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G = C₁₁⋊C₅  order 55 = 5·11

The semidirect product of C₁₁ and C₅ acting faithfully

metacyclic, supersoluble, monomial, Z-group, 5-hyperelementary

Aliases: C₁₁⋊C₅, SmallGroup(55,1)

Series: Derived ►Chief ►Lower central ►Upper central

Generators and relations for C₁₁⋊C₅
 G = < a,b | a¹¹=b⁵=1, bab^-1=a³ >

Character table of C₁₁⋊C₅

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

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

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

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

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

G:=TransitiveGroup(11,3);

C₁₁⋊C₅ is a maximal subgroup of   F₁₁
C₁₁⋊C₅ is a maximal quotient of   C₁₁⋊C₂₅

Matrix representation of C₁₁⋊C₅ ►in GL₅(𝔽₃)

G:=sub<GL(5,GF(3))| [2,2,2,0,2,2,2,1,1,1,2,1,0,1,2,0,1,0,0,0,0,1,2,1,1],[1,0,0,0,0,0,0,0,1,0,2,2,1,1,1,0,0,1,0,0,0,1,2,1,1] >;

C₁₁⋊C₅ in GAP, Magma, Sage, TeX

C_{11}\rtimes C_5

% in TeX

G:=Group("C11:C5");

// GroupNames label

G:=SmallGroup(55,1);

// by ID

G=gap.SmallGroup(55,1);

# by ID

G:=PCGroup([2,-5,-11,81]);

// Polycyclic

G:=Group<a,b|a^11=b^5=1,b*a*b^-1=a^3>;

// generators/relations

Export

Subgroup lattice of C₁₁⋊C₅ in TeX
Character table of C₁₁⋊C₅ in TeX