order	110
isoclinism	isoclinic class of D₁₁
automorphism	Aut(G) = C₄×AGL(1,𝔽₁₁) (order 440) · Inn(G) = D₁₁ · Out(G) = C₄×C₅
holomorph	G ⋊ Aut(G) = AGL(1,𝔽₅)×#11925892⋊C₂
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁

Aliases

C₅×D₁₁

Splittings

Fitting, socle, Hall	C₅×C₁₁ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂×C₅

	subgroup	G/H
center, hypercenter	C₅	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₅

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 55

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(110, 4);