Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C961 · Schur multiplier (H2) = C2 |
| direct product | D32×C961 |
| unambiguous semidirect product | (C3×D3)⋊(C2×C961) |
| unambiguous semidirect product | (C3⋊D3)⋊(C2×C961) |
| Fitting, Hall | C32×C961 ⋊ C22 |
| derived, Sylow | C32 ⋊ C22×C961 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C961 | D32 |
| commutator, hypocenter | C32 | C22×C961 |
| Frattini | C31 | D32×C31 |
| Fitting | C32×C961 | C22 |
| socle, cosocle | C32×C31 | C22×C31 |
| prime radical | D32×C31 | C31 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C961 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5766 |
8649 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 36);