C₃×#332 #4579

order	192
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	Aut(G) = C₂³×D₄² (order 512) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂⁵
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 192

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 138);