Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C961 · Schur multiplier (H2) = C2 |
| direct product | A4×C961 |
| unambiguous semidirect product | C22⋊(C3×C961) |
| Fitting, Hall | C22×C961 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C961 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C961 | A4 |
| commutator, hypocenter | C22 | C3×C961 |
| Frattini | C31 | A4×C31 |
| Fitting | C22×C961 | C3 |
| socle, cosocle | C22×C31 | C3×C31 |
| prime radical | A4×C31 | C31 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C961 | |
15 conjugacy classes of subgroups.
3844 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×C961⋊C3, C3×A4×C961 |
| maximal normal subgroup of | A4×C961⋊C3, C3×A4×C961 |
| maximal quotient of | C22⋊C9×C961, C3×A4×C961 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 11);