C₂×C₃²×C₃⋊D₃ #66481

order	324
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃²

Aliases

direct product	C₂×C₃²×C₃⋊D₃
unambiguous semidirect product	(C₂×C₃)⋊(C₃²×D₃)

	subgroup	G/H
center, hypercenter	C₂×C₃²	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃⁴	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₃²

356 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 3 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 173);