Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | ΓL(1,𝔽8)×#564 |
| Fitting, Hall | C7×#564 ⋊ C3 |
| Sylow | C7 ⋊ C3×#564 |
344 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 39 points:
(2,3,4)(5,7,6)(10,16)(11,19)(13,17)(14,21)(24,25,28,31)(26,29,34,32)(27,35,36,30)(33,38,39,37);(1,2,3,5,4,6,7)(8,9,12,15)(10,17,16,13)(11,14,19,21)(18,23,22,20)(24,25)(26,32)(27,35)(28,31)(29,34)(30,36)(33,37)(38,39);(8,10,12,16)(9,13,15,17)(11,18,19,22)(14,20,21,23)(24,26)(25,29)(27,33)(28,34)(30,37)(31,32)(35,38)(36,39);(8,11)(9,14)(10,18)(12,19)(13,20)(15,21)(16,22)(17,23)(24,27,28,36)(25,30,31,35)(26,33,34,39)(29,37,32,38)95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10014);