Finite Group DatabasebetaFinite Group Databasebeta| order | 19420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic971⋊C5 |
| unambiguous semidirect product | (C971⋊C5)⋊C4 |
| derived, Sylow | C971 ⋊ C4×C5 |
| Hall | C971⋊C5 ⋊ C4 |
| Hall | Dic971 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D971⋊C5 |
| commutator, hypocenter | C971 | C4×C5 |
| Fitting, socle, cosocle | C2×C971 | C2×C5 |
| prime radical | C2×C971⋊C5 | C2 |
| LCS | G ▷ C971 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3884 |
Polycyclic presentation:
2,5,971,2|a^2=d,c^a=c^970,c^b=c^341214 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19420, 2);