Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | SD32×D21 |
| Fitting | C3×C7×SD32 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×SD32 |
| Sylow | C7 ⋊ D3×SD32 |
| Sylow | C3 ⋊ D7×SD32 |
180 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5839);