C₂×#6094 #88154

order	416
isoclinism	isoclinic class of Dic₂₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₂×C₈×C₁₃ ⋊ C₂
Sylow	C₁₃ ⋊ C₂×M₁₆

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 3 generators on 23 points:

(3,4,5,8,6,7,9,10)(11,12,14,16,18,20,22,23,21,19,17,15,13);(1,2)(4,7)(8,10)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 121);