C₃×#352 #4599

order	192
nilpotency class	4
isoclinism	isoclinic class of AΣL(1,𝔽₁₆)
automorphism	Aut(G) = C₂²×B(4,𝔽₂) (order 256) · Inn(G) = #99 · Out(G) = C₂³
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

68 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)(3,9)(4,12,13,7)(5,8)(6,10,14,16)(11,15)(17,18,19);(1,3,5,11)(2,6,8,14)(4,10,13,16)(7,9,12,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 158);