C₃×#3750 #88841

order	432
isoclinism	isoclinic class of #634
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₃³ ⋊ C₄⋊C₄

220 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 488);