C₂×#1055 #6098

order	208
isoclinism	isoclinic class of D₁₃
automorphism	Aut(G) = C₂×D₄×AGL(1,𝔽₁₃) (order 2496) · Inn(G) = D₁₃ · Out(G) = C₂²×C₃×D₄
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

C₁₃ ⋊ C₂×C₈

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 2 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 9);