Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #89419⋊C3 |
| Hall | #89419 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #389 |
| Sylow | C7 ⋊ C3×#389 |
340 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^3,3,2^3,7|a^2=g,b^2=f,c^2=e,b^a=bg,h^a=h^6,c^b=cfg,h^d=h^2104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 841);