direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14×Dic6, C42⋊4Q8, C28.55D6, C84.71C22, C42.48C23, C6⋊(C7×Q8), C21⋊7(C2×Q8), C3⋊1(Q8×C14), C4.11(S3×C14), (C2×C84).16C2, (C2×C28).10S3, (C2×C12).4C14, (C2×C14).36D6, C12.11(C2×C14), C6.1(C22×C14), C22.8(S3×C14), C14.38(C22×S3), (C2×C42).47C22, (Dic3×C14).8C2, Dic3.1(C2×C14), (C2×Dic3).3C14, (C7×Dic3).13C22, C2.3(S3×C2×C14), (C2×C4).4(S3×C7), (C2×C6).8(C2×C14), SmallGroup(336,184)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14×Dic6
G = < a,b,c | a14=b12=1, c2=b6, ab=ba, ac=ca, cbc-1=b-1 >
Subgroups: 120 in 76 conjugacy classes, 54 normal (18 characteristic)
C1, C2, C2, C3, C4, C4, C22, C6, C6, C7, C2×C4, C2×C4, Q8, Dic3, C12, C2×C6, C14, C14, C2×Q8, C21, Dic6, C2×Dic3, C2×C12, C28, C28, C2×C14, C42, C42, C2×Dic6, C2×C28, C2×C28, C7×Q8, C7×Dic3, C84, C2×C42, Q8×C14, C7×Dic6, Dic3×C14, C2×C84, C14×Dic6
Quotients: C1, C2, C22, S3, C7, Q8, C23, D6, C14, C2×Q8, Dic6, C22×S3, C2×C14, S3×C7, C2×Dic6, C7×Q8, C22×C14, S3×C14, Q8×C14, C7×Dic6, S3×C2×C14, 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)
(1 186 264 230 88 162 42 129 18 120 201 174)(2 187 265 231 89 163 29 130 19 121 202 175)(3 188 266 232 90 164 30 131 20 122 203 176)(4 189 253 233 91 165 31 132 21 123 204 177)(5 190 254 234 92 166 32 133 22 124 205 178)(6 191 255 235 93 167 33 134 23 125 206 179)(7 192 256 236 94 168 34 135 24 126 207 180)(8 193 257 237 95 155 35 136 25 113 208 181)(9 194 258 238 96 156 36 137 26 114 209 182)(10 195 259 225 97 157 37 138 27 115 210 169)(11 196 260 226 98 158 38 139 28 116 197 170)(12 183 261 227 85 159 39 140 15 117 198 171)(13 184 262 228 86 160 40 127 16 118 199 172)(14 185 263 229 87 161 41 128 17 119 200 173)(43 308 333 285 111 152 248 216 84 58 319 270)(44 295 334 286 112 153 249 217 71 59 320 271)(45 296 335 287 99 154 250 218 72 60 321 272)(46 297 336 288 100 141 251 219 73 61 322 273)(47 298 323 289 101 142 252 220 74 62 309 274)(48 299 324 290 102 143 239 221 75 63 310 275)(49 300 325 291 103 144 240 222 76 64 311 276)(50 301 326 292 104 145 241 223 77 65 312 277)(51 302 327 293 105 146 242 224 78 66 313 278)(52 303 328 294 106 147 243 211 79 67 314 279)(53 304 329 281 107 148 244 212 80 68 315 280)(54 305 330 282 108 149 245 213 81 69 316 267)(55 306 331 283 109 150 246 214 82 70 317 268)(56 307 332 284 110 151 247 215 83 57 318 269)
(1 245 42 54)(2 246 29 55)(3 247 30 56)(4 248 31 43)(5 249 32 44)(6 250 33 45)(7 251 34 46)(8 252 35 47)(9 239 36 48)(10 240 37 49)(11 241 38 50)(12 242 39 51)(13 243 40 52)(14 244 41 53)(15 313 261 105)(16 314 262 106)(17 315 263 107)(18 316 264 108)(19 317 265 109)(20 318 266 110)(21 319 253 111)(22 320 254 112)(23 321 255 99)(24 322 256 100)(25 309 257 101)(26 310 258 102)(27 311 259 103)(28 312 260 104)(57 232 284 122)(58 233 285 123)(59 234 286 124)(60 235 287 125)(61 236 288 126)(62 237 289 113)(63 238 290 114)(64 225 291 115)(65 226 292 116)(66 227 293 117)(67 228 294 118)(68 229 281 119)(69 230 282 120)(70 231 283 121)(71 92 334 205)(72 93 335 206)(73 94 336 207)(74 95 323 208)(75 96 324 209)(76 97 325 210)(77 98 326 197)(78 85 327 198)(79 86 328 199)(80 87 329 200)(81 88 330 201)(82 89 331 202)(83 90 332 203)(84 91 333 204)(127 279 184 147)(128 280 185 148)(129 267 186 149)(130 268 187 150)(131 269 188 151)(132 270 189 152)(133 271 190 153)(134 272 191 154)(135 273 192 141)(136 274 193 142)(137 275 194 143)(138 276 195 144)(139 277 196 145)(140 278 183 146)(155 298 181 220)(156 299 182 221)(157 300 169 222)(158 301 170 223)(159 302 171 224)(160 303 172 211)(161 304 173 212)(162 305 174 213)(163 306 175 214)(164 307 176 215)(165 308 177 216)(166 295 178 217)(167 296 179 218)(168 297 180 219)
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), (1,186,264,230,88,162,42,129,18,120,201,174)(2,187,265,231,89,163,29,130,19,121,202,175)(3,188,266,232,90,164,30,131,20,122,203,176)(4,189,253,233,91,165,31,132,21,123,204,177)(5,190,254,234,92,166,32,133,22,124,205,178)(6,191,255,235,93,167,33,134,23,125,206,179)(7,192,256,236,94,168,34,135,24,126,207,180)(8,193,257,237,95,155,35,136,25,113,208,181)(9,194,258,238,96,156,36,137,26,114,209,182)(10,195,259,225,97,157,37,138,27,115,210,169)(11,196,260,226,98,158,38,139,28,116,197,170)(12,183,261,227,85,159,39,140,15,117,198,171)(13,184,262,228,86,160,40,127,16,118,199,172)(14,185,263,229,87,161,41,128,17,119,200,173)(43,308,333,285,111,152,248,216,84,58,319,270)(44,295,334,286,112,153,249,217,71,59,320,271)(45,296,335,287,99,154,250,218,72,60,321,272)(46,297,336,288,100,141,251,219,73,61,322,273)(47,298,323,289,101,142,252,220,74,62,309,274)(48,299,324,290,102,143,239,221,75,63,310,275)(49,300,325,291,103,144,240,222,76,64,311,276)(50,301,326,292,104,145,241,223,77,65,312,277)(51,302,327,293,105,146,242,224,78,66,313,278)(52,303,328,294,106,147,243,211,79,67,314,279)(53,304,329,281,107,148,244,212,80,68,315,280)(54,305,330,282,108,149,245,213,81,69,316,267)(55,306,331,283,109,150,246,214,82,70,317,268)(56,307,332,284,110,151,247,215,83,57,318,269), (1,245,42,54)(2,246,29,55)(3,247,30,56)(4,248,31,43)(5,249,32,44)(6,250,33,45)(7,251,34,46)(8,252,35,47)(9,239,36,48)(10,240,37,49)(11,241,38,50)(12,242,39,51)(13,243,40,52)(14,244,41,53)(15,313,261,105)(16,314,262,106)(17,315,263,107)(18,316,264,108)(19,317,265,109)(20,318,266,110)(21,319,253,111)(22,320,254,112)(23,321,255,99)(24,322,256,100)(25,309,257,101)(26,310,258,102)(27,311,259,103)(28,312,260,104)(57,232,284,122)(58,233,285,123)(59,234,286,124)(60,235,287,125)(61,236,288,126)(62,237,289,113)(63,238,290,114)(64,225,291,115)(65,226,292,116)(66,227,293,117)(67,228,294,118)(68,229,281,119)(69,230,282,120)(70,231,283,121)(71,92,334,205)(72,93,335,206)(73,94,336,207)(74,95,323,208)(75,96,324,209)(76,97,325,210)(77,98,326,197)(78,85,327,198)(79,86,328,199)(80,87,329,200)(81,88,330,201)(82,89,331,202)(83,90,332,203)(84,91,333,204)(127,279,184,147)(128,280,185,148)(129,267,186,149)(130,268,187,150)(131,269,188,151)(132,270,189,152)(133,271,190,153)(134,272,191,154)(135,273,192,141)(136,274,193,142)(137,275,194,143)(138,276,195,144)(139,277,196,145)(140,278,183,146)(155,298,181,220)(156,299,182,221)(157,300,169,222)(158,301,170,223)(159,302,171,224)(160,303,172,211)(161,304,173,212)(162,305,174,213)(163,306,175,214)(164,307,176,215)(165,308,177,216)(166,295,178,217)(167,296,179,218)(168,297,180,219)>;
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), (1,186,264,230,88,162,42,129,18,120,201,174)(2,187,265,231,89,163,29,130,19,121,202,175)(3,188,266,232,90,164,30,131,20,122,203,176)(4,189,253,233,91,165,31,132,21,123,204,177)(5,190,254,234,92,166,32,133,22,124,205,178)(6,191,255,235,93,167,33,134,23,125,206,179)(7,192,256,236,94,168,34,135,24,126,207,180)(8,193,257,237,95,155,35,136,25,113,208,181)(9,194,258,238,96,156,36,137,26,114,209,182)(10,195,259,225,97,157,37,138,27,115,210,169)(11,196,260,226,98,158,38,139,28,116,197,170)(12,183,261,227,85,159,39,140,15,117,198,171)(13,184,262,228,86,160,40,127,16,118,199,172)(14,185,263,229,87,161,41,128,17,119,200,173)(43,308,333,285,111,152,248,216,84,58,319,270)(44,295,334,286,112,153,249,217,71,59,320,271)(45,296,335,287,99,154,250,218,72,60,321,272)(46,297,336,288,100,141,251,219,73,61,322,273)(47,298,323,289,101,142,252,220,74,62,309,274)(48,299,324,290,102,143,239,221,75,63,310,275)(49,300,325,291,103,144,240,222,76,64,311,276)(50,301,326,292,104,145,241,223,77,65,312,277)(51,302,327,293,105,146,242,224,78,66,313,278)(52,303,328,294,106,147,243,211,79,67,314,279)(53,304,329,281,107,148,244,212,80,68,315,280)(54,305,330,282,108,149,245,213,81,69,316,267)(55,306,331,283,109,150,246,214,82,70,317,268)(56,307,332,284,110,151,247,215,83,57,318,269), (1,245,42,54)(2,246,29,55)(3,247,30,56)(4,248,31,43)(5,249,32,44)(6,250,33,45)(7,251,34,46)(8,252,35,47)(9,239,36,48)(10,240,37,49)(11,241,38,50)(12,242,39,51)(13,243,40,52)(14,244,41,53)(15,313,261,105)(16,314,262,106)(17,315,263,107)(18,316,264,108)(19,317,265,109)(20,318,266,110)(21,319,253,111)(22,320,254,112)(23,321,255,99)(24,322,256,100)(25,309,257,101)(26,310,258,102)(27,311,259,103)(28,312,260,104)(57,232,284,122)(58,233,285,123)(59,234,286,124)(60,235,287,125)(61,236,288,126)(62,237,289,113)(63,238,290,114)(64,225,291,115)(65,226,292,116)(66,227,293,117)(67,228,294,118)(68,229,281,119)(69,230,282,120)(70,231,283,121)(71,92,334,205)(72,93,335,206)(73,94,336,207)(74,95,323,208)(75,96,324,209)(76,97,325,210)(77,98,326,197)(78,85,327,198)(79,86,328,199)(80,87,329,200)(81,88,330,201)(82,89,331,202)(83,90,332,203)(84,91,333,204)(127,279,184,147)(128,280,185,148)(129,267,186,149)(130,268,187,150)(131,269,188,151)(132,270,189,152)(133,271,190,153)(134,272,191,154)(135,273,192,141)(136,274,193,142)(137,275,194,143)(138,276,195,144)(139,277,196,145)(140,278,183,146)(155,298,181,220)(156,299,182,221)(157,300,169,222)(158,301,170,223)(159,302,171,224)(160,303,172,211)(161,304,173,212)(162,305,174,213)(163,306,175,214)(164,307,176,215)(165,308,177,216)(166,295,178,217)(167,296,179,218)(168,297,180,219) );
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)], [(1,186,264,230,88,162,42,129,18,120,201,174),(2,187,265,231,89,163,29,130,19,121,202,175),(3,188,266,232,90,164,30,131,20,122,203,176),(4,189,253,233,91,165,31,132,21,123,204,177),(5,190,254,234,92,166,32,133,22,124,205,178),(6,191,255,235,93,167,33,134,23,125,206,179),(7,192,256,236,94,168,34,135,24,126,207,180),(8,193,257,237,95,155,35,136,25,113,208,181),(9,194,258,238,96,156,36,137,26,114,209,182),(10,195,259,225,97,157,37,138,27,115,210,169),(11,196,260,226,98,158,38,139,28,116,197,170),(12,183,261,227,85,159,39,140,15,117,198,171),(13,184,262,228,86,160,40,127,16,118,199,172),(14,185,263,229,87,161,41,128,17,119,200,173),(43,308,333,285,111,152,248,216,84,58,319,270),(44,295,334,286,112,153,249,217,71,59,320,271),(45,296,335,287,99,154,250,218,72,60,321,272),(46,297,336,288,100,141,251,219,73,61,322,273),(47,298,323,289,101,142,252,220,74,62,309,274),(48,299,324,290,102,143,239,221,75,63,310,275),(49,300,325,291,103,144,240,222,76,64,311,276),(50,301,326,292,104,145,241,223,77,65,312,277),(51,302,327,293,105,146,242,224,78,66,313,278),(52,303,328,294,106,147,243,211,79,67,314,279),(53,304,329,281,107,148,244,212,80,68,315,280),(54,305,330,282,108,149,245,213,81,69,316,267),(55,306,331,283,109,150,246,214,82,70,317,268),(56,307,332,284,110,151,247,215,83,57,318,269)], [(1,245,42,54),(2,246,29,55),(3,247,30,56),(4,248,31,43),(5,249,32,44),(6,250,33,45),(7,251,34,46),(8,252,35,47),(9,239,36,48),(10,240,37,49),(11,241,38,50),(12,242,39,51),(13,243,40,52),(14,244,41,53),(15,313,261,105),(16,314,262,106),(17,315,263,107),(18,316,264,108),(19,317,265,109),(20,318,266,110),(21,319,253,111),(22,320,254,112),(23,321,255,99),(24,322,256,100),(25,309,257,101),(26,310,258,102),(27,311,259,103),(28,312,260,104),(57,232,284,122),(58,233,285,123),(59,234,286,124),(60,235,287,125),(61,236,288,126),(62,237,289,113),(63,238,290,114),(64,225,291,115),(65,226,292,116),(66,227,293,117),(67,228,294,118),(68,229,281,119),(69,230,282,120),(70,231,283,121),(71,92,334,205),(72,93,335,206),(73,94,336,207),(74,95,323,208),(75,96,324,209),(76,97,325,210),(77,98,326,197),(78,85,327,198),(79,86,328,199),(80,87,329,200),(81,88,330,201),(82,89,331,202),(83,90,332,203),(84,91,333,204),(127,279,184,147),(128,280,185,148),(129,267,186,149),(130,268,187,150),(131,269,188,151),(132,270,189,152),(133,271,190,153),(134,272,191,154),(135,273,192,141),(136,274,193,142),(137,275,194,143),(138,276,195,144),(139,277,196,145),(140,278,183,146),(155,298,181,220),(156,299,182,221),(157,300,169,222),(158,301,170,223),(159,302,171,224),(160,303,172,211),(161,304,173,212),(162,305,174,213),(163,306,175,214),(164,307,176,215),(165,308,177,216),(166,295,178,217),(167,296,179,218),(168,297,180,219)]])
126 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 6A | 6B | 6C | 7A | ··· | 7F | 12A | 12B | 12C | 12D | 14A | ··· | 14R | 21A | ··· | 21F | 28A | ··· | 28L | 28M | ··· | 28AJ | 42A | ··· | 42R | 84A | ··· | 84X |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 6 | 6 | 7 | ··· | 7 | 12 | 12 | 12 | 12 | 14 | ··· | 14 | 21 | ··· | 21 | 28 | ··· | 28 | 28 | ··· | 28 | 42 | ··· | 42 | 84 | ··· | 84 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 6 | 6 | 6 | 6 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 6 | ··· | 6 | 2 | ··· | 2 | 2 | ··· | 2 |
126 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | + | - | |||||||||
| image | C1 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | S3 | Q8 | D6 | D6 | Dic6 | S3×C7 | C7×Q8 | S3×C14 | S3×C14 | C7×Dic6 |
| kernel | C14×Dic6 | C7×Dic6 | Dic3×C14 | C2×C84 | C2×Dic6 | Dic6 | C2×Dic3 | C2×C12 | C2×C28 | C42 | C28 | C2×C14 | C14 | C2×C4 | C6 | C4 | C22 | C2 |
| # reps | 1 | 4 | 2 | 1 | 6 | 24 | 12 | 6 | 1 | 2 | 2 | 1 | 4 | 6 | 12 | 12 | 6 | 24 |
Matrix representation of C14×Dic6 ►in GL4(𝔽337) generated by
| 273 | 0 | 0 | 0 |
| 0 | 273 | 0 | 0 |
| 0 | 0 | 295 | 0 |
| 0 | 0 | 0 | 295 |
| 0 | 336 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 0 | 0 | 336 | 335 |
| 0 | 0 | 1 | 1 |
| 189 | 35 | 0 | 0 |
| 183 | 148 | 0 | 0 |
| 0 | 0 | 147 | 45 |
| 0 | 0 | 44 | 190 |
G:=sub<GL(4,GF(337))| [273,0,0,0,0,273,0,0,0,0,295,0,0,0,0,295],[0,1,0,0,336,1,0,0,0,0,336,1,0,0,335,1],[189,183,0,0,35,148,0,0,0,0,147,44,0,0,45,190] >;
C14×Dic6 in GAP, Magma, Sage, TeX
C_{14}\times {\rm Dic}_6 % in TeX
G:=Group("C14xDic6"); // GroupNames label
G:=SmallGroup(336,184);
// by ID
G=gap.SmallGroup(336,184);
# by ID
G:=PCGroup([6,-2,-2,-2,-7,-2,-3,336,1082,266,8069]);
// Polycyclic
G:=Group<a,b,c|a^14=b^12=1,c^2=b^6,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations