  We discuss essential dimension of group schemes, with particular attention to
infinitesimal group schemes. We prove that the essential dimension of a group
scheme of finite type over a field k is at least equal to the difference
between the dimension of its Lie algebra and its dimension. Furthermore, we
show that the essential dimension of a trigonalizable group scheme of length
p^{n} over a field of characteristic p>0 is at most n. We give several
examples.
