See examples in Groups.mw
FG_test(S,{timing},$)::boolean test if S is group.FG_testnumeric(S,p,$)::boolean numerically test if S is group.FG_group(S,nmax,$)::G generate matrix group from a given set
(unit element in S is not required), where nmax::posint:=2*|S|
is the maximun number of elements (technical limitation).FG_mulTable(G,$)::Matrix calculate the multiplication table.FG_invTable(G,$)::Vector calculate the inversion table.FG_mulinvTable(G,$)::Matrix,Vector calculate the multiplication and inversion tables
by faster algorithm; works only for rational elements (space groups).FG_cyclic(g,n,$)::preS returns the set g^i,i=0..n-1.FG_orbitC(G,h,$)::S returns the orbit of matrix h
by g*h*gi action for all g in G (conjugacy class).FG_factor(G,H,$)::S is suppossed to return the right factor G/H,
but current implementation uses incorrect algorithm (a possible workaround is to use generators).FG_testInvSG(S,G,$)::boolean test if S is invariant subgroup of G.FG_testSDP(G,G1,G0,$)::boolean test if G is semidirect product
of G1 and G0 with G0 being the invariant subgroup.FG_testDP(G,G1,G0,$)::boolean test if G is direct product of G1 and G0.