direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C7×C3⋊C16, C3⋊C112, C6.C56, C21⋊3C16, C84.8C4, C42.3C8, C56.4S3, C168.7C2, C12.2C28, C24.3C14, C28.5Dic3, C8.2(S3×C7), C14.2(C3⋊C8), C4.2(C7×Dic3), C2.(C7×C3⋊C8), SmallGroup(336,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C3 — C7×C3⋊C16 |
Generators and relations for C7×C3⋊C16
G = < a,b,c | a7=b3=c16=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C7×C3⋊C16
►Regular action on 336 points
Generators in S336
(1 167 262 297 242 285 203)(2 168 263 298 243 286 204)(3 169 264 299 244 287 205)(4 170 265 300 245 288 206)(5 171 266 301 246 273 207)(6 172 267 302 247 274 208)(7 173 268 303 248 275 193)(8 174 269 304 249 276 194)(9 175 270 289 250 277 195)(10 176 271 290 251 278 196)(11 161 272 291 252 279 197)(12 162 257 292 253 280 198)(13 163 258 293 254 281 199)(14 164 259 294 255 282 200)(15 165 260 295 256 283 201)(16 166 261 296 241 284 202)(17 330 62 95 70 104 211)(18 331 63 96 71 105 212)(19 332 64 81 72 106 213)(20 333 49 82 73 107 214)(21 334 50 83 74 108 215)(22 335 51 84 75 109 216)(23 336 52 85 76 110 217)(24 321 53 86 77 111 218)(25 322 54 87 78 112 219)(26 323 55 88 79 97 220)(27 324 56 89 80 98 221)(28 325 57 90 65 99 222)(29 326 58 91 66 100 223)(30 327 59 92 67 101 224)(31 328 60 93 68 102 209)(32 329 61 94 69 103 210)(33 156 240 135 189 127 315)(34 157 225 136 190 128 316)(35 158 226 137 191 113 317)(36 159 227 138 192 114 318)(37 160 228 139 177 115 319)(38 145 229 140 178 116 320)(39 146 230 141 179 117 305)(40 147 231 142 180 118 306)(41 148 232 143 181 119 307)(42 149 233 144 182 120 308)(43 150 234 129 183 121 309)(44 151 235 130 184 122 310)(45 152 236 131 185 123 311)(46 153 237 132 186 124 312)(47 154 238 133 187 125 313)(48 155 239 134 188 126 314)
(1 233 65)(2 66 234)(3 235 67)(4 68 236)(5 237 69)(6 70 238)(7 239 71)(8 72 240)(9 225 73)(10 74 226)(11 227 75)(12 76 228)(13 229 77)(14 78 230)(15 231 79)(16 80 232)(17 125 302)(18 303 126)(19 127 304)(20 289 128)(21 113 290)(22 291 114)(23 115 292)(24 293 116)(25 117 294)(26 295 118)(27 119 296)(28 297 120)(29 121 298)(30 299 122)(31 123 300)(32 301 124)(33 276 64)(34 49 277)(35 278 50)(36 51 279)(37 280 52)(38 53 281)(39 282 54)(40 55 283)(41 284 56)(42 57 285)(43 286 58)(44 59 287)(45 288 60)(46 61 273)(47 274 62)(48 63 275)(81 156 194)(82 195 157)(83 158 196)(84 197 159)(85 160 198)(86 199 145)(87 146 200)(88 201 147)(89 148 202)(90 203 149)(91 150 204)(92 205 151)(93 152 206)(94 207 153)(95 154 208)(96 193 155)(97 165 142)(98 143 166)(99 167 144)(100 129 168)(101 169 130)(102 131 170)(103 171 132)(104 133 172)(105 173 134)(106 135 174)(107 175 136)(108 137 176)(109 161 138)(110 139 162)(111 163 140)(112 141 164)(177 257 217)(178 218 258)(179 259 219)(180 220 260)(181 261 221)(182 222 262)(183 263 223)(184 224 264)(185 265 209)(186 210 266)(187 267 211)(188 212 268)(189 269 213)(190 214 270)(191 271 215)(192 216 272)(241 324 307)(242 308 325)(243 326 309)(244 310 327)(245 328 311)(246 312 329)(247 330 313)(248 314 331)(249 332 315)(250 316 333)(251 334 317)(252 318 335)(253 336 319)(254 320 321)(255 322 305)(256 306 323)
(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)
G:=sub<Sym(336)| (1,167,262,297,242,285,203)(2,168,263,298,243,286,204)(3,169,264,299,244,287,205)(4,170,265,300,245,288,206)(5,171,266,301,246,273,207)(6,172,267,302,247,274,208)(7,173,268,303,248,275,193)(8,174,269,304,249,276,194)(9,175,270,289,250,277,195)(10,176,271,290,251,278,196)(11,161,272,291,252,279,197)(12,162,257,292,253,280,198)(13,163,258,293,254,281,199)(14,164,259,294,255,282,200)(15,165,260,295,256,283,201)(16,166,261,296,241,284,202)(17,330,62,95,70,104,211)(18,331,63,96,71,105,212)(19,332,64,81,72,106,213)(20,333,49,82,73,107,214)(21,334,50,83,74,108,215)(22,335,51,84,75,109,216)(23,336,52,85,76,110,217)(24,321,53,86,77,111,218)(25,322,54,87,78,112,219)(26,323,55,88,79,97,220)(27,324,56,89,80,98,221)(28,325,57,90,65,99,222)(29,326,58,91,66,100,223)(30,327,59,92,67,101,224)(31,328,60,93,68,102,209)(32,329,61,94,69,103,210)(33,156,240,135,189,127,315)(34,157,225,136,190,128,316)(35,158,226,137,191,113,317)(36,159,227,138,192,114,318)(37,160,228,139,177,115,319)(38,145,229,140,178,116,320)(39,146,230,141,179,117,305)(40,147,231,142,180,118,306)(41,148,232,143,181,119,307)(42,149,233,144,182,120,308)(43,150,234,129,183,121,309)(44,151,235,130,184,122,310)(45,152,236,131,185,123,311)(46,153,237,132,186,124,312)(47,154,238,133,187,125,313)(48,155,239,134,188,126,314), (1,233,65)(2,66,234)(3,235,67)(4,68,236)(5,237,69)(6,70,238)(7,239,71)(8,72,240)(9,225,73)(10,74,226)(11,227,75)(12,76,228)(13,229,77)(14,78,230)(15,231,79)(16,80,232)(17,125,302)(18,303,126)(19,127,304)(20,289,128)(21,113,290)(22,291,114)(23,115,292)(24,293,116)(25,117,294)(26,295,118)(27,119,296)(28,297,120)(29,121,298)(30,299,122)(31,123,300)(32,301,124)(33,276,64)(34,49,277)(35,278,50)(36,51,279)(37,280,52)(38,53,281)(39,282,54)(40,55,283)(41,284,56)(42,57,285)(43,286,58)(44,59,287)(45,288,60)(46,61,273)(47,274,62)(48,63,275)(81,156,194)(82,195,157)(83,158,196)(84,197,159)(85,160,198)(86,199,145)(87,146,200)(88,201,147)(89,148,202)(90,203,149)(91,150,204)(92,205,151)(93,152,206)(94,207,153)(95,154,208)(96,193,155)(97,165,142)(98,143,166)(99,167,144)(100,129,168)(101,169,130)(102,131,170)(103,171,132)(104,133,172)(105,173,134)(106,135,174)(107,175,136)(108,137,176)(109,161,138)(110,139,162)(111,163,140)(112,141,164)(177,257,217)(178,218,258)(179,259,219)(180,220,260)(181,261,221)(182,222,262)(183,263,223)(184,224,264)(185,265,209)(186,210,266)(187,267,211)(188,212,268)(189,269,213)(190,214,270)(191,271,215)(192,216,272)(241,324,307)(242,308,325)(243,326,309)(244,310,327)(245,328,311)(246,312,329)(247,330,313)(248,314,331)(249,332,315)(250,316,333)(251,334,317)(252,318,335)(253,336,319)(254,320,321)(255,322,305)(256,306,323), (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)>;
G:=Group( (1,167,262,297,242,285,203)(2,168,263,298,243,286,204)(3,169,264,299,244,287,205)(4,170,265,300,245,288,206)(5,171,266,301,246,273,207)(6,172,267,302,247,274,208)(7,173,268,303,248,275,193)(8,174,269,304,249,276,194)(9,175,270,289,250,277,195)(10,176,271,290,251,278,196)(11,161,272,291,252,279,197)(12,162,257,292,253,280,198)(13,163,258,293,254,281,199)(14,164,259,294,255,282,200)(15,165,260,295,256,283,201)(16,166,261,296,241,284,202)(17,330,62,95,70,104,211)(18,331,63,96,71,105,212)(19,332,64,81,72,106,213)(20,333,49,82,73,107,214)(21,334,50,83,74,108,215)(22,335,51,84,75,109,216)(23,336,52,85,76,110,217)(24,321,53,86,77,111,218)(25,322,54,87,78,112,219)(26,323,55,88,79,97,220)(27,324,56,89,80,98,221)(28,325,57,90,65,99,222)(29,326,58,91,66,100,223)(30,327,59,92,67,101,224)(31,328,60,93,68,102,209)(32,329,61,94,69,103,210)(33,156,240,135,189,127,315)(34,157,225,136,190,128,316)(35,158,226,137,191,113,317)(36,159,227,138,192,114,318)(37,160,228,139,177,115,319)(38,145,229,140,178,116,320)(39,146,230,141,179,117,305)(40,147,231,142,180,118,306)(41,148,232,143,181,119,307)(42,149,233,144,182,120,308)(43,150,234,129,183,121,309)(44,151,235,130,184,122,310)(45,152,236,131,185,123,311)(46,153,237,132,186,124,312)(47,154,238,133,187,125,313)(48,155,239,134,188,126,314), (1,233,65)(2,66,234)(3,235,67)(4,68,236)(5,237,69)(6,70,238)(7,239,71)(8,72,240)(9,225,73)(10,74,226)(11,227,75)(12,76,228)(13,229,77)(14,78,230)(15,231,79)(16,80,232)(17,125,302)(18,303,126)(19,127,304)(20,289,128)(21,113,290)(22,291,114)(23,115,292)(24,293,116)(25,117,294)(26,295,118)(27,119,296)(28,297,120)(29,121,298)(30,299,122)(31,123,300)(32,301,124)(33,276,64)(34,49,277)(35,278,50)(36,51,279)(37,280,52)(38,53,281)(39,282,54)(40,55,283)(41,284,56)(42,57,285)(43,286,58)(44,59,287)(45,288,60)(46,61,273)(47,274,62)(48,63,275)(81,156,194)(82,195,157)(83,158,196)(84,197,159)(85,160,198)(86,199,145)(87,146,200)(88,201,147)(89,148,202)(90,203,149)(91,150,204)(92,205,151)(93,152,206)(94,207,153)(95,154,208)(96,193,155)(97,165,142)(98,143,166)(99,167,144)(100,129,168)(101,169,130)(102,131,170)(103,171,132)(104,133,172)(105,173,134)(106,135,174)(107,175,136)(108,137,176)(109,161,138)(110,139,162)(111,163,140)(112,141,164)(177,257,217)(178,218,258)(179,259,219)(180,220,260)(181,261,221)(182,222,262)(183,263,223)(184,224,264)(185,265,209)(186,210,266)(187,267,211)(188,212,268)(189,269,213)(190,214,270)(191,271,215)(192,216,272)(241,324,307)(242,308,325)(243,326,309)(244,310,327)(245,328,311)(246,312,329)(247,330,313)(248,314,331)(249,332,315)(250,316,333)(251,334,317)(252,318,335)(253,336,319)(254,320,321)(255,322,305)(256,306,323), (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) );
G=PermutationGroup([[(1,167,262,297,242,285,203),(2,168,263,298,243,286,204),(3,169,264,299,244,287,205),(4,170,265,300,245,288,206),(5,171,266,301,246,273,207),(6,172,267,302,247,274,208),(7,173,268,303,248,275,193),(8,174,269,304,249,276,194),(9,175,270,289,250,277,195),(10,176,271,290,251,278,196),(11,161,272,291,252,279,197),(12,162,257,292,253,280,198),(13,163,258,293,254,281,199),(14,164,259,294,255,282,200),(15,165,260,295,256,283,201),(16,166,261,296,241,284,202),(17,330,62,95,70,104,211),(18,331,63,96,71,105,212),(19,332,64,81,72,106,213),(20,333,49,82,73,107,214),(21,334,50,83,74,108,215),(22,335,51,84,75,109,216),(23,336,52,85,76,110,217),(24,321,53,86,77,111,218),(25,322,54,87,78,112,219),(26,323,55,88,79,97,220),(27,324,56,89,80,98,221),(28,325,57,90,65,99,222),(29,326,58,91,66,100,223),(30,327,59,92,67,101,224),(31,328,60,93,68,102,209),(32,329,61,94,69,103,210),(33,156,240,135,189,127,315),(34,157,225,136,190,128,316),(35,158,226,137,191,113,317),(36,159,227,138,192,114,318),(37,160,228,139,177,115,319),(38,145,229,140,178,116,320),(39,146,230,141,179,117,305),(40,147,231,142,180,118,306),(41,148,232,143,181,119,307),(42,149,233,144,182,120,308),(43,150,234,129,183,121,309),(44,151,235,130,184,122,310),(45,152,236,131,185,123,311),(46,153,237,132,186,124,312),(47,154,238,133,187,125,313),(48,155,239,134,188,126,314)], [(1,233,65),(2,66,234),(3,235,67),(4,68,236),(5,237,69),(6,70,238),(7,239,71),(8,72,240),(9,225,73),(10,74,226),(11,227,75),(12,76,228),(13,229,77),(14,78,230),(15,231,79),(16,80,232),(17,125,302),(18,303,126),(19,127,304),(20,289,128),(21,113,290),(22,291,114),(23,115,292),(24,293,116),(25,117,294),(26,295,118),(27,119,296),(28,297,120),(29,121,298),(30,299,122),(31,123,300),(32,301,124),(33,276,64),(34,49,277),(35,278,50),(36,51,279),(37,280,52),(38,53,281),(39,282,54),(40,55,283),(41,284,56),(42,57,285),(43,286,58),(44,59,287),(45,288,60),(46,61,273),(47,274,62),(48,63,275),(81,156,194),(82,195,157),(83,158,196),(84,197,159),(85,160,198),(86,199,145),(87,146,200),(88,201,147),(89,148,202),(90,203,149),(91,150,204),(92,205,151),(93,152,206),(94,207,153),(95,154,208),(96,193,155),(97,165,142),(98,143,166),(99,167,144),(100,129,168),(101,169,130),(102,131,170),(103,171,132),(104,133,172),(105,173,134),(106,135,174),(107,175,136),(108,137,176),(109,161,138),(110,139,162),(111,163,140),(112,141,164),(177,257,217),(178,218,258),(179,259,219),(180,220,260),(181,261,221),(182,222,262),(183,263,223),(184,224,264),(185,265,209),(186,210,266),(187,267,211),(188,212,268),(189,269,213),(190,214,270),(191,271,215),(192,216,272),(241,324,307),(242,308,325),(243,326,309),(244,310,327),(245,328,311),(246,312,329),(247,330,313),(248,314,331),(249,332,315),(250,316,333),(251,334,317),(252,318,335),(253,336,319),(254,320,321),(255,322,305),(256,306,323)], [(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)]])
168 conjugacy classes
| class | 1 | 2 | 3 | 4A | 4B | 6 | 7A | ··· | 7F | 8A | 8B | 8C | 8D | 12A | 12B | 14A | ··· | 14F | 16A | ··· | 16H | 21A | ··· | 21F | 24A | 24B | 24C | 24D | 28A | ··· | 28L | 42A | ··· | 42F | 56A | ··· | 56X | 84A | ··· | 84L | 112A | ··· | 112AV | 168A | ··· | 168X |
| order | 1 | 2 | 3 | 4 | 4 | 6 | 7 | ··· | 7 | 8 | 8 | 8 | 8 | 12 | 12 | 14 | ··· | 14 | 16 | ··· | 16 | 21 | ··· | 21 | 24 | 24 | 24 | 24 | 28 | ··· | 28 | 42 | ··· | 42 | 56 | ··· | 56 | 84 | ··· | 84 | 112 | ··· | 112 | 168 | ··· | 168 |
| size | 1 | 1 | 2 | 1 | 1 | 2 | 1 | ··· | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | ··· | 1 | 3 | ··· | 3 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 3 | ··· | 3 | 2 | ··· | 2 |
168 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||||||||||
| image | C1 | C2 | C4 | C7 | C8 | C14 | C16 | C28 | C56 | C112 | S3 | Dic3 | C3⋊C8 | S3×C7 | C3⋊C16 | C7×Dic3 | C7×C3⋊C8 | C7×C3⋊C16 |
| kernel | C7×C3⋊C16 | C168 | C84 | C3⋊C16 | C42 | C24 | C21 | C12 | C6 | C3 | C56 | C28 | C14 | C8 | C7 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 6 | 4 | 6 | 8 | 12 | 24 | 48 | 1 | 1 | 2 | 6 | 4 | 6 | 12 | 24 |
Matrix representation of C7×C3⋊C16 ►in GL2(𝔽337) generated by
| 52 | 0 |
| 0 | 52 |
| 0 | 336 |
| 1 | 336 |
| 59 | 30 |
| 89 | 278 |
G:=sub<GL(2,GF(337))| [52,0,0,52],[0,1,336,336],[59,89,30,278] >;
C7×C3⋊C16 in GAP, Magma, Sage, TeX
C_7\times C_3\rtimes C_{16} % in TeX
G:=Group("C7xC3:C16"); // GroupNames label
G:=SmallGroup(336,3);
// by ID
G=gap.SmallGroup(336,3);
# by ID
G:=PCGroup([6,-2,-7,-2,-2,-2,-3,84,50,69,8069]);
// Polycyclic
G:=Group<a,b,c|a^7=b^3=c^16=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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