C₄×C₈×Dic₃ #69747

order	384
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₄²×C₈ · Schur multiplier (H₂) = C₄³

Aliases

C₄×C₈×Dic₃

C₃ ⋊ C₄²×C₈

408 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 384

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 2323);