C₃×#340 #4587

order	192
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂×#6628842 (order 1024) · Inn(G) = D₄ · Out(G) = C₂²×#120
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₂³

Aliases

114 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 146);