Finite Group DatabasebetaFinite Group Databasebeta| order | 5340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#13184069 |
| Fitting, socle, Hall | C3×C5×C89 ⋊ C4 |
| derived, Hall | C5×C89 ⋊ C3×C4 |
| Hall | C3×C89 ⋊ AGL(1,𝔽5) |
| Sylow | C89 ⋊ C3×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ Dic89 |
| Sylow | C5 ⋊ C3×Dic89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13184069 |
| commutator, hypocenter | C5×C89 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C89 | C4 |
| LCS | G ▷ C5×C89 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
543 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5340, 14);