Group 3.1 - Z
3
Name
Z
3
Order
3
Exponent
3
Cyclic
yes
Abelian
yes
Elementary
yes
Abelian Invariants
[ 3 ]
p-Group
yes (3)
Rank
1
Nilpotent
yes
Supersoluble
yes
Soluble
yes
Simple
yes
Perfect
no
Permutation Representation
<
(1,2,3)
>
Degree
3
Transitive
yes
Primitive
yes
Regular
yes
Cayley Table:
1
2
3
1
1
2
3
2
2
3
1
3
3
1
2
Elements:
1 = ()
2 = (1,2,3)
3 = (1,3,2)
Centre:
3.1
= <
(1,2,3)
>
Commutator Subgroup:
1
Frattini Subgroup:
1
Composition Series
<
(1,2,3)
>
<
()
>
Chief Series
<
(1,2,3)
>
<
()
>
Maximal Subgroups
<
()
>
