C₂×C₅×C₇ #602

order	70
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄ (order 24) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄
holomorph	G ⋊ Aut(G) = C₂×AGL(1,𝔽₅)×AGL(1,𝔽₇)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 70

A minimal faithful permutation representation — 1 generator on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(70, 4);