Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C4×C7×C22⋊A4 |
| Fitting, Hall | C24×C4×C7 ⋊ C3 |
| derived | C24 ⋊ C3×C4×C7 |
| Sylow | C24×C4 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C7 | C22⋊A4 |
| commutator, hypocenter | C24 | C3×C4×C7 |
| Frattini | C2 | C2×C7×C22⋊A4 |
| Fitting | C24×C4×C7 | C3 |
| socle | C25×C7 | C2×C3 |
| prime radical | C2×C7×C22⋊A4 | C2 |
| cosocle | C25 | C2×C3×C7 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C4×C7 | |
524 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11607);