g := PSL(2,27); invols := [ [g| (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 20)(2, 15)(3, 17)(4, 19)(5, 14)(6, 12)(7, 8)(9, 25)(10, 18)(11, 21)(13, 23)(16, 24)(22, 28)(26, 27) , (1, 12)(2, 28)(3, 13)(4, 18)(5, 23)(6, 8)(7, 24)(9, 10)(11, 15)(14, 22)(16, 19)(17, 20)(21, 25)(26, 27) ], [g| (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 20)(2, 15)(3, 17)(4, 19)(5, 14)(6, 12)(7, 8)(9, 25)(10, 18)(11, 21)(13, 23)(16, 24)(22, 28)(26, 27) , (1, 10)(2, 9)(3, 8)(4, 7)(5, 6)(11, 28)(12, 27)(13, 26)(14, 25)(15, 24)(16, 23)(17, 22)(18, 21)(19, 20) ], [g| (1, 2)(3, 14)(4, 11)(5, 17)(6, 8)(7, 12)(9, 27)(10, 22)(13, 24)(15, 20)(16, 23)(18, 28)(19, 21)(25, 26) , (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 20)(2, 15)(3, 17)(4, 19)(5, 14)(6, 12)(7, 8)(9, 25)(10, 18)(11, 21)(13, 23)(16, 24)(22, 28)(26, 27) ], [g| (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 20)(2, 15)(3, 17)(4, 19)(5, 14)(6, 12)(7, 8)(9, 25)(10, 18)(11, 21)(13, 23)(16, 24)(22, 28)(26, 27) , (1, 14)(2, 16)(3, 18)(4, 13)(5, 11)(6, 7)(8, 24)(9, 17)(10, 20)(12, 22)(15, 23)(19, 28)(21, 27)(25, 26) ], [g| (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 20)(2, 15)(3, 17)(4, 19)(5, 14)(6, 12)(7, 8)(9, 25)(10, 18)(11, 21)(13, 23)(16, 24)(22, 28)(26, 27) , (1, 24)(2, 13)(3, 20)(4, 9)(5, 12)(6, 22)(7, 17)(8, 10)(11, 27)(14, 15)(16, 26)(18, 19)(21, 28)(23, 25) ], [g| (1, 3)(2, 13)(4, 14)(5, 19)(6, 24)(7, 9)(8, 25)(10, 11)(12, 16)(15, 23)(17, 20)(18, 21)(22, 26)(27, 28) , (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 20)(2, 15)(3, 17)(4, 19)(5, 14)(6, 12)(7, 8)(9, 25)(10, 18)(11, 21)(13, 23)(16, 24)(22, 28)(26, 27) ], [g| (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 7)(2, 21)(3, 28)(4, 9)(5, 24)(6, 18)(8, 20)(10, 12)(11, 15)(13, 27)(14, 16)(17, 22)(19, 25)(23, 26) , (1, 12)(2, 28)(3, 13)(4, 18)(5, 23)(6, 8)(7, 24)(9, 10)(11, 15)(14, 22)(16, 19)(17, 20)(21, 25)(26, 27) ], [g| (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 7)(2, 21)(3, 28)(4, 9)(5, 24)(6, 18)(8, 20)(10, 12)(11, 15)(13, 27)(14, 16)(17, 22)(19, 25)(23, 26) , (1, 14)(2, 16)(3, 18)(4, 13)(5, 11)(6, 7)(8, 24)(9, 17)(10, 20)(12, 22)(15, 23)(19, 28)(21, 27)(25, 26) ], [g| (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 7)(2, 21)(3, 28)(4, 9)(5, 24)(6, 18)(8, 20)(10, 12)(11, 15)(13, 27)(14, 16)(17, 22)(19, 25)(23, 26) , (1, 26)(2, 15)(3, 27)(4, 25)(5, 19)(6, 13)(7, 11)(8, 23)(9, 12)(10, 28)(14, 20)(16, 17)(18, 24)(21, 22) ], [g| (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 25)(2, 22)(3, 11)(4, 8)(5, 17)(6, 23)(7, 13)(9, 14)(10, 27)(12, 15)(16, 28)(18, 21)(19, 24)(20, 26) , (1, 12)(2, 28)(3, 13)(4, 18)(5, 23)(6, 8)(7, 24)(9, 10)(11, 15)(14, 22)(16, 19)(17, 20)(21, 25)(26, 27) ], [g| (1, 2)(3, 9)(4, 18)(5, 27)(6, 7)(8, 21)(10, 17)(11, 14)(12, 16)(13, 23)(15, 28)(19, 26)(20, 24)(22, 25) , (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 25)(2, 22)(3, 11)(4, 8)(5, 17)(6, 23)(7, 13)(9, 14)(10, 27)(12, 15)(16, 28)(18, 21)(19, 24)(20, 26) ], [g| (1, 6)(2, 10)(3, 5)(4, 13)(7, 8)(9, 16)(11, 17)(12, 19)(14, 28)(15, 24)(18, 26)(20, 21)(22, 27)(23, 25) , (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 25)(2, 22)(3, 11)(4, 8)(5, 17)(6, 23)(7, 13)(9, 14)(10, 27)(12, 15)(16, 28)(18, 21)(19, 24)(20, 26) ], [g| (1, 9)(2, 18)(3, 20)(4, 28)(5, 7)(6, 19)(8, 16)(10, 12)(11, 26)(13, 17)(14, 25)(15, 27)(21, 22)(23, 24) , (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 25)(2, 22)(3, 11)(4, 8)(5, 17)(6, 23)(7, 13)(9, 14)(10, 27)(12, 15)(16, 28)(18, 21)(19, 24)(20, 26) ], [g| (1, 22)(2, 19)(3, 4)(5, 15)(6, 24)(7, 8)(9, 20)(10, 17)(11, 23)(12, 14)(13, 18)(16, 28)(21, 26)(25, 27) , (1, 28)(2, 12)(3, 21)(4, 5)(6, 17)(7, 14)(8, 20)(9, 11)(10, 15)(13, 25)(16, 27)(18, 23)(19, 26)(22, 24) , (1, 10)(2, 9)(3, 8)(4, 7)(5, 6)(11, 28)(12, 27)(13, 26)(14, 25)(15, 24)(16, 23)(17, 22)(18, 21)(19, 20) ] ];