C₃×#367 #4614

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 173);