C₅×Dic₁₃ #63114

order	260
isoclinism	isoclinic class of D₁₃
automorphism	Aut(G) = C₂×C₄×AGL(1,𝔽₁₃) (order 1248) · Inn(G) = D₁₃ · Out(G) = C₂²×C₃×C₄
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

C₅×Dic₁₃

derived, Sylow	C₁₃ ⋊ C₄×C₅
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);(6,8,7,9)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(260, 2);