The vector space tensor product 
of two group representations of a group 
is also a representation of 
. An element 
of 
acts on a basis element 
by
 |
If 
is a finite group and 
is a faithful representation,
then any representation is contained in 
for some 
. If 
is a representation of 
and 
is a representation of 
, then 
is a representation of 
, called the external
tensor product. The regular tensor product is a special case, with the diagonal
embedding of 
in 
.
