C₂×#4018 #65806

order	320
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

Fitting	C₂×C₄²×C₅ ⋊ C₂
Sylow	C₅ ⋊ C₂×#117

330 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 4 generators on 19 points:

(3,4,5,6)(7,8,10,11,9)(13,17)(16,19);(1,2)(12,14,15,18)(13,16,17,19);(8,9)(10,11)(12,13)(14,16)(15,17)(18,19);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1144);