Maximal wild monodromy in unequal characteristic

Let R be a complete discrete valuation ring of mixed characteristic $(0,p)$ with fraction field K. We study stable models of p-cyclic covers of ${\mathbb{P}}_K^1$. First, we determine the monodromy extension, the monodromy group, its filtration and the Swan conductor for special covers of arbitrarily high genus with potential good reduction. In the case $p=2$ we consider hyperelliptic curves of genus 2.