Finite Group DatabasebetaFinite Group Databasebeta| order | 33165 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C11 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×C67⋊C11 |
| unambiguous semidirect product | (C32×C67)⋊(C5×C11) |
| unambiguous semidirect product | (C32×C5×C67)⋊C11 |
| Fitting, socle, Hall | C32×C5×C67 ⋊ C11 |
| derived, Sylow | C67 ⋊ C32×C5×C11 |
| Hall | C32×C67 ⋊ C5×C11 |
| Hall | C5×C67 ⋊ C32×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | C67⋊C11 |
| commutator, cosocle, hypocenter | C67 | C32×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C67 | C11 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C32×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3015 |
765 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33165, 10);