Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C4⋊Q8×C3⋊D9 |
| Fitting | C3×C9×C4⋊Q8 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×C4⋊Q8 |
1450 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 20341);