Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C32 |
| direct product | D3×C3⋊#4183 |
| Fitting, derived, Sylow | C32×AΣL(1,𝔽27) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×AΣL(1,𝔽27) | C22 |
| Frattini | C32 | D3×C3⋊(C3⋊D3) |
| socle | C33 | C2×#272 |
| LCS | G ▷ C32×AΣL(1,𝔽27) | |
| UCS | C1 | |
1753 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #72243790, D3×#13091647, D3×#11757735 |
| maximal normal subgroup of | D3×#13091647, D3×#11757735 |
Past the SmallGroups library coverage — no SmallGroups id.