C₂²⋊Dic₁₃ #6108

order	208
isoclinism	isoclinic class of Dic₂₆
automorphism	Aut(G) = #120×AGL(1,𝔽₁₃) (order 4992) · Inn(G) = C₂×D₁₃ · Out(G) = C₃×C₄×D₄
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₂²⋊Dic₁₃

C₁₃ ⋊ C₂²⋊C₄

34 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:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 19);