Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C22 |
| direct product | C22×C11×A4 |
| Fitting, socle, Hall | C24×C11 ⋊ C3 |
| derived | C22 ⋊ C22×C3×C11 |
| Sylow | C24 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C11 | A4 |
| commutator, cosocle, hypocenter | C22 | C22×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C24×C11 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C22×C11 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 165);