Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of C3⋊D3×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C3⋊D3×D11 |
| Fitting, socle | C22×C32×C11 ⋊ C22 |
| derived, Hall | C32×C11 ⋊ C24 |
| Sylow | C11 ⋊ C23×C3⋊D3 |
| Sylow | C32 ⋊ C23×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊D3×D11 |
| commutator, cosocle, hypocenter | C32×C11 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C11 | C22 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C22 | |
804 conjugacy classes of subgroups.
| transitive degree | μt(G) = 396 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3⋊D3×AGL(1,𝔽11), D11×#3811 |
| maximal normal subgroup of | C22×C3⋊D3×AGL(1,𝔽11), D11×#3811 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 686);