C₂²×#685 #66121

order	320
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

Fitting	C₂³×C₄×C₅ ⋊ C₂
Sylow	C₅ ⋊ C₂²×C₂²⋊C₄

674 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1459);