Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C312 · Schur multiplier (H2) = C2×C31 |
| direct product | A4×C312 |
| unambiguous semidirect product | C22⋊(C3×C312) |
| Fitting, socle, Hall | C22×C312 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C312 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C312 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C312 |
| Frattini | C1 | G |
| Fitting, socle | C22×C312 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C312 | |
170 conjugacy classes of subgroups.
3844 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×C31×C31⋊C3, A4×#15668333, A4×#15668332, … |
| maximal normal subgroup of | A4×C31×C31⋊C3, A4×#15668333, A4×#15668332, … |
| maximal quotient of | C312×C22⋊C9, C3×A4×C312 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 58);