C₃×#323 #4570

order	192
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	Aut(G) = C₂×#23900 (order 512) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂²×D₄
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₂²

Aliases

98 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 129);