Brauer's 14th Problem and Dyson's Tenfold Way

We consider Brauer’s 14th Problem in the context of “Real” structures on finite groups and their antilinear representations. The problem is to count the number of characters of each different type using “group theory”. While Brauer’s original problem deals only with three types (real, complex and quaternionic), here we consider the ten types coming from Dyson’s tenfold way.