Summary
An algorithm for the determination of all integral classes of reducible integral matrix groups of given dimension from those of lower dimension is described. For dimensionn=4 there are 567 such classes.
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Brown, H., Neubüser, J. & Zassenhaus, H. On integral groups. Numer. Math. 19, 386–399 (1972). https://doi.org/10.1007/BF01404921
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DOI: https://doi.org/10.1007/BF01404921