C₂×C₈×Dic₃ #5098

order	192
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂×D₃×#347042 (order 6144) · Inn(G) = D₃ · Out(G) = C₂×#347042
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₈×Dic₃

C₃ ⋊ C₂×C₄×C₈

162 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 657);