C₂×#1057 #6121

order	208
isoclinism	isoclinic class of #261
automorphism	Aut(G) = D₄×AGL(1,𝔽₁₃) (order 1248) · Inn(G) = #261 · Out(G) = 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 32);