C₂×#208 #921

order	96
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×D₃×B(4,𝔽₂) (order 768) · Inn(G) = C₂×D₃ · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₃ ⋊ C₂×M₁₆

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 13 points:

(1,2)(3,4,5)(7,10)(11,13);(4,5)(6,7,8,11,9,10,12,13);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 128);