C₂×#3928 #64876

order	320
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	Aut(G) = AGL(1,𝔽₅)×#131 (order 640) · Inn(G) = AGL(1,𝔽₅) · Out(G) = #131
homology	Abelianization (H₁) = C₂×C₃₂ · Schur multiplier (H₂) = C₂

Aliases

C₅ ⋊ C₂×C₃₂

34 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 2 generators on 39 points:

(4,5,6,7)(8,9,10,14,11,15,18,24,12,16,19,25,21,27,30,34,13,17,20,26,22,28,31,35,23,29,32,36,33,37,38,39);(1,2)(3,4,5,7,6)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 214);