An overview of Lie groups

Group	Manifold	$∘$	Comment
`CircleGroup`	real or complex `Circle`, `Sphere`	`*`
`GeneralLinearGroup`	`InvertibleMatrices`	`*`
`HeisenbergGroup`	`HeisenbergMatrices`	`*`
`OrthogonalGroup`	`OrthogonalMatrices`	`*`	This can be interpreted as all rotations and reflections.
`PowerLieGroup`	`PowerManifold`	`∘`	`^` is a constructor
`ProductLieGroup`	`ProductManifold`	`∘`	`×` of two Lie groups is a constructor
`LeftSemidirectProductLieGroup`	`ProductManifold`	`∘`	`⋉` of 2 Lie groups is a constructor, similarly `⋊` for the right variant
`SpecialEuclideanGroup`	`Rotations⋉Euclidean`	`∘`	Analogously you can also use a `⋊` if you prefer tuples `(t,R)` having the rotation matrix in the second component
`SpecialLinearGroup`	`DeterminantOneMatrices`	`*`
`SpecialOrthogonalGroup`	`Rotations`	`*`
`SpecialUnitaryGroup`	`GeneralUnitaryMatrices`	`*`
`SymplecticGroup`	`SymplecticMatrices`	`*`
`TranslationGroup`	`Euclidean`	`+`
`UnitaryGroup`	`UnitaryMatrices`	`*`