Finite Group DatabasebetaFinite Group Databasebeta| order | 32580 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(#13108656⋊C5) |
| unambiguous semidirect product | (C22⋊#13108656)⋊C5 |
| derived, Hall | C22×C181 ⋊ C5×C9 |
| Hall | C22⋊#13108656 ⋊ C5 |
| Hall | C22×C181⋊C5 ⋊ C9 |
| Hall | C181⋊C5 ⋊ C22⋊C9 |
| Sylow | C181 ⋊ C5×C22⋊C9 |
| Sylow | C22 ⋊ #13108656⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊((C181⋊C3)⋊C5) |
| commutator, hypocenter | C22×C181 | C5×C9 |
| Fitting, socle, cosocle | C22×C3×C181 | C3×C5 |
| prime radical | C22×C3×C181⋊C5 | C3 |
| LCS | G ▷ C22×C181 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,2^2,181,3|a^3=f,c^a=d,d^a=cd,e^a=e^132,e^b=e^59204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32580, 26);