Operational Group (PolishGrupa Operacyjna, abbreviated GO) was the highest level of tactical division of the Polish Army before and during World War II and the Polish Defence War. It was corps-sized, although various Operational Groups varied in size.
The group of upper triangular n by n matrices is a solvable Lie group of dimension n(n + 1)/2.
The group U(1)×SU(2)×SU(3) is a Lie group of dimension 1+3+8=12 that is the gauge group of the standard model, whose dimension corresponds to the 1 photon + 3 vector bosons + 8 gluons of the standard model.
The group of smooth maps from a manifold to a finite dimensional group is called a gauge group, and is used in quantum field theory and Donaldson theory.