Finite Group DatabasebetaFinite Group Databasebeta| order | 19780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic989 |
| unambiguous semidirect product | C23⋊(C5×Dic43) |
| unambiguous semidirect product | C43⋊(C5×Dic23) |
| derived, Hall | C23×C43 ⋊ C4×C5 |
| Hall | C5×C23×C43 ⋊ C4 |
| Hall | C5×C43 ⋊ Dic23 |
| Hall | C5×C23 ⋊ Dic43 |
| Sylow | C43 ⋊ C5×Dic23 |
| Sylow | C23 ⋊ C5×Dic43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D989 |
| commutator, hypocenter | C23×C43 | C4×C5 |
| Frattini | C2 | C5×D989 |
| Fitting, socle, prime radical | C2×C5×C23×C43 | C2 |
| cosocle | C2×C23×C43 | C2×C5 |
| LCS | G ▷ C23×C43 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19780 |
4960 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19780, 4);