order	468
isoclinism	isoclinic class of D₃×D₁₃⋊C₃
automorphism	Aut(G) = D₃×AGL(1,𝔽₁₃) (order 936) · Inn(G) = G · Out(G) = C₂
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₁₃⋊C₃
unambiguous semidirect product	D₁₃⋊(C₃×D₃)
unambiguous semidirect product	(D₃×D₁₃)⋊C₃
unambiguous semidirect product	(C₃×D₁₃⋊C₃)⋊C₂
unambiguous semidirect product	(D₃×C₁₃⋊C₃)⋊C₂
unambiguous semidirect product	(C₃⋊(D₁₃⋊C₃))⋊C₂

Splittings

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃	C₂²×C₃
LCS	G ▷ C₃×C₁₃
UCS	C₁

44 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 39

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 31);