Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22⋊Q8×D21 |
| Fitting | C3×C7×C22⋊Q8 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×C22⋊Q8 |
| Sylow | C7 ⋊ D3×C22⋊Q8 |
| Sylow | C3 ⋊ D7×C22⋊Q8 |
644 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11009);