order	160
isoclinism	isoclinic class of #700
automorphism	Aut(G) = AGL(1,𝔽₅)×B(4,𝔽₂) (order 1280) · Inn(G) = C₂×AGL(1,𝔽₅) · Out(G) = #120
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product	C₂×C₂²⋊AGL(1,𝔽₅)
unambiguous semidirect product	D₅⋊(C₂²⋊C₄)
unambiguous semidirect product	(C₂×AGL(1,𝔽₅))⋊C₂²

Splittings

Fitting	C₂³×C₅ ⋊ C₄
Sylow	C₅ ⋊ C₂×C₂²⋊C₄

132 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 3 generators on 11 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 212);