Finite Group DatabasebetaFinite Group Databasebeta| order | 3762 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×D33 |
| unambiguous semidirect product | C3⋊(D11×C19⋊C3) |
| unambiguous semidirect product | C11⋊(D3×C19⋊C3) |
| unambiguous semidirect product | (C19×D33)⋊C3 |
| Fitting, socle, derived | C3×C11×C19 ⋊ C2×C3 |
| Hall | C3×C11×C19⋊C3 ⋊ C2 |
| Hall | C11×C19 ⋊ C3×D3 |
| Hall | C3×C19⋊C3 ⋊ D11 |
| Sylow | C19 ⋊ C3×D33 |
| Sylow | C11 ⋊ D3×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C19 | C2×C3 |
| LCS | G ▷ C3×C11×C19 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 627 |
162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3762, 24);