direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C11⋊Q16, C22⋊2Q16, C44.20D4, Q8.7D22, C44.16C23, Dic22.10C22, C11⋊3(C2×Q16), C22.55(C2×D4), (C2×C4).54D22, (C2×C22).43D4, C11⋊C8.9C22, (C2×Q8).3D11, (Q8×C22).3C2, C4.9(C11⋊D4), (C2×C44).38C22, (C2×Dic22).8C2, C4.16(C22×D11), (Q8×C11).7C22, C22.24(C11⋊D4), (C2×C11⋊C8).6C2, C2.19(C2×C11⋊D4), SmallGroup(352,138)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C11⋊Q16
G = < a,b,c,d | a2=b11=c8=1, d2=c4, ab=ba, ac=ca, ad=da, cbc-1=b-1, bd=db, dcd-1=c-1 >
Subgroups: 266 in 60 conjugacy classes, 33 normal (17 characteristic)
C1, C2, C2, C4, C4, C22, C8, C2×C4, C2×C4, Q8, Q8, C11, C2×C8, Q16, C2×Q8, C2×Q8, C22, C22, C2×Q16, Dic11, C44, C44, C2×C22, C11⋊C8, Dic22, Dic22, C2×Dic11, C2×C44, C2×C44, Q8×C11, Q8×C11, C2×C11⋊C8, C11⋊Q16, C2×Dic22, Q8×C22, C2×C11⋊Q16
Quotients: C1, C2, C22, D4, C23, Q16, C2×D4, D11, C2×Q16, D22, C11⋊D4, C22×D11, C11⋊Q16, C2×C11⋊D4, C2×C11⋊Q16
►Regular action on 352 points
Generators in S352
(1 89)(2 90)(3 91)(4 92)(5 93)(6 94)(7 95)(8 96)(9 97)(10 98)(11 99)(12 100)(13 101)(14 102)(15 103)(16 104)(17 105)(18 106)(19 107)(20 108)(21 109)(22 110)(23 111)(24 112)(25 113)(26 114)(27 115)(28 116)(29 117)(30 118)(31 119)(32 120)(33 121)(34 122)(35 123)(36 124)(37 125)(38 126)(39 127)(40 128)(41 129)(42 130)(43 131)(44 132)(45 133)(46 134)(47 135)(48 136)(49 137)(50 138)(51 139)(52 140)(53 141)(54 142)(55 143)(56 144)(57 145)(58 146)(59 147)(60 148)(61 149)(62 150)(63 151)(64 152)(65 153)(66 154)(67 155)(68 156)(69 157)(70 158)(71 159)(72 160)(73 161)(74 162)(75 163)(76 164)(77 165)(78 166)(79 167)(80 168)(81 169)(82 170)(83 171)(84 172)(85 173)(86 174)(87 175)(88 176)(177 265)(178 266)(179 267)(180 268)(181 269)(182 270)(183 271)(184 272)(185 273)(186 274)(187 275)(188 276)(189 277)(190 278)(191 279)(192 280)(193 281)(194 282)(195 283)(196 284)(197 285)(198 286)(199 287)(200 288)(201 289)(202 290)(203 291)(204 292)(205 293)(206 294)(207 295)(208 296)(209 297)(210 298)(211 299)(212 300)(213 301)(214 302)(215 303)(216 304)(217 305)(218 306)(219 307)(220 308)(221 309)(222 310)(223 311)(224 312)(225 313)(226 314)(227 315)(228 316)(229 317)(230 318)(231 319)(232 320)(233 321)(234 322)(235 323)(236 324)(237 325)(238 326)(239 327)(240 328)(241 329)(242 330)(243 331)(244 332)(245 333)(246 334)(247 335)(248 336)(249 337)(250 338)(251 339)(252 340)(253 341)(254 342)(255 343)(256 344)(257 345)(258 346)(259 347)(260 348)(261 349)(262 350)(263 351)(264 352)
(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)
(1 252 23 241 12 263 34 230)(2 251 24 240 13 262 35 229)(3 250 25 239 14 261 36 228)(4 249 26 238 15 260 37 227)(5 248 27 237 16 259 38 226)(6 247 28 236 17 258 39 225)(7 246 29 235 18 257 40 224)(8 245 30 234 19 256 41 223)(9 244 31 233 20 255 42 222)(10 243 32 232 21 254 43 221)(11 253 33 242 22 264 44 231)(45 208 78 186 56 219 67 197)(46 207 79 185 57 218 68 196)(47 206 80 184 58 217 69 195)(48 205 81 183 59 216 70 194)(49 204 82 182 60 215 71 193)(50 203 83 181 61 214 72 192)(51 202 84 180 62 213 73 191)(52 201 85 179 63 212 74 190)(53 200 86 178 64 211 75 189)(54 199 87 177 65 210 76 188)(55 209 88 187 66 220 77 198)(89 340 111 329 100 351 122 318)(90 339 112 328 101 350 123 317)(91 338 113 327 102 349 124 316)(92 337 114 326 103 348 125 315)(93 336 115 325 104 347 126 314)(94 335 116 324 105 346 127 313)(95 334 117 323 106 345 128 312)(96 333 118 322 107 344 129 311)(97 332 119 321 108 343 130 310)(98 331 120 320 109 342 131 309)(99 341 121 330 110 352 132 319)(133 296 166 274 144 307 155 285)(134 295 167 273 145 306 156 284)(135 294 168 272 146 305 157 283)(136 293 169 271 147 304 158 282)(137 292 170 270 148 303 159 281)(138 291 171 269 149 302 160 280)(139 290 172 268 150 301 161 279)(140 289 173 267 151 300 162 278)(141 288 174 266 152 299 163 277)(142 287 175 265 153 298 164 276)(143 297 176 275 154 308 165 286)
(1 144 12 133)(2 145 13 134)(3 146 14 135)(4 147 15 136)(5 148 16 137)(6 149 17 138)(7 150 18 139)(8 151 19 140)(9 152 20 141)(10 153 21 142)(11 154 22 143)(23 166 34 155)(24 167 35 156)(25 168 36 157)(26 169 37 158)(27 170 38 159)(28 171 39 160)(29 172 40 161)(30 173 41 162)(31 174 42 163)(32 175 43 164)(33 176 44 165)(45 89 56 100)(46 90 57 101)(47 91 58 102)(48 92 59 103)(49 93 60 104)(50 94 61 105)(51 95 62 106)(52 96 63 107)(53 97 64 108)(54 98 65 109)(55 99 66 110)(67 111 78 122)(68 112 79 123)(69 113 80 124)(70 114 81 125)(71 115 82 126)(72 116 83 127)(73 117 84 128)(74 118 85 129)(75 119 86 130)(76 120 87 131)(77 121 88 132)(177 342 188 331)(178 343 189 332)(179 344 190 333)(180 345 191 334)(181 346 192 335)(182 347 193 336)(183 348 194 337)(184 349 195 338)(185 350 196 339)(186 351 197 340)(187 352 198 341)(199 309 210 320)(200 310 211 321)(201 311 212 322)(202 312 213 323)(203 313 214 324)(204 314 215 325)(205 315 216 326)(206 316 217 327)(207 317 218 328)(208 318 219 329)(209 319 220 330)(221 298 232 287)(222 299 233 288)(223 300 234 289)(224 301 235 290)(225 302 236 291)(226 303 237 292)(227 304 238 293)(228 305 239 294)(229 306 240 295)(230 307 241 296)(231 308 242 297)(243 265 254 276)(244 266 255 277)(245 267 256 278)(246 268 257 279)(247 269 258 280)(248 270 259 281)(249 271 260 282)(250 272 261 283)(251 273 262 284)(252 274 263 285)(253 275 264 286)
G:=sub<Sym(352)| (1,89)(2,90)(3,91)(4,92)(5,93)(6,94)(7,95)(8,96)(9,97)(10,98)(11,99)(12,100)(13,101)(14,102)(15,103)(16,104)(17,105)(18,106)(19,107)(20,108)(21,109)(22,110)(23,111)(24,112)(25,113)(26,114)(27,115)(28,116)(29,117)(30,118)(31,119)(32,120)(33,121)(34,122)(35,123)(36,124)(37,125)(38,126)(39,127)(40,128)(41,129)(42,130)(43,131)(44,132)(45,133)(46,134)(47,135)(48,136)(49,137)(50,138)(51,139)(52,140)(53,141)(54,142)(55,143)(56,144)(57,145)(58,146)(59,147)(60,148)(61,149)(62,150)(63,151)(64,152)(65,153)(66,154)(67,155)(68,156)(69,157)(70,158)(71,159)(72,160)(73,161)(74,162)(75,163)(76,164)(77,165)(78,166)(79,167)(80,168)(81,169)(82,170)(83,171)(84,172)(85,173)(86,174)(87,175)(88,176)(177,265)(178,266)(179,267)(180,268)(181,269)(182,270)(183,271)(184,272)(185,273)(186,274)(187,275)(188,276)(189,277)(190,278)(191,279)(192,280)(193,281)(194,282)(195,283)(196,284)(197,285)(198,286)(199,287)(200,288)(201,289)(202,290)(203,291)(204,292)(205,293)(206,294)(207,295)(208,296)(209,297)(210,298)(211,299)(212,300)(213,301)(214,302)(215,303)(216,304)(217,305)(218,306)(219,307)(220,308)(221,309)(222,310)(223,311)(224,312)(225,313)(226,314)(227,315)(228,316)(229,317)(230,318)(231,319)(232,320)(233,321)(234,322)(235,323)(236,324)(237,325)(238,326)(239,327)(240,328)(241,329)(242,330)(243,331)(244,332)(245,333)(246,334)(247,335)(248,336)(249,337)(250,338)(251,339)(252,340)(253,341)(254,342)(255,343)(256,344)(257,345)(258,346)(259,347)(260,348)(261,349)(262,350)(263,351)(264,352), (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), (1,252,23,241,12,263,34,230)(2,251,24,240,13,262,35,229)(3,250,25,239,14,261,36,228)(4,249,26,238,15,260,37,227)(5,248,27,237,16,259,38,226)(6,247,28,236,17,258,39,225)(7,246,29,235,18,257,40,224)(8,245,30,234,19,256,41,223)(9,244,31,233,20,255,42,222)(10,243,32,232,21,254,43,221)(11,253,33,242,22,264,44,231)(45,208,78,186,56,219,67,197)(46,207,79,185,57,218,68,196)(47,206,80,184,58,217,69,195)(48,205,81,183,59,216,70,194)(49,204,82,182,60,215,71,193)(50,203,83,181,61,214,72,192)(51,202,84,180,62,213,73,191)(52,201,85,179,63,212,74,190)(53,200,86,178,64,211,75,189)(54,199,87,177,65,210,76,188)(55,209,88,187,66,220,77,198)(89,340,111,329,100,351,122,318)(90,339,112,328,101,350,123,317)(91,338,113,327,102,349,124,316)(92,337,114,326,103,348,125,315)(93,336,115,325,104,347,126,314)(94,335,116,324,105,346,127,313)(95,334,117,323,106,345,128,312)(96,333,118,322,107,344,129,311)(97,332,119,321,108,343,130,310)(98,331,120,320,109,342,131,309)(99,341,121,330,110,352,132,319)(133,296,166,274,144,307,155,285)(134,295,167,273,145,306,156,284)(135,294,168,272,146,305,157,283)(136,293,169,271,147,304,158,282)(137,292,170,270,148,303,159,281)(138,291,171,269,149,302,160,280)(139,290,172,268,150,301,161,279)(140,289,173,267,151,300,162,278)(141,288,174,266,152,299,163,277)(142,287,175,265,153,298,164,276)(143,297,176,275,154,308,165,286), (1,144,12,133)(2,145,13,134)(3,146,14,135)(4,147,15,136)(5,148,16,137)(6,149,17,138)(7,150,18,139)(8,151,19,140)(9,152,20,141)(10,153,21,142)(11,154,22,143)(23,166,34,155)(24,167,35,156)(25,168,36,157)(26,169,37,158)(27,170,38,159)(28,171,39,160)(29,172,40,161)(30,173,41,162)(31,174,42,163)(32,175,43,164)(33,176,44,165)(45,89,56,100)(46,90,57,101)(47,91,58,102)(48,92,59,103)(49,93,60,104)(50,94,61,105)(51,95,62,106)(52,96,63,107)(53,97,64,108)(54,98,65,109)(55,99,66,110)(67,111,78,122)(68,112,79,123)(69,113,80,124)(70,114,81,125)(71,115,82,126)(72,116,83,127)(73,117,84,128)(74,118,85,129)(75,119,86,130)(76,120,87,131)(77,121,88,132)(177,342,188,331)(178,343,189,332)(179,344,190,333)(180,345,191,334)(181,346,192,335)(182,347,193,336)(183,348,194,337)(184,349,195,338)(185,350,196,339)(186,351,197,340)(187,352,198,341)(199,309,210,320)(200,310,211,321)(201,311,212,322)(202,312,213,323)(203,313,214,324)(204,314,215,325)(205,315,216,326)(206,316,217,327)(207,317,218,328)(208,318,219,329)(209,319,220,330)(221,298,232,287)(222,299,233,288)(223,300,234,289)(224,301,235,290)(225,302,236,291)(226,303,237,292)(227,304,238,293)(228,305,239,294)(229,306,240,295)(230,307,241,296)(231,308,242,297)(243,265,254,276)(244,266,255,277)(245,267,256,278)(246,268,257,279)(247,269,258,280)(248,270,259,281)(249,271,260,282)(250,272,261,283)(251,273,262,284)(252,274,263,285)(253,275,264,286)>;
G:=Group( (1,89)(2,90)(3,91)(4,92)(5,93)(6,94)(7,95)(8,96)(9,97)(10,98)(11,99)(12,100)(13,101)(14,102)(15,103)(16,104)(17,105)(18,106)(19,107)(20,108)(21,109)(22,110)(23,111)(24,112)(25,113)(26,114)(27,115)(28,116)(29,117)(30,118)(31,119)(32,120)(33,121)(34,122)(35,123)(36,124)(37,125)(38,126)(39,127)(40,128)(41,129)(42,130)(43,131)(44,132)(45,133)(46,134)(47,135)(48,136)(49,137)(50,138)(51,139)(52,140)(53,141)(54,142)(55,143)(56,144)(57,145)(58,146)(59,147)(60,148)(61,149)(62,150)(63,151)(64,152)(65,153)(66,154)(67,155)(68,156)(69,157)(70,158)(71,159)(72,160)(73,161)(74,162)(75,163)(76,164)(77,165)(78,166)(79,167)(80,168)(81,169)(82,170)(83,171)(84,172)(85,173)(86,174)(87,175)(88,176)(177,265)(178,266)(179,267)(180,268)(181,269)(182,270)(183,271)(184,272)(185,273)(186,274)(187,275)(188,276)(189,277)(190,278)(191,279)(192,280)(193,281)(194,282)(195,283)(196,284)(197,285)(198,286)(199,287)(200,288)(201,289)(202,290)(203,291)(204,292)(205,293)(206,294)(207,295)(208,296)(209,297)(210,298)(211,299)(212,300)(213,301)(214,302)(215,303)(216,304)(217,305)(218,306)(219,307)(220,308)(221,309)(222,310)(223,311)(224,312)(225,313)(226,314)(227,315)(228,316)(229,317)(230,318)(231,319)(232,320)(233,321)(234,322)(235,323)(236,324)(237,325)(238,326)(239,327)(240,328)(241,329)(242,330)(243,331)(244,332)(245,333)(246,334)(247,335)(248,336)(249,337)(250,338)(251,339)(252,340)(253,341)(254,342)(255,343)(256,344)(257,345)(258,346)(259,347)(260,348)(261,349)(262,350)(263,351)(264,352), (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), (1,252,23,241,12,263,34,230)(2,251,24,240,13,262,35,229)(3,250,25,239,14,261,36,228)(4,249,26,238,15,260,37,227)(5,248,27,237,16,259,38,226)(6,247,28,236,17,258,39,225)(7,246,29,235,18,257,40,224)(8,245,30,234,19,256,41,223)(9,244,31,233,20,255,42,222)(10,243,32,232,21,254,43,221)(11,253,33,242,22,264,44,231)(45,208,78,186,56,219,67,197)(46,207,79,185,57,218,68,196)(47,206,80,184,58,217,69,195)(48,205,81,183,59,216,70,194)(49,204,82,182,60,215,71,193)(50,203,83,181,61,214,72,192)(51,202,84,180,62,213,73,191)(52,201,85,179,63,212,74,190)(53,200,86,178,64,211,75,189)(54,199,87,177,65,210,76,188)(55,209,88,187,66,220,77,198)(89,340,111,329,100,351,122,318)(90,339,112,328,101,350,123,317)(91,338,113,327,102,349,124,316)(92,337,114,326,103,348,125,315)(93,336,115,325,104,347,126,314)(94,335,116,324,105,346,127,313)(95,334,117,323,106,345,128,312)(96,333,118,322,107,344,129,311)(97,332,119,321,108,343,130,310)(98,331,120,320,109,342,131,309)(99,341,121,330,110,352,132,319)(133,296,166,274,144,307,155,285)(134,295,167,273,145,306,156,284)(135,294,168,272,146,305,157,283)(136,293,169,271,147,304,158,282)(137,292,170,270,148,303,159,281)(138,291,171,269,149,302,160,280)(139,290,172,268,150,301,161,279)(140,289,173,267,151,300,162,278)(141,288,174,266,152,299,163,277)(142,287,175,265,153,298,164,276)(143,297,176,275,154,308,165,286), (1,144,12,133)(2,145,13,134)(3,146,14,135)(4,147,15,136)(5,148,16,137)(6,149,17,138)(7,150,18,139)(8,151,19,140)(9,152,20,141)(10,153,21,142)(11,154,22,143)(23,166,34,155)(24,167,35,156)(25,168,36,157)(26,169,37,158)(27,170,38,159)(28,171,39,160)(29,172,40,161)(30,173,41,162)(31,174,42,163)(32,175,43,164)(33,176,44,165)(45,89,56,100)(46,90,57,101)(47,91,58,102)(48,92,59,103)(49,93,60,104)(50,94,61,105)(51,95,62,106)(52,96,63,107)(53,97,64,108)(54,98,65,109)(55,99,66,110)(67,111,78,122)(68,112,79,123)(69,113,80,124)(70,114,81,125)(71,115,82,126)(72,116,83,127)(73,117,84,128)(74,118,85,129)(75,119,86,130)(76,120,87,131)(77,121,88,132)(177,342,188,331)(178,343,189,332)(179,344,190,333)(180,345,191,334)(181,346,192,335)(182,347,193,336)(183,348,194,337)(184,349,195,338)(185,350,196,339)(186,351,197,340)(187,352,198,341)(199,309,210,320)(200,310,211,321)(201,311,212,322)(202,312,213,323)(203,313,214,324)(204,314,215,325)(205,315,216,326)(206,316,217,327)(207,317,218,328)(208,318,219,329)(209,319,220,330)(221,298,232,287)(222,299,233,288)(223,300,234,289)(224,301,235,290)(225,302,236,291)(226,303,237,292)(227,304,238,293)(228,305,239,294)(229,306,240,295)(230,307,241,296)(231,308,242,297)(243,265,254,276)(244,266,255,277)(245,267,256,278)(246,268,257,279)(247,269,258,280)(248,270,259,281)(249,271,260,282)(250,272,261,283)(251,273,262,284)(252,274,263,285)(253,275,264,286) );
G=PermutationGroup([[(1,89),(2,90),(3,91),(4,92),(5,93),(6,94),(7,95),(8,96),(9,97),(10,98),(11,99),(12,100),(13,101),(14,102),(15,103),(16,104),(17,105),(18,106),(19,107),(20,108),(21,109),(22,110),(23,111),(24,112),(25,113),(26,114),(27,115),(28,116),(29,117),(30,118),(31,119),(32,120),(33,121),(34,122),(35,123),(36,124),(37,125),(38,126),(39,127),(40,128),(41,129),(42,130),(43,131),(44,132),(45,133),(46,134),(47,135),(48,136),(49,137),(50,138),(51,139),(52,140),(53,141),(54,142),(55,143),(56,144),(57,145),(58,146),(59,147),(60,148),(61,149),(62,150),(63,151),(64,152),(65,153),(66,154),(67,155),(68,156),(69,157),(70,158),(71,159),(72,160),(73,161),(74,162),(75,163),(76,164),(77,165),(78,166),(79,167),(80,168),(81,169),(82,170),(83,171),(84,172),(85,173),(86,174),(87,175),(88,176),(177,265),(178,266),(179,267),(180,268),(181,269),(182,270),(183,271),(184,272),(185,273),(186,274),(187,275),(188,276),(189,277),(190,278),(191,279),(192,280),(193,281),(194,282),(195,283),(196,284),(197,285),(198,286),(199,287),(200,288),(201,289),(202,290),(203,291),(204,292),(205,293),(206,294),(207,295),(208,296),(209,297),(210,298),(211,299),(212,300),(213,301),(214,302),(215,303),(216,304),(217,305),(218,306),(219,307),(220,308),(221,309),(222,310),(223,311),(224,312),(225,313),(226,314),(227,315),(228,316),(229,317),(230,318),(231,319),(232,320),(233,321),(234,322),(235,323),(236,324),(237,325),(238,326),(239,327),(240,328),(241,329),(242,330),(243,331),(244,332),(245,333),(246,334),(247,335),(248,336),(249,337),(250,338),(251,339),(252,340),(253,341),(254,342),(255,343),(256,344),(257,345),(258,346),(259,347),(260,348),(261,349),(262,350),(263,351),(264,352)], [(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)], [(1,252,23,241,12,263,34,230),(2,251,24,240,13,262,35,229),(3,250,25,239,14,261,36,228),(4,249,26,238,15,260,37,227),(5,248,27,237,16,259,38,226),(6,247,28,236,17,258,39,225),(7,246,29,235,18,257,40,224),(8,245,30,234,19,256,41,223),(9,244,31,233,20,255,42,222),(10,243,32,232,21,254,43,221),(11,253,33,242,22,264,44,231),(45,208,78,186,56,219,67,197),(46,207,79,185,57,218,68,196),(47,206,80,184,58,217,69,195),(48,205,81,183,59,216,70,194),(49,204,82,182,60,215,71,193),(50,203,83,181,61,214,72,192),(51,202,84,180,62,213,73,191),(52,201,85,179,63,212,74,190),(53,200,86,178,64,211,75,189),(54,199,87,177,65,210,76,188),(55,209,88,187,66,220,77,198),(89,340,111,329,100,351,122,318),(90,339,112,328,101,350,123,317),(91,338,113,327,102,349,124,316),(92,337,114,326,103,348,125,315),(93,336,115,325,104,347,126,314),(94,335,116,324,105,346,127,313),(95,334,117,323,106,345,128,312),(96,333,118,322,107,344,129,311),(97,332,119,321,108,343,130,310),(98,331,120,320,109,342,131,309),(99,341,121,330,110,352,132,319),(133,296,166,274,144,307,155,285),(134,295,167,273,145,306,156,284),(135,294,168,272,146,305,157,283),(136,293,169,271,147,304,158,282),(137,292,170,270,148,303,159,281),(138,291,171,269,149,302,160,280),(139,290,172,268,150,301,161,279),(140,289,173,267,151,300,162,278),(141,288,174,266,152,299,163,277),(142,287,175,265,153,298,164,276),(143,297,176,275,154,308,165,286)], [(1,144,12,133),(2,145,13,134),(3,146,14,135),(4,147,15,136),(5,148,16,137),(6,149,17,138),(7,150,18,139),(8,151,19,140),(9,152,20,141),(10,153,21,142),(11,154,22,143),(23,166,34,155),(24,167,35,156),(25,168,36,157),(26,169,37,158),(27,170,38,159),(28,171,39,160),(29,172,40,161),(30,173,41,162),(31,174,42,163),(32,175,43,164),(33,176,44,165),(45,89,56,100),(46,90,57,101),(47,91,58,102),(48,92,59,103),(49,93,60,104),(50,94,61,105),(51,95,62,106),(52,96,63,107),(53,97,64,108),(54,98,65,109),(55,99,66,110),(67,111,78,122),(68,112,79,123),(69,113,80,124),(70,114,81,125),(71,115,82,126),(72,116,83,127),(73,117,84,128),(74,118,85,129),(75,119,86,130),(76,120,87,131),(77,121,88,132),(177,342,188,331),(178,343,189,332),(179,344,190,333),(180,345,191,334),(181,346,192,335),(182,347,193,336),(183,348,194,337),(184,349,195,338),(185,350,196,339),(186,351,197,340),(187,352,198,341),(199,309,210,320),(200,310,211,321),(201,311,212,322),(202,312,213,323),(203,313,214,324),(204,314,215,325),(205,315,216,326),(206,316,217,327),(207,317,218,328),(208,318,219,329),(209,319,220,330),(221,298,232,287),(222,299,233,288),(223,300,234,289),(224,301,235,290),(225,302,236,291),(226,303,237,292),(227,304,238,293),(228,305,239,294),(229,306,240,295),(230,307,241,296),(231,308,242,297),(243,265,254,276),(244,266,255,277),(245,267,256,278),(246,268,257,279),(247,269,258,280),(248,270,259,281),(249,271,260,282),(250,272,261,283),(251,273,262,284),(252,274,263,285),(253,275,264,286)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 8A | 8B | 8C | 8D | 11A | ··· | 11E | 22A | ··· | 22O | 44A | ··· | 44AD |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 44 | 44 | 22 | 22 | 22 | 22 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D4 | Q16 | D11 | D22 | D22 | C11⋊D4 | C11⋊D4 | C11⋊Q16 |
| kernel | C2×C11⋊Q16 | C2×C11⋊C8 | C11⋊Q16 | C2×Dic22 | Q8×C22 | C44 | C2×C22 | C22 | C2×Q8 | C2×C4 | Q8 | C4 | C22 | C2 |
| # reps | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 4 | 5 | 5 | 10 | 10 | 10 | 10 |
Matrix representation of C2×C11⋊Q16 ►in GL5(𝔽89)
| 88 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 37 | 88 | 0 | 0 |
| 0 | 78 | 34 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 88 | 0 | 0 | 0 | 0 |
| 0 | 2 | 40 | 0 | 0 |
| 0 | 11 | 87 | 0 | 0 |
| 0 | 0 | 0 | 66 | 78 |
| 0 | 0 | 0 | 60 | 48 |
| 88 | 0 | 0 | 0 | 0 |
| 0 | 17 | 48 | 0 | 0 |
| 0 | 83 | 72 | 0 | 0 |
| 0 | 0 | 0 | 51 | 15 |
| 0 | 0 | 0 | 52 | 38 |
G:=sub<GL(5,GF(89))| [88,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,37,78,0,0,0,88,34,0,0,0,0,0,1,0,0,0,0,0,1],[88,0,0,0,0,0,2,11,0,0,0,40,87,0,0,0,0,0,66,60,0,0,0,78,48],[88,0,0,0,0,0,17,83,0,0,0,48,72,0,0,0,0,0,51,52,0,0,0,15,38] >;
C2×C11⋊Q16 in GAP, Magma, Sage, TeX
C_2\times C_{11}\rtimes Q_{16} % in TeX
G:=Group("C2xC11:Q16"); // GroupNames label
G:=SmallGroup(352,138);
// by ID
G=gap.SmallGroup(352,138);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,96,218,86,579,159,69,11525]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^11=c^8=1,d^2=c^4,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations