  An algebra with identities $(a,b,c)=(a,c,b)=(b,a,c)$ is called {\it
assosymmetric}, where $(x,y,z)=(xy)z-x(yz)$ is associator. We study
$S_n$-module, $A_n$-module and $GL_n$-module structures of free assosymmetric
algebra.
