All set theoretic functions described in chapter Domains are also applicable to permutation groups. This section describes which functions are implemented specially for permutation groups. Functions not mentioned here are handled by the default methods described in the respective sections.
Random( G )
To compute a random element in a permutation group G GAP computes a stabilizer chain for G, takes on each level a random representative and returns the product of those. All elements of G are chosen with equal probability by this method.
Size( G )
Size calls StabChain (see StabChain), if necessary, and
returns the product of the indices of the stabilizer chain (see
Stabilizer Chains).
Elements( G )
Elements calls StabChain (see StabChain), if necessary, and
enumerates the elements of G as described in Stabilizer Chains. It
returns the set of those elements.
Intersection( G1, G2 )
Intersection first computes stabilizer chains for G1 and G2 for a
common base. If either group already has a stabilizer chain a basechange
is performed (see MakeStabChain). Intersection enumerates the
elements of G1 and G2 using a backtrack algorithm, eliminating whole
cosets of stabilizers in the stabilizer chains if possible (see
PermGroupOps.SubgroupProperty). It builds a stabilizer chain for the
intersection.
GAP 3.4.4