An overview of Lie groups

Alphabetical list of Lie groups

GroupManifold$∘$Comment
GeneralLinearGroupInvertibleMatrices*
HeisenbergGroupHeisenbergMatrices*
OrthogonalGroupOrthogonalMatrices*This can be interpreted as all rotations and reflections.
SpecialEuclideanGroupRotationsEuclideanAnalogously you can also use a if you prefer tuples (t,R) having the rotation matrix in the second component
SpecialOrthogonalGroupRotations*
SpecialUnitaryGroupGeneralUnitaryMatrices*
TranslationGroupEuclidean+
UnitaryGroupUnitaryMatrices*