According to a result of \textit{A. Delandtsheer} and \textit{J. Doyen} [Private Communication], if G is a block-transitive automorphism group of a 2-\((v,k,\lambda)\) design, then G acts primitively on points, unless there exist two integers \(\beta\), \(\gamma\) such that \[ v=\frac{\binom{k}{2}-\beta}{\beta} \times \frac{\binom{k}{2}- \gamma}{\gamma}. \] In the special case when \(k=6\) and \(\lambda =1\), this implies that G can act imprimitively on points only if \(v=91\) or 196. It is known that when \(v=91\) there are groups acting imprimitively on a 2- (91,6,1) design (see [\textit{A. R. Camina}, Discrete Math. 57, 1-7 (1985; Zbl 0586.05004)], [\textit{W. H. Mills}, Util. Math. 7, 73-75 (1975; Zbl 0312.05009)]). In this paper, we show that any block-transitive 2- (196,6,1) design has to be flag-transitive, hence primitive on points. We believe that it is still undecided whether or not there exist any 2- (196,6,1) designs.