Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D12×#611 |
| Fitting | C22×C3×C4×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ D42 |
1378 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 16606);