C₃×#4174 #92270

order	486
isoclinism	isoclinic class of #4174
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

Fitting, Sylow	C₃×AΣL(1,𝔽₂₇) ⋊ C₂
derived	H(3,𝔽₃) ⋊ C₂×C₃²

	subgroup	G/H
center, socle, hypercenter	C₃²	(C₃⋊D₃)⋊C₃
commutator, cosocle, hypocenter	H(3,𝔽₃)	C₂×C₃²
Frattini	C₃²	C₃²×D₃
Fitting	C₃×AΣL(1,𝔽₂₇)	C₂
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₃²

165 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 27

A minimal faithful permutation representation — 2 generators on 12 points:

(5,11,10,8,9,12);(1,2,3)(4,5,8)(6,10,12)(7,9,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 115);