direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3×C20⋊Q8, C60⋊6Q8, C12⋊6Dic10, C20⋊(C3×Q8), C15⋊14(C4⋊Q8), C6.48(Q8×D5), Dic5⋊1(C3×Q8), (C3×Dic5)⋊8Q8, C4⋊1(C3×Dic10), C6.175(D4×D5), C10.21(C6×D4), C30.77(C2×Q8), C10.10(C6×Q8), C30.334(C2×D4), C4⋊Dic5.11C6, Dic5.6(C3×D4), (C4×Dic5).1C6, C2.7(C6×Dic10), (C2×C12).232D10, (C3×Dic5).53D4, (C2×Dic10).4C6, C6.45(C2×Dic10), C10.D4.2C6, (C2×C30).346C23, (C2×C60).267C22, (C6×Dic10).15C2, (C12×Dic5).11C2, (C6×Dic5).238C22, C5⋊2(C3×C4⋊Q8), C2.4(C3×Q8×D5), C2.11(C3×D4×D5), (C5×C4⋊C4).5C6, C4⋊C4.4(C3×D5), (C2×C20).4(C2×C6), (C3×C4⋊C4).11D5, (C2×C4).37(C6×D5), (C15×C4⋊C4).12C2, C22.46(D5×C2×C6), (C3×C4⋊Dic5).25C2, (C2×Dic5).9(C2×C6), (C2×C10).29(C22×C6), (C3×C10.D4).7C2, (C2×C6).342(C22×D5), SmallGroup(480,681)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×C20⋊Q8
G = < a,b,c,d | a3=b20=c4=1, d2=c2, ab=ba, ac=ca, ad=da, cbc-1=b11, dbd-1=b9, dcd-1=c-1 >
Subgroups: 384 in 136 conjugacy classes, 74 normal (38 characteristic)
C1, C2, C3, C4, C4, C22, C5, C6, C2×C4, C2×C4, C2×C4, Q8, C10, C12, C12, C2×C6, C15, C42, C4⋊C4, C4⋊C4, C2×Q8, Dic5, Dic5, C20, C20, C2×C10, C2×C12, C2×C12, C2×C12, C3×Q8, C30, C4⋊Q8, Dic10, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C4×C12, C3×C4⋊C4, C3×C4⋊C4, C6×Q8, C3×Dic5, C3×Dic5, C60, C60, C2×C30, C4×Dic5, C10.D4, C4⋊Dic5, C5×C4⋊C4, C2×Dic10, C3×C4⋊Q8, C3×Dic10, C6×Dic5, C6×Dic5, C2×C60, C2×C60, C20⋊Q8, C12×Dic5, C3×C10.D4, C3×C4⋊Dic5, C15×C4⋊C4, C6×Dic10, C3×C20⋊Q8
Quotients: C1, C2, C3, C22, C6, D4, Q8, C23, D5, C2×C6, C2×D4, C2×Q8, D10, C3×D4, C3×Q8, C22×C6, C3×D5, C4⋊Q8, Dic10, C22×D5, C6×D4, C6×Q8, C6×D5, C2×Dic10, D4×D5, Q8×D5, C3×C4⋊Q8, C3×Dic10, D5×C2×C6, C20⋊Q8, C6×Dic10, C3×D4×D5, C3×Q8×D5, C3×C20⋊Q8
►Regular action on 480 points
Generators in S480
(1 141 178)(2 142 179)(3 143 180)(4 144 161)(5 145 162)(6 146 163)(7 147 164)(8 148 165)(9 149 166)(10 150 167)(11 151 168)(12 152 169)(13 153 170)(14 154 171)(15 155 172)(16 156 173)(17 157 174)(18 158 175)(19 159 176)(20 160 177)(21 134 403)(22 135 404)(23 136 405)(24 137 406)(25 138 407)(26 139 408)(27 140 409)(28 121 410)(29 122 411)(30 123 412)(31 124 413)(32 125 414)(33 126 415)(34 127 416)(35 128 417)(36 129 418)(37 130 419)(38 131 420)(39 132 401)(40 133 402)(41 263 354)(42 264 355)(43 265 356)(44 266 357)(45 267 358)(46 268 359)(47 269 360)(48 270 341)(49 271 342)(50 272 343)(51 273 344)(52 274 345)(53 275 346)(54 276 347)(55 277 348)(56 278 349)(57 279 350)(58 280 351)(59 261 352)(60 262 353)(61 116 315)(62 117 316)(63 118 317)(64 119 318)(65 120 319)(66 101 320)(67 102 301)(68 103 302)(69 104 303)(70 105 304)(71 106 305)(72 107 306)(73 108 307)(74 109 308)(75 110 309)(76 111 310)(77 112 311)(78 113 312)(79 114 313)(80 115 314)(81 201 246)(82 202 247)(83 203 248)(84 204 249)(85 205 250)(86 206 251)(87 207 252)(88 208 253)(89 209 254)(90 210 255)(91 211 256)(92 212 257)(93 213 258)(94 214 259)(95 215 260)(96 216 241)(97 217 242)(98 218 243)(99 219 244)(100 220 245)(181 385 443)(182 386 444)(183 387 445)(184 388 446)(185 389 447)(186 390 448)(187 391 449)(188 392 450)(189 393 451)(190 394 452)(191 395 453)(192 396 454)(193 397 455)(194 398 456)(195 399 457)(196 400 458)(197 381 459)(198 382 460)(199 383 441)(200 384 442)(221 368 467)(222 369 468)(223 370 469)(224 371 470)(225 372 471)(226 373 472)(227 374 473)(228 375 474)(229 376 475)(230 377 476)(231 378 477)(232 379 478)(233 380 479)(234 361 480)(235 362 461)(236 363 462)(237 364 463)(238 365 464)(239 366 465)(240 367 466)(281 331 437)(282 332 438)(283 333 439)(284 334 440)(285 335 421)(286 336 422)(287 337 423)(288 338 424)(289 339 425)(290 340 426)(291 321 427)(292 322 428)(293 323 429)(294 324 430)(295 325 431)(296 326 432)(297 327 433)(298 328 434)(299 329 435)(300 330 436)
(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)
(1 355 249 464)(2 346 250 475)(3 357 251 466)(4 348 252 477)(5 359 253 468)(6 350 254 479)(7 341 255 470)(8 352 256 461)(9 343 257 472)(10 354 258 463)(11 345 259 474)(12 356 260 465)(13 347 241 476)(14 358 242 467)(15 349 243 478)(16 360 244 469)(17 351 245 480)(18 342 246 471)(19 353 247 462)(20 344 248 473)(21 299 109 190)(22 290 110 181)(23 281 111 192)(24 292 112 183)(25 283 113 194)(26 294 114 185)(27 285 115 196)(28 296 116 187)(29 287 117 198)(30 298 118 189)(31 289 119 200)(32 300 120 191)(33 291 101 182)(34 282 102 193)(35 293 103 184)(36 284 104 195)(37 295 105 186)(38 286 106 197)(39 297 107 188)(40 288 108 199)(41 93 237 150)(42 84 238 141)(43 95 239 152)(44 86 240 143)(45 97 221 154)(46 88 222 145)(47 99 223 156)(48 90 224 147)(49 81 225 158)(50 92 226 149)(51 83 227 160)(52 94 228 151)(53 85 229 142)(54 96 230 153)(55 87 231 144)(56 98 232 155)(57 89 233 146)(58 100 234 157)(59 91 235 148)(60 82 236 159)(61 449 410 432)(62 460 411 423)(63 451 412 434)(64 442 413 425)(65 453 414 436)(66 444 415 427)(67 455 416 438)(68 446 417 429)(69 457 418 440)(70 448 419 431)(71 459 420 422)(72 450 401 433)(73 441 402 424)(74 452 403 435)(75 443 404 426)(76 454 405 437)(77 445 406 428)(78 456 407 439)(79 447 408 430)(80 458 409 421)(121 326 315 391)(122 337 316 382)(123 328 317 393)(124 339 318 384)(125 330 319 395)(126 321 320 386)(127 332 301 397)(128 323 302 388)(129 334 303 399)(130 325 304 390)(131 336 305 381)(132 327 306 392)(133 338 307 383)(134 329 308 394)(135 340 309 385)(136 331 310 396)(137 322 311 387)(138 333 312 398)(139 324 313 389)(140 335 314 400)(161 277 207 378)(162 268 208 369)(163 279 209 380)(164 270 210 371)(165 261 211 362)(166 272 212 373)(167 263 213 364)(168 274 214 375)(169 265 215 366)(170 276 216 377)(171 267 217 368)(172 278 218 379)(173 269 219 370)(174 280 220 361)(175 271 201 372)(176 262 202 363)(177 273 203 374)(178 264 204 365)(179 275 205 376)(180 266 206 367)
(1 410 249 61)(2 419 250 70)(3 408 251 79)(4 417 252 68)(5 406 253 77)(6 415 254 66)(7 404 255 75)(8 413 256 64)(9 402 257 73)(10 411 258 62)(11 420 259 71)(12 409 260 80)(13 418 241 69)(14 407 242 78)(15 416 243 67)(16 405 244 76)(17 414 245 65)(18 403 246 74)(19 412 247 63)(20 401 248 72)(21 81 109 158)(22 90 110 147)(23 99 111 156)(24 88 112 145)(25 97 113 154)(26 86 114 143)(27 95 115 152)(28 84 116 141)(29 93 117 150)(30 82 118 159)(31 91 119 148)(32 100 120 157)(33 89 101 146)(34 98 102 155)(35 87 103 144)(36 96 104 153)(37 85 105 142)(38 94 106 151)(39 83 107 160)(40 92 108 149)(41 198 237 287)(42 187 238 296)(43 196 239 285)(44 185 240 294)(45 194 221 283)(46 183 222 292)(47 192 223 281)(48 181 224 290)(49 190 225 299)(50 199 226 288)(51 188 227 297)(52 197 228 286)(53 186 229 295)(54 195 230 284)(55 184 231 293)(56 193 232 282)(57 182 233 291)(58 191 234 300)(59 200 235 289)(60 189 236 298)(121 204 315 178)(122 213 316 167)(123 202 317 176)(124 211 318 165)(125 220 319 174)(126 209 320 163)(127 218 301 172)(128 207 302 161)(129 216 303 170)(130 205 304 179)(131 214 305 168)(132 203 306 177)(133 212 307 166)(134 201 308 175)(135 210 309 164)(136 219 310 173)(137 208 311 162)(138 217 312 171)(139 206 313 180)(140 215 314 169)(261 384 362 339)(262 393 363 328)(263 382 364 337)(264 391 365 326)(265 400 366 335)(266 389 367 324)(267 398 368 333)(268 387 369 322)(269 396 370 331)(270 385 371 340)(271 394 372 329)(272 383 373 338)(273 392 374 327)(274 381 375 336)(275 390 376 325)(276 399 377 334)(277 388 378 323)(278 397 379 332)(279 386 380 321)(280 395 361 330)(341 443 470 426)(342 452 471 435)(343 441 472 424)(344 450 473 433)(345 459 474 422)(346 448 475 431)(347 457 476 440)(348 446 477 429)(349 455 478 438)(350 444 479 427)(351 453 480 436)(352 442 461 425)(353 451 462 434)(354 460 463 423)(355 449 464 432)(356 458 465 421)(357 447 466 430)(358 456 467 439)(359 445 468 428)(360 454 469 437)
G:=sub<Sym(480)| (1,141,178)(2,142,179)(3,143,180)(4,144,161)(5,145,162)(6,146,163)(7,147,164)(8,148,165)(9,149,166)(10,150,167)(11,151,168)(12,152,169)(13,153,170)(14,154,171)(15,155,172)(16,156,173)(17,157,174)(18,158,175)(19,159,176)(20,160,177)(21,134,403)(22,135,404)(23,136,405)(24,137,406)(25,138,407)(26,139,408)(27,140,409)(28,121,410)(29,122,411)(30,123,412)(31,124,413)(32,125,414)(33,126,415)(34,127,416)(35,128,417)(36,129,418)(37,130,419)(38,131,420)(39,132,401)(40,133,402)(41,263,354)(42,264,355)(43,265,356)(44,266,357)(45,267,358)(46,268,359)(47,269,360)(48,270,341)(49,271,342)(50,272,343)(51,273,344)(52,274,345)(53,275,346)(54,276,347)(55,277,348)(56,278,349)(57,279,350)(58,280,351)(59,261,352)(60,262,353)(61,116,315)(62,117,316)(63,118,317)(64,119,318)(65,120,319)(66,101,320)(67,102,301)(68,103,302)(69,104,303)(70,105,304)(71,106,305)(72,107,306)(73,108,307)(74,109,308)(75,110,309)(76,111,310)(77,112,311)(78,113,312)(79,114,313)(80,115,314)(81,201,246)(82,202,247)(83,203,248)(84,204,249)(85,205,250)(86,206,251)(87,207,252)(88,208,253)(89,209,254)(90,210,255)(91,211,256)(92,212,257)(93,213,258)(94,214,259)(95,215,260)(96,216,241)(97,217,242)(98,218,243)(99,219,244)(100,220,245)(181,385,443)(182,386,444)(183,387,445)(184,388,446)(185,389,447)(186,390,448)(187,391,449)(188,392,450)(189,393,451)(190,394,452)(191,395,453)(192,396,454)(193,397,455)(194,398,456)(195,399,457)(196,400,458)(197,381,459)(198,382,460)(199,383,441)(200,384,442)(221,368,467)(222,369,468)(223,370,469)(224,371,470)(225,372,471)(226,373,472)(227,374,473)(228,375,474)(229,376,475)(230,377,476)(231,378,477)(232,379,478)(233,380,479)(234,361,480)(235,362,461)(236,363,462)(237,364,463)(238,365,464)(239,366,465)(240,367,466)(281,331,437)(282,332,438)(283,333,439)(284,334,440)(285,335,421)(286,336,422)(287,337,423)(288,338,424)(289,339,425)(290,340,426)(291,321,427)(292,322,428)(293,323,429)(294,324,430)(295,325,431)(296,326,432)(297,327,433)(298,328,434)(299,329,435)(300,330,436), (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), (1,355,249,464)(2,346,250,475)(3,357,251,466)(4,348,252,477)(5,359,253,468)(6,350,254,479)(7,341,255,470)(8,352,256,461)(9,343,257,472)(10,354,258,463)(11,345,259,474)(12,356,260,465)(13,347,241,476)(14,358,242,467)(15,349,243,478)(16,360,244,469)(17,351,245,480)(18,342,246,471)(19,353,247,462)(20,344,248,473)(21,299,109,190)(22,290,110,181)(23,281,111,192)(24,292,112,183)(25,283,113,194)(26,294,114,185)(27,285,115,196)(28,296,116,187)(29,287,117,198)(30,298,118,189)(31,289,119,200)(32,300,120,191)(33,291,101,182)(34,282,102,193)(35,293,103,184)(36,284,104,195)(37,295,105,186)(38,286,106,197)(39,297,107,188)(40,288,108,199)(41,93,237,150)(42,84,238,141)(43,95,239,152)(44,86,240,143)(45,97,221,154)(46,88,222,145)(47,99,223,156)(48,90,224,147)(49,81,225,158)(50,92,226,149)(51,83,227,160)(52,94,228,151)(53,85,229,142)(54,96,230,153)(55,87,231,144)(56,98,232,155)(57,89,233,146)(58,100,234,157)(59,91,235,148)(60,82,236,159)(61,449,410,432)(62,460,411,423)(63,451,412,434)(64,442,413,425)(65,453,414,436)(66,444,415,427)(67,455,416,438)(68,446,417,429)(69,457,418,440)(70,448,419,431)(71,459,420,422)(72,450,401,433)(73,441,402,424)(74,452,403,435)(75,443,404,426)(76,454,405,437)(77,445,406,428)(78,456,407,439)(79,447,408,430)(80,458,409,421)(121,326,315,391)(122,337,316,382)(123,328,317,393)(124,339,318,384)(125,330,319,395)(126,321,320,386)(127,332,301,397)(128,323,302,388)(129,334,303,399)(130,325,304,390)(131,336,305,381)(132,327,306,392)(133,338,307,383)(134,329,308,394)(135,340,309,385)(136,331,310,396)(137,322,311,387)(138,333,312,398)(139,324,313,389)(140,335,314,400)(161,277,207,378)(162,268,208,369)(163,279,209,380)(164,270,210,371)(165,261,211,362)(166,272,212,373)(167,263,213,364)(168,274,214,375)(169,265,215,366)(170,276,216,377)(171,267,217,368)(172,278,218,379)(173,269,219,370)(174,280,220,361)(175,271,201,372)(176,262,202,363)(177,273,203,374)(178,264,204,365)(179,275,205,376)(180,266,206,367), (1,410,249,61)(2,419,250,70)(3,408,251,79)(4,417,252,68)(5,406,253,77)(6,415,254,66)(7,404,255,75)(8,413,256,64)(9,402,257,73)(10,411,258,62)(11,420,259,71)(12,409,260,80)(13,418,241,69)(14,407,242,78)(15,416,243,67)(16,405,244,76)(17,414,245,65)(18,403,246,74)(19,412,247,63)(20,401,248,72)(21,81,109,158)(22,90,110,147)(23,99,111,156)(24,88,112,145)(25,97,113,154)(26,86,114,143)(27,95,115,152)(28,84,116,141)(29,93,117,150)(30,82,118,159)(31,91,119,148)(32,100,120,157)(33,89,101,146)(34,98,102,155)(35,87,103,144)(36,96,104,153)(37,85,105,142)(38,94,106,151)(39,83,107,160)(40,92,108,149)(41,198,237,287)(42,187,238,296)(43,196,239,285)(44,185,240,294)(45,194,221,283)(46,183,222,292)(47,192,223,281)(48,181,224,290)(49,190,225,299)(50,199,226,288)(51,188,227,297)(52,197,228,286)(53,186,229,295)(54,195,230,284)(55,184,231,293)(56,193,232,282)(57,182,233,291)(58,191,234,300)(59,200,235,289)(60,189,236,298)(121,204,315,178)(122,213,316,167)(123,202,317,176)(124,211,318,165)(125,220,319,174)(126,209,320,163)(127,218,301,172)(128,207,302,161)(129,216,303,170)(130,205,304,179)(131,214,305,168)(132,203,306,177)(133,212,307,166)(134,201,308,175)(135,210,309,164)(136,219,310,173)(137,208,311,162)(138,217,312,171)(139,206,313,180)(140,215,314,169)(261,384,362,339)(262,393,363,328)(263,382,364,337)(264,391,365,326)(265,400,366,335)(266,389,367,324)(267,398,368,333)(268,387,369,322)(269,396,370,331)(270,385,371,340)(271,394,372,329)(272,383,373,338)(273,392,374,327)(274,381,375,336)(275,390,376,325)(276,399,377,334)(277,388,378,323)(278,397,379,332)(279,386,380,321)(280,395,361,330)(341,443,470,426)(342,452,471,435)(343,441,472,424)(344,450,473,433)(345,459,474,422)(346,448,475,431)(347,457,476,440)(348,446,477,429)(349,455,478,438)(350,444,479,427)(351,453,480,436)(352,442,461,425)(353,451,462,434)(354,460,463,423)(355,449,464,432)(356,458,465,421)(357,447,466,430)(358,456,467,439)(359,445,468,428)(360,454,469,437)>;
G:=Group( (1,141,178)(2,142,179)(3,143,180)(4,144,161)(5,145,162)(6,146,163)(7,147,164)(8,148,165)(9,149,166)(10,150,167)(11,151,168)(12,152,169)(13,153,170)(14,154,171)(15,155,172)(16,156,173)(17,157,174)(18,158,175)(19,159,176)(20,160,177)(21,134,403)(22,135,404)(23,136,405)(24,137,406)(25,138,407)(26,139,408)(27,140,409)(28,121,410)(29,122,411)(30,123,412)(31,124,413)(32,125,414)(33,126,415)(34,127,416)(35,128,417)(36,129,418)(37,130,419)(38,131,420)(39,132,401)(40,133,402)(41,263,354)(42,264,355)(43,265,356)(44,266,357)(45,267,358)(46,268,359)(47,269,360)(48,270,341)(49,271,342)(50,272,343)(51,273,344)(52,274,345)(53,275,346)(54,276,347)(55,277,348)(56,278,349)(57,279,350)(58,280,351)(59,261,352)(60,262,353)(61,116,315)(62,117,316)(63,118,317)(64,119,318)(65,120,319)(66,101,320)(67,102,301)(68,103,302)(69,104,303)(70,105,304)(71,106,305)(72,107,306)(73,108,307)(74,109,308)(75,110,309)(76,111,310)(77,112,311)(78,113,312)(79,114,313)(80,115,314)(81,201,246)(82,202,247)(83,203,248)(84,204,249)(85,205,250)(86,206,251)(87,207,252)(88,208,253)(89,209,254)(90,210,255)(91,211,256)(92,212,257)(93,213,258)(94,214,259)(95,215,260)(96,216,241)(97,217,242)(98,218,243)(99,219,244)(100,220,245)(181,385,443)(182,386,444)(183,387,445)(184,388,446)(185,389,447)(186,390,448)(187,391,449)(188,392,450)(189,393,451)(190,394,452)(191,395,453)(192,396,454)(193,397,455)(194,398,456)(195,399,457)(196,400,458)(197,381,459)(198,382,460)(199,383,441)(200,384,442)(221,368,467)(222,369,468)(223,370,469)(224,371,470)(225,372,471)(226,373,472)(227,374,473)(228,375,474)(229,376,475)(230,377,476)(231,378,477)(232,379,478)(233,380,479)(234,361,480)(235,362,461)(236,363,462)(237,364,463)(238,365,464)(239,366,465)(240,367,466)(281,331,437)(282,332,438)(283,333,439)(284,334,440)(285,335,421)(286,336,422)(287,337,423)(288,338,424)(289,339,425)(290,340,426)(291,321,427)(292,322,428)(293,323,429)(294,324,430)(295,325,431)(296,326,432)(297,327,433)(298,328,434)(299,329,435)(300,330,436), (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), (1,355,249,464)(2,346,250,475)(3,357,251,466)(4,348,252,477)(5,359,253,468)(6,350,254,479)(7,341,255,470)(8,352,256,461)(9,343,257,472)(10,354,258,463)(11,345,259,474)(12,356,260,465)(13,347,241,476)(14,358,242,467)(15,349,243,478)(16,360,244,469)(17,351,245,480)(18,342,246,471)(19,353,247,462)(20,344,248,473)(21,299,109,190)(22,290,110,181)(23,281,111,192)(24,292,112,183)(25,283,113,194)(26,294,114,185)(27,285,115,196)(28,296,116,187)(29,287,117,198)(30,298,118,189)(31,289,119,200)(32,300,120,191)(33,291,101,182)(34,282,102,193)(35,293,103,184)(36,284,104,195)(37,295,105,186)(38,286,106,197)(39,297,107,188)(40,288,108,199)(41,93,237,150)(42,84,238,141)(43,95,239,152)(44,86,240,143)(45,97,221,154)(46,88,222,145)(47,99,223,156)(48,90,224,147)(49,81,225,158)(50,92,226,149)(51,83,227,160)(52,94,228,151)(53,85,229,142)(54,96,230,153)(55,87,231,144)(56,98,232,155)(57,89,233,146)(58,100,234,157)(59,91,235,148)(60,82,236,159)(61,449,410,432)(62,460,411,423)(63,451,412,434)(64,442,413,425)(65,453,414,436)(66,444,415,427)(67,455,416,438)(68,446,417,429)(69,457,418,440)(70,448,419,431)(71,459,420,422)(72,450,401,433)(73,441,402,424)(74,452,403,435)(75,443,404,426)(76,454,405,437)(77,445,406,428)(78,456,407,439)(79,447,408,430)(80,458,409,421)(121,326,315,391)(122,337,316,382)(123,328,317,393)(124,339,318,384)(125,330,319,395)(126,321,320,386)(127,332,301,397)(128,323,302,388)(129,334,303,399)(130,325,304,390)(131,336,305,381)(132,327,306,392)(133,338,307,383)(134,329,308,394)(135,340,309,385)(136,331,310,396)(137,322,311,387)(138,333,312,398)(139,324,313,389)(140,335,314,400)(161,277,207,378)(162,268,208,369)(163,279,209,380)(164,270,210,371)(165,261,211,362)(166,272,212,373)(167,263,213,364)(168,274,214,375)(169,265,215,366)(170,276,216,377)(171,267,217,368)(172,278,218,379)(173,269,219,370)(174,280,220,361)(175,271,201,372)(176,262,202,363)(177,273,203,374)(178,264,204,365)(179,275,205,376)(180,266,206,367), (1,410,249,61)(2,419,250,70)(3,408,251,79)(4,417,252,68)(5,406,253,77)(6,415,254,66)(7,404,255,75)(8,413,256,64)(9,402,257,73)(10,411,258,62)(11,420,259,71)(12,409,260,80)(13,418,241,69)(14,407,242,78)(15,416,243,67)(16,405,244,76)(17,414,245,65)(18,403,246,74)(19,412,247,63)(20,401,248,72)(21,81,109,158)(22,90,110,147)(23,99,111,156)(24,88,112,145)(25,97,113,154)(26,86,114,143)(27,95,115,152)(28,84,116,141)(29,93,117,150)(30,82,118,159)(31,91,119,148)(32,100,120,157)(33,89,101,146)(34,98,102,155)(35,87,103,144)(36,96,104,153)(37,85,105,142)(38,94,106,151)(39,83,107,160)(40,92,108,149)(41,198,237,287)(42,187,238,296)(43,196,239,285)(44,185,240,294)(45,194,221,283)(46,183,222,292)(47,192,223,281)(48,181,224,290)(49,190,225,299)(50,199,226,288)(51,188,227,297)(52,197,228,286)(53,186,229,295)(54,195,230,284)(55,184,231,293)(56,193,232,282)(57,182,233,291)(58,191,234,300)(59,200,235,289)(60,189,236,298)(121,204,315,178)(122,213,316,167)(123,202,317,176)(124,211,318,165)(125,220,319,174)(126,209,320,163)(127,218,301,172)(128,207,302,161)(129,216,303,170)(130,205,304,179)(131,214,305,168)(132,203,306,177)(133,212,307,166)(134,201,308,175)(135,210,309,164)(136,219,310,173)(137,208,311,162)(138,217,312,171)(139,206,313,180)(140,215,314,169)(261,384,362,339)(262,393,363,328)(263,382,364,337)(264,391,365,326)(265,400,366,335)(266,389,367,324)(267,398,368,333)(268,387,369,322)(269,396,370,331)(270,385,371,340)(271,394,372,329)(272,383,373,338)(273,392,374,327)(274,381,375,336)(275,390,376,325)(276,399,377,334)(277,388,378,323)(278,397,379,332)(279,386,380,321)(280,395,361,330)(341,443,470,426)(342,452,471,435)(343,441,472,424)(344,450,473,433)(345,459,474,422)(346,448,475,431)(347,457,476,440)(348,446,477,429)(349,455,478,438)(350,444,479,427)(351,453,480,436)(352,442,461,425)(353,451,462,434)(354,460,463,423)(355,449,464,432)(356,458,465,421)(357,447,466,430)(358,456,467,439)(359,445,468,428)(360,454,469,437) );
G=PermutationGroup([[(1,141,178),(2,142,179),(3,143,180),(4,144,161),(5,145,162),(6,146,163),(7,147,164),(8,148,165),(9,149,166),(10,150,167),(11,151,168),(12,152,169),(13,153,170),(14,154,171),(15,155,172),(16,156,173),(17,157,174),(18,158,175),(19,159,176),(20,160,177),(21,134,403),(22,135,404),(23,136,405),(24,137,406),(25,138,407),(26,139,408),(27,140,409),(28,121,410),(29,122,411),(30,123,412),(31,124,413),(32,125,414),(33,126,415),(34,127,416),(35,128,417),(36,129,418),(37,130,419),(38,131,420),(39,132,401),(40,133,402),(41,263,354),(42,264,355),(43,265,356),(44,266,357),(45,267,358),(46,268,359),(47,269,360),(48,270,341),(49,271,342),(50,272,343),(51,273,344),(52,274,345),(53,275,346),(54,276,347),(55,277,348),(56,278,349),(57,279,350),(58,280,351),(59,261,352),(60,262,353),(61,116,315),(62,117,316),(63,118,317),(64,119,318),(65,120,319),(66,101,320),(67,102,301),(68,103,302),(69,104,303),(70,105,304),(71,106,305),(72,107,306),(73,108,307),(74,109,308),(75,110,309),(76,111,310),(77,112,311),(78,113,312),(79,114,313),(80,115,314),(81,201,246),(82,202,247),(83,203,248),(84,204,249),(85,205,250),(86,206,251),(87,207,252),(88,208,253),(89,209,254),(90,210,255),(91,211,256),(92,212,257),(93,213,258),(94,214,259),(95,215,260),(96,216,241),(97,217,242),(98,218,243),(99,219,244),(100,220,245),(181,385,443),(182,386,444),(183,387,445),(184,388,446),(185,389,447),(186,390,448),(187,391,449),(188,392,450),(189,393,451),(190,394,452),(191,395,453),(192,396,454),(193,397,455),(194,398,456),(195,399,457),(196,400,458),(197,381,459),(198,382,460),(199,383,441),(200,384,442),(221,368,467),(222,369,468),(223,370,469),(224,371,470),(225,372,471),(226,373,472),(227,374,473),(228,375,474),(229,376,475),(230,377,476),(231,378,477),(232,379,478),(233,380,479),(234,361,480),(235,362,461),(236,363,462),(237,364,463),(238,365,464),(239,366,465),(240,367,466),(281,331,437),(282,332,438),(283,333,439),(284,334,440),(285,335,421),(286,336,422),(287,337,423),(288,338,424),(289,339,425),(290,340,426),(291,321,427),(292,322,428),(293,323,429),(294,324,430),(295,325,431),(296,326,432),(297,327,433),(298,328,434),(299,329,435),(300,330,436)], [(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)], [(1,355,249,464),(2,346,250,475),(3,357,251,466),(4,348,252,477),(5,359,253,468),(6,350,254,479),(7,341,255,470),(8,352,256,461),(9,343,257,472),(10,354,258,463),(11,345,259,474),(12,356,260,465),(13,347,241,476),(14,358,242,467),(15,349,243,478),(16,360,244,469),(17,351,245,480),(18,342,246,471),(19,353,247,462),(20,344,248,473),(21,299,109,190),(22,290,110,181),(23,281,111,192),(24,292,112,183),(25,283,113,194),(26,294,114,185),(27,285,115,196),(28,296,116,187),(29,287,117,198),(30,298,118,189),(31,289,119,200),(32,300,120,191),(33,291,101,182),(34,282,102,193),(35,293,103,184),(36,284,104,195),(37,295,105,186),(38,286,106,197),(39,297,107,188),(40,288,108,199),(41,93,237,150),(42,84,238,141),(43,95,239,152),(44,86,240,143),(45,97,221,154),(46,88,222,145),(47,99,223,156),(48,90,224,147),(49,81,225,158),(50,92,226,149),(51,83,227,160),(52,94,228,151),(53,85,229,142),(54,96,230,153),(55,87,231,144),(56,98,232,155),(57,89,233,146),(58,100,234,157),(59,91,235,148),(60,82,236,159),(61,449,410,432),(62,460,411,423),(63,451,412,434),(64,442,413,425),(65,453,414,436),(66,444,415,427),(67,455,416,438),(68,446,417,429),(69,457,418,440),(70,448,419,431),(71,459,420,422),(72,450,401,433),(73,441,402,424),(74,452,403,435),(75,443,404,426),(76,454,405,437),(77,445,406,428),(78,456,407,439),(79,447,408,430),(80,458,409,421),(121,326,315,391),(122,337,316,382),(123,328,317,393),(124,339,318,384),(125,330,319,395),(126,321,320,386),(127,332,301,397),(128,323,302,388),(129,334,303,399),(130,325,304,390),(131,336,305,381),(132,327,306,392),(133,338,307,383),(134,329,308,394),(135,340,309,385),(136,331,310,396),(137,322,311,387),(138,333,312,398),(139,324,313,389),(140,335,314,400),(161,277,207,378),(162,268,208,369),(163,279,209,380),(164,270,210,371),(165,261,211,362),(166,272,212,373),(167,263,213,364),(168,274,214,375),(169,265,215,366),(170,276,216,377),(171,267,217,368),(172,278,218,379),(173,269,219,370),(174,280,220,361),(175,271,201,372),(176,262,202,363),(177,273,203,374),(178,264,204,365),(179,275,205,376),(180,266,206,367)], [(1,410,249,61),(2,419,250,70),(3,408,251,79),(4,417,252,68),(5,406,253,77),(6,415,254,66),(7,404,255,75),(8,413,256,64),(9,402,257,73),(10,411,258,62),(11,420,259,71),(12,409,260,80),(13,418,241,69),(14,407,242,78),(15,416,243,67),(16,405,244,76),(17,414,245,65),(18,403,246,74),(19,412,247,63),(20,401,248,72),(21,81,109,158),(22,90,110,147),(23,99,111,156),(24,88,112,145),(25,97,113,154),(26,86,114,143),(27,95,115,152),(28,84,116,141),(29,93,117,150),(30,82,118,159),(31,91,119,148),(32,100,120,157),(33,89,101,146),(34,98,102,155),(35,87,103,144),(36,96,104,153),(37,85,105,142),(38,94,106,151),(39,83,107,160),(40,92,108,149),(41,198,237,287),(42,187,238,296),(43,196,239,285),(44,185,240,294),(45,194,221,283),(46,183,222,292),(47,192,223,281),(48,181,224,290),(49,190,225,299),(50,199,226,288),(51,188,227,297),(52,197,228,286),(53,186,229,295),(54,195,230,284),(55,184,231,293),(56,193,232,282),(57,182,233,291),(58,191,234,300),(59,200,235,289),(60,189,236,298),(121,204,315,178),(122,213,316,167),(123,202,317,176),(124,211,318,165),(125,220,319,174),(126,209,320,163),(127,218,301,172),(128,207,302,161),(129,216,303,170),(130,205,304,179),(131,214,305,168),(132,203,306,177),(133,212,307,166),(134,201,308,175),(135,210,309,164),(136,219,310,173),(137,208,311,162),(138,217,312,171),(139,206,313,180),(140,215,314,169),(261,384,362,339),(262,393,363,328),(263,382,364,337),(264,391,365,326),(265,400,366,335),(266,389,367,324),(267,398,368,333),(268,387,369,322),(269,396,370,331),(270,385,371,340),(271,394,372,329),(272,383,373,338),(273,392,374,327),(274,381,375,336),(275,390,376,325),(276,399,377,334),(277,388,378,323),(278,397,379,332),(279,386,380,321),(280,395,361,330),(341,443,470,426),(342,452,471,435),(343,441,472,424),(344,450,473,433),(345,459,474,422),(346,448,475,431),(347,457,476,440),(348,446,477,429),(349,455,478,438),(350,444,479,427),(351,453,480,436),(352,442,461,425),(353,451,462,434),(354,460,463,423),(355,449,464,432),(356,458,465,421),(357,447,466,430),(358,456,467,439),(359,445,468,428),(360,454,469,437)]])
102 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 6A | ··· | 6F | 10A | ··· | 10F | 12A | 12B | 12C | 12D | 12E | 12F | 12G | 12H | 12I | ··· | 12P | 12Q | 12R | 12S | 12T | 15A | 15B | 15C | 15D | 20A | ··· | 20L | 30A | ··· | 30L | 60A | ··· | 60X |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | ··· | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 10 | 10 | 10 | 10 | 20 | 20 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
102 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | - | + | + | - | + | - | ||||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C3 | C6 | C6 | C6 | C6 | C6 | D4 | Q8 | Q8 | D5 | D10 | C3×D4 | C3×Q8 | C3×Q8 | C3×D5 | Dic10 | C6×D5 | C3×Dic10 | D4×D5 | Q8×D5 | C3×D4×D5 | C3×Q8×D5 |
| kernel | C3×C20⋊Q8 | C12×Dic5 | C3×C10.D4 | C3×C4⋊Dic5 | C15×C4⋊C4 | C6×Dic10 | C20⋊Q8 | C4×Dic5 | C10.D4 | C4⋊Dic5 | C5×C4⋊C4 | C2×Dic10 | C3×Dic5 | C3×Dic5 | C60 | C3×C4⋊C4 | C2×C12 | Dic5 | Dic5 | C20 | C4⋊C4 | C12 | C2×C4 | C4 | C6 | C6 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 1 | 2 | 2 | 2 | 4 | 2 | 2 | 4 | 2 | 2 | 2 | 2 | 6 | 4 | 4 | 4 | 4 | 8 | 12 | 16 | 2 | 2 | 4 | 4 |
Matrix representation of C3×C20⋊Q8 ►in GL6(𝔽61)
| 13 | 0 | 0 | 0 | 0 | 0 |
| 0 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 47 | 0 | 0 | 0 |
| 0 | 0 | 0 | 47 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 1 | 0 | 0 |
| 0 | 0 | 42 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 43 | 9 |
| 0 | 0 | 0 | 0 | 52 | 18 |
| 22 | 46 | 0 | 0 | 0 | 0 |
| 12 | 39 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 7 | 35 | 0 | 0 | 0 | 0 |
| 16 | 54 | 0 | 0 | 0 | 0 |
| 0 | 0 | 59 | 55 | 0 | 0 |
| 0 | 0 | 31 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(61))| [13,0,0,0,0,0,0,13,0,0,0,0,0,0,47,0,0,0,0,0,0,47,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,42,0,0,0,0,1,18,0,0,0,0,0,0,43,52,0,0,0,0,9,18],[22,12,0,0,0,0,46,39,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[7,16,0,0,0,0,35,54,0,0,0,0,0,0,59,31,0,0,0,0,55,2,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
C3×C20⋊Q8 in GAP, Magma, Sage, TeX
C_3\times C_{20}\rtimes Q_8 % in TeX
G:=Group("C3xC20:Q8"); // GroupNames label
G:=SmallGroup(480,681);
// by ID
G=gap.SmallGroup(480,681);
# by ID
G:=PCGroup([7,-2,-2,-2,-3,-2,-2,-5,168,344,590,555,142,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^20=c^4=1,d^2=c^2,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^11,d*b*d^-1=b^9,d*c*d^-1=c^-1>;
// generators/relations