W:free(s0,s1,s2,s3); W.relations:s0^2,s1^2,s2^2,s3^2,(s0*s2)^2,(s1*s3)^2,(s0*s3)^2, (s0*s1)^4,(s1*s2)^3,(s2*s3)^5; A:=empty; i:=0; while (length(A) lt 7) do i:=i+1; K:=low index subgroups(W,0,seq(i,i);genset=1); if (length(K) ne 0) then print 'Found',length(K),'subgroups of index',i; end; for j=1 to length(K) do f,imf,kerf=cosact homomorphism(W,); h0=; h3=; h03=h0 meet h3; if (order(h3) eq 48) and (order(h0) eq 120) and (order(h03) eq 6) then print ' Core of number',j,'is sparse, of index',order(imf); A=append(A,K[j]); end; end; end; print 'Some subgroups of W whose Cores are sparse:'; print A; save 'w435'; quit;