C₃×#382 #5256

order	192
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 8192
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²×C₄

Aliases

154 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 192

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 815);