C₃⋊(C₉⋊C₁₆) #88385

order	432
isoclinism	isoclinic class of C₃⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₁₆ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product	C₃⋊(C₉⋊C₁₆)
unambiguous semidirect product	C₉⋊(C₃⋊C₁₆)

C₃×C₉ ⋊ C₁₆

50 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 432

A minimal faithful permutation representation — 3 generators on 28 points:

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

Polycyclic presentation:

2^4,3^3|a^2=b,b^2=c,c^2=d,e^3=g^2,e^a=e^2g,f^a=f^2,g^a=g^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 32);