metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C15⋊3Q32, C5⋊2Dic24, C20.4D12, C10.9D24, C40.11D6, C60.52D4, C30.12D8, C24.43D10, Dic60.4C2, Dic12.1D5, C120.20C22, C8.19(S3×D5), C3⋊1(C5⋊Q32), C5⋊2C16.1S3, C6.4(D4⋊D5), C2.7(C5⋊D24), C4.4(C5⋊D12), C12.54(C5⋊D4), (C5×Dic12).1C2, (C3×C5⋊2C16).1C2, SmallGroup(480,24)
Series: Derived ►Chief ►Lower central ►Upper central
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 >
Smallest permutation representation of C5⋊Dic24
►Regular action on 480 points
Generators in S480
(1 403 250 458 199)(2 200 459 251 404)(3 405 252 460 201)(4 202 461 253 406)(5 407 254 462 203)(6 204 463 255 408)(7 409 256 464 205)(8 206 465 257 410)(9 411 258 466 207)(10 208 467 259 412)(11 413 260 468 209)(12 210 469 261 414)(13 415 262 470 211)(14 212 471 263 416)(15 417 264 472 213)(16 214 473 265 418)(17 419 266 474 215)(18 216 475 267 420)(19 421 268 476 217)(20 218 477 269 422)(21 423 270 478 219)(22 220 479 271 424)(23 425 272 480 221)(24 222 433 273 426)(25 427 274 434 223)(26 224 435 275 428)(27 429 276 436 225)(28 226 437 277 430)(29 431 278 438 227)(30 228 439 279 432)(31 385 280 440 229)(32 230 441 281 386)(33 387 282 442 231)(34 232 443 283 388)(35 389 284 444 233)(36 234 445 285 390)(37 391 286 446 235)(38 236 447 287 392)(39 393 288 448 237)(40 238 449 241 394)(41 395 242 450 239)(42 240 451 243 396)(43 397 244 452 193)(44 194 453 245 398)(45 399 246 454 195)(46 196 455 247 400)(47 401 248 456 197)(48 198 457 249 402)(49 319 105 361 192)(50 145 362 106 320)(51 321 107 363 146)(52 147 364 108 322)(53 323 109 365 148)(54 149 366 110 324)(55 325 111 367 150)(56 151 368 112 326)(57 327 113 369 152)(58 153 370 114 328)(59 329 115 371 154)(60 155 372 116 330)(61 331 117 373 156)(62 157 374 118 332)(63 333 119 375 158)(64 159 376 120 334)(65 335 121 377 160)(66 161 378 122 336)(67 289 123 379 162)(68 163 380 124 290)(69 291 125 381 164)(70 165 382 126 292)(71 293 127 383 166)(72 167 384 128 294)(73 295 129 337 168)(74 169 338 130 296)(75 297 131 339 170)(76 171 340 132 298)(77 299 133 341 172)(78 173 342 134 300)(79 301 135 343 174)(80 175 344 136 302)(81 303 137 345 176)(82 177 346 138 304)(83 305 139 347 178)(84 179 348 140 306)(85 307 141 349 180)(86 181 350 142 308)(87 309 143 351 182)(88 183 352 144 310)(89 311 97 353 184)(90 185 354 98 312)(91 313 99 355 186)(92 187 356 100 314)(93 315 101 357 188)(94 189 358 102 316)(95 317 103 359 190)(96 191 360 104 318)
(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 88 25 64)(2 87 26 63)(3 86 27 62)(4 85 28 61)(5 84 29 60)(6 83 30 59)(7 82 31 58)(8 81 32 57)(9 80 33 56)(10 79 34 55)(11 78 35 54)(12 77 36 53)(13 76 37 52)(14 75 38 51)(15 74 39 50)(16 73 40 49)(17 72 41 96)(18 71 42 95)(19 70 43 94)(20 69 44 93)(21 68 45 92)(22 67 46 91)(23 66 47 90)(24 65 48 89)(97 433 121 457)(98 480 122 456)(99 479 123 455)(100 478 124 454)(101 477 125 453)(102 476 126 452)(103 475 127 451)(104 474 128 450)(105 473 129 449)(106 472 130 448)(107 471 131 447)(108 470 132 446)(109 469 133 445)(110 468 134 444)(111 467 135 443)(112 466 136 442)(113 465 137 441)(114 464 138 440)(115 463 139 439)(116 462 140 438)(117 461 141 437)(118 460 142 436)(119 459 143 435)(120 458 144 434)(145 417 169 393)(146 416 170 392)(147 415 171 391)(148 414 172 390)(149 413 173 389)(150 412 174 388)(151 411 175 387)(152 410 176 386)(153 409 177 385)(154 408 178 432)(155 407 179 431)(156 406 180 430)(157 405 181 429)(158 404 182 428)(159 403 183 427)(160 402 184 426)(161 401 185 425)(162 400 186 424)(163 399 187 423)(164 398 188 422)(165 397 189 421)(166 396 190 420)(167 395 191 419)(168 394 192 418)(193 316 217 292)(194 315 218 291)(195 314 219 290)(196 313 220 289)(197 312 221 336)(198 311 222 335)(199 310 223 334)(200 309 224 333)(201 308 225 332)(202 307 226 331)(203 306 227 330)(204 305 228 329)(205 304 229 328)(206 303 230 327)(207 302 231 326)(208 301 232 325)(209 300 233 324)(210 299 234 323)(211 298 235 322)(212 297 236 321)(213 296 237 320)(214 295 238 319)(215 294 239 318)(216 293 240 317)(241 361 265 337)(242 360 266 384)(243 359 267 383)(244 358 268 382)(245 357 269 381)(246 356 270 380)(247 355 271 379)(248 354 272 378)(249 353 273 377)(250 352 274 376)(251 351 275 375)(252 350 276 374)(253 349 277 373)(254 348 278 372)(255 347 279 371)(256 346 280 370)(257 345 281 369)(258 344 282 368)(259 343 283 367)(260 342 284 366)(261 341 285 365)(262 340 286 364)(263 339 287 363)(264 338 288 362)
G:=sub<Sym(480)| (1,403,250,458,199)(2,200,459,251,404)(3,405,252,460,201)(4,202,461,253,406)(5,407,254,462,203)(6,204,463,255,408)(7,409,256,464,205)(8,206,465,257,410)(9,411,258,466,207)(10,208,467,259,412)(11,413,260,468,209)(12,210,469,261,414)(13,415,262,470,211)(14,212,471,263,416)(15,417,264,472,213)(16,214,473,265,418)(17,419,266,474,215)(18,216,475,267,420)(19,421,268,476,217)(20,218,477,269,422)(21,423,270,478,219)(22,220,479,271,424)(23,425,272,480,221)(24,222,433,273,426)(25,427,274,434,223)(26,224,435,275,428)(27,429,276,436,225)(28,226,437,277,430)(29,431,278,438,227)(30,228,439,279,432)(31,385,280,440,229)(32,230,441,281,386)(33,387,282,442,231)(34,232,443,283,388)(35,389,284,444,233)(36,234,445,285,390)(37,391,286,446,235)(38,236,447,287,392)(39,393,288,448,237)(40,238,449,241,394)(41,395,242,450,239)(42,240,451,243,396)(43,397,244,452,193)(44,194,453,245,398)(45,399,246,454,195)(46,196,455,247,400)(47,401,248,456,197)(48,198,457,249,402)(49,319,105,361,192)(50,145,362,106,320)(51,321,107,363,146)(52,147,364,108,322)(53,323,109,365,148)(54,149,366,110,324)(55,325,111,367,150)(56,151,368,112,326)(57,327,113,369,152)(58,153,370,114,328)(59,329,115,371,154)(60,155,372,116,330)(61,331,117,373,156)(62,157,374,118,332)(63,333,119,375,158)(64,159,376,120,334)(65,335,121,377,160)(66,161,378,122,336)(67,289,123,379,162)(68,163,380,124,290)(69,291,125,381,164)(70,165,382,126,292)(71,293,127,383,166)(72,167,384,128,294)(73,295,129,337,168)(74,169,338,130,296)(75,297,131,339,170)(76,171,340,132,298)(77,299,133,341,172)(78,173,342,134,300)(79,301,135,343,174)(80,175,344,136,302)(81,303,137,345,176)(82,177,346,138,304)(83,305,139,347,178)(84,179,348,140,306)(85,307,141,349,180)(86,181,350,142,308)(87,309,143,351,182)(88,183,352,144,310)(89,311,97,353,184)(90,185,354,98,312)(91,313,99,355,186)(92,187,356,100,314)(93,315,101,357,188)(94,189,358,102,316)(95,317,103,359,190)(96,191,360,104,318), (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), (1,88,25,64)(2,87,26,63)(3,86,27,62)(4,85,28,61)(5,84,29,60)(6,83,30,59)(7,82,31,58)(8,81,32,57)(9,80,33,56)(10,79,34,55)(11,78,35,54)(12,77,36,53)(13,76,37,52)(14,75,38,51)(15,74,39,50)(16,73,40,49)(17,72,41,96)(18,71,42,95)(19,70,43,94)(20,69,44,93)(21,68,45,92)(22,67,46,91)(23,66,47,90)(24,65,48,89)(97,433,121,457)(98,480,122,456)(99,479,123,455)(100,478,124,454)(101,477,125,453)(102,476,126,452)(103,475,127,451)(104,474,128,450)(105,473,129,449)(106,472,130,448)(107,471,131,447)(108,470,132,446)(109,469,133,445)(110,468,134,444)(111,467,135,443)(112,466,136,442)(113,465,137,441)(114,464,138,440)(115,463,139,439)(116,462,140,438)(117,461,141,437)(118,460,142,436)(119,459,143,435)(120,458,144,434)(145,417,169,393)(146,416,170,392)(147,415,171,391)(148,414,172,390)(149,413,173,389)(150,412,174,388)(151,411,175,387)(152,410,176,386)(153,409,177,385)(154,408,178,432)(155,407,179,431)(156,406,180,430)(157,405,181,429)(158,404,182,428)(159,403,183,427)(160,402,184,426)(161,401,185,425)(162,400,186,424)(163,399,187,423)(164,398,188,422)(165,397,189,421)(166,396,190,420)(167,395,191,419)(168,394,192,418)(193,316,217,292)(194,315,218,291)(195,314,219,290)(196,313,220,289)(197,312,221,336)(198,311,222,335)(199,310,223,334)(200,309,224,333)(201,308,225,332)(202,307,226,331)(203,306,227,330)(204,305,228,329)(205,304,229,328)(206,303,230,327)(207,302,231,326)(208,301,232,325)(209,300,233,324)(210,299,234,323)(211,298,235,322)(212,297,236,321)(213,296,237,320)(214,295,238,319)(215,294,239,318)(216,293,240,317)(241,361,265,337)(242,360,266,384)(243,359,267,383)(244,358,268,382)(245,357,269,381)(246,356,270,380)(247,355,271,379)(248,354,272,378)(249,353,273,377)(250,352,274,376)(251,351,275,375)(252,350,276,374)(253,349,277,373)(254,348,278,372)(255,347,279,371)(256,346,280,370)(257,345,281,369)(258,344,282,368)(259,343,283,367)(260,342,284,366)(261,341,285,365)(262,340,286,364)(263,339,287,363)(264,338,288,362)>;
G:=Group( (1,403,250,458,199)(2,200,459,251,404)(3,405,252,460,201)(4,202,461,253,406)(5,407,254,462,203)(6,204,463,255,408)(7,409,256,464,205)(8,206,465,257,410)(9,411,258,466,207)(10,208,467,259,412)(11,413,260,468,209)(12,210,469,261,414)(13,415,262,470,211)(14,212,471,263,416)(15,417,264,472,213)(16,214,473,265,418)(17,419,266,474,215)(18,216,475,267,420)(19,421,268,476,217)(20,218,477,269,422)(21,423,270,478,219)(22,220,479,271,424)(23,425,272,480,221)(24,222,433,273,426)(25,427,274,434,223)(26,224,435,275,428)(27,429,276,436,225)(28,226,437,277,430)(29,431,278,438,227)(30,228,439,279,432)(31,385,280,440,229)(32,230,441,281,386)(33,387,282,442,231)(34,232,443,283,388)(35,389,284,444,233)(36,234,445,285,390)(37,391,286,446,235)(38,236,447,287,392)(39,393,288,448,237)(40,238,449,241,394)(41,395,242,450,239)(42,240,451,243,396)(43,397,244,452,193)(44,194,453,245,398)(45,399,246,454,195)(46,196,455,247,400)(47,401,248,456,197)(48,198,457,249,402)(49,319,105,361,192)(50,145,362,106,320)(51,321,107,363,146)(52,147,364,108,322)(53,323,109,365,148)(54,149,366,110,324)(55,325,111,367,150)(56,151,368,112,326)(57,327,113,369,152)(58,153,370,114,328)(59,329,115,371,154)(60,155,372,116,330)(61,331,117,373,156)(62,157,374,118,332)(63,333,119,375,158)(64,159,376,120,334)(65,335,121,377,160)(66,161,378,122,336)(67,289,123,379,162)(68,163,380,124,290)(69,291,125,381,164)(70,165,382,126,292)(71,293,127,383,166)(72,167,384,128,294)(73,295,129,337,168)(74,169,338,130,296)(75,297,131,339,170)(76,171,340,132,298)(77,299,133,341,172)(78,173,342,134,300)(79,301,135,343,174)(80,175,344,136,302)(81,303,137,345,176)(82,177,346,138,304)(83,305,139,347,178)(84,179,348,140,306)(85,307,141,349,180)(86,181,350,142,308)(87,309,143,351,182)(88,183,352,144,310)(89,311,97,353,184)(90,185,354,98,312)(91,313,99,355,186)(92,187,356,100,314)(93,315,101,357,188)(94,189,358,102,316)(95,317,103,359,190)(96,191,360,104,318), (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), (1,88,25,64)(2,87,26,63)(3,86,27,62)(4,85,28,61)(5,84,29,60)(6,83,30,59)(7,82,31,58)(8,81,32,57)(9,80,33,56)(10,79,34,55)(11,78,35,54)(12,77,36,53)(13,76,37,52)(14,75,38,51)(15,74,39,50)(16,73,40,49)(17,72,41,96)(18,71,42,95)(19,70,43,94)(20,69,44,93)(21,68,45,92)(22,67,46,91)(23,66,47,90)(24,65,48,89)(97,433,121,457)(98,480,122,456)(99,479,123,455)(100,478,124,454)(101,477,125,453)(102,476,126,452)(103,475,127,451)(104,474,128,450)(105,473,129,449)(106,472,130,448)(107,471,131,447)(108,470,132,446)(109,469,133,445)(110,468,134,444)(111,467,135,443)(112,466,136,442)(113,465,137,441)(114,464,138,440)(115,463,139,439)(116,462,140,438)(117,461,141,437)(118,460,142,436)(119,459,143,435)(120,458,144,434)(145,417,169,393)(146,416,170,392)(147,415,171,391)(148,414,172,390)(149,413,173,389)(150,412,174,388)(151,411,175,387)(152,410,176,386)(153,409,177,385)(154,408,178,432)(155,407,179,431)(156,406,180,430)(157,405,181,429)(158,404,182,428)(159,403,183,427)(160,402,184,426)(161,401,185,425)(162,400,186,424)(163,399,187,423)(164,398,188,422)(165,397,189,421)(166,396,190,420)(167,395,191,419)(168,394,192,418)(193,316,217,292)(194,315,218,291)(195,314,219,290)(196,313,220,289)(197,312,221,336)(198,311,222,335)(199,310,223,334)(200,309,224,333)(201,308,225,332)(202,307,226,331)(203,306,227,330)(204,305,228,329)(205,304,229,328)(206,303,230,327)(207,302,231,326)(208,301,232,325)(209,300,233,324)(210,299,234,323)(211,298,235,322)(212,297,236,321)(213,296,237,320)(214,295,238,319)(215,294,239,318)(216,293,240,317)(241,361,265,337)(242,360,266,384)(243,359,267,383)(244,358,268,382)(245,357,269,381)(246,356,270,380)(247,355,271,379)(248,354,272,378)(249,353,273,377)(250,352,274,376)(251,351,275,375)(252,350,276,374)(253,349,277,373)(254,348,278,372)(255,347,279,371)(256,346,280,370)(257,345,281,369)(258,344,282,368)(259,343,283,367)(260,342,284,366)(261,341,285,365)(262,340,286,364)(263,339,287,363)(264,338,288,362) );
G=PermutationGroup([[(1,403,250,458,199),(2,200,459,251,404),(3,405,252,460,201),(4,202,461,253,406),(5,407,254,462,203),(6,204,463,255,408),(7,409,256,464,205),(8,206,465,257,410),(9,411,258,466,207),(10,208,467,259,412),(11,413,260,468,209),(12,210,469,261,414),(13,415,262,470,211),(14,212,471,263,416),(15,417,264,472,213),(16,214,473,265,418),(17,419,266,474,215),(18,216,475,267,420),(19,421,268,476,217),(20,218,477,269,422),(21,423,270,478,219),(22,220,479,271,424),(23,425,272,480,221),(24,222,433,273,426),(25,427,274,434,223),(26,224,435,275,428),(27,429,276,436,225),(28,226,437,277,430),(29,431,278,438,227),(30,228,439,279,432),(31,385,280,440,229),(32,230,441,281,386),(33,387,282,442,231),(34,232,443,283,388),(35,389,284,444,233),(36,234,445,285,390),(37,391,286,446,235),(38,236,447,287,392),(39,393,288,448,237),(40,238,449,241,394),(41,395,242,450,239),(42,240,451,243,396),(43,397,244,452,193),(44,194,453,245,398),(45,399,246,454,195),(46,196,455,247,400),(47,401,248,456,197),(48,198,457,249,402),(49,319,105,361,192),(50,145,362,106,320),(51,321,107,363,146),(52,147,364,108,322),(53,323,109,365,148),(54,149,366,110,324),(55,325,111,367,150),(56,151,368,112,326),(57,327,113,369,152),(58,153,370,114,328),(59,329,115,371,154),(60,155,372,116,330),(61,331,117,373,156),(62,157,374,118,332),(63,333,119,375,158),(64,159,376,120,334),(65,335,121,377,160),(66,161,378,122,336),(67,289,123,379,162),(68,163,380,124,290),(69,291,125,381,164),(70,165,382,126,292),(71,293,127,383,166),(72,167,384,128,294),(73,295,129,337,168),(74,169,338,130,296),(75,297,131,339,170),(76,171,340,132,298),(77,299,133,341,172),(78,173,342,134,300),(79,301,135,343,174),(80,175,344,136,302),(81,303,137,345,176),(82,177,346,138,304),(83,305,139,347,178),(84,179,348,140,306),(85,307,141,349,180),(86,181,350,142,308),(87,309,143,351,182),(88,183,352,144,310),(89,311,97,353,184),(90,185,354,98,312),(91,313,99,355,186),(92,187,356,100,314),(93,315,101,357,188),(94,189,358,102,316),(95,317,103,359,190),(96,191,360,104,318)], [(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)], [(1,88,25,64),(2,87,26,63),(3,86,27,62),(4,85,28,61),(5,84,29,60),(6,83,30,59),(7,82,31,58),(8,81,32,57),(9,80,33,56),(10,79,34,55),(11,78,35,54),(12,77,36,53),(13,76,37,52),(14,75,38,51),(15,74,39,50),(16,73,40,49),(17,72,41,96),(18,71,42,95),(19,70,43,94),(20,69,44,93),(21,68,45,92),(22,67,46,91),(23,66,47,90),(24,65,48,89),(97,433,121,457),(98,480,122,456),(99,479,123,455),(100,478,124,454),(101,477,125,453),(102,476,126,452),(103,475,127,451),(104,474,128,450),(105,473,129,449),(106,472,130,448),(107,471,131,447),(108,470,132,446),(109,469,133,445),(110,468,134,444),(111,467,135,443),(112,466,136,442),(113,465,137,441),(114,464,138,440),(115,463,139,439),(116,462,140,438),(117,461,141,437),(118,460,142,436),(119,459,143,435),(120,458,144,434),(145,417,169,393),(146,416,170,392),(147,415,171,391),(148,414,172,390),(149,413,173,389),(150,412,174,388),(151,411,175,387),(152,410,176,386),(153,409,177,385),(154,408,178,432),(155,407,179,431),(156,406,180,430),(157,405,181,429),(158,404,182,428),(159,403,183,427),(160,402,184,426),(161,401,185,425),(162,400,186,424),(163,399,187,423),(164,398,188,422),(165,397,189,421),(166,396,190,420),(167,395,191,419),(168,394,192,418),(193,316,217,292),(194,315,218,291),(195,314,219,290),(196,313,220,289),(197,312,221,336),(198,311,222,335),(199,310,223,334),(200,309,224,333),(201,308,225,332),(202,307,226,331),(203,306,227,330),(204,305,228,329),(205,304,229,328),(206,303,230,327),(207,302,231,326),(208,301,232,325),(209,300,233,324),(210,299,234,323),(211,298,235,322),(212,297,236,321),(213,296,237,320),(214,295,238,319),(215,294,239,318),(216,293,240,317),(241,361,265,337),(242,360,266,384),(243,359,267,383),(244,358,268,382),(245,357,269,381),(246,356,270,380),(247,355,271,379),(248,354,272,378),(249,353,273,377),(250,352,274,376),(251,351,275,375),(252,350,276,374),(253,349,277,373),(254,348,278,372),(255,347,279,371),(256,346,280,370),(257,345,281,369),(258,344,282,368),(259,343,283,367),(260,342,284,366),(261,341,285,365),(262,340,286,364),(263,339,287,363),(264,338,288,362)]])
57 conjugacy classes
| class | 1 | 2 | 3 | 4A | 4B | 4C | 5A | 5B | 6 | 8A | 8B | 10A | 10B | 12A | 12B | 15A | 15B | 16A | 16B | 16C | 16D | 20A | 20B | 20C | 20D | 20E | 20F | 24A | 24B | 24C | 24D | 30A | 30B | 40A | 40B | 40C | 40D | 48A | ··· | 48H | 60A | 60B | 60C | 60D | 120A | ··· | 120H |
| order | 1 | 2 | 3 | 4 | 4 | 4 | 5 | 5 | 6 | 8 | 8 | 10 | 10 | 12 | 12 | 15 | 15 | 16 | 16 | 16 | 16 | 20 | 20 | 20 | 20 | 20 | 20 | 24 | 24 | 24 | 24 | 30 | 30 | 40 | 40 | 40 | 40 | 48 | ··· | 48 | 60 | 60 | 60 | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 2 | 2 | 24 | 120 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 10 | 10 | 10 | 10 | 4 | 4 | 24 | 24 | 24 | 24 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
57 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | + | - | + | + | + | - | + | - | |
| image | C1 | C2 | C2 | C2 | S3 | D4 | D5 | D6 | D8 | D10 | D12 | Q32 | C5⋊D4 | D24 | Dic24 | S3×D5 | D4⋊D5 | C5⋊D12 | C5⋊Q32 | C5⋊D24 | C5⋊Dic24 |
| kernel | C5⋊Dic24 | C3×C5⋊2C16 | C5×Dic12 | Dic60 | C5⋊2C16 | C60 | Dic12 | C40 | C30 | C24 | C20 | C15 | C12 | C10 | C5 | C8 | C6 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 8 | 2 | 2 | 2 | 4 | 4 | 8 |
Matrix representation of C5⋊Dic24 ►in GL6(𝔽241)
| 51 | 1 | 0 | 0 | 0 | 0 |
| 240 | 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 | 156 | 0 | 0 | 0 | 0 |
| 193 | 237 | 0 | 0 | 0 | 0 |
| 0 | 0 | 114 | 136 | 0 | 0 |
| 0 | 0 | 105 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 205 | 236 |
| 0 | 0 | 0 | 0 | 182 | 206 |
| 165 | 49 | 0 | 0 | 0 | 0 |
| 192 | 76 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 211 | 0 | 0 |
| 0 | 0 | 233 | 219 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 37 |
| 0 | 0 | 0 | 0 | 185 | 216 |
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
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