C₁₇×Dic₅ #66767

order	340
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂×C₁₆×AGL(1,𝔽₅) (order 640) · Inn(G) = D₅ · Out(G) = C₂²×C₁₆
homology	Abelianization (H₁) = C₄×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

C₁₇×Dic₅

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

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 340

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,24,25,26);(18,20,19,21)(23,26)(24,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(340, 1);