metabelian, supersoluble, monomial, A-group
Aliases: C11⋊Dic11, C112⋊3C4, C22.3D11, C2.(C11⋊D11), (C11×C22).2C2, SmallGroup(484,6)
Series: Derived ►Chief ►Lower central ►Upper central
| C112 — C11⋊Dic11 |
Generators and relations for C11⋊Dic11
G = < a,b,c | a11=b22=1, c2=b11, ab=ba, cac-1=a-1, cbc-1=b-1 >
121C4
11Dic11
11Dic11
11Dic11
11Dic11
11Dic11
11Dic11
11Dic11
11Dic11
11Dic11
11Dic11
11Dic11
11Dic11
Smallest permutation representation of C11⋊Dic11
►Regular action on 484 points
Generators in S484
(1 160 272 305 482 49 114 409 183 387 37)(2 161 273 306 483 50 115 410 184 388 38)(3 162 274 307 484 51 116 411 185 389 39)(4 163 275 308 463 52 117 412 186 390 40)(5 164 276 287 464 53 118 413 187 391 41)(6 165 277 288 465 54 119 414 188 392 42)(7 166 278 289 466 55 120 415 189 393 43)(8 167 279 290 467 56 121 416 190 394 44)(9 168 280 291 468 57 122 417 191 395 23)(10 169 281 292 469 58 123 418 192 396 24)(11 170 282 293 470 59 124 397 193 375 25)(12 171 283 294 471 60 125 398 194 376 26)(13 172 284 295 472 61 126 399 195 377 27)(14 173 285 296 473 62 127 400 196 378 28)(15 174 286 297 474 63 128 401 197 379 29)(16 175 265 298 475 64 129 402 198 380 30)(17 176 266 299 476 65 130 403 177 381 31)(18 155 267 300 477 66 131 404 178 382 32)(19 156 268 301 478 45 132 405 179 383 33)(20 157 269 302 479 46 111 406 180 384 34)(21 158 270 303 480 47 112 407 181 385 35)(22 159 271 304 481 48 113 408 182 386 36)(67 344 372 102 439 462 231 151 245 310 213)(68 345 373 103 440 441 232 152 246 311 214)(69 346 374 104 419 442 233 153 247 312 215)(70 347 353 105 420 443 234 154 248 313 216)(71 348 354 106 421 444 235 133 249 314 217)(72 349 355 107 422 445 236 134 250 315 218)(73 350 356 108 423 446 237 135 251 316 219)(74 351 357 109 424 447 238 136 252 317 220)(75 352 358 110 425 448 239 137 253 318 199)(76 331 359 89 426 449 240 138 254 319 200)(77 332 360 90 427 450 241 139 255 320 201)(78 333 361 91 428 451 242 140 256 321 202)(79 334 362 92 429 452 221 141 257 322 203)(80 335 363 93 430 453 222 142 258 323 204)(81 336 364 94 431 454 223 143 259 324 205)(82 337 365 95 432 455 224 144 260 325 206)(83 338 366 96 433 456 225 145 261 326 207)(84 339 367 97 434 457 226 146 262 327 208)(85 340 368 98 435 458 227 147 263 328 209)(86 341 369 99 436 459 228 148 264 329 210)(87 342 370 100 437 460 229 149 243 330 211)(88 343 371 101 438 461 230 150 244 309 212)
(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)(463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484)
(1 235 12 224)(2 234 13 223)(3 233 14 222)(4 232 15 221)(5 231 16 242)(6 230 17 241)(7 229 18 240)(8 228 19 239)(9 227 20 238)(10 226 21 237)(11 225 22 236)(23 147 34 136)(24 146 35 135)(25 145 36 134)(26 144 37 133)(27 143 38 154)(28 142 39 153)(29 141 40 152)(30 140 41 151)(31 139 42 150)(32 138 43 149)(33 137 44 148)(45 352 56 341)(46 351 57 340)(47 350 58 339)(48 349 59 338)(49 348 60 337)(50 347 61 336)(51 346 62 335)(52 345 63 334)(53 344 64 333)(54 343 65 332)(55 342 66 331)(67 129 78 118)(68 128 79 117)(69 127 80 116)(70 126 81 115)(71 125 82 114)(72 124 83 113)(73 123 84 112)(74 122 85 111)(75 121 86 132)(76 120 87 131)(77 119 88 130)(89 289 100 300)(90 288 101 299)(91 287 102 298)(92 308 103 297)(93 307 104 296)(94 306 105 295)(95 305 106 294)(96 304 107 293)(97 303 108 292)(98 302 109 291)(99 301 110 290)(155 449 166 460)(156 448 167 459)(157 447 168 458)(158 446 169 457)(159 445 170 456)(160 444 171 455)(161 443 172 454)(162 442 173 453)(163 441 174 452)(164 462 175 451)(165 461 176 450)(177 320 188 309)(178 319 189 330)(179 318 190 329)(180 317 191 328)(181 316 192 327)(182 315 193 326)(183 314 194 325)(184 313 195 324)(185 312 196 323)(186 311 197 322)(187 310 198 321)(199 416 210 405)(200 415 211 404)(201 414 212 403)(202 413 213 402)(203 412 214 401)(204 411 215 400)(205 410 216 399)(206 409 217 398)(207 408 218 397)(208 407 219 418)(209 406 220 417)(243 382 254 393)(244 381 255 392)(245 380 256 391)(246 379 257 390)(247 378 258 389)(248 377 259 388)(249 376 260 387)(250 375 261 386)(251 396 262 385)(252 395 263 384)(253 394 264 383)(265 428 276 439)(266 427 277 438)(267 426 278 437)(268 425 279 436)(269 424 280 435)(270 423 281 434)(271 422 282 433)(272 421 283 432)(273 420 284 431)(274 419 285 430)(275 440 286 429)(353 472 364 483)(354 471 365 482)(355 470 366 481)(356 469 367 480)(357 468 368 479)(358 467 369 478)(359 466 370 477)(360 465 371 476)(361 464 372 475)(362 463 373 474)(363 484 374 473)
G:=sub<Sym(484)| (1,160,272,305,482,49,114,409,183,387,37)(2,161,273,306,483,50,115,410,184,388,38)(3,162,274,307,484,51,116,411,185,389,39)(4,163,275,308,463,52,117,412,186,390,40)(5,164,276,287,464,53,118,413,187,391,41)(6,165,277,288,465,54,119,414,188,392,42)(7,166,278,289,466,55,120,415,189,393,43)(8,167,279,290,467,56,121,416,190,394,44)(9,168,280,291,468,57,122,417,191,395,23)(10,169,281,292,469,58,123,418,192,396,24)(11,170,282,293,470,59,124,397,193,375,25)(12,171,283,294,471,60,125,398,194,376,26)(13,172,284,295,472,61,126,399,195,377,27)(14,173,285,296,473,62,127,400,196,378,28)(15,174,286,297,474,63,128,401,197,379,29)(16,175,265,298,475,64,129,402,198,380,30)(17,176,266,299,476,65,130,403,177,381,31)(18,155,267,300,477,66,131,404,178,382,32)(19,156,268,301,478,45,132,405,179,383,33)(20,157,269,302,479,46,111,406,180,384,34)(21,158,270,303,480,47,112,407,181,385,35)(22,159,271,304,481,48,113,408,182,386,36)(67,344,372,102,439,462,231,151,245,310,213)(68,345,373,103,440,441,232,152,246,311,214)(69,346,374,104,419,442,233,153,247,312,215)(70,347,353,105,420,443,234,154,248,313,216)(71,348,354,106,421,444,235,133,249,314,217)(72,349,355,107,422,445,236,134,250,315,218)(73,350,356,108,423,446,237,135,251,316,219)(74,351,357,109,424,447,238,136,252,317,220)(75,352,358,110,425,448,239,137,253,318,199)(76,331,359,89,426,449,240,138,254,319,200)(77,332,360,90,427,450,241,139,255,320,201)(78,333,361,91,428,451,242,140,256,321,202)(79,334,362,92,429,452,221,141,257,322,203)(80,335,363,93,430,453,222,142,258,323,204)(81,336,364,94,431,454,223,143,259,324,205)(82,337,365,95,432,455,224,144,260,325,206)(83,338,366,96,433,456,225,145,261,326,207)(84,339,367,97,434,457,226,146,262,327,208)(85,340,368,98,435,458,227,147,263,328,209)(86,341,369,99,436,459,228,148,264,329,210)(87,342,370,100,437,460,229,149,243,330,211)(88,343,371,101,438,461,230,150,244,309,212), (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)(463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484), (1,235,12,224)(2,234,13,223)(3,233,14,222)(4,232,15,221)(5,231,16,242)(6,230,17,241)(7,229,18,240)(8,228,19,239)(9,227,20,238)(10,226,21,237)(11,225,22,236)(23,147,34,136)(24,146,35,135)(25,145,36,134)(26,144,37,133)(27,143,38,154)(28,142,39,153)(29,141,40,152)(30,140,41,151)(31,139,42,150)(32,138,43,149)(33,137,44,148)(45,352,56,341)(46,351,57,340)(47,350,58,339)(48,349,59,338)(49,348,60,337)(50,347,61,336)(51,346,62,335)(52,345,63,334)(53,344,64,333)(54,343,65,332)(55,342,66,331)(67,129,78,118)(68,128,79,117)(69,127,80,116)(70,126,81,115)(71,125,82,114)(72,124,83,113)(73,123,84,112)(74,122,85,111)(75,121,86,132)(76,120,87,131)(77,119,88,130)(89,289,100,300)(90,288,101,299)(91,287,102,298)(92,308,103,297)(93,307,104,296)(94,306,105,295)(95,305,106,294)(96,304,107,293)(97,303,108,292)(98,302,109,291)(99,301,110,290)(155,449,166,460)(156,448,167,459)(157,447,168,458)(158,446,169,457)(159,445,170,456)(160,444,171,455)(161,443,172,454)(162,442,173,453)(163,441,174,452)(164,462,175,451)(165,461,176,450)(177,320,188,309)(178,319,189,330)(179,318,190,329)(180,317,191,328)(181,316,192,327)(182,315,193,326)(183,314,194,325)(184,313,195,324)(185,312,196,323)(186,311,197,322)(187,310,198,321)(199,416,210,405)(200,415,211,404)(201,414,212,403)(202,413,213,402)(203,412,214,401)(204,411,215,400)(205,410,216,399)(206,409,217,398)(207,408,218,397)(208,407,219,418)(209,406,220,417)(243,382,254,393)(244,381,255,392)(245,380,256,391)(246,379,257,390)(247,378,258,389)(248,377,259,388)(249,376,260,387)(250,375,261,386)(251,396,262,385)(252,395,263,384)(253,394,264,383)(265,428,276,439)(266,427,277,438)(267,426,278,437)(268,425,279,436)(269,424,280,435)(270,423,281,434)(271,422,282,433)(272,421,283,432)(273,420,284,431)(274,419,285,430)(275,440,286,429)(353,472,364,483)(354,471,365,482)(355,470,366,481)(356,469,367,480)(357,468,368,479)(358,467,369,478)(359,466,370,477)(360,465,371,476)(361,464,372,475)(362,463,373,474)(363,484,374,473)>;
G:=Group( (1,160,272,305,482,49,114,409,183,387,37)(2,161,273,306,483,50,115,410,184,388,38)(3,162,274,307,484,51,116,411,185,389,39)(4,163,275,308,463,52,117,412,186,390,40)(5,164,276,287,464,53,118,413,187,391,41)(6,165,277,288,465,54,119,414,188,392,42)(7,166,278,289,466,55,120,415,189,393,43)(8,167,279,290,467,56,121,416,190,394,44)(9,168,280,291,468,57,122,417,191,395,23)(10,169,281,292,469,58,123,418,192,396,24)(11,170,282,293,470,59,124,397,193,375,25)(12,171,283,294,471,60,125,398,194,376,26)(13,172,284,295,472,61,126,399,195,377,27)(14,173,285,296,473,62,127,400,196,378,28)(15,174,286,297,474,63,128,401,197,379,29)(16,175,265,298,475,64,129,402,198,380,30)(17,176,266,299,476,65,130,403,177,381,31)(18,155,267,300,477,66,131,404,178,382,32)(19,156,268,301,478,45,132,405,179,383,33)(20,157,269,302,479,46,111,406,180,384,34)(21,158,270,303,480,47,112,407,181,385,35)(22,159,271,304,481,48,113,408,182,386,36)(67,344,372,102,439,462,231,151,245,310,213)(68,345,373,103,440,441,232,152,246,311,214)(69,346,374,104,419,442,233,153,247,312,215)(70,347,353,105,420,443,234,154,248,313,216)(71,348,354,106,421,444,235,133,249,314,217)(72,349,355,107,422,445,236,134,250,315,218)(73,350,356,108,423,446,237,135,251,316,219)(74,351,357,109,424,447,238,136,252,317,220)(75,352,358,110,425,448,239,137,253,318,199)(76,331,359,89,426,449,240,138,254,319,200)(77,332,360,90,427,450,241,139,255,320,201)(78,333,361,91,428,451,242,140,256,321,202)(79,334,362,92,429,452,221,141,257,322,203)(80,335,363,93,430,453,222,142,258,323,204)(81,336,364,94,431,454,223,143,259,324,205)(82,337,365,95,432,455,224,144,260,325,206)(83,338,366,96,433,456,225,145,261,326,207)(84,339,367,97,434,457,226,146,262,327,208)(85,340,368,98,435,458,227,147,263,328,209)(86,341,369,99,436,459,228,148,264,329,210)(87,342,370,100,437,460,229,149,243,330,211)(88,343,371,101,438,461,230,150,244,309,212), (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)(463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484), (1,235,12,224)(2,234,13,223)(3,233,14,222)(4,232,15,221)(5,231,16,242)(6,230,17,241)(7,229,18,240)(8,228,19,239)(9,227,20,238)(10,226,21,237)(11,225,22,236)(23,147,34,136)(24,146,35,135)(25,145,36,134)(26,144,37,133)(27,143,38,154)(28,142,39,153)(29,141,40,152)(30,140,41,151)(31,139,42,150)(32,138,43,149)(33,137,44,148)(45,352,56,341)(46,351,57,340)(47,350,58,339)(48,349,59,338)(49,348,60,337)(50,347,61,336)(51,346,62,335)(52,345,63,334)(53,344,64,333)(54,343,65,332)(55,342,66,331)(67,129,78,118)(68,128,79,117)(69,127,80,116)(70,126,81,115)(71,125,82,114)(72,124,83,113)(73,123,84,112)(74,122,85,111)(75,121,86,132)(76,120,87,131)(77,119,88,130)(89,289,100,300)(90,288,101,299)(91,287,102,298)(92,308,103,297)(93,307,104,296)(94,306,105,295)(95,305,106,294)(96,304,107,293)(97,303,108,292)(98,302,109,291)(99,301,110,290)(155,449,166,460)(156,448,167,459)(157,447,168,458)(158,446,169,457)(159,445,170,456)(160,444,171,455)(161,443,172,454)(162,442,173,453)(163,441,174,452)(164,462,175,451)(165,461,176,450)(177,320,188,309)(178,319,189,330)(179,318,190,329)(180,317,191,328)(181,316,192,327)(182,315,193,326)(183,314,194,325)(184,313,195,324)(185,312,196,323)(186,311,197,322)(187,310,198,321)(199,416,210,405)(200,415,211,404)(201,414,212,403)(202,413,213,402)(203,412,214,401)(204,411,215,400)(205,410,216,399)(206,409,217,398)(207,408,218,397)(208,407,219,418)(209,406,220,417)(243,382,254,393)(244,381,255,392)(245,380,256,391)(246,379,257,390)(247,378,258,389)(248,377,259,388)(249,376,260,387)(250,375,261,386)(251,396,262,385)(252,395,263,384)(253,394,264,383)(265,428,276,439)(266,427,277,438)(267,426,278,437)(268,425,279,436)(269,424,280,435)(270,423,281,434)(271,422,282,433)(272,421,283,432)(273,420,284,431)(274,419,285,430)(275,440,286,429)(353,472,364,483)(354,471,365,482)(355,470,366,481)(356,469,367,480)(357,468,368,479)(358,467,369,478)(359,466,370,477)(360,465,371,476)(361,464,372,475)(362,463,373,474)(363,484,374,473) );
G=PermutationGroup([[(1,160,272,305,482,49,114,409,183,387,37),(2,161,273,306,483,50,115,410,184,388,38),(3,162,274,307,484,51,116,411,185,389,39),(4,163,275,308,463,52,117,412,186,390,40),(5,164,276,287,464,53,118,413,187,391,41),(6,165,277,288,465,54,119,414,188,392,42),(7,166,278,289,466,55,120,415,189,393,43),(8,167,279,290,467,56,121,416,190,394,44),(9,168,280,291,468,57,122,417,191,395,23),(10,169,281,292,469,58,123,418,192,396,24),(11,170,282,293,470,59,124,397,193,375,25),(12,171,283,294,471,60,125,398,194,376,26),(13,172,284,295,472,61,126,399,195,377,27),(14,173,285,296,473,62,127,400,196,378,28),(15,174,286,297,474,63,128,401,197,379,29),(16,175,265,298,475,64,129,402,198,380,30),(17,176,266,299,476,65,130,403,177,381,31),(18,155,267,300,477,66,131,404,178,382,32),(19,156,268,301,478,45,132,405,179,383,33),(20,157,269,302,479,46,111,406,180,384,34),(21,158,270,303,480,47,112,407,181,385,35),(22,159,271,304,481,48,113,408,182,386,36),(67,344,372,102,439,462,231,151,245,310,213),(68,345,373,103,440,441,232,152,246,311,214),(69,346,374,104,419,442,233,153,247,312,215),(70,347,353,105,420,443,234,154,248,313,216),(71,348,354,106,421,444,235,133,249,314,217),(72,349,355,107,422,445,236,134,250,315,218),(73,350,356,108,423,446,237,135,251,316,219),(74,351,357,109,424,447,238,136,252,317,220),(75,352,358,110,425,448,239,137,253,318,199),(76,331,359,89,426,449,240,138,254,319,200),(77,332,360,90,427,450,241,139,255,320,201),(78,333,361,91,428,451,242,140,256,321,202),(79,334,362,92,429,452,221,141,257,322,203),(80,335,363,93,430,453,222,142,258,323,204),(81,336,364,94,431,454,223,143,259,324,205),(82,337,365,95,432,455,224,144,260,325,206),(83,338,366,96,433,456,225,145,261,326,207),(84,339,367,97,434,457,226,146,262,327,208),(85,340,368,98,435,458,227,147,263,328,209),(86,341,369,99,436,459,228,148,264,329,210),(87,342,370,100,437,460,229,149,243,330,211),(88,343,371,101,438,461,230,150,244,309,212)], [(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),(463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484)], [(1,235,12,224),(2,234,13,223),(3,233,14,222),(4,232,15,221),(5,231,16,242),(6,230,17,241),(7,229,18,240),(8,228,19,239),(9,227,20,238),(10,226,21,237),(11,225,22,236),(23,147,34,136),(24,146,35,135),(25,145,36,134),(26,144,37,133),(27,143,38,154),(28,142,39,153),(29,141,40,152),(30,140,41,151),(31,139,42,150),(32,138,43,149),(33,137,44,148),(45,352,56,341),(46,351,57,340),(47,350,58,339),(48,349,59,338),(49,348,60,337),(50,347,61,336),(51,346,62,335),(52,345,63,334),(53,344,64,333),(54,343,65,332),(55,342,66,331),(67,129,78,118),(68,128,79,117),(69,127,80,116),(70,126,81,115),(71,125,82,114),(72,124,83,113),(73,123,84,112),(74,122,85,111),(75,121,86,132),(76,120,87,131),(77,119,88,130),(89,289,100,300),(90,288,101,299),(91,287,102,298),(92,308,103,297),(93,307,104,296),(94,306,105,295),(95,305,106,294),(96,304,107,293),(97,303,108,292),(98,302,109,291),(99,301,110,290),(155,449,166,460),(156,448,167,459),(157,447,168,458),(158,446,169,457),(159,445,170,456),(160,444,171,455),(161,443,172,454),(162,442,173,453),(163,441,174,452),(164,462,175,451),(165,461,176,450),(177,320,188,309),(178,319,189,330),(179,318,190,329),(180,317,191,328),(181,316,192,327),(182,315,193,326),(183,314,194,325),(184,313,195,324),(185,312,196,323),(186,311,197,322),(187,310,198,321),(199,416,210,405),(200,415,211,404),(201,414,212,403),(202,413,213,402),(203,412,214,401),(204,411,215,400),(205,410,216,399),(206,409,217,398),(207,408,218,397),(208,407,219,418),(209,406,220,417),(243,382,254,393),(244,381,255,392),(245,380,256,391),(246,379,257,390),(247,378,258,389),(248,377,259,388),(249,376,260,387),(250,375,261,386),(251,396,262,385),(252,395,263,384),(253,394,264,383),(265,428,276,439),(266,427,277,438),(267,426,278,437),(268,425,279,436),(269,424,280,435),(270,423,281,434),(271,422,282,433),(272,421,283,432),(273,420,284,431),(274,419,285,430),(275,440,286,429),(353,472,364,483),(354,471,365,482),(355,470,366,481),(356,469,367,480),(357,468,368,479),(358,467,369,478),(359,466,370,477),(360,465,371,476),(361,464,372,475),(362,463,373,474),(363,484,374,473)]])
124 conjugacy classes
| class | 1 | 2 | 4A | 4B | 11A | ··· | 11BH | 22A | ··· | 22BH |
| order | 1 | 2 | 4 | 4 | 11 | ··· | 11 | 22 | ··· | 22 |
| size | 1 | 1 | 121 | 121 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | - | |
| image | C1 | C2 | C4 | D11 | Dic11 |
| kernel | C11⋊Dic11 | C11×C22 | C112 | C22 | C11 |
| # reps | 1 | 1 | 2 | 60 | 60 |
Matrix representation of C11⋊Dic11 ►in GL4(𝔽89) generated by
| 42 | 1 | 0 | 0 |
| 11 | 13 | 0 | 0 |
| 0 | 0 | 76 | 1 |
| 0 | 0 | 6 | 20 |
| 75 | 76 | 0 | 0 |
| 35 | 7 | 0 | 0 |
| 0 | 0 | 54 | 62 |
| 0 | 0 | 16 | 53 |
| 9 | 68 | 0 | 0 |
| 59 | 80 | 0 | 0 |
| 0 | 0 | 68 | 3 |
| 0 | 0 | 1 | 21 |
G:=sub<GL(4,GF(89))| [42,11,0,0,1,13,0,0,0,0,76,6,0,0,1,20],[75,35,0,0,76,7,0,0,0,0,54,16,0,0,62,53],[9,59,0,0,68,80,0,0,0,0,68,1,0,0,3,21] >;
C11⋊Dic11 in GAP, Magma, Sage, TeX
C_{11}\rtimes {\rm Dic}_{11} % in TeX
G:=Group("C11:Dic11"); // GroupNames label
G:=SmallGroup(484,6);
// by ID
G=gap.SmallGroup(484,6);
# by ID
G:=PCGroup([4,-2,-2,-11,-11,8,482,7043]);
// Polycyclic
G:=Group<a,b,c|a^11=b^22=1,c^2=b^11,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations
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