order	192
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂×D₃×#131 (order 384) · Inn(G) = D₃ · Out(G) = C₂×#131
homology	Abelianization (H₁) = C₂×C₃₂ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃⋊C₃₂
unambiguous semidirect product	(C₂×C₃)⋊C₃₂

Splittings

C₃ ⋊ C₂×C₃₂

34 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2)(4,5)(6,7,8,12,9,13,16,22,10,14,17,23,19,25,28,32,11,15,18,24,20,26,29,33,21,27,30,34,31,35,36,37);(1,2)(3,4,5)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 57);