Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#11721773 |
| Fitting | C22×C3×C8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×#135 |
1330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 20374);