Finite Group DatabasebetaFinite Group Databasebeta| order | 32580 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#16813740 |
| unambiguous semidirect product | C3⋊(C3×#16813740) |
| Fitting, socle, Hall | C32×C5×C181 ⋊ C4 |
| derived | C3×C5×C181 ⋊ C3×C4 |
| Hall | C32×C181 ⋊ Dic5 |
| Hall | C5×C181 ⋊ C3×Dic3 |
| Sylow | C181 ⋊ C3×Dic15 |
| Hall | C32×C5 ⋊ #10624382 |
| Sylow | C32 ⋊ #16813740 |
| Sylow | C5 ⋊ C3×C3⋊#10624382 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#16813740 |
| commutator, hypocenter | C3×C5×C181 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C181 | C4 |
| prime radical | C32×C5×D181 | C2 |
| cosocle | C3×C5×D181 | C2×C3 |
| LCS | G ▷ C3×C5×C181 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
2079 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32580, 201);