Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3×C4 |
| direct product | C2×#11723529 |
| Sylow | C33 ⋊ C2×#127 |
3420 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 43254);