Function table_of_marks 

pub fn table_of_marks(
    degree: usize,
    gens: &[Perm],
    cap: usize,
) -> Option<(Vec<u128>, Vec<Vec<u128>>)>

The table of marks of G = ⟨gens⟩ — the Burnside-ring analogue of the character table. Rows and columns are the conjugacy classes of subgroups (ordered by increasing order); the (i,j) entry is the mark m(H_i, H_j) = the number of H_i-fixed points in the transitive action of G on the cosets G/H_j, computed as (1/|H_j|)·|{g ∈ G : g⁻¹ H_i g ⊆ H_j}|. Returns (subgroup_class_orders, marks).

The complete invariant of the category of G-sets: every finite G-set decomposes uniquely into the transitive ones G/H_j, and the marks record how each subgroup sees each. With this ordering the matrix is triangular with diagonal [N_G(H_i):H_i], hence invertible. Where character_table classifies the LINEAR representations of G, the table of marks classifies its PERMUTATION representations. Exact integer arithmetic. None when |G| > cap.