Finite Group DatabasebetaFinite Group Databasebeta| order | 5994 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C32×#66526⋊C2 |
| Fitting, socle | C32×C37 ⋊ C2×C9 |
| derived, Sylow | C37 ⋊ C2×C32×C9 |
| Hall | C32×#66526 ⋊ C2 |
| Hall | D37 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #66526⋊C2 |
| commutator, hypocenter | C37 | C2×C32×C9 |
| Frattini | C1 | G |
| Fitting, socle | C32×C37 | C2×C9 |
| prime radical | C32×D37⋊C3 | C3 |
| cosocle | C37⋊C3 | C2×C33 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C32 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 333 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#66526⋊C2, C32×AGL(1,𝔽37), #72276564 |
| maximal normal subgroup of | C3⋊D3×#66526⋊C2, C32×AGL(1,𝔽37), #72276564 |
Past the SmallGroups library coverage — no SmallGroups id.