C₃×D₃×C₃⋊D₃ #66474

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

Aliases

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

Fitting, socle, Sylow	C₃⁴ ⋊ C₂²
derived	C₃³ ⋊ C₂²×C₃

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

224 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 3 generators on 12 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 166);