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The zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis(ABJ) and related theories, with at least $\mathcal{N}=6$ supersymmetry inthree dimensions, are examined in detail. Starting from well-known dualitiesbetween theories with orthogonal and symplectic gauge groups and those withunitary gauge groups, we gauge their one-form symmetries or their subgroups andobtain new dualities. One side of the latter involves theories with specialorthogonal and symplectic gauge groups, and the other side involves theorieswith unitary gauge groups; there is a discrete quotient on one or both sides ofthe duality. We study the refined superconformal indices of such theories andmap the symmetries across the dualities, with particular attention to theirdiscrete part. As a generalisation, we also find a new duality between acircular quiver with a discrete quotient of alternating special orthogonal andsymplectic gauge groups and a three-dimensional $\mathcal{N}=4$ circular(Kronheimer-Nakajima) quiver with unitary gauge groups, whose Higgs or Coulombbranch describes an instanton on a singular orbifold.

Zero-form and one-form symmetries of the ABJ and related theories