Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#19153446⋊C2 |
| Fitting, socle | C3×C312 ⋊ C22×C3 |
| derived, Sylow | C312 ⋊ C22×C32 |
| Hall | C3×#15668333 ⋊ C22 |
| Hall | D312 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19153446⋊C2 |
| commutator, cosocle, hypocenter | C312 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C312 | C22×C3 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C3 | |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 558 |
321 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 144);