C₃×#430 #5304

order	192
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	Aut(G) = C₂×#511819 (order 1024) · Inn(G) = C₂×D₄ · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

102 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 863);