Q1) If it is mentioned something like "a group $G$ consists of $p^2$ conjugate subgroups of order $q$" (as an example), is there a possible way to represent $G$ as isomorphic to some group by using a general representation?
Usually we can write that $G$ is isomorphic to $Z_q$ or something like that when you know some details about the group $G$. But here since it says there are $p^2$ number of sub groups what I want to know is whether it will be possible to represent all of them using up to isomorphism by some general group or will I have to know the values of $p$ and $q$ and consider them case by case?
Q2) Is there a guidance book or website where I can get a clear knowledge on determining groups up to isomorphism for a given group order? A fully explanatory guide with worked examples too if possible. (Even video lessons are ok).
Please help me in this regard.
Thanks a lot in advance.