Finite Group DatabasebetaFinite Group Databasebeta| order | 990 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×AGL(1,𝔽11) |
| unambiguous semidirect product | D11⋊(C5×C9) |
| unambiguous semidirect product | (C11⋊C5)⋊(C2×C9) |
| unambiguous semidirect product | (C9×D11)⋊C5 |
| Fitting, Hall | C9×C11 ⋊ C2×C5 |
| derived, Sylow | C11 ⋊ C2×C5×C9 |
| Hall | C9×C11⋊C5 ⋊ C2 |
| Hall | C9×D11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×C9 |
| Hall | D11 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | AGL(1,𝔽11) |
| commutator, hypocenter | C11 | C2×C5×C9 |
| Frattini | C3 | C3×AGL(1,𝔽11) |
| Fitting | C9×C11 | C2×C5 |
| socle, cosocle | C3×C11 | C2×C3×C5 |
| prime radical | C3×AGL(1,𝔽11) | C3 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 99 |
99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(990, 1);