C₂×D₃×C₁₁ #3611

order	132
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂²×C₅×D₃ (order 120) · Inn(G) = D₃ · Out(G) = C₂²×C₅
holomorph	G ⋊ Aut(G) = AGL(1,𝔽₁₁)×#3811
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₃×C₁₁
unambiguous semidirect product	C₃⋊(C₂²×C₁₁)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₁₁)

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₁

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 66

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(132, 8);