direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C3×C7⋊C16, C7⋊3C48, C21⋊2C16, C42.2C8, C84.5C4, C56.6C6, C24.4D7, C14.3C24, C168.5C2, C28.8C12, C12.5Dic7, C6.2(C7⋊C8), C8.2(C3×D7), C4.2(C3×Dic7), C2.(C3×C7⋊C8), SmallGroup(336,4)
Series: Derived ►Chief ►Lower central ►Upper central
| C7 — C3×C7⋊C16 |
Generators and relations for C3×C7⋊C16
G = < a,b,c | a3=b7=c16=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C3×C7⋊C16
►Regular action on 336 points
Generators in S336
(1 263 132)(2 264 133)(3 265 134)(4 266 135)(5 267 136)(6 268 137)(7 269 138)(8 270 139)(9 271 140)(10 272 141)(11 257 142)(12 258 143)(13 259 144)(14 260 129)(15 261 130)(16 262 131)(17 195 209)(18 196 210)(19 197 211)(20 198 212)(21 199 213)(22 200 214)(23 201 215)(24 202 216)(25 203 217)(26 204 218)(27 205 219)(28 206 220)(29 207 221)(30 208 222)(31 193 223)(32 194 224)(33 57 128)(34 58 113)(35 59 114)(36 60 115)(37 61 116)(38 62 117)(39 63 118)(40 64 119)(41 49 120)(42 50 121)(43 51 122)(44 52 123)(45 53 124)(46 54 125)(47 55 126)(48 56 127)(65 307 173)(66 308 174)(67 309 175)(68 310 176)(69 311 161)(70 312 162)(71 313 163)(72 314 164)(73 315 165)(74 316 166)(75 317 167)(76 318 168)(77 319 169)(78 320 170)(79 305 171)(80 306 172)(81 289 232)(82 290 233)(83 291 234)(84 292 235)(85 293 236)(86 294 237)(87 295 238)(88 296 239)(89 297 240)(90 298 225)(91 299 226)(92 300 227)(93 301 228)(94 302 229)(95 303 230)(96 304 231)(97 276 336)(98 277 321)(99 278 322)(100 279 323)(101 280 324)(102 281 325)(103 282 326)(104 283 327)(105 284 328)(106 285 329)(107 286 330)(108 287 331)(109 288 332)(110 273 333)(111 274 334)(112 275 335)(145 243 191)(146 244 192)(147 245 177)(148 246 178)(149 247 179)(150 248 180)(151 249 181)(152 250 182)(153 251 183)(154 252 184)(155 253 185)(156 254 186)(157 255 187)(158 256 188)(159 241 189)(160 242 190)
(1 109 83 42 314 19 243)(2 244 20 315 43 84 110)(3 111 85 44 316 21 245)(4 246 22 317 45 86 112)(5 97 87 46 318 23 247)(6 248 24 319 47 88 98)(7 99 89 48 320 25 249)(8 250 26 305 33 90 100)(9 101 91 34 306 27 251)(10 252 28 307 35 92 102)(11 103 93 36 308 29 253)(12 254 30 309 37 94 104)(13 105 95 38 310 31 255)(14 256 32 311 39 96 106)(15 107 81 40 312 17 241)(16 242 18 313 41 82 108)(49 290 287 262 190 196 163)(50 164 197 191 263 288 291)(51 292 273 264 192 198 165)(52 166 199 177 265 274 293)(53 294 275 266 178 200 167)(54 168 201 179 267 276 295)(55 296 277 268 180 202 169)(56 170 203 181 269 278 297)(57 298 279 270 182 204 171)(58 172 205 183 271 280 299)(59 300 281 272 184 206 173)(60 174 207 185 257 282 301)(61 302 283 258 186 208 175)(62 176 193 187 259 284 303)(63 304 285 260 188 194 161)(64 162 195 189 261 286 289)(65 114 227 325 141 154 220)(66 221 155 142 326 228 115)(67 116 229 327 143 156 222)(68 223 157 144 328 230 117)(69 118 231 329 129 158 224)(70 209 159 130 330 232 119)(71 120 233 331 131 160 210)(72 211 145 132 332 234 121)(73 122 235 333 133 146 212)(74 213 147 134 334 236 123)(75 124 237 335 135 148 214)(76 215 149 136 336 238 125)(77 126 239 321 137 150 216)(78 217 151 138 322 240 127)(79 128 225 323 139 152 218)(80 219 153 140 324 226 113)
(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)| (1,263,132)(2,264,133)(3,265,134)(4,266,135)(5,267,136)(6,268,137)(7,269,138)(8,270,139)(9,271,140)(10,272,141)(11,257,142)(12,258,143)(13,259,144)(14,260,129)(15,261,130)(16,262,131)(17,195,209)(18,196,210)(19,197,211)(20,198,212)(21,199,213)(22,200,214)(23,201,215)(24,202,216)(25,203,217)(26,204,218)(27,205,219)(28,206,220)(29,207,221)(30,208,222)(31,193,223)(32,194,224)(33,57,128)(34,58,113)(35,59,114)(36,60,115)(37,61,116)(38,62,117)(39,63,118)(40,64,119)(41,49,120)(42,50,121)(43,51,122)(44,52,123)(45,53,124)(46,54,125)(47,55,126)(48,56,127)(65,307,173)(66,308,174)(67,309,175)(68,310,176)(69,311,161)(70,312,162)(71,313,163)(72,314,164)(73,315,165)(74,316,166)(75,317,167)(76,318,168)(77,319,169)(78,320,170)(79,305,171)(80,306,172)(81,289,232)(82,290,233)(83,291,234)(84,292,235)(85,293,236)(86,294,237)(87,295,238)(88,296,239)(89,297,240)(90,298,225)(91,299,226)(92,300,227)(93,301,228)(94,302,229)(95,303,230)(96,304,231)(97,276,336)(98,277,321)(99,278,322)(100,279,323)(101,280,324)(102,281,325)(103,282,326)(104,283,327)(105,284,328)(106,285,329)(107,286,330)(108,287,331)(109,288,332)(110,273,333)(111,274,334)(112,275,335)(145,243,191)(146,244,192)(147,245,177)(148,246,178)(149,247,179)(150,248,180)(151,249,181)(152,250,182)(153,251,183)(154,252,184)(155,253,185)(156,254,186)(157,255,187)(158,256,188)(159,241,189)(160,242,190), (1,109,83,42,314,19,243)(2,244,20,315,43,84,110)(3,111,85,44,316,21,245)(4,246,22,317,45,86,112)(5,97,87,46,318,23,247)(6,248,24,319,47,88,98)(7,99,89,48,320,25,249)(8,250,26,305,33,90,100)(9,101,91,34,306,27,251)(10,252,28,307,35,92,102)(11,103,93,36,308,29,253)(12,254,30,309,37,94,104)(13,105,95,38,310,31,255)(14,256,32,311,39,96,106)(15,107,81,40,312,17,241)(16,242,18,313,41,82,108)(49,290,287,262,190,196,163)(50,164,197,191,263,288,291)(51,292,273,264,192,198,165)(52,166,199,177,265,274,293)(53,294,275,266,178,200,167)(54,168,201,179,267,276,295)(55,296,277,268,180,202,169)(56,170,203,181,269,278,297)(57,298,279,270,182,204,171)(58,172,205,183,271,280,299)(59,300,281,272,184,206,173)(60,174,207,185,257,282,301)(61,302,283,258,186,208,175)(62,176,193,187,259,284,303)(63,304,285,260,188,194,161)(64,162,195,189,261,286,289)(65,114,227,325,141,154,220)(66,221,155,142,326,228,115)(67,116,229,327,143,156,222)(68,223,157,144,328,230,117)(69,118,231,329,129,158,224)(70,209,159,130,330,232,119)(71,120,233,331,131,160,210)(72,211,145,132,332,234,121)(73,122,235,333,133,146,212)(74,213,147,134,334,236,123)(75,124,237,335,135,148,214)(76,215,149,136,336,238,125)(77,126,239,321,137,150,216)(78,217,151,138,322,240,127)(79,128,225,323,139,152,218)(80,219,153,140,324,226,113), (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( (1,263,132)(2,264,133)(3,265,134)(4,266,135)(5,267,136)(6,268,137)(7,269,138)(8,270,139)(9,271,140)(10,272,141)(11,257,142)(12,258,143)(13,259,144)(14,260,129)(15,261,130)(16,262,131)(17,195,209)(18,196,210)(19,197,211)(20,198,212)(21,199,213)(22,200,214)(23,201,215)(24,202,216)(25,203,217)(26,204,218)(27,205,219)(28,206,220)(29,207,221)(30,208,222)(31,193,223)(32,194,224)(33,57,128)(34,58,113)(35,59,114)(36,60,115)(37,61,116)(38,62,117)(39,63,118)(40,64,119)(41,49,120)(42,50,121)(43,51,122)(44,52,123)(45,53,124)(46,54,125)(47,55,126)(48,56,127)(65,307,173)(66,308,174)(67,309,175)(68,310,176)(69,311,161)(70,312,162)(71,313,163)(72,314,164)(73,315,165)(74,316,166)(75,317,167)(76,318,168)(77,319,169)(78,320,170)(79,305,171)(80,306,172)(81,289,232)(82,290,233)(83,291,234)(84,292,235)(85,293,236)(86,294,237)(87,295,238)(88,296,239)(89,297,240)(90,298,225)(91,299,226)(92,300,227)(93,301,228)(94,302,229)(95,303,230)(96,304,231)(97,276,336)(98,277,321)(99,278,322)(100,279,323)(101,280,324)(102,281,325)(103,282,326)(104,283,327)(105,284,328)(106,285,329)(107,286,330)(108,287,331)(109,288,332)(110,273,333)(111,274,334)(112,275,335)(145,243,191)(146,244,192)(147,245,177)(148,246,178)(149,247,179)(150,248,180)(151,249,181)(152,250,182)(153,251,183)(154,252,184)(155,253,185)(156,254,186)(157,255,187)(158,256,188)(159,241,189)(160,242,190), (1,109,83,42,314,19,243)(2,244,20,315,43,84,110)(3,111,85,44,316,21,245)(4,246,22,317,45,86,112)(5,97,87,46,318,23,247)(6,248,24,319,47,88,98)(7,99,89,48,320,25,249)(8,250,26,305,33,90,100)(9,101,91,34,306,27,251)(10,252,28,307,35,92,102)(11,103,93,36,308,29,253)(12,254,30,309,37,94,104)(13,105,95,38,310,31,255)(14,256,32,311,39,96,106)(15,107,81,40,312,17,241)(16,242,18,313,41,82,108)(49,290,287,262,190,196,163)(50,164,197,191,263,288,291)(51,292,273,264,192,198,165)(52,166,199,177,265,274,293)(53,294,275,266,178,200,167)(54,168,201,179,267,276,295)(55,296,277,268,180,202,169)(56,170,203,181,269,278,297)(57,298,279,270,182,204,171)(58,172,205,183,271,280,299)(59,300,281,272,184,206,173)(60,174,207,185,257,282,301)(61,302,283,258,186,208,175)(62,176,193,187,259,284,303)(63,304,285,260,188,194,161)(64,162,195,189,261,286,289)(65,114,227,325,141,154,220)(66,221,155,142,326,228,115)(67,116,229,327,143,156,222)(68,223,157,144,328,230,117)(69,118,231,329,129,158,224)(70,209,159,130,330,232,119)(71,120,233,331,131,160,210)(72,211,145,132,332,234,121)(73,122,235,333,133,146,212)(74,213,147,134,334,236,123)(75,124,237,335,135,148,214)(76,215,149,136,336,238,125)(77,126,239,321,137,150,216)(78,217,151,138,322,240,127)(79,128,225,323,139,152,218)(80,219,153,140,324,226,113), (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([[(1,263,132),(2,264,133),(3,265,134),(4,266,135),(5,267,136),(6,268,137),(7,269,138),(8,270,139),(9,271,140),(10,272,141),(11,257,142),(12,258,143),(13,259,144),(14,260,129),(15,261,130),(16,262,131),(17,195,209),(18,196,210),(19,197,211),(20,198,212),(21,199,213),(22,200,214),(23,201,215),(24,202,216),(25,203,217),(26,204,218),(27,205,219),(28,206,220),(29,207,221),(30,208,222),(31,193,223),(32,194,224),(33,57,128),(34,58,113),(35,59,114),(36,60,115),(37,61,116),(38,62,117),(39,63,118),(40,64,119),(41,49,120),(42,50,121),(43,51,122),(44,52,123),(45,53,124),(46,54,125),(47,55,126),(48,56,127),(65,307,173),(66,308,174),(67,309,175),(68,310,176),(69,311,161),(70,312,162),(71,313,163),(72,314,164),(73,315,165),(74,316,166),(75,317,167),(76,318,168),(77,319,169),(78,320,170),(79,305,171),(80,306,172),(81,289,232),(82,290,233),(83,291,234),(84,292,235),(85,293,236),(86,294,237),(87,295,238),(88,296,239),(89,297,240),(90,298,225),(91,299,226),(92,300,227),(93,301,228),(94,302,229),(95,303,230),(96,304,231),(97,276,336),(98,277,321),(99,278,322),(100,279,323),(101,280,324),(102,281,325),(103,282,326),(104,283,327),(105,284,328),(106,285,329),(107,286,330),(108,287,331),(109,288,332),(110,273,333),(111,274,334),(112,275,335),(145,243,191),(146,244,192),(147,245,177),(148,246,178),(149,247,179),(150,248,180),(151,249,181),(152,250,182),(153,251,183),(154,252,184),(155,253,185),(156,254,186),(157,255,187),(158,256,188),(159,241,189),(160,242,190)], [(1,109,83,42,314,19,243),(2,244,20,315,43,84,110),(3,111,85,44,316,21,245),(4,246,22,317,45,86,112),(5,97,87,46,318,23,247),(6,248,24,319,47,88,98),(7,99,89,48,320,25,249),(8,250,26,305,33,90,100),(9,101,91,34,306,27,251),(10,252,28,307,35,92,102),(11,103,93,36,308,29,253),(12,254,30,309,37,94,104),(13,105,95,38,310,31,255),(14,256,32,311,39,96,106),(15,107,81,40,312,17,241),(16,242,18,313,41,82,108),(49,290,287,262,190,196,163),(50,164,197,191,263,288,291),(51,292,273,264,192,198,165),(52,166,199,177,265,274,293),(53,294,275,266,178,200,167),(54,168,201,179,267,276,295),(55,296,277,268,180,202,169),(56,170,203,181,269,278,297),(57,298,279,270,182,204,171),(58,172,205,183,271,280,299),(59,300,281,272,184,206,173),(60,174,207,185,257,282,301),(61,302,283,258,186,208,175),(62,176,193,187,259,284,303),(63,304,285,260,188,194,161),(64,162,195,189,261,286,289),(65,114,227,325,141,154,220),(66,221,155,142,326,228,115),(67,116,229,327,143,156,222),(68,223,157,144,328,230,117),(69,118,231,329,129,158,224),(70,209,159,130,330,232,119),(71,120,233,331,131,160,210),(72,211,145,132,332,234,121),(73,122,235,333,133,146,212),(74,213,147,134,334,236,123),(75,124,237,335,135,148,214),(76,215,149,136,336,238,125),(77,126,239,321,137,150,216),(78,217,151,138,322,240,127),(79,128,225,323,139,152,218),(80,219,153,140,324,226,113)], [(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)]])
120 conjugacy classes
| class | 1 | 2 | 3A | 3B | 4A | 4B | 6A | 6B | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 14A | 14B | 14C | 16A | ··· | 16H | 21A | ··· | 21F | 24A | ··· | 24H | 28A | ··· | 28F | 42A | ··· | 42F | 48A | ··· | 48P | 56A | ··· | 56L | 84A | ··· | 84L | 168A | ··· | 168X |
| order | 1 | 2 | 3 | 3 | 4 | 4 | 6 | 6 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 12 | 12 | 12 | 12 | 14 | 14 | 14 | 16 | ··· | 16 | 21 | ··· | 21 | 24 | ··· | 24 | 28 | ··· | 28 | 42 | ··· | 42 | 48 | ··· | 48 | 56 | ··· | 56 | 84 | ··· | 84 | 168 | ··· | 168 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 7 | ··· | 7 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 7 | ··· | 7 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
120 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 | C3 | C4 | C6 | C8 | C12 | C16 | C24 | C48 | D7 | Dic7 | C3×D7 | C7⋊C8 | C3×Dic7 | C7⋊C16 | C3×C7⋊C8 | C3×C7⋊C16 |
| kernel | C3×C7⋊C16 | C168 | C7⋊C16 | C84 | C56 | C42 | C28 | C21 | C14 | C7 | C24 | C12 | C8 | C6 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 8 | 8 | 16 | 3 | 3 | 6 | 6 | 6 | 12 | 12 | 24 |
Matrix representation of C3×C7⋊C16 ►in GL4(𝔽337) generated by
| 208 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 144 | 336 |
| 0 | 0 | 145 | 336 |
| 111 | 0 | 0 | 0 |
| 0 | 191 | 0 | 0 |
| 0 | 0 | 153 | 27 |
| 0 | 0 | 151 | 184 |
G:=sub<GL(4,GF(337))| [208,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,144,145,0,0,336,336],[111,0,0,0,0,191,0,0,0,0,153,151,0,0,27,184] >;
C3×C7⋊C16 in GAP, Magma, Sage, TeX
C_3\times C_7\rtimes C_{16} % in TeX
G:=Group("C3xC7:C16"); // GroupNames label
G:=SmallGroup(336,4);
// by ID
G=gap.SmallGroup(336,4);
# by ID
G:=PCGroup([6,-2,-3,-2,-2,-2,-7,36,50,69,10373]);
// Polycyclic
G:=Group<a,b,c|a^3=b^7=c^16=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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