,254),(195,268,210,253),(211,350,226,335),(212,349,227,334),(213,348,228,333),(214,347,229,332),(215,346,230,331),(216,345,231,360),(217,344,232,359),(218,343,233,358),(219,342,234,357),(220,341,235,356),(221,340,236,355),(222,339,237,354),(223,338,238,353),(224,337,239,352),(225,336,240,351),(271,477,286,462),(272,476,287,461),(273,475,288,460),(274,474,289,459),(275,473,290,458),(276,472,291,457),(277,471,292,456),(278,470,293,455),(279,469,294,454),(280,468,295,453),(281,467,296,452),(282,466,297,451),(283,465,298,480),(284,464,299,479),(285,463,300,478),(361,433,376,448),(362,432,377,447),(363,431,378,446),(364,430,379,445),(365,429,380,444),(366,428,381,443),(367,427,382,442),(368,426,383,441),(369,425,384,440),(370,424,385,439),(371,423,386,438),(372,422,387,437),(373,421,388,436),(374,450,389,435),(375,449,390,434)], [(1,344,177,372),(2,345,178,373),(3,346,179,374),(4,347,180,375),(5,348,151,376),(6,349,152,377),(7,350,153,378),(8,351,154,379),(9,352,155,380),(10,353,156,381),(11,354,157,382),(12,355,158,383),(13,356,159,384),(14,357,160,385),(15,358,161,386),(16,359,162,387),(17,360,163,388),(18,331,164,389),(19,332,165,390),(20,333,166,361),(21,334,167,362),(22,335,168,363),(23,336,169,364),(24,337,170,365),(25,338,171,366),(26,339,172,367),(27,340,173,368),(28,341,174,369),(29,342,175,370),(30,343,176,371),(31,477,196,406),(32,478,197,407),(33,479,198,408),(34,480,199,409),(35,451,200,410),(36,452,201,411),(37,453,202,412),(38,454,203,413),(39,455,204,414),(40,456,205,415),(41,457,206,416),(42,458,207,417),(43,459,208,418),(44,460,209,419),(45,461,210,420),(46,462,181,391),(47,463,182,392),(48,464,183,393),(49,465,184,394),(50,466,185,395),(51,467,186,396),(52,468,187,397),(53,469,188,398),(54,470,189,399),(55,471,190,400),(56,472,191,401),(57,473,192,402),(58,474,193,403),(59,475,194,404),(60,476,195,405),(61,213,328,433),(62,214,329,434),(63,215,330,435),(64,216,301,436),(65,217,302,437),(66,218,303,438),(67,219,304,439),(68,220,305,440),(69,221,306,441),(70,222,307,442),(71,223,308,443),(72,224,309,444),(73,225,310,445),(74,226,311,446),(75,227,312,447),(76,228,313,448),(77,229,314,449),(78,230,315,450),(79,231,316,421),(80,232,317,422),(81,233,318,423),(82,234,319,424),(83,235,320,425),(84,236,321,426),(85,237,322,427),(86,238,323,428),(87,239,324,429),(88,240,325,430),(89,211,326,431),(90,212,327,432),(91,130,295,261),(92,131,296,262),(93,132,297,263),(94,133,298,264),(95,134,299,265),(96,135,300,266),(97,136,271,267),(98,137,272,268),(99,138,273,269),(100,139,274,270),(101,140,275,241),(102,141,276,242),(103,142,277,243),(104,143,278,244),(105,144,279,245),(106,145,280,246),(107,146,281,247),(108,147,282,248),(109,148,283,249),(110,149,284,250),(111,150,285,251),(112,121,286,252),(113,122,287,253),(114,123,288,254),(115,124,289,255),(116,125,290,256),(117,126,291,257),(118,127,292,258),(119,128,293,259),(120,129,294,260)], [(1,242,177,141),(2,261,178,130),(3,250,179,149),(4,269,180,138),(5,258,151,127),(6,247,152,146),(7,266,153,135),(8,255,154,124),(9,244,155,143),(10,263,156,132),(11,252,157,121),(12,241,158,140),(13,260,159,129),(14,249,160,148),(15,268,161,137),(16,257,162,126),(17,246,163,145),(18,265,164,134),(19,254,165,123),(20,243,166,142),(21,262,167,131),(22,251,168,150),(23,270,169,139),(24,259,170,128),(25,248,171,147),(26,267,172,136),(27,256,173,125),(28,245,174,144),(29,264,175,133),(30,253,176,122),(31,85,196,322),(32,74,197,311),(33,63,198,330),(34,82,199,319),(35,71,200,308),(36,90,201,327),(37,79,202,316),(38,68,203,305),(39,87,204,324),(40,76,205,313),(41,65,206,302),(42,84,207,321),(43,73,208,310),(44,62,209,329),(45,81,210,318),(46,70,181,307),(47,89,182,326),(48,78,183,315),(49,67,184,304),(50,86,185,323),(51,75,186,312),(52,64,187,301),(53,83,188,320),(54,72,189,309),(55,61,190,328),(56,80,191,317),(57,69,192,306),(58,88,193,325),(59,77,194,314),(60,66,195,303),(91,345,295,373),(92,334,296,362),(93,353,297,381),(94,342,298,370),(95,331,299,389),(96,350,300,378),(97,339,271,367),(98,358,272,386),(99,347,273,375),(100,336,274,364),(101,355,275,383),(102,344,276,372),(103,333,277,361),(104,352,278,380),(105,341,279,369),(106,360,280,388),(107,349,281,377),(108,338,282,366),(109,357,283,385),(110,346,284,374),(111,335,285,363),(112,354,286,382),(113,343,287,371),(114,332,288,390),(115,351,289,379),(116,340,290,368),(117,359,291,387),(118,348,292,376),(119,337,293,365),(120,356,294,384),(211,463,431,392),(212,452,432,411),(213,471,433,400),(214,460,434,419),(215,479,435,408),(216,468,436,397),(217,457,437,416),(218,476,438,405),(219,465,439,394),(220,454,440,413),(221,473,441,402),(222,462,442,391),(223,451,443,410),(224,470,444,399),(225,459,445,418),(226,478,446,407),(227,467,447,396),(228,456,448,415),(229,475,449,404),(230,464,450,393),(231,453,421,412),(232,472,422,401),(233,461,423,420),(234,480,424,409),(235,469,425,398),(236,458,426,417),(237,477,427,406),(238,466,428,395),(239,455,429,414),(240,474,430,403)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 6A | 6B | 6C | 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 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 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 | 4 | 6 | 6 | 10 | 10 | 12 | 20 | 30 | 30 | 60 | 2 | 2 | 2 | 2 | 2 | 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 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | - | + | + | + | + | + | - | - | + | + | - | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | S3 | Q8 | D4 | Q8 | D5 | D6 | D6 | D10 | D10 | C3⋊D4 | Dic10 | S3×Q8 | S3×D5 | D4×D5 | Q8×D5 | C2×S3×D5 | S3×Dic10 | D15⋊Q8 | D5×C3⋊D4 |
| kernel | Dic15⋊1Q8 | Dic3×Dic5 | Dic15⋊5C4 | C6.Dic10 | C5×Dic3⋊C4 | C30.4Q8 | C2×C15⋊Q8 | C6×Dic10 | C2×Dic10 | C5×Dic3 | C3×Dic5 | Dic15 | Dic3⋊C4 | C2×Dic5 | C2×C20 | C2×Dic3 | C2×C12 | Dic5 | Dic3 | C10 | C2×C4 | C6 | C6 | C22 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 1 | 4 | 2 | 4 | 8 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
Matrix representation of Dic15⋊1Q8 ►in GL6(𝔽61)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 1 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 60 |
| 0 | 0 | 0 | 0 | 45 | 17 |
| 60 | 0 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 60 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 29 |
| 0 | 0 | 0 | 0 | 19 | 34 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 60 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 32 | 4 |
| 0 | 0 | 0 | 0 | 3 | 29 |
| 39 | 8 | 0 | 0 | 0 | 0 |
| 8 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 29 |
| 0 | 0 | 0 | 0 | 19 | 34 |
G:=sub<GL(6,GF(61))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,60,0,0,0,0,1,0,0,0,0,0,0,0,1,45,0,0,0,0,60,17],[60,0,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,60,60,0,0,0,0,0,0,27,19,0,0,0,0,29,34],[0,60,0,0,0,0,1,0,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,32,3,0,0,0,0,4,29],[39,8,0,0,0,0,8,22,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,27,19,0,0,0,0,29,34] >;
Dic15⋊1Q8 in GAP, Magma, Sage, TeX
{\rm Dic}_{15}\rtimes_1Q_8 % in TeX
G:=Group("Dic15:1Q8"); // GroupNames label
G:=SmallGroup(480,403);
// by ID
G=gap.SmallGroup(480,403);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,120,254,219,58,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^30=c^4=1,b^2=a^15,d^2=c^2,b*a*b^-1=a^-1,a*c=c*a,d*a*d^-1=a^19,c*b*c^-1=a^15*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations