Finite Group DatabasebetaFinite Group Databasebeta| order | 32164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(C43⋊#595) |
| unambiguous semidirect product | C43⋊(C11⋊#595) |
| Fitting, socle, derived, Hall | C11×C17×C43 ⋊ C4 |
| Hall | C17×C43 ⋊ Dic11 |
| Hall | C11×C43 ⋊ #595 |
| Hall | C11×C17 ⋊ Dic43 |
| Sylow | C43 ⋊ C11⋊#595 |
| Sylow | C17 ⋊ Dic473 |
| Sylow | C11 ⋊ C43⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C17×C43 | C4 |
| prime radical, cosocle | C11×D17×C43 | C2 |
| LCS | G ▷ C11×C17×C43 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8041 |
Polycyclic presentation:
2^2,11,17,43|a^2=b,c^a=c^10,d^a=d^13,e^a=e^42,d^b=d^162368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32164, 15);