C₃×C₉×C₃⋊D₃ #92383

order	486
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₉ · Schur multiplier (H₂) = C₃²

Aliases

direct product	C₃×C₉×C₃⋊D₃
unambiguous semidirect product	C₃⋊(C₃×D₃×C₉)

Fitting, Sylow	C₃³×C₉ ⋊ C₂
derived	C₃² ⋊ C₂×C₃×C₉

288 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 228);