D₃×Dic₆ #3794

order	144
automorphism	Aut(G) = C₂×D₃²×D₄ (order 576) · Inn(G) = C₂×D₃² · Out(G) = C₂³
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

direct product	D₃×Dic₆
unambiguous semidirect product	(C₃×D₃)⋊Q₈

C₃² ⋊ C₂×Q₈

82 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 137);