Finite Group DatabasebetaFinite Group Databasebeta| order | 3996 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C4 · Schur multiplier (H2) = C33 |
| direct product | C32×#3866⋊C3 |
| Fitting, socle | C32×C37 ⋊ C3×C4 |
| derived, Sylow | C37 ⋊ C33×C4 |
| Hall | C32×C37⋊C3 ⋊ C4 |
| Hall | #3866 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #3866⋊C3 |
| commutator, hypocenter | C37 | C33×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C37 | C3×C4 |
| prime radical | C32×D37⋊C3 | C2 |
| cosocle | D37 | C2×C33 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C32 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 333 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3866⋊C3, C32×AGL(1,𝔽37) |
| maximal normal subgroup of | C3⋊D3×#3866⋊C3, C32×AGL(1,𝔽37) |
Past the SmallGroups library coverage — no SmallGroups id.