Prove that the notion of group isomorphism is transitive.

My proof so far:

Suppose G, H, and K are groups.

Let the function f be the isomorphism from G onto H, then

with f is onto and 1-1.

That equation should be .
Now let the function t be the isomorphism from H onto K, then

with t is onto and 1-1.

That equation should be .
My plan is to get a function, say X, such that

That equation should be .
First I tried with X = f(t), but it doesn't really work out, so am I at least doing something right here?