My newbie impression when studying finite group theory is that geometric aspects are not very prevalent. Cayley graphs play quite some role for visualising finite groups, but compared to the study of infinite groups in geometric group theory, geometric aspects seem to be marginal.
I therefore wonder:
(1) Why is geometry less interesting when studying finite groups (if this is really the case)?
(2) Could it (nevertheless) be interesting to delve into geometric group theory when studying finite groups?
I find GGT particularly interesting, but as I am currently working in finite group theory I am not sure how advisable it is to hope for connections. Finite groups are special cases of finitely generated infinite groups, but I am not sure if these are uninteresting cases from the GGT viewpoint.
Thank you for any clarifications and hints!