order	253
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₅×C₁₁ (order 220) · Inn(G) = C₁ · Out(G) = C₂²×C₅×C₁₁
holomorph	G ⋊ Aut(G) = AGL(1,𝔽₁₁)×AGL(1,𝔽₂₃)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₅₃
abelian	C₁₁×C₂₃

Subgroups

4 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 253

A minimal faithful permutation representation — 1 generator on 34 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(253, 2);