Finite Group DatabasebetaFinite Group Databasebeta| order | 32580 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(#10624382⋊C5) |
| unambiguous semidirect product | (C9⋊#10624382)⋊C5 |
| Fitting, derived, Hall | C9×C181 ⋊ C4×C5 |
| Hall | C9×C181⋊C5 ⋊ C4 |
| Hall | C9⋊#10624382 ⋊ C5 |
| Hall | C181⋊C5 ⋊ Dic9 |
| Sylow | C181 ⋊ C5×Dic9 |
| Sylow | C9 ⋊ #10624382⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C181 | C4×C5 |
| Frattini | C3 | C3⋊(#10624382⋊C5) |
| socle | C3×C181 | C5×Dic3 |
| prime radical | C3×D181⋊C5 | D3 |
| cosocle | C9×D181 | C2×C5 |
| LCS | G ▷ C9×C181 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,3,181,3|a^2=c,d^3=f^2,d^a=d^2f,e^a=e^162,f^a=f^2,e^b=e^59,e^c=e^180141 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32580, 23);