Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×D27⋊C3 |
| Fitting, Sylow | C32×C27⋊C3 ⋊ C22 |
| derived | C32×C27 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C27 | C22×C3 |
| Frattini | C9 | C3×D3×C3⋊D3 |
| Fitting | C32×C27⋊C3 | C22 |
| socle | C33 | C2×C3×D9 |
| LCS | G ▷ C32×C27 | |
| UCS | C1 | |
484 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 65 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 | C3⋊D3×AGL(1,ℤ/27), D32×D27⋊C3 |
| maximal normal subgroup of | C3⋊D3×AGL(1,ℤ/27), D32×D27⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.