C₃×#347 #4594

order	192
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	Aut(G) = C₂×#2010 (order 256) · Inn(G) = C₄² · Out(G) = C₂×D₄
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₁

Aliases

46 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 153);