C₃×#322 #4569

order	192
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) = C₂×#234591 (order 1024) · Inn(G) = C₂² · Out(G) = C₂×#2021
homology	Abelianization (H₁) = C₃×C₄×C₈ · Schur multiplier (H₂) = C₄

Aliases

66 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 128);