Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C961⋊C9) |
| unambiguous semidirect product | C961⋊(C22⋊C9) |
| derived, Hall | C22×C961 ⋊ C9 |
| Sylow | C961 ⋊ C22⋊C9 |
| Sylow | C22 ⋊ C961⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C22⋊(C961⋊C3) |
| commutator, hypocenter | C22×C961 | C9 |
| Frattini | C3×C31 | C22⋊(C31⋊C3) |
| Fitting, cosocle | C22×C3×C961 | C3 |
| socle, prime radical | C22×C3×C31 | C31⋊C3 |
| LCS | G ▷ C22×C961 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17298 |
Polycyclic presentation:
3,2^2,31,3,31|a^3=e,d^31=f^2,b^a=c,c^a=bc,d^a=d^25f,f^a=f^253852 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 12);