C₂²×D₅₅ #89197

order	440
isoclinism	isoclinic class of D₅₅
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×D₅₅

	subgroup	G/H
center, hypercenter	C₂²	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂³
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₁	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂²

64 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 50);