Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D3×C22⋊C4×D9 |
| Fitting | C3×C9×C22⋊C4 ⋊ C22 |
| Sylow | C3×C9 ⋊ C22×C22⋊C4 |
2154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D9×#120 |
| maximal normal subgroup of | D3×D9×#120 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 14453);