Finite Group DatabasebetaFinite Group Databasebeta| order | 32164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C43⋊#595 |
| unambiguous semidirect product | C43⋊(C11×#595) |
| Fitting, socle, Hall | C11×C17×C43 ⋊ C4 |
| derived, Hall | C17×C43 ⋊ C4×C11 |
| Hall | C11×C43 ⋊ #595 |
| Hall | C11×C17 ⋊ Dic43 |
| Sylow | C43 ⋊ C11×#595 |
| Sylow | C17 ⋊ C11×Dic43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C43⋊#595 |
| commutator, hypocenter | C17×C43 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C17×C43 | C4 |
| prime radical | C11×D17×C43 | C2 |
| cosocle | D17×C43 | C2×C11 |
| LCS | G ▷ C17×C43 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8041 |
2398 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32164, 11);