#6881⋊C₂ #92194

order	486
isoclinism	isoclinic class of #6881⋊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	#6881	C₂
socle	C₃	#4178
LCS	G ▷ #733
UCS	C₁

30 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:

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

Polycyclic presentation:

2,3^5|b^3=e,c^3=f^2,d^3=f^2,c^a=c^2f,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, 39);