#6860⋊C₂ #92202

order	486
isoclinism	isoclinic class of #6860⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#6860	C₂
Frattini	C₃³	C₃⋊D₃
socle	C₃²	#272
LCS	G ▷ #6860
UCS	C₁

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 81

A minimal faithful permutation representation — 3 generators on 18 points:

(2,5)(3,8)(4,9)(6,7)(11,13)(12,16)(14,18)(15,17);(1,3,8)(2,4,6)(5,7,9)(10,15,13,12,18,14,16,11,17);(1,8,5,9,7,6,4,2,3)(10,11,13)(12,15,14)(16,18,17)

Polycyclic presentation:

2,3^5|b^3=e^2,c^3=e^2f,b^a=b^2e,c^a=c^2ef^2,d^a=de^2f,e^a=e^2,f^a=f^2,c^b=cd,d^b=def,d^c=df

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 47);