Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×D3×C22⋊D11 |
| Fitting | C22×C32×C11 ⋊ C22 |
| Hall | C32×C11 ⋊ C2×D4 |
| Sylow | C11 ⋊ C3×D3×D4 |
| Sylow | C32 ⋊ C2×C22⋊D11 |
232 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 264 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 503);