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G = C30.SD16order 480 = 25·3·5

14th non-split extension by C30 of SD16 acting via SD16/C4=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C60.10Q8, C20.2Dic6, C12.1Dic10, C30.14SD16, C153C811C4, C155(C4.Q8), C4.7(C15⋊Q8), C20.42(C4×S3), (C2×C30).30D4, (C2×C20).59D6, C12.10(C4×D5), C6.6(Q8⋊D5), C4⋊Dic3.9D5, C4⋊Dic5.9S3, C30.26(C4⋊C4), C60.126(C2×C4), (C2×C12).59D10, C6.6(D4.D5), C53(C12.Q8), C32(C20.Q8), C10.6(D4.S3), (C2×C60).185C22, C4.11(D30.C2), C10.6(Q82S3), C6.4(C10.D4), C2.3(C20.D6), C2.3(C30.D4), C2.3(Dic155C4), C10.10(Dic3⋊C4), C22.16(C15⋊D4), (C2×C4).190(S3×D5), (C5×C4⋊Dic3).8C2, (C3×C4⋊Dic5).8C2, (C2×C153C8).13C2, (C2×C6).48(C5⋊D4), (C2×C10).48(C3⋊D4), SmallGroup(480,62)

Series: Derived Chief Lower central Upper central

C1C60 — C30.SD16
C1C5C15C30C2×C30C2×C60C3×C4⋊Dic5 — C30.SD16
C15C30C60 — C30.SD16
C1C22C2×C4

Generators and relations for C30.SD16
 G = < a,b,c | a30=b8=1, c2=a15, bab-1=a-1, cac-1=a11, cbc-1=b3 >

Subgroups: 268 in 72 conjugacy classes, 40 normal (38 characteristic)
C1, C2 [×3], C3, C4 [×2], C4 [×2], C22, C5, C6 [×3], C8 [×2], C2×C4, C2×C4 [×2], C10 [×3], Dic3, C12 [×2], C12, C2×C6, C15, C4⋊C4 [×2], C2×C8, Dic5, C20 [×2], C20, C2×C10, C3⋊C8 [×2], C2×Dic3, C2×C12, C2×C12, C30 [×3], C4.Q8, C52C8 [×2], C2×Dic5, C2×C20, C2×C20, C2×C3⋊C8, C4⋊Dic3, C3×C4⋊C4, C5×Dic3, C3×Dic5, C60 [×2], C2×C30, C2×C52C8, C4⋊Dic5, C5×C4⋊C4, C12.Q8, C153C8 [×2], C6×Dic5, C10×Dic3, C2×C60, C20.Q8, C3×C4⋊Dic5, C5×C4⋊Dic3, C2×C153C8, C30.SD16
Quotients: C1, C2 [×3], C4 [×2], C22, S3, C2×C4, D4, Q8, D5, D6, C4⋊C4, SD16 [×2], D10, Dic6, C4×S3, C3⋊D4, C4.Q8, Dic10, C4×D5, C5⋊D4, Dic3⋊C4, D4.S3, Q82S3, S3×D5, C10.D4, D4.D5, Q8⋊D5, C12.Q8, D30.C2, C15⋊D4, C15⋊Q8, C20.Q8, C30.D4, C20.D6, Dic155C4, C30.SD16

Smallest permutation representation of C30.SD16
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)
(1 245 394 99 41 89 129 439)(2 244 395 98 42 88 130 438)(3 243 396 97 43 87 131 437)(4 242 397 96 44 86 132 436)(5 241 398 95 45 85 133 435)(6 270 399 94 46 84 134 434)(7 269 400 93 47 83 135 433)(8 268 401 92 48 82 136 432)(9 267 402 91 49 81 137 431)(10 266 403 120 50 80 138 430)(11 265 404 119 51 79 139 429)(12 264 405 118 52 78 140 428)(13 263 406 117 53 77 141 427)(14 262 407 116 54 76 142 426)(15 261 408 115 55 75 143 425)(16 260 409 114 56 74 144 424)(17 259 410 113 57 73 145 423)(18 258 411 112 58 72 146 422)(19 257 412 111 59 71 147 421)(20 256 413 110 60 70 148 450)(21 255 414 109 31 69 149 449)(22 254 415 108 32 68 150 448)(23 253 416 107 33 67 121 447)(24 252 417 106 34 66 122 446)(25 251 418 105 35 65 123 445)(26 250 419 104 36 64 124 444)(27 249 420 103 37 63 125 443)(28 248 391 102 38 62 126 442)(29 247 392 101 39 61 127 441)(30 246 393 100 40 90 128 440)(151 351 317 285 219 204 374 472)(152 350 318 284 220 203 375 471)(153 349 319 283 221 202 376 470)(154 348 320 282 222 201 377 469)(155 347 321 281 223 200 378 468)(156 346 322 280 224 199 379 467)(157 345 323 279 225 198 380 466)(158 344 324 278 226 197 381 465)(159 343 325 277 227 196 382 464)(160 342 326 276 228 195 383 463)(161 341 327 275 229 194 384 462)(162 340 328 274 230 193 385 461)(163 339 329 273 231 192 386 460)(164 338 330 272 232 191 387 459)(165 337 301 271 233 190 388 458)(166 336 302 300 234 189 389 457)(167 335 303 299 235 188 390 456)(168 334 304 298 236 187 361 455)(169 333 305 297 237 186 362 454)(170 332 306 296 238 185 363 453)(171 331 307 295 239 184 364 452)(172 360 308 294 240 183 365 451)(173 359 309 293 211 182 366 480)(174 358 310 292 212 181 367 479)(175 357 311 291 213 210 368 478)(176 356 312 290 214 209 369 477)(177 355 313 289 215 208 370 476)(178 354 314 288 216 207 371 475)(179 353 315 287 217 206 372 474)(180 352 316 286 218 205 373 473)
(1 466 16 451)(2 477 17 462)(3 458 18 473)(4 469 19 454)(5 480 20 465)(6 461 21 476)(7 472 22 457)(8 453 23 468)(9 464 24 479)(10 475 25 460)(11 456 26 471)(12 467 27 452)(13 478 28 463)(14 459 29 474)(15 470 30 455)(31 289 46 274)(32 300 47 285)(33 281 48 296)(34 292 49 277)(35 273 50 288)(36 284 51 299)(37 295 52 280)(38 276 53 291)(39 287 54 272)(40 298 55 283)(41 279 56 294)(42 290 57 275)(43 271 58 286)(44 282 59 297)(45 293 60 278)(61 372 76 387)(62 383 77 368)(63 364 78 379)(64 375 79 390)(65 386 80 371)(66 367 81 382)(67 378 82 363)(68 389 83 374)(69 370 84 385)(70 381 85 366)(71 362 86 377)(72 373 87 388)(73 384 88 369)(74 365 89 380)(75 376 90 361)(91 159 106 174)(92 170 107 155)(93 151 108 166)(94 162 109 177)(95 173 110 158)(96 154 111 169)(97 165 112 180)(98 176 113 161)(99 157 114 172)(100 168 115 153)(101 179 116 164)(102 160 117 175)(103 171 118 156)(104 152 119 167)(105 163 120 178)(121 347 136 332)(122 358 137 343)(123 339 138 354)(124 350 139 335)(125 331 140 346)(126 342 141 357)(127 353 142 338)(128 334 143 349)(129 345 144 360)(130 356 145 341)(131 337 146 352)(132 348 147 333)(133 359 148 344)(134 340 149 355)(135 351 150 336)(181 402 196 417)(182 413 197 398)(183 394 198 409)(184 405 199 420)(185 416 200 401)(186 397 201 412)(187 408 202 393)(188 419 203 404)(189 400 204 415)(190 411 205 396)(191 392 206 407)(192 403 207 418)(193 414 208 399)(194 395 209 410)(195 406 210 391)(211 450 226 435)(212 431 227 446)(213 442 228 427)(214 423 229 438)(215 434 230 449)(216 445 231 430)(217 426 232 441)(218 437 233 422)(219 448 234 433)(220 429 235 444)(221 440 236 425)(222 421 237 436)(223 432 238 447)(224 443 239 428)(225 424 240 439)(241 309 256 324)(242 320 257 305)(243 301 258 316)(244 312 259 327)(245 323 260 308)(246 304 261 319)(247 315 262 330)(248 326 263 311)(249 307 264 322)(250 318 265 303)(251 329 266 314)(252 310 267 325)(253 321 268 306)(254 302 269 317)(255 313 270 328)

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

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

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

60 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D4E4F5A5B6A6B6C8A8B8C8D10A···10F12A12B12C12D12E12F15A15B20A20B20C20D20E···20L30A···30F60A···60H
order1222344444455666888810···1012121212121215152020202020···2030···3060···60
size11112221212202022222303030302···2442020202044444412···124···44···4

60 irreducible representations

dim1111122222222222224444444444
type+++++-++++---++-++--
imageC1C2C2C2C4S3Q8D4D5D6SD16D10Dic6C4×S3C3⋊D4Dic10C4×D5C5⋊D4D4.S3Q82S3S3×D5D4.D5Q8⋊D5D30.C2C15⋊Q8C15⋊D4C30.D4C20.D6
kernelC30.SD16C3×C4⋊Dic5C5×C4⋊Dic3C2×C153C8C153C8C4⋊Dic5C60C2×C30C4⋊Dic3C2×C20C30C2×C12C20C20C2×C10C12C12C2×C6C10C10C2×C4C6C6C4C4C22C2C2
# reps1111411121422224441122222244

Matrix representation of C30.SD16 in GL6(𝔽241)

02400000
1520000
001100
00240000
00002400
00000240
,
421080000
931990000
0013111100
0022111000
0000022
00001138
,
41850000
1562000000
009223400
0014214900
000057237
0000210184

G:=sub<GL(6,GF(241))| [0,1,0,0,0,0,240,52,0,0,0,0,0,0,1,240,0,0,0,0,1,0,0,0,0,0,0,0,240,0,0,0,0,0,0,240],[42,93,0,0,0,0,108,199,0,0,0,0,0,0,131,221,0,0,0,0,111,110,0,0,0,0,0,0,0,11,0,0,0,0,22,38],[41,156,0,0,0,0,85,200,0,0,0,0,0,0,92,142,0,0,0,0,234,149,0,0,0,0,0,0,57,210,0,0,0,0,237,184] >;

C30.SD16 in GAP, Magma, Sage, TeX

C_{30}.{\rm SD}_{16}
% in TeX

G:=Group("C30.SD16");
// GroupNames label

G:=SmallGroup(480,62);
// by ID

G=gap.SmallGroup(480,62);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,28,141,148,675,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c|a^30=b^8=1,c^2=a^15,b*a*b^-1=a^-1,c*a*c^-1=a^11,c*b*c^-1=b^3>;
// generators/relations

׿
×
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