I've got quite a few practice problems for finding class numbers and structures of imaginary quadratic number fields. For instance, I've just been trying to find the class structure of $\displaystyle \mathbb{Q}(\sqrt{-34})$ and I've got an answer of $\displaystyle C_4$, the cyclic group of order 4. Is there a reference online that gives the class structure for "small" imaginary quadratic number fields (so that I can check my answers)? I've found that the class numbers are given at, for instance, Tables of small class numbers of imaginary quadratic fields but obviously this doesn't give you all the information. For instance it says that the class number of $\displaystyle \mathbb{Q}(\sqrt{-34})$ is 4 but the class structure could then be either $\displaystyle C_2 \times C_2$ or $\displaystyle C_4$.