Finite Group DatabasebetaFinite Group Databasebeta| order | 19420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D971⋊C5 |
| unambiguous semidirect product | D971⋊(C2×C5) |
| unambiguous semidirect product | (C2×D971)⋊C5 |
| unambiguous semidirect product | (C971⋊C5)⋊C22 |
| unambiguous semidirect product | (C2×C971⋊C5)⋊C2 |
| Fitting, socle | C2×C971 ⋊ C2×C5 |
| derived, Sylow | C971 ⋊ C22×C5 |
| Hall | C971⋊C5 ⋊ C22 |
| Hall | C2×D971 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D971⋊C5 |
| commutator, cosocle, hypocenter | C971 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C971 | C2×C5 |
| LCS | G ▷ C971 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1942 |
214 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19420, 8);