Finite Group DatabasebetaFinite Group Databasebeta| order | 9020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×(C11⋊C5)⋊D41 |
| unambiguous semidirect product | (C2×C11⋊C5)⋊D41 |
| Fitting, socle | C2×C11×C41 ⋊ C2×C5 |
| derived, Hall | C11×C41 ⋊ C22×C5 |
| Hall | C41×C11⋊C5 ⋊ C22 |
| Hall | C2×D451 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C2×C5×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C11⋊C5)⋊D41 |
| commutator, hypocenter | C11×C41 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C41 | C2×C5 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
302 conjugacy classes — view the full character table.
| maximal subgroup of | D3×(C11⋊C5)⋊D41, C2×C3×(C11⋊C5)⋊D41, C2×C3⋊((C11⋊C5)⋊D41) |
| maximal normal subgroup of | C2×C3×(C11⋊C5)⋊D41 |
| maximal quotient of | D3×(C11⋊C5)⋊D41, C2×C3×(C11⋊C5)⋊D41, C2×C3⋊((C11⋊C5)⋊D41) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9020, 62);