Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C3 |
| direct product | C22×#89021 |
| Sylow | C33 ⋊ C22×#41 |
5964 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47648);