Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C22×C3 |
| direct product | C9×B(4,𝔽2)⋊C3 |
| Fitting | C9×B(4,𝔽2) ⋊ C3 |
| derived | H(5,𝔽2) ⋊ C2×C3×C9 |
| Sylow | B(4,𝔽2) ⋊ C3×C9 |
234 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7272);