Finite Group DatabasebetaFinite Group Databasebeta| order | 516 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C43 · Schur multiplier (H2) = C2 |
| direct product | A4×C43 |
| unambiguous semidirect product | C22⋊(C3×C43) |
| Fitting, socle, Hall | C22×C43 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C22×C43 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C43 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 172 |
172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(516, 10);