C₄⋊#168 #3936

order	160
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = C₂×AGL(1,𝔽₅)×#120 (order 1280) · Inn(G) = C₂×D₅ · Out(G) = C₂×C₄×D₄
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

C₅ ⋊ C₄⋊C₈

38 conjugacy classes of subgroups.

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

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

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

Polycyclic presentation:

2^5,5|a^2=c,b^2=d,c^2=e,b^a=bd,f^a=f^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 11);