C₂×#3941 #65254

order	320
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

Fitting	C₂×C₅×C₄⋊C₄ ⋊ C₂
Sylow	C₅ ⋊ C₂×#102

202 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 592);