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G = C11×Dic10order 440 = 23·5·11

Direct product of C11 and Dic10

direct product, metacyclic, supersoluble, monomial, 2-hyperelementary

Aliases: C11×Dic10, C554Q8, 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

C1C10 — C11×Dic10
C1C5C10C110C11×Dic5 — C11×Dic10
C5C10 — C11×Dic10
C1C22C44

Generators and relations for C11×Dic10
 G = < a,b,c | a11=b20=1, c2=b10, ab=ba, ac=ca, cbc-1=b-1 >

5C4
5C4
5Q8
5C44
5C44
5Q8×C11

Smallest permutation representation of C11×Dic10
Regular action on 440 points
Generators in S440
(1 294 191 338 224 78 423 351 403 43 399)(2 295 192 339 225 79 424 352 404 44 400)(3 296 193 340 226 80 425 353 405 45 381)(4 297 194 321 227 61 426 354 406 46 382)(5 298 195 322 228 62 427 355 407 47 383)(6 299 196 323 229 63 428 356 408 48 384)(7 300 197 324 230 64 429 357 409 49 385)(8 281 198 325 231 65 430 358 410 50 386)(9 282 199 326 232 66 431 359 411 51 387)(10 283 200 327 233 67 432 360 412 52 388)(11 284 181 328 234 68 433 341 413 53 389)(12 285 182 329 235 69 434 342 414 54 390)(13 286 183 330 236 70 435 343 415 55 391)(14 287 184 331 237 71 436 344 416 56 392)(15 288 185 332 238 72 437 345 417 57 393)(16 289 186 333 239 73 438 346 418 58 394)(17 290 187 334 240 74 439 347 419 59 395)(18 291 188 335 221 75 440 348 420 60 396)(19 292 189 336 222 76 421 349 401 41 397)(20 293 190 337 223 77 422 350 402 42 398)(21 104 179 310 252 210 380 142 276 124 94)(22 105 180 311 253 211 361 143 277 125 95)(23 106 161 312 254 212 362 144 278 126 96)(24 107 162 313 255 213 363 145 279 127 97)(25 108 163 314 256 214 364 146 280 128 98)(26 109 164 315 257 215 365 147 261 129 99)(27 110 165 316 258 216 366 148 262 130 100)(28 111 166 317 259 217 367 149 263 131 81)(29 112 167 318 260 218 368 150 264 132 82)(30 113 168 319 241 219 369 151 265 133 83)(31 114 169 320 242 220 370 152 266 134 84)(32 115 170 301 243 201 371 153 267 135 85)(33 116 171 302 244 202 372 154 268 136 86)(34 117 172 303 245 203 373 155 269 137 87)(35 118 173 304 246 204 374 156 270 138 88)(36 119 174 305 247 205 375 157 271 139 89)(37 120 175 306 248 206 376 158 272 140 90)(38 101 176 307 249 207 377 159 273 121 91)(39 102 177 308 250 208 378 160 274 122 92)(40 103 178 309 251 209 379 141 275 123 93)
(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)
(1 111 11 101)(2 110 12 120)(3 109 13 119)(4 108 14 118)(5 107 15 117)(6 106 16 116)(7 105 17 115)(8 104 18 114)(9 103 19 113)(10 102 20 112)(21 396 31 386)(22 395 32 385)(23 394 33 384)(24 393 34 383)(25 392 35 382)(26 391 36 381)(27 390 37 400)(28 389 38 399)(29 388 39 398)(30 387 40 397)(41 83 51 93)(42 82 52 92)(43 81 53 91)(44 100 54 90)(45 99 55 89)(46 98 56 88)(47 97 57 87)(48 96 58 86)(49 95 59 85)(50 94 60 84)(61 364 71 374)(62 363 72 373)(63 362 73 372)(64 361 74 371)(65 380 75 370)(66 379 76 369)(67 378 77 368)(68 377 78 367)(69 376 79 366)(70 375 80 365)(121 403 131 413)(122 402 132 412)(123 401 133 411)(124 420 134 410)(125 419 135 409)(126 418 136 408)(127 417 137 407)(128 416 138 406)(129 415 139 405)(130 414 140 404)(141 421 151 431)(142 440 152 430)(143 439 153 429)(144 438 154 428)(145 437 155 427)(146 436 156 426)(147 435 157 425)(148 434 158 424)(149 433 159 423)(150 432 160 422)(161 289 171 299)(162 288 172 298)(163 287 173 297)(164 286 174 296)(165 285 175 295)(166 284 176 294)(167 283 177 293)(168 282 178 292)(169 281 179 291)(170 300 180 290)(181 307 191 317)(182 306 192 316)(183 305 193 315)(184 304 194 314)(185 303 195 313)(186 302 196 312)(187 301 197 311)(188 320 198 310)(189 319 199 309)(190 318 200 308)(201 230 211 240)(202 229 212 239)(203 228 213 238)(204 227 214 237)(205 226 215 236)(206 225 216 235)(207 224 217 234)(208 223 218 233)(209 222 219 232)(210 221 220 231)(241 326 251 336)(242 325 252 335)(243 324 253 334)(244 323 254 333)(245 322 255 332)(246 321 256 331)(247 340 257 330)(248 339 258 329)(249 338 259 328)(250 337 260 327)(261 343 271 353)(262 342 272 352)(263 341 273 351)(264 360 274 350)(265 359 275 349)(266 358 276 348)(267 357 277 347)(268 356 278 346)(269 355 279 345)(270 354 280 344)

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

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

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

143 conjugacy classes

class 1  2 4A4B4C5A5B10A10B11A···11J20A20B20C20D22A···22J44A···44J44K···44AD55A···55T110A···110T220A···220AN
order1244455101011···112020202022···2244···4444···4455···55110···110220···220
size112101022221···122221···12···210···102···22···22···2

143 irreducible representations

dim11111122222222
type+++-++-
imageC1C2C2C11C22C22Q8D5D10Dic10Q8×C11D5×C11D5×C22C11×Dic10
kernelC11×Dic10C11×Dic5C220Dic10Dic5C20C55C44C22C11C5C4C2C1
# reps121102010122410202040

Matrix representation of C11×Dic10 in GL2(𝔽661) generated by

810
081
,
624215
53589
,
26831
455393
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

Subgroup lattice of C11×Dic10 in TeX

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