Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of D9×C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C4 |
| direct product | Dic9×C42⋊C3 |
| derived | C42×C9 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×C42⋊C3 |
| commutator, hypocenter | C42×C9 | C3×C4 |
| Frattini, socle | C23×C3 | D3×A4 |
| Fitting, cosocle | C2×C42×C9 | C2×C3 |
| prime radical | C2×C3×C42⋊C3 | D3 |
| LCS | G ▷ C42×C9 | |
| UCS | C1 ◁ C2 | |
186 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2872);