D₁₀₄ #6096

order	208
isoclinism	isoclinic class of #6095
automorphism	Aut(G) = AGL(1,ℤ/8)×AGL(1,𝔽₁₃) (order 4992) · Inn(G) = D₅₂ · Out(G) = C₂²×C₃×C₄
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

D₁₀₄

Fitting	C₈×C₁₃ ⋊ C₂
Sylow	C₁₃ ⋊ D₈

22 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 21 points:

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

Polycyclic presentation:

2^4,13|b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 7);