Group 8.2 - Z₂xZ₄

Name	Z₂xZ₄
Order	8
Exponent	4
Cyclic	no
Abelian	yes
Elementary	no
Abelian Invariants	[ 2, 4 ]
p-Group	yes (2)
Rank	2
Nilpotent	yes
Supersoluble	yes
Soluble	yes
Simple	no
Perfect	no

Permutation Representation

< (1,2), (3,4,5,6) >

Degree	6
Transitive	no
Primitive	no
Regular	no

Cayley Table:

	1	2	3	4	5	6	7	8
1	1	2	3	4	5	6	7	8
2	2	3	4	1	6	7	8	5
3	3	4	1	2	7	8	5	6
4	4	1	2	3	8	5	6	7
5	5	6	7	8	1	2	3	4
6	6	7	8	5	2	3	4	1
7	7	8	5	6	3	4	1	2
8	8	5	6	7	4	1	2	3

Elements:

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

Centre:	8.2 = < (3,4,5,6), (1,2) >
Commutator Subgroup:	1
Frattini Subgroup:	2.1 = < (3,5)(4,6) >

Composition Series

< (3,4,5,6), (3,5)(4,6), (1,2) >

< (3,5)(4,6), (1,2) >

Chief Series

< (1,2), (3,4,5,6) >

< (3,5)(4,6), (1,2) >

Maximal Subgroups

< (3,4,5,6), (3,5)(4,6) >

< (1,2), (3,5)(4,6) >

< (1,2)(3,4,5,6), (3,5)(4,6) >