C₉×C₃⋊D₉ #92288

order	486
isoclinism	isoclinic class of C₃⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₃

Aliases

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

Fitting, Sylow	C₃×C₉² ⋊ C₂
derived	C₃×C₉ ⋊ C₂×C₉

108 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)(4,5,7,6,8,10,9,11,12)(14,16)(15,19)(17,18)(20,21);(1,2,3);(13,21,16,19,18,17,15,14,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 133);