C₉×Dic₁₂ #88466

order	432
isoclinism	isoclinic class of #204
automorphism	Aut(G) = C₂×C₃×D₃×AGL(1,ℤ/8) (order 1152) · Inn(G) = D₁₂ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×Dic₁₂

C₃×C₉ ⋊ Q₁₆

62 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2,3)(4,5,7,6,8,10,9,11,12)(13,15,22,26,17,24,16,23)(14,18,25,28,20,27,19,21);(2,3)(13,14,17,20)(15,21,24,28)(16,25,22,19)(18,26,27,23)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 113);