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We report on some computations with nilpotent orbits in simple Lie algebrasof exceptional type within the SLA package of GAP4. Concerning reachablenilpotent orbits our computations firstly confirm the classification of suchorbits in Lie algebras of exceptional type by Elashvili and Grelaud, secondlythey answer a question by Panyushev, and thirdly they show in what way a recentresult of Yakimova for the Lie algebras of classical type extends to theexceptional types. The second topic of this note concerns abelianizations ofcentralizers of nilpotent elements. We give tables with their dimensions.

Computations with nilpotent orbits in SLA