Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of D11×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, Hall | C11×3−1+2 ⋊ C22 |
| derived | C9×C11 ⋊ C22×C3 |
| Sylow | 3−1+2 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C9×C11 | C22×C3 |
| Frattini | C3 | C3×D3×D11 |
| Fitting | C11×3−1+2 | C22 |
| socle | C3×C11 | C2×C3×D3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 99 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/9)×AGL(1,𝔽11), C2×D11×AGL(1,ℤ/9) |
| maximal normal subgroup of | AGL(1,ℤ/9)×AGL(1,𝔽11), C2×D11×AGL(1,ℤ/9) |
| maximal quotient of | C2×D11×AGL(1,ℤ/9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 34);