Finite Group DatabasebetaFinite Group Databasebeta| order | 32509 |
| automorphism | ? |
| homology | Abelianization (H1) = C19×C29 · Schur multiplier (H2) = C1 |
| direct product | C19×C59⋊C29 |
| unambiguous semidirect product | C59⋊(C19×C29) |
| unambiguous semidirect product | (C19×C59)⋊C29 |
| Fitting, socle, Hall | C19×C59 ⋊ C29 |
| derived, Sylow | C59 ⋊ C19×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C59⋊C29 |
| commutator, cosocle, hypocenter | C59 | C19×C29 |
| Frattini | C1 | G |
| Fitting, socle | C19×C59 | C29 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C19 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1121 |
589 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32509, 1);