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real peresentation Real representation of finite groups

I want to know if there is complete theory on real representation of finite groups.

say,given

Say, given a finite group G,can G, can we know all the injections from G to GL(n,R) for a particular n.?
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real peresentation of finite groups

I want to know if there is complete theory on real representation of finite groups.

say,given a finite group G,can we know all the injections from G to GL(n,R) for a particular n.