  For any characteristic zero coefficient field, an irreducible representation
of a finite $p$-group can be assigned a Roquette $p$-group, called the
genotype. This has already been done by Bouc and Kronstein in the special cases
Q and C. A genetic invariant of an irrep is invariant under group isomorphism,
change of coefficient field, Galois conjugation, and under suitable inductions
from subquotients. It turns out that the genetic invariants are precisely the
invariants of the genotype. We shall examine relationships between some genetic
invariants and the genotype. As an application, we shall count Galois conjugacy
classes of certain kinds of irreps.
