Finite Group DatabasebetaFinite Group Databasebeta| order | 4940 |
| isoclinism | isoclinic class of C19⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C19⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C19⋊(C13×AGL(1,𝔽5)) |
| Fitting, socle, Hall | C5×C13×C19 ⋊ C4 |
| derived, Hall | C5×C19 ⋊ C4×C13 |
| Hall | C13×C19 ⋊ AGL(1,𝔽5) |
| Hall | C5×C13 ⋊ Dic19 |
| Sylow | C19 ⋊ C13×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C13×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C19⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C19 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C19 | C4 |
| LCS | G ▷ C5×C19 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
533 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4940, 14);