Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C32 · Schur multiplier (H2) = C29×C3 |
| direct product | C2×C32×#1009 |
| Fitting | C2×C33×#41 ⋊ C2 |
| Sylow | C33 ⋊ C2×H(5,𝔽2) |
6044 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
486 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47784);