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The structure of the first homology group of a cyclic covering of a knot isan important invariant well known in the knot theory. In the last century, H.Seifert developed a general approach to compute the homology group of thecovering. Based on his ideas R. Fox found explicit form for$H_{1}(M_{n},\mathbb{Z}),$ where $M_{n}$ is an $n$-fold cyclic covering over aknot $K$ admitting genus one Seifert surface.  The aim of the present paper is to find the structure of$H_{1}(M_{n},\mathbb{Z})$ for $2$-bridge knots admitting genus two Seifertsurface. The result is given explicitly in terms of Alexander polynomial of theknot.

Homology group of branched cyclic covering over a 2-bridge knot of genus two