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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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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 );