C₃×#418 #5292

order	192
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	Aut(G) = C₂×#72216616 (order 2048) · Inn(G) = C₂×D₄ · Out(G) = C₂²×#120
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²×C₄

Aliases

190 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 851);