C₃×#443 #5317

order	192
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂³×AGL(1,ℤ/8) (order 256) · Inn(G) = D₄ · Out(G) = C₂⁵
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

106 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 876);