Complex reflection subgroups of real reflection groups (Q1588408)

Let \(V\) be an \(n\)-dimensional complex vector space, \(G\) an irreducible rank \(n\) complex, but not complexified, reflection group in \(V\), and \(W\) an irreducible rank \(2n\) finite real reflection group in \(_\mathbb{R} V\) such that \(G<W\) and \(W\) is minimal for \(G\). The author finds, up to isomorphism, all pairs \(G<W\).