Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | D9×(C3⋊D3)⋊C9 |
| Fitting, Sylow | C9×C32⋊C9 ⋊ C22 |
| derived | C32×C9 ⋊ C22×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D9×(C3⋊D3)⋊C3 |
| commutator, hypocenter | C32×C9 | C22×C9 |
| Frattini, socle | C33 | C3×D32 |
| Fitting | C9×C32⋊C9 | C22 |
| prime radical | C3×D9×C3⋊D3 | C3 |
| cosocle | C33×C9 | C22×C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C3 | |
331 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 331 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #72254045, #72254047, #72254050, … |
| maximal normal subgroup of | #72254045, #72254047, #72254050, … |
Past the SmallGroups library coverage — no SmallGroups id.