I am trying to work out the structure of the class groups for discriminants of some simple forms.
I am interested in the cases where the discriminant is a prime number and where it is of the form $d = p_1 p_2^2 \dots p_n^2$ for $p_i$ primes.
The class number for these discriminants has a simple form and so I am wondering if this extends to the structure of the group in any way.