order	208
isoclinism	isoclinic class of Dic₂₆
automorphism	Aut(G) = B(4,𝔽₂)×AGL(1,𝔽₁₃) (order 9984) · Inn(G) = C₂×D₁₃ · Out(G) = C₃×#525
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×Dic₂₆
unambiguous semidirect product	(C₂×C₁₃)⋊Q₈

Splittings

C₁₃ ⋊ C₂×Q₈

38 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 35);