Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#10589918 |
| Fitting | C22×C3×Q8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ #536 |
966 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19709);