Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C34 |
| direct product | C2×C3×#4177⋊C3 |
| Fitting | C2×C3×#6910 ⋊ C2 |
| derived | C3×C9 ⋊ C22×C33 |
| Sylow | C3×#6910 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #4177⋊C3 |
| commutator, cosocle, hypocenter | C3×C9 | C22×C33 |
| Frattini | C32 | C2×C33×D3 |
| Fitting | C2×C3×#6910 | C2 |
| socle | C2×C32 | C3×(C3⋊D3)⋊C3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C2×C3 | |
1040 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221916 |
Past the SmallGroups library coverage — no SmallGroups id.