Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×D9×#137 |
| Fitting | C3×C9×#137 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×#137 |
834 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19570);