C₂×C₃×D₃₉ #90877

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

Aliases

direct product	C₂×C₃×D₃₉
unambiguous semidirect product	(C₂×C₃)⋊(C₃×D₁₃)

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

44 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 156

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2)(4,5)(6,7,8)(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)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 52);