Representation theory of finite groups  From Wikipedia, the free
encyclopedia   (Redirected from Representation of a finite
group) Jump to: navigation, search  In mathematics,
representation theory is a technique for analyzing abstract
groups in terms of groups of linear transformations. See the
article on group representations for an introduction. This
article discusses the representation theory of groups that have
a finite number of elements.  Basic definitions[edit]  All the
linear representations in this article are finite-dimensional
and assumed to be complex unless otherwise stated. A
representation of G is a group homomorphism ρ:G → GL(n,C) from G
to the general linear group GL(n,C). Thus to specify a
representation, we just assign a square matrix to each element
of the group, in such a way that the matrices behave in the same
way as the group elements when multiplied together.  We say that
ρ is a real representation of G if the matrices are real, i.e.
if ρ(G) ⊂ GL(n,R).  Other formulations[edit]  A re