C₂×#819 #5107

order	192
isoclinism	isoclinic class of #204
automorphism	Aut(G) = C₂×D₃×#23882 (order 3072) · Inn(G) = D₁₂ · Out(G) = C₂²×#120
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

106 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 666);