C₃×#357 #4604

order	192
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	Aut(G) = C₂³×#442 (order 512) · Inn(G) = D₈ · Out(G) = C₂³×C₄
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

66 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 96

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 163);