C₂²×#170 #4135

order	160
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	Aut(G) = AGL(1,𝔽₅)×#5934 (order 3840) · Inn(G) = AGL(1,𝔽₅) · Out(G) = #5934
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₅ ⋊ C₂²×C₈

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 210);