C₂²×Dic₁₃ #6132

order	208
isoclinism	isoclinic class of D₁₃
automorphism	Aut(G) = AGL(1,𝔽₁₃)×#5934 (order 29952) · Inn(G) = D₁₃ · Out(G) = C₂×C₃×#5934
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×Dic₁₃

C₁₃ ⋊ C₂²×C₄

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 43);