The symmetric Galois group conjecture for Tutte polynomials of connected matroids

Let $M$ be a finite connected matroid with positive rank $n=r(M)$, and let $K$ be a field of characteristic zero. The symmetric Galois group conjecture. The Galois group of the Tutte polynomial $T_M(x,y)$ over $K(y)$ is the symmetric group of degree $n$. This is suggested by computations for every biconnected graph of order at most $10$. The claim concerns the Galois group of the bivariate Tutte polynomial for arbitrary finite connected matroids and is presented as a conjectural generalization of those computations.