Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | Q8×C7⋊SL(2,𝔽3) |
| Fitting, Hall | C7×Q82 ⋊ C3 |
| Sylow | Q82 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ Q8×SL(2,𝔽3) |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
85 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10073);