order	208
automorphism	Aut(G) = C₂×D₄×AGL(1,𝔽₁₃) (order 2496) · Inn(G) = C₂²×D₁₃ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₄×D₁₃

Splittings

Fitting	D₄×C₁₃ ⋊ C₂
Sylow	C₁₃ ⋊ C₂×D₄

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 52

A minimal faithful permutation representation — 3 generators on 17 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)(15,17);(14,15)(16,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 39);