Group 8.3 - Z₂xZ₂xZ₂

Name Z2xZ2xZ2 Order 8 Exponent 2 Cyclic no Abelian yes Elementary yes Abelian Invariants [ 2, 2, 2 ] p-Group yes (2) Rank 3 Nilpotent yes Supersoluble yes Soluble yes Simple no Perfect no

Permutation Representation

Cayley Table:

Elements:

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

Composition Series

Chief Series

Maximal Subgroups