C₂×#3930 #65189

order	320
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₂×C₅×C₁₆ ⋊ C₂
Sylow	C₅ ⋊ C₂×M₃₂

90 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 3 generators on 23 points:

(3,4,6,7,5)(8,9,10,14,11,15,16,21,12,13,17,19,18,20,22,23);(1,2)(4,5)(6,7)(9,13)(14,19)(15,20)(21,23);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 527);