C₂²×C₂²⋊D₅ #4152

order	160
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = AGL(1,𝔽₅)×#72209641 (order 30720) · Inn(G) = C₂×D₅ · Out(G) = #72215537
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂²×C₂²⋊D₅

Fitting	C₂⁴×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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 227);