Exercise 2, § 5

If G is a finite group of order n, the number of automorphisms of G is $\leq n^{\log n / \log 2}$ (show that there exists a generating set $\{a_1, a_2, \ldots, a_m\}$ of G such that $a_i$ does not belong to the subgroup generated by $a_1, a_2, \ldots, a_{i-1}$ for $2 \leq i \leq m$; deduce that $2^m \leq n$ and that the number of automorphisms of G is $\leq n^m$).