C₂²×D₃×C₉ #6272

order	216
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂×C₃×D₃×S₄ (order 864) · Inn(G) = D₃ · Out(G) = C₂×C₃×S₄
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂²×D₃×C₉
unambiguous semidirect product	C₃⋊(C₂³×C₉)
unambiguous semidirect product	(C₂×C₃)⋊(C₂²×C₉)

106 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(216, 109);