Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C3 |
| direct product | C3×#10592731 |
| Fitting | C33×#120 ⋊ C2 |
| Sylow | C33 ⋊ B(4,𝔽2) |
1708 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13165994, C3×D3×#5032, #72220851, … |
| maximal normal subgroup of | C3×D3×#5032, #72220851, #72220980 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 29133);