order	468
isoclinism	isoclinic class of C₃⋊D₃₉
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃⋊D₃₉
unambiguous semidirect product	(C₂×C₃)⋊D₃₉
unambiguous semidirect product	(C₂×C₁₃)⋊(C₃⋊D₃)

Splittings

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₃₉
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃	C₂
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 234

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2)(4,5)(7,8)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21);(1,2)(3,4,5)(9,10,12,14,16,18,20,21,19,17,15,13,11);(6,7,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 54);