I have given a group and I have to prepare the character table of this given group. I know that firstly I have to find the conjugacy classes of the given group. The group is below:
$T_{4n}=\{a,b:a^{2n}=1, a^n=b^2=1, b^{-1}ab=a^{-1}\}$
and I need to find for $n=5$ i.e. $T_{20}$. I think there is a case about $n$, if $n$ is odd or $n$ is even. I hope that I can prepare the character table after finding the conjugacy classes.
How can I find conjugacy classes of this group?
Thanks for any help...