C₃×C₅² #659

order	75
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×GL(2,𝔽₅) (order 960) · Inn(G) = C₁ · Out(G) = C₂×GL(2,𝔽₅)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅

Aliases

C₃×C₅²

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 75

A minimal faithful permutation representation — 2 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(75, 3);