Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C32×#5791 |
| Fitting | C23×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ #525 |
2924 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45231);