| Download
Worksheets related to Applied Discrete Structures
Project: Applied Discrete Structures
Views: 15786Image: ubuntu2004
Symmetric group of order 4! as a permutation group
[(), (1,2), (1,2,3,4), (1,3)(2,4), (1,3,4), (2,3,4), (1,4,3,2), (1,3,4,2), (1,3,2,4), (1,4,2,3), (1,2,4,3), (2,4,3), (1,4,3), (1,4)(2,3), (1,4,2), (1,3,2), (1,3), (3,4), (2,4), (1,4), (2,3), (1,2)(3,4), (1,2,3), (1,2,4)]
[[(), 1], [(1,2), -1], [(1,2,3,4), -1], [(1,3)(2,4), 1], [(1,3,4), 1], [(2,3,4), 1], [(1,4,3,2), -1], [(1,3,4,2), -1], [(1,3,2,4), -1], [(1,4,2,3), -1], [(1,2,4,3), -1], [(2,4,3), 1], [(1,4,3), 1], [(1,4)(2,3), 1], [(1,4,2), 1], [(1,3,2), 1], [(1,3), -1], [(3,4), -1], [(2,4), -1], [(1,4), -1], [(2,3), -1], [(1,2)(3,4), 1], [(1,2,3), 1], [(1,2,4), 1]]
[(), 1]
[(1,2), -1]
[(1,2,3,4), -1]
[(1,3)(2,4), 1]
[(1,3,4), 1]
[(2,3,4), 1]
[(1,4,3,2), -1]
[(1,3,4,2), -1]
[(1,3,2,4), -1]
[(1,4,2,3), -1]
[(1,2,4,3), -1]
[(2,4,3), 1]
[(1,4,3), 1]
[(1,4)(2,3), 1]
[(1,4,2), 1]
[(1,3,2), 1]
[(1,3), -1]
[(3,4), -1]
[(2,4), -1]
[(1,4), -1]
[(2,3), -1]
[(1,2)(3,4), 1]
[(1,2,3), 1]
[(1,2,4), 1]
[1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 8, 8, 8, 12, 24]
[(), (1,3)(2,4), (2,4,3), (1,4)(2,3), (1,2)(3,4), (1,4,2), (1,2,3), (1,3,4), (2,3,4), (1,3,2), (1,4,3), (1,2,4)]
Permutation Group with generators [(1,2,3,4), (1,3)]
8
* a b c d e f g h
+----------------
a| a b c d e f g h
b| b a f h g c e d
c| c e d g h b a f
d| d h g a f e c b
e| e c b f a d h g
f| f g h e d a b c
g| g f a c b h d e
h| h d e b c g f a
* () (1,3) (1,2,3,4) (1,3)(2,4) (1,2)(3,4) (1,4)(2,3) (1,4,3,2) (2,4)
+----------------------------------------------------------------------------------------
()| () (1,3) (1,2,3,4) (1,3)(2,4) (1,2)(3,4) (1,4)(2,3) (1,4,3,2) (2,4)
(1,3)| (1,3) () (1,4)(2,3) (2,4) (1,4,3,2) (1,2,3,4) (1,2)(3,4) (1,3)(2,4)
(1,2,3,4)| (1,2,3,4) (1,2)(3,4) (1,3)(2,4) (1,4,3,2) (2,4) (1,3) () (1,4)(2,3)
(1,3)(2,4)| (1,3)(2,4) (2,4) (1,4,3,2) () (1,4)(2,3) (1,2)(3,4) (1,2,3,4) (1,3)
(1,2)(3,4)| (1,2)(3,4) (1,2,3,4) (1,3) (1,4)(2,3) () (1,3)(2,4) (2,4) (1,4,3,2)
(1,4)(2,3)| (1,4)(2,3) (1,4,3,2) (2,4) (1,2)(3,4) (1,3)(2,4) () (1,3) (1,2,3,4)
(1,4,3,2)| (1,4,3,2) (1,4)(2,3) () (1,2,3,4) (1,3) (2,4) (1,3)(2,4) (1,2)(3,4)
(2,4)| (2,4) (1,3)(2,4) (1,2)(3,4) (1,3) (1,2,3,4) (1,4,3,2) (1,4)(2,3) ()