aut := sub<Sym(24)|(2,17,21)(3,8,6)(5,13,16)(10,20,14)(11,15,24)(18,22,23),
(1,13)(2,22)(3,12)(4,23)(5,8)(6,9)(7,10)(11,17)(14,18)(15,21)(16,24)(19,20)>;

g := sub<aut|(1,23)(2,13)(3,19)(4,17)(5,14)(6,24)(7,8)(9,12)(10,21)(11,22)(15,18)(16,20),
(1,6,23)(2,20,17)(3,24,8)(4,5,14)(7,15,22)(12,16,21)>;

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