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Let S5 denote the symmetric group on 5 letters, and let Ŝ5 denote a non-trivial double cover of S5 whose Sylow 2-subgroups are generalized quaternion groups. We determine the universal deformation rings R(S5,V) and R(Ŝ5,V) for each mod 2 representation V of S5 that belongs to the principal 2-modular block of S5 and whose stable endomorphism ring is given by scalars when it is inflated to Ŝ5. We show that for these V, a question raised by the first author and Chinburg concerning the relation of the universal deformation ring of V to the Sylow 2-subgroups of S5 and Ŝ5, respectively, has an affirmative answer.

Bleher, Frauke M. and Jennifer B. Froelich. Universal Deformation Rings for the Symmetric Group S5 and One of its Double Covers. Journal of Pure and Applied Algebra 215, no. 4 (2011): 523-530. doi: 10.1016/j.jpaa.2010.06.004

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