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G = C11×C52C8order 440 = 23·5·11

Direct product of C11 and C52C8

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

Aliases: C11×C52C8, C52C88, C555C8, 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

C1C5 — C11×C52C8
C1C5C10C20C220 — C11×C52C8
C5 — C11×C52C8
C1C44

Generators and relations for C11×C52C8
 G = < a,b,c | a11=b5=c8=1, ab=ba, ac=ca, cbc-1=b-1 >

5C8
5C88

Smallest permutation representation of C11×C52C8
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)
(1 244 265 51 226)(2 245 266 52 227)(3 246 267 53 228)(4 247 268 54 229)(5 248 269 55 230)(6 249 270 45 231)(7 250 271 46 221)(8 251 272 47 222)(9 252 273 48 223)(10 253 274 49 224)(11 243 275 50 225)(12 236 62 286 41)(13 237 63 276 42)(14 238 64 277 43)(15 239 65 278 44)(16 240 66 279 34)(17 241 56 280 35)(18 242 57 281 36)(19 232 58 282 37)(20 233 59 283 38)(21 234 60 284 39)(22 235 61 285 40)(23 346 132 367 153)(24 347 122 368 154)(25 348 123 369 144)(26 349 124 370 145)(27 350 125 371 146)(28 351 126 372 147)(29 352 127 373 148)(30 342 128 374 149)(31 343 129 364 150)(32 344 130 365 151)(33 345 131 366 152)(67 393 99 414 220)(68 394 89 415 210)(69 395 90 416 211)(70 396 91 417 212)(71 386 92 418 213)(72 387 93 408 214)(73 388 94 409 215)(74 389 95 410 216)(75 390 96 411 217)(76 391 97 412 218)(77 392 98 413 219)(78 200 424 110 323)(79 201 425 100 324)(80 202 426 101 325)(81 203 427 102 326)(82 204 428 103 327)(83 205 429 104 328)(84 206 419 105 329)(85 207 420 106 330)(86 208 421 107 320)(87 209 422 108 321)(88 199 423 109 322)(111 335 181 405 436)(112 336 182 406 437)(113 337 183 407 438)(114 338 184 397 439)(115 339 185 398 440)(116 340 186 399 430)(117 341 187 400 431)(118 331 177 401 432)(119 332 178 402 433)(120 333 179 403 434)(121 334 180 404 435)(133 357 299 165 378)(134 358 300 155 379)(135 359 301 156 380)(136 360 302 157 381)(137 361 303 158 382)(138 362 304 159 383)(139 363 305 160 384)(140 353 306 161 385)(141 354 307 162 375)(142 355 308 163 376)(143 356 298 164 377)(166 312 198 264 291)(167 313 188 254 292)(168 314 189 255 293)(169 315 190 256 294)(170 316 191 257 295)(171 317 192 258 296)(172 318 193 259 297)(173 319 194 260 287)(174 309 195 261 288)(175 310 196 262 289)(176 311 197 263 290)
(1 78 297 403 72 360 32 36)(2 79 287 404 73 361 33 37)(3 80 288 405 74 362 23 38)(4 81 289 406 75 363 24 39)(5 82 290 407 76 353 25 40)(6 83 291 397 77 354 26 41)(7 84 292 398 67 355 27 42)(8 85 293 399 68 356 28 43)(9 86 294 400 69 357 29 44)(10 87 295 401 70 358 30 34)(11 88 296 402 71 359 31 35)(12 231 205 264 439 219 307 145)(13 221 206 254 440 220 308 146)(14 222 207 255 430 210 298 147)(15 223 208 256 431 211 299 148)(16 224 209 257 432 212 300 149)(17 225 199 258 433 213 301 150)(18 226 200 259 434 214 302 151)(19 227 201 260 435 215 303 152)(20 228 202 261 436 216 304 153)(21 229 203 262 437 217 305 154)(22 230 204 263 438 218 306 144)(45 429 198 114 413 162 370 236)(46 419 188 115 414 163 371 237)(47 420 189 116 415 164 372 238)(48 421 190 117 416 165 373 239)(49 422 191 118 417 155 374 240)(50 423 192 119 418 156 364 241)(51 424 193 120 408 157 365 242)(52 425 194 121 409 158 366 232)(53 426 195 111 410 159 367 233)(54 427 196 112 411 160 368 234)(55 428 197 113 412 161 369 235)(56 275 109 317 332 92 380 129)(57 265 110 318 333 93 381 130)(58 266 100 319 334 94 382 131)(59 267 101 309 335 95 383 132)(60 268 102 310 336 96 384 122)(61 269 103 311 337 97 385 123)(62 270 104 312 338 98 375 124)(63 271 105 313 339 99 376 125)(64 272 106 314 340 89 377 126)(65 273 107 315 341 90 378 127)(66 274 108 316 331 91 379 128)(133 352 278 252 320 169 187 395)(134 342 279 253 321 170 177 396)(135 343 280 243 322 171 178 386)(136 344 281 244 323 172 179 387)(137 345 282 245 324 173 180 388)(138 346 283 246 325 174 181 389)(139 347 284 247 326 175 182 390)(140 348 285 248 327 176 183 391)(141 349 286 249 328 166 184 392)(142 350 276 250 329 167 185 393)(143 351 277 251 330 168 186 394)

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

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

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

176 conjugacy classes

class 1  2 4A4B5A5B8A8B8C8D10A10B11A···11J20A20B20C20D22A···22J44A···44T55A···55T88A···88AN110A···110T220A···220AN
order1244558888101011···112020202022···2244···4455···5588···88110···110220···220
size1111225555221···122221···11···12···25···52···22···2

176 irreducible representations

dim11111111222222
type+++-
imageC1C2C4C8C11C22C44C88D5Dic5C52C8D5×C11C11×Dic5C11×C52C8
kernelC11×C52C8C220C110C55C52C8C20C10C5C44C22C11C4C2C1
# reps112410102040224202040

Matrix representation of C11×C52C8 in GL2(𝔽881) generated by

2370
0237
,
327880
328880
,
386233
402495
G:=sub<GL(2,GF(881))| [237,0,0,237],[327,328,880,880],[386,402,233,495] >;

C11×C52C8 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

Export

Subgroup lattice of C11×C52C8 in TeX

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