We define the theta group associated to a simple coherent sheaf \({\mathcal F}\) on a hyperkähler manifold X of Kummer type or OG6 type, provided \(g^{*}({\mathcal F})\) is isomorphic to \({\mathcal F}\) for every automorphism g of X acting trivially on \(H^2(X)\) . Note that this condition is satisfied if \({\mathcal F}\) is invertible, if \({\mathcal F}\) is one of the rank 4 stable vector bundles on general polarized HK fourfolds with certain discrete invariants constructed in O’Grady (Modular sheaves on hyperkähler fourfolds of Kummer type, arXiv:2203.03987 [math.AG], 2022), or if \({\mathcal F}\) is the tangent bundle. We compute the commutator pairings of theta groups of line bundles and the rank 4 modular vector bundles of O’Grady (the commutator pairing of the tangent bundle is trivial). We have been motivated by the quest for an explicit description of locally complete families of polarized varieties of Kummer (or OG6) type.