Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C3⋊D3×#896 |
| Fitting | C33×C4⋊C4 ⋊ C22 |
| Sylow | C33 ⋊ C2×C22⋊Q8 |
2228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 42057);