Finite Group DatabasebetaFinite Group Databasebeta| order | 33759 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C11 |
| direct product | C31⋊C3×C112⋊C3 |
| unambiguous semidirect product | (C31⋊(C112⋊C3))⋊C3 |
| unambiguous semidirect product | (C31×C112⋊C3)⋊C3 |
| unambiguous semidirect product | (C112×C31⋊C3)⋊C3 |
| Fitting, socle, derived, Hall | C112×C31 ⋊ C32 |
| Sylow | C112 ⋊ C3×C31⋊C3 |
| Sylow | C31 ⋊ C3×C112⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C31 | C32 |
| LCS | G ▷ C112×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1023 |
559 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33759, 10);