Descendants library for the groups of order 19683 (GRPS39)

This dataset provides the descendant p-groups used by the GAP package GRPS39 to give complete or partial access to the 5,937,876,645 groups of order 19,683 = 3⁹. The library contains the groups of 3-power order 3¹ through 3⁸ (directories Desc_3, Desc_9, Desc_27, Desc_81, Desc_243, Desc_729, Desc_2187, Desc_6561) that serve as immediate ancestors in the p-group generation algorithm, together with the descendant data needed to reconstruct the corresponding groups of order 3⁹. The groups were generated using the p-group generation algorithm of O'Brien (1990), as implemented in the ANUPQ package for GAP, using computational methods developed for the 2021 enumeration of the groups of order 1024. Information on groups not explicitly constructed was calculated using the cohomological methods of Eick and O'Brien (1999). This data was produced for and used in the 2022 enumeration of the groups of order 19,683 (Burrell, 2022).