metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23⋊2Q16, Q8.D23, C4.4D46, C46.10D4, C92.4C22, Dic46.2C2, C23⋊C8.C2, (Q8×C23).1C2, C2.7(C23⋊D4), SmallGroup(368,17)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23⋊Q16
G = < a,b,c | a23=b8=1, c2=b4, bab-1=a-1, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C23⋊Q16
►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)
(1 323 47 300 25 346 91 277)(2 345 48 322 26 368 92 299)(3 344 49 321 27 367 70 298)(4 343 50 320 28 366 71 297)(5 342 51 319 29 365 72 296)(6 341 52 318 30 364 73 295)(7 340 53 317 31 363 74 294)(8 339 54 316 32 362 75 293)(9 338 55 315 33 361 76 292)(10 337 56 314 34 360 77 291)(11 336 57 313 35 359 78 290)(12 335 58 312 36 358 79 289)(13 334 59 311 37 357 80 288)(14 333 60 310 38 356 81 287)(15 332 61 309 39 355 82 286)(16 331 62 308 40 354 83 285)(17 330 63 307 41 353 84 284)(18 329 64 306 42 352 85 283)(19 328 65 305 43 351 86 282)(20 327 66 304 44 350 87 281)(21 326 67 303 45 349 88 280)(22 325 68 302 46 348 89 279)(23 324 69 301 24 347 90 278)(93 236 168 190 122 259 153 213)(94 235 169 189 123 258 154 212)(95 234 170 188 124 257 155 211)(96 233 171 187 125 256 156 210)(97 232 172 186 126 255 157 209)(98 231 173 185 127 254 158 208)(99 253 174 207 128 276 159 230)(100 252 175 206 129 275 160 229)(101 251 176 205 130 274 161 228)(102 250 177 204 131 273 139 227)(103 249 178 203 132 272 140 226)(104 248 179 202 133 271 141 225)(105 247 180 201 134 270 142 224)(106 246 181 200 135 269 143 223)(107 245 182 199 136 268 144 222)(108 244 183 198 137 267 145 221)(109 243 184 197 138 266 146 220)(110 242 162 196 116 265 147 219)(111 241 163 195 117 264 148 218)(112 240 164 194 118 263 149 217)(113 239 165 193 119 262 150 216)(114 238 166 192 120 261 151 215)(115 237 167 191 121 260 152 214)
(1 127 25 98)(2 128 26 99)(3 129 27 100)(4 130 28 101)(5 131 29 102)(6 132 30 103)(7 133 31 104)(8 134 32 105)(9 135 33 106)(10 136 34 107)(11 137 35 108)(12 138 36 109)(13 116 37 110)(14 117 38 111)(15 118 39 112)(16 119 40 113)(17 120 41 114)(18 121 42 115)(19 122 43 93)(20 123 44 94)(21 124 45 95)(22 125 46 96)(23 126 24 97)(47 173 91 158)(48 174 92 159)(49 175 70 160)(50 176 71 161)(51 177 72 139)(52 178 73 140)(53 179 74 141)(54 180 75 142)(55 181 76 143)(56 182 77 144)(57 183 78 145)(58 184 79 146)(59 162 80 147)(60 163 81 148)(61 164 82 149)(62 165 83 150)(63 166 84 151)(64 167 85 152)(65 168 86 153)(66 169 87 154)(67 170 88 155)(68 171 89 156)(69 172 90 157)(185 346 208 323)(186 347 209 324)(187 348 210 325)(188 349 211 326)(189 350 212 327)(190 351 213 328)(191 352 214 329)(192 353 215 330)(193 354 216 331)(194 355 217 332)(195 356 218 333)(196 357 219 334)(197 358 220 335)(198 359 221 336)(199 360 222 337)(200 361 223 338)(201 362 224 339)(202 363 225 340)(203 364 226 341)(204 365 227 342)(205 366 228 343)(206 367 229 344)(207 368 230 345)(231 277 254 300)(232 278 255 301)(233 279 256 302)(234 280 257 303)(235 281 258 304)(236 282 259 305)(237 283 260 306)(238 284 261 307)(239 285 262 308)(240 286 263 309)(241 287 264 310)(242 288 265 311)(243 289 266 312)(244 290 267 313)(245 291 268 314)(246 292 269 315)(247 293 270 316)(248 294 271 317)(249 295 272 318)(250 296 273 319)(251 297 274 320)(252 298 275 321)(253 299 276 322)
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), (1,323,47,300,25,346,91,277)(2,345,48,322,26,368,92,299)(3,344,49,321,27,367,70,298)(4,343,50,320,28,366,71,297)(5,342,51,319,29,365,72,296)(6,341,52,318,30,364,73,295)(7,340,53,317,31,363,74,294)(8,339,54,316,32,362,75,293)(9,338,55,315,33,361,76,292)(10,337,56,314,34,360,77,291)(11,336,57,313,35,359,78,290)(12,335,58,312,36,358,79,289)(13,334,59,311,37,357,80,288)(14,333,60,310,38,356,81,287)(15,332,61,309,39,355,82,286)(16,331,62,308,40,354,83,285)(17,330,63,307,41,353,84,284)(18,329,64,306,42,352,85,283)(19,328,65,305,43,351,86,282)(20,327,66,304,44,350,87,281)(21,326,67,303,45,349,88,280)(22,325,68,302,46,348,89,279)(23,324,69,301,24,347,90,278)(93,236,168,190,122,259,153,213)(94,235,169,189,123,258,154,212)(95,234,170,188,124,257,155,211)(96,233,171,187,125,256,156,210)(97,232,172,186,126,255,157,209)(98,231,173,185,127,254,158,208)(99,253,174,207,128,276,159,230)(100,252,175,206,129,275,160,229)(101,251,176,205,130,274,161,228)(102,250,177,204,131,273,139,227)(103,249,178,203,132,272,140,226)(104,248,179,202,133,271,141,225)(105,247,180,201,134,270,142,224)(106,246,181,200,135,269,143,223)(107,245,182,199,136,268,144,222)(108,244,183,198,137,267,145,221)(109,243,184,197,138,266,146,220)(110,242,162,196,116,265,147,219)(111,241,163,195,117,264,148,218)(112,240,164,194,118,263,149,217)(113,239,165,193,119,262,150,216)(114,238,166,192,120,261,151,215)(115,237,167,191,121,260,152,214), (1,127,25,98)(2,128,26,99)(3,129,27,100)(4,130,28,101)(5,131,29,102)(6,132,30,103)(7,133,31,104)(8,134,32,105)(9,135,33,106)(10,136,34,107)(11,137,35,108)(12,138,36,109)(13,116,37,110)(14,117,38,111)(15,118,39,112)(16,119,40,113)(17,120,41,114)(18,121,42,115)(19,122,43,93)(20,123,44,94)(21,124,45,95)(22,125,46,96)(23,126,24,97)(47,173,91,158)(48,174,92,159)(49,175,70,160)(50,176,71,161)(51,177,72,139)(52,178,73,140)(53,179,74,141)(54,180,75,142)(55,181,76,143)(56,182,77,144)(57,183,78,145)(58,184,79,146)(59,162,80,147)(60,163,81,148)(61,164,82,149)(62,165,83,150)(63,166,84,151)(64,167,85,152)(65,168,86,153)(66,169,87,154)(67,170,88,155)(68,171,89,156)(69,172,90,157)(185,346,208,323)(186,347,209,324)(187,348,210,325)(188,349,211,326)(189,350,212,327)(190,351,213,328)(191,352,214,329)(192,353,215,330)(193,354,216,331)(194,355,217,332)(195,356,218,333)(196,357,219,334)(197,358,220,335)(198,359,221,336)(199,360,222,337)(200,361,223,338)(201,362,224,339)(202,363,225,340)(203,364,226,341)(204,365,227,342)(205,366,228,343)(206,367,229,344)(207,368,230,345)(231,277,254,300)(232,278,255,301)(233,279,256,302)(234,280,257,303)(235,281,258,304)(236,282,259,305)(237,283,260,306)(238,284,261,307)(239,285,262,308)(240,286,263,309)(241,287,264,310)(242,288,265,311)(243,289,266,312)(244,290,267,313)(245,291,268,314)(246,292,269,315)(247,293,270,316)(248,294,271,317)(249,295,272,318)(250,296,273,319)(251,297,274,320)(252,298,275,321)(253,299,276,322)>;
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), (1,323,47,300,25,346,91,277)(2,345,48,322,26,368,92,299)(3,344,49,321,27,367,70,298)(4,343,50,320,28,366,71,297)(5,342,51,319,29,365,72,296)(6,341,52,318,30,364,73,295)(7,340,53,317,31,363,74,294)(8,339,54,316,32,362,75,293)(9,338,55,315,33,361,76,292)(10,337,56,314,34,360,77,291)(11,336,57,313,35,359,78,290)(12,335,58,312,36,358,79,289)(13,334,59,311,37,357,80,288)(14,333,60,310,38,356,81,287)(15,332,61,309,39,355,82,286)(16,331,62,308,40,354,83,285)(17,330,63,307,41,353,84,284)(18,329,64,306,42,352,85,283)(19,328,65,305,43,351,86,282)(20,327,66,304,44,350,87,281)(21,326,67,303,45,349,88,280)(22,325,68,302,46,348,89,279)(23,324,69,301,24,347,90,278)(93,236,168,190,122,259,153,213)(94,235,169,189,123,258,154,212)(95,234,170,188,124,257,155,211)(96,233,171,187,125,256,156,210)(97,232,172,186,126,255,157,209)(98,231,173,185,127,254,158,208)(99,253,174,207,128,276,159,230)(100,252,175,206,129,275,160,229)(101,251,176,205,130,274,161,228)(102,250,177,204,131,273,139,227)(103,249,178,203,132,272,140,226)(104,248,179,202,133,271,141,225)(105,247,180,201,134,270,142,224)(106,246,181,200,135,269,143,223)(107,245,182,199,136,268,144,222)(108,244,183,198,137,267,145,221)(109,243,184,197,138,266,146,220)(110,242,162,196,116,265,147,219)(111,241,163,195,117,264,148,218)(112,240,164,194,118,263,149,217)(113,239,165,193,119,262,150,216)(114,238,166,192,120,261,151,215)(115,237,167,191,121,260,152,214), (1,127,25,98)(2,128,26,99)(3,129,27,100)(4,130,28,101)(5,131,29,102)(6,132,30,103)(7,133,31,104)(8,134,32,105)(9,135,33,106)(10,136,34,107)(11,137,35,108)(12,138,36,109)(13,116,37,110)(14,117,38,111)(15,118,39,112)(16,119,40,113)(17,120,41,114)(18,121,42,115)(19,122,43,93)(20,123,44,94)(21,124,45,95)(22,125,46,96)(23,126,24,97)(47,173,91,158)(48,174,92,159)(49,175,70,160)(50,176,71,161)(51,177,72,139)(52,178,73,140)(53,179,74,141)(54,180,75,142)(55,181,76,143)(56,182,77,144)(57,183,78,145)(58,184,79,146)(59,162,80,147)(60,163,81,148)(61,164,82,149)(62,165,83,150)(63,166,84,151)(64,167,85,152)(65,168,86,153)(66,169,87,154)(67,170,88,155)(68,171,89,156)(69,172,90,157)(185,346,208,323)(186,347,209,324)(187,348,210,325)(188,349,211,326)(189,350,212,327)(190,351,213,328)(191,352,214,329)(192,353,215,330)(193,354,216,331)(194,355,217,332)(195,356,218,333)(196,357,219,334)(197,358,220,335)(198,359,221,336)(199,360,222,337)(200,361,223,338)(201,362,224,339)(202,363,225,340)(203,364,226,341)(204,365,227,342)(205,366,228,343)(206,367,229,344)(207,368,230,345)(231,277,254,300)(232,278,255,301)(233,279,256,302)(234,280,257,303)(235,281,258,304)(236,282,259,305)(237,283,260,306)(238,284,261,307)(239,285,262,308)(240,286,263,309)(241,287,264,310)(242,288,265,311)(243,289,266,312)(244,290,267,313)(245,291,268,314)(246,292,269,315)(247,293,270,316)(248,294,271,317)(249,295,272,318)(250,296,273,319)(251,297,274,320)(252,298,275,321)(253,299,276,322) );
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)], [(1,323,47,300,25,346,91,277),(2,345,48,322,26,368,92,299),(3,344,49,321,27,367,70,298),(4,343,50,320,28,366,71,297),(5,342,51,319,29,365,72,296),(6,341,52,318,30,364,73,295),(7,340,53,317,31,363,74,294),(8,339,54,316,32,362,75,293),(9,338,55,315,33,361,76,292),(10,337,56,314,34,360,77,291),(11,336,57,313,35,359,78,290),(12,335,58,312,36,358,79,289),(13,334,59,311,37,357,80,288),(14,333,60,310,38,356,81,287),(15,332,61,309,39,355,82,286),(16,331,62,308,40,354,83,285),(17,330,63,307,41,353,84,284),(18,329,64,306,42,352,85,283),(19,328,65,305,43,351,86,282),(20,327,66,304,44,350,87,281),(21,326,67,303,45,349,88,280),(22,325,68,302,46,348,89,279),(23,324,69,301,24,347,90,278),(93,236,168,190,122,259,153,213),(94,235,169,189,123,258,154,212),(95,234,170,188,124,257,155,211),(96,233,171,187,125,256,156,210),(97,232,172,186,126,255,157,209),(98,231,173,185,127,254,158,208),(99,253,174,207,128,276,159,230),(100,252,175,206,129,275,160,229),(101,251,176,205,130,274,161,228),(102,250,177,204,131,273,139,227),(103,249,178,203,132,272,140,226),(104,248,179,202,133,271,141,225),(105,247,180,201,134,270,142,224),(106,246,181,200,135,269,143,223),(107,245,182,199,136,268,144,222),(108,244,183,198,137,267,145,221),(109,243,184,197,138,266,146,220),(110,242,162,196,116,265,147,219),(111,241,163,195,117,264,148,218),(112,240,164,194,118,263,149,217),(113,239,165,193,119,262,150,216),(114,238,166,192,120,261,151,215),(115,237,167,191,121,260,152,214)], [(1,127,25,98),(2,128,26,99),(3,129,27,100),(4,130,28,101),(5,131,29,102),(6,132,30,103),(7,133,31,104),(8,134,32,105),(9,135,33,106),(10,136,34,107),(11,137,35,108),(12,138,36,109),(13,116,37,110),(14,117,38,111),(15,118,39,112),(16,119,40,113),(17,120,41,114),(18,121,42,115),(19,122,43,93),(20,123,44,94),(21,124,45,95),(22,125,46,96),(23,126,24,97),(47,173,91,158),(48,174,92,159),(49,175,70,160),(50,176,71,161),(51,177,72,139),(52,178,73,140),(53,179,74,141),(54,180,75,142),(55,181,76,143),(56,182,77,144),(57,183,78,145),(58,184,79,146),(59,162,80,147),(60,163,81,148),(61,164,82,149),(62,165,83,150),(63,166,84,151),(64,167,85,152),(65,168,86,153),(66,169,87,154),(67,170,88,155),(68,171,89,156),(69,172,90,157),(185,346,208,323),(186,347,209,324),(187,348,210,325),(188,349,211,326),(189,350,212,327),(190,351,213,328),(191,352,214,329),(192,353,215,330),(193,354,216,331),(194,355,217,332),(195,356,218,333),(196,357,219,334),(197,358,220,335),(198,359,221,336),(199,360,222,337),(200,361,223,338),(201,362,224,339),(202,363,225,340),(203,364,226,341),(204,365,227,342),(205,366,228,343),(206,367,229,344),(207,368,230,345),(231,277,254,300),(232,278,255,301),(233,279,256,302),(234,280,257,303),(235,281,258,304),(236,282,259,305),(237,283,260,306),(238,284,261,307),(239,285,262,308),(240,286,263,309),(241,287,264,310),(242,288,265,311),(243,289,266,312),(244,290,267,313),(245,291,268,314),(246,292,269,315),(247,293,270,316),(248,294,271,317),(249,295,272,318),(250,296,273,319),(251,297,274,320),(252,298,275,321),(253,299,276,322)]])
62 conjugacy classes
| class | 1 | 2 | 4A | 4B | 4C | 8A | 8B | 23A | ··· | 23K | 46A | ··· | 46K | 92A | ··· | 92AG |
| order | 1 | 2 | 4 | 4 | 4 | 8 | 8 | 23 | ··· | 23 | 46 | ··· | 46 | 92 | ··· | 92 |
| size | 1 | 1 | 2 | 4 | 92 | 46 | 46 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
62 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | - | + | + | - | |
| image | C1 | C2 | C2 | C2 | D4 | Q16 | D23 | D46 | C23⋊D4 | C23⋊Q16 |
| kernel | C23⋊Q16 | C23⋊C8 | Dic46 | Q8×C23 | C46 | C23 | Q8 | C4 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 2 | 11 | 11 | 22 | 11 |
Matrix representation of C23⋊Q16 ►in GL4(𝔽1289) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 32 | 1 |
| 0 | 0 | 171 | 811 |
| 597 | 692 | 0 | 0 |
| 597 | 597 | 0 | 0 |
| 0 | 0 | 1004 | 141 |
| 0 | 0 | 73 | 285 |
| 1266 | 827 | 0 | 0 |
| 827 | 23 | 0 | 0 |
| 0 | 0 | 177 | 213 |
| 0 | 0 | 331 | 1112 |
G:=sub<GL(4,GF(1289))| [1,0,0,0,0,1,0,0,0,0,32,171,0,0,1,811],[597,597,0,0,692,597,0,0,0,0,1004,73,0,0,141,285],[1266,827,0,0,827,23,0,0,0,0,177,331,0,0,213,1112] >;
C23⋊Q16 in GAP, Magma, Sage, TeX
C_{23}\rtimes Q_{16} % in TeX
G:=Group("C23:Q16"); // GroupNames label
G:=SmallGroup(368,17);
// by ID
G=gap.SmallGroup(368,17);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-23,40,61,46,182,97,42,8804]);
// Polycyclic
G:=Group<a,b,c|a^23=b^8=1,c^2=b^4,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export