order	144
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×D₃×#120 (order 384) · Inn(G) = C₂×D₃ · Out(G) = C₂²×D₄
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×C₄⋊Dic₃
unambiguous semidirect product	C₄⋊(C₃×Dic₃)

Splittings

C₃² ⋊ C₄⋊C₄

60 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 78);