C₃×#4181 #92290

order	486
isoclinism	isoclinic class of #4181
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

Fitting, Sylow	C₃×C₃²⋊C₉ ⋊ C₂
derived	C₃²⋊C₉ ⋊ C₂×C₃

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

156 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 135);