Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of D11×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×D11×S4 |
| unambiguous semidirect product | (C11×S4)⋊(C2×C3) |
| unambiguous semidirect product | (C11⋊S4)⋊(C2×C3) |
| unambiguous semidirect product | (A4×D11)⋊(C2×C3) |
| Fitting, socle | C22×C3×C11 ⋊ C2×D3 |
| derived | C11×A4 ⋊ C22×C3 |
| Sylow | C11 ⋊ C2×C3×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D11×S4 |
| commutator, cosocle, hypocenter | C11×A4 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C11 | C2×D3 |
| LCS | G ▷ C11×A4 | |
| UCS | C1 ◁ C3 | |
140 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 132 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | C3×S4×AGL(1,𝔽11), D3×D11×S4 |
| maximal normal subgroup of | C3×S4×AGL(1,𝔽11), D3×D11×S4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 659);