Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C32×Q8×D12 |
| Fitting | C33×C4×Q8 ⋊ C2 |
| Sylow | C33 ⋊ D4×Q8 |
1960 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45015);