C₁₃² #4289

order	169
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₃×#72210882 (order 26208) · Inn(G) = C₁ · Out(G) = C₃×#72210882
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₃

Aliases

C₁₃²

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 169

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13);(14,15,16,17,18,19,20,21,22,23,24,25,26)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(169, 2);