Finite Group DatabasebetaFinite Group Databasebeta| order | 3762 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(#4294⋊C2) |
| unambiguous semidirect product | #4294⋊D11 |
| derived, Hall | C11×C19 ⋊ C2×C9 |
| Hall | C11×#4294 ⋊ C2 |
| Hall | D209 ⋊ C9 |
| Hall | #4294 ⋊ D11 |
| Sylow | C19 ⋊ C9×D11 |
| Sylow | C11 ⋊ #4294⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C11⋊(D19⋊C3) |
| commutator, hypocenter | C11×C19 | C2×C9 |
| Fitting, socle, cosocle | C3×C11×C19 | C2×C3 |
| prime radical | C3×D209 | C3 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1881 |
Polycyclic presentation:
2,3,11,19,3|b^3=e,c^a=c^10,d^a=d^18,d^b=d^11162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3762, 4);