Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×D3×Q8×D9 |
| Fitting | C2×C3×Q8×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C23×Q8 |
2706 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30816);