C₉⋊C₃₂ #63353

order	288
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = C₂×C₈×AGL(1,ℤ/9) (order 864) · Inn(G) = D₉ · Out(G) = C₂×C₃×C₈
homology	Abelianization (H₁) = C₃₂ · Schur multiplier (H₂) = C₁

Aliases

C₉⋊C₃₂

C₉ ⋊ C₃₂

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 2 generators on 41 points:

(2,4)(3,7)(5,6)(8,9)(10,11,12,16,13,17,20,26,14,18,21,27,23,29,32,36,15,19,22,28,24,30,33,37,25,31,34,38,35,39,40,41);(1,9,4,7,6,5,3,2,8)

Polycyclic presentation:

2^5,3^2|a^2=b,b^2=c,c^2=d,d^2=e,f^3=g^2,f^a=f^2g,g^a=g^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 1);