order	88
isoclinism	isoclinic class of D₁₁
automorphism	Aut(G) = D₄×AGL(1,𝔽₁₁) (order 880) · Inn(G) = D₁₁ · Out(G) = C₅×D₄
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×Dic₁₁
unambiguous semidirect product	(C₂×C₁₁)⋊C₄

Splittings

C₁₁ ⋊ C₂×C₄

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 88

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(88, 6);