Finite Group DatabasebetaFinite Group Databasebeta| order | 32547 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C3×C571⋊C19 |
| unambiguous semidirect product | (C3×C571)⋊C19 |
| Fitting, socle, Hall | C3×C571 ⋊ C19 |
| derived, Sylow | C571 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C571⋊C19 |
| commutator, cosocle, hypocenter | C571 | C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C571 | C19 |
| LCS | G ▷ C571 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1713 |
147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32547, 2);