  The group U_n(F) of all nxn unipotent upper-triangular matrices over F has
derived length d := Ceiling(log_2 (n)), equivalently 2^{d-1} < n <= 2^d. We
prove that U_n(F) has a 3-generated subgroup of derived length d, and it has a
2-generated subgroup of derived length d if and only if (21/32)* 2^d < n <=
2^d.
