Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×#13091647 |
| Fitting | C2×#10624930 ⋊ C2 |
| derived | C3×AΣL(1,𝔽27) ⋊ C22×C3 |
| Sylow | #10624930 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #13091647 |
| commutator, cosocle, hypocenter | C3×AΣL(1,𝔽27) | C22×C3 |
| Frattini | C32 | C2×C3×C3⋊(C3⋊D3) |
| Fitting | C2×#10624930 | C2 |
| socle | C2×C3 | C3×C3⋊#272 |
| LCS | G ▷ C3×AΣL(1,𝔽27) | |
| UCS | C1 ◁ C2 | |
1243 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#13091647, C2×#72221953, C2×#72221901, … |
| maximal normal subgroup of | C2×#72221953, C2×C3×#13091647, C2×#72221905 |
| maximal quotient of | D3×#13091647, C2×C3×#13091647 |
Past the SmallGroups library coverage — no SmallGroups id.