Spin group and almost commutative geometry

For Connes’ spectral triples, the group of automorphisms lifted to the Hilbert space is defined and used to fluctuate the metric. A few commutative examples are presented including Chamseddine and Connes’ spectral unification of gravity and electromagnetism. One almost commutative example is treated: the full standard model. Here the lifted automorphisms explain O’Raifeartaigh’s reduction $SU(2)\times U(3)\mathrm{/}{\text{zz}}_2\mathrm{.}$