C₁₃×Dic₅ #63113

order	260
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂×C₃×C₄×AGL(1,𝔽₅) (order 480) · Inn(G) = D₅ · Out(G) = C₂²×C₃×C₄
homology	Abelianization (H₁) = C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

C₁₃×Dic₅

derived, Sylow	C₅ ⋊ C₄×C₁₃
Hall	C₅×C₁₃ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 260

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(260, 1);