order	208
automorphism	Aut(G) = C₂×S₄×AGL(1,𝔽₁₃) (order 7488) · Inn(G) = C₂²×D₁₃ · Out(G) = C₂²×C₃×D₃
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Q₈×D₁₃

Splittings

Fitting	Q₈×C₁₃ ⋊ C₂
Sylow	C₁₃ ⋊ C₂×Q₈

38 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 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)(14,16,17,21)(15,18,19,20);(14,15,17,19)(16,20,21,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 41);