C₃×C₇×C₁₁ #6596

order	231
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₅ (order 120) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₅
holomorph	G ⋊ Aut(G) = D₃×AGL(1,𝔽₇)×AGL(1,𝔽₁₁)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₃₁
abelian	C₃×C₇×C₁₁

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 231

A minimal faithful permutation representation — 1 generator on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(231, 2);