C₂²×#676 #66071

order	320
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting	C₂²×C₅×C₈ ⋊ C₂
Sylow	C₅ ⋊ C₂²×M₁₆

298 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1409);