Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×#10596669 |
| Fitting | C22×C33×C4 ⋊ C22 |
| Sylow | C33 ⋊ #585 |
3786 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47607);