metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C11⋊2Q32, C44.6D4, C8.7D22, Q16.D11, C22.11D8, C88.5C22, Dic44.2C2, C11⋊C16.C2, C2.7(D4⋊D11), C4.4(C11⋊D4), (C11×Q16).1C2, SmallGroup(352,35)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C11⋊Q32
G = < a,b,c | a11=b16=1, c2=b8, bab-1=a-1, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C11⋊Q32
►Regular action on 352 points
Generators in S352
(1 324 310 98 60 221 267 274 26 290 45)(2 46 291 27 275 268 222 61 99 311 325)(3 326 312 100 62 223 269 276 28 292 47)(4 48 293 29 277 270 224 63 101 313 327)(5 328 314 102 64 209 271 278 30 294 33)(6 34 295 31 279 272 210 49 103 315 329)(7 330 316 104 50 211 257 280 32 296 35)(8 36 297 17 281 258 212 51 105 317 331)(9 332 318 106 52 213 259 282 18 298 37)(10 38 299 19 283 260 214 53 107 319 333)(11 334 320 108 54 215 261 284 20 300 39)(12 40 301 21 285 262 216 55 109 305 335)(13 336 306 110 56 217 263 286 22 302 41)(14 42 303 23 287 264 218 57 111 307 321)(15 322 308 112 58 219 265 288 24 304 43)(16 44 289 25 273 266 220 59 97 309 323)(65 178 145 129 206 115 252 82 239 170 337)(66 338 171 240 83 253 116 207 130 146 179)(67 180 147 131 208 117 254 84 225 172 339)(68 340 173 226 85 255 118 193 132 148 181)(69 182 149 133 194 119 256 86 227 174 341)(70 342 175 228 87 241 120 195 134 150 183)(71 184 151 135 196 121 242 88 229 176 343)(72 344 161 230 89 243 122 197 136 152 185)(73 186 153 137 198 123 244 90 231 162 345)(74 346 163 232 91 245 124 199 138 154 187)(75 188 155 139 200 125 246 92 233 164 347)(76 348 165 234 93 247 126 201 140 156 189)(77 190 157 141 202 127 248 94 235 166 349)(78 350 167 236 95 249 128 203 142 158 191)(79 192 159 143 204 113 250 96 237 168 351)(80 352 169 238 81 251 114 205 144 160 177)
(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)
(1 145 9 153)(2 160 10 152)(3 159 11 151)(4 158 12 150)(5 157 13 149)(6 156 14 148)(7 155 15 147)(8 154 16 146)(17 346 25 338)(18 345 26 337)(19 344 27 352)(20 343 28 351)(21 342 29 350)(22 341 30 349)(23 340 31 348)(24 339 32 347)(33 190 41 182)(34 189 42 181)(35 188 43 180)(36 187 44 179)(37 186 45 178)(38 185 46 177)(39 184 47 192)(40 183 48 191)(49 247 57 255)(50 246 58 254)(51 245 59 253)(52 244 60 252)(53 243 61 251)(54 242 62 250)(55 241 63 249)(56 256 64 248)(65 298 73 290)(66 297 74 289)(67 296 75 304)(68 295 76 303)(69 294 77 302)(70 293 78 301)(71 292 79 300)(72 291 80 299)(81 214 89 222)(82 213 90 221)(83 212 91 220)(84 211 92 219)(85 210 93 218)(86 209 94 217)(87 224 95 216)(88 223 96 215)(97 116 105 124)(98 115 106 123)(99 114 107 122)(100 113 108 121)(101 128 109 120)(102 127 110 119)(103 126 111 118)(104 125 112 117)(129 332 137 324)(130 331 138 323)(131 330 139 322)(132 329 140 321)(133 328 141 336)(134 327 142 335)(135 326 143 334)(136 325 144 333)(161 275 169 283)(162 274 170 282)(163 273 171 281)(164 288 172 280)(165 287 173 279)(166 286 174 278)(167 285 175 277)(168 284 176 276)(193 315 201 307)(194 314 202 306)(195 313 203 305)(196 312 204 320)(197 311 205 319)(198 310 206 318)(199 309 207 317)(200 308 208 316)(225 257 233 265)(226 272 234 264)(227 271 235 263)(228 270 236 262)(229 269 237 261)(230 268 238 260)(231 267 239 259)(232 266 240 258)
G:=sub<Sym(352)| (1,324,310,98,60,221,267,274,26,290,45)(2,46,291,27,275,268,222,61,99,311,325)(3,326,312,100,62,223,269,276,28,292,47)(4,48,293,29,277,270,224,63,101,313,327)(5,328,314,102,64,209,271,278,30,294,33)(6,34,295,31,279,272,210,49,103,315,329)(7,330,316,104,50,211,257,280,32,296,35)(8,36,297,17,281,258,212,51,105,317,331)(9,332,318,106,52,213,259,282,18,298,37)(10,38,299,19,283,260,214,53,107,319,333)(11,334,320,108,54,215,261,284,20,300,39)(12,40,301,21,285,262,216,55,109,305,335)(13,336,306,110,56,217,263,286,22,302,41)(14,42,303,23,287,264,218,57,111,307,321)(15,322,308,112,58,219,265,288,24,304,43)(16,44,289,25,273,266,220,59,97,309,323)(65,178,145,129,206,115,252,82,239,170,337)(66,338,171,240,83,253,116,207,130,146,179)(67,180,147,131,208,117,254,84,225,172,339)(68,340,173,226,85,255,118,193,132,148,181)(69,182,149,133,194,119,256,86,227,174,341)(70,342,175,228,87,241,120,195,134,150,183)(71,184,151,135,196,121,242,88,229,176,343)(72,344,161,230,89,243,122,197,136,152,185)(73,186,153,137,198,123,244,90,231,162,345)(74,346,163,232,91,245,124,199,138,154,187)(75,188,155,139,200,125,246,92,233,164,347)(76,348,165,234,93,247,126,201,140,156,189)(77,190,157,141,202,127,248,94,235,166,349)(78,350,167,236,95,249,128,203,142,158,191)(79,192,159,143,204,113,250,96,237,168,351)(80,352,169,238,81,251,114,205,144,160,177), (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), (1,145,9,153)(2,160,10,152)(3,159,11,151)(4,158,12,150)(5,157,13,149)(6,156,14,148)(7,155,15,147)(8,154,16,146)(17,346,25,338)(18,345,26,337)(19,344,27,352)(20,343,28,351)(21,342,29,350)(22,341,30,349)(23,340,31,348)(24,339,32,347)(33,190,41,182)(34,189,42,181)(35,188,43,180)(36,187,44,179)(37,186,45,178)(38,185,46,177)(39,184,47,192)(40,183,48,191)(49,247,57,255)(50,246,58,254)(51,245,59,253)(52,244,60,252)(53,243,61,251)(54,242,62,250)(55,241,63,249)(56,256,64,248)(65,298,73,290)(66,297,74,289)(67,296,75,304)(68,295,76,303)(69,294,77,302)(70,293,78,301)(71,292,79,300)(72,291,80,299)(81,214,89,222)(82,213,90,221)(83,212,91,220)(84,211,92,219)(85,210,93,218)(86,209,94,217)(87,224,95,216)(88,223,96,215)(97,116,105,124)(98,115,106,123)(99,114,107,122)(100,113,108,121)(101,128,109,120)(102,127,110,119)(103,126,111,118)(104,125,112,117)(129,332,137,324)(130,331,138,323)(131,330,139,322)(132,329,140,321)(133,328,141,336)(134,327,142,335)(135,326,143,334)(136,325,144,333)(161,275,169,283)(162,274,170,282)(163,273,171,281)(164,288,172,280)(165,287,173,279)(166,286,174,278)(167,285,175,277)(168,284,176,276)(193,315,201,307)(194,314,202,306)(195,313,203,305)(196,312,204,320)(197,311,205,319)(198,310,206,318)(199,309,207,317)(200,308,208,316)(225,257,233,265)(226,272,234,264)(227,271,235,263)(228,270,236,262)(229,269,237,261)(230,268,238,260)(231,267,239,259)(232,266,240,258)>;
G:=Group( (1,324,310,98,60,221,267,274,26,290,45)(2,46,291,27,275,268,222,61,99,311,325)(3,326,312,100,62,223,269,276,28,292,47)(4,48,293,29,277,270,224,63,101,313,327)(5,328,314,102,64,209,271,278,30,294,33)(6,34,295,31,279,272,210,49,103,315,329)(7,330,316,104,50,211,257,280,32,296,35)(8,36,297,17,281,258,212,51,105,317,331)(9,332,318,106,52,213,259,282,18,298,37)(10,38,299,19,283,260,214,53,107,319,333)(11,334,320,108,54,215,261,284,20,300,39)(12,40,301,21,285,262,216,55,109,305,335)(13,336,306,110,56,217,263,286,22,302,41)(14,42,303,23,287,264,218,57,111,307,321)(15,322,308,112,58,219,265,288,24,304,43)(16,44,289,25,273,266,220,59,97,309,323)(65,178,145,129,206,115,252,82,239,170,337)(66,338,171,240,83,253,116,207,130,146,179)(67,180,147,131,208,117,254,84,225,172,339)(68,340,173,226,85,255,118,193,132,148,181)(69,182,149,133,194,119,256,86,227,174,341)(70,342,175,228,87,241,120,195,134,150,183)(71,184,151,135,196,121,242,88,229,176,343)(72,344,161,230,89,243,122,197,136,152,185)(73,186,153,137,198,123,244,90,231,162,345)(74,346,163,232,91,245,124,199,138,154,187)(75,188,155,139,200,125,246,92,233,164,347)(76,348,165,234,93,247,126,201,140,156,189)(77,190,157,141,202,127,248,94,235,166,349)(78,350,167,236,95,249,128,203,142,158,191)(79,192,159,143,204,113,250,96,237,168,351)(80,352,169,238,81,251,114,205,144,160,177), (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), (1,145,9,153)(2,160,10,152)(3,159,11,151)(4,158,12,150)(5,157,13,149)(6,156,14,148)(7,155,15,147)(8,154,16,146)(17,346,25,338)(18,345,26,337)(19,344,27,352)(20,343,28,351)(21,342,29,350)(22,341,30,349)(23,340,31,348)(24,339,32,347)(33,190,41,182)(34,189,42,181)(35,188,43,180)(36,187,44,179)(37,186,45,178)(38,185,46,177)(39,184,47,192)(40,183,48,191)(49,247,57,255)(50,246,58,254)(51,245,59,253)(52,244,60,252)(53,243,61,251)(54,242,62,250)(55,241,63,249)(56,256,64,248)(65,298,73,290)(66,297,74,289)(67,296,75,304)(68,295,76,303)(69,294,77,302)(70,293,78,301)(71,292,79,300)(72,291,80,299)(81,214,89,222)(82,213,90,221)(83,212,91,220)(84,211,92,219)(85,210,93,218)(86,209,94,217)(87,224,95,216)(88,223,96,215)(97,116,105,124)(98,115,106,123)(99,114,107,122)(100,113,108,121)(101,128,109,120)(102,127,110,119)(103,126,111,118)(104,125,112,117)(129,332,137,324)(130,331,138,323)(131,330,139,322)(132,329,140,321)(133,328,141,336)(134,327,142,335)(135,326,143,334)(136,325,144,333)(161,275,169,283)(162,274,170,282)(163,273,171,281)(164,288,172,280)(165,287,173,279)(166,286,174,278)(167,285,175,277)(168,284,176,276)(193,315,201,307)(194,314,202,306)(195,313,203,305)(196,312,204,320)(197,311,205,319)(198,310,206,318)(199,309,207,317)(200,308,208,316)(225,257,233,265)(226,272,234,264)(227,271,235,263)(228,270,236,262)(229,269,237,261)(230,268,238,260)(231,267,239,259)(232,266,240,258) );
G=PermutationGroup([[(1,324,310,98,60,221,267,274,26,290,45),(2,46,291,27,275,268,222,61,99,311,325),(3,326,312,100,62,223,269,276,28,292,47),(4,48,293,29,277,270,224,63,101,313,327),(5,328,314,102,64,209,271,278,30,294,33),(6,34,295,31,279,272,210,49,103,315,329),(7,330,316,104,50,211,257,280,32,296,35),(8,36,297,17,281,258,212,51,105,317,331),(9,332,318,106,52,213,259,282,18,298,37),(10,38,299,19,283,260,214,53,107,319,333),(11,334,320,108,54,215,261,284,20,300,39),(12,40,301,21,285,262,216,55,109,305,335),(13,336,306,110,56,217,263,286,22,302,41),(14,42,303,23,287,264,218,57,111,307,321),(15,322,308,112,58,219,265,288,24,304,43),(16,44,289,25,273,266,220,59,97,309,323),(65,178,145,129,206,115,252,82,239,170,337),(66,338,171,240,83,253,116,207,130,146,179),(67,180,147,131,208,117,254,84,225,172,339),(68,340,173,226,85,255,118,193,132,148,181),(69,182,149,133,194,119,256,86,227,174,341),(70,342,175,228,87,241,120,195,134,150,183),(71,184,151,135,196,121,242,88,229,176,343),(72,344,161,230,89,243,122,197,136,152,185),(73,186,153,137,198,123,244,90,231,162,345),(74,346,163,232,91,245,124,199,138,154,187),(75,188,155,139,200,125,246,92,233,164,347),(76,348,165,234,93,247,126,201,140,156,189),(77,190,157,141,202,127,248,94,235,166,349),(78,350,167,236,95,249,128,203,142,158,191),(79,192,159,143,204,113,250,96,237,168,351),(80,352,169,238,81,251,114,205,144,160,177)], [(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)], [(1,145,9,153),(2,160,10,152),(3,159,11,151),(4,158,12,150),(5,157,13,149),(6,156,14,148),(7,155,15,147),(8,154,16,146),(17,346,25,338),(18,345,26,337),(19,344,27,352),(20,343,28,351),(21,342,29,350),(22,341,30,349),(23,340,31,348),(24,339,32,347),(33,190,41,182),(34,189,42,181),(35,188,43,180),(36,187,44,179),(37,186,45,178),(38,185,46,177),(39,184,47,192),(40,183,48,191),(49,247,57,255),(50,246,58,254),(51,245,59,253),(52,244,60,252),(53,243,61,251),(54,242,62,250),(55,241,63,249),(56,256,64,248),(65,298,73,290),(66,297,74,289),(67,296,75,304),(68,295,76,303),(69,294,77,302),(70,293,78,301),(71,292,79,300),(72,291,80,299),(81,214,89,222),(82,213,90,221),(83,212,91,220),(84,211,92,219),(85,210,93,218),(86,209,94,217),(87,224,95,216),(88,223,96,215),(97,116,105,124),(98,115,106,123),(99,114,107,122),(100,113,108,121),(101,128,109,120),(102,127,110,119),(103,126,111,118),(104,125,112,117),(129,332,137,324),(130,331,138,323),(131,330,139,322),(132,329,140,321),(133,328,141,336),(134,327,142,335),(135,326,143,334),(136,325,144,333),(161,275,169,283),(162,274,170,282),(163,273,171,281),(164,288,172,280),(165,287,173,279),(166,286,174,278),(167,285,175,277),(168,284,176,276),(193,315,201,307),(194,314,202,306),(195,313,203,305),(196,312,204,320),(197,311,205,319),(198,310,206,318),(199,309,207,317),(200,308,208,316),(225,257,233,265),(226,272,234,264),(227,271,235,263),(228,270,236,262),(229,269,237,261),(230,268,238,260),(231,267,239,259),(232,266,240,258)]])
46 conjugacy classes
| class | 1 | 2 | 4A | 4B | 4C | 8A | 8B | 11A | ··· | 11E | 16A | 16B | 16C | 16D | 22A | ··· | 22E | 44A | ··· | 44E | 44F | ··· | 44O | 88A | ··· | 88J |
| order | 1 | 2 | 4 | 4 | 4 | 8 | 8 | 11 | ··· | 11 | 16 | 16 | 16 | 16 | 22 | ··· | 22 | 44 | ··· | 44 | 44 | ··· | 44 | 88 | ··· | 88 |
| size | 1 | 1 | 2 | 8 | 88 | 2 | 2 | 2 | ··· | 2 | 22 | 22 | 22 | 22 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
46 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | - | |
| image | C1 | C2 | C2 | C2 | D4 | D8 | D11 | Q32 | D22 | C11⋊D4 | D4⋊D11 | C11⋊Q32 |
| kernel | C11⋊Q32 | C11⋊C16 | Dic44 | C11×Q16 | C44 | C22 | Q16 | C11 | C8 | C4 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 2 | 5 | 4 | 5 | 10 | 5 | 10 |
Matrix representation of C11⋊Q32 ►in GL4(𝔽353) generated by
| 258 | 1 | 0 | 0 |
| 288 | 101 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 231 | 151 | 0 | 0 |
| 23 | 122 | 0 | 0 |
| 0 | 0 | 203 | 273 |
| 0 | 0 | 10 | 163 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 270 | 192 |
| 0 | 0 | 159 | 83 |
G:=sub<GL(4,GF(353))| [258,288,0,0,1,101,0,0,0,0,1,0,0,0,0,1],[231,23,0,0,151,122,0,0,0,0,203,10,0,0,273,163],[1,0,0,0,0,1,0,0,0,0,270,159,0,0,192,83] >;
C11⋊Q32 in GAP, Magma, Sage, TeX
C_{11}\rtimes Q_{32} % in TeX
G:=Group("C11:Q32"); // GroupNames label
G:=SmallGroup(352,35);
// by ID
G=gap.SmallGroup(352,35);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,96,73,103,218,116,122,579,297,69,11525]);
// Polycyclic
G:=Group<a,b,c|a^11=b^16=1,c^2=b^8,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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