Finite Group DatabasebetaFinite Group Databasebeta| order | 5620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C22×C281⋊C5 |
| unambiguous semidirect product | (C22×C281)⋊C5 |
| Fitting, socle, Hall | C22×C281 ⋊ C5 |
| derived, Sylow | C281 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C281⋊C5 |
| commutator, hypocenter | C281 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C281 | C5 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C22 | |
20 conjugacy classes of subgroups.
244 conjugacy classes — view the full character table.
| maximal subgroup of | A4×C281⋊C5, C2×D3×C281⋊C5, C22×C3×C281⋊C5, … |
| maximal normal subgroup of | A4×C281⋊C5, C22×C3×C281⋊C5, C22×C5×C281⋊C5 |
| maximal quotient of | C2×D3×C281⋊C5, C22×C3×C281⋊C5, C22×C281⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5620, 10);