Several neurodegenerative diseases such as Alzheimer's, Parkinson's, and Huntington's diseases are associated with amyloid fibrils formed by different polypeptides. We probe the structure and stability of oligomers of different sizes of the fragment Abeta(16-22) of the Alzheimer beta-amyloid peptide using atomic-detail molecular dynamics simulations with explicit solvent. We find that only large oligomers form a stable beta-sheet aggregate, the minimum nucleus size being of the order of 8-16 peptides. This effect is attributed to better hydrophobic contacts and a better shielding of backbone-backbone hydrogen bonds from the solvent in bigger assemblies. Moreover, the observed stability of beta-sheet aggregates with a different number of layers can be explained on the basis of their solvent-accessible surface area. Depending on the stacking interface between the sheets, we observe straight or twisted structures, which could be linked to the experimentally observed polymorphism of amyloid fibrils. To compare our 32-mer structure to experimental data, we calculate its x-ray diffraction pattern. Good agreement is found between experimentally and theoretically determined reflections, suggesting that our model indeed closely resembles the structures found in vitro.