C₃×#327 #4574

order	192
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	Aut(G) = C₂³×#120 (order 256) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

90 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)(3,7,8,5)(4,6)(9,10)(11,13)(12,15)(14,16)(17,18,19);(1,3)(2,5)(4,8)(6,7)(10,13)(11,16)(14,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 133);