direct product, metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C11×Dic10, C55⋊4Q8, C44.3D5, C220.5C2, C20.1C22, C22.13D10, Dic5.1C22, C110.18C22, C5⋊(Q8×C11), C4.(D5×C11), C2.3(D5×C22), C10.1(C2×C22), (C11×Dic5).3C2, SmallGroup(440,29)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C11×Dic10
G = < a,b,c | a11=b20=1, c2=b10, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C11×Dic10
►Regular action on 440 points
Generators in S440
(1 307 288 192 377 21 404 145 67 94 351)(2 308 289 193 378 22 405 146 68 95 352)(3 309 290 194 379 23 406 147 69 96 353)(4 310 291 195 380 24 407 148 70 97 354)(5 311 292 196 361 25 408 149 71 98 355)(6 312 293 197 362 26 409 150 72 99 356)(7 313 294 198 363 27 410 151 73 100 357)(8 314 295 199 364 28 411 152 74 81 358)(9 315 296 200 365 29 412 153 75 82 359)(10 316 297 181 366 30 413 154 76 83 360)(11 317 298 182 367 31 414 155 77 84 341)(12 318 299 183 368 32 415 156 78 85 342)(13 319 300 184 369 33 416 157 79 86 343)(14 320 281 185 370 34 417 158 80 87 344)(15 301 282 186 371 35 418 159 61 88 345)(16 302 283 187 372 36 419 160 62 89 346)(17 303 284 188 373 37 420 141 63 90 347)(18 304 285 189 374 38 401 142 64 91 348)(19 305 286 190 375 39 402 143 65 92 349)(20 306 287 191 376 40 403 144 66 93 350)(41 101 137 163 396 424 234 271 338 213 245)(42 102 138 164 397 425 235 272 339 214 246)(43 103 139 165 398 426 236 273 340 215 247)(44 104 140 166 399 427 237 274 321 216 248)(45 105 121 167 400 428 238 275 322 217 249)(46 106 122 168 381 429 239 276 323 218 250)(47 107 123 169 382 430 240 277 324 219 251)(48 108 124 170 383 431 221 278 325 220 252)(49 109 125 171 384 432 222 279 326 201 253)(50 110 126 172 385 433 223 280 327 202 254)(51 111 127 173 386 434 224 261 328 203 255)(52 112 128 174 387 435 225 262 329 204 256)(53 113 129 175 388 436 226 263 330 205 257)(54 114 130 176 389 437 227 264 331 206 258)(55 115 131 177 390 438 228 265 332 207 259)(56 116 132 178 391 439 229 266 333 208 260)(57 117 133 179 392 440 230 267 334 209 241)(58 118 134 180 393 421 231 268 335 210 242)(59 119 135 161 394 422 232 269 336 211 243)(60 120 136 162 395 423 233 270 337 212 244)
(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)
(1 273 11 263)(2 272 12 262)(3 271 13 261)(4 270 14 280)(5 269 15 279)(6 268 16 278)(7 267 17 277)(8 266 18 276)(9 265 19 275)(10 264 20 274)(21 103 31 113)(22 102 32 112)(23 101 33 111)(24 120 34 110)(25 119 35 109)(26 118 36 108)(27 117 37 107)(28 116 38 106)(29 115 39 105)(30 114 40 104)(41 369 51 379)(42 368 52 378)(43 367 53 377)(44 366 54 376)(45 365 55 375)(46 364 56 374)(47 363 57 373)(48 362 58 372)(49 361 59 371)(50 380 60 370)(61 384 71 394)(62 383 72 393)(63 382 73 392)(64 381 74 391)(65 400 75 390)(66 399 76 389)(67 398 77 388)(68 397 78 387)(69 396 79 386)(70 395 80 385)(81 439 91 429)(82 438 92 428)(83 437 93 427)(84 436 94 426)(85 435 95 425)(86 434 96 424)(87 433 97 423)(88 432 98 422)(89 431 99 421)(90 430 100 440)(121 412 131 402)(122 411 132 401)(123 410 133 420)(124 409 134 419)(125 408 135 418)(126 407 136 417)(127 406 137 416)(128 405 138 415)(129 404 139 414)(130 403 140 413)(141 169 151 179)(142 168 152 178)(143 167 153 177)(144 166 154 176)(145 165 155 175)(146 164 156 174)(147 163 157 173)(148 162 158 172)(149 161 159 171)(150 180 160 170)(181 258 191 248)(182 257 192 247)(183 256 193 246)(184 255 194 245)(185 254 195 244)(186 253 196 243)(187 252 197 242)(188 251 198 241)(189 250 199 260)(190 249 200 259)(201 292 211 282)(202 291 212 281)(203 290 213 300)(204 289 214 299)(205 288 215 298)(206 287 216 297)(207 286 217 296)(208 285 218 295)(209 284 219 294)(210 283 220 293)(221 356 231 346)(222 355 232 345)(223 354 233 344)(224 353 234 343)(225 352 235 342)(226 351 236 341)(227 350 237 360)(228 349 238 359)(229 348 239 358)(230 347 240 357)(301 326 311 336)(302 325 312 335)(303 324 313 334)(304 323 314 333)(305 322 315 332)(306 321 316 331)(307 340 317 330)(308 339 318 329)(309 338 319 328)(310 337 320 327)
G:=sub<Sym(440)| (1,307,288,192,377,21,404,145,67,94,351)(2,308,289,193,378,22,405,146,68,95,352)(3,309,290,194,379,23,406,147,69,96,353)(4,310,291,195,380,24,407,148,70,97,354)(5,311,292,196,361,25,408,149,71,98,355)(6,312,293,197,362,26,409,150,72,99,356)(7,313,294,198,363,27,410,151,73,100,357)(8,314,295,199,364,28,411,152,74,81,358)(9,315,296,200,365,29,412,153,75,82,359)(10,316,297,181,366,30,413,154,76,83,360)(11,317,298,182,367,31,414,155,77,84,341)(12,318,299,183,368,32,415,156,78,85,342)(13,319,300,184,369,33,416,157,79,86,343)(14,320,281,185,370,34,417,158,80,87,344)(15,301,282,186,371,35,418,159,61,88,345)(16,302,283,187,372,36,419,160,62,89,346)(17,303,284,188,373,37,420,141,63,90,347)(18,304,285,189,374,38,401,142,64,91,348)(19,305,286,190,375,39,402,143,65,92,349)(20,306,287,191,376,40,403,144,66,93,350)(41,101,137,163,396,424,234,271,338,213,245)(42,102,138,164,397,425,235,272,339,214,246)(43,103,139,165,398,426,236,273,340,215,247)(44,104,140,166,399,427,237,274,321,216,248)(45,105,121,167,400,428,238,275,322,217,249)(46,106,122,168,381,429,239,276,323,218,250)(47,107,123,169,382,430,240,277,324,219,251)(48,108,124,170,383,431,221,278,325,220,252)(49,109,125,171,384,432,222,279,326,201,253)(50,110,126,172,385,433,223,280,327,202,254)(51,111,127,173,386,434,224,261,328,203,255)(52,112,128,174,387,435,225,262,329,204,256)(53,113,129,175,388,436,226,263,330,205,257)(54,114,130,176,389,437,227,264,331,206,258)(55,115,131,177,390,438,228,265,332,207,259)(56,116,132,178,391,439,229,266,333,208,260)(57,117,133,179,392,440,230,267,334,209,241)(58,118,134,180,393,421,231,268,335,210,242)(59,119,135,161,394,422,232,269,336,211,243)(60,120,136,162,395,423,233,270,337,212,244), (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), (1,273,11,263)(2,272,12,262)(3,271,13,261)(4,270,14,280)(5,269,15,279)(6,268,16,278)(7,267,17,277)(8,266,18,276)(9,265,19,275)(10,264,20,274)(21,103,31,113)(22,102,32,112)(23,101,33,111)(24,120,34,110)(25,119,35,109)(26,118,36,108)(27,117,37,107)(28,116,38,106)(29,115,39,105)(30,114,40,104)(41,369,51,379)(42,368,52,378)(43,367,53,377)(44,366,54,376)(45,365,55,375)(46,364,56,374)(47,363,57,373)(48,362,58,372)(49,361,59,371)(50,380,60,370)(61,384,71,394)(62,383,72,393)(63,382,73,392)(64,381,74,391)(65,400,75,390)(66,399,76,389)(67,398,77,388)(68,397,78,387)(69,396,79,386)(70,395,80,385)(81,439,91,429)(82,438,92,428)(83,437,93,427)(84,436,94,426)(85,435,95,425)(86,434,96,424)(87,433,97,423)(88,432,98,422)(89,431,99,421)(90,430,100,440)(121,412,131,402)(122,411,132,401)(123,410,133,420)(124,409,134,419)(125,408,135,418)(126,407,136,417)(127,406,137,416)(128,405,138,415)(129,404,139,414)(130,403,140,413)(141,169,151,179)(142,168,152,178)(143,167,153,177)(144,166,154,176)(145,165,155,175)(146,164,156,174)(147,163,157,173)(148,162,158,172)(149,161,159,171)(150,180,160,170)(181,258,191,248)(182,257,192,247)(183,256,193,246)(184,255,194,245)(185,254,195,244)(186,253,196,243)(187,252,197,242)(188,251,198,241)(189,250,199,260)(190,249,200,259)(201,292,211,282)(202,291,212,281)(203,290,213,300)(204,289,214,299)(205,288,215,298)(206,287,216,297)(207,286,217,296)(208,285,218,295)(209,284,219,294)(210,283,220,293)(221,356,231,346)(222,355,232,345)(223,354,233,344)(224,353,234,343)(225,352,235,342)(226,351,236,341)(227,350,237,360)(228,349,238,359)(229,348,239,358)(230,347,240,357)(301,326,311,336)(302,325,312,335)(303,324,313,334)(304,323,314,333)(305,322,315,332)(306,321,316,331)(307,340,317,330)(308,339,318,329)(309,338,319,328)(310,337,320,327)>;
G:=Group( (1,307,288,192,377,21,404,145,67,94,351)(2,308,289,193,378,22,405,146,68,95,352)(3,309,290,194,379,23,406,147,69,96,353)(4,310,291,195,380,24,407,148,70,97,354)(5,311,292,196,361,25,408,149,71,98,355)(6,312,293,197,362,26,409,150,72,99,356)(7,313,294,198,363,27,410,151,73,100,357)(8,314,295,199,364,28,411,152,74,81,358)(9,315,296,200,365,29,412,153,75,82,359)(10,316,297,181,366,30,413,154,76,83,360)(11,317,298,182,367,31,414,155,77,84,341)(12,318,299,183,368,32,415,156,78,85,342)(13,319,300,184,369,33,416,157,79,86,343)(14,320,281,185,370,34,417,158,80,87,344)(15,301,282,186,371,35,418,159,61,88,345)(16,302,283,187,372,36,419,160,62,89,346)(17,303,284,188,373,37,420,141,63,90,347)(18,304,285,189,374,38,401,142,64,91,348)(19,305,286,190,375,39,402,143,65,92,349)(20,306,287,191,376,40,403,144,66,93,350)(41,101,137,163,396,424,234,271,338,213,245)(42,102,138,164,397,425,235,272,339,214,246)(43,103,139,165,398,426,236,273,340,215,247)(44,104,140,166,399,427,237,274,321,216,248)(45,105,121,167,400,428,238,275,322,217,249)(46,106,122,168,381,429,239,276,323,218,250)(47,107,123,169,382,430,240,277,324,219,251)(48,108,124,170,383,431,221,278,325,220,252)(49,109,125,171,384,432,222,279,326,201,253)(50,110,126,172,385,433,223,280,327,202,254)(51,111,127,173,386,434,224,261,328,203,255)(52,112,128,174,387,435,225,262,329,204,256)(53,113,129,175,388,436,226,263,330,205,257)(54,114,130,176,389,437,227,264,331,206,258)(55,115,131,177,390,438,228,265,332,207,259)(56,116,132,178,391,439,229,266,333,208,260)(57,117,133,179,392,440,230,267,334,209,241)(58,118,134,180,393,421,231,268,335,210,242)(59,119,135,161,394,422,232,269,336,211,243)(60,120,136,162,395,423,233,270,337,212,244), (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), (1,273,11,263)(2,272,12,262)(3,271,13,261)(4,270,14,280)(5,269,15,279)(6,268,16,278)(7,267,17,277)(8,266,18,276)(9,265,19,275)(10,264,20,274)(21,103,31,113)(22,102,32,112)(23,101,33,111)(24,120,34,110)(25,119,35,109)(26,118,36,108)(27,117,37,107)(28,116,38,106)(29,115,39,105)(30,114,40,104)(41,369,51,379)(42,368,52,378)(43,367,53,377)(44,366,54,376)(45,365,55,375)(46,364,56,374)(47,363,57,373)(48,362,58,372)(49,361,59,371)(50,380,60,370)(61,384,71,394)(62,383,72,393)(63,382,73,392)(64,381,74,391)(65,400,75,390)(66,399,76,389)(67,398,77,388)(68,397,78,387)(69,396,79,386)(70,395,80,385)(81,439,91,429)(82,438,92,428)(83,437,93,427)(84,436,94,426)(85,435,95,425)(86,434,96,424)(87,433,97,423)(88,432,98,422)(89,431,99,421)(90,430,100,440)(121,412,131,402)(122,411,132,401)(123,410,133,420)(124,409,134,419)(125,408,135,418)(126,407,136,417)(127,406,137,416)(128,405,138,415)(129,404,139,414)(130,403,140,413)(141,169,151,179)(142,168,152,178)(143,167,153,177)(144,166,154,176)(145,165,155,175)(146,164,156,174)(147,163,157,173)(148,162,158,172)(149,161,159,171)(150,180,160,170)(181,258,191,248)(182,257,192,247)(183,256,193,246)(184,255,194,245)(185,254,195,244)(186,253,196,243)(187,252,197,242)(188,251,198,241)(189,250,199,260)(190,249,200,259)(201,292,211,282)(202,291,212,281)(203,290,213,300)(204,289,214,299)(205,288,215,298)(206,287,216,297)(207,286,217,296)(208,285,218,295)(209,284,219,294)(210,283,220,293)(221,356,231,346)(222,355,232,345)(223,354,233,344)(224,353,234,343)(225,352,235,342)(226,351,236,341)(227,350,237,360)(228,349,238,359)(229,348,239,358)(230,347,240,357)(301,326,311,336)(302,325,312,335)(303,324,313,334)(304,323,314,333)(305,322,315,332)(306,321,316,331)(307,340,317,330)(308,339,318,329)(309,338,319,328)(310,337,320,327) );
G=PermutationGroup([[(1,307,288,192,377,21,404,145,67,94,351),(2,308,289,193,378,22,405,146,68,95,352),(3,309,290,194,379,23,406,147,69,96,353),(4,310,291,195,380,24,407,148,70,97,354),(5,311,292,196,361,25,408,149,71,98,355),(6,312,293,197,362,26,409,150,72,99,356),(7,313,294,198,363,27,410,151,73,100,357),(8,314,295,199,364,28,411,152,74,81,358),(9,315,296,200,365,29,412,153,75,82,359),(10,316,297,181,366,30,413,154,76,83,360),(11,317,298,182,367,31,414,155,77,84,341),(12,318,299,183,368,32,415,156,78,85,342),(13,319,300,184,369,33,416,157,79,86,343),(14,320,281,185,370,34,417,158,80,87,344),(15,301,282,186,371,35,418,159,61,88,345),(16,302,283,187,372,36,419,160,62,89,346),(17,303,284,188,373,37,420,141,63,90,347),(18,304,285,189,374,38,401,142,64,91,348),(19,305,286,190,375,39,402,143,65,92,349),(20,306,287,191,376,40,403,144,66,93,350),(41,101,137,163,396,424,234,271,338,213,245),(42,102,138,164,397,425,235,272,339,214,246),(43,103,139,165,398,426,236,273,340,215,247),(44,104,140,166,399,427,237,274,321,216,248),(45,105,121,167,400,428,238,275,322,217,249),(46,106,122,168,381,429,239,276,323,218,250),(47,107,123,169,382,430,240,277,324,219,251),(48,108,124,170,383,431,221,278,325,220,252),(49,109,125,171,384,432,222,279,326,201,253),(50,110,126,172,385,433,223,280,327,202,254),(51,111,127,173,386,434,224,261,328,203,255),(52,112,128,174,387,435,225,262,329,204,256),(53,113,129,175,388,436,226,263,330,205,257),(54,114,130,176,389,437,227,264,331,206,258),(55,115,131,177,390,438,228,265,332,207,259),(56,116,132,178,391,439,229,266,333,208,260),(57,117,133,179,392,440,230,267,334,209,241),(58,118,134,180,393,421,231,268,335,210,242),(59,119,135,161,394,422,232,269,336,211,243),(60,120,136,162,395,423,233,270,337,212,244)], [(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)], [(1,273,11,263),(2,272,12,262),(3,271,13,261),(4,270,14,280),(5,269,15,279),(6,268,16,278),(7,267,17,277),(8,266,18,276),(9,265,19,275),(10,264,20,274),(21,103,31,113),(22,102,32,112),(23,101,33,111),(24,120,34,110),(25,119,35,109),(26,118,36,108),(27,117,37,107),(28,116,38,106),(29,115,39,105),(30,114,40,104),(41,369,51,379),(42,368,52,378),(43,367,53,377),(44,366,54,376),(45,365,55,375),(46,364,56,374),(47,363,57,373),(48,362,58,372),(49,361,59,371),(50,380,60,370),(61,384,71,394),(62,383,72,393),(63,382,73,392),(64,381,74,391),(65,400,75,390),(66,399,76,389),(67,398,77,388),(68,397,78,387),(69,396,79,386),(70,395,80,385),(81,439,91,429),(82,438,92,428),(83,437,93,427),(84,436,94,426),(85,435,95,425),(86,434,96,424),(87,433,97,423),(88,432,98,422),(89,431,99,421),(90,430,100,440),(121,412,131,402),(122,411,132,401),(123,410,133,420),(124,409,134,419),(125,408,135,418),(126,407,136,417),(127,406,137,416),(128,405,138,415),(129,404,139,414),(130,403,140,413),(141,169,151,179),(142,168,152,178),(143,167,153,177),(144,166,154,176),(145,165,155,175),(146,164,156,174),(147,163,157,173),(148,162,158,172),(149,161,159,171),(150,180,160,170),(181,258,191,248),(182,257,192,247),(183,256,193,246),(184,255,194,245),(185,254,195,244),(186,253,196,243),(187,252,197,242),(188,251,198,241),(189,250,199,260),(190,249,200,259),(201,292,211,282),(202,291,212,281),(203,290,213,300),(204,289,214,299),(205,288,215,298),(206,287,216,297),(207,286,217,296),(208,285,218,295),(209,284,219,294),(210,283,220,293),(221,356,231,346),(222,355,232,345),(223,354,233,344),(224,353,234,343),(225,352,235,342),(226,351,236,341),(227,350,237,360),(228,349,238,359),(229,348,239,358),(230,347,240,357),(301,326,311,336),(302,325,312,335),(303,324,313,334),(304,323,314,333),(305,322,315,332),(306,321,316,331),(307,340,317,330),(308,339,318,329),(309,338,319,328),(310,337,320,327)]])
143 conjugacy classes
| class | 1 | 2 | 4A | 4B | 4C | 5A | 5B | 10A | 10B | 11A | ··· | 11J | 20A | 20B | 20C | 20D | 22A | ··· | 22J | 44A | ··· | 44J | 44K | ··· | 44AD | 55A | ··· | 55T | 110A | ··· | 110T | 220A | ··· | 220AN |
| order | 1 | 2 | 4 | 4 | 4 | 5 | 5 | 10 | 10 | 11 | ··· | 11 | 20 | 20 | 20 | 20 | 22 | ··· | 22 | 44 | ··· | 44 | 44 | ··· | 44 | 55 | ··· | 55 | 110 | ··· | 110 | 220 | ··· | 220 |
| size | 1 | 1 | 2 | 10 | 10 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 10 | ··· | 10 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
143 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | + | + | - | |||||||
| image | C1 | C2 | C2 | C11 | C22 | C22 | Q8 | D5 | D10 | Dic10 | Q8×C11 | D5×C11 | D5×C22 | C11×Dic10 |
| kernel | C11×Dic10 | C11×Dic5 | C220 | Dic10 | Dic5 | C20 | C55 | C44 | C22 | C11 | C5 | C4 | C2 | C1 |
| # reps | 1 | 2 | 1 | 10 | 20 | 10 | 1 | 2 | 2 | 4 | 10 | 20 | 20 | 40 |
Matrix representation of C11×Dic10 ►in GL2(𝔽661) generated by
| 81 | 0 |
| 0 | 81 |
| 624 | 215 |
| 535 | 89 |
| 268 | 31 |
| 455 | 393 |
G:=sub<GL(2,GF(661))| [81,0,0,81],[624,535,215,89],[268,455,31,393] >;
C11×Dic10 in GAP, Magma, Sage, TeX
C_{11}\times {\rm Dic}_{10} % in TeX
G:=Group("C11xDic10"); // GroupNames label
G:=SmallGroup(440,29);
// by ID
G=gap.SmallGroup(440,29);
# by ID
G:=PCGroup([5,-2,-2,-11,-2,-5,220,461,226,8804]);
// Polycyclic
G:=Group<a,b,c|a^11=b^20=1,c^2=b^10,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export