C₃×#4169 #92249

order	486
isoclinism	isoclinic class of #4169
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃²

Aliases

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

	subgroup	G/H
center, hypercenter	C₃	#4169
commutator, cosocle, hypocenter	C₃×C₉	C₂×C₃²
Frattini	C₃²	C₃²×D₃
Fitting	C₃×C₃²⋊C₉	C₂
socle	C₃³	C₃×D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₃

138 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 94);