Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42×C7 · Schur multiplier (H2) = C2×C4 |
| direct product | C42×C7×A4 |
| Fitting, Hall | C22×C42×C7 ⋊ C3 |
| derived | C22 ⋊ C3×C42×C7 |
| Sylow | C22×C42 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42×C7 | A4 |
| commutator, hypocenter | C22 | C3×C42×C7 |
| Frattini | C22 | C22×C7×A4 |
| Fitting | C22×C42×C7 | C3 |
| socle | C24×C7 | C22×C3 |
| prime radical | C22×C7×A4 | C22 |
| cosocle | C24 | C22×C3×C7 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C42×C7 | |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10030);