 In the non-trivial case ( is not the identity) this means that is conjugation of operations by the reflection (a rotation axis and the direction of rotation are replaced by their "mirror image").The group of semilinear transformations on a vector space over a field , often denoted , is isomorphic to a semidirect product of the linear group (a normal subgroup of ), and the automorphism group of .In crystallography, the space group of a crystal splits as the semidirect product of the point group and the translation group if and only if the space group is symmorphic.