Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
| direct product | D9×C3⋊(C3⋊D9) |
| Fitting, derived, Sylow | C32×C92 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C92 | C22 |
| Frattini | C32 | D3×C3⋊(C3⋊D3) |
| socle | C34 | D32 |
| LCS | G ▷ C32×C92 | |
| UCS | C1 | |
1666 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 1666 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | #72254059, #72254062, #72254064, … |
| maximal normal subgroup of | #72254059, #72254062, #72254064, … |
Past the SmallGroups library coverage — no SmallGroups id.