  We prove, for primes $p\ge5$, two inequalities between the fundamental
invariants of Brauer $p$-blocks of finite quasi-simple groups: the number of
characters in the block, the number of modular characters, the number of height
zero characters, and the number of conjugacy classes of a defect group and of
its derived subgroup. For this, we determine these invariants explicitly, or at
least give bounds for them for several classes of classical groups.
