Finite Group DatabasebetaFinite Group Databasebeta| order | 33165 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C11 · Schur multiplier (H2) = C3 |
| direct product | C3×C5×C11×C67⋊C3 |
| unambiguous semidirect product | (C5×C11×C67)⋊C32 |
| unambiguous semidirect product | (C3×C5×C11×C67)⋊C3 |
| Fitting, socle | C3×C5×C11×C67 ⋊ C3 |
| derived, Sylow | C67 ⋊ C32×C5×C11 |
| Hall | C5×C11×C67 ⋊ C32 |
| Hall | C11×C67 ⋊ C32×C5 |
| Hall | C5×C67 ⋊ C32×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C11 | C67⋊C3 |
| commutator, cosocle, hypocenter | C67 | C32×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C11×C67 | C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C3×C5×C11 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11055 |
4125 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33165, 12);