Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C31 · Schur multiplier (H2) = C2 |
| direct product | C22×C31×C31⋊C9 |
| derived | C31 ⋊ C22×C9×C31 |
| Hall | C22×C312 ⋊ C9 |
| Sylow | C312 ⋊ C22×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C31 | C31⋊C3 |
| commutator, hypocenter | C31 | C22×C9×C31 |
| Frattini | C3 | C22×C31×C31⋊C3 |
| Fitting, socle, prime radical | C22×C3×C312 | C3 |
| cosocle | C3×C31 | C22×C3×C31 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C22×C3×C31 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1116 |
4836 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 91);