I wondered the class group $G_{29}$ of the cyclotomotic field $\Bbb Q(\zeta_{29})$ today (29 October) which is the second non-trivial class group of the sequence of fields $\Bbb Q(\zeta_p)$ where$\zeta_p=\exp(\frac{2\pi i}p)$.
For now, I found its class number in the list of Wikipedia: $$|G_{29}|=8.$$
It also contains the quadratic subfield $\Bbb Q(\sqrt{29})$ if I am not wrong.
I am very far from the main computation. I have no ideas now. Thank you for any help.