order	132
isoclinism	isoclinic class of D₃×D₁₁
automorphism	Aut(G) = D₃×AGL(1,𝔽₁₁) (order 660) · Inn(G) = G · Out(G) = C₅
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₁₁
unambiguous semidirect product	(D₃×C₁₁)⋊C₂
unambiguous semidirect product	(C₃×D₁₁)⋊C₂
unambiguous semidirect product	D₃₃⋊C₂

Splittings

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

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 33

A minimal faithful permutation representation — 2 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(132, 5);