Finite Group DatabasebetaFinite Group Databasebeta| order | 5620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#11765499 |
| Fitting, socle, Hall | C5×C281 ⋊ C4 |
| derived, Sylow | C281 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #11765499 |
| commutator, hypocenter | C281 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C281 | C4 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
370 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5620, 11);