Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D3×D27⋊C3 |
| Fitting, Sylow | C32×C27⋊C3 ⋊ C22 |
| derived | C3×C27 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×D27⋊C3 |
| commutator, cosocle, hypocenter | C3×C27 | C22×C32 |
| Frattini | C9 | C32×D32 |
| Fitting | C32×C27⋊C3 | C22 |
| socle | C33 | C2×C3×D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C3 | |
475 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 475 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D27⋊C3, C3×D3×AGL(1,ℤ/27) |
| maximal normal subgroup of | D32×D27⋊C3, C3×D3×AGL(1,ℤ/27) |
Past the SmallGroups library coverage — no SmallGroups id.