Group 2.1 - Z
2
Name
Z
2
Order
2
Exponent
2
Cyclic
yes
Abelian
yes
Elementary
yes
Abelian Invariants
[ 2 ]
p-Group
yes (2)
Rank
1
Nilpotent
yes
Supersoluble
yes
Soluble
yes
Simple
yes
Perfect
no
Permutation Representation
<
(1,2)
>
Degree
2
Transitive
yes
Primitive
yes
Regular
yes
Cayley Table:
1
2
1
1
2
2
2
1
Elements:
1 = ()
2 = (1,2)
Centre:
2.1
= <
(1,2)
>
Commutator Subgroup:
1
Frattini Subgroup:
1
Composition Series
<
(1,2)
>
<
()
>
Chief Series
<
(1,2)
>
<
()
>
Maximal Subgroups
<
()
>
