The quantization of chiral fermions on a 3-manifold in an external gauge potential is known to lead to an abelian extension of the gauge group. In this article, we concentrate on the case of Ω3G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega ^3 G$$\\end{document} of based smooth maps on a 3-sphere taking values in a compact Lie group G. There is a crossed module constructed from an abelian extension Ω3G^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widehat{\\Omega ^3 G}$$\\end{document} of this group and a group of automorphisms acting on it as explained in a recent article by Mickelsson and Niemimäki. We shall construct a representation of this crossed module in terms of a representation of Ω3G^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widehat{\\Omega ^3 G}$$\\end{document} on a space of functions of gauge potentials with values in a fermionic Fock space and a representation of the automorphism group of Ω3G^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widehat{\\Omega ^3 G}$$\\end{document} as outer automorphisms of the canonical anticommutation relations algebra in the Fock space.