order	144
isoclinism	isoclinic class of #204
automorphism	Aut(G) = C₂×D₃×AGL(1,ℤ/8) (order 384) · Inn(G) = D₁₂ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

C₃×Dic₁₂

Splittings

C₃² ⋊ Q₁₆

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3)(4,5,6)(7,20,10,9,11,17,16,18)(8,22,13,12,14,15,19,21);(5,6)(7,14,11,8)(9,22,18,15)(10,13,16,19)(12,17,21,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 73);