order	220
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂²×C₅×AGL(1,𝔽₅) (order 400) · Inn(G) = D₅ · Out(G) = C₂³×C₅
homology	Abelianization (H₁) = C₄×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

C₁₁×Dic₅

Splittings

derived, Sylow	C₅ ⋊ C₄×C₁₁
Hall	C₅×C₁₁ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 220

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(220, 3);