order	96
isoclinism	isoclinic class of #204
automorphism	Aut(G) = D₃×#23882 (order 1536) · Inn(G) = D₁₂ · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

C₂×Dic₁₂

Splittings

C₃ ⋊ C₂×Q₁₆

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 112);