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G = Dic308C4order 480 = 25·3·5

2nd semidirect product of Dic30 and C4 acting via C4/C2=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: Dic308C4, C60.201D4, C30.10Q16, C6.1Dic20, C2.1Dic60, C22.7D60, C30.16SD16, C10.1Dic12, (C2×C40).4S3, (C2×C24).4D5, (C2×C8).2D15, C4.7(C4×D15), C20.82(C4×S3), (C2×C120).6C2, C12.50(C4×D5), (C2×C30).99D4, (C2×C6).13D20, (C2×C4).70D30, C605C4.1C2, C60.187(C2×C4), (C2×C10).13D12, (C2×C20).384D6, C6.1(C40⋊C2), C53(C2.Dic12), C2.1(C24⋊D5), C10.1(C24⋊C2), C10.31(D6⋊C4), C1514(Q8⋊C4), (C2×C12).386D10, C12.98(C5⋊D4), C32(C20.44D4), C20.98(C3⋊D4), C4.19(C157D4), (C2×Dic30).1C2, C2.7(D303C4), C30.73(C22⋊C4), (C2×C60).471C22, C6.16(D10⋊C4), SmallGroup(480,176)

Series: Derived Chief Lower central Upper central

C1C60 — Dic308C4
C1C5C15C30C60C2×C60C605C4 — Dic308C4
C15C30C60 — Dic308C4
C1C22C2×C4C2×C8

Generators and relations for Dic308C4
 G = < a,b,c | a60=c4=1, b2=a30, bab-1=cac-1=a-1, cbc-1=a15b >

Subgroups: 500 in 84 conjugacy classes, 41 normal (39 characteristic)
C1, C2 [×3], C3, C4 [×2], C4 [×3], C22, C5, C6 [×3], C8, C2×C4, C2×C4 [×2], Q8 [×3], C10 [×3], Dic3 [×3], C12 [×2], C2×C6, C15, C4⋊C4, C2×C8, C2×Q8, Dic5 [×3], C20 [×2], C2×C10, C24, Dic6 [×3], C2×Dic3 [×2], C2×C12, C30 [×3], Q8⋊C4, C40, Dic10 [×3], C2×Dic5 [×2], C2×C20, C4⋊Dic3, C2×C24, C2×Dic6, Dic15 [×3], C60 [×2], C2×C30, C4⋊Dic5, C2×C40, C2×Dic10, C2.Dic12, C120, Dic30 [×2], Dic30, C2×Dic15 [×2], C2×C60, C20.44D4, C605C4, C2×C120, C2×Dic30, Dic308C4
Quotients: C1, C2 [×3], C4 [×2], C22, S3, C2×C4, D4 [×2], D5, D6, C22⋊C4, SD16, Q16, D10, C4×S3, D12, C3⋊D4, D15, Q8⋊C4, C4×D5, D20, C5⋊D4, C24⋊C2, Dic12, D6⋊C4, D30, C40⋊C2, Dic20, D10⋊C4, C2.Dic12, C4×D15, D60, C157D4, C20.44D4, C24⋊D5, Dic60, D303C4, Dic308C4

Smallest permutation representation of Dic308C4
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)
(1 210 31 240)(2 209 32 239)(3 208 33 238)(4 207 34 237)(5 206 35 236)(6 205 36 235)(7 204 37 234)(8 203 38 233)(9 202 39 232)(10 201 40 231)(11 200 41 230)(12 199 42 229)(13 198 43 228)(14 197 44 227)(15 196 45 226)(16 195 46 225)(17 194 47 224)(18 193 48 223)(19 192 49 222)(20 191 50 221)(21 190 51 220)(22 189 52 219)(23 188 53 218)(24 187 54 217)(25 186 55 216)(26 185 56 215)(27 184 57 214)(28 183 58 213)(29 182 59 212)(30 181 60 211)(61 242 91 272)(62 241 92 271)(63 300 93 270)(64 299 94 269)(65 298 95 268)(66 297 96 267)(67 296 97 266)(68 295 98 265)(69 294 99 264)(70 293 100 263)(71 292 101 262)(72 291 102 261)(73 290 103 260)(74 289 104 259)(75 288 105 258)(76 287 106 257)(77 286 107 256)(78 285 108 255)(79 284 109 254)(80 283 110 253)(81 282 111 252)(82 281 112 251)(83 280 113 250)(84 279 114 249)(85 278 115 248)(86 277 116 247)(87 276 117 246)(88 275 118 245)(89 274 119 244)(90 273 120 243)(121 398 151 368)(122 397 152 367)(123 396 153 366)(124 395 154 365)(125 394 155 364)(126 393 156 363)(127 392 157 362)(128 391 158 361)(129 390 159 420)(130 389 160 419)(131 388 161 418)(132 387 162 417)(133 386 163 416)(134 385 164 415)(135 384 165 414)(136 383 166 413)(137 382 167 412)(138 381 168 411)(139 380 169 410)(140 379 170 409)(141 378 171 408)(142 377 172 407)(143 376 173 406)(144 375 174 405)(145 374 175 404)(146 373 176 403)(147 372 177 402)(148 371 178 401)(149 370 179 400)(150 369 180 399)(301 475 331 445)(302 474 332 444)(303 473 333 443)(304 472 334 442)(305 471 335 441)(306 470 336 440)(307 469 337 439)(308 468 338 438)(309 467 339 437)(310 466 340 436)(311 465 341 435)(312 464 342 434)(313 463 343 433)(314 462 344 432)(315 461 345 431)(316 460 346 430)(317 459 347 429)(318 458 348 428)(319 457 349 427)(320 456 350 426)(321 455 351 425)(322 454 352 424)(323 453 353 423)(324 452 354 422)(325 451 355 421)(326 450 356 480)(327 449 357 479)(328 448 358 478)(329 447 359 477)(330 446 360 476)
(1 373 334 266)(2 372 335 265)(3 371 336 264)(4 370 337 263)(5 369 338 262)(6 368 339 261)(7 367 340 260)(8 366 341 259)(9 365 342 258)(10 364 343 257)(11 363 344 256)(12 362 345 255)(13 361 346 254)(14 420 347 253)(15 419 348 252)(16 418 349 251)(17 417 350 250)(18 416 351 249)(19 415 352 248)(20 414 353 247)(21 413 354 246)(22 412 355 245)(23 411 356 244)(24 410 357 243)(25 409 358 242)(26 408 359 241)(27 407 360 300)(28 406 301 299)(29 405 302 298)(30 404 303 297)(31 403 304 296)(32 402 305 295)(33 401 306 294)(34 400 307 293)(35 399 308 292)(36 398 309 291)(37 397 310 290)(38 396 311 289)(39 395 312 288)(40 394 313 287)(41 393 314 286)(42 392 315 285)(43 391 316 284)(44 390 317 283)(45 389 318 282)(46 388 319 281)(47 387 320 280)(48 386 321 279)(49 385 322 278)(50 384 323 277)(51 383 324 276)(52 382 325 275)(53 381 326 274)(54 380 327 273)(55 379 328 272)(56 378 329 271)(57 377 330 270)(58 376 331 269)(59 375 332 268)(60 374 333 267)(61 201 170 433)(62 200 171 432)(63 199 172 431)(64 198 173 430)(65 197 174 429)(66 196 175 428)(67 195 176 427)(68 194 177 426)(69 193 178 425)(70 192 179 424)(71 191 180 423)(72 190 121 422)(73 189 122 421)(74 188 123 480)(75 187 124 479)(76 186 125 478)(77 185 126 477)(78 184 127 476)(79 183 128 475)(80 182 129 474)(81 181 130 473)(82 240 131 472)(83 239 132 471)(84 238 133 470)(85 237 134 469)(86 236 135 468)(87 235 136 467)(88 234 137 466)(89 233 138 465)(90 232 139 464)(91 231 140 463)(92 230 141 462)(93 229 142 461)(94 228 143 460)(95 227 144 459)(96 226 145 458)(97 225 146 457)(98 224 147 456)(99 223 148 455)(100 222 149 454)(101 221 150 453)(102 220 151 452)(103 219 152 451)(104 218 153 450)(105 217 154 449)(106 216 155 448)(107 215 156 447)(108 214 157 446)(109 213 158 445)(110 212 159 444)(111 211 160 443)(112 210 161 442)(113 209 162 441)(114 208 163 440)(115 207 164 439)(116 206 165 438)(117 205 166 437)(118 204 167 436)(119 203 168 435)(120 202 169 434)

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

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

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

126 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D4E4F5A5B6A6B6C8A8B8C8D10A···10F12A12B12C12D15A15B15C15D20A···20H24A···24H30A···30L40A···40P60A···60P120A···120AF
order1222344444455666888810···10121212121515151520···2024···2430···3040···4060···60120···120
size1111222606060602222222222···2222222222···22···22···22···22···22···2

126 irreducible representations

dim111112222222222222222222222222
type+++++++++-++++-+-+-
imageC1C2C2C2C4S3D4D4D5D6SD16Q16D10C4×S3C3⋊D4D12D15C4×D5C5⋊D4D20C24⋊C2Dic12D30C40⋊C2Dic20C4×D15C157D4D60C24⋊D5Dic60
kernelDic308C4C605C4C2×C120C2×Dic30Dic30C2×C40C60C2×C30C2×C24C2×C20C30C30C2×C12C20C20C2×C10C2×C8C12C12C2×C6C10C10C2×C4C6C6C4C4C22C2C2
# reps11114111212222224444444888881616

Matrix representation of Dic308C4 in GL3(𝔽241) generated by

100
078128
0113170
,
100
0156238
07985
,
17700
08435
05157
G:=sub<GL(3,GF(241))| [1,0,0,0,78,113,0,128,170],[1,0,0,0,156,79,0,238,85],[177,0,0,0,84,5,0,35,157] >;

Dic308C4 in GAP, Magma, Sage, TeX

{\rm Dic}_{30}\rtimes_8C_4
% in TeX

G:=Group("Dic30:8C4");
// GroupNames label

G:=SmallGroup(480,176);
// by ID

G=gap.SmallGroup(480,176);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,85,92,422,100,2693,18822]);
// Polycyclic

G:=Group<a,b,c|a^60=c^4=1,b^2=a^30,b*a*b^-1=c*a*c^-1=a^-1,c*b*c^-1=a^15*b>;
// generators/relations

׿
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𝔽