Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#10589678 |
| Fitting | C3×C4×Q8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ #548 |
940 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18745);