metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.3Q8, Dic3⋊Dic7, C42.18D4, C6.12D28, C14.3Dic6, C6.3Dic14, C21⋊3(C4⋊C4), C3⋊1(C4⋊Dic7), C2.3(C21⋊Q8), C14.14(C4×S3), C42.13(C2×C4), C7⋊2(Dic3⋊C4), (C7×Dic3)⋊2C4, (C2×C14).11D6, (C2×C6).11D14, C2.5(S3×Dic7), C6.5(C2×Dic7), C2.3(C3⋊D28), C14.6(C3⋊D4), (C2×C42).8C22, (C6×Dic7).4C2, (C2×Dic3).3D7, (C2×Dic7).3S3, C22.10(S3×D7), (C2×Dic21).7C2, (Dic3×C14).4C2, SmallGroup(336,47)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.Dic6
G = < a,b,c | a14=b12=1, c2=a7b6, bab-1=a-1, ac=ca, cbc-1=a7b-1 >
Smallest permutation representation of C14.Dic6
►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 89 284 201 146 17 47 169 166 82 328 125)(2 88 285 200 147 16 48 182 167 81 329 124)(3 87 286 199 148 15 49 181 168 80 330 123)(4 86 287 198 149 28 50 180 155 79 331 122)(5 85 288 197 150 27 51 179 156 78 332 121)(6 98 289 210 151 26 52 178 157 77 333 120)(7 97 290 209 152 25 53 177 158 76 334 119)(8 96 291 208 153 24 54 176 159 75 335 118)(9 95 292 207 154 23 55 175 160 74 336 117)(10 94 293 206 141 22 56 174 161 73 323 116)(11 93 294 205 142 21 43 173 162 72 324 115)(12 92 281 204 143 20 44 172 163 71 325 114)(13 91 282 203 144 19 45 171 164 84 326 113)(14 90 283 202 145 18 46 170 165 83 327 126)(29 237 193 280 308 247 133 217 107 59 313 254)(30 236 194 279 295 246 134 216 108 58 314 253)(31 235 195 278 296 245 135 215 109 57 315 266)(32 234 196 277 297 244 136 214 110 70 316 265)(33 233 183 276 298 243 137 213 111 69 317 264)(34 232 184 275 299 242 138 212 112 68 318 263)(35 231 185 274 300 241 139 211 99 67 319 262)(36 230 186 273 301 240 140 224 100 66 320 261)(37 229 187 272 302 239 127 223 101 65 321 260)(38 228 188 271 303 252 128 222 102 64 322 259)(39 227 189 270 304 251 129 221 103 63 309 258)(40 226 190 269 305 250 130 220 104 62 310 257)(41 225 191 268 306 249 131 219 105 61 311 256)(42 238 192 267 307 248 132 218 106 60 312 255)
(1 278 54 64)(2 279 55 65)(3 280 56 66)(4 267 43 67)(5 268 44 68)(6 269 45 69)(7 270 46 70)(8 271 47 57)(9 272 48 58)(10 273 49 59)(11 274 50 60)(12 275 51 61)(13 276 52 62)(14 277 53 63)(15 320 116 308)(16 321 117 295)(17 322 118 296)(18 309 119 297)(19 310 120 298)(20 311 121 299)(21 312 122 300)(22 313 123 301)(23 314 124 302)(24 315 125 303)(25 316 126 304)(26 317 113 305)(27 318 114 306)(28 319 115 307)(29 80 140 206)(30 81 127 207)(31 82 128 208)(32 83 129 209)(33 84 130 210)(34 71 131 197)(35 72 132 198)(36 73 133 199)(37 74 134 200)(38 75 135 201)(39 76 136 202)(40 77 137 203)(41 78 138 204)(42 79 139 205)(85 184 172 105)(86 185 173 106)(87 186 174 107)(88 187 175 108)(89 188 176 109)(90 189 177 110)(91 190 178 111)(92 191 179 112)(93 192 180 99)(94 193 181 100)(95 194 182 101)(96 195 169 102)(97 196 170 103)(98 183 171 104)(141 261 330 247)(142 262 331 248)(143 263 332 249)(144 264 333 250)(145 265 334 251)(146 266 335 252)(147 253 336 239)(148 254 323 240)(149 255 324 241)(150 256 325 242)(151 257 326 243)(152 258 327 244)(153 259 328 245)(154 260 329 246)(155 218 294 231)(156 219 281 232)(157 220 282 233)(158 221 283 234)(159 222 284 235)(160 223 285 236)(161 224 286 237)(162 211 287 238)(163 212 288 225)(164 213 289 226)(165 214 290 227)(166 215 291 228)(167 216 292 229)(168 217 293 230)
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), (1,89,284,201,146,17,47,169,166,82,328,125)(2,88,285,200,147,16,48,182,167,81,329,124)(3,87,286,199,148,15,49,181,168,80,330,123)(4,86,287,198,149,28,50,180,155,79,331,122)(5,85,288,197,150,27,51,179,156,78,332,121)(6,98,289,210,151,26,52,178,157,77,333,120)(7,97,290,209,152,25,53,177,158,76,334,119)(8,96,291,208,153,24,54,176,159,75,335,118)(9,95,292,207,154,23,55,175,160,74,336,117)(10,94,293,206,141,22,56,174,161,73,323,116)(11,93,294,205,142,21,43,173,162,72,324,115)(12,92,281,204,143,20,44,172,163,71,325,114)(13,91,282,203,144,19,45,171,164,84,326,113)(14,90,283,202,145,18,46,170,165,83,327,126)(29,237,193,280,308,247,133,217,107,59,313,254)(30,236,194,279,295,246,134,216,108,58,314,253)(31,235,195,278,296,245,135,215,109,57,315,266)(32,234,196,277,297,244,136,214,110,70,316,265)(33,233,183,276,298,243,137,213,111,69,317,264)(34,232,184,275,299,242,138,212,112,68,318,263)(35,231,185,274,300,241,139,211,99,67,319,262)(36,230,186,273,301,240,140,224,100,66,320,261)(37,229,187,272,302,239,127,223,101,65,321,260)(38,228,188,271,303,252,128,222,102,64,322,259)(39,227,189,270,304,251,129,221,103,63,309,258)(40,226,190,269,305,250,130,220,104,62,310,257)(41,225,191,268,306,249,131,219,105,61,311,256)(42,238,192,267,307,248,132,218,106,60,312,255), (1,278,54,64)(2,279,55,65)(3,280,56,66)(4,267,43,67)(5,268,44,68)(6,269,45,69)(7,270,46,70)(8,271,47,57)(9,272,48,58)(10,273,49,59)(11,274,50,60)(12,275,51,61)(13,276,52,62)(14,277,53,63)(15,320,116,308)(16,321,117,295)(17,322,118,296)(18,309,119,297)(19,310,120,298)(20,311,121,299)(21,312,122,300)(22,313,123,301)(23,314,124,302)(24,315,125,303)(25,316,126,304)(26,317,113,305)(27,318,114,306)(28,319,115,307)(29,80,140,206)(30,81,127,207)(31,82,128,208)(32,83,129,209)(33,84,130,210)(34,71,131,197)(35,72,132,198)(36,73,133,199)(37,74,134,200)(38,75,135,201)(39,76,136,202)(40,77,137,203)(41,78,138,204)(42,79,139,205)(85,184,172,105)(86,185,173,106)(87,186,174,107)(88,187,175,108)(89,188,176,109)(90,189,177,110)(91,190,178,111)(92,191,179,112)(93,192,180,99)(94,193,181,100)(95,194,182,101)(96,195,169,102)(97,196,170,103)(98,183,171,104)(141,261,330,247)(142,262,331,248)(143,263,332,249)(144,264,333,250)(145,265,334,251)(146,266,335,252)(147,253,336,239)(148,254,323,240)(149,255,324,241)(150,256,325,242)(151,257,326,243)(152,258,327,244)(153,259,328,245)(154,260,329,246)(155,218,294,231)(156,219,281,232)(157,220,282,233)(158,221,283,234)(159,222,284,235)(160,223,285,236)(161,224,286,237)(162,211,287,238)(163,212,288,225)(164,213,289,226)(165,214,290,227)(166,215,291,228)(167,216,292,229)(168,217,293,230)>;
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), (1,89,284,201,146,17,47,169,166,82,328,125)(2,88,285,200,147,16,48,182,167,81,329,124)(3,87,286,199,148,15,49,181,168,80,330,123)(4,86,287,198,149,28,50,180,155,79,331,122)(5,85,288,197,150,27,51,179,156,78,332,121)(6,98,289,210,151,26,52,178,157,77,333,120)(7,97,290,209,152,25,53,177,158,76,334,119)(8,96,291,208,153,24,54,176,159,75,335,118)(9,95,292,207,154,23,55,175,160,74,336,117)(10,94,293,206,141,22,56,174,161,73,323,116)(11,93,294,205,142,21,43,173,162,72,324,115)(12,92,281,204,143,20,44,172,163,71,325,114)(13,91,282,203,144,19,45,171,164,84,326,113)(14,90,283,202,145,18,46,170,165,83,327,126)(29,237,193,280,308,247,133,217,107,59,313,254)(30,236,194,279,295,246,134,216,108,58,314,253)(31,235,195,278,296,245,135,215,109,57,315,266)(32,234,196,277,297,244,136,214,110,70,316,265)(33,233,183,276,298,243,137,213,111,69,317,264)(34,232,184,275,299,242,138,212,112,68,318,263)(35,231,185,274,300,241,139,211,99,67,319,262)(36,230,186,273,301,240,140,224,100,66,320,261)(37,229,187,272,302,239,127,223,101,65,321,260)(38,228,188,271,303,252,128,222,102,64,322,259)(39,227,189,270,304,251,129,221,103,63,309,258)(40,226,190,269,305,250,130,220,104,62,310,257)(41,225,191,268,306,249,131,219,105,61,311,256)(42,238,192,267,307,248,132,218,106,60,312,255), (1,278,54,64)(2,279,55,65)(3,280,56,66)(4,267,43,67)(5,268,44,68)(6,269,45,69)(7,270,46,70)(8,271,47,57)(9,272,48,58)(10,273,49,59)(11,274,50,60)(12,275,51,61)(13,276,52,62)(14,277,53,63)(15,320,116,308)(16,321,117,295)(17,322,118,296)(18,309,119,297)(19,310,120,298)(20,311,121,299)(21,312,122,300)(22,313,123,301)(23,314,124,302)(24,315,125,303)(25,316,126,304)(26,317,113,305)(27,318,114,306)(28,319,115,307)(29,80,140,206)(30,81,127,207)(31,82,128,208)(32,83,129,209)(33,84,130,210)(34,71,131,197)(35,72,132,198)(36,73,133,199)(37,74,134,200)(38,75,135,201)(39,76,136,202)(40,77,137,203)(41,78,138,204)(42,79,139,205)(85,184,172,105)(86,185,173,106)(87,186,174,107)(88,187,175,108)(89,188,176,109)(90,189,177,110)(91,190,178,111)(92,191,179,112)(93,192,180,99)(94,193,181,100)(95,194,182,101)(96,195,169,102)(97,196,170,103)(98,183,171,104)(141,261,330,247)(142,262,331,248)(143,263,332,249)(144,264,333,250)(145,265,334,251)(146,266,335,252)(147,253,336,239)(148,254,323,240)(149,255,324,241)(150,256,325,242)(151,257,326,243)(152,258,327,244)(153,259,328,245)(154,260,329,246)(155,218,294,231)(156,219,281,232)(157,220,282,233)(158,221,283,234)(159,222,284,235)(160,223,285,236)(161,224,286,237)(162,211,287,238)(163,212,288,225)(164,213,289,226)(165,214,290,227)(166,215,291,228)(167,216,292,229)(168,217,293,230) );
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)], [(1,89,284,201,146,17,47,169,166,82,328,125),(2,88,285,200,147,16,48,182,167,81,329,124),(3,87,286,199,148,15,49,181,168,80,330,123),(4,86,287,198,149,28,50,180,155,79,331,122),(5,85,288,197,150,27,51,179,156,78,332,121),(6,98,289,210,151,26,52,178,157,77,333,120),(7,97,290,209,152,25,53,177,158,76,334,119),(8,96,291,208,153,24,54,176,159,75,335,118),(9,95,292,207,154,23,55,175,160,74,336,117),(10,94,293,206,141,22,56,174,161,73,323,116),(11,93,294,205,142,21,43,173,162,72,324,115),(12,92,281,204,143,20,44,172,163,71,325,114),(13,91,282,203,144,19,45,171,164,84,326,113),(14,90,283,202,145,18,46,170,165,83,327,126),(29,237,193,280,308,247,133,217,107,59,313,254),(30,236,194,279,295,246,134,216,108,58,314,253),(31,235,195,278,296,245,135,215,109,57,315,266),(32,234,196,277,297,244,136,214,110,70,316,265),(33,233,183,276,298,243,137,213,111,69,317,264),(34,232,184,275,299,242,138,212,112,68,318,263),(35,231,185,274,300,241,139,211,99,67,319,262),(36,230,186,273,301,240,140,224,100,66,320,261),(37,229,187,272,302,239,127,223,101,65,321,260),(38,228,188,271,303,252,128,222,102,64,322,259),(39,227,189,270,304,251,129,221,103,63,309,258),(40,226,190,269,305,250,130,220,104,62,310,257),(41,225,191,268,306,249,131,219,105,61,311,256),(42,238,192,267,307,248,132,218,106,60,312,255)], [(1,278,54,64),(2,279,55,65),(3,280,56,66),(4,267,43,67),(5,268,44,68),(6,269,45,69),(7,270,46,70),(8,271,47,57),(9,272,48,58),(10,273,49,59),(11,274,50,60),(12,275,51,61),(13,276,52,62),(14,277,53,63),(15,320,116,308),(16,321,117,295),(17,322,118,296),(18,309,119,297),(19,310,120,298),(20,311,121,299),(21,312,122,300),(22,313,123,301),(23,314,124,302),(24,315,125,303),(25,316,126,304),(26,317,113,305),(27,318,114,306),(28,319,115,307),(29,80,140,206),(30,81,127,207),(31,82,128,208),(32,83,129,209),(33,84,130,210),(34,71,131,197),(35,72,132,198),(36,73,133,199),(37,74,134,200),(38,75,135,201),(39,76,136,202),(40,77,137,203),(41,78,138,204),(42,79,139,205),(85,184,172,105),(86,185,173,106),(87,186,174,107),(88,187,175,108),(89,188,176,109),(90,189,177,110),(91,190,178,111),(92,191,179,112),(93,192,180,99),(94,193,181,100),(95,194,182,101),(96,195,169,102),(97,196,170,103),(98,183,171,104),(141,261,330,247),(142,262,331,248),(143,263,332,249),(144,264,333,250),(145,265,334,251),(146,266,335,252),(147,253,336,239),(148,254,323,240),(149,255,324,241),(150,256,325,242),(151,257,326,243),(152,258,327,244),(153,259,328,245),(154,260,329,246),(155,218,294,231),(156,219,281,232),(157,220,282,233),(158,221,283,234),(159,222,284,235),(160,223,285,236),(161,224,286,237),(162,211,287,238),(163,212,288,225),(164,213,289,226),(165,214,290,227),(166,215,291,228),(167,216,292,229),(168,217,293,230)]])
54 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 6A | 6B | 6C | 7A | 7B | 7C | 12A | 12B | 12C | 12D | 14A | ··· | 14I | 21A | 21B | 21C | 28A | ··· | 28L | 42A | ··· | 42I |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 6 | 6 | 7 | 7 | 7 | 12 | 12 | 12 | 12 | 14 | ··· | 14 | 21 | 21 | 21 | 28 | ··· | 28 | 42 | ··· | 42 |
| size | 1 | 1 | 1 | 1 | 2 | 6 | 6 | 14 | 14 | 42 | 42 | 2 | 2 | 2 | 2 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 4 | 4 | 4 | 6 | ··· | 6 | 4 | ··· | 4 |
54 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | - | - | + | - | + | + | - | + | - | |||
| image | C1 | C2 | C2 | C2 | C4 | S3 | D4 | Q8 | D6 | D7 | Dic6 | C4×S3 | C3⋊D4 | Dic7 | D14 | Dic14 | D28 | S3×D7 | S3×Dic7 | C3⋊D28 | C21⋊Q8 |
| kernel | C14.Dic6 | C6×Dic7 | Dic3×C14 | C2×Dic21 | C7×Dic3 | C2×Dic7 | C42 | C42 | C2×C14 | C2×Dic3 | C14 | C14 | C14 | Dic3 | C2×C6 | C6 | C6 | C22 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 3 | 2 | 2 | 2 | 6 | 3 | 6 | 6 | 3 | 3 | 3 | 3 |
Matrix representation of C14.Dic6 ►in GL4(𝔽337) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 228 | 228 |
| 0 | 0 | 109 | 143 |
| 30 | 15 | 0 | 0 |
| 322 | 15 | 0 | 0 |
| 0 | 0 | 312 | 276 |
| 0 | 0 | 71 | 25 |
| 286 | 72 | 0 | 0 |
| 123 | 51 | 0 | 0 |
| 0 | 0 | 319 | 177 |
| 0 | 0 | 160 | 18 |
G:=sub<GL(4,GF(337))| [1,0,0,0,0,1,0,0,0,0,228,109,0,0,228,143],[30,322,0,0,15,15,0,0,0,0,312,71,0,0,276,25],[286,123,0,0,72,51,0,0,0,0,319,160,0,0,177,18] >;
C14.Dic6 in GAP, Magma, Sage, TeX
C_{14}.{\rm Dic}_6 % in TeX
G:=Group("C14.Dic6"); // GroupNames label
G:=SmallGroup(336,47);
// by ID
G=gap.SmallGroup(336,47);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-3,-7,24,121,55,490,10373]);
// Polycyclic
G:=Group<a,b,c|a^14=b^12=1,c^2=a^7*b^6,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=a^7*b^-1>;
// generators/relations
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