direct product, metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C3×Dic28, C21⋊5Q16, C56.5C6, C24.2D7, C168.2C2, C42.25D4, C6.15D28, C12.54D14, C84.61C22, Dic14.3C6, C8.(C3×D7), C7⋊4(C3×Q16), C4.10(C6×D7), C2.5(C3×D28), C28.33(C2×C6), C14.19(C3×D4), (C3×Dic14).3C2, SmallGroup(336,62)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×Dic28
G = < a,b,c | a3=b56=1, c2=b28, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C3×Dic28
►Regular action on 336 points
Generators in S336
(1 274 117)(2 275 118)(3 276 119)(4 277 120)(5 278 121)(6 279 122)(7 280 123)(8 225 124)(9 226 125)(10 227 126)(11 228 127)(12 229 128)(13 230 129)(14 231 130)(15 232 131)(16 233 132)(17 234 133)(18 235 134)(19 236 135)(20 237 136)(21 238 137)(22 239 138)(23 240 139)(24 241 140)(25 242 141)(26 243 142)(27 244 143)(28 245 144)(29 246 145)(30 247 146)(31 248 147)(32 249 148)(33 250 149)(34 251 150)(35 252 151)(36 253 152)(37 254 153)(38 255 154)(39 256 155)(40 257 156)(41 258 157)(42 259 158)(43 260 159)(44 261 160)(45 262 161)(46 263 162)(47 264 163)(48 265 164)(49 266 165)(50 267 166)(51 268 167)(52 269 168)(53 270 113)(54 271 114)(55 272 115)(56 273 116)(57 301 201)(58 302 202)(59 303 203)(60 304 204)(61 305 205)(62 306 206)(63 307 207)(64 308 208)(65 309 209)(66 310 210)(67 311 211)(68 312 212)(69 313 213)(70 314 214)(71 315 215)(72 316 216)(73 317 217)(74 318 218)(75 319 219)(76 320 220)(77 321 221)(78 322 222)(79 323 223)(80 324 224)(81 325 169)(82 326 170)(83 327 171)(84 328 172)(85 329 173)(86 330 174)(87 331 175)(88 332 176)(89 333 177)(90 334 178)(91 335 179)(92 336 180)(93 281 181)(94 282 182)(95 283 183)(96 284 184)(97 285 185)(98 286 186)(99 287 187)(100 288 188)(101 289 189)(102 290 190)(103 291 191)(104 292 192)(105 293 193)(106 294 194)(107 295 195)(108 296 196)(109 297 197)(110 298 198)(111 299 199)(112 300 200)
(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)
(1 173 29 201)(2 172 30 200)(3 171 31 199)(4 170 32 198)(5 169 33 197)(6 224 34 196)(7 223 35 195)(8 222 36 194)(9 221 37 193)(10 220 38 192)(11 219 39 191)(12 218 40 190)(13 217 41 189)(14 216 42 188)(15 215 43 187)(16 214 44 186)(17 213 45 185)(18 212 46 184)(19 211 47 183)(20 210 48 182)(21 209 49 181)(22 208 50 180)(23 207 51 179)(24 206 52 178)(25 205 53 177)(26 204 54 176)(27 203 55 175)(28 202 56 174)(57 274 85 246)(58 273 86 245)(59 272 87 244)(60 271 88 243)(61 270 89 242)(62 269 90 241)(63 268 91 240)(64 267 92 239)(65 266 93 238)(66 265 94 237)(67 264 95 236)(68 263 96 235)(69 262 97 234)(70 261 98 233)(71 260 99 232)(72 259 100 231)(73 258 101 230)(74 257 102 229)(75 256 103 228)(76 255 104 227)(77 254 105 226)(78 253 106 225)(79 252 107 280)(80 251 108 279)(81 250 109 278)(82 249 110 277)(83 248 111 276)(84 247 112 275)(113 333 141 305)(114 332 142 304)(115 331 143 303)(116 330 144 302)(117 329 145 301)(118 328 146 300)(119 327 147 299)(120 326 148 298)(121 325 149 297)(122 324 150 296)(123 323 151 295)(124 322 152 294)(125 321 153 293)(126 320 154 292)(127 319 155 291)(128 318 156 290)(129 317 157 289)(130 316 158 288)(131 315 159 287)(132 314 160 286)(133 313 161 285)(134 312 162 284)(135 311 163 283)(136 310 164 282)(137 309 165 281)(138 308 166 336)(139 307 167 335)(140 306 168 334)
G:=sub<Sym(336)| (1,274,117)(2,275,118)(3,276,119)(4,277,120)(5,278,121)(6,279,122)(7,280,123)(8,225,124)(9,226,125)(10,227,126)(11,228,127)(12,229,128)(13,230,129)(14,231,130)(15,232,131)(16,233,132)(17,234,133)(18,235,134)(19,236,135)(20,237,136)(21,238,137)(22,239,138)(23,240,139)(24,241,140)(25,242,141)(26,243,142)(27,244,143)(28,245,144)(29,246,145)(30,247,146)(31,248,147)(32,249,148)(33,250,149)(34,251,150)(35,252,151)(36,253,152)(37,254,153)(38,255,154)(39,256,155)(40,257,156)(41,258,157)(42,259,158)(43,260,159)(44,261,160)(45,262,161)(46,263,162)(47,264,163)(48,265,164)(49,266,165)(50,267,166)(51,268,167)(52,269,168)(53,270,113)(54,271,114)(55,272,115)(56,273,116)(57,301,201)(58,302,202)(59,303,203)(60,304,204)(61,305,205)(62,306,206)(63,307,207)(64,308,208)(65,309,209)(66,310,210)(67,311,211)(68,312,212)(69,313,213)(70,314,214)(71,315,215)(72,316,216)(73,317,217)(74,318,218)(75,319,219)(76,320,220)(77,321,221)(78,322,222)(79,323,223)(80,324,224)(81,325,169)(82,326,170)(83,327,171)(84,328,172)(85,329,173)(86,330,174)(87,331,175)(88,332,176)(89,333,177)(90,334,178)(91,335,179)(92,336,180)(93,281,181)(94,282,182)(95,283,183)(96,284,184)(97,285,185)(98,286,186)(99,287,187)(100,288,188)(101,289,189)(102,290,190)(103,291,191)(104,292,192)(105,293,193)(106,294,194)(107,295,195)(108,296,196)(109,297,197)(110,298,198)(111,299,199)(112,300,200), (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), (1,173,29,201)(2,172,30,200)(3,171,31,199)(4,170,32,198)(5,169,33,197)(6,224,34,196)(7,223,35,195)(8,222,36,194)(9,221,37,193)(10,220,38,192)(11,219,39,191)(12,218,40,190)(13,217,41,189)(14,216,42,188)(15,215,43,187)(16,214,44,186)(17,213,45,185)(18,212,46,184)(19,211,47,183)(20,210,48,182)(21,209,49,181)(22,208,50,180)(23,207,51,179)(24,206,52,178)(25,205,53,177)(26,204,54,176)(27,203,55,175)(28,202,56,174)(57,274,85,246)(58,273,86,245)(59,272,87,244)(60,271,88,243)(61,270,89,242)(62,269,90,241)(63,268,91,240)(64,267,92,239)(65,266,93,238)(66,265,94,237)(67,264,95,236)(68,263,96,235)(69,262,97,234)(70,261,98,233)(71,260,99,232)(72,259,100,231)(73,258,101,230)(74,257,102,229)(75,256,103,228)(76,255,104,227)(77,254,105,226)(78,253,106,225)(79,252,107,280)(80,251,108,279)(81,250,109,278)(82,249,110,277)(83,248,111,276)(84,247,112,275)(113,333,141,305)(114,332,142,304)(115,331,143,303)(116,330,144,302)(117,329,145,301)(118,328,146,300)(119,327,147,299)(120,326,148,298)(121,325,149,297)(122,324,150,296)(123,323,151,295)(124,322,152,294)(125,321,153,293)(126,320,154,292)(127,319,155,291)(128,318,156,290)(129,317,157,289)(130,316,158,288)(131,315,159,287)(132,314,160,286)(133,313,161,285)(134,312,162,284)(135,311,163,283)(136,310,164,282)(137,309,165,281)(138,308,166,336)(139,307,167,335)(140,306,168,334)>;
G:=Group( (1,274,117)(2,275,118)(3,276,119)(4,277,120)(5,278,121)(6,279,122)(7,280,123)(8,225,124)(9,226,125)(10,227,126)(11,228,127)(12,229,128)(13,230,129)(14,231,130)(15,232,131)(16,233,132)(17,234,133)(18,235,134)(19,236,135)(20,237,136)(21,238,137)(22,239,138)(23,240,139)(24,241,140)(25,242,141)(26,243,142)(27,244,143)(28,245,144)(29,246,145)(30,247,146)(31,248,147)(32,249,148)(33,250,149)(34,251,150)(35,252,151)(36,253,152)(37,254,153)(38,255,154)(39,256,155)(40,257,156)(41,258,157)(42,259,158)(43,260,159)(44,261,160)(45,262,161)(46,263,162)(47,264,163)(48,265,164)(49,266,165)(50,267,166)(51,268,167)(52,269,168)(53,270,113)(54,271,114)(55,272,115)(56,273,116)(57,301,201)(58,302,202)(59,303,203)(60,304,204)(61,305,205)(62,306,206)(63,307,207)(64,308,208)(65,309,209)(66,310,210)(67,311,211)(68,312,212)(69,313,213)(70,314,214)(71,315,215)(72,316,216)(73,317,217)(74,318,218)(75,319,219)(76,320,220)(77,321,221)(78,322,222)(79,323,223)(80,324,224)(81,325,169)(82,326,170)(83,327,171)(84,328,172)(85,329,173)(86,330,174)(87,331,175)(88,332,176)(89,333,177)(90,334,178)(91,335,179)(92,336,180)(93,281,181)(94,282,182)(95,283,183)(96,284,184)(97,285,185)(98,286,186)(99,287,187)(100,288,188)(101,289,189)(102,290,190)(103,291,191)(104,292,192)(105,293,193)(106,294,194)(107,295,195)(108,296,196)(109,297,197)(110,298,198)(111,299,199)(112,300,200), (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), (1,173,29,201)(2,172,30,200)(3,171,31,199)(4,170,32,198)(5,169,33,197)(6,224,34,196)(7,223,35,195)(8,222,36,194)(9,221,37,193)(10,220,38,192)(11,219,39,191)(12,218,40,190)(13,217,41,189)(14,216,42,188)(15,215,43,187)(16,214,44,186)(17,213,45,185)(18,212,46,184)(19,211,47,183)(20,210,48,182)(21,209,49,181)(22,208,50,180)(23,207,51,179)(24,206,52,178)(25,205,53,177)(26,204,54,176)(27,203,55,175)(28,202,56,174)(57,274,85,246)(58,273,86,245)(59,272,87,244)(60,271,88,243)(61,270,89,242)(62,269,90,241)(63,268,91,240)(64,267,92,239)(65,266,93,238)(66,265,94,237)(67,264,95,236)(68,263,96,235)(69,262,97,234)(70,261,98,233)(71,260,99,232)(72,259,100,231)(73,258,101,230)(74,257,102,229)(75,256,103,228)(76,255,104,227)(77,254,105,226)(78,253,106,225)(79,252,107,280)(80,251,108,279)(81,250,109,278)(82,249,110,277)(83,248,111,276)(84,247,112,275)(113,333,141,305)(114,332,142,304)(115,331,143,303)(116,330,144,302)(117,329,145,301)(118,328,146,300)(119,327,147,299)(120,326,148,298)(121,325,149,297)(122,324,150,296)(123,323,151,295)(124,322,152,294)(125,321,153,293)(126,320,154,292)(127,319,155,291)(128,318,156,290)(129,317,157,289)(130,316,158,288)(131,315,159,287)(132,314,160,286)(133,313,161,285)(134,312,162,284)(135,311,163,283)(136,310,164,282)(137,309,165,281)(138,308,166,336)(139,307,167,335)(140,306,168,334) );
G=PermutationGroup([[(1,274,117),(2,275,118),(3,276,119),(4,277,120),(5,278,121),(6,279,122),(7,280,123),(8,225,124),(9,226,125),(10,227,126),(11,228,127),(12,229,128),(13,230,129),(14,231,130),(15,232,131),(16,233,132),(17,234,133),(18,235,134),(19,236,135),(20,237,136),(21,238,137),(22,239,138),(23,240,139),(24,241,140),(25,242,141),(26,243,142),(27,244,143),(28,245,144),(29,246,145),(30,247,146),(31,248,147),(32,249,148),(33,250,149),(34,251,150),(35,252,151),(36,253,152),(37,254,153),(38,255,154),(39,256,155),(40,257,156),(41,258,157),(42,259,158),(43,260,159),(44,261,160),(45,262,161),(46,263,162),(47,264,163),(48,265,164),(49,266,165),(50,267,166),(51,268,167),(52,269,168),(53,270,113),(54,271,114),(55,272,115),(56,273,116),(57,301,201),(58,302,202),(59,303,203),(60,304,204),(61,305,205),(62,306,206),(63,307,207),(64,308,208),(65,309,209),(66,310,210),(67,311,211),(68,312,212),(69,313,213),(70,314,214),(71,315,215),(72,316,216),(73,317,217),(74,318,218),(75,319,219),(76,320,220),(77,321,221),(78,322,222),(79,323,223),(80,324,224),(81,325,169),(82,326,170),(83,327,171),(84,328,172),(85,329,173),(86,330,174),(87,331,175),(88,332,176),(89,333,177),(90,334,178),(91,335,179),(92,336,180),(93,281,181),(94,282,182),(95,283,183),(96,284,184),(97,285,185),(98,286,186),(99,287,187),(100,288,188),(101,289,189),(102,290,190),(103,291,191),(104,292,192),(105,293,193),(106,294,194),(107,295,195),(108,296,196),(109,297,197),(110,298,198),(111,299,199),(112,300,200)], [(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)], [(1,173,29,201),(2,172,30,200),(3,171,31,199),(4,170,32,198),(5,169,33,197),(6,224,34,196),(7,223,35,195),(8,222,36,194),(9,221,37,193),(10,220,38,192),(11,219,39,191),(12,218,40,190),(13,217,41,189),(14,216,42,188),(15,215,43,187),(16,214,44,186),(17,213,45,185),(18,212,46,184),(19,211,47,183),(20,210,48,182),(21,209,49,181),(22,208,50,180),(23,207,51,179),(24,206,52,178),(25,205,53,177),(26,204,54,176),(27,203,55,175),(28,202,56,174),(57,274,85,246),(58,273,86,245),(59,272,87,244),(60,271,88,243),(61,270,89,242),(62,269,90,241),(63,268,91,240),(64,267,92,239),(65,266,93,238),(66,265,94,237),(67,264,95,236),(68,263,96,235),(69,262,97,234),(70,261,98,233),(71,260,99,232),(72,259,100,231),(73,258,101,230),(74,257,102,229),(75,256,103,228),(76,255,104,227),(77,254,105,226),(78,253,106,225),(79,252,107,280),(80,251,108,279),(81,250,109,278),(82,249,110,277),(83,248,111,276),(84,247,112,275),(113,333,141,305),(114,332,142,304),(115,331,143,303),(116,330,144,302),(117,329,145,301),(118,328,146,300),(119,327,147,299),(120,326,148,298),(121,325,149,297),(122,324,150,296),(123,323,151,295),(124,322,152,294),(125,321,153,293),(126,320,154,292),(127,319,155,291),(128,318,156,290),(129,317,157,289),(130,316,158,288),(131,315,159,287),(132,314,160,286),(133,313,161,285),(134,312,162,284),(135,311,163,283),(136,310,164,282),(137,309,165,281),(138,308,166,336),(139,307,167,335),(140,306,168,334)]])
93 conjugacy classes
| class | 1 | 2 | 3A | 3B | 4A | 4B | 4C | 6A | 6B | 7A | 7B | 7C | 8A | 8B | 12A | 12B | 12C | 12D | 12E | 12F | 14A | 14B | 14C | 21A | ··· | 21F | 24A | 24B | 24C | 24D | 28A | ··· | 28F | 42A | ··· | 42F | 56A | ··· | 56L | 84A | ··· | 84L | 168A | ··· | 168X |
| order | 1 | 2 | 3 | 3 | 4 | 4 | 4 | 6 | 6 | 7 | 7 | 7 | 8 | 8 | 12 | 12 | 12 | 12 | 12 | 12 | 14 | 14 | 14 | 21 | ··· | 21 | 24 | 24 | 24 | 24 | 28 | ··· | 28 | 42 | ··· | 42 | 56 | ··· | 56 | 84 | ··· | 84 | 168 | ··· | 168 |
| size | 1 | 1 | 1 | 1 | 2 | 28 | 28 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
93 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | + | - | |||||||||
| image | C1 | C2 | C2 | C3 | C6 | C6 | D4 | D7 | Q16 | C3×D4 | D14 | C3×D7 | C3×Q16 | D28 | C6×D7 | Dic28 | C3×D28 | C3×Dic28 |
| kernel | C3×Dic28 | C168 | C3×Dic14 | Dic28 | C56 | Dic14 | C42 | C24 | C21 | C14 | C12 | C8 | C7 | C6 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 2 | 2 | 2 | 4 | 1 | 3 | 2 | 2 | 3 | 6 | 4 | 6 | 6 | 12 | 12 | 24 |
Matrix representation of C3×Dic28 ►in GL2(𝔽337) generated by
| 128 | 0 |
| 0 | 128 |
| 108 | 224 |
| 113 | 69 |
| 214 | 46 |
| 96 | 123 |
G:=sub<GL(2,GF(337))| [128,0,0,128],[108,113,224,69],[214,96,46,123] >;
C3×Dic28 in GAP, Magma, Sage, TeX
C_3\times {\rm Dic}_{28} % in TeX
G:=Group("C3xDic28"); // GroupNames label
G:=SmallGroup(336,62);
// by ID
G=gap.SmallGroup(336,62);
# by ID
G:=PCGroup([6,-2,-2,-3,-2,-2,-7,144,169,223,867,69,10373]);
// Polycyclic
G:=Group<a,b,c|a^3=b^56=1,c^2=b^28,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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