g := PGL(2,13); invols := [ [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 11)(2, 4)(3, 6)(5, 8)(7, 9)(10, 14)(12, 13) , (1, 2)(3, 7)(4, 12)(5, 9)(6, 13)(8, 14)(10, 11) ], [g| (1, 12)(2, 4)(3, 14)(5, 9)(6, 10)(7, 8)(11, 13) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 11)(2, 4)(3, 6)(5, 8)(7, 9)(10, 14)(12, 13) ], [g| (1, 14)(2, 7)(3, 5)(4, 9)(6, 8)(10, 11) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 11)(2, 4)(3, 6)(5, 8)(7, 9)(10, 14)(12, 13) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 11)(2, 4)(3, 6)(5, 8)(7, 9)(10, 14)(12, 13) , (1, 4)(2, 9)(3, 14)(5, 11)(7, 13)(8, 10) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 8)(2, 12)(3, 9)(4, 14)(5, 6)(7, 13)(10, 11) , (1, 12)(2, 11)(3, 10)(4, 9)(5, 8)(6, 7)(13, 14) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 8)(2, 12)(3, 9)(4, 14)(5, 6)(7, 13)(10, 11) , (1, 7)(2, 5)(3, 8)(4, 10)(6, 9)(11, 13)(12, 14) ], [g| (1, 5)(2, 3)(4, 14)(6, 8)(7, 10)(9, 12)(11, 13) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 8)(2, 12)(3, 9)(4, 14)(5, 6)(7, 13)(10, 11) ], [g| (1, 4)(2, 5)(3, 10)(6, 12)(8, 14)(9, 11) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 8)(2, 12)(3, 9)(4, 14)(5, 6)(7, 13)(10, 11) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 8)(2, 12)(3, 9)(4, 14)(5, 6)(7, 13)(10, 11) , (1, 14)(4, 5)(6, 11)(7, 9)(8, 13)(10, 12) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 8)(2, 12)(3, 9)(4, 14)(5, 6)(7, 13)(10, 11) , (1, 4)(2, 9)(3, 14)(5, 11)(7, 13)(8, 10) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 8)(2, 10)(3, 4)(5, 9)(6, 14)(7, 11)(12, 13) , (1, 12)(2, 11)(3, 10)(4, 9)(5, 8)(6, 7)(13, 14) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 8)(2, 10)(3, 4)(5, 9)(6, 14)(7, 11)(12, 13) , (1, 9)(2, 3)(4, 8)(5, 13)(6, 10)(7, 14)(11, 12) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 8)(2, 10)(3, 4)(5, 9)(6, 14)(7, 11)(12, 13) , (1, 4)(2, 9)(3, 14)(5, 11)(7, 13)(8, 10) ], [g| (1, 7)(2, 4)(3, 10)(5, 13)(8, 11)(9, 12) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 8)(2, 10)(3, 4)(5, 9)(6, 14)(7, 11)(12, 13) ], [g| (1, 14)(2, 7)(3, 5)(4, 9)(6, 8)(10, 11) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 8)(2, 10)(3, 4)(5, 9)(6, 14)(7, 11)(12, 13) ], [g| (1, 9)(2, 7)(3, 12)(4, 10)(5, 6)(8, 11)(13, 14) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 14)(2, 8)(3, 10)(4, 12)(5, 6)(7, 11)(9, 13) ], [g| (1, 10)(2, 6)(3, 14)(4, 11)(5, 8)(7, 12) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 14)(2, 8)(3, 10)(4, 12)(5, 6)(7, 11)(9, 13) ], [g| (1, 7)(3, 9)(4, 6)(5, 12)(10, 13)(11, 14) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 14)(2, 8)(3, 10)(4, 12)(5, 6)(7, 11)(9, 13) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 14)(2, 8)(3, 10)(4, 12)(5, 6)(7, 11)(9, 13) , (1, 4)(2, 9)(3, 14)(5, 11)(7, 13)(8, 10) ], [g| (1, 8)(2, 5)(3, 13)(4, 9)(7, 12)(11, 14) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 13)(2, 7)(3, 8)(4, 14)(5, 12)(6, 10)(9, 11) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 13)(2, 7)(3, 8)(4, 14)(5, 12)(6, 10)(9, 11) , (1, 6)(2, 10)(3, 11)(4, 14)(7, 12)(9, 13) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 13)(2, 7)(3, 8)(4, 14)(5, 12)(6, 10)(9, 11) , (1, 11)(2, 13)(3, 4)(5, 6)(7, 10)(8, 12) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 5)(3, 14)(4, 8)(6, 9)(10, 11)(12, 13) , (1, 12)(2, 11)(3, 10)(4, 9)(5, 8)(6, 7)(13, 14) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 5)(3, 14)(4, 8)(6, 9)(10, 11)(12, 13) , (1, 7)(2, 5)(3, 8)(4, 10)(6, 9)(11, 13)(12, 14) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 5)(3, 14)(4, 8)(6, 9)(10, 11)(12, 13) , (1, 8)(2, 6)(3, 12)(4, 13)(5, 7)(9, 11)(10, 14) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 5)(3, 14)(4, 8)(6, 9)(10, 11)(12, 13) , (1, 11)(2, 13)(3, 4)(5, 6)(7, 10)(8, 12) ], [g| (1, 11)(2, 7)(3, 14)(5, 10)(6, 13)(9, 12) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 5)(3, 14)(4, 8)(6, 9)(10, 11)(12, 13) ], [g| (1, 10)(2, 7)(4, 8)(5, 11)(6, 12)(9, 13) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 5)(3, 14)(4, 8)(6, 9)(10, 11)(12, 13) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 5)(3, 14)(4, 8)(6, 9)(10, 11)(12, 13) , (1, 14)(4, 5)(6, 11)(7, 9)(8, 13)(10, 12) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 5)(3, 14)(4, 8)(6, 9)(10, 11)(12, 13) , (1, 4)(2, 9)(3, 14)(5, 11)(7, 13)(8, 10) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(2, 13)(4, 9)(5, 12)(8, 11)(10, 14) , (1, 7)(2, 5)(3, 8)(4, 10)(6, 9)(11, 13)(12, 14) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(2, 13)(4, 9)(5, 12)(8, 11)(10, 14) , (1, 8)(2, 6)(3, 12)(4, 13)(5, 7)(9, 11)(10, 14) ], [g| (1, 6)(3, 7)(4, 10)(5, 11)(8, 12)(9, 14) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(2, 13)(4, 9)(5, 12)(8, 11)(10, 14) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(2, 13)(4, 9)(5, 12)(8, 11)(10, 14) , (1, 11)(2, 13)(3, 4)(5, 6)(7, 10)(8, 12) ], [g| (1, 9)(2, 8)(3, 7)(4, 6)(10, 14)(11, 13) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(2, 13)(4, 9)(5, 12)(8, 11)(10, 14) ], [g| (1, 4)(2, 11)(3, 7)(5, 12)(6, 9)(8, 13) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(2, 13)(4, 9)(5, 12)(8, 11)(10, 14) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(2, 13)(4, 9)(5, 12)(8, 11)(10, 14) , (1, 14)(4, 5)(6, 11)(7, 9)(8, 13)(10, 12) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(2, 13)(4, 9)(5, 12)(8, 11)(10, 14) , (1, 4)(2, 9)(3, 14)(5, 11)(7, 13)(8, 10) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 4)(2, 12)(3, 8)(6, 11)(7, 14)(10, 13) , (1, 7)(2, 5)(3, 8)(4, 10)(6, 9)(11, 13)(12, 14) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 4)(2, 12)(3, 8)(6, 11)(7, 14)(10, 13) , (1, 8)(2, 6)(3, 12)(4, 13)(5, 7)(9, 11)(10, 14) ], [g| (1, 4)(2, 6)(5, 9)(7, 10)(11, 12)(13, 14) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 4)(2, 12)(3, 8)(6, 11)(7, 14)(10, 13) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 4)(2, 12)(3, 8)(6, 11)(7, 14)(10, 13) , (1, 11)(2, 13)(3, 4)(5, 6)(7, 10)(8, 12) ], [g| (2, 11)(3, 8)(5, 9)(6, 12)(7, 13)(10, 14) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 4)(2, 12)(3, 8)(6, 11)(7, 14)(10, 13) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 4)(2, 12)(3, 8)(6, 11)(7, 14)(10, 13) , (1, 14)(4, 5)(6, 11)(7, 9)(8, 13)(10, 12) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 4)(2, 12)(3, 8)(6, 11)(7, 14)(10, 13) , (1, 4)(2, 9)(3, 14)(5, 11)(7, 13)(8, 10) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(3, 7)(4, 10)(5, 11)(8, 12)(9, 14) , (1, 7)(2, 5)(3, 8)(4, 10)(6, 9)(11, 13)(12, 14) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(3, 7)(4, 10)(5, 11)(8, 12)(9, 14) , (1, 9)(2, 3)(4, 8)(5, 13)(6, 10)(7, 14)(11, 12) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(3, 7)(4, 10)(5, 11)(8, 12)(9, 14) , (1, 3)(2, 7)(4, 6)(5, 14)(8, 9)(12, 13) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(3, 7)(4, 10)(5, 11)(8, 12)(9, 14) , (1, 4)(2, 9)(3, 14)(5, 11)(7, 13)(8, 10) ], [g| (2, 13)(3, 7)(4, 14)(5, 8)(9, 10)(11, 12) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(3, 7)(4, 10)(5, 11)(8, 12)(9, 14) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 6)(3, 7)(4, 10)(5, 11)(8, 12)(9, 14) , (1, 14)(4, 5)(6, 11)(7, 9)(8, 13)(10, 12) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 4)(2, 11)(3, 7)(5, 12)(6, 9)(8, 13) , (1, 9)(2, 3)(4, 8)(5, 13)(6, 10)(7, 14)(11, 12) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 4)(2, 11)(3, 7)(5, 12)(6, 9)(8, 13) , (1, 11)(2, 13)(3, 4)(5, 6)(7, 10)(8, 12) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 4)(2, 11)(3, 7)(5, 12)(6, 9)(8, 13) , (1, 6)(2, 10)(3, 11)(4, 14)(7, 12)(9, 13) ], [g| (2, 11)(3, 8)(5, 9)(6, 12)(7, 13)(10, 14) , (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 4)(2, 11)(3, 7)(5, 12)(6, 9)(8, 13) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 4)(2, 11)(3, 7)(5, 12)(6, 9)(8, 13) , (1, 4)(2, 9)(3, 14)(5, 11)(7, 13)(8, 10) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 13)(2, 4)(3, 12)(5, 14)(6, 7)(10, 11) , (1, 11)(2, 13)(3, 4)(5, 6)(7, 10)(8, 12) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 13)(2, 4)(3, 12)(5, 14)(6, 7)(10, 11) , (1, 14)(4, 5)(6, 11)(7, 9)(8, 13)(10, 12) ], [g| (1, 7)(2, 3)(4, 13)(5, 8)(6, 12)(9, 14)(10, 11) , (1, 13)(2, 4)(3, 12)(5, 14)(6, 7)(10, 11) , (1, 4)(2, 9)(3, 14)(5, 11)(7, 13)(8, 10) ] ];