metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C21⋊1Q16, C28.7D6, C12.7D14, C42.10D4, Dic6.2D7, C84.25C22, Dic14.2S3, C4.18(S3×D7), C3⋊2(C7⋊Q16), C7⋊2(C3⋊Q16), C21⋊C8.2C2, C6.10(C7⋊D4), C2.7(C21⋊D4), (C7×Dic6).2C2, C14.10(C3⋊D4), (C3×Dic14).2C2, SmallGroup(336,38)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C21⋊Q16
G = < a,b,c | a21=b8=1, c2=b4, bab-1=a-1, cac-1=a8, cbc-1=b-1 >
Smallest permutation representation of C21⋊Q16
►Regular action on 336 points
Generators in S336
(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)
(1 308 58 287 31 329 78 264)(2 307 59 286 32 328 79 263)(3 306 60 285 33 327 80 262)(4 305 61 284 34 326 81 261)(5 304 62 283 35 325 82 260)(6 303 63 282 36 324 83 259)(7 302 43 281 37 323 84 258)(8 301 44 280 38 322 64 257)(9 300 45 279 39 321 65 256)(10 299 46 278 40 320 66 255)(11 298 47 277 41 319 67 254)(12 297 48 276 42 318 68 253)(13 296 49 275 22 317 69 273)(14 295 50 274 23 316 70 272)(15 315 51 294 24 336 71 271)(16 314 52 293 25 335 72 270)(17 313 53 292 26 334 73 269)(18 312 54 291 27 333 74 268)(19 311 55 290 28 332 75 267)(20 310 56 289 29 331 76 266)(21 309 57 288 30 330 77 265)(85 228 148 179 107 251 140 208)(86 227 149 178 108 250 141 207)(87 226 150 177 109 249 142 206)(88 225 151 176 110 248 143 205)(89 224 152 175 111 247 144 204)(90 223 153 174 112 246 145 203)(91 222 154 173 113 245 146 202)(92 221 155 172 114 244 147 201)(93 220 156 171 115 243 127 200)(94 219 157 170 116 242 128 199)(95 218 158 169 117 241 129 198)(96 217 159 189 118 240 130 197)(97 216 160 188 119 239 131 196)(98 215 161 187 120 238 132 195)(99 214 162 186 121 237 133 194)(100 213 163 185 122 236 134 193)(101 212 164 184 123 235 135 192)(102 211 165 183 124 234 136 191)(103 231 166 182 125 233 137 190)(104 230 167 181 126 232 138 210)(105 229 168 180 106 252 139 209)
(1 110 31 88)(2 118 32 96)(3 126 33 104)(4 113 34 91)(5 121 35 99)(6 108 36 86)(7 116 37 94)(8 124 38 102)(9 111 39 89)(10 119 40 97)(11 106 41 105)(12 114 42 92)(13 122 22 100)(14 109 23 87)(15 117 24 95)(16 125 25 103)(17 112 26 90)(18 120 27 98)(19 107 28 85)(20 115 29 93)(21 123 30 101)(43 157 84 128)(44 165 64 136)(45 152 65 144)(46 160 66 131)(47 168 67 139)(48 155 68 147)(49 163 69 134)(50 150 70 142)(51 158 71 129)(52 166 72 137)(53 153 73 145)(54 161 74 132)(55 148 75 140)(56 156 76 127)(57 164 77 135)(58 151 78 143)(59 159 79 130)(60 167 80 138)(61 154 81 146)(62 162 82 133)(63 149 83 141)(169 336 198 315)(170 323 199 302)(171 331 200 310)(172 318 201 297)(173 326 202 305)(174 334 203 313)(175 321 204 300)(176 329 205 308)(177 316 206 295)(178 324 207 303)(179 332 208 311)(180 319 209 298)(181 327 210 306)(182 335 190 314)(183 322 191 301)(184 330 192 309)(185 317 193 296)(186 325 194 304)(187 333 195 312)(188 320 196 299)(189 328 197 307)(211 257 234 280)(212 265 235 288)(213 273 236 275)(214 260 237 283)(215 268 238 291)(216 255 239 278)(217 263 240 286)(218 271 241 294)(219 258 242 281)(220 266 243 289)(221 253 244 276)(222 261 245 284)(223 269 246 292)(224 256 247 279)(225 264 248 287)(226 272 249 274)(227 259 250 282)(228 267 251 290)(229 254 252 277)(230 262 232 285)(231 270 233 293)
G:=sub<Sym(336)| (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), (1,308,58,287,31,329,78,264)(2,307,59,286,32,328,79,263)(3,306,60,285,33,327,80,262)(4,305,61,284,34,326,81,261)(5,304,62,283,35,325,82,260)(6,303,63,282,36,324,83,259)(7,302,43,281,37,323,84,258)(8,301,44,280,38,322,64,257)(9,300,45,279,39,321,65,256)(10,299,46,278,40,320,66,255)(11,298,47,277,41,319,67,254)(12,297,48,276,42,318,68,253)(13,296,49,275,22,317,69,273)(14,295,50,274,23,316,70,272)(15,315,51,294,24,336,71,271)(16,314,52,293,25,335,72,270)(17,313,53,292,26,334,73,269)(18,312,54,291,27,333,74,268)(19,311,55,290,28,332,75,267)(20,310,56,289,29,331,76,266)(21,309,57,288,30,330,77,265)(85,228,148,179,107,251,140,208)(86,227,149,178,108,250,141,207)(87,226,150,177,109,249,142,206)(88,225,151,176,110,248,143,205)(89,224,152,175,111,247,144,204)(90,223,153,174,112,246,145,203)(91,222,154,173,113,245,146,202)(92,221,155,172,114,244,147,201)(93,220,156,171,115,243,127,200)(94,219,157,170,116,242,128,199)(95,218,158,169,117,241,129,198)(96,217,159,189,118,240,130,197)(97,216,160,188,119,239,131,196)(98,215,161,187,120,238,132,195)(99,214,162,186,121,237,133,194)(100,213,163,185,122,236,134,193)(101,212,164,184,123,235,135,192)(102,211,165,183,124,234,136,191)(103,231,166,182,125,233,137,190)(104,230,167,181,126,232,138,210)(105,229,168,180,106,252,139,209), (1,110,31,88)(2,118,32,96)(3,126,33,104)(4,113,34,91)(5,121,35,99)(6,108,36,86)(7,116,37,94)(8,124,38,102)(9,111,39,89)(10,119,40,97)(11,106,41,105)(12,114,42,92)(13,122,22,100)(14,109,23,87)(15,117,24,95)(16,125,25,103)(17,112,26,90)(18,120,27,98)(19,107,28,85)(20,115,29,93)(21,123,30,101)(43,157,84,128)(44,165,64,136)(45,152,65,144)(46,160,66,131)(47,168,67,139)(48,155,68,147)(49,163,69,134)(50,150,70,142)(51,158,71,129)(52,166,72,137)(53,153,73,145)(54,161,74,132)(55,148,75,140)(56,156,76,127)(57,164,77,135)(58,151,78,143)(59,159,79,130)(60,167,80,138)(61,154,81,146)(62,162,82,133)(63,149,83,141)(169,336,198,315)(170,323,199,302)(171,331,200,310)(172,318,201,297)(173,326,202,305)(174,334,203,313)(175,321,204,300)(176,329,205,308)(177,316,206,295)(178,324,207,303)(179,332,208,311)(180,319,209,298)(181,327,210,306)(182,335,190,314)(183,322,191,301)(184,330,192,309)(185,317,193,296)(186,325,194,304)(187,333,195,312)(188,320,196,299)(189,328,197,307)(211,257,234,280)(212,265,235,288)(213,273,236,275)(214,260,237,283)(215,268,238,291)(216,255,239,278)(217,263,240,286)(218,271,241,294)(219,258,242,281)(220,266,243,289)(221,253,244,276)(222,261,245,284)(223,269,246,292)(224,256,247,279)(225,264,248,287)(226,272,249,274)(227,259,250,282)(228,267,251,290)(229,254,252,277)(230,262,232,285)(231,270,233,293)>;
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), (1,308,58,287,31,329,78,264)(2,307,59,286,32,328,79,263)(3,306,60,285,33,327,80,262)(4,305,61,284,34,326,81,261)(5,304,62,283,35,325,82,260)(6,303,63,282,36,324,83,259)(7,302,43,281,37,323,84,258)(8,301,44,280,38,322,64,257)(9,300,45,279,39,321,65,256)(10,299,46,278,40,320,66,255)(11,298,47,277,41,319,67,254)(12,297,48,276,42,318,68,253)(13,296,49,275,22,317,69,273)(14,295,50,274,23,316,70,272)(15,315,51,294,24,336,71,271)(16,314,52,293,25,335,72,270)(17,313,53,292,26,334,73,269)(18,312,54,291,27,333,74,268)(19,311,55,290,28,332,75,267)(20,310,56,289,29,331,76,266)(21,309,57,288,30,330,77,265)(85,228,148,179,107,251,140,208)(86,227,149,178,108,250,141,207)(87,226,150,177,109,249,142,206)(88,225,151,176,110,248,143,205)(89,224,152,175,111,247,144,204)(90,223,153,174,112,246,145,203)(91,222,154,173,113,245,146,202)(92,221,155,172,114,244,147,201)(93,220,156,171,115,243,127,200)(94,219,157,170,116,242,128,199)(95,218,158,169,117,241,129,198)(96,217,159,189,118,240,130,197)(97,216,160,188,119,239,131,196)(98,215,161,187,120,238,132,195)(99,214,162,186,121,237,133,194)(100,213,163,185,122,236,134,193)(101,212,164,184,123,235,135,192)(102,211,165,183,124,234,136,191)(103,231,166,182,125,233,137,190)(104,230,167,181,126,232,138,210)(105,229,168,180,106,252,139,209), (1,110,31,88)(2,118,32,96)(3,126,33,104)(4,113,34,91)(5,121,35,99)(6,108,36,86)(7,116,37,94)(8,124,38,102)(9,111,39,89)(10,119,40,97)(11,106,41,105)(12,114,42,92)(13,122,22,100)(14,109,23,87)(15,117,24,95)(16,125,25,103)(17,112,26,90)(18,120,27,98)(19,107,28,85)(20,115,29,93)(21,123,30,101)(43,157,84,128)(44,165,64,136)(45,152,65,144)(46,160,66,131)(47,168,67,139)(48,155,68,147)(49,163,69,134)(50,150,70,142)(51,158,71,129)(52,166,72,137)(53,153,73,145)(54,161,74,132)(55,148,75,140)(56,156,76,127)(57,164,77,135)(58,151,78,143)(59,159,79,130)(60,167,80,138)(61,154,81,146)(62,162,82,133)(63,149,83,141)(169,336,198,315)(170,323,199,302)(171,331,200,310)(172,318,201,297)(173,326,202,305)(174,334,203,313)(175,321,204,300)(176,329,205,308)(177,316,206,295)(178,324,207,303)(179,332,208,311)(180,319,209,298)(181,327,210,306)(182,335,190,314)(183,322,191,301)(184,330,192,309)(185,317,193,296)(186,325,194,304)(187,333,195,312)(188,320,196,299)(189,328,197,307)(211,257,234,280)(212,265,235,288)(213,273,236,275)(214,260,237,283)(215,268,238,291)(216,255,239,278)(217,263,240,286)(218,271,241,294)(219,258,242,281)(220,266,243,289)(221,253,244,276)(222,261,245,284)(223,269,246,292)(224,256,247,279)(225,264,248,287)(226,272,249,274)(227,259,250,282)(228,267,251,290)(229,254,252,277)(230,262,232,285)(231,270,233,293) );
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)], [(1,308,58,287,31,329,78,264),(2,307,59,286,32,328,79,263),(3,306,60,285,33,327,80,262),(4,305,61,284,34,326,81,261),(5,304,62,283,35,325,82,260),(6,303,63,282,36,324,83,259),(7,302,43,281,37,323,84,258),(8,301,44,280,38,322,64,257),(9,300,45,279,39,321,65,256),(10,299,46,278,40,320,66,255),(11,298,47,277,41,319,67,254),(12,297,48,276,42,318,68,253),(13,296,49,275,22,317,69,273),(14,295,50,274,23,316,70,272),(15,315,51,294,24,336,71,271),(16,314,52,293,25,335,72,270),(17,313,53,292,26,334,73,269),(18,312,54,291,27,333,74,268),(19,311,55,290,28,332,75,267),(20,310,56,289,29,331,76,266),(21,309,57,288,30,330,77,265),(85,228,148,179,107,251,140,208),(86,227,149,178,108,250,141,207),(87,226,150,177,109,249,142,206),(88,225,151,176,110,248,143,205),(89,224,152,175,111,247,144,204),(90,223,153,174,112,246,145,203),(91,222,154,173,113,245,146,202),(92,221,155,172,114,244,147,201),(93,220,156,171,115,243,127,200),(94,219,157,170,116,242,128,199),(95,218,158,169,117,241,129,198),(96,217,159,189,118,240,130,197),(97,216,160,188,119,239,131,196),(98,215,161,187,120,238,132,195),(99,214,162,186,121,237,133,194),(100,213,163,185,122,236,134,193),(101,212,164,184,123,235,135,192),(102,211,165,183,124,234,136,191),(103,231,166,182,125,233,137,190),(104,230,167,181,126,232,138,210),(105,229,168,180,106,252,139,209)], [(1,110,31,88),(2,118,32,96),(3,126,33,104),(4,113,34,91),(5,121,35,99),(6,108,36,86),(7,116,37,94),(8,124,38,102),(9,111,39,89),(10,119,40,97),(11,106,41,105),(12,114,42,92),(13,122,22,100),(14,109,23,87),(15,117,24,95),(16,125,25,103),(17,112,26,90),(18,120,27,98),(19,107,28,85),(20,115,29,93),(21,123,30,101),(43,157,84,128),(44,165,64,136),(45,152,65,144),(46,160,66,131),(47,168,67,139),(48,155,68,147),(49,163,69,134),(50,150,70,142),(51,158,71,129),(52,166,72,137),(53,153,73,145),(54,161,74,132),(55,148,75,140),(56,156,76,127),(57,164,77,135),(58,151,78,143),(59,159,79,130),(60,167,80,138),(61,154,81,146),(62,162,82,133),(63,149,83,141),(169,336,198,315),(170,323,199,302),(171,331,200,310),(172,318,201,297),(173,326,202,305),(174,334,203,313),(175,321,204,300),(176,329,205,308),(177,316,206,295),(178,324,207,303),(179,332,208,311),(180,319,209,298),(181,327,210,306),(182,335,190,314),(183,322,191,301),(184,330,192,309),(185,317,193,296),(186,325,194,304),(187,333,195,312),(188,320,196,299),(189,328,197,307),(211,257,234,280),(212,265,235,288),(213,273,236,275),(214,260,237,283),(215,268,238,291),(216,255,239,278),(217,263,240,286),(218,271,241,294),(219,258,242,281),(220,266,243,289),(221,253,244,276),(222,261,245,284),(223,269,246,292),(224,256,247,279),(225,264,248,287),(226,272,249,274),(227,259,250,282),(228,267,251,290),(229,254,252,277),(230,262,232,285),(231,270,233,293)]])
39 conjugacy classes
| class | 1 | 2 | 3 | 4A | 4B | 4C | 6 | 7A | 7B | 7C | 8A | 8B | 12A | 12B | 12C | 14A | 14B | 14C | 21A | 21B | 21C | 28A | 28B | 28C | 28D | ··· | 28I | 42A | 42B | 42C | 84A | ··· | 84F |
| order | 1 | 2 | 3 | 4 | 4 | 4 | 6 | 7 | 7 | 7 | 8 | 8 | 12 | 12 | 12 | 14 | 14 | 14 | 21 | 21 | 21 | 28 | 28 | 28 | 28 | ··· | 28 | 42 | 42 | 42 | 84 | ··· | 84 |
| size | 1 | 1 | 2 | 2 | 12 | 28 | 2 | 2 | 2 | 2 | 42 | 42 | 4 | 28 | 28 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 12 | ··· | 12 | 4 | 4 | 4 | 4 | ··· | 4 |
39 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | - | + | - | - | |||
| image | C1 | C2 | C2 | C2 | S3 | D4 | D6 | D7 | Q16 | C3⋊D4 | D14 | C7⋊D4 | C3⋊Q16 | S3×D7 | C7⋊Q16 | C21⋊D4 | C21⋊Q16 |
| kernel | C21⋊Q16 | C21⋊C8 | C3×Dic14 | C7×Dic6 | Dic14 | C42 | C28 | Dic6 | C21 | C14 | C12 | C6 | C7 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 2 | 2 | 3 | 6 | 1 | 3 | 3 | 3 | 6 |
Matrix representation of C21⋊Q16 ►in GL6(𝔽337)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 110 | 34 | 0 | 0 |
| 0 | 0 | 77 | 33 | 0 | 0 |
| 0 | 0 | 0 | 0 | 335 | 196 |
| 0 | 0 | 0 | 0 | 294 | 1 |
| 324 | 13 | 0 | 0 | 0 | 0 |
| 324 | 324 | 0 | 0 | 0 | 0 |
| 0 | 0 | 104 | 256 | 0 | 0 |
| 0 | 0 | 275 | 233 | 0 | 0 |
| 0 | 0 | 0 | 0 | 115 | 156 |
| 0 | 0 | 0 | 0 | 330 | 222 |
| 56 | 262 | 0 | 0 | 0 | 0 |
| 262 | 281 | 0 | 0 | 0 | 0 |
| 0 | 0 | 95 | 27 | 0 | 0 |
| 0 | 0 | 190 | 242 | 0 | 0 |
| 0 | 0 | 0 | 0 | 115 | 156 |
| 0 | 0 | 0 | 0 | 330 | 222 |
G:=sub<GL(6,GF(337))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,110,77,0,0,0,0,34,33,0,0,0,0,0,0,335,294,0,0,0,0,196,1],[324,324,0,0,0,0,13,324,0,0,0,0,0,0,104,275,0,0,0,0,256,233,0,0,0,0,0,0,115,330,0,0,0,0,156,222],[56,262,0,0,0,0,262,281,0,0,0,0,0,0,95,190,0,0,0,0,27,242,0,0,0,0,0,0,115,330,0,0,0,0,156,222] >;
C21⋊Q16 in GAP, Magma, Sage, TeX
C_{21}\rtimes Q_{16} % in TeX
G:=Group("C21:Q16"); // GroupNames label
G:=SmallGroup(336,38);
// by ID
G=gap.SmallGroup(336,38);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-3,-7,48,73,55,218,116,50,490,10373]);
// Polycyclic
G:=Group<a,b,c|a^21=b^8=1,c^2=b^4,b*a*b^-1=a^-1,c*a*c^-1=a^8,c*b*c^-1=b^-1>;
// generators/relations
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