C₃×#366 #4613

order	192
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	Aut(G) = C₂×#495725 (order 1024) · Inn(G) = D₈ · Out(G) = C₂×C₄×D₄
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

46 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,3,4)(6,10)(7,11)(8,14)(12,20)(13,18)(15,19)(16,17)(21,22,23);(5,6,11,17,8,12,15,18,9,13,19,20,14,16,7,10)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 172);