Group 5.1 - Z₅

Name	Z₅
Order	5
Exponent	5
Cyclic	yes
Abelian	yes
Elementary	yes
Abelian Invariants	[ 5 ]
p-Group	yes (5)
Rank	1
Nilpotent	yes
Supersoluble	yes
Soluble	yes
Simple	yes
Perfect	no

Permutation Representation

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

Degree	5
Transitive	yes
Primitive	yes
Regular	yes

Cayley Table:

	1	2	3	4	5
1	1	2	3	4	5
2	2	3	4	5	1
3	3	4	5	1	2
4	4	5	1	2	3
5	5	1	2	3	4

Elements:

1 = ()
2 = (1,2,3,4,5)
3 = (1,3,5,2,4)
4 = (1,4,2,5,3)
5 = (1,5,4,3,2)

Centre:	5.1 = < (1,2,3,4,5) >
Commutator Subgroup:	1
Frattini Subgroup:	1

Composition Series

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

Chief Series

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

Maximal Subgroups