$SO(12)$ is the special orthogonal group in dimension 12.
$Spin(12)$ is the spin group in dimension 12.
In the classification of simple Lie groups this is the entry D6.
rotation groups in low dimensions:
see also
(…)
Discussion as a gauge group in grand unified theory (see there):
S. Rajpoot and P. Sithikong, Implications of the $SO(12)$ gauge symmetry for grand unification, Phys. Rev. D 23, 1649 (1981) (doi:10.1103/PhysRevD.23.1649)
Takaaki Nomura and Joe Sato, Standard(-like) Model from an $SO(12)$ Grand Unified Theory in six-dimensions with $S^2$ extra-space, Nucl.Phys.B811:109-122, 2009 (arXiv:0810.0898)
Takaaki Nomura, Physics beyond the standard model with $S^2$ extra-space, 2009 (pdf, pdf)
Cheng-Wei Chiang, Takaaki Nomura, Joe Sato, Gauge-Higgs unification models in six dimensions with $S^2/\mathbb{Z}_2$ extra space and GUT gauge symmetry (arXiv:1109.5835)
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