Finite Group DatabasebetaFinite Group Databasebeta| order | 33462 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×C11⋊#11759813 |
| unambiguous semidirect product | C11⋊(C3×#11759813) |
| Fitting, socle | C3×C11×C132 ⋊ D3 |
| derived | C11×#92789 ⋊ C2×C3 |
| 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, hypercenter | C3 | C11⋊#11759813 |
| commutator, cosocle, hypocenter | C11×#92789 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C132 | D3 |
| LCS | G ▷ C11×#92789 | |
| UCS | C1 ◁ C3 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 858 |
1032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33462, 84);