Increasingly-large datasets (for example, the resting-state fMRI data from the Human Connectome Project) are demanding analyses that are problematic because of the sheer scale of the aggregate data. We present two approaches for applying group-level PCA; both give a close approximation to the output of PCA applied to full concatenation of all individual datasets, while having very low memory requirements regardless of the number of datasets being combined. Across a range of realistic simulations, we find that in most situations, both methods are more accurate than current popular approaches for analysis of multi-subject resting-state fMRI studies. The group-PCA output can be used to feed into a range of further analyses that are then rendered practical, such as the estimation of group-averaged voxelwise connectivity, group-level parcellation, and group-ICA. Copyright 2014 Elsevier Inc. All rights reserved.