Odd degree number fields with odd class number

For any fixed odd integer n >= 3, we study the 2-torsion of the ideal class groups of certain families of degree n number fields. We show that (up to a tail estimate) the average size of the 2-torsion in these families matches the predictions given by the Cohen-Lenstra-Martinet-Malle heuristics, which predict the distribution of class groups of number fields. As a consequence, we find that for any odd n >= 3, there exist infinitely many number fields of degree n and associated Galois group S_n whose class number is odd. This talk is based on joint work with Arul Shankar and Ila Varma.