C₅×#595 #66771

order	340
isoclinism	isoclinic class of #595
automorphism	Aut(G) = C₄×AGL(1,𝔽₁₇) (order 1088) · Inn(G) = #595 · Out(G) = C₄²
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

Fitting, socle, Hall	C₅×C₁₇ ⋊ C₄
derived, Sylow	C₁₇ ⋊ C₄×C₅

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 85

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(340, 5);