{5, 0, 1, 0, 0, 0, 0}

Table of Percent Abundance (row: Lie-type, col: Group Factor):

11722	{1⇿2,2⇿3,3⇿4,4⇿5,4⇿6}
1141	{1⇿2,2⇿3,3⇿4,4⇿5,1⇿5,1⇿6}
10327	{1⇿2,2⇿3,3⇿4,4⇿5,1⇿6}
3730	{1⇿2,2⇿3,3⇿4,4⇿5,3⇿6}
782	{1⇿2,2⇿3,3⇿4,4⇿5,1⇿4,1⇿6}
789	{1⇿2,2⇿3,3⇿4,4⇿5,4⇿6,1⇿5}
69	{1⇿2,2⇿3,3⇿4,4⇿5,1⇿3,1⇿6}
55	{1⇿2,2⇿3,3⇿4,4⇿5,1⇿3,4⇿6}
58	{1⇿2,2⇿3,3⇿4,4⇿5,1⇿3,3⇿6}
22	{1⇿2,2⇿3,3⇿4,4⇿5,1⇿4,3⇿6}
16	{1⇿2,2⇿3,3⇿4,4⇿5,3⇿6,1⇿6}
2	{1⇿2,2⇿3,3⇿4,4⇿5,1⇿3,2⇿5,1⇿6}
4	{1⇿2,2⇿3,3⇿4,4⇿5,1⇿3,1⇿5,1⇿6}
11	{1⇿2,2⇿3,3⇿4,4⇿5,4⇿6,1⇿4}
5	{1⇿2,2⇿3,3⇿4,4⇿5,4⇿6,1⇿5,1⇿6}
2	{1⇿2,2⇿3,3⇿4,4⇿5,1⇿3,1⇿4,2⇿5,1⇿6}
1	{1⇿2,2⇿3,3⇿4,4⇿5,1⇿4,3⇿6,1⇿6}

Created with Wolfram Mathematica 9.0