C₂×C₅×D₁₁ #6357

order	220
isoclinism	isoclinic class of D₁₁
automorphism	Aut(G) = C₂×C₄×AGL(1,𝔽₁₁) (order 880) · Inn(G) = D₁₁ · Out(G) = C₂×C₄×C₅
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₅×D₁₁

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₅

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 110

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(220, 12);