C₂²×D₂₀ #4140

order	160
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) order 61440
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂²×D₂₀

Fitting	C₂²×C₄×C₅ ⋊ C₂
Sylow	C₅ ⋊ C₂²×D₄

236 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 4 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 215);