C₃³×C₃⋊D₃ #92412

order	486
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³ · Schur multiplier (H₂) = C₃⁴

Aliases

direct product	C₃³×C₃⋊D₃
unambiguous semidirect product	C₃⋊(C₃³×D₃)

Fitting, socle, Sylow	C₃⁵ ⋊ C₂
derived	C₃² ⋊ C₂×C₃³

	subgroup	G/H
center, hypercenter	C₃³	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₃³
Frattini	C₁	G
Fitting, socle	C₃⁵	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₃³

1584 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 54

A minimal faithful permutation representation — 3 generators on 15 points:

(7,8,9)(11,12)(14,15);(4,5,6)(13,14,15);(1,2,3)(10,11,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 257);