C₂×C₃×C₁₉ #1177

order	114
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₉ (order 36) · Inn(G) = C₁ · Out(G) = C₂²×C₉
holomorph	G ⋊ Aut(G) = C₂×D₃×AGL(1,𝔽₁₉)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₄
abelian	C₂×C₃×C₁₉

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 114

A minimal faithful permutation representation — 1 generator on 24 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)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(114, 6);