C₅²×C₇ #4309

order	175
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×C₇

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 175

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(175, 2);