  We study the gauging of the orthosymplectic algebras OSp(6|4)xSO(2) and its
"dual" OSp(2|4)x SO(6), both based on supergravities with the same exceptional
coset SO*(12)/U(6), and gauge group SO(6)xSO(2). The two dual theories are
obtained by two different truncations of gauged N=8 AdS_4 supergravity. We
explicitly study the gauge sector of the two dual theories with the most
general group allowed by supersymmetry. In the ungauged (super-Poincar\'e) case
they exhibit the same (large) black-hole attractor solutions with dual
relations between the 1/N-BPS and non-BPS configurations. The N=6 gravity
multiplet has also the exceptional property to be a {\em zero-center module} of
OSp(6|4), as it is the case for superconformal Yang--Mills theory in four
dimensions based on SU(2,2|n) (PSU(2,2|4) for n=4) or OSp(n|4).
