= Ramification groups of the splitting field of T3 minus 2 over Q3
{title2=$G_0=S_3,\quad G_1=C_3,\quad G_2=1$}
For $L=\mathbb Q_3(\zeta_3,\alpha)$ with $\alpha^3=2$, the shifted cubic for $\alpha+1$ and quadratic for $\zeta_3-1$ are <Eisenstein>. Their compositum is totally ramified of degree six. The element $\pi=(\zeta_3-1)/(\alpha+1)$ has <valuation> one. Order-three automorphisms move it with <valuation> two and transpositions with <valuation> one. The lower breaks are zero and one, the upper breaks zero and one-half, and the <different exponent from ramification groups> is seven.
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