Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of A4×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×Dic11 |
| unambiguous semidirect product | C11⋊(C3×C4×A4) |
| unambiguous semidirect product | (C22×Dic11)⋊C32 |
| unambiguous semidirect product | (C22×C3×Dic11)⋊C3 |
| derived | C22×C11 ⋊ C32×C4 |
| Hall | C22×Dic11 ⋊ C32 |
| Sylow | C11 ⋊ C3×C4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | A4×D11 |
| commutator, hypocenter | C22×C11 | C32×C4 |
| Frattini | C2 | C3×A4×D11 |
| Fitting, socle | C23×C3×C11 | C2×C3 |
| prime radical | C2×C3×C11×A4 | C2 |
| cosocle | C23×C11 | C2×C32 |
| LCS | G ▷ C22×C11 | |
| UCS | C1 ◁ C2×C3 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 396 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 457);