Finite Group DatabasebetaFinite Group Databasebeta| order | 3996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊(#66526⋊C2) |
| Fitting, socle | C2×C3×C37 ⋊ C2×C9 |
| derived | C3×C37 ⋊ C22×C9 |
| Hall | C3×#66526 ⋊ C22 |
| Sylow | C37 ⋊ C2×D3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(#66526⋊C2) |
| commutator, hypocenter | C3×C37 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C37 | C2×C9 |
| prime radical | C2×C3⋊(D37⋊C3) | C3 |
| cosocle | C3×C37⋊C3 | C22×C3 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 222 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#66526⋊C2 |
| maximal normal subgroup of | C2×D3×#66526⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.