D₁₃⋊C₈ #6117

order	208
isoclinism	isoclinic class of #261
automorphism	Aut(G) = D₄×AGL(1,𝔽₁₃) (order 1248) · Inn(G) = #261 · Out(G) = C₃×D₄
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

D₁₃⋊C₈

C₁₃ ⋊ C₂×C₈

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:

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

Polycyclic presentation:

2^4,13|a^2=c,b^2=d,c^2=d,e^a=e^8,e^c=e^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 28);