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G = C₁₅  order 15 = 3·5

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C₁₅, also denoted Z₁₅, SmallGroup(15,1)

Series: Derived ►Chief ►Lower central ►Upper central

Generators and relations for C₁₅
 G = < a | a¹⁵=1 >

Character table of C₁₅

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

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

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

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

G:=TransitiveGroup(15,1);

C₁₅ is a maximal subgroup of   D₁₅  F₁₆  He₅⋊C₃  C₃₁⋊C₁₅
C₁₅ is a maximal quotient of   F₁₆  C₃₁⋊C₁₅

Matrix representation of C₁₅ ►in GL₁(𝔽₃₁) generated by

G:=sub<GL(1,GF(31))| [19] >;

C₁₅ in GAP, Magma, Sage, TeX

C_{15}

% in TeX

G:=Group("C15");

// GroupNames label

G:=SmallGroup(15,1);

// by ID

G=gap.SmallGroup(15,1);

# by ID

G:=PCGroup([2,-3,-5]);

// Polycyclic

G:=Group<a|a^15=1>;

// generators/relations

Export

Subgroup lattice of C₁₅ in TeX
Character table of C₁₅ in TeX