order	104
isoclinism	isoclinic class of D₁₃
automorphism	Aut(G) = D₄×AGL(1,𝔽₁₃) (order 1248) · Inn(G) = D₁₃ · Out(G) = C₂×C₃×D₄
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₂×Dic₁₃

Splittings

C₁₃ ⋊ C₂×C₄

16 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(104, 7);