C₃×#444 #5318

order	192
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	Aut(G) = C₂×#3003 (order 256) · Inn(G) = C₂×D₄ · Out(G) = C₂×D₄
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

104 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)(4,12,14,16,15,8,13,10)(17,18,19);(1,3)(2,5)(4,10)(6,9)(7,11)(8,13)(12,14)(15,16);(1,4,6,14,7,15,5,13)(2,8,3,10,9,12,11,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 877);