C₂×C₁₃×C₃⋊D₃ #90878

order	468
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

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

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₃

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 53);