Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of D3×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D3×C9×D9 |
| Fitting, Sylow | C3×C92 ⋊ C22 |
| derived | C3×C9 ⋊ C22×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D3×D9 |
| commutator, hypocenter | C3×C9 | C22×C9 |
| Frattini | C32 | C3×D32 |
| Fitting | C3×C92 | C22 |
| socle | C33 | C2×C3×D3 |
| prime radical | C3×D3×D9 | C3 |
| cosocle | C32×C9 | C22×C3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C9 | |
156 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D92, C2×D3×C9×D9, D3×#92265, … |
| maximal normal subgroup of | D3×D92, C2×D3×C9×D9, D3×#92265, … |
| maximal quotient of | C9×#6189, C9×Dic3×D9, C9×(C3⋊D9)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 419);