C₂×C₄×D₁₁ #4337

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) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₄×D₁₁

Fitting	C₂×C₄×C₁₁ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂²×C₄

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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 28);