Dic₁₁⋊C₄ #4320

order	176
isoclinism	isoclinic class of Dic₂₂
automorphism	Aut(G) = C₂⁴×AGL(1,𝔽₁₁) (order 1760) · Inn(G) = C₂×D₁₁ · Out(G) = C₂³×C₅
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

Dic₁₁⋊C₄

C₁₁ ⋊ C₄⋊C₄

26 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 176

A minimal faithful permutation representation — 2 generators on 19 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 11);