Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C33 |
| direct product | C22⋊Q8×C3⋊(C3⋊D3) |
| Fitting | C33×C22⋊Q8 ⋊ C2 |
| Sylow | C33 ⋊ C2×C22⋊Q8 |
4508 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, 45818);