Finite Group DatabasebetaFinite Group Databasebeta| order | 19780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C43⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C43⋊(AGL(1,𝔽5)×C23) |
| Fitting, socle, Hall | C5×C23×C43 ⋊ C4 |
| derived, Hall | C5×C43 ⋊ C4×C23 |
| Hall | C23×C43 ⋊ AGL(1,𝔽5) |
| Hall | C5×C23 ⋊ Dic43 |
| Sylow | C43 ⋊ AGL(1,𝔽5)×C23 |
| Sylow | C5 ⋊ C23×Dic43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C43⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C43 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C23×C43 | C4 |
| prime radical | D5×C23×C43 | C2 |
| cosocle | D5×C43 | C2×C23 |
| LCS | G ▷ C5×C43 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4945 |
2047 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19780, 12);