Our main goal is to determine the general solution of the functional equation \[ f 1 ( x y ) + f 2 ( x y − 1 ) = f 3 ( x ) + f 4 ( y ) + f 5 ( x ) f 6 ( y ) , f i ( t x y ) = f i ( t y x ) ( i = 1 , 2 ) \begin {array}{*{20}{c}} {{f_1}(xy) + {f_2}(x{y^{ - 1}}) = {f_3}(x) + {f_4}(y) + {f_5}(x){f_6}(y),} \\ {{f_i}(txy) = {f_i}(tyx)\qquad (i = 1,2)} \\ \end {array} \] where f i {f_i} are complex-valued functions defined on a group. This equation contains, among others, an equation of H. Swiatak whose general solution was not known until now and an equation studied by K.S. Lau in connection with a characterization of Rao’s quadratic entropies. Special cases of this equation also include the Pexider, quadratic, d’Alembert and Wilson equations.