GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
#The Hat (upper Teardrop) orbifold M := [ [1,2,3], [1,2,4], [1,3,4] ]; G := Group( (1,2) ); iso := rec( 1 := G ); mu := [ [ [3], [1,3], [1,2,3], [1,3,4], x -> (1,2) ], [ [3], [1,3], [1,3,4], [1,2,3], x -> (1,2) ] ]; dim := 4;