The paper is concerned with the character theory of finite groups of Lie type.
The irreducible characters of a group 𝐺 of Lie type are partitioned in Lusztig series.
We provide a simple formula for an upper bound of the maximal size of a Lusztig series for classical groups with connected center; this is expressed for each group 𝐺 in terms of its Lie rank and defining characteristic.
When 𝐺 is specified as and 𝑞 is large enough, we determine explicitly the maximum of the sizes of the Lusztig series of 𝐺.
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