Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C9 |
| direct product | C3×D3×C9⋊D9 |
| Fitting, Sylow | C32×C92 ⋊ C22 |
| derived | C3×C92 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×C9⋊D9 |
| commutator, cosocle, hypocenter | C3×C92 | C22×C3 |
| Frattini | C32 | C3×D3×C3⋊D3 |
| Fitting | C32×C92 | C22 |
| socle | C34 | C2×C3⋊D3 |
| LCS | G ▷ C3×C92 | |
| UCS | C1 ◁ C3 | |
978 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 978 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/9)×C9⋊D9, C3×D3×#92314, C3×D3×D92, … |
| maximal normal subgroup of | C3×D3×#92314, C3×D3×D92, D32×C9⋊D9, … |
| maximal quotient of | AGL(1,ℤ/9)×C9⋊D9 |
Past the SmallGroups library coverage — no SmallGroups id.