Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C961⋊#157 |
| Fitting, derived, Hall | C32×C961 ⋊ C4 |
| Sylow | C961 ⋊ #157 |
| Sylow | C32 ⋊ Dic961 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C32×C961 | C4 |
| Frattini | C31 | C31⋊#157 |
| socle | C32×C31 | Dic31 |
| prime radical | C3⋊D3×C31 | D31 |
| cosocle | C3⋊D3×C961 | C2 |
| LCS | G ▷ C32×C961 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5766 |
Polycyclic presentation:
2^2,3^2,31^2|a^2=b,e^31=f^30,c^a=cd^2,d^a=c^2d^2,e^a=e^30f,f^a=f^30,c^b=c^2,d^b=d^22886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 33);