Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| derived, Sylow | C312 ⋊ C22×C9 |
| Hall | C31×C31⋊C9 ⋊ C22 |
| Hall | D312 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D31×D31⋊C3 |
| commutator, hypocenter | C312 | C22×C9 |
| Fitting, socle, cosocle | C3×C312 | C22×C3 |
| prime radical | C3×D312 | C3 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 558 |
561 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 67);