Group 9.1 - Z₉

Name Z9 Order 9 Exponent 9 Cyclic yes Abelian yes Elementary no Abelian Invariants [ 9 ] p-Group yes (3) Rank 1 Nilpotent yes Supersoluble yes Soluble yes Simple no Perfect no

Permutation Representation

Cayley Table:

Elements:

• 1 = ()
• 2 = (1,2,3,4,5,6,7,8,9)
• 3 = (1,3,5,7,9,2,4,6,8)
• 4 = (1,4,7)(2,5,8)(3,6,9)
• 5 = (1,5,9,4,8,3,7,2,6)
• 6 = (1,6,2,7,3,8,4,9,5)
• 7 = (1,7,4)(2,8,5)(3,9,6)
• 8 = (1,8,6,4,2,9,7,5,3)
• 9 = (1,9,8,7,6,5,4,3,2)

Composition Series

Chief Series

Maximal Subgroups