C₃×#108 #851

order	96
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂²×AGL(1,ℤ/8) (order 128) · Inn(G) = D₄ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

30 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 58);