Finite Group DatabasebetaFinite Group Databasebeta| order | 9820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C22×C491⋊C5 |
| unambiguous semidirect product | (C22×C491)⋊C5 |
| Fitting, socle, Hall | C22×C491 ⋊ C5 |
| derived, Sylow | C491 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C491⋊C5 |
| commutator, cosocle, hypocenter | C491 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C491 | C5 |
| LCS | G ▷ C491 | |
| UCS | C1 ◁ C22 | |
20 conjugacy classes of subgroups.
412 conjugacy classes — view the full character table.
| maximal subgroup of | A4×C491⋊C5, C2×D3×C491⋊C5, C22×C3×C491⋊C5 |
| maximal normal subgroup of | A4×C491⋊C5, C22×C3×C491⋊C5 |
| maximal quotient of | C2×D3×C491⋊C5, C22×C3×C491⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9820, 9);