C₃×D₉⋊C₉ #92251

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

Aliases

direct product	C₃×D₉⋊C₉
unambiguous semidirect product	(C₃×D₉)⋊C₉

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

90 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 96);