The following sections describe functions that compute certain subgroups
of a given group, e.g., SylowSubgroup computes a Sylow subgroup of a
group (see Centralizer, Centre, Closure, CommutatorSubgroup,
ConjugateSubgroup, Core, DerivedSubgroup, FittingSubgroup,
FrattiniSubgroup, NormalClosure, NormalIntersection, Normalizer,
PCore, PrefrattiniSubgroup, Radical, SylowSubgroup,
TrivialSubgroup).
They return group records as described in Group Records for the computed subgroups. Some functions may not terminate if the given group has an infinite set of elements, while other functions may signal an error in such cases.
Here the term ``subgroup'' is used in a mathematical sense. But in GAP, every group is either a parent group or a subgroup of a unique parent group. If you compute a Sylow subgroup S of a group U with parent group G then S is a subgroup of U but its parent group is G (see More about Groups and Subgroups).
Further sections describe functions that return factor groups of a given group (see FactorGroup and CommutatorFactorGroup).
GAP 3.4.4