Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C9 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C9×#994 |
| Fitting | C2×C9×H(5,𝔽2) ⋊ C3 |
| Sylow | C2×H(5,𝔽2) ⋊ C3×C9 |
764 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
342 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30896);