C₁₁⋊C₁₆ #4310

order	176
isoclinism	isoclinic class of D₁₁
automorphism	Aut(G) = C₂×C₄×AGL(1,𝔽₁₁) (order 880) · Inn(G) = D₁₁ · Out(G) = C₂×C₄×C₅
homology	Abelianization (H₁) = C₁₆ · Schur multiplier (H₂) = C₁

Aliases

C₁₁⋊C₁₆

C₁₁ ⋊ C₁₆

	subgroup	G/H
center, Frattini, hypercenter	C₈	D₁₁
commutator, hypocenter	C₁₁	C₁₆
Fitting, cosocle	C₈×C₁₁	C₂
socle, prime radical	C₂×C₁₁	C₈
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₈

10 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 176

A minimal faithful permutation representation — 2 generators on 27 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,14,17,15,18,20,23,16,19,21,24,22,25,26,27);(1,2,4,6,8,10,11,9,7,5,3)

Polycyclic presentation:

2^4,11|a^2=b,b^2=c,c^2=d,e^a=e^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 1);