metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic15⋊7Q8, Dic6⋊5Dic5, C15⋊11(C4×Q8), C3⋊2(Q8×Dic5), C6.6(Q8×D5), C10.6(S3×Q8), C20.57(C4×S3), C30.17(C2×Q8), C60.133(C2×C4), (C5×Dic6)⋊12C4, (C2×C20).108D6, C2.3(D15⋊Q8), C4⋊Dic5.11S3, (C2×Dic6).8D5, C4.10(S3×Dic5), C30.13(C4○D4), (C2×C12).110D10, C5⋊6(Dic6⋊C4), (C2×C30).34C23, (C10×Dic6).8C2, (C2×Dic5).91D6, C12.13(C2×Dic5), C6.Dic10.8C2, C10.1(D4⋊2S3), C2.1(D20⋊S3), C6.8(C22×Dic5), (C2×C60).192C22, C30.117(C22×C4), C6.20(Q8⋊2D5), Dic3.4(C2×Dic5), (C2×Dic3).84D10, (C4×Dic15).13C2, (Dic3×Dic5).17C2, (C6×Dic5).19C22, (C10×Dic3).18C22, (C2×Dic15).181C22, C10.116(S3×C2×C4), C2.10(C2×S3×Dic5), C22.30(C2×S3×D5), (C2×C4).202(S3×D5), (C3×C4⋊Dic5).10C2, (C2×C6).46(C22×D5), (C2×C10).46(C22×S3), (C5×Dic3).26(C2×C4), SmallGroup(480,420)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic15⋊7Q8
G = < a,b,c,d | a30=c4=1, b2=a15, d2=c2, bab-1=a-1, ac=ca, dad-1=a11, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 492 in 140 conjugacy classes, 70 normal (32 characteristic)
C1, C2, C3, C4, C4, C22, C5, C6, C2×C4, C2×C4, Q8, C10, Dic3, Dic3, C12, C12, C2×C6, C15, C42, C4⋊C4, C2×Q8, Dic5, C20, C20, C2×C10, Dic6, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C30, C4×Q8, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C5×Q8, C4×Dic3, Dic3⋊C4, C3×C4⋊C4, C2×Dic6, C5×Dic3, C3×Dic5, Dic15, Dic15, C60, C2×C30, C4×Dic5, C4⋊Dic5, C4⋊Dic5, Q8×C10, Dic6⋊C4, C6×Dic5, C5×Dic6, C10×Dic3, C2×Dic15, C2×C60, Q8×Dic5, Dic3×Dic5, C6.Dic10, C3×C4⋊Dic5, C4×Dic15, C10×Dic6, Dic15⋊7Q8
Quotients: C1, C2, C4, C22, S3, C2×C4, Q8, C23, D5, D6, C22×C4, C2×Q8, C4○D4, Dic5, D10, C4×S3, C22×S3, C4×Q8, C2×Dic5, C22×D5, S3×C2×C4, D4⋊2S3, S3×Q8, S3×D5, Q8×D5, Q8⋊2D5, C22×Dic5, Dic6⋊C4, S3×Dic5, C2×S3×D5, Q8×Dic5, D20⋊S3, D15⋊Q8, C2×S3×Dic5, Dic15⋊7Q8
►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 40 16 55)(2 39 17 54)(3 38 18 53)(4 37 19 52)(5 36 20 51)(6 35 21 50)(7 34 22 49)(8 33 23 48)(9 32 24 47)(10 31 25 46)(11 60 26 45)(12 59 27 44)(13 58 28 43)(14 57 29 42)(15 56 30 41)(61 237 76 222)(62 236 77 221)(63 235 78 220)(64 234 79 219)(65 233 80 218)(66 232 81 217)(67 231 82 216)(68 230 83 215)(69 229 84 214)(70 228 85 213)(71 227 86 212)(72 226 87 211)(73 225 88 240)(74 224 89 239)(75 223 90 238)(91 193 106 208)(92 192 107 207)(93 191 108 206)(94 190 109 205)(95 189 110 204)(96 188 111 203)(97 187 112 202)(98 186 113 201)(99 185 114 200)(100 184 115 199)(101 183 116 198)(102 182 117 197)(103 181 118 196)(104 210 119 195)(105 209 120 194)(121 326 136 311)(122 325 137 310)(123 324 138 309)(124 323 139 308)(125 322 140 307)(126 321 141 306)(127 320 142 305)(128 319 143 304)(129 318 144 303)(130 317 145 302)(131 316 146 301)(132 315 147 330)(133 314 148 329)(134 313 149 328)(135 312 150 327)(151 274 166 289)(152 273 167 288)(153 272 168 287)(154 271 169 286)(155 300 170 285)(156 299 171 284)(157 298 172 283)(158 297 173 282)(159 296 174 281)(160 295 175 280)(161 294 176 279)(162 293 177 278)(163 292 178 277)(164 291 179 276)(165 290 180 275)(241 466 256 451)(242 465 257 480)(243 464 258 479)(244 463 259 478)(245 462 260 477)(246 461 261 476)(247 460 262 475)(248 459 263 474)(249 458 264 473)(250 457 265 472)(251 456 266 471)(252 455 267 470)(253 454 268 469)(254 453 269 468)(255 452 270 467)(331 412 346 397)(332 411 347 396)(333 410 348 395)(334 409 349 394)(335 408 350 393)(336 407 351 392)(337 406 352 391)(338 405 353 420)(339 404 354 419)(340 403 355 418)(341 402 356 417)(342 401 357 416)(343 400 358 415)(344 399 359 414)(345 398 360 413)(361 448 376 433)(362 447 377 432)(363 446 378 431)(364 445 379 430)(365 444 380 429)(366 443 381 428)(367 442 382 427)(368 441 383 426)(369 440 384 425)(370 439 385 424)(371 438 386 423)(372 437 387 422)(373 436 388 421)(374 435 389 450)(375 434 390 449)
(1 208 453 129)(2 209 454 130)(3 210 455 131)(4 181 456 132)(5 182 457 133)(6 183 458 134)(7 184 459 135)(8 185 460 136)(9 186 461 137)(10 187 462 138)(11 188 463 139)(12 189 464 140)(13 190 465 141)(14 191 466 142)(15 192 467 143)(16 193 468 144)(17 194 469 145)(18 195 470 146)(19 196 471 147)(20 197 472 148)(21 198 473 149)(22 199 474 150)(23 200 475 121)(24 201 476 122)(25 202 477 123)(26 203 478 124)(27 204 479 125)(28 205 480 126)(29 206 451 127)(30 207 452 128)(31 112 260 309)(32 113 261 310)(33 114 262 311)(34 115 263 312)(35 116 264 313)(36 117 265 314)(37 118 266 315)(38 119 267 316)(39 120 268 317)(40 91 269 318)(41 92 270 319)(42 93 241 320)(43 94 242 321)(44 95 243 322)(45 96 244 323)(46 97 245 324)(47 98 246 325)(48 99 247 326)(49 100 248 327)(50 101 249 328)(51 102 250 329)(52 103 251 330)(53 104 252 301)(54 105 253 302)(55 106 254 303)(56 107 255 304)(57 108 256 305)(58 109 257 306)(59 110 258 307)(60 111 259 308)(61 415 159 390)(62 416 160 361)(63 417 161 362)(64 418 162 363)(65 419 163 364)(66 420 164 365)(67 391 165 366)(68 392 166 367)(69 393 167 368)(70 394 168 369)(71 395 169 370)(72 396 170 371)(73 397 171 372)(74 398 172 373)(75 399 173 374)(76 400 174 375)(77 401 175 376)(78 402 176 377)(79 403 177 378)(80 404 178 379)(81 405 179 380)(82 406 180 381)(83 407 151 382)(84 408 152 383)(85 409 153 384)(86 410 154 385)(87 411 155 386)(88 412 156 387)(89 413 157 388)(90 414 158 389)(211 347 300 423)(212 348 271 424)(213 349 272 425)(214 350 273 426)(215 351 274 427)(216 352 275 428)(217 353 276 429)(218 354 277 430)(219 355 278 431)(220 356 279 432)(221 357 280 433)(222 358 281 434)(223 359 282 435)(224 360 283 436)(225 331 284 437)(226 332 285 438)(227 333 286 439)(228 334 287 440)(229 335 288 441)(230 336 289 442)(231 337 290 443)(232 338 291 444)(233 339 292 445)(234 340 293 446)(235 341 294 447)(236 342 295 448)(237 343 296 449)(238 344 297 450)(239 345 298 421)(240 346 299 422)
(1 62 453 160)(2 73 454 171)(3 84 455 152)(4 65 456 163)(5 76 457 174)(6 87 458 155)(7 68 459 166)(8 79 460 177)(9 90 461 158)(10 71 462 169)(11 82 463 180)(12 63 464 161)(13 74 465 172)(14 85 466 153)(15 66 467 164)(16 77 468 175)(17 88 469 156)(18 69 470 167)(19 80 471 178)(20 61 472 159)(21 72 473 170)(22 83 474 151)(23 64 475 162)(24 75 476 173)(25 86 477 154)(26 67 478 165)(27 78 479 176)(28 89 480 157)(29 70 451 168)(30 81 452 179)(31 227 260 286)(32 238 261 297)(33 219 262 278)(34 230 263 289)(35 211 264 300)(36 222 265 281)(37 233 266 292)(38 214 267 273)(39 225 268 284)(40 236 269 295)(41 217 270 276)(42 228 241 287)(43 239 242 298)(44 220 243 279)(45 231 244 290)(46 212 245 271)(47 223 246 282)(48 234 247 293)(49 215 248 274)(50 226 249 285)(51 237 250 296)(52 218 251 277)(53 229 252 288)(54 240 253 299)(55 221 254 280)(56 232 255 291)(57 213 256 272)(58 224 257 283)(59 235 258 294)(60 216 259 275)(91 448 318 342)(92 429 319 353)(93 440 320 334)(94 421 321 345)(95 432 322 356)(96 443 323 337)(97 424 324 348)(98 435 325 359)(99 446 326 340)(100 427 327 351)(101 438 328 332)(102 449 329 343)(103 430 330 354)(104 441 301 335)(105 422 302 346)(106 433 303 357)(107 444 304 338)(108 425 305 349)(109 436 306 360)(110 447 307 341)(111 428 308 352)(112 439 309 333)(113 450 310 344)(114 431 311 355)(115 442 312 336)(116 423 313 347)(117 434 314 358)(118 445 315 339)(119 426 316 350)(120 437 317 331)(121 418 200 363)(122 399 201 374)(123 410 202 385)(124 391 203 366)(125 402 204 377)(126 413 205 388)(127 394 206 369)(128 405 207 380)(129 416 208 361)(130 397 209 372)(131 408 210 383)(132 419 181 364)(133 400 182 375)(134 411 183 386)(135 392 184 367)(136 403 185 378)(137 414 186 389)(138 395 187 370)(139 406 188 381)(140 417 189 362)(141 398 190 373)(142 409 191 384)(143 420 192 365)(144 401 193 376)(145 412 194 387)(146 393 195 368)(147 404 196 379)(148 415 197 390)(149 396 198 371)(150 407 199 382)
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), (1,40,16,55)(2,39,17,54)(3,38,18,53)(4,37,19,52)(5,36,20,51)(6,35,21,50)(7,34,22,49)(8,33,23,48)(9,32,24,47)(10,31,25,46)(11,60,26,45)(12,59,27,44)(13,58,28,43)(14,57,29,42)(15,56,30,41)(61,237,76,222)(62,236,77,221)(63,235,78,220)(64,234,79,219)(65,233,80,218)(66,232,81,217)(67,231,82,216)(68,230,83,215)(69,229,84,214)(70,228,85,213)(71,227,86,212)(72,226,87,211)(73,225,88,240)(74,224,89,239)(75,223,90,238)(91,193,106,208)(92,192,107,207)(93,191,108,206)(94,190,109,205)(95,189,110,204)(96,188,111,203)(97,187,112,202)(98,186,113,201)(99,185,114,200)(100,184,115,199)(101,183,116,198)(102,182,117,197)(103,181,118,196)(104,210,119,195)(105,209,120,194)(121,326,136,311)(122,325,137,310)(123,324,138,309)(124,323,139,308)(125,322,140,307)(126,321,141,306)(127,320,142,305)(128,319,143,304)(129,318,144,303)(130,317,145,302)(131,316,146,301)(132,315,147,330)(133,314,148,329)(134,313,149,328)(135,312,150,327)(151,274,166,289)(152,273,167,288)(153,272,168,287)(154,271,169,286)(155,300,170,285)(156,299,171,284)(157,298,172,283)(158,297,173,282)(159,296,174,281)(160,295,175,280)(161,294,176,279)(162,293,177,278)(163,292,178,277)(164,291,179,276)(165,290,180,275)(241,466,256,451)(242,465,257,480)(243,464,258,479)(244,463,259,478)(245,462,260,477)(246,461,261,476)(247,460,262,475)(248,459,263,474)(249,458,264,473)(250,457,265,472)(251,456,266,471)(252,455,267,470)(253,454,268,469)(254,453,269,468)(255,452,270,467)(331,412,346,397)(332,411,347,396)(333,410,348,395)(334,409,349,394)(335,408,350,393)(336,407,351,392)(337,406,352,391)(338,405,353,420)(339,404,354,419)(340,403,355,418)(341,402,356,417)(342,401,357,416)(343,400,358,415)(344,399,359,414)(345,398,360,413)(361,448,376,433)(362,447,377,432)(363,446,378,431)(364,445,379,430)(365,444,380,429)(366,443,381,428)(367,442,382,427)(368,441,383,426)(369,440,384,425)(370,439,385,424)(371,438,386,423)(372,437,387,422)(373,436,388,421)(374,435,389,450)(375,434,390,449), (1,208,453,129)(2,209,454,130)(3,210,455,131)(4,181,456,132)(5,182,457,133)(6,183,458,134)(7,184,459,135)(8,185,460,136)(9,186,461,137)(10,187,462,138)(11,188,463,139)(12,189,464,140)(13,190,465,141)(14,191,466,142)(15,192,467,143)(16,193,468,144)(17,194,469,145)(18,195,470,146)(19,196,471,147)(20,197,472,148)(21,198,473,149)(22,199,474,150)(23,200,475,121)(24,201,476,122)(25,202,477,123)(26,203,478,124)(27,204,479,125)(28,205,480,126)(29,206,451,127)(30,207,452,128)(31,112,260,309)(32,113,261,310)(33,114,262,311)(34,115,263,312)(35,116,264,313)(36,117,265,314)(37,118,266,315)(38,119,267,316)(39,120,268,317)(40,91,269,318)(41,92,270,319)(42,93,241,320)(43,94,242,321)(44,95,243,322)(45,96,244,323)(46,97,245,324)(47,98,246,325)(48,99,247,326)(49,100,248,327)(50,101,249,328)(51,102,250,329)(52,103,251,330)(53,104,252,301)(54,105,253,302)(55,106,254,303)(56,107,255,304)(57,108,256,305)(58,109,257,306)(59,110,258,307)(60,111,259,308)(61,415,159,390)(62,416,160,361)(63,417,161,362)(64,418,162,363)(65,419,163,364)(66,420,164,365)(67,391,165,366)(68,392,166,367)(69,393,167,368)(70,394,168,369)(71,395,169,370)(72,396,170,371)(73,397,171,372)(74,398,172,373)(75,399,173,374)(76,400,174,375)(77,401,175,376)(78,402,176,377)(79,403,177,378)(80,404,178,379)(81,405,179,380)(82,406,180,381)(83,407,151,382)(84,408,152,383)(85,409,153,384)(86,410,154,385)(87,411,155,386)(88,412,156,387)(89,413,157,388)(90,414,158,389)(211,347,300,423)(212,348,271,424)(213,349,272,425)(214,350,273,426)(215,351,274,427)(216,352,275,428)(217,353,276,429)(218,354,277,430)(219,355,278,431)(220,356,279,432)(221,357,280,433)(222,358,281,434)(223,359,282,435)(224,360,283,436)(225,331,284,437)(226,332,285,438)(227,333,286,439)(228,334,287,440)(229,335,288,441)(230,336,289,442)(231,337,290,443)(232,338,291,444)(233,339,292,445)(234,340,293,446)(235,341,294,447)(236,342,295,448)(237,343,296,449)(238,344,297,450)(239,345,298,421)(240,346,299,422), (1,62,453,160)(2,73,454,171)(3,84,455,152)(4,65,456,163)(5,76,457,174)(6,87,458,155)(7,68,459,166)(8,79,460,177)(9,90,461,158)(10,71,462,169)(11,82,463,180)(12,63,464,161)(13,74,465,172)(14,85,466,153)(15,66,467,164)(16,77,468,175)(17,88,469,156)(18,69,470,167)(19,80,471,178)(20,61,472,159)(21,72,473,170)(22,83,474,151)(23,64,475,162)(24,75,476,173)(25,86,477,154)(26,67,478,165)(27,78,479,176)(28,89,480,157)(29,70,451,168)(30,81,452,179)(31,227,260,286)(32,238,261,297)(33,219,262,278)(34,230,263,289)(35,211,264,300)(36,222,265,281)(37,233,266,292)(38,214,267,273)(39,225,268,284)(40,236,269,295)(41,217,270,276)(42,228,241,287)(43,239,242,298)(44,220,243,279)(45,231,244,290)(46,212,245,271)(47,223,246,282)(48,234,247,293)(49,215,248,274)(50,226,249,285)(51,237,250,296)(52,218,251,277)(53,229,252,288)(54,240,253,299)(55,221,254,280)(56,232,255,291)(57,213,256,272)(58,224,257,283)(59,235,258,294)(60,216,259,275)(91,448,318,342)(92,429,319,353)(93,440,320,334)(94,421,321,345)(95,432,322,356)(96,443,323,337)(97,424,324,348)(98,435,325,359)(99,446,326,340)(100,427,327,351)(101,438,328,332)(102,449,329,343)(103,430,330,354)(104,441,301,335)(105,422,302,346)(106,433,303,357)(107,444,304,338)(108,425,305,349)(109,436,306,360)(110,447,307,341)(111,428,308,352)(112,439,309,333)(113,450,310,344)(114,431,311,355)(115,442,312,336)(116,423,313,347)(117,434,314,358)(118,445,315,339)(119,426,316,350)(120,437,317,331)(121,418,200,363)(122,399,201,374)(123,410,202,385)(124,391,203,366)(125,402,204,377)(126,413,205,388)(127,394,206,369)(128,405,207,380)(129,416,208,361)(130,397,209,372)(131,408,210,383)(132,419,181,364)(133,400,182,375)(134,411,183,386)(135,392,184,367)(136,403,185,378)(137,414,186,389)(138,395,187,370)(139,406,188,381)(140,417,189,362)(141,398,190,373)(142,409,191,384)(143,420,192,365)(144,401,193,376)(145,412,194,387)(146,393,195,368)(147,404,196,379)(148,415,197,390)(149,396,198,371)(150,407,199,382)>;
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), (1,40,16,55)(2,39,17,54)(3,38,18,53)(4,37,19,52)(5,36,20,51)(6,35,21,50)(7,34,22,49)(8,33,23,48)(9,32,24,47)(10,31,25,46)(11,60,26,45)(12,59,27,44)(13,58,28,43)(14,57,29,42)(15,56,30,41)(61,237,76,222)(62,236,77,221)(63,235,78,220)(64,234,79,219)(65,233,80,218)(66,232,81,217)(67,231,82,216)(68,230,83,215)(69,229,84,214)(70,228,85,213)(71,227,86,212)(72,226,87,211)(73,225,88,240)(74,224,89,239)(75,223,90,238)(91,193,106,208)(92,192,107,207)(93,191,108,206)(94,190,109,205)(95,189,110,204)(96,188,111,203)(97,187,112,202)(98,186,113,201)(99,185,114,200)(100,184,115,199)(101,183,116,198)(102,182,117,197)(103,181,118,196)(104,210,119,195)(105,209,120,194)(121,326,136,311)(122,325,137,310)(123,324,138,309)(124,323,139,308)(125,322,140,307)(126,321,141,306)(127,320,142,305)(128,319,143,304)(129,318,144,303)(130,317,145,302)(131,316,146,301)(132,315,147,330)(133,314,148,329)(134,313,149,328)(135,312,150,327)(151,274,166,289)(152,273,167,288)(153,272,168,287)(154,271,169,286)(155,300,170,285)(156,299,171,284)(157,298,172,283)(158,297,173,282)(159,296,174,281)(160,295,175,280)(161,294,176,279)(162,293,177,278)(163,292,178,277)(164,291,179,276)(165,290,180,275)(241,466,256,451)(242,465,257,480)(243,464,258,479)(244,463,259,478)(245,462,260,477)(246,461,261,476)(247,460,262,475)(248,459,263,474)(249,458,264,473)(250,457,265,472)(251,456,266,471)(252,455,267,470)(253,454,268,469)(254,453,269,468)(255,452,270,467)(331,412,346,397)(332,411,347,396)(333,410,348,395)(334,409,349,394)(335,408,350,393)(336,407,351,392)(337,406,352,391)(338,405,353,420)(339,404,354,419)(340,403,355,418)(341,402,356,417)(342,401,357,416)(343,400,358,415)(344,399,359,414)(345,398,360,413)(361,448,376,433)(362,447,377,432)(363,446,378,431)(364,445,379,430)(365,444,380,429)(366,443,381,428)(367,442,382,427)(368,441,383,426)(369,440,384,425)(370,439,385,424)(371,438,386,423)(372,437,387,422)(373,436,388,421)(374,435,389,450)(375,434,390,449), (1,208,453,129)(2,209,454,130)(3,210,455,131)(4,181,456,132)(5,182,457,133)(6,183,458,134)(7,184,459,135)(8,185,460,136)(9,186,461,137)(10,187,462,138)(11,188,463,139)(12,189,464,140)(13,190,465,141)(14,191,466,142)(15,192,467,143)(16,193,468,144)(17,194,469,145)(18,195,470,146)(19,196,471,147)(20,197,472,148)(21,198,473,149)(22,199,474,150)(23,200,475,121)(24,201,476,122)(25,202,477,123)(26,203,478,124)(27,204,479,125)(28,205,480,126)(29,206,451,127)(30,207,452,128)(31,112,260,309)(32,113,261,310)(33,114,262,311)(34,115,263,312)(35,116,264,313)(36,117,265,314)(37,118,266,315)(38,119,267,316)(39,120,268,317)(40,91,269,318)(41,92,270,319)(42,93,241,320)(43,94,242,321)(44,95,243,322)(45,96,244,323)(46,97,245,324)(47,98,246,325)(48,99,247,326)(49,100,248,327)(50,101,249,328)(51,102,250,329)(52,103,251,330)(53,104,252,301)(54,105,253,302)(55,106,254,303)(56,107,255,304)(57,108,256,305)(58,109,257,306)(59,110,258,307)(60,111,259,308)(61,415,159,390)(62,416,160,361)(63,417,161,362)(64,418,162,363)(65,419,163,364)(66,420,164,365)(67,391,165,366)(68,392,166,367)(69,393,167,368)(70,394,168,369)(71,395,169,370)(72,396,170,371)(73,397,171,372)(74,398,172,373)(75,399,173,374)(76,400,174,375)(77,401,175,376)(78,402,176,377)(79,403,177,378)(80,404,178,379)(81,405,179,380)(82,406,180,381)(83,407,151,382)(84,408,152,383)(85,409,153,384)(86,410,154,385)(87,411,155,386)(88,412,156,387)(89,413,157,388)(90,414,158,389)(211,347,300,423)(212,348,271,424)(213,349,272,425)(214,350,273,426)(215,351,274,427)(216,352,275,428)(217,353,276,429)(218,354,277,430)(219,355,278,431)(220,356,279,432)(221,357,280,433)(222,358,281,434)(223,359,282,435)(224,360,283,436)(225,331,284,437)(226,332,285,438)(227,333,286,439)(228,334,287,440)(229,335,288,441)(230,336,289,442)(231,337,290,443)(232,338,291,444)(233,339,292,445)(234,340,293,446)(235,341,294,447)(236,342,295,448)(237,343,296,449)(238,344,297,450)(239,345,298,421)(240,346,299,422), (1,62,453,160)(2,73,454,171)(3,84,455,152)(4,65,456,163)(5,76,457,174)(6,87,458,155)(7,68,459,166)(8,79,460,177)(9,90,461,158)(10,71,462,169)(11,82,463,180)(12,63,464,161)(13,74,465,172)(14,85,466,153)(15,66,467,164)(16,77,468,175)(17,88,469,156)(18,69,470,167)(19,80,471,178)(20,61,472,159)(21,72,473,170)(22,83,474,151)(23,64,475,162)(24,75,476,173)(25,86,477,154)(26,67,478,165)(27,78,479,176)(28,89,480,157)(29,70,451,168)(30,81,452,179)(31,227,260,286)(32,238,261,297)(33,219,262,278)(34,230,263,289)(35,211,264,300)(36,222,265,281)(37,233,266,292)(38,214,267,273)(39,225,268,284)(40,236,269,295)(41,217,270,276)(42,228,241,287)(43,239,242,298)(44,220,243,279)(45,231,244,290)(46,212,245,271)(47,223,246,282)(48,234,247,293)(49,215,248,274)(50,226,249,285)(51,237,250,296)(52,218,251,277)(53,229,252,288)(54,240,253,299)(55,221,254,280)(56,232,255,291)(57,213,256,272)(58,224,257,283)(59,235,258,294)(60,216,259,275)(91,448,318,342)(92,429,319,353)(93,440,320,334)(94,421,321,345)(95,432,322,356)(96,443,323,337)(97,424,324,348)(98,435,325,359)(99,446,326,340)(100,427,327,351)(101,438,328,332)(102,449,329,343)(103,430,330,354)(104,441,301,335)(105,422,302,346)(106,433,303,357)(107,444,304,338)(108,425,305,349)(109,436,306,360)(110,447,307,341)(111,428,308,352)(112,439,309,333)(113,450,310,344)(114,431,311,355)(115,442,312,336)(116,423,313,347)(117,434,314,358)(118,445,315,339)(119,426,316,350)(120,437,317,331)(121,418,200,363)(122,399,201,374)(123,410,202,385)(124,391,203,366)(125,402,204,377)(126,413,205,388)(127,394,206,369)(128,405,207,380)(129,416,208,361)(130,397,209,372)(131,408,210,383)(132,419,181,364)(133,400,182,375)(134,411,183,386)(135,392,184,367)(136,403,185,378)(137,414,186,389)(138,395,187,370)(139,406,188,381)(140,417,189,362)(141,398,190,373)(142,409,191,384)(143,420,192,365)(144,401,193,376)(145,412,194,387)(146,393,195,368)(147,404,196,379)(148,415,197,390)(149,396,198,371)(150,407,199,382) );
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)], [(1,40,16,55),(2,39,17,54),(3,38,18,53),(4,37,19,52),(5,36,20,51),(6,35,21,50),(7,34,22,49),(8,33,23,48),(9,32,24,47),(10,31,25,46),(11,60,26,45),(12,59,27,44),(13,58,28,43),(14,57,29,42),(15,56,30,41),(61,237,76,222),(62,236,77,221),(63,235,78,220),(64,234,79,219),(65,233,80,218),(66,232,81,217),(67,231,82,216),(68,230,83,215),(69,229,84,214),(70,228,85,213),(71,227,86,212),(72,226,87,211),(73,225,88,240),(74,224,89,239),(75,223,90,238),(91,193,106,208),(92,192,107,207),(93,191,108,206),(94,190,109,205),(95,189,110,204),(96,188,111,203),(97,187,112,202),(98,186,113,201),(99,185,114,200),(100,184,115,199),(101,183,116,198),(102,182,117,197),(103,181,118,196),(104,210,119,195),(105,209,120,194),(121,326,136,311),(122,325,137,310),(123,324,138,309),(124,323,139,308),(125,322,140,307),(126,321,141,306),(127,320,142,305),(128,319,143,304),(129,318,144,303),(130,317,145,302),(131,316,146,301),(132,315,147,330),(133,314,148,329),(134,313,149,328),(135,312,150,327),(151,274,166,289),(152,273,167,288),(153,272,168,287),(154,271,169,286),(155,300,170,285),(156,299,171,284),(157,298,172,283),(158,297,173,282),(159,296,174,281),(160,295,175,280),(161,294,176,279),(162,293,177,278),(163,292,178,277),(164,291,179,276),(165,290,180,275),(241,466,256,451),(242,465,257,480),(243,464,258,479),(244,463,259,478),(245,462,260,477),(246,461,261,476),(247,460,262,475),(248,459,263,474),(249,458,264,473),(250,457,265,472),(251,456,266,471),(252,455,267,470),(253,454,268,469),(254,453,269,468),(255,452,270,467),(331,412,346,397),(332,411,347,396),(333,410,348,395),(334,409,349,394),(335,408,350,393),(336,407,351,392),(337,406,352,391),(338,405,353,420),(339,404,354,419),(340,403,355,418),(341,402,356,417),(342,401,357,416),(343,400,358,415),(344,399,359,414),(345,398,360,413),(361,448,376,433),(362,447,377,432),(363,446,378,431),(364,445,379,430),(365,444,380,429),(366,443,381,428),(367,442,382,427),(368,441,383,426),(369,440,384,425),(370,439,385,424),(371,438,386,423),(372,437,387,422),(373,436,388,421),(374,435,389,450),(375,434,390,449)], [(1,208,453,129),(2,209,454,130),(3,210,455,131),(4,181,456,132),(5,182,457,133),(6,183,458,134),(7,184,459,135),(8,185,460,136),(9,186,461,137),(10,187,462,138),(11,188,463,139),(12,189,464,140),(13,190,465,141),(14,191,466,142),(15,192,467,143),(16,193,468,144),(17,194,469,145),(18,195,470,146),(19,196,471,147),(20,197,472,148),(21,198,473,149),(22,199,474,150),(23,200,475,121),(24,201,476,122),(25,202,477,123),(26,203,478,124),(27,204,479,125),(28,205,480,126),(29,206,451,127),(30,207,452,128),(31,112,260,309),(32,113,261,310),(33,114,262,311),(34,115,263,312),(35,116,264,313),(36,117,265,314),(37,118,266,315),(38,119,267,316),(39,120,268,317),(40,91,269,318),(41,92,270,319),(42,93,241,320),(43,94,242,321),(44,95,243,322),(45,96,244,323),(46,97,245,324),(47,98,246,325),(48,99,247,326),(49,100,248,327),(50,101,249,328),(51,102,250,329),(52,103,251,330),(53,104,252,301),(54,105,253,302),(55,106,254,303),(56,107,255,304),(57,108,256,305),(58,109,257,306),(59,110,258,307),(60,111,259,308),(61,415,159,390),(62,416,160,361),(63,417,161,362),(64,418,162,363),(65,419,163,364),(66,420,164,365),(67,391,165,366),(68,392,166,367),(69,393,167,368),(70,394,168,369),(71,395,169,370),(72,396,170,371),(73,397,171,372),(74,398,172,373),(75,399,173,374),(76,400,174,375),(77,401,175,376),(78,402,176,377),(79,403,177,378),(80,404,178,379),(81,405,179,380),(82,406,180,381),(83,407,151,382),(84,408,152,383),(85,409,153,384),(86,410,154,385),(87,411,155,386),(88,412,156,387),(89,413,157,388),(90,414,158,389),(211,347,300,423),(212,348,271,424),(213,349,272,425),(214,350,273,426),(215,351,274,427),(216,352,275,428),(217,353,276,429),(218,354,277,430),(219,355,278,431),(220,356,279,432),(221,357,280,433),(222,358,281,434),(223,359,282,435),(224,360,283,436),(225,331,284,437),(226,332,285,438),(227,333,286,439),(228,334,287,440),(229,335,288,441),(230,336,289,442),(231,337,290,443),(232,338,291,444),(233,339,292,445),(234,340,293,446),(235,341,294,447),(236,342,295,448),(237,343,296,449),(238,344,297,450),(239,345,298,421),(240,346,299,422)], [(1,62,453,160),(2,73,454,171),(3,84,455,152),(4,65,456,163),(5,76,457,174),(6,87,458,155),(7,68,459,166),(8,79,460,177),(9,90,461,158),(10,71,462,169),(11,82,463,180),(12,63,464,161),(13,74,465,172),(14,85,466,153),(15,66,467,164),(16,77,468,175),(17,88,469,156),(18,69,470,167),(19,80,471,178),(20,61,472,159),(21,72,473,170),(22,83,474,151),(23,64,475,162),(24,75,476,173),(25,86,477,154),(26,67,478,165),(27,78,479,176),(28,89,480,157),(29,70,451,168),(30,81,452,179),(31,227,260,286),(32,238,261,297),(33,219,262,278),(34,230,263,289),(35,211,264,300),(36,222,265,281),(37,233,266,292),(38,214,267,273),(39,225,268,284),(40,236,269,295),(41,217,270,276),(42,228,241,287),(43,239,242,298),(44,220,243,279),(45,231,244,290),(46,212,245,271),(47,223,246,282),(48,234,247,293),(49,215,248,274),(50,226,249,285),(51,237,250,296),(52,218,251,277),(53,229,252,288),(54,240,253,299),(55,221,254,280),(56,232,255,291),(57,213,256,272),(58,224,257,283),(59,235,258,294),(60,216,259,275),(91,448,318,342),(92,429,319,353),(93,440,320,334),(94,421,321,345),(95,432,322,356),(96,443,323,337),(97,424,324,348),(98,435,325,359),(99,446,326,340),(100,427,327,351),(101,438,328,332),(102,449,329,343),(103,430,330,354),(104,441,301,335),(105,422,302,346),(106,433,303,357),(107,444,304,338),(108,425,305,349),(109,436,306,360),(110,447,307,341),(111,428,308,352),(112,439,309,333),(113,450,310,344),(114,431,311,355),(115,442,312,336),(116,423,313,347),(117,434,314,358),(118,445,315,339),(119,426,316,350),(120,437,317,331),(121,418,200,363),(122,399,201,374),(123,410,202,385),(124,391,203,366),(125,402,204,377),(126,413,205,388),(127,394,206,369),(128,405,207,380),(129,416,208,361),(130,397,209,372),(131,408,210,383),(132,419,181,364),(133,400,182,375),(134,411,183,386),(135,392,184,367),(136,403,185,378),(137,414,186,389),(138,395,187,370),(139,406,188,381),(140,417,189,362),(141,398,190,373),(142,409,191,384),(143,420,192,365),(144,401,193,376),(145,412,194,387),(146,393,195,368),(147,404,196,379),(148,415,197,390),(149,396,198,371),(150,407,199,382)]])
66 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 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 | 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 | 2 | 2 | 6 | 6 | 6 | 6 | 10 | 10 | 10 | 10 | 15 | 15 | 15 | 15 | 30 | 30 | 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 |
66 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | + | - | + | + | - | - | + | - | + | - | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | S3 | Q8 | D5 | D6 | D6 | C4○D4 | Dic5 | D10 | D10 | C4×S3 | D4⋊2S3 | S3×Q8 | S3×D5 | Q8×D5 | Q8⋊2D5 | S3×Dic5 | C2×S3×D5 | D20⋊S3 | D15⋊Q8 |
| kernel | Dic15⋊7Q8 | Dic3×Dic5 | C6.Dic10 | C3×C4⋊Dic5 | C4×Dic15 | C10×Dic6 | C5×Dic6 | C4⋊Dic5 | Dic15 | C2×Dic6 | C2×Dic5 | C2×C20 | C30 | Dic6 | C2×Dic3 | C2×C12 | C20 | C10 | C10 | C2×C4 | C6 | C6 | C4 | C22 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 8 | 1 | 2 | 2 | 2 | 1 | 2 | 8 | 4 | 2 | 4 | 1 | 1 | 2 | 2 | 2 | 4 | 2 | 4 | 4 |
Matrix representation of Dic15⋊7Q8 ►in GL6(𝔽61)
| 59 | 46 | 0 | 0 | 0 | 0 |
| 49 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 60 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 52 | 59 | 0 | 0 | 0 | 0 |
| 40 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 23 | 0 | 0 |
| 0 | 0 | 27 | 54 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 60 | 0 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 50 | 42 |
| 0 | 0 | 0 | 0 | 0 | 11 |
| 9 | 2 | 0 | 0 | 0 | 0 |
| 21 | 52 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 31 |
| 0 | 0 | 0 | 0 | 15 | 49 |
G:=sub<GL(6,GF(61))| [59,49,0,0,0,0,46,1,0,0,0,0,0,0,18,1,0,0,0,0,60,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[52,40,0,0,0,0,59,9,0,0,0,0,0,0,7,27,0,0,0,0,23,54,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[60,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,50,0,0,0,0,0,42,11],[9,21,0,0,0,0,2,52,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,12,15,0,0,0,0,31,49] >;
Dic15⋊7Q8 in GAP, Magma, Sage, TeX
{\rm Dic}_{15}\rtimes_7Q_8 % in TeX
G:=Group("Dic15:7Q8"); // GroupNames label
G:=SmallGroup(480,420);
// by ID
G=gap.SmallGroup(480,420);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,120,422,219,100,1356,18822]);
// 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^11,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations