Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×D9×#235 |
| Fitting | C22×C3×C4×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C22×#41 |
2834 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30766);