In what representation do fields in a gauge theory lie?

I'm currently learning about gauge theory and am getting confused about where all the fields of a given theory take values in.

Given some $G$-gauge theory, the gauge fields take values in the adjoint representation of $G$. What representation the do matter fields take values in, such as bosonic and fermionic fields? For fermionic fields this has something to do with the spin group, but what is the connection with $G$?

Could anyone give me a brief rundown? The sources I'm looking at are mixing the Poincare group and symmetry groups and it's getting confusing, I'd like just a clear statement about where these fields lie if possible!

Answer

Matter fields transform under the fundamental representation of the gauge group G, while the gauge fields transform under the adjoint representation of the same group. The Poincare group is different from the gauge group in the sense that it is a global symmetry group (i.e the generated transformations are not dependent on $x^\mu$) whereas gauge groups are local symmetry groups where the generated transformations are dependent on $x^\mu$.