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