direct product, metacyclic, nilpotent (class 3), monomial, 2-elementary
Aliases: Q16×C23, C8.C46, Q8.C46, C184.3C2, C46.16D4, C92.19C22, C4.3(C2×C46), C2.5(D4×C23), (Q8×C23).2C2, SmallGroup(368,26)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Q16×C23
G = < a,b,c | a23=b8=1, c2=b4, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of Q16×C23
►Regular action on 368 points
Generators in S368
(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)
(1 78 139 288 301 97 65 359)(2 79 140 289 302 98 66 360)(3 80 141 290 303 99 67 361)(4 81 142 291 304 100 68 362)(5 82 143 292 305 101 69 363)(6 83 144 293 306 102 47 364)(7 84 145 294 307 103 48 365)(8 85 146 295 308 104 49 366)(9 86 147 296 309 105 50 367)(10 87 148 297 310 106 51 368)(11 88 149 298 311 107 52 346)(12 89 150 299 312 108 53 347)(13 90 151 277 313 109 54 348)(14 91 152 278 314 110 55 349)(15 92 153 279 315 111 56 350)(16 70 154 280 316 112 57 351)(17 71 155 281 317 113 58 352)(18 72 156 282 318 114 59 353)(19 73 157 283 319 115 60 354)(20 74 158 284 320 93 61 355)(21 75 159 285 321 94 62 356)(22 76 160 286 322 95 63 357)(23 77 161 287 300 96 64 358)(24 267 168 338 252 129 193 225)(25 268 169 339 253 130 194 226)(26 269 170 340 231 131 195 227)(27 270 171 341 232 132 196 228)(28 271 172 342 233 133 197 229)(29 272 173 343 234 134 198 230)(30 273 174 344 235 135 199 208)(31 274 175 345 236 136 200 209)(32 275 176 323 237 137 201 210)(33 276 177 324 238 138 202 211)(34 254 178 325 239 116 203 212)(35 255 179 326 240 117 204 213)(36 256 180 327 241 118 205 214)(37 257 181 328 242 119 206 215)(38 258 182 329 243 120 207 216)(39 259 183 330 244 121 185 217)(40 260 184 331 245 122 186 218)(41 261 162 332 246 123 187 219)(42 262 163 333 247 124 188 220)(43 263 164 334 248 125 189 221)(44 264 165 335 249 126 190 222)(45 265 166 336 250 127 191 223)(46 266 167 337 251 128 192 224)
(1 193 301 168)(2 194 302 169)(3 195 303 170)(4 196 304 171)(5 197 305 172)(6 198 306 173)(7 199 307 174)(8 200 308 175)(9 201 309 176)(10 202 310 177)(11 203 311 178)(12 204 312 179)(13 205 313 180)(14 206 314 181)(15 207 315 182)(16 185 316 183)(17 186 317 184)(18 187 318 162)(19 188 319 163)(20 189 320 164)(21 190 321 165)(22 191 322 166)(23 192 300 167)(24 139 252 65)(25 140 253 66)(26 141 231 67)(27 142 232 68)(28 143 233 69)(29 144 234 47)(30 145 235 48)(31 146 236 49)(32 147 237 50)(33 148 238 51)(34 149 239 52)(35 150 240 53)(36 151 241 54)(37 152 242 55)(38 153 243 56)(39 154 244 57)(40 155 245 58)(41 156 246 59)(42 157 247 60)(43 158 248 61)(44 159 249 62)(45 160 250 63)(46 161 251 64)(70 121 112 259)(71 122 113 260)(72 123 114 261)(73 124 115 262)(74 125 93 263)(75 126 94 264)(76 127 95 265)(77 128 96 266)(78 129 97 267)(79 130 98 268)(80 131 99 269)(81 132 100 270)(82 133 101 271)(83 134 102 272)(84 135 103 273)(85 136 104 274)(86 137 105 275)(87 138 106 276)(88 116 107 254)(89 117 108 255)(90 118 109 256)(91 119 110 257)(92 120 111 258)(208 294 344 365)(209 295 345 366)(210 296 323 367)(211 297 324 368)(212 298 325 346)(213 299 326 347)(214 277 327 348)(215 278 328 349)(216 279 329 350)(217 280 330 351)(218 281 331 352)(219 282 332 353)(220 283 333 354)(221 284 334 355)(222 285 335 356)(223 286 336 357)(224 287 337 358)(225 288 338 359)(226 289 339 360)(227 290 340 361)(228 291 341 362)(229 292 342 363)(230 293 343 364)
G:=sub<Sym(368)| (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), (1,78,139,288,301,97,65,359)(2,79,140,289,302,98,66,360)(3,80,141,290,303,99,67,361)(4,81,142,291,304,100,68,362)(5,82,143,292,305,101,69,363)(6,83,144,293,306,102,47,364)(7,84,145,294,307,103,48,365)(8,85,146,295,308,104,49,366)(9,86,147,296,309,105,50,367)(10,87,148,297,310,106,51,368)(11,88,149,298,311,107,52,346)(12,89,150,299,312,108,53,347)(13,90,151,277,313,109,54,348)(14,91,152,278,314,110,55,349)(15,92,153,279,315,111,56,350)(16,70,154,280,316,112,57,351)(17,71,155,281,317,113,58,352)(18,72,156,282,318,114,59,353)(19,73,157,283,319,115,60,354)(20,74,158,284,320,93,61,355)(21,75,159,285,321,94,62,356)(22,76,160,286,322,95,63,357)(23,77,161,287,300,96,64,358)(24,267,168,338,252,129,193,225)(25,268,169,339,253,130,194,226)(26,269,170,340,231,131,195,227)(27,270,171,341,232,132,196,228)(28,271,172,342,233,133,197,229)(29,272,173,343,234,134,198,230)(30,273,174,344,235,135,199,208)(31,274,175,345,236,136,200,209)(32,275,176,323,237,137,201,210)(33,276,177,324,238,138,202,211)(34,254,178,325,239,116,203,212)(35,255,179,326,240,117,204,213)(36,256,180,327,241,118,205,214)(37,257,181,328,242,119,206,215)(38,258,182,329,243,120,207,216)(39,259,183,330,244,121,185,217)(40,260,184,331,245,122,186,218)(41,261,162,332,246,123,187,219)(42,262,163,333,247,124,188,220)(43,263,164,334,248,125,189,221)(44,264,165,335,249,126,190,222)(45,265,166,336,250,127,191,223)(46,266,167,337,251,128,192,224), (1,193,301,168)(2,194,302,169)(3,195,303,170)(4,196,304,171)(5,197,305,172)(6,198,306,173)(7,199,307,174)(8,200,308,175)(9,201,309,176)(10,202,310,177)(11,203,311,178)(12,204,312,179)(13,205,313,180)(14,206,314,181)(15,207,315,182)(16,185,316,183)(17,186,317,184)(18,187,318,162)(19,188,319,163)(20,189,320,164)(21,190,321,165)(22,191,322,166)(23,192,300,167)(24,139,252,65)(25,140,253,66)(26,141,231,67)(27,142,232,68)(28,143,233,69)(29,144,234,47)(30,145,235,48)(31,146,236,49)(32,147,237,50)(33,148,238,51)(34,149,239,52)(35,150,240,53)(36,151,241,54)(37,152,242,55)(38,153,243,56)(39,154,244,57)(40,155,245,58)(41,156,246,59)(42,157,247,60)(43,158,248,61)(44,159,249,62)(45,160,250,63)(46,161,251,64)(70,121,112,259)(71,122,113,260)(72,123,114,261)(73,124,115,262)(74,125,93,263)(75,126,94,264)(76,127,95,265)(77,128,96,266)(78,129,97,267)(79,130,98,268)(80,131,99,269)(81,132,100,270)(82,133,101,271)(83,134,102,272)(84,135,103,273)(85,136,104,274)(86,137,105,275)(87,138,106,276)(88,116,107,254)(89,117,108,255)(90,118,109,256)(91,119,110,257)(92,120,111,258)(208,294,344,365)(209,295,345,366)(210,296,323,367)(211,297,324,368)(212,298,325,346)(213,299,326,347)(214,277,327,348)(215,278,328,349)(216,279,329,350)(217,280,330,351)(218,281,331,352)(219,282,332,353)(220,283,333,354)(221,284,334,355)(222,285,335,356)(223,286,336,357)(224,287,337,358)(225,288,338,359)(226,289,339,360)(227,290,340,361)(228,291,341,362)(229,292,342,363)(230,293,343,364)>;
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), (1,78,139,288,301,97,65,359)(2,79,140,289,302,98,66,360)(3,80,141,290,303,99,67,361)(4,81,142,291,304,100,68,362)(5,82,143,292,305,101,69,363)(6,83,144,293,306,102,47,364)(7,84,145,294,307,103,48,365)(8,85,146,295,308,104,49,366)(9,86,147,296,309,105,50,367)(10,87,148,297,310,106,51,368)(11,88,149,298,311,107,52,346)(12,89,150,299,312,108,53,347)(13,90,151,277,313,109,54,348)(14,91,152,278,314,110,55,349)(15,92,153,279,315,111,56,350)(16,70,154,280,316,112,57,351)(17,71,155,281,317,113,58,352)(18,72,156,282,318,114,59,353)(19,73,157,283,319,115,60,354)(20,74,158,284,320,93,61,355)(21,75,159,285,321,94,62,356)(22,76,160,286,322,95,63,357)(23,77,161,287,300,96,64,358)(24,267,168,338,252,129,193,225)(25,268,169,339,253,130,194,226)(26,269,170,340,231,131,195,227)(27,270,171,341,232,132,196,228)(28,271,172,342,233,133,197,229)(29,272,173,343,234,134,198,230)(30,273,174,344,235,135,199,208)(31,274,175,345,236,136,200,209)(32,275,176,323,237,137,201,210)(33,276,177,324,238,138,202,211)(34,254,178,325,239,116,203,212)(35,255,179,326,240,117,204,213)(36,256,180,327,241,118,205,214)(37,257,181,328,242,119,206,215)(38,258,182,329,243,120,207,216)(39,259,183,330,244,121,185,217)(40,260,184,331,245,122,186,218)(41,261,162,332,246,123,187,219)(42,262,163,333,247,124,188,220)(43,263,164,334,248,125,189,221)(44,264,165,335,249,126,190,222)(45,265,166,336,250,127,191,223)(46,266,167,337,251,128,192,224), (1,193,301,168)(2,194,302,169)(3,195,303,170)(4,196,304,171)(5,197,305,172)(6,198,306,173)(7,199,307,174)(8,200,308,175)(9,201,309,176)(10,202,310,177)(11,203,311,178)(12,204,312,179)(13,205,313,180)(14,206,314,181)(15,207,315,182)(16,185,316,183)(17,186,317,184)(18,187,318,162)(19,188,319,163)(20,189,320,164)(21,190,321,165)(22,191,322,166)(23,192,300,167)(24,139,252,65)(25,140,253,66)(26,141,231,67)(27,142,232,68)(28,143,233,69)(29,144,234,47)(30,145,235,48)(31,146,236,49)(32,147,237,50)(33,148,238,51)(34,149,239,52)(35,150,240,53)(36,151,241,54)(37,152,242,55)(38,153,243,56)(39,154,244,57)(40,155,245,58)(41,156,246,59)(42,157,247,60)(43,158,248,61)(44,159,249,62)(45,160,250,63)(46,161,251,64)(70,121,112,259)(71,122,113,260)(72,123,114,261)(73,124,115,262)(74,125,93,263)(75,126,94,264)(76,127,95,265)(77,128,96,266)(78,129,97,267)(79,130,98,268)(80,131,99,269)(81,132,100,270)(82,133,101,271)(83,134,102,272)(84,135,103,273)(85,136,104,274)(86,137,105,275)(87,138,106,276)(88,116,107,254)(89,117,108,255)(90,118,109,256)(91,119,110,257)(92,120,111,258)(208,294,344,365)(209,295,345,366)(210,296,323,367)(211,297,324,368)(212,298,325,346)(213,299,326,347)(214,277,327,348)(215,278,328,349)(216,279,329,350)(217,280,330,351)(218,281,331,352)(219,282,332,353)(220,283,333,354)(221,284,334,355)(222,285,335,356)(223,286,336,357)(224,287,337,358)(225,288,338,359)(226,289,339,360)(227,290,340,361)(228,291,341,362)(229,292,342,363)(230,293,343,364) );
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)], [(1,78,139,288,301,97,65,359),(2,79,140,289,302,98,66,360),(3,80,141,290,303,99,67,361),(4,81,142,291,304,100,68,362),(5,82,143,292,305,101,69,363),(6,83,144,293,306,102,47,364),(7,84,145,294,307,103,48,365),(8,85,146,295,308,104,49,366),(9,86,147,296,309,105,50,367),(10,87,148,297,310,106,51,368),(11,88,149,298,311,107,52,346),(12,89,150,299,312,108,53,347),(13,90,151,277,313,109,54,348),(14,91,152,278,314,110,55,349),(15,92,153,279,315,111,56,350),(16,70,154,280,316,112,57,351),(17,71,155,281,317,113,58,352),(18,72,156,282,318,114,59,353),(19,73,157,283,319,115,60,354),(20,74,158,284,320,93,61,355),(21,75,159,285,321,94,62,356),(22,76,160,286,322,95,63,357),(23,77,161,287,300,96,64,358),(24,267,168,338,252,129,193,225),(25,268,169,339,253,130,194,226),(26,269,170,340,231,131,195,227),(27,270,171,341,232,132,196,228),(28,271,172,342,233,133,197,229),(29,272,173,343,234,134,198,230),(30,273,174,344,235,135,199,208),(31,274,175,345,236,136,200,209),(32,275,176,323,237,137,201,210),(33,276,177,324,238,138,202,211),(34,254,178,325,239,116,203,212),(35,255,179,326,240,117,204,213),(36,256,180,327,241,118,205,214),(37,257,181,328,242,119,206,215),(38,258,182,329,243,120,207,216),(39,259,183,330,244,121,185,217),(40,260,184,331,245,122,186,218),(41,261,162,332,246,123,187,219),(42,262,163,333,247,124,188,220),(43,263,164,334,248,125,189,221),(44,264,165,335,249,126,190,222),(45,265,166,336,250,127,191,223),(46,266,167,337,251,128,192,224)], [(1,193,301,168),(2,194,302,169),(3,195,303,170),(4,196,304,171),(5,197,305,172),(6,198,306,173),(7,199,307,174),(8,200,308,175),(9,201,309,176),(10,202,310,177),(11,203,311,178),(12,204,312,179),(13,205,313,180),(14,206,314,181),(15,207,315,182),(16,185,316,183),(17,186,317,184),(18,187,318,162),(19,188,319,163),(20,189,320,164),(21,190,321,165),(22,191,322,166),(23,192,300,167),(24,139,252,65),(25,140,253,66),(26,141,231,67),(27,142,232,68),(28,143,233,69),(29,144,234,47),(30,145,235,48),(31,146,236,49),(32,147,237,50),(33,148,238,51),(34,149,239,52),(35,150,240,53),(36,151,241,54),(37,152,242,55),(38,153,243,56),(39,154,244,57),(40,155,245,58),(41,156,246,59),(42,157,247,60),(43,158,248,61),(44,159,249,62),(45,160,250,63),(46,161,251,64),(70,121,112,259),(71,122,113,260),(72,123,114,261),(73,124,115,262),(74,125,93,263),(75,126,94,264),(76,127,95,265),(77,128,96,266),(78,129,97,267),(79,130,98,268),(80,131,99,269),(81,132,100,270),(82,133,101,271),(83,134,102,272),(84,135,103,273),(85,136,104,274),(86,137,105,275),(87,138,106,276),(88,116,107,254),(89,117,108,255),(90,118,109,256),(91,119,110,257),(92,120,111,258),(208,294,344,365),(209,295,345,366),(210,296,323,367),(211,297,324,368),(212,298,325,346),(213,299,326,347),(214,277,327,348),(215,278,328,349),(216,279,329,350),(217,280,330,351),(218,281,331,352),(219,282,332,353),(220,283,333,354),(221,284,334,355),(222,285,335,356),(223,286,336,357),(224,287,337,358),(225,288,338,359),(226,289,339,360),(227,290,340,361),(228,291,341,362),(229,292,342,363),(230,293,343,364)]])
161 conjugacy classes
| class | 1 | 2 | 4A | 4B | 4C | 8A | 8B | 23A | ··· | 23V | 46A | ··· | 46V | 92A | ··· | 92V | 92W | ··· | 92BN | 184A | ··· | 184AR |
| order | 1 | 2 | 4 | 4 | 4 | 8 | 8 | 23 | ··· | 23 | 46 | ··· | 46 | 92 | ··· | 92 | 92 | ··· | 92 | 184 | ··· | 184 |
| size | 1 | 1 | 2 | 4 | 4 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 |
161 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | |||||
| image | C1 | C2 | C2 | C23 | C46 | C46 | D4 | Q16 | D4×C23 | Q16×C23 |
| kernel | Q16×C23 | C184 | Q8×C23 | Q16 | C8 | Q8 | C46 | C23 | C2 | C1 |
| # reps | 1 | 1 | 2 | 22 | 22 | 44 | 1 | 2 | 22 | 44 |
Matrix representation of Q16×C23 ►in GL2(𝔽47) generated by
| 28 | 0 |
| 0 | 28 |
| 0 | 34 |
| 29 | 7 |
| 39 | 16 |
| 40 | 8 |
G:=sub<GL(2,GF(47))| [28,0,0,28],[0,29,34,7],[39,40,16,8] >;
Q16×C23 in GAP, Magma, Sage, TeX
Q_{16}\times C_{23} % in TeX
G:=Group("Q16xC23"); // GroupNames label
G:=SmallGroup(368,26);
// by ID
G=gap.SmallGroup(368,26);
# by ID
G:=PCGroup([5,-2,-2,-23,-2,-2,920,941,926,5523,2768,58]);
// Polycyclic
G:=Group<a,b,c|a^23=b^8=1,c^2=b^4,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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