Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C9 · Schur multiplier (H2) = C29 |
| direct product | D3×C9×H(5,𝔽2) |
| Fitting | C3×C9×H(5,𝔽2) ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×H(5,𝔽2) |
2860 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
459 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 31012);