C₃⁴×D₃ #92411

order	486
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃⁴ · Schur multiplier (H₂) = C₃⁶

Aliases

direct product	C₃⁴×D₃
unambiguous semidirect product	C₃⋊(C₂×C₃⁴)

Fitting, socle, Sylow	C₃⁵ ⋊ C₂
derived	C₃ ⋊ C₂×C₃⁴

	subgroup	G/H
center, hypercenter	C₃⁴	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃⁴
Frattini	C₁	G
Fitting, socle	C₃⁵	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃⁴

1968 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 162

A minimal faithful permutation representation — 4 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 256);