Function rational_class_count 

pub fn rational_class_count(
    degree: usize,
    gens: &[Perm],
    cap: usize,
) -> Option<usize>

The number of rational conjugacy classes — classes C fixed by the whole Galois group (g ~ g^t for every t coprime to ord(g)), i.e. the singleton galois_class_orbits. By Burnside’s rationality theorem this equals the number of rational-valued irreducible characters. Strictly refines real_class_count (real = closed under the single element t = −1): rational ⟹ real, and the counts differ exactly when a character is real but irrational (e.g. A₅’s golden-ratio degree-3 pair). None when |G| > cap.