C₃×C₃⋊Dic₉ #66404

order	324
isoclinism	isoclinic class of C₃⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₃⋊Dic₉
unambiguous semidirect product	C₃⋊(C₃×Dic₉)

derived	C₃×C₉ ⋊ C₃×C₄
Sylow	C₃²×C₉ ⋊ C₄

90 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 96);