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G = C₁₃⋊C₃  order 39 = 3·13

The semidirect product of C₁₃ and C₃ acting faithfully

metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary

Aliases: C₁₃⋊C₃, SmallGroup(39,1)

Series: Derived ►Chief ►Lower central ►Upper central

Generators and relations for C₁₃⋊C₃
 G = < a,b | a¹³=b³=1, bab^-1=a⁹ >

Character table of C₁₃⋊C₃

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

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

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

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

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

G:=TransitiveGroup(13,3);

C₁₃⋊C₃ is a maximal subgroup of   C₁₃⋊C₆  C₁₃⋊A₄  C₉₁⋊C₃  C₉₁⋊₄C₃
C₁₃⋊C₃ is a maximal quotient of   C₁₃⋊C₉  C₁₃⋊A₄  C₉₁⋊C₃  C₉₁⋊₄C₃

Matrix representation of C₁₃⋊C₃ ►in GL₃(𝔽₃) generated by

G:=sub<GL(3,GF(3))| [0,2,2,2,1,0,0,2,1],[1,0,0,1,2,2,2,1,0] >;

C₁₃⋊C₃ in GAP, Magma, Sage, TeX

C_{13}\rtimes C_3

% in TeX

G:=Group("C13:C3");

// GroupNames label

G:=SmallGroup(39,1);

// by ID

G=gap.SmallGroup(39,1);

# by ID

G:=PCGroup([2,-3,-13,37]);

// Polycyclic

G:=Group<a,b|a^13=b^3=1,b*a*b^-1=a^9>;

// generators/relations

Export

Subgroup lattice of C₁₃⋊C₃ in TeX
Character table of C₁₃⋊C₃ in TeX