Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #89341⋊C3 |
| Hall | #89341 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #333 |
| Sylow | C7 ⋊ C3×#333 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^2,3,2^4,7|a^2=e,b^2=fg,d^2=fg,e^2=g,b^a=bd,d^a=df,h^a=h^6,d^b=dfg,e^b=eg,h^c=h^271 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 109);