Finite Group DatabasebetaFinite Group Databasebeta| order | 9020 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×Dic11⋊C5 |
| unambiguous semidirect product | Dic11⋊(C5×C41) |
| unambiguous semidirect product | (C11⋊C5)⋊(C4×C41) |
| derived, Sylow | C11 ⋊ C4×C5×C41 |
| Hall | C41×C11⋊C5 ⋊ C4 |
| Hall | C41×Dic11 ⋊ C5 |
| Hall | C11×C41 ⋊ C4×C5 |
| Hall | C11⋊C5 ⋊ C4×C41 |
| Hall | Dic11 ⋊ C5×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | AGL(1,𝔽11) |
| commutator, hypocenter | C11 | C4×C5×C41 |
| Frattini | C2 | C41×AGL(1,𝔽11) |
| Fitting, socle | C2×C11×C41 | C2×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C41 | |
24 conjugacy classes of subgroups.
902 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C41×Dic11⋊C5, C41×C3⋊(Dic11⋊C5) |
| maximal normal subgroup of | C3×C41×Dic11⋊C5 |
| maximal quotient of | C3×C41×Dic11⋊C5, C41×C3⋊(Dic11⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9020, 22);