Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of D11×AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | D11×AGL(1,𝔽9) |
| Fitting, socle, derived, Hall | C32×C11 ⋊ C2×C8 |
| Sylow | C11 ⋊ C2×AGL(1,𝔽9) |
| Sylow | C32 ⋊ C8×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C11 | C2×C8 |
| prime radical | C3⋊D3×D11 | C4 |
| cosocle | C11×#157 | C22 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 99 |
63 conjugacy classes — view the full character table.
| maximal subgroup of | D11×AΓL(1,𝔽9), AGL(1,𝔽9)×AGL(1,𝔽11) |
| maximal normal subgroup of | D11×AΓL(1,𝔽9), AGL(1,𝔽9)×AGL(1,𝔽11) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 652);