order	208
isoclinism	isoclinic class of Dic₂₆
automorphism	Aut(G) = #120×AGL(1,𝔽₁₃) (order 4992) · Inn(G) = C₂×D₁₃ · Out(G) = C₂×C₃×#41
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×C₂²⋊D₁₃
unambiguous semidirect product	C₂³⋊D₁₃

Splittings

Fitting	C₂³×C₁₃ ⋊ C₂
Sylow	C₁₃ ⋊ C₂×D₄

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 104

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 44);