C₃×#344 #4591

order	192
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	Aut(G) = C₂×#63011 (order 512) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂⁵
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₂²

Aliases

90 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)(3,9,10,6)(4,8)(5,7)(11,15,16,13)(12,14)(17,18,19);(1,3,4,11,5,10,12,16)(2,6,8,13,7,9,14,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 150);