C₃×C₇² #3863

order	147
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×#10621462 (order 4032) · Inn(G) = C₁ · Out(G) = C₂×C₃×#10621462
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

C₃×C₇²

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 147

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(147, 6);