order	175
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄×C₅ (order 120) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄×C₅
holomorph	G ⋊ Aut(G) = AGL(1,𝔽₇)×AGL(1,ℤ/25)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₇₅
abelian	C₇×C₂₅

Subgroups

6 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 175

A minimal faithful permutation representation — 1 generator on 32 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)(26,27,28,29,30,31,32)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(175, 1);