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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 exceptionalcoset SO*(12)/U(6), and gauge group SO(6)xSO(2). The two dual theories areobtained by two different truncations of gauged N=8 AdS_4 supergravity. Weexplicitly study the gauge sector of the two dual theories with the mostgeneral group allowed by supersymmetry. In the ungauged (super-Poincar\'e) casethey exhibit the same (large) black-hole attractor solutions with dualrelations between the 1/N-BPS and non-BPS configurations. The N=6 gravitymultiplet has also the exceptional property to be a {\em zero-center module} ofOSp(6|4), as it is the case for superconformal Yang--Mills theory in fourdimensions based on SU(2,2|n) (PSU(2,2|4) for n=4) or OSp(n|4).

Exceptional N=6 and N=2 AdS_4 Supergravity, and Zero-Center Modules