Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C29 |
| direct product | C2×C7×#1009 |
| Fitting | C2×C3×C7×#41 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×H(5,𝔽2) |
| Sylow | C3 ⋊ C2×C7×H(5,𝔽2) |
1796 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
378 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11648);