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We study an invariant of a 3-manifold which consists of Reidemeister torsionfor linear representations which pass through a finite group. We show a Dehnsurgery formula on this invariant and compute that of a Seifert manifold over$S^2$. As a consequence we obtain a necessary condition for a result of Dehnsurgery along a knot to be Seifert fibered, which can be applied even in a casewhere abelian Reidemeister torsion gives no information.

Reidemeister torsion for linear representations and Seifert surgery on knots