On invariant rings of the groups generated by reflections with respect to the skewstrate lines

The basic polinomial invariants of a transformation group $H$ of the affine space $V$ are found in the case when $H$ satisfies the following conditions:
a) $H$ acts on some non-cylindrical algebraic gypersuface $F\subset V$;
b) $H$ is generated by affine reflections with respect to strate lines, some two of which are skew;
c) for every gyperplane $P \subset V$ there exist at most one strate line $L$ such that the reflection with respect to $L$ in the direction of $P$ belongs to $H$.