Finite Group DatabasebetaFinite Group Databasebeta| order | 32580 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20266771⋊C5 |
| derived, Sylow | C181 ⋊ C4×C5×C9 |
| Hall | #13108656⋊C5 ⋊ C4 |
| Hall | #20266771 ⋊ C5 |
| Hall | #10624382⋊C5 ⋊ C9 |
| Hall | #13108656 ⋊ C4×C5 |
| Hall | C181⋊C5 ⋊ C4×C9 |
| Hall | #10624382 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (#10624382⋊C3)⋊C5 |
| commutator, hypocenter | C181 | C4×C5×C9 |
| Fitting, socle | C3×C181 | C3×C4×C5 |
| prime radical | C3×D181⋊C5 | C2×C3 |
| cosocle | C3×D181 | C2×C3×C5 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,2,181,3|a^2=d,b^3=f,e^a=e^162,e^b=e^132,e^c=e^59,e^d=e^180189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32580, 20);