order	192
automorphism	Aut(G) = C₂×D₃×AGL(1,ℤ/16) (order 1536) · Inn(G) = D₃×D₈ · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₃×D₁₆

Splittings

Fitting	C₃×D₁₆ ⋊ C₂
Sylow	C₃ ⋊ C₂×D₁₆

98 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 469);