C₉×D₈ #3682

order	144
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂×C₃×AGL(1,ℤ/8) (order 192) · Inn(G) = D₄ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₈

33 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 25);