Finite Group DatabasebetaFinite Group Databasebeta| order | 32580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D5×#13108656⋊C2 |
| unambiguous semidirect product | (C5×#13108656⋊C2)⋊C2 |
| unambiguous semidirect product | (D5×#13108656)⋊C2 |
| unambiguous semidirect product | (C5⋊(#13108656⋊C2))⋊C2 |
| derived, Hall | C5×C181 ⋊ C22×C9 |
| Hall | C5×#13108656 ⋊ C22 |
| Hall | D5×D181 ⋊ C9 |
| Hall | #13108656 ⋊ C2×D5 |
| Sylow | C181 ⋊ C2×C9×D5 |
| Sylow | C5 ⋊ C2×#13108656⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D5×D181⋊C3 |
| commutator, hypocenter | C5×C181 | C22×C9 |
| Fitting, socle, cosocle | C3×C5×C181 | C22×C3 |
| prime radical | C3×D5×D181 | C3 |
| LCS | G ▷ C5×C181 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
432 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32580, 34);