C₂×C₅×C₁₇ #4293

order	170
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₄×C₁₆ (order 64) · Inn(G) = C₁ · Out(G) = C₄×C₁₆
holomorph	G ⋊ Aut(G) = C₂×AGL(1,𝔽₅)×AGL(1,𝔽₁₇)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₇₀
abelian	C₂×C₅×C₁₇

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 170

A minimal faithful permutation representation — 1 generator on 24 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)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(170, 4);