Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×Q8×C22⋊D7 |
| Fitting | C22×C3×C7×Q8 ⋊ C2 |
| Hall | C3×C7 ⋊ D4×Q8 |
| Sylow | C7 ⋊ C3×D4×Q8 |
560 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10446);