C₉⋊C₁₆ #3658

order	144
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = C₂×C₄×AGL(1,ℤ/9) (order 432) · Inn(G) = D₉ · Out(G) = C₂×C₃×C₄
homology	Abelianization (H₁) = C₁₆ · Schur multiplier (H₂) = C₁

Aliases

C₉⋊C₁₆

C₉ ⋊ C₁₆

15 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:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 1);