C₂×D₅×D₁₁ #89194

order	440
isoclinism	isoclinic class of D₅×D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×D₅×D₁₁
unambiguous semidirect product	(D₅×C₁₁)⋊C₂²
unambiguous semidirect product	(C₅×D₁₁)⋊C₂²
unambiguous semidirect product	D₅₅⋊C₂²

	subgroup	G/H
center, hypercenter	C₂	D₅×D₁₁
commutator, cosocle, hypocenter	C₅×C₁₁	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁	C₂²
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂

64 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 47);