Algebra using sage

Question

Can anyone help in writing a code to find the list of idempotent and primitive elements of a group algebra, the examples goes like this. Let $p$ be an odd prime such that $\bar2$ generates $U(\mathbf{Z}_{p^2})$ and $G=<a>*<b>$ an abelian group, with $o(a) = p^2$ and $o(b)=p$. Then $\mathbf{F_2}G$ has four inequivalent minimal codes, namely, the ones generated by the idempotents $e_0=\hat{G}$, $e_1=\hat{b}-\hat{<a>*<b>}$(note: its a big hat), $e_2=\hat{a}-\hat{G}$ and $e_3=\hat{<a^p>*<b>}-\hat{G}$.