Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×D3×#1004 |
| Fitting | C2×C33×D4 ⋊ C22 |
| Sylow | C33 ⋊ C2×H(5,𝔽2) |
4214 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
243 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#5077, D3×#10591510, D3×#10596675, … |
| maximal normal subgroup of | C3×D3×#5077, D3×#10591510, D3×#10596675, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47612);