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Permutations of S5 With Table

The document lists all 120 permutations of the set S = {1, 2, 3, 4, 5} in two-line notation. Additionally, it includes a group multiplication table formed from a selected subset of these permutations. This provides a comprehensive overview of the permutations and their interactions within the group.

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christian olpindo
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16 views8 pages

Permutations of S5 With Table

The document lists all 120 permutations of the set S = {1, 2, 3, 4, 5} in two-line notation. Additionally, it includes a group multiplication table formed from a selected subset of these permutations. This provides a comprehensive overview of the permutations and their interactions within the group.

Uploaded by

christian olpindo
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Permutations and Group Table for S =

{1, 2, 3, 4, 5}
This document contains all 120 permutations of the set S = {1, 2, 3, 4, 5} in two-line
notation. Below the permutations is a group multiplication table formed from a selected
subset of these permutations.

All 120 Permutations of S in Two-Line Notation


1. (1 2 3 4 5)
(1 2 3 4 5)
2. (1 2 3 4 5)
(1 2 3 5 4)
3. (1 2 3 4 5)
(1 2 4 3 5)
4. (1 2 3 4 5)
(1 2 4 5 3)
5. (1 2 3 4 5)
(1 2 5 3 4)
6. (1 2 3 4 5)
(1 2 5 4 3)
7. (1 2 3 4 5)
(1 3 2 4 5)
8. (1 2 3 4 5)
(1 3 2 5 4)
9. (1 2 3 4 5)
(1 3 4 2 5)
10. (1 2 3 4 5)
(1 3 4 5 2)
11. (1 2 3 4 5)
(1 3 5 2 4)
12. (1 2 3 4 5)
(1 3 5 4 2)
13. (1 2 3 4 5)
(1 4 2 3 5)
14. (1 2 3 4 5)
(1 4 2 5 3)
15. (1 2 3 4 5)
(1 4 3 2 5)
16. (1 2 3 4 5)
(1 4 3 5 2)
17. (1 2 3 4 5)
(1 4 5 2 3)
18. (1 2 3 4 5)
(1 4 5 3 2)
19. (1 2 3 4 5)
(1 5 2 3 4)
20. (1 2 3 4 5)
(1 5 2 4 3)
21. (1 2 3 4 5)
(1 5 3 2 4)
22. (1 2 3 4 5)
(1 5 3 4 2)
23. (1 2 3 4 5)
(1 5 4 2 3)
24. (1 2 3 4 5)
(1 5 4 3 2)
25. (1 2 3 4 5)
(2 1 3 4 5)
26. (1 2 3 4 5)
(2 1 3 5 4)
27. (1 2 3 4 5)
(2 1 4 3 5)
28. (1 2 3 4 5)
(2 1 4 5 3)
29. (1 2 3 4 5)
(2 1 5 3 4)
30. (1 2 3 4 5)
(2 1 5 4 3)
31. (1 2 3 4 5)
(2 3 1 4 5)
32. (1 2 3 4 5)
(2 3 1 5 4)
33. (1 2 3 4 5)
(2 3 4 1 5)
34. (1 2 3 4 5)
(2 3 4 5 1)
35. (1 2 3 4 5)
(2 3 5 1 4)
36. (1 2 3 4 5)
(2 3 5 4 1)
37. (1 2 3 4 5)
(2 4 1 3 5)
38. (1 2 3 4 5)
(2 4 1 5 3)
39. (1 2 3 4 5)
(2 4 3 1 5)
40. (1 2 3 4 5)
(2 4 3 5 1)
41. (1 2 3 4 5)
(2 4 5 1 3)
42. (1 2 3 4 5)
(2 4 5 3 1)
43. (1 2 3 4 5)
(2 5 1 3 4)
44. (1 2 3 4 5)
(2 5 1 4 3)
45. (1 2 3 4 5)
(2 5 3 1 4)
46. (1 2 3 4 5)
(2 5 3 4 1)
47. (1 2 3 4 5)
(2 5 4 1 3)
48. (1 2 3 4 5)
(2 5 4 3 1)
49. (1 2 3 4 5)
(3 1 2 4 5)
50. (1 2 3 4 5)
(3 1 2 5 4)
51. (1 2 3 4 5)
(3 1 4 2 5)
52. (1 2 3 4 5)
(3 1 4 5 2)
53. (1 2 3 4 5)
(3 1 5 2 4)
54. (1 2 3 4 5)
(3 1 5 4 2)
55. (1 2 3 4 5)
(3 2 1 4 5)
56. (1 2 3 4 5)
(3 2 1 5 4)
57. (1 2 3 4 5)
(3 2 4 1 5)
58. (1 2 3 4 5)
(3 2 4 5 1)
59. (1 2 3 4 5)
(3 2 5 1 4)
60. (1 2 3 4 5)
(3 2 5 4 1)
61. (1 2 3 4 5)
(3 4 1 2 5)
62. (1 2 3 4 5)
(3 4 1 5 2)
63. (1 2 3 4 5)
(3 4 2 1 5)
64. (1 2 3 4 5)
(3 4 2 5 1)
65. (1 2 3 4 5)
(3 4 5 1 2)
66. (1 2 3 4 5)
(3 4 5 2 1)
67. (1 2 3 4 5)
(3 5 1 2 4)
68. (1 2 3 4 5)
(3 5 1 4 2)
69. (1 2 3 4 5)
(3 5 2 1 4)
70. (1 2 3 4 5)
(3 5 2 4 1)
71. (1 2 3 4 5)
(3 5 4 1 2)
72. (1 2 3 4 5)
(3 5 4 2 1)
73. (1 2 3 4 5)
(4 1 2 3 5)
74. (1 2 3 4 5)
(4 1 2 5 3)
75. (1 2 3 4 5)
(4 1 3 2 5)
76. (1 2 3 4 5)
(4 1 3 5 2)
77. (1 2 3 4 5)
(4 1 5 2 3)
78. (1 2 3 4 5)
(4 1 5 3 2)
79. (1 2 3 4 5)
(4 2 1 3 5)
80. (1 2 3 4 5)
(4 2 1 5 3)
81. (1 2 3 4 5)
(4 2 3 1 5)
82. (1 2 3 4 5)
(4 2 3 5 1)
83. (1 2 3 4 5)
(4 2 5 1 3)
84. (1 2 3 4 5)
(4 2 5 3 1)
85. (1 2 3 4 5)
(4 3 1 2 5)
86. (1 2 3 4 5)
(4 3 1 5 2)
87. (1 2 3 4 5)
(4 3 2 1 5)
88. (1 2 3 4 5)
(4 3 2 5 1)
89. (1 2 3 4 5)
(4 3 5 1 2)
90. (1 2 3 4 5)
(4 3 5 2 1)
91. (1 2 3 4 5)
(4 5 1 2 3)
92. (1 2 3 4 5)
(4 5 1 3 2)
93. (1 2 3 4 5)
(4 5 2 1 3)
94. (1 2 3 4 5)
(4 5 2 3 1)
95. (1 2 3 4 5)
(4 5 3 1 2)
96. (1 2 3 4 5)
(4 5 3 2 1)
97. (1 2 3 4 5)
(5 1 2 3 4)
98. (1 2 3 4 5)
(5 1 2 4 3)
99. (1 2 3 4 5)
(5 1 3 2 4)
100. (1 2 3 4 5)
(5 1 3 4 2)
101. (1 2 3 4 5)
(5 1 4 2 3)
102. (1 2 3 4 5)
(5 1 4 3 2)
103. (1 2 3 4 5)
(5 2 1 3 4)
104. (1 2 3 4 5)
(5 2 1 4 3)
105. (1 2 3 4 5)
(5 2 3 1 4)
106. (1 2 3 4 5)
(5 2 3 4 1)
107. (1 2 3 4 5)
(5 2 4 1 3)
108. (1 2 3 4 5)
(5 2 4 3 1)
109. (1 2 3 4 5)
(5 3 1 2 4)
110. (1 2 3 4 5)
(5 3 1 4 2)
111. (1 2 3 4 5)
(5 3 2 1 4)
112. (1 2 3 4 5)
(5 3 2 4 1)
113. (1 2 3 4 5)
(5 3 4 1 2)
114. (1 2 3 4 5)
(5 3 4 2 1)
115. (1 2 3 4 5)
(5 4 1 2 3)
116. (1 2 3 4 5)
(5 4 1 3 2)
117. (1 2 3 4 5)
(5 4 2 1 3)
118. (1 2 3 4 5)
(5 4 2 3 1)
119. (1 2 3 4 5)
(5 4 3 1 2)
120. (1 2 3 4 5)
(5 4 3 2 1)
Group Multiplication Table (Subset of S₅)
◦ ρ₀ ρ₁ ρ₂ ρ₃ ρ₄
ρ₀ ρ₀ ρ₁ ρ₂ ρ₃ ρ₄
ρ₁ ρ₁ ρ₀ - - -
ρ₂ ρ₂ - ρ₀ - -
ρ₃ ρ₃ - - ρ₀ -
ρ₄ ρ₄ - - - ρ₀

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