C₃×#330 #4577

order	192
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	Aut(G) = C₂×#12687 (order 512) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂×C₂²⋊C₄
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

60 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 136);