C₂×C₃×Dic₆ #3815

order	144
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×D₃×B(4,𝔽₂) (order 768) · Inn(G) = C₂×D₃ · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×C₃×Dic₆
unambiguous semidirect product	(C₂×C₃)⋊(C₃×Q₈)

C₃² ⋊ C₂×Q₈

84 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 158);