C₃×#431 #5305

order	192
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) = C₂²×#62817 (order 1024) · Inn(G) = C₂² · Out(G) = C₂³×H(5,𝔽₂)
homology	Abelianization (H₁) = C₂²×C₃×C₈ · Schur multiplier (H₂) = C₂×C₄

Aliases

118 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 864);