D₉⋊H(3,𝔽₃) #92261

order	486
isoclinism	isoclinic class of D₉⋊H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃²

Aliases

unambiguous semidirect product	D₉⋊H(3,𝔽₃)
unambiguous semidirect product	(C₃×AGL(1,ℤ/9))⋊C₃

91 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 54

A minimal faithful permutation representation — 2 generators on 18 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 106);