Bilbao Crystallographic Server arrow Classify the Subgroups arrow Classes of Subgroups

Classes of Conjugate Subgroups

Let G be a group, and H1 and H2 two of its subgroups of the same cristallographic space-group type (G > H1, G > H2). The subgroups H1 and H2 are conjugate subgroups of G if there exists an element g of the group G such that

g-1 H1 g = H2

In this way the subgroups of the same crystallographic space-group type and of the same index of the group G are distributed into sets of conjugate subgroups with respect to G. These sets are the classes of conjugate subgroups.

Bilbao Crystallographic Server
http://www.cryst.ehu.es 		For comments, please mail to
administrador.bcs@ehu.eus