C₂×C₃²×H(3,𝔽₃) #92406

order	486
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃⁴ · Schur multiplier (H₂) = C₃⁷

Aliases

direct product	C₂×C₃²×H(3,𝔽₃)
unambiguous semidirect product	(C₂×C₃²)⋊C₃³

	subgroup	G/H
center, socle	C₂×C₃³	C₃²
commutator, Frattini, cosocle	C₃	C₂×C₃⁴
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃³ ◁ G

900 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 162

A minimal faithful permutation representation — 4 generators on 17 points:

(1,2)(6,7,8);(3,4,5);(10,12,15)(13,17,16);(9,10,13)(11,12,16)(14,15,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 251);