order	104
isoclinism	isoclinic class of D₁₃
automorphism	Aut(G) = C₂²×AGL(1,𝔽₁₃) (order 624) · Inn(G) = D₁₃ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₄×D₁₃

Splittings

Fitting	C₄×C₁₃ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₄

16 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 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)(14,15,16,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(104, 5);