Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×#4183⋊C3 |
| Fitting | C2×C3×#6909 ⋊ C2 |
| derived | AΣL(1,𝔽27) ⋊ C22×C32 |
| Sylow | C3×#6909 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #4183⋊C3 |
| commutator, cosocle, hypocenter | AΣL(1,𝔽27) | C22×C32 |
| Frattini | C32 | C2×C32×C3⋊D3 |
| Fitting | C2×C3×#6909 | C2 |
| socle | C2×C32 | C3×#272 |
| LCS | G ▷ AΣL(1,𝔽27) | |
| UCS | C1 ◁ C2×C3 | |
1342 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#13091647, C2×#72221905, C2×C3×#13091107, … |
| maximal quotient of | AGL(1,𝔽7)×#4183⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.