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

Aliases

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

Splittings

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

126 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)(13,14,16)(15,17,20,19,18,21);(1,2,3)(14,17,18)(16,20,21)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 93);