In this note we study the linear symmetry group LS(f) of a Boolean function f of n variables, that is, the set of all £ GLn(2) which leave f invariant, where GLn (2) is the general linear group on the field of two elements. The main problem is that of concrete reproesentation: which subgroups G of GLn(2) can be represented as G=LS(f) for some n-ary k=valued Boolean function f. We call such subgroups linearly representable. The main results of the note may be summarized sa follows: We give a necessary and sufficient condition that a subgroup of GLn(2) is linearly representable and obtain some results on linear representability of its subgroups. Our results generalize some theorems from P.Clote and E. Kranakis [SIAMJ. Comut. 20 (1991) 553-590]; A Kisielewicz [J. Algebra 199 (1998) 379-4031].