C₃²×C₃⋊C₁₆ #88582

order	432
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₆ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×C₃⋊C₁₆
unambiguous semidirect product	C₃⋊(C₃²×C₁₆)

derived	C₃ ⋊ C₃²×C₁₆
Sylow	C₃³ ⋊ C₁₆

92 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 2 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 229);