C₂×C₇×C₁₁ #3901

order	154
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₅ (order 60) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₅
holomorph	G ⋊ Aut(G) = C₂×AGL(1,𝔽₇)×AGL(1,𝔽₁₁)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₅₄
abelian	C₂×C₇×C₁₁

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 154

A minimal faithful permutation representation — 1 generator on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(154, 4);