Group 4.2 - Z₂xZ₂

Name	Z₂xZ₂
Order	4
Exponent	2
Cyclic	no
Abelian	yes
Elementary	yes
Abelian Invariants	[ 2, 2 ]
p-Group	yes (2)
Rank	2
Nilpotent	yes
Supersoluble	yes
Soluble	yes
Simple	no
Perfect	no

Permutation Representation

< (1,2), (3,4) >

Degree	4
Transitive	no
Primitive	no
Regular	no

Cayley Table:

	1	2	3	4
1	1	2	3	4
2	2	1	4	3
3	3	4	1	2
4	4	3	2	1

Elements:

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

Centre:	4.2 = < (3,4), (1,2) >
Commutator Subgroup:	1
Frattini Subgroup:	1

Composition Series

< (3,4), (1,2) >

Chief Series

< (1,2), (3,4) >

Maximal Subgroups

< (1,2)(3,4) >