Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | #90326⋊C3 |
| Fitting | C7×C22⋊Q8 ⋊ C2×C3 |
| Hall | #90326 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #554 |
| Sylow | C7 ⋊ C3×#554 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^4,3,2^2,7|c^2=f,d^2=f,b^a=bg,d^a=dg,h^a=h^6,d^b=dg,d^c=df,h^e=h^289 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6661);