Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #123×D27 |
| Fitting | C27×#123 ⋊ C2 |
| Sylow | C27 ⋊ C2×#123 |
684 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2457);