Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of D11×PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
| direct product | D11×PSU(3,𝔽2) |
| Fitting, socle, Hall | C32×C11 ⋊ C2×Q8 |
| Sylow | C11 ⋊ C2×PSU(3,𝔽2) |
| Sylow | C32 ⋊ Q8×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C11×C3⋊D3 | C23 |
| Fitting, socle, hypocenter | C32×C11 | C2×Q8 |
| prime radical | C3⋊D3×D11 | C22 |
| LCS | G ▷ C11×C3⋊D3 ▷ C32×C11 | |
| UCS | C1 | |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 99 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | PSU(3,𝔽2)×AGL(1,𝔽11), D11×PSU(3,𝔽2)⋊C3, D11×AΓL(1,𝔽9) |
| maximal normal subgroup of | PSU(3,𝔽2)×AGL(1,𝔽11), D11×PSU(3,𝔽2)⋊C3, D11×AΓL(1,𝔽9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 658);