  In the paper of Yu. A. Mikhalchishina for an arbitrary virtual link $L$ three
groups $G_{1,r}(L)$, $r>0$, $G_{2}(L)$ and $G_{3}(L)$ were defined. In the
present paper these groups for the virtual trefoil are investigated. The
structure of these groups are found out and the fact that some of them are not
isomorphic to each other is proved. Also we prove that $G_3$ distinguishes the
Kishino knot from the trivial knot. The fact that these groups have the lower
central series which does not stabilize on the second term is noted. Hence we
have a possibility to study these groups using quotients by terms of the lower
central series and to construct representations of these groups in rings of
formal power series. It allows to construct an invariants for virtual knots.
