Finite Group DatabasebetaFinite Group Databasebeta| order | 22420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1121 |
| unambiguous semidirect product | C19⋊(C5×Dic59) |
| unambiguous semidirect product | C59⋊(C5×Dic19) |
| derived, Hall | C19×C59 ⋊ C4×C5 |
| Hall | C5×C19×C59 ⋊ C4 |
| Hall | C5×C59 ⋊ Dic19 |
| Hall | C5×C19 ⋊ Dic59 |
| Sylow | C59 ⋊ C5×Dic19 |
| Sylow | C19 ⋊ C5×Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1121 |
| commutator, hypocenter | C19×C59 | C4×C5 |
| Frattini | C2 | C5×D1121 |
| Fitting, socle, prime radical | C2×C5×C19×C59 | C2 |
| cosocle | C2×C19×C59 | C2×C5 |
| LCS | G ▷ C19×C59 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22420 |
5620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22420, 4);