C₃×#335 #4582

order	192
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂²×#3003 (order 512) · Inn(G) = D₄ · Out(G) = C₂³×D₄
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₂

Aliases

54 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 141);