metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C21⋊7Q16, C4.4D42, C28.12D6, C42.37D4, Q8.2D21, C12.12D14, C84.4C22, Dic42.2C2, C7⋊3(C3⋊Q16), C3⋊3(C7⋊Q16), (C3×Q8).1D7, (C7×Q8).3S3, C21⋊C8.1C2, (Q8×C21).1C2, C6.19(C7⋊D4), C2.7(C21⋊7D4), C14.19(C3⋊D4), SmallGroup(336,104)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C21⋊7Q16
G = < a,b,c | a21=b8=1, c2=b4, bab-1=a-1, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C21⋊7Q16
►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)
(1 312 62 285 30 325 79 270)(2 311 63 284 31 324 80 269)(3 310 43 283 32 323 81 268)(4 309 44 282 33 322 82 267)(5 308 45 281 34 321 83 266)(6 307 46 280 35 320 84 265)(7 306 47 279 36 319 64 264)(8 305 48 278 37 318 65 263)(9 304 49 277 38 317 66 262)(10 303 50 276 39 316 67 261)(11 302 51 275 40 336 68 260)(12 301 52 274 41 335 69 259)(13 300 53 294 42 334 70 258)(14 299 54 293 22 333 71 257)(15 298 55 292 23 332 72 256)(16 297 56 291 24 331 73 255)(17 296 57 290 25 330 74 254)(18 295 58 289 26 329 75 253)(19 315 59 288 27 328 76 273)(20 314 60 287 28 327 77 272)(21 313 61 286 29 326 78 271)(85 216 150 180 115 241 132 195)(86 215 151 179 116 240 133 194)(87 214 152 178 117 239 134 193)(88 213 153 177 118 238 135 192)(89 212 154 176 119 237 136 191)(90 211 155 175 120 236 137 190)(91 231 156 174 121 235 138 210)(92 230 157 173 122 234 139 209)(93 229 158 172 123 233 140 208)(94 228 159 171 124 232 141 207)(95 227 160 170 125 252 142 206)(96 226 161 169 126 251 143 205)(97 225 162 189 106 250 144 204)(98 224 163 188 107 249 145 203)(99 223 164 187 108 248 146 202)(100 222 165 186 109 247 147 201)(101 221 166 185 110 246 127 200)(102 220 167 184 111 245 128 199)(103 219 168 183 112 244 129 198)(104 218 148 182 113 243 130 197)(105 217 149 181 114 242 131 196)
(1 107 30 98)(2 108 31 99)(3 109 32 100)(4 110 33 101)(5 111 34 102)(6 112 35 103)(7 113 36 104)(8 114 37 105)(9 115 38 85)(10 116 39 86)(11 117 40 87)(12 118 41 88)(13 119 42 89)(14 120 22 90)(15 121 23 91)(16 122 24 92)(17 123 25 93)(18 124 26 94)(19 125 27 95)(20 126 28 96)(21 106 29 97)(43 165 81 147)(44 166 82 127)(45 167 83 128)(46 168 84 129)(47 148 64 130)(48 149 65 131)(49 150 66 132)(50 151 67 133)(51 152 68 134)(52 153 69 135)(53 154 70 136)(54 155 71 137)(55 156 72 138)(56 157 73 139)(57 158 74 140)(58 159 75 141)(59 160 76 142)(60 161 77 143)(61 162 78 144)(62 163 79 145)(63 164 80 146)(169 327 205 314)(170 328 206 315)(171 329 207 295)(172 330 208 296)(173 331 209 297)(174 332 210 298)(175 333 190 299)(176 334 191 300)(177 335 192 301)(178 336 193 302)(179 316 194 303)(180 317 195 304)(181 318 196 305)(182 319 197 306)(183 320 198 307)(184 321 199 308)(185 322 200 309)(186 323 201 310)(187 324 202 311)(188 325 203 312)(189 326 204 313)(211 257 236 293)(212 258 237 294)(213 259 238 274)(214 260 239 275)(215 261 240 276)(216 262 241 277)(217 263 242 278)(218 264 243 279)(219 265 244 280)(220 266 245 281)(221 267 246 282)(222 268 247 283)(223 269 248 284)(224 270 249 285)(225 271 250 286)(226 272 251 287)(227 273 252 288)(228 253 232 289)(229 254 233 290)(230 255 234 291)(231 256 235 292)
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), (1,312,62,285,30,325,79,270)(2,311,63,284,31,324,80,269)(3,310,43,283,32,323,81,268)(4,309,44,282,33,322,82,267)(5,308,45,281,34,321,83,266)(6,307,46,280,35,320,84,265)(7,306,47,279,36,319,64,264)(8,305,48,278,37,318,65,263)(9,304,49,277,38,317,66,262)(10,303,50,276,39,316,67,261)(11,302,51,275,40,336,68,260)(12,301,52,274,41,335,69,259)(13,300,53,294,42,334,70,258)(14,299,54,293,22,333,71,257)(15,298,55,292,23,332,72,256)(16,297,56,291,24,331,73,255)(17,296,57,290,25,330,74,254)(18,295,58,289,26,329,75,253)(19,315,59,288,27,328,76,273)(20,314,60,287,28,327,77,272)(21,313,61,286,29,326,78,271)(85,216,150,180,115,241,132,195)(86,215,151,179,116,240,133,194)(87,214,152,178,117,239,134,193)(88,213,153,177,118,238,135,192)(89,212,154,176,119,237,136,191)(90,211,155,175,120,236,137,190)(91,231,156,174,121,235,138,210)(92,230,157,173,122,234,139,209)(93,229,158,172,123,233,140,208)(94,228,159,171,124,232,141,207)(95,227,160,170,125,252,142,206)(96,226,161,169,126,251,143,205)(97,225,162,189,106,250,144,204)(98,224,163,188,107,249,145,203)(99,223,164,187,108,248,146,202)(100,222,165,186,109,247,147,201)(101,221,166,185,110,246,127,200)(102,220,167,184,111,245,128,199)(103,219,168,183,112,244,129,198)(104,218,148,182,113,243,130,197)(105,217,149,181,114,242,131,196), (1,107,30,98)(2,108,31,99)(3,109,32,100)(4,110,33,101)(5,111,34,102)(6,112,35,103)(7,113,36,104)(8,114,37,105)(9,115,38,85)(10,116,39,86)(11,117,40,87)(12,118,41,88)(13,119,42,89)(14,120,22,90)(15,121,23,91)(16,122,24,92)(17,123,25,93)(18,124,26,94)(19,125,27,95)(20,126,28,96)(21,106,29,97)(43,165,81,147)(44,166,82,127)(45,167,83,128)(46,168,84,129)(47,148,64,130)(48,149,65,131)(49,150,66,132)(50,151,67,133)(51,152,68,134)(52,153,69,135)(53,154,70,136)(54,155,71,137)(55,156,72,138)(56,157,73,139)(57,158,74,140)(58,159,75,141)(59,160,76,142)(60,161,77,143)(61,162,78,144)(62,163,79,145)(63,164,80,146)(169,327,205,314)(170,328,206,315)(171,329,207,295)(172,330,208,296)(173,331,209,297)(174,332,210,298)(175,333,190,299)(176,334,191,300)(177,335,192,301)(178,336,193,302)(179,316,194,303)(180,317,195,304)(181,318,196,305)(182,319,197,306)(183,320,198,307)(184,321,199,308)(185,322,200,309)(186,323,201,310)(187,324,202,311)(188,325,203,312)(189,326,204,313)(211,257,236,293)(212,258,237,294)(213,259,238,274)(214,260,239,275)(215,261,240,276)(216,262,241,277)(217,263,242,278)(218,264,243,279)(219,265,244,280)(220,266,245,281)(221,267,246,282)(222,268,247,283)(223,269,248,284)(224,270,249,285)(225,271,250,286)(226,272,251,287)(227,273,252,288)(228,253,232,289)(229,254,233,290)(230,255,234,291)(231,256,235,292)>;
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), (1,312,62,285,30,325,79,270)(2,311,63,284,31,324,80,269)(3,310,43,283,32,323,81,268)(4,309,44,282,33,322,82,267)(5,308,45,281,34,321,83,266)(6,307,46,280,35,320,84,265)(7,306,47,279,36,319,64,264)(8,305,48,278,37,318,65,263)(9,304,49,277,38,317,66,262)(10,303,50,276,39,316,67,261)(11,302,51,275,40,336,68,260)(12,301,52,274,41,335,69,259)(13,300,53,294,42,334,70,258)(14,299,54,293,22,333,71,257)(15,298,55,292,23,332,72,256)(16,297,56,291,24,331,73,255)(17,296,57,290,25,330,74,254)(18,295,58,289,26,329,75,253)(19,315,59,288,27,328,76,273)(20,314,60,287,28,327,77,272)(21,313,61,286,29,326,78,271)(85,216,150,180,115,241,132,195)(86,215,151,179,116,240,133,194)(87,214,152,178,117,239,134,193)(88,213,153,177,118,238,135,192)(89,212,154,176,119,237,136,191)(90,211,155,175,120,236,137,190)(91,231,156,174,121,235,138,210)(92,230,157,173,122,234,139,209)(93,229,158,172,123,233,140,208)(94,228,159,171,124,232,141,207)(95,227,160,170,125,252,142,206)(96,226,161,169,126,251,143,205)(97,225,162,189,106,250,144,204)(98,224,163,188,107,249,145,203)(99,223,164,187,108,248,146,202)(100,222,165,186,109,247,147,201)(101,221,166,185,110,246,127,200)(102,220,167,184,111,245,128,199)(103,219,168,183,112,244,129,198)(104,218,148,182,113,243,130,197)(105,217,149,181,114,242,131,196), (1,107,30,98)(2,108,31,99)(3,109,32,100)(4,110,33,101)(5,111,34,102)(6,112,35,103)(7,113,36,104)(8,114,37,105)(9,115,38,85)(10,116,39,86)(11,117,40,87)(12,118,41,88)(13,119,42,89)(14,120,22,90)(15,121,23,91)(16,122,24,92)(17,123,25,93)(18,124,26,94)(19,125,27,95)(20,126,28,96)(21,106,29,97)(43,165,81,147)(44,166,82,127)(45,167,83,128)(46,168,84,129)(47,148,64,130)(48,149,65,131)(49,150,66,132)(50,151,67,133)(51,152,68,134)(52,153,69,135)(53,154,70,136)(54,155,71,137)(55,156,72,138)(56,157,73,139)(57,158,74,140)(58,159,75,141)(59,160,76,142)(60,161,77,143)(61,162,78,144)(62,163,79,145)(63,164,80,146)(169,327,205,314)(170,328,206,315)(171,329,207,295)(172,330,208,296)(173,331,209,297)(174,332,210,298)(175,333,190,299)(176,334,191,300)(177,335,192,301)(178,336,193,302)(179,316,194,303)(180,317,195,304)(181,318,196,305)(182,319,197,306)(183,320,198,307)(184,321,199,308)(185,322,200,309)(186,323,201,310)(187,324,202,311)(188,325,203,312)(189,326,204,313)(211,257,236,293)(212,258,237,294)(213,259,238,274)(214,260,239,275)(215,261,240,276)(216,262,241,277)(217,263,242,278)(218,264,243,279)(219,265,244,280)(220,266,245,281)(221,267,246,282)(222,268,247,283)(223,269,248,284)(224,270,249,285)(225,271,250,286)(226,272,251,287)(227,273,252,288)(228,253,232,289)(229,254,233,290)(230,255,234,291)(231,256,235,292) );
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)], [(1,312,62,285,30,325,79,270),(2,311,63,284,31,324,80,269),(3,310,43,283,32,323,81,268),(4,309,44,282,33,322,82,267),(5,308,45,281,34,321,83,266),(6,307,46,280,35,320,84,265),(7,306,47,279,36,319,64,264),(8,305,48,278,37,318,65,263),(9,304,49,277,38,317,66,262),(10,303,50,276,39,316,67,261),(11,302,51,275,40,336,68,260),(12,301,52,274,41,335,69,259),(13,300,53,294,42,334,70,258),(14,299,54,293,22,333,71,257),(15,298,55,292,23,332,72,256),(16,297,56,291,24,331,73,255),(17,296,57,290,25,330,74,254),(18,295,58,289,26,329,75,253),(19,315,59,288,27,328,76,273),(20,314,60,287,28,327,77,272),(21,313,61,286,29,326,78,271),(85,216,150,180,115,241,132,195),(86,215,151,179,116,240,133,194),(87,214,152,178,117,239,134,193),(88,213,153,177,118,238,135,192),(89,212,154,176,119,237,136,191),(90,211,155,175,120,236,137,190),(91,231,156,174,121,235,138,210),(92,230,157,173,122,234,139,209),(93,229,158,172,123,233,140,208),(94,228,159,171,124,232,141,207),(95,227,160,170,125,252,142,206),(96,226,161,169,126,251,143,205),(97,225,162,189,106,250,144,204),(98,224,163,188,107,249,145,203),(99,223,164,187,108,248,146,202),(100,222,165,186,109,247,147,201),(101,221,166,185,110,246,127,200),(102,220,167,184,111,245,128,199),(103,219,168,183,112,244,129,198),(104,218,148,182,113,243,130,197),(105,217,149,181,114,242,131,196)], [(1,107,30,98),(2,108,31,99),(3,109,32,100),(4,110,33,101),(5,111,34,102),(6,112,35,103),(7,113,36,104),(8,114,37,105),(9,115,38,85),(10,116,39,86),(11,117,40,87),(12,118,41,88),(13,119,42,89),(14,120,22,90),(15,121,23,91),(16,122,24,92),(17,123,25,93),(18,124,26,94),(19,125,27,95),(20,126,28,96),(21,106,29,97),(43,165,81,147),(44,166,82,127),(45,167,83,128),(46,168,84,129),(47,148,64,130),(48,149,65,131),(49,150,66,132),(50,151,67,133),(51,152,68,134),(52,153,69,135),(53,154,70,136),(54,155,71,137),(55,156,72,138),(56,157,73,139),(57,158,74,140),(58,159,75,141),(59,160,76,142),(60,161,77,143),(61,162,78,144),(62,163,79,145),(63,164,80,146),(169,327,205,314),(170,328,206,315),(171,329,207,295),(172,330,208,296),(173,331,209,297),(174,332,210,298),(175,333,190,299),(176,334,191,300),(177,335,192,301),(178,336,193,302),(179,316,194,303),(180,317,195,304),(181,318,196,305),(182,319,197,306),(183,320,198,307),(184,321,199,308),(185,322,200,309),(186,323,201,310),(187,324,202,311),(188,325,203,312),(189,326,204,313),(211,257,236,293),(212,258,237,294),(213,259,238,274),(214,260,239,275),(215,261,240,276),(216,262,241,277),(217,263,242,278),(218,264,243,279),(219,265,244,280),(220,266,245,281),(221,267,246,282),(222,268,247,283),(223,269,248,284),(224,270,249,285),(225,271,250,286),(226,272,251,287),(227,273,252,288),(228,253,232,289),(229,254,233,290),(230,255,234,291),(231,256,235,292)]])
57 conjugacy classes
| class | 1 | 2 | 3 | 4A | 4B | 4C | 6 | 7A | 7B | 7C | 8A | 8B | 12A | 12B | 12C | 14A | 14B | 14C | 21A | ··· | 21F | 28A | ··· | 28I | 42A | ··· | 42F | 84A | ··· | 84R |
| order | 1 | 2 | 3 | 4 | 4 | 4 | 6 | 7 | 7 | 7 | 8 | 8 | 12 | 12 | 12 | 14 | 14 | 14 | 21 | ··· | 21 | 28 | ··· | 28 | 42 | ··· | 42 | 84 | ··· | 84 |
| size | 1 | 1 | 2 | 2 | 4 | 84 | 2 | 2 | 2 | 2 | 42 | 42 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
57 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | + | - | - | - | |||
| image | C1 | C2 | C2 | C2 | S3 | D4 | D6 | D7 | Q16 | C3⋊D4 | D14 | D21 | C7⋊D4 | D42 | C21⋊7D4 | C3⋊Q16 | C7⋊Q16 | C21⋊7Q16 |
| kernel | C21⋊7Q16 | C21⋊C8 | Dic42 | Q8×C21 | C7×Q8 | C42 | C28 | C3×Q8 | C21 | C14 | C12 | Q8 | C6 | C4 | C2 | C7 | C3 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 2 | 2 | 3 | 6 | 6 | 6 | 12 | 1 | 3 | 6 |
Matrix representation of C21⋊7Q16 ►in GL4(𝔽337) generated by
| 70 | 323 | 0 | 0 |
| 14 | 262 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 332 | 3 | 0 | 0 |
| 216 | 5 | 0 | 0 |
| 0 | 0 | 311 | 181 |
| 0 | 0 | 283 | 0 |
| 242 | 274 | 0 | 0 |
| 63 | 95 | 0 | 0 |
| 0 | 0 | 204 | 16 |
| 0 | 0 | 116 | 133 |
G:=sub<GL(4,GF(337))| [70,14,0,0,323,262,0,0,0,0,1,0,0,0,0,1],[332,216,0,0,3,5,0,0,0,0,311,283,0,0,181,0],[242,63,0,0,274,95,0,0,0,0,204,116,0,0,16,133] >;
C21⋊7Q16 in GAP, Magma, Sage, TeX
C_{21}\rtimes_7Q_{16} % in TeX
G:=Group("C21:7Q16"); // GroupNames label
G:=SmallGroup(336,104);
// by ID
G=gap.SmallGroup(336,104);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-3,-7,48,73,55,218,116,50,964,10373]);
// Polycyclic
G:=Group<a,b,c|a^21=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
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