C₃×#328 #4575

order	192
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	Aut(G) = C₂³×#120 (order 256) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

80 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)(3,7,8,5)(4,6)(10,13,14,15)(17,18,19);(1,3,4,8)(2,5,6,7)(9,10)(11,15)(12,14)(13,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 134);