C₃×#346 #4593

order	192
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) = C₂²×#2010 (order 512) · Inn(G) = C₂² · Out(G) = C₂²×#120
homology	Abelianization (H₁) = C₃×C₄×C₈ · Schur multiplier (H₂) = C₂

Aliases

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 2 generators on 23 points:

(5,6,7,11,8,12,13,18,9,10,14,16,15,17,19,20)(21,22,23);(1,2,3,4)(6,10)(11,16)(12,17)(18,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 152);