  In this paper, we define the notion of a virtually symmetric representation
of representations of virtual braid groups and prove that many known
representations are equivalent to virtually symmetric. Using one such
representation, we define the notion of virtual link groups which is an
extension of virtual link groups defined by Kauffman. Moreover, we introduce
the concept of marked Gauss diagrams as a generalisation of Gauss diagrams and
their interpretation in terms of knot-like diagrams. We extend the definition
of virtual link groups to marked Gauss diagrams and define their peripheral
structure. We define $C_m$-groups and prove that every group presented by a
$1$-irreducible $C_1$-presentation of deficiency $1$ or $2$ can be realized as
the group of a marked Gauss diagram.
