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(1,2,3,4,5,6,7,8,9,10,11,12)
(1,3,5,7,9,11)(2,4,6,8,10,12)
(1,3,5,7,9,11)(2,4,6,8,10,12)
(1,12,11,10,9,8,7,6,5,4,3,2)
(1,11,9,7,5,3)(2,12,10,8,6,4)
true
Group([ (1,2,3,4,5,6,7,8,9,10,11,12) ])
[ (1,5,9)(2,6,10)(3,7,11)(4,8,12), (1,4,7,10)(2,5,8,11)(3,6,9,12) ] ->
[ f3, f1*f2 ]
12
[ (), (1,9,5)(2,10,6)(3,11,7)(4,12,8), (1,5,9)(2,6,10)(3,7,11)(4,8,12),
(1,11,9,7,5,3)(2,12,10,8,6,4), (1,7)(2,8)(3,9)(4,10)(5,11)(6,12),
(1,3,5,7,9,11)(2,4,6,8,10,12), (1,12,11,10,9,8,7,6,5,4,3,2),
(1,8,3,10,5,12,7,2,9,4,11,6), (1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,10,7,4)(2,11,8,5)(3,12,9,6), (1,6,11,4,9,2,7,12,5,10,3,8),
(1,2,3,4,5,6,7,8,9,10,11,12) ]
[ 1, 9, 5, 11, 7, 3, 12, 8, 4, 10, 6, 2 ]
true
[ [ 4, 7, 12 ], [ 4, 8, 11 ], [ 3, 8, 12 ], [ 2, 6, 9 ], [ 1, 6, 10 ],
[ 2, 5, 10 ], [ 1, 5, 8 ], [ 5, 9, 12 ], [ 1, 4, 9 ], [ 3, 7, 10 ],
[ 2, 7, 11 ], [ 3, 6, 11 ] ]
[ [ 4, 8, 12 ], [ 2, 6, 10 ], [ 1, 5, 9 ], [ 3, 7, 11 ] ]
(1,11)(2,10)(3,9)(4,8)(5,7)
Group([ (1,2,3,4,5,6,7,8,9,10,11,12), (1,11)(2,10)(3,9)(4,8)(5,7) ])
[ (1,3)(4,12)(5,11)(6,10)(7,9), (1,2)(3,12)(4,11)(5,10)(6,9)(7,8) ] ->
[ f1, f1*f2 ]
(1,5)(2,10)(4,8)(7,11)
Group([ (1,2,3,4,5,6,7,8,9,10,11,12), (1,11)(2,10)(3,9)(4,8)(5,7),
(1,5)(2,10)(4,8)(7,11) ])
[ (1,5)(2,4)(6,12)(7,11)(8,10), (1,4,7,10)(2,5,8,11)(3,6,9,12),
(2,6)(3,11)(5,9)(8,12) ] -> [ f1*f2^2*f3, f4, f1 ]
(1,3,5,7,9,11)(2,4,6,8,10,12)
(1,2)(3,12)(4,11)(5,10)(6,9)(7,8)
(1,4)(2,3)(5,12)(6,11)(7,10)(8,9)
<group of size 48 with 5 generators>
[ (1,4,7,10)(2,9,8,3)(5,12,11,6), (1,3)(4,12)(5,11)(6,10)(7,9),
(1,4,7,10)(2,5,8,11)(3,6,9,12) ] ->
[ [ (1,9)(2,8)(3,7)(4,6)(10,12), (1,10,7,4)(2,11,8,5)(3,12,9,6),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,9,5)(2,10,6)(3,11,7)(4,12,8) ] ->
[ (1,6)(2,5)(3,4)(7,12)(8,11)(9,10), (1,10,7,4)(2,11,8,5)(3,12,9,6),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12) ],
[ (1,2,3,4,5,6,7,8,9,10,11,12), (1,11)(2,10)(3,9)(4,8)(5,7) ] ->
[ (1,12,11,10,9,8,7,6,5,4,3,2), (1,3)(4,12)(5,11)(6,10)(7,9) ],
[ (1,2,3,4,5,6,7,8,9,10,11,12), (1,11)(2,10)(3,9)(4,8)(5,7) ] ->
[ (1,2,3,4,5,6,7,8,9,10,11,12), (1,8)(2,7)(3,6)(4,5)(9,12)(10,11) ] ]
<group with 2 generators>
[ (1,8)(2,7)(3,6)(4,5)(9,12)(10,11), (1,10,7,4)(2,11,8,5)(3,12,9,6),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,9,5)(2,10,6)(3,11,7)(4,12,8) ] ->
[ (1,9)(2,8)(3,7)(4,6)(10,12), (1,10,7,4)(2,11,8,5)(3,12,9,6),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,9,5)(2,10,6)(3,11,7)(4,12,8) ]
[ (2,12)(3,11)(4,10)(5,9)(6,8), (1,4,7,10)(2,5,8,11)(3,6,9,12),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12) ] ->
[ (1,9)(2,8)(3,7)(4,6)(10,12), (1,10,7,4)(2,11,8,5)(3,12,9,6),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,9,5)(2,10,6)(3,11,7)(4,12,8) ]
(1,3,5,7,9,11)(2,4,6,8,10,12)
(1,4)(2,3)(5,12)(6,11)(7,10)(8,9)
(1,6)(2,5)(3,4)(7,12)(8,11)(9,10)
(1,11,9,7,5,3)(2,12,10,8,6,4)
(1,11)(2,10)(3,9)(4,8)(5,7)
(1,9)(2,8)(3,7)(4,6)(10,12)
(1,11,9,7,5,3)(2,12,10,8,6,4)
(1,11)(2,10)(3,9)(4,8)(5,7)
(1,9)(2,8)(3,7)(4,6)(10,12)
true
[ (1,6,11,4,9,2,7,12,5,10,3,8), (1,11)(2,10)(3,9)(4,8)(5,7) ] ->
[ (1,2,3,4,5,6,7,8,9,10,11,12), (1,11)(2,10)(3,9)(4,8)(5,7) ]
[ (1,6,11,4,9,2,7,12,5,10,3,8), (1,11)(2,10)(3,9)(4,8)(5,7) ] ->
[ (1,12,11,10,9,8,7,6,5,4,3,2), (1,11)(2,10)(3,9)(4,8)(5,7) ]
<group with 2 generators>
(1,3,5,7,9,11)(2,4,6,8,10,12)
(1,2)(3,12)(4,11)(5,10)(6,9)(7,8)
(1,4)(2,3)(5,12)(6,11)(7,10)(8,9)
<action homomorphism>
<group with 1 generators>
2
[ IdentityMapping( Group([ (1,2,3,4,5,6,7,8,9,10,11,12),
(1,11)(2,10)(3,9)(4,8)(5,7) ]) ),
[ (1,9)(2,8)(3,7)(4,6)(10,12), (1,10,7,4)(2,11,8,5)(3,12,9,6),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,9,5)(2,10,6)(3,11,7)(4,12,8) ] ->
[ (1,3)(4,12)(5,11)(6,10)(7,9), (1,10,7,4)(2,11,8,5)(3,12,9,6),
(1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,9,5)(2,10,6)(3,11,7)(4,12,8) ] ]
true
true
true
true
true
true
true
[ 4, 7, 12 ]
[ [ 4, 7, 12 ], [ 4, 8, 11 ], [ 3, 8, 12 ], [ 2, 6, 9 ], [ 1, 6, 10 ],
[ 2, 5, 10 ], [ 1, 5, 8 ], [ 5, 9, 12 ], [ 1, 4, 9 ], [ 3, 7, 10 ],
[ 2, 7, 11 ], [ 3, 6, 11 ], [ 2, 7, 10 ], [ 3, 6, 10 ], [ 2, 6, 11 ],
[ 5, 8, 12 ], [ 1, 4, 8 ], [ 4, 9, 12 ], [ 1, 6, 9 ], [ 2, 5, 9 ],
[ 1, 5, 10 ], [ 4, 7, 11 ], [ 3, 7, 12 ], [ 3, 8, 11 ] ]
Group([ (1,7,4,10,2,8,5,11,3,9,6,12)(13,24,18,21,15,23,17,20,14,22,16,19),
(1,16)(2,17)(3,18)(4,14)(5,15)(6,13)(7,22)(8,23)(9,24)(10,20)(11,21)(12,19)
])
[ (2,12)(3,11)(4,10)(5,9)(6,8), (1,8)(2,7)(3,6)(4,5)(9,12)(10,11) ] ->
[ (1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24),
(1,19)(2,20)(3,21)(4,22)(5,23)(6,24)(7,16)(8,17)(9,18)(10,14)(11,15)(12,13)
]
(1,8,6,10,3,7,5,12,2,9,4,11)(13,23,16,21,14,24,17,19,15,22,18,20)
(1,18)(2,16)(3,17)(4,13)(5,14)(6,15)(7,24)(8,22)(9,23)(10,19)(11,20)(12,21)
Sym( [ 1 .. 24 ] )
true
<permutation group with 4 generators>
true
[ (1,22)(2,23)(3,24)(4,20)(5,21)(6,19)(7,14)(8,15)(9,13)(10,17)(11,18)(12,16),
(1,7,4,10,2,8,5,11,3,9,6,12)(13,24,18,21,15,23,17,20,14,22,16,19) ] ->
[ (1,13)(2,15)(3,14)(4,18)(5,17)(6,16)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19),
(1,7,4,10,2,8,5,11,3,9,6,12)(13,19,16,22,14,20,17,23,15,21,18,24) ]
(1,12,6,9,3,11,5,8,2,10,4,7)(13,24,18,21,15,23,17,20,14,22,16,19)
(1,13)(2,15)(3,14)(4,18)(5,17)(6,16)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)
(1,13)(2,15)(3,14)(4,18)(5,17)(6,16)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)
(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)
(1,19)(2,21)(3,20)(4,24)(5,23)(6,22)(7,13)(8,15)(9,14)(10,18)(11,17)(12,16)
(1,23)(2,22)(3,24)(4,20)(5,19)(6,21)(7,17)(8,16)(9,18)(10,14)(11,13)(12,15)
Group([ (1,8,6,10,3,7,5,12,2,9,4,11)(13,23,16,21,14,24,17,19,15,22,18,20) ])
<permutation group with 5 generators>
288
true
(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)
()
(1,2,3,4,5,6,7,8,9,10,11,12)
(13,14,15,16,17,18,19,20,21,22,23,24)
(1,6,11,4,9,2,7,12,5,10,3,8)(13,18,23,16,21,14,19,24,17,22,15,20)
(1,16)(2,17)(3,18)(4,19)(5,20)(6,21)(7,22)(8,23)(9,24)(10,13)(11,14)(12,15)
<permutation group of size 1152 with 5 generators>
(1,2,3,4,5,6,7,8,9,10,11,12)(13,24,23,22,21,20,19,18,17,16,15,14)
(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)(12,24)
Group([ (1,2,3,4,5,6,7,8,9,10,11,12)(13,24,23,22,21,20,19,18,17,16,15,14),
(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)(12,24)
])
true
(1,17)(2,22)(3,15)(4,20)(5,13)(6,18)(7,23)(8,16)(9,21)(10,14)(11,19)(12,24)
(1,19)(2,14)(3,21)(4,16)(5,23)(6,18)(7,13)(8,20)(9,15)(10,22)(11,17)(12,24)
(1,23,7,17)(2,22,8,16)(3,21,9,15)(4,20,10,14)(5,19,11,13)(6,18,12,24)
(1,19,7,13)(2,14,8,20)(3,21,9,15)(4,16,10,22)(5,23,11,17)(6,18,12,24)
(1,17,4,20,7,23,10,14)(2,22,5,13,8,16,11,19)(3,15,6,18,9,21,12,24)
Group([ (1,2,3,4,5,6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24),
(1,17)(2,22)(3,15)(4,20)(5,13)(6,18)(7,23)(8,16)(9,21)(10,14)(11,19)(12,24)
])
Group([ (1,2,3,4,5,6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24),
(1,19)(2,14)(3,21)(4,16)(5,23)(6,18)(7,13)(8,20)(9,15)(10,22)(11,17)(12,24)
])
Group([ (1,2,3,4,5,6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24),
(1,23,7,17)(2,22,8,16)(3,21,9,15)(4,20,10,14)(5,19,11,13)(6,18,12,24) ])
Group([ (1,2,3,4,5,6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24),
(1,19,7,13)(2,14,8,20)(3,21,9,15)(4,16,10,22)(5,23,11,17)(6,18,12,24) ])
Group([ (1,2,3,4,5,6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24),
(1,17,4,20,7,23,10,14)(2,22,5,13,8,16,11,19)(3,15,6,18,9,21,12,24) ])
<permutation group of size 4608 with 7 generators>