Finite Group DatabasebetaFinite Group Databasebeta| order | 5994 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×#66526 |
| Fitting, socle, derived | C32×C37 ⋊ C2×C9 |
| Hall | C32×#66526 ⋊ C2 |
| Sylow | C37 ⋊ C9×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C37 | C2×C9 |
| prime radical | C3⋊D3×C37⋊C3 | C3 |
| cosocle | C32×C37⋊C3 | C2×C3 |
| LCS | G ▷ C32×C37 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 333 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#66526⋊C2 |
| maximal normal subgroup of | C3⋊D3×#66526⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.