C₂²×Dic₉ #3702

order	144
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = AGL(1,ℤ/9)×#5934 (order 10368) · Inn(G) = D₉ · Out(G) = C₃×#5934
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×Dic₉

C₉ ⋊ C₂²×C₄

81 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 45);