  We discuss a grand unified theory (GUT) based on a $USp(32)$ GUT gauge group
broken to its subgroups including a special subgroup. A GUT based on an
$SO(32)$ GUT gauge group has been discussed on six-dimensional (6D) orbifold
space $M^4\times T^2/\mathbb{Z}_2$. It is inspired by the $SO(32)$ string
theory behind the $SU(16)$ GUT whose $SU(16)$ is broken to a special subgroup
$SO(10)$. Alternative direction is to embed an $SU(16)$ gauge group into a
$USp(32)$ GUT gauge group, which is inspired by a non-supersymmetric
symplectic-type $USp(32)$ string theory. In a $USp(32)$ GUT, one generation of
the SM fermions is embedded into a 6D bulk Weyl fermion in a $USp(32)$ defining
representation. For a three generation model, all the 6D and 4D gauge anomalies
in the bulk and on the fixed points are canceled out without exotic chiral
fermions at low energies. The SM Higgs scalar is embedded into a 6D bulk scalar
field in a $USp(32)$ adjoint representation.
