C₃×#364 #4611

order	192
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂²×#575 (order 256) · Inn(G) = D₄ · Out(G) = C₂⁵
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₁

Aliases

46 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 170);