Finite Group DatabasebetaFinite Group Databasebeta| order | 9020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C22×#14555919 |
| Fitting, socle, Hall | C22×C11×C41 ⋊ C5 |
| derived, Hall | C11×C41 ⋊ C22×C5 |
| Hall | C22×C41 ⋊ C11⋊C5 |
| Hall | C22×C11 ⋊ C41⋊C5 |
| Sylow | C41 ⋊ C22×C11⋊C5 |
| Sylow | C11 ⋊ C22×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #14555919 |
| commutator, hypocenter | C11×C41 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C11×C41 | C5 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C22 | |
40 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#14555919, C2×D3×#14555919, C22×C3×#14555919 |
| maximal normal subgroup of | A4×#14555919, C22×C3×#14555919 |
| maximal quotient of | C2×D3×#14555919, C22×C3×#14555919 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9020, 70);