Finite Group DatabasebetaFinite Group Databasebeta| order | 19590 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1959 |
| unambiguous semidirect product | C3⋊(C5×D653) |
| unambiguous semidirect product | C653⋊(C5×D3) |
| Fitting, socle, Hall | C3×C5×C653 ⋊ C2 |
| derived, Hall | C3×C653 ⋊ C2×C5 |
| Hall | C5×C653 ⋊ D3 |
| Sylow | C653 ⋊ C5×D3 |
| Hall | C3×C5 ⋊ D653 |
| Sylow | C3 ⋊ C5×D653 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1959 |
| commutator, cosocle, hypocenter | C3×C653 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C653 | C2 |
| LCS | G ▷ C3×C653 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9795 |
4905 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19590, 6);