order	176
isoclinism	isoclinic class of D₁₁
automorphism	Aut(G) = #120×AGL(1,𝔽₁₁) (order 3520) · Inn(G) = D₁₁ · Out(G) = C₅×#120
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

direct product	C₄×Dic₁₁
unambiguous semidirect product	C₁₁⋊C₄²

Splittings

C₁₁ ⋊ C₄²

30 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 10);