#Be patient! This example may take a while.
#You may need to press `return' for more memory.
K:=QuillenComplex(SymmetricGroup(10),3);
Print(Size(K),"\n");
Y:=RegularCWComplex(K);
C:=CocriticalCellsOfRegularCWComplex(Y,3);;
n:=0;;Print(Length(Filtered(C,c->c[1]=n)),"\n");
n:=1;;Print(Length(Filtered(C,c->c[1]=n)),"\n");
n:=2;;Print(Length(Filtered(C,c->c[1]=n)),"\n"); 
G:=FundamentalGroup(Y,"no Tietze simplification");
Print(G,"\n");
relgens:=List(RelatorsOfFpGroup(G), LetterRepAssocWord);;
relgens:=Flat(relgens);
Apply(relgens,AbsInt);
relgens:=SSortedList(relgens);;
FF:=FreeGroup(Length(relgens));
B:=[];;j:=0;;
for i in [1..25253] do
 if i in relgens then
 j:=j+1;; Add(B,GeneratorsOfGroup(FF)[j]);
 else Add(B,One(FF)); fi;
od;
F:=FreeGroupOfFpGroup(G);
hom:=GroupHomomorphismByImages(F,FF, GeneratorsOfGroup(F),B);;
S:=List(RelatorsOfFpGroup(G),u->Image(hom,u));;
Q:=FF/S;
Print(AbelianInvariants(Q),"\n");
Print(SimplifiedFpGroup(Q),"\n");
NQ:=NilpotentQuotient(Q,2);;
Print(IsAbelian(NQ),"\n"); 
