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) = C₂³

Aliases

C₂×D₄₄

Splittings

Fitting	C₂×C₄×C₁₁ ⋊ C₂
Sylow	C₁₁ ⋊ C₂×D₄

54 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 29);