C₂×C₅×C₉ #777

order	90
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄ (order 24) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄
holomorph	G ⋊ Aut(G) = C₂×AGL(1,𝔽₅)×AGL(1,ℤ/9)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₀
abelian	C₂×C₅×C₉

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 90

A minimal faithful permutation representation — 1 generator on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(90, 4);