C₈×Dic₆ #4678

order	192
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂³×D₃×#120 (order 1536) · Inn(G) = C₂×D₃ · Out(G) = C₂⁴×D₄
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

C₃ ⋊ C₈×Q₈

102 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 237);