Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#10621035 |
| Fitting | C22×C3×C4×C7 ⋊ C22 |
| Hall | C3×C7 ⋊ C22×C22⋊C4 |
| Sylow | C7 ⋊ C2×D3×C22⋊C4 |
| Sylow | C3 ⋊ C2×D7×C22⋊C4 |
1348 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, 9140);