Finite Group DatabasebetaFinite Group Databasebeta| order | 3762 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D11×C19⋊C3 |
| unambiguous semidirect product | C11⋊(C2×C3×C19⋊C3) |
| unambiguous semidirect product | (C19×D11)⋊C32 |
| unambiguous semidirect product | (C3×C19×D11)⋊C3 |
| Fitting, socle | C3×C11×C19 ⋊ C2×C3 |
| derived, Hall | C11×C19 ⋊ C2×C32 |
| Hall | C3×C11×C19⋊C3 ⋊ C2 |
| Hall | C19×D11 ⋊ C32 |
| Sylow | C19 ⋊ C32×D11 |
| Sylow | C11 ⋊ C2×C3×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D11×C19⋊C3 |
| commutator, cosocle, hypocenter | C11×C19 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C19 | C2×C3 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 627 |
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3762, 20);