Thread: Subgroups, isomorphic

Let H be a subgroup of G and let a be in G. Show that aHa^-1 is a subgroup of G that is isomorphic to H.
I want to show aHa^-1 is 1-1, onto and has a homomorphism property.
Ok so my problem with this is that with isomorphisms before I generally had a function that I worked from, so it was easier to show 1-1, onto, and c(ab)=c(a)c(b), but without a funcction, I get stuck beginning.

Let by
Clearly onto and well defined.
To check injectivity, suppose then simply multiply on the left by a and on the right by to conclude
we need only check it is a homomorphism

proving the isomorphism