C₃⋊#4181 #92336

order	486
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₃²

Aliases

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₃⋊D₉)
commutator, Fitting, cosocle, hypocenter	C₃×C₃²⋊C₉	C₂
Frattini	C₃²	C₃⋊(C₃⋊D₃)
socle	C₃³	C₃⋊D₃
LCS	G ▷ C₃×C₃²⋊C₉
UCS	C₁ ◁ C₃

207 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 54

A minimal faithful permutation representation — 4 generators on 21 points:

(2,3)(5,7)(6,10)(8,9)(11,12)(14,16)(17,21)(18,20);(14,17,18)(16,20,21);(1,2,3);(4,12,7,10,9,8,6,5,11)(13,14,16)(15,18,20)(17,21,19)

Polycyclic presentation:

2,3^5|b^3=e^2,b^a=b^2e,c^a=c^2,d^a=d^2,e^a=e^2,d^b=df

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 181);