Finite Group DatabasebetaFinite Group Databasebeta| order | 32580 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(Dic181⋊C5) |
| unambiguous semidirect product | Dic1629⋊C5 |
| derived, Hall | C9×C181 ⋊ C4×C5 |
| Hall | C9×C181⋊C5 ⋊ C4 |
| Hall | Dic1629 ⋊ C5 |
| Hall | C181⋊C5 ⋊ Dic9 |
| Sylow | C181 ⋊ C5×Dic9 |
| Sylow | C9 ⋊ Dic181⋊C5 |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,181,2,3|a^2=e,b^3=f^2,b^a=b^2f,d^a=d^180,f^a=f^2,d^c=d^59384 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32580, 14);