C₉×Dic₆ #6207

order	216
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×C₃×D₃×D₄ (order 288) · Inn(G) = C₂×D₃ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×Dic₆
unambiguous semidirect product	C₃⋊(Q₈×C₉)

C₃×C₉ ⋊ Q₈

42 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(216, 44);