C₃×#341 #4588

order	192
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂×#394102 (order 1024) · Inn(G) = D₄ · Out(G) = C₂×#392
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₂²

Aliases

90 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 147);