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G = C5⋊Dic24order 480 = 25·3·5

The semidirect product of C5 and Dic24 acting via Dic24/Dic12=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C153Q32, C52Dic24, C20.4D12, C10.9D24, C40.11D6, C60.52D4, C30.12D8, C24.43D10, Dic60.4C2, Dic12.1D5, C120.20C22, C8.19(S3×D5), C31(C5⋊Q32), C52C16.1S3, C6.4(D4⋊D5), C2.7(C5⋊D24), C4.4(C5⋊D12), C12.54(C5⋊D4), (C5×Dic12).1C2, (C3×C52C16).1C2, SmallGroup(480,24)

Series: Derived Chief Lower central Upper central

C1C120 — C5⋊Dic24
C1C5C15C30C60C120C3×C52C16 — C5⋊Dic24
C15C30C60C120 — C5⋊Dic24
C1C2C4C8

Generators and relations for C5⋊Dic24
 G = < a,b,c | a5=b48=1, c2=b24, bab-1=a-1, ac=ca, cbc-1=b-1 >

12C4
60C4
6Q8
30Q8
4Dic3
20Dic3
12C20
12Dic5
3Q16
5C16
15Q16
2Dic6
10Dic6
6C5×Q8
6Dic10
4C5×Dic3
4Dic15
15Q32
5C48
5Dic12
3C5×Q16
3Dic20
2Dic30
2C5×Dic6
5Dic24
3C5⋊Q32

Smallest permutation representation of C5⋊Dic24
Regular action on 480 points
Generators in S480
(1 55 447 393 189)(2 190 394 448 56)(3 57 449 395 191)(4 192 396 450 58)(5 59 451 397 145)(6 146 398 452 60)(7 61 453 399 147)(8 148 400 454 62)(9 63 455 401 149)(10 150 402 456 64)(11 65 457 403 151)(12 152 404 458 66)(13 67 459 405 153)(14 154 406 460 68)(15 69 461 407 155)(16 156 408 462 70)(17 71 463 409 157)(18 158 410 464 72)(19 73 465 411 159)(20 160 412 466 74)(21 75 467 413 161)(22 162 414 468 76)(23 77 469 415 163)(24 164 416 470 78)(25 79 471 417 165)(26 166 418 472 80)(27 81 473 419 167)(28 168 420 474 82)(29 83 475 421 169)(30 170 422 476 84)(31 85 477 423 171)(32 172 424 478 86)(33 87 479 425 173)(34 174 426 480 88)(35 89 433 427 175)(36 176 428 434 90)(37 91 435 429 177)(38 178 430 436 92)(39 93 437 431 179)(40 180 432 438 94)(41 95 439 385 181)(42 182 386 440 96)(43 49 441 387 183)(44 184 388 442 50)(45 51 443 389 185)(46 186 390 444 52)(47 53 445 391 187)(48 188 392 446 54)(97 265 323 341 223)(98 224 342 324 266)(99 267 325 343 225)(100 226 344 326 268)(101 269 327 345 227)(102 228 346 328 270)(103 271 329 347 229)(104 230 348 330 272)(105 273 331 349 231)(106 232 350 332 274)(107 275 333 351 233)(108 234 352 334 276)(109 277 335 353 235)(110 236 354 336 278)(111 279 289 355 237)(112 238 356 290 280)(113 281 291 357 239)(114 240 358 292 282)(115 283 293 359 193)(116 194 360 294 284)(117 285 295 361 195)(118 196 362 296 286)(119 287 297 363 197)(120 198 364 298 288)(121 241 299 365 199)(122 200 366 300 242)(123 243 301 367 201)(124 202 368 302 244)(125 245 303 369 203)(126 204 370 304 246)(127 247 305 371 205)(128 206 372 306 248)(129 249 307 373 207)(130 208 374 308 250)(131 251 309 375 209)(132 210 376 310 252)(133 253 311 377 211)(134 212 378 312 254)(135 255 313 379 213)(136 214 380 314 256)(137 257 315 381 215)(138 216 382 316 258)(139 259 317 383 217)(140 218 384 318 260)(141 261 319 337 219)(142 220 338 320 262)(143 263 321 339 221)(144 222 340 322 264)
(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)
(1 285 25 261)(2 284 26 260)(3 283 27 259)(4 282 28 258)(5 281 29 257)(6 280 30 256)(7 279 31 255)(8 278 32 254)(9 277 33 253)(10 276 34 252)(11 275 35 251)(12 274 36 250)(13 273 37 249)(14 272 38 248)(15 271 39 247)(16 270 40 246)(17 269 41 245)(18 268 42 244)(19 267 43 243)(20 266 44 242)(21 265 45 241)(22 264 46 288)(23 263 47 287)(24 262 48 286)(49 301 73 325)(50 300 74 324)(51 299 75 323)(52 298 76 322)(53 297 77 321)(54 296 78 320)(55 295 79 319)(56 294 80 318)(57 293 81 317)(58 292 82 316)(59 291 83 315)(60 290 84 314)(61 289 85 313)(62 336 86 312)(63 335 87 311)(64 334 88 310)(65 333 89 309)(66 332 90 308)(67 331 91 307)(68 330 92 306)(69 329 93 305)(70 328 94 304)(71 327 95 303)(72 326 96 302)(97 185 121 161)(98 184 122 160)(99 183 123 159)(100 182 124 158)(101 181 125 157)(102 180 126 156)(103 179 127 155)(104 178 128 154)(105 177 129 153)(106 176 130 152)(107 175 131 151)(108 174 132 150)(109 173 133 149)(110 172 134 148)(111 171 135 147)(112 170 136 146)(113 169 137 145)(114 168 138 192)(115 167 139 191)(116 166 140 190)(117 165 141 189)(118 164 142 188)(119 163 143 187)(120 162 144 186)(193 419 217 395)(194 418 218 394)(195 417 219 393)(196 416 220 392)(197 415 221 391)(198 414 222 390)(199 413 223 389)(200 412 224 388)(201 411 225 387)(202 410 226 386)(203 409 227 385)(204 408 228 432)(205 407 229 431)(206 406 230 430)(207 405 231 429)(208 404 232 428)(209 403 233 427)(210 402 234 426)(211 401 235 425)(212 400 236 424)(213 399 237 423)(214 398 238 422)(215 397 239 421)(216 396 240 420)(337 447 361 471)(338 446 362 470)(339 445 363 469)(340 444 364 468)(341 443 365 467)(342 442 366 466)(343 441 367 465)(344 440 368 464)(345 439 369 463)(346 438 370 462)(347 437 371 461)(348 436 372 460)(349 435 373 459)(350 434 374 458)(351 433 375 457)(352 480 376 456)(353 479 377 455)(354 478 378 454)(355 477 379 453)(356 476 380 452)(357 475 381 451)(358 474 382 450)(359 473 383 449)(360 472 384 448)

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

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

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

57 conjugacy classes

class 1  2  3 4A4B4C5A5B 6 8A8B10A10B12A12B15A15B16A16B16C16D20A20B20C20D20E20F24A24B24C24D30A30B40A40B40C40D48A···48H60A60B60C60D120A···120H
order12344455688101012121515161616162020202020202424242430304040404048···4860606060120···120
size11222412022222222244101010104424242424222244444410···1044444···4

57 irreducible representations

dim111122222222222444444
type+++++++++++-+-+++-+-
imageC1C2C2C2S3D4D5D6D8D10D12Q32C5⋊D4D24Dic24S3×D5D4⋊D5C5⋊D12C5⋊Q32C5⋊D24C5⋊Dic24
kernelC5⋊Dic24C3×C52C16C5×Dic12Dic60C52C16C60Dic12C40C30C24C20C15C12C10C5C8C6C4C3C2C1
# reps111111212224448222448

Matrix representation of C5⋊Dic24 in GL6(𝔽241)

5110000
24000000
001000
000100
000010
000001
,
41560000
1932370000
0011413600
00105900
0000205236
0000182206
,
165490000
192760000
002221100
0023321900
00002537
0000185216

G:=sub<GL(6,GF(241))| [51,240,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[4,193,0,0,0,0,156,237,0,0,0,0,0,0,114,105,0,0,0,0,136,9,0,0,0,0,0,0,205,182,0,0,0,0,236,206],[165,192,0,0,0,0,49,76,0,0,0,0,0,0,22,233,0,0,0,0,211,219,0,0,0,0,0,0,25,185,0,0,0,0,37,216] >;

C5⋊Dic24 in GAP, Magma, Sage, TeX

C_5\rtimes {\rm Dic}_{24}
% in TeX

G:=Group("C5:Dic24");
// GroupNames label

G:=SmallGroup(480,24);
// by ID

G=gap.SmallGroup(480,24);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,28,85,120,135,142,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c|a^5=b^48=1,c^2=b^24,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C5⋊Dic24 in TeX

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