C₃×#432 #5306

order	192
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) = C₂²×#62817 (order 1024) · Inn(G) = C₂³ · Out(G) = C₂⁷
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

110 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 96

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 865);