Go

G = C₁₃  order 13

Cyclic group

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

Aliases: C₁₃, also denoted Z₁₃, SmallGroup(13,1)

Series: Derived ►Chief ►Lower central ►Upper central ►Jennings

Generators and relations for C₁₃
 G = < a | a¹³=1 >

Character table of C₁₃

(1 2 3 4 5 6 7 8 9 10 11 12 13)

G:=sub<Sym(13)| (1,2,3,4,5,6,7,8,9,10,11,12,13)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13) );

G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13)]])

G:=TransitiveGroup(13,1);

C₁₃ is a maximal subgroup of   D₁₃  C₁₃⋊C₃  C₁₆₉  C₃³⋊C₁₃
C₁₃ is a maximal quotient of   C₁₆₉  C₃³⋊C₁₃

Matrix representation of C₁₃ ►in GL₁(𝔽₅₃) generated by

G:=sub<GL(1,GF(53))| [13] >;

C₁₃ in GAP, Magma, Sage, TeX

C_{13}

% in TeX

G:=Group("C13");

// GroupNames label

G:=SmallGroup(13,1);

// by ID

G=gap.SmallGroup(13,1);

# by ID

G:=PCGroup([1,-13]:ExponentLimit:=1);

// Polycyclic

G:=Group<a|a^13=1>;

// generators/relations

Export

Subgroup lattice of C₁₃ in TeX
Character table of C₁₃ in TeX