Computing subgroups of finite soluble groups
CRISP (Computing with Radicals, Injectors, Schunck classes and Projectors) provides algorithms for computing subgroups of finite soluble groups related to group classes. In particular, it allows computing F-radicals and F-injectors for Fitting classes (and Fitting sets) F, F-residuals for formations F, and X-projectors for Schunck classes X. In order to carry out these computations, the group classes F and X must be given by an algorithm which decides membership in the group class. Moreover, CRISP contains algorithms for the computation of normal subgroups invariant under a prescribed set of automorphisms and belonging to a given group class. This includes an improved method to compute the set of all normal subgroups of a finite soluble group, its characteristic subgroups, and the socle and p-socles for given primes p.