For instance, the unitary group $U(1)$ is useful in quantum physics, the special orthogonal group $SO(3,1)$ is useful in special relativity, $SU(2)$ for electroweak force and $SU(3)$ for chromodynamics, etc.
Is there a use for $GL(4,R)$ or $GL^+(4,R)$ as a fundamental group in physics?
