order	192
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂²×D₃×C₈ (order 192) · Inn(G) = D₃ · Out(G) = C₂²×C₈
homology	Abelianization (H₁) = C₂×C₃₂ · Schur multiplier (H₂) = C₂

Aliases

D₃×C₃₂

Splittings

Fitting	C₃×C₃₂ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₃₂

34 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 2 generators on 35 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 5);