Group 16.5 - Z₂xZ₂xZ₂xZ₂

Name Z2xZ2xZ2xZ2 Order 16 Exponent 2 Cyclic no Abelian yes Elementary yes Abelian Invariants [ 2, 2, 2, 2 ] p-Group yes (2) Rank 4 Nilpotent yes Supersoluble yes Soluble yes Simple no Perfect no

Permutation Representation

Cayley Table:

Elements:

• 1 = ()
• 2 = (7,8)
• 3 = (5,6)
• 4 = (5,6)(7,8)
• 5 = (3,4)
• 6 = (3,4)(7,8)
• 7 = (3,4)(5,6)
• 8 = (3,4)(5,6)(7,8)
• 9 = (1,2)
• 10 = (1,2)(7,8)
• 11 = (1,2)(5,6)
• 12 = (1,2)(5,6)(7,8)
• 13 = (1,2)(3,4)
• 14 = (1,2)(3,4)(7,8)
• 15 = (1,2)(3,4)(5,6)
• 16 = (1,2)(3,4)(5,6)(7,8)

Composition Series

Chief Series

Maximal Subgroups