direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C11×C5⋊C8, C5⋊C88, C55⋊2C8, C10.C44, C22.2F5, C110.2C4, Dic5.2C22, C2.(C11×F5), (C11×Dic5).4C2, SmallGroup(440,15)
Series: Derived ►Chief ►Lower central ►Upper central
| C5 — C11×C5⋊C8 |
Generators and relations for C11×C5⋊C8
G = < a,b,c | a11=b5=c8=1, ab=ba, ac=ca, cbc-1=b3 >
Smallest permutation representation of C11×C5⋊C8
►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 74 265 51 297)(2 75 266 52 287)(3 76 267 53 288)(4 77 268 54 289)(5 67 269 55 290)(6 68 270 45 291)(7 69 271 46 292)(8 70 272 47 293)(9 71 273 48 294)(10 72 274 49 295)(11 73 275 50 296)(12 162 308 236 375)(13 163 298 237 376)(14 164 299 238 377)(15 165 300 239 378)(16 155 301 240 379)(17 156 302 241 380)(18 157 303 242 381)(19 158 304 232 382)(20 159 305 233 383)(21 160 306 234 384)(22 161 307 235 385)(23 251 228 153 367)(24 252 229 154 368)(25 253 230 144 369)(26 243 231 145 370)(27 244 221 146 371)(28 245 222 147 372)(29 246 223 148 373)(30 247 224 149 374)(31 248 225 150 364)(32 249 226 151 365)(33 250 227 152 366)(34 66 116 279 340)(35 56 117 280 341)(36 57 118 281 331)(37 58 119 282 332)(38 59 120 283 333)(39 60 121 284 334)(40 61 111 285 335)(41 62 112 286 336)(42 63 113 276 337)(43 64 114 277 338)(44 65 115 278 339)(78 424 363 200 139)(79 425 353 201 140)(80 426 354 202 141)(81 427 355 203 142)(82 428 356 204 143)(83 429 357 205 133)(84 419 358 206 134)(85 420 359 207 135)(86 421 360 208 136)(87 422 361 209 137)(88 423 362 199 138)(89 415 210 168 343)(90 416 211 169 344)(91 417 212 170 345)(92 418 213 171 346)(93 408 214 172 347)(94 409 215 173 348)(95 410 216 174 349)(96 411 217 175 350)(97 412 218 176 351)(98 413 219 166 352)(99 414 220 167 342)(100 403 324 434 179)(101 404 325 435 180)(102 405 326 436 181)(103 406 327 437 182)(104 407 328 438 183)(105 397 329 439 184)(106 398 330 440 185)(107 399 320 430 186)(108 400 321 431 187)(109 401 322 432 177)(110 402 323 433 178)(122 387 260 194 319)(123 388 261 195 309)(124 389 262 196 310)(125 390 263 197 311)(126 391 264 198 312)(127 392 254 188 313)(128 393 255 189 314)(129 394 256 190 315)(130 395 257 191 316)(131 396 258 192 317)(132 386 259 193 318)
(1 78 386 403 172 380 31 36)(2 79 387 404 173 381 32 37)(3 80 388 405 174 382 33 38)(4 81 389 406 175 383 23 39)(5 82 390 407 176 384 24 40)(6 83 391 397 166 385 25 41)(7 84 392 398 167 375 26 42)(8 85 393 399 168 376 27 43)(9 86 394 400 169 377 28 44)(10 87 395 401 170 378 29 34)(11 88 396 402 171 379 30 35)(12 231 337 46 419 188 106 414)(13 221 338 47 420 189 107 415)(14 222 339 48 421 190 108 416)(15 223 340 49 422 191 109 417)(16 224 341 50 423 192 110 418)(17 225 331 51 424 193 100 408)(18 226 332 52 425 194 101 409)(19 227 333 53 426 195 102 410)(20 228 334 54 427 196 103 411)(21 229 335 55 428 197 104 412)(22 230 336 45 429 198 105 413)(56 275 138 317 323 92 240 149)(57 265 139 318 324 93 241 150)(58 266 140 319 325 94 242 151)(59 267 141 309 326 95 232 152)(60 268 142 310 327 96 233 153)(61 269 143 311 328 97 234 154)(62 270 133 312 329 98 235 144)(63 271 134 313 330 99 236 145)(64 272 135 314 320 89 237 146)(65 273 136 315 321 90 238 147)(66 274 137 316 322 91 239 148)(67 356 125 183 351 160 368 285)(68 357 126 184 352 161 369 286)(69 358 127 185 342 162 370 276)(70 359 128 186 343 163 371 277)(71 360 129 187 344 164 372 278)(72 361 130 177 345 165 373 279)(73 362 131 178 346 155 374 280)(74 363 132 179 347 156 364 281)(75 353 122 180 348 157 365 282)(76 354 123 181 349 158 366 283)(77 355 124 182 350 159 367 284)(111 290 204 263 438 218 306 252)(112 291 205 264 439 219 307 253)(113 292 206 254 440 220 308 243)(114 293 207 255 430 210 298 244)(115 294 208 256 431 211 299 245)(116 295 209 257 432 212 300 246)(117 296 199 258 433 213 301 247)(118 297 200 259 434 214 302 248)(119 287 201 260 435 215 303 249)(120 288 202 261 436 216 304 250)(121 289 203 262 437 217 305 251)
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), (1,74,265,51,297)(2,75,266,52,287)(3,76,267,53,288)(4,77,268,54,289)(5,67,269,55,290)(6,68,270,45,291)(7,69,271,46,292)(8,70,272,47,293)(9,71,273,48,294)(10,72,274,49,295)(11,73,275,50,296)(12,162,308,236,375)(13,163,298,237,376)(14,164,299,238,377)(15,165,300,239,378)(16,155,301,240,379)(17,156,302,241,380)(18,157,303,242,381)(19,158,304,232,382)(20,159,305,233,383)(21,160,306,234,384)(22,161,307,235,385)(23,251,228,153,367)(24,252,229,154,368)(25,253,230,144,369)(26,243,231,145,370)(27,244,221,146,371)(28,245,222,147,372)(29,246,223,148,373)(30,247,224,149,374)(31,248,225,150,364)(32,249,226,151,365)(33,250,227,152,366)(34,66,116,279,340)(35,56,117,280,341)(36,57,118,281,331)(37,58,119,282,332)(38,59,120,283,333)(39,60,121,284,334)(40,61,111,285,335)(41,62,112,286,336)(42,63,113,276,337)(43,64,114,277,338)(44,65,115,278,339)(78,424,363,200,139)(79,425,353,201,140)(80,426,354,202,141)(81,427,355,203,142)(82,428,356,204,143)(83,429,357,205,133)(84,419,358,206,134)(85,420,359,207,135)(86,421,360,208,136)(87,422,361,209,137)(88,423,362,199,138)(89,415,210,168,343)(90,416,211,169,344)(91,417,212,170,345)(92,418,213,171,346)(93,408,214,172,347)(94,409,215,173,348)(95,410,216,174,349)(96,411,217,175,350)(97,412,218,176,351)(98,413,219,166,352)(99,414,220,167,342)(100,403,324,434,179)(101,404,325,435,180)(102,405,326,436,181)(103,406,327,437,182)(104,407,328,438,183)(105,397,329,439,184)(106,398,330,440,185)(107,399,320,430,186)(108,400,321,431,187)(109,401,322,432,177)(110,402,323,433,178)(122,387,260,194,319)(123,388,261,195,309)(124,389,262,196,310)(125,390,263,197,311)(126,391,264,198,312)(127,392,254,188,313)(128,393,255,189,314)(129,394,256,190,315)(130,395,257,191,316)(131,396,258,192,317)(132,386,259,193,318), (1,78,386,403,172,380,31,36)(2,79,387,404,173,381,32,37)(3,80,388,405,174,382,33,38)(4,81,389,406,175,383,23,39)(5,82,390,407,176,384,24,40)(6,83,391,397,166,385,25,41)(7,84,392,398,167,375,26,42)(8,85,393,399,168,376,27,43)(9,86,394,400,169,377,28,44)(10,87,395,401,170,378,29,34)(11,88,396,402,171,379,30,35)(12,231,337,46,419,188,106,414)(13,221,338,47,420,189,107,415)(14,222,339,48,421,190,108,416)(15,223,340,49,422,191,109,417)(16,224,341,50,423,192,110,418)(17,225,331,51,424,193,100,408)(18,226,332,52,425,194,101,409)(19,227,333,53,426,195,102,410)(20,228,334,54,427,196,103,411)(21,229,335,55,428,197,104,412)(22,230,336,45,429,198,105,413)(56,275,138,317,323,92,240,149)(57,265,139,318,324,93,241,150)(58,266,140,319,325,94,242,151)(59,267,141,309,326,95,232,152)(60,268,142,310,327,96,233,153)(61,269,143,311,328,97,234,154)(62,270,133,312,329,98,235,144)(63,271,134,313,330,99,236,145)(64,272,135,314,320,89,237,146)(65,273,136,315,321,90,238,147)(66,274,137,316,322,91,239,148)(67,356,125,183,351,160,368,285)(68,357,126,184,352,161,369,286)(69,358,127,185,342,162,370,276)(70,359,128,186,343,163,371,277)(71,360,129,187,344,164,372,278)(72,361,130,177,345,165,373,279)(73,362,131,178,346,155,374,280)(74,363,132,179,347,156,364,281)(75,353,122,180,348,157,365,282)(76,354,123,181,349,158,366,283)(77,355,124,182,350,159,367,284)(111,290,204,263,438,218,306,252)(112,291,205,264,439,219,307,253)(113,292,206,254,440,220,308,243)(114,293,207,255,430,210,298,244)(115,294,208,256,431,211,299,245)(116,295,209,257,432,212,300,246)(117,296,199,258,433,213,301,247)(118,297,200,259,434,214,302,248)(119,287,201,260,435,215,303,249)(120,288,202,261,436,216,304,250)(121,289,203,262,437,217,305,251)>;
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), (1,74,265,51,297)(2,75,266,52,287)(3,76,267,53,288)(4,77,268,54,289)(5,67,269,55,290)(6,68,270,45,291)(7,69,271,46,292)(8,70,272,47,293)(9,71,273,48,294)(10,72,274,49,295)(11,73,275,50,296)(12,162,308,236,375)(13,163,298,237,376)(14,164,299,238,377)(15,165,300,239,378)(16,155,301,240,379)(17,156,302,241,380)(18,157,303,242,381)(19,158,304,232,382)(20,159,305,233,383)(21,160,306,234,384)(22,161,307,235,385)(23,251,228,153,367)(24,252,229,154,368)(25,253,230,144,369)(26,243,231,145,370)(27,244,221,146,371)(28,245,222,147,372)(29,246,223,148,373)(30,247,224,149,374)(31,248,225,150,364)(32,249,226,151,365)(33,250,227,152,366)(34,66,116,279,340)(35,56,117,280,341)(36,57,118,281,331)(37,58,119,282,332)(38,59,120,283,333)(39,60,121,284,334)(40,61,111,285,335)(41,62,112,286,336)(42,63,113,276,337)(43,64,114,277,338)(44,65,115,278,339)(78,424,363,200,139)(79,425,353,201,140)(80,426,354,202,141)(81,427,355,203,142)(82,428,356,204,143)(83,429,357,205,133)(84,419,358,206,134)(85,420,359,207,135)(86,421,360,208,136)(87,422,361,209,137)(88,423,362,199,138)(89,415,210,168,343)(90,416,211,169,344)(91,417,212,170,345)(92,418,213,171,346)(93,408,214,172,347)(94,409,215,173,348)(95,410,216,174,349)(96,411,217,175,350)(97,412,218,176,351)(98,413,219,166,352)(99,414,220,167,342)(100,403,324,434,179)(101,404,325,435,180)(102,405,326,436,181)(103,406,327,437,182)(104,407,328,438,183)(105,397,329,439,184)(106,398,330,440,185)(107,399,320,430,186)(108,400,321,431,187)(109,401,322,432,177)(110,402,323,433,178)(122,387,260,194,319)(123,388,261,195,309)(124,389,262,196,310)(125,390,263,197,311)(126,391,264,198,312)(127,392,254,188,313)(128,393,255,189,314)(129,394,256,190,315)(130,395,257,191,316)(131,396,258,192,317)(132,386,259,193,318), (1,78,386,403,172,380,31,36)(2,79,387,404,173,381,32,37)(3,80,388,405,174,382,33,38)(4,81,389,406,175,383,23,39)(5,82,390,407,176,384,24,40)(6,83,391,397,166,385,25,41)(7,84,392,398,167,375,26,42)(8,85,393,399,168,376,27,43)(9,86,394,400,169,377,28,44)(10,87,395,401,170,378,29,34)(11,88,396,402,171,379,30,35)(12,231,337,46,419,188,106,414)(13,221,338,47,420,189,107,415)(14,222,339,48,421,190,108,416)(15,223,340,49,422,191,109,417)(16,224,341,50,423,192,110,418)(17,225,331,51,424,193,100,408)(18,226,332,52,425,194,101,409)(19,227,333,53,426,195,102,410)(20,228,334,54,427,196,103,411)(21,229,335,55,428,197,104,412)(22,230,336,45,429,198,105,413)(56,275,138,317,323,92,240,149)(57,265,139,318,324,93,241,150)(58,266,140,319,325,94,242,151)(59,267,141,309,326,95,232,152)(60,268,142,310,327,96,233,153)(61,269,143,311,328,97,234,154)(62,270,133,312,329,98,235,144)(63,271,134,313,330,99,236,145)(64,272,135,314,320,89,237,146)(65,273,136,315,321,90,238,147)(66,274,137,316,322,91,239,148)(67,356,125,183,351,160,368,285)(68,357,126,184,352,161,369,286)(69,358,127,185,342,162,370,276)(70,359,128,186,343,163,371,277)(71,360,129,187,344,164,372,278)(72,361,130,177,345,165,373,279)(73,362,131,178,346,155,374,280)(74,363,132,179,347,156,364,281)(75,353,122,180,348,157,365,282)(76,354,123,181,349,158,366,283)(77,355,124,182,350,159,367,284)(111,290,204,263,438,218,306,252)(112,291,205,264,439,219,307,253)(113,292,206,254,440,220,308,243)(114,293,207,255,430,210,298,244)(115,294,208,256,431,211,299,245)(116,295,209,257,432,212,300,246)(117,296,199,258,433,213,301,247)(118,297,200,259,434,214,302,248)(119,287,201,260,435,215,303,249)(120,288,202,261,436,216,304,250)(121,289,203,262,437,217,305,251) );
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)], [(1,74,265,51,297),(2,75,266,52,287),(3,76,267,53,288),(4,77,268,54,289),(5,67,269,55,290),(6,68,270,45,291),(7,69,271,46,292),(8,70,272,47,293),(9,71,273,48,294),(10,72,274,49,295),(11,73,275,50,296),(12,162,308,236,375),(13,163,298,237,376),(14,164,299,238,377),(15,165,300,239,378),(16,155,301,240,379),(17,156,302,241,380),(18,157,303,242,381),(19,158,304,232,382),(20,159,305,233,383),(21,160,306,234,384),(22,161,307,235,385),(23,251,228,153,367),(24,252,229,154,368),(25,253,230,144,369),(26,243,231,145,370),(27,244,221,146,371),(28,245,222,147,372),(29,246,223,148,373),(30,247,224,149,374),(31,248,225,150,364),(32,249,226,151,365),(33,250,227,152,366),(34,66,116,279,340),(35,56,117,280,341),(36,57,118,281,331),(37,58,119,282,332),(38,59,120,283,333),(39,60,121,284,334),(40,61,111,285,335),(41,62,112,286,336),(42,63,113,276,337),(43,64,114,277,338),(44,65,115,278,339),(78,424,363,200,139),(79,425,353,201,140),(80,426,354,202,141),(81,427,355,203,142),(82,428,356,204,143),(83,429,357,205,133),(84,419,358,206,134),(85,420,359,207,135),(86,421,360,208,136),(87,422,361,209,137),(88,423,362,199,138),(89,415,210,168,343),(90,416,211,169,344),(91,417,212,170,345),(92,418,213,171,346),(93,408,214,172,347),(94,409,215,173,348),(95,410,216,174,349),(96,411,217,175,350),(97,412,218,176,351),(98,413,219,166,352),(99,414,220,167,342),(100,403,324,434,179),(101,404,325,435,180),(102,405,326,436,181),(103,406,327,437,182),(104,407,328,438,183),(105,397,329,439,184),(106,398,330,440,185),(107,399,320,430,186),(108,400,321,431,187),(109,401,322,432,177),(110,402,323,433,178),(122,387,260,194,319),(123,388,261,195,309),(124,389,262,196,310),(125,390,263,197,311),(126,391,264,198,312),(127,392,254,188,313),(128,393,255,189,314),(129,394,256,190,315),(130,395,257,191,316),(131,396,258,192,317),(132,386,259,193,318)], [(1,78,386,403,172,380,31,36),(2,79,387,404,173,381,32,37),(3,80,388,405,174,382,33,38),(4,81,389,406,175,383,23,39),(5,82,390,407,176,384,24,40),(6,83,391,397,166,385,25,41),(7,84,392,398,167,375,26,42),(8,85,393,399,168,376,27,43),(9,86,394,400,169,377,28,44),(10,87,395,401,170,378,29,34),(11,88,396,402,171,379,30,35),(12,231,337,46,419,188,106,414),(13,221,338,47,420,189,107,415),(14,222,339,48,421,190,108,416),(15,223,340,49,422,191,109,417),(16,224,341,50,423,192,110,418),(17,225,331,51,424,193,100,408),(18,226,332,52,425,194,101,409),(19,227,333,53,426,195,102,410),(20,228,334,54,427,196,103,411),(21,229,335,55,428,197,104,412),(22,230,336,45,429,198,105,413),(56,275,138,317,323,92,240,149),(57,265,139,318,324,93,241,150),(58,266,140,319,325,94,242,151),(59,267,141,309,326,95,232,152),(60,268,142,310,327,96,233,153),(61,269,143,311,328,97,234,154),(62,270,133,312,329,98,235,144),(63,271,134,313,330,99,236,145),(64,272,135,314,320,89,237,146),(65,273,136,315,321,90,238,147),(66,274,137,316,322,91,239,148),(67,356,125,183,351,160,368,285),(68,357,126,184,352,161,369,286),(69,358,127,185,342,162,370,276),(70,359,128,186,343,163,371,277),(71,360,129,187,344,164,372,278),(72,361,130,177,345,165,373,279),(73,362,131,178,346,155,374,280),(74,363,132,179,347,156,364,281),(75,353,122,180,348,157,365,282),(76,354,123,181,349,158,366,283),(77,355,124,182,350,159,367,284),(111,290,204,263,438,218,306,252),(112,291,205,264,439,219,307,253),(113,292,206,254,440,220,308,243),(114,293,207,255,430,210,298,244),(115,294,208,256,431,211,299,245),(116,295,209,257,432,212,300,246),(117,296,199,258,433,213,301,247),(118,297,200,259,434,214,302,248),(119,287,201,260,435,215,303,249),(120,288,202,261,436,216,304,250),(121,289,203,262,437,217,305,251)]])
110 conjugacy classes
| class | 1 | 2 | 4A | 4B | 5 | 8A | 8B | 8C | 8D | 10 | 11A | ··· | 11J | 22A | ··· | 22J | 44A | ··· | 44T | 55A | ··· | 55J | 88A | ··· | 88AN | 110A | ··· | 110J |
| order | 1 | 2 | 4 | 4 | 5 | 8 | 8 | 8 | 8 | 10 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 | 55 | ··· | 55 | 88 | ··· | 88 | 110 | ··· | 110 |
| size | 1 | 1 | 5 | 5 | 4 | 5 | 5 | 5 | 5 | 4 | 1 | ··· | 1 | 1 | ··· | 1 | 5 | ··· | 5 | 4 | ··· | 4 | 5 | ··· | 5 | 4 | ··· | 4 |
110 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 |
| type | + | + | + | - | ||||||||
| image | C1 | C2 | C4 | C8 | C11 | C22 | C44 | C88 | F5 | C5⋊C8 | C11×F5 | C11×C5⋊C8 |
| kernel | C11×C5⋊C8 | C11×Dic5 | C110 | C55 | C5⋊C8 | Dic5 | C10 | C5 | C22 | C11 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 10 | 10 | 20 | 40 | 1 | 1 | 10 | 10 |
Matrix representation of C11×C5⋊C8 ►in GL4(𝔽881) generated by
| 168 | 0 | 0 | 0 |
| 0 | 168 | 0 | 0 |
| 0 | 0 | 168 | 0 |
| 0 | 0 | 0 | 168 |
| 0 | 0 | 0 | 880 |
| 1 | 0 | 0 | 880 |
| 0 | 1 | 0 | 880 |
| 0 | 0 | 1 | 880 |
| 502 | 551 | 601 | 380 |
| 222 | 50 | 329 | 1 |
| 831 | 552 | 880 | 602 |
| 501 | 272 | 379 | 330 |
G:=sub<GL(4,GF(881))| [168,0,0,0,0,168,0,0,0,0,168,0,0,0,0,168],[0,1,0,0,0,0,1,0,0,0,0,1,880,880,880,880],[502,222,831,501,551,50,552,272,601,329,880,379,380,1,602,330] >;
C11×C5⋊C8 in GAP, Magma, Sage, TeX
C_{11}\times C_5\rtimes C_8 % in TeX
G:=Group("C11xC5:C8"); // GroupNames label
G:=SmallGroup(440,15);
// by ID
G=gap.SmallGroup(440,15);
# by ID
G:=PCGroup([5,-2,-11,-2,-2,-5,110,42,4404,414]);
// 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^3>;
// generators/relations
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