Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | D3×#4207⋊C3 |
| Fitting, Sylow | C3×3−1+4 ⋊ C22 |
| derived | C32×C9 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C9 | C22×C32 |
| Frattini | C3 | C32×D3×C3⋊D3 |
| Fitting | C3×3−1+4 | C22 |
| socle | C32 | C2×C32×C3⋊D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 | |
1568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | #72243364, #72243812, D3×#13091662, … |
| maximal normal subgroup of | D3×(#4207⋊C2)⋊C3 |
| maximal quotient of | D3×#13091521, #72243364, #72243994, … |
Past the SmallGroups library coverage — no SmallGroups id.