  Let N be a nilpotent Lie group and K a compact subgroup of the automorphism
group Aut(N) of N. It is well-known that if (KnN,N) is a Gelfand pair then N is
at most 2-step nilpotent Lie group. The notion of Gelfand pair was generalized
when K is a non-compact group. In this work, we give an example of a 3-step
nilpotent Lie group and a non-compact subgroup K of Aut(N) such that (K nN,N)
is a generalized Gelfand pair.
