Doubts when looking for possible PhD supervisors
To know about a research group reputation, you have to follow their research works (most likely that there will be a dedicated webpage for their group which lists their works). If it is not a research group then you have to shortlist a few professors and visit their webpages to know more about their works.

Now, before emailing anybody, you have to come to a decision point and zero in on few works that they have published or are working on. This will give you a focus area. Further, you have to understand them a bit and if you find them too much intriguing then you should email them.

Further questions on how to email professors can be browsed in academia SE.