Another FOSS option is maxima, although like everything else in maxima, support for group theory is a bit weird and isn’t exactly comprehensive. https://maxima.

Another FOSS option is maxima, although like everything else in maxima, support for group theory is a bit weird and isn’t exactly comprehensive. https://maxima.sourceforge.io/docs/manual/maxima_151.html https://maxima.sourceforge.io/docs/manual/maxima_151.html and https://maxima.sourceforge.io/docs/manual/maxima_147.html#Item_003a-Symmetries_002fnode_002fIntroduction-to-Symmetries https://maxima.sourceforge.io/docs/manual/maxima_147.html#It... And on the paid side, if you have access to it, mathematica has group theory support also and a bunch of named groups implemented right out of the box including the Monster group and the Conway groups https://reference.wolfram.com/language/guide/GroupTheory.html https://reference.wolfram.com/language/guide/GroupTheory.htm...