Dic₅×D₁₁ #89164

order	440
isoclinism	isoclinic class of D₅×D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

Dic₅×D₁₁

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×D₁₁
commutator, hypocenter	C₅×C₁₁	C₂×C₄
Fitting, socle, cosocle	C₂×C₅×C₁₁	C₂²
prime radical	C₂×C₅×D₁₁	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂

32 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 17);