GroupD4:=MatrixGroup<11,IntegerRing()|
[1,0,0,0,0,0,0,0,0,0,0, 1,1,1,1,0,0,0,0,0,0,0, -1,0,0,-1,0,0,0,0,0,0,0, -1,0,-1,0,0,0,0,0,0,0,0,  0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
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[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1]>;

GroupD5:=MatrixGroup<11,IntegerRing()|
[1,0,0,0,0,0,0,0,0,0,0, 1,1,1,1,0,0,0,0,0,0,0, -1,0,0,-1,0,0,0,0,0,0,0, -1,0,-1,0,0,0,0,0,0,0,0,  0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1]>;

GroupD6:=MatrixGroup<11,IntegerRing()|
[1,0,0,0,0,0,0,0,0,0,0, 1,1,1,1,0,0,0,0,0,0,0, -1,0,0,-1,0,0,0,0,0,0,0, -1,0,-1,0,0,0,0,0,0,0,0,  0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1]>;

GroupD7:=MatrixGroup<11,IntegerRing()|
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[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
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[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1]>;

GroupD8:=MatrixGroup<11,IntegerRing()|
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[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
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[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
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[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,0,1]>;

GroupD9:=MatrixGroup<11,IntegerRing()|
[1,0,0,0,0,0,0,0,0,0,0, 1,1,1,1,0,0,0,0,0,0,0, -1,0,0,-1,0,0,0,0,0,0,0, -1,0,-1,0,0,0,0,0,0,0,0,  0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,0,1, 0,0,0,0,0,0,0,0,0,1,0]>;




//Transpose Group
TransGroup:=function(G)
local R,d;
R:=CoefficientRing(G);
d:=Degree(G);
H:=MatrixGroup<d,R|{Transpose(G.k):k in [1..#Generators(G)]}>;
return H;
end function;

//Minimal Group

IsMinimalE:=function(G,Exceptional)
H:={};
for i in [1..#Exceptional] do
	Include(~H,SetToIndexedSet(Orbit(TransGroup(G),Exceptional[i])));
end for;
H:=SetToIndexedSet(H);
for i in [1..#H] do
	if #H[i] eq 1 then
		return false;
	end if;
end for;
for r in [1..#H] do
	Matrix:=RMatrixSpace(IntegerRing(),#H[r],#H[r])!0;
	for j in [1..#H[r]-1] do
		for k in [j+1..#H[r]] do
			product:=0;
			for t in [2..9] do
				product:=product-H[r][j][t]*H[r][k][t];
			end for;
			product:=product+H[r][j][1]*H[r][k][1];
			Matrix[j,k]:=product;
		end for;
	end for;
	if IsZero(Matrix) eq true then
		return false;
	end if;
end for;
return true;
end function;

IsMinimalD:=function(G,Exceptional)
H:={};
for i in [1..#Exceptional] do
	Include(~H,SetToIndexedSet(Orbit(TransGroup(G),Exceptional[i])));
end for;
H:=SetToIndexedSet(H);
for i in [1..#H] do
	if #H[i] eq 1 then
		return false;
	end if;
end for;
for r in [1..#H] do
	Matrix:=RMatrixSpace(IntegerRing(),#H[r],#H[r])!0;
	for j in [1..#H[r]-1] do
		for k in [j+1..#H[r]] do
			product:=0;
			for t in [3..Degree(G)] do
				product:=product-H[r][j][t]*H[r][k][t];
			end for;
			product:=product+H[r][j][1]*H[r][k][2]+H[r][j][2]*H[r][k][1];
			Matrix[j,k]:=product;
		end for;
	end for;
	if IsZero(Matrix) eq true then
		return false;
	end if;
end for;
return true;
end function;



//H1 group cohomology

C0Matrix:=function(M)
local l;
l:=IdentityMatrix(BaseRing(M),Dimension(M));
return HorizontalJoin([Transpose(ActionGenerator(M,k))-l:k in [1..Nagens(M)]]);
end function;

add_block:=procedure(~M,i,j,M2)
local rows,cols,block;
rows:=NumberOfRows(M2);
cols:=NumberOfColumns(M2);
block:=ExtractBlock(M,i,j,rows,cols);
InsertBlock(~M,block+M2,i,j);
end procedure;

C1Matrix:=function(M)
local K,d,G,RG,r,s,rel,w,C1,g,si,sg;
K:=BaseRing(M);
d:=Dimension(M);
G:=Group(M);
RG:=Relations(FPGroup(G));
r:=#Generators(G);
s:=#RG;
C1:=RMatrixSpace(K,r*d,s*d)!0;

for i in [1..s] do
rel:=RG[i]; w:=LHS(rel)*RHS(rel)^(-1);
si:=(i-1)*d+1;
	for g in [1..r] do
		sg :=(Abs(g)-1)*d+1;
		if Abs(Eltseq(w)[1]) eq g then
			if Eltseq(w)[1] gt 0 then
				mattemp:=IdentityMatrix(K,d);
				add_block(~C1,sg,si,Transpose(mattemp));
			end if;
			if Eltseq(w)[1] lt 0 then
				mattemp:=(-1)*ActionGenerator(M,-Eltseq(w)[1])^(-1);
				add_block(~C1,sg,si,Transpose(mattemp));
			end if;
		end if;
			for h in [2..#w] do
				if Abs(Eltseq(w)[h]) eq g then
					mattemp:=IdentityMatrix(K,d);
				for t in [1..h-1] do
					mattemp:=mattemp*ActionGenerator(M,Abs(Eltseq(w)[t]))^(Sign(Eltseq(w)[t]));
				end for;
				if Eltseq(w)[h] lt 0 then
					mattemp:=mattemp*(-1)*ActionGenerator(M,-Eltseq(w)[h])^(-1);
				end if;
				add_block(~C1,sg,si,Transpose(mattemp));
			end if;
		end for;
	end for;
end for;
return C1;
end function;


IsH1:=function(G)
local List,M,C0,C1,H1;
List:=Subgroups(G);

for i in [2..#List] do

	M:=GModule(List[#List-i+2]`subgroup);

	C0:=C0Matrix(M);

	C1:=C1Matrix(M);

	H1:=quo<Nullspace(C1)|RowSpace(C0)>;

	if #H1 ne 1 then

		return false;

	end if;

end for;

return true;

end function;


//get conic matrix
IsConic:=function(h,H)
local Matrix;
Matrix:=RMatrixSpace(IntegerRing(),#H[h],#H[h])!0;
for i in [1..#H[h]] do
	for j in [1..#H[h]] do
		product:=0;
		for t in [3..10] do
			product:=product-H[h][i][t]*H[h][j][t];
		end for;
		product:=product+H[h][i][1]*H[h][j][2]+H[h][i][2]*H[h][j][1];
		Matrix[i,j]:=product;
	end for;
end for;
return Matrix;
end function;


//intersection of 2 orbit D type
Inter2OrbitD:=function(m,n,H)
local Matrix;
Matrix:=RMatrixSpace(IntegerRing(),#H[m],#H[n])!0;
for i in [1..#H[m]] do
	for j in [1..#H[n]] do
		product:=0;
		for t in [3..Degree(Group(Parent(H[1][1])))] do
			product:=product-H[m][i][t]*H[n][j][t];
		end for;
		product:=product+H[m][i][1]*H[n][j][2]+H[m][i][2]*H[n][j][1];
		Matrix[i,j]:=product;
	end for;
end for;
return Matrix;
end function;

//invariant space under the group action
InvSpace:=function(H)
local G,R,d,M,S;
G:=TransGroup(H);
R:=CoefficientRing(G);

d:=Degree(G);

M:=G.1-IdentityMatrix(R,d);
S:=Nullspace(M);
if NumberOfGenerators(G) ge 2 then
	for i in [1..NumberOfGenerators(G)] do
		M:=G.i-IdentityMatrix(R,d);
		S:=S meet Nullspace(M);
	end for;
end if;
return S;
end function;

IsMinimalInv:=function(G,H)
local Inv,TInv;
Inv:=InvSpace(G);
TInv:=InvSpace(H);
return Inv eq TInv;
end function;



ReadResult:=procedure(G,Exceptional)
//Orbit decomposition of exceptional set
H:={@ @};

for i in [1..#Exceptional] do

	Include(~H,SetToIndexedSet(Orbit(TransGroup(G),Exceptional[i])));

end for;

S:=TransGroup(Stabilizer(TransGroup(G),H[1][1]));

H:=SetToIndexedSet(H);

G;

for i in [1..#H] do
	i;
	H[i];
	"Intersection Matrix: ";
	IsConic(i,H);
	"Stabilizer Group Name: ";
	GroupName(TransGroup(Stabilizer(TransGroup(G),H[i][1])));
	TransGroup(Stabilizer(TransGroup(G),H[i][1]));
end for;
end procedure;