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Given a countable group $X$ we study the algebraic structure of itssuperextension $\lambda(X)$. This is a right-topological semigroup consistingof all maximal linked systems on $X$ endowed with the operation $$\mathcalA\circ\mathcal B=\{C\subset X:\{x\in X:x^{-1}C\in\mathcal B\}\in\mathcal A\}$$that extends the group operation of $X$. We show that the subsemigroup$\lambda^\circ(X)$ of free maximal linked systems contains an open dense subsetof right cancelable elements. Also we prove that the topological center of$\lambda(X)$ coincides with the subsemigroup $\lambda^\bullet(X)$ of allmaximal linked systems with finite support. This result is applied to show thatthe algebraic center of $\lambda(X)$ coincides with the algebraic center of $X$provided $X$ is countably infinite. On the other hand, for finite groups $X$ oforder $3\le|X|\le5$ the algebraic center of $\lambda(X)$ is strictly largerthan the algebraic center of $X$.

Algebra in superextension of groups, II: cancelativity and centers