C₃⋊#4183 #92340

order	486
isoclinism	isoclinic class of C₃⋊#4183
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₃²

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×AΣL(1,𝔽₂₇)	C₂
Frattini	C₃²	C₃⋊(C₃⋊D₃)
socle	C₃²	#272
LCS	G ▷ C₃×AΣL(1,𝔽₂₇)
UCS	C₁

207 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 12 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 185);