direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C11⋊C16, C22⋊C16, C44.3C8, C88.3C4, C8.21D22, C8.4Dic11, C88.21C22, C11⋊2(C2×C16), C4.3(C11⋊C8), (C2×C88).9C2, C22.8(C2×C8), (C2×C22).2C8, (C2×C8).9D11, C44.38(C2×C4), (C2×C44).11C4, C22.2(C11⋊C8), (C2×C4).8Dic11, C4.10(C2×Dic11), C2.2(C2×C11⋊C8), SmallGroup(352,17)
Series: Derived ►Chief ►Lower central ►Upper central
| C11 — C2×C11⋊C16 |
Generators and relations for C2×C11⋊C16
G = < a,b,c | a2=b11=c16=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×C11⋊C16
►Regular action on 352 points
Generators in S352
(1 84)(2 85)(3 86)(4 87)(5 88)(6 89)(7 90)(8 91)(9 92)(10 93)(11 94)(12 95)(13 96)(14 81)(15 82)(16 83)(17 262)(18 263)(19 264)(20 265)(21 266)(22 267)(23 268)(24 269)(25 270)(26 271)(27 272)(28 257)(29 258)(30 259)(31 260)(32 261)(33 314)(34 315)(35 316)(36 317)(37 318)(38 319)(39 320)(40 305)(41 306)(42 307)(43 308)(44 309)(45 310)(46 311)(47 312)(48 313)(49 185)(50 186)(51 187)(52 188)(53 189)(54 190)(55 191)(56 192)(57 177)(58 178)(59 179)(60 180)(61 181)(62 182)(63 183)(64 184)(65 237)(66 238)(67 239)(68 240)(69 225)(70 226)(71 227)(72 228)(73 229)(74 230)(75 231)(76 232)(77 233)(78 234)(79 235)(80 236)(97 273)(98 274)(99 275)(100 276)(101 277)(102 278)(103 279)(104 280)(105 281)(106 282)(107 283)(108 284)(109 285)(110 286)(111 287)(112 288)(113 137)(114 138)(115 139)(116 140)(117 141)(118 142)(119 143)(120 144)(121 129)(122 130)(123 131)(124 132)(125 133)(126 134)(127 135)(128 136)(145 204)(146 205)(147 206)(148 207)(149 208)(150 193)(151 194)(152 195)(153 196)(154 197)(155 198)(156 199)(157 200)(158 201)(159 202)(160 203)(161 244)(162 245)(163 246)(164 247)(165 248)(166 249)(167 250)(168 251)(169 252)(170 253)(171 254)(172 255)(173 256)(174 241)(175 242)(176 243)(209 352)(210 337)(211 338)(212 339)(213 340)(214 341)(215 342)(216 343)(217 344)(218 345)(219 346)(220 347)(221 348)(222 349)(223 350)(224 351)(289 327)(290 328)(291 329)(292 330)(293 331)(294 332)(295 333)(296 334)(297 335)(298 336)(299 321)(300 322)(301 323)(302 324)(303 325)(304 326)
(1 111 155 173 218 57 237 20 315 332 129)(2 130 333 316 21 238 58 219 174 156 112)(3 97 157 175 220 59 239 22 317 334 131)(4 132 335 318 23 240 60 221 176 158 98)(5 99 159 161 222 61 225 24 319 336 133)(6 134 321 320 25 226 62 223 162 160 100)(7 101 145 163 224 63 227 26 305 322 135)(8 136 323 306 27 228 64 209 164 146 102)(9 103 147 165 210 49 229 28 307 324 137)(10 138 325 308 29 230 50 211 166 148 104)(11 105 149 167 212 51 231 30 309 326 139)(12 140 327 310 31 232 52 213 168 150 106)(13 107 151 169 214 53 233 32 311 328 141)(14 142 329 312 17 234 54 215 170 152 108)(15 109 153 171 216 55 235 18 313 330 143)(16 144 331 314 19 236 56 217 172 154 110)(33 264 80 192 344 255 197 286 83 120 293)(34 294 121 84 287 198 256 345 177 65 265)(35 266 66 178 346 241 199 288 85 122 295)(36 296 123 86 273 200 242 347 179 67 267)(37 268 68 180 348 243 201 274 87 124 297)(38 298 125 88 275 202 244 349 181 69 269)(39 270 70 182 350 245 203 276 89 126 299)(40 300 127 90 277 204 246 351 183 71 271)(41 272 72 184 352 247 205 278 91 128 301)(42 302 113 92 279 206 248 337 185 73 257)(43 258 74 186 338 249 207 280 93 114 303)(44 304 115 94 281 208 250 339 187 75 259)(45 260 76 188 340 251 193 282 95 116 289)(46 290 117 96 283 194 252 341 189 77 261)(47 262 78 190 342 253 195 284 81 118 291)(48 292 119 82 285 196 254 343 191 79 263)
(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)
G:=sub<Sym(352)| (1,84)(2,85)(3,86)(4,87)(5,88)(6,89)(7,90)(8,91)(9,92)(10,93)(11,94)(12,95)(13,96)(14,81)(15,82)(16,83)(17,262)(18,263)(19,264)(20,265)(21,266)(22,267)(23,268)(24,269)(25,270)(26,271)(27,272)(28,257)(29,258)(30,259)(31,260)(32,261)(33,314)(34,315)(35,316)(36,317)(37,318)(38,319)(39,320)(40,305)(41,306)(42,307)(43,308)(44,309)(45,310)(46,311)(47,312)(48,313)(49,185)(50,186)(51,187)(52,188)(53,189)(54,190)(55,191)(56,192)(57,177)(58,178)(59,179)(60,180)(61,181)(62,182)(63,183)(64,184)(65,237)(66,238)(67,239)(68,240)(69,225)(70,226)(71,227)(72,228)(73,229)(74,230)(75,231)(76,232)(77,233)(78,234)(79,235)(80,236)(97,273)(98,274)(99,275)(100,276)(101,277)(102,278)(103,279)(104,280)(105,281)(106,282)(107,283)(108,284)(109,285)(110,286)(111,287)(112,288)(113,137)(114,138)(115,139)(116,140)(117,141)(118,142)(119,143)(120,144)(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)(145,204)(146,205)(147,206)(148,207)(149,208)(150,193)(151,194)(152,195)(153,196)(154,197)(155,198)(156,199)(157,200)(158,201)(159,202)(160,203)(161,244)(162,245)(163,246)(164,247)(165,248)(166,249)(167,250)(168,251)(169,252)(170,253)(171,254)(172,255)(173,256)(174,241)(175,242)(176,243)(209,352)(210,337)(211,338)(212,339)(213,340)(214,341)(215,342)(216,343)(217,344)(218,345)(219,346)(220,347)(221,348)(222,349)(223,350)(224,351)(289,327)(290,328)(291,329)(292,330)(293,331)(294,332)(295,333)(296,334)(297,335)(298,336)(299,321)(300,322)(301,323)(302,324)(303,325)(304,326), (1,111,155,173,218,57,237,20,315,332,129)(2,130,333,316,21,238,58,219,174,156,112)(3,97,157,175,220,59,239,22,317,334,131)(4,132,335,318,23,240,60,221,176,158,98)(5,99,159,161,222,61,225,24,319,336,133)(6,134,321,320,25,226,62,223,162,160,100)(7,101,145,163,224,63,227,26,305,322,135)(8,136,323,306,27,228,64,209,164,146,102)(9,103,147,165,210,49,229,28,307,324,137)(10,138,325,308,29,230,50,211,166,148,104)(11,105,149,167,212,51,231,30,309,326,139)(12,140,327,310,31,232,52,213,168,150,106)(13,107,151,169,214,53,233,32,311,328,141)(14,142,329,312,17,234,54,215,170,152,108)(15,109,153,171,216,55,235,18,313,330,143)(16,144,331,314,19,236,56,217,172,154,110)(33,264,80,192,344,255,197,286,83,120,293)(34,294,121,84,287,198,256,345,177,65,265)(35,266,66,178,346,241,199,288,85,122,295)(36,296,123,86,273,200,242,347,179,67,267)(37,268,68,180,348,243,201,274,87,124,297)(38,298,125,88,275,202,244,349,181,69,269)(39,270,70,182,350,245,203,276,89,126,299)(40,300,127,90,277,204,246,351,183,71,271)(41,272,72,184,352,247,205,278,91,128,301)(42,302,113,92,279,206,248,337,185,73,257)(43,258,74,186,338,249,207,280,93,114,303)(44,304,115,94,281,208,250,339,187,75,259)(45,260,76,188,340,251,193,282,95,116,289)(46,290,117,96,283,194,252,341,189,77,261)(47,262,78,190,342,253,195,284,81,118,291)(48,292,119,82,285,196,254,343,191,79,263), (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)>;
G:=Group( (1,84)(2,85)(3,86)(4,87)(5,88)(6,89)(7,90)(8,91)(9,92)(10,93)(11,94)(12,95)(13,96)(14,81)(15,82)(16,83)(17,262)(18,263)(19,264)(20,265)(21,266)(22,267)(23,268)(24,269)(25,270)(26,271)(27,272)(28,257)(29,258)(30,259)(31,260)(32,261)(33,314)(34,315)(35,316)(36,317)(37,318)(38,319)(39,320)(40,305)(41,306)(42,307)(43,308)(44,309)(45,310)(46,311)(47,312)(48,313)(49,185)(50,186)(51,187)(52,188)(53,189)(54,190)(55,191)(56,192)(57,177)(58,178)(59,179)(60,180)(61,181)(62,182)(63,183)(64,184)(65,237)(66,238)(67,239)(68,240)(69,225)(70,226)(71,227)(72,228)(73,229)(74,230)(75,231)(76,232)(77,233)(78,234)(79,235)(80,236)(97,273)(98,274)(99,275)(100,276)(101,277)(102,278)(103,279)(104,280)(105,281)(106,282)(107,283)(108,284)(109,285)(110,286)(111,287)(112,288)(113,137)(114,138)(115,139)(116,140)(117,141)(118,142)(119,143)(120,144)(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)(145,204)(146,205)(147,206)(148,207)(149,208)(150,193)(151,194)(152,195)(153,196)(154,197)(155,198)(156,199)(157,200)(158,201)(159,202)(160,203)(161,244)(162,245)(163,246)(164,247)(165,248)(166,249)(167,250)(168,251)(169,252)(170,253)(171,254)(172,255)(173,256)(174,241)(175,242)(176,243)(209,352)(210,337)(211,338)(212,339)(213,340)(214,341)(215,342)(216,343)(217,344)(218,345)(219,346)(220,347)(221,348)(222,349)(223,350)(224,351)(289,327)(290,328)(291,329)(292,330)(293,331)(294,332)(295,333)(296,334)(297,335)(298,336)(299,321)(300,322)(301,323)(302,324)(303,325)(304,326), (1,111,155,173,218,57,237,20,315,332,129)(2,130,333,316,21,238,58,219,174,156,112)(3,97,157,175,220,59,239,22,317,334,131)(4,132,335,318,23,240,60,221,176,158,98)(5,99,159,161,222,61,225,24,319,336,133)(6,134,321,320,25,226,62,223,162,160,100)(7,101,145,163,224,63,227,26,305,322,135)(8,136,323,306,27,228,64,209,164,146,102)(9,103,147,165,210,49,229,28,307,324,137)(10,138,325,308,29,230,50,211,166,148,104)(11,105,149,167,212,51,231,30,309,326,139)(12,140,327,310,31,232,52,213,168,150,106)(13,107,151,169,214,53,233,32,311,328,141)(14,142,329,312,17,234,54,215,170,152,108)(15,109,153,171,216,55,235,18,313,330,143)(16,144,331,314,19,236,56,217,172,154,110)(33,264,80,192,344,255,197,286,83,120,293)(34,294,121,84,287,198,256,345,177,65,265)(35,266,66,178,346,241,199,288,85,122,295)(36,296,123,86,273,200,242,347,179,67,267)(37,268,68,180,348,243,201,274,87,124,297)(38,298,125,88,275,202,244,349,181,69,269)(39,270,70,182,350,245,203,276,89,126,299)(40,300,127,90,277,204,246,351,183,71,271)(41,272,72,184,352,247,205,278,91,128,301)(42,302,113,92,279,206,248,337,185,73,257)(43,258,74,186,338,249,207,280,93,114,303)(44,304,115,94,281,208,250,339,187,75,259)(45,260,76,188,340,251,193,282,95,116,289)(46,290,117,96,283,194,252,341,189,77,261)(47,262,78,190,342,253,195,284,81,118,291)(48,292,119,82,285,196,254,343,191,79,263), (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) );
G=PermutationGroup([[(1,84),(2,85),(3,86),(4,87),(5,88),(6,89),(7,90),(8,91),(9,92),(10,93),(11,94),(12,95),(13,96),(14,81),(15,82),(16,83),(17,262),(18,263),(19,264),(20,265),(21,266),(22,267),(23,268),(24,269),(25,270),(26,271),(27,272),(28,257),(29,258),(30,259),(31,260),(32,261),(33,314),(34,315),(35,316),(36,317),(37,318),(38,319),(39,320),(40,305),(41,306),(42,307),(43,308),(44,309),(45,310),(46,311),(47,312),(48,313),(49,185),(50,186),(51,187),(52,188),(53,189),(54,190),(55,191),(56,192),(57,177),(58,178),(59,179),(60,180),(61,181),(62,182),(63,183),(64,184),(65,237),(66,238),(67,239),(68,240),(69,225),(70,226),(71,227),(72,228),(73,229),(74,230),(75,231),(76,232),(77,233),(78,234),(79,235),(80,236),(97,273),(98,274),(99,275),(100,276),(101,277),(102,278),(103,279),(104,280),(105,281),(106,282),(107,283),(108,284),(109,285),(110,286),(111,287),(112,288),(113,137),(114,138),(115,139),(116,140),(117,141),(118,142),(119,143),(120,144),(121,129),(122,130),(123,131),(124,132),(125,133),(126,134),(127,135),(128,136),(145,204),(146,205),(147,206),(148,207),(149,208),(150,193),(151,194),(152,195),(153,196),(154,197),(155,198),(156,199),(157,200),(158,201),(159,202),(160,203),(161,244),(162,245),(163,246),(164,247),(165,248),(166,249),(167,250),(168,251),(169,252),(170,253),(171,254),(172,255),(173,256),(174,241),(175,242),(176,243),(209,352),(210,337),(211,338),(212,339),(213,340),(214,341),(215,342),(216,343),(217,344),(218,345),(219,346),(220,347),(221,348),(222,349),(223,350),(224,351),(289,327),(290,328),(291,329),(292,330),(293,331),(294,332),(295,333),(296,334),(297,335),(298,336),(299,321),(300,322),(301,323),(302,324),(303,325),(304,326)], [(1,111,155,173,218,57,237,20,315,332,129),(2,130,333,316,21,238,58,219,174,156,112),(3,97,157,175,220,59,239,22,317,334,131),(4,132,335,318,23,240,60,221,176,158,98),(5,99,159,161,222,61,225,24,319,336,133),(6,134,321,320,25,226,62,223,162,160,100),(7,101,145,163,224,63,227,26,305,322,135),(8,136,323,306,27,228,64,209,164,146,102),(9,103,147,165,210,49,229,28,307,324,137),(10,138,325,308,29,230,50,211,166,148,104),(11,105,149,167,212,51,231,30,309,326,139),(12,140,327,310,31,232,52,213,168,150,106),(13,107,151,169,214,53,233,32,311,328,141),(14,142,329,312,17,234,54,215,170,152,108),(15,109,153,171,216,55,235,18,313,330,143),(16,144,331,314,19,236,56,217,172,154,110),(33,264,80,192,344,255,197,286,83,120,293),(34,294,121,84,287,198,256,345,177,65,265),(35,266,66,178,346,241,199,288,85,122,295),(36,296,123,86,273,200,242,347,179,67,267),(37,268,68,180,348,243,201,274,87,124,297),(38,298,125,88,275,202,244,349,181,69,269),(39,270,70,182,350,245,203,276,89,126,299),(40,300,127,90,277,204,246,351,183,71,271),(41,272,72,184,352,247,205,278,91,128,301),(42,302,113,92,279,206,248,337,185,73,257),(43,258,74,186,338,249,207,280,93,114,303),(44,304,115,94,281,208,250,339,187,75,259),(45,260,76,188,340,251,193,282,95,116,289),(46,290,117,96,283,194,252,341,189,77,261),(47,262,78,190,342,253,195,284,81,118,291),(48,292,119,82,285,196,254,343,191,79,263)], [(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)]])
112 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 8A | ··· | 8H | 11A | ··· | 11E | 16A | ··· | 16P | 22A | ··· | 22O | 44A | ··· | 44T | 88A | ··· | 88AN |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 11 | ··· | 11 | 16 | ··· | 16 | 22 | ··· | 22 | 44 | ··· | 44 | 88 | ··· | 88 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 11 | ··· | 11 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
112 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | ||||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | C8 | C16 | D11 | Dic11 | D22 | Dic11 | C11⋊C8 | C11⋊C8 | C11⋊C16 |
| kernel | C2×C11⋊C16 | C11⋊C16 | C2×C88 | C88 | C2×C44 | C44 | C2×C22 | C22 | C2×C8 | C8 | C8 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 4 | 4 | 16 | 5 | 5 | 5 | 5 | 10 | 10 | 40 |
Matrix representation of C2×C11⋊C16 ►in GL3(𝔽353) generated by
| 352 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
| 1 | 0 | 0 |
| 0 | 34 | 352 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 0 | 19 | 46 |
| 0 | 339 | 334 |
G:=sub<GL(3,GF(353))| [352,0,0,0,1,0,0,0,1],[1,0,0,0,34,1,0,352,0],[1,0,0,0,19,339,0,46,334] >;
C2×C11⋊C16 in GAP, Magma, Sage, TeX
C_2\times C_{11}\rtimes C_{16} % in TeX
G:=Group("C2xC11:C16"); // GroupNames label
G:=SmallGroup(352,17);
// by ID
G=gap.SmallGroup(352,17);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,24,50,69,11525]);
// Polycyclic
G:=Group<a,b,c|a^2=b^11=c^16=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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