Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of D3×(C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | D3×(C3⋊D3)⋊C9 |
| unambiguous semidirect product | (D3×C3⋊D3)⋊C9 |
| Fitting, Sylow | C3×C32⋊C9 ⋊ C22 |
| derived | C33 ⋊ C22×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×(C3⋊D3)⋊C3 |
| commutator, hypocenter | C33 | C22×C9 |
| Frattini | C32 | C3×D32 |
| Fitting | C3×C32⋊C9 | C22 |
| socle | C33 | C2×C3×D3 |
| prime radical | C3×D3×C3⋊D3 | C3 |
| cosocle | C34 | C22×C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C3 | |
184 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 421);