We study fixed point properties of the automorphism group universal Coxeter Aut(Wn). In particular, we prove that whenever Aut(Wn) acts by isometries on complete d-dimensional CAT(0) space with d<⌊n2⌋, then it must fix a point. also does not have Kazhdan’s property (T). Further, strong restrictions are obtained homomorphisms to groups do contain copy Sym(n).