metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C21⋊2Q16, C6.9D28, C3⋊2Dic28, C12.8D14, C42.11D4, C28.25D6, C84.11C22, Dic14.1S3, Dic42.3C2, C3⋊C8.D7, C4.4(S3×D7), C7⋊1(C3⋊Q16), C14.4(C3⋊D4), C2.7(C3⋊D28), (C3×Dic14).1C2, (C7×C3⋊C8).1C2, SmallGroup(336,39)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3⋊Dic28
G = < a,b,c | a3=b56=1, c2=b28, bab-1=a-1, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C3⋊Dic28
►Regular action on 336 points
Generators in S336
(1 314 146)(2 147 315)(3 316 148)(4 149 317)(5 318 150)(6 151 319)(7 320 152)(8 153 321)(9 322 154)(10 155 323)(11 324 156)(12 157 325)(13 326 158)(14 159 327)(15 328 160)(16 161 329)(17 330 162)(18 163 331)(19 332 164)(20 165 333)(21 334 166)(22 167 335)(23 336 168)(24 113 281)(25 282 114)(26 115 283)(27 284 116)(28 117 285)(29 286 118)(30 119 287)(31 288 120)(32 121 289)(33 290 122)(34 123 291)(35 292 124)(36 125 293)(37 294 126)(38 127 295)(39 296 128)(40 129 297)(41 298 130)(42 131 299)(43 300 132)(44 133 301)(45 302 134)(46 135 303)(47 304 136)(48 137 305)(49 306 138)(50 139 307)(51 308 140)(52 141 309)(53 310 142)(54 143 311)(55 312 144)(56 145 313)(57 278 200)(58 201 279)(59 280 202)(60 203 225)(61 226 204)(62 205 227)(63 228 206)(64 207 229)(65 230 208)(66 209 231)(67 232 210)(68 211 233)(69 234 212)(70 213 235)(71 236 214)(72 215 237)(73 238 216)(74 217 239)(75 240 218)(76 219 241)(77 242 220)(78 221 243)(79 244 222)(80 223 245)(81 246 224)(82 169 247)(83 248 170)(84 171 249)(85 250 172)(86 173 251)(87 252 174)(88 175 253)(89 254 176)(90 177 255)(91 256 178)(92 179 257)(93 258 180)(94 181 259)(95 260 182)(96 183 261)(97 262 184)(98 185 263)(99 264 186)(100 187 265)(101 266 188)(102 189 267)(103 268 190)(104 191 269)(105 270 192)(106 193 271)(107 272 194)(108 195 273)(109 274 196)(110 197 275)(111 276 198)(112 199 277)
(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)
(1 226 29 254)(2 225 30 253)(3 280 31 252)(4 279 32 251)(5 278 33 250)(6 277 34 249)(7 276 35 248)(8 275 36 247)(9 274 37 246)(10 273 38 245)(11 272 39 244)(12 271 40 243)(13 270 41 242)(14 269 42 241)(15 268 43 240)(16 267 44 239)(17 266 45 238)(18 265 46 237)(19 264 47 236)(20 263 48 235)(21 262 49 234)(22 261 50 233)(23 260 51 232)(24 259 52 231)(25 258 53 230)(26 257 54 229)(27 256 55 228)(28 255 56 227)(57 122 85 150)(58 121 86 149)(59 120 87 148)(60 119 88 147)(61 118 89 146)(62 117 90 145)(63 116 91 144)(64 115 92 143)(65 114 93 142)(66 113 94 141)(67 168 95 140)(68 167 96 139)(69 166 97 138)(70 165 98 137)(71 164 99 136)(72 163 100 135)(73 162 101 134)(74 161 102 133)(75 160 103 132)(76 159 104 131)(77 158 105 130)(78 157 106 129)(79 156 107 128)(80 155 108 127)(81 154 109 126)(82 153 110 125)(83 152 111 124)(84 151 112 123)(169 321 197 293)(170 320 198 292)(171 319 199 291)(172 318 200 290)(173 317 201 289)(174 316 202 288)(175 315 203 287)(176 314 204 286)(177 313 205 285)(178 312 206 284)(179 311 207 283)(180 310 208 282)(181 309 209 281)(182 308 210 336)(183 307 211 335)(184 306 212 334)(185 305 213 333)(186 304 214 332)(187 303 215 331)(188 302 216 330)(189 301 217 329)(190 300 218 328)(191 299 219 327)(192 298 220 326)(193 297 221 325)(194 296 222 324)(195 295 223 323)(196 294 224 322)
G:=sub<Sym(336)| (1,314,146)(2,147,315)(3,316,148)(4,149,317)(5,318,150)(6,151,319)(7,320,152)(8,153,321)(9,322,154)(10,155,323)(11,324,156)(12,157,325)(13,326,158)(14,159,327)(15,328,160)(16,161,329)(17,330,162)(18,163,331)(19,332,164)(20,165,333)(21,334,166)(22,167,335)(23,336,168)(24,113,281)(25,282,114)(26,115,283)(27,284,116)(28,117,285)(29,286,118)(30,119,287)(31,288,120)(32,121,289)(33,290,122)(34,123,291)(35,292,124)(36,125,293)(37,294,126)(38,127,295)(39,296,128)(40,129,297)(41,298,130)(42,131,299)(43,300,132)(44,133,301)(45,302,134)(46,135,303)(47,304,136)(48,137,305)(49,306,138)(50,139,307)(51,308,140)(52,141,309)(53,310,142)(54,143,311)(55,312,144)(56,145,313)(57,278,200)(58,201,279)(59,280,202)(60,203,225)(61,226,204)(62,205,227)(63,228,206)(64,207,229)(65,230,208)(66,209,231)(67,232,210)(68,211,233)(69,234,212)(70,213,235)(71,236,214)(72,215,237)(73,238,216)(74,217,239)(75,240,218)(76,219,241)(77,242,220)(78,221,243)(79,244,222)(80,223,245)(81,246,224)(82,169,247)(83,248,170)(84,171,249)(85,250,172)(86,173,251)(87,252,174)(88,175,253)(89,254,176)(90,177,255)(91,256,178)(92,179,257)(93,258,180)(94,181,259)(95,260,182)(96,183,261)(97,262,184)(98,185,263)(99,264,186)(100,187,265)(101,266,188)(102,189,267)(103,268,190)(104,191,269)(105,270,192)(106,193,271)(107,272,194)(108,195,273)(109,274,196)(110,197,275)(111,276,198)(112,199,277), (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), (1,226,29,254)(2,225,30,253)(3,280,31,252)(4,279,32,251)(5,278,33,250)(6,277,34,249)(7,276,35,248)(8,275,36,247)(9,274,37,246)(10,273,38,245)(11,272,39,244)(12,271,40,243)(13,270,41,242)(14,269,42,241)(15,268,43,240)(16,267,44,239)(17,266,45,238)(18,265,46,237)(19,264,47,236)(20,263,48,235)(21,262,49,234)(22,261,50,233)(23,260,51,232)(24,259,52,231)(25,258,53,230)(26,257,54,229)(27,256,55,228)(28,255,56,227)(57,122,85,150)(58,121,86,149)(59,120,87,148)(60,119,88,147)(61,118,89,146)(62,117,90,145)(63,116,91,144)(64,115,92,143)(65,114,93,142)(66,113,94,141)(67,168,95,140)(68,167,96,139)(69,166,97,138)(70,165,98,137)(71,164,99,136)(72,163,100,135)(73,162,101,134)(74,161,102,133)(75,160,103,132)(76,159,104,131)(77,158,105,130)(78,157,106,129)(79,156,107,128)(80,155,108,127)(81,154,109,126)(82,153,110,125)(83,152,111,124)(84,151,112,123)(169,321,197,293)(170,320,198,292)(171,319,199,291)(172,318,200,290)(173,317,201,289)(174,316,202,288)(175,315,203,287)(176,314,204,286)(177,313,205,285)(178,312,206,284)(179,311,207,283)(180,310,208,282)(181,309,209,281)(182,308,210,336)(183,307,211,335)(184,306,212,334)(185,305,213,333)(186,304,214,332)(187,303,215,331)(188,302,216,330)(189,301,217,329)(190,300,218,328)(191,299,219,327)(192,298,220,326)(193,297,221,325)(194,296,222,324)(195,295,223,323)(196,294,224,322)>;
G:=Group( (1,314,146)(2,147,315)(3,316,148)(4,149,317)(5,318,150)(6,151,319)(7,320,152)(8,153,321)(9,322,154)(10,155,323)(11,324,156)(12,157,325)(13,326,158)(14,159,327)(15,328,160)(16,161,329)(17,330,162)(18,163,331)(19,332,164)(20,165,333)(21,334,166)(22,167,335)(23,336,168)(24,113,281)(25,282,114)(26,115,283)(27,284,116)(28,117,285)(29,286,118)(30,119,287)(31,288,120)(32,121,289)(33,290,122)(34,123,291)(35,292,124)(36,125,293)(37,294,126)(38,127,295)(39,296,128)(40,129,297)(41,298,130)(42,131,299)(43,300,132)(44,133,301)(45,302,134)(46,135,303)(47,304,136)(48,137,305)(49,306,138)(50,139,307)(51,308,140)(52,141,309)(53,310,142)(54,143,311)(55,312,144)(56,145,313)(57,278,200)(58,201,279)(59,280,202)(60,203,225)(61,226,204)(62,205,227)(63,228,206)(64,207,229)(65,230,208)(66,209,231)(67,232,210)(68,211,233)(69,234,212)(70,213,235)(71,236,214)(72,215,237)(73,238,216)(74,217,239)(75,240,218)(76,219,241)(77,242,220)(78,221,243)(79,244,222)(80,223,245)(81,246,224)(82,169,247)(83,248,170)(84,171,249)(85,250,172)(86,173,251)(87,252,174)(88,175,253)(89,254,176)(90,177,255)(91,256,178)(92,179,257)(93,258,180)(94,181,259)(95,260,182)(96,183,261)(97,262,184)(98,185,263)(99,264,186)(100,187,265)(101,266,188)(102,189,267)(103,268,190)(104,191,269)(105,270,192)(106,193,271)(107,272,194)(108,195,273)(109,274,196)(110,197,275)(111,276,198)(112,199,277), (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), (1,226,29,254)(2,225,30,253)(3,280,31,252)(4,279,32,251)(5,278,33,250)(6,277,34,249)(7,276,35,248)(8,275,36,247)(9,274,37,246)(10,273,38,245)(11,272,39,244)(12,271,40,243)(13,270,41,242)(14,269,42,241)(15,268,43,240)(16,267,44,239)(17,266,45,238)(18,265,46,237)(19,264,47,236)(20,263,48,235)(21,262,49,234)(22,261,50,233)(23,260,51,232)(24,259,52,231)(25,258,53,230)(26,257,54,229)(27,256,55,228)(28,255,56,227)(57,122,85,150)(58,121,86,149)(59,120,87,148)(60,119,88,147)(61,118,89,146)(62,117,90,145)(63,116,91,144)(64,115,92,143)(65,114,93,142)(66,113,94,141)(67,168,95,140)(68,167,96,139)(69,166,97,138)(70,165,98,137)(71,164,99,136)(72,163,100,135)(73,162,101,134)(74,161,102,133)(75,160,103,132)(76,159,104,131)(77,158,105,130)(78,157,106,129)(79,156,107,128)(80,155,108,127)(81,154,109,126)(82,153,110,125)(83,152,111,124)(84,151,112,123)(169,321,197,293)(170,320,198,292)(171,319,199,291)(172,318,200,290)(173,317,201,289)(174,316,202,288)(175,315,203,287)(176,314,204,286)(177,313,205,285)(178,312,206,284)(179,311,207,283)(180,310,208,282)(181,309,209,281)(182,308,210,336)(183,307,211,335)(184,306,212,334)(185,305,213,333)(186,304,214,332)(187,303,215,331)(188,302,216,330)(189,301,217,329)(190,300,218,328)(191,299,219,327)(192,298,220,326)(193,297,221,325)(194,296,222,324)(195,295,223,323)(196,294,224,322) );
G=PermutationGroup([[(1,314,146),(2,147,315),(3,316,148),(4,149,317),(5,318,150),(6,151,319),(7,320,152),(8,153,321),(9,322,154),(10,155,323),(11,324,156),(12,157,325),(13,326,158),(14,159,327),(15,328,160),(16,161,329),(17,330,162),(18,163,331),(19,332,164),(20,165,333),(21,334,166),(22,167,335),(23,336,168),(24,113,281),(25,282,114),(26,115,283),(27,284,116),(28,117,285),(29,286,118),(30,119,287),(31,288,120),(32,121,289),(33,290,122),(34,123,291),(35,292,124),(36,125,293),(37,294,126),(38,127,295),(39,296,128),(40,129,297),(41,298,130),(42,131,299),(43,300,132),(44,133,301),(45,302,134),(46,135,303),(47,304,136),(48,137,305),(49,306,138),(50,139,307),(51,308,140),(52,141,309),(53,310,142),(54,143,311),(55,312,144),(56,145,313),(57,278,200),(58,201,279),(59,280,202),(60,203,225),(61,226,204),(62,205,227),(63,228,206),(64,207,229),(65,230,208),(66,209,231),(67,232,210),(68,211,233),(69,234,212),(70,213,235),(71,236,214),(72,215,237),(73,238,216),(74,217,239),(75,240,218),(76,219,241),(77,242,220),(78,221,243),(79,244,222),(80,223,245),(81,246,224),(82,169,247),(83,248,170),(84,171,249),(85,250,172),(86,173,251),(87,252,174),(88,175,253),(89,254,176),(90,177,255),(91,256,178),(92,179,257),(93,258,180),(94,181,259),(95,260,182),(96,183,261),(97,262,184),(98,185,263),(99,264,186),(100,187,265),(101,266,188),(102,189,267),(103,268,190),(104,191,269),(105,270,192),(106,193,271),(107,272,194),(108,195,273),(109,274,196),(110,197,275),(111,276,198),(112,199,277)], [(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)], [(1,226,29,254),(2,225,30,253),(3,280,31,252),(4,279,32,251),(5,278,33,250),(6,277,34,249),(7,276,35,248),(8,275,36,247),(9,274,37,246),(10,273,38,245),(11,272,39,244),(12,271,40,243),(13,270,41,242),(14,269,42,241),(15,268,43,240),(16,267,44,239),(17,266,45,238),(18,265,46,237),(19,264,47,236),(20,263,48,235),(21,262,49,234),(22,261,50,233),(23,260,51,232),(24,259,52,231),(25,258,53,230),(26,257,54,229),(27,256,55,228),(28,255,56,227),(57,122,85,150),(58,121,86,149),(59,120,87,148),(60,119,88,147),(61,118,89,146),(62,117,90,145),(63,116,91,144),(64,115,92,143),(65,114,93,142),(66,113,94,141),(67,168,95,140),(68,167,96,139),(69,166,97,138),(70,165,98,137),(71,164,99,136),(72,163,100,135),(73,162,101,134),(74,161,102,133),(75,160,103,132),(76,159,104,131),(77,158,105,130),(78,157,106,129),(79,156,107,128),(80,155,108,127),(81,154,109,126),(82,153,110,125),(83,152,111,124),(84,151,112,123),(169,321,197,293),(170,320,198,292),(171,319,199,291),(172,318,200,290),(173,317,201,289),(174,316,202,288),(175,315,203,287),(176,314,204,286),(177,313,205,285),(178,312,206,284),(179,311,207,283),(180,310,208,282),(181,309,209,281),(182,308,210,336),(183,307,211,335),(184,306,212,334),(185,305,213,333),(186,304,214,332),(187,303,215,331),(188,302,216,330),(189,301,217,329),(190,300,218,328),(191,299,219,327),(192,298,220,326),(193,297,221,325),(194,296,222,324),(195,295,223,323),(196,294,224,322)]])
48 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 | ··· | 28F | 42A | 42B | 42C | 56A | ··· | 56L | 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 | 42 | 42 | 42 | 56 | ··· | 56 | 84 | ··· | 84 |
| size | 1 | 1 | 2 | 2 | 28 | 84 | 2 | 2 | 2 | 2 | 6 | 6 | 4 | 28 | 28 | 2 | 2 | 2 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 6 | ··· | 6 | 4 | ··· | 4 |
48 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | - | - | + | + | - | |
| image | C1 | C2 | C2 | C2 | S3 | D4 | D6 | D7 | Q16 | C3⋊D4 | D14 | D28 | Dic28 | C3⋊Q16 | S3×D7 | C3⋊D28 | C3⋊Dic28 |
| kernel | C3⋊Dic28 | C7×C3⋊C8 | C3×Dic14 | Dic42 | Dic14 | C42 | C28 | C3⋊C8 | C21 | C14 | C12 | C6 | C3 | C7 | C4 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 2 | 2 | 3 | 6 | 12 | 1 | 3 | 3 | 6 |
Matrix representation of C3⋊Dic28 ►in GL6(𝔽337)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 112 | 0 | 0 |
| 0 | 0 | 9 | 335 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 336 | 0 | 0 | 0 | 0 |
| 1 | 110 | 0 | 0 | 0 | 0 |
| 0 | 0 | 278 | 275 | 0 | 0 |
| 0 | 0 | 154 | 59 | 0 | 0 |
| 0 | 0 | 0 | 0 | 311 | 39 |
| 0 | 0 | 0 | 0 | 216 | 0 |
| 332 | 9 | 0 | 0 | 0 | 0 |
| 222 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 257 | 205 | 0 | 0 |
| 0 | 0 | 194 | 80 | 0 | 0 |
| 0 | 0 | 0 | 0 | 71 | 197 |
| 0 | 0 | 0 | 0 | 166 | 266 |
G:=sub<GL(6,GF(337))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,9,0,0,0,0,112,335,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,336,110,0,0,0,0,0,0,278,154,0,0,0,0,275,59,0,0,0,0,0,0,311,216,0,0,0,0,39,0],[332,222,0,0,0,0,9,5,0,0,0,0,0,0,257,194,0,0,0,0,205,80,0,0,0,0,0,0,71,166,0,0,0,0,197,266] >;
C3⋊Dic28 in GAP, Magma, Sage, TeX
C_3\rtimes {\rm Dic}_{28} % in TeX
G:=Group("C3:Dic28"); // GroupNames label
G:=SmallGroup(336,39);
// by ID
G=gap.SmallGroup(336,39);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-3,-7,48,73,79,218,50,490,10373]);
// Polycyclic
G:=Group<a,b,c|a^3=b^56=1,c^2=b^28,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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