#(3p+1)/2 algebras
Append( LIE_DATA[7], [
[7,3,4,"<a,b,c|ca-bab,cb,pa-bab,pb-wbaa,pc-xbaaa,class=4>",[[6,1],[4,1],[5,w],[6,1],[],[7,x],[5,1],[6,1],[7,-w],[7,w],[7,1],[],[],[],[],[],[7,-w]],"x~-x",,"7.1624"],
[7,3,4,"<a,b,c|ca-bab,cb,pa-bab,pb-wbaa-xbaaa,pc-ybaaa,class=4>",[[6,1],[4,1],[5,w,7,x],[6,1],[],[7,y],[5,1],[6,1],[7,-w],[7,w],[7,1],[],[],[],[],[],[7,-w]],"x ne 0, unique y so that y^2=2w^3, [x,y]~[-x,y]","p=±3 mod 8","7.1625"],
[7,3,4,"<a,b,c|ca-bab,cb,pa-wbab,pb-wbaa,pc-xbaaa,class=4>",[[6,w],[4,1],[5,w],[6,1],[],[7,x],[5,1],[6,1],[7,-1],[7,w],[7,1],[],[],[],[],[],[7,-1]],"x~-x",,"7.1626"],
[7,3,4,"<a,b,c|ca-bab,cb,pa-wbab,pb-wbaa-xbaaa,pc-ybaaa,class=4>",[[6,w],[4,1],[5,w,7,x],[6,1],[],[7,y],[5,1],[6,1],[7,-1],[7,w],[7,1],[],[],[],[],[],[7,-1]],"x ne 0, unique y so that y^2=2w^2, [x,y]~[-x,y]","p=±1 mod 8","7.1627"]
]);