Finite Group DatabasebetaFinite Group Databasebeta| order | 33759 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C31⋊(C112⋊C9) |
| unambiguous semidirect product | C112⋊(C31⋊C9) |
| derived, Hall | C112×C31 ⋊ C9 |
| Sylow | C112 ⋊ C31⋊C9 |
| Sylow | C31 ⋊ C112⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C31⋊(C112⋊C3) |
| commutator, hypocenter | C112×C31 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C112×C31 | C3 |
| LCS | G ▷ C112×C31 | |
| UCS | C1 ◁ C3 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3069 |
Polycyclic presentation:
3,11^2,31,3|a^3=e,b^a=b^9c^5,c^a=b^6c,d^a=d^53759 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33759, 6);