system 0 has group of order 4
{0,1,2,3}{4,5,6,7}{8,9,10}
{0,2,4,8}{1,5,9,7}{3,6,10}
{0,4,9,6}{1,3,5,8}{2,7,10}
{0,5,2,9}{1,6,4,10}{3,7,8}
{0,7,5,10}{1,4,3,9}{2,6,8}