Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C9 · Schur multiplier (H2) = C27 |
| direct product | C24×C22⋊C9 |
| derived | C22 ⋊ C24×C9 |
| Sylow | C26 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C3 | A4 |
| commutator, hypocenter | C22 | C24×C9 |
| Frattini | C3 | C24×A4 |
| Fitting, socle, prime radical | C26×C3 | C3 |
| cosocle | C22×C3 | C24×C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C24×C3 | |
2196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8264);