C₂×C₃×C₃⋊(C₃⋊D₃) #66482

order	324
isoclinism	isoclinic class of C₃⋊(C₃⋊D₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₃³

Aliases

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

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊(C₃⋊D₃)
commutator, cosocle, hypocenter	C₃³	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃⁴	C₂
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂×C₃

436 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 4 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 174);