  It was shown by Lubotzky in 2014 that automorphism invariant subsets of
finite simple groups which contain identity are always word images. In this
article, we study word maps on finite nilpotent groups and show that for
arbitrary finite groups, the number of automorphism invariant subsets
containing identity which are not word images, referred to as word image
impostors, may be arbitrarily larger than the number of actual word images. In
the course of it, we construct a $2$-exhaustive set of word maps on nilpotent
groups of class $2$ and demonstrate its minimality in some cases.
