Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D7×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C24 |
| direct product | Dic7×C22⋊A4 |
| derived | C24×C7 ⋊ C3×C4 |
| Hall | C24×Dic7 ⋊ C3 |
| Sylow | C7 ⋊ C4×C22⋊A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×C22⋊A4 |
| commutator, hypocenter | C24×C7 | C3×C4 |
| Fitting, socle, cosocle | C25×C7 | C2×C3 |
| prime radical | C2×C7×C22⋊A4 | C2 |
| LCS | G ▷ C24×C7 | |
| UCS | C1 ◁ C2 | |
524 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11496);