Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#11722478 |
| Fitting | C22×C3×C4×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×H(5,𝔽2) |
2930 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13164733 |
| maximal normal subgroup of | C2×#13164733 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30771);