Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D3×#4174 |
| Fitting, Sylow | C32×AΣL(1,𝔽27) ⋊ C22 |
| derived | C3×H(3,𝔽3) ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D3×(C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C22×C32 |
| Frattini | C32 | C32×D32 |
| Fitting | C32×AΣL(1,𝔽27) | C22 |
| socle | C33 | C2×(C3⋊D3)⋊C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
1388 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 1388 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | #72243719, C3×#72214502, D3×#13091645, … |
| maximal normal subgroup of | D3×#13091645, D3×#13091661, D3×#11757735, … |
Past the SmallGroups library coverage — no SmallGroups id.