C₂×D₁₀₄ #88157

order	416
isoclinism	isoclinic class of #6095
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₁₀₄

Fitting	C₂×C₈×C₁₃ ⋊ C₂
Sylow	C₁₃ ⋊ C₂×D₈

76 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:

(3,4,8,10,6,9,5,7)(11,12,14,16,18,20,22,23,21,19,17,15,13);(1,2)(4,7)(5,8)(9,10)(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, 124);