C₃×#410 #5284

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) = C₂²×C₄

Aliases

158 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)(3,9,11,6)(4,7)(5,8)(10,15,16,13)(12,14)(17,18,19);(1,3)(2,6)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 843);