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G = C2order 2

Cyclic group

p-group, cyclic, elementary abelian, simple, monomial, rational

Aliases: C2, also denoted Z2, SmallGroup(2,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C2
C1 — C2
C1 — C2
C1 — C2
C1 — C2

Generators and relations for C2
 G = < a | a2=1 >


Character table of C2

 class 12
 size 11
ρ111    trivial
ρ21-1    linear of order 2 faithful

Permutation representations of C2
Regular action on 2 points - transitive group 2T1
Generators in S2
(1 2)

G:=sub<Sym(2)| (1,2)>;

G:=Group( (1,2) );

G=PermutationGroup([(1,2)])

G:=TransitiveGroup(2,1);

Polynomial with Galois group C2 over ℚ
actionf(x)Disc(f)
2T1x2+1-22

Matrix representation of C2 in GL1(ℤ) generated by

-1
G:=sub<GL(1,Integers())| [-1] >;

C2 in GAP, Magma, Sage, TeX

C_2
% in TeX

G:=Group("C2");
// GroupNames label

G:=SmallGroup(2,1);
// by ID

G=gap.SmallGroup(2,1);
# by ID

G:=PCGroup([1,-2]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^2=1>;
// generators/relations

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