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G = C₂  order 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

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

Character table of C₂

(1 2)

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

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

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

G:=TransitiveGroup(2,1);

C₂ is a maximal subgroup of
 C₄
 D_p: S₃  D₅  D₇  D₁₁  D₁₃  D₁₇  D₁₉  D₂₃ ...
C₂ is a maximal quotient of
 C₄  S₅  PGL₂(𝔽₇)
 D_p: S₃  D₅  D₇  D₁₁  D₁₃  D₁₇  D₁₉  D₂₃ ...

Matrix representation of C₂ ►in GL₁(ℤ) generated by

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

Export

Subgroup lattice of C₂ in TeX
Character table of C₂ in TeX