order	176
isoclinism	isoclinic class of Dic₂₂
automorphism	Aut(G) = B(4,𝔽₂)×AGL(1,𝔽₁₁) (order 7040) · Inn(G) = C₂×D₁₁ · Out(G) = C₅×#120
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×Dic₂₂
unambiguous semidirect product	(C₂×C₁₁)⋊Q₈

Splittings

C₁₁ ⋊ C₂×Q₈

38 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 176

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 27);