GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
gap> START_TEST("HAP library"); gap> K:=QuillenComplex(SymmetricGroup(7),2); Simplicial complex of dimension 2. gap> Size(K); 11291 gap> Y:=RegularCWComplex(K);; gap> C:=CriticalCells(Y);; gap> n:=0;;Length(Filtered(C,c->c[1]=n)); 1 gap> n:=1;;Length(Filtered(C,c->c[1]=n)); 0 gap> n:=2;;Length(Filtered(C,c->c[1]=n)); 160 gap> STOP_TEST( "tst.tst", 1000 );