C₅²×C₉ #6569

order	225
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×GL(2,𝔽₅) (order 2880) · Inn(G) = C₁ · Out(G) = C₂×C₃×GL(2,𝔽₅)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅

Aliases

C₅²×C₉

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 225

A minimal faithful permutation representation — 2 generators on 19 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14);(15,16,17,18,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(225, 4);