direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C10×Dic11, C110⋊4C4, C22⋊3C20, C10.16D22, C110.16C22, C55⋊11(C2×C4), C11⋊5(C2×C20), C22.(C5×D11), (C2×C22).3C10, (C2×C110).2C2, C2.2(C10×D11), (C2×C10).2D11, C22.12(C2×C10), SmallGroup(440,27)
Series: Derived ►Chief ►Lower central ►Upper central
| C11 — C10×Dic11 |
Generators and relations for C10×Dic11
G = < a,b,c | a10=b22=1, c2=b11, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C10×Dic11
►Regular action on 440 points
Generators in S440
(1 159 106 149 83 111 52 215 23 177)(2 160 107 150 84 112 53 216 24 178)(3 161 108 151 85 113 54 217 25 179)(4 162 109 152 86 114 55 218 26 180)(5 163 110 153 87 115 56 219 27 181)(6 164 89 154 88 116 57 220 28 182)(7 165 90 133 67 117 58 199 29 183)(8 166 91 134 68 118 59 200 30 184)(9 167 92 135 69 119 60 201 31 185)(10 168 93 136 70 120 61 202 32 186)(11 169 94 137 71 121 62 203 33 187)(12 170 95 138 72 122 63 204 34 188)(13 171 96 139 73 123 64 205 35 189)(14 172 97 140 74 124 65 206 36 190)(15 173 98 141 75 125 66 207 37 191)(16 174 99 142 76 126 45 208 38 192)(17 175 100 143 77 127 46 209 39 193)(18 176 101 144 78 128 47 210 40 194)(19 155 102 145 79 129 48 211 41 195)(20 156 103 146 80 130 49 212 42 196)(21 157 104 147 81 131 50 213 43 197)(22 158 105 148 82 132 51 214 44 198)(221 386 320 364 298 331 276 419 243 408)(222 387 321 365 299 332 277 420 244 409)(223 388 322 366 300 333 278 421 245 410)(224 389 323 367 301 334 279 422 246 411)(225 390 324 368 302 335 280 423 247 412)(226 391 325 369 303 336 281 424 248 413)(227 392 326 370 304 337 282 425 249 414)(228 393 327 371 305 338 283 426 250 415)(229 394 328 372 306 339 284 427 251 416)(230 395 329 373 307 340 285 428 252 417)(231 396 330 374 308 341 286 429 253 418)(232 375 309 353 287 342 265 430 254 397)(233 376 310 354 288 343 266 431 255 398)(234 377 311 355 289 344 267 432 256 399)(235 378 312 356 290 345 268 433 257 400)(236 379 313 357 291 346 269 434 258 401)(237 380 314 358 292 347 270 435 259 402)(238 381 315 359 293 348 271 436 260 403)(239 382 316 360 294 349 272 437 261 404)(240 383 317 361 295 350 273 438 262 405)(241 384 318 362 296 351 274 439 263 406)(242 385 319 363 297 352 275 440 264 407)
(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)
(1 221 12 232)(2 242 13 231)(3 241 14 230)(4 240 15 229)(5 239 16 228)(6 238 17 227)(7 237 18 226)(8 236 19 225)(9 235 20 224)(10 234 21 223)(11 233 22 222)(23 243 34 254)(24 264 35 253)(25 263 36 252)(26 262 37 251)(27 261 38 250)(28 260 39 249)(29 259 40 248)(30 258 41 247)(31 257 42 246)(32 256 43 245)(33 255 44 244)(45 283 56 272)(46 282 57 271)(47 281 58 270)(48 280 59 269)(49 279 60 268)(50 278 61 267)(51 277 62 266)(52 276 63 265)(53 275 64 286)(54 274 65 285)(55 273 66 284)(67 292 78 303)(68 291 79 302)(69 290 80 301)(70 289 81 300)(71 288 82 299)(72 287 83 298)(73 308 84 297)(74 307 85 296)(75 306 86 295)(76 305 87 294)(77 304 88 293)(89 315 100 326)(90 314 101 325)(91 313 102 324)(92 312 103 323)(93 311 104 322)(94 310 105 321)(95 309 106 320)(96 330 107 319)(97 329 108 318)(98 328 109 317)(99 327 110 316)(111 331 122 342)(112 352 123 341)(113 351 124 340)(114 350 125 339)(115 349 126 338)(116 348 127 337)(117 347 128 336)(118 346 129 335)(119 345 130 334)(120 344 131 333)(121 343 132 332)(133 358 144 369)(134 357 145 368)(135 356 146 367)(136 355 147 366)(137 354 148 365)(138 353 149 364)(139 374 150 363)(140 373 151 362)(141 372 152 361)(142 371 153 360)(143 370 154 359)(155 390 166 379)(156 389 167 378)(157 388 168 377)(158 387 169 376)(159 386 170 375)(160 385 171 396)(161 384 172 395)(162 383 173 394)(163 382 174 393)(164 381 175 392)(165 380 176 391)(177 408 188 397)(178 407 189 418)(179 406 190 417)(180 405 191 416)(181 404 192 415)(182 403 193 414)(183 402 194 413)(184 401 195 412)(185 400 196 411)(186 399 197 410)(187 398 198 409)(199 435 210 424)(200 434 211 423)(201 433 212 422)(202 432 213 421)(203 431 214 420)(204 430 215 419)(205 429 216 440)(206 428 217 439)(207 427 218 438)(208 426 219 437)(209 425 220 436)
G:=sub<Sym(440)| (1,159,106,149,83,111,52,215,23,177)(2,160,107,150,84,112,53,216,24,178)(3,161,108,151,85,113,54,217,25,179)(4,162,109,152,86,114,55,218,26,180)(5,163,110,153,87,115,56,219,27,181)(6,164,89,154,88,116,57,220,28,182)(7,165,90,133,67,117,58,199,29,183)(8,166,91,134,68,118,59,200,30,184)(9,167,92,135,69,119,60,201,31,185)(10,168,93,136,70,120,61,202,32,186)(11,169,94,137,71,121,62,203,33,187)(12,170,95,138,72,122,63,204,34,188)(13,171,96,139,73,123,64,205,35,189)(14,172,97,140,74,124,65,206,36,190)(15,173,98,141,75,125,66,207,37,191)(16,174,99,142,76,126,45,208,38,192)(17,175,100,143,77,127,46,209,39,193)(18,176,101,144,78,128,47,210,40,194)(19,155,102,145,79,129,48,211,41,195)(20,156,103,146,80,130,49,212,42,196)(21,157,104,147,81,131,50,213,43,197)(22,158,105,148,82,132,51,214,44,198)(221,386,320,364,298,331,276,419,243,408)(222,387,321,365,299,332,277,420,244,409)(223,388,322,366,300,333,278,421,245,410)(224,389,323,367,301,334,279,422,246,411)(225,390,324,368,302,335,280,423,247,412)(226,391,325,369,303,336,281,424,248,413)(227,392,326,370,304,337,282,425,249,414)(228,393,327,371,305,338,283,426,250,415)(229,394,328,372,306,339,284,427,251,416)(230,395,329,373,307,340,285,428,252,417)(231,396,330,374,308,341,286,429,253,418)(232,375,309,353,287,342,265,430,254,397)(233,376,310,354,288,343,266,431,255,398)(234,377,311,355,289,344,267,432,256,399)(235,378,312,356,290,345,268,433,257,400)(236,379,313,357,291,346,269,434,258,401)(237,380,314,358,292,347,270,435,259,402)(238,381,315,359,293,348,271,436,260,403)(239,382,316,360,294,349,272,437,261,404)(240,383,317,361,295,350,273,438,262,405)(241,384,318,362,296,351,274,439,263,406)(242,385,319,363,297,352,275,440,264,407), (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), (1,221,12,232)(2,242,13,231)(3,241,14,230)(4,240,15,229)(5,239,16,228)(6,238,17,227)(7,237,18,226)(8,236,19,225)(9,235,20,224)(10,234,21,223)(11,233,22,222)(23,243,34,254)(24,264,35,253)(25,263,36,252)(26,262,37,251)(27,261,38,250)(28,260,39,249)(29,259,40,248)(30,258,41,247)(31,257,42,246)(32,256,43,245)(33,255,44,244)(45,283,56,272)(46,282,57,271)(47,281,58,270)(48,280,59,269)(49,279,60,268)(50,278,61,267)(51,277,62,266)(52,276,63,265)(53,275,64,286)(54,274,65,285)(55,273,66,284)(67,292,78,303)(68,291,79,302)(69,290,80,301)(70,289,81,300)(71,288,82,299)(72,287,83,298)(73,308,84,297)(74,307,85,296)(75,306,86,295)(76,305,87,294)(77,304,88,293)(89,315,100,326)(90,314,101,325)(91,313,102,324)(92,312,103,323)(93,311,104,322)(94,310,105,321)(95,309,106,320)(96,330,107,319)(97,329,108,318)(98,328,109,317)(99,327,110,316)(111,331,122,342)(112,352,123,341)(113,351,124,340)(114,350,125,339)(115,349,126,338)(116,348,127,337)(117,347,128,336)(118,346,129,335)(119,345,130,334)(120,344,131,333)(121,343,132,332)(133,358,144,369)(134,357,145,368)(135,356,146,367)(136,355,147,366)(137,354,148,365)(138,353,149,364)(139,374,150,363)(140,373,151,362)(141,372,152,361)(142,371,153,360)(143,370,154,359)(155,390,166,379)(156,389,167,378)(157,388,168,377)(158,387,169,376)(159,386,170,375)(160,385,171,396)(161,384,172,395)(162,383,173,394)(163,382,174,393)(164,381,175,392)(165,380,176,391)(177,408,188,397)(178,407,189,418)(179,406,190,417)(180,405,191,416)(181,404,192,415)(182,403,193,414)(183,402,194,413)(184,401,195,412)(185,400,196,411)(186,399,197,410)(187,398,198,409)(199,435,210,424)(200,434,211,423)(201,433,212,422)(202,432,213,421)(203,431,214,420)(204,430,215,419)(205,429,216,440)(206,428,217,439)(207,427,218,438)(208,426,219,437)(209,425,220,436)>;
G:=Group( (1,159,106,149,83,111,52,215,23,177)(2,160,107,150,84,112,53,216,24,178)(3,161,108,151,85,113,54,217,25,179)(4,162,109,152,86,114,55,218,26,180)(5,163,110,153,87,115,56,219,27,181)(6,164,89,154,88,116,57,220,28,182)(7,165,90,133,67,117,58,199,29,183)(8,166,91,134,68,118,59,200,30,184)(9,167,92,135,69,119,60,201,31,185)(10,168,93,136,70,120,61,202,32,186)(11,169,94,137,71,121,62,203,33,187)(12,170,95,138,72,122,63,204,34,188)(13,171,96,139,73,123,64,205,35,189)(14,172,97,140,74,124,65,206,36,190)(15,173,98,141,75,125,66,207,37,191)(16,174,99,142,76,126,45,208,38,192)(17,175,100,143,77,127,46,209,39,193)(18,176,101,144,78,128,47,210,40,194)(19,155,102,145,79,129,48,211,41,195)(20,156,103,146,80,130,49,212,42,196)(21,157,104,147,81,131,50,213,43,197)(22,158,105,148,82,132,51,214,44,198)(221,386,320,364,298,331,276,419,243,408)(222,387,321,365,299,332,277,420,244,409)(223,388,322,366,300,333,278,421,245,410)(224,389,323,367,301,334,279,422,246,411)(225,390,324,368,302,335,280,423,247,412)(226,391,325,369,303,336,281,424,248,413)(227,392,326,370,304,337,282,425,249,414)(228,393,327,371,305,338,283,426,250,415)(229,394,328,372,306,339,284,427,251,416)(230,395,329,373,307,340,285,428,252,417)(231,396,330,374,308,341,286,429,253,418)(232,375,309,353,287,342,265,430,254,397)(233,376,310,354,288,343,266,431,255,398)(234,377,311,355,289,344,267,432,256,399)(235,378,312,356,290,345,268,433,257,400)(236,379,313,357,291,346,269,434,258,401)(237,380,314,358,292,347,270,435,259,402)(238,381,315,359,293,348,271,436,260,403)(239,382,316,360,294,349,272,437,261,404)(240,383,317,361,295,350,273,438,262,405)(241,384,318,362,296,351,274,439,263,406)(242,385,319,363,297,352,275,440,264,407), (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), (1,221,12,232)(2,242,13,231)(3,241,14,230)(4,240,15,229)(5,239,16,228)(6,238,17,227)(7,237,18,226)(8,236,19,225)(9,235,20,224)(10,234,21,223)(11,233,22,222)(23,243,34,254)(24,264,35,253)(25,263,36,252)(26,262,37,251)(27,261,38,250)(28,260,39,249)(29,259,40,248)(30,258,41,247)(31,257,42,246)(32,256,43,245)(33,255,44,244)(45,283,56,272)(46,282,57,271)(47,281,58,270)(48,280,59,269)(49,279,60,268)(50,278,61,267)(51,277,62,266)(52,276,63,265)(53,275,64,286)(54,274,65,285)(55,273,66,284)(67,292,78,303)(68,291,79,302)(69,290,80,301)(70,289,81,300)(71,288,82,299)(72,287,83,298)(73,308,84,297)(74,307,85,296)(75,306,86,295)(76,305,87,294)(77,304,88,293)(89,315,100,326)(90,314,101,325)(91,313,102,324)(92,312,103,323)(93,311,104,322)(94,310,105,321)(95,309,106,320)(96,330,107,319)(97,329,108,318)(98,328,109,317)(99,327,110,316)(111,331,122,342)(112,352,123,341)(113,351,124,340)(114,350,125,339)(115,349,126,338)(116,348,127,337)(117,347,128,336)(118,346,129,335)(119,345,130,334)(120,344,131,333)(121,343,132,332)(133,358,144,369)(134,357,145,368)(135,356,146,367)(136,355,147,366)(137,354,148,365)(138,353,149,364)(139,374,150,363)(140,373,151,362)(141,372,152,361)(142,371,153,360)(143,370,154,359)(155,390,166,379)(156,389,167,378)(157,388,168,377)(158,387,169,376)(159,386,170,375)(160,385,171,396)(161,384,172,395)(162,383,173,394)(163,382,174,393)(164,381,175,392)(165,380,176,391)(177,408,188,397)(178,407,189,418)(179,406,190,417)(180,405,191,416)(181,404,192,415)(182,403,193,414)(183,402,194,413)(184,401,195,412)(185,400,196,411)(186,399,197,410)(187,398,198,409)(199,435,210,424)(200,434,211,423)(201,433,212,422)(202,432,213,421)(203,431,214,420)(204,430,215,419)(205,429,216,440)(206,428,217,439)(207,427,218,438)(208,426,219,437)(209,425,220,436) );
G=PermutationGroup([[(1,159,106,149,83,111,52,215,23,177),(2,160,107,150,84,112,53,216,24,178),(3,161,108,151,85,113,54,217,25,179),(4,162,109,152,86,114,55,218,26,180),(5,163,110,153,87,115,56,219,27,181),(6,164,89,154,88,116,57,220,28,182),(7,165,90,133,67,117,58,199,29,183),(8,166,91,134,68,118,59,200,30,184),(9,167,92,135,69,119,60,201,31,185),(10,168,93,136,70,120,61,202,32,186),(11,169,94,137,71,121,62,203,33,187),(12,170,95,138,72,122,63,204,34,188),(13,171,96,139,73,123,64,205,35,189),(14,172,97,140,74,124,65,206,36,190),(15,173,98,141,75,125,66,207,37,191),(16,174,99,142,76,126,45,208,38,192),(17,175,100,143,77,127,46,209,39,193),(18,176,101,144,78,128,47,210,40,194),(19,155,102,145,79,129,48,211,41,195),(20,156,103,146,80,130,49,212,42,196),(21,157,104,147,81,131,50,213,43,197),(22,158,105,148,82,132,51,214,44,198),(221,386,320,364,298,331,276,419,243,408),(222,387,321,365,299,332,277,420,244,409),(223,388,322,366,300,333,278,421,245,410),(224,389,323,367,301,334,279,422,246,411),(225,390,324,368,302,335,280,423,247,412),(226,391,325,369,303,336,281,424,248,413),(227,392,326,370,304,337,282,425,249,414),(228,393,327,371,305,338,283,426,250,415),(229,394,328,372,306,339,284,427,251,416),(230,395,329,373,307,340,285,428,252,417),(231,396,330,374,308,341,286,429,253,418),(232,375,309,353,287,342,265,430,254,397),(233,376,310,354,288,343,266,431,255,398),(234,377,311,355,289,344,267,432,256,399),(235,378,312,356,290,345,268,433,257,400),(236,379,313,357,291,346,269,434,258,401),(237,380,314,358,292,347,270,435,259,402),(238,381,315,359,293,348,271,436,260,403),(239,382,316,360,294,349,272,437,261,404),(240,383,317,361,295,350,273,438,262,405),(241,384,318,362,296,351,274,439,263,406),(242,385,319,363,297,352,275,440,264,407)], [(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)], [(1,221,12,232),(2,242,13,231),(3,241,14,230),(4,240,15,229),(5,239,16,228),(6,238,17,227),(7,237,18,226),(8,236,19,225),(9,235,20,224),(10,234,21,223),(11,233,22,222),(23,243,34,254),(24,264,35,253),(25,263,36,252),(26,262,37,251),(27,261,38,250),(28,260,39,249),(29,259,40,248),(30,258,41,247),(31,257,42,246),(32,256,43,245),(33,255,44,244),(45,283,56,272),(46,282,57,271),(47,281,58,270),(48,280,59,269),(49,279,60,268),(50,278,61,267),(51,277,62,266),(52,276,63,265),(53,275,64,286),(54,274,65,285),(55,273,66,284),(67,292,78,303),(68,291,79,302),(69,290,80,301),(70,289,81,300),(71,288,82,299),(72,287,83,298),(73,308,84,297),(74,307,85,296),(75,306,86,295),(76,305,87,294),(77,304,88,293),(89,315,100,326),(90,314,101,325),(91,313,102,324),(92,312,103,323),(93,311,104,322),(94,310,105,321),(95,309,106,320),(96,330,107,319),(97,329,108,318),(98,328,109,317),(99,327,110,316),(111,331,122,342),(112,352,123,341),(113,351,124,340),(114,350,125,339),(115,349,126,338),(116,348,127,337),(117,347,128,336),(118,346,129,335),(119,345,130,334),(120,344,131,333),(121,343,132,332),(133,358,144,369),(134,357,145,368),(135,356,146,367),(136,355,147,366),(137,354,148,365),(138,353,149,364),(139,374,150,363),(140,373,151,362),(141,372,152,361),(142,371,153,360),(143,370,154,359),(155,390,166,379),(156,389,167,378),(157,388,168,377),(158,387,169,376),(159,386,170,375),(160,385,171,396),(161,384,172,395),(162,383,173,394),(163,382,174,393),(164,381,175,392),(165,380,176,391),(177,408,188,397),(178,407,189,418),(179,406,190,417),(180,405,191,416),(181,404,192,415),(182,403,193,414),(183,402,194,413),(184,401,195,412),(185,400,196,411),(186,399,197,410),(187,398,198,409),(199,435,210,424),(200,434,211,423),(201,433,212,422),(202,432,213,421),(203,431,214,420),(204,430,215,419),(205,429,216,440),(206,428,217,439),(207,427,218,438),(208,426,219,437),(209,425,220,436)]])
140 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 5A | 5B | 5C | 5D | 10A | ··· | 10L | 11A | ··· | 11E | 20A | ··· | 20P | 22A | ··· | 22O | 55A | ··· | 55T | 110A | ··· | 110BH |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 10 | ··· | 10 | 11 | ··· | 11 | 20 | ··· | 20 | 22 | ··· | 22 | 55 | ··· | 55 | 110 | ··· | 110 |
| size | 1 | 1 | 1 | 1 | 11 | 11 | 11 | 11 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 11 | ··· | 11 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
140 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | ||||||||
| image | C1 | C2 | C2 | C4 | C5 | C10 | C10 | C20 | D11 | Dic11 | D22 | C5×D11 | C5×Dic11 | C10×D11 |
| kernel | C10×Dic11 | C5×Dic11 | C2×C110 | C110 | C2×Dic11 | Dic11 | C2×C22 | C22 | C2×C10 | C10 | C10 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 4 | 8 | 4 | 16 | 5 | 10 | 5 | 20 | 40 | 20 |
Matrix representation of C10×Dic11 ►in GL4(𝔽661) generated by
| 247 | 0 | 0 | 0 |
| 0 | 660 | 0 | 0 |
| 0 | 0 | 660 | 0 |
| 0 | 0 | 0 | 660 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 660 |
| 0 | 0 | 488 | 174 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 197 | 371 |
| 0 | 0 | 225 | 464 |
G:=sub<GL(4,GF(661))| [247,0,0,0,0,660,0,0,0,0,660,0,0,0,0,660],[1,0,0,0,0,1,0,0,0,0,1,488,0,0,660,174],[1,0,0,0,0,1,0,0,0,0,197,225,0,0,371,464] >;
C10×Dic11 in GAP, Magma, Sage, TeX
C_{10}\times {\rm Dic}_{11} % in TeX
G:=Group("C10xDic11"); // GroupNames label
G:=SmallGroup(440,27);
// by ID
G=gap.SmallGroup(440,27);
# by ID
G:=PCGroup([5,-2,-2,-5,-2,-11,100,10004]);
// Polycyclic
G:=Group<a,b,c|a^10=b^22=1,c^2=b^11,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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