<<"Desktop/Groupoid/MatrixManifolds.m" 
G2[];

comb3=Subsets[Range[7], {3}]

Clear[x, y];
A = C3;
B=C13;
N[MatrixCommutator[A, B]]//MatrixForm

MatrixExp[z*A] //MatrixForm
MatrixExp[z*B]//MatrixForm

g1=FullSimplify[MatrixExp[x*A].MatrixExp[y*B]];
g2=FullSimplify[MatrixExp[y*B].MatrixExp[x*A]];

g1//MatrixForm
g2//MatrixForm

g1=== g2

Clear[x,y]
w = {1, 1, 2.3, 1, 1, 1,1, 1};
Table[
ParametricPlot3D[{actionG2[g1/.{x->u, y->v},w][[comb3[[i]][[1]]]],actionG2[g1/.{x->u, y->v},w][[comb3[[i]][[2]]]],actionG2[g1/.{x->u, y->v},w][[comb3[[i]][[3]]]]} , {u, 0, 2*Pi}, {v,0, 2*Pi*((Sqrt[3])/2)}]
, {i, 1, Length[comb3]}]

Clear[x,y]
w = {1, 1, 2.3, 1, 1, 1,1, 1};
Table[
ParametricPlot3D[{actionG2[g2/.{x->u, y->v},w][[comb3[[i]][[1]]]],actionG2[g2/.{x->u, y->v},w][[comb3[[i]][[2]]]],actionG2[g2/.{x->u, y->v},w][[comb3[[i]][[3]]]]} , {u, 0, 2*Pi}, {v,0, 2*Pi*((Sqrt[3])/2)}]
, {i, 1, Length[comb3]}]