Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C9 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×D4×C9×A4 |
| unambiguous semidirect product | C4⋊(C22×C9×A4) |
| Fitting | C23×D4×C9 ⋊ C3 |
| Sylow | C23×D4 ⋊ C3×C9 |
1167 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30886);