Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D961⋊C5 |
| unambiguous semidirect product | D961⋊(C2×C5) |
| unambiguous semidirect product | (C2×D961)⋊C5 |
| unambiguous semidirect product | (C961⋊C5)⋊C22 |
| unambiguous semidirect product | (C2×C961⋊C5)⋊C2 |
| Fitting | C2×C961 ⋊ C2×C5 |
| derived, Sylow | C961 ⋊ C22×C5 |
| Hall | C961⋊C5 ⋊ C22 |
| Hall | C2×D961 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D961⋊C5 |
| commutator, cosocle, hypocenter | C961 | C22×C5 |
| Frattini | C31 | C2×D31⋊C5 |
| Fitting | C2×C961 | C2×C5 |
| socle | C2×C31 | D31⋊C5 |
| LCS | G ▷ C961 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1922 |
212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 8);