Finite Group DatabasebetaFinite Group Databasebeta| order | 33759 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C31 · Schur multiplier (H2) = C3×C11 |
| direct product | C3×C31×C112⋊C3 |
| unambiguous semidirect product | C112⋊(C32×C31) |
| unambiguous semidirect product | (C3×C112)⋊(C3×C31) |
| Fitting, socle | C3×C112×C31 ⋊ C3 |
| derived, Sylow | C112 ⋊ C32×C31 |
| Hall | C112×C31 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C31 | C112⋊C3 |
| commutator, cosocle, hypocenter | C112 | C32×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112×C31 | C3 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C3×C31 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3069 |
3999 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33759, 11);