Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of D9×AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C9×C11 ⋊ C22×C5 |
| Hall | C9×C11⋊C5 ⋊ C22 |
| Hall | D9×D11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×D9 |
| Sylow | C11 ⋊ C2×C5×D9 |
| Sylow | C9 ⋊ C2×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C11 | C22×C5 |
| Frattini | C3 | D3×AGL(1,𝔽11) |
| socle | C3×C11 | C2×C5×D3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 99 |
66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 13);