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G = C₂₁  order 21 = 3·7

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C₂₁, also denoted Z₂₁, SmallGroup(21,2)

Series: Derived ►Chief ►Lower central ►Upper central

Generators and relations for C₂₁
 G = < a | a²¹=1 >

Character table of C₂₁

(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21)

G:=sub<Sym(21)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21) );

G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21)]])

G:=TransitiveGroup(21,1);

C₂₁ is a maximal subgroup of   D₂₁  C₇⋊C₉

Matrix representation of C₂₁ ►in GL₁(𝔽₄₃) generated by

G:=sub<GL(1,GF(43))| [40] >;

C₂₁ in GAP, Magma, Sage, TeX

C_{21}

% in TeX

G:=Group("C21");

// GroupNames label

G:=SmallGroup(21,2);

// by ID

G=gap.SmallGroup(21,2);

# by ID

G:=PCGroup([2,-3,-7]);

// Polycyclic

G:=Group<a|a^21=1>;

// generators/relations

Export

Subgroup lattice of C₂₁ in TeX
Character table of C₂₁ in TeX