Finite Group DatabasebetaFinite Group Databasebeta| order | 22420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×C59⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C59⋊(C19×AGL(1,𝔽5)) |
| Fitting, socle, Hall | C5×C19×C59 ⋊ C4 |
| derived, Hall | C5×C59 ⋊ C4×C19 |
| Hall | C19×C59 ⋊ AGL(1,𝔽5) |
| Hall | C5×C19 ⋊ Dic59 |
| Sylow | C59 ⋊ C19×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C19×Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C59⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C59 | C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C59 | C4 |
| prime radical | D5×C19×C59 | C2 |
| cosocle | D5×C59 | C2×C19 |
| LCS | G ▷ C5×C59 | |
| UCS | C1 ◁ C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5605 |
2299 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22420, 12);