C₃×#3676 #88517

order	432
isoclinism	isoclinic class of Dic₁₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

134 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)(4,9,11,10,5,7,6,12,8)(18,20);(5,7)(6,10)(8,9)(11,12)(13,16,15,14)(17,18)(19,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 164);