Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of C9⋊AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C9⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C2×C9)⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C2×C11⋊C5)⋊D9 |
| unambiguous semidirect product | (C2×D99)⋊C5 |
| Fitting | C2×C9×C11 ⋊ C2×C5 |
| derived, Hall | C9×C11 ⋊ C22×C5 |
| Hall | C9×C11⋊C5 ⋊ C22 |
| Hall | C2×D99 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×D9 |
| Sylow | C11 ⋊ C2×C5×D9 |
| Sylow | C9 ⋊ C2×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C9⋊AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C9×C11 | C22×C5 |
| Frattini | C3 | C2×C3⋊AGL(1,𝔽11) |
| Fitting | C2×C9×C11 | C2×C5 |
| socle | C2×C3×C11 | C5×D3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 17);