g := PSL(2,19); invols := [ [g| (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 12)(2, 3)(4, 15)(5, 17)(6, 9)(7, 10)(8, 18)(11, 19)(13, 14)(16, 20) , (1, 18)(2, 7)(3, 9)(4, 12)(5, 10)(6, 16)(8, 20)(11, 14)(13, 17)(15, 19) ], [g| (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 12)(2, 3)(4, 15)(5, 17)(6, 9)(7, 10)(8, 18)(11, 19)(13, 14)(16, 20) , (1, 19)(2, 16)(3, 12)(4, 18)(5, 9)(6, 13)(7, 14)(8, 17)(10, 20)(11, 15) ], [g| (1, 3)(2, 12)(4, 18)(5, 14)(6, 20)(7, 11)(8, 15)(9, 16)(10, 19)(13, 17) , (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 12)(2, 3)(4, 15)(5, 17)(6, 9)(7, 10)(8, 18)(11, 19)(13, 14)(16, 20) ], [g| (1, 7)(2, 15)(3, 4)(5, 8)(6, 19)(9, 11)(10, 12)(13, 16)(14, 20)(17, 18) , (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 12)(2, 3)(4, 15)(5, 17)(6, 9)(7, 10)(8, 18)(11, 19)(13, 14)(16, 20) ], [g| (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 12)(2, 3)(4, 15)(5, 17)(6, 9)(7, 10)(8, 18)(11, 19)(13, 14)(16, 20) , (1, 12)(2, 11)(3, 10)(4, 9)(5, 8)(6, 7)(13, 20)(14, 19)(15, 18)(16, 17) ], [g| (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 15)(2, 11)(3, 17)(4, 8)(5, 12)(6, 13)(7, 16)(9, 19)(10, 14)(18, 20) , (1, 12)(2, 11)(3, 10)(4, 9)(5, 8)(6, 7)(13, 20)(14, 19)(15, 18)(16, 17) ], [g| (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 15)(2, 11)(3, 17)(4, 8)(5, 12)(6, 13)(7, 16)(9, 19)(10, 14)(18, 20) , (1, 16)(2, 10)(3, 11)(4, 7)(5, 19)(6, 9)(8, 14)(12, 17)(13, 15)(18, 20) ], [g| (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 15)(2, 11)(3, 17)(4, 8)(5, 12)(6, 13)(7, 16)(9, 19)(10, 14)(18, 20) , (1, 18)(2, 7)(3, 9)(4, 12)(5, 10)(6, 16)(8, 20)(11, 14)(13, 17)(15, 19) ], [g| (1, 13)(2, 16)(3, 18)(4, 7)(5, 17)(6, 10)(8, 12)(9, 19)(11, 14)(15, 20) , (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 20)(2, 9)(3, 17)(4, 10)(5, 18)(6, 7)(8, 11)(12, 14)(13, 15)(16, 19) ], [g| (1, 7)(2, 18)(3, 10)(4, 17)(5, 9)(6, 20)(8, 16)(11, 19)(12, 13)(14, 15) , (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 20)(2, 9)(3, 17)(4, 10)(5, 18)(6, 7)(8, 11)(12, 14)(13, 15)(16, 19) ], [g| (1, 15)(2, 19)(3, 5)(4, 6)(7, 10)(8, 14)(9, 16)(11, 12)(13, 20)(17, 18) , (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 20)(2, 9)(3, 17)(4, 10)(5, 18)(6, 7)(8, 11)(12, 14)(13, 15)(16, 19) ], [g| (1, 8)(2, 15)(3, 7)(4, 18)(5, 19)(6, 14)(9, 17)(10, 11)(12, 13)(16, 20) , (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 6)(2, 4)(3, 17)(5, 10)(7, 9)(8, 14)(11, 19)(12, 20)(13, 16)(15, 18) ], [g| (1, 10)(2, 9)(3, 8)(4, 7)(5, 6)(11, 20)(12, 19)(13, 18)(14, 17)(15, 16) , (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 6)(2, 4)(3, 17)(5, 10)(7, 9)(8, 14)(11, 19)(12, 20)(13, 16)(15, 18) ], [g| (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 18)(2, 10)(3, 12)(4, 5)(6, 15)(7, 11)(8, 16)(9, 19)(13, 14)(17, 20) , (1, 12)(2, 11)(3, 10)(4, 9)(5, 8)(6, 7)(13, 20)(14, 19)(15, 18)(16, 17) ], [g| (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 18)(2, 10)(3, 12)(4, 5)(6, 15)(7, 11)(8, 16)(9, 19)(13, 14)(17, 20) , (1, 18)(2, 7)(3, 9)(4, 12)(5, 10)(6, 16)(8, 20)(11, 14)(13, 17)(15, 19) ], [g| (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 8)(2, 4)(3, 11)(5, 16)(6, 13)(7, 17)(9, 18)(10, 12)(14, 19)(15, 20) , (1, 12)(2, 11)(3, 10)(4, 9)(5, 8)(6, 7)(13, 20)(14, 19)(15, 18)(16, 17) ], [g| (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 8)(2, 4)(3, 11)(5, 16)(6, 13)(7, 17)(9, 18)(10, 12)(14, 19)(15, 20) , (1, 10)(2, 18)(3, 13)(4, 8)(5, 16)(6, 19)(7, 20)(9, 15)(11, 17)(12, 14) ], [g| (1, 12)(2, 8)(3, 5)(4, 14)(6, 20)(7, 16)(9, 13)(10, 17)(11, 18)(15, 19) , (1, 17)(2, 3)(4, 6)(5, 14)(7, 9)(8, 19)(10, 11)(12, 16)(13, 18)(15, 20) , (1, 6)(2, 4)(3, 17)(5, 10)(7, 9)(8, 14)(11, 19)(12, 20)(13, 16)(15, 18) , (1, 8)(2, 12)(3, 16)(4, 13)(5, 7)(6, 18)(9, 14)(10, 15)(11, 20)(17, 19) ] ];