direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C11×C5⋊2C8, C5⋊2C88, C55⋊5C8, C44.4D5, C20.2C22, C10.2C44, C110.5C4, C220.6C2, C22.2Dic5, C4.2(D5×C11), C2.(C11×Dic5), SmallGroup(440,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C5 — C11×C5⋊2C8 |
Generators and relations for C11×C5⋊2C8
G = < a,b,c | a11=b5=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C11×C5⋊2C8
►Regular action on 440 points
Generators in S440
(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)
(1 130 365 214 246)(2 131 366 215 247)(3 132 367 216 248)(4 122 368 217 249)(5 123 369 218 250)(6 124 370 219 251)(7 125 371 220 252)(8 126 372 210 253)(9 127 373 211 243)(10 128 374 212 244)(11 129 364 213 245)(12 236 42 204 428)(13 237 43 205 429)(14 238 44 206 419)(15 239 34 207 420)(16 240 35 208 421)(17 241 36 209 422)(18 242 37 199 423)(19 232 38 200 424)(20 233 39 201 425)(21 234 40 202 426)(22 235 41 203 427)(23 229 55 410 350)(24 230 45 411 351)(25 231 46 412 352)(26 221 47 413 342)(27 222 48 414 343)(28 223 49 415 344)(29 224 50 416 345)(30 225 51 417 346)(31 226 52 418 347)(32 227 53 408 348)(33 228 54 409 349)(56 280 186 399 430)(57 281 187 400 431)(58 282 177 401 432)(59 283 178 402 433)(60 284 179 403 434)(61 285 180 404 435)(62 286 181 405 436)(63 276 182 406 437)(64 277 183 407 438)(65 278 184 397 439)(66 279 185 398 440)(67 149 311 97 292)(68 150 312 98 293)(69 151 313 99 294)(70 152 314 89 295)(71 153 315 90 296)(72 154 316 91 297)(73 144 317 92 287)(74 145 318 93 288)(75 146 319 94 289)(76 147 309 95 290)(77 148 310 96 291)(78 302 108 321 263)(79 303 109 322 264)(80 304 110 323 254)(81 305 100 324 255)(82 306 101 325 256)(83 307 102 326 257)(84 308 103 327 258)(85 298 104 328 259)(86 299 105 329 260)(87 300 106 330 261)(88 301 107 320 262)(111 335 161 385 140)(112 336 162 375 141)(113 337 163 376 142)(114 338 164 377 143)(115 339 165 378 133)(116 340 155 379 134)(117 341 156 380 135)(118 331 157 381 136)(119 332 158 382 137)(120 333 159 383 138)(121 334 160 384 139)(166 272 198 353 391)(167 273 188 354 392)(168 274 189 355 393)(169 275 190 356 394)(170 265 191 357 395)(171 266 192 358 396)(172 267 193 359 386)(173 268 194 360 387)(174 269 195 361 388)(175 270 196 362 389)(176 271 197 363 390)
(1 38 386 403 32 320 153 136)(2 39 387 404 33 321 154 137)(3 40 388 405 23 322 144 138)(4 41 389 406 24 323 145 139)(5 42 390 407 25 324 146 140)(6 43 391 397 26 325 147 141)(7 44 392 398 27 326 148 142)(8 34 393 399 28 327 149 143)(9 35 394 400 29 328 150 133)(10 36 395 401 30 329 151 134)(11 37 396 402 31 330 152 135)(12 271 277 46 305 94 161 369)(13 272 278 47 306 95 162 370)(14 273 279 48 307 96 163 371)(15 274 280 49 308 97 164 372)(16 275 281 50 298 98 165 373)(17 265 282 51 299 99 155 374)(18 266 283 52 300 89 156 364)(19 267 284 53 301 90 157 365)(20 268 285 54 302 91 158 366)(21 269 286 55 303 92 159 367)(22 270 276 45 304 93 160 368)(56 415 84 292 338 210 420 189)(57 416 85 293 339 211 421 190)(58 417 86 294 340 212 422 191)(59 418 87 295 341 213 423 192)(60 408 88 296 331 214 424 193)(61 409 78 297 332 215 425 194)(62 410 79 287 333 216 426 195)(63 411 80 288 334 217 427 196)(64 412 81 289 335 218 428 197)(65 413 82 290 336 219 429 198)(66 414 83 291 337 220 419 188)(67 114 253 207 355 430 344 258)(68 115 243 208 356 431 345 259)(69 116 244 209 357 432 346 260)(70 117 245 199 358 433 347 261)(71 118 246 200 359 434 348 262)(72 119 247 201 360 435 349 263)(73 120 248 202 361 436 350 264)(74 121 249 203 362 437 351 254)(75 111 250 204 363 438 352 255)(76 112 251 205 353 439 342 256)(77 113 252 206 354 440 343 257)(100 319 385 123 236 176 183 231)(101 309 375 124 237 166 184 221)(102 310 376 125 238 167 185 222)(103 311 377 126 239 168 186 223)(104 312 378 127 240 169 187 224)(105 313 379 128 241 170 177 225)(106 314 380 129 242 171 178 226)(107 315 381 130 232 172 179 227)(108 316 382 131 233 173 180 228)(109 317 383 132 234 174 181 229)(110 318 384 122 235 175 182 230)
G:=sub<Sym(440)| (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), (1,130,365,214,246)(2,131,366,215,247)(3,132,367,216,248)(4,122,368,217,249)(5,123,369,218,250)(6,124,370,219,251)(7,125,371,220,252)(8,126,372,210,253)(9,127,373,211,243)(10,128,374,212,244)(11,129,364,213,245)(12,236,42,204,428)(13,237,43,205,429)(14,238,44,206,419)(15,239,34,207,420)(16,240,35,208,421)(17,241,36,209,422)(18,242,37,199,423)(19,232,38,200,424)(20,233,39,201,425)(21,234,40,202,426)(22,235,41,203,427)(23,229,55,410,350)(24,230,45,411,351)(25,231,46,412,352)(26,221,47,413,342)(27,222,48,414,343)(28,223,49,415,344)(29,224,50,416,345)(30,225,51,417,346)(31,226,52,418,347)(32,227,53,408,348)(33,228,54,409,349)(56,280,186,399,430)(57,281,187,400,431)(58,282,177,401,432)(59,283,178,402,433)(60,284,179,403,434)(61,285,180,404,435)(62,286,181,405,436)(63,276,182,406,437)(64,277,183,407,438)(65,278,184,397,439)(66,279,185,398,440)(67,149,311,97,292)(68,150,312,98,293)(69,151,313,99,294)(70,152,314,89,295)(71,153,315,90,296)(72,154,316,91,297)(73,144,317,92,287)(74,145,318,93,288)(75,146,319,94,289)(76,147,309,95,290)(77,148,310,96,291)(78,302,108,321,263)(79,303,109,322,264)(80,304,110,323,254)(81,305,100,324,255)(82,306,101,325,256)(83,307,102,326,257)(84,308,103,327,258)(85,298,104,328,259)(86,299,105,329,260)(87,300,106,330,261)(88,301,107,320,262)(111,335,161,385,140)(112,336,162,375,141)(113,337,163,376,142)(114,338,164,377,143)(115,339,165,378,133)(116,340,155,379,134)(117,341,156,380,135)(118,331,157,381,136)(119,332,158,382,137)(120,333,159,383,138)(121,334,160,384,139)(166,272,198,353,391)(167,273,188,354,392)(168,274,189,355,393)(169,275,190,356,394)(170,265,191,357,395)(171,266,192,358,396)(172,267,193,359,386)(173,268,194,360,387)(174,269,195,361,388)(175,270,196,362,389)(176,271,197,363,390), (1,38,386,403,32,320,153,136)(2,39,387,404,33,321,154,137)(3,40,388,405,23,322,144,138)(4,41,389,406,24,323,145,139)(5,42,390,407,25,324,146,140)(6,43,391,397,26,325,147,141)(7,44,392,398,27,326,148,142)(8,34,393,399,28,327,149,143)(9,35,394,400,29,328,150,133)(10,36,395,401,30,329,151,134)(11,37,396,402,31,330,152,135)(12,271,277,46,305,94,161,369)(13,272,278,47,306,95,162,370)(14,273,279,48,307,96,163,371)(15,274,280,49,308,97,164,372)(16,275,281,50,298,98,165,373)(17,265,282,51,299,99,155,374)(18,266,283,52,300,89,156,364)(19,267,284,53,301,90,157,365)(20,268,285,54,302,91,158,366)(21,269,286,55,303,92,159,367)(22,270,276,45,304,93,160,368)(56,415,84,292,338,210,420,189)(57,416,85,293,339,211,421,190)(58,417,86,294,340,212,422,191)(59,418,87,295,341,213,423,192)(60,408,88,296,331,214,424,193)(61,409,78,297,332,215,425,194)(62,410,79,287,333,216,426,195)(63,411,80,288,334,217,427,196)(64,412,81,289,335,218,428,197)(65,413,82,290,336,219,429,198)(66,414,83,291,337,220,419,188)(67,114,253,207,355,430,344,258)(68,115,243,208,356,431,345,259)(69,116,244,209,357,432,346,260)(70,117,245,199,358,433,347,261)(71,118,246,200,359,434,348,262)(72,119,247,201,360,435,349,263)(73,120,248,202,361,436,350,264)(74,121,249,203,362,437,351,254)(75,111,250,204,363,438,352,255)(76,112,251,205,353,439,342,256)(77,113,252,206,354,440,343,257)(100,319,385,123,236,176,183,231)(101,309,375,124,237,166,184,221)(102,310,376,125,238,167,185,222)(103,311,377,126,239,168,186,223)(104,312,378,127,240,169,187,224)(105,313,379,128,241,170,177,225)(106,314,380,129,242,171,178,226)(107,315,381,130,232,172,179,227)(108,316,382,131,233,173,180,228)(109,317,383,132,234,174,181,229)(110,318,384,122,235,175,182,230)>;
G:=Group( (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), (1,130,365,214,246)(2,131,366,215,247)(3,132,367,216,248)(4,122,368,217,249)(5,123,369,218,250)(6,124,370,219,251)(7,125,371,220,252)(8,126,372,210,253)(9,127,373,211,243)(10,128,374,212,244)(11,129,364,213,245)(12,236,42,204,428)(13,237,43,205,429)(14,238,44,206,419)(15,239,34,207,420)(16,240,35,208,421)(17,241,36,209,422)(18,242,37,199,423)(19,232,38,200,424)(20,233,39,201,425)(21,234,40,202,426)(22,235,41,203,427)(23,229,55,410,350)(24,230,45,411,351)(25,231,46,412,352)(26,221,47,413,342)(27,222,48,414,343)(28,223,49,415,344)(29,224,50,416,345)(30,225,51,417,346)(31,226,52,418,347)(32,227,53,408,348)(33,228,54,409,349)(56,280,186,399,430)(57,281,187,400,431)(58,282,177,401,432)(59,283,178,402,433)(60,284,179,403,434)(61,285,180,404,435)(62,286,181,405,436)(63,276,182,406,437)(64,277,183,407,438)(65,278,184,397,439)(66,279,185,398,440)(67,149,311,97,292)(68,150,312,98,293)(69,151,313,99,294)(70,152,314,89,295)(71,153,315,90,296)(72,154,316,91,297)(73,144,317,92,287)(74,145,318,93,288)(75,146,319,94,289)(76,147,309,95,290)(77,148,310,96,291)(78,302,108,321,263)(79,303,109,322,264)(80,304,110,323,254)(81,305,100,324,255)(82,306,101,325,256)(83,307,102,326,257)(84,308,103,327,258)(85,298,104,328,259)(86,299,105,329,260)(87,300,106,330,261)(88,301,107,320,262)(111,335,161,385,140)(112,336,162,375,141)(113,337,163,376,142)(114,338,164,377,143)(115,339,165,378,133)(116,340,155,379,134)(117,341,156,380,135)(118,331,157,381,136)(119,332,158,382,137)(120,333,159,383,138)(121,334,160,384,139)(166,272,198,353,391)(167,273,188,354,392)(168,274,189,355,393)(169,275,190,356,394)(170,265,191,357,395)(171,266,192,358,396)(172,267,193,359,386)(173,268,194,360,387)(174,269,195,361,388)(175,270,196,362,389)(176,271,197,363,390), (1,38,386,403,32,320,153,136)(2,39,387,404,33,321,154,137)(3,40,388,405,23,322,144,138)(4,41,389,406,24,323,145,139)(5,42,390,407,25,324,146,140)(6,43,391,397,26,325,147,141)(7,44,392,398,27,326,148,142)(8,34,393,399,28,327,149,143)(9,35,394,400,29,328,150,133)(10,36,395,401,30,329,151,134)(11,37,396,402,31,330,152,135)(12,271,277,46,305,94,161,369)(13,272,278,47,306,95,162,370)(14,273,279,48,307,96,163,371)(15,274,280,49,308,97,164,372)(16,275,281,50,298,98,165,373)(17,265,282,51,299,99,155,374)(18,266,283,52,300,89,156,364)(19,267,284,53,301,90,157,365)(20,268,285,54,302,91,158,366)(21,269,286,55,303,92,159,367)(22,270,276,45,304,93,160,368)(56,415,84,292,338,210,420,189)(57,416,85,293,339,211,421,190)(58,417,86,294,340,212,422,191)(59,418,87,295,341,213,423,192)(60,408,88,296,331,214,424,193)(61,409,78,297,332,215,425,194)(62,410,79,287,333,216,426,195)(63,411,80,288,334,217,427,196)(64,412,81,289,335,218,428,197)(65,413,82,290,336,219,429,198)(66,414,83,291,337,220,419,188)(67,114,253,207,355,430,344,258)(68,115,243,208,356,431,345,259)(69,116,244,209,357,432,346,260)(70,117,245,199,358,433,347,261)(71,118,246,200,359,434,348,262)(72,119,247,201,360,435,349,263)(73,120,248,202,361,436,350,264)(74,121,249,203,362,437,351,254)(75,111,250,204,363,438,352,255)(76,112,251,205,353,439,342,256)(77,113,252,206,354,440,343,257)(100,319,385,123,236,176,183,231)(101,309,375,124,237,166,184,221)(102,310,376,125,238,167,185,222)(103,311,377,126,239,168,186,223)(104,312,378,127,240,169,187,224)(105,313,379,128,241,170,177,225)(106,314,380,129,242,171,178,226)(107,315,381,130,232,172,179,227)(108,316,382,131,233,173,180,228)(109,317,383,132,234,174,181,229)(110,318,384,122,235,175,182,230) );
G=PermutationGroup([[(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)], [(1,130,365,214,246),(2,131,366,215,247),(3,132,367,216,248),(4,122,368,217,249),(5,123,369,218,250),(6,124,370,219,251),(7,125,371,220,252),(8,126,372,210,253),(9,127,373,211,243),(10,128,374,212,244),(11,129,364,213,245),(12,236,42,204,428),(13,237,43,205,429),(14,238,44,206,419),(15,239,34,207,420),(16,240,35,208,421),(17,241,36,209,422),(18,242,37,199,423),(19,232,38,200,424),(20,233,39,201,425),(21,234,40,202,426),(22,235,41,203,427),(23,229,55,410,350),(24,230,45,411,351),(25,231,46,412,352),(26,221,47,413,342),(27,222,48,414,343),(28,223,49,415,344),(29,224,50,416,345),(30,225,51,417,346),(31,226,52,418,347),(32,227,53,408,348),(33,228,54,409,349),(56,280,186,399,430),(57,281,187,400,431),(58,282,177,401,432),(59,283,178,402,433),(60,284,179,403,434),(61,285,180,404,435),(62,286,181,405,436),(63,276,182,406,437),(64,277,183,407,438),(65,278,184,397,439),(66,279,185,398,440),(67,149,311,97,292),(68,150,312,98,293),(69,151,313,99,294),(70,152,314,89,295),(71,153,315,90,296),(72,154,316,91,297),(73,144,317,92,287),(74,145,318,93,288),(75,146,319,94,289),(76,147,309,95,290),(77,148,310,96,291),(78,302,108,321,263),(79,303,109,322,264),(80,304,110,323,254),(81,305,100,324,255),(82,306,101,325,256),(83,307,102,326,257),(84,308,103,327,258),(85,298,104,328,259),(86,299,105,329,260),(87,300,106,330,261),(88,301,107,320,262),(111,335,161,385,140),(112,336,162,375,141),(113,337,163,376,142),(114,338,164,377,143),(115,339,165,378,133),(116,340,155,379,134),(117,341,156,380,135),(118,331,157,381,136),(119,332,158,382,137),(120,333,159,383,138),(121,334,160,384,139),(166,272,198,353,391),(167,273,188,354,392),(168,274,189,355,393),(169,275,190,356,394),(170,265,191,357,395),(171,266,192,358,396),(172,267,193,359,386),(173,268,194,360,387),(174,269,195,361,388),(175,270,196,362,389),(176,271,197,363,390)], [(1,38,386,403,32,320,153,136),(2,39,387,404,33,321,154,137),(3,40,388,405,23,322,144,138),(4,41,389,406,24,323,145,139),(5,42,390,407,25,324,146,140),(6,43,391,397,26,325,147,141),(7,44,392,398,27,326,148,142),(8,34,393,399,28,327,149,143),(9,35,394,400,29,328,150,133),(10,36,395,401,30,329,151,134),(11,37,396,402,31,330,152,135),(12,271,277,46,305,94,161,369),(13,272,278,47,306,95,162,370),(14,273,279,48,307,96,163,371),(15,274,280,49,308,97,164,372),(16,275,281,50,298,98,165,373),(17,265,282,51,299,99,155,374),(18,266,283,52,300,89,156,364),(19,267,284,53,301,90,157,365),(20,268,285,54,302,91,158,366),(21,269,286,55,303,92,159,367),(22,270,276,45,304,93,160,368),(56,415,84,292,338,210,420,189),(57,416,85,293,339,211,421,190),(58,417,86,294,340,212,422,191),(59,418,87,295,341,213,423,192),(60,408,88,296,331,214,424,193),(61,409,78,297,332,215,425,194),(62,410,79,287,333,216,426,195),(63,411,80,288,334,217,427,196),(64,412,81,289,335,218,428,197),(65,413,82,290,336,219,429,198),(66,414,83,291,337,220,419,188),(67,114,253,207,355,430,344,258),(68,115,243,208,356,431,345,259),(69,116,244,209,357,432,346,260),(70,117,245,199,358,433,347,261),(71,118,246,200,359,434,348,262),(72,119,247,201,360,435,349,263),(73,120,248,202,361,436,350,264),(74,121,249,203,362,437,351,254),(75,111,250,204,363,438,352,255),(76,112,251,205,353,439,342,256),(77,113,252,206,354,440,343,257),(100,319,385,123,236,176,183,231),(101,309,375,124,237,166,184,221),(102,310,376,125,238,167,185,222),(103,311,377,126,239,168,186,223),(104,312,378,127,240,169,187,224),(105,313,379,128,241,170,177,225),(106,314,380,129,242,171,178,226),(107,315,381,130,232,172,179,227),(108,316,382,131,233,173,180,228),(109,317,383,132,234,174,181,229),(110,318,384,122,235,175,182,230)]])
176 conjugacy classes
| class | 1 | 2 | 4A | 4B | 5A | 5B | 8A | 8B | 8C | 8D | 10A | 10B | 11A | ··· | 11J | 20A | 20B | 20C | 20D | 22A | ··· | 22J | 44A | ··· | 44T | 55A | ··· | 55T | 88A | ··· | 88AN | 110A | ··· | 110T | 220A | ··· | 220AN |
| order | 1 | 2 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | 10 | 11 | ··· | 11 | 20 | 20 | 20 | 20 | 22 | ··· | 22 | 44 | ··· | 44 | 55 | ··· | 55 | 88 | ··· | 88 | 110 | ··· | 110 | 220 | ··· | 220 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 5 | 5 | 5 | 5 | 2 | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 5 | ··· | 5 | 2 | ··· | 2 | 2 | ··· | 2 |
176 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||||||
| image | C1 | C2 | C4 | C8 | C11 | C22 | C44 | C88 | D5 | Dic5 | C5⋊2C8 | D5×C11 | C11×Dic5 | C11×C5⋊2C8 |
| kernel | C11×C5⋊2C8 | C220 | C110 | C55 | C5⋊2C8 | C20 | C10 | C5 | C44 | C22 | C11 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 10 | 10 | 20 | 40 | 2 | 2 | 4 | 20 | 20 | 40 |
Matrix representation of C11×C5⋊2C8 ►in GL2(𝔽881) generated by
| 237 | 0 |
| 0 | 237 |
| 327 | 880 |
| 328 | 880 |
| 386 | 233 |
| 402 | 495 |
G:=sub<GL(2,GF(881))| [237,0,0,237],[327,328,880,880],[386,402,233,495] >;
C11×C5⋊2C8 in GAP, Magma, Sage, TeX
C_{11}\times C_5\rtimes_2C_8 % in TeX
G:=Group("C11xC5:2C8"); // GroupNames label
G:=SmallGroup(440,3);
// by ID
G=gap.SmallGroup(440,3);
# by ID
G:=PCGroup([5,-2,-11,-2,-2,-5,110,42,8804]);
// Polycyclic
G:=Group<a,b,c|a^11=b^5=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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