C₃×#413 #5287

order	192
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	Aut(G) = C₂×#7622880 (order 1024) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂³×D₄
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂³

Aliases

150 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 846);