C₃×#131 #971

order	96
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) = C₂³×S₄ (order 192) · Inn(G) = C₂² · Out(G) = C₂³×D₃
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

62 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 178);