Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C22×C961⋊C5 |
| unambiguous semidirect product | (C22×C961)⋊C5 |
| Fitting, Hall | C22×C961 ⋊ C5 |
| derived, Sylow | C961 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C961⋊C5 |
| commutator, cosocle, hypocenter | C961 | C22×C5 |
| Frattini | C31 | C22×ΓL(1,𝔽32) |
| Fitting | C22×C961 | C5 |
| socle | C22×C31 | ΓL(1,𝔽32) |
| LCS | G ▷ C961 | |
| UCS | C1 ◁ C22 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3844 |
788 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 9);