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G = C₁₉  order 19

Cyclic group

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

Aliases: C₁₉, also denoted Z₁₉, SmallGroup(19,1)

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

Generators and relations for C₁₉
 G = < a | a¹⁹=1 >

Character table of C₁₉

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

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

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

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

G:=TransitiveGroup(19,1);

C₁₉ is a maximal subgroup of   D₁₉  C₁₉⋊C₃  C₃₆₁
C₁₉ is a maximal quotient of   C₃₆₁

Matrix representation of C₁₉ ►in GL₁(𝔽₁₉₁) generated by

G:=sub<GL(1,GF(191))| [150] >;

C₁₉ in GAP, Magma, Sage, TeX

C_{19}

% in TeX

G:=Group("C19");

// GroupNames label

G:=SmallGroup(19,1);

// by ID

G=gap.SmallGroup(19,1);

# by ID

G:=PCGroup([1,-19]:ExponentLimit:=1);

// Polycyclic

G:=Group<a|a^19=1>;

// generators/relations

Export

Subgroup lattice of C₁₉ in TeX
Character table of C₁₉ in TeX