C₄×#676 #64976

order	320
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

Fitting	C₄×C₅×C₈ ⋊ C₂
Sylow	C₅ ⋊ C₄×M₁₆

142 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 314);