Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×#66431 |
| Fitting, Sylow | C32×C92 ⋊ C22 |
| derived | C32×C9 ⋊ C22×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #66431 |
| commutator, hypocenter | C32×C9 | C22×C9 |
| Frattini | C32 | C3×#1113 |
| Fitting | C32×C92 | C22 |
| socle | C34 | C2×C3×D3 |
| prime radical | C3×#66431 | C3 |
| cosocle | C33×C9 | C22×C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C9 | |
610 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72259340, D32×C9×D9, D9×#66431, … |
| maximal normal subgroup of | #72259340, D32×C9×D9, D9×#66431, … |
Past the SmallGroups library coverage — no SmallGroups id.