direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C6×Dic14, C42⋊3Q8, C12.55D14, C42.38C23, C84.62C22, C7⋊4(C6×Q8), C21⋊6(C2×Q8), C14⋊3(C3×Q8), C4.11(C6×D7), (C2×C84).11C2, (C2×C28).15C6, C28.34(C2×C6), (C2×C6).36D14, (C2×C12).10D7, C22.8(C6×D7), (C6×Dic7).8C2, Dic7.6(C2×C6), (C2×Dic7).7C6, C6.38(C22×D7), (C2×C42).37C22, C14.15(C22×C6), (C3×Dic7).13C22, C2.3(C2×C6×D7), (C2×C4).4(C3×D7), (C2×C14).25(C2×C6), SmallGroup(336,174)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C6×Dic14
G = < a,b,c | a6=b28=1, c2=b14, ab=ba, ac=ca, cbc-1=b-1 >
Subgroups: 208 in 76 conjugacy classes, 54 normal (18 characteristic)
C1, C2, C2, C3, C4, C4, C22, C6, C6, C7, C2×C4, C2×C4, Q8, C12, C12, C2×C6, C14, C14, C2×Q8, C21, C2×C12, C2×C12, C3×Q8, Dic7, C28, C2×C14, C42, C42, C6×Q8, Dic14, C2×Dic7, C2×C28, C3×Dic7, C84, C2×C42, C2×Dic14, C3×Dic14, C6×Dic7, C2×C84, C6×Dic14
Quotients: C1, C2, C3, C22, C6, Q8, C23, C2×C6, D7, C2×Q8, C3×Q8, C22×C6, D14, C3×D7, C6×Q8, Dic14, C22×D7, C6×D7, C2×Dic14, C3×Dic14, C2×C6×D7, C6×Dic14
►Regular action on 336 points
Generators in S336
(1 238 320 154 259 110)(2 239 321 155 260 111)(3 240 322 156 261 112)(4 241 323 157 262 85)(5 242 324 158 263 86)(6 243 325 159 264 87)(7 244 326 160 265 88)(8 245 327 161 266 89)(9 246 328 162 267 90)(10 247 329 163 268 91)(11 248 330 164 269 92)(12 249 331 165 270 93)(13 250 332 166 271 94)(14 251 333 167 272 95)(15 252 334 168 273 96)(16 225 335 141 274 97)(17 226 336 142 275 98)(18 227 309 143 276 99)(19 228 310 144 277 100)(20 229 311 145 278 101)(21 230 312 146 279 102)(22 231 313 147 280 103)(23 232 314 148 253 104)(24 233 315 149 254 105)(25 234 316 150 255 106)(26 235 317 151 256 107)(27 236 318 152 257 108)(28 237 319 153 258 109)(29 59 188 138 209 288)(30 60 189 139 210 289)(31 61 190 140 211 290)(32 62 191 113 212 291)(33 63 192 114 213 292)(34 64 193 115 214 293)(35 65 194 116 215 294)(36 66 195 117 216 295)(37 67 196 118 217 296)(38 68 169 119 218 297)(39 69 170 120 219 298)(40 70 171 121 220 299)(41 71 172 122 221 300)(42 72 173 123 222 301)(43 73 174 124 223 302)(44 74 175 125 224 303)(45 75 176 126 197 304)(46 76 177 127 198 305)(47 77 178 128 199 306)(48 78 179 129 200 307)(49 79 180 130 201 308)(50 80 181 131 202 281)(51 81 182 132 203 282)(52 82 183 133 204 283)(53 83 184 134 205 284)(54 84 185 135 206 285)(55 57 186 136 207 286)(56 58 187 137 208 287)
(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)
(1 188 15 174)(2 187 16 173)(3 186 17 172)(4 185 18 171)(5 184 19 170)(6 183 20 169)(7 182 21 196)(8 181 22 195)(9 180 23 194)(10 179 24 193)(11 178 25 192)(12 177 26 191)(13 176 27 190)(14 175 28 189)(29 273 43 259)(30 272 44 258)(31 271 45 257)(32 270 46 256)(33 269 47 255)(34 268 48 254)(35 267 49 253)(36 266 50 280)(37 265 51 279)(38 264 52 278)(39 263 53 277)(40 262 54 276)(41 261 55 275)(42 260 56 274)(57 98 71 112)(58 97 72 111)(59 96 73 110)(60 95 74 109)(61 94 75 108)(62 93 76 107)(63 92 77 106)(64 91 78 105)(65 90 79 104)(66 89 80 103)(67 88 81 102)(68 87 82 101)(69 86 83 100)(70 85 84 99)(113 249 127 235)(114 248 128 234)(115 247 129 233)(116 246 130 232)(117 245 131 231)(118 244 132 230)(119 243 133 229)(120 242 134 228)(121 241 135 227)(122 240 136 226)(123 239 137 225)(124 238 138 252)(125 237 139 251)(126 236 140 250)(141 301 155 287)(142 300 156 286)(143 299 157 285)(144 298 158 284)(145 297 159 283)(146 296 160 282)(147 295 161 281)(148 294 162 308)(149 293 163 307)(150 292 164 306)(151 291 165 305)(152 290 166 304)(153 289 167 303)(154 288 168 302)(197 318 211 332)(198 317 212 331)(199 316 213 330)(200 315 214 329)(201 314 215 328)(202 313 216 327)(203 312 217 326)(204 311 218 325)(205 310 219 324)(206 309 220 323)(207 336 221 322)(208 335 222 321)(209 334 223 320)(210 333 224 319)
G:=sub<Sym(336)| (1,238,320,154,259,110)(2,239,321,155,260,111)(3,240,322,156,261,112)(4,241,323,157,262,85)(5,242,324,158,263,86)(6,243,325,159,264,87)(7,244,326,160,265,88)(8,245,327,161,266,89)(9,246,328,162,267,90)(10,247,329,163,268,91)(11,248,330,164,269,92)(12,249,331,165,270,93)(13,250,332,166,271,94)(14,251,333,167,272,95)(15,252,334,168,273,96)(16,225,335,141,274,97)(17,226,336,142,275,98)(18,227,309,143,276,99)(19,228,310,144,277,100)(20,229,311,145,278,101)(21,230,312,146,279,102)(22,231,313,147,280,103)(23,232,314,148,253,104)(24,233,315,149,254,105)(25,234,316,150,255,106)(26,235,317,151,256,107)(27,236,318,152,257,108)(28,237,319,153,258,109)(29,59,188,138,209,288)(30,60,189,139,210,289)(31,61,190,140,211,290)(32,62,191,113,212,291)(33,63,192,114,213,292)(34,64,193,115,214,293)(35,65,194,116,215,294)(36,66,195,117,216,295)(37,67,196,118,217,296)(38,68,169,119,218,297)(39,69,170,120,219,298)(40,70,171,121,220,299)(41,71,172,122,221,300)(42,72,173,123,222,301)(43,73,174,124,223,302)(44,74,175,125,224,303)(45,75,176,126,197,304)(46,76,177,127,198,305)(47,77,178,128,199,306)(48,78,179,129,200,307)(49,79,180,130,201,308)(50,80,181,131,202,281)(51,81,182,132,203,282)(52,82,183,133,204,283)(53,83,184,134,205,284)(54,84,185,135,206,285)(55,57,186,136,207,286)(56,58,187,137,208,287), (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), (1,188,15,174)(2,187,16,173)(3,186,17,172)(4,185,18,171)(5,184,19,170)(6,183,20,169)(7,182,21,196)(8,181,22,195)(9,180,23,194)(10,179,24,193)(11,178,25,192)(12,177,26,191)(13,176,27,190)(14,175,28,189)(29,273,43,259)(30,272,44,258)(31,271,45,257)(32,270,46,256)(33,269,47,255)(34,268,48,254)(35,267,49,253)(36,266,50,280)(37,265,51,279)(38,264,52,278)(39,263,53,277)(40,262,54,276)(41,261,55,275)(42,260,56,274)(57,98,71,112)(58,97,72,111)(59,96,73,110)(60,95,74,109)(61,94,75,108)(62,93,76,107)(63,92,77,106)(64,91,78,105)(65,90,79,104)(66,89,80,103)(67,88,81,102)(68,87,82,101)(69,86,83,100)(70,85,84,99)(113,249,127,235)(114,248,128,234)(115,247,129,233)(116,246,130,232)(117,245,131,231)(118,244,132,230)(119,243,133,229)(120,242,134,228)(121,241,135,227)(122,240,136,226)(123,239,137,225)(124,238,138,252)(125,237,139,251)(126,236,140,250)(141,301,155,287)(142,300,156,286)(143,299,157,285)(144,298,158,284)(145,297,159,283)(146,296,160,282)(147,295,161,281)(148,294,162,308)(149,293,163,307)(150,292,164,306)(151,291,165,305)(152,290,166,304)(153,289,167,303)(154,288,168,302)(197,318,211,332)(198,317,212,331)(199,316,213,330)(200,315,214,329)(201,314,215,328)(202,313,216,327)(203,312,217,326)(204,311,218,325)(205,310,219,324)(206,309,220,323)(207,336,221,322)(208,335,222,321)(209,334,223,320)(210,333,224,319)>;
G:=Group( (1,238,320,154,259,110)(2,239,321,155,260,111)(3,240,322,156,261,112)(4,241,323,157,262,85)(5,242,324,158,263,86)(6,243,325,159,264,87)(7,244,326,160,265,88)(8,245,327,161,266,89)(9,246,328,162,267,90)(10,247,329,163,268,91)(11,248,330,164,269,92)(12,249,331,165,270,93)(13,250,332,166,271,94)(14,251,333,167,272,95)(15,252,334,168,273,96)(16,225,335,141,274,97)(17,226,336,142,275,98)(18,227,309,143,276,99)(19,228,310,144,277,100)(20,229,311,145,278,101)(21,230,312,146,279,102)(22,231,313,147,280,103)(23,232,314,148,253,104)(24,233,315,149,254,105)(25,234,316,150,255,106)(26,235,317,151,256,107)(27,236,318,152,257,108)(28,237,319,153,258,109)(29,59,188,138,209,288)(30,60,189,139,210,289)(31,61,190,140,211,290)(32,62,191,113,212,291)(33,63,192,114,213,292)(34,64,193,115,214,293)(35,65,194,116,215,294)(36,66,195,117,216,295)(37,67,196,118,217,296)(38,68,169,119,218,297)(39,69,170,120,219,298)(40,70,171,121,220,299)(41,71,172,122,221,300)(42,72,173,123,222,301)(43,73,174,124,223,302)(44,74,175,125,224,303)(45,75,176,126,197,304)(46,76,177,127,198,305)(47,77,178,128,199,306)(48,78,179,129,200,307)(49,79,180,130,201,308)(50,80,181,131,202,281)(51,81,182,132,203,282)(52,82,183,133,204,283)(53,83,184,134,205,284)(54,84,185,135,206,285)(55,57,186,136,207,286)(56,58,187,137,208,287), (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), (1,188,15,174)(2,187,16,173)(3,186,17,172)(4,185,18,171)(5,184,19,170)(6,183,20,169)(7,182,21,196)(8,181,22,195)(9,180,23,194)(10,179,24,193)(11,178,25,192)(12,177,26,191)(13,176,27,190)(14,175,28,189)(29,273,43,259)(30,272,44,258)(31,271,45,257)(32,270,46,256)(33,269,47,255)(34,268,48,254)(35,267,49,253)(36,266,50,280)(37,265,51,279)(38,264,52,278)(39,263,53,277)(40,262,54,276)(41,261,55,275)(42,260,56,274)(57,98,71,112)(58,97,72,111)(59,96,73,110)(60,95,74,109)(61,94,75,108)(62,93,76,107)(63,92,77,106)(64,91,78,105)(65,90,79,104)(66,89,80,103)(67,88,81,102)(68,87,82,101)(69,86,83,100)(70,85,84,99)(113,249,127,235)(114,248,128,234)(115,247,129,233)(116,246,130,232)(117,245,131,231)(118,244,132,230)(119,243,133,229)(120,242,134,228)(121,241,135,227)(122,240,136,226)(123,239,137,225)(124,238,138,252)(125,237,139,251)(126,236,140,250)(141,301,155,287)(142,300,156,286)(143,299,157,285)(144,298,158,284)(145,297,159,283)(146,296,160,282)(147,295,161,281)(148,294,162,308)(149,293,163,307)(150,292,164,306)(151,291,165,305)(152,290,166,304)(153,289,167,303)(154,288,168,302)(197,318,211,332)(198,317,212,331)(199,316,213,330)(200,315,214,329)(201,314,215,328)(202,313,216,327)(203,312,217,326)(204,311,218,325)(205,310,219,324)(206,309,220,323)(207,336,221,322)(208,335,222,321)(209,334,223,320)(210,333,224,319) );
G=PermutationGroup([[(1,238,320,154,259,110),(2,239,321,155,260,111),(3,240,322,156,261,112),(4,241,323,157,262,85),(5,242,324,158,263,86),(6,243,325,159,264,87),(7,244,326,160,265,88),(8,245,327,161,266,89),(9,246,328,162,267,90),(10,247,329,163,268,91),(11,248,330,164,269,92),(12,249,331,165,270,93),(13,250,332,166,271,94),(14,251,333,167,272,95),(15,252,334,168,273,96),(16,225,335,141,274,97),(17,226,336,142,275,98),(18,227,309,143,276,99),(19,228,310,144,277,100),(20,229,311,145,278,101),(21,230,312,146,279,102),(22,231,313,147,280,103),(23,232,314,148,253,104),(24,233,315,149,254,105),(25,234,316,150,255,106),(26,235,317,151,256,107),(27,236,318,152,257,108),(28,237,319,153,258,109),(29,59,188,138,209,288),(30,60,189,139,210,289),(31,61,190,140,211,290),(32,62,191,113,212,291),(33,63,192,114,213,292),(34,64,193,115,214,293),(35,65,194,116,215,294),(36,66,195,117,216,295),(37,67,196,118,217,296),(38,68,169,119,218,297),(39,69,170,120,219,298),(40,70,171,121,220,299),(41,71,172,122,221,300),(42,72,173,123,222,301),(43,73,174,124,223,302),(44,74,175,125,224,303),(45,75,176,126,197,304),(46,76,177,127,198,305),(47,77,178,128,199,306),(48,78,179,129,200,307),(49,79,180,130,201,308),(50,80,181,131,202,281),(51,81,182,132,203,282),(52,82,183,133,204,283),(53,83,184,134,205,284),(54,84,185,135,206,285),(55,57,186,136,207,286),(56,58,187,137,208,287)], [(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)], [(1,188,15,174),(2,187,16,173),(3,186,17,172),(4,185,18,171),(5,184,19,170),(6,183,20,169),(7,182,21,196),(8,181,22,195),(9,180,23,194),(10,179,24,193),(11,178,25,192),(12,177,26,191),(13,176,27,190),(14,175,28,189),(29,273,43,259),(30,272,44,258),(31,271,45,257),(32,270,46,256),(33,269,47,255),(34,268,48,254),(35,267,49,253),(36,266,50,280),(37,265,51,279),(38,264,52,278),(39,263,53,277),(40,262,54,276),(41,261,55,275),(42,260,56,274),(57,98,71,112),(58,97,72,111),(59,96,73,110),(60,95,74,109),(61,94,75,108),(62,93,76,107),(63,92,77,106),(64,91,78,105),(65,90,79,104),(66,89,80,103),(67,88,81,102),(68,87,82,101),(69,86,83,100),(70,85,84,99),(113,249,127,235),(114,248,128,234),(115,247,129,233),(116,246,130,232),(117,245,131,231),(118,244,132,230),(119,243,133,229),(120,242,134,228),(121,241,135,227),(122,240,136,226),(123,239,137,225),(124,238,138,252),(125,237,139,251),(126,236,140,250),(141,301,155,287),(142,300,156,286),(143,299,157,285),(144,298,158,284),(145,297,159,283),(146,296,160,282),(147,295,161,281),(148,294,162,308),(149,293,163,307),(150,292,164,306),(151,291,165,305),(152,290,166,304),(153,289,167,303),(154,288,168,302),(197,318,211,332),(198,317,212,331),(199,316,213,330),(200,315,214,329),(201,314,215,328),(202,313,216,327),(203,312,217,326),(204,311,218,325),(205,310,219,324),(206,309,220,323),(207,336,221,322),(208,335,222,321),(209,334,223,320),(210,333,224,319)]])
102 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | 4B | 4C | 4D | 4E | 4F | 6A | ··· | 6F | 7A | 7B | 7C | 12A | 12B | 12C | 12D | 12E | ··· | 12L | 14A | ··· | 14I | 21A | ··· | 21F | 28A | ··· | 28L | 42A | ··· | 42R | 84A | ··· | 84X |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 7 | 7 | 7 | 12 | 12 | 12 | 12 | 12 | ··· | 12 | 14 | ··· | 14 | 21 | ··· | 21 | 28 | ··· | 28 | 42 | ··· | 42 | 84 | ··· | 84 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 14 | 14 | 14 | 14 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
102 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 | C3 | C6 | C6 | C6 | Q8 | D7 | C3×Q8 | D14 | D14 | C3×D7 | Dic14 | C6×D7 | C6×D7 | C3×Dic14 |
| kernel | C6×Dic14 | C3×Dic14 | C6×Dic7 | C2×C84 | C2×Dic14 | Dic14 | C2×Dic7 | C2×C28 | C42 | C2×C12 | C14 | C12 | C2×C6 | C2×C4 | C6 | C4 | C22 | C2 |
| # reps | 1 | 4 | 2 | 1 | 2 | 8 | 4 | 2 | 2 | 3 | 4 | 6 | 3 | 6 | 12 | 12 | 6 | 24 |
Matrix representation of C6×Dic14 ►in GL3(𝔽337) generated by
| 336 | 0 | 0 |
| 0 | 129 | 0 |
| 0 | 0 | 129 |
| 336 | 0 | 0 |
| 0 | 219 | 319 |
| 0 | 56 | 257 |
| 1 | 0 | 0 |
| 0 | 176 | 267 |
| 0 | 197 | 161 |
G:=sub<GL(3,GF(337))| [336,0,0,0,129,0,0,0,129],[336,0,0,0,219,56,0,319,257],[1,0,0,0,176,197,0,267,161] >;
C6×Dic14 in GAP, Magma, Sage, TeX
C_6\times {\rm Dic}_{14} % in TeX
G:=Group("C6xDic14"); // GroupNames label
G:=SmallGroup(336,174);
// by ID
G=gap.SmallGroup(336,174);
# by ID
G:=PCGroup([6,-2,-2,-2,-3,-2,-7,144,506,122,10373]);
// Polycyclic
G:=Group<a,b,c|a^6=b^28=1,c^2=b^14,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations