order	208
isoclinism	isoclinic class of D₁₃
automorphism	Aut(G) = C₂³×AGL(1,𝔽₁₃) (order 1248) · Inn(G) = D₁₃ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

C₈×D₁₃

Splittings

Fitting	C₈×C₁₃ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₈

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 104

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 4);