There sure is, and a major connection at that.
Consider a finite set of n elements. The symmetric group of this set is said to have a degree of n. The symmetric group of degree n (Sn) is the Galois group of the general polynomial of degree n. In order for there to be a formula involving radicals that solve the general polynomial of degree n, such as the quadratic equation when n = 2, that polynomial's corresponding Galois group must be solvable. S5 is not a solvable group. Therefore, the Galois group of the general polynomial of degree 5 is not solvable. Thus the general polynomial of degree 5 has no general formula to solve it using radicals.
This was huge result, and one of the first real applications, for group theory, since that problem had stumped mathematicians for centuries.
