Copied to
clipboard

## G = C10×C3⋊C16order 480 = 25·3·5

### Direct product of C10 and C3⋊C16

Series: Derived Chief Lower central Upper central

 Derived series C1 — C3 — C10×C3⋊C16
 Chief series C1 — C3 — C6 — C12 — C24 — C120 — C5×C3⋊C16 — C10×C3⋊C16
 Lower central C3 — C10×C3⋊C16
 Upper central C1 — C2×C40

Generators and relations for C10×C3⋊C16
G = < a,b,c | a10=b3=c16=1, ab=ba, ac=ca, cbc-1=b-1 >

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

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

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

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

240 conjugacy classes

 class 1 2A 2B 2C 3 4A 4B 4C 4D 5A 5B 5C 5D 6A 6B 6C 8A ··· 8H 10A ··· 10L 12A 12B 12C 12D 15A 15B 15C 15D 16A ··· 16P 20A ··· 20P 24A ··· 24H 30A ··· 30L 40A ··· 40AF 60A ··· 60P 80A ··· 80BL 120A ··· 120AF order 1 2 2 2 3 4 4 4 4 5 5 5 5 6 6 6 8 ··· 8 10 ··· 10 12 12 12 12 15 15 15 15 16 ··· 16 20 ··· 20 24 ··· 24 30 ··· 30 40 ··· 40 60 ··· 60 80 ··· 80 120 ··· 120 size 1 1 1 1 2 1 1 1 1 1 1 1 1 2 2 2 1 ··· 1 1 ··· 1 2 2 2 2 2 2 2 2 3 ··· 3 1 ··· 1 2 ··· 2 2 ··· 2 1 ··· 1 2 ··· 2 3 ··· 3 2 ··· 2

240 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 type + + + + - + - image C1 C2 C2 C4 C4 C5 C8 C8 C10 C10 C16 C20 C20 C40 C40 C80 S3 Dic3 D6 Dic3 C3⋊C8 C3⋊C8 C5×S3 C3⋊C16 C5×Dic3 S3×C10 C5×Dic3 C5×C3⋊C8 C5×C3⋊C8 C5×C3⋊C16 kernel C10×C3⋊C16 C5×C3⋊C16 C2×C120 C120 C2×C60 C2×C3⋊C16 C60 C2×C30 C3⋊C16 C2×C24 C30 C24 C2×C12 C12 C2×C6 C6 C2×C40 C40 C40 C2×C20 C20 C2×C10 C2×C8 C10 C8 C8 C2×C4 C4 C22 C2 # reps 1 2 1 2 2 4 4 4 8 4 16 8 8 16 16 64 1 1 1 1 2 2 4 8 4 4 4 8 8 32

Matrix representation of C10×C3⋊C16 in GL3(𝔽241) generated by

 87 0 0 0 143 0 0 0 143
,
 1 0 0 0 0 240 0 1 240
,
 165 0 0 0 0 30 0 30 0
G:=sub<GL(3,GF(241))| [87,0,0,0,143,0,0,0,143],[1,0,0,0,0,1,0,240,240],[165,0,0,0,0,30,0,30,0] >;

C10×C3⋊C16 in GAP, Magma, Sage, TeX

C_{10}\times C_3\rtimes C_{16}
% in TeX

G:=Group("C10xC3:C16");
// GroupNames label

G:=SmallGroup(480,130);
// by ID

G=gap.SmallGroup(480,130);
# by ID

G:=PCGroup([7,-2,-2,-5,-2,-2,-2,-3,140,80,102,15686]);
// Polycyclic

G:=Group<a,b,c|a^10=b^3=c^16=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

׿
×
𝔽