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G = C₁₁  order 11

Cyclic group

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

Aliases: C₁₁, also denoted Z₁₁, SmallGroup(11,1)

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

Generators and relations for C₁₁
 G = < a | a¹¹=1 >

Character table of C₁₁

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

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

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

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

G:=TransitiveGroup(11,1);

C₁₁ is a maximal subgroup of   D₁₁  C₁₁⋊C₅  C₁₂₁  C₂₃⋊C₁₁
C₁₁ is a maximal quotient of   C₁₂₁  C₂₃⋊C₁₁

Matrix representation of C₁₁ ►in GL₁(𝔽₂₃) generated by

G:=sub<GL(1,GF(23))| [8] >;

C₁₁ in GAP, Magma, Sage, TeX

C_{11}

% in TeX

G:=Group("C11");

// GroupNames label

G:=SmallGroup(11,1);

// by ID

G=gap.SmallGroup(11,1);

# by ID

G:=PCGroup([1,-11]:ExponentLimit:=1);

// Polycyclic

G:=Group<a|a^11=1>;

// generators/relations

Export

Subgroup lattice of C₁₁ in TeX
Character table of C₁₁ in TeX