Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of A4×C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | A4×C42⋊C3 |
| unambiguous semidirect product | (C22×C42⋊C3)⋊C3 |
| unambiguous semidirect product | (C42×A4)⋊C3 |
| unambiguous semidirect product | (C22⋊(C42⋊C3))⋊C3 |
| Fitting, derived, Sylow | C22×C42 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×C42 | C32 |
| Frattini | C22 | A42 |
| socle | C24 | C3×A4 |
| LCS | G ▷ C22×C42 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
32 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5127);