Let W be the Atkin-Lehner group of the modular curve that Shimura attached to each real quadratic field of discrimiant N. In a recent paper we completely characterise when a canonical generator of the group W lies in the centre of W. There we also propose a conjecture that predicts that W is either a Hall-Higman extra-special 2-group or a Pauli group, if the centre of W is cyclic. In this talk we discuss the case N = 60, where W is the Pauli group of 16 elements.
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