Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#6472 |
| Fitting | C3×C7×M16 ⋊ C22 |
| Hall | C3×C7 ⋊ C2×#137 |
| Sylow | C7 ⋊ D3×#137 |
| Sylow | C3 ⋊ C2×#6472 |
516 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 8544);