Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #395⋊ΓL(1,𝔽8) |
| Fitting, Hall | C7×#395 ⋊ C3 |
| Sylow | #395 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ #395⋊C3 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2,3,2^4,7,2|a^2=h,c^2=h,d^2=h,c^a=ce,d^a=def,c^b=cd,d^b=c,e^b=f,f^b=ef,g^b=g^2,d^c=dh62 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4357);