Finite Group DatabasebetaFinite Group Databasebeta| order | 33462 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C11⋊#11759813) |
| unambiguous semidirect product | C11⋊(C3⋊#11759813) |
| Fitting, socle | C3×C11×C132 ⋊ D3 |
| derived, Hall | C3×C11×#92789 ⋊ C2 |
| Hall | C11×C132 ⋊ C3⋊D3 |
| Hall | C3×#92789 ⋊ D11 |
| Sylow | C132 ⋊ C3⋊D33 |
| Sylow | C11 ⋊ C3⋊#11759813 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C11×#92789 | C2 |
| Fitting, socle | C3×C11×C132 | D3 |
| LCS | G ▷ C3×C11×#92789 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 858 |
Polycyclic presentation:
2,3^2,11,13^2|b^a=b^2,c^a=c^2,d^a=d^10,e^a=f,f^a=e,e^b=e^3,f^b=f^9993 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33462, 106);