order	96
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₈ (order 32) · Inn(G) = C₁ · Out(G) = C₂²×C₈
holomorph	G ⋊ Aut(G) = D₃×AGL(1,ℤ/32)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

Subgroups

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 1 generator on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)(33,34,35)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 2);