direct product, metacyclic, nilpotent (class 3), monomial, 2-elementary
Aliases: C11×C2.D8, C8⋊1C44, C88⋊5C4, C22.14D8, C44.10Q8, C22.7Q16, C4⋊C4.3C22, (C2×C8).3C22, C4.7(C2×C44), C2.2(C11×D8), C4.2(Q8×C11), (C2×C88).13C2, C44.44(C2×C4), (C2×C22).49D4, C22.13(C4⋊C4), C2.2(C11×Q16), C22.11(D4×C11), (C2×C44).118C22, C2.4(C11×C4⋊C4), (C11×C4⋊C4).10C2, (C2×C4).21(C2×C22), SmallGroup(352,56)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C11×C2.D8
G = < a,b,c,d | a11=b2=c8=1, d2=b, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >
Smallest permutation representation of C11×C2.D8
►Regular action on 352 points
Generators in S352
(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)
(1 102)(2 103)(3 104)(4 105)(5 106)(6 107)(7 108)(8 109)(9 110)(10 100)(11 101)(12 84)(13 85)(14 86)(15 87)(16 88)(17 78)(18 79)(19 80)(20 81)(21 82)(22 83)(23 74)(24 75)(25 76)(26 77)(27 67)(28 68)(29 69)(30 70)(31 71)(32 72)(33 73)(34 342)(35 343)(36 344)(37 345)(38 346)(39 347)(40 348)(41 349)(42 350)(43 351)(44 352)(45 56)(46 57)(47 58)(48 59)(49 60)(50 61)(51 62)(52 63)(53 64)(54 65)(55 66)(89 145)(90 146)(91 147)(92 148)(93 149)(94 150)(95 151)(96 152)(97 153)(98 154)(99 144)(111 162)(112 163)(113 164)(114 165)(115 155)(116 156)(117 157)(118 158)(119 159)(120 160)(121 161)(122 133)(123 134)(124 135)(125 136)(126 137)(127 138)(128 139)(129 140)(130 141)(131 142)(132 143)(166 196)(167 197)(168 198)(169 188)(170 189)(171 190)(172 191)(173 192)(174 193)(175 194)(176 195)(177 233)(178 234)(179 235)(180 236)(181 237)(182 238)(183 239)(184 240)(185 241)(186 242)(187 232)(199 250)(200 251)(201 252)(202 253)(203 243)(204 244)(205 245)(206 246)(207 247)(208 248)(209 249)(210 221)(211 222)(212 223)(213 224)(214 225)(215 226)(216 227)(217 228)(218 229)(219 230)(220 231)(254 284)(255 285)(256 286)(257 276)(258 277)(259 278)(260 279)(261 280)(262 281)(263 282)(264 283)(265 321)(266 322)(267 323)(268 324)(269 325)(270 326)(271 327)(272 328)(273 329)(274 330)(275 320)(287 338)(288 339)(289 340)(290 341)(291 331)(292 332)(293 333)(294 334)(295 335)(296 336)(297 337)(298 309)(299 310)(300 311)(301 312)(302 313)(303 314)(304 315)(305 316)(306 317)(307 318)(308 319)
(1 246 158 221 133 186 98 196)(2 247 159 222 134 187 99 197)(3 248 160 223 135 177 89 198)(4 249 161 224 136 178 90 188)(5 250 162 225 137 179 91 189)(6 251 163 226 138 180 92 190)(7 252 164 227 139 181 93 191)(8 253 165 228 140 182 94 192)(9 243 155 229 141 183 95 193)(10 244 156 230 142 184 96 194)(11 245 157 231 143 185 97 195)(12 313 74 338 59 277 38 267)(13 314 75 339 60 278 39 268)(14 315 76 340 61 279 40 269)(15 316 77 341 62 280 41 270)(16 317 67 331 63 281 42 271)(17 318 68 332 64 282 43 272)(18 319 69 333 65 283 44 273)(19 309 70 334 66 284 34 274)(20 310 71 335 56 285 35 275)(21 311 72 336 57 286 36 265)(22 312 73 337 58 276 37 266)(23 287 48 258 346 323 84 302)(24 288 49 259 347 324 85 303)(25 289 50 260 348 325 86 304)(26 290 51 261 349 326 87 305)(27 291 52 262 350 327 88 306)(28 292 53 263 351 328 78 307)(29 293 54 264 352 329 79 308)(30 294 55 254 342 330 80 298)(31 295 45 255 343 320 81 299)(32 296 46 256 344 321 82 300)(33 297 47 257 345 322 83 301)(100 204 116 219 131 240 152 175)(101 205 117 220 132 241 153 176)(102 206 118 210 122 242 154 166)(103 207 119 211 123 232 144 167)(104 208 120 212 124 233 145 168)(105 209 121 213 125 234 146 169)(106 199 111 214 126 235 147 170)(107 200 112 215 127 236 148 171)(108 201 113 216 128 237 149 172)(109 202 114 217 129 238 150 173)(110 203 115 218 130 239 151 174)
(1 55 102 66)(2 45 103 56)(3 46 104 57)(4 47 105 58)(5 48 106 59)(6 49 107 60)(7 50 108 61)(8 51 109 62)(9 52 110 63)(10 53 100 64)(11 54 101 65)(12 137 84 126)(13 138 85 127)(14 139 86 128)(15 140 87 129)(16 141 88 130)(17 142 78 131)(18 143 79 132)(19 133 80 122)(20 134 81 123)(21 135 82 124)(22 136 83 125)(23 111 74 162)(24 112 75 163)(25 113 76 164)(26 114 77 165)(27 115 67 155)(28 116 68 156)(29 117 69 157)(30 118 70 158)(31 119 71 159)(32 120 72 160)(33 121 73 161)(34 98 342 154)(35 99 343 144)(36 89 344 145)(37 90 345 146)(38 91 346 147)(39 92 347 148)(40 93 348 149)(41 94 349 150)(42 95 350 151)(43 96 351 152)(44 97 352 153)(166 284 196 254)(167 285 197 255)(168 286 198 256)(169 276 188 257)(170 277 189 258)(171 278 190 259)(172 279 191 260)(173 280 192 261)(174 281 193 262)(175 282 194 263)(176 283 195 264)(177 321 233 265)(178 322 234 266)(179 323 235 267)(180 324 236 268)(181 325 237 269)(182 326 238 270)(183 327 239 271)(184 328 240 272)(185 329 241 273)(186 330 242 274)(187 320 232 275)(199 338 250 287)(200 339 251 288)(201 340 252 289)(202 341 253 290)(203 331 243 291)(204 332 244 292)(205 333 245 293)(206 334 246 294)(207 335 247 295)(208 336 248 296)(209 337 249 297)(210 309 221 298)(211 310 222 299)(212 311 223 300)(213 312 224 301)(214 313 225 302)(215 314 226 303)(216 315 227 304)(217 316 228 305)(218 317 229 306)(219 318 230 307)(220 319 231 308)
G:=sub<Sym(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), (1,102)(2,103)(3,104)(4,105)(5,106)(6,107)(7,108)(8,109)(9,110)(10,100)(11,101)(12,84)(13,85)(14,86)(15,87)(16,88)(17,78)(18,79)(19,80)(20,81)(21,82)(22,83)(23,74)(24,75)(25,76)(26,77)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,342)(35,343)(36,344)(37,345)(38,346)(39,347)(40,348)(41,349)(42,350)(43,351)(44,352)(45,56)(46,57)(47,58)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(89,145)(90,146)(91,147)(92,148)(93,149)(94,150)(95,151)(96,152)(97,153)(98,154)(99,144)(111,162)(112,163)(113,164)(114,165)(115,155)(116,156)(117,157)(118,158)(119,159)(120,160)(121,161)(122,133)(123,134)(124,135)(125,136)(126,137)(127,138)(128,139)(129,140)(130,141)(131,142)(132,143)(166,196)(167,197)(168,198)(169,188)(170,189)(171,190)(172,191)(173,192)(174,193)(175,194)(176,195)(177,233)(178,234)(179,235)(180,236)(181,237)(182,238)(183,239)(184,240)(185,241)(186,242)(187,232)(199,250)(200,251)(201,252)(202,253)(203,243)(204,244)(205,245)(206,246)(207,247)(208,248)(209,249)(210,221)(211,222)(212,223)(213,224)(214,225)(215,226)(216,227)(217,228)(218,229)(219,230)(220,231)(254,284)(255,285)(256,286)(257,276)(258,277)(259,278)(260,279)(261,280)(262,281)(263,282)(264,283)(265,321)(266,322)(267,323)(268,324)(269,325)(270,326)(271,327)(272,328)(273,329)(274,330)(275,320)(287,338)(288,339)(289,340)(290,341)(291,331)(292,332)(293,333)(294,334)(295,335)(296,336)(297,337)(298,309)(299,310)(300,311)(301,312)(302,313)(303,314)(304,315)(305,316)(306,317)(307,318)(308,319), (1,246,158,221,133,186,98,196)(2,247,159,222,134,187,99,197)(3,248,160,223,135,177,89,198)(4,249,161,224,136,178,90,188)(5,250,162,225,137,179,91,189)(6,251,163,226,138,180,92,190)(7,252,164,227,139,181,93,191)(8,253,165,228,140,182,94,192)(9,243,155,229,141,183,95,193)(10,244,156,230,142,184,96,194)(11,245,157,231,143,185,97,195)(12,313,74,338,59,277,38,267)(13,314,75,339,60,278,39,268)(14,315,76,340,61,279,40,269)(15,316,77,341,62,280,41,270)(16,317,67,331,63,281,42,271)(17,318,68,332,64,282,43,272)(18,319,69,333,65,283,44,273)(19,309,70,334,66,284,34,274)(20,310,71,335,56,285,35,275)(21,311,72,336,57,286,36,265)(22,312,73,337,58,276,37,266)(23,287,48,258,346,323,84,302)(24,288,49,259,347,324,85,303)(25,289,50,260,348,325,86,304)(26,290,51,261,349,326,87,305)(27,291,52,262,350,327,88,306)(28,292,53,263,351,328,78,307)(29,293,54,264,352,329,79,308)(30,294,55,254,342,330,80,298)(31,295,45,255,343,320,81,299)(32,296,46,256,344,321,82,300)(33,297,47,257,345,322,83,301)(100,204,116,219,131,240,152,175)(101,205,117,220,132,241,153,176)(102,206,118,210,122,242,154,166)(103,207,119,211,123,232,144,167)(104,208,120,212,124,233,145,168)(105,209,121,213,125,234,146,169)(106,199,111,214,126,235,147,170)(107,200,112,215,127,236,148,171)(108,201,113,216,128,237,149,172)(109,202,114,217,129,238,150,173)(110,203,115,218,130,239,151,174), (1,55,102,66)(2,45,103,56)(3,46,104,57)(4,47,105,58)(5,48,106,59)(6,49,107,60)(7,50,108,61)(8,51,109,62)(9,52,110,63)(10,53,100,64)(11,54,101,65)(12,137,84,126)(13,138,85,127)(14,139,86,128)(15,140,87,129)(16,141,88,130)(17,142,78,131)(18,143,79,132)(19,133,80,122)(20,134,81,123)(21,135,82,124)(22,136,83,125)(23,111,74,162)(24,112,75,163)(25,113,76,164)(26,114,77,165)(27,115,67,155)(28,116,68,156)(29,117,69,157)(30,118,70,158)(31,119,71,159)(32,120,72,160)(33,121,73,161)(34,98,342,154)(35,99,343,144)(36,89,344,145)(37,90,345,146)(38,91,346,147)(39,92,347,148)(40,93,348,149)(41,94,349,150)(42,95,350,151)(43,96,351,152)(44,97,352,153)(166,284,196,254)(167,285,197,255)(168,286,198,256)(169,276,188,257)(170,277,189,258)(171,278,190,259)(172,279,191,260)(173,280,192,261)(174,281,193,262)(175,282,194,263)(176,283,195,264)(177,321,233,265)(178,322,234,266)(179,323,235,267)(180,324,236,268)(181,325,237,269)(182,326,238,270)(183,327,239,271)(184,328,240,272)(185,329,241,273)(186,330,242,274)(187,320,232,275)(199,338,250,287)(200,339,251,288)(201,340,252,289)(202,341,253,290)(203,331,243,291)(204,332,244,292)(205,333,245,293)(206,334,246,294)(207,335,247,295)(208,336,248,296)(209,337,249,297)(210,309,221,298)(211,310,222,299)(212,311,223,300)(213,312,224,301)(214,313,225,302)(215,314,226,303)(216,315,227,304)(217,316,228,305)(218,317,229,306)(219,318,230,307)(220,319,231,308)>;
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), (1,102)(2,103)(3,104)(4,105)(5,106)(6,107)(7,108)(8,109)(9,110)(10,100)(11,101)(12,84)(13,85)(14,86)(15,87)(16,88)(17,78)(18,79)(19,80)(20,81)(21,82)(22,83)(23,74)(24,75)(25,76)(26,77)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,342)(35,343)(36,344)(37,345)(38,346)(39,347)(40,348)(41,349)(42,350)(43,351)(44,352)(45,56)(46,57)(47,58)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(89,145)(90,146)(91,147)(92,148)(93,149)(94,150)(95,151)(96,152)(97,153)(98,154)(99,144)(111,162)(112,163)(113,164)(114,165)(115,155)(116,156)(117,157)(118,158)(119,159)(120,160)(121,161)(122,133)(123,134)(124,135)(125,136)(126,137)(127,138)(128,139)(129,140)(130,141)(131,142)(132,143)(166,196)(167,197)(168,198)(169,188)(170,189)(171,190)(172,191)(173,192)(174,193)(175,194)(176,195)(177,233)(178,234)(179,235)(180,236)(181,237)(182,238)(183,239)(184,240)(185,241)(186,242)(187,232)(199,250)(200,251)(201,252)(202,253)(203,243)(204,244)(205,245)(206,246)(207,247)(208,248)(209,249)(210,221)(211,222)(212,223)(213,224)(214,225)(215,226)(216,227)(217,228)(218,229)(219,230)(220,231)(254,284)(255,285)(256,286)(257,276)(258,277)(259,278)(260,279)(261,280)(262,281)(263,282)(264,283)(265,321)(266,322)(267,323)(268,324)(269,325)(270,326)(271,327)(272,328)(273,329)(274,330)(275,320)(287,338)(288,339)(289,340)(290,341)(291,331)(292,332)(293,333)(294,334)(295,335)(296,336)(297,337)(298,309)(299,310)(300,311)(301,312)(302,313)(303,314)(304,315)(305,316)(306,317)(307,318)(308,319), (1,246,158,221,133,186,98,196)(2,247,159,222,134,187,99,197)(3,248,160,223,135,177,89,198)(4,249,161,224,136,178,90,188)(5,250,162,225,137,179,91,189)(6,251,163,226,138,180,92,190)(7,252,164,227,139,181,93,191)(8,253,165,228,140,182,94,192)(9,243,155,229,141,183,95,193)(10,244,156,230,142,184,96,194)(11,245,157,231,143,185,97,195)(12,313,74,338,59,277,38,267)(13,314,75,339,60,278,39,268)(14,315,76,340,61,279,40,269)(15,316,77,341,62,280,41,270)(16,317,67,331,63,281,42,271)(17,318,68,332,64,282,43,272)(18,319,69,333,65,283,44,273)(19,309,70,334,66,284,34,274)(20,310,71,335,56,285,35,275)(21,311,72,336,57,286,36,265)(22,312,73,337,58,276,37,266)(23,287,48,258,346,323,84,302)(24,288,49,259,347,324,85,303)(25,289,50,260,348,325,86,304)(26,290,51,261,349,326,87,305)(27,291,52,262,350,327,88,306)(28,292,53,263,351,328,78,307)(29,293,54,264,352,329,79,308)(30,294,55,254,342,330,80,298)(31,295,45,255,343,320,81,299)(32,296,46,256,344,321,82,300)(33,297,47,257,345,322,83,301)(100,204,116,219,131,240,152,175)(101,205,117,220,132,241,153,176)(102,206,118,210,122,242,154,166)(103,207,119,211,123,232,144,167)(104,208,120,212,124,233,145,168)(105,209,121,213,125,234,146,169)(106,199,111,214,126,235,147,170)(107,200,112,215,127,236,148,171)(108,201,113,216,128,237,149,172)(109,202,114,217,129,238,150,173)(110,203,115,218,130,239,151,174), (1,55,102,66)(2,45,103,56)(3,46,104,57)(4,47,105,58)(5,48,106,59)(6,49,107,60)(7,50,108,61)(8,51,109,62)(9,52,110,63)(10,53,100,64)(11,54,101,65)(12,137,84,126)(13,138,85,127)(14,139,86,128)(15,140,87,129)(16,141,88,130)(17,142,78,131)(18,143,79,132)(19,133,80,122)(20,134,81,123)(21,135,82,124)(22,136,83,125)(23,111,74,162)(24,112,75,163)(25,113,76,164)(26,114,77,165)(27,115,67,155)(28,116,68,156)(29,117,69,157)(30,118,70,158)(31,119,71,159)(32,120,72,160)(33,121,73,161)(34,98,342,154)(35,99,343,144)(36,89,344,145)(37,90,345,146)(38,91,346,147)(39,92,347,148)(40,93,348,149)(41,94,349,150)(42,95,350,151)(43,96,351,152)(44,97,352,153)(166,284,196,254)(167,285,197,255)(168,286,198,256)(169,276,188,257)(170,277,189,258)(171,278,190,259)(172,279,191,260)(173,280,192,261)(174,281,193,262)(175,282,194,263)(176,283,195,264)(177,321,233,265)(178,322,234,266)(179,323,235,267)(180,324,236,268)(181,325,237,269)(182,326,238,270)(183,327,239,271)(184,328,240,272)(185,329,241,273)(186,330,242,274)(187,320,232,275)(199,338,250,287)(200,339,251,288)(201,340,252,289)(202,341,253,290)(203,331,243,291)(204,332,244,292)(205,333,245,293)(206,334,246,294)(207,335,247,295)(208,336,248,296)(209,337,249,297)(210,309,221,298)(211,310,222,299)(212,311,223,300)(213,312,224,301)(214,313,225,302)(215,314,226,303)(216,315,227,304)(217,316,228,305)(218,317,229,306)(219,318,230,307)(220,319,231,308) );
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)], [(1,102),(2,103),(3,104),(4,105),(5,106),(6,107),(7,108),(8,109),(9,110),(10,100),(11,101),(12,84),(13,85),(14,86),(15,87),(16,88),(17,78),(18,79),(19,80),(20,81),(21,82),(22,83),(23,74),(24,75),(25,76),(26,77),(27,67),(28,68),(29,69),(30,70),(31,71),(32,72),(33,73),(34,342),(35,343),(36,344),(37,345),(38,346),(39,347),(40,348),(41,349),(42,350),(43,351),(44,352),(45,56),(46,57),(47,58),(48,59),(49,60),(50,61),(51,62),(52,63),(53,64),(54,65),(55,66),(89,145),(90,146),(91,147),(92,148),(93,149),(94,150),(95,151),(96,152),(97,153),(98,154),(99,144),(111,162),(112,163),(113,164),(114,165),(115,155),(116,156),(117,157),(118,158),(119,159),(120,160),(121,161),(122,133),(123,134),(124,135),(125,136),(126,137),(127,138),(128,139),(129,140),(130,141),(131,142),(132,143),(166,196),(167,197),(168,198),(169,188),(170,189),(171,190),(172,191),(173,192),(174,193),(175,194),(176,195),(177,233),(178,234),(179,235),(180,236),(181,237),(182,238),(183,239),(184,240),(185,241),(186,242),(187,232),(199,250),(200,251),(201,252),(202,253),(203,243),(204,244),(205,245),(206,246),(207,247),(208,248),(209,249),(210,221),(211,222),(212,223),(213,224),(214,225),(215,226),(216,227),(217,228),(218,229),(219,230),(220,231),(254,284),(255,285),(256,286),(257,276),(258,277),(259,278),(260,279),(261,280),(262,281),(263,282),(264,283),(265,321),(266,322),(267,323),(268,324),(269,325),(270,326),(271,327),(272,328),(273,329),(274,330),(275,320),(287,338),(288,339),(289,340),(290,341),(291,331),(292,332),(293,333),(294,334),(295,335),(296,336),(297,337),(298,309),(299,310),(300,311),(301,312),(302,313),(303,314),(304,315),(305,316),(306,317),(307,318),(308,319)], [(1,246,158,221,133,186,98,196),(2,247,159,222,134,187,99,197),(3,248,160,223,135,177,89,198),(4,249,161,224,136,178,90,188),(5,250,162,225,137,179,91,189),(6,251,163,226,138,180,92,190),(7,252,164,227,139,181,93,191),(8,253,165,228,140,182,94,192),(9,243,155,229,141,183,95,193),(10,244,156,230,142,184,96,194),(11,245,157,231,143,185,97,195),(12,313,74,338,59,277,38,267),(13,314,75,339,60,278,39,268),(14,315,76,340,61,279,40,269),(15,316,77,341,62,280,41,270),(16,317,67,331,63,281,42,271),(17,318,68,332,64,282,43,272),(18,319,69,333,65,283,44,273),(19,309,70,334,66,284,34,274),(20,310,71,335,56,285,35,275),(21,311,72,336,57,286,36,265),(22,312,73,337,58,276,37,266),(23,287,48,258,346,323,84,302),(24,288,49,259,347,324,85,303),(25,289,50,260,348,325,86,304),(26,290,51,261,349,326,87,305),(27,291,52,262,350,327,88,306),(28,292,53,263,351,328,78,307),(29,293,54,264,352,329,79,308),(30,294,55,254,342,330,80,298),(31,295,45,255,343,320,81,299),(32,296,46,256,344,321,82,300),(33,297,47,257,345,322,83,301),(100,204,116,219,131,240,152,175),(101,205,117,220,132,241,153,176),(102,206,118,210,122,242,154,166),(103,207,119,211,123,232,144,167),(104,208,120,212,124,233,145,168),(105,209,121,213,125,234,146,169),(106,199,111,214,126,235,147,170),(107,200,112,215,127,236,148,171),(108,201,113,216,128,237,149,172),(109,202,114,217,129,238,150,173),(110,203,115,218,130,239,151,174)], [(1,55,102,66),(2,45,103,56),(3,46,104,57),(4,47,105,58),(5,48,106,59),(6,49,107,60),(7,50,108,61),(8,51,109,62),(9,52,110,63),(10,53,100,64),(11,54,101,65),(12,137,84,126),(13,138,85,127),(14,139,86,128),(15,140,87,129),(16,141,88,130),(17,142,78,131),(18,143,79,132),(19,133,80,122),(20,134,81,123),(21,135,82,124),(22,136,83,125),(23,111,74,162),(24,112,75,163),(25,113,76,164),(26,114,77,165),(27,115,67,155),(28,116,68,156),(29,117,69,157),(30,118,70,158),(31,119,71,159),(32,120,72,160),(33,121,73,161),(34,98,342,154),(35,99,343,144),(36,89,344,145),(37,90,345,146),(38,91,346,147),(39,92,347,148),(40,93,348,149),(41,94,349,150),(42,95,350,151),(43,96,351,152),(44,97,352,153),(166,284,196,254),(167,285,197,255),(168,286,198,256),(169,276,188,257),(170,277,189,258),(171,278,190,259),(172,279,191,260),(173,280,192,261),(174,281,193,262),(175,282,194,263),(176,283,195,264),(177,321,233,265),(178,322,234,266),(179,323,235,267),(180,324,236,268),(181,325,237,269),(182,326,238,270),(183,327,239,271),(184,328,240,272),(185,329,241,273),(186,330,242,274),(187,320,232,275),(199,338,250,287),(200,339,251,288),(201,340,252,289),(202,341,253,290),(203,331,243,291),(204,332,244,292),(205,333,245,293),(206,334,246,294),(207,335,247,295),(208,336,248,296),(209,337,249,297),(210,309,221,298),(211,310,222,299),(212,311,223,300),(213,312,224,301),(214,313,225,302),(215,314,226,303),(216,315,227,304),(217,316,228,305),(218,317,229,306),(219,318,230,307),(220,319,231,308)]])
154 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 8A | 8B | 8C | 8D | 11A | ··· | 11J | 22A | ··· | 22AD | 44A | ··· | 44T | 44U | ··· | 44BH | 88A | ··· | 88AN |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 | 44 | ··· | 44 | 88 | ··· | 88 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 |
154 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | + | + | - | |||||||||
| image | C1 | C2 | C2 | C4 | C11 | C22 | C22 | C44 | Q8 | D4 | D8 | Q16 | Q8×C11 | D4×C11 | C11×D8 | C11×Q16 |
| kernel | C11×C2.D8 | C11×C4⋊C4 | C2×C88 | C88 | C2.D8 | C4⋊C4 | C2×C8 | C8 | C44 | C2×C22 | C22 | C22 | C4 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 10 | 20 | 10 | 40 | 1 | 1 | 2 | 2 | 10 | 10 | 20 | 20 |
Matrix representation of C11×C2.D8 ►in GL4(𝔽89) generated by
| 64 | 0 | 0 | 0 |
| 0 | 64 | 0 | 0 |
| 0 | 0 | 39 | 0 |
| 0 | 0 | 0 | 39 |
| 88 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 88 | 87 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 64 |
| 0 | 0 | 57 | 64 |
| 25 | 4 | 0 | 0 |
| 66 | 64 | 0 | 0 |
| 0 | 0 | 87 | 42 |
| 0 | 0 | 19 | 2 |
G:=sub<GL(4,GF(89))| [64,0,0,0,0,64,0,0,0,0,39,0,0,0,0,39],[88,0,0,0,0,88,0,0,0,0,1,0,0,0,0,1],[88,1,0,0,87,1,0,0,0,0,0,57,0,0,64,64],[25,66,0,0,4,64,0,0,0,0,87,19,0,0,42,2] >;
C11×C2.D8 in GAP, Magma, Sage, TeX
C_{11}\times C_2.D_8 % in TeX
G:=Group("C11xC2.D8"); // GroupNames label
G:=SmallGroup(352,56);
// by ID
G=gap.SmallGroup(352,56);
# by ID
G:=PCGroup([6,-2,-2,-11,-2,-2,-2,528,553,1327,5283,117]);
// Polycyclic
G:=Group<a,b,c,d|a^11=b^2=c^8=1,d^2=b,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations
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