Finite Group DatabasebetaFinite Group Databasebeta| order | 9020 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C4×#14555916 |
| Fitting, Hall | C4×C11×C41 ⋊ C5 |
| derived, Hall | C11×C41 ⋊ C4×C5 |
| Hall | C4×C41 ⋊ C11⋊C5 |
| Hall | C4×C11 ⋊ C41⋊C5 |
| Sylow | C41 ⋊ C4×C11⋊C5 |
| Sylow | C11 ⋊ C4×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14555916 |
| commutator, hypocenter | C11×C41 | C4×C5 |
| Frattini | C2 | C2×#14555916 |
| Fitting | C4×C11×C41 | C5 |
| socle | C2×C11×C41 | C2×C5 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×#14555916, Dic3×#14555916 |
| maximal normal subgroup of | C3×C4×#14555916 |
| maximal quotient of | C3×C4×#14555916, Dic3×#14555916 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9020, 7);