Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | D9×C3⋊AGL(1,ℤ/9) |
| Fitting, Sylow | C3×C9×3−1+2 ⋊ C22 |
| derived | C3×C92 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C92 | C22×C3 |
| Frattini | C32 | C3×D3×C3⋊D3 |
| Fitting | C3×C9×3−1+2 | C22 |
| socle | C33 | C3×D32 |
| LCS | G ▷ C3×C92 | |
| UCS | C1 | |
598 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#92314, AGL(1,ℤ/9)×C3⋊AGL(1,ℤ/9), D9×#92299, … |
| maximal normal subgroup of | AGL(1,ℤ/9)×C3⋊AGL(1,ℤ/9), D3×D9×AGL(1,ℤ/9) |
| maximal quotient of | D9×#92314, D9×#92299, D9×#92303 |
Past the SmallGroups library coverage — no SmallGroups id.