Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×C3⋊(#4183⋊C3) |
| Fitting | C2×C3×#6909 ⋊ C2 |
| derived | C3×AΣL(1,𝔽27) ⋊ C22×C3 |
| Sylow | C3×#6909 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(#4183⋊C3) |
| commutator, cosocle, hypocenter | C3×AΣL(1,𝔽27) | C22×C3 |
| Frattini | C32 | C2×C3×C3⋊(C3⋊D3) |
| Fitting | C2×C3×#6909 | C2 |
| socle | C2×C32 | C3×#272 |
| LCS | G ▷ C3×AΣL(1,𝔽27) | |
| UCS | C1 ◁ C2 | |
1302 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221905 |
| maximal normal subgroup of | C2×#72221905 |
| maximal quotient of | C2×#72221909 |
Past the SmallGroups library coverage — no SmallGroups id.