C₄²×Dic₃ #4930

order	192
isoclinism	isoclinic class of D₃
automorphism	Aut(G) order 73728
homology	Abelianization (H₁) = C₄³ · Schur multiplier (H₂) = C₄³

Aliases

direct product	C₄²×Dic₃
unambiguous semidirect product	C₃⋊C₄³

C₃ ⋊ C₄³

258 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 489);