C₃×Dic₉ #1079

order	108
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = C₂²×AGL(1,ℤ/9) (order 216) · Inn(G) = D₉ · Out(G) = C₂²×C₃
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

derived	C₉ ⋊ C₃×C₄
Sylow	C₃×C₉ ⋊ C₄

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(108, 6);