#6882⋊C₂ #92195

order	486
isoclinism	isoclinic class of #6882⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	#733	C₂×C₃
Frattini	C₃×C₉	C₃×D₃
Fitting	#6882	C₂
socle	C₃	#4178
prime radical	#733⋊C₂	C₃
LCS	G ▷ #733
UCS	C₁

29 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 27 points:

(2,20,26,7,19,25,9,14,17,5,18,21,8,27,16,22,6,15)(3,12,24,10,11,23)(4,13);(1,9,5,4,8,7,13,2,22)(3,19,25,11,18,15,24,6,21)(10,26,14,23,17,20,12,16,27)

Polycyclic presentation:

2,3^5|b^3=e,c^3=f,d^3=f^2,c^a=c^2f^2,d^a=d^2ef,f^a=f^2,c^b=cd,d^b=df,d^c=def,e^c=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 40);