Finite Group DatabasebetaFinite Group Databasebeta| order | 32580 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #20266815⋊C5 |
| Fitting, socle, derived, Hall | C32×C181 ⋊ C4×C5 |
| Hall | C32×C181⋊C5 ⋊ C4 |
| Hall | #20266815 ⋊ C5 |
| Hall | C181⋊C5 ⋊ #157 |
| Sylow | C181 ⋊ C5×#157 |
| Sylow | C32 ⋊ #10624382⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C181 | C4×C5 |
| prime radical | C3⋊(C3⋊(D181⋊C5)) | C2 |
| cosocle | C3⋊D543 | C2×C5 |
| LCS | G ▷ C32×C181 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,3^2,181|a^2=c,d^a=de,e^a=de^2,f^a=f^162,f^b=f^59,d^c=d^2,e^c=e^2,f^c=f^180111 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32580, 126);