Group 4.1 - Z₄

Name Z4 Order 4 Exponent 4 Cyclic yes Abelian yes Elementary no Abelian Invariants [ 4 ] p-Group yes (2) Rank 1 Nilpotent yes Supersoluble yes Soluble yes Simple no Perfect no

Permutation Representation

Cayley Table:

Elements:

• 1 = ()
• 2 = (1,2,3,4)
• 3 = (1,3)(2,4)
• 4 = (1,4,3,2)

Composition Series

Chief Series

Maximal Subgroups