C₃⋊(D₉⋊C₉) #92293

order	486
isoclinism	isoclinic class of C₃⋊AGL(1,ℤ/9)
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₃

Aliases

C₃⋊(D₉⋊C₉)

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

90 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 21 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 138);